Intertemporal Risk Management Decisions of Farmers under Preference, Market, and Policy Dynamics

The stochastic trend model reduces to a deterministic time trend model if β₀ ≠ 0
andσ_η² = σ_ς² = 0 . If β₀ = 0 , then it reduces to a constant mean regression model.

Estimation and Simulation for Yields and Prices

Applying the stochastic trend model to our yield and price data using maximum
likelihood estimation programmed in GAUSS, we find there is no stochastic trend in the yield for
Whitman County but there is one for Grant County. The stochastic trend also exists in the
Portland cash prices and CBOT futures prices (Table 1).

For Grant County yield, cash price and futures price, the significance of estimated σ_η
confirms the existence of a random walk in the mean component. However, the insignificance of
estimated σ_ς shows such stochastic variation doesn’t exist within the mean of the trend. For
Whitman County yield, however, the trend is generally a deterministic time trend and there is no
significant randomness in the slope of the time trend. The simple linear regression model with a
deterministic time trend appears to be a good model for Whitman County yield⁴.

The plots of predicted values versus actual values show that in general the stochastic
trend models fit the data well by capturing the long-run variation in the trend for wheat yield in
Grant County (Figure 3) and cash prices (Figure 4)⁵. The 95 percent confidence intervals include
nearly all of the realizations.

For the distributions of yield and prices, we conduct normality tests first on the
detrended data. Results fail to reject the null hypothesis of normality. We also estimate the
stochastic trend model including non-normal errors. The estimates of the non-normal parameters
are not statistically different from zero, confirming that the data follow a normal distribution.

⁴ We further tested for autocorrelation within the series before applying the time trend and found no
evidence.

⁵ Similar pattern is also shown for wheat futures prices.

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