Working Paper: NBER ID: w14086
Authors: Anirban Basu; Daniel Polsky; Willard G. Manning
Abstract: Under the assumption of no unmeasured confounders, a large literature exists on methods that can be used to estimating average treatment effects (ATE) from observational data and that spans regression models, propensity score adjustments using stratification, weighting or regression and even the combination of both as in doubly-robust estimators. However, comparison of these alternative methods is sparse in the context of data generated via non-linear models where treatment effects are heterogeneous, such as is in the case of healthcare cost data. In this paper, we compare the performance of alternative regression and propensity score-based estimators in estimating average treatment effects on outcomes that are generated via non-linear models. Using simulations, we find that in moderate size samples (n= 5000), balancing on estimated propensity scores balances the covariate means across treatment arms but fails to balance higher-order moments and covariances amongst covariates, raising concern about its use in non-linear outcomes generating mechanisms. We also find that besides inverse-probability weighting (IPW) with propensity scores, no one estimator is consistent under all data generating mechanisms. The IPW estimator is itself prone to inconsistency due to misspecification of the model for estimating propensity scores. Even when it is consistent, the IPW estimator is usually extremely inefficient. Thus care should be taken before naively applying any one estimator to estimate ATE in these data. We develop a recommendation for an algorithm which may help applied researchers to arrive at the optimal estimator. We illustrate the application of this algorithm and also the performance of alternative methods in a cost dataset on breast cancer treatment.
Keywords: propensity scores; nonlinear response models; healthcare expenditures
JEL Codes: C01; C21; I10
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Balancing on estimated propensity scores (C51) | Balances covariate means across treatment arms (C90) |
| Balancing on estimated propensity scores (C51) | Does not ensure balance in higher-order moments and covariances among covariates (C46) |
| Inconsistent estimators due to model misspecification (C51) | IPW estimator is prone to inconsistency (C51) |
| No single estimator is consistent across all data generating mechanisms (C51) | Potential biases in the estimates (C51) |
| Traditional regression methods (C29) | May not adequately capture the underlying data generating mechanisms (C51) |
| At least one of the models used is correctly specified (C52) | Doubly robust estimators could offer advantages (C51) |