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Time Consistent Control in Non-Linear Models

  • Steven Ambler

    ()

    (Université du Québec à Montréal public)

  • Florian Pelgrin

This paper shows how to use optimal control theory to derive time-consistent optimal government policies in nonlinear dynamic general equilibrium models. It extends the insight of Cohen and Michel (1988), who showed that in _linear_ models time-consistent policies can be found by imposing a linear relationship between predetermined state variables and the costate variables from private agents' maximization problems. We use an analogous procedure based on the Den Haan and Marcet (1990) technique of parameterized expectations, which replaces nonlinear functions of expected future costates by flexible functions of current states. This leads to a nonlinear relationship between current state and costate variables, which is verified in equilibrium to an arbitrarily close degree of approximation. The optimal control problem of the government is recursive, unlike the Ramsey (1927) problem which is common in the optimal taxation literature. We use a model of public investment to illustrate the technique

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 282.

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Date of creation: 11 Nov 2005
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Handle: RePEc:sce:scecf5:282
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  1. Soderlind, Paul, 1999. "Solution and estimation of RE macromodels with optimal policy," European Economic Review, Elsevier, vol. 43(4-6), pages 813-823, April.
  2. Chari, V V & Kehoe, Patrick J, 1993. "Sustainable Plans and Mutual Default," Review of Economic Studies, Wiley Blackwell, vol. 60(1), pages 175-95, January.
  3. den Haan, Wouter J & Marcet, Albert, 1990. "Solving the Stochastic Growth Model by Parameterizing Expectations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 31-34, January.
  4. S. B. Aruoba & Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2005. "Comparing Solution Methods for Dynamic Equilibrium Economies," Levine's Bibliography 122247000000000855, UCLA Department of Economics.
  5. Benhabib, Jess & Rustichini, Aldo, 1997. "Optimal Taxes without Commitment," Journal of Economic Theory, Elsevier, vol. 77(2), pages 231-259, December.
  6. Per Krusell & Anthony A Smith, Jr., 2001. "Consumption Savings Decisions with Quasi-Geometric Discounting," Levine's Working Paper Archive 625018000000000251, David K. Levine.
  7. Paul Klein & Per Krusell & José-V�ctor R�os-Rull, 2008. "Time-Consistent Public Policy," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 789-808.
  8. V.V. Chari & Patrick J. Kehoe, 1989. "Sustainable plans," Staff Report 122, Federal Reserve Bank of Minneapolis.
  9. Andrew Blake & Tatiana Kirsanova, 2008. "Discretionary Policy and Multiple Equilibria in LQ RE Models," Discussion Papers 0813, Exeter University, Department of Economics.
  10. Gilles Oudiz & Jeffrey Sachs, 1985. "International Policy Coordination in Dynamic Macroeconomic Models," NBER Chapters, in: International Economic Policy Coordination, pages 274-330 National Bureau of Economic Research, Inc.
  11. V. V. Chari & Patrick J. Kehoe, 1998. "Optimal fiscal and monetary policy," Staff Report 251, Federal Reserve Bank of Minneapolis.
  12. Wouter J. den Haan & Albert Marcet, 1993. "Accuracy in simulations," Economics Working Papers 42, Department of Economics and Business, Universitat Pompeu Fabra.
  13. Steve Ambler & Alain Paquet, 1993. "Fiscal Spending Shocks, Endogenous Government Spending and Real Business Cycles," Cahiers de recherche CREFE / CREFE Working Papers 14, CREFE, Université du Québec à Montréal.
  14. Jinill Kim & Sunghyun Henry Kim, 1999. "Spurious Welfare Reversals in International Business Cycle Models," Virginia Economics Online Papers 319, University of Virginia, Department of Economics.
  15. Cohen, Daniel & Michel, Philippe, 1988. "How Should Control Theory Be Used to Calculate a Time-Consistent Government Policy?," Review of Economic Studies, Wiley Blackwell, vol. 55(2), pages 263-74, April.
  16. Ambler, Steve & Paquet, Alain, 1997. "Recursive methods for computing equilibria of general equilibrium dynamic Stackelberg games," Economic Modelling, Elsevier, vol. 14(2), pages 155-173, April.
  17. Benhabib, Jess & Velasco, Andres, 1996. "On the optimal and best sustainable taxes in an open economy," European Economic Review, Elsevier, vol. 40(1), pages 135-154, January.
  18. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
  19. Debortoli, Davide & Nunes, Ricardo, 2006. "On Linear Quadratic Approximations," MPRA Paper 544, University Library of Munich, Germany, revised Jul 2006.
  20. Bernheim, B. Douglas & Ray, Debraj, 1989. "Markov perfect equilibria in altruistic growth economies with production uncertainty," Journal of Economic Theory, Elsevier, vol. 47(1), pages 195-202, February.
  21. Salvador Ortigueira, 2006. "Markov-Perfect Optimal Taxation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(1), pages 153-178, January.
  22. Judd, Kenneth L. & Guu, Sy-Ming, 1997. "Asymptotic methods for aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1025-1042, June.
  23. repec:cup:cbooks:9780521441964 is not listed on IDEAS
  24. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
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