Machine Learning Instrument Variables for Causal Inference

Instrumental variables (IVs) are a commonly used technique for causal inference from observational data. In practice, the variation induced by raw IVs can be limited, and many marketing researchers flag the resulting imprecision or bias in the estimates of causal effects, which renders the approach ineffective for policy decisions. We confront this challenge by formulating the problem of constructing strong instrumental variables from raw (and potentially weak) exogenous data as a machine learning problem. The method is designed for settings in which researchers begin with a set of exogenous instruments and seek to improve their relevance by learning their optimal transformations. We provide formal asymptotic theory and show root-n consistency and asymptotic efficiency of our estimators. We show that, for linear models with homoskedasticity, this translates to a standard supervised learning problem. We apply the method to two real-world data sets. First, we revisit recent criticisms concerning the use of political cycles as instruments for identifying the causal effect of advertising. Although researchers argue that political cycles are weak IVs—citing first stage F-statistics below 10 for most product categories—we demonstrate that the issue stems from model misspecification in the first stage and that our approach effectively resolves it. Second, we use the ready-to-eat cereal industry data set to compare estimates derived from the original instruments to those obtained using our proposed method. In this setting, raw instruments fail to statistically identify customer heterogeneity parameters, whereas our approach introduces sufficient variation to successfully identify them.

History: Olivier Toubia served as the senior editor.

Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mksc.2023.0340.