I'm having trouble understanding how to interpret the results of the Pedroni test of cointegration in panels. I'm using the pco R package.

I call the function like this:

pedroni99(Y = unstack(pdf, y ~ iso), X = unstack(pdf, x ~ iso), kk = 0, type.stat = 1, ka = 15)

And get the following result:

[1] "Pedroni(1999) panel tests for cointegration"

                 empirical  standardized
nipanel       5.485297e+00 -6.103495e+00
rhopanel     -9.151844e+03 -1.134516e+03
tpanelnonpar -2.550723e+02 -1.927592e+02
tpanelpar    -2.254923e+05 -1.805847e+05
rhogroup     -9.471852e+03 -1.449308e+03
tgroupnonpar -2.619853e+02 -3.037890e+02
tgrouppar    -2.560885e+02 -2.964693e+02

How do I interpret the empirical vs standardized values for each test? I've read here that the first test is supposed to diverge to positive infinity, and the other to negative infinity, under the null. What are the results supposed to say?


1 Answer 1


Looking at the help file of the pedroni99 function and Pedroni's 1999 paper (especially pages 665-666), we find that

The standardized values of the test statistics are asymptotically normal (0,1) under $H_0$

and the null hypotheses seem are "No cointegration". If your sample is large enough to invoke asymptotic arguments, you can compare the test statistics with appropriate tail quantiles of the standard normal distribution. You will reject $H_0$ of 6 out of 7 flavors (the 1 flavor that you cannot reject is $\nu$ panel) for any common significance level (10%, 5%, 1%), as the absolute values of your test statistics are higher than the 95%, 97.5% and 99.5% quantiles of the standard normal distribution, respectively.

  • 1
    $\begingroup$ @AchintyaAgarwal, I have edited my answer to clarify. $\endgroup$ Mar 22, 2021 at 18:47
  • $\begingroup$ Thank you very much for this helpful answer! Can you explain how you used the fact that the standardized values are normally distributed under the null, along with the results in my original post, to conclude that we can reject H0 for all but 1 test? That is, what comparison are you making between the "empirical" and "standardized" values? My thought was that the empirical values should be outside 2 (or however many to exclude 90 or 95 or 99 % of the data) standard deviations of the standardized values - is that right? $\endgroup$ Mar 22, 2021 at 18:51
  • $\begingroup$ Ah, gotcha. Thanks for the clarification! (Sorry, I meant to write more in my comment and couldn't edit after 5 minutes.) $\endgroup$ Mar 22, 2021 at 18:52
  • $\begingroup$ @RichardHardy , could you please clarify your nipanel statistic interpretation? Perhaps I am missing or misreading something, but the standardized nipanel value equals -6.1 (approx), which would suggest rejecting $H_0$. $\endgroup$
    – Tomas
    Jul 14, 2022 at 15:27
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    $\begingroup$ @Tomas, hm, I wonder what I was thinking back when I wrote the answer. Looking at this today, it seems to me you are right. But I hesitate to state this firmly, as I would need to look more deeply into it. (It is not a test I have ever used myself.) $\endgroup$ Jul 15, 2022 at 10:00

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