A Discontinuity Test of Endogeneity *

Abstract This paper develops a nonparametric test of endogeneity without the need of instrumental variables. The test ensues from the novel observation that the potentially endogenous variable x is often of a nature such that the distribution of the unobservable q conditional on x and covariates z is discontinuous in x at a known value in its range. This relationship arises, for example, when x is subject to corner solutions, default contracts, social norms or law imposed restrictions, and may be argued using both economic theory and empirical evidence. If also x has a continuous effect on the dependent variable y, any discontinuity of y that is not accounted by the discontinuities in the covariates z is evidence that q and y are dependent conditional on z, i.e. it is evidence of the endogeneity of x. The analysis develops the test statistics and derives the asymptotic distribution for three versions of the test: linear, partially linear (nonparametric only on x but not on covariates) and non-parametric. Finally, the partially linear version of the test is applied to the estimation of the effect of maternal smoking on birth weight and on the probability of low birth weight (LBW). For the most detailed specification in the literatur