## Whether Low Unemployment Is Inflationary

Is Low Unemployment Inflationary?

R O B E R T O C H A N G The author is a research officer in the macropolicy section of the Atlanta Fed’s research department. He thanks Robert Eisenbeis, Frank King, Mary Rosenbaum, and Eric Leeper for useful comments and suggestions.

F ROM A VARIETY OF PERSPECTIVES, THE MACROECONOMIC PERFORMANCE OF THE U.S. ECONOMY

HAS BEEN VERY SATISFACTORY IN RECENT YEARS. IN PARTICULAR, BROAD-BASED MEASURES OF

INFLATION HAVE STABILIZED BETWEEN 21⁄2 AND 3 PERCENT WHILE UNEMPLOYMENT HAS FALLEN

BELOW 51⁄2 PERCENT. HOWEVER, MANY OBSERVERS REMAIN UNEASY, BELIEVING THAT THE CUR-

RENT SITUATION IS FRAGILE AND TEMPORARY. THIS BELIEF IS, IN TURN, ROOTED IN A LESS OBVIOUS VIEW

THAT THE CURRENT RATE OF UNEMPLOYMENT IS “TOO LOW” TO BE CONSISTENT WITH LOW AND STABLE

INFLATION.

4 Federal Reser ve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 1997

This state of affairs becomes most visible on the first Friday of every month, when the Bureau of Labor Statistics releases the latest data on employment and unemployment in the United States. Recently, these data releases have often been followed by sharp changes in financial markets. In particular, markets have taken lower-than-expected unemployment rates to mean that inflation is about to accelerate, resulting in falling stock prices and increasing interest rates.

The average citizen would find this to be a rather strange ritual. Isn’t low unemployment good for the coun- try? And why is low unemployment supposed to lead to higher inflation anyway? These are important and diffi- cult questions. An influential economic theory, however, argues that the answers are easy and widely found in macroeconomics textbooks. Low unemployment, this the- ory implies, is unambiguously “good” only up to a point. If unemployment falls below this point, known as the nonaccelerating inflation rate of unemployment (NAIRU), inflation tends to accelerate.1 Opinions about the current location of the NAIRU vary, but many pub- lished estimates place it close to 6 percent.2 Since recent unemployment figures have been consistently below that

range, adherents to this theory predict that inflation will accelerate.

So far these predictions have turned out to be wrong. That their failure should not be a surprise is one of the themes of this article. More precisely, this article argues that the concept of the NAIRU is of very limited use for pre- dicting inflation, understanding its causes, or forming pol- icy. There is both empirical and theoretical support for this view. On the empirical side, the article discusses evidence showing that the NAIRU is highly variable and that there is a great deal of uncertainty about where it is at any particu- lar point in time. These findings imply that, in practice, one cannot know if unemployment is above or below that value supposedly consistent with stable inflation. On the theo- retical side, this article argues that even if such a value became known, it would be irrelevant. Contemporary eco- nomic theory implies that movements of the unemployment rate may be positively or negatively related to inflation, depending on the nature of the fundamental shocks caus- ing the unemployment changes. Identifying such shocks is possible and helpful for predicting the inflation implica- tions of unemployment changes; but given that these shocks can be identified, whether current unemployment

1. It is worth noting that several authors have also used the term natural rate to refer to the NAIRU. To avoid confusion, this arti- cle will make a distinction between the two concepts. The distinction is important because, as discussed below, the natural rate concept developed by Friedman (1968) and Phelps (1968) is not the same as the NAIRU concept, although their values may coincide.

2. For instance, the Congressional Budget Office (1996, 5) recently estimated that the NAIRU was 5.8 percent in 1995. 3. The Friedman-Phelps view further implies that the monetary authority can keep the unemployment rate permanently below

its natural rate only by perpetually engineering unexpected increases in inflation. If people’s expectations of inflation are rel- atively slow to adjust, ever-accelerating inflation is required. This implication does not hold true if expectations of inflation are fully “rational,” as first demonstrated by the work of Lucas (1972) and Sargent and Wallace (1976).

5Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 1997

is above or below the NAIRU provides no additional useful information about prospective changes in inflation.

The Phillips Curve, the Natural Rate, and the NAIRU

T he idea that unemployment may be too low to be consistent with stable inflation is of relatively recent vintage. Its origins can be traced to the

1960s and 1970s discussion about how to interpret the then recently discovered “Phillips curve,” an empirical association between inflation and unemployment. Some aspects of this debate are useful for the discussion that comes later.

As some readers may recall, Phillips’s (1958) analy- sis of almost a century of U.K. data shocked the econom- ics profession. Phillips focused on the relationship between wages and unemployment and discovered the striking fact that the rate of change in nominal wages had a negative correlation with unemployment. Soon after- ward, Samuelson and Solow (1960) showed that a similar relation held in U.S. data. Moreover, Samuelson and Solow argued that changes in nominal wages were posi- tively related to overall inflation, thus recasting the wage- unemployment relation discovered by Phillips into the inverse relation between price inflation and unemploy- ment commonly known as the Phillips curve.

The discovery of the Phillips curve generated a heat- ed debate about its implications for economic policy. In particular, research focused on whether a monetary authority such as the Federal Reserve could “buy” less unemployment at the cost of faster inflation. Some argued that the existence of a Phillips curve implied that unemployment could be permanently lowered if inflation were kept at a permanently higher level. Others, in par- ticular Friedman (1968) and Phelps (1968), argued that there was an inflation-unemployment trade-off in the short run but not in the long run. In justifying their the- sis, Friedman and Phelps coined the term “natural rate of unemployment.”

To understand Friedman and Phelps’s argument, con- sider first an economy without price surprises, so actual inflation is always equal to previously expected inflation. In such an economy, some workers would always be observed to be unemployed and looking for a job. This phenomenon may simply reflect the fact that, since work- ers and jobs are heterogeneous, unemployed workers and

firms may take time to search for adequate matches. Hence, even if inflation were always perfectly foreseen, the economy would experience a positive rate of unem- ployment that Friedman and Phelps called “natural.”

What if inflation were not perfectly foreseen? Friedman and Phelps argued that unexpectedly high inflation would make actual unemployment fall below its natural rate, but only in the short run. This decline would happen, in particular, if wage contracts had been negoti- ated on the basis of previously expected inflation, in which case an inflation surprise would reduce real (inflation- adjusted) wages and stimulate employment. One im- plication is that a monetary authority could indeed “buy” lower unemployment by inducing inflation to rise above previ- ously expected infla- tion. But this effect would be only tempo- r a r y b e c a u s e e c o – nomic agents would eventually learn to f o r e c a s t i n f l a t i o n c o r re c t l y, a n d t h e difference between expected inflation and actual inflation would tend to disappear.3

Although unexpected accelerations in inflation, engendered by monetary policy, may “cause” unemploy- ment to fall below the natural rate, the converse need not hold. Given monetary policy, the Friedman-Phelps theory had no implications for whether movements in the unem- ployment rate have an independent effect on inflation.

In subsequent research, a subtly but clearly different view on the relation between inflation and unemploy- ment emerged. According to this view, inflation tends to accelerate whenever unemployment falls below a partic- ular number, which has come to be known as the “nonac- celerating inflation rate of unemployment,” or NAIRU.

The NAIRU concept was first proposed by Modigliani and Papademos, who posited the existence of a rate of unemployment “such that, as long as unemployment is above it, inflation can be expected to decline” (1975, 142).

Contemporary economic theory implies that movements of the un- employment rate may be positively or negatively related to inflation, depending on the nature of the fundamental shocks causing the unemployment changes.

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C H A R T 1 Inflation and Unemployment, 1955-96 (Monthly)

6 Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 1997

The intuition is that low unemployment is likely to inten- sify wage pressures and consequently to result in a gen- eralized wage increase. Assuming that firms manage to pass this cost increase to consumers in the form of high- er prices, a fall in unemployment is likely to be associat- ed with an increase in inflation. Similarly, an increase in unemployment must result in a fall in inflation. There must therefore be a level of unemployment such that inflation can be expected to remain constant; this level is the NAIRU.

Readers may note that the Friedman-Phelps natural rate and the NAIRU are different concepts. Friedman and Phelps defined the natural rate as an equilibrium whose value was determined by the characteristics of the labor market. In contrast, the NAIRU is posited as an empirical value rather than an equilibrium value. More important- ly, the theory of the NAIRU implies that low unemploy- ment may cause inflation to increase independently of the causes of the low unemployment and, in particular, of monetary policy; this is not an implication of the Friedman-Phelps natural rate theory.

The NAIRU concept pervades current policy discus- sions and is the main concern of this article. Since Modigliani and Papademos’s article numerous studies have, not surprisingly, focused on the estimation of the NAIRU. If there were in fact a strong, stable relation between unemployment, a known NAIRU, and inflation, then one could compare current unemployment with the NAIRU to accurately predict future inflation. But this is not the world we live in, as the discussion below will show.

A First Look at the NAIRU

T o understand the details and some of the problems associated with estimating the NAIRU, it is helpful to have a broad idea of the historical behavior of

unemployment and inflation. Chart 1 depicts the behav- ior of civilian unemployment and the inflation rate since 1955. The most notable aspect of this chart is the dra- matic increase in inflation that started in the mid-sixties and ended in the early eighties, and the subsequent dis- inflation. In 1965 inflation was less than 2 percent a year; in 1980 it surpassed 13 percent. Much of the increase is widely believed to have been caused by the oil shocks of 1973 and 1979, and in fact the chart shows a rapid increase in inflation following each of these dates. It has to be noted, though, that the increase in inflation actual- ly started much earlier. The trend toward higher inflation was broken around 1980, and the first half of the 1980s witnessed a rapid decrease in inflation toward the 4 to 6 percent range. This change in inflation behavior has been widely attributed to strongly contractionary monetary policy starting in October 1979 and called, accordingly, the “Volcker deflation.” Finally, inflation since 1991 has been surprisingly stable at around 3 percent.

In Chart 1, unemployment shows a slightly upward trend over the 1955-96 period but considerable variation around its trend. Until the early seventies, unemployment was about 5 percent on average. Its fluctuations were much larger during the decade following the first oil shock; average unemployment during that period was 71⁄2 percent, and it surpassed 10 percent in 1982, reflecting the contractionary effects of the Volcker deflation. Since 1984 unemployment has been declining, averaging a little less than 6 percent.

In Chart 1 it is not obvious that there may be a spe- cial level of the unemployment rate above which inflation would be expected to decline. However, the Modigliani- Papademos definition of the NAIRU suggests a different and more informative way to look at the same data. Their definition implies that inflation is expected to decline

7Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 1997

whenever unemployment is above the NAIRU. Hence there should be a negative relation between expected changes in inflation and the difference between unem- ployment and the NAIRU. If, in addition, this relation is assumed to be linear, a plausible hypothesis for inflation, unemployment, and the NAIRU is given by

Et[π(t + 1) – π(t)] = b[u(t) – u*], (1)

where π(t) denotes the inflation rate in period t, u(t) the unemployment rate in period t, u* the NAIRU, b a coeffi- cient whose expected sign is negative, and Et[.] is short notation for “expectation given information available up to period t.” That is, provided that b is indeed negative, an equation such as (1) implies that, if this month’s unemployment is above the NAIRU u*, inflation should be expected to decline next month. Neither b nor u* are directly observable; instead, they must be inferred from the data.

Versions of equation (1) are the basis of most attempts to estimate the NAIRU. The intuition for work of this kind, and some of the problems associated with it, can be grasped from a scatter diagram of unemployment against subsequent changes in inflation, such as Chart 2. Each point in the chart represents a particular month’s unemployment rate, measured against the horizontal axis, and the subsequent month’s change in inflation, measured against the vertical axis. In particular, observa- tions above the horizontal axis represent months in which inflation increased. If equation (1) were to hold in the data, the observations depicted in Chart 2 would be dis- tributed around a line of negative slope that intersects the horizontal axis at precisely the NAIRU, u*.

At first glance the chart suggests that there is a neg- ative relation between the unemployment rate and sub-

sequent changes in inflation, in particular for extreme values of the unemployment rate. When unemployment has been below 5 percent, inflation has historically increased more often than decreased. Conversely, unem- ployment rates above 8 percent have been mostly asso- ciated with falling inflation rates. However, the relationship in the middle range of unemployment rates between 5 and 8 percent is much less clear: for each value of unemployment in that range, the number of observations above the horizontal axis is about the same as the number of observations below it. Hence, if the NAIRU is defined as “a rate of unemployment such that inflation is as likely to increase as to decrease,” Chart 2 suggests that the data are not likely to yield a very precise estimate of the NAIRU.

A closer look at Chart 2 should reveal a second aspect of the data that is relevant for this discussion: the relationship between changes in inflation and unemploy- ment, and by inference the NAIRU, has moved signifi- cantly over time. To illustrate this behavior, observations in Chart 2 are distinguished by different symbols corre- sponding to three different subperiods, 1955-73, 1974-83, and 1984-96. Splitting the sample in this way is loosely motivated by the fact that the oil shocks of 1973 and 1979 and the Volcker disinflation were large, unusual events that affected both unemployment and inflation.

It is clear that the observations in Chart 2 are not just randomly distributed across the three periods under consideration. Observations before 1974, the squares in the chart, appear mostly to the left, showing that unem- ployment was relatively low. Observations between 1974 and 1983, depicted as diamonds, appear to the right, because unemployment in that period was relatively high. Finally, observations from 1984 on, marked by triangles, are in the middle part of the chart. Using these data to

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1955–73

1974–83

1984–96

C H A R T 2 Unemployment versus Inflation Changes, 1955-96

8 Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 1997

look for a value of the unemployment rate at which infla- tion is “as likely to increase as to decrease,” it is hard to deny that the value is different for each of the three peri- ods considered. In other words, Chart 2 suggests that the NAIRU has not been constant. It seems to have been lower in the first period than in the second and to have fallen after 1983 (although not to the pre-1974 level). Chart 2 thus suggests that the NAIRU is an elusive num- ber. Its precise location is difficult to infer from the data, and it moves around over time. These conclusions, obtained from the visual inspection of Chart 2, are con- firmed by more formal statistical evidence, to which the discussion now turns.

There Is No Reliable NAIRU Estimate

T o understand the statistical estimation of the NAIRU, start by supposing that equation (1) is true. Estimating the NAIRU then amounts to esti-

mating the parame- ters b and u* in (1), which requires some quick manipulations. To simplify notation, define the change of the monthly infla- tion rate, ∆π(t + 1) = π(t + 1) – π(t). A minor difficulty is that the left-hand side of (1) is not the observed value of ∆π(t + 1) but its expected value con- ditional on informa- tion available up to

period t, which is unobservable. To handle this problem, let e(t + 1) = ∆π(t + 1) – Et∆π (t + 1) denote the error in predicting ∆π(t + 1). One can now replace the left- hand side of (1) by the difference between the observed change in inflation and the error in predicting it, ∆π (t + 1) – e(t + 1). Finally, define c = bu*. Inserting these definitions in (1), one obtains

∆π(t + 1) = – c + bu(t) + e(t + 1). (2)

Equation (2) is very useful. It is a linear equation, and its parameters b and c can be estimated using ordi- nary least squares.4 Since c is equal to bu*, an estimate of u* is simply given by the estimate of c divided by the estimate of b. This way of estimating the NAIRU is fairly common in the literature.5

Once an equation such as (2) has been estimated, standard statistical techniques allow assessment of the precision of the estimated coefficients c and b and con- sequently the precision of the estimated NAIRU u*. The degree of precision is usually summarized using confi-

dence intervals. A 95 percent confidence interval for u*, in particular, provides upper and lower bounds for the unemployment rate that should contain u* with 95 per- cent probability. Standard techniques are also available for testing whether assuming that b, c, and the NAIRU are constant, as is implicit in equations (1) and (2). Recalling the discussion of Chart 2, it is clear that testing for the stability of the NAIRU is particularly important given that the data suggest that the NAIRU has changed over time.

Equation (1) is unduly restrictive in that it restricts the expected change in inflation to respond only to the current value of unemployment relative to the NAIRU. It may be more realistic to assume that the expected change in inflation also responds to past unemployment, as would be the case if increases in wages were translat- ed only gradually to consumer prices. Similarly, people’s expectations concerning the change in inflation may depend on current and previous changes in inflation. These considerations imply that lags of unemployment, relative to NAIRU, and lags of inflation changes should be included as explanatory variables in (1). Accordingly, the following generalization of (1) was analyzed:

Et∆π (t + 1) = b0[u(t) – u*] + b1[u(t – 1) (3) – u*] + … + b11[u(t – 11) – u* + a0∆π(t) + … + a11 ∆π(t – 11).

The alphas and betas are coefficients to be estimat- ed, in addition to the NAIRU, u*. In contrast to (1), equa- tion (3) allows the expected change in inflation between periods t and (t + 1) to be influenced by the deviations of unemployment from the NAIRU in the previous twelve months. Also, the expected change of inflation can be influenced by the twelve previous changes in inflation.

The coefficients of (3) were estimated by ordinary least squares. For brevity, details are omitted and only the main findings are reported here. For the full 1955-96 sam- ple displayed in Chart 1, NAIRU was estimated to be 6.14. This estimate is close to others found previously.6 A sec- ond finding was that this estimate of NAIRU is rather imprecise: a 95 percent confidence interval is given by the range of unemployment rates between 5.38 and 6.90.

The wide range for the location of the NAIRU is con- sistent with the lack of precision found in previous work. Indeed, the results presented here are on the optimistic side. In a recent, convincing paper Staiger, Stock, and Watson examined a large number of alternative proce- dures and concluded, “Our main finding is that the nat- ural rate is measured quite imprecisely. For example, we find that a typical value of the NAIRU in 1990 is 6.2 per- cent, with a 95 percent confidence interval for the NAIRU in 1990 being 5.1 to 7.7 percent” (1996, 2).

Readers may note that Staiger, Stock, and Watson’s “typical” confidence interval is much larger than the one estimated here. In fact, for a specification very close to

If there were a strong, stable relation between unemployment, a known NAIRU, and inflation, then one could compare current unemployment with the NAIRU to predict future inflation. But this is not the world we live in.

4. A property of expectations conditional on an information set is that prediction errors are independent of any variable in the information set (see Goldberger 1991, chap. 5). Since e(t + 1) is a prediction error and u(t) is assumed to be known by the pub- lic at t, e(t + 1) and u(t) must be independent. This condition guarantees that OLS estimates of b and c are at least consistent (see Goldberger 1991, chap. 13.)

5. Recent examples include Weiner (1993), Tootell (1994), Fuhrer (1995), and Staiger, Stock, and Watson (1996). 6. See footnote 5 for published estimates. 7. Two reasons underlie the differences between the estimates given here and those of Staiger, Stock, and Watson. The first is that

they include in their regressions additional explanatory variables intended to control for supply shocks and Nixon-era price controls. The second reason is that Staiger, Stock, and Watson assumed that the error term in the estimated equation is normally distributed and derived exact confidence intervals based on that assumption. This study did not assume normality and derived approximate intervals based on the so-called Delta method, which is valid in large samples. For a description of the Delta method, see Goldberger (1991, 102).

8. The test is a standard one for stability of coefficients over time, as described by Harvey (1989, chap. 2). 9. For example, the assumption in the text is that s(t) is equal to some positive number, say n, for the 1974-83 subperiod. If one

estimates (2) the regression constant c is equal to bu* – n, and the true value of the NAIRU should be calculated to be (c – n)/b and not c/b. Hence the standard procedure would overestimate the NAIRU for the 1974-83 subperiod.

9Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 1997

(3), Staiger, Stock, and Watson argue that perhaps a bet- ter way to estimate a 95 percent confidence interval yields an interval from 4.74 to 8.31.7

From the perspective of policy analysis, the main implication of these findings is that the range of uncer- tainty about the location of the NAIRU is often too large to be useful. Consider, in particular, the recent debate about whether the unemployment rate signals increasing inflation. Since unemployment has been in the 5.5 to 6.5 percent range for the last three years, there is no way to tell, on the basis of observed data, whether current unem- ployment is above or below the NAIRU; it is well within the confidence bands.

Returning to equation (3), further analysis shows that the coefficients and hence the implied value of the NAIRU have changed over time. One can test and easily reject the hypothesis that the coefficients of (3) are con- stant over the three subperiods underlying the discussion of Chart 2 above, namely 1955-73, 1974-83, and 1984- present.8 Estimates of the NAIRU were at 5.91 for the first subperiod, 7.44 for the second, and 6.04 for the most recent subperiod. Hence the statistical analysis is consis- tent with the hypotheses obtained from the visual inspec- tion of Chart 2. It also agrees with most of the literature.

The instability of the NAIRU raises further difficul- ties. Estimating a moving NAIRU requires specifying how the NAIRU moves over time but, unfortunately, current economic theory provides little guidance on the econom- ic determinants of changes in the NAIRU. As a conse- quence, recent studies have focused on models in which the u* is viewed as slowly varying over time but in a way that has no relation with other economic events. This strategy does imply that the NAIRU’s location at different times can be estimated and its changes predicted. However, there are at least two important problems with it. The first is that the work of Staiger, Stock, and Watson has shown that forecasts of the NAIRU obtained in this manner are also subject to very wide confidence inter- vals. For example, when they estimated a version of (3) allowing u* to be a smooth function of time, they found

the 95 percent confidence interval for u* in January 1990 to be 4.17 to 8.91.

The second problem is that the instability of the esti- mated NAIRU may be a symptom of a deeper problem, namely, that equations such as (1) and (3) may be incor- rectly specified. To illustrate this problem, assume in equation (1) that the NAIRU is in fact constant. The hypothesis expressed by that equation is that inflation next month is expected to be the same as it is this month, unless this month’s unemployment deviates from the NAIRU. Intuition suggests that such a hypothesis is too extreme: even if there is no such deviation, it may be the case that inflation is not expected to stay the same. For example, it is plausible that people’s expectations of inflation would have increased following the oil shocks of 1973 and 1979 even if the unemployment rate had not deviated from the NAIRU. Conversely, it is likely that expectations of inflation decreased following the October 1979 Federal Reserve announcement of a change toward money targets to fight accelerating inflation.

These considerations suggest that (1) should be changed to something like

Etπ(t + 1) – π(t) = s(t) + b[u(t) – u*], (4)

where s(t) represents the expected change in inflation when unemployment is at the NAIRU. As shown by Chart 1, s(t) was probably a positive number during the subperiod from 1974 to 1983 in which inflation was accel- erating. Suppose that s(t) was zero until 1973, a positive number between 1974 and 1983, and a negative number since 1984. Then it is not hard to show that the estimat- ed NAIRU for the second subperiod would be higher than that for the first or third subperiods, just as indicated before.9 But this would just be the result of the incorrect omission of s(t), for the earlier assumption was that the NAIRU had stayed constant at u* for the whole 1955-96 period.

Some researchers have tried to deal with this speci- fication problem by adding measures of supply shocks, or