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Quantile Regression Model with Unknown Censoring Point

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Abstract

The paper introduces an estimator for the linear censored quantile regression model when the censoring point is an unknown function of a set of regressors. The objective function minimized is convex and the minimization problem is a linear programming problem, for which there is a global minimum. The suggested procedure applies also to the special case of a fixed known censoring point. Under fairly weak conditions the estimator is shown to have n-convergence rate and is asymptotically normal. In the special case of a fixed censoring point it is asymptotically equivalent to the estimator suggested by Powell (1984, 1986a). A Monte Carlo study performed shows that the suggested estimator has very desirable small sample properties. It precisely corrects for the bias induced by censoring, even when there is a large amount of censoring, and for relatively small sample sizes. The estimator outperforms that suggested by Powell in cases where both apply.

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  • Moshe Buchinsky & Jinyong Hahn, 1995. "Quantile Regression Model with Unknown Censoring Point," Cowles Foundation Discussion Papers 1096, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1096
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d10/d1096.pdf
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    1. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-1460, November.
    2. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    3. Chamberlain, G., 1991. "Quantile Regression, Censoring, And The Structure Of Wages," Harvard Institute of Economic Research Working Papers 1558, Harvard - Institute of Economic Research.
    4. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    5. Buchinsky, Moshe, 1995. "Estimating the asymptotic covariance matrix for quantile regression models a Monte Carlo study," Journal of Econometrics, Elsevier, vol. 68(2), pages 303-338, August.
    6. Nawata, Kazumitsu, 1990. "Robust estimation based on grouped-adjusted data in censored regression models," Journal of Econometrics, Elsevier, vol. 43(3), pages 337-362, March.
    7. James Tobin, 1956. "Estimation of Relationships for Limited Dependent Variables," Cowles Foundation Discussion Papers 3R, Cowles Foundation for Research in Economics, Yale University.
    8. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    9. Moon, Choon-Geol, 1989. "A Monte Carlo Comparison of Semiparametric Tobit Estimators," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(4), pages 361-382, Oct.-Dec..
    10. Honore, Bo E. & Powell, James L., 1994. "Pairwise difference estimators of censored and truncated regression models," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 241-278.
    11. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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    4. Roger White & Bedassa Tadesse, 2011. "International Migration and Economic Integration," Books, Edward Elgar Publishing, number 14318.
    5. Golan, Amos & Judge, George & Perloff, Jeffrey, 1997. "Estimation and inference with censored and ordered multinomial response data," Journal of Econometrics, Elsevier, vol. 79(1), pages 23-51, July.

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