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Finite Sample Inference for the Maximum Score Estimand

Author

Listed:
  • Adam Rosen

    (Institute for Fiscal Studies and Duke University)

  • Takuya Ura

    (Institute for Fiscal Studies)

Abstract
We provide a ?nite sample inference method for the structural parameters of a semiparametric binary response model under a conditional median restriction originally studied by Manski (1975, 1985). Our inference method is valid for any sample size and irrespective of whether the structural parameters are point identi?ed or partially identi?ed, for example due to the lack of a continuously distributed covariate with large support. Our inference approach exploits distributional properties of observable outcomes conditional on the observed sequence of exogenous variables. Moment inequalities conditional on this size n sequence of exogenous covariates are constructed, and the test statistic is a monotone function of violations of sample moment inequalities. The critical value used for inference is provided by the appropriate quantile of a known function of n independent Rademacher random variables. Simulation studies compare the performance of the test to two alternative tests using an infeasible likelihood ratio statistic and Horowitz’s (1992) smoothed maximum score estimator.

Suggested Citation

  • Adam Rosen & Takuya Ura, 2020. "Finite Sample Inference for the Maximum Score Estimand," CeMMAP working papers CWP22/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:22/20
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    References listed on IDEAS

    as
    1. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    2. Delgado, Miguel A. & Rodriguez-Poo, Juan M. & Wolf, Michael, 2001. "Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator," Economics Letters, Elsevier, vol. 73(2), pages 241-250, November.
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