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Estimating and testing a quantile regression model with interactive effects
Institution:1. Department of Economics, Stanford University, 579 Serra Mall, Stanford, CA 94305, United States;2. Department of Economics, University of Kentucky, 335A College of Business and Economics, KY 40506, United States;1. Department of Economics, National Chengchi University, Taipei 116, Taiwan;2. Department of Finance and CRETA, National Taiwan University, Taipei 106, Taiwan;1. Department of Economics, Duke University, Durham, NC, USA;2. Department of Economics, Northern Illinois University, DeKalb, IL, USA;3. Department of Economics, Harvard University, Cambridge, MA, USA;1. Department of Economics, MIT, 50 Memorial Drive, Cambridge, MA 02142, United States;2. Boston University, Department of Economics, 270 Bay State Road, Boston, MA 02215, United States;3. Department of Economics, Yale University, 37 Hillhouse Avenue, New Haven, CT 06520, United States;4. NBER, 1050 Massachusetts Avenue, Cambridge, MA 02138, United States
Abstract:This paper proposes a quantile regression estimator for a model with interactive effects potentially correlated with covariates. We provide conditions under which the estimator is asymptotically Gaussian and we investigate the finite sample performance of the method. An approach to testing the specification against a competing fixed effects specification is introduced. The paper presents an application to study the effect of class size and composition on educational attainment. The evidence suggests that while smaller classes are beneficial for low performers, larger classes are beneficial for high performers. The fixed effects specification is rejected in favor of the interactive effects specification.
Keywords:Quantile regression  Panel data  Interactive effects  Instrumental variables
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