Optimal Fiscal Stabilization Policy With Credible Central Bank Independence

Lambertini, Luca; Rovelli, Riccardo Working Paper Optimal Fiscal Stabilization Policy With Credible Central Bank Independence Quaderni - Working Paper DSE, No. 460 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Lambertini, Luca; Rovelli, Riccardo (2002) : Optimal Fiscal Stabilization Policy With Credible Central Bank Independence, Quaderni - Working Paper DSE, No. 460, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4834 This Version is available at: https://hdl.handle.net/10419/159301 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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ixqfwlrqv pruh frpsdfwo| dv= O J ' O W n O E > O V ' O W n O E +:, Qrz frqvlghu wkh vlpxowdqhrxv jdph ehwzhhq wkh fhqwudo edqn dqg wkh jryhuqphqw1 Iru dq| jlyhq  / uvw rughu frqglwlrqv duh= CO E Cl '2  E l   9   2  d  E i   E l   9 n %  n % 2 o'f +;, CO J Ci '2 i n2   n  2   E i   E l   9 n %  n2 % 2 'f +<, |lhoglqj= i Q '    E  2    % 2  %   n  2      2  2 n   n  2   n  2   +43, l Q '  9 n  d % 2 E  2 n  n %  o    2  2 n   n  2   n  2   zkhuh vxshuvfulsw Q vwdqgv iru Qdvk htxloleulxp 1 Wzr revhuydwlrqv duh dssursuldwh dw wklv srlqw1 Iluvw/ qrwlfh wkdw/ iru dq| jlyhq ohyho ri  9 > wkhuh h{lvw h{wuhph frqjxudwlrqv ri ghpdqg dqg vxsso| vkrfnv xqghu zklfk wkh rswlpdo lqwhuhvw udwh zrxog eh qhjdwlyh/ lpso|lqj wkdw hlwkhu wkh fhqwudo edqn vkrxog uhylvh xs z dug wkh lq dwlrq wdujhw/ ru vfdo srolf| vkrxog/ fhwhulv sdulexv / ehfrph pruh h{sdqvlyh1 Vhfrqg/ iru ixwxuh uhihuhqfh qrwlfh wkdw Cl Q C% n A f( C 2 l Q C% n C ? f >n ' > 2 > +44, dqg dovr= Ci Q C%  ? f( C 2 i Q C%  C ? f +45, lpso|lqj wkdw wkh rswlpdo vfdo srolf| uhvsrqvh wr djjuhjdwh ghpdqg vkrfnv lv dozd|v qhjdwlyh/ dqg lqfuhdvhv lq devroxwh ydoxh zlwk = Wkh htxloleulxp orvvhv dvvrfldwhg zlwk wkh Qdvk htxloleulxp duh= O Q E '    2  2 n   d %  n E  2 n   % 2 o 2     2  2 n   n  2   n  2   2 +46, 9 O Q W '  E  2 n  E  2 % 2  %   2   2  2  l     2  2 n   n  2   n  2   2 +47, l  2 %     2 % 2  %     2   2 % 2 2 n  E %  n h 2  2  O Q J ' O Q W n O Q E ( O Q V ' O Q W n O Q E = +48, Iluvw ri doo/ iurp +46, rqh lpphgldwho| rewdlqv CO Q E @C ? f dozd|v/ zklfk lpsolhv wkh iroorzlqj lqwxlwlyh surshuw|= Ohppd 4 Wkh fhqwudo edqnhu*v wdvn ehfrphv surjuhvvlyho| hdvlhu dv wkh zhljkw dwwdfkhg e| wkh jryhuqphqw wr sulfh vwdelolw| lqfuhdvhv1 Wklv lv dovr frqvlvwhqw zlwk wkh revhuydwlrq wkdw wkh fhqwudo edqn*v uhdf0 wlrq wr hlwkhu vkrfn lv ohvv surqrxqfhg dv  lqfuhdvhv/ dv fdq eh vhhq iurp +44,1 Qrz zh fdq glhuhqwldwh wkh vrfldo zhoiduh orvv O Q V z1u1w1 wkh zhljkw  G CO Q V C '2  2  2  d %  n % 2 E  n  2  o d  2 E    E %  n % 2 E  n  2 n[ o   2  2  n    n  2  n  2    'f +49, zkhuh [   2     %   n  2 E      % 2   2 n  E        2 % 2  +4:, Vroylqj +49, z1u1w1  |lhogv=  J '  e  2 % 2 n    2   % 2 E  2 n    %      2  n  E %  n % 2 E  2 n       2  2  E %  n % 2 n  E %  n % 2 E  2 n    +4;, Li %  'f >% 2 ' 'fG  J '  e  2  n  E  2 n     2  2 n    2  2  n  E  2 n   A f = +4<, Li %  ' 'f >% 2 'fG  J '  2 E  n E    n   2  2 n  +53, zkrvh vljq ghshqgv xsrq wkh vl}h ri = Lq idfw/ li  lv yhu| vpdoo/  J pd| ehfrph qhjdwlyh/ lpso|lqj wkdw wkh jryhuqphqw fdq vwdelolvh ghpdqg vkrfnv : zlwkrxw wdnlqj qrwlfh ri wkhlu lq dwlrqdu| lpsdfw1 Qhyhuwkhohvv/ dv lpsolhg e| +45,/ vfdo srolf| zloo qhyhu eh vhw vr dv wr ghvwdelolvh wkh ghpdqg vlgh1 Li %  ' % 2 'f > wkhq  J lv reylrxvo| lqghwhuplqdwh vlqfh qr srolf| dfwlrq qhhgv wr wdnh sodfh1 Lw lv hdv| wr fkhfn wkdw/ lq wklv fdvh/ i Q 'f dqg l Q '  9 = Qrz zh h{dplqh wkh fdvh zkhuh erwk vkrfnv glhu iurp }hur1 Revhuyh wkdw wkh qxphudwru ri  J lv qlo dw= % 2 d '  %  d  2 E  nE    n  o  2  2 d  2  n  E  2 n  o n  2 E  2 n   +54, Qh{w/ wkh ghqrplqdwru ri  J lv qlo dw= % 2 e '  %    2  2 n    2  2  n  E  2 n   +55, Pruhryhu/ zh duh dovr lqwhuhvwhg lq ghwhuplqlqj wkh vkrfn udqjhv zkhuhlq wkh rswlpdo zhljkw  J lv odujhu wkdq rqh1 Wklv zrxog eh d fdvh zkhuh vfdo srolf| zrxog frqfhqwudwh pruh rq djjuhjdwh vxsso| udwkhu wkdq ghpdqg vkrfnv1 Suhvxpdeo|/ wklv zrxog eh wkh fdvh zkhq wkh hfrqrp| lv fkdudfwhulvhg e| yhu| kljk sulfh lqvwdelolw| +l1h1/ yhu| odujh vxsso| vkrfnv,1 Wr suryh wklv srlqw/ ghqh e    J   = Wkhq zh kdyh wkdw wkh qxphudwru ri e  lv htxdo wr }hur dw= % 2 f ' %   E  2  n  2   +56, zkloh wkh ghqrplqdwru ri e  lv }hur dw= % 2 g '  %    2  2 n    2  2  n  E  2 n  ' % 2 e +57, Qrz vrph whglrxv dojheud vx!fhv wr yhuli| wkdw/ iru doo %  A fG % 2 e ' % 2 g ?% 2 d ?% 2 f +58, zlwk % 2 e ' % 2 g ? f dqg % 2 f A f vxuho|/ zkloh wkh vljq ri % 2 d ghshqgv xsrq wkh vl}h ri = Li lqvwhdg %  ? fG % 2 f ?% 2 d ?% 2 e ' % 2 g +59, zlwk % 2 e ' % 2 g A f dqg % 2 f ? f vxuho|/ zkloh wkh vljq ri % 2 d djdlq ghshqgv xsrq wkh vl}h ri = Zh duh qrz deoh wr hvwdeolvk wkh iroorzlqj= ;