Average and Quantile Effects in Nonseparable Panel Models

Authors

  • Victor Chernozhukov,

    1. Dept. of Economics, Massachusetts Institute of Technology, Cambridge, MA 02142, U.S.A.; vchern@mit.edu
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  • Iván Fernández-Val,

    1. Dept. of Economics, Boston University, Boston, MA 02215, U.S.A.; ivanf@bu.edu
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  • Jinyong Hahn,

    1. Dept. of Economics, University of California, Los Angeles, Los Angeles, CA 90095, U.S.A.; hahn@econ.ucla.edu
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  • Whitney Newey

    1. Dept. of Economics, Massachusetts Institute of Technology, Cambridge, MA 02142, U.S.A.; wnewey@mit.edu
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    • We thank J. Angrist, G. Chamberlain, D. Chetverikov, B. Frandsen, B. Graham, J. Hausman, and many seminar participants for comments. Brad Larsen and Seongyeon Chang provided capable research assistance. Parts of this paper were given at the 2007 CEMMAP Microeconometrics: Measurement Matters Conference, the Shanghai Lecture of the 2010 World Congress of the Econometric Society, and conferences in between. We gratefully acknowledge research support from the NSF.


Abstract

Nonseparable panel models are important in a variety of economic settings, including discrete choice. This paper gives identification and estimation results for nonseparable models under time-homogeneity conditions that are like “time is randomly assigned” or “time is an instrument.” Partial-identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with time effects. It is shown that the usual, linear, fixed-effects estimator is not a consistent estimator of the identified average effect, and a consistent estimator is given. A simple estimator of identified quantile treatment effects is given, providing a solution to the important problem of estimating quantile treatment effects from panel data. Bounds for overall effects in static and dynamic models are given. The dynamic bounds provide a partial-identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity. The impact of T, the number of time periods, is shown by deriving shrinkage rates for the identified set as T grows. We also consider semiparametric, discrete-choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds. Computationally convenient methods for semiparametric models are presented. We propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples. We give empirical illustrations.

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