grows soft white wheat which has no actively traded futures contract, the Chicago Board of
Trade (CBOT) September wheat futures contact is chosen by the farmer for hedging. We pick
the mid-week price of the first week (Wednesday or Thursday) of September to develop our
dataset.
Deterministic Trend vs. Stochastic Trend
Because of the multiple time dimensions involved in GEU specification and dynamic
programming, simulation of yield data could affect the final optimization results to a large extent.
Specifying a pattern that is consistent with real processes is critical in this study.
From the time series plots of Whitman County and Grant County yield (Figure 1) for
1972 to 2003, an upward trend is visible for the last 32 years. There are possibly two sources of
randomness that influence the county yield time series. One is the stochastic technology changes
that will determine the “mean” yield in any given year, and the other is the random weather that
moves the yield around the “mean”. For multi-period analysis, we need to model the long-run
inter-year randomness from technology changes as well as the short-run random effects brought
by weather. A stochastic trend model would be more appropriate than any deterministic trend
models in that it incorporates both types of randomness.
Moss and Shonkwiler (1993) developed a single time-dependent stochastic trend model.
Their model transforms the error term rather than the dependent variable to incorporate the
possibility of both non-stationary data and non-normal errors in corn yield variation. The model
is also general enough to include both the standard deterministic time trend and normal errors as
special cases. This model is adopted for our analysis.
Similarly for wheat cash and futures prices (Figure 2), the long-run unpredictable
balance of supply and demand determines the annual price trend, and short-run information at
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