To investigate potential bias in the use of the conventional linear instrumental variables (IV) method for the estimation of causal effects in inherently nonlinear regression settings.
Smoking Supplement to the 1979 National Health Interview Survey, National Longitudinal Alcohol Epidemiologic Survey, and simulated data.
Potential bias from the use of the linear IV method in nonlinear models is assessed via simulation studies and real world data analyses in two commonly encountered regression setting: (1) models with a nonnegative outcome (e.g., a count) and a continuous endogenous regressor; and (2) models with a binary outcome and a binary endogenous regressor.
The simulation analyses show that substantial bias in the estimation of causal effects can result from applying the conventional IV method in inherently nonlinear regression settings. Moreover, the bias is not attenuated as the sample size increases. This point is further illustrated in the survey data analyses in which IV‐based estimates of the relevant causal effects diverge substantially from those obtained with appropriate nonlinear estimation methods.
We offer this research as a cautionary note to those who would opt for the use of linear specifications in inherently nonlinear settings involving endogeneity.