  Loss functions are widely used to compare several competing forecasts.
However, forecast comparisons are often based on mismeasured proxy variables
for the true target. We introduce the concept of exact robustness to
measurement error for loss functions and fully characterize this class of loss
functions as the Bregman class. For such exactly robust loss functions,
forecast loss differences are on average unaffected by the use of proxy
variables and, thus, inference on conditional predictive ability can be carried
out as usual. Moreover, we show that more precise proxies give predictive
ability tests higher power in discriminating between competing forecasts.
Simulations illustrate the different behavior of exactly robust and non-robust
loss functions. An empirical application to US GDP growth rates demonstrates
that it is easier to discriminate between forecasts issued at different
horizons if a better proxy for GDP growth is used.
