are independently distributed, the standard deviation of the composed error term is:
2 _ 2-2 . 2( (11/2)
σ = (σv + σu )
Clearly, the greater the deviation from the frontier, the greater the
variance of total production. Therefore, combining this result with (6) above shows that a higher
level of inefficiency leads to a greater willingness-to-pay for insurance.
While this result allows for predictions of aggregate effects, detecting individual cases of
adverse selection requires a firm-specific measure of inefficiency. Jondrow, Lovell, Materov, and
Schmidt (1982) derive such a measure from the expectation of u, conditional on each firms'
realization of ε. In the composite normal/half normal case described above, the expected value of
E(u∖εi) = εi(-σU) + σu σ f (εσu)( 1 - F(εσu))
u for each farm is written:
where f is the normal density function, and F is the normal distribution function. Subtracting the
expectation of u from the residual ε; gives the value of the random component of the deviation
from the best-practice frontier: v i. Subtracting this random deviation from the predicted level of
output and dividing the result by the actual level of output yields an index of efficiency for each
observation.
This vector of efficiency indices allow the econometric estimation of the factors that
contribute to the willingness-to-pay for insurance according to the theoretical model of equation
(6). Namely, the willingness-to-pay is a function of the variation in output, an index of technical
efficiency, various indicators of growers’ attitudes towards risk, and their tendency to self insure
through diversification or other means. As in JC, proxy variables for these factors include such