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Lecture 08-2005

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

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1 Estimation of Production Functions: Fixed Effects in Panel Data Lecture VIII I. Analysis of Covariance A. Looking at a representative regression model * 1, 1, it it it it y x z u i N t T α β γ = + + + = = K K Where it x and it z are 1 1 k × and 2 1 k × vectors of exogenous variables and * α , β and γ are estimated parameters, and it u is an independently and identically distributed (iid) error term with mean 0 and variance 2 u σ . 1. It is well known that ordinary least squares (OLS) regressions of it y on it x and it z are best linear unbiased estimators (BLUE) of * α , β , and γ . 2. However, the results are corrupted if we do not observe it z . Specifically if the covariance of it x and it z are correlated, then OLS estimates of the β are biased. 3. 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 it z . a. For example if it i z z = (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 ( ) ( ) ( ) , 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 = + + . Since , 1 it i t i z z z = = ( ) ( ) , 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 b. Similarly if it t z z = (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 ( ) ( ) ( ) it i it i it i it i y y x x z z u u β γ = + + Since it i z z = ( ) ( ) 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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AEB 6184–Production Economics Lecture VIII Professor Charles B. Moss
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Lecture 08-2005 - Estimation of Production Functions Fixed...

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