Causal diagrams for empirical legal research: a methodology for identifying causation, avoiding bias and interpreting results

Abstract

In this paper we introduce methodology-causal directed acyclic graphs-that empirical researchers can use to identify causation, avoid bias, and interpret empirical results. This methodology has become popular in a number of disciplines, including statistics, biostatistics, epidemiology and computer science, but has yet to appear in the empirical legal literature. Accordingly we outline the rules and principles underlying this new methodology and then show how it can assist empirical researchers through both hypothetical and real-world examples found in the extant literature. While causal directed acyclic graphs are certainly not a panacea for all empirical problems, we show they have potential to make the most basic and fundamental tasks, such as selecting covariate controls, relatively easy and straightforward.

Figure A.1. Directed Acyclic Graph with Mutually Independent Errors but with an Unobserved Variable, U

Figure A.2. Directed Acyclic Graph with Unobservable Errors that Violate the Mutual Independence Assumption; Errors, ε₂ and ε_Y, are Correlated

Figure 1. A Simple Underlying Causal Structure

Figure 2. A More Complex Set of Structural Relationships

Figure 3. A Directed Acyclic Graph with Five Variables (Pearl 2009, 15)

Figure 4. Causal Directed Acyclic Graph with Unobserved Variable, U₁

Note: Controlling for X₂ satisfies the back-door criterion for the effect of X₂ on Y.

Figure 5

Directed Acyclic Graph with Two Unobserved Covariates. Note: Adjusting for X₃, a “collider” variable induces correlation between U₁ and U₂ and confounds the results of X₄ on Y.