Simple closed form Anderson-Rubin confidence sets

摘要

This note provides simple rules and formulas for deriving closed form confidence sets by inverting the Anderson-Rubin (AR) test in the important case of one endogenous covariate and one instrument. I demonstrate that these confidence sets can be easily constructed using standard output from three regressions: the first stage, the reduced form, and a modified reduced form. The procedure is the same for a wide variety of standard error estimators. Furthermore, I provide graphical intuition for the confidence sets that we get from inverting the AR test using instrumental confidence regions within the coordinate system of the first stage and reduced form slope coefficients.