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Do Instrumental Variables Belong in Propensity Scores?

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Jay Bhattacharya
William B. Vogt

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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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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0343.

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Date of creation: Sep 2007
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Handle: RePEc:nbr:nberte:0343

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
I1 - Health, Education, and Welfare - - Health
I2 - Health, Education, and Welfare - - Education

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  1. Heckman, James J. & Robb, Richard Jr., 1985. "Alternative methods for evaluating the impact of interventions : An overview," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 239-267. [Downloadable!] (restricted)
  2. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March. [Downloadable!] (restricted)
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  3. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-49, September. [Downloadable!] (restricted)
  4. Hidehiko Ichimura & Christopher Taber, 2001. "Propensity-Score Matching with Instrumental Variables," American Economic Review, American Economic Association, vol. 91(2), pages 119-124, May. [Downloadable!] (restricted)
  5. Jay Bhattacharya & Azeem Shaikh & Edward Vytlacil, 2005. "Treatment Effect Bounds: An Application to Swan-Ganz Catheterization," NBER Working Papers 11263, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  6. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, 05. [Downloadable!] (restricted)
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