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< In the mixture model, likelihood ratios are bounded.
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> In the mixture model, likelihood ratios are bounded.  Besides justifying the
> first-order approach (which simplifies exposition), our main use of the mixture
> assumption is its implication that the benchmark appearing in the solution to
> the second-best problem is the uninformed optimum.  Absent the mixture
> assumption, the form of the optimal compensation is the same but the benchmark
> loses its simple interpretation.
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> 
> The mixture model assumption plays two roles in this analysis.  First, as noted
> in the literature, it implies that any first-order solution is a solution of
> the underlying agency model.  Second, the mixture model assumption implies that the benchmark in the
> solution can be chosen to be the uninformed optimum.  One interpretation of the
> mixture model is that it assumes that the marginal impact of effort on the
> joint distribution of signal and returns is proportional to the average impact of effort.  This gives
> the link between the first-order condition (which is in terms of the marginal
> impact of effort) and the excess over the uninformed optimum (which is related
> to the average impact of effort).  Absent the mixture model assumption, the
> optimal contract can still be interpreted as the excess return over a
> benchmark, but the benchmark is not necessarily the uninformed optimum and may
> depend on the signal (which is okay since the signal is observed in the
> second-best, but not consistent with the usual choice of a benchmark in
> practice as an uninformed portfolio).\footnote{This result that any optimal
> contract rewards excess
> returns over
> a benchmark even without assuming a mixture model is still valid even if the
> first-order approach fails and there are non-locally-binding incentive
> compatibility constraints.  The general first-order condition for the
> principal's problem may put weights on both local and non-local changes.
> Combining the weighted average of the corresponding density changes from
> the optimum and dividing by $p(e)$ gives the appropriate change from the
> optimum to the benchmark.}