Unit-root and Johansen- lack of normal distribution. Please help!

[Anastazja Stachwiuk]

I have a question concerning unit-root data and normal distribution. As an assignment, I am checking the long-term relationship between unemployment rates and labor force participation rate. First I used the DF-GLS and KPSS test, and I proved that my data has unit-root at levels and is stationary at first differences. Now I am supposed to use the Johansen cointegration test. As far as I read, it requires normal distribution. Is it possible that my variables with unit-root do not have a normal distribution, and stationary first-differences do? If yes, should I use first differences to Johansen test? 2) I am obligated to run tests on all econometric problems such as autocorrelation, heteroskedasticity etc. should I do it on data with unit root or again stationary first differences? Sorry for trivial questions, but it is my first time. Thank you very much in advance, you will save my life!

[Justin Niakamal]

You can do the Engle-Granger method if you're only looking at two series. The Johansen test is typically used for more than two series. You should not use first differences when doing the Johansen test. Variables that are I~(0) do not have a trend. Cointegration is when two (or more series) share the same stochastic long-run trend. They move together ('co'). They also need to share the same order of integration. In other words, you have two series that are both I~(1).

Absent of any statistical test, I wouldn't expect there to be a cointegrating relationship between the unemployment rate and labor force participation rate. They clearly do not share the same long-run trend, and any test that suggests otherwise is likely a spurious relationship. This applies in the US, at least (I can't speak to other countries). The unemployment rate is a very cyclical indicator, whereas the labor force participation rate (in the long run) has moved in tandem with demographic forces. You can visualize this by creating a scatter plot of the two. There's no clear linear combination. Arguably, there is a short-run relationship. That is to say the labor force participation declines during a recession and rises during an expansion, but the labor force participation rate has been steadily declining for the last two decades, and that has a lot to do with an aging workforce. I wouldn't worry about normality.

I am obligated to run tests on all econometric problems such as autocorrelation, heteroskedasticity etc. should I do it on data with unit root or again stationary first differences?

I'm not really sure what this refers to.

[Anastazja Stachwiuk]

Thank you very much for your answer, it is extremely helpful. The last part is connected with the fact that I want to run VAR and I need to fill some requirements, such as stationarity of variables etc. I need to also check the autocorrelation between residuals and heteroskedasticity in order to check whether my results are not biased. Am I right? One more time thank you so much!