Solving the stochastic growth model by backsolving with a particular nonlinear form for the decision rule

Backsolving is a class of methods that generate simulated values for exogenous forcing processes in a stochastic equilibrium model from specified assumed distributions for Euler-equation disturbances. It can be thought of as a way to force the approximation error generated by inexact choice of decision rule or boundary condition into distortions of the distribution of the exogenous shocks in the simulations rather than into violations of the Euler equations as with standard approaches. Here it is applied to a one-sector neoclassical growth model with decision rule generated from a linear-quadratic approximation.