The Structuralist Perspective on Real Exchange Rate, Share Price Level and Employment Path: What Room is Left for Money?

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1 {ref.: NewSchool2003-D14} The Structuralst Perspectve on Real Exchange Rate, Share Prce Level and Employment Path: What Room s Left for Money? by Edmund S. Phelps, Han Teck Hoon and Gylf Zoega * The current sluggsh performance of the US economy follows one of the more remarkable booms n modern hstory. The late 1990s was a perod of smultaneous output and productvty growth, 1 low unemployment and stable nflaton, culmnatng n an unemployment rate of only 3.9% n the fourth quarter of the year The absence of rsng nflaton durng ths perod came as a surprse to many snce the level of the natural rate of unemployment was commonly estmated to be n the range of 5-6% by the md 1990s. The non-nflatonary boom, however, remnds one of another epsode where nonmonetary forces were strongly at work, namely, the non-deflatonary slump n Europe and elsewhere n the 1980s and 90s, whch appeared to sgnal a move to a hgher natural rate of unemployment. The modelng of such structural slumps and booms s the task that we have tackled n a number of papers n recent years, the book Structural Slumps beng a major mlestone. 2 The theory set out n Structural Slumps models the supply sde of the economy and provdes mcroeconomc foundatons for a movng natural rate of unemployment. Involuntary unemployment occurs, snce ncentve wages and consequent job ratonng are allowed, and ths unemployment s structural, not a result of defcent aggregate demand. The determnng structure ncludes tax rates and regulatons, the focus of supply-sde (SS) theory, and ncludes fluctuatons n techncal progress, the focus of real busness cycle (RBC) theory, but ncludes much more. The mplcatons exhbt some sharp dfferences from those of Keynesan theory and some strkng parallels, as we shall see. What bascally characterzes the structuralst perspectve and dfferentates t from RBC and SS models s ts vew of busness lfe: the mperfect nformaton, the busness assets frms need and the expectatons they have to form. A frm ncurs costs to acqure and retan employees (workers who know ther job, have learned the ropes) and customers (buyers who know how to reach t), not just equpment and plant. The rate of nvestment n each asset s a functon of the value, or shadow prce, placed by frms on that asset and the cost of nvestng n t. A raft of non-monetary fundamentals world real nterest rates, expectatons for techncal advances and thus productvty growth, enttlements, the *McVckar Professor of Poltcal Economy, Columba Unversty, Assocate Professor of Economcs, Sngapore Management Unversty, and Reader, Brkbeck College, Unversty of London. 1 In the rate of growth of output per man-hour n the busness sector ranged between 2.3% and 3%. 2 Edmund Phelps, Structural Slumps: The Modern Equlbrum Theory of Unemployment, Interest and Assets, Cambrdge, Mass., Harvard Unversty Press, 1994.

2 2 stocks of the busness assets, the wealth of the workers, tax rates, the poltcal clmate, nvestor trust, etc. drve the values placed on the busness assets, the cost of nvestng n them, and thus the rates of nvestment n them. 3 Our baselne models of busness-asset nvestment and the employment path are restrcted to the case of nter-temporal equlbrum: more accurately, to a punctuated equlbrum n whch, nfrequently or more frequently as the case may be, a wholly unforeseen shft n one or more of the fundamentals occasonally occurs a parametrc shft or even a loss of some knd of captal causng jumps n the real values of each of the busness assets onto ther new correct-expectatons tme-paths. Yet some of the key forces among these fundamentals, such as the vsons of (each of) the economy s entrepreneurs about future proft opportuntes and the judgments of fnancers and professonal nvestors, are planly speculatve, unobservable, unmeasurable; moreover, the consequences of both these unobservable forces and the observable ones, such as the world real nterest rate and the long-term natonal productvty trend, for the values (the shadow prces) entrepreneurs put on the customer, the employee and much else are lkewse unobservable. Ths s a problem for testng and usng the theory, as t was for testng and usng Keynes s theory. 4 Two recent papers of ours meet that problem by hypotheszng that the net overall nfluence of these unobservable forces on the assets shadow prces (and thus on the employment path) s reflected, alongsde the net nfluence of some related observable forces, by the level of the stock market. Snce ether the level of employment or ts growth s an ncreasng functon of every one of the (three) shadow prces, t s plausble that an ncrease n the current ndex of real share prces, nterpreted as the current shadow prce of the representatve basket of the frms several busness assets, s also expansonary for employment on the average. The papers found a statstcal relatonshp between the frst dfference of employment and the real share prce ndex taken as a rato to some ndcator of the cost of nvestng n employees and customers. 5 An alternatve measure of the unobservable share prces s total market captalzaton as a share of GDP. The fgure below shows the relatonshp (cross secton) between market captalzaton and the employment rate. 3 The employee model, also called the turnover-tranng model or quttng model, derves from Phelps, Money Wage Dynamcs and Labor Market Equlbrum, Journal of Poltcal Economy, 76, August The customer model orgnates n Phelps and Sdney Wnter, Optmal Prce Polcy under Atomstc Competton, n Phelps, et al., Mcroeconomc Foundatons of Employment and Inflaton Theory, Keynes, whose theory gave center stage to the unpredctablty and unobservablty of entrepreneurs vsons and optmsm, expressed skeptcsm that statstcal analyses, such as those Jan Tnbergen began to undertake, would be valuable n forecastng employment swngs or n testng hs theory s explanaton of them. Subsequent practconers avoded the problem by treatng nvestment demand as exogenous. It was not untl James Tobn ntroduced hs Q rato that emprcal work sought to capture the role of entrepreneurs expectatons on nvestment, essentally by relocatng the exogenety from nvestment demand to the stock market. 5 Davd Jestaz, Jean-Paul Ftouss, Edmund Phelps and Gylf Zoega, Roots of the Recent Recoveres: Labor Market Reforms or Prvate Sector Forces? Brookngs Papers on Economc Actvty, no. 1, 2000, , and Edmund Phelps and Gylf Zoega, Structural Booms: Productvty Expectatons and Asset Valuatons, Economc Polcy, no. 32, Aprl 2001,

3 3 3.0 stock-m arket cap talzaton as a rato 2.5 to G D P (2001) 2.0 Sw 1.5 UK Ne Sp Fr It Ge US Ca Be Sw e Aus De Ja em ploym ent as a rato to labor force (2002) Fgure 1. Employment and the Stock Market A clear postve relatonshp s vsble. Note that Swtzerland s way off the lne. The very hgh value of stock market captalzaton n Swtzerland would lead us to predct an even hgher employment rate. However, n accordance wth our theory, the supply functon may be convex and only asymptotcally approaches full employment, n whch case the poston of Swtzerland n the fgure may not come as a bg surprse. The present paper, n pursung that strategy, faces up to some questons. Frst, there s another asset prce, whch we neglected n the two prevous papers, namely, the real exchange rate. In the customer-market model, an apprecaton (strengthenng) of the real exchange rate n a country causes frms to moderate ther prce markups, thus pullng up the product wage and employment an upward move along what s called the wage curve: the real apprecaton may hence lower the natural rate of unemployment! Ths s the provocatve hypothess at the heart of ths paper. So we ask whether employment rses n response to a strengthened real exchange rate just as t rses n response to a strengthenng of real share prces. The queston s especally nterestng snce, as s well known, monetary theores of economc actvty say that the stock market and the foregn exchange market pull n opposng drectons: In those Keynesan and monetarst models, a strengthenng of real share prces ncreases economc actvty by boostng effectve demand but a strengthenng (apprecaton) of the real exchange rate decreases actvty by cuttng effectve demand. 6 Real exchange rates are typcally reported n the form of ndces that enable a comparson over tme but not across countres. For ths reason we use data from the World Bank on 6 Makng hs case for a flexble exchange rate, Mlton Fredman famously argued that, to paraphrase t a lttle, f expected future proft prospects deterorate and so share prces drop, thus threatenng nvestment demand, the real exchange rate wll drop just enough to offset the drop n share prces, thus holdng or returnng employment to some fxed preternatural level a natural rate taken to be nvarant or smply the prevous employment level. The Mundell-Flemng model ncely demonstrates that proposton and the Dornbusch model modfes t.

4 4 hypothetcal exchange rates that would gve purchasng-power party (PPP) between a country and the US. The rato of ths hypothetcal exchange rate and the actual exchange rate observed n foregn exchange markets can be used to test our hypothess on the relatonshp between real exchange rates and the natural rate of employment and unemployment. In Fgure 2 we show the relatonshp between the real exchange rate defned as descrbed n the prevous paragraph and the employment rate (one mnus the rate of unemployment) n a cross secton of the same OECD economes. 1.4 real exchange rate (2001) 1.2 Ja Sw 1.0 US UK De Swe 0.8 Sp Fr It Ge Ca Aus Be Ne employment as a rato to labor force (2002) Fgure 2. Employment and real exchange rates Note the upward-slopng relatonshp: A real exchange rate apprecaton appears to go hand n hand wth hgher employment rates when domestc output becomes relatvely more expensve, the rate of employment goes up, nstead of fallng as Keynesan theory mght lead us to beleve. Though not perfect, the relatonshp s surprsngly strong (correlaton s 0.68). We take ths smple graph to be ndcatve that the relatonshp between real exchange rates and employment may be more nvolved than the textbook verson of the open-economy (New) Keynesan model would lead one to beleve. In Part I we lay out the theory and the answer to the key queston whether a real exchange rate apprecaton tends to rase or lower the rate of employment. Fgure 2 appears to mply that a stronger real exchange rate acts to rase the employment rate. However, t s not clear whether t s the cause or the effect? After all, our model also says that a weakenng of proft prospects and the consequent drop n nvestment and ultmately employment causes a weaker real exchange rate as well as lower real share prces. From a forecastng standpont, ths dstncton makes lttle dfference: Ether way, whether as causes or effects, the strength of the real exchange rate and of the real share-prce level are theory-grounded predctors of where present forces are takng the economy one or

5 5 two years ahead absent a shft n the wnds. A weak real exchange rate, lke a weak stock market, spells weak actvty ahead. In Part II, we consder the mplcatons of our model for the conduct of monetary polcy. Clearly, a central bank faces a dauntng task durng structural booms and slumps because the underlyng natural rate of unemployment s changng over tme. Our model yelds a soluton for the domestc real nterest rate that s compatble wth the endogenously determned natural rate of unemployment. Ths s the natural rate of nterest, dscussed by Knut Wcksell. By keepng the short-term real nterest rate n tandem wth the natural rate of nterest, a central bank s able to control the equlbrum nflaton rate and keep the economy along a path of tme-varyng natural rate of unemployment. The natural rate of nterest could, therefore, serve as the gudng lght of a central bank s nterest rate polcy durng structural booms and slumps! Part III examnes the data and fnds that a real exchange rate apprecaton may rase the employment rate, hence provdng support for our theoretcal predcton and castng doubt on the smplest versons of the Keynesan model. The result s a rather hopeful step n the confrmaton of our structuralst model. We fnd that a weaker real exchange rate, n shelterng frms from overseas compettors, nvtes hgher markups effectvely, a contracton n the supply of output and jobs whch causes employment to contract, not expand as n the monetary vews. Part IV takes a look at recent US experence, n partcular, t asks whether the current slump s of a structuralst nature. Agan, the results are promsng. The economc boom experenced n the US n the late 1990s s almost entrely explaned by our model, whle the peterng out of that boom and the recent rse n unemployment s also to a large extent compatble wth our model. I. Theory Here we set out a model of the small open economy n whch all frms, foregn and domestc, operate n a market subject to nformatonal frctons. We frst examne a case where, ntally all the relevant customers of natonal frms frms that produce only wth natonal labor are natonals. Although the small open economy s too small, by defnton, to affect perceptbly the world real rate of nterest, changes n demand by ts natonal customers wll certanly be felt by natonal frms, and so wll the exchange rate and the real nterest rate n terms of the goods suppled by natonal frms and ther prce. Wth regard to the -th frm, we let x, a contnuous varable, denote (the sze of) ts customer stock; let c s denote the amount of consumer output t supples per customer; and let p denote ts prce, say, n unts of the domestc good. We wll let p denote the prce at the other domestc frms and p e denote the prce that the frm and ts customers expect s beng charged by other domestc frms (all measured n unts of the domestc good). We ntroduce a varable e, where e tells us how many unts of the foregn good

6 6 must be gven up n exchange for one unt of the domestc good. Consequently, an ncrease n e s a real exchange rate apprecaton. In product-market equlbrum, by defnton, every frm and ts customers have correct expectatons about the other frms, that s, p=p e. Wth ther expectatons thus dentcal n product-market equlbrum, the dentcally stuated domestc frms wll then behave alke, so that p =p=p e. A frm, n maxmzng the value of ts shares, has to strke a balance between the benefts of a hgh prce, whch are ncreased revenue and reduced cost, thus ncreased proft, n the present, and the benefts of a low prce, whch are an ncreased proft base n the future as customers elsewhere gradually learn of the frm's prce advantage. The key dynamc s therefore the law of moton of the frm's customer stock, (1) d x/dt=g( t p/p t, e t ) x ; g 1 <0; g 11 0; g 2 <0; g 22 0; g(1,1)=0. t t The jont assumpton that g 1 <0; g 11 0 means that the margnal returns to prce concessons are non-ncreasng, n the sense that successve prce reductons of an equal amount by frm yeld a non-ncreasng sequence of ncrements to the exponental growth rate of customers. The nequalty g 2 <0 mples a gan of customers at the expense of foregn supplers when the real exchange rate deprecates though successve weakenng of the real exchange rate yelds a non-ncreasng sequence of ncrements to the exponental growth rate of customers snce g What the sgn of g 12 s relates to the queston of what the effect of foregn competton on domestc frms' market power s. Suppose that e<1 so there has been a real exchange rate deprecaton, hence foregn goods are sellng at a premum. Then each dentcally stuated domestc frm s ncreasng ts market share at the expense of foregn supplers. In such an envronment, a reducton n p, gven p, can be expected to generate a smaller ncrease n the rate of nflow of customers compared to a stuaton where e>1 (and each dentcally stuated domestc frm s losng customers to foregn supplers). Snce stffer foregn competton (hgher e) confers a hgher margnal return to a prce concesson, frm s nduced to go further n reducng ts markup, holdng other thngs constant. In our theory, therefore, the assumpton that g 2 <0; g 22 <0 taken alone or jontly wth g 12 <0 mples that an apprecaton of the real exchange rate wll lead to lower domestc markups and hence ncreased output suppled due to the ncreased competton that domestc producers face from foregn supplers. It turns out that our key theoretcal results below wll depend on the assumpton of g 2 <0; g 22 <0; and g 12 <0. Because of ths assumpton, a real exchange apprecaton wll rase the margnal beneft of cuttng domestc prces n terms of retanng more customers and such prce cuts wll appear n the labor market as upward shfts of the labor demand curve, rasng employment and reducng unemployment (that s, the natural rate of unemployment). The reader may want to pause to contemplate the assumpton for a few seconds. It mples that when domestc goods are relatvely expensve, the margnal beneft from cuttng prces n terms of customers recruted s greater, hence prces are lower gven nomnal wages, the real demand wage s hgher, and so s the rate of

7 7 employment n equlbrum. Intutvely, hgh domestc prces may have made consumers aware or suspcous of further prce ncreases. When customers pay closer attenton to prce decsons, ths ncreases the gan domestc frms reap from prce cuts n the form of an expanded market share and the loss nflcted on the domestc market share from prce ncreases. The reader mght wonder whether a polcy of prcng to market mght not nullfy our results. If foregn producers sell ther output n our market at a fxed domestc prce that does not respond to changes n the (nomnal) exchange rate, so the degree of exchange rate pass-through s zero, the real exchange rate wll be unchanged. In contrast, when foregn producers fx the foregn prce of ther product, or at any rate do not change t equ-proportonately n response to a nomnal exchange rate change, and allow the domestc (mport) prce to fluctuate, the real exchange rate s bound to fluctuate. The hgh correlaton n the data between nomnal and real exchange rates suggests that the latter scenaro s by no means unrealstc so our model has applcablty despte our abstractng from prcng to market behavor. The degree of exchange rate pass-through s hgh when (nomnal) exchange rate changes are perceved to have a large permanent component. 7 The representatve frm has to choose the prce at whch to sell to ts current customers. Rasng ts prce causes a decrease, and lowerng the prce an ncrease, n the quantty demanded by ts current customers accordng to a per-customer demand relatonshp, D(p /p,c s ), where c s n ths context s set equal to the average expendture per customer, c d, at the other frms. For smplcty, we assume that D(p /p,c s ) s homogeneous of degree one n total sales, c s, and so we wrte c s =η(p /p) c s ; η (p /p)<0; η (1)=1. Each frm chooses the path of ts real prce or, equvalently, the path of ts supply per customer to ts consumers, to maxmze the present dscounted value of ts cash flows. The maxmum at the -th frm s the value of the frm, V, whch depends upon x : : s r s ds 0 V 0 max [( pt / pt ) ς ] η( pt / pt ) ct xt exp dt, 0 where ς s the unt cost. The maxmzaton s subject to the dfferental equaton gvng the moton of the stock of customers of the -th frm as a functon of ts relatve, or real, prce and the real exchange rate gven by (1) and an ntal x 0. The current-value Hamltonan s expressed as s [( p / p) ς ] η( p / p) c x + q g( p / p, p / p t ) x *, 7 Kenneth Froot and Paul Klemperer, 1989, Exchange Rate Pass-Through When Market Share Matters, Amercan Economc Revew, Vol. 79, No. 4, p Usng a customer-market model smlar to ours, Froot and Klemperer show that the extent of prcng to the market depends on the expected persstence of nomnal exchange rate changes. A transent apprecaton of the domestc currency may nduce foregn producers to rase the domestc (mport) prce of ther output n order to beneft further from the temporarly hgh value of the currency snce the future loss matters less due to the expectaton that the value of the currency wll be lower whle a permanent apprecaton rases both the beneft and cost of rasng current prces, hence leavng the foregn prce unchanged, and the domestc (mport) prce lower.

8 8 * where q s the shadow prce, or worth, of an addtonal customer and p s the prce charged by the foregn suppler expressed n our domestc currency. The frst-order condton for optmal p s s s c x c x (2) η ( p / p) + [( p / p) ς ] η'( p / p) + p p * x * x q [ g1 ( p / p, p / p ) + g2( p / p, p / p ) ] = 0. * p p Another two necessary frst-order condtons (whch are also suffcent under our assumptons) from solvng the optmal control problem are: (3) * s dq / dt = [ r g( p / p, p / p )] q [( p / p) ς ] η( p / p) c, r ds s 0 (4) lmexp q x = 0. t t t t We can readly show that margnal q s equal to average q so we have q = V / x. Equatng p to p, and settng q =q, delvers the condton on consumer-good supply per frm for product-market equlbrum: (5) 1+[η(1)/ η (1)]-ς = -(q/c s )[1 / η (1)][ g 1 (1,e)+eg 2 (1,e)]; η(1)=1. The expresson on the LHS of (5) s the algebrac excess of margnal revenue over margnal cost, a negatve value n customer-market models as the frm supples more than called for by the statc monopolst's formula for maxmum current proft, gvng up some of the maxmum current proft for the sake of ts longer-term nterests. An ncrease n q means that profts from future customers are hgh so that each frm reduces ts prce (equvalently ts markup) n order to ncrease ts customer base. Hence lower prces n the Phelps-Wnter model are a form of nvestment, an nvestment n market share. Note also the role played by the real exchange rate (e). If stffer foregn competton leads to reduced market power of domestc frms, then a hgher e leads domestc frms to ncrease ther output even further beyond the pont where current margnal revenue equals margnal cost as dctated by a statc monopolst. Ths channel s present f ether g 12 (1,e)<0 or g 22 (1,e)<0. Alternatve specfcatons of the labor market gve rse to a unt cost ς that s a rsng functon of c s x / Λ. One assumpton s to suppose that there s a wage curve that s generated from a shrkng vew of the labor market. Another alternatve s to suppose that there s a neoclasscal labor supply that s postvely sloped n the (employment, real wage) plane. From (5), we can express consumer-good supply per customer relatve to productvty, c s /Λ, n terms of q/ Λ, e, and x, that s, c s /Λ =Ω(q/Λ, e, x). It s straghtforward to show that 0<ε q/λ = dln(c s /Λ)/dln(q/Λ)<1; ε e = dln(c s /Λ)/dlne>0; and

9 9-1< ε x = dln(c s /Λ)/dlnx <0, where ε j denotes the partal elastcty of c s /Λ wth respect to the varable j. As explaned before, an ncrease n q makes nvestments n customers through reducng the markup attractve and so expands output. An ncrease n e, that s, a real exchange rate apprecaton causes markups to decrease as domestc frms face stffer competton from foregn supplers and consequently leads to ncreases n output and employment. Fnally, wth rsng margnal costs, an ncrease n the number of customers at each frm leads to a less than proportonate declne n the amount of output suppled per customer. Notng that we can express the markup, say, μ as beng equal to1/ς, we can say that our theory mples that, for gven x, the markup s nversely related to q/λ and e so we wrte μ=m(q/λ, e). Gven x, there s a monotoncally negatve relatonshp between the natural rate of employment and the markup so we can wrte 1 un = Θ( q / Λ, e); Θ q / Λ > 0; Θe > 0. In a dagram wth q/λ and e on the two axes, the so- ( 1 un ) contour s downward slopng wth a move n the North-east drecton mplyng a move to a hgher level of 1 un. Fnally we sketch the mechansms of savng, nvestment and asset valuaton n the captal market. Households have to plan how much of ncome to save, puttng ther savngs n domestc shares; any excess s nvested overseas and any defcency mples the placement of shares overseas. Frms have to plan ther accumulaton of customers, ssung (retrng) a share for each customer ganed (lost); any excess of customers over the domestc populaton mples some customers are overseas and any defcency means that foregn frms have a share of the market. Snce the stock of customers, hence shares, s sluggsh, the level of the share prce must clear the asset market. In a symmetrc stuaton across frms, (3) smplfes to (6) [1- ς] c s /q + (dq/dt)/q + g(1,e) = r. Ths equaton n the frm's nstantaneous rate of return to nvestment n ts stock of assets, whch are customers, s an ntertemporal condton of captal-market equlbrum: t s entaled by correct expectatons of dq/dt, r and e at all future dates. We wll make the assumpton that ntally all shares ssued by domestc frms are held by natonals. Drawng upon the Blanchard-Yaar model of fnte-lved dynastes subject to exponental mortalty, t s argued that the economy here satsfes an Euler-type dfferental equaton n the rate of change of consumpton per customer, c d. Consumpton growth s governed by the excess of the nterest rate over the rate of pure tme preference, denoted ρ, and by the rato of (nonhuman) wealth, denoted W, to consumpton. Upon settng customers' consumpton per customer equal to the output suppled to them per customer, c s, we obtan (7) d c s /dt = (r ρ) c s θ(θ + ρ )W, where θ denotes the nstantaneous probablty of death and W = qx here. In requrng here that q at each moment be at such a level as to make the path of planned consumpton (ts

10 10 growth as well as ts level) consstent wth the path of output from (5), we are requrng that the market where goods are exchanged for shares (at prce q) be n equlbrum. No household wll fnd the prevalng share prce dfferent from what s expected. Fnally, for nternatonal captal-market equlbrum wth perfect captal moblty, we must satsfy the real nterest party condton, whch states that any excess of domestc real nterest rate, r, over the exogenously gven world real rate of nterest, r*, must be met by an exact amount of expected rate of real exchange deprecaton. Ths equaton s: (8) r = r* - (de/dt)/e. Equatons (5) to (8) gve us four equatons n the four varables: c s /Λ, q/λ, e and x. However, usng the relaton c s /Λ =Ω(q/Λ, e, x) derved from (5), we can reduce the system to three dynamc equatons n the three varables: q/λ, e and x, the last beng a slow-movng varable. We proceed to do the necessary substtutons to obtan the 3 by 3 dynamc system but t wll turn out convenent to present an analyss of a subsystem treatng the state varable x as frozen at ts ntal value. 8 In a dagram nvolvng q/λ and e on the two axes and depctng the two statonary loc assocated wth equatons (7) and (8), we can then show how an adjustment of x, n response to an economc shock, shfts the two loc to reach a sort of quas-long run steady state where e s back to one, hence satsfyng the purchasng power party n the (quas) long run. A. The 3 by 3 Dynamc System The dynamcs of the system can be descrbed by the behavor of the endogenous varables q/λ, e and x after substtutng out for c s /Λ usng c s /Λ =Ω(q/Λ, e, x): (9) (dq/dt)/q = [(1+ ε e )/(1- ε q/λ + ε e )]f(q/λ, e, x)+ [ε e /(1- ε q/λ + ε e )]h(q/λ, e, x), (10) (de/dt)/e = [(1- ε q/λ )/(1- ε q/λ + ε e )]h(q/λ, e, x)- [ε q/λ /(1- ε q/λ + ε e )]f(q/λ, e, x), (11) (dx/dt)/x = g(1,e), where f(q/λ, e, x) = -[1-Υ(Ω(q/Λ, e, x)x)][ Ω(q/Λ, e, x)/( q/λ)]+ ρ+ [θ(θ + ρ )qx/( Λ Ω(q/Λ, e, x))] [1+ ε x ]g(1,e), h(q/λ, e, x) = r* - ρ - [θ(θ + ρ )qx/( Λ Ω(q/Λ, e, x))] + ε x g(1,e). The lnearzed dynamc system around the steady-state ((q/λ) ss, e ss, x ss ), where e ss =1 and x ss =1 s gven by: 8 A complete characterzaton of the 3x3 system s done n Hoon, Han Teck and Edmund Phelps, A Structuralst Model of the Small Open Economy n the Short, Medum and Long Run, Dscusson Paper No , March 2002, Department of Economcs, Columba Unversty.

11 11 (12) [(dq/dt)/q (de/dt)/e (dx/dt)/x] = A[(q/Λ) - (q/λ) ss e 1 x - x ss ] where [ ]' denotes a column vector, and the 3 by 3 matrx A contans the followng elements: a 11 = [(1+ ε e )/(1- ε q/λ + ε e )]{f q/λ + [ε e /(1+ ε e )] h q/λ }, a 12 = [(1+ ε e )/(1- ε q/λ + ε e )]{f e + [ε e /(1+ ε e )] h e }, a 13 = [(1+ ε e )/(1- ε q/λ + ε e )]{f x + [ε e /(1+ ε e )] h x }, a 21 = [(1- ε q/λ )/(1- ε q/λ + ε e )]h q/λ - [ε q/λ /(1- ε q/λ + ε e )]f q/λ, a 22 = [(1- ε q/λ )/(1- ε q/λ + ε e )]h e - [ε q/λ /(1- ε q/λ + ε e )]f e, a 23 = [(1- ε q/λ )/(1- ε q/λ + ε e )]h x - [ε q/λ /(1- ε q/λ + ε e )]f x, a 31 = 0, a 32 = g e, a 33 = 0. We have g e <0 as a real exchange rate apprecaton leads to a flow decrease of customers (so dx/dt<0 when e>1), and we can readly check that f q/λ >0, h q/λ <0, f x >0, and h x <0. In conjuncton wth the followng two assumptons, we obtan sgns for f e and h e, whch provde suffcent condtons for a unque perfect foresght path: Assumpton 1: Ceters parbus, an ncrease n e rases the rate of return to holdng a share n the domestc frm by rasng the quas-rent, [1- ς] c s, taken as a rato to q, by more than t decreases the rate at whch the customer base shrnks, g e. Assumpton 2: Ceters parbus, an ncrease n e reduces the customer's requred rate of nterest through shrnkng the (nonhuman) wealth to consumpton rato, θ(θ + ρ )(qx/c s ), by more than t ncreases the requred nterest rate through rasng the growth rate of consumpton, - ε x g e. Under Assumptons 1 and 2, we also have f e <0 and h e >0. We can then sgn the elements n the matrx A as follows: Lemma 1: a 11 >0, a 12 <0, a 13 >0, a 21 <0, a 22 >0, a 23 <0, a 31 =0, a 32 <0 and a 33 =0. B. The 2 by 2 Dynamc System

12 12 The two equatons we examne are the lnearzed versons of (9) and (10), where we treat x as gven. Then, t s straghtforward to see that the slope of the statonary q locus s gven by de dt q& = a / 0 and the slope of the statonary e locus s gven by / = 0 11 a12 > / dt = 0 = a21 / a22 > 0 de e&. Snce both q and e are jumpy varables, the case where the statonary e locus s steeper than the statonary q locus n the (q,e) plane---wth q on the horzontal axs and e on the vertcal axs---gves rse to multple ratonal expectatons equlbra. We wll focus on the case where we obtan unque ratonal expectatons equlbrum, whch requres that the determnant gven by a11a22 a12a21 be postve. Ths mples that the statonary q locus must be steeper than the statonary e locus for unque ratonal expectatons equlbrum. We depct ths case n Fgure 3, where we also draw a contour depctng the natural rate of employment, 1 u n = Θ( q / Λ, e) gong through the ntersecton pont. A real exchange rate deprecaton, n shelterng our economy from nternatonal competton, nvtes an ncrease n the markup, whch translates nto a declne of the real product wage and, gven an upward slopng wage curve, leads to a declne n employment. Hence a real-exchange-rate deprecaton can be seen to be a cause of the employment contracton. There s, however, also a sense n whch a real-exchange-rate deprecaton s also an effect, possbly alongsde a declne of the stock market, of worsened prospects for jobs and output due an adverse exogenous shock. To llustrate ths, let us consder the consequences of an unantcpated jump n the exogenously gven * external real rate of nterest, r. In terms of Fgure 3, we can readly check that the statonary q locus, whch s the steeper locus, shfts to the left snce at any gven e, a lower q s now requred to satsfy the asset prcng condton. On the other hand, the statonary e locus shfts to the rght as a hgher q s requred to support a hgher domestc real nterest rate, whch must now be equated to a hgher external real nterest rate. The result, as we see n Fgure 4, s an unambguous declne n the real exchange rate and the real share prce, and the so- ( 1 un ) contour passng through the new ntersecton pont les closer to the orgn. Hence, the declne n the real exchange rate, and a depressed stock market as well, must correspond to worsened job prospects n our theory. 9 II. Monetary polcy Is t concevable, theoretcally and emprcally as we wll show below that n an era of nflaton targetng (mplct or explct) where economc agents have come to form expectatons of nflaton that are largely borne out by experence, that the marked swngs of the actual unemployment rate reflect prmarly movements of the natural rate of unemployment? Accordng to the Fredman-Phelps expectatons-augmented Phllps curve, f the actual nflaton rate equals the expected rate of nflaton, the actual 9 To get to the quas-long run steady state where e s back to 1, we note that as customers are ganed so x ncreases, both the statonary q locus and the statonary e locus gradually shft left to ntersect at the orgnal level of 1 wth a lower q.

13 13 unemployment rate movement reflects swngs n the natural rate of unemployment. We have spelled out a model of structural booms and slumps whch can explan nonnflatonary booms such as the one seen n the Unted States n the late 1990s and non-deflatonary slumps such as the one seen n Europe n the 1980s and, n some countres, the 1990s. It s worthwhle to make a comment here about the sort of errors that a Central Bank gnorng the lessons of our structuralst analyss here s prone to make. Let us wrte the Taylor rule as follows: (13) = + a π π ) b( u u ), t ( t t n where a and b are postve constants and s the short-term nomnal nterest rate. Suppose that we observe an epsode where an expectaton of brght future prospects leads to a boomng stock market together wth a real exchange rate apprecaton such as the US economy experenced n the second half of the nnetes. Accordng to our theory, both the rse of q/λ and e has the effect of lowerng u n. In the extreme case that helps make our pont most starkly, suppose that the actual declne of u observed was entrely the result of the declne of u n but the Central Bank attrbutes t entrely to a fall relatve to u n, that s, a fall of u- u n. Then, although a correct applcaton of the Taylor rule would suggest that the short-term nomnal nterest rate be left unchanged on account of employment or output stablzaton, a Central Bank that does not see that the boomng stock market and the stronger real exchange rate has lowered the natural rate of unemployment would ncorrectly rase the short-term nomnal nterest rate to a level that s not justfable. 10 Woodford (2003) has shown that general-equlbrum models featurng the Taylor rule can usefully be solved to show that the equlbrum rate of nflaton s a functon of the current and expected future gaps between the natural rate of nterest and the ntercept term n the Taylor rule ( n (13)). 11 To prevent the nflaton rate from ether rsng or fallng, t would be necessary to adjust the ntercept term n tandem wth the natural rate of nterest. It s, therefore, useful to know how the domestc real nterest rate, r, whch s our natural rate of nterest, moves wth the real share prce (normalzed by productvty) and the real exchange rate. By takng note that c s / Λ = Ω( q / Λ, e, x), we can, through varous substtutons, obtan an expresson for the natural rate of nterest : 10 The short-term nomnal nterest rate should nevertheless be rased n tandem wth a rse of the natural rate of nterest n accordance wth an upward adjustment of the ntercept term n the Taylor rule n (13). 11 Mchael Woodford, Interest and Prces: Foundatons of a Theory of Monetary Polcy, 2003, Prnceton, Prnceton Unversty Press.

14 14 (14) 1 θ ( θ + ρ)( q / Λ) x ( ε x ε q / Λ ) ε e r = { ρ + } + g(1, e) + r * [1 ε + ε ] Ω( q / Λ, e, x) [1 ε + ε ] [1 ε + ε ] ε q [1 ε q / Λ q / Λ / Λ e 1 μ { + ε ] q / Λ e 1 } Ω( q / Λ, e, x), where, μ, the markup s a functon of q / Λ, e, x. It s readly checked from (14) that a rse n q, holdng other thngs constant, s assocated wth a hgher natural rate of nterest. Intutvely, a hgher q rases the wealth to per capta consumpton rato and also ncreases the rate of growth of per capta consumpton, consequently ncreasng the household s requred real rate of nterest. A real exchange rate apprecaton, however, has an ambguous effect on the natural rate of nterest as t lowers the wealth to per capta consumpton rato but ncreases the rate of growth of a representatve household s consumpton. If the former effect domnates, whch s a suffcent condton for saddlepath stablty, then a real exchange rate apprecaton n our model lowers the natural rate * of nterest. In steady state, of course, we have r = r. In an era of structural slumps and booms when the natural rate of unemployment s shftng, a central bank that keeps the short-term real nterest rate n tandem wth the natural rate of nterest wll be able to control the equlbrum rate of nflaton. Gven a stable nflaton rate, movements of the actual rate of unemployment wll then reflect prmarly movements n the natural rate of unemployment. Equvalently, the sze of the gap between the short-term real nterest rate and the natural rate of nterest wll be a measure of the deflatonary pressure faced by the economy. (A postve gap mples deflatonary pressure whereas a negatve gap mples nflatonary pressure.) A recent paper by two European Central Bank economsts dscuss the consequences of takng nto account movements n the natural rate of nterest n smple monetary polcy rules. 12 q / Λ e q / Λ e III. Evdence on Employment and the Real Exchange Rate We have seen that the model outlned n Part I of ths paper yelds a postve relatonshp between the real exchange rate and employment, whch goes aganst the Keynesan dea that real-exchange-rate deprecatons mprove compettveness and cause employment to expand. In our customer-market model, real-exchange-rate apprecatons nduce domestc frms to moderate the consequent dran of customers to foregn supplers by cuttng ther mark-up, whch mples an ncrease of the demand wage n terms of domestc product. The upward shft n the demand-wage schedule pulls the economy rghtwards and upwards along ts wage curve, causng employment as well as the product wage to ncrease. We now wsh to test our proposton emprcally. The countres ncluded n our statstcal study are Australa, Austra, Belgum, Canada, 12 See Ncola Gammarol and Natacha Valla, May 2003, The Natural Real Rate of Interest n the Euro Area, European Central Bank Workng Paper Seres.

15 15 Denmark, Fnland, France, Germany, Italy, Japan, the Netherlands, Norway, Span, Sweden, the U.K. and the U.S. We have data on both share prces and real (effectve) exchange rates for these countres for the perod We now measure the exchange rate by the real effectve exchange rate compled by the IMF (relatve prce of consumer goods, Internatonal Fnancal Statstcs). As before, an ncrease n the value of the exchange-rate varable mples a real-exchange-rate apprecaton. Accordng to Keynesan theory an elevaton of the real exchange rate rases the foregn prce of our product and reduces the domestc prce of mports, whch makes the aggregate demand for domestc output fall, hence also employment. In contrast, structuralst theory gves the converse predcton: an elevaton of the real exchange rate rases employment. The estmated equaton s of the error-correcton varety, γ s 2 * ol (15) Δf ( ut ) = β j1 α + γ 1e t γ 3( 1+ rt 1 ) + γ 4 pt 1 f ( u t 1 ) + βj2δπ t + β j3δet t 1 where s the country ndex and t denotes the years (=1,2,, 10; t=1976, 77,. 2000). The equaton postulates a long-run relatonshp between unemployment, on the one hand, and real exchange rates, real share prces s, world real nterest rates r* (measured n decmals) and real ol prces p ol, on the other hand. 13 Ths represents an upward-slopng supply (convex) curve n the employment/real exchange rate and the employment/real share prce planes. Inflaton and exchange-rate shocks push unemployment off ts longrun equlbrum path but assumng that β 1 s postve, unemployment gradually converges back to ts long-run equlbrum followng such shocks. 14 The speed of adjustment towards equlbrum s measured by the coeffcent β 1, whch we hope wll take a value somewhere between zero and one. The functon f s a non-lnear functon of the unemployment rate; (u 0.5-1)/0.5, followng Bean (1994) 15. The dea s to capture the (strct) convexty of the wage-settng relatonshp each consecutve fall n unemployment requres ever larger shfts of labor demand. Note that α s a country-specfc fxed effect that captures any omtted country-specfc effects. Whle each country has ts own fxed effect, ndex, groups of countres share a senstvty coeffcent β 1, as well as the senstvty to nflaton shocks (β 2 ) and changes n the real exchange rate (β 3 ) We should note that the results are robust to the excluson of the ol-prce varable, whch dd not appear n the theoretcal model above. 14 Note that we allow for a short-term effect of real-exchange-rate changes on unemployment to capture any short-run Keynesan effect as well as a long-run relatonshp between the two varables. 15 Charles R. Bean, European Unemployment: A Retrospectve, 38, Aprl 1994.

16 16 Note that unemployment can be above ts equlbrum path when prce nflaton s fallng and above the path when prce nflaton s rsng. The nflaton term at the end of the equaton s meant to capture ths monetary effect. The table below has the defnton of the varables. Table 1. Defnton of varables. u e s r* p ol π Unemployment rate. Source: OECD. Real effectve (trade weghted) exchange rate, measurng the relatve prce of domestc and foregn consumer goods. Source: IMF. Real share prces normalzed by real GDP per employed worker. Source. IMF. World real rate of nterest (weghted average of G7 yeld on government bonds). Source: IMF. Real prce of ol. Source: Ctbase. Inflaton (GDP deflator). Source: IMF. The equaton was estmated wth a panel of 326 observatons. The reported estmates were derved usng weghted least squares. Table 2 has the coeffcent estmates γ 1, γ 2, γ 3 and γ 4. Table 2. Estmaton results. Coeffcent Estmate t-statstc γ γ γ γ The results n the table are consstent wth predctons of our structuralst model. Frst, an apprecaton of the real exchange rate causes the steady-state unemployment rate to fall (t=4.12). Second, an elevaton of real stock prces also lowers unemployment (t=8.27). An ncrease n the world real rate of nterest rases unemployment (t=9.09). Fnally, an ncrease n the real prce of ol causes unemployment to rse (t=4.93). The reader may wonder why we nclude real share prces and the world real rate of nterest sde by sde snce the former should encapsulate the latter. Our reason for dong

17 17 ths s smple: f share prces are suffcently volatle due to rratonal speculaton, ths may dwarf the contractonary effects of real nterest rates. Table 3 has the group-specfc coeffcents. Table 3. Further estmaton results group effects Areas Senstvty coeffcent Inflaton shock Real exchange shock Estmate t-statstc Estmate t-statstc Estmate t-statstc Australa Europe* Japan Scandnava ** Canada U.S * Includng Denmark ** Excludng Denmark Table 3 shows that the Keynesan short-term effect of surprse nflaton measured by the frst dfference of the (prce) nflaton rate causes unemployment to fall for all country groups. The employment effect of the nflaton shock s smallest n Japan, then n the U.S. and roughly the same n the other four areas. The short-term unemployment effect of a real exchange rate apprecaton s less robust. The sgn of the estmated coeffcent s also only correct n Japan. The speed of adjustment to steady state s greatest n Australa, the U.S. and Canada and much smaller n Europe, Scandnava and Japan. Ths confrms our pror expectatons. Importantly, the results from estmatng equaton (15) confrm a negatve assocaton between real exchange rates and the unemployment rate as suggested by structuralst theory. We have so far omtted one mportant varable n our model of Secton I. Ths s the market share of domestc producers, x. Clearly, domestc output and employment are an ncreasng functon of the market share. The reason for ths omsson s smply lack of data. However, we dd experment wth calculatng the market share by assumng that t takes the value 1 n year 1978 all domestc customers are customers of domestc frms and then updatng t usng the followng dfference equaton: et (16) xt = xt xt 1 e where e denotes the average real exchange rate over the perod whch s our proxy for the PPP real exchange rate and the number 0.2 s only a rough guesstmate of the responsveness of the market share to real exchange rates. The equaton suggests

18 18 that an elevated (that s apprecated) real exchange rate makes customers drft away to foregn frms whle a lower value of e makes new customers jon domestc frms. Includng the market share x n equaton (15) gave a negatve coeffcent wth a t-rato of Ths suggests that a larger market share goes together wth lower unemployment (hence hgher employment rate and hgher output). Ths s what we expected. Apart from ths, the results were qualtatvely unaffected. We now turn to the most recent employment experence of the Unted States n lght of our theory. IV. The 1990s boom n the Unted States We start by plottng the rate of employment n the Unted States (one mnus the rate of unemployment) aganst the S&P500 ndex (n logs), when the share ndex has been normalzed by labor productvty (all sectors) and the consumer prce ndex. Ths s Fgure 5 below Fgure 5. Share prces (normalzed) and employment n the Unted States 1.00 employment rate employment rate share prces (normalsed) 7.5 log of share prces Employment rate defned as one mnus the rate of unemployment (n decmals). Share prces are S&P500 normalzed by the CPI ndex (1995=1) and a measure of labor productvty (1995=1). The value of the normalzed share-prce seres n 1995 s 470, whch s then also the value of the unnormalzed seres. It comes as a pleasant surprse that the long swngs n the two seres are clearly related. We should note that a postve relatonshp between the two seres has also been dscovered for many other countres (see Phelps and Zoega (2001)). The persstent

19 19 unemployment found n a number of Contnental economes s smultaneously reflected n the falure of stock prces (normalzed) to recover. Gong back to Fgure 5, the fall n the employment rate n the US n the early 1970s corresponded to a fall n the normalzed share prce wth a common trough n year 1975 and then agan n year There followed a jont recovery peakng n year 2000, followed by a declne n both seres. There are also nstances when the two seres go separate ways: Employment expanded n the late 1960s, the late 1970s and the late 1980s wthout a correspondng elevaton of stock prces. It follows that these may possbly have brought n rsng nflaton snce a rse n employment above ts non-nflatonary level or natural rate creates rsng nflaton n our model. The recesson n also seems to ft ths mould although wth the reverse sgn employment fell wthout a correspondng fall n stock prces. In contrast, the rse n share prces n the late 1990s appears not fully reflected n the employment rate. At ts peak n year 2000, the employment rate had not yet reached the peak of the late 1960s, although the stock market was much hgher. Smlarly, the employment rate n 2003 s lower than what we would expect from the stock market, whch s stll hgh by hstorcal standards. In lght of our theory, ths may suggest that employment could expand wthout rskng nflaton. (More on ths later.) Fgure 6 shows the nflaton rate and ts frst dfference over the same perod. Fgure 6. Prce and wage nflaton n the US 0.15 Prce nflaton 0.10 Wage nflaton 0.10 prce nflaton wage nflaton change of wage nflaton ch an g e o f prce nflato n Inflaton (n decmals) s measured as the rate of change of the CPI from last quarter of the prevous year to the last quarter of the current year. The perods of rsng prce nflaton are the late 1960s, the late 1970s and to a lesser extent the late 1980s. These perods correspond to those when employment expanded wthout any accompanyng elevaton of share prces. In contrast, the nflaton shock n the md 1970s s clearly caused by the ol prce hkes n Wage nflaton also pcked up n the late 1970s and the late 1980s. Interestngly, wage nflaton rose n the late 1990s to a greater extent than prce nflaton the real wage rose durng ths perod.

20 20 Phllps Curves If share prces truly affect the level of the natural rate of unemployment they should be of use n explanng and predctng nflaton. As a prelude, we plot n Fgure 7 the relatonshp between the frst dfference of the nflaton rate (CPI and wages) that s unexpected nflaton and the employment rate. Not surprsngly, there emerges no clear relatonshp between the two varables. The data clearly reject the jont hypothess of an expectatons-augmented Phllps curve and a constant natural rate of unemployment. Fgure 7. The (non) relatonshp between nflaton and employment n the US 0.06 prce nflaton 0.04 (frst dfferences) Prce Phllps curve wage nflaton (frst dfferences) Wage Phllps curve employment rate employment rate The ncorporaton of share prces should help clarfy the relatonshp between nflaton and employment f changes n share prces go hand n hand wth changes n the nonobservable natural rate of unemployment. To test for ths we now resort to regresson analyss. The estmated equaton has the followng form (17) ( 1 u ) ( s g e ) ( 1 u ) π t = α0+ απ 1 t 1+ β t γ1 t + γ 2 t + γ3 t + φδ t + εt where π denotes nflaton (ether prce nflaton (CPI) or wage nflaton), 1-u s the employment rate, s s the SP500 share prce ndex normalzed by labor productvty, g s the rate of (labor) productvty growth and e s the (trade-weghted) effectve real exchange rate. We also nclude the frst dfference of the employment rate because a rapd expanson or a rapd convergence to steady state s more prone to generatng rsng nflaton. The results follow n the table below.