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Often we are taught that growth rates are stationary. Or at least, this is what I have often been taught.

But I've a set of macroeconomic variables, in levels, which I transform and take natural log differences with a lag of 4 (to produce % y/y growth rates). I use the ADF test to check for a unit root, and in each case I fail to reject the null of non-stationarity.

I've tried searching on Google, but does anyone have any literature or anything on this topic? I've found a couple of papers by Stock & Watson where they assume they have stationary variables because they have y/y growth rates, even though tests for a unit root show the presence of one. Is this really something that is justifiable? Surely if the ADF test, or some other tests, indicates non-stationarity, you cannot really proceed assuming you have stationary variables?

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  • $\begingroup$ Sometimes the non-stationarity can come in a different form ( trend stationary)) in which case, a unit root test could possibly miss it. (ADF looks for difference stationarity ). Also, there is the augmented DF test that could give different results and other unit root test that treat the null differently. I don't know the answer to your question ( your growth rates are indicating stationaary wen you expect them to be non-stationary ? ) but I glanced at this link and it may be slightly useful. . mayoral.iae-csic.org/timeseries_bgse12/slides_intrononstat.pdf . I hope it helps some. $\endgroup$ – mlofton Aug 23 '18 at 16:54
  • $\begingroup$ Thanks for the link. I'll check it out. Sorry I made a few mistakes in my first post; I'd expect y/y growth rates to be stationary, but in my case I have found they are not when using the Augmented-Dickey-Fuller test. $\endgroup$ – eBopBob Aug 23 '18 at 17:18
  • $\begingroup$ I have had my own problems with unit root tests with different ones giving different results. Maybe try a few other tests ( there are many. KPSS, perron and others ) and see if they give conflicting results. Unit root tests are problematic because they are not robust to different tests because some tests have the null as stationary and others have it as not-stationary. Good luck with your problem. $\endgroup$ – mlofton Aug 24 '18 at 3:59
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I do ADF tests, not find out about stationarity, but to convince others. I found that this test doesn't bring any value beyond what's obvious. Are GPD growth rates stationary? Maybe, maybe not. You could argue that China's real GDP cannot sustain at current level for next 50 years. On the other hand interest rates (growth rates of bond prices) were at the same order of magnitude today as they were 2000 years ago. Whether you model them as stationary or not depends on the series and the context of your problem. You can't make a general statement about all macroeconomic series' stationarity. Having said that, prices are almost always non-stationary, and their growth rates often are.

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