Homework 3

Continuing from the previous Homework 2 on estimating the generalized production functions of Zellner and Revankar [1970], the Box-Cox functional form is given as:

Q^(θ) = β₁ + β₂K^(λ) + β₃L^(λ) + ε

Estimate and interpret the Box-Cox production function based on the estimate (variable) rate of returns to scale and elasticity of substitution, respectively.

Many classical functional forms are possible by setting the Box-Cox transformation parameters. For example, if θ, λ -> 0, then it is the Cobb-Douglas form. Formulate and test for the most appropriate functional forms for this study.

A particular case of interest is the following generalized production function:

ln(Q) + θQ = β₁ + β₂K^(λ) + β₃L^(λ) + ε

Estimate and interpret this model, and test λ -> 0 (i.e., generalized Cobb-Douglas).