k-Class instrumental variables quantile regression

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 $$k=1$$ 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 ).