Growth and slowdown of nations: what role for the elasticity of substitution?

Although the importance of the elasticity of substitution between capital and labor (σ) has long been recognized in several branches of economics, it has received too little attention in the growth literature. This paper aims to partly rectify this omission by exploring the growth potentials with σ as a yardstick and studying how different values of σ impact upon the balanced growth paths in theoretical model. When σ is high, the incremental capital is easily substituted for labor, resulting in a nearly equiproportionate increase in both factors. Under constant returns to scale, diminishing returns sets-in very slowly, and the marginal and average products of capital can remain sufficiently large so that output can grow indefinitely. The theoretical model is built upon the work of de La Grandville and Solow (2004) who show that perpetual growth is possible in the Solow (1956) model even without technological progress, if value of σ exceeds a critical value that is greater than unity ( cH σ ). I extend the model to show that output level, capital stock and consumption follow perpetual decline if σ is less than another critical value ( cL σ ) that lies between zero and unity. The critical values depend on saving, population growth and depreciation rates, and the initial share of capital in total output; hence each country has at most one critical value. I show that the above results also carry into in a model of endogenous saving, and analytically prove that the balanced growth path exists only if σ lies between two critical values- cL σ and cH σ . I calibrate the critical value of σ from the data for each country. These values are then compared to σˆ ’s estimated from country time series data. A number of countries, mainly from Africa, have ˆ cL σ <σ . Average per capita output growth in these countries is either negative or very low. Although many countries have cH σ indicating bright growth potential, none of them has ˆ σ sufficiently large (i.e., ˆ cH σ >σ ).