# A New Approach to Estimating the Natural Rate of Unemployment

**INTRODUCTION**

The non-accelerating inflation rate of unemployment (NAIRU) is frequently employed in fiscal and monetary policy deliberations. The U.S. Congressional Budget Office uses estimates of the NAIRU to compute potential GDP, that in turn is used to make budget projections that affect decisions about federal spending and taxation. Central banks consider estimates of the NAIRU to determine the likely course of inflation and what actions they should take to preserve price stability. A problem with the use of the NAIRU in policy formation is that it is thought to change over time (Ball and Mankiw 2002; Cohen, Dickens, and Posen 2001; Stock 2001; Gordon 1997, 1998). But estimates of the NAIRU and its time variation are remarkably imprecise and are far from robust (Staiger, Stock, and Watson 1997, 2001; Stock 2001).

NAIRU estimates are obtained from estimates of the Phillips curve— the relationship between the inflation rate, on the one hand, and the unemployment rate, measures of inflationary expectations, and variables representing supply shocks on the other. Typically, inflationary expectations are proxied with several lags of inflation and the unemployment rate is entered with lags as well. The NAIRU is recovered as the constant in the regression divided by the coefficient on unemployment (or the sum of the coefficient on unemployment and its lags).

The notion that the NAIRU might vary over time goes back at least to Perry (1970), who suggested that changes in the demographic composition of the labor force would change the NAIRU. He adjusted the unemployment rate to account for this. By 1990 several authors, including Gordon (1990) and Abraham (1987), had suggested that the NAIRU was probably lower in the 1960s than in the 1970s and 1980s. This adjustment was initially accommodated by adding dummy variables or splines for certain periods to the Phillips curve regression. However, when it began to appear that the U.S. NAIRU was coming down in the 1990s, new methods were developed to track its changes. Staiger, Stock, and Watson (1997), Gordon (1997, 1998) and Stock and Watson (1999) applied time-varying coefficient models and structural break models to NAIRU estimation, and typically found evidence that it rose in the late 1960s or early 1970s and declined in the 1990s.1 However, the timing and the magnitudes of the estimated changes differed markedly depending on the specification used. Furthermore, confidence bounds on the estimated NAIRUs were so large that the estimates had little value for policy.

This paper presents a new approach to estimating time variation in the NAIRU. A major problem with Phillips curve-based estimates is that the complicated relationship between inflation, its own lags, supply shocks, and unemployment and its lags makes it possible to explain any particular incidence of high or low inflation a number of different ways. This problem is the root cause of both the lack of robust results and the large confidence intervals around NAIRU estimates derived from Phillips curve estimates. This paper explores an alternative source of information about time variation in the NAIRU. To the extent that such changes are due to changes in the efficiency of the labor market, these changes are reflected not just in the relationship between inflation and unemployment, but also in the relationship between unemployment and job vacancies. That relationship is much simpler and consequently much easier to model in a robust fashion. Combined estimates of the Phillips curve and Beveridge curve—the relationship between unemployment and vacancies—yield remarkably consistent estimates of the timing of changes in the NAIRU. The next section provides a brief introduction to the literature on the Beveridge curve and on how it has shifted over time. It argues that because the Beveridge curve is much simpler and potentially better fitting than the Phillips curve, it provides a better basis for discerning shifts in the efficiency of the labor market’s functioning. These shifts appear to be quite large. The second section develops a theory linking shifts in the Beveridge curve to shifts in the NAIRU. The third section presents estimates of the Beveridge curve model developed in the second section. These estimates turn out to be very robust and motivate the model developed in the fourth section.

The fourth section presents estimates of a linearized version of the model using a Kalman filter. The filtered series is essentially a weighted average of the residuals of the Beveridge and Phillips curves that has been scaled to satisfy an identifying constraint—this constraint is that the coefficient on the filtered variable must be the same as minus the coefficient on the unemployment rate in the Phillips curve. As might be expected, given how precisely the Beveridge curve is estimated, the filter puts nearly all the weight on the Beveridge curve residuals. Estimates of a restricted version of the model suggest that the information from the Beveridge curve adds significantly to the explanatory power of the Phillips curve.

The Beveridge curve and Phillips curve NAIRUs look fairly similar, a result which supports the theory behind both curves. Confidence intervals that account for both forecast and parametric uncertainty are about 40 percent larger for Phillips curve NAIRU series than for series derived from the combined Beveridge curve-Phillips curve model. While estimates of the magnitude of the fluctuations in the NAIRU based on the joint Beveridge curve-Phillips curve model are still fairly uncertain, there is little uncertainty about the timing of the fluctuations.