Download 1 Economic way of thinking

1
Economic way of thinking
• CMD, Lagos 22-26 Nov 2010
• Monday: The economic way of thinking, basic tools of economic analysis: Reading Chapter 1-3
• Tuesday: NIPA, SAMs Reading: Chapters 5
• Wed: Growth models Reading: Chapter 6,7
• Thursday: Short-run equilibrium models. Reading: 8-10
• Friday: Computable models: Reading: Chapter 12,19
• We will find a way to have fun learning this material!
1.1
Schedule
• 8:00-9:00 am Free discussion, Q&A
• 9:00-11:00 am Class presentation
• 11:00-11:30 Coffee break
• 11:30-1:00 am Class presentation
• 1:00-1:30 Q&A Evals
• 1:30-2:30 pm Lunch discussion
• 2:30-5:00 Lab practicum
• Questions during class presentation are encouraged!
• Specialization and trade is how society become well off
• Proper incentives are necessary for good outcomes
• Good Institutions align self and social interest
• Trade-offs must be evaluated at the margin in terms of opportunity costs
• Laws of Supply and Demand are difficult to repeal
• Root cause of inflation is government deficit
• Once we start thinking of economic growth it is hard to think about anything else
• Applying these ideas can be rewarding!
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1.2
1.3
The father of modern economics
Wealth of Nations and Economic Growth
Everyone used2. to
be poor
Everyone
Used to Be Poor
1.4
Why are we no longer as poor...
!"#$%&'&()&*'&
• Why don’t we still live in trees or caves?
• Why is the average life span of a human being more than 25 yrs?
• All of our families “escaped” poverty as some point.
• Industrial Revolution beginning in England around 1750, started it all.
• Brad Delong estimates per capital income for last million years at just more than $124. Very low; less
than a dollar a day.
• Life is better in Lagos! Why is this?
1.5
Adam Smith: Specialization and trade
• ...is why do we not still live in caves!
2
1.6
Specialization and trade
• Cave painting by Cro-Magnon man in Lascaux, France
1.7
Smith Earns 20£ of Fame
• Adam Smith will replace composer Edward Elgar on the twenty-pound note next spring
• Awkward, absent-minded and had no head for business, according to his obituary in The Times.
• Kidnapped by gypsies, never married, lived with his mother
• Died in 1790, having lived out his days as a quiet Customs official
• Adam Smith widely recognized as the father of modern economics
Example Who was the first Scotsman to appear on a Bank of England note?
• Answer: Adam Smith is the first!
3
1.8
Pin Factory
1.9
Smith on Self-interest
• It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but
from their regard to their own interest.” The Wealth of Nations
• Preferences are not defined over the preferences of other agents
• There is no utility function for firms
• Nor for government
• Only for consumers
Example Why do firms and governments exist in economic theory?
• Answer: To serve consumers!
1.10
Taking Prisoners to Australia
1.11
Incentives
• English ship captains paid to transport prisoners to the fatal shore
• Paid per head by British govt...given rations of food
4
• Incentive: starve the convicts to death and sell their rations
• British changed their incentive system
• Captains paid per delivered prisoners
• Did the change in the incentive structure make any difference?
• Death rate fall from over 33% to less than 1%
1.12
Competition makes self interest work!
Competition forces telcos to reduce tariff on data service
–Internet users in for good times (19 Nov 2010)
by Ben Uzor Jr.
Going by the increasing number of undersea cables, both finance and market watchers say the nation’s highly
competitive telecommunications market appears poised for a tariff war. Speaking...
1.13
Skepticism about markets and free trade
• Samuelson Free-Trade only true and nontrivial insight economists have to offer
• Wealth of nations derives from specialization and trade
• LDCs specialization in relatively labor-intensive branches of production
• Marxists, following Lenin, believed that foreign trade provided vent for surplus
• Neoclassicals: gains from trade nonnegative and growth comes from and k and technology
ExampleHow does trade stimulate savings and investment?
• Specialization encourages application of capital
1.14
A chicken and egg story
• Average chicken in US produces 300 eggs per month
• In Mexico the number is 30...why such a difference?
• No incentive to apply capital.
• Opportunity cost of labor is low
• Wages should be low to reflect low opportunity cost
• Otherwise...those willing to work will not be able to.
ExampleWhy does a barber in Lagos earn so much less than a barber in NYC?
• Answer: Productivity? Capital? Opportunity costs?
5
1.15
Opportunity costs
• Opportunity cost is only true cost
• Applies to everything
• How much of one thing must be given up to get another
• Goods priced below their opportunity costs are usually wasted!
• Values are determined in markets and markets only
Example Is a free lunch ever a good idea?
• Answer: No some people will just waste the food...
1.16
Fundamental theorem of economics
• Free markets efficiently allocate scarce resources
• Efficiency defined by the Pareto principle
• No one can be made better off without someone becoming worse off
• A basic tenet “if an individual thinks he or she is better then he or she is better off.”
• The economic way of thinking is stylized, and not for everyone
• Often criticized as having a libertarian bias
• Also criticized by behavioral economists as unrealistic
ExampleIf the economic way of thinking is so bad, why do we use it?
• Answer: To build tractable mathematical models to undertake policy experiments
1.17
Economic theory
• All economic well being must be resolved at the level of the individual
• Many policies hurt some individuals and help others; these are not Pareto optimal
• However, compensation is possible
• We allow side payments to those who are hurt
• Who makes these payments? Those who gain
Example Show that theft is not Pareto optimal
• Answer: Thief cannot compensate the victim and still be better off. Hence theft is not Pareto optimal, even
if the thief is poor and deserving
1.18
At what margin?
• Margin means “extra” or “additional”
• Some politicians want mandatory executions for drug dealers. . .
• At the margin the incentive to murder the arresting police offer increased
• Booksellers on Amazon were upset when Amazon allowed used copies to be sold along side of the new ones
• This simply caused marginal cost to buyers to be reduced
ExampleWhat happened then?
• Answer: Amazon sold, predictably, more books!
6
1.19
Supply and Demand
• Government cannot repeal these laws easily
• Always unintended consequences
• PL 480: give away food...drove African farmers out of business
• Rent control results in fewer available apartments
• “Cheap food”, minimum wages, untargetted public assistance...all bad
• Distort market signals and lead to bad allocation of resources
ExampleIf government should not alter market prices, how should the poor be helped?
• Answer: Through lump-sum transfers that do not disturb decisions at the margin.
1.20
Growth
1.21
Rich and poor countries
• Lack of proper incentives
• High fertility and rapid population growth
• Lack of institutions that provide incentives to economic growth
• Govt bureaucracy, corruption and interference (red tape)
• Chiefs, priests and thieves–all get by on transfers
Example Are import licenses ever a good idea?
• Answer: No...policymakers cannot know what is best for individuals. Alka Seltzer: bourgeois remedy or rural
necessity?
7
1.22
Economics takes a dim view of chiefs, priests and theives
1.23
The best and worst
Example In which country would a person face a lower opportunity cost for holding cash? Zimbabwe or
Nigeria?
• Answer: Nigeria by far.
8
1.24
Demand
1.25
Demand curve: x = αB/p
1.26
Demand and Supply
1.27
Demand curve: x = αB/p
• Can be read in two ways:
• Horizontally: How much buyers are willing and able to purchase at a given price.
• Vertically: The maximum price for which buyers are willing to pay for a given quantity.
• Key to demand: substitution
• As price rises consumers substitute other goods
Example α = 0.4, B = 200, price, p = 25, quantity demanded is
• Answer: q = (0.4)200/25 = 3.2
9
Consuming Nations 2008
United States
China
Japan
India
Russia
Germany
Brazil
Saudi Arabia
Mexico
France
Iran
1.28
Consumption
(1000 b/day)
population
millions
bbl/year
per capita
19,497.95
7,831.00
4,784.85
2,962.00
2,916.00
2,569.28
2,485.00
2,376.00
2,128.46
1,986.26
1,741.00
314
1345
127
1198
140
82
193
25
109
62
74
22.6
2.1
13.7
0.9
7.6
11.4
4.7
33.7
7.1
11.6
8.6
Where does demand come from?
• Utility maximization subject to a budget constraint
• Rational consumers will choose this combination
• Tastes and preferences are subjective and will vary among consumers
• Expectation of a higher price for a good in the future increases current demand for the good.
• Social welfare measured by the consumers themselves
• Utility fundamental in economics
Example In a two-good world U = xα y 1−α
1.29
Utility
• The α is the preference parameter and can be shown to be equal to the share of the budget the consumer will
spend on the first good.
• By definition, the rest of the budget is spent on the second good.
• Marginal utility is the change in total utility as one good increases while holding the other good constant.
Example In a two-good world α = 0.4, B = 200, price, p = 25, total utility is
• Answer: (3.20.4 )(1200.6 ) = 28.16
1.30
Economic theory of markets
• Simplest example of a prisoner of war camp
• Nazis have Allied prisoners and given them a ration of one pack of cigarettes and one chocolate each day
• The way we tell if an individual i is better off or not is to define a utility function. A simple example is the
square-root function
√
Example Let U = xy where x is chocolate and y is cigarettes. Let x = 8 and y = 88. What is utility?
p
√
• Answer: U = 8(88) = 144 = 12
10
1.31
Consumers’ Problem
• Budget constraint
• Indifference curve
• Rationality: marginal utility per dollar same for all goods
• Geometically: tangency condition
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• Slope of the of indifference curve
•
•
1.32
The slope of an indifference curve
Show@8a, b, c, d, e, f, g, g1, h<D
y
4
x0 , y0
3
2
Indifference curve
x1 , y1
1
1
1.33
U=
√
2
xy → indifference:Ū =
√
3
xy
• Take two points on the difference curve U0 and U1 subtract and square
U12 = U02 = x1 y1 − x0 y0 = 0
• Add and subtract x0 y1 to get
0 = x1 y1 + [x0 y1 − x0 y1 ] − x0 y0
• or:
0 = (x1 − x0 )y1 + (y1 − y0 )x0
• Rearranging terms
−(x1 − x0 )y1 = (y1 − y0)x0
1.34
U=
√
xy → indifference:Ū =
√
xy
• Rearranging terms
−(x1 − x0 )y1 = (y1 − y0)x0
• Now divide by x1 − x0 = ∆x
• So that
∆y
= −y1 /x0
∆x
11
4
x
• As x1 → x0 , y1 → y0
• We have
1.35
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dx
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The slope of anShow@8a,
indifference
curve
b, c, d, e, f, g, g1, h<D
y
4
x0 , y0
3
2
Indifference curve
x1 , y1
1
1
1.36
2
3
4
x
The budget constraint
• Equation is linear B = px x + py y
• First say px /py = p
• So then B = px + y
• Next put the budget constraint in standard slope-intecept form.
• Here the slope is −p and the intercept is B
• We then have
y = −px + B
1.37
Tangency condition
• To get the highest utility, the consumer must be
• In the feasible region of the budget constraint
• On an indifference curve that is tangent to the budget constraint
• Any non-tangent indifference curve will give lower utility
• Budget constraint defines the feasible choice and tangency condition defines the optimal choice
• Tangency condition: p = y/x
1.38
To summarize
• Taking budget and relative prices as given...
• Consumer chooses goods to maximize utility
• The tangency condition means consumer will set marginal rate of substitution = relative price of good 1 in
terms of good Example Is there an easy way to see the tangency condition?
• Answer: Same as saying that marginal utility divided by price is same for every good
12
1.39
Marginal utility of good x
• Change in utility with respect to increase of a unit of good x, holding the consumption of good y constant
• Marginal utility is same as marginal benefit
• Marginal utility always declines.
Example When someone buys a good at price p what do we know about his marginal utility of that good?
• Answer: It must be at least as great as the marginal utility of buying any other good at its given price!
1.40
Square roots not for everyone
• Economic agents don’t have identical preferences
• Must introduce a more general utility function to capture this
• The Cobb Douglas is the most general form of utility studied in these lectures and is written
U = xα y 1−α
• The α is the preference parameter
• Its equal to the share of the budget the consumer will spend on the first good.
• The rest of the budget is spent on the second good.
• The square root is a special case of the CD with α = 0.5
1.41
Tangency condition for CD utility function
• For the utility function
U = xα y 1−α
• The tangency condition is given as
p=
α y
1−αx
• Determined as a simple calculus problem
Example What if α = 0.5?
• Answer: We have the square root utility tangency condition
1.42
Deriving the demand curves
• Solve simultaneously
y = −px + B
α y
p=
1−αx
• First write the tangency condition as
(1 − α)px = αy
• And then substitute in the budget constraint for y
(1 − α)px = α(−px + B)
• Simplify to get
x=
αB
p
y = (1 − α)B
13
1.43
Deriving the demand curve
• General form of the demand equation is “share of income times the budget divided by price”
• If the price of the second good can be equal to one the budget B must be defined in terms of the that good!
• Utility is then found by substituting the demand functions into the utility function
U =(
1.44
α
αB α
) [(1 − α)B](1−α) = ( )α (1 − α)(1−α) B
p
p
Consumer’s problem
y
7
6
Indifference
5
4
Solution x = 4.2, y = 2.4
3
2
1
Budget constraint
2
1.45
4
6
8
10
x
Challenge
Example
• Price of good 1 = 3 price of good 2 = 4
• Budget is 12
• Utility is square root
• Solve for demand for both goods and total utility
• Answer: x = (1/2)12/3 = 2, y = (1/2)(12)/4 = 3/2, U =
1.46
√
3
Challenge 2
Example
• Price of good 1 = 3 price of good 2 = 4
• Budget is 12
• Utility is CD with α = 0.2
• Solve for demand for both goods and total utility with p = 3/4
• Answer: x = (1/5)(12/4)/(3/4) = 4/5, y = (4/5)(12/4) = 12/5, U = (4/5)1/5 (12/5)4/5 = 1.93
14
1.47
Supply
1.48
Supply
• Why is the supply curve upward sloping?
• The cost of producing a good is not equal across all suppliers
• Low price, a good is produced and sold only by the lowest cost suppliers
• High price, a good is also produced and sold by higher cost suppliers
• Crossing price is where new technology is adopted
Example How are rising supply curves consistent with constant returns to scale technology?
• Answer: Factor prices rise (they are take as given on a supply curve)
1.49
Supply
• Supply curves can be read in two ways
• Horizontally: How much suppliers are willing and able to sell at a given price
• Vertically: The minimum price for which suppliers are willing to sell a given quantity
Example Will producers ever take accept a price that is lower than the price on the supply curve?
• Answer:
Yes...profits are maximized over time so that if a loss now leads to higher sales later, rational
producers will sell at a loss today
1.50
Producers’ Problem
• Taking factor prices and quantity demanded as given
• Maximize profits by finding the right capital-labor ratio
15
• Production function is same mathematical form as utility x = Lβ K (1−β)
• Budget constraint becomes isocost function C = wL + rK
• w is the wage rate,L is the labor demand, r cost of capital and K is demand for capital
β
K/L
1−β
• Solve problem in same way: tangency condition:
1.51
= w/r
Producers’ problem
K
7
6
Expansion path
Isoquant
5
More capital intensive
4
3
Less capital intensive
2
1
Isocost curve
2
1.52
4
6
8
10
L
Marginal productivity conditions
• Instead of demand for goods we have the factor demand equations
rK = (1 − β)px
wl = βpx
• Also known as the marginal productivity conditions
Example If the value of output is 10 and the real wage rate is 2 and the cost of capital is 1/5, what is demand
for labor and the demand for capital? The share of labor is 2/5.
• Answer: L = (2/5)(10)/2 = 2, K = (3/5)(10)/(1/5) = 30.
1.53
As price of energy rise
Other inputs
7
Less energy intensive
6
5
More energy intensive
4
3
Isoquant
2
1
Isocost
2
4
6
16
8
10
Energy
Table 1: Regional Oil Costs
Saudi Arabia $2 per bbl
Nigeria
Russia
Alaska
North Sea
US
Canada (shale)
$5 per bbl
$7 per bbl
$10 per bbl
$12 per bbl
$22.5 per bbl
$33 per bbl
Source: Cowan and Tabarrock
1.54
Substitution in production
Other inputs
7
Less energy intensive
6
5
More energy intensive
4
3
Isoquant
2
1
Isocost
2
1.55
4
6
Market supply curve
• Made up of individual supply curves summed horizontally
1.56
Six oil shocks
17
8
10
Energy
1.57
Elasticity
• Economists use elasticity to avoid having to deal with units
• Also good for how growth rates affect each other
• Similar to a derivative...only in percent terms
• Elasticity is just percent change of the dependent variable with respect to the percent change in the independent
variable.
dY /Y
Y X =
dX/X
1.58
Example
Example As the expression for some economic quantity, demand, supply or really anything else
Y = mX + b
Calculate the elasticity of Y with respect to X.
• Answer: Compute
Y X =
1.59
dY X
= mX/Y
dX Y
Elasticity of a straight line
• Is not constant unless it goes through the origin
• If intercept is positive, then X increases more slowly than Y
• Elasticity is less than one
• Only if intercept is zero with the elasticity be equal to one
Example What is the elasticity of demand with respect to price of the demand curve x = αB/p
• Answer: dx/dp = −αB/p2 dx/dpp/x = −αB/p2 p/x or dx/dpp/x = −(x/p)(p/x) = 1
1.60
Elasticity of discrete functions
• With a continuous function, this work fine.
• But when no function is given, use the discrete form
•
1
Y X =
∆Y /Y
∆X/X
• Here is it easy to see that we are just working with a ratio of percent changes.
1 The
calculus form is when the ∆X goes to zero; that is:
lim∆X→0
∆Y /Y
dY /Y
=
∆X/X
dX/X
18
1.61
Example
Example Let’s say the demand curve is
q = −4p + 6
Calculate the elasticity of demand with respect to price at p = 1
• Answer: The slope dq/dp = −4 and p = 1 gives q = 2.Hence the elasticity is = −4(1/2) = −2. It will be
different at a different p.
1.62
Geometry
• Elasticity can be visualized as the slope of the tangent to a function divided by the slope of the chord line.
• Slope of a line from the origin to the point at which the elasticity is to be determined.
• In figure below slope of the chord line is 1 and the slope of the function is 1/2 so the elasticity at the point
x = 1 is = 1/2
1.63
Geometry of elasticity
Elasticity = slope of function/slope of chord
6
5
4
function
3
slope
chord
2
1
0
0
5
10
15
19
20
25
30
35
1.64
Perfectly or infinitely elastic
1.65
Perfectly or infinitely inelastic function
1.66
Don’t confuse axes
• It makes a big difference which variable is on which axis.
• Note that we have consistently defined at the elasticity of the y variable with respect to the x variable.
• It is easiest to stick with this convention.
• It is the same for slopes: it is always the rise (difference in the y-axis variable) over the run (difference in the
x-axis variable.)
Example What is an elasticity, really?
• Answer: In words it is “responsiveness”. In math it is a slope on steroids!
20
2
2.1
NIPA
National Income and Product Accounts
• GDP=gross domestic product: market value of all final goods (sold but not resold) produced in a year (or
quarter) by domestic factors of production (labor, land and capital).
• Final: does not include intermediate goods.
• Period of time means that GDP is flow not a stock.
• Domestic factors of production: factors owned by both nationals and foreigners but operated inside the political
boundary of the country.
• GNP Gross national product: factors of production owned by nationals.
Example What is the difference between GDP and GNP
• Answer: GDP = GNP + net foreign factor payments.
2.2
Definitions
Definition GNP is the value of all final goods and services produced by factors of production owned by the
citizens of a country in a given time period
Definition GDP is the value of all final goods and services produced factors of production within the borders
of a country in a given time period
Plumbing Diagram
Plumbing diagram
Demand
Firms Value added
Firm savings 2.3
HH NNP GDP Savings
Per savings
Capital Market Dep
M
C
I
21
Plumbing Diagram
Plumbing diagram
Demand
Firm savings Profit tax Firms Value added
Ind tax Transfers HH Govt Personal tax PI SS 2.4
DI Savings
Per savings
Capital Market C
NNP GDP Deifict
Dep
I
22
NI G
2.5
Plumbing Diagram
Plumbing diagram
Demand
Firm savings Profit tax Firms Value added
Govt Personal tax PI SS HH DI Savings
Per savings
Capital Market NI Ind tax Transfers NNP GDP Deifict
Dep
M
C
2.6
I
G
Plumbing Diagram
C = household consump/on I = investment (firms, households, govt, foreign) G = Govt X exports = M = imports S = savings T = tax Y = income E = expenditure Star (*) means foreign; subscripts F, G and H refer to firms, government and households •  We have the following rela/onships: •  EF=YF, EH=YH , EG=YG, E* =Y* and SF+SH+SG+S* = I • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
23
E
2.7
Plumbing Diagram
C = household consump/on I = investment (firms, households, govt, foreign) G = Govt X exports = M = imports S = savings T = tax Y = income E = expenditure Star (*) means foreign; subscripts F, G and H refer to firms, government and households •  We have the following rela/onships: •  EF=YF, EH=YH , EG=YG, E* =Y* and SF+SH+SG+S* = I • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
2.8
Vector and matrix Notation
Definition A matrix : is rectangular array of numbers with n rows and m columns. Definition A scalar is
matrix with n and m both equal to one. If n = 1 but m is greater than one 1, the matrix is called a row vector
and is written X = xj with j as the column index. If m = 1 but n is greater than one 1, the matrix is called a
column vector and is written X = xi with i as the row index.
2.9
»
a.
Examples
2
0
1
3
–
»
b.
2
0
1
3
1
2
–
»
c.
a11
a21
a12
a22
–
• First is square with n = 2 and m = 2,
• Second is rectangular, n = 2 and m = 3.
• Third is written with its row-column index arow,col explicit so that aij is the element in the ith row and jth
column.
2.10
More definitions
• The only restriction on n and m is that the be integers, i.e., whole numbers greater than or equal to one.
There are some important special cases
Definition A transpose of a matrix reverses its row column index
M T = mji
the transpose of a row vector is a column vector and vice-versa.
• This is important in matrix multiplication
24
2.11
Operations
Definition Scalar multiplication. The product of a scalar z and a matrix A = {aij } is zA = B{zaij }
• Note the convenient way we have represented the matrix A as the row-column index on the same, but lowercase
letter, aij . The matrix B is the product and is the same size as A was before it was multiplied.
2.12
Example of scalar multiplication
Example
»
• Let z = 3; and A =
2
0
1
3
–
.
»
• We then have zA = B where B =
6
0
3
9
–
• Expands or contracts a vector along same direction
2.13
Scalar multiplication
2.14
Matrix multiplication
Definition The product of two matrices, A and B is equal to C so long as A and B must “conform” to
multiplication.
• Column index of A must be equal to the row index of B.
• The dimension of C is then the row index of A and the column index of B.
• To get the first element of C, that is c11 take the first row of A and multiply it element-by-element times the
first column of B and the add up the results
P
• cij = m
k=1 aik bkj
»
–
»
–
»
–
2 1
1 2
5 8
• Example The product of the matrix
and
is
.
0 3
3 4
9 12
• The matrices conform since both are 2 × 2 and thus the column index of the first matrix is equal to the row
index of the second.
25
2.15
Matrix multiplication example
»
a
c
b
d
»
1
0
2
−1
• Example
• Example
–»
– »
–
y
ax + bz ay + bw
=
w
cx + dz cy + dw
3
2
–
–
»
1
5
−12 12
−3 4
−2
2 5=
14
−6
4
3
−1
x
z
2.16
Properties of Matrix Multiplication
2.17
Vector Spaces are different from Rn
• Matrix multiplication is finicky about the order of multiplication.
• While we normally think that ab = ba, it is not true for matrices (except for some special cases).
• If we reverse the order we get an entirely different matrix.
• We use the terms postmultiply to indicate multiplication from the right and premultiply to indicate multiplication from the left.
2.18
More on rules of multiplication
• Possible to multiply rectangular matrices IF they conform
• Above a and b do conform because a is a 2 × 2 and b is a 2 × 3.
• The product matrix c is a 2 × 3.
• Reversing the order of matrix multiplication doesn’t work
• The column index of b is 3 and this does not agree with the row index of a = 2
• Two row (column) vectors cannot be multiplied times each other
• A special case: row × col vector
• Called a scalar, inner or dot product.
2.19
Social Accounting Matrices
• SAMs are always nominal, measured in LCU (not physical units).
• The SAM for the base year both real and nominal.
• SAMs have at most 4 agents: firms, households, government and foreign.
• Each agent has a row and column.
• When income (rows) = expenditure (columns) for all agents of the SAM, then total savings is equal to total
investment.
Example What if the sum of savings is not equal to invest?
• Answer: You have made a mistake! Try to find and fix it.
26
2.20
A Simple SAM
A Social Accounting Matrix with 2 goods (No savings or Investment)
Firms-x
Firms-y
VA
rKx
wLx
rKy
wLy
px
y
Firms-x
Firms-y
HHolds
profits
wages
Total
Households
αB
(1 − α)B
Total
px
y
B
rK̄
wL̄
B
Note: Bars over variables indicate total factor supply.
2.21
SAMs
• Gross value of production (GVP) is the row sum for the firms
• The GDP is GVP less intermediate goods, plus government wages
• PI is sum of household row/column
• Government deficit is negative of government savings
• The foreign deficit is foreign savings (total imports less total exports)
• SAM balanced when income is equal to expenditure for all agents
• Sum of savings equal investment
2.22
Foreign savings
• We call this foreign savings because it is owed to foreigners since we didn’t pay for all of our imports with
exports
• Foreigners are therefore “saving” in our country
• the sum of firm savings, households saving, government savings and foreign savings is equal to investment
• The government deficit is the negative of government savings
• When firms operate they have some payments that are contractual, intermediates, wages, indirect taxes, profit
taxes, foreign factor payments
• Twin towers: foreign and govt deficits related
2.23
SAMs make essential link
• First foray into macroeconomics.
• So far have assumed that B, budget of consumer is given. Have assumed that C, costs of firms is also given.
• Now link the two by saying that consumer’s income comes from their ownership of the factors of production
• Note that in SAM we have Kx the capital needed to produce x and Ky taken as given.
Example Where do w and r come from
• Answer: The are determined in the labor and capital markets
27
2.24
Balancing a SAM
GDP Accounts
GDP
C
I
G
E
M
200
105
50
70
75
112
Source: National Statistical Institute
2.25
Public Sector
Public Sector Income and Expenditure
Government revenue
Direct Taxes
Firms
HH
Indirect taxes
Tariffs
42.5
22.3
9
13.3
4
16
Government expenditure
Goods and services
Wages
Transfers
Interest
Foreign
Domestic
Source: Ministry of Finance
2.26
Balance of Payments
Foreign Income and Expenditure
Exports
Imports
Transfers
Factor payments
Firms
Govt
75
92
5
20
8
12
Source: Central Bank
2.27
Steps in Balancing a SAM
• Make sure GDP = Value Added
• Split imports into competitive and non-competitive
• Calculate exports net of competitive imports
• Subtract government wages from G in NIPA
• Fill in first row (estimate intermediates)
• Compute first row sum
28
Non comp Imports
Firms
Consumption
Investment
Factor payments
77
12
15
30
20
89
45
25
2
17
12
5
• Make this first column sum and determine total VA
Example Must each row-column pair have a residual to balance?
• Answer: Yes...one number in each pair must be calculated
2.28
Balancing income and expenditure for firms
Firms
HH
Inv
Govt
Foreign
Total
Firms
HH
Savings
Govt
Foreign
30
157
90
20
45
40
225
Total
225
18
20
• VA is the residual
2.29
Next step: balance the HH account
• HH income: VA, gov wages, domestic and foreign transfers
• Note that G in government spending does count wages
• But not transfers
• Difference between HH expenditure and HH income is savings
• This is the residual for the HH column
ExampleWhy did we not use savings as a residual for firms?
• Answer: We could have if we have the information on payout of profits in the form of dividends.
2.30
Balancing income and expenditure for HH
Firms
HH
Inv
Govt
Foreign
Total
Firms
HH
Savings
Govt
Foreign
30
157
90
20
45
32
40
5
225
194
18
20
72
17
15
Total
225
194
HH savings is the residual
29
2.31
Third step: balance the Govt
• Government income is taxes of all forms
• Direct tax on firms (not yet included) and HH
• Indirect (sales or VAT) tax and tariffs
• Govt expenditure: Goods from firms, wages
• Transfers, interest payments
ExampleIs the residual again savings?
• Answer: Yes! Govt savings is just the current surplus of the public sector
2.32
Balancing income and expenditure for govt-expenditure
Firms
HH
Labor
Capital
Transfers
Savings
Govt
Foreign
Total
2.33
2.34
Firms
HH
Inv
Govt
Foreign
Total
30
157
45.8
111.2
90
20
45
32
25
5
2
-46.5
40
5
225
194
71
116
7
18
20
72
17
15
7.5
30
12
225
194
57.5
43
5
42.5
Balancing income and expenditure for govt-income
Firms
HH
Inv
Govt
Foreign
Total
Firms
HH
Savings
Govt
Tax-direct
Tax-indirect
Tariffs
Foreign
30
157
90
20
40
5
225
194
72
17
13.3
45
32
-46.5
7.5
3.8
15
7.5
30
12
Total
225
194
57.5
43
18
9
4
5
20
42.5
22.3
4
16.3
Balancing the foreign sector
• Foreign sector income is derived from our imports
• Their expenditure is our exports and net foreign transfers
• Non-competitive imports are made up of factor payments (profits, wages and rents)
• and goods and services
30
• Remember that exports are net of competitive imports
Example What is the residual?
• Answer: Foreign savings...just the current account deficit
• Balancing income and expenditure for foreign
Firms
HH
Inv
Govt
Foreign
Total
Firms
HH
Savings
Govt
Foreign
Imports
Factor payments
30
157
90
20
72
17
15
15
45
32
-46.5
40
5
32
7.5
30
225
194
57.5
42.5
77
27
20
Total
225
18
20
12
8
12
12
194
57.5
43
77
Foreign savings is the residual
2.35
Finishing up
• The easy part is to balance investment and savings
• It should automatically balance
• How? By Walras’ law!
• This is a mathematical property of matrices
• Its always true
P
•
Si = I is not and independent
P
ExampleWhat if
Si 6= I? How do we fix it?
• Answer: It can’t be fixed directly, the problem lies in firms, HH, Govt or Foreign!
2.36
Balanced SAM
Firms
HH
Savings
Govt
Foreign
Total
Firms
HH
Inv
Govt
Foreign
Total
30
157
90
20
72
17
15
194
45
32
-46.5
40
5
32
7.5
30
57.5
12
43
225
194
57.5
42.5
77
77
18
20
225
Saving and investment balance!
31
2.37
5 Aggregates
• GNP - depreciation = NNP
• NNP - indirect taxes = NI
• NI - retained earnings + corporate and social security taxes + transfers and interest payment = PI
• PI - direct taxes = PDI
• GDP = GNP + net foreign factor payments
• Know these!
2.38
SAMs and NIPA
• Gross value of production is the row sum for the firms.
• The GDP is GVP less intermediate goods, plus government wages.
• GNP is GDP less foreign factor payments.
• Net national product is GNP less depreciation.
• National income is NNP less sales tax.
• Personal income is NI less retained earnings less corporate direct taxes (profit tax) less social security contributions (payroll taxes) plus transfers (social security, welfare, unemployment compensation) plus interest on
government debt.
• Personal disposable income is PI less direct taxes on households.
Example Is savings is included in expenditure?
• Answer: Yes!
2.39
Foreign Savings
• The foreign deficit is foreign savings (total imports less total exports).
• We call this foreign savings because it is owed to foreigners since
• We didn’t pay for all of our imports with exports.
• Foreigners are therefore “saving” in our country.
• The sum of firm savings, households saving, government savings and foreign savings is equal to investment.
• The import row for firms includes intermediates and foreign factor payments.
ExampleIs foreign savings related to the balance of payments?
• Answer: Yes...it is the current account surplus
32
2.40
GOS
• Firms get revenues from all agents
• Expenditure is on intermediates, labor, pagyments to govt and imports
• The difference between income and these contractually obligated payments is the Gross Operating Surplus
(GOS)
• Out of GOS is paid income to households for capital services
• Firms must make a decision as to how much retained earnings they want for future investment
• Everything that firm does not pay out they put into the capital market. So that inflows into the capital market
(banks and investment banks) consist of the depreciation fund and retained earnings.
• During a recession, PI is greater than NI but during good times PI is less than NI.
• Example Is the relationship between PI and NI stabilizing or destabilizing?
• Answer: Stabilizing! This is an example of an automatic stabilizer.
3
3.1
Growth
Lack of capital
• Every year 1.8 million children die from diarrhea.
• Preventing these deaths requires only one thing: economic growth
• Health and wealth go together.
• While GDP does not measure well being perfectly..
• GDP highly correlated with other measures
• Infant and maternal mortality, life expectancy, literacy, poverty alleviation and income distribution
• Answer: The higher the GDP per capita
3.2
Population
• For low-income countries 1/3 population is under age 15
• High-income countries less than a fifth
• Growing by 200,000 people a day
• Between 1980 and 2030, the population of low- and middle-income countries will more than double to 7.0 billion
• 1 billion for high-income countries.
• Converge to 9 billion by 2050
• Population models some of the best in social sciences
33
3.3
Introduction
Growth and Health
• China: GDP per capita grew by 10%
• Catch-up growth: takes advantage of ideas, technologies, ormethods of management already in existence
!"#$%&'&()&'*&
• Cutting-edge growth: Primarily about developing new ideas
• China catching up
• Solow model about exogenous technological change
• Endogenous growth about investing in education
Example Why did Solow in the Nobel prize?
• Answer: Because he saw that capital accumulation alone was insufficient
3.4
Hats
3.5
Hats
• Growth rates or percent changes of the underlying level variable
• GDP is 100 in 2000 and grows to 106 in 2001
• Total percentage change (106-100)/100 = 0.06 or 6 percent
• Made up of “dots” and levels, ẋ = ∆x/∆t where x is the level
• Hats are related to logarithms and they follow the same rules
• If have y = ln(x) then the derivative of y is
dy
dt
=
dx/dt
x
= x̂
• Elasticity can be thought of as comparisons of growth rates
• Know your hat rules...saves a lot of time and effort
34
3.6
Multiplication
• Let
x = yz
where x, y and z are levels of the three variables
x̂ = ŷ + ẑ
• If levels are multiplied, then the hats are added Example Nominal GDP grows at 6% but inflation is 4%. What
is the approximate growth rate of real GDP?
• Answer: 2 %
3.7
Division
• Let
x = y/z
x̂ = ŷ − ẑ
• Levels are divided: hats are subtracted Example Output per worker is defined as ρ = X/L where X is GDP
and L is employment. We know that productivity usually grows at around 1%. If employment grows by 2%,
what is the growth rate of GDP?
• Answer: 3%
Example
• Let Y = C + I where C = 80 and I = 20.C is growing at 4% and I is growth at 2%.The rate of growth of Y is
• Answer: 0.8(4)+0.2(2)=3.6 but...next time Example Let Y = C +I where C = 83.2 and I = 20.4.C is growing
at 4% and I is growth at 2%.Y grows at
• Answer: [83.20/(83.2+20.4)]4+[20.4/(83.2+20.40)]2=3.61
...and so on with weights changing each time
3.8
Average rate of growth
•
xt = (1 + g)t x0
where x is any variable and x0 is the initial value and the final value is xt .
• We can calculate the average growth rate, g, by solving this equation
xt
g = ( )1/t − 1
x0
• Rules only apply for “small” changes; for large changes they are only approximations
3.9
Rule 7 Average rate of growth
Example
2005
=
1
2006
=
2
2007
=
3
What is the average rate of growth?
• Answer: (last/first) raised to inverse number of growth periods then subtract one = (3/1)1/2 − 1 = 0.73
Be careful about parentheses on these!
35
Table 2: Years to double
Annual rate of growth
0
1
2
3
4
7
3.10
Years to Double
never
70
35
23.3
17.5
10
Doubling time
• Growth path given by
xt = x0 (1 + g)t
where x is any variable and x0 is the initial value
• Solve for t with
(
xt
)=2
x0
• Take ln of both sides and not that ln(1 + g) ≈ (1 + g)
tg = ln 2 = 0.693147
• Doubling time t = 0.69/gor “rule of 70”
3.11
Doubling time
Example A country is growing at 3.5 percent. Approximately how long will it take for income to double?
• Answer: 70/3.5 = 20 years Example A country is growing at 3.5 percent. Approximately how long will it
take for income to triple?
• Answer: 100 (ln 3)/3.5 = 31.4 years
• Small differences in growth rates make big differences over time!
3.12
Growth widely divergent
• Two Growth Miracles
• Japan: annual rate of real growth 1950-70 = 8.5
• South Korea: annual rate of real growth 1950-70 = 7.2
• Argentina 1900: one of the richest countries in the world
• Now: per capita real GDP is 1/3 that of the U.S
• Nigeria: hardly changed since 1954
• Until recently
36
3.13
What is needed
• The factors of Production
• Physical capital: the stock of tools, structures, and equipment.
• Human capital: is the productive knowledge and skills that workers acquire through education, training and
experience
• Technological knowledge: knowledge about how the world works that is used to produce goods and services
• Good institutions: property rights, good governance, legal system
Honest Government: The Good and the Bad
• Competitive exchange rate!
3.14
Corruption
!"#$%&'(&)*&(+&
37
Government:
3.15Honest
Corruption
3.16
The Good and the Bad
Compound Growth
Appendix
•  Compound Growth: The Shortcut
!"#$%&'(&)*&+,&
If the growth rate is r percent and we grow for n
years then:
r #
&
Ending Value = Starting Value ' $1 +
!
100
%
"
n
!"#$%&'(&)*&'+&
38
3.17
Years to Goal
Appendix
•  Use Excel’s Goal Seek to work backward to find,
for example: number of years to reach a certain
level of GDP.
!  The ending value in cell B6 is fixed at 1,000,000.
Excel then calculates the value of the variable in
B2, that will give this result.
!"#$%&'(&)*&'+&
3.18
Growth Models
• Pond is like capital stock
• Output related to capital stock
• Investment related to output
• Plowback ratio is s
• Can still predict how large capital stock will get
3.19
Production function
• Y = F (A, K, eL)
• Y = GDP , A = technological change, K = capital stock
• eL is Human capital: education × Labor
• For homework use a square root production function Y =
• You will show that this function has diminishing returns
• This explains why poor countries can grow so quickly
ExampleCan bombing a country raise its growth rate?
• Answer: Of course, but it is not recommended.
39
√
K
3.20
Growth Equals Investment Minus Depreciation
Diminishing•  Capital
returns
Output, Y
20
When K = 100 Y= 10
Y= K
15
10
Consumption = (1- 0.3) x 10 = 7
5
I = 0.3·Y
3
2
I=3
0
3.21
0
100
200
Capital, K
400
12.12
Slide 12 of 73
300
Capital alone cannot determine growth
•  Capital Increases or Decreases Until Investment = Depreciation
Y
Dep = 0.02·K
8
6
I = 0.3·Y
4.5
4
At K = 400, Inv. < Dep. ! # K
3
2
At K = 100, Inv. > Dep.! " K
0
3.22
0
100
200 225
300
400
12.16
K
Slide 16 of 73
Solow Steady
State
$%&!'()(*!+(,&)!-!.&/01)2!03,!456/%&6!7&22(32!
!  !"#$%&!&'(&'%&()$*+,&()*)$&$-.'/'01'.23&"&'(&'%&()$*+,&()*)$&$-.'/'01'.24&
"#
68&
Y= K
A)$*+,&()*)$&B@&<&5>&
"#!
;<&8486=!#
58&
!
I = 0.3 K
>&
?@&<&66>&&
!
8&&&&&&&&&&&&588&&&&&&688&& &988&&&&&&&&&&&:88&
40
!#
56467& Slide 27 of 73
3.23
Transient
• In 1950, South Korea was poorer than Nigeria.
• 1950s: the investment rate was less than 10%.
• 1970s: Investment rate more than doubled.
• 1990s: Investment rate increased to over 35%.
• South Korea’s GDP increased rapidly.
• As GDP reached Western levels, the growth rate has slowed.
Example Why such a difference?
• Answer:
Incentives! Low real interest rates, low marginal tax rates, trustworthy govt, secure property
rights.(Necessary, but may not be sufficient)
The Solow Model – Details and Further Lessons
3.24
GDP higher with higher investment rates
3.25
Variable capital-output ratio
• Solow model has variable v with diminishing returns
• Diminishing returns means that eventually capital and output will cease growing.
• Therefore, other factors must be responsible for long-run economic growth.
• Human capital: knowledge, skills, experience
• Technological knowledge: better ideas
ExampleIs human capital subject to diminishing returns?
• Answer: Of course...Technological change is not!
41
Slide 32 of 73
3.26
Solow
HumanThe
capital
3.27
More investment
Model and Catch-Up Growth
12.19
Slide 19 of 73
Figure 7.6 An Increase in A Increases Output Holding K Constant
Cowen/Tabarrok: Modern Principles: Macroeconomics, First Edition
Copyright © 2010 by Worth Publishers
42
3.28
Higher Steady State
3.29
Cowen/Tabarrok: Modern Principles: Macroeconomics, First Edition
Data on Investment and Growth
Figure 7.8 When Capital Is in the Steady State, Output Is in the Steady State
Copyright © 2010 by Worth Publishers
Figure 7.10 GDP per Capita is Higher in Countries with Higher Investment Rates
Cowen/Tabarrok: Modern Principles: Macroeconomics, First Edition
Copyright © 2010 by Worth Publishers
43
3.30
Convergence
3.31
All at once!
Figure 7.11 Conditional Convergence
Cowen/Tabarrok: Modern Principles: Macroeconomics, First Edition
Copyright © 2010 by Worth Publishers
Figure 7.12 Better Ideas Generate More Output and More Capital Accumulation
Cowen/Tabarrok: Modern Principles: Macroeconomics, First Edition
Copyright © 2010 by Worth Publishers
44
3.32
Solow-step by step
Figure A7.1
Cowen/Tabarrok: Modern Principles: Macroeconomics, First Edition
Copyright © 2010 by Worth Publishers
45
3.33
Solow-step by step
3.34
Solow-step by step
Figure A7.2
Cowen/Tabarrok: Modern Principles: Macroeconomics, First Edition
Copyright © 2010 by Worth Publishers
Figure A7.3
Cowen/Tabarrok: Modern Principles: Macroeconomics, First Edition
Copyright © 2010 by Worth Publishers
46
3.35
Solow-step by step
Figure A7.4
Cowen/Tabarrok: Modern Principles: Macroeconomics, First Edition
Copyright © 2010 by Worth Publishers
3.36
Solow-step by step
Introduction
•  Economic Growth is Not a Smooth Process
!  Real GDP grew at an average rate of 3% over the
past 50 years. Growth wasn’t smooth.
Figure A7.4
Cowen/Tabarrok: Modern Principles: Macroeconomics, First Edition
Copyright © 2010 by Worth Publishers
3.37
Growth Not Smooth
47
Slide 2 of 51
•  Economic Growth is Not a Smooth Process (cont.)
!  We now turn to deviations from the average:
booms and recessions.
3.38
4
Recesssions
New Keynesian Models
Slide 3 of 51
• Solow growth rate: is an economy’s potential growth rate,
• Prices are perfectly flexible
• Note that the Solow model’s output does not depend on the price level or inflation
• Distribution between wages and profits does matter
• Solow model can be thought of the supply side
• The demand side can be determined by the New Keynesian model
Example Does the Solow output ever deviate from the potential path?
• Answer: Yes...when there are shocks to technology, the shares of income or population growth
4.1
Demand side is given by Keynes.
• Keynesian policy prescription: unemployment → deficit
• Inflation → surplus.
• Doesn’t allow for stagflation simultaneous presence of inflation and unemployment.
• Keynes’ main theoretical contribution: underemployment equilibrium.
• Keynes said no: wages and prices in the short run are sticky and don’t adjust.
• Formally the Keynesian model is a fixed price model. Wages and prices are fixed in the short run.
4.2
Keynes and Say’s Law
• Classical theory unemployment was impossible because of Say’s Law ,
• Supply creates its own demand..
• Thus if there were unemployment, wage would fall and full employment would be restored
• Keynes argued if there was a deficiency aggregate demand falling wages would not help
• Investment would drop off with no expectation that what was produced could be sold
Example Did Keynes agree that wages would ultimately adjust to bring about full employment?
• Answer: Yes..in the long run.
48
4.3
Keynes’ contribution
• Keynes’ most important theoretical contribution: consumption function.
• Economists would claim that consumption is a function of price.
• Keynes: disposable income
• Radical interpretation
• Most economists believed that income was fixed and prices were variable.
Example Did Keynes reverse classical causality?
• Answer: Yes...
4.4
Evidence
• In labor market, unions made sure that real wages were not flexible.
• Adam Smith had concentrated on a perfectly competitive farmers’ market
• There the quantities were fixed and the price were variable.
• But a farmers’ market is not a good basis on which to build a theory of a complex economy
• Monopolistic competition and lack of perfect competition meant that prices were more rigid than Smith had
supposed.
• Markets in the Keynesian model are said to be quantity clearing not price clearing.
4.5
Aggregate demand
• Y=C+I+G+E-M
• C consumption (70-80 percent)
• I investment (15-30 percent)
• G government expenditure (10-40 percent)
• E exports (5-40 percent)
• M imports (5-45 percent)
• C, I and G all have imports in them
4.6
Keynesian model
• Keynesian model has to do with the short run level aggregate demand.
Y = C + I + G + E − er M
where Y = GDP, C consumption, I investment E − er M the current account or net exports.
• Each of the variables on the right-hand side is in the SAM as snapshot
Example Could this be written using the balance of payments?
• Answer: Yes...
Y = C + I + G + E + CA orY = C + I + G − fk (i − i∗ )
where
49
Table 3: A Social Accounting Matrix
Firms
4.7
Firms
HHolds
Savings
100
Total
100
Household
80
Investment
20
20
100
Total
100
100
20
20
Consumption function
• C = C̄ + cYd
• Where =C̄ is autonomous consumption and c is the marginal propensity to consume. Disposable income is Yd .
• The consumption function is calibrated to the SAM.
• We must know the marginal propensity to consume, c, which is usually given by fitting a regression line through
points on a scatter diagram.
• The slope of the regression line is the marginal propensity to consume.
• Since the scatter diagram covers many years, not just the year of the SAM, we can use the slope, but not the
intercept.
Example Is the intercept of the consumption function fixed?
• Answer: No...it too must move over time.
4.8
Consumption function calibration example
• Calibration: MPC or c = 0.7.
• The consumption function C = C̄ + cYd becomes 80 = C̄ + 0.7(100). This gives C̄ = 10.
4.9
Calibrated model
• The simplest calibrated Keynesian model
Y =C +I
C = C̄ + cY
• With the parameters inserted.
Y = C + 20
C = 10 + 0.7Y
• The variable list is V (Y, C) and the parameter list is P (I, C̄, c).
• This is a coherent model since there are as many entries in the variable list as equations of the model.
50
4.10
Comparative statics
• Formally, a multiplier is the change in the equilibrium values of the variables with respect to a change in one
and only one parameter.
• The “multiplier” is usually thought as
• but logically, we also have
∆C ∆Y ∆C
,
,
∆I ∆C̄ ∆C̄
∆Y
∆I
and
∆Y
∆c
∆C
.
∆c
and
Example How many multipliers are there?
• Answer: The number of variables × the number of parameters (here it is 6)
4.11
Solving the model
• Done by “substituting upward”. Take the second equation and substitute it into the first.
Y = C̄ + cY + I
• This is called a “reduced form” of the model
• To solve for the multiplier write the reduced and then subtract
Y1 = C̄ + cY1 + I1
Y0 = C̄ + cY0 + I0
Y1 − Y0 = c(Y1 − Y0 ) + I1 − I0
∆Y = c∆Y + ∆I
• So the multiplier is
∆Y
1
=
∆I
1−c
4.12
The multiplier
• The multiplier is a direct consequence of the Keynesian consumption function
• Income increases directly because of a rise in investment.
• In the Keynesian model, then, there are two types of demand, induced demand and autonomous demand
• Rising incomes affect consumption through the consumption function.
• Now we have a direct and indirect impact on demand.
• The first is the rise investment and induces an increase in consumption demand
Example Here investment is exogenous. What determines investment
• Answer: Here is where the schools of thought differ
4.13
Standard theory
• Decision maker is rational, learns from mistakes
• Investment and savings are determined by intertemporal trade-off between today’s and tomorrow’s goods
• Investment can be crowded out if return to investment is low
• Can be reduced by taxes, present and future
• Also can be “crowded out” by a rise in the interest rate
Example What was Keynes theory of investment?
• Answer: That investment is determined by “animal spirits”
51
4.14
Animal spirits
• Means people make investment decisions unaided by mathematical, i.e., rational models.
• When deciding whether to invest, they don’t calculate probabilities
• Instead are guided by the seat of their pants, hunches, heuristics and gut feelings.
• None of this, said Keynes, can be put into a formal model. He just took investment as given.
• Keynes agreed, but said animal spirits often overwhelm this rational trade-off and even though the model says
“no go”, people will invest anyway.
Example Does this mean that investment is volatile?
• Answer: Yes! Most volatile component of the aggregate demand and that is generally true
4.15
Calibrating the investment function
• Start with I = I¯ − bi where b is a response parameter and i interest rate
• Determined elasticity: usually in the range of 3 percent
• Elasticity- percent change in investment demand with respect to a one percentage point change in i
• Solve for the b that gives this
• ∆I = −b∆i
•
∆I/I
∆i
= −b/I
• If elasticity is 3, then
• b = 3I
4.16
Calibrating the investment function
• Once b is determined
• Then use I = I¯ − bi to solve for I¯
• Note that this requires a base period interest rate
Example If elasticity = 3, I = 100, i = 0.05, then what is the calibrated investment function?
• Answer: I = 160 − 300i
4.17
Calibrating the money demand function
• Start with Ms = Y /v = M d = km y − hi where h is a response parameter and i interest rate
• Determined elasticity: usually in the range of 3 percent
• Elasticity- percent change in money demand with respect to a one percentage point change in i
• Solve for the h that gives this
• ∆M d = −h∆i
•
∆M d/M d
∆i
= −h/M d
• If elasticity is 3, then
• h = 3M d
52
Table 4: A Social Accounting Matrix
Firms
Firms
HHolds
Labor
Capital
Savings
Govt
Foreign
Total
4.18
HHolds
80
Invest
20
145
79.8
65.3
48
30
Govt
50
10
10
Foreign
25
-30
5
30
30
30
175
155
20
Total
175
155
89.8
65.3
20
30
30
Calibrating the money demand function
• Once h is determined
• Then use M d = km y − hi to solve for km
• Note that this requires a base period interest rate
Example If elasticity = 3, Ms = 1000, i = 0.05, then what is the calibrated investment function? Velocity is
2.
• Answer: 1000 = km 2000 − 3000i gives k = 2
4.19
Calibrating the Money function
• Start with I¯ − bi where b is a response parameter and i interest rate
• Determined elasticity: usually in the range of 3 percent
• Elasticity- percent change in investment demand with respect to a one percentage point change in i
• Solve for the b that gives this
• ∆I = −b∆i
•
∆I/I
∆i
= −b/I
• If elasticity is 3, then
• b = 3I
4.20
Adding govt and foreign
4.21
Calibrating govt and foreign sectors
• G is a policy variable, a parameter set by the rule above
• The tax rate, t, needs to be calibrated. Here it is 30/155 = 0.19.
• Must define consumption as a function of disposable income
53
• Yd = (Yh + Tr )(1 − t)
• Imports are given by the marginal propensity to import multiplied by income or M = mf Y
• Exports is given by the real exchange rate,
∗
• er = epp where e is the nominal locals/foreign currency exchange rate, p∗ is the foreign price and p is the
domestic price or GDP deflator
4.22
Investment
• Investment is made up of structures, equipment, residential and inventories.
• Investing in bond or stock is not an investment; that is savings.
• Investment is demand for real goods and services.
• Investment demand is depends on the interest rate in the form of
I = I¯ − bi
where I¯ is autonomous investment and b is the interest sensitivity of investment.
• Can also depend on capacity utilization u = Y /Q.
Example How does this investment function capture animal spirits?
• Answer: Through the I¯ term.
4.23
The Keynesian model-real side
X =C +I +G+E
Y = C + I + G + E − ep∗ /pM
C = C̄ + c(Y + Tr )(1 − t)
G = Ḡ
I = I¯ − bi
E = E0 ep∗ /p
ep∗
mf Y f
p
p = (1 + tau)(emf + wl)
M=
¯ b, i, E(0), e, p∗ , mf )
V (X, Y, C, G, I, E, M, p) P (C̄, c, Tr , t, G, I,
4.24
The Calibrated Keynesian model-real side
C = 17.5 + .5(Y + 10)(1 − 0.19)
G = 50
I = 25 − 100i
E = 25(ep∗ /p)
M = (ep∗ /p)0.171X
p = 1.59(e0.171 + 0.46)
54
4.25
Simplifying assumptions
• No intermediate goods
• No indirect taxes or tariffs
• A single household
• No firms savings (even for depreciation)
• No government wages
• No interest payments
• No foreign transfers!
4.26
Exchange rates and competitiveness
• Exchange rates are analyzed with supply and demand diagrams. See the text for illustration of how exchange
rates are determined.
• Taking hats of the real exchange rate equation
er =
ep∗
p
• we have
eˆr = ê + pˆ∗ − p̂
• Here “up is down” meaning that a higher real exchange rate (8 is higher than 6) is a weaker exchanger rate.
• We could also say that when prices of goods go up domestically that our current is “weaker”
• Larger number of dollars required to buy the same good.
Example Foreign inflation is 3 percent and domestic inflation is 10 percent. If the nominal exchange rate e
remains fixed, then the real exchange rate will appreciate by
• Answer: 7 percent.
4.27
Fixed and flexible exchange rates
• We use appreciation/depreciation for floating exchange rates and devaluation/revaluation for fixed exchange
rates.
• Appreciation is good for importers (including tourists) and bad for exporters.
• Get fewer units of local currency for their dollars
• Hence, IMF always recommends devaluation if there is a balance of payments crisis
• This is not evil; it is just logic
• Local government resist it however, since they believe that devaluations signal weakness and cause inflation
Example What is the major drawback of devaluation?
• Answer: Can spark a financial crisis!
55
4.28
Marshall-Lerner conditions and J − curve
• ML conditions: real devaluation must improve the trade balance
• If exports do no increase a devaluation will worsen the current account
• Need time for the devaluation to affect exports
• Current account could first decrease and then increase as exports rise
• If ML conditions do not hold comparative statics of the model will not be correct
• Devaluation must be expansionary
ExampleWhat is the relationship between the current account surplus and time called
• Answer: The J − curve
4.29
J-curve
800 Current account surplus 600 400 200 0 0 5 10 15 20 25 30 -­‐200 -­‐400 Time Shocks to AD in the New Keynesian Model
•  Other Factors that Shift the AD Curve (cont.)
4.30
Aggregate Demand
Slide 37 of 51
56
4.31
Money
4.32
Financial SAM
Firms
HH
Govt
Banks
Fed
Foreign
Wealth
Total
Firms
trade credits
equities
HH
installment
bank loans
rediscount
loans
net worth
bank loans
Govt
bonds
bonds
Banks
deposits
deposits
Fed
cash
cash
Foreign
capital flight
capital flight
Capital
Kf
Kh
Kg
bonds
reserves
bonds
discount
foreign reserves
bonds
K*
net worth
net worth
0
0
net worth
------------------------------------- Liabilities ----------------------------------------
Total
|
|
|
Assets
|
|
|
Financial SAM 2007
(initial stocks)
Real SAM 2007
Financial SAM 2008
(final stocks)
4.33
The players in the Financial SAM
• Firms
• Households
• Govts
• Foreign
• Commercial banks including non-bank financial institutions (mutual funds, hedge funds, securities firms, insurance companies, pension funds)
• Central banks
• Last two are new but are “fictitious”
4.34
Assets
• Firms loan to households, govts and foreigners
• HH loan to firms (stocks), govts and foreigners (ignore HH-HH loans)
• Banks loans to firms, HH, govt and foreigners
• CB loans to banks and govt
• Assets include physical capital
– Firms: structures, equipment and inventories
– HH: Residential structures
– Govt: Infrastructure
57
– Foreigners:
– Banks: included in firms (so zero in the SAM)
– Central Bank: included in govt (also zero in the SAM)
• Assets are along the rows liabilities down columns
4.35
Private sector
• Savings+ banks loans -investment = accumulation of gross financial assets
• Saving - investment = accumulation of net financial assets
• Firms finance investment by issuing stock + using net business savings + bank loans
• Firms deposits in banks and cash usually linked to needs for working capital
• Wealth of firms is actually owned by households but still computed separately
• HH finance residential investment by borrowing from banks and using their savings
• If not investing then savings is accumulation of net financial assets
• Financial surplus negative for firms and positive for households
4.36
Financial sector
• Banks make profits by making loans to firms and households at the market interest rate paying depositors less
• Commercial Banks aim is to make profits by keeping excess bank reserves as low as possible
• Central bank’s job is to manage the monetary base in the interests of maintaining low inflation and macroeconomic stability.
• Open market operations buying-selling bonds
• Changing the discount or federal funds rate to control bank reserves
• Changing the reserve requirement to control bank reserves
• International reserves are part of the monetary base!
4.37
Govt
• Issues government bonds to finance deficit
• Fed buys them and resells them to public to control reserves through open-market operations
• If no bonds resold, then banking reserves rise by the amount of the fiscal deficit
• Defined as government investment - govt savings.
• Wealth can be positive negative or zero
• Be sure to keep foreign and bank reserves separate
58
4.38
Foreign sector
• Not complete wealth of foreign sector
• Only what is kept in our country
• Buys government bonds (makes loans to government)
• Sells foreign exchange to Central Bank in foreign currency markets
• Can also make loans to firms
• Loans in dollars taken to central bank and traded for local currency
• Foreign capital holdings are liabilities for foreigners
• Change in money supply = change in base × money multiplier 1/r
4.39
Demand for money
• Classical economists said demand for money = 0
• True in static model with rational agents
• Dynamic model money demand is due liquidity preference
• Money is a liquid asset: no transaction costs
Example You want to buy a house. Does it cost your any money?
• Answer: No! Your demand for money will be the same before and after the house purchase. You sell other
assets, bonds, stocks, etc. to buy the house.
4.40
Simplified demand for money
• Taken as a function of income and the interest rate
• Is real demand
• M d/P = L(i, Y ) where: P is the price level Y is real national income i is a measure of interest rates on
non-monetary assets L(R, Y ) is the aggregate demand of real monetary assets
• Note “real” price level doubles and nominal demand for money also doubles
Example L(R, Y ) = kY − hi where k = 1/2 and h = 10 The supply of money is 150. What is the equilibrium
interest rate if GDP = 450?
• Answer: 150 = 450/2 − 10i i = 7.5 %
59
4.41
Money demand curve
4.42
Money demand curve
4.43
Disequilibrium in money market
• When there is an excess supply of monetary assets like bonds, loans, and deposit
• There is an excess demand for interest bearing assets, bonds, stocks
• Excess supply of monetary assets are willing to offer interest-bearing assets at lower interest rates.
• HH and firms more willing to hold additional monetary assets as interest rates falls
Example What does it mean for the opportunity cost (price) of money to rise?
• Answer: The interest rate has risen.
60
4.44
Applying hat rules
• Mv = P Y
• M̂ + v̂ = P̂ + Ŷ
• Velocity usually assumed to be constant (roughly) v̂ = 0
• If income also constant
• M̂ = P̂
• In the long run, the rate of growth of the money supply is equal to the rate of inflation
4.45
Equilibrium in the money market
4.46
Equilibrium in the money market
61
4.47
Change in income
4.48
Exchange Rate
• Let the price level (GDP deflator) be defined as:
p = (1 + τ )C
where p = price τ is mark-up and
• C is unit cost
C = wl + pA + e(1 + t∗ )p∗ A∗
where w = wage rate, l = labor per unit of output, A = intermediate goods, e = nominal exchange rate, t∗ is
the tariff rate and p∗ is the foreign price.
4.49
Exchange Rate
• With a change in e, we have a change in C which leads to a change in the price level
p̂ = Ĉ
Since wage don’t immediately adjust with the exchange rate
• The real exchange rate
er =
ep∗
p
• Using hat rules
êr = ê + p̂∗ − p̂
4.50
Exchange Rate
• With foreign inflation = 0
p̂∗ = 0
• Since wages do not immediately adjust with the exchange rate
êr = ê − p̂ > 0
• And the real exchange rate depreciates
• But the rise in exports creates inflation so there is overshooting
62
4.51
Dynamics of the Real Exchange Rate
• Consider an increase in the money supply
• Once a CB action is announced, the dollar moves on international currency markets within minutes
• Domestic prices do not move as quickly
• The LCU has lower value–depreciates immediately
• As prices begin to rise exchange rate appreciates again
• Overshooting
4.52
Exchange rates
• Floating exchange rate: determined primarily by market forces
• Most countries have “fear of floating”
• Probability of a financial crisis conditional on having a rapid liberalization is greater than probability of having
a financial crisis
• Floating exchange rates are most common
• Must ease into floating exchange rates gradually
• Yet floating regimes only regimes consistent with economic theory
Example What is the relationship between the spot and forward exchange rates?
• Answer: F/S − 1 = re − r∗
4.53
Fixed exchange rate systems take three forms
• Fixed (pegged) exchange rate: the central bank has promised to convert its currency at a fixed rate
• Dollarization: occurs when a foreign country uses the U.S. as its currency
• Panama, Ecuador, El Salvador (effectively China)
• Disadvantage: the country must buy and save sufficient dollars
• Once in place, the country receives U.S. monetary policy
• Avoids episodes of high inflation
Example Do low interest rates in the US improve competitiveness of countries tied to the dollar?
• Answer: Yes...as dollar depreciates so too all currencies tied to it!
4.54
Problem with pegs
• Thailand, Indonesia, Brazil, and Argentina attempted pegs to the U.S. dollar
• All broken by speculators
• Argentina couldn’t control inflation...had to eventually break the peg
• To maintain the currency at the pegged rate central bank must be prepared to buy large amounts of LCU with
U.S. dollars
• Govt spending cannot exceed taxation by more than what would match US inflation
63
4.55
Overshooting
• Occurs in both fixed and flexible exchange rates
• In fixed exchange rates domestic price simply rises
• In flexible the real value of the money supply falls
• Interest rate rises and attracts foreign capital
• Real exchange rate appreciates as a result.
Example What is the main implication of overshooting?
• Answer: Nominal exchange rates very volatile as a result
4.56
Price adjustment
4.57
Overshooting
• Only happens when the forward rate in S =
F
r e −r∗+1
changes!
• When spot rate changes...quite possible!
• How to predict? Depends on expectation of change in money supply
• Will money supply continue to increase? If so then forward rate will rise
• If not, then F will stay
• Depends on whether money supply increase is permanent or transitory
• If transitory inflation will dissipate and spot rate will come back to where it was
64
4.58
Exchange rate volatility
4.59
Overshooting
• Only happens when the forward rate in S =
F
r e −r∗+1
changes!
• When spot rate changes...quite possible!
• How to predict? Depends on expectation of change in money supply
• Will money supply continue to increase? If so then forward rate will rise
• If not, then F will stay
• Depends on whether money supply increase is permanent or transitory
• If transitory inflation will dissipate and spot rate will come back to where it was
Example Do speculator help or hurt?
• Answer: In flexible exchange rates they limit the ability of governments to overspend.
4.60
Financial crisis
• Government debt increases some 86 percent in the 3 years following a crisis
• Usually 10 times the bailout costs (which can be negative)
• In past private sectors have not trusted own govts enough to loan them money
• Prefer to finance developed country budget deficits
• Explosion of domestic borrowing at beginning of 21st century
• Thresholds of external debt fall because of this!
Example What are ways in which the governments extract revenue from individuals?
• Answer: Direct tax, indirect tax, inflation tax, financial repression excess seigniorage
65
4.61
Financially Repressed Systems
• Banking crisis are a form of government default on domestic debt
• Financial repression is major form of taxation
• Keep interest rates low and prevent capital flight through currency controls
• Banks are vehicles to squeeze taxes from citizens by paying lower than market interest rates
• Governments then stuff debt into the banks by way of reserve requirements
• Govt can finance a part of its debt at a very low interest rate
Example What are prescribed assets?
• Answer: Nothing more than a form of hidden taxation
4.62
Financially Repressed Systems
• If the govt creates inflation, the cost of borrowing through forced reserves increases
• India did this in the 1970s
• Capped bank interest at 5 percent and then ran 20 percent inflation
• Sometimes govt default on domestic debt on top of this
• This forces banks to default on their own liabilities
• Reneges on deposit insurance
ExampleIf this is just taxation, what is wrong with it?
• Answer: First it can spark a financial crisis and second it is a hidden form of taxation
4.63
Inflation targeting
• Sometimes central banks target inflation rather than the money supply
• Use the interest rate to stop inflation
• Money supply becomes endogenous
• Demand for money rises and falls with income
• Higher than expected inflation causes an appreciation as central bank responds
• Even if CB does not target inflation, then private sector will!
• Banks will raise their interest rates with inflation to keep real interest rate positive
66
4.64
Financial crisis
• How do developing countries get into trouble
• Have to call on the IMF as the lender of last resort?
• The root of all balance of payment crises is negative government savings.
• Most poor countries have difficulty borrowing from their own private sectors,
• Situation is improving as inflation is lower throughout the world.
• Mexico has been able to float debt at very low long-term interest rates recently, for example.
• If there is a deficit, government saving is negative and G > T .
ExampleThis has an expansionary effect on GDP! What’s wrong with that?
• Answer: Imports increase as GDP increases. If exports don’t increase, we have a foreign deficit (positive
government savings).
5
Open Economy Macroeconomics
5.1
Debt
5.2
Main Characteristics of LDCs
• Greater exposure to supply shocks
• Trade volatility
• Procyclicality of capital inflows
• And domestic fiscal and monetary policy
• Lower credibility for price stability and default risk
• Imperfect institutions
Example What economic concepts apply?
• Answer: Asymmetric information, imperfect capital markets, default risk and moral hazard with respect to
institutions
5.3
Specific Macroeconomic Problems
• Dutch disease for successful primary exporters
• Contractionary effects of devaluation-elongated J-curve
• Financial repression
• Inflation tax
• Capital and exchange controls
• Choice of exchange rate regime
Example Have emerging markets have largely escaped these problems?
• Answer: Some...not all
67
5.4
Washington Consensus-Helped?
• Competitive exchange rate
• Fiscal Discipline
• Low marginal tax rates
• SOE producing public not private goods
• Defense of property and adequate titles
• Labor market deregulation
ExampleHow do these measures help?
• Answer: Avoid financial crisis, encourage capital inflow, prevent macroeconomic populism
5.5
Openness
• Current and capital account liberalization
• Solves inducement to invest
• No longer depends on the extent of local market
• Allowed LDCs to share in Giant Pool of Money
Example When did the globalization of finance begin?
• Answer: In the late 1970s with the syndicated bank loans that recycled petrodollars to oil-importers and
success waves after 1990 and again after 2003.
5.6
US Financial Crisis
• Infected by so-called toxic assets originating in the United States.
• Call for a fundamental rethinking of macroeconomic theory?
• Developing countries tend to be subject to more volatility than rich countries
• In exchange rates, production and financial flows
• Local markets are thin and subject to internal and external shocks
• Attempted to address income inequality by protecting labor unions
• And...macroeconomics populism
Example Are these measures not helpful?
• Answer: In the short run yes, but in the longer term they can hurt the people they are intended to help
5.7
Debt Intolerance
• Weak institutional structure
• Problematic political system
• External borrowing becomes tempting
• Avoid hard decisions about spending and taxation
• Emerging markets can experience duress at levels easily handled by more advanced countries
• Can give rise to serial debt default relapses
68
5.8
History
• 1800-2009 250 sovereign external debt default episodes
• At least 68 cases of default on domestic public debt
• About $1.9 trillion in foreign exchange transactions take place on a typical day.
• Most trades are speculative.
• Daily price movements are set largely by psychology and expectations.
• Some traders are simply guessing what other traders are going to do.
Example Can central banks protect themselves from financial crisis?
• Answer: Central banks have a difficult time manipulating currencies effectively enough.
5.9
Sequence of events
• Spiraling interest rates on external debt
• Political resistance to repaying foreign creditors
• Loss in market confidence
• Default occurs far below 60 percent debt/GDP in Masstarich treaty
• Depends on history of default and inflation
Example What is the vulnerability to marignal increse in debt to GDP
• Answer: Highly dependent: Japan’s debt is 170 % of GDP but not considered problematic
5.10
Emerging Market Defaults
• Far lower levels of debt to GDP in many countries in
• Argentina (2001) (51 percent) or Mexico 1982 (47 percent)
• Ecuador (2008) also
• Exceed 100 percent of GDP in 16 percent of episodes
• Markets don’t allow it to get that high
• Half of all defaults were below 60 percent and 20 percent were below 40 percent of GDP
Example Thresholds are biased upward?
• Answer: Yes...real exchange rate depreciates rapidly causes debt measures to rise
69
5.11
Defaulter Borrow more than Non Defaulter
• Takes two to tango: must be complicit in this time is difference
• Highest debt intolerance borrow most especially when measured by Exports/GDP
• Thresholds depends on repayment and inflation history
• Capital flow cycles end in ugly events
• Different levels of intolerance give rise to
• When debt/GDP is about 30-35 percent of GDP risk of a credit event increases significantly
Example Measure vulnerability
• Answer: Institutional investor rating of sovereign debt and debt ratio both important
5.12
IIR
• Compiled twice a year...banks, securities and economists
• Scale 0 to 100 default on govt obligations
• Market based so fairly accurate
• Private plus public: private becomes public after the fact
• 2000 lots of public debt issued to domestic private sector
• Correlations between 100-IRR and debt ratio for all grouping positive and mostly signfiicant
Example What is mean and standard deviation of IRR?
• Answer: 47.6 and 25.9 for 90 countries 1979-2007
5.13
3 Clubs
• At or above 73.5 is club A: least vulnerable:
• Essentially a horizontal BP curve
• Club C: IIR 21.7 or below: grants and official loans
• The countries are so debt intolerant that mkts only give sporadic opportunity to borrow
• Remaining countries are in B: indeterminate
• Default risk not trivial: crisis can be triggered by self fulfilling expectations
• Not shut out of debt markets and so intolerance rises with debt ratio
Example How can B be further
• Answer: Type I: above mean but with debt ratio for 35 %. Type II: above 35%. Type II: below mean but
with debt below 35%. Most debt intolerant type IV: below mean and greater then 35% of GDP.
70
5.14
Type IV has greatest problems
• Can “degraduate” to class C easily
• Early 2000 Argentina’s IIR was 44 and D/Y = 0.51
• By 2003 Argentina’s rating dropped to 15 and moved to club C.
• Club A may lose members after latest crisis
• Patient vulnerability and dose of debt can lead to debt intolerance
• Will to repay can collapse
Example How does one graduate to a higher club?
• Answer: Not easily...maybe with decade of impeccable repayment and low D/Y .
5.15
Implications of Debt Intolerance
• Failure to take DI into account leads to underestimation of effect of shocks
• On loss of market confidence
• On willingness to repay–and another
• Country with weak internal structures makes it susceptible to wide macroeconomics swings
• And...slower growth path
Example Is constrained access to international capital markets cause or effect?
• Answer: Effect of debt intolerance!
5.16
3 Causes of DI
• Soft factors: institutions, corruption and governance
• Risk-sharing benefits of market integration modest-even without taking into account cyclical factors
• Pro-cyclical inflows required emerging markets to tighten monetary and fiscal policy in a recession (in contrast
to rich countries)
• This suggests to many that having limited and stable access to borrowing might actually be welfare enhancing
relative to boom bus
• Example Are LDCs hampered by limited access to debt markets?
• Answer: Yes...but DI limits benefits of debt
5.17
Capital Inflows
• Debt, equity and direct foreign investment
• Firms often come in with large amounts of cash
• Derivatives blur the categories
• Hard to accurately separated different capital inflows
• Countries can mislabel inflows as FDI when they are actually debt
ExampleWhat is the fundamental problem?
• Answer: Non-indexed debt
71
5.18
Indicators of DI
• Domestic currency substitution
• Dollarization–defactor or dejure
• Indexization of domestic financial instruments.
• Drop in reserves sent abroad
5.19
Escaping High Ratios of External Debt
• Rapid growth
• Sizeable and prolonged repayment (unwinding)
• Central error to think this can really happen
• Fiscal stimulus packages are begin implemented
• Widening deficits push countries toward debt intolerance thresholds
• Balance of payments crisis result
Example How have most emerging markets reduced their D/Y?
• Answer: Via restructuring or default
72