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International Trade Notes: 10 October 2016
Preliminary Draft
Notes on the Pure Theory of International Trade
Houston H. Stokes
Note: These "preliminary notes" are geared to the books
1. International Economics 6th edition by Robert Dunn and John Mutti, Routledge (2004)
2. Advanced International Trade: Theory and Evidence by Robert Feenstra Princeton (2004,2016).
3. International Economics by Robert Mundell (1968) Columbia University
4. International Economics Robert Feenstra & Alan Taylor Worth 2008
as well as various key articles in the Handbook of International Economics series. The goal of these notes is to
provide a "living" editable document so that students can add material to the basic outline that hopefully will
focus the discussion. These notes should be treated as preliminary. Key math setups are given. Please report
any errors.
Notes on the Pure Theory of International Trade ............................ 1
1. Introduction .................................................. 2
2. Why Nations Trade - Gains from Trade .............................. 11
3. Modern Theory of Trade. ........................................ 22
4. Basis for Trade: The Ricardian Model vs the Hechscher-Ohlin Models ........ 26
Stopler- Samuelson Theorem – Preliminary graphical analysis. .................. 34
Math Treatment of Two Factor Model (See Chapter 1 of Feenstra) Optional topic. .. 36
Magnification Effect. How do changes in product prices impact factor prices?
Optional topic. ................................................ 38
Effect of changes in Endowments on Industry outputs .................... 40
Simple Model of Trade in Intermediate Inputs ......................... 44
Estimation setup .............................................. 46
Example Code and results from B34S, Rats and Stata: .................... 51
Note e ' e values reported for B34S and Rats agree. Stata made an "adjustment." ...... 75
STOPSTOP ........................ Error! Bookmark not defined.
Code for Leverage Plots with OLS, GAM and Marspline ................... 75
Edited output from Leverage Plots ................................. 76
Selected Leverage Plots. ......................................... 79
6. Extensions to H-O model suggested by Vanek .......................... 91
7. H-O Theory, increasing returns and the Gravity Model................... 119
8. Alternative approaches to trade theory contrasted to Original HO Model. ..... 128
9. The Theory of Protection ....................................... 133
10. Arguments for Protection ...................................... 138
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International Trade Notes: 10 October 2016
11. Mundell Policy Equation .......................................
12. Regional Blocks => Discriminatory Trade Liberalization ................
13. Commercial Policy ...........................................
14 Trade of Less Developed Countries ................................
15 International Mobility of Labor and Capital .........................
16. Balance of Payments Accounting .................................
17. Market for Foreign Exchange ...................................
18. Impact of trade on determination of National Income ...................
19. Alternative Models of Balance of Payments or Exchange Rate Determination ..
20. Balance of Payments adjustment with fixed exchange rates ...............
21. Balance of Payments Adjustment through exchange rate changes ..........
22. The theory of flexible exchange rates ..............................
23. International Monetary Experience 1880-1940 .......................
24 The International Monetary System 1945-1973 ........................
25 International Monetary Relations 1973 - Present ......................
143
147
148
151
152
154
155
161
162
164
167
168
169
173
175
1. Introduction
International Trade is concerned with exchange. Important topics include the mechanisms by
which trade between countries is caused and the resulting effect on the countries after trade is
opened. In the Ricardian Model Trade is caused by comparative or absolute advantage.
Production conditions are different in the two countries that are not restricted to have the same
technology. The Heckscher-Ohlin approach assumes
1. Two goods and two factors of production where the factors can move between industries.
2. One good is labor intensive while the other is capital intensive.
3. The relative abundance of the factors of production differs by countries. Home country
abundant in capital, foreign country abundant in labor.
4. Final products can move between countries. Factors of production cannot move.
5. The technologies used in the two countries the same.
6. Consumer tastes are the same in the two countries
These assumptions can be modified and the effects shown.
Effects of trade:
Welfare changes in both countries. Who gains and by how much? Large and small
country assumptions impact the analysis. Can growth actually lower a countries welfare?
The distribution of income changes in both countries. Who owns the factors? Trade
alters the relative income of owners of factors of production. Are the factors mobile both
into and out of the country?
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International Trade Notes: 10 October 2016
Factor prices change in both countries. Will factor prices adjust so as to be equalized?
Why is factor price equalization so important? How does persistent wage differentials
drive immigration? Under what assumptions does immigration of workers lead to
PL / PK , to PL / PK constant, to PL / PK ?
The range of goods produced changes in both countries. What is the consumption gain
from trade? The production gain from trade? Under what conditions will countries with
same tastes and same production conditions trade? Who gains from trade inside the
country? Who loses?
Under what assumptions will the relative prices of goods to change after trade, the
relative price of factors change?
Key aspects of trade policy include:
-
The effect of tariff on international trade.
-
The effect of free trade areas (NAFTA), customs unions and economic unions on welfare.
Why do we need a theory of international trade?
Macroeconomics assumes:
1. economic agents maximize their self interest,
2. such agents are rational.
In trade theory more assumptions are needed.
Within a nation state it is assumed that labor and capital are free to move among regions. This
may not be the case across countries. What does this “restriction” cost?
Within a nation state there are normally no government-imposed barriers to shipment of goods
(tariff). Between countries there are many barriers including tariffs, regulations (steering wheel
construction laws forced Rolls Royce to buy parts from GM in the 1960’s. Cars had to be crash
tested, even if they were high priced and hand made.)
The state of the economy within a nation state is usually the same for all regions. Across
countries, differences in a countries position in the business cycle can have major ramifications.
(In the EU zone Germany and Greece are in different “phases”.)
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International Trade Notes: 10 October 2016
Within a country there is only one currency. Exchange rate changes complicate the analysis. (In
world of fixed exchange rate and perfect capital mobility there is only one interest rate. In a
world of flexible exchange rates, different interest rates across countries are possible.)
[3 Table 1-2] Trade /GDP ratio and GDP (billions) in 2005
Hong Kong 192%
$178
Malaysia 111%
$130
Switzerland 49% $366
South Korea 42% $788
Germany
38% $2,782
Canada
36% $1,115
China
33% $2,229
Mexico
31% $768
UK
28% $2,193
France
27% $2,110
India
20% $785
Japan
14% $4,506
US
13% $12,455
US share is low compared to most other countries but has increased substantially in recent years.
US is now being impacted by the world to an increased degree. Politically workers displaced by
foreign competition have become active! These political issues have been impacting the EU
zone, which allows labor to be mobile, as well as the US.
Table 1
Ratios of Merchandise Trade to GDP (percent)
Country
1890
1913
1960
1970
1980
Australia
15.7
21.0
13.0
11.5
13.6
Canada
12.8
17.0
14.5
18.0
24.1
Denmark
24.0
30.7
26.9
23.3
26.8
France
14.2
15.5
9.9
11.9
16.7
Germany
15.9
19.9
14.5
16.5
21.6
Italy
9.7
14.4
10.0
12.8
19.3
Japan
5.1
12.5
8.8
8.3
11.8
Norway
21.8
25.5
24.9
27.6
30.8
Sweden
23.6
21.2
18.8
19.7
25.0
United Kingdom 27.3
29.8
15.3
16.5
20.3
United Statesb 5.6
6.1
3.4
4.1
8.8
Notes: Merchandise trade is measured as the average of imports and exports
1990
13.4
22.0
24.3
17.1
24.0
15.9
8.4
28.8
23.5
20.6
8.0
In recent years the development of container shipping has lowered costs and reduced theft. In
1959 .627 tons per man hours which increased to 4,234 tons per man hour in 1976 [4, page 14)
In the period 1970-2000 the total capital outflows of the US increased from 10.88 to 580.65.
Inflows from 6.24 to 1024.23. These numbers are greater for UK (3.16 to 777.68 and 1.64 to
801.58). This data is nominal, not real!
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International Trade Notes: 10 October 2016
US faces increased vulnerability to foreign shocks (such as 1974 oil price shock). As of 2016,
the EU and the China slow-down are the biggest risks. Changes is exchange rates under the
flexible exchange rate system provides a damper of shocks to the US economy. (In early 1980's
high US interest rates attracted capital from abroad causing the dollar to appreciate and making
sales overseas more difficult.)
Recent experience in the fall of 2008 indicates how vulnerable the world economy is to the
financial system. The degree of leverage in many parts of the world has caused a general loss of
confidence in financial institutions. The distribution of income has become a political problem
with no easy solution without a political census on what is the best policy. Political pressure in
2016 to raise tariffs might push us back to what we experienced after the Smoot Hawley tariff in
1930.
The real side is being impacted by the monetary side to a degree not seen for a long time.
Euro now gives Europe one currency like the US. The EEC is like what was setup in the US in
1796. US now faces a potential economic rival.
"Pure Theory" of International Trade provides a framework by which all kinds of exchanges can
be analyzed, both graphically and using statistical (econometric) methods.
"Monetary Theory" of International trade is concerned with balance of payments adjustment.
Increasingly it appears that the monetary side can have substantial real side effects. It remains to
be seen if the crisis of the fall of 2008 will result in higher tariffs such as were enacted in the US
and other countries in 1932 and which proved so damaging.
Positive Economics
- Develops a framework of analysis
- Constructs various alternative hypothesis
- Tests hypothesis
Normative Economics
- Determines what ought to be
- Can lay out costs and benefits (defense vs welfare)
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International Trade Notes: 10 October 2016
- Want to look at gains from exchange.
- Want to look at the costs and benefits of differing policies.
Trade can be shown from supply and demand analysis.
Figure 1
Def: An indifference curve drawn on the X and Y diagram contains the locus of points showing
different bundles of X and Y to which the consumer (country) is indifferent. Assume barter ratio
is fixed. Country at f producing and consuming oc of steel and od of food. The domestic relative
P
P
price line is a a'. The world relative price line is a a'' . World steel domestic steel causing
Pfood
Pfood
producers to stop producing food and go 100% to steel (o a). At position g the country consumes
ob of steel and gives up ab of steel to get oe of food. Trade moved the country from U1 to U2.
Trade is caused by the relative price differing between regions. As a result of trade steel workers
gain and food workers need to change jobs. The country as a whole gains. Political question:
“How are gains distributed?” What is the cost of changing jobs? Can it be done?
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International Trade Notes: 10 October 2016
Figure 2
For complements the indifference curve approaches a 900 angle. For substitutes the indifference
curve approaches a 1800 angle.
The above analysis assumes we have a community indifference curve. A major unsolved problem
in economics is how to construct the community indifference curve.
Key idea: Normative economics is in the indifference curve and changes:
- Over time
- Due to advertising
- Due to consumption itself
Trade theory assumes exchange in the presence of some fixed factor. The fixed factor does not
have to be location related. Examples are land, tastes, skills, climate.
Gains from trade can arise:
Due to changing consumption patterns as a result of changes in relative prices.
Changes in the degree by which a country specializes.
Both changes in consumption patterns and specialization.
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International Trade Notes: 10 October 2016
Key idea: "Under what conditions can trade gain one country more than another? Who gains in
the country?
Changes is specialization imply changes in the returns to factors and thus possible dislocation.
This can cause political problems. Wheat farmers in Mass lost out to Iowa when US Constitution
outlawed internal tariffs. Historic international trade models assumed perfect competition and
constant returns to scale. Assuming increasing returns was not studied sufficiently. The effect of
Monopolistic Competition can be added to the H-O model to explain trade between relatively similar
countries.
Growth. Sources of growth in the United States include:
Population (immigration)
Education (increases in technology)
Resources
Will of People (WWII increased productivity)
Some assumptions used to simplify analysis. (How sensitive are results to these assumptions?)
Neutrality of Money: Real variables determined independently of monetary variables.
Each sector looks at relative prices not absolute prices (which are a function of money
supply).
All prices are flexible (determined by competition)
Assume initially the amount of factors of production are fixed.
Assume initially that factors are immobile between countries.
Assume initially that same technology is available to all consumers.
Assume that initial income patterns are known.
Assume initially no barriers to trade in form of transportation, information,
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International Trade Notes: 10 October 2016
communication.
Key questions:
Direction of trade
Volume of trade and prices of traded goods
Effects of trade restrictions
Effect of free trade and restricted trade on welfare
Approaches:
- Partial equilibrium approach uses supply and demand. The problem is that as
you move on the supply and demand curve, the assumptions underlying these curves are not met
resulting in the curves shifting. (See Above figure)
- General Equilibrium Approach. Uses production possibility curve (PPP),
Community indifference curves, and relative price line to determine trade welfare. This approach
will be the main focus of the course.
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International Trade Notes: 10 October 2016
Technical problems in Trade Analysis:
Time period of analysis. If the period is too short, then substitutes cannot be developed
and analysis leads to misleading results. Example. Gas crisis in 1974. Gas prices
increased and in the short run people drove old cars. In the longer run more fuel efficient
cars were produced and demand for gas fell. => Negative balance of payments effects of
an increase in import prices are most severe in the short run.
Simultaneity Both supply and demand may be shifting. Need to identify the supply and
demand curves using 2SLS or 3SLS methods.
Errors of Measurement. Trade data may be poor. Example: US used value of disks and
manuals to measure software sales.
Aggregate elasticity. Aggregate elasticity measures biased toward zero since greatest
price fluctuation is observed in goods with inelastic response => goods with inelastic S &
D are likely to be given too much weight in the calculation of the aggregate price index.
Adjustment. During the time path of adjustment we may see points not on the true curve.
Elasticity measurement is critical. Assume two countries initially in equilibrium. The
home country (A) imports X and exports Y. Define the income elasticity of demand in A
as:
aI (X / X ) /(I / I )
If BI AI then as A and B grow the balance of payments will move against B. It will be in B's
interest to have growth in A increase. => Economic stagnation in the foreign country implies
balance of payments problems in the home country. The lower the income elasticity of demand,
the faster a country can grow and still maintain balance of payments equilibrium.
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International Trade Notes: 10 October 2016
2. Why Nations Trade - Gains from Trade
- Nations trade because they benefit from it.
- Adam Smith stressed that nations traded due to absolute advantage. Absolute cost
advantage => the real cost (labor ) was less in one country than another. Smith was thinking in
terms of labor theory of value. Modern economics (not Marxism) discards this approach and
looks at other costs of production such as land and capital.
- Assuming labor is mobile, labor is the only input and competition within a single
country => goods will trade at prices that are a direct proportion of their labor costs. This further
assumes away retraining problems. But between countries labor may not be mobile due to a
number of reasons.
- Ricardo stated that absolute advantage was not a necessary condition for trade. Trade
could occur due to comparative advantage. Ricardo's example involved the number of hours to
produce two goods:
Cloth
Wine
Portugal
90
80
England
100
120
Portugal has absolute advantage in both goods since it takes less labor to produce cloth and wine
than England. This does not mean that England cannot benefit from trade
In Portugal 90 hours of labor get you 9/8 of a wine barrel or 1C = (9/8)W.
In England 100 hours of labor get you 5/6 of a wine barrel or 1C = (5/6)W.
=> Portugal sell wine, England sell cloth which suggests that it would be desirable for labor in
Portugal (England) to move into production of wine (cloth).
Define ai and ai* as the # of hours for the ith good in the home (Portugal) and foreign country
(England).
a1 a2 90 80
* *
a1 a2 100 120
2
2
i 1
i 1
Assume L and L* are the labor in the home and foreign country. L Li and L* L*i
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International Trade Notes: 10 October 2016
MPPLi 1/ ai and MPPL* 1/ ai* Assume cloth is on the x axis and pi and pi* are the prices of
i
the ith good in home and foreign country, The slope of the budget lines that are tangent to the
indifference curves imply that in the absence of trade
a1 / a2 p1 / p2 90 / 80 1.125 and a1* / a2* p1* / p2* 100 /120 .8333 in the two countries.
This suggests that cloth (good 1) is relatively expensive in the home country Portugal and wine (
good 2) is relatively expensive in the foreign country England. => England sell cloth and
Portugal sell wine.
Define the world price in terms of the relative price of good 1 (here cloth). If
P a1 / a2 ( P a1* / a2* ) then the home (foreign) country will produce both cloth and wine.
If a1 / a2 P a1* / a2* then the home country will specialize in cloth and the foreign country in
wine. Note: comparative advantage determines the wages in each country. Absolute advantage
determines the level of wages across countries.
Can setup example in terms of 1 unit of labor.
England
Germany
Broadcloth
10
10
Linen
15
20
-=> in England 10 broadcloth = 15 Linen
in Germany 10 broadcloth = 20 Linen
- English broadcloth producers should exchange broadcloth for linen in Germany.
Broadcloth produces will benefit if they can obtain more than 15 linen for 10 broadcloth. German
linen producers note that to get broadcloth in Germans they have to trade 20 linen but if they
trade with England they can only give up 15 linen for 10 broadcloth.
Mill introduced demand to allow us to determine how much each country would trade.
Specie Flow Mechanism. Assume national money is determined by gold stocks. Assume a two
country world where trade is initially in balance. Here prices in each country are stable. Assume
next that increased demand for A's goods causes gold to flow in. PA / PB causes demand for A's
goods to fall and demand for B's goods to rise. Specie Flow mechanism implies that
| A | | B | 1 (Marshall Lerner Condition). If this condition is not met, all gold will flow from B
to A. This classical adjustment mechanism relied on change in gold flows to change national
money to change prices and costs. This theory did not deal with output and unemployment
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International Trade Notes: 10 October 2016
effects. Note: Two gold standard papers written by Neuburger and Stokes will be discussed in
class later this term.
Managed Adjustment. Keynes suggested that a change in demand could change the demand for
imports (exports) without a change in prices. Taussig noted that before WWI the system
appeared to adjust faster that the level of gold flows would suggest. Neuburger-Stokes (1979)
presented time series evidence that suggested that central banks were using interest rate policy to
speed the adjustment without having to resort to the level of gold flows that would other wise
occur. The current paper (2016) documents that the effect of gold flows on interest rates was
relatively small in comparison to interest rates in other countries in a model of the UK, Germany
and France.)
Historical notes: Earl Hamilton studied gold flows from the new world to Spain and hence to
France and England. During wars (such as the Bullionist Controversy) many countries suspended
the gold standard. In this century the gold standard was suspended during WWI. After the war
the UK went back on gold at the overvalued prewar rate. The economic return was protracted and
slow. In the late 20's the world moved into depression and countries moved off gold. After WWII
the world moved to the gold exchange standard. Here countries pegged to either the pound or the
dollar which in turn pegged to gold. Major problems included adjustment, confidence, and
liquidity. In the fall of 1967 at the Rio Conference the SDR was setup. The SDR paid interest.
No country was required to accept more that 2 times its quota. The SDR was designed to solve
the liquidity problem. It did not address the confidence or adjustment problem. In Nov 1967 the
pound was devalued from $2.80 to $2.40. In the 20's exchange rates moved in part as a result of
changes in prices. This led to purchasing power parity theory or the "law of one price." The
problem is that this theory is not general. It does not look at changes in demand, at changes in
capital flows and at technological changes, all of which impact on exchange rates. Define as
the dollar price of one unit of the foreign currency. Theory suggests that:
( Pf / Pd ) or that foreign inflation is associated with devaluation of the
foreign currency.
Technological changes (lower domestic prices) A glut of domestic
goods floods the market requiring the exchange rate to depreciate to allow country to
sell goods.
Capital inflow Home currency has strengthened (appreciated).
In 30's moved away from PPP since there were other causes of exchange rate movements. These
included large scale speculative capital flows, competitive devaluations by both deficit and
surplus countries and problems of exchange stability due to fears. Expectations can alter 's in
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International Trade Notes: 10 October 2016
countries.
- Before trade the relative prices of goods in A and B differ. After trade they adjust to be
the same. Assume ( PXA / PYA ) ( PXB / PYB ) . This implies that A is willing to sell Y to
B and import X from B. The gains from trade include a consumption effect and a possible
production effect. Assuming no changes in production in each country, trade can still result in a
gain for both countries. If as a result of trade production changes in both countries there can be a
still further production effect. To accurately measure the gains from trade we need:
Community indifference curves in each country.
Production functions in each country (Production possibility curves)
Offer Curves (derived from community indifference curves and production possibility
curves to determine the world trade price).
It is important to know how to derive these curves.
Partial equilibrium analysis such as figure 1 can be used to attempt to measure the gains from
trade but there are serious problems in moving along country supply and demand curves without
the curves themselves shifting. This course will use general equilibrium approach. Basic
diagram is given in figure 3. We assume diminishing returns to scale which is seen by the
country having a production possibility curve which is bowed outward. The country starts at k
with oc of food and oi of steel. After trade with no production change the country is on higher
indifference curve and consuming oe of food and on of steel. If production changes, country
produces at g. Here food is ob and steel is of. After trade country gives up bd of food to get fp of
steel. Country now on highest indifference curve. We assume here that the world trade price
does not change as a result of trade (small country assumption).
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International Trade Notes: 10 October 2016
Figure 3
As we move down the PPC we give up more and more food to get steel. The relative price of
steel is increasing relative to food. The factor use more intensively in steel production will see
its price increase relative to the factor used most intensively in food. => movements along the
PPC are not costless. If trade opens up such that the price of steel increases relative to food.
Producers of food will loose relative to producers of steel. => Stopler Samuelson that states that
free trade will reduce the income of the scarce factor of production and increase the income of
the abundant factor of production in each country. For an example if Chinese steel is reduced in
price US steel production will go down and the value of steel mills will fall.
The PPC is derived from the Edgeworth Box with the inputs on the axis. If the isoquants for x
any y are tangent along the diagonal then we have constant returns to scale. The tangent points
in this case imply the relative price of the inputs is the same in the production of x and y.
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International Trade Notes: 10 October 2016
Figure 4 shows equilibrium in a closed economy assuming constant returns to scale production.
Here in contrast to figure 3 we have a straight line production possibility curve.
Figure 4
Country reaches U2 by producing oa food and ob steel. Country is at point
C on the production possibility curve. Without trade country cannot get to U3.
Figure 5 shows effect of trade. Country was consuming and producing at k. After
trade county reached higher indifference curve at g. Steel consumption increased from ob to om
and food consumption did not change much. Country production point was now all Food and no
steel. Na of food was sold for om of steel.
Figure 5
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International Trade Notes: 10 October 2016
Historical Development of Trade Theory
- Trade theory developed in four areas:
I.
II.
III.
IV.
Balance of payments and theory of employment
Fluctuating Exchange rates
Price Theory and International trade
Commercial Policy and The Theory of International Trade
I. Balance of payments and Theory of Employment
- Prior to Keynes - Monetary theory (specie flow mechanism) suggested that system
adjusted automatically. Gold out => P d , P f and trade adjusts. The classical theory did have
a role for interest rates. The mechanism was Gold M P, costs not output,
employment
- Keynes attacked theory suggesting could have unemployment and over production.
- New theory. An external event which causes exports => imports without Pd.
The mechanism was exports => level of aggregate demand => imports . This theory
covered the balance of payments effects being either or depending on Ia and Ib where
Ii is the income elasticity of the i th country.
- Taussig before WWI noted that the system appeared to adjust faster than gold flows
would suggest. He had no theory to explain what was happening. Neuburger and Stokes in
"The Relationship between Interest Rates and Gold Flows Under the Gold Standard: A
New Empirical Approach," , Economica, Vol. 46, August 1979, pp. 261-279.
presented evidence that that is consistent with governments using a variety of policies to force
adjustment without a gold flow. Their 2016 paper expands on this result.
- After WWI elasticity measurements appeared to be low. Why did trade adjust? The
Keynesian approach provided a missing link.
- Keynesian theory independent of banking policy and implied that banks cannot
influence the system. The Keynesian theory did have antecedents in Ricardo and others.
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International Trade Notes: 10 October 2016
- Capital flow effects. Keynesian theory => unless a disturbance (such as a capital flow)
disturbs the circular flow of income (via a change in investment), it will have no effect on the
system. The classical theory treated all flows as the same. In classical theory the gold flow =>
M and M => changes in prices and the balance of payments etc.
II. Fluctuating Exchange Rates
- During WWI gold standard suspended. After war world's return to the gold standard was
protracted and slow. Next the world moved into depression => a period of fluctuating rates.
- In 20's exchange rate moved as a result of war causing prices to increase. This led to
purchasing power parity theory (see contributions of Officer) that codified the "law of one price."
PPP => exchange rates had to move. Problems with PPP included 1. not looking at effects of
shifts in international demand on exchange rates, 2. not looking at effects of capital flows on
exchange rates, 3. difficulty in selecting just what price should be used in the index.
- In 30's many countries found depression caused changes in the exchange rate.
There was a move away from PPP since here changes in the price level was not the cause of
exchange rate movements. The income of all countries fell in the depression but not all countries
balance of payments were effected the same. Keynesian theory on the effect of induced income
changes implied: Balance of payments deficit => Y down => imports down => balance of
payments improves. This line of reasoning suggested that changes in the exchange rate would not
adjust the balance of payments. The situation was complicated by:
- large scale speculative capital flows.
- Competitive devaluation by both deficit and surplus countries.
- Problems with exchange stability due to fear => .
III. Price Theory and International Trade
- Classical theory measured gain from trade as difference between international rate of
exchange on commodities and the rate that would prevail in the absence of international trade.
Gain = the savings in resources from trade. This theory rested on the labor theory of value.
- Haberler postulated production possibility curve. Leontief added indifference curves
which allowed measurement of the gains from trade. The new approach got away from real costs
theories and depended on the ratio of the marginal costs of the two products.
- Viner attacked the new approach on the grounds that the PPC (or production
substitution curve) assumed fixed quantities of factors. In Viner's view, P changes caused
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International Trade Notes: 10 October 2016
changes in factor prices. Since as we move along the PPC curve relative prices of factors changes
(except in constant returns to scale case) => supply of factors must change. Viner wanted to look
at the "real cost" of supplying factors. Viner further noted that the country indifference curves
depend on the distribution of goods. Since international trade changes the distribution of goods
=> Country indifference curves shift as a result of trade. This important point is moot if we
assume homogenous tastes for all consumers in the country.
- Samuelson (in 1939 Canadian Journal of Economics and Political Science) showed that
after trade, each country if it wants can obtain more of every good while performing less of every
production service. => cannot measure the gain but it is a gain never the less. Samuelson showed
that some degree of trade can make the country better. This leaves open the possibility of an
optimum tariff.
- The more modern H-O Theory shows how trade based on factor endowments alters the
distribution of income. H-O Theory argues that in many cases trade originates from the fact that
one country had a large supply of one factor. This is contrast to the Ricardian Theory that focused
on technology differences in the countries. Using the basic H-O assumptions of two goods, two
factors and the same technology in each country and constant returns to scale, the H-O model
argues that assuming trade in a good that uses one factor intensively => returns to owners of
that factor relative to other factor owners. H-O Theory showed that assuming constant returns
to scale, except for some cases involving complete specialization, trade tended to equalize
relative factor returns in the two trading countries. Ohlin showed how changes in relative factor
prices might change factor supplies in the longer run. H-O theory can assume fixed factors
supplies or variable factor supplies. Recent advances in theory have extended the analysis to the
increasing returns case (Krugman, Helpman) that refine the arguments for trade and for
protection. Use of the H-O-V Model allows adding more inputs and setting up tests of the
Leontief hypothesis using econometric methods.
Looking only at one country producing goods yi i 1, , N where there are N goods. If there are
two factors of production yi fi ( Li Ki ) L1 L2 L and K1 K2 K . Assuming the "even
case" which implies an equal number of goods and factors and maximizing the production of
good 2 conditional on good 1 we note that y2 h( y1 , L, K ) which defines the production
possibility curve. If y 2 is a concave function of y1 then 2h( y1 , L, K ) / y12 0 which indicates
that as we increase production of good 1 the rate of increase in good 2 is reduced, giving the
concave shape of the production possibility curve. (See figure 3 of these notes).
Mill introduced demand which allows us to determine how much each country would trade.
IV Theory of Tariffs
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International Trade Notes: 10 October 2016
- Tariffs and terms of trade. Between WWI and WWII shaky foundation for free trade. In
30's US raised tariffs as did other countries. Samuelson showed that using the optimum tariff (to
be defined later) that assumes the elasticity of supply of the foreign country is not => country
putting up tariff could gain at expense of the other country. Scitovsky showed how such a tariff
increased gains from retaliation. => all countries try to gain = all countries lose. Such a result
might lead to tariff bargaining. A tariff is like a monopoly. Some gain, some lose. In a tariff war
the bigger countries are at an advantage.
- Tariffs and the distribution of income. Tariff => certain groups gain. StolperSamuelson (RES Nov 41) showed that regardless of tariff effects on the terms of trade and real
income as a whole, protection increases return and relative share of factor of production most
important in protected industry. Proved for 2 good, 2 factor case. In more than 2 good world
cannot tell for sure what will happen since can have complementary relationships. In the 19th
century agriculture was governed by land. A tariff on manufacturing made labor relatively scarce
=> raised return of the working class. This became the "pauper labor" argument for tariffs.
'Pauper Labor" theory not the whole story!! In the Heckscher-Ohlin Model the abundant factor
gains from trade and the scarce factor loses from trade.
V Commercial policy
- Mercantilists thought trade was an outlet for a countries surplus production and a
way to get gold.
- Classical theory argued against mercantilism. In their view trade was to satisfy
wants. A shift in emphasis from exports to imports. In classical view, exports to obtain gold not
necessarily the right thing to do since P . The goal was not a surplus but balance. In an N
country world only N-1 countries can be successful multilateral mercantilists. Only one can be a
successful bilateral mercantilist!
- Keynes attacked the classical view that export surplus was not a good thing.
Keynes argues exports => gold =>Yd => increased welfare of country. This argument
assumes that initially you had unemployment. In Keynes view mercantilists were OK when they
argued that exports should be a vent for over production. Keynes noted that not all countries
could run a balance of payments surplus. Keynes felt that a policy of trade restriction is a
treacherous policy, even in the short run.
Summary.
- Meade integrated income (multiplier) and price theory of balance of payments.
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International Trade Notes: 10 October 2016
He argued looking at two policy targets (internal balance, external balance). To obtain these
goals required two instruments. => # of targets = # of instruments.
- Mundell principle of effective market classification => use instrument where it
is most effective.
- Meade argued that there is no one rate of exchange. There is one equilibrium
rate corresponding to each level of interest rates and income. As interest rates increase, with a
fixed level of income, capital will be attracted in. This will appreciate the exchange rate. Given
interest rates, if income were to increase => demand for exports would increase implying a
depreciation of the exchange rate.
- Alexander looked at income effects on the balance of payments. A balance of
payments surplus => total production > total absorption (C + I in real terms). If a devaluation is
to improve trade balance it must reduce absorption. This argument is irrespective of elasticities.
Absorption theory => balance of payments only if hoarding goes up since only in this way can
we forestall imports as a result of income increasing due to exports . This theory has a
Keynesian flavor.
- If at full employment and have a devaluation due to a prior deficit, then
absorption theory suggests balance of payments will not improve because Y cannot increase. The
devaluation has converted demand for the import good to demand for the domestic good. =>
cannot rely only on to help external balance without policies to reduce absorption. Unless
absorption then country will have nothing to sell! Key idea: Demand is not the only thing to
look at. Supply is also important.
- Problems with absorption theory. The theory as stated implicitly assumes a
neutral monetary policy or one that maintains the interest rate by changes in M. If this is not
done: deficit => devaluation => demand of domestic consumers for foreign goods , domestic
demand => balance of payments gets worse since absorption had to have increased. If were at
less than full employment could have domestic income > absorption and get an
improvement in the balance of payments. If drop neutral monetary policy assumption the
increased domestic demand => id => capital comes in and balance of payments improves.
Metzler Case. Stolper-Samuelson showed how a large factor could gain absolutely as well as
relatively from a tariff. Logic: tariff=> internal price of protected good => value of scarce
factor goes . As a counter example, Metzler showed protection may not increase price of the
importable good since it may improve the terms of trade sufficiently to shift not only the external
terms of trade (price ratio of exports relative to imports without tariff) but also the internal terms
of trade in favor of exportables => buy more of the foreign good.
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International Trade Notes: 10 October 2016
3. Modern Theory of Trade.
- Moved away from theory based only on labor theory of value.
- Initial Assumptions (to be relaxed later):
- Perfect Competition in both commodity and factor markets.
- Given quantities of the factors of production (assume population and capital
growth are zero)
- Technology is given.
- Zero transport costs and no barriers to trade.
- Given tastes and preferences.
-Factors of production are perfectly mobile among industries within each country
but are immobile between countries.
- Opportunity cost of one unit of X is the amount of Y that you have to give to produce
one more unit of X. From opportunity cost you get the production possibility curve which
defines the maximum amount of X given Y or conversely the maximum amount of Y given X.
- Production possibility curves show constant returns to scale if they are straight
lines from the upper left to the lower right. (See figure 2-1).
- Production possibility curves show decreasing returns to scale if they are convex
to the origin. (See figure 2.6).
- Production possibility curves show increasing returns to scale if they are concave
to the origin.
- Community Indifference Curves shows the locus of points showing the consumption of
X and Y to which the community is indifferent. To derive these curves requires assumptions be
made on the distribution of income within a country. => all policy implications have to be
somewhat qualified.
- With constant returns to scale, trade drives country to complete specialization (See
figure 2-4)
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International Trade Notes: 10 October 2016
- With decreasing returns to scale trade does not in general drive a country to complete
specialization. (See figure 2-6).
- With increasing returns to scale there can be specialization in the wrong direction.
Figure 5B Specialization in right/wrong direction assuming increasing returns.
- The Offer Curve plots the quantities that countries will be willing to export at different
prices. Intersection of the offer curves sets the international trade price.
- Draw Increasing, constant and decreasing returns to scale production
possibility curves. Recent research by Krugman and others have discussed the implications of
product differentiation (monopolistic competition and economies of scale) on the results obtained
using the 2 by 2 case and constant returns to scale.
- Draw Gains from trade in case of increasing returns, constant returns
and decreasing returns in two cases: 1. where there is no change in production (only
Consumption gain) and 2. when there is consumption and production gains. (See book figure 2-9
as a basis upon which to draw). Show specialization in the right and wrong direction.
- Draw the derivation of the offer curve in the case of constant returns to
scale (see book figure 2-9) and decreasing returns to scale.
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International Trade Notes: 10 October 2016
- Draw determination of the equilibrium terms of trade. (see book figure 210
- Define the coefficient elasticity of the offer curve => e = % change in
quantity demanded / % change in the terms of trade. In figure 2-11 we see e= in segment Oa, e
> 1 in segment ab and at b e = 1 since for small movements the % change in the terms of trade % change in the quantity demanded. In the segment bc e< 1. The elasticity of demand the foreign
countries offer curves determines whether the optimum tariff is 0 (if e= ). In trade the small
country assumption => that e < for the domestic country but that e = for the foreign
country.
- Define the coefficient of elasticity of demand as
e = % change in Q demanded / % change in terms of trade
- For a straight line offer curve e =
- For a curved (yet positively sloped) offer curve
e>0
- For a negatively sloped offer curve e < 0 (See figure 2-11).
- If the offer curve is not a straight line => can have the possibility of an
optimum tariff. Complications will occur if the other country "fights
back.
- Distribution of the gains from trade. The lower e for the foreign country the more the
gains from trade accrue to the home country. Take of a small county trading with the United
States. The small country sees the US offer curve as having e = . Here no matter what the
small country does, the US price is always the same. This will be shown to be true in the case
when the small country places a tariff on the US. If e < , then as the tariff reduces quantity, the
foreign country lowers price. Hence the price net of the tariff falls.
- Effects of trade. If there are production changes due to trade opening,
resources will be reallocated. Mechanism: Assume country A exports X and imports Y. After
trade, production of X will increase and production of Y will fall. Inputs used more intensively in
the production of X will increase in value relative to prices of inputs used intensively in the
production of Y. This is will cause changes in income and may have an impact on demand within
the country. Those gaining from trade should be able to compensate those hurt by trade. After
trade a country tends to specialize in the direction of the good in which it has a comparative
advantage. Changes in the production mix are checked by increasing costs.
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International Trade Notes: 10 October 2016
- Figure 2.10 shows general equilibrium determination of world relative
price. Figure 2.9 can be modified to show total gain consumption gain and production gain.
Figure 2-8 shows partial equilibrium approach to same problem.
- Unless the country is driven to complete specialization after trade
(PXA/PYA) = (PXB/PYB). At a later date we will show that the prices of inputs are related to the
prices of final products.
- A movement along the production possibility curve may take a great deal
of time and involve much retraining and human cost. There may be political pressures against
such moves. The 2008 US election showed that even within a state there are winners and losers
of opening trade.
- In the real world with many countries, transport costs and many products
analysis can proceed if for each country goods are ranked by their relative comparative
advantage. Usually a country exports the good for which it has the greatest comparative
advantage and imports goods for which it has the least comparative advantage. The heavier (or
more perishable) a good the more likely it will not be traded.
- It is hoped that through trade there can be a reduction of tensions (war). This was
an important motivation for the development of the European Common Market and in recent
times TPP.
- Free Trade Area. No tariffs between country A and B. A and B maintain separate
tariffs for the rest of the world.
- Customs Union. No tariffs between country A and B. A and B maintain a
common tariff for the rest of the world.
- Economic Union. => Customs union with labor mobility.
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4. Basis for Trade: The Ricardian Model vs the Hechscher-Ohlin Models
-The Ricardian Model stresses that trade is due to technological differences across
countries. The Hechscher-Ohlin model stress that trade is due to differences in factor
endowments. After first looking at the Ricardian Model using math (See Feenstra Chapter 1), the
Heckscher-Ohlin Model is discussed.
- Let
ai labor needed for production of good i in the home country.
ai* labor needed for production of good i in the foreign country
L and L* are the labor in the home and foreign country. The marginal product of
labor in each industry is 1 / ai . If pi the price of the product in industry i and workers are paid
their marginal product, then in equilibrium
p1 / a1 p2 / a2 . The slopes of the production
possibility curve in each country is a1 / a2 and a1* / a2* . If the home country has a comparative
advantage in good 1, then a1 / a2 a1* / a2* or relatively less labor needed in good 1 in home
country. Define p as the relative price of good 1 or p p1 / p2 .
Figure 4.1 Ricardian Model
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- Define A p a* a1* / a2* and C =p a a1 / a2 If p is below A and C, then both countries produce
good 2. For C<p<A then the home country produces good 1 and the foreign country produces
good 2. Point D ( L / a1 ) / L* / a2* ) q1 / q2* .
- Heckscher-Ohlin theory, which assumes two countries, two goods and two factors of
production, is one explanation of why relative prices of goods differ before trade. Basic idea:
Countries differ in the amounts of various factors of production (land, labor, capital) that they
possess. Relative scarcity impacts relative factor prices and hence production patterns.
- Theory predicts that a nation's export (import) list will include commodities
whose production requires factors that are relatively abundant (scarce) in relation to other
nations. (Exception is case there tastes out weight production conditions.)
- => Comparative Advantage determined by supply side. Later we will show a
situation where by "tastes outweigh production conditions." Here demand conditions are
overwhelming supply conditions.
- H-O theory predicts that trade will increase the price of the abundant factor and
decrease the price of the scarce factor. Assuming two factors L and K, then in equilibrium
(PLA/PKA) = (PLB/PKB). This condition holds unless one or both countries are driven to complete
specialization.
- If we assume indifference curves are the same in all countries (same tastes) =>
supply conditions will drive trade.
- Because a nation's comparative advantage is based on relative factor
endowment, over time it could change. Physical capital could be accumulated. Human capital
could change (more education, trained workers come into country). (After WWII Germany had
ruined physical capital but there was still human capital in the population still living.)
- Formal assumptions
- Perfect competition in both commodity and factor markets. (=> price = MC and
full employment in both countries)
- Factors of production immobile internationally but mobile nationally.
- Same tastes in both countries.
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- Transport costs are zero, no tariffs.
- State of technology given and the same in both countries.
- Constant returns to scale exist in both industries. (Note in the Cobb-Douglas
case Q L K . The production function shows decreasing returns to scale, constant returns to
scale of increasing returns to scale as ( ) is < 1, = 1 or > 1.
- Commodities can be unambiguously ranked in terms of factor intensity.
- Discussion of assumptions. Constant returns to scale => that is all inputs go up by a
factor then output goes up by . Proof:
Q ' ( L) ( K )
L K
Q
Isoquants are shown in figure 3-4
- The assumption of identical production functions does not mean that all
countries operate using the same mix of labor and capital. Figure 3-5 shows isoquants for wheat
(W1 W2) and cloth (C1 C2). Initial budget line is MN. (Can buy OM of land or ON of labor. At
these relative prices, country will maximize wheat production at E or cloth production at J. Note
that the country cannot do both at the same time. Given this budget line, cloth in labor intensive
and wheat is land intensive at E. Next assume that the price of land becomes relatively cheaper
relative to labor. The budget line rotates clockwise to RS. Given the setup the same amount of
cloth is produced (C1) but in a more land intensive way at K. Substantially more wheat is
produced (at W2) in a more land intensive way. Note that the slope of MN represents the factorprice ratio. In this case, even with a shift in relative factor prices, wheat is still more land
intensive than cloth. If isoquants are drawn where the wheat isoquant shows a high degree of
substitution between land and labor while the cloth isoquant shows that land and labor are more
complementary, then a reversal in factor intensity is possible.
- Derivation of the production possibility curve
- Place two figure 3.1's back to back to form Edgeworth Box. In figure 3-6 line
OO' is the contract curve. It is always more efficient to move from a position such as Z off the
contract curve to a position such as Q on the contract curve. Points P, Q and R trace out the
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International Trade Notes: 10 October 2016
production possibility curve. Point Z becomes a point inside the production possibility curve.
- Along the contract curve the marginal rate of substitution between labor and land
in the production of wheat is the same as the marginal rate of substitution of labor and land in
the production of cloth.
- Define MPP i j as the increase in the production of j for one more input of i. In
equilibrium MPP 1 j / P1 = MPP 2 j / P2 where 1 and 2 are inputs.
- Slope of the isoquant = MPP 1 j / MPP 2 j
- Slope of isocost = P1 / P2
- Note: We assume that input 2 is on the vertical axis. (As you get close to
vertical axis MPP of that input 0 => slope . As you get to horizontal axis slope of
isocqant 0 => MPP of that input goes to 0.)
- Along the contract curve slopes of isoquants are the same. => (MPP 1 j / MPP 2 j)
= (MPP 1 i / MPP 2 i ) and are equal to the ratios of the input prices P1 / P2
- Figure 3-7 shows effect on production possibility curve of increasing inputs land
and labor.
- Slope of PPC = marginal rate of transformation MRT. In equilibrium MRT =
ratio of good prices.
- In consumption theory we have
[MUx / Px] = [MUy / Py]
- Slope of indifference curve = MUx / MUy
- In equilibrium ratios of MU, prices and MRT are the same in both countries. =>
If the assumptions of the analysis are true you will get factor price equalization. For further
detail see classic papers by Stolper-Samuelson in 1941 and 1948.
- As the economy moves to equilibrium there are income effects. Owners of
factors of production having price increases (decreases) will have their relative incomes increase
(decrease). Because it is impossible to make interpersonal comparisons of utility, cannot tell if
national welfare went up. If all persons have the same utility functions and because income went
up => winners get more than losers lose. If all persons do not have same utility functions, then
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International Trade Notes: 10 October 2016
compensation principle can be used.
- Compensation principle. Can winners pay losers to accept the change? Will
they? In practice owners of scarce factors of production favor protection since free trade will
lower their rent. In the United States free trade usually impacts unskilled labor negatively. =>
labor often favors higher tariffs.
- The predictions of H-O theory require that adjustment is complete. In the short
run all factors of production in the import competing industry may be hurt. Since these industries
are in specific regions, may have negative regional effects.
- Trade is a substitute for factor mobility. H-O theory => can either have factor mobility
or international trade. Factor mobility alters the relative prices of factor prices. Rybczynski
Theorem show conditions under which relative factor prices do not have to move when one input
increases. European economic community allows labor to be mobile but when times get tough in
one region labor can go home. EEC found cultural effects of labor mobility. NAFTA allows
Mexican workers not to come to the US to produce but to produce in Mexico and send goods
here.
- Rybczynski Theorem shows conditions under which an increase in one factor of
production does not lead to the relative price of this factor going down. (See figure 3.9). Assume
the economy is on the contract curve and that on the axis of the Edgeworth box is Labor and
Capital. Assume that labor is on the horizontal axis. Given the production of X and Y does not
change and K is labor intensive, then if L => [PL/PK] . If on the other hand the production of
the capital intensive good Y goes down and the production of the labor intensive good X goes up,
then the capital released from the production of Y will combine with the new labor such that it is
possible that [PL/PK] remains unchanged. This theorem shows that immigration of labor does not
necessarily result in a decrease in the wage rate. There are three possible cases. The Rybczynski
line can be drawn on the production possibility diagram. In order for [PL/Pk] to stay constant,
when the input used most intensively in the production of C goes up, the output of food must
decrease to release the other input to now combine with the more plentiful input. See figure 3.9
-Leontief Paradox. Leontief expected that the United States would export goods that were
capital intensive and import goods that were labor intensive. We found the converse. Why?
(Later using the H-O-V theory we will discuss whether in fact Leontief setup the econometric
model correctly.
- US labor may have more (human) capital attached than labor in other countries.
=> cannot just measure labor.
- H-O theory assumes same tariff on all goods. US tariffs are relatively higher on
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International Trade Notes: 10 October 2016
labor intensive good than capital intensive goods.
- Leontief may have statistical error such that the there may not be a significant
difference between the two capital/labor ratios.
- Reversal. The H-O theory assumes that all goods can be ranked in terms of their
capital intensity and that the ranking is the same for all price ratios of capital and labor. The usual
case is:
Figure 4.2 Non Reversal Case
Figure 4.2 shows the usual case. For relative price # 1 X=Y=1. If (Pk/PL) =>
than x=1 is less expensive than y=1. Hence (PX/PY) and (PK/PL) are positively related.
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International Trade Notes: 10 October 2016
Figure 4.3 shows a factor intensity reversal.
Assume two goods X and Y. X has low substitutability of capital and labor while
Y has high substitutability of capital and labor. In figure 4.3 for isocost line BB [PL/PK] > than
[PL/PK] for AA. For BB good Y is relatively more capital intensive than X, for AA good Y is
relatively more labor intensive than X. => H-O assumption of ranking goods in terms of their
capital intensive does not hold and the prediction of H-O on the intensive of the exports of the
United States will not necessarily hold. The importance of a reversal is that some for one P X / PY
value there are two values of P L / PK.
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International Trade Notes: 10 October 2016
Scale induced factor intensity reversal. Analysis to date has assumed that
( PK / PL ) 0 and showed under what conditions it was possible for a reversal to take place.
Now assume ( PK / PL ) 0 and look at figure 8. Here as the isocost shifts out, X continues to be
capital intensive and Y continues to be labor intensive. This is the usual case. Figure 9 shows
what happens when there is a factor intensity reversal even without a change in relative factor
prices. Here due to scale effects at relatively low level of output X is relative capital intensive
and Y is relatively labor intensive. At higher levels of output the situation reverses. Example: A
small garden may be labor intensive. As the scale of operation increases, the production process
becomes more capital intensive.
Figure 4.4 Reversal due to scale
- Since Leontief looked only at labor and capital, all natural resources were
lumped into capital. This may have biased the results.
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Stopler- Samuelson Theorem – Preliminary graphical analysis.
The real return to a nation’s scarce factor of production will
rise with the imposition of a tariff. Logic: Nation 2 the K
abundant nation) imposes an import tariff on commodity X (its L
p
intensive commodity). x for domestic producers and consumers
py
which implies that the real wage of labor (Nation 2’s scare
K
factor) will increase. The tariff results in an increase in
L
in the production of both goods causing the wage of labor to
increase as domestic production of import protected good X
increases.
The Edgeworth box which shows endowments has tangency points of
the two isoquants that can be moverd to the production frontier
(see figure 3.9 of supplementary graphs) If there is not
complete specialization there is a maping from the relative
prices of goods to relative prices of factors. Factor price
P
equalization can occur due to movement of inputs that change k
PL
P
or trade opening of trade that changes X . A quick analysis is
PY
shown below:
- Heckscher-Ohlin - Factor price Adjustment. H-O theory shows how trade tends to
equalize good prices and factor prices (in the absence of complete specialization.) Figure 11A &
11B shows the conditions under which factor prices adjust (11A) and do not adjust (11B). In 11A
The initial endowments of the countries (RI and RII) are more similar than in figure 11B.
AI
=> complete specialization of X in country I
AII
=> complete specialization of X in country II
BI
=> complete specialization of Y in country I
BII
=> complete specialization of Y in country II
In figure 11A BII < BI < AII < AI while in figure 11B
BII < AII < BI < AI
Because of complete specialization in figure 11B you never can get to the zone between AII - BI
=> need factor mobility.
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International Trade Notes: 10 October 2016
Figure 11 R1 and R2 are the endowment ratios in country 1 and 2.
Obstacles to factor price equalization from trade
- Many countries - will only cause problems if all productions functions are not the same.
- Many products and factors - to equalize all factors need an equal number of traded products.
- Imperfect competition - To get equalization need MC = price of product and factors being paid
the value of their marginal product.
- Increasing returns to scale breaks down perfect competition since one producer dominates.
- Different production functions in different countries ruins equalization since one country will
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International Trade Notes: 10 October 2016
have an edge.
- Increasing marginal productivity of factors of production => the price of factors =/ VMP of
factor.
- Factor intensity reversals cause problems due to: 1. lack of homogeneity since will not get
straight line expansion paths and 2. due to one good's isoquant curve being positioned inside
another good's isoquant curve. If a country expands and there is a reversal there will be a switch
in the good having comparative advantage.
If trade does not equalize factor prices, factors can move!
Even if factor prices adjust, the formerly scare factor owners will lose relative to the
formerly abundant factor owners. This change in the relative position of factor owners sets the
stage for political pressure for tariffs. Since the welfare of the country goes up with free trade =>
gainers should be able to compensate losers. Problem: it may take time to adjust.
Math Treatment of Two Factor Model (See Chapter 1 of Feenstra) Optional topic.
yi f i ( Li , K i ), i 1, 2
L1 L2 L
(M1)
K1 K 2 K
G ( p1 , p2 , L, K ) max y1 , y2 p1 y1 p2 y2 s.t. y2 h( y1 , L, K )
We assume perfect competition in product and factor markets. This assumption implies that each
industry is producing to maximize GDP. By substituting the constraint into the GDP objective
function and choosing y1 to maximize
p1 y1 p2h( y1, L, K )
(M2)
gives the first order condition p1 p2 (h / y1 ) 0 or
p
p1
h
y
2
p2
y1
y1
(M3)
or in words the economy will produce where the relative price of good 1 equals the slope of the
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International Trade Notes: 10 October 2016
production possibility curve. Equation M3 can be seen if we divide the first order condition by
p2 Differentiation of the GDP function (M1) produces
y
G
y
yi p1 1 p2 2 ,
pi
pi
pi
(M4)
Due to the "envelope theorem" the terms inside
sum to 0 resulting in G / pi yi .
In words
the derivative of the GDP function with respect to the price of good i is the output of good i.
The envelope theorem can be seen once we note that p1y1 p2y2 from M3. Moving all terms
to the left hand side and dividing by pi shows that
0 for small movements of
yi induced
by changes in pi .
The unit cost function
ci (w, r ) min Li ,Ki 0 wLi rKi | fi ( Li , Ki ) 1
(M5)
is the dual of the production function fi ( Li , Ki ) . The solution of the maximization of the unit
cost function is
ci (w, r ) waiL raiK
(M6)
where aiL yi Li and aiK yi Ki at the equilibrium
ci
a
a
aiL w iL r iK
w
w
w
ci
a
a
aiK w iL r iK
r
r
r
(M7)
ci
c
aiL , i aiK since the terms inside =0. In words, at equilibrium, aiL and aiK are
w
r
the derivatives of the unit cost function with respect to the wage and interest rate, The
assumption that profits equal zero (perfect competition) and full employment produces four
nonlinear equations that solve w, r , y1, y2 .
Gives
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International Trade Notes: 10 October 2016
p1 c1 ( w, r )
p2 c2 ( w, r )
(M7 & M8)
a1L y1 a2 L y2 L
a1K y1 a2 K y2 K
The first two equations indicate that provided there are no reversals and both goods are produced,
each price vector p ( p1, p2 ) corresponds to a unique wage and interest rate independent of
factor endowments. Using the Ricardian model, however, this would not be the case, since any
increase in L / K would lower wages.
If we totally differentiate the zero profit condition we get equation 1.9 of Feenstra (2016) which
is M9 below.
The Samuelson factor price equalization theorem (1949) requires the two sector model. The
reason trade can equalize factor prices is that a labor intensive country can keep exporting the
labor intensive product so that the wages of labor are kept high.
Magnification Effect. How do changes in product prices impact factor prices? Optional
topic.
First differentiate the zero profit equations (M7).
dpi aiL dw aik dr
(M9)
Which can be transformed to
dpi waiL dw raiK dr
(M10)
pi
ci w
ci r
wa
ra
dw
Note d ln w
. Define iL iL and iK iK or in words the cost share of labor and
w
ci
ci
dp
dw
dr
, rˆ
capital in industry i. Given ci waiL raiK iL iK 1 . Define pˆ i i , wˆ
pi
w
r
which implies
pˆ i iL wˆ iK rˆ, i 1, 2
(M11)
which can be solved as
38
International Trade Notes: 10 October 2016
pˆ1 1L 1K wˆ
ˆ
p2 2 L 2 K rˆ
1
wˆ 1L 1K pˆ1 1 2 K 1K pˆ1
ˆ
r 2 L 2 K pˆ 2 | | 2 L 1L pˆ 2
| | (1L 2 K 1K 2 L )
(M12)
1L (1 2 L ) (1 1L ) 2 L
1L 2 L 2 K 1K
If industry 1 is labor intensive => 1L 2 L | | 0 .
Assume the price of good 1 increases so pˆ ( pˆ1 pˆ 2 ) 1
2 K pˆ1 1K pˆ 2 ( 2 K 1K ) pˆ1 1K ( pˆ1 pˆ 2 )
( pˆ pˆ 2 )
pˆ1 1K 1
pˆ1
| |
( 2 K 1K )
( 2 K 1K )
(M13)
1L pˆ 2 2 L pˆ1 (1L 2 L ) pˆ 2 2 L ( pˆ1 pˆ 2 )
( pˆ pˆ 2 )
pˆ 2 2 L 1
pˆ 2
| |
(1L 2 L )
(1L 2 L )
(M14)
wˆ
rˆ
Wages increases more than price of good 1 since wˆ pˆ1 pˆ 2 . Since both w / p1 and w / p2
workers can buy more of both good 1 and good 2 (real wage up). Since r / p1 and r / p2 the
real return to capital has fallen due to p1 and p2 increasing.
Stopler-Samuelson 1941 theorem "An increase in the relative price of a good will increase the
real return to the factor used intensively in that good and reduce the real return to the other
factor."
wˆ pˆ1 pˆ 2 rˆ
(M15)
Which is called the "magnification effect" by Jones (1965) since any change in product prices has
a magnified effect on the factor prices. Assume tariffs are lowered so that import prices fall this
will result in effects on wage rates that are greater than product price changes. Later we will
show the conditions of the Rybczynski theorem that shows when increased trade is not changing
39
International Trade Notes: 10 October 2016
input prices.
Effect of changes in Endowments on Industry outputs
Holding product prices fixed implies that aiL and aiK do not change. From (M8)
a1L dy1 a2 L dy2 dL
(E1)
a1L dy1 a2 K dy2 dK
Which can be rewritten as
y1a1L dy1 y2 a2 L dy2 dL
L y1
L y2
L
(E2)
y1a1K dy1 y2 a2 K dy2 dK
K y1
K y2
K
Define dyi / yi yˆi , iL ( yi aiL / L) Li / L and iK ( yi aiK / K ) Ki / K where 1 j 2 j 1 .
And rewrite (E2) as
1L yˆ1 2 L yˆ 2 Lˆ
(E3)
1K yˆ1 2 K yˆ 2 Kˆ
And solve
1L 2 L yˆ1 Lˆ
yˆ ˆ
1K 2 K 2 K
(E4)
yˆ1 1 2 K 2 L Lˆ
ˆ
y2 | | 1K 1L Kˆ
(E5)
| | 1L2 K 2 L1L
1L (1 1K ) (1 1L )1K
(E6)
1L 1K 2 K 2 L
40
International Trade Notes: 10 October 2016
Since industry 1 is labor intensive (1L 1K ) 0 | | 0 . Given that labor is increasing
(immigration) and with a fixed capital stock => Lˆ 0 and Kˆ 0 since factor prices and product
prices are fixed, then
2 K
Lˆ Lˆ 0
(2 K 2 L )
1K
yˆ 2
Lˆ 0
(2 K 2 L )
yˆ1
(E7)
Which proves the Rybczynski theorem that the labor intensive industry, 1, increases production
(using up the new labor) and the capital intensive industry, 2, decreases production thus releasing
capital to combine with this newly more abundant labor force.
When oil was discovered off the Dutch coast. Industries using oil expanded while other
industries not using oil contracted. This was called the "Dutch disease."
Remark: The Rybczynski theorem assumes that both goods are produced (in the zone of
diversification) and there are no reversals (either relative price reversals or scale reversals).
For any endowment vector (L, K), there is a unique y1 , y2 such that when (a1L a1K ) and (a2 L a2 K )
are multiplied by this vector all endowments will be used. See (M8).
Under what conditions will all outputs be > 0? Consult Feenstra Figure 1.9. The (L' K) must lie
inside the vectors (a1L a1K ) and (a2 L a2 K ) . For example if too much labor is added, even if
industry 2 completely stops, not enough capital can be released to hold relative factor prices
constant.
Proof that the Rybczynski line is straight. From (E1) assume dK 0 which implies
dy
a
a1L dy1 a2 K dy2 0 . The slope of the Rybczynski line is 2 1K and fixed since
dy1
a2 K
a1K and a2 K are fixed by assumption.
5. Effect on Wages of Outsourcing Intermediate Inputs; Developing an Empirical Model
The goal of this section is to present the key ideas in Feenstra (2004) chapter 4 regarding
modeling outsourcing. Preliminary empirical results will also be presented that extend his models
reported in his Tables 4.4 and 4.5. The paper "The Impact of Outsourcing and High-Technology
41
International Trade Notes: 10 October 2016
Capital on Wages: Estimates for the United States 1979-1990" by Robert Feenstra and Gorden
Hanson Quarterly Journal of Economics Vol 114 # 3 (August 1999) pp 907-940 should also be
consulted. Feenstra has provided his data and Stata programs which helps in the replication.
B34S data files are also distributed to aid in the replication and extension of this important work.
- Since the 1980's the wage of skilled workers has increased relative to unskilled
workers. We want to look at the effect of outsourcing to try to explain what has occurred.
- Assume an input is outsourced and is thus lower cost.
- Option 1 is to use the Stopler-Samuelson 1941 Theorem, to show how if a traded good
price increases the price of the input used most intensively will increase relative to the other
input.
- Option 2 use Heckscher-Ohlin-Vanek approach and compute the change in factor
content of trade and the associated changes in factor prices. Assume w t is the equilibrium wage
in a county in year t and F t is the factor content of exports where endowments are given.
Deardoff-Staiger (1988) show that
( w2 w1 )( F 2 F 1 ) 0
(5.1)
Which implies that a higher content of imports for some factor k , or Fk2 Fk1 0 or
( Fk2 Fk1 ) 0 will be associated with a falling wage for that factor or ( wk2 w1k ) 0. The same
effect as immigration on labor wage. Borjas, Freeman and Katz (1997) find that immigration into
the US during 1980-1995 explains 25% to 50% of the relative wage of high school dropouts. The
increasing factor content of imports from less-developed countries also reduces the wage of high
school drop outs but less than immigration.
-Option 3 is to directly model the presence of traded intermediate inputs caused by firms
splitting their production across several countries. Key idea Trade in intermediate inputs can
have an effect on production and factor prices that is different from trade in final goods.
-
A fall in the price of imported intermediate inputs decreases the relative wage of the
factor used intensively in those imports in the home country. (See Stopler-Samuelson).
(Note in this setup the intermediate input is produced in the foreign and domestic
country.)
-
Since the US outsources production of labor intensive intermediate goods, this suggests a
fall in the wage of unskilled labor in the United States since there is now less demand for
the domestically produced intermediate input. Feenstra (page 117) argues what while
42
International Trade Notes: 10 October 2016
unskilled labor in the home country (US) are the most disadvantaged, their real wages
may in fact increase never the less due to possible lower prices of the final product.
-
Assuming a continuum of inputs and the 1980 Dornbusch-Fisher-Samuelson model. The
US is more abundant in skilled labor than abroad. Their model predicts that the growth of
capital or technology abroad will lead to increased outsourcing of labor intensive inputs
from the US and increase the relative wage of skilled labor in both countries. Reason.
capital and or technology implies the marginal product of foreign labor (both skilled
and unskilled) goes up leading to more outsourcing. In the US unskilled labor wages fall
relative to skilled wages.
-
In period 1979-1995 real wages of those with HS fell 13.4%, those with less that 12 years
of school fell 20.2% and those with 16 or more years of school increased by 3.4%.
-
See Figures 4.1 & 4.2. There has been both an increase in the relative wage of
nonproduction to production (manufacturing) workers and an increase in the relative
employment of nonproduction to production workers. The only explanation is that there
has been a movement outward of the demand curve for more skilled workers. The bulk
of the increase in relative demand has occurred within the manufacturing industries.
-
This suggests that trade cannot be a dominant explanation of the wage and employment
shifts because the movements between industries are smaller than the movements within
industries.
-
Stopler-Samuelson suggests that if the price of skill intensive products (computers)
increases then the relative wages of skilled workers will increase but the prices of
computers fell and the relative wages of skilled workers increased. Data from Lawrence
and Slaughter (1993) showed that the relative prices of goods produced in low skilled
(production) worker intensive industries increased. => Price movements due to
international competition could not explain the wage movements.
-
Trade however can shift the structure of production within an industry and thus on factor
demand within an industry.
43
International Trade Notes: 10 October 2016
Simple Model of Trade in Intermediate Inputs
See Feenstra 2004 Chapter 4
y1 unskilled labor intensive input
y2 skilled labor intensive input
Li Unskilled labor
H i skilled labor
K i Capital
pi price of input i
xi 0 ( 0) import (export) of input i.
yi fi ( Li , H i , Ki ),
i 1, 2
(4.2)
Given the price of traded inputs p ( p1 p2 ) and holding capital fixed the production of the
final good yn in terms of inputs 1 and 2 is
(5.2)
yn f n ( y1 x1 , y2 x2 )
Where x1 0 implies import of input 1 x2 0 implies exports of input 2.
Ignoring additional labor and capital used in the final "bundling" stage for production of the final
product,
L1 L2 Ln , H1 H 2 H n , K1 K 2 K n
(4.3)
Optimal output assuming perfect competition maximizes
Gn ( Ln , H n , K n pn , p) max xi , Li , Hi , Ki pn f n ( y1 x1, y2 x2 ) p1 x1 p2 x2
(4.4)
subject to the resource constraints (4.3) and the production technology (4.2)
- The question becomes how will a drop in the relative price of imported inputs affect
factor prices?
For locally produced inputs to be competitive to those produced abroad, assume zero profit
condition for producing inputs yi for i 1, 2
44
International Trade Notes: 10 October 2016
pi ci (w, q, r )
(5.5)
Totally differencing (5.5) following Jones (1965) express the percent change in prices pˆ i and as
a function of the percent change in input prices wˆ , qˆ , rˆ where ij = cost share of factor j in the
production of input i.
ij
1.
j
pˆ1 1L wˆ 1H qˆ 1K rˆ
pˆ 2 2 L wˆ 2 H qˆ 2 K rˆ
(5.6)
With two equations and three unknowns ( wˆ , qˆ , rˆ) no solution is possible unless we assume
capital has equal shares in the two industries (1K 2 K ) and subtract
pˆ1 pˆ 2 (1L 2 L ) wˆ (1H 2 H )qˆ
(1L 2 L )( wˆ qˆ )
(5.7)
Note that (1K 2 K ) (1L 1H ) (2 L 2 H ) or (1L 2 L ) (1H 2 H )
since
ij
1.
j
Activity 1 involves unskilled labor => (1L 2 L ) 0 . The importance of this is that it shows
that a decrease in the relative price of the unskilled labor intensive import 1 ( pˆ1 pˆ 2 ) 0
leads to a decrease in the relative wage of unskilled labor in the domestic country ( wˆ qˆ ) 0
( wˆ qˆ )
( pˆ1 pˆ 2 )
(1L 2 L )
(5.8)
In summary, a drop in the price of the imported unskilled labor intensive input 1 leads to a fall in
the relative wage of unskilled labor or ( w / q) .
What happens to the price of the final product pn ? Define pn cn ( p1, p2 ) = unit cost that is the
dual of the production function yn f n ( y1, y2 ) . The change in the final good price is a weighted
average of the input prices
pˆ n n1 pˆ1 n 2 pˆ 2
(5.9)
45
International Trade Notes: 10 October 2016
( pˆ1 pˆ 2 ) 0 pˆ1 pˆ n pˆ 2 or ( pˆ n pˆ1 ) 0 .
We have shown that the relative price of the final product rises relative to the price of the
imported input. In the US in the 1980's domestic prices rose faster than import prices.
Note we are comparing import and domestic prices within an industry. While the relative wage of
unskilled workers falls in both countries, their real wages need not fall.
Estimation setup
Since (5.4) is linear homogeneous it can be written as
(5.10)
pnGn ( Ln , H n , Kn , 1, p / pn )
A measure of real value-added including real net exports becomes
Yn Gn ( Ln , H n , Kn , 1, p / pn )
(5.11)
Given that the capital stock and output are fixed in the short run, we define a short-run cost
function
Cn ( w, q, K n , Yn , p / pn ) min Ln , H n wLn qH n s.t.(5.11)
(5.12)
Note than any structural variables that shift the production function and affect costs should be
included. In the empirical implementation imported intermediate inputs will be measured by
expenditure on imported inputs for each industry. Structural variables in industry n will be
denoted as zn . Feenstra uses the translog production function
M
ln C 0 i ln wi
i 1
K
K
k ln xk
k 1
1 M M
ij ln wi ln w j
2 i 1 j 1
K
M K
1
k l ln xk ln xl i k ln wi ln xk
2 k 1 l 1
i 1 k 1
(5.13)
k 1, , K = inputs/shift parameters.
wi = optimally chosen inputs for i 1, , M , xk
There are two optimally chosen inputs, skilled and unskilled labor. The objective is to calculate
the effect on the percent change in costs if the price of one labor input changes.
46
International Trade Notes: 10 October 2016
ln C C wi
ln wi wi C
(5.14)
Differentiating (5.13) with respect to ln wi produces a short run model which was estimated in
Feenstra 4.4
M
K
j 1
k 1
si i i j ln w j i k ln xk i 1,
(4.17)
,M
Feenstra imposed symmetry i j j i and the requirement that (5.13) was homogenious of degree
M
one in wages which implied
i 1
i
M
M
i 1
i 1
1, i j i k 0 .
Assume a cross section of countries. Equation (4.17) can be estimated over time, for a single year
or for the change between two years. Feenstra used this latter approach for the years 1979 and
1990. This approach assumed the same cost function applied across the industries. Feenstra also
made the usual assumption of dropping the wage terms to estimate a wage share of skilled labor
SnH 0 k ln Kn ln Yn z 'zn n 1, , N
(4.18)
in table 4.4.
Basic idea page 118 “The decision of companies tp purchase intermediate inputs from overseas
will most certainly affect their employment at home and can be expected to differentially affect
skilled versus unskilled workers. With firms in industrial countries facing a higher relative wage
for unskilled labor than that found abroad, the activities that are outsourced would be would be
those that use a large amount amount of unskilled labor such as assembly of components and
other repitive tasks. Moving these activitied overseas will reduce the the relative demand for
unskilled laboer in the industrial country, in much the same way as replacing these workers with
automated production” Page 122 discusses right hand side variables. Outsourcing and computer
share have a positive effect. Rquation very sensitive. We look at
Looks at 447 industries. In some runs drops computers. Dependent variable = change in non
production wage share in industry . Controls include shipments Y and change in ln K/Y). is
structural variable., outsourcing Equation is not stable.
Table 4.5 looks at log change in industry price. “Slight changes in the data such as dropping the
computer industry have dramatic effects on the results.”
Feenstra (page 133) a drop in the price of imported intermediates has effects that are
47
International Trade Notes: 10 October 2016
observationally equivalent to the effect of skilled-based technological change.”
Files Problem_4.2.do code and data_Chp4.dta are available on class ftp location. This problem
is not discussed in Feenstra 2016.
// set mem 300m
* Annotated October 2014
log using log_4_2.log,replace
// use d:\feenstra_course\chap4\data_Chp4,clear
use c:\feenstra_course\chap4\data_Chp4,clear
// use e:\feenstra_course\chap4\data_Chp4,clear
* use /usr/local/lib/hhsfiles/data_Chp4,clear
drop if year==1972|year==1987
drop if sic72==2067|sic72==2794|sic72==3483
egen wagebill=sum(pay), by(year)
gen share=pay/wagebill
sort sic72 year
by sic72: gen lagshare=share[_n-1]
gen ashare=(share+lagshare)/2
by sic72: gen lagnwsh=nwsh[_n-1]
gen chanwsh=(nwsh-lagnwsh)*100/11
gen
gen
gen
gen
gen
gen
gen
gen
gen
gen
gen
gen
gen
gen
gen
wchanwsh=chanwsh*ashare
wdlky=dlky*ashare
wdly=dly*ashare
wdsimat1a=dsimat1a*ashare
wdsimat1b=dsimat1a*ashare
diffout=dsimat1a-dsimat1b
wdiffout=(dsimat1a-dsimat1b)*ashare
wcosh_exp=dofsh*ashare
htsh_exp=dhtsh-dofsh
whtsh_exp=(dhtsh-dofsh)*ashare
wcosh_exa=dofsh1*ashare
htsh_exa=dhtsh1-dofsh1
whtsh_exa=(dhtsh1-dofsh1)*ashare
wcosh=ci*ashare
whtsh=dhtsh*ashare
* Check with the first column of Table 4.4 *
tabstat wchanwsh wdlky wdly wdsimat1a wcosh_exp whtsh_exp wcosh_exa whtsh_exa wcosh whtsh,
stats(mean)
tabstat chanwsh dlky dly dsimat1a dofsh htsh_exp dofsh1 htsh_exa ci dhtsh, stats(mean)
* Reproduce the rest of the columns in Table 4.4 *
* replicates table 4.4 col 2
regress chanwsh dlky dly dsimat1a dofsh htsh_exp [aw=ashare], cluster (sic2)
* test ols
regress chanwsh dlky dly dsimat1a dofsh htsh_exp
* replicates table 4.4 col 3
regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa [aw=ashare], cluster (sic2)
* test ols
regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa
* replicates table 4.4 col 4
regress chanwsh dlky dly dsimat1a ci dhtsh [aw=ashare], cluster (sic2)
* test ols
regress chanwsh dlky dly dsimat1a ci dhtsh
48
International Trade Notes: 10 October 2016
* To instead distinguish narrow and other outsourcing, we can reproduce column (1) of table III
in Feenstra and Hanson, 1999 *
tabstat wchanwsh wdlky wdly wdsimat1b wdiffout wcosh_exp whtsh_exp wcosh_exa whtsh_exa wcosh
whtsh, stats(sum)
* Reproduce the rest of the columns in Table III *
regress chanwsh dlky dly dsimat1b diffout dofsh htsh_exp [aw=ashare], cluster (sic2)
regress chanwsh dlky dly dsimat1b diffout dofsh1 htsh_exa [aw=ashare], cluster (sic2)
regress chanwsh dlky dly dsimat1b diffout ci dhtsh [aw=ashare], cluster (sic2)
log close
* clear
exit
Note the relatively low R2 terms. This model was estimated with Stata which uses the weighted
regression coefficients on the raw data in a manner that is not used in Rats.
.
. * replicates table 4.4 col 2
. regress chanwsh dlky dly dsimat1a dofsh htsh_exp [aw=ashare], cluster (sic2)
(sum of wgt is
1.0000e+00)
Linear regression
Number of obs
F(5, 19)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
6.72
0.0009
0.1557
.38912
(Std. Err. adjusted for 20 clusters in sic2)
-----------------------------------------------------------------------------|
Robust
chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0467948
.0113832
4.11
0.001
.0229695
.0706201
dly |
.0197383
.0063797
3.09
0.006
.0063853
.0330912
dsimat1a |
.1966658
.0962066
2.04
0.055
-.004697
.3980286
dofsh |
.19534
.0915302
2.13
0.046
.0037651
.3869148
htsh_exp | -.0650465
.1371193
-0.47
0.641
-.3520404
.2219474
_cons |
.2028764
.0428851
4.73
0.000
.1131169
.292636
-----------------------------------------------------------------------------. * test ols
. regress chanwsh dlky dly dsimat1a dofsh htsh_exp
Source |
SS
df
MS
-------------+---------------------------------Model | 4.87604716
5 .975209432
Residual | 99.6927448
441 .226060646
-------------+---------------------------------Total | 104.568792
446 .234459175
Number of obs
F(5, 441)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
447
4.31
0.0008
0.0466
0.0358
.47546
-----------------------------------------------------------------------------chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0194616
.010929
1.78
0.076
-.0020179
.0409411
dly |
.0016347
.0087081
0.19
0.851
-.0154799
.0187492
dsimat1a |
.0854863
.0403379
2.12
0.035
.006208
.1647647
dofsh |
.1773819
.078036
2.27
0.024
.0240132
.3307505
htsh_exp | -.0063895
.1034685
-0.06
0.951
-.2097421
.1969632
_cons |
.3044169
.0345396
8.81
0.000
.2365342
.3722995
-----------------------------------------------------------------------------.
. * replicates table 4.4 col 3
. regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa [aw=ashare], cluster (sic2)
(sum of wgt is
1.0000e+00)
Linear regression
Number of obs
F(5, 19)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
8.01
0.0003
0.1592
.38832
(Std. Err. adjusted for 20 clusters in sic2)
49
International Trade Notes: 10 October 2016
-----------------------------------------------------------------------------|
Robust
chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0444529
.0113121
3.93
0.001
.0207764
.0681293
dly |
.0173278
.0062906
2.75
0.013
.0041613
.0304942
dsimat1a |
.2207528
.0999711
2.21
0.040
.0115109
.4299947
dofsh1 |
.4309753
.1671453
2.58
0.018
.0811362
.7808144
htsh_exa |
.0052436
.0712031
0.07
0.942
-.1437862
.1542735
_cons |
.2064394
.0397614
5.19
0.000
.1232178
.289661
-----------------------------------------------------------------------------. * test ols
. regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa
Source |
SS
df
MS
-------------+---------------------------------Model | 4.42334831
5 .884669662
Residual | 100.145444
441 .227087174
-------------+---------------------------------Total | 104.568792
446 .234459175
Number of obs
F(5, 441)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
447
3.90
0.0018
0.0423
0.0314
.47654
-----------------------------------------------------------------------------chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0210034
.0110506
1.90
0.058
-.000715
.0427218
dly |
.0009338
.0089879
0.10
0.917
-.0167306
.0185982
dsimat1a |
.0899303
.0407687
2.21
0.028
.0098053
.1700553
dofsh1 |
.2866326
.1631938
1.76
0.080
-.0341015
.6073667
htsh_exa | -.0076398
.1360646
-0.06
0.955
-.2750554
.2597758
_cons |
.3244891
.0375708
8.64
0.000
.250649
.3983292
-----------------------------------------------------------------------------.
. * replicates table 4.4 col 4
. regress chanwsh dlky dly dsimat1a ci dhtsh [aw=ashare], cluster (sic2)
(sum of wgt is
1.0000e+00)
Linear regression
Number of obs
F(5, 19)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
11.87
0.0000
0.1885
.38148
(Std. Err. adjusted for 20 clusters in sic2)
-----------------------------------------------------------------------------|
Robust
chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0399279
.0087378
4.57
0.000
.0216396
.0582162
dly |
.0100379
.0062332
1.61
0.124
-.0030084
.0230841
dsimat1a |
.1346024
.0883067
1.52
0.144
-.0502257
.3194306
ci |
.0180834
.0066465
2.72
0.014
.0041722
.0319946
dhtsh |
.0324624
.0519
0.63
0.539
-.0761655
.1410904
_cons |
.1569685
.0446895
3.51
0.002
.0634323
.2505048
-----------------------------------------------------------------------------. * test ols
. regress chanwsh dlky dly dsimat1a ci dhtsh
Source |
SS
df
MS
-------------+---------------------------------Model | 6.52521799
5
1.3050436
Residual | 98.0435739
441 .222321029
-------------+---------------------------------Total | 104.568792
446 .234459175
Number of obs
F(5, 441)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
447
5.87
0.0000
0.0624
0.0518
.47151
-----------------------------------------------------------------------------chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0185285
.0105271
1.76
0.079
-.0021611
.0392181
dly | -.0008842
.0086306
-0.10
0.918
-.0178465
.0160781
dsimat1a |
.0523652
.0414966
1.26
0.208
-.0291904
.1339207
ci |
.013381
.0043628
3.07
0.002
.0048065
.0219555
dhtsh |
.0870111
.0613731
1.42
0.157
-.0336091
.2076312
_cons |
.2455871
.037316
6.58
0.000
.1722479
.3189263
------------------------------------------------------------------------------
.
In Table 4.4 Feenstra is estimating equation 4.18
For more details see the assignment sheet.
50
International Trade Notes: 10 October 2016
Example Code and results from B34S, Rats and Stata:
/;
/; Uses Align to insure 447 obs
/;
b34sexec options ginclude('Feenstra_ch4.mac') member(table4_4A);
b34srun;
/; b34sexec data set dropmiss; b34srun;
b34sexec matrix;
/; call loaddata;
call get(chanwsh dlky dly dsimat1a dofsh dofsh1 htsh_exp htsh_exa
ci dhtsh
);
big=
'chanwsh dlky dly dsimat1a dofsh dofsh1 htsh_exp htsh_exa ci dhtsh';
call align(argument(big));
mod4_42='
mod4_42='
mod4_43='
mod4_44='
chanwsh
chanwsh
chanwsh
chanwsh
dlky
dlky
dlky
dlky
dly
dly
dly
dly
dsimat1a dofsh htsh_exp';
dsimat1a dofsh htsh_exp';
dsimat1a dofsh1 htsh_exa';
dsimat1a ci dhtsh';
n=namelist(argument(big));
do i=1,10;
call describe(argument(n(i)) :print);
enddo;
/; call tabulate(argument(mod4_42));
/; call tabulate(argument(mod4_43));
/; call tabulate(argument(mod4_44));
call olsq(
argument(mod4_42)
call gamfit(
argument(mod4_42)
call marspline(argument(mod4_42)
call
ppreg(argument(mod4_42)
:print :white);
:print );
:print);
:print);
call olsq(
argument(mod4_43)
call gamfit(
argument(mod4_43)
call marspline(argument(mod4_43)
call
ppreg(argument(mod4_43)
:print :white);
:print );
:print);
:print);
call olsq(
argument(mod4_44)
call gamfit(
argument(mod4_44)
call marspline(argument(mod4_44)
call
ppreg(argument(mod4_44)
:print :white);
:print );
:print);
:print);
b34srun;
Note: If Feenstra_ch4.mac is on your computer, unless it is in c:\b34slm, do not use ginclude.
Note: The Stata code [aw=share] weights the regression including the constant by multiplying buy
51
International Trade Notes: 10 October 2016
sharei . What effect does this transformation have if the variables are not appropriate? Note that Rats
and B34S and other software divide the right and left hand sides by
52
sharei .
International Trade Notes: 10 October 2016
Example code from Problem _4_2.do
set mem 300m
log using log_4_2.log,replace
use d:\feenstra_course\chap4\data_Chp4,clear
* use /usr/local/lib/hhsfiles/data_Chp4,clear
drop if year==1972|year==1987
drop if sic72==2067|sic72==2794|sic72==3483
egen wagebill=sum(pay), by(year)
gen share=pay/wagebill
sort sic72 year
by sic72: gen lagshare=share[_n-1]
gen ashare=(share+lagshare)/2
by sic72: gen lagnwsh=nwsh[_n-1]
gen chanwsh=(nwsh-lagnwsh)*100/11
gen
gen
gen
gen
gen
gen
gen
gen
gen
gen
gen
gen
gen
gen
gen
wchanwsh=chanwsh*ashare
wdlky=dlky*ashare
wdly=dly*ashare
wdsimat1a=dsimat1a*ashare
wdsimat1b=dsimat1a*ashare
diffout=dsimat1a-dsimat1b
wdiffout=(dsimat1a-dsimat1b)*ashare
wcosh_exp=dofsh*ashare
htsh_exp=dhtsh-dofsh
whtsh_exp=(dhtsh-dofsh)*ashare
wcosh_exa=dofsh1*ashare
htsh_exa=dhtsh1-dofsh1
whtsh_exa=(dhtsh1-dofsh1)*ashare
wcosh=ci*ashare
whtsh=dhtsh*ashare
* Check with the first column of Table 4.4 *
tabstat wchanwsh wdlky wdly wdsimat1a wcosh_exp whtsh_exp wcosh_exa whtsh_exa wcosh whtsh,
stats(mean)
tabstat chanwsh dlky dly dsimat1a dofsh htsh_exp dofsh1 htsh_exa ci dhtsh, stats(mean)
* Reproduce the rest of the columns in Table 4.4 *
* replicates table 4.4 col 2
regress chanwsh dlky dly dsimat1a dofsh htsh_exp [aw=ashare], cluster (sic2)
* test ols
regress chanwsh dlky dly dsimat1a dofsh htsh_exp
regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa [aw=ashare], cluster (sic2)
* test ols
regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa
regress chanwsh dlky dly dsimat1a ci dhtsh [aw=ashare], cluster (sic2)
* test ols
regress chanwsh dlky dly dsimat1a ci dhtsh
* To instead distinguish narrow and other outsourcing, we can reproduce column (1) of table III
in Feenstra and Hanson, 1999 *
tabstat wchanwsh wdlky wdly wdsimat1b wdiffout wcosh_exp whtsh_exp wcosh_exa whtsh_exa wcosh
whtsh, stats(sum)
* Reproduce the rest of the columns in Table III *
regress chanwsh dlky dly dsimat1b diffout dofsh htsh_exp [aw=ashare], cluster (sic2)
53
International Trade Notes: 10 October 2016
regress chanwsh dlky dly dsimat1b diffout dofsh1 htsh_exa [aw=ashare], cluster (sic2)
regress chanwsh dlky dly dsimat1b diffout ci dhtsh [aw=ashare], cluster (sic2)
log close
* clear
exit
Table 4.5 in Feenstra(2004) (same as Table 4.1 in Feenstra(2016) estimates equation 4.24 which
calculates the implied change in factor prices assuming labor and capital are optimally selected or
Cn 4. ( wn , qn , rn , Yn , p / pn ) min Ln ,H n Kn wn Ln , qn H n rn K n
(4.19)
Total factor productivity is
(4.22)
TFPn (nl ln wn nH ln qn nk ln rn ) ln pn
Where the cost shares sum to unity and is the first difference. While 4.22 could be
estimated for the cost shares, a better strategy is to estimate
ln pn TFPn nL L nH H nK K
(4.24)
Where L , H , K are the change in factor prices that are mandated by the change in product
prices which is the dependent variable in (4.24). If these values are what occurred it is due to the
linkage between product and factor prices mandated by the Stopler Samuelson theory.
File problem_3_a.do estimates Feenstra (2004) equation 4.5 or Feenstra (2016) eq 4.1. OLS
models are run to test how the results might change if weighting was not used. Run2.b34 uses
GAM, MARS and PPREG on the models in Table 4.5 / 4.1
// set mem 3m
log using log_4_3a.log,replace
// use d:\feenstra_course\chap4\data_Chp4.dta, clear
use c:\feenstra_course\chap4\data_Chp4.dta, clear
// use e:\feenstra_course\chap4\data_Chp4.dta, clear
* use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
keep if year==1990
drop if sic72==2067
drop if sic72==2794
drop if sic72==3483
gen etfp=ptfp-err
gen adj1=1/(1-amesh)
gen etfp1=adj1*etfp
gen dlpvad1=adj1*dlpvad
gen apsh1=adj1*apsh
gen ansh1=adj1*ansh
gen aksh1=adj1*aksh
gen mshxpr=amsh*dlpmx
gen eshxpr=aosh*dlpe
54
International Trade Notes: 10 October 2016
* Reproduce Table 4.5 *
gen dlp34=dlp-mshxpr-eshxpr
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model
regress dlp34 ptfp apsh ansh aksh , robust
preserve
drop if sic72==3573
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model
regress dlp34 ptfp apsh ansh aksh , robust
regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp apsh ansh aksh mshxpr eshxpr, robust
restore
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
* OLS Model
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
log close
* clear *
exit
Results are given below. Note that in Feenstra (2016, 90) he appeared to back away from his research in
Table 4.1. “The estimates in table 4.1 are troubling because they show that the estimates of are quite
far off the mark: they do not reflect the actual changes in wages that occurred in the United States
during the 1980’s, are are quite sensitive to the data used used and specificatiuonb of the regression.
Run2.b34 shows alternative estimators on the table 4.1 data. More research is needed on this important
topic. The output from run2.b34 or run2.out is available on the class ftp location. More detail on this
problem is given later in the class notes. The results shown next show how much of a difference using
a weighted regression makes in “improving” the results. See that the R squared improved to .8957 from
.6967.
.
.
. * Reproduce Table 4.5 *
.
. gen dlp34=dlp-mshxpr-eshxpr
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(4, 442)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
106.29
0.0000
0.8957
.80656
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.9631819
.0702093
-13.72
0.000
-1.101168
-.8251963
55
International Trade Notes: 10 October 2016
apsh |
3.062598
1.22198
2.51
0.013
.6609845
5.464212
ansh |
2.294716
1.430073
1.60
0.109
-.5158719
5.105305
aksh |
7.887571
.7810006
10.10
0.000
6.352634
9.422507
_cons | -.7051116
.3006016
-2.35
0.019
-1.295898
-.1143256
-----------------------------------------------------------------------------.
. * OLS Model
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression
Number of obs
F(4, 442)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
110.62
0.0000
0.6967
.91728
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.6790007
.0709856
-9.57
0.000
-.8185121
-.5394894
apsh |
3.455601
.8328199
4.15
0.000
1.818822
5.09238
ansh |
3.905478
1.754048
2.23
0.026
.4581676
7.352789
aksh |
7.394156
.71982
10.27
0.000
5.979461
8.808851
_cons | -.7849882
.1904677
-4.12
0.000
-1.159323
-.4106534
-----------------------------------------------------------------------------.
. preserve
. drop if sic72==3573
(1 observation deleted)
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is
9.8179e-01)
Linear regression
Number of obs
F(4, 441)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
92.17
0.0000
0.8059
.74139
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.7531151
.0751891
-10.02
0.000
-.9008886
-.6053416
apsh |
2.427856
1.162844
2.09
0.037
.142451
4.713261
ansh |
4.086394
1.722144
2.37
0.018
.7017647
7.471024
aksh |
8.058291
.9411699
8.56
0.000
6.208556
9.908027
_cons | -.8249273
.2930995
-2.81
0.005
-1.400973
-.2488819
-----------------------------------------------------------------------------. * OLS Model
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression
Number of obs
F(4, 441)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
135.75
0.0000
0.6696
.87366
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.6043067
.0418654
-14.43
0.000
-.6865873
-.5220261
apsh |
3.156235
.7864841
4.01
0.000
1.610513
4.701958
56
International Trade Notes: 10 October 2016
ansh |
4.954764
1.5334
3.23
0.001
1.941084
7.968443
aksh |
7.396599
.7390641
10.01
0.000
5.944073
8.849124
_cons | -.8377685
.1852263
-4.52
0.000
-1.201804
-.4737325
-----------------------------------------------------------------------------.
. regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is
9.8179e-01)
Linear regression
Number of obs
F(5, 440)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
10.85
0.0000
0.4289
1.2034
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------apsh |
3.605277
1.88524
1.91
0.056
-.0999163
7.310471
ansh |
6.202674
4.036466
1.54
0.125
-1.730475
14.13582
aksh |
9.535214
2.18722
4.36
0.000
5.236518
13.83391
mshxpr |
1.219304
.2471334
4.93
0.000
.7335958
1.705013
eshxpr | -.9301182
.9150299
-1.02
0.310
-2.728491
.8682541
_cons | -1.929187
.9147773
-2.11
0.036
-3.727063
-.1313111
-----------------------------------------------------------------------------. * OLS Model
. regress dlp apsh ansh aksh mshxpr eshxpr, robust
Linear regression
Number of obs
F(5, 440)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
24.65
0.0000
0.3400
1.2384
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------apsh |
5.629626
1.284501
4.38
0.000
3.105105
8.154147
ansh |
7.727702
2.065437
3.74
0.000
3.668354
11.78705
aksh |
8.611022
1.272484
6.77
0.000
6.110121
11.11192
mshxpr |
1.448936
.1923696
7.53
0.000
1.070858
1.827013
eshxpr |
.0327104
.533676
0.06
0.951
-1.01616
1.081581
_cons | -2.629372
.6429471
-4.09
0.000
-3.893001
-1.365743
-----------------------------------------------------------------------------. restore
.
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(4, 443)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9998
.07762
-----------------------------------------------------------------------------|
Robust
dlpvad1 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp1 | -1.000041
.0006831 -1463.88
0.000
-1.001384
-.9986986
apsh1 |
4.680657
.0157718
296.77
0.000
4.64966
4.711654
ansh1 |
5.482807
.0194677
281.64
0.000
5.444547
5.521068
aksh1 |
3.952538
.0083407
473.89
0.000
3.936146
3.96893
57
International Trade Notes: 10 October 2016
-----------------------------------------------------------------------------. * OLS Model
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
Linear regression
Number of obs
F(4, 443)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9988
.1685
-----------------------------------------------------------------------------|
Robust
dlpvad1 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp1 | -.9992624
.0042216 -236.70
0.000
-1.007559
-.9909655
apsh1 |
4.666086
.0550321
84.79
0.000
4.55793
4.774243
ansh1 |
5.437375
.0644382
84.38
0.000
5.310733
5.564018
aksh1 |
3.953762
.0221871
178.20
0.000
3.910157
3.997367
-----------------------------------------------------------------------------.
. regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(6, 440)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9999
.0262
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp | -1.000358
.000677 -1477.55
0.000
-1.001689
-.9990273
apsh |
4.700013
.011911
394.60
0.000
4.676603
4.723422
ansh |
5.443315
.0314405
173.13
0.000
5.381523
5.505107
aksh |
3.972308
.0150284
264.32
0.000
3.942772
4.001845
mshxpr |
.9974072
.0023115
431.50
0.000
.9928643
1.00195
eshxpr |
.9961108
.0057421
173.47
0.000
.9848254
1.007396
_cons |
.0010799
.005423
0.20
0.842
-.0095784
.0117382
-----------------------------------------------------------------------------. * OLS Model
. regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
Linear regression
Number of obs
F(6, 440)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9989
.05637
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp | -.9984327
.0024469 -408.04
0.000
-1.003242
-.9936236
apsh |
4.71449
.0145206
324.68
0.000
4.685952
4.743028
ansh |
5.443702
.0521618
104.36
0.000
5.341185
5.546219
aksh |
4.000907
.044225
90.47
0.000
3.913988
4.087825
mshxpr |
.9907738
.0089715
110.44
0.000
.9731416
1.008406
eshxpr |
.996285
.0058313
170.85
0.000
.9848243
1.007746
_cons | -.0023481
.007124
-0.33
0.742
-.0163494
.0116532
-----------------------------------------------------------------------------.
. log close
58
International Trade Notes: 10 October 2016
name: <unnamed>
log: C:\feenstra_course\chap4\log_4_3a.log
log type: text
closed on: 15 Jun 2016, 15:29:31
-------------------------------------------------------------------------------------------------------------------. * clear *
. exit
end of do-file
. do "C:\feenstra_course\chap4\Problem_4_2.do"
. // set mem 300m
.
. * Annotated October 2014
.
. log using log_4_2.log,replace
-------------------------------------------------------------------------------------------------------------------name: <unnamed>
log: C:\feenstra_course\chap4\log_4_2.log
log type: text
opened on: 15 Jun 2016, 15:30:45
.
. // use d:\feenstra_course\chap4\data_Chp4,clear
. use c:\feenstra_course\chap4\data_Chp4,clear
(Matrl Cons (72 SIC), 67-92)
. // use e:\feenstra_course\chap4\data_Chp4,clear
. * use /usr/local/lib/hhsfiles/data_Chp4,clear
. drop if year==1972|year==1987
(900 observations deleted)
. drop if sic72==2067|sic72==2794|sic72==3483
(6 observations deleted)
.
. egen wagebill=sum(pay), by(year)
. gen share=pay/wagebill
.
. sort sic72 year
. by sic72: gen lagshare=share[_n-1]
(447 missing values generated)
. gen ashare=(share+lagshare)/2
(447 missing values generated)
.
. by sic72: gen lagnwsh=nwsh[_n-1]
(447 missing values generated)
. gen chanwsh=(nwsh-lagnwsh)*100/11
(447 missing values generated)
.
. gen wchanwsh=chanwsh*ashare
(447 missing values generated)
. gen wdlky=dlky*ashare
(447 missing values generated)
59
International Trade Notes: 10 October 2016
. gen wdly=dly*ashare
(447 missing values generated)
. gen wdsimat1a=dsimat1a*ashare
(447 missing values generated)
. gen wdsimat1b=dsimat1a*ashare
(447 missing values generated)
. gen diffout=dsimat1a-dsimat1b
. gen wdiffout=(dsimat1a-dsimat1b)*ashare
(447 missing values generated)
. gen wcosh_exp=dofsh*ashare
(447 missing values generated)
. gen htsh_exp=dhtsh-dofsh
. gen whtsh_exp=(dhtsh-dofsh)*ashare
(447 missing values generated)
. gen wcosh_exa=dofsh1*ashare
(447 missing values generated)
. gen htsh_exa=dhtsh1-dofsh1
. gen whtsh_exa=(dhtsh1-dofsh1)*ashare
(447 missing values generated)
. gen wcosh=ci*ashare
(447 missing values generated)
. gen whtsh=dhtsh*ashare
(447 missing values generated)
.
. * Check with the first column of Table 4.4 *
.
. tabstat wchanwsh wdlky wdly wdsimat1a wcosh_exp
stats(mean)
whtsh_exp
wcosh_exa
whtsh_exa
wcosh
whtsh,
stats | wchanwsh
wdlky
wdly wdsim~1a wcosh_~p whtsh_~p wcosh_~a whtsh_~a
wcosh
whtsh
---------+--------------------------------------------------------------------------------------------------mean | .0008702 .0015802 .0034469 .0009452 .0005605 .0003231 .0001573 .0003704 .0146791
.0008836
------------------------------------------------------------------------------------------------------------. tabstat chanwsh dlky dly dsimat1a dofsh htsh_exp dofsh1 htsh_exa ci dhtsh, stats(mean)
stats |
chanwsh
dlky
dly dsimat1a
dofsh htsh_exp
dofsh1 htsh_exa
ci
dhtsh
---------+--------------------------------------------------------------------------------------------------mean |
.377241 .8334145 1.180938 .3791446 -.0020403 .1839697 -.0127181 .1451851 3.596809
.1819293
------------------------------------------------------------------------------------------------------------. * Reproduce the rest of the columns in Table 4.4 *
.
. * replicates table 4.4 col 2
. regress chanwsh dlky dly dsimat1a dofsh htsh_exp [aw=ashare], cluster (sic2)
(sum of wgt is
1.0000e+00)
60
International Trade Notes: 10 October 2016
Linear regression
Number of obs
F(5, 19)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
6.72
0.0009
0.1557
.38912
(Std. Err. adjusted for 20 clusters in sic2)
-----------------------------------------------------------------------------|
Robust
chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0467948
.0113832
4.11
0.001
.0229695
.0706201
dly |
.0197383
.0063797
3.09
0.006
.0063853
.0330912
dsimat1a |
.1966658
.0962066
2.04
0.055
-.004697
.3980286
dofsh |
.19534
.0915302
2.13
0.046
.0037651
.3869148
htsh_exp | -.0650465
.1371193
-0.47
0.641
-.3520404
.2219474
_cons |
.2028764
.0428851
4.73
0.000
.1131169
.292636
-----------------------------------------------------------------------------. * test ols
. regress chanwsh dlky dly dsimat1a dofsh htsh_exp
Source |
SS
df
MS
-------------+---------------------------------Model | 4.87604716
5 .975209432
Residual | 99.6927448
441 .226060646
-------------+---------------------------------Total | 104.568792
446 .234459175
Number of obs
F(5, 441)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
447
4.31
0.0008
0.0466
0.0358
.47546
-----------------------------------------------------------------------------chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0194616
.010929
1.78
0.076
-.0020179
.0409411
dly |
.0016347
.0087081
0.19
0.851
-.0154799
.0187492
dsimat1a |
.0854863
.0403379
2.12
0.035
.006208
.1647647
dofsh |
.1773819
.078036
2.27
0.024
.0240132
.3307505
htsh_exp | -.0063895
.1034685
-0.06
0.951
-.2097421
.1969632
_cons |
.3044169
.0345396
8.81
0.000
.2365342
.3722995
-----------------------------------------------------------------------------.
. * replicates table 4.4 col 3
. regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa [aw=ashare], cluster (sic2)
(sum of wgt is
1.0000e+00)
Linear regression
Number of obs
F(5, 19)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
8.01
0.0003
0.1592
.38832
(Std. Err. adjusted for 20 clusters in sic2)
-----------------------------------------------------------------------------|
Robust
chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0444529
.0113121
3.93
0.001
.0207764
.0681293
dly |
.0173278
.0062906
2.75
0.013
.0041613
.0304942
dsimat1a |
.2207528
.0999711
2.21
0.040
.0115109
.4299947
dofsh1 |
.4309753
.1671453
2.58
0.018
.0811362
.7808144
htsh_exa |
.0052436
.0712031
0.07
0.942
-.1437862
.1542735
_cons |
.2064394
.0397614
5.19
0.000
.1232178
.289661
-----------------------------------------------------------------------------. * test ols
. regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa
Source |
SS
df
MS
Number of obs
61
=
447
International Trade Notes: 10 October 2016
-------------+---------------------------------Model | 4.42334831
5 .884669662
Residual | 100.145444
441 .227087174
-------------+---------------------------------Total | 104.568792
446 .234459175
F(5, 441)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
3.90
0.0018
0.0423
0.0314
.47654
-----------------------------------------------------------------------------chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0210034
.0110506
1.90
0.058
-.000715
.0427218
dly |
.0009338
.0089879
0.10
0.917
-.0167306
.0185982
dsimat1a |
.0899303
.0407687
2.21
0.028
.0098053
.1700553
dofsh1 |
.2866326
.1631938
1.76
0.080
-.0341015
.6073667
htsh_exa | -.0076398
.1360646
-0.06
0.955
-.2750554
.2597758
_cons |
.3244891
.0375708
8.64
0.000
.250649
.3983292
-----------------------------------------------------------------------------.
. * replicates table 4.4 col 4
. regress chanwsh dlky dly dsimat1a ci dhtsh [aw=ashare], cluster (sic2)
(sum of wgt is
1.0000e+00)
Linear regression
Number of obs
F(5, 19)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
11.87
0.0000
0.1885
.38148
(Std. Err. adjusted for 20 clusters in sic2)
-----------------------------------------------------------------------------|
Robust
chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0399279
.0087378
4.57
0.000
.0216396
.0582162
dly |
.0100379
.0062332
1.61
0.124
-.0030084
.0230841
dsimat1a |
.1346024
.0883067
1.52
0.144
-.0502257
.3194306
ci |
.0180834
.0066465
2.72
0.014
.0041722
.0319946
dhtsh |
.0324624
.0519
0.63
0.539
-.0761655
.1410904
_cons |
.1569685
.0446895
3.51
0.002
.0634323
.2505048
-----------------------------------------------------------------------------. * test ols
. regress chanwsh dlky dly dsimat1a ci dhtsh
Source |
SS
df
MS
-------------+---------------------------------Model | 6.52521799
5
1.3050436
Residual | 98.0435739
441 .222321029
-------------+---------------------------------Total | 104.568792
446 .234459175
Number of obs
F(5, 441)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
447
5.87
0.0000
0.0624
0.0518
.47151
-----------------------------------------------------------------------------chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0185285
.0105271
1.76
0.079
-.0021611
.0392181
dly | -.0008842
.0086306
-0.10
0.918
-.0178465
.0160781
dsimat1a |
.0523652
.0414966
1.26
0.208
-.0291904
.1339207
ci |
.013381
.0043628
3.07
0.002
.0048065
.0219555
dhtsh |
.0870111
.0613731
1.42
0.157
-.0336091
.2076312
_cons |
.2455871
.037316
6.58
0.000
.1722479
.3189263
-----------------------------------------------------------------------------.
. * To instead distinguish narrow and other outsourcing, we can reproduce column (1) of table III in
Feenstra and Han
> son, 1999 *
.
. tabstat wchanwsh wdlky wdly wdsimat1b wdiffout wcosh_exp whtsh_exp wcosh_exa whtsh_exa wcosh whtsh,
62
International Trade Notes: 10 October 2016
stats(sum)
stats | wchanwsh
wdlky
wdly wdsim~1b wdiffout wcosh_~p whtsh_~p wcosh_~a whtsh_~a
wcosh
---------+--------------------------------------------------------------------------------------------------sum | .3889885 .7063639 1.540769 .4225266 .1998607 .2505536 .1444164 .0703266 .1655768
6.561565
------------------------------------------------------------------------------------------------------------stats |
whtsh
---------+---------sum |
.39497
-------------------.
. * Reproduce the rest of the columns in Table III *
.
. regress chanwsh dlky dly dsimat1b diffout dofsh htsh_exp [aw=ashare], cluster (sic2)
(sum of wgt is
1.0000e+00)
Linear regression
Number of obs
F(6, 19)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
7.00
0.0005
0.1627
.38794
(Std. Err. adjusted for 20 clusters in sic2)
-----------------------------------------------------------------------------|
Robust
chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0421152
.0141103
2.98
0.008
.0125821
.0716483
dly |
.0178086
.0080568
2.21
0.040
.0009456
.0346716
dsimat1b |
.2454613
.1692732
1.45
0.163
-.1088315
.5997541
diffout |
.121362
.0457066
2.66
0.016
.025697
.2170271
dofsh |
.2060218
.1021206
2.02
0.058
-.0077192
.4197627
htsh_exp | -.0392957
.1289341
-0.30
0.764
-.309158
.2305665
_cons |
.206945
.0415146
4.98
0.000
.120054
.2938361
-----------------------------------------------------------------------------.
. regress chanwsh dlky dly dsimat1b diffout dofsh1 htsh_exa [aw=ashare], cluster (sic2)
(sum of wgt is
1.0000e+00)
Linear regression
Number of obs
F(6, 19)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
7.37
0.0004
0.1650
.38742
(Std. Err. adjusted for 20 clusters in sic2)
-----------------------------------------------------------------------------|
Robust
chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0408212
.0141101
2.89
0.009
.0112884
.070354
dly |
.0159677
.0078375
2.04
0.056
-.0004365
.0323718
dsimat1b |
.2653356
.175142
1.51
0.146
-.1012407
.6319119
diffout |
.1537718
.0502819
3.06
0.006
.0485307
.259013
dofsh1 |
.4207269
.1707522
2.46
0.023
.0633383
.7781154
htsh_exa |
.0143582
.07223
0.20
0.845
-.1368209
.1655373
_cons |
.2137716
.0390531
5.47
0.000
.1320326
.2955107
-----------------------------------------------------------------------------.
. regress chanwsh dlky dly dsimat1b diffout ci dhtsh [aw=ashare], cluster (sic2)
63
International Trade Notes: 10 October 2016
(sum of wgt is
1.0000e+00)
Linear regression
Number of obs
F(6, 19)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
14.96
0.0000
0.1995
.37933
(Std. Err. adjusted for 20 clusters in sic2)
-----------------------------------------------------------------------------|
Robust
chanwsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlky |
.0331274
.0119999
2.76
0.012
.0080113
.0582434
dly |
.0068629
.0087795
0.78
0.444
-.0115128
.0252386
dsimat1b |
.1928059
.1657117
1.16
0.259
-.1540328
.5396445
diffout |
.0380044
.0539983
0.70
0.490
-.0750153
.1510241
ci |
.0186984
.0068931
2.71
0.014
.0042711
.0331258
dhtsh |
.0519438
.0512489
1.01
0.324
-.0553214
.1592091
_cons |
.1612801
.0401323
4.02
0.001
.0772822
.2452781
-----------------------------------------------------------------------------.
. log close
name: <unnamed>
log: C:\feenstra_course\chap4\log_4_2.log
log type: text
closed on: 15 Jun 2016, 15:30:45
-------------------------------------------------------------------------------------------------------------------.
. * clear
. exit
end of do-file
. do "C:\feenstra_course\chap4\Problem_4_3_b.do"
. // set mem 3m
. capture log close
. log using log_4_3b.log,replace
-------------------------------------------------------------------------------------------------------------------name: <unnamed>
log: C:\feenstra_course\chap4\log_4_3b.log
log type: text
opened on: 15 Jun 2016, 15:31:29
.
. // use d:\feenstra_course\Chap4\data_Chp4, clear
. use c:\feenstra_course\Chap4\data_Chp4, clear
(Matrl Cons (72 SIC), 67-92)
. // use d:\feenstra_course\Chap4\data_Chp4, clear
. // use e:\feenstra_course\Chap4\data_Chp4, clear
.
.
. keep if year==1990
(1,350 observations deleted)
. drop if sic72==2067
(1 observation deleted)
. drop if sic72==2794
(1 observation deleted)
64
International Trade Notes: 10 October 2016
. drop if sic72==3483
(1 observation deleted)
. gen etfp=ptfp-err
. gen adj1=1/(1-amesh)
. gen etfp1=adj1*etfp
. gen dlpvad1=adj1*dlpvad
. gen apsh1=adj1*apsh
. gen ansh1=adj1*ansh
. gen aksh1=adj1*aksh
. gen t4dlpvad=(dlpvad+etfp)*adj1
. preserve
.
. * Reproduce the first column of Table IV *
. * generating difference measure of outsourcing *
.
. gen dsimatd1=dsimat1a-dsimat1b
.
. * generating difference measure of high tech share *
.
. gen dhtdsh=dhtsh-dofsh
.
. * check whether we are using the right variable as described in table II *
.
. sum dsimatd1 dhtdsh dofsh [aw=mvshipsh]
Variable |
Obs
Weight
Mean
Std. Dev.
Min
Max
-------------+----------------------------------------------------------------dsimatd1 |
447 .998730832
.1598317
.3220691 -1.763297
2.735888
dhtdsh |
447 .998730832
.1281193
.1962393 -.0841524
.9744269
dofsh |
447 .998730832
.1983744
.244483 -.3634307
.8313999
.
. regress t4dlpvad dsimat1b dsimatd1 dofsh dhtdsh [aw=mvshipsh], cluster(sic2)
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(4, 19)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
5.40
0.0044
0.1534
.14521
(Std. Err. adjusted for 20 clusters in sic2)
-----------------------------------------------------------------------------|
Robust
t4dlpvad |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dsimat1b |
.0635024
.030585
2.08
0.052
-.0005128
.1275177
dsimatd1 |
.0788136
.0472159
1.67
0.111
-.0200103
.1776375
dofsh |
.1665693
.0658945
2.53
0.021
.0286505
.3044881
dhtdsh |
.075982
.0722494
1.05
0.306
-.0752377
.2272016
_cons |
4.262727
.0322917
132.01
0.000
4.19514
4.330314
-----------------------------------------------------------------------------.
. * Reproduce Table V using the coefficients in column(1) of Table IV *
65
International Trade Notes: 10 October 2016
.
. gen wt=mvshipsh^.5
. gen apsh5=apsh1*wt
. gen ansh5=ansh1*wt
. gen aksh5=aksh1*wt
. gen narrout=dsimat1b*wt*_coef[dsimat1b]
. gen diffout=dsimatd1*wt*_coef[dsimatd1]
. gen comsh=dofsh*wt*_coef[dofsh]
. gen difcom=dhtdsh*wt*_coef[dhtdsh]
.
. sum narrout diffout comsh difcom
Variable |
Obs
Mean
Std. Dev.
Min
Max
-------------+--------------------------------------------------------narrout |
447
.0004107
.0012838 -.0077687
.0131523
diffout |
447
.0005548
.0012192 -.0053996
.0156501
comsh |
447
.0012452
.0021439 -.0028531
.0110437
difcom |
447
.0004038
.0007386 -.0009354
.0064305
.
. regress narrout apsh5 ansh5 aksh5, noconstant
Source |
SS
df
MS
-------------+---------------------------------Model | .000211586
3 .000070529
Residual | .000598861
444 1.3488e-06
-------------+---------------------------------Total | .000810447
447 1.8131e-06
Number of obs
F(3, 444)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
447
52.29
0.0000
0.2611
0.2561
.00116
-----------------------------------------------------------------------------narrout |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------apsh5 | -.0095155
.0093511
-1.02
0.309
-.0278934
.0088624
ansh5 |
.0986666
.0147744
6.68
0.000
.0696303
.127703
aksh5 |
.0026378
.003536
0.75
0.456
-.0043116
.0095872
-----------------------------------------------------------------------------. regress diffout apsh5 ansh5 aksh5, noconstant
Source |
SS
df
MS
-------------+---------------------------------Model | .000185525
3 .000061842
Residual | .000615016
444 1.3852e-06
-------------+---------------------------------Total | .000800542
447 1.7909e-06
Number of obs
F(3, 444)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
447
44.65
0.0000
0.2317
0.2266
.00118
-----------------------------------------------------------------------------diffout |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------apsh5 |
.0203644
.0094764
2.15
0.032
.0017403
.0389885
ansh5 |
.0628478
.0149723
4.20
0.000
.0334224
.0922732
aksh5 | -.0011399
.0035834
-0.32
0.751
-.0081824
.0059026
-----------------------------------------------------------------------------. regress comsh apsh5 ansh5 aksh5, noconstant
Source |
SS
df
MS
-------------+---------------------------------Model | .001395044
3 .000465015
Residual | .001347998
444 3.0360e-06
Number of obs
F(3, 444)
Prob > F
R-squared
66
=
=
=
=
447
153.17
0.0000
0.5086
International Trade Notes: 10 October 2016
-------------+---------------------------------Total | .002743042
447 6.1366e-06
Adj R-squared
Root MSE
=
=
0.5053
.00174
-----------------------------------------------------------------------------comsh |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------apsh5 | -.0049722
.0140295
-0.35
0.723
-.0325447
.0226004
ansh5 |
.2480141
.0221661
11.19
0.000
.2044505
.2915777
aksh5 |
.0007009
.0053051
0.13
0.895
-.0097253
.0111272
-----------------------------------------------------------------------------. regress difcom apsh5 ansh5 aksh5, noconstant
Source |
SS
df
MS
-------------+---------------------------------Model | .000099567
3 .000033189
Residual | .000216627
444 4.8790e-07
-------------+---------------------------------Total | .000316194
447 7.0737e-07
Number of obs
F(3, 444)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
447
68.02
0.0000
0.3149
0.3103
.0007
-----------------------------------------------------------------------------difcom |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------apsh5 |
.0259448
.0056241
4.61
0.000
.0148915
.036998
ansh5 |
.0069214
.0088859
0.78
0.436
-.0105422
.0243851
aksh5 |
.0043305
.0021267
2.04
0.042
.0001509
.0085102
-----------------------------------------------------------------------------.
. restore
.
. * Reproduce column (2) of Table IV *
.
. preserve
.
. * generating difference measure of outsourcing *
.
. gen dsimatd1=dsimat1a-dsimat1b
.
. * generate difference measure of high tech share with ex ante rental price *
.
. gen dhtdsh1=dhtsh1-dofsh1
.
. * check whether we are using the right variable as described in table II *
.
. sum dsimatd1 dhtdsh1 dofsh1 [aw=mvshipsh]
Variable |
Obs
Weight
Mean
Std. Dev.
Min
Max
-------------+----------------------------------------------------------------dsimatd1 |
447 .998730832
.1598317
.3220691 -1.763297
2.735888
dhtdsh1 |
447 .998730832
.1643722
.1506561
.0204334
.9001704
dofsh1 |
447 .998730832
.0534329
.124323 -.2700591
.3795505
.
. regress t4dlpvad dsimat1b dsimatd1 dofsh1 dhtdsh1 [aw=mvshipsh], cluster(sic2)
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(4, 19)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
2.42
0.0844
0.1089
.14898
(Std. Err. adjusted for 20 clusters in sic2)
67
International Trade Notes: 10 October 2016
-----------------------------------------------------------------------------|
Robust
t4dlpvad |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dsimat1b |
.0795164
.034676
2.29
0.033
.0069387
.1520942
dsimatd1 |
.11368
.0440198
2.58
0.018
.0215455
.2058144
dofsh1 |
.1924159
.1083624
1.78
0.092
-.0343891
.4192209
dhtdsh1 | -.0477944
.0820494
-0.58
0.567
-.2195258
.1239369
_cons |
4.294261
.0385949
111.27
0.000
4.213481
4.375041
-----------------------------------------------------------------------------.
. * Reproduce column (3) of Table IV *
.
. * generating difference measure of high tech share *
.
. gen dhtdsh=dhtsh-dofsh
.
. regress t4dlpvad dsimat1b dsimatd1 ci dhtsh [aw=mvshipsh], cluster(sic2)
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(4, 19)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
5.96
0.0028
0.2129
.14002
(Std. Err. adjusted for 20 clusters in sic2)
-----------------------------------------------------------------------------|
Robust
t4dlpvad |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dsimat1b |
.0404059
.0295213
1.37
0.187
-.0213829
.1021947
dsimatd1 |
.0351687
.0488208
0.72
0.480
-.0670145
.1373518
ci |
.0081792
.0045064
1.82
0.085
-.0012528
.0176112
dhtsh |
.093074
.0496036
1.88
0.076
-.0107475
.1968955
_cons |
4.243861
.0334856
126.74
0.000
4.173775
4.313947
-----------------------------------------------------------------------------.
Example Code to Test WLS with "junk" data. Test case shows how WLS can give "significant"
but misleading answers. WLS is shown with Rats and Stata. Note that Stata uses a non standard
weighting system. B34S first build a random left hands side variable and a random right hand side
variable and a random vector of "weights" to form a "junk" model. Next OLS and weignted least
squares are run in three software systems. The results speak for themselves.
/;
/; B34S-Stata-Rats
/;
b34sexec matrix;
* tests weighted regression ;
* illustrates how weighted least squares can give "significance";
n=10000;
k=4;
y=rn(array(n:));
w=abs(rn(array(n:)));
x=rn(array(n,k:));
/;
/; OLS Model
/;
68
International Trade Notes: 10 October 2016
/; quick way to go to weighted least squares assuming
/; vector or matrix input
call olsq(y x :print :savex);
ww=1./afam(sqrt(w));
%xnew=transpose(transpose(afam(%x))*ww);
%ynew=afam(%y)*ww;
call print('Weighted Least Squares':);
call olsq(%ynew %xnew :noint :print);
/; pass data to test WLS with Stata and Rats
call dmfput(y,w :file 'file_1.dmf'
:member file1
:comment 'y and w for weighted regression test'
);
call dmfput(x
:file 'file_2.dmf'
:member file2
);
b34srun;
/;
/; test reading the save
/;
b34sexec data file('file_1.dmf') filef=fdmf
dmfmember(file1)
;
b34srun;
b34sexec data file('file_2.dmf') filef=fdmf
dmfmember(file2)
;
b34srun;
/;
/; Merge the two DMF files
/;
b34sexec merge
file1('file_1.dmf')
file2('file_2.dmf')
file3('file_3.dmf')
member1(file1) member2(file2) member3(file3)
outfmt=formatted
/;
comment('Test of effect of Weighted Regression')
;
b34srun;
/;
/; illustrate a read of a DMF into the matrix Command
/;
b34sexec matrix;
call dmfget(:file 'file_3.dmf' :member file3 :print);
b34srun;
/;
b34sexec data file('file_3.dmf') filef=fdmf; b34srun;
/;
/; This is the best way to go
/;
b34sexec options open('statdata.do') unit(28) disp=unknown$ b34srun$
b34sexec options clean(28)$ b34srun$
b34sexec options open('stata.do') unit(29) disp=unknown$ b34srun$
b34sexec options clean(29)$ b34srun$
b34sexec pgmcall idata=28 icntrl=29$
stata$
pgmcards$
//
uncomment if do not use /e
//
log using stata.log, text
//
describe
regress y m1*
regress y m1* [aw=1/w]
b34sreturn$
69
International Trade Notes: 10 October 2016
b34seend$
b34sexec options close(28); b34srun;
b34sexec options close(29); b34srun;
b34sexec options
dodos('stata /e stata.do');
b34srun;
b34sexec options npageout
writeout('output from stata',' ',' ')
copyfout('stata.log')
dodos('erase stata.do','erase stata.log','erase statdata.do') $
b34srun$
/$ user places RATS commands between
/$
PGMCARDS$
/$
note: user RATS commands here
/$
B34SRETURN$
/$
b34sexec
b34sexec
b34sexec
b34sexec
options
options
options
options
open('rats.dat') unit(28) disp=unknown$ b34srun$
open('rats.in') unit(29) disp=unknown$ b34srun$
clean(28)$ b34srun$
clean(29)$ b34srun$
b34sexec pgmcall$
rats
pcomments('* ',
'* Data passed from B34S(r) system to RATS',
'*
',
"display @1 %dateandtime() @33 ' Rats Version ' %ratsversion()"
'* ') $
PGMCARDS$
*
linreg y
# constant m1col__1 m1col__2 m1col__3 m1col__4
linreg(spread=w) y
# constant m1col__1 m1col__2 m1col__3 m1col__4
b34sreturn$
b34srun $
b34sexec options close(28)$ b34srun$
b34sexec options close(29)$ b34srun$
b34sexec options
/$
dodos(' rats386 rats.in rats.out ')
dodos('start /w /r
rats32s rats.in /run')
dounix('rats
rats.in rats.out')$ B34SRUN$
b34sexec options npageout
WRITEOUT('Output from RATS',' ',' ')
COPYFOUT('rats.out')
dodos('ERASE rats.in','ERASE rats.out','ERASE
dounix('rm
rats.in','rm
rats.out','rm
$
Results
B34SI Matrix Command. d/m/y 15/ 8/10. h:m:s 21:18:32.
=>
* TESTS WEIGHTED REGRESSION $
=>
* ILLUSTRATES HOW WEIGHTED LEAST SQUARES CAN GIVE "SIGNIFICANCE"$
=>
N=10000$
70
rats.dat')
rats.dat')
International Trade Notes: 10 October 2016
=>
K=4$
=>
Y=RN(ARRAY(N:))$
=>
W=ABS(RN(ARRAY(N:)))$
=>
X=RN(ARRAY(N,K:))$
=>
CALL OLSQ(Y X :PRINT :SAVEX)$
Results for the OLS Model of 10,000 observations on "junk" data.
Ordinary Least Squares Estimation
Dependent variable
Centered R**2
Adjusted R**2
Residual Sum of Squares
Residual Variance
Standard Error
Total Sum of Squares
Log Likelihood
Mean of the Dependent Variable
Std. Error of Dependent Variable
Sum Absolute Residuals
F( 4,
9995)
F Significance
1/Condition XPX
Maximum Absolute Residual
Number of Observations
Variable
Col____1
Col____2
Col____3
Col____4
CONSTANT
Lag
0
0
0
0
0
Coefficient
-0.21613705E-01
0.99455008E-02
-0.25503089E-01
-0.83857056E-02
-0.11056801E-01
Y
1.283800318883199E-003
8.841139958492355E-004
10083.5816512905
1.00886259642727
1.00442152327958
10096.5435971802
-14231.0024774754
-1.106035532484140E-002
1.00486582947752
8006.64281307591
3.21201963864575
0.987921184267561
0.945609242214882
4.03166296169811
10000
SE
0.10089154E-01
0.10155609E-01
0.99336699E-02
0.10068969E-01
0.10044510E-01
=>
WW=1./AFAM(SQRT(W))$
=>
%XNEW=TRANSPOSE(TRANSPOSE(AFAM(%X))*WW)$
=>
%YNEW=AFAM(%Y)*WW$
=>
CALL PRINT('Weighted Least Squares':)$
t
-2.1422713
0.97931108
-2.5673381
-0.83282667
-1.1007806
Weighted Least Squares
Weighted Least Squares of above model that will be validated with Rats and Stata below.
=>
CALL OLSQ(%YNEW %XNEW :NOINT :PRINT)$
Ordinary Least Squares Estimation
Dependent variable
Centered R**2
Adjusted R**2
Residual Sum of Squares
Residual Variance
Standard Error
Total Sum of Squares
Log Likelihood
Mean of the Dependent Variable
Std. Error of Dependent Variable
Sum Absolute Residuals
F( 4,
9995)
F Significance
1/Condition XPX
Maximum Absolute Residual
Number of Observations
Variable
Col____1
Col____2
Col____3
Col____4
Col____5
=>
=>
=>
=>
Lag
0
0
0
0
0
Coefficient
0.13243375
0.32195210
0.31666619E-01
-0.15003716
0.60455770E-01
%YNEW
0.125430978105311
0.125080975495248
104592.075351771
10.4644397550546
3.23487863065287
119592.705359240
-25926.7988036037
-1.522589703452888E-002
3.45839075041880
14772.8577916210
358.371550665769
0.999999999999874
0.255815512089038
110.962446369039
10000
SE
0.98266760E-02
0.11437311E-01
0.95544411E-02
0.11766487E-01
0.97906901E-02
t
13.476963
28.149282
3.3143350
-12.751228
6.1748221
CALL DMFPUT(Y,W :FILE 'file_1.dmf'
:MEMBER FILE1
:COMMENT 'y and w for weighted regression test'
)$
71
International Trade Notes: 10 October 2016
=>
=>
=>
CALL DMFPUT(X
:FILE 'file_2.dmf'
:MEMBER FILE2
)$
B34S Matrix Command Ending. Last Command reached.
Space available in allocator
Number variables used
Number temp variables used
B34SI 8.11E
Variable
Y
W
CONSTANT
(D:M:Y)
# Cases
1
2
3
14856808, peak space used
49, peak number used
45, # user temp clean
15/ 8/10 (H:M:S) 21:18:32
Mean
581397
51
0
DATA STEP
Std Deviation
10000 -0.1106035532E-01
10000 0.7897850809
10000
1.000000000
Variance
1.004865829
0.5970220007
0.000000000
Variable
M1COL__1
M1COL__2
M1COL__3
M1COL__4
CONSTANT
(D:M:Y)
# Cases
1
2
3
4
5
15/ 8/10 (H:M:S) 21:18:33
Mean
3.460313180
3.646702144
1.000000000
Maximum
0.9913245780
0.9783507125
1.022557394
0.9952855480
0.000000000
Number of observations in data file
10000
Current missing variable code
1.000000000000000E+031
Data begins on (D:M:Y) 2: 1:1960 ends 2: 1:****.
Frequency is
1
PAGE
2
PAGE
3
Minimum
-4.001602802
0.3183224533E-04
1.000000000
Data from Matrix Command
Variance
0.9956528401
0.9891161269
1.011215800
0.9976399892
0.000000000
PAGE
1
DATA STEP
Std Deviation
10000 0.4888179470E-02
10000 0.2011437524E-03
10000 -0.2136661813E-02
10000 -0.5438502297E-02
10000
1.000000000
Maximum
1.009755335
0.3564352694
0.000000000
Number of observations in data file
10000
Current missing variable code
1.000000000000000E+031
Data begins on (D:M:Y) 2: 1:1960 ends 2: 1:****.
Frequency is
B34SI 8.11E
Data from Matrix Command
3.689869729
3.785540146
3.964659396
3.611193295
1.000000000
Minimum
-3.764639466
-4.161275084
-3.849832359
-3.935043696
1.000000000
1
B34SI Matrix Command. d/m/y 15/ 8/10. h:m:s 21:18:33.
=>
CALL DMFGET(:FILE 'file_3.dmf' :MEMBER FILE3 :PRINT)$
DMF File Name
Member
Created on date
Time
Number of series
Number of observations
Frequency
File format is FORMATTED
Base Date d/m/y
Header
Number of comments
file_3.dmf
FILE3
15/ 8/10
21:18:32
6
10000
1.00000000000000
2/ 1/1960
Data from Matrix Command
1
Comments:
Series:
Y
W
M1COL__1
M1COL__2
M1COL__3
M1COL__4
Type
0
0
0
0
0
0
Label:
B34S Matrix Command Ending. Last Command reached.
Space available in allocator
Number variables used
Number temp variables used
B34SI 8.11E
Variable
Y
W
M1COL__1
M1COL__2
M1COL__3
M1COL__4
CONSTANT
(D:M:Y)
# Cases
1
2
3
4
5
6
7
14856979, peak space used
14, peak number used
7, # user temp clean
15/ 8/10 (H:M:S) 21:18:34
Mean
10000 -0.1106035532E-01
10000 0.7897850809
10000 0.4888179470E-02
10000 0.2011437524E-03
10000 -0.2136661813E-02
10000 -0.5438502297E-02
10000
1.000000000
Std Deviation
1.004865829
0.5970220007
0.9956528401
0.9891161269
1.011215800
0.9976399892
0.000000000
100370
14
0
DATA STEP
Data from Matrix Command
Variance
Maximum
1.009755335
0.3564352694
0.9913245780
0.9783507125
1.022557394
0.9952855480
0.000000000
Number of observations in data file
10000
Current missing variable code
1.000000000000000E+031
Data begins on (D:M:Y) 2: 1:1960 ends 2: 1:****.
Frequency is
output from stata
72
3.460313180
3.646702144
3.689869729
3.785540146
3.964659396
3.611193295
1.000000000
1
Minimum
-4.001602802
0.3183224533E-04
-3.764639466
-4.161275084
-3.849832359
-3.935043696
1.000000000
International Trade Notes: 10 October 2016
___ ____ ____ ____ ____ (R)
/__
/
____/
/
____/
___/
/
/___/
/
/___/
11.1
Statistics/Data Analysis
Copyright 2009 StataCorp LP
StataCorp
4905 Lakeway Drive
College Station, Texas 77845 USA
800-STATA-PC
http://www.stata.com
979-696-4600
[email protected]
979-696-4601 (fax)
Single-user Stata perpetual license:
Serial number: 30110535901
Licensed to: Houston H. Stokes
University of Illinois at Chicago
Notes:
1.
2.
(/m# option or -set memory-) 120.00 MB allocated to data
Stata running in batch mode
. do stata.do
. * File built by B34S
. run statdata.do
on 15/ 8/10
at
21:18:34
Stata validates the B34S results. Note command setup.
.
regress y m1*
Source |
SS
df
MS
-------------+-----------------------------Model | 12.9619459
4 3.24048647
Residual | 10083.5817 9995
1.0088626
-------------+-----------------------------Total | 10096.5436 9999 1.00975534
Number of obs
F( 4, 9995)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
10000
3.21
0.0121
0.0013
0.0009
1.0044
-----------------------------------------------------------------------------y |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------m1col__1 | -.0216137
.0100892
-2.14
0.032
-.0413905
-.0018369
m1col__2 |
.0099455
.0101556
0.98
0.327
-.0099615
.0298525
m1col__3 | -.0255031
.0099337
-2.57
0.010
-.0449751
-.0060311
m1col__4 | -.0083857
.010069
-0.83
0.405
-.0281229
.0113515
_cons | -.0110568
.0100445
-1.10
0.271
-.0307461
.0086325
-----------------------------------------------------------------------------.
regress y m1* [aw=1/w]
(sum of wgt is
1.3529e+05)
Source |
SS
df
MS
-------------+-----------------------------Model | 866.267364
4 216.566841
Residual |
7730.9091 9995 .773477649
-------------+-----------------------------Total |
8597.17646
9999
.859803627
Number of obs
F( 4, 9995)
Prob > F
R-squared
Adj R-squared
=
=
=
=
=
10000
279.99
0.0000
0.1008
0.1004
Root MSE
=
.87948
-----------------------------------------------------------------------------y |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------m1col__1 |
.1324338
.0098267
13.48
0.000
.1131715
.151696
m1col__2 |
.3219521
.0114373
28.15
0.000
.2995327
.3443715
m1col__3 |
.0316666
.0095544
3.31
0.001
.012938
.0503952
m1col__4 | -.1500372
.0117665
-12.75
0.000
-.1731018
-.1269725
_cons |
.0604558
.0097907
6.17
0.000
.041264
.0796475
-----------------------------------------------------------------------------.
end of do-file
73
International Trade Notes: 10 October 2016
Output from RATS
Rats used to validate B34S and Stata results.
*
* Data passed from B34S(r) system to RATS
*
display @1 %dateandtime() @33 ' Rats Version ' %ratsversion()
08/15/2010 21:18
Rats Version
7.30000
*
CALENDAR(IRREGULAR)
ALLOCATE
10000
OPEN DATA rats.dat
DATA(FORMAT=FREE,ORG=OBS,
$
MISSING=
0.1000000000000000E+32
) / $
Y
$
W
$
M1COL__1
$
M1COL__2
$
M1COL__3
$
M1COL__4
$
CONSTANT
SET TREND = T
TABLE
Series
Obs
Mean
Std Error
Minimum
Y
10000
-0.011060
1.004866
-4.001603
W
10000
0.789785
0.597022
0.000032
M1COL__1
10000
0.004888
0.995653
-3.764639
M1COL__2
10000
0.000201
0.989116
-4.161275
M1COL__3
10000
-0.002137
1.011216
-3.849832
M1COL__4
10000
-0.005439
0.997640
-3.935044
TREND
10000
5000.500000
2886.895680
1.000000
Maximum
3.460313
3.646702
3.689870
3.785540
3.964659
3.611193
10000.000000
*
linreg y
# constant m1col__1 m1col__2 m1col__3 m1col__4
Linear Regression - Estimation by Least Squares
Dependent Variable Y
Usable Observations 10000
Degrees of Freedom 9995
Centered R**2
0.001284
R Bar **2
0.000884
Uncentered R**2
0.001405
T x R**2
14.048
Mean of Dependent Variable
-0.011060355
Std Error of Dependent Variable 1.004865829
Standard Error of Estimate
1.004421523
Sum of Squared Residuals
10083.581651
Regression F(4,9995)
3.2120
Significance Level of F
0.01207882
Log Likelihood
-14231.00248
Durbin-Watson Statistic
1.980979
Variable
Coeff
Std Error
T-Stat
Signif
********************************************************************************
1. Constant
-0.011056801 0.010044510
-1.10078 0.27101868
2. M1COL__1
-0.021613705 0.010089154
-2.14227 0.03219575
3. M1COL__2
0.009945501 0.010155609
0.97931 0.32745000
4. M1COL__3
-0.025503089 0.009933670
-2.56734 0.01026268
5. M1COL__4
-0.008385706 0.010068969
-0.83283 0.40496239
linreg(spread=w) y
# constant m1col__1 m1col__2 m1col__3 m1col__4
Linear Regression - Estimation by Weighted Least Squares
Dependent Variable Y
Usable Observations 10000
Degrees of Freedom 9995
Centered R**2
0.125431
R Bar **2
0.125081
Uncentered R**2
0.125448
T x R**2
1254.479
Mean of Dependent Variable
-0.015225897
Std Error of Dependent Variable 3.458390750
Standard Error of Estimate
3.234878631
Sum of Squared Residuals
104592.07535
Log Likelihood
-22690.72492
Durbin-Watson Statistic
1.952328
Variable
Coeff
Std Error
T-Stat
Signif
********************************************************************************
1. Constant
0.060455770 0.009790690
6.17482 0.00000000
2. M1COL__1
0.132433752 0.009826676
13.47696 0.00000000
3. M1COL__2
0.321952098 0.011437311
28.14928 0.00000000
4. M1COL__3
0.031666619 0.009554441
3.31434 0.00092188
5. M1COL__4
-0.150037162 0.011766487
-12.75123 0.00000000
B34S normal exit on Date (D:M:Y) 15/ 8/10
at Time (H:M:S) 21:18:40Results:
74
International Trade Notes: 10 October 2016
Note e ' e values reported for B34S and Rats agree. Stata made an "adjustment."
Code for Leverage Plots with OLS, GAM and Marspline
/;
/; Uses Align to insure 447 obs
/;
b34sexec options ginclude('Feenstra_ch4.mac') member(table4_4A);
b34srun;
b34sexec matrix;
call echooff;
call get(chanwsh dlky dly dsimat1a dofsh dofsh1 htsh_exp htsh_exa
ci dhtsh
);
big=
'chanwsh dlky dly dsimat1a dofsh dofsh1 htsh_exp htsh_exa ci dhtsh';
call align(argument(big));
mod4_42='
mod4_42='
mod4_43='
mod4_44='
chanwsh
chanwsh
chanwsh
chanwsh
dlky
dlky
dlky
dlky
dly
dly
dly
dly
dsimat1a dofsh htsh_exp';
dsimat1a dofsh htsh_exp';
dsimat1a dofsh1 htsh_exa';
dsimat1a ci dhtsh';
n=namelist(argument(big));
datamean=1;
dopass1=1;
dopass2=0;
if(datamean.ne.0)then;
do i=1,10;
call describe(argument(n(i)) :print);
enddo;
endif;
if(dopass1.ne.0)then;
call load(contrib);
call contribi;
/;
/; specific settings
/;
do_ppexp=0;
_m=8;
iols=2;
/; _mi=1;
_mi=2;
_nk=40;
/; ppreg code
_m=30;
iols=2;
/; iols=4;
isave=1;
/; rf code
_mtry=2;
_mtree=200;
call character(fsv_info,'1. Model 1');
75
International Trade Notes: 10 October 2016
call character(l_hand_s,'chanwsh');
call character(_args, 'dlky dly dsimat1a dofsh htsh_exp');
call character(_argsg,'dlky dly dsimat1a dofsh htsh_exp');
call contribl;
call contribd;
endif;
/; call tabulate(argument(mod4_42));
/; call tabulate(argument(mod4_43));
/; call tabulate(argument(mod4_44));
if(dopass2.ne.0)then;
call olsq(
chanwsh
call gamfit(
chanwsh
call marspline(chanwsh
call
ppreg(chanwsh
argument(mod4_42)
argument(mod4_42)
argument(mod4_42)
argument(mod4_42)
:print :white);
:print );
:print :mi 3 :nk 20);
:print);
call olsq(
chanwsh
call gamfit(
chanwsh
call marspline(chanwsh
call
ppreg(chanwsh
argument(mod4_43)
argument(mod4_43)
argument(mod4_43)
argument(mod4_43)
:print :white);
:print );
:print :mi 3 :nk 20);
:print);
call olsq(
chanwsh
call gamfit(
chanwsh
call marspline(chanwsh
call
ppreg(chanwsh
endif;
argument(mod4_44)
argument(mod4_44)
argument(mod4_44)
argument(mod4_44)
:print :white);
:print );
:print :mi 3 :nk 20);
:print);
b34srun;
Edited output from Leverage Plots
Settings for Leverage plots
Mars Models
Number of knots for MARS
(_knots)
Number of interactions
(_mi)
Max span between each knot (_ms=0)
C_rows / r_rows print setting
Plot setting
16
2
0
0
2
GAM Models
Degree of Polynomial for forecasts (degmod)
Default degree of GAM model (_gdf)
6
2.000000000000000
PPREG Models
Number of trees
(_m)
Exploratory Projection Pursuit turned off
OLS, GAM and MARS plotted
Plots produced in WMF form
Data saved in SCA fsv format
30
(do_ppexp=0)
(iols=2)
(ihp=0)
(isave=1)
Leverage effect of target variable (iversion=1)
Grids placed on graphs
(igrid=1)
Show graphs (ishow=1)
Data to write in fsv file
(fsv_info) 1. Model 1
Left hand side variable
Right hand side variables
_ARGS
= dlky dly dsimat1a dofsh htsh_exp
_ARGSG
= dlky dly dsimat1a dofsh htsh_exp
GAM right hand side variables
(l_hand_s) chanwsh
(_args)
(_argsg)
Ordinary Least Squares Estimation using QR Method
Dependent variable
CHANWSH
Centered R**2
4.663004197990550E-02
Adjusted R**2
3.582085878239876E-02
Residual Sum of Squares
99.69274477778127
Residual Variance
0.2260606457546060
Standard Error
0.4754583533335028
Total Sum of Squares
104.5687919355227
76
International Trade Notes: 10 October 2016
Log Likelihood
Mean of the Dependent Variable
Std. Error of Dependent Variable
Sum Absolute Residuals
F( 5,
441)
F Significance
QR Rank Check variable (eps) set as
Maximum Absolute Residual
Number of Observations
-298.9114424425495
0.3772410371879195
0.4842098457728058
154.2697623492203
4.313928363306974
0.9992344947238444
2.220446049250313E-16
2.423346113505557
447
-2 * ln(Maximum of Likelihood Function)
Akaike Information Criterion (AIC)
Scwartz Information Criterion (SIC)
Akaike (1970) Finite Prediction Error
Generalized Cross Validation
Hannan & Quinn (1979) HQ
Shibata (1981)
Rice (1984)
Variable
DLKY
DLY
DSIMAT1A
DOFSH
HTSH_EXP
CONSTANT
Lag
0
0
0
0
0
0
Coefficient
0.19461621E-01
0.16346747E-02
0.85486338E-01
0.17738186
-0.63894988E-02
0.30441686
597.8228848850989
611.8228848850989
640.5407950473939
0.2290950168385605
0.2291363007988864
0.2341227407534938
0.2290135572121456
0.2291787236270834
SE
0.10929047E-01
0.87081211E-02
0.40337870E-01
0.78035999E-01
0.10346851
0.34539594E-01
t
1.7807244
0.18771841
2.1192576
2.2730773
-0.61753074E-01
8.8135623
Using MARS note the number of time any knot figures in model. Also compare e ' e values for
different models.
Multivariate Autoregressive Splines Analysis
Model Estimated using Hastie-Tibshirani GPL routines in
CRAN General Public License (GPL) Library.
Version - 1 March 2006.
Left Hand Side Variable
Penalty cost per degree of freedom
Threshold for Forward stepwise Stopping
Rank Test Tolerance
Max # of Knots (nk)
Max interaction (mi)
Number of Observations
Number of right hand Variables
tolbx
set as
stopfac gcv/gcvnull > stopfac => stop
prevcrit set as
CHANWSH
3.000
0.1000E-03
0.1000E-12
16
2
447
5
1.000000000000000E-09
10.00000000000000
10000000000.00000
Series
Lag
DLKY
0
DLY
0
DSIMAT1A 0
DOFSH
0
HTSH_EXP 0
Min
-13.03
-13.96
-3.900
-0.3634
-0.8415E-01
Mean
0.5129
0.3948
0.3653
0.1801
0.1540
Max
14.73
22.53
2.970
0.8314
0.9744
GCV with only the constant
Total sum of squares
Final gcv
Variance of Y Variable
R**2 (1 - (var(res)/var(y)))
Residual Sum of Squares
Residual Variance
Residual Standard Error
Sum Absolute Residuals
Max Absolute Residual
# of coefficients after last fwd step
0.2349848679602379
104.5687919355228
0.2243541985438403
0.2344591747433244
9.800778114759146E-02
94.32023666063806
0.2114803512570358
0.4598699286287763
151.8419819292555
2.356771963985708
6
MARS Model Coefficients
CHANWSH
=
+
0.11234242
+
0.33196963
+
0.16270845
-0.70342093
+
0.19893933
SE
0.22430248
* max(
DLKY{ 0}
* max(
DOFSH{ 0}
* max(DSIMAT1A{ 0}
* max(
DLKY{ 0}
* max( -0.47806446E-01
* max(
5.1820626
* max( -0.47806446E-01
-
5.1592455
,
-0.47806446E-01,
0.20999895
,
-0.38131475E-01,
DOFSH{ 0}
,
DLY{ 0}
,
DOFSH{ 0}
,
0.0)
0.0)
0.0)
0.0)
0.0)
0.0)
0.0)
Importance
#
0.36260299E-01
0.29373323E-01
0.86699033E-01
0.57208979E-01
0.22217457
6.18
3.82
3.82
2.84
-3.16
447
23
332
287
39
100.000
5.145
74.273
64.206
8.725
99.886
100.000
74.278
82.687
1
2
3
4
5
0.64517991E-01
3.08
87
19.463
80.530
6
Analysis of GCV, RSS and KNOT by Variable before prune step
Obs
1
2
3
4
5
6
7
_GCV
0.2308
0.2306
0.2320
0.2345
0.2355
0.2373
0.2394
_RSS
100.4
98.08
96.41
95.22
93.38
91.87
90.47
_KNOT
_VAR
5.159
DLKY
-0.4781E-01 DOFSH
0.2100
DSIMAT1A
-0.3813E-01 DLKY
5.182
DLY
-7.413
DLY
3.993
DLY
_LAG
0
0
0
0
0
0
0
77
t
Non Zero
%
International Trade Notes: 10 October 2016
Generalized Additive Models (GAM) Analysis
Reference: Generalized Additive Models by Hastie and Tibshirani. Chapman (1990)
Model estimated using CRAN General Public License (GPL) routines.
Gaussian additive model assumed
Identity link - yhat = x*b + sum(splines)
Response variable ....
Number of observations:
Residual Sum of Squares
# iterations
# smooths/variable
Mean Squared Residual
df of deviance
Scale Estimate
Primary
tolerence
Secondary tolerance
R square
Total sum of Squares
Model df
-----------1.
2.00
2.00
2.00
2.00
2.00
----11.0
coef
---0.307945
0.182242E-01
0.759133E-03
0.742341E-01
0.195753
-.177332E-01
CHANWSH
447
96.78912935189766
1
12
0.2165304907201290
435.9990210388421
0.2219939143929292
1.000000000000000E-09
1.000000000000000E-09
7.439755628449879E-02
104.5687919355228
st err
z score
-----------0.3423E-01
8.997
0.1083E-01
1.683
0.8629E-02 0.8797E-01
0.3997E-01
1.857
0.7733E-01
2.531
0.1025
-.1729
nl pval
-------
lin_res
-------
0.7998
0.5792
0.7106
0.6579
0.7457
97.50
97.17
97.34
97.27
97.40
Name
---intcpt
DLKY
DLY
DSIMAT1A
DOFSH
HTSH_EXP
Lag
--0
0
0
0
0
Projection Pursuit Regression
Number of Observations
Number of right hand side variables
Maximum number of trees
Minimum number of trees
Number of left hand side variables
Level of fit
Max number of Primary
Iterations (maxit)
Max number of Secondary Iterations (mitone)
Number of cj Iterations (mitcj)
Smoother tone control (alpha)
Span
Convergence (CONV) set as
Left Hand Side Variable
Series
CHANWSH
Mean
0.3772
Max
2.972
447
6
30
30
1
2
200
200
10
0.000000000000000E+00
0.000000000000000E+00
5.000000000000000E-03
CHANWSH
Min
-1.184
Right Hand Side Variables
#
1
2
3
4
5
6
Series
DLKY
DLY
DSIMAT1A
DOFSH
HTSH_EXP
CONSTANT
Lag
0
0
0
0
0
0
Mean
0.5129
0.3948
0.3653
0.1801
0.1540
1.000
Max
14.73
22.53
2.970
0.8314
0.9744
1.000
Min
-13.03
-13.96
-3.900
-0.3634
-0.8415E-01
1.000
Given # of trees
# primary
iterations used
# secondary iterations used
# cj iterations used
Residual sum of squares
Total
sum of squares
Mean of the Dependent Variable
Std. Error of Dependent Variable
Sum Absolute Residuals
Maximum Absolute Residual
Residual Variance
Variable Importance for Model with # Trees
Series Number
Importance
1
1.00000
2
0.582809
3
0.547460
5
0.397385
4
0.343518
6
0.00000
30
2
3
2
45.74746740785981
104.5687919355227
0.3772410371879195
0.4842098457728058
102.4741977233084
1.592191521771080
0.1037357537593193
30
For Random Forest method note effect on e ' e of bagging and averaging. Note mtry was set as
2!
Random Forest Analysis Ver. 3.1 - 30 May 2009 build
Regression option selected.
Number of Observations
447
78
International Trade Notes: 10 October 2016
Number of right hand side variables
5
Maximum number of trees (maxtree)
200
Maximum number of nodes (nrnodes)
179
Number of Variables to select at each node (mtry) 2
Minimum node size (ndsize)
5
Left Hand Side Variable
CHANWSH
Series
CHANWSH
Mean
0.3772
Max
2.972
Min
-1.184
Right Hand Side Variables
#
1
2
3
4
5
Series
Lag
DLKY
0
DLY
0
DSIMAT1A
0
DOFSH
0
HTSH_EXP
0
Mean
0.5129
0.3948
0.3653
0.1801
0.1540
Max
14.73
22.53
2.970
0.8314
0.9744
Total Sum of Squares
Sum of Squared Residuals for last bagged model
Sum of Squared Residuals for averaged OOB model
Sum of Squared Residuals for averaged model
Centered R**2 for %YHAT
Centered R**2 for %YHAT2
Centered R**2 for %YHAT3
Min
-13.03
-13.96
-3.900
-0.3634
-0.8415E-01
104.5687919355227
85.36903992005276
111.6020632996678
39.00181645337509
0.1836088154036296
-6.725975536259265E-02
0.6270224057152378
Importance Analysis
For details see Hastie-Tibshirani-Friedman (2009, 594)
Variable importance based on Randomization
1
0.0000000
2
0.0000000
3
0.0000000
4
0.0000000
5
0.0000000
Variable importance based on Gini
1
4268.8911
2
3955.2716
3
4179.0395
4
1710.9527
5
1407.7635
Selected Leverage Plots.
It appears that there are thresholds. Only select graphs are shown.
79
International Trade Notes: 10 October 2016
Prediction L everage of D L K Y
[ lag= 0 , i nt= 2, o=M edians]
1.4
1.2
Contribution
1
M
A
R
S
Y
H
A
T
.8
.6
.4
.2
-10
-5
0
DLK Y
80
5
10
15
O
L
S
_
Y
H
A
T
G
A
M
_
Y
H
A
T
International Trade Notes: 10 October 2016
Prediction L everage of D L Y
[ lag= 0 , int= 2, o=M edians]
.44
.42
Contribution
.40
M
A
R
S
Y
H
A
T
.38
.36
.34
O
L
S
_
Y
H
A
T
G
A
M
_
Y
H
A
T
.32
.30
-15
-10
-5
0
5
DLY
10
15
20
Table 4.5 represents another approach that assumes a long run cost function where both types of
labor and capital are jointly solved from
Cn ( wn , qn , rn , Yn , p / pn ) min Ln , H n , Kn wn Ln qn H n rn K n s.t. (4.14)
(4.19)
Here factor prices differ across industries. (4.19) is linearly homogeneous in inputs and can be
written as
Cn (wn , qn , rn , Yn , zn ) Yn cn ( wn , qn , rn , zn )
(4.20)
Where we replaced ( p / pn ) by zn that includes other structural variables. Note that
cn (wn , qn , rn , zn ) is the unit cost function and
pn cn (wn , qn , rn , zn ), n 1,
,N
(4.21)
81
International Trade Notes: 10 October 2016
(4.21) shows that both product prices and structural change ( zn ) can affect factor prices. Taking
the difference between the log change in factor and product prices and noting that the cost shares
sum to 1.0, total factor productivity is
TFPn (nL ln wn nH ln qn nK ln rn ) ln pn
(4.22)
Which can be used to form the estimating equation
ln pn TFPn nL ln wn nH ln qn nK ln rn n 1,
,N
(4.23)
If the data are factor shares nj then the implied change in factor prices L , H , K can be
estimated from
ln pn TFPn nL L nH H nK K n 1,
,N
(4.24)
Which has been used in Table 4.5. L , H , K can be interpreted as the change in factor prices
that are mandated by the change in product prices. A code template for further investigation of
whether there are nonlinearities in the model that have caused the model not to work well is
Code Template for Estimation of a Long Run Model
b34sexec options ginclude('Feenstra_ch4.mac') member(ch4_3_a);
b34srun;
b34sexec matrix;
call loaddata;
call olsq(
dlp34 ptfp apsh ansh aksh :print :white);
call gamfit(
dlp34 ptfp apsh ansh aksh :print );
call marspline(dlp34 ptfp apsh ansh aksh :print);
call
ppreg(dlp34 ptfp apsh ansh aksh :print);
b34srun;
Stata Template
// set mem 3m
log using log_4_3a.log,replace
// use d:\feenstra_course\chap4\data_Chp4.dta, clear
// use c:\feenstra_course\chap4\data_Chp4.dta, clear
use data_Chp4.dta, clear
// use e:\feenstra_course\chap4\data_Chp4.dta, clear
* use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
keep if year==1990
82
International Trade Notes: 10 October 2016
drop if sic72==2067
drop if sic72==2794
drop if sic72==3483
gen etfp=ptfp-err
gen adj1=1/(1-amesh)
gen etfp1=adj1*etfp
gen dlpvad1=adj1*dlpvad
gen apsh1=adj1*apsh
gen ansh1=adj1*ansh
gen aksh1=adj1*aksh
gen mshxpr=amsh*dlpmx
gen eshxpr=aosh*dlpe
* Reproduce Table 4.5 reprinted at 4.1 in new edition.
gen dlp34=dlp-mshxpr-eshxpr
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model
regress dlp34 ptfp apsh ansh aksh , robust
preserve
drop if sic72==3573
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model without sic72
regress dlp34 ptfp apsh ansh aksh , robust
regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp apsh ansh aksh mshxpr eshxpr, robust
restore
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
* OLS Model
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
log close
* clear *
exit
___ ____ ____ ____ ____ (R)
/__
/
____/
/
____/
___/
/
/___/
/
/___/
14.2
Statistics/Data Analysis
Special Edition
Copyright 1985-2015 StataCorp LP
StataCorp
4905 Lakeway Drive
College Station, Texas 77845 USA
800-STATA-PC
http://www.stata.com
979-696-4600
[email protected]
979-696-4601 (fax)
Single-user Stata perpetual license:
Serial number: 401406202087
Licensed to: Houston H. Stokes
University of Illinois Chicago
Notes:
1.
2.
3.
Stata is running in batch mode.
Unicode is supported; see help unicode_advice.
Maximum number of variables is set to 5000; see help set_maxvar.
83
International Trade Notes: 10 October 2016
. do Problem_4_3_a.do
.
. // set mem 3m
.
. log using log_4_3a.log,replace
------------------------------------------------------------------------------name: <unnamed>
log: D:\class\E514\log_4_3a.log
log type: text
opened on: 10 Oct 2016, 10:11:28
.
. // use d:\feenstra_course\chap4\data_Chp4.dta, clear
. // use c:\feenstra_course\chap4\data_Chp4.dta, clear
. use data_Chp4.dta, clear
(Matrl Cons (72 SIC), 67-92)
. // use e:\feenstra_course\chap4\data_Chp4.dta, clear
. * use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
.
. keep if year==1990
(1,350 observations deleted)
. drop if sic72==2067
(1 observation deleted)
. drop if sic72==2794
(1 observation deleted)
. drop if sic72==3483
(1 observation deleted)
. gen etfp=ptfp-err
. gen adj1=1/(1-amesh)
. gen etfp1=adj1*etfp
. gen dlpvad1=adj1*dlpvad
. gen apsh1=adj1*apsh
. gen ansh1=adj1*ansh
. gen aksh1=adj1*aksh
. gen mshxpr=amsh*dlpmx
. gen eshxpr=aosh*dlpe
.
.
. * Reproduce Table 4.5 *
.
. gen dlp34=dlp-mshxpr-eshxpr
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(4, 442)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
106.29
0.0000
0.8957
.80656
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.9631819
.0702093
-13.72
0.000
-1.101168
-.8251963
apsh |
3.062598
1.22198
2.51
0.013
.6609845
5.464212
ansh |
2.294716
1.430073
1.60
0.109
-.5158719
5.105305
aksh |
7.887571
.7810006
10.10
0.000
6.352634
9.422507
_cons | -.7051116
.3006016
-2.35
0.019
-1.295898
-.1143256
-----------------------------------------------------------------------------.
. * OLS Model
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression
Number of obs
F(4, 442)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
110.62
0.0000
0.6967
.91728
-----------------------------------------------------------------------------|
Robust
84
International Trade Notes: 10 October 2016
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.6790007
.0709856
-9.57
0.000
-.8185121
-.5394894
apsh |
3.455601
.8328199
4.15
0.000
1.818822
5.09238
ansh |
3.905478
1.754048
2.23
0.026
.4581676
7.352789
aksh |
7.394156
.71982
10.27
0.000
5.979461
8.808851
_cons | -.7849882
.1904677
-4.12
0.000
-1.159323
-.4106534
-----------------------------------------------------------------------------.
. preserve
. drop if sic72==3573
(1 observation deleted)
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is
9.8179e-01)
Linear regression
Number of obs
F(4, 441)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
92.17
0.0000
0.8059
.74139
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.7531151
.0751891
-10.02
0.000
-.9008886
-.6053416
apsh |
2.427856
1.162844
2.09
0.037
.142451
4.713261
ansh |
4.086394
1.722144
2.37
0.018
.7017647
7.471024
aksh |
8.058291
.9411699
8.56
0.000
6.208556
9.908027
_cons | -.8249273
.2930995
-2.81
0.005
-1.400973
-.2488819
-----------------------------------------------------------------------------. * OLS Model without sic72
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression
Number of obs
F(4, 441)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
135.75
0.0000
0.6696
.87366
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.6043067
.0418654
-14.43
0.000
-.6865873
-.5220261
apsh |
3.156235
.7864841
4.01
0.000
1.610513
4.701958
ansh |
4.954764
1.5334
3.23
0.001
1.941084
7.968443
aksh |
7.396599
.7390641
10.01
0.000
5.944073
8.849124
_cons | -.8377685
.1852263
-4.52
0.000
-1.201804
-.4737325
-----------------------------------------------------------------------------.
. regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is
9.8179e-01)
Linear regression
Number of obs
F(5, 440)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
10.85
0.0000
0.4289
1.2034
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------apsh |
3.605277
1.88524
1.91
0.056
-.0999163
7.310471
ansh |
6.202674
4.036466
1.54
0.125
-1.730475
14.13582
aksh |
9.535214
2.18722
4.36
0.000
5.236518
13.83391
mshxpr |
1.219304
.2471334
4.93
0.000
.7335958
1.705013
eshxpr | -.9301182
.9150299
-1.02
0.310
-2.728491
.8682541
_cons | -1.929187
.9147773
-2.11
0.036
-3.727063
-.1313111
-----------------------------------------------------------------------------. * OLS Model
. regress dlp apsh ansh aksh mshxpr eshxpr, robust
Linear regression
Number of obs
F(5, 440)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
24.65
0.0000
0.3400
1.2384
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
85
International Trade Notes: 10 October 2016
apsh |
5.629626
1.284501
4.38
0.000
3.105105
8.154147
ansh |
7.727702
2.065437
3.74
0.000
3.668354
11.78705
aksh |
8.611022
1.272484
6.77
0.000
6.110121
11.11192
mshxpr |
1.448936
.1923696
7.53
0.000
1.070858
1.827013
eshxpr |
.0327104
.533676
0.06
0.951
-1.01616
1.081581
_cons | -2.629372
.6429471
-4.09
0.000
-3.893001
-1.365743
-----------------------------------------------------------------------------. restore
.
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(4, 443)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9998
.07762
-----------------------------------------------------------------------------|
Robust
dlpvad1 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp1 | -1.000041
.0006831 -1463.88
0.000
-1.001384
-.9986986
apsh1 |
4.680657
.0157718
296.77
0.000
4.64966
4.711654
ansh1 |
5.482807
.0194677
281.64
0.000
5.444547
5.521068
aksh1 |
3.952538
.0083407
473.89
0.000
3.936146
3.96893
-----------------------------------------------------------------------------. * OLS Model
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
Linear regression
Number of obs
F(4, 443)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9988
.1685
-----------------------------------------------------------------------------|
Robust
dlpvad1 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp1 | -.9992624
.0042216 -236.70
0.000
-1.007559
-.9909655
apsh1 |
4.666086
.0550321
84.79
0.000
4.55793
4.774243
ansh1 |
5.437375
.0644382
84.38
0.000
5.310733
5.564018
aksh1 |
3.953762
.0221871
178.20
0.000
3.910157
3.997367
-----------------------------------------------------------------------------.
. regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(6, 440)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9999
.0262
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp | -1.000358
.000677 -1477.55
0.000
-1.001689
-.9990273
apsh |
4.700013
.011911
394.60
0.000
4.676603
4.723422
ansh |
5.443315
.0314405
173.13
0.000
5.381523
5.505107
aksh |
3.972308
.0150284
264.32
0.000
3.942772
4.001845
mshxpr |
.9974072
.0023115
431.50
0.000
.9928643
1.00195
eshxpr |
.9961108
.0057421
173.47
0.000
.9848254
1.007396
_cons |
.0010799
.005423
0.20
0.842
-.0095784
.0117382
-----------------------------------------------------------------------------. * OLS Model
. regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
Linear regression
Number of obs
F(6, 440)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9989
.05637
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp | -.9984327
.0024469 -408.04
0.000
-1.003242
-.9936236
apsh |
4.71449
.0145206
324.68
0.000
4.685952
4.743028
ansh |
5.443702
.0521618
104.36
0.000
5.341185
5.546219
aksh |
4.000907
.044225
90.47
0.000
3.913988
4.087825
mshxpr |
.9907738
.0089715
110.44
0.000
.9731416
1.008406
eshxpr |
.996285
.0058313
170.85
0.000
.9848243
1.007746
86
International Trade Notes: 10 October 2016
_cons | -.0023481
.007124
-0.33
0.742
-.0163494
.0116532
-----------------------------------------------------------------------------.
. log close
name: <unnamed>
log: D:\class\E514\log_4_3a.log
log type: text
closed on: 10 Oct 2016, 10:11:29
------------------------------------------------------------------------------. * clear *
. exit
Code Template for Estimation of a Long Run Model
b34sexec options include('Feenstra_ch4.mac') member(ch4_3_a);
b34srun;
b34sexec matrix;
call loaddata;
call olsq(
dlp34 ptfp apsh ansh aksh :print :white);
call gamfit(
dlp34 ptfp apsh ansh aksh :print );
call marspline(dlp34 ptfp apsh ansh aksh :print);
call
ppreg(dlp34 ptfp apsh ansh aksh :print);
b34srun;
Variable
YEAR
SIC72
EMP
PAY
PRODE
PRODH
PRODW
VADD
MATERIAL
INVENT
INVEST
ENERGY
CAP
EQUIP
PLANT
PISHIP
PIINV
PIEN
VSHIP
PIMAT
CI
SIC2
IMAT
SIMAT1A
SIMAT1B
DSIMAT1A
DSIMAT1B
DLY
NWSH
MVSHIPSH
04
DLKY
APSH
01
ANSH
02
AMESH
AMSH
AOSH
02
AKSH
01
DLP
DLPE
01
DHTSH
Label
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Year ranges from 58 to 97
4 digit SIC code
Total employment in 1000s
Total payroll in $1,000,000
Production workers in 1000s
Production worker hours in 1,000,000
Production worker wages in $1,000,000
Total value added in $1,000,000
Total cost of materials in $1,000,000
End-of-year inventories in $1,000,000
Total capital expenditure in $1,000,000
Cost of electric & fuels in $1,000,000
Total real capital stock in $1,000,000
Real capital: equipment in $1,000,000
Real capital: structures in $1,000,000
Deflator for VSHIP 1987=1.000
Deflator for INVEST 1987=1.000
Deflator for ENERGY 1987=1.000
Total value of shipments in $1,000,000
Deflator for MATCOST 1987=1.000
computer investment/total investment
2 digit SIC code
imported materials
Share of imported mat -broad outsourcing
share of imported mat - 2-digit industry
change in outsourcing (broad)
change in outsourcing (narrow)
change in log real shipments
nonproduction share of the total wages
industry share of total manfg shipments
# Cases
Mean
Std. Dev.
Variance
Maximum
Minimum
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
433
447
447
447
447
447
447
447
1990.00
3015.57
39.2085
1054.33
27.0548
54.2481
607.053
2959.26
3469.51
875.567
228.052
126.855
2702.68
1646.90
1055.78
1.11687
1.08237
1.06987
6412.92
1.12898
5.55268
29.6174
23.3486
0.118441
0.485957E-01
0.365305
0.157793
0.394762
0.372574
0.223430E-02
0.00000
608.388
62.8485
1892.61
41.5547
83.9769
1040.94
5191.26
9619.80
2098.71
545.062
352.896
5862.97
3676.64
2300.93
0.837093E-01
0.241873E-01
0.167540E-01
13641.7
0.481798E-01
5.48071
6.09484
109.734
0.875671E-01
0.749496E-01
0.563151
0.473762
3.76272
0.120623
0.496680E-02
0.00000
370136.
3949.93
0.358198E+07
1726.79
7052.12
0.108355E+07
0.269491E+08
0.925406E+08
0.440458E+07
297093.
124535.
0.343745E+08
0.135177E+08
0.529427E+07
0.700725E-02
0.585027E-03
0.280697E-03
0.186097E+09
0.232130E-02
30.0382
37.1470
12041.7
0.766799E-02
0.561745E-02
0.317139
0.224450
14.1581
0.145500E-01
0.246691E-04
1990.00
3999.00
631.100
18381.6
487.700
979.200
9789.90
39504.4
145885.
32271.6
4396.40
4327.90
59407.3
38087.0
31042.8
1.53300
1.11900
1.25700
170775.
1.52700
43.4804
39.0000
1399.06
0.659710
0.628002
2.96951
2.73056
22.5287
0.873336
0.703875E-01
1990.00
2011.00
0.400000
13.9000
0.100000
0.300000
8.70000
27.6000
10.7000
7.90000
0.400000
0.800000
19.9000
4.40000
12.2000
0.822000
0.937000
1.02200
44.5000
1.01400
0.00000
20.0000
0.00000
0.00000
0.00000
-3.90025
-4.14979
-13.9630
0.109044
0.230466E-
31 change in log capital stock/shipments
32 average production share
447
447
0.512945
0.132555
3.13639
0.574340E-01
9.83696
0.329867E-02
14.7261
0.364086
-13.0257
0.115928E-
33 average non-production share
447
0.722582E-01
0.393782E-01
0.155065E-02
0.270142
0.638309E-
34 aosh + amsh
35 average material share
36 average energy share
447
447
447
0.512149
0.487772
0.243771E-01
0.123647
0.127229
0.328570E-01
0.152887E-01
0.161873E-01
0.107958E-02
0.890473
0.877148
0.275952
0.171757
0.151759
0.213427E-
37 average capital share
447
0.283037
0.843416E-01
0.711350E-02
0.636899
0.738303E-
38 change in log price
39 change in log energy price
447
447
3.54611
3.12686
1.70410
0.912518
2.90397
0.832688
11.7933
8.40714
-12.9502
0.860887E-
40 (capital=pstk x ex post rental price)
447
0.334085
0.376402
0.141678
1.27976
87
-0.301242
International Trade Notes: 10 October 2016
DHTSH1
DOFSH
DOFSH1
DLPMX
DLPVAD
PTFP
ADLHW
ADLNW
ADLPK
ERR
ETFP
ADJ1
ETFP1
41
42
43
44
45
46
47
48
49
50
51
52
53
(capital=pstk x ex ante rental price)
change in office equipment/total capital
change in office equipment/total capital
change in log material price
change in log value-added
primary TFP
annual change in log production wage
annual chage in log non-production wage
annual change in log capital price
error as defined in (4.26) of Chapter 4
ptfp-err
1.0/(1.0-amesh)
adj1*etfp
447
447
447
447
447
447
447
447
447
447
447
447
447
0.210975
0.180127
0.352378E-01
3.58936
1.77040
0.408978
4.71405
5.43687
3.95370
0.464305E-01
0.362547
2.24364
1.00142
88
0.245414
0.307711
0.151631
0.887371
1.65821
1.64672
0.00000
0.00000
0.00000
1.10714
1.46871
0.889095
3.55532
0.602279E-01
0.946862E-01
0.229921E-01
0.787427
2.74968
2.71169
0.00000
0.00000
0.00000
1.22575
2.15711
0.790491
12.6403
1.21186
0.831400
0.379551
7.67960
10.5839
14.0399
4.71405
5.43687
3.95370
4.49691
14.8904
9.13017
32.8904
-0.209675
-0.363431
-0.270059
-1.81683
-12.6178
-5.01075
4.71405
5.43687
3.95370
-4.63585
-7.65468
1.20737
-10.8290
International Trade Notes: 10 October 2016
B34S 9
(D:M:Y)
DLPVAD1
APSH1
01
ANSH1
01
AKSH1
MSHXPR
ESHXPR
02
DLP34
CONSTANT
10/10/16 (H:M:S) 10:24: 4
3.35799
0.270372
3.56748
0.903109E-01
56 adj1*ansh
447
0.143112
57 adj1*aksh
58 amsh*dlpmx
59 aosh*dlpe
447
447
447
0.586515
1.69937
0.763338E-01
60 dlp-mshxpr-eshxpr
61
447
447
1.77040
1.00000
CALL LOADDATA$
=>
CALL OLSQ(
Ordinary Least Squares Estimation
Dependent variable
Centered R**2
Adjusted R**2
Residual Sum of Squares
Residual Variance
Standard Error
Total Sum of Squares
Log Likelihood
Mean of the Dependent Variable
Std. Error of Dependent Variable
Sum Absolute Residuals
F( 4,
442)
F Significance
1/Condition XPX
Maximum Absolute Residual
Number of Observations
Variable
PTFP
APSH
ANSH
AKSH
CONSTANT
Lag
0
0
0
0
0
Coefficient
-0.67900074
3.4556009
3.9054785
7.3941559
-0.78498817
-29.1263
0.305658E-
0.558816E-01
0.312275E-02
0.389831
0.266251E-
0.109801
0.515041
0.115698
0.120563E-01
0.265268
0.133861E-01
0.920277
3.39471
1.21165
0.277150
-1.58880
0.206717E-
1.65821
0.00000
2.74968
0.00000
CALL GAMFIT(
:PRINT :WHITE)$
DLP34
0.6967466663385627
0.6940022922782783
371.8964985643850
0.8413947931320926
0.9172757454179701
1226.355846031963
-593.1542618937680
1.770400132847875
1.658214939272056
297.4930711130872
253.8818145899300
1.000000000000000
6.550394423061074E-04
5.408266825961406
447
White SE
0.70587514E-01
0.82814894
1.7442105
0.71578284
0.18939943
DLP34 PTFP APSH ANSH AKSH
t
-9.6192754
4.1726805
2.2391097
10.330166
-4.1446174
:PRINT )$
Generalized Additive Models (GAM) Analysis
Reference: Generalized Additive Models by Hastie and Tibshirani. Chapman (1990)
Model estimated using CRAN General Public License (GPL) routines.
Gaussian additive model assumed
Identity link - yhat = x*b + sum(splines)
Response variable ....
Number of observations:
Residual Sum of Squares
# iterations
# smooths/variable
Mean Squared Residual
df of deviance
Scale Estimate
Primary
tolerence
Secondary tolerance
R square
Total sum of Squares
Model df
-----------1.
3.00
3.00
3.00
3.00
----13.0
=>
coef
----1.04728
-.665252
4.03542
5.63971
7.58671
DLP34
447
300.2070345290874
1
15
0.6716041040919182
434.0021682741188
0.6917178218784257
1.000000000000000E-09
1.000000000000000E-09
0.7552039764800347
1226.355846031963
st err
z score
-----------0.1685
-6.217
0.2421E-01 -27.48
0.7551
5.344
1.133
4.979
0.4869
15.58
CALL MARSPLINE(DLP34 PTFP APSH ANSH AKSH
nl pval
-------
lin_res
-------
1.000
0.1748
0.8573
1.000
346.8
300.8
304.0
325.1
:PRINT)$
Multivariate Autoregressive Splines Analysis
89
2
14.9729
0.488378
447
1.000000000000000E+31
DLP34 PTFP APSH ANSH AKSH
PAGE
12.7269
0.815606E-02
Matrix Command. d/m/y 10/10/16. h:m:s 10:24: 4.
=>
=>
Feenstra Chap4 4_3a Data
447
447
Number of observations in data file
Current missing variable code
Note: Missing data in the data file
B34S
DATA STEP
54 adj1*dlpvad
55 adj1*apsh
Name
---intcpt
PTFP
APSH
ANSH
AKSH
Lag
--0
0
0
0
10.5839
1.00000
-12.6178
1.00000
International Trade Notes: 10 October 2016
Model Estimated using Hastie-Tibshirani GPL routines in
CRAN General Public License (GPL) Library.
Version - 1 March 2006.
Left Hand Side Variable
Penalty cost per degree of freedom
Threshold for Forward stepwise Stopping
Rank Test Tolerance
Max # of Knots (nk)
Max interaction (mi)
Number of Observations
Number of right hand Variables
tolbx
set as
stopfac gcv/gcvnull > stopfac => stop
prevcrit set as
DLP34
2.000
0.1000E-03
0.1000E-12
5
1
447
4
1.000000000000000E-09
10.00000000000000
10000000000.00000
Series
PTFP
APSH
ANSH
AKSH
Min
-5.011
0.1159E-01
0.6383E-02
0.7383E-01
Lag
0
0
0
0
Mean
0.4090
0.1326
0.7226E-01
0.2830
Max
14.04
0.3641
0.2701
0.6369
GCV with only the constant
Total sum of squares
Final gcv
Variance of Y Variable
R**2 (1 - (var(res)/var(y)))
Residual Sum of Squares
Residual Variance
Residual Standard Error
Sum Absolute Residuals
Max Absolute Residual
# of coefficients after last fwd step
2.755841979409840
1226.355846031963
0.8411019886991933
2.749676784825029
0.7056440275681013
360.9851676062820
0.8093837838705881
0.8996575925709670
306.7363667559480
3.945752605427743
5
MARS Model Coefficients
DLP34
=
-1.2359379
+
0.57809246
+
12.581184
-7.1731181
=>
CALL
SE
1.1612470
* max(
PTFP{ 0}
* max(
3.1126752
* max(
AKSH{ 0}
* max( 0.41347152
-
PPREG(DLP34 PTFP APSH ANSH AKSH
3.1126752
PTFP{ 0}
0.41347152
AKSH{ 0}
,
,
,
,
0.0)
0.0)
0.0)
0.0)
0.13135952
0.77496252E-01
0.31013665E-01
1.9014328
0.62994727
:PRINT)$
Projection Pursuit Regression
Number of Observations
Number of right hand side variables
Maximum number of ridge functions
Minimum number of ridge functions
Number of left hand side variables
Level of fit
Max number of Primary
Iterations (maxit)
Max number of Secondary Iterations (mitone)
Number of cj Iterations (mitcj)
Smoother tone control (alpha)
Span
Convergence (CONV) set as
Left Hand Side Variable
Series
DLP34
Mean
1.770
Max
10.58
447
5
20
20
1
2
200
200
10
0.000000000000000E+00
0.000000000000000E+00
5.000000000000000E-03
DLP34
Min
-12.62
Right Hand Side Variables
#
1
2
3
4
5
Series
PTFP
APSH
ANSH
AKSH
CONSTANT
Lag
0
0
0
0
0
Mean
0.4090
0.1326
0.7226E-01
0.2830
1.000
Given # of ridge functions
# primary
iterations used
# secondary iterations used
# cj iterations used
Residual sum of squares
Total
sum of squares
Mean of the Dependent Variable
Std. Error of Dependent Variable
Sum Absolute Residuals
Maximum Absolute Residual
Residual Variance
Max
14.04
0.3641
0.2701
0.6369
1.000
Min
-5.011
0.1159E-01
0.6383E-02
0.7383E-01
1.000
20
1
7
2
179.3691430157083
1226.355846031963
1.770400132847875
1.658214939272056
210.3559765757928
2.456771179577403
0.4058125407595211
Variable Importance for Model with # ridge functions
Series Number
Importance
1
1.00000
3
0.885062
4
0.760611
2
0.636560
5
0.00000
20
90
t
8.84
-15.9
18.6
6.61
-11.3
Non Zero
447
23
423
23
423
%
100.000
5.145
94.631
5.145
94.631
Importance
#
85.560
100.000
35.497
61.089
1
2
3
4
5
International Trade Notes: 10 October 2016
Stata Template
// set mem 3m
log using log_4_3a.log,replace
// use d:\feenstra_course\chap4\data_Chp4.dta, clear
// use c:\feenstra_course\chap4\data_Chp4.dta, clear
use data_Chp4.dta, clear
// use e:\feenstra_course\chap4\data_Chp4.dta, clear
* use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
keep if year==1990
drop if sic72==2067
drop if sic72==2794
drop if sic72==3483
gen etfp=ptfp-err
gen adj1=1/(1-amesh)
gen etfp1=adj1*etfp
gen dlpvad1=adj1*dlpvad
gen apsh1=adj1*apsh
gen ansh1=adj1*ansh
gen aksh1=adj1*aksh
gen mshxpr=amsh*dlpmx
gen eshxpr=aosh*dlpe
* Reproduce Table 4.5 reprinted at 4.1 in new edition.
gen dlp34=dlp-mshxpr-eshxpr
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model
regress dlp34 ptfp apsh ansh aksh , robust
preserve
drop if sic72==3573
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model without sic72
regress dlp34 ptfp apsh ansh aksh , robust
regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp apsh ansh aksh mshxpr eshxpr, robust
restore
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
* OLS Model
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
log close
* clear *
91
International Trade Notes: 10 October 2016
exit
___ ____ ____ ____ ____ (R)
/__
/
____/
/
____/
___/
/
/___/
/
/___/
14.2
Statistics/Data Analysis
Special Edition
Copyright 1985-2015 StataCorp LP
StataCorp
4905 Lakeway Drive
College Station, Texas 77845 USA
800-STATA-PC
http://www.stata.com
979-696-4600
[email protected]
979-696-4601 (fax)
Single-user Stata perpetual license:
Serial number: 401406202087
Licensed to: Houston H. Stokes
University of Illinois Chicago
Notes:
1.
2.
3.
Stata is running in batch mode.
Unicode is supported; see help unicode_advice.
Maximum number of variables is set to 5000; see help set_maxvar.
. do Problem_4_3_a.do
.
. // set mem 3m
.
. log using log_4_3a.log,replace
------------------------------------------------------------------------------name: <unnamed>
log: D:\class\E514\log_4_3a.log
log type: text
opened on: 10 Oct 2016, 10:11:28
.
. // use d:\feenstra_course\chap4\data_Chp4.dta, clear
. // use c:\feenstra_course\chap4\data_Chp4.dta, clear
. use data_Chp4.dta, clear
(Matrl Cons (72 SIC), 67-92)
. // use e:\feenstra_course\chap4\data_Chp4.dta, clear
. * use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
.
. keep if year==1990
(1,350 observations deleted)
. drop if sic72==2067
(1 observation deleted)
. drop if sic72==2794
(1 observation deleted)
. drop if sic72==3483
(1 observation deleted)
. gen etfp=ptfp-err
. gen adj1=1/(1-amesh)
. gen etfp1=adj1*etfp
. gen dlpvad1=adj1*dlpvad
. gen apsh1=adj1*apsh
. gen ansh1=adj1*ansh
. gen aksh1=adj1*aksh
. gen mshxpr=amsh*dlpmx
. gen eshxpr=aosh*dlpe
.
.
. * Reproduce Table 4.5 *
.
. gen dlp34=dlp-mshxpr-eshxpr
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(4, 442)
Prob > F
R-squared
Root MSE
=
=
=
=
=
92
447
106.29
0.0000
0.8957
.80656
International Trade Notes: 10 October 2016
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.9631819
.0702093
-13.72
0.000
-1.101168
-.8251963
apsh |
3.062598
1.22198
2.51
0.013
.6609845
5.464212
ansh |
2.294716
1.430073
1.60
0.109
-.5158719
5.105305
aksh |
7.887571
.7810006
10.10
0.000
6.352634
9.422507
_cons | -.7051116
.3006016
-2.35
0.019
-1.295898
-.1143256
-----------------------------------------------------------------------------.
. * OLS Model
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression
Number of obs
F(4, 442)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
110.62
0.0000
0.6967
.91728
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.6790007
.0709856
-9.57
0.000
-.8185121
-.5394894
apsh |
3.455601
.8328199
4.15
0.000
1.818822
5.09238
ansh |
3.905478
1.754048
2.23
0.026
.4581676
7.352789
aksh |
7.394156
.71982
10.27
0.000
5.979461
8.808851
_cons | -.7849882
.1904677
-4.12
0.000
-1.159323
-.4106534
-----------------------------------------------------------------------------.
. preserve
. drop if sic72==3573
(1 observation deleted)
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is
9.8179e-01)
Linear regression
Number of obs
F(4, 441)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
92.17
0.0000
0.8059
.74139
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.7531151
.0751891
-10.02
0.000
-.9008886
-.6053416
apsh |
2.427856
1.162844
2.09
0.037
.142451
4.713261
ansh |
4.086394
1.722144
2.37
0.018
.7017647
7.471024
aksh |
8.058291
.9411699
8.56
0.000
6.208556
9.908027
_cons | -.8249273
.2930995
-2.81
0.005
-1.400973
-.2488819
-----------------------------------------------------------------------------. * OLS Model without sic72
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression
Number of obs
F(4, 441)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
135.75
0.0000
0.6696
.87366
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.6043067
.0418654
-14.43
0.000
-.6865873
-.5220261
apsh |
3.156235
.7864841
4.01
0.000
1.610513
4.701958
ansh |
4.954764
1.5334
3.23
0.001
1.941084
7.968443
aksh |
7.396599
.7390641
10.01
0.000
5.944073
8.849124
_cons | -.8377685
.1852263
-4.52
0.000
-1.201804
-.4737325
-----------------------------------------------------------------------------.
. regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is
9.8179e-01)
Linear regression
Number of obs
F(5, 440)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
10.85
0.0000
0.4289
1.2034
-----------------------------------------------------------------------------|
Robust
93
International Trade Notes: 10 October 2016
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------apsh |
3.605277
1.88524
1.91
0.056
-.0999163
7.310471
ansh |
6.202674
4.036466
1.54
0.125
-1.730475
14.13582
aksh |
9.535214
2.18722
4.36
0.000
5.236518
13.83391
mshxpr |
1.219304
.2471334
4.93
0.000
.7335958
1.705013
eshxpr | -.9301182
.9150299
-1.02
0.310
-2.728491
.8682541
_cons | -1.929187
.9147773
-2.11
0.036
-3.727063
-.1313111
-----------------------------------------------------------------------------. * OLS Model
. regress dlp apsh ansh aksh mshxpr eshxpr, robust
Linear regression
Number of obs
F(5, 440)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
24.65
0.0000
0.3400
1.2384
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------apsh |
5.629626
1.284501
4.38
0.000
3.105105
8.154147
ansh |
7.727702
2.065437
3.74
0.000
3.668354
11.78705
aksh |
8.611022
1.272484
6.77
0.000
6.110121
11.11192
mshxpr |
1.448936
.1923696
7.53
0.000
1.070858
1.827013
eshxpr |
.0327104
.533676
0.06
0.951
-1.01616
1.081581
_cons | -2.629372
.6429471
-4.09
0.000
-3.893001
-1.365743
-----------------------------------------------------------------------------. restore
.
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(4, 443)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9998
.07762
-----------------------------------------------------------------------------|
Robust
dlpvad1 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp1 | -1.000041
.0006831 -1463.88
0.000
-1.001384
-.9986986
apsh1 |
4.680657
.0157718
296.77
0.000
4.64966
4.711654
ansh1 |
5.482807
.0194677
281.64
0.000
5.444547
5.521068
aksh1 |
3.952538
.0083407
473.89
0.000
3.936146
3.96893
-----------------------------------------------------------------------------. * OLS Model
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
Linear regression
Number of obs
F(4, 443)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9988
.1685
-----------------------------------------------------------------------------|
Robust
dlpvad1 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp1 | -.9992624
.0042216 -236.70
0.000
-1.007559
-.9909655
apsh1 |
4.666086
.0550321
84.79
0.000
4.55793
4.774243
ansh1 |
5.437375
.0644382
84.38
0.000
5.310733
5.564018
aksh1 |
3.953762
.0221871
178.20
0.000
3.910157
3.997367
-----------------------------------------------------------------------------.
. regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(6, 440)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9999
.0262
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp | -1.000358
.000677 -1477.55
0.000
-1.001689
-.9990273
apsh |
4.700013
.011911
394.60
0.000
4.676603
4.723422
ansh |
5.443315
.0314405
173.13
0.000
5.381523
5.505107
aksh |
3.972308
.0150284
264.32
0.000
3.942772
4.001845
mshxpr |
.9974072
.0023115
431.50
0.000
.9928643
1.00195
94
International Trade Notes: 10 October 2016
eshxpr |
.9961108
.0057421
173.47
0.000
.9848254
1.007396
_cons |
.0010799
.005423
0.20
0.842
-.0095784
.0117382
-----------------------------------------------------------------------------. * OLS Model
. regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
Linear regression
Number of obs
F(6, 440)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9989
.05637
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp | -.9984327
.0024469 -408.04
0.000
-1.003242
-.9936236
apsh |
4.71449
.0145206
324.68
0.000
4.685952
4.743028
ansh |
5.443702
.0521618
104.36
0.000
5.341185
5.546219
aksh |
4.000907
.044225
90.47
0.000
3.913988
4.087825
mshxpr |
.9907738
.0089715
110.44
0.000
.9731416
1.008406
eshxpr |
.996285
.0058313
170.85
0.000
.9848243
1.007746
_cons | -.0023481
.007124
-0.33
0.742
-.0163494
.0116532
-----------------------------------------------------------------------------.
. log close
name: <unnamed>
log: D:\class\E514\log_4_3a.log
log type: text
closed on: 10 Oct 2016, 10:11:29
------------------------------------------------------------------------------. * clear *
. exit
Code Template for Estimation of a Long Run Model
b34sexec options include('Feenstra_ch4.mac') member(ch4_3_a);
b34srun;
b34sexec matrix;
call loaddata;
call olsq(
dlp34 ptfp apsh ansh aksh :print :white);
call gamfit(
dlp34 ptfp apsh ansh aksh :print );
call marspline(dlp34 ptfp apsh ansh aksh :print);
call
ppreg(dlp34 ptfp apsh ansh aksh :print);
b34srun;
Variable
YEAR
SIC72
EMP
PAY
PRODE
PRODH
PRODW
VADD
MATERIAL
INVENT
INVEST
ENERGY
CAP
EQUIP
PLANT
PISHIP
PIINV
PIEN
VSHIP
PIMAT
CI
SIC2
IMAT
Label
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Year ranges from 58 to 97
4 digit SIC code
Total employment in 1000s
Total payroll in $1,000,000
Production workers in 1000s
Production worker hours in 1,000,000
Production worker wages in $1,000,000
Total value added in $1,000,000
Total cost of materials in $1,000,000
End-of-year inventories in $1,000,000
Total capital expenditure in $1,000,000
Cost of electric & fuels in $1,000,000
Total real capital stock in $1,000,000
Real capital: equipment in $1,000,000
Real capital: structures in $1,000,000
Deflator for VSHIP 1987=1.000
Deflator for INVEST 1987=1.000
Deflator for ENERGY 1987=1.000
Total value of shipments in $1,000,000
Deflator for MATCOST 1987=1.000
computer investment/total investment
2 digit SIC code
imported materials
# Cases
Mean
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
433
1990.00
3015.57
39.2085
1054.33
27.0548
54.2481
607.053
2959.26
3469.51
875.567
228.052
126.855
2702.68
1646.90
1055.78
1.11687
1.08237
1.06987
6412.92
1.12898
5.55268
29.6174
23.3486
95
Std. Dev.
0.00000
608.388
62.8485
1892.61
41.5547
83.9769
1040.94
5191.26
9619.80
2098.71
545.062
352.896
5862.97
3676.64
2300.93
0.837093E-01
0.241873E-01
0.167540E-01
13641.7
0.481798E-01
5.48071
6.09484
109.734
Variance
0.00000
370136.
3949.93
0.358198E+07
1726.79
7052.12
0.108355E+07
0.269491E+08
0.925406E+08
0.440458E+07
297093.
124535.
0.343745E+08
0.135177E+08
0.529427E+07
0.700725E-02
0.585027E-03
0.280697E-03
0.186097E+09
0.232130E-02
30.0382
37.1470
12041.7
Maximum
Minimum
1990.00
3999.00
631.100
18381.6
487.700
979.200
9789.90
39504.4
145885.
32271.6
4396.40
4327.90
59407.3
38087.0
31042.8
1.53300
1.11900
1.25700
170775.
1.52700
43.4804
39.0000
1399.06
1990.00
2011.00
0.400000
13.9000
0.100000
0.300000
8.70000
27.6000
10.7000
7.90000
0.400000
0.800000
19.9000
4.40000
12.2000
0.822000
0.937000
1.02200
44.5000
1.01400
0.00000
20.0000
0.00000
International Trade Notes: 10 October 2016
SIMAT1A
SIMAT1B
DSIMAT1A
DSIMAT1B
DLY
NWSH
MVSHIPSH
04
DLKY
APSH
01
ANSH
02
AMESH
AMSH
AOSH
02
AKSH
01
DLP
DLPE
01
DHTSH
DHTSH1
DOFSH
DOFSH1
DLPMX
DLPVAD
PTFP
ADLHW
ADLNW
ADLPK
ERR
ETFP
ADJ1
ETFP1
24
25
26
27
28
29
30
Share of imported mat -broad outsourcing
share of imported mat - 2-digit industry
change in outsourcing (broad)
change in outsourcing (narrow)
change in log real shipments
nonproduction share of the total wages
industry share of total manfg shipments
447
447
447
447
447
447
447
0.118441
0.485957E-01
0.365305
0.157793
0.394762
0.372574
0.223430E-02
0.875671E-01
0.749496E-01
0.563151
0.473762
3.76272
0.120623
0.496680E-02
0.766799E-02
0.561745E-02
0.317139
0.224450
14.1581
0.145500E-01
0.246691E-04
0.659710
0.628002
2.96951
2.73056
22.5287
0.873336
0.703875E-01
0.00000
0.00000
-3.90025
-4.14979
-13.9630
0.109044
0.230466E-
31 change in log capital stock/shipments
32 average production share
447
447
0.512945
0.132555
3.13639
0.574340E-01
9.83696
0.329867E-02
14.7261
0.364086
-13.0257
0.115928E-
33 average non-production share
447
0.722582E-01
0.393782E-01
0.155065E-02
0.270142
0.638309E-
34 aosh + amsh
35 average material share
36 average energy share
447
447
447
0.512149
0.487772
0.243771E-01
0.123647
0.127229
0.328570E-01
0.152887E-01
0.161873E-01
0.107958E-02
0.890473
0.877148
0.275952
0.171757
0.151759
0.213427E-
0.843416E-01
0.711350E-02
0.636899
0.738303E-
1.70410
0.912518
2.90397
0.832688
11.7933
8.40714
-12.9502
0.860887E-
0.376402
0.245414
0.307711
0.151631
0.887371
1.65821
1.64672
0.00000
0.00000
0.00000
1.10714
1.46871
0.889095
3.55532
0.141678
0.602279E-01
0.946862E-01
0.229921E-01
0.787427
2.74968
2.71169
0.00000
0.00000
0.00000
1.22575
2.15711
0.790491
12.6403
37 average capital share
447
0.283037
38 change in log price
39 change in log energy price
447
447
3.54611
3.12686
40
41
42
43
44
45
46
47
48
49
50
51
52
53
447
447
447
447
447
447
447
447
447
447
447
447
447
447
(capital=pstk x ex post rental price)
(capital=pstk x ex ante rental price)
change in office equipment/total capital
change in office equipment/total capital
change in log material price
change in log value-added
primary TFP
annual change in log production wage
annual chage in log non-production wage
annual change in log capital price
error as defined in (4.26) of Chapter 4
ptfp-err
1.0/(1.0-amesh)
adj1*etfp
0.334085
0.210975
0.180127
0.352378E-01
3.58936
1.77040
0.408978
4.71405
5.43687
3.95370
0.464305E-01
0.362547
2.24364
1.00142
96
1.27976
1.21186
0.831400
0.379551
7.67960
10.5839
14.0399
4.71405
5.43687
3.95370
4.49691
14.8904
9.13017
32.8904
-0.301242
-0.209675
-0.363431
-0.270059
-1.81683
-12.6178
-5.01075
4.71405
5.43687
3.95370
-4.63585
-7.65468
1.20737
-10.8290
International Trade Notes: 10 October 2016
B34S 9
(D:M:Y)
DLPVAD1
APSH1
01
ANSH1
01
AKSH1
MSHXPR
ESHXPR
02
DLP34
CONSTANT
10/10/16 (H:M:S) 10:24: 4
3.35799
0.270372
3.56748
0.903109E-01
56 adj1*ansh
447
0.143112
57 adj1*aksh
58 amsh*dlpmx
59 aosh*dlpe
447
447
447
0.586515
1.69937
0.763338E-01
60 dlp-mshxpr-eshxpr
61
447
447
1.77040
1.00000
CALL LOADDATA$
=>
CALL OLSQ(
Ordinary Least Squares Estimation
Dependent variable
Centered R**2
Adjusted R**2
Residual Sum of Squares
Residual Variance
Standard Error
Total Sum of Squares
Log Likelihood
Mean of the Dependent Variable
Std. Error of Dependent Variable
Sum Absolute Residuals
F( 4,
442)
F Significance
1/Condition XPX
Maximum Absolute Residual
Number of Observations
Variable
PTFP
APSH
ANSH
AKSH
CONSTANT
Lag
0
0
0
0
0
Coefficient
-0.67900074
3.4556009
3.9054785
7.3941559
-0.78498817
-29.1263
0.305658E-
0.558816E-01
0.312275E-02
0.389831
0.266251E-
0.109801
0.515041
0.115698
0.120563E-01
0.265268
0.133861E-01
0.920277
3.39471
1.21165
0.277150
-1.58880
0.206717E-
1.65821
0.00000
2.74968
0.00000
CALL GAMFIT(
:PRINT :WHITE)$
DLP34
0.6967466663385627
0.6940022922782783
371.8964985643850
0.8413947931320926
0.9172757454179701
1226.355846031963
-593.1542618937680
1.770400132847875
1.658214939272056
297.4930711130872
253.8818145899300
1.000000000000000
6.550394423061074E-04
5.408266825961406
447
White SE
0.70587514E-01
0.82814894
1.7442105
0.71578284
0.18939943
DLP34 PTFP APSH ANSH AKSH
t
-9.6192754
4.1726805
2.2391097
10.330166
-4.1446174
:PRINT )$
Generalized Additive Models (GAM) Analysis
Reference: Generalized Additive Models by Hastie and Tibshirani. Chapman (1990)
Model estimated using CRAN General Public License (GPL) routines.
Gaussian additive model assumed
Identity link - yhat = x*b + sum(splines)
Response variable ....
Number of observations:
Residual Sum of Squares
# iterations
# smooths/variable
Mean Squared Residual
df of deviance
Scale Estimate
Primary
tolerence
Secondary tolerance
R square
Total sum of Squares
Model df
-----------1.
3.00
3.00
3.00
3.00
----13.0
=>
coef
----1.04728
-.665252
4.03542
5.63971
7.58671
DLP34
447
300.2070345290874
1
15
0.6716041040919182
434.0021682741188
0.6917178218784257
1.000000000000000E-09
1.000000000000000E-09
0.7552039764800347
1226.355846031963
st err
z score
-----------0.1685
-6.217
0.2421E-01 -27.48
0.7551
5.344
1.133
4.979
0.4869
15.58
CALL MARSPLINE(DLP34 PTFP APSH ANSH AKSH
nl pval
-------
lin_res
-------
1.000
0.1748
0.8573
1.000
346.8
300.8
304.0
325.1
:PRINT)$
Multivariate Autoregressive Splines Analysis
97
2
14.9729
0.488378
447
1.000000000000000E+31
DLP34 PTFP APSH ANSH AKSH
PAGE
12.7269
0.815606E-02
Matrix Command. d/m/y 10/10/16. h:m:s 10:24: 4.
=>
=>
Feenstra Chap4 4_3a Data
447
447
Number of observations in data file
Current missing variable code
Note: Missing data in the data file
B34S
DATA STEP
54 adj1*dlpvad
55 adj1*apsh
Name
---intcpt
PTFP
APSH
ANSH
AKSH
Lag
--0
0
0
0
10.5839
1.00000
-12.6178
1.00000
International Trade Notes: 10 October 2016
Model Estimated using Hastie-Tibshirani GPL routines in
CRAN General Public License (GPL) Library.
Version - 1 March 2006.
Left Hand Side Variable
Penalty cost per degree of freedom
Threshold for Forward stepwise Stopping
Rank Test Tolerance
Max # of Knots (nk)
Max interaction (mi)
Number of Observations
Number of right hand Variables
tolbx
set as
stopfac gcv/gcvnull > stopfac => stop
prevcrit set as
DLP34
2.000
0.1000E-03
0.1000E-12
5
1
447
4
1.000000000000000E-09
10.00000000000000
10000000000.00000
Series
PTFP
APSH
ANSH
AKSH
Min
-5.011
0.1159E-01
0.6383E-02
0.7383E-01
Lag
0
0
0
0
Mean
0.4090
0.1326
0.7226E-01
0.2830
Max
14.04
0.3641
0.2701
0.6369
GCV with only the constant
Total sum of squares
Final gcv
Variance of Y Variable
R**2 (1 - (var(res)/var(y)))
Residual Sum of Squares
Residual Variance
Residual Standard Error
Sum Absolute Residuals
Max Absolute Residual
# of coefficients after last fwd step
2.755841979409840
1226.355846031963
0.8411019886991933
2.749676784825029
0.7056440275681013
360.9851676062820
0.8093837838705881
0.8996575925709670
306.7363667559480
3.945752605427743
5
MARS Model Coefficients
DLP34
=
-1.2359379
+
0.57809246
+
12.581184
-7.1731181
=>
CALL
SE
1.1612470
* max(
PTFP{ 0}
* max(
3.1126752
* max(
AKSH{ 0}
* max( 0.41347152
-
PPREG(DLP34 PTFP APSH ANSH AKSH
3.1126752
PTFP{ 0}
0.41347152
AKSH{ 0}
,
,
,
,
0.0)
0.0)
0.0)
0.0)
0.13135952
0.77496252E-01
0.31013665E-01
1.9014328
0.62994727
:PRINT)$
Projection Pursuit Regression
Number of Observations
Number of right hand side variables
Maximum number of ridge functions
Minimum number of ridge functions
Number of left hand side variables
Level of fit
Max number of Primary
Iterations (maxit)
Max number of Secondary Iterations (mitone)
Number of cj Iterations (mitcj)
Smoother tone control (alpha)
Span
Convergence (CONV) set as
Left Hand Side Variable
Series
DLP34
Mean
1.770
Max
10.58
447
5
20
20
1
2
200
200
10
0.000000000000000E+00
0.000000000000000E+00
5.000000000000000E-03
DLP34
Min
-12.62
Right Hand Side Variables
#
1
2
3
4
5
Series
PTFP
APSH
ANSH
AKSH
CONSTANT
Lag
0
0
0
0
0
Mean
0.4090
0.1326
0.7226E-01
0.2830
1.000
Given # of ridge functions
# primary
iterations used
# secondary iterations used
# cj iterations used
Residual sum of squares
Total
sum of squares
Mean of the Dependent Variable
Std. Error of Dependent Variable
Sum Absolute Residuals
Maximum Absolute Residual
Residual Variance
Max
14.04
0.3641
0.2701
0.6369
1.000
Min
-5.011
0.1159E-01
0.6383E-02
0.7383E-01
1.000
20
1
7
2
179.3691430157083
1226.355846031963
1.770400132847875
1.658214939272056
210.3559765757928
2.456771179577403
0.4058125407595211
Variable Importance for Model with # ridge functions
Series Number
Importance
1
1.00000
3
0.885062
4
0.760611
2
0.636560
20
98
t
8.84
-15.9
18.6
6.61
-11.3
Non Zero
447
23
423
23
423
%
100.000
5.145
94.631
5.145
94.631
Importance
#
85.560
100.000
35.497
61.089
1
2
3
4
5
International Trade Notes: 10 October 2016
5
0.00000
B34S Matrix Command Ending. Last Command reached.
Space available in allocator
Number variables used
Number temp variables used
99856943, peak space used
145, peak number used
41, # user temp clean
133856
145
0
99
International Trade Notes: 10 October 2016
B34S 9
(D:M:Y)
10/10/16 (H:M:S) 10:24: 4
DATA STEP
100
Feenstra Chap4 4_3a Data
PAGE
3
International Trade Notes: 10 October 2016
Stata Template
// set mem 3m
log using log_4_3a.log,replace
// use d:\feenstra_course\chap4\data_Chp4.dta, clear
// use c:\feenstra_course\chap4\data_Chp4.dta, clear
use data_Chp4.dta, clear
// use e:\feenstra_course\chap4\data_Chp4.dta, clear
* use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
keep if year==1990
drop if sic72==2067
drop if sic72==2794
drop if sic72==3483
gen etfp=ptfp-err
gen adj1=1/(1-amesh)
gen etfp1=adj1*etfp
gen dlpvad1=adj1*dlpvad
gen apsh1=adj1*apsh
gen ansh1=adj1*ansh
gen aksh1=adj1*aksh
gen mshxpr=amsh*dlpmx
gen eshxpr=aosh*dlpe
* Reproduce Table 4.5 reprinted at 4.1 in new edition.
gen dlp34=dlp-mshxpr-eshxpr
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model
regress dlp34 ptfp apsh ansh aksh , robust
preserve
drop if sic72==3573
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model without sic72
regress dlp34 ptfp apsh ansh aksh , robust
regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp apsh ansh aksh mshxpr eshxpr, robust
restore
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
* OLS Model
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
log close
* clear *
101
International Trade Notes: 10 October 2016
exit
___ ____ ____ ____ ____ (R)
/__
/
____/
/
____/
___/
/
/___/
/
/___/
14.2
Statistics/Data Analysis
Special Edition
Copyright 1985-2015 StataCorp LP
StataCorp
4905 Lakeway Drive
College Station, Texas 77845 USA
800-STATA-PC
http://www.stata.com
979-696-4600
[email protected]
979-696-4601 (fax)
Single-user Stata perpetual license:
Serial number: 401406202087
Licensed to: Houston H. Stokes
University of Illinois Chicago
Notes:
1.
2.
3.
Stata is running in batch mode.
Unicode is supported; see help unicode_advice.
Maximum number of variables is set to 5000; see help set_maxvar.
. do Problem_4_3_a.do
.
. // set mem 3m
.
. log using log_4_3a.log,replace
------------------------------------------------------------------------------name: <unnamed>
log: D:\class\E514\log_4_3a.log
log type: text
opened on: 10 Oct 2016, 10:11:28
.
. // use d:\feenstra_course\chap4\data_Chp4.dta, clear
. // use c:\feenstra_course\chap4\data_Chp4.dta, clear
. use data_Chp4.dta, clear
(Matrl Cons (72 SIC), 67-92)
. // use e:\feenstra_course\chap4\data_Chp4.dta, clear
. * use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
.
. keep if year==1990
(1,350 observations deleted)
. drop if sic72==2067
(1 observation deleted)
. drop if sic72==2794
(1 observation deleted)
. drop if sic72==3483
(1 observation deleted)
. gen etfp=ptfp-err
. gen adj1=1/(1-amesh)
. gen etfp1=adj1*etfp
. gen dlpvad1=adj1*dlpvad
. gen apsh1=adj1*apsh
. gen ansh1=adj1*ansh
. gen aksh1=adj1*aksh
. gen mshxpr=amsh*dlpmx
. gen eshxpr=aosh*dlpe
.
.
. * Reproduce Table 4.5 *
.
. gen dlp34=dlp-mshxpr-eshxpr
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(4, 442)
Prob > F
R-squared
Root MSE
=
=
=
=
=
102
447
106.29
0.0000
0.8957
.80656
International Trade Notes: 10 October 2016
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.9631819
.0702093
-13.72
0.000
-1.101168
-.8251963
apsh |
3.062598
1.22198
2.51
0.013
.6609845
5.464212
ansh |
2.294716
1.430073
1.60
0.109
-.5158719
5.105305
aksh |
7.887571
.7810006
10.10
0.000
6.352634
9.422507
_cons | -.7051116
.3006016
-2.35
0.019
-1.295898
-.1143256
-----------------------------------------------------------------------------.
. * OLS Model
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression
Number of obs
F(4, 442)
Prob > F
R-squared
Root MSE
=
=
=
=
=
447
110.62
0.0000
0.6967
.91728
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.6790007
.0709856
-9.57
0.000
-.8185121
-.5394894
apsh |
3.455601
.8328199
4.15
0.000
1.818822
5.09238
ansh |
3.905478
1.754048
2.23
0.026
.4581676
7.352789
aksh |
7.394156
.71982
10.27
0.000
5.979461
8.808851
_cons | -.7849882
.1904677
-4.12
0.000
-1.159323
-.4106534
-----------------------------------------------------------------------------.
. preserve
. drop if sic72==3573
(1 observation deleted)
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is
9.8179e-01)
Linear regression
Number of obs
F(4, 441)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
92.17
0.0000
0.8059
.74139
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.7531151
.0751891
-10.02
0.000
-.9008886
-.6053416
apsh |
2.427856
1.162844
2.09
0.037
.142451
4.713261
ansh |
4.086394
1.722144
2.37
0.018
.7017647
7.471024
aksh |
8.058291
.9411699
8.56
0.000
6.208556
9.908027
_cons | -.8249273
.2930995
-2.81
0.005
-1.400973
-.2488819
-----------------------------------------------------------------------------. * OLS Model without sic72
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression
Number of obs
F(4, 441)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
135.75
0.0000
0.6696
.87366
-----------------------------------------------------------------------------|
Robust
dlp34 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------ptfp | -.6043067
.0418654
-14.43
0.000
-.6865873
-.5220261
apsh |
3.156235
.7864841
4.01
0.000
1.610513
4.701958
ansh |
4.954764
1.5334
3.23
0.001
1.941084
7.968443
aksh |
7.396599
.7390641
10.01
0.000
5.944073
8.849124
_cons | -.8377685
.1852263
-4.52
0.000
-1.201804
-.4737325
-----------------------------------------------------------------------------.
. regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is
9.8179e-01)
Linear regression
Number of obs
F(5, 440)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
10.85
0.0000
0.4289
1.2034
-----------------------------------------------------------------------------|
Robust
103
International Trade Notes: 10 October 2016
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------apsh |
3.605277
1.88524
1.91
0.056
-.0999163
7.310471
ansh |
6.202674
4.036466
1.54
0.125
-1.730475
14.13582
aksh |
9.535214
2.18722
4.36
0.000
5.236518
13.83391
mshxpr |
1.219304
.2471334
4.93
0.000
.7335958
1.705013
eshxpr | -.9301182
.9150299
-1.02
0.310
-2.728491
.8682541
_cons | -1.929187
.9147773
-2.11
0.036
-3.727063
-.1313111
-----------------------------------------------------------------------------. * OLS Model
. regress dlp apsh ansh aksh mshxpr eshxpr, robust
Linear regression
Number of obs
F(5, 440)
Prob > F
R-squared
Root MSE
=
=
=
=
=
446
24.65
0.0000
0.3400
1.2384
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------apsh |
5.629626
1.284501
4.38
0.000
3.105105
8.154147
ansh |
7.727702
2.065437
3.74
0.000
3.668354
11.78705
aksh |
8.611022
1.272484
6.77
0.000
6.110121
11.11192
mshxpr |
1.448936
.1923696
7.53
0.000
1.070858
1.827013
eshxpr |
.0327104
.533676
0.06
0.951
-1.01616
1.081581
_cons | -2.629372
.6429471
-4.09
0.000
-3.893001
-1.365743
-----------------------------------------------------------------------------. restore
.
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(4, 443)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9998
.07762
-----------------------------------------------------------------------------|
Robust
dlpvad1 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp1 | -1.000041
.0006831 -1463.88
0.000
-1.001384
-.9986986
apsh1 |
4.680657
.0157718
296.77
0.000
4.64966
4.711654
ansh1 |
5.482807
.0194677
281.64
0.000
5.444547
5.521068
aksh1 |
3.952538
.0083407
473.89
0.000
3.936146
3.96893
-----------------------------------------------------------------------------. * OLS Model
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
Linear regression
Number of obs
F(4, 443)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9988
.1685
-----------------------------------------------------------------------------|
Robust
dlpvad1 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp1 | -.9992624
.0042216 -236.70
0.000
-1.007559
-.9909655
apsh1 |
4.666086
.0550321
84.79
0.000
4.55793
4.774243
ansh1 |
5.437375
.0644382
84.38
0.000
5.310733
5.564018
aksh1 |
3.953762
.0221871
178.20
0.000
3.910157
3.997367
-----------------------------------------------------------------------------.
. regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is
9.9873e-01)
Linear regression
Number of obs
F(6, 440)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9999
.0262
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp | -1.000358
.000677 -1477.55
0.000
-1.001689
-.9990273
apsh |
4.700013
.011911
394.60
0.000
4.676603
4.723422
ansh |
5.443315
.0314405
173.13
0.000
5.381523
5.505107
aksh |
3.972308
.0150284
264.32
0.000
3.942772
4.001845
mshxpr |
.9974072
.0023115
431.50
0.000
.9928643
1.00195
104
International Trade Notes: 10 October 2016
eshxpr |
.9961108
.0057421
173.47
0.000
.9848254
1.007396
_cons |
.0010799
.005423
0.20
0.842
-.0095784
.0117382
-----------------------------------------------------------------------------. * OLS Model
. regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
Linear regression
Number of obs
F(6, 440)
Prob > F
R-squared
Root MSE
=
>
=
=
=
447
99999.00
0.0000
0.9989
.05637
-----------------------------------------------------------------------------|
Robust
dlp |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------etfp | -.9984327
.0024469 -408.04
0.000
-1.003242
-.9936236
apsh |
4.71449
.0145206
324.68
0.000
4.685952
4.743028
ansh |
5.443702
.0521618
104.36
0.000
5.341185
5.546219
aksh |
4.000907
.044225
90.47
0.000
3.913988
4.087825
mshxpr |
.9907738
.0089715
110.44
0.000
.9731416
1.008406
eshxpr |
.996285
.0058313
170.85
0.000
.9848243
1.007746
_cons | -.0023481
.007124
-0.33
0.742
-.0163494
.0116532
-----------------------------------------------------------------------------.
. log close
name: <unnamed>
log: D:\class\E514\log_4_3a.log
log type: text
closed on: 10 Oct 2016, 10:11:29
------------------------------------------------------------------------------. * clear *
. exit
Code Template for Estimation of a Long Run Model
b34sexec options include('Feenstra_ch4.mac') member(ch4_3_a);
b34srun;
b34sexec matrix;
call loaddata;
call olsq(
dlp34 ptfp apsh ansh aksh :print :white);
call gamfit(
dlp34 ptfp apsh ansh aksh :print );
call marspline(dlp34 ptfp apsh ansh aksh :print);
call
ppreg(dlp34 ptfp apsh ansh aksh :print);
b34srun;
Variable
YEAR
SIC72
EMP
PAY
PRODE
PRODH
PRODW
VADD
MATERIAL
INVENT
INVEST
ENERGY
CAP
EQUIP
PLANT
PISHIP
PIINV
PIEN
VSHIP
PIMAT
CI
SIC2
IMAT
Label
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Year ranges from 58 to 97
4 digit SIC code
Total employment in 1000s
Total payroll in $1,000,000
Production workers in 1000s
Production worker hours in 1,000,000
Production worker wages in $1,000,000
Total value added in $1,000,000
Total cost of materials in $1,000,000
End-of-year inventories in $1,000,000
Total capital expenditure in $1,000,000
Cost of electric & fuels in $1,000,000
Total real capital stock in $1,000,000
Real capital: equipment in $1,000,000
Real capital: structures in $1,000,000
Deflator for VSHIP 1987=1.000
Deflator for INVEST 1987=1.000
Deflator for ENERGY 1987=1.000
Total value of shipments in $1,000,000
Deflator for MATCOST 1987=1.000
computer investment/total investment
2 digit SIC code
imported materials
# Cases
Mean
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
447
433
1990.00
3015.57
39.2085
1054.33
27.0548
54.2481
607.053
2959.26
3469.51
875.567
228.052
126.855
2702.68
1646.90
1055.78
1.11687
1.08237
1.06987
6412.92
1.12898
5.55268
29.6174
23.3486
105
Std. Dev.
0.00000
608.388
62.8485
1892.61
41.5547
83.9769
1040.94
5191.26
9619.80
2098.71
545.062
352.896
5862.97
3676.64
2300.93
0.837093E-01
0.241873E-01
0.167540E-01
13641.7
0.481798E-01
5.48071
6.09484
109.734
Variance
0.00000
370136.
3949.93
0.358198E+07
1726.79
7052.12
0.108355E+07
0.269491E+08
0.925406E+08
0.440458E+07
297093.
124535.
0.343745E+08
0.135177E+08
0.529427E+07
0.700725E-02
0.585027E-03
0.280697E-03
0.186097E+09
0.232130E-02
30.0382
37.1470
12041.7
Maximum
Minimum
1990.00
3999.00
631.100
18381.6
487.700
979.200
9789.90
39504.4
145885.
32271.6
4396.40
4327.90
59407.3
38087.0
31042.8
1.53300
1.11900
1.25700
170775.
1.52700
43.4804
39.0000
1399.06
1990.00
2011.00
0.400000
13.9000
0.100000
0.300000
8.70000
27.6000
10.7000
7.90000
0.400000
0.800000
19.9000
4.40000
12.2000
0.822000
0.937000
1.02200
44.5000
1.01400
0.00000
20.0000
0.00000
International Trade Notes: 10 October 2016
SIMAT1A
SIMAT1B
DSIMAT1A
DSIMAT1B
DLY
NWSH
MVSHIPSH
04
DLKY
APSH
01
ANSH
02
AMESH
AMSH
AOSH
02
AKSH
01
DLP
DLPE
01
DHTSH
DHTSH1
DOFSH
DOFSH1
DLPMX
DLPVAD
PTFP
ADLHW
ADLNW
ADLPK
ERR
ETFP
ADJ1
ETFP1
24
25
26
27
28
29
30
Share of imported mat -broad outsourcing
share of imported mat - 2-digit industry
change in outsourcing (broad)
change in outsourcing (narrow)
change in log real shipments
nonproduction share of the total wages
industry share of total manfg shipments
447
447
447
447
447
447
447
0.118441
0.485957E-01
0.365305
0.157793
0.394762
0.372574
0.223430E-02
0.875671E-01
0.749496E-01
0.563151
0.473762
3.76272
0.120623
0.496680E-02
0.766799E-02
0.561745E-02
0.317139
0.224450
14.1581
0.145500E-01
0.246691E-04
0.659710
0.628002
2.96951
2.73056
22.5287
0.873336
0.703875E-01
0.00000
0.00000
-3.90025
-4.14979
-13.9630
0.109044
0.230466E-
31 change in log capital stock/shipments
32 average production share
447
447
0.512945
0.132555
3.13639
0.574340E-01
9.83696
0.329867E-02
14.7261
0.364086
-13.0257
0.115928E-
33 average non-production share
447
0.722582E-01
0.393782E-01
0.155065E-02
0.270142
0.638309E-
34 aosh + amsh
35 average material share
36 average energy share
447
447
447
0.512149
0.487772
0.243771E-01
0.123647
0.127229
0.328570E-01
0.152887E-01
0.161873E-01
0.107958E-02
0.890473
0.877148
0.275952
0.171757
0.151759
0.213427E-
37 average capital share
447
0.283037
0.843416E-01
0.711350E-02
0.636899
0.738303E-
38 change in log price
39 change in log energy price
447
447
3.54611
3.12686
1.70410
0.912518
2.90397
0.832688
11.7933
8.40714
-12.9502
0.860887E-
40
41
42
43
44
45
46
47
48
49
50
51
52
53
447
447
447
447
447
447
447
447
447
447
447
447
447
447
0.376402
0.245414
0.307711
0.151631
0.887371
1.65821
1.64672
0.00000
0.00000
0.00000
1.10714
1.46871
0.889095
3.55532
0.141678
0.602279E-01
0.946862E-01
0.229921E-01
0.787427
2.74968
2.71169
0.00000
0.00000
0.00000
1.22575
2.15711
0.790491
12.6403
(capital=pstk x ex post rental price)
(capital=pstk x ex ante rental price)
change in office equipment/total capital
change in office equipment/total capital
change in log material price
change in log value-added
primary TFP
annual change in log production wage
annual chage in log non-production wage
annual change in log capital price
error as defined in (4.26) of Chapter 4
ptfp-err
1.0/(1.0-amesh)
adj1*etfp
0.334085
0.210975
0.180127
0.352378E-01
3.58936
1.77040
0.408978
4.71405
5.43687
3.95370
0.464305E-01
0.362547
2.24364
1.00142
106
1.27976
1.21186
0.831400
0.379551
7.67960
10.5839
14.0399
4.71405
5.43687
3.95370
4.49691
14.8904
9.13017
32.8904
-0.301242
-0.209675
-0.363431
-0.270059
-1.81683
-12.6178
-5.01075
4.71405
5.43687
3.95370
-4.63585
-7.65468
1.20737
-10.8290
International Trade Notes: 10 October 2016
B34S 9
(D:M:Y)
DLPVAD1
APSH1
01
ANSH1
01
AKSH1
MSHXPR
ESHXPR
02
DLP34
CONSTANT
10/10/16 (H:M:S) 10:24: 4
3.35799
0.270372
3.56748
0.903109E-01
56 adj1*ansh
447
0.143112
57 adj1*aksh
58 amsh*dlpmx
59 aosh*dlpe
447
447
447
0.586515
1.69937
0.763338E-01
60 dlp-mshxpr-eshxpr
61
447
447
1.77040
1.00000
CALL LOADDATA$
=>
CALL OLSQ(
Ordinary Least Squares Estimation
Dependent variable
Centered R**2
Adjusted R**2
Residual Sum of Squares
Residual Variance
Standard Error
Total Sum of Squares
Log Likelihood
Mean of the Dependent Variable
Std. Error of Dependent Variable
Sum Absolute Residuals
F( 4,
442)
F Significance
1/Condition XPX
Maximum Absolute Residual
Number of Observations
Variable
PTFP
APSH
ANSH
AKSH
CONSTANT
Lag
0
0
0
0
0
Coefficient
-0.67900074
3.4556009
3.9054785
7.3941559
-0.78498817
-29.1263
0.305658E-
0.558816E-01
0.312275E-02
0.389831
0.266251E-
0.109801
0.515041
0.115698
0.120563E-01
0.265268
0.133861E-01
0.920277
3.39471
1.21165
0.277150
-1.58880
0.206717E-
1.65821
0.00000
2.74968
0.00000
CALL GAMFIT(
:PRINT :WHITE)$
DLP34
0.6967466663385627
0.6940022922782783
371.8964985643850
0.8413947931320926
0.9172757454179701
1226.355846031963
-593.1542618937680
1.770400132847875
1.658214939272056
297.4930711130872
253.8818145899300
1.000000000000000
6.550394423061074E-04
5.408266825961406
447
White SE
0.70587514E-01
0.82814894
1.7442105
0.71578284
0.18939943
DLP34 PTFP APSH ANSH AKSH
t
-9.6192754
4.1726805
2.2391097
10.330166
-4.1446174
:PRINT )$
Generalized Additive Models (GAM) Analysis
Reference: Generalized Additive Models by Hastie and Tibshirani. Chapman (1990)
Model estimated using CRAN General Public License (GPL) routines.
Gaussian additive model assumed
Identity link - yhat = x*b + sum(splines)
Response variable ....
Number of observations:
Residual Sum of Squares
# iterations
# smooths/variable
Mean Squared Residual
df of deviance
Scale Estimate
Primary
tolerence
Secondary tolerance
R square
Total sum of Squares
Model df
-----------1.
3.00
3.00
3.00
3.00
----13.0
=>
coef
----1.04728
-.665252
4.03542
5.63971
7.58671
DLP34
447
300.2070345290874
1
15
0.6716041040919182
434.0021682741188
0.6917178218784257
1.000000000000000E-09
1.000000000000000E-09
0.7552039764800347
1226.355846031963
st err
z score
-----------0.1685
-6.217
0.2421E-01 -27.48
0.7551
5.344
1.133
4.979
0.4869
15.58
CALL MARSPLINE(DLP34 PTFP APSH ANSH AKSH
nl pval
-------
lin_res
-------
1.000
0.1748
0.8573
1.000
346.8
300.8
304.0
325.1
:PRINT)$
Multivariate Autoregressive Splines Analysis
107
2
14.9729
0.488378
447
1.000000000000000E+31
DLP34 PTFP APSH ANSH AKSH
PAGE
12.7269
0.815606E-02
Matrix Command. d/m/y 10/10/16. h:m:s 10:24: 4.
=>
=>
Feenstra Chap4 4_3a Data
447
447
Number of observations in data file
Current missing variable code
Note: Missing data in the data file
B34S
DATA STEP
54 adj1*dlpvad
55 adj1*apsh
Name
---intcpt
PTFP
APSH
ANSH
AKSH
Lag
--0
0
0
0
10.5839
1.00000
-12.6178
1.00000
International Trade Notes: 10 October 2016
Model Estimated using Hastie-Tibshirani GPL routines in
CRAN General Public License (GPL) Library.
Version - 1 March 2006.
Left Hand Side Variable
Penalty cost per degree of freedom
Threshold for Forward stepwise Stopping
Rank Test Tolerance
Max # of Knots (nk)
Max interaction (mi)
Number of Observations
Number of right hand Variables
tolbx
set as
stopfac gcv/gcvnull > stopfac => stop
prevcrit set as
DLP34
2.000
0.1000E-03
0.1000E-12
5
1
447
4
1.000000000000000E-09
10.00000000000000
10000000000.00000
Series
PTFP
APSH
ANSH
AKSH
Min
-5.011
0.1159E-01
0.6383E-02
0.7383E-01
Lag
0
0
0
0
Mean
0.4090
0.1326
0.7226E-01
0.2830
Max
14.04
0.3641
0.2701
0.6369
GCV with only the constant
Total sum of squares
Final gcv
Variance of Y Variable
R**2 (1 - (var(res)/var(y)))
Residual Sum of Squares
Residual Variance
Residual Standard Error
Sum Absolute Residuals
Max Absolute Residual
# of coefficients after last fwd step
2.755841979409840
1226.355846031963
0.8411019886991933
2.749676784825029
0.7056440275681013
360.9851676062820
0.8093837838705881
0.8996575925709670
306.7363667559480
3.945752605427743
5
MARS Model Coefficients
DLP34
=
-1.2359379
+
0.57809246
+
12.581184
-7.1731181
=>
CALL
SE
1.1612470
* max(
PTFP{ 0}
* max(
3.1126752
* max(
AKSH{ 0}
* max( 0.41347152
-
PPREG(DLP34 PTFP APSH ANSH AKSH
3.1126752
PTFP{ 0}
0.41347152
AKSH{ 0}
,
,
,
,
0.0)
0.0)
0.0)
0.0)
0.13135952
0.77496252E-01
0.31013665E-01
1.9014328
0.62994727
:PRINT)$
Projection Pursuit Regression
Number of Observations
Number of right hand side variables
Maximum number of ridge functions
Minimum number of ridge functions
Number of left hand side variables
Level of fit
Max number of Primary
Iterations (maxit)
Max number of Secondary Iterations (mitone)
Number of cj Iterations (mitcj)
Smoother tone control (alpha)
Span
Convergence (CONV) set as
Left Hand Side Variable
Series
DLP34
Mean
1.770
Max
10.58
447
5
20
20
1
2
200
200
10
0.000000000000000E+00
0.000000000000000E+00
5.000000000000000E-03
DLP34
Min
-12.62
Right Hand Side Variables
#
1
2
3
4
5
Series
PTFP
APSH
ANSH
AKSH
CONSTANT
Lag
0
0
0
0
0
Mean
0.4090
0.1326
0.7226E-01
0.2830
1.000
Given # of ridge functions
# primary
iterations used
# secondary iterations used
# cj iterations used
Residual sum of squares
Total
sum of squares
Mean of the Dependent Variable
Std. Error of Dependent Variable
Sum Absolute Residuals
Maximum Absolute Residual
Residual Variance
Max
14.04
0.3641
0.2701
0.6369
1.000
Min
-5.011
0.1159E-01
0.6383E-02
0.7383E-01
1.000
20
1
7
2
179.3691430157083
1226.355846031963
1.770400132847875
1.658214939272056
210.3559765757928
2.456771179577403
0.4058125407595211
Variable Importance for Model with # ridge functions
Series Number
Importance
1
1.00000
3
0.885062
4
0.760611
2
0.636560
20
108
t
8.84
-15.9
18.6
6.61
-11.3
Non Zero
447
23
423
23
423
%
100.000
5.145
94.631
5.145
94.631
Importance
#
85.560
100.000
35.497
61.089
1
2
3
4
5
International Trade Notes: 10 October 2016
5
0.00000
B34S Matrix Command Ending. Last Command reached.
Space available in allocator
Number variables used
Number temp variables used
99856943, peak space used
145, peak number used
41, # user temp clean
133856
145
0
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International Trade Notes: 10 October 2016
B34S 9
(D:M:Y)
10/10/16 (H:M:S) 10:24: 4
DATA STEP
110
Feenstra Chap4 4_3a Data
PAGE
3
International Trade Notes: 10 October 2016
6. Extensions to H-O model suggested by Vanek
(Math treatment by Feenstra)
Assume C countries ( i 1, , C ) , N industries ( j 1, , N ) and M factors indexed by
(k 1, , M ) or l 1, , M ) . Define A [a j k ]' the requirements of labor and capital to produce
one unit of good j using input k. Assuming the 2 by 2 case with Labor L and capital K
a1L a2 L
A
Matrix A includes both direct primary factors A used in production and indirect
a1K a2 K
factors used through intermediate production.
Remark: [In input-output analysis: Define B as the N by N input-output matrix. Define d j = final
demand in industry j and x j = production of good j. Total production needs to take into account
N
final demand and intermediate demand. x j a ji xi d j or
i 1
d j (1 a jj ) x j
N
a
i 1 i j
x .
(6.1)
ji i
Define B such that ( I B ) x d . Final production of goods x ( I B) 1 d . In terms of the
primary and indirect factors, A A( I B)1 ]
Define Y i = outputs of the N industries in country i, Di = demands for N industries in country i
and T i Y i Di net exports. (Can think of Di as absorption).
Remark: [ S. Alexander (See Dunn-Mutti page 400) argued that if Y i Di it was not possible to
export. Other writers have stressed the fact that it was important to determine if the economy was
at full employment or not. If an economy is at full employment then the only way to increase
exports is to reduce absorption.]
Factor content of trade is F i AT i . Define an individual component of F i as Fki . where >0
(<0) determines if the k factor is exported (imported).
Goal of HOV theory is to relate factor content of trade in country i to the underlying factor
endowments.
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International Trade Notes: 10 October 2016
AY i V i = demand for factors in country i.
ADi demand for factors in country i that are consumed domestically.
Assuming product prices are equalized across countries => consumption vectors are proportional
=> can simplify the analysis. Define s i =share of country i. D i s i D w , AD i s i AD w . If trade
is balanced, s i = country i's share of world GDP.
Given world consumption = world production,
AD i s i AD w s i AY w s iV w .
(6.2)
This proves the HOV theorem relating to the factor content of trade F i . Recall V i = total
demand for factors in country i. If F i 0 this implies that factor content of trade greater than
countries consumption share times total world factor demand.
F i AT i V i s iV w
(6.3)
for the kth factor. Equation (6.3) is the basic HOV theorem. Equations (6.19) and (6.25) extend
the HOV model by allowing for factor productivity differences in the A matrix across countries.
Fki Vki ski Vkw
(6.4)
A country i is abundant in factor k if
Vki
si
Vkw
(6.5)
Looking at two elements of the factor content of trade vector
Fki K i si K w
(6.6)
FLi Li si LW
K w ( K i Fki ) / si
(6.7)
Lw ( Li Fl i ) / si
which can be transformed to
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International Trade Notes: 10 October 2016
Ki
si K i
K w ( K i Fki )
Li
s i Li
Lk ( Li Fl i )
Ki
Li
K w Lw
(6.8)
Ki
Li
( K i Fki ) ( Li Fl i )
Define capital to be abundant relative to labor if
( K i / K w ) ( Li / Lw )
(6.9)
which simplifies to the Leamer (1980) Theorem "If capital is abundant relative to labor in
country i then the HOV theorem for all inputs is
F i AT i V i siV w
(6.10)
and for the k th input
Fki Vki ski Vkw
(6.11)
Leamer's 1980 theorem states that if capital is abundant relative to labor in country i, then
Ki
Li
K w Lw
(6.12)
or
Ki Kw
w
Li
L
(6.13)
From (6.7) and (6.13) we have proved that the capital/labor ratio embodied in production for
country i exceeds the capital/labor ratio embodied in consumption" if country i is capital
abundant.
( K i / Li ) [( K i Fki ) / ( Li FLi )]
(6.14)
Strict equality holds if there is no trade and FKi FLi 0 . Feenstra page 40 reports that (6.14)
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International Trade Notes: 10 October 2016
holds for the US in 1947. => No Leontief paradox! The Leamer theorem does not require
balanced trade!
To fully test the Leontief paradox requires data on T i , A, V i and V w . If the number of factors
equals the number of goods we can estimate net exports as
T i A1 (V i siV w )
(6.15)
taking A1 from (6.3) as data. The estimated coefficients should estimate the relative abundance
of each factor (V i s iV w ) . (Note: This is the usual OLS model Y=XB where X A1 ) If the
number of goods is greater than the number of factors, we can estimate T i (adjusted net exports
of each industry) as a function of A' (their labor and capital requirements).
T i A'
(6.16)
ˆ ( AA ') 1 AT i ( AA ') 1 (V i s iV w )
(6.17)
Feenstra (2004, 43) and others have argued that this less than optimum formulation gives a
"contaminated estimate" of the vector of relative factor endowments that could be less than zero.
Leamer using an alternative approach treated (V i s iV w ) as data and using data for all C
countries estimated
M
T ji jk (Vki s iVkw ) i 1, C
(6.18)
k 1
which is not a test of Leontief. For details on this and other possible approaches, see Freenstra
(2004, 44-60).
In an important extension Trefler (1993) assumed different productivity of factors across
countries. Let ki represent the relative productivity of i th country for the k th factor relative to the
US.
Looking at all countries, equation (6.4) becomes
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International Trade Notes: 10 October 2016
C
Fki kiVki si kjVk j , i 1, , C; k 1, , M
(6.19)
j 1
which restates the HOV theory in equation (6.3).
There are MC equations but since both sides sum to 0.0, we drop one country and solve for
M(C-1) parameters using an inverse. Equation (6.19) holds as an identity. Given the assumptions
of the model, it is thus not testable. Of interest is whether the assumptions are warranted.
One way to proceed is to see if the solutions generated by the inverse are all greater than
0.0. Any value < 0.0 is not reasonable. Another way to proceed is to assume factor price
equalization and see if the estimated relative labor productivity ki follows relative wage
differences across countries. The empirical results for this hypothesis for the factor labor are
given in figure 2.4 on page 51 of Feenstra and tend to support Trefler (1993).
Research Ideas: It would be interesting to generate figure 2.4 for other factors and see what
countries are off the line. Figure 2.4 suggests that relative wages in Canada are above what
Canadian labor productivity would imply. Hong Kong, Finland, France etc being below the line
are more productive in labor than their relative wages. Another research question might be to
look at trends over time.
Trefler (1995) approached the same general problem using a method involving
differences in the factor requirements matrix Ai across countries. One simplifying assumption is
to assume a uniform amount change across countries defined as i . In his 1993 paper defined ki
to resent the relative productivity of i th country for the k th factor relative to the US. In the 1995
paper if i 1 then the i th country is less technologically advanced than the US. In terms of the
US technology matrix
i Ai AUS
(6.20)
Starting from the factor requirement equation for total production in country i
AiY i V i
(6.21)
we define factors needed for trade.
C
AiT i AiY i Ai Di V i Ai ( si D w ) V i Ai si Y j
j 1
115
(6.22)
International Trade Notes: 10 October 2016
Using (6.20) we multiply both sides of (6.22) by i to express the factor content of trade of the
i th country in terms of US factor requirements matrix.
C
i AiT i AUST i F iUS iV i i Ai si Y j
(6.23)
j 1
Looking at all countries we note
C
A
C
C
j 1
j 1
Y j j A jY j jV j
US
j 1
(6.24)
which allows simplification of the last term in (6.23). Equation (6.23) can now be written as
C
i AiT i AUST i F iUS iV i si jV j .
(6.25).
j 1
Equation (6.25) is a restatement of the HOV theorem when we allow for uniform technological
differences across countries. Equation (6.25) needs to be estimated to get the best i values.
Trefler's results are given in Table 2.5. Significance can be measured for each estimate. The
estimates i themselves are of interest.
Summary of Selected Factor Content Research:
Equation (6.3) is the HOV Model assuming no productivity parameters
Equation (6.19) allows individual country individual factor productivity adjustments.
Equation (6.25) imposes a country-wide adjustment to all the elements of the
A matrix for a specific country.
Trefler (1998) looked at bilateral trade.
He assumed that output of every good is exported to each country in proportion to the
purchasing country's GDP.
Define X i j as gross exports of goods from country i to country j . This is related to net exports
Ti
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International Trade Notes: 10 October 2016
T i X i j X ji
i j
(6.26)
i j
The bilaterial export assumption ( s j GDP j / GDP w Y j / Y w ) implies
X i j s jY i
(6.27)
Define F i j as the factor content of exports from country i to country j .
F i j Ai X i j
(6.28)
Using (6.21) equation (6.27) becomes
F i j s j AiY i s jV i
(6.29)
which can be transformed to relative endowments of country i
V i si V j (1 si )V i si V j V i s j s i V j
j i
j
j i
(6.30)
j i
From equation (6.31) we prove the Trefler (1998) theorem that is an identity if the assumptions
of the derivation are correct.
V i si V j F i j F ji
j
j i
(6.31)
j i
The left term is the relative factor endowments. On the right the first term is the factor content for
trade from country i to all countries. The second term on the right is the factor content from
country of imports for all countries to country i .
Feenstra contains a number of other tests on trade which are not treated here due to time
limitations.
It appears although the data fails the rigid assumptions of same tastes and same production
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International Trade Notes: 10 October 2016
conditions of the H-O model, that with adjustments the theory can be made to work.
If the number of goods equals the number of factors, it is possible to have factor price
equalization.
If the number of factors is > number of goods factor price equalization does not hold!
If the number of factors is < number of goods "there is a wide range of possible factor
endowments across countries such that factor prices equalization continues to hold, provided that
technologies are the same across countries. However the amount of production occurring in each
country is indeterminate when factor prices are equalized."
Many concerns remain. One key issue is that the H-O theory was developed to explain
trade in final goods not intermediate goods. With "outsourcing" increasing, this assumption is not
realistic. Outsourcing is usually implemented as a means by which labor intensive intensive can
be produced.
Econometrically a drop in the price of imported intermediate goods implies effects that
are observationally equivalent to the effect of skill-based technological change.
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International Trade Notes: 10 October 2016
7. H-O Theory, increasing returns and the Gravity Model.
Figure 5B shows specialization in right and wrong direction with increasing returns. While the
H-O theory suggested that factor endowments drove trade between countries, the majority of
trade currently is between similar countries. Krugman attempted to explain this finding by
investigating the effects of assuming monopolistic competition and increasing returns.
- Monopolistic competition assumes that each firm sets MC=MR where the MR curve is
downwardly sloped and firms enter an industry if profits are positive. It is assumed that at
equilibrium P=AR=AC. Following Feenstra (2004 139) Assume labor is the only input, w is the
equilibrium wage, w is the marginal cost and ci is the consumption of the i th good. Assume
there are L consumers. We initially assume an additive symmetric utility function
N
v(ci ) v ' 0, v " 0 or U v (ci ) . Dropping subscripts, at equilibrium the supply of each good
i 1
equals the demand or y Lc For the ith good
y Lc
(7.0)
Li yi
(7.1)
AC wL / y w / y w
(7.2)
TC w w y
(7.3)
MC w
(7.4)
p AC p / w [a / ( Lc )]
(7.5)
1
MR MC pi 1 w
(7.6)
p
w
( 1)
(7.7)
Solving (7.5) and (7.7) for p / w and c
c
( a a ) / ( L )
(7.8)
p/w
( ) / ( 1)
(7.9)
Remark: (7.8) and (7.9) solve for the intersection point of the ZZ and PP curves. Equation (7.7)
plots as the PP curve in Feenstra figure 5.2 or the figure below. PP is upward sloped and
indicates that as demand increases resulting in c , then equilibrium ( p / w) from (7.9). Note
that we have a downward sloped AC curve. In a graph with p on the y axis and q on the x axis an
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International Trade Notes: 10 October 2016
p
as we
w
move up the curve. Assume two identical countries start trading. This is like L* 2 L . From
(7.8) we see that Equation (7.5) plots on the graphs as ZZ and is the firms average cost curve.
outward shift in the demand curve implies everything else equal resulting in
The next task is to determine the equilibrium number of firms N.
N
N
i 1
i 1
L Li ( yi ) N ( y ) N ( Lc )
N
1
[( / L) c)
(7.10)
(7.11)
which is a function of the equilibrium consumption c which in turn depends on and .
Graphical analysis of the model that shows how p/w and c are determined is shown
below. Assume that di / dci 0 or that reduced consumption implies a movement up the
demand curve and thus an increase in in most cases. This insures that the PP curve showing
the locus of points that solves p / w ( / ( 1)) is upward sloped. Remember that 0 . If
1 then as it increases from 1.1 to 1.2 to 1.3 assuming = 1, p / w ( / ( 1))
decreases from (1.1/.1)=11, to (1.2/.2) =6 to (1.3/.3) = 4.333. The ZZ curve which is the firm's
average cost curve is downward sloped and solves (6.5) or p / w / Lc . Increased
consumption with increasing returns to scale implies that average cost will fall. Increasing the
population L will shift ZZ to Z' Z' and result in a decrease in both p / w and c . In words,
consumption of the ith good falls due to individuals spreading their expenditure over more goods.
This lowers p / w .
Equations (7.8) and (7.9) can provide insight into dynamics. Looking at (7.8) assume
there is an increase in L. The initial effect is to lower p / w , but this is not an equilibrium value.
The solution will involve a move down the PP curve and a fall in which from (7.9) will lower
c,
Notes for a future setup: In a later setup we will use a CES utility curve that makes a flat PP
curve. Here as L we find that ci but p / w does not change.
Using the Krugman assumptions the result of assuming two identical countries with increasing
returns that are trading finds:
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International Trade Notes: 10 October 2016
L implies ci . Number of firms N since for each country full employment requires
L N ( y ) and economies of scale allow y to increase more than proportionally than the
increase in L. This can be seen when we note that p / w implies that y as increased returns
to scale kick in. In summary the increase in y as firms exploit economies of scale necessarily
implies a reduction in the number of firms in each country. Think of it as the firms are
capitalizing on the increased profits obtainable from the increasing returns to scale. It pays for
them to specialize due to increased demand.
=> opening trade between countries indeed implies that firms must exit in each, while the
remaining firms expand their output and take advantage of scale economies.
Krugman's model makes two predictions concerning the impact of trade productivity of
firms: The scale effect as surviving firms expand their outputs and the selection effect as some
firms are forced to exit. The evidence is that the scale effect is not all that large. Increased USCanada trade had only a small effect on scale. It appears that the gains to scale were not all that
big in the first place. The selection effect suggests that if the least efficient firms exit this will
result in an increase in average industry productivity. (This is outside Krugman's model that did
not allow for differences in productivity among firms to simplify the analysis.) The evidence is
that productivity in Canada increased but that there was a small scale effect.
Models have been suggested by Head-Reis (see Feenstra (2004 143)) to impose a model
with no scale effect. Note "If the elasticity of demand for product varieties is constant then firm
scale will not change at all due to tariffs or trade liberalization." To impose this restriction use a
CES utility function:
N
U ci(( 1)/ ) .
(7.12)
i 1
The elasticity of substitution between products is equal to 1 which when N is large
equals the elasticity of demand . In this model di / dci 0 which implies a flat PP curve and
no scale effect. Another implication is that the markup of prices over marginal costs is fixed or
pi
w ( 1)
(7.13)
since limn . Equation (7.13) comes directly from a simple transformation of (7.7). This
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International Trade Notes: 10 October 2016
can be seen by looking at the implications of a flat PP curve. In such a world the profit equation
is
y
.
1
py w( y ) w
(7.14)
Equation (7.14) can be derived if we note:
w
py w(a y ) y
w( a y )
1
y w
wa w y
1
y y ( 1)
w
a
1
(7.15)
y
w
a
1
Assuming no extra normal profits in the long run for monopolistic competition => output will be
fixed
y ( 1) / .
(7.16)
Equation (7.16) insures the term on the right of (7.14) in [ ]) = 0. (Note that the w can be
normalized to 1.0.) The number of products N produced can be solved from the
identity L N ( y ) as
N L / ( y )
(7.17)
and does not change because of the CES assumption. (7.11) can be derived from (7.17) is we use
(7.0). (7.17) illustrates there is no selection effect on the production side. But more varieties are
consumed due to imports. Melitz and Yeaple allow for heterogeneous firms and thus allow for
the selection effect even with a CES utility function.
Summary: The theory is attempting to explain trade between similar countries but is still short of
explaining most of what is happening. More work needs to be done in developing the theory and
then performing tests. In the last 20 years a major effort has been made to test pure theory trade
models. Key articles on the reading list will point to how to proceed with research in this area.
The goal of future research might be to explain what has happened and to make predictions on
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International Trade Notes: 10 October 2016
what might occur in the future.
Why does all this matter? In the past 20 years the ratio of skilled wages to unskilled
wages has increased in many countries in addition to the US. This has led to political
ramifications. How is this to be explained? What is to be done about it? An argument made by
Feenstra and others is that "movements in product prices (combined with growth in productivity)
are fully consistent with the increase in the relative wage of skilled labor in the United States." A
number of authors "have argued that the variables most highly correlated with the movement in
wages over the 1980s and 1990s are neither trade prices nor outsourcing nor high-technology
capital, but rather, a sharp increase in the price of skill-intensive nontraded goods in the United
States as well as a decrease in the price of unskilled-intensive nontradables. This finding poses a
challenge to those who believe that either trade of technology is responsible for the change in
wages and will no doubt be an important area for further research." Feenstra (134).
Gravity Equation Research
Assume two countries that have similar production conditions and tastes operating under
monopolistic competition :
- Gravity equation => bilaterial trade between two countries is directly proportional to
the product of the countries' GDP. => larger countries trade more. => more similar countries
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International Trade Notes: 10 October 2016
trade more.
Assume production of two countries sums to 10.
Case one assumes the sizes were equal. 5*5 = 25.
Case 2 assumes sizes were 1 and 9. 1*9=9.
Case 1 implies more trade.
Define X i j as trade from i to j . It can be proved, given all countries have the same price, that
Xij X
ji
2
w Y iY
Y
j
(7.18)
N
Proof: Assume N products and C countries. Total GDP in each country is Y i yki and
k 1
Yj
world GDP is Y Y . Define s as country j's share of world expenditure so that s w .
Y
i 1
Assume all countries producing different products and demand are identical and homothetic.
C
w
i
j
j
Remark: [A homothetic utility function states that the point at which a ray from the origin of an
indifference map intersects each indifference curve will find a constant rate of transformation
(slope). In words MU y / MU x constant .]
Exports from country i to country j of product k is
X kij s j yki .
(7.19)
For all products
N
N
k 1
k 1
X ij X kij s j yki s jY i
Y jY i
s j siY w X ji
w
Y
(7.20)
- An important question is if the assumptions needed for this result are too binding to be
of use in empirical models. Focusing on size,
X ij X ji 2 s i s jY w
(7.21)
or two countries of unequal size will not trade as much as two countries of the same size.
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International Trade Notes: 10 October 2016
- Assume a region "A" such as OECD with two countries.
Y A Y i Y j .
(7.22)
Their relative shares are
siA Y i / Y A , s jA Y i / Y A , s A Y A / Y w .
(7.23)
The size equation can be expressed as
X ij X ji
2 siAs jAs A
YA
(7.24)
Squaring the identity
s iA s jA 1
(7.25)
implies that
2siAs jA [1 ( siA )2 ( s jA )2 ].
(7.26)
Substituting back into (7.24) proves the Helpman 1987 theorem that states that if countries are
completely specialized in their outputs, tastes are identical and homothetic and there is free trade
then the volume of trade is:
Volume of Trade in A
s A 1 ( siA ) 2
A
GDP
iA
(7.27)
The term 1 ( s iA ) 2 is a "size dispersion index" that shows how trade is related to the
iA
relative size of countries. In the more than two country case look at pairs of countries and define
A [i, j ]. The above equation is usually expressed in logs (Feenstra 2004, 147) or
2
X ij X ji
Yi Y j
i
j
ln i
ln(
s
s
)
ln[1
i
i
j
j
j
Y Y
Y Y Y Y
For empirical work using fixed effect models the form
125
2
(7.28)
International Trade Notes: 10 October 2016
2
X tij X t ji
Yt i Yt j
i
j
ln i
ij ln( st st ) ln[1 i
i
j
j
j
Yt Yt
Yt Yt Yt Yt
2
(7.29)
has been used. The second term, if present assumes country shares are not constant, while if this
term is not present the implicit assumption is that the shares are constant and are in the ij term.
Helpman' model assumes 1 which is tested by the above form. Results for this and other
related models are shown in Feenstra (2004 148-).
- Summary: The Monopolistic Competition model assumes each country will be
exporting varieties of the differentiated product to another. It is assumed that such countries are
completely specialized in that product but could costlessly move to another product =>
intraindustry trade.
Equation Estimated in Table 5.2
ln X ji 1 ln Y i 2 ln Y j ij ln d ij
Where Y = income ij indicator of trade between two provences, d ij = distance Some
models added border effect and a indicator of US trade. Border effect was negative , X = trade.
A border effect implies that prices not equalized across i and j.
Remark: [(H-O model only in an extreme case has complete specialization and never has
intraindustry trade. When there is a continuum of goods H-O can result in complete
specialization. Feenstra asserts that factor prices will not be equal. Johnson shows a special case
where they might be). Common assumption of Monopolistic competition model and H-O
Continuum of goods model is that # of goods exceeds # factors.]
- Simple Heckscher-Ohlin Model does not allow for intraindustry trade unless there is a
continum of goods produced.
-H-O models with a continuum of goods => more goods than factors.
- Using the gains from trade. A country can gain from trade in the following cases:
- Same production conditions, different tastes.
- Different production conditions, same tastes
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International Trade Notes: 10 October 2016
- Different production conditions, different tastes where tastes do not outweigh
production conditions .
- Different production conditions, different tastes where tastes do outweigh
production conditions.
- Same production conditions and same tastes implies no gains from trade are
possible. (Does this work for marriages?)
Figure 2.7 is the basic diagram. Form this base the above cases can be drawn.
- The gains from trade can be broken down into the production gain and the
consumption gain. The consumption gain refers to the gain that occurs when the production of
all goods in a country stays the same after trade opens but the consumption pattern changes. If
production does not change, then there are usually fewer political repercussions of trade. Note
that politicians never complain about the consumption gain, only the costs of obtaining the
production gain. The production gain arises as the mix of goods produced changes as a result of
trade opening. Figure 9 below shows these gains
Figure 9.
Initially the country is at a for consumption and production. After trade opens the country moves
to a higher indifference curve at b but still produces at a. When production of X relative to y
increases the country gets to c. The diagram makes the small country assumption. If this is not
the case, the terms of trade may deteriorate as production of X increases.
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International Trade Notes: 10 October 2016
8. Alternative approaches to trade theory contrasted to Original HO Model.
- Product cycle of a new good - Vernon.
- 1. Product development and sale in the US
- 2. Growth in US exports as foreign demand increases.
- 3. Decline in US exports as foreign firms begin to produce for their home
markets.
- 4. US becomes a new importer as foreign prices fall.
- Examples Radios, television, synthetic fibers, transistors, pocket
calculators. Product cycle theory is short run and dynamic.
- Multinationals. If the product is developed by a multinational, the
production may move overseas at once. Note that the product cycle theory is not in conflict with
comparative advantage since the US may have a comparative advantage in science and research
technology. Continuing product improvements may allow the US to maintain its role as a
producer. Since technology and capital are mobile the US may lose its production role.
Technology may be stolen!!
- Economies of Scale Considerations - Krugman.
- Products such as aircraft may require large fixed cost to get going. Firms in these
industries may require larger markets (and not proceed unless such markets are available). The
large startup costs insulate such firms from stages 3-4 of the product cycle.
- Economists have argued that anti trust laws should not be used to prevent US
firms from cooperating on major research efforts.
- Preference Similarity Hypothesis - Linder.
- => Countries will export good which has a large domestic market. => countries
will find that the most promising markets are those which have preference similarities to their
home market. This analysis explains gains from trade in the same tastes different production
conditions case but in addition considers the case where a country both imports and exports the
same product class, but different models. (US imports cars but also exports cars of different
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International Trade Notes: 10 October 2016
design. Linder model does not explain why production originates in one country.
- Border Trade.
- Trade based on similarities in consumer preferences implies that similar
products may cross a border in both directions. Often the product is not quite the same. Shipping
costs for bulk products may explain this circumstance.
- Changes in Factor Supplies.
- Figure 10-1 in Dunn and Mutti shows neutral growth. Here the same % increase
in factor supplies cause PPC to move out. Exports increase. Relative prices of food and cloth
remain the same. This analysis assumes a number of things:
- Income elasticity of demand for all goods is unity.
- Constant returns to scale. (If one good had increasing returns, then the
same % increase in both factors would not increase the production of both good the same
percentage.
- Analysis assumes that world trade prices do not change (small country
assumption.)
- Figure 10-2 in Dunn and Mutti shows same conditions except that
demand does not go up by the same percentage as factors of production increased. If final
consumption point is along GQ' = > then we have trade biased growth. If final consumption is
along Q'K then trade is anti-trade biased growth.
- The production expansion path OPP' assumes that the terms of trade
remain the same. If the terms of trade move against the country, then the expansion path will be
steeper than OPP'. Immiserizing growth (see figure 10-4 is an extreme case. Here welfare of the
country actually falls. This can cause substantial political problems!
- Immiserizing growth can occur due to:
- The country increasing production.
- World trade prices moving against the country which by
increasing production tries to stay ahead.
- Increases of one factor of production.
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International Trade Notes: 10 October 2016
- Figure 10-2 shows effect on PPC of increasing one factor of production. Cloth is
relative labor intensive in comparison to wheat. An increase in labor (immigration went up)
causes the PPC to move out. The increase in the potential cloth output (C1C2/OC1 is
proportionately greater that the increase in potential food output F2F1/OF1. The effect of this
change is that at the same world trade price the expansion path can no longer be a straight line.
- A complete analysis looks at both production and consumption effects. Increased
supply may cause world trade prices to change. Changes in income inside the home country may
have effects on consumption patterns. From figure 10-3 we add indifference curves and generate
the new offer curves shown on figure 10.3 These are drawn on figure 10 below.
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International Trade Notes: 10 October 2016
Figure 10
- Offer curve analysis. Initial offer curve for home country was OA. The offer
curve of the rest of the world is ORest of World. The world trade relative price is OT and the
home country exports OC1 of cloth for OF1 of food. As a result of the production possibility
curve moving out, the home country offer curve moves to OA'. If the small country assumption
was in effect, the rest of the world offer curve would be OT and the home country would sell
OC3 of cloth and be at point E2. Since the rest of the world offer curve is not completely elastic,
then the terms of trade move against the home country ( Pc / Pf ) and the equilibrium point
becomes the new terms of trade line OT'. Immiserizing growth (see figure 10-4) is the extreme
situation. Prebisch argued that this occurred for less developed countries in the 60's. This fact has
been controversial.
- Changes in technology shift the PPC and can be handled like changes in factor
supplies.
- Changes in demand can shift community indifference curve and cause changes
in relative prices.
- Transport Costs. Have assumed that transport costs are zero. This assumption
implies that trade will equalize commodity prices at home and abroad for traded goods and
assuming do not have complete specialization. Transport costs imply that price of good in foreign
exporting country is less that price in domestic country. => transport costs lower gains from
trade. In some cases transport costs preclude trade. IMF data suggests that transport costs have
fallen from about 9% of the value to trade to 6% of the value of trade in the last 40 years. Time to
deliver a product also makes some products not able to be exported.
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International Trade Notes: 10 October 2016
- Dumping. Defined as selling a good in one market below the cost charged in
another market. For a consumer in a given market, dumping is a gain. For the domestic producer
of the domestic good being imported, dumping is seen as "unfair." For the i t h good
MR i (1 (1/ i )) AR
If | i | , then MRi ARi Pi . If id and i f are domestic and foreign elasticities of demand
for the ith good, then | i f | | id | implies that Pi f Pi d
Different elasticities of demand suggest market segmentation. Dumping => a gain to importing
consumers but is usually protested by competing domestic firms.
- Cartels. Cartels attempt to reduce supply and raise price. This action will tend to
be more successful if:
- The price elasticity of demand for the product is low (=> no close
substitutes). In the case of oil initially people were "stuck" with cars that had low mileage. Over
time as energy efficient cars were built demand elasticity changed.
- The elasticity of supply for products from outside the cartel is low (new
firms cannot enter easily). In the long run firms may be more likely to be able to enter.
- A few members of the cartel must be willing to reduce production. Some
way must be found to monitor production and assign quotas This has been a problem within
OPEC.
- The cartel must be congenial and small enough to work together.
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International Trade Notes: 10 October 2016
9. The Theory of Protection
- National money supplies were historically linked with gold. With increasing population
and growth outstripping increases in the gold stock, governments were anxious to increase gold
reserves. Arguments were been made for bilateral mercantilism where a country ran a surplus
with each and every other country. Since in an N country world, at most there can be 1 successful
bilateral mercantilism, argument shifted to multilateral mercantilism. where on balance a country
ran a surplus but not necessarily with all countries. Tariffs have been used to restrict imports.
Retaliation often negates first round effects. Import "regulations" or "standards" have been used
to achieve the same goals.
- Partial Equilibrium Analysis - Small country assumption
(Small country assumption assumes that country has no effect on the world trade price) See
figure 5-1. We assume area under demand curve = consumer welfare.
- Initially free trade at world price = Pw. Country produces 0Q1. Country consumes
OQ4. Imports Q1Q4.
- Tariff increases such that (1 ) Pw Pt . Domestic producers able to produce
Q2Q1 more. Domestic consumers consume Q3Q4 less.
As result of tariff imports now Q2Q3. Tariff proceeds [Q2Q3] * [PT-Pw]. b = producer surplus
gain. d = consumer surplus loss. c = gov gain due to tariff. After tariff consumer surplus loss =
a+b+c+d . But other sectors gain. a = producers gain, c= government gain b+d = consumers loss.
Deadweight loss = reduction in imports * tariff * .5
= (Q3Q4 + Q1Q2)*(PT-PW)* .5 + b+c.
Assumes straight line demand and supply curves.
=> total consumer loss = a+b+c+d. If consumers get benefit of tariff from government then
a+b+d is the loss. Producers gain b. => consumers and producers are often on different sides of
the politics of tariffs.
- Non Trade Barriers. Regulations regarding packaging may hinder foreign firms. In late
50's size of headlights limited high priced Italian cars from being sold in the US. Crash testing
limited low volume cars. RR had to import steering columns from GM. When the requirement is
not in the home market => costs of compliance cannot be shifted/shared.
- Quotas. Although GATT outlawed quotas have "Voluntary Export Restraints" (VERs).
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International Trade Notes: 10 October 2016
VER can be used to convince Congress not to place tariff on good. See figure 5-2. In the absence
of a quota would import Q1Q4 = 40. VER limits imports to Q2Q3 = 25. Producer surplus = a.
Deadweight loss = b + d. c goes to foreign country exporter who has the right to ship to domestic
country. In 1950s and 1960s oil companies were given limited rights to ship oil to the US and
earn area c. If treasury auctioned quota right, could recapture the monopoly rent. Same holds for
NBC's right to channel 5!! Producers can upgrade products to sell a limited number of top of the
line products. Producers can send parts to the US and put them together on US soil.
- Subsidies. US producers are given a subsidy of S per unit. In figure 5-3 => supply curve
shifts from S to S'. => Domestic producers can sell Q1Q2 more. Imports now Q2Q4 not Q1Q4.
Total subsidy = S * OQ2 (paid for by taxes) of which producers get a. b is the deadweight loss
since it represents an inefficiency in resource use. The subsidy is less inefficient than a tariff
since the level of consumption was the same as before the subsidy. (There is no area d that occurs
with the tariff since the tariff implies an increase in price. Subsidies are deemed less politically
defensible.
- Lerner "The Symmetry Between Import and Export Taxes" (Caves and Johnson # 11.
A tax or subsidy on trade involves a divergence between foreign and domestic price
ratios. Equal taxes on exports and imports create the same divergence between foreign and
domestic price ratios (if trade is in balance) so the real effect of import and export taxes are
symmetrical.
[tariff] +
[import subsidy]
= 0 effect on price
[tariff]
=
[consumption tax] + [production subsidy]
[export tax]
=
[production tax] +
[devaluation] + [import subsidy]
= 0 effect on imports
[devaluation]
= [tariff] + [export subsidy]
[consumption subsidy]
= [consumption tax] + [production subsidy]
[tariff] + [export subsidy] + [appreciation] = 0
[export tax]
= [tariff] + [appreciation]
[appreciation]
= [consumption subsidy] + [production tax]
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International Trade Notes: 10 October 2016
[import subsidy]
= [consumption subsidy] + [production tax]
- Large Country Case - Here tariff => foreign price
-Figure 5-4 shows partial equilibrium analysis. Assume A is the home country and B is
the foreign country. If there was no trade between A and B, the price of oats would be higher in
A than B. With free trade are initially at price PW. B sells q1q4 ) to A. Assume next that country A
places a tariff of T on imports from B. Price is not PW+T since B's price falls as tariff drives B
down its supply curve. B's price is now P0. In A this is P0 + T. The effect is that A imports Q2Q3.
Area c = tariff collected. d+b = deadweight loss and a = production subsidy. In A domestic
production goes up by Q1Q2 and consumption goes down by Q3Q4.
- Elastic supply. If B had a perfectly elastic supply curve, then the price in A after
the tariff would rise the full amount of the tariff. A would not be able to drive the price lower in
B. A has no power over the price it pays!
- Inelastic supply. If B had a perfectly inelastic supply curve and none of the
product was sold in B, then the effect of a tariff is to lower the price B gets. A sees the same
price. Tariff collections rise but producers in A do not see any increase in sales. This may be the
case in some primary product producing countries. Here foreign country pays the tariff.
- Inelastic supply - export tax. In 1973 oil producing countries imposed an export
tax and collected more money from the developed countries who need the oil and initially
imported what they had in the past, but at a higher cost.
- General Equilibrium Analysis. (See figure 5-5)
- Small Country Case. Country initially at P1 for production and C1 for
consumption. The world relative price line is TT. Tariff on the imported good (food) raises the
relative price of food. Hence as [PF / PC] the relative price line gets flatter and moves to EE.
Tariff has driven a wedge between domestic and world price. The new domestic price => food
production in country as move along PPC to P2. Consumption is now at C2 on indifference
curve i1.
- Large Country Case. See figure 5-6. Initially at P1 for production and C1 for
consumption. As a result of tariff domestically [PF/PC] but due to large country assumption
and assuming that the foreign country has supply elasticity < => that the world [PF/PC] .
Due to the domestic price [PF/PC] production shifts to P3 but foreign imports are made at the
new world price. Final consumption point C3 is where indifference curve i3 is tangent to the new
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International Trade Notes: 10 October 2016
domestic price ratio.
- Offer Curve Analysis. Figure 6-2 shows the initial position E. Here A supplied
OC of cloth for OF of food. The terms of trade are represented by OE. Country A now places a
tariff on B => A's offer curve shifts to OA'. Without retaliation, A hopes to obtain the new
relative price OE'. Point E' is selected such that A's indifference curve (not drawn) is tangent to
B's offer curve. If B retaliates to get back to the original price we move to E"(not shown in ed #
6). Here trade will fall. If B has elasticity of supply of , then the effect of A's tariff in would be
no change in the terms of trade and equilibrium since A cannot change prices.
- Dynamics of Offer Curve Adjustment.
Usually assume Walrusian adjustment => Excess demand causes price to rise.
Can have Marshallian adjustment where excess demand => supply
to increase.
- Effective rate of Protection for industry j,
ej
t j (ai j ti )
i
1 ai j
i
e j effective rate of protection in industry j
ti nominal tariff in industry i
ai j share of inputs from industry i in industry j
Case 1. Value added 50%. Tariff = 33%
=> effective rate of protection = .33/(1-.50) = 66%
Case 2.
tariff on motor cycle
tariff imported steel
tariff on imported chrome
share of steel
= 40%
= 60%
= 50%
= .2
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International Trade Notes: 10 October 2016
share of chrome
% value added
= .22
= 10% 1 ai j
i
effective rate of protection on value added =
[.4 - [(.2*.6) + (.22 * .5)]]/.1 = 1.7 => 170%
without tariffs on imported steel and chrome would be .4/.1 =400%
- Export Subsidies. Governments have various means by which they can stimulate
exports. In the 60's JFK gave "tied aid" that required that the foreign country buy American
goods (usually military hardware). Other schemes include direct payments to export firms which
is illustrated in figure 5-7 for a country facing world demand elasticity = | | . Here the world
price is P0. In the absence of any intervention the country would export c. As a result of the
subsidy the export firms have a price of P1 . The higher price increases exports by d + b ( and
reduces domestic consumption by b. Note that the subsidy is not available for domestic sales so
the firm raises the domestic price which cuts off b of domestic sales. The deadweight loss is b
(loss of domestic consumer surplus) and d (the loss of productive efficiency which results from
producing goods at a cost (the area under the supply curve) which is higher than the revenue
received from foreign firms. If the small country assumption was not in effect, the effect of the
subsidy might be to reduce the world price.
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International Trade Notes: 10 October 2016
10. Arguments for Protection
- Protectionism and free trade have always been in conflict in the United States. Labor
used to be pro free trade but in recent years labor has tried to secure tariffs to "save jobs." In the
25 years after WWII, there was a consensus to reduce tariffs. In this era the United States was
economically dominant. JFK made major progress in pushing for free trade. Now protectionism
has become far more popular since the world trade market is much more competitive. A number
of arguments are made for tariffs.
- Protection of a way of life. The scissors statement in the book on page 142 was a plea
to protect an industry from becoming extinct. The statement did not make any attempt to measure
the costs of the tariff against the benefits. No attempt was made to make a security argument.
- Increase Output and Employment. These arguments assume that the country will have a
net increase of jobs = the protected jobs. What will happen is that there will be less jobs due to
the reduction in real income. In the tariff analysis we showed the deadweight loss (d+b) in figure
6-1. There is no way to get around this cost. In a country with flexible exchange rates, a tariff
will initially make the balance of payments go more into surplus but, exchange rate changes will
nullify this gain. Mechanism: Tariff reduces demand for foreign currency which will fall in
value making imports cheaper for a range of goods. The fall in the exchange rate nullifies the
effect of the tariff.
- Closing a Trade Deficit. In the short run tariffs on non essential items are sometimes
used. In the long run these policies are usually not effective.
- Pauper Labor. The argument is made that foreign labor is less expensive => US labor
need protection. Argument assumes that 1. labor is the only input and 2. there are no differences
in labor productivity 3. that wages rates have not adjusted for differences in productivity.
Argument also ignores that exchange rates adjust to compensate for differences in unit labor
costs across countries. Key factor is not wage rates but unit labor costs.
- Heckscher-Ohlin - Factor price Adjustment. H-O theory shows how trade tends to
equalize good prices and factor prices (in the absence of complete specialization.) Figure 11A &
11B shows the conditions under which factor prices adjust (11A) and do not adjust (11B). In 11A
The initial endowments of the countries (RI and RII) are more similar than in figure 11B.
AI
=> complete specialization of X in country I
AII
=> complete specialization of X in country II
BI
=> complete specialization of Y in country I
BII
=> complete specialization of Y in country II
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International Trade Notes: 10 October 2016
In figure 11A BII < BI < AII < AI while in figure 11B
BII < AII < BI < AI
Because of complete specialization in figure 11B you never can get to the zone between AII - BI
=> need factor mobility.
Obstacles to factor price equalization from trade
- Many countries - will only cause problems if all productions functions are not the same.
- Many products and factors - to equalize all factors need an equal number of traded products.
- Imperfect competition - To get equalization need MC = price of product and factors being paid
the value of their marginal product.
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International Trade Notes: 10 October 2016
- Increasing returns to scale breaks down perfect competition since one producer dominates.
- Different production functions in different countries ruins equalization since one country will
have an edge.
- Increasing marginal productivity of factors of production => the price of factors =/ VMP of
factor.
- Factor intensity reversals cause problems due to: 1. lack of homogeneity since will not get
straight line expansion paths and 2. due to one good's isoquant curve being positioned inside
another good's isoquant curve. If a country expands and there is a reversal there will be a switch
in the good having comparative advantage.
If trade does not equalize factor prices, factors can move!
Even if factor prices adjust, the formerly scare factor owners will lose relative to the
formerly abundant factor owners. This change in the relative position of factor owners sets the
stage for political pressure for tariffs. Since the welfare of the country goes up with free trade =>
gainers should be able to compensate losers. Problem: it may take time to adjust.
Terms of trade argument. Figure 6-2 shows initially the world is at E. Country A seeing
that the elasticity of B's offer curve is not perfectly elastic, decides to impose an "optimum" tariff
and move to E'. B does not let this pass and itself passes a tariff moving the world to E". If B did
not react, then from A's nationalistic perspective the move to E' is in its interest. OPEC's oil price
increases are similar to export taxes. Here OPEC wanted to get the tariff gains. The primary
product producing countries have been interested in raising the value of their products. They
have suspected that demand for their products has not been growing worldwide as fast as the
demand for the products of the developed countries. What is the optimum tariff? If the other
countries offer curve has an elasticity | | , => optimum tariff = 0. If the elasticity = 1, then
there is no limit to the amount of tariff that can be applied by one country since no matter what
the tariff, the other country supplies the same amount. For an example see figure 6-2. The
optimum point is where country A's trade indifference curve is tangent to country B's offer curve.
The analysis assumes no retaliation.
Infant Industry Argument. Argues that start up industries or infant industries need special
protection. Over time the learning curve will => that the PPC curve will shift out and the firm
will be competitive. Firms fear that attempts to develop an industry will be defeated by vigorous
price competition from existing firms. Argument can be traced to Alexander Hamilton's "Report
on Manufactures" (1791). While argument appears to have appeal:
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International Trade Notes: 10 October 2016
- How do we tell in advance if an industry will ever grow up and have the PPC shift out?
- Will the eventual gains outweigh the costs of protection?
- Why does the market not finance the startup? Why is the government needed?
- If the wrong industry is selected the country will be saddled with a continuing burden.
Many infant industries remain dependent.
Industrial Strategy. Krugman has developed an argument that is an extension of infant
industry and product cycle argument. Protectionism is advocated for new or emerging industries
while extensive research is carried out or until sufficient economies of scale are realized.
Protection of such industries may discourage foreign firms from entering the field. It is suggested
that the United States may thus be able to gain permanent dominance of the market. Krugman
looked an Japan and detected that this was their strategy.
- Why does the market not finance such an industry?
- How is Washington going to "beat the market" and pick a winner?
How has Japan been doing recently in picking winners?
Secondary Arguments for Protectionism.
- National Defense. This argument was recognized by Adam Smith "defense is
more important than opulence." If the product is storable a better strategy might be to buy on the
world market at a low price and store the product. It is costly for a country to become self
sufficient. International dependence may be a means by which to avoid war. An argument can be
made to protect an industry to maintain skills in the work force.
- Cultural or Social Values. Country may want to protect a way of life. What is the
cost?
- Protection to Correct Distortions in the Domestic Market. Figure 6-5 illustrates
the situation.
D
SP
Pw
= domestic demand.
= domestic supply curve.
= world price.
With no tariff the domestic production = OA, domestic consumption = OF and domestic imports
= AF. We assume that SP does not include external economies in the production of the good that,
if present, would make the supply curve SS. Solution is to impost a tariff raising the price to PT
such that domestic production = OB, domestic consumption = OC and domestic imports = BC.
Problem is that tariff induces a deadweight loss of shaded area. A better policy might be to
141
International Trade Notes: 10 October 2016
provide a domestic production subsidy of GE. Here domestic consumption = OF, domestic
imports = BF and domestic production = OB. The domestic distortion argument has been
suggested by economists that think that wages in manufacturing in some developing countries are
> that wages for the same labor in agriculture. If true this would imply that the social cost of
labor is < than the private cost and suggest a tariff to protect manufacturing. Others suggest that
the market is paying a higher wage in the city due to differences in skills of to pay people for the
disutility of working in that location.
- Anti-dumping tariffs. Can place a tariff to correct an artificially low price due to
dumping. If dumping is long run, the country as a while gains while the industry facing the
dumped product is hurt. If dumping is short run (goal to drive domestic competing firm out of
business) can have a case to use a tariff to counter dumping.
- Scientific Tariff. Arguments have been made to apply a tariff to "equalize the
costs of production at home and abroad." This would cancel the gains from trade. These
arguments are usually made in political campaigns.
- Revenues. Tariffs have been used as a source of revenues. (US in late 1700's)
and in many developing countries having no income tax. The problem is that the export sector is
hurt. In Nigeria farmers in Palm Oil, Ground nuts and Coca were required to sell their produce
to marketing boards at a low price which in turn were the only one that could legally export. The
result was that agricultural, output was below that which could be realized if the world trade
price was used. Since the marketing boards price paid to farmers never changed. Farmers did not
get a higher price in lean years and a lower price in good years. => farmer faced the full effect of
changes in the crop. HHS argued that the government go into the palm oil business and gradually
raise the price that farmers obtained.
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International Trade Notes: 10 October 2016
11. Mundell Policy Equation
The Mundell policy equation listed on page 41 of his International Economics (1968)
provides a way to unify a great deal of the pure trade theory that was first introduced as graphs.
The policy equation can be simplified by assuming some effects to be zero. The basic equation is
(1 ma mb )T I (a b 1)P Ia' ta Ib' tb ma X a* mbX b*
'
'
ya ya
tca xb xb' tcb Ya ya
t pa X b xb' t pb B
(11.1)
which shows how changes in transfers (T), changes in the terms of trade (P), changes in tariffs
in countries a and b (ta , tb ) , changes in consumption taxes in a and b (tca , tcb ) , changes in
production taxes in a and b (t pa , t pb ) , changes in the balance of payments (B), and changes in
productivity in countries a and b ( X i* ) are related. Define T > (<0) as a lending of funds from
country a to country b in terms of X goods. P is the price of Y in terms of X. If we define Da
domestic expenditure in a, then
Da xa Pya X a PYa T
Db
xb
X
T
yb b Yb
P
P
P
where demand in a (b) is defined in X (Y) goods. Small letters define consumption ( xa , ya ) while
capital letters ( X a , Ya ) denote production
Country a (b) exports good X (Y).
i and i' are the elasticity and Hicks real income constant elasticities respectively. These are in
absolute value form. We note that mi is the marginal propensity to spend on imports in the ith
country.
i i' mi
(11.2)
ya' compensated elasticity of supply of y in a. The elasticity of supply in b is defined as
b b 1
(11.3)
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International Trade Notes: 10 October 2016
Since country a imports y then
y
Y
a ya a ya a
I
I
(11.4)
which leads to
ya
Y
( ya ma ) a
I
I
ya
' Ya
ya
I
I
a' a ma ( ya ma )
'
ya
(11.5)
The policy equation provides a way to apply the theory used in the graphs since the parameters of
the equation can be estimated. In terms of the Mundell equation, the Marshall-Lerner exchange
rate stability relationships is just
I ( a b 1) P B
(11.6)
Define the terms of trade P as the foreign price / the domestic price. B implies an increased
surplus or reduced deficit. I = amount of imports. Assume exchange stability or
a b 1 where we assume i is the absolute value of the elasticity of demand for imports of
the ith country. The above equation suggests that if the terms of trade move against the country
( P ) the balance of payments improves B . Assume a is Germany and b is the UK. After
WW I Germany was required to make a payment to the UK, One way to do this would be to
place a tariff on UK goods or
T
a' I
ta (1 ma mb )
(11.7)
or have the UK grow and Germany not grow
T
mb
*
X b (1 ma mb )
(11.8)
If the terms of trade are to remain fixed, the only way for country A to grow faster than country B
is for the marginal propensity to import in A to be less than in B because ma X a* mb X b* .
Suppose country a wishes to know the rate at which it must tax import goods to relieve
disequilibrium caused by an increase in productivity in the foreign country b then
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International Trade Notes: 10 October 2016
'
ya ya
tca mbX b* 0
(11.9)
or
tca
mb
*
'
X b ya ya
(11.10)
If China is country b who has mb 0 then no tax change is needed. However if Chinese buy
more from the US (country a) then the consumption tax in the US must be lowered to stimulate
demand for Chinese goods.
The effect on the terms of trade of a tariff is
P
a'
ta (a b 1)
(11.11)
Unless b the effect of a tariff increase in country a is to improve the terms of trade for
country a which implies that P or in words the price of the foreign good/domestic good falls.
The effect on the domestic price ratio ( Pta ) of a tariff change is
( Pta )
P
a'
( ma 1)
P ta
1
b
ta
ta
(a b 1) (a b 1)
(11.12)
if we assume P and t a initially were 1. A tariff raises the domestic price of imports if the sum of
the foreign demand for imports, b plus the domestic marginal propensity to import, ma is
greater than one. Other interesting related items are
U a / X a* 1 I (P / X a* ) ,
(11.13)
which relates changes in utility in country A to the growth of productivity in country A. Multiply
out to get
U a X a* I P
(11.14)
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International Trade Notes: 10 October 2016
which highlights the result that the gain in productivity comes at the cost of a loss in the terms of
trade. If X a* I P we have immeriserizing growth!
The effect of a production tax in country a on the imported good y, increases demand for the
foreign good and worsens the terms of trade.
ya
P Ya
t py I (a b 1)
'
(11.15)
The effect of a consumption tax in country a on the imported good has the reverse effect
'
ya ya
P
tca I (a b 1)
(11.16)
The policy equation allows us to net out the effect of a number of policy instruments being
applied. The basic idea is that any policy will cause either excess demand or excess supply which
requires some other variable to change. The advantage of the policy equation is that more than
one policy can be changed at the same time. For further details and extensions see Mundell
(1968)
Application: Since WW II the US has tried to promote growth of first Europe and later other
sectors of the world. Assuming the US is country A and that there is US growth X a* 0 , the
policy equation suggests that unless we can get growth going in the rest of the world (B), the
terms of trade are going to move against the US.
A country can grow faster than the rest of the world if its marginal; propensity to import is lower.
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International Trade Notes: 10 October 2016
12. Regional Blocks => Discriminatory Trade Liberalization
- United States has the following trading classes:
- Free trade (NAFTA)
- Most favored nation status
- tariff not at MFN level
- embargo
- Free Trade Area. Easiest to setup since do not have to agree on a common tariff but
there is always the problem of reshipment of goods. Usually setup when the countries are quite
different and a common tariff makes little sense and/or when the countries are quite far apart and
the reshipment problem is less.
- Customs Union. (free trade area with a common tariff) avoids the reshipment problem.
Customs union has trade creation and trade diversion. Trade diversion arises from the higher
costs of trading from the new partner country rather than a third lower cost country outside the
customs union. Trade creation is the added trade with the partner country that was not possible in
the past.
- Economic Union. (Customs union with capital and labor freely mobile). An economic
union is a large step toward one economy. The United States became an economic union when
the constitution was passed since tariffs between the states were outlawed and capital and labor
were freely mobile. Figure 7-1 shows trade creation and diversion due to a customs union. Before
the customs union was formed between France and Germany, France had a tariff T which was
added to the US supply curve SUS. At that time imports were Q2Q3 from the US. After the
formation of the customs union, there was trade diversion from the US which was the low cost
producer to Germany. Imports are now Q1Q4 from Germany. Total consumer surplus increases by
a + b + c + d. The French government loses c + e of tariff revenue. The efficiency gains for the
expansion of trade = b + d. The result of the customs union was that local producers lost sales but
customers gained. Since e = the loss and b + d = the gain, if e > (<) (b + d) then on balance the
customs union hurt (helped) country.
- Dynamic Effects. Europe noted that in many cases the complete output from an industry
in one country was less than the output from one firm. => Form the EEC to allow bigger firms
since the market would be bigger. Another gain from the common market was that national firms
faced increased competition. New changes in the works include:
- Removal of border controls.
- Standardization of industrial standards (TV).
- Removal of limitations on movement of professional people (common licensing
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standards for doctors etc)
- Standardization of legal systems.
- Removal of capital controls.
- Removal of restrictions on trade in services such as banking, insurance and air transport.
- All cross country government procurement.
Major problem with economic unification - Distribution of the seignorage. How do we
coordinate monetary policy? What happens if different parts of Europe want a different rate of
monetary growth?
13. Commercial Policy
- The rise of nationalism in the Western world (1500-1800) associated with mercantilism
and close and detailed regulation of trade. The objective was to amass gold to increase the
national money supply. The classical economists fought against these theories. They argued that
imports were desirable. To get imports you had to export. In the UK the Corn Laws were
repealed in 1846. UK was a leader in the free trade movement which reached a peak in 1870
when Germany, France and Italy wanted tariff protection for their new industries against the
established UK industries.
- Period 1875 - 1914 European countries developed preferential relationships with their
colonies.
- Protectionist tide swelled until middle of depression.
Tariffs over the history of the United States. In the period 1789-1934 tariffs set by
Congress and were in general relatively quite high. Tariff of 1789 was designed to generate
revenue. After 1812 Southern and Western interests who exported agricultural good and
imported manufacturing goods, wanted low tariffs. Eastern and Mid Atlantic States wanted
higher tariffs to protect their industry. In 1828 Southerners added high tariffs on manufacturing
goods usually imported into the East in the hopes the tariff would fail. The south wanted low
tariffs while the North wanted high tariffs to protect their industry. Much to their surprise the
"Tariff of the Abominations" passed. In 1833 some of the worst tariff abominations were
removed.
After the civil war Southerners had little political power. Tariffs were raised since the
North was in power and remained high until the Underwood tariff of the 1920's. In 1930 SmootHawley tariff passed. Trade soon fell. In 1934 President Roosevelt was given the authority to
negotiate bilateral tariff agreements (Reciprocal Trade Agreements Act). In the period 1934-1947
agreements with 29 nations were made. All agreements stressed the unconditional most-favored
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nation clause and the chief supplier rule where the US only negotiated with the countries who
were the chief supplier of the product. By many agreements the US was able to lower world
tariffs.
After WWII there was a move toward multilateralism. The International Trade
Organization, International Monetary Fund and the World Bank were setup. The Reciprocal
Trade Agreement provided the authorization for the United States to participate under the GATT
agreement which was established in 1947. The main principle of GATT is nondiscrimination.
However if all countries get the same tariff on a product but not all products get the same tariff,
and all countries do not produce the same range of products, there is a possibility that what
appears nondiscriminatory is in fact discriminatory.
In the period 1933 - 1960's tariffs fell from ~ 53% to 10%. 1962 Trade Expansion Act
authorized Kennedy Round. Eventually in 1967 tariffs were cut about 35%. While most
reductions were across the board, there were special cases for individual countries. Trade
Expansion Act provided "adjustment assistance" to workers impacted. This good idea did not
work out too well in practice due to administrative problems. Workers may have problems
learning new skills. How do we tell it is foreign competition that was the problem? An escape
clause in the act allowing firms to partition for relief provided a warning to foreign firms that a
tariff was possible. Many foreign firms a voluntary limits on exports to the United States. In the
negotiations many countries questioned whether tariffs contained water and as a result tariff
reductions were not meaningful.
The Tokyo Round began in 1973 and was completed in 1979. The President was
authorized to reduce tariffs up to 60% and eliminate "nuisance tariffs." After the Tokyo round the
European Community reduced tariffs 29%, Japan reduced tariffs 49%, the United States reduced
rates 31% and all industrial countries reduced 34%. The US participated in the Tokyo Round
under the 1974 Trade Reform Act which again contained an "escape clause" and "adjustment"
help and gave the President's hand in dealing with certain unfair trading practices. The President
was authorized to give special treatment to developing countries in the form of a Generalized
System of Preferences. Only some commodities qualified to be on the GSP list.
The Uruguay Round began in 1986 and as concerned with trade in services, intellectual
property rights, and Voluntary Export Restraints. GATT passed in late 1995.
The 1988 Omnibus Trade Act included provisions allowing retaliation against the exports
of countries whose governments do not make reasonable efforts to enforce U. S. patents and
copyrights within their borders (Super 301).
During the Clinton years NAFTA open trade with Canada and Mexico. So far this
legislation has been a success. Bush II wants fast track authority to extend trade with other South
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American Countries.
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14 Trade of Less Developed Countries
Issues: In the 60's primary product producers felt that the terms of trade were moving
against them. That the prices of primary products were low and that production in the developed
countries prevented industry from developing in the developing countries.
In recent period many of same countries have experienced rapid growth. Two
types of countries:
- Those that have partially or totally broken away from the past trading pattern and
now export manufactured goods.
- Those that still export primary products (OPEC).
Price instability of primary product producing countries:
Competitive markets more volatile than oligopolies.
Elasticities of demand and supply are lower for primary products than
manufactured products (use Mundell equation to determine the effect on growth.
Possible policies:
- Marketing boards => Government gets the profits. Farmer's earnings fluctuate as yield
changes.
- Buffer stock system. (Clinton released oil from US reserve in May 1996).
- Figure 10-3 Shows decline in concentration of merchandise for least developed
countries. Many countries tried to reduce impact of foreign trade by a policy of import
substitution. A costly way to proceed. Infant industry argument a temporary import substitution
policy.
- "Four tigers" (Hong Kong, Taiwan, Singapore, South Korea) were countries that
pursued an export-led growth policy. Indonesia, Thailand, Malaysia and China also were
successful. Countries exported labor intensive goods.
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15 International Mobility of Labor and Capital
Without mobility of labor => high wages can persist is a labor scarce region.
If a country is driven to complete specialization BEFORE factor prices are equalized =>
need labor mobility to equalize relative factor prices.
Trade and factor mobility are close substitutes.
AFL-CIO supports immigration restrictions to raise wages. Also support protectionism.
If production patterns stay the same more labor immigrating => PL/PK . If the
production of the capital intensive good goes down, it is possible to release enough capital to
combine with the now more abundant labor to keep PL/PK fixed.
Assume Y = F(K, LABOR, LAND, TECHNOLOGY)
K includes education and training
LABOR = a(population) where a = labor force participation
rate
Y/C = output per capita
Y/C = F(K/LABOR, LAND/LABOR, TECHNOLOGY
(Y/C) / (K/LABOR) > 0
(Y/C) / (LAND/LABOR) > 0
(Y/C) / (TECHNOLOGY) > 0
It is in the interest of the US to let in highly educated and talented immigrants. Reverse brain
drain.
Most of the world's largest firms are multinationals. Direct investment of capital by Multi
National Corporations) MNC improves the world's allocation of capital. Owners of capital in
capital scare countries may not want foreign capital to come in since relative return on capital
will fall. Their position in society may change!!
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MNC adjust prices and move money to reduce taxes.
Source Country Issues:
- Return to labor goes down in country exporting capital.
- For tax reduction reasons, MNC may "over" export capital to reduce tax.
- Home country labor force feels export of capital => export of jobs.
- Source country may feel that in many cases host country pressures MNC to
distort trade flows.
Host country issues:
- Host country gains BUT does it get a fair deal? How controls this capital?
- MNC may improve host countries ability to export by developing a capability to
produce certain products.
- Host country may not get its "share" of research.
- Host countries often complain that MNC's change prices in order of avoid taxes.
Money can be moved from one country to another in "payment" of input goods.
- Host countries try to impose their laws on MNC that are under different laws.
- Developing countries, increasingly find it difficult to borrow funds. Have turned
to MNCs as a source of capital.
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16. Balance of Payments Accounting
CA
= current account
KA
= capital account
d(FXR)
= change in country's foreign exchange reserves
CA + KA
= d(FXR)
Under fixed exchange rates d(FXR) =/ 0
Under flexible exchange rates d(FXR) ~ 0.
Y = C + I + G +(X-M)
Y = C + Sp + T
I + (X-M) = Sp + (T-G)
I -(Sp + (T - G)) = M - X
T - G = Sg
St = Sp + Sg
=> I - St = M - X
=> Excess of investment over total savings = imports - exports
Assume a sharp decline in US total savings caused by large government budget deficits and
lower personal savings.
=> I > St implies that M > X
System will come into equilibrium at a higher interest rate. US investing more than it saves, a
capital inflow. Rest of world is the mirror image.
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17. Market for Foreign Exchange
XRr
= real effective exchange rate
XRn
= nominal effective exchange rate
Pd
= domestic price level
Prow
= price level for rest of world
XRr
= (XRn * Pd) / Prow
Purchasing power parity (PPP) => nominal exchange rates should move to just offset changes in
inflation.
Change notation to be specific
St
= dollar price of one unit of the foreign currency for delivery today
F
dollar price of one unit of the foreign currency for delivery in t+n
t+n t =
e
expected spot rate in period t for period t+n
t + nS t =
itd
=
90 day interest rate in domestic county
it f
=
90 day interest rate in foreign country
Be careful how the exchange rate is defined!!
Equilibrium Interest parity condition
t
St (1 itd ) t n Ft (1 it f )
Interest Parity Diagram shows parity condition graphically along diagonal line.
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Positions 1, 2 and 3 are outflows while positions 4, 5 and 6 are inflows. Along the parity line are
no flow points.
1 =>
2 =>
3 =>
4 =>
5 =>
6 =>
Define
making it on exchange
> loss on interest
making it on both exchange and interest
making it on interest
> loss on exchange
making it on exchange
> loss on interest
making it on both interest and exchange
making it on interest
> loss on exchange
t n
Ft * t St (1 itd ) /(1 it f )
Inflow condition
t
St (1 itd ) t n Ft (1 it f )
or
t n
Ft * t n Ft
Outflow condition
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International Trade Notes: 10 October 2016
t
St (1 itd ) t n Ft (1 it f )
or
t n
Ft * t n Ft
Outflow:
1. Buy foreign currency spot.
2. Buy foreign security.
3. Sell enough of foreign currency forward to bring back principle and interest in
period t+n.
4. In 90 days unwind forward contract.
Equilibrium spot speculation condition
t
St (1 itd ) t n Ste (1 it f )
Which can be written as
t n
Ft * t n Ste
Inflow condition
t
St (1 itd )
t n
Ste (1 it f )
or
t n
Ft *
t n
Ste
Outflow condition
t
St (1 itd ) t n Ste (1 it f )
or
t n
Ft *
t n
Ste
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International Trade Notes: 10 October 2016
Outflow:
1. Buy foreign currency spot.
2. Buy foreign security.
3. In 90 days bring funds home hopefully at a rate
t n
St n t n Ste
Forward speculation
Do nothing if
t n
Ft t n Ste
Sell forward if
t n
Ft
e
t n t
Buy forward if
t n
Ft
e
t n t
S
S
Define:
Ca t
= desired stock of forward contracts held by arbitragers in period t.
Cs t
= desired stock of forward contracts held by forward speculators in period t.
Cŝ t
= desired stock of domestic currency held by spot speculators in period t.
Ca t (t n Ft t n Ft * ) where 0
Cs t (t n Ft t n Ste ) where 0
Csˆ t Z (t n Ste t n Ft * ) where Z < 0
With no intervention
| Cat | | Cs t | and Ca t Cs t
|t n Ste t n Ft * | = return to spot speculation
|t n Ste t n Ft | = return to forward speculation
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|t n Ft t n Ft * | = return to arbitrage
Return to spot speculation = return to arbitrage plus return to forward speculation.
|t n Ste t n Ft * | = |t n Ft t n Ft * | + |t n Ste t n Ft |
Non intervention cases
t n
Ft *
t n
Ste t n Ft
t n
Ft
t n
Ste
t n Ft *
Intervention cases
t n
Ft* t n Ste
t n
Ft t n Ft*
t n
t n
Ft t n Ste
t n
t n
Ste
t n
t n
Ft
Ste
Ft*
Ft*t n Ft
See Stokes (1973 figures 1 and 2)
Define dMd = new flow of money to the domestic country due to forward intervention, then
(dropping subscripts)
dMd = dF[( Se/ F)Z + ] where
dMd = dI[( Se/ I)Z + 1] where
and I = the dollar amount of forward contracts of the foreign currency sold by the central bank.
The key problem is the sign of Se/ F.
If Se/ F < 0 => central bank causes F to fall but the market believes that the attempt will fail
and as a result Se rises.
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Tension index based on hypothesis that not all values for
tn
Ft
tn
Ft* imply the same degree
of tension in the market. Weighing each market as wi for n countries the weighted tension index
t is defined as
t i 1 wi [[(iti itd ) /(1 iti )]2 [( Fi t Si t ) / Si t ]2 ].5 / n
n
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18. Impact of trade on determination of National Income
Under assumptions of fixed exchange rate the business cycles of major trading partners
tend to be linked.
=> Recession in UK causes less demand for US goods which in turn shows US
production.
=> Small countries do not export business cycles.
=> During Vietnam war US inflation caused an outflow of money from the US.
causing world wide inflation.
=> If Canada knows the US is moving into recession, it can adopt an expansionary
fiscal policy.
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19. Alternative Models of Balance of Payments or Exchange Rate Determination
- Under fixed exchange rates a balance of payments deficit => loss of reserves.
- If M > X => a recessionary factor. Loss of competitiveness.
- Balance of payments deficit for US => stock of US dollars builds up outside country.
US central bank forced to sell foreign currency for US dollars. => reduction is US money supply.
- Trade surplus => expansionary effects.
- In the 60' and 70' the US sterilized US deficits. => no domestic effects of the deficit. =>
caused the world to bear burden of adjustment.
Keynesian View of balance of payments
BOT = Px* Qx - Pm* Qm
Q m = F(Yd, XR r) Qm/ Yd > 0, Q m / (XR r ) > 0
XR r = foreign price of domestic money. UK def
Qx = F(Yf, XRr) Q f / Yf > 0, Q f / (XR f ) < 0
BOT = Px * F(Yf, XR r) - Pm* F(Yd, XR r)
+ - - + BOT = F(Px, Pm,Yd, Yf, XRr)
KA
= capital account
+ - - +
= F(rd, rf, riskd, riskf)
+ - - + - + - - +
BOP = F(Px, Pm, Yd, Yf, XRr, rd, rf, risk d, risk f)
Monetarist Approach to balance of payments
- Excess money creation drives down domestic interest rate => BOP deficit =>
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money flows out to adjust system.
- In recent years velocity has been changing up, then down. => hard to determine
the appropriate increase in money supply.
- Figure 13-2 shows US dollar appreciation in period 80-85 due to tight US
monetary policy. The exchange rate also appreciated in the period 95-2000, After 2000 US
growth and government deficits together with lower foreign growth causes the effective
exchange rate to depreciate.
In a world of flexible exchange rates speculative flows of money have a large impact.
Economists have not been able to effectively model these flows.
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20. Balance of Payments adjustment with fixed exchange rates
Hume "Specie flow mechanism"
=> Money linked to gold. Deficit => money flows out increasing domestic
interest rate, and lowering domestic prices, reduces domestic income.
=>Sets into motion corrective forces that will adjust system.
Need IS/LM/BB analysis to under stand what happens.
IS Curve => locus of points where S=I
LM Curve => locus of points where Money Demand = money supply
BB Curve => locus of points where BOP=0
IS curve goes from upper left to lower right. See fig 16-1.
Assumptions: I/ r < 0, S/ Y > 0
Points to right (left) or IS are points of excess supply or S > I. (excess demand or S < I).
Assume any point on r, Y axis. Move right. Here Y up => S up. Since r = fixed then S > I.
In order to increase I, need to move down. As r falls I increases.
The more sensitive investment is to interest rates, the flatter the IS. IS curve drawn on Y r
axis where r is real interest rate.
LM curve goes from lower left to upper right. Figure 16-2. Points to right (left) are points of
excess demand (supply).
Assumptions Ms = m1 + m2 where
m1 = transactions demand for money,
m2 = speculative demand for money
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m1 / Y > 0, m2 / r < 0
The more sensitive the speculative demand for money is to interest rates the flatter the
LM. The less sensitive the transactions demand to income the flatter the LM.
Ms up => LM to right.
P up
=> LM to left.
BB curve goes from lower left to upper right. See figure 16-6. Assert a point. Move right. => Y
up causes BOP < 0. r must increase to attract capital into country.
The more sensitive capital flows are to changes in r the flatter the BB.
The less sensitive the BOP to changes in Y the flatter the BB.
If the dollar price of the foreign currency goes up => BB moves right.
Figures 16-3 shows closed economy equilibrium where IS=LM. We assume away
problem that IS a function of real interest rate r and LM is function of nominal interest rate i. If
we were to assume
r (P)e / P i
then Mundell draws GG such that difference between IS and GG is (P)e / P . If this world
equilibrium is where LM = GG.
Figure 16-4 shows effect of fiscal policy.
Figure 16-5 shows effect of monetary policy.
Both curves assume Y is below full employment. If Y is at full employment fiscal policy will
move IS right. Prices will increase and LM will move left resulting is same level of income but
higher interest rates.
Figure 16-7 shows open economy equilibrium where BB, IS and LM intersect.
Figure 16-8 shows domestic equilibrium at A but at a BOP deficit since are to right of
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BB.
Figure 16-9 shows money flowing out of country causing LM to move left to equilibrium.
Figure 16-10 shows Brenton Woods adjustment. Here central bank moves LM by
reducing money supply. After adjustment Y down , r up.
Figure 16-11 shows fiscal policy being used to adjust system. Here after adjustment Y
down and r down.
Mundell "Principle of Effective Market Classification" => use the instrument that is most
effective in adjusting the system.
Figure 16-12 shows that if LM is flatter than BB = > use monetary policy rather than
fiscal policy since there will be less of a loss of income. A steep BB curve => BOP not sensitive
to changes in interest rates.
Figure 16-13 shows that if LM is steeper than BB => use fiscal policy to adjust a deficit
since here need to move IS right not left as in case of figure 16-12. A flat BB => the BOP
payments sensitive to interest rate changes!
Figure 16-14 shows Mundell diagram. y axis is government surplus. On horizontal axis is
interest rate.
- Along FF have balance of payments equilibrium. To left (right) have deficit
(surplus).
- Along DD have domestic equilibrium. To left (right) of DD have recession
(inflation).
Slopes of FF and DD represent relative impacts of monetary and fiscal policy on
equilibrium. Note that fiscal policy is relatively strong at achieving domestic balance and
monetary policy is relatively effective at achieving BOP equilibrium.
Figure 16-15 Shows how if fiscal policy (monetary policy) is used on the BOP (domestic
balance), system moves away from equilibrium.
Figure 16-16 shows Reagan policy. Tight money to help BOP, expansionary fiscal policy
to help obtain domestic balance.
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21. Balance of Payments Adjustment through exchange rate changes
Marshall-Lerner Case. We have assumed that if the domestic price of one unit of the foreign
currency goes up, then exports up, imports go down and the BOP improves. This is exchange
stability and forms the basis of the Mundell Equation.
If the demand for imports and exports is inelastic => as foreign prices go up will buy less
but spend more. On export side as price fall exports increase but prices fall faster.
Figure 17-3 shows a small country facing a horizontal supply curve. Devaluation shifts up
supply curve. On import side elasticity = │1│. Demand curve for exports is vertical. Devaluation
has no effect.
Figure 17-4 shows case where D for exports is not completely inelastic. Here devaluation
helps since demand for imports is │1│ and demand for exports is not 0.
Figure 17-5 same as figure 17-3 except on import side elasticity < │1│.
Figure 17-6 shows small country case. Devaluation will improve BOP.
Figure 17-7 shows country with no power as an importer but some power as an exported.
Devaluation will help.
Figure 17-8 shows that a devaluation moves BB right and IS up. IS moves up since
because prices of imports have risen, demand for domestic production will increase.
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22. The theory of flexible exchange rates
Figure 18-10 shows a monetary expansion with fixed exchange rates. The resulting initial
fall in interest rates causes money to flow out of the country. LM shifts back. Monetary policy
will not work with fixed exchange rates if there is capital mobility.
Figure 18-11 shows effect of fiscal policy expansion with perfect capital mobility and
fixed exchange rates. Here IS shifts and increases interest rates. The capital inflow increases the
money supply and the LM drops.
Figure 18-12 shows effect of not complete capital mobility (BB is still flatter that LM)..
Here BB has a positive slope. Fiscal policy is still strong but interest rates have risen.
In Figure 18-13 still less capital mobility. Here BB steeper than LM. Here if IS shifts right
there is a balance of payments deficit since we are to the right of the BB. This causes money to
leave the country and the LM curve shifts up. Fiscal policy is not powerful here.
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23. International Monetary Experience 1880-1940
- Reasons that gold flows were not large under the gold standard were:
- The mint par exchange rate was $4.866 = L-1.00. The cost of shipping was $.026
per pound sterling equivalent. This implies that the gold points were $4.866 + .026. When the
spot exchange moved toward gold export point for UK of $4.84 = -l 1, US traders regarded the
pound as cheap and bought pounds. Since the market knew that the dollar price of the pound
could only stay the same or go up, they made capital flows into the UK in the hope that the
exchange rate would rise. These flows bid of the rate and did not require gold flows to adjust the
system.
- Central banks moved interest rates to limit flows.
- Capital flows were sensitive and moved in a equilibrating direction as discussed
above.
- The gold standard required flexibility of wages and prices and tolerance for
swings income and employment.
- World merchandise exports tripled from 1876-1880 to 1911-1913.
- Gold standard discipline. Any nations ability to expand its money supply is limited by
its balance of payments position. If M increases too much, the country will lose gold and cause a
internal deflation. The total money stock of the world is linked to gold discoveries. => a tendency
for world wide deflation. Gold discoveries (California 1949 and South Africa 1890) were
unrelated to need. This is the main weakness of the Gold Standard.
- Some concerns:
- Relatively satisfactory performance of the world economy in the pre 1914 period may be
due to factors other than the gold standard. In a period of high growth a country with a balance of
payments problem might just grow a little slower. In a static world such an adjustment would me
much harder.
- The gold standard worked much better in the central countries of Europe than in the
developing countries where the gold standard tended to exaggerate the swings in the economy. In
a boom the UK made capital exports to developing countries and bought raw materials.
Developing countries gained by both. In less good times, capital flows fell and in addition the
price of the export goods fell. This hurt the developing country on two fronts.
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- The large capital flows did lessen the need to make adjustments in wages and prices
since the capital flows were in the equilibrating direction.
- Many of the central bank "did not play by the rules." They intervened in blocking gold
shipments and did not always let the gold flows influence central bank discount rates.
- While the supply of gold was linked to money supplies, many countries had paper
currency. Triffin estimated that 90% of the increase in the money supplies in the period 18731913 were from paper money.
- During WWI the gold standard ceased to exist. This implied that the linkage of the
economies was no longer there. The debtor nation (US) came out of the war a creditor nation.
These changes made starting over again in 1918 difficult.
- The period 1919 to 1926 was a period of fluctuating exchange rates as many countries
delayed their return to the discipline of the gold standard. Key question what parity rates should
be set?
- When the war time pound peg was removed in 1919, the pound fell to $3.81. In 1920
inflation drove is still further down to $3.38. The UK government decided to reduce wages and
prices in the UK. => tight money (high interest rates) high taxes. BUT wages and prices were not
as flexible as anticipated. The UK fought is way back to the prewar parity but at a high cost in
terms of lost growth and high unemployment. Unions resisted wage cuts. The UK faced growing
competition in its basic export industries and needed to develop new export goods.
- The United States in the 20's had a balance of payments surplus. Under the rules this
would => US prices would increase but the Federal Reserve attempted to sterilize these flows by
selling bonds. This action shifted the burden of adjustment on the UK. The United States showed
that it was unable to allow foreign determination of domestic economic variables.
- In April 1925 Churchill, the Chancellor of the Exchequer, returned the UK to the prewar
parity rate and announced that the UK would again redeem its notes in gold and allow gold to
freely flow. Speculators anticipating this even had been moving funds in to the UK. After the
announcement, these funds moved out of the country. The UK still had to maintain deflationary
pressure to hold the rate. Keynes attached this policy arguing that the UK not allow "the tides of
gold to play what tricks they like with the internal price level." Keynes wanted a managed paper
standard. "The gold standard is already a barbarous relic... advocates of the ancient standard do
not observe how remote it is from the spirit and requirement of the age. A well regulated nonmetallic standard has slipped in unnoticed..."
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International Trade Notes: 10 October 2016
- France was more economically hurt by WWI than the UK. In 1919 the Franc was
floating and lost 50% of its value going from $.183 to $.092 in the period March to December,
well below its prewar rate of $.193. The French government did not have sufficient taxes and
hoped German reparations would pay. As French prices increased due to the deficit, the Franc
fell still further. Changes in the exchange rate fed expectations and the domestic price level was
driven up. The Franc fell to $0.035 in March 1924. A conservative government led by Poincare
borrowed from J. P. Morgan and bit up the Franc to $0.065 in April 1994, but was driven from
office in May 1924. In the next 2 years there were 6 changes in the government. In 1926 a wave
of selling hit the Franc as it fell to $0.0205 partially in response the German problems with
hyperinflation. Poincare came back into power and stabilized the Franc at $0.0392 as France
offered to buy and sell Francs to maintain that rate. France was effectively no longer on a flexible
exchange rate system. As a result of the stabilization policy confidence was restored and capital
flowed back to France.
- The UK which chose to maintain their fixed exchange rate system suffered recession
and hardship, while in France there was full employment. => UK citizens saw the costs in
maintaining a fixed exchange rate system. France, Belgium and Italy saw the costs on inflation.
Figure 19-3 shows the exchange rate in the UK while figure 19-5 shows what happened in
France. Figure 19-7 shows countries struggling back on to then off the gold standard.
- Problems of going back on the gold standard:
- Countries had difficulty setting the appropriate exchange rate. It was too high
=> needed recession to maintain it. If it was too low = surplus.
- There was concern regarding whether there was enough gold being discovered.
To save on gold countries encouraged to hold L- and $ which in turn were pegged to gold.
- Many countries were reluctant to play by the rules of the gold standard. Surplus
countries fearing inflation neutralized gold inflows so prices would not increase. Deficit
countries attempted to avoid the deflation consequences of gold outflows. Changes in social
attitudes made the price system less flexible.
- In 1928 France prohibited the central bank from issuing the Franc backed by
anything but gold. This action caused problems for the gold exchange standard since whenever
France had a surplus, it demanded gold. French gold reserves rose in 1929, 1930 and 1931.
- In 1931 growing depression led to "hot" money flows. In September 1931 after
a near naval mutiny, the UK went off gold. The UK government had no stomach for another dose
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of classical medicine. The restored gold standard failed because nations were never able to
reestablish the closely knit, highly integrated world economy that had evolved in the prewar
period. Countries rejected interdependence and sough in various ways to go it alone.
- In the 30's countries attempted to manage the float. Some countries tried to peg
their currencies to the pound (Sterling Area) others resorted to various exchange controls. In the
US wholesale prices fell 30% and 23% of the work force was out of work as national income fell
45% and exports fell 38%. In the US FDR wanted to raise prices. This was done by raising the
price of gold from $20.67 to $35.00. FDR imposed an embargo on gold exports (taking the US
off gold) and required all private gold to be turned in (prior to the price of gold being raised).
(This was repealed in 1974). This action abrogated "gold clauses" in contracts. The effect was a
huge gold inflow in to the US and miners found and sold gold to the US treasury. Figure 19-9
shows how this caused the gold price of the pound to increase helping US exports and limiting
US imports.
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International Trade Notes: 10 October 2016
24 The International Monetary System 1945-1973
- At the 1944 Bretton Woods conference the IMF was setup to help maintain an exchange
rate system (1945-1973). Goals of the IMF were to 1. Provide an orderly method of regulation of
exchange rates, 2. Provide a supplementary supply of international reserves, 3. Provide a
mechanism for the adjustment of balance of payments disturbances. All these goals impacted on
national sovereignty and autonomy.
- Each member pegs its currency to the US dollar.
- Each member agreed to keep its spot rate within +
_ 1% of par. => the countries central
bank had to stand ready to intervene.
- The IMF provided a mechanism by which exchange rates could be changed. Wanted the
advan
did not have to be put in the situation of having to deflate internally as the UK had to do when it
went back on gold.
- While exchange controls were outlawed under article VIII, article XIV allowed a
"transition period" that has expended for many years.
- Adjustment problems In the prewar period deficit countries had to take action at once
while surplus countries could wait. Under the IMF scarce currency provision a currency can be
declared scarce (from a surplus country) giving other countries the right to adopt discriminatory
provisions. => force adjustment costs on both surplus and deficit countries.
- In period 1945-1958 there was a dollar shortage as the US ran balance of payments
surplus. The US gave $30 billion to Europe alone under the Marshall plan. By 1958 the US was
running a deficit. In 1949 the Pound was depreciated 30% from $4.03 to $2.80.
- After 1958 there was a dollar surplus. Figure 20-1 shows Japanese yen, French franc,
Italian lira and Swiss franc.
- The need for an international money led to the rise of the Eurocurrency market.
This was essentially unregulated banking since there was no formal reserve requirement. The
only thing stopping the expansion is if Eurodollars are placed in an American bank which would
trade them into the US currency, the "reserve" base of the Eurodollar.
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International Trade Notes: 10 October 2016
- Reasons for Eurodollar Market
- Until the mid 60's regulation Q limited the amount American banks could pay on time
deposits to 4%. Eurobanks not subject to this law could pay more than 4%.
- In the 60' LBJ imposed a tax on foreign bond issues in New York and placed restrictions
on loans to foreigners by U. S. banks. => US firms needing money in Europe borrowed from the
Eurodollar market.
- Nations with exchange controls and legal restrictions on their citizens moved into the
Eurodollar market.
- US banks were required to maintain reserves in the US which they did not get interest
on. => US banks had an incentive to move to Eurodollar market.
- The Eurocurrency market played a major role in financing the Oil shock of the 70's.
Many countries made a major mistake in borrowing long term for oil => a large buildup of debt.
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International Trade Notes: 10 October 2016
25 International Monetary Relations 1973 - Present
- US dollar float was relative stable in the period 75-76. In 1977 a new US secretary of
the treasury stated that he thought the dollar was too strong and that it should float down. This
statement led to the US dollar floating down. Higher US inflation in 1978 made matters worse.
Paul Volcker became the newly appointed chairman of the Federal Reserve Board and started
tightening US monetary policy. Starting in 1981, capital began to flow into the United States and
the dollar appreciated 40%. => a disastrous decline in the cost and price competitiveness of US
firms operating in international markets.
- The US dollar appreciated because of tight money and high US interest rates due to
sales of government bonds to finance the tax cut. During Don Reagan the dollar floated relatively
cleanly while under Baker there was more US intervention to lower the value of the dollar.
- The historical record under the flexible exchange rate period shows more volatility than
was initially expected. Large "hot" capital flows are certainly part of the problem. The possibility
of a "dual rate system" where trade had one exchange rate and capital had a freely floating rate
would be easily circumvented since invoicing could be adjusted to move capital.
- A return to the gold standard puts the world at the mercy of gold production in South
African and Russia.
- Key lesson. Open economies cannot escape some degree of vulnerability to
macroeconomic shocks that originate abroad and policy independence will always be partially
constrained by balance of payments or exchange rate considerations. Economic isolation has
great costs!!
- Europe has attempted to limit the degree of fluctuation across countries.
i:j = i price of one unit of j's currency.
[A:B] = [A:C]*[C:B]
[$:M]
= [$:L-][L-:K][K:E][E:M]
- European Monetary system has a new currency (European Currency Unit or ECU) made
up of a basket of currencies. Goal is for the ECU to replace national currencies. Problems might
occur if one section of the European Monetary system wanted more inflation than another
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International Trade Notes: 10 October 2016
section. Mundell argued for optimum currency areas.
- In 1976 the SDR which was once linked to the gold content of the US dollar became
equal to a basket of currencies. .5720 US dollar, .4530 Deutsche mark, .8000 French franc,
31.8000 4. Japanese yen, .0812 Pound sterling.
- The Latin American debt crisis continues to be a problem. While most debtor countries
were able to make interest payments in the 70'2, this was not the case in the 80's when defaults
threatened US banks.
- The disintegration of the Soviet bloc remains a problem. How are these countries to be
integrated into the world financial system? Will the US continue to play a major international
role or will it retreat into isolationism? How interested will the US be in the third world countries
now the cold war is over?
Can we explain exchange rate movements? See page 469. No one theory will explain
everything.
Purchasing Power Parity clearly works for hyper inflations but is not the whole story.
Interest Rate Parity almost never holds. This suggests the AA curve is not flat! If the SS curve
was flat is would suggest that S e F or that the forward rate is an unbiased predictor of the spot
rate. A flat SS curve and flat AA curve is not possible at one time.
Monetarist Models argue that the exchange rates depreciate if the domestic money supply
increases and appreciates in response to an increase in total output. Dornbusch in the 80's argued
that this is not a complete answer either.
Changes in exchange rates can impact certain sectors more than other sectors. The EU
tries to correct for this.
See page 489-491 for a list of pressing problems.
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