k-Class Instrumental Variables Quantile Regression

With standard 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. Computation is fast, and the "LIML" k reliably reduces median bias compared to the k=1 benchmark across a variety of data-generating processes, especially with greater degrees of overidentification. We also revisit some empirical estimates of consumption Euler equations. All code is provided online.