Objective To examine the settings of simulation evidence supporting use of nonlinear two‐stage residual inclusion (2SRI) instrumental variable (IV) methods for estimating average treatment effects (ATE) using observational data and investigate potential bias of 2SRI across alternative scenarios of essential heterogeneity and uniqueness of marginal patients. Study Design Potential bias of linear and nonlinear IV methods for ATE and local average treatment effects (LATE) is assessed using simulation models with a binary outcome and binary endogenous treatment across settings varying by the relationship between treatment effectiveness and treatment choice. Principal Findings Results show that nonlinear 2SRI models produce estimates of ATE and LATE that are substantially biased when the relationships between treatment and outcome for marginal patients are unique from relationships for the full population. Bias of linear IV estimates for LATE was low across all scenarios. Conclusions Researchers are increasingly opting for nonlinear 2SRI to estimate treatment effects in models with binary and otherwise inherently nonlinear dependent variables, believing that it produces generally unbiased and consistent estimates. This research shows that positive properties of nonlinear 2SRI rely on assumptions about the relationships between treatment effect heterogeneity and choice.