Frisch–Waugh–Lovell theorem-type results for the k-Class and 2SGMM estimators

Abstract

The Frisch–Waugh–Lovell (FWL) theorem shows that for the least squares estimator, parameter estimates from full and partial models are identically same. I show that in linear regression models with a mix of exogenous and endogenous regressors, FWL theorem-type results hold for the k-class estimators (including LIML) and the two-step optimal GMM estimator.