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Lecture 08-2005

# Lecture 08-2005 - Estimation of Production Functions Fixed...

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Estimation of Production Functions: Fixed Effects in Panel Data Lecture VIII

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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 .

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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

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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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