Theoretical literature in finance has shown that quantifying the risk of financial time series amounts to measuring their expected shortfall, also known as tail Value at Risk. Unfortunately, little empirical work has been devoted to the problem of modeling and inference of such risk measures...

In this paper, we present methods for deriving testable implication from models with multiple equilibria. Our framework includes many economic models with a one-dimensional endogenous variable---examples are macroeconomic growth models (Solow, 1956), partial equilibrium models, and games of...

Survey data on expectations frequently find evidence that forecasts are biased, rejecting the joint hypothesis of rational expectations and symmetric loss. While the literature has attempted to explain this bias through forecasters' strategic behavior, we propose a simpler explanation based on...