The Demand for Specialty-Crop Insurance: Adverse Selection and Moral Hazard

a multi-input model that takes into account both the output and risk effects of additional input
use. To the extent that θ measures unobservable producer decisions, a lower value of θ reduces
the level of income. With the DARA assumption, this means that lower θ values result in a higher
willingness-to-pay for insurance, ceteris paribus. This result also suggests that more specific
assumptions about the distribution of ε can provide insight as to the potential factors that
influence the willingness-to-pay for insurance. Furthermore, if two producers are identical in
every other observable respect, a difference in willingness-to-pay that is caused by factors within
the distribution of ε can suggest an alternative indicator of adverse selection in crop insurance.³

Specifically, assume that the random error term, ε, is composed of the two elements
suggested in (1) above in the following form: ^ε = ^{v -} | ^u |. With this definition, the effect of
climate on output is a random normal variable: v ~ N(0,σ²_v), and managerial quality, or the proxy
for the effect of adverse selection ( u ) follows a half-normal distribution:

so that the function f above describes a stochastic production frontier. Because this technology
defines a frontier along which only the most efficient producers lie, the greater the individual
realization of u, the greater is the deviation from the best practice frontier. Assuming that v and u

Despite many authors’ arguments to the contrary, as QKS suggest the difference between moral hazard (MH)
and adverse selection (AS) in agricultural crop insurance is unobservable as the decisions to insure and to plant are
made simultaneously. Attempts to differentiate between the two largely rest on semantic arguments as to the timing of
each decision. For our purposes, AS is interpreted as flowing from hidden information about inherent producer
characteristics, while MH results from specific input decisions unknown to the insurer.

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