APPENDICES
1. ORGINAL DATA OF USED VARIABLE IN TAYLOR
RULE
|
years
|
GDPt
|
EXCHt
|
Mt
|
INFt
|
GDP tar
|
INF tar
|
|
1995
|
337.2
|
297.69
|
62.9
|
48.249
|
324.897
|
38.386
|
|
1996
|
431.4
|
304.16
|
75.6
|
13.434
|
411.751
|
8.736
|
|
1997
|
562.4
|
304.67
|
92.5
|
11.689
|
546.526
|
16.615
|
|
1998
|
632.1
|
330.72
|
97.8
|
6.842
|
605.629
|
-5.958
|
|
1999
|
677
|
349.53
|
104.2
|
-2.423
|
606.991
|
2.057
|
|
2000
|
732.2
|
430.49
|
119.5
|
3.901
|
676.099
|
5.832
|
|
2001
|
799.4
|
443.74
|
130.7
|
3.366
|
741.872
|
-0.219
|
|
2002
|
872.7
|
471.93
|
144.3
|
1.975
|
797.439
|
6.165
|
|
2003
|
993
|
516.07
|
167.5
|
7.445
|
992.597
|
7.677
|
|
2004
|
1,206
|
577.52
|
187.4
|
11.951
|
1,206.23
|
10.236
|
|
2005
|
1,440
|
557.81
|
218.4
|
9.122
|
1,439.83
|
5.608
|
|
2006
|
1,716
|
551.8
|
286
|
8.831
|
1,716.32
|
12.138
|
|
2007
|
2,046
|
547
|
375.1
|
9.081
|
2,049.26
|
6.579
|
|
2008
|
2,577
|
546.8
|
384.1
|
15.436
|
2,565.29
|
22.323
|
|
2009
|
2,990
|
568.27
|
402
|
10.4
|
2,964.07
|
5.737
|
|
2010
|
3,282
|
813
|
516.7
|
6.4
|
3,278.26
|
0.227
|
Source: NBR, NISR, MINECOFIN
AND
http://www.economywatch.com/economic-statistics/Rwanda/General
Government Total Expenditure Percentage GDP/
1. VALUES OF ALL USED VARIABLES IN TAYLOR RULE
|
obs
|
MT
|
M1
|
IG
|
IG1
|
YG
|
YG1
|
DEXCH
|
DEXCH1
|
|
1995
|
62.9
|
NA
|
-9.863
|
NA
|
12.303
|
NA
|
NA
|
NA
|
|
1996
|
75.6
|
62.9
|
-4.698
|
-9.863
|
19.649
|
12.303
|
6.47
|
NA
|
|
1997
|
92.5
|
75.6
|
4.926
|
-4.698
|
15.874
|
19.649
|
0.51
|
6.47
|
|
1998
|
97.8
|
92.5
|
-12.8
|
4.926
|
26.471
|
15.874
|
26.05
|
0.51
|
|
1999
|
104.2
|
97.8
|
4.48
|
-12.8
|
70.009
|
26.471
|
18.81
|
26.05
|
|
2000
|
119.5
|
104.2
|
1.931
|
4.48
|
56.101
|
70.009
|
80.96
|
18.81
|
|
2001
|
130.7
|
119.5
|
-3.585
|
1.931
|
57.528
|
56.101
|
13.25
|
80.96
|
|
2002
|
144.3
|
130.7
|
4.19
|
-3.585
|
75.261
|
57.528
|
28.19
|
13.25
|
|
2003
|
167.5
|
144.3
|
0.232
|
4.19
|
0.403
|
75.261
|
44.14
|
28.19
|
|
2004
|
187.4
|
167.5
|
-1.715
|
0.232
|
-0.23
|
0.403
|
61.45
|
44.14
|
|
2005
|
218.4
|
187.4
|
-3.514
|
-1.715
|
0.17
|
-0.23
|
-19.71
|
61.45
|
|
2006
|
286
|
218.4
|
3.307
|
-3.514
|
-0.32
|
0.17
|
-6.01
|
-19.71
|
|
2007
|
375.1
|
286
|
-2.502
|
3.307
|
-3.26
|
-0.32
|
-4.8
|
-6.01
|
|
2008
|
384.1
|
375.1
|
6.887
|
-2.502
|
11.71
|
-3.26
|
-0.2
|
-4.8
|
|
2009
|
402
|
384.1
|
-4.663
|
6.887
|
25.93
|
11.71
|
21.47
|
-0.2
|
|
2010
|
516.7
|
402
|
-6.173
|
-4.663
|
3.74
|
25.93
|
244.73
|
21.47
|
Source of basic data: NBR, NISR, MINECOFIN and are done in
E-VIEWS 3.1
Where: MT = Current money stock
M1= Previous money stock
IG= Current inflation gap
IG1= Previous inflation gap
YG= Current output gap
YG1= Previous output gap
DEXCH= Current variation of exchange
DEXCH1= Previous variation of exchange
2. AIC AND SIC FOR FINDING USED LAGS
|
|
|
|
AIC
|
|
SIC
|
|
|
CHOOSEN LAG
|
|
|
LAG
|
INT
|
INT AND TRE
|
NONE
|
INT
|
INT AND TRE
|
NONE
|
|
|
MT
|
0
|
9.641715
|
9.688929
|
9.50839
|
9.736122
|
9.830539
|
9.555593
|
LAG IS 0
|
|
|
1
|
9.866872
|
9.887956
|
9.724115
|
10.00381
|
10.07054
|
9.815408
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
M1
|
0
|
9.296327
|
9.208122
|
9.206107
|
9.387621
|
9.345063
|
9.251754
|
LAG IS 0
|
|
|
1
|
9.458962
|
9.25416
|
9.374977
|
9.589335
|
9.427991
|
9.461892
|
|
|
|
|
|
|
|
|
|
|
|
|
IG
|
0
|
6.206957
|
6.322018
|
6.14714
|
6.301364
|
6.463628
|
6.194343
|
|
|
|
1
|
6.064265
|
6.142289
|
6.01912
|
6.201206
|
6.324877
|
6.110414
|
LAG IS 1
|
|
|
|
|
|
|
|
|
|
|
|
IG1
|
0
|
6.143109
|
6.098601
|
6.039519
|
6.234403
|
6.235541
|
6.085166
|
|
|
|
1
|
6.097979
|
5.82158
|
5.845228
|
6.097979
|
5.99541
|
5.932143
|
LAG IS 1
|
|
|
|
|
|
|
|
|
|
|
|
YG
|
0
|
9.560466
|
9.683185
|
9.419062
|
9.65176
|
9.820126
|
9.464709
|
LAG IS 1
|
|
|
1
|
9.790076
|
9.907057
|
9.637297
|
9.920449
|
10.08089
|
9.724212
|
|
|
|
|
|
|
|
|
|
|
|
|
YG1
|
0
|
9.612163
|
9.763314
|
9.458669
|
9.699078
|
9.893687
|
9.502127
|
|
|
|
1
|
9.872514
|
10.02692
|
9.706344
|
9.993741
|
10.18856
|
9.787161
|
LAG IS 0
|
|
|
|
|
|
|
|
|
|
|
|
DEXCH
|
0
|
11.61242
|
11.63065
|
11.53175
|
11.69933
|
11.76102
|
11.57521
|
|
|
|
1
|
11.88346
|
11.84749
|
11.78135
|
12.00469
|
12.00912
|
11.86217
|
LAG IS 0
|
|
|
|
|
|
|
|
|
|
|
|
DEXCH1
|
0
|
9.755819
|
9.832075
|
9.856065
|
9.842734
|
9.962448
|
9.899522
|
|
|
|
1
|
9.988968
|
9.93752
|
10.04704
|
10.11019
|
10.09916
|
10.12786
|
LAG IS 0
|
|
|
|
|
|
|
|
|
|
|
|
R
|
0
|
10.02276
|
10.10345
|
9.930729
|
10.09511
|
10.21197
|
9.966901
|
|
|
|
1
|
10.31132
|
10.20734
|
10.22258
|
10.40209
|
10.32838
|
10.2831
|
LAG IS 0
|
|
|
|
|
|
|
|
|
|
|
|
R1
|
0
|
10.1346
|
10.10586
|
9.995851
|
10.19512
|
10.19663
|
10.02611
|
|
|
|
1
|
10.46616
|
9.93182
|
10.32152
|
10.53191
|
10.01948
|
10.36535
|
LAG IS 1
|
Source of basic data: NBR, NISR and MINECOFIN
2(100/n)0.25 = 1.8, this shows that we stop at lag
1.
3. ERROR CORRECTION MODEL
DMT=B0+ B1DM1 +B2DIG +B3DIG1 +B4DYG +B5DYG1 + B6DDEXCH +
B7DDEXCH1 + DR
|
Dependent Variable: MT-MT(-1)
|
|
Method: Least Squares
|
|
Date: 09/19/11 Time: 10:01
|
|
Sample(adjusted): 1998 2010
|
|
Included observations: 13 after adjusting endpoints
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
C
|
28.09017
|
8.530250
|
3.293007
|
0.0110
|
|
IG-IG(-1)
|
0.499831
|
0.999226
|
0.500218
|
0.6304
|
|
YG-YG(-1)
|
-0.317961
|
0.348275
|
-0.912961
|
0.3879
|
|
DEXCH-DEXCH(-1)
|
0.222279
|
0.125268
|
1.774425
|
0.1139
|
|
RESID-RESID(-1)
|
0.515337
|
0.312843
|
1.647271
|
0.1381
|
|
R-squared
|
0.527088
|
Mean dependent var
|
32.63077
|
|
Adjusted R-squared
|
0.290633
|
S.D. dependent var
|
35.03913
|
|
S.E. of regression
|
29.51134
|
Akaike info criterion
|
9.891149
|
|
Sum squared resid
|
6967.352
|
Schwarz criterion
|
10.10844
|
|
Log likelihood
|
-59.29247
|
F-statistic
|
2.229121
|
|
Durbin-Watson stat
|
1.000899
|
Prob(F-statistic)
|
0.155471
|
Source: Done in E-VIEWS 3.1
After estimating the error correction model, it is found that all
probabilities are greater than 5% this verifies that each explanatory variable
has an effect on explained variable (MT).
4. RAMSEY RESET TEST FOR MODEL SPECIFICATION
|
Ramsey RESET Test:
|
|
F-statistic
|
31.08468
|
Probability
|
0.061410
|
|
Log likelihood ratio
|
58.04147
|
Probability
|
0.072100
|
|
|
|
|
|
|
Test Equation:
|
|
Dependent Variable: MT
|
|
Method: Least Squares
|
|
Date: 09/19/11 Time: 09:53
|
|
Sample: 1997 2010
|
|
Included observations: 14
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
C
|
4.001070
|
197.2238
|
0.020287
|
0.9857
|
|
MT(-1)
|
4.339922
|
7.446307
|
0.582829
|
0.6190
|
|
IG
|
-5.797933
|
12.89962
|
-0.449465
|
0.6971
|
|
IG(-1)
|
-8.277322
|
19.41283
|
-0.426384
|
0.7113
|
|
YG
|
-1.842925
|
4.348232
|
-0.423833
|
0.7129
|
|
YG(-1)
|
1.287048
|
2.608869
|
0.493336
|
0.6706
|
|
DEXCH
|
0.255345
|
0.632645
|
0.403615
|
0.7256
|
|
DEXCH(-1)
|
-0.784084
|
1.650993
|
-0.474917
|
0.6817
|
|
FITTED^2
|
-0.046524
|
0.054793
|
-0.849073
|
0.4853
|
|
FITTED^3
|
0.000276
|
0.000205
|
1.347810
|
0.3101
|
|
FITTED^4
|
-6.66E-07
|
3.58E-07
|
-1.858988
|
0.2041
|
|
FITTED^5
|
5.56E-10
|
2.38E-10
|
2.338133
|
0.1443
|
|
R-squared
|
0.999651
|
Mean dependent var
|
230.4429
|
|
Adjusted R-squared
|
0.997732
|
S.D. dependent var
|
137.8947
|
|
S.E. of regression
|
6.567172
|
Akaike info criterion
|
6.370419
|
|
Sum squared resid
|
86.25550
|
Schwarz criterion
|
6.918183
|
|
Log likelihood
|
-32.59293
|
F-statistic
|
520.8801
|
|
Durbin-Watson stat
|
2.655976
|
Prob(F-statistic)
|
0.001918
|
Source: Done in E-VIEWS 3.1
Ramsey RESET Test, as all probabilities are greater than 5%, this
shows that the model is well specified.
5. AUTOCORRELATION TEST OF DARBIN WATSON (DW)
DW TABLE
0
4
2
(1.177) (1.732)
(2.268) (2.823)
dL du
4-du 4-dL
Source: statistical tables
DW =2.461915 =where the DW is placed on table.
DW is in the indecision zone near no autocorrelation zone, so DW
is associated in the zone of no autocorrelation.
6. TEST FOR COINTEGRATION
In econometric literature, it is not clear whether
cointegration should be applied to only series integrated of the same order.
Though Verbeck (2004) noted that the concept of cointegration can be applied to
(nonstationary) integrated time series only and Dickey et al, quoted by
Gujarati (2004), stipulated that Cointegration deals with the relationship
among a group of variables, where (unconditionally) each has a unit root,
however Brooks (2004) stressed that it is also possible to combine levels and
first differenced terms in a VECM. The later therefore illustrates that
cointegration can exist among variables not integrated of the same order.
Heij et al (2004) stated by gujarati (2009) developed the
mathematical proof of this view where they asserted that a cointegration
relationship exists between stationary and nonstationary variables. If their
mathematical proof is put in simple terms, there are three possibilities in VAR
with many variables: If m: the number of variables, r = rank of the matrix of
coefficients and also the number of cointegration relations, therefore:
· If all variables are stationary, r = m and all roots
lie outside the unit cycle
· If all variables are not stationary, r = 0, there are m
unit roots or m stochastic trends.
· If some variables are stationary and others not
stationary, r = 0< r < m, there are m-r unit roots, the polynomial have
m-r common stochastic trends and there are r cointegrating relations.
As all variables are stationary, Johansen cointegration test
has been used to determine whether there exist a long-run relationship between
these variables. This test was preferred to Engle-Granger approach because in
case of six variables we may have more than one cointegrating relationship
(Brooks, 2004).
| 
