The Integrated Instrumental Variables Estimator: Exploiting Nonlinearities for Identification of Linear Models

Abstract

A new estimator for linear models with endogenous regressors and strictly exogenous instruments is proposed. The new estimator, called the Integrated Instrumental Variables (IIV) estimator, only requires minimal assumptions to identify the true parameters, thereby providing a potential robust alternative to classical Instrumental Variables (IV) methods when instruments and endogenous variables are partially uncorrelated (i.e. weak identi cation holds) but are non-linearly dependent. The IIV estimator is simple to compute, as it can be written as a weighted least squares estimator and it does not require to solve an ill-posed problem and the subsequent regularization. Monte Carlo evidence suggests that the IIV estimator can be a valuable alternative to IV and optimal IV in nite samples under weak identi cation. An application to estimating the elasticity of intertemporal substitution highlights the merits of the proposed approach over classical IV methods.