## Abstract (may include machine translation)

The Bregman class of loss functions is characterized by the property that the con-

ditional mean is the unrestricted optimal forecast for any Bregman loss. Similarly,

generalized piecewise linear (GPL) loss functions all give rise to a given quantile as

the unrestricted optimal forecast. Using the identification theory in Lieli and Stinch-

combe (2013), we argue that Bregman losses are still potentially distinguishable if

restrictions are placed on the set of allowable forecasts; e.g., off-support forecasts are

excluded. In contrast, GPL loss functions remain observationally equivalent even in

such forecasting environments—here the failure of identification is more fundamental.

Motivated by these examples, we conclude by asking partly open questions about the

nonparametric identifiability of loss functions.

ditional mean is the unrestricted optimal forecast for any Bregman loss. Similarly,

generalized piecewise linear (GPL) loss functions all give rise to a given quantile as

the unrestricted optimal forecast. Using the identification theory in Lieli and Stinch-

combe (2013), we argue that Bregman losses are still potentially distinguishable if

restrictions are placed on the set of allowable forecasts; e.g., off-support forecasts are

excluded. In contrast, GPL loss functions remain observationally equivalent even in

such forecasting environments—here the failure of identification is more fundamental.

Motivated by these examples, we conclude by asking partly open questions about the

nonparametric identifiability of loss functions.

Original language | American English |
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Publisher | Central European University, Department of Economics |

State | Published - 2016 |

### Publication series

Name | Working papers |
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