autocorrelated error-term. The i.i.d. form of the proposed estimator limits those RMSE increases to 0.141
and 0.188 (variance-contaminated autocorrelated), and to 0.126 and 0.260 (log-normal autocorrelated).
Comparable RMSEs are found under the EGB2.
In short, the efficiency gains in the estimation of the slope parameter resulting from the use of
either the EGB2 or the i.i.d. from of the proposed estimator, in relation to OLS, are reduced to about 50%
if the underlying error-term is non-normally distributed and autocorrelated. The relative reduction is even
more severe in comparison to the standard maximum likelihood autocorrelated normal-error estimator and,
in the 0.8 autocorrelation log-normal error term scenario, the later is actually more efficient (Table 2). This
illustrates the importance of a partially adaptive estimator that can account for both error term non-
normality and autocorrelation/ heteroskedasticity: The autocorrelated form of the proposed estimator fully
recovers the efficiency losses, producing slope-estimator RMSEs that are similar to those obtained under
the i.i.d. non-normal underlying error-term scenarios. These RMSEs are 50 to 75% lower than those
obtained with the standard maximum likelihood autocorrelated normal estimator and 25 to 80% lower than
those obtained under the EGB2 or the i.i.d. form of the proposed estimator (Table 2).
Agricultural Economics Applications
Simple Time Series Models OfAgricultural Commodity Prices
An issue of interest for agricultural economists is whether real commodity prices have been declining
through time and if price variability has changed over time making the production of a particular crop more risky.
Both, the normal-error regression model and the proposed partially adaptive (i.e. non-normal error) regression
model are used to analyze this issue in the case of annual (1950-1999) U.S. corn and soybean prices.
The two price series are adjusted for inflation to the year 2000 using the producer price index for all
agricultural products (USDA/NASS, http://www.usda.gov /nass/, March 2001). Both series are stationary
according to augmented Dickey-Fuller unit root tests. OLS models assuming second-degree polynomial time
trends (i.e. Xβ = β0 + β1 t + β2t2; t=1,...,50) are first estimated using Gauss 386i lreg procedure (Table 3).
Durbin-Watson tests indicate first order positive autocorrelation in both cases. Therefore, standard tenth-order
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