Dear all,

 

I am writing because I am facing discrepancies between the outputs of the Johansen cointegration tests in Gretl and R. Concretely, both softwares yield exactly the same test statistics, but the critical values are different (therefore, the decision about the number of cointegration vectors not always coincide). Attached is a data with 62 yearly observations where the two first columns are treated as endogenous variables (GDP and NDB) and the last is a dummy variable treated as exogenous. I don't include restricted drift.

 

 

 

I guess most of you are familiar with R. In R the code is the following:

 

johansen<-ca.jo(data[1:2], type = "trace", ecdet = "none", K = 6, spec = "longrun", dumvar = data[3])
summary(johansen)

 

And the output is this,

###################### 
# Johansen-Procedure # 
###################### 

Test type: trace statistic , with linear trend 

Eigenvalues (lambda):
[1] 0.30869583 0.09632144

Values of teststatistic and critical values of test:

          test 10pct  5pct  1pct
r <= 1 |  5.67  6.50  8.18 11.65
r = 0  | 26.35 15.66 17.95 23.52

Eigenvectors, normalised to first column:
(These are the cointegration relations)

           baGDP.l6   bdNDB.l6
baGDP.l6  1.0000000  1.0000000
bdNDB.l6 -0.2013471 -0.3513728

Weights W:
(This is the loading matrix)

          baGDP.l6   bdNDB.l6
baGDP.d -0.2046459 0.05197298
bdNDB.d  0.6099287 0.74570305

Sent: Friday, February 01, 2019 at 12:15 PM
From: "Allin Cottrell" <cottrell@wfu.edu>
To: "Gretl list" <gretl-users@lists.wfu.edu>
Subject: Re: [Gretl-users] Discrepancy between R and Gretl in Johansen cointegration

On Fri, 1 Feb 2019, Sven Schreiber wrote:

> OK, so gretl and the tsDyn package for R seem to agree about the
> p-values [...]

Here's a replication and extension of Sven's exercise. It's not
trivial to get R's tsDyn and urca packages to perform the same test
but I think I've succeeded. Note that using

include="const"

in tsDyn is equivalent to

ecdet="none"

in urca.

<hansl>
open denmark
coint2 4 LRM LRY --quiet

foreign language=R --send-data
require(tsDyn)
cidat <- gretldata[,1:2] # again LRM LRY
ve <- VECM(cidat, lag=3, estim="ML", include="const")
ve_test0 <- rank.test(ve, r_null=0, type="trace")
ve_test0
ve_test1 <- rank.test(ve, r_null=1, type="trace")
ve_test1
require(urca)
test2 <- ca.jo(cidat, type="trace", K=4, ecdet=c("none"))
summary(test2)
end foreign
</hansl>

The relevant portions of the output:

---------------------------

gretl (omitting the presumably more reliable small-sample p-values
that gretl provides):

Rank Eigenvalue Trace test p-value Lmax test p-value
0 0.19415 11.904 [0.1633] 11.009 [0.1557]
1 0.017402 0.89533 [0.3440] 0.89533 [0.3440]

R, tsDyn:
Test of rank 0 versus 2 (trace test), p-value: 0.1633226.
Test of rank 1 versus 2 (trace test), p-value: 0.344037.

R, urca:
Test type: trace statistic , with linear trend

Values of teststatistic and critical values of test:

test 10pct 5pct 1pct
r <= 1 | 0.9 6.50 8.18 11.65
r = 0 | 11.9 15.66 17.95 23.52

---------------------------

Gretl and tsDyn are clearly agreed. What about urca? Note that the
two tests appear in the opposite order relative to gretl and tsDyn.

a) Since "test" = 0.9 is less than "10pct" = 6.50, H0 is not
rejected at the 10% level. Agreed, since gretl and tsDyn show
p-value = 0.344.

b) Since "test" = 11.9 is less than "10pct" = 15.66, H0 is not
rejected at the 10% level. Agreed, since gretl and tsDyn show
p-value = 0.1633.

So I think we await a fully-specified example of disagreement
between R::urca and R::tsDyn or gretl.

Allin
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