Federal Reserve Bank of San Francisco

FRBSF Economic Letter

1999-09 | March 12, 1999

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Economic Activity and Inflation

Bharat Trehan

This Letter reviews four papers on the relationship between inflation and economic activity that were presented at a recent macroeconomics workshop organized by the Federal Reserve Bank of San Francisco and the Stanford Institute of Economic Policy Research. The papers focused on the Phillips curve, named for A.W. Phillips (1958); he showed that a plot of (wage) inflation against unemployment for the U.K. produced a downward-sloping curve, indicating that higher unemployment was accompanied by lower inflation. The nature of this relationship has been studied and debated extensively, reflecting its importance for numerous policy issues. For instance, policymakers would like to know how much unemployment would increase if they tried to reduce inflation by some amount. This relationship also plays a key role in forecasting inflation in many Keynesian models.

Does the Phillips curve always slope downwards?

Haldane and Quah begin by showing that 50 years of postwar U.K. data do–at first glance–exhibit a negative relationship between unemployment and inflation, much as Phillips found in data through 1957. However, they then demonstrate that this relationship conceals two quite different relationships that held during the pre-1980 and post-1980 subperiods. Before 1980, the unemployment rate moved relatively little and was generally below 4%, while the inflation rate was fairly volatile and appears to have been centered around 10%. A plot of inflation against unemployment over that period would produce a vertical Phillips curve. After 1980, unemployment moved around more, ranging between 4% and 12%, while inflation varied less than the prior period, remaining below 10% most of the time. Here, the Phillips curve appears horizontal. Note that unemployment is higher on average while inflation is lower in the second subsample than in the first, which is why we get an apparently downward-sloping Phillips curve for the overall postwar period.

Other data sets Haldane and Quah examined also reveal differing relationships between inflation and unemployment. For instance, over periods that approximate the length of the business cycle, U.S. data reveal a negative relationship between the two variables, while U.K. data exhibit no such relationship.

Finding different relationships between unemployment and inflation in different data sets suggests that the conventional downward-sloping Phillips curve is not a fundamental economic relationship and prompts a search for the features of the economy responsible for the changing patterns observed in the data. In their theoretical work, the authors show how differences in policymakers’ beliefs about the economy can lead to differences in the observed Phillips curve. First, they present a model economy where it is optimal for fully informed policymakers to reduce the rate of inflation when unemployment is low and to raise the rate of inflation when unemployment is high. Intuitively, periods of low unemployment (for instance) make it less costly to reduce inflation. However, while such behavior tends to stabilize both output and inflation, the result is a Phillips curve that is upward sloping! The authors then show that this prediction can change if policymakers do not know exactly how the economy functions. For instance, a conventionally sloped Phillips curve can emerge if policymakers are mistaken about the nature of the tradeoff between inflation and unemployment.

According to the authors, the “mistakes” they focus on are meant to describe the changing beliefs of the British authorities in the postwar era. At first, monetary authorities probably believed that there was a long-run tradeoff between inflation and unemployment. Later, they realized that this belief was incorrect, but still believed there was a fixed short-run tradeoff between inflation and unemployment which they could exploit. More recently, they have abandoned this belief as well. The authors show that these beliefs have different implications for the behavior of output and inflation generated by their model, and that the predictions from their model are consistent with some (but not all) of the patterns observed in the data.

Learning about the tradeoff

Sargent’s paper also emphasizes the role of changing beliefs and uses these changes to explain variations in the U.S. inflation rate since the 1960s. A key feature of his paper is that these changes in policymakers’ beliefs occur because of their analysis of incoming data about the economy.

As in the Haldane and Quah paper, Sargent assumes that monetary policymakers attempt to minimize fluctuations in inflation and unemployment around some target levels. He further assumes that policymakers can control the rate of inflation reasonably well, but they do not know exactly how variations in the rate of inflation will affect the unemployment rate. More formally, they do not know the “true” model. They try to learn the “truth” by statistically estimating the relationship between inflation and unemployment–a Phillips curve–using all the available data. They reestimate this relationship each period when new data come in. Policymakers also believe that this relationship tends to shift over time, so they employ estimation techniques that de-emphasize older data. Finally, each period they use the latest estimates of the Phillips curve to determine the optimal rate of inflation.

Typically (but not always), the Phillips curve estimated by policymakers shows a tradeoff between inflation and unemployment, which tends to reflect the tradeoff between surprise inflation and unemployment inherent in the “true” model. (This kind of model will be described in more detail in the discussion of the paper by Ireland below.) In an attempt to exploit this tradeoff, policymakers tend to push the inflation rate to a relatively high level.

However, Sargent’s model economy does not settle down at this point. The economy is subject to random shocks, so the shape of the estimated Phillips curve keeps changing. (The assumption that older data get de-emphasized is important here.) Eventually, the estimated Phillips curve appears vertical, that is, the data suggest that there is no tradeoff between inflation and unemployment. Optimizing policymakers then reduce inflation to near zero (the target level). Sargent interprets the reduction in U.S. inflation during the 1980s as just such an event: Sometime in the late 1970s, incoming data began to suggest that the U.S. Phillips curve was vertical; policymakers responded by lowering the inflation rate.

Sargent’s analysis suggests that, unfortunately, the reduction in inflation is not likely to be permanent. This is because policymakers’ belief in a vertical Phillips curve does not last. At some point, incoming data again begin to suggest a tradeoff between unemployment and inflation, and policymakers respond by trying to exploit the perceived tradeoff once again. (Recall that the perceived tradeoff reflects the tradeoff between unemployment and surprise inflation in the “true” model.) The whole cycle then repeats itself. Simulations of his model show the economy cycling between periods of high and low inflation, which mirrors changes in policymakers’ beliefs about the Phillips curve.

Declining inflation: a lucky break?

The two papers discussed so far attribute changes in inflation–and in the correlation between economic activity and inflation–to changes in policymakers’ understanding of the economy. In sharp contrast, Ireland suggests that the observed variation in inflation originated in events that had little to do with monetary policy.

Ireland uses a well-known model of inflation due to Robert Barro and David Gordon. In the Barro-Gordon model, surprise inflation leads to a reduction in the unemployment rate. Policymakers have an incentive to exploit this tradeoff, that is, to create surprise inflation in order to push the unemployment rate below the level where market forces would take it–this level is referred to as the natural rate of unemployment. However, the public recognizes the temptation faced by the government and adjusts its expectations of inflation accordingly. In equilibrium, then, the economy ends up with higher than optimal inflation and unemployment at the natural rate.

An important assumption of this model is that the gap between the natural rate and the unemployment rate desired by policymakers varies positively with the natural rate. This means, for instance, that the higher the natural rate, the greater the amount by which policymakers want to reduce unemployment. Since a greater reduction in unemployment can be obtained only by greater (surprise) inflation, the end result is that inflation varies positively with the natural rate.

Using data for the 1960-1990 period, Ireland shows that the long-run relationship between U.S. inflation and unemployment is consistent with the predictions of the Barro-Gordon model. While the short-run relationship found in the data is not consistent with the model, Ireland believes that this is not fatal for the theory, since the model being used is very simple. Thus, the model can be used to explain the behavior of inflation as follows: A series of negative shocks pushed the natural rate up during the 1970s. Policymakers responded by pushing the inflation rate up, as implied by the model. Positive shocks during the 1980s and 1990s then pushed the natural rate down; policymakers responded by lowering the inflation rate. Thus, Ireland argues that the rise in inflation during the 1970s reflected bad luck rather than unusually bad policy, while the reduction in inflation over the last two decades reflects good luck rather than good policy.

A better way to predict inflation

Gali and Gertler focus on the role firms play in determining the behavior of the inflation rate. Their model is a variant of recent “New Keynesian” models of the macroeconomy. In these models, firms are assumed to have some monopoly power in the market, which allows them a degree of freedom in setting prices for their products. These firms determine the price they will charge by looking not only at current costs of production, but also at anticipated costs, since prices cannot be adjusted instantaneously. Because changes in costs are related to changes in output over the business cycle, these models imply that prices should change before output does. However, U.S. data show that changes in prices typically lag changes in output over the business cycle.

Gali and Gertler make several changes to the basic New Keynesian model to improve its ability to predict inflation. First, they assume that some firms are backward-looking and use simple rules of thumb to set prices. In addition, they employ a measure of the firms’ marginal cost in order to predict inflation, on the grounds that this is what matters for inflation in the New Keynesian models, rather than more common measures of the output gap used in earlier empirical work.

Gali and Gertler show that their model does quite well in explaining the behavior of U.S. inflation over the 1960-1996 period. Further, their estimates suggest that relatively few U.S. firms are backward-looking. This result is important because the existence of backward-looking firms often has been proposed as the reason for the empirical finding that prices tend to be “sticky,” that is, for the empirical finding that the price level tends to change more slowly than is easily explained a priori. Their finding implies that the observed stickiness in prices results from the fact that real marginal costs are sticky. Stated more generally, sticky prices reflect the fact that the variables that firms look at in order to set prices themselves change slowly in response to changes in economic conditions.

Summing up

Though the underlying issues are far from settled, the papers presented at this workshop provide some interesting insights about the relationship between economic activity and inflation. Haldane and Quah argue that the conventional, downward-sloping Phillips curve does not represent a fundamental relationship, and that the relationship we observe will change as policymakers’ beliefs about the economy change. Sargent’s message is consistent, though his paper focuses on the role of learning. Policymakers learn about the economy by reestimating the Phillips curve as new data come in and vary the rate of inflation in response to these changing estimates. Ireland offers a plausible, alternative explanation for the observed variations in U.S. inflation: Inflation went up during the 1970s and came down in the 1980s because of the nature of the shocks hitting the economy and not because policymakers learned something about how the economy functions. Finally, the Gali and Gertler paper suggests that attempts to use economic activity to forecast inflation will do better if one accounts for the relationship between firms’ marginal costs and inflation.

Bharat Trehan
Research Officer


Barro, Robert J., and David B. Gordon. 1983. “A Positive Theory of Monetary Policy in a Natural Rate Model.” Journal of Political Economy 91 pp. 589-610.

Gali, Jordi, and Mark Gertler. 1998. “Inflation Dynamics: A Structural Econometric Analysis.” Mimeo. New York University.

Haldane, Andrew, and Danny Quah. 1998. “U.K. Phillips Curves and Monetary Policy.” Mimeo. Bank of England.

Ireland, Peter. 1998. “Does the Time Consistency Problem Explain the Behavior of U.S. Inflation?” Mimeo. Boston College.

Phillips, A.W. 1958. “The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957.” Economica 25 pp. 283-299.

Sargent, Thomas. 1999. “The Temporary (?) Conquest of American Inflation.” Mimeo. Stanford University.

Opinions expressed in FRBSF Economic Letter do not necessarily reflect the views of the management of the Federal Reserve Bank of San Francisco or of the Board of Governors of the Federal Reserve System. This publication is edited by Sam Zuckerman and Anita Todd. Permission to reprint must be obtained in writing.

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