Studying a principal-agent game in which the agent alone observes the
state of the world and reports it, but the moral hazard is not reducib
le, shows that, if the principal uses all signals, then no solution ex
ists, i.e. there is no contract that elicits truth-telling and motivat
es the agent to exert effort. When the principal does not use signals
on the state of the world that seem irrelevant, a solution exists in w
hich some of the ex post signals on outcome are not used, even though
they obey the informativeness condition of Holmstrom (Bell Journal of
Economics, 1979, 10, 74-91).