<p>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:
$$\alpha + (1-\alpha)=1$$</p>

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

<p>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.</p>

CC BY-SA 3.0
2016-04-24T14:09:10.540Z
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
CC BY-SA 3.0
2016-04-24T14:20:17.913Z
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
CC BY-SA 3.0
2016-04-24T15:19:33.103Z
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.
Graeme Walsh
CC BY-SA 3.0
2016-04-24T15:48:08.737Z
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
CC BY-SA 3.0
2016-05-06T06:48:23.653Z
Thanks for all your help and the book recommendation, too :)
Übel Yildmar
<macroeconomics><cobb-douglas><rbc>
Given a standard Cobb-Douglas production function, how to estimate the output elasticity of labour and capital by country?
Übel Yildmar
# Given a standard Cobb-Douglas production function, how to estimate the output elasticity of labour and capital by country?

(Asked by: username_0 on 2016-04-24)

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.

**Tags:** macroeconomics, cobb-douglas, rbc

> **Comments:**
> **username_1**: 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.  
> **username_1**: 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 $\alpha , \beta$  
> **username_2**: 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 @username_1 is mentioned as a basic variant, but system estimation is probably a better way to go.  
> **username_1**: I assumed the approach I gave would be a bit simple. Thanks for the reference @username_2. I will check it out as well. I've never had a need to do such a thing.  
> **username_0**: Thanks for all your help and the book recommendation, too :)  

---

## 0 answers

