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To further elaborate on my question, assume that I have a time series dataset of Tax X and Tax Y, where in Tax X is paid by 100% of the sample while Tax Y is paid by 75%. Both taxes differ with regards to how they are implemented and collected, but are ultimately based on business revenues. Now if I am trying to figure out the relationship between Tax Y and Tax X to estimate Tax Y for the 25% of the sample for which there is no Tax Y data, is it kosher to regress Tax Y on Tax X? It is clear to see that Tax X is not causing Tax Y and that both taxes are being determined by individual business revenues, which is not known.

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There can be a linear relationship between variables with no causal relation directly involved. It's fair to check if the linear model is a good fit in order to make estimations.

I personally don't know any single model which needs something like "direct causality assumption".

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  • $\begingroup$ Interesting. I don't have too much experience with time series data, but I was under the impression that since you have a greater degree of ability to identify and establish things like Granger causality, regression specifications with spurious relationships like the one I laid out were not considered useful. $\endgroup$ – Naj S May 28 '15 at 20:42
  • $\begingroup$ +1 In the absence of a causal idnetification strategy, linear regression is just a handy descriptive or predictive tool. Apply as necessary, where necessary. $\endgroup$ – conjugateprior May 28 '15 at 22:20

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