HUNGARY VS
EUROZONE
ECO310b, Final project
Elizaveta Krylova
Evgeniia Samsonova
Lyuuboslava Kehayova
Zhaklin Dib
Hungary vs Eurozone
2
Content
INTRODUCTION ............................................................................................................................3
PRELIMINARY RESULT IS STATA ..............................................................................................4
ONE-MONTH INTEREST RATES .................................................................................................5
UNIT ROOT TESTING ...................................................................................................................5
COINTEGRATION........................................................................................................................ 13
ENGLE’S METHOD:..................................................................................................................... 13
JOHANSEN’S TEST ...................................................................................................................... 16
ERROR CORRECTION MODEL ................................................................................................. 17
SERIAL CORRELATION ............................................................................................................. 20
FINAL MODEL ............................................................................................................................. 23
THREE MONTH INTEREST RATES ........................................................................................... 24
UNIT ROOT TESTING ................................................................................................................. 24
COINTEGRATION........................................................................................................................ 30
ENGLE’S METHOD ...................................................................................................................... 30
JOHANSEN’S TEST ...................................................................................................................... 33
ERROR CORRECTION MODEL ................................................................................................. 34
SERIAL CORRELATION ............................................................................................................. 36
FINAL MODEL ............................................................................................................................. 38
CONCLUSION ............................................................................................................................... 38
Hungary vs Eurozone
3
Introduction
The Project’s aim is to determine whether there is any correlation between the interest
rates in Hungary and the Eurozone. As Hungary is a member of the European Union from 2004,
we expect to observe the long-term convergence.
We will test the model of cointegrated time-series and expect to observe a stable long-run
relationship between the two countries interest rates. The data was collected from the Hungarian
Central Bank (MNB) website and the EURIBOR-Interbank Offered Rate website. The following
variables were chosen to comprise the data between January 2005 and December 2015.






hg_i1 – monthly averages of interest rates with maturity of 1 month for Hungary
eu_i1 – monthly averages of interest rates with maturity of 1 month for Eurozone
hg_i3 – monthly averages of interest rates with maturity of 3 months for Hungary
eu_i3 – monthly averages of interest rates with maturity of 3 months for Eurozone
Dcrisis – a dummy variable that accounts for the economic crisis in 2007m9 – 2009m11
Drec – a dummy variable that accounts for the legal proceedings of the European
Commission launched against Hungary that caused a recession (2012m1 – 2013m6).
Hungary vs Eurozone
Preliminary result is STATA
First of all we can check whether there is any convergence between HG_i1 and EU_i1,
and between HG_i3 and EU_i3. For that we will do the following command:
. tsline HG_i1 EU_i1
. tsline HG_i3 EU_i3
4
Hungary vs Eurozone
We indeed observe some correlation but only in the case with the 3-month interest rates
and still need to do the tests.
One-month interest rates
Unit Root Testing
To check whether there are some non-stationary variables we need to run the DickeyFuller test. All variables must be a Random Walk model but we need to identify whether it is
Case A (a pure random walk, no drift, no trend), Case B (a random walk with a drift), or Case C
(a random walk with a drift and a trend).
We will start with HG_i1 variable. First of all, we need to identify where there is a unit
root in general. For that we run the Dickey-Fuller test without lags to see the general situation:
. gen t=m(2005m1)+_n-1
. format t %tm
. tsset t
time variable: t, 2005m1 to 2014m12
delta: 1 month
This is our hypothesis:
H0: There exists a unit root (i.e. HG_i1is non-stationary)
5
Hungary vs Eurozone
6
HA: There is no unit root (i.e. HG_i1is stationary)
Rule: Reject H0 iff MacKinnon p-value < α, where α = 5%
As we can observe from the STATA output MacKinnon p-value = 0.8681 > α=0.05 =>
We do not reject H0 => There exists a unit root. We observe that αhat (_cons) p-value = 0.132 >
α, βhat (_trend) p-value = 0.130 > α, that means that both are insignificant with α = 5%. We need
to run the Dickey-Fuller test with lags to identify the Case.
The MacKinnon p-value is 0.8510 > α = 0.05, hence we do not reject the Ho and
conclude that there exists a unit root. We will proceed with two steps: checking for trend and
then checking for drift.
Hungary vs Eurozone
7
Checking for a drift:
H0 : αhat = 0 (It is not individually significant, no drift)
HA: αhat ≠ 0 (It is individually significant, the drift exists)
Rule: Reject H0 iff αhat p-value < α, where α=5%
Here αhat p-value=0.094 > α = 0.05. Therefore, there is no drift in HG_i1.
Now, we check whether there is a trend:
H0 : β_trend = 0 (It is not individually significant, there is no trend)
HA: β_trend ≠ 0 (It is individually significant, the trend exists)
Rule: Reject H0 iff β_trend p-value < α, where α=5%
As we can observe from the STATA output β_trend p-value=0.078 > α = 0.05. Therefore,
there is no trend in HG_i1.
We can conclude that there is a Case A unit root random walk with no time trend and no
drift.
Since there is a unit root we need to cure HG_i1 and first, check the unit root in
differenced HG_i1.
Hungary vs Eurozone
8
We see that two lags are enough to run the regression. Because LD p-value = 0.093 > α =
0.05, so we will rerun the test:
Hungary vs Eurozone
9
As we can observe from STATA output MacKinnon p-value = 0.0000 < α = 0.05, hence,
we reject the Ho. We observe that the _trend p-value = 0.173 > α = 0.05 (insignificant) and
_cons p-value = 0.379 > α = 0.05 (insignificant). Therefore, we can conclude that the unit root in
HG_i1 was cured and there is no time trend and no drift. The stationary variable that we will use
is d. HG_i1.
Unit Root Testing and Curing for EU_i1
As with the EU_i1 variable we will follow the same steps to identify whether there is a
unit root in EU_i1 and if so, cure it. For that we run the Dickey-Fuller test without lags to see the
general situation:
Ho: There exists a unit root (i.e. EU_i1 is non-stationary)
Ha: There is no unit root (i.e. EU_i1 is stationary)
Rule: Reject Ho iff MacKinnon p-value < α, where α = 5%
Hungary vs Eurozone 10
We observe that the MacKinnon p-value = 0.8207 > α = 0.05, hence, we do not reject the
Ho and conclude that there exists a unit root. Furthermore, we observe that αhat (_cons) p-value
= 0.134 > α = 0.05, βhat (_trend) p-value = 0.074 > α = 0.05, so both are insignificant and as a
result, we have a random walk with no time trend and no drift. But we will do further tests with
lags to prove it.
Hungary vs Eurozone 11
The MacKinnon p-value is 0.0972 > α = 0.05. Therefore, we do not reject the Ho and
conclude that there exists a unit root.
We will proceed with two steps: checking for trend and then checking for drift.
Checking for a drift:
Ho: αhat = 0 (It is not individually significant, there is no drift)
Ha: αhat ≠ 0 (It is individually significant, the drift exists)
Rule: Reject Ho iff αhat p-value < α, where α = 5%
Hungary vs Eurozone 12
Here αhat p-value = 0.005 < α = 0.05. Therefore, there is a drift in EU_i1.
Checking for a trend:
Ho: β_trend = 0 (It is not individually significant, no trend)
Ha: β_trend ≠ 0 (It is individually significant, the trend exists)
Rule: Reject Ho iff β_trend p-value < α, where α=5%
Here β_trend p-value = 0.006 < α = 0.05. Therefore, there is a time trend in EU_i1.
We can conclude that there is a Case C unit root random walk with a time trend and a
drift.
Since there is a unit root we need to cure EU_i1 and first, check the unit root in
differenced EU_i1.
As we can observe from STATA output MacKinnon p-value = 0.0198 < α = 0.05, hence
we reject the Ho and we see that the _trend p-value = 0.659 > α = 0.05 (insignificant) and _cons
p-value = 0.869 > α = 0.05 (insignificant), so we can conclude that the unit root in EU_i1 was
cured and there is no time trend and no drift. The stationary variable that we will use is d.
EU_i1.
Hungary vs Eurozone 13
Cointegration
We proved that during the last several tests the order of integration of the pair HG_i1 and
EU_i1 is the same – I(1). This is sufficient for us to proceed with the tests for cointegration. We
will start with Engle’s test and Johansen’s test to determine whether there is cointegration
between HG_i1 and EU_i1.
Engle’s Method:
H0: unit root exists, no cointegration, the residuals are non-stationary;
HA: unit root doesn’t exist, cointegration exists, the residuals are stationary;
Rule: Reject Ho iff MacKinnon p-value < α = 5%
Hungary vs Eurozone 14
As we can see, since the MacKinnon p-value = 0.8676 > α = 0.05, we do not reject the
Ho and there is no cointegration.
Since we cannot reject Ho, we can try to rerun the regression with a time variable and a
uhat2.
Hungary vs Eurozone 15
Hungary vs Eurozone 16
Still, the MacKinnon p-value = 0.8540 > α = 0.05 and we cannot reject the Ho, there is no
cointegration between the interest rates. However, since Johansen’s test is considered more
reliable, we will also run it.
Johansen’s test
First, we need to complete a lag determination test.
As we can see from the output, we should chose lags(3), due to the star indicators.
Now, we can check for cointegration:
Hungary vs Eurozone 17
Since the star is in from of the rank1, we choose the following hypothesis:
H0: there is “1” cointegration between hg_i1 and eu_i1;
HA: there is “2” cointegration between hg_i1 and eu_i1;
If |trace statistics| > |critical value|, reject Ho and conclude that there is an I(1)
cointegration.
|2.6698| < |3.76|, hence, do not reject the H0, there is cointegration I(1) between HG_i1
and EU_i1.
Error Correction Model
Since HG_i1 and EU_i1 are both random walk (nonstationary, unit root) variables
(integrated of order 1, I(1)) are cointegrated, then we can formulate an error correction model.
Our command .reg hg_i1 eu_i1 is a superior regression as both of the variables have unit roots
(as we checked with Dickey-Fuller tests) but there is a long term stable equilibrium relationship
between these series and our regression becomes meaningful. Once we established cointegration,
we can check the short-run dynamics in an error-correction model, so we will create a new
variable sradj that represents a lagged error (sradj = l.uhat). We also need to create a
combination of dummy variables and a lagged error: sradj_dcrisis (equals to its multiplication),
sragj_drec (equals to its multiplication).
Hungary vs Eurozone 18
We observe that the coefficient in front of the sradj variable is negative, it value
indicates that the proportion of disequilibrium is corrected each time period.
. gen dcrisis = (t>=2007m9)*(t<=2009m11)
. gen drec = (t>=2012m1)*(t<=2013m6)
Hungary vs Eurozone 19
Now we will generate the following variables:
. gen sradj_dcrisis = sradj * dcrisis
. gen sradj_drec = sradj * drec
And run the regression with new variables:
In this model almost every variable is insignificant and R2adj = 3,6%. We definitely need
to improve the model but first check for serial correlation.
Hungary vs Eurozone 20
Serial Correlation
If we run Breusche – Godfrey test, we see that there is serial correlation:
Rule: Reject H0 iff p-value for lag < α = 0.05
Here, p-value for the second lag = 0.0012< α = 0.05, so we reject H0 and conclude that there
is serial correlation of at least AR(2) type, which needs to be cured. We add lag 2 periods hg_i1
and eu_i1 and rerun the regression and the bgodfrey test.
Hungary vs Eurozone 21
Here, dcrisis variable is totally insignificant, so we drop it and rerun the regression:
Hungary vs Eurozone 22
Indeed, the model improved
d.Eu_i1 p-value = 0.922 > α = 0.05 – insignificant and its coefficient is negative, s
L2.d.hg_i1 p-value = 0.037 < α = 0.05 – significant
L2.d.eu_i1 p-value = 0.000 < α = 0.05 – significant
Drec p-value = 0.023 < α = 0.05 – significant
Sradj p-value = 0.096 > α = 0.05 – insignificant, but! could be significant at α = 0.1
Sradj_dcrisis p-value = 0.000 < α = 0.05 – significant
Sradj_drec p-value = 0.037 < α = 0.05 – significant
_cons p-value = 0.105 > α = 0.05 – insignificant.
In our case, since sradj=0.023, the long run equilibrium adjustment will take place in less than
three months.
Hungary vs Eurozone 23
Indeed, all lags p-values are insignificant and we can conclude that there is no serial
correlation and the model is cured.
Final Model
Now, we have arrived at our best, final model – most of the variables are significant,
the model is free of Serial Correlation, and the R2adj is 22.09%.
Hungary vs Eurozone 24
Three Month Interest Rates
Unit Root Testing
We will check for unit roots in all variables to see if any variable is non-stationary. We
start by assuming that each variable may have Case 3 Random Walk model with a drift and time
trend. We run Dickey-Fuller test without lags to test eu_i3.
. dfuller eu_i3, trend regress
Dickey-Fuller test for unit root
=
119
Interpolated Dickey-Fuller
1% Critical
5% Critical
10% Critical
Value
Value
Value
Test
Statistic
Z(t)
Number of obs
-1.584
-4.034
-3.447
-3.147
MacKinnon approximate p-value for Z(t) = 0.7988
D.eu_i3
eu_i3
L1.
_trend
_cons
Coef.
-.0238857
-.0014341
.1135051
Std. Err.
.0150834
.0006923
.0670715
t
-1.58
-2.07
1.69
P>|t|
0.116
0.041
0.093
[95% Conf. Interval]
-.0537602
-.0028052
-.0193384
.0059888
-.000063
.2463486
Those are our hypothesis:
H0: There exists a unit root and eu_i3 is non-stationary
HA: There exists NO unit root and eu_i3 is stationary
Rule: Reject H0 if and only if MacKinnon p-value < α, where we assume that α=5%
As we can observe from the STATA output MacKinnon p-value = 0.7988 > α=0.05 =>
We do not reject H0 => There exists a unit root. The _trend is significant at α=0.05. The _cons is
not significant at α=0.05, its value is 0.093, so we should run the augmented Dickey-Fuller Test
with lags.
Hungary vs Eurozone 25
. dfuller eu_i3, trend regress lags(4)
Augmented Dickey-Fuller test for unit root
Test
Statistic
1% Critical
Value
-2.609
-4.035
Z(t)
Number of obs
=
115
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.448
-3.148
MacKinnon approximate p-value for Z(t) = 0.2758
D.eu_i3
eu_i3
L1.
LD.
L2D.
L3D.
L4D.
_trend
_cons
Coef.
-.0306224
.7540449
-.1414612
.1410562
-.0144459
-.0012834
.1321693
Std. Err.
.0117376
.0939126
.1181025
.1179007
.0950554
.0005495
.0541034
t
-2.61
8.03
-1.20
1.20
-0.15
-2.34
2.44
P>|t|
0.010
0.000
0.234
0.234
0.879
0.021
0.016
[95% Conf. Interval]
-.0538884
.5678938
-.3755607
-.0926435
-.2028622
-.0023725
.0249269
-.0073565
.940196
.0926384
.3747559
.1739704
-.0001943
.2394118
The McKinnon p-value is 0.2758 (which is very high). Therefore, we do not reject the
Ho and we conclude that there is a unit root in eu_i3.
We will proceed with two steps: checking for a trend and then checking for a drift.
Checking for the trend:
H0: β_trend = 0 (It is not individually significant, no trend)
HA: β_trend ≠ 0 (It is individually significant, trend exists)
Rule: Reject H0 if and only if β_trend p-value < α, where α=5%
As we can observe from the STATA output β_trend p-value=0.021 < α. Therefore, there
is a trend in eu_i3.
Checking for the drift:
Hungary vs Eurozone 26
H0: α = 0 (It is not individually significant, no drift)
HA: α ≠ 0 (It is individually significant, drift exists)
Rule: Reject H0 if and only if αhat p-value < α, where α=5%
As we can observe from the STATA output α p-value=0.016 < α. Therefore, there is a
drift in eu_i3.
So, we can conclude that there is a unit root CASE 3, which means that we have a model
of random walk with trend and drift.
Since there is a unit root we need to cure eu_i3 and check for the unit root in differenced
eu_i3:
. dfuller d.eu_i3, trend regress lags(4)
Augmented Dickey-Fuller test for unit root
Z(t)
Test
Statistic
1% Critical
Value
-3.605
-4.035
Number of obs
=
114
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.448
-3.148
MacKinnon approximate p-value for Z(t) = 0.0294
D2.eu_i3
D.eu_i3
L1.
LD.
L2D.
L3D.
L4D.
_trend
_cons
Coef.
-.3185119
.1002422
-.0554522
.0729414
.0513269
-.0002155
.0077181
Std. Err.
.088358
.1071253
.1049256
.0986837
.0968435
.0003771
.0260365
t
-3.60
0.94
-0.53
0.74
0.53
-0.57
0.30
P>|t|
0.000
0.352
0.598
0.461
0.597
0.569
0.767
[95% Conf. Interval]
-.4936713
-.1121212
-.263455
-.1226875
-.1406541
-.0009631
-.0438961
-.1433526
.3126055
.1525507
.2685702
.243308
.000532
.0593324
As we can observe from STATA output MacKinnon p-value = 0.0294 < α = 0.05, hence
we reject the Ho and we see that the _trend p-value = 0.569 > α = 0.05 (insignificant) and _cons
p-value = 0.767 > α = 0.05 (insignificant), so we can conclude that the unit root in eu_i3 was
cured and there is no time trend and no drift. The stationary variable that we will use is d. eu_i3.
Then, we proceed by testing hg_i3.
Hungary vs Eurozone 27
We run a Dickey-Fuller test with no lags.
. dfuller hg_i3, trend regress
Dickey-Fuller test for unit root
Number of obs
Test
Statistic
1% Critical
Value
-1.540
-4.034
Z(t)
=
119
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.447
-3.147
MacKinnon approximate p-value for Z(t) = 0.8149
D.hg_i3
hg_i3
L1.
_trend
_cons
Coef.
-.0482736
-.0024555
.4123704
Std. Err.
.0313388
.0018544
.2963817
t
-1.54
-1.32
1.39
P>|t|
0.126
0.188
0.167
[95% Conf. Interval]
-.110344
-.0061285
-.1746509
.0137968
.0012174
.9993916
There is our hypothesis:
H0: There exists a unit root and hg_i3 is non – stationary.
HA: There is no unit root and hg_i3 is stationary.
Rule: Reject H0 if and only if MacKinnon p-value < α, where α=5%.
As we can observe from the STATA output MacKinnon p-value=0.8149 >α. Therefore,
there exists a unit root in hg_i3. Since, the trend is insignificant at α=5% with p-value (trend)
=0.188 we drop it.
Hungary vs Eurozone 28
. dfuller hg_i3, regress
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-0.947
-3.504
=
119
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-2.889
-2.579
MacKinnon approximate p-value for Z(t) = 0.7721
D.hg_i3
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
hg_i3
L1.
-.0243108
.0256679
-0.95
0.346
-.0751447
.026523
_cons
.1021472
.182115
0.56
0.576
-.258522
.4628164
However, the MacKinnon p-value is still high, therefore, we run the regression with lags:
Hungary vs Eurozone 29
The MacKinnon p-value is 0.8723 > α = 0.05, therefore, we do not reject the H0 and
conclude that there is a unit root.
We will proceed with checking for drift:
Ho: αhat = 0 (It is not individually significant, there is no drift)
Ha: αhat ≠ 0 (It is individually significant, the drift exists)
Rule: Reject Ho iff αhat p-value < α, where α = 5%
Here αhat p-value = 0.730 > α = 0.05. Therefore, there is no drift in hg_i3.
We can conclude that there is a Case A unit root random walk with no time trend and no
drift.
Since there is a unit root, we check whether it still exists in differenced hg_i3.
. dfuller d.hg_i3, trend regress
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-13.785
-4.034
=
118
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.448
-3.148
MacKinnon approximate p-value for Z(t) = 0.0000
D2.hg_i3
D.hg_i3
L1.
_trend
_cons
Coef.
-1.229403
-.0014839
.0195019
Std. Err.
.0891851
.0014894
.1019863
t
-13.78
-1.00
0.19
P>|t|
0.000
0.321
0.849
[95% Conf. Interval]
-1.406062
-.0044342
-.1825133
-1.052745
.0014664
.2215171
We observe that the MacKinnon p-value = 0.0000 < α=0.05. Furthermore, we see that the
_trend and the _cons are both insignificant with p-value (trend) = 0.321 and p-value (cons) =
0.849 > α=5%. Therefore, the unit root in hg_i3 is cured.
The order of integration is the same and is I(1) because it was enough to do only the
first differencing.
Hungary vs Eurozone 30
Cointegration
We proved that during the last several tests that the order of integration of the pair eu_i3
and hg_i3 is the same - I(1). This is sufficient for us to proceed with the tests for cointegration.
We will start with Engle’s Method to check whether cointegration exists.
Engle’s Method
H0: unit root exists, no cointegration, the residuals are non-stationary;
HA: unit root doesn’t exist, cointegration exists , the residuals are stationary;
Rule: Reject H0 iff MacKinnon p-value < α=5%
Hungary vs Eurozone 31
. reg hg_i3 eu_i3
Source
SS
df
MS
Model
Residual
148.012649
365.938747
1
118
148.012649
3.10117583
Total
513.951397
119
4.3189193
hg_i3
Coef.
eu_i3
_cons
.7036051
5.448796
Std. Err.
.1018457
.2485246
t
6.91
21.92
Number of obs
F( 1,
118)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
120
47.73
0.0000
0.2880
0.2820
1.761
P>|t|
[95% Conf. Interval]
0.000
0.000
.5019229
4.95665
.9052874
5.940943
. predict uhat, res
. dfuller uhat, trend regress lags(4)
Augmented Dickey-Fuller test for unit root
Z(t)
Test
Statistic
1% Critical
Value
-1.748
-4.035
Number of obs
=
115
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.448
-3.148
MacKinnon approximate p-value for Z(t) = 0.7293
D.uhat
Coef.
uhat
L1.
LD.
L2D.
L3D.
L4D.
_trend
_cons
-.0599868
-.1189027
.2017545
.2126869
-.0496742
-.001588
.07365
Std. Err.
.0343183
.096026
.095052
.0960623
.095026
.0016195
.1134315
t
-1.75
-1.24
2.12
2.21
-0.52
-0.98
0.65
P>|t|
0.083
0.218
0.036
0.029
0.602
0.329
0.518
[95% Conf. Interval]
-.1280116
-.3092429
.013345
.0222748
-.2380321
-.0047982
-.151191
.008038
.0714374
.3901641
.403099
.1386838
.0016222
.2984909
We observe that the MacKinnon p-value = 0.7293 > α=0.05, hence, we do not reject Ho.
Therefore, we conclude that there is no cointegration. We proceed with the Jonahsen’s Test as it
is more reliable when it comes to testing cointegration.
Since we cannot reject Ho, we can try to rerun the regression with a time variable and a
uhat2.
Hungary vs Eurozone 32
Hungary vs Eurozone 33
Still, the MacKinnon p-value = 0.8093 > α = 0.05 and we cannot reject the Ho, there is no
cointegration between the interest rates. However, since Johansen’s test is considered more
reliable, we will also run it.
Johansen’s Test
This test adds three criteria for cointegration identification – SBIC, HQIC, and AIC.
First, we need to complete a lag determination test.
. varsoc hg_i3 eu_i3 , maxlag(4)
Selection-order criteria
Sample: 2005m5 - 2014m12
lag
0
1
2
3
4
LL
LR
-448.77
-50.383
-9.98071
-8.40882
-4.50306
Endogenous:
Exogenous:
796.77
80.805*
3.1438
7.8115
Number of obs
df
4
4
4
4
p
0.000
0.000
0.534
0.099
FPE
8.13479
.009063
.004838*
.005046
.005056
AIC
7.7719
.972121
.344495*
.386359
.387984
HQIC
7.79118
1.02994
.440857*
.521266
.561436
=
116
SBIC
7.81938
1.11455
.581873*
.718689
.815265
hg_i3 eu_i3
_cons
.
We observe that there appears a star in the second lag in AIC with a value of 0.344495.
Next, we run a vecrank test for cointegration:
H0: there exists “1” cointegration
HA: there exists “2” cointegration
Rule: Reject H0 iff |trace statistic| > |critical value|.
Hungary vs Eurozone 34
Since |1.1927| < |3.76|, we do not reject the null and conclude that “1” cointegration
exists between eu_i3 and hg_i3.
Therefore, after performing both tests, we can conclude that there is cointegration I(1)
between the three month interest rates of the Central Bank of Hungary and the European Central
Bank.
Error Correction Model
Since HG_i3 and EU_i3 are both random walk (nonstationary, unit root) variables
(integrated of order 1, I(1)) are cointegrated, then we can formulate an error correction model.
Our command .reg hg_i3 eu_i3 is a superior regression as both of the variables have unit
roots (as we checked with Dickey-Fuller tests) but there is a long term stable equilibrium
relationship between these series and our regression becomes meaningful. Once we established
cointegration, we can check the short-run dynamics in an error-correction model.
Hungary vs Eurozone 35
As we can see, dcrisis is not significant, hence, we can drop it. Now, we can drop it.
As we can see, adjusted R-squared is higher.
Hungary vs Eurozone 36
This is not our final model, since we need to check it for serial correlation.
Serial Correlation
We run the Breusch-Godfrey test.
Rule: Reject H0 iff p-value for lag < α = 0.05
Here, p-value for the first lag = 0.0032< α = 0.05, so we reject H0 and conclude that there is
serial correlation of at least AR(1) type, which needs to be cured. We add lag 1 period hg_i3 and
eu_i3 and rerun the regression and the bgodfrey test.
Hungary vs Eurozone 37
Indeed, the model improved
d.Eu_i3 p-value = 0.278 > α = 0.05 – insignificant and its coefficient is negative;
L.d.hg_i3 p-value = 0.002 < α = 0.05 – significant
L.d.eu_i3 p-value = 0.392 > α = 0.05 – insignificant
Drec p-value = 0.093 > α = 0.05 – insignificant, but! could be significant at α = 0.1;
Sradj p-value = 0.355 > α = 0.05 – insignificant;
Sradj_dcrisis p-value = 0.638 > α = 0.05 – insignificant;
Sradj_drec p-value = 0.125 > α = 0.05 – insignificant;
_cons p-value = 0.516 > α = 0.05 – insignificant.
Considering the fact the sradj = 0.355, we can assume that the long run equilibrium adjustment
will take almost one year.
Hungary vs Eurozone 38
Final Model
Now, we have arrived at our best, final model – most of the variables are significant,
the model is free of Serial Correlation, and the R2adj is 6.62%.
Conclusion
To conclude, after running the test on interest rates with a maturity of 1 month and 3
months to investigate the relationship between the MNB and EURIBOR interbank interest rates,
we observe a long-run cointegration between them. No matter that Hungary is a new member of
the European Union, its interest rates are tight to the Euro board rates.
The final models do not appear flawless, due to the fact that not all of the variables
appear to be significant, however, they have no serial correlation and do have some cointegration
between them.
Our dummy variables, being drisis and drec, were chosen correctly, since their products
were significant. This means that the crisis of 2007 and the recession of 2012 in Hungary have
attributed to disruptions in the long-run convergence between interbank interest rates.
Overall our models still seek some corrections, nevertheless, show the existence of stable
long-run cointegration between interbank interest rates of Hungary and Eurozone.