[Paper Review] Robust Uniform Inference for Quantile Treatment Effects in Regression Discontinuity Designs

Harold D. Chiang, Yu‐Chin Hsu+1 more|arXiv (Cornell University)|Feb 15, 2017

Statistical Methods and Inference35 references4 citations

TL;DR

This paper develops a unified framework for robust uniform inference on quantile treatment effects in fuzzy regression discontinuity designs, enabling inference that is robust to large bandwidths. It extends existing methods to handle uniform inference for CDF and quantile processes, validated through simulations and an empirical application to the Oklahoma pre-K program, offering improved reliability in causal inference under model uncertainty.

ABSTRACT

The practical importance of inference with robustness against large bandwidths for causal effects in regression discontinuity and kink designs is widely recognized. Existing robust methods cover many cases, but do not handle uniform inference for CDF and quantile processes in fuzzy designs, despite its use in the recent literature in empirical microeconomics. In this light, this paper extends the literature by developing a unified framework of inference with robustness against large bandwidths that applies to uniform inference for quantile treatment effects in fuzzy designs, as well as all the other cases of sharp/fuzzy mean/quantile regression discontinuity/kink designs. We present Monte Carlo simulation studies and an empirical application for evaluations of the Oklahoma pre-K program.

Motivation & Objective

• To address the gap in robust inference methods for uniform quantile treatment effects in fuzzy regression discontinuity designs.
• To extend existing bandwidth-robust inference to handle cumulative distribution function (CDF) and quantile process inference.
• To provide a unified methodological framework applicable to all combinations of sharp/fuzzy and mean/quantile regression discontinuity/kink designs.
• To ensure inference remains valid even when bandwidths are large, improving robustness in empirical applications.

Proposed method

• The authors develop a uniform inference procedure based on a multiplier central limit theorem for empirical processes under weak dependence.
• They construct a bandwidth-robust test statistic that accounts for potential bias in local polynomial estimation of quantile regression functions.
• The method employs a wild bootstrap procedure to approximate the asymptotic distribution of the test statistic under the null hypothesis.
• It integrates the use of kernel-based weighting and local linear estimation to improve finite-sample performance.
• The framework allows for inference over a range of quantiles simultaneously, ensuring uniform coverage across the conditional quantile process.
• Theoretical justification is provided through weak convergence results under minimal regularity conditions, ensuring broad applicability.

Experimental results

Research questions

• RQ1 Can robust uniform inference be developed for quantile treatment effects in fuzzy regression discontinuity designs?
• RQ2 How can inference be made robust to large bandwidths in the context of quantile and CDF processes?
• RQ3 What is the finite-sample performance of the proposed method compared to existing alternatives?
• RQ4 Does the method maintain correct coverage rates across different quantiles and design configurations?
• RQ5 Can the framework be unified across all variants of regression discontinuity and kink designs?

Key findings

• The proposed method achieves uniform coverage rates close to nominal levels across a range of quantiles, even with large bandwidths.
• Monte Carlo simulations show that the method maintains correct size and exhibits good power in finite samples.
• The empirical application to the Oklahoma pre-K program reveals significant positive treatment effects at the median and upper quantiles of children's test scores.
• The method outperforms conventional inference procedures in terms of robustness to bandwidth choice and model misspecification.
• The wild bootstrap approximation effectively captures the sampling distribution of the test statistic, ensuring reliable critical values.
• Theoretical results confirm the validity of the inference procedure under weak regularity conditions, supporting broad empirical use.