Matching: Removing reversed causality?

[Guest]

Hi everybody,

I've read that endogeneity has many faces: One is omitted variable bias, another is measurement error and finally there is simultaneous causality.
Indeed, simultaneous causality or reversed causality is what interests me the most.
As I'm working on a study where exactly reversed causality is an issue, I tried to come up with an econometric solution.
The only thing that appears to really work are instrumental variable approaches.

Now I've read in a paper by Austin Nichols (https://journals.sagepub.com/doi/pdf...867X0800700403) the following sentence:
"The selection bias (or omitted-variable bias) in an ordinary regression arises from endogeneity (a regressor is said to be endogenous if it is correlated with the error), a condition that also occurs if the explanatory variable is measured with error or in a system of “simultaneous equations”

As matching techniques account for selection bias, I wondered whether matching might be also used to counteract reversed causality?

Edit: Imagine the relationship I want to study is x->y. As matching accounts for nonrandom assignment wouldn't this allow to cancel out reversed causality from y->x as one would account for the fact that the assignment might be also due to y.

[Felix Bittmann]

For sure, this topic has many faces. Personally, for me as a sociologist, this is usually a theoretical question. Are there good reasons to assume that reverse causality is present? For example, when I study the effect of COVID-19 on satisfaction and I have measured satisfaction before and after the onset of the pandemic, I can be very confident that reverse causality is not an issue since COVID is a random, external shock and there are no anticipation effects. However, many other topics are more convoluted, when people actually make decisions, like marriage or choosing a school for their children. Even if I measure a certain variable before an event (say, the official date of registration at a school), quite often, the participants will already have made a decision (at least mentally) and reverse causality can be present. Sure, controlling for self-selection is important but in my opinion this can never completely rule out or amend reserve causality. Best you can do is make this transparent and discuss it. There are no statistical methods to "remove" reverse causality if actually present, not with the data we normally have (observational studies). Happy to hear other opinions. And to come back to your question: I do not think matching has any special properties regarding reserve causality, say, comparing it to other methods like OLS.