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Endogenous Sampling and Matching Method in Duration Models


  • Takeshi Amemiya

    (Edward Ames Edmonds Professor of Economics, Stanford University, Department of Economics (E-mail:

  • Xinghua Yu

    (Stanford University, Department of Economics (E-mail:


Endogenous sampling with matching (also called gmixed sampling h) occurs when the statistician samples from the non-right- censored subset at a predetermined proportion and matches on one or more exogenous variables when sampling from the right-censored subset. This is widely applied in the duration analysis of firm failures, loan defaults, insurer insolvencies, and so on, due to the low frequency of observing non-right-censored samples (bankrupt, default, and insolvent observations in respective examples). However, the common practice of using estimation procedures intended for random sampling or for the qualitative response model will yield either an inconsistent or inefficient estimator. This paper proposes a consistent and efficient estimator and investigates its asymptotic properties. In addition, this paper evaluates the magnitude of asymptotic bias when the model is estimated as if it were a random sample or an endogenous sample without matching. This paper also compares the relative efficiency of other commonly used estimators and provides a general guideline for optimally choosing sample designs. The Monte Carlo study with a simple example shows that random sampling yields an estimator of poor finite sample properties when the population is extremely unbalanced in terms of default and non-default cases while endogenous sampling and mixed sampling are robust in this situation.

Suggested Citation

  • Takeshi Amemiya & Xinghua Yu, 2006. "Endogenous Sampling and Matching Method in Duration Models," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 24(2), pages 1-32, November.
  • Handle: RePEc:ime:imemes:v:24:y:2006:i:2:p:1-32

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    References listed on IDEAS

    1. Amemiya, Takeshi, 2001. "Endogenous Sampling in Duration Models," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 19(3), pages 77-96, November.
    2. Luoma, M & Laitinen, EK, 1991. "Survival analysis as a tool for company failure prediction," Omega, Elsevier, vol. 19(6), pages 673-678.
    3. Palepu, Krishna G., 1986. "Predicting takeover targets : A methodological and empirical analysis," Journal of Accounting and Economics, Elsevier, vol. 8(1), pages 3-35, March.
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    Cited by:

    1. Gerard J. Berg & Johan Vikström, 2014. "Monitoring Job Offer Decisions, Punishments, Exit to Work, and Job Quality," Scandinavian Journal of Economics, Wiley Blackwell, vol. 116(2), pages 284-334, April.

    More about this item


    Duration models; Endogenous sampling with matching; Maximum likelihood estimator; Manski-Lerman estimator; Asymptotic distribution;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies


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