The simple geometry of transmission and stabilization in closed and open economy

Transcription

1 The simple geomery of ransmission and sabilizaion in closed and open economy Giancarlo Corsei European Universiy Insiue, Universiy of Rome III and CEPR Paolo Peseni Federal Reserve Bank of New York, NBER and CEPR November 24 Absrac This paper provides an inroducion o he recen lieraure on macroeconomic sabilizaion in closed and open economy. We inroduce a sylized heoreical framework, and illusrae is main properies wih he help of an inuiive graphical apparaus. Among he issues we discuss: opimal moneary policy and he welfare gains from macroeconomic sabilizaion; inernaional ransmission of real and moneary shocks and he role of exchange rae pass-hrough; he design of opimal exchange rae regimes and moneary coordinaion among inerdependen economies. JEL classicaion: E3, E52, F42 Keywords: opimal moneary policy, nominal rigidiies, exchange rae pass-hrough, inernaional cooperaion. Preliminary and incomplee. We hank Pierpaolo Benigno, Ken Rogo, Lars Svensson, Cedric Tille, and Mike Woodford for useful commens and suggesions. We also hank Raymond Guieras and Kahryn Vasilaky for excellen research assisance. Corsei's work on his paper is par of he Pierre Werner Chair Programme on Moneary Union, a he Rober Schuman Cener of he European Universiy Insiue. Financial suppor from he programme is graefully acknowledged. Corsei's work on he projec is also par of he research nework on `The Analysis of Inernaional Capial Markes: Undersanding Europe's Role in he Global Economy', funded by he European Commission under he Research Training Nework Programme (Conrac No. HPRN-CT ). The views expressed here are hose of he auhors, and do no necessarily reec he posiion of he Federal Reserve Bank of New York, he Federal Reserve Sysem, or any oher insiuion wih which he auhors are aliaed.

2 . Inroducion The pas decade has winessed rapid and subsanial developmens in he lieraure on macroeconomic sabilizaion in closed and open economies, wih poenially far-reaching implicaions for he design and conduc of moneary policy. Despie imporan dierences in emphasis and syle, a number of ighly relaed research agendas (from he `new neo-classical' synhesis o he `neo-wicksellian' moneary economics, he `new open-economy macroeconomics', and so on) have focused on he properies of choice-heoreic models wih imperfecly compeiive labor and/or produc markes and nominal rigidiies. An explici aemp o provide a synhesis beween elemens from real business cycle models and shor-run `Keynesian' wage and/or price inerias is he minimum common denominaor of he vas array of DSGE (for `dynamic sochasic general-equilibrium') models ha have recenly proliferaed in academic research, and have found ferile grounds among cenral banks and policy insiuions. This paper is mean o provide an inroducion o hese new research srands, deliberaely (bu no exclusively) argeed oward a non-specialis audience. In fac, our objecive is o use a sylized heoreical framework o analyze macroeconomic sabilizaion and ransmission, and visualize some key resuls wih he help of an inuiive graphical apparaus. Wihou aemping o provide an exhausive overview of he lieraure (a ask well beyond he scope of a `simple geomery'), an imporan goal of our exercise is pedagogical: scholars, pracioners and policy analyss unineresed in unraveling echnical deails may nd in our graphs a useful ool o `inspec he mechanism' and convey imporan resuls from more complex models in a ransparen and immediae fashion. Transparency and immediacy are achieved via resricions on he specicaion of preferences and echnology, which allow us o mainain analyical racabiliy and focus on he subsance of he argumen wihou sacricing heoreical coherence. On he negaive side, parameric resricions may well hamper he degree of generaliy and robusness of he heoreical framework. Thus, when necessary, in he ex we will commen on our key assumpions, o make sure ha he general principles conveyed by our analysis are no confused wih model-specic resuls. Very few equaions and only exremely inuiive ones appear in he main ex. Relaively advanced readers are referred o he Appendices where full-edged versions of he models described in he main ex, wih complee algebraic deails, are available. This paper is organized as follows. The nex hree secions delve ino building he main analyical and graphical ools in a closed-economy seing, covering boh normaive and posiive issue. Secion 2 describes he basic macroeconomic model. Secion 3 analyzes he ransmission of moneary policy, characerizes macroeconomic sabilizaion and provides elemens for a welfare analysis. Secion 4 discusses and exends he basic model; non-specialis readers may skip his Secion and proceed direcly o Secion 5 wihou sacrice of exposiional coninuiy. The following secions of he paper reconsider he concepual apparaus analyzed in he closedeconomy case in he conex of a wo-counry world model. Secion 5 secion describes he global economy and inroduces alernaive price-seing regimes. Secion 6 revisis he radiional view of he sabilizaion properies of exchange rae movemens. Secion 7 discusses he inernaional dimensions of opimal moneary policy, linking hem o he choice of he exchange rae regime. Secion 8 discusses a few exensions of he model and Secion 9 concludes. 2

3 2. A basic macroeconomic model We sar by developing a sylized closed-economy macroeconomic model. The economy consiss of households, rms, and he governmen. There is no exernal rade in goods or asses. The populaion size is normalized o one, so ha we can use he same noaion for aggregae and per capia variables. The model is fully specied in Appendix I, which also derives and characerizes he general equilibrium allocaion. Households have idenical preferences. They derive uiliy from consuming he producs supplied by he rms, and disuiliy from supplying labor o he rms in exchange for wage incomes. There may also be oher elemens aecing he households' welfare, for insance uiliy from real money balances, bu in our discussion we disregard hem as quaniaively negligible. A any poin in ime, uiliy is: U = ln C ` (2.) where C is consumpion and ` is hours worked. The parameer measures he discomfor associaed wih labor eor, so ha he marginal rae of subsiuion beween consumpion and = C: (2.2) du= There are many varieies (or `brands') of he consumpion good. Each rm produces a single variey, which is an imperfec subsiue o all oher varieies. As rms have marke power over he supply of heir producs, hey se prices as markups over marginal coss. Labor is he only inpu in producion. Produciviy (oupu per uni labor) is subjec o economy-wide shocks. The labor marke is assumed o be perfecly compeiive. We allow for nominal price rigidiies in he shor run. For simpliciy, we assume ha rms prese he price of heir own produc a he beginning of each period, and sand ready o mee curren demand a his price during he period. In mos of our analysis we will absrac from governmen consumpion: he governmen only redisribues revenue. The moneary auhoriy ses he counry's moneary policy. 2.. The srucure of he economy Our model can be synhesized by means of hree schedules, as illusraed in Figure : Aggregae Demand, Aggregae Supply, and he Naural Rae. Figure plos labor eor ` on he horizonal axis and consumpion C on he verical axis. Le P denoe he consumer price index associaed wih he consumpion baske C. Wihou invesmen or governmen spending, C coincides wih he aggregae demand in real erms, while P C is aggregae nominal spending. Le denoe a variable ha synhesizes he eec of moneary policy (whaever he policy insrumens used) on aggregae nominal spending P C. We can refer o as he aggregae moneary sance of he counry. The Aggregae Demand `AD' equaion can hen be wrien as: We analyze governmen spending shocks in Secion 4.4. P C = (2.3) 3

4 Wih prices P prese in he shor run, aggregae demand C moves one-o-one wih he policy variable. In erms of Figure, he `AD' is a horizonal line: given he price level P, a higher moneary sance ranslaes ino higher real consumpion C. By he same oken, given he moneary sance, consumpion is higher he lower he price level. Nex, le Z denoe labor produciviy. The Aggregae Supply `AS' equaion relaes oupu (which in equilibrium is equal o demand) o oal employmen measured in erms of hours worked: C = Z` (2.4) Holding C consan, shocks o produciviy Z lead o ucuaions in aggregae employmen `. In Figure, he `AS' schedule is a ray from he origin wih slope deermined by he produciviy parameer Z: higher produciviy ranslaes ino a seeper line. A any poin in ime, he inersecion beween `AD' and `AS' deermines he equilibrium allocaion of consumpion C and labor ` for given values of he exogenous variables and Z, as well as for a given price level P. Of course, he price level is an endogenous variable in our sysem. We herefore need o analyze opimal pricing by rms. Suppose prices were perfecly exible in he shor run. Imperfecly compeiive rms would hen se prices by charging an opimal markup over heir marginal coss. Labor being he only inpu in producion, marginal coss are labor coss per uni of produc, i.e. he wage rae, W, divided by he labor produciviy Z. The markup charged by he rm is a funcion of is monopoly power in he produc marke, in iself a funcion of he degree of subsiuabiliy of he variey produced by he rm relaive o all oher varieies. Le denoe he elasiciy of subsiuion beween dieren varieies of he consumpion good. We assume ha is sucienly large o capure he idea ha varieies of he same consumpion good are good subsiues for each oher bu no \oo" large (oherwise all varieies would subsanially be similar in he eye of he consumers, and a rm would have no monopoly power a all in seing he price of is produc). Specically, we assume < <. The opimal price charged by he represenaive rm would hen be: P flex = markup z } { marg. cos z} { W Z Inerpreing he expression above, if he elasiciy of subsiuion were very high, prices would be equal o marginal coss W=Z. Bu if were relaively small (close o one), rms would face very inelasic demand curves for heir producs, and would be able o exploi heir signican marke power by charging very high prices relaive o he producion coss. Moreover, wih a perfecly compeiive labor marke, he equilibrium wage rae in unis of consumpion (W=P ) mus be equal o he marginal rae of subsiuion beween consumpion and leisure of he represenaive agen (2.2). 2 I follows ha he nominal wage is proporional o nominal spending: (2.5) W = P C (2.6) 2 If he labor marke were imperfecly compeiive, here would be a wedge (labor marke markup) beween real wage and marginal rae of subsiuion, reecing workers' marke power. 4

5 Combining (2.5) and (2.6), in equilibrium he pro-maximizing produc price P flex is deermined as follows: P flex = P flex C Z Now, replacing C wih Z` according o (2.4) in he previous expression and rearranging, we obain: (2.7) ` = ` (2.8) Equaion (2.8) denes he `naural' or `poenial' rae of employmen, `, as he level of employmen ha would prevail in an economy wihou nominal rigidiies. 3 The naural rae depends on he monopolisic disorions in he economy: he higher, he lower he equilibrium markup, and he higher he equilibrium level of employmen. Observe ha, while he naural rae of employmen is consan, he naural rae of oupu Z ` (dened as oupu in an economy wihou nominal rigidiies) will ucuae as a funcion of produciviy Z. In Figure, we depic he `Naural Rae' or `NR' as a hird schedule: a verical line above he consan `. Figure illusraes he ex-price equilibrium where `AD' and `AS' cross each oher corresponding o he naural rae of employmen. Once C and ` are deermined a he inersecion of `AS' and `NR', he price level P adjuss for any level of he moneary sance o make sure ha `AD' inersecs he oher wo schedules a he equilibrium poin. In our seing, however, prices are no exible in he shor run. Raher, rms se heir prices opimally based on heir expeced marginal coss, 4 and are unable o modify hem once hey observe he acual realizaions of W and Z: 5 P = W E (2.9) Z Of course, when prices are prese, unanicipaed changes in marginal coss can reduce or raise he ex-pos pros of he rm. 6 We now show ha sicky-price employmen is equal o he naural rae in expeced erms. To see his, recall ha W = P C and P C = from (2.6) and (2.3). Combine hese expressions 3 This resul can be generalized o he case of non-linear disuiliy of labor eor. In Secion 4.4 for insance we assume ha ha U = ln C `+ =( + ). In his case he naural rae of employmen is a consan equal o [( ) =] =+. For more general model specicaions, he naural rae need no be consan, and consequenly he graphical represenaion of he equilibrium allocaion urns ou o be less sraighforward. For a generalizaion of our graphical apparaus o he case in which he naural rae depends on consumpion see Corsei and Peseni As discussed in Appendix, produc prices are opimally prese o maximize he discouned value of he rm's pros. While in general his problem is quie complex, i grealy simplies in our seing. 5 In wha follows, E(X) will refer o he expeced value of he variable X based on informaion available a he ime expecaions are aken. Wih one-period nominal rigidiies, he expression E(X) is shorhand for E (X ). 6 The ex-pos gross markup is P=(W=Z), or ( ) E(W=Z)=(W=Z). As long as he shocks are no oo large, rms' ex-pos markups will remain above one. Noe ha in a model wihou monopolisic disorions any increase in marginal cos would lower he ex-pos markup below one, promping rms o adjus heir prices in response o he shock: in ha framework, nominal rigidiies would be inconsisen wih he raional behavior of rms. 5

6 wih (2.9) o rewrie he opimal good price as follows: P = E Z (2.) Nex, muliply boh sides by C and use (2.4) and (2.3) o wrie: = E Z` (2.) Z Rearranging and aking expecaions, we obain: =Z E (`) = E E (=Z) = = ` (2.2) On average, expeced employmen is equal o is naural rae wih idenical rms, his is rue boh in he aggregae and a rm level. An inuiive inerpreaion of (2.2) is ha in equilibrium rms choose prices as o insure ha, on average, hey will operae on heir ex-price supply curve: we will reurn on his poin in Secion To sum up: he `Aggregae Demand' equaion (2.3) relaes nominal spending o he sance of moneary policy. The `Aggregae Supply' equaion (2.4) relaes aggregae supply o employmen. Prices in he shor run are se such ha, in expecaion, he economy operaes along he `Naural Rae' equaion (2.2). In he long run, when prices are exible, he `NR' equaion deermines labor `, he `AS' equaion deermines consumpion C given ` and Z, and he `AD' equaion (2.3) deermines he price level P given C and Welfare properies of he marke allocaion We can now use our graphical apparaus o analyze changes in welfare as a resul of macroeconomic shocks, by shifing he hree schedules in Figure. Specically, given he uiliy funcion (2.), he indierence curves in he space (`; C) are convex and upward sloping, wih slope proporional o consumpion according o (2.2). In Figure he dashed curve is he indierence curve associaed wih he equilibrium. Uiliy is increasing as we move upwards or weswards, corresponding o higher consumpion level for any given labor eor or lower labor eor for any given consumpion level. In he presence of monopolisic disorions in he produc marke, an economy operaing a he naural rae ` will no be Pareo ecien: he equilibrium level of employmen and oupu will be subopimally low, as rms conrac heir supply of goods o exploi heir monopoly power and maximize heir pros. We can provide a simple graphical represenaion of his poin. In Figure, he indierence curve ha goes hrough he equilibrium poin crosses he `AS' locus from above. Tha is, a he equilibrium C = Z `, he marginal rae of subsiuion (measured by he slope of he indierence curve of he represenaive household) is smaller han he marginal rae of ransformaion (he slope of he aggregae supply locus): dc d` du=;c= ` = Cj C= ` = Z = Z < Z (2.3) 7 In more complex models, expeced employmen need no be a he naural rae in any period. Neverheless, opimal price seing is such ha employmen converges o he naural rae asympoically. 6

7 This illusraes a general and crucial feaure of economies wih monopolisic power in producion. Inuiively, due o monopolisic disorions, in equilibrium he disuiliy from a marginal increase in labor eor is lower han he uiliy from higher revenue. In he absence of monopolisic disorions, he equilibrium in he model would correspond o a poin in which he indierence curve is angen o he `AS' locus. To see his, assume ha produc varieies are highly subsiuable, i.e. le become inniely large, so ha he monopoly power of rms is arbirarily small. Expression (2.3) shows ha in equilibrium he slope of he indierence curve will be idenical o he slope of he `AS' locus, and equal o Z. Indeed, he Pareo-ecien level of employmen is =. The previous poin is illusraed in Figure 2. One can easily visualize he eec of srucural reforms reducing monopolisic disorions in he economy as a righward shif of he `Naural Rae' verical locus. As is apparen from (2.2), ` is increasing in, he elasiciy of subsiuion across varieies ha is inversely relaed o he size of he equilibrium markup in he economy. For any given produciviy Z, reducing rms' marke power raises oupu and herefore consumpion, owards heir Pareo-ecien level. For any given moneary sance, he price level P falls. The equilibrium moves from poin O o poin X. 3. Transmission and sabilizaion in closed economy In his secion we use our apparaus o analyze he macroeconomic eecs of produciviy and moneary shocks. We address his issue in wo seps. We rs sudy he macroeconomic response o shocks when prices are exible. Then we reconsider he same shock in he conex of an economy wih sicky prices. Throughou he analysis, we will focus on posiive shocks, dened as unexpeced increases in Z and (wih he undersanding ha he analysis of a negaive shock will be perfecly symmeric) The ex-price equilibrium benchmark Wih exible prices, an increase in Z does no aec he equilibrium level of employmen, which remains consan a `. Given `, a shock o Z raises he equilibrium level of oupu in proporion, generaing excess supply in he economy. If nominal spending does no change, he price level P needs o fall enough o boos consumpion demand o he new level of oupu. Figure 3 illusraes graphically he eec of he posiive produciviy shock jus described. Le O be he iniial equilibrium allocaion. An increase in Z ils he `AS' locus upwards: higher produciviy raises he level of consumpion ha is susainable a any given employmen level. Wih employmen a ` and no change in he moneary sance, prices fall in response o he excess supply, shifing he `AD' locus upward. The new equilibrium, A in he Figure, corresponds o higher consumpion (he segmen OA measures he increase in C) and lower prices, while employmen remains unchanged a is naural rae `. Clearly, wih exible prices moneary shocks have no eec on he equilibrium allocaion: and P always move insananeously in he same proporion, leaving consumpion and he `AD' locus unchanged. 8 A very parial lis of references includes Chrisiano, Eichenbaum and Evans, 999, 24, Clarida Gali and Gerler 2, 2, Gali 22, Goodfriend and King 2, Walsh 999 and Woodford 23. 7

8 3.2. Nominal price rigidiies and he eeciveness of moneary policy The equilibrium response o produciviy shocks in an economy where prices are sicky in he shor run is quie dieren from he ex-price benchmark characerized above. If P is inexible, aggregae demand is pinned down by moneary policy : wihou a change in, consumpion is consan in real erms during he period. Hence, ucuaions in produciviy ha are no mached by changes in aggregae demand canno bu ranslae ino changes in shor-run employmen and oupu. Relaive o he naural rae of employmen and oupu, a posiive produciviy shock opens boh an employmen and a labor gap. Figure 3 illusraes hese poins. Wihou price exibiliy, a produciviy shock ha roaes he `AS' locus upwards does no cause any fall in prices, hence is no mached by a proporional upward movemen of he `AD' locus. Unless is raised by he moneary auhoriies, he new shor-run equilibrium will correspond o poin B in which he new `AS' locus crosses he (unchanged) `AD' locus. Employmen falls below ` while oupu falls below Z `. As shown in he Figure, a produciviy shock opens an employmen gap OB, ha in our economy is proporional o he oupu gap OA. 9 Noe ha he appropriae measure of oupu gap in our conex is he dierence beween he amoun of resources ha could be produced and consumed under exible prices, and he analogous amoun in he presence of nominal rigidiies. Moneary policy can be eecive in his framework. Provided moneary auhoriies are able o observe or predic Z wih accuracy, and can use appropriae policy insrumens, hey can engineer a moneary expansion o raise and bring he economy o operae exacly as if prices were exible. Figure 4 shows wha happens when policymakers use moneary insrumens as o raise in proporion wih Z: he `AD' curve shifs up by he amoun OA and closes he employmen and he oupu gap. As a resul, he shor-run inexibiliy of prices does no preven he economy from operaing a he naural rae. More general analyical frameworks shed ligh on oher possible policy rade-os ha make moneary policy less eecive han suggesed by he above analysis. Namely, cos push and secoral shocks, dual wage and price rigidiies as well as invesmen dynamics may rule ou ha moneary policy arge he ex-price allocaion exacly. Ye, he main principles esablished in his secion remain valid. Namely, he moneary sance ha brings employmen and oupu o heir naural raes is expansionary when he economy experiences a produciviy shock ha opens a negaive employmen and oupu gap (by symmery, i will conracionary in he presence of an adverse produciviy shock ha would lead o overheaing of he economy a unchanged demand condiions). Inuiively, he produciviy boom makes an increasing amoun of resources poenially available for consumpion. Bu if prices do no fall, consumers whose nominal incomes are unchanged will be unable o purchase hese addiional producs. Hence he need for a moneary simulus, ha generaes aggregae demand and brings he economy back o poenial. 9 Wih P xed during he period, here is no shor-run inaion (deaion) in response o posiive (negaive) oupu gaps. However, one could obain some responsiveness of he AD o produciviy shocks by allowing for an imperfec degree of shor-run price exibiliy wihou changing he message from our resuls above. If prices could parially respond o excess supply, a fall in he price level would somewha raise AD, moving he equilibrium allocaion closer o he naural rae. Bu unless he economy is free of nominal rigidiies, he economy would no operae a is (consrained-) ecien level (see Secion 4.3). 8

9 3.3. Opimal moneary policy and macroeconomic sabilizaion A he end of he previous subsecion, we have seen ha policymakers informed abou he sae of he economy Z could use moneary insrumens o move aggregae demand C oward is ex-price level for a given price level P. Would such a policy conduc be opimal? To address his quesion, we need o accoun for he endogenous response of opimal prices o he conduc of policymakers. So far, we have used our apparaus o analyze he performance of he macroeconomy a given prese prices. Ye, as shown in (2.) above, prices are endogenous: forward-looking rms se he prices of heir producs on he basis of heir expecaions abou boh economic fundamenals and policy variables. In wha follows we analyze he policy implicaions of his behavior, and characerize he `opimal' moneary sance by welfare-maximizing moneary auhoriies able o make credible commimens. To perform such exercise, we need o specify a welfare meric: in our model, i is naural o assume ha he objecive funcion of he policymakers coincides wih he expeced uiliy of he naional represenaive agen: W = EU = E (ln C `) (3.) Now recall ha in a marke equilibrium expeced employmen is consan and equal o is naural rae. Thus, using he equilibrium expression for opimal prese prices, he welfare crierion simplies o: W = E (ln C) ` = E (ln ) E (ln P ) ` = E (ln ) ln E + consan (3.2) Z Maximizing he above expression wih respec o yields: solved by: =Z E (=Z) = (3.3) = Z (3.4) where is an arbirary posiive parameer ha rms know when hey se heir prices. The previous condiion characerizes an opimal moneary policy sance up o he scale of nominal variables in he economy. The opimal policy consiss in a commimen o provide a nominal anchor for he economy,, and deviae from such sance only when produciviy shocks in he economy hreaen o desabilize marginal coss and move employmen and oupu far from heir poenial levels. In our framework, by responding fully and sysemaically o Z, such policy compleely eliminaes uncerainy in marginal coss, hus in pros. Prices are sabilized a he level P = = ( ). I is sraighforward o resae he resuls above in erms of inaion raes, raher han price levels. Suppose ha he moneary auhoriies se he nominal anchor according o: = P ( + e) (3.5) In expression (3.4), need no be consan over ime: i can represen any deerminisic process ha rms can predic when hey ake heir expecaions. 9

10 where P is he lagged price level observed a he ime expecaions are aken, and e is he `desired' rae of inaion i.e. he (implici or explici) inaion arge of he policymakers, which may be equal o zero. Given he above nominal anchor, in he absence of shocks (Z = ) rms would opimally se heir prices equal o in each period: he economy would exhibi a consan inaion rae equal o e: P P = ( + e) (3.6) Bu his is precisely he oucome ha would prevail in he presence of shocks o Z, provided ha he moneary auhoriies implemen (3.4). In he nex subsecion, we will show ha his is no necessarily he case when he economy is subjec o insucien sabilizaion. If moneary auhoriies implemen he opimal moneary sance (3.4), nominal rigidiies are inconsequenial, in he sense ha whaever is he level of predeermined prices, policymakers can simulae aggregae demand o close he oupu gap and push he economy oward poenial. In erms of Figure 4, any sochasic roaion of he `AS' locus is perfecly mached by a corresponding shif in he `AD' locus, so ha in he shor run he equilibrium always lies along he `NR' verical line above he naural rae. Noe ha under he opimal policy consumpion will no be consan, bu raher ucuae wih produciviy, perfecly maching he ex-price allocaion The coss of insucien sabilizaion: inecienly high markups and low purchasing power Having esablished wha an opimal policy looks like in he framework of our model, we can now urn our aenion o a dieren issue: wha are he consequences of adoping a subopimal moneary policy no aimed a sabilizaion? We will show ha insucien sabilizaion ranslae ino subopimally high markups and price levels making a case for `price sabiliy' in he design of opimal sabilizaion policies. We will discuss oher ypes of coss in he nex secion. To provide a graphical reamen, wihou loss of generaliy consider an economy where Z is a random variable ha can rise or fall by he same amoun wih equal probabiliy /2, wih E (Z) =. Figure 5 depics he wo possible `AS' lines, corresponding o a high and a low level of Z. They inersec he `NR' locus a poins A and A, respecively. For convenience, we also draw he `AS' line corresponding o he average level of produciviy E(Z) =. The laer inersecs he `NR' locus a poin O, wih AO = O A. Observe ha, were he opimal policy (3.4) in place, employmen would be consan a is naural level `, and consumpion would be high or low depending on he realizaion of he produciviy shock. We are ineresed in sudying he equilibrium allocaion when policymaking deviaes from he opimal moneary sance. For insance, suppose ha during each period moneary auhoriies se he curren moneary sance according o: = Z (3.7) where is a consan parameer wih. Clearly = corresponds o he opimal policy response o shocks (3.4). For any value of dieren from one, he moneary response o shock will be inecien. We also assume ha moneary auhoriies se according o (3.5) above.

11 To focus sharply on our argumen, i is convenien o carry ou our analysis under he exreme assumpion ha does no respond a all o he oupu gap, i.e. =. Wih sicky prices, consumpion will be consan bu employmen will hen be ucuaing wih Z: i will be below he naural rae when he shock is posiive, above he naural rae when he shock is negaive. These poins are illusraed in Figure 5, where we include wo `AD' lines, drawn for dieren price levels: he upper AD line is drawn for a price level P B, he lower AD line for a higher price level P F > P B. The `AD' locus corresponding o P B inersecs he `NR' locus a poin O, he `AD' locus corresponding o P F inersecs he `NR' locus a poin Q ha lies below O. For a consan moneary sance =, consumpion is lower when prices are equal o P F. For each level of P, he shor-run equilibrium will lie where he corresponding `AD' locus crosses eiher he lower `AS' (if he shock is negaive) or he higher `AS' (if he shock is posiive). When P = P B he economy will operae eiher a B or a B. When P = P F he economy will operae eiher a F or a F. Wha will he equilibrium level of P be? To he exen ha a higher variance of shocks does no modify average produciviy, one may be emped o conjecure ha uncerainy would no aec prices: rms would se prices equal o P B, as if he produciviy level was consan and equal o E(Z) =, i.e., he average of low and high produciviy. The upper `AD' line in Figure 5 has been drawn precisely under such assumpion. Noe ha, corresponding o his `AD' line, aggregae consumpion is equal o he average of high and low consumpion wih exible prices. Is his an equilibrium? We could easily show ha his is no he case by considering he pricing equaion direcly. There is however an inuiive way o approach his issue using our graph. Recall ha rms opimally prese prices o ensure ha, on average, hey operae on heir supply schedule. As discussed above, an imporan implicaion of such behavior is ha he expeced employmen be equal o is naural rae. Bu Figure 5 clearly suggess ha his condiion is violaed when pricing is done in reference o average produciviy, i.e. when P = P B. In fac, consider he wo possible equilibria on he upper `AD' line. When he produciviy shock is posiive, rms' employmen falls by he segmen BO. Bu when he shock is negaive, employmen increases by a much larger amoun, equal o he segmen OB > OB. Taking he average of he wo employmen levels wih equal probabiliy, i follows ha a P B he expeced employmen gap will be posiive, i.e. expeced employmen will be above he naural rae: E(`)j P =PB > ` (3.8) In oher words, a P B each rm is supplying \oo much" relaive o he level of oupu ha maximizes is expeced discouned pros. Each rm has herefore an incenive o cu back on is producion plans, raising is price: P B canno be he equilibrium price level. Given he disribuion of Z, equilibrium pricing always equaes he average gap beween employmen and is naural rae o zero. In our example his principle has a simple geomerical inerpreaion: given he wo `AS' curves corresponding o he wo dieren realizaions of he produciviy process, and holding consan, prices (and he `AD' schedule) mus be se such Holding =, he equilibrium price level is: P j = = E Z since, wih E (Z) =, E (=Z) >.

12 ha he low and high employmen allocaion are perfecly symmeric around `. In Figure 5, his happens in correspondence o he lower `AD' curve, based on he higher price index P F. In his case, when he produciviy shock is posiive employmen falls by he segmen F Q, and when he shock is negaive employmen increases by he segmen QF, wih F Q = QF. 2 Ulimaely, Figure 5 sheds ligh on one of he key reasons why insucien sabilizaion can reduce naional welfare. Facing uncerainy in marginal coss, rms raise heir average markup and charge a higher prices. As a resul, a subopimally high price level reduces households' purchasing power: failing o sabilize he economy will no aec expeced disuiliy from labor eors (which is kep consan by rms' opimal pricing), bu will reduce he expeced uiliy from consumpion. 3 By using he expression for opimal pricing, he equilibrium inaion will be: P P = ( + e) E Z > ( + e) (3.9) The inequaliy sign follows as a sraighforward implicaions of he Jensen's inequaliy. 4 Higher markups and prices imply ha he realized inaion rae will be higher han he argeed rae of inaion. Noe ha, since he growh of moneary sance is rebased in each period relaive o price level realized in he previous period, moneary auhoriies de faco le grow a a rae equal o he realized rae of inaion. Comparison of (3.6) wih (3.9) highlighs he reason why macroeconomic sabilizaion and price sabiliy can be hough of as wo faces of he same coin. Observe ha he above resuls can be easily generalized o economies where he deviaion from he opimal policy is `smaller', for some < < in (3.7). Even if moneary auhoriies reac somewha o produciviy shocks, bu fall shor of sabilizing marginal coss and oupu compleely, average markups and prices will sill be subopimally high. Furhermore, for any given subopimal moneary policy, he higher he variance of he shock (he furher away are he wo `AS' lines from each oher), he higher he equilibrium level of prices (hus, he lower he equilibrium `AD'). I follows ha, for a given moneary sance, changes in he variance of he shocks from one period o anoher lead o adjusmen in prices creaing emporary ucuaions of inaion. 2 Observe he dierence in he macroeconomic implicaions of produciviy uncerainy and noise in he conduc of moneary policy. Holding produciviy consan, opimal pricing is no aeced by he variance of, bu only by is expeced value: = P j Z consan = E E Z Z Hence moneary noise in he form of i:i:d: shocks o do no aler expeced marginal coss. In erms of our graph: moneary noise ranslaes ino sochasic shifs of he `AD' curve, raising or lowering consumpion along he `AS' curve. Bu, dieren from he case of produciviy shocks, i:i:d: shifs of he `AD' curve do no aler expeced employmen. 3 In principle, one canno rule ou ha for paricular parameerizaions of preferences and echnology subopimal sabilizaion policies pu downward pressure on prices. However, he specicaions commonly adoped by he lieraure yield resuls consisen wih he one discussed in he ex. 4 More generally, he prese price level will be increasing in he variance of he produciviy shock. An inuiive explanaion of his resul is he following. Uncerainy abou marginal coss ends o reduce expeced discouned pros (hese are a concave funcion of produciviy). However, by raising he prese price, a rm can reduce he sensiiviy of discouned pro o shocks o marginal coss. 2

13 4. The closed-economy model: discussion and exensions 4.. Time consisency and opimal policy The opimal moneary policy sance characerized above is no ime consisen. To see his, consider once again Figure 2, depicing an equilibrium a poin O where acual employmen is a is naural rae. From our discussion above, we know ha his allocaion will prevail if moneary policies follow he opimal moneary rule. The problem wih such allocaion is ha monopoly disorions resul ino a subopimal level of welfare: in equilibrium he indierence curve cus he `AS' curve from above. Once prices are se, ex-pos uiliy could be increased hrough a furher moneary expansion ha moves he equilibrium o he righ of `, up o he poin X a which he indierence curve is angen o he `AS' locus. This is precisely wha policymakers would do if hey re-opimized heir moneary sance in a discreionary manner. Dene as discreion he moneary sance ha solves he problem: max [ln ln P `] (4.) Comparing (3.2) wih he above expression, noe ha here is no expecaion operaor in (4.): he moneary auhoriies now ake expecaions and prices as given, independen of heir decisions. The rs order condiion of he above problem is: discreion P Z according o which he opimal moneary policy under discreion pushes labor eor ` owards is Pareo-opimal level =, as discussed in Secion 2.2. There is however a crucial problem in solving for an equilibrium wih discreionary moneary policy in our seing. Using (4.2) o solve for P in (2.), we obain: discreion Z = = E discreion Z This condiion canno be par of a raional-expecaions equilibrium. In fac, ake expecaions on boh sides of (4.3): he wo sides are equal only when = ( ) =, i.e. for!. Oherwise, whaever he price level chosen by he rms, here is always an incenive for he policymakers o expand moneary policy above privae expecaions. To obain a raional expecaions equilibrium, he above model could be modied o accoun for welfare coss from realized inaion in (4.). 5 This would correspond o he radiional Kydland-Presco/Barro- Gordon model of inaionary bias. 6 Oher conribuions in he lieraure analyze moneary policy in economies where disorionary (Pigouvian) ax and subsidies can eliminae he disorions caused by monopoly power, hence making he opimal policy ime-consisen. Suppose ha he governmen can impose a ax on rms pros a he rae = =, rebaing he ax revenue o households in a lump-sum 5 For insance, in Albanesi, Chari and Chrisiano 23 which inaion leads o a cosly reducion in consumpion purchases because of he operaion of he cash in advance consrain. 6 See he original aricles by Kydland and Presco, and Barro and Gordon. (4.2) (4.3) 3

14 fashion. Then rms' opimaliy will ensure ha prices are equal o: P = W ( ) E = E Z Z (4.4) Under hese condiions, he moneary sance = Z is boh he opimal rule as dened in (3.4) and he opimal moneary policy under discreion discreion as derived in (4.2). The price level P is equal o and in equilibrium here is no longer an incenive for he policymakers o deviae from he opimal sabilizaion policy. The economy operaes a an ecien (rs-bes) naural rae of employmen, equal o =, where he indierence curve in our graph is angen o he AS curve. The inuiion underlying his resul is sraighforward. There are wo disorions in he economy: nominal price rigidiies and monopoly power in producion. The governmen needs a leas wo insrumens o achieve eciency: on he aggregae demand side of he economy, moneary policy eliminaes he negaive consequences of xed prices; on he aggregae supply side of he economy, scal policy eliminaes supply-side disorions due o monopolisic compeiion. The appropriae moneary and scal sance allows he policymakers o bring he economy o a rs-bes allocaion Moneary policy and ineres raes So far we have characerized moneary policy in erms of an index of moneary sance, bu we have inenionally lef unspecied he issue of how policymakers can conrol. We now provide some examples of policy insrumens corresponding o a given sance. The mos immediae case is one in which policymakers conrol money supply. In he model specied in our appendix, wih logarihmic uiliy of consumpion as in expression (2.), and money-balance providing uiliy also in logarihmic form, is simply proporional o he money sock: a moneary expansion leads o a one-o-one change in nominal spending. Wha if he moneary auhoriies se ineres raes? As shown in Appendix, when privae agens can hold a nominal bond whose reurn is direcly conrolled by he governmen, opimal consumpion and bond holdings imply: P C = ( + i) E P + C + The previous opimaliy condiion is a sandard Euler equaion. On he lef hand side we have he marginal uiliy of nominal wealh oday. This has o be equal o he expeced marginal uiliy of nominal wealh omorrow (he erm under expecaions), adjused o accoun for deviaions of he curren nominal ineres rae i from he `naural' real rae of ineres =, a funcion of he rae of ime preference. Using our deniion = P C, we can derive he nominal ineres rae corresponding o he implemenaion of moneary policies ha sabilize he oupu gap providing a nominal anchor for he economy, namely = Z. We obain + i = + (4.5) Z E(=Z + ) (4.6) 4

15 The nominal ineres depends on hree elemens: he `naural' real ineres rae, =; he nominal anchor + =; and he curren response by moneary auhoriies o produciviy shocks, boh curren and anicipaed. The rs elemen is exogenously given, independen of policymakers' decisions. The laer has been characerized in our analysis above: he nominal ineres rae falls when Z increases above is average, opening an oupu gap. 7 This ranslaes ino a lower real ineres rae, raising consumpion demand in he shor run. 8 In general, he ineres rae policy has o be chosen o rule ou self-validaing increases in inaion, and o guaranee a unique saionary raional expecaions equilibrium. In oher words, i is necessary ha P + =P converges o he inaion arge + e regardless of he curren level of inaion. When inaion grows above arge, moneary auhoriies mus reac by raising nominal raes in he curren period, and in all he fuure period unil he price level has compleely converged o he nominal anchor couneracing he eec of expeced inaion on curren demand. This is he essence of he so-called `Taylor principle'. 9 The economy will hen approach a seady sae such ha: + i = + e (4.7) 4.3. Inaion variabiliy and he Phillips curve In he previous secions we have proceeded under he exreme assumpion ha no price adjusmen is possible in he shor run. However, we could easily revisi our analysis by allowing some parial adjusmen of shor run-prices owards heir equilibrium level. In doing so, we would derive a Phillips Curve ha is, a posiive relaion beween he oupu gap and curren inaion. Suppose ha rms ener he period wih a prese price, bu now hese prices can be modied afer observing he realizaion of he shocks. Adjusing prices, however, enails some cos. In his case each rm will choose o adjus is price only parially. For simpliciy we will iniially discuss he case in which he adjusmen is symmeric across all rms. This sligh modicaion of our seup enables us o discuss a few imporan resuls. A rs resul is ha, provided ha he moneary auhoriies implemen he opimal policy sance = Z, here will be no price adjusmen in equilibrium. As shown above, when opimally se, moneary policy reac o shocks by sabilizing marginal coss compleely. Bu wih consan marginal coss, here is no incenive for rms o change prices in he shor run. Opimal moneary policies make nominal rigidiies irrelevan in equilibrium: he oher side of he same coin is ha price exibiliy is irrelevan oo. A an opimum, he inaion rae will be consan, and equal o he desired inaion rae. There will be no inaion variabiliy beween periods. A second resul is ha insucien sabilizaion will induce some shor-run variabiliy of inaion raes. Suppose ha moneary auhoriies deviae from he opimal rules. Marginal 7 We absrac from produciviy growh. Wih produciviy growh he analysis would remain subanially similar, once he naural real ineres rae is appropriaely adjused. 8 If he nominal anchor is oo low, he fac he nominal ineres rae canno be negaive (a zero lower bound on he ineres rae i > ) may complicae he implemenaion of opimal sabilizaion policy. See for insance Krugman 998, Svensson 23 and Eggersson and Woodford The original conribuion is Taylor

16 coss will hen no be compleely sabilized. Bu wih variable marginal coss rms have an incenive o change heir price in he shor run. Moreover, marginal coss and he oupu gap will be posiively relaed o each oher: high marginal coss (which are no be mached oneo-one by higher prices) lead o a fall in employmen, hence o a posiive oupu gap. Lower marginal coss have he opposie eec. Hence, produciviy shocks ha are no compleely ose by moneary policymakers open oupu gaps. The laer are associaed wih ucuaions of inaion, above and below rend. In addiion o raising he average markups, imperfec sabilizaion also raises he variabiliy of inaion. Wih parial adjusmen of prices, our model generaes a Phillips curve. 2 Above we have shown ha subopimally high average markups are a componen of he welfare coss of insucien sabilizaion leading o deviaions of employmen and consumpion from heir benchmark levels under price exibiliy. There are oher componens relaed o inaion variabiliy. To he exen ha he process of price adjusmen requires real resources and absorbs labor inpus ha would oherwise be employed in he producion secor, inaion variabiliy per se will raise average disuiliy of labor for any level of consumpion. Mos imporan, when price adjusmen is asymmeric across rms, in response o a shock here will be dieren prices for goods ha are however symmeric in preferences and echnology, i.e. ha should have he same price in equilibrium. In his case, he dispersion of inaion raes in he economy will induce disorions in relaive prices, reducing welfare. 2 Throughou our exercises, we have considered economies where opimally designed sabilizaion policies can eliminae disorions associaed wih nominal rigidiies. I is worh reieraing ha his is generally no he case, as policymakers usually do no have enough or ecien insrumens o reach heir objecives, and herefore face policy rade-os. The lieraure has discussed several examples of economies wih policy rade-os, especially in he framework of model wih saggered price adjusmen, where cos-push inaion may preven moneary policies from supporing ecien allocaion wih complee price sabiliy Transmission of scal shocks To conclude he presenaion of he closed-economy model, we consider wo modicaions of our baseline seup. Firs, we modify he specicaion of he uiliy funcion (2.) and pose: U = ln C `+ + To he exen ha is posiive, he marginal disuiliy of labor eor is no longer a consan. The key implicaion of his modicaion is ha an increase in labor eor is now associaed wih an increase in he real wage (and marginal cos). In fac, he wage equaion (2.6) is now: (4.8) W = P C` (4.9) 2 I is easy o verify ha a posiive exogenous moneary shocks will raise employmen above is naural rae, inducing a emporary increase in inaion. 2 Many conribuions in he lieraure inroduce nominal rigidiies allowing for saggered price adjusmen or shor-run coss of nominal price adjusmen, leading o explici inaion dynamics. The condiion of opimal pricing ypically includes a erms reecing conemporaneous expecaions of fuure price adjusmen. 6

17 Second, we inroduce public demand in he model and consider he macroeconomic eecs of governmen purchases of goods nanced wih lump-sum axes. 22 In wha follows, we dene g as he raio of governmen spending o aggregae consumpion, or: g = G C. (4.) How does our graphical apparaus change under he new assumpions? In he presence of governmen spending, he `AS' equaion (2.4) becomes: C ( + g) = Z` (4.) An increase in governmen spending ils he `AS' locus downward (similar o a negaive produciviy shock): for any given level of privae consumpion, agens need o work more o accommodae boh privae and public demand. There is no eec on he `AD' locus, according o which only privae nominal spending P C is aeced by he moneary sance. In he ligh of he previous secion, his poin is sraighforward when he insrumen of moneary policy is he nominal ineres rae (in fac, equaion (4.5) holds regardless of he presence of governmen spending). 23 Finally, boh modicaions of he baseline model aec he naural rae `NR' locus. In fac, i is possible o show ha under exible prices he naural rae is: `flex = ` + ( + g) + (4.2) where ` is he same consan dened in (2.8). 24 Figure 6 illusraes he eecs of an unanicipaed permanen scal expansion. The economy sars o a poin O. In he shor run, he increase in g ils he `AS' locus downward. Since shor-run prices are predeermined and (by assumpion) here is no change in he moneary sance, consumpion does no change eiher. Insead, he economy moves along he `AD' locus, and employmen increases in andem wih governmen spending by an amoun OA. 25 In he long run, real wages and marginal coss adjus upward o reec he permanen increase in demand for goods. As a resul, oupu increases by less han public spending, so ha he supply of goods available for privae consumpion goods falls while prices increase. In Figure 6, he higher real wages shif he `NR' locus o he righ: for any level of consumpion, agens are now willing o supply more labor. A he same ime, prices P increase for any level of he moneary sance, so 22 Public spending can be assumed o be purely dissipaive, wih no impac on households' uiliy. Alernaively, i can be assumed ha governmen spending eners households' uiliy in an addiively separable way, so ha an increase in public spending has no eec on he marginal uiliy of consumpion or he marginal disuiliy of labor eor. 23 Aggregae money demand may be a funcion of boh privae and public consumpion. Under his assumpion he `AD' locus could sill be independen of governmen spending, provided ha scal expansions are accommodaed by moneary policy. 24 Noably, under hese simple modicaions of he model i is no longer rue ha E(`) = `flex. In fac, one can show ha: E(`) = ` + [E ( + g)] 2+ + E ( + g) Noice ha he oupu muliplier of a governmen expansion is. To obain `Keynesian' scal mulipliers above one he model needs o be modied e.g. o allow for non-opimizing agens, or overlapping generaions of households. 7

18 ha he `AD' locus shifs downward. Thus, he economy reaches an equilibrium such as poin B, corresponding o lower consumpion and higher oupu levels relaive o he iniial seady-sae allocaion (poin ): higher public spending crowds ou privae spending and generaes inaion. In welfare erms he new allocaion is Pareo inferior o he previous equilibrium, unless here are direc uiliy gains from higher public consumpion. 5. Exchange raes and prices in open economy: more building blocks We now exend our analysis o he sudy of inerdependen, open economies. The model is fully specied in Appendix II. Relaive o he closed-economy model analyzed above, here are a leas wo new imporan feaures o consider. Firs, he equivalence of oupu and consumpion is no longer valid. Firms sell in wo markes, domesically and abroad. Modelling nominal rigidiies raises imporan issues abou rms' pricing behavior. Are produc prices prese in domesic currency only? Or, raher, do rms x wo ses of prices, one for he domesic marke and he oher for he expor marke (provided ha produc markes are sucienly segmened so ha consumers canno arbirage price dierenials)? A second dierence is ha, in addiion o he macroeconomic disorions associaed wih nominal rigidiies and monopoly power in producion, here is now a new disorion relaed o a counry's monopoly power on is erms of rade, ha is, he relaive price of foreign raded goods in erms of domesic raded goods. Firms ignore he impac of heir pricing and producion decisions on he overall counry's erms of rade. A decenralized equilibrium reecs his ineciency, adding a furher dimension o he policy problem. In wha follows we build a wo-counry general-equilibrium heoreical framework. Our graphical apparaus in he wo-counry case is o a large exen similar o he one developed for closed-economy analysis. However, because of a number of feaures specic o inerdependen economies, we will modify he inerpreaion of several variables, and reconsider our resuls abou he design of ecien sabilizaion policies. 5.. Exending he basic model o he world economy The world economy consiss of wo counries of equal size, Home and Foreign, each producing a counry-specic ype of good ha is raded worldwide. Counries and ypes of goods are denoed by he same leer, H and F, respecively. Similarly o he closed-economy case, in each counry monopolisic compeiors produce imperfecly subsiuable varieies of he same naional good, employing a linear echnology wih labor as he only inpu in producion. Households consume boh naional and foreign goods. In boh counries he elasiciy of subsiuion beween dieren varieies of he same ype of goods () is higher han he elasiciy of subsiuion beween ypes of goods H and F, ha we posi equal o one. In each counry here is a counry-specic produciviy shock. To he exen ha macroeconomic shocks are no perfecly correlaed across counries, naional residens in he wo counries bene from having access o some kind of risk-sharing mechanism. For simpliciy, and o minimize analyical dierences wih respec o he closed-economy case, we proceed by posiing from he sar ha asses markes are complee, so ha agens can achieve full consumpion 8