Transcript Structural VAR Modelling Of Monetary Policy For Small Open

Structural VAR Modelling
Of Monetary Policy
For Small Open Economies:
The Turkish Case
Agata STĘPIEŃ
Bilge Kagan OZDEMIR
Renata SADOWSKA
Winfield TURPIN
Introduction
VAR methodology:
i.
Produces efficient results for small closed
economies
ii. Provides uncertain empirical results for small
open economies
- on account of the effects of monetary policy shocks -
AIM: to present why SVAR
methodology is better than VAR
We investigate the utility
of the structural VAR approach in
conventional empirical puzzles:
i. The price puzzle
ii. The liquidity puzzle
iii. The exchange rate puzzle
Empirical Puzzles
• Result from the recursive structure implied by the
standard identification procedure of VAR models
• Non-recursive identification schemes effectively
solve these puzzles:
Non-recursive VAR’s are called structural VAR (SVAR) models.
Price Puzzle
Sims (1992)
In various empirical VAR studies, a contractionary
monetary shock causes a persistent increase in
price level rather than a decrease.
This odd response of the price level to a
restrictive monetary policy shock is called “the
price puzzle”
The Liquidity Puzzle
Leeper & Gordon (1992)
A similar anomaly has been observed in the
response of interest rates to a shock to
monetary aggregates. Following an
expansionary shock to the money variable,
the interest rate exhibits a positive response
creating “the liquidity puzzle”.
The Exchange Rate Puzzle
Grilli and Roubini (1995) & Sims (1992)
In an open economy environment a
positive innovation in interest rates seems
to result in a depreciation of the local
currency rather than an appreciation. This is
“the exchange rate puzzle”.
The data
All of our estimations use monthly data for Turkey covering the period 1997:1
to 2004:12
IPI : Industrial production index
P : Wholesale price index
M : Monetary aggregate (M1)
R : Short-term interest rates (overnight rates)
REDEX : Real effective exchange rate index
EX : Nominal exchange rate
All variables are in logarithm levels except the short-term rate.
Structural VAR methodology
Structural VAR methodology
• pth order reduced form VAR:
yt  A1 yt 1  ........ Ap yt k  et
yt - n x 1 vector of endogenous variables
Ai - the coefficient vector of lagged variables yt - p
et - the vector of serially uncorrelated reduced form errors
with (etet`) = Σ
• the more compact form:
A( L) yt  et
A(L) - a matrix polynomial in the lag operator L
the structural form of VAR:
B( L) yt  ut
where:
B(L) - a pth order matrix polynomial in the lag operator
B( L)  B0  B1 L  B2 L2  ...  BP LP
ut - nx1 vector of structural innovations, with:
Eut ut'   
ut – serially uncorrelated and diagonal
• The relationship between the structural and the reduced
model
B0A(L)=B(L)
B0e=u
Σ=(B0-1)Ω(B0-1)
Imposing parameter restictions
Cholesky decomposition - orthogonalizing the covariance
matrix of reduced form residuals 
- gives an exactly identified system,
- implies a recursive structure among the variables of the
system.
structural VAR
- allows us to use a non-recursive structure
- we identify the model by imposing short-run restrictions on
B0, or long-run restrictions on B1
Kim and Roubini (2000): indentification = at least n(n+1)/2
restrictions on B0
Determining the set of restrictions on B0
2 approaches:
(i) an explicit macroeconomic model (Gal (1992))
(ii) choosing restrictions based on the structure of the
economy ((Leeper et al. (1996) and Kim and Roubini
(2000)).
- restrictions, which produce the results consistent with
economic theories,
- restrictions, which are not rejected by data.
VAR MODEL
Lag order selection
. varsoc
R lIPI lOP lM lP lREDEX
Selection order criteria
Sample: 1997m5 2004m12
Number of obs
=
92
+---------------------------------------------------------------------------+
|lag |
LL
LR
df
p
FPE
AIC
HQIC
SBIC
|
|----+----------------------------------------------------------------------|
| 0 | -144.842
1.1e-06
3.27918
3.34556
3.44364 |
| 1 | 560.092 1409.9
36 0.000 5.2e-13 -11.2629 -10.7982* -10.1116* |
| 2 | 613.131 106.08
36 0.000 3.6e-13 -11.6333 -10.7703 -9.49523 |
| 3 | 653.409 80.557
36 0.000 3.4e-13* -11.7263 -10.4651 -8.60145 |
| 4 | 689.552 72.286* 36 0.000 3.5e-13 -11.7294* -10.0699 -7.61777 |
+---------------------------------------------------------------------------+
Endogenous: R lIPI lOP lM lP lREDEX
Exogenous: _cons
FPE - the final prediction error,
AIC - Akaike's information criterion,
BIC - the Bayesian information criterion,
HQIC - the Hannan and Quinn information criterion
VAR model - results
. var R lIPI lOP lM lP lREDEX, lag(1/3)
Vector autoregression
Sample: 1997m4 2004m12
Log likelihood = 661.0898
FPE
= 3.24e-13
Det(Sigma_ml) = 2.70e-14
No. of obs
AIC
HQIC
SBIC
Equation
Parms
RMSE
R-sq
chi2
P>chi2
---------------------------------------------------------------R
19
13.2301
0.6380
163.8826
0.0000
lIPI
19
.061535
0.7297
251.0798
0.0000
lOP
19
.035396
0.9984
59819.36
0.0000
lM
19
.064749
0.9967
28285.83
0.0000
lP
19
.011552
0.9998
586895.1
0.0000
lREDEX
19
.033824
0.9253
1152.253
0.0000
----------------------------------------------------------------
=
93
= -11.76537
= -10.51187
= -8.660894
-----------------------------------------------------------------------------|
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------R
|
R
|
L1 |
.3995304
.1014779
3.94
0.000
.2006374
.5984235
L2 |
.1809653
.1187785
1.52
0.128
-.0518363
.4137668
L3 |
.15915
.118526
1.34
0.179
-.0731568
.3914567
lIPI
|
L1 |
13.37996
21.50408
0.62
0.534
-28.76726
55.52718
L2 |
6.803307
20.3533
0.33
0.738
-33.08843
46.69504
L3 | -19.84411
19.33525
-1.03
0.305
-57.74049
18.05228
lOP
|
L1 |
13.18471
74.09397
0.18
0.859
-132.0368
158.4062
L2 | -3.072712
111.4021
-0.03
0.978
-221.4168
215.2713
L3 |
1.81071
79.20603
0.02
0.982
-153.4302
157.0517
lM
|
L1 | -30.20778
19.80261
-1.53
0.127
-69.02018
8.60462
L2 | -18.16114
21.20074
-0.86
0.392
-59.71382
23.39154
(-)
L3 |
57.92457
19.6259
2.95
0.003
19.45851
96.39063
lP
|
L1 | -65.59419
125.1523
-0.52
0.600
-310.8882
179.6998
L2 |
.4824675
193.7531
0.00
0.998
-379.2667
380.2316
L3 |
38.10159
114.4841
0.33
0.739
-186.2831
262.4863
lREDEX
|
L1 |
24.63748
72.7621
0.34
0.735
-117.9736
167.2486
L2 | -52.32018
110.568
-0.47
0.636
-269.0294
164.389
L3 |
10.48087
74.28239
0.14
0.888
-135.1099
156.0717
_cons
|
233.4477
159.4269
1.46
0.143
-79.02332
545.9188
-------------+----------------------------------------------------------------
lIPI
|
R
|
lIPI
lOP
lM
lP
lREDEX
L1 |
-.0011091
.000472
-2.35
0.019
-.0020341
-.000184
L2 |
-.0010219
.0005525
-1.85
0.064
-.0021047
.0000609
L3 |
-.0000996
.0005513
-0.18
0.857
-.00118
.0009809
L1 |
.2043341
.1000175
2.04
0.041
.0083033
.4003649
L2 |
.2637963
.0946652
2.79
0.005
.078256
.4493366
L3 |
-.1599971
.0899301
-1.78
0.075
-.3362569
.0162626
L1 |
.1363438
.3446182
0.40
0.692
-.5390954
.811783
L2 |
-.0293313
.5181417
-0.06
0.955
-1.04487
.9862078
L3 |
-.4743676
.3683948
-1.29
0.198
-1.196408
.247673
L1 |
-.2818191
.0921038
-3.06
0.002
-.4623393
-.1012989
L2 |
-.0029148
.0986067
-0.03
0.976
-.1961804
.1903507
L3 |
.1458815
.091282
1.60
0.110
-.0330278
.3247909
L1 |
-.4241252
.5820954
-0.73
0.466
-1.565011
.7167609
L2 |
.6964245
.9011644
0.77
0.440
-1.069825
2.462674
L3 |
.2978765
.5324765
0.56
0.576
-.7457583
1.341511
L1 |
-.117054
.3384235
-0.35
0.729
-.7803519
.5462439
L2 |
.0968535
.5142622
0.19
0.851
-.9110818
1.104789
L3 |
-.3506112
.3454945
-1.01
0.310
-1.027768
.3265457
|
|
|
|
|
lOP
|
R
|
lIPI
lOP
lM
lP
lREDEX
L1 |
.0011678
.0002715
4.30
0.000
.0006356
.0016999
L2 |
-.0008104
.0003178
-2.55
0.011
-.0014332
-.0001875
L3 |
.0011107
.0003171
3.50
0.000
.0004892
.0017323
L1 |
.012352
.057532
0.21
0.830
-.1004087
.1251127
L2 |
-.0109391
.0544533
-0.20
0.841
-.1176655
.0957873
L3 |
-.0732841
.0517295
-1.42
0.157
-.1746721
.028104
L1 |
1.333208
.1982311
6.73
0.000
.9446823
1.721734
L2 |
-.9057044
.2980452
-3.04
0.002
-1.489862
-.3215465
L3 |
.6686133
.2119079
3.16
0.002
.2532815
1.083945
L1 |
.0881565
.0529799
1.66
0.096
-.0156822
.1919953
L2 |
.0251405
.0567205
0.44
0.658
-.0860296
.1363106
L3 |
.0643267
.0525072
1.23
0.221
-.0385855
.1672388
L1 |
-.4812317
.3348327
-1.44
0.151
-1.137492
.1750283
L2 |
.79044
.5183674
1.52
0.127
-.2255415
1.806421
L3 |
-.6453991
.3062909
-2.11
0.035
-1.245718
-.0450799
L1 |
-.1132399
.1946678
-0.58
0.561
-.4947818
.268302
L2 |
-.0643379
.2958137
-0.22
0.828
-.644122
.5154462
L3 |
.4465974
.1987352
2.25
0.025
.0570836
.8361113
|
|
|
|
|
lM
|
R
|
lIPI
lOP
lM
lP
lREDEX
L1 |
-.0002212
.0004966
-0.45
0.656
-.0011946
.0007522
L2 |
.0004955
.0005813
0.85
0.394
-.0006438
.0016349
L3 |
-.0000379
.0005801
-0.07
0.948
-.0011748
.001099
L1 |
.1994379
.1052423
1.90
0.058
-.0068332
.405709
L2 |
-.1596862
.0996103
-1.60
0.109
-.3549188
.0355464
L3 |
.2012161
.0946279
2.13
0.033
.0157488
.3866833
L1 |
.369864
.3626205
1.02
0.308
-.3408591
1.080587
L2 |
.1119453
.5452086
0.21
0.837
-.9566439
1.180535
L3 |
-.3698579
.3876392
-0.95
0.340
-1.129617
.389901
L1 |
.4052211
.0969152
4.18
0.000
.2152709
.5951714
L2 |
.2263902
.1037577
2.18
0.029
.0230288
.4297516
L3 |
.2045462
.0960504
2.13
0.033
.0162909
.3928015
L1 |
-.8188753
.6125032
-1.34
0.181
-2.01936
.3816089
L2 |
1.453369
.9482399
1.53
0.125
-.4051467
3.311885
L3 |
-.5771145
.5602923
-1.03
0.303
-1.675267
.5210382
L1 |
.2498104
.3561022
0.70
0.483
-.4481371
.947758
L2 |
.1801751
.5411264
0.33
0.739
-.8804131
1.240763
L3 |
-.160013
.3635426
-0.44
0.660
-.8725434
.5525175
|
|
|
|
|
lP
|
R
|
lIPI
lOP
lM
(-)
lP
lREDEX
L1 |
.0002657
.0000886
3.00
0.003
.0000921
.0004394
L2 |
-.0002623
.0001037
-2.53
0.011
-.0004655
-.000059
L3 |
.000144
.0001035
1.39
0.164
-.0000588
.0003468
L1 |
-.0203368
.0187759
-1.08
0.279
-.0571368
.0164632
L2 |
-.0050536
.0177711
-0.28
0.776
-.0398843
.029777
L3 |
-.0010808
.0168822
-0.06
0.949
-.0341693
.0320077
L1 |
.2226912
.0646937
3.44
0.001
.095894
.3494885
L2 |
-.3624083
.0972685
-3.73
0.000
-.553051
-.1717656
L3 |
.1525029
.0691571
2.21
0.027
.0169573
.2880484
L1 |
.0503055
.0172902
2.91
0.004
.0164172
.0841938
L2 |
-.0221363
.018511
-1.20
0.232
-.0584172
.0141445
L3 |
.0114683
.017136
0.67
0.503
-.0221175
.0450542
L1 |
1.338255
.1092742
12.25
0.000
1.124081
1.552429
L2 |
-.3782558
.1691716
-2.24
0.025
-.7098261
-.0466855
L3 |
-.0231389
.0999595
-0.23
0.817
-.2190559
.172778
L1 |
.0515253
.0635308
0.81
0.417
-.0729927
.1760433
L2 |
-.0944245
.0965402
-0.98
0.328
-.2836398
.0947907
L3 |
.0192958
.0648582
0.30
0.766
-.1078238
.1464155
|
|
|
|
|
lREDEX
|
R
|
(+)
lIPI
lOP
lM
lP
lREDEX
L1 |
-.0010795
.0002594
-4.16
0.000
-.001588
-.000571
L2 |
.0006899
.0003037
2.27
0.023
.0000948
.0012851
L3 |
-.0009764
.000303
-3.22
0.001
-.0015703
-.0003825
L1 |
-.0380951
.0549767
-0.69
0.488
-.1458476
.0696573
L2 |
-.0258617
.0520347
-0.50
0.619
-.1278478
.0761244
L3 |
.1137401
.049432
2.30
0.021
.0168552
.210625
L1 |
-.0400498
.1894266
-0.21
0.833
-.4113191
.3312195
L2 |
.3524744
.2848075
1.24
0.216
-.2057379
.9106868
L3 |
-.3852534
.2024959
-1.90
0.057
-.7821382
.0116313
L1 |
-.0514458
.0506268
-1.02
0.310
-.1506725
.0477809
L2 |
-.0421617
.0542012
-0.78
0.437
-.1483941
.0640707
L3 |
-.039677
.050175
-0.79
0.429
-.1380183
.0586643
L1 |
.6439002
.319961
2.01
0.044
.0167882
1.271012
L2 |
-.8925327
.4953439
-1.80
0.072
-1.863389
.0783236
L3 |
.4943425
.2926869
1.69
0.091
-.0793132
1.067998
L1 |
1.32148
.1860216
7.10
0.000
.9568841
1.686075
L2 |
-.3721302
.282675
-1.32
0.188
-.926163
.1819025
L3 |
-.2428434
.1899083
-1.28
0.201
-.6150568
.1293701
|
|
|
|
|
. varstable
The stability
of the model
Eigenvalue stability condition
+----------------------------------------+
|
Eigenvalue
|
Modulus
|
|--------------------------+-------------|
|
.9941794 + .0143843i |
.994283
|
|
.9941794 - .0143843i |
.994283
|
|
.8836465 + .1336579i |
.893698
|
|
.8836465 - .1336579i |
.893698
|
|
.6276038 + .4060743i |
.747518
|
|
.6276038 - .4060743i |
.747518
|
| -.3011287 + .5766123i |
.650508
|
| -.3011287 - .5766123i |
.650508
|
| -.6301265
|
.630126
|
|
.6223038
|
.622304
|
|
.3939734 + .4414872i |
.591714
|
|
.3939734 - .4414872i |
.591714
|
|
.1893117 + .5121128i |
.545984
|
|
.1893117 - .5121128i |
.545984
|
| -.2825017 + .3782144i |
.472073
|
| -.2825017 - .3782144i |
.472073
|
| -.0001588 + .3392226i |
.339223
|
| -.0001588 - .3392226i |
.339223
|
+----------------------------------------+
All the eigenvalues lie inside the unit
circle
VAR satisfies stability condition
Lagrange Multiplier test for
autocorrelation in the
residuals of VAR model
. varlmar
Lagrange-multiplier test
+--------------------------------------+
| lag |
chi2
df
Prob > chi2 |
|------+-------------------------------|
|
1 |
50.2262
36
0.05795
|
|
2 |
35.3152
36
0.50097
|
+--------------------------------------+
H0: no autocorrelation at lag order
Impulse-response functions
for VAR model
irf, lIPI, R
irf, lIPI, lREDEX
.2
50
0
0
-.2
-50
-.4
0
2
4
6
8
0
2
4
step
95% CI
6
8
step
impulse response function (irf)
95% CI
Graphs by irfname, impulse variable, and response variable
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
irf, lP, lREDEX
irf, lP, R
3
200
2
0
1
-200
0
-400
0
2
4
6
8
0
2
step
95% CI
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
4
6
step
95% CI
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
8
irf, R, R
irf, R, lREDEX
1
0
-.001
.5
-.002
-.003
0
0
2
4
6
8
0
2
step
95% CI
4
6
8
step
impulse response function (irf)
95% CI
Graphs by irfname, impulse variable, and response variable
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
irf, lREDEX, R
irf, lREDEX, lREDEX
200
2
100
1
0
0
-100
-200
-1
0
2
4
6
8
0
2
step
95% CI
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
4
6
step
95% CI
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
8
Structural VAR
1st model
Equations:
•eOP = 
•eIPI = eOP + 
•eP = eIPI + 
• eR = eOP + eIPI + eREDEX + 
•eREDEX = eOP + eR + 
. svar lOP lIPI lP R lREDEX, aeq(A)
Estimating short-run parameters
Sample:
1997m3
2004m12
LR test of overidentifying restrictions
Number of obs
Log likelihood
LR chi2( 8)
Prob > chi2
=
=
=
=
94
-7512.638
16001.667
0.0000
-------------------------------------------------------------------------Equation
Obs Parms
RMSE
R-sq
chi2
P
-------------------------------------------------------------------------lOP
94
11
.038518
0.9980
47749.65
0.0000
lIPI
94
11
.063011
0.6828
202.3791
0.0000
lP
94
11
.012667
0.9998
459943
0.0000
R
94
11
13.2022
0.5966
139.0212
0.0000
lREDEX
94
11
.035579
0.9093
942.5407
0.0000
-------------------------------------------------------------------------VAR Model lag order selection statistics
---------------------------------------FPE
AIC
HQIC
SBIC
6.872e-11 -9.2169243
-8.6158416
-7.7288263
LL
488.19544
Det(Sigma_ml)
2.121e-11
-----------------------------------------------------------------------------|
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------a_2_1
|
_cons |
.118268
.1031421
1.15
0.252
-.0838868
.3204229
-------------+---------------------------------------------------------------a_4_1
|
_cons |
-72.5256
.3379927 -214.58
0.000
-73.18806
-71.86315
-------------+---------------------------------------------------------------a_5_1
|
_cons | -1.369489
.1313077
-10.43
0.000
-1.626847
-1.11213
-------------+---------------------------------------------------------------a_3_2
|
_cons |
.0155035
.1024283
0.15
0.880
-.1852522
.2162592
-------------+---------------------------------------------------------------a_4_3
|
_cons |
127.3628
.8188706
155.53
0.000
125.7579
128.9678
-------------+---------------------------------------------------------------a_5_4
|
(+)
_cons |
.0620754
.0018962
32.74
0.000
.058359
.0657917
-------------+---------------------------------------------------------------a_4_5
|
_cons | -22.80443
.248202
-91.88
0.000
-23.2909
-22.31796
------------------------------------------------------------------------------
Results
nd
2
Equations:
model
•eIPI = eOP + 
•eP = eIPI + 
• eR = eOP + eIPI + eREDEX + 
•eREDEX = eOP + eIPI + eP + eR + 
. svar lOP lIPI lP R lREDEX, aeq(A)
Sample: 1997m3 2004m12
Number of obs
=
94
Log likelihood
= -7660.8406
LR test of overidentifying restrictions
LR chi2( 6)
= 16298.072
Prob > chi2
=
0.0000
-------------------------------------------------------------------------Equation
Obs Parms
RMSE
R-sq
chi2
P
-------------------------------------------------------------------------lOP
94
11
.038518
0.9980
47749.65
0.0000
lIPI
94
11
.063011
0.6828
202.3791
0.0000
lP
94
11
.012667
0.9998
459943
0.0000
R
94
11
13.2022
0.5966
139.0212
0.0000
lREDEX
94
11
.035579
0.9093
942.5407
0.0000
-------------------------------------------------------------------------VAR Model lag order selection statistics
---------------------------------------FPE
AIC
HQIC
SBIC
LL
Det(Sigma_ml)
6.872e-11 -9.2169243
-8.6158416
-7.7288263
488.19544
2.121e-11
-----------------------------------------------------------------------------|
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------a_2_1
|
_cons |
1.01558
.1031421
9.85
0.000
.8134252
1.217735
-------------+---------------------------------------------------------------a_4_1
|
_cons |
1.251037
.1571423
7.96
0.000
.943044
1.559031
-------------+---------------------------------------------------------------a_5_1
|
_cons |
.4819695
.1485563
3.24
0.001
.1908045
.7731345
-------------+---------------------------------------------------------------a_3_2
|
_cons |
1.073148
.0723666
14.83
0.000
.9313118
1.214984
-------------+---------------------------------------------------------------a_5_2
|
_cons | -2.099263
.2086427
-10.06
0.000
-2.508195
-1.690331
-------------+---------------------------------------------------------------a_4_3
|
_cons |
1.762008
.1202497
14.65
0.000
1.526322
1.997693
-------------+---------------------------------------------------------------a_5_3
|
_cons |
.5360897
.1105982
4.85
0.000
.3193211
.7528582
-------------+---------------------------------------------------------------a_5_4
|
_cons | -.0125239
.0443363
-0.28
0.778
-.0994214
.0743736
-------------+---------------------------------------------------------------a_4_5
|
_cons |
1.574081
.0619692
25.40
0.000
1.452623
1.695538
------------------------------------------------------------------------------
Results
Impulse-response functions
for SVAR model
irf, lIPI, R
irf, lIPI, lREDEX
50
.3
.2
.1
0
0
-.1
-50
0
2
4
6
8
0
2
4
step
95% CI
6
8
6
8
step
irf
95% CI
Graphs by irfname, impulse variable, and response variable
irf
Graphs by irfname, impulse variable, and response variable
irf, lP, R
irf, lP, lREDEX
3
100
0
2
-100
1
-200
0
-300
0
2
4
6
95% CI
Graphs by irfname, impulse variable, and response variable
8
0
2
4
step
step
irf
95% CI
Graphs by irfname, impulse variable, and response variable
irf
irf, R, R
irf, R, lREDEX
1
.001
0
.5
-.001
-.002
0
0
2
4
6
8
0
step
2
4
6
8
6
8
step
95% CI
irf
95% CI
irf
Graphs by irfname, impulse variable, and response variable
Graphs by irfname, impulse variable, and response variable
irf, lREDEX, lREDEX
irf, lREDEX, R
2
200
100
1
0
0
-100
-1
-200
0
2
4
6
Graphs by irfname, impulse variable, and response variable
0
2
4
step
step
95% CI
8
irf
95% CI
Graphs by irfname, impulse variable, and response variable
irf
3rd model
Equations:
•eIPI = eOP + 
•eP = eOP + eIPI + 
•eM = eP + eR + 
•eR = eOP + eM + eREDEX + 
•eREDEX = eOP + eIPI + eP + eM + eR + 
Results
VAR Model lag order selection statistics
---------------------------------------FPE
AIC
HQIC
SBIC
LL
Det(Sigma_ml)
3.598e-13 -11.636792
-10.784347
-9.5263982
624.92921
6.770e-14
-----------------------------------------------------------------------------|
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------a_2_1
|
_cons |
.0135702
.1031421
0.13
0.895
-.1885846
.2157251
-------------+---------------------------------------------------------------a_3_1
|
_cons | -.1462277
.1031516
-1.42
0.156
-.3484012
.0559457
-------------+---------------------------------------------------------------a_5_1
|
_cons |
39.04031
.3636957
107.34
0.000
38.32748
39.75314
-------------+---------------------------------------------------------------a_6_1
|
_cons |
2.069827
.1633726
12.67
0.000
1.749622
2.390031
-------------+---------------------------------------------------------------a_3_2
|
_cons |
.0009657
.1031421
0.01
0.993
-.2011892
.2031205
-------------+---------------------------------------------------------------a_6_2
|
_cons |
.1058091
.1034304
1.02
0.306
-.0969108
.3085291
-------------+---------------------------------------------------------------a_4_3
|
(+)
_cons |
1.949205
.2572013
7.58
0.000
1.445099
2.45331
-------------+---------------------------------------------------------------a_6_3
|
_cons |
20.60607
1.519741
13.56
0.000
17.62744
23.58471
-------------+---------------------------------------------------------------a_5_4
|
_cons |
34.16626
.0843784
404.92
0.000
34.00088
34.33163
-------------+---------------------------------------------------------------a_6_4
|
_cons | -15.77592
1.177115
-13.40
0.000
-18.08303
-13.46882
-------------+---------------------------------------------------------------a_4_5
|
_cons |
.0816462
.0058645
13.92
0.000
.070152
.0931405
-------------+---------------------------------------------------------------a_6_5
|
(+)
_cons | -.0073892
.0085119
-0.87
0.385
-.0240723
.0092939
-------------+---------------------------------------------------------------a_5_6
|
_cons |
113.1403
.9599074
117.87
0.000
111.2589
115.0217
------------------------------------------------------------------------------
Impulse-response functions
for money in SVAR model
irf, lM, lIPI
irf, lM, R
.2
40
20
0
0
-.2
-20
-40
-.4
0
2
4
6
8
0
2
4
step
95% CI
irf
95% CI
Graphs by irfname, impulse variable, and response variable
Graphs by irfname, impulse variable, and response variable
irf, lM, lP
.3
.2
.1
0
0
6
step
2
4
6
step
95% CI
Graphs by irfname, impulse variable, and response variable
irf
8
irf
8
irf, lM, lM
1
.5
0
0
2
4
6
8
step
95% CI
irf
Graphs by irfname, impulse variable, and response variable
irf, lM, lREDEX
.1
2.776e-17
-.1
-.2
-.3
0
2
4
6
step
95% CI
Graphs by irfname, impulse variable, and response variable
irf
8
CONCLUSIONS
Comparison
of responses functions
for VAR and SVAR models
SVAR responses functions:
irf, lIPI, R
irf, lIPI, lREDEX
50
.3
.2
.1
0
0
-.1
-50
0
2
4
6
8
0
2
4
step
95% CI
6
8
step
irf
95% CI
Graphs by irfname, impulse variable, and response variable
irf
Graphs by irfname, impulse variable, and response variable
VAR responses functions:
irf, lIPI, R
irf, lIPI, lREDEX
50
.2
0
0
-.2
-50
-.4
0
2
4
6
8
0
2
step
95% CI
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
4
6
step
95% CI
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
8
SVAR responses functions:
irf, lP, lREDEX
irf, lP, R
3
100
0
2
-100
1
-200
0
-300
0
2
4
6
8
0
2
4
step
6
step
95% CI
irf
95% CI
Graphs by irfname, impulse variable, and response variable
irf
Graphs by irfname, impulse variable, and response variable
VAR responses functions:
irf, lP, R
irf, lP, lREDEX
200
3
0
2
1
-200
0
-400
0
2
4
6
8
0
2
95% CI
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
4
6
step
step
95% CI
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
8
8
SVAR responses functions:
irf, R, R
irf, R, lREDEX
1
.001
0
.5
-.001
-.002
0
0
2
4
6
8
0
2
4
step
6
step
95% CI
irf
95% CI
Graphs by irfname, impulse variable, and response variable
irf
Graphs by irfname, impulse variable, and response variable
VAR responses functions:
irf, R, R
irf, R, lREDEX
1
0
-.001
.5
-.002
0
-.003
0
2
4
6
8
0
2
step
95% CI
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
4
6
step
95% CI
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
8
8
SVAR responses functions:
irf, lREDEX, R
irf, lREDEX, lREDEX
200
2
100
1
0
0
-100
-200
-1
0
2
4
6
8
0
2
4
step
95% CI
6
8
step
irf
95% CI
Graphs by irfname, impulse variable, and response variable
irf
Graphs by irfname, impulse variable, and response variable
VAR responses functions:
irf, lREDEX, R
irf, lREDEX, lREDEX
200
2
100
1
0
0
-100
-1
-200
0
2
4
6
8
0
2
step
95% CI
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
4
6
step
95% CI
impulse response function (irf)
Graphs by irfname, impulse variable, and response variable
8
Why SVAR is better than VAR?
VAR MODELS:
• it is often difficult to draw any conclusion from the large number of
coefficient estimates in a VAR system,
• vector autoregressions have the status of „reduced form'' and, thus, are
merely vehicles to summarize the dynamic properties of the data,
• the parameters do not have an economic meaning and are subject
to the so-called „Lucas critique'‘.
SVAR MODELS:
• SVAR’s do not contain fixed-coefficient expectational rules. They
are best thought of as giving linear approximations to the behavior of the
private sector and monetary authorities. The private behavior they model
thus implicitly includes dynamics arising from revision in forecasting
rules as well as other sources of dynamics.