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Okun’s law and anelastic relaxation in advanced and developing economies

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Abstract

We show that the anelastic form of Okun’s law describes the output-unemployment relationship in a large number of advanced and developing counties well, and find two novel forms of this relationship: a Voigt-form of Okun’s law as well as a purely dynamical form of Okun’s law with no long-term output-unemployment tradeoff. We also find that the time-dependence in the anelastic form of Okun’s law reconciles the conflicting observations of general linearity and occasional nonlinearity by generalizing the output-unemployment relationship from a simple line to an ellipse known as an Okun loop.

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Data availability

The data used in this study were obtained from the World Economic Outlook (WEO) databases of the International Monetary Fund (IMF).

Notes

  1. See, for example, Gordon (1984); Hamada and Kurosaka (1984); Knoester (1986); Kaufman (1988); Prachowny (1993); Weber (1995); Moosa (1997); Lee (2000); Sögner and Stiassny (2002); Schnabel (2002); Knotek (2007); Malley and Molana (2008); Balakrishnan et al. (2010); Wen and Chen (2012); Ball et al. (2017).

  2. “Our principal conclusions are that Okun’s Law is a strong relationship in most countries, and one that is fairly stable over time. We find some deviations from a fixed Okun’s Law, but they are usually modest in size.” Ball et al. (2019).

  3. See, for example, Gordon (2010); Balakrishnan et al. (2010); Cazes et al. (2011); Manyika et al. (2011); Meyer and Tasci (2012) and references therein.

  4. The unemployment gap is the deviation of unemployment from trend, where the trend is often associated with the natural rate of unemployment. The output gap is the the deviation of the natural logarithm of real gross domestic product (real GDP) from trend, where the trend is often associated with the natural logarithm of potential real GDP.

  5. The data for real GDP are WEO Subject Code NDP_R and the unemployment data are WEO Subject Code LUR. The unemployment and output gaps were taken to be the cyclic component of the Hodrick-Prescott (HP) filter of the unemployment time series and natural logarithm of the real output time series, respectively. The smoothing parameter, \(\lambda\), for the HP filter was taken to be 100, in keeping with common practice for annual data. To avoid an issue with the end-point of the HP filter we employed the approach of Ball et al. (2017) of calculating the gaps using the IMF’s projections through 2021 but only using gaps through 2015 when performing the regressions.

  6. Differences reflect our use of the publicly-available April 2016 database and their use of the July database from the same year.

  7. See, for example, Knotek (2007); Daly and Hobijn (2010); Owyang and Sekhposyan (2012); Hawkins (2014); Obst (2019); Hawkins and Li (2021, 2022).

  8. See, for example, Knotek (2007), Obst (2019), and references therein.

  9. By “ideal elasticity” we are referring to the notion of elasticity given by Hooke’s law (\(\epsilon = J \sigma\) where \(\epsilon\) is strain and \(\sigma\) is stress) and the similar proportional relationship between \(\tilde{u}\) and \(\tilde{y}\) shown in Eq. (1). The question of what to do when solids did not conform to Hooke’s law due to time-dependence of the response is the basis of anelasticity. Our anelastic development of Okun’s law in terms of anelasticity develops the ansatz that phenomena that share assumptions—here, the three postulates of ideal elasticity—will have a common mathematical description. We are not saying, for example, that the unemployment gap is an economic form of material deformation; rather, that Okun’s law is formally similar to the variety of processes in condensed-matter physics (e.g., magnetic, dielectric, and anelastic relaxations) that involve time-dependent relaxations toward newly established equilibria that follow from a change in a driving force and can be described in terms of linear-response theory.

  10. This is a summary of theory that has appeared elsewhere (c.f., Hawkins (2014) and Hawkins and Li (2021, 2022)), and is included here for a self-contained appreciation of the results shown in Sect. 4.2. The extension of these discussions here to include the Voigt model and the slope of the Okun loop given by Eq. (7) is new.

  11. The loops for the member of the advanced economies group that are also in the EU15 were discussed in a recent communication on the EU15 (Hawkins and Li 2022) and are included here for completeness.

  12. Examples of the use of partial-adjustment models in the study of Okun’s law include Gordon (1984); Kaufman (1988); Weber (1995); Moosa (1997); Sögner and Stiassny (2002); Knotek (2007); Stock and Volger-Ludwig (2010); Källman and Nordell (2012); Ball et al. (2017).

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Acknowledgements

My thanks to Sarah Baig, Ciecie Chen, Michael Chen, Charles Fondecave, Yunzhen Huang, Jose Lawani, Chaitali Mandavia, Smin Na, Kiarash Rahmati, Layly Roodsari, Christopher Tice-Raskin, Hiroyuki Tominaga, Deborah Yam, Amanda Yao, and Zhi Zuo  for their excellent research assistance. I also thank Prof. Martha Olney for the Economics Undergraduate Researcher Program that enabled the participation of these research assistants in this project.

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  1. Department of Economics, University of California, Berkeley, CA, 94720, USA

    Raymond J. Hawkins

  2. Wyant College of Optical Sciences, University of Arizona, Tucson, AZ, 85721, USA

    Raymond J. Hawkins

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Hawkins, R.J. Okun’s law and anelastic relaxation in advanced and developing economies. Evolut Inst Econ Rev (2024). https://doi.org/10.1007/s40844-024-00280-4

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