Executive MBA Program
Macroeconomics
Professor: Martin Eichenbaum
TA: Riccardo Bianchi Vimercati
Assignment 3
Question 1 – The Taylor rule and monetary policy
Suppose the Fed follows the Taylor rule given by
? = ? + ?∗ − (? − ?∗) + 0.5 (? − ?∗).
Here ? denotes the nominal interest rate, ? is the inflation rate, and ? is the cu
ent
unemployment rate. Assume that the long-run average value of the real interest rate ?∗ is 0.03,
the target rate of inflation ?∗ is 0.02, and the long-run (or natural) unemployment level ?∗ is
0.04.
Note that in class we used a Taylor rule with output gap
?∗−?
?∗
instead of the deviation of
unemployment rate from the natural level ? − ?∗. These are equivalent formulations of the
Taylor rule since both terms measure deviation of the cu
ent economic conditions relative to
some long-run value, so don’t get confused.
Note that when unemployment is at its natural level and inflation is on target, the nominal
interest rate is equal to 0.05.
Suppose that unemployment is 0.04 and inflation grows from 0.02 to 0.04 (four percent):
(a) What will the Fed set the nominal interest rate to if it follows the Taylor rule? What does the
Fed have to do to
ing about the change in the nominal interest rate? Specifically, will it
have to buy or sell bonds. Explain your answer.
(b) What will the real interest be after the Fed acts? Did it go up or down? State the Taylor
Principle and relate your finding about the change in the real interest rate to the Taylor
Principle.
The following graph shows that after the great recession, the Fed was not following the Taylor
ule due to the Zero-Lower Bound (ZLB) constraint on nominal interest rates. Cu
ently the
federal funds rate is at 0.016, while inflation is at 0.022 and the unemployment rate is 0.042.
(c) As the economy recovers, the Fed is increasing interest rates towards the Taylor rule
prescription. Determine what that rate is under the following scenarios:
i. The natural unemployment rate is 0.04.
ii. The natural unemployment rate is lower at 0.03 (President Trump’s prefe
ed
number).
For cases (i) and (ii), discuss whether monetary policy is getting looser or tighter.
Suppose now that the long-run value of the real interest rate ?∗ falls to 0.01, so that the Taylor
ule now is:
? = ? + 0.01 − (? − XXXXXXXXXX (? − 0.02).
(d) With this lower real interest rate, Fed officials are wo
ied the ZLB on nominal interest rates
will be more likely to bind when the unemployment rate rises. Suppose that cu
ent inflation
is at 0.02. Holding inflation at its target level, for what value of the unemployment rate is the
ZLB now binding?
(e) Explain why and how a change in the inflation target could help reduce the problem that the
ZLB is more likely to bind in the future if the economy gets hit by shocks that increase the
unemployment rate.
(f) Based on your answer to (d) and (e) would you favour raising the inflation target? As part of
your answer please discuss possible downsides of raising the target inflation rate.
Question 2 – Fiscal policy and the government budget
The Economic Report of the President can be obtained on the web at
https:
www.gpo.gov/fdsys
owse/collection.action?collectionCode=ERP
Consider the 2018 report. In this exercise, you will use data from the appendix (downloadable in
excel format) to take a closer look at the government budget.
a. Using the data from Table B-18, plot the government deficit or surplus and the gross
federal debt in the same graph, both as a percentage of GDP, from 1947 until the most
ecent date (use the left vertical axis for gross federal debt and the right vertical axis for
government deficit). How can you explain the years where the federal government was
unning a deficit but the debt-to-GDP ratio was decreasing?
. Now compare the Federal government’s budget between 2000 and 2015. Express the
main components of Federal spending and receipts each year as fractions of GDP. (Use
the GDP data from Table B-2 and the budget data from table B-19. Table B-2 only has
values for GDP starting from 2002. GDP in 2000 and 2001 was respectively 10,284.8
and 10,621.8 billions). Use information you computed about the main components of
Federal spending and receipts to answer the following questions:
i. What accounts for the increase in the deficit between 2000 and 2004?
ii. What accounts for the decrease in the deficit between 2004 and 2007?
iii. How would you characterize the reason for rise in the deficit during the great
ecession?
iv. What accounts for the decrease in the deficit between 2011 and 2015?
https:
www.gpo.gov/fdsys
owse/collection.action?collectionCode=ERP