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The question seems to involve two things that really ought to be considered separately. First is whether one can infer causality from an observational study, and on that you might contrast the views of, say, Pearl (2009), who argues yes so long as you can model the process properly, versus the view @propofol, who will find many allies in experimental disciplines and who may share some of the thoughts expressed in (a rather obscure but nonetheless good) essay by Gerber et al (2004). Second, assuming that you do think that causality can be inferred from observational data, you might wonder whether propensity score methods are useful in doing so. Propensity score methods include various conditioning strategies as well as inverse propensity weighting. A nice review is given by Lunceford and Davidian (2004). They have good properties but certain assumptions are required (most specifically, "conditional independence") for them to be consistent.

A little wrinkle though: propensity score matching and weighting are also used in the analysis of randomized experiments when, for example, there is an interest in computing "indirect effects" and also when there are problems of potentially non-random attrition or drop out (in which case what you have resembles an observational study).

References

Gerber A, et al. 2004. "The illusion of learning from observational research." In Shapiro I, et al, Problems and Methods in the Study of Politics, Cambridge University Press.

Lunceford JK, Davidian M. 2004. "Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study." Statistics in Medicine 23(19):2937–2960.

Pearl J. 2009. Causality (2nd Ed.), Cambridge University Press.

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