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Time-Consistent Control in Non-Linear Models


  • 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.

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. 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.
    2. Christophe Gouel & Sébastien Jean, 2015. "Optimal Food Price Stabilization in a Small Open Developing Country," World Bank Economic Review, World Bank Group, vol. 29(1), pages 72-101.
    3. Richard Dennis, 2013. "Asset Prices, Business Cycles, and Markov-Perfect Fiscal Policy when Agents are Risk-Sensitive," Working Papers 2013_15, Business School - Economics, University of Glasgow.
    4. 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.
    5. Kankanamge, Sumudu & Weitzenblum, Thomas, 2016. "Time-consistent unemployment insurance," TSE Working Papers 16-657, Toulouse School of Economics (TSE).
    6. 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.
    7. repec:eee:reecon:v:71:y:2017:i:3:p:399-410 is not listed on IDEAS

    More about this item


    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
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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