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Department of Economics
University of California, Berkeley
Spring 2013
Professor Christina Romer
Professor David Romer
ECONOMICS 134
Macroeconomic Policy from the Great Depression to Today
SUGGESTED ANSWERS TO PROBLEM SET 2
1. Describe the short-run effect on real output, the exchange rate and net exports
a. Increase in investment demand for a given real interest rate
Since the question asks about the effect of the change in investment demand on the real exchange
rate and net exports, we need to work with the open economy version of the IS-MP model. Thus
planned expenditure is E = C(Y-T) + I(r) + G + CF(r). An increase in investment demand for a
given real interest rate, r, is reflected in a shift up of the planned expenditure curve in the
Keynesian cross (figures are on the following page). Since the level of output people are willing
to purchase for any given real interest rate is now higher, the IS curve shifts to the right in the ISMP diagram. With Y higher, the central bank raises the real interest rate, which corresponds to a
move along the MP curve. The higher interest rate depresses planned expenditure by reversing
some of the investment increase and by lowering net capital outflows. In the IS-MP diagram, it
corresponds to a move along the new IS curve from the point (Y1, r0) to the point (Y2,r1). In the
Keynesian cross diagram, it corresponds to a downward shift in the planned expenditure curve
from E1 to E2. This analysis establishes that the increase in investment demand raises output.
To determine the effect of the increase in investment demand on the exchange rate and net
exports, we can reason through the effects using the equations of the model or we can use the net
capital outflows and net exports diagrams. These are two different ways of doing the same thing.
To reason through the effects, recall that the increase in investment raises output, causing the Fed
to raise the real interest rate. Since net capital outflows are a decreasing function of the real
interest rate, they fall. Net exports equal net capital outflows. Thus net exports must also fall. And
in order for net exports to fall, we know that the exchange rate must rise.
Intuitively, the higher real interest rate makes U.S. assets more attractive, decreasing capital
outflows and increasing inflows. Thus net capital outflows fall. Since there is more demand for
U.S. assets, there is more demand for dollars. So the dollar appreciates, making U.S. goods
relatively more expensive. This reduces exports and increases imports. Therefore net exports fall
along with net capital outflows.
We can also use the net capital outflows and net exports diagrams to derive the same results.
Again, the shift in the IS curve increases output, which causes the central bank to raise interest
rates. Since net capital outflows are a decreasing function of the real interest rate, they are lower
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at the new real interest rate, r1. One can see this by comparing the horizontal lines between the ISMP diagram and the net capital outflows diagram.
Net exports equal net capital outflows. Net capital outflows are lower, so net exports must also be
lower. The vertical lines connecting the net capital outflows diagram to the net exports diagram
show this decline. Finally, the net exports diagram shows that the decline in net exports is
accompanied by an increase in the exchange rate. In other words, the dollar appreciates.
E
Y=E
E1
E2
E0
Y
r
r
MP
r1
r0
Y0
Y2
Y1
CF(r)
IS1
IS0
Y
CF
ε
NX(ε)
NX
2
b. The central bank decides to set a lower real interest rate for any given level of output.
The change in central bank policy corresponds to a downward shift of the MP curve. Thus the
real interest rate and output fall. As the net capital outflows diagram shows, the decrease in the
real interest rate increases net capital outflows. Thus net exports must also increase, which can
only occur if the exchange rate falls (i.e., the dollar depreciates).
Intuitively, the decision by the Fed to lower real interest rates makes investing in the U.S. less
attractive, increasing capital outflows and decreasing inflows. As demand for dollars falls, the
exchange rate declines, and hence U.S. exports become cheaper and imports more expensive. So
net exports rise.
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c. The demand for money increases
Since we are using the IS-MP model, changes to money demand have no effect on the real
interest rate or output. The Fed matches the increase in money demand with an increase in money
supply so that the real interest rate remains unchanged. Since the real interest is unchanged, net
capital outflows, net exports, and the exchange rate are also unchanged.
2. Foreign central banks tighten, raising foreign real interest rates
a. Effect on CF(r)
Higher foreign real interest rates make foreign investment more attractive. Thus for any given
domestic real interest rate, capital outflows will be higher and inflows lower. Since net capital
outflows will be higher for any r, the net capital outflows schedule shifts to the right.
r
CF1(r)
CF0(r)
CF
b. Effect on Y and r
The increase in net capital outflows corresponds to an upward shift of the planned expenditures
curve in the Keynesian cross. Thus the IS curve shifts to the right, and output and the real interest
rate rise. (See figures on page 6.)
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c. Effect on net exports and the real exchange rate.
First consider the effect of the increase in foreign real interest rates on net capital outflows. There
are two forces affecting net capital outflows:
(1) For any given r, the increase in foreign interest rates means net capital outflows are
higher, i.e. the CF(r) schedule shifts right (part a).
(2) r increases as the economy moves up the MP curve. The increase in r lowers net capital
outflows as the economy moves up the new net capital outflows schedule.
It must be the case that (1) dominates (2) such that net capital outflows rise. Showing this is hard.
Here is one argument. Suppose for a moment that it isn’t true, and that r rises so much that net
capital outflows fall. In this case, both CF and I are lower than before, and so the planned
expenditure line in the Keynesian cross shifts down. But this means that Y is lower, which means
that the MP equation, r = r(Y), implies that r is lower – a contradiction. A similar argument rules
out the possibility that net capital flows are unchanged. Thus, the only possibility is that they rise.
Since net exports equal net capital outflows, net exports must also rise. And in order for net
exports to rise, we know that the exchange rate must fall.
We can also try to use the net capital outflows and net exports diagrams to derive the same results
(see figures on the following page). Unfortunately, from the figures alone it is not possible to
show that net capital outflows and thus net exports must increase: it is perfectly possible to draw
a figure in which the CF(r) schedule shifts by a small enough amount that net capital outflows fall.
But the discussion above suggests that such a figure would not be an accurate depiction of our
model.
5
E
Y=E
E1
E2
E0
Y
r
r
MP
r1
r0
CF1(r)
IS1
IS0
Y0
Y2
Y1
CF0(r)
Y
CF
ε
NX(ε)
NX
Figures for question 2, parts b and c.
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3. Potential output falls because of reduced productivity
a. Effect on the IS-MP diagram in the short run
Even though the question asks about the short
run effects in the IS-MP diagram, we start with
the IA-AD figure. The change in productivity
has two effects on the AD-IA diagram in the
short run. First, the reduction in potential output
is a supply shock and corresponds to a decline in
potential output from Y! to Y! . Second, the fall
in productivity is an unfavorable inflation shock.
Recall that an inflation shock is any disturbance
that changes the way that firms set their prices.
The fall in productivity means that firms
produce less with the same amount of inputs, so
firm costs are higher. This means that firms
increase their prices more, and so inflation today
increases. In our IA-AD figure this unfavorable
inflation shock shifts the IA curve up from IA !
to IA! .
Moving to the IS-MP diagram, remember that
the MP curve is given by the interest rate rule
r = r(Y, π) and that r is increasing in inflation.
In response to the increase in inflation the
central bank raises the interest rate for any level
of output. In our graph this appears as a shift
upward of the MP curve. The IS curve does not
move. In the short run the drop in productivity
reduces output from Y! to Y! and increases the
interest rate from r! to r! .
Notice that even though the IA curve shifted up, we drew it so that IA! does not cross the AD
curve at the new level of potential output, Y! . This is only one of several ways to draw this
response. Short-run output Y! could be above, below, or equal to the new potential output.
b. Impact on output and inflation in the long run
Since we have assumed that Y! is greater than the new level of potential output, Y! , inflation will
continue to increase and output will continue to fall. This is reflected in further upward shifts of
the IA curve. Inflation will continue to rise until the IA curve intersects the AD curve at the new
level of potential output, Y! . Notice that as the IA curve shifts up the MP curve also shifts up. The
central bank reacts to higher inflation by raising the real interest rate, moving the economy along
the AD curve. If you had drawn the first part so that short run output was equal to potential output
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(Y! = Y! ) then there would be no inflation dynamics in the long run. If you had drawn the first
part so that short run output was less than potential output (Y! > Y! ), then inflation would
decrease and output would rise until output reached Y! .
4. Output and money growth regression
The problem with this statement is that the regression residuals are uncorrelated with money
growth by construction. Using OLS gives a regression line that fits the data in such a way that the
residuals are guaranteed to be uncorrelated with the right hand side variables, in this case money
growth. Unfortunately, if there is an omitted variable that is correlated with money growth, then
the coefficient estimated by the computer will be a bad estimate of the actual (causal) effect of
money on output. And since the regression residuals are uncorrelated with money growth by
construction, they cannot tell us whether or not we should be concerned about omitted variables
bias.
It might help to consider again the underlying model Δ𝑌! = 𝑎 + 𝑏 Δ𝑀! + 𝑢! . Here b is the true
(causal) effect of money growth on output growth and 𝑢! captures everything else that affects
output growth. In order for our OLS regression to give us estimates of these true parameters we
need it to be true that there is no correlation between 𝑢! , the model’s true residual, and Δ𝑀! .
Omitted variable bias would mean that there is a variable Z that we are placing in u that is
correlated with Δ𝑀! (fiscal policy could be such a variable). If we run a regression with a model
that has omitted variable bias then the regression will not give us estimates of the true parameter
b. This means the estimated residuals will differ systematically from the true residuals. Thus, the
correlation between the estimated residuals and Δ𝑀! does not tell us about the correlation
between the true residuals and Δ𝑀! .
5. True / false / uncertain
It was possible to get full credit for this problem by answering true, false or uncertain. The
explanation was the crucial part of your answer.
If you answered true or uncertain, your answer should have focused on the U.S experience in the
depression. The depression in the U.S. was in large part caused by domestic aggregate demand
shocks. Early in the depression (1929-1930) these were primarily shocks to consumer and
investor demand (IS shocks) related to the stock market crash. Thereafter, the dominant shocks
came from waves of increasingly severe banking panics that increased the demand for highpowered money. In our model, these banking panics correspond to repeated upward shifts of the
LM curve. As Friedman and Schwartz emphasize, the Fed was mostly passive even as prices and
output declined rapidly. The Fed’s passivity contributed to the depression both by not mitigating
the banking panics and by lowering inflation expectations.
Other than in October 1931 (right after Britain went off the gold standard), it is not obvious that
the gold standard was a constraint on Fed actions. The U.S. had large gold reserves and the Fed
could probably have significantly expanded the money supply without endangering them. Hence,
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one can plausibly argue that the gold standard played a small or uncertain role in the Great
Depression in the U.S.
A good explanation for an answer of 'false' would have emphasized that even if the gold standard
played a relatively unimportant role in the depression in the U.S., it was important to the
transmission of the depression around the world. When the U.S. raised interest rates in 1928,
other countries were also forced to tighten monetary policy if they wished to stay on the gold
standard. Perhaps more importantly, the gold standard then prevented countries from responding
to banking panics and output declines with expansionary policy. Outside of the U.S. and France,
gold reserves were low and expansionary monetary or fiscal policy risked provoking gold
outflows. Strong evidence of the importance of the gold standard as a constraint on expansionary
policy comes from the fact that most countries began to recover from the depression when they
abandoned the gold standard.
6. Empirical question
a.
This question asked you to obtain two different measures of real GDP beginning in 2006:Q4.
Both measures are computed by the Bureau of Economic Analysis (BEA), a division of the U.S.
Department of Commerce. It was possible to download these series directly from the BEA (table
1.17.6). Real GDP as measured on the expenditure side could be downloaded from the online
database FRED, but real GDP measured on the income side (gross domestic income) could not
be. Note that real GDP measured on the income side is available only through 2012:Q3.
b.
The table below shows the two series’ growth rates by quarter at an annual rate.
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Real GDP, Expenditure side
Date
2006:Q4
2007:Q1
2007:Q2
2007:Q3
2007:Q4
2008:Q1
2008:Q2
2008:Q3
2008:Q4
2009:Q1
2009:Q2
2009:Q3
2009:Q4
2010:Q1
2010:Q2
2010:Q3
2010:Q4
2011:Q1
2011:Q2
2011:Q3
2011:Q4
2012:Q1
2012:Q2
2012:Q3
2012:Q4
Levels
(2005
dollars)
13038
13056
13174
13270
13326
13267
13311
13187
12884
12711
12701
12747
12873
12948
13020
13104
13181
13184
13265
13307
13441
13506
13549
13653
13657
Real GDP, Income side
Growth rate at an Growth rate at an Levels Growth rate at an Growth rate at an
annual rate (exact annual rate (log
(2005 annual rate (exact annual rate (log
calculation)
approximation) dollars)
calculation)
approximation)
0.54%
3.65%
2.95%
1.70%
-1.77%
1.32%
-3.66%
-8.89%
-5.25%
-0.31%
1.45%
4.03%
2.34%
2.24%
2.60%
2.39%
0.08%
2.48%
1.28%
4.09%
1.96%
1.25%
3.11%
0.13%
0.54%
3.58%
2.91%
1.69%
-1.78%
1.32%
-3.73%
-9.31%
-5.39%
-0.31%
1.44%
3.95%
2.31%
2.22%
2.57%
2.36%
0.08%
2.45%
1.27%
4.01%
1.94%
1.24%
3.06%
0.13%
13301
13214
13232
13189
13237
13321
13284
13195
12857
12660
12580
12602
12758
12933
12984
13107
13144
13229
13243
13235
13379
13506
13481
13533
-2.58%
0.55%
-1.29%
1.45%
2.58%
-1.13%
-2.64%
-9.84%
-5.99%
-2.52%
0.70%
5.04%
5.62%
1.56%
3.85%
1.13%
2.61%
0.42%
-0.24%
4.45%
3.83%
-0.72%
1.55%
-2.61%
0.54%
-1.30%
1.44%
2.55%
-1.14%
-2.68%
-10.36%
-6.18%
-2.55%
0.70%
4.92%
5.47%
1.55%
3.78%
1.12%
2.58%
0.42%
-0.24%
4.35%
3.76%
-0.73%
1.54%
c.
There are many interesting things to see by comparing the two series. For instance:
•
•
•
•
The two measures can differ quite significantly. There are many instances when one
series says the economy is growing and the other shows the economy to be stagnant or
shrinking.
2007 looks much worse using the income-side measure than the expenditure-side
measure.
As measured on the income side, the decline in real GDP is significantly more rapid in
late 2008 and early 2009. In 2008:Q4, real GDP on the income side declines by almost a
percentage point more than real GDP as measured on the expenditure side.
Since recovery began in late 2009, real GDP as measured on the expenditure side paints a
picture of more consistent growth than real GDP measured on the income side. Measured
on the expenditure side, there have been no quarters with negative growth since 2009.
Measured on the income side, growth has been negative in two quarters (2011:Q3 and
2012:Q2).
Finally, it is also interesting that we don’t yet have an income-side estimate for 2012:Q4 even
though the product-side number has been available for more than a month.
7. e
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8. b
9. c