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Structured ambiguity and model misspecification

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  • Hansen, Lars Peter
  • Sargent, Thomas J.

Abstract

A decision maker is averse to not knowing a prior over a set of restricted structured models (ambiguity) and suspects that each structured model is misspecified. The decision maker evaluates intertemporal plans under all of the structured models and, to recognize possible misspecifications, under unstructured alternatives that are statistically close to them. Likelihood ratio processes are used to represent unstructured alternative models, while relative entropy restricts a set of unstructured models. A set of structured models might be finite or indexed by a finite-dimensional vector of unknown parameters that could vary in unknown ways over time. We model such a decision maker with a dynamic version of variational preferences and revisit topics including dynamic consistency and admissibility.

Suggested Citation

  • Hansen, Lars Peter & Sargent, Thomas J., 2022. "Structured ambiguity and model misspecification," Journal of Economic Theory, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:jetheo:v:199:y:2022:i:c:s0022053120301587
    DOI: 10.1016/j.jet.2020.105165
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    References listed on IDEAS

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    1. Lars Peter Hansen & Thomas J Sargent, 2014. "Beliefs, Doubts and Learning: Valuing Macroeconomic Risk," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 10, pages 331-377, World Scientific Publishing Co. Pte. Ltd..
    2. Wang, Shaoping & Li, Ang & Wen, Kuangyu & Wu, Ximing, 2020. "Robust kernels for kernel density estimation," Economics Letters, Elsevier, vol. 191(C).
    3. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    4. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    5. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    6. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    7. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Misspecification," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 6, pages 155-216, World Scientific Publishing Co. Pte. Ltd..
    8. Lars Peter Hansen & Thomas J Sargent, 2014. "Doubts or Variability?," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 7, pages 217-256, World Scientific Publishing Co. Pte. Ltd..
    9. Epstein, Larry G. & Ji, Shaolin, 2014. "Ambiguous volatility, possibility and utility in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 269-282.
    10. Lars Peter Hansen & Thomas J Sargent, 2014. "Fragile Beliefs and the Price of Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 9, pages 293-330, World Scientific Publishing Co. Pte. Ltd..
    11. Lars Peter Hansen, 2007. "Beliefs, Doubts and Learning: Valuing Economic Risk," NBER Working Papers 12948, National Bureau of Economic Research, Inc.
    12. Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2006. "Dynamic variational preferences," Journal of Economic Theory, Elsevier, vol. 128(1), pages 4-44, May.
    13. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    14. Lars Peter Hansen & Jianjun Miao, 2018. "Aversion to ambiguity and model misspecification in dynamic stochastic environments," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 115(37), pages 9163-9168, September.
    15. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Permanent Income and Pricing," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 3, pages 33-81, World Scientific Publishing Co. Pte. Ltd..
    16. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345, January.
    17. Geweke, John & Amisano, Gianni, 2011. "Optimal prediction pools," Journal of Econometrics, Elsevier, vol. 164(1), pages 130-141, September.
    18. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    19. Hansen, Lars Peter & Szőke, Bálint & Han, Lloyd S. & Sargent, Thomas J., 2020. "Twisted probabilities, uncertainty, and prices," Journal of Econometrics, Elsevier, vol. 216(1), pages 151-174.
    20. Waggoner, Daniel F. & Zha, Tao, 2012. "Confronting model misspecification in macroeconomics," Journal of Econometrics, Elsevier, vol. 171(2), pages 167-184.
    21. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
    22. Hansen, Lars Peter & Sargent, Thomas J., 2007. "Recursive robust estimation and control without commitment," Journal of Economic Theory, Elsevier, vol. 136(1), pages 1-27, September.
    23. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    24. Lars Peter Hansen & Thomas J Sargent, 2014. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 4, pages 83-143, World Scientific Publishing Co. Pte. Ltd..
    25. Lars Peter Hansen, 2012. "Dynamic Valuation Decomposition Within Stochastic Economies," Econometrica, Econometric Society, vol. 80(3), pages 911-967, May.
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    2. Ilke AYDOGAN & Loïc BERGER & Valentina BOSETTI & Ning LIU, 2022. "Three layers of uncertainty," Working Papers 2022-iRisk-01, IESEG School of Management.
    3. Ilke Aydogan & Loïc Berger & Valentina Bosetti & Ning Liu, 2023. "Three layers of uncertainty," Post-Print hal-03031751, HAL.
    4. Cosmin L. Ilut & Martin Schneider, 2022. "Modeling Uncertainty as Ambiguity: a Review," NBER Working Papers 29915, National Bureau of Economic Research, Inc.
    5. Szőke, Bálint, 2022. "Estimating robustness," Journal of Economic Theory, Elsevier, vol. 199(C).

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    More about this item

    Keywords

    Ambiguity; Misspecification; Relative entropy; Robustness; Variational preferences; Structured and unstructured models;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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