Lecture 11-2005

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

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Unformatted text preview: Stochastic Production Functions II: Maximum Likelihood Lecture XI Normal-Half Normal Model Assumptions about Errors: ( 29 2 ~ 0, i v v N σ ( 29 * 2 ~ 0, i u u N σ and independent i i v u Distribution functions: The distribution function of v follows the standard zero-mean normal distribution function ( 29 2 2 1 exp 2 2 v v v f v σ πσ =- ÷ The half-normal distribution is represented by ( 29 2 2 2 exp 2 2 u v u g u σ πσ =- ÷ Assuming independence ( 29 ( 29 ( 29 2 2 2 2 2 , exp 2 2 2 u v u v u v f u v f v g u πσ σ σ σ = =-- ÷ Since ε = v - u , or by definition of the composed error term ( 29 ( 29 2 2 2 2 2 , exp 2 2 2 u v u v u u f u ε ε πσ σ σ σ + ÷ =-- ÷ Integrating u out, we obtain the marginal distribution function for ε From Weinstein ( 29 ( 29 X X Y Y X x Y y μ σ μ σ- =- = x...
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Lecture 11-2005 - Stochastic Production Functions II...

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