Rational Expectations and General Equilibrium

Equilibrium is then considered that condition in Rational Expectations and Ceneral Equilibrium TO THE EDITOR: Cl.rristopher Phelan's "A l)clbnse of Ilational Expcctations/General Equilibrium Analysis against Austrian Objections" (Fall r987) has provided thtreaders ofthisjournal with a fair and reasorrable cxplanation ofuencral cquilibrium theory ancl the rational expectations hypothcsis. Hc also intcndcd to answer Austrian-school critics of gcneral equilibrium ancl rational cxpcctations.'As onc of tl-rosc critics, I would like to takc this opportunity to look into the equilibriunr issuc a littlc dccper, and tease out some additional problems crnbcddcd in the equilibrium framcwork which Phclan so competerltl\' dcscribecl. Phclan statcs that the major sourccs of Austrian objections are simply misunderstandings about thc nature and purposc ofthc conccpt ofequilibriunr. Thc rnost comnlon rnisundcrstanding, according to Phelan, is to belicvc equilibrium reprcscnts thc conring to rest of a systcnl ovcr timc. Using Hotcllinq's classic cxample of two hot-dog vcndors attenrpting to find thc optimal location on a bcach, he dernonstrates that equilibriunr means no such thinq. Rathcr, equilibriunr is that state of affairs in which minds or stratcgies becomr. coordinatcd. On this point, howcvcr, nlost Austrians agree (or -ifiould agree ) with Phclan. Certainly Hayck dcfincs cqr.rilibrium this way.'Moreover, Mises soes to somc lcngths to distirrguish betwecn thc notions of what he calls the plain state of rest (markct clcaring), the final statc of rest (that which the markct always tcnds toward, but never reaches), and thc cvcnly rotating econom\' (Miscs's label lor qeneral equilibrium). Thc very fact that the economy is "rotating" (i.c., all market transactions arc constantly repeated) irnplies not a state of rcst, br-rt a "ccasclcss flux" of coordir-rated cxpectations and markct activity. As Phclan emphasizes twicc in his paper, such a construct is a timclcss world.' The conccpt of general equilibrium (GE), Phelan cxplains, assumes given prcfcrcnces, known production functions, rnd an initial set of cndowments. Morcovcr, agents rre trcatcd as pricc takers-their individual actions cannot influence markct priccs. He assures Lls that this basic n'rodel can bc "cxtendcd" to allow for "tirnc" if we so dcsirc. Just as two different goods are considcred spatially uniquc with uniquc prices (an apple in this bin and an orangc in the other), so thcy can be considercd tcmporally uniquc (an apple today and one tomorrow), with unique prices. Her-rcc, "timc" can bc formally incorporated into the rnodel by trcating it as a variable in thc samc way wc trcat spacc. 220 stllc most preferred feasibly attainable path over all goodsd condition, Phelan continues, requires a set of,fua contracts specifying at the beginning the delivery of.3lr given date, which holds for all goods and all tinr. d beginning. Though this is "obviously a huge ebmecb points out that at least the model builder finds it "'$fu: can now talk about "time" without having to chengs fr librium model. Because we are now dealing with the fucure, drc mnd way to introduce expectations and uncertainty si&d ratus he has erected. One alternative is to simply utidd tainty in the world" and treat expectations as &e ouE (that is, as if the agents themselves were convid dd mentally adopted the model the economist uses to cql such a bizarre world, the individuals will be able pcrGd and attain a rational expectations equiJibrium. Morw be the same as that which occurs at the temporal beg-though this may seem outrageous," Phelan assurc G. toward explaining phenomena such as infletion orr itt Finally, if the theorist feels compelled to deal wifir by simply specifying a series ofArrow-Habn-Debrcuo the beginning which hang probabilistic weights o d Phelan once again explains that this leads to the semo equilibrium models. Now I don't know how all this amounts t() an 2rr5*rl standings or objections. In particular, I think Phdalc stract model building adds little to what Friedmm rtainly remains quite naive and outdated, especiallyifc current debates in the epistemology and the philqqo*t than continue my objection on methodologicel gro{r*, arguments dealing with a matter that Mr- Phelanmryd internal consistency ofthe Chicago schooli gener:l e Standard Chicago price theory has traditiondly bo, ful than GE theory. This is so because it relies @, etti partial equilibrium concepts (that is, it srudies isoldir single firm or industry rather than the entire syv,em { e Melvin Reder has pointed out,a Chicago-school moddl he calls the "Tight Prior Equilibrium": a state of aE makers so allocate the resources under their control tll allocation such that any one decision maker could heltl creased without a reduction occurring in the erpool other decision maker." In other words, indiridu:b acr reto-optimal manner. In addition, the prices at wLitl Lctters 22 r Equilibrium is then considered that condition in rvhich cach agcnt chooses his most prefi:rrcd fcasibly attainablc path over all goods and tinres. To justify this corrdition. Phelan corrtirru(.s. requirc5 a sct of futurcs colltracts- a scric: of contracts specitying at the beginning the delivery ola givcn good or input at a givcn date, which holds for all goods and all timc, and is enforccd from the bcginning. Though this is "obviously a huge absrracrion from reality," Phclan points out that at lcast the model builder finds it "quitc attractivc" becausc he can now talk about "timc" without having to change fundamcntally his cqui- librium model. Because we arc now dealing with the futurc, the modcl builder rnust find a way to introduce expcctations and unccrtainty without forsaking the apparatus he has crected. Onc alternative is to simply avoid the "undcrlying uncertai'rty in the world" and trcat expectations as thc outcomc of the rnodcl itself (that is, as ilthe agents themselvcs were convinccd of the RE hypothesis and mcntally adopted the nodcl thc economist uscs to explain their bchavior). In such a bizarrc world, thc individuals will bc able pcrlictly to predict the futr.rre and attain a rational cxpectations cquilibriunr. Moreover, this equilibrirrm will be thc same as that which occurs ar the temporal bcginning of thc model. ,,Although this nray sccnl outrageous," Phelan assures us, it goes "a lons lvay toward cxplaining phenomena such as inflation or interest ratcs." Fi,ally, if the thcorist fccls compciled to dcal with u,ccrtai,ty, he can do so by si.,ply specifying a scrics of Arrow-Hahn-l)ebrcu conrirtacrcy corltr.rcts at the beginni,g which hang probabilistic weights o.r all furure possibilitres. Phelan orrce again explains that this leads to the samc olrtcorlc as thc formcr equilibrium modcls. Now I do,'t know how all this amounts to an answcr to Austria,,risundcrsta,dings or objections. I, particular, I thi'k Phelan's cxplicit dcfense of abstract nrodcl building adds littlc to what Friedman said in the r95os; it certainly rcmains quite naive and outdatcd, espe cially if onc takes into account thc currcnt dcbates in the epistcmology and the philosophy ofscie,cc. But rather than continue my objectio, o, methoclological grou,ds, let mc advance somc ar[Jumcnts dcaling with a nratter that Mr. Phelan may take rnore seriously: the internal consistcncy of thc Chicago school's gcncral use of equilibrium. Sta,dard chicago price thcory has traditio.rally bee. considered more uscful than GE thcory. This is so bccause it rclies or rcteris paribus analysis a,d partial equilibrium concepts (that is, it studics isolated phcnomcna such as a single frrm ,r industry rather than the entirc systcnr all at o,cc). Morcovcr, as Mclvi' Rcdcr has poi'ted out,r Chicago-school ,rodel buildcrs enrploy what he calls the "Tight Prior Equilibrium": a sratc of aftairs rvhcrcby "decisio, makcrs so allocate thc resourccs under thcir control that therc is no alternativc allocation such that any onc clecision maker could havc his expcctcd utility increascd without a reduction occurring in thc expcctcd utility of at lcast or-rc other dccisior-r nrakcr." I, other words, i,dividuals arc assunte.d to act i, a parcto-optimal nlanncr. Irr addition, thc priccs at which indivicluals currently 222 Critical Reuicw' Spriry/Sunmrer t9E8 transact are considerccl market-clcaring priccs atrd arc trcated as "goocl approximations to thcir long-run compctitivc cquilibrium values." Thcy thcrelore nrcasure the truc opportulity costs ofaltcrnativc resourcc allocation. Reder points out that the Tight Prior Equilibrium allows the theorist to lirrk inclividual optinlization dccisions with ccononty-widc wcllare conclusions. This l-rolds bccause thc individual nrarket price is thought to rcflect thc lull opporturliry cost of thc good's alternative uscs. But lct's take this one step further. If the pricc of a good in an isolatcd markct (i) clears the markct; (ii) is consistcnt with optimization by every individual decision maker; (iii) rcflccts the full opportunity cost of alternative uscs; and (iv) is assumed to hold in tl-re long rur-r, thcn the plals of thc agcnts wili be fully coordinatcd: the systcm u'ill bc in equilibriunr. As such, all markct activity, accorcling to this view, rs deemcd e{Iicicnt-indeed, Pareto optimal. Here, as (ieorge Stigler has had occasion to remind us, wc havc the bcst of all worlds. It is not clough, howcvcr, to view markets iu isolation fron each other. Usc of partial cquilibrium supplemcnted by Tight Prior assumPtions allows thc Chicago tl-reorist to talk about thc overall pcrformance of the economic systcm. But Tight Prior analysis is consistcnt or,/y wherl all the othcr industries, hcld constant by rcttris pdriltus, arc in cquilibrium.'Therr, by Walras's law, the isolatcd industry ul1der examillation is also in equilibrium, and, in lact, pricc nlust cqurl opportttrrity cost. What we havc herc, ILichard Fink argues, is rcally scctoral GE theory. As "Microecononrics concentratcs Jack Hirshlcifer says in his standard textbook: mainly upon cquilibriurn states <.lf particular rnarkets, presun'ring arr eqttilibriunr of the rnarkct systcm as a whole-"" On thc other harrd, if all thc other industries arc not actlrally in cquilibrium, the bridge betwcel thc partial and thc gcneral collapses. And to assunlc otherwise leads one to engagc in inconsistent (JE analysis. In fact, as long as rr:alworld industrics are composcd of finns and cngage in ntonetary cxchange and monettry calculation, thcy are trcccssarily in a statc of discquilibrium: for ip a statc of affairs charactcrized by the con'rplete and optimal coordination of the mcntal and stratcllic cconomic activities of all individuals, rnoney:rs a scneral medilrnt of cxchangc and tool of ccononic calculatiotr becomes con-rplctely Llseless. A gencral mcclittnr of cxchangc and urlit of ccononric calculation ceascs to exist in general ccluilibrium.' To continuc to trcat a merkct pricc as reflccting opportunity costs (in order to ntakc welfarc assessmcnts) uudcr thcsc conclitions mcalls to cr-rgage'i1 i1consistent ()E analysis. In this casc, its policy cottclusions caunot bc supported by thcory, bccause thc thcory itselfis iuconsistcnt. why is this so? It secms that thc chicago yiew colluscs lrarkct clcarinq with rnarket cquilibriunr. Markct clearipg occurs wheu the quantitv of a good supplied cquals thc cluarltity demanded. Market clcaring, then, is a rcccssary but not sulhcicnt cot'rdition lor nrarket cquilibrium, bccause a currelltly cleared market docs not ncccssarily inrply that tl-rc luturc actiolls of thc buycrs a1d sellcrs in cvery markct :rro rlso ini.: .:.: : :, thJtCUrr(.nt,tippIicsilllJJ(,Ill,I]].].:,,., ccrnirrg tolltorrow nrly Jiti..r ,lr.r.:. . 'Thus. w hilc thcrc is r srror)- qlr.;::. . clc.rr, it w.ruld bc rrri:takt.rr ru ., .: ::.:. . - Now the Tight Prior Equilibriunr r: . -r: r .: :r: -- ' - : ory as it is part of Cl-ricaeo pricc rh;.:'. ,:. ,-:.:.: . with the GE framework. But how can rhe RE modd est rates in a world characterized by intertempa-el only does the model fail to account for moner- (:nd I believe inflation is primarily a monetary phenorrErn say about interest rates. Because thc GE franrcu.ork nroJ.l. -. j. l ' tttodt'ls good. irr spJcc (J [,..,rur. Ph-]..r. ,,, structecl as the "ou.,n rates of returr't i.:,,-.. :. i -" Bccausc the Arrow-Hahn-I)cbrcr.r tll:r:. ... :,. -: : ratc as a discount rate uscd to cl(jterllltni ::i ::--- : nt.rd,'l ultirrrrtely lrck: .r capir.rl rlru. :. through spacc, so, irr qencr:rl r-qurlrbr:i.::. i' : rnove, in principle, forward ancl b.rck..,.:: j _:. :.:. -, l{ather than capital thcory, GE rh.or-. .: : - , _ - merely "a theory of location clo.rkc-d Lrni.: : -r..:. -,positivc intcrcst ratcs and ncqativc inr.:..: : ::-: -,l ditTc'rent points ill "timc." Hos c.rn :.r-': r .r. i discuss thc cveryday rvorld? I do rrot cxpcct Phclarl to rcspolr.l L.r' ::-.::'- - - framework-hc has done such a qoo.l-t.,: . . r - _ ' - . ... into thc llttcr. My point is to sho\\ tir.: ::._ . : : major problerns of (lE analvsis. lJr-rr :i :: -i, - ,. : . world, or is used inconsistcntll.. c.rn ir r-:'. -:: .. ,.. tive valuc? Maybe so. On the othcr hand, if onc m:rint.rirr. rl:l: '.. - .-- a fully coordinatcd norld (bur erogtn,,.:. .. , ..--: final equilibriunt)-an cnrpirical clainr i:-.::. ., -tions and inrplications of thc rnoclel in:i:.:: , r - RE analysis models tl'rc rvorlcl .ls \rnr . : withotrt truc Llncertainty and cr;rit.rl soo:. .,. -:- -: :. likc firms, n)oncy, or nlollc.tarv c:ilcul.rr:,:r - ::--: world; r-rclr are wc nroving tor,vard ii rrr .l-.-. -:.-:. _ Letters 223 sellers in evcry market are also intertemporally coordinatcd. It simply mcans that current supplics and dcmands mcsh in a singlc markct. Expectations conccrning tomorrow rnay differ clrastically from today. Thus, whilc thcrc is a strong cmpirical tcndcncy for unhanrpercd nrarkcts to clear, it would be rnistaken to conclude that n'rarkets tend to be cquilibratcd. Now thc Tight Prior Equilibriunr is just as much a part of Chicago I{E theory as it is part of Cl.ricago pricc tl.rcory. In adclition, Phelan rightly links RE with the GE franrer,vork. But how can the RE model explain inflation or intcrcst ratcs in a world charactcrizcd by intertenrporal general equilibrium? Not only docs thc nroclcl fail to account for money (and thcrcforc inflation-if you bclieve inflation is primarily a monetary phcnomcnon); it has nothing much to say about intcrest ratcs- Bccausc thc GE frarncr,,.ork nrodcls goods in "time" in thc same way as it models goods in spacc (a fcaturc Phclan applauds), interest rates must be constructcd as the "own rates of return" for each and every good in thc system. Bccausc thc Arrow-Hahn-L)ebreu tranrcwork cannot account for the interest ratc as a discount rate usccl to cleternrine the present value ofcapital goods, the model ultimatcly lacks a capital thcory.n Just as onc l'noves back and forth through space, so, in general equilibriunr (RE or otherwise), individuals can nrovc, in principlc, lorwarcl ancl backr.vard in time. Rather than capital thcory, GE thcory providcs, according to Tylcr Cowcn, mcrcly "a thcory of location cloakccl undcr a differcnt namc." In such a system positive interest rates and ncgativc intcrcst rrtcs crn e'xist for the samc good at diffcrcnt points in "time." Horv can such a rnodcl bc uscd mcaningfully to discuss thc evcryday u'orld? I do not expect Phelan to responcl by trying to diflcrcntiatc RE from the GE has done such a qood job showing how r-rcatly thc fornrcr fits into thc latter. My point is to show that the RE rnodel suffers from all the major problems of GE analysis. Ilut if indecd it docs not dcscribe thc rcal worlcl, or is uscd inconsistcntly, c:rn it nevcrtheless be salvaged by its predictive value? Maybe so. On thc othcr hand, if onc maintains that wc arc alrvays nroving toward such :r fully coordinated rvorld (but cxogenous shocks kccp us lrom attaining thc final cquilibriurn)-an cn'rpirical claim-thcn lvc havc to evaluate the assumptions and in-rplications of thc nrodel in thcir own right. RE analysis rnodels the worlcl as onc of fully coordinated cxpectations, withorrt truc unccrtainty ancl capital goods, without basic market institutions like firms, nloney, or nlonctarv calculation. I contcnd wc do not live in that world; nor are we nroving toward it in any degrcc inraginablc. framcwork-hc Dayid L. Prychitko D ep artment oJ Econ omi c s Ccorge Mason Utiuersity Fairfax, Virginia USA 224 Critical Reuiew' Spting/Summer t988 cHliISTopHER rttrraN NOTES I. See J. 4. Kurt Schuler, "Father Time's Revenge on Economics," cnrllcat nr- 8. _, Mr. Prr.chitkr. ., :-:::. .-. - .r vIEw r, no. r (Winter 1986-7), and David L. Prychitko, "Ludwig Lach- is in mann and the Farther Reaches of Austrian Economics," CRITICAL REVIEW I, no. 3 (Summer 1987). I should mention at the outset that there is no ..Austrian" position on the equilibrium issue. In addition homogeneous to the above, see Roger Garrison's "The Kaleidic World of Ludwig Lachmann," cRITICAL REvIEw r, no. 3 (Summer 1987), and Pete Boettke, Steve Horwitz, and David L. Prychitko, "Beyond Equilibrium Economics: Reflections on rhe uniqueness of the Austrian Tradition," Market Process 4, no. z (Fall 1986). See, for example, F. A. Hayek, "Economics and Knowledge," in his Iadiuidualism and Economic Order (Chictgo: University of Chicago Press, libriurn advocates mean bv cqr-ur:l::-.:: -. Austrians cnough credit, that rhci :- :. :. : 1948),33-56. Ludwig von Mises, Human Action (Chicago: Contemporary Books, ry66),244-5o. Mises relegates the use of the equilibrium construct to that of a "thought experiment": the fictitious world of equilibrium is contrasted with our dynamic, uncertain everyday world in order to elicit a better understanding of the everyday world. "In order to grasp the function ofentrepreneurship and the meaning ofprofit and loss," for example, "we construct a system from which they are entirely absent' This image is mereiy a tool for our thinking- It is not the description of a possible and realizable state of affairs" (248)' Rothbard, however, seems to confuse the Misesian notion of the final state of rest with the evenly rotating economy, in that he believes the market is always tending toward (but never reaches) the latter (see Murray N. Rothbard, Man, Economy, and Stare [Los Angeles: Nash Publishing, r97o], 44tn29, 274-76)Melvin Reder, "Chicago Economics: Permanence and Change," Journal oJEconomic Literature zo (March r98z): r-38. See Richard H. Fink, "General and Partial Equilibrium Theory in Bork's Antitrust Analysis," Contemporary Policy Issues 3 (Winter 1984-85): rzzo. These ideas are elaborated in his "Resale Price Maintenance: A Market Process Approach" (Ph.D. dissertation, New York University, t988). ed. (Englewood Cliffs, Jack Hirshleifer, Price Theory and Applications, znd See N.J.: Prentice Hall, r98o), r9. 7. Once again, sincc rt7r11, F. H. Hahn: "The Walrasian economy that we have been considering, although one where the auctioneer regulates the terms at which goods shall exchange, is essentially one of barter-" As cited in Paul Davidson, Money and the Real Wotld (London: Macmillan, 1978), r4r' See Tyler Cowen, "The Rate of Return in General Equilibrium: A Critique," Journal oJ Post-Keynesian Economics 4, no. 4: 6o8- t7 - Cf., e.g., cquilibrium, I must enrp[.1'17. ::],. -_ not say whcther this is truc becau., ::- , r " . :,,. libriurrris.Thcrnisutlderstatrc]irlsI'..,:::l:-'group has a "better" understandin: , : ::. : _: wh:rr a gcilcrll cquilibrirrrrr rlt(, r:,: . .. ... librium," and hon,unfoundccl crrriri.::. -.: -. Thc point is that to a GE thc.on.i. .. : l.l librium is not a real-rvorld phcnonr..r:, r. .--..,: : anothcr. or lor a wholr ccorr,,:rrr 1, -. livcs arrd brc.rthes or:l1 in his rrro.l.l. I: .. cls. That is, whcrc a givcn nrodrl c:r: :_.'. - : , comes, equilibriunr outcomcs arc rh. :.:: for the imaginary inhabitants oithc n. -:. .-. :,--.r .- .. . : _ ... .: l only outcontes that rnake scr:.. Prychitko lrBuc. thrt :rr)c( .,'rr:- :.. -. money which are r]ot prcsent in rh.,:_... :. ntudclt. thlt rltcsc trr.rrkt rs rp1.r hc ::. thcy arc in cqrrilibrium nrakcs t-or rr:::-, r_:.::- :-no idca wl-rethcr actual rnarkcts :lr. :i'. -i::: :.-: this cvcrr nt('ans. hut sinrplv hq..rLt.. ,. : characteristic ofthc real rvorld cioe. i:!.: :t_.r : .: are the . ing in a vacuunr clon't predict rhc ttll ,,i = t:,. -: into how thc world r,vorks. To be fair, howcvc'r, I rvill qr:c-': ri..: , : nrodels do much morc than lcave otrr ..:: :i- -: l most of thc charactcristics of thc r.-.r1 -,'.,:._ : ,- " -. C)n sonrc querstions, such :rs tht- rolc t,: ::::. _to agrcc, while on othcrs I u.or,rld .lis.r_:.. :. rcgardirrg r,i lrar is irrtt.rr.srir:q. Nevertheless, we should consider our alternrur money or innovation or another field r*'here Pn-cti ing, we can either try to create models, GE or notdeficiency and increase our understanding ofrbr Ft and talk in fuzzy enough terms thar w-e hide the I anywhere. Economics is hard, and I for one crnffi using imprecise language. (An econornics pafter x may be judged inapplicable, but it is ar leasr clear sl the Austrians think they can make progress u,i6o then I wish them all the luck in the *'orld- tbr I