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Inequality Constraints in Recursive Economies

Author

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  • Pontus Rendahl

Abstract

Dynamic models with inequality constraints pose a challenging problem for two major reasons: Dynamic Programming techniques often necessitate a non established differentiability of the value function, while Euler equation based techniques have problematic or unknown convergence properties. This paper aims to resolve these two concerns: An "envelope theorem" is presented that establishes the differentiability of any element in the convergent sequence of approximate value functions when inequality constraints may bind. As a corollary, convergence of an iterative procedure on the Euler equation, usually referred to as time iteration, is ascertained. This procedure turns out to be very convenient from a computational perspective; dynamic economic problems with inequality constraints can be solved reliably and extremely efficiently by exploiting the theoretical insights provided by the paper.

Suggested Citation

  • Pontus Rendahl, 2006. "Inequality Constraints in Recursive Economies," Economics Working Papers ECO2006/6, European University Institute.
    • Handle: RePEc:eui:euiwps:eco2006/6
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    Cited by:

    1. Pontus Rendahl, 2012. "Asset‐Based Unemployment Insurance," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 743-770, August.
    2. Hintermaier, Thomas & Koeniger, Winfried, 2010. "The method of endogenous gridpoints with occasionally binding constraints among endogenous variables," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 2074-2088, October.
    3. Emilio Espino & Thomas Hintermaier, 2009. "Asset trading volume in a production economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(2), pages 231-258, May.
    4. Michael Grill & Johannes Brumm, 2010. "Computing Equilibria in Dynamic Models with Occasionally Binding Constraints," 2010 Meeting Papers 695, Society for Economic Dynamics.

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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