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Time-Consistent Control in Non-Linear Models

Listed author(s):
  • Steve Ambler
  • Florian Pelgrin

We show how to use optimal control theory to derive optimal time-consistent Markov-perfect government policies in nonlinear dynamic general equilibrium models, extending the result of Cohen and Michel (1988) for models with quadratic objective functions and linear dynamics. We replace private agents' costates by flexible functions of current states in the government's maximization problem. The functions are verified in equilibrium to an arbitrarily close degree of approximation. They can be found numerically by perturbation or projection methods. We use a stochastic model of optimal public spending to illustrate the technique.

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File URL: http://www.bankofcanada.ca/wp-content/uploads/2010/02/wp07-3.pdf
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Paper provided by Bank of Canada in its series Staff Working Papers with number 07-3.

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Length: 32 pages
Date of creation: 2007
Handle: RePEc:bca:bocawp:07-3
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Web page: http://www.bank-banque-canada.ca/

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  6. Chari, V V & Kehoe, Patrick J, 1990. "Sustainable Plans," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 783-802, August.
  7. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, July.
  8. 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.
  9. Andrew P. Blake & Tatiana Kirsanova, 2012. "Discretionary Policy and Multiple Equilibria in LQ RE Models," Review of Economic Studies, Oxford University Press, vol. 79(4), pages 1309-1339.
  10. 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.
  11. Benhabib, Jess & Rustichini, Aldo, 1997. "Optimal Taxes without Commitment," Journal of Economic Theory, Elsevier, vol. 77(2), pages 231-259, December.
  12. Currie,David & Levine,Paul, 2009. "Rules, Reputation and Macroeconomic Policy Coordination," Cambridge Books, Cambridge University Press, number 9780521104609, Diciembre.
  13. 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.
  14. 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.
  15. 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.
  16. V. V. Chari & Patrick J. Kehoe, 1993. "Sustainable Plans and Mutual Default," Review of Economic Studies, Oxford University Press, vol. 60(1), pages 175-195.
  17. 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.
  18. 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.
  19. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," Review of Economic Studies, Oxford University Press, vol. 61(1), pages 3-17.
  20. Debortoli, Davide & Nunes, Ricardo, 2006. "On Linear Quadratic Approximations," MPRA Paper 544, University Library of Munich, Germany, revised Jul 2006.
  21. 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.
  22. 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.
  23. Daniel Cohen & Philippe Michel, 1988. "How Should Control Theory Be Used to Calculate a Time-Consistent Government Policy?," Review of Economic Studies, Oxford University Press, vol. 55(2), pages 263-274.
  24. Paul Klein & Per Krusell & José-Víctor Ríos-Rull, 2008. "Time-Consistent Public Policy," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 789-808.
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