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

Jann, Ben (2020). Influence functions continued. A framework for estimating standard errors in reweighting, matching, and regression adjustment (University of Bern Social Sciences Working Papers 35). Bern: University of Bern, Department of Social Sciences

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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.

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