# Problem Set 4 ECN 101 – Intermediate Macroeconomics Spring ```Problem Set 4
ECN 101 – Intermediate Macroeconomics
Spring 2004
Professor &Ograve;scar Jord&agrave;
DUE DATE: May 24, 2004
Multiple Choice Questions
Questions associated to chapters 10, 11 and 13 primarily. The website is:
http://bcs.worthpublishers.com/mankiw5/
Numerical Questions
1. Assume that the demand for real money balance (M/P) is M/P = 0.6Y - 100i,
where Y is national income and i is the nominal interest rate. The real interest rate
r is fixed at 3 percent by the investment and saving functions. The expected
inflation rate equals the rate of nominal money growth.
a. If Y is 1,000, M is 100, and the growth rate of nominal money is 1
percent, what must i and P be?
b. If Y is 1,000, M is 100, and the growth rate of nominal money is 2
percent, what must i and P be?
2. Assume that the long-run aggregate supply curve is vertical at Y = 3,000 while
the short-run aggregate supply curve is horizontal at P = 1.0. The aggregate
demand curve is Y = 3(M/P) and M = 1,000.
a. If the economy is initially in long-run equilibrium, what are the values of P and Y?
b. Now suppose a supply shock moves the short-run aggregate supply
curve to P = 1.5. What are the new short-run P and Y?
c. If the aggregate demand curve and long-run aggregate supply curves are
unchanged, what are the long-run equilibrium P and Y after the supply shock?
d. Suppose that after the supply shock the Fed wanted to hold output
at its long-run level. What level of M would be required? If this level of M were
maintained, what would be long-run equilibrium P and Y?
3. Suppose you are an economist working for the Federal Reserve when droughts in
the southeast and floods in the Midwest substantially reduce food production in
the United States. Use the aggregate demand/aggregate supply model to
supply shock assuming that your top priority is maintaining full employment in
the economy. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium
1
Problem Set 4
ECN 101 – Intermediate Macroeconomics
Spring 2004
Professor &Ograve;scar Jord&agrave;
values; iv. the direction the curves shift; and v. the terminal equilibrium values.
State in words what happens to prices and output as a combined result of the
supply shock and the recommended Fed accommodation.
Computer Questions – This Part is Due June 7
This section is a little more involved than usual, hence the expanded due date. Hopefully,
you will also find it more interesting. The EXCEL file for this part of the homework is
labeled “ps4.xls” and contains the following data (further details are available in the
EXCEL file) extracted from the St. Louis Fed website:
•
•
•
•
•
•
•
DPIC96: Real Disposable Income
GDPC96: Real Gross Domestic Product
GDPPOT2: Real Potential Gross Domestic Product
PCECC96: Real Personal Consumption Expenditures
PCECTPI: PCE deflator
TB3: 3-month T-Bill Rate
Recession: 1 if recession, 0 otherwise.
a) The first goal will be to construct an estimate of the Phillips Curve. Recall, the
Phillips curve can be expressed as:
π = π e + γ (Y − Y )
For this purpose, you will need to construct the yearly rate of inflation using the
PCE deflator. One way to do this is by using the usual logarithmic approximation:
π t = ln( PCE Deflator ) t − ln( PCE Deflator ) t −4
and noticing that the data is in quarterly frequency. As an approximation to πe you
can use πt-1.
Next you will need to construct Y − Y , i.e., the difference between actual and
potential output, also called the output gap. This can be easily calculated, in
percentage, by constructing the following logarithmic difference:
GAPt = 100 &times; (ln( rGDP ) − ln( rGD P ))
You are now in a position to calculate the coefficient γ by doing a scatter plot of
(π t − π t −1 ) on GAPt and fitting a trend line in EXCEL with the option “set
intercept to = 0” selected. For this part you should report the scatter plot with the
regression line and the regression output.
2
Problem Set 4
ECN 101 – Intermediate Macroeconomics
Spring 2004
Professor &Ograve;scar Jord&agrave;
b) The second item in the agenda will consist in fitting a Taylor rule to the data and
finding the sensitivity of interest rates to variations in the output gap. From the
previous part, you have already calculated all the variables that you will need. To
be sure, here is one way to write down the Taylor rule (the actual coefficients
proposed by Taylor are somewhat different but I use slightly different data. Also
notice that I am lagging inflation and the output gap to indicate that the central
bank observed these variables with a one quarter delay):
it = 4 + (π t −1 − 2) + β (Yt −1 − Yt −1 )
As you can see, I have assumed that if inflation goes up by 1% above the inflation
target (2%), nominal interest rates will be raised by 1%. If inflation and output are
at their targeted levels, then nominal interest rates will be set at 4%.
To estimate the coefficient β you will need to construct an adjusted, nominal
interest rate series by taking the current three-month T-Bill rate and subtracting 2
and the lagged rate of inflation (i.e. moving to the left hand side of the previous
expression the terms 4 + (π t −1 − 2) . Notice that Yt − Yt was already calculated as
the variable GAPt in the previous question so all you need to do is make sure that
you use its lag, rather than the current value. Similar to part a), you will need to
do a scatter plot of the adjusted interest rate series just described on to the lag of
the variable GAPt. Be sure to add a trend line with the “set intercept” option
selected. This will give you an estimate of β. Report the scatter plot with trend
line and the regression output.
c) Using the previous part, check to see how well your estimated Taylor rule does
historically. For that purpose you will need to create a series of predicted interest
rates as follows:
iˆt = 4 + (π t −1 − 2) + βˆGAPt −1
where the “hats” denote estimates. Do a “line” plot of the actual series for the
three-month T-Bill, the series predicted by the expression just described, and the
series “recession” times 20 (so that you can see more clearly where the recession
periods are). Report the line plot and comment on how well you predict interest
rates with this simple Taylor rule, and the relation between your predictions and
the actual interest rate over the business cycle. Be sure to label your X-axis so that
the dates show.
d) This one is an easy one. Use the data on personal consumption expenditures and
personal income to calculate the consumption rate over time (a crude
approximation to the marginal propensity to consume). Call this φˆ . Do a simple
plot over time (make sure that you put the dates on the x-axis) and calculate the
average over the sample.
e) Suppose that the IS curve is given by:
3
Problem Set 4
ECN 101 – Intermediate Macroeconomics
Spring 2004
Professor &Ograve;scar Jord&agrave;
Y = a + φˆ(Y − T ) + G − 2i
and the Taylor rule is given by your estimates in part c) by
i = 4 + (π − 2) + βˆ (Y − Y )
Solve for the aggregate demand curve Y as a function of I and calculate the
following multipliers (notice that you do not actually need the specific values of a
or Y to answer this question since they do not enter in the multipliers):
a) The government expenditures multiplier
b) The tax multiplier
c) The slope of the aggregate demand curve
4
```