We provide a finite sample inference method for the structural parameters of Manski's semiparametric binary response model under a conditional median restriction. This is achieved by exploiting distributional properties of observable outcomes conditional on the observed sequence of exogenous variables. Moment inequalities conditional on the size n sequence of exogenous covariates are constructed, and the proposed test statistic is a monotone function of violations of the corresponding sample moment inequalities. The critical value used for inference is provided by the appropriate quantile of a known function of n independent Bernoulli random variables and does not require the use of a cube root asymptotic approximation employing a point estimator of the target parameter. Simulation studies demonstrate favourable finite sample performance of the test in comparison to several existing approaches. Empirical use is illustrated with an application to the classical setting of transportation choice.

We examine the use of instrumental variable (IV) methods to measure the effect of a ceteris paribus change in an endogenous variable on an ordered outcome. Specifically, we use these methods to investigate the effect of neighborhood characteristics on subjective well-being (SWB) among participants in the Moving to Opportunity (MTO) housing voucher experiment. We find that the estimated positive effect of a decrease in neighborhood poverty on SWB is sensitive to the specification of the first-stage auxiliary equation for endogenous neighborhood poverty. Our results highlight the influential role of control function restrictions in complete triangular models.