Although the importance of the elasticity of substitution between capital and labor (σ) has long been recognized in several branches of economics, it has not received enough attention in the growth literature. de La Grandville (1989) showed theoretically that at any stage of an economy's development, the growth rate of income per capita is increasing with σ. The higher is σ, the greater the similarity between capital and labor in the production function, and thus diminishing returns set in very slowly. To the best of our knowledge, this is the first paper that tests the hypothesis that growth rate is increasing with the value of σ at the cross-country level. We estimate σ for 90 countries from direct estimation of the normalized CES production function and then include these estimators as an explanatory variable in cross-country growth regression. We investigate the sign and significance of the coefficient of σ conditioning on country characteristics, initial conditions, and a set of policy variables. After accounting for endogeneity and the fact that σ is a “generated” regressor, we find strong support for the hypothesis. The result is robust to both Leamer's (1983) extreme value analysis and Bayesian model averaging. About a fifth to a quarter of the growth rate differential between East Asia and Sub-Saharan Africa can be explained by σ alone.
The elasticity of substitution between capital and labor (σ) is a second-order parameter of the production function but has a first-order effect on economic growth. Although the importance of this elasticity has long been recognized in several branches of economics, it has received very little attention in the growth literature. de La Grandville (1989) was the first to systematically explore the relationship between σ and economic growth. He showed theoretically that at any stage of an economy's development, the growth rate of income per capita is an increasing function of σ. 1 Intuitively, the mechanism for this hypothesis is the following: for an increase in σ, the incremental capital is more easily substituted for labor, thus leading to a more equiproportionate increase in both factors; consequently, diminishing returns to capital set in very slowly. In short, a larger σ allows an economy to rapidly accumulate capital without substantially lowering its marginal product. This hypothesis readily extends to understanding the differential growth performances among countries. If two countries have different values of σ but otherwise share the same initial conditions, such as the capital–labor ratio, and the population growth and savings rates, then the country with the larger value of σ will experience a higher growth rate. To the best of our knowledge, ours is the first paper that tests the hypothesis of the positive effect of σ on the growth rate at the cross-country level. 2
The hypothesis is tested in a Barro-type cross-country growth regression framework that regresses the growth rate of per capita real GDP on σ and a set of variables related to growth. In the first step, σ is obtained for 90 countries by estimating the normalized CES production function for each country separately using respective country time series. These estimated values of σ are then included in a cross-country growth regression in the second step, and the sign and significance of the coefficient of σ are investigated after controlling for other explanatory variables. Since σ is a “generated” regressor, the OLS estimator of the variance of the coefficient of σ in the second-step cross-country regression is inconsistent, and the asymptotic t-statistic overstates the true value. For correct inference, the standard error of the coefficient of σ is adjusted by the correction proposed by Murphy and Topel (1985). However, it is not known that the Murphy–Topel (M–T) correction is appropriate in the presence of endogenous regressors; therefore, the second-step equation is also estimated by 2SLS, an alternative to the M–T correction, by instrumenting both σ and other endogenous variables. The instruments for σ are the percentage of union workers and the share of general government consumption in GDP, which is a proxy for inclination to socialist ideas. The relevance and validity of the instruments are discussed in detail in Section 3.2. We also employ an alternation identification strategy proposed by Lewbel (2012) that does not rely on exclusion restrictions but exploits the heteroskedasticity for identification.
After controlling for country characteristics, initial conditions, and a set of policy variables, we find a positive and significant coefficient of σ that indicates strong support for the hypothesis. The result is robust in a variety of ways including both Leamer's (1983) extreme value analysis and Bayesian model averaging. Finally, σ can explain about a fifth to a quarter of the growth rate differential between East Asia and Sub-Saharan Africa.
The rest of the paper proceeds as follows. Section 2 discusses the importance of σ in economic growth. Section 3 discusses the analytical framework and econometric issues associated with testing the hypothesis. The data set is discussed in Section 4. Section 5 discusses estimation and summary statistics of the estimated values of σ. The results are presented in Section 6. Finally, Section 7 concludes.
Although there are some recent theoretical advances on the importance of σ in economic growth, empirical research is scant. This paper finds strong support for the hypothesis of the positive effect of σ on the growth rate at the cross-country level. The results are robust in a variety of ways including the extreme value analysis and Bayesian model averaging. We find that σ can explain about a fifth to a quarter of the growth rate differential between East Asia and Sub-Saharan Africa. In addition, values of σ for the countries substantially depart from unity. It is suggested that both theoretical and empirical research on economic growth should pay more attention to the role of this neglected parameter, and reconsider the usefulness of the Cobb–Douglas production function in growth theory.
