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Beyond Okun’s law: output growth and labor market flows

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Abstract

This paper studies the relationship between the change in the unemployment rate and output growth using an approach based on labor market flows. The framework shows why the Okun coefficient may be constant/time varying and/or symmetric/asymmetric and that the outcome depends upon the behavior of the labor flows in response to growth. The encompassing framework nests the conditions to determine the properties of the Okun coefficient without the need to rely on retrospective arbitrary dating of recessions. The framework also highlights the potential misspecification in conventional models of Okun’s Law unless stringent conditions are assumed about the behavior of labor flows. The empirical analysis is based on the stock-consistent labor market flows data developed by the Bureau of Labor Statistics for the period 1990:2–2017:3.

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Notes

  1. Knotek (2007) in his survey of the Okun relationship for the USA concluded that the Okun relationship has changed over time and is different during expansions and contractions, while Owyang and Sekhposyan (2012) show that during recent US recessions—including the Great Recession—unemployment appears to be more sensitive to economic growth than before. Cazes et al. (2013) also find that the Okun coefficient varies over time for the USA (and other countries). Bayesian methods were applied by Huang and Lin (2008) (to a model with time-varying parameters that can take any functional form) and by Grant (2017) (to a gap model which allows for stochastic volatility in the output gap), and both provide further evidence of time variation in the Okun coefficient.

  2. Pereira (2013) concludes on the basis of an analysis of US data that there are asymmetries in the Okun relationship with a weaker relationship during periods of expansion. Valadkhani and Smyth (2015) analyzing US data also find asymmetries and a weakening of the Okun relationship since the early 1980s. Furthermore, Belaire-Franch and Peiró (2015) examine US (and the UK) data and conclude that there is an asymmetry in the relationship between unemployment and the business cycle.

  3. This subsection draws in part upon some ideas presented in section II of Dixon et al. (2015).

  4. These equations also show that \(\Delta p_{t}=0,\) when \(nu_{t}=en_{t}.\) In this case, \(\Delta u_{t}\) collapses to \(eu_{t}+en_{t}\) and \(\Delta u_{t}=0\) when \(en_{t}=-eu_{t}.\) Thus, we note in passing that for labor market equilibrium (\(\Delta p_{t}=\Delta u_{t}=0)\), we require the absolute value of the three net flows to be equal: \(nu_{t}=-eu_{t}=en_{t}.\)

  5. Ball et al. (2017) only allows for two lags: \(\Delta y_{t-1}\) and \(\Delta y_{t-2}.\) Using aggregate data on the change in the unemployment rate (\(\Delta u\)) and output growth (\(\Delta y\))  we find, following the lag specification in Ball et al. (2017), an impact Okun effect of − 0.153 and a long-run effect of 0.455 (similar to results reported in that paper). When an aggregate model was estimated allowing for more general lag effects, we find that the fit is greatly improved (adjusted \(R^{2}\) increased from 0.507 to 0.605), but the Okun coefficient remains similar being − 0.167 on impact and − 0.411 in the long run.

  6. We note that we could have specified the system as a VARX and use lagged net flows. We have estimated this option, but the system with the lagged unemployment rate is parsimonious (less extraneous terms) and the fit was better and less volatile.

  7. In general, the approach discussed here can be generalized as a VAR. Writing \(\Delta u_{t}=G_{t-1}X_{t}\) where \(G_{t-1}\) is a (1x3) vector \([1,(1-u_{t-1}),u_{t-1}]\) and \(X_{t}\) is a (3x1) vector of flows \([eu_{t},nu_{t},en_{t}]^{^{\prime }}\) then a VAR net flows model like \(X_{t}=A+B\Delta y_{t}+DX_{t-1}+\epsilon _{t},\) where A, B, D are coefficient matrices, and \(\epsilon \) is a vector of errors, will yield time-varying Okun coefficients \(\beta _{t}=G_{t-1}B.\)

  8. The specification adopted here follows Zakoïan (1994) and Glosten et al. (1993) modeling of the asymmetric response of stock prices to good/bad news.

  9. Real GDP data is US Bureau of Economic Analysis, Real Gross Domestic Product, retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/GDPC1 , November 6, 2017. The series is in Billions of Chained 2009 Dollars, Seasonally Adjusted Annual Rate. The growth rate is measured as the change in real GDP (quarter on previous quarter) expressed as a percentage.

  10. Further information on the BLS’s stock-consistent data set may be found in Frazis et al. (2005). The (seasonally adjusted) CPS flows data are publicly available on the Internet at http://www.bls.gov/cps/cps_flows.htm. For examples of published work using this data set, see Barnichon and Nekarda (2012), Boon et al. (2008), Demiralp et al. (2011), Dixon et al. (2011) and Gyourko and Tracy (2014).

  11. The BLS notes that, in January 2000, the large flow from ‘marginal’ to employment, to account for population changes, is affected by ‘changes associated with population controls.’ We checked the influence of this one outlier (in a sample of 330 quarterly observations) and found that it had no significant effect on the analysis.

  12. In our empirical analysis, we have not taken into account the age composition of the labor force because BLS stock-consistent flows data are not available disaggregated by age. Previous studies, e.g., Zanin (2014) and Dixon et al. (2017), have estimated more traditional Okun relationships, finding that for younger workers the change in unemployment is more sensitive to economic growth than it is for prime age and older workers. This suggests that the net flows in the labor market, particularly in the net flows from employment to unemployment for younger workers, will likely be more volatile. For an example of a paper at a regional level, see Zanin and Calabrese (2017) for a study exploring the link between labor market transitions and regional level GDP.

  13. See Zanin and Marra (2012) for criticism of rolling regressions in this context.

  14. Michail 2019 argues that it is important to examine whether time variation is present in the mean or in the variance equation. We have estimated our model assuming no time variation in the mean, but allowing for the presence of GARCH errors. Our estimated results, based on Bollerslev–Wooldridge robust quasi-maximum likelihood standard errors, clearly rejected time-varying volatility in net flows.

  15. The extensive literature on Okun’s law suggests that the relevant explanation(s) for asymmetry in the Okun coefficient must be to do with differences in the way average hours, labor productivity, labor force participation and the process by which workers are matched to jobs respond to positive or negative shocks to GDP. In his 1962 paper, Okun himself focused attention on the first three items, while more recent literature has also examined asymmetries resulting from differences in job hiring and search practices, including scarring effects of unemployment.

  16. Note that these results based on stock-consistent flows are not dissimilar to the results in the Ball et al. (2017) study which showed that the Okun coefficient was asymmetric with estimated values of − 0.535 in recessions and − 0.248 in other periods (p. 1422, Table 3 last column). Our study takes these results further by identifying the net flows that matter.

  17. See also Krueger (2017) and Elsby et al. (2015) on the drop in the US participation rate.

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Authors and Affiliations

  1. Melbourne Institute of Applied Economic and Social Research, University of Melbourne, Melbourne, Australia

    G. C. Lim

  2. Department of Economics, University of Melbourne, Melbourne, Australia

    Robert Dixon

  3. Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute, Rotterdam, The Netherlands

    Jan C. van Ours

  4. Department of Economics, University of Melbourne, Melbourne, Australia

    Jan C. van Ours

  5. CEPR, London, UK

    Jan C. van Ours

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  1. G. C. Lim
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Appendix: allowing for population changes

Appendix: allowing for population changes

In our theory Sect. 2.1, we ignore population growth, i.e., we assume that the population at the beginning of the month is the same as the population at the end of the month: \(P_{t-1}=P_{t}\). This simplifies the math but is not stock consistent as in reality population is not a constant. Let \(g_{t}\) be the rate of growth in the population.

$$\begin{aligned} P_{t}&=(1+g_{t})P_{t-1}\\ g_{t}&=\frac{P_{t}-P_{t-1}}{P_{t-1}} \end{aligned}$$

Then, the stock-consistent definition of the change in the participation rate is

$$\begin{aligned} \Delta p_{t}&=\frac{L_{t}}{P_{t}}-\frac{L_{t-1}}{P_{t-1}}\frac{P_{t} }{P_{t}}=\frac{1}{P_{t}}\left( L_{t}-L_{t-1}(1+g_{t})\right) \\&=\frac{(L_{t}-L_{t-1}-L_{t-1}g_{t})}{P_{t}}=\frac{\Delta L_{t}}{P_{t} }-\frac{L_{t-1}g_{t}}{P_{t}} \end{aligned}$$

Putting this in net flow terms:

$$\begin{aligned} \frac{\Delta p_{t}}{p_{t}}&=\frac{\Delta p_{t}}{L_{t}/P_{t}}=\frac{\Delta L_{t}}{L_{t}}-\frac{L_{t-1}}{L_{t}}g_{t}\\&=(nu_{t}-en_{t})-\frac{L_{t-1}}{L_{t}}g_{t} \end{aligned}$$

shows that predictions of \(\frac{\Delta p_{t}}{p_{t}}\) using (\(nu_{t}-en_{t}) \) will be (systematically) greater than actual by \(\frac{L_{t-1}}{L_{t}}g_{t} \). Treating \(g_{t}\) as exogenously determined and manipulating the terms gives:

$$\begin{aligned} \frac{\Delta p_{t}}{p_{t}}=(nu_{t}-en_{t})(1+g_{t})-g_{t} \end{aligned}$$

In our predictions of the participation rate represented in Fig. 5, we have taken actual population growth into account:

$$\begin{aligned} {\widehat{p}}_{t}&=\frac{p_{t-1}}{(1-{\widehat{\Phi }}_{t})}\\ {\widehat{\Phi }}_{t}&=({\widehat{nu}}_{t}-{\widehat{en}}_{t})(1+g_{t})-g_{t} \end{aligned}$$

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Lim, G.C., Dixon, R. & van Ours, J.C. Beyond Okun’s law: output growth and labor market flows. Empir Econ 60, 1387–1409 (2021). https://doi.org/10.1007/s00181-019-01794-2

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