Particle Filter Methods for Nonlinear Macroeconomic Models

Abstract

Structural models -- that is, statistical models of the macroeconomy which incorporate an underlying economic structure -- are widely used in central banking and other areas of applied macroeconomics. Because of technical difficulties in solving this type of model, they are typically used in linearised form. This thesis presents two new methods for solving and estimating nonlinear approximations of structural macromodels. The first method is designed for use with second-order approximations. Second-order approximations can be calculated relatively easily, and the proposed method allows them to be taken to the data with a high degree of efficiency compared to standard methods, by using a partially adapted particle filter. I demonstrate its effectiveness using an estimated asset pricing model. The second approach involves a novel method for approximating the nonlinear model solution. It is more accurate than a second-order approximation, and can be used with the fully adapted particle filter. This means that the second method is faster than the available alternatives. In the second half of the thesis, I use it to analyse two topics in applied macroeconomics. First, I find that incorporating a nonlinear consumption habit response and heteroscedastic shocks provides a considerable improvement in a standard New Keynesian model's ability to fit US data. Second, I demonstrate that a nonlinear response to risk can partially explain the dynamics of the Australia–US exchange rate.