Estimating Causal Effects in Linear Regression Models With Observational Data: The Instrumental Variables Regression Model

Abstract

Instrumental variable methods are an underutilized tool to enhance causal inference in psychology. By way of incorporating predictors of the predictors (called "instruments" in the econometrics literature) into the model, instrumental variable regression (IVR) is able to draw causal inferences of a predictor on an outcome. We show that by regressing the outcome y on the predictors x and the predictors on the instruments, and modeling correlated disturbance terms between the predictor and outcome, causal inferences can be drawn on y on x if the IVR model cannot be rejected in a structural equation framework. We provide a tutorial on how to apply this model using ML estimation as implemented in structural equation modeling (SEM) software. We additionally provide code to identify instruments given a theoretical model, to select the best subset of instruments when more than necessary are available, and we guide researchers on how to apply this model using SEM. Finally, we demonstrate how the IVR model can be estimated using a number of estimators developed in econometrics