Quantile Regression with Panel Data

56 Pages Posted: 23 Mar 2015 Last revised: 22 Jun 2024

See all articles by Bryan S. Graham

Bryan S. Graham

University of California, Berkeley - Department of Economics; National Bureau of Economic Research (NBER)

Jinyong Hahn

University of California, Los Angeles

Alexandre Poirier

Georgetown University - Department of Economics

James L. Powell

University of California, Berkeley

Date Written: March 2015

Abstract

We propose a generalization of the linear quantile regression model to accommodate possibilities afforded by panel data. Specifically, we extend the correlated random coefficients representation of linear quantile regression (e.g., Koenker, 2005; Section 2.6). We show that panel data allows the econometrician to (i) introduce dependence between the regressors and the random coefficients and (ii) weaken the assumption of comonotonicity across them (i.e., to enrich the structure of allowable dependence between different coefficients). We adopt a “fixed effects” approach, leaving any dependence between the regressors and the random coefficients unmodelled. We motivate different notions of quantile partial effects in our model and study their identification. For the case of discretely-valued covariates we present analog estimators and characterize their large sample properties. When the number of time periods (T) exceeds the number of random coefficients (P), identification is regular, and our estimates are √N-consistent. When T=P, our identification results make special use of the subpopulation of stayers – units whose regressor values change little over time – in a way which builds on the approach of Graham and Powell (2012). In this just-identified case we study asymptotic sequences which allow the frequency of stayers in the population to shrink with the sample size. One purpose of these “discrete bandwidth asymptotics” is to approximate settings where covariates are continuously-valued and, as such, there is only an infinitesimal fraction of exact stayers, while keeping the convenience of an analysis based on discrete covariates. When the mass of stayers shrinks with N, identification is irregular and our estimates converge at a slower than √N rate, but continue to have limiting normal distributions. We apply our methods to study the effects of collective bargaining coverage on earnings using the National Longitudinal Survey of Youth 1979 (NLSY79). Consistent with prior work (e.g., Chamberlain, 1982; Vella and Verbeek, 1998), we find that using panel data to control for unobserved worker heteroegeneity results in sharply lower estimates of union wage premia. We estimate a median union wage premium of about 9 percent, but with, in a more novel finding, substantial heterogeneity across workers. The 0.1 quantile of union effects is insignificantly different from zero, whereas the 0.9 quantile effect is of over 30 percent. Our empirical analysis further suggests that, on net, unions have an equalizing effect on the distribution of wages.

Suggested Citation

Graham, Bryan S. and Hahn, Jinyong and Poirier, Alexandre and Powell, James L., Quantile Regression with Panel Data (March 2015). NBER Working Paper No. w21034, Available at SSRN: https://ssrn.com/abstract=2583583

Bryan S. Graham (Contact Author)

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Jinyong Hahn

University of California, Los Angeles ( email )

405 Hilgard Avenue
Box 951361
Los Angeles, CA 90095-1361
United States

Alexandre Poirier

Georgetown University - Department of Economics ( email )

Washington, DC 20057
United States

James L. Powell

University of California, Berkeley

310 Barrows Hall
Berkeley, CA 94720
United States

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