978-0133836790 Chapter 16 Part 2

d. Potential output declines while actual output remains unchanged.

e. The Fed revises its (implicit) inflation target downward.

ANSWERS TO APPLIED PROBLEMS

24. If the Fed has an interest-rate target, why will an increase in the demand for reserves lead to a

rise in the money supply? Use a graph of the market for reserves to explain.

25. Since monetary policy changes made through the fed funds rate occur with a lag,

policymakers are usually more concerned with adjusting policy according to changes in the

forecasted or expected inflation rate, rather than the current inflation rate. In light of this,

suppose that monetary policymakers employ the Taylor rule to set the fed funds rate, where

the inflation gap is defined as the difference between expected inflation and the target

inflation rate. Assume that the weights on both the inflation and output gaps are ½ the

equilibrium real fed funds rate is 2%, the inflation rate target is 2%, and the output gap is

1%.

a. If the expected inflation rate is 4%, then at what target should the fed funds rate be set

according to the Taylor rule?



b. Suppose half of Fed economists forecast inflation to be 3%, and half of Fed economists

forecast inflation to be 5%. If the Fed uses the average of these two forecasts as its

measure of expected inflation, then at what target should the fed funds rate be set

according to the Taylor rule?

e

c. Now suppose half of Fed economists forecast inflation to be 0%, and half forecast

inflation to be 8%. If the Fed uses the average of these two forecasts as its measure of

expected inflation, then at what target should the fed funds rate be set according to the

Taylor rule?

e

d. Given your answers to parts (a)–(c) above, do you think it is a good idea for monetary

policymakers to use a strict interpretation of the Taylor rule as a basis for setting policy?

Why or why not?

Probably not. In the situation in part (a), it is assumed that there is very little uncertainty

ANSWERS TO DATA ANALYSIS PROBLEMS

1. The Fed’s maximum employment mandate is generally interpreted as an attempt to achieve

an unemployment rate that is as close as possible to the natural rate and inflation that is

close to its 2% goal for personal consumption expenditure price inflation. Go to the St. Louis

Federal Reserve FRED database, and find data on the personal consumption expenditure

price index (PCECTPI), the unemployment rate (UNRATE), and a measure of the natural

rate of unemployment (NROU). For the price index, adjust the units setting to “Percent

Change From Year Ago” to convert the data to the inflation rate; for the unemployment rate,

change the frequency setting to “Quarterly.” Download the data into a spreadsheet.

Calculate the unemployment gap and inflation gap for each quarter. Then, using the inflation

gap, create an average inflation gap measure by taking the average of the current inflation

gap and the gaps for the previous three quarters. Now apply the following (admittedly

arbitrary and ad hoc) test to the data from 2000:Q1 through the most recent data available:

If the unemployment gap is larger than 1.0 for two or more consecutive quarters, and/ or the

average inflation gap is larger in absolute value than 0.5 for two or more consecutive

quarters, consider the mandate “violated.”

a. Based on this ad hoc test, in which quarters has the Fed “violated” the price stability

portion of its mandate? In which quarters has the Fed “violated” the maximum

employment mandate?

b. Is the Fed currently “in violation” of its mandate?

c. Interpret your results. What do your response to part (a) and the data imply about the

challenge that monetary policymakers face in achieving the Fed’s mandate perfectly at

all times?

It is clearly very difficult to meet the objectives set forth in the Fed’s mandate, even

somewhat minor in that they do not last for long, or do not significantly deviate from the

noted thresholds too much.

Date

Unemp. Gap

Avg. Four Qtr.

Inflation Gap

2000-01-01

-1.01

-0.2

2000-04-01

-1.11

0.1

2000-07-01

-1.01

0.4

2000-10-01

-1.10

0.5

2001-01-01

-0.80

0.4

2001-04-01

-0.60

0.4

2001-07-01

-0.20

0.2

2001-10-01

0.50

-0.1

2002-01-01

0.70

-0.4

2002-04-01

0.80

-0.8

2002-07-01

0.70

-0.8

2002-10-01

0.90

-0.7

2003-01-01

0.90

-0.2

2003-04-01

1.10

-0.1

2003-07-01

1.10

0.0

2003-10-01

0.80

0.0

2004-01-01

0.70

-0.2

2004-04-01

0.60

0.0

2004-07-01

0.40

0.2

2004-10-01

0.40

0.4

2005-01-01

0.30

0.6

2005-04-01

0.10

0.6

2005-07-01

0.00

0.8

2005-10-01

0.00

0.8

2006-01-01

-0.30

1.0

2006-04-01

-0.40

1.1

2006-07-01

-0.40

1.0

2006-10-01

-0.60

0.7

2007-01-01

-0.50

0.5

2007-04-01

-0.50

0.3

2007-07-01

-0.30

0.1

2007-10-01

-0.20

0.5

2008-01-01

0.00

0.8

2008-04-01

0.30

1.1

2008-07-01

1.00

1.5

2008-10-01

1.90

1.1

2009-01-01

3.30

0.3

2009-04-01

4.25

-0.8

2009-07-01

4.52

-2.0

2009-10-01

4.79

-2.1

2010-01-01

4.65

-1.5

2010-04-01

4.42

-1.0

2010-07-01

4.30

-0.4

2010-10-01

4.38

-0.3

2011-01-01

3.76

-0.4

2011-04-01

3.84

-0.3

2011-07-01

3.73

0.1

2011-10-01

3.32

0.4

2012-01-01

2.90

0.6

2012-04-01

2.88

0.4

2012-07-01

2.64

0.1

2012-10-01

2.41

-0.2

2013-01-01

2.28

-0.4

2013-04-01

2.05

-0.6

2013-07-01

1.72

-0.7

2013-10-01

1.50

-0.9

2014-01-01

1.20

-0.9

consumption expenditure price index (PCECTPI), real GDP (GDPC1), an estimate of

potential GDP (GDPPOT), and the federal funds rate (DFF). For the price index, adjust the

units setting to “Percent Change From Year Ago” to convert the data to the inflation rate;

for the federal funds rate, change the frequency setting to “Quarterly.” Download the data

into a spreadsheet. Assuming the inflation target is 2%, calculate the inflation gap and the

output gap for each quarter, from 2000 until the most recent quarter of data available.

Calculate the output gap as the percentage deviation of output from the potential level of

output.

a. Use the output and inflation gaps to calculate, for each quarter, the fed funds rate

predicted by the Taylor rule. Assume that the weights on inflation stabilization and output

stabilization are both ½ (see the formula in the chapter). Compare the current (quarterly

average) federal funds rate to the federal funds rate prescribed by the Taylor rule. Does

the Taylor rule accurately predict the current rate? Briefly comment.

b. Create a graph that compares the predicted Taylor rule values with the actual quarterly

federal funds rate averages. How well, in general, does the Taylor rule prediction fit the

average federal funds rate? Briefly explain.

c. Based on the results from the 2008–2009 period, explain the limitations of the Taylor

rule as a formal policy tool. How do these limitations help explain the use of

nonconventional monetary policy during this period?

d. Suppose Congress changes the Fed’s mandate to a hierarchical one in which inflation

stabilization takes priority over output stabilization. In this context, recalculate the

predicted Taylor rule value for each quarter since 2000, assuming that the weight on

inflation stabilization is ¾ and the weight on output stabilization is ¼. Create a graph

showing the Taylor rule prediction calculated in part (a), the prediction using new

“hierarchical” Taylor rule, and the fed funds rate. How, if at all, does changing the

mandate change the predicted policy paths? How would the fed funds rate be affected by

a hierarchical mandate? Briefly explain.

-4

-2

0

2

4

6

8

2000-01-01

2000-09-01

2001-05-01

2002-01-01

2002-09-01

2003-05-01

2004-01-01

2004-09-01

2005-05-01

2006-01-01

2006-09-01

2007-05-01

2008-01-01

2008-09-01

2009-05-01

2010-01-01

2010-09-01

2011-05-01

2012-01-01

2012-09-01

Taylor Rule

Fed Funds Rate