Federal Reserve Bank of MinneapolisInstitute for Empirical Macroeconomics

Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the method of undetermined coeecients. The innovation here is to demonstrate that log-linearizing the nonlinear equations can usually be done without the need for explicit diierentiation, to extend the method of undetermined coeecients to models with more endogenous state variables than ex-pectational equations, to provide a general solution and to provide frequency-domain techniques to calculate the second order properties of the model in its HP-ltered version without resorting to simulations. Since the method is an Euler-equation based approach rather than an approach based on solving a social planners problem, models with externalities or distortionary taxation do not pose additional problems. MATLAB programs to carry out the calculations in this paper are made available. This paper should be useful for researchers and Ph.D. students alike. for helpful comments. This paper was completed while visiting the Institute for Empirical Macroeconomics at the Federal Reserve Bank of Minneapolis: I am grateful for its hospitality. Any views expressed here are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.