Aggregate Supply, Output Fluctuations and Policy Neutrality

Transcription

1 Douglas Hibbs Macro Thory Aggrgat Supply, Output Fluctuations and Policy Nutrality In this lctur I ll illustrat how svral spci c routs by which nominal misprcptions may caus output uctuations can b viwd as variations on th basic stup of th famous Lucas supply function. Along th way I ll giv a brif history of th Phillips curv, and I will show how it conncts to, and ultimatly ld to, th subsqunt txtbook Lucas supply quation. Thn w ll look at th implications of Lucasian supply functions for montary policy "nutrality" an implication of Lucas sminal work that was quickly sharpnd by Barro, Sargnt and Wallac, and comprisd a major assault on traditional Kynsian modls which faturd sluggish adjustmnt of nominal wags and prics as a ky sourc of businss cycls. Subsqunt lcturs will build upon ths foundations. Unlss notd othrwis, all lowr cas variabls dnot corrsponding uppr cas variabls in natural log form. Nominal Adjustmnt Thoris of Businss Cycls Nominal adjustmnt thoris of th businss cycl oprat through an aggrgat supply quation. Th undrlying imprfctions in information about prics and/or th mony supply could logically originat with th procss of wag formation in th labor markt, or with production dcisions in th goods markt, or both. Th bnchmark quation is th supply function found in most intrmdiat macroconomics txtbooks (with random disturbancs and othr xognous in uncs omittd): q S t = q t + [p t E (p t ji t )] ; > 0 () whr q S is log aggrgat supply, q is log "potntial", "normal" or "natural" output th log output lvl that would b ground out by a comptitiv conomy

2 in quilibrium, p is log output pric, and E (p t ji t ) is th xpctation of pric conditiond on th tim t information st of agnts (which I shall somtims writ as E t X), whr it is assumd that I t is rstrictd to outcoms ralizd at t and arlir. 2 Th natural log output lvl, qt ; is known to all agnts, and dviations of log output supply from q ar drivn by pric (or in ation) 3 "surpriss". Th sam assrtd supply modl could radily b obtaind from a simpl wag-formation stup.. A Labor Markt Viw Using q.() as th bnchmark, in th labor markt viw w hav q S t = q t + (p t ^w) : (2) Output dviats from potntial in proportion to movmnts in th productivityadjustd ral wag. Th log nominal wag (nt of productivity) 4, ^w; is dtrmind by xpctd log pric ^w = E t p t ; (3) Oftn q is modlld as a linar trnd (as Lucas did in svral paprs), which would b consistnt with what w usd to obtain stylizd rsults in th growth thory lcturs. Hnc on th balancd growth path with labor growing at rat n and tchnology at rat g;output grows at rat q = (g + n) ; and log natural output is thrfor q t = q 0 + (g + n) t: 2 In arlir lcturs it was oftn positd that th tim t information st includd outcoms ralizd up to and including tim t: Kp th nw assumption in mind. 3 Dviating th pric trms in () givs th sam modl with in ation surpriss in plac of log pric surpriss. 4 Rcall that in a comptitiv stting with tchnology growing xponntially A t = A 0 ( + g) t th ral wag can b xprssd in discrt tim as W t Qt = A t F 0 P t A t N t t : ^w t can b thought of as log Wt A t : Kt A t N t K t A t N t 2

3 which gts us back to q.(). As a simpl illustrativ motivation of th labor markt viw, considr a production tchnology in which labor is th only ndognous input: Q S t = A t N t : (4) Lt log labor dmand, n D, b obtaind from th FOC for static pro t maximization: which givs log labor dmand as n D t = Q 0 (N t ) = A t N t = W t P t ; (5) ( ) [ln + (p t ^w)] ; ^w [ ^w ln A t ] : (6) Using ths simpl rlations w arriv at th log aggrgat supply function qt S = qt + ( ) (p t ^w) ; (7) h i which is q.(2) with qt = ln + ln A ( ) t and =. Output thrfor ( ) travls up th production function on th back of falling ral wags. (Whnc th kn-jrk raction from conomists to output and mploymnt problms: "cut wags".) Whn wags ar formd according to w arriv at th bnchmark supply function in (). ^w t = E t p t (8).2 An Historical Divrsion on th Phillips Curv A prcursor of th modrn aggrgat supply function was th famous Phillips curv (aftr A.W. Phillips, Economica, 958), which basd on historical vidnc idnti d a convx rlation btwn wag in ation or pric in ation and th rat of unmploymnt ^w w t = a bu t (9) p t p t = a bu t (0) 3

4 u bing th log of th unmploymnt rat, U. Mony wag in ation and unmploymnt wr rgardd by many as baring a "trad-o rlationship a viw that two giants of conomics Paul Samulson and Robrt Solow argud (with subtl rsrvations) providd policy authoritis with somthing lik a "mnu of choics" for aggrgat dmand policy. (Samulson and Solow, AER, 960). Almost simultanously (a common occurrnc in scinc) Milton Fridman (AER, 968) and Edmund Phlps (Economica, 967) pointd out that a ral variabl lik unmploymnt could only b rlatd to a nominal variabl lik th wag in ation rat whn th in ation xpctations a cting wag formation laggd bhind actual in ation dvlopmnts. 5 This viw yildd xpctations augmntd Phillips curv quations lik and w t w t = a b U t U (t) + c Et (p t p t ) () p t p t = a b U t U (t) + c Et (p t p t ) ; (2) whr U(t), is th so-calld natural rat of unmploymnt, which you can tak to b th unmploymnt rat whn output is at quilibrium, qt. Expctd in ation was commonly modlld adaptivly (cf. th Consumption lctur nots on Fridman s adaptiv xpctations proposal for modlling prmannt incom), and many studis attmptd to dtrmin whthr or not th co cint c was lss than :0 or not, which was considrd informativ about th slop of th short- and long-run Phillips curv and, indd, whthr a long-run Phillips curv "trad-o " xistd at all. 6 All this has gon by th boards undr mor modrn viws. No on sriously ntrtains th ida anymor that thr could possibly b a stabl "mnu of choics" allowing policy makrs to us aggrgat dmand policy to slct combinations of unmploymnt and in ation, as tracd out by a stabl, downward sloping Phillips curv schdul in in ation-unmploymnt spac. By Okun s law (Arthur Okun,962 ASA, and takn from th start to b a statistical rathr than a structural rlation) w know that unmploymnt and output gnrally bar clos association to on anothr (q t qt ) = k U t U(t) 5 Th ida that xpctations ntr th story, howvr, can b tracd back furthr; at last to Ludwig von Miss (Th Thory of Mony and Crdit, 953). 6 Thomas Sargnt mad on of his arly impacts on th conomics profssion (JPE, 976) by pointing out that th magnitud of "c" was irrlvant to th trad-o viw whn xpctations wr modlld adaptivly, or modlld in any othr fashion that did not corrspond to a rational modl of xpctation formation in Muth s (Economtrica, 96) sns. (3) 4

5 whr in US data is in th vicinity of 0.02 to By th 970s what was onc studid in Phillips curv fashion was mor commonly writtn as an aggrgat supply rlation, which amounts to intrchanging in ation and unmploymnt on th lft- and right-sids of q.(2), and using Okun s law to substitut out U t : U (t) U t U(t) a = b b (p t p t ) + c b E t (p t p t ) (4) (q t qt ) = k a b + b (p t p t ) c b E t (p t p t ) : (5) At c = (prsumd undr rationality of xpctations) q t = k a b + q t + b [(p t p t ) E t (p t p t )] ; (6) which up to a scalar is obsrvationally quivalnt to th supply schdul in q.(). 2 Th Lucas Supply Modl Th bnchmark aggrgat supply function on o r in macroconomics originats with Lucas (JET, 972 ; AER,973 and Lucas and Rapping, JPE, 969). Th mchanics and logical foundation laid out in th 973 papr ar spcially famous, and you should b thoroughly familiar with thm. Th main (and quit prpostrous) ida said to takn as a "mtaphor" rathr than as a plausibl dscription of any ral world conomy is that producrs cannot distinguish th rlativ pric movmnts thy want to rspond to from gnral pric movmnts (in ation). Thy rationally attmpt to mak th distinction, but thr is of cours tmporary slippag (inhrntly transitory "surpriss") which givs th statistical apparanc of a upward sloping aggrgat supply curv. Obsrving an upward sloping supply curv in data, policy-makrs consquntly might rronously try to xploit it by jacking up aggrgat dmand in th hops of incrasing ral incoms. [Graph] 7 In othr words, masurd on an annual basis output is dprssd around 2.0 to 2.5 prcntag points for ach xtra prcntag point of unmploymnt. Th magnitud of this statistical paramtr is clarly contingnt on th institutional stting. It tnds to b much biggr in many postwar Europan macroconomis than in th US. Think about th rlationship th othr way around, and ask yourslf why might unmploymnt tnd to fall lss during booms and ris lss during busts in Europ than in Amrica? And if this b tru, why might th natural rat of unmploymnt (structural unmploymnt) b highr in th lattr stting. 5

6 2. Th Stat of th World Goods ar tradd in physically isolatd comptitiv markts ("islands"). Dmand is distributd unvnly across th markts, which yilds rlativ as wll as gnral pric movmnts. Producrs hav prfct, instantanous information about own-pric in thir own markt, but imprfct information about th prics producrs fac in othr markts and, hnc, imprfct information about th gnral pric lvl. Aggrgat Dmand is Kynsian (IS-LM), and so it can b shiftd by movmnts in M, G, T and X. To kp simpl th partitioning of nominal output, Y, into ral quantitis, Q, and prics, P, it is assumd that dmand is unit lastic. This allows us to plug into th quantity idntity Y P Q = M V (7) V = Y M = :0 (8) so that nominal spnding quals th mony supply 8 and w can writ th log aggrgat dmand quation Y = M; (9) 2.2 Dmand in Markt i Dmand for th rprsntativ good in markt i is q D t = m t p t : (20) Q D i = Q Pi " D i ; D log Normal (2) P whr th stup imposs th (inssntial) simplifying assumption that =, so that aggrgat pric is just th gomtric man P = J i=p J i (22) 8 M might b thought of quit broadly as any variabl a cting aggrgat dmand, rathr than as th mony supply pr s. Th important point is that aggrgat dmand is unit lastic. Stting vlocity to :0 is just don for convninc, without loss of gnrality. W could carry aggrgat dmand vlocity shocks throughout th story. 6

7 and log aggrgat pric is p = J JX p i = p i : (23) i= Markt-spci c log dmand is thrfor q D i = q (p i p) + D i ; D ln D 0; 2 D (24) 2.3 Supply in Markt i To motivat simply th Lucas supply function from highly simpli d rst principls, imagin that production possibilitis for th rprsntativ good ar Q S i = A (t) N i " S i ; 2 (0; ) ; " S log Normal (25) whr N is producrs own labor, A is th stat of tchnology and w abstract from othr inputs to production. Producr utility is givn by U i = P i ^w i P N i ; > (26) whr ^w i = P iq i P A (t) is ral incom from production nt of th scular ris in productivity. U i implis that producrs hav constant, unit marginal utility of nt incom. Substituting for incom, utility is U i = P in i " S i P N i : (27) P and P i (aggrgat pric and local markt pric) ar xognous to local producrs, so having substitutd out ^w i w hav but on i = P in i P " S i N i = 0; (28) ) P i" S i P = N ( ) : Taking logs and nding n i w obtain 9 9 Not that n now grows ind ntily with A! 7

8 n i = ( ) (p i p) + S i ; S ln " S 0; 2 (29) S Th log supply function in markt i is found by taking th log of q.(25) and using (29) to substitut for n i : q S i = ln A + ( ) (p i p) + ( ) S i : (30) 2.4 Equilibrium Pric W now nd quilibrium pric. As usual, quat supply and dmand and solv for p i 8 >< >: q D i = q S i (3) q (pi p) + D i = h i ln A + (p ( ) i p) + ( ) S i which aftr a bit of boring algbra givs p i as p i = p ( ) ln A + ( ) q + 9 >= >; ; (32) ( ) D i S i : (33) By th assumption of unit lasticity of dmand for th rprsntativ good in markt i (rcall w unit pric lasticity of dmand, = ; in q.(2)) E (p i ) p i = p: (34) Hnc on th right-sid of q.(33) it must b tru that th sum of th trms aftr th rst aftr th aggrgat pric trm p hav zro unconditional xpctation ( ) ( ) ( ) E ln A + q + D i S i = 0: (35) Sinc D i and S i ar random shocks to local markt dmand and supply, rspctivly, with zro xpctd valu, w hav ( ) ( ) E q = ln A (36) ) E (q) = ln A: (37) 8

9 In this motivation of supply, E (q) is clarly th aggrgat potntial or "natural" output lvl, q(t), of q.(), which corrsponds to log output lvl producd whn th macroconomy on its balancd growth path Notional and Bhavioral Local Markt Supply Consistnt with q S i in (30) and q t in (37), notional supply in th Lucas stup is q S it = q t + (p it p t ) + ( ) S it; (38) whr = > 0 is a composit supply paramtr composd of th "dp", ( ) fundamntal paramtrs of production and utility. Eq.(38) is th quation that producrs would lov to us to mak production dcisions; thy d lik to jack up output whn rlativ prics ar running in thir favor ("to mak hay whil th sun shins" as Amricans say), and tak lisur whn rlativ pric dvlopmnts ar running against thm. But, as notd in th stat of th world, producrs ar not sur what th aggrgat pric lvl, p; is instantanously. Hnc thy ar not sur whthr a movmnt in p it rprsnts a rlativ pric shift or just in ation of th gnral pric lvl. Blow w shall s that bhavioral supply function that actually drivs production dcisions is th x-ant rational xpctation of q.(38): q S it = q t + [p it E (p t ji it )] (39) whr is a paramtr to b drivd shortly, and E (p t ji it ) is th xpctation of p t conditiond on th information availabl to producrs in markt i at dcision tim t. What gnrats rationally E (p t ji it )? Lt s writ down xplicitly what producrs know: p it = p t + r it, r it (p it p t ); local markt pric is by d nition gnral pric plus a rlativ pric shock, r it. p t = E (p t ji it ) + " P t 0; 2 ; normal; whit; producrs do not mak systmatic mistaks ovr tim producrs xpctations ar P rational. 0 Hnc, if as arlir, q t = ln [A 0 F (K ; N )] + ln ( + g) t thn th ("dp") paramtrs of production and utility, and ; undrly th convrgnt stocks of K and N and th rat of scular growthln ( + g). 9

10 Sinc r it (p it p t ) = p it E (pt ji it ) + " P t 0; 2 r ; normal; whit, r it + " P t = [pit E (p t ji it )]; producrs know that xpctation rrors in gauging th rlativ pric shock of intrst will qual th sum of rlativ pric shocks and aggrgat pric shocks. Cov r it ; " P t = 0; by plausibl assumption of th stup (by producrs historical obsrvation), rlativ and gnral pric shocks hav zro covarianc. So how do th producrs stimat r it th rlativ pric movmnt thy want to rgulat supply with from th obsrvd dviation of p it from xpctd p t ;which thy know is qual to th composit rror r it + " P t? This qustion is known as th signal xtraction problm a commonplac concpt among lctrical nginrs sinc th 940s, but quit a novlty in conomics whn Lucas was writing back in th arly 970s. On way to approach th signal xtraction problm is to assum that producrs hav a quadratic loss function, that is, at ach dcision priod thy want to minimiz (r i br i ) 2. This would lad dirctly to a last-squars computation of th bst linar unbiasd (quadratic loss minimizing) prdictor from historical data, that is from data in priods t 0 < t: r it 0 = b r it 0 + " P t 0 = b fp t [p it E (p t ji it )]g b OLS = Cov r it 0; r it 0 + " P t 0 V ar (r it 0 + " P t ) 0 (40) (4) = b 2 r b 2 r + d 2 " P ; t 0 < t: Hnc at dcision priod t producrs would stimat th rlativ pric movmnt of intrst, r it, from th obsrvd composit xpctation dviation r it + " P t = [p it E (p t ji it )] by computing br it = b 2 r b 2 r + d 2 " P r it + " P t (42) = b 2 r b 2 r + d 2 " P [p it E (p t ji it )] : Sinc th xpctd valus of r it 0 and " P t0 ar both zro and thy hav zro covarianc, on may in principl omit th constant (intrcpt) from th linar projction quation: constant = r it 0 b (r it 0) + " P t =

11 It follows that th rational local markt bhavioral supply function would b q S it = q t + b 2 r b 2 r + d 2 " P [p it E (p t ji it )] (43) whr at q.(39). c 2 r c 2 r+ d 2 " P = q t + [p it E (p t ji it )] ; is what I lablld whn I positd th bhavioral supply function A scond way to rationaliz = c 2 r c 2 r + d 2 " P is to forgt about assuming a quadratic loss function and just apply a thorm from statistics (Cf. Mood, Graybill and Bos, many ditions, chaptr 5) which shows that if r it and p it ar jointly normally distributd, th conditional xpctation of r it givn ralization of p it is c 2 r c 2 r + d 2 " P [p it E (p t ji it )]. Eithr way, on gts to th rsult in q.(43). I lik th formr motivation, as it dos not dpnd on joint distribution assumptions (which wr assumd along th way in th stup, with appal to this thorm in mind), though of cours th rational I favor dos imput a loss function to th agnts. Lucas usd th joint normality projction, and most of th sorcrr s apprntics sm to hav followd suit. Taking th man (unconditional xpctation) of q.(43) across local markts at tim t givs th oprativ Aggrgat Supply function 2 q S t = q t + b 2 r b 2 r + d 2 " P [p t E (p t ji t )] : (44) Not wll th implications of this aggrgat supply schdul. [Graph of LRAS, SRAS] As gnral pric variability gts larg by comparison to rlativ pric variability, producrs no longr rspond vry much to surprising pric movmnts pric surpriss that in a rgim of low gnral pric variability (low rlativ to historical calibrations of rlativ pric variability) would licit changs to production. As c 2 r c 2 r+ d 2 " P! 0, that is, whn all pric movmnts historically originat with th gnral pric lvl, th supply schdul is vrtical in th pric-output spac, intrscting th output axis at th natural rat, qt c. By contrast as 2 r c 2 r + d!, 2 " P 2 Notic that by substracting p t from ach pric trm within brackts in q.(44) w obtain output supply (qual to actual output at quilibrium) in trms of th gap btwn actual and xpctd rats of in ation: q t = q t + [(p t p t ) (E (p t ji t ) p t )]. This is analogoust to th Phillips curv of q.(6).

12 that is, in a historical rgim of zro gnral pric in ation in which all pric movmnts ar rlativ pric shifts, producrs will rspond fully to an unxpctd pric movmnt in proportion = pr unit pric surpris. ( ) Th ratio of rlativ to gnral pric variability is clarly contingnt on th montary policy-rgim. This statmnt will bcom (mor) obvious blow. 2.6 Aggrgat Equilibrium Th aggrgat pric lvl is ndognous; mony (th gnric aggrgat dmand policy variabl of th modl) is th only xognous variabl in this stylizd macroconomy. W nd aggrgat quilibrium in th usual way by quating supply to dmand: q S t = q D t g ) q t (45) qt + [p it E (p t ji t )] = (m t p t ) g ) q t ; (46) whr rcall c = 2 r c 2 r+ d = c2 r 2 ( ) c " P 2 r+ d : You may radily con rm that 2 " th solutions for p P t and q t ar p t = + m t + + E (p t ji t ) + qt (47) q t = + m t + E (p t ji t ) + + q t : (48) Eq.(47) is th x-post solution for ralizd aggrgat pric. Ex-ant, bfor p t is ralizd, it must b tru by rationality of xpctations that th quation for x-post quilibrium pric holds in conditional xpctation 3 : E(p t ji t ) = + E(m t ji t ) + + E (p t ji t ) + qt : (49) It follows that 2 E(p t ji t ) E (p t ji t ) 5 = + E(m t ji t ) + q t E(p t ji t ) = E(m t ji t ) qt : (50) 3 Rmmbr that agnts ar assumd to know th natural output lvl, qt along with paramtrs of utility and production. 2

13 Using th quations for ralizd aggrgat pric(q. 47) and xpctd aggrgat pric (q. 50), w s that th solution for p t can b writtn p t = + m t + + [E(m t ji t ) q t ] + qt (5) p t = + E(m t ji t ) + + m t q t : (52) Th quilibrium solution for output in q.(48) thrfor is q t = + m t + [E(m t ji t ) qt ] + + q t (53) q t = qt + + [m t E(m t ji t )] : (54) Equation (54) just maps th arlir rsult for pric surpriss back onto mony th xognous policy instrumnt in th stylizd macroconomy. Th intrprtation is thrfor prcisly th sam: Only montary surpriss (or, mor gnrally, surprising aggrgat dmand shifts) can gnrat dviations of log output from its "natural" lvl. And undr th strict intrprtation of th Lucas modl, vn th ct of montary surpriss will b dampd monotonically as th ratio of rlativ pric variability to gnral pric variability falls. (Rcall = c2 r ). ( ) c 2 r + d2 " Hnc, thr is no scop for systmatic, and consquntly prdictabl, montary P policy to a ct th ral conomy. This is th cor of th famous Lucas-Sagnt- Wallac "policy nutrality" proposition, and you should undrstand its logical foundation thoroughly. Lucas "isolatd markts" story motivating policy nutrality is, of cours, prpostrous. If information about th gnral pric lvl wr of importanc to producrs, or to any anyon ls for that mattr, it could b supplid at almost no cost at mor or lss th sam frquncy as asst pric quotations. Yt th main mssag of th story has considrabl mrit. Agnts in th conomy (th agnts of principals) surly do tak pains to avoid bing foold by gnral pric in ation and th montary xpansions that crat it. Th famous ssay by Lucas dvloping th nutrality proposition in svral policy and forcasting sttings (th Lucas critiqu ) is still prhaps th bst plac to larn about its rang and powr (Carngi-Rochstr sris, 976). 3

14 But all is not lost for policy activism. You should familiariz yourslf with th oldr nw Kynsian modls that giv th authoritis som capacity to a ct th ral conomy bcaus of institutionally dtrmind sluggishnss of wag adjustmnt, (lading xampls ar Fischr, JPE, 977 and Taylor, 979 AER, 979), as wll as subsqunt nw Kynsian modls that look to inrtia in product pricing (for xampl, Mankiw, QJE, 985 and Ball t al. BPEA, 988). Finally, not that on could trac th c 2 r c 2 r+ d 2 " P componnt of th composit aggrgat supply paramtr back to th volatility of mony (volatility of aggrgat dmand policy) bcaus, asid from potntial output, it is mony that ultimatly drivs th pric lvl (q.52). c Douglas A. Hibbs, Jr. 4