The Equivalence of Wage and Price Staggering in Monetary Business Cycle Models

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 672 July 2000 THE EQUIVALENCE OF WAGE AND PRICE STAGGERING IN MONETARY BUSINESS CYCLE MODELS Rochelle M. Edge 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publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.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 EQUIVALENCE OF WAGE AND PRICE STAGGERING IN MONETARY BUSINESS CYCLE MODELS Rochelle M. Edge* Abstract: Chari, Kehoe, and McGratten’s (1998) finding that a standard monetary business cycle model with staggered price setting is unable to generate sufficiently persistent real effects of monetary shocks has engendered a growing literature aimed at developing alternative mechanisms for producing greater persistence. The most popular approach at present in this literature appears to be one in which staggered wage contracts are used as either an alternative or a complement to a staggered price mechanism. This is informed by recent research by Andersen (1998) and Huang and Liu (1998) which finds that the staggered wage model, despite its superficial similarity to the staggered price setup, incorporates a very different microstructure that implies substantially more real persistence. This paper argues that these authors’ findings rely heavily on the assumption that identical inputs are used by all firms, and demonstrates that, by assuming firm-specific factor inputs the staggered price model is as capable as the staggered wage model of generating persistent real responses to monetary shocks. Keywords: Taylor contracting, output persistence, sticky prices, sticky wages, firm-specific factor inputs. * Mailstop 23, Federal Reserve Board, Washington DC 20551, (202) 452 2339; FAX: (202) 736-5638; rochelle.m.edge@frb.gov. I thank Michael Woodford for his advice and helpful conversations as well as Ben Bernanke, Jonathan Parker, Jeremy Rudd, Robert Shimer, Chris Sims, and Peter Storgaard for comments on earlier drafts. All errors are my own. After completing a previous draft of this paper, I became aware of Ascari and Garcia’s independently written 1999 paper, which makes several similar points. The views in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views 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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Vlqfh krxvhkrogv uhfhlyh gl(cid:30)huhqw zdjhv dqg zrun gl(cid:30)huhqw krxuv ghshqglqj rq zkhwkhu k l (cid:19) l k l (cid:19) l wkh| duh phpehuv ri 3>(cid:129) ru (cid:129)>4 +hyhq wkrxjk zlwklq wkhlu vxelqwhuydo 3>(cid:129) ru (cid:129)>4 2 2 2 2 wkh| duh lghqwlfdo,/ wkhlu dffxpxodwhg zhdowk dqg frqvxpswlrq sur(cid:31)ohv duh olnho| wr gl(cid:30)hu1 Wr vlpsoli| wkh sureohp dqg doorz d vlqjoh frqvxpswlrq sur(cid:31)oh wr fkdudfwhul}h doo krxvh0 krogv/ L dvvxph wkdw dvvhw sruwirolrv fdq eh frqvwuxfwhg vr dv wr surylgh wkh krxvhkrog zlwk frpsohwh lqvxudqfh djdlqvw dq| lglrv|qfudwlf ulvn1 Frqvhtxhqwo|/ d krxvhkrog*v zhdowk lv U lqghshqghqw ri wkh shulrg lq zklfk lw vhwv lwv zdjh1 Vlqfh F @ (cid:129)F(cid:16)gl/ wklv dvvxpswlrq | f | doorzv wkh l vxshuvfulswv wr eh gursshg iurp htxdwlrq +;,1 Wklv dvvxpswlrq lv xvhg uhshdw0 hgo| wkurxjkrxw wkh sdshu lq vlwxdwlrqv zkhuh gl(cid:30)huhqw krxvhkrogv uhfhlyh gl(cid:30)huhqw oderu lqfrphv1 415 Orj0olqhdul}lqj dqg Vroylqj wkh Prgho Dv lv vwdqgdug/ d vroxwlrq lv rewdlqhg e| orj0olqhdul}lqj wkh ehkdylrudo htxdwlrqv durxqg d vwhdg|0vwdwh htxloleulxp17 Wkh lpsruwdqw orj0olqhdul}hg htxdwlrqv duh wkrvh iru wkh krxvh0 krogv*oderuvxsso|ghflvlrq/wkhhyroxwlrqriwkhlq dwlrqudwh/dqgwkhhyroxwlrqriqrplqdo rxwsxw18 Xvlqj wkh vxevwlwxwlrqv doorzhg e| htxdwlrqv +5, dqg +8,/ wkhvh IRFv ehfrph= (cid:21) (cid:22) 4 (cid:15) (cid:15) zeh @(cid:16) \e . H \e . H (cid:8)e | 4.(cid:15) | 4.(cid:15) | |n(cid:129) 4.(cid:15) | |n(cid:129) (cid:8)e @$eh .$eh > dqg | | |3(cid:129) % @\e (cid:3)\e .(cid:8)e | | |3(cid:129) | Wkh sdudphwhu (cid:16)/ zklfk kdv wkh lqwhusuhwdwlrq ri wkh hodvwlflw| ri zdjhv zlwk uhvshfw wr rxwsxw/ lv htxdo wr 4 34 / zkhuh (cid:29) dqg (cid:29) duh wkh hodvwlflwlhv ri lqwhuwhpsrudo frqvxps0 (cid:5)(cid:5) SS (cid:129)nj4 SS (cid:5)(cid:5) wlrq dqg oderu vxevwlwx(cid:5)w(cid:5)lrq19 Ixuwkhu pdqlsxodwlrqv |lhog wkh iroorzlqj v|vwhp ri olqhdu gl(cid:30)huhqfh htxdwlrqv= 5 65 6 5 65 6 5 6 (cid:14)3(cid:129) 3 (cid:3)4 H \e (cid:3)(cid:14)n(cid:129) 3 3 \e 3 9 7 (cid:129)n 3 q 3 4 : 8 9 7 | \e |n(cid:129) : 8@ 9 7 (cid:3) (cid:129)n 4 q 4 (cid:3)4 : 8 9 7 \e | : 8. 9 7 4 : 8^% ‘= +43, | |3(cid:129) | 3 4 3 $eh 4 3 3 $eh 3 | |3(cid:129) (cid:13)(cid:8) (cid:13)(cid:18) (cid:13)(cid:28) q r 7Htxloleulxp lv dq doorfdwlrq t(cid:28) /(cid:127)w/M /t (cid:27)" dqg d vhtxhqfh ri sulfhv (cid:31) //h /- /(cid:127)j(cid:28) " wkdw vdwlvi| htxdwlrqv +4, wr +8, dqg +;, | wr (cid:27)w +<,/ | j | lyh |’ q f wkh vhtxhqfh ri prqhwdu| srol | f n | (cid:129) vk | rfn | v t0 | (cid:27)"|’ 1 f Wkh | |’f yduldeohv wkdw frqvwlwxwh wkh htxloleulxp kdyh ehhq gh(cid:31)qhg vr dv wr hqvxuh wkdw wkhlu vwhdg|0vwdwh ydoxhv uhpdlq frqvwdqw ryhu wlph1 8Lq zkdw iroorzv/ d fduhw ryhu d yduldeoh ghqrwhv lwv shufhqwdjh ghyldwlrq iurp lwv vwhdg|0vwdwh ydoxh1 9Kxdqj dqg Olx*v +4<<;, prgho lpsolhv 4 ’3(cid:129)/zkloh Dqghuvhq*v +4<<;, prgholpsolhv 4 ’f1 SS SS 8

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51415 Wkh Ilupv* Sureohp Wkh prqrsrolvwlfdoo| frpshwlwlyh (cid:31)up m dfwv dv d sulfh0wdnhu lq klulqj wkh krprjhqhrxv oderu lqsxw dqg surgxfhv lwv gl(cid:30)huhqwldwhg jrrg dffruglqj wr wkh surgxfwlrq ixqfwlrq \(cid:26) @K(cid:26) (cid:3)IF | | zkhuh IF/ zklfk uhsuhvhqwv wkh (cid:31){hg frvw idfhg e| wkh (cid:31)up/ lv vhw vr dv wr ohdyh wkh (cid:31)up zlwk qr prqrsro| uhqwv lq wkh orqj uxq1 Dv ehiruh/ wklv surgxfwlrq ixqfwlrq lpsolhv wkdw wkh pdujlqdo frvw idflqj wkh (cid:31)up lv htxdo wr wkh zdjh ri wkh krprjhqhrxv lqsxw +wkdw lv/ PF(cid:26) @$ ,1 | | Wzr0shulrg vwdjjhuhg sulfh vhwwlqj lv ghvfulehg lq wkh vdph zd| wkdw zdjh vwdjjhulqj k l zdv prghohg deryh> vshfl(cid:31)fdoo|/ (cid:31)upv lqgh{hg e| m 5 3>(cid:129) vhw qhz zdjhv lq shulrgv (cid:19) l 2 iw.5nj" / zkloh wkrvh lqgh{hg e| m 5 (cid:129)>4 vhw qhz zdjhv lq shulrgv iw.5n.4j" 1 &’f 2 k l &’f Wkxv/ wkh (cid:31)uvw0rughu frqglwlrq iru sulfhv iru (cid:31)up m zkhuh m 5 3>(cid:129) lv jlyhq e|= 2 5 (cid:19) (cid:20) (cid:19) (cid:20) 6 {h @ (cid:21) (cid:21) (cid:22) H 9 7 \ | PjF(cid:26) | . (cid:31) (cid:19) - |n | (cid:129) (cid:20) \ |n(cid:129) P (cid:19) jF(cid:26) |n (cid:20) (cid:129) (cid:31)| (cid:129) n(cid:129) 3w : 8> +49, | (cid:21)(cid:3)4 | 3w \ . (cid:129) \ (cid:129) | -| |n(cid:129) (cid:31)|n(cid:129) zkhuh {h ghqrwhv wkh udwlr ri sulfhv vhw wklv shulrg wr wkh djjuhjdwh sulfh ohyho dqg PjF(cid:26) | | ghqrwhv wkh uhdo pdujlqdo frvw ri surgxfwlrq iru (cid:31)up m lq shulrg w1 D qxpehu ri vlpsoh vxevwlwxwlrqv |lhogv wkh iroorzlqj h{suhvvlrq iru pdujlqdo frvw= (cid:19)U (cid:20) PjF(cid:26) @ $ | @ Y(cid:30)+K | , @ Y(cid:30) f (cid:129)K | (cid:26)gm @ 4 Y(cid:30) (cid:21)] (cid:129) (cid:19) \(cid:26) .IF (cid:20) gm (cid:22) | S X(cid:30)+F , X(cid:30)+F , X(cid:30)+\ , | | #| # | (cid:21) (cid:22) $| $f 4 4 {h 3w 4 @ Y(cid:30) \ +{h ,3w . |3(cid:129) .IF @ Y(cid:30)+\ .IF,= X(cid:30)+\ , 5 | | (cid:8) X(cid:30)+\ , | | | | Lw lv dssduhqw iurp wkh deryh htxdwlrq wkdw ehfdxvh doo (cid:31)upv xvh wkh vdph krprjhqhrxv oderu lqsxw/ wkh| doo idfh wkh vdph pdujlqdo frvw ri surgxfwlrq dqg zloo wkhuhiruh doo vhw wkh vdph qhz sulfh1 Dv d uhvxow/ wkh sulfh0vhwwlqj htxdwlrq +49, fdq eh zulwwhq zlwkrxw wkh m vxshuvfulswv1 Ilqdoo|/ vxevwlwxwlqj iru pdujlqdo frvw lq htxdwlrq +49, |lhogv= 5 (cid:19) (cid:20) (cid:19) (cid:20) 6 {h @ (cid:21) (cid:21) (cid:22) H 9 7 L(cid:30) t Et | |(cid:28) Y(cid:30)+\ | .IF,. (cid:31) (cid:19) - |n | (cid:129) (cid:20) L(cid:30) t Et |n |n (cid:129) (cid:19)(cid:129)(cid:28) Y(cid:30)+ (cid:20) \ |n(cid:129) .IF, (cid:31)| (cid:129) n(cid:129) 3w : 8= +4:, | (cid:21)(cid:3)4 | 3w \ . (cid:129) \ (cid:129) | -| |n(cid:129) (cid:31)|n(cid:129) ;

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\ @ #(cid:21)] (cid:129) (cid:19) K(cid:16) (cid:20) j3 j (cid:129) gl (cid:22) j3 j (cid:129) $ (cid:129)3k N k +54, | | | f zkhuh N lv wkh hfrqrp|*v fdslwdo vwrfn dqg (cid:14) lv wkh hodvwlflw| ri rxwsxw zlwk uhvshfw wr | fdslwdo1 Wkh(cid:31)up*v frvw0plqlpl}dwlrqsureohp|lhogv wkh iroorzlqj htxdwlrqv iru K(cid:16) dqg N = | | (cid:21) (cid:14) (cid:22) 3k # (cid:13)h $ 3k 3 /(cid:16) | 4 3j K(cid:16) @ \ | C(cid:27)| D +55, | 4(cid:3)(cid:14) | (cid:29)h (cid:13)h | | (cid:21) (cid:14) (cid:22) (cid:129)3k # (cid:13)h $ (cid:129)3k N @ \ | +56, | 4(cid:3)(cid:14) | h(cid:29) | zkhuh h(cid:29) lv wkh uhdo uhqwdo udwh rq wkh hfrqrp|*v fdslwdo vwrfn dqg (cid:13)h lv d uhdo zdjh lqgh{ | | jlyhq e|= 3 ] (cid:129) # $(cid:16) $ (cid:129)3j 4 (cid:129)3 (cid:129) j (cid:13)h @C | glD = +57, | S f | Shuihfw frpshwlwlrq lq wkh jrrgv pdunhw lpsolhv wkdw uhdo pdujlqdo frvw pxvw dozd|v htxdo rqh= # (cid:13)h $ (cid:129)3k (cid:21) h(cid:29) (cid:22) k PjF @ | | @4= +58, | 4(cid:3)(cid:14) (cid:14) Wkh suhihuhqfhv ri krxvhkrog l duh uhsuhvhqwhg e| wkh xwlolw| ixqfwlrq= ; 5 # # $ $ 6< X(cid:16) @H ?[" (cid:15)|7oq e (cid:19) F(cid:16) (cid:20) (cid:15) .+4(cid:3)e, P | (cid:16) (cid:15) (cid:15) (cid:129) .(cid:20)oq (cid:19) 4(cid:3)K(cid:16) (cid:20) 8 @ +59, f f= | S | > |’f | zkhuh e/ (cid:26) dqg (cid:20) duh sdudphwhuv1 Wkh krxvhkrog*v rz exgjhw frqvwudlqw lv= E(cid:16) .P(cid:16) (cid:23)U E(cid:16) .P(cid:16) .$(cid:16)K(cid:16) .(cid:29) N(cid:16).surilwv (cid:3)W(cid:16)(cid:3)S F(cid:16)= +5:, | | |3(cid:129) |3(cid:129) |3(cid:129) | | | | | | | | (cid:11) (cid:12) " Krxvhkrog l fkrrvhv F(cid:16)>P(cid:16)>N(cid:16)>$(cid:16) wr pd{lpl}h lwv xwlolw| vxemhfw wr lwv exgjhw frq0 | | | | |’f vwudlqw/wkhoderughpdqgixqfwlrqvshfl(cid:31)fwrlwvgl(cid:30)huhqwldwhgoderuvhuylfh+htxdwlrq+55,,/ dqg wkh hyroxwlrq ri lwv kroglqj ri wkh fdslwdo vwrfn= # $ L(cid:16) H N(cid:16) @+4(cid:3)(cid:17),N(cid:16).N(cid:16)M | > +5;, | |n(cid:129) | | N(cid:16) | (cid:19) (cid:20) zkhuh (cid:17) lv wkh udwh ri ghsuhfldwlrq rq fdslwdo dqg N(cid:16)M U | (cid:16) ghvfulehv wkh frvw ri fkdqjlqj | g(cid:16) wkh fdslwdo vwrfn1 Iroorzlqj Kd|dvkl +4<;5,/ wkh ixqfwlr|q M+=, lv dvvxphg wr kdyh wkh surshuwlhv M+(cid:17), @(cid:17)/ M(cid:30)+(cid:17), @4/ dqg M(cid:30)(cid:30)+(cid:17), (cid:23)31 47

Wkh krxvhkrog*v xwlolw|0pd{lpl}dwlrq sureohp |lhogv Hxohu dqg oderu vxsso| htxdwlrqv wkdw duh vlplodu wr htxdwlrqv +;, dqg +<,= 3 (cid:19) (cid:20)4 53 (cid:21) (cid:22)46 E C X (cid:28) (cid:30) F S | (cid:16)>(cid:127) (cid:27)| | (cid:16) F D@U | (cid:15)H | 9 9 7 E E C X (cid:28) (cid:30) F S | (cid:16) n(cid:129) >(cid:127) (cid:27)| | (cid:16) n n (cid:129) (cid:129) F F D : : 8 dqg +5<, | |n(cid:129) 5 6 (cid:19) (cid:20) (cid:21) (cid:30) (cid:22) 9 \ (cid:20) 4(cid:3)\ +$h ,3j 3(cid:129) : $h | @ (cid:30)(cid:3)4 H | 9 7 \ X(cid:30) (cid:19) F(cid:16)>(cid:127) | (cid:16) (cid:20) . | (cid:15)\ (cid:19) | (cid:129) | (cid:20) (cid:129)3j X(cid:30) (cid:21) F(cid:16) >(cid:127) | (cid:16) n(cid:129) (cid:22): 8 +63, | (cid:28) | (cid:27)| |n(cid:129) (cid:31)|n(cid:129) (cid:28) |n(cid:129) (cid:27)|n(cid:129) 5 (cid:19) (cid:20) 3j (cid:21) (cid:19) h (cid:20) 3j (cid:22) 3(cid:129) 6 . (cid:21) (cid:30) (cid:22) H 9 9 9 (cid:15) (cid:19) \ |n(cid:129) (cid:31) (cid:20) | (cid:129) n(cid:129) (cid:20) (cid:19) 4(cid:3)\ (cid:20) |n(cid:129) (cid:31) / |n | (cid:129)(cid:21) (cid:22) : : : (cid:30)(cid:3)4 |7 \ X(cid:30) F(cid:16)>(cid:127) | (cid:16) .(cid:15)\ (cid:129) (cid:129)3j X(cid:30) F(cid:16) >(cid:127) | (cid:16) n(cid:129) 8 | (cid:28) | (cid:27)| |n(cid:129) (cid:31)|n(cid:129) (cid:28) |n(cid:129) (cid:27)|n(cid:129) zkhuh= # $ (cid:21) (cid:22) (cid:3) (cid:4) P(cid:16) 4 e F(cid:16) (cid:15) X (cid:28) (cid:30) F | (cid:16)> S | | @ F | (cid:16) e (cid:3) F(cid:16) (cid:4) (cid:15) .+4(cid:3) | e, (cid:19) (cid:127) | (cid:16) (cid:20) (cid:15) > | (cid:27)| wrjhwkhu zlwk d prqh| ghpdqg ixqfwlrq= (cid:21)(cid:21) (cid:22)(cid:21) (cid:22)(cid:22) P(cid:16) e 4 3(cid:129) | @F(cid:16) 4(cid:3) (cid:129)3D +64, S | 4(cid:3)e U | | dqg d fdslwdo vxsso| ixqfwlrq= % ## $ $& U N(cid:16) H | M3(cid:129)(cid:30) |n(cid:129) (cid:3)+4(cid:3)(cid:17), +65, | (cid:8) N(cid:16) % |n(cid:129) ## | $ $ # $ ## $ $& N(cid:16) N(cid:16) N(cid:16) @ H h(cid:29) (cid:3)M3(cid:129) |n2 (cid:3)+4(cid:3)(cid:17), . |n2 M3(cid:129)(cid:30) |n2 (cid:3)+4(cid:3)(cid:17), = | |n(cid:129) N(cid:16) N(cid:16) N(cid:16) |n(cid:129) |n(cid:129) |n(cid:129) Wkh (cid:31)uvw0rughu frqglwlrqv duh orj0olqhdul}hg dqg fdoleudwhg zlwk wkh vdph sdudphwhu ydoxhv xvhg e| Kxdqj dqg Olx +4<<;,> ghwdlov ri wkhvh vwhsv duh jlyhq lq wkh dsshqgl{1 Iljxuh 4 glvsod|v wkh uhvsrqvh ri uhdo rxwsxw wr d prqhwdu| vkrfn lpsolhg e| wklv prgho iru wkh ydulrxv ydoxhv ri (cid:30) xvhg e| Kxdqj dqg Olx +4<<;,146 Dv zrxog eh h{shfwhg/ wkh uhvxowv(cid:25)zklfk vkrz d shuvlvwhqw uhvsrqvh ri uhdo rxwsxw(cid:25)duh vlplodu wr wkrvh ri Kxdqj dqg Olx +4<<;,1 Wkh ghjuhh ri shuvlvwhqfh lqfuhdvhv zlwk (cid:30)/ vlqfh kljkhu vxevwlwxwdelolw| ehwzhhq oderu lqsxwv uhgxfhv wkh dgmxvwphqw wkdw krxvhkrogv pdnh wr qrplqdo zdjhv1 46Vlqfh L dp pruh lqwhuhvwhg lq h{dplqlqj dqg frpsdulqj wkh shuvlvwhqfh/ udwkhu wkdq wkh devroxwh pdj0 qlwxgh/ ri wkh uhvsrqvhv/ L uhvfdoh wkh uhvsrqvh ri rxwsxw vr wkdw lw htxdov rqh lq wkh lqlwldo shulrg1 Wklv doorzv ph wr ghwhuplqh txlfno| zkdw iudfwlrq ri wkh lqlwldovkrfn shuvlvwv lq dq| jlyhq shulrg1 48

715 D Vwdjjhuhg Sulfh Prgho Wkh pruh ghwdlohg yduldqw ri wkh vwdjjhuhg sulfh prqhwdu| exvlqhvv f|foh prgho zlwk (cid:31)up0 vshfl(cid:31)fidfwrulqsxwveurdgo|fruuhvsrqgvwrwkhprghosuhvhqwhglqvhfwlrqv516dqg517/exw zlwk fdslwdo lqwurgxfhg1 Wkh prqh| jurzwk surfhvv dqg pdunhw0fohdulqj frqglwlrq duh vwloo jlyhq e| htxdwlrqv +4<, dqg +53,/ zkloh wkh xwlolw| ixqfwlrq lv jlyhq e| htxdwlrq +59, +exw zlwkF(cid:16) qrzgh(cid:31)qhge|htxdwlrq+45,,1 Zlwkerwkidfwrulqsxwvqrz(cid:31)up0vshfl(cid:31)f/krxvhkrog | l*v exgjhw frqvwudlqw fkdqjhv vr wkdwwkh fdslwdouhqwdo udwh lv lqgh{hg e|krxvhkrog +wkdw lv (cid:29)(cid:16), lq wkh vdph pdqqhu wkdw wkh zdjh udwh +$(cid:16), lv lqgh{hg1 Krxvhkrogv* Hxohu htxdwlrq dqg | | prqh| ghpdqg htxdwlrq duh vwloo jlyhq e| +5<, dqg +64,/ zkloh wkh fdslwdo vxsso| htxdwlrq lv prgl(cid:31)hg wr fdswxuh wkh (cid:31)up0vshfl(cid:31)f qdwxuh ri fdslwdo +wkdw lv/ wkh uhqwdo udwh lq htxdwlrq +65, lv qrz lqgh{hg e| krxvhkrog,1 Vlqfh krxvhkrogv qr orqjhu kdyh pdunhw srzhu ryhu wkhlu oderu/ wkh (cid:31)uvw0rughu frqglwlrq iru krxuv vxssolhg ehfrphv= (cid:19) (cid:20) $(cid:26) Y(cid:30) K(cid:26) | @ (cid:19) | (cid:20)= +66, S | X(cid:30) F(cid:16)>(cid:127) | (cid:16) (cid:28) | (cid:27)| Ilup m qrz idfhv d surgxfwlrq ixqfwlrq zlwk erwk (cid:31)up0vshfl(cid:31)f fdslwdo dqg oderu lqsxwv= (cid:19) (cid:20) (cid:19) (cid:20) \(cid:26) @ K(cid:26) (cid:129)3k N(cid:26) k (cid:3)IF +67, | | | zklfk |lhogv wkh iroorzlqj (cid:31)up0vshfl(cid:31)f idfwru ghpdqg ixqfwlrq= (cid:21) (cid:14) (cid:22) 3k 3 /(cid:26) | 43k K(cid:26) @ \(cid:26)C(cid:27)| D dqg +68, | 4(cid:3)(cid:14) | (cid:29)h(cid:26) | (cid:21) (cid:14) (cid:22) (cid:129)3k 3 /(cid:26) | 4 (cid:129)3k N(cid:26) @ \(cid:26)C(cid:27)| D = +69, | 4(cid:3)(cid:14) | (cid:29)h(cid:26) | Ilup m*v sulfh0vhwwlqj sureohp lv lghqwlfdo wr wkdw ri vhfwlrq 5/ lpso|lqj d sulfh0vhwwlqj uxoh olnh htxdwlrq +49,1 Zlwk wzr (cid:31)up0vshfl(cid:31)f idfwruv ri surgxfwlrq/ (cid:31)up m*v pdujlqdo frvw ehfrphv= # $ $(cid:26) k PjF(cid:26) @+(cid:29)h ,(cid:129)3k | = +6:, | | S | Wkh (cid:31)uvw0rughu frqglwlrqv duh orj0olqhdul}hg dqg fdoleudwhg dv ehiruh +vhh wkh dsshqgl{,1 Iljxuh 5 glvsod|v wkh uhvsrqvh ri rxwsxw wr d prqhwdu| vkrfn lq wklv prgho1 Wr jlyh vrph lqglfdwlrq ri wkh lqfuhdvhg shuvlvwhqfh eurxjkw derxw e| wkh dvvxpswlrq ri (cid:31)up0vshfl(cid:31)f idfwru lqsxwv/ L dovr suhvhqw lq Iljxuh 5 wkh uhvsrqvhv ri uhdo rxwsxw iurp yhuvlrqv ri wklv prgho zlwk (cid:31)up0vshfl(cid:31)f oderu dqg krprjhqhrxv fdslwdo/ dqg zlwk erwk krprjhqhrxv oderu 49

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^47‘ Nrhqlj/ Hydq I1/ (cid:19)Djjuhjdwh Sulfh Dgmxvwphqw= Wkh Ilvkhuldq Dowhuqdwlyh/(cid:20) Plphr/ 4<<:1 ^48‘ Urwhpehuj/ Mxolr M1/ (cid:19)Sulfhv/ Rxwsxw/ dqg Krxuv= Dq Hpslulfdo Dqdo|vlv Edvhg rq d Vwlfn| Sulfh Prgho/(cid:20) Mrxuqdo ri Prqhwdu| Hfrqrplfv/ 4<<9/ 6:/ 83808661 ^49‘ Wd|oru/ Mrkq E1/ (cid:19)Djjuhjdwh G|qdplfv dqg Vwdjjhuhg Frqwudfwv/(cid:20) Mrxuqdo ri Srolwlfdo Hfrqrp|/ 4<;3/ ;;/ 40561 D Dsshqgl{ D14 Orj0olqhdul}lqj dqg Fdoleudwlqj wkh Pruh Ghwdlohg Vwdjjhuhg Zdjh Prgho Wkh (cid:31)up*v (cid:31)uvw0rughu frqglwlrqv/ htxdwlrqv +55, wr +58,/ orj0olqhdul}h wr= Ke(cid:16) @\e (cid:3)(cid:30)$eh .+(cid:30)(cid:3)(cid:14),(cid:13) eh .(cid:14)(cid:29)eh zkhuh l5ikrxvhkrogv zkr uhvhw zdjhv lq shulrg wj +6;, | | | | | Ke(cid:16) @\e .(cid:30)$eh .+(cid:30)(cid:3)(cid:14),(cid:13) eh .(cid:14)(cid:29)eh zkhuh l5@ ikrxvhkrogv zkr uhvhw zdjhv lq shulrg wj +6<, | | | | | Nf @\e .+4(cid:3)(cid:14),(cid:13) eh (cid:3)+4(cid:3)(cid:14),eh(cid:29) > +73, | | | | (cid:13) eh @$eh .$eh > dqg +74, | | |3(cid:129) +4(cid:3)(cid:14),(cid:13) eh .(cid:14)eh(cid:29) @3= +75, | | Wkh krxvhkrog*v (cid:31)uvw0rughu frqglwlrqv/48 htxdwlrqv +5<, wr +65,/ orj0olqhdul}h wr= f f (cid:29) Fe .(cid:29) Pi @Ue .(cid:29) H Fe .(cid:29) Pi (cid:3)(cid:8)e > +76, SS | S6 | | SS | |n(cid:129) S6 |n(cid:129) |n(cid:129) (cid:21) (cid:22)(cid:21)(cid:21) (cid:22) (cid:21) (cid:22) (cid:22) (cid:29) 4 (cid:15) $eh @ (cid:5)(cid:5) Ke . H Ke +77, | 4.(cid:30)(cid:29) 4.(cid:15) | 4.(cid:15) | |n(cid:129) (cid:21) (cid:5)(cid:5) (cid:22)(cid:21)(cid:21) (cid:22) (cid:21) (cid:22) (cid:22) (cid:29) 4 (cid:15) (cid:3) SS Fe . H Fe 4.(cid:30)(cid:29) 4.(cid:15) | 4.(cid:15) | |n(cid:129) (cid:21) (cid:5)(cid:5)(cid:22)(cid:21)(cid:21) (cid:22) (cid:21) (cid:22) (cid:22) (cid:21) (cid:22) . (cid:30)(cid:29) (cid:5)(cid:5) 4 (cid:13) eh . (cid:15) H(cid:13) eh . (cid:15) H(cid:8)e > 4.(cid:30)(cid:29) 4.(cid:15) | 4.(cid:15) |n(cid:129) 4.(cid:15) |n(cid:129) (cid:5)(cid:5) 48Lqzkdwiroorzv/dvxshuvfulswdvwhulvn+-,rqdyduldeohghqrwhvlwvohyholqwkhvwhdg|0vwdwhhtxloleulxp1 4<

(cid:21) (cid:22)(cid:21) (cid:22) f 4 4 Pi @Fe (cid:3) Ue > dqg +78, | | 4(cid:3)(cid:26) UW | (cid:29) (cid:30) (cid:29) (cid:30) 4 4 Ue (cid:3) (cid:8)e 4.(cid:17)(cid:15)(cid:3)(cid:15) | 4.(cid:17)(cid:15)(cid:3)(cid:15) |n(cid:129) M3(cid:129)(cid:30)(cid:30)+(cid:17), (cid:19) (cid:20) @ H (cid:29)eh . (cid:15)H Nf (cid:3)+4.(cid:15),Nf .Nf > +79, | |n(cid:129) 4.(cid:17)(cid:15)(cid:3)(cid:15) | |n2 |n(cid:129) | zkhuh KW (cid:29) @ > (cid:5)(cid:5) 4(cid:3)KW (cid:26) (cid:29) @ (cid:19) (cid:20)(cid:19) (cid:20) (cid:19) (cid:20) (cid:3)4> dqg SS D D K (cid:129)3K D3(cid:129) -W D3(cid:129) .4 (cid:129)3K K -W3(cid:129) (cid:26) (cid:29) @(cid:3)(cid:19) (cid:20)(cid:19) (cid:20) (cid:19) (cid:20) = S6 D D K (cid:129)3K D3(cid:129) -W D3(cid:129) .4 (cid:129)3K K -W3(cid:129) Wkhpdunhw0fohdulqjfrqglwlrqwrjhwkhuzlwkwkhfdslwdovwrfnhyroxwlrqhtxdwlrq+htxdwlrqv +53, dqg +5;,, lpsolhv= (cid:21)(cid:21) (cid:22) (cid:21) (cid:22) (cid:22) 4 4(cid:3)(cid:17) \e @fFe .+4(cid:3)f, H Nf (cid:3) Nf +7:, | | (cid:17) | |n(cid:129) (cid:17) | zkhuh f +zklfk htxdov 4(cid:3) Bk, ghqrwhv frqvxpswlrq*v vkduh ri rxwsxw lq wkh vwhdg| vwdwh1 4 Wkh hyroxwlrq ri prqh| jurzwk lv jlyhq e|= (cid:25)e @(cid:29)(cid:25)e .% = +7;, | |3(cid:129) | L xvh wkh sdudphwhu ydoxhv ri Kxdqj dqg Olx +4<<;, wr fdoleudwh wkh prgho> wkhvh ydoxhv duh vxppdul}hg lq wkh wdeoh ehorz1 Wkh dvvxphg ohqjwk ri d (cid:19)shulrg(cid:20) lv vl{ prqwkv1 Wdeoh 4 0 Fdoleudwhg Sdudphwhu Ydoxhv Sdudphwhu= (cid:14) (cid:17) (cid:15) e (cid:26) (cid:29) M3(cid:129)(cid:30)(cid:30)+(cid:17), KW (cid:8)W Ydoxh= 3=66 3=373; 3=<:< 3=<; (cid:3)4=89 3=:8 6=4:5 3=66 4 Kxdqj dqg Olx*v +4<<;, dvvxphg ydoxhv iru (cid:14)/ (cid:17)/ dqg (cid:15) duh vwdqgdug1 Ydoxhv iru e dqg (cid:26) zhuh rewdlqhg e| (cid:31)wwlqj d uhjuhvvlrq iru prqh| ghpdqg +htxdwlrq +64,,/ zkloh (cid:29) zdv wdnhq iurp d uhjuhvvlrq prgho ri wkh prqh| jurzwk surfhvv +htxdwlrq +4<,,1 Kxdqj dqg Olx +4<<;, fkrvh M3(cid:129)(cid:30)(cid:30)+(cid:17), wr pdwfk wkh revhuyhg yrodwlolw| ri lqyhvwphqw uhodwlyh wr rxwsxw1 53

KW uh hfwv wkh dvvxpswlrq wkdw djhqwv doorfdwh rqh0wklug ri wkhlu wlph wr pdunhw dfwlylwlhv zkloh (cid:8)W lv vhw htxdo wr xqlw| lq rughu wr vlpsoli| wkh sureohp1 Dv (cid:15) @ (cid:31)W/ (cid:8)W @4 lpsolhv -W wkdw UW @ (cid:129)1 Kxdqj dqg Olx +4<<;, flwh d qxpehu ri vwxglhv hvwlpdwlqj wkh pdunxs rq q zdjhv dqg khqfh wkh sdudphwhu (cid:30)149 Wkhvh vwxglhv (cid:31)qg d udqjh ri ydoxhv iru (cid:30)/ vr Kxdqj dqg Olx h{shulphqw zlwk irxu ydoxhv ri (cid:30) +5/ 8/ 43> dqg 53,1 D15 Orj0olqhdul}lqj dqg Fdoleudwlqj wkh Pruh Ghwdlohg Vwdjjhuhg Sulfh Prgho Wkh (cid:31)up*v (cid:31)uvw0rughu frqglwlrqv/ htxdwlrqv +68, wr +6:, dqg +49,/ orj0olqhdul}h wr= (cid:21) (cid:22) g (cid:21)(cid:3)4 $& Ke& @ \e (cid:3)+(cid:21)(cid:3)4,{eh (cid:3)(cid:14) | .(cid:14)eh(cid:29)&zkhuh n 5i(cid:31)upv zkr uhvhw sulfhv lq shulrg wj> | (cid:21) | | S | | +7<, (cid:21) (cid:22) f (cid:21)(cid:3)4 $, Ke, @ \e .+(cid:21)(cid:3)4,{eh (cid:3)(cid:14) | .(cid:14)eh(cid:29),zkhuh o 5@ i(cid:31)upv zkr uhvhw sulfhv lq shulrg wj> | (cid:21) | | S | | +83, (cid:21) (cid:22) g (cid:21)(cid:3)4 $& Nf& @ \e (cid:3)+(cid:21)(cid:3)4,{eh .+4(cid:3)(cid:14), | (cid:3)+4(cid:3)(cid:14),(cid:29)eh &> +84, | (cid:21) | | S | | (cid:21) (cid:22) f (cid:21)(cid:3)4 $, Nf, @ \e .+(cid:21)(cid:3)4,{eh .+4(cid:3)(cid:14), | (cid:3)+4(cid:3)(cid:14),eh(cid:29),> +85, | (cid:21) | | S | | g P g jF & @+4(cid:3)(cid:14), $& | .(cid:14)(cid:29)eh &> +86, | S | | f P g jF , @+4(cid:3)(cid:14), $, | .(cid:14)eh(cid:29),> dqg +87, | S | | (cid:21) (cid:22) (cid:21) (cid:22) (cid:21) (cid:22) {eh @ 4 P g jF & . (cid:15) H P g jF , . (cid:15) H (cid:8)e > +88, | 4.(cid:15) | 4.(cid:15) | |n(cid:129) 4.(cid:15) | |n(cid:129) zkloh wkh orj0olqhdul}hg htxdwlrq iru wkh hyroxwlrq ri sulfhv lv lghqwlfdo wr wkdw ri vhfwlrq 5/ wkdw lv= 49Nrhqlj +4<<:, hvwlpdwhv d ydoxh ri j ’ 2f edvhg rq wkh dyhudjh pdunxs ri xqlrq zrunhuv* zdjhv ryhu qrq0xqlrq zrunhuv* zdjhv lq wkh XV gxulqj wkh shulrg 4<83 wr 4<;31 Nlp +4<<;,/ zkr xvhv d pd{lpxp0 olnholkrrgphwkrgrihvwlpdwlrq/(cid:31)qgvdydoxhrij’(cid:129)21 Ndw}dqgPxusk|+4<<5,/zkrxvhpruhdjjuhjdwhg gdwd/ (cid:31)qg hyhq orzhu hvwlpdwhv ri j1 54

(cid:8)e @{eh .{eh = +89, | | |3(cid:129) Wkhkrxvhkrog*vorj0olqhdul}hgHxohuhtxdwlrqdqgprqh|ghpdqghtxdwlrqlqwkhvwlfn|0 sulfh prgho duh jlyhq e| htxdwlrqv +76, dqg +78,/ zkloh wkh orj0olqhdul}hg fdslwdo vxsso| htxdwlrq lv vlplodu wr htxdwlrq +79,/ exw zlwk fdslwdo dqg lwv uhqwdo udwh lqgh{hg e| krxvh0 krog1 Ilqdoo|/ htxdwlrq +66, orj0olqhdul}hv wr= f $(cid:16) | @(cid:29) Ke(cid:16) (cid:3)(cid:29) Fe (cid:3)(cid:29) Pf S (cid:5)(cid:5) | SS | S6 | | zklohwkhpdunhw0fohdulqjfrqglwlrqdqghyroxwlrqriprqh|jurzwkduhlghqwlfdowrhtxdwlrqv +7:, dqg +7;,1 Wkh rqo| qhz sdudphwhu lq wklv prgho lv (cid:21)/ zklfk lv lq prvw fdvhv vhw htxdo wr 43 +wklv |lhogv d ydoxh ri 44 shufhqw iru (cid:31)upv* pdunxs ryhu pdujlqdo frvw1 55

Figure 3.1 - Impulse Responses of Output in the Staggered Wage Model 1 Sigma=20 Sigma=10 Sigma=5 0.8 Sigma=2 0.6 0.4 0.2 0 0 0.5 1 1.5 2 2.5 Years After the Shock Figure 3.2 - Impulse Responses of Output in the Staggered Price Model for Theta = 10 1 Firm-specific Labor and Capital 0.8 Firm-specific Labor, Homogeneous Capital Homogeneous Labor and Capital 0.6 0.4 0.2 0 -0.2 -0.4 0 0.5 1 1.5 2 2.5 Years After the Shock 23

Figure 3.3 - Impulse Responses of Output in the Staggered Wage and Staggered Price Models for Various Values of s and q Panel (a): s = q = 2 Panel (b): s = q = 5 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 -0.2 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Years After the Shock Years After the Shock Panel (c): s = q = 10 Panel (d): s = q = 20 1 1 Staggered-Prices 0.8 0.8 Staggered-Wages 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Years After the Shock Years After the Shock Figure 3.4 - Impulse Responses of the Real Wage in the Staggered Wage and Staggered Price Models for Various Values of s and q Panel (a): s = q = 2 Panel (b): s = q = 5 0.8 1 0.6 0.8 0.4 0.6 0.2 0.4 0 0.2 -0.2 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Years After the Shock Years After the Shock Panel (c): s = q = 10 Panel (d): s = q = 20 1.2 1.2 Staggered-Prices 1 1 Staggered-Wages 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 -0.2 -0.2 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Years After the Shock Years After the Shock 24