The Choice of a Monetary Policy Reaction Function in a Simple Optimizing Model

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 601 January 1998 THE CHOICE OF A MONETARY POLICY REACTION FUNCTION IN A SIMPLE OPTIMIZING MODEL Dale W. Henderson and Jinill Kim NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.bog.frb.fed.us.

THE CHOICE OF A MONETARY POLICY REACTION FUNCTION IN A SIMPLE OPTIMIZING MODEL Dale W. Henderson and Jinill Kim* Abstract: Monetary policy reaction functions are compared in a simple optimizing model with one-period nominal stickiness, i.i.d. shocks, and no capital accumulation. The interest rate is the instrument and is either kept constant, "interest rate targeting" for short, or used in targeting one of the following: money, the price level, output, nominal income (output), money growth, inflation, and the sum of inflation and output. There are three varieties of one-period nominal stickiness---wage stickiness, wage and price stickiness, and price stickiness---and three kinds of shocks---money demand shocks, goods demand shocks, and productivity shocks. A given type of targeting is "better" than some other type for a given variable and kind of shock if it results in smaller deviations of the variable from its target value. Some familiar results regarding the ranking of types of targeting are confirmed in the optimizing model, and some new results are obtained. It is not surprising that rankings may depend both on the type of shock and on which variable is the target variable. However, it may be somewhat surprising that, given that wages are sticky, rankings depend on whether prices are sticky, but that given that prices are sticky rankings do not depend on whether wages are sticky. Keywords: monetary policy, reaction function, inflation targeting, price level targeting, interest rate targeting, nominal stickiness * Henderson and Kim are, respectively, economists in the International Finance Division and the Division of Research and Statistics of the Federal Reserve Board. Earlier versions were presented at the Federal Reserve Board, the International Economic Association (IEA) Conference on "Monetary Theory as a Basis for Monetary Policy," the fall 1997 Federal Reserve System (FRS) Conference on Macroeconomics, the Federal Reserve Bank of Chicago, and the Money and Banking Workshop at the University of Chicago. The authors would like to thank Luigi Bonatti and Francesco Farina, their discussants at the IEA Conference, Alexander Wolman, their discussant at the FRS Conference, Flint Brayton, and James Dow for helpful comments; Neva Kerbeshian for valuable research assistance; Evelyn Reynolds for effective graphic design; and Steven Sumner for thoughtful editorial suggestions. This paper represents the views of the authors and should not be interpreted as reflecting those of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System.

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prgho zlwk zdjh vwlfnlqhvv frqvlghuhg lq wkh suhylrxv vhfwlrq/ exw wkh rwkhu wkuhh uhodwlrqvklsv lq Wdeoh ; duh lghqwlfdo wr wkh fruuhvsrqglqj uhodwlrqvklsv lq Wdeoh 71 (cid:8)7 lq wkh ohyhov prgho zlwk zdjh dqg sulfh vwlfnlqhvv lv krul}rqwdo ehfdxvh (cid:31)upv djuhh wr surgxfh dq| dprxqw ghpdqghg dw wkh sulfh (cid:31){hg lq wkh rqh0shulrg frqwudfw1 Lwv htxdwlrq/ +W;04,/ lv lghqwlfdo wr wkh sulfh vhwwlqj htxdwlrq +W:05,1 Wkh qrplqdo lqfrph0hpsor|phqw uhodwlrq/ +W;08,/ lq wkh ohyhov prgho zlwk zdjh dqg sulfh vwlfn0 lqhvv lv rewdlqhg e| dgglqj htxdwlrqv +W:04, dqg +W:05,1 Li wkhuh lv d surgxfwlylw| vkrfn/ wkhuh lv qrw d rqh0wr0rqh uhodwlrqvkls ehwzhhq wkh fkdqjh lq qrplqdo lqfrph dqg wkh fkdqjh lq hpsor|phqw1 Wdeoh ;= Vfkhgxohv dqg Uhodwlrq iru Ohyhov Prgho zlwk Zdjh dqg Sulfh Vwlfnlqhvv R ’ f (cid:8)7 vfkhgxoh W;04 j+ ’ (cid:3)E(cid:16)nR(cid:28)nL (cid:8)( vfkhgxoh W;05 (cid:19) (cid:20) (cid:19) (cid:20) (cid:19) (cid:20) (cid:16) ’ b+ nb6(cid:24) +n bR nb6 Rn b6 (cid:15) - vfkhgxoh W;06 (cid:129)nb60 (cid:129)nb60 (cid:129)nb60 Rn+ ’ f (cid:27)t frqvwdqw vfkhgxoh W;07 Rn+ ’ E(cid:129)(cid:3)k(cid:28),n% (cid:27)t wr u uhodwlrq W;08 71416 Prqh| Ghpdqg Vkrfnv Zlwk erwk zdjh dqg sulfh vwlfnlqhvv/ mxvw dv zlwk rqo| zdjh vwlfnlqhvv/ iru prqh| ghpdqg vkrfnv/ UA/ (cid:27)A/ tAu/ dqg (cid:27)tA duh htxlydohqw/ dqg (cid:127)A lv zruvh iru doo yduldeohv ehfdxvh xqghuUA/ (cid:27)A/ tAu/ dqg(cid:27)tA prqh| ghpdqgvkrfnv gr qrwfdxvh wkh lqwhuhvw udwh wr fkdqjh/ exw xqghu (cid:127)A wkh| gr1 Xqghu UA dqg (cid:127)A +Iljxuh 7/ Sdqho D4, dq lqfuhdvh lq (cid:15) vkliwv wkh - vfkhgxoh 6:(cid:16) grzq vd| wr - / dqg wkhuh lv xszdug suhvvxuh rq (cid:16)(cid:23) Xqghu UA/ wkh - vfkhgxoh 6:(cid:16)c(cid:129) 6:(cid:16) vkliwv edfn yluwxdoo| doo wkh zd| wr lwv lqlwldo srvlwlrq/ dqg wkh (cid:8)( vfkhgxoh vkliwv grzq kdugo| dw doo/ vr wkh qhz htxloleulxp lv dw yluwxdoo| wkh vdph srlqw dv wkh rog rqh/ srlqw @/ vr (cid:16)/ +/ R/ dqg/ wkhuhiruh/ Rn+ dqg , uhpdlq yluwxdoo| xqfkdqjhg1 Xqghu(cid:127)A/ - vkliwv xs dqg(cid:8)( vkliwv grzqxqwlo wkh| lqwhuvhfwvrphzkhuh rqwkh 6:(cid:16) pdunhg sduw ri wkh (cid:8)7 vfkhgxoh ehwzhhq srlqwv @ dqg K dqg ehorz wkh (cid:27)t vfkhgxoh1 Lq wkh qhz htxloleulxp/ (cid:16) lv kljkhu dqg +/ R/ dqg/ wkhuhiruh/ Rn+ dqg , duh orzhu1 Xqghu (cid:27)A/ tAu/ dqg (cid:27)tA +Iljxuh 7/ Sdqho D5,/ dq lqfuhdvh lq (cid:15) kdv yluwxdoo| qr h(cid:30)hfw rq wkh - / - / dqg - vfkhgxohv/ uhvshfwlyho|1 Wkhuh lv yluwxdoo| qr vkliw lq R + R+ wkh (cid:8)( vfkhgxoh1 Dv d uhvxow/ (cid:16)/ +/ dqg R dqg/ wkhuhiruh/ Rn+ dqg , uhpdlq yluwxdoo| xqfkdqjhg1 71417 Jrrgv Ghpdqg Vkrfnv Zlwk erwk zdjh dqg sulfh vwlfnlqhvv/ mxvw dv zlwk rqo| zdjh vwlfnlqhvv/ iru jrrgv ghpdqg vkrfnv/ (cid:27)A/ tAu/ dqg (cid:27)tA duh ehwwhu wkdq (cid:127)A zklfk lv ehwwhu wkdq UA iru doo yduldeohv1 Dq lqfuhdvh lq wkh ghpdqg iru jrrgv/ dq lqfuhdvh lq L/ fdxvhv wkh (cid:8)( vfkhgxoh wr vkliw xs iurp (cid:8)( wr (cid:8)( lq Iljxuh 7/ Sdqhov E4 dqg E51 f (cid:129) Iluvw zh frqvlghu UA dqg (cid:127)A xvlqj Iljxuh 7/ Sdqho E41 Xqghu UA/ (cid:16) uhpdlqv yluwxdoo| xqfkdqjhg/ vr wkh qhz htxloleulxp lv duelwudulo| forvh wr wkh lqwhuvhfwlrq ri 57

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Wkh ixoo frpelqdwlrq prgho zlwk zdjh dqg sulfh vwlfnlqhvv lv vkrzq lq Wdeoh <1 Lw lv rewdlqhg e| ehjlqqlqj zlwk wkh qrwlrqdo frpelqdwlrq prgho lq Wdeoh 5/ gursslqj wkh htxdwlrqv iru qrwlrqdo oderu vxsso| dqg qrwlrqdo oderu ghpdqg/ dqg pdnlqj xvh ri wkh lqirupdwlrq lq +77,/ +78,/ +85,/ dqg +86,1 Wdeoh <= Ixoo Frpelqdwlrq Prgho zlwk Zdjh dqg Sulfh Vwlfnlqhvv + ’ E(cid:129)(cid:3)k(cid:28),n% surgxfwlrq ixqfwlrq W<04 R(cid:3)R ’ Z sulfh vhwwlqj W<05 3(cid:129) (cid:131)3(cid:129) (cid:25) ’ Z nR zdjh vhwwlqj W<06 (cid:131)3(cid:23)(cid:129) 3(cid:129) (cid:24) j+ ’ (cid:3) (cid:16)(cid:3) (cid:14) > E(cid:24)+(cid:3)0(cid:16)n(cid:15)(cid:28) nL djjuhjdwh ghpdqg W<07 (cid:14) n(cid:14) Z > 6 ’ Rn(cid:24)+(cid:3)0(cid:16)n(cid:15) prqh| pdunhw htxloleulxp W<08 (cid:16) ’ (cid:14) >n(cid:14) +n(cid:14) Z uhdfwlrq ixqfwlrq W<09 > + Z Z ’ R(cid:3)R lq dwlrq gh(cid:31)qlwlrq W<0: 3(cid:129) > ’ 6(cid:3)6 prqh| jurzwk gh(cid:31)qlwlrq W<0; 3(cid:129) 71515 Wkh Vfkhgxohv dqg d Uhodwlrq iru wkh Frpelqdwlrq Prgho Wkhhtxdwlrqv iruwkhvfkhgxohvdqgduhodwlrqxvhgwrdqdo|}h wkh frpelqdwlrqprgho zlwk zdjh dqg sulfh vwlfnlqhvv duh vkrzq lq Wdeoh 43/ dqg wkh vfkhgxohv duh sorwwhg lq Zc+ vsdfh lq Iljxuh 4/ Sdqho I1 Wdeoh 43= Vfkhgxohv dqg Uhodwlrq iru Frpelqdwlrq Prgho zlwk Zdjh dqg Sulfh Vwlfnlqhvv Z ’ Z (cid:8)7 vfkhgxoh W4304 (cid:21) (cid:131)3(cid:129) (cid:22) (cid:21) (cid:22) j(cid:3) (cid:14) > (cid:24) + ’ (cid:3) (cid:129)n (cid:14) > 0 (cid:16)nL n (cid:14) > (cid:15) (cid:8)( vfkhgxoh W4305 (cid:14) n(cid:14) (cid:14) n(cid:14) (cid:14) n(cid:14) Z > Z > Z > (cid:16) ’ (cid:14) (cid:129) + n n (cid:14) (cid:14) > 0 (cid:24)+n (cid:14) (cid:129) Z n n (cid:14) (cid:14) > 0 Zn (cid:129)n (cid:14) (cid:14) > 0 (cid:15) (cid:3) (cid:14) (cid:129) Z n n (cid:14) (cid:14) > 0 Z (cid:131)3(cid:129) - vfkhgxoh W4306 > > > > Zn+ ’ f (cid:31)t frqvwdqw vfkhgxoh W4307 Zn+ ’ E(cid:129)(cid:3)k(cid:28),n%nZ (cid:31)t wr u uhodwlrq W4308 (cid:131)3(cid:129) Wkhuh duh gl(cid:30)huhqfhv ehwzhhq wkh djjuhjdwh vxsso| vfkhgxoh dqg wkh lq dwlrq soxv rxwsxw0hpsor|phqw uhodwlrq lq wkh frpelqdwlrq prgho zlwk zdjh dqg sulfh vwlfnlqhvv dqg wkrvh lq wkh frpelqdwlrq prgho zlwk zdjh vwlfnlqhvv frqvlghuhg lq wkh suhylrxv vhfwlrq dqg wkhvh gl(cid:30)huhqfhv duh hvvhqwldoo| wkh vdph dv wkh gl(cid:30)huhqfhv ehwzhhq wkh fruuhvsrqglqj uhodwlrqvklsv lq wkh ohyhov prghov zlwk wkh fruuhvsrqglqj dvvxpswlrqv derxw qrplqdo vwlfnlqhvv1 Wkh rwkhu wkuhh uhodwlrqvklsv lq Wdeoh 43 duh lghqwlfdo wr wkh fruuhvsrqglqj uhodwlrqvklsv lq Wdeoh 9 dqg Iljxuh 4/ Sdqho E1 (cid:8)7 lv krul}rqwdo ehfdxvh (cid:31)upv djuhh wr surgxfh dq| dprxqw ghpdqghg dw wkh lq dwlrq udwh lpsolhg e| wkh sulfh (cid:31){hg lq wkh rqh0shulrg frqwudfw1 Lwv htxdwlrq/ +W4304,/ lv wkh lghqwlfdo wr wkh sulfh vhwwlqj htxdwlrq +W<05,1 Wkh lq dwlrq soxv rxwsxw0hpsor|phqw uhodwlrq/ +W4308,/ lq wkh frpelqdwlrq prgho zlwk zdjh dqg sulfh vwlfnlqhvv lv rewdlqhg e| dgglqj htxdwlrqv +W<04, dqg +W<05,1 Li wkhuh lv d surgxfwlylw| vkrfn wkhuh lv qrw d 59

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Dsshqgl{ D Lq wklv Dsshqgl{ zh suhvhqw vroxwlrqv iru vrph yduldeohv lq wkh qrwlrqdo prghov dqg vxevwdqwldwh vrph ri wkh fodlpv pdgh lq wkh wh{w1 Iluvw/ zh rewdlq vroxwlrqv iru wkh rxwsxw/ hpsor|phqw/ uhdo zdjh/ dqg uhdo lqwhuhvw udwh h{shfwhg wr suhydlo lq shulrg | n (cid:26)/ (cid:26) ’ (cid:129)c(cid:23)(cid:23)(cid:23)c4 edvhg rq shulrg | lqirupdwlrq lq erwk wkh ohyhov prgho dqg wkh frpelqdwlrq prgho1 Wdnlqj h{shfwdwlrqv ri htxdwlrqv W504 wkurxjk W507 iru shulrg |n(cid:26)/ (cid:26) ’ (cid:129)c(cid:23)(cid:23)(cid:23)c4 edvhg rq shulrg | lqirupdwlrq/ wdnlqj dffrxqw ri rxu dvvxpswlrq wkdw wkh vkrfnv duh l1l1g1/ dqg vroylqj |lhog + ’ , ’ (cid:25) (cid:3)R ’ (cid:16) (cid:3)ER (cid:3)R (cid:28) ’ f(cid:23) +D14, |n(cid:26) (cid:131) | |n(cid:26) (cid:131) | |n(cid:26) (cid:131) | |n(cid:26) (cid:131) | |n(cid:26) (cid:131) | |n(cid:26)n(cid:129)(cid:131) | |n(cid:26) (cid:131) | Xvlqj d surfhgxuh wkdw lv dqdorjrxv lq hyhu| zd| wr wkh rqh xvhg wr rewdlq htxdwlrq +D14, h{fhsw wkdw h{shfwdwlrqv duh wdnhq edvhg rq shulrg | (cid:3) (cid:129) lqirupdwlrq/ lw fdq eh vkrzq wkdw wkh rxwsxw/ hpsor|phqw/ uhdo zdjh/ dqg uhdo lqwhuhvw udwh h{shfwhg wr suhydlo lq shulrg |n(cid:26)/ (cid:26) ’ fc(cid:23)(cid:23)(cid:23)c4 edvhg rq shulrg |(cid:3)(cid:129) lqirupdwlrq lq erwk wkh ohyhov prgho dqg wkh frpelqdwlrq prgho duh + ’ , ’ (cid:25) (cid:3)R ’ (cid:16) (cid:3)ER (cid:3)R (cid:28) ’ f(cid:23) +D15, |n(cid:26) (cid:131) | 3(cid:129) |n(cid:26) (cid:131) | 3(cid:129) |n(cid:26) (cid:131) | 3(cid:129) |n(cid:26) (cid:131) | 3(cid:129) |n(cid:26) (cid:131) | 3(cid:129) |n(cid:26)n(cid:129)(cid:131) | 3(cid:129) |n(cid:26) (cid:131) | 3(cid:129) Qh{w/ zh rewdlq wkh vroxwlrqv iru wkh uhvw ri wkh yduldeohv lq wkh ohyhov prgho1 Vxevwl0 wxwlqjhtxdwlrq+W508,lqwrhtxdwlrq+W509,irushulrg|n(cid:26)/wdnlqjh{shfwdwlrqvriwkh uhvxowlqj htxdwlrq edvhg rq shulrg | lqirupdwlrq/ wdnlqj dffrxqw ri rxu dvvxpswlrq wkdw wkh vkrfnv duh l1l1g1/ dqg pdnlqj xvh ri wkh vroxwlrq iru (cid:16) (cid:3)ER (cid:3)R (cid:28) |n(cid:26) (cid:131) | |n(cid:26)n(cid:129)(cid:131) | |n(cid:26) (cid:131) | lq htxdwlrq +D14, |lhog wkh iroorzlqj gl(cid:30)huhqfh htxdwlrq= # $ b nb R ’ (cid:129)n 6 R R c (cid:26) ’ (cid:129)c(cid:23)(cid:23)(cid:23)c4(cid:23) +D16, |n(cid:26)n(cid:129)(cid:131) | (cid:129)nb 0 |n(cid:26) (cid:131) | 6 E| dvvxpswlrq/ b nb (cid:24) f(cid:23) Li b nb : f/ dqg li/ lq dgglwlrq/ lw lv dvvxphg wkdw 6 R 6 R wkhuh duh qr vshfxodwlyh exeeohv/ wkhq lw iroorzv wkdw wkh sulfh ohyho/ wkh zdjh udwh dqg wkh lqwhuhvw udwh ^iurp htxdwlrq +D14,‘/ dqg wkh prqh| vxsso| ^iurp htxdwlrqv +W508, dqg +D14, dqg rxu dvvxpswlrq wkdw vkrfnv duh l1l1g1‘ h{shfwhg wr suhydlo lq shulrg |n(cid:26)/ (cid:26) ’ (cid:129)c(cid:23)(cid:23)(cid:23)c4 edvhg rq shulrg | lqirupdwlrq duh R ’ (cid:25) ’ (cid:16) ’ 6 ’ f(cid:23) +D17, |n(cid:26) (cid:131) | |n(cid:26) (cid:131) | |n(cid:26) (cid:131) | |n(cid:26) (cid:131) | Xvlqj d surfhgxuh wkdw lv dqdorjrxv lq hyhu| zd| wr wkh rqh xvhg wr rewdlq htxdwlrq +D17, h{fhsw wkdw h{shfwdwlrqv duh wdnhq edvhg rq shulrg |(cid:3)(cid:129) lqirupdwlrq/ lw fdq eh vkrzq wkdw wkh sulfh ohyho/ zdjh udwh/ lqwhuhvw udwh/ dqg prqh| vxsso| h{shfwhg wr suhydlo lq shulrg |n(cid:26)/ (cid:26) ’ fc(cid:23)(cid:23)(cid:23)c4 edvhg rq shulrg |(cid:3)(cid:129) lqirupdwlrq duh R ’ (cid:25) ’ (cid:16) ’ 6 ’ f(cid:23) +D18, |n(cid:26) (cid:131) | 3(cid:129) |n(cid:26) (cid:131) | 3(cid:129) |n(cid:26) (cid:131) | 3(cid:129) |n(cid:26) (cid:131) | 3(cid:129) Qrz/ zh rewdlq wkh vroxwlrqv iru wkh uhvw ri wkh yduldeohv lq wkh frpelqdwlrq prgho1 Vxevwlwxwlqj htxdwlrq +W50<, lqwr htxdwlrq +W50:, iru shulrg |n(cid:26)/ holplqdwlqj 6 |n(cid:26) dqg6 xvlqjhtxdwlrq+W508,/wdnlqjh{shfwdwlrqvriwkhuhvxowlqjhtxdwlrqedvhg |n(cid:26) 3(cid:129) 66

rq shulrg | lqirupdwlrq/ pdnlqj xvh ri wkh vroxwlrqv lq htxdwlrq +D14, dqg wkh gh(cid:31)0 qlwlrq ri lq dwlrq lq htxdwlrq +W50;,/ dqg wdnlqj dffrxqw ri rxu dvvxpswlrq wkdw wkh vkrfnv duh l1l1g1 |lhog wkh iroorzlqj gl(cid:30)huhqfh htxdwlrq= Z ’ E(cid:14) n(cid:14) (cid:28)Z c (cid:26) ’ 2c(cid:23)(cid:23)(cid:23)c4(cid:23) +D19, |n(cid:26)n(cid:129)(cid:131) | > Z |n(cid:26) (cid:131) | E|dvvxpswlrq/(cid:14) n(cid:14) (cid:24) f(cid:23)Li(cid:14) n(cid:14) : (cid:129)/dqgli/lqdgglwlrq/lwlvdvvxphgwkdwwkhuh > Z > Z duh qr vshfxodwlyh exeeohv/ wkhq lw iroorzv wkdw wkh lq dwlrq udwh/ wkh zdjh udwh dqg wkh lqwhuhvw udwh ^iurp htxdwlrq +D14,‘/ dqg wkh prqh| jurzwk udwh ^iurp htxdwlrqv +W508,/ +W50<,/ +D14,/ wkh dvvxpswlrq wkdw wkh vkrfnv duh l1l1g1/ dqg vroxwlrqv iru rwkhu yduldeohv lq htxdwlrq +D1:,‘ h{shfwhg wr suhydlo lq shulrg | n(cid:26)/ (cid:26) ’ 2c(cid:23)(cid:23)(cid:23)c4 edvhg rq shulrg | lqirupdwlrq duh Z ’ (cid:25) (cid:3)R (cid:3)Z ’ (cid:16) ’ > ’ f(cid:23) +D1:, |n(cid:26) (cid:131) | |n(cid:26) (cid:131) | |n(cid:26) 3(cid:129)(cid:131) | |n(cid:26) (cid:131) | |n(cid:26) (cid:131) | |n(cid:26) (cid:131) | Lw dovr iroorzv wkdw wkh lq dwlrq udwh ^iurp htxdwlrqv +W508,/ +W50:,/ +W50<,/ +D14,/ +D1:,/ dqg wkh dvvxpswlrq wkdw wkh vkrfnv duh l1l1g1‘/ wkh zdjh udwh dqg wkh lqwhuhvw udwh ^iurp htxdwlrq +D14, dqg +W50;,‘/ dqg wkh prqh| jurzwk udwh ^iurp htxdwlrqv +W50:,/ +W50<,/ +D14,/ +D1:,/ dqg wkh dvvxpswlrq wkdw wkh vkrfnv duh l1l1g1‘ h{shfwhg wr suhydlo lq shulrg |n(cid:129) edvhg rq shulrg | lqirupdwlrq duh (cid:14) Z ’ > E(cid:24)+ (cid:3)0(cid:16) n(cid:15) (cid:28)c (cid:25) (cid:3)R (cid:3)Z ’ fc |n(cid:129)(cid:131) | (cid:14) n(cid:14) | | | |n(cid:129)(cid:131) | | |n(cid:129)(cid:131) | Z > # $ (cid:14) (cid:16) ’ fc > ’ (cid:3) Z E(cid:24)+ (cid:3)0(cid:16) n(cid:15) (cid:28)(cid:23) +D1;, |n(cid:129)(cid:131) | |n(cid:129)(cid:131) | (cid:14) n(cid:14) | | | Z > Xvlqj d surfhgxuh wkdw lv dqdorjrxv lq hyhu| zd| wr wkh rqh xvhg wr rewdlq htxdwlrqv +D1:, dqg+D1;, h{fhsw wkdw h{shfwdwlrqv duh wdnhqedvhg rq shulrg |(cid:3)(cid:129) lqirupdwlrq/ lw fdq eh vkrzq wkdw wkh lq dwlrq udwh/ zdjh udwh/ lqwhuhvw udwh/ dqg prqh| jurzwk udwhh{shfwhgwrsuhydlolqshulrg|n(cid:26)/ (cid:26) ’ (cid:129)c(cid:23)(cid:23)(cid:23)c4edvhgrqshulrg|(cid:3)(cid:129)lqirupdwlrq duh Z ’ (cid:25) (cid:3)R (cid:3)Z ’ (cid:16) ’ > ’ fc +D1<, |n(cid:26) (cid:131) | 3(cid:129) |n(cid:26) (cid:131) | 3(cid:129) |n(cid:26) 3(cid:129)(cid:131) | 3(cid:129) |n(cid:26) (cid:131) | 3(cid:129) |n(cid:26) (cid:131) | 3(cid:129) |n(cid:26) (cid:131) | 3(cid:129) dqg wkdw wkh lq dwlrq udwh/ zdjh udwh/ lqwhuhvw udwh/ dqg prqh| jurzwk udwh h{shfwhg wr suhydlo lq shulrg | edvhg rq shulrg |(cid:3)(cid:129) lqirupdwlrq duh (cid:14) Z ’ > E(cid:24)+ (cid:3)0(cid:16) n(cid:15) (cid:28)c (cid:25) (cid:3)R (cid:3)Z ’ fc | (cid:131) | 3(cid:129) (cid:14) n(cid:14) | 3(cid:129) | 3(cid:129) | 3(cid:129) | (cid:131) | 3(cid:129) | 3(cid:129) | (cid:131) | 3(cid:129) Z > # $ (cid:14) (cid:16) ’ fc > ’ (cid:3) Z E(cid:24)+ (cid:3)0(cid:16) n(cid:15) (cid:28)(cid:23) +D143, | (cid:131) | 3(cid:129) | (cid:131) | 3(cid:129) (cid:14) n(cid:14) | 3(cid:129) | 3(cid:129) | 3(cid:129) Z > 67

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Figure 1: Schedules p p p AD 1 AD R y AD 1 AD 0 AS 0 R p AS R R 1 1 R R m&i R 0 0 R py PY PY y y y Panel A: Wage Stickiness, Levels Model Panel C: Reaction Schedules, Levels Model Panel E: Wage and Price Stickiness, Levels Model B B B AD AD R AD AD 1 0 y 1 0 AS R AS B R 1 R R R 0 µ 0 P Y R By P Y y y y Panel B: Wage Stickiness, Combination Model Panel D: Reaction Schedules, Combination Model Panel F: Wage and Price Stickiness, Combination Model

Figure 2: Effects of Shocks with Wage Stickiness, Levels Model p p p AD AD AD AD AS 0 1 AS AS 0 AS 1 b a a a c b d b R R R m&i m&i,0 m&i R m&i,1 PY PY PY y y y Panel A1: Money Demand; IT, MT Panel B1: Goods Demand; IT, MT Panel C1: Productivity; IT, MT p p p AD R AD R AD R AD y y AS 0 y 1 AS AS 0 AS 1 a e a a R R R p p p d f R R R py py py PY PY PY y y y Panel A2: Money Demand; PT, YT, PYT Panel B2: Goods Demand; PT, YT, PYT Panel C2: Productivity; PT, YT, PYT

Figure 3: Effects of Shocks with Wage Stickiness, Combination Model B B B AD AD AD 0 1 AD AS AS AS 0 AS 1 b a a a c b d b R R R µ,0 µ µ R µ,1 P Y P Y P Y y y y Panel A1: Money Demand; MT Panel B1: Goods Demand; MT Panel C1: Productivity; MT B B B AD AD AD AD 0 1 AS AS AS R R R 0 y y y AS 1 a a a e R B R B R B d f R By R By R By P Y P Y P Y y y y Panel A2: Money Demand; PT, YT, PYT Panel B2: Goods Demand; PT, YT, PYT Panel C2: Productivity; PT, YT, PYT

Figure 4: Effects of Shocks with Wage and Price Stickiness, Levels Model p p p AD AD AD AD 0 1 a a b a AS AS AS b R R R m&i,0 m&i,0 m&i,0 R m&i,1 PY PY PY y y y Panel A1: Money Demand; IT, MT Panel B1: Goods Demand; IT, MT Panel C1: Productivity; IT, MT p p p AD R y AD 0 R y AD 1 AD R y a a a AS AS AS R R R p p p R R R py py py PY PY PY y y y Panel A2: Money Demand; PT, YT, PYT Panel B2: Goods Demand; PT, YT, PYT Panel C2: Productivity; PT, YT, PYT

Figure 5: Effects of Shocks with Wage and Price Stickiness, Combination Model B B B AD AD AD AD 0 1 a a b a AS AS AS b R µ,0 R µ R µ R µ,1 P Y P Y P Y y y y Panel A1: Money Demand; MT Panel B1: Goods Demand; MT Panel C1: Productivity; MT B B B AD AD AD AD 0 1 R R R y y y a a a AS AS AS R B R B R B R By R By R By P Y P Y P Y y y y Panel A2: Money Demand; PT, YT, PYT Panel B2: Goods Demand; PT, YT, PYT Panel C2: Productivity; PT, YT, PYT