Confusing Results

[turkhanali]

Dear Friends on the Forum,

I having trying to study the long run money demand parameter stability for the past weeks. Unfortunately, I am stuck now. I used CATS2.0 to estimate the the our variables which long of nominal m2 (LM2) seasonally adjusted quarterly industrial index and CPI and 3 month TB rate, there is strong evidence of one cointegration relationship among these variables.(the results does not change quantitatively with one or two lags)
I(1)-ANALYSIS
p-r r Eig.Value Trace Trace* Frac95 P-Value P-Value*
4 0 0.796 242.194 238.579 53.945 0.000 0.000
3 1 0.147 35.687 35.310 35.070 0.043 0.047
2 2 0.072 15.020 14.926 20.164 0.230 0.236
1 3 0.040 5.316 5.305 9.142 0.260 0.261
.
FM.SRC estimated the one cointegrating vector as follows:
@Fm(DET=constant,lag=1)
#lm2 lysa lp tb3
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. Constant -3.620764727 0.501383973 -7.22154 0.00000000
2. LYSA 0.332544826 0.063331524 5.25086 0.00000015
3. LP 3.342603405 0.168816818 19.80018 0.00000000
4. TB3 -0.030868098 0.006618349 -4.66402 0.00000310

Then I checked with Gauss code (because FM.SRC does not have option of stability test) the results shows that it is not stables because Lc SupF and MeanF all have p-value less than 0.05.

In addition I used FMOLS.SRC by Kai Carstensen(2006) the results are as follows:

Sample from 1977:01 until 2009:03

Variable Coefficient standard error t statistic
*********************************************************************************
Constant -5.1986533 0.9509016 -5.4670779
LYSA 0.1427528 0.1201116 1.1885011
LP 3.8731548 0.3201702 12.0971760
TB3 -0.0435931 0.0125521 -3.4729865

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

STABILITY TESTS
Trimmed sample from 1981:04 until 2004:04 . Maximal F statistic in 1986:03 .
SupF test: 16.3478395854
MeanF test: 10.3134932961
Lc test: 0.8810960352

=================================================================================
You can see that the sharp difference in terms of coefficient of LYSA., in the later case it is not significant at all while it is significant in the first case. (I use the gauss code of Hansen get the same results as FM.SRC, not reported here).

As rejection of Hansen's Lc test also indicates rejection of the null of cointegration. Plus SupF and MeanF also reports that the stability is rejected. Giving this case, What I should Do? I hope some of you may guide in this regard.

Then I have done JJ test with Eviews, the evidence of cointegration is not so strong: there is cointegration when lag=1 but not with lag=2. (LR test indicates lag=1)

To make M results more robust I also used FMOLS, FIML and DOLS approch to do the residual based cointegration test, all of them are unable to reject the no cointegration hypothesis. For instance,

@Fm(DET=constant,lag=2)
#lm2 lysa lp tb3

set ecmfmt / = lm2 - %beta(1) - %beta(2)*lysa - %beta(3)*lp - %beta(4)*tb3
@DFUNIT ecmfmt
@kpss ecmfmt
Dickey-Fuller Unit Root Test, Series ECMFMT
Regression Run From 1977:02 to 2009:03
Observations 131
With intercept
Using 0 lags on the differences

Sig Level Crit Value
1%(**) -3.48100
5%(*) -2.88349
10% -2.57834

T-Statistic -2.23754


KPSS Test for Stationarity about Level, Series ECMFMT
From 1977:01 to 2009:03
Observations 131

Sig Level Crit Value
1%(**) 0.739000
2.5% 0.574000
5%(*) 0.463000
10% 0.347000

Lags TestStat
4 0.241037 (*** This KPSS results seems indicates cointegration)

And also did using @johmle.SRC and SWOLS.SRC they are not able to rejected the null of nu cointegration

Then I used ARDL of Pesaran Shin as follows:

***ARDL TEST of SHIN
set dlm1 = lm1 - lm1{1}
set dlm2 = lm2 -lm2{1}
set dlp = lp - lp{1}
set dlysa = lysa-lysa{1}
set dtb3 = tb3 -tb3{1}
set rm2 = lm2 - lp

smpl
LINREG dlm2
# CONSTANT dlm2{1} dlm2{2} dlysa dlysa{1} dlysa{2} dlp dlp{1} dlp{2} dtb3 dtb3{1} dtb3{2} lm2{1} lysa{1}lp{1} tb3{1}
exclude(Title="F test")
# lm2{1} lysa{1} lp{1} tb3{1}
Linear Regression - Estimation by Least Squares
Dependent Variable DLM2
Quarterly Data From 1977:04 To 2009:03
Usable Observations 128 Degrees of Freedom 112
Centered R**2 0.189987 R Bar **2 0.081503
Uncentered R**2 0.713797 T x R**2 91.366
Mean of Dependent Variable 0.0327052220
Std Error of Dependent Variable 0.0242700535
Standard Error of Estimate 0.0232599936
Sum of Squared Residuals 0.0605950576
Regression F(15,112) 1.7513
Significance Level of F 0.05091727
Log Likelihood 308.33249
Durbin-Watson Statistic 2.001718

Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. Constant 0.443130040 0.175421521 2.52609 0.01293160
2. DLM2{1} 0.126169560 0.104627605 1.20589 0.23040058
3. DLM2{2} -0.002985383 0.107602295 -0.02774 0.97791522
4. DLYSA 0.018092587 0.049122759 0.36831 0.71333454
5. DLYSA{1} 0.029598364 0.051265639 0.57735 0.56485991
6. DLYSA{2} -0.014626687 0.051986376 -0.28136 0.77895640
7. DLP -0.044502340 0.324398470 -0.13718 0.89113152
8. DLP{1} 0.006103499 0.307947010 0.01982 0.98422226
9. DLP{2} 0.090424801 0.292580306 0.30906 0.75785025
10. DTB3 -0.009397716 0.004203226 -2.23583 0.02734492
11. DTB3{1} 0.002651879 0.004127117 0.64255 0.52182930
12. DTB3{2} -0.000342481 0.004055767 -0.08444 0.93285492
13. LM2{1} 0.028122504 0.029488421 0.95368 0.34229962
14. LYSA{1} 0.026507689 0.017245712 1.53706 0.12709905
15. LP{1} -0.199270982 0.111118421 -1.79332 0.07562040
16. TB3{1} 0.002064652 0.001772406 1.16489 0.24654006


F test

Null Hypothesis : The Following Coefficients Are Zero
LM2 Lag(s) 1
LYSA Lag(s) 1
LP Lag(s) 1
TB3 Lag(s) 1
F(4,112)= 2.01080 with Significance Level 0.09776800

This does not support for cointegration too.

Finally W I used the Gregory and Hansen (1996) cointegration test with regime shifts.

The results shows that non of ADF*, Zt* and Za* test does not reject the null hypothesis (I mean all the value I got not negative enough to reject the null hypothesis).

Having tried all of the available test. I am in cross road and confusing and don't what to do? I am really your help on these issues.

Your comments and suggestions are highly appreciated.

[TomDoan]

Have you looked into the possible I(2) behavior of the data? (Chapter 5 of the CATS manual). log CPI in many countries seems to show I(2) behavior more than I(1), and that could cause confusing I(1) results.

[turkhanali]

Dear Tom,

I have checked all the variables and all are I(1). the JJ test test indicates one cointegration but Grogery and Hansen (1996) Test can not reject the null.

Residual test from FMOLS, CCR and DOLS all doest reject the null of no cointegration. But Hansen(1992) of P-value of Lc is greater than 0.2.

If the JJ test indicates cointegration, but Grogery and Hanse (1996) does not reject of the null of null cointegration, Is that logic?

Thank very much for your reply.

[TomDoan]

To sum it up, it would seem as if there is no strong evidence of a stable money demand function in the data. Lack of a result is still a result.

[turkhanali]

Tom,

Thanks for your reply.

I have checked the literature, there are vast studies shows that there is cointegration among these variables. However, none of them performed these test I have done except the JJ test. Maybe it is something good for me write.