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Heteroskedasticity and Distributional Assumptions in the Censored Regression Model

  • James B. McDonald

    ()

    (Department of Economics, Brigham Young University)

  • Hieu Nguyen

    ()

    (Department of Economics, Brigham Young University)

Data censoring causes ordinary least squares estimators of linear models to be biased and inconsistent. The Tobit estimator yields consistent estimators in the presence of data censoring if the errors are normally distributed. However, non-normality or heteroskedasticity results in the Tobit estimators being inconsistent. Various estimators have been proposed for circumventing the normality assumption. Some of these estimators include censored least absolute deviations (CLAD), symmetrically censored least squares (SCLS), and partially adaptive estimators. CLAD and SCLS will be consistent in the presence of heteroskedasticity; however, SCLS performs poorly in the presence of asymmetric errors. This paper extends the partially adaptive estimation approach to accommodate possible heteroskedasticity as well as non-normality. A simulation study is used to investigate the estimators’ relative efficiency in these settings. The partially adaptive censored regression estimators have little efficiency loss for censored normal errors and appear to outperform the Tobit and semiparametric estimators for non-normal error distributions and be less sensitive to the presence of heteroskedasticity. An empirical example is considered which supports these results.

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Paper provided by Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory in its series BYU Macroeconomics and Computational Laboratory Working Paper Series with number 2012-09.

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Length: 24 pages
Date of creation: Aug 2012
Date of revision:
Handle: RePEc:byu:byumcl:201209
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  1. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
  2. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
  3. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
  4. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
  5. Butler, Richard J, et al, 1990. "Robust and Partially Adaptive Estimation of Regression Models," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 321-27, May.
  6. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
  7. Paarsch, Harry J., 1984. "A Monte Carlo comparison of estimators for censored regression models," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 197-213.
  8. McDonald, James B. & Xu, Yexiao J., 1996. "A comparison of semi-parametric and partially adaptive estimators of the censored regression model with possibly skewed and leptokurtic error distributions," Economics Letters, Elsevier, vol. 51(2), pages 153-159, May.
  9. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-60, November.
  10. Stephen R. Cosslett, 2004. "Efficient Semiparametric Estimation of Censored and Truncated Regressions via a Smoothed Self-Consistency Equation," Econometrica, Econometric Society, vol. 72(4), pages 1277-1293, 07.
  11. Greene, William H, 1981. "On the Asymptotic Bias of the Ordinary Least Squares Estimator of the Tobit Model," Econometrica, Econometric Society, vol. 49(2), pages 505-13, March.
  12. McDonald, James B., 1989. "Partially adaptive estimation of ARMA time series models," International Journal of Forecasting, Elsevier, vol. 5(2), pages 217-230.
  13. Newey, Whitney K., 1987. "Specification tests for distributional assumptions in the Tobit model," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 125-145.
  14. 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.
  15. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
  16. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(03), pages 428-457, December.
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