Im trying to understand the difference between an OLS estimation model and a Propensity Score Matching (PSM) Technique. I understand that, essentially, what the PSM does is comparing treatment and control individuals based on their similarity according to a propensity score. Where the propensity score is calculated given a set of explanatory variables. Comparing this to OLS, does including explanatory variables in a regression lead to the creation of a more similar treatment and control group on which to estimate the effect of the treatment. In other words, would the following text make sense:
Ideally, we would like to compare two sets of identical students (having completed the same STEM degree in the same university) varying only in terms of gender. This kind of framework would prevent for any potential bias arising from the impact of unobserved factors that vary across gender and influence STEM persistence. For example, if males in the sample achieved higher average university grades compared to females, not accounting for this factor could lead to an upward bias in estimating the influence of gender on STEM persistence. Hence, leveraging a set of socio-demographic, socio-economic and education background control variables we set out to obtain two groups that ideally, given these controls, differ solely in terms of gender. The foundational assumption in our study is that the selection process is completely based on observables. In other words that our specification accounts for all conceivable unobservable variables that may differ across genders and impact STEM persistence.
I tried researching but was not able to find any answer.