Exponential Tilting with Weak Instruments: Estimation and Testing

Abstract

This article analyses exponential tilting estimator with weak instruments in a nonlinear framework. Our paper differs from the previous literature in the context of consistency proof. Tests that are robust to the identification problem are also analysed. These are Anderson–Rubin and Kleibergen types of test statistics. We also conduct a simulation study wherein we compare empirical likelihood and continuous updating-based tests with exponential tilting (ET)-based ones. The designs involve GARCH(1,1) and contaminated structural errors. We find that ET-based Kleibergen test has the best size among these competitors.