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Identifying Multiple Marginal Effects With A Single Instrument

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  • Caetano, Carolina
  • Escanciano, Juan Carlos

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.

Suggested Citation

  • Caetano, Carolina & Escanciano, Juan Carlos, 2021. "Identifying Multiple Marginal Effects With A Single Instrument," Econometric Theory, Cambridge University Press, vol. 37(3), pages 464-494, June.
  • Handle: RePEc:cup:etheor:v:37:y:2021:i:3:p:464-494_2
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    Cited by:

    1. Fusejima, Koki, 2024. "Identification of multi-valued treatment effects with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 238(1).
    2. Michael Mueller-Smith & Benjamin Pyle & Caroline Walker, 2023. "Estimating the Impact of the Age of Criminal Majority: Decomposing Multiple Treatments in a Regression Discontinuity Framework," Working Papers 23-01, Center for Economic Studies, U.S. Census Bureau.
    3. Feng, Junlong, 2024. "Matching points: Supplementing instruments with covariates in triangular models," Journal of Econometrics, Elsevier, vol. 238(1).
    4. Carolina Caetano & Gregorio Caetano & Juan Carlos Escanciano, 2023. "Regression discontinuity design with multivalued treatments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(6), pages 840-856, September.

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