Linear Panel Models Lecture

Linear Panel Models Lecture - Imbens/Wooldridge, Lecture...

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Imbens/Wooldridge, Lecture Notes 2, Summer ’07 What s New in Econometrics ? NBER , Summer 2007 Lecture 2 , Monday , July 30th , 11 . 00 - 12 . 30 am Linear Panel Data Models These notes cover some recent topics in linear panel data models. They begin with a “modern” treatment of the basic linear model, and then consider some embellishments, such as random slopes and time-varying factor loads. In addition, fully robust tests for correlated random effects, lack of strict exogeneity, and contemporaneous endogeneity are presented. Section 4 considers estimation of models without strictly exogenous regressors, and Section 5 presents a unified framework for analyzing pseudo panels (constructed from repeated cross sections). 1 . Quick Overview of the Basic Model Most of these notes are concerned with an unobserved effects model defined for a large population. Therefore, we assume random sampling in the cross section dimension. Unless stated otherwise, the asymptotic results are for a fixed number of time periods, T , with the number of cross section observations, N , getting large. For some of what we do, it is critical to distinguish the underlying population model of interest and the sampling scheme that generates data that we can use to estimate the population parameters. The standard model can be written, for a generic i in the population, as y it t x it c i u it , t 1,. .., T , (1.1) where t is a separate time period intercept (almost always a good idea), x it is a 1 K vector of explanatory variables, c i is the time-constant unobserved effect, and the u it : t T are idiosyncratic errors. Thanks to Mundlak (1978) and Chamberlain (1982), we view the c i as random draws along with the observed variables. Then, one of the key issues is whether c i is correlated with elements of x it . It probably makes more sense to drop the i subscript in (1.1), which would emphasize that the equation holds for an entire population. But (1.1) is useful to emphasizing which factors change only across t , which change only change across i , and which change across i and t .It is sometimes convenient to subsume the time dummies in x it . Ruling out correlation (for now) between u it and x it , a sensible assumption is contemporaneous exogeneity conditional on c i : E u it | x it , c i 0, t T . (1.2) This equation really defines in the sense that under (1.1) and (1.2), 1
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Imbens/Wooldridge, Lecture Notes 2, Summer ’07 E y it | x it , c i t x it c i , (1.3) so the j are partial effects holding fixed the unobserved heterogeneity (and covariates other than x tj ). As is now well known, is not identified only under (1.2). Of course, if we added Cov x it , c i 0 for any t , then is identified and can be consistently estimated by a cross section regression using period t . But usually the whole point is to allow the unobserved effect to be correlated with time-varying x it .
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Linear Panel Models Lecture - Imbens/Wooldridge, Lecture...

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