Cluster Jackknife Instrumental Variables Estimation

Abstract Researchers commonly use jackknife-based instrumental variables estimators to eliminate the many-instruments bias of two-stage least squares. Where inference must be clustered, however, the jackknife fails to eliminate the bias. We propose a cluster-jackknife approach in which first-stage predicted values for each observation are constructed from a regression that leaves out the observation’s entire cluster. The cluster-jackknife instrumental variables estimator (CJIVE) eliminates many-instruments bias, and consistently estimates causal effects in the traditional linear model and local average treatment effects in the heterogeneous treatment effects framework. We illustrate the method in an application estimating the effects of pre-trial detention in Miami-Dade County.