Re: xtpedroni

[Paula Castellanos]

Hi,

I have implemented the command xtpedroni in Stata to check for cointegration. xtpedroni is a user written command and appears in 'The Stata Journal' - https://www.econ.uzh.ch/dam/jcr:0000...3e4/sj14-3.pdf (page 684 in the journal or page 238 in pdf)

I am unsure how to interpret the cointegration statistics. All test statistics are distributed N(0,1) under a null of no cointegration.


Stata returns:

Test Stats	Panel	Group
v	1.29	.
rho	-7.286	-5.6
t	-11.37	-12.46
adf	-7.311	-6.243

I would really really appreciate any assistance, please?

Kind regards,

Paula

[Paula Castellanos]

So I e-mailed the author of the xtpedroni code and here is what he had to say:

"The test statistics for the cointegration tests have been normalized to the N(0,1) distribution (as the command states under the output), and so to find the p-values you would follow the exact same procedure as you would with any other standard normal test statistic (z score). Look into the normal(z) function of stata."

Again, I am a little unsure of the next step of interpreting the cointegration statistics. Can anyone help?

[Jesse Wursten]

The values you see are normally distributed. If you want the corresponding p-values, you can type e.g.

di 1-normal(1.29)

Which will give you the pvalue for the panel-v, .09852533. Hence, you cannot reject the H0 of no cointegration at 5%.

[Paula Castellanos]

The values you see are normally distributed. If you want the corresponding p-values, you can type e.g.

di 1-normal(1.29)

Which will give you the pvalue for the panel-v, .09852533. Hence, you cannot reject the H0 of no cointegration at 5%.

Hi Jesse,

Thank you for your response.

I have applied your method to other journal articles in the hope of replicating their results, however it doesn't. I am at a loss as to what the issue could be as your command seemed perfect.

[Jesse Wursten]

Hi Jesse,

Thank you for your response.

How would I check 1% or 10% significance?

The same way. E.g.
0.0985 > 0.01 (not significant at 1%)
0.0985 > 0.05 (not significant at 5%)
0.0985 < 0.10 (significant at 10%)

[William Lisowski]

In general, given a p-value for a test statistic, you compare the p-value to the desired significance level. Since 0.098 > 0.05 it is not significant at the 5% level. Since 0.098 > 0.01 it is not signficant at the 1% level. Since 0.098 < 0.10 it is significant at the 10% level.

With that said, I think perhaps the test is meant to be a two-tailed test, so the p-value of a z-score of 1.29 is really

. di 2*(1-normal(1.29))
.19705066

and the results are not significant at the 10% level.

Note that all the other tests will be significant at all of the usual levels.

. di %10.8f 2*(1-normal(5.6))
0.00000002

My knowledge of xtpedroni and the interpretation of the various tests is non-existent, however, so I'll leave it to others to explain the meaning of these differing results.

[Andrew Musau]

Just a cautionary note which might (or might not) resolve the issue above. The p-value that Jesse obtains in #3

di 1-normal(1.29)

is a one-tailed test. Stata in most cases reports two-tailed p-values. So you need to multiply your p-values by two for correct inference

2*(1-normal(1.29))

Edit: Crossed with William

[Paula Castellanos]

Just a cautionary note which might (or might not) resolve the issue above. The p-value that Jesse obtains in #3



is a one-tailed test. Stata in most cases reports two-tailed p-values. So you need to multiply your p-values by two for correct inference

2*(1-normal(1.29))

Edit: Crossed with William

Hi Andrew,

Thanks for your response (and thanks to everyone else too).

When I try your code in Stata it says, '2 is not a valid command name'.

[Andrew Musau]

Apologies, should be

di 2*(1-normal(1.29))

where di is short for display. Also, you may want to take a look at this calculator to make sure that you are getting the correct values with Stata

http://www.socscistatistics.com/pval...tribution.aspx

[Paula Castellanos]

Apologies, should be

di 2*(1-normal(1.29))

where di is short for display.

Thanks.

In one journal I am trying to replicate they run Pedroni statistic. They get a value of -0.53 and their associated p-value is 0.35. Unfortunately, neither your or Jesse's solutions return a p-value of 0.35 when I run them. I am at a loss.

I thank you both for your patience and trying (and excuse my poor English)

Paula

[Andrew Musau]

You should check the distribution of the Pedroni statistic in that paper. The one produced by Stata is distributed as N(0,1) but maybe if someone else programmed it in a different software, then it may follow a different distribution. That said, the values you report are very close to a t-distribution with one degree of freedom

  di ttail(1, 0.529)
.34511755

Alternatively

. di 1-ttail(1, -0.529)
.34511755

Say I round off 0.529 to 2 decimal places, I have 0.53. On the other hand, the p-value rounds off to 0.35 (one tailed this time).

Hope this helps!

[Paula Castellanos]

You should check the distribution of the Pedroni statistic in that paper. The one produced by Stata is distributed as N(0,1) but maybe if someone else programmed it in a different software, then it may follow a different distribution. That said, the values you report are very close to a t-distribution with one degree of freedom

di ttail(1, 0.529)
.34511755

Alternatively

. di 1-ttail(1, -0.529)
.34511755

Say I round off 0.529 to 2 decimal places, I have 0.53. On the other hand, the p-value rounds off to 0.35 (one tailed this time).

Hope this helps!

Hi Andrew,

I appreciate your time. So your code worked for this value and corroborated the papers p-value. I tried verifying their other p-values but was unable too and I have double checked the distribution used by the paper.

Thank you for your time though

[Anat Tchetchik]

Hey all,
I read the above corresponding and then read https://www.econ.uzh.ch/dam/jcr:0000...3e4/sj14-3.pdf in The Stata Journal (2014) 14, Number 3, pp. 684–692
I am still not sure whether the -xtpedroni- command for panel co-integration is a one or two-tailed test
Does anyone know?
Many thanks,
Anat

[Andrew Musau]

Hi Anat. Usually there has to be a justification for reporting a one-tailed p-value, and most test commands would otherwise report two-tailed p-values. In this paper, the authors do not explicitly state the p-values, but you can infer that these are two-tailed tests. On p.691, the authors state

All the tests, except the panel t and ADF statistics, are significant at least at the 10% level

.

Taking the panel t test statistic (t=1.434), note that the one tailed p-value is significant at the 10% level whereas the two-tailed is not.

*ONE-TAILED
.  di (1-normal(1.434))
.07578613

*TWO-TAILED
.  di 2*(1-normal(1.434))
.15157226

[Anat Tchetchik]

Hi Andrew, I can see your point, however, I have contacted Timothy Neal, the author of this code asking him about it here is his my question and his reply:

I am using your command –xtpedroni- in Stata 14.1 In order to interpret the results I am not sure whether the test is one or two-sided

Prof. Neal's answered:

It should be one-tailed..

so.. I really don't know what to say..