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November 19, 2012

Compensation Growth and Slack in the Current Economic Environment

M. Henry Linder, Richard Peach, and Robert Rich

Following a significant slowing during the recent recession, growth in various labor compensation measures has stabilized during the past two to three years. This stabilization is puzzling because it’s widely held that a significant amount of slack remains in the economy. Accordingly, this large amount of slack should result in a further slowing in compensation (wage) growth. In this post, we show that there’s a very mild trade-off between compensation growth and resource slack, even though slack is sizable. Consequently, the observation that there’s slow but steady growth in labor compensation measures is consistent with a large amount of slack in the current economic environment.

    Our analysis is based on the estimation of a nonlinear wage-inflation Phillips curve that draws upon the modeling approach outlined in a Boston Fed paper by Fuhrer, Olivei, and Tootell. The key feature of the nonlinear Phillips curve is that the impact of a change in slack depends on the level of slack. These features are illustrated in the chart below, where the slope of the Phillips curve becomes steeper as the unemployment rate moves further below the natural rate of unemployment (higher resource utilization), while the slope becomes flatter as the unemployment rate moves further above it (lower resource utilization).


    Why might the Phillips curve flatten out as the unemployment rate rises further above the natural rate of unemployment? As a reminder, what matters for labor market decisions is the real wage rate—the nominal wage adjusted for the price level (or cost of living). One explanation for the flattening of the Phillips curve is downward real wage rigidity—that is, a more sluggish response of real wages when the unemployment rate is high (see the Boston Fed paper by Holden and Wulfsberg for a more detailed discussion of theories of real wage resistance during an economic downturn). In a situation of high unemployment, wage growth becomes relatively stable around the recent level of underlying inflation, so that real wages don’t fall sufficiently to clear the labor market.

    Our Phillips curve model relates four-quarter growth in nominal compensation per hour (for the nonfarm business sector) to economic slack, controlling for movements in trend productivity growth and expected inflation. Our measure of slack is the Congressional Budget Office (CBO) estimate of the unemployment gap—the percentage point deviation between the actual unemployment rate and the CBO estimate of the natural rate of unemployment. For trend productivity growth, we use an average of the (annualized) quarterly growth rate of productivity. For expected inflation, we construct a ten-year personal consumption expenditure (PCE) survey measure by adjusting the Survey of Professional Forecasters’ ten-year expected CPI inflation series to account for the average differential between CPI and PCE inflation. As the chart below shows, expected inflation has been extremely stable during the post-1997 period. To provide additional observations for estimation and to conduct the analysis in a low-inflation environment with well-anchored expectations, we use data that cover the period from 1997 through the present.


    Our model relates economic slack to an adjusted compensation measure, where we subtract the values of trend productivity growth and expected inflation from the compensation growth series. This adjustment imposes the standard restriction that increases in the real wage rate equal increases in labor productivity in the long run. The chart below provides a scatter plot of the adjusted compensation growth series and the unemployment gap. Negative (positive) values of the unemployment gap represent conditions in which unemployment is below (above) the natural rate of unemployment.


    An examination of the scatter plot shows that the general shape of the data points bears a close resemblance to the chart of the nonlinear Phillips curve, and estimation of the model provides evidence of a statistically significant nonlinear relationship between (adjusted) compensation growth and slack. To better illustrate the nature of the estimated nonlinearity, we consider a comparison based on the same percentage point change in the unemployment gap. If the gap were to move from -1 percentage point to -3 percentage points, then the four-quarter growth rate of compensation would increase by 2.2 percentage points. If the unemployment gap were to move from 3 percentage points (the current CBO estimate) to 1 percentage point, then the rate would increase only by 1 percentage point.

    We also consider two additional criteria to evaluate the nonlinear Phillips curve model—within-sample fit and out-of-sample forecast performance. The within-sample fit is based on estimation of the model using data from the full sample to compare the predicted and actual values of growth in compensation per hour. The out-of-sample forecast performance is based on estimation of the model only using data through 2007:Q4 on the unemployment gap, trend productivity growth, and expected inflation. With the resulting estimated model, we input the actual values of the unemployment gap, trend productivity growth, and expected inflation during the post-2007:Q4 period to generate forecasts of compensation growth. The first forecast corresponds to compensation growth from 2008:Q1 to 2009:Q1.

    The next chart plots the four-quarter change in compensation growth, the within-sample predictions, and the post-2007:Q4 out-of-sample forecasts. While the within-sample predictions fail to track some short-run movements in compensation growth, they do capture the general movements in the series. Moreover, both the within-sample predictions and out-of-sample forecasts capture the magnitude of the decline in compensation growth since 2008 as well as its subsequent stability.


    Our analysis suggests that a nonlinear wage-inflation Phillips curve fits the data well during the post-1997 episode and complements the results of Fuhrer, Olivei, and Tootell, who find evidence of a nonlinear relationship between price inflation and activity gap measures. An important conclusion from our analysis is that recent stability in the growth rate of labor compensation measures may not be informative about the extent of slack or its change. That is, stability in labor compensation measures doesn’t imply that the output gap has closed, while changes in the output gap may only have a modest impact on compensation growth.

    In an inflation environment where actual and expected price changes are low, someone might interpret the earlier scatter plot as reflective of downward nominal wage rigidity—the idea that workers and firms have incentives to avoid reductions in nominal wages. However, the nonlinearity between wage growth and slack appears to be evident in other episodes in which large fluctuations in real activity were accompanied by high inflation and high compensation growth (this point is also discussed by Fuhrer, Olivei, and Tootell). Thus, the mild trade-off between compensation/wage growth and resource slack when slack is sizable isn’t unique to recent experience. Moreover, the source of the nonlinearity must stem from downward real wage rigidity, as downward nominal wage rigidity can generate this feature only in a low-inflation environment.

    We recognize that our analysis comes with important caveats, which include the use of a model based on a simple, parsimonious specification as well as the study of a single, short sample period. Nevertheless, if the nonlinear relationship between slack and wage/price inflation is an important feature of the data, then it will be critical for policymakers to identify other indicators that may be more responsive to slack and provide a quick and more reliable read on its movements.

The views expressed in this post are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System. Any errors or omissions are the responsibility of the authors.

M. Henry Linder is a research associate in the Research and Statistics Group of the Federal Reserve Bank of New York.

Richard Peach is a senior vice president in the Research and Statistics Group of the Federal Reserve Bank of New York.

Robert Rich
is an assistant vice president in the Research and Statistics Group of the Federal Reserve Bank of New York.
Posted by Blog Author at 07:00:00 AM in Forecasting, Macroecon, Unemployment, Wages

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