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Finite Sample Inference for the Maximum Score Estimand

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Document pages: 34 pages

Abstract: We provide a finite sample inference method for the structural parameters ofa semiparametric binary response model under a conditional median restrictionoriginally studied by Manski (1975, 1985). Our inference method is valid forany sample size and irrespective of whether the structural parameters are pointidentified or partially identified, for example due to the lack of acontinuously distributed covariate with large support. Our inference approachexploits distributional properties of observable outcomes conditional on theobserved sequence of exogenous variables. Moment inequalities conditional onthis size n sequence of exogenous covariates are constructed, and the teststatistic is a monotone function of violations of sample moment inequalities.The critical value used for inference is provided by the appropriate quantileof a known function of n independent Rademacher random variables. Weinvestigate power properties of the underlying test and provide simulationstudies to support the theoretical findings.

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