12 Dynamic Models with Sticky Prices

Transcription

1 Economics 314 Coursebook, 2014 Jeffrey Parker 12 Dynamic Models wih Sicky Prices Chaper 12 Conens A. Topics and Tools... 1 B. Undersanding Romer's Chaper Romer s building blocks... 3 Macroeconomic equilibrium wih predeermined prices... 8 Macroeconomic equilibrium wih fixed prices... 9 Evaluaion of he Fischer and Taylor models Calvo model Caplin-Spulber model Danziger-Golosov-Lucas model Mankiw and Reis: sicky informaion vs. sicky prices C. Suggesions for Furher Reading Original papers on wage-conracing models Papers on opimal indexing Seminal papers on sicky prices Oher heoreical approaches o price adjusmen D. Works Cied in Tex A. Topics and Tools In Romer s Chaper 6, we sudied a firm s decision o change prices vs. keeping prices sicky as hough he price change were an isolaed even ha would happen only once. Firms in he Chaper 6 model have a pre-se menu price of ambiguous origin, hen decide wheher or no o change i aking ino accoun he curren period s profis a he pre-exising price vs. he opimal price. A more complee model would consider he implicaions of oday s price seing for fuure profis as well as curren profis. The price ha he firm ses oday wheher i be he pre-exising price or a newly changed one becomes he pre-se menu price for he nex period, so i has an effec ha exends beyond he curren period. Chaper 7 explores dynamic models of price-seing using he ools ha we developed in Chaper 6.

2 Secion 7.1 develops a general framework for opimal price-seing in a dynamic model. This framework is hen applied o alernaive siuaions in subsequen secions. Secion 7.2 examines a predeermined-price model in which firms make pricing decisions for wo periods a a ime, hough hey may se a differen price for he firs and second period. There are wo groups of firms ha se prices a differen imes wih one group making wo-period pricing decisions in even periods and he oher in odd periods, so in each period half of he prices are newly se and half were se one period before. Secion 7.3 considers a fixed-price model ha is idenical o he predeerminedprice model excep ha firms se he same price for he firs and second periods on heir price conrac. Secion 7.4 examines a workhorse model of he lieraure, he Calvo model, in which a fracion α of randomly chosen firms re-se heir prices each period. For example, if α = 25%, hen a firm would have a 25% chance of re-seing is price in any given quarer, so on average he firm ses is price once per year. The models of Secions 7.2 hrough 7.4 are all have ime-dependen pricing, in which he decision o change price does no depend on economic condiions. In he real world, i is likely ha a large shock would cause firms o change heir pricing sraegies regardless of how long heir exising prices had been in effec. In oher words, he lengh of ime over which prices are fixed (or he probabiliy ha a firm reses is price) is endogenous. Secion 7.5 considers wo imporan models wih sae-dependen pricing. Price sickiness alone canno explain a widely observed phenomenon of modern economies: inflaion ineria. Empirical evidence suggess ha inflaion is someimes sicky, which canno be caused by menu coss. (For example, menu coss presen no impedimen o firms in reducing inflaion from a posiive value o zero, bu in fac firms seem o coninue raising prices even afer aggregae-demand growh slows down.) Afer a digression on empirical sudies of price sickiness (which are covered in Coursebook Chaper 13), Secion 7.7 covers several models ha aim o explain inflaion ineria. Secions 7.8 and 7.9 hen conclude he chaper by summarizing a canonical new Keynesian model and variaions on i. B. Undersanding Romer's Chaper 7 Par B of Romer s Chaper 6 examined he incenives of each individual firm in deciding wheher o change is price or keep i fixed. In Chaper 7, we embed hese firms ino a macroeconomic model and consider he macroeconomic implicaions of price sickiness. 12 2

3 Romer s building blocks Romer begins in Secion 7.1 by developing a dynamic version of he imperfec compeiion model of Secion 6.5. This model is based on uiliy maximizaion by households and profi maximizaion by firms, so is microfoundaions are quie compleely developed. Mos of he elemens of his model are familiar from he imperfec compeiion model of Chaper 6, bu some ake slighly new forms. For example, he uiliy funcion (7.1) is a discree-ime lifeime uiliy funcion similar o ones we used in he Diamond growh model, he real-business-cycle model, and he new Keynesian model in Chaper 6. Uiliy is an addiively separable sum of uiliy from consumpion and disuiliy from labor. The addiiviy of he uiliy funcion simplifies he analysis by making he marginal uiliy of consumpion independen of labor and vice versa. The condiion V > 0 means ha more work leads o more disuiliy (working is disliked), and V > 0 implies ha he more you work, he greaer is he marginal disuiliy of work. These condiions are he flip-side of an assumpion ha leisure has posiive bu diminishing marginal uiliy. The discoun facor in equaion (7.1) is wrien simply as β (0,1). As noed in he discussion of he imperfec compeiion model of Chaper 6, you can hink of β as equal o 1/(1 + ρ) if you wish, wih ρ being he marginal rae of ime preferences; i is jus a more compac noaion. Equaion (7.4) is he firs-order condiion relaing o he rade-off beween consumpion a ime and labor a ime. I says ha he marginal disuiliy of working (he lef-hand side) mus equal he marginal uiliy of he goods ha can be bough wih an addiional uni of work (he righ-hand side). The new Keynesian IS curve in equaion (7.7) is he same one we derived in Romer s equaion (6.8). As wih radiional IS curves, i slopes downward in (Y, r) space. The heory of he firm in he discussion on pages 316 hrough 318 is a lile ricky. We usually simply assume ha each firm maximizes he presen value of is sream of profis. Here, he firm is assumed o maximize he uiliy of is sream of profis o he shareholders. Wih a compeiive credi marke, hese assumpions are equivalen. To see his, consider Romer s equaion (2.47) in he discussion of he Diamond model on page 79. This equaion applies o he equilibrium beween consumpion in periods 1 and 2. Solving i for 1 + r + 1 yields ( C1, ) ( ) θ θ C U 2, + 1 C1, 1+ r = ( 1+ρ ) = ( 1+ρ ) = ( 1 +ρ). + 1 θ θ C1, C2, + 1 U C2, + 1 (1) 12 3

4 The righ-hand equaliy in equaion (1) follows direcly from he definiion of he uiliy funcion. In he Diamond model, individuals live for only wo periods, so he only relevan comparison is beween and + 1. The owners of firms in he new Keynesian model are longer-lived, so we mus also consider consumpion radeoffs beween more disan poins in ime. If we were o generalize equaion (1) o reflec he radeoff beween consumpion a ime zero and ime, he corresponding equaion would be U ( C0 ) ( rs) ( ) (2) s= 1 U ( C ) 1+ r 1+ = 1 +ρ. Taking he reciprocals of boh sides of equaion (2) yields ( C ) ( ) 1 1 U = 1+ r 1+ρ U C 0. (3) If, as we suggesed above, he discoun facor β can be hough of as 1/(1 + ρ), hen we can rewrie (3) as ( C ) ( ) 1 U =β =λ. 1+ r U C 0 (4) This λ erm is defined by Romer in ex in he paragraph below equaion (7.8). From he derivaion above, we can see ha i serves he same role as he usual discoun facor involving he ineres rae. In paricular, if he ineres rae were consan beween ime 0 and ime, equaion (4) would simplify o ( C ) ( ) 1 U =β =λ. 1+ r U C 0 (5) Thus, he λ erm in equaion (7.9) can be inerpreed as a discoun facor in which he equilibrium ineres rae from he consumpion side of he model has been subsiued in. Anoher poenially confusing componen of equaion (7.9) is q, which denoes he probabiliy ha a price se oday has no been changed periods laer. This probabiliy depends on he firm s fuure decisions abou wheher or no o change price he decisions we analyzed in he previous secion. In he remaining secions of Chaper 7, Romer looks a several alernaive models for q, including ime-dependen 12 4

5 models in which he paern of price-changing is exogenous (as wih fixed-lengh conracs) and sae-dependen models in which he decision o change prices depends on economic condiions. For now, we simply rea q as a parameer, leaving is deerminaion unspecified. This leads us o Romer s maximand shown in equaion (7.9), which is more complex han i appears because of uncerainy. By making a couple of reasonable simplifying assumpions and using a second-order Taylor series approximaion o he effec of prices on profis, he arrives a equaion (7.14), which has a useful inuiive inerpreaion. * To undersand his equaion you need o be very clear abou wha p i and p represen. p i is he price ha he firm ses now, knowing ha i will be in place boh in he curren period and (probably) in some fuure periods. * p is he price ha would be ideal for he firm o se for period if i were o * se he price independenly for each period. Firms would se p = p in every period if here were no coss of price adjusmen. Equaion (7.14) shows ha he firm should se a price ha equals he average of he ideal prices in each fuure period, weighed in proporion o he probabiliy ha he curren price will sill be in effec during ha fuure period. For example, if i is known ha he newly se price will be in effec for wo periods, hen he opimal price for he firm o se is he (unweighed) average beween he desired price in he firs period and he desired price in he second period. If he new price will be in effec for he firs period and here is a 50% chance i will be in effec for he second period (bu no any longer), hen he firm should se he price a a weighed average of he wo ideal prices wih a 2/3 weigh given o he curren period and a 1/3 weigh o he second. Equaion (7.14) and is cerainy-equivalen form (7.15) are cenral o he dynamic new Keynesian model. They describe he soluion o a basic problem: how o se a price ha will carry over ino fuure ime periods. The soluion is a logical one: se a price ha is he average of he prices you ll wan in he fuure. The final piece of he puzzle in his secion is he somewha crypic paragraph a he boom of page 318. He assers ha he profi-maximizing real price is proporional o he real wage. If we can se a disinc price for period, hen we would wan o maximize R in equaion (7.8). We can derive Romer s resul easily by maximizing equaion (7.8) wih respec o (P i /P) and seing he resul equal o zero: η η 1 dr Pi W Pi = Y ( 1 η ) +η. d( Pi / P) P P P (6) 12 5

6 The derivaive in (6) can equal zero only if he brackeed expression is zero, which implies or η Pi W Pi 1 = η ( η ) P P P η 1 P i P η W =. (7) η 1 P Equaion (7), which is idenical o Romer s equaion (6.55), demonsraes he asserion ha he desired price is proporional o he real wage. From Romer s equaion (7.6), W P = BY (8) γ+θ 1. Plugging (8) ino (7) yields Pi P η = B Y η 1 γ+θ 1, or in log erms, η pi p = b+ ln + ( γ+θ 1 ) y. η 1 (9) This corresponds o Romer s equaion (7.16) for p* wih c = ln[η/(η 1)], b = ln(b), and φ = (γ + θ 1). Obviously, c + b ` 0 in general. However, Romer is correc in saying ha seing c + b = 0 does no change he fundamenal resul and i keeps he algebra simple. Romer s equaions (7.17) and (7.18) give us he building blocks we need in order o proceed wih he analysis of macro models wih sicky prices. All ha remains is o specify he paern of price sickiness. Romer considers he basic paerns of price sickiness shown in Table 1. Romer has adaped each of hese models in simplified form using common noaion. This means ha Romer s versions of hese models do no correspond exacly o he versions in he original sources. However, he basic conclusions of he models are represenaive of hose of he more widely varying models in he lieraure. 12 6

7 The predeermined-price model is a cousin of he wage-conrac model developed in a seminal paper by Sanley Fischer (1977). In his model, prices are se for wo periods a a ime, wih half of he firms in he economy seing heir prices in even periods and he oher half in odd periods. The price a firm ses for he firs of he wo periods is no necessarily he same as he price se for he second. Romer calls his model he predeermined-price model. He shows ha moneary policy can have a posiive counercyclical role under hese assumpions (as in Fischer s original wageconrac model). Moneary shocks have real effecs ha las wo periods. Table 1. Classificaion of price-seing regimes under imperfec compeiion. Model Secion Descripion Predeermined Prices se for wo periods a a ime. May se a differen 7.2 prices (Fischer) price for firs and second periods. Fixed prices Prices se for wo periods. Same price mus be se for 7.3 (Taylor) boh periods of conrac. Calvo 7.4 Consan (exogenous) probabiliy of firm re-seing price in any period. Caplin-Spulber 7.5 Models how firms decide when o change prices in simple, consan inflaion seing. Danziger- Exends he Caplin-Spulber model o allow for differences across firms and idiosyncraic demand shocks. 7.5 Golosov-Lucas Chrisiano- Eichenbaum- Evans 7.7 Adds indexaion of price changes ino he Calvo model so ha inflaion beween price reviews he firm raises prices a he previous period s inflaion rae. Mankiw-Reis 7.7 Like predeermined prices excep firms se prices when hey receive new macroeconomic informaion, which happens randomly wih probabiliy α per period. Model number wo is based on anoher wage-conrac model originally due o John Taylor (1979). Romer calls his he fixed-price model. This model also has overlapping price seing for wo periods a a ime. I differs from he predeerminedprice model in ha firms are consrained o se he same price for he wo periods raher han a differen price for he firs and second periods of he conrac. This model has similar implicaions for moneary policy, bu leads o quie a differen dynamic response o a moneary shock. In he predeermined-price model, moneary effecs lased only as long as he longes price conrac (wo periods). In he fixedprice case, he real effecs of he moneary shock are longer lasing, damping ou o zero only asympoically. The Calvo model allows he duraion of any paricular price o vary raher han being fixed a wo periods. In each period, he firm changes is price wih probabiliy α and keeps i consan wih probabiliy 1 α. This model has properies ha are 12 7

8 similar o he Taylor model, bu i allows derivaion of he new Keynesian Phillips curve. The nex group of models allow he frequency of price change o be deermined by he agen s need o change prices, raher han according o a sric and exogenous schedule. In he Caplin-Spulber model, agens adjus prices when he gap beween heir exising price and heir opimal price becomes large enough. While Romer does no presen all of he underlying logic o jusify his behavior, he does use his model o show ha money can be neural under sicky prices. The Danziger-Golosov-Lucas model builds on he idea of sae-dependen pricing o consider a seing in which firms experience moneary shocks and shocks o heir individual demand curves, as in he Lucas model of he previous chaper. One shorcoming of he Calvo and oher ime-dependen models is ha hey canno explain inflaion ineria, he empirically observed endency of inflaion o persis when moneary growh slows or sops. Menu coss make i very easy o sop changing prices, so dropping he rae of inflaion o zero should be cosless. The final wo models aemp o explain inflaion sickiness. Chrisiano, Eichenbaum, and Evans allow firms in he Calvo model o index heir prices o las period s inflaion rae when in periods where hey do no make an explici price change. In he Mankiw and Reis (2002) model, firms se a pricing policy for he indeerminae fuure based on heir curren informaion. As in he predeermined price model, hey may se a differen level of price for each period, so for example hey may se a policy of increasing price by 2% each year indefiniely. A randomly seleced share α of firms receives new macroeconomic informaion each period and, when hey receive new informaion, reformulaes sraegies. In his model, he adjusmen coss do no resul from changing prices bu raher from acquiring deailed macroeconomic informaion and reformulaing a dynamic pricing policy. Macroeconomic equilibrium wih predeermined prices As described in Table 1, agens in he predeermined-price model se prices in advance for each of he nex wo periods. The reasons for his price sickiness are no addressed unil laer, bu one can mos easily hink of his price sickiness as fixederm conracs ha are esablished every wo periods. 1 Romer adops he (poenially confusing) noaion ha p is he price se for period by he half of he people who se prices a he end of period 1 and p 2 is he period price se by he oher half of he economy who esablished heir prices a he end of period 2. The superscrips here are no exponens, so do no hink of he p 2 erm as a square. Once you ge he noaion down, he algebra on pages 320 and 321 should be prey easy o undersand. The law of ieraed projecions a he boom of page 320 warrans some discussion. Wha his law says is ha your curren (2012) expecaion of he price ha will 12 8

9 prevail in he year 2014 canno be differen han your curren (2012) expecaion of he price ha you will expec in 2013 o prevail in If you have raional expecaions, hen your expecaion of he 2014 price will only change from 2012 o 2013 due o new informaion ha becomes available in Since you do no, by definiion, have ha informaion now, you canno anicipae how your expecaion will change and E 2012 [E 2013 [P 2014 ]] = E 2012 [P 2014 ]. 1 The soluion of he model is summarized by equaions (7.27) and (7.28). The former shows ha he price level in period depends on he expecaions of he period money supply during he wo periods in which he prices for he curren period were se ( 2 and 1). The laer shows ha he deviaion of oupu from is seady-sae value (by normalizaion, his value is one, or zero in log erms) is due o wo money-surprise erms. The firs of hese measures he change in he predicion abou he curren money supply based on informaion ha arrived las period; he laer is he deviaion of he curren money supply from wha was expeced las period. Romer describes wo key implicaions of hese resuls. The firs is ha, in conras o Lucas s model, here is a posiive role for counercyclical moneary policy here. Shocks ha are one period old sill affec real oupu (hrough E 1 m E 2 m ). The cenral bank can observe hese shocks and respond by changing he money supply in period. This moneary-policy reacion is a change in m E 1 m ha brings y back o is seady-sae level (zero). The second key resul is ha a modified version of moneary neuraliy coninues o hold in his model. Changes in he money supply ha people know abou more han wo periods in advance have a proporional effec on prices and no effec on oupu. Consider he effec of an unexpeced, one-ime, permanen increase in he money supply happening a dae. This will affec oupu in and + 1, bu from periods + 2 onward, prices will be proporionaely higher and oupu will be unaffeced by he shock. Thus, he non-neuraliy of money in his model has a finie lifeime equal o he lengh of he conrac he longes amoun of ime in advance ha prices are se. Macroeconomic equilibrium wih fixed prices Romer s hird model of his secion is based on Taylor s overlapping wageconrac model. As in he case of he Fischer model, Romer adaps he model o look a overlapping price seing raher han wage-seing, and o do so mus ake explici accoun of imperfec compeiion in he produc marke. 1 For a deailed mahemaical discussion of he law of ieraed projecions, see Sargen (1987), Chaper X, Secion

10 I is imporan o keep in mind he difference beween fixed and predeermined prices as Romer uses he erms. In each case, firms se prices for wo-period inervals, wih half of he firms seing prices in even-numbered periods and half in odd-numbered periods. However, in he fixed-price model, he firms mus decide on a single level of price o prevail in boh of he upcoming periods. Wih predeermined prices hey are able o specify a differen price for he firs and second periods. This seemingly minor aleraion of he price-seing srucure has a subsanial effec on he dynamic behavior of he model. Equaion (7.32) shows ha firms seing prices oday (for he nex wo periods) se a price ha is based on he average of he price se las period and heir expecaions of he price o be se nex period, along wih he curren money supply. To undersand he raionale for his, hink abou he markes in which he currenly se price x will prevail. During he firs period, firms seing x will be compeing wih firms who se prices las period a x 1. Since he oher half of he marke has a prese price of x 1, firms will no wan o deviae oo much from his price les hey lose oo much of he marke (if x > x 1 ) or fail o ake advanage of profi opporuniies afforded by heir compeiors overpricing (if x < x 1 ). Similarly, during he second period ha he price currenly being se will be in effec, i will be compeing agains he price o be se nex period, abou which our curren expecaion is E [x + 1 ]. For similar reasons, hey would like o keep x fairly close o E [x + 1 ]. Thus, over he wo periods, he average price agains which we expec he currenly se price o compee is he average of x 1 and E [x + 1 ], which is he firs par of (7.32). The second par shows he effec of he opimal long-run price, which under our simple normalizaion is m. In long-run equilibrium wih no moneary shocks, x = x 1 = E [x + 1 ] = m, which shows ha money is neural in he long run in his model. The mehod of undeermined coefficiens, which Romer uses o solve he fixedprice model, may be familiar o you from he real-business-cycle chaper. We posi a hypoheical soluion such as (7.33), hen use he properies of he model o demonsrae he correspondence beween he parameers of he soluion (µ, λ, and ν) and he parameers of he original model (in his case, jus φ). The mahemaical derivaion carried hrough o equaion (7.44) execues his procedure. The only difficul aspec of his derivaion is he fac ha he equaion for λ in erms of φ is quadraic, which means ha here are wo differen values of λ ha solve he model. Romer noes ha one value is greaer han one and he oher is less han one in absolue value, and ha only he value ha is less han one leads o a sable equilibrium. The use of sabiliy o choose which of wo possible roos is appropriae for equilibrium is an exension of Samuelson s correspondence principle, which argues ha because equilibrium in he acual economy is sable raher han 12 10

11 explosive, we are jusified in ignoring possible parameer values ha lead o explosive behavior. The fixed-price model implies ha moneary shocks will have long-lived effecs on oupu. Insead of he runcaed impac of he predeermined-price model, where oupu is affeced for a finie number of periods, he effecs of a moneary shock in his model will die away gradually, converging on neuraliy only asympoically. The relaionship beween he mean lag in he effec of moneary policy and he lengh of he conrac is called he conrac muliplier. Since inflaion and oupu flucuaions are more persisen han our models ofen predic, he conrac muliplier in a Taylor-ype model has been proposed as a poenial explanaion. 2 While lag operaors are exremely useful for many asks in ime-series analysis, hey are no crucial here. I does no seem worh your ime o read and learn he maerial abou hem on pages , so you may skip his secion. Evaluaion of he Fischer and Taylor models The Fischer and Taylor models were criicized on several grounds. One was he ad-hoc naure of he lengh of he price (wage) conrac. Why should agens se prices or wages for wo periods raher han one, when uiliy would be higher if hey se hem in each period? Anoher case of $50 bills lying on he sidewalk? A considerable lieraure on he opimal lengh of conracs ensued. 3 Models of conrac lengh commonly assume ha here are fixed negoiaion coss ha mus be incurred each ime a conrac is negoiaed (or he price is se, in our conex). Because of hese fixed coss, agens will fix prices/wages for a finie conrac period. The lengh of he conrac period is deermined by sriking a balance beween he disequilibrium coss of being away from he opimal price or wage (which rises wih longer conracs) and he per-period negoiaion cos (which rises wih shorer conracs). Anoher common criicism was ha he models exclude he possibiliy of indexed conracs, which would allow prices or wages o respond fully o moneary changes and hus eliminae he source of non-neuraliy in he model. An indexed conrac could make he price or wage a funcion of he money supply, similar o cos-ofliving adjusmens based on he acual CPI. Wih appropriaely indexed conracs, markes would always clear. This means ha indexed conracs would lead o welfare gains, so agens would have a srong incenive o use hem raher han he predeermined-price or fixed-price arrangemens ha are assumed by Fischer and Taylor. Alhough his was an imporan criicism, oher economiss argued ha in he labormarke conex, indexed conracs migh have o be unreasonably complex in order 2 For example, see Chari, Kehoe, and McGraan (2000). 3 An excellen and quie readable paper is Gray (1978)

12 o fully offse changes in he money supply. I migh be difficul o design indexing rules ha would allow for boh moneary shocks and also changes in produciviy or in he relaive demand for he produc. Ulimaely, he mos damning evidence agains he Fischer and Taylor wageconrac models (which does no apply o he price-based versions in Romer) was ha boh models rely on srongly counercyclical real wages o produce heir basic resuls. In boh cases, a conrac wage ha urns ou o be oo high, given he price level ha ends up prevailing in he period, leads o a high real wage ha causes firms o reduce employmen and oupu and leads o a recession. Since real wages seem o be mildly procyclical raher han srongly counercyclical, hese models have los much of heir iniial populariy. Calvo model The Fischer and Taylor models are boh adapaions from early wage-conrac models. Mos of he price-sickiness lieraure has used variaions on Guillermo Calvo s model. This model is very racable and, as a firs approximaion, seems reasonably realisic. Whereas he Fischer and Taylor models feaure a fixed schedule of daes a which firms adjus prices, he Calvo model assumes a fixed probabiliy α ha each firm s price will be adjused in any period. This means ha he probabiliy ha he currenly-se price is sill in effec j periods laer is ( 1 ) j j q = α, since for he price o say in force for j period he firm mus be in he 1 α share of he populaion ha does no adjus is price for j periods in a row. If x is he price se in period by he share α of firms ha se heir price anew, hen he average price is p =α x + ( 1 α ) p 1, as in Romer s equaion (7.53). The remaining analysis on pages 330 and 331 uses a ime-series rick o derive he new Keynesian Phillips curve (7.60). This equaion is similar o he Friedman-Phelps Phillips curve and he Lucas supply curve in ha i shows a shor-run posiive relaionship beween he difference beween acual and expeced inflaion and he difference beween oupu and naural oupu. Caplin-Spulber model The Caplin-Spulber model differs from he Fischer and Taylor models in ha here is no fixed frequency a which prices are se. Insead, agens change prices when heir desired price ges far enough from heir exising price. This is an example of sae-dependen raher han ime-dependen pricing. Under cerain quie resricive assumpions, one can show ha he Ss pricing rule of he Caplin-Spulber model is 12 12

13 opimal. (See he ciaions in Romer.) In paricular, he model is usually applied o a siuaion of seady inflaion of he general (average) price level. 4 Under an Ss rule, firms keep prices consan unil he difference beween acual and desired price reaches some rigger hreshold s, hen hey rese he price. However, hey do no rese he price o he curren desired price because ha price will be ou of dae an insan laer. Insead, hey overshoo heir curren desired price and se he price S unis above i. As inflaion coninues, heir fixed price gradually falls in relaion o he desired price, which rises wih he general price level in he economy. Evenually, heir relaive price falls o s, a which poin anoher price increase is riggered. You can hink of he dynamic behavior of a single firm s price in he Ss model as being a sep funcion of ime ha moves above and below an upward-sloping line, which represens he seady increase in he desired price. When he desired-price line ges far enough above he previous sep, he agen raises price and leaps above he line, saying here unil he desired-price line caches up and again moves far enough above. Ineresingly, money is neural in he Caplin-Spulber model because an unusually large increase in he money supply pushes more firms above he price-adjusmen hreshold. Alhough each firm s price is fixed for a finie period of ime, as in Romer s varians of he Fischer and Taylor models, he aggregae price level is perfecly flexible. This comes abou because he lengh of he price conrac is endogenous. A moneary shock makes i more or less desirable o change prices, hus causing he average price level o respond direcly o he shock. Danziger-Golosov-Lucas model We won spend much ime alking abou his model. The cenral idea here is ha if firms face boh aggregae shocks and relaive-price shocks, hen a moneary shock will induce some hose firms whose prices are furhes from he opimal price o adjus. This means ha he iniial price adjusmen will be faser han if he firms were randomly seleced as in he Calvo model. Mankiw and Reis: sicky informaion vs. sicky prices Mankiw and Reis (2002) presen a model ha aemps o correc several implicaions of he new Keynesian Phillips curve ha are boh counerinuiive and counerfacual. Romer discusses he problem of inflaion ineria a he end of Secion 7.6. However, his is only one of hree problems ha Mankiw and Reis discuss and ry o solve in heir paper. They also consider he counerfacual implicaion of some 4 Recen papers have applied sae-dependen models using simulaion echniques o ge around he complexiy ha precludes analyic soluion in all bu simple cases. See Dosey, King, and Wolman (1999), Dosey and King (2005), and Caballero and Engel (2007)

14 sicky-price models ha a credible disinflaion (reducion in inflaion) can be expansionary and he discrepancy beween he speed of adjusmen of inflaion o changes in moneary policy beween he implicaions of sicky-price models and he empirical evidence. Laurence Ball (1994) looks carefully a he implicaions of a simple sicky-price model for sudden disinflaions. He finds ha while a credible deflaion, in which he cenral bank lowers he money supply over ime and prices mus fall, leads o he expeced recession, a credible disinflaion, in which he cenral bank reduces he rae of growh of he money supply from a posiive value o zero, leads no only o no recession bu acually causes oupu o be above full employmen. Ball explains he inuiion of he difference beween he effecs of deflaion and disinflaion as follows: To undersand he difference beween deflaion and disinflaion, recall why he former reduces oupu: prices se before deflaion is announced are oo high once money begins o fall. In he case of disinflaion, he overhang of prese prices is a less serious problem. Prices se before an announcemen of disinflaion are se higher han he curren money sock in anicipaion of furher increases in money. However, he overhang of high prices is easily overcome if money growh, while falling, remains posiive for some ime. The level of money quickly caches up o he highes prese price and can hen be sabilized coslessly. (Ball 1994, ) Essenially, price sickiness does no imply inflaion sickiness, which means ha a reducion in money growh has differen effecs han a change in he level of he money supply. Fuhrer and Moore (1995) argue ha he sicky price model implies no persisence in inflaion, whereas he daa indicae ha he auocorrelaions of he inflaion rae are quie high. Again, i is prices ha are sicky in he heoreical model, whereas he daa seem o indicae sickiness of inflaion. Finally, Mankiw (2001) compares he heoreical ime-pah of he response of inflaion o changes in money growh o economerically esimaed responses. He finds ha sicky-price heory suggess ha inflaion should adjus quickly o changes in money growh, bu he evidence suggess ha adjusmen is slow. Mankiw and Reis replace he assumpion of sicky prices wih one of sicky informaion. Because i is informaion ha is sicky raher han prices, his model inroduces sickiness or persisence ino inflaion. They do his by resricing he frequency wih which firms can adop new pricing sraegies. In each period, a fracion α of firms receives curren macroeconomic informaion and updaes is pricing sraegy and he remaining fracion (1 α) keeps is old pric

15 ing policy inac. Thus, α share of firms are seing heir price a he level ha is currenly opimal and (1 α) are using older informaion. Similarly, in he previous period, α share had he opporuniy o rese pricing policy and (1 α) did no, so he share (1 α) 2 are using informaion more han one period old. Following he same logic, (1 α) i is he share of firms whose informaion and pricing policies are a leas i periods old and 1 (1 α) i = λ i is he fracion ha has updaed less han i periods ago. The algebra of he remainder of he las paragraph on page 349 is complex, bu he logic is sraighforward. By obaining he expression for a in equaion (7.81), Romer solves for he equilibrium oupu expression using (7.78). This expression shows ha oupu is a funcion of moneary policy shocks exending back ino he indefinie pas. The Mankiw-Reis model exhibis considerable inflaion persisence due o he ineracion of nominal and real rigidiy. The persisence is in inflaion raes raher han price levels because of he predeermined-price naure of he individual pricing policies ha firms adop. Moreover, simulaions in he Mankiw and Reis (2002) show ha he model can lead o a delayed reacion o moneary policy in which he maximum effec of policy changes on oupu do no occur immediaely. In a more recen follow-up o heir 2002 paper, Mankiw and Reis (2006) examine he abiliy of macro models o reproduce hree sylized facs abou modern business cycles: (1) inflaion rises when oupu is above is rend level, (2) real wages are smooher han labor produciviy, and (3) mos real variables have gradual, humpshaped responses o shocks. They find ha in order o explain hese hree phenomena, more han simply sicky informaion of price seers is required. They inroduce addiional informaion sickiness (or inaeniveness ) in household consumpion planning in workers labor supply decisions. Only if all hree forms of inaeniveness are presen in he model can he hree sylized facs all be explained. C. Suggesions for Furher Reading Original papers on wage-conracing models Fischer, Sanley, Long-Term Conracs, Raional Expecaions, and he Opimal Money Supply Rule, Journal of Poliical Economy 85(1), February 1977, Taylor, John B., Aggregae Dynamics and Saggered Conracs, Journal of Poliical Economy 88(1), February 1980, Barro, Rober J., Long-Term Conracing, Sicky Prices, and Moneary Policy, Journal of Moneary Economics 3, July 1977,

16 Papers on opimal indexing Gray, Jo Anna, Wage Indexaion: A Macroeconomic Approach, Journal of Moneary Economics 2(2), April 1976, Gray, Jo Anna, On Indexaion and Conrac Lengh, Journal of Poliical Economy 86(1), February 1978, Karni, Edi, On Opimal Wage Indexaion, Journal of Poliical Economy 91(2), April 1983, Blanchard, Olivier, Wage Indexing Rules and he Behavior of he Economy, Journal of Poliical Economy 87(4), Augus 1979, Vroman, Susan B., Inflaion Uncerainy and Conrac Duraion, Review of Economics and Saisics 71(4), November 1989, Seminal papers on sicky prices Mankiw, N. Gregory, Small Menu Coss and Large Business Cycles: A Macroeconomic Model of Monopoly, Quarerly Journal of Economics 100(2), May 1986, Akerlof, George A., and Jane L. Yellen, A Near-Raional Model of he Business Cycle, wih Wage and Price Ineria, Quarerly Journal of Economics 100(Supplemen), 1985, Oher heoreical approaches o price adjusmen Barro, Rober J., A Theory of Monopolisic Price Adjusmen, Review of Economic Sudies 34(1), January 1972, Roemberg, Julio J., Monopolisic Price Adjusmen and Aggregae Oupu, Review of Economic Sudies 44(4), Ocober 1982, D. Works Cied in Tex Ball, Laurence Credible Disinflaion wih Saggered Price Seing. American Economic Review 84 (1): Caballero, Ricardo J, and Eduardo M. R. A. Engel Price Sickiness in Ss Models: New Inerpreaions of Old Resuls. Journal of Moneary Economics 54S:S100-S121. Chari, V. V., Parick J. Kehoe, and Ellen R. McGraan Sicky Price Models of he Business Cycle: Can he Conrac Muliplier Solve he Persisence Problem? Economerica 68 (5): Dosey, Michael, and Rober G. King Implicaions of Sae-Dependen Pricing for Dynamic Macroeconomic Models. Journal of Moneary Economics 52 (1):

17 Dosey, Michael, Rober G. King, and Alexander L. Wolman Sae- Dependen Pricing and he General Equilibrium Dynamics of Money and Oupu. Quarerly Journal of Economics 114 (2): Fischer, Sanley Long-Term Conracs, Raional Expecaions, and he Opimal Money Supply Rule. Journal of Poliical Economy 85 (1): Fuhrer, Jeffrey, and George Moore Inflaion Persisence. Quarerly Journal of Economics 110 (1): Gray, JoAnna On Indexaion and Conrac Lengh. Journal of Poliical Economy 86 (1):1-18. Mankiw, N. Gregory The Inexorable and Myserious Tradeoff Beween Inflaion and Unemploymen. Economic Journal 111 (471):C45-C61. Mankiw, N. Gregory, and Ricardo Reis Sicky Informaion and Sicky Prices: A Proposal o Replace he New Keynesian Phillips Curve. Quarerly Journal of Economics 117 (4): Pervasive Sickiness. American Economic Review. March 96 (2): Sargen, Thomas J Macroeconomic Theory. Second ed. Boson: Academic Press. Taylor, John B Saggered Wage Seing in a Macro Model. American Economic Review 69 (2):