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The Academy of Economic Studies Bucharest Doctoral School of Banking and Finance

The Academy of Economic Studies Bucharest Doctoral School of Banking and Finance. DISSERTATION PAPER CENTRAL BANK REACTION FUNCTION MSc. Student: ANDRA SERBAN Supervisor: Prof. MOISĂ ALTĂR. Contents. Introduction Review of the concepts The optimal linear regulator problem

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The Academy of Economic Studies Bucharest Doctoral School of Banking and Finance

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  1. The Academy of Economic Studies BucharestDoctoral School of Banking and Finance DISSERTATION PAPER CENTRAL BANK REACTION FUNCTION MSc. Student: ANDRA SERBAN Supervisor: Prof. MOISĂ ALTĂR

  2. Contents • Introduction • Review of the concepts • The optimal linear regulator problem • Model specification • Empirical estimation • Conclusion

  3. Introduction The purpose of this paper was to determine an explicit instrument rule and to compare it to an optimal monetary policy rule (reaction function) .

  4. Review of the concepts Reaction function: describes the systematic components of economic policy in a formal model, i.e. equation. (DJC Smant 2003)

  5. General approach In this approach, reaction functions are not different than policy rules, specifying how the central bank should adjust its instrument(s) as a function of the state of the economy.

  6. Rudebusch and Svensson (1998) describes 2 types of rules: • Instrument rules: The monetary policy instrument is expressesd as an explicit function of available information 2. Targeting rules Central bank is assigned to minimize a loss function that is increasing in the deviation between a target variable and the target level for this variable.

  7. Instrument rules: It = C + B(L)Zt-1 +Ut C – vector of constant B(L) – polynomial distributed lag Zt-1 – the central bank information at t-1 It – the central bank policy instruments Ut – white noise It : - the interest rate Taylor (1993), (1999); Henderson-McKibbin (1993) - the monetary aggregate McCallum (1984), (1987); Meltzer (1984), (1987) - domestic credit Jaffee and Russell (1976); Keeton(1979); Stiglitz Weiss (1981)

  8. Targeting rules where β- discount factor, 0<β<1 Et- expectation operator x - targeting variable x* - target level for variable x it - instrument

  9. Optimal control approach More specifically, reaction functions can be regarded as solutions to an optimal control approach to monetary policy. Tinbergen (1952), Theil (1964), Klein (1965)

  10. THE OPTIMAL LINEAR REGULATOR PROBLEM

  11. THE OPTIMAL LINEAR REGULATOR PROBLEM If the system admits a solution (V, W, R) so that R is semipositive defined (R0) and A+BF has the |eigenvalues|<1, than the command ut=FXt stabilize the system and minimize the cost J(u).

  12. From the system we obtain the Matrix Riccati Difference equation: which is solved by the DLQRRICCATI (Discrete Linear Quadratic Regulator) algorithm in Matlab

  13. MODEL SPECIFICATION The model is an extension of Ball(1998) for an open economy: IS

  14. The Loss Function Acording to Rudenbusch and Svensson (1998) I considered the following cost function of the central bank  :

  15. Empirical estimation • The data sample covers the period 1996:01 – 2002:12 • All time series are based on monthly observation.

  16. TIME SERIES USED

  17. TIME SERIES USED

  18. Unit Root Tests model

  19. IS estimation

  20. System estimation by WTSLS Equation: INFL=C(1)*INFL(-1)+C(2)*DIF_CSR(-1)+C(3)*DUMCENTRAT+ +C(4)*OUTPUT_GAP(-1)+C(5) Observations: 82 R-squared 0.819670 Mean dependent var 0.035248 Adjusted R-squared0.810302S.D. dependent var0.036597 S.E. of regression0.015940Sum squared resid0.019564 Durbin-Watson stat1.731411 Equation: DIF_CSR=C(6)*DIF_CSR(-1)+C(7)*RRA+C(8)*DUMCENTRAT Observations: 82 R-squared 0.604270 Mean dependent var -0.003343 Adjusted R-squared0.594252S.D. dependent var0.057243 S.E. of regression0.036463Sum squared resid0.105032 Durbin-Watson stat 1.992943 Equation: DIF_RA=C(9)+C(10)*INFL(-1)+C(11)*DIF_CSR(-1)+DIF_RA(-1)*C(12) Observations: 82 R-squared 0.628309 Mean dependent var -0.000269 Adjusted R-squared 0.614013 S.D. dependent var 0.005344 S.E. of regression 0.003320 Sum squared resid 0.000860 Durbin-Watson stat 2.044055

  21. Estimated Model IS • OUTPUT_GAP =0.655049*OUTPUT_GAP(-1) -0.247160*RRA(-1)+ +0.179965* DIF_CSR PHILLIPS • INFL=0.638493*INFL(-1)+ 0.284684*DIF_CSR(-1)-0.099128*DUMCENTRAT +0.176756*OUTPUT_GAP(-1)+0.012691 REAL EXCHANGE RATE EQUATION • DIF_CSR=0.173626*DIF_CSR(-1) -0.455091*RRA+0.466524*DUMCENTRAT IR • DIF_RA=-0.001541+ 0.590841*DIF_RA(-1)+ 0. 042867*INFL(-1)+ +0.055321*DIF_CSR(-1)

  22. The Loss Function For =0.9 and c=0.2 a+b=0.8

  23. The evolution of the coefficients in the reaction function for different weights put on inflation

  24. Optimal Taylor rules it = rr* + Πt + α (Πt – Π*) + (y -y*)t Taylor (1993): α=0.5 , =0.5 Taylor (1999): α=0.5 , =1 Henderson-McKibbin (1993): α=1 , =2 Ball (1997): α=0.82 , =1.13 Ball (1998): α=0.82 , =1.04 (open economy)

  25. Conclusion For different combination of weights (a,b), put on deviation of output from its natural trend and deviation of inflation from its target, I found: 1 ≤ ≤2 and 0.5≤ α ≤2.88, results comparable to those existing in the literature.

  26. Conclusion Considering a=0.2 and b=0.6 the optimal rule is: it =1,561*(y -y*)t + 1,8097* (Πt – Π*) +0,9565*(CSRt -CSRt-1 ) -0,1714*DUM+2,3923*K+5,0057*λ compared to the explicit IR: DIF_RA=-0.001541+ 0.590841*DIF_RA(-1)+ 0. 042867*INFL(-1)+0.055321*DIF_CSR(-1)

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