Transcript VAR

VAR
Małgorzata Bednarek
Maria Derezińska
Magdalena Sadowska
Theory
About VAR

Sims critique
Validity of interrelated analytical exercises (common in reality
where everything depends on everything) implicit incorrect analysis of
applications if econometric inquiry is dependent on prior theoretical
restrictions
Vector autoregression (VAR model) is possible to deal with
dynamic relationships between macroeconomic variables, where causality
may be mutual

Vector autoregression
xt =Π1xt -1+...+Πkxt -k+ΦDt +εt
εt ~NID(0, Ω)
Applications of vector autoregressions


Forecasting
VAR models allow complete flexibility in specifying the
correlation between future, present and past
Causality tests



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Granger tests
Sims tests
Both tests are implications of the same null hypothesis. In the
model joint significance of all lags except the lags of variable
supposed to be a cause is tested
Hypothesis-seeking
Data characterization
Impulse response analysis
Monetary and fiscal policy analysis
VAR diagnosis
•
Testing for number of lags
•
Testing for VAR stability
•
Testing for Granger causality
•
Testing for autocorrelation
Empirical results
Model

In our model we analyze the potential for lending and consumption booms
in Hungary
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DATA SOURCES:
OECD Maxdata database,
extension of papers: Brzoza-Brzezina (2004) and Susan Schadler, Zuzana
Murgasova, Rachel van Elkan (2004 )
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DATA: quarterly dataset for Hungary for period 1996-2004

1. lloan - logarithm of total nominal loans to the private sector
2. lrate - logarithm of Nominal interest rate
3. lgdp - logarithm of GDP at constant prices
4. lcon - logarithm of Private Consumption, Volume
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Vector Autoregression for Hungary with consumption (quarterly
dataset October 1995 - May 2004)
Sample:
1996q2
2004q2
-------------------------------------------------------------------------Equation
Obs Parms
RMSE
R-sq
chi2
P
-------------------------------------------------------------------------lloan
23
12
.001624
0.9960
5721.318
0.0000
lrate
23
12
.742514
0.4584
19.46434
0.0533
lgdp
23
12
.000417
0.9980
11602.81
0.0000
lcon
23
12
.004917
0.9998
96633.75
0.0000
-------------------------------------------------------------------------Model lag order selection statistics
-----------------------------------FPE
AIC
HQIC
1.362e-17 -27.9393
-27.34332
SBIC
-25.569572
LL
369.30194
Det(Sigma_ml)
1.329e-19
-----------------------------------------------------------------------------|
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------lloan
|
lloan
|
L1 |
.6797655
.1784921
3.81
0.000
.3299274
1.029604
L2 |
.1464823
.2067421
0.71
0.479
-.2587247
.5516893
lrate
|
L1 | -.0000959
.0007495
-0.13
0.898
-.001565
.0013732
L2 | -.0012674
.0007255
-1.75
0.081
-.0026895
.0001546
lgdp
|
L1 | -.1985731
.7957318
-0.25
0.803
-1.758179
1.361033
L2 |
.2478325
.688455
0.36
0.719
-1.101514
1.597179
lcon
|
L1 |
.0266011
.0772088
0.34
0.730
-.1247254
.1779276
L2 | -.0134382
.0670136
-0.20
0.841
-.1447824
.117906
_q_2
| -.0015721
.001348
-1.17
0.243
-.0042141
.0010698
_q_3
| -.0016634
.00163
-1.02
0.307
-.0048582
.0015313
_q_4
|
-.001651
.0007053
-2.34
0.019
-.0030334
-.0002686
_cons
|
.269556
1.732104
0.16
0.876
-3.125306
3.664418
-------------+---------------------------------------------------------------lrate
|
lloan
|
L1 | -6.605417
81.60332
-0.08
0.935
-166.545
153.3342
L2 |
115.7716
94.51868
1.22
0.221
-69.48158
301.0249
lrate
|
L1 |
.3951908
.3426723
1.15
0.249
-.2764345
1.066816
L2 | -.1638084
.3317012
-0.49
0.621
-.8139309
.486314
lgdp
|
L1 | -145.4654
363.794
-0.40
0.689
-858.4885
567.5577
L2 | -455.4286
314.749
-1.45
0.148
-1072.325
161.4681
lcon
|
L1 | -28.46556
35.29845
-0.81
0.420
-97.64925
40.71812
L2 |
36.38052
30.63737
1.19
0.235
-23.66762
96.42867
_q_2
|
.503419
.6162614
0.82
0.414
-.7044312
1.711269
_q_3
|
.5327072
.7452087
0.71
0.475
-.927875
1.993289
_q_4
|
-.472785
.3224592
-1.47
0.143
-1.104793
.1592233
_cons
|
1293.563
791.8863
1.63
0.102
-258.5061
2845.631
var lloan lrate lgdp lcon, exog(_q*)
Parameters of VAR model in standard form
have no structural interpretations !!
lgdp
lloan
|
|
L1 |
.076064
.0458807
1.66
0.097
-.0138604
.1659885
L2 | -.0677189
.0531422
-1.27
0.203
-.1718757
.0364379
lrate
|
L1 |
.0000754
.0001927
0.39
0.696
-.0003022
.000453
L2 | -.0001645
.0001865
-0.88
0.378
-.00053
.0002011
lgdp
|
L1 |
.9302852
.2045396
4.55
0.000
.529395
1.331175
L2 |
-.160274
.1769645
-0.91
0.365
-.5071181
.1865701
lcon
|
L1 |
.0047614
.0198462
0.24
0.810
-.0341365
.0436592
L2 |
.000569
.0172256
0.03
0.974
-.0331925
.0343305
_q_2
|
.0001349
.0003465
0.39
0.697
-.0005442
.000814
_q_3
|
.0000478
.000419
0.11
0.909
-.0007734
.000869
_q_4
|
.0000322
.0001813
0.18
0.859
-.0003231
.0003876
_cons
|
.5750082
.4452303
1.29
0.197
-.297627
1.447643
-------------+---------------------------------------------------------------lcon
|
lloan
|
L1 |
-1.00662
.5403622
-1.86
0.062
-2.065711
.0524706
L2 |
1.114147
.6258854
1.78
0.075
-.1125662
2.34086
lrate
|
L1 | -.0035271
.0022691
-1.55
0.120
-.0079745
.0009203
L2 | -.0021112
.0021965
-0.96
0.336
-.0064162
.0021938
lgdp
|
L1 |
2.890635
2.408977
1.20
0.230
-1.830874
7.612143
L2 | -4.470218
2.08421
-2.14
0.032
-8.555195
-.3852413
lcon
|
L1 |
1.085324
.2337399
4.64
0.000
.6272024
1.543446
L2 | -.0913518
.2028751
-0.45
0.653
-.4889797
.306276
_q_2
|
.0017963
.0040808
0.44
0.660
-.0062019
.0097944
_q_3
| -.0179587
.0049346
-3.64
0.000
-.0276304
-.008287
_q_4
| -.0144019
.0021353
-6.74
0.000
-.0185869
-.0102169
_cons
|
4.021655
5.243726
0.77
0.443
-6.255859
14.29917
Table 1: Testing for number of lags
varsoc lloan lrate lgdp lcon, maxlag(3)
Selection order criteria
endogenous variables:
lloan lrate lgdp lcon
constant included in models
Sample: 1996q3
Obs = 20
2004q2, with gaps
------------------------------------------------------------------------------lag
LL
LR
df
p
FPE
AIC
HQIC
SBIC
------------------------------------------------------------------------------0
182.019
.
.
.
2.18e-13
-17.8019
-17.763
-17.6028
1
287.577 211.116
16 0.000 2.94e-17
-26.7577
-26.5633
-25.762
2
303.730
32.305
16 0.009 3.66e-17
-26.773
-26.4231
-24.9806
3
362.188 116.917*
16 0.000 1.08e-18* -31.0188* -30.5134* -28.4299*
Source: OECD maxdata 2004
Table 2: Testing for VAR stability
varstable
Eigenvalue stability condition
---------------------------------------------Eigenvalue
Modulus
----------------------------------------------.3669971 + .44064736
|
.57346052
-.3669971 - .44064736
|
.57346052
.3679289 + .43235172
|
.56771447
.3679289 - .43235172
|
.56771447
.8478558 + .14019235
|
.85936801
.8478558 - .14019235
|
.85936801
.9212941
|
.92129405
.4716963
|
.47169626
Source: OECD maxdata 2004

All the eigenvalues lie inside the unit circle, which means that VAR satisfies
stability condition.
Table 3: Testing for autocorrelation
vargranger
H0: no autocorrelation at lag order j
------------------------------------j
chi2
df
p
------------------------------------1
26.0522
16
0.05330
2
9.4846
16
0.03212
Source: OECD maxdata 2004
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In this test a 0 hypothesis tells that there is no autocorrelation at lag of
order j.
We test it at the 5% level so the p-values bigger than 0,05 means that
there is no autocorrelation in the model.
Table 4: Testing for Granger causality
varlmar
Granger causality Wald tests
---------------------------------------------------------------------------Equation
Excluded
chi2
df
Prob > chi2
---------------------------------------------------------------------------lloan
lrate
7.1690
2
0.0278
lloan
lgdp
0.1414
2
0.9318
lloan
lcon
0.8457
2
0.6552
lloan
ALL
19.0689
6
0.0040
---------------------------------------------------------------------------lrate
lloan
2.7777
2
0.2494
lrate
lgdp
3.3249
2
0.1897
lrate
lcon
6.3980
2
0.0408
lrate
ALL
6.8007
6
0.3397
---------------------------------------------------------------------------lgdp
lloan
2.7658
2
0.2509
lgdp
lrate
0.9085
2
0.6349
lgdp
lcon
2.7804
2
0.2490
lgdp
ALL
24.7132
6
0.0004
---------------------------------------------------------------------------lcon
lloan
3.8855
2
0.1433
lcon
lrate
11.6411
2
0.0030
lcon
lgdp
4.7092
2
0.0949
lcon
ALL
14.4984
6
0.0245
Source: OECD maxdata 2004
Graph 1: The temporal change of consumption in Hungary
(impulse- lcon, response- lloan)
varirf graph irf, i(lloan) r(lcon)
irf, lcon, lloan
.4
.2
0
-.2
0
2
4
6
step
95% CI
Graphs by irfname, impulse variable, and response
variable
Source: OECD maxdata 2004
irf
8
Graph 2: The permanent change of consumption in Hungary
(impulse- lcon, response- lloan)
varirf graph oirf, i(lloan) r(lcon)
irf, lcon, lloan
.001
.0005
0
-.0005
0
2
4
6
step
95% CI
Graphs by irfname, impulse variable, and response variable
Source: OECD maxdata 2004
orthogonalized irf
8
Graph 4: Trend line of interest rate since 1995q4 and
prediction for period (2004q1 till 2008q2)
0
19
95
19 q4
97
19 q1
98
19 q2
99
20 q3
00
20 q4
02
20 q1
03
20 q2
04
20 q3
05
20 q4
07
20 q1
08
q2
-1
-2
-3
-4
-5
-6
-7
-8
Source: OECD maxdata 2004
lrate
Graph 5: Trend line of a number of loans since 1995q4
and prediction for period (2004q1 till 2008q2)
2,73
2,72
2,71
2,7
2,69
2,68
2,67
2,66
2,65
2,64
2,63
Source: OECD maxdata 2004
2008q2
2007q1
2005q4
2004q3
2003q2
2002q1
2000q4
1999q3
1998q2
1997q1
1995q4
lloan
Graph 6: Trend line of GDP since 1995q4 and prediction for
period (2004q1 till 2008q2)
2,72
2,715
2,71
2,705
2,7
2,695
2,69
2,685
2,68
Source: OECD maxdata 2004
2008q2
2007q1
2005q4
2004q3
2003q2
2002q1
2000q4
1999q3
1998q2
1997q1
1995q4
lgdp
Graph 7: Trend line of consumption since 1995q4 and
prediction for period (2004q1 till 2008q2)
6
5
4
3
2
1
19
95
19 q4
97
19 q1
98
19 q2
99
20 q3
00
20 q4
02
20 q1
03
20 q2
04
20 q3
05
20 q4
07
20 q1
08
q2
0
Source: OECD maxdata 2004
lcon
Graph 8: Predicted trend lines for consumption and loans for period
2004q1 till 2008q2
6
5
4
3
LOANS
CONS
2
1
20
04
q
20 1
04
q
20 3
05
q
20 1
05
q
20 3
06
q
20 1
06
q
20 3
07
q
20 1
07
q
20 3
08
q1
0
Source: OECD maxdata 2004
Both trend lines seem to be very stable. While consumption is slightly
increasing the predicted amount of loans stays fairly constant and with hardly
noticeable the tendency to decrease.
Table 5: Comparison between data on consumption and
prediction (quarterly dataset January 2004 - October 2004)
January 04
April 04
July 04
October 04
OECD data
5,00739
5,01837
5,02886
5,03924
Prediction
5,00739
5,01784
5,01058
5,00267
Standard
Error
0
0,000106
0,003635
0,007257
Source: OECD maxdata 2004
Arguments for no lending boom
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There is no empirical evidence for the near future threat
according a possible lending boom in Hungary.
Undoubtedly , after the EURO adoption, the interest rate will
have to accommodate to the one in EMU but some adjustments
have already been accomplished.
There is smaller deviation from the interest rate of EMU
Hungary still have less developed financial market than the old
member state
Forecast is based on the internal outcome of the past events in
Hungary. Awareness of an external shock or unexpected twist in
domestic economy is the key issue for ruling elites.
The end
Now is time for applause! 