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ON THE RECOVERABILITY OF FORECASTERS’ PREFERENCES

Published online by Cambridge University Press:  12 November 2012

Robert P. Lieli  and
Maxwell B. Stinchcombe
Robert P. Lieli*
Affiliation:
Central European University and Magyar Nemzeti Bank
Maxwell B. Stinchcombe
Affiliation:
University of Texas–Austin
*
*Address correspondence to Robert P. Lieli, Department of Economics, Central European University, Nádor u. 9, 1051 Budapest, Hungary; e-mail: lielir@ceu.hu.
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Abstract

We study the problem of identifying a forecaster’s loss function from observations on forecasts, realizations, and the forecaster’s information set. Essentially different loss functions can lead to the same forecasts in all situations, though within the class of all continuous loss functions, this is strongly nongeneric. With the small set of exceptional cases ruled out, generic nonparametric preference recovery is theoretically possible, but identification depends critically on the amount of variation in the conditional distributions of the process being forecast. There exist processes with sufficient variability to guarantee identification, and much of this variation is also necessary for a process to have universal identifying power. We also briefly address the case in which the econometrician does not fully observe the conditional distributions used by the forecaster, and in this context we provide a practically useful set identification result for loss functions used in forecasting binary variables.

Type
Articles
Information
Econometric Theory , Volume 29 , Issue 3 , June 2013 , pp. 517 - 544
Copyright
Copyright © Cambridge University Press 2012 

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Footnotes

We thank David Hendry, Ivana Komunjer, Michael McCracken, Ulrich Müller, and two anonymous referees for useful comments. All errors are our responsibility.

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