Better the devil you know: Improved forecasts from imperfect models

Many important economic decisions are based on a parametric forecasting model that is known to be good but imperfect. We propose methods to improve out-of-sample forecasts from a misspecified model by estimating its parameters using a form of local M estimation (thereby nesting local OLS and local MLE), drawing on information from a state variable that is correlated with the misspecification of the model. We theoretically consider the forecast environments in which our approach is likely to offer improvements over standard methods, and we find significant forecast improvements from applying the proposed method across four distinct empirical analyses including volatility forecasting, risk management, and yield curve forecasting.