This chapter explains how the key difficulty that arises when the Bayesian estimation of DSGE models is extended from linear to nonlinear models is the evaluation of the likelihood function, and focuses on the use of particle filters to accomplish this task. The basic bootstrap particle filtering algorithm is remarkably straightforward, but may perform quite poorly in practice. Thus, much of the literature about particle filters focuses on refinements of the bootstrap filter that increases the efficiency of the algorithm. The accuracy of the particle filter can be improved by choosing other proposal distributions. While the tailoring (or adaption) of the proposal distributions tends to require additional computations, the number of particles can often be reduced drastically, which leads to an improvement in efficiency.
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