Abstract

Introduction It is common in the literature on instrumental variables to remark upon the difficulty of knowing or demonstrating that a potential instrument is exogenous, in the sense of being uncorrelated with the disturbances [Bartels, 1991, Johnston, 1972]. It is also widely recognized that exogeneity is an assumption embedded in the model specification [Engle, et al, 1984], hence, it rests on subjective judgment and, like other structural assumptions of causation and "zero-restrictions", it cannot be tested in purely observational studies. The purpose of this note is to show that despite its elusive nature, exogeneity can nevertheless be given some empirical test. The test is not guaranteed to detect all violations of exogeneity but it can, in certain circumstances, screen away real bad choices of would-be instruments. 2 An Instrumental Inequality Definition 2.1 (exogeneity) A variable z is said to be exogenous relative to an ordered

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