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Time-Consistent Control in Non-Linear Models

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  • Steve Ambler
  • Florian Pelgrin

Abstract

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.

Suggested Citation

  • Steve Ambler & Florian Pelgrin, 2007. "Time-Consistent Control in Non-Linear Models," Staff Working Papers 07-3, Bank of Canada.
    • Handle: RePEc:bca:bocawp:07-3
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    References listed on IDEAS

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    Cited by:

    1. Richard Dennis, 2013. "Asset Prices, Business Cycles, and Markov-Perfect Fiscal Policy when Agents are Risk-Sensitive," CAMA Working Papers 2013-69, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    2. Kankanamge, Sumudu & Weitzenblum, Thomas, 2016. "Time-consistent unemployment insurance," TSE Working Papers 16-657, Toulouse School of Economics (TSE).
    3. Mário Amorim Lopes & Fernando A. C. C. Fontes & Dalila A. C. C. Fontes, 2013. "Optimal Control of Infinite-Horizon Growth Models — A direct approach," FEP Working Papers 506, Universidade do Porto, Faculdade de Economia do Porto.
    4. Ambler, Steve & Bouakez, Hafedh & Cardia, Emanuela, 2017. "Does the crowding-in effect of public spending on private consumption undermine neoclassical models?," Research in Economics, Elsevier, vol. 71(3), pages 399-410.
    5. Christophe Gouel & Sébastien Jean, 2015. "Optimal Food Price Stabilization in a Small Open Developing Country," The World Bank Economic Review, World Bank, vol. 29(1), pages 72-101.
    6. Dennis, Richard & Kirsanova, Tatiana, 2014. "Computing Markov-Perfect Optimal Policies in Business-Cycle Models," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-64, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    7. Dennis, Richard & Kirsanova, Tatiana, 2016. "Computing Markov-Perfect Optimal Policies In Business-Cycle Models," Macroeconomic Dynamics, Cambridge University Press, vol. 20(7), pages 1850-1872, October.
    8. Dennis, Richard, 2022. "Computing time-consistent equilibria: A perturbation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    9. Christophe Gouel, 2013. "Rules versus Discretion in Food Storage Policies," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 95(4), pages 1029-1044.
    10. Novales, Alfonso & Pérez, Rafaela & Ruiz, Jesús, 2014. "Optimal time-consistent fiscal policy in an endogenous growth economy with public consumption and capital," Journal of Macroeconomics, Elsevier, vol. 42(C), pages 104-117.

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    More about this item

    Keywords

    Fiscal policy; Monetary policy framework;

    JEL classification:

    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy; Modern Monetary Theory
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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