Existence and Uniqueness of Perturbation Solutions in DSGE Models

We prove the existence of unique solutions for all undetermined coefficients of nonlinear perturbations of arbitrary order in a wide class of discrete time DSGE models under standard regularity and saddle stability assumptions for linear approximations. Our result follows from the straightforward application of matrix analysis to our perturbation derived with Kronecker tensor calculus. Additionally, we relax the assumptions needed for the local existence theorem of perturbation solutions and prove that the local solution is independent of terms first order in the perturbation parameter.