Questions
(1) Estimate the regression model (E) using the OLS estimator and provide a summary report of the result (i.e., the estimated equation with the standard errors and/or t-ratios with other relevant statistics).
(2) Interpret each coefficient estimate and comment on its individual significance.
(3) Test if the model as a whole is significant using an F statistic.
It has been suggested that the group of big companies and the group of small companies may have different production technologies and hence different labour-demand functions. To implement this suggestion, generate a dummy variable Dt = 1 if the output (Q) of company t is greater than or equal to $110m and Dt = 0 otherwise.
(4) Using the dummy variable, D, test if the two groups (i.e., one group of the companies with Q ≥ $110m and the other group) have the same labour-demand function.
(5) Estimate the model that combines the labour-demand functions of the two groups (i.e., the model with the intercept and slope dummy-variable terms) using the OLS method and provide a summary report. Interpret each coefficient and comment on its significance.
(6) If the production technology exhibits the specific characteristic called "homotheticity", budget shares for input are independent of output at given input prices. Test if the production function for the big-company group exhibits this characteristic. (Use the model reported in the previous question.)
(7) Test for heteroscedasticity in the model reported in Question (5) using the Koenker version of the Breusch-Pagan test. If the test result indicates anything in your answer to Question (5) is wrong, correct the answer.
(8) Test if the variances of the error terms in the two groups' models are the same using the Goldfelt-Quandt test for heteroscedasticity.
(9) Re-estimate the model in Question (5) using the WLS method, assuming that the variance of the random error term, V(ut) = σ2 t, is given by ln σ2t = α1 + α2 lnQt.
Provide a summary report of the estimation result and compare it with the OLS estimation result including possible reasons for significant differences, if any.
Download:- Regression model.xlsx