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 often is desirable for robustness against misspecification and against highly variable observations. Stability exponents are determined and compared for a wide variety of estimators and economietric 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 constructed.