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Chapter 18: Expectations and Macroeconomics Instructor’s Manual Chapter 18: Expectations and Macroeconomics Problem 1 The Phillips curve is an empirical relationship between the unemployment rate and the rate of wage inflation. The neoclassical wage equation, on the other hand, is a theoretical construct explaining how wage inflation and unemployment may be related in the short run, given expectations of price inflation. The Phillips curve relationship can be obtained from the neoclassical wage equation only if expectations of price inflation are constant. If the inflation rate were to become very high, it is unreasonable to assume that future inflation rates will be constant. This means that once people start observing high inflation, they will begin to expect even higher inflation rates in the future. Higher expectations of inflation will be built into wage contracts that firms and workers enter into, and will push up the wage inflation rate. Hence, we would start observing wage inflation without a corresponding reduction in the unemployment rate as the Phillips curve predicts. In other words, the Phillips curve relationship would cease to hold in a world where inflationary expectations were not constant. Problem 2 E w P g cU U * . We can see that an P w The new-Keynesian wage equation is P E increase in increases the rate of nominal wage inflation for a given level of unemployment P holding other variables constant. In other words, an increase in expected inflation shifts the Phillips curve to the right. During both the 1969-1979 and 1979-1989 periods we observed increasing nominal wage inflation during periods of steady or increasing unemployment, which could be caused by an increase in the expected inflation rate. Problem 3 The parameter c in the neoclassical wage equation: w P E g c(U U * ) , w P determines how fast the nominal wage rate adjusts to restore balance whenever unemployment is different from its natural rate. Recall that the classical model says that wages and prices adjust instantaneously because economic agents react very quickly to profit opportunities; therefore, unemployment is always at its natural rate. In the neoclassical wage equation, if people react quickly whenever unemployment is different from U*, this means that the speed of adjustment of nominal wage inflation to the gap (U - U*) is very high. In the limiting case when c is infinite, the adjustment is instantaneous, and the neoclassical wage equation behaves like the classical one. 207 Instructor’s Manual Chapter 18: Expectations and Macroeconomics Problem 4 w 5% 4% 2U 6% . w a. The Phillips curve equation is b. It must be true that 4% 5% 4% 2U 6% or U = 8.5%. c. The short run aggregate supply curve is d. No. Unemployment is above its natural rate and output growth is below its natural rate because price inflation is significantly below the expected inflation rate. Eventually, expected inflation will fall which will decrease unemployment back to its natural rate of 6% and increase output growth to its natural rate of 5%. P 4% 5% 4% 5% P = -2%. Problem 5 The NAIRU, or the non-accelerating inflationary rate of unemployment, is the level of unemployment that can be maintained by the Federal Reserve without putting upward or downward pressure on the current inflation rate. In other words, the NAIRU is the unemployment rate when actual price inflation equals expected price inflation. Unfortunately, the NAIRU is not observable. There is always some uncertainty as to the unemployment rate that the Fed should try to target if its goal is inflation stability. Because of this uncertainty, there is always a chance the Fed is targeting the wrong unemployment rate and, as a result, in danger of either accelerating inflation or maintaining a level of unemployment that is too high. Problem 6 The natural rate of employment is the employment rate consistent with the natural rate of growth of GDP. The natural rate of unemployment is the unemployment rate consistent with search costs in the labor market (see Chapter 7). If the productivity growth rate and labor supply both increase, but the increase in productivity growth is not enough to absorb the increased labor pool, then both rates will increase. Problem 7 The theory of rational expectations says that agents do not make predictable, or systematic, errors in forming their expectations. As a result, though agents may make mistakes in the future, they are as likely to be too high as too low. Thus, mistakes can be made, but on average expectations are correct. If expectations are consistently too high or too low, this new information will be adopted by agents and their expectations will change accordingly. 208 Instructor’s Manual Chapter 18: Expectations and Macroeconomics Problem 8 In the short run, an increase in the money growth rate increases the dynamic aggregate demand curve, increasing price inflation and output growth above its natural rate. This increase in price inflation without any change in nominal wage inflation reduces unemployment below its natural rate. See Figure 18.4 in the text. In the long run, agents increase their expected inflation rate and wage inflation increases. As a result, the short run aggregate supply curve shifts to the left, eventually reducing output growth back to its natural rate. The increase in the expected price level increases the unemployment rate for a given level of price inflation, eventually returning unemployment to its natural rate. See Figure 18.5 in the text. Problem 9 In order to reduce unemployment, the Fed will have to increase the rate of money growth and price inflation above its current levels. This will reduce unemployment temporarily. However, the economy is not in a long run equilibrium when unemployment is at 5% but when it is at 6%. Eventually, inflation expectations and wages will adjust to this increase in the inflation rate, shifting the Phillips curve to the right and increasing the unemployment rate back toward its natural rate. If the Fed persists in attempting to reduce unemployment below its natural rate by undertaking a series of increases in the money growth rate, it will lead to a series of increases in the price inflation rate. Hence, targeting an unemployment rate that is too low can lead to accelerating inflation. Problem 10 A policy that permanently reduces unemployment below its natural rate is one that permanently increases GDP growth above the natural rate. Consider Figure 3 below which shows how this can be done using a certain type of monetary policy. P P LRAS SRAS1 C P/P)2 SRAS0 P/P)Et+2 = (P/P)1 P/P)Et+1 = P/P)Et = (P/P)0 B AD1 A AD0 Y/Y)0 = g Y/Y)1 Figure 3 209 Y Y Instructor’s Manual Chapter 18: Expectations and Macroeconomics Suppose the economy is in long-run equilibrium at point A. If the current year is year t, and the economy is at A in the year (t-1) as well, then the expected inflation rate is (P/P)Et = (P/P)0. Now suppose the Fed increases the rate of money creation in the year t+1 so that the aggregate demand curve shifts from AD0 to AD1, i.e., the aggregate demand curve for the year t+1 is AD1. Since people were expecting the rate of inflation in year t+1 to be (P/P)0, the relevant short-run aggregate supply curve for the year is still SRAS0. Therefore, the economy will move from A to B along SRAS0. In year t+1, GDP growth will increase above g, and unemployment will fall below its natural rate. The actual inflation rate will be (P/P)1. In the following year (i.e., t+2), the expected inflation rate will be (P/P)1. Since the expected inflation rate has increased, and unemployment has fallen below its natural rate, the nominal wage inflation rate will increase in t+2. This will shift the year t+2 short-run aggregate supply curve to SRAS1. If the aggregate demand curve remains at AD1 from year t+1 onwards, then expectations will soon adjust and take the economy to the long-run equilibrium point C. Compared to the case where expectations are rational, the only difference here will be that the adjustment towards C will take longer. So, if the Fed is to permanently decrease the unemployment rate below the natural rate, it will have to keep pushing the AD curve to the right, i.e., increase the rate of money creation every period. In other words, the Fed has to increase the money supply at an increasing rate.1 Problem 11 First, the traditional Keynesian model ignored the effects of inflation expectations and how changes in these expectations can affect the relationship between inflation of unemployment. Second, the traditional Keynesian model ignored the natural rate of unemployment, arguing that the Fed can keep unemployment at any level if it chooses the proper level of inflation. Obviously, the fact that the expected inflation rate and the natural rate of unemployment, neither of which the Fed controls, are important factors in the tradeoff between inflation and unemployment suggests that it is very difficult, maybe impossible, to reliably control the unemployment rate using monetary policy. This has the effect of “surprising” people every period, since they look backwards in forming their expectations. Had expectations been rational, such a policy would have had no permanent effect as price expectations would be adjusted every period in anticipation of the Fed's actions. 1 210 Instructor’s Manual Chapter 18: Expectations and Macroeconomics Problem 12 This is a good question for class discussion. a. What Friedman is saying here is that money neutrality holds in the long run, meaning that the Fed can control nominal variables by changing the money supply but it cannot control real variables by changing the money supply. Thus, the tradeoff between inflation and unemployment does exist, but it only exists in the short run, because unemployment eventually returns to its natural rate, and the tradeoff is unstable, because changes in expected inflation can change the tradeoff. b. If the Fed tries to target a nominal interest rate, it may lead to exploding inflation. Consider the following example. Suppose that there is an increase in productivity that increases the natural rate of output growth, reduces the natural rate of unemployment, and increases real and nominal interest rates. What will happen if the Fed tries to target nominal interest rates and prevent this increase in interest rates from occuring? The Fed will be forced to increase the money supply to drive nominal interest rates down. However, this will eventually increase inflation and expected inflation, putting more upward pressure on nominal interest rates. This will once again force the Fed to increase the money supply to keep interest rates from rising and the whole process will continue to repeat itself. The end result of this policy to target nominal interest rates will be significantly higher inflation over time. Accelerating inflation will end only when the Fed gives up its interest rate target. Thus, the Fed cannot target nominal interest rates over long periods of time Problem 13 First, the Fed has imperfect information about the economy, such as the future state of the economy or what exactly the natural rate of unemployment is. As a result, it is prone to making mistakes because of this imperfect information. Second, the public’s expectations are not constant but will vary with changes in monetary policy. Thus, the results of policy can be unpredictable depending upon how agents form their expectations. Third, there are long logs in policy. The time between when a policy is enacted and when it actually has some effect on the economy can be so long that by the time the policy has an effect it may no longer be needed or it might be the wrong policy. Fourth, if the Fed tries to stabilize output and unemployment after aggregate supply shocks, the end result will be very high levels of inflation and will lead to inflationary expectations that may be very costly to remove over time. Problem 14 A class discussion is useful here. 211