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Okun’s law and anelastic relaxation in economics

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Abstract

We unify the gap, difference and dynamic versions of Okun’s law using the theory of anelasticity. This theory provides a straightforward and parsimonious approach to macroeconomic model construction that we illustrate by treating the time-dependence of Okun’s law generated by labor migration. We also show how this approach provides a natural way of expressing the phenomena of macroeconomic friction due to the kinetic adjustment of microeconomic variables.

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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) and Ball et al. (2012).

  2. Studies of Okun’s law by policymakers includes Schnabel (2002), Balakrishnan et al. (2010), Wen and Chen (2012) and Ball et al. (2012).

  3. While the preponderance of prior research and the current literature expresses unemployment as a function of output, reversal of this causality has been discussed by researchers (Gordon 1984; Prachowny 1993; Lee 2000; Malley and Molana 2008, for example).

  4. 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. 2012).

  5. These formal assumptions are the postulates developed by Nowick and Berry (1972) for general anelasticity, adapted herein to Okun’s law.

  6. For examples in the natural sciences (magnetic, dielectric and anelastic relaxation) and economics (bank-product price and macroeconomic relaxation) see Dattagupta (1987), Hawkins and Arnold (2000), Hawkins and Aoki (2009) and references therein.

  7. As noted by Ball et al. (2012), these values for the HP-filter \(\lambda \) are commonly used for quarterly data.

  8. The importance of migration effects on Okun’s law in Austria, Germany, the US, Switzerland and Sweden is discussed by Sögner and Stiassny (2002),

  9. This model is based on Weidlich and Haag (1983) was developed in Haag and Weidlich (1984, 1986), and Weidlich and Haag (1987) and elaborated further in Weidlich and Haag (1988), Weidlich and Munz (1990) and Munz and Weidlich (1990) Further references for these and related sociodynamic models can be found in Weidlich (2000) and Helbing (2010). Recent extensions of this approach include Schweitzer (Schweitzer 2003, Chapter 9) and the literature linking the work of Weidlich and coworkers with the macroeconomics of Aoki (1996, 2000) and Aoki and Yoshikawa (2005, 2007) found in the work of Tabata, Eshima and Takagi (Tabata and Eshima 2004, 2009; Tabata et al. 2001, 2010, 2011).

  10. A major early study (Weidlich and Haag 1988) applying this model to Germany, France, Israel, Italy and Sweden found both the mobility \(\nu \) and the dynamic utility \(\mu _i\) to be functions of employment participation and availability measures.

  11. See, for example, Weidlich and Haag (1983), Aoki (1996), Weidlich (2000), Helbing (2010) and references therein.

  12. Another way of expressing this is that individuals are responding to endogenous changes in social fields that follow directly from the dynamic utility functions. A discussion of social-field theory in a master and Fokker–Planck equation context can be found in Helbing (2010, chapter 9). We note as well that the equations for a standard anelastic economy assume the relaxation time \(\tau _y\) is independent of time. Thus, the change described above is most correctly seen as an effectively instantaneous (on the time-scale of \(\tau _y\)) change in the state of the economy from one level of \(\tau _y\) to another.

  13. See Hawkins and Arnold (2000) and references therein.

  14. Since internal friction measures the loss of output associated with a change in unemployment it can be seen as a generalization of the concept of the sacrifice ratio from the usual output loss associated with a change in inflation to a wider range of structural changes that result in a loss of output.

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Acknowledgments

I thank Prof. Lawrence Ball of Johns Hopkins University and Drs. Daniel Leigh and Prakash Loungani of the International Monetary Fund for sharing the unemployment data, output data and Hodrick–Prescott results used in their paper (Ball et al. 2012). Their contribution materially improved this paper: all errors in the use or interpretation of their data are mine. I also thank Prof. Masanao Aoki for his pioneering work in macroeconomics without which this work would not have been possible and for his guidance and friendship.

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    Raymond J. Hawkins

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Hawkins, R.J. Okun’s law and anelastic relaxation in economics. J Econ Interact Coord 10, 151–161 (2015). https://doi.org/10.1007/s11403-014-0128-2

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