IDEAS home Printed from https://ideas.repec.org/a/tpr/jeurec/v1y2003i1p68-123.html
   My bibliography  Save this article

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

Author

Listed:
  • Evan W. Anderson

    (University of North Carolina,)

  • Lars Peter Hansen

    (University of Chicago,)

  • Thomas J. Sargent

    (New York University and Hoover Institution,)

Abstract

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
    as

    Download full text from publisher

    File URL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1542-4774/issues
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    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

    Lists

    This item is featured on the following reading lists, Wikipedia, or ReplicationWiki pages:
    1. Recursive Macroeconomic Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tpr:jeurec:v:1:y:2003:i:1:p:68-123. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kelly McDougall (email available below). General contact details of provider: https://direct.mit.edu/journals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.