Solving the Beck and Wieland model with optimal experimentation in DualPC

Abstract

Currently, there is a renewed interest in the use of optimal experimentation (adaptive control) in economics. Example are found in [Amman, H. M. & Kendrick, D. A. (1999). Should macroeconomic policy makers consider parameter covariances. Computational Economics 14, 263–267; Amman, H. M. & Kendrick, D. A. (2003). Mitigation of the Lucas critique with stochastic control methods. Journal of Economic Dynamics and Control 27, 2035–2057; Cosimano, T. F. Optimal experimentation and the perturbation method in the neighborhood of the augmented linear regulator problem. Journal of Economics, Dynamics and Control (in press); Cosimano, T. F., & Gapen, M. T. (2005b). Recursive methods of dynamic linear economics and optimal experimentation using the perturbation method, Working paper. Notre Dame, Indiana, USA: Department of Finance, University of Notre Dame; Cosimano, T. F., & Gapen, M. T. (2005a). Program notes for optimal experimentation and the perturbation method in the neighborhood of the augmented linear regulator problem, Working paper. Notre Dame, Indiana, USA: Department of Finance, University of Notre Dame; Cosimano, T. F., & Gapen, M. T. (2006). An algorithm for approximating optimal experimentation problems using the perturbation method, Working paper. Notre Dame, Indiana, USA: Department of Finance, University of Notre Dame; Tesfaselassie, M. F., Schaling, E., & Eijffinger, S. (2007). Learning about the term structure and optimal rules for inflation targeting, Working paper. Tilburg, The Netherlands: Tilburg University; Tucci, M. P. (1997). Adaptive control in the presence of time-varying parameters. Journal of Economic Dynamics and Control, 22, 39–47; Wieland, V. (2000a). Learning by doing and the value of optimal experimentation. Journal of Economic Dynamics and Control, 24, 501–543; Wieland, V., (2000b). Monetary policy, parameter uncertainty and optimal learning. Journal of Monetary Economics, 46, 199–228] . In this paper we present the Beck & Wieland model [Beck, G., & Wieland, V. (2002). Learning and control in a changing economic environment. Journal of Economic Dynamics and Control, 26, 1359–1378] and the methodology to solve this model with time-varying parameters using the various control methods described in [Kendrick, D. A. (1981). Stochastic control for economic models (1st ed.), New York, NY, USA: McGraw-Hill Book Company; Kendrick, D. A. (2002). Stochastic control for economic models (2nd ed.) Available at url: http://www.eco.utexas.edu/faculty/Kendrick] . Furthermore, we also provide numerical results using the DualPC software [Amman, H. M., & Kendrick, D. A. (1999). The DualI/DualPC software for optimal control models: User’s guide. Working paper, Austin, TX 78712, USA: Center for Applied Research in Economics, University of Texas] and show first evidence that optimal experimentation or Dual Control may produce better results than Expected Optimal Feedback.