Instrumental Variables and the Sign of the Average Treatment Effect

57 Pages Posted: 14 Feb 2019

See all articles by Cecilia Machado

Cecilia Machado

Getulio Vargas Foundation (FGV)

Azeem Shaikh

University of Chicago

Edward Vytlacil

Yale University - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: January 16, 2018

Abstract

This paper considers identification and inference about the sign of the average effect of a binary endogenous regressor (or treatment) on a binary outcome of interest when a binary instrument is available. In this setting, the average effect of the endogenous regressor on the outcome is sometimes referred to as the average treatment effect (ATE). We consider four different sets of assumptions: instrument exogeneity, instrument exogeneity and monotonicity on the outcome equation, instrument exogeneity and monotonicity on the equation for the endogenous regressor, or instrument exogeneity and monotonicity on both the outcome equation and the equation for the endogenous regressor. For each of these sets of conditions, we characterize when (i) the distribution of the observed data is inconsistent with the assumptions and (ii) the distribution of the observed data is consistent with the assumptions and the sign of ATE is identified. A distinguishing feature of our results is that they are stated in terms of a reduced form parameter from the population regression of the outcome on the instrument. In particular, we find that the reduced form parameter being far enough, but not too far, from zero, implies that the distribution of the observed data is consistent with our assumptions and the sign of ATE is identified, while the reduced form parameter being too far from zero implies that the distribution of the observed data is inconsistent with our assumptions. For each set of restrictions, we also develop methods for simultaneous inference about the consistency of the distribution of the observed data with our restrictions and the sign of the ATE when the distribution of the observed data is consistent with our restrictions. We show that our inference procedures are valid uniformly over a large class of possible distributions for the observed data that include distributions where the instrument is arbitrarily “weak.” A novel feature of the methodology is that the null hypotheses involve unions of moment inequalities.

Keywords: Average Treatment Effect, Endogeneity, Instrumental Variables, Union of Moment In-equalities, Bootstrap, Uniform Validity, Multiple Testing, Familywise Error Rate, Gatekeeping

JEL Classification: C12, C31, C35, C36

Suggested Citation

Machado, Cecilia and Shaikh, Azeem and Vytlacil, Edward J., Instrumental Variables and the Sign of the Average Treatment Effect (January 16, 2018). University of Chicago, Becker Friedman Institute for Economics Working Paper No. 2019-18, Available at SSRN: https://ssrn.com/abstract=3334009 or http://dx.doi.org/10.2139/ssrn.3334009

Cecilia Machado

Getulio Vargas Foundation (FGV) ( email )

R. Dr. Neto de Araujo 320 cj 1307
Rio de Janeiro, Rio de Janeiro 22250-900
Brazil

Azeem Shaikh (Contact Author)

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Edward J. Vytlacil

Yale University - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8281
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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