Deck 25: Monetary Policy: a Summing up

Question 1

Taxes, inflation, and home ownership
In this chapter, we discussed the effect of inflation on the effective capital-gains tax rate on the sale of a home. In this question, we explore the effect of inflation on another feature of the tax code-the deductibility of mortgage interest.
Suppose you have a mortgage of $50,000. Expected inflation is
and the nominal interest rate on your mortgage is i. Consider two cases.
a. What is the real interest rate you are paying on your mortgage in each case
b. Suppose you can deduct nominal mortgage interest payments from your income before paying income tax (as is the case in the United States). Assume that the tax rate is 25%. So, for each dollar you pay in mortgage interest, you pay 25 cents less in taxes, in effect getting a subsidy from the government for your mortgage costs. Compute, in each case, the real interest rate you are paying on your mortgage, taking this subsidy into account.
c. Considering only the deductibility of mortgage interest (and not capital-gains taxation), is inflation good for homeowners in the United States

Answer 1

(a) To calculate the real interest rate we can use the approximation. This states that the real interest rate is equal to the nominal interest rate minus inflation.
Case i: Therefore, the real interest rate is 4%.
Case ii: Therefore, the real interest rate is 4%.
(b) To calculate mortgage interest payments we will use the $50,000 given. We will first calculate how much interest is accumulated at 4% and at 14%, as mortgages use nominal interest rate.
Case i: Therefore, the real interest rate is 3%.
Case ii: Therefore, the real interest rate is 1.5%.
(c) Considering only the deductibility of mortgage interest rate, inflation is good for homeowners.

Question 2

Inflation targets
Consider a central bank that has an inflation target,
The Phillips curve is given by
a. If the central bank is able to keep the inflation rate equal to the target inflation rate every period, will there be dramatic fluctuations in unemployment
b. Is the central bank likely to be able to hit its inflation target every period
c. Suppose the natural rate of unemployment,
changes frequently. How will these changes affect the central bank's ability to hit its inflation target Explain.

Answer 2

(a) If the central bank is able to keep the inflation rate equal to the target inflation rate, there will not be dramatic fluctuations in unemployment. In fact, if the inflation rate is always equal to the target inflation rate, then the unemployment rate will always be equal of to the natural rate of unemployment.
(b) No, it is unlikely that the central bank will hit its target rate of inflation each period. There are many variables that can cause the inflation rate to fluctuate in the short term. Also, the Phillips curve does not hold exactly. There are situations where the inflation rate will increase even when the unemployment is above the natural rate of unemployment. In this case, the central bank needs to determine if it will let inflation increase to decrease the unemployment rate or decrease inflation and cause the unemployment rate to increase.
(c) If the natural rate of unemployment changes frequently it will be very hard for the central bank to hit its target rate of inflation. If the natural rate of unemployment changes, the target level of inflation might not cause the intended effect anymore. In a situation where the natural rate of unemployment is changing frequently, it will be hard to determine exactly what level of inflation to target. There is a chance that by the time you reach the target level of inflation that the natural level of unemployment will have changed.

Question 3

Suppose you have been elected to Congress. One day, one of your colleagues makes the following statement:
The Fed chair is the most powerful economic policy maker in the United States. We should not turn over the keys to the economy to someone who was not elected and therefore has no accountability. Congress should impose an explicit Taylor rule on the Fed. Congress should choose not only the target inflation rate but the relative weight on the inflation and unemployment targets. Why should the preferences of an individual substitute for the will of the people, as expressed through the democratic and legislative processes
Do you agree with your colleague Discuss the advantages and disadvantages of imposing an explicit Taylor rule on the Fed.

Answer 3

I disagree with my colleague. Implementing a Taylor rule on the central bank has many downsides. Currently, the mandate of the Federal Reserve states that it will effectively promote maximum employment, stable prices, and moderate long-term interest rates. Thus, the Fed does target employment and inflation as it would under a Taylor rule. However, imposing an explicit Taylor rule would break the separation between politics and the central bank. This means that the Fed would now be subject the political pressures, which would almost assuredly decrease its credibility. Also, using an explicit Taylor rule would limit the Fed's power to act under unusual circumstances such as a currency crisis or a situation where it needs to change the composition monetary and fiscal policy.
The benefits of using a Taylor rule fewer than the negatives. However, using a Taylor rule would give a very strong set of expectations for consumers and investors. The calculations used under the Taylor rule would let consumers know exactly what to expect in the coming quarters. The economy would be transparent, allowing anybody to analyze the long term path that an economy will follow.

Question 4

Inflation targeting and the Taylor rule in the IS-LM model
Consider a closed economy in which the central bank follows an interest rate rule. The IS relation is given by
Where r is the real interest rate.
The central bank sets the nominal interest rate according to the rule
Where
is expected inflation,
is the target rate of inflation, and Y n is the natural level of output. Assume that a 1 and b 0. The symbol i* is the target interest rate the central bank chooses when expected inflation equals the target rate and output equals the natural level. The central bank will increase the nominal interest rate when expected inflation rises above the target, or when output rises above the natural level.
(Note that the Taylor rule described in this chapter uses actual inflation instead of expected inflation, and it uses unemployment instead of output. The interest rate rule we use in this problem simplifies the analysis and does not change the basic results.)
Real and nominal interest rates are related by
a. Define the variable
Use the definition of the real interest rate to express the interest rate rule as
(Hint: Subtract
from each side of the nominal interest rate rule and rearrange the right-hand side of the equation.)
b. Graph the IS relation in a diagram, with r on the vertical axis and Y on the horizontal axis. In the same diagram, graph the interest rate rule (in terms of the real interest rate) you derived in part (a) for given values of
and Y n. Call the interest rate rule the monetary policy (MP) relation.
c. Using the diagram you drew in part (b), show that an increase in government spending leads to an increase in output and the real interest rate in the short run.
d. Now consider a change in the monetary policy rule. Suppose the central bank reduces its target inflation rate,
. How does the fall in
affect the MP relation (Remember that a 1.) What happens to output and the real interest rate in the short run

Question 5

Consider the economy described in Problem 6.
a. Suppose the economy starts with
Now suppose there is an increase in
Assume that Y n does not change. Using the diagram you drew in Problem 6(b), show how the increase in
affects the MP relation. (Again, remember that a 7 1.) What happens to output and the real interest rate in the short run
b. Without attempting to model the dynamics of inflation explicitly, assume that inflation and expected inflation will increase over time if Y Y n , and that they will decrease over time if Y Y n. Given the effect on output you found in part (a), will
tend to return to the target rate of inflation,
over time
c. Redo part (a), but assuming this time that a 1. How does the increase in
affect the MP relation when a 1 What happens to output and the real interest rate in the short run
d. Again assume that inflation and expected inflation will increase over time if Y Yn , and that they will decrease over time if Y Yn. Given the effect on output you found in part (c), will
tend to return to the target rate of inflation,
over time Is it sensible for the parameter a (in the interest rate rule) to have values less than 1

Question 6

Current monetary policy
Problem 10 in Chapter 4 asked you to consider the cur-rent stance of monetary policy. Here, you are asked to do so again, but with the additional understanding of monetary policy you have gained in this and previous chapters. Go to the Web site of the Federal Reserve Board of Governors (www.federalreserve.gov) and download either the press release you considered in Chapter 4 (if you did problem 10) or the most recent press release of the Federal Open Market Committee (FOMC).
a. What is the stance of monetary policy, as described in the press release
b. Is there evidence that the FOMC considers both inflation and unemployment in setting interest rate policy, as would be implied by the Taylor rule
c. Does any of the language of the press release seem to be aimed at increasing the credibility of the Fed (as committed to low inflation) or at affecting inflation expectations

Question 7

Using the information in this chapter, label each of the following statements true, false, or uncertain. Explain briefly.
a. The most important argument in favor of a positive rate of inflation in OECD countries is seignorage. b. The Fed should target M2 growth because it moves quite closely with inflation.
c. Fighting inflation should be the Fed's only purpose.
d. Because most people have little trouble distinguishing between nominal and real values, inflation does not distort decision making.
e. The Fed uses reserve requirements as its primary instrument of monetary policy.
f. The higher the inflation rate, the higher the effective tax rate on capital gains.

Question 8

Explain how each of the developments listed in (a) through (d) would affect the demand for M 1 and M 2. a. Banks reduce penalties on early withdrawal from time deposits.
b. The government forbids the use of money market funds for check-writing purposes.
c. The government legislates a tax on all ATM transactions.
d. Congress decides to impose a tax on all transactions involving government securities with maturities of more than one year.