Solving and simulating unbalanced growth models using linearization about the current state

- We detail a method of solving and simulating DSGE models which is more accurate than the traditional method of linearizing about the steady state.
- Our method takes longer, but is able to sole and simulate unbalanced growth models which cannot be solved using any other current method.
- While the execution time is longer it is not prohibitively so, and the results are much more accurate, at least when measured by Euler errors.

This paper presents an adjustment to commonly used linear approximation methods for dynamic stochastic general equilibrium (DSGE) models. Policy functions approximated around the steady state will be inaccurate away from the steady state. In some cases the model may not have a well-defined steady state, or the nature of the steady state may be at odds with its off-steady-state dynamics. We show how to simulate a DSGE model with no well-defined steady state by approximating about the current state. Our method minimizes the error associated with a finite-order Taylor-series expansion of the model's characterizing equations. This method is easily implemented and has the advantage of mimicking highly non-linear behavior. It also requires choosing N out of 2N possible roots from a matrix quadratic equations and the choice of this root not obvious away from the steady state. However, simulations show that using the same criteria as when linearizing about the steady state yield reasonable, well-fitting results.