To examine the settings of simulation evidence supporting use of nonlinear two‐stage residual inclusion (2) instrumental variable () methods for estimating average treatment effects () using observational data and investigate potential bias of 2 across alternative scenarios of essential heterogeneity and uniqueness of marginal patients.
Potential bias of linear and nonlinear methods for and local average treatment effects () 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.
Results show that nonlinear 2 models produce estimates of and 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 estimates for was low across all scenarios.
Researchers are increasingly opting for nonlinear 2 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 2 rely on assumptions about the relationships between treatment effect heterogeneity and choice.