Decomposition of Labor Productivity Growth: A Multilateral Production Frontier Approach

Decomposition of Labor Productivity Growth: A Multilateral Production Frontier Approach

This paper develops a parametric decomposition framework of labor productivity growth relaxing the assumption of labor-specific efficiency.

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The productivity fall observed in many developed and developing countries during the 60’s and early 70’s triggered an intense public debate aimed to unravel the internal mechanism of productivity growth. This heated debate had resulted to an enormous theoretical and empirical literature directed to the investigation of the proximate causes of the observed differences in per-capita income across developing and developed countries. Most researchers used the cross-sectional version of the familiar growth accounting framework of Solow (1957) to decompose country variations in the levels of output per worker into parts attributed to the variation in the factors of production and productivity growth. The results lead to the conclusion that the residual productivity rather than factor accumulation accounts for most of the income and growth differences across nations (see Caselli (2005) and the references cited therein). This finding although it uncovers the proximate causes of income differentials is unsatisfactory in the sense that the ultimate causes that lead to different levels of productivity are not explained. If we accept that productivity differences are large, then we are left with a shortage of convincing explanation for this result. The later is important as different sources of productivity differentials require different policy measures to enhance economic growth either in developed or developing nations (Prescott, 1988).

Since much of these productivity variations represents differences in technological structures, then there should be an adequate explanation why non-rival innovations do not diffuse across borders. And if they do, then why we still observe differences in measured productivity rates. If there is a uniform worldwide production frontier, then all of the observed differences in productivity reflect a gap from this frontier. Obviously there are strong barriers to adoption across countries related to the institutional and cultural environment preventing many countries from using that common technological structure. Olson (1982) and Krusell and Rios-Rull (1996) argue, that vested interest groups are lobbying for market power, protection from competition, limiting factor mobility and then blocking adoption of rival technologies through a political process. Parente and Prescott (1999) provide a theoretical model where the existence of monopoly power extend beyond the traditional deadweight loss affecting the adoption of new technologies as well as the appropriate use of technologies already adopted.

Relative recently economic growth literature questions the above perspective, recognizing that the technology frontier is not uniform. In other words, it admits that not every country face the same technological conditions. According to this perception countries choose the best production technologies available to them given their internal economic and structural conditions. Obviously factor endowments as well as the institutional and cultural environment affect these choices as some technologies may be less productive than others. For instance, ICT technologies enhance social welfare through structural transformation in production networks and social customs but at the same time require human capital, i.e., high literacy rates, to function properly. Basu and Weil (1998) and Acemoglou and Zilibotti (2001), explored the appropriateness of technology paradigm to explain differences in income levels and economic convergence. They both conclude that developed countries invent new technologies that are compatible with their own resource endowments and these technologies do not work appropriately in developing countries with a different input mix. This implies that the adoption of a modern technology by poor countries do not raise their productivity levels as it is inappropriate to them. So the assumption of the same technological structure may not be adequate to explain productivity variations and empirical work should take that into account.

Under both paradigms, one would expect all countries to operate on their own or to the common technological frontier being thus fully efficient. Empirical evidence though suggest that rather the opposite is true. Several authors suggest that rarely countries are exploring fully the potential of the existing technology operating far from their respective production frontier (e.g., Färe et al., 1994; Kumar and Russell, 2002; Los and Timmer, 2005; Badunenko et al., 2008). Theoretical models of explaining inefficiency in resource utilization, focus on the role of institutions and social structures to explain why the common or country-specific production technology is not utilized appropriately by individual countries. Apart of the availability of the technology, other factors must be present such as strong investment, a well trained work force, R&D activity, trading relationships, a receptive political structure that Abramovitz (1986) summarizes under the term social capability. However, all these elements of efficiency determination are not affecting the efficient use of all inputs in the same manner. For instance, lack of working experience affects rather more intensively labor efficiency than capital utilization. Nevertheless empirical studies, besides analyzing labor productivity differentials, they utilize an aggregate output or input inefficiency index. Important information, valuable from a policy perspective, can be gained by providing an empirical analysis focusing exclusively on labor-specific efficiency.

Probably the most important aspect related with resource utilization and therefore productivity differentials across countries, recognized by many researcher, is the role of human capital. Inspired by the early approaches on human capital theory (Schultz, 1961; Becker, 1975), many empirical researchers have focused on the important role played by educational levels in the efficiency of input utilization and hence on the growth process. In these early theoretical contributions schooling is viewed as an investment in skills having a direct effect on labor productivity as well as an indirect one through the improvement of worker’s ability to work efficiently (Welch, 1970). Griliches (1970) and Jorgenson and Fraumeni (1993) found that a significant portion of differentials is attributed directly to increases in educational levels. On the other hand, Welch (1970) and Bartel and Lichtenberg (1987), among others, found that highly educated workers have a comparative advantage with regard to the implementation of new technologies exhibiting therefore higher efficiency levels. Recently the development of detailed educational data by Barro and Lee (1993; 2001) and the formulation of endogenous growth models by Lucas (1988) and Romer (1990), enabled the empirical analysis on the role of education in economic growth. All of these studies on growth accounting again indicated that a significant portion of measured productivity growth is attributed directly to increases in educational levels of the labor force (e.g., Benhabib and Spiegel, 1994; O’Neil, 1995; Bils and Klenow, 2000). Regardless of the nature and the aims of these studies, they provided unshaken evidence about the important role played by human capital in the growth process, suggesting that it is an important element of any productivity decomposition analysis and it should be included in any empirical research.

Motivated by the works of Färe et al., (1994), Kumar and Russell (2002) and Henderson and Russell (2005), we attempt in this paper to contribute in the relevant literature providing a theoretically consistent parametric decomposition of labor productivity growth. According to these studies labor productivity is decomposed into the rates of growth of factor intensities and TFP. However, shifts in relative capital-labor prices and the biases of technological change are also important possibilities for changes in the growth rate of factor intensities. Taking that into account, our decomposition framework provides a more detailed analysis of changes in labor productivity across countries. First, we focus on labor-specific inefficiency rather than an output efficiency measure which is more relevant when labor productivity growth is analyzed. The proposed index for measuring labor-specific technical and allocative efficiency is based on Kopp’s (1981) orthogonal non-radial index of technical efficiency modified in a parametric frontier framework. Then the derived index of labor-specific efficiency is used to provide a complete decomposition framework of labor productivity growth. 

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