Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: May, 2015, Volume 83, Issue 3

Identification of Nonseparable Triangular Models With Discrete Instruments
p. 1199-1210

X. D'Haultfœuille and P. Février

We study the identification through instruments of a nonseparable function that relates a continuous outcome to a continuous endogenous variable. Using group and dynamical systems theories, we show that full identification can be achieved under strong exogeneity of the instrument and a dual monotonicity condition, even if the instrument is discrete. When identified, the model is also testable. Our results therefore highlight the identifying power of strong exogeneity when combined with monotonicity restrictions.

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Supplemental Material

Supplement to "Identification of Nonseparable Triangular Models with Discrete Instruments"

This supplement discusses the link with group theory and the freeness and nonfreeness properties.  It then discusses the extension to a multivariate X. The third section gathers all proofs.