Spatial Aggregation and Weather Risk Management

Also, the data suggests that the variance of aggregate yields was significantly less than
the variance of the individual yields.

⁶ The disperse nature of rainfall in the summer months, which is frequently generated by
spatially sporadic thunderstorms, contributes to the insurance portfolio’s ability to self-
diversify. On aggregate however, rainfall and temperature tend to be highly correlated
during drought events.

⁷ In addition, preliminary analysis strongly supported the spatial aggregation hypothesis.
Preliminary analysis was conducted by regressing individual district detrended yields on
the temperature and temperature-squared indexes for all districts. The average of the
district adjusted R-squares was 0.366, versus 0.526 for aggregated yields. The average
correlation of the temperature effects across all districts was 0.72, and the average
correlation of the residuals was 0.52.

⁸ This procedure does not impose any distributional assumptions on the residuals but
removes their central tendency (VB 2004). While OLS is inefficient when errors are not
normally distributed, the econometric properties of an uninterrupted series independent
variable as well as the level of skewness typical of corn yields can permit OLS to
generate better crop yield coefficient estimates than many robust regression methods
(Swinton and King 1991).

⁹ The assumptions of BA are that the historical index time series is stationary, and
statistically consistent with the prevailing climate during the contract period (i.e., the
historical distribution of weather accurately reflects the true underlying distribution), and
that the values are independent across different years (Jewson and Brix 2005).

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