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Instrumental variables and the sign of the average treatment effect

Author

Listed:
  • Machado, Cecilia
  • Shaikh, Azeem M.
  • Vytlacil, Edward J.

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.

Suggested Citation

  • Machado, Cecilia & Shaikh, Azeem M. & Vytlacil, Edward J., 2019. "Instrumental variables and the sign of the average treatment effect," Journal of Econometrics, Elsevier, vol. 212(2), pages 522-555.
    • Handle: RePEc:eee:econom:v:212:y:2019:i:2:p:522-555
    DOI: 10.1016/j.jeconom.2018.04.007
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    References listed on IDEAS

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    1. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    2. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    3. Ivan A. Canay & Azeem M. Shaikh, 2016. "Practical and theoretical advances in inference for partially identified models," CeMMAP working papers 05/16, Institute for Fiscal Studies.
    4. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    5. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    6. Jason Abrevaya & Jerry A. Hausman & Shakeeb Khan, 2010. "Testing for Causal Effects in a Generalized Regression Model With Endogenous Regressors," Econometrica, Econometric Society, vol. 78(6), pages 2043-2061, November.
    7. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
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    11. Bhattacharya, Jay & Shaikh, Azeem M. & Vytlacil, Edward, 2012. "Treatment effect bounds: An application to Swan–Ganz catheterization," Journal of Econometrics, Elsevier, vol. 168(2), pages 223-243.
    12. Martin Huber & Giovanni Mellace, 2015. "Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 398-411, May.
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    Keywords

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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