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.

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.

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.

This paper uses the marginal treatment effect (MTE) to unify the nonparametric literature on treatment effects with the econometric literature on structural estimation using a nonparametric analog of a policy invariant parameter; to generate a variety of treatment effects from a common semiparametric functional form; to organize the literature on alternative estimators; and to explore what policy questions commonly used estimators in the treatment effect literature answer. A fundamental asymmetry intrinsic to the method of instrumental variables (IV) is noted. Recent advances in IV estimation allow for heterogeneity in responses but not in choices, and the method breaks down when both choice and response equations are heterogeneous in a general way.

Conventional analyses of single spell duration models control for unobservables using a random effect estimator with the distribution of unobservables selected by ad hoc criteria. Both theoretical and empirical examples indicate that estimates of structural parameters obtained from conventional procedures are very sensitive to the choice of mixing distribution. Conventional procedures overparameterize duration models. We develop a consistent nonparametric maximum likelihood estimator for the distribution of unobservables and a computational strategy for implementing it. For a sample of unemployed workers our estimator produces estimates in concordance with standard search theory while conventional estimators do not. ECONOMIC THEORIES of search unemployment (Lippman and McCall [34]; Flinn and Heckman [14]), job turnover (Jovanovic [25]), mortality (Harris [17]), labor supply (Heckman and Willis [23]) and marital instability (Becker [3]) produce structural distributions for durations of occupancy of states. These theories generate qualitative predictions about the effects of changes in parameters on these structural distributions, and occasionally predict their functional forms.2 In order to test economic theories about durations and recover structural parameters, it is necessary to account for population variation in observed and unobserved variables unless it is assumed a priori that individuals are homogeneous.3 In every microeconomic study in which the hypothesis of heterogeneity is subject to test, it is not rejected. Temporally persistent unobserved components are an empirically important fact of life in microeconomic data (Heckman [19]). Since the appearance of papers by Silcock [39] and Blumen, Kogan, and McCarthy [5], social scientists have been aware that failure to adequately control for population heterogeneity can produce severe bias in structural estimates of duration models. Serious empirical analysts attempt to control for these unob

"This paper estimates semiparametric reduced-form neoclassical models of life-cycle fertility in Sweden.... The estimated model integrates aspects of life cycle fertility that have previously been studied in isolation of each other: completed fertility, childlessness, interbirth intervals, and the time series of annual birth rates. The main objective of this paper is to determine which aspects of life cycle fertility, if any, are sensitive to male income and female wages."