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Lecture 09-2005

# Lecture 09-2005 - Estimation of Production Functions Random...

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1 Estimation of Production Functions: Random Effects in Panel Data Lecture IX I. Basic Setup A. Regression analysis typically assumes that a large number of factors affect the value of the dependent variable, while some of the variables are measured directly in the model the remaining variables can be summarized by a random distribution: [] () it it it it it it it it it yx z Ez x z Ez α βγε αγ β ε =+ + + + + + 1. When “numerous observations” on individuals are observed over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods. 2. Going back to the panel specification * it it it it i t it v vu αβ αλ = ++ =++ We further assume that [ ] [ ] [ ] [][][] 0 iti t it ii t ti t EEE u E Eu Eu λ === == 2 if 0i f ij E σ αα =  =  2 if f ts E λλ = = 2 if , 0O t h e r w i s e u it js Euu = = = 0 i it t it it it Ex E u x ′′′ = The variance of it y on it x based on the assumption above is 2222 yu σσσ = These variances ( 2 , 2 , and 2 u ) are the components of the overall variance. Thus, this kind of model is typically referred to as a

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Lecture 09-2005 - Estimation of Production Functions Random...

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