Propensity Score Weights - Differ by Period

Dear all,

Apologies if my query format is incorrect as this is my first post.

I am currently conducting a difference-in-difference analysis on panel data (2 pre and 2 post treatment periods). The goal is a doubly robust DiD regression, weighting for a propensity score/inverse probability of treatment. The analysis regards the provision of piped water to households and the subsequent effects on child health status.

Having perused statlist for a number of hours this evening, it is apparent that employing an xtreg, fe is superior to the standard reg command, due to the panel data format of the data (subsequently individual unobservables are differenced out, and not simply aggregate unobservables).

A number of methods to estimate the propensity score have been made use, such as the popular psmatch2 as well as standard logistic regression on the probability of treatment.

The issue concerns the weighting requirements of the xtreg, fe model - it must be constant within the group variable through time. Both the Psmatch2 package and the logistic regression produce a propensity score for treatment reflective of the characteristics specific to that period (i.e. the propensity scores between periods 1 and 2 differ as the characteristics used to compute them change through time).

How might one calculate a singular pre-treatment propensity score on the basis of pre-treatment characteristics, regardless of period. If rephrased, how might one generate a propensity score that, for each category, does not differ between periods 1 and 2. I have considered averaging the two, though this seems archaic.

All support is much appreciated

Thanks and regards

Thanks and Regards