* Testing OLS Model for Cobb-Douglas Production Function
*
* Keywords:
*     regression, multiple, ols, log, f-test, cobb-douglas, production
*
* Description:
*     We illustrate how to estimate an OLS Regression Models for Cobb-Douglas
*     Production Function and test an imposed restriction with an F-test
*
* Author(s):
*     Skif Pankov
*
* Source:
*    Damodar N. Gujarati and Dawn C. Porter, Basic Econometrics - 5th Edition
*    McGraw-Hill International Edition, Chapter 8, Example 8.3 (page 250)
*
sample 1 20

* Reading the datafile and naming the variables
read (data_8.3.shd) gdp emp cap

* Generating logs of variables
genr lngdp = log(gdp)
genr lnemp = log(emp)
genr lncap = log(cap)

* Running OLS regression of lngdp on lnemp and lncap, specifying that it is a
* log-log regression and including residual summary statistics into output
ols lngdp lnemp lncap / loglog rstat 

* Testing the restriction lnemp + lncap = 1 (constant returns to scale)
test lnemp + lncap = 1 
end

stop

* Note: 
*     The value of F-statistic will be greater that the book value by 0.02 - 
*     this is because SHAZAM uses more accurate values of sums of squared 
*     errors