The possibility that correlations are unstable over time is a matter of fact. Just for example we can consider that models included in these articles: https://www.sciencedirect.com/science/article/abs/pii/S1059056011000207
At the other side we know that correlation not imply causation, however sometime is possible to identify causal effects from correlational measures.
Therefore the question: causal effects can be time varying?
The reply seem yes. However unstable correlation can reveal misspecification problems and these are very relevant in causal inference. Moreover I think that causal effects descend from data generating mechanism/models and them sound like “laws of nature”. Usually we imagine them as stable. Time varying is not a problem for moments in general, then not for correlations. However I fear that for causal effects the story can be different.
Upload: From the reply of Elenchus i consider useful to add something. First, as causal effect I consider the average causal effect usually intended in social science; in related statistic-causal models randomness is the rule (see here: do(x) operator meaning?).
The answer depends somewhat on whether you're talking about the nature of the universe or the nature of modelling.
I’m interested in both. However my question starting from modeling side more than philosophic one. I never seen a causal model that consider time varying effects. For example in Causal Inference in Statistics a primer – Pearl Glymour Jewel (2016), such effects are not considered. Relevant to say that nor time varying correlations/moments/regression coefficients are. I do not know if it is so due to the introduction level of the book or more substantial motivations exist. However I checked even in the more advanced book: Causality – Pearl (2009); in it something like "time-varying treatments" are considered but not "time varying effect". The treatment can be structured in more or less complex manner, so naturally it can change over time also. My question is if the outcome can be different after the same treatment/intervention only because we repeat the same intervention at two different moments.
In regression side, if I estimate two times the same regression model on two different dataset, dataset that change only for the period considered, the parameters can be significantly different. This is the idea behind the Chow test for stability of coefficients. So, I discovered a, or some, time break/s. This can happen for several reason. However I can properly deal with this problem with a time varying coefficient regression model.
Passing to causal model side, from here (Is it appropriate to use "time" as a causal variable in a DAG?) I understand that, even if in some cases the time can be part of the causal model, time per se cannot have causal effects. So the reply on my question seems:
No, causal effects cannot change over time. If in the data, for the same causal model, something like instability regression coefficients happen, it mean that the causal model is wrong and we have to rethink it. Causal model that deal with time varying causal effect (time varying structural parameters) is a nonsense.
It is so?