  Empirical research typically involves a robustness-efficiency tradeoff. A
researcher seeking to estimate a scalar parameter can invoke strong assumptions
to motivate a restricted estimator that is precise but may be heavily biased,
or they can relax some of these assumptions to motivate a more robust, but
variable, unrestricted estimator. When a bound on the bias of the restricted
estimator is available, it is optimal to shrink the unrestricted estimator
towards the restricted estimator. For settings where a bound on the bias of the
restricted estimator is unknown, we propose adaptive shrinkage estimators that
minimize the percentage increase in worst case risk relative to an oracle that
knows the bound. We show that adaptive estimators solve a weighted convex
minimax problem and provide lookup tables facilitating their rapid computation.
Revisiting five empirical studies where questions of model specification arise,
we examine the advantages of adapting to -- rather than testing for --
misspecification.
