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Abstract:
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Consider the model y=Xß+e subject to Rß=r, such that e~N(0,V) - V diagonal of unequal elements - and X is a matrix of constants of size nxk. Both E(ß)=ß* and cov(ß*) - ß restricted - may be drawn from Akaike's or White's solutions for non-restricted models introducing an estimated V* from OLS residuals. Although these solutions converge to efficient estimators of ß* when n goes to infinity, there is little evidence about their performance for small sample sizes (n< 50). The paper compares six estimators of ß* and computes by simulation the sum of squares s=(ß*-ß)'(ß*-ß) for n={5, 10, 15, 20, 25, 50} and k=4. The findings suggest that OLS is the most efficient estimator for extremely small samples (5< n< 10), whereas White's estimator corrected by Davidson-Mac Kinnon's factor is the most efficient for small- to medium-sized samples (25< n< 50). Results are ambiguous for 10< n< 25.
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