1 The empirical relationship and its demise (?)

Transcription

1 BURNABY SIMON FRASER UNIVERSITY BRITISH COLUMBIA Paul Klein Office: WMC 3635 Phone: (778) paul klein URL: Economics 305 Intermediate Macroeconomic Theory Fall 2013 Lecture 6: The Phillips curve and the credibility problem 1 The empirical relationship and its demise (?) Williamson documents the withering away of the relationship between inflation and output. In the 1960s and 1970s it seemed like an inevitable fact of life. In the 1980s and 1990s it seemed to weaken almost to the point of disappearing. Well, perhaps not quite. Has it returned? As it happens, the theoretical literature is mostly focussed on (1) explaining why there is a short-run but not a long-run relationship between output and inflation and (2) what the implication of the Phillips curve are for the conduct of (optimal) monetary policy. The focus is typically not on why inflation went down or why the Phillips curve relationship disappeared or weakened over time. An partial exception is a fascinating book by Sargent (2001) where he argues that, occasionally, supply shocks can hit the economy that make the inflation output trade off seem more adverse (increasing output costs more in terms of inflation), persuading policy makers to choose lower inflation rates. So a disappearance of the Phillips relationship leads to lower inflation. Perhaps this is what happened in the 1970s. But how did the trade off remain adverse for so long? It s been three decades now. 1

2 2 The expectations augmented Phillips curve and the credibility problem The work of Lucas (1972) was a culmination of a literature that tried to formalize the notion that anticipated increases in the money supply should increase prices but not output, and that surprise increases in the money supply should increase output (and later inflation as well). On average, so this school of thought contended, output and employment should be at their natural rates and these rates are independent of the average rate of inflation. A popular specification, found in Kydland and Prescott (1977), is the following. y t = a(π t π e t) + y (1) where y t is (log) output or employment in period t, λ is a positive constant, π t is the inflation rate and π e t is the forecasted or expected inflation rate, and y is the (log of the) natural output level. For simplicity, suppose a = 1 and y = 0. Now suppose policy makers care about inflation and unemployment. They dislike both according to the loss function L(π t, y t ) = (y t y) 2 + λπ 2 t (2) where y > 0 is the socially desired level of output and λ > 0 is a parameter determining how much the policy maker dislikes inflation. What is the equilibrium here? Suppose the private sector moves first, forming expectations about inflation. Next the government moves, setting inflation. This is a dynamic game, and we can solve it backwards. So take π e t as given and substitute the constraint (1) into the objective function (2) (which we are minimizing, not maximizing). We get (π t π e t y) 2 + λπ 2 t. Taking first order conditions, setting to zero and rearranging, we get π t = πe t + y Now suppose the private sector wants to have correct expectations and that it is aware that what it expects will affect the outcome. This is an awkward situation, but it has a solution: 2

3 the private sector will set its inflationary expectations in such a way as to make it optimal for the policy maker to exactly fulfill these expectations. Conceptually, there might me many ways of doing this, or none. But in this context there is only one rational expectations equilibrium, where, by definition, expectations equal outcomes. When they do, we have π e t = π t and hence Solving for optimal inflation, we get π e t = πe t + y π t = π e t = y λ. Notice that a real inflation hater (λ = + ) will set inflation equal to zero. So will a policy maker who is quite happy with the natural rate of output (y = y = 0). Notice also that the equilibrium is not very attractive from the point of view of the policy maker. Inflation is positive, but since expectations are exactly fulfilled, output is equal to its natural rate. The policy maker would prefer to make a binding promise to set inflation equal to zero no matter what. If this promise is credible and is kept, then the policy maker achieves a better outcome. But the promise is not credible. Once expectations are formed, the policy maker would like to surprise people in order to achieve an output level closer to y. This is the time inconsistency or credibility problem. The result is an inflationary bias a tendency for inflation to be above the socially desirable level without any desirable effect on output. 2.1 Diagrammatic depiction of the credibility problem Consider Figure 1. Every circle represents an indifference curve of the policy maker. (These indifference curves are circles if λ = 1, otherwise they are ellipses.) Every upwards sloping line represents a Phillips curve; each one being associated with a separate fixed value of inflation expectations π e. Recall that y t = π t π e t so that the slope of each Phillips curve is the same (and equal to one) but that the intercept, π e is different for each. 3

4 The downwards sloping line joins the points of tangency between a Phillips curve and an indifference curve; each point on this line is an optimal choice for some given level of expected inflation. The intersection between this line and the rational expectations line y = 0 is the equilibrium point: (ȳ, 0). y ȳ ȳ π Figure 1: The credibility problem in monetary policy 3 Solving the credibility problem Several solutions to the credibility problem have been discussed in the literature. Most of them involve some form of delegation. Hiring a thug. This idea is simply and beautifully developed in Vickers (1985). An alternative is the idea that a policy maker may have a reputation for good behavior, and that the incentive to keep on behaving well is to avoid losing this reputation. This idea is developed in Barro and Gordon (1983). In practice, what governments have done since the early 1990s is to delegate monetary policy making to central banks, instructing them to target inflation. New Zealand and Canada have been the pioneers here. Australia, the UK, Sweden and recently Norway have followed. 4

5 Given the above discussion, it might appear that the government should delegate to an authority that cares only about inflation and not about unemployment (λ = + ). This is not quite the case, however. A popular view in the literature, and in central bank circles, is that, although monetary policy can do nothing to influence long run average employment and output, it can and should stabilize output. And there might be a trade off between stable output and stable inflation. This idea is formalized in Rogoff (1985). There output depends on a random (supply) shock whose value is not known when inflation expectations are formed, but which is known to the central bank when it sets inflation. This means that the central bank can respond to a negative supply shock by a surprise inflation and to a positive supply shock by a surprise deflation (or disinflation), thereby stabilizing output. It is not clear as we saw in the discussion of real business cycle models why the stabilization of output should be desirable. But many central bankers seems to think that it is. In any case, Rogoff s formalization consists in the following: y t = π t π e t + ε t where ε t is a random variable with mean zero, representing a supply shock. The optimization problem now changes a bit. Here is the minimand: (π t π e t y + ε t ) 2 + λπ 2 t. The solution, for given inflationary expectations, is π t = πe t + y ε t. 1 + λ Meanwhile, inflationary expectations, although rational, will not always be correct, since they cannot be based on ε t. The best that can be achieved is to be correct on average, i.e. π e t = πe t + y Thus, in equilibrium, π t = y λ ε t Rogoff s conclusion from this is that, although you do want to delegate monetary policy to a central banker who is more conservative (has a higher λ) than you do, you don t want to take 5

6 this too far. You want to eliminate the inflationary bias, but choosing an infinitely conservative central banker would cause output to fluctuate more than you would like, since this central banker would respond less than you would to a supply shock. So Rogoff concludes that you should delegate monetary policy to a central banker who is somewhat more conservative than you are but not to a monetary fascist. Notice, by the way, that Rogoff s model implies a negative relationship between inflation and unemployment in equilibrium: when inflation is above its mean, output is below its mean! We could augment the model to include a demand shock one that affects inflation without affecting output directly (except via inflation). This would lead to a positive relationship between output and inflation. In any case, an ingenious device described in Persson and Tabellini (1993) shows that a sufficiently sophisticated contract with the monetary policy authority can achieve both zero average inflation and the optimal degree of stabilization. It involves letting the central banker (who is assumed to care about inflation and output in the same way that society as a whole does) pay a penalty that is linear in inflation. This removes the inflation bias without affecting incentives to stabilize. 6

7 References Barro, R. J. and D. B. Gordon (1983). Rules, discretion and reputation in a model of monetary policy. Journal of Monetary Economics 12, Kydland, F. E. and E. C. Prescott (1977). Rules rather than discretion: The inconsistency of optimal plans. Journal of Political Economy 85 (3), Lucas, R. E. (1972). Expectations and the neutrality of money. Journal of Economic Theory 4, Persson, T. and G. Tabellini (1993). Designing institutions for monetary stability. Carnegie- Rochester Conference Series on Public Policy 39, Rogoff, K. (1985). The optimal degree of commitment to an intermediate monetary target. Quarterly Journal of Economics 100 (4), Sargent, T. J. (2001). The Conquest of American Inflation. Princeton University Press. Vickers, J. (1985). Delegation and the theory of the firm. Economic Journal Supplement 95,