Top-down versus bottom-up macroeconomics

Transcription

1 DG ECFIN's 6 h Annual Research Conference (ARC 29) SESSION C "Revisiing he economic paradigm" Crisis and reform Brussels, 5-6 Ocober 29 Paul De Grauwe Universiy of Leuven Top-down versus boom-up macroeconomics (Keynoe address) Ocober 29 Copyrigh ress wih he auhor

2 TOP-DOWN VERSUS BOTTOM-UP MACROECONOMICS Paul De Grauwe Universiy of Leuven Absrac: I disinguish wo ypes of macroeconomic models. The firs ype are op-down models in which some or all agens are capable of undersanding he whole picure and use his superior informaion o deermine heir opimal plans. The second ype are boom-up models in which all agens experience cogniive limiaions. As a resul, hese agens are only capable of undersanding and using small bis of informaion. These are models in which agens use simple rules of behavior. These models are no devoid of raionaliy. Agens in hese models behave raionally in ha hey are willing o learn from heir misakes. These wo ypes of models produce a radically differen macroeconomic dynamics. I analyze hese differences. JEL codes : E, E32, D83 Keywords : DSGE-model, imperfec informaion, heurisics, animal spiris Ocober 29 This paper was prepared for he DG ECFIN's Annual Research Conference of 29. I am graeful o Yunus Aksoy, Tony Akinson, Sephan Fahr, Daniel Gros, Richard Harrison, Romain Houssa, Pablo Rovira Kalwasser, Chrisian Keuschnigg, Alan Kirman, Giovanni Lombardo, Lars Ljungqvis, Parick Minford, John Muellbauer, Ilbas Pelin, Frank Smes, Leopold von Thadden, David Vines, and Tony Yaes for heir commens and suggesions.

3 . Inroducion One of he surprising developmens in macroeconomics is he sysemaic incorporaion of he paradigm of he uiliy maximizing forward looking and fully informed agen ino macroeconomic models. This developmen sared wih he raional expecaions revoluion of he 97s, which augh us ha macroeconomic models can only be acceped if agens expecaions are consisen wih he underlying model srucure. The real business cycle heory (RBC) inroduced he idea ha macroeconomic models should be micro-founded, i.e. should be based on dynamic uiliy maximizaion. While RBC models had no place for price rigidiies and oher ineria, he New Keynesian School sysemaically inroduced rigidiies of all kinds ino similar micro-founded models. These developmens occurred in he ivory owers of academia for several decades unil in recen years hese models were implemened empirically in such a way ha hey have now become ools of analysis in he boardrooms of cenral banks. The mos successful implemenaion of hese developmens are o be found in he Dynamic Sochasic General Equilibrium models (DSGE-models) ha are increasingly used in cenral banks for policy analysis (see Smes and Wouers(23), Chrisiano, e al.(27), Smes and Wouers(27), Adjemian, e al. (27)). These developmens are surprising. While macroeconomic heory enhusiasically embraced he view ha agens fully undersand he srucure of he underlying models in which hey operae, oher sciences like psychology and neurology increasingly uncovered he cogniive limiaions of individuals (see e.g. Damasio(23), Kahneman (22), Camerer e al. (25), Kahneman and Thaler (26) and Della Vigna(27)). We learn from hese sciences ha agens only undersand small bis and pieces of he world in which hey live, and insead of maximizing coninuously aking all available informaion ino accoun, agens use simple rules (heurisics) in guiding heir behaviour and heir forecass abou he fuure (see Gabaix, Laibson, Moloche, and Weinberg, 26). The recen financial crisis seems o suppor he view ha agens have limied undersanding of he big picure. If hey had undersood he full complexiy of he financial sysem hey would have undersood he lehal riskiness of he asses hey massively ook in heir porfolios. In order o undersand he naure of differen macroeconomic models i is useful o make a disincion beween op-down and boom-up sysems. In is mos general 2

4 definiion a op-down sysem is one in which one or more agens fully undersand he sysem. These agens are capable of represening he whole sysem in a blueprin ha hey can sore in heir mind. Depending on heir posiion in he sysem hey can use his blueprin o ake over he command, or hey can use i o opimize heir own privae welfare. These are sysems in which here is a one o one mapping of he informaion embedded in he sysem and he informaion conained in he brain of one (or more) individuals. An example of such a op-down sysem is a building ha can be represened by a blueprin and is fully undersood by he archiec. Boom-up sysems are very differen in naure. These are sysems in which no individual undersands he whole picure. Each individual undersands only a very small par of he whole. These sysems funcion as a resul of he applicaion of simple rules by he individuals populaing he sysem. Mos living sysems follow his boom-up logic (see he beauiful descripion of he growh of he embryo by Dawkins(29)). The marke sysem is also a boom-up sysem. The bes descripion made of his boom-up sysem is sill he one made by Hayek(945). Hayek argued ha no individual exiss who is capable of undersanding he full complexiy of a marke sysem. Insead individuals only undersand small bis of he oal informaion. The main funcion of markes consiss in aggregaing his diverse informaion. If here were individuals capable of undersanding he whole picure, we would no need markes. This was in fac Hayek s criicism of he socialis economiss who ook he view ha he cenral planner undersood he whole picure, and would herefore be able o compue he whole se of opimal prices, making he marke sysem superfluous. My conenion is ha he raional expecaions models are he inellecual heirs of hese cenral planning models. No in he sense ha individuals in hese raional expecaions models aim a planning he whole, bu in he sense ha, as he cenral planner, hey undersand he whole picure. These individuals use his superior informaion o obain he opimum opimorum for heir own privae welfare. In his sense hey are op-down models. In his paper I will conras he raional expecaions op-down model wih a boomup macroeconomic model. This will be a model in which agens have cogniive limiaions and do no undersand he whole picure (he underlying model). Insead hey only undersand small bis and pieces of he whole model and use simple rules o 3

5 guide heir behavior. I will inroduce raionaliy in he model hrough a selecion mechanism in which agens evaluae he performance of he rule hey are following and decide o swich or o sick o he rule depending on how well he rule performs relaive o oher rules. The modeling approach presened in his paper is no he only possible one o model agens behaviour under imperfec informaion. In fac, a large lieraure has emerged aemping o inroduce imperfec informaion ino macroeconomic models. These aemps have been based mainly on he saisical learning approach pioneered by Sargen(993) and Evans and Honkapohja(2). This lieraure leads o imporan new insighs (see e.g. Gaspar and Smes(26), Orphanides and Williams(24), Milani(27a)). However, I feel ha his approach sill loads individual agens wih oo many cogniive skills ha hey probably do no posses in he real world. In a way i can be argued ha he saisical learning models are also op-down models, in which agens ambiion is o learn he secres of he whole picure, which in hese models hey ypically achieve asympoically (in heaven?). The purpose of his paper is o conras he dynamics of he op-down and he boomup models, and o draw some policy conclusions. Secion 2 presens he boom-up model, which will be called behavioural model. The nex hree secions hen discuss he differen implicaions he behavioural model has when conrased wih he raional expecaions model. The paper is concluded wih a discussion of some mehodological issues. See he fascinaing book of Gigerenzer and Todd(999) on he use of simple heurisics as compared o saisical (regression) learning. 4

6 2. A behavioural macroeconomic model In his secion he modeling sraegy is described. This is done by presening a sandard aggregae-demand-aggregae supply model augmened wih a Taylor rule. The novel feaure of he model is ha agens use simple rules, heurisics, o forecas he fuure. These rules are subjeced o an adapive learning mechanism, i.e., agens endogenously selec he forecasing rules ha have delivered he highes performance ( finess ) in he pas. This selecion mechanism acs as a disciplining device on he kind of rules ha are accepable. Since agens use differen heurisics one obains heerogeneiy. This, as will be shown, creaes endogenous business cycles. This behavioural model is conrased wih a similar model ha incorporaes raional expecaions, and ha is inerpreed as a sylized version of DSGE-models. This comparison will make i possible o focus on some crucial differences in he ransmission of shocks, in paricular of moneary policy shocks. 2. The model The model consiss of an aggregae demand equaion, an aggregae supply equaion and a Taylor rule. The aggregae demand equaion is specified in he sandard way, i.e. y ~ a E y ( a) y a2 ( r E ) () ~ where y is he oupu gap in period, r is he nominal ineres rae, is he rae of inflaion, and is a whie noise disurbance erm. E ~ is he expecaions operaor where he ilde above E refers o expecaions ha are no formed raionally. This process will be specified subsequenly. I follow he procedure inroduced in DSGEmodels of adding a lagged oupu in he demand equaion. This is usually jusified by invoking habi formaion. I keep his assumpion here as I wan o compare he behavioural model wih he DSGE-raional expecaions model. However, I will show in secion 4 ha I do no really need his ineria-building device o generae ineria in he endogenous variables. 5

7 The aggregae supply equaion can be derived from profi maximizaion of individual producers. As in DSGE-models a Calvo pricing rule and some indexaion rule used in adjusing prices is assumed. This leads o a lagged inflaion variable in he equaion 2. The supply curve can also be inerpreed as a New Keynesian Philips curve: ~ b E ( b b y (2) ) 2 Finally he Taylor rule describes he behaviour of he cenral bank r c * ( ) c y c r u (3) 2 3 where * is he inflaion arge which for he sake of convenience will be se equal o. Noe ha, as is commonly done, he cenral bank is assumed o smooh he ineres rae. This smoohing behaviour is represened by he lagged ineres rae in equaion (3). Ideally, he Taylor rule should be formulaed using a forward looking inflaion variable, i.e. cenral banks se he ineres rae on he basis of heir forecass abou he rae of inflaion. This was no done here in order o mainain simpliciy in he model. Inroducing heurisics in forecasing oupu Agens are assumed o use simple rules (heurisics) o forecas he fuure oupu and inflaion. The way I proceed is as follows. I sar wih a very simple forecasing heurisics and apply i o he forecasing rules of fuure oupu. I assume wo ypes of forecasing rules. A firs rule can be called a fundamenalis one. Agens esimae he seady sae value of he oupu gap (which is normalized a ) and use his o forecas he fuure oupu gap. (In a laer exension, i will be assumed ha agens do no know he seady sae oupu gap wih cerainy and only have biased esimaes of i). A second forecasing rule is an exrapolaive one. This is a rule ha does no presuppose ha agens know he seady sae oupu gap. They are agnosic abou i. Insead, hey exrapolae he previous observed oupu gap ino he fuure. The wo rules are specified as follows ~ f The fundamenalis rule is defined by E y (4) 2 I is now sandard in DSGE-models o use a pricing equaion in which marginal coss ener on he righ hand side. Such an equaion is derived from profi maximisaion in a world of imperfec compeiion. I can be shown ha under cerain condiions he aggregae supply equaion (3) is equivalen o such a pricing equaion (see Gali(28), Smes and Wouers(23)). 6

8 ~ e The exrapolaive rule is defined by E y y (5) This kind of simple heurisic has ofen been used in he behavioural finance lieraure where agens are assumed o use fundamenalis and charis rules (see Brock and Hommes(997), Branch and Evans(26), De Grauwe and Grimaldi(26)). I is probably he simples possible assumpion one can make abou how agens, which experience cogniive limiaions, use rules ha embody limied knowledge o guide heir behavior. In his sense hey are boom-up rules. They only require agens o use informaion hey undersand, and do no require hem o undersand he whole picure. Thus he specificaion of he heurisics in (4) and (5) should no be inerpreed as a realisic represenaion of how agens forecas. Raher is i a parsimonious represenaion of a world where agens do no know he Truh (i.e. he underlying model). The use of simple rules does no mean ha he agens are dumb and ha hey do no wan o learn from heir errors. I will specify a learning mechanism laer in his secion in which hese agens coninuously ry o correc for heir errors by swiching from one rule o he oher. The marke forecas is obained as a weighed average of hese wo forecass, i.e. ~ E y ~ E y ~ ~ f e f, E y c, E (7) f, y (8) c, and (9) f, e, where f, and e, are he probabiliies ha agens use a fundamenalis, respecively, an exrapolaive rule. A mehodological issue arises here. The forecasing rules (heurisics) inroduced here are no derived a he micro level and hen aggregaed. Insead, hey are imposed ex pos, on he demand and supply equaions. This has also been he approach in he learning lieraure pioneered by Evans and Honkapohja(2). Ideally one would like o derive he heurisics from he micro-level in an environmen in which agens experience cogniive problems. Our knowledge abou how o model his behaviour a 7

9 he micro level and how o aggregae i is oo skechy, however, and I have no ried o do so 3. As indicaed earlier, agens are raional in he sense ha hey coninuously evaluae heir forecas performance. I apply noions of discree choice heory (see Anderson, de Palma, and Thisse, (992) and Brock & Hommes(997)) in specifying he procedure agens follow in his evaluaion process. Discree choice heory analyzes how agens decide beween differen alernaives. The heory akes he view ha agens are boundedly raional, i.e. uiliy has a deerminisic componen and a random componen. Agens compue he forecas performance of he differen heurisics as follows: U U f, e, ~ 2 k yk E f, k yk k ~ 2 k yk Ee, k yk k () () where U f, and U e, are he forecas performances (uiliies) of he fundamenaliss and exrapolaors, respecively. These are defined as he mean squared forecasing errors (MSFEs) of he opimisic and pessimisic forecasing rules; k are geomerically declining weighs. Applying discree choice heory he probabiliy ha an agen will use he fundamenalis forecasing rule is given by he expression (Anderson, de Palma, and Thisse, (992) and Brock-Hommes(997)): f, exp U f, (2) exp( U ) exp( U ) f, e, Similarly he probabiliy ha an agen will use he exrapolaive forecasing rule is given by: e, e, exp( U f, ) exp( U e, ) exp U (3) Equaion (2) says ha as he pas forecas performance of he fundamenaliss improves relaive o ha of he exrapolaors agens are more likely o selec he fundamenalis rule abou he oupu gap for heir fuure forecass. As a resul he f, 3 Psychologiss and brains scieniss sruggle o undersand how our brain processes informaion. There is as ye no generally acceped model we could use o model he micro-foundaions of informaion processing. There are some aemps o provide micro-foundaions of models wih agens experiencing cogniive limiaions, hough. See e.g. Kirman, (992), Delli Gai, e al.(25). 8

10 probabiliy ha agens use he fundamenalis rule increases. Equaion (3) has a similar inerpreaion. The parameer γ measures he inensiy of choice. I paramerizes he exen o which he deerminisic componen of uiliy deermines acual choice. When γ = uiliy is purely sochasic. In ha case agens decide o be fundamenalis or exrapolaor by ossing a coin and he probabiliy o be fundamenalis (or exrapolaor) is exacly.5. When γ = uiliy is fully deerminisic and he probabiliy of using a fundamenalis rule is eiher or. The parameer γ can also be inerpreed as expressing a willingness o learn from pas performance. When γ = his willingness is zero; i increases wih he size of γ. Noe ha his selecion mechanism is he disciplining device inroduced in his model on he kind of rules of behaviour ha are accepable. Only hose rules ha pass he finess es remain in place. The ohers are weeded ou. In conras wih he disciplining device implici in raional expecaions models which implies ha agens have superior cogniive capaciies, we do no have o make such an assumpion here. I should also be sressed ha alhough individuals use simple rules in forecasing he fuure, his does no mean ha hey fail o learn. In fac he finess crierion used should be inerpreed as a learning mechanism based on rial and error. When observing ha he rule hey use performs less well han he alernaive rule, agens are willing o swich o he more performing rule. Pu differenly, agens avoid making sysemaic misakes by consanly being willing o learn from pas misakes and o change heir behavior. This also ensures ha he marke forecass are unbiased. The mechanism driving he selecion of he rules inroduces a self-organizing dynamics in he model. I is a dynamics ha is beyond he capaciy of any one individual in he model o undersand. In his sense i is a boom-up sysem. I conrass wih he mainsream macroeconomic models in which i is assumed ha some or all agens can ake a bird s eye view and undersand he whole picure. These agens no only undersand he whole picure bu also use his whole picure o decide abou heir opimal behaviour. Thus here is a one-o-one correspondence beween he oal informaion embedded in he world and he individual brains. Inroducing heurisics in forecasing inflaion 9

11 Agens also have o forecas inflaion. A similar simple heurisics is used as in he case of oupu gap forecasing, wih one rule ha could be called a fundamenalis rule and he oher an exrapolaive rule. (See Brazier e al. (26) for a similar seup). The fundamenalis rule is based on he announced inflaion arge, i.e. agens using his rule have confidence in he credibiliy of his rule and use i o forecas inflaion. The exrapolaive rule is used by agens who do no rus he announced inflaion arge. Insead hey exrapolae inflaion from he pas ino he fuure. The fundamenalis rule will be called an inflaion argeing rule. I consiss in using he cenral bank s inflaion arge o forecas fuure inflaion, i.e. ~ ar * E (7) * where he inflaion arge is normalized o be equal o ex The exrapolaors are defined by E (8) The marke forecas is a weighed average of hese wo forecass, i.e. or ~ ~ ar ~ ex E E E (9) ar, ex, E (2) * ar, ex, and (2) ar, ex, The same selecion mechanism is used as in he case of oupu forecasing o deermine he probabiliies of agens rusing he inflaion arge and hose who do no rus i and rever o exrapolaion of pas inflaion, i.e. ar, ex, exp U ar, (22) exp( U ) exp( U ) ar, ex, exp U ex, (23) exp( U ) exp( U ) ar, ex, where U ar, and U ex, are he weighed averages of pas squared forecas errors of using argeer and exrapolaor rules, respecively. These are defined in he same way as in () and ().

12 This inflaion forecasing heurisics can be inerpreed as a procedure of agens o find ou how credible he cenral bank s inflaion argeing is. If his is very credible, using he announced inflaion arge will produce good forecass and as a resul, he probabiliy ha agens will rely on he inflaion arge will be high. If on he oher hand he inflaion arge does no produce good forecass (compared o a simple exrapolaion rule) he probabiliy ha agens will use i will be small. The soluion of he model is found by firs subsiuing (3) ino () and rewriing in marix noaion. This yields: u a r c a y a b y E E a a b y c a c a b ~ ~ or vbzczebz A~ r (4) where bold characers refer o marices and vecors. The soluion for Z is given by vbzczeba Z~ r (5) The soluion exiss if he marix A is non-singular, i.e. if (-a 2 c 2 )a 2 b 2 c. The sysem (5) describes he soluion for y and given he forecass of y and. The laer have been specified in equaions (4) o (3) and can be subsiued ino (5). Finally, he soluion for r is found by subsiuing y and obained from (5) ino (3). My research sraegy consiss in comparing he dynamics of his behavioural model wih he same srucural model (aggregae demand equaion (), aggregae supply equaion (2) and Taylor rule equaion (3)) under raional expecaions which we inerpre as a sylized DSGE-model. The model consising of equaions () o (3) can be wrien in marix noaion as follows: u r y a a b r E y E E a a b r y c c a b

13 Ω Z Z Ω Φ E Z Λ Z v (6) Φ E Z Λ Z v (7) This model can be solved under raional expecaions using he Binder-Pesaran(996) procedure. 2.2 Calibraing he model I proceed by calibraing he model. In appendix A he parameers used in he calibraion exercise are presened. The model was calibraed in such a way ha he ime unis can be considered o be monhs. A sensiiviy analysis of he main resuls o changes in he some of he parameers of he model will be presened. The hree shocks (demand shocks, supply shocks and ineres rae shocks) are i.i.d. wih sandard deviaions of.5%. 3. Animal spiris, learning and forgefulness In his secion simulaions of he behavioural model in he ime domain are presened and inerpreed. The upper panel of Figure shows he ime paern of oupu produced by he behavioural model. A srong cyclical movemen in he oupu gap can be observed. The lower panel of Figure shows a variable called animal spiris 4. I represens he evoluion of he fracions of he agens who exrapolae a posiive oupu gap. Thus when he curve reaches + all agens are exrapolaing a posiive oupu gap; when he curve reaches no agens are exrapolaing a posiive oupu gap. In fac in ha case hey all exrapolae a negaive oupu gap. Thus he curve shows he degree of opimism and pessimism of agens who make forecass of he oupu gap. Combining he informaion of he wo panels in figure i can be seen ha he model generaes endogenous waves of opimism and pessimism. During some periods opimiss (i.e. agens who exrapolae posiive oupu gaps) dominae and his ranslaes ino above average oupu growh. These opimisic periods are followed by pessimisic ones when pessimiss (i.e. agens who exrapolae negaive oupu gaps) dominae and he growh rae of oupu is below average. These waves of opimism 4 See Mario Nui (29)on he differen inerpreaions of Animal Spiris. The locus classicus is Keynes(936). See also Farmer(26) and he recen book of Akerlof and Shiller(29). 2

14 and pessimism are essenially unpredicable. Oher realizaions of he shocks produce differen cycles wih he same general characerisics. These endogenously generaed cycles in oupu are made possible by a self-fulfilling mechanism ha can be described as follows. A series of random shocks creaes he possibiliy ha one of he wo forecasing rules, say he exrapolaing one, delivers a higher payoff, i.e. a lower mean squared forecas error (MSFE). This aracs agens ha were using he fundamenalis rule. If he successful exrapolaion happens o be a posiive exrapolaion, more agens will sar exrapolaing he posiive oupu gap. The conagion-effec leads o an increasing use of he opimisic exrapolaion of he oupu-gap, which in urn simulaes aggregae demand. Opimism is herefore selffulfilling. A boom is creaed. A some poin, negaive sochasic shocks and/or he reacion of he cenral bank hrough he Taylor rule make a den in he MSFE of he opimisic forecass. Fundamenalis forecass may become aracive again, bu i is equally possible ha pessimisic exrapolaion becomes aracive and herefore fashionable again. The economy urns around. These waves of opimism and pessimism can be undersood o be searching (learning) mechanisms of agens who do no fully undersand he underlying model bu are coninuously searching for he ruh. An essenial characerisic of his searching mechanism is ha i leads o sysemaic correlaion in beliefs (e.g. opimisic exrapolaions or pessimisic exrapolaions). This sysemaic correlaion is a he core of he booms and buss creaed in he model. Noe, however, ha when compued over a significanly large period of ime he average error in he forecasing goes o zero. In his sense, he forecas bias ends o disappear asympoically. The resuls concerning he ime pah of inflaion are shown in figure 2. Firs concenrae on he lower panel of figure 2. This shows he fracion of agens using he exrapolaor heurisics, i.e. he agens who do no rus he inflaion arge of he cenral bank. One can idenify wo regimes. There is a regime in which he fracion of exrapolaors flucuaes around 5% which also implies ha he fracion of forecasers using he inflaion arge as heir guide (he inflaion argeers ) is around 5%. This is sufficien o mainain he rae of inflaion wihin a narrow band of approximaely + and % around he cenral bank s inflaion arge. There is a second regime hough which occurs when he exrapolaors are dominan. During his regime he rae of inflaion flucuaes significanly more. Thus he inflaion argeing of he cenral bank 3

15 is fragile. I can be undermined when forecasers decide ha relying on pas inflaion movemens produces beer forecas performances han relying on he cenral bank s inflaion arge. This can occur quie unpredicably as a resul of sochasic shocks in supply and/or demand. We will reurn o he quesion of how he cenral can reduce his loss of credibiliy. Figure : Oupu gap in behavioural model 4

16 Figure 2 Inflaion in behavioural model The simulaions repored in he previous secion assumed a given se of numerical values of he parameers of he model. I was found ha for his se of parameer values animal spiris (measured by he movemens in he fracion of opimisic exrapolaors) emerge and affec he flucuaions of he oupu gap. The correlaion coefficien beween he fracion of opimiss and he oupu gap in he simulaion repored in figure is.86. One would like o know how his correlaion evolves when one changes he parameer values of he model. I concenrae on wo parameer values here, he inensiy of choice parameer,, and he memory agens have when calculaing he performance of heir forecasing. The laer is represened by he parameer k in equaions ()-() and is a series of declining weighs aached o pas forecas errors. I define k ( ) (and ). The parameer can k 5

17 hen be inerpreed as a measure of he memory of agens. When = here is no memory; i.e. only las period s performance maers in evaluaing a forecasing rule; when = here is infinie memory, i.e. all pas errors, however far in he pas, obain he same weigh. The resuls of he sensiiviy analysis are shown in figure 3. The lef hand panel shows he correlaion beween he oupu gap and he fracion of opimisic exrapolaors (animal spiris) for increasing values of he inensiy of choice parameer,. I can be seen ha when is zero (i.e. he swiching mechanism is purely sochasic), his correlaion is zero. The inerpreaion is ha in an environmen in which agens decide purely randomly, i.e. hey do no reac o he performance of heir forecasing rule, here are no sysemaic waves of opimism and pessimism (animal spiris) ha can influence he business cycle. When increases, he correlaion increases sharply. Thus in an environmen in which agens learn from heir misakes, animal spiris arise. Thus one needs a minimum level of raionaliy (in he sense of a willingness o learn) for animal spiris o emerge and o influence he business cycle. I appears from figure 3 ha his is achieved wih relaively low levels of γ. The righ hand panel shows he correlaion beween he oupu gap and he fracion of opimiss for increasing values of he memory parameer. I can be seen ha when = he correlaion is zero. This is he case where agens aach he same weigh o all pas observaions, however, far in he pas hey occur. Pu differenly, when agens have infinie memory; hey forge nohing. In ha case animal spiris do no occur. Thus one needs some forgefulness (which is a cogniive limiaion) o produce animal spiris. Noe ha he degree of forgefulness does no have o be large. For values of below.98 he correlaions beween oupu and animal spiris are quie high. Having presened he main feaures of he behavioural (boom up) model I now proceed o show how his model leads o a view of macroeconomic dynamics ha conrass grealy wih he view obained from he raional expecaions (op down) macroeconomic models. I concenrae on hree areas. The firs one has o do wih he business cycle heories implici in he behavioural and he raional expecaions models. The second one focuses on he naure of he uncerainy in he wo models and he hird one on he implicaions for moneary policies. 6

18 Figure 3 Correlaions beween oupu gap and fracion of opimiss 4. Two differen business cycle heories The behavioural and raional expecaions macroeconomic models lead o very differen views on he naure of business cycle. Business cycle movemens in he raional expecaions (DSGE) models arise as a resul of exogenous shocks (in produciviy and preferences) and lags in he ransmission of hese shocks o oupu and inflaion. Thus ineria in oupu and inflaion are he resul of he lagged ransmission of exogenous shocks. One could call he ineria (and he business cycles) inroduced in he DSGE-model exogenously creaed phenomena 5. In conras, he behavioural model presened here is capable of generaing ineria (and business cycles) wihou imposing lags in he ransmission process. This could be called endogenous ineria. This difference beween he wo models is illusraed by analyzing he behavioural and he raional models in he absence of lags in he ransmission process in he demand and he supply equaions. This is achieved by seing he parameers of he forward looking variables a = in equaion () and b = in equaion (2). The same i.i.d. shocks are hen applied in boh he behavioural and 5 In a way i can be said ha he lags in he ransmission mechanism inroduce an exogenous, some may say an ad-hoc, elemen ino he logic of he DSGE-model. To give an example, Calvo pricing in which firms are consrained o adjus prices insananeously (Chrisiano, Eichenbaum and Evans (2)) is rouinely imposed in DSGE models. I is clear, however, ha such a resricion comes from ouside he logic of he model. In a world where everybody undersands he model and each oher s raionaliy, which is a he core of he DSGE-models, agens would wan o go immediaely o he opimal plan using he opimal price. They would no wan o accep such a resricion. 7

19 he raional models and he auocorrelaion coefficiens of he simulaed series of oupu gaps and inflaion are compued. The resuls are shown in able. I can be seen ha he behavioural model produces ineria (posiive auocorrelaion) in he oupu gap and in inflaion even if here are no lags in he ransmission of shocks. The raional model produces no ineria in he oupu gap and in inflaion. Table also shows he auocorrelaion coefficiens obained in models ha assume lags in he ransmission. These coefficiens are obained when a =.5 in equaion () and b =.5 in equaion (2). These are also he numerical values assumed in all he simulaions repored in he previous secion. One now observes ha ineria in he oupu gap and in inflaion increases in boh models. However, i can be concluded ha all of he ineria obained in he raional model is he resul of he lags in he ransmission process. This is no he case in he behavioural model where mos of he ineria is produced endogenously. Table : Auocorrelaion coefficiens in oupu gap and inflaion No lags in ransmission behavioural model raional model oupu gap.77.7 inflaion Lags in ransmission behavioural model raional model oupu gap inflaion.9.6 Noe: he auocorrelaion coefficiens are he averages obained from simulaing he model imes, each ime over periods. I can also be seen from able ha even when he coefficiens a and b of he forward looking variables of he model are se a.5, he raional model produces less ineria han he behavioural model. The sensiiviy of he auocorrelaion coefficiens o hese parameers is explored more exhausively in figure 4. This shows he auocorrelaion coefficiens as a funcion of a and b. I can be observed ha in he behavioural model he auocorrelaion coefficiens are no very sensiive o he a and b. This conrass a grea deal wih he resuls of he raional model, where he sensiiviy is very high. When a and b are close o (i.e. no or weak lags in he ransmission process) he auocorrelaion coefficiens are very low (very low ineria). 8

20 In order o produce ineria in he raional model which is of he same magniude as in he behavioural model, a and b mus be smaller han.5. This difference beween he wo models is quie fundamenal. In he raional expecaions model and in he absence of lags in he ransmission, agens immediaely find he opimal levels of oupu and inflaion afer some unanicipaed shock. This resuls from heir op-down posiion, i.e. hey can insananeously compue he effecs his shock has on all he variables of he model making i possible o compue he opimal plan oday and in he fuure. In order o produce he required ineria (and he business cycle movemens), lags in he ransmission prevening insananeous adjusmen o he opimal plan, are necessary. The conras wih he behavioural model is grea. Agens in his model do no fully undersand how he shock will be ransmied. They have no op-down posiion. As a resul hey follow a procedure (heurisics ogeher wih a selecion mechanism) ha funcions as a rial and error learning mechanism aimed a revealing he informaion abou shocks and he ransmission process. This is a slow boom-up process ha uses backward evaluaion processes. I generaes an endogenous ineria (and business cycle) ino he model. The ineria obained in he behavioural model could also be called informaional ineria. In conras o he raional expecaions model, agens in he behavioural model experience an informaional problem. They do no fully undersand he naure of he shock nor is ransmission. They ry o undersand i by applying a rial and error learning rule, bu hey never succeed in fully undersanding he complexiy of he world. This cogniive problem hen creaes he ineria in oupu and prices. Thus one obains very differen heories of he business cycles in he wo models 6 6 Criics of he heurisic model presened here may argue ha he comparison beween he raional and he behavioural model is unfair for he raional model. Indeed he heurisic model generaes ineria because he evaluaion and selecion process of he differen heurisics is backward looking. This is he reason why he behavioural model does no need lags in he ransmission process o generae ineria. However, i can be argued ha his evaluaion and selecion process can only be backward looking, and as a resul, he lags ha are presen in he behavioural model are wihin he logic of ha model. This conrass wih he lags inroduced in he raional model: hey come from ouside he model. See Milani(27b) who makes a similar poin conrasing raional expecaions models wih learning models. 9

21 Figure 4: Auocorrelaion coefficiens of oupu gap and inflaion Behavioural model Raional model auocorrelaion oupu auocorrelaion oupu auocorr y.5.4 auocorr y a and b a and b auocorrelaion inflaion auocorrelaion inflaion auocorr p.5.4 auocorr p a and b a and b Noe: see noe of able ; we have always se a = b Mankiw and Reis(22), (26) have inroduced a similar concep which hey call sicky informaion. There is a difference wih he concep of informaional ineria used in he presen paper hough. In Mankiw and Reis(22) informaion ineria arises because agens do no immediaely have access o he correc informaion. Once hey obain he informaion hey se heir plans opimally exacly as hey would do in a raional expecaions model wihou delays in he informaion flow. Thus in Mankiw and Reis(22) he failure o undersand is emporary. Afer a while raional expecaions re-esablishes iself. The differen naures of he business cycles in he DSGE-models and he behavioural model also have policy implicaions. In he DSGE-models now favoured by cenral banks, business cycle movemens in oupu and prices originae from price and wage sickiness. In order o reduce his kind of volailiy more flexibiliy in prices and wages is required. Tha is why many cenral banks call for more flexibiliy. In a more flexible world, cenral banks will no be called upon so ofen o sabilize oupu, and hereby se price sabiliy a risk. 2

22 In he behavioural model, business cycle movemens in oupu arise from informaional ineria. Thus, even if prices and wages become more flexible, his will no necessarily reduce he business cycle movemens in oupu. As a resul, sociey s desire o sabilize oupu will no be reduced. And cenral banks ha ineviably respond o hese desires will face he need o sabilize oupu a he risk of reducing price sabiliy. 5. The naure of uncerainy in he wo models The behavioural and he raional expecaions models produce a differen view abou he naure of uncerainy. We illusrae his feaure by presening impulse responses o shocks. Here I focus on he impulse responses o an ineres rae shock, defined as plus one sandard deviaion of he shock in he Taylor equaion. The peculiariy of he behavioural model is ha for he same parameers of he model he impulse responses are differen for each realizaion of he sochasic shocks. This conrass wih he raional expecaions model where he impulse response funcions are no sensiive o he realizaion of he sochasic shocks (keeping he parameers unchanged). Figure 5 shows he mean impulse responses o an ineres rae shock. These were consruced by simulaing he model, imes wih, differen realizaions of he shocks. The mean and median responses ogeher wih he sandard deviaions were hen compued. Figure 5 shows he mean and median response (he doed lines are + and 2 sandard deviaions from he mean response), exhibiing he sandard resul of an ineres rae shock on oupu and inflaion. However, he uncerainy surrounding his resul is considerable a leas in he shor run. This conrass wih he raional expecaions model which does no show such uncerainy (see figure 6). 2

23 Figure 5: Mean impulse responses o ineres rae shock in he behavioural model Noe: The doed lines represen he impulse responses wih +/- 2 sandard deviaions Figure 6: Impulse responses o ineres rae shock in raional model 22

24 Where does his uncerainy come from? No from parameer uncerainy. The same parameers are used in consrucing all our impulse responses. The answer is ha in his behavioural model each realizaion of he shocks creaes differen waves of opimism and pessimism (animal spiris). One could also call hese marke senimens. Thus a shock ha occurs in one simulaion happens in a differen marke senimen han he same shock in anoher simulaion. In addiion, he shock iself affecs marke senimens. As a resul, he shor-erm effecs of he same ineres rae shock become very hard o predic. Anoher way o inerpre his resul is o say ha he iming of he shock is imporan. The same shocks applied a differen imes can have very differen shor-erm effecs on inflaion and oupu. In oher words, hisory maers. Noe ha he uncerainy abou he impulse responses ends o disappear in he long run, as he effec of shorerm differences in marke senimens disappears 7. The previous discussion leads o he conclusion ha he naure of he uncerainy in he wo models is very differen. In he op down srucure of he raional expecaions models, agens capable of overseeing he whole picure, compue wih grea precision how hese shocks are ransmied. The quesion ha arises here is wheher he precision obained in his model does no creae an illusion among he praciioners of hese models abou wha one can know in economics. The conras wih he behavioural model is grea. The boom up srucure of his model is one in which agens have only limied informaion. These agens wih limied and heerogeneous informaion, follow rules of behaviour ha when ineracing wih oher rules lead o grea complexiy and a grea amoun of uncerainy abou how an ineres rae shock is ransmied. In fac our resuls sugges ha even if 7 This difference in he naure of uncerainy in a behavioural and a raional expecaions model has everyhing o do wih he fac ha he former has non-linear feaures while he laer is linear. Thus he addiional uncerainy produced by he behavioural model, i.e. he dependence of he impulse response funcions on he sae of he economy is he oucome of is non-lineariy. Raional expecaions models including he DSGE-models radiionally impose some linearizaion procedure. This is done for he sake of mahemaical simpliciy. I leads o a problem hough. If he microfoundaion of he model leads o a non-linear model, i is imporan o know how his non-lineariy (which is par of he micro-foundaion) affecs he dynamics generaed by he model. Eliminaing hese non-lineariies amouns o desroying informaion ha is relevan o predic he ransmission of shocks. This may no maer much for he long run, bu since he DSGE-models have he ambiion of forecasing he ransmission process, i is of significan imporance. 23

25 one knows he parameers of he model wih cerainy, i will no be possible o predic how a given shock in he ineres rae applied a a paricular ime will be ransmied in he economy. 6. The role of oupu sabilizaion Modern macroeconomics in general, and DSGE-models in paricular, have provided he inellecual foundaion of inflaion argeing. Unil he erupion of he financial crisis in 27, inflaion argeing sraegies had become he undispued policy framework modern cenral banks should adop. And mos did. The official holders of macroeconomic wisdom declared ha his sep owards inflaion argeing consiued a grea vicory of macroeconomics as a science (Woodford(29)). From now on we would be living in a more sable macroeconomic environmen, a Grea Moderaion. How hings can change so quickly. Inflaion argeing, of course, does no imply ha here is no role for oupu sabilizaion. DSGE-modelers who have pu a New Keynesian flavor in heir models, have always sressed ha wage and price rigidiies provide a raionale for oupu sabilizaion by cenral banks (see Clarida, e al(999), Gali(28)). This idea has found is reflecion in flexible inflaion argeing (Svensson(997), Woodford(22)). Because of he exisence of rigidiies, a cenral bank should no aemp o keep inflaion close o is arge all he ime. When sufficienly large shocks occur ha lead o deparures of inflaion from is arge, he cenral bank should follow a sraegy of gradual reurn of inflaion o is arge. The raionale is ha in a world of wage and price rigidiies oo abrup aemps o bring back inflaion o is arge would require such high increases in he ineres rae as o produce oo srong declines in oupu. Oupu sabilizaion in he DSGE-world, however, is very much circumscribed. The need o sabilize arises because of he exisence of rigidiies in prices ha makes i necessary o spread ou price movemens over longer periods. The limied scope for oupu sabilizaion is based on a model characerized by a sable equilibrium. There is no consideraion of he possibiliy ha he equilibrium may be unsable or ha flucuaions in oupu have a differen origin han price rigidiies. Should he scope for oupu sabilizaion be enlarged? In order o shed some ligh on his issue we derive 24

26 he radeoff beween oupu and inflaion variabiliy in he conex of he behavioural model, and we formulae some policy conclusions. The radeoffs are consruced as follows. The model was simulaed, imes and he average oupu and inflaion variabiliies were compued for differen values of he Taylor rule parameers. Figure 7 shows how oupu variabiliy (panel a) and inflaion variabiliy (panel b) change as he oupu coefficien (c 2 ) in he Taylor rule increases from o. Each line represens he oucome for differen values of he inflaion coefficien (c ) in he Taylor rule. Panel a showing he evoluion of oupu variabiliy exhibis he expeced resul, i.e. as he oupu coefficien (c 2 ) increases (inflaion argeing becomes less sric) oupu variabiliy ends o decrease. One would now expec ha his decline in oupu variabiliy resuling from more acive sabilizaion comes a he cos of more inflaion variabiliy. This, however, is no found in panel b. One observes ha he relaionship is non-linear. As he oupu coefficien is increased from zero, inflaion variabiliy firs declines. Only when he oupu coefficien increases beyond a cerain value (in a range.6-.8) inflaion variabiliy sars increasing. Thus he cenral bank can reduce boh oupu and inflaion variabiliy when i moves away from sric inflaion argeing (c 2 =) and engages in some oupu sabilizaion. No oo much hough. Too much oupu sabilizaion urns around he relaionship and increases inflaion variabiliy. Figure 7 allows us o consruc he radeoffs beween oupu and inflaion variabiliy. These are shown in figure 8 for differen values of he inflaion parameer c. Take he radeoff AB. This is he one obained for c =. Sar from poin A on he radeoff. In poin A, he oupu parameer c 2 = (sric inflaion argeing). As oupu sabilizaion increases we firs move downwards. Thus increased oupu sabilizaion by he cenral bank reduces oupu and inflaion variabiliy. The relaion is non-linear, however. A some poin, wih oo high an oupu sabilizaion parameer, he radeoff curve sars increasing, becoming a normal radeoff, i.e. a lower oupu variabiliy is obained a he cos of increased inflaion variabiliy. 25

27 Figure 7: Oupu and inflaion variabiliy Panel a Panel b 26

28 Figure 8: Trade-offs in he behavioural model B A How can we inerpre hese resuls? Le us sar from he case of sric inflaion argeing, i.e. he auhoriies se c 2 =. There is no aemp a sabilizing oupu a all. The ensuing oupu variabiliy inensifies he waves of opimism and pessimism (animal spiris) which in urn feed back on oupu volailiy. These larges waves lead o higher inflaion variabiliy. Thus, some oupu sabilizaion is good; i reduces boh oupu and inflaion variabiliy by prevening oo large swings in animal spiris. Wih no oupu sabilizaion a all (c 2 =) he forces of animal spiris are so high ha he high oupu variabiliy also increases inflaion volailiy hrough he effec of he oupu gap on inflaion (supply equaion). Too much oupu sabilizaion, however, reduces he sabilizaion bonus provided by a credible inflaion arge. When he cenral bank aaches oo much imporance o oupu sabilizaion i creaes more scope for beer forecasing performance of he inflaion exrapolaors, leading o more inflaion variabiliy. Figure 8 also ells us somehing imporan abou inflaion argeing. We noe ha increasing he inflaion parameer in he Taylor rule (c ) has he effec of shifing he radeoffs downwards, i.e. he cenral bank can improve he radeoffs by reacing more 27

29 srongly o changes in inflaion 8. The cenral bank achieves his improvemen in he radeoff because by reacing more inensely o changes in inflaion i reduces he probabiliy ha inflaion exrapolaors will end o dominae he marke, and as a resul i reduces he probabiliy ha inflaion argeing looses credibiliy. Such a loss of credibiliy desabilizes boh inflaion and oupu. Thus mainaining credibiliy of inflaion argeing is an imporan source of macroeconomic sabiliy in our behavioural model. The previous resuls sugges ha here is a relaionship beween he parameers c and c 2 in he Taylor equaion and he credibiliy of he inflaion arge. This relaionship can be analyzed in more deail. Inflaion credibiliy can be given a precise definiion in he model. I can be defined as he fracion of agens who use he inflaion arge o forecas inflaion ( inflaion argeers ). Thus when more agens use he announced inflaion arge o forecas inflaion, credibiliy increases. Figure 9 presens he relaionship beween inflaion credibiliy and he parameers c and c 2. On he horizonal axis he parameer c 2 (oupu parameer) is se ou; on he verical axis he inflaion credibiliy. The laer is obained by simulaing he model, imes and compuing he mean fracions of inflaion argeers for differen values of he c and c 2. Each curve represens he relaion beween credibiliy and he oupu parameer (c 2 ) for differen values of he inflaion parameer (c ). I has a non-linear feaure, i.e. when he oupu parameer c 2 increases his has he effec of firs increasing inflaion credibiliy unil a maximum is reached. Then credibiliy sars declining when c 2 increases furher. This non-linear feaure is found for all values of c. Noe ha he maximum poins obained in figure 9 correspond o he minimum poin of he radeoffs in figure 8. These resuls have he following inerpreaion. When he cenral bank increases is effor o sabilize oupu his has a firs a posiive effec on he credibiliy of is inflaion arge. The reason, as was discussed earlier, is ha by sabilizing oupu, he cenral bank also reduces he ampliude of he waves of opimism and pessimism hereby sabilizing oupu and inflaion. Inflaion credibiliy is maximized when c 2 is in a range beween.5 and. Beyond ha range furher aemps o sabilize oupu reduce inflaion credibiliy for he reasons given earlier. The ineresing aspec of his 8 A similar resul on he imporance of sric inflaion is also found in Gaspar, Smes and Vesin(26) who use a macromodel wih saisical learning. 28

30 resul is ha he opimal values of c 2 are in a range ofen found in economeric sudies of he Taylor equaion. Thus cenral banks seem o apply a degree of oupu sabilizaion ha is consisen wih our heory of animal spiris. Finally figure 9 shows ha for increasing values of c he credibiliy curves increase. Thus a cenral bank can improve is inflaion credibiliy by reacing more srongly o changes in inflaion. This feaure hen underlies he resul found in figure 8 ha higher values of c improve he radeoff beween inflaion and oupu variabiliy. Figure 9 Inflaion credibiliy and oupu sabilizaion One can conclude ha he behavioural model provides a differen perspecive abou he need o sabilize oupu. This is a model ha creaes endogenous movemens of he business cycle ha are correlaed wih waves of opimism and pessimism. They are also unrelaed o he exisence of wage and price rigidiies. These waves of opimism and pessimism boh influence he oupu gap and in urn are also influenced by he oupu gap. We show his wo-way causaliy feaure in able 2 were he resuls of a Granger causaliy es on he oupu gap and he animal spiris (as defined in secion 3) are presened. I can be seen ha one canno rejec he hypoheses ha animal spiris Granger cause he oupu gap and ha he oupu gap Granger causes he animal spiris. 29

31 This wo-way causaliy beween oupu gap and animal spiris creaes he possibiliy for he cenral bank o reduce he waves of opimism and pessimism by reducing he volailiy of oupu. In doing so, he cenral bank creaes a more sable macroeconomic environmen ha also helps o sabilize inflaion. Table 2: Pairwise Granger Causaliy Tess Null Hypohesis: Obs F-Saisic Probabiliy Oupu does no Granger Cause opimism E-4 Opimism does no Granger Cause oupu E-5 7. An exension of he behavioural model The behavioural model discussed in he previous secions uses he assumpion ha he fundamenalis forecasers of he oupu gap know is seady sae value. In his secion we drop his assumpion. Insead i will be assumed ha because agens do no fully undersand how he oupu gap is deermined, heir forecass are biased. Some agens are opimisic and sysemaically bias he oupu gap upwards, ohers are pessimisic and sysemaically bias he oupu gap downwards. ~ op The opimiss are defined by E y g (4b) The pessimiss are defined by ~ E pes y g (4c) where g > expresses he degree of bias in esimaing he oupu gap. The rule used by he exrapolaors remains unchanged. For he sake of convenience i is repeaed here, i.e. ~ c E y y (5) The model now has hree forecasing rules. As before a selecion mechanism is assumed, whereby agens can swich beween hese hree rules. This implies firs ha agens compue he performance (uiliy) of using hese hree rules. For he opimisic and pessimisic rules his becomes U op, k k ~ y E y 2 (8) k op, k k 3

32 U pes, k ~ y E y 2 (9) k k pes, k k The performance (uiliy) of he exrapolaing rule was defined in equaion () The corresponding probabiliies of using he hree rules now are: op, pes, exp U op, exp( U ) exp( U ) exp( U ) (2) op, pes, exp U pes, exp( U ) exp( U ) exp( U ) (2) op, pes, c, c, c, exp U c, exp( U ) exp( U ) exp( U ) (22) op, pes, c, The model was simulaed in he ime domain using he same calibraion as in he previous version of he model. The resuls are shown in figure. They are qualiaively he same as in he previous version, i.e. he model generaes similar endogenous business cycles ha are based on waves of opimism and pessimism. The oher resuls of he model (no shown here) are also similar in naure, i.e. he uncerainy surrounding he impulse responses and he naure of he radeoffs. 3

33 Figure : Oupu gap and animal spiris in a hree-agen model 8. Animal Spiris: heory and empirics The concep of animal spiris, i.e. waves of opimism and pessimism, has played a cenral role in he behavioural macroeconomic model presened in he previous secions. Is here an empirical counerpar for his concep? There is one, and i is widely used in day-o-day macroeconomic analysis. Many counries use survey based consumer and/or business senimen indicaors as a ool of analyzing he business cycle and as a predicive insrumen. The bes-known senimen indicaor in he US is he Michigan Consumer Confidence indicaor which has been in use since he 95s. The firs measures of consumer confidence were developed by George Kaona in he lae 94s (see Kaona(95)). Since hen similar indicaors have been implemened in a large number of counries (see 32