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**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

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Introduction

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**- 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 -

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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

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**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.

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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”

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**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”.

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**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”.

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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.

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**Structural VAR methodology**

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**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

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**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)

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**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)/ restrictions on B0

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**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.

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VAR MODEL

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**Lag order selection FPE - the final prediction error,**

. varsoc R lIPI lOP lM lP lREDEX Selection order criteria Sample: 1997m m Number of obs = |lag | LL LR df p FPE AIC HQIC SBIC | | | | 0 | e | | 1 | e * * | | 2 | e | | 3 | e-13* | | 4 | * e * | 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

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**VAR model - results . var R lIPI lOP lM lP lREDEX, lag(1/3) **

Vector autoregression Sample: 1997m m No. of obs = Log likelihood = AIC = FPE = 3.24e HQIC = Det(Sigma_ml) = 2.70e SBIC = Equation Parms RMSE R-sq chi2 P>chi2 R lIPI lOP lM lP lREDEX

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**------------------------------------------------------------------------------**

| Coef. Std. Err z P>|z| [95% Conf. Interval] R | L1 | L2 | L3 | lIPI | L1 | L2 | L3 | lOP | L1 | L2 | L3 | lM | L1 | L2 | (-) L3 | lP | L1 | L2 | L3 | lREDEX | L1 | L2 | L3 | _cons |

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**-------------+----------------------------------------------------------------**

lIPI | R | L1 | L2 | L3 | L1 | L2 | L3 | lOP | L1 | L2 | L3 | lM | L1 | L2 | L3 | lP | L1 | L2 | L3 | lREDEX | L1 | L2 | L3 | _cons |

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**-------------+----------------------------------------------------------------**

lOP | R | L1 | L2 | L3 | lIPI | L1 | L2 | L3 | L1 | L2 | L3 | lM | L1 | L2 | L3 | lP | L1 | L2 | L3 | lREDEX | L1 | L2 | L3 | _cons |

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**-------------+----------------------------------------------------------------**

lM | R | L1 | L2 | L3 | lIPI | L1 | L2 | L3 | lOP | L1 | L2 | L3 | L1 | L2 | L3 | lP | L1 | L2 | L3 | lREDEX | L1 | L2 | L3 | _cons |

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**-------------+----------------------------------------------------------------**

lP | R | L1 | L2 | L3 | lIPI | L1 | L2 | L3 | lOP | L1 | L2 | L3 | lM | (-) L1 | L2 | L3 | L1 | L2 | L3 | lREDEX | L1 | L2 | L3 | _cons |

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**-------------+----------------------------------------------------------------**

lREDEX | R | (+) L1 | L2 | L3 | lIPI | L1 | L2 | L3 | lOP | L1 | L2 | L3 | lM | L1 | L2 | L3 | lP | L1 | L2 | L3 | L1 | L2 | L3 | _cons |

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**The stability of the model**

. varstable Eigenvalue stability condition | Eigenvalue | Modulus | | | | i | | | i | | | i | | | i | | | i | | | i | | | i | | | i | | | | | | | | | i | | | i | | | i | | | i | | | i | | | i | | | i | | | i | | All the eigenvalues lie inside the unit circle VAR satisfies stability condition The stability of the model

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

. varlmar Lagrange-multiplier test | lag | chi2 df Prob > chi2 | | | | 1 | | | 2 | | H0: no autocorrelation at lag order

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**Impulse-response functions for VAR model**

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Structural VAR

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**1st model Equations: eOP = eIPI = eOP + eP = eIPI + **

eR = eOP + eIPI + eREDEX + eREDEX = eOP + eR +

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**Results . svar lOP lIPI lP R lREDEX, aeq(A)**

Estimating short-run parameters Sample: 1997m m Number of obs = Log likelihood = LR test of overidentifying restrictions LR chi2( 8) = Prob > chi = Equation Obs Parms RMSE R-sq chi P lOP lIPI lP R lREDEX VAR Model lag order selection statistics FPE AIC HQIC SBIC LL Det(Sigma_ml) 6.872e e-11 | Coef. Std. Err z P>|z| [95% Conf. Interval] a_2_ | _cons | a_4_ | _cons | a_5_ | _cons | a_3_ | _cons | a_4_ | _cons | a_5_ | (+) _cons | a_4_ | _cons | Results

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**2nd model Equations: eIPI = eOP + eP = eIPI + **

eR = eOP + eIPI + eREDEX + eREDEX = eOP + eIPI + eP + eR +

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**Results . svar lOP lIPI lP R lREDEX, aeq(A)**

Sample: 1997m m Number of obs = Log likelihood = LR test of overidentifying restrictions LR chi2( 6) = Prob > chi = Equation Obs Parms RMSE R-sq chi P lOP lIPI lP R lREDEX VAR Model lag order selection statistics FPE AIC HQIC SBIC LL Det(Sigma_ml) 6.872e e-11 | Coef. Std. Err z P>|z| [95% Conf. Interval] a_2_ | _cons | a_4_ | _cons | a_5_ | _cons | a_3_ | _cons | a_5_ | _cons | a_4_ | _cons | a_5_ | _cons | a_5_ | _cons | a_4_ | _cons | Results

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**Impulse-response functions for SVAR model**

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**3rd model Equations: eIPI = eOP + eP = eOP + eIPI + **

eM = eP + eR + eR = eOP + eM + eREDEX + eREDEX = eOP + eIPI + eP + eM + eR +

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**Results VAR Model lag order selection statistics**

FPE AIC HQIC SBIC LL Det(Sigma_ml) 3.598e e-14 | Coef. Std. Err z P>|z| [95% Conf. Interval] a_2_ | _cons | a_3_ | _cons | a_5_ | _cons | a_6_ | _cons | a_3_ | _cons | a_6_ | _cons | a_4_ | (+) _cons | a_6_ | _cons | a_5_ | _cons | a_6_ | _cons | a_4_ | _cons | a_6_ | (+) _cons | a_5_ | _cons | Results

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**Impulse-response functions for money in SVAR model**

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CONCLUSIONS

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**of responses functions**

Comparison of responses functions for VAR and SVAR models

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**SVAR responses functions:**

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**SVAR responses functions:**

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**SVAR responses functions:**

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**SVAR responses functions:**

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**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.

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