# Exact computation of GMM estimators for instrumental variable quantile regression models

## TL;DR

This paper introduces an exact computational method for GMM estimators in instrumental variable quantile regression models by formulating the problem as a mixed integer quadratic program, demonstrated through simulations and real data.

## Contribution

The paper presents a novel formulation that allows for exact GMM estimation in IVQR models using mixed integer quadratic programming.

## Key findings

- Exact GMM estimators can be computed efficiently.
- The method outperforms approximate algorithms in accuracy.
- Application to demand for fish illustrates practical usefulness.

## Abstract

We show that the generalized method of moments (GMM) estimation problem in instrumental variable quantile regression (IVQR) models can be equivalently formulated as a mixed integer quadratic programming problem. This enables exact computation of the GMM estimators for the IVQR models. We illustrate the usefulness of our algorithm via Monte Carlo experiments and an application to demand for fish.