In this paper, a new estimator is proposed for discrete choice models with choice-based sampling. The estimator is efficient and can incorporate information on the marginal choice probabilities in a straightforward manner and for that case leads to a procedure that is computationally and intuitively more appealing than the estimators that have been proposed before. The idea is to start with a flexible parametrization of the distribution of the explanatory variables and then rewrite the estimator to remove dependence on these parametric assumptions.
Orley Ashenfelter, Janet Currie, Henry S. Farber, Matthew Spiegel, An Experimental Comparison of Dispute Rates in Alternative Arbitration Systems, Econometrica, Vol. 60, No. 6 (Nov., 1992), pp. 1407-1433