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AEB 6184 – Direct Estimation of Cost Functions. Elluminate 11. Formulation of the Cobb-Douglas Cost Function. Starting with the basic Cobb-Douglas production function formulation Forming the Lagrangian. Solving for x 1 in terms of x 2
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AEB 6184 – Direct Estimation of Cost Functions Elluminate 11
Formulation of the Cobb-Douglas Cost Function • Starting with the basic Cobb-Douglas production function formulation • Forming the Lagrangian
Solving for x1 in terms of x2 • Substituting this result into the production function and solving for x2
Estimation • Defining a two equation system • Next, we construct an error matrix with 45 rows and 2 columns
Maximum likelihood estimation is then • The variance matrix for the estimates is given by the Hessian matrix at the optimal value by the Cramer-Rao lower bound.
Exercise • Extend the Cobb-Douglas function two four inputs and refit the KLEM data. • Implement the same estimation for the Constant Elasticity of Substitution function.