تجمع سرمایه انسانی و حقوق و دستمزد نسبی در سراسر کشور

Most of the growth accounting literature relies on an aggregate production function to determine the contribution of factors of production relative to that of total factor productivity (TFP) in explaining differences in incomes across countries. I show that the importance of TFP in accounting for cross-country income differences depends crucially on how skilled and unskilled labor are aggregated. Further, cross-country evidence on the relationship between relative wages and relative endowments of skilled and unskilled labor suggests that the two types of labor should not be aggregated into a single factor of production. Growth accounting decomposition using a commonly used nested-CES aggregate production function that allows skilled and unskilled labor to be used as separate factors of production results in a significantly greater role for TFP in accounting for income differences across countries than that found by past studies. The finding that different aggregate production functions lead to significantly different conclusions about the role of TFP in accounting for cross-country income differences calls for a more general approach to understanding such differences.

Most of the growth accounting literature relies on the use of an aggregate production function (APF) in order to evaluate the contributions of human capital, physical capital and total factor productivity (TFP) to differences in incomes across countries.1 In this paper, I show that the relative importance of TFP in accounting for cross-country income differences depends crucially depends on how skilled and unskilled labor are aggregated. Previous studies, such as Klenow and Rodríguez–Clare, 1997 and Hall and Jones, 1999, aggregate skilled and unskilled labor into a single factor of production, human capital, when evaluating the importance of TFP. To begin with, I show that the importance of TFP depends on the value of the substitution parameter used for the aggregation by these studies.2 To do so, using data for 51 countries, I consider a growth accounting exercise similar to that of Hall and Jones (1999) under different values for the substitution parameter and, for each country, compute TFP relative to that of the US.3 Relative TFP for all countries increases when the substitution parameter is decreased from 1 (skilled and unskilled labor are perfect substitutes) to 0.75 (imperfect substitutes), indicating that the degree of substitutability between skilled and unskilled labor plays a crucial role for determining the importance of TFP in accounting for cross-country income differences.4 Given the importance of the substitution parameter for the aggregate production function used in the above exercise, it becomes imperative to determine the value of the parameter that should be used for the aggregation. Using cross-country data, I plot the logarithm of relative wages against the logarithm of the ratio of the two types of labor and find that the slope, which provides an estimate of the substitution parameter for this particular aggregation, varies systematically with GDP per worker: low income countries have a steeper slope than high income countries.5 In other words, the relation between relative wages and relative endowments of skilled and unskilled labor varies systematically across countries.6 This evidence suggests that aggregation of the two types of labor into a single factor of production using a common substitution parameter will not be able to match this systematic cross-country difference in the relationship between relative wages and relative endowments of skilled and unskilled labor. A natural question to ask, then, is whether using aggregate production functions that allow for skilled and unskilled labor to be used as separate inputs for growth accounting would lead to conclusions that differ from those obtained by Hall and Jones (1999). The two-level or nested-CES class of aggregate production functions provide a generalization of the aggregation used by Hall and Jones.7 Based on estimates obtained using data for the US (Krusell et al., 2000) and cross-country panel data (Duffy et al., 2004), the literature on capital-skill complementarity has argued in favor of one nesting of this class of production functions. I employ this preferred APF for the growth accounting exercise and investigate whether doing so results in significant changes in the importance of TFP in explaining cross-country income differences. When aggregating the two types of labor into a single input, for the Hall and Jones growth accounting exercise, the labor share of income is assumed to be constant across countries while country-specific relative wages of skilled and unskilled labor are used to compute the relative efficiency of the two types of labor. To ensure comparability of results with the previous exercise, for the preferred variant of the nested-CES APF, I use estimates of the substitution parameters from Duffy et al. (2004) and calibrate the two share parameters of the production function to match the country-specific relative wages of skilled and unskilled labor and the common labor share of income.8 These parameter values are then used to compute the TFP for each country relative to that for the US, and the results obtained are compared with that for the aggregation used in the previous exercise. Relative to the Hall and Jones aggregation, using the preferred APF for growth accounting increases the importance of TFP in explaining cross-country income differences. The contribution of TFP in explaining differences in incomes increases from 54% (Hall and Jones aggregation) to 111% (preferred aggregation).9 To put it differently, a growth accounting exercise using the preferred aggregation concludes that differences in factors of production cannot explain any of the cross-country differences in GDP per worker. These results suggest that the choice of the aggregation plays a crucial role in determining the relative importance of TFP in explaining cross-country income differences. The rest of this paper is organized as follows: Section 2 provides a description of the cross-country data and illustrates the importance of the substitution parameter for the conclusions from a growth accounting exercise when skilled and unskilled are aggregated into a single factor of production. Section 3 explores the relationship between relative wages and relative endowments of skilled and unskilled labor to determine the substitution parameter for the aggregate production function used for growth accounting in the previous section. In Section 4, the implications for the relative importance of TFP in explaining cross-country income differences using a commonly used nested-CES APF are presented and discussed. Section 5 concludes.

This paper highlights the importance of the assumptions used for aggregating skilled and unskilled labor for growth accounting exercises. It is shown that when aggregating the two types of labor to construct a single factor of production, human capital, the assumption about the substitution parameter used for the aggregation plays a crucial role for the conclusions about the importance of total factor productivity relative to that of availability of factors of production in accounting for cross-country income differences. While differences in TFP are relatively more important for the Hall and Jones (1999) aggregation with perfect substitutability between skilled and unskilled labor, the relative importance of differences in availability of factors of production increases when the value of the substitution parameter for the aggregate production function used by them is decreased. Given the importance of this parameter for the aggregate production function used by Hall and Jones, it becomes imperative to determine its value for undertaking the aggregation. To do so, I investigate the relationship between relative wages and relative endowments of skilled and unskilled labor using data from Caselli and Coleman (2006), and find that the two types of labor are not perfect substitutes in production. Moreover, and importantly, I find that there are systematic cross-country differences in the relationship between relative wages and relative endowments of the two types of labor. This suggests that the substitution parameter for the aggregation used by Hall and Jones varies systematically with GDP per worker across countries. Hence, this aggregation, which uses a common substitution parameter to aggregate skilled and unskilled labor to construct human capital, is found to be inconsistent with the data. The nested-CES class of aggregate production functions provide a generalization of the aggregation used by Hall and Jones (1999). These APFs allow skilled and unskilled labor to be used as separate factors rather than be aggregated into a single factor of production. Given that past empirical studies, investigating the role of capital-skill complementarity, have argued in favor of one variant of the nested-CES aggregate production function, I use this APF to undertake a growth accounting exercise. Comparing the results from growth accounting exercises using different aggregate production functions, I find that the relative importance of TFP in explaining differences in incomes across countries depends crucially on the APF used for the growth accounting exercise. While one APF implies that about 60% of the difference in GDP per worker can be explained by differences in factors of production, the preferred aggregation suggests that none of the differences can be attributed to such differences. Thus we require a consensus on the aggregate production function that should be used for evaluating the role of factors of production and TFP in explaining differences in GDP per worker across countries.39 The findings also call for a more general approach to understanding differences in incomes as well as use of technologies across countries. Since the aggregation of skilled and unskilled labor plays a crucial role in determining the sources of cross-country income differences, understanding the relationship between a country’s skill distribution and technology adoption becomes all the more important. Acemoglu and Zilibotti (1999) provide an example of such an approach where they explore the link between availability of skilled and unskilled labor and technology use based on the idea that technologies used by low income countries may be ‘inappropriate’ given their skill distribution. Acemoglu (2003) extends this line of reasoning to argue that the higher relative price of skilled to unskilled labor in low income countries could be a result of these countries using technologies that are complementary to skilled labor. High income countries are constantly innovating, and hence the relative wage of skilled to unskilled labor does not vary as much with the relative endowment of skilled and unskilled labor for these countries as it does for technology adopting, low income countries. This may provide a reason for the finding in this paper that skilled and unskilled labor are almost perfect substitutes in production for high income countries, but are imperfect substitutes for low income countries.