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Censored Probit Estimation with Correlation near the Boundary: A Useful Reparameteriztion


  • Terza, Joseph V.
  • Tsai, Wei-Der


The conventional computational algorithms for full information maximum likelihood (FIML) estimation of the censored probit model (see Farber, 1983), will sometimes fail to converge when the estimated value of the correlation coefficient (ñ) approaches ±1; even when the true value of ñ is not at a boundary. We show that a simple reparametrization of the censored probit model may afford straightforward Newton-Raphson convergence to the true FIML estimate for cases in which likelihood maximization under the conventional censored probit parameterization would have failed. Moreover, our method avoids the computational and inferential complications that arise in alternative methods that, based on a specified criterion, suggest fixing the estimated value of ñ at -1 or +1. For the purpose of illustration the method is used to estimate the determinants of elderly parents’ receipt of informal care from their children.

Suggested Citation

  • Terza, Joseph V. & Tsai, Wei-Der, 2006. "Censored Probit Estimation with Correlation near the Boundary: A Useful Reparameteriztion," Review of Applied Economics, Review of Applied Economics, vol. 2(1).
  • Handle: RePEc:ags:reapec:50278

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    References listed on IDEAS

    1. Richard P. Chaykowski & George A. Slotsve & J. S. Butler, 1992. "A Simultaneous Analysis of Grievance Activity and Outcome Decisions," ILR Review, Cornell University, ILR School, vol. 45(4), pages 724-737, July.
    2. Meng, Chun-Lo & Schmidt, Peter, 1985. "On the Cost of Partial Observability in the Bivariate Probit Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 71-85, February.
    3. Butler, J. S., 1997. "Censored probit models do not fail randomly: A Monte Carlo study," Economics Letters, Elsevier, vol. 57(1), pages 33-37, November.
    4. Henry S. Farber & Michelle J. White, 1990. "Medical Malpractice: An Empirical Examination of the Litigation Process," NBER Working Papers 3428, National Bureau of Economic Research, Inc.
    5. Joseph Terza, 2009. "Parametric Nonlinear Regression with Endogenous Switching," Econometric Reviews, Taylor & Francis Journals, vol. 28(6), pages 555-580.
    6. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
    7. Kenkel, D., 1988. "The Demand For Preventive Medical Care," Papers 3-88-4, Pennsylvania State - Department of Economics.
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    Cited by:

    1. Terza, Joseph V. & Basu, Anirban & Rathouz, Paul J., 2008. "Two-stage residual inclusion estimation: Addressing endogeneity in health econometric modeling," Journal of Health Economics, Elsevier, vol. 27(3), pages 531-543, May.

    More about this item


    sample selection; endogenous treatment effects; endogenous switching; qualitative dependent variables; informal elderly care; Research Methods/ Statistical Methods; I12; C24; C63;

    JEL classification:

    • I12 - Health, Education, and Welfare - - Health - - - Health Behavior
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques


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