Flexible nonlinear inference with endogenous explanatory variables

Hamilton's (2001) flexible nonlinear inference is not valid with endogenous explanatory variables. Hence, this paper proposes a framework to approach endogeneity problems in the flexible nonlinear inference. We develop two estimation procedures, namely, joint estimation and two-step estimation procedures. The parameters in both models can be estimated by maximum likelihood or numerical Bayesian method. Our approach can be used in handling endogeneity and nonlinearity in the oil-macro relationship or in the monetary policy rule.