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Unformatted text preview: Quantile Regression Estimation of a Model with Interactive Effects * Matthew Harding and Carlos Lamarche June 24, 2010 Abstract This paper proposes a quantile regression estimator for a panel data model with interactive effects potentially correlated with the independent variables. We provide conditions under which the slope parameter estimator is asymptotically Gaussian. Monte Carlo studies are carried out to investigate the finite sample performance of the proposed method in comparison with other candidate methods. The paper presents an empirical application of the method to study the effect of class size and class composition on educational attainment. The findings suggest that (i) a change in the gender composition of a class impacts differently low- and high-performing students; (ii) while smaller classes are beneficial for low performers, larger classes are beneficial for high performers; (iii) reductions in class size do not seem to impact mean and median student performance. JEL: C23, C33 Keywords: Quantile Regression; Panel data; Interactive effects; Instrumental variables. * We are grateful to seminar participants at Stanford University and the University of Oklahoma for useful comments, and to Michele Pellizzari for providing the data for the empirical section. The R software for the method introduced in this paper (as well as the other methods discussed in this paper) are available upon request and for download from the authors websites. Corresponding author: Department of Economics, Stanford University, 579 Serra Mall, Stanford, CA 94305; Phone: (650) 723-4116; Fax: (650) 725-5702; Email: firstname.lastname@example.org Department of Economics, University of Oklahoma, 729 Elm Avenue, Norman, OK 73019; Phone: (405) 325-5857; Email: email@example.com 2 1. Introduction Panel data models which account for the confounding effect of unobservable individual effects have become the models of choice in many applied areas of economics from microeconomics to finance. Recent papers have focused on relaxing the traditional fixed effects framework by allowing for multiple interactive effects (Bai, 2009; Pesaran, 2006). The natural extension of the classical panel data models with N cross-sectional units and T time periods (Hsiao 2003, Baltagi 2008) is thus y it = x it + i f t + u it , where i is an r 1 vector of factor loadings and f t corresponds to the r common time-varying factors, and where both i and f t are latent variables. Although this extension substantially increases the flexibility of controlling for unobserved heterogeneity, the existing estimation approaches are designed for Gaussian models and do not offer the possibility of estimating heterogeneous covariate effects, which may be of interest to applied researchers. For example, Bandiera, Larcinese, and Rasul (2010) argue for the use of heterogeneous effects in the design of educational policies....
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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.
- Fall '08