Optimized Inference in Regression Kink Designs

TL;DR

This paper introduces a new method for constructing nonparametric confidence intervals in regression kink designs that improves finite sample coverage and efficiency, is data-driven, and handles shape constraints effectively.

Contribution

It develops a half-length optimal linear minimax estimator-based interval that addresses coverage issues and enhances efficiency in regression kink analysis.

Findings

Demonstrates improved finite sample coverage in simulations

Shows efficiency gains over existing procedures

Valid across various distributions of the assignment variable

Abstract

We propose a method to remedy finite sample coverage problems and improve upon the efficiency of commonly employed procedures for the construction of nonparametric confidence intervals in regression kink designs. The proposed interval is centered at the half-length optimal, numerically obtained linear minimax estimator over distributions with Lipschitz constrained conditional mean function. Its construction ensures excellent finite sample coverage and length properties which are demonstrated in a simulation study and an empirical illustration. Given the Lipschitz constant that governs how much curvature one plausibly allows for, the procedure is fully data driven, computationally inexpensive, incorporates shape constraints and is valid irrespective of the distribution of the assignment variable.