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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
or https://arxiv.org/ftp/arxiv/papers/1705/1705.02479.pdf

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?).

Then:

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?

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    $\begingroup$ Yes, I think you've got it now. I just remembered Samantha Kleinberg's work though, which I haven't yet read. She incorporates more temporal information into her models than others. There's a book, and a few papers. Here's a link to one arxiv.org/abs/1205.2634 $\endgroup$
    – Elenchus
    Commented Sep 11, 2020 at 9:58
  • $\begingroup$ Also just reiterating @Bob D's comment - time is never a cause $\endgroup$
    – Elenchus
    Commented Sep 11, 2020 at 10:00

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The answer depends somewhat on whether you're talking about the nature of the universe or the nature of modelling. To quote from McElreath's Statistical Rethinking 2, "Nothing in the real world - excepting controversial interpretations of quantum physics - is actually random. Presumably, if we had more information, we could exactly predict everything". Modelling, on the other hand, is full of randomness - but that randomness describes our uncertainty about the nature of the universe more than randomness in real processes.

With an impossibly good causal model which accurately captures the nature of the universe, it's hard to say - there may or may not be causal effects which change over time; a physicist could give a better answer to that. For a causal model constructed by human beings, if we are seeing changes in causal effects over time, then the model is not explaining part of the process - there is some variable that the cause or effect is dependent on that is missing from the model. Remember the adage "all models are wrong, but some are useful".

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    $\begingroup$ Exactly, it all depends on the level of granuality you are looking at a causal effect. Time is never a cause. Sometimes assuming some time-depending parametric smoothing over the covariate space might be a more and sometimes aless adequate assumption to capture confounding. $\endgroup$
    – persephone
    Commented Sep 8, 2020 at 15:08
  • $\begingroup$ @Elenchus. The first part of your reply deal with the opportunity/necessity of consider the randomness in the model. I do not argue pro or cons of this, however I consider randomness in causal models that I interested in. As causal effect I consider the "average causal effect" usually intended in social science. $\endgroup$
    – markowitz
    Commented Sep 10, 2020 at 11:11
  • $\begingroup$ In the second part it seems me that you sustain a position like: if causal effect change over time … something went wrong (misspecification). This sound like: no time varying causal effect can exist, even if them can appear in some, eventually useful, model. I understand correctly what you said? $\endgroup$
    – markowitz
    Commented Sep 10, 2020 at 11:12
  • $\begingroup$ Hmm, I'm not sure. Let me have another go. No model we'll ever come up with will be able to capture the true causal effect of anything - that would rely on being able to understand things beyond the scope of our knowledge and ability to measure. The representations in our models tend to be high-level, and randomness represents our uncertainty about the low-level. If in a model we're using we see an effect change, then there's causal information missing from the model - our representation of the true causes was complete enough to be useful at one time, but not complete enough to be useful later $\endgroup$
    – Elenchus
    Commented Sep 10, 2020 at 11:48
  • $\begingroup$ I think you were closer with the second part than the first - the first part was trying to describe how models depict reality, more than being about the randomness you might use in your model $\endgroup$
    – Elenchus
    Commented Sep 10, 2020 at 11:51

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