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Do Instrumental Variables Belong in Propensity Scores?

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  • Jay Bhattacharya
  • William B. Vogt

Abstract

Propensity score matching is a popular way to make causal inferences about a binary treatment in observational data. The validity of these methods depends on which variables are used to predict the propensity score. We ask: "Absent strong ignorability, what would be the effect of including an instrumental variable in the predictor set of a propensity score matching estimator?" In the case of linear adjustment, using an instrumental variable as a predictor variable for the propensity score yields greater inconsistency than the naive estimator. This additional inconsistency is increasing in the predictive power of the instrument. In the case of stratification, with a strong instrument, propensity score matching yields greater inconsistency than the naive estimator. Since the propensity score matching estimator with the instrument in the predictor set is both more biased and more variable than the naive estimator, it is conceivable that the confidence intervals for the matching estimator would have greater coverage rates. In a Monte Carlo simulation, we show that this need not be the case. Our results are further illustrated with two empirical examples: one, the Tennessee STAR experiment, with a strong instrument and the other, the Connors' (1996) Swan-Ganz catheterization dataset, with a weak instrument.

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  • Jay Bhattacharya & William B. Vogt, 2007. "Do Instrumental Variables Belong in Propensity Scores?," NBER Technical Working Papers 0343, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0343
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    Citations

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    Cited by:

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    5. Steiner Peter M. & Kim Yongnam, 2016. "The Mechanics of Omitted Variable Bias: Bias Amplification and Cancellation of Offsetting Biases," Journal of Causal Inference, De Gruyter, vol. 4(2), pages 1-22, September.
    6. Bisakha Sen & Stephen Mennemeyer & Lisa C. Gary, 2009. "The Relationship Between Neighborhood Quality and Obesity Among Children," NBER Working Papers 14985, National Bureau of Economic Research, Inc.
    7. Rebecca Riley & Hilary Metcalf & John Forth, 2013. "The business case for equal opportunities," Industrial Relations Journal, Wiley Blackwell, vol. 44(3), pages 216-239, May.
    8. Chabé-Ferret, Sylvain, 2012. "Matching vs Differencing when Estimating Treatment Effects with Panel Data: the Example of the Effect of Job Training Programs on Earnings," TSE Working Papers 12-356, Toulouse School of Economics (TSE).
    9. Steven Lawry & Cyrus Samii & Ruth Hall & Aaron Leopold & Donna Hornby & Farai Mtero, 2014. "The Impact of Land Property Rights Interventions on Investment and Agricultural Productivity in Developing Countries: a Systematic Review," Campbell Systematic Reviews, John Wiley & Sons, vol. 10(1), pages 1-104.
    10. Pearl Judea, 2013. "Linear Models: A Useful “Microscope” for Causal Analysis," Journal of Causal Inference, De Gruyter, vol. 1(1), pages 155-170, June.
    11. Bryan Keller, 2020. "Variable Selection for Causal Effect Estimation: Nonparametric Conditional Independence Testing With Random Forests," Journal of Educational and Behavioral Statistics, , vol. 45(2), pages 119-142, April.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • I1 - Health, Education, and Welfare - - Health
    • I2 - Health, Education, and Welfare - - Education

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