How to adjust standard errors when the final estimates are reported on a screened sample based on propensity score?

[Hirakjyoti Basak]

I want to estimate the causal effect of a treatment variable D (which is binary) on outcome variable (Y) using covariates (X). That is I want to run a regression like:

reg Y D X

However, instead of running the regression on the full sample, I want to first generate propensity scores for D based on covariates X and then keep only those observations with propensity score lying strictly between 0.1 and 0.9.

That is, I want to run the above regression on the sample screened based on the propensity score. While I can manually screen the sample by dropping the observations with pscore outside 0.1 to 0.9 range and then run the regression on the remaining sample, the final standard errors will not be quite right as it will not be reflecting the fact that the sample has been screened using propensity score which in turn has been estimated. Thus I wanted to know how to ensure in STATA that the final estimates of the regression have standard errors which account for the fat that the sample is screened based in the propensity score?

Thank you.

[David Radwin]

I'm not sure why you need to adjust the standard errors of the regression after matching. For example, the Stata code in appendix SA2 of the following article doesn't make any such correction.

DuGoff, E.H., Schuler, M., and Stuart, E.A. (2014). Generalizing Observational Study Results: Applying Propensity Score Methods to Complex Surveys. Health Services Research, 49(1): 284–303. https://onlinelibrary.wiley.com/doi/...475-6773.12090

That said, your standard errors will likely (but not necessarily) be larger than if you included the whole sample because you dropped some cases. That's not necessarily a bad thing. But you might choose a different criterion for dropping cases, like cases outside common support or all unmatched cases. See the article above and also these:

Ho, D.E., Imai, K., King, G., and Stuart, E.A. (2007). Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference. Political Analysis, 15(3): 199–236.

Sekhon, J.S. (2009). Opiates for the matches: Matching methods for causal inference. Annual Review of Political Science, 12: 487-508.