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This paper investigates a property of estimators called stability. The stability exponent of an estimator is deﬁned to be a measure of the eﬀect of any single observation in the sample on the realized value of the estimator. High stability is often desirable for robustness against misspeciﬁcation and against highly variable observations. Stability exponents are determined and compared for a wide variety of estimators and econometric models. They are found to depend on the maximal moment exponent (i.e., the number of ﬁnite moments) of the estimator’s influence curve. Since it is possible often to construct estimators with speciﬁed influence curves, estimators with diﬀerent stability exponents can be construed.
Andrews, Donald W.K., "Stability Comparisons of Estimators" (1984). Cowles Foundation Discussion Papers. 946.