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The effects of globalization and technology on the elasticity of substitution

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Abstract

The elasticity of substitution between capital and labor (\(\sigma\)) is usually considered a “deep parameter”. This paper shows, in contrast, that \(\sigma\) is affected by both globalization and technology, and that different intensities in these drivers have different consequences for the OECD and the non-OECD economies. In the OECD, we find that the elasticity of substitution between capital and labor is below unity; that it increases along with the degree of globalization; but it decreases with the level of technology. Although results for the non-OECD area are more heterogeneous, we find that technology enhances the substitutability between capital and labor. We also find evidence of a non-significant impact of the capital-output ratio on the labor share irrespective of the degree of globalization (which would be consistent with an average aggregate Cobb–Douglas technology). Given the relevance of \(\sigma\) for economic growth and the functional distribution of income, the intertwined linkage among globalization, technology and the elasticity of substitution should be taken into account in any policy makers’ objective function.

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Notes

  1. This type of production functions has also been used, among others, by Sato and Hoffman (1968) and Jones and Manuelli (1990). In addition to the VES production functions, Antony (2010) mentions the possibility of using flexible functional forms, such as translog or quadratic production functions. These flexible forms, however, share the problem of having a large number of parameters to be estimated or calibrated.

  2. Independent in spite that trade and associated activities, such as foreign direct investment (FDI), are among the main sources of technological transfer (Coe and Helpman 1995; Falvey et al. 2004), and it can also spur innovation by increasing the extent of the market (Sachs 2000).

  3. A detailed derivation of Eq. (2) from (1) can be found in Bentolila and Saint-Paul (2003), pp. 6–7, and Young and Lawson (2014), p. 23. For the sake of intuition, we follow the latter and define \(\sigma\) as a positive parameter.

  4. This is known as the “capital-skill complementarity hypothesis”. Formal and empirical evidence can be found in Griliches (1969), Goldin and Katz (1996) and Caselli and Coleman (2001).

  5. These production functions are based on the idea from de La Grandville (1989) of normalizing CES production functions.

  6. A dual elasticity of substitution is chosen in this section for the sake of simplicity. The important fact is that changes in the capital-labor ratio can affect the value of \(\sigma\). Antony’s-type production functions do not have any structural model behind and do not provide clear indications about how increases in the capital-labor ratio affect \(\sigma\). Our paper, therefore, has to be seen essentially as an empirical exercise on the determinants of \(\sigma\) leaving the specific policy implications for further research.

  7. For a detailed overview on System GMM, and its advantages over standard panel data techniques and Difference GMM, see Bond et al. (2001) and Roodman (2009).

  8. Accordingly, both samples are estimated allowing for just four lags of endogenous variables and using the “collapse” instruments option available in the xtabond2 Stata command developed by David Roodman. Table A4 and Figures A8 and A9 in the “Online Appendix” present the results when 3 and 5 lags are used.

  9. Tables A2 and A3 in the “Online Appendix” show the main descriptive statistics by group of countries. Given data availability, our analysis considers 24 OECD countries (621 observations) and 27 non-OECD countries (650 observations).

  10. To complement this information, Figure A1 in the “Online Appendix” shows the evolution of the labor income share, the capital-output ratio and the KOF index taking as initial value the weighted average at 1970. TFP is not included in this figure, as its variation is within country (the index is equal to 1 for all the countries in 2005), thus making different values between groups uninformative.

  11. To complement this general information, Figures A2–A4 in the “Online Appendix” present country specific correlation coefficients of the capital-output ratio, the KOF index of globalization, and TFP with respect to the labor income share (to provide the most global picture, these figures contain information for a wider sample than the one that we could actually use in the analysis due to data limitations). Clear pictures emerge in the first two cases, with worldwide positive and negative correlations across all economies. On the contrary, there is a much disperse result regarding TFP, with a negative correlation in most OECD countries, and a not so clear negative relationship in the non-OECD countries.

  12. As a goodness check, note that the persistence coefficients obtained by the BB estimator lie between the ones estimated by POLS and 2FE (see Bond 2002). They are the largest ones under the POLS estimation (0.84 in the OECD and 0.96 in the non-OECD areas, respectively), the lowest ones under the 2FE estimation (0.66 and 0.79), and take a middle position when estimated by System GMM (0.72 and 0.82). We credit the latter and conclude that the labor share in the non-OECD area is more persistent than in the OECD countries.

  13. The extent to which the process of globalization affects a particular country is certainly shaped by the trade policies and the institutional framework in which these policies are developed (which affect the costs and profits of economic activities). However, country-specific trade policies and the design of institutions are not forward looking but rather reactive to global and domestic changes. It is from this perspective that we consider globalization as an exogenous driver of the influence exerted by the capital-output ratio on the labor share. This interpretation is reinforced by the results presented in columns [2] and [6] in Table A4, and Figure A7 in the “Online Appendix”, which are robust when globalization is considered endogenous.

  14. Figure A5 in the “Online Appendix” shows the Kernel density functions of the KOF and TFP indices in the OECD and non-OECD countries, with the shaded areas indicating the selected values. For the OECD economies, they range from 40 to 100% for the KOF index, and from \(-0.35\) to 0.18 for the TFP; for the non-OECD economies, they go from 22 to 68% for the KOF index, and range between \(-0.34\) and 0.38 for the TFP. Note that the wider interval in the non-OECD group implies a larger volatility of the TFP, and does not reflect at all a better technological level.

  15. It is worth outlining the differences of significance between Table 2 and Fig. 2. While we find a significant impact of the marginal effects in Fig. 2, most of the coefficients in Table 2 are insignificant. For a benchmark model like \(Y=\beta _0+\beta _1X+\beta _2Z+\beta _3XZ+\epsilon\), Brambor et al. (2006) explain this result as follows: “even more important to remember is that the analyst is not directly interested in the significance or insignificance of the model parameters per se anyway. Instead, the analyst who employs a multiplicative interaction model is typically interested in the marginal effect of X on Y. In the case of [our model], this is \(\frac{\partial Y}{\partial X}=\beta _1+\beta _3Z\). As a result, the analyst really wants to know the standard error of this quantity and not the standard error of \(\beta _0\), \(\beta _1\), \(\beta _2\), or \(\beta _3\). The standard error of interest is:

    $$\begin{aligned} \hat{\sigma }_{\frac{\partial Y}{\partial X}}=\sqrt{\mathrm {var}(\hat{\beta _1})+Z^2\mathrm {var}(\hat{\beta _3})+2Z\mathrm {cov}(\hat{\beta _1}\hat{\beta _3}) } \end{aligned}$$

    If the covariance term is negative, as is often the case, then it is entirely possible for \(\beta _1+\beta _3Z\) to be significant for substantively relevant values of Z even if all of the model parameters are insignificant.” (Brambor et al. 2006, p. 70.)

  16. Given that Antony’s production functions lack an explicit transmission mechanism, it is worth noting that additional factors could also play a role on this relationship. Disentangling such factors is left for further research.

  17. In the event of slow capital stock changes and a counter-cyclical behavior of the labor share, yearly data analysis could reflect a spurious positive correlation between the capital-output ratio and the labor income share. To exclude this possibility, Figure A6 in the “Online Appendix” shows the marginal effects for a 3 years average static model estimated by System GMM. It can be observed that our results are robust both for the OECD and the non-OECD countries and, thus, we can safely rule out the possibility of a spurious positive correlation.

  18. Income and region classifications follows the World Bank system. Regarding income levels, we have created three groups in the following way: (i) high income \(=\) High Income OECD \(+\) High Income non-OECD, (ii) Middle Income \(=\) Upper Middle Income, and (iii) Low Income \(=\) Low Income \(+\) Lower Middle Income.

  19. We are aware that some authors have warned against the study of country-specific coefficients in an isolated way (Pedroni 2007; Eberhardt and Teal 2013). For this reason, we will not focus on the specific information obtained for a given country, but on the existence of potential patterns across countries for different average globalization levels. In any case, let us note that our results are robust to the estimation method and no significant differences appear when we use the Chudik and Pesaran (2015) Dynamic CMG estimator (CMG1 and CMG2). We use the CMG estimates because of the larger number of countries included in this estimation.

  20. The graphical analysis in this section is based on Eberhardt and Presbitero (2015). The replication files can be accessed at Markus Eberhardt’s personal website: https://sites.google.com/site/medevecon/publications-and-working-papers (by clicking “Replication data and do-files” below Eberhardt and Presbitero 2015).

  21. Although we have tried to use alternative proxies for technological change, we have not found an alternative that covers enough sample to undertake a reliable robustness check.

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Acknowledgements

We acknowledge helpful comments from three anonymous referees, which have led to significant improvements in the original version of this paper. Pedro Trivín acknowledges the warm hospitality received from the School of Economics and Finance of Queen Mary University of London, where the bulk of this work was developed. We are grateful to Ángel López, Matteo Fragetta, the participants in the XXIX Italian Conference of Labor Economics, the XI Spanish Conference of Labor Economics, the 39th SAEe, and the Economics Seminars at Ryerson University. We are also grateful to the Spanish Ministry of Economy and Competitiveness for financial support through Grant ECO2016-75623-R.

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  1. Departament d’Economia Aplicada, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Hector Sala

  2. IZA, Bonn, Germany

    Hector Sala

  3. Departament d’Economia, Universitat de Girona, 17071, Girona, Spain

    Pedro Trivín

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Correspondence to Hector Sala.

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Sala, H., Trivín, P. The effects of globalization and technology on the elasticity of substitution. Rev World Econ 154, 617–647 (2018). https://doi.org/10.1007/s10290-018-0315-7

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