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.
Cross-sectional dispersion; endogenous uncertainty; monotone likelihood ratio property; nonlinear transformations; risk; second moments; volatility;
- C19: Other
- D83: Search • Learning • Information and Knowledge • Communication • Belief
- E32: Business Fluctuations • Cycles
- G13: Contingent Pricing • Futures Pricing
Ludwig Straub, and Robert Ulbricht, “Endogenous Second Moments: A Unified Approach to Fluctuations in Risk, Dispersion, and Uncertainty”, TSE Working Paper, n. 16-664, June 2016, revised March 2018.
TSE Working Paper, n. 16-664, June 2016, revised March 2018