Dale J. Poirier

Partial observability in bivariate probit models

This study investigates random utility models in which the observed binary outcome does not reflect the binary choice of a single decision-maker, but rather the joint unobserved binary choices of two decision-makers. Under the usual normality assumptions, the model that arises for the observed binary outcome is not a univariate probit model, but rather a bivariate probit model in which only one of the four possible outcomes is observed. Estimation and identification issues are discussed, and the implications for sample selectivity problems are noted.

Piecewise Regression Using Cubic Splines

Abstract Spline theory and piecewise regression theory are integrated to provide a framework in which structural change is viewed as occurring in a smooth fashion. Specifically, structural change occurs at given points through jump discontinuities in the third derivative of a continuous piecewise cubic estimating function. Testing procedures are developed for detecting structural change as well as linear or quadratic segments. Finally, the techniques developed are illustrated empirically in a learning-by-doing model.

REVISING BELIEFS IN NONIDENTIFIED MODELS

A Bayesian analysis of a nonidentified model is always possible if a proper prior on all the parameters is specified. There is, however, no Bayesian free lunch. The “price†is that there exist quantities about which the data are uninformative, i.e., their marginal prior and posterior distributions are identical. In the case of improper priors the analysis is problematic—resulting posteriors can be improper. This study investigates both proper and improper cases through a series of examples.

The Use of the Box-Cox Transformation in Limited Dependent Variable Models

Abstract The general limited dependent variable model discussed in this article permits skewness in a pretruncated variable by transforming it within the class of Box-Cox transformations. As a by-product this general model also provides a convenient nesting framework for statistically distinguishing between numerous limited dependent variable models. An application to a model of the supply of bilateral foreign aid illustrates the ability of the general model to empirically distinguish between competing specifications.

Probit with Dependent Observations

Estimation of limited dependent variable models with dependent observations has received relatively little attention due to the computational complexity of the maximum likelihood estimator. We develop a computationally attractive and relatively efficient estimator for this case that utilises the orthogonality conditions. The resulting Generalized Conditional Moment (GCM) estimators can be applied with a known or an unknown disturbance covariance matrix. Although the paper considers only the probit model, the approach is easily generalized to other limited dependent variable models.

On the appropriateness of endogenous switching

Abstract This study argues that there has been confusion in the econometrics literature over switching regression models with endogenous switching, and that this confusion can cause serious interpretation problems when the model is employed in applied work.

Bayesian analysis of logit models using natural conjugate priors

Abstract This study provides a Bayesian investigation of conditional logit and multinomial logit models based on a conjugate prior which has many appealing computational properties. A one-parameter ‘neutral’ prior is developed which concentrates prior mass over the region corresponding to equiprobable alternatives. This prior is particularly attractive in sensitivity analysis. An empirical example of occupational choice illustrates the proposed techniques.

A Note on the Interpretation of Regression Coefficients within a Class of Truncated Distributions

DESPITE THE INTENSE ACTIVITY in the area of estimation of limited dependent variable (LDV) models (see, for example, the Fall 1976 issue of the Annals of Economic and Social Measurement), the interpretation of regression coefficients in truncated regression models has been largely ignored. This issue should not be taken lightly since the obvious interpretation which equates regression coefficients to partial derivatives of the conditional mean of the dependent variable is unfortunately incorrect. One specific implication of the results presented here is that whenever the dependent variable y in the usual classical linear normal regression model is truncated above and/or below, then the effect of the fth regressor on the conditional mean of y is proportional to, but not equal to, the fth regression coefficient. However, more generally this note presents a simple expression for the effect of the fth regressor on any conditional moment of y in terms of a generalized LDV model introduced by Poirier [3]. Poirier introduced a general LDV model which permitted skewness in a pre-truncated variable by transforming it within the class of transformations suggested by Box and Cox

A Bayesian analysis of nested logit models

Abstract This study provides a Bayesian analysis of estimation, testing, and prediction in nested logit models. Tractable families of informative priors are introduced. The discussion advocates explicit treatment of prior information often used informally by non-Bayesian empirical researchers.

An Econometric Model of Birth Inputs and Outputs for Native Americans

This paper presents a new model of the birth process of Native Americans with seven endogenous variables: four birth inputs maternal smoking (S), drinking (D), prenatal care (PC), and weight gain (WG), and three birth outputs gestational age (G), birth length (BL), and birth weight (BW). The model is a seven-equation simultaneous model with three endogenous dummies S, D, and PC. The data are taken from the NLSY. We find that the four birth inputs are determined jointly and dependently among S, D, and PC, but independently of WG. S has negative systematic correlation with G. D and PC appear to have no sizeable systematic effect on G, BL, or BW. Except for the sizeable and positive correlation between the unexplained parts of S and G, there seem to be no unexplained common effects between the birth inputs and outputs. Moreover, G appears dependent on the exogenous size of the mother. BL is affected by the inputs mainly through WG. BW is affected by the inputs through their effects on G. Except for maternal weight, there is little correlation between the remaining exogenous variables and BW. Finally, the predictive density of BW for a typical pregnancy gives a mean weight of 3.240kg.