Vania Esady, Bradley Speigner and Boromeus Wanengkirtyo

The general unemployment rate is one of the most widely used economic slack indicators to measure the state of the business cycle. A large empirical literature on phillips curve The estimate has explored whether more general definitions of labor utilization are more informative than this simple measure. in a new paper, we investigate whether the unemployment duration distribution contains useful information for modeling the dynamics of inflation. More specifically, short and long term unemployment (for long term unemployment we mean people who are unemployed for 27 weeks or more) play separate roles in the Phillips curve?

The literature on the estimation of the Phillips curve tends to suggest that long-term unemployment (LTU) is less relevant to inflation than short-term unemployment (STU). One possible explanation is that labor market attachment decreases with the duration of unemployment, and therefore a higher share of long-term unemployment may weaken wage competition. Next, we explore the different roles of short- and long-run unemployment in shaping inflation behavior, highlighting in particular the interaction between unemployment duration and nonlinearity in the Phillips curve.

Simulating a simple Phillips curve

To help illustrate the mechanism, we consider a simple Phillips curve model with two key ingredients: (i) the LTU share increases in deep recessions and (ii) a slope that is convex with respect to aggregate unemployment. Therefore, by assumption, the effects of a change in STU or LTU on inflation are bound to be the same at a given level of aggregate unemployment.

Figure 1 shows the results of simulating this Phillips curve configuration using US data. By design, a convex Phillips curve slope is generated when plotting inflation against aggregate unemployment (left-hand side). However, the interaction of nonlinearity with the state dependence of LTU participation results in an interesting implication: the degree of convexity is exacerbated for LTU (right-hand side) and attenuated for STU (middle).

Our framework offers a simple explanation. At the start of a recession, STU is the first to go up and this causes the slope of the Phillips curve to fall. Therefore, by the time LTU begins to rise, the economy will have already transitioned to a flatter region of the Phillips curve. Thus, the effect of LTU on inflation is likely to be smaller simply because it rises after STU, leading to the misperception that LTU does not affect inflation much in recessions. Conversely, however, declines in LTU are likely to occur when the economy is in a steep region of the Phillips curve, creating marked inflationary pressure.

Graph 1: Simulated Phillips curve

Source: Authors’ calculation.

Further econometric research

Our next step is to perform a more rigorous statistical analysis. To do so, we adopt an empirical strategy that combines two popular methodologies from the recent literature, allowing us to jointly estimate the curvature of the Phillips curve, as well as identify separate slopes for STU and LTU rates. First, we apply a flexible estimation method based on local projections which can be easily adapted to handle rich unemployment dynamics in the presence of state agencies on the Phillips curve. Second, we take advantage of cross-sectional information to further aid the identification of the Phillips curve, making use of state-level data rather than aggregate data, as in McLeay and Tenreyro (2019). We constructed US statewide unemployment rates by duration between 1994 and 2017 using the Current Population Survey and merged them with statewide inflation rates constructed by Hazell et al (2022) based on US CPI microdata

We found? The empirical results in Graph 2 reflect the simulation exercise described above, showing that the slopes of the Phillips curve with respect to STU (Graph 2a) and LTU (Graph 2b) diverge more significantly during expansions (blue line) when the The labor market is tight, with LTU showing a larger and more immediate maximum effect on inflation than STU. We do not find a large significant difference between LTU and STU during periods of high unemployment (red line) when the effect of both unemployment measures on inflation is estimated to be relatively weak. The maximum inflationary impact of LTU in the low unemployment regime is around four times higher than when unemployment is high, whereas it is only twice for STU.

Graph 2: Response of aggregate inflation to unemployment

Source: Authors’ calculation.

Further discussion and policy implications

What are the possible macroeconomic channels that could explain our findings? We offer two tentative ideas.

Firstly, to the extent that the CMUs are relatively more disconnected from the labor market (Krueger et al (2014)), the search and comparison process is likely to be more difficult and less efficient than for STUs as a whole, making recruitment more expensive for companies. If such recruitment difficulties are resolved with higher salary offers from companies, this would increase inflationary pressure. However, there are several measurement problems with the data that may mean that the LTU job search rates are not very different from those of the STU (Abraham (2014)page 281).

There is also a different demand-side channel that could provide a basis for why the LTU is an important barometer of inflationary pressure. Being unemployed is often a negative impact on income and household consumption responds accordingly. The literature shows that consumption responds more strongly the more persistent the shock (Jappelli and Pistaferri (2010)). The longer individuals remain unemployed, the more persistent they are likely to perceive the income shock, implying that a reduction in LTU may be associated with a relatively large adjustment in aggregate demand.

Regardless of the underlying explanation, from a purely statistical perspective, our results show that dividing aggregate unemployment into different duration categories in Phillips curve models can help practitioners better explain inflation dynamics. The question we have discussed is important in the context of the large fluctuations in the long-term share of total unemployment that have occurred during the downturns that followed the 2008 recession and the most recent pandemic. Policymakers and econometricians can benefit from including long-term unemployment as part of the inflation-relevant measure of economic capacity, particularly when labor markets are tight.

vania esada works in the Bank’s Current Economic Conditions Division and Bradley Speigner and Boromeus Wanengkirtyo work in the Bank’s Structural Economics Division.

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