Occasionally Misspecified

When fitting a particular Economic model on a sample of data, the model may turn out to be heavily misspecified for some observations. This can happen because of unmodelled idiosyncratic events, such as an abrupt but short-lived change in policy. These outliers can significantly alter estimates and inferences. A robust estimation is desirable to limit their influence. For skewed data, this induces another bias which can also invalidate the estimation and inferences. This paper proposes a robust GMM estimator with a simple bias correction that does not degrade robustness significantly. The paper provides finite-sample robustness bounds, and asymptotic uniform equivalence with an oracle that discards all outliers. Consistency and asymptotic normality ensue from that result. An application to the "Price-Puzzle," which finds inflation increases when monetary policy tightens, illustrates the concerns and the method. The proposed estimator finds the intuitive result: tighter monetary policy leads to a decline in inflation.