Bridging TSLS and JIVE

Abstract

Economists often implement TSLS to handle endogeneity. The bias of TSLS is severe when the number of instruments is large. Hence, JIVE has been proposed to reduce bias of over-identified TSLS. However, both methods have critical drawbacks. While over-identified TSLS has a large bias with a large degree of overidentification, JIVE is unstable. In this paper, I bridge the optimization problems of TSLS and JIVE, solve the connected problem and propose a new estimator TSJI. TSJI has a user-defined parameter $\lambda$. By approximating the bias of the TSJI up to op(1/N), I find a $\lambda$ value that produces approximately unbiased TSJI. TSJI with the selected $\lambda$ value not only has the same first order distribution as TSLS when the number of first-stage and second-stage regressors are fixed, but also is consistent and asymptotically normal under many-instrument asymptotics. Under three different simulation settings, I test TSJI against TSLS and JIVE with instruments of different strengths. TSJI clearly outperforms TSLS and JIVE in simulations. I apply TSJI to two empirical studies. TSJI mostly agrees with TSLS and JIVE, but it also gives different conclusions from TSLS and JIVE for specific cases