The central bank cost constraint and output inflation variability: a note on Cecchetti and Ehrmann Abstract

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1 The cenral bank co conrain and oupu inflaion variabiliy: a noe on Cecchei and Ehrmann 000 Oama Sweidan Aian Profeor of Economic Fadwa Kalaji Aian Profeor of Economic Abrac The goal of hi paper i o exend he model of Cecchei and Ehrmann 000 o udy he cae of developing counrie ha have a conrain in conducing heir moneary policie. Conrary o Cecchei and Ehrmann 000 model, our model how ha he exience of uch a conrain i.e. co rericion allow he aggregae demand hock o affec he oupu inflaion variabiliy. Our model alo how ha adding a moneary policy co rericion o he cenral bank lo funcion lead o eiher a eeper or flaer efficien fronier. Thi implie ha he effec of moneary policy o offe aggregae demand and upply hock i reduced. Ciaion: Sweidan, Oama and Fadwa Kalaji, (005) "The cenral bank co conrain and oupu inflaion variabiliy: a noe on Cecchei and Ehrmann 000." Economic Bullein, Vol. 5, No. pp. 6 Submied: Augu, 005. Acceped: November 9, 005. URL: hp:// 05E0000A.pdf

2 . Inroducion Cenral bank policymaker in any counry in he world, developed and developing alike, eek he ame goal; namely o abilize oupu and price abou ome pah ha i expeced o be opimal. Developed counrie do no have echnical conrain in applying moneary policy i.e. open marke operaion. However, developing counrie have. Thi echnical difference i due o he fac ha developed counrie have well-developed and ophiicaed financial marke compared o developing counrie. One of he major and crucial iue in recen ime i ha cenral bank in developing counrie, engaged in conducing moneary policy by uing indirec conrol, find ha hey hould inervene and creae heir own inrumen o conduc open marke operaion becaue heir financial marke are underdeveloped. Thi enail a high co in he form of negaive profi. Thi iue raie he queion abou he validiy and coninuiy of uch policie in hee counrie. Lieraure how a lack of academic udie in hi area of reearch. We believe hi lack of inere em from he fac ha economi are more inereed in decribing he behavior of moneary policy in developed counrie i.e. he U.S and EMU. Hence, he goal of hi paper i o focu on he effec of uch conrain on he oupu-inflaion variabiliy.. Policy Formulaion Recen reearch in moneary economic focue on finding he opimal moneary policy, i.e. he level of he inere rae, ha minimize a quadraic lo funcion (ee, for example, Taylor (979), Cecchei (998), Cecchei and Ehrmann (000)). The conribuion of hi paper i o expand he quadraic lo funcion by adding a hird preference, conien wih a real cae, o minimize he flucuaion of cenral bank co. The policy arge i o minimize () ubjec o (), (3) and (4) below: * * * LE[ α ( π π ) + η( y y ) + ( α η)( c c ) ] () y γ m + γd + () π c m + d ω (3) ψ m (4) Equaion () i a general form of a quadraic lo funcion for one period 3. E denoe he mahemaical expecaion. π *, y * and c * are he deired level of inflaion, oupu and cenral bank co of conducing moneary policy, repecively. The parameer α, η and (-α-η) are he weigh of inere. Equaion (4) how ha co ha a negaive relaion wih he money upply (m ) becaue iuing more ecuriie i.e. cerificae of depoi (conracionay moneary policy) mean higher value of inere paymen on hoe ecuriie. Equaion () and (3) decribe he dynamic rucure of he economy (oupu and inflaion). d and are aggregae demand and upply hock, repecively. The ource of Equaion () o (3) i Cecchei and Ehrmann (000), bu adjued wih equaion (4) o mee he goal of hi paper. We replaced inere rae by money upply becaue we arge he former by he laer. 3. Cenral Bank Loe and Moneary Policy Cenral bank loe can arie in one of wo way: fir, operaing loe which occur when operaing co exceed operaing income. Operaing co include mainly he inere rae paid on all accoun and inrumen. On he oher hand, operaing income encompae income For more deail abou he counrie ha have ued cenral bank ecuriie and he counrie ha have wiched o cenral bank ecuriie ee Quinyn (994). Daa from he cenral bank of Jordan provide evidence, for more deail ee Sweidan and Maghyereh (005). 3 For more deail abou muliperiod funcion ee Dimar, Gavin and Kydland (999).

3 from local and foreign invemen. Second, valuaion loe which mean loe ariing from he revaluaion of ae and liabiliie. For he purpoe of he curren paper, we believe ha moneary policy will be ineffecive when a cenral bank operae wih uch ignifican operaing loe. However, loe ariing from revaluaion do no have he ame effec a operaing loe. Real world evidence which come from wo neighboring counrie, Jordan and Irael may clarify hi poin furher. The daa in Table (I), below, from boh counrie over he period ( ) how ha he Cenral Bank of Jordan (CBJ) and he Bank of Irael (BOI) uffered ne loe. Bu, he main difference beween he wo counrie i ha he loe in Jordan are relaed o he moneary policy ielf. During he period ( ) he CBJ inervened aggreively in he marke by creaing cerificae of depoi o aborb he exce liquidiy. Cerificae of depoi are non-income earning inrumen ued in he conduc of open marke operaion. Thi move wa aken a a ime when inere rae were high, averaging 8%. Thi coniued a high co o he CBJ. For hi reaon, he CBJ uffered ignifican loe during he period under udy. We are herefore, led o believe ha hee loe may puh he moneary auhoriy in Jordan o eae i moneary policy. Table (I) The CBJ and he BIO Ne Loe over he Period ( ) Year Loe/Profi in he CBJ Million JD Loe/Profi in he BIO Million NIS S Source: annual repor of he CBJ and he BOI, differen iue. Loe/Profi in he CBJ Million $ Loe/Profi in he BIO Million $ , ,943-4., , ,03.9 In he cae of he BOI, he balance hee how ha foreign exchange reerve coniue he main ae of he BOI, amouning o almo 87% of oal ae. Conequenly, he exchange rae regime allow he rae o move wihin a wide band. The wide exchange rae flucuaion led he BOI o uffer loe over he period ( ). Thi ugge ha he loe in he BOI are relaed o exchange rae differenial (revaluaion). Moreover, he daa from he BOI how ha he main moneary inrumen in Irael are: moneary loan; depoi aucion and reaury bill. Some of hee inrumen are income-earning ae which guaranee ome revenue o he BOI. Evidence from he conolidaed balance hee of he Federal Reerve Syem, how ha he U.S. governmen ecuriie are he large caegory of i ae, i i approximaely 90.0%. Thi implie ha hee ecuriie are income-earning ae. Furhermore, in a recen udy, Dalon and Dziobek (005) illurae ha cenral bank of everal developing counrie uch a Brazil and Chile uffered loe becaue of he inere differenial beween he co of domeic liabiliie and reurn on heir ae. Overall, here i no doub ha conducing a moneary policy in any counry ha ome co. Neverhele, he evidence how ha adoping a moneary policy ha goe much beyond convenional cenral banking funcion caue loe o he cenral bank. If hi i he cae, one may queion he effecivene of an independen moneary policy when

4 financial marke are no ye fully developed. Therefore, we believe hee cenral bank hould re-evaluae and minimize he co of heir moneary policy. 4. Reul Appendix A demonrae he reul of he opimizaion problem aed above. We compare he reul of hi opimizaion problem (including moneary policy conrain) wih he reul of Cecchei and Ehrmann (000) (wihou conrain). I i clear ha he original model by Cecchei and Ehrmann (000), equaion (A5), how ha he moneary policy offe aggregae demand hock, one-for-one relaionhip (a 0 ). However, he exience of a conrain in applying moneary policy i.e. co conrain make moneary policy unable o offe compleely an aggregae demand hock, equaion (A0), (a <). Furhermore, he reul illurae ha he value of b, equaion (A), i le han b 0, equaion (A6). Thi mean ha he repone of moneary policy o upply hock can be decribed a limied or conervaive. Thee wo oucome lead o he concluion ha a rericed moneary policy lead o more flucuaion in he economy. And ha i i unable o puh he economy back o he equilibrium. Moreover, hi reul i alo confirmed by calculaing he variabiliy of oupu ( y) and inflaion ( π). The original model, Cecchei and Ehrmann (000) in equaion ( (A7) and (A8) ), conclude ha he variabiliy of boh oupu and inflaion depend only on he variance of he aggregae upply hock ( ), and no on he variance of he aggregae demand hock ( d). However, wih a conervaive moneary policy he reul will be changed. I i clear from Appendix A, equaion ( (A) and (A3) ), ha oupu and inflaion variabiliy are affeced by boh he aggregae demand and upply hock ( d, ). Given he value of γ, ω and ψ, he addiional preference (co conrain) in cenral bank lo funcion implie ha he policymaker have preference diperion. Thi analyi aume ha he policymaker focu more on he co of moneary policy a a prioriy. A a reul, hey have wo cenario: eiher o give aenion o he co of moneary policy and oupu variabiliy; or o he co of moneary policy and inflaion variabiliy. If he cenral bank place a fixed weigh on argeing inflaion, oupu ocillae. However, if he cenral bank place a fixed weigh on he oupu hen inflaion rae flucuae. Thi analyi poulae ha he exience of he co conrain in he lo funcion force he cenral bank o concenrae on one of wo arge eiher oupu or inflaion. From a echnical poin of view, he efficien fronier 4 could be eiher eep or fla, equaion (A5), which depend on he preference of he cenral bank. In um, he exience of co conrain in performing moneary policy, limi he abiliy of moneary policy o affec aggregae demand. In addiion, adoping a igh moneary policy i coly. 5. Concluion Thi paper how ha he exience of conrain in conducing moneary policy, i.e. high moneary policy co, lead o eiher a eeper or a flaer efficien fronier. Thi mean inefficien moneary policy; i effec o offe aggregae demand and upply hock i mall. Thi heoreical analyi hed ligh on he fac ha developing counrie which adop an economic adjumen program wih a conrained (non-well developed) moneary policy, are unable o conrol oupu and inflaion variabiliy efficienly. Moreover, combaing inflaion under uch circumance i exremely expenive. 4 Thi fronier how he rade-off beween oupu and inflaion variabiliy, for more deail ee Cecchei, Flore- Lagune and Kraue (004). 3

5 Appendix A Cecchei and Ehrmann 000 model α π π * + α y y * (A) [ ] L E ( ) ( )( ) ( r d ) y γ + (A) ( r d ) ω π (A3) Opimizaion reul r a0 d + b0 (A4) ( α ) γ ( α ) γ α + a 0 (A5) α + b 0 αω α + + ( α ) ( α ) γ γ y ( γb0 ) π + (A6) (A7) ( ω b ) (A8) 0 The opimizaion reul of he model in hi paper m ad b (A9) α + ηγ a (A0) α + ηγ + ( α η) ψ ηγ αω b (A) α + ηγ + ( α η) ψ y ( γ a γ ) d + ( γb ) (A) ( a ) d + ( ω b ) π + (A3) The lope of he oupu-inflaion variabiliy rade-off y π y π γ α ηγ α( + ωγ ) ( α )( + ωγ ) ( + ωγ ) + ( γ + )( α ) ( + ωγ ) + ( ω + )( α ) η ψ η ψ wihou conrain wih conrain (A4) (A5) 4

6 Reference. Cecchei, S., A. Flore-Lagune and S. Kraue (004), Ha Moneary Policy Become More Efficien? A Cro Counry Analyi, Naional Bureau of Economic Reearch, Working Paper 0973, December.. Cecchei, S. G. and M. Ehrmann (000), Doe Inflaion Targeing Increae Oupu Volailiy? An Inernaional Comparion of Policymaker Preference and Oucome, Cenral Bank of Chile, Working Paper No. 69, April. 3. Cecchei, S. (998), Policy Rule and Targe: Framing he Cenral Banker Problem, Economic Policy Review, Federal Reerve Bank of New York. 4. Dalon, J. and C. Dziobek (005) Cenral Bank Loe and Experience in Seleced Counrie, IMF Working Paper No. WP/05/7, April, Wahingon. 5. Dimar, R, W. Gavin and F. Kydland (999), The Inflaion-Oupu Variabiliy Tradeoff and Price-Level Targe, Review, Federal Reerve Bank of Sain Loui, January/February. 6. Quinyn, M. (994) Governmen Securiie veru Cenral Bank Securiie in Developing Open Marke Operaion, IMF Working Paper No. 94/6, May, Wahingon. 7. Sweidan, O. and A. Maghyereh (005) Moneary Policy and he Cenral Bank Securiie, Applied Economic Leer, (Forhcoming). 8. Taylor, J. B. (979), Eimaion and Conrol of Macroeconomic Model wih Raional Expecaion, Economerica, 47. 5