Estimation of a semiparametric recursive bivariate probit model in the presence of endogeneity

Abstract

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

Testing the hypothesis of absence of unobserved confounding in semiparametric bivariate probit models

“…These regressors have to induce variation in y 1i , not to directly affect y 2i , and be independent of (ε 1i , ε 2i ) given covariates. However, under correct model specification, this restriction may not be necessary in estimation (Marra and Radice 2011;Wilde 2000).…”

“…Following previous work on the subject (Wooldridge 2010; Marra and Radice 2011;Sobotka et al 2013), we specified a semiparametric recursive bivariate probit model with main terms only. The description of the variables used in the model are reported in Table 5.…”

“…The nonparametric specification for age arises from the fact that this covariate embodies productivity and life-cycle effects that are likely to affect child non-linearly. Wooldridge (2010) considered a model for fertility that contains linear and quadratic terms in age, whereas Marra and Radice (2011) and Sobotka et al (2013) specified a model containing a smooth function of age. Here, we found non-linear effects of age that are almost identical to those reported in Marra and Radice (2011); results are available upon request.…”

“…Wooldridge (2010) considered a model for fertility that contains linear and quadratic terms in age, whereas Marra and Radice (2011) and Sobotka et al (2013) specified a model containing a smooth function of age. Here, we found non-linear effects of age that are almost identical to those reported in Marra and Radice (2011); results are available upon request. The quantity of interest is the average treatment effect (ATE) of ed on child, which measures the effect of ed on the probability of having at least one child, i.e.…”

“…However the lack of user-friendly software makes them unfeasible for practitioners. The need for methods flexibly modeling covariate effects arises from the observation that all parameter estimates are inconsistent when the relationship between observed confounders and outcome is mismodeled (Marra and Radice 2011;Chib et al 2009). …”