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A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection


  • Evan W. Anderson

    (University of North Carolina,)

  • Lars Peter Hansen

    (University of Chicago,)

  • Thomas J. Sargent

    (New York University and Hoover Institution,)


A representative agent fears that his model, a continuous time Markov process with jump and diffusion components, is misspecified and therefore uses robust control theory to make decisions. Under the decision maker's approximating model, cautious behavior puts adjustments for model misspecification into market prices for risk factors. We use a statistical theory of detection to quantify how much model misspecification the decision maker should fear, given his historical data record. A semigroup is a collection of objects connected by something like the law of iterated expectations. The law of iterated expectations defines the semigroup for a Markov process, while similar laws define other semigroups. Related semigroups describe (1) an approximating model; (2) a model misspecification adjustment to the continuation value in the decision maker's Bellman equation; (3) asset prices; and (4) the behavior of the model detection statistics that we use to calibrate how much robustness the decision maker prefers. Semigroups 2, 3, and 4 establish a tight link between the market price of uncertainty and a bound on the error in statistically discriminating between an approximating and a worst case model. (JEL: C00, D51, D81, E1, G12) Copyright (c) 2003 The European Economic Association.

Suggested Citation

  • Evan W. Anderson & Lars Peter Hansen & Thomas J. Sargent, 2003. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 68-123, March.
  • Handle: RePEc:tpr:jeurec:v:1:y:2003:i:1:p:68-123

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    References listed on IDEAS

    1. Ulrich Erlenmaier & Hans Gersbach, 2001. "Flexible Majority Rules," CESifo Working Paper Series 464, CESifo Group Munich.
    2. Persson, Torsten & Tabellini, Guido, 2002. "Political economics and public finance," Handbook of Public Economics,in: A. J. Auerbach & M. Feldstein (ed.), Handbook of Public Economics, edition 1, volume 3, chapter 24, pages 1549-1659 Elsevier.
    3. Persson, Torsten & Tabellini, Guido, 1999. "Political economics and macroeconomic policy," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 22, pages 1397-1482 Elsevier.
    4. Casella, Alessandra, 2005. "Storable votes," Games and Economic Behavior, Elsevier, vol. 51(2), pages 391-419, May.
    5. Hans Gersbach, 2002. "Democratic Mechanisms: Double Majority Rules and Flexible Agenda Costs," CESifo Working Paper Series 749, CESifo Group Munich.
    6. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Oxford University Press, vol. 38(2), pages 175-208.
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    More about this item

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates


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    1. Recursive Macroeconomic Theory


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