In this paper we document that realized variation measures constructed from high-frequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized volatility are substantive. Even...

Single equation instrumental variable models for discrete outcomes are shown to be set not point identifying for the structural functions that deliver the values of the discrete outcome. Identified sets are derived for a general nonparametric model and sharp set identification is demonstrated....

This paper develops methods for evaluating marginal policy changes. We characterize how the effects of marginal policy changes depend on the direction of the policy change, and show that marginal policy effects are fundamentally easier to identify and to estimate than conventional treatment...