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A quantile correlated random coefficients panel data model


  • 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)


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 v 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 v 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. Supplement for CWP34/16

Suggested Citation

  • Bryan S. Graham & Jinyong Hahn & Alexandre Poirier & James L. Powell, 2016. "A quantile correlated random coefficients panel data model," CeMMAP working papers CWP34/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:34/16

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    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Antonio F. Galvao & Jiaying Gu & Stanislav Volgushev, 2018. "On the Unbiased Asymptotic Normality of Quantile Regression with Fixed Effects," Papers 1807.11863,
    2. Patrick Kline & Raffaele Saggio & Mikkel S{o}lvsten, 2018. "Leave-out estimation of variance components," Papers 1806.01494,, revised Aug 2019.

    More about this item


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

    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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