Econometrica: Jul 2015, Volume 83, Issue 4

A Test of Exogeneity Without Instrumental Variables in Models With Bunching
p. 1581-1600

C. Caetano

This paper presents a test of the exogeneity of a single explanatory variable in a multivariate model. It does not require the exogeneity of the other regressors or the existence of instrumental variables. The fundamental maintained assumption is that the model must be continuous in the explanatory variable of interest. This test has power when unobservable confounders are discontinuous with respect to the explanatory variable of interest, and it is particularly suitable for applications in which that variable has bunching points. An application of the test to the problem of estimating the effects of maternal smoking in birth weight shows evidence of remaining endogeneity, even after controlling for the most complete covariate specification in the literature.

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Supplemental Material

Supplement to “A Test of Exogeneity Without Instrumental Variables in Models With Bunching”

This supplement provides details of the implementation of the test statistic described in Section 3.1 in the manuscript.  It also develops the theorems that describe the test statistic's asymptotic behavior.  Finally, it presents a Monte Carlo study of the small sample behavior of the test statistic using real data (the same dataset used in the paper's Section 3).

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Supplement to "A Test Exogeneity without Instrumental Variables in Models with Bunching"

This zip file contains the replication files for the manuscript.

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