Homework 4

Generalized Production Function Revisited

Continuing from the previous Homework 2, we recall that the generalized Cobb-Douglas (GCD) functional form is written as:

ln(Q) + θQ = β₁ + β₂ln(K) + β₃ln(L) + ε

In addition to the maximum likelihood method, the model could be estimated using OLS, IV or 2SLS, and GMM methods. However, OLS is biased because Q and ln(Q) are endogenous as they are correlated with the model error e. For IV and GMM estimations, the instrumental variables include predetermined regressors: constant, ln(K), ln(L), K, L, and possibly their interactions.

Formulate and estimate the above generalized Cobb-Douglas functional form using OLS, IV, and GMM methods. How the problem of heteroscedasticity is handled?

Compare and interpret the GMM estimators (in terms of factor elasticities) with the maximum likelihood estimators obtained from the previous homework.