Using the “Chandrasekhar Recursions” for Likelihood Evaluation of DSGE Models
In likelihood-based estimation of linearized Dynamic Stochastic General Equilibrium (DSGE) models, the evaluation of the Kalman Filter dominates the running time of the entire algorithm. In this paper, we revisit a set of simple recursions known as the “Chandrasekhar Recursions” developed by Morf (Fast Algorithms for Multivariate Systems, Ph.D. thesis, Stanford University, 1974) and Morf et al. (IEEE Trans Autom Control 19:315–323, 1974) for evaluating the likelihood of a Linear Gaussian State Space System. We show that DSGE models are ideally suited for the use of these recursions, which work best when the number of states is much greater than the number of observables. In several examples, we show that there are substantial benefits to using the recursions, with likelihood evaluation up to five times faster. This gain is especially pronounced in light of the trivial implementation costs—no model modification is required. Moreover, the algorithm is complementary with other approaches.
KeywordsKalman Filter Likelihood estimation Computational techniques
JEL ClassificationC18 C63 E20
This paper uses material from Chapter 1 of my dissertation at the University of Pennsylvania. I am deeply indebted to my advisor, Frank Schorfheide, for his guidance. I also thank, without implication, participants at the Research Computing Seminar at the Fed Board and John Roberts for comments.
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