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Influence functions continued. A framework for estimating standard errors in reweighting, matching, and regression adjustment

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  • Ben Jann

Abstract

In Jann (2019) I provided some reflections on influence functions for linear regression (with an application to regression adjustment). Based on an analogy to variance estimation in the generalized method of moments (GMM), I extend the discussion in this paper to maximum-likelihood models such as logistic regression and then provide influence functions for a variety of treatment effect estimators such as inverse-probability weighting (IPW), regression adjustment (RA), inverse-probability weighted regression adjustment (IPWRA), exact matching (EM), Mahalanobis distance matching (MD), and entropy balancing (EB). The goal of this exercise is to provide a framework for standard error estimation in all these estimators.

Suggested Citation

  • Ben Jann, 2020. "Influence functions continued. A framework for estimating standard errors in reweighting, matching, and regression adjustment," University of Bern Social Sciences Working Papers 35, University of Bern, Department of Social Sciences, revised 31 Aug 2020.
    • Handle: RePEc:bss:wpaper:35
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    File URL: https://boris.unibe.ch/142529/15/jann-2020-IF.pdf
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    References listed on IDEAS

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    1. Hainmueller, Jens, 2012. "Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies," Political Analysis, Cambridge University Press, vol. 20(1), pages 25-46, January.
    2. Ben Jann, 2019. "Influence functions for linear regression (with an application to regression adjustment)," University of Bern Social Sciences Working Papers 32, University of Bern, Department of Social Sciences, revised 30 Mar 2019.
    3. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    4. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    5. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    6. Zhao Qingyuan & Percival Daniel, 2017. "Entropy Balancing is Doubly Robust," Journal of Causal Inference, De Gruyter, vol. 5(1), pages 1-19, March.
    7. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, January.
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    Cited by:

    1. Ben Jann, 2021. "dstat: A new command for the analysis of distributions," 2021 Stata Conference 1, Stata Users Group.
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    More about this item

    Keywords

    influence function; sampling variance; standard error; generalized method of moments; maximum likelihood; logistic regression; inverse-probability weighting; inverse-probability weighted regression adjustment; exact matching; Mahalanobis distance matching; entropy balancing; average treatment effect; causal inference;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • 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
    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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