Important overlooked IVs in spatial models

Spatial models often contain additional endogenous variables as regressors. The complete system determining these variables is typically not known to the researcher, and so maximum likelihood or Bayesian estimation methods are precluded. This leaves instrumental variable estimation. In all likelihood, the system may contain certain forms of nonlinearities. These nonlinearities might arise because of endogenous weighting matrices, functional form differences in the endogenous variables, etc. The existence of such nonlinearities strongly suggests the use of nonlinear forms of the instruments. Issues of this sort were pointed out in Kelejian and Piras (Spatial econometrics, Elsevier, Amsterdam, 2017) and Kelejian (Lett Spat Resour Sci 9(1):113–136, 2016). However, thus far Monte Carlo results relating to efficiencies gained by the use of nonlinear instrumental variables are not available. This is unfortunate because these efficiencies can be quite extensive. The purpose of this paper is to fill this void.