lect20_06apr24 - Imbens, Lecture Notes 20, ARE213 Spring...

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Imbens, Lecture Notes 20, ARE213 Spring ’06 1 ARE213 Econometrics Spring 2006 UC Berkeley Department of Agricultural and Resource Economics Panel Data I: Random Effects Panel or longitudinal data sets consists of repeated observations for the same units, Frms, individuals or other economic agents. Typically the observations are at different points in time. Let Y it denote the outcome for unit i in period t , and X it a vector of explanatory variables. The index i denotes the unit and runs from 1 to N , and the index t denotes time and runs from 1 to T . Typically T is relatively small (as small as two), and N is relatively large. As a result, when we try to approximate sampling distributions for estimators, we typically approximate them using large N asymptotics, keeping T Fxed. (Recently there has been some work looking at asymptotic approximations where T/N α for some 0 <α< 1.) Here we will mainly look at balanced panels, where T is the same for each unit. An unbalanced panel has potentially different numbers of observations for each unit. This may arise because of units dropping out of the sample, or more directly for Frms going out of business. The key issue with panel data is that Y it and Y is tend to be correlated even conditional on the covariates X it and X is . Let us look at this in a linear model setting: Y it = X ± it β + c i + ε it . The presence of c i , the unobserved individual effect, creates this correlation even with the ε it uncorrelated over time and units. The two main approaches to dealing with such issues are fxed effects and random effects . The labels are somewhat of a misnomer. These effects are not Fxed or random. They are both unobserved , individual-specifc , time-invariant quantities that can be viewed as random variables. The key distinction is whether we allow for dependence between the
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This note was uploaded on 08/01/2008 for the course ARE 213 taught by Professor Imbens during the Spring '06 term at University of California, Berkeley.

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lect20_06apr24 - Imbens, Lecture Notes 20, ARE213 Spring...

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