Covariate Distribution Balance via Propensity Scores

Abstract

The propensity score plays an important role in causal inference with observational data. However, it is well documented that under slight model misspecifications, propensity score estimates based on maximum likelihood can lead to unreliable treatment effect estimators. To address this practical limitation, this article proposes a new framework for estimating propensity scores that mimics randomize control trials (RCT) in settings where only observational data is available. More specifically, given that in RCTs the joint distritbution of covariates are balanced between treated and not-treated groups, we propose to estimate the propensity score by maxizing the covariate distribution balance. The proposed propensity score estimators, which we call the integrated propensity score (IPS), are data-driven, do not rely on tuning parameters such as bandwidths, admit an asymptotic linear representation, and can be used to estimate many different treatment effect measures in a unified manner. We derive the asymptotic properties of inverse probability weighted estimators for the average, distributional and quantile treatment effects based on the IPS and illustrate their relative performance via Monte Carlo simulations and three empirical applications. An implementation of the proposed methods is provided in the new package IPS for R.

Abadie's Kappa and Weighting Estimators of the Local Average Treatment Effect

“…In particular, numerous papers have used this result to estimate mean covariate values for compliers (e.g., Angrist et al, 2013;Dahl et al, 2014;Bisbee et al, 2017) and to approximate the conditional mean of Y given D and X for this subpopulation (e.g., Cruces and Galiani, 2007;Angrist et al, 2013;Goda et al, 2017). On the other hand, the implications of Lemma 1(b) and (c) have been considered almost exclusively in the econometrics literature, where several papers have used these results to identify and estimate τ LATE and quantile treatment effects (e.g., Frölich and Melly, 2013;Abadie and Cattaneo, 2018;Sant'Anna et al, 2020;Singh and Sun, 2021).…”

“…where both sets of weights, N i=1 κ i1 −1 κ i1 and N i=1 κ i0 −1 κ i0 , sum to unity across i. The normalized estimator is also considered by Abadie and Cattaneo (2018) and Sant'Anna et al (2020).…”

“…Abadie (2003)'s theorem has been highly influential in applied work, and it is now routinely used to estimate mean covariate values for compliers (e.g., Angrist et al, 2013;Dahl et al, 2014;Bisbee et al, 2017) and to approximate the conditional mean of an outcome of interest in this subpopulation (e.g., Cruces and Galiani, 2007;Angrist et al, 2013;Goda et al, 2017). At the same time, it is surprisingly uncommon among practitioners to use methods based on kappa weighting to estimate the LATE, even though Abadie (2003)'s result has also spurred a growing literature in econometrics, which indeed focuses on the LATE and its quantile counterparts (e.g., Frölich and Melly, 2013;Abadie and Cattaneo, 2018;Sant'Anna et al, 2020;Singh and Sun, 2021).…”

“…To do this, we assume that the researcher adopts a parametric model for the instrument propensity score and estimates the unknown parameters by maximum likelihood (cf. Sant'Anna et al, 2020). In a unified framework of M-estimation, our weighting estimators are asymptotically normal, and we derive their asymptotic variances.…”

“…We recommend that applied researchers with access to a binary instrumental variable either restrict their attention to normalized weighting estimators or consider other flexible approaches to estimation. These could include covariate balancing estimators of the LATE, as studied by Sant'Anna et al (2020) and Heiler (2021), and doubly robust estimators of this parameter, as recommended by Tan (2006), Uysal (2011), Ogburn et al (2015), Belloni et al (2017), Singh andSun (2021), andSłoczyński et al (2022).…”