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LAURENCE B A L LNew York UniversityN . GREGORY M A N K I WHarvard UniversityD A V I D ROMERPrinceton University

The New KeynesianEconomics and the Output-Infation Trade-08IN T H E E A R L Y 1980s, the Keynesian view of business cycles was introuble. T he problem w as not n ew empirical eviden ce against K eynesiantheories, but weakness in the theories themselves. ' According to theKeyn esian view, fluctuations in ou tput a rise largely from fluctuations innominal aggregate dem and . The se changes in dema nd hav e real effectsbec ause nominal wages and prices ar e rigid. But in Keyne sian models ofthe 1970s, the crucial norninal rigidities were assumed rather than

We thank Toshiki Jinushi, David Johnson, and David Weil for research assistance;Ray F air, Paul Wac htel, and mem bers of the Brookings Panel for helpful discuss ions; andthe National Sc ience Foundation for financial suppo rt.1. Keynesian models of wage and price adjustm ent based on Phillips curves providedpoor fits to the data of the early-to-mid-1970s. But subseq uent m odifications of the m odels,such as the addition of supply shocks, have led to fairly good performances. See thediscussions ~ I IOlivier J . Blancha rd, "Why Does Money Affect Output? A Survey ,"Working Pap er 2285 (National Bureau of E conom ic Researc h, June 1987); and R obert J .

Gordon, "Postwar Developments in Business Cycle Theory: An Unabashedly New-Keynesian Perspective," Keynote L ecture , 18th CIR ET Conference, Zurich, Septembe r1987.


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2 Brookings Papers on Economic Activity, 1 I988explained-assumed directly, a s in disequilibrium m ode ls, or introducedthrough theoretically arbitrary assumptions about labor contracts . 'Inde ed, it wa s clearly in the interests of agents to eliminate th e rigiditiesthey were assumed to cre ate . If wages, for exam ple, were set above themarket-clea ring level, firms could increase profits by reducin g wag es.Microeconomics teaches us t o reject models in which, as Robert L uca sputs i t, "there ar e $500 bills on the sidew alk." Th us the 1970s and early1980s saw many economists turn away from Keynesian theories andtoward new classical models with flexible wage s and prices.

But Key nesian economics has m ade much progress in the past fewyears. Re cent rese arch has produced models in which optimizing agentscho ose to cre ate nominal rigidities. This accom plishme nt derives largelyfrom a cen tral insight: nominal rigidities, and h enc e the real effects ofnominal dem and shoc ks, can b e large even if the frictions preventing fullnominal flexibility ar e slight. Seemingly minor as pec ts of the ec ono my ,suc h as cos ts of price adjustme nt and the asynchronized timing of pricechanges by different firms, ca n explain large nonn eutralities.Theoretical demonstrations that K eynesian m odels can be reconciledwith microeconomics do not constitute proof that Keynesian theoriesar e correct. Inde ed, a weak nes s of recent mode ls of nominal rigidities isthat they do not appear to have novel empir ical implications. AsLawrence Summ ers argues:While word s like me nu co sts an d overlapping con tra cts ar e often heard, l i tt le ifany empirical work has demonstrated connect ion between the extent of thes ephen om ena and th e pattern of cyclical fluctuations. It is difficult to think of anyanom alies that Keyn esian researc h in the "nominal rigidities" tradition hasre solved , o r of any new phenomena that it has rende red c ~ m pr eh en s i b l e . ~The purpose of this paper is to provide evidence supporting newKeynesian theories. We point out a s imple prediction of Keynesian

2. For disequil ibrium models, see Robert J . Bar ro an d Her sch e l I . Grossman, "AGeneral Disequil ibrium Model of Inco me and Emp loym ent," American Economic Review,vol. 61 (Mar ch 1971), pp. 82-93; an d E. Malinvaud , The T11eor.y of Un enlp loym entReconsidered (Basil Blackwell , 1977). Fo r contra ct mod els, see Stanley Fisch er, "Long -Term C ont racts , Rat ional Expecta t ion s and the Optimal Money Supply Rule , ' ' Journal ofPolitical Economy, vol . 85 (Feb ruar y 1977), pp. 191-205; an d Jo Ann a G ray , "OnIndexat ion and Con t ract Length ," Journal of Political Econ om y, vol . 86 (Feb ruary 1978),pp. 1-18.3 . Lawren ce H . Sum me rs , "Should Keynesian E conom ics Dispense wi th the Ph il lipsCu rv e?" i n R o d Cro ss , ed . , Un emp loym ent, Hystere sis, and the NattrralRate Hypothesis(Basil Blac kwe ll, 1988), p. 12.


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3aurence Bal l , N . Gregory Mankiw, and Dalsid Romermodels that contradicts other leading macro econom ic theories and showthat i t holds in actual economies. In doing so, we point out a "newphenomenon" that Key nesian theories "render com prehens ible."

T he prediction that we test co nce rns th e effects of steady inflation. InKey nesian mo dels, nominal sho cks have real effects because nominalprices change infrequ ently. An increas e in the averag e rate of inflationcauses firms to adjust prices mo re frequently to ke ep up with the risingprice level. In turn, m ore frequent price chan ges imply that prices ad justmo re quickly to nominal s hocks, and th us that the sho cks have sm allerreal effects. We test this prediction by examining the relation betweenave rage inflation and the size of the real effects of nominal s hoc ks bothacross countries and over time. We measure the effects of nominalshock s by the slope of the short-run Phillips cur ve.

Othe r prominent macroeconom ic theories do not predict that averageinflation affects the slop e of th e Phillips cu rv e. In particular, o ur empiricalwork provides a sharp test between the Keynesian explanation for thePhillips curve and the leading new classical alternative, the Lucasimperfect information mo del.4 Ind eed , on e goal of this pap er is to redoLu cas's famo us analysis and dramatically reinterpret his results. Lu casand later authors show that countries with highly variable aggregatedemand have steep Phillips curves. That is, nominal shocks in thesecountries have li t t le effect on output. Lucas interprets this finding asevidence that highly variable demand reduces the perceived relativeprice changes resulting from nominal sho cks . W e provide a Key nesianinterpretation of Lu cas's result: more variable de ma nd, like high ave rageinflation, leads to more frequent price adjustment. We then test thediffering implications of the two theories for the effects of averageinflation. Ou r results are con sistent with the K eynesian explanation forthe Phillips cu rv e and inconsistent with the classical explana tion.

In addition to providing evidence about m acroecon omic theories, ou rfinding that aver age inflation affects the sho rt-run o utput-inflation trade -off is important for policy. For example, it is likely that the trade-offfacing policymakers in the United State s has changed as a consequenc eof disinflation in the 1980s. Our estimates imply that a reduction in

4. Robert E. Lucas, Jr . , "Expectat ions and the Neutral i ty of Money," Joltrnal ofEconomic Theory, vol. 4 (April 1972), pp. 103-24; L uc as , "Som e International Ev iden ceon Output-Inflation Tradeoffs," American Economic Review, vol. 63 (June 1973), pp.326-34.


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4 Brookings Papers o n Econom ic Ac t iv ity , 1:1988average inflation from 10 perc ent to 5 percent substantially alters theshort-run impact of aggregate dem and .The body of the paper consists of three major sections. The firstdiscusses the new res earch that provides m icroeconomic foundationsforKe ynesia n theor ies . Th e second presents am odel ofpr ice ad jus tment .I t dem onstrates the connection betwe en ave rage inf lation and t he slopeof the Phillips curve and contrasts this result with the predictions ofother the ories. The third section provides both cros s-country and t imeseries evidenc e that s upports the predictions of the model.

New Keynesian TheoriesAccording to Keynesian econo mics, f luctuations in employment and

outp ut arise largely from fluctuations in nominal aggregate dem and . Th ereason that nominal shock s ma tter is that nominal wages and prices arenot fully flexible. The se views a re the basis fo r conventiona l ac cou nts ofmacroeconomic e vents . F or exam ple, the consen sus explanation for the1982 recession is slow growth in nominal demand resulting from tightmonetary policy. Th e research program described he re is modest in thesense that it seeks to strengthen the foundations of this conventionalthinking, not t o provide a new theory of fluctuations. In particular, itsgoal is to an swe r the theo retical question of how nom inal rigidities arisefrom optimizing behavior, since the absen ce of an answ er in the 1970swas largely responsible for the decline of Keynesian econom ics.

In the following discussion we first describe t he c entra l point of therecent literature: large nominal rigidities a re possible ev en if th e frictionspreventing full nominal flexibility are small. We next describe somephe nom ena that greatly strengthe n the basic argu m ent, including rigidi-ties in real wages and prices and asynchronized timing of price cha nge s.We then discuss two innovations in recent models that are largelyresponsible for their succe ss: the introduction of impe rfect competitionand an em phasis on price a s well as wage rigidity. Finally, we a rgue thatthe ideas in recent work are indispensable for a plausible Keynesianac co un t of fluctuations.'

5 . Som e of the ideas of this l i terature are discussed informally by earl ier Keyn esian


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5aurence Ball, N. Gregory Mankiw , arzd Dcrvid Rotner

S M A L L N O M I N A L F R I C T I O N S A N D L A R G E N O M I N A L R I G I D I T I E SThe recent literature on nominal rigidities enters an argument that

Keynesians appeared to be losing. Members of the new classical schoolthat developed in the 1970s challenged Keynesians to explain therigidities in Keynesian models. In response, Keynesians sometimescited costs of adjusting prices. But as the classicals pointed out, thesecosts, while surely present, appear small. Indeed, the frequently men-tioned "menu costs"-the costs of printing new menus and catalogs, ofreplacing price tags, and so on-sound trivial. Thus the impediments tonominal flexibility in actual economies appear too small to provide afoundation for Keynesian models.

A common but mistaken response is that there are many obvioussources of large wage and price rigidities: implicit contracts, customermarkets, efficiency wages, insider-outsider relationships, and so on. Theproblem is that these phenomena imply rigidities in real wages andprices, while the Keynesian theory depends on rigidities in nominalwages and prices. Real rigidities are no impediment to complete flexibilityof nominal prices, because full adjustment to a nominal shock does notrequire any change in real prices. The absence of models of nominalrigidity reflects the microeconomic proposition that agents do not careabout nominal magnitudes. The only apparent departures from thisproposition in actual economies are the small costs of nominal adjust-ment.

Thus recent work begins with the premise that it is inexpensive toreduce nominal rigidity and asks how substantial rigidity nonethelessarises. The central answer of the literature is presented by Mankiw,Akerlof and Yellen, Blanchard and Kiyotaki, and Ball and R ~ m e r . ~Journal of Economic Literature, vol. 19 (June 1981), pp. 493-530, and the discu ssion ofexterna lities from nominal rigidity in Charles L. Schultze, "M icroeconomic Efficiencyand Nominal Wage Stickiness," American Economic Review, vol. 75 (March 1983,pp. 1-15.

6. N. G regory M ankiw, "Small Menu Costs and Large Business Cycles: A Macroec-onomic Moael of Monopo ly," Qi~arterly ournal o f Econom ics, vol. 100 (May 1985), pp.529-37; Geo rge A. Akerlof and Jane t L . Yellen, "A Near-Rationa l Model of the BusinessCycle, with Wage and Price Inertia," Quizrrerly Jolirnal of Econo mic s, vol. 100 (1985,


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6 Brookings Papers on Econornic Activity, 1.1988Second-O rder Private Co sts and First-Order Business Cyc les. Mankiw

and Akerlof and Yellen make a simple but imp ortant point. The y stud yimperfectly competitive econom ies and sh ow that the cost of nominalrigidities to price setters ca n be m uch smaller than the m acroecon omiceffects. An exam ple that i l lustrates the cos t to price setters is a firm thatinitially se ts its price at the profit-maximizing level but d oe s not adjus tafter the money supply falls. We let n(*)den ote the firm's profits a s afunction of its price an d let P be the firm's predeterm ined price and P*its profit-maximizing price, which it would set if it adjusted. Using aTaylor ex pan sion , we ca n approxim ate the firm's profit !oss from notadjusting as

But since P*maxim izes profits, r 1 ( P * )s ze ro . Thus the profit loss fromnonad justmen t is second order-that is, proportional to the square of(P* - P ) . As long as the predetermined price is close to the profit-maximizing pric e, the cost of price rigidity t o the firm is sm all.

But rigidity can have first-order macroe conom ic effects. An increasein nominal money with nom inal prices fixed leads to a first-order incre asein real aggregate dem and , and hence in real ou tput. F or exam ple, if theaggregate deman d cu rve is simply Y = M I P , rigid prices imply a cha ngein output proportional to the change in m oney.

Th e effect on social welfare is also first ord er, as follows from theassum ption of imperfect competition. Un der imperfect compe tition, theprofit-maximizing price is socially sub optim al. Th e price is too high andoutput is too low. Thus a t P* the first derivativ e of welfare with resp ectto th e firm's price is negative: welfare w ould rise if the piic e fell belowP*. Non adjustme nt to a fall in money implies P greater than P * ; giventhe ne gative first de rivative of welfar e, the welfare loss is first ord er.

~ e k u s ehe cost of r ig idity to a price set te r is second order while themacroeconomic effects are first order, the latter can be much larger.This finding resolv es the puzzle of why price setters refuse t o incur thesmall costs of reducing the bu siness cycle through more flexible prices.Despite the large macroeconomic effects, the private incentives aresmall.Aggregate Dernand Externali t ies . Blanchard and Kiyotaki providean im portant interpretation of the result in Mankiw and A kerlof-Yellen:


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7a u r en ce Ball, IV. G r e g o y Mn n k i i v , a n d Dabbid Ro me rthe macroeconomic effects of nominal rigidity differ from the privatecos ts because rigidity has an "aggregate dem and externality." A fewequations make this clear . Suppos e the dem and for the product of firm idep end s on aggregate spending and on the firm's relative price:

Fo r simplicity, aggregate dem and is given by a quan tity equation7

Combining equations 2 and 3 yields

According to equation 4, firm i's demand depends on its relative priceand on real money, which determines aggregate demand. Changes inreal money shift the demand curve facing firm i, and the firm's pricedetermines its position on the demand c urv e.If M falls and firm i doe s not ad just, the seco nd-o rder cost t o firm i isthat P,IP does not adjust to the new profit-maximizing level. Theexternality is that rigidity in firm i's p rice co ntribu tes t o rigidity in theaggregate price level. Given the fall in nominal money, rigidity in Pimplies a first-order fall in real money, which reduces demand for allfirms' goods . In other word s, there is an externality because ad justmentof all prices would prev ent a fall in real aggregate de m an d, but e ach firmis a small part of the economy and thus ignores this macroeconomicbenefit.

T he imp ortan ce of the e xtern ality is illustrated by a firm in a reces sioncaused by tight m one y. To the firm, the recession mean s an inward shiftof its demand curve and a resulting first-order loss in profits. The firmwould very much like to shift i ts dem and cu rve back o ut, but of cour seit can not do so by changing its price. In stea d, price adjustmen t wouldyield only the seco nd- orde r gain from o ptimally dividing the losses from

7. The only essential feature of equation 3 is the negative relation betwe en Y and P.We can interpretM as simply a shift term in the aggregate deman d equation . Thu s, as wediscuss below. the resu lts in recent pap ers conc ern the effects of any sho ck to aggregate


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8 Broohirlgs Pnprrs on E C O I I O I I Z ~ Cc t ~ v i t y ,1:1988the recession betw een reduced sales and a lower pr ice. Th e recessionwould end a nd ev eryo ne would be m uch bet ter off if all firms adjust ed.But eac h firm believes that it cann ot end the recession and therefore m ayfail to adjust eve n if the costs of adjustmen t a re muc h sm aller than t hecos ts of the recession.

This argument resembles standard microeconomic analyses of exter-nalities. C onsi der the classic exam ple of pollution. Pollution w ould begreatly reduced, and social welfare greatly improved, if each personincurred th e small cost of walking to the tras h can at the end of the block.But each individual ignores this when he throws his wrapper on thestree t bec ause he is only one of many polluters. Be cau se of externalities,ec on om ist s d o not find highly inefficient levels of pollution puzzling e ve nthough the costs of reducing pollution are small. For similar reasons,highly inefficient nom inal rigidities a re not a my ste ry ev en though m en ucosts are smal l.

Exte rnal i t ie s f iom Fluctuations in Dernand. Key nesians believe notonly that sh ock s to nominal aggregate dem and ca use large fluctuationsin outp ut and welfare, but a lso that th ese fluctuations are inefficient, andthus that s tabilization of dem and is desirable. The models surv eyed sofar do not provide a foundation for this view. As explained above,nonadjustm ent of prices t o a fall in dem and leads to large reductions inoutput and welfare. But nonadjustrnent to a rise in demand leads tohigher output an d, because output is init ially too low un der im perfectcom petition, t o higher welfare. 'Thus the implications of fluctuations foraverage welfare, an d hence the desirability of reducing fluctuations, ar eunclear. In dee d, Ball and R om er show tha t the first-order welfare effectsof fluctuations av erag e to zero , which mea ns that the first order-secondo r d e r d istin ctio n i s i rr el ev an t to th is i s s ~ e . ~

Non etheless, Ball and Ro me r show , by comparing the average socialand private costs of nominal rigidity, that small nominal frictions aresufficient for large reductions in average welfare. The private cost isfluctuations of a firm's re lative price aro und t he profit-maxim izing leve l.The social cost is the private cost plus the cost of fluctuations in realaggregate dem and . Gre ater flexibility would stabilize real dem an d, buteac h firm ignores its effect on the va riance of dem and , just as it ignoresits effect on the level of dem and aft er a given shoc k. Although both the


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9ar~renceBall , N . Gregoy Mankirt ' , and David Rorneraverage social and average pr ivate costs are second order , Ball andRo me r show that the former may be m uchla rger: fluctuationsin aggregatedem and ca n be m uch m ore costly than f luctuations in relative pr ices. Asa re sult , small frictions can p rev ent firms from a doptin g greater flexibilityeve n if busine ss cyc les a re highly inefficient.

S T I L L L A R G E R R I G I D I T I E STh e papers discussed so far establish that nominal r igidit ies c an be

far larger than the fr ictions that ca use them . But a s we now des cr ibe, thesimple models in these pa pers can no t fully explain nonneu tralities of thesize and persistence ob served in actual econo mies. Therefore, we turnto more com plicated models that inco rporate realis tic phen om ena thatmagnify no minal rigidities. Th ese ph en om ena include rigidities in realwages and prices an d asynch ronized timing of price chang es by differentfirms.

R e a l R i g i d i t i e ~ .As we argue above, real rigidities alone are noimpediment to full nominal flexibility. But Ball and R om er sho w that ahigh degree of real rigidity, defined as sm all resp on ses of real wages andreal pr ices to changes in real dem and, greatly increases the n onneutral-ities arising from small nominal friction^.^

This finding is important because, although models with nominalfrictions but no real rigidities can in principle produce large nominalr igidit ies , they do so only for implausible parameter values. Mostimportant, large rigidities arise only if labor supply is highly elastic,while labor supply elasticities in actual economies appear small. Therole of labor supply is illustrated by a hypothetical economy withimperfect competit ion and menu costs in the goods market but aWalrasian labor ma rke t. If men u cos ts led to nominal price rigidity, the nnominal shocks would cause large shifts in labor demand. But if laborsupply were inelastic, these shifts in labor demand would cause largechanges in the real wage an d th ereby create large incentives for pricesette rs to adjust their price s. As a resu lt, nominal rigidity wo uld n ot bean equilibrium.While for plausible param eter values nominal frictions alone prod ucelittle nominal rigidity, Ball and R om er sh ow that conside rable rigidity

9 . Laurence Ball and David Romer, "Real Rigidities and the Non-Neutra l i ty of


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10 B r o o k i n g s P a p e r s o n E c o n or n ic Activity, 1:1988can arise if the frictions are combined with real rigidities arising fromefficiency wages, cu stom er ma rkets , and the l ike. For exam ple, substan-tial nominal rigidity c an a rise from a com bination of real rigidity in thelabor market and im perfect competi t ion and menu costs in the good sma rket. If firms pay efficiency wa ges , for instan ce, the n real wages m aybe set above the marke t-clearing level, so that worke rs are off their laborsupply c ur ve s. In this situation a fall in labor dem and c an greatly redu ceem ploym ent witho ut a large fall in th e real wage ev en if labor sup ply isinelastic.

T he im po rtan ce of real rigidities fo r explaining nom inal rigidities isnot set t led, because there is no consensus about the sources andmag nitudes of real rigidities in actual econo mie s. In particular, phenom -en a like efficiency wages a nd cu sto m er marke ts increa se nom inal rigidityto the exten t that they redu ce desired respo nses of real wages and realprices t o dema nd shifts, but e conom ists ar e sti ll unsure of the sizes ofthese effects. Further research on real rigidities will lead to a betterunde rstand ing of nominal rigidities.

S tagge r e d Pr ic e Se t t in g . Even when real rigidities are added, themod els surveyed so far can not fully explain the size and persiste nce ofthe real effects of nominal shoc ks. In thes e m odels, the effects of sho cksare eliminated when nominal prices adjust. In actual eco nom ies, reces-sions following severe dem and contract ions can last for several ye ars,and while individual prices ar e fixed for substantial periods, these periodsare general ly shorter than several years. Th us m odels with st icky pricesmust explain why the effects of shocks persist af ter all prices a re cha nged.

An e xplanation is provided by the l i terature on stagge red price se tting,which show s that iffirms change prices at different t imes, the adjustme ntof the aggregate price level to sho cks ca n take m uch longer than the t imebetwee n adjustm ents of e ach individual price. o Th e "price level inertia"caused by staggering implies that nominal shocks can have large andlong-lasting real e ffects even if individual prices c han ge frequ ently.

10. John B. Taylor, "Staggered Wage Setting in a Macro Mode1,"American EconomicRev iew, vol. 69 (May 1979,Papers and procee dings , 1978) ,pp. 108-13; Tay lor, "Aggrega teDynamics and Staggered Contracts," J o ~ ~ r n u lf Political Economy, vol. 88 (February1980),pp . 1-23; Olivier J . Blan chard, "Price Asynchronization a nd Price L,evel Inertia,"in Rudiger DornbuschandMarioHenrique Simonsen, eds. , I n ju t ion , Debt , and lndexa t ion(M IT Pres s, 1983), pp . 3-24; Olivier J . Blanchard, "The Wage Price Spiral," Quarter/>>Journal of Economics, vol . 101 (Augu st 1986),pp . 543-65.


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11ailrence Bcill, N . Gregory Ma n k i w , and David RornerA simple examp le makes clear the imp ortance of the t iming of price

chan ges. Sup pose first that e ver y firm adjusts i ts price o n the first of eachmo nth, so that price setting is synchron ized. If the money supply fallson Jun e 10, output is reduced from June 10 to July 1, beca use nominalprices are fixed during this period. But on July 1 all prices adjust inproportion to the fall in mo ney, an d the rec ession en ds.

N ow suppo se that half of all firms se t prices on the first of each m onthand half o n the fifteenth. If the m oney supply falls on Ju ne 10, then onJun e 15 half th e firms have an opp ortunity to adjust their prices. B ut inthis c ase they may c ho ose to ma ke li tt le adjustm ent. B ecau se half of allnominal prices remain fixed, adjustment of the other prices implieschan ges in relative prices, which firms may not w ant. (In con trast , if allprices cha nge sim ultaneou sly, full nominal adjustm ent doe s not affectrelative prices.) If the Ju ne 15 price setters m ake li tt le ad justme nt, thenthe othe r firms make lit tle adjustm ent when their turn co m es on July 1,because they d o not desire relat ive price changes ei ther . And s o on. T heprice level declines slowly as the result of small decr eas es eve ry firstand fifteenth, and th e real effects of the fall in m one y die out slow ly. Insho rt, price adjustm ent is slow becau se neither grou p of firms is willingto be the first to m ake large cuts ."

As Blanchard e mp hasizes , if staggering oc cur s among firms at differ-ent points in a chain of production, i ts effects are strengthened.12 A

11. A natural question is why firms change prices at different times if this exac erba tesaggregate fluctuations. One obvious answer is that different firms receive shocks atdifferent times and face different costs of price adjustment. Laurence Ball and DavidRomer, "The Equilibrium and Optimal Timing of Price Changes," Working Paper 2412(NB ER , Octo ber 1987), show th at, beca use of externalities from stagg ering, idiosyncraticshocks can lead to staggering even if synchronized price setting is Pareto superior. Butidiosyncratic sh ocks can not explain all staggering. Fo r exam ple, some firms with tw o-yearlabor contracts set wages in even years and some set them in odd years, and this does notcorrespon d to deterministic tw o-year cycles in the arrival of sh ock s. Another explanationfor staggering is that it arises from firms' efforts to gain information. This source ofstaggering is discussed in Arthur M . Okun, Prices and Quuntities: A Mac roeco nom icAnulysis (Brookings, 1981), and formalized in L aurence Ball and S tephen G . Cecch etti,"Imperfect Information and Staggered Price Setting," Working Paper 2201 (N BE R, April1987). Fo r exam ple, a firm wants to s et wages in line with the wages of oth er firms. If allwages are s et simultaneously, e ach firm is unsure of what wage to set beca use it does notknow what others will do. This gives each firm an incentive to set its wage shortly afterthe oth ers . The desire of each firm to "bat last," as Okun puts it, can lead in equilibriumto a uniform distribution of signing da tes .12. Blanchard, "Price Asynchronization."


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12 Bioo king s P c~ pe is r1 Ecorlomic Activity, 1:1988firm's profit-maximizing price is tied t o both the prices of its inpu ts andthe prices of goods for which its prod uct is an input (the latter influencedem and for the firm's produce). Th us a firm does not wan t to adjust i tsprice to a sh ock if these oth er prices d o not adjust at the sa me time. Thisreluctance to make asy nchronized adjustmen ts causes price level inertia.Blanchard show s that the degree of inertia increases the longer the chainof production: i t takes a long time for the gradual adjustme nt of prices tomake its way through a complicated sy stem .

Th e li terature on staggered price setting com plemen ts that o n nominalrigidities arising from menu co sts . Th e degree of rigidity in the ag gregateprice level depends o n both the frequency and the timing of individualprice changes. M enu costs c ause prices to adjust infrequently. For agiven frequency of individual adjustment, staggering slows the adjust-ment of the pric e level. Larg e aggregate rigidities ca n thu s be explainedby a combination of staggering and nominal frictions: the former mag-nifies the rigidities arising from the la tter .

Asymmetric Effects ofDemund Shocks . We co nclude this part of ourdiscu ssion by m entioning a little-explored possibility for strengtheningKeynesian m odels. Th e models surveyed imply symm etric responses ofthe econo my to rises and falls in nominal aggregate dema nd . Fo r examp le,in menu cos t models the range of shocks to which prices d o not adjust issym metric around ze ro, and so is the range of possible chan ges in ou tpu t.But traditional Keynesian models often imply asymmetric effects ofdem and shifts. In undergraduate texts, for exam ple, the aggregate supplycurve is often draw n so that de creases in demand lead to large outputlosse s while the effects of incre ases ar e mostly dissipated through higherprices. Such asymmetries are intuitively appealing, and they greatlystrengthen the Keynesian view that demand stabilization is desirable:stabilization raises the average levels of output and emp loyme nt as wellas reducing the va rianc es. It is unclear w heth er plausible modificationsof new Ke ynesian m odels can produc e asymm etries. Asym metric effectsof sho cks could arise from asym m etric price rigidity-prices that aresticky dow nw ard but not upward-but this is ano ther appealing notiontha t is difficult to form aliz e."

13. Tim ur Kura n show s that asym metries in firms' profit functions, which many menucost models ignore, can lead to asymmetric price rigidity. But the asymmetries appearsmall. See Timur Kuran, "Asymmetric Price Rigidity and Inflationary Bias," AmericanEconotnic R e l i e n , , vol. 73 (June 1983), pp. 373-82; Ku ran , "Price Adju stmen t Costs ,


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Laltrrrlce Bal l , N . G r e g o r y M a n k i w , a n d D a v i d R o rn er

THE NEW A S S U M P T I O N S I N NEW K E Y N E S I A N M O D E L SAside from the specific arguments outlined above, recent research

establishes the general point that nominal rigidities can result fromoptimizing choices of agents in well-specified models. This contrastswith the ad hoc im position of rigidities in many of the K eyn esia n mo delsof the 1970s. Recent progress is largely a result of two innovations inmodeling: the introduc tion of imperfect competit ion and greater em pha-sis on price r athe r than wage rigidities.

Imperfect Compet i t ion . Microeconom ists have long recognized thatsticky prices and perfect competit ion a re incompatible. 141n acom petit ivemarket , a f i rm d oes not set i ts price, but acce pts the price quoted by theWalrasian auctioneer. Only under imperfect competit ion, when firmsset prices, does i t make sense to as k whe ther a firm adjusts i ts price to ashock. Nonetheless, Keynesian models of the 1970s, most clearlydisequilibrium m odels, im posed nominal rigidities on o therwise Wa lras-ian econom ies. Th e resul t was e mb arrassm ents in the form of unappeal-ing results or the need for additional arbitrary assum ptions. M any rece ntmo dels simply generalize earlier mode ls by allowing the firms' dem andcurves to slope down. This single modification sweeps away many ofthe problems with older models. Specifically, the new models withimperfect competition offer six advantage s:

-Private cos ts of rigidity are secon d order. Un der perfect comp eti-t ion, the gains from nominal adjustment are large. For example, ifnominal demand r ises and prices do not adjust , there is exce ss dem and.In this s ituatio n, an individual firm c an ra ise its price significantly andstill sell as much output as before, which implies a Barge increase inprofits. In c ontr ast , under imperfect com petition a higher price alwaysimplies lower sales. Sta rting from the profit-maximizing price-qllantitycombination, the gains from trading off price and sales after a sha ck a resecond order .Anticipated Inflation, and Output," Quarterly Journcll of Econonzics, vol. 101 (Ma y 1986),pp . 407-18.14. Se e, for example, Kenneth J . Arr ow , "Toward a Theory of Price Adjustm ent," inMoses Abramovitz and others, eds., The Allocation of Economic Resources: Essuys in


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14 Brookings Ptrprrs 011Economic Act i~ i t y ,1:1988-Output is demarld det erm ine d. W hen price rigidity is imp osed o n a

Walrasian market, so that the market does not clear, i t is natural toassu me that quant ity equals the smaller of supply and dem and , so thatoutput falls below the Walrasian level when price is either above orbelow the W alrasian level. But Keyn esians believe that whe n prices arerigid, increase s in dem an d, which mean prices below W alrasian levels,raise ou tput , just as decreases in dem and reduce output . This resul t isbuilt into many K eynes ian m odels through the unappealing assump tionthat output is demand determined even if demand e xcee ds supply. Forexam ple, in the G ray-Fisch er contract model, firms hire a s much lab oras they wa nt, regardless of the prefe rences of workers.15 In co ntra st ,under imperfect com peti tion, demand determinat ion arises natural ly.Firms set prices and then meet d em an d. Crucially, if dem and rises, firmsar e happy to sell mo re eve n if they d o not a djust their prices, becauseunde r imperfect com petition price initially exceeds marginal co st. Thu schanges in demand always c ause change s in output in the same direct ion.

-Booms raise welfa re. Under perfect competit ion, the equilibriumlevel of outpu t in the abs enc e of shocks is efficient. Thu s increas es inoutput resulting from positive shocks, as well as decreases resultingfrom negat ive shoc ks, reduce welfare. In the Gray-Fischer m odel , forexample, half the welfare loss from the business cycle occurs whenworkers are required to work m ore than they w ant . In actual eco nom ies,unusually high output and em ploym ent mean that the econ om y is doingwe11.16 And this is the ca se in m odels of impe rfect com petitio n. S inceimperfect competit ion pushes the no-shock level of output below thesocial optimu m, welfare rises wh en ou tput rises abo ve this level.

-Wage r igidity cau ses une mp loym ent through low aggregate de-m a n d . In 1970s models with sticky nominal wages, unem ploym ent occ urswhen prices fall short of the level expected wh en wages were set , s o thatreal wages rise and firms move up their labor dem and cur ve s. In actualeconom ies, however, f i rms often appear to reduce em ployment becausedemand for their output is low, not because real wages are high. Thisfact is not necessarily a problem for Keynesian theories if the goodsma rket is imperfectly com petit ive. In this cas e, a firm's lab or dema nd

15. Fischer, "Long-Term C ont racts ," and Gray, "On Indexation."16. Of course economists worry that low unemployment may be inflationary. Butsticky-price models with perfect competition imply that low unemploy ment is undesirableper se.


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15a u r en c~Bal l , N . Grrgoty Motlkitt', ntitl Drrlsid Romrrdepen ds on real aggregate dem and a s well as the real wage, becau sechanges in aggregate demand shift the firm's product demand (seeequation 2).-Real wa ges need rlot be counter ~cyc lical.mpe rfect com petit ion canremed y an embarrassing em pirical failure of traditional m odels based o nsticky nominal wages-the cyclical beh avior of real wa ges. We ca ntautologically write P = k W I M P L , where P is the price level, W is th ewage, M P L is the marginal product of labor, and p i s the m arkup of priceover marginal cost. If the markup is constant and marginal product oflabor is diminishing, as many 1970s mode ls assum ed, th en the real wage,WIP = M P L I k , must be countercycl ical . In actual economies, how ever,real wages ap pea r acyclical or ab it procyclical. This fact ca n be exp lainedif the m arginal produ ct of labor is cons tan t, as suggested by H all, or ifthe markup is countercyclical, as suggested by Rotemb erg and Sa lone rand by B ils.I7 Th us there need not be a l ink betwe en cha nges inemploym ent and change s in real wages.

-Nom inal rigidities hav e aggre giite de m an d exrerncilit ies. A s w ehave explained, since real aggregate d ema nd affects the deman d c urvesfacing individual firms, no minal rigidities ha ve extern alities. R igidity inone firm's price contributes to rigidity in the price level, which causesfluctuations in real aggregate d em and an d thu s h arm s all firms. The seexternalit ies ar e crucial to the finding that small frictions can hav e largemacroeconomic effects . Th e external it ies depend on imperfect compe-tit ion, for under perfect com petit ion, aggregate dem and is irrelevant toindividual firms bec au se they ca n sell all they wa nt at the going price.

Prodlrct Ma rke t Rigidities. Keynes and most K eynesians emphasizerigidities in nominal wa ges. But re cent wo rk fo cu ses largely on rigiditiesin product prices. T he change offers two adva ntage s.

-Goods are sold in spot m ark ets . Although there is clearly muchnominal wage rigidity in actu al economies-in U .S . labor con tracts, forexam ple, wages are set up to three years in advance-the allocativeeffects of this rigidity are uncle ar. T he implicit co ntra cts literature sh ow sthat i t may be efficient for contract signers to make employment

17. Robert E. Hal l , "Market S t ructure and Mac roec onon ~ic luctuat ions ," BPEA,2: 1986, pp. 285-322; Julio J . Rotemb erg and Gar th Saloner. "A Supergame-TheoreticModel of Price Wars during Boom s," Arnericclrl Ecorlornic re vie^,, vol. 76 (June 1986),pp. 390-407; Mar k Bils, "Cyclical Pricing of Dura ble Luxu ries ," Work ing Pa per 83(Univers i ty of Roche ster Center for Econo mic R esearch , M ay 1987) .


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16 Brookilzgs Papers on Economic Activity, 1:1988indepe ndent of wag es. T hat is, given long-term relationships with theirwo rke rs, firms inay cho ose the efficient amou nt of employm ent ratherthan m oving along their labor dem and curve s whe n real wages cha nge. 8In many product m arke ts, on the other hand , buyers clearly ope rate ontheir deman d cu rves. Fo r example, the local shoe store has no agreement ,explicit or implict , from its customers to buy the efficient number ofshoes regardless of the prices. Instead, rigidity in the storek pricesaffects its sale s of shoe s.

-Real wag es need not be countercyclical. As we argue above,acyclical real wage s are possible e ven if nominal rigidities oc cu r only inwag es. But it is easie st to explain acyclical o r procyclical real wages ifprices a s well as wages ar e sticky. In this case , the effect of a sho ck onreal wages dep end s on the relative sizes of the adjustme nts of prices andwages .

Des pite the adva ntages of studying rigidities in goods m ark ets, we a reambivalent about the deem phasis of labor m arkets, because the apparentrigidities in nominal wages may have important allocative effects.Fu rthe r resea rch o n the relative impo rtance of wage and price rigiditiesis needed .

D I S C U S S I O NWe c onclud e this section by discussing seve ral issues conce rning the

impo rtance of recent theories and their plausibili ty.The Importance of Nom inal Rigidit ies. Nom inal rigidities are essen -

tial for explaining important features of business cycles. As we haveem phasize d, real effects of nominal disturbances , su ch as chang es in themoney stock, depend on so me nominal imperfect ion. Th e only prominentalternative to nominal rigidities is imperfect information about theaggregate price leve l, an exp lanation that many econ om ists find implau-sible. It is possible, of cou rse , to maintain that m oney is neutral in theshort run-that Paul Vo lcker, for exam ple, had nothing to do with the1982 recession-but this also app ears unrealistic to many econo m ists.

18. Ear ly exposit ions o f th ~ sdeaappear inMart inNei lBai ly , "WagesandEmploymentunder Uncer ta in Dem and," Review of Econonzic Stud ies , vol. 41 (Jan uar y 1974), pp. 37-50; Costa s Azariadis, "Implicit Con tracts and Und erem ploym ent Equil ibria," Journal ofPolitical Economy, vol. 83 (D ec em ber 1975), pp. 1183-1202; and Robe rt E. Hal l , "The


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17a ~ r r e n c eBtrll, N . Gr ego ry Marzkiw, arztl D m i d R o n z ~ rT hu s it is difficult to exp lain th e relation of ou tpu t to nom inal variableswitho ut nom inal rigidities.

No min al rigidities a re also importa nt fo r explaining the effects of realshocks to aggregate dem and, resul ting, for exa mp le, from changes ingovernment spending or in the ex pectat ions of investors. The point isclear if we inte rpret M in the aggregate dem and equa tion, Y = MIP, a ssimply a shift term, in which ca se real disturbances that shift dem andaffect output through the sam e channels a s changes in mone y.

Not all explanations for the output effects of real demand shocksdepend o n nominal imperfections. Robe rt Barro's model of gov ernm entpurchases , for one, does not . 9 But such explanations in vok e implausiblylarge labor supply elasticities. Th us nom inal rigidities, while not the on lyexplanation for the effects of real dem and, a re perhaps the most appeal-ing.

In the rnodels w e hav e su rvey ed, slow adjustment of prices impliesthat shock s cause temporary deviations of output and em ployment fromtheir "natural rates." Rece nt ly, how ever, models ofhy sterr sis , in whichshocks have permanent effects , have become popular . For example,Blanchard and Sum me rs argue that the natural rate of unemployment inEurope an countr ies changes when a ctual unemp!oyment chang es, sothat the re is no uniqu e level to which une mp loym ent returns.?O If thes etheories a re co rrect, then nom inal rigidities can not fully explain unem -ployment , because nominal prices eventual ly adjust to shocks; someadditional explanation, s uch as th e insider-outsider model in Blancha rdand Summers, is needed for the persistence of unemployment . Butnominal rigidities may be crucial for explaining the initial impulses inunem ploymen t. Fo r exa mp le, after rising during the late 1970s, unem -ployme nt in Britain has rem ained high, suggesting hyste resis. Bu t thebest explana tion for the original increase is arguably a conventional o ne:slow adjustment of wages and prices to shoc ks like t ight mone tary policyand increases in import prices.

The Importance of Externali t ies j iom Rigidity . Externalit ies fromnominai rigidity, the cen tral eleme nt of menu cost m odels, a re essential

19. Robert J . Barro , "Output Effects o f Governm ent Purchases ," Jorlrncrl ofPoliticn1Economy, vol. 89 (D ece mb er 1981), pp. 1086-1 121.20. Olivier J . Blanchard and Lawrence Sum mer s , "Hysteres is and the EuropeanUneniployment Problem," in Stanley Fisch er, ed. , N B E R M a c r o r c o n o n ~ i c s A n n u n l ,1986(MIT Pr es s, 1986), pp . 15-78.


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18 Brookings Papers on Ecotlor?z ic Act iv i ty , 1 :I988for a plausible the ory of rigidities. If rigidities ex ist, on e of the followingstatements must be true: rigidities do not impose large costs on theeco nom y; rigidities hav e large cos ts to the firms and w orke rs who cre atethem, but these are exceeded by the costs of reducing rigidities; orrigidities ha ve small private co sts , and so sm all frictions ar e sufficient tocreate them, but externalit ies from rigidity impose large costs on theeconomy. The problem with the first statement is the difficulty ofexplaining apparently costly events, such as rises in unemploymentfollowing mon etary con traction s, without nominal rigidities. The secondseems implausible: i t would not be costly for magazine publishers toprint new prices every ye arra ther tha n every four years, a s they typical lydo .21 hu s the third s tatem ent is the best hope for explaining rigidities.

W h a t A re Men u Costs? Models of nominal rigidity depend on somecos t of full flexibili ty, albeit a small on e. T he term menu cos t may bemisleading because the physical costs of printing menus and catalogsmay not be the most important barriers to flexibili ty. Perhaps moreimp ortant is the lost co nven ience of fixing prices in nominal terms-thecos t of learning to think in real term s and of computing the nominal pricechanges corresponding to desired real price changes. More generally,we can view infrequent revision of nominal prices as a rule s f thum b thatis m ore convenient than cont inuous revision. Th us , rather than referringto m enus, we can state the central argument of recent papers as follows.Firm s take the c onvenient shor tcut of infrequently reviewing and chang -ing prices . T he resulting profit loss is sm all, so firms ha ve little incentiveto eliminate the shortcut, but externalit ies make the macroeconomiceffects large.

At a somewhat deeper level , we can interpret the convenience offixing nominal rather than real prices as that of using the medium ofexchange, dol lars, as au ni t of accoun t .'*Alternatively, followin g Ak erlo fand Y ellen, we ca n view simple rules of thum b as arising from "near-

21. S tephen G . Cecchett i , "The Frequency of Price Adjustment: A Study of theNewsstand Prices of Magazines," Jorunal o f Econometr ics, vol. 31 (Augu st 1986), pp .255-74. T he co st of reducing nom inal wage rigidity m ay be significant if rigidity is red uce dthrough shorte r labor contra cts, which require more frequ ent negotiations betwee n unionsand m anag eme nt. But wage rigidity can also be reduc ed through grea ter indexation o r byhaving the nominal w age change m ore often ove r the life of a contrac t , neither of whichappears to have large cost s .22. Bennett T. McCallum, "On 'Real ' and 'St icky-Price' Theories of the BusinessCycle," Journ~11f M o n ey , Credit , c~rtd onhirzg, vol. 18 (N ove mb er 1986). pp. 397-414.


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19aurence Ball , N . Gregory Mankiw, alzd David Ronzerrationality ," a small d ep a rt ur e f ro m full o p t i m i ~ a t i o n . ~ ~n any c ase, theprecise sou rce offrictions is not importan t. Th e effects of nominal shoc ksare th e sam e wh ether rigidity a rises from printing c os ts, near-rationality ,o r something else.

Inflation, the Frequency of Adjustment, and the Phillips CurveRe cen t resea rch sh ow s that no mina l rigidity is possible in principle-

that on e can cons truct a m odel with firm microeconomic fou ndations inwhich rational agents choose substantial rigidity. But the validity ofKeynesian theories is not thereby establ ished. F or these theories to beconv incing, they m ust hnve empirical implications that contradict o thermacroecon omic theories, and the se predict ions must be confirmed byevidenc e. This section derives implications of recent K eyne sian m odels,and the next section tests them. As explained in the introduction, themain prediction is that the real effects of nominal shocks are smallerwhen average inflation is higher. Higher average inflation erodes thefrictions that cause nonneutralit ies, for example by causing more fre-quen t wage and price adjustm ents.

This section studies a specific model of the class described in theprevious section. In the mod el, a cost of price adjustm ent leads firms tochange prices at intervals rather than continuously. In addition toproviding a basis for the empirical tests of the next m ajor section, themo del is of theoretical in teres t. Pre viou s models of nominal rigidity arehighly stylized; for example, most menu cost models are static. Ourmodel is dynamic and has the appealing feature that the price leveladjusts slowly over t ime to a nominal shoc k. Th e speed of adjustm ent ,which is treated a s exog enou s in older Key nesian m odels, is endogen ous.It depends on the frequency of price adjustment by individual firms,which in tu rn is derived f rom pro f i t -m ax im iz a t i~ n . ~~

We first present the model and show that high average inflationreduc es the outp ut effects of nominal sho cks . W e also show that highlyvariable aggregate demand reduces these effects. We then investigate

23. Akerlof and Yellen, "A Near-Rational Mo del."24. Th e speed of adjustment is also endogenous in Laurenc e B all, "Externalities fromContract Length," American Econornic Review,vol. 77 (Se pte m ber 1987), pp. 615-29.


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20 Brookings Papers on Econowzic Act iv i ty , 1 :I988the model's quantitative implications by calculating the real effects ofshocks for a range of plausible parameter values. The results suggestthat the effects of average inflation and demand variability are large.Nex t w e argue that the implications of our model are robust: they c arryov er to broad classes of other Keyn esian mo dels.

Finally, we co mp are the predictions of K eynesian the ories with thoseof models in the new classical or equilibrium tradition, focusing onLucas's model of imperfect information. Like our model, Lucas'spredicts th at the size of the real effects of shock s depen ds negatively onthe variance of aggregate dema nd . Since this prediction is com mon toKey nesian and new classical theories, testing it empirically, as L uca sand oth ers hav e don e, is not useful for distinguishing betwe en the tw otheories. C rucially, Luc as's model differs from o urs by predicting thatthe effects of shoc ks do not dep end on av erag e inflation. This differenceleads to the tests of the models in the next s ection.

T H E M O D E L A N D Q U A L I T A T I V E R E S U L T SOur model of price adjustment is similar in spirit to those of John

Taylor and Olivier Blanchard." Th e model is set in continuous time.Th e econom y con tains imperfectly co mp etitive firms that change pricesat discrete intervals rather than continuou sly, bec aus e adjustments arecostly. Price setting is staggered, with an equal proportion of firmschanging prices at every instant. T he crucial dep artu re from Tay lor andBlanchard is that the length of t ime betwee n price changes, and he ncethe rate at which the price level adjusts to sh ock s, is endogenou s. Thu swe can study the determinants of the speed of adjustment.

Consider the behavior of a representative firm, firm i. Rather thanderive a profit function from specific cost and demand functions, wesimply ass um e that firm i's profits depen d on th ree variables: agg regatespending in the eco nom y, y ; firm i's relative price, p, - p ; and a firm-specific shock, & (all variables are in logs). Th e aggregate price level pis defined simply as the average of prices across firms. Aggregatespending y affects firm i's profits by shifting the demand curve that itfaces. When aggregate spending rises, the firm sells more at a given

25. Taylor, "Staggered Wage Setting" and "Aggregate Dynamics and StaggeredContracts"; and Blanchard, "Price Asynchronization" and "Wage Price Spiral."


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Laurence Ball , N . Gregory M ankiw , and David Ronzer 2 1relative price. T he term pi - p affects the firm's profits by determ iningthe position on the demand curve at which it operates. And 0, is anidiosyncrat ic shock to ei ther dema nd o r costs ( the presence of O i is notneeded for our main qualitative results, but i t strongly affects thequantitative results of the next se ction).

W e assu m e that th e elasticity of firm i's profit-maximizing real price,p? - p, with respect to y is a positive constant, v . Without loss ofgenerality, w e as su m e that the e lasticity of p.? - p with respect to 0, isone , and that 0, has z ero m ean. T hus w e can w rite the profit-maximizingreal price a s

where y is the natura l rate of output-the level at wh ich, if 0, equa ls i tsme an, the firm desires a relative price of one . (Relative prices eq ual toon e is the condition for a sym me tric equilibrium of the econo my wh enprices ar e flexible.)26

If price adjustment were costless, firm i would set pi = p h t everyinstant . We assume, however, that an adjustment cost leads f i rms tochange prices only at intervals of length A , which for simplicity isconstan t ove r t ime (later in this section we discuss th e implications ofallowing A to vary). S pecifically, eac h price change ha s a fixed cost F ,so adjustm ent costs pe r period are FIX.

As noted above, an equal proportion of firms sets prices at everyinstan t.27 f firm i sets a price a t t , i t choo ses the price and A to maximizeits exp ected profits, averaged o ve r the life of the price (from t to t + A).Maximizing profits is equivalent to minimizing profit losses from twosources: adjustment costs and deviations of price from the profit-

26. As an example offoundations for equation 5 , suppose that firm i's demand equationis y, = y - ~ ( p , p) (demand depends on aggregate spending and the firm's relative price),and that its log costs are yy, + (1 - e + ey)O,. This implies equation 5 with v = (y - 1)/(1- E +ey) and y = [l/(y- I)] In [(E- l ) / ~ ]the coefficient on 0, in the cost function ischosen to satisfy the normalization that the coefficient on 0, in equation 5 is one). Fordeeper microfoundations, see Ball and Romer, "Equilibrium and Optimal Timing of PriceChanges," where a price-setting rule like equation 5 is derived from utility and productionfunctions.27. We assume that price setting is staggered so that inflation is smooth. If all firmschanged prices at the same times, the aggregate price level would remain constant betweenadjustments and thenjump discretely. Wedonot model the sources ofstaggeringexplicitly;


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22 Brookings Pupers on Econotnic Act i t~i ty , :1988maximizing level. W e approx imate the latter by !A K (p, - P ? ) ~ ,whereK is the negative of the second derivative of profits with respectt o p ? - pi.Th us firm i's lo ss per unit of time is

M inimization of equation 6 implies a sim ple rule for choosing pi:

That is, a firm sets its price to the average of its expected profit-maximizing prices for the period w hen the price is in effect. We d escribethe m ore complicated determ ination of A below.

T o study the effects of nominal sh ock s, we m ust introduce a stochas ticnominal variable. We as sum e that the log of nominal aggregate dem and ,x = y + p , is exogenou s and follows the continuous-time analogue of arandom walk with drift:

where W ( t )is a W iener process. Th e first term in the expression for x ( t )captures trend growth of g per unit t ime; the second captures randomwalk innovations with variance qf.per unit t ime. Our analysis belowfocuses on the effects of the parameters g and oxon the economy. Amonetarist interpretation of equation 8 is that x ( t ) = m ( t ) + V-thevelocity of money is cons tant, and aggregate dem and is driven by rand omwalk movements in the money stock. A more g eneral interpretation isthat a variety of exo gen ous variables-fiscal policy, the exp ectatio ns ofinv es tor s, and so on-drive x ( t ) .

We make two final assumptions. First , the natural rate of outputgrows smoothly at rate I*.:(9 ) y ( t ) = pt.Along with the process for x ( t ) , this implies that average inflation isg - p. Sec ond , the firm-specific disturbances, the 0, 's, are un correlatedacross firms and follow con tinuous-time random walks wh ose inno va-tions hav e mean zero and variance ui per unit t ime.2s

28. More precisely, we assum e that 0, follows a stationary process and consider the


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Laurence Bal l , N . Gregory Mankiw, and David Rorner 23Tlze Belzavior of the Economy for a Given Frequency of Price

Changes . Below we show that average inflation, by influencing theinterval betwe en p rice chan ges, affects th e output-inflation trade-off inour m odel. A preliminary s tep is to solve for the behavior of the econo myfor a given interva l, A. We d o this by combining our assumptions aboutprice setting by individual firms and th en ag gregating. T he beh avio r ofindividual firms determines the behavior of the price level. A s describedab ov e, the behavior of price level-which eac h firm, being sm all, takesas given-in turn deter min es the beh avio r of firms. T he condition forequilibrium is that individual and ag gregate beh avio r are con sisten t; thatis, th at profit-maximizing price-setting rules fo r individual firms giventhe behavior of the price level in fact yield that behavior of the pricelevel. Th e details are com plicated, so we leave them for the app endix.H ere we simply present ou r main results.

Th e solution for the behavior of the price level takes the form

where d Z ( t - s ) = u , d W ( t - s ) is the innov ation in aggregate demandat t - s . T he first term in equ ation 10 cap tur es averag e inflation of g - p,and the second captures the effects of sh ocks. Th e term M J ( ~ ; A )ives theeffect of a demand shock a t t - s on th e price level at t .

Th e appendix derives the expression that defines w p ) . We ca nno t findan analytic solution to the exp ression and therefo re solve it numerically;the appendix describes how. We find when we solve for w(*)hat ,assuming v < l , w ( s ; A ) equals zero when s = 0 , increases with s , andapproaches one as s app roac hes infinity. That is , the immediate effect ofa shock o n the price level is zero (beca use a n infinitesimal propo rtion offirms changes prices a t t ) ;the effect of the sh ock grows o ver time; andasym ptotically the s hoc k is passed one-for-one into prices.

Th e crucial result ab out w e ) concerns the frequency of price changes:when v < 1 , w( s ; A)is decrea sing in A. A longer interval between changesin individual prices leads to slower adjustment of the aggregate pricelevel-for any s , a smaller proportion of a shoc k at t - s is passed intoprices by tSz9

29 . If v > 1 , firms want to adjust their prices more than one-for-one with real output;


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24 Brookings Papers on Economic Activ i ty , 1 :I988Th e behavior of real output follows directly from th e behavior of the

price level, the stochastic process for aggregate dem an d, and th e identityy = x - p :

Th e sizes of the real effects of nominal sho cks ar e given by 1 - this(-);is the theo retical counterpart of the parameter that we estim ate in thefollowing sectio n.

Finally, equation 11 implies a n expression fo r the variance of ou tput:(12) E{b(t) - B(t)12}= CT;j [ I - a.(s;A)12ds.

s =o

Th e variance of outpu t depen ds on the variance of demand shock s, o,and the size of the effects of sh ock s, 1 - This result is also used in( 0 ) .the empirical wo rk of the next major section.

The Equilibrium Frequency of Price Changes. We now derive acondition defining the equilibrium interval between price changes.Co nsid er firm i's problem of choosing its interval, A,, given that all oth erfirms in the economy choose an interval A. The value of a firm's lossfunction, L (equation 6), is affected by bo th Xi and A; the latte r matt ersbec aus e it determine s the b ehavior of the price level. Minimization ofL(Ai,A) with res pect to hi yields the first-order con dition dL(Ai,A)/dAi= 0.A sym metric Na sh equilibrium for A, AE is defined imp licitly by settingA, = A in this condition:

In other words, an interval A is an equilibrium if, when A is chosenthrough out the eco nom y, it is in firm i's interest to choose A as well.30

Bec ause we can find w(*) only nu me rically, we must also find the30 . Solving for the equilibrium interval between price changes is different from thecommon exercise of solving for the socially optimal interval. See, for example, Gray, "On

Indexation" (which focuses on the interval between wage changes-that is, the length oflabor contracts). The equilibrium and optimal intervals differ because, as we stress in thefirst section, firms' choices of the frequency of price adjustment have externalities. SeeBall, "Externalities from Contract Length," for a further discussion of this point.


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25a~ t re t l c eBall , N . G re gory Mankiw, and Drivid Rornerequilibrium A num erically, as described in the appen dix. W e find that Ais decrea sing in -ir, a,,and a,,where 7i = g - p is the av erag e inflationrate. Thus the interval between price changes decreases the higherave rage inflation. High inflation ca uses a firm's profit-maximizing nom -inal price to change rapidly, which raises the benefits from frequentadjustment. The interval A also decreases the greater the variances ofaggregate and firm-specific shocks. When either variance is large, afirm's future profit-maximizing price is highly u ncer tain, so the firm do esnot w ish to fix its price for long .

Th ese results, along with the results ab out th e effects of A , imply thatthe Phillips cu rve is stee per when 5,a,,o r a,is larger. Higher averageinflation re duc es th e interval betw een p rice cha ng es , which in turn raiseswe ), the proportion of a sho ck that is passed into prices. A larger va rianceof aggregate or firm-specific shock s also red uces A and thus raises w(-).These results imply that increases in -ir, a,,or a, lead to decreases in1 - we), the real effects of shocks. These predictions lead to theempirical tests of the next section.

Q U A N T I T A T I V E R E S U L T SWe now ask whether the effects of inflation and demand variability

identified abov e are quantitatively impo rtant. W e d o so by computingthe interval between price chang es and the real effects of shocks for arange of plausible param eter v alues .

Choice o f Parameters . Since our focus is the effects of averageinflation, g - p,and the standard deviat ion o fde m and ,a,,we experimentwith wide ranges of values of these parameters (g and p affect the resu ltsonly through their difference). This leaves three other parameters forwhich w e need baseline values: FIK , the ratio of the cost of changingprices to the negative of the second derivative of the profit function (Fand K en ter only through their ratio); a,,the s tand ard deviation of firm-specific shocks; and v , the elasticity of a firm's profit-maximizing realprice with respect t o aggregate outp ut.

We choose baseline parameters by experimenting with values ofFIK, a,,and v to find a com bination that implies plausible sizes for thereal effects of shock s. We then ask w hether these param eter values arerealistic. Fin ally, we investigate rob us tne ss by calculating the effects of


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26 Brook ings Pap e rs on Ec or lomic Ac t i v it y , 1.1988It is difficult to measure F and K direct ly, so we take an indirect

app roa ch . In a mod el of steady inflation and no sho cks (u,= u, = O),FIK determines the frequency of price cha nges . With FIK = 0.00015,firms chan ge prices every five quarters und er stea dy 3 percent inflationand every two quarters under steady 12pe rcent nflat ion. Microeconom iceviden ce suggests that actual intervals betw een p rice change s typicallyaverage two ye ars or more. T hus ou r baseline value of FIK is conserva-tive. W e certainly do not assum e menu co sts that are too large to beccxrlsistent with p rice setting in actu al econom ies.31

To pick a value for u,,we use the fact that u, equals the standarddeviation of m ove m ents in profit-maximizing price s, the p:'s, ac ro ssfirms. This leads us to use data on relative price variabili ty to gaugeplausible values of u,.Vining and Elwertowski report a 4-5 percentstandard deviation of annual relative price movements across highlydisaggregate (8-digit) co m pon en ts of the U . S . consum er pr ice index; th isis consistent with our assum ption of u, = 3 percent .32

Finally, there is li tt le qu antitative evidence conce rning the size of v,the e lasticity of profit-maximizing relative prices with resp ect to aggre-gate outpu t. Ho we ver , our cho ice of a small elasticity, 0.1, is consistentwith the common view that relative prices vary li t t le in response toaggregate fluctuations. Our baseline parameters are therefore FIK =0.00015, a,= 3 percent , and v = 0.1.

Results. Tab le 1 sho w s the effects of average inflation, g - p., andthe variabili ty of de m an d, u,,when F l K , a,,and v equa l their baselinevalues. F or wide ranges of g - p and u,, he table show s two figures.

31. For microeconomic evidence on price behavior, see Cecchetti , "The Freque ncyof Price Adjustment"; Anil K. Kashyap, "Sticky Prices: New Evidence from RetailCatalogs" (M IT, Novem ber 1987); and W . A. H. Godle-yan dC . Gillion, "Pricing Behaviorin Manufacturing Industry," National Institute Econornic Revie w, no. 33 (August 1965),pp . 43-47.32. Daniel R. Vining, Jr . , and Thom as C . Elwertowski, "The Relationship betweenRelative Prices and the General Price Level," American Economic Review, vol. 66(Sep tem ber 1976), pp. 699-708. As a mea sure of a,,Vining and Elwertowski's figure hasboth an upward and a downward bias. The upward bias occurs because staggered priceadjustme nt cau ses actual prices, the p ,'s, to vary ac ross firms even w hen profit-maximizingprices, the p;"'s, do not. As a result, the standard deviation of p,, which Vining andElwertowski m easure, is greater than the standard deviation of p : , which equals a,.T henegative bias in that variation acro ss compo nents of the C P I, eve n if these ar e highlydisag grega ted, is less than varia tion ac ros s individual prices. It is difficult to tell the relative


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Lorircnce Ball, N . Gregory M a n k i w , ond David Xorner 27Table 1. Effect of a Nominal Shock on Real Output and the Equilibrium Intervalbetween Price ChangesaAverageinflationrate , Dernanrl variability, a,(percent)g-)J,(percent) 0 1 3 5 10 20

Source : Authors ' ca lcu la t~o ns . ee t ex t descrip t ion .a. Th e table shows the effects of changing values of g - b a n d o,wh e n FIK, oe,and v equal their basel ine values.FIK is the rat io of the cost of changing prlces to minus th e secon d derivat ive of the profi t funct io n; oe is the standardd e v i a l ~o n of f i rm-spec~f ic hocks : and r i s the e las t i c i ty of a f i rm 's prof i t -max~m~zingeal prlce with respect toaggregate output . Basel ine values: FIK = 0.00015: oH = 3 percent : and r = 0.1. For each entry in the table, thefirst n umb er is the percentage effect of a 1 percent nominal shock o n real output af ter s ix months , the num ber inp a r e n th e s e s is t h e e q u ~ l ~b r l u mnterva l e tween pr lce changes , A . In weeks.

Th e first is the perc entage effect of a 1 perce nt change in dem and on realoutput six mo nths late r. A value of zero would m ean that prices adjustfully to the shock ; a value of on e would mean that prices d o not adjustat all . We refer to this figure as simply the real effect of a sho ck . Thefigure in parentheses is the equilibrium interva l betw een price c hang es,A , in weeks. As we explain above, inflation and demand variabili tyinfluence the rea l effects of shoc ks through their effects on A .

Table 1 shows that realistic increases in average inflation havequantitatively important effects. With u, = 3 percent , roughly thestandard deviation of nominal G N P growth for the postwar UnitedStates, the interval between price changes is 28 w ee ks if g - p. = 0, butfalls to 19 weeks if g - p. = 10 percent and 6 weeks if g - p. = 100pe rce nt. As a result , the real effect of a shoc k is 0.50 for g - p = 0,0 . 3 0 f o r g - p = l ope rcen t , andO.O1 fo rg - p = 100percent .


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28 Brookings Prrpers or1 Ecorzomic Acti~,ity, :1988Table 2. The Effects of Changes in FIK, v , and a, on the Slope of the Phillips Curveand the Equilibrium Interval between Price Changes

Average inflationrate."Parameter valrres g - C L5 20FIK v (perc ent ) percent percent

Sourc e: .4uihors ' calculat ion


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Laurence Ball, N . Gregory Ma nkiw , an d David Rorner 29unchanged for g - p. = 5 percen t . These l ines show how the parametersaffect the strength of the link between average inflation and the realeffect of a s hoc k.

R O B U S T N E S STraditional Keynesian models, such as textbook models of price

adjustment or the staggered co ntracts models of Fischer and T aylor, donot share the key predictions of ou r Th ese older theories treatthe degree of nominal rigidity (for exam ple, the length of labor co ntr ac tsor the ad justment speed of the price level) as fixed p aram eters ; thus theyrule out the ch annel through which ave rage inflation affects the output-inflation trade-off. On the oth er han d, o ur central results ap pea r to berob ust implications of Ke yne sian theo ries in which th e degre e of rigidityis endogenou s. T he intuition for the effects of inflation on th e frequencyof price adjustmen t, and of this frequenc y on the size of nonne utralit ies,is not tied to the specific assu mp tions of our m ode l.

One assu mption of our model that requ ires attention is that the intervalbetween price chan ges is constant o ver t ime. This assump tion is ad hoc:given ou r other assu mp tions, firms could increase profits by varying theinterval based on the realizations of sh ocks. In addition, th e assum ptionis unrealistic, b ecause firms in actual econo mies d o not alway s changeprices at fixed interv als.

We now consider the alternative assum ption that firms can freely varythe timing of price cha nge s. This assu mp tion of com plete flexibility isalso far from realistic. M ost w ages are ad justed at co nstant intervals ofa year. There appears to be greater flexibility in the timing of pricechan ges , but the limited evide nce sugg ests that it is not com plete. M ailorder companies change prices at fixed times during the year, eventhough they issue catalogs much more frequently than they changeprices, and thus could vary the dates of adjustments without issuingextr a catalogs. In addition, a broad range of industries appe ars to havea preferred time of the year, often Janu ary, for price chang es.34

It is not yet possible to solve a mo del like ou rs with flexible timing,33 . For a textbook mode l , see Rudiger Dornbusch and Stanley F ischer, Macroeco-nomics , 4th ed . (McGraw-Hill, 1987).34 . For evidence on mail order catalogs, see Ka shya p, "Sticky Prices." For evidenceon industries' preferred months for price changes, see Julio J. Rotemberg and Garth


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30 Brooking3 Pupc.r s or1 Erorzornic Activity, 1 :I988but suggestive results are available for simpler models. I n particular, aliteratu re beginning with Shesh inski and W eiss presen ts partial-equilib-riun-1mo dels in which a firm ch oos es to follow an "Ss" rule for adjustingits price: whe never inflation pushe s i ts real price outside so me b oun ds,it adjusts i ts nominal price to return the real price t o a target level. The semodels reproduce a crucial implication of our model: higher averageinflation leads to mo re frequen t price c hange s. H igh inflation cause s afirm's real price t o chan ge rapidly, so , for given Ss boun ds, the price hi tsthe bo unds mo re often. H igh inflation also cau ses the firm to widen itsbounds, which reduces the frequency of price changes, but does notfully offset the first effect.'Fo r our main argument to hold, the more frequen t chang es in individualprices that result from higher inflation must lead in turn to fasteradju stm ent of the aggregate price leve l. Intuition clearly sugg ests a linkbetw een the frequen cy of individual adjustm ent and the speed of aggre-gate ad,justmen t, but th e difficulty of studying ge nera l equilibrium w ithflexible timing preclud es a definitive proof. In dee d, in on e prom inentspecial ca se , the l ink does not ex ist . And rew Caplin and Daniel Spu lbersh ow that if we usslrrne that firms follow Ss rules with constant boun ds,and if aggregate deman d is nondecrea sing, then th e aggregate price leveladju sts imm ediately to nominal shocks-nominal sho cks ar e neu tral.Because aggregate adjustment is always instantaneous, i ts speed isobviously independent of the frequency of indiv idual pr ice ~ h a n g e s . ~ "Current research suggests that the Caplin-Spulber result does nothold unde r realistic con ditions. Th ere exist exa mp les in which firms donot follow Ss rules with constant bo unds , and s o a shock to the moneysupply is not neu tral, eith er if ther e is som e pers isten ce t o inflation or iffirms' optimal nominal prices som etime s fall. And when nonne utralit iesexist , i t appears plausible that their size depends on the frequency ofindividual price adjustm ent. Th us , overall , models of price adjustm entwith flexible timing app ear c ons isten t with the predictions of our mode l.37

35. Th e link betwe en inflation an d the frequenc y of adjustment is establish ed for thecase of consta nt inflat ion in Eytan Sheshinski and Yora m W eiss, "Inflat ion and Cos ts ofPrice Adjustment," Review, of Econ omic Studies , vol. 44 (Jun e 1977), pp. 287-303. Anexten sion to the case of stochastic inflation is presented by An drew S . Caplin and EytanSheshinski, "Optimality of ( s ,S) Pricing Policies" (Prince ton University, 1987).

36. Andrew S. Caplin and Daniel F. Spulb er, "Menu Cos ts and the Neutral ity ofMoney , " Quar te r l y Journal of Economics, vol. 102 (N ove mb er 1987), pp. 703-25.


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Lactrence Ball, ,V. Gregory Monkiw, and Dnvid Ronler 3 1Another robustness issue concerns the nature of the friction that

prev ents nominal flexibility. In ou r m ode l, the friction is a fixed cos t ofprice a djustmen t. An alternative view is that the technological cos ts ofmaking prices highly flexible are negligible but that for some reason,such as convenience, the desire to avoid com putat ion c osts, o r habit,price setters nonetheless follow rules that focus on nominal prices.38Without a theory that predicts the particular rules of thum b that pricesetters follow, theories of this type do not make precise predictionsconcerning the relationship betwee n average inflation and the de gree ofprice flexibility. But it appears that under reasonable interpretationsthese theo ries imply th at higher inflation increas es nominal flexibility.As average inflation rises, s o does th e cost of following a rule-of-thumbpricing policy stated in nominal term s, as d oes th e evidenc e that keepinga fixed nominal price is not equivalent to keeping a fixed real price.Although price set ter s may con tinue to follow rules of thu m b, they willincreasingly think in terms of real rather than nominal magnitudes.Nom inal price flexibility will thus incre ase.

T H E P R E D I C T I O N S OF NEW C L A S S I C A L T H E O R I E STh e prediction of Key nesia n m odels that av erag e inflation affects the

output-inflation trade-off is important because it is inconsistent withalternative macroeconomic models in the new classical tradition. Wenow review the predictions of new classical models, focusing on Lu ca s'simperfect information the or y. L ike K eyn esian mod els of nominal rigid-ity, Lu ca s's mod el is designed to explain the effects of nominal sh ock son output-that is, to generate a short-run Phillips curve . But Luc as'smodel has different implications abou t w hat de termines the size of theeffects.

In Luca s's model, agents wish to change their output in respon se tochanges in their relative prices, but not in response to changes in theaggregate price level. When an agent observes a change in his price,how ever, he cannot tell wh ether i t results from a relative o r an aggregate

optimal prices, see Blanchard, "Why Does Money Affect Output?" and Tsiddon, "The(Mis)behavior of the Aggregate Price Level" (Columbia U niversity, 1987). The se au thorsestablish results for the special case in which a firm's optimal price m oves on e-for-one


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32 Brookings Paper s on Economic Activity, 1 :I988mo vem ent. H e acts upon his best gu ess, which is that part of the chang ecomes from each source. Since agents interpret any price change aspartly relative, chang es that in fact result from a nominal shock hav eeffects on ou tput.

In Lu ca s's mo del, the size of the effects of nominal shocks depen dson the relative magnitudes of nominal and idiosy ncratic real sho cks . Inparticular, if nominal shocks are large, agents attribute most of themo vem ents in their prices to nominal sh ock s, and respond lit tle. Th us alarge variance of nominal aggregate demand leads to a steep Phillipscurv e. Luca s prese nts cross-coun try evidence supporting this predictionin his famo us 1973 paper. W e sho w, how eve r, that Key nesian m odelsmak e the sam e prediction, although the reason-a large variance ofaggregate dem and causes mo re frequent price changes-is very different.Because both Keynesian and new classical theories explain Lucas'sresults, his test does not he lp to distinguish betwee n them.

T he effect of ave rage inflation o n the output-inflation trade-off doesdistinguish Key nesian and new classical models. Theories of nominalrigidities predict that high inflation m akes the Phillips cur ve s tee pe r. InLu ca s's imperfect information mo del, averag e inflation is irrelevant tothe output-inflation trade-off, because only the variances of randomvariables, not the means, affect the uncertainty that agents face. Thisdifference between the theories is the basis for our empirical wo rk. (Asimple correlation be twe en ave rage inflation and the slope of the Phillipscurve is consistent with Lucas's model, because average inflation iscorrelated with the variance of demand, which affects the slope. Theissue is whether there is a relation between average inflation and theslope after we c ontrol for the variance of dem and .)

Another difference between the predictions of Keynesian and newclassical theories co ncerns the effects of idiosyncratic shoc ks. Accordingto Lucas, a large variance of relative price shocks increases the realeffects of nominal shocks, because it raises the proportion of theseshocks tha t agents misperceive a s real. Our model predicts that a largevariance of idiosyncratic shocks, like a large variance of aggregateshock s, leads to m ore frequent price changes and thu s reduces the effectsof nominal sho cks . If one could con struc t a measu re of the variance offirm-specific shocks, which we do not attempt in this paper, thenestimating the relation b etw een this variable and the slope of the P hillipscurve would be a nother test between the tw o competing theories.


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Larlrrncr Bnll, N.G re gory Mank iw , and Dr~\xiclKornrr 33model is real business-cycle theory 3 9 This theory attributes all f luctua-tions in output to real disturbances and assumes that nominnl distur-bances are s imply passed into pr ices. Becau se nominal shocks have n ocau sal role in outpu t fluctu atio ns, it is difficult for the the ory to explainthe ob served po sitive correlation s of real and nominal variab les, muchless the effect of average inflation on the strength of these c orrelations.King and Plosser have devised a real business-cycle model in whichoutpu t moves with nominal money through rev erse causality: the bankingsystem creates inside money in anticipation of outpu t mo vem ents. B utas Mankiw points o ut , the m odel predicts that th e aggregate price levelfillls w hen ou tpu t r i~ e s . ~ O T h useal businejs-cycle models do not appea rto provide an alternative explana tion of the results that we repo rt below.

International Evidence

We examine here how the trade-off betwcen output and inflationvaries across countries. Our goal is to test the theoretical resultsdiscussed in the previous section. In particular, we wish to examinewhether in countries with high rates of inflation, changes in aggregatedemand have relatively small effects on outpu t and instead are reflectedquickly in pric es.

Our analysis is divided into two parts . First we descr ibe the d ata andpresen t the basic results. W e estimate th e output-inflation trade-off for43 industrialized countries and examine the relationship between thetrade-off and a verage inflation and de man d variability. Then w e consid ereconom etr ic issues raised by our procedure and exam ine variations o nour basic test .

D A T A A N D B A S I C R E S I J L T ST h e d a t a we exam ine, originally from Intrrnational Financial Statis-

tics of the International Mo netary Fu nd , are from the IM F databank of39 . For a recent real business-cycle model, see Edward C. Prescott, "Theory Aheadof Business Cycle Measurement," Federal Reserve Bank of Adinneapolis Qrtnrterly

R ev i ew , vo l. 10 (Fall 1986), pp. 9-22.40. Robert G. King and Charles I . Plosser, "Money, Credit, and Prices in a RealBusinessCycle," Americiln Ec ono mic Reviertl,vol. 7 4(Ju ne 1984), pp. 363-80: N . GregoryMankiw, "Real Business Cycles: A Neo-Keynesian Perspective," Jorrrnal of Econornic


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34 Brookings Papers o n Economic Act i l i ty , 1:1988Data Resources, Inc. All the data are annual. Depending on the country,output is real GNP or real GDP, whichever is available. We denote thelog of output as y and the log of the corresponding nominal quantity asx. The log of the price level is thenp = x - y .

We wanted the most extensive possible sample oflarge, industrialized,free market economies. We used the following five criteria for choosingthe sample of countries: the population had to be at least one million; atleast 10 percent of output had to be in manufacturing; not more than 30percent of output could be in agriculture; data had to be available at leastback to 1963; the economy had to be largely unplanned. Information onthe first three criteria was taken from the IMF's Yearbook of Nat iona lAccount S tat is t ics and the International Firzancial Statistics Yearbooks;data for the year 1965 were used for these criteria. The fifth criterion isobviously open to interpretation. It led us to exclude such countries asCzechoslovakia, East Germany, and Yugoslavia.

The countries are listed in table 3, together with the period of time forwhich data are available. We present here some sample statistics foreach country: the mean and standard deviation for real growth, inflation,and the growth in nominal demand. We see from this table that there issubstantial variation in the macroeconomic experiences of these coun-tries. For example, Panama had the lowest average inflation rate, lessthan 3 percent a year, while Argentina and Brazil each had averageinflation exceeding 40 percent a year.

Es timating the Outpu t - In ju t ion Trade-o f f . We express the short-runoutput-inflation trade-off by estimating the following equation:(14) y , = constant + 7 Axt + X y t l + ?/ Tim e .The log of real GNP is regressed on its own lag, a time trend, and thechange in nominal GNP. This sort of equation has been used widely,both by new classical macroeconomists such as Robert Lucas and byKeynesian macroeconomists such as Charles S~hul tze .~ 'quation 14 isthe empirical counterpart of equation 12 of our theoretical model. Itdiffers from equation 12 by the use of discrete rather than continuoustime and by summarizing the effects of past demand movements through

41. Lucas, "Some International Evidence"; Charles L. Schultze, "Cross-Countryand Cross-Temporal Differences in Inflation Responsiveness," American EconomicReview, vol. 74 (May 1984,Papers and Proceed ings, 1983),pp . 160-65.


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Laurerlce Ball, N . Gregory M an kiw , arzd David Rorner 35Table 3. Descriptive Statistics on Inflation and Output, Various Countries, SelectedPeriods, 1948-86

Rea l grori'th In.& tioil No rni i~a l rowthC o ~ r n t r y ,Sainpleperiod Mecin Stnndarddevicitiort Mecin S t a i ~ d a r ddeviation Menil S tn i~ i lnrdi i e ~ ~ i n t i o i ~ArgentinaAustraliaAustriaBelgiumBoliviaBrazilCanadaColombiaCosta RicaDenmarkDominican RepublicEcuadorEl SalvadorFinlandFranceGermanyGreeceGuatemalaIcelandIranIrelandIsraelItalyJamaicaJapanMexicoNetherlandsNicaraguaNorwayPanamaPeruPhilippinesPortugalSingaporeSouth AfricaSpainSwedenSwitzerlandTunisiaUnited KingdomUnited StatesVenezuelaZaireAcross-country valuesMeanStandard deviation

Source: Authors ' calculat~ons ith dara from International Monetary Fund, Inlernnt ionnl Financi r ii Sfa f i s f~r sT hedata were obtained from the IM F data bank of Data Resources, Inc All daia are annual. Depending on the country.output is real G NP or real GDP, w h~c heve r s available. Growth rates are coinputed as differences in ioga r~t hmswith the log of real output as y and the log of nominal output as .r: the log of the price level is p = .r - y . F or


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Lazrreizce Ball , N . Gregory Mankiw, ctnd Drtvid Roiner 37the term in lagged real ou tp ut . W e discuss this specification of the ou tpu t-inflation trade-off furth er in th e seco nd p art of this sec tion.

Th e coefficient of the chang e in nominal dem and , 7 , i s the parameterof central interest . I t tel ls us how much of a shock to nominal GNPshows up in output in the first year. If T = 1, then all of the c hang e innominal GN P shows up in real GN P; if T = 0, then all the cha nge innominal GN P shows up in pr ices .

Table 4 presen ts the estimated v alue of 7 for the 43 coun tr ies , togetherwith th e estimated standard errors . F or each co untry, the entire availabletime ser ies is used in the estimation. Table 4 also presents th e estimatedvalue of 7 for two subsam ples. W e use 1972-73 as the cutoff be twe en thetwo subsamples. T he ear ly 1970s are of ten considered a t ime of majorstructural change; certainly many empirical macroeconomic relation-ships broke dow n. W e therefore wanted to see whether the t rade-of fparameter T changed an d, if so , whe ther the ch anges could be explained.

Table 4 sho ws sub stantial variation in the output-inflation trade-offacross countr ies . Th e mean value of T for ou r 43 coun tries is 0.242 andthe standard deviation is 0.272. The t

40 new keynesian

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