Solutions to PSet 5. October 6, More on the AS/AD Model

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1 Solutions to PSet 5 October 6, 207 More on the AS/AD Model. If there is a zero interest rate lower bound, is fiscal policy more or less effective than otherwise? Explain using the AS/AD model. Is the United States currently at the zero lower bound? Explain. If there is a zero interest rate lower bound, the AD curve is a vertical line: if there is a change in prices, r does not change (since is set to zero) and thus also investment and output don t change. If there is an expansionary fiscal policy (an increase in spending G), the AD curve shifts to the right, but the absence of crowding out effects (an increase in the interest rate that causes I to go down) makes this policy even more effective than in the standard case of r > 0. The United States is currently at the zero lower bound, as can be seen in Figure. Since the last recession, given that output was low and inflation was low and stable, the Fed had chosen a low interest rate in an effort to try to stimulate the economy.

2 2 Figure : Output, Inflation, and the Interest Rate 970 I IV 2. What would the shape of the AD curve be if the Fed cared much more about output than about the price level? Why? How would the effects on output of a change in the price of imports PM differ in this case versus the case in which the Fed cared much more about the price level than about output? Show graphically using the AS/AD model. If the Fed cared much more about output than about the price level, then in the equation for the Fed rule we would have b < a. This means that the central bank will react to price changes only if these changes are substantial, to avoid negative effects on output due to the increase in the interest rate. This implies that the Fed is willing to accept high changes in P to keep output stable. This clearly implies that the AD has a very steep slope. If there is an increase in the price of imports, the aggregate level of prices goes up. If the Fed cares more about output, then its response will be mild: it will increase the interest rate by few basis points. If instead the Fed cares more about price stability than production, then the response will be stronger and it will increase the interest rate a lot to keep prices stable, at the cost of reducing investment and thus output. You can see the opposite situation (a decline in the price of imports) graphically in Figure 2, where again, price declines less and so the output impact is greater.

3 3 Figure 2: A decline in the price of imports 3. From the Board of Governors website, the 0 year nominal rate of interest is 2.3 percent and the 0 year real (inflation indexed) rate of interest is 0.44 percent. What is the implicit 0 year expected rate of inflation at an annual rate? Should borrowers and lenders be more concerned about real interest rates than about nominal interest rates? Why or why not? Let r N be the nominal interest rate, and r R be the real interest rate. Let p e be expected inflation. Then,

4 4 ( + r N ) = ( + r R )( + p e ) + p e = + r N + r R p e = + r N + r R p e = + r N + r R p e = p e The implicit expected inflation rate is.86%. Borrowers and lenders care about real interest rates because they represent the true value of what they are getting paid back, or paying back in terms of the goods and services they can buy. If the price level is going up at 0%, and I am getting paid back 5% on my loans, then I am worse off in real terms, even though I am getting a nominal rate of 5%. The real interest rate adjusts for the price level, and so borrowers and lenders will care more about that. 4. Do you think the Fed rule calls for an increase in the interest rate the next time the Fed meets? Explain your answer. What are possible arguments against your answer? Looking at Figure, it seems that output is growing while inflation remains stable and low. In general, implementation of the Fed rule would call for an increase in the interest rate given the increase in output. However, since these are the first periods of growth after a severe recession, the Fed might want to wait before increasing the interest rate. Note that ( + r N ) = ( + r R )( + p e ) ( + r N ) = + r R + p e + r R p e r N = r R + p e + r R p e Since r R p e is generally close to zero, a reasonable (and fast) approximation for calculating the expected inflation rate is p e r N r R = =

5 5 Unemployment. Why might there be unemployment if wages are sticky downward? Why might wages be sticky downward? Give at least four reasons. With sticky wages, if labor demand decreases but wages do not decrease, then the supply of labor will exceed the demand. This excess supply would persist because so long as wages don t adjust downward, and there would be unemployment. There are many reasons why wages might be sticky downward. Implicit/social contracts prevent firms from cutting wages because it hurts morale and therefore productivity. Explicit contracts may keep wages fixed at the agreed-upon level. Minimum wage laws will fix wages for a fraction of workers. Firms may have imperfect information and not react to changes in the economy right away so that it takes time for wages to adjust. Finally, employers may keep wages higher than the market-clearing rate to provide incentives to employees to work harder (efficiency wages theory). 2. Plot the monthly unemployment rate from January 948 through August 207 (BLS website). What are the periods that you would consider the economy to have been roughly at full employment? Figure 3: Unemployment Rate I would consider the following periods to be roughly at full employment: , , , , , , Some people argue that the actual unemployment rate is higher than the government estimates it to be. What is this argument? The unemployment rate would be higher if it included discouraged workers. Discouraged workers stopped looking for a job because they could not find a job but they still want to

6 6 work. These people are not officially unemployed because they are not counted as in the labor force, though arguably they truly are. 4. Some people argue that the actual unemployment rate is lower than the government estimates it to be. What is this argument? The unemployment rate may be lower because there are people who are looking for a job and have received job offers but have not accepted them because they are hoping for a higher wage that is above the market wage. These people should not be counted as unemployed because they are not willing to work at the market wage. The Phillips Curve. The Phillips Curve broke down in the 970 s. What does this mean and why is it perhaps a misleading statement? Explain the breakdown using the AS/AD model. The Phillips Curve illustrates the inverse relationship between the inflation rate and the rate of unemployment: when unemployment is high, inflation is low, and vice versa. This relationship held very strongly in the 950s and 960s. But for much of the 970s both inflation and unemployment moved in the same direction, rising and falling together. This is what is meant by the Phillips Curve broke down. This statement might be misleading for two reasons. First, by the end of the 970s the rate of inflation fell as unemployment rose, so the relationship may not have broken down entirely. Even if the graphical representation of the Phillips relationship became messy, the underlying association between inflation and employment could remain. Second, it might be misleading because it attributes a sense of historical accuracy to the Phillips Curve that may be undeserved. The mid-century stability of the AS curve allowed fluctuations of the AD curve to trace-out a robust and inverse relationship of the unemployment rate and the rate of inflation: when inflation declined, unemployment rose; when unemployment declined, inflation rose. As price shocks hit the economy in the 970s, the AS curve began to shift at the same time the AD curve shifted, distorting the Phillips relationship. The Phillips curve holds for a given AS curve, and so it represents a short-run trade-off that can vary over time as fundamentals change. 2. The U.S. unemployment rate is currently a little over 4 percent, a value that most economists think is close to full employment. Inflation is modest, below the Fed s

7 7 target of 2 percent. Is the low unemployment rate and the low rate of inflation inconsistent with the Phillips Curve? Why or why not? No, the current low unemployment rate and the low rate of inflation are not inconsistent with the Phillips Curve. As mentioned above, the Phillips curve holds for a given AS curve, and so it represents a short-run trade-off that can vary over time as fundamentals change. For instance, as Figure 4 shows, one fundamental that changed in the last years is the price of oil, which is at historically low prices. Figure 4: Price of Crude Oil WTI (NYMEX) Price End of day Commodity Futures Price Quotes for Crude Oil WTI (NYMEX)