This paper describes a method for solving, estimating and testing a fully specified nonlinear stochastic equilibrium model by simulation in the context of an asset pricing model. A nonlinear stochastic asset pricing model with production and money is formulated, which aims to explain observed empirical relations between inflation and asset returns. Complete solution paths to the equilibrium model are generated through a back-jards mapping simulation method that does not call for any approximation procedures. The parameters of the model are estimated by simulation talking account of a broad range of dynamics of the model, and over-identifying restrictions of the model are tested by extending GMM procedures