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Missing Wage Inflation? Downward Wage Rigidity and the Natural Rate of Unemployment

Yuto Iwasaki, Ichiro Muto (Bank of Japan) , Mototsugu Shintani (University of Tokyo)

Research LAB No. 18-E-3, September 25, 2018

Keywords : wage; natural rate of unemployment; downward wage rigidity; Phillips curve; nonlinear DSGE model

JEL Classification : E24, E31, E32

Contact:yuuto.iwasaki@boj.or.jp (Yuto Iwasaki)

Summary

In recent years, advanced economies, including Japan, have experienced a weak response of wage inflation to the decline in the unemployment rate (i.e. missing wage inflation). In this study, we investigate whether downward wage rigidity (DWR) in recession periods can be a source of this weak wage response. Specifically, we jointly estimate the degree of DWR as well as the natural rate of unemployment using a nonlinear DSGE model with asymmetric adjustment costs. We show that wage adjustment costs are highly asymmetric in Japan, the euro area, and the UK; especially, a clear L-shaped wage Phillips curve between wage inflation and the unemployment gap (i.e. the actual unemployment rate minus the natural rate) is obtained in Japan. We argue that missing wage inflation is attributable to DWR and wage inflation is likely to reappear under the tight labor market conditions.

1. Missing wage inflation and downward wage rigidity

During the recovery from the Global Financial Crisis (GFC hereafter), advanced economies, including Japan, have experienced a weak response of wage inflation to the decline in the unemployment rate (i.e. missing wage inflation), as shown in Figure 1. Central bankers have expressed concerns over this weak wage response since it has created a weak inflationary environment in which the inflation rate has persistently remained below the central bank target1. However, there are still few analyses that attempt to identify the possible causes in detail.

Figure 1. Wage inflation and unemployment rate

Accordingly, in this study, we outline the analysis in Iwasaki, Muto, and Shintani (2018) [PDF 2,675KB], which attempted to reveal the mechanism behind missing wage inflation. In that paper, we investigated whether downward wage rigidity (DWR hereafter) can be a cause of missing wage inflation. We learn from textbook macroeconomics that the slope of the wage Phillips curve, which indicates the relationship between wage inflation and the unemployment gap (i.e. the deviation of the actual rate from the natural rate), becomes quite flat at low rates of wage inflation in the presence of DWR, as illustrated in Figure 2. This implies that wage inflation is irresponsive not only to negative shocks but also to positive shocks to labor market conditions under a low wage inflation environment.

Figure 2. Downward wage rigidity and the wage Phillips curve

Intuitively, irresponsiveness of wage inflation to positive shocks to labor market conditions, just mentioned above, can be interpreted as follows. Suppose that the economic situation has recovered after a prolonged recession in which wage increases were impossible and a firm has made sufficient profit to raise wages. In this situation, however, if the firm expects that it will be highly difficult to cut wages in a future recession due to e.g. the resistance of workers, it may hesitate to raise current wages. This causes a situation where wage inflation is weak in spite of an economic recovery and the tightened labor market conditions.2

In order to take DWR into account, an asymmetric wage adjustment cost function is introduced into the DSGE model.3 Wage adjustment costs represent how difficult it is to change wages. Most of the previous literature employs a quadratic adjustment cost function, which is shown in Figure 3, based on the assumption that the cost of increasing and cutting wages is the same as long as the revision rate is the same. Contrastingly, our model allows the possibility that cutting wages is more difficult than increasing wages, thus enabling us to estimate the shape of the asymmetric wage adjustment cost functions.

Figure 3. Asymmetric adjustment cost function (conceptual scheme)

  1. See, for example, Yellen (2014), Constâncio (2017), Haldane (2017), Cunliffe (2017). FRB Chairman Powell also pointed out that, in spite of the decline in the unemployment rate, inflation has continued to run below their 2 percent target possibly because the relationship between the unemployment rate and inflation, known as the Phillips curve, has weakened in recent years (Powell (2018).)
  2. Elsby (2009) was the first to explain why DWR in a past recession can lead to upward wage rigidity in the present. Krugman (2018) also stresses the importance of this mechanism in understanding the wage inflation dynamics after the GFC.
  3. Our model follows the models developed by Kim and Ruge-Murcia (2009, 2011) and Aruoba, Bocola, and Schorfheide (2017).

2. Estimation results of DWR and natural rate of unemployment

In our estimation, we use data for Japan, the euro area, the UK, and the U.S. spanning from 1970Q2 to 2017Q3. We estimate our nonlinear DSGE model using a particle filter with MCMC.

Figure 4 summarizes the estimation results for the wage adjustment cost functions for the four major economies. Due to the presence of DWR, wage adjustment costs are highly asymmetric in Japan, the euro area, and the UK. In contrast, the wage adjustment cost in the U.S. is almost symmetric and large both in an upward and downward direction.

Figure 4. Estimated wage adjustment cost function

Next, we estimate the natural rate of unemployment using these wage adjustment cost functions. Following the definition in the New Keynesian model, we define the natural rate of unemployment as the rate that would be realized if wages are flexible, i.e. the cost of wage adjustment is zero. As this cannot be observed directly, we conduct counterfactual simulation using an estimated DSGE model with wage adjustment cost to obtain the path of unemployment in a zero wage adjustment costs economy.

Figure 5 shows the results for Japan. Compared to the actual unemployment rates, which increased substantially during the recession from the late 1990s to the first half of 2000s as well as during the period following the GFC in 2008, the increases in the estimated natural rate of unemployment are relatively mild. As a result, the obtained unemployment gap took persistently large positive values during these periods. The reason for the occurrence of slack in these two periods is that, due to the presence of DWR, the declines in wage inflation in response to a large negative shock were smaller than they would have been under flexible wage adjustment costs, which then led to an excess supply of labor, i.e. increases in the unemployment gap. However, the unemployment gap has shrunk and turned negative in recent years, implying that tightness in Japan's labor market has increased.

Figure 5. Natural rate of unemployment and unemployment gap (Japan)

3. Wage Phillips curve and "Missing Wage Inflation"

Figure 6 shows the wage Phillips curve by plotting wage inflation and the unemployment gap. The figure clearly shows that the wage Phillips curve in Japan is L-shaped: it bends around the point where the unemployment gap is almost zero. The slope is almost linear where the unemployment rate is negative, but almost flat where the unemployment gap is positive. Therefore, the wage Phillips curve is nonlinear and the slope is dependent on the level of the unemployment gap.

Figure 6. Estimated wage Phillips curve (Japan)

It is generally expected that tightened labor market conditions lead to an increase in wage inflation, but such expectations are based on a linear wage Phillips curve. Our results, however, indicate that, in the presence of DWR, the wage Phillips curve becomes flat at low level of wage inflation and wage inflation is not responsive to the degree of labor market slack as long as the unemployment gap is positive.

Additionally, we investigate whether missing wage inflation can be explained by these mechanisms. In Figure 7, we present recent developments in wage inflation and the unemployment gap.

Figure 7. Wage Phillips curve and the developments after the GFC

In the case of Japan, since 2009Q3, when the unemployment rate peaked, the unemployment gap has declined substantially throughout the recovery phases following the GFC, but wage inflation has remained almost unchanged. This is because the combinations of wage inflation and the unemployment gap during this period move along the flat part of the wage Phillips curve, i.e. the base of the L-shape, due to the presence of strong DWR. That is, in this period, forward-looking firms might have tempered wage increases based on the expectations that reducing wages in a future recession would be highly difficult.

The data for 2017Q3, which is the end of the sample period, shows that the combination of the wage inflation and the unemployment gap is located around the kink point of the wage Phillips curve. This suggests that wage inflation is likely to reappear in the not too distant future.

In the euro area, the situation is almost the same as in Japan: the obtained wage Phillips curve is nonlinear and, since the European Debt Crisis, wage inflation and the unemployment gap have moved along the flat part of the wage Phillips curve. Therefore, wage inflation is almost unchanged despite the decline in the unemployment gap. This indicates that, as in Japan, DWR had a sizable effect on wage inflation. In the UK, although it is not as clear as in Japan and the euro area, a nonlinear wage Phillips curve is obtained, and wage inflation and the unemployment gap can be regarded as evolving roughly in line with the flat part of the wage Phillips curve.

Finally, the situation is quite different in the U.S. In other words, there is no clear relationship between wage inflation and the unemployment gap. Since the GFC, the unemployment gap has declined almost monotonically but the wage inflation rate has fluctuated substantially. As a result, it is difficult to find a clear relationship between wage inflation and the unemployment rate. One possible explanation for this is that the wage Phillips curve in the U.S. may have been under the situation where exogenous labor supply shocks frequently shifted the curve.4

  1. 4Iwasaki, Muto, and Shintani (2018) points out that the labor supply shock variance in the U.S. is much larger than in other countries and that there actually exists a linear wage Phillips curve in the U.S. once the distortionary impact of labor supply shocks is eliminated. However, our results imply that the degree of DWR has increased somewhat in the post-crisis period. For details, please refer to Iwasaki, Muto, and Shintani (2018).

4. Conclusion

This article presents results based on Iwasaki, Muto, and Shintani (2018), which investigated whether DWR can explain missing wage inflation.

Our results indicate the possibility that missing wage inflation is caused by the flattening of the wage Phillips curve due to DWR in Japan, the euro area, and the UK. Especially in the case of Japan, an L-shaped wage Phillips curve between wage inflation and the unemployment gap is clearly observed and, since the GFC, the combinations of wage inflation and the unemployment gap have moved along the flat part of the curve. However, the level of the unemployment gap is getting close to the kink point, implying that the tightened labor market conditions might lead to a rise in wage inflation.

However, it should be noted that our model omits other possible mechanisms that can affect the estimates of the natural rate of unemployment and DWR. For example, this analysis does not take account of factors such as the adaptive inflation expectations formation and time variation in trend inflation. Accordingly, when they are taken into consideration, the degree of DWR might be estimated differently. In addition, the degree of DWR might be different across different types of workers, e.g. regular/non-regular workers. Especially, it is observed that, in advanced countries including Japan, the rise in the ratio of non-regular workers has been depressing the increase in aggregate wage inflation in recent years. This implies that, if the composition effects are adjusted, wage inflation would have been higher than the unadjusted rate. Based on this inference, once the types of workers are controlled, the degree of DWR might be higher than reported in our paper.

Reference

  • Aruoba, S. Boragan, Luigi Bocola and Frank Schorfheide (2017), "Assessing DSGE model nonlinearities," Journal of Economic Dynamics and Control, 83(1), pp. 34-54.
  • Iwasaki, Yuto, Ichiro Muto, and Mototsugu Shintani (2018), "Missing Wage Inflation? Estimating the Natural Rate of Unemployment in a Nonlinear DSGE Model, [PDF 2,675KB]" IMES Discussion Paper, No.2018-E-8.
  • Constâncio, Vitor (2017), "Understanding and overcoming low inflation, (Link to an external website)" remarks at the conference on "Understanding inflation: lessons from the past, lessons for the future?" Frankfurt am Main, September 21 and 22.
  • Cunliffe, Jon (2017), "The Phillips curve: lower, flatter or in hiding? [PDF 368KB] (Link to an external website)" speech at Oxford Economics Society, November 14.
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  • Kim, Jinill and Francisco J. Ruge-Murcia (2011), "Monetary policy when wages are downwardly rigid: Friedman meets Tobin," Journal of Economic Dynamics and Control, 35(12), pp. 2064-2077.
  • Krugman, Paul (2018), "Is the Great Recession still holding down wages? (Link to an external website)" New York Times, May 4.
  • Powell, Jerome (2018), "The outlook for the U.S. economy, (Link to an external website)" remarks at the Economic Club of Chicago, Chicago, Illinois, April 6.
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