Jiacheng Li and Sean Myers (Working), A Hansen-Jagannathan Bound for Beliefs.
Abstract: What can forecast errors tell us about deviations from full-information rational expectations (FIRE)? For a large class of belief models, we show that commonly studied moments of forecast errors have a "problem of arbitrariness": any belief model that deviates from FIRE can match these moments if we apply the model to some latent component of the forecasted variable (e.g., extrapolation of a latent trend in yields rather than extrapolation of yields). Thus, even a belief model with an arbitrarily small deviation from FIRE can match any values of these moments. To address this problem, we propose a new moment, the forecast error Sharpe ratio (FESR). We use a variant of the Hansen-Jagannathan bound to show that the empirical FESR provides a lower bound on the magnitude of the required deviation from FIRE and that this bound can be used to evaluate a belief model across all possible latent variables. Applying this framework to professional forecasts of the 10-year yield, we find that the minimum required deviation from FIRE is substantially larger than the deviations generated by models of learning and behavioral expectations for standard parameter values, with some notable exceptions
