Structural VAR Modelling Of Monetary Policy For Small Open Economies: The Turkish Case

1
Structural VAR Modelling Of Monetary Policy For
Small Open Economies The Turkish Case

• Agata STEPIEN
• Bilge Kagan OZDEMIR
• Renata SADOWSKA
• Winfield TURPIN

2
Introduction
3
VAR methodology

• Produces efficient results for small closed
  economies
• Provides uncertain empirical results for small
  open economies
• - on account of the effects of monetary policy
  shocks -

4
AIM to present why SVAR methodology is better
than VAR We investigate the utility of the
structural VAR approach in conventional empirical
puzzles

• The price puzzle
• The liquidity puzzle
• The exchange rate puzzle

5
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 VARs are called structural VAR
  (SVAR) models.

6
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

7
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.

8
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.

9
The data

• All of our estimations use monthly data for
  Turkey covering the period 19971 to 200412
• 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.

10
Structural VAR methodology
11
Structural VAR methodology

• pth order reduced form VAR
• 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) S
• the more compact form
• A(L) - a matrix polynomial in the lag operator L

12

• the structural form of VAR
• where
• B(L) - a pth order matrix polynomial in the lag
  operator
• ut - nx1 vector of structural innovations, with
  
• ut serially uncorrelated and diagonal
• The relationship between the structural and the
  reduced model
• B0A(L)B(L)
• B0eu
• S(B0-1)O(B0-1)

13

• 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(n1)/2 restrictions on B0

14

• 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.

15
VAR MODEL
16
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,

17
VAR model - results

• . var R lIPI lOP lM lP lREDEX, lag(1/3)
•  
• Vector autoregression
•  
• Sample 1997m4 2004m12
  No. of obs 93
• Log likelihood 661.0898
  AIC -11.76537
• FPE 3.24e-13
  HQIC -10.51187
• Det(Sigma_ml) 2.70e-14
  SBIC -8.660894
•  
• Equation Parms RMSE R-sq
  chi2 Pgtchi2
• --------------------------------------------------
  --------------
• 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
• --------------------------------------------------
  --------------

18

• --------------------------------------------------
  ----------------------------
• Coef. Std. Err. z
  Pgtz 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

19
-------------------------------------------------
---------------------------- lIPI R
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 lIPI 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 lOP 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 lM
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 lP 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 lREDEX 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 _cons
2.833139 .74151 3.82 0.000
1.379806 4.286472 ----------------------------
-------------------------------------------------
20
-------------------------------------------------
---------------------------- lOP R
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 lIPI 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 lOP 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 lM
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 lP
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 lREDEX 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 _cons
.4718347 .426531 1.11 0.269
-.3641508 1.30782 ---------------------------
--------------------------------------------------
21
-------------------------------------------------
---------------------------- lM R
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 lIPI 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 lOP 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 lM
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 lP
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 lREDEX 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 _cons -2.266752
.7802453 -2.91 0.004 -3.796005
-.7374992 ---------------------------------------
--------------------------------------
22
-------------------------------------------------
---------------------------- lP R
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 lIPI 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 lOP 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 lM
(-) 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 lP 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 lREDEX 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 _cons
.494224 .1392004 3.55 0.000
.2213962 .7670517 ----------------------------
-------------------------------------------------
23
-------------------------------------------------
---------------------------- lREDEX R
() 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 lIPI 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 lOP
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 lM
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 lP 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 lREDEX 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 _cons
.2481114 .4075865 0.61 0.543
-.5507434 1.046966 ----------------------------
--------------------------------------------------

24
The stability of the model

• . varstable
•  
• 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

25
Lagrange Multiplier test for autocorrelation
in the residuals of VAR model

• . varlmar
•  
• Lagrange-multiplier test
• --------------------------------------
• lag chi2 df Prob gt chi2
• -------------------------------------
• 1 50.2262 36 0.05795
• 2 35.3152 36 0.50097
• --------------------------------------
• H0 no autocorrelation at lag order

26
Impulse-response functions for VAR model
27
(No Transcript)
28
(No Transcript)
29
Structural VAR
30
1st model
Equations

• eOP ?
• eIPI eOP ?
• eP eIPI ?
• eR eOP eIPI eREDEX ?
• eREDEX eOP eR ?

31
. svar lOP lIPI lP R lREDEX, aeq(A) Estimating
short-run parameters   Sample 1997m3 2004m12
Number of obs 94
Log
likelihood -7512.638 LR test of
overidentifying restrictions LR chi2( 8)
16001.667
Prob gt 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 Pgtz 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
32
2nd model
Equations

• eIPI eOP ?
• eP eIPI ?
• eR eOP eIPI eREDEX ?
• eREDEX eOP eIPI eP eR ?

33
. 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 gt 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 Pgtz 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
34
Impulse-response functionsfor SVAR model
35
(No Transcript)
36
(No Transcript)
37
3rd model
Equations

• eIPI eOP ?
• eP eOP eIPI ?
• eM eP eR ?
• eR eOP eM eREDEX ?
• eREDEX eOP eIPI eP eM eR ?

38
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
  Pgtz 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
• -------------------------------------------------
  ----------------------------

39
Impulse-response functionsfor money in SVAR model
40
(No Transcript)
41
(No Transcript)
42
CONCLUSIONS
43
Comparison of responses functions for VAR and
SVAR models
44
SVAR responses functions
VAR responses functions
45
SVAR responses functions
VAR responses functions
46
SVAR responses functions
VAR responses functions
47
SVAR responses functions
VAR responses functions
48
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
• SVARs 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.