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Quantile regression with panel data

Author

Listed:
  • Bryan S. Graham

    (Institute for Fiscal Studies and University of California, Berkeley)

  • Jinyong Hahn

    (Institute for Fiscal Studies)

  • Alexandre Poirier

    () (Institute for Fiscal Studies and University of Iowa)

  • James L. Powell

    () (Institute for Fiscal Studies and University of California, Berkeley)

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 vN - 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 vN 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 heterogeneity 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. Supporting material is available in a supplementary appendix here.

Suggested Citation

  • Bryan S. Graham & Jinyong Hahn & Alexandre Poirier & James L. Powell, 2015. "Quantile regression with panel data," CeMMAP working papers CWP12/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:12/15
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    References listed on IDEAS

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    8. Francis Vella & Marno Verbeek, 1998. "Whose wages do unions raise? A dynamic model of unionism and wage rate determination for young men," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(2), pages 163-183.
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    Citations

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    Cited by:

    1. Jorge E. Galán, 2020. "The benefits are at the tail: uncovering the impact of macroprudential policy on growth-at-risk," Working Papers 2007, Banco de España;Working Papers Homepage.
    2. Victor Chernozhukov & Iv'an Fern'andez-Val & Martin Weidner, 2018. "Network and Panel Quantile Effects Via Distribution Regression," Papers 1803.08154, arXiv.org, revised Jun 2020.
    3. Manuel Arellano & Stéphane Bonhomme, 2016. "Nonlinear panel data estimation via quantile regressions," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 61-94, October.
    4. Frantisek Cech & Jozef Barunik, 2017. "Measurement of Common Risk Factors: A Panel Quantile Regression Model for Returns," Working Papers IES 2017/20, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Sep 2017.
    5. Callaway, Brantly & Li, Tong & Oka, Tatsushi, 2018. "Quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods," Journal of Econometrics, Elsevier, vol. 206(2), pages 395-413.
    6. Pietro Santoleri, 2019. "Innovation and job creation in (high-growth) new firms," LEM Papers Series 2019/31, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.

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    More about this item

    Keywords

    Panel Data; Quantile Regression; Fixed Effects; Difference-in-Differences; Union Wage Premium; Discrete Bandwidth Asymptotics; Decomposition Analysis;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
    • J51 - Labor and Demographic Economics - - Labor-Management Relations, Trade Unions, and Collective Bargaining - - - Trade Unions: Objectives, Structure, and Effects

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