Estimating causal effects in bivariate probit instrumental variable models often faces challenges with standard maximum likelihood (MLE) methods. These approaches can produce inaccurate parameter estimates and fail to provide straightforward measures of uncertainty for causal quantities, even when correctly specified. This note addresses these limitations by demonstrating that Bayesian estimation offers superior accuracy for key parameters and facilitates the direct calculation of treatment effects along with their full measure of uncertainty.

Data & Methods:

The study utilizes bivariate probit models within an instrumental variables framework to analyze scenarios involving binary treatments and outcomes. Unlike relying on standard MLE approaches which are common but potentially flawed, the investigation employs Bayesian estimation techniques as a robust alternative.

Key Findings:

Bayesian methods provide more reliable estimates compared to traditional maximum likelihood estimation in these complex models. The approach successfully calculates causal quantities of interest directly with associated measures of uncertainty.

Why It Matters:

For political scientists working with binary dependent variables and needing precise identification of treatment effects, this note suggests Bayesian estimation as a preferable method over standard MLE for achieving accurate results and quantifying uncertainty.