Asymptotically robust permutation-based randomization confidence intervals for parametric OLS regression

Randomization inference provides exact finite sample tests of sharp null hypotheses which fully specify the distribution of outcomes under counterfactual realizations of treatment, but the sharp null is often considered restrictive as it rules out unspecified heterogeneity in treatment response. However, a growing literature shows that tests based upon permutations of regressors using pivotal statistics can remain asymptotically valid when the assumption regarding the permutation invariance of the data generating process used to motivate them is actually false. For experiments where potential outcomes involve the permutation of regressors, these results show that permutation-based randomization inference, while providing exact tests of sharp nulls, can also have the same asymptotic validity as conventional tests of average treatment effects with unspecified heterogeneity and other forms of specification error in treatment response. This paper extends this work to the consideration of interactions between treatment variables and covariates, a common feature of published regressions, as well as issues in the construction of confidence intervals and testing of subsets of treatment effects.