Lecture 11-2005 - Stochastic Production Functions II:...

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Stochastic Production Functions II: Maximum Likelihood Lecture XI I. Estimating the Stochastic Production Function Using Maximum Likelihood A. Normal-Half Normal Model 1. Assumptions about Errors: a. ( ) 2 ~0 , iv vN σ . b. ( ) * , i uN 2 u , where * N denotes the nonnegative half-normal. c. and are independent of each other and the regressors i v i u 2. Distribution functions: a. The distribution function of follows the standard zero-mean normal distribution function v () 2 2 1 exp 2 2 v v v fv πσ ⎛⎞ =− ⎜⎟ ⎝⎠ b. The half-normal distribution is represented by 2 2 2 exp 2 2 u v u gu c. Assuming independence ( ) ( ) 22 2 ,e x p uv u v fuv fvgu 2 πσσ == d. Since vu ε = , or by definition of the composed error term 2 2 2 x p 2 u v u u fu πσ σ + e. Integrating out, we obtain the marginal distribution function for u (1) From Weinstein ( ) X X Y Y X x Y y μ = = x is distributed normal, while is distributed half- normal y 2 1 exp 2 2 1 0 x fx y f ya gy a F π ≥− = ⎡⎤ −− ⎣⎦ <−
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This note was uploaded on 07/15/2011 for the course AEB 6184 taught by Professor Staff during the Fall '09 term at University of Florida.

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Lecture 11-2005 - Stochastic Production Functions II:...

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