2SLS vs 2SRI: Appropriate methods for rare outcomes and/or rare exposures

Using Monte-Carlo simulations, we compare the two-stage least-squares estimator with two-stage residual inclusion estimators, with varying forms of residuals, to estimate the local average treatment effect parameter for a binary outcome and endogenous binary treatment model in the presence of binary covariates and a binary instrumental variable. We vary the rarity of both the outcome and the treatment and find different estimators to produce the least bias in different settings. We develop guidance for applied researchers and illustrate the utility of this guidance with estimating the effects of long-term care insurance on a variety of binary health care use outcomes among the near-elderly using the Health and Retirement Study.