How to Maximize the Likelihood Function for a DSGE Model
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This paper extends two optimization routines to deal with objective functions for DSGE models. The optimization routines are (1) a version of Simulated Annealing developed by Corana A, Marchesi M, Ridella (ACM Trans Math Softw 13(3):262–280, 1987), and (2) the evolutionary algorithm CMA-ES developed by Hansen, Müller, Koumoutsakos (Evol Comput 11(1), 2003). Following these extensions, we examine the ability of the two routines to maximize the likelihood function for a sequence of test economies. Our results show that the CMA-ES routine clearly outperforms Simulated Annealing in its ability to find the global optimum and in efficiency. With ten unknown structural parameters in the likelihood function, the CMA-ES routine finds the global optimum in 95% of our test economies compared to 89% for Simulated Annealing. When the number of unknown structural parameters in the likelihood function increases to 20 and 35, then the CMA-ES routine finds the global optimum in 85 and 71% of our test economies, respectively. The corresponding numbers for Simulated Annealing are 70 and 0%.
KeywordsCMA-ES optimization routine Multimodel objective function Nelder–Mead simplex routine Non-convex search space Resampling Simulated Annealing
JEL ClassificationsC61 C88 E30
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