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Does Productivity Affect Unemployment? A Time-Frequency Analysis for the US

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Wavelet Applications in Economics and Finance

Part of the book series: Dynamic Modeling and Econometrics in Economics and Finance ((DMEF,volume 20))

Abstract

The effect of increased productivity on unemployment has long been disputed both theoretically and empirically. Although economists mostly agree on the long run positive effects of labor productivity, there is still much disagreement over the issue as to whether productivity growth is good or bad for employment in the short run. Does productivity growth increase or reduce unemployment? This paper try to answer this question by using the property of wavelet analysis to decompose economic time series into their time scale components, each associated to a specific frequency range. We decompose the relevant US time series data in different time scale components and consider co-movements of productivity and unemployment over different time horizons. In a nutshell, we conclude that, according to US post-war data, productivity creates unemployment in the short and medium terms, but employment in the long run.

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Notes

  1. 1.

    See the volume by Cooley (1995), and see also Backus and Kehoe (1992) among the others.

  2. 2.

    For details of the evaluations, see Gong and Semmler (2006, ch.6).

  3. 3.

    For example in Gallegati et al. (2011) where wavelet analysis is applied to the wage Phillips curve for the US.

  4. 4.

    Most of the attention of economic researchers who work on productivity has been devoted to measurement issues and to resolve the problem of data consistency, as there are many different approaches to the measurement of productivity linked to the choice of data, notably the combination of employment, hours worked and GDP (see for example the OECD Productivity Manual, 2001).

  5. 5.

    “At short term scales, I think, something sort of Keynesian is a good approximation, and surely better than anything straight neoclassical. At very long scales, the interesting questions are best studied in a neoclassical framework…. At the 5–10 years time scale, we have to piece things together as best as we can, and look for an hybrid model that will do the job” (Solow 2000, p. 156).

  6. 6.

    “The nature of the mechanism that link [unemployment and productivity growth] changes with the time frame adopted” because one needs “to distinguish between an analysis of the forces shaping long-term equilibrium paths of output, employment and productivity on the one hand and the forces causing temporary deviations from these equilibrium paths on the other hand” (Landmann 2004, p. 35).

  7. 7.

    Qualitative similar results are also provided using time domain techniques separating long-run trends from short run phenomena.

  8. 8.

    For example Gençay et al. (2005), Gençay et al. (2010), Kim and In (2005), Fernandez (2005), Crowley and Mayes (2008), Gallegati (2008), Ramsey et al. (2010), Gallegati et al. (2011).

  9. 9.

    Wavelets, their generation, and their potential use are discussed in intuitive terms in Ramsey (2010), while Gençay et al. (2001) generate an excellent development of wavelet analysis and provide many interesting economic examples. Percival and Walden (2000) provide a more technical exposition with many examples of the use of wavelets in a variety of fields, but not in economics.

  10. 10.

    The CWT has been computed using the MatLab package developed by Grinsted et al. (2004). MatLab programs for performing the bias-rectified wavelet power spectrum and partial wavelet coherence are provided by Ng and Kwok at http://www.cityu.edu.hk/gcacic/wavelet.

  11. 11.

    The statistical significance of the results obtained through wavelet power analysis was first assessed by Torrence and Compo (1998) by deriving the empirical (chi-squared) distribution for the local wavelet power spectrum of a white or red noise signal using Monte Carlo simulation analysis.

  12. 12.

    As with other types of transforms, the CWT applied to a finite length time series inevitably suffers from border distortions; this is due to the fact that the values of the transform at the beginning and the end of the time series are always incorrectly computed, in the sense that they involve missing values of the series which are then artificially prescribed; the most common choices are zero padding extension of the time series by zeros or periodization. Since the effective support of the wavelet at scale λ is proportional to λ, these edge effects also increase with λ. The region in which the transform suffers from these edge effects is called the cone of influence. In this area of the time-frequency plane the results are unreliable and have to be interpreted carefully (see Percival and Walden 2000).

  13. 13.

    We use quarterly data for the US between 1948: 1 and 2013: 4 from the Bureau of Labor Statistics. Labor productivity is defined as output per hour of all persons in the Nonfarm Business Sector, Index 1992 = 100, and transformed into its growth rate as \(400 {\ast}\mathit{ln}(x_{t}/x_{t-1}\)). Unemployment rate is defined as percent Civilian Unemployment Rate.

  14. 14.

    The number of the papers applying the DWT is far greater than those using the CWT. As a matter of fact, the preference for DWT in economic applications can be explained by the ability of the DWT to facilitate a more direct comparison with standard econometric tools than is permitted by the CWT, e.g. time scales regression analysis, homogeneity test for variance, nonparametric analysis.

  15. 15.

    Their dimensions change according to their scale: the windows stretch for large values of λ to measure the low frequency movements and compress for small values of λ to measure the high frequency movements.

  16. 16.

    Since the J components obtained by the application of MODWT are not orthogonal, they do not sum up to the original variable.

  17. 17.

    Detail levels D 1 and D 2, represent the very short-run dynamics of a signal (and contains most of the noise of the signal), levels D 3 and D 4 roughly correspond to the standard business cycle time period (Stock and Watson 1999), while the medium-run component is associated to level D 5. Finally, the smooth component S 5 captures oscillations with a period longer than 16 years corresponding to the low-frequency components of a signal.

  18. 18.

    Although a standard assumption in economics is that the delay between variables is fixed, the phase relationship may well be scale dependent and vary continuously over time (e.g. in Ramsey and Lampart 1998a,b; Gallegati and Ramsey 2013).

  19. 19.

    This leading behavior is consistent with the findings reported in the previous section using wavelet coherence.

  20. 20.

    Thus, we test for frequency dependence of the regression parameter by using timescale regression analysis since the approaches used to detect and model frequency dependence such as spectral regression approaches (Hannan 1963; Engle 1974, 1978) present several shortcomings because of their use of the Fourier transformation. For examples of the use of this procedure in economics, see Ramsey and Lampart (1998a,b), Gallegati et al. (2011).

  21. 21.

    This estimated magnitude of the impact of growth on unemployment is in line with those obtained in previous studies. For example, Pissarides and Vallanti (2007) a panel of OECD countries estimate that a 1 % decline in the growth rate leads to a 1.3–1.5 % increase in unemployment.

  22. 22.

    Recently, a negative long-run relationship between productivity growth and unemployment has also been obtained by Schreiber (2009) using a co-breaking approach and Miyamoto and Takahashi (2011) using band-pass filtering.

  23. 23.

    The traditional nonlinear regression model introduce nonlinear functions of dependent variables using a limited range of transformed variables to the model (quadratic terms, cubic terms or piecewise constant function). An example of a methodology testing for nonlinearity without imposing any a priory assumption about the shape of the relationship is the smooth transition regression used in Eliasson (2001).

  24. 24.

    See Fox (2000a,b) for a discussion on nonparametric regression methods.

  25. 25.

    The smoothing parameter controls the flexibility of the loess regression function: large values of produce the smoothest functions that wiggle the least in response to fluctuations in the data, the smaller the smoothing parameter is, the closer the regression function will conform to the data

  26. 26.

    We use different smoothing parameters, but our main findings do not show excess sensitivity to the choice of the span in the loess function within what appear to be reasonable ranges of smoothness (i.e. between 0.4 and 0.8).

  27. 27.

    Embodied technical change is embedded in (new) capital goods or jobs and can benefit only jobs that explicitly invest in new technology. By contrast, disembodied technical change is not tied to any factor of production and can benefit all existing jobs. According to the “capitalization” effect an increase in growth raises the capitalized value of those returns obtained from creating jobs, thereby reducing the equilibrium rate of unemployment by increasing the job-finding rate. The second effect is the creative destruction, according to which an increase in growth raises the equilibrium level of unemployment both directly, by raising the job-separation rate, and indirectly, by discouraging the creation of job vacancies.

  28. 28.

    These long run effects maybe also based on the sluggishness of real wage adjustments as suggested by models where wage setting depends on backward looking reservation wages (Blanchard and Katz 1999). Results compatible with this evidence are reported in Gallegati et al. (2011) where wages do not adjust fully to productivity changes in the long-run.

  29. 29.

    Higher productivity growth is often accompanied by structural change wherein “old jobs” are replaced by “new ones” since technology could enhance the demands for new products.

  30. 30.

    Indeed, the relationship between productivity and the unemployment rate may appear weaker when we reduce the time period used for aggregating data (see Steindel and Stiroh 2001).

  31. 31.

    A statement like this goes back to David Ricardo who has pointed out that if machinery is substituted for labor unemployment is likely to increase.

  32. 32.

    This point is made clear in a simple text book illustration by Blanchard (2005).

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Acknowledgements

The paper has been presented at the Workshop on “Frequency domain research in macroeconomics and finance”, held at the Bank of Finland, Helsinki, 20–21 October 2011. We thank all participants for valuable comments and suggestions, particularly Jouko Vilmunen and Patrick Crowley.

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Authors and Affiliations

  1. DISES and SIEC, Polytechnic University of Marche, Ancona, Italy

    Marco Gallegati & Mauro Gallegati

  2. Department of Economics, New York University, New York, NY, USA

    James B. Ramsey

  3. Department of Economics, New School for Social Research, New York, NY, USA

    Willi Semmler

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  1. Marco Gallegati
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  2. Mauro Gallegati
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  4. Willi Semmler
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Correspondence to Marco Gallegati .

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Editors and Affiliations

  1. Faculty of Economics "G. Fuà", Polytechnic University of Marche, Ancona, Italy

    Marco Gallegati

  2. New School for Social Research, The New School University, New York, New York, USA

    Willi Semmler

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Gallegati, M., Gallegati, M., Ramsey, J.B., Semmler, W. (2014). Does Productivity Affect Unemployment? A Time-Frequency Analysis for the US. In: Gallegati, M., Semmler, W. (eds) Wavelet Applications in Economics and Finance. Dynamic Modeling and Econometrics in Economics and Finance, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-07061-2_2

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