1. 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

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. 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: 1. 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) Taylor (1993), (1999); Henderson-McKibbin (1993) - the monetary aggregate - the monetary aggregate McCallum (1984), (1987); Meltzer (1984), (1987) - domestic credit - 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 i t - instrument

9. Optimal control approach More specifically, reaction functions can be regarded as solutions to an optimal control approach to monetary policy. 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. 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: 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 The data sample covers the period 1996:01 – 2002:12 All time series are based on monthly observation. All time series are based on monthly observation.

16. TIME SERIES USED Symbol Semnification PI Industrial Production Chained Index Seasonal Adjusted PI_95 Industrial Production Index computed by taking Dec 1995 as basis LN_PI_95 Log(PI_95) HPTREND_PI The trend of LN_PI_95 computed using a Hodrick Prescott filter OUTPUT_GAP The difference between LN_PI_95 and its trend IPC Consumer Price Chained Index IPC_F Consumer Price Chained Index US

17. IPC_95Consumer Price Index computed by taking Dec 1995 as basis IPC_95_FConsumer Price Index computed by taking Dec 1995 as basis INFLLog(IPC) CSNNominal Exchange Rate CSRReal Exchange Rate = log(CSN*IPC_95_F/IPC_95) DIF_CSRFirst difference of CSR RALending rate for non-bank customers DIF_RAFirst difference of RA RRAReal lending rate for non-bank customers EXPNETNet exports DUMCENTRATdummy variable that takes the value of 1 in March 1997 and 1/(no.of observations - 1) elsewhere.

18. TIME SERIES USED

20. Unit Root Tests SeriesOrder of Integration Level of Significance ADFPP OUTPUT_GAPI(0) 1% INFLI(0) 1% CSRI(1) 1% DIF_CSRI(0) 1% RAI(1) 1% DIF_RAI(0) 1% RRAI(0) 1% model

21. IS estimation Dependent Variable: OUTPUT_GAP Method: Least Squares Date: 07/01/03 Time: 10:45 Sample(adjusted): 1996:02 2002:12 Included observations: 83 after adjusting endpoints VariableCoefficientStd. Error t-StatisticProb. OUTPUT_GAP(-1)0.6550490.0828587.905.6670.0000 RRA(-1)-0.2471600.124724-1.981.6540.0510 DIF_CSR0.1799650.0648652.774.4480.0069 R-squared0.570380 Mean dependent var0.000877 Adjusted R-squared0.559639 S.D. dependent var0.049507 S.E. of regression0.032853 Akaike info criterion-3.958.076 Sum squared resid0.086345 Schwarz criterion-3.870.648 Log likelihood1.672.602 Durbin-Watson stat2.035.637

22. 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) +C(4)*OUTPUT_GAP(-1)+C(5) Observations: 82 R-squared0.819670 Mean dependent var0.035248 Adjusted R-squared0.810302 S.D. dependent var0.036597 S.E. of regression0.015940 Sum squared resid0.019564 Durbin-Watson stat1.731411 Equation: DIF_CSR=C(6)*DIF_CSR(-1)+C(7)*RRA+C(8)*DUMCENTRAT Observations: 82 R-squared0.604270 Mean dependent var-0.003343 Adjusted R-squared0.594252 S.D. dependent var0.057243 S.E. of regression0.036463 Sum squared resid0.105032 Durbin-Watson stat1.992943 Equation: DIF_RA=C(9)+C(10)*INFL(-1)+C(11)*DIF_CSR(-1)+DIF_RA(-1)*C(12 ) Observations: 82 R-squared0.628309 Mean dependent var-0.000269 Adjusted R-squared0.614013 S.D. dependent var0.005344 S.E. of regression0.003320 Sum squared resid0.000860 Durbin-Watson stat2.044055

23. CoefficientStd. Errort-StatisticProb. C(1)0.5732730.0620739.235.4740.0000 C(2)0.2533450.0357757.081.6600.0000 C(3)-0.1179390.018424-6.401.3400.0000 C(4)0.2117750.0505014.193.5110.0000 C(5)0.0150950.0027155.560.4360.0000 C(6)0.1736260.0765202.269.0230.0242 C(7)-0.4550910.162430-2.801.7670.0055 C(8)0.4665240.0455091.025.1230.0000 C(9)-0.0015410.000601-2.564.1240.0110 C(10)0.0428670.0134043.198.0550.0016 C(11)0.0553210.0068438.084.1990.0000 C(12)0.5908410.0936026.312.2480.0000 Determinant residual covariance3.01E-12

24. E stimated Model IS OUTPUT_GAP =0.655049*OUTPUT_GAP(-1) -0.247160*RRA(-1)+ OUTPUT_GAP =0.655049*OUTPUT_GAP(-1) -0.247160*RRA(-1)+ +0.179965* DIF_CSR +0.179965* DIF_CSRPHILLIPS INFL=0.638493*INFL(-1)+ 0.284684*DIF_CSR(-1)-0.099128*DUMCENTRAT +0.176756*OUTPUT_GAP(-1)+0.012691 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 DIF_CSR=0.173626*DIF_CSR(-1) -0.455091*RRA+0.466524*DUMCENTRATIR DIF_RA=-0.001541+ 0.590841*DIF_RA(-1)+ 0. 042867*INFL(-1)+ +0.055321*DIF_CSR(-1) DIF_RA=-0.001541+ 0.590841*DIF_RA(-1)+ 0. 042867*INFL(-1)+ +0.055321*DIF_CSR(-1)

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

28. ab THE OPTIMAL RULES 0.80 it =1,9907*(y -y*)t + 0,5732* (Πt – Π*) +0,3483*(CSRt - CSRt -1 )+ + 0,1372*DUM+3,039*K+λ 0.40.4 it =1,7671*(y -y*)t + 1,1673* (Πt – Π*) +0,643*(CSRt - CSRt -1 ) -0,0151*DUM+2,6545*K+3,1173*λ 0.20.6 it =1,561*(y -y*)t + 1,8097* (Πt – Π*) +0,9565*(CSRt - CSRt -1 ) -0,1714*DUM+2,3923*K+5,0057*λ 00.8 it =1,1829*(y -y*)t + 3,8226* (Πt – Π*) +1,9006*(CSRt - CSRt -1 ) -0,6181*DUM+2,2098*K+9,1849*λ

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

30. 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)

31. 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.

32. 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)