Linear Panel Models Slides

Linear Panel Models Slides - WNE 7/30/07 #2 Whats New in...

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What’s New in Econometrics? Lecture 2 Linear Panel Data Models Jeff Wooldridge NBER Summer Institute, 2007 1. Overview of the Basic Model 2. New Insights Into Old Estimators 3. Behavior of Estimators without Strict Exogeneity 4. IV Estimation under Sequential Exogeneity 5. Pseudo Panels from Pooled Cross Sections 1
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1 . Overview of the Basic Model Unless stated otherwise, the methods discussed in these slides are for the case with a large cross section and small time series. For a generic i in the population, y it t x it c i u it , t 1,. .., T , (1) where t is a separate time period intercept, x it is a 1 K vector of explanatory variables, c i is the time-constant unobserved effect, and the u it : t 1,. .., T are idiosyncratic errors. We view the c i as random draws along with the observed variables. An attractive assumption is contemporaneous exogeneity conditional on c i : E u it | x it , c i 0, t 1,. .., T . (2) 2
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This equation defines in the sense that under (1) and (2), E y it | x it , c i t x it c i , (3) so the j are partial effects holding c i fixed. Unfortunately, is not identified only under (2). If we add the strong assumption Cov x it , c i 0 , then is identified. Allow any correlation between x it and c i by assuming strict exogeneity conditional on c i : E u it | x i 1 , x i 2 ,..., x iT , c i 0, t 1,. .., T , (4) which can be expressed as E y it | x i , c i E y it | x it , c i t x it c i . (5) If x it : t 1,. .., T has suitable time variation, can be consistently estimated by fixed effects (FE) or first differencing (FD), or generalized least 3
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squares (GLS) or generalized method of moments (GMM) versions of them. Make inference fully robust to heteroksedasticity and serial dependence, even if use GLS. With large N and small T , there is little excuse not to compute “cluster” standard errors. Violation of strict exogeneity: always if x it contains lagged dependent variables, but also if changes in u it cause changes in x i , t 1 (“feedback effect”). Sequential exogeneity condition on c i : E u it | x i 1 , x i 2 ,..., x it , c i 0, t 1,. .., T (6) or, maintaining the linear model, E y it | x i 1 ,..., x it , c i E y it | x it , c i . (7) Allows for lagged dependent variables and other 4
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feedback. Generally, is identified under sequential exogeneity. (More later.) The key “random effects” assumption is E c i | x i E c i . (8) Pooled OLS or any GLS procedure, including the RE estimator, are consistent. Fully robust inference is available for both. It is useful to define two
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Linear Panel Models Slides - WNE 7/30/07 #2 Whats New in...

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