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AEB 6184 – Direct Estimation of Cost Functions

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

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  1. AEB 6184 – Direct Estimation of Cost Functions Elluminate 11

  2. Formulation of the Cobb-Douglas Cost Function • Starting with the basic Cobb-Douglas production function formulation • Forming the Lagrangian

  3. Solving for x1 in terms of x2 • Substituting this result into the production function and solving for x2

  4. Input demands and cost function

  5. Estimation • Defining a two equation system • Next, we construct an error matrix with 45 rows and 2 columns

  6. 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.

  7. Estimation using the KLEM dataset

  8. 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.

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