Often
researchers wish to analyze nonlinear dynamic discretetime stochastic models This chapter
provides a toolkit for solving such models easily
building on loglinearizing the necessary equa
tions characterizing the equilibrium and solving for the recursive equilibrium law of motion with
the method of undetermined coecients This chapter contains nothing substantially new In
stead
the chapter simplies and unies existing approaches to make them accessible for a wide
audience
showing how to loglinearizing the nonlinear equations without the need for explicit
dierentiation
how to use the method of undetermined coecients for models with a vector of
endogenous state variables
to provide a general solution by characterizing the solution with a
matrix quadratic equation and solving it
and to provide frequencydomain techniques to cal
culate the second order properties of the model in its HPltered version without resorting to
simulations Since the method is an Eulerequation 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 chap
ter are made available This chapter should be useful for researchers and PhD students alike