Universiä der Bundeswehr Münhen Insiu für Volkswirshafslehre Friedrih L. Sell Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs 4. Jg. 22, Nr.
Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs Friedrih L. Sell # Universiä der Bundeswehr Münhen # Insiu für Volkswirshafslehre, insb. Makroökonomik und Wirshafspoliik, Werner-Heisenberg-Weg 39, 85577 Neubiberg, e-mail: friedrih.sell@unibw-muenhen.de.
Conen INTRODUCTION 2 2 CLEARING KEY NOTIONS: CONFIDENCE VERSUS SUSICION; SCETICISM/ESSIMISM VERSUS OTIMISM 4 3 THE MODEL 9 4 A SIMULATION EXERCISE 2 5 EMIRICAL EVIDENCE? 25 6 SOME CONCLUSIONS AND THE SCOE FOR FUTURE RESEARCH 26 REFERENCES 27
Absra Indiaors of "rus", "onfidene", "opimism" or "senimen" among onsumers and/or invesors, are published oninuousl in he mass media. More imporanl, hese indies seem no onl o refle how he sae of he real eonom is pereived b privae agens, bu an also help predi he fuure ourse of he business le. Moreover, in eonomeri analses he have even been found o "ause" business aivi. In his paper, we firs make an aemp o lear all of he above menioned noions and o inerpre heir eonomi onen. We hus inend o provide a heoreial foundaion for how "pessimism" and "opimism", in onjunion wih esimaion errors ommied b privae agens, an drive he real eonom. Furhermore, he model presened is apable of inorporaing he revision of expeaions of privae agens hrough Baesian updaing, o reae a full endogenized business le. The resuls ahieved in simulaion experimens onfirm he possibili of onsan, rising and delining osillaions in he growh rae of onsumpion and inome. Ke words: Business Cles, Raional Beliefs, Baesian Updaing, Consumer Behaviour. Die wirshaflihe Fahpresse und die Massenmedien berihen koninuierlih über die Enwiklung von Indikaoren, welhe Auskunf geben sollen über das "Verrauen", die "Zuversih", den "Opimismus" oder shlih die "Gefühlslage" bei Konsumenen und/oder Invesoren. Dieses Indikaoren sheinen nih nur die Ansih der privaen Akeure über den Zusand der Ökonomie widerzuspiegeln, sondern können auh dazu verwende werden, den Verlauf des Konjunkurzklus zu prognosizieren. Ökonomerishe Analsen haben gezeig, daß sie in der Lage sind, den Verlauf der wirshaflihen Enwiklung zu "verursahen". In diesem Beirag sollen zunäs eine Reihe der o. a. Begriffe geklär und ihr ökonomisher Gehal inerpreier werden. Anshließend unernehmen wir den Versuh, den Gang der wirshaflihen Enwiklung im Zklus durh das Zusammenspiel von "Opimismus" bzw. "essimismus" einerseis und das Aufreen besimmer Erwarungsfehler andererseis zu erklären. Das Modell bedien sih eines Baesianishen Lernprozesses und kreier einen völlig endogenen Konjunkurzklus. Numerishe Simulaionen zeigen, daß durh das Modell konsane, zunehmende sowie abnehmende Oszillaionen des Konsum- und des Einkommenswahsums erzeug werden können. Shlagwore: Konjunkurzklus, Raionale Überzeugung, Baesianishes Lernen, Konsumverhalen. JEL-Klassifikaion: E32, E37, E2, E27
2 Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs "Then I saw her fae Now I' m a believer No a rae of doub in m mind I' m in love I' m a believer I ouldn' leave her if I ried" Neil Diamond, 966 INTRODUCTION i I is fair o sa ha heories of he business le are no reall booming in our profession. On he oher hand, he business sie and he large publi group ineresed in "ommerial affairs", are greal onerned wih ime series whih repor on he "business limae" as he IFO index, "onsumers' senimen" index of onsumer senimen, ICS, olleed and ompiled b he Universi of Mihigan Surve Researh Cener, "onsumers onfidene" he index of he US Conferene Board and of he EU ommission or likewise, "invesors onfidene" Mussler 2, p. 7. All of hese indies inend o grasp he opinions of onsumers and invesors on he sae of he eonom and heir expeaions owards he fuure, during a business le. The noions being used here are mosl loaed in he semanis of psholog and of subjeive judgemens raher han in a world of "raional expeaions", whih anno be fooled b poliiians ssemaiall. ii The same publi does no ake muh ineres in he highl sophisiaed heoreial and empirial onribuions b professional and aademi eonomiss. This sae of he ar seems o be quie unsaisfaor. The disipline of explaining he business le is dominaed oda b and large, b approahes whih have heir foundaions in he new lassial maroeonomis NCM. Wh do no we have a brief look a he NCM and heir aemp o onribue o he heor of he business le? Ineresingl, he earl papers of he NCM are in need of so-alled "propagaion iii mehanisms" o reae a business le. This is due o he fa ha he Luas suppl funion onl allows he explanaion of real oupu effes wheher posiive or negaive, in he onsequene of unexpeed monear shoks whih, b definiion, are sohasi and anno be aniipaed ssemaiall. The indued "real movemens are of no longer duraion han he duraion of he shok" Luas 994, p. 8. If he naural oupu is assoiaed wih a normal usage of apaiies, onl a downswing or an upswing from here an be explained wihou reurring o "propagaion elemens". To explain he business le however, he main hallenge is o be able o sa wh and when we have he urning poins.
Inroduion 3 Two main "propagaion elemens" are found in he business le models of he NCM: "one mehanism sems from he presene of oss of firms of adjusing heir soks of apial and labour rapidl. The presene of hese oss is known o make i opimal for firms o spread ou over ime heir response o he relaive prie signals he reeive. Tha is, suh a mehanism auses a firm o onver he seriall un-orrelaed foreass errors in prediing relaive pries ino seriall orrelaed movemens in faor demands and oupu. A seond propagaion mehanism is alread presen in he mos lassial of eonomi growh models. Households' opimal aumulaion plans for laims on phsial apial and oher asses onver seriall un-orrelaed impulses ino seriall orrelaed demands for he aumulaion of real asses" Luas/Sargen 988, p. 33. In laer papers, persisene of effes is due o "informaion lags" and/or "aeleraor effes" Luas 994, p. 8. As iljoo 992, p. 4 pus i, i is quesionable wheher, in he Luas model "suppliers raher han demanders mispereive mone shoks for relaive prie shoks". Generall spoken, he NCM model b and large negles he informaion sruure on he side of demanders and more preisel, on he side of onsumers. I is sriking o see ha NCM as far as i was mean o onribue o he heor of business les hough based on "expeaions", has been unable o apure he effes of "surprise" and "disappoinmen" beond he framework of he Luas suppl funion. The sri inerpreaion of he raional expeaion hpohesis REH has also prevened auhors of NCM o idenif he relevane and signifiane of "opimism" and "pessimism" as priors, or raional srong beliefs of eonomi agens. There is perhaps one exempion: Burdekin and Langdana 995, pp. 48-69 make a srong, bu in m view, fruiless effor o inrodue opimism whih, b he wa, he all "onfidene", an error in semanis as shown below, ino a REH model. Insead of apuring opimism as a srong belief or prior see below, he preend ha "onfidene inludes idiosnrai respondenspeifi informaion, ha is, an idiosnrai shok, he auhor in he urren ime period in addiion o he mahemaial foreass.... Thus,... we see 'onfidene' as apuring addiional informaion no e readil available in onemporaneous daa" ibid., p. 47. Obviousl, we find here a severe onfusion beween he belief iself and he wa believers learn from new informaion. One ma argue ha NCM wen beond he earl onribuions of he laer Nobel prize winner, Rober E. Luas Jr Furhermore, i ould be saed ha models of "real business les" as in he seminal paper of Long and losser 983 are of he NCM pe, as he work wih raional expeaions. This argumen is somehow misleading; in hese models "business les arise from ehnolog shoks and ineremporal labor, leisure, and onsumpion subsiuions in response o hese surprises" Kades 985, p. 22. Tehnolog shoks, as a soure for business les, follow he radiion of Knu Wiksell's lassial onribuion, iv alhough being surprising simple beause no-
4 Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs bod an expe hem. This makes a srong differene o he aiude of agens in he "old" NCM models, where agens are involved in a game agains he monear auhori. An auhori whih, b he wa, makes announemens on whih i an hea. Tehnolog shoks anno raise expeaions and are, almos b definiion, unexpeed. Here, I am afraid, NCM is less aurae han in man oher pars of is heor! There is no muh omfor o be gained from oher srands of business le heor eiher. While a number of papers "sueeded" in inroduing he REH ino models of he business le roued in Kenesian maroeonomis as for example Dornbush's and Fisher's modifiaion 994 of he poliial business le model of Nordhaus 975 "in fa, no exising Kenesian maroeonomi model inorporaes... an eonomi model of learning" Luas and Sargen 988, p. 36. One should no exend his affirmaion auiousl o he whole lass of models whih do no sril follow he NCM. I will be he aim of his paper o do he job in his field. We will aemp o reonsider on he one hand, he fores whih drove he business le in Samuelson's seminal paper of 939 onsumers' and invesors' demand, aking ino aoun on he oher hand, he role also of expeaions and of learning in a framework differen from and ompeing wih he REH. The paper is organised as follows: The nex seion haper 2 is devoed o lear he noions of onfidene/suspiion on he one hand and of pessimism and opimism on he oher. We show how opimism/pessimism have been inegraed ino he heor of finane and of ompeiion on goods' markes e. I is also disussed wheher opimism pessimism an be idenified wih risk love aversion and wheher i is due o informaional defiienies and/or asmmeries. Chaper 3 hen presens our own model of he business le, wih privae onsumpion as he main driving fore of eonomi aivi. We ome up wih a differene equaion of seond order for onsumpion and inome growh raes insead of inome levels in he radiion of Samuelson's seminal paper 939, whih is ompliaed b he fa ha agens hold differen aiudes during alernaive phases of he le, bu are also willing o revise heir expeaions b appling Baesian learning/updaing. Chaper 4 presens some simulaion experimens. Chaper 5 quesions he empirial evidene of our houghs. The final haper 6 addresses onlusions and opens quesions for fuure researh. 2 CLEARING KEY NOTIONS: CONFIDENCE VERSUS SUSICION; SCETICISM/ESSIMISM VERSUS OTIMISM In he framework of game heor "rus" or "onfidene" an be modelled and/or inerpreed as a pariular subjeive probabili assigned b he prinipal in he even ha he agen implemens he required level of inpu, are e., whih is he aion desired b he prinipal Demougin 999,
2 Clearing Ke Noions: Confidene versus Suspiion; Sepiism/essimism versus Opimism 5 p. 35. Boh plaers find hemselves in an agen relaionship haraerised b "moral hazard and adverse seleion" ibid., p. 33 and an be aken o be risk-neural see below a brief disussion on he aiude owards risk among opimiss and pessimiss. I is pial for suh a game o find a rade-off for he heaing sraeg of he agen; on he one hand he dire shor-erm gain of heaing ma exeed he ren of implemening he required inpu bu, on he oher hand a he longerm risk ha he game ends. Hene ex-ane, i is no lear wheher he expeed presen value of heaing dominaes vis-à-vis implemening. In our onex, we are more ineresed in game siuaions where he plaers are exluding exepions no in an agen relaionship, bu onfroned wih he lassial prisoners dilemma in a Kdland/reso/Barro/Gordon world. Wha sor of meaning an rus or onfidene have here? Obviousl, onfidene has o be linked o he issue of expeaions. Aording o he view pu forward b Maaß and Sell 998, p. 52, onfidene or likewise onfiden expeaions, an persis even if a enral bank dares o hea he publi as long as heaing is regarded onl as a ransior phenomenon and i implies "he belief b privae agens ha an aual monear arge deviaion b he enral bank will be 'healed' b a ompensaing poli in he near fuure so ha he medium o long-erm ahievemens in he field of prie sabili is pu in danger" ibid.. Ye, onfidene or rus is no he opposie o sepiism/pessimism he firs being some sor of weaker pessimism as some papers end o argue impliil, bu suspiiousl. Aordingl, sepiism or pessimism mahes opimism Allen/Faulhaber 988, p. 398. As our paper is no onerned wih onfidene/rus versus suspiion/disrus in he firs plae, we shall onenrae he following on he noions of opimism and pessimism. When doing so, we are aware of he fa ha a number of papers menion "pessimism" or "opimism" in heir ile see for example Drazen 988 or Tallon 2, bu reading hose papers, i soon beomes apparen ha he are no reall ineresed in eiher of heses erms. If one would sill be ineresed o relae he noion of onfidene o he aiude of opimism, he answer is sraighforward: Conrar o he observaion of onfidene, where a leas one individual has o be onfiden in someone else, opimism pessimism in omparison, has o do wih he lak of self-onfidene. Moreover, in he definiion of Heifez and Spiegel 2, pp. and 2, "opimiss overesimae he posiive impa of heir own aions, pessimiss underesimae i, and onl realiss assess i orrel". An ineresing resul from game heor is ha "an opimis who overesimaes he reurn o his aions, behaves more "aggressivel" han a realis and hooses a higher level of aion". Furhermore, when he aions "of one individual impose a posiive exernali on he paoff of rivals, he aggressive behaviour of he opimis riggers a favourable aggressive be-
6 Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs haviour from rivals" ibid.. This mehanism obviousl no onl has a srong link o he phenomenon of he business le, bu i also fis niel ino he explanaion paerns of he new growh heor. Enrepreneurs, who are unrealisiall opimisi abou he produivi of heir own firms, mus no neessaril be fored ou of business. As Manove 995, p. 5 explains, opimism regarding produivi of inpu faors "reaes an inenive for agens o inrease heir savings raes and work effor whih an lead o a larger sead-sae inome". The mehanism involved works like an inverse Luas riique effe, where new fas rigger new expeaions and hene, an adjused behaviour of agens. Opposed o his, in he Manove model speifi expeaions rigger new beha v- iour, hus new eonomi fas. A negaive side effe of he Manove pe of opimism is ha enrepreneurs hire oo man exernal resoures negaive effiien effe, whih in onsequene, will be overuilised ibid., p. 8. The same applies o heir inernal resoures effor, savings, bu his an be undersood as a posiive inenive effe. A number of auhors idenif he aiude of opimism wih he observaion "ha mos people are overonfiden abou heir own relaive abiliies, and unreasonabl opimisi abou heir fuures" Camerer/Lovallo 999, p. 36. v As a resul, eonomi agens end o exeue eonomi deisions like business and/or marke enr whih, wihou misjudging one's own relaive skills, migh no have ourred. I seems as if opimism omes in here as sor of illusion and/or missing realism, as he subjes onerned "seem o negle he fa ha he are ompeing wih a referene group of subjes who all hink he are skilled oo" ibid., p. 37. Max Weber, b he wa, has apparenl been a srong opponen o an "naive" opimism among philosophers; as Hennis 2, p. 7 repors, he blamed some of his olleagues for heir aemp o find he road o happiness and jusie in siene. "Who would believe in ha", he is quoed, "onl grea hildren on heir reading desk or in press rooms" ibid.. Saisiall spoken, a majori of agens preend o be above he average in skills, alhough, if he rai is smmeriall disribued, onl half of hem an be. Opimiss are blamed for no hinking ha "everbod else is hinking he same wa" ibid., p. 35. We will demonsrae below ha his inerpreaion of opimism/pessimism gives a raher narrow view of he relevan issue, if a all. Beause, if he mehanism ied would no exis, one ould hardl explain onsumers opimism in a maroeonomi framework. Anoher possibili o differeniae beween onfidene and opimism is pu forward b Ripperger 998: As in he ase of hopes, opimism is relaed o exogenous risks wih he imporan impliaion ha in priniple no onra an be made wih he agen who possibl riggers he unerain
2 Clearing Ke Noions: Confidene versus Suspiion; Sepiism/essimism versus Opimism 7 evens. As opposed o his, onfidene is relaed o endogenous risks, ha is in siuaions where he risk aken b some agen is dependen of he behaviour of anoher agen. In priniple, a onra an be signed beween hese wo agens ibid., p. 38. Suh a onra see above ma bu mus no be one beween an agen and a prinipal. Also eonomeriians end o idenif opimism pessimism wih overesimaion underesimaion; as Rasmusen 998 explains, "if poliies are used more where he are more effeive a he margin, hen boh asual empiriism and ordinar leas squares esimaes are biased owards opimism abou he poliies" ibid., p. 65. The anals ma fail in his prediions if he does no ake ino aoun ha imes and plaes for a poli are no idenial. The hoel ax revenue ase serves as a good example: "A sae's hoel ax is eiher high or low, rading off revenue agains harm o ourism. In 25 saes, he high hoel ax would rise $ in revenue per apia more han he low ax, and hose saes adop he ax. In he oher 25 saes, he higher ax would so disourage business ha he hange in ax revenue per apia would be $. The anals noies ha he 25 saes wih he high ax have $ higher revenue per apia, a differene ha is saisiall signifian. He herefore advises all saes o impose high axes, even hough, in ruh, he added benefi in he former low ax saes, he auhor is zero. He has overesimaed he benefi of inreasing he poli's inensi" ibid., p. 76. Ye, o be overonfiden in he impa of one's own aions, or o overesimae he effeiveness of a poli adopion, does no over all aspes of opimism. There are opimiss who do no a a all in he sense of an enrepreneur or of an adviser o he poli-maker, bu simpl as onsumers. In heir model, Allen and Faulhaber onsider a wo-periods-deision problem and he define opimism as an iniial belief 988, p. 397 or prior ibid., p. 4, whih is he probabili assigned b onsumers o he quali of a good/quali of he inpus used. If his probabili is hosen as one zero, one an speak of exreme opimism pessimism whih makes learning impossible, as experiene is ignored ibid., p. 4. Bu for reasonable values for ha probabili, onsumers have he possibili o observe he performane of he good in period and hene o learn: "observaions of he oupu lead hem o revise hese beliefs" ibid., p. 397. This informaion will hen affe heir willingness o pa for he good in period 2. Building up he repuaion of a firm means, in his framework, having a good firs period performane. Opimism/pessimism and onsumers have more in ommon. The opimism of single onsumers will be reinfored and hene ranslaed ino a growing onsumer demand on he maroeonomi level one he well-known bandwagon effes Sell 997, pp. 8- ome ino pla. Wha has been used o be framed "herding" in modern analsis of inernaional finanial rises Sell 2, has a orol-
8 Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs lar in he leader-follower relaionship in onsumpion behaviour. Bandwagon effes an work in boh direions and so onribue o undersanding wh onsumers beliefs end o homogenise during boh he upswing and he downswing phase of he business le. Burdekin and Langdana 995, p. 45 onlude ha here is an "enhaning aali effe of onsumer senimen. Therefore, fluuaions in explanaor variables ha are no simulaneousl aompanied b fluuaions in senimen, migh have a disproporionael lower effe on overall eonomi aivi". Cauious opimiss or pessimiss are, as he model explains, able o learn. Then, he should be apable o avoid he onfirmaion bias whih is mean o be "he enden o seek informaion ha onfirms one's own views and overlook evidene ha ma disonfirm hese views" Heifez/Spiegel 2, p. 9. An imporan onlusion emerges here: Opimiss, like pessimiss, are no irraional individuals. Raher he make foreass buil on he same pas se of informaion, assigning differen weighs never he less, o he omponens of his informaion. A ruial quesion, however, is o explain how opimiss/pessimiss learn from presen and fuure reali. More preisel, he quesion has o be raised how he learning proess an be modelled in suh a wa ha he "irraionali" of adapive expeaions an be avoided. One proposal saes ha agens have o orre heir iniial beliefs b adoping he Baesian rule of learning Demougin 999, p. 37. In finane, opimism and pessimism an be found being used as erms used o desribe speifi aiudes on he par of he marke pariipans onerning apial markes. Some auhors relae opimism/pessimism o unerain, ohers o risk. To Wakker 99, p. 459, for example, "a pessimis dislikes unerain, hene he reduion of unerain hrough hedging will lead o addiional appreiaion. An opimis, who expes unerain o urn ou favourable, will no appreiae he reduion of unerain hrough hedging". Opposing his, Anderson 986, p. 83 defines "he more opimisi agen in he sense of higher expeed period prie ondiional on privae informaion", being someone who "invess more in he risk asse han he less opimisi agen". On he oher hand, "an agen being pessimisi abou he period prie will hus find i opimal o inves his whole wealh in he riskless asse raher han in he risk asse" ibid.. Anderson also sresses however, ha "he mos opimisi informaion he mos pessimisi informaion, he auhor is no neessaril he mos reliable from a soial poin of view" ibid., p. 85. In a reen paper, Kle and Wang 997, p. 274 reah an exraordinar resul whih somehow his he REH: In a model of wo risk-neural speulaive raders, he "overonfiden rader ma make a higher expeed profi and uili han his raional opponen... and a higher profi and uili han if he were also raional". Moreover, his ouome is no jus shor-lived and he "survival of overonfidene is due o he fa ha overonfidene as like a ommimen devie o aggressive rading" ibid., a resul whih niel omplemens he posiive exernaliies ied above.
3 The Model 9 Opimism is an issue in he business of making foreass on finanial markes as well; "he anals's deision o issue opimisi earnings foreass is based on a omparison of he oss and benefis of doing so. The benefis are derived primaril from higher brokerage ommissions and beer ma n- agemen relaions; he oss relae o anals repuaion and legal liabili. When he oss of issuing an opimisi foreas are high relaive o he benefis of doing so, opimism will be less apparen or absen" Espahbodi e al. 2, p. 3. The quesion as o wha ma ause hese differen aiudes arises. Is opimism pessimism refleing a risk-loving risk-averse haraer of agens? Or is i ha informaion is imperfe on he one hand and he aess o i asmmerial on he oher? Or is informaion smmerial, bu he valuaion of is onen asmmerial? Basiall, we follow he answer given o heses quesions b Kurz 994; opimism or pessimism are no hinged upon differen levels of informaion and/or upon an asmmeri aess o informaion: "agens ma exhibi drasi differenes in beliefs even when he have he same informaion" ibid., p. 878. Opimism or pessimism do no refle analogousl o he modelling of rus in an agen relaionship see above risk-neurali an be assigned o ever plaer differen risk aiudes, bu he formaion of a "ondiional probabili belief.. abou he fuure sequene of random variables" ibid., p. 879. Though informaion on pas daa is he same for everbod, no all agens "hold he same probabili belief and make he same foreass" ibid., p. 878. I seems indeed, ha valuaion plas a major role: "imporan bu infrequen evens ma be assigned differen, he auhor signifian probabiliies" ibid., p. 893 b differen agens. These probabiliies are grounded in "subjeive rieria whih represen individual heories abou he environmen" ibid., p. 894. The impression one aquires from he enormousl rih hough heerogeneous lieraure dealing wih srong beliefs like opimism or pessimism, is refreshing and enouraging. Can i be ha, based on his pe of "orreable irraionali", we ma ge loser o he lues of business les and eonomi growh? 3 THE MODEL If we wan o profi from he insighs he relevan lieraure has o offer and if we also wan o implemen in a model of he business le an observaion of he da-o-da eonomi behaviour, vi auious opimiss and pessimiss should be presen in he model. We need heir prior aiude o undersand upward and downward fores in he eonom, bu we also need hem o be learning individuals who are eiher surprised he pessimiss or disappoined he opimiss. Oherwise, we ould no explain he ore issue in an heor of he business le: he urning poins! If he slised fa on business les upswings onsiue wo hirds, downswings one hird of one full -
Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs le oninues o work, opimism is a suffiien and neessar ondiion for he long-erm growh perspeives of modern eonomies whih "pure raionali" ould fulfil, a bes, o a less degree. Whih are our assumpions? Firs, like in Zorn and Marin 986, p. 66, "all individuals are assumed o be risk neural whih fouses he analsis on differenes in individuals' beliefs raher han heir aiudes owards risk". Seond: While i is rue ha "in praie, soie is omposed of heerogeneous individuals who ma differ from one anoher in heir degree of opimism/pessimism" Heifez/Spiegel 2, p. 9, during an upswing/downswing of he eonom, he majori of he individuals will share he same aiude. This assumpion omes as a sor of mirror o anoher assumpion made b Zorn and Marin: "he more unerain an ouome he more heerogeneous are beliefs" ibid., p. 67. In oher words: The more all relevan indiaors poin a an eonomi upswing downswing, he more ind i- viduals will "onver" o opimism pessimism. Likewise, one ma sa ha opimism pessimism is endogenized b he business le iself. Third: A German proverb sas: "Opimismus is ansekend" opimism is onagious. This is an essenial of he model whih an addiionall explain wh here is a srong enden o homogenise beliefs during he upswing downswing of he le. I helps o explain reinforing effes, bu of ourse i anno help in explaining he urning poins. Fourh: How are opimisi pessimisi beliefs assoiaed o eah oher? There are onl wo pes of belief, one assigning a high probabili o higher eonomi growh and he oher, a omplemenar probabili - assigning a low probabili o higher eonomi growh. More preisel: If < and [ ] prob < for prob [ > ] and where, - sand for subjeive probabiliies. Fifh: As in Gran/Karni 2, p., we assume ha he deisions makers' beliefs opimism versus pessimism, are represened b hese subjeive probabiliies. Moreover, aording o hese auhors, "he subjeive probabiliies are he unique represenaion of deision-makers' beliefs" ibid., p. 3. In our onex, hose agens whih give values of higher han.5, shall be idenified as opimiss, while hose who give values of less han or equal o.5, respeivel, are idenified as pessimiss. The expeed inome growh given beliefs Zorn/Marin 986, p. 66 hen is: 2 E [ ] e
3 The Model This assumpion has several impliaions: All in all, we have o ake ino aoun wih regard o he same observaion period hree differen growh raes. The firs is he aual growh rae,. The seond is he growh rae assigned o he opimis, and he omplemenar growh rae assigned o he pessimis,. The hird is he expeed growh rae, e ompued as given b equaion 2 wih 3 and > For onveniene, we define: 4 and wih ; > Opimism pessimism hene, has alwas wo omponens: he ourrene of a desired feared growh rae on he one hand and he assigned likelihood o ha iniden on he oher. How is he onsumpion funion formalised? Agens deide on he rae of expendiure growh in period 2, based on pas onsumpion growh and on experienes made in period, in onjunion wih heir own expeaions regarding inome growh [ ] e f ; expeaions, in urn, depend on weighed alulaions vis-à-vis o period : 5 [ ] [ ] [ ] f f e or, enred on period : 6 [ ] [ ] [ ] f f 2 2 e vii Colleing erms gives: 7 [ ] [ ] 2 e f f The firs erm of he onsumpion funion on he righ hand side of 7 brings in he so-alled "habi persisene hpohesis", inrodued firs b Brown in 952 Sell 982, p. 49 and provided wih empirial evidene in man eonomeri sudies see for example Lüdeke e al. 983, pp. 42-5 and, more reenl, Dnan 993. The seond erm on he righ hand side apures posiive
2 Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs surprises viii or negaive disillusions wih regard o inome growh in he immediae pas. In line wih Carroll e al 994, p. 47, we suspe ha "i is no longer lear ha all relevan informaion abou he expeed urren growh rae of onsumpion should be onained in he lagged growh rae of onsumpion". Noie ha he onsumpion funion an neiher be onfounded wih a random walk he seond erm on he righ hand side an never beome/be redued o he error erm u or a funion of i nor is he implied learning proess idenial o adapive expeaions. Also, we do no agree wih hose who make a disinion beween "Rule-of-humb" onsumers on he one hand and "Raional lifele" onsumers Carroll e al. 994, pp. 4/2 on he oher. I is hardl oneivable o reae wo pes of raionali in a Luas-Barro-Sargen-Wallae world a leas, for he vas majori of eonomiss!. As opposed o his, in our framework, opimism and pessimism belong o he same aegor of irraionali. Sixh: If a pessimis an opimis is surprised disappoined, he onomian revision of his expeaions an indue he lower upper urning poin of he business le. If a pessimis opimis is onfirmed b he eonomi realiies, his reinfores he downswing upswing of he business le. This assumpion should be explained furher. The hree relevan growh raes menioned above an be relaed o eah oher in he following four ix inequaliies: i ii e < < e < < iii e > > iv e > > In he firs ase, "bad news is onfirmed", a siuaion where he overwhelming majori of onsumers anno bu refrain from heir demand. The seond ase leads o he lower urning poin, as a "posiive surprise" will make pessimiss rehink heir aiude. Mos likel, if good news is reprodued several imes, he will swih o beome opimiss. The hird ase ours in an opimisi environmen and is assoiaed wih "disillusion and disappoinmen" on he side of he opimiss. Again, if bad news is reprodued, opimiss ma swih o beome pessimiss and he upper urning poin of he business le is reahed. In he las ase, "good news is onfirmed" and bak he judgemen of an opimisi environmen so ha he upswing of he eonom will be fosered.
3 The Model 3 In he following Table we have pu ogeher all four ases; as one an see, he are he resul no onl of differen pes of errors, bu also he onsequene of differen aiudes. Noie ha in priniple, a hird row dediaed o he "neurals" exiss, who, almos b definiion, have raional expeaions. There errors an hene onl be due o unforeseen shoks, as i is mainained in he NCM or in "Monearism II". Wih hese slised ases we are able o haraerise he pial four phases of a full business le. Table : Errors Commied b Opimis, essimiss and Neurals Tpe of Error Overesimaion Underesimaion Agens < e < - < e > e - < e < essimiss "bad news are onfirmed" "posiive surprise" - < < e - > e reession end of reession Opimiss > e > "disillusion and disappoinmen" > > e "good news are onfirmed" > e end of boom > > e boom Neurals - e radiionall: Monearism II radiionall: Monearism II Soure: Own ompilaion. Le us make a heurisi numerial example for eah of he aforemenioned ases and le onsumer demand in he pas grow a he rae of oal inome growh; we sar a.3 ; 2.25 ;.3 ;.6 ;.4 ;.3 ; wih he las ase iv, whih is loaed in an upswing phase of he eonom ha is, is posiive, bu small and agens are opimisi bu no euphori is modes: 8.3 f.3 f [.3 { [.6.25.3 ] [.4.25 ]}] [.32 ] >.28 >. 268
4 Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs Remember ha in his siuaion we find ourselves alread in an opimisi environmen for he onsumers, so ha he opimiss are onfirmed in heir beliefs. Tha is wh he upswing of he eonom is baked, or even reinfored. Wha, if iii he opimiss are disappoined? This resul an be ahieved easil now wih.3 ; 2.25 ;.3 ;.9 ;. ;.8 ;, whenever he boom of he le is almos reahed so ha opimism is "oo srong" and hene is ver high. is posiive and high and agens' 9.3 f.3 f [.3 { [.9.25.8 ] [..25 ]}] [.22 ] <.322 <. 33 For a numerial example of he las wo ases, we have o bear in mind ha he eonom is now in a reession. A he ver boom of he business le, pessimism is deep means is high and expeed growh is exremel low is high. This firs relevan siuaion an be illusraed b he following numbers suppose he variables/parameers are now.25; 2.25;.25 ;.;.9 ;.3 ;.5 and leads o he phenomenon ha ii pessimiss are posiivel surprised:.25.25 f f [.25 { [..25.3 ] [.9.25.5 ]}] [.42 ] >.28 >. 2 The las of our ases i represens a siuaion during eonomi reession, long before reahing he boom of he le means is moderae and is low or insignifian and an subsaniae he ase where he pessimiss are onfirmed suppose he numbers are now.25 ; 2.25 ;.25 ;.4 ;.6 ;.3 ; :.25.25 f f [.25 { [.4.25.3 ] [.6.25 ]}] [.2 ] <.25 <. 262 Before we proeed o furher assumpions, i is worh hinking abou he implied densi funions whih an be assigned o he differen subjeive probabiliies in our four senarios. Suppose in he firs plae, ha eonomi growh raes are disribued smmeriall following, b and large, a normal disribuion. In Figure we have depied he ases whih sand for agens' opimism, in Figure 2 we have he wo ases for pessimism, respeivel.
3 The Model 5 Figure : roba bilisi Inerpreaion of essimism Opimism - -..3 /o [ ] - - -.4.3 /o [ ] - Soure: Own ompilaion. In eah of he Figures, opimism or pessimism is represened geomeriall b he surfae under he disribuion and o he lef of he riial pas inome growh raes, j, given a pessimisi or opimisi senario. Noie ha j o, p sand for he opimisi o and for he pessimisi p siuaion he numbers are.3 and.25 respeivel and is he supersrip sanding for "riial". Analiall, he orresponding expression is: j 2 d prob [ ] ; j o, p f
6 Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs Figure 2: robabilisi Inerpreaion of essimism essimism - -.6.25 /p [ ] - - -.9.25 /p [ ] - Soure: Own ompilaion. Sevenh: The revision of opimisi or pessimisi expeaions follows he rules of Baesian updaing. x This is supposed o be he mos sophisiaed assumpion of he model, being, a he same ime, ompleel indispensable. Oherwise, onsumers would no be learning and would herefore be affeed b wha pshologiss are used o all "perseverane". Firs of all i riviall implies ha: 3 [, ] g In order o learn or, likewise, o updae he subjeive probabiliies, agens have o ake ino aoun favourable or less favourable informaion abou he ourse of he eonom; if he informaion apured is favourable unfavourable, opimism pessimism should be mainained orreed upwards. Wha should be he ardsik for a favourable unfavourable eonomi developmen? Our suggesion is o ake he long-run sead sae growh rae of he eonom, dee a favourable unfavourable piee of informaion xi hen is: *. A simple means o
3 The Model 7 4 q, * i i > * < * ; i > * The aual growh raes of he eonom in onsideraion fluuae around he long-run sead sae growh rae of he eonom, *, as i is depied in Figure 3. The laer an be derived eiher from a neo-lassial, or from a new growh heor model. Assuming, for onveniene, zero populaion growh in eiher ase, he per apia growh equals he absolue growh rae. The numbers hosen orrespond o our numerial example. Figure 3: Growh Cles and he Sead Sae.3.275.25 * Soure: Own ompilaion. The upper and lower numbers for eonomi growh we make use of in Figure 3, are hose we alread applied in our examples i hrough iv; he equilibrium or rend growh rae for inome and onsumpion, *, is assumed o be.275 and is loaed smmeriall beween he inerim upper and lower bounds. In doing so, we are a lile more "onservaive" han Luas 99, p. 23, who argues wih a benhmark value of onsumpion growh of.3. Again, aording o him, one sandard deviaion of he log of onsumpion, is abou.3, wo-sigma even.25 whih would impl in our ase bounding edges in he neighbourhood of.45 and.45 no marked in Figure 3. Baesian updaing hen has, for a disree period, he following form: xii
Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs 8 5 q q q q q q > < < > If onsumers observe he eonom all he wa o period, hen: 6 q q q q q q > < < > essimism, hene, inreases if unfavourable informaion is observed b privae onsumers. No onl, are ime-varian, bu are also as our numerial examples ended o suppor,,. The mos simple approah saes see above ha: 7 [ ] [ ],, h, As our numerial examples ended o sugges, opimism pessimism alwas has wo omponens: he ourrene of an expeed feared iniden plus he assoiaed probabili. These omponens are no independen, bu orrelae wih eah oher. In Figure 4, we have depied his relaionship in he firs quadran. The posiive orrelaion ma be srong hen he line is seep aording o α or weak hen he line is fla aording o ' α. In eah ase he line an onl sar one a minimal probabili has been surpassed. In quadran four he falling line represens a oninuum of probabiliies, onsrained b he adding-up ondiion. Quadran hree enompasses he 45 degree line, whih helps o ranslae he resuls of he firs and of he fourh quadran ino he seond quadran. The main resul of he seond quadran is o show ha he subjeive probabili hosen b he pessimis opimis, impliil deermines beause, basiall, he numbers have o add up he size of he expeed feared iniden. 8 a,b ; b a b a > 9,d ; d ; d d > From ha we an onlude ha eiher:
3 The Model 9 2 d a b or d 2 b a d b Figure 4: Growh Expeaions as a Funion of Opimism essimism - - [ ] α α [ ] - - [] Soure: Own ompilaion. Before we an proeed o he soluion of he model, we should lose i. Thus far, we have a enaive explanaion of onsumer behaviour under he influene of opimism and pessimism. For onveniene, we resri ourselves o a losed eonom wih privae ransaions onl. The usual definiion holds: 22 Y C I The model, however, is formulaed in growh raes and no in levels. Hene we ransform 22 ino:
Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs 2 23 i Y I Y C If we posulae as done impliil above in he numerial examples ha inome growh equals onsumpion growh: 24 hen 23 beomes 25 Y / I Y C i i Y I Y C We define: 26 Y I ; Y C β β If boh of hese shares are assumed onsan, we ahieve: 27 i β β 28 i As a resul, he analsis of shor-erm and long-erm inome, or likewise invesmen developmen, an be redued o he analsis of inome growh. Given his resul, our ke equaion from above simplifies o: 29 [ ] 2 e f f All in all, he model onains 8 endogenous variables and 3 exogenous variables. When speifing he funion. f in 29 as a linear funion. γ, inroduing 4 ino 6 and he laer ino 8 and 9 whih ener ogeher ino 29, equaion 29 is an inhomogenous differene equaion of he seond order. Inroduing: 3 2 b a
4 A Simulaion Exerise 2 and 3 2 2 d d 2 d d gives: 2 32 γ [ d b d a 2d ] 2 From he logi of he model, in equilibrium, he likelihood for pessimism and for opimism should be abou he same. Hene, * 33, 5 Then, we ge, for : 2 * * * 34 γ [,5 a,25b,5,25d ] From 34 we an onlude ha he erm in brakes neessaril equals zero. Hene, 35 d b 2 a As 4 and 6 are formulaed as oningen equaions, a sraighforward soluion of he homogenous problem of 32 is somehow ompliaed. Therefore, we proeed o a simulaion exerise whih neiher eliminaes an imporan informaion of he model, nor is a hindering faor for an indeph analsis of he properies of he le. The parameer resriion found in 35 is aomplished in all simulaion experimens. 4 A SIMULATION EXERCISE As Luas has observed, an sensiive model of he business le should no onradi speifi regulariies whih were observed as o-movemens among differen aggregae ime series 994, p. 27. Wha abou hese o-movemens in our model? The following experimens have primaril a heurisi aim: Firs of all we inend o show ha he model is able o reae under plausible parameer assumpions les of he real growh rae onsumpion or likewise inome. Seondl, we shall demonsrae ha he model an as well "produe" i onverging osillaions boh a a higher and a a lower new equilibrium, ii exploding osillaions as iii permanen osillaions. Figures 5 and 7 are ases for i, Figures 9 and are ases for ii, and Figures 6 and 8 are ases for iii.
22 Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs Figure 5: Cles of he Real Growh Rae Case,4,35,3,25,2,5,,5 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 22 23 24 25 γ *.33;.275;.5; i.8; a.2; b.5;.3; d.5 Soure: Own alulaion. Figure 6: Cles of he Real Growh Rae Case 2,5,45,4,35,3,25,2,5,,5 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 22 23 24 25 γ *.44;.275;.5; i.8; a.2; b.5;.3; d.5 Soure: Own alulaion.
4 A Simulaion Exerise 23 Figure 7: Cles of he Real Growh Rae Case 3,6,5,4,3,2, -, -,2 -,3 -,4 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 22 23 24 25 γ *.55;.275;.5; i.8; a.2; b.5;.3; d.5 Soure: Own alulaion. Figure 8: Cles of he Real Growh Rae Case 4,5,5 -,5 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 22 23 24 25 - -,5-2 -2,5 γ *.66;.275;.5; i.8; a.2; b.5;.3; d.5 Soure: Own alulaion.
24 Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs Figure 9: Cles of he Real Growh Rae Case 5 4E 2E -2E 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 22 23 24 25-4E -6E -8E -E2 γ *.77;.275;.5; i.8; a.2; b.5;.3; d.5 Soure: Own alulaion. Figure : Cles of he Real Growh Rae Case 6,2E9 E9 8E8 6E8 4E8 2E8-2E8-4E8-6E8-8E8 -E9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 22 23 24 25 γ *.88;.275;.5; i.8; a.2; b.5;.3; d.5 Soure: Own alulaion.
5 Empirial Evidene? 25 In all of he above experimens, we have mainained all parameers onsan wih he exepion of γ; he laer, we have inreased from.33 in Figure 5 up o.88 in Figure. 5 EMIRICAL EVIDENCE? The majori of papers inending o make use of indiaors whih ould refle onsumers' beliefs, draw on measures of so-alled "onsumer onfidene" Aemoglu/So 994, p. or "onsumer senimen" Delorme Jr e al. 2, p. 864. The Gallup-Surve, for example, akes ino aoun and laer averages over hem responses o five quesions given b onsumers who were asked abou heir las ear experienes wih "general eonomi ondiions" and heir "household finanes", he "expeaions of hange" in hese variables over he nex ear and, finall abou wheher "i is a good ime o make a major purhase" Aemoglu/So 994, p. 3. However, ompuing a simple average of hese responses is like omparing apples wih pears: Whereas having posiive negaive expeaions regarding he fuure in he forward looking answers reveals, b and large, he size of opimism pessimism among he inerviewed people, he bakward looking answers and also he answer wih regard o he propensi o purhase in he presen give some hin as o wha exen people were surprised disillusioned in he immediae pas. The mulidimensionali of ombining differen aiudes wih differen pes of errors ges los, if one simpl idenifies low high onfidene wih "onsumers being depressed glad and pessimisi opimisi abou he urren sae of he eonom" Delorme Jr e al. 2, p. 866. In his simplisi view, pessimism opimism is "aused" b a good bad expeed sae of he eonom and i is no longer possible o explain he business le as being driven b srong privae beliefs among privae agens and he orresponding updaing of hese beliefs aording o he developmen of he eonom. If agens are eiher jus "pessimisi" or "opimisi", hen here is no room for explaining he urningpoins in he business le. The ICS Universi of Mihigan is based also on he responses o five quesions; "among he five quesions used o ompile he index are wo major omponens: One refles onsumer assessmens of urren eonomi ondiions; anoher fouses on expeaions abou he fuure Kinse/Collins 99, p. 26. Theses wo omponens of he ICS "make up wo separae indies alled he index of onsumer expeaions ICE and he index of urren eonomi ondiions ICEC ibid.. This separaion is an improvemen, bu sill: How are expeaions owards he fuure and he perepion of he presen relaed o eah oher? In a raional expeaions framework Kinse and Collins 99, pp. 29-24 esimae he ICE as, among oher hings, a funion of he ICEC. This proedure is, if a all, onl half wa of explaining he disillusion of opimiss/posiive surprise of pessimiss. Raher i is in line wih wo of our four senarios in Table : "good bad news is onfirmed".
26 Opimism, essimism and he Unforeseen: Modelling an Endogenous Business Cle Driven b Srong Beliefs Nowihsanding hese shoromings, man of hose papers ome up basiall wih a orre me s- sage: No onl is he sae of he eonom refleed in onsumers' onfidene, bu also "onsumer senimen auses fluuaions in GN" Masusaka/Sboordone 995, p. 297. Empirial invesigaions suppor he presumpion ha onsumer onfidene is posiivel negaivel orrelaed wih good bad news from he real maro-eonom Delorme Jr e al. 2, p. 866. I an also be shown ha indiaors of onsumers' onfidene do work as leading indiaors for he hange in he onsumpion of goods ibid., p. 868. There is also eonomeri evidene for he hpohesis ha "exogenous hanges in onsumer senimen have real effes on oupu" Masusaka/Sboordone 995, p. 37. Wh his an be and how i an be, were ke quesions addressed in his paper. 6 SOME CONCLUSIONS AND THE SCOE FOR FUTURE RE- SEARCH I seems as if no onl posiive or negaive "surprises" in a Luas-Barro-Sargen-Wallae world an indue signifian real effes on he suppl side of he eonom. In our model, where he eonom is driven b he growh of onsumpion and invesmen plas a merel passive role, posiive surprises among pessimiss and disillusions among opimiss, are he kes for he explanaion of he urning poins during a business le. The onfirmaion of good bad news helps o explain he persisene of a boom reession. This insigh is boh onsisen wih he long lasing upswing of he US eonom during he Clinon ears, as also wih he reluane of he European eonom o ahieve a more dnami momenum. This paper an be undersood as onl a firs sep ino a broad field of researh, boh on a heoreial and on an empirial basis. Mos likel, we eonomiss should learn more abou srong beliefs of eonomi agens suh as "opimism" and "pessimism". I is also more han likel ha a disipline suh as psholog, an onribue o a beer undersanding of hese human aiudes. In pariular, we should analse in more deph, he preondiions for he likelihood of agens swihing from one mood o anoher. Wha abou persisene and hseresis effes, whih we have no ouhed a all in our exposiion? Also, he indiaors menioned and used in he presen b researh insiues for he prediion of eonomi growh and onsumpion expendiures purposes, should be revised aording o a horough idenifiaion of iems. Judgemens of privae agens wih regard o he presen sae of he eonom, he fuure prospes of growh and, finall, wih regard o he expeed or unexpeed ahievemens in he immediae pas, should be olleed and analsed separael and no be aggregaed o a diffuse measure of "onfidene".
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