Abstract
The predictive squared error risk behavior of a restricted least squares estimator (RLS), pre-test estimator (PT), and Stein rule (SR) estimator are each compared to the behavior of the OLS estimator when relevant variables are omitted. Risk superiority conditions dependent on prior constraint error and this model specification error in a two-dimensional parameter space are exhibited. Among the consequences of this model misspecification, it is found that (i) perfectly correct prior constraints do not ensure risk superiority of any of the alternatives to OLS, (ii) the risk difference between OLS and PT is no longer bounded, and (iii) the SR no longer dominates OLS. The usefulness of risk superiority hypothesis tests based on the doubly non-centralF distribution is examined.
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