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Polarization of the worldwide distribution of productivity

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Abstract

We employ data envelopment analysis (DEA) methods to construct the world production frontier, which is in turn used to decompose (labor) productivity growth into components attributable to technological change (shift of the production frontier), efficiency change (movements toward or away from the frontier), physical capital deepening, and human capital accumulation over the 1965–2007 period. Using this decomposition, we provide new findings on the causes of polarization (the emergence of bimodality) and divergence (increased variance) of the world productivity distribution. First, unlike earlier studies, we find that efficiency change is the unique driver of the emergence of a second (higher) mode. Second, while earlier studies attributed the overall change in the distribution exclusively to physical capital accumulation, we find that technological change and human capital accumulation are also significant factors explaining this change in the distribution (most notably the emergence of a long right-hand tail). Robustness exercises indicate that these revisions of earlier findings are attributable to the addition of (more recent) years and a much greater number of countries included in our sample. We also check to see whether our results are changed by a correction for the downward bias in the DEA construction of the frontier, concluding that these corrections affect none of our major findings (essentially because the level correction roughly washes out in changes.)

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Notes

  1. This notion is much narrower than the polarization concept studied in the microeconomic analysis of the distribution of income. The latter concept (see, e.g., Duclos et al. 2004) is much richer, entailing psychological notions like alienation and within-group identification. Our usage, however, is consistent with that in the macroeconomic literature (see, e.g., Quah 1997).

  2. Bimodality could be the result of convergence clubs, but bimodality is neither necessary nor sufficient for club convergence, as pointed out by Pittau et al. (2010), Battisti and Parmeter (forthcoming), and others. For examples that look at movements between groups see Bianchi (1997) and Henderson et al. (2008).

  3. The idea behind Diewert’s sequential production set is that it represents the “state of technological knowledge” at a point in time, which is assumed not to depreciate: that is, technological innovations cannot be “forgotten” in subsequent years. Kumar and Russell (2002) did not impose this restriction—they used only current-period data to construct the current-period production frontier—and found some implosion of the frontier at low levels of capitalization. Following HR, we believe it is more reasonable to preclude such implosion.

  4. While there are several approaches to efficiency measurement, DEA is one of the most commonly employed. The other frequently employed method is Stochastic Frontier Analysis (SFA). For comparisons of these two approaches, see, for example, Gong and Sickles (1992); Bojanic et al. (1998); Cubbin and Tzanidakis (1998); Badunenko et al. (2012), and Park and Lesourd (2000).

  5. We drop the i subscript from e it , defined in Eq. (2), for better readability.

  6. Unlike HR and many other studies in this area, we adopt the view of Caselli (2005) that some oil-rich countries are among the most productive in the world and should be retained in the sample.

  7. This finding is also consistent with the Basu and Weil (1998) approach to modeling the growth process, in which each level of capitalization is associated with a unique “appropriate technology”, and technological innovations in a country are aimed at improving productivity in that country’s region of input space. See also Los and Timmer (2005).

  8. More systematic comparisons are discussed in the robustness tests in Sect. 5.

  9. For all estimated distributions, we employ a Gaussian kernel and the Sheather and Jones (1991) method for choice of the optimal bandwidth.

  10. Percentages are obtained by subtracting 1 from the index and multiplying by 100. Because of compounding, the contributions of individual components do not, of course, sum to the total productivity change.

  11. The corresponding median contributions in HR are −1, 1.5, 29.4, and 14.7.

  12. We should note that there were large efficiency improvements in Ghana.

  13. For further details, see Hall and York (2001), Henderson et al. (2008), and Silverman (1981).

  14. For further details, see Fan and Ullah (1999), Li (1996), and Pagan and Ullah (1999).

  15. The p value in HR is obtained using the standard Silverman test, which has been shown to be conservative, in the sense that the true asymptotic level is less than the nominal one. When employing the calibrated Silverman test with the original HR data and set-up, the p value is equal to 0.028. Therefore the null that the counterfactual distribution incorporating only efficiency changes is uni-modal is rejected using the calibrated test for the HR sample as well.

  16. The long tails in these distributions are attributable to exceptionally large productivity values for a few countries: especially Luxembourg and Singapore, and to a lesser extent, Hong Kong, Norway, and Ireland.

  17. The omitted countries, none of which determines the shape of the production frontier in 1965 or 2007, are Germany, Dominican Republic, and Yugoslavia.

  18. We thank a referee for drawing our attention to this possibility.

  19. The USA efficiency score increases to 0.99, compared to 0.74 in the original sample.

  20. See, e.g., the comprehensive treatments of DEA and related production-frontier methods in Färe et al. (1985, 1994), and Charnes et al. (1994) as well as the pioneering paper by Farrell (1957).

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Authors and Affiliations

  1. Cologne Graduate School in Management, Economics and Social Sciences, University of Cologne, Richard-Strauss-Str. 2, 50931, Cologne, Germany

    Oleg Badunenko

  2. Department of Economics, Finance and Legal Studies, University of Alabama, Box 870224, Tuscaloosa, AL, 35487-0224, USA

    Daniel J. Henderson

  3. Department of Economics, University of California, Riverside, CA, 92521-0427, USA

    R. Robert Russell

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  1. Oleg Badunenko
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  2. Daniel J. Henderson
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  3. R. Robert Russell
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Correspondence to R. Robert Russell.

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Badunenko, O., Henderson, D.J. & Russell, R.R. Polarization of the worldwide distribution of productivity. J Prod Anal 40, 153–171 (2013). https://doi.org/10.1007/s11123-012-0328-5

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