Volailiy as link beween risk and memory in Economics, Economerics and Neuroeconomics: an applicaion for he Bolivian Inflaion Rae 1938-2012 María Edih Chacón B. maredihc@homail.com Teacher and researcher CIDES UMSA. La Paz, Bolivia. Erneso Sheriff B. sheriff@ciede.ne Teacher and researcher CIDES UMSA and UPB. La Paz, Bolivia. Experimenal and Behavioral Economics: Oher Neuroeconomics Economerics: Time Series ABSTRACT This paper provides an indicaor ha measures memory as a sock. Memory affecs economic decisions hus he memory indicaor is useful o help in applied work, i was buil according o he sae of he ar in Psychology and Neuroeconomics and i is presened as a ime series; i is a recursive one and i is represened by an accumulaed measure of he volailiy. Many heories of risk have used volailiy indicaors o represen risk in he applied work. Risk valuaion is associaed o volailiy and i is very sensiive o periods in which i is measured; i is very sensiive oo o he ype of daa associaed o volailiy. In his paper we found ha he memory affecs risk valuaions and he link beween hem is a special kind of volailiy i.e. accumulaed volailiy wih an endogenous iniializaion period and compaible wih many Psychological hypoheses. The developed indicaor is compaible wih he economerics of saionary series, inegraed series and fracional inegraed series. These conribuions help o improve he sudy of hyseresis in applied economics, o develop more consisen links beween memory and risk in Neuroeconomics and, o obain more confiden ime series models in economerics using he new indicaor. 1
Volailiy as link beween risk and memory in Economics, Economerics and Neuroeconomics: an applicaion for he Bolivian Inflaion Rae 1938-2012 María Edih Chacón B. & Erneso Sheriff B. Index ABSTRACT... 1 1. Inroducion... 3 2. Psychology and Neuroeconomics of links beween Risk and Memory... 3 3. Volailiy and risk in economics... 7 4. Economic memory and an innovaive ime series indicaor for economic memory... 9 5. Memory and risk in he sudy of Bolivian inflaion rae... 13 6. Conclusions... 18 References... 19 Appendix : Mone Carlo Simulaions wih economic memory indicaor... 22 Simulaions wih uni roo series... 22 Simulaions wih saionary series... 24 Simulaions wih long memory saionary series... 25 2
1. Inroducion In his paper we presen an indicaor ha measures memory as a sock. Memory affecs economic decisions hus he memory indicaor was buil according o he sae of he ar in Psychology and Neuroeconomics and i is presened as a ime series; i is a recursive one and i is represened by an accumulaed measure of he volailiy. The paper is organized as follow. In secion 2 we discuss abou he links beween memory and risk aking accoun he heoreical and empirical work in Psychology and Neuroeconomics and is relaion wih economic decisions. In secion 3 we discuss abou he relaionship beween risk and volailiy in economics; in applied work hese differen conceps are aken as synonymous and we disagree wih ha approach inroducing memory as facor behind risk aversion and volailiy. In secion 4 we develop a memory indicaor aking he form of a recursive variance and we show is properies and we inroduce Monecarlo simulaions for a variey of ime series wih he new memory indicaor. In secion 5 we ake he Bolivian inflaion rae o explain is hisorical evoluion using differen memory indicaors wih a variable saring period reflecing ha indicaor is useful in he sudy of credibiliy. Finally secion 6 is dedicaed o show some conclusions. 2. Psychology and Neuroeconomics of links beween Risk and Memory Risk eiher as concep, consruc, paradigm, heory or macro heory is a erm of mulidisciplinary characer wih growing and recurren presence in diverse sciences 1. In his paper we will rea he risk in an enclosed way, saring from he revision of he conribuions in hree sciences Economy, Psychology, and Neuroeconomics in order o arrive o a definiion of Risk concep and hen o relae i wih Memory. 1 In Anhropology risk was opic of ineres for Mary Douglas, Wildavsky, Dake, Marris among ohers. The invesigaions in his field begun around 1980 being cenral concep for he elaboraion of he call culural heory of he risks he same one ha emphasizes he funcion of he social and culural conex in which people live like decisive of he learning of behaviors, beliefs, values and social represenaions, in his sense he risk is conceived like a "social consrucion" whose esimae, valuaion and behaviors presen culure variaions o culure. In Sociology risk is a caegory applied o he social analysis o undersand he conemporary socieies, in his ask hey highligh he conribuions of Luhmann, Giddens, Beck, Casel, Bourdieu, Rosanvallon, as well as Alaszewski, Budgen, Ekberg, Green, Zinn who sand ou in he creaion of a subdiscipline, he sociology of he risk. In general lines he social heories of he risk are susained in he idea of he "impermanence and hisoriciy of he phenomena". 3
In Economy i has been considered he risk and he uncerainy regarding he fuure, as subsanial elemens ha affec he relaive decisions o economic ends 2. In his fac resides he imporance of he sudy of he Risk. This concern has been capured in he formulaion of heories and explanaory models in which differen variables are ariculaed, in his conex hey sand ou wo focuses, he firs one ha is debaed in he supposiions of he raionaliy aking as focal poin "he individual hing" and he second, he insiuionalism proposal ha emphasizes he normaive marks in which he aciviy and he economic facs ake place. Wih he word "risk" we refer o hose decisions hose ha i is admied he possibiliy of esimae he consequences or alernaive resuls of an acion, ha is o say is relaive probabiliies. Alhough i is no possible o deermine he resul a priori on he oher hand i is spoken of uncerainy when i is no possible o deermine wih accuracy he resuls of he acions by no means assigning hem a probabiliy (Casro, e al., 2005, p. 238). In spie of his disincion, he economic heory oulines ha he relaive decisions o economic ends are always uncerain, because he agens have a "imperfec knowledge" abou he fuure (Marínez Franzoni, 2008, p. 24). In his logic he queries are guided abou he facors ha influence in he economic behavior, hey are considered very varied aspecs, such as radical doub, hope, fear, emoions, expecaions, and opinions regarding he fuure o inerpre marke behaviors, invesmen, employmen, consumpion, saving, liquidiy among many ohers 3. Wih his hemaic one inerface has been creaed wih he Psychology, firs discipline inside he human sciences ha i approached he "phenomenon of he risk" relaing i wih is percepion, he heories formulaed in his respec hey bolsered his invesigaion line saring from he decade of he years 1960, he discussion beween he objeciviy and subjeciviy of he risk 4, cenered in good measure he debaes 5. In his environmen i's 2 Risk was a cenral opic in he work of many auhors like Adam Smih, Schumpeer, Keynes, Von Neumann, Morgensern, Allais, Arrow, Pra, Sen, Sigliz among ohers. See (Mas-Colell & Whinson, 1995). 3 For example Keynes (1936) disinguishes among objecive and subjecive facors. The objecive facors are: a change in he wage uni; a change in he difference beween income and ne income; accidenal changes in capial goods value no considered when calculaing he ne income; changes in he discoun rae; changes in fiscal policy; changes in he expecaions abou he relaionship beween he presen level and he fuure of he income. The subjecive facors or reasons are: cauion (o form a reserve for coningencies); forecas (o anicipae income and consumpion); calculaion; Improvemen (o enjoy a growing consumpion); independence (sensaion of being able o sill make hings wihou inenion of specific acion); enerprise (o inves in speculaive projecs or business); pride (o bequeah a forune); avarice (Keynes, 1936, pp. 87-106). 4 The Dicionary of Pedagogy and Psychology (Ed. Culural, Madrid, 2006; 293) defines he word risk like "possible inciden, linked or concomian o a siuaion or aciviy can be objecive if i depends on he 4
remarkable he conribuions of wo currens: cogniive ha highlighs he imporance of he processes of aenion, sensaion, percepion, memory, hough, reasoning, language, beliefs, heurisic paerns and, he socioculural one ha emphasizes he influence of he social and symbolic environmen in he consrucion of inferences abou he risk. In he cogniive psychology memory highlighs as cenral hemaic, for example Mayer (1981) defines is sudy environmen as "scienific Analysis of he menal processes and human memory srucures wih he purpose of undersanding he human behavior", undersanding in his case as synonymous memory and knowledge. Memory becomes one of he more sudied opics; i is opical of ineres ha a he presen ime couns wih enormous invesigaive producion, which responds o he following quesions in general erms: How he human memory works? Are here differen ypes of memory? (Carwrigh, 2001). In his work we define memory as persisence of he informaion hrough he ime 6. Using a compuaional meaphor 7 we can describe informaion process in hree sages in he human memory sysem; o ranslae he daa in such a way ha allow ha he daa ener in he sysem, o sore or o reain he informaion hrough he ime and o recover and, o locae and o give he informaion when i is needed 8. I implies a series of processes ha hey impac in he consrucion and reconsrucion of his informaion (Canda Moreno, 2006). In his logical José Alameda 9 noices ha we only have memory of he informaion ha is assised and probabiliy ha an even akes place or subjecive if i is considered correc or incorrec he possibiliy ha i happens". I is disinguished among objecive risk when i is considered characerisic of he ask ha is carried ou and subjecive o ha people feel, has o do wih heir fears, individual or collecive insecuriies (Marínez Tavisco, 2009, p. 3). 5 Lisón, C. 2007:319 apud (Chacón, 2011). 6 In his definiion we considered as basic he disincions wrien by Von Foerser (1969) among sorage, recovery (sorage, rerieval), recogniion and memory (recogniion and recall); and prevens abou a confusion beween he vehicle of a poenial informaion wih he informaion iself, or he resuls of cerain operaions and he operaions hemselves. The human processor makes hrough neuronal mechanisms - maerial biophysical srucures, bioelecric, biochemisry - o fulfill funcions as hose of exracing informaion, o reain he same one, o idenify experiences and o classify hem inside oher previous ones, o make symbolic represenaions of hose experiences (Calle, 1977, pp. 95-132). 7 A model ha allows o design hypohesis and precise supposiions abou processes ha are no obvious for he direc experience (Carreero, 2001, p. 127). 8 The means ha he organism has developed o reain he informaion are known by he name of memory. In he case of he human beings exiss evidence of several memory mechanisms, in his way we have sensorial memory or buffer ha work while he percepual analyzer acs, shor erm memory ha allows o mainain alive images is inerpreaion according o he emporary conex in which hey ake place and he long erm memory ha implies a mechanism of permanen sorage (Mercado, 1978, pp. 67-75) 9 See (Alameda, 2000). 5
seleced according o variables as heir relevance, bigger caegorical adapaion, moivaion and emoional conen, being he aenion relaed wih processes of conrol of simuli o guide and o conrol he behavior. The relaionship risk - memory, becomes eviden when considering ha he way in which is coded, organize, sore and recover he informaion i will deermine he behavior of people, he organism ask help o he memory o inerpre informaion diffused in he ime in such a way ha he sense of cerain sensorial enrance, i can depend on evens happened lile ime before. (Cores, c 2000, p. 20). I makes reference o he sequence of behaviors in he differen sages ha i supposes he course of evens from he risk o disaser 10, describes a diversiy of such reacions as: eluion, concern, "psychological barrier", negaion, increduliy, anxiey, vulnerabiliy feelings and less defense sensaion, passiviy among ohers, ofen due o he poen effec associaed wih he rauma of evens ha hey implied damage, los, damages o he well-being and survival, in many cases hese feelings sill coninue when heir consequences have already been suffered, i is also observed ha he ideas and beliefs regarding he poenialiy of suffering "damage of he fuure '' hey can say so much in he memory in exposed people and even in non-exposed people o similar siuaions. The invesigaions in he field of he Neuroeconomics - a discipline ha originaes in he evens ha followed o he revoluion from he neoclassical economy in he 1930's and o he birh of cogniive neurosciences in he 1990's whose objec is o deermine how he human being makes decisions keeping in mind he operaion and neuronal brain aciviy - show ha exis differeniaed areas ha drive he accepance or search and aversion or eluion of risks. These are he nucleus accumbens for he pleasan emoions and anerior insula, nucleus parabranquial, sriaum, amygdala, halamus, gray periacueducus associaed o relaive negaive emoions o he loss, damage, hreaens 11. The damages of he cerebral amygdala are relaed wih lack of wisdom o ake risk money in bes; he lack of good operaion of he cerebral amygdala akes o no assising signs of risk, 10 The sages are: WARNING before he impac, THREAT, laer on in he ime in he measure ha he risk is developed and i shows direc indicaions of he disaser in which can become, IMPACT, momen of occurrence of he even, INVENTORY, recoun immediaely afer he impac, RESCUE, rescue and saving works and, RECOVERY laer sage o he even, prolonged in he ime where he reconsrucion of he los environmen is aemped. (Cores, c 2000, p. 19) 11 See (Yacubian e al.2006), (Dayan & Seymour, 2009, pp. 180-183). 6
while he excess in he work of his makes he individual o exaggerae he risks. When he simuli are perceived as "familiar, he amygdala remains in calm, ha which faciliaes he learning and he memorizaion - associaed o he hippocampus - of new informaion, bu when he simuli are ignored or hreaening, he level of anxiey of he brain rises, cenering he aenion in he immediae siuaion, his generaes a defensive behavior for he curren momen (Taylor, 2009, p. 37). The experiences of McGauch (1966) and Landfield (1973) have checked he role of he hippocampus specifically in he memory in he sorage and recovery of informaion linked o acivaion sysems (arousal) relaive o he medial sepum, he reicular formaion and he jagged region CA4 CA3. Douglas (1967) poins ou ha he hippocampus is relaed wih he memory of shor duraion, he area behind of he convoluion of he hippocampus paricipaes in he formaion of images, exercising inhibiory conrol in such a way ha he code of each curren siuaion depends on he percepual facors and of he analogy wih previous memoirs (Calle, 1977, pp. 122-123). 3. Volailiy and risk in Economics In he economic models he subjeciviy is expressed wih erms like "aiude o he risk" or "risk olerance", empirically i designaes he elecions of a person refleced paramerically, in urn hey sugges ha he behavior is moivaed for example by a sable consruc as he personaliy. However, one of he observed inconveniences is ha he same person can manifes differences in aking risks when he siuaions are changed: finances, healh, securiy, career, ehics, recreaion, work, social decisions. Consequenly or oher labels are used o designae hese variaions, or i becomes necessary o find a form of measuring he aiude o he risk so ha i shows he sabiliy hrough differen domains (Weber & Johnson, 2009, p. 133). The economiss Kenneh Arrow and James Pra derived a risk aversion measure independen of uiliy funcion; hey conneced risk aversion wih risk premium. They defined wo indexes ha specified how he risks ha a person akes can change as weighs of incremens. This measure of risk aversion is called Arrow Pra coefficien (absolue and relaive) (Varian, 1992, pp. 208-230) and (Weber & Johnson, 2009, p. 133). u"( w) R( w) u'( w) 7
Where R is he Absolue Risk Aversion coefficien, u is he uiliy funcion and w is he value of a risky income. The risk aversion supposiion implies ha E( w) E U ( w) relaive cos for risk, according o he Arrow-Pra condiion, is: U. So, he CR 1 V ( w) 2 2 E( w) Where ρ is he relaive coefficien of risk aversion (R/w), V(w) he variance of a risky income and E(w) he expeced value of w. In he previous secion we esablished ha many facors (neurological and psychological) are behind he curren value of ρ including memory. Tradiionally in he applied work ρ is aken as a consan including he specific assumpion ha ρ is consan so in order o evaluae he risk premium he main effors are focused in he variance calculaion and forecas. The lieraure of financial economerics is prolific, aking accoun of deerminisic condiional variance mehods o sochasic variance ones ( (Weber & Johnson, 2009, p. 134). As i was esablished ha ρ depends of memory, he calculaion of V and E are relaed wih memory oo in differen ways. In he specific case of V, memory affecs he horizon of calculus of V and he value of V iself. Usually V comes from an ARCH/GARCH ype model or sae/space model boh wihou an exogenous variable linked o memory (Tsay, 2005). The radiional economeric approach akes accoun saionary and no saionary series undersanding ha long infinie memory refers o non-saionary daa and shor memory refers o saionary daa, fracional inegraed series le work wih shor and long non-infinie memory. The neuroeconomic lesson of his ar is ha he hisory of non-saionary daa always affecs he curren value so is memory is infinie; his is compaible wih he psychological heory exposed before. Neverheless he economeric approach only le us o label he series as shor run, infinie run or large memory series wihou give us an amoun of memory in every period of ime. In Appendix we show differen Monecarlo simulaed series for saionary (shor and long memory) series and for non-saionary series. We can reformulae he Risk Premium as follow: 1 V ( w, M ) CR ( M ) 2 E( w, M 2 ) 8
Where M is he curren amoun of memory. V may change wih M or no depending of he ime properies of w. If w is a non-saionary ime series hen is memory is infinie and he amoun of M would deerminae he curren value of V. Tradiional variance models may incorporae M as exogenous argumen in order o predic V. 4. Economic memory and an innovaive ime series indicaor for economic memory "The memory is he capaciy ha has an alive organism - or a sociey - of conserving a prin of is experiences and of reacing in a siuaion in a such way ha keeps relaionship wih ha warehouse of experiences, ha which pus in relaion o he memory wih he informaion and he knowledge" (Del Rey Morao, 2005, p. 239). As we can see in he previous secion, memory has been considered synonym of knowledge or a leas an indispensable condiion for his. From he perspecive of he Cogniive Psychology, i can be defined as a process ha is par of he human sysem of prosecuion of informaion whose funcion implies he regisraion, sorage and recovery of daa (Ellis, 1986). I can be conceived as a consrucive process in which he adapaive variaion is he rule, his means ha he informaion doesn' ener direcly o he conscience, neiher i reproduces lierally, bu raher i follows differen phases in which are elaboraed and hey reconsruc inegraive unis, he informaion is conained in srucures ha ac as reference marks ha deermine he organizaion lines, relaionship and operaion of he behavior (Mahoney, 1983). The cogniive srucures ha make possible he memory spread o inroduce prejudices and disorions, since hey are inerconneced wih judges, beliefs, emoions and ineress of he fellows, i shows he qualiy mulimodal of he human memory, so much in he regisraion momen or code of informaion like when upgrading he impressions (Soliz Macias, 2005). These phenomena are suppored by experimenal sudies in which i is explained ha given a siuaion simulus, oulines are acivaed ha include in heir conained informaion and oher people's represenaions, denominaed by some auhors "inrusions" or "false alarms". Also he inerference phenomena and inhibiion have been commened (Guiérrez Calvo, 1988, pp. 81-109). 9
The recovery 12 or evocaion, in general don' ake place in a conscious way, his aspec has given place o disinguish among informaion "available" ha canno recover in direc form having sill been coded and regisered successfully and "accessible" he one ha recovers volunarily. The recovery will depend on several such aspecs as: he ype of ask, he level of he individual's developmen, he prominence of ousanding indicaions (emoional or percepual) he frequency in he repeiion of he even and he way how hese daa are organized, ha is o say he order in he regisraion phase will deermine he easiness and recovery speed, as well as he possibiliy o carry ou differen manipulaions and classificaions 13. A very imporan class of srucures is hose ha represen he classificaion in he ime. The aduls spread o build he evens of heir experience in a mark of emporal reference, in which he facs and life experiences of he pas are linked and hey anicipae he fuure evens, his explains he imporance of wha is generally denominaed "experience". The accumulaed informaion is used o anicipae he evens o come and o form expecaions 14. Consequenly, wha we denominae economic memory refers o he prins of relaive experiences o a specific economic phenomenon. Take as example he inflaion rae. Long periods of inflaion or violen acceleraions of he inflaion consiue by he ligh of he previous paragraphs, simuli ha are sored in he memory of long erm ha hey affec he behavior of people every ime ha "hey exrac" his informaion. In his way, he emporary ouline in conjuncion wih he memory of long erm would preven o consider he effec of a violen inflaionary acceleraion and/or a long period wih high inflaion raes, as a phenomenon ha has ransiory effecs in he behavior of he economic agens. In inflaionary conexs and pos inflaionary, he behavior of people can be drawn by he ligh of he emporary ouline and he memory of long erm: escape of he naional money, indexaion of conracs, speculaion, high risk discoun, ec. These srucures will serve as reference marks ha hey will impac in he aking of decisions, expecaions and fuure behaviors. 12 "The recovery of informaion of he memory is a sampling insance wih subsiuion, in his sampling class he producion of knowledge doesn' eliminae he informaion in he Long erm Memory, he effec of his sampling leads o he producion of a copy of he required informaion leaving inac he originally regisered copy" (Soliz Macias, 2005). 13 See (Soliz Macias, 2005), (Case, 1984) and (Carreero, 2001). 14 See (Carreero, 2001) and (Del Rey Morao, 2005). 10
Now we presen an indicaor ha measures he sae of he economic memory in each momen of he ime, sensiive o he longiude of he memory, associaed in urn o he credibiliy around he formaion of a new process generaor of daa for he economic variable sudied. We will call o his indicaor MEMON. MEMON is useful o show how slow i is he speed wih which ges los he memory of raumaic acceleraions of a specific economic variable. Taking ino accoun he characerisics of he "economic memory" commened lines up and, he fac ha he variabiliy of an or more variable i is a facor ha affecs he risk, he measure of appropriae volailiy i would be ha ha evaluaes i in an accumulaive way in he ime and no in a momen of he same one. Following Harvey and Shepard (Harvey & Shepard, 1993) he variances are also random variable and herefore, hey also possess emporary properies. An accumulaed measure of he variabiliy reflecs he variaion average of a variable making use of he whole memory ha one has of his variable, since a predicion of shor erm (for example a moving average) i would no reflec oally he risk involved in he same one. On he oher hand, when an economic series diminishes (for example, he inflaion rae when concluding a hyperinflaion), he risk ha he agens assign o he variables correlaed wih he economic variable doesn' diminish in he same proporion, reflecing a long memory as for he variabiliy of he economic variable sudied. I inends like a measure of he volailiy of an economic series o is recursive variance defined as: MEMON i 0 ( X ) 0 1 2 Where, 0 is he period of iniializaion of he agen's memory. A srong acceleraion in an economic variable (X) drives up is recursive average (µ), causing in urn ha he whole variance increases. However, when X reurns o is iniial levels, sill when he recursive mean also reurns o is iniial levels, he variance won' reurn o he same speed a his iniial level reproducing he phenomenon of asymmery behind many economic series wih hyseresis. So ha he recursive variance begins a reversion oward he exisen level before he acceleraion of X (for example a hyperinflaion), X for every period should always be smaller han is recursive mean in he nex periods. MEMON measures he sae of he economic memory in each momen of he ime, i is sensiive o he longiude of he memory, associaed in urn o he credibiliy around he 11
formaion of a new daa generaing process for any variable X. MEMON also reflecs he accumulaive effec in he ime of variaions in X, asymmeric beween periods of high levels of X and laer periods of low levels of X, and independen of he observed value of X in a momen of he ime. H is he period of iniializaion of he agen's memory. If in he period =1 a credible change of policy akes place (for example he Bolivian sabilizaion in Augus of 1985), he represenaive agen will refer from now on her M percepions. M will be calculaed from he period =1 and will more represenaive of he given curren risk for he new policy scene because he change was credible. The imporance of memory is cenral when valuing risks. The saring period from which he risk is valued deermines differen dynamics o he evoluion of he valuaion of macroeconomic risk. The memory of macroeconomic risk, represened as inflaionary memory, is bound sill, o macroeconomic shocks of a very remoe pas. The incorporaion of he memory of he agens in he valuaion of he risk can make more relaive he imporance of anoher group of psychological deerminans of he currency subsiuion (for example) which are he preferences, ha is o say, o simply prefer he foreign currency for pleasure. In he Appendix we draw sochasic saionary (shor and long memory) and non-saionary ime series and heir MEMON indicaor in red lines. We can see ha in he case of shor memory saionary daa he memory remains consan among periods afer a shor period of iniializaion. Even when he daa varies around an aracor 15 (say mean, median, ec.) he memory indicaor changes in a minimal way, he memory is shor and he effec of shock doesn remain along he ime, his is he radiional definiion of a shor memory saionary daa and MEMON reflecs i wih he addiion ha i shows he amoun of memory in every single period and i is a sochasic variable oo. The mos surprising resul we can see for he case of long memory saionary daa and for non-saionary daa (infinie memory). In hese cases MEMON moves in asymmeric way reflecing all innovaions sored as informaion for he fuure, when a shock ends MEMON doesn back o is iniial posiion or akes several periods o achieve ha. 15 Following (Granger, 1993). 12
5. Memory and risk in he sudy of Bolivian inflaion rae In spie of he abundan maerial ha exiss on he opic, he concep of inflaionary memory i has been linked o several meanings of he same one, i has had a non-explici formalizaion in he economic modeling. On one hand he inflaionary memory is linked wih he persisence of he inflaion. In oher words, when he economic foundaions no longer suppored big inflaion raes, he inflaion rae coninued being high. Tha phenomenon was known as inerial inflaion and i was linked o he memory of he economic agens ha hey coninued incorporaing in heir conracs, indexing formulas (indexaion) similar o hose used in inflaionary periods. Alhough his phenomenon (he inerial inflaion and heir persisence) has been research objec, is link wih he inflaionary memory in ime series has been weakly formalized incorporaing dynamic oulines mainly in he inflaion equaions. This dynamic srucure generally incorporaed finie and decreasing lags of he inflaion rae deermining a very shor memory ha mus drain, in he wors of he cases, some monhs afer of he sabilizaion program in absence of new shocks. Anoher linking of he inflaionary memory has o do wih he credibiliy. The design of many sabilizaion programs looked for o erase he inflaionary memory of he public in such a way ha is eliminaed he previously menioned ineria and he behavior "inflaionary" sill using indexaion mechanisms when he same ones were no longer necessary. The cenral argumen, appropriae wih he previous one, i was ha he mos orhodox sabilizaion were more effecive in presence of an inflaionary memory erased by he own sabilizaion program. The associaions of cerain ype of economic decisions wih he inflaionary memory have a horizon of shor and medium erm, bu he associaions of cerain hyseresis phenomena o he inflaionary memory were less frequen. During he high inflaion experience in Lain America many economic variables - paricularly real variables as consumpion, invesmen, expors, unemploymen and holding of real balances - showed negaive raes of growh because he macroeconomic chaos where he inflaion played an imporan role. Once reached he sabilizaion, he recovery of hese variables was much slower ha he reducion of he inflaion rae. Even when all he foundaions of such variables were already in he previous levels o he crisis, he same ones had no sill recovered heir iniial levels. The 13
inflaionary memory has been behind hese phenomena, in such a way ha in horizons of medium long erm, his variable coninues affecing he economic agens' decisions. In cerain momen of he developmen of he ar in his opic, i was associaed his inflaionary memory o he persisence of he inflaion ha in definiive is a opic separaed from wha implies he inflaionary memory jus as we are reaing. The persisence of he inflaion, ha is o say, he presence of inflaion raes above wha he foundaions would deermine, is parly a consequence of he inflaionary memory bu i canno be undersood as he inflaionary memory by iself. Indeed, many economic real variables, as consumpion, invesmen, expors, employmen and holding of real balances, faced violen urndowns because he macroeconomic crisis where he inflaion played a cenral role. Afer he successful sabilizaions, he recovery of hese variables was much slower ha he reducion of he inflaion rae. Even when all he foundaions of such variables were already in he previous levels o he crisis, he same ones had no sill recovered heir iniial levels. For i, we say ha he inflaionary memory has been behind hese phenomena, in such a way ha in horizons of medium long erm, his variable coninues affecing he economic agens' decisions. Anoher field of ineres is abou expecaions. An expecaion is an informed predicion of fuure facs (Sheffrin, 1985). The expecaions have been cenral in he heoreical developmens of he las 50 years, beginning in he definiions and formalizaions made in pioneer works of Allais (1958), Cagan(1956), Friedman(1956) and Muh (1961) 16. From he psychological poin of view, he expecaion is one of he four variables inside moivaional heory; i allows predicing he behavior of a person in any given siuaion. In his heory, he expecaion refers o he subjecive anicipaions of he individuals abou he resul of heir behavior; he individual esimaes he probabiliy ha a paricular reinforcemen happens if he/she behaves in cerain way in a cerain siuaion (Kazdin, 2001). The expecaions are based on he previous experience of an individual and hey spread o reflec he form in ha a person feels regarding a opic, no for force hey are based on all he perinen objecive daa neiher in he real esimae, based on rue facs. The formaion of expecaions is influenced by he percepive seleciviy. This process refers o he elecion of informaion ha comes from he facs; he seleciviy is guided in urn by 16 See (Sheffrin, 1985). 14
hose "personal consrucions" or schemaic paerns elaboraed by he fellow. They serve as base o organize he preliminary design of an individual, guiding is sraegies of facing a given siuaion (Shulman, 1988). Kazdin (2001) has poined ou how he expecaions in he field of he clinical invesigaion influence in he behavior of he fellows, hese effecs were denominaed "effecs of noninenional expecaions", o emphasize ha he researcher canno make nohing o influence in he answers of he fellows. The expecaions can lead o modify he posure, he voice one, he facial expressions, he form of giving he insrucions, and o influence in he answers of he paricipans in an experimen. If we make an exrapolaion o he economic behavior, i is jusified he meaning of he economiss in he sense ha he expecaions can sill influence in he economic variables when heir foundaions have no suffered movemen. The effecs of he expecaions received considerable aenion by he middle of he 1960 s, in he conex of he invesigaion in social psychology, hey were carried ou works in human and in primaes idenifying he characerisics of he fellows and how hey behave, ha is o say if hey ac in a professional, compeen, and relaxed way, and hey were relaed wih he magniude of he effecs of he expecaion (Rosenhal, 1966, 1976 menioned by Kazdin, 2001). The heoreical work of he economiss around he expecaions, alhough i has been inense from he menioned conribuions, has concenraed heir effors in o consruc models wih expecaions, ha is o say, in adoping cerain mahemaical and saisical supposiions o inroduce he expecaions in he economic models. In ha way, he economic hypoheses of expecaions don' ell us how he agens form heir expecaions, hey show us simply formulaions ha reflec a "as if hey made i". Lucas's developmens in 1976 and laer uned in a remarkable way he form of incorporaing he expecaions in he economic models. I responded o he episemological endencies of he ime and i ook ino accoun many aspecs referred o he imperfec, asymmeric and expensive informaion ha was reaed in previous papers (Sheriff & Chacón, 2007). Alhough hese conribuions are objec of coninuous revisions and amplificaions, i is clear ha here are many aspecs ha have no been sill incorporae in a formal way, alhough inuiive. Such i is he case of he memory. The shocks of credibiliy would only make unnecessary he use of las informaion for he predicion of he inflaion in presence of raional expecaions. In absence of shocks of credibiliy and supposing ha he expecaions are raional, he definiion of he vecor of informaion available I in he period {-1} is large, since i includes quaniaive informaion 15
and qualiaive informaion (conex or saes of he naure). So, differen poliical conexs and differen economic policies would lead o differen inflaion forecass. The consideraion of he concep of inflaionary memory refleced by MEMON prevens o make indiscriminae use of dummy variables o cach an isolaed even of economic policies and allow working in a more consisen way according o he principles of Psychology and Neuroeconomics. INFAND 1.2 1.0 0.8 0.6 0.4 0.2 0.0-0.2 40 45 50 55 60 65 70 75 80 85 90 95 00 05 10 Ilusraion 1: Bolivian inflaion rae (12 monh) 1938-2012 The inflaion rae in Bolivia is he hisory of recurren high inflaion periods mos of hem showing hyperinflaionary dynamics. As we can see in Char 1, he inflaion rae 17 series has many characerisics uncomforable in ime series: long rends, cycles, non-linear rends, condiional variance, and many ouliers, i is no clear if i shows seasonaliy. We ll use MEMON o improve he knowledge of he Bolivian inflaion rae. 17 Measured as P/(1+P) where P is he curren inflaion rae. 16
1.2 1.0 0.8 0.6 0.4 0.2 0.0 INFAND.07.06.05.04.03.02.01 MEMON2-0.2 1940 1950 1960 1970 1980 1990 2000 2010.00 1940 1950 1960 1970 1980 1990 2000 2010.14.12.10.08.06.04.02 MEMON_56.14.12.10.08.06.04.02 MEMON_86.00 1940 1950 1960 1970 1980 1990 2000 2010.00 1940 1950 1960 1970 1980 1990 2000 2010 Ilusraion 2: Memory indicaors for Bolivian inflaion rae 1938-2012 We calculaed MENOF for many assumpions abou he iniial period 0. In firs place we ook 0 as he firs single period wih exising daa; his assumpion implies an agen wih infinie memory. The char looks like simulaed chars for non-saionary daa (in fac INFAND is non-saionary according uni roo es). The memory sock (MEMON2) increases wih acceleraion in inflaion rae and rends o decay when he shocks end bu, wih new acceleraions he memory sock increases again. When Bolivia suppor a high inflaion process in he middle of 1950 s a sabilizaion program was adoped (called Eder Plan) in 1956 (December) and he inflaion rae fall quickly and he amoun of memory was decaying slowly. The memory abou his episode was sill presen when a hyperinflaion process begun a he beginning of he 1980 s explaining why he people overreac o he firs populis essays of sabilizaion. More ye, when he definiive sabilizaion was finally successful beween 1985 (Augus 29) and 1986 (January 15) 18 he memory sock (MEMON2) begun o decay slowly again and by he middle of 2013 he hyperinflaionary process apparenly was no forgoen and is far from is iniial levels of 1983. I can help o explain why many real Bolivian macro variables suffered hyseresis afer he sabilizaion process for a very long 18 The sabilizaion program called NPE (Nueva Políica Económica in Spanish) was inroduced in augus 29, 1985 bu he inflaion rae had a new crisis on December 85 and i was necessary a new adjus in January 86. 17
period. Many people preferring foreign money for ransacions and savings; speculaive aiudes in price formaion; very risk aversion o risk invesmens. If we incorporaed MEMON2 in formal models for hese real macro variables maybe he explanaion power will be improved. MEMON_56 was calculaed assuming ha Eder s Plan was credible and erased he inflaionary memory of Bolivian people. So, he calculus of MEMON_56 ook a new 0 in 1957. In ha hypoheical case we can see ha he 1974 s acceleraion (wih rural massacre included) under Banzer s dicaorial period affeced he memory indicaor wih a smooh urbulence bu he hyperinflaionary period was no forgoen ye even in 2013. Under assumpion ha NPE Program was full credible 19 MEMON_86 shows ha he hyperinflaionary process was forgoen around 2005. MEMON_86 helps o explain why he preference for domesic money is currenly dynamic bu in he period 1995 2000 wih similar moneary policy he preference for domesic money was minimal. In focus groups we can deec ha young agens 20 don ake accoun he hyperinflaionary process in heir decisions and oher whose were able o ake decisions in 1985 are very sensiive ye and off course ake accoun even now he hyperinflaionary process. 6. Conclusions In his paper a memory indicaor was developed measuring memory as a sock. The indicaor (called here MEMON) was consruced aking accoun he new encouner poins beween Psychology, Economics and Neuroeconomics. The memory indicaor akes he form of a recursive variance reflecing an asymmerical componen of volailiy. Volailiy is showing here as encouner poin beween risk and memory: how he memory affecs he measuremen of volailiy affecs in ime he risk premium forecasing. We saw for he Bolivian case how differen is he memory sock when a credible program is adoped and i is feasible o find differen measures of risk according of he memory saring period of he economic agens. Memory affecs economic decisions hus he memory indicaor is useful o help in applied work, i is able o be incorporaed as exogenous variable especially when non-saionary daa or long memory saionary daa are presen. A researcher can find 0 wih an insiuional 19 Undersanding as credible a memory erase afer sabilizaion program meaning a new value of 0. 20 People wih average age less han 35 years specially. 18
approach, qualiaive mehods or quaniaive ones (randomly or wih bes fi crieria searching, ec.). Models for variance can include MEMON as exogenous variable oo and i can improve he models because he memory indicaor reproduces some non-lineariies, rends and srucural changes. References Alameda, J., 2000. Aención, Percepción y Memoria., Madrid.: Universidad de Huelva. Calle, J., 1977. Sisema nervioso y sisemas de información. neurocibernéica del cerebro. Madrid: Pirámide. Canda Moreno, F. (., 2006. Diccionario de Pedagogía y Psicología. Madrid: Culural S.a.. Carreero, M., 2001. Inroducción a la Psicología Cogniiva. 2 ed. Buenos Aires: Grupo Ediorial Aique. Case, R., 1984. desarrollo inelecual: una reinerpreación sisemáica. En: Lecuras de Psicología del pensamieno. Madrid: Alianza. Casro, L., Casro, M. & Morales, J., 2005. Meodología de las ciencias sociales. Madrid: Tecnos. Chacón, M. E., 2011. Una revisión de las concepciones de riesgo, La Paz: CIDES. Cores, E., c 2000. La percepción psicológica del riesgo y el desasre. México: Fundación para la Gesión del Riesgo, FGR. Dayan, P. & Seymour, B., 2009. Values and Acions in Aversión, por, (2009) Ed. USA: Elsevier, pp. 175-188.. En: Neuroeconomics. San Diego: Academic Press, pp. 175-188. Del Rey Morao, J., 2005. La memoria caj negra de la comunicación, Madrid: s.n. Ellis, A., 1986. Fundamenos del aprendizaje y procesos cogniivos del hombre. México: Trillas. 19
Glimcher, P., Camerer, C., Fehr, E. & Poldrack, R., 2009. A brief hisory of neuroeconomics. En: P. Glimcher, C. Camerer, E. Fehr & R. Poldrack, edis. Neuroeconomics. Oxford: Elsevier, pp. 1-12. Granger, C., 1993. Wha are we learning abou he long-run?. The Economic Journal, Marzo.pp. 307-317. Guiérrez Calvo, M., 1988. Efecos inferenciales de la acivación, ipicidad e implicación en el aprendizaje de exos. Cogniiva, pp. 81-109. Harvey, A. & Shepard, N., 1993. The economerics of sochasic volailiy, Oxford: Oxford Universiy. Kazdin, A., 2001. Méodos de invesigación en psicología clínica. México: Pearson Educación. Keynes, J., 1936. The General Theory of Employmen, Ineres and Money. London: Macmillan. Mahoney, M., 1983. Cognición y modificación de conduca. México: Trillas. Marínez Franzoni, J., 2008. Arañando bienesar? Trabajo remunerado, proección social y familias en América Cenral. Quio: Colección CLACSO-CROP. Marínez Tavisco, J., 2009. Riesgo Y Sociedad. Ponencia De La Jornada De Indicadores De Seguridad.. Palmas de la Gran Canaria: Academia Canaria De Seguridad - Universidad De La Laguna, Las Palmas De Gran Canaria, 27/4/2009.. Mas-Colell, A. & Whinson, M. D., 1995. Microeconomic Theory. Oxford: Oxford Universiy Press. Mercado, S., 1978. Procesamieno Humano De La Información. México: Trillas. Peerson, R., 2007. Inside The Invenor s Brain. New York: Wiley. Pla, M. & Padoa-Schioppa, C., 2009. Neuronal Represenaions Of Value (2009) Usa: Elsevier, Pp. 441-462.. En: Neuroeconomics. San Diego: Academic Press, pp. 441-462. Sheffrin, S., 1985. Expecaivas Racionales. Madrid: Alianza Ediorial. 20
Sheriff, E. & Chacón, E., 2007. Psicología y economía: cómo procesan la información los agenes económicos. ABC Economía y Finanzas, pp. 74-78. Shulman, B., 1988. La erapia cogniiva y la psicología individual de Alfred Adler. En: Cognición y psicoerapia. Barcelona: Paidos. Smirnov, A. A., Rubinsein, S. L., Leoniev, A. N. & Tieplov, B. M., 1960. Psicología. México: Grijalbo. Smih, V. L., 2009. Experimenal economics and neuroeconomics. En: P. Glimcher, C. Camerer, E. Fehr & R. Poldrack, edis. Neuroeconomics. Oxford: Elsevier, pp. 15-19. Soliz Macias, V. H., 2005. Invesigación sobre flucuaciones de la memoria, México: UNAM. Taylor, J., 2009. Un Aaque De Lucidez. Buenos Aires: Sudamericana. Tsay, R. S., 2005. Analysis of financial me series. New Jersey: Wiley. Varian, H., 1992. Análisis Microeconómico. Barcelona: Bosch. Vigosky, L. S., 1985. Obras Escogidas Tomo III. Moscú: Comisión Ediorial para la edición en lengua rusa, Academia de Ciencias Pedagógicas de la URSS.. Weber, E. U. & Johnson, E. J., 2009. Decisions under uncerainy: psychological, economic and neuroeconomic explanaions of risk preference. En: Neuroeconomics. San Diego: Academic Press, p. 133. 21
Appendix : Mone Carlo Simulaions wih economic memory indicaor Simulaions wih uni roo series Y Y 1 u. Number of simulaions:2000. (Memory indicaor is prined in red) 22
23
Simulaions wih saionary series Y Y 1 u, 0.5. Number of simulaions:2000. (Memory indicaor is prined in red) 24
Simulaions wih long memory saionary series Y red) Y 1 u,0.5 0.99. Number of simulaions:2000. (Memory indicaor is prined in 25