Using Stochastic Processes for Causal Inference

Abstract

We provide a framework for identification, estimation, and testing in general causal models with endogeneity by rephrasing the instrumental variable model as dependent stochastic processes. This shift in perspective has analytical benefits and allows us to solve several open problems in the literature.

First, we provide a proof of Pearl's conjecture, showing that the validity of an instrument cannot be tested without structural assumptions when the treatment is continuous; using the stochastic process framework, we are furthermore able to show that already weak continuity- or monotonicity restrictions reestablish testability.

Second, we provide a tractable procedure for estimating sharp bounds on causal effects which is flexible enough to incorporate structural assumptions into the estimation process in a unified manner.

It is based on the stochastic process representation of instrumental variable models and constructs an infinite dimensional linear program on the paths of these processes, the solution to which provides the counterfactual bounds. Finally, we also point to further applications of this framework: dynamic causal effects and continuous analogues of the LATE concept.

About Florian Gunsilius

Postdoctoral Associate in the Department of Economics at MIT. I will join

the Department of Economics at the University of

Michigan Opens external as an Assistant Professor in the Fall

of 2020.