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Labor quality, natural unemployment, and US inflation
The Quarterly Review of Economics and Finance 40 (2000) 325–336
Labor quality, natural unemployment, and US inflation David B. Crary* Department of Economics, Eastern Michigan University, Ypsilanti, MI 48197, USA
Abstract The recent combination of low inflation and low unemployment has led some to question whether the short-run, Phillips curve trade-off is dead. We argue that the improved trade-off has resulted, in part, from improved labor quality in the form of increased average years of work experience and education, and use these variables to calculate new estimates of the natural unemployment rate. Based on evidence from inflation equations, we find strong support for a time-varying natural unemployment rate, and find that our measure based on labor quality outperforms other leading measures of natural unemployment. © 2000 Bureau of Economic and Business Research, University of Illinois. All rights reserved.
1. Introduction The natural unemployment rate plays a crucial role in the Friedman (1968) and Phelps (1968) version of the Phillips curve, which includes a vertical long-run curve at which inflation expectations are realized. At the natural unemployment rate or NAIRU (for nonaccelerating inflation rate of unemployment) inflation remains stable, but if unemployment is below the natural rate inflation accelerates. The recent combination of unusually low inflation and unemployment has led some to question the short-run trade-off between inflation and unemployment, and the concept of a natural unemployment rate. Galbraith (1997), for example, suggested in his title that it was, “Time to Ditch the NAIRU,” due in part to the profession’s inability to agree on how to measure natural unemployment. Stiglitz (1997) and Gordon (1997) argue that natural unemployment remains a very important policy concept, and that recent declines in the natural unemployment rate help explain recent declines in inflation. Staiger, Stock, and Watson (1997) find weak support for a time-varying
* Tel.: ⫹1-734-487-0001. E-mail address: [email protected] (D.B. Crary). 1062-9769/00/$ – see front matter © 2000 Bureau of Economic and Business Research, University of Illinois. All rights reserved. PII: S 1 0 6 2 - 9 7 6 9 ( 0 0 ) 0 0 0 4 3 - 0
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NAIRU, and suggest that the confidence interval around NAIRU is so wide as to make it a nearly meaningless policy concept. Favorable supply factors have contributed to declining inflation, as discussed by the Congressional Budget Office (1999), the Council of Economic Advisers (1999, pp. 88 –95), and Gordon (1998a), but these sources suggest that a decline in NAIRU has also been a contributing factor. Disagreement has arisen on how to measure natural unemployment, however. Perry (1970) and Gordon (1982) focused on demographic factors as determining NAIRU, but Gordon (1997, 1998a) has since abandoned the demographic approach in favor of residual-based estimates from inflation equations. The Congressional Budget Office (1994), or C.B.O., has continued Gordon’s demographic approach, but its measure of NAIRU has shown relatively little decline in recent years. We offer a new approach of basing estimates of NAIRU on labor quality in the form of average years of education and work experience. These variables are available from the US Department of Labor (1993) as part of its multifactor productivity analysis. Our labor-quality measure of NAIRU has declined considerably more in recent years than those available from CBO (1994) and Gordon (1998a), and compares favorably to their measures in explaining past and recent inflation. Section 2 describes and compares time-varying estimates of NAIRU from the CBO (1994), Gordon (1998a), and the new series offered in this paper. The third section evaluates the ability of these time-varying measures and two fixed measures of NAIRU to explain past inflation. Conclusions and policy implications are discussed in Section 4.
2. Estimating NAIRU Most modern explanations of inflation are based on the natural-unemployment-rate, inflation-expectations models of Friedman (1968) and Phelps (1968), with a leading example being the “triangular model” used by Gordon (1997, 1998a). The three parts of the “triangular model” are demand pressure, inflation expectations, and supply-shock variables such as oil price inflation. The demand pressure variable is most often based on the civilian unemployment rate, and can either be this rate itself, or an unemployment gap where the rate is taken relative to an estimate of NAIRU. Often, the inflation equation is used to estimate NAIRU, with a fixed-NAIRU derived as the constant term in the inflation equation divided by the coefficient on the unemployment rate. As discussed below, variations on this approach were used to produce time-varying measures of NAIRU available from the Congressional Budget Office (1994) and Gordon (1997, 1998a), and the new series offered here. 2.1. CBO shares The Congressional Budget Office (1994) used the “triangular inflation model” to estimate a fixed natural unemployment rate for married males. Next, the fixed rate for married males was used to estimate fixed natural unemployment rates for each of 28 different demographic groups,1 based on the relationship between actual unemployment rates for each group and that for married males. The 28 group-specific estimates of fixed NAIRUs were then weighted by their labor-force shares to produce an aggregate NAIRU that varies over time. This
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approach was first developed by Gordon (1982), and served as the basis of the “Textbook NAIRU” discussed by Gordon (1997, p. 22). 2.2. Gordon residual Gordon (1997, pp. 20 –23) rejected the “shares” approach to estimating NAIRU in favor of a “stochastic time-varying parameters regression model.” In the new approach, NAIRU is allowed to change over time, based on residuals from the inflation equation and subject to an imposed smoothness constraint. Thus, Gordon replaced labor-based estimates of NAIRU with a residual approach to estimating NAIRU. Because it is based on equation residuals, Gordon’s NAIRU varies with the measure of inflation from which the residuals are taken, as shown in his Fig. 4 (Gordon, 1997). In addition, a judgment has to be made on how much to let NAIRU vary each period in response to the residuals as shown and discussed by Gordon (1998a, Fig. 2).2 2.3. Labor quality As discussed in most macroeconomic textbooks including Gordon (1998b, pp. 383–389), natural unemployment is influenced by the amount of structural and frictional unemployment at any time. The CBO shares approach to estimating NAIRU assumes that structural and frictional unemployment differs across demographic groups, with the relative differences being stable over time. For example, teenagers are likely to have a higher natural unemployment rate than middle-aged men, because teenagers are likely to have less work experience (structural) and are likely to be moving in and out of the labor force more frequently (frictional). Perry (1970, p. 435) questioned the stability of relative differences in natural unemployment by demographic groups, based on his finding that, “. . . as the relative size of an age-sex group has grown, its relative unemployment rate has generally worsened.” The recent dissatisfaction with the CBO shares approach was thus foreshadowed by Perry’s comments nearly 30 years ago. The shares approach probably captures some of the movement in NAIRU over time, but perhaps not enough of the movement. We take an alternate approach to estimating an aggregate NAIRU, by focusing on aggregate measures of labor quality in the form of average years of work experience and average years of education for the labor force.3 Workers with more work experience and with more education are likely to have more marketable skills, and thus be subject to less structural unemployment. As shown in Fig. 1, sizable changes have occurred in labor quality as measured by average years of work experience and education. Average work experience, with a mean value of 16.27 years, ranged from a high of 18.1 years in 1963 to a low of 15.2 years in the mid-1980s. This decline, of about 3 years in average work experience from the early1960s through the mid-1980s, occurred as baby boomers and an increasing number of women entered the labor market with below-average years of work experience. As these groups have aged, average work experience for the labor force as a whole has increased by 1 year, or by one-third of the previous decline. If additional work experience increases marketable skills, changes in work experience increased structural unemployment from the early 1960s through the mid-1980s, and have partially reversed the increase since then. Fortunately, while average work experience was declining, average years of education
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Fig. 1. Adjustment to NAIRU for years of experience and education
have shown a steady upward trend from 10.9 years in 1962 to 13.4 years in recent years, with a mean of 12.34 years. Data from the Bureau of Labor Statistics indicates a strong inverse relationship between unemployment rates and level of education for those 25 years old and above. For 1997, the unemployment rate was 8.1% for those without a high school education, 4.3% for high school graduates with no college, 3.3% for those with some college, and 2.0% for those with a college degree. Thus, the upward trend in average educational attainment of labor has probably reduced structural unemployment, and partially offset increased structural unemployment from the decline in average work experience. The upward trend in years of education has leveled off, however. From 1962 to 1985, average education levels increased by about 1 year each decade, but the increase was only about one-half year in the most recent decade with no increase in the past 4 years. The Labor Quality NAIRU was estimated based on a variation of the inflation equation discussed in the next section. Variables for years of experience and education were added as explanatory variables in the inflation equation, with a constant term included, and the civilian unemployment rate used as the demand variable. NAIRU was then calculated from the coefficients for the constant term, years of education YED, and years of work experience YWX, divided by the absolute value of the coefficient for the unemployment rate, 0.6864, as follows: Labor Quality NAIRU ⫽ [19.1321 ⫺ 0.5373 YED ⫺ 0.5080 YWX]/0.6864 (5.596)
(0.193)
(0.187)
(0.089)
Standard errors are shown in parentheses below the coefficients. The two labor quality variables each had expected negative signs, and were statistically significant at the 1% level. This indicates that higher education and higher work experience lower the natural unemployment rate and thus lower inflation for a given level of unemployment.
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Fig. 2. Alternate measures of natural unemployment
Fig. 1 shows how much the Labor Quality NAIRU was adjusted relative to its mean value to reflect deviations in education and work experience from their mean values: a 1-year increase in work experience reduces natural unemployment by 0.74% points (0.5373/0.6864) and a 1-year increase in education reduces natural unemployment by 0.78% points (0.5080/ 0.6864). The combined adjustment ranges from ⫺0.33% in 1970 to ⫹0.52% in 1980, with the largest absolute adjustment of ⫺0.78% in 1998. Shimer (1998) and Summers (1986) have argued against adjusting natural unemployment rates for changes in educational attainment, in part, because such adjustments would produce a strong secular decline in natural unemployment that has not been observed. Although different approaches were used, our demographic adjustment for education alone is very similar to that shown in Shimer (1998, Chart 11). However, our results suggest that, until the 1980s, the downward trend in natural unemployment, from increased education, was more than offset by declining average years of work experience.4
2.4. Comparison of time-varying NAIRU series As shown in Fig. 2, the three estimates of NAIRU show substantially different patterns. The one common element is that all three reached their highest values in the late 1970s and early 1980s and has declined by large amounts since those peaks. The C.B.O. measure shows a steady upward trend of 75 basis points from 1962 to 1978, followed by a steady downward trend of 61 basis points from 1978 to 1998. The Gordon measure fluctuates within a very
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narrow 22 basis point range between 6.16 and 6.38% from 1962 to 1991, followed by a rapid decline to 5.63% by 1998. The C.B.O. and Gordon measures each have a range of 75 basis points, but in 1962 they start out 70 basis points apart. The labor quality measure has a much wider range of 129 basis points, had values between the other two measures in the 1960s, above them for most of the 1970s and 1980s, and below them for most of the 1990s. Values for 1998 range from a high of 5.71% for the C.B.O. measure to 5.63 for Gordon, and a low of 5.39 for the labor quality measure.
3. Evaluating alternate measures of NAIRU Given substantial differences between the three measures of NAIRU, it is important to identify criteria by which to evaluate them. Three criteria seem appropriate: 1. Is the measure based on labor characteristics that can be used to predict future levels of NAIRU? 2. By how much does it improve our ability to explain inflation? 3. Does it perform well in inflation equations for different aggregate price measures? The CBO Shares and the Labor Quality series meet Criterion (1), whereas the Gordon Residual series does not. Because the Gordon series is derived from residuals from the inflation equation, it provides a useful measure against which to evaluate other NAIRU series on Criteria (2) and (3), however, and will be used for this purpose. For comparison purposes, we also estimate inflation equations using two fixed-rate-NAIRU measures, one is based on the civilian unemployment rate and the other is based on the unemployment rate for married males. The married-male rate is used because it is an important component in the CBO calculation of NAIRU. Except for the CBO measure, the NAIRU measures are estimated in part from constant terms from an unconstrained version of the inflation equation, and the constant term is then suppressed when a labor gap veriable based on NAIRU is used in the inflation equations reported in Tables 1 and 2. An adjusted CBO NAIRU is also used, with its value increased by 0.2 percentage points based on the constant term in an unconstrained version of the equation with the labor gap calculated from the CBO NAIRU. In evaluating the alternate measures of NAIRU, we use an inflation equation based on those reported in Gordon (1997, 1998a), which were the basis for estimating Gordon’s residual-based estimate of NAIRU.5 Gordon’s triangular model of inflation includes variables to capture expected inflation, demand pressure, and supply shocks. A 24-quarter lag on inflation, split into six 1-year inflation rates, is used as a proxy for expected inflation. The demand pressure variable is an unemployment gap measured as the unemployment rate minus a measure of NAIRU. Supply shocks include: (1) the deviation of productivity growth from its trend rate; (2) the annual rate of change in the relative price of imports; (3) the annual rate of change in the relative price of food and energy for personal consumption spending; and (4) dummy variables for the Nixon wage and price controls, with “on” equal to 0.8 for the 1971Q3–1972Q3 period when controls were strictly enforced, and “off” equal to 0.4, 1.6, 1.6, and 0.4, respectively, for the 1974Q2–1975Q1 period after their removal. Two different aggregate price measures are used to test the ability of the different
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Table 1 GDP inflation equations using alternate labor gap variables (1962q1–1996q4: labor variables identified at top of columns) Explanatory variables
Lags Fixed NAIRU
Time-varying measures of NAIRU
UR URMM C.B.O. (6.18%) (3.56%) shares Past GDP inflation (constrained ⫽ 1.0) Labor gap variable Deviation in productivity growth Relative inflation: imports Relative inflation: food & energy Nixon controls “on” Nixon controls “off” S.E.E. S.S.R. D.W. Comparison of equationsb F-stat compared to UR equation F-stat compared to Labor Quality Eq. Out-of-sample forecasts 1997q1–1998q4 mean error 1997q1–1998q4 root mean squared error
1–24 1.0** 1.0** 1.0** 0–4 ⫺0.55** ⫺0.70** ⫺0.60** 0–1 ⫺0.11** ⫺0.10** ⫺0.10** 1–4 0.10** 0.07** 0.08** 0 0.23** 0.24** 0.25** 0 ⫺1.66** ⫺1.70** ⫺1.52** 0 1.25** 1.64** 1.61** 0.69 0.71 0.69 57.62 61.71 58.28 1.86 1.87 1.86
Adj. C.B.O. Gordon Labor sharesa residuala quality 1.0** ⫺0.63** ⫺0.10** 0.09** 0.22** ⫺1.70** 1.38** 0.68 56.46 1.89
0 8.58** 1.38 ⫺2.45 9.84** 19.12** 11.33** 7.20** ⫺0.65 0.85
⫺0.79 0.92
⫺0.65 0.85
⫺0.67 0.88
1.0** ⫺0.58** ⫺0.11** 0.10** 0.24** ⫺1.73** 1.26** 0.67 54.45 1.96
1.0** ⫺0.69** ⫺0.10** 0.09** 0.22** ⫺1.63** 1.46** 0.66 53.29 1.98
⫺6.66* ⫺9.10** 2.64 0 ⫺0.39 0.67
⫺0.41 0.70
Inflation rates are quarterly log changes in price levels multiplied by 400 to yield annual percent changes. Significant levels are indicated by ** for 1%, * for 5%, and ⫹ for 10%. a The Adj. CBO Shares measure of NAIRU was increased by ⫹0.2 based on the constant from an unconstrained version of the GDP equation. This gives it a mean value of 6.17, compared to the unadjusted mean of 5.97. b Critical values for the F-test (1,121) are 6.85 for 1%, 3.92 for 5%, and 2.75 for 10% confidence levels. Shaded areas indicate equations that show improvement compared to the reference equation in the F-tests.
measures of NAIRU to explain inflation. The first is the chain-weighted GDP price index with results shown in Table 1, and the second is the chain-weighted price index for personal consumption expenditures (PCE) with results shown in Table 2. In the tables, lag periods are indicated for each explanatory variable, and notes at the bottom of the tables discuss slight changes to the Gordon specification with respect to trend productivity and lags on food and energy prices. As indicated at the top of each column, a total of six different NAIRU estimates were used to calculate unemployment gaps, in what is otherwise the same inflation equation. UR uses a fixed NAIRU of 6.18% based on the civilian unemployment rate, URMM uses a fixed NAIRU of 3.56% based on the unemployment rate for married males, and the other four columns use unemployment gaps calculated from measures of NAIRU discussed above and shown in Fig. 2. As discussed by Gordon (1997, p. 24), the constant is excluded from equations using an unemployment gap as the labor variable, because the constant term from unconstrained estimates of equations are used to calculate the various measures of NAIRU. Coefficients on lagged inflation are constrained to sum to one, because NAIRU is supposed to yield actual inflation equal to expected inflation in the absence of supply shocks. Results reported in Tables 1 and 2 indicate that this is a very powerful model for explaining inflation. Although not reported in the tables due to use of constrained estimation,
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Table 2 PCE inflation equations using alternate labor gap variables (1962q1–1996q4: labor variables identified at top of columns) Explanatory variables
Lags Fixed NAIRU
Time-varying measures of NAIRU
UR URMM C.B.O. (6.18%) (3.56%) shares Past PCE inflation (constrained ⫽ 1.0) Labor gap variable Deviation in productivity growth Relative inflation: imports Relative inflation: food & energy Nixon controls “on” Nixon controls “off” S.E.E. S.S.R. D.W. Comparison of equationsb F-stat compared to UR equation F-stat compared to Labor Quality Eq. Out-of-sample forecasts 1997q1–1998q4 mean error 1997q1–1998q4 root mean squared error
1–24 1.0** 1.0** 1.0** 0–4 ⫺0.47** ⫺0.60** 0.54** 0–1 ⫺0.04 ⫺0.02 ⫺0.03 1–4 0.06* 0.03 0.05* 0 0.81** 0.81** 0.81** 0 ⫺1.51** ⫺1.55** ⫺1.40** 0 0.81 1.15* 1.09* 0.74 0.75 0.73 66.51 67.81 64.30 1.44 1.48 1.46
Adj. C.B.O. sharesa
Gordon residuala
1.0** 1.0** ⫺0.58** ⫺0.51** ⫺0.03 ⫺0.03 0.06** 0.07** 0.78** 0.80** ⫺1.59** ⫺1.62** 0.88⫹ 0.80⫹ 0.72 0.72 62.77 62.79 1.49 1.49
Labor quality 1.0** ⫺0.65** ⫺0.03 0.07** 0.77** ⫺1.54** 0.95* 0.70 59.38 1.54
0 23.7 ⫺4.02* ⫺6.81* ⫺6.77* ⫺12.96** 14.52** 17.17** 10.02** 6.89** 6.94** 0.00 ⫺0.82 0.95
⫺0.96 1.06
⫺0.75 0.89
⫺0.86 0.99
⫺0.60 0.77
⫺0.62 0.79
Inflation rates are quarterly log changes in price levels multiplied by 400 to yield annual percent changes. Significant levels are indicated by ** for 1%, * for 5%, and ⫹ for 10%. a The Adj. CBO Shares measure of NAIRU was increased by ⫹0.2 based on the constant from an unconstrained version of the GDP equation. This gives it a mean value of 6.17, compared to the unadjusted mean of 5.97. b Critical values for the F-test (1,121) are 6.85 for 1%, 3.92 for 5%, and 2.75 for 10% confidence levels. Shaded areas indicate equations that show improvement compared to the reference equation in the F-tests.
90% or more of the variance in the inflation rate was explained by each equation. In Table 1 for GDP inflation, coefficients for every explanatory variable have the expected signs, and are significantly different from zero at the 1% confidence level. The standard-error-ofestimate ranges from a low of 66 basis points for the labor quality equation to 71 basis points for the married-male equation. In Table 2 for PCE inflation, all coefficients again have the correct signs, and those for past inflation, labor gap, food and energy inflation, and controls “on” are all significant at the 1% confidence level. Coefficients on import inflation are significant at the 1% level for the three time-varying NAIRU equations, and at the 5% level in all except the URMM equation. The controls “off” variable is significant at the 5% level in three equations, and at the 10% level in two additional equations. For PCE inflation, the standard-error-of-estimate ranges from a low of 70 basis points for the labor quality equation to a high of 75 basis points for the married-male equation. The key question in our analysis is, “How well do the different labor measures perform in explaining inflation?” Based on the sum squared residuals (S.S.R.) for GDP inflation (Table 1), the ranking from best to worst is Labor Quality, Gordon Residual, Adjusted CBO Shares, UR, CBO shares, and URMM. For PCE inflation (Table 2), the ranking is similar except that the CBO measure outperforms UR, and the Adjusted CBO. Shares slightly
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outperform the Gordon measure to take second place after the Labor Quality measure. In comparing best to worst specifications, reductions of 14 and 12% in S.S.R. statistics were achieved, respectively, for GDP inflation and PCE inflation. F-statistics were calculated to test significance levels for using alternate measures of NAIRU in the equations, and these are shown in the second panel, toward the bottom of each table. In Table 1 for example, the higher S.S.R. for the URMM than the UR equation produces an F-statistic of 8.58. This indicates that URMM results are worse at a 1% significance level than those for UR in explaining GDP inflation. For PCE inflation (Table 2), URMM results are worse than those for UR, but not at the 10% significance level. It was surprising to find that URMM performed worse than UR. The unemployment rate for married males is often viewed as being a more stable measure of labor market tightness than UR, and was therefore used as the basis for the CBO (1994) calculation of NAIRU. Related to this, it was surprising to find that C.B.O. Shares performed worse than UR for GDP inflation, although it did perform better than UR at the 5% level for PCE inflation. The three remaining time-varying measures of NAIRU showed improvements compared to the fixed NAIRU for UR. For the Adjusted CBO measure, improvement compared to UR was not significant at the 10% level for GDP inflation but was significant at the 5% level for PCE inflation. The Gordon measure of natural unemployment showed improvement compared to UR that was significant at the 5% level for both measures of inflation. Finally, the Labor Quality measure of NAIRU performed significantly better than UR at the 1% level for both measures of inflation. In the second row of F-tests, for GDP inflation, the Labor Quality measure performed better at the 1% level than all other measures except Gordon, and for PCE inflation, it performed better at the 1% level than all other measures of NAIRU. As indicated by Gordon (1998a, Fig. 1), his residual based approach to estimating NAIRU is sensitive to the inflation equation from which it is measured. This helps explain why his measure of NAIRU from the GDP inflation equation, which is used here, considerably outperforms the Adjusted C.B.O. measure in the GDP inflation equation, but not for the PCE inflation equation. As a second test of the various measures of NAIRU, we look at their performance in out-of-sample forecasts. Recent questions about NAIRU were prompted by declining inflation rates despite exceptionally low unemployment rates. Thus, many Phillips curve models of inflation have significantly overpredicted inflation in recent years. Gordon (1998a) finds that much of the improved trade-off is due to favorable supply shocks captured by his equations, with the remaining overprediction due to changes in price measurement methods, omitted supply shocks, and declines in NAIRU. The equations from Tables 1 and 2, which were estimated for the period ending in the fourth quarter of 1996, were used to generate ex-post forecasts for the eight quarters in 1997 and 1998. Results from these forecasts are shown in the bottom panel of each table. For both inflation measures, each of the six equations produces overpredictions of inflation. The mean error for GDP inflation ranges from an overprediction of 39 basis points for Gordon’s NAIRU to 79 basis points for the married-male unemployment rate, whereas that for PCE inflation ranges from an overprediction of 60 basis points to 96 basis points for the same two unemployment measures. Rankings of the unemployment measures based on root-mean-squared-errors follow the same pattern as those for the mean errors. Performance for the married-male rate and for the
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Adjusted CBO NAIRU is considerably worse and slightly worse, respectively, than the general unemployment rate. The unadjusted CBO measure has the same out-of-sample error measures as UR for GDP inflation, and slightly lower error measures for PCE inflation. The Gordon and Labor Quality measures of NAIRU both perform considerably better than the general unemployment rate. Thus, recent large declines in the Labor Quality and Gordon measures of NAIRU provide significant improvement in our ability to explain the low inflation in recent years. The Gordon measure slightly outperforms the Labor Quality measure, but this is due in part to the fact that Gordon’s NAIRU was originally estimated from a sample period that ended in the second quarter of 1998, and thus included six of the eight quarters in our “out-of-sample” forecast.
4. Conclusion This paper has demonstrated that the concept of NAIRU remains a very useful tool for measuring labor market tightness and inflationary pressure. Empirical results provide strong support for use of a time-varying NAIRU rather than a fixed NAIRU, but indicate that accurately measuring NAIRU is a challenge. Gordon’s time-varying-parameters measure of NAIRU provides a useful benchmark for evaluating measures of NAIRU derived from labor market characteristics. The weakness of Gordon’s approach is that it is entirely backward looking, and is not useful in predicting future values of NAIRU or in explaining why NAIRU has changed (see Gordon, 1997, p. 30). This paper offered a new approach to estimating a time-varying NAIRU that focuses on labor quality in the form of average years of work experience and average years of education of the labor force. These new estimates appear to be a promising alternative to NAIRU estimates that are currently available. In the three criteria suggested for evaluating alternate measures of NAIRU, the new Labor Quality NAIRU performed well. First, like the CBO measure but unlike the Gordon measure, the new measure provides a labor-based explanation for changes in NAIRU. Second, the Labor Quality NAIRU significantly outperforms the CBO NAIRU in explaining inflation for GDP and PCE at the 1% confidence level. Third, although the Labor Quality NAIRU does not significantly outperform the Gordon measure for GDP inflation, the Labor Quality measure significantly outperforms the Gordon measure in explaining PCE inflation at the 1% confidence measure. Finally, the Gordon and Labor Quality NAIRU measures produce sizable reductions in out-of-sample forecast errors compared to the other four measures of labor market tightness. Reliable estimates of NAIRU are desirable for use as a macroeconomic policy target, and because the CBO relies heavily on estimates of NAIRU in producing annual reports to Congress on budgetary and economic projections.6 Results from this paper suggest that estimates of NAIRU can be improved significantly by using the labor-quality approach offered here. This new approach provides a much different view of past movements in NAIRU than the CBO and Gordon approaches. In contrast to the gradual rise and fall in the CBO NAIRU, the Labor Quality NAIRU showed a much more pronounced rise in the early 1970s, a relatively stable NAIRU in the 1980s, and a much more dramatic decline in the past decade. From 1988 to 1998, the labor quality NAIRU declined 97 basis points to 5.39%,
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compared to a decline of only 29 basis points to 5.71% for the CBO NAIRU. In the next 5 to 10 years, further improvements in labor quality could lower NAIRU to 5% or below compared to a fairly steady estimate of between 5.7 and 5.6% for the CBO NAIRU. Results from this paper need to be tested further, but they offer a promising start to providing more accurate measures of NAIRU, a better explanation of past inflation, and a better guide for policy making in the future.
Notes 1. The 28 demographic groups are white and nonwhite, and male and female, for seven different age categories: 16 –19, 20 –24, 25–34, 35– 44,45–54, 55– 64, and 65 and over. 2. The remainder of this paper uses Gordon’s (1998a) NAIRU for the chain-weighted GDP deflator with the smoothness constraint of standard deviation ⫽ 0.09. We thank Gordon for supplying these data to us. 3. These data were developed to help identify sources of US productivity growth, and are described in US Department of Labor (1993, pp. 9 –12, and 56 – 67). The Department of Labor uses source data from the Current Population Survey, Social Security Administration, Internal Revenue Service, and population censuses to estimate the composition of the labor force by different levels of education and work experience. Annual data for average years of experience and education are calculated using weights based on estimated total hours worked for each group. Updated measures of these data were provided by Larry Rosenblum of the Bureau of Labor Statistics. The annual data were converted to quarterly data by taking a five-quarter, centered-moving-average of quarterly data set equal to the annual data for each year. 4. A referee for this article suggested inclusion of the female share of the labor force, as an additional demographic adjustment. The female share of the labor force shows a strong upward trend as does average years of education, with a 0.99 correlation coefficient between these two variables. The correlation coefficient between each of these variables and the average years of experience is ⫺0.87. When the female share was included in the inflation equation, together with years of education and years of experience, it had an insignificant positive impact, there was a slight reduction in the experience coefficient, and the education coefficient doubled in size but became insignificant due to the extreme colinearity between this variable and the female share variable. The net impact of these variables on the Labor Quality NAIRU continued to be virtually the same as that shown in Figs. 1 and 2, however. 5. Several modifications have been made to Gordon’s specification. First, the deviation of productivity growth from trend uses the average growth over the past thirty-two quarters as trend growth, while Gordon sets trend growth equal to the average growth between cyclical peaks. This alternate specification of trend productivity growth was suggested by Robert Arnold of the Congressional Budget Office. Second, Gordon includes lags of 0 – 4 on the relative inflation for food and energy, but we have dropped
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insignificant lagged values. Finally, the sample period has been shortened by six quarters to provide eight quarters for use in out-of-sample forecasts. 6. The Congressional Budget Office typically makes its 10-year budget projections based on the unemployment rate moving to a level slightly above NAIRU and remaining at that level for an extended period. See for example, Congressional Budget Office (1999, Fig. 1–1).
Acknowledgments The author thanks Robert Arnold of the Congressional Budget Office, Robert Gordon of Northwestern University, and Larry Rosenblum of the Bureau of Labor Statistics for providing data used in this paper. In addition, Robert Arnold and two anonymous referees provided valuable comments on this paper.
References Congressional Budget Office. (1994). Re-estimating the NAIRU. In The Economic and Budget Outlook: An Update (p. 59 – 63). Washington, DC: US Government Printing Office. Congressional Budget Office. (1999). The Economic and Budget Outlook: Fiscal Years 2000 –2009. Washington, DC: US Government Printing Office. Council of Economic Advisers. (1999). Economic Report of the President. Washington, DC: US Government Printing Office. Friedman, M. (1968). The role of monetary policy. Am Econ Rev, 58, 1–17. Galbraith, J. K. (1997). Time to ditch the NAIRU. J Econ Perspectives, 11, 93–108. Gordon, R. J. (1982). Inflation, flexible exchange rates, and the natural unemployment rate. In Baily, M. N. (Ed.). Workers, Jobs and Inflation (p. 88 –152). Washington, DC: Brookings Institution. Gordon, R. J. (1998a). Foundations of the Goldilocks economy: supply shocks and the time-varying NAIRU. Brookings Papers on Economic Activity, 29, 297–346. Gordon, R. J. (1998b). Macroeconomics. New York: Addison–Wesley. Gordon, R. J. (1997). “The time-varying NAIRU and its implications for economic policy. J Econ Perspectives, 11, 11–32. Perry, G. L. (1970). Changing labor markets and inflation. Brookings Papers on Economic Activity, 3, 411– 41. Phelps, E. S. (1968). Money-wage dynamics and labor-market equilibrium. J Polit Econ 76, 678 –711. Shimer, R. (1998). Why is the US unemployment rate so much lower? In Bernanke, B. S. & Rotemberg, J. J. (Eds.). NBER Macroeconomics Annual 1998 Cambridge, MA: MIT Press, 11– 61. Staiger, D., Stock, J. H., & Watson, M. W. (1997). The NAIRU, unemployment and monetary policy. The Journal of Economic Perspectives, 11, 33–50. Stiglitz, J. (1997). Reflections on the natural rate hypothesis. J Econ Perspect, 11, 3–10. Summers, L. (1986). Why is the unemployment rate so very high near full employment? Brookings Papers on Economic Activity, 1985, 17, 339 – 83. US Department of Labor. (1993). Labor Composition and US Productivity Growth, 1948 –90, (Bulletin2426) Washington, DC: US Government Printing Office.
Labor quality, natural unemployment, and US inflation David B. Crary* Department of Economics, Eastern Michigan University, Ypsilanti, MI 48197, USA
Abstract The recent combination of low inflation and low unemployment has led some to question whether the short-run, Phillips curve trade-off is dead. We argue that the improved trade-off has resulted, in part, from improved labor quality in the form of increased average years of work experience and education, and use these variables to calculate new estimates of the natural unemployment rate. Based on evidence from inflation equations, we find strong support for a time-varying natural unemployment rate, and find that our measure based on labor quality outperforms other leading measures of natural unemployment. © 2000 Bureau of Economic and Business Research, University of Illinois. All rights reserved.
1. Introduction The natural unemployment rate plays a crucial role in the Friedman (1968) and Phelps (1968) version of the Phillips curve, which includes a vertical long-run curve at which inflation expectations are realized. At the natural unemployment rate or NAIRU (for nonaccelerating inflation rate of unemployment) inflation remains stable, but if unemployment is below the natural rate inflation accelerates. The recent combination of unusually low inflation and unemployment has led some to question the short-run trade-off between inflation and unemployment, and the concept of a natural unemployment rate. Galbraith (1997), for example, suggested in his title that it was, “Time to Ditch the NAIRU,” due in part to the profession’s inability to agree on how to measure natural unemployment. Stiglitz (1997) and Gordon (1997) argue that natural unemployment remains a very important policy concept, and that recent declines in the natural unemployment rate help explain recent declines in inflation. Staiger, Stock, and Watson (1997) find weak support for a time-varying
* Tel.: ⫹1-734-487-0001. E-mail address: [email protected] (D.B. Crary). 1062-9769/00/$ – see front matter © 2000 Bureau of Economic and Business Research, University of Illinois. All rights reserved. PII: S 1 0 6 2 - 9 7 6 9 ( 0 0 ) 0 0 0 4 3 - 0
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NAIRU, and suggest that the confidence interval around NAIRU is so wide as to make it a nearly meaningless policy concept. Favorable supply factors have contributed to declining inflation, as discussed by the Congressional Budget Office (1999), the Council of Economic Advisers (1999, pp. 88 –95), and Gordon (1998a), but these sources suggest that a decline in NAIRU has also been a contributing factor. Disagreement has arisen on how to measure natural unemployment, however. Perry (1970) and Gordon (1982) focused on demographic factors as determining NAIRU, but Gordon (1997, 1998a) has since abandoned the demographic approach in favor of residual-based estimates from inflation equations. The Congressional Budget Office (1994), or C.B.O., has continued Gordon’s demographic approach, but its measure of NAIRU has shown relatively little decline in recent years. We offer a new approach of basing estimates of NAIRU on labor quality in the form of average years of education and work experience. These variables are available from the US Department of Labor (1993) as part of its multifactor productivity analysis. Our labor-quality measure of NAIRU has declined considerably more in recent years than those available from CBO (1994) and Gordon (1998a), and compares favorably to their measures in explaining past and recent inflation. Section 2 describes and compares time-varying estimates of NAIRU from the CBO (1994), Gordon (1998a), and the new series offered in this paper. The third section evaluates the ability of these time-varying measures and two fixed measures of NAIRU to explain past inflation. Conclusions and policy implications are discussed in Section 4.
2. Estimating NAIRU Most modern explanations of inflation are based on the natural-unemployment-rate, inflation-expectations models of Friedman (1968) and Phelps (1968), with a leading example being the “triangular model” used by Gordon (1997, 1998a). The three parts of the “triangular model” are demand pressure, inflation expectations, and supply-shock variables such as oil price inflation. The demand pressure variable is most often based on the civilian unemployment rate, and can either be this rate itself, or an unemployment gap where the rate is taken relative to an estimate of NAIRU. Often, the inflation equation is used to estimate NAIRU, with a fixed-NAIRU derived as the constant term in the inflation equation divided by the coefficient on the unemployment rate. As discussed below, variations on this approach were used to produce time-varying measures of NAIRU available from the Congressional Budget Office (1994) and Gordon (1997, 1998a), and the new series offered here. 2.1. CBO shares The Congressional Budget Office (1994) used the “triangular inflation model” to estimate a fixed natural unemployment rate for married males. Next, the fixed rate for married males was used to estimate fixed natural unemployment rates for each of 28 different demographic groups,1 based on the relationship between actual unemployment rates for each group and that for married males. The 28 group-specific estimates of fixed NAIRUs were then weighted by their labor-force shares to produce an aggregate NAIRU that varies over time. This
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approach was first developed by Gordon (1982), and served as the basis of the “Textbook NAIRU” discussed by Gordon (1997, p. 22). 2.2. Gordon residual Gordon (1997, pp. 20 –23) rejected the “shares” approach to estimating NAIRU in favor of a “stochastic time-varying parameters regression model.” In the new approach, NAIRU is allowed to change over time, based on residuals from the inflation equation and subject to an imposed smoothness constraint. Thus, Gordon replaced labor-based estimates of NAIRU with a residual approach to estimating NAIRU. Because it is based on equation residuals, Gordon’s NAIRU varies with the measure of inflation from which the residuals are taken, as shown in his Fig. 4 (Gordon, 1997). In addition, a judgment has to be made on how much to let NAIRU vary each period in response to the residuals as shown and discussed by Gordon (1998a, Fig. 2).2 2.3. Labor quality As discussed in most macroeconomic textbooks including Gordon (1998b, pp. 383–389), natural unemployment is influenced by the amount of structural and frictional unemployment at any time. The CBO shares approach to estimating NAIRU assumes that structural and frictional unemployment differs across demographic groups, with the relative differences being stable over time. For example, teenagers are likely to have a higher natural unemployment rate than middle-aged men, because teenagers are likely to have less work experience (structural) and are likely to be moving in and out of the labor force more frequently (frictional). Perry (1970, p. 435) questioned the stability of relative differences in natural unemployment by demographic groups, based on his finding that, “. . . as the relative size of an age-sex group has grown, its relative unemployment rate has generally worsened.” The recent dissatisfaction with the CBO shares approach was thus foreshadowed by Perry’s comments nearly 30 years ago. The shares approach probably captures some of the movement in NAIRU over time, but perhaps not enough of the movement. We take an alternate approach to estimating an aggregate NAIRU, by focusing on aggregate measures of labor quality in the form of average years of work experience and average years of education for the labor force.3 Workers with more work experience and with more education are likely to have more marketable skills, and thus be subject to less structural unemployment. As shown in Fig. 1, sizable changes have occurred in labor quality as measured by average years of work experience and education. Average work experience, with a mean value of 16.27 years, ranged from a high of 18.1 years in 1963 to a low of 15.2 years in the mid-1980s. This decline, of about 3 years in average work experience from the early1960s through the mid-1980s, occurred as baby boomers and an increasing number of women entered the labor market with below-average years of work experience. As these groups have aged, average work experience for the labor force as a whole has increased by 1 year, or by one-third of the previous decline. If additional work experience increases marketable skills, changes in work experience increased structural unemployment from the early 1960s through the mid-1980s, and have partially reversed the increase since then. Fortunately, while average work experience was declining, average years of education
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Fig. 1. Adjustment to NAIRU for years of experience and education
have shown a steady upward trend from 10.9 years in 1962 to 13.4 years in recent years, with a mean of 12.34 years. Data from the Bureau of Labor Statistics indicates a strong inverse relationship between unemployment rates and level of education for those 25 years old and above. For 1997, the unemployment rate was 8.1% for those without a high school education, 4.3% for high school graduates with no college, 3.3% for those with some college, and 2.0% for those with a college degree. Thus, the upward trend in average educational attainment of labor has probably reduced structural unemployment, and partially offset increased structural unemployment from the decline in average work experience. The upward trend in years of education has leveled off, however. From 1962 to 1985, average education levels increased by about 1 year each decade, but the increase was only about one-half year in the most recent decade with no increase in the past 4 years. The Labor Quality NAIRU was estimated based on a variation of the inflation equation discussed in the next section. Variables for years of experience and education were added as explanatory variables in the inflation equation, with a constant term included, and the civilian unemployment rate used as the demand variable. NAIRU was then calculated from the coefficients for the constant term, years of education YED, and years of work experience YWX, divided by the absolute value of the coefficient for the unemployment rate, 0.6864, as follows: Labor Quality NAIRU ⫽ [19.1321 ⫺ 0.5373 YED ⫺ 0.5080 YWX]/0.6864 (5.596)
(0.193)
(0.187)
(0.089)
Standard errors are shown in parentheses below the coefficients. The two labor quality variables each had expected negative signs, and were statistically significant at the 1% level. This indicates that higher education and higher work experience lower the natural unemployment rate and thus lower inflation for a given level of unemployment.
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Fig. 2. Alternate measures of natural unemployment
Fig. 1 shows how much the Labor Quality NAIRU was adjusted relative to its mean value to reflect deviations in education and work experience from their mean values: a 1-year increase in work experience reduces natural unemployment by 0.74% points (0.5373/0.6864) and a 1-year increase in education reduces natural unemployment by 0.78% points (0.5080/ 0.6864). The combined adjustment ranges from ⫺0.33% in 1970 to ⫹0.52% in 1980, with the largest absolute adjustment of ⫺0.78% in 1998. Shimer (1998) and Summers (1986) have argued against adjusting natural unemployment rates for changes in educational attainment, in part, because such adjustments would produce a strong secular decline in natural unemployment that has not been observed. Although different approaches were used, our demographic adjustment for education alone is very similar to that shown in Shimer (1998, Chart 11). However, our results suggest that, until the 1980s, the downward trend in natural unemployment, from increased education, was more than offset by declining average years of work experience.4
2.4. Comparison of time-varying NAIRU series As shown in Fig. 2, the three estimates of NAIRU show substantially different patterns. The one common element is that all three reached their highest values in the late 1970s and early 1980s and has declined by large amounts since those peaks. The C.B.O. measure shows a steady upward trend of 75 basis points from 1962 to 1978, followed by a steady downward trend of 61 basis points from 1978 to 1998. The Gordon measure fluctuates within a very
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narrow 22 basis point range between 6.16 and 6.38% from 1962 to 1991, followed by a rapid decline to 5.63% by 1998. The C.B.O. and Gordon measures each have a range of 75 basis points, but in 1962 they start out 70 basis points apart. The labor quality measure has a much wider range of 129 basis points, had values between the other two measures in the 1960s, above them for most of the 1970s and 1980s, and below them for most of the 1990s. Values for 1998 range from a high of 5.71% for the C.B.O. measure to 5.63 for Gordon, and a low of 5.39 for the labor quality measure.
3. Evaluating alternate measures of NAIRU Given substantial differences between the three measures of NAIRU, it is important to identify criteria by which to evaluate them. Three criteria seem appropriate: 1. Is the measure based on labor characteristics that can be used to predict future levels of NAIRU? 2. By how much does it improve our ability to explain inflation? 3. Does it perform well in inflation equations for different aggregate price measures? The CBO Shares and the Labor Quality series meet Criterion (1), whereas the Gordon Residual series does not. Because the Gordon series is derived from residuals from the inflation equation, it provides a useful measure against which to evaluate other NAIRU series on Criteria (2) and (3), however, and will be used for this purpose. For comparison purposes, we also estimate inflation equations using two fixed-rate-NAIRU measures, one is based on the civilian unemployment rate and the other is based on the unemployment rate for married males. The married-male rate is used because it is an important component in the CBO calculation of NAIRU. Except for the CBO measure, the NAIRU measures are estimated in part from constant terms from an unconstrained version of the inflation equation, and the constant term is then suppressed when a labor gap veriable based on NAIRU is used in the inflation equations reported in Tables 1 and 2. An adjusted CBO NAIRU is also used, with its value increased by 0.2 percentage points based on the constant term in an unconstrained version of the equation with the labor gap calculated from the CBO NAIRU. In evaluating the alternate measures of NAIRU, we use an inflation equation based on those reported in Gordon (1997, 1998a), which were the basis for estimating Gordon’s residual-based estimate of NAIRU.5 Gordon’s triangular model of inflation includes variables to capture expected inflation, demand pressure, and supply shocks. A 24-quarter lag on inflation, split into six 1-year inflation rates, is used as a proxy for expected inflation. The demand pressure variable is an unemployment gap measured as the unemployment rate minus a measure of NAIRU. Supply shocks include: (1) the deviation of productivity growth from its trend rate; (2) the annual rate of change in the relative price of imports; (3) the annual rate of change in the relative price of food and energy for personal consumption spending; and (4) dummy variables for the Nixon wage and price controls, with “on” equal to 0.8 for the 1971Q3–1972Q3 period when controls were strictly enforced, and “off” equal to 0.4, 1.6, 1.6, and 0.4, respectively, for the 1974Q2–1975Q1 period after their removal. Two different aggregate price measures are used to test the ability of the different
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Table 1 GDP inflation equations using alternate labor gap variables (1962q1–1996q4: labor variables identified at top of columns) Explanatory variables
Lags Fixed NAIRU
Time-varying measures of NAIRU
UR URMM C.B.O. (6.18%) (3.56%) shares Past GDP inflation (constrained ⫽ 1.0) Labor gap variable Deviation in productivity growth Relative inflation: imports Relative inflation: food & energy Nixon controls “on” Nixon controls “off” S.E.E. S.S.R. D.W. Comparison of equationsb F-stat compared to UR equation F-stat compared to Labor Quality Eq. Out-of-sample forecasts 1997q1–1998q4 mean error 1997q1–1998q4 root mean squared error
1–24 1.0** 1.0** 1.0** 0–4 ⫺0.55** ⫺0.70** ⫺0.60** 0–1 ⫺0.11** ⫺0.10** ⫺0.10** 1–4 0.10** 0.07** 0.08** 0 0.23** 0.24** 0.25** 0 ⫺1.66** ⫺1.70** ⫺1.52** 0 1.25** 1.64** 1.61** 0.69 0.71 0.69 57.62 61.71 58.28 1.86 1.87 1.86
Adj. C.B.O. Gordon Labor sharesa residuala quality 1.0** ⫺0.63** ⫺0.10** 0.09** 0.22** ⫺1.70** 1.38** 0.68 56.46 1.89
0 8.58** 1.38 ⫺2.45 9.84** 19.12** 11.33** 7.20** ⫺0.65 0.85
⫺0.79 0.92
⫺0.65 0.85
⫺0.67 0.88
1.0** ⫺0.58** ⫺0.11** 0.10** 0.24** ⫺1.73** 1.26** 0.67 54.45 1.96
1.0** ⫺0.69** ⫺0.10** 0.09** 0.22** ⫺1.63** 1.46** 0.66 53.29 1.98
⫺6.66* ⫺9.10** 2.64 0 ⫺0.39 0.67
⫺0.41 0.70
Inflation rates are quarterly log changes in price levels multiplied by 400 to yield annual percent changes. Significant levels are indicated by ** for 1%, * for 5%, and ⫹ for 10%. a The Adj. CBO Shares measure of NAIRU was increased by ⫹0.2 based on the constant from an unconstrained version of the GDP equation. This gives it a mean value of 6.17, compared to the unadjusted mean of 5.97. b Critical values for the F-test (1,121) are 6.85 for 1%, 3.92 for 5%, and 2.75 for 10% confidence levels. Shaded areas indicate equations that show improvement compared to the reference equation in the F-tests.
measures of NAIRU to explain inflation. The first is the chain-weighted GDP price index with results shown in Table 1, and the second is the chain-weighted price index for personal consumption expenditures (PCE) with results shown in Table 2. In the tables, lag periods are indicated for each explanatory variable, and notes at the bottom of the tables discuss slight changes to the Gordon specification with respect to trend productivity and lags on food and energy prices. As indicated at the top of each column, a total of six different NAIRU estimates were used to calculate unemployment gaps, in what is otherwise the same inflation equation. UR uses a fixed NAIRU of 6.18% based on the civilian unemployment rate, URMM uses a fixed NAIRU of 3.56% based on the unemployment rate for married males, and the other four columns use unemployment gaps calculated from measures of NAIRU discussed above and shown in Fig. 2. As discussed by Gordon (1997, p. 24), the constant is excluded from equations using an unemployment gap as the labor variable, because the constant term from unconstrained estimates of equations are used to calculate the various measures of NAIRU. Coefficients on lagged inflation are constrained to sum to one, because NAIRU is supposed to yield actual inflation equal to expected inflation in the absence of supply shocks. Results reported in Tables 1 and 2 indicate that this is a very powerful model for explaining inflation. Although not reported in the tables due to use of constrained estimation,
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Table 2 PCE inflation equations using alternate labor gap variables (1962q1–1996q4: labor variables identified at top of columns) Explanatory variables
Lags Fixed NAIRU
Time-varying measures of NAIRU
UR URMM C.B.O. (6.18%) (3.56%) shares Past PCE inflation (constrained ⫽ 1.0) Labor gap variable Deviation in productivity growth Relative inflation: imports Relative inflation: food & energy Nixon controls “on” Nixon controls “off” S.E.E. S.S.R. D.W. Comparison of equationsb F-stat compared to UR equation F-stat compared to Labor Quality Eq. Out-of-sample forecasts 1997q1–1998q4 mean error 1997q1–1998q4 root mean squared error
1–24 1.0** 1.0** 1.0** 0–4 ⫺0.47** ⫺0.60** 0.54** 0–1 ⫺0.04 ⫺0.02 ⫺0.03 1–4 0.06* 0.03 0.05* 0 0.81** 0.81** 0.81** 0 ⫺1.51** ⫺1.55** ⫺1.40** 0 0.81 1.15* 1.09* 0.74 0.75 0.73 66.51 67.81 64.30 1.44 1.48 1.46
Adj. C.B.O. sharesa
Gordon residuala
1.0** 1.0** ⫺0.58** ⫺0.51** ⫺0.03 ⫺0.03 0.06** 0.07** 0.78** 0.80** ⫺1.59** ⫺1.62** 0.88⫹ 0.80⫹ 0.72 0.72 62.77 62.79 1.49 1.49
Labor quality 1.0** ⫺0.65** ⫺0.03 0.07** 0.77** ⫺1.54** 0.95* 0.70 59.38 1.54
0 23.7 ⫺4.02* ⫺6.81* ⫺6.77* ⫺12.96** 14.52** 17.17** 10.02** 6.89** 6.94** 0.00 ⫺0.82 0.95
⫺0.96 1.06
⫺0.75 0.89
⫺0.86 0.99
⫺0.60 0.77
⫺0.62 0.79
Inflation rates are quarterly log changes in price levels multiplied by 400 to yield annual percent changes. Significant levels are indicated by ** for 1%, * for 5%, and ⫹ for 10%. a The Adj. CBO Shares measure of NAIRU was increased by ⫹0.2 based on the constant from an unconstrained version of the GDP equation. This gives it a mean value of 6.17, compared to the unadjusted mean of 5.97. b Critical values for the F-test (1,121) are 6.85 for 1%, 3.92 for 5%, and 2.75 for 10% confidence levels. Shaded areas indicate equations that show improvement compared to the reference equation in the F-tests.
90% or more of the variance in the inflation rate was explained by each equation. In Table 1 for GDP inflation, coefficients for every explanatory variable have the expected signs, and are significantly different from zero at the 1% confidence level. The standard-error-ofestimate ranges from a low of 66 basis points for the labor quality equation to 71 basis points for the married-male equation. In Table 2 for PCE inflation, all coefficients again have the correct signs, and those for past inflation, labor gap, food and energy inflation, and controls “on” are all significant at the 1% confidence level. Coefficients on import inflation are significant at the 1% level for the three time-varying NAIRU equations, and at the 5% level in all except the URMM equation. The controls “off” variable is significant at the 5% level in three equations, and at the 10% level in two additional equations. For PCE inflation, the standard-error-of-estimate ranges from a low of 70 basis points for the labor quality equation to a high of 75 basis points for the married-male equation. The key question in our analysis is, “How well do the different labor measures perform in explaining inflation?” Based on the sum squared residuals (S.S.R.) for GDP inflation (Table 1), the ranking from best to worst is Labor Quality, Gordon Residual, Adjusted CBO Shares, UR, CBO shares, and URMM. For PCE inflation (Table 2), the ranking is similar except that the CBO measure outperforms UR, and the Adjusted CBO. Shares slightly
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outperform the Gordon measure to take second place after the Labor Quality measure. In comparing best to worst specifications, reductions of 14 and 12% in S.S.R. statistics were achieved, respectively, for GDP inflation and PCE inflation. F-statistics were calculated to test significance levels for using alternate measures of NAIRU in the equations, and these are shown in the second panel, toward the bottom of each table. In Table 1 for example, the higher S.S.R. for the URMM than the UR equation produces an F-statistic of 8.58. This indicates that URMM results are worse at a 1% significance level than those for UR in explaining GDP inflation. For PCE inflation (Table 2), URMM results are worse than those for UR, but not at the 10% significance level. It was surprising to find that URMM performed worse than UR. The unemployment rate for married males is often viewed as being a more stable measure of labor market tightness than UR, and was therefore used as the basis for the CBO (1994) calculation of NAIRU. Related to this, it was surprising to find that C.B.O. Shares performed worse than UR for GDP inflation, although it did perform better than UR at the 5% level for PCE inflation. The three remaining time-varying measures of NAIRU showed improvements compared to the fixed NAIRU for UR. For the Adjusted CBO measure, improvement compared to UR was not significant at the 10% level for GDP inflation but was significant at the 5% level for PCE inflation. The Gordon measure of natural unemployment showed improvement compared to UR that was significant at the 5% level for both measures of inflation. Finally, the Labor Quality measure of NAIRU performed significantly better than UR at the 1% level for both measures of inflation. In the second row of F-tests, for GDP inflation, the Labor Quality measure performed better at the 1% level than all other measures except Gordon, and for PCE inflation, it performed better at the 1% level than all other measures of NAIRU. As indicated by Gordon (1998a, Fig. 1), his residual based approach to estimating NAIRU is sensitive to the inflation equation from which it is measured. This helps explain why his measure of NAIRU from the GDP inflation equation, which is used here, considerably outperforms the Adjusted C.B.O. measure in the GDP inflation equation, but not for the PCE inflation equation. As a second test of the various measures of NAIRU, we look at their performance in out-of-sample forecasts. Recent questions about NAIRU were prompted by declining inflation rates despite exceptionally low unemployment rates. Thus, many Phillips curve models of inflation have significantly overpredicted inflation in recent years. Gordon (1998a) finds that much of the improved trade-off is due to favorable supply shocks captured by his equations, with the remaining overprediction due to changes in price measurement methods, omitted supply shocks, and declines in NAIRU. The equations from Tables 1 and 2, which were estimated for the period ending in the fourth quarter of 1996, were used to generate ex-post forecasts for the eight quarters in 1997 and 1998. Results from these forecasts are shown in the bottom panel of each table. For both inflation measures, each of the six equations produces overpredictions of inflation. The mean error for GDP inflation ranges from an overprediction of 39 basis points for Gordon’s NAIRU to 79 basis points for the married-male unemployment rate, whereas that for PCE inflation ranges from an overprediction of 60 basis points to 96 basis points for the same two unemployment measures. Rankings of the unemployment measures based on root-mean-squared-errors follow the same pattern as those for the mean errors. Performance for the married-male rate and for the
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Adjusted CBO NAIRU is considerably worse and slightly worse, respectively, than the general unemployment rate. The unadjusted CBO measure has the same out-of-sample error measures as UR for GDP inflation, and slightly lower error measures for PCE inflation. The Gordon and Labor Quality measures of NAIRU both perform considerably better than the general unemployment rate. Thus, recent large declines in the Labor Quality and Gordon measures of NAIRU provide significant improvement in our ability to explain the low inflation in recent years. The Gordon measure slightly outperforms the Labor Quality measure, but this is due in part to the fact that Gordon’s NAIRU was originally estimated from a sample period that ended in the second quarter of 1998, and thus included six of the eight quarters in our “out-of-sample” forecast.
4. Conclusion This paper has demonstrated that the concept of NAIRU remains a very useful tool for measuring labor market tightness and inflationary pressure. Empirical results provide strong support for use of a time-varying NAIRU rather than a fixed NAIRU, but indicate that accurately measuring NAIRU is a challenge. Gordon’s time-varying-parameters measure of NAIRU provides a useful benchmark for evaluating measures of NAIRU derived from labor market characteristics. The weakness of Gordon’s approach is that it is entirely backward looking, and is not useful in predicting future values of NAIRU or in explaining why NAIRU has changed (see Gordon, 1997, p. 30). This paper offered a new approach to estimating a time-varying NAIRU that focuses on labor quality in the form of average years of work experience and average years of education of the labor force. These new estimates appear to be a promising alternative to NAIRU estimates that are currently available. In the three criteria suggested for evaluating alternate measures of NAIRU, the new Labor Quality NAIRU performed well. First, like the CBO measure but unlike the Gordon measure, the new measure provides a labor-based explanation for changes in NAIRU. Second, the Labor Quality NAIRU significantly outperforms the CBO NAIRU in explaining inflation for GDP and PCE at the 1% confidence level. Third, although the Labor Quality NAIRU does not significantly outperform the Gordon measure for GDP inflation, the Labor Quality measure significantly outperforms the Gordon measure in explaining PCE inflation at the 1% confidence measure. Finally, the Gordon and Labor Quality NAIRU measures produce sizable reductions in out-of-sample forecast errors compared to the other four measures of labor market tightness. Reliable estimates of NAIRU are desirable for use as a macroeconomic policy target, and because the CBO relies heavily on estimates of NAIRU in producing annual reports to Congress on budgetary and economic projections.6 Results from this paper suggest that estimates of NAIRU can be improved significantly by using the labor-quality approach offered here. This new approach provides a much different view of past movements in NAIRU than the CBO and Gordon approaches. In contrast to the gradual rise and fall in the CBO NAIRU, the Labor Quality NAIRU showed a much more pronounced rise in the early 1970s, a relatively stable NAIRU in the 1980s, and a much more dramatic decline in the past decade. From 1988 to 1998, the labor quality NAIRU declined 97 basis points to 5.39%,
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compared to a decline of only 29 basis points to 5.71% for the CBO NAIRU. In the next 5 to 10 years, further improvements in labor quality could lower NAIRU to 5% or below compared to a fairly steady estimate of between 5.7 and 5.6% for the CBO NAIRU. Results from this paper need to be tested further, but they offer a promising start to providing more accurate measures of NAIRU, a better explanation of past inflation, and a better guide for policy making in the future.
Notes 1. The 28 demographic groups are white and nonwhite, and male and female, for seven different age categories: 16 –19, 20 –24, 25–34, 35– 44,45–54, 55– 64, and 65 and over. 2. The remainder of this paper uses Gordon’s (1998a) NAIRU for the chain-weighted GDP deflator with the smoothness constraint of standard deviation ⫽ 0.09. We thank Gordon for supplying these data to us. 3. These data were developed to help identify sources of US productivity growth, and are described in US Department of Labor (1993, pp. 9 –12, and 56 – 67). The Department of Labor uses source data from the Current Population Survey, Social Security Administration, Internal Revenue Service, and population censuses to estimate the composition of the labor force by different levels of education and work experience. Annual data for average years of experience and education are calculated using weights based on estimated total hours worked for each group. Updated measures of these data were provided by Larry Rosenblum of the Bureau of Labor Statistics. The annual data were converted to quarterly data by taking a five-quarter, centered-moving-average of quarterly data set equal to the annual data for each year. 4. A referee for this article suggested inclusion of the female share of the labor force, as an additional demographic adjustment. The female share of the labor force shows a strong upward trend as does average years of education, with a 0.99 correlation coefficient between these two variables. The correlation coefficient between each of these variables and the average years of experience is ⫺0.87. When the female share was included in the inflation equation, together with years of education and years of experience, it had an insignificant positive impact, there was a slight reduction in the experience coefficient, and the education coefficient doubled in size but became insignificant due to the extreme colinearity between this variable and the female share variable. The net impact of these variables on the Labor Quality NAIRU continued to be virtually the same as that shown in Figs. 1 and 2, however. 5. Several modifications have been made to Gordon’s specification. First, the deviation of productivity growth from trend uses the average growth over the past thirty-two quarters as trend growth, while Gordon sets trend growth equal to the average growth between cyclical peaks. This alternate specification of trend productivity growth was suggested by Robert Arnold of the Congressional Budget Office. Second, Gordon includes lags of 0 – 4 on the relative inflation for food and energy, but we have dropped
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insignificant lagged values. Finally, the sample period has been shortened by six quarters to provide eight quarters for use in out-of-sample forecasts. 6. The Congressional Budget Office typically makes its 10-year budget projections based on the unemployment rate moving to a level slightly above NAIRU and remaining at that level for an extended period. See for example, Congressional Budget Office (1999, Fig. 1–1).
Acknowledgments The author thanks Robert Arnold of the Congressional Budget Office, Robert Gordon of Northwestern University, and Larry Rosenblum of the Bureau of Labor Statistics for providing data used in this paper. In addition, Robert Arnold and two anonymous referees provided valuable comments on this paper.
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