Labour-augmenting technical change data for alternative elasticities of substitution, growth, slowdown, and distribution dynamics

We solve the standard production function with constant elasticity of substitution (CES) for its labour augmenting technology term. We make capital stock data and insert them together with data from Penn World Tables (PWT9.1). This provides labour augmenting technology levels and growth rates for alternative elasticities of substitution for 70 countries, 1950-2017. The percentage growth rates of labour-augmenting technical change (LATC) are shown to fall over time (productivity slowdown) for all elasticity values in a panel data analysis. They converge to a panel average of 2.67% and 1% depending on the inclusion of human capital and the elasticity of substitution assumed. The standard growth result of a GDP growth rate equal to that of LATC and labour input holds only for LATC based on low elasticities of substitution indicating that the economies are not in steady-states. The correlation of LATC growth rates with total factor productivity growth from PWT9.1 is strongest (0.893) for LATC data based on an elasticity of substitution of 0.8. Matching the labour/capital share ratios from CES functions with those of PWT9.1 reveals a range of elasticities of substitution for each country, mostly between 0.8 and 1.2 or somewhat lower for developing countries. If the MPL-to-wage ratio is 1.6, the elasticities of substitution vary around 0.8. Using the human-capital corrected LATC growth with CES = 0.8, 13 of 69 countries have a productivity slowdown defined as growth rate below mean in the long run; the USA is not among them indicating that the US productivity slowdown is mainly one of human capital. Dynamics of coefficient of variation and kernel density distributions for LATC growth rates shows that there is neither technological convergence nor divergence.