Introduction

Takeshi Amemiya made basic contributions to the econometrics of discrete choice and limited dependent variable models. His fundamental 1973 paper on the censored normal regression model was the first systematic application in econometrics of the uniform law of large numbers and the central limit theorems required to establish consistency and asymptotic normality of nonlinear econometric models. That paper and his later work on nonlinear least squares are summarized in his magisterial text Advanced Econometrics (1985). His research and his text set the standard for a generation of econometricians, and provided the framework for modern structural econometric analysis of index models or latent variable models.

Latent variable models of the type analyzed by Amemiya arise in wellposed economic problems. The latent variables can be utilities, potential wages (or home wages as in Gronau 1974 and Heckman 1974) or potential profitability. This class of models, which originates in psychology in the work of Thurstone (1930, 1959), has been widely developed in the econometrics of discrete choice (see McFadden 1981, and the survey of index models in labor economics presented by Heckman and MaCurdy 1985). Amemiya provided the econometric foundations for the application of these methods to numerous economic problems.

This paper uses the latent variable or index model of econometrics and psychometrics to impose structure on the model of Neyman (1923)–Fisher (1935)–Cox (1958)–Rubin (1978) of potential outcomes used to define treatment effects.