The paper considers the spatial auto-regressive (SAR) model in the presence of endogenous and exogenous regressors. The instrumental variable (IV) estimators are commonly recommended when dealing with endogenous regressors, as the ordinary least squares (OLS) estimators are inconsistent in such scenarios. The paper revisits this recommendation in the context of the SAR model, particularly when the instruments are weak or when several instruments are involved. Drawing inspiration from the concept of model averaging and Hansen’s work in 2017 (see Hansen BE, Econom Rev 36(6–9):840–852, 2017), the paper employs Hausman-Wu statistic for exogeneity to blend OLS and 2SLS estimators and, through a weighted average with the weight inversely proportional to the Hausman statistic for exogeneity, proposes a Stein-like shrinkage estimator. When the number of endogenous variables exceeds two, the shrinkage estimator is shown to outperform the 2SLS estimator in terms of having lower asymptotic risk. The study also provides insights from Monte Carlo simulations, particularly regarding small sample sizes, and illustrates that the shrinkage estimator exhibits substantially reduced finite sample median squared error relative to the standard 2SLS estimator.