Facts and figures about UK taxes, benefits and public spending.
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Analysis of the fiscal choices an independent Scotland would face.
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Reforming the tax system for the 21st century.
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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. Point identification is typically not achieved by imposing parametric restrictions. The extent of an identified set varies with the strength and support of instruments and typically shrinks as the support of a discrete outcome grows. The paper extends the analysis of structural quantile functions with endogenous arguments to cases in which there are discrete outcomes.This paper is a revised version of the original issued in December 2008.