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Time Consistent Control in Non-Linear Models

Author

Listed:
  • Steven Ambler

    (Université du Québec à Montréal public)

  • Florian Pelgrin

Abstract

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

Suggested Citation

  • Steven Ambler & Florian Pelgrin, 2005. "Time Consistent Control in Non-Linear Models," Computing in Economics and Finance 2005 282, Society for Computational Economics.
    • Handle: RePEc:sce:scecf5:282
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    File URL: http://repec.org/sce2005/up.18673.1107179786.pdf
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    Cited by:

    1. 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.
    2. 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.
    3. Kankanamge, Sumudu & Weitzenblum, Thomas, 2016. "Time-consistent unemployment insurance," TSE Working Papers 16-657, Toulouse School of Economics (TSE).
    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. 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.
    6. 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.
    7. 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.
    8. 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).
    9. Dennis, Richard, 2022. "Computing time-consistent equilibria: A perturbation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    10. 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.

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    Keywords

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    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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