This project will compute efficiency bounds for a large class of semiparametric discrete choice models. (These models relax some of the distributional assumptions, which are not supported by economic theory, that occur in traditional models of discrete choice.) Efficiency bounds provide benchmarks for evaluating the performance of alternative statistical estimation strategies by providing lower bounds on the variability of any estimate. It is expected that the project will show that a large class of existing estimators are not efficient relative to the benchmark bounds on estimator variance. The project will identify strategies for improving upon the existing estimators through exploitation of qualitative shape restrictions on the choice probabilities -- restrictions that are ignored by most existing methodologies. This project will provide important guidance for future improvements in the econometric methods available for analysis of discrete behavior.