Other scenarios of interest in our study include the two special cases of the GEU base
model, CES-EU optimization with α= ρ=-1 andβ= 0.89, and MR-EU optimization with
α=ρ=1 and β= 0.89. The former refers to the case where the farmer is more risk averse and
has smaller intertemporal substitution preference in consumption, while the latter refers to the
case when he/she is risk neutral and has perfect intertemporal substitution preference.
Besides the CES-EU and MR-EU, a multi-period additive EU (MA-EU) optimization is
also examined. The utility function in this case is the standard constant relative risk aversion
Cα
utility function Ut = where α = -1, which implies a relative risk aversion coefficient equal
α
to 2. This utility function has been widely used in static single-period risk analyses (Mahul, 2003;
Wang, Makus, and Chen, 2004; Coble, Heifner, and Zuniga, 2000). It is also easy to extend the
model from single-period to multi-period as in equation (7), but note that this multi-period
version has a static nature.
(7)
MaxUt =
(MA-EU)
Table 3 lists results of the Whitman County and Grant County farmers’ optimal choice
on risk management portfolios using the four different models. In general, we see that
parameterization of intertemporal preferences determines the model specification, and the model
specification is very important in modeling farmer’s risk management behavior and finding the
optimal portfolios for farmers’ intertemporal decision.
For the optimal choice of crop insurance, the highest coverage of 85% is favored in all
cases. This result is consistent with the model setting since the insurance is subsidized by the
government and no premium loading is charged. The farmer purchases the highest available level
so as to enjoy the most protection against yield risk and receive the highest subsidy. Also, the
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