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The Magic's Gone

A hard look at the data shows that the famous Phillips curve does no better at forecasting inflation than a simple look at the past.

September 1, 2001


Douglas Clement Senior Writer

The following is based on work by Minneapolis Fed visiting scholars Andrew Atkeson and Lee E. Ohanian, both professors of economics at the University of California, Los Angeles. Their paper appears in the Winter 2001 Quarterly Review, published by the Minneapolis Fed's Research Department.

We've all been there: Stuck in a relationship that's going nowhere. What was once so special now seems empty and lifeless. The spark has faded, the magic's gone. And so it is—according to a new analysis by Minneapolis Fed visiting scholars—with the Phillips curve, a line that described the relationship between unemployment and inflation. Once upon a time ...

Birth of a notion

In 1958, New Zealand economist A.W. Phillips published "The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957." The paper examined nearly a century's worth of data and found a striking inverse correlation between wage inflation and unemployment rates, a relationship summarized by the eponymous curve, showing that in Britain, high rates of unemployment were seen at times of low wage inflation, and vice versa.

The data were clear and the relationship seemed to make sense: When unemployment is high, workers tend to be less aggressive in pushing for higher pay. Conversely, when the job market is tight, employers have to promise higher wages to draw workers. As Phillips put it:

"When the demand for labour is high and there are very few unemployed, we should expect employers to bid wage rates up quite rapidly, each firm and each industry being continually tempted to offer a little above the prevailing rates to attract the most suitable labour from other firms and industries."

Higher wages could in turn lead to more inflation, both directly through their impact on the costs of production and indirectly by raising incomes, leading consumers to bid up the price of products.

The Phillips curve—supported and elaborated by Paul Samuelson, Robert Solow and other prominent economists—quickly became economics gospel and, among other uses, was employed by policymakers to predict future inflation on the basis of current unemployment.

Challenging the curve

But Milton Friedman, Edmund Phelps, Robert Lucas and other economists didn't buy it. The simplistic linking of inflation and unemployment, they argued, didn't make sense on a theoretical level. What matters to both workers and employers in making decisions about supplying and demanding labor are real (inflation-adjusted) wages, not nominal wages, said the Phillips curve critics. If workers expect inflation of a certain level, they'll implicitly calculate their purchasing power and supply labor accordingly. The same is true for employers estimating the real costs of hiring more workers. So while some people might make a few short-term employment changes on the basis of nominal wage changes, in the long-run the labor market will adjust to real wage conditions, independent of inflation.

These theorists argued that the predictive ability of a simple Phillips curve is further limited because people's expectations about inflation change under different economic conditions, so a reliable or stable relationship between rates of inflation and unemployment is unlikely. Significant productivity increases or price declines in imports, for example, alter perceptions about inflation and unemployment, making it unwise to assume that relationships that obtained before will work in the future.

Indeed, the economic conditions of the 1970s brought about stagflation—with simultaneous high unemployment and high inflation—and provided evidence that the simple Phillips curve wasn't quite as reliable a guide as once thought.

Improved conventional wisdom

To cope with these theoretical and practical objections but still preserve what they perceived as a kernel of truth, Phillips curve advocates suggested a more complex version. The new model posited that an economy tends to have a natural rate of unemployment at which annual price increases are steady—that is, inflation is a constant. If unemployment drops below this natural rate, the rate of inflation will increase. If unemployment moves above the natural rate, the inflation rate will decline.

According to this new understanding, a high rate of unemployment (above the natural rate) isn't linked to low inflation, per se, but to a decrease in the inflation rate (below whatever it is when unemployment is at its natural rate). That natural unemployment rate came to be known by the accurate, if ungainly, term nonaccelerating inflation rate of unemployment (NAIRU), and the new model linking unemployment rates and changes in inflation rates was called a NAIRU Phillips curve.

No one had an exact measure of the nonaccelerating rate, and it seemed clear that the rate could change if economic conditions varied (in fact, reducing labor market rigidities could theoretically lower the NAIRU), but in recent times the NAIRU Phillips relationship has replaced its predecessor, becoming the new-and-improved conventional wisdom about unemployment/inflation linkages.

Indeed, during the 1990s and on into the new century, as unemployment rates have dropped and stayed low, both economists and policymakers have shown their implicit faith—and fear—that inflation will soon return. They warn of "overheating" the economy-conjuring images of a boiler set to explode, unleashing the scalding wrath of inflation. The stock market, too, seems to believe in NAIRU (or believes that the Fed does), regularly greeting news of rising wages or dropping unemployment with plunges in stock prices, as analysts fear the Fed will pull in the economy's reins by raising interest rates to stem "inevitable" inflation.

A closer look

This abiding faith in a stable link between unemployment and inflation is the subject of close empirical scrutiny in Andrew Atkeson and Lee Ohanian's paper in the Winter 2001 edition of the Quarterly Review. In "Are Phillips Curves Useful for Forecasting Inflation?" the Minneapolis Fed visiting scholars point out that many academics and government officials still hold close to some version of an inflation/unemployment relationship, and that Phillips curve analysis continues to carry substantial weight in Federal Open Market Committee (FOMC) inflation forecasts. Their task was to evaluate whether data support the use of such a tool. Is some version of the Phillips relationship still magic?

Atkeson and Ohanian first look at the classic Phillips curve relationship, seeing if the data fit the original Phillips theory. They analyze U.S. data on inflation and unemployment in two different time periods, from 1959 to 1969 and then from 1970 to 1999. In the earlier time span, the 1960s, they find that, indeed, there is a clear negative relationship between the unemployment rate at a given point in time and inflation over the next four quarters: a classic Phillips curve similar to that seen in the British data for the preceding century.

But their scatter plot of unemployment and subsequent inflation data for the next 30 years shows virtually no correlation (see Chart 1). Apparently, whatever relationship existed in the 1960s had disappeared. "Moreover," note the authors, "any inflation forecast for post-1970s data based on the 1960s [data] clearly would be inaccurate." The classic Phillips curve is dead. Q.E.D. R.I.P.

Chart 1 The Breakdown in an Early Phillips Curve
Quarterly Unemployment as a Percentage of the U.S. Labor Force vs. Changes in the Implicit Price Deflator for U.S. GDP Over the Next Four Quarters, 1st Quarter 1959-1st Quarter 1999

Chart-Breakdown in an Early Phillips Curve

Source: U.S. Departments of Labor and Commerce

Long live the curve

Well, that was too easy. After all, Friedman, et al., had already undercut the theoretical basis of the simple Phillips curve. And stagflation sent it to an early empirical grave. But what about the more sophisticated version? Atkeson and Ohanian take a similar graphical look at a NAIRU Phillips curve, plotting the unemployment rate against changes in the subsequent inflation rate—essentially asking whether a high unemployment rate can predict not low inflation, but a decrease in inflation. Here again they look at the data for two different time periods, from 1960 to 1983, and then from 1984 to 1999.

In the early time span, they find, there is a negative relationship between unemployment and subsequent changes in inflation. Specifically, the data indicate that when unemployment is about 6 percent, the inflation rate will neither rise nor fall—the NAIRU—but if unemployment drops to 5 percent, inflation is forecast to rise 0.6 of a percentage point over the following year. (Note that this isn't saying prices will rise 0.6 percent, but that the inflation rate itself—4 percent, 7 percent, whatever it might be—will increase by 0.6 of a percentage point.)

But over the following 15-year time span—our recent history—the data show very little relationship. In a graphical description, the line that best fits the data points has flattened out, meaning that large changes in unemployment in this later time period forecast very little change in inflation. So, while an unemployment rate of 4 percent in the early time span would have led to a prediction of a 1 point increase in inflation, a similar unemployment rate in more recent years would forecast just a one-quarter point increase (see Chart 2).

Chart 2 A Shift in the Textbook NAIRU Phillips Curve
Quarterly Unemployment as a Percentage of the U.S. Labor Force vs. Difference Between Change in the Implicit Price Deflator for U.S. GDP Over the Next Four Quarters and Its Change Over the Previous Four Quarters,
1st Quarter 1960-1st Quarter 1999

Chart-Shift in Textbook NAIRU Phillips Curve

Source: U.S. Departments of Labor and Commerce

Things have changed, evidently, to make the measurable relationship between these variables so different in one time period compared with the other. Atkeson and Ohanian indicate that lower volatility in the business cycle, monetary policy and inflation since the 1980s might have altered the economic environment sufficiently to weaken the unemployment/inflation change link and diminish the predictive power of the NAIRU Phillips curve.

Putting NAIRU to the test

To an econometrician, this begs a question: Is the underlying relationship "stable" enough, can we depend upon it, to serve as an accurate predictor of inflation in the current economic environment? The graphs indicate that the relationship is not as strong as once it was, but is it strong enough to be useful?

The litmus test that Atkeson and Ohanian use is straightforward. A given forecasting model will be considered useful if it can do a better job of forecasting inflation than simply predicting that next year's inflation rate will be the same as last year's. If a complex model can't outdo this simple "rear-view mirror," then it's not worth the computer time.

They apply the test to three different variations of the NAIRU Phillips curve over the 1984-1999 period, seeing statistically if any of them do a better job of predicting inflation than simply projecting forward last year's inflation. They look at: (1) a textbook NAIRU Phillips curve that says that changes in inflation are proportional to the previous year's unemployment rate, (2) a more sophisticated NAIRU Phillips curve that incorporates lagged values of unemployment and inflation rates as well as present values and (3) a still more complex NAIRU Phillips curve that tries to forecast changes in inflation using a broad economic index incorporating 85 indicators of economic activity. (They also try out several different inflation measures—the consumer price index (CPI), the "core" CPI, which excludes food and energy, and a price deflator for personal consumption expenditures—to see if the Phillips curve variations are better at forecasting one or another measure of inflation.)

The authors find that the simple rearview mirror does basically just as well or better than the three NAIRU Phillips curve variations. In fact, the rearview model is 88 percent more accurate than the textbook NAIRU curve, at least 4 percent better than the activity index model and essentially just as good as the unemployment rate version. In other words, the models aren't at all useful for forecasting inflation. A policymaker trying to guess at next year's inflation rate could come up with an equally good estimate simply by looking at last year's inflation rate. Why hire an economist?

Greenbook predictions

Atkeson and Ohanian then take the bull by the horns, examining inflation forecasts produced by staff of the Federal Reserve System's Board of Governors. While acknowledging that complex econometric models are only one of a number of inputs used by Fed staff in constructing the inflation forecasts that appear in their Greenbook reports prepared for FOMC meetings, Atkeson and Ohanian emphasize that the models are again based on a NAIRU Phillips curve relationship. So they subject the Greenbook forecasts to the same test: Does the Fed model do a better job at predicting inflation than the simple rearview mirror?

Because the Greenbooks are not made public for several years, the researchers can analyze Greenbook forecasts only from 1984 to 1996, not the full period used in the previous tests, but again they find that the Fed model does no better (and no worse) than their litmus test. Comparing inflation rate predictions to actual inflation rates for both forecasting models reveals that the complicated NAIRU Phillips curve econometrics used by the Fed's Board of Governors has no real inflation-predicting edge over a naive glance at the past year's inflation rate. The ratio of prediction errors for the Fed and naive models is 1.01—basically, they do equally well.

The bottom line

So what should economists and policymakers conclude from this? One clear implication is that existing Phillips curve-based forecasting models simply don't work in the current economic environment. "For the last 15 years," say the authors, "economists have not produced a version of the Phillips curve that makes more accurate inflation forecast than those from a naive model."

Does that imply that more effort should go into building a better model, a more sophisticated, insightful forecasting tool that can hone in on the proper variables that will illustrate the underlying though elusive unemployment/inflation link? Atkeson and Ohanian say no. Enough is enough. Theorists and applied economists have looked high and low for a stable relationship between the two, but whatever link once existed—in Phillips' British data or America's 1960s economy, for example—no longer obtains, and further efforts are likely to be fruitless. "The search for yet another Phillips curve-based forecasting model," they conclude, "should be abandoned."

The Phillips curve magic that once seemed to give policymakers a clear signpost is now gone. Time to move on.

Douglas Clement
Senior Writer

Douglas Clement was a managing editor at the Minneapolis Fed, where he wrote about research conducted by economists and other scholars associated with the Minneapolis Fed and interviewed prominent economists.