Inference for instrumental variables: a randomization inference approach

The method of instrumental variables provides a framework to study causal effects in both randomized experiments with non‐compliance and in observational studies where natural circumstances produce as if random nudges to accept treatment. Traditionally, inference for instrumental variables relied on asymptotic approximations of the distribution of the Wald estimator or two‐stage least squares, often with structural modelling assumptions and/or moment conditions. We utilize the randomization inference approach to instrumental variables inference. First, we outline the exact method, which uses the randomized assignment of treatment in experiments as a basis for inference but lacks a closed form solution and may be computationally infeasible in many applications. We then provide an alternative to the exact method, the almost exact method, which is computationally feasible but retains the advantages of the exact method. We also review asymptotic methods of inference, including those associated with two‐stage least squares, and analytically compare them with randomization inference methods. We also perform additional comparisons by using a set of simulations. We conclude with three different applications from the social sciences.