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Endogenous Second Moments: A Unified Approach to Fluctuations in Risk, Dispersion, and Uncertainty

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  • Straub, Ludwig
  • Ulbricht, Robert

Abstract

Many important statistics in macroeconomics and finance—such as cross-sectional dispersions, risk, volatility, or uncertainty—are second moments. In this paper, we explore a mechanism by which second moments naturally and endogenously fluctuate over time as nonlinear transformations of fundamentals. Specifically, we provide general results that characterize second moments of transformed random variables when the underlying fundamentals are subject to distributional shifts that affect their means, but not their variances. We illustrate the usefulness of our results with a series of applications to (1) the cyclicality of the cross-sectional dispersions of macroeconomic variables, (2) the dispersion of MRPKs, (3) security pricing, and (4) endogenous uncertainty in Bayesian inference problems.

Suggested Citation

  • Straub, Ludwig & Ulbricht, Robert, 2016. "Endogenous Second Moments: A Unified Approach to Fluctuations in Risk, Dispersion, and Uncertainty," TSE Working Papers 16-664, Toulouse School of Economics (TSE), revised Mar 2018.
    • Handle: RePEc:tse:wpaper:30521
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    2. Schaal, Edouard & Taschereau-Dumouchel, Mathieu, 2023. "Herding through booms and busts," Journal of Economic Theory, Elsevier, vol. 210(C).
    3. Cosmin Ilut & Matthias Kehrig & Martin Schneider, 2018. "Slow to Hire, Quick to Fire: Employment Dynamics with Asymmetric Responses to News," Journal of Political Economy, University of Chicago Press, vol. 126(5), pages 2011-2071.

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    More about this item

    Keywords

    Cross-sectional dispersion; endogenous uncertainty; monotone likelihood ratio property; nonlinear transformations; risk; second moments; volatility;
    All these keywords.

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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