Estimation in a generalization of bivariate probit models with dummy endogenous regressors

Abstract

Summary The purpose of this paper is to provide guidelines for empirical researchers who use a class of bivariate threshold crossing models with dummy endogenous variables. A common practice employed by the researchers is the specification of the joint distribution of unobservables as a bivariate normal distribution, which results in a bivariate probit model. To address the problem of misspecification in this practice, we propose an easy‐to‐implement semiparametric estimation framework with parametric copula and nonparametric marginal distributions. We establish asymptotic theory, including root‐n normality, for the sieve maximum likelihood estimators that can be used to conduct inference on the individual structural parameters and the average treatment effect (ATE). In order to show the practical relevance of the proposed framework, we conduct a sensitivity analysis via extensive Monte Carlo simulation exercises. The results suggest that estimates of the parameters, especially the ATE, are sensitive to parametric specification, while semiparametric estimation exhibits robustness to underlying data‐generating processes. We then provide an empirical illustration where we estimate the effect of health insurance on doctor visits. In this paper, we also show that the absence of excluded instruments may result in identification failure, in contrast to what some practitioners believe.

Testing identifying assumptions in bivariate probit models

“…To illustrate the usefulness of the tests developed in Section 4, we apply the methodology to data sets of two policy relevant recent papers. First, we use the data set Zimmer (2017) and Han and Lee (2019) used to analyze the effect of access to health insurance on individuals' decision to visit a doctor. The second application revisits Gao et al (2018) to analyze how land tenure arrangements affect Chinese farmers' adoption of straw retention.…”

“…The second application revisits Gao et al (2018) to analyze how land tenure arrangements affect Chinese farmers' adoption of straw retention. Han and Lee (2019) analyze the impact of health insurance coverage on individual's decision to visit a doctor. In this example, Y and D are indicators for whether an individual has a doctor visit, and is covered by private health insurance, respectively.…”

“…The data comes from the 2010 wave of the Medical Expenditure Panel Survey (MEPS). As in Han and Lee (2019), we focus on all the visits that occurred in January 2010, restrict the sample to contain individuals with age between 25 and 64 years, and exclude those who have retained any federal or state insurance in 2010. Furthermore, self-employed or unemployed individuals are excluded from the analysis.…”

“…We briefly discuss these parameters' identification in Section 3. SeeHan and Vytlacil (2017),Han and Lee (2019),Mourifié and Méango (2014) for detailed identification results. Note that Li et al (2019) provide conditions for identification by functional form in the absence of an instrument.…”

Seawater salinity modeling using bivariate probit regression

“…Bivariate probit regression is a data analysis used to analyze response variables that are qualitative, quantitative or a combination of both [6]. However, in everyday life cases are often encountered, the response variable is a qualitative variable or a dummy variable by taking two or more possible values, such as decisions, such as the decision to choose "yes" or "no" [7]. .…”