Inference on quantile processes with a finite number of clusters

TL;DR

This paper proposes a new inference method for quantile processes with a finite number of heterogeneous clusters, enabling reliable hypothesis testing without extensive cluster matching.

Contribution

It introduces a distributional symmetry-based randomization test that works with few clusters and does not require parameter tuning, broadening inference capabilities.

Findings

Performs well with as few as five clusters

Controls size asymptotically in heterogeneous settings

Applicable to quantile treatment effects and beyond

Abstract

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.