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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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    References listed on IDEAS

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    1. Cosmin Ilut & Matthias Kehrig & Martin Schneider, 2014. "Slow to Hire, Quick to Fire: Employment Dynamics with Asymmetric Responses to News," Department of Economics Working Papers 150113, The University of Texas at Austin, Department of Economics, revised Dec 2014.
    2. Jorg Dopke & Sebastian Weber, 2010. "The within-distribution business cycle dynamics of German firms," Applied Economics, Taylor & Francis Journals, vol. 42(29), pages 3789-3802.
    3. Benjamin Moll, 2014. "Productivity Losses from Financial Frictions: Can Self-Financing Undo Capital Misallocation?," American Economic Review, American Economic Association, vol. 104(10), pages 3186-3221, October.
    4. Laura Veldkamp & Anna Orlik, 2014. "Uncertainty Shocks and the Role of the Black Swan," 2014 Meeting Papers 275, Society for Economic Dynamics.
    5. Ezra Oberfield & Devesh Raval, 2012. "Micro data and macro technology," Working Paper Series WP-2012-11, Federal Reserve Bank of Chicago.
    6. Bachmann, Ruediger & Bayer, Christian, 2009. "Firm-specific productivity risk over the business cycle: facts and aggregate implications," Discussion Paper Series 1: Economic Studies 2009,15, Deutsche Bundesbank.
    7. Tatsuro Senga, 2014. "A New Look at Uncertainty Shocks: Imperfect Information and Misallocation," UTokyo Price Project Working Paper Series 042, University of Tokyo, Graduate School of Economics.
    8. Rainer Klump & Peter McAdam & Alpo Willman, 2007. "Factor Substitution and Factor-Augmenting Technical Progress in the United States: A Normalized Supply-Side System Approach," The Review of Economics and Statistics, MIT Press, vol. 89(1), pages 183-192, February.
    9. Döpke, Jörg & Funke, Michael & Holly, Sean & Weber, Sebastian, 2005. "The cross-sectional dynamics of German business cycles: a bird's eye view," Discussion Paper Series 1: Economic Studies 2005,23, Deutsche Bundesbank.
    10. Straub, Ludwig & Ulbricht, Robert, 2015. "Endogenous Uncertainty and Credit Crunches," TSE Working Papers 15-604, Toulouse School of Economics (TSE), revised Dec 2017.
    11. Bachmann, Rüdiger & Bayer, Christian, 2013. "‘Wait-and-See’ business cycles?," Journal of Monetary Economics, Elsevier, vol. 60(6), pages 704-719.
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    Cited by:

    1. Cosmin Ilut & Matthias Kehrig & Martin Schneider, 2014. "Slow to Hire, Quick to Fire: Employment Dynamics with Asymmetric Responses to News," Department of Economics Working Papers 150113, The University of Texas at Austin, Department of Economics, revised Dec 2014.

    More about this item

    Keywords

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

    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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