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Time-consistent control in nonlinear models

  • Ambler, Steve
  • Pelgrin, Florian

The paper shows how to use optimal control to compute optimal time-consistent Markovian government policies in nonlinear dynamic general equilibrium models. It extends Cohen and Michel's (1988) results for the linear-quadratic case. The method involves replacing private agents' costate variables with flexible functions of current state variables in the government's maximization problem. The functions hold in equilibrium to an arbitrarily close approximation. They can be found numerically by perturbation or projection methods. A stochastic model of optimal public spending illustrates the technique.

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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 34 (2010)
Issue (Month): 10 (October)
Pages: 2215-2228

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Handle: RePEc:eee:dyncon:v:34:y:2010:i:10:p:2215-2228
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

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  1. V.V. Chari & Patrick J. Kehoe, 1989. "Sustainable plans," Staff Report 122, Federal Reserve Bank of Minneapolis.
  2. Ambler, Steve & Paquet, Alain, 1996. "Fiscal spending shocks, endogenous government spending, and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 237-256.
  3. Den Haan, Wouter J & Marcet, Albert, 1994. "Accuracy in Simulations," Review of Economic Studies, Wiley Blackwell, vol. 61(1), pages 3-17, January.
  4. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing Solution Methods for Dynamic Equilibrium Economies," PIER Working Paper Archive 04-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  5. Per Krusell & Anthony A. Smith, Jr., 2003. "Consumption--Savings Decisions with Quasi--Geometric Discounting," Econometrica, Econometric Society, vol. 71(1), pages 365-375, January.
  6. Blake, Andrew P. & Kirsanova, Tatiana, 2006. "Discretionary Policy and Multiple Equilibria in LQ RE Models," MPRA Paper 21901, University Library of Munich, Germany, revised 01 Apr 2010.
  7. Lawrence J. Christiano & Jonas D.M. Fisher, 1994. "Algorithms for solving dynamic models with occasionally binding constraints," Working Paper Series, Macroeconomic Issues 94-6, Federal Reserve Bank of Chicago.
  8. Debortoli, Davide & Nunes, Ricardo, 2006. "On Linear Quadratic Approximations," MPRA Paper 544, University Library of Munich, Germany, revised Jul 2006.
  9. 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.
  10. Benhabib, J. & Rustichini, A., 1996. "Optimal Taxes Without Commitment," Working Papers 96-18, C.V. Starr Center for Applied Economics, New York University.
  11. 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.
  12. Söderlind, Paul, 1998. "Solution and Estimation of RE Macromodels with Optimal Policy," SSE/EFI Working Paper Series in Economics and Finance 256, Stockholm School of Economics.
  13. 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.
  14. 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.
  15. Kim, Jinill & Kim, Sunghyun Henry, 2003. "Spurious welfare reversals in international business cycle models," Journal of International Economics, Elsevier, vol. 60(2), pages 471-500, August.
  16. repec:cup:cbooks:9780521441964 is not listed on IDEAS
  17. V. V. Chari & Patrick E. Kehoe, 1990. "Sustainable Plans and Mutual Default," IMF Working Papers 90/22, International Monetary Fund.
  18. 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.
  19. 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.
  20. 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.
  21. V. V. Chari & Patrick J. Kehoe, 1998. "Optimal fiscal and monetary policy," Staff Report 251, Federal Reserve Bank of Minneapolis.
  22. 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.
  23. 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.
  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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