Sample selection bias as a specification error This paper discusses the bias that results from using non-randomly selected samples to estimate behavioral relationships as an ordinary specification error or «omitted variables» bias. A simple consistent two stage estimator is considered that enables analysts to utilize simple regression methods to estimate behavioral functions by least squares methods. The asymptotic distribution of the estimator is derived.

The Importance of Noncognitive Skills: Lessons from the GED Testing Program by James J. Heckman and Yona Rubinstein. Published in volume 91, issue 2, pages 145-149 of American Economic Review, May 2001

This paper explores the robustness of the essential economic conclusions of the Roy model of self-selection and income inequality to relaxation of its normality assumptions. A log concave version of the model reproduces most of the main results. Log convex cases offer counterexamples. The authors show that in a Roy economy, random assignment is inegalitarian and Pareto inefficient. They consider nonparametric identifiability of latent skill distributions with cross-section and panel data. The authors' analysis proves nonparametric identifiability for the closely related competing risks model.

The major contributions of twentieth century econometrics to knowledge were the definition of causal parameters within well-defined economic models in which agents are constrained by resources and markets and causes are interrelated, the analysis of what is required to recover causal parameters from data (the identification problem), and clarification of the role of causal parameters in policy evaluation and in forecasting the effects of policies never previously experienced. This paper summarizes the development ofthese ideas by the Cowles Commission, the response to their work by structural econometricians and VAR econometricians, and the response to structural and VAR econometrics by calibrators, advocates of natural and social experiments, and by nonparametric econometricians and statisticians.

This paper considers the formulation and estimation of simultaneous equation models with both discrete and continuous endogenous variables.The statistical model proposed here is sufficiently rich to encompass the álassjcai simultaneous equation model for continuous endogenous variables and more recent models for purely discrete endogenous variables as special cases of a more general model.Interest in discrete data has been ftsledby a rapid growth in the availability of microeconomic data sets coupled with a growing awareness of the importance of discrete choice models for the analysis of uiicroeconomic problems (see McFadden, 1976).To date, the only available statistical models for the analysis of discrete endogenous variables have been developed for the purely discrete case.The log-linear or logistic model of Goodman (1970) as expanded by Raberman (1974) and Nerlove and Press (1976) is one Vol.II, 1967; Lord and Novick, cbs.16-20, 1967.)It is argued in this paper that this class of statistical models provides a natural framework for generating simultaneous equation models with both discrete and continuous random variables.In contrast, the framework of Goodman, while convenient for formulating descriptive models for discrete data, offers a much less natural apparatus for analyzing econometric structural equation models.This is so primarily because the simultaneous equation model is inherently an unconditional representation of behavioral equations while the model of Goodman is designed to facilitate the analysis of conditional representations, and does not lend itself to the unconditional formulations required in simultaneous equation theory.The structure of this paper is in four parts.in part one general models are discussed.Dummy endogenous variables are introduced in two distinct roles: (1) as proxies for unobserved latent variables and (2) as direct shifters of behavioral equations.Five models incorporating such dummy variables are discussed.Part two, also the longest section, presents a complete analysis of the most novel and most general of the five models presented in part one.This is a model with both continuous and discrete endogenous variables.The issues of identification and estimation are discussed together by proving the existence of consistent estimators.Maximum likelihood estimators and alternative estimators are discussed.In part three, a brief discussion of a multivariate probit model with structural shift is presented.Part four presents a comparison between the models developed in this paper and the models of Goodman and Nerlove and Press.