[Gretl-devel] VECM estimation: gretl vs JMulTi
Riccardo Jack Lucchetti
r.lucchetti at univpm.it
Thu Aug 31 05:20:32 EDT 2006
On Thu, August 31, 2006 10:49, Sven Schreiber wrote:
>> Please try to reproduce the Denmark example you find in Johansen's book. The
>> data are available as denmark.gdt among gretl example datasets. JMulTi seems
>> to do strange things with VECMs. I exported the denmark dataset to JMulTi
>> format via the new ad-hoc facility: then, I could reproduce the same results
>> we have in gretl for almost everything (descriptives, VARs, etc.) but VECMs
>> proved impossible. I understand you know the main developer of JMulTi
>> personally: it may be a good idea to ask his opinion if/when we're certain
>> that results are indeed different.
>
> A quick check doesn't show any problems, exactly the same output. I
> suspect that you get bitten by different conventions w.r.t. lag
> specification, deterministics etc.
> But I don't have Johansen's book with me here right now, so what's the
> exact specification you're having trouble with?
Attached you will find gretl's and JMulTi's output for what I believe should
be the same model. You will see the numbers are similar, but definitely not
something you could blame floating-point rounding for. I am using JMulTi 4.04,
as the latest version doesn't like my version of java.
Riccardo "Jack" Lucchetti
Dipartimento di Economia
Facoltà di Economia "G. Fuà"
Ancona
-------------- next part --------------
VECM system, lag order 2
Maximum likelihood estimates, observations 1974:3-1987:3 (T = 53)
Cointegration rank = 1
Case 2: Restricted constant
Cointegrating vectors (standard errors in parentheses)
LRM(-1) 1.0000
(0.0000)
LRY(-1) -1.0329
(0.12805)
IBO(-1) 5.2069
(0.50735)
IDE(-1) -4.2159
(1.0051)
const -6.0599
(0.79464)
Log-likelihood = 669.115
Determinant of covariance matrix = 1.27152e-16
AIC = -23.5893
BIC = -21.9535
HQC = -22.9602
Equation 1: d_LRM
VARIABLE COEFFICIENT STDERROR T STAT P-VALUE
d_LRM_1 0.262771 0.146270 1.796 0.07913 *
d_LRY_1 -0.144254 0.131686 -1.095 0.27915
d_IBO_1 -0.0401148 0.377610 -0.106 0.91587
d_IDE_1 -0.670698 0.499446 -1.343 0.18604
S1 -0.0576527 0.00946248 -6.093 <0.00001 ***
S2 -0.0163050 0.00845625 -1.928 0.06016 *
S3 -0.0408586 0.00807873 -5.058 <0.00001 ***
EC1 -0.212955 0.0592981 -3.591 0.00081 ***
Mean of dependent variable = 0.00775739
Standard deviation of dep. var. = 0.0330857
Sum of squared residuals = 0.0204556
Standard error of residuals = 0.0196457
Unadjusted R-squared = 0.659708
Durbin-Watson statistic = 2.07569
First-order autocorrelation coeff. = -0.0438555
Equation 2: d_LRY
VARIABLE COEFFICIENT STDERROR T STAT P-VALUE
d_LRM_1 0.602668 0.153164 3.935 0.00029 ***
d_LRY_1 -0.142828 0.137893 -1.036 0.30584
d_IBO_1 -0.290609 0.395408 -0.735 0.46618
d_IDE_1 -0.182561 0.522987 -0.349 0.72866
S1 -0.0268262 0.00990849 -2.707 0.00955 ***
S2 0.00784216 0.00885483 0.886 0.38052
S3 -0.0130827 0.00845951 -1.547 0.12899
EC1 0.115022 0.0620931 1.852 0.07053 *
Mean of dependent variable = 0.00333981
Standard deviation of dep. var. = 0.0252391
Sum of squared residuals = 0.0224293
Standard error of residuals = 0.0205717
Unadjusted R-squared = 0.334755
Durbin-Watson statistic = 1.96451
First-order autocorrelation coeff. = 0.00942197
Equation 3: d_IBO
VARIABLE COEFFICIENT STDERROR T STAT P-VALUE
d_LRM_1 0.0573489 0.0578902 0.991 0.32715
d_LRY_1 0.144224 0.0521184 2.767 0.00818 ***
d_IBO_1 0.310660 0.149449 2.079 0.04338 **
d_IDE_1 0.203769 0.197669 1.031 0.30812
S1 -0.000400021 0.00374503 -0.107 0.91541
S2 0.00762196 0.00334679 2.277 0.02757 **
S3 0.00462651 0.00319737 1.447 0.15484
EC1 0.0231772 0.0234688 0.988 0.32864
Mean of dependent variable = -0.00111367
Standard deviation of dep. var. = 0.00980228
Sum of squared residuals = 0.00320415
Standard error of residuals = 0.00777532
Unadjusted R-squared = 0.367037
Durbin-Watson statistic = 1.61592
First-order autocorrelation coeff. = 0.174104
Equation 4: d_IDE
VARIABLE COEFFICIENT STDERROR T STAT P-VALUE
d_LRM_1 0.0613395 0.0390156 1.572 0.12291
d_LRY_1 0.0177406 0.0351257 0.505 0.61598
d_IBO_1 0.264939 0.100723 2.630 0.01163 **
d_IDE_1 0.212009 0.133221 1.591 0.11852
S1 -0.00482995 0.00252400 -1.914 0.06204 *
S2 -0.00117799 0.00225560 -0.522 0.60406
S3 -0.00288469 0.00215490 -1.339 0.18740
EC1 0.0294111 0.0158170 1.859 0.06951 *
Mean of dependent variable = -0.000383719
Standard deviation of dep. var. = 0.00689651
Sum of squared residuals = 0.00145539
Standard error of residuals = 0.00524025
Unadjusted R-squared = 0.41339
Durbin-Watson statistic = 1.95973
First-order autocorrelation coeff. = 0.0155449
Cross-equation covariance matrix
d_LRM d_LRY d_IBO d_IDE
d_LRM 0.00038595 0.00022597 -6.5007e-05 -2.9101e-05
d_LRY 0.00022597 0.00042320 -1.2151e-05 -2.7357e-05
d_IBO -6.5007e-05 -1.2151e-05 6.0456e-05 1.0517e-05
d_IDE -2.9101e-05 -2.7357e-05 1.0517e-05 2.7460e-05
determinant = 1.27152e-16
-------------- next part --------------
*** Thu, 31 Aug 2006 11:12:09 ***
VEC REPRESENTATION
endogenous variables: LRM LRY IBO IDE
exogenous variables:
deterministic variables: CONST S1 S2 S3
endogenous lags (diffs): 1
exogenous lags: 0
sample range: [1974 Q3, 1987 Q3], T = 53
estimation procedure: One stage. Johansen approach
Lagged endogenous term:
=======================
d(LRM) d(LRY) d(IBO) d(IDE)
---------------------------------------------------
d(LRM)(t-1)| 0.196 0.486 0.081 0.036
| (0.141) (0.155) (0.056) (0.039)
| {0.165} {0.002} {0.149} {0.365}
| [1.388] [3.130] [1.443] [0.906]
d(LRY)(t-1)| -0.164 -0.122 0.141 0.020
| (0.131) (0.145) (0.052) (0.037)
| {0.213} {0.400} {0.007} {0.577}
| [-1.245] [-0.842] [2.716] [0.558]
d(IBO)(t-1)| -0.026 0.111 0.310 0.374
| (0.334) (0.368) (0.132) (0.093)
| {0.938} {0.764} {0.019} {0.000}
| [-0.077] [0.300] [2.343] [4.016]
d(IDE)(t-1)| -0.583 -0.424 0.212 0.154
| (0.485) (0.535) (0.192) (0.135)
| {0.229} {0.428} {0.269} {0.254}
| [-1.202] [-0.793] [1.105] [1.142]
---------------------------------------------------
Deterministic term:
===================
d(LRM) d(LRY) d(IBO) d(IDE)
-------------------------------------------------
S1(t)| -0.051 -0.014 -0.003 -0.002
| (0.008) (0.008) (0.003) (0.002)
| {0.000} {0.097} {0.398} {0.318}
| [-6.711] [-1.660] [-0.845] [-0.998]
S2(t)| -0.015 0.011 0.007 -0.001
| (0.008) (0.009) (0.003) (0.002)
| {0.072} {0.232} {0.035} {0.700}
| [-1.798] [1.196] [2.109] [-0.385]
S3(t)| -0.037 -0.005 0.003 -0.001
| (0.007) (0.008) (0.003) (0.002)
| {0.000} {0.525} {0.268} {0.496}
| [-5.158] [-0.635] [1.108] [-0.681]
-------------------------------------------------
Loading coefficients:
=====================
d(LRM) d(LRY) d(IBO) d(IDE)
-------------------------------------------------
ec1(t-1)| -0.274 -0.003 0.030 -0.003
| (0.039) (0.043) (0.015) (0.011)
| {0.000} {0.948} {0.050} {0.757}
| [-7.092] [-0.065] [1.956] [-0.310]
-------------------------------------------------
Estimated cointegration relation(s):
====================================
ec1(t-1)
-------------------
LRM(t-1)| 1.000
| (0.000)
| {0.000}
| [0.000]
LRY(t-1)| -0.981
| (0.137)
| {0.000}
| [-7.143]
IBO(t-1)| 4.602
| (0.544)
| {0.000}
| [8.460]
IDE(t-1)| -2.412
| (1.078)
| {0.025}
| [-2.238]
CONST | -6.535
| (0.851)
| {0.000}
| [-7.680]
-------------------
VAR REPRESENTATION
modulus of the eigenvalues of the reverse characteristic polynomial:
|z| = ( 5.6567 5.6567 1.7701 1.7701 1.4970 1.0000 1.0000 1.0000 )
Legend:
=======
Equation 1 Equation 2 ...
------------------------------------------
Variable 1 | Coefficient ...
| (Std. Dev.)
| {p - Value}
| [t - Value]
Variable 2 | ...
...
------------------------------------------
Lagged endogenous term:
=======================
LRM LRY IBO IDE
-------------------------------------------------
LRM(t-1)| 0.922 0.484 0.111 0.032
| (0.146) (0.161) (0.058) (0.041)
| {0.000} {0.003} {0.056} {0.428}
| [6.302] [3.002] [1.909] [0.792]
LRY(t-1)| 0.105 0.881 0.112 0.024
| (0.137) (0.151) (0.054) (0.038)
| {0.442} {0.000} {0.039} {0.534}
| [0.769] [5.850] [2.068] [0.622]
IBO(t-1)| -1.287 0.098 1.448 0.359
| (0.379) (0.417) (0.150) (0.106)
| {0.001} {0.815} {0.000} {0.001}
| [-3.398] [0.234] [9.654] [3.400]
IDE(t-1)| 0.078 -0.417 0.140 1.163
| (0.494) (0.544) (0.196) (0.138)
| {0.875} {0.444} {0.474} {0.000}
| [0.157] [-0.766] [0.716] [8.437]
LRM(t-2)| -0.196 -0.486 -0.081 -0.036
| (0.141) (0.155) (0.056) (0.039)
| {0.165} {0.002} {0.149} {0.365}
| [-1.388] [-3.130] [-1.443] [-0.906]
LRY(t-2)| 0.164 0.122 -0.141 -0.020
| (0.131) (0.145) (0.052) (0.037)
| {0.213} {0.400} {0.007} {0.577}
| [1.245] [0.842] [-2.716] [-0.558]
IBO(t-2)| 0.026 -0.111 -0.310 -0.374
| (0.334) (0.368) (0.132) (0.093)
| {0.938} {0.764} {0.019} {0.000}
| [0.077] [-0.300] [-2.343] [-4.016]
IDE(t-2)| 0.583 0.424 -0.212 -0.154
| (0.485) (0.535) (0.192) (0.135)
| {0.229} {0.428} {0.269} {0.254}
| [1.202] [0.793] [-1.105] [-1.142]
-------------------------------------------------
Deterministic term:
===================
LRM LRY IBO IDE
-------------------------------------------------
S1 (t)| -0.051 -0.014 -0.003 -0.002
| (0.000) (0.000) (0.000) (0.000)
| {0.000} {0.000} {0.000} {0.000}
| [0.000] [0.000] [0.000] [0.000]
S2 (t)| -0.015 0.011 0.007 -0.001
| (0.000) (0.000) (0.000) (0.000)
| {0.000} {0.000} {0.000} {0.000}
| [0.000] [0.000] [0.000] [0.000]
S3 (t)| -0.037 -0.005 0.003 -0.001
| (0.000) (0.000) (0.000) (0.000)
| {0.000} {0.000} {0.000} {0.000}
| [0.000] [0.000] [0.000] [0.000]
CONST | 1.790 0.018 -0.196 0.022
| (0.000) (0.000) (0.000) (0.000)
| {0.000} {0.000} {0.000} {0.000}
| [0.000] [0.000] [0.000] [0.000]
-------------------------------------------------
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