* OLS Model for Cobb-Douglas Production Function * * Keywords: * regression, ols, log, cobb-douglas, production function, f-test * * Description: * We illustrate how to estimate an OLS Model for Cobb-Douglas Production * Function and test restrictions on its coefficients using an F-test * * Author(s): * Noel Roy * Skif Pankov * * Source: * William H. Greene, Econometric Analysis - 7th Edition * Pearson International Edition, Chapter 5, Example 5.4 (page 164) * sample 1 27 * Reading the datafile and retrieving names of the variables read (TableF5-3.shd) / names * Generating logs of data genr lny=log(valueadd) genr lnl=log(labour) genr lnk=log(capital) * Running an OLS regression of lny on lnl and lnk (Cobb-Douglas production * function) ols lny lnl lnk / pcov * Testing the null hypothesis that the production function exhibits constant * returns to scale - that lnl+lnk = 1 test lnl+lnk=1 * Estimate the "translog" model using ols genr ln2l=lnl**2/2 genr ln2k=lnk**2/2 genr lnllnk=lnl*lnk ols lny lnl lnk ln2l ln2k lnllnk / pcov * Testing the null hypothesis for the cobb-douglas model, which implies * that the coefficients on the additional variables in the unrestricted * model are jointly equal to zero test test ln2l=0 test ln2k=0 test lnllnk=0 end * Testing the null hypothesis that the translog production function * exhibits constant returns to scale test test lnk+lnl=1 test ln2l+ln2k+2*lnllnk=0 end * Estimaitng the Cobb-Douglas production function with the restriction * beta2=1 by generating variables genr lnyl = lny-lnl ols lnyl lnk * Estimaitng the Cobb-Douglas production function with the restriction * beta2=1 by imposing the linear restriction directly ols lny lnl lnk / restrict restrict lnl=1 end * Calculating the capital elasticity of output, and its standard error by * finding the mean values for lnl and lnk (OLS estimates) and then * testing the value of the function that defines the capital elasticity * ?stat lnl /mean=lnlbar ?stat lnk /mean=lnkbar ?ols lny lnl lnk ln2l ln2k lnllnk test lnk+ln2k*lnkbar+lnllnk*lnlbar stop