  I introduce a generic method for inference on entire quantile and regression
quantile processes in the presence of a finite number of large and arbitrarily
heterogeneous clusters. The method asymptotically controls size by generating
statistics that exhibit enough distributional symmetry such that randomization
tests can be applied. The randomization test does not require ex-ante matching
of clusters, is free of user-chosen parameters, and performs well at
conventional significance levels with as few as five clusters. The method tests
standard (non-sharp) hypotheses and can even be asymptotically similar in
empirically relevant situations. The main focus of the paper is inference on
quantile treatment effects but the method applies more broadly. Numerical and
empirical examples are provided.
