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what happens if my dependent variable is correlated with my time variable in a regression. I'm trying to add a time variable to control for trend but I notice that my dependent variable also increases over time.

Is it common or wrong to interact the time variable with your dependent variable?

How do I avoid spurious regression ( I'm not very knowledgeable on this I must admit)

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    $\begingroup$ Welcome to CV, Alice Work! Possibly of interest: De Boef, S. and Keele, L. (2008). Taking time seriously. American Journal of Political Science, 52(1):184–200. $\endgroup$
    – Alexis
    Dec 4 '18 at 4:22
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    $\begingroup$ " but I notice that my dependent variable also increases over time." Why 'but', what is the problem with this? If you have (positive) correlation between some dependent variable and time then isn't this the case by definition. $\endgroup$ Dec 4 '18 at 23:13
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    $\begingroup$ Did you mean to write independent variable the first or second time that you wrote dependent variable? $\endgroup$ Dec 4 '18 at 23:21
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    $\begingroup$ @Carl From the cited paper "Another important advantage of ECMs is that variables are parameterized in terms of changes, helping us to avoid spurious findings if the stationarity of the series is in question due to strongly autoregressive or near-integrated data, for example (De Boef 2001; De Boef and Granato 1997)." $\endgroup$
    – Alexis
    Dec 5 '18 at 1:07
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    $\begingroup$ @Carl The "path length for discovering physics" seems to be more or less irrelevant to the original question. $\endgroup$
    – Alexis
    Dec 5 '18 at 16:45