NBER WORKING PAPER SERIES AGGREGATE SUPPLY AND POTENTIAL OUTPUT. Assaf Razin. Working Paper

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1 NBER WORKING PAPER SERIES AGGREGATE SUPPL AND POTENTIAL OUTPUT Assaf Razi Workig Paper 094 hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 050 Massachuses Aveue Cambridge MA 038 February 004 The paper was wrie while Assaf Razi was a visiig scholar i he Hog Kog Isiue for Moeary Research. The Isiue s hospialy is ackowledged. I am graeful for Lars Svesso for isighful commes. The views expressed herei are hose of he auhors ad o ecessarily hose of he Naioal Bureau of Ecoomic Research. 004 by Assaf Razi. All righs reserved. Shor secios of ex o o exceed wo paragraphs may be quoed wihou explici permissio provided ha full credi icludig oice is give o he source.

2 Aggregae Supply ad Poeial Oupu Assaf Razi NBER Workig Paper No. 094 February 004 JEL No. E E E60 ABSTRACT The New-Keyesia aggregae supply derives from micro-foudaios a iflaio-dyamics model very much like he radiio i he moeary lieraure. Iflaio is primarily affeced by: (i) ecoomic slack; (ii) expecaios; (iii) supply shocks; ad (iv) iflaio persisece. This paper exeds he New Keyesia aggregae supply relaioship o iclude also flucuaios i poeial oupu as a addiioal deermia of he relaioship. Implicaios for moeary rules ad o he esimaio of he Phillips curve are poied ou. Assaf Razi Eia Berglas School of Ecoomics Tel Aviv Uiversiy Tel Aviv ISRAEL ad NBER razi@pos.au.ac.il

3 . Iroducio The New Keysia aggregae supply relaioship ypically liks iflaio surprises wih flucuaios i he oupu gap bu here is o idepede role for he flucuaios i poeial oupu. Based o such cosruc micro-based moeary rules do o have he poeial oupu as arge; he moeary rules arges are exclusively iflaio raes ad oupu gaps. Aoher brach i he iflaio lieraure is cocered wih he log-erm level of poeial oupu. The lieraure pois ou o he log ru coss of iflaio based o some cross-coury evidece. Fidigs poi o some hreshold effecs i he relaioship bewee iflaio ad growh. Cosequely above cerai coury-specific iflaio hresholds growh is egaively affeced by mea iflaio. [e.g. see Barro (995) ad Kha ad Sehadji (00)]. However his log ru chael hrough which moeary policy affec poeial oupu is o cosidered i his paper. Raher he paper demosraes how o brig he poeial oupu io he aggregae supply relaioship by icorporaig he effecs of ivesme i capaciy o aggregae supply. The aalysis is coduced i a opimizaio-based New Keyesia framework a la Blachard ad Kiyoaki (987) employig he aalyical ools i he lucid exposiio of Woodford (003). Specifically he model feaures imperfec compeiio i he produc marke i which he producers mark up oupu prices over margial coss ad also mark dow wages below he margial produciviy of labor. We hus derive a versio of he Markups of prices over wages i our model which ur ou o be couer-cyclical a very proouced pheomeo i he Europea markes as oed by Cohe ad Farhi (00). They oe ha Europea firms i bad imes maage o keep he prices high while heir US couerpars are pressed io cus ad discous of various forms. This is why he produc marke versio of he Phillips curve (i.e. he relaio bewee iflaio ad he oupu gap) i Europe seems o be relaively more sable empirically ha he labor marke versio (i.e. he relaio bewee wage growh ad uemployme).

4 Evidely he equilibrium relaio bewee iflaio ad excess capaciy is sigificaly iflueced by he degree of compeiio i he produc marke. A key feaure of such a equilibrium is he degree of sraegic ieracios bewee firms ha se heir prices ex ae ad oher domesic ad foreig firms ha se heir prices so as o clear he markes ex pos. This marke-orgaizaio feaure deermies i ur he degree of price sickiess. Udersadig why omial chages have real cosequeces (why a shor ru aggregae supply relaioship exiss) has log bee a ceral cocer of macroecoomic research. Lucas (973) proposes a model i which he effec arises because ages i he ecoomy are uable o disiguish perfecly bewee aggregae ad idiosycraic shocks. He ess his model a he aggregae level by showig ha he Phillips curve is seeper i couries wih more variable aggregae maximal demad. Followig Lucas Ball Makiw ad Romer (988) show ha sicky-price Keyesia models predic ha he Phillips curve should be seeper i couries wih higher average raes of iflaio ad ha his predicio oo receives empirical suppor. Lougai Razi ad ue (00) ad Razi ad ue (00) show ha boh Lucas s ad Ball-Makiw-Romer s esimaes of he Phillips curve slope deped o he degree of capial accou resricios. The remaider of he paper is orgaised as follows. Secio lays ou he New- Keyesia aalyical framework. Secio 3 derives he aggregae supply relaioship. Secio 4 cocludes wih implicaios of he aggregae supply relaioship o opimisig moeary rules ad o he empirical lieraure. The Aalyical Framework Cosider a closed ecoomy wih a represeaive household ha is edowed wih a coiuum of goods-specific skills uiformly disribued o he ui ierval [0 ] o be supplied o a differeiaed produc idusry. As a cosumer he represeaive household has access o cosumpio of boh domesic goods (disribued o [0 ]). The household seeks o maximize a discoued sum of expeced uiliies: 3

5 E s s [ u( C ; ξ ) ( v( h ( j); ξ ) dj φ( M / )] β s s 0 s s s P where β is he subjecive discou facor C is he Dixi-Sigliz (977) idex of household cosumpio P he Dixi-Sigliz price idex M/P he demad for real balaces ξ a preferece shock ad h(j) he supply of ype-j labor o he producio of good of variey j. As usual we defie he cosumpio idex ad is correspodig price idex respecively as C 0 c θ θ θ ( j) θ dj ad P p dj 0 θ θ ( j) () where c(j) represes domesic cosumpio of he jh good ad p(j) he domesic-currecy price of c(j). The elasiciy of subsiuio amog he differe goods is θ> ad he umber of goods ha are produced is equal o. For our purpose he releva uiliy-maximizig codiios iclude a ira-emporal codiio for he choice of labor supply of ype j: vh u ( h ( j) ξ ) ( C ; ξ ) c ( j) ; w () P ad a ier-emporal codiio for he cosumpio-savig choice: u u c c ( C ; ) ( C ; ξ ) ξ β ( r ) (3) 4

6 whre r is he real rae of ieres i period. As i he Dixi-Sigliz (977) model demad for good j saisfies θ p ( j) y ( j) (4) P The producio fucio assumes he form y [ ] ( j) k ( j) f A h ( j) / k ( j) where A is a radom labor-augmeig produciviy shock. We follow Woodford (003 chaper 5) ad assume (for racabiliy) ha here is a separae capial sock k (j) for each good raher ha a sigle real marke for capial services ha each producer has access o. Ivesme spedig is i he amou I ( j) I[ k ( j) / k ( j) ] k ( ) j where he fucio I[ ] is a covex fucio as i he sadard ivesme cos-of-adjusme exbooks. I (j) represes purchases by producer j of a Dixi-Sigliz composie good: I θ θ θ 0 i ( j) I ( j) θ di θ > For simpliciy he elasiciy of subsiuio θ is he same as i he case of cosumpio purchases. The variable cos of supplyig y (j) is w f [ y ( j) k ( j) ] which implies a (real) margial cos of / s ( j) P A f w ( j) ( y ( j) / k ( j) ) [ f ]. 5

7 6 By usig equaio () we ca replace he real wage above by he margial rae of subsiuio. Imposig symmery across firms (so ha we ca drop he idex j) he above equaio ca be rewrie as ( ) ( ) ( ) ( ) [ ] c h k y f f A C u A k k y f v A C y k s / ; ; / ; ξ ζ ξ (5). Price Seig Firms are moopolisically compeiive i he goods markes ad each oe of hem behaves like a moopso i he labor marke (wih producer j as he sole demader for labor of ypej). A fracio γ of he moopolisically compeiive firms ses heir prices flexibly a p supplyig y ; whereas he remaiig fracio - γ ses heir prices oe period i advace (i period ) a p supplyig y. I he former case he price is marked up above he margial cos by a facor of > θ θ µ so ha ( ). 0 ; A I y k s P p ξ µ (6a) I he laer case p will be chose o maximize expeced discoued profi ( ) h w y p i E ( ) [ ] / k p P f w p P i E θ θ θ θ where we have used he iverse demad fucio from equaio (4) for y ad he iverse producio fucio for h. Oe ca show ha p saisfies ( ) 0 A I y k s P p P i E ξ µ θ (6b)

8 This codiio has a iuiive ierpreaio. I he special case of perfec ceraiy his is ohig bu a sadard equaio describig price as a mark-up over margial cos like equaio (6a). Wih uceraiy i ca be ierpreed as a weighed average of price markups over margial cos. This expeced value is equal o zero. Wih price-pre-seig he firm is commied o supply accordig o he realized demad. Hece he realizaio of shocks will affec acual oupu wih egaive shocks leadig o excess capaciy ad posiive shocks o over-capaciy. Our model predics ha he mark-ups of he producers who pre-se heir prices will be couer-cyclical. Negaive demad shocks will iduce he flex-price firms o adjus heir prices dowward aracig demad away from ad hus lowerig he margial coss ad jackig up he price mark-ups of fix-price firms. Give p ad p he aggregae price idex i equaio () ca be rewrie as: [ ( ) ] θ θ γp γ p θ. P ( ). The Labor Marke The marke for each ype of goods-specific skill of labor service is characerized by workers as wage-akers ad producers as wage-makers as i he moopsoy case. Figure describes equilibrium i oe such marke. The dowward-slopig margial-produciviy curve is he demad for labor. Supply of labor S h is implicily deermied by he uiliy-maximizig codiio for h i.e. see equaio (). The upward-slopig margial facor cos curve is he margial cos chage from he producer poi of view. I lies above he supply curve because Woodford (003) assumes he Calvo price-seig framework. He derives a aggregae supply block cosisig wih muliple dyamic equaios. Our assumed price seig framework yields a sigleequaio aggregae supply relaioship. This simple form focuses aeio o he coefficie of he poeial oupu variable i he aggregae supply relaioship. 7

9 i order o elici more hours of work he producer has o offer a higher wage o oly o ha (margial) hour bu also o all he (ira-margial) exisig hours. Equilibrium employme occurs a a poi where he margial facor coss is equal o he margial produciviy. Equilibrium wage is give by B wih he worker' real wage marked dow below her margial produc by a disace AB. Full employme obais because workers are offered a wage accordig o heir supply schedule. This is why our Phillips curve will be saed i erms of excess capaciy (produc marke versio) raher ha uemployme (labor marke versio). I fac he model ca also accommodae uemployme by iroducig a labor uio which has moopoly power o bargai o behalf of he workers wih he moopsoisic firms over he equilibrium wage. I such case he equilibrium wage will lie somewhere bewee S h ad M P h ad uemployme ca arise so ha he labor marke versio of he Phillips curve ca be derived as well. To simplify he aalysis we assume i his paper ha he workers are wage-akers. I he limiig case where he producers behave perfecly compeiive i he labor marke he real wage becomes equal o he margial produciviy of labor ad he margial cos of labor curve is o sesiive o θ oupu chages. Thus wih a cosa mark-up he Phillips curve becomes fla i.e. o relaio exiss bewee iflaio ad excess capaciy. θ 8

10 W/P Figure : Labor Marke Equilibrium Margial Facor Cos Labor Supply Mark Dow Margial Produciviy h.3 Ivesme Profi maximizaio by producer j yields a firs-order codiio for ivesme P I' [ k ( j) / k ( j)] E ( ) { q ( j) ( k ( j) / k ( j)) I'[ k ( j) / k ( j)] I[ k ( j) / k ( j)]} i P where q is he shadow value (because here is o ay real marke) of a addiioal ui of capial. 3 I is wrie i a Bellma-like equaio as follows. q ( j) w ( j) f ( A h ( j)/ k ( j) ( A h ( j)/ ( k ( j) )) ( A h ( j)/ k ( j) )) ( ) A f A h ( j)/ k ( j) (7) Noe ha if a real marke were o exis q (j) i equaio (7) will be equal o he margial produciviy of capial as expeced. 3 See Woodford (003 chaper 5). 9

11 .4 Poeial Oupu Poeial oupu is defied as he price-flexible level of oupu. I he case where all prices are fully flexible (i.e. γ ) oupu will aai is aural level implicily defied by µ s( K I ; ξ A ). Noe ha depeds o he capial sock K ad o curre ivesme I. 3. Aggregae Supply ad Ivesme This secio derives he aggregae supply relaioship. I has is roos i he expecaios-augmeed Phillips curve of he kid hypohesized by Friedma (968) ad Phelps (970) for boh closed ad ope ecoomies. [see also Ball Makiw ad Romer (988) ad Robers (995).] I order o obai a racable soluio we log-liearize he equilibrium codiios aroud he seady sae. I he seady sae ξ 0 ad A Ā. We assume ha β(r) ad i r (i.e. iflaio is se equal o zero i he shock-free seady sae). Defie xˆ log x x x ~ as he proporioal deviaio of ay variable x from is deermiisic seady x x sae value x. We ca he log-liearize he model equaios aroud he deermiisic seady sae equilibrium. where s s ω ( ) ( ) yˆ yˆ σ yˆ yˆ σ Iˆ ωp k k (8) 0

12 ω ω w ω p ω w vhh ω p v h f f ad σ cu u cc c Log-liearizig he wo price-seig equaios [( a) ( 6b) ] (7)] ad usig equaio (8) yields: ( P ) ( P ) ( )( y ˆ log σ ˆ ) σ Iˆ ω ( kˆ kˆ ) p 6 he ivesme rule [equaio log ω (6a ) ( P ) E [ ( P ) ( )( y ˆ log ˆ ) Iˆ p ( kˆ kˆ σ σ ω )] log ω (6b ) Defie as sadard he iflaio rae by l( P / P ) ( π ) ( P ) E log( P ) π E. log π so ha Equaios (6a ) ad (6b ) ca be combied o obai he lik bewee iflaio surprise ad flucuaios i oupu gap ivesme ad he sock of capial as follows. π E ( π ) γ ω σ θω ( γ ) ( ˆ ˆ ) σ ωp Iˆ Kˆ θω θω (9) Real margial coss icrease wih a rise i he curre level of ecoomic aciviy; hus hey are affeced by flucuaios i he aggregae capial sock ad ivesme demad. Cosequely he flucuaios i ivesme ad he capial sock are egaively correlaed wih surprise iflaio holdig cosa he oupu gap. 4. Aggregae Supply ad Poeial Oupu

13 Poeial oupu is defied as he hypoheical oupu level ha would resul if prices ad wages are compleely flexible bu oher disorios like axes ad imperfec compeiio are lef i place. Tha is poeial oupu is ormally lower ha he efficie oupu level (he Pareo-opimal oupu level). The level of poeial oupu is solved implicily from: ( ) A I y k s ; ξ µ Log-liearizig he equaio ad rearragig yields: [ ] p u I K ˆ ˆ σ ω σ ω (0) where A da d u ξ ζ ξ ς ζ ς is a shock erm. Rearragig erms i equaio (0) ad subsiuig he resulig relaioship io equaio (9) yields he aggregae supply relaioship we are seekig as follows. Equaio () demosraes ha he flucuaios i poeial oupu are egaively correlaed wih iflaio surprises for a give realizaio of he shock ad a give level of he oupu p u I K ˆ ) ( ˆ σ ω σ ω ( ) ( ) ( ) u E ˆ ˆ ˆ θω σ ω θω σ ω γ γ π π ()

14 gap. This meas ha he iflaio-oupu radeoff is hree-dimesioal: amog iflaio oupu gaps ad poeial oupu. I he absece of ivesme however he aggregae supply relaioship reduces o he coveioal relaioship bewee surprise iflaio ad he oupu gap: π E ( π ) γ ( γ ) ω σ θω ( ˆ ˆ ) () Therefore he iflaio-oupu rade-off becomes wo-dimesioal: bewee iflaio raes ad oupu gaps. 4. Coclusio The New-Keyesia aggregae supply derives from micro-foudaios a iflaio-dyamics model very much like he radiio i he moeary lieraure. Iflaio is primarily affeced by: (i) ecoomic slack; (ii) expecaios; (iii) supply shocks; ad (iv) iflaio persisece. This paper exeds he New Keyesia aggregae supply relaioship o iclude also flucuaios i poeial oupu as a addiioal deermia of he relaioship. Should poeial oupu become a arge variable for ceral baks? Should ceral baks respod o poeial oupu? Firs oe has o be clear wha "arge variable" ad "respodig" meas. The mos useful defiiio of "argeig" a variable is ha he variable is a "arge variable" i he sese ha i is a argume i he loss fucio o be miimized (ad he loss fucio is icreasig i he disace bewee he arge variable ad he "arge level" for he variable). There is aoher use of "argeig a variable" as meaig "respodig o a variable" where he laer meas ha he variable i quesio is a argume i he reacio fucio ha represes he equilibrium isrume seig as a fucio of he sae of he ecoomy. The problem is ha he 3

15 relaio bewee he loss fucio ad he correspodig opimal reacio fucio (he reacio fucio ha miimizes he loss fucio) is complex ad ypically o oe-o-oe. Wha eer i he loss fucio are he arge variables. Wha eer io he reacio fucio are he deermias of (he forecass of) he arge variables ha is he predeermied variables ha describe he sae of he ecoomy. Typically a arge variable eers he reacio fucio oly if he variable is also a predeermied sae variable (which i is i some models). Also he coefficies i he reacio fucio are complex ad o moooic fucios of he parameers of he loss fucio ad he res of he model. Thus should poeial oupu be a arge variable i he sese of idepedely eerig io he loss fucio? I he presece of capial goods i he model he aswer could be ha poeial oupu could eer as a separae argume ad also o he exe ha i eers io he oupu gap. Tha is he oupu gap should be oe of he arge variables (wih a zero arge level meaig ha he arge for oupu is poeial oupu). I pracice hough moeary policy probably have a raher complex effec o poeial oupu eve i he shor ru. Thus ay aemp o sar sysemaically affec poeial oupu for isace aempig o icrease i owards he Pareo opimal level of oupu could lead dow he iflaio-bias lae of Kydlad-Presco ad Barro-Gordo. Oher policies ha moeary policy like fiscal policies srucural policies ha reduce regulaory barriers ad improve compeiio or subsidies o research raiig ad educaio seem o be beer desiged o affec poeial oupu. The framework of aalysis ha could give a aswer o hese quesios could usefully be he oe pursued by Woodford (003) who skilfully reduces a dyamic opimizaio problem of 4

16 he choice of he desired moeary rule based o he represeaive cosumer s welfare io a liear-quadraic opimizaio problem. Exedig his framework o a aalysis of he ieracios bewee moeary ad fiscal policies Beigo ad Woodford (003)) he cosraied-efficie allocaio is achieved whe oupu is equal o he would be price-flex o-wedge disorios level wih a zero price dispersio (or oher coss of iflaio) ad real value of he iiial goverme omial deb equal o he deermiisic seady sae real deb. I he broader-scoped framework ha is specified i his paper A cojecured quadraicliear opimal problem is o miimize a carefully derived loss fucio subjec o hree cosrais: () Aggregae- supply relaioship; () Goverme deb dyamics ad 3) he dyamic low goverig he poeial accumulaio of he sock of capial. The cojecured loss fucio is he discoued value of a weighed sum of squared deviaios of iflaio from a zero level (so as o miimize disorig price dispersio amog firms of ideical echologies ad demad schedules) he squared deviaios i oupu from arge oupu ad he level of he oupu arge. The arge oupu level is likely o be differe from poeial oupu uder moopolisic compeiio because of he exisece of a wedge bewee he margial produciviy of labor ad he leisure/cosumpio margial rae of subsiuio. My iuiio is ha sice his paper demosraes ha poeial oupu improves he iflaiooupu gap rade-off he ask of he moeary auhoriy which rades off iflaio ad oupu gaps is faciliaed if hey arge poeial oupu as well as he iflaio flucuaios ad he oupu gaps. Therefore a Taylor-like ieres rule which arges o oly he flucuaios i iflaio raes ad oupu gaps bu also he flucuaios i poeial oupu is boud o raise he measure of cosumer. The broader-scope aggregae supply ha is derived i his paper has also implicaios for he empirical lieraure. The New Keyesia Phillips curve has araced reewed ieres also i much of he empirical research. Gali ad Gerler (999) ad Gali Gerler ad Lopez- Salida(00) prese evidece ha US ad Europe iflaio dyamics are cosise wih a varia of he New Keyesia Phillips Curve. Poeial oupu plays a role i he aalysis oly o he exe ha i is eeded o measure he oupu gap. Thus he revised versio of he aggregae supply relaioship which icludes poeial oupu as oe of he iflaio-oupu rade-off s deermias has a obvious implicaio for he empirical lieraure as well. A ew esimaio sraegy o come o grip wih he broader scope of iflaio-oupu rade off is warraed. 5

17 6

18 Refereces () Ball Laurece (993) Wha Deermies he Sacrifice Raio? i N. Gregory Makiw (ed.) Moeary Policy (Uiversiy of Chicago Press 994). () Ball Laurece N.Greg Makiw ad David Romer 988 The ew Keyesia ecoomics ad he oupu-iflaio rade-off Brookigs Papers o Ecoomic Aciviy (3) Beigo Pierpaolo ad Michael Woodford (003) Opimal Moeary ad Fiscal Policy: A Liear-Quadraic Approach NBER Workig Paper (4) Blachard Olivier ad Nobu Kiyoaki 987 Moopolisic compeiio ad he effecs of aggregae demad America ecoomic Review (5) Cohe Daiel ad Emmauel Farhi 00 The Phillips curve across he Alaic: I is he price curves ha differ CEPR discussio paper 300 December. (6) Dixi Aviash ad Joseph E. Sigliz Moopolisic compeiio ad opimum produc diversiy America Ecoomic Review (7) Friedma Milo The role of moeary policy America Ecoomic Review (8) Gali Jordi ad Mark Gerler (999) Iflaio Dyamics: A Srucural Ecoomeric Approach Joural of Moeary Ecoomics 44 () Ocober 95-. (9) Gali Jordi Mark Gerler ad David Lopez-Salido(00) Europea Iflaio Dyamics Europea Ecoomic Review 45 (7) Jue (0) Gordo Rober J. 98. Why Soppig Iflaio may be Cosly: Evidece from Fouree Hisorical episodes i Rober E. Hall (ed.) Iflaio: Causes ad Cures Uiversiy of Chicago Press () Kha Mohsi S. ad Sehadji Abdelhak S. (00) Threshold Effecs i he Relaioship Bewee Iflaio ad Growh IMF Saff Papers () Lae Philip R. 00 The ew ope ecoomy macroecoomics: a survey Joural of Ieraioal Ecoomics (3) Lougai Prakash Assaf Razi ad Chi-Wa ue (00) Capial mobiliy ad he oupu-iflaio radeoff Joural of Developme Ecoomics (4) Lucas Rober E. (973) Some Ieraioal Evidece o Oupu-Iflaio Tradeoffs America Ecoomic Review 63 (Jue)

19 (5) Kha Mohsi ad Sehadji (00) Threshold Effecs i he Relaioship Bewee Iflaio ad Growh IMF Saff Papers. (6) Obsfeld Maurice. ad Keeh Rogoff (996) Foudaios of ieraioal macroecoomics Chaper 0 (MIT Press Cambridge). (7) Oku Arhur (978) Efficie Disiflaioary Policies America Ecoomic Review (8) Phelps Ned.S. (970) Microecoomic foudaios of employme heory (Noro New ork). (9) Razi Assaf ad Chi-Wa ue (00) The New Keyesia Phillips Curve: Closed Ecoomy vs. Ope Ecoomy Ecoomics Leers (0) Woodford Michael (003) Ieres ad Prices: Foudaios of a Theory of Moeary Policy Priceo Uiversiy Press. () Zhag Lawrece Huiya (00) Sacrifice Raios wih Log-Lived Effecs Johs Hopkis Uiversiy Workig Paper. 8