Using non-binding experiments to estimate causal effects using instrumental variables regression: A tutorial

Often, causal effects of interest in psychological research involve causes that cannot be randomly assigned. Instrumental variables (IV) regression, a cornerstone of the econometric literature on causal inference with nonrandom causes, allows for unbiased causal inference in the face of several threats to the validity of causal inference using ordinary least squares regression. IV is enabled by an instrument – a third variable that affects the outcome only through its influence on the hypothesized cause. One way to study causal effects in psychology is thus the random assignment of an intervention that drives change in the cause of interest but is otherwise unrelated to the outcome, followed by IV analysis to produce a valid causal effect. Moreover, IV regression models can be estimated straightforwardly as structural equation models (SEMs). Based on open data from a recently published study in the economics literature, this tutorial outlines the use of SEM to estimate the causal effect of a behavior of interest, exercise, on an outcome of interest, academic performance, enabled by an instrument – a randomly-distributed free gym card – that constitutes a random, non-binding manipulation of exercise. The role of covariates in IV is discussed, and R code is provided for all analyses.