Optimal monetary and fiscal policy under discretion in the new Keynesian model: A technical appendix to Great expectations and the end of the Depression

This paper details the microfoundations of the model presented in Staff Report no. 234, “Great Expectations and the End of the Depression.” It defines the Markov perfect equilibrium formally in the nonlinear model, discusses in some detail the approximation method used and the order of accuracy of this approximation, and gives proofs of two propositions not proved in Staff Report no. 234. In addition, this paper states a proposition that shows the equivalence between the linear quadratic approximation in Staff Report no. 234 and a first order approximation to the exact nonlinear conditions of the government in the Markov perfect equilibrium defined here.