Can propensity score analysis correct for reverse causation or simultaneity

Question

I have data where I suspect there may be reverse causation (Y => X) or simultaneity (Y <=> X). Does the technique of propensity score analysis help to account for this effect? I feel that as part of the technique we are constructing a "control" equivalent sample (through propensity scores) which is counterfactual to any hypothesised simultaneity relationship.

EDIT : Thanks. Can I add a bit more context? I have data on the sale price of houses (Y) in a neighbourhood and the local grocery retail provision (X). I am looking to see if the brand of the retail provision has an effect on the sales price of houses (in the UK this is known as a Waitrose effect, after a premium retailer brand (https://www.lloydsbankinggroup.com/Media/Press-Releases/2018-press-releases/lloyds-bank/090618_Supermarkets_LB/). My concern is that there might be simultaneity, with retail brands locating in areas with high house prices (Y => X) and also the presence of a particular retail brand raising house prices (X => Y). But maybe my concern is actually a selection bias, where certain retail brands are bias to select certain types of areas (high affluence/low affluence) and PS can correct for this?

Answer 1

No. Matching methods in this case have the same fragility as regression. They do not automagically control for any endogeneity sources.

In assessment of treatment effect, both matching and regression base on the same Conditional Independence Assumption (CIA) (Angrist and Pishke, 2008), which is:

$$ \{Y_{0i}, Y_{1i} \} \perp \! \! \! \perp c_i | X_i $$

As long as treatment depends on outcome it is a straight violation of CIA and estimator in both methods is biased.

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Angrist, Joshua D., and Jörn-Steffen Pischke. Mostly harmless econometrics: An empiricist's companion. Princeton university press, 2008.