Lucas Imerfect Infrmatn Mdel 93 Lucas Imerfect Infrmatn Mdel The Lucas mdel was the frst f the mdern, mcrfundatns mdels f aggregate suly and macrecnmcs It bult drectly n the Fredman-Phels analyss f the Phlls curve that we have studed e It led t the Lucas suly curve n whch yt y b Smlar suly curves can (and wll) be derved frm ther sets f assumtns Key assumtn: Lucas mdel assumes erfect rce flexblty, but merfect nfrmatn Rmer resents n terms f yeman farmer rductn rather than havng exlct frms Ths s nt an mrtant assumtn Can derve smlar mdel wth frms and wages Key assumtn: Market structure Ecnmy s cmsed f a large number f gds Each gd s rduced by a large number f frms (rather than beng a mnly as n the merfect cmettn mdel) Key assumtn: There are tw knds f randm shcks Aggregate shcks that affect AD curve (M) Gd-secfc shcks that affect demand fr ndvdual gd (z ) but average ut t zer acrss all gds Husehld behavr U C L Prductn functn: Y L Budget cnstrant: PC PY Ths s crtcal: C s an ndex f cnsumtn by a reresentatve rducer f gd, nt cnsumtn f gd Husehld buys all gds, but sells nly gd P Puttng tgether: U Y Y P Prce-takng husehlds, s they take bth P and P as gven Nte the dfference ntrduced by the cmettn assumtn rather than the lygly mdel Utlty maxmzatn:
94 Lucas Imerfect Infrmatn Mdel du P Y 0 dy P P Y P In lg terms: y Ths s the suly curve fr gd Aggregate and sngle-gd demand Demand fr gd s gven by y y z Aggregate demand: ym y m z Ths s exactly the same demand curve as n the lygly mdel, excet we nw have a randm, gd-secfc shck z Aggregatn and equlbrum Assume that and y y are the lg-average rce and quantty ndexes What matters t rducers s ther relatve rce: r If they can bserve bth and, then the mdel can be slved drectly Settng demand = suly fr each market: m z m z / Snce s the average f all the values, when we average acrss all markets z 0 S slutn s = m and mney s neutral Aggregate utut s y = 0 (Y = ) Nte that ths s fully effcent n cmarsn t lygly mdel because there s n mnly behavr here Lucas assumes that agents have merfect nfrmatn They knw the rce f the gd they sell They dn t knw all the rces f the gds that they buy Ths s rbably farly realstc because mst ele are mre secalzed n the gds they sell than the nes they buy Sgnal-extractn rblem
Lucas Imerfect Infrmatn Mdel 95 Agents bserve but nt Must attemt t nfer and r frm Knwn varable r (sgnal lus nse) Under merfect nfrmatn, suly curve becmes y Er Shcks Assume that the aggregate shck m s nrmally dstrbuted wth mean zer and varance V m Lcal shcks z are nrmal wth mean zer and varance V z Frm agent s ersectve, we cnsder and r as unbserved randm functns f m and z r Otmal sgnal-extractn rule: Er E V, where V r and V are the V varances f r and frm the agent s vewnt s sgnal-t-nse rat: hw much f what we hear s the sgnal r as V sed t the nse V? Nte what haens t E r when V becmes large r small N aggregate-rce varatn means rat = and all shcks are assumed t be lcal Suly curve s elastc because agents assume shcks are relatve and resnd strngly Infnte aggregate-rce varatn (r zer lcal-rce varatn) means rat = 0 and all shcks are assumed t the aggregate Suly curve s nelastc because agents assume shcks are aggregate and dn t resnd Values f V r and V are endgenus, deendng n hw r and resnd t shcks Lucas suly curve Plug sgnal-extractn rule back nt suly curve y E V Averagng acrss all : y E b E V Nte smlarty t mdern Phlls curve relatng u u n t e Vz Usng methds yu need nt learn, we can shw that V V V V case that r z m n the
96 Lucas Imerfect Infrmatn Mdel Shw grah f SRAS and AD, wth SRAS assng thrugh y = 0 and = E() Nte crss-cuntry mlcatns: Cuntres wth hgh V m wll have nelastc AS curves relatve t cuntres Equlbrum wth lw V m Ths s the bass fr the emrcal wrk n Lucas s aer f the week (and als the Ball, Mankw, and Rmer aer fr next week) AS: ybe AD: ym Slvng tgether yelds b be m b mbe b m E b b b b y m E b b What are exectatns f? Ratnal exectatns hythess says that agents frm exectatns n a way that s cnsstent wth mdel They dn t knw the shcks m and z, but they d knw the mdel and the ceffcents f the mdel b b b b b b b E E Em b b b E Em b b bb E E m b b E Em b b E E m E Em E E Em E Thus, b y m Em b b m Em b b Shw settng f E() and thus SRAS based n AD curve crresndng t E(m)
Lucas Imerfect Infrmatn Mdel 97 Plcy neffectveness rstn The utut equatn shws that nly unantcated changes n aggregate demand affect real utut. If m and E(m) g u by the same amunt, then mney s neutral: Effect n y s zer Effect n s ne Ths undermnes the case fr cuntercyclcal AD lcy, because f ele crrectly recgnze the need fr lcy as quckly as lcymaker des, then they wll fx the ecnmy n ther wn and any lcy change wll affect nly Ths was hghly cntrversal cnclusn f Lucas mdel n early 970s, rejected by Keynesans, leadng t new Keynesan mdels wth gd mcrfundatns but wth stve rle fr macrecnmc stablzatn lcy Emrcal evdence was ntally stve (Barr), but later mst evdence demnstrated that even lcy changes that were crrectly antcatable had real effects