Identification and estimation of nonparametric panel data regressions with measurement error

Abstract

This paper provides a constructive argument for identification of nonparametric panel data models with measurement error in a continuous explanatory variable. The approach point identifies all structural elements of the model using only observations of the outcome and the mismeasured explanatory variable; no further external variables such as instruments are required. In the case of two time periods, restricting either the structural or the measurement error to be independent over time allows past explanatory variables or outcomes to serve as instruments. Time periods have to be linked through serial dependence in the latent explanatory variable, but the transition process is left nonparametric. The paper discusses the general identification result in the context of a nonlinear panel data regression model with additively separable fixed effects. It provides a nonparametric plug-in estimator, derives its uniform rate of convergence, and presents simulation evidence for good performance in finite samples. * First version: January 31, 2011. I am particularly indebted to Susanne Schennach, Chris Hansen, Alan Bester, and Azeem Shaikh, and thank them for their advice, encouragement and comments. I also thank Stephane Bonhomme, Federico Bugni, Jean-Marie Dufour, Kirill Evdokimov, Jean-Pierre Florens, Xavier D'Haultfoeuille, James Heckman, Roger Koenker, Arthur Lewbel, Elie Tamer and participants of various conferences and seminars for helpful discussions. Remaining errors are my own. I gratefully acknowledge financial support from the ESRC Centre for Microdata Methods and Practice at IFS (ES/I0334021/1).

Earnings and Consumption Dynamics: A Nonlinear Panel Data Framework

“…Then it is easy to see that y i1 , y i3 , and y i5 are conditionally independent given η i3 . As a result, identification arguments based on "Hidden Markov" structures (Hu and Schennach (2008), Wilhelm (2015)) can be applied.…”

“…Part (iii) is a high-level assumption. See Wilhelm (2015) for more primitive conditions. By Assumption S1(ii) we have, almost surely in y 1 ,…”

Microeconomic models with latent variables: applications of measurement error models in empirical industrial organization and labor economics

“…8 Therefore, it doesn't really matter which one of fX t 1 ; X t ; X t+1 g is treated as measurement or instrument for X t . Applications of nonparametric identi…cation of such a hidden Markov model or, in general, the 3-measurement model can be found in Hu, Kayaba, andShum (2013), Feng and, Wilhelm (2013), and Hu and Sasaki (2014), etc.…”

Earnings and consumption dynamics: a nonlinear panel data framework

“…33 C Technical Appendix C.1 Summary of the argument in Wilhelm (2012) We consider model (1)- (2) with T = 3. We omit i subscripts for conciseness.…”

“…Nonparametric identification can be established in our setup by building on a recent literature on nonlinear models with latent variables. Identification of the earnings process builds on Hu and Schennach (2008) and Wilhelm (2012). 5 Identification of the consumption rule relies on novel arguments, which extend standard instrumental-variables methods (as in Blundell et al, 2008, for example) to our nonparametric setup.…”