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A simple consistent test of conditional symmetry in symmetrically trimmed tobit models

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  • Tao Chen

    ()
    (Department of Economics, University of Waterloo, Ontario, Canada)

  • Gautam Tripathi

    ()
    (CREA, Universit├ę de Luxembourg)

Abstract

We propose a "weighted and sample-size adjusted" Kolmogorov-Smirnov type statistic to test the assumption of conditional symmetry maintained in the symmetrically trimmed least-squares (STLS) approach of Powell (1986b), which is widely used to estimate censored or truncated regression models without making distributional assumptions. The statistic proposed here is consistent and computationally easy to implement because, unlike traditional Kolmogorov-Smirnov statistics, it is not optimized over an uncountable set. Moreover, it does not require any nonparametric smoothing, although we test the validity of a conditional feature. We also propose a bootstrap procedure to obtain the p-values and critical values that are required to carry out the test in practical applications. Results from a simulation study suggest that our test can work very well even in small to moderately sized samples. As an empirical illustration, we apply our test to two datasets that have been used in the literature to estimate censored regression models using Powell's STLS approach, to check whether the assumption of conditional symmetry is supported by these datasets.

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Bibliographic Info

Paper provided by Center for Research in Economic Analysis, University of Luxembourg in its series CREA Discussion Paper Series with number 14-04.

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Date of creation: 2014
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Handle: RePEc:luc:wpaper:14-04

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  1. Hanan G. Jacoby & Rinku Murgai & Saeed Ur Rehman, 2004. "Monopoly Power and Distribution in Fragmented Markets: The Case of Groundwater," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 783-808.
  2. Newey, Whitney K., 1987. "Specification tests for distributional assumptions in the Tobit model," Journal of Econometrics, Elsevier, Elsevier, vol. 34(1-2), pages 125-145.
  3. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, Elsevier, vol. 32(1), pages 143-155, June.
  4. Zheng, John Xu, 1998. "Consistent Specification Testing For Conditional Symmetry," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 14(01), pages 139-149, February.
  5. Santos Silva, J M C, 2001. "Influence Diagnostics and Estimation Algorithms for Powell's SCLS," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 19(1), pages 55-62, January.
  6. Tao Chen & Gautam Tripathi, 2011. "Testing Conditional Symmetry Without Smoothing," Working papers, University of Connecticut, Department of Economics 2011-01, University of Connecticut, Department of Economics.
  7. Delgado, Miguel A. & Carlos Escanciano, J., 2007. "Nonparametric tests for conditional symmetry in dynamic models," Journal of Econometrics, Elsevier, Elsevier, vol. 141(2), pages 652-682, December.
  8. Hyndman, R.J. & Yao, Q., 1998. "Nonparametric Estimation and Symmetry Tests for Conditional Density Functions," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 17/98, Monash University, Department of Econometrics and Business Statistics.
  9. Lee, Myoung-Jae, 1995. "Semi-parametric Estimation of Simultaneous Equations with Limited Dependent Variables: A Case Study of Female Labour Supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 10(2), pages 187-200, April-Jun.
  10. Wojciech Kopczuk, 2007. "Bequest and Tax Planning: Evidence from Estate Tax Returns," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 122(4), pages 1801-1854, November.
  11. Khan, Shakeeb & Powell, James L., 2001. "Two-step estimation of semiparametric censored regression models," Journal of Econometrics, Elsevier, Elsevier, vol. 103(1-2), pages 73-110, July.
  12. Jolliffe, Dean, 2002. "The Gender Wage Gap in Bulgaria: A Semiparametric Estimation of Discrimination," Journal of Comparative Economics, Elsevier, vol. 30(2), pages 276-295, June.
  13. Honore, Bo E. & Kyriazidou, Ekaterini & Udry, Christopher, 1997. "Estimation of Type 3 Tobit models using symmetric trimming and pairwise comparisons," Journal of Econometrics, Elsevier, Elsevier, vol. 76(1-2), pages 107-128.
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