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Efficiently Weighted Estimation of Tail and Interquantile Expectations

Tail expectations have recently attracted much attention in economics for their ability to capture risk. We develop a semiparametric estimator for the joint estimation of (nonlinear) models of tail expectations with some tail quantile as left or right threshold, and interquantile expectations, partial expectations between two thresholding quantiles. The joint estimator of these quantities can be used to test for heterogeneity in the conditional distribution, with special attention to distinct tail behavior. We derive efficient weights and asymptotic properties of the estimator for time-series data. The estimator does not require the specification of the conditional distribution and its computation relies on standard techniques. In an empirical application in finance we test for a disproportionate contribution of tail events to the average abnormal return of portfolio strategies.