Agata STĘPIEŃ Bilge Kagan OZDEMIR Renata SADOWSKA Winfield TURPIN Structural VAR Modelling Of Monetary Policy For Small Open Economies: The Turkish Case Agata STĘPIEŃ Bilge Kagan OZDEMIR Renata SADOWSKA Winfield TURPIN

Introduction

- on account of the effects of monetary policy shocks - 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 -

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

Non-recursive VAR’s are called structural VAR (SVAR) models. 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 - 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) - a matrix polynomial in the lag operator L

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) 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 FPE - the final prediction error, . 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 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 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

------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- 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 | 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 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

-------------+---------------------------------------------------------------- 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 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

-------------+---------------------------------------------------------------- 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 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

-------------+---------------------------------------------------------------- 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 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

-------------+---------------------------------------------------------------- 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 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 ------------------------------------------------------------------------------

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 | | .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 The stability of the model

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

Structural VAR

1st model Equations: eOP =  eIPI = eOP +  eP = eIPI +  eR = eOP + eIPI + eREDEX +  eREDEX = eOP + eR + 

Results . 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 > 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 | .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

2nd model Equations: eIPI = eOP +  eP = eIPI +  eR = eOP + eIPI + eREDEX +  eREDEX = eOP + eIPI + eP + eR + 

Results . 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

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 Results

Impulse-response functions for money in SVAR model

CONCLUSIONS

of responses functions Comparison of responses functions for VAR and SVAR models

SVAR responses functions:

SVAR responses functions:

SVAR responses functions:

SVAR responses functions:

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.