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A maximum likelihood approach to combining forecasts

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  • Levy, Gilat
  • Razin, Ronny

Abstract

We model an individual who wants to learn about a state of the world. The individual has a prior belief and has data that consist of multiple forecasts about the state of the world. Our key assumption is that the decision maker identifies explanations that could have generated this data and among these focuses on those that maximize the likelihood of observing the data. The decision maker then bases her final prediction about the state on one of these maximum likelihood explanations. We show that in all the maximum likelihood explanations, moderate forecasts are just statistical derivatives of extreme ones. Therefore, the decision maker will base her final prediction only on the information conveyed in the relatively extreme forecasts. We show that this approach to combining forecasts leads to a unique prediction, and a simple and dynamically consistent way to aggregate opinions.

Suggested Citation

  • Levy, Gilat & Razin, Ronny, 2021. "A maximum likelihood approach to combining forecasts," LSE Research Online Documents on Economics 104116, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:104116
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    File URL: http://eprints.lse.ac.uk/104116/
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    References listed on IDEAS

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    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    2. Gilat Levy & Ronny Razin, 2012. "When do simple policies win?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(3), pages 621-637, April.
    3. Benjamin Golub & Matthew O. Jackson, 2012. "How Homophily Affects the Speed of Learning and Best-Response Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1287-1338.
    4. Gilboa, Itzhak & Schmeidler, David, 2010. "Simplicity and likelihood: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1757-1775, September.
    5. Ran Spiegler, 2016. "Bayesian Networks and Boundedly Rational Expectations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(3), pages 1243-1290.
    6. Levy, Gilat & Razin, Ronny, 2013. "Dynamic legislative decision making when interest groups control the agenda," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1862-1890.
    7. Matthew Rabin & Dimitri Vayanos, 2010. "The Gambler's and Hot-Hand Fallacies: Theory and Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 730-778.
    8. , & , & ,, 2016. "Fragility of asymptotic agreement under Bayesian learning," Theoretical Economics, Econometric Society, vol. 11(1), January.
    9. Roberta De Filippis & Antonio Guarino & Philippe Jehiel & Toru Kitagawa, 2016. "Updating ambiguous beliefs in a social learning experiment," CeMMAP working papers 18/16, Institute for Fiscal Studies.
    10. Pietro Ortoleva, 2012. "Modeling the Change of Paradigm: Non-Bayesian Reactions to Unexpected News," American Economic Review, American Economic Association, vol. 102(6), pages 2410-2436, October.
    11. Benjamin Enke & Florian Zimmermann, 2019. "Correlation Neglect in Belief Formation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 313-332.
    12. Jeffrey S. Rosenthal & Martin J. Osborne & Matthew A. Turner, 2000. "Meetings with Costly Participation," American Economic Review, American Economic Association, vol. 90(4), pages 927-943, September.
    13. Erik Eyster & Georg Weizsäcker, 2011. "Correlation Neglect in Financial Decision-Making," Discussion Papers of DIW Berlin 1104, DIW Berlin, German Institute for Economic Research.
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    Cited by:

    1. Olivier Compte, 2023. "Belief formation and the persistence of biased beliefs," Papers 2310.08466, arXiv.org.
    2. Marcos R. Fernandes, 2024. "Combining Combined Forecasts: a Network Approach," Papers 2406.13749, arXiv.org.
    3. Kfir Eliaz & Simone Galperti & Ran Spiegler, 2022. "False Narratives and Political Mobilization," Papers 2206.12621, arXiv.org.

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    More about this item

    Keywords

    maximum likelihood; combining forecasts; misspecified models;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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