Chapter 13 Causal inference
In this chapter, we present some Bayesian methods to perform inference on causal effects. The point of departure is the set of identification conditions, which are the assumptions that allow us to express the estimand—the causal or statistical quantity of interest—as a unique function of the observable data distribution. These identification conditions are conceptually distinct from the econometric or statistical framework used to perform inference once those conditions are satisfied. In other words, the assumptions necessary for identification do not constrain whether we apply a Frequentist or a Bayesian approach for estimation and inference.
Identification addresses the question: Can the causal effect be expressed as a function of the observable data distribution under certain assumptions? Once the causal effect is identified in terms of the observed data distribution, we can proceed with statistical inference using either Frequentist methods or Bayesian methods. These inferential frameworks differ in how they estimate and quantify uncertainty but operate on the same identified causal effect. Thus, the identification assumptions are logically prior to, and independent of, whether we adopt a Frequentist or a Bayesian inferential paradigm.
We now present the underlying identification assumptions employed in popular strategies such as randomized controlled trials, conditional independence, and instrumental variables, among others, as well as the Bayesian inferential framework used to estimate causal effects in these settings.
We emphasize that this chapter provides only an introduction to causal inference and does not aim to offer an in-depth treatment. There are excellent texts on causal inference, such as Angrist and Pischke (2009), Angrist and Pischke (2014), Guido W. Imbens and Rubin (2015), Hernán and Robins (2020), Cunningham (2021), and Victor Chernozhukov et al. (2024). We recommend that readers consult these references for a deeper understanding of the concepts and tools introduced here.