Lecture08-2011

# Lecture08-2011 - Outline Analysis of Covariance Pooling...

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Outline Analysis of Covariance Pooling Assumptions Estimation of Production Functions: Fixed Eﬀects in Panel Data : Lecture VIII Charles B. Moss 1 1 University of Florida September 20, 2011 Charles B. Moss Estimation of Production Functions: Fixed Eﬀects in Panel Dat a

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Outline Analysis of Covariance Pooling Assumptions 1 Analysis of Covariance Individual Eﬀects Time Eﬀects Modiﬁed Ordinary Least Squares 2 Pooling Assumptions Empirical Procedure Computations Corn Estimates Diﬀerent Intercepts - Same Slope Same Slopes - Same Intercept Testing for Pooling Dummy Variable Formulation Sweeping the Data Charles B. Moss Estimation of Production Functions: Fixed Eﬀects in Panel Dat a
Outline Analysis of Covariance Pooling Assumptions Individual Eﬀects Time Eﬀects Modiﬁed Ordinary Least Squares Analysis of Covariance Looking at a representative regression model y it = α * + β 0 x it + γ 0 z it + u it i = 1 , ··· N t = 1 , T (1) 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 . 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 . Charles B. Moss Estimation of Production Functions: Fixed Eﬀects in Panel Dat a

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Outline Analysis of Covariance Pooling Assumptions Individual Eﬀects Time Eﬀects Modiﬁed Ordinary Least Squares Individual Eﬀects 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 y it - y i , t - 1 = β 0 ( x it - x i , t - 1 ) + γ 0 ( z it - z i , t - 1 ) + ( u it - u i , t - 1 ) (2) Since z it = z i , t - 1 = z i y it - y i , t - 1 = β 0 ( x it - x i , t - 1 ) + ( u it - u i , t - 1 ) i = 1 , ··· N t = 2 , T (3) Charles B. Moss Estimation of Production Functions: Fixed Eﬀects in Panel Dat a
Outline Analysis of Covariance Pooling Assumptions Individual Eﬀects Time Eﬀects Modiﬁed Ordinary Least Squares Time Eﬀects 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 y it - ¯ y i = β 0 ( x it - ¯ x i ) + γ 0 ( z it - ¯ z i ) + ( u it - ¯ u i ) (4) Again z it = ¯ z i y it - ¯ y i = β 0 ( x it - ¯ x i ) + ( u it - ¯ u i ) ¯ y i = 1 T T X t =1 y it ¯ x i = 1 T T X t =1 x it ¯ u i = 1 T T X t =1 u it (5) Charles B. Moss Estimation of Production Functions: Fixed Eﬀects in Panel Dat a

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Outline Analysis of Covariance Pooling Assumptions Individual Eﬀects Time Eﬀects
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Lecture08-2011 - Outline Analysis of Covariance Pooling...

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