Lecture 08-2005 - Estimation of Production Functions Fixed Effects in Panel Data Lecture VIII Analysis of Covariance Looking at a representative

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Unformatted text preview: Estimation of Production Functions: Fixed Effects in Panel Data Lecture VIII Analysis of Covariance Looking at a representative regression model It is well known that ordinary least squares (OLS) regressions of y on x and z are best linear unbiased estimators (BLUE) of α, β, and γ * 1, 1, it it it it y x z u i N t T α β γ ′ ′ = + + + = = K K However, the results are corrupted if we do not observe z . Specifically if the covariance of x and z are correlated, then OLS estimates of the β are biased. However, if repeated observations of a group of individuals are available (i.e., panel or longitudinal data) they may us to get rid of the effect of z . For example if z it = z i (or the unobserved variable is the same for each individual across time), the effect of the unobserved variables can be removed by first-differencing the dependent and independent variables ( 29 ( 29 ( 29 , 1 , 1 , 1 , 1 it i t it i t it i t it i t y y x x z z u u β γ---- ′- =- +- +- , 1 it i t i z z z- = = ( 29 ( 29 , 1 , 1 , 1 1, 2, it i t it i t it i t y y x x u u i N t T β--- ′- =- +- = = L L Similarly if z it = z t (or the unobserved variables are the same for every individual at a any point in time) we can derive a consistent estimator by subtracting the mean of the dependent and independent variables for each individual ( 29 ( 29 ( 29 it i it i it i it i y y x x z z u u β γ- =- +- +- it i z z = ( 29 ( 29 1 1 1 1 1 1 it i it i it i T i it t T i it t T i it t y y x x u u y y T x x T u u T β = = = ′- =- +- = = = ∑ ∑ ∑...
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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 08-2005 - Estimation of Production Functions Fixed Effects in Panel Data Lecture VIII Analysis of Covariance Looking at a representative

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