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I'm doing a regression between Institutional Investment and Total Debt for 500 companies over 2000-2022. Basically, it's panel data. I get the results of the regression and I see that the two are correlated. Now, please guide me as to how I check if that correlation is also a causation with X affecting Y or Y affecting X?

I read over the internet and I found that causality can be checked only if there is a exogenous shock to the system. In my case, I could say that the 2008 Crisis and COVID Crisis were outside shocks to the system. The data for 2007-2009 and 2020-2022 has the effect of those shocks.

However, how do I use this information statistically and reflect it in data to arrive at an conclusion? My apologies for not being precise in my question as I'm new to statistics. Thank you!

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2 Answers 2

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To argue that this relationship is causal, you need an exogenous shock which only affects X and does not directly affect Y. Moreover, the shock should not affect other factors related to Y, otherwise the effect you will measure will be that of X and other factors. This is something that as Frank Harrell says cannot be proved via data, but about which you have to persuade your audience.

For example, if I want to measure the effect of working from home on wages, Covid (an exogenous shock) might be an interesting idea, since many people suddenly started working from home. However, Covid changed a number of things, for example forcing children to learn from home, which might in turn lower people's productivity. I will have trouble persuading people that this is a useful exogenous shock, since Covid changed a large number of factors affecting productivity (out of which working from home is just one). Perhaps I can focus on people without children to rule out this particular rival theory, but there will be many others I have to think of.

Finally, if you want to strengthen your argument about causality (rather than just correlation), it might be helpful to propose a mechanism -- through what channel does X affect Y? For example, once it was understood how exactly certain chemicals in cigarettes degraded the body, the case that smoking actually causes lung cancer became much stronger (it took 3 decades from first studies until policymakers and the public were persuaded of a causal link).

Good luck with your study!

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  • $\begingroup$ Thank you very much! Beautifully explained. Now, assume I find an exogenous shock that effects only one variable. How do I proceed? What statistical methods and techniques would you suggest I use. I'm sorry for asking such basic questions. I've just started studying Statistics. $\endgroup$ Aug 25, 2023 at 13:54
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    $\begingroup$ You can't "find" an exogenous shock variable in the sense I think you mean. The only way to provide evidence of one variable causing changes in another is to design an experiment. No statistical method can extract causality from your data if your data is not from a well-controlled experimental design. (cont.) $\endgroup$
    – Sointu
    Aug 25, 2023 at 15:14
  • $\begingroup$ ...however, is you have data with, say, long follow-up with the same variables measured many times during different time periods, and you observe changes in X every time right after you observe changes in Y, I think most of your fellow researchers would be willing to agree it's a reasonable theory that Y changing has something to do with X changing, all other things being equal. $\endgroup$
    – Sointu
    Aug 25, 2023 at 15:17
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    $\begingroup$ Hi @wolterskluver, I am not sure what your exact setting is, but perhaps Instrumental variables could be of use to you, or this discussion about some successful natural experiments. $\endgroup$
    – Dudelstein
    Aug 25, 2023 at 18:54
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    $\begingroup$ @wolterskluver please accept an answer if you found it satisfactory, thank you! $\endgroup$
    – Dudelstein
    Aug 27, 2023 at 10:12
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As has been discusssed extensively, evidence for causation does not come from data. It comes from understanding the data generating process, the meaning of the measurements, the subject matter context, the study design, and in short on the ability to rule out alternative explanations.

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  • $\begingroup$ Thank you for the instant response. I understand your point that data can not be used to conclusively prove causality. However, what if I were to say I want to see whether X follows Y or vice-versa without taking causality into account. For example, in a 10 year data for X and Y, X always shows a drop after a drop in Y and a rise after a rise in Y. This can be observed from data. Right? How do I make a similar deduction in my above case? $\endgroup$ Aug 25, 2023 at 12:48
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    $\begingroup$ That might be used to RULE out causality: If X follows Y, then X cannot cause Y (although even there, there might be exceptions that I am not thinking of), but it is possible for X to follow Y with no causal relationship at all. But, in the real world, things are rarely so simple, certainly not in subjects like economics (your example), psychology, sociology etc. It could even be causal in one direction in one company and the other direction in another company. $\endgroup$
    – Peter Flom
    Aug 25, 2023 at 13:10
  • $\begingroup$ @PeterFlom That clears a lot of questions in my mind. Thank You. However, if I remove causality from the equation, is there a way to establish whether X follows Y or vice-versa through a statistical method? Being able to rule out causality is also helpful in my case. $\endgroup$ Aug 25, 2023 at 13:20
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    $\begingroup$ I think "follows" refers to temporality here - you know the temporal sequence of events you're interested in. From that sequence you know which things happened before and after X -and you know the latter could not have caused X, you don't need a statistical test for that. $\endgroup$
    – Sointu
    Aug 25, 2023 at 13:32
  • $\begingroup$ Lack of correlation is also not proof of non-causality. Data alone cannot answer this type of question @wolterskluver $\endgroup$
    – Firebug
    Aug 26, 2023 at 15:16

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