ESTIMATION OF EFFICIENT REGRESSION MODELS FOR APPLIED AGRICULTURAL ECONOMICS RESEARCH

A log-normal error term distribution is unimodal but not symmetric. It exhibits positive degrees of
kurtosis and skewness. The RMSE of the proposed slope-parameter estimator is 0.050, approximately 20%
of the RMSE of the OLS estimator. According to McDonald and White criteria, this is an “impressive”
performance, only comparable to the EGB2’s 0.05 RMSE. All other alternative estimation techniques
produce RMSE’s of 0.11 and above.

In summary, the estimator proposed in this study performs very favorably in comparison with the
16 estimating techniques evaluated by McDonald and White according to the standards applied by these
authors and independently established in previous studies (Newey; Hsieh and Manski). It clearly excels
when the underlying error-term distribution is asymmetric. This implies a potential for efficiency gains
when using the proposed estimator under conditions of error-term non-normality and
heteroskedasticity/autocorrelation, or in a disturbance related equations set up.

When the variance-contaminated error-terms are simulated to be heteroskedastic, the slope
estimation efficiency (i.e. the RMSEs) of the EGB2 and of the proposed estimator are not substantially
affected, and the modeling of heteroskedasticity with the proposed estimator, by letting σ =α1+α2I (where I
is the binomial index variable known to affect the error-term variance), only produces modest efficiency
gains (Table 2). Under log-normal heteroskedastic errors, however, the EGB2 and the i.i.d form of the
proposed estimator are substantially less efficient in comparison to the log-normal homoscedastic scenario.
Their RMSEs increase from 0.054 and 0.050 to 0.117 and 0.104, respectively. In contrast, a RMSE of
0.202 is obtained when estimating a heteroskedastic but normally distributed error-term model specification
by maximum likelihood. The modeling of heteroskedasticicy with the non-i.i.d. form of the proposed
estimator recovers the lost estimation efficiency gains. The resulting RMSE of 0.052 is 25% of the RMSE
obtained with the heteroskedastic normal model.

In contrast, failure to model autocorrelation (ρ=0.5 and ρ=0.8) reduces the slope estimation
efficiency of all estimators. The RMSEs increase to 0.320 and 0.388, respectively, when OLS is used
under a variance-contaminated autocorretaled error-term, and to 0.334 and 0.439 under a log-normal

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