UCLA

Since the seminal work of Rosenbaum and Rubin (1983), the propensity score (the probability of receiving treatment given covariates) has played a major role in improving the credibility of causal effect estimation in observational data. Propensity scores have been used for stratification, matching, and weighting, demonstrating their capacity to improve balance in the distribution of covariates across treatment groups. More recently, balance estimators that directly target balance through calibration or optimization have gained acceptance due to their superior in-sample performance.

While one of the primary strengths of these balancing methods lies in reducing the reliance on a correctly specified outcome model, one of their drawbacks is their relative inefficiency resulting from weight variability. An advisable alternative is then to utilize prognostic scores (predicted untreated potential outcomes given covariates) to augment the weighting estimator, thereby recovering some lost efficiency without purely depending on an outcome model.

In this paper, I demonstrate the use of a prognostic propensity score weighting (PPSW) as a conceptually simple yet effective alternative to traditional propensity score weighting. Instead of predicting the treatment status given covariates, the PPS predicts the treatment status based on estimates of the control potential outcome. This approach addresses only the portion of covariate imbalance relevant to de-biasing the treatment effect of interest.

I compare the performance of PPSW with other causal effect estimators through simulations and an empirical application, illustrating that the method can offer a practical alternative for researchers dealing with hard-to-balance and distracting covariates.