ESTIMATION OF EFFICIENT REGRESSION MODELS FOR APPLIED AGRICULTURAL ECONOMICS RESEARCH

functions of time, respectively. Likelihood ratio and t tests do not reject Ho: σji = 0 at the 20% level of
statistical significance, suggesting that the error terms are homoskedastic in both cases. Since βc1 and βc2 are not
statistically significant at the 20% level, and second degree polynomial regression specifications are
susceptible to multicollinearity, a final model [NSUR-AR(1)] is estimated without βc2 (Table 3), in which
the linear time-trend parameter βc1 is statistically different from zero at the 5% level.

The NSUR-AR(1) model is the most statistically efficient model currently achievable by an applied
researcher dealing with the simple issue of whether real commodity prices have been declining over time.
However, the previously discussed Monte Carlo simulation results suggest that the non-normal regression
modeling techniques described above offer the potential for increased efficiency, i.e. slope parameter
estimators with lower standard errors. The NSUR-AR(1) model is expanded to allow for the possibility of
error term skewness and kurtosis. This expanded model [NNSUR-AR(1)] is estimated by maximizing the
concentrated log-likelihood function given in equation (6), setting m=2. This log-likelihood is a function of
the same parameters as the NSUR-AR(1) model, plus the parameters accounting a potential non-normality in
the error term distributions of the corn (Θc and μ c) and soybean (Θs and μ s) models.

The statistical significance of the non-normality parameters is verified through the most reliable
likelihood ratio tests. The concentrated log-likelihood function for the NSUR-AR(1) model reaches a
maximum value of 36.92, versus 52.55 in the case of the NNSUR-AR(1) model. Thus, the likelihood ratio
test statistic for Ho: Θc=μ c=Θs=μ s=0 is χ²(4) = -2×(36.92-52.55) = 31.26 allows for rejection of Ho at the
1% level. The non-normal SUR-AR(1) regression model is statistically superior to the normal SUR-AR(1)
model. If the NNSUR-AR(1) model is restricted to only allow for non-normality in the error term of the corn
price regression, the maximum value of the log-likelihood function decreases from 52.55 to 42.89, resulting a χ²(2)
test statistic of -2×(42.89-52.55) = 19.32, and rejection of Ho: Θs=μ s=0 at the 1% level. Alternatively, the χ²(2)
test statistic for Ho: Θc=μ c=0 is -2×(46.12-52.55) = 12.86 rejects Ho at the 1% level as well. The previous
results indicate that the error terms of both the corn and the soybean price models are non-normally distributed.

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