Nice quote from EconJeff on propensity score matching. The idea that somehow matching buys you causality in a situation in which you’d snicker at the idea that OLS does seems to be distressingly common.
Matching is not a design or an identifying assumption. Rather, it is one of several estimators that can be use when assuming selection on observed variables or unconfoundedness (or ignorability, or conditional independence, or whatever else your particular discipline or sub-field happens to call it this week). The key to evaluating an analysis based on an assumption of selection on observed variables is a careful consideration of the set of conditioning variables used in the analysis to deal with the problem of non-random selection into treatment. Estimator choice, e.g. matching versus linear regression versus inverse propensity weighting, is not unimportant, and can be very important for specific data generating processes, but what really matters in general is the set of conditioning variables.