# Given a standard Cobb-Douglas production function, how to estimate the output elasticity of labour and capital by country?

Given a standard Cobb-Douglas production function: $$Y_t=(A_t L_t)^{\alpha} K_t^{1-\alpha}$$ Moreover, the production function has constant returns to scale: $$\alpha + (1-\alpha)=1$$

How to estimate the output elasticity of labour ($\alpha$) and the output elasticity of capital $(1-\alpha)$?

I would like to estimate the output elasticity of labour and capital for a specific group of countries (US, Germany, Korea, Japan) for my RBC model.

• Are you asking how to interpret the values of exponents or are you asking how to estimate the appropriate value of alpha for a given country? I suspect the later - just want to make sure.
– 123
Apr 24 '16 at 14:09
• This might be a naive approach but it should work: 1. linearize your function s.t. $$Y_t=(A_t L_t)^{\alpha} K_t^{1-\alpha}$$ becomes: $$ln(Y_t)=ln(A_t) \space +\alpha ln(L_t)\space+ \beta ln(K_t)$$ now run OLS regression and recover the coefficients $\alpha , \beta$
– 123
Apr 24 '16 at 14:20
• There's a chapter dedicated (Ch 9) to the estimation of production functions (not only Cobb-Douglas form) in Berndt's The Practice of Econometrics (1991). The approach suggested above by @123 is mentioned as a basic variant, but system estimation is probably a better way to go. Apr 24 '16 at 15:19
• I assumed the approach I gave would be a bit simple. Thanks for the reference @Graeme Walsh. I will check it out as well. I've never had a need to do such a thing.
– 123
Apr 24 '16 at 15:48
• Thanks for all your help and the book recommendation, too :) May 6 '16 at 6:48