A Numerical Procedure to Estimate Real Business Cycle Models Using Simulated Annealing

  • Willi Semmler
  • Gang Gong
Part of the Advances in Computational Economics book series (AICE, volume 6)


This paper presents a numerical procedure to estimate a stochastic growth model of real business cycle type where the decision rules are not analytically solvable. The statistical estimation of this type of models faces the difficulty that the relationship is not explicit between the estimated parameters and the objective function for the estimation (for example, the distance function in GMM estimation). Furthermore, multiple local optima may exist since the objective function is often nonlinear in parameters. To circumvent these problems, we introduce a global optimization algorithm, the simulated annealing, that searches the parameter space recursively for the global optimum. When this algorithm is employed, along with an appropriate approximation method of dynamic programming to numerically compute the decision rules, the estimation turns out to be efficient. The estimation of structural parameters with statistical methods appears to us a necessary step to empirically evaluate RBC models.


Simulated Annealing Stochastic Dynamic Programming Business Cycle Theory Real Business Cycle Macroeconomic Time Series 
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  1. Altug, S., 1989, ‘Time to build and aggregate fluctugtions: Some new evidence’, International Economic Review 30, 889–920.CrossRefGoogle Scholar
  2. Burnside, C., M. Eichenbaum, and S. Rebelo, 1993, ‘Labor hoarding and the business cycle’, Journal of Political Economy 101, 245–273.CrossRefGoogle Scholar
  3. Chow, G.C., 1991, ‘Dynamic optimization without dynamic programming’, Econometric Research Program, Research Memorandum, No. 361, Princeton: Princeton University.Google Scholar
  4. Chow, G.C., 1993a, `Statistical estimation and testing of a real business cycle model’, Econometric Research Program, Research Memorandum, No. 365, Princeton: Princeton University.Google Scholar
  5. Chow, G.C., 1993b, `Optimum control without solving the Bellman equation’, Journal of Economic Dynamics and Control 17, 621–630.CrossRefGoogle Scholar
  6. Christiano, L.J., 1987, `Dynamic properties of two approximate solutions to a particular growth model’, Research Department Working Papers, No. 338, Federal Reserve Bank of Minneapolis.Google Scholar
  7. Christiano, L.J., 1988, `Why does inventory fluctuate so much?’, Journal of Monetary Economics 21, 247–280.CrossRefGoogle Scholar
  8. Christiano, L.J. and M. Eichenbaum, 1992, ‘Current real business cycle theories and aggregate labor market fluctuation’, American Economic Review 82, 431–472.Google Scholar
  9. Corana, A., M.C. Martini, and S. Ridella, 1987, `Minimizing multimodal functions of continuous variables with the simulating annealing algorithm’, ACM Transactions on Mathematical Software 13, 262–280.CrossRefGoogle Scholar
  10. Eichenbaum, M., 1991, `Real business cycle theory: Wisdom or whimsy?’, Journal of Economic Dynamics and Control 15, 607–626.CrossRefGoogle Scholar
  11. Goffe, W.L., G. Ferrier, and J. Rogers, 1991, ‘Global optimization of statistical functions’, in H.M. Amman, D.A. Belsley, and L.F. Pau (Eds), Computational Economics and Econometrics, Vol. 1, Dordrecht: Kluwer.Google Scholar
  12. Hansen, G.H., 1985, `Indivisible labor and business cycle’, Journal of Monetary Economics 16, 309–327.CrossRefGoogle Scholar
  13. Hansen, L.P., 1982, ‘Large sample properties of generalized methods of moments estimators’, Econometrica 50, 1029–1054.CrossRefGoogle Scholar
  14. Hansen, L.P. and K.J. Singleton, 1982, ‘Generalized instrument variables estimation of nonlinear rational expectations models’, Econometrica 50, 1268–1286.Google Scholar
  15. Newey, W.K. and K.D. West, 1987, ‘A simple, positive semi-definite, heteroskedastcity and autocorrelation consistent covariance matrix’, Econometric 55, 703–708.CrossRefGoogle Scholar
  16. King, R.G., C.I. Plosser, and S.T. Rebelo, 1988, `Production, growth and business cycles I: The basic neo-classical model’, Journal of Monetary Economics 21, 195–232.CrossRefGoogle Scholar
  17. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.M., and Teller, E., 1953, `Equation of state calculation by fast computing machines’, The Journal of Chemical Physics 21, 1087–1092.CrossRefGoogle Scholar
  18. Semmler, W., 1995, ‘Solving nonlinear dynamic models by interative dynamic programming’, Computational Economics 8, 127–154.CrossRefGoogle Scholar
  19. Semmler, W. and G. Gong, 1994, `Estimating and evaluating equilibrium business cycle models’, Working Papers Series, No. 56, Department of Economics, New School for Social Research.Google Scholar
  20. Semmler, W. and G. Gong, 1996a, ‘Estimating parameters of real business cycle models’, Journal of Economic Behavior and Organization, 30.Google Scholar
  21. Semmler, W. and G. Gong, 1996b, ‘Estimating stochastic growth models: A comparison of different data sets’, New School for Social Research, Memeo.Google Scholar
  22. Singleton, K., 1988, `Econometric issues in the analysis of equilibrium business cycle models’, Journal of Monetary Economics 21, 361–386.CrossRefGoogle Scholar
  23. Taylor, J.B. and H. Uhlig, 1990, ‘Solving nonlinear stochastic growth models: A comparison of alternative solution methods’, Journal of Business and Economic Statistics 8 (1), 1–17.Google Scholar

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© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Willi Semmler
  • Gang Gong

There are no affiliations available

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