Individual Decision-Making and Inflation Persistence

Transcription

1 Individual Decision-Making and Inflaion Persisence Gerald Karl Josef Seidel - 0 -

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3 Individual Decision-Making and Inflaion Persisence Disseraion zur Erlangung des akademischen Grades Dokor der Wirschafs- und Sozialwissenschafen (Dr. rer. pol.) vorgeleg im Fachbereich Wirschafswissenschafen der Universiä Kassel von Gerald Karl Josef Seidel Ersguacher Professor Dr. Björn Frank, Universiä Kassel Zweiguacher Professor Dr. Jochen Michaelis, Universiä Kassel Tag der Dispuaion: 0. März 04 I

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5 Acknowledgemens During my research on his disseraion, I received suppor from many people o whom I am very much indebed. Firs, I would like o hank my supervisor Professor Dr. Björn Frank for his excellen suppor and coninuous encouragemen. He provided me wih academic advice almos wenyfour-seven. Whaever quesion I had, he never los his enormous paience and direced me o a good soluion. I am especially graeful o him for awakening and wheing my ineres in he field of behavioral and experimenal economics. I am also graeful o Professor Dr. Jochen Michaelis. I very much enjoyed he inspiring and challenging discussions wih him on moneary macroeconomics, from which I grealy benefied. Similarly, I wan o hank Professor Dr. Peer Spahn. Having been his suden a he Universiy of Hohenheim a Sugar, he coined my way of macroeconomic hinking, providing me wih insighs from sandard New Keynesian as well as from compeing heories. When I worked for him as research and eaching assisan, he graned me a huge amoun of academic freedom (as for he conduc of classroom-experimens), and especially encouraged and suppored my raining in quaniaive mehods. As he work on a disseraion is an ineracive process, I am graeful o my academic eachers and colleagues, especially a he Universiy of Hohenheim and he Universiy of Mannheim, for many fruiful discussions. Similarly, I wan o hank he paricipans of conferences (such as of Verein für Socialpoliik, Economic Science Associaion, and Gesellschaf für Experimenelle Wirschafsforschung) and research seminars (e.g., a he Universiy of Tübingen and he Universiy of Zürich) where I presened early pars of my disseraion or relaed work, for ineresing discussions and helpful commens. Finally, I received a lo of emoional suppor and encouragemen from many friends and relaives, for which I am mos graeful. Especially, I am deeply indebed o my beloved parens o whom I dedicae my disseraion. I

6 Conens Acknowledgemens... I Conens... II Lis of Figures... IV. Inroducion..... Moivaion..... Srucure of he Thesis Endogenous Inflaion The Role of Expecaions and Sraegic Ineracion..... Absrac..... Inroducion Models of Aggregae Supply The New Keynesian Phillips Curve The Taylor (979) Model Aggregae Demand: Opimal Cenral Bank Policy Endogenous Inflaion in a New Keynesian World Endogenous Inflaion in a Taylor-Type Economy Simulaion Resuls Conclusions Appendix Muli-Period Conracs and Inflaion Dynamics Absrac Inroducion The Muli-Period Saggered Conrac Model Simulaion of he Model Taking he Hybrid Phillips Curve as a Benchmark Conclusion II

7 4. Fair Behavior and Inflaion Persisence Absrac Inroducion The Fuhrer and Moore Model and he Driscoll and Holden Criique The Exension of Driscoll and Holden s (003) Idea Discussion and Conclusions Fairness, Efficiency, Risk, and Time Absrac Inroducion The Model General Srucure Households Uiliy Producion Bargaining Soluion Measuring Fairness and Efficiency Resuls The Impac of Time Preference The Impac of Risk Aversion The Impac of Relaive Produciviy Discussion Conclusions References Zusammenfassung (Summary in German) Moivaion Fragesellungen und Vorgehensweise in meiner Arbei III

8 Lis of Figures. Impuls Response o u(=)=; Taylor (979) Model : k=0.5, ρ= Impulse Response o u(=)=; New Keynesian Phillips Curve: k=0.5, ρ= Response of Oupu o u(=)=; Taylor/New Keynesian PC: k=0.5, ρ= Response of Inflaion o u(=)=; Taylor/New Keynesian PC: k=0.5, ρ= Response of Inrinsic Inflaion o u(=)=; Taylor/New Keynesian PC 9.6 Auocorrelaion of Inrinsic Inflaion - α=, β=0.96, k=0.5, ρ= Auocorrelaion of Inrinsic Inflaion - α=, β=0.98, k=0.5, ρ=0 3.8 Auocorrelaion of Inrinsic Inflaion - α=, β=0.96, k=0.5, ρ= Auocorrelaion of Inrinsic Inflaion - α=0.5, β=0.96, k=0.5, ρ= Auocorrelaion of Inrinsic Inflaion - α=, β=0.96, k=0.5, ρ=0 34. Auocorrelaion of Inrinsic Inflaion - α=, β=0.96, k=0., ρ=0 35. Auocorrelaion of Inrinsic Inflaion - α=, β=0.96, k=0.8, ρ= Auocorrelaion of Inrinsic Inflaion - α=, β=0.94, k=0.5, ρ= Impulse Response (supply-led shock) Impulse Response (demand-led shock) Benchmark Hybrid Phillips Curve (supply-led shock) Benchmark Hybrid Phillips Curve (demand-led shock) Srucure of he Model Soluion o Bargaining wih Ouside Opion Case Soluion of Bargaining wih Ouside Opion Case Soluion o Bargaining wih Ouside Opion Case Soluion of Bargaining wih Ouside Opion Case Measuring Donaion Measuring Oupu and Welfare. 70 IV

9 5.4. Effecs of Parameer Change on Donaion (Baseline Parameerizaion) Effecs of Parameer Change on New Equilibrium (Baseline Parameerizaion) Effecs of Parameer Change on he Expeced Uiliy of A Effecs of Parameer Change on Producion Effecs of Parameer Change on B s Aspiraion-Oucome-Spread Effecs of Parameer Change on Welfare Effecs of Time Preference on Donaion d Effecs of Time Preference on New Equilibrium Effecs of Time Preference on he Expeced Uiliy of A Effecs of Time Preference on Producion Effecs of Time Preference on B s Aspiraion-Oucome-Spread Effecs of Time Preference on Welfare Effecs of Risk Aversion on Donaion d Effecs of Risk Aversion on New Equilibrium Effecs of Risk Aversion on he Expeced Uiliy of A Effecs of Risk Aversion on Producion Effecs of Risk Aversion on B s Aspiraion-Oucome-Spread Effecs of Risk Aversion on Welfare Effecs of Parial Oupu Elasiciy on Donaion d Effecs of Parial Oupu Elasiciy on New Equilibrium Effecs of Parial Oupu Elasiciy on he Expeced Uiliy of A Effecs of Parial Oupu Elasiciy on Producion Effecs of Parial Oupu Elasiciy on B s Aspiraion-Oucome-Spread Effecs of Parial Oupu Elasiciy on Welfare V

10 . Inroducion.. Moivaion The radiional main ask of cenral banks is o preserve price sabiliy. In doing so, he cenral bank deermines he economy-wide budge consrain wihin which decenralized decison-makers can se or bargain over nominal prices and wages. A he same ime cenral banks are supposed o pursue heir main ask of price sabiliy in a way ha does no harm he real economy, especially oupu and employmen, more han necessary (or arguable) for he achievemen of he main goal. As decenralized markes are highly complex, he ask of cenral banks is complex as well. Therefore, a srand of moneary lieraure developed ha suggess cenral bankers o 'experimen' when pursuing moneary policy. Experimenaion in his conex means o apply moneary insrumens more courageously o induce more variaion in inflaion, oupu and unemploymen, and, hereby, o learn more abou he srengh of he rade-off beween inflaion and oupu/unemploymen. Of course, experimenaion and learning in moneary policy can only be fruiful if he general srucure of he rade-off especially in ineremporal perspecive - is known. A his sage, he quesion arises wheher inflaion should be hough o be driven only by expeced fuure inflaion and he curren sae of he real economy, usually represened by he oupu gap or he deviaion of real marginal coss from seady sae, or wheher i is addiionally influenced by pas inflaion. Indeed, a significan number of empirical sudies come o he conclusion ha inflaion is auo-correlaed, i.e., i is persisen. For cenral banks, however, i is of grea relevance wheher his persisency of inflaion is 'inrinsic', an original and 'srucural' feaure of he economy 3, or wheher i is merely caused by he persisence of See, e.g., Beck and Wieland (00), Cogley, Colacio, Hansen, and Sargen (008), Cogley, Colacio, and Sargen (007) and Wieland (000a, 000b). See, e.g., Gali and Gerler (999), Rudebusch and Svensson (999), Gali, Gerler and Lopez-Salido (00), McAdam and Willman (004), and Chrisiano, Eichenbaum, and Evans (005). 3 The concep of 'insrinsic' inflaion persisence is closely relaed o Lucas' (976) claim for a sound microfoundaion of eonomic models. The exisence and degree of 'inrinsic' inflaion persisence is one ha does no depend on he policy of he cenral bank or on specific demand and supply shocks economic decision-makers are faced o. Speaking more echnically, an inrinsic inflaion persisence model is 'srucural' in he (narrow) sense of Lucas (976) if is fundamenal 'deep' parameers, namely hose ha encode inflaion persisence, are consan over ime and do no differ accross various policy regimes (Benai 009).

11 oher driving forces, namely expeced inflaion and real oupu (or real marginal cos, respecively). The laer case is ofen referred o as 'exrinsic' or 'inheried' inflaion persisence (see, e.g., Fuhrer 006). Exrinsic/inheried inflaion persisence can be considered o be he easier case for policy makers. If policy makers by he way in which hey ac or by modificaion of marke regulaions are able o reduce he persisence in he driving forces of inflaion, he ineremporal policy rade-off vanishes. If he pah of he real economy is brough back o is seady-sae, inflaion is brough back o is desired value, i.e., (slighly above) zero, as well. Being no longer confroned o ineremporal rade-offs, he policy-makers find hemselves in he siuaion of he 'divine coincidence' (see, e.g., Blanchard and Gali 007). Is persisence in inflaion expecaion, in one of he driving forces of inflaion, an empirically realisic and heoreically adequae assumpion? From a microeconomic as well as from a macroeconomic poin of view, he formaion of adapive expecaions canno be rejeced a priori. Especially in he conex of moneary economics wih is complex relaions i is hardly possible ha individuals are able o acquire and o process all relevan informaions (Sargen 993, p.3). Raionaliy urns ou o be 'bounded' (Simon 959, Gigerenzer and Selen 00). Consequenly, many macroeconomic models rely eiher on explicily adapive expecaion (e.g., Ireland 000, Robers 005) or on conceps of learning (e.g., Evans and Honkapohja 00, Bullard and Mira 00). Alernaively, he idea of raional expecaions is formally mainained bu informaion is assumed o be 'sicky', i.e., i is assumed o slowly disseminae among individuals (Mankiw and Reis 00). In he sicky informaion case, individuals have differen saes of informaion, resuling in consequences similar o ha of (parially) adapive expecaions. In whaever kind of way adapive inflaion expecaion migh be moivaed, i is challenged by he fac ha cenral banks use o announce heir policy arges (as a moneary aggregae or direc inflaion goal) so ha individuals (and organizaions) receive a clear orienaions in expecaion formaion. In doing so, he informaion processing requiremens are limied. And, a leas in he case of an independen cenral bank, he credibiliy of he cenral bank should no be a major problem of policy announcemens (Rogoff 985, Cukierman 99, Bomfim e al. 997, Huh and Lansing 000) 4. Also in respec o 'sicky informaion' hese 4 An alernaive opinion, however wih a focus on he specific siuaion of he Volcker disinflaion, is expressed in Ergec and Levin (003).

12 objecions are generally in line wih empirical findings: Alhough some auhors find evidence for 'sicky informaion' (Carroll 003, Klenow and Willis 007), i does no seem o be he limiing facor as prices are found o be more ofen reviewed han changed (Fabiani e al. 005, Coibion 00). As sickiness in inflaion expecaions is no he (finally) convincing reason ha explains acual inflaion dynamics, could inflaion persisence be inheried from sluggish effecs in he real secor? Indeed, Chrisiano, Eichenbaum and Evans (005) include adjusmen coss o invesmen in heir model ha resul in he sluggishness of oupu (and, consequenly, in inflaion). Sluggish responses of he real secor o shocks can also be caused by habi formaion in consumpion 5, where households' uiliy depends on he change rae raher han on he level of consumpion. Chrisiano, Eichenbaum and Evans (005) allow for habi consumpion, oo. However, he quaniaive effecs of hese ypes of real secor sluggishness are minor o and mainly depended on ha of backward-looking price indexaion (Collard and Dellas 006). Backward-looking price indexaion is a source of inrinsic inflaion persisence (Chrisiano, Eichenbaum and Evans 005, Seinsson 003, Smes and Wouers 003, 007) 6. If firms do no reopimize prizes every period bu (a leas parially) se prizes according o pas inflaion, pas inflaion will be a source of curren inflaion (in addiion o expeced fuure inflaion and he curren oupu gap) as described by he 'hybrid Phillips curve'. As he assumpion of pure price indexaion is somewha arbirary from a heoreical poin of view and hardly suppored by empirical evidence (Blanchard 009), is counerpar in he labor marke (wih poenial effecs on price-seing) wage indexaion can be observed in several OECD counries (Du Caju e al. 009). As inflaion persisence is no solely found in such counries wih formal or informal wage indexaion, indexaion should no be considered as a dominan source of sicky inflaion. In addiion, (a leas) formal schemes of wage indexaions can be avoided by regulaory means. Insofar, inflaion persisence caused by wage indexaion is no inrinsic in a narrow sense and of minor heoreical ineres. A quie inuiive mechanism o generae inflaion persisence is presened by Sheedy (00). If in a New Keynesian ype sicky-price model firms are no more randomly seleced o updae prices (as assumed by Calvo (983)) bu insead he probabiliy of a price change 5 Alhough imposing habi formaion in consumpion could be regarded as arbirary a firs glance, i is in line wih behavioral heories of he 'aspiraion level' (see, e.g., Simon 957). 6 In a sric sense, inflaion persisence generaed by backward-looking indexaion is only inrinsic/srucural as far as indexaion is policy-invarian and only caused by preferences, echnology and resource consrains. 3

13 increases wih he price duraion, pas inflaion will have an (equally direced) effec on curren inflaion. The influence of pas on curren inflaion is caused by a selecion effec on he various firms' abiliy of having been able or no o adap heir prices o shocks in recen periods: If a ransiory cos-push or demand shock occurs, firms ha are able o reac immediaely and change heir money prices, will raise hem and hereby he overall price level. All oher firms have o say wih heir money prices se in earlier periods. In he nex period, he laer firms will, if hey are able o change heir prices, 'cach up' o he overall price level ha remains comparably high due o price sickiness. In conras, he former firms will, if being able, 'roll back' heir money prices as he previous period's shock is no more in effec and he previously se prices appear o be oo high. If he hazard funcion of price changes is upward-sloping, i.e., if recenly se prices are less probably o be revised han older ones, he 'cach up' effec will dominae he 'roll back' effec, This resuls in a furher increase of he overall price level, (indirecly) caused by he shock in he previous period. 7 Inflaion appears o be sluggish. Unforunaely, Sheedy (00) excludes (for echnical reasons) models wih fixed price duraions 8 from his analysis, in conras o empirical evidence for seasonaliy in price changes (Nakamura and Seinsson 008, Dhyne e al. 005). More problemaically, he effec of lagged on curren inflaion is generally mirrowed by an impac of he wo-periods ahead expeced inflaion wih opposie sign. 9 However, neiher a dampening effec of fuure expeced nor of pas inflaion on curren inflaion is in line wih convenional wisdom. 0 Finally, as he slope of he hazard funcion ha governs he degree of inrinsic inflaion persisence empirically changes over ime, Sheedy's (00) model migh be criicized no o be (sricly) 'srucural' in Lucas' (976) sense (Benai 009). In recen years, he model by Ergec, Henderson and Levin (000) (EHL) evolved as he main framework for he analysis of moneary policy. In exension of he basic New Keynesian 7 In conras, a downward-sloping hazard funcion causes an effec of pas on curren inflaion wih a negaive sign. 8 A prominen example for a model wih fixed price duraion is he saggered price model by Taylor (979). 9 Similarily, he effec of he wo-periods lagged inflaion is mirrowed by he hree-periods ahead expeced inflaion and so on. 0 Of course, high inflaion expecaions can moivae he cenral bank o pursue a conracionary policy already in he curren period. Such a reacion, however, refers o he demand side of he economy and should be modelled by an appropriae cenral bank's policy funcion; i should no affec (he sign of) he Phillips curve coefficiens. In addiion, Sheedy (00) finds empirical evicende for a cyclical hazard funcion wih some coefficiens no being significanly differen from zero, in conras o he assumpion of an upward-sloping hazard funcion wih coefficiens generally being posiive. A similar criique applies o Fuhrer and Moore (995), Gali and Gerler (999), and Blanchard and Gali (007) (Benai 009). 4

14 model where only goods are differeniaed and sold a a monopolisically compeiive goods marke a prices ha are saggered according o he Calvo (983) mechanism, Ergec, Henderson and Levin (000) also assume ha labor services are differeniaed and wages are se in he same saggered way. Again, households opimize he presen value of uiliy and firms maximize heir iner-emporal profis. This resuls in wo differen ypes of Phillips curves, wih one describing he dynamics of prices and he oher one he dynamics of nominal wages. Whereas price as well as nominal wage inflaion is driven by heir own one-period-ahead expeced value and by he oupu gap, price inflaion is increased and nominal wage inflaion is decreased by a posiive real wage gap. The real wage gap is definded as he deviaion of he acual real wage from is (hypoheical) level in he absence of any nominal rigidiies. The inuiion behind he influence of he real wage gap is ha monopolisic compeiion ogeher wih nominal saggering drives a wedge beween he real wage and he rae of subsiuion (wage markup) as well as beween he real wage and he marginal produc of labor (price markup). Wih a posiive real wage gap (and he wage markup assumed o be a is desired level), he price markup is under is desired level so ha firms ha are o se prices in he curren period will increase prices and foser inflaion (e vice versa). Mos imporan from a policy perspecive, cenral banks are no more able a he same ime and wihin one period o bring price inflaion, wage inflaion and oupu back o heir seady-sae value. The sabilizaion of nominal and real aggregaes urns ou o be an ineremporal rade-off, he 'divine coincidence' (in a sric sense) is broken. However, Blanchard and Gali (007) show ha a weaker form of he 'divine coincidence' can be esablished if policy makers focus on a composie price-wage-inflaion rae. In his case, sabilizing a weighed average of price and wage inflaion is equal o sabilizing he disance of he oupu o is 'naural' level (in he absence of nominal rigidiies) 3. So, he pracical meaning of he generally exising ineremporal policy rade-off remains conroversal. As a naural consequence, a similar ambiguiy applies o he quesion wheher he EHL model exhibis inrinsic inflaion persisence. As he (pure) EHL price Phillips curve does no depend on pas (price) inflaion (bu on he curren real wage gap), is raional expecaions soluion exhibis inrinsic inflaion persisence depending on he degree of real wage rigidiy 3 For specific parameer values, even he full 'divine coincidence' emerges for he composie price-wage-inflaion and he (pure) oupu gap (Gali 008, p. 36 ff.) 5

15 induced by he acual parameerizaion (Knell 03) 4. Blanchard and Gali (007) find a similar posiive relaion beween real wage rigidiy (being imposed on heir model) and inrinsic inflaion persisence. The laer findings migh be regarded as he condenced resuls of he research on inflaion persisence in he las decade: As a lo of effor has been dedicaed o his opic, an enormous progress has been made in he undersanding of he driving forces behind inflaion persisence. Clearly, real wage rigidiy plays a major role in explaning sluggish inflaion. Ye, no all aspecs of his complex opic are fully undersood. Wih he following essays I ry o shed a leas a lile more ligh on some opics relaed o inflaion persisence... Srucure of he Thesis Chaper Endogenous Inflaion The Role of Expecaions and Sraegic Ineracion compares he capabiliy of wo differen models of nominal saggering o produce inflaion persisence. Calvo (983) assumes ha an (infiniely) large number of firms adjus heir prices infrequenly, each firm only in a period ha is deermined by a fixed probabiliy. In conras, Taylor (979) relies on he idea of an economy in which only wo (ypes of) firms se heir prices in an alernaing manner. Whereas he Calvo (983) model is more flexible and could be regarded as a generalizaion of Taylor (979), he laer fis quie well o he empirical evidence on seasonaliy in price changes (Nakamura and Seinsson 008, Dhyne e al. 005) 5. The major difference, however, is ha he Phillips curve derived from he Taylor (979) specificaion includes an addiional erm of lagged oupu whereas his lagged erm disappears in he Calvo (983) Phillips curve due o he assumpion of an infiniely large number of firms and an approximaion in is derivaion. Taking his difference seriously, I evalue boh ypes of Phillips curves in a framework wih a 'imeless' opimizing cenral bank (Jensen and McCallum 00). In doing so, I amend he resuls of Kiley (00) who found ha he Calvo (983) model shows more persisence afer a money supply shock han he Taylor (979) counerpar. In conras, I find ha in he 4 Naurally, he raional expecaions soluion does no include an inflaion expecaion erm and is insofar closely relaed o he radiional 'riangle' model (Gordon 998). 5 Dhyne e al. (005) repor ha price changes are especially likely in January and Sepember (wih an average duraion of price spells from 4 o 5 quarers). 6

16 Taylor (979) case a 'imeless' opimizing cenral bank will ac more carefully knowing ha a policy induced effecs on he oupu gap will influence inflaion even in he following period. Even furher, he cenral bank will be aware ha firms expec he effec of he curren oupu gap on nex-period inflaion and, in urn, will moderae heir price seing behavior (and inflaion) addiionally. This more complex ineremporal ineracion beween price seing firms and he cenral bank in he Taylor (979) case resuls in more persisen inflaion han in a model economy wih Calvo (983) saggering. This resul is compaible wih ha of Dixon and Kara (006) who criicize Kiley (00) for comparing boh models wih an inappropriae parameerizaion. Chaper 3 Muli-Period Conracs and Inflaion Dynamics exends he analysis on he capabiliy of he Taylor model o generae a realisic degree of inflaion persisence. As Taylor (980) has been especially successful in generaing persisence of he oupu gap by employing muliple, i.e., more han wo conracs, overlapping each oher, I derive he Phillips curve resuling from hree and four overlapping nominal conracs. In doing so, he number of leads and lags of inflaion and he oupu gap ha governs curren inflaion is exended. In conras o he wo-period Taylor-ype Phillips curve, in my model version wih muli-period saggered conracs pas inflaion does influence curren inflaion. However, he muli-period model version predics pas inflaion o affec curren price dynamics wih a negaive sign. This means ha pas (posiive) inflaion should ceeris paribus have a disinflaionary effec on he curren period. Alhough his specific resul is in conras o economic inuiion, he proposed muli-period model version is sill a candidae o (exrinsically) generae persisen inflaion due o srong and long-lasing effecs of he pas oupu gap on curren inflaion. Similarily, Coenen and Wieland (005) sae ha he muli-period version of he Taylor model reasonably well fis he Euro area daa. To challenge and o complemen Coenen and Wieland's (005) resuls, I generae impulse response funcions on grounds of heir unconsrained VAR(3) regression and of he muli-period Taylor-ype Phillips curve, esimaed by he same daa, and compare i o impulse responses of a hybrid Phillips curve. The simulaion resuls show ha in he case of a demand as well as of a supply shock he hybrid Phillips curve much beer resembles inflaions dynamics based on he unconsrained VAR regression han he muli-period Taylor model. The Taylor-ype model especially fails o generae sufficien persisence in inflaion dynamics and urning poins ha follow several periods afer he shock. The urning poin of he Taylor-based inflaion impulse response even precedes ha of he oupu gap. 7

17 Chaper 4 Fair Behavior and Inflaion Persisence conribues o he discussion abou he foundaion of he hybrid Phillips curve. I reviews he criique of Driscoll and Holden (003) on Fuhrer and Moore (995) and exends heir argumens ino an alernaive direcion. Fuhrer and Moore (995) argued ha (under he condiion of wo-period alernaing wage saggering) wage seers se heir nominal conrac wage so ha is real value equals he real value of he nominal wages ha are se by oher wage seers in he previous period (and are sill valid) and of wages ha will be se in he nex period. (Addiionally, hey assume he curren oupu gap o influence he curren real wage aspiraion.) Assuming fixed price markups, Fuhrer and Moore (995) derived a hybrid Phillips curve ha relaes curren inflaion no only o fuure expeced inflaion and he curren (and pas) oupu gap bu also o pas inflaion. Driscoll and Holden (003), however, had been able o show ha, if one akes Fuhrer and Moore's (995) wage seing reasoning lierally, heir model collapses o ha of Taylor (980) where lagged inflaion has no impac on curren inflaion. While aking Driscoll and Holden's (003) criique seriously, I exend heir real wage equaion by a erm ha accouns for inequaliy aversion. Based on Falk and Fischbacher (006), I assume ha he real wage aspiraion of wage seers is (addiionally) increased if hey experienced lower wages in he previous period han oher wage seers (e vice versa). In doing so, I relae he saggered wage seing model o he broad experimenal lieraure ha finds evidence for oher-regarding preferences, and I complemen macroeconomic research ha applies relaed assumpions such as efficiency wages (Danhine and Kurmann 006) or wage norms (Gerler and Trigari 009). I find ha wih a moderae degree of inequiy aversion, he modified wage seing equaion resuls in a hybrid Phillips curve ha is (observably) equal o he one originally presened by Fuhrer and Moore (995), i.e., ha is able o generae inrinsic inflaion persisence. In chaper 5 Fairness, Efficiency, Risk, and Time I presen a model ha allows o analyse he relaionship (especially) beween fairness aiudes and ime preference (impaience). The scope of his analysis is o conribue o bridging he gap beween empirical evidence from experimenal economics and macroeconomic modelling (as advocaed by Akerlof 00). One impedimen o incorporaing behavioral aspecs o sandard macroeconomics is ha several behavioral models capure differen deviaions from fully raional and uiliy- 8

18 maximizing behavior, however, up o now one general framework is missing ha reas all known behavioral aspecs in an inegraed way. Therefore, many radiional heoriss rejec behaviorally moivaed modificaions of preferences as 'arbirary' and call for an endogenous modelling of such effecs. A second challenge is ha modern macroeconomic models are mosly based on ineremporally opimizing agens, whereas models of oher-regarding preferences do no capure he aspec of ime preference. Therefore, I presen a model ha builds on purely uiliy-maximizing agens where (observably) fair behavior is an endogenous oucome and ime preference is explicily modelled. In he model, wo individuals have o ake acion in wo periods. In he firs period, he wo individuals are endowed wih differen amouns of goods. The beer endowed individual can donae a share of his endowmen o his less endowed counerpar. In he second period, he wo individuals are able o join in a common producion employing specific human capial which hey can build by means of he goods hey received in he firs period. The produced goods will be disribued among he wo individuals as agreed on before he producion by alernaing-offer bargaining (Såhl 97, Rubinsein 98). If he wo individuals do no agree on a common producion, hey direcly can consume heir endowmen from period. The same is rue in he case ha a leas one of he individuals has o leave he model world afer he firs period which makes common producion impossible. The leave of one individual will ake place wih a small bu posiive probabiliy o induce uncerainy abou he 'fuure' (second period) and, hereby, ime preference. The model oucome indicaes ha (seemlingly) fair behavior and ime preference are negaively correlaed. The more an individual is impaien, he less he is willing o donae a share of his endowmen o his poorer counerpar. In conras, a higher ime preference moivaes he poorer individual o increase her aspiraion of receiving a donaion from he beer endowed individual. This means ha a higher ime preference leads o sronger disribuive conflics in an economy which is indirecly suppored by experimenal evidence (Güh e al. 008). A second imporan finding is ha fairness aiudes are posiively affeced by efficiency. Beer endowed individuals are willing o donae more o oher individuals he higher producive hey will be in he second period. Complemenarily, producive bu less endowed individuals aspire higher donaions from heir beer endowed counerpars. Ineresingly, he model presened in chaper 5 exhibis some srucural similariies o he macroeconomic model by Erceg, Henderson and Levin (000): A cenral assumpion in 9

19 boh models is ha agens opimize heir (expeced) uiliy due o ineremporal consrains, more precisely, due o own decisions ha are valid for more han one period. Fundamenal o boh models as well is ha individuals offer heir human capial wih some degree of monopolisic power. This raises he quesion wheher he EHL model iself could be regarded as a model of ineremporal fairness. A leas, he quesion should be discussed wheher real wage rigidiy (which migh be an indicaor for fairness aiudes) is an oucome of wo combined ypes of nominal rigidies or wheher fairness aiudes may induce (or increase and/or spill over) he rigidiy of a leas one of he nominal variables. The laer conjecure would be in line wih empirical findings ha wages and prices feed ino each oher and ha wage and price changes are linked more closely bu ake place less frequen, he higher he labor cos share of he firm is (Druan e al. 009). In any case, he model presened in chaper 5 provides valuable insighs in he relaionship beween fairness aiudes and ime preference, wih boh aspecs being modelled explicily. 0

20 . Endogenous Inflaion The Role of Expecaions and Sraegic Ineracion.. Absrac Macroeconomic flucuaions are always he resul of complex ineracive processes. For his reason, our challenge of he widely used New Keynesian Phillips Curve builds on Taylor's (979) version, which provides room for a richer sequenial and ineracive srucure. We show ha he Taylor model can be fruifully complemened by he assumpion of a imeless opimizing cenral bank. The macroeconomic equilibrium exhibis a significan degree of inflaion ineria which is an endogenous economic oucome and no merely he consequence of exogenous persisence in aggregae real aciviy. This resul amends earlier work by Kiley (00) who found he New Keynesian Phillips curve o show more persisen reacions han is Taylor (979) companion when being exposed o an exogenous moneary shocks. JEL classificaion: E 3, E 58, C 6, D 84, L 6. Keywords: Inflaion persisence, endogenous dynamics, imeless opimizaion, cenral bank behavior, saggered conracs... Inroducion Following he seminal paper by Fuhrer and Moore (995), a vas number of empirical sudies showed ha pas inflaion is an imporan and significan variable in explaining curren inflaion. 6 In conras, heoreical Phillips curve models derived from microeconomic principles relae curren inflaion only o fuure expeced inflaion as well as curren and/or pas excess demand bu no o pas inflaion. 7 If one akes such Phillips curve equaions as a 6 See, e.g., Gali and Gerler (999), Rudebusch and Svensson (999), Gali, Gerler and Lopez-Salido (00), McAdam and Willman (004), and Chrisiano, Eichenbaum, and Evans (005). 7 One major excepion is Sheedy (00). He is able o derive a Phillips curve where curren inflaion is influenced by lagged inflaion. However, he one-period lagged inflaion erm is generally mirrowed by a wo-period ahead

21 descripion of an independen economic relaionship, hey ell us ha he dynamics of inflaion is auoregressive only o ha degree o which is he excess demand, he main driving force. The perspecive of aking he Phillips curve independenly of is economic environmen, however, is hardly in line wih he real economic world. In realiy, aggregae supply (as desribed by he Phillips curve) is only one side of he economy, which is no independen from is counerpar. Workers and capial owners, whose decision-making is represened in a sylized form by he Phillips curve, are concerned abou and confroned o aggregae demand condiions, o which hey reac in an ineracive way. In paricular, workers and capial owners form expecaions on fuure demand in he economy. In order o cope wih his ineracive srucure of an economy, we ry o endogenize inflaion expecaions, which are a main variable in modern ypes of he Phillips curve. As economic counerpar we inroduce a cenral bank ha minimizes a social loss funcion, characerized by he quadraic deviaions from zero-inflaion and seady-sae growh. We pursue in ha way in order o analyze he endogenous dynamics of inflaion. The respecive procedure, i.e., dynamically opimizing he cenral bank s social welfare funcion while aking he Phillips curve as consrain, is quie well-known in he moneary policy lieraure. For example, Svensson (999) and Vesin (00) used his mehod o compare differen moneary policy sraegies. The purpose of his paper is a slighly differen one. Insead of comparing wo differen policy sraegies, we analyse how he enire model economy is affeced when he srucure of is supply side is varied. Aggregae supply is mos frequenly represened by he sandard New Keynesian Phillips curve (e.g., Gali 00), which describes curren inflaion as a funcion of merely curren excess demand and fuure expeced inflaion. In conras, Taylor (979) provides a much simpler alernaive. Taylor (979) s model is less general and only based on quasimicrofoundaion. This simpliciy, however, allows Taylor (979) o absain from approximaions ha ignore sraegic ineracions beween individual price seers. As a consequence, Taylor (979) provides a somewha richer inflaion dynamic han he sandard New Keynesian Phillips curve. More precisely, in Taylor (979) inflaion depends no only on curren excess demand and inflaion expecaions bu also on pas excess demand. inflaion expecaion erm of opposie sign. This does, in our view, no mee he sylized facs of inflaion dynamics.

22 This seemingly small difference is of grea consequence. A deviaion of oupu from seady-sae does no only aler curren inflaion bu also causes disinflaion in he nex period o be cosly. In addiion, his fuure consequence is even anicipaed in presen ime, as described by inflaion expecaions being aken as explanaory variable. Therefore, we expec ha his seemingly small modificaion by Taylor (979) is imporan in an ineracive perspecive wih endogenous cenral bank behavior. Whereas he difference beween he sandard New Keynesian Phillips curve and he Taylor (979) model already has been sudied in respec o exogenous moneary shocks (Kiley 00) 8, we analyse he wo differen Phillips curve seings in a model economy wih endogenous moneary policy. In his case of endogenous policy, he individuals, who are represened by eiher of he Phillips curves, anicipae ha he cenral bank will minimize he social loss from inflaion and unemploymen in an ineremporal perspecive. In oher words, hey do no merely reac on exogenous evens. We can show ha, in conras o Kiley (00) s work, he Taylor (979) model urns ou o endogenously produce more inflaion ineria han is New Keynesian counerpar. The remainder of he paper is organized as follows: In he nex secion, he wo differen versions of he Phillips curve are derived. The mehodology will be explained in secion.4 and applied o he wo alernaives in secions.5 and.6. In secion.7 he resuls are simulaed and visualized. Secion.8 concludes..3. Models of Aggregae Supply In he following secion, we derive he wo slighly differen ypes of Phillips curves from microeconomic principles. Firs, we describe he widely used New Keynesian Phillips curve. As we are ineresed in inflaion dynamics, we concenrae on he price seing mechanism and leave ou oher aspecs of economic decision-making. 9 Secondly, we provide inuiion for he Taylor (979) ype of nominal dynamics. 8 Dixon and Kara (006) criicize Kiley (00) for comparing boh models wih an inappropriae parameerizaion. 9 For he enire microfoundaion of he New Keynesian Phillips curve, including aspecs of consumpion and labor supply, see, e.g., Gali (008) or Sbordone e al. (00). 3

23 .3.. The New Keynesian Phillips Curve The New Keynesian Phillips Curve is based on Calvo s (983) model of parial price adjusmen. Calvo (983) assumes ha firms adjus heir prices infrequenly. Furhermore, he assumes ha opporuniies o do so arrive according o an exogenous Poisson process where (-ω) is he consan probabiliy ha a firm can adjus prices in he curren period. Roemberg (987) claims ha represenaive firms i ry o minimize he ineremporal sum of squared deviaions of heir (fixed) prices o he profi maximizing prices of he respecive period. 0 He shows ha firms se prices according o x j0 j j E p * (.) j where x is he price ha is opimal for he adjusing firms, β is he discoun facor represening ime preference, ω he firm s probabiliy of currenly being inhibied from adjusing prices, and Ep*+j is he curren expecaion of he j period s ahead price level ha would be profi-maximizing in he absence of any price-seing resricions. Equaion (.) describes he adjused prices o be a weighed average of he curren and fuure expeced arge prices p*+j. The currenly adjusing firms opimal price x can be rewrien as weighed average of he curren arge prices p* and he expeced opimal price of he following period s adjusing firms, Ex+, x p * E x. (. ) Assuming ha he arge price level p* depends on curren oupu y as well as on he curren aggregae price level p, equaion (. ) can be replaced by x y p E x (. ) 0 For furher deails, see also Walsh (003). 4

24 where γ is a posiive consan coefficien, which depends on he goods price elasiciies of demand, and ν caches influences on pricing oher han price level and aggregae demand. Hereby, ν=ρ ν- + ε is a sable firs order sochasic process. The dynamics of he aggregae price level, in urn, can approximaely be described by p x p (.) if he number of firms is sufficienly large. The equaions (. ) and (.) can be reformulaed and combined o describe he inflaion dynamics of he model: If we ake equaion (.) and is one period s ahead expecaions o eliminae x and Ex+ from equaion (. ) we receive p p p y E p p (.3) which can be rewrien as y E (.3 ) as π=p-p-. Simplifying noaion, we ge E ky u (.3 ) where ky is inended o represen he curren demand side effecs and u=ρ u- + ε all oher, mainly he curren cos push effecs on inflaion dynamics. The derivaion of his Calvo (983) ype Phillips curve is based on criical assumpions. Especially equaion (.) is an appropriae approximaion of aggregae price dynamics only if excess demand varies jus moderaely and if he number of firms is large, i.e, if price seing of In conras o sandard noaion he effecs of excess demand are normalized o ky insead of ky. This noaion is comparable o he one of he Taylor (979) model where k(y +y -) represens demand side effecs on inflaion. 5

25 a single firm does no influence he aggregae price level and specific demand for anoher firm s good o a significan exen. If hese assumpions are no me, he derived descripion of inflaion dynamics lacks of imporan sraegic ineracion effecs ha exis in he real world. Furhermore, one should hink abou eliminaing he aggregae price level in equaion (. ) by ieraively insering he curren and han lagged versions of equaion (.): This procedure shows ha price adjusmen also depends on pas values of excess demand. Alogeher we see ha, due o he sequenial srucure of he price seing process, he influence of pas values on curren aggregae inflaion is in line wih he poenial sraegic effecs menioned above. As Calvo s (983) parial adjusmen model can be solved only wih approximaions poenially disregarding sraegic ineracion effecs, we sugges o addiionally analyse he earlier and more simple Taylor (979) model which does no compel o use he menioned approximaions..3.. The Taylor (979) Model Insead of parial price adjusmen, he Taylor (979) model relies on he idea of an economy where wo (ypes of) firms se alernaely heir prices. The sequenial srucure of he pricing decisions is deerminisic. Firms se prices p such ha hey cover he average of he conrac wages x 3 ha are currenly valid, plus a mark-up μ p x x. (.4) The variables represen log values, and, for simpliciy, he mark-up is se o μ=0. Workers orienae heir wage aspiraion on he curren sae of he business cycle, y. As he expeced real wage during he nominal wage conrac period is ½[(x-p)+(x-Ep+)], unions se nominal wages according o For a relaed discussion of he limiaions of firs order linear approximaions, see Michaelis (03). 3 In he Taylor (979) model x represens he opimal nominal wage o be se by he workers or a union, repecively, whereas in he Calvo (983) model i sands for he opimal price o se by he firm(s) in charge. As nominal wages in he former and nominal prices in he laer model are he respecive microeconomic key variable, i is in our case - no unprecise bu economically appropriae o use he same label for hem. In doing so, we are in line wih sandard noaion. 6

26 x p E p y (.5) where δ is he wage elasiciy of aggregae demand. Insering he wage seing equaion (.5) in he (simplified) price equaion (.4), we ge p 4 p 4 p 4 E p 4 p y y. (.6) Subracing (¾ p + ¼ p-) from equaion (.6), deviding he resul by ¼, and noing ha π=p-p-, we ge E y y (.6 ) To make equaion (.6 ) comparable o equaion (.3 ), we discoun he variables of he former equaion o presen ime, simplify by aking δ=k, and add u o represen cos push effecs on inflaion E ky ky u (.6 ) where u=ρ u- + ε, again, is a sable auoregressive process. The saggered price ype Phillips curve according o Taylor (979) has a srucure similar o he parial price adjusmen Phillips curve ha follows from Calvo (983)..4. Aggregae Demand: Opimal Cenral Bank Policy As argued above, from our poin of view i is no sufficien o appraise he wo derived ypes of Phillips curves independenly from demand side condiions. Aggregae demand is no purely exogenously given bu ineracs wih aggregae supply which we describe by he Phillips curve. Therefore, we will evaluae he wo derived ypes of Phillips curves by confroning hem o aggregae demand, which is governed by he cenral bank. 7

27 In line wih he general course of acion in he moneary policy lieraure, we assume ha he cenral bank minimizes a social loss funcion l, which depends on inflaion π and oupu y as nominal and real variable, respecively: l y (.7) The social loss is a weighed sum of he squared deviaion of (curren) inflaion π from price sabiliy, π=0, and oupu y from is seady-sae pah where α is a posiive coefficien. We assume ha he cenral bank is perfecly able o conrol he aggregae oupu level y by is policy insrumens while we, as usual, absain from modelling he ransmission process explicily. Hereby, we also absrac from possible problems of he adopion of policy insrumens. Alhough mos cenral banks are no exposed o direcly binding resricions in he conduc of heir fuure moneary policy (Clarida, Gali, and Gerler 999, p. 97), we claim ha he cenral bank does no pursue a discreionary policy. In conras, we propose ha he cenral bank adops a policy sraegy which is opimal over an infinie horizon. Moreover, we assume he cenral bank o ake even a imeless perspecive 4, i.e., o operae in a way ha is no only opimal in respec o he fuure bu also from he pas poin of view. This means ha he cenral bank does no ake individuals price or wage seing decisions as given bu punishes hem if hey did no adap o is course of macroeconomic sabilizaion. In oher words, he moneary auhoriy pursues is sraegy of ineremporally minimizing social loss as if i was already credible in previous periods. 5 Speaking in formal erms, he cenral bank will dynamically opimize is loss funcion subjec o he respecive Phillips curve being he consrain. 6 Using Lagrangian, we ge L E 0 y F (.8) 4 For deails on he imeless perspecive, see Jensen and McCallum, For relaed problems of credibiliy and heir possible soluion, see, e.g., Walsh (003), Chaper For mehodological issues, see Currie and Levine (993) and Woodford (999). 8

28 where ½ф is he muliplier associaed wih he consrain a ime and F represens equaion (.3 ) or (.6 ), respecively. Differeniaing he Lagrangian o π and y and seing he resuls equal o zero, yields he opimaliy condiions. As will be shown in he nex secion he differeniaion wih respec o π provides differen resuls for =0 and >0. This is he case because he expecaions of presen inflaion, E-π, have already been deermined one period ago and, herefore are cancelled ou when differeniaing wih respec o =0. As he cenral bank is assumed o adop a imeless perspecive, only he condiions for >0 are applied and he resuls for =0 are ignored..5. Endogenous Inflaion in a New Keynesian World In his secion we use he mehod described above and apply i o he case of he sandard New Keynesian Phillips curve. Wih he Lagrangian being L E y ky u (.8 ) 0 he firs order condiions resul in, 0 (.9.) 0 (.9.), y k, 0 (.9.3) Combining he firs order condiions o eliminae he muliplier ф, we receive he condiions for he cenral bank s opimal policy y, 0 (.0.) k y, y 0 (.0.) k k 9

29 As he cenral bank is conducing is moneary policy in a imeless perspecive, i will ignore he presen ime condiion and ac according o equaion (.0.) from he very beginning. By rewriing (.0.) as k y (.0. ) one can see ha a imeless cenral bank maximizes is welfare by increasing he oupu gap proporionally o he curren level of inflaion. Hereby, he policy reacion will be he sronger, he more effecive a reducion in aggregae demand is for he reducion of inflaion and he weaker he social preferences for real oupu are. Insering he opimal policy condiion (.0.) ino he Phillips curve yields a sochasic difference equaion for y which describes he ime pah of excess demand as an endogenous policy resul y b C y E y bc k b C u (.) where bc ½α(+β)+k. The sable soluion of (.) is y C y C u (.) wih and C C b C bc C k b C k k 4 4k C 4 k 4k 0

30 as ηc є (0,). This resul, in urn, can be combined wih he opimaliy condiion (.0.) which yields he endogenous inflaion dynamics, resuling from he ineracions on he macroeconomic level C C u u k (.3) or C u u k k k k (.3 ) Thus, in a New Keynesian world inflaion urns ou o be a sable AR()-process, wih an increase in he cos pressure (Δu>0) driving curren inflaion upwards (as ηc<0)..6. Endogenous Inflaion in a Taylor-Type Economy Afer having derived he endogenous resuls for he New Keynesian benchmark, we proceed in he same way for an economy in which prices are se in line wih Taylor (979). From he modified Lagrangian 0 u ky ß ky y E L (.4) he firs order condiions are derived, which for 0 L are he same as in he New Keynesian economy 0, (.5.) 0, (.5.)

31 L bu differ for 0 y y k k, 0. (.5.3) Concenraing on he relevan case of a imeless moneary policy sraegy, we ge he opimal condiion or, (.6) k k E y y 0 y k E. (.6 ) Compared o he New Keynesian benchmark case (equaion.0. ), an opimally working cenral bank will reac on average half a period earlier on inflaion (and even process inflaion expecaions) when i is confroned wih Taylor-ype price seers (equaion.6 ). By insering he opimal policy condiion (.6) ino he aggregae supply equaion following from Taylor (979), we, again, ge a sochasic difference equaion ha describes he endogenous ime pah for y y k b T y k b T E y k b T E u k b T u (.7) where bt α(+β)+k β - (+β) and Eu+=ρu. For appropriae parameer 7 values, he difference equaion (.7) yields a single sable soluion which is y Ty T u (.8) 7 For a ime discoun facor β = 0.96 (assumed conrac lengh: year) η T є (0; ) if k є (0.44; 0.939). If he cenral bank has no ime preference, β =, here is always a single and sable soluion for all posiive values of k, however, η T > 0 only for k <.

32 3 wih k k k k k k k k k b b T T T and k k b k T T T T. To deermine he endogenous dynamics of inflaion, we subsiue ou y from (.8) by insering he opimal policy (.6), and we receive T T T u u k. (.9) In he Taylor (979) world, he endogenous ime pah of inflaion depends on lagged inflaion and he previous period s change in cos push pressure. For (ηt-)<0, he previous period s inflaion has a deflaionary influence on he curren period bu increases inflaion, again, anoher period laer. An increase in he cos pressure fuels inflaion wih a lag of one period. In conras, in he New Keynesian world (equaion.3), lagged inflaion increases curren inflaion and only in he direcly following period; he inflaionary effec of an increase in cos pressure occurs wihou delay. These resuls are surprising a firs glance. As an opimally operaing cenral bank in a Taylor (979) economy (equaion.6 ) is parly forward-looking and fighs inflaion on average half a period earlier han in a New Keynesian economy (equaion.0. ), one migh expec ha endogenous inflaion depends on shorer lags in he former case. Equaions (.3) and (.9), however, show he opposie. As a cenral bank in he Taylor (979) economy knows ha a curren reducion in excess demand reduces inflaion also in he following period, i will apply is policy insrumens in a more careful and emporarily exended way han a cenral bank in a New Keynesian economy. In he laer environmen aggregae demand direcly influences

33 inflaion only in he curren period (equaion.3 ). In boh cases, he policy effecs are reinforced by he forward-looking behavior of he price or wage seers. Clear predicions, however, are hard o derive from he analyical soluion only, which depends on a bundle of parameers. This fac reflecs he high complexiy of a macroeconomic sysem in which a forward-looking cenral bank ineracs wih forward-looking agens in an economy wih overlapping conracs. Therefore, in he nex secion he resuls are simulaed for a broad range of parameer values..7. Simulaion Resuls In his secion we will conduc impulse response exercises o ge a more precise idea how oupu and inflaion evolve endogenously in reacion o a cos push shock of size % of is equilibrium value. Thereby, we proceed in he following way: Firs, we explain he simulaion exercise and describe he resuls for he Taylor (979) economy. Secondly, we compare he resuls o ha of a New Keynesian economy and give some explanaions for he observed differences. Thirdly, we briefly refer o variaions in he parameers in order o show ha he obained resuls are robus for a broad parameer range. Saring poin of he simulaion is an economy in equilibrium 8 and in absence of shocks. In period, he cos push erm is increase by % over is equilibrium value. The values for inflaion and excess demand are compued for he nex 0 periods according o he respecive dynamic soluions for he endogenous ime pah: Taylor economy: y Ty T u (.8) ~ T T T k in * u u y y u (.9 ) ~ k (.9 ) New Keynesian economy: y C y C u (.) C Cu u k (.3) ky u (.9 ) in 8 I.e., log-values of inflaion and excess demand are zero. 4

34 where in is inrinsic inflaion, i.e., he fracion of inflaion ha is no caused by excess demand or a cos push shock. Noe ha our noion of inrinsic inflaion is slighly differen from he noion of inrinsic inflaion persisence (see, e.g., Fuhrer 006). Whereas inrinsic inflaion persisence refers o inflaion ineria ha is no explained by he persisence of he oupu gap or of inflaion expecaions, inrinsic inflaion describes ha fracion of he curren inflaion level ha is no (direcly) caused by he oupu gap. Insead, i is due o he ineracion beween he moneary auhoriy and he decenralized wage and price seers in he marke (whom we assume o apply raional expecaions (Muh 96, Lucas 976)). We use, here, he similar noion inrinsic inflaion as we are ineresed in wha drives inflaion dynamics apar from he direc influence of he well-known sources. A special issue is he inflaion oucome in he Taylor (979) economy (equaion.9). In his paricular case he analyically precise inflaion dynamics are dominaed by a cycling paern. This cycling effec is due o he overlapping srucure of he Taylor (979) model and he merely sylized microfoundaions of is agens (equaion.4 and.5). In order o sress he medium erm business cycle aspecs of he model economy he somewha arificial cycling componen is removed. This smoohing procedure is done by subracing he seady-sae * ampliude of he cycling componen,. As sandard seing, we fix he relevan parameers as follows: The cenral bank s relaive preference for aggregae oupu compared o price sabiliy is. The discoun facor, reflecing ime preference, is 0. 96; herefore, he corresponding rae of ime preference is 4% per period. The responsiveness coefficien 9 of inflaion on excess demand, which reflecs he inverse of he marke power of he price or wage seers, is k Finally, he cos push shock is assumed no o show auocorrelaion, 0, in he sandard case. Black lines show he ime pah of oupu, purple lines describe he dynamics of inflaion or smoohed inflaion, respecively, whereas orange lines represen he purely inrinsic inflaion. 9 As inflaion and excess demand are denoed in log values, his coefficien is approximaely equal o he inflaion elasiciy of excess demand. 5

35 Solid lines are he endogenous oucome of he Taylor economy, dashed lines refer o he New Keynesian world. As we see in figure., he cenral bank in he Taylor (979) world immediaely fighs agains he inflaionary pressure of he cos push shock aking place in period. This is done by he reducion of aggregae oupu, i.e., by creaing an oupu gap. This oupu gap is smoohly reduced in he subsequen periods and, provided ha here is no furher supply side shock, converges o is seady-sae. Smoohed inflaion is increased as a consequence of he iniial cos push. However, his effec is parially offse by he lack of aggregae demand as inended by he moneary auhoriy. Due o he sluggish influence of excess demand on inflaion, he iniial rise of prices is revered o deflaion in period, before he sae of price sabiliy is approached again. Inrinsic inflaion, which is driven by fuure inflaion expecaions, is pushed o is negaive range as he deflaionary policy reacion on he cos push is correcly anicipaed by price seers. From hen on also inrinsic inflaion converges back o is equilibrium pah. Oupu gap and (negaive) inrinsic inflaion influence smoohed inflaion o a comparable degree. Figure.: Impuls Response o u(=)=; Taylor (979) Model : k=0.5, ρ=0. 6

36 Figure. shows ha in he New Keynesian world he endogenous reacions of oupu and inflaion on he cos push shock are similar o ha of he Taylor (979) economy. Only he ampliude of inflaion seems o be smaller in he New Keynesian case. For deails, however, le us direcly compare he respecive variables in he following. Figure.3 shows how he cenral bank reduces oupu in response o a cos push shock. The policy acion is clearly sronger in he New Keynesian case. This in line wih our predicions. A Taylor (979) world cenral bank more carefully reduces excess demand, knowing ha his reducion will have he same inflaion reducing effecs in he nex period as i had in he curren one. Inflaion dynamics has a similar srucure in boh ype of economies, as figure.4 shows. In he Taylor (979) economy, however, he cenral bank leaves more room o shif he cos push shock ino prices. Consequenly, deflaion in he subsequen period occurs o a somewha minor exen. The resuls for inflaion are in line wih wha we have learned abou he differen oupu dynamics of boh economies (figure.3). Figure.: Impulse Response o u(=)=; New Keynesian Phillips Curve: k=0.5, ρ=0. 7

37 Figure.3: Response of Oupu o u(=)=; Taylor/New Keynesian PC: k=0.5, ρ=0. Figure.4: Response of Inflaion o u(=)=; Taylor/New Keynesian PC: k=0.5, ρ=0. 8

38 Figure.5: Response of Inrinsic Inflaion o u(=)=; Taylor/New Keynesian PC. So, are differences in inflaion dynamics only he direc resul of differen oupu reacions in he wo economies? Figure.5 shows ha in boh economies inrinsic inflaion, which is neiher due o excess demand nor cos push bu solely driven by expecaions, increases in a similar way when a cos push shock occured. However, inrinsic inflaion converges more smoohly back o equilibrium in he New Keynesian world. In order o beer undersand his fac, we will consider he auocorrelaion of inrinsic inflaion. Figure.6 shows he firs order auoregression coefficiens of inrinsic inflaion (aken period by period). The blue columns represen he New Keynesian economy, he yellow ones are he resuls in he Taylor (979) world. We find ha auocorrelaion of inrinsic inflaion is higher in he Taylor (979) world, even if only o a small bu consan exen. The only excepion of his fac we find in period. Here, he Taylor (979) economy shows by far a much smaller degree of auocorrelaion han he New Keynesian economy, and i is especially smaller han is own auocorrelaion in he following periods. This effec can be explained by he addiional oupu lag in he Taylor (979) ype Phillips curve. Price seers know ha he reducion in excess demand, pursued o figh cos push inflaion, will dampen prices also in he second bu no anymore in he hird period. Consequenly, inflaion expecaions are already reduced in period. One can resume ha he Taylor (979) ype Phillips curve, due o is exra lag, is one period in delay in geing he urn-around back o equilibrium. 9

39 Figure.6: Auocorrelaion of Inrinsic Inflaion - α=, β=0.96, k=0.5, ρ=0. Bu is wha we observe in figure.6 a general resul? In order o see wheher he finding ha he Taylor (979) economy experiences a higher degree of auocorrelaion in inrinsic inflaion migh only be due o he specific parameerizaion, we vary each of he main four parameers, while keeping he oher hree parameers consan. (The parameer variaions are α=0.5, α=; β=0.94, β=0.98; k=0., k=0.8; ρ=0.5). As a resul, we see ha he levels of auocorrelaion vary when he parameers are varied, however, he srucure of he endogenous dynamics mainly remains unchanges. For deails, we refer o he Appendix where, he sake of clariy, we have moved o he respecive figures. One major excepion from finding qualiaively unchanged resuls when we vary he parameers, is he case of a ime preference of Figure.7 shows ha, when ime preference is low, auocorrelaion is lile higher in he New Keynesian han in he Taylor (979) case. As individuals wih low ime preference assess fuure evens lower han presen or even pas ones, he lagged oupu erm of he Taylor ype Phillips curve receives a higher weigh. This migh be he reason why in he presence of low ime preference a Taylor (979) economy converges especially fas o equilibrium. 30

40 Figure.7: Auocorrelaion of Inrinsic Inflaion - α=, β=0.98, k=0.5, ρ=0. Remarkable is also he endogenous oucome for an auocorrelaed cos push shock (ρ=0.5). Figure.8 exhibis ha he auoregression coefficien of inrinsic inflaion is no consan over ime. I is highes direcly afer he occurrence of he cos push shock and hen converges o he value of he auocorrelaion of he shock iself. The laer, however, does no preven a Taylor (979) economy from experiencing a higher auocorrelaion of inrinsic inflaion han he New Keynesian one. 3

41 Figure.8: Auocorrelaion of Inrinsic Inflaion - α=, β=0.96, k=0.5, ρ= Conclusions Nominal as well as real macroeconomic flucuaions are always he resul of complex ineracive processes. For his reason, we challenged in he conex of our model economy - he widely used New Keynesian Phillips Curve by he (seemingly more simple) version developed by Taylor (979). The simpler approach, however, proved o provide more room for a richer sequenial and ineracive srucure. Exposing he Taylor (979) model o a imeless opimizing cenral bank, we are able o reproduce a significan degree of inflaion ineria which is endogenous in he spiri of an ineracive economy and no merely he consequence of exogenous persisence in real oupu. We pursued our analysis in he perspecive of an endogenous economic sysem. Thereby, we amended earlier work by Kiley (00) who also considered he New Keynesian Phillips curve and is Taylor (979) companion. In conras o our approach, Kiley (00) represened he economy s demand side by exogenous moneary shocks which, of course, do no depend on price and wage seers behavior. Thus, in his approach inflaion is a direc response o exogenous shocks, whereas in our case he pah of inflaion is deermined by a goal- 3

42 oriened cenral bank which ries o offse undesirable exogenous shocks. Insofar, i is no surprising ha Kiley (00) finds he New Keynesian Phillips curve o creae more inflaion persisence han he Taylor (979) model, whereas we for mos parameer values came o he opposie resul. A beer knowledge abou causes and characerisics of inflaion persisence is necessary for a precise, arge-oriened moneary policy. Therefore, we carried ou simulaions o disenangle cos push, aggregae demand and inflaion expecaions as disinc sources of inflaion ineria and o ge an impression of heir relaive imporance. The major insigh from our model, however, is more general: Sraegic ineracion, prevalen beween he cenral bank and price seers as well as among price seers, is a major candidae o explain he slaggness inflaion dynamics. 33

43 .9. Appendix Figure.9: Auocorrelaion of Inrinsic Inflaion - α=0.5, β=0.96, k=0.5, ρ=0. Figure.0: Auocorrelaion of Inrinsic Inflaion - α=, β=0.96, k=0.5, ρ=0. 34

44 Figure.: Auocorrelaion of Inrinsic Inflaion - α=, β=0.96, k=0., ρ=0. Figure.: Auocorrelaion of Inrinsic Inflaion - α=, β=0.96, k=0.8, ρ=0. 35