Optimal Monetary Policy with Informational Frictions *

Transcription

1 Opmal Moneary Polcy wh Informaonal Frcons * George-Maros Angeleos MIT and NBER Jennfer La O Columba and NBER Sepember 0, 207 Absrac Ths paper sudes opmal polcy n a busness-cycle seng n whch frms have a blurry undersandng of he sae of he economy due o nformaonal or cognve consrans. The laer are no only he source of nomnal rgdy bu also an mpedmen n he coordnaon of producon. The opmal allocaon hus dffers from famlar Ramsey benchmarks Lucas and Sokey, 983; Correa, Ncoln, and Teles, 2008 n manners ha may be msnerpreed as a call for macroeconomc sablzaon. Furhermore, convenonal polcy nsrumens serve new funcons: hey manpulae he frms collecon and use of nformaon or her cognve effors. Despe hese facs, he opmal axes are smlar o hose n he aforemenoned benchmarks and he opmal moneary polcy replcaes flexble-prce allocaons. On he oher hand, he raonale for prce sably falls apar: replcang flexble-prce allocaons and mnmzng relave-prce dsorons become equvalen o a ceran form of leanng agans he wnd. JEL codes: E32, E52, D6, D83. Keywords: busness cycles, ncomplee nformaon, raonal naenon, bounded raonaly, opmal polcy, prce sably. * Ths paper exends, and subsumes, an earler draf ha concerned he same opc bu conaned a narrower mehodologcal conrbuon Angeleos and La O, 202. We benefed from commens receved n numerous conferences and semnars. We hank Rober Kng and Phlppe Bacchea for dscussng early versons of our paper. We are parcularly graeful o he edor, Harald Uhlg, and hree anonymous referees for dealed and consrucve feedback on he laes verson. We fnally hank Karhk Sasry for research asssance. Emal: angele@m.edu, jenlao@columba.edu.

2 Inroducon How should fscal and moneary polcy respond o busness cycles? The leraure has suded hs queson exensvely, bu ypcally only under srong assumpons abou wha economc agens know and how well hey can comprehend wha s gong on n he economy. In parcular, he Ramsey and he New-Keynesan frameworks alke assume ha agens have common knowledge of he underlyng aggregae shocks and her consequences, of how deep or long a recesson mgh be, and so on. In hs paper, we depar from hs radon by leng frms have a blurry undersandng of he sae of he economy due o nformaonal, or cognve, frcons. Crucally, we le such frcons nerfere wh boh he frms prce-seng decsons and her npu choces. We hus accommodae boh a form of nomnal rgdy and an mperfecon n he coordnaon of producon. We hen proceed o make wo conrbuons: one mehodologcal and one appled. On he mehodologcal fron, we exend he prmal approach of he Ramsey leraure, and he resuls of Lucas and Sokey 983, Char, Chrsano, and Kehoe 994 and, especally, Correa, Ncoln, and Teles 2008, o sengs ha accommodae nformaonal, cognve, and coordnaon frcons. On he appled fron, we hghlgh how convenonal polcy nsrumens can serve new funcons; we sudy how he consdered frcons affec he socally opmal allocaon and he polces ha mplemen ; and fnally we explan why he raonale for he desrably of prce sably s urned upsde down once he nformaon, or cognve, consrans of he frms are aken no consderaon. Background. The frcons consdered n hs paper are easly movaed. Even f arbrarly rch daa s readly avalable n he publc doman, agens may lack he me and he cognve capacy needed for fully dgesng all he avalable daa. A number of auhors have hus argued ha he accommodaon of nosy, and heerogeneous, nformaon need no be nerpreed oo lerally; nsead, can be he formal represenaon of he dffculy ha he agens face n comprehendng wha s gong on n he economy and n coordnang her behavor wh ha of ohers. 2 Such frcons offer a compellng subsue o Calvo-lke scky prces Mankw and Res, 2002; Woodford, 2003a; Mackowak and Wederhol, 2009, as well as a powerful complemen o hem Nmark, They help explan he observed nera n he response employmen and oupu o echnology shocks Angeleos and La O, 200, he volaly of unemploymen Venkaeswaran, 204, and oher salen feaures of he busness-cycle daa Lorenzon, 2009; Angeleos, Collard, and Dellas, 205. They mpede coordnaon Morrs and Shn, 2002, 2003, aenuae generalequlbrum effecs Angeleos and Lan, 207, and open o door o forces ha resemble anmal sprs Angeleos and La O, 203; Benhabb, Wang, and Wen, 205; Huo and Takayama, 205. They make he economy behave as f he agens were myopc Angeleos and Lan, 206a, offerng a resoluon o some of he paradoxcal predcons of he New-Keynesan framework. Las bu no leas, he assumed frcons are conssen wh he observed heerogeney n forecass and her response o shocks Mankw, Res, and Wolfers, 2004; Cobon and Gorodnchenko, 205. Ball, Mankw, and Res 2005, Adam 2007 and Pacello and Wederhol 204 are exempons, whch are dscussed n due course. 2 See, ner ala, Angeleos and Lan 207, 206b, Morrs and Shn 2002, 2003, Sms 2003, 200, Trole 205, and Woodford 2003a, 2009.

3 Despe hese mporan advances, he normave mplcaons of he consdered frcons are less well undersood. To he bes of our knowledge, our paper s ndeed he frs o sudy how he polcy lessons of he Ramsey and New-Keynesan paradgms are affeced by leng frms face such frcons when makng boh her producon and prce-seng decsons. 3 Framework. Our framework resembles hose found n eher he Ramsey leraure on opmal fscal polcy Lucas and Sokey, 983; Char, Chrsano, and Kehoe, 994 or he relaed New-Keynesan leraure on opmal moneary polcy Correa, Ncoln, and Teles, I feaures a represenave household, cenralzed markes, and a connuum of monopolscally compeve frms, each producng a dfferenaed commody ha eners he producon of he fnal good. I also allows he planner o conrol wo knds of polcy nsrumens: a rch se of lnear axes se by he fscal auhory and he nomnal neres rae se by he moneary auhory. There are, however, hree key dfferences beween our framework and he aforemenoned works. Frs, he prce of each frm s measurable n a nosy, prvae sgnal of he sae of Naure. Second, some of he frm s npu choces mus also be measurable n he aforemenoned sgnal. Thrd, he sochasc srucure of ha sgnal s flexble and can be endogenously chosen by he frm. The frs feaure, whch s common o Woodford 2003a, Mankw and Res 2002, and Mackowak and Wederhol 2009, represens a form of nomnal rgdy. Alhough hs feaure offers an appealng alernave o scky prces and menu coss, does no alone upse he key normave lessons of he New-Keynesan paradgm: when he only modfcaon s n he formalzaon of he nomnal rgdy, he resuls of Correa, Ncoln, and Teles 2008 reman nac. The second feaure, whch s novel vs- -vs all he aforemenoned works, nroduces a real frcon. Because each frm mus fx some of her npus on he bass of a blurry and dosyncrac undersandng of he underlyng sae of Naure and of he equlbrum choces of he oher frms, producon can no more be perfecly coordnaed across he frms, regardless of polcy and regardless of wheher nomnal rgdy nerferes wh he workngs of he prce mechansm. As we explan n due course, s hs knd of mperfecon n he coordnaon of producon, and only hs, whch s responsble for he novely of lessons we delver n hs paper. The hrd feaure s useful for wo reasons. Frs, allows us o nes a varey of nformaon specfcaons ha have appeared n pror work and o esablsh our resuls wh a hgh degree of generaly. Second, faclaes he renerpreaon of he assumed prvae sgnals as he produc of raonal naenon Sms, 2003, 200, or as he cognve saes ha represen how well he agens comprehend wha s gong on n he economy and how o bes respond Trole, 205. Mehods and Resuls. The rchness of our framework precludes a closed-form soluon of he equlbrum regardless of polcy. Alhough such racably has played a cenral role n pror work, s neher necessary nor useful for our purposes. To he conrary, by allowng for an essenally arbrary specfcaon of he frms sgnals and by showng how one can adap he prmal approach from he Ramsey leraure o he envronmens of neres, we are able o no only bypass he need for racably, bu also delver he key lessons wh a hgh level of ransparency. 3 Noe he emphass on boh : Ball, Mankw, and Res 2005, Adam 2007 and Pacello and Wederhol 204 have suded opmal moneary polcy n sengs ha allow he nformaonal frcon o mpede he adjusmen of nomnal prces bu assume away from he frms producon decsons. 2

4 We hus sar by characerzng he enre se of allocaons ha can be mplemened as markebased equlbra wh he help of he avalable polcy nsrumens. For pedagogcal reasons, we do so under wo scenaros. The one allows he nformaon, or cognve, consrans o be he source of boh nomnal and real frcon, n he sense explaned above. The oher shus down he nomnal frcon by leng he prce of each frm be conngen on he rue sae of Naure. Alhough he second scenaro s less realsc and precludes moneary polcy from havng real effec, s nsrumenal for undersandng, no only he opmal axes, bu also he opmal moneary polcy under he frs scenaro. Adopng, or perhaps paraphrasng, he ermnology used n he New-Keynesan leraure, we refer o he allocaons ha are mplemenable under he frs scenaro as scky-prce allocaons and o he ones under he second scenaro as flexble-prce allocaons. We nex proceed o characerze he soluon of a relaxed problem, whch allows he planner o drecly conrol how each frm maps her prvae sgnal o her acons. Ths relaxed problem resembles he one suded n Correa, Ncoln, and Teles 2008, excep for one key dfference: he heerogeney of he sgnals and he assocaed mperfecon n he coordnaon of producon precludes he planner from aanng eher he frs bes or he knd of second bes ha s relevan n ha paper and n he Ramsey leraure more generally Lucas and Sokey, 983; Char, Chrsano, and Kehoe, 994. Tha sad, by characerzng he soluon o hs relaxed problem and by showng ha hs soluon belongs o he appropraely redefned ses of he flexble- and scky-prce allocaons, we are able o shed ample lgh on he naure of he opmal allocaon and of he combnaon of axes and moneary polcy ha mplemen ha allocaons as an equlbrum. The followng lessons emerge: Famlar polcy nsrumens serve new funcons: hey help he planner manpulae no only how frms ac on he bass of her dosyncrac knowledge of he sae of economy bu also how much aenon hey pay o he ongong economc condons or how much cognve effor hey pu n undersandng how hey should respond. Because of he underlyng frcon, he observable properes of he opmal allocaon dffer from he relevan benchmarks denfed n Lucas and Sokey 983, Char, Chrsano, and Kehoe 994, and Correa, Ncoln, and Teles The dfference s evden n boh he cross secon of he frms and he aggregae me seres. In he cross secon, he planner affords some dsperson n margnal producs n order o allow each frm o ulze her own prvae nformaon, or o do wha s bes gven her cognve ables. In he me seres, he planner allows he economy o vary wh shocks ha resemble anmal sprs or senmens as formalzed n Angeleos and La O 203 and Benhabb, Wang, and Wen 205. Despe he aforemenoned noveles n he naure of he opmal allocaon and n he funcons of he ax nsrumens, he opmal ax polcy remans he same as n Lucas and Sokey 983 and Char, Chrsano, and Kehoe 994. For a famlar class of preferences and echnologes, he opmal wedges, and hence also he opmal axes, are ndeed nvaran wh he sae of he economy. Ths s because once he polcy has been se so as o balance he underlyng ax and monopoly dsorons here s no furher welfare gan n fac, here s ypcally a src welfare loss from ryng o manpulae how frms respond o her sgnals. 3

5 The opmal moneary polcy replcaes flexble prces. Ths exends a resul from Correa, Ncoln, and Teles 2008 o he envronmens we are neresed n. As n ha paper and conrary o wha may be suggesed by exbook reamens of he New-Keynesan framework, he opmaly of replcang flexble-prce allocaons holds rue despe he fac ha he dsoron relave o he frs bes s non-zero and may even vary wh he busness cycle. The reason s ha, a leas wh he allowed ax nsrumens, he se of flexble-prce allocaons conans he soluon o he relaxed plannng problem descrbed above. The opmal moneary polcy does no nduce prce sably. Insead, nduces a negave relaon beween he prce level and real economc acvy. Ths resul holds despe he fac ha he underlyng flexble-prce allocaons can and should be replcaed. I s herefore orhogonal o he more convenonal argumens ha jusfy a deparure from prce sably eher by prevenng he replcaon of he opmal flexble-prce allocaon 4 or by leng moneary polcy subsue for mssng ax nsrumens. 5 Insead, s a drec mplcaon of leng he frms make he bes possble use of her dosyncrac knowledge or undersandng of wha s gong on n he economy and of how much hey should produce. Our las resul can hus be read as a revson of he so-called dvne concdence. On he one hand, we preserve dvne concdence n he sense ha, n our seng, he replcaon of flexble prces acheves wo goals a once: frs, elmnaes he oupu gap relave o an approprae reference pon; and second, mnmzes relave-prce dsorons or maxmzes producon effcency, properly defned. On he oher hand, we urn dvne concdence on s head by equang he second goal, and he replcaon of flexble prces, wh a ceran deparure from prce sably. Relaedly, we also qualfy he reference pon relave o whch he oupu gap has o be measured. I s neher he frs bes ha appears n exbook reamens of he New-Keynesan framework, nor he ype of second bes suded n Lucas and Sokey 983 and Correa, Ncoln, and Teles Insead, s a hrd bes ha ncorporaes he underlyng nformaonal/cognve frcon and as a resul may dsplay exoc observable properes. The defnon and he characerzaon of hs reference pon are negral pars of our conrbuon. Layou. The res of he paper s organzed as follows. Secon 2 ses up our framework and dscusses he key assumpons ha dfferenae our paper from he prevous leraure. Secon 3 defnes he scky-prce and flexble-prce scenaros ha are approprae o consder n our conex. Secon 4 characerzes and compares he se of allocaons ha can be mplemened as marke-based equlbra n each of hese wo scenaros. Secon 5 defnes and characerzes he relaxed plannng problem ha helps denfy he opmal allocaon; also derves our key lessons regardng opmal axes and opmal moneary polcy. Secon 6 endogenzes he nformaon or cognve frcon. Secon 7 concludes. The Appendx conans all proofs as well as a racable example ha llusraes some of he broader nsghs n a sharper form. 4 E.g., by combnng scky prces wh scky wages, or by resrcng he polcy maker o follow a Taylor rule ha s no suffcenly sophscaed alhough perhaps more realsc. 5 E.g., by nroducng markup shocks shorcus for forces ha rgger neffcen busness cycles under flexble prces and by prevenng he planner from offseng hese shocks wh he rgh ax nsrumens. 4

6 2 The Framework In hs secon, we nroduce our framework. We frs descrbe he componens of he envronmen ha are nvaran o he nformaon srucure. We nex formalze he nformaonal frcon and s wo faces he nomnal and he real. We fnally commen on some of he dsnc quales of our framework, as well as on some of s lmaons. 2. The underlyng envronmen Tme s dscree and perods are ndexed by {0,, 2,...}. There s a represenave household, whch pools all he ncome n he economy and makes he consumpon, capal accumulaon, and labor supply decsons. There s a connuum of monopolscally compeve frms, ndexed by I = [0, ]. These frms produce dfferenaed goods, whch are used by a compeve real secor as nermedae npus no he producon of a fnal good. The laer n urn can be used for hree purposes: as consumpon; as nvesmen no capal; or as an nermedae npu n he producon of he dfferenaed goods. Fnally, here s a governmen, whch lacks lump-sum axaon bu can levy a varey of dsoronary axes and can ssue boh a conngen and non-conngen deb. Saes of Naure. In each perod, Naure draws a random varable s from a fne se S. Ths varable s mean o conan no only nnovaons n aggregae TFP and governmen spendng bu also any oher aggregae aggregae nnovaon n he cross-secon of he sgnals upon whch he frms can ac more on hs below. The aggregae sae of he economy, or he sae of Naure, n perod s comprsed by he hsory of draws of s τ for all τ {0,..., }. The sae s herefore an elemen of S S 0... S and s henceforh denoed by s s 0,..., s. Is uncondonal probably s denoed by µs. Tax and deb nsrumens. The governmen lacks access o boh lump-sum axaon and frm-specfc axes. I can noneheless mpose four knds of economy-wde axes: a proporonal ax on consumpon a rae τ c ; a proporonal ax on labor ncome a rae τ l ; a proporonal ax on capal ncome, ne of deprecaon, a rae τ k ; and a 00% ax on dsrbued profs. In addon, he governmen can ssue and rade wh he represenave household wo knds of deb nsrumens. The frs s a one-perod, non-conngen, deb nsrumen ha coss dollar n perod and pays ou + R n perod ; R herefore denoes he nomnal neres rae beween and +. The second s a complee se of sae-conngen asses or Arrow secures. These are ndexed by s S +, hey cos Q,s dollars n perod, and hey pay ou dollar n perod + f sae s s realzed and 0 oherwse. Ther correspondng quanes are denoed by D,s. The quany of he non-conngen deb, on he oher hand, s denoed by B. I follows ha he nomnal value of all deb ssued a he end of perod s B + s S + Q,sD,s, whle he nomnal lably of he governmen n he begnnng of perod + s + R B + D,s +. The household. We adop he followng noaon: K denoes he capal sock accumulaed by he end of perod ; L denoes he labor supply n perod ; r and w denoe he pre-ax real values of he renal rae of capal and he wage rae n perod, respecvely; C and X denoe he perod- real 5

7 levels of consumpon and nvesmen, respecvely; and fnally P denoes he perod- prce level.e., he nomnal prce of he fnal good. The household s perod- budge consran can hus be expressed, n nomnal erms, as follows: +τ c P C +P X +B + Q,s D,s = τ l P w L + τ k P r K ++R B +D,s s Ss The law of moon of he capal sock, on he oher hand, s gven by K = δk + X, where δ [0, ] s he deprecaon rae of capal. Fnally, he household s preferences are gven by her expecaon of β UC, L, s where β 0, and U s srcly ncreasng and srcly concave n C, L. =0 The frms. The nermedae goods, and he monopolsc frms producng hem, are ndexed by [0, ]. Take frm, ha s, he frm ha produces varey. Is oupu n perod s denoed by y and s gven by y = As F k, h, l, where As s an exogenous aggregae producvy shock, 6 F s a CRS producon funcon, k s he capal npu, h s he fnal-good npu or maerals, and l s he labor npu. The frm faces a proporonal ax on revenue, a rae τ r. Is nomnal prof ne of axes s herefore gven by Π = τ r p y P r k P h P w l, where p denoes he nomnal prce of he nermedae good, P denoes he nomnal prce of he fnal good also, he prce level, and r and w denoe, respecvely, he real renal rae of capal and he real wage rae. The fnal good, n urn, s produced by a compeve real secor, whose oupu s a CES aggregaor of all he nermedae varees: [ Y = I y ] d, where Y denoes he quany of he fnal good and > s he elascy of subsuon across he nermedae varees. 7 The governmen. The governmen s perod- budge consran, n nomnal erms, s gven by + R B + D,s + P G = B + s S + Q,s D,s + T 6 We rule ou dosyncrac producvy shocks mosly for exposonal reasons; see Appendx B for an example ha accommodaes such shocks. 7 Clearly, he nomnal profs of he real secor are gven by P Y p I y d and are zero n equlbrum. Also, we could have nroduced he aggregae producvy shock n 6

8 where G = Gs s he exogenous real level of governmen spendng and T s he nomnal level of ax revenue, gven by T = τ r P Y + τ c P C + τ l P w L + τ k P r k + Π d Wh some abuse of noaon, we le D = D,s s S + and Q = Q,s s S +. We hus denfy he fscal-polcy nsrumens n perod wh τ r, τ l, τ k, τ c, B, D, he axes and he deb ssuances, and he moneary-polcy nsrumen wh R, he nomnal neres rae. To smplfy he exposon and keep he analyss comparable o ha of Correa, Ncoln, and Teles 2008, we absrac from he zero lower bound on he nomnal neres rae. We fnally bypass he ssue suded n Sraub and Wernng 204 and guaranee he valdy of he opmaly of a zero ax on capal ncome by allowng he governmen o ax fully he nal capal sock. Marke Clearng. Marke clearng n he goods marke or, equvalenly, he resource consran of he economy s gven by C + H + X + G = Y, where X I x d denoes aggregae nvesmen and H I h d denoes he aggregae quany of he fnal good used as nermedae npu. Marke clearng n he labor marke, on he oher hand, s gven by l d = L. 2.2 The nformaonal, or cognve, frcon I Throughou, we le he aggregae quanes C, L, X, K, Y, he wage w, he renal rae r, he asse prces Q, he aggregae prce level P, and he polcy nsrumens τ r, τ l, τ k, τ c, B, D, R be measurable n s, for all. We nex defne our frconless or complee-nformaon benchmark by he scenaro n whch he frm-specfc varables p, k, h, l, y are also measurable n s, for all and all. Ths scenaro, whch s commonplace n he leraure, s akn o leng he realzed sae of Naure no only be perfecly known o each of he frms bu also common knowledge o hem: when a frm acs, knows ha every frm knows s, knows ha every frm knows ha every frm knows s, and so on. We fnally depar from hs benchmark and accommodae he sough-afer frcon by requrng ha he frms mus nsead ac on he bass of an nosy, and dosyncrac, sgnal of s. More specfcally, he frcon akes he followng form. For every, every realzaon of s, and every frm, Naure draws a random varable from a fne se Ω accordng o some probably dsrbuon φ. The jon probably of he par, s s denoed by φ, s, he probably of condonal on s s denoed by φ s, and he probably of s condonal on s denoed by φs. Condonal on s, he draws of are..d. across frms and a law of large number apples so ha φ s s also he realzed fracon of he populaon ha receves he sgnal when he underlyng sae s s. 8 Fnally, whle he varable l s allowed o be measurable n boh and s, he vecor p, k, h s resrced o be measurable only n, for all and all. 8 See Uhlg 996 for an applcable law of large numbers wh a connuum of draws. 7

9 Requrng ha p be measurable n raher han s nroduces he same knd of nomnal rgdy as he one feaured n Mankw and Res 2002, Woodford 2003a, Adam 2007, Mackowak and Wederhol 2009, Pacello and Wederhol 204, and a growng leraure ha replaces Calvo-lke scky prces wh an nformaonal frcon. 9 Relave o hs leraure, he key nnovaon here s o add a real frcon by requrng ha k, h be also measurable n. As wll become clear, our resuls depend on he neracon of he wo rgdes. Fnally, leng l and hereby also y adjus o s guaranees ha supply can mee demand for all realzaons of uncerany. 2.3 Dscusson By requrng ha he frms make ceran choces on he bass of dspersed prvae nformaon abou he underlyng sae of Naure, we connec o a long radon n macroeconomcs ha sudes sland economes, ha s, economes n whch nformaon and radng s geographcally segmened Lucas, 972; Townsend, 983; Presco and Ros-Rull, 992. There are, however, wo suble and conneced dfferences. Frs, hese earler works manan he assumpon of he sandard Arrow-Debreu framework ha agens can condon her choces on he rue prces. By conras, our framework allows he frms o ac on he bass of an mperfec observaon, or undersandng, of he npu prces hey ransac a. Second, hese earler works formalzed he nformaonal frcon as he produc of resrced marke parcpaon. In parcular, hey prevened he endogenous aggregaon of nformaon ha would have obaned n a complee Arrow-Debreu seng by leng only a small, and non-represenave, sample of he populaon rade n any parcular marke a any pon of me and by precludng he parcpans of one marke o observe he oucomes of oher markes. Accordngly, hs allowed nformaon o heerogeneous across markes bu resrced o be homogeneous whn markes. By conras, we allow markes o be cenralzed and nformaon o be heerogeneous whn markes; moreover, we enrely bypass he ssue of he endogenous aggregaon of nformaon by recasng he nformaon frcon as a cognve frcon. These modelng choces are no srcly needed for he polcy lessons of hs paper. An early ncarnaon of our paper Angeleos and La O, 2008 had obaned smlar resuls for a varan economy ha feaured segmened markes and allowed frms o condon her choces on he acual npu prces. The curren formulaon, however, perms us o connec o a growng leraure ha nerpres he nosy sgnal ha an agen receves abou he sae of he economy as he formal represenaon of he agen s bounded capacy o pay aenon o avalable daa Sms, 2003; Woodford, 2003a; Mackowak and Wederhol, 2009, o comprehend wha s gong on around her, o form belefs abou he behavor of ohers, and o fgure ou her own course of acon Trole, 205; Angeleos and Lan, 207. We fnd hs nerpreaon o be appealng no only on concepual grounds bu also on emprcal grounds: hese days he mos bndng consran seems o be lmed me and cognve capaces raher han he unavalably of daa. Ths nerpreaon s also suppored by expermenal evdence Khaw, Sevens, and Woodford, 206. To enhance hs nerpreaon, Secon 6 exends he analyss o he case n whch each frm 9 See also Chwe 999 for an earler, and overlooked, conrbuon ha emphaszes how lack of common knowledge can raonalze moneary non-neurarly. 8

10 chooses opmally he jon dsrbuon of he sgnal wh he sae s, subjec o a cos. Ths can be hough of as he choce of how much aenon o pay o he avalable daa or how much cognve effor o exer owards undersandng wha s gong on n he economy. 0 For he me beng, however, we rea φ, he jon dsrbuon of he sgnal and he sae, as exogenous. Our framework s oherwse fully flexble. For nsance, he sae s and he sgnal do no have o be Gaussan. Furhermore, s may become known a he end of each perod, wh any oher fne lag, or never. Also, may, bu does no have o, be measurable n τ for all τ > : ha s, frms can suffer from mperfec recall Woodford, 2009; Pavan, 206. Las bu no leas, s may conan all of he followng: nnovaons o curren fundamenals, news abou fuure fundamenals Beaudry and Porer, 2006; Jamovch and Rebelo, 2009, correlaed errors n belefs of he fundamenals or nose shocks Lorenzon, 2009; Angeleos and La O, 200, or more exoc shocks o hgher-order belefs. The laer ype of shock decouples varaon n equlbrum expecaons of economc oucomes from varaon n fundamenals or frs-order belefs hereof, and can hus be nerpreed as a produc of senmens or anmal sprs Angeleos and La O, 203; Benhabb, Wang, and Wen, 205; Huo and Takayama, 205. Whle no srcly needed, hs flexbly s useful for wo reasons. Frs, helps clarfy he precse naure and he robusness of our resuls. Second, perms us o nes a plehora of more specal nformaon srucures ha have been used prevously n he leraure. For nsance, consder Woodford 2003a, Adam 2007, Nmark 2008, and Angeleos and La O 200. These papers sudy models n whch each frm observes a new prvae sgnal of he underlyng aggregae fundamenal n each perod, possbly n combnaon wh a publc sgnal. To nes hese sengs, we may absrac from he governmen spendng shock and suppose ha each frm receves a par of sgnals a, z n each perod, where a = log A + ϵ s he prvae sgnal of he underlyng aggregae TFP, z = log A +u s he publc sgnal, ϵ s dosyncrac nose, and u s aggregae nose; and fnally le s = log A τ, u τ τ and = a τ, z τ τ. Alernavely, consder models wh scky nformaon as n Mankw and Res 2002 and Ball, Mankw, and Res These sengs are drecly nesed n our framework by leng φ assgn probably λ o =, s and probably λ o =, where λ 0, s he probably wh whch a frm updaes s nformaon se wh he perfec observaon of he underlyng sae and λ s he probably wh whch he frm s suck wh her old nformaon se. Consder nex he forms of raonal naenon found n Sms 2003, Mackowak and Wederhol 2009, and Pacello and Wederhol 204, he varans proposed by Mya and Wallace 202 and Pavan 206, he model of fxed observaon coss found n Alvarez, Lpp, and Pacello 20, and he model of cosly conemplaon consdered n Trole 205. For our purposes, hese sengs bol down o endogenzng he jon dsrbuon of he sae s and he sgnal n a varey of ways, all 0 Clearly, he accommodaon of hese deas s anoher feaure ha dsngushes our framework, and he relaed works menoned n hs paragraph, from he earler leraure on sland economes. If he underlyng TFP shock s perssen, hs specfcaon allows for gradual learnng and perssen dynamcs n hgherorder belefs, as n Woodford 2003a, Angeleos and La O 200, and Huo and Takayama 205. Alernavely, one can assume ha he underlyng TFP becomes common knowledge a he end of each perod and le = s a τ, z τ τ. Fnally, s possble o recas a as frm-specfc TFP, whch self serves as a nosy prvae sgnal of aggregae TFP; hs was acually he case n earler versons of hs paper Angeleos and La O,

11 of whch are nesed n he exended framework of Secon 6. The followng pon s also worh emphaszng. By allowng frms o have no only nosy bu also heerogeneous nformaon abou s, our framework accommodaes hgher-order uncerany. By conras, hgh-order uncerany s a foror ruled ou n he RBC and New-Keynesan frameworks because all frms are assumed o share he same nformaon a all mes. As emphaszed elsewhere, 2 rulng ou hgher-order uncerany s synonymous o mposng perfec coordnaon: s as f all he economc agens can congregae n a room, alk o one anoher, and flawlessly coordnae her choces. Conversely, a key qualy of our framework s ha allows for mperfecon n he coordnaon of he frms producon and prcng choces. Ths mperfecon urns ou o be key o some of our polcy lessons mos noably, he subopmaly of prce sably. Nowhsandng he aforemenoned flexbly, our framework absracs from markup shocks and from labor or capal marke frcons. The raonale s he followng. In he New Keynesan leraure, such feaures are ofen nroduced n conjuncon wh approprae resrcons on he ax nsrumens so as o jusfy a moneary polcy ha devaes from replcang flexble-prce allocaons. Had we made he same assumpons as n ha leraure, we would have recovered he famlar argumen ha such a devaon s desrable only when moneary polcy subsues for mssng ax nsrumens. By absracng from markup shocks and he lke, we nsead ensure ha he nsghs delvered n hs paper are orhogonal o wha s already known. 3 3 Scky Prces, Flexble Prces, and Feasbly: Defnons We vew he accommodaon of he dual role of he nformaonal frcon he nomnal rgdy assocaed wh he resrcon ha p be measurable n and he real rgdy assocaed wh he resrcon ha k and h also be measurable n as a defnng feaure of our framework. Accordngly, we are prmarly neres n he scenaro n whch boh roles are acve. To undersand he opmal polcy under hs scenaro, s neverheless nsrumenal o sudy he alernave scenaro n whch he nomnal rgdy s arfcally shu down by leng p be measurable n s. Borrowng, and somewha paraphrasng, he ermnology of he New-Keynesan leraure, we henceforh refer o he former scenaro he one of neres as scky prces and o he laer one as flexble prces. In hs secon, we delneae he wo roles of he nformaonal frcon and defne he ses of allocaons, prces, and polces ha can be par of an equlbrum under each scenaro. 3. Scky-Prce Equlbra We henceforh represen an allocaon by a sequence ξ {ξ.} =0, where ξ. {k., h., l., y.; K., H., L., Y., C.} 2 See, among ohers, he dscussons n Morrs and Shn 2002, 2003, Angeleos and La O 203 and Angeleos and Lan 206b, Ths, however, does no mean ha here are no addonal nsghs o be derved from sudyng he neracon of he aforemenoned feaures wh nformaonal frcons: see Pacello and Wederhol 204 and Angeleos, Iovno, and La O 206 for examples. 0

12 s a vecor of funcons ha map he realzaons of uncerany o he quanes chosen by he ypcal frm for he frs four componens of ξ and he aggregae quanes for he remanng fve componens. We smlarly represen a prce sysem by a sequence ϱ {ϱ.} =0, where ϱ. {p., P., r., w., Q.} s a vecor of funcons ha map he realzaons of uncerany o he nomnal prce se by he ypcal frm, he aggregae prce level, he real wage rae, he real renal rae of capal, and he nomnal prces of he Arrow secures. We fnally represen a polcy wh a sequence θ = {θ.} =0, where { } θ. τ r., τ l., τ k., τ c., B., D., R. s a vecor of funcons ha map he realzaons of uncerany o he varous polcy nsrumens, Throughou our analyss, we le he doman of K., H., L., Y., C., P., r., w., Q., τ r., τ l., τ k., τ c., B., D., and R. be S. Ths means ha all he aggregae oucomes, he real wages, he real neres rae, he asse prces, and he polcy nsrumens are measurable n s. We nex embed he real aspec of he nformaonal frcon by assumng ha he doman of he funcons k and h s Ω ; hs smply means ha k and h are resrced o be measurable n. By conras, he doman of l and y s Ω S ; hs means ha he labor npu and he oupu of a frm are allowed o respond o he realzed sae. We fnally embed a nomnal frcon, or le prces be nformaonally scky, by requrng ha p be measurable n or, equvalenly, ha he doman of p. be Ω. For fuure reference, we collec he relevan frm-level measurably resrcons n he followng wo properes. Propery. The frm-level quanes sasfy h = h, k = k, l = l, s, y = y, s, for all, all, and all realzaons of uncerany. Propery 2. The prces sasfy for all, all, and all realzaons of uncerany. p = p Properes and 2 are, n effec, a defnon of he knd of allocaons and prces ha are nformaonally feasble under he scenaro of neres. Noe n parcular ha k, h, and p are prevened from beng conngen on peces of nformaon ha are conaned n j for some j bu are no conaned n. In hs sense, nformaon canno be ransferred from one frm o anoher. Ths s he key resrcon ha dsngushes our analyss from Correa, Ncoln, and Teles 2008 and more generally from he Ramsey polcy paradgm: n ha paradgm, s as f nformaon can be ransferred from one agen o anoher nsananeously and whou any resrcon. 4,5 4 Le us emphasze once agan ha he ssue a sake s orhogonal o eher he queson of how precse he avalable nformaon s a any gven pon, or he queson of how nformaon evolves over me. The Arrow-Debreu framework and he Ramsey paradgm can accommodae a lo of rchness n hese wo dmensons, bu do no allow for dfferen agens o have dfferen nformaon and o face hgher-order uncerany. 5 Properes and 2 mpose no only he relevan nformaonal frcon bu also a ceran symmery: wo frms can choose

13 In he res of hs secon, we formulae he household s and he frm s problems and defne he equlbrum of he economy. Throughou, we resrc aenon o rples ξ, ϱ, θ ha sasfy Properes and 2. Consder frs he household. The saemen of her problem s sandard. 6 Household s Problem. The household chooses {C., L., K., B., D.} so as o maxmze her expeced uly, W = β µ s [ U C s, L s, s ], =0 s subjec o her budge consran, + τ c s C { s + Xs + P s B s + } Qs + Ds + = τ l s w s L s + s + + τ k s r s K s + { + R s P s B s + Ds }, s, and he law of moon for capal, where K s = δk s + X s, s. Consder nex he ypcal monopolsc frm. Her ex ane valuaon s gven by [ ] V E β Ms Π, s { P s = β Ms Π, s P s φ, s }, =0 Ms =0,s U c s + τ c s s he prcng kernel, U c s s a shorcu for c U C s, L s, s, and Π, s τ r s p P s y, s h w s l, s rs k s he frm s real prof ne of he revenue ax. The demand faced by he monopols s gven by 7 y, s = p Y s. P s We may hus express he monopols s problem as follows. dfferen quanes and/or prces only f hey have dfferen ypes. Ths s whou any loss of generaly gven he assumed convexy n echnology and preferences. 6 To ease he noaon, we henceforh drop he subscrp from he funcons C., L., ec, excep for few occasons n whch s useful o make explc he dependence on. 7 As usual, condon here as well as condon 3 n he sequel follow from opmaly n he real secor. 2

14 Monopols s Problem. The ypcal monopols chooses he plan {p, k, h, l, y} so as o maxmze her valuaon, { [ β Ms τ r s p P s y, s h w s l, s ] rs k φ, s },,s subjec o he echnology, and he demand for her produc, y, s = A s F k, h, l, s, s,, y, s = p P s Y s, s,. Fnally, snce he cross-seconal dsrbuon of he sgnal n perod and sae s s gven by φ. s, he followng properes are self-evden: aggregae oupu s gven by Y s = [ Ω he prce level he prce of he fnal good by P s = [ y, s Ω p φ he marke for he fnal good clears f and only f φ s ] s ], s ; 2, s ; 3 C s + Xs + G s + Ω h φ s = Y s, s ; 4 he marke for labor clears f and only f l φ s = L s Ω, s ; 5 and he marke for capal clears f and only f k φ s = K s Ω, s. 6 We can hus defne an equlbrum as follows. Defnon. A scky-prce equlbrum s a rple ξ, ϱ, θ of allocaons, prces, and polces ha sasfy Properes and 2 and are such ha: {C, L, K, B, D } solves he household s problem; {p, k, h, l, y } solves he frm s problem; he quany of he fnal good s gven by 2 and s prce by 3; he governmen s budge consran s sasfed; v all markes clear, namely, condons 4, 5, and 6 are sasfed. 3

15 3.2 Flexble-prce Equlbra: Defnon We qualfed he equlbra defned n he prevous subsecon as scky-prce equlbra n order o underscore he nomnal frcon ha s embedded n Propery 2. We nex consder he alernave scenaro n whch hs frcon s shu down. We say ha prces are flexble, or ha he nomnal rgdy s absen, when p can be measurable n boh and s. Formally, we denfy hs scenaro by replacng Propery 2 wh he followng. Propery 2. The prces sasfy p = p, s for all, all, and all realzaons of uncerany. Accordngly, he monopols s problem s reformulaed wh p, s n he place of ps. Smlarly, condon 3 s adjused as follows: P s = We herefore arrve a he he followng defnon. p, s φ s Defnon 2. A flexble-prce equlbrum s a rple ξ, ϱ, θ of allocaons, prces, and polces ha sasfy Properes and 2 and are such ha: {C, L, K, B, D } solves he household s problem; {p, k, h, l, y } solves he frm s problem; he quany of he fnal good s gven by 2 and s prce by 7; he governmen s budge consran s sasfed; v all markes clear. In a nushell, he defnon of flexble-prce equlbra s he same as ha of scky-prce equlbra, excep ha we have replaced Propery 2 wh Propery 2. Remark. Our flexble-prce scenaro preserves he real frcon and removes he nomnal one. The damercally oppose scenaro would preserve he nomnal frcon ye remove he real one; hs can be accommodaed by mananng Propery 2 and replacng Propery wh a varan ha allows k, h, l o be measurable n boh and s. As wll become clear n due course, hs scenaro helps reveal ha he resuls of Correa, Ncoln, and Teles 2008 drecly exend o sengs n whch he nformaonal frcon s he source of only nomnal rgdy, whch n urn underscores he sgnfcance of accommodang he real rgdy formalzed n Propery Feasbly We conclude hs secon wh one addonal defnon, whose meanng s self-evden. Defnon 3. An allocaon ξ s feasble f and only f sasfes Propery and resource consrans 2, 4, 5 and 6. 4

16 4 Scky vs Flexble Prces: Characerzaon and Replcaon Wha s he enre se of he allocaons ha can be mplemened as par of an equlbrum wh some polcy? In hs secon we address hs queson under boh he flexble-prce and he scky-prce scenaro. By allowng he polcy o be arbrary, he analyss n hs secon delvers hree key nsghs whch are nsrumenal o he lessons we develop n he followng secon abou opmal polcy. Frs, we hghlgh how he avalable polcy nsrumens can serve a new funcon, 8 namely, how hey can manpulae he manner n whch each frm ulzes her dosyncrac nformaon, or responds o her cognve sae, and hereby also nfluence he cross-seconal dsperson n producon ha orgnaes from he underlyng frcon. Second, we shed lgh on whch ax nsrumens are mssng and on wheher moneary polcy can subsue for hem once prces are scky. Thrd, we show ha, under a mld qualfcaon, every allocaon ha s par of flexble-prce equlbrum s also par of a scky-prce equlbrum. 4. Flexble-Prce Allocaons Consder any flexble-prce equlbrum. The characerzaon of he household s problem s sandard. Is soluon s pnned down by he combnaon of he usual ransversaly condon along wh he followng se of frs-order condons: U l s = U c s τ l s + τ c s w s, s 8 [ { Ms = βe Ms + δ + τ k s + r s +} ] s, s 9 Ms = β + R s [ ] E Ms + + π s + s, s 0 Ms Qs + = βms + + π s +, s, s + where Ms U cs +τ c s and πs+ P s+ P s. The frs condon s he opmaly condon for labor; he second s he Euler equaon for capal; he hrd s he Euler equaon for he non-conngen bond; and he las s he Euler equaon for he sae-conngen secures. The characerzaon of he monopols s problem s slghly more exoc because of he nose and heerogeney n he sgnal upon whch he npus k and h mus be chosen. To conserve on noaon, we henceforh le, for z {l, h, k}, MP z, s y, s As Y s z F k, h, l, s. In he eyes of he planner, MP z represens he margnal produc of npu z n frm, expressed n erms of he fnal good; n he eyes of he frm, capures he correspondng margnal revenue produc once 8 By new we mean relave o he sandard Ramsey paradgm, whch rules ou he knd of nformaonal, or cognve, frcons we have accommodaed here. 5

17 s mulpled by, he recprocal of one plus he monopoly markup. As shown n he Appendx, we can hen express he frs-order condons of he frm as follows: τ r s MP l, s ws = 0,, s 2 [ { E Ms τ r s MP h, s } ] = 0, 3 [ { E Ms τ r s MP k, s ] rs } = 0,. 4 These condons have a smple nerpreaon. The frm seeks o equae he cos of each npu wh s afer-ax margnal revenue produc. The only dfference among he hree condons s he exen o whch hs goal s acheved. Because labor s conngen on he realzed sae s, s margnal revenue produc s equaed wh he real wage sae-by-sae. By conras, he oher wo condons hold only on average, ha s, n expecaon condonal on he frm s sgnal. Ths bears a smlary o models wh me-o-buld or adjusmen coss: n hose models, oo, here s an npu whose margnal produc s equaed o he user cos only n expecaon. There s, however, a key dfference: n hose models, expecaons are conngen on he same nformaon se; n our seng, by conras, expecaons are conngen on heerogeneous nformaon. I s hs heerogeney n nformaon, and he resulng heerogeney n npu choces, ha ushers n a coordnaon frcon n producon. Ths n urn ulmaely drves our resul regardng he subopmaly of prce sably. Movng on, noe ha he combnaon of he aforemenoned opmaly condons, he marke clearng condons 4-6, and he governmen budge consran s necessary and suffcen for a sysem of prces, allocaons, and polces o consue an equlbrum. Solvng ou for he prces and he polcy nsrumens, we reach he followng resul. Proposon. A feasble allocaon s par of a flexble-prce equlbrum f and only f he followng wo properes hold. The allocaon sasfes β µ s [ U c s C s + U l s L s ] = 0. 5,s For every, here exs funcons ψ r, ψ l, ψ c, ψ k : S R + such ha ψ r s MP l, s ψ l s = 0, s 6 [ E ψ r s MP h, s ψ c s ] = 0 7 [ E ψ r s MP k, s ψ k s ] = 0 8 Necessy s sraghforward. Condon 5 follows from combnng he neremporal budge consran of he governmen wh he opmaly condons of he household. 9 Condons 6-8 follow from combnng he opmaly condons of he household wh hose of he frms and leng ψ l s = U ls τ l s, ψc s = U cs + τ c s, ψk s = U cs + τ c s r s τ k s, 9 9 Whou serous loss of generaly, we assume ha D 0 = 0 and B 0 = K 0, whch explans why he rgh hand sde of condon 5 s zero. 6

18 and ψ r s = U cs τ r s + τ c s = ψ c s τ r s, 20 where rs denoes he ne-of-axes reurn o savngs. The above equaons reveal ha he vecor ψ r, ψ l, ψ c, ψ k capures he wedges nduced by he ax nsrumens. To prove suffcency, and o undersand why hese wedges are free varables under he planner s conrol, noe he followng. Pck any allocaon ξ ha s feasble and sasfes condon 5. Once such an allocaon s fxed, he pahs for U c s and U l s are also fxed. Sll, he planner can nduce any par of values for he wedges ψ c and ψ l by choosng appropraely he values of he axes τ c and τ l. Furhermore, he planner can rvally sasfy he household s opmaly condons by leng r, he ne-of-axes renal rae of capal, and w, he ne-of-axes wage rae, be such ha ψ c s = βe [ ψ c s + δ + r s + s ] and ψ l s = ws ψ c s, s. Noe nex ha any par of values for ψ r and ψ k can be nduced by seng appropraely he values for τ r and τ k, whle he frm s opmaly condons are sasfed provded ha condons 6-8 hold. The argumen s compleed n he Appendx by reverse-engneerng he enre prce sysem and he asse porfolos ha suppor he consdered allocaon n an equlbrum. Le us now expand on he meanng of Proposon and on s relaon o exsng resuls from he Ramsey leraure. Condon 5 s fully famlar from ha leraure: denfes he aggregae quanes ha are conssen wh he neremporal budge balance for he governmen, opmaly for he household and he frms, and marke clearng. I can hus been read as an on-he-equlbrum represenaon of he neremporal governmen budge, expressed n erms of he consdered allocaon alone. Imporanly, hs condon encapsulaes he fac ha axaon s dsoronary: f lump-sum axaon were avalable, he aforemenoned condon would be vod. Consder nex condons 6-8. When he nformaon, or cognve, frcon s absen, as n he analyses of Lucas and Sokey 983, Char, Chrsano, and Kehoe 994, and Correa, Ncoln, and Teles 2008, he frms can condon her npu choces on he rue underlyng sae of he economy. As a resul, he aforemenoned condons reduce o he followng: MP l, s = ψl s ψ r s, MP h, s = ψc s ψ r s, and MP k, s = ψk s ψ r s,,, s. And snce he ψ s are free varables, he above are sasfed f and only f he margnal produc of each npu s equaed across all frms a all daes and all saes of naure. Ths defnes wha we call perfec coordnaon n he producon sde of he economy. I also means ha he sole role of he avalable ax nsrumens under complee nformaon s o conrol he wedges beween he common MRTs of he frms and he correspondng MRSs of he household. When nsead he nformaonal frcon s presen, each frm mus condon her opmal choce of ceran npus on a nosy and dosyncrac knowledge, or undersandng, of wha s gong on n he economy ha s, on he prvae sgnal of he sae s. As a resul, he margnal producs of hese npus need no be equaed n he cross secon of frms. Ths dsperson n margnal producs and n he underlyng heerogeney n npu choces are ndcaons of he ms-coordnaon of producon across frms. The correspondng hallmark a he macro level s an aggregae TFP loss: for gven 7

19 aggregae quanes of capal and labor, he aggregae quany of he fnal good ha goes o consumpon and nvesmen s depressed relave o he benchmark characerzed n Lucas and Sokey 983, Char, Chrsano, and Kehoe 994, and Correa, Ncoln, and Teles Ths aggregae TFP loss s he resul of he msallocaon of resources nduced by frms nably o condon her choces on he same nformaon se. Under such crcumsances, he avalable ax nsrumens sar playng a new role. Because he aggregae sae s correlaed wh he sgnal receved by he ypcal frm, he conngency of he axes on he former nfluences how he opmal choces of he frm respond o he laer. Ths enables he planner o conrol no only he macro level busness cycle.e., he covaraon of aggregae oupu wh he underlyng sae bu also he mcro-level ms-coordnaon.e., he aforemenoned heerogeney n npu choces and he resulng dsperson n margnal produc. I s hs new role of he axes ha s encoded no condons 6-8. An example. We llusrae he precedng nsghs n he Appendx wh he help of an example ha adms a closed-form characerzaon of he log-lnearzed flexble-prce allocaons. In hs example, we absrac from capal accumulaon, shu down any shocks o governmen spendng, and mpose homohec preferences and Cobb-Douglas echnology. We also le he ax sysem be such ha he relevan wedges are log-lnear funcons of aggregae producvy and aggregae oupu only. We fnally assume ha he nformaon srucure s Gaussan. To be concree, le us heren make he addonal assumpon ha he nformaon conaned n abou A can be summarzed n wo suffcen sascs, one gven by a = log A + ξ and anoher gven by z = log A + u, where ξ s dosyncrac nose and u s common nose, boh orhogonal o log A. As n Morrs and Shn 2002 and Angeleos and La O 200, one can hen hnk of a and z as, respecvely, prvae and publc sgnals abou he underlyng fundamenal. For our purposes, however, s bes o hnk of z more broadly as a proxy for correlaed errors n he frms equlbrum belefs of aggregae economc oucomes. For nsance, z could be he lm of a prvae sgnal ha has a vanshng dosyncrac error and a non-vanshng common error. 20 I s hen easy o show he followng resul. Frs, for any ax srucure, here exss scalars γ 0, γ a, γ u R such ha equlbrum GDP s gven by log GDP s = γ 0 + γ a log A + γ u u. 2 Second, he coeffcens γ a and γ u, whch measure he elasces of aggregae oupu o he underlyng TFP and o he nose, can ake a wde range of values n R 2 ; dfferen values for hese elasces are suppored by dfferen conngences of he axes on aggregae producvy and oupu. Ths resul llusraes how he planner can use axes o nfluence he exen o whch he busness cycle s drven by fundamenal or non-fundamenal forces. As shown n he Appendx, hs nsgh exends o a larger class of nformaon srucures, whch allows he frms o observe an essenally arbrary se of Gaussan sgnals no only abou he underlyng fundamenal bu also abou one anoher s nformaon. The resul saed above connues o hold, excep ha now u has o be re-nerpreed 20 I s also possble o re-cas a as frm-specfc TFP, whch self serves as a prvae sgnal of aggregae TFP. 8

20 as a proxy for all aggregae varaon n he equlbrum expecaons of Y ha s orhogonal o he underlyng varaon n A. Such varaon n equlbrum expecaons of Y reflecs correlaed movemens n eher frs- or hgher-order belefs of A. I can hus capure no only he nose shocks suded n Lorenzon 2009, Angeleos and La O 200, and Barsky and Sms 20, bu also he senmen shocks suded n Angeleos and La O 203, Benhabb, Wang, and Wen 205, and Huo and Takayama 205. In fac, here exss a ax polcy ha nsulaes he economy from such exoc, belefs-drven flucuaons and ha also nduces he same covaraon beween aggregae oupu and aggregae TFP as he one ha s opmal accordng o Lucas and Sokey 983 and Correa, Ncoln, and Teles And ye, as wll be shown n he nex secon, such a polcy s no opmal once he underlyng frcon s properly accouned for n he planner s calculaon of socal welfare. The basc nuon s he followng. To nsulae aggregae oupu from such belefs shocks, he frms would have o dsregard any sgnal ha s correlaed wh hese shocks, such as he sgnal z n he example gven above. Bu hs would mean dsregardng socally valuable nformaon. In parcular, by leng frms condon her choces on he aforemenoned sgnal, he planner can aan a hgher degree of coordnaon n producon; ha s, she can reduce he dsperson n he cross-seconal allocaon of resources, he resulng dsperson n margnal producs, and he assocaed TFP loss a he aggregae level. To sum up, he consdered example llusraes, no only he novel roles ha convenonal ax nsrumens can play n he presence of nformaonal/cognve frcons, bu why he opmal plan may feaure more exoc flucuaons han hose famlar from he sandard Ramsey and New-Keynesan paradgms. Ths, of course, rases he queson of how exacly he opmal plan s deermned. We address hs queson n he nex secon; n he remander of he curren secon, we characerze he se of allocaons ha can be mplemened as par of a scky-prce equlbrum and compare o s flexble-prce counerpar. 4.2 Scky-Prce Allocaons We now add back he nomnal frcon Propery 2 and sudy how hs modfes he se of mplemenable allocaons. Clearly, he addon of he nomnal frcon does no aler he opmaly condons of he household, he budge consrans, and he marke-clearng condons. The mplemenably consran n par of Proposon herefore remans nac. Par, on he oher hand, has o be modfed so as o ake no accoun how he nomnal frcon nerferes wh frm opmaly. A dealed characerzaon of he frm s problem can be found n he Appendx. The key dfference from he flexble-prce scenaro s ha he realzed monopoly markup can flucuae around he deal one nsofar as he polcy nsrumens and he assocaed allocaons respond o conngences no conaned n he nformaon upon whch he frm condons her prce. As a resul, here now exss 9