Randomization inference is quickly becoming a widely used statistical approach in the social, behavioral, and natural sciences. In the setting of regression kink designs, Ganong and J¨ager (2018) propose a randomization test that is constructed based on random kink points, assigned by a policy. The limitation of their method is that researchers are assumed to know the policy data generating process that selects the kink point and use that distribution to simulate critical values for the test. Although the randomization test has exact size under such an assumption, the test is no longer valid even asymptotically if the researcher misspecifies the policy assignment distribution. The first contribution of this paper is to provide a general framework for randomization tests based on policy assignments of individuals into treatment and control groups. Our framework includes not only regression discontinuity and kink designs but also bunching and difference-in-differences models. Our proposed test controls size in large samples even when the researcher does not know the policy assignment distribution; it retains the exactness property of the randomization test when the policy distribution is known.
