Advertisement

Computational Economics

, Volume 35, Issue 2, pp 127–154 | Cite as

How to Maximize the Likelihood Function for a DSGE Model

  • Martin Møller Andreasen
Article

Abstract

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%.

Keywords

CMA-ES optimization routine Multimodel objective function Nelder–Mead simplex routine Non-convex search space Resampling Simulated Annealing 

JEL Classifications

C61 C88 E30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Altig, D., Christiano, L. J., Eichenbaum, M., & Linde, J. (2005). Firm-specific capital, nominal rigidities and the business cycle. NBER working paper no 11034 (pp. 1–50).Google Scholar
  2. An S., Schorfheide F. (2007) Bayesian analysis of DSGE models. Econometric Reviews 26(2–4): 113–172CrossRefGoogle Scholar
  3. Andreasen, M. M. (2008). Ensuring the validity of the micro foundation in DSGE models. Working Paper.Google Scholar
  4. Auger, A., & Hansen, N. (2005). A restart CMA evolution strategy with increasing population size. Proceedings of the IEEE Congress on Evolutionary Computation, CEC (pp. 1769–1776).Google Scholar
  5. Christiano L.J., Eichenbaum M., Evans C.L. (2005) Nominal rigidities and the dynamic effects of a shock to monetary policy. Journal of Political Economy 113: 1–45CrossRefGoogle Scholar
  6. Corana A., Marchesi M., Ridella S. (1987) Minimizing multimodal functions of continuous variables with “simulated annealing” algorithm. ACM Transactions on Mathematical Software 13(3): 262–280CrossRefGoogle Scholar
  7. Fernández-Villaverde J., Rubio-Ramírez J.F. (2007) Estimating macroeconomic models: A likelihood approach. Review of Economic Studies 74: 1–46CrossRefGoogle Scholar
  8. Goffe W.L., Ferrier G.D., Rogers J. (1994) Global optimization of statistical functions with simulated annealing. Journal of Econometrics 60: 65–99CrossRefGoogle Scholar
  9. Hansen, N. (2005). The CMA evolution strategy: A tutorial. Working Paper.Google Scholar
  10. Hansen, N., & Kern, S. (2004). Evaluating the CMA evolution strategy on multimodal test functions. In Eighth international conference on parallel problem from nature, PPSN VIII, (pp. 282–291). Berlin: Springer.Google Scholar
  11. Hansen N., Müller S.D., Koumoutsakos P. (2003) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evolutionary Computation 11(1): 1–18CrossRefGoogle Scholar
  12. Justiniano A., Primiceri G.E. (2008) The time-varying volatility of macroeconomic fluctuations. The American Economic Review 98(3): 604–641CrossRefGoogle Scholar
  13. Kern S., Muller S.D., Hansen N., Buche D., Ocenasek J., Koumoutsakos P. (2004) Learning probability distributions in continuous evolutionary algorithms—A comparative review. Natural Computing 3(1): 77–112CrossRefGoogle Scholar
  14. Lagarias J.C., Reeds J.A., Wright M.H., Wright P.E. (1998) Convergence properties of the nelder-mead simplex method in low dimensions. SIAM Journal of Optimization 9(1): 112–147CrossRefGoogle Scholar
  15. Muller S.D., Hansen N., Koumoutsakos P. (2002). Increasing the serial and the parallel performance of the CMA-evolution strategy with large populations. In Seventh international conference on parallel problem solving from nature PPSN VII, Proceedings (pp. 422–431). Berlin: Springer.Google Scholar
  16. Rossi G. D. (2004). Maximum likelihood estimation of the cox-ingersoll-ross model using particle filters. Working Paper.Google Scholar
  17. Salamon, P., Sibani, P., & Frost, R. (2002). Facts, conjectures and improvements for simulated annealing. Philadelphia: Society for Industrial and Applied Mathematics.Google Scholar
  18. Schmitt-Grohé S., Uribe M. (2004) Solving dynamic general equilibrium models using a second-order approximation to the policy function. Journal of Economic Dynamics and Control 28: 755–775CrossRefGoogle Scholar
  19. Schmitt-Grohé, S., Uribe, M. (2006). Optimal inflation stabilization in a medium-scale macroeconomic model. Working Paper (pp. 1–59).Google Scholar
  20. Smets F., Wouters R. (2007) Shocks and frictions in US business cycles: A bayesian DSGE approach. American Economic Review 97(3): 586–606CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.School of Economics and ManagementAarhus University and CREATESÅrhusDenmark

Personalised recommendations