A practical comparison of the bivariate probit and linear IV estimators

► IV and BP estimates differ when treatment probabilities are close to 0 or 1, or when sample sizes are below 5000. ► Differences between estimates can reflect differences between plim (Linear IV) and ATE. ► Bootstrapping confidence intervals are recommended when sample sizes are below 10,000. ► A goodness-of-fit score test can help detect misspecifications of the BP model.