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Nonlinear two-stage residual inclusion (2SRI) estimators have become increasingly favored over traditional linear two-stage least squares (2SLS) methods for instrumental variables analysis of empirical models with inherently nonlinear dependent variables. Rising adoption of nonlinear 2SRI is largely attributable to simulation evidence showing that nonlinear 2SRI generates consistent estimates of population average treatment effects in nonlinear models, while 2SLS and nonlinear 2SPS do not. However, while it is believed that consistency of 2SRI for population average treatment effects is a general result, current evidence is limited to simulations performed under unique and restrictive settings with regards to treatment effect heterogeneity and conditions underlying treatment choices. This research contributes by describing existing simulation evidence and investigating the ability to generate absolute estimates of population average treatment effects (ATE) and local average treatment effects (LATE) using common IV estimators using Monte Carlo simulation methods across 10 alternative scenarios of treatment effect heterogeneity and sorting-on-the-gain. Additionally, estimates for the effect of ACE/ARBs on 1-year survival for Medicare beneficiaries with acute myocardial infarction are generated and compared across alternative linear and nonlinear IV estimators. Simulation results show that, while 2SLS generates unbiased and consistent estimates of LATE across all scenarios, nonlinear 2SRI generates unbiased estimates of ATE only under very restrictive settings. If marginal patients are unique in terms of treatment effectiveness, then nonlinear 2SRI cannot be expected to generate unbiased or consistent estimates of ATE unless all factors related to treatment effect heterogeneity are fully measured.