k-Class instrumental variables quantile regression

Abstract

With mean instrumental variables regression, k-class estimators have the potential to reduce bias, which is larger with weak instruments. With instrumental variables quantile regression, weak instrument-robust estimation is even more important because there is less guidance for assessing instrument strength. Motivated by this, we introduce an analogous k-class of estimators for instrumental variables quantile regression. We show the first-order asymptotic distribution under strong instruments is equivalent for all conventional choices of k. We evaluate finite-sample median bias in simulations for a variety of k, including the k for the conventional k-class estimator corresponding to limited information maximum likelihood (LIML). Computation is fast for all k, and compared to the \(k=1\) benchmark estimator (analogous to 2SLS), using the LIML k reliably reduces median bias in a variety of data-generating processes, especially when the degree of overidentification is larger. We also revisit some empirical estimates of consumption Euler equations derived from quantile utility maximization. All code is provided online (https://kaplandm.github.io).