Distribution theory for the analysis of binary choice under uncertainty with nonparametric estimation of expectations (Q1209890)

The paper deals with the estimator of preferences previously introduced by Manski, analyzing its asymptotic sampling behavior. \textit{C. F. Manski} [Nonparametric and semiparametric methods in econometrics and statistics. Proc. 5th Int. Symp., Econ. Theory Econ., Durham/NC (USA) 1988, 259-275 (1991; Zbl 0757.62018)] introduced a two-stage, semiparametric estimator applicable if expectations are fulfilled and are conditioned only on variables observed by the researcher. Manski's estimator leads to a consistent estimator of preference parameters if the population is sufficiently regular and if the expectations estimate is chosen appropriately. The present paper solves a further question referred to the influence that a nonparametric estimation of expectations has in the parametric estimation of preferences. After setting out the estimation problem and presenting the estimator, a theorem is proved showing that, given six assumptions, the preference estimate enjoys the classical asymptotic properties of \(\sqrt{N}\)- consistency, \(\sqrt{N}\)-asymptotic unbiasedness and asymptotic normality. According to my opinion this paper is an interesting new contribution to the asymptotic analysis of preferences estimation.