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In this paper, I consider identification of treatment effects when the treatment is endogenous. The use of instrumental variables is a popular solution to deal with endogeneity, but this may give misleading answers when the instrument is invalid. I show that when the instrument is invalid due to correlation with the first stage unobserved heterogeneity, a second (also possibly invalid) instrument allows to partially identify not only the local average treatment effect but also the entire potential outcomes distributions for compliers. I exploit the fact that the distribution of the observed outcome in each group defined by the treatment and the instrument is a mixture of the distributions of interest. I write the identified set in the form of conditional moment inequalities, and provide an easily implementable inference procedure. Under some (testable) tail restrictions, the potential outcomes distributions are point-identified for compliers. Finally, I illustrate my methodology on data from the National Longitudinal Survey of Young Men to estimate returns to college using college proximity as (potential) instrument. I find that a college degree increases the average hourly wage of the compliers by 38-79%.

This paper discusses the empirical content of the exogeneity (zero-covariance) assumption, the key assumption for identification in the linear IV model. Contrary to the general belief, we show that whenever the outcome is bounded, the exogeneity assumption imposes some testable restrictions on the observables, namely the linear instrumental inequalities (LII). The LII can therefore be used to test the instrument validity. The test can be easily implemented using existing inferential methods for testing multiple inequalities. Whenever, the causal effect parameter is random, an additional critical condition that trivially holds in the linear IV model is required for the IV estimand to identify the average treatment effect (ATE). We show that when this critical condition holds while the exogeneity assumption does not, the magnitude of the violations of the LII allows us to derive (informative) bounds on the ATE. We also derive testable implications of this critical condition which when violated implies that the usual IV estimand cannot be interpreted as the ATE or as the local ATE. We illustrate our results by testing the validity of various instruments present in the literature.
This paper proposes a new set of testable implications of the instrumental variable (IV) independence assumption: generalized instrumental inequalities. In our leading case with binary outcome, we show that the generalized instrumental inequalities are necessary and sufficient to detect all observable violations of the IV independence assumption. To test the generalized instrumental inequalities, we propose an approach combining a sample splitting procedure and intersection bounds inferential methods. This idea allows one to easily implement the test using the Stata packages of Chernozhukov, Kim, Lee, and Rosen (2015) or Andrews, Kim and Shi (2016). We apply our proposed strategy to assess the validity of the IV independence assumption for various instruments used in the return to college literature.

Research in progress
  • "Bounding Treatment Effects using Unconditional Moment Restrictions" (joint with Lixiong Li and Ismael Mourifié).
  • "Class Size and Student Performance: At what cost? Evidence from Greece" (joint with Kala Krishna, Rigissa Megalokonomou and Yingyan Zhao).
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