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IDENTIFYING MULTIPLE MARGINAL EFFECTS WITH A SINGLE INSTRUMENT

Published online by Cambridge University Press:  19 May 2020

Carolina Caetano  and
Juan Carlos Escanciano
Carolina Caetano*
Affiliation:
University of Georgia
Juan Carlos Escanciano
Affiliation:
Universidad Carlos III de Madrid
*
Address correspondence to Carolina Caetano, Department of Economics, University of Georgia, 620 South Lumpkin Street Athens, GA30602, USA; e-mail: [email protected].
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Abstract

This paper proposes a new strategy for the identification of the marginal effects of an endogenous multivalued variable (which can be continuous, or a vector) in a model with an Instrumental Variable (IV) of lower dimension, which may even be a single binary variable, and multiple controls. Despite the failure of the classical order condition, we show that identification may be achieved by exploiting heterogeneity of the “first stage” in the controls through a new rank condition that we term covariance completeness. The identification strategy justifies the use of interactions between instruments and controls as additional exogenous variables and can be straightforwardly implemented by parametric, semiparametric, and nonparametric two-stage least squares estimators, following the same generic algorithm. Monte Carlo simulations show that the estimators have excellent performance in moderate sample sizes. Finally, we apply our methods to the problem of estimating the effect of air quality on house prices, based on Chay and Greenstone (2005, Journal of Political Economy 113, 376–424). All methods are implemented in a companion Stata software package.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 3 , June 2021 , pp. 464 - 494
Copyright
© Cambridge University Press 2020

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Footnotes

*

We would like to thank Gregorio Caetano, Alon Bergman, Kenneth Chay, Matias Cattaneo, Pedro Sant’Anna, and and Robin Sickles for helpful discussions. We are thankful to the Co-Editor and three referees for suggestions, which have helped us to significantly improve the presentation. We would also like to thank seminar participants at many institutions as well as guests at our institutions for useful comments. This paper subsumes part of the working paper “Identifying Multiple Marginal Effects with a Single Binary Instrument or by Regression Discontinuity,” dated May 25, 2015. Research funded to Juan Carlos Escanciano by the Spanish Grant PGC2018-096732-B-I00.

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