Team Kenya
Outline
1.
2.
3.
4.
5.
Lessons learnt
Case of Kenya: Overview
Test for Stationarity of CPI variable
VAR analysis
Policy insights
1. Lessons Learnt
• How to test for stationarity using appropriate
models, that is, testing for validity of including
trend and/or constant term.
• Testing for stability / stationarity of a VAR
model.
• How to use Eviews.
• How to interpret impulse response functions.
2. Case of Kenya: Overview
• Study period 2000:1 to 2013:3
• Data source: Central Bank of Kenya and Kenya
National Bureau of Statistics
• Frequency of data: Quarterly
• Variables: CPI, M3, RGDP, TB3, e, libor, oilprice
• Methodology: Granger causality, Johansen
cointegration test, impulse response analysis
2. Test for Stationarity of CPI variable
• Step 1: View time graph of variable
CPI
160
DCPI
8
140
6
120
4
100
2
80
0
60
-2
40
00 01 02 03 04 05 06 07 08 09 10 11 12 13
00 01 02 03 04 05 06 07 08 09 10 11 12 13
2. Test for Stationarity of CPI variable
• Step 2: Conduct ADF test using trend and intercept
Null Hypothesis: CPI has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, maxlag=10)
Augmented Dickey-Fuller test statistic
Test critical values:
1% level
5% level
10% level
t-Statistic
Prob.*
-1.976710
-4.140858
-3.496960
-3.177579
0.6003
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(CPI)
Method: Least Squares
Date: 06/04/14 Time: 10:53
Sample (adjusted): 2000Q3 2013Q3
Included observations: 53 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
CPI(-1)
D(CPI(-1))
C
@TREND("2000Q1")
-0.077218
0.387609
3.118543
0.160511
0.039064
0.130121
1.447449
0.069631
-1.976710
2.978831
2.154510
2.305153
0.0537
0.0045
0.0361
0.0254
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
0.282098
0.238145
1.548395
117.4789
-96.29686
6.418141
0.000939
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
1.735849
1.773967
3.784787
3.933488
3.841970
2.006769
F3 = 2.656 against CV = 6.50
Indicating that the trend
term is not significant
2. Test for Stationarity of CPI variable
• Step 3: Conduct ADF test using intercept
Null Hypothesis: CPI has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=10)
Augmented Dickey-Fuller test statistic
Test critical values:
1% level
5% level
10% level
t-Statistic
Prob.*
1.248345
-3.560019
-2.917650
-2.596689
0.9981
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(CPI)
Method: Least Squares
Date: 06/04/14 Time: 11:05
Sample (adjusted): 2000Q3 2013Q3
Included observations: 53 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
CPI(-1)
D(CPI(-1))
C
0.010781
0.362481
0.185867
0.008636
0.135141
0.719489
1.248345
2.682239
0.258333
0.2177
0.0099
0.7972
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
0.204246
0.172416
1.613807
130.2187
-99.02521
6.416744
0.003307
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
1.735849
1.773967
3.850008
3.961534
3.892895
1.933581
F3 = 0.033 against CV = 8.73
Indicating that the constant
term is not significant
2. Test for Stationarity of CPI variable
• Step 4: Conduct ADF test without trend or intercept
Null Hypothes is : CPI has a unit root
Exogenous : None
Lag Length: 1 (Autom atic - bas ed on SIC, m axlag=10)
Augm ented Dickey-Fuller tes t s tatis tic
Tes t critical values :
1% level
5% level
10% level
t-Statis tic
Prob.*
3.437860
-2.609324
-1.947119
-1.612867
0.9998
*MacKinnon (1996) one-s ided p-values .
Augm ented Dickey-Fuller Tes t Equation
Dependent Variable: D(CPI)
Method: Leas t Squares
Date: 06/04/14 Tim e: 11:09
Sam ple (adjus ted): 2000Q3 2013Q3
Included obs ervations : 53 after adjus tm ents
Variable
Coefficient
Std. Error
t-Statis tic
Prob.
CPI(-1)
D(CPI(-1))
0.012790
0.361140
0.003720
0.133800
3.437860
2.699099
0.0012
0.0094
R-s quared
Adjus ted R-s quared
S.E. of regres s ion
Sum s quared res id
Log likelihood
Durbin-Wats on s tat
0.203184
0.187560
1.598973
130.3925
-99.06056
1.932729
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
1.735849
1.773967
3.813606
3.887957
3.842198
Conclusion: CPI is non
stationary
2. Test for Stationarity of CPI variable
• Step 5: Conduct ADF test on DCPI
Null Hypothes is : D(CPI) has a unit root
Exogenous : Cons tant, Linear Trend
Lag Length: 0 (Autom atic - bas ed on SIC, m axlag=10)
Augm ented Dickey-Fuller tes t s tatis tic
Tes t critical values :
1% level
5% level
10% level
t-Statis tic
Prob.*
-4.940998
-4.140858
-3.496960
-3.177579
0.0010
*MacKinnon (1996) one-s ided p-values .
Augm ented Dickey-Fuller Tes t Equation
Dependent Variable: D(CPI,2)
Method: Leas t Squares
Date: 06/04/14 Tim e: 11:11
Sam ple (adjus ted): 2000Q3 2013Q3
Included obs ervations : 53 after adjus tm ents
Variable
Coefficient
Std. Error
t-Statis tic
D(CPI(-1))
C
@TREND("2000Q1")
-0.653044
0.400286
0.026002
0.132168
0.464715
0.015194
-4.940998
0.861358
1.711390
R-s quared
Adjus ted R-s quared
S.E. of regres s ion
Sum s quared res id
Log likelihood
F-s tatis tic
Prob(F-s tatis tic)
0.328098
0.301222
1.592777
126.8469
-98.33000
12.20782
0.000048
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Wats on s tat
Prob.
0.0000
0.3932
0.0932
-0.015094
1.905397
3.823774
3.935300
3.866661
1.934941
Conclusion: CPI is I(1)
3. Estimate a VAR
•
Step 1: Estimate unresticted VAR on log(rgdp) log(m3) tb3 log(e) log(cpi) and
exogenous variables c libor log(oilprice) and 2 lags
•
Step 2: Test lag length criteria
VAR Lag Order Selection Criteria
Endogenous variables: LOG(RGDP) LOG(M3) TB3 LOG(E) LOG(CPI)
Exogenous variables: C LIBOR LOG(OILPRICE)
Date: 06/04/14 Time: 11:37
Sample: 2000Q1 2013Q3
Included observations: 51
Lag
LogL
0
1
2
3
4
156.8417
396.8381
437.2993
455.5089
497.3937
LR
NA
404.6999
60.29507
23.56530
45.99114*
FPE
AIC
SC
HQ
2.64e-09
5.83e-13
3.33e-13
4.80e-13
3.00e-13*
-5.562420
-13.99365
-14.59997
-14.33368
-14.99583*
-4.994236
-12.47850*
-12.13784
-10.92458
-10.63975
-5.345300
-13.41467
-13.65912*
-13.03096
-13.33124
* indicates lag order selected by the criterion
LR: sequential modified LR test statistic (each test at 5% level)
FPE: Final prediction error
AIC: Akaike information criterion
SC: Schwarz information criterion
HQ: Hannan-Quinn information criterion
Choose lag length of 1
3. Estimate a VAR
•
Step 3: Estimate unresticted VAR on log(rgdp) log(m3) tb3 log(e) log(cpi) and
exogenous variables c libor log(oilprice) and 1 lag
•
Step 4: Test for VAR stability
Roots of Characteristic Polynomial
Endogenous variables: LOG(RGDP) LOG(M3) TB3 L...
Exogenous variables: C LIBOR LOG(OILPRICE)
Lag specification: 1 1
Date: 06/04/14 Time: 11:46
Root
0.964622
0.805908
0.664349 - 0.101053i
0.664349 + 0.101053i
0.172220
No root lies outside the unit circle.
VAR satisfies the stability condition.
Modulus
0.964622
0.805908
0.671991
0.671991
0.172220
3. Estimate a VAR
Vector Autoregres s ion Es tim ates
Date: 06/04/14
Tim e: 11:46
Sam ple (adjus ted): 2000Q2 2013Q3
Included obs ervations : 54 after adjus tm ents
Standard errors in ( ) & t-s tatis tics in [ ]
LOG(RGDP)
LOG(M3)
TB3
LOG(E)
LOG(CPI)
LOG(RGDP(-1))
0.056730
(0.13577)
[ 0.41784]
-0.013630
(0.05418)
[-0.25155]
16.27575
(5.63528)
[ 2.88819]
-0.403484
(0.11029)
[-3.65847]
-0.000919
(0.06307)
[-0.01457]
LOG(M3(-1))
0.113207
(0.08576)
[ 1.32012]
0.976757
(0.03422)
[ 28.5400]
-8.366150
(3.55938)
[-2.35045]
0.239617
(0.06966)
[ 3.43979]
0.086950
(0.03984)
[ 2.18263]
TB3(-1)
-0.003709
(0.00165)
[-2.24725]
-0.000590
(0.00066)
[-0.89567]
0.812446
(0.06850)
[ 11.8597]
-0.001364
(0.00134)
[-1.01727]
-0.000392
(0.00077)
[-0.51092]
LOG(E(-1))
-0.061476
(0.10411)
[-0.59050]
-0.100757
(0.04155)
[-2.42503]
22.43778
(4.32113)
[ 5.19257]
0.649062
(0.08457)
[ 7.67498]
0.034232
(0.04836)
[ 0.70781]
LOG(CPI(-1))
0.379994
(0.13801)
[ 2.75342]
0.049095
(0.05508)
[ 0.89137]
-1.245256
(5.72821)
[-0.21739]
-0.066447
(0.11211)
[-0.59272]
0.776453
(0.06411)
[ 12.1111]
C
9.142041
(1.43465)
[ 6.37232]
0.697822
(0.57256)
[ 1.21878]
-202.7438
(59.5471)
[-3.40477]
3.970861
(1.16539)
[ 3.40732]
-0.500845
(0.66646)
[-0.75150]
LIBOR
0.010233
(0.00461)
[ 2.22054]
-0.003220
(0.00184)
[-1.75098]
0.116433
(0.19127)
[ 0.60872]
0.000467
(0.00374)
[ 0.12471]
-0.002266
(0.00214)
[-1.05868]
LOG(OILPRICE)
-0.027779
(0.03627)
[-0.76582]
0.013560
(0.01448)
[ 0.93672]
4.573956
(1.50556)
[ 3.03804]
-0.064894
(0.02947)
[-2.20238]
0.050155
(0.01685)
[ 2.97648]
0.956539
0.949925
0.072205
0.039619
144.6310
102.0425
-3.483054
-3.188390
12.66318
0.177050
0.999314
0.999210
0.011500
0.015812
9575.953
151.6449
-5.320183
-5.025519
13.48751
0.562508
0.826484
0.800080
124.3934
1.644446
31.30082
-99.15323
3.968638
4.263303
7.800000
3.677827
0.872000
0.852522
0.047645
0.032183
44.76779
113.2671
-3.898783
-3.604119
4.350034
0.083804
0.997315
0.996907
0.015582
0.018405
2441.120
143.4441
-5.016449
-4.721785
4.399869
0.330919
Determ inant res id covariance (dof adj.)
Determ inant res id covariance
Log likelihood
Akaike inform ation criterion
Schwarz criterion
2.72E-13
1.22E-13
419.7278
-14.06399
-12.59067
R-s quared
Adj. R-s quared
Sum s q. res ids
S.E. equation
F-s tatis tic
Log likelihood
Akaike AIC
Schwarz SC
Mean dependent
S.D. dependent
4. Analyse the VAR results
• Step 1: Estimate impulse response functions
Response to Cholesky One S.D. Innov ations ± 2 S.E.
Response of LOG(RGDP) to LOG(M3)
Response of LOG(RGDP) to TB3
Response of LOG(RGDP) to LOG(E)
.008
.008
.008
.004
.004
.004
.000
.000
.000
-.004
-.004
-.004
-.008
-.008
-.008
-.012
-.012
1
2
3
4
5
6
7
8
9
-.012
1
10
2
Response of LOG(CPI) to LOG(M3)
3
4
5
6
7
8
9
1
10
Response of LOG(CPI) to TB3
.008
.008
.004
.004
.004
.000
.000
.000
-.004
-.004
-.004
-.008
-.008
-.008
-.012
-.012
•
•
•
•
•
2
3
4
5
6
7
8
9
10
3
4
5
6
7
8
9
10
9
10
Response of LOG(CPI) to LOG(E)
.008
1
2
-.012
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
M3 has no impact on GDP.
TB3 has negative impact on GDP four quarters after initial shock.
Exchange rate has negative impact on GDP 5-6 quarters after the initial shock.
M3 positively impacts on CPI after 5 quarters and persists thereafter.
Interest rates and exchange rates have no significant impact on CPI.
7
8
4. Analyse the VAR results
• Step 2: Variance Decomposition
Variance Decomposition of LOG(RGDP):
Perio...
S.E.
LOG(RGDP) LOG(M3)
1
2
3
4
5
6
7
8
9
10
0.039619
0.040530
0.041621
0.042451
0.043129
0.043713
0.044218
0.044653
0.045027
0.045349
100.0000
95.65326
91.73790
88.52697
85.81665
83.54043
81.64444
80.06744
78.75009
77.64127
0.000000
0.247354
0.642520
1.045370
1.399053
1.692048
1.932420
2.132909
2.304879
2.456835
Variance Decomposition of LOG(CPI):
Perio...
S.E.
LOG(RGDP) LOG(M3)
1
2
3
4
5
6
7
8
9
10
0.015812
0.022265
0.027146
0.031242
0.034825
0.038019
0.040897
0.043505
0.045879
0.048048
16.02663
16.61828
18.07977
19.13435
19.55334
19.45527
19.02880
18.43483
17.78248
17.13479
0.949970
0.593378
0.939783
1.949628
3.454488
5.243297
7.114605
8.913332
10.54433
11.96566
TB3
LOG(E)
LOG(CPI)
0.000000
1.651738
2.993515
3.824021
4.330049
4.645795
4.850849
4.990448
5.090050
5.164158
0.000000
0.073331
0.667772
1.749625
3.015615
4.233845
5.297103
6.180979
6.900189
7.482448
0.000000
2.374319
3.958297
4.854010
5.438635
5.887883
6.275190
6.628220
6.954794
7.255293
TB3
LOG(E)
LOG(CPI)
1.811368
1.480150
1.206363
1.065535
1.032843
1.075125
1.165823
1.285588
1.420967
1.562971
1.474381
2.360067
2.672514
2.581965
2.386412
2.321459
2.508390
2.965746
3.647522
4.482093
79.73766
78.94812
77.10157
75.26852
73.57292
71.90485
70.18238
68.40050
66.60471
64.85449
Cholesky Ordering: LOG(RGDP) LOG(M3) TB3 LOG(E) LOG(CPI)
• After 10 quarters, 77.6%
of variations in GDP is
attributed to itself, 7.5%
to exchange rate, 7.3%
to CPI, 5.2% to interest
rates and 2.5% to M3.
• After 10 quarters, 64.8%
of variations in CPI is
attributed to itself,
17.1% to GDP, 11.9% to
M3, 4.5% to exchange
rates and 1.5% to
interest rates.
4. Analyse the VAR results
• Step 3: Granger Causality test
Pairwise Granger Causality Tests
Date: 06/04/14 Time: 12:13
Sample: 2000Q1 2013Q3
Lags: 2
Null Hypothesis:
Obs
F-Statistic
Prob.
LOG(M3) does not Granger Cause LOG(RGDP)
LOG(RGDP) does not Granger Cause LOG(M3)
53
23.1552
2.26228
9.E-08
0.1151
TB3 does not Granger Cause LOG(RGDP)
LOG(RGDP) does not Granger Cause TB3
53
2.94042
3.58396
0.0624
0.0354
LOG(E) does not Granger Cause LOG(RGDP)
LOG(RGDP) does not Granger Cause LOG(E)
53
1.36514
3.01192
0.2651
0.0586
LOG(CPI) does not Granger Cause LOG(RGDP)
LOG(RGDP) does not Granger Cause LOG(CPI)
53
28.0732
4.79411
8.E-09
0.0126
TB3 does not Granger Cause LOG(M3)
LOG(M3) does not Granger Cause TB3
53
2.01766
0.18146
0.1441
0.8346
LOG(E) does not Granger Cause LOG(M3)
LOG(M3) does not Granger Cause LOG(E)
53
6.06863
2.64862
0.0045
0.0811
LOG(CPI) does not Granger Cause LOG(M3)
LOG(M3) does not Granger Cause LOG(CPI)
53
1.60881
3.48525
0.2107
0.0386
LOG(E) does not Granger Cause TB3
TB3 does not Granger Cause LOG(E)
53
3.87927
0.10084
0.0274
0.9043
LOG(CPI) does not Granger Cause TB3
TB3 does not Granger Cause LOG(CPI)
53
1.15447
2.65575
0.3238
0.0806
LOG(CPI) does not Granger Cause LOG(E)
LOG(E) does not Granger Cause LOG(CPI)
53
1.78699
0.27778
0.1784
0.7587
• M3 and CPI granger
cause GDP, while TB3
and exchange rates do
not cause granger GDP.
• M3 granger causes CPI.
4. Analyse the VAR results
• Step 4: Cointegration test
13.2
13.0
12.8
12.6
.08
12.4
.04
12.2
.00
-.04
-.08
-.12
00
01
02
03
04
05
Residual
06
07
Actual
08
09
10
11
12
13
Fitted
• Residual seems stationary, therefore, variables are cointegrated.
5. Policy insights
• Excessive money is not good for inflation in
the medium-term.
• Raising short-term interest rates and
depreciating the shilling will impact negatively
on growth in the short term.
• Thank you for listening