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An augmented first-order approach for incentive problems

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  • Philipp Renner

Abstract

Incentive constraints are constraints that are optimization problems themselves. If these problems are non convex then the first order approach fails. We propose an alternative solution method where we use the value function as an additional constraint. This ensures that all solutions are incentive compatible. To get the value function we use a function interpolator like sparse grids. We demonstrate our approach by solving two examples from the literature were it was shown that the first order approach fails.

Suggested Citation

  • Philipp Renner, 2020. "An augmented first-order approach for incentive problems," Working Papers 297498586, Lancaster University Management School, Economics Department.
    • Handle: RePEc:lan:wpaper:297498586
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    References listed on IDEAS

    as
    1. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    2. J. A. Mirrlees, 1999. "The Theory of Moral Hazard and Unobservable Behaviour: Part I," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 3-21.
    3. Philipp Renner & Karl Schmedders, 2015. "A Polynomial Optimization Approach to Principal–Agent Problems," Econometrica, Econometric Society, vol. 83, pages 729-769, March.
    4. Chade, Hector & Swinkels, Jeroen M., 2020. "The no-upward-crossing condition, comparative statics, and the moral-hazard problem," Theoretical Economics, Econometric Society, vol. 15(2), May.
    5. Araujo, Aloisio & Moreira, Humberto, 2001. "A general Lagrangian approach for non-concave moral hazard problems," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 17-39, February.
    6. Arpad Abraham & Nicola Pavoni, 2008. "Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending: A Recursive Formulation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(4), pages 781-803, October.
    7. Johannes Brumm & Simon Scheidegger, 2017. "Using Adaptive Sparse Grids to Solve High‐Dimensional Dynamic Models," Econometrica, Econometric Society, vol. 85, pages 1575-1612, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    incentive constraints; first order approach; parametric optimization; value function approach;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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