Abstract
This note identifies a moral hazard environment in which a piecewise linear compensation
scheme is optimal. Both the principal and the agent have CARA utility, mean output
is increasing in the agent's non-contractible input, and output is distributed according
to a Laplace distribution, which resembles a normal distribution (e.g. it is symmetric
about the mean), but has fatter tails. The key property of the Laplace distribution
is that the likelihood ratio is a piecewise constant, where the discontinuity occurs
at the mean. The value of this approach is twofold: First, a tractable, empirically-observed
wage scheme emerges as the equilibrium in a simple static contracting model. Second,
the optimal piecewise linear scheme cleanly separates insurance and incentive provision.
The linearity at output levels away from the mean captures insurance, while the jump
at the mean captures incentive provision. Hence, this model is well-suited for studying
a wide variety of principal-agent problems in risky environments subject to moral
hazard, such as the effect of risk and moral hazard considerations on employment relationships
in developing economies.
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