Hi Eric,

I can certainly help answer the first question - the answer is that it is completely fine (and possibly more correct) to run PSM followed by OLS.

If you assume that matching is a preprocessing method used to adjust the data prior to regression analysis (as proposed by Ho, Imai, King, & Stuart, 2017) – then you can proceed as you would have done prior to matching (i.e. conduct regressions etc). Andrew Gelman certainly argues that this is the only way to go:

https://statmodeling.stat.columbia.edu/2014/06/22/matching-regression-matching-regression/

As for question #2, what exactly do you mean? Are you intending to use the same matching variables as contols in your path analysis? This has already been answered in an excellent post by Holger Steinmetz here in researchgate:

https://www.researchgate.net/post/What-is-the-role-of-control-variables-in-SEM

Hope this helps!

Tanya

Reference:

Ho, D. E., Imai, K., King, G., & Stuart, E. A. (2007). Matching as nonparametric preprocessing for reducing model dependence in parametric causal inference. Political analysis, 15(3), 199-236.

Yeap! I agree. Propensity is a preprocessing method. You do what you have to do at this stage to prepare for the outcome analysis stage. Do not conflate both. You can use matching vars in your outcome analysis - it is for double-robust estimation.