Why does the real interest rate, not the nominal interest rate, have intertemporal-substitution effects on consumption and saving? Does the same result apply for intertemporal substitution of labour supply?
The nominal rate cannot determine the opportunity cost of consuming goods today rather than in the future. Only the real interest rate can do that, because it takes into account changes in the future price of goods. The same argument applies to the labour supply decision, which is also based on the opportunity cost of current vs. future leisure.
What is the Livingston survey of inflationary expectations? What are the pluses and minuses of using this type of information to measure the expected inflation rate, πet?
The Livingston survey is survey of 50 economists concerning inflation forecasts. The forecast uses “experts” as opposed to households. The extent to which household expectations relate to those of the experts is not known. Also, how do we determine whether the sample chosen is representative of the entire group? On the other hand, to the extent that decision makers are looking at these forecasts when formulating their own expectations, the survey is an economical way and reliable source of information.
3. Which of the following statements is correct?
a. A constant rate of increase in the price level, P, will lead to a continuous rise in the nominal interest rate, i.
b. A continuous increase in the inflation rate, π, will lead to a continuous rise in the nominal interest rate, i.
a. false. A constant rate of inflation will be incorporated into a constant nominal rate.
true. A growing rate of inflation will cause corresponding changes in i.
4. Why does the actual real interest rate, r, generally differ from the expected real interest rate, ret? How does this relation depend on whether bonds prescribe the nominal or real interest rate?
The actual rate can only be determined after the fact, when actual inflation rates can be measured. Before the fact, inflation rates can only be predicted.
5. Define the real interest rate, r. Why does it differ from the nominal interest rate, i, in the presence of inflation?
The real interest rate is the nominal interest rate – inflation. Positive rates of inflation change the purchasing power of money over time, reducing the real value of interest. Higher nominal rates are needed to compensate lenders for this loss in purchasing power.
6. Can the government always increase its real revenue from printing money by raising the money growth rate, μ? How does the answer depend on the responsiveness of real money demand, Md/P, to the nominal interest rate, i?
Government revenue from printing money increases with m, but decreases with respect to real balances, (see equation 12.22 on page 233) Higher m will lead to higher nominal rates, which reduce money demand. The more sensitive money demand is to these nominal rates, the more it will reduce the government’s real revenue from printing money.
7. In 1925, a group of swindlers induced the Waterlow Company, a British manufacturer of bank notes, to print and deliver to them £3 million worth of Portuguese currency (escudos). Since the company also printed the legitimate notes for the Bank of Portugal, the counterfeit notes were indistinguishable from the real thing (except that the serial numbers were duplicates of those from a previous series of legitimate notes). Before the fraud was discovered, £1 million worth of the fraudulent notes had been introduced into circulation in Portugal. After the scheme unravelled (because someone noticed the duplication of serial numbers), the Bank of Portugal made good on the fraudulent notes by exchanging them for newly printed, valid notes. The Bank subsequently sued the Waterlow Company for damages. The company was found liable, but the key question was the amount of damages. The Bank argued that the damages were £1 million (less funds collected from the swindlers). The other side contended that the Bank suffered only negligible real costs in having to issue an additional £1 million worth of money to redeem the fraudulent notes. (Note that the currency was purely a paper issue, with no convertibility into gold or anything else.) Thus, the argument was that the only true costs to the Bank were the expenses for paper and printing.
Which side do you think was correct? (The House of Lords determined in 1932 that £1 million was the correct measure. For discussions of this fascinating episode in monetary economics, see Ralph Hawtrey, 1932, and Murray Bloom, 1966.)
The counterfeiting was sufficient to create some inflation and higher nominal interest rates, which would ultimately lead to lower real money balances. By equation 12.22, we see that this would have reduced government’s ability to increase revenue from the creation of money. In a sense, the competition hurt government’s profits!
8. Suppose that the monetary authority wants to keep the nominal interest rate, i, constant. Assume that the real interest rate, r, is fixed. However, the real demand for money, Md/P, shifts around a great deal.
a. How should the monetary authority vary the nominal quantity of money, M, if the real demand for money, Md/P, increases temporarily? What if the real demand increases permanently?
b. How does the price level, P, behave in your answers to question a? What should the monetary authority do if it wants to dampen fluctuations of P, as well as maintain a constant nominal interest rate, i?
a. and b. If there is a temporary increase in money demand then people will want to increase their money balances; this would cause a onetime reduction in the price level. This does not affect nominal interest rates however, because the one time change in the price level has no effect on the growth rate of money. Therefore, by the equation i=r+p, the nominal interest rate will not change.
However, if the central bank wanted to prevent even a one‐time change in the price level, they would have to grow the nominal money supply temporarily, and then shrink it once the event is over. If the public recognizes the temporary nature of the increased money supply growth, then there will be no change in prices or interest rates. A credible announcement of its intentions will help calm inflationary fears.
The FED attempted something very similar to this in the months leading up to the Y2K scare. They allowed the money supply to grow quickly before the year 1999 ended, and reduced the growth rate in the following period. If the increase in money demand is permanent, then the increase in money supply must also be permanent.
Once again, there should be no effects on either prices or nominal interest rates, as in figure 12.9. One way for the central bank to gain credibility is to announce a target for inflation. Countries that do this credibly have an essentially passive monetary policy that accommodates changes in money demand without causing inflation. The nominal interest rate changes only in response to changes in the real interest rate.
9. What are the effects on the price level, P, and the nominal interest rate, i, from the following events?
a. A once-and-for-all increase in the nominal quantity of money, M;
b. A once-and-for-all increase in the money growth rate, μ;
c. A credible announcement that the money growth rate, μ, will rise beginning one year in the future.
The price level increases proportionately, but nominal interest rates do not change.
The increase in the money growth rate causes a similar increase in inflation and nominal interest rates. The price level “jumps” during the transition to a higher level.
Prices increase because of the reduction in money demand, nominal interest rates rise.
10. How would the hypothesis of rational expectations help us to measure the expected inflation rate, πet? What seem to be the pluses and minuses of this approach?
Rational expectations allow us to make use of all available information to identify the expected rate during the period in question. However, it is also difficult to determine the extent to which decision makers will actually attempt to gather and process this information. Sophisticated statistical models using data that is difficult to gather and interpret may help the forecaster formulate their own expectations, but won’t necessarily explain how decision makers formulate their forecasts.
11. Suppose that the money-demand function takes the form:
Md/P = D(Y,i) = Y•ψ(i)
That is, for a given nominal interest rate, i, a doubling of real GDP, Y, doubles the real quantity of money demanded, Md/P.
a. Consider the relation across countries between the growth rate of money (currency), μ, and the inflation rate, π, as shown in Figure 12.1 in Barro, R. et al (2017). How does the growth rate of real GDP, ΔY/Y, affect the relationship between μ and π?
b. What is the relation between μ and π for a country in which the nominal interest rate, i, has increased?
c. Suppose that the expected real interest rate, ret, is given. What is the relation between μ and π for a country in which the expected inflation rate, πet, has increased?
