Abstract
The lack of a clear classification structure and the use of a variety of names for the same solution method for stochastic control models in economics, create communications inefficiencies in the field. A proposal is made for a classification system based on a number of attributes of these models including stochastic elements, solution classes, estimation method, forward-looking variables and policies-to-parameters effects. Tables are provided which categorize some well-known example models into this structure. Our work focuses on models with quadratic criterion functions and linear systems equations and without game theory elements. Thus it is a mere start of a larger effort which is much needed since there has been a proliferation of stochastic control models in economics in recent years.
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References
Abel, A.B. (1975). A Comparison of three control algorithms to the Monetarist-Fiscalist debate. Annals of Economic and Social Measurement, 4, 239–252.
Adam, K. (2003). Optimal Monetary Policy with Imperfect Common Knowledge, Paper Presented at the Conference of the Society of Computational Economics Conference, Seattle, http://www.depts.washington.edu/sce2003.
Amman, H.M. and Kendrick, D.A. (1996). Forward looking variables in deterministic control. Annals of Operations Research, 68, 141–159.
Amman, H.M. and Kendrick, D.A. (1999a). Linear quadratic optimization for models with rational expectations. Macroeconomic Dynamics, 3, 534–543.
Amman, H.M. and Kendrick, D.A. (1999b). Should macroeconomic policy makers consider parameter covariances. Computational Economics, 14, 263–267.
Amman, H.M. and Kendrick, D.A. (1999c). The Duali/Dualpc Software for Optimal Control Models: User's Guide, Center for Applied Research in Economics, The University of Texas, Austin, Texas, http://www.eco.utexas.edu/faculty/Kendrick.
Amman, H.M. and Kendrick, D.A. (2000). Stochastic policy design in a learning environment with rational expectations. Journal of Optimization Theory and Applications, 105, 509–520.
Amman, H.M. and Kendrick, D.A. (2003). Mitigation of the Lucas critique with stochastic control methods. Journal of Economic Dynamics and Control, 27, 2035–2057.
Anderson, G. and Moore, G. (1985). A linear algebraic procedure for solving linear perfect foresight models. Economics Letters, 17, 247–252.
Aoki, M. (1967). Optimization of Stochastic Systems, Academic Press, New York.
Basar, T. and Olsder, G.J. (1999). Dynamic Noncooperative Game Theory, SIAM Series in Classics in Applied Mathematics, Philadelphia.
Backus, D. and Driffill, J. (1986). The Consistency of Optimal Policy in Stochastic Rational Expectation Models, Discussion Paper No. 124, Centre for Economic Policy Research, London.
Beck, G.W. and Wieland, V. (2002). Learning and control in a changing economic environment. Journal of Economic Dynamics and Control, 26, 1359–1378.
Becker, R.G., Dwolatzky, B., Karakitsos, E. and Rustem, B. (1986). The simultaneous use of Rival models in policy optimization. The Economic Journal, 96, 425–448.
Blanchard, O.J. and Kahn, C.M. (1980). The solution of linear difference models under rational expectations. Econometrica, 48, 1305–1311.
Brainard, W. (1967). Uncertainty and the effectiveness of policy. American Economic Review, 57, 411–425.
Bullard, J. and Mitra, K. (2002). Learning about monetary policy rules. Journal of Monetary Economics, 49, 1105–1129.
Chow, G.C. (1973). Effects of uncertainty on optimal control policies. International Economic Review, 14, 632–645.
Chow, G.C. (1975). Analysis and Control of Dynamic Systems, Wiley, New York.
Chow, G.C. (1997). Dynamic Economics, Oxford University Press, Oxford, UK.
Coenen, G., Levin, A. and Wieland, V. (2001). Data Uncertainty and the Role of Money as an Information Variable for Monetary Policy, European Central Bank Working Paper No. 84, Frankfurt, Germany.
Coenen, G. and Wieland, V. (2001). Evaluating Information Variables for Monetary Policy in a Noisy Economic Environment, European Central Bank, presented at the Seventh International Confernce of the Society for Computational Economics Conference,Yale University, New Haven, CT.
Cosimano, T.F. (2003). Optimal Experimentation and the Perturbation Method in the Neightborhood of the Augmented Linear Regulator, working paper, Department of Finance, University of Notre Dame, Norte Dame, IN.
Cosimano, T.F. and Gapen, M.T. (2005). Recursive Methods of Dynamic Linear Economics and Optimal Experimentation using the Perturbation Method, working paper, Department of Finance, University of Notre Dame, IN.
Craine, R. (1979). Optimal monetary policy with uncertainty. Journal of Economic Dynamics and Control, 1, 59–83.
Craine, R., Havenner, A. and Tinsley, P. (1976). Optimal macroeconomic control policies. Annals of Economic and Social Measurement, 5, 191–204.
Deissenberg, C. (1987). On the minmax Lyapunov stabilization of uncertain economies. Journal of Economic Dynamics and Control, 11, 229–234.
Evans, G. and Honkapohja, S. (2001). Convergence in monetary inflation models with heterogeneous learning rules. Macroeconomic Dynamics, 5, 1–31.
Fair, R.C. (1978). The use of optimal control techniques to measure economic performance. International Economic Review, 19, 289–309.
Fair, R.C. and Taylor, J.B. (1993). Solution and maximum likelihood estimation of dynamic rational expectations models. Econometrica, 52, 1169–1185.
Farison, J.B., Graham, R.E. and Shelton, R.C. (1967). Identification and control of linear discrete systems. IEEE Transactions on Automatic Control, AC-12, 438–442.
Fisher, P.G., Holly, S. and Hughes Hallett, A.J. (1986). Efficient solution techniques for dynamic nonlinear rational expectations models. Journal of Economic Dynamics and Control, 10, 139–145.
Giannoni, M. (2002). Robust optimal monetary policy in a forward-looking model. Macroeconomic Dynamics, 6, 111–144.
Hall, R.E. and Taylor, J.B. (1993). Macroeconomics, 4th edition, W. W. Norton & Company, New York.
Hansen, L.P. and Sargent, T.J. (2001). Robust Control and Economic Model Uncertainty, draft downloaded from Sargents web site at http://homepages.nyu.edu/∼ts43/.
Healey, A.J. and Summers, S. (1974). A suboptimal method for feedback control of the St. Louis Econometric model. Trans. ASME, J. Dynam. Syst., Meas. Control, 96, 446–454.
Henderson, D. and Turnovsky, S.J. (1972). Optimal macroeconomic policy adjustment under conditions of risk. Journal of Economic Theory, 4, 58–72.
Herbert, R.D. (1998). Observers and Macroeconomic Systems, Kluwer Academic Publishers, Boston/Dordrecht/London.
Holt, C.C. (1962). Linear decision rules for economic stabilization and growth. Quarterly Journal of Economics, 76, 20–45.
Hughes-Hallett, A. and McAdam, P. (eds.) (1999). Analyses in Macroeconomic Modeling, Kluwer Academic Publishers, Boston/Dordrecht/London.
Juillard, M. (1996). DYNARE: A Program for the Resolution and Simulation of Dynamic Models with Forward Variables through the Use of a Relaxation Algorithm, CEPREMAP Working Paper No. 9602, Paris.
Kalchbrenner, J. and Tinsley, P. (1976). On the use of feedback control in the design of aggregrate monetary policy. American Economic Review, 66, 349–355.
Karakitsos, E. and Rustem, B. (1984). Optimally derived fixed rules and indicators. Journal of Economic Dynamics and Control, 8, 33–64.
Karakitsos E. and Rustem, B. (1985). Optimal fixed rules and simple feedback laws for nonlinear econometric models. Automatica, 21, 169–180.
Kendrick, D.A. and Majors, J. (1974). Stochastic control with uncertain macroeconomic parameters. Automatica, 10, 587–594.
Kendrick, D.A. (1981). Stochastic Control for Economic Models, McGraw-Hill Book Company, New York, see also Kendrick (2002).
Kendrick, D.A. (1982). Caution and probing in a macroeconomic model. Journal of Economic Dynamics and Control, 4, 149–170.
Kendrick, D.A. (2002). Stochastic Control for Economic Models, Second Edition available at http://www.eco.utexas.edu/faculty/Kendrick.
Kendrick, D.A. (2005). Stochastic control for economic models: Past, present and paths ahead. Journal of Economic Dynamics and Control, 29, 3–30.
Kozicki, S. and Tinsley, P. (2001). Term structure views of monetary policy under alternative models of agent expectations. Journal of Economic Dynamics and Control, 25, 149–184.
Kydland, F. and Prescott, E.C. (1982). Time to build and aggregate fluctations. Econometrica, 50, 1345–1370.
Lee, M.H. (1998). Analysis of Optimal Macroeconomic Policy Design, Ph.D. Dissertation, Department of Economics, The University of Texas, Austin, Texas 78712.
Levin, A., Wieland, V. and Williams, J.C. (2003). The performance of forward-looking monetary policy rules under model uncertainty. American Economic Review, 93, 622–645.
Levine, P. and Currie, D. (1987). The design of feedback rules in linear stochastic rational expectations models. Journal of Economic Dynamics and Control, 11, 1–28.
Ljung, L., Pflug, G. and Walk, H. (1992). Stochastic Approximation and Optimization of Random Systems, Birkhauser, Berlin.
Ljung, L. and Soderstrom, T. (1983). Theory and Practice of Recursive Identification, M.I.T. Press, Cambridge, Mass.
Lucas, R. (1976). Econometric policy evaluation: A critique, in K. Brunner and A.H. Meltzer (eds.), The Phillips Curve and the Labor Markets, 19–46, Supplemental series to the Journal of Monetary Economics.
MacRae, E.C. (1972). Linear decision with experimentation. Annals of Economic and Social Measurement, 1, 437–447.
MacRae, E.C. (1975). An adaptive learning role for multiperiod decision problems. Econometrica, 43, 893–906.
Marcet, A. and Sargent, T.J. (1989). Convergence of least squares learning mechanisms in self-referential linear stochastic models. Journal of Economic Theory, 48, 337–368.
Mercado, P.R. and Kendrick, D.A. (1999). Computational Methods for Macro Policy Analysis: Hall and Taylor's Model in Duali, Chapter 8 in Hughes-Hallett and McAdam (1999), 179–206.
Mizrach, B. (1991). Non-convexities in a stochastic control problem with learning. Journal of Economic Dynamics and Control, 15, 515–538.
Norman, A.L. (1976). First order dual control. Annals of Economic and Social Measurement, 5, 311–321.
Norman, A.L. (1979). Dual Control of Perfect Observations, 343–349 in J.N.L. Janssen, L.M. Pau and A. Straszak (eds.), Models and Decision Making in National Economies, North-Holland, Amsterdam.
Norman, A. (1981). On the control of structural models, and “A Reply”. Journal of Econometrics, 15, 13–24, 29.
Onatski, A. and Stock, J.H. (2002). Robust monetary policy under model uncertainty in a small model of the U.S. economy. Macroeconomic Dynamics, 6, 85–110.
Oudiz, G. and Sachs, J. (1985). International policy coordination in dynamic in dynamic macroeconomic models, in W.H. Buiter and R.C. Marston (eds.), International Economic Policy Coordination, Cambridge University Press, Cambridge, U.K.
Pearlman, J.G., Currie, D.A. and Levine, P.L. (1986). Rational expectations models with partial information. Economic Modeling, 3, 90–125.
Phillips, A.W. (1954). Stabilization policy in a closed economy. Economic Journal, 64, 290–323.
Pindyck, R.S. (1972). An application of the linear quadratic tracking problem to economic stabilization policy. IEEE Trans. Autom. Control, AC-17, 287–300.
Pindyck, R.S. (1973a). Optimal Planning for Economic Stabilization, North-Holland, Amsterdam.
Pindyck, R.S. (1973b). Optimal policies for economic stabilization. Econometrica, 41, 529–560.
Pitchford, J.D. and Turnovsky, S.J. (eds.) (1977). Applications of Control Theory to Economic Analysis, North Holland, Amsterdam.
Prescott, E.C. (1972). The multi-period control problem under uncertainty. Econometrica, 40, 1043–1058.
Rausser, G. and Pekelman, D. (1978). Adaptive control: Survey of methods and applications. Management Science, 9, 89–120.
Rustem, B. (1992). A constrained min-max algorithm for rival models of the same economic system. Math Programming, 53, 279–295.
Rustem, B. (1998). Algorithms for Nonlinear Programming and Multiple Objective Decisions, John Wiley & Sons, New York.
Rustem, B. and Howe, M.A. (2002). Algorithms for Worst-Case Design with Applications to Risk Management, forthcoming, Princeton University Press.
Rustem, B., Wieland, V. and Zakovic, S. (2001). A Continuous Min-Max Problem and Its Application to Inflation Targeting, Ch. 11, pp. 201–219 in Zaccour (2002).
Sargent, T.J. and Wallace, N. (1975). ‘Rational’ expectations, the optimal monetary instruments, and the optimal money supply rule. Journal of Political Economy, 83, 241–254.
Sargent, T. (1978). Estimation of dyanmic labor demand schedules under rational expectations. Journal of Political Economy, 86, 1009–1044.
Sarris, A.H. (1973). A Bayesian approach to the estimaton of time-varying regression coefficients. Annals of Economic and Social Measurement, 2, 501–523.
Shupp, F.R. (1972). Uncertainty and stabilization policies for a nonlinear macroeconomic model. Quarterly Journal of Economics, 80, 94–110.
Shupp, F.R. (1976c). Uncertainty and optimal stabilization policies. J. Public Finances, 6, 243–253.
Simon, H.A. (1956). Dynamic programming under uncertainty with a quadratic criterion function. Econometrica, 24, 74–81.
Sims, C.A. (2002). Solving linear rational expectations models. Computational Economics, 20, 1–20.
Soderlind, P. (1999). Solution and estimation of RE macromodels with optimal policy. European Economic Review, 43, 813–823.
Soderstrom, U. (2002). Monetary policy with uncertain parameters. Scandinavian Journal of Economics, 104, 124–145.
Swamy, P.A.V.B. and Tinsley, P. (1980). Linear prediction and estimation methods for regression models with stationary stochastic coefficients. Journal of Econometrics, 12, 103–142.
Taylor, J.B. (1974). Asymptotic properties of multiperiod control rules in the linear regression model. International Economic Review, 15, 472–482.
Taylor, J.B. (1993). Macroeconomic Policy in a World Economy, W. W. Norton & Company, New York.
Taylor, J.B. (1993). Discretion versus policy rules in practice, Carnegie-Rochester Conference Series on Public Policy, 39, 195–214.
Taylor, J.B. (ed.) (1999). Monetary Policy Rules, University of Chicago Press, Chicago.
Tetlow, R. and von zur Muehlen, P. (2001a). Robust monetary policy with misspecified models: Does model uncertainty always call for attenuated policy? Journal of Economic Dynamics and Control, 25, 911–949.
Tetlow, R. and von zur Muehlen, P. (2001b). Avoiding Nash Inflation: Bayesian and Robust Reponses to Model Uncertainty, working paper, Board of Governors of the Federal Reserve System, Washington, D.C.
Tetlow, R. and von zur Muehlen, P. (2001c). Simplicity versus optimality: The choice of monetary policy rules when agents must learn. Journal of Economic Dynamics and Control, 25, 245–279.
Theil, H. (1957). A note on certainty equivalence in dynamic planning. Econometrica, 25, 346–349.
Tinsley, P. (1971). A variable adjustment model of labor demand. International Economic Review, 12, 481–510.
Tinsley, P., Craine, R. and Havenner, A. (1974). On NEREF Solutions of Macroeconomic Tracking Problems, 3d NBER Stochastic Control Conf., Washington.
Tinsley, P., von zur Muehlen, P. and Fries, G. (1982). The short-run volatility of money stock targeting. Journal of Monetary Economics, 215–237.
Tucci, M. (1989). Time-varying Parameters in Adaptive Control, Ph.D. Dissertation, Dept. of Economics, University of Texas, Austin, Texas, 78712.
Tucci, M. (1997). Adaptive control in the presence of time-varying parameters. Journal of Economic Dynamics and Control, 22, 39–47.
Tucci, M. (2004). The Rational Expectation Hypothesis, Time-varying Parameters and Adaptive Control, Springer, Dordrecht, The Netherlands.
Turnovsky, S.J. (1973). Optimal stabilization policies for deterministic and stochastic linear systems. Review of Economic Studies, 40, 79–96.
Turnovsky, S.J. (1975). Optimal choice of monetary instruments in a linear economic model with stochastic coefficients. J. Money Credit Banking, 7, 51–80.
Turnovsky, S.J. (1977). Optimal Control of Linear Systems with Stochastic Coefficients and Additive Disturbances, Ch. 11, in Pitchford and Turnovsky (1977).
von zur Muehlen, P. (1982). Activist vs Non-Activist Monetary Policy: Optimal Rules Under Extreme Uncertainty, reprinted in Finance and Economic Discussion Series, No. 2002–02 (2001) and downloadable from www.federalreserve.gov/pubs/feds/.
Wieland, V. (2000a). Learning by doing and the value of optimal experimentation. Journal of Economics Dynamics and Control, 24, 501–543.
Wieland, V. (2000b). Monetary policy, parameter uncertainty and optimal learning. Journal of Monetary Economics, 46, 199–228.
Woodford, M. and Svensson, L.E.O. (2003). Indicator variables for optimal policy. Journal of Monetary Economics, 50, 619–720.
Zaccour, G. (2002). Decision and Control in Management Science, Essays in Honor of Alan Haurie, Kluwer Academic Publishers, Boston/Dordrecht/London.
Zadrozny, P. and Chen, B. (1999). Perturbation Solutions of Nonlinear Rational Expectations Models, presented at the Fifth International Conference of the Society for Computational Economics, Boston College, and June 1999.
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Kendrick, D.A., Amman, H.M. A Classification System for Economic Stochastic Control Models. Comput Econ 27, 453–481 (2006). https://doi.org/10.1007/s10614-005-9000-8
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DOI: https://doi.org/10.1007/s10614-005-9000-8