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Francisco Vazquez-Grande vazquez-grande@chicagobooth.edu
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This paper solves a new learning problem in a model with long-run risk, where both, the level and persistence of consumption growth are unobserved. We introduce a new methodology to quantify the effects of learning about parameter uncertainty and latent variables. The representative consumer chooses state variables that are sufficient statistics of the learning problems and, conditioning on her information set, forms posterior distributions of the states and future consumption growth. We present a novel numerical approach, which approximates the agent's continuation-value and solves a series of nested dynamic programming problems. The problems are nested by imposing that solutions for learning problems converge to the solution of the problem without learning as uncertainty disappears. Keeping preference parameters constant, maximum Sharpe ratios increase significantly from .07 in the benchmark case without learning to .45 in the learning economy.
Lars P. Hansen (co-chair) Ruey S. Tsay (co-chair) Homer J. Livingston Distinguished Service Professor H.G.B. Alexander Professor of Econometrics & Statistics Department of Economics, University of Chicago Booth School of Business, University of Chicago lhansen@uchicago.edu Ruey.Tsay@chicagobooth.edu +1 (773) 702-8170 +1 (773) 702-6750 Pietro Veronesi Kenneth L. Judd Roman Family Professor of Finance Paul H. Bauer Senior Fellow Booth School of Business, University of Chicago Hoover Institution, Stanford University pietro.veronesi@chicagobooth.edu judd@hoover.stanford.edu +1 (773) 702-6348 +1 (650) 723-5866
November 19th, 2009