# Decentralization Estimators for Instrumental Variable Quantile Regression Models

## TL;DR

This paper introduces a decomposition approach for IVQR models that simplifies estimation by breaking it into convex quantile regressions, enabling faster and more accessible causal effect estimation.

## Contribution

It presents a novel decomposition method that transforms the complex IVQR estimation into convex sub-problems, improving efficiency and implementation.

## Key findings

- Decomposition into convex quantile regressions simplifies IVQR estimation.
- New identification results for IVQR models.
- Proposed estimators are fast, easy to implement, and tuning-free.

## Abstract

The instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen, 2005) is a popular tool for estimating causal quantile effects with endogenous covariates. However, estimation is complicated by the non-smoothness and non-convexity of the IVQR GMM objective function. This paper shows that the IVQR estimation problem can be decomposed into a set of conventional quantile regression sub-problems which are convex and can be solved efficiently. This reformulation leads to new identification results and to fast, easy to implement, and tuning-free estimators that do not require the availability of high-level "black box" optimization routines.