3.3 Estimation of long run model 3.3.1 Co-integration
test
Co-integration is a statistical property of a collection of
time series variables X1, X2... Xk. First, all of the series must be integrated
of order 1, second, if a linear combination of this collection is integrated of
order zero, then the collection is said to be co-integrated. With Johansen
approach, we use trace and Maximum Eigenvalue tests to justify co-integration.
If two or more series are themselves non-stationary but a linear combination of
them is stationary, the series are said to be co-integrated. (KASAI,
2009:43).
54
Date: 08/12/16 Time: 12:59
Sample (adjusted): 1997 2015
Included observations: 19 after adjustments Trend assumption:
Linear deterministic trend Series: LNGCE LNGDP INT INF LNEXCHR
Lags interval (in first differences): 1 to 1
Unrestricted Co-integration Rank Test (Trace)
Hypothesize
d Trace 0.05
Critical
No. of CE(s) Eigenvalue Statistic Value Prob.**
|
None *
|
0.986335
|
149.9639
|
69.81889
|
0.0000
|
|
At most 1 *
|
0.862347
|
68.39784
|
47.85613
|
0.0002
|
|
At most 2 *
|
0.614846
|
30.72045
|
29.79707
|
0.0390
|
|
At most 3
|
0.446337
|
12.59231
|
15.49471
|
0.1306
|
|
At most 4
|
0.069054
|
1.359523
|
3.841466
|
0.2436
|
Trace test indicates 3 co-integrating eqn(s) at the 0.05 level *
denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis
(1999) p-values
Unrestricted Co-integration Rank Test (Maximum Eigenvalue)
Hypothesize
d Max-Eigen 0.05
Critical
No. of CE(s) Eigenvalue Statistic Value Prob.**
|
None *
|
0.986335
|
81.56606
|
33.87687
|
0.0000
|
|
At most 1 *
|
0.862347
|
37.67739
|
27.58434
|
0.0018
|
|
At most 2
|
0.614846
|
18.12814
|
21.13162
|
0.1251
|
|
At most 3
|
0.446337
|
11.23279
|
14.26460
|
0.1429
|
|
At most 4
|
0.069054
|
1.359523
|
3.841466
|
0.2436
|
55
Max-eigenvalue test indicates 2 co-integrating eqn(s) at the 0.05
level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Co-integrating Coefficients (normalized by
b'*S11*b=I):
|
LNGCE
|
LNGDP
|
INT
|
INF
|
LNEXCHR
|
|
42.28232
|
-30.85109
|
-4.837431
|
0.013107
|
-4.937743
|
|
0.717548
|
-3.422595
|
1.791842
|
0.614326
|
3.563539
|
|
2.098782
|
-3.153853
|
-0.823262
|
-0.111838
|
8.181454
|
|
-26.75212
|
25.13077
|
-0.712632
|
0.155683
|
-3.249637
|
|
-20.33113
|
20.86315
|
-0.252021
|
0.018610
|
-3.100465
|
Source: World Bank indicators1995-2015 and author's computation
Table 5: Long run Johansen Co-integration test output
3.3.2 Interpretation of Johansen Co-integration test
output
Trace test indicates 3 co-integrating eqn(s) at the 0.05 level
and the
Max-eigenvalue test indicates 2 co-integrating eqn(s) at the 0.05
level
From these findings, the researcher concluded that variables have
a long run relationship.
56
3.3.3 Long run output
Dependent Variable: LNGCE Method: Least Squares
Date: 08/11/16 Time: 20:33 Sample: 1995 2015
Included observations: 21
Variable Coefficient Std. Error t-Statistic Prob.
LNGDP 0.867339 0.032528 26.66452
0.0000
INT -0.032394 0.019717 1.642904
0.0499
INF -0.040527 0.002049 0.257232
0.0303
LNEXCHR -0.025767 0.065889 -0.391066
0.0409
C 0.371652 0.394843 0.941266
0.3606
R-squared 0.998411 Mean dependent var
7.124936
Adjusted R-squared 0.998014 S.D. dependent var
0.812793
S.E. of regression 0.036223 Akaike info criterion -3.593979
Sum squared resid 0.020994 Schwarz criterion -3.345284
Log likelihood 42.73678 Hannan-Quinn criter. -3.540006
F-statistic 2513.431 Durbin-Watson stat 1.347986
Prob(F-statistic) 0.000000
Source: World Bank indicators1995-2015 and author's
computation
Table 6: Long run output effect of changes in GDP,
INT, INF, and EXCHR on Gross Consumption Expenditure
| 
