Doubts or variability?

Reinterpreting most of the market price of risk as a price of model uncertainty eradicates a link between asset prices and measures of the welfare costs of aggregate fluctuations that was proposed by Hansen, Sargent, and Tallarini [17], Tallarini [30], Alvarez and Jermann [1]. Prices of model uncertainty contain information about the benefits of removing model uncertainty, not the consumption fluctuations that Lucas [22] and [23] studied. A max-min expected utility theory lets us reinterpret Tallarini's risk-aversion parameter as measuring a representative consumer's doubts about the model specification. We use model detection instead of risk-aversion experiments to calibrate that parameter. Plausible values of detection error probabilities give prices of model uncertainty that approach the Hansen and Jagannathan [11] bounds. Fixed detection error probabilities give rise to virtually identical asset prices as well as virtually identical costs of model uncertainty for Tallarini's two models of consumption growth.

[1]  Robert E. Lucas,et al.  Models of business cycles , 1987 .

[2]  M. Obstfeld.  Evaluating Risky Consumption Paths: the Role of Intertemporal Substitutability , 1994 .

[3]  R. Shiller,et al.  Consumption, Asset Markets, and Macroeconomic Fluctuations , 1982 .

[4]  Evan L. Porteus,et al.  Temporal Resolution of Uncertainty and Dynamic Choice Theory , 1978 .

[5]  P. Weil.  Nonexpected Utility in Macroeconomics , 1990 .

[6]  Lars Peter Hansen,et al.  Robust estimation and control under commitment , 2005, J. Econ. Theory.

[7]  N. Kocherlakota.  Disentangling the Coefficient of Relative Risk Aversion from the Elasticity of Intertemporal Substitution: An Irrelevance Result , 1990 .

[8]  M. Marinacci,et al.  A Smooth Model of Decision Making Under Ambiguity , 2003 .

[9]  Massimo Marinacci,et al.  Dynamic variational preferences , 2006, J. Econ. Theory.

[10]  T. Sargent,et al.  Robust Control and Model Uncertainty , 2001 .

[11]  K. Narendra,et al.  Discounted Linear Exponential Quadratic Gaussian Control , 1995 .

[12]  Lars Peter Hansen,et al.  Robustness and US Monetary , 2008 .

[13]  Ravi Jagannathan,et al.  Implications of Security Market Data for Models of Dynamic Economies , 1990, Journal of Political Economy.

[14]  Lars Peter Hansen,et al.  Robust control and model misspecification , 2006, J. Econ. Theory.

[15]  Tomasz Strzalecki,et al.  Axiomatic Foundations of Multiplier Preferences , 2009 .

[16]  Lars Peter Hansen,et al.  Recursive Robust Estimation and Control Without Commitment , 2007, J. Econ. Theory.

[17]  Massimo Marinacci,et al.  Uncertainty averse preferences , 2011, J. Econ. Theory.

[18]  Robert E. Lucas,et al.  Macroeconomic Priorities , 2003 .

[19]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[20]  J. Pratt.  RISK AVERSION IN THE SMALL AND IN THE LARGE11This research was supported by the National Science Foundation (grant NSF-G24035). Reproduction in whole or in part is permitted for any purpose of the United States Government. , 1964 .

[21]  T. Sargent,et al.  Robust Permanent Income and Pricing , 1999 .

[22]  J. Cochrane,et al.  Where is the market going ? Uncertain facts and novel theories , 1997 .

[23]  T. Sargent,et al.  ROBUST PERMANENT INCOME AND PRICING WITH FILTERING , 2002, Macroeconomic Dynamics.

[24]  A. Rustichini,et al.  Ambiguity Aversion, Robustness, and the Variational Representation of Preferences , 2006 .

[25]  T. Sargent,et al.  Fragile beliefs and the price of model uncertainty , 2006 .

[26]  Thomas D. Tallarini.  Risk-sensitive real business cycles☆ , 2000 .

[27]  Larry G. Epstein,et al.  Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework , 1989 .

[28]  Lars Peter Hansen,et al.  A QUARTET OF SEMIGROUPS FOR MODEL SPECIFICATION, ROBUSTNESS, PRICES OF RISK, AND MODEL DETECTION , 2003 .

[29]  Larry G. Epstein,et al.  Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis , 1991, Journal of Political Economy.

[30]  James Dolmas.  Risk Preferences and the Welfare Cost of Business Cycles , 1998 .