We conduct an extensive Monte Carlo experiment to examine the finite sample properties of maximum-likelihood-based inference in the bivariate probit model with an endogenous dummy. We analyse the relative performance of alternative exogeneity tests, the impact of distributional misspecification and the role of exclusion restrictions to achieve parameter identification in practice. The results allow us to infer important guidelines for applied econometric practice. Copyright (c) Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2007.

Rigby & Stasinopoulos (2005) introduced generalized additive models for location, scale and shape (GAMLSS) where the response distribution is not restricted to belong to the exponential family and its parameters can be specified as functions of additive predictors that allows for several types of covariate effects (e.g., linear, non-linear, random and spatial effects).In many empirical situations, however, modeling simultaneously two or more responses conditional on some covariates can be of considerable relevance. In this article, we extend the scope of GAMLSS by introducing a bivariate copula additive model with continuous margins for location, scale and shape. The framework permits the copula dependence and marginal distribution parameters to be estimated simultaneously and, like in GAMLSS, each parameter to be modeled using an additive predictor. Parameter estimation is achieved within a penalized likelihood framework using a trust region algorithm with integrated automatic multiple smoothing parameter selection. The proposed approach allows for straightforward inclusion of potentially any parametric continuous marginal distribution and copula function. The models can be easily used via the copulaReg() function in the R package SemiParBIVProbit.The usefulness of the proposal is illustrated on two case studies (which use electricity price and demand data, and birth records) and on simulated data.

The classic recursive bivariate probit model is of particular interest to researchers since it allows for the estimation of the treatment effect that a binary endogenous variable has on a binary outcome in the presence of unobservables. In this article, the authors consider the semiparametric version of this model and introduce a model fitting procedure which permits to estimate reliably the parameters of a system of two binary outcomes with a binary endogenous regressor and smooth functions of continuous covariates. They illustrate the empirical validity of the proposal through an extensive simulation study. The approach is applied to data from a survey, conducted in Botswana, on the impact of education on women's fertility. Some studies suggest that the estimated effect could have been biased by the possible endogeneity arising because unobservable confounders (e.g., ability and motivation) are associated with both fertility and education. The Canadian Journal of Statistics 39: 259–279; 2011 © 2011 Statistical Society of Canada

We introduce a framework for estimating the effect that a binary treatment has on a binary outcome in the presence of unobserved confounding. The methodology is applied to a case study which uses data from the Medical Expenditure Panel Survey and whose aim is to estimate the effect of private health insurance on health care utilization. Unobserved confounding arises when variables which are associated with both treatment and outcome are not available (in economics this issue is known as endogeneity). Also, treatment and outcome may exhibit a dependence which cannot be modeled using a linear measure of association, and observed confounders may have a non-linear impact on the treatment and outcome variables.The problem of unobserved confounding is addressed using a two-equation structural latent variable framework, where one equation essentially describes a binary outcome as a function of a binary treatment whereas the other equation determines whether the treatment is received.Non-linear dependence between treatment and outcome is dealt with by using copula functions, whereas covariate-response relationships are flexibly modeled using a spline approach.Related model fitting and inferential procedures are developed, and asymptotic arguments presented.