Friedman and Lucas. Class handout. Giovanni Di Bartolomeo University of Teramo

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1 Class hando Fridman and cas Giovanni Di Barolomo Univrsiy of Tramo. Monarism I: Fridman According o h Phillips mn, h govrnmn can rdc h nmploymn ra by incrasing inflaion. Howvr, in h 970s, Milon Fridman and Edmnd Phlps poind o ha a prmann rdcion in h nmploymn ra shold also b associad o a prmann chang in h ral wag. Why his shold b h cas bcas inflaion was highr, appard o rly on sysmaic irraionaliy in h labor mark: wag inflaion, in fac, wold vnally cach p and lav h ral wag, and nmploymn, nchangd. Expcaions rrors shold hn b h main cas of dviaion in nmploymn from h naral ra, h ra drmind by ral facors indpndnly of prics and h inflaion ra. owr nmploymn cold only b aaind as long as wag inflaion and inflaion xpcaions laggd bhind acal inflaion. As a consqnc, dviaions from h naral ra wr sn o b only a mporary ocom (xpcaion rrors will b soon or lar corrcd). Evnally, nmploymn wold rrn o is naral ra. According o his viw, h Phillips crv ms b vrical in h long rn, and xpansiv dmand policis wold only b a cas of inflaion, no a cas of prmannly lowr nmploymn. Fridman and Phlps viw can b formally dscribd by sing Phillips crv agmnd wih xpcaions drivd in h prvios hando (s also Appndix A): π π + α () ( ) or π π + ( α)( ) whr > 0 is h naral ra of nmploymn. As in h conomy hr ar many disorions (xrnaliis, mark powrs, imprfc informaion) h naral ra is sbopimal. Ths govrnmn wold lik o rdc i. Howvr, his is no possibl a las in h long rn. Fridman dfins h long rn as h priod of im ndd o h priva scor o corrcly forcas h variabls (i.., h im ha i is ndd o h xpcaions o adjs and fi h acal vals in macroconomics hs long rn mans π π ). As a consqnc, qaion () implis ha in h long rn h nmploymn ra is qal o h naral on. Clarly, his also mans ha, in h long rn (whn priva scor corrcly forcass inflaion), hr is no room for h policymakrs amp o rdc nmploymn. In ohr words, in h long rn monary policy is nral. W ar going o dfin h concp of long rn sd in macroconomics dfind by Fridman. Howvr, i is worh noicing ha in microconomics h Marshall s long rn is sally dfind as h im ha is ndd o adjs all prodcion inps; in h shor rn capial is insad givn, whras labor can b adjsd. Morovr, somims h rm mdim rn is sd, i is associad o h firms nry: in h shor rn firms can mark in h compiiv mark, MCMR; in h long rn hr ar no incniv o nr, as xra-profis ar zro, MCACMR. MC and MR sand for marginal cos and rvn, whil AC sands for avrag cos.

2 Inflaion xpcaions ar s a priod in advanc wih rspc o acal inflaion, π in fac indicas h inflaion h priva scor xpcs whn nominal wags ar bargaind (or prics s). Formally, h priva scor ss π a priod, hn a obsrvs π. Thn a :. If π π, xpcaions wr corrc.. If π > π, h priva scor has ndrsimad inflaion. 3. If π < π, h priva scor has ndrsimad inflaion. W can assm ha in h cas, h priva scor dos no rvis h xpcaions; in h cas, h priva scor rviss h xpcaions pward; in h cas 3, h priva scor rviss h xpcaions downward. Th adjsmn procss proposd by Fridman 3 is dscribd by h following figr. Inflaion ra (π) 0 RPC π π 8 6 E E E 3 < π > π Firs bs 4 E 0 PC PC PC Unmploymn ra () Figr Assm, now, ha h govrnmn amps o rdc nmploymn by raising inflaion (as in h classical Tinbrgn s approach). 4 Th conomy movs from E 0 o E. As in E <, h inflaion ra is grar han h xpcd on (π > π ), 5 i.., h workrs hav ndrsimad h inflaion ra. Workrs rvis hir xpcaions and h Phillips crv movs prigh (from PC o PC). Facing h nw consrain, i is opimal for h govrnmn o choos E (whr boh nmploymn and inflaion ar highr). 6 Howvr, in E, workrs hav again ndrsimad h inflaion ra and S h prvios hando. 3 Indd, in h figr dscribs a Fridman-kind adjsmn, which mphasizs h policy gam bwn wag-srs and h govrnmn. W also assm ha workrs parially ak accon for monary policy (as w will lar clarify). In h original Fridman modl inflaion acclras bcas of an asymmry bwn workrs and firms. In sing h nominal wags, workrs hav o forcas h gnral pric indx o ry o fix ral wags. By conras firm corrcly fix prics as mployrs ar only concrnd wih hir own prics and h nominal wag o comp h labor cos. 4 By dfici spnding or incrasing h qaniy of mony. Rcall ha h Phillips crv xprssd in rms of op is h aggrga spply and ha govrnmn can mov h qilibrim along h AS crv (choosing h inflaion ra) by shifing h aggrga dmand (IS/M modl). 5 S qaion (). 6 I is worh noicing ha if h govrnmn dos no chang h inflaion ra (i.., abo 5% is kp), h nmploymn will rais from 3.8% o abo 6.3% (i.., h nmploymn ra fond in h PC if inflaion is 5%).

3 hs hav o rvis xpcaions; hnc h Phillips crv shifs o PC. Th procss conins nil poin E 3, which rprsns h long rn as hr π π. Th ral ffcs of h govrnmn s amp o forc h naral ra vanish in h long rn, b inflaion is now prmannly highr. Morovr, i is worh noicing ha inflaion is vn highr han h val associad o h iniial amp o rdc h naral ra of nmploymn sinc i hn raiss from E o E 3 (inflaion acclraion). As Fridman said, inflaion is always and vrywhr a monary phnomnon. As a consqnc, Fridman and monarism rjc h s of fiscal policy as a ool of dmand managmn and hold ha h govrnmn's rol in h gidanc of h conomy shold b rsricd svrly. Excssiv xpansion of h mony spply is also inhrnly inflaionary, and ha monary ahoriis shold hs focs solly on mainaining pric sabiliy. Exampl. Considr h following hr-qaion conomy: () (3) + α ( π π ) ( ) π + (4) π π Eqaion () is h inflaion-xpcaion agmnd Phillips crv; qaion (3) is h policymakr s loss (in ach priod h policymakr aims o minimiz h sqard dviaions from is args: zro inflaion and an nmploymn ra qal o ); 7 qaion (4) is h rl sd by h wag-srs o s xpcd inflaion (in ach insan of im workrs assm ha inflaion omorrow will b h sam as inflaion oday, hs inflaion xpcd oday is qal o inflaion obsrvd ysrday!!!). Assming ha α/, 4, 3 (i.., h policymakr dsirs a lowr nmploymn ra), and ha in priod zro and π 0 3. How do h conomy volv? 0 A im on xpcaions ar givn π π0 3, hs h policymakr facs h following Phillips crv: (5) ( π ) Exrcis. Dmonsra ha h opimal policy a im implis π 3. and 3.6. A im wo, according o qaion (4), xpcaions ar qal o priod on obsrvd inflaion, i.., π π 3., h Phillips crv is hn: (6) ( π ) Exrcis. Dmonsra ha h opimal policy a im implis π 3.36 and 3.68, whil opimal policy a im hr implis abo π 3.49 and In gnral, a im, givn h xpcaions π, opimal policy implis: (7) π ( ) ( ) π + π π + whr α. 7 In Figr, was zro. 3 and π + + +

4 Exrcis 3. If a im 4 π 4 3.6, how mch ar inflaion and nmploymn a im 5? ong-rn inflaion is fond by sing (7) and (4), hy imply (8) ( ) π π Eqaion (8) is a firs ordr diffrnc qaion, which solvd givs: (9) π R, i.., 4% in or cas. Th solion of (8) is no sraighforward wiho som mah fondaions. Eqaion (8) dscribs h volion along im of inflaion. This volion can b also xplosiv (b no in or cas), i.., inflaion can grow infinily (hyprinflaion). Howvr, hr is an asy way o solv i assm ha h qaion convrgs o a givn val in h long rn, vry far in h fr (.g., π π ), hn on priod afr convrgnc, by dfiniion, inflaion shold b again π, i.., π + π, b qaion (8) shold hold also a +, hn: (0) π ( ) π ( ) i.., π π Solving (8) for π, on gs (9), which is h long-rn inflaion if qaion (8) convrg ohrwis h inflaion grows forvr. ù. Sagflaion In h 950s and 960s, dvlopd conomis volv flcaing arond a long-rm growh rnd, ypically involving shifs ovr im bwn priods of rlaivly rapid conomic growh (xpansion or boom) associad wih high inflaion ras, and priods of rlaiv sagnaion or dclin (conracion or rcssion) associad wih low, or vn ngaiv, inflaion ras. 8 Kynsian policis hn prscribd o frz h conomy in xpansion o avoid h cos of inflaion by rdcing h mony spply and o fl i whn rcssion occrs by pmping mony ino h conomy. In h 970 somhing nw mrgd: boh h inflaion ra and h nmploymn ra wr prsisnly high. Economiss calld his nw siaion sagflaion. Thr ar diffrn inrpraions of sagflaion, in h 970s probably h roos of simlanosly high inflaion and nmploymn wr rahr nclar. Fridman s xplanaion is a mix of spply shocks and bad policis. In 973 h Organizaion of Prolm Exporing Conris (OPEC) consraind h worldwid spply of oil, casing an oil crisis, a spply shock. 9 Oil crisis, combind wih h ovrall nrgy shorag ha characrizd h 970s, rsld in acal or rlaiv scarciy of raw marials. Th pric conrols rsld in shorags a h poin of prchas, casing, for xampl, qs of consmrs a fling saions and incrasd prodcion coss for indsry. Th nmploymn ra ros. No ha highr prodcion coss implis coris paribs a lowr labor dmand and, if ral wags do no fall down, nmploymn incrass. Th govrnmn amping o rsor low nmploymn pshd pric pward, as wll as xpcaions, and hs obaining high inflaion wiho affcing nmploymn. 8 Th wors conomic crisis of h 900s was h Gra Dprssion (99-39). 9 Oil shock cam wih ohr disrbancs as h nd of h Bron Woods sysm and h Nixon s policis ha imposd wag and pric conrols in 97, casing an iniial wav of cos-psh shocks in commodiis, which was blamd for casing spiraling prics. 4

5 Figr dscribs Fridman s viw. Figr Assm ha h Phillips Crv is PC, h qilibrim is E 0, whr h govrnmn policy is opimal (h inflaion ra is 3.3% and h nmploymn ra is.4%). Th 970s oil crisis shifs h Phillips crv on h lf o PC, if h govrnmn conins o kp h inflaion ra a.4%, nmploymn jmps o 3.8% (poin E ). Th Kynsian govrnmn inrprs h incras in nmploymn as a dmand-drivn rcssion; hrfor, h govrnmn pmps mony ino h conomy o fac h crisis moving h conomy along h Phillips crv. As xpcd by h Kynsian govrnmn, nmploymn bgins o fall and inflaion o rais (poin E ). Thrafr, wih srpris for h govrnmn, boh inflaion and nmploymn grow as wag-srs rvis hir xpcaions (poin E 3 ) and, following Fridman monaris viw, conin o grow nil poin E 5. A nw phnomnon mrgs: Sagflaion. Figr 3 is vocaiv. Inflaion ra (π) PC PC PC Unmploymn ra () Figr 3 5

6 Th figr shows h Phillips crvs associad o h 960s, h firs half of h 970s and h scond half of h 970s. 3. Monarism II (Nw Classical Economics): cas Th implici assmpion of Fridman is ha xpcaions ar slggish: workrs obsrv hir rrors and rvis hir xpcaions wiho flly considring ha h govrnmn, as nmploymn is now highr, will again amp o incras inflaion o rdc i. This implis ha hy ar sbjcd o sysmaical rrors, i.. workrs ar fools!!! Rconsidr h Fridman adjsmn pah in dails,.g., in poin E of Figr, workrs ndrsand ha hy hav ndrsimad inflaion (hir xpcaions wr abo 4% and inflaion is 5%); hy hs rvis pward π, sing inflaion xpcaions qal o h crrn inflaion ra (5%). Workrs forcas is o b in A in h nx priod. Howvr, if h workrs rvis xpcaions is sch a mannr, in h nx priod for h policymakr will b opimal o frhr incras inflaion (o abo 6%) moving h conomy in E, whr workrs again ndrsima h inflaion ra. Thn wag-srs rvis hir xpcaions o 6% (o achiv A ) and again will b cha by h policymakr, who ss inflaion o abo 6.8% o achiv E 3, and so on. Ar wag-srs acally fools? Bob cas in h 970s says no. cas poin is ha h wagsrs anicipa h policymakr s bhavior. For insanc, if h conomy is E, hy anicipa ha by sing inflaion xpcaions a 5%, hy will wrongly forcas inflaion; hy, in fac, corrcly ndrsand ha in his cas h policymakr has an incniv o frhr incras inflaion o 6%. Morovr, hy also ndrsand ha vn hy s xpcaions a 6%, again xpcaions will b wrong, as h policymakr sill has an incniv o rais inflaion. Thy can bliv only o a fr inflaion qal o abo 7.5%, as in his cas policymakr has no incniv o fool hm, and hs will s hir xpcaions accordingly. If xpcd inflaion is 7.5%, in fac, h Phillips crv immdialy shifs o PC, and inflaion will b 7.5%, i.., corrcly anicipad. Inflaion ra (π) 0 RPC 8 E 3 E 4 Firs bs 6 4 E A A E E 0 PC PC PC PC Unmploymn ra () Figr 4 6

7 cas ida is vn srongr. If h prfrncs ar hos dscrib in Figr 4, wag-srs anicipas ha h policymakr aims o infla h conomy o rdc nmploymn, i.. mov o poin E, and hs, hy anicipa an inflaion ra qal o 7.5%. In ohr words, policymakrs canno s h Phillips rad-off: any amps o do i will b anicipad and will only imply highr inflaion. Th implicaion of h cas poin of viw is ha only nxpcd policis may hav som ral ffc (cas proposiion). For insanc, random policis canno b anicipad and hs will mporary shif h nmploymn ra. Howvr, do random policis b sfl? By conras anicipad policy will hav no ffc. W now rconsidr h hr-qaion modl o show how o solv a raional xpcaions modl. π π + α () ( ) () ( ) π + (3) π E π Eqaion (3) dscribs raional xpcaions. I implis ha xpcaions ar on avrag corrc and hs workrs ar no sbjcd o sysmaic rrors. Th modl rns as follows. A, workrs form hir xpcaions; ha is, hy ms forcas fr inflaion. Afr xpcaions ar formd (rcall ha his mans h shif of h Phillips crv is s), h policymakr chooss is opimal policy (i.., h policymakr chooss a poin along h Phillips crv). Howvr, whn w considr h workrs problm w nd o ak accon of h fac ha hy anicipa also h possibl policymakr s policy. Ths, o solv h workrs problm w nd o solv bfor h policymakr problm for a givn xpcaion abo inflaion. Formally, w solv h problm by backward indcion. Th policymakr problm is asy o solv, minimiz () sbjc o () wih rspc o π, givn π. I follows (s qaion (7)): (4) π As workrs ar raional, hy anicipa ha givn π, h policymakr s opimal policy will imply (4); hn hy can anicipa ha π α (5) ( π π) Mor in dails, aking h xpcd val: π + + E E + + α (6) ( π π) Eπ + + E E + + α (7) ( π π) + (8) ( ) π π No ha E π π. Now compar (8) o (9), wha dos i man? 7

8 By sing (8) ino (4), i follows (9) Morovr, by sing (8) and (9) w obain (0) π I is worh noicing ha E π π. Now considr a small varian of h modl dscribd abov by assming ha h policymakr sill aims o minimiz () sbjc o () wih rspc o π, b is policy is affcd by a sochasic disrbanc (a sor of masrmn rror), so opimal policy is 0 () ( ) π + π + ε + A, ε is nknown, w assm ha ε is normally disribd wih zro man and fini varianc (formally, ε (0, σ ) ). No ha E ( ) 0 ε. N ε Expcd inflaion is: () ( π ) ( ) E + E E E + π + ( ε) π π i.., inflaion xpcaions ar h sam as prvios cas (his is no srang sinc workrs canno prdic h disrbanc; indd, hir bs prdicion is o assm ha i is zro). Howvr, by sing () and (), acal inflaion will b (3) ( + ) ( ) π + + ε π + ε + which is diffrn from (0), b qal on avrag ( E π ( ) ). Exrcis 4. By sing (3), find acal and xpcd nmploymn ras and discss h cas s policy nraliy proposiion. 0 Opimal inflaion is h sam as bfor pls a disrbanc. 8

9 Appndix Eqaion () Considr from h labor mark qilibrim (drivd in h prvios hando): p p + α (4) ( ) Thn sm and sbrac p, p p p + p + α (5) ( ) Dfin inflaion as h diffrnc bwn h (log)pric lvls and obain π π + α (6) ( ) Solvd for π, qaion (6) is (7) π πr + ( α)( ) As qaion (). 9