Spatial Aggregation and Weather Risk Management

argument. If weather events across locations are highly correlated, but other yield effects
are relatively less correlated, then relatively more variation (i.e. risk) in yields can be
attributed to weather events as yields are aggregated. Empirically, the relevant question
for the re/insurer is whether the differences in the correlations of weather effects and
other yield effects are significant enough to see substantial differences in WD hedging
effectiveness as the level of aggregation increases.

There are good reasons to believe that WD hedging may be more effective as the
level of aggregation is increased. First, aggregating yields should have a diversifying
effect across locations. Popp, Rudstrom and Manning (2005), for instance, find that the
risk of farm-level yields is substantially higher than county-level yields. This is partly
due to the diversifying effect as yields are aggregated over individual farms.⁵ Second,
weather events tend to be highly spatially correlated.⁶ For example, the average
correlation between the temperature indexes used in this study (the temperature indexes
are described in section 5) across locations was 0.755.⁷

Yields, Weather Indexes, Derivatives, and Pricing

Failure to account for technological advancements in crop production can produce
misleading hedging results. Significant trends in historical yields may produce spurious
hedge ratios which are not representative of the underlying optimal hedge ratio
distribution. To account for changes in technology district level yields are detrended
using a simple log-linear trend model (VB 2004)⁸

(6)              log(Y_t^tr) = α₀ +α₁(t-1971),     t=1971,1972,...,2002.

Detrended yields to 2002 equivalents are calculated as

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