ESTIMATION OF EFFICIENT REGRESSION MODELS FOR APPLIED AGRICULTURAL ECONOMICS RESEARCH



of -5.77 and -1.46 points, and standard deviations of 3.55 and 3.07, respectively. They were somewhat less
kurtotic and asymmetric, with implied probabilities of basis realizations below (above) one standard deviation
from their means of 5.9% and 7.1% (9.1% and 10.3%), respectively. In short, the probability of a high
positive basis during the planting season was much higher during the 1985 Farm Bill period, and it is almost
negligible in the current policy period, as it could be inferred from the data (Figure 3).

The estimated conditional distributions of the West Texas cotton basis during the harvesting and
marketing season (Figure 5) are nearly normal under all the three policy periods analyzed. They show lower
means (-6.08 vs. -5.77, -2.43 vs. -1.46, and -3.74 vs. -2.62, respectively) and standard deviations (2.64 vs.
3.55, 2.13 vs. 3.07, and 1.59 vs. 2.83, respectively) than during the planting season. Because of the stronger
non-normality in the August-to-February distributions, however, these reduced standard deviations do not
imply a lower overall degree of dispersion in the distribution of the basis in this case (Figures 4 and 5).

This is empirically important since, under error term non-normality, normal-error models such as the
NHAR(4), provide consistent estimates for the error term variance (note the similarity in the variance
estimates from the FNHAR(4) and the FNNHAR(4) models in Table 5), which would be misinterpreted as
appropriate measures of the degree of dispersion of the distribution. For example, from the relatively large
negative value of the variance shifter for the harvesting and marketing season (
σ2sD) in the FNHAR(4) model,
one would falsely conclude that the distribution of the basis during this season exhibits a much lower overall
degree of dispersion about its mean value.

Concluding Remarks

Agricultural economics research often involves the estimation of regression models with a limited
amount of data, and more precise and realistic statistical inferences from these models are always useful.
As illustrated above, the non-normal error multiple regression model evaluated in this study can provide for
substantially more precise and realistic statistical inferences than the currently available estimation
techniques that assume normality. Since many dependent variables of interest to agricultural economists,
such as commodity prices, crop acreage, yields, product supply, profits, etc., are likely non-normally

21



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