Correlated Random Effects

Correlated Random Effects - CORRELATED RANDOM EFFECTS...

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Unformatted text preview: CORRELATED RANDOM EFFECTS MODELS WITH UNBALANCED PANELS Jeffrey M. Wooldridge Department of Economics Michigan State University East Lansing, MI 48824-1038 wooldri1@msu.edu July 2009 I presented an earlier version of this paper, called Nonlinear Correlated Random Effects Models with Unbalanced Panels, at the 15 th Conference on Panel Data, Bonn, Germany, July 3-5, 2009. I thank Simon Quinn for helpful comments. 1 Abstract : I propose some strategies for allowing unobserved heterogeneity to be correlated with observed covariates and sample selection for unbalanced panels. The methods are extensions of the Chamberlain-Mundlak approach for balanced panels. Even for nonlinear models, in many cases the estimators can be implemented using standard software. The framework suggests straightforward tests of correlation between heterogeneity and the covariates, as well as sample selection that is correlation with unobserved shocks while allowing selection to be correlated with the observed covariates and unobserved heterogeneity. 2 1 . Introduction Correlated random effects (CRE) approaches to nonlinear panel data models are popular with empirical researchers, partly because of their simplicity but also because recent research (for example, Blundell and Powell (2003), Altonji and Matzkin (2005), and Wooldridge (2005)) shows that quantities of interest usually called average marginal effects (AMEs) or average partial effects (APEs) are identified under nonparametric restrictions on the distribution of heterogeneity given the covariate process. (Exchangeability is one such restriction, but it is not the only one.) Wooldridge (2002) shows how the CRE approach applies to commonly used models, such as unobserved effects probit, tobit, and count models. Papke and Wooldridge (2008) propose simple CRE methods when the response variable is a fraction or proportion. The leading competitor to CRE approaches are so-called fixed effects (FE) methods, which, for the purposes of this paper, treat the heterogeneity as parameters to be estimated. (Perhaps a better characterization is that the FE approach studies the properties of the fixed population parameters and, more recently, average partial effects, when heterogeneity is handled via estimating separate parameters for each population unit.) As is well known, except in some very special cases, estimating unobserved heterogeneity for each unit in the sample generally suffer from the incidental parameters problem both in estimating population parameters and APEs. Some headway has been made in obtaining bias-corrected versions of fixed effects estimators for nonlinear models for example, Hahn and Newey (2004) and Fernandez-Val (2008). These methods are promising, but they currently have several practical shortcomings. First, the number of time periods needed for the bias adjustments to work well is often greater than is available in many applications. Second, an important point is that recent 3 bias adjustments include the assumptions of stationarity and weak dependence; in some cases,...
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Correlated Random Effects - CORRELATED RANDOM EFFECTS...

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