<p>The problem of endogeneity remains central to research in economics and econometrics. The authors propose a model averaging method for regression models with endogenous regressors. Given the high dimensionality of instruments, the authors utilize a low-dimensional representation of the instrument set via factor instrumental variables. With a set of candidate models differing in the choices of factor instrumental variables and exogenous regressors, the authors combine the generalized method of moments estimators from each candidate model, using weights that minimize a cross-validation criterion. The authors prove the asymptotic optimality of the proposed method in the sense that it minimizes the squared estimation loss. The efficacy of the method is demonstrated through extensive simulation studies.</p>