The Blessings of Multiple Causes

Abstract

Causal inference from observational data often assumes "ignorability," that all confounders are observed. This assumption is standard yet untestable. However, many scientific studies involve multiple causes, different variables whose effects are simultaneously of interest. We propose the deconfounder, an algorithm that combines unsupervised machine learning and predictive model checking to perform causal inference in multiple-cause settings. The deconfounder infers a latent variable as a substitute for unobserved confounders and then uses that substitute to perform causal inference. We develop theory for the deconfounder, and show that it requires weaker assumptions than classical causal inference. We analyze its performance in three types of studies: semi-simulated data around smoking and lung cancer, semi-simulated data around genome-wide association studies, and a real dataset about actors and movie revenue. The deconfounder provides a checkable approach to estimating closer-to-truth causal effects.

Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance for Empirical Practice in Economics

“…There is some connection between this identification strategy and the multiple causes approach in [Wang and Blei, 2018]. They assume that there is an unobserved confounder that affects both causes.…”

Flexible Sensitivity Analysis for Observational Studies Without Observable Implications

“…This would require generalizing the factorization in Equation (5). In some special cases, for example, where the unobserved confounding can be represented as latent factors of the observed distribution of treatments (Wang and Blei, 2018), more parsimonious sensitivity factorizations may be possible, e.g., following D'Amour (2019). A final extension would extend our sensitivity analysis to observational studies with missing data.…”

Comment on: “The Blessings of Multiple Causes” by Yixin Wang and David M. Blei

“…See Angrist, Graddy, and Imbens (2000) for an interpretation in the modern causal inference literature. We show that the Wang and Blei (2018) multiple causes ideas bring new insights to this setting, but that they will not be a panacea.…”

“…We congratulate the authors of Wang and Blei (2018) on a thought-provoking article on causal inference in settings with unobserved confounders. We expect that their ideas will lead to further developments in this important area.…”

“…In this comment, we offer some thoughts on one such direction. Specifically, we explore the relevance of the Wang and Blei (2018) multiple causes ideas for a canonical problem in economics, namely the identification of demand functions in simultaneous equations (supply and demand) models. This is an old problem in economics, going back to the origins of the field of econometrics in the 1920s.…”