Columbia University. Department of Economics Discussion Paper Series. Good Jobs, Bad Jobs, and Trade Liberalization. Donald R. Davis James Harrigan

Transcription

1 Columba Unversty Department of Economcs Dscusson Paper Seres Good Jobs, Bad Jobs, and Trade Lberalzaton Donald R. Davs James Harrgan Dscusson Paper No.: Department of Economcs Columba Unversty Ne York, NY 0027 June 2007

2 Good Jobs, Bad Jobs, and Trade Lberalzaton Donald R. Davs Columba Unversty and NBER James Harrgan Federal Reserve Bank of Ne York, Columba Unversty, and NBER May 5, 2007 Abstract Globalzaton threatens good jobs at good ages, accordng to overhelmng publc sentment. Yet professonal dscusson often rules out such concerns a pror. We nstead offer a frameork to nterpret and address these concerns. We develop a model n hch monopolstcally compettve frms pay effcency ages, and these frms dffer n both ther techncal capablty and ther montorng ablty. Heterogenety n the ablty of frms to montor effort leads to dfferent ages for dentcal orkers good jobs and bad jobs as ell as equlbrum unemployment. Wage heterogenety combnes th dfferences n techncal capablty to generate an equlbrum sze dstrbuton of frms. As n Meltz (2003), trade lberalzaton ncreases aggregate effcency through a frm selecton effect. Ths effcency-enhancng selecton effect, hoever, puts pressure on many good jobs, n the sense that the hgh-age jobs at any level of techncal capablty are the least lkely to survve trade lberalzaton. In a central case, trade rases the average real age but leads to a loss of many good jobs and to a steady-state ncrease n unemployment. The ves expressed n ths paper are those of the authors and do not necessarly reflect the poston of the Federal Reserve Bank of Ne York or the Federal Reserve System. Donald Davs gratefully acknoledges support of the Natonal Scence Foundaton. We are grateful for dscussons th Elhanan Helpman and Oleg Itskhok.

3 Good Jobs, Bad Jobs, and Trade Lberalzaton I. Introducton Treasury Secretary Henry M. Paulson, Jr., speakng n March 2007, cted a Pe Research Center survey to the effect that more and more Amercans seem to doubt that trade brngs greater benefts than costs. Whle the publc n the survey as roughly evenly splt on the overall benefts of freer trade, among those statng an opnon there as an overhelmng sentment that trade costs jobs and loers ages. A central concept n publc dscussons of globalzaton s that of a good job, a job that pays a hgh age, offers generous benefts, and provdes job securty. Such jobs are the subject of envy for those n lesser jobs, and nduce a feelng of good fortune n those ho have them. In economsts terms, good jobs have an element of rent that bad jobs lack. The benchmark model of labor demand used n most general equlbrum trade models has no place for such a concept: orkers are pad ther margnal product. Trade models typcally explan changes n ages n response to lberalzaton as the consequence of endogenous changes n margnal products. These models rule out a pror any dscusson of good and bad jobs. Our ve s that trade economsts are mssng an opportunty to address publc concerns, and adequately understand publc atttudes, by neglectng models here trade lberalzaton mght affect the ncdence of labor market rents. In ths paper, e offer such an analyss by combnng the effcency age model of Shapro and Stgltz (984) th the trade model of Meltz (2003). The Shapro-Stgltz model explans labor market rents and unemployment as arsng from asymmetrc nformaton: frms montor ther orkers effort mperfectly, and n equlbrum use hgh ages to nduce orkers to value ther jobs suffcently that the orkers on t rsk beng fred for shrkng. The Meltz frameork features equlbrum product market rents, and the dstrbuton of these rents s affected by trade lberalzaton. In our combned model, frms dffer n both ther ablty to montor orkers and n ther underlyng productvty, and the nteracton of these to forms of heterogenety mples novel, Remarks by Treasury Secretary Henry M. Paulson, Jr. before the Economc Club of Washngton, March, 2007; Free Trade Agreements Get a Mxed Reve, December 9, 2006, Pe Research Center For the People and Press. Lest t be thought that the perspectve on job and age losses s a partsan Democratc ve, t s notable that Republcans also responded that freer trade costs jobs and loers ages respectvely by margns of three- and fourto-one.

4 and provocatve, possbltes for adjustment to trade lberalzaton. Heterogenety n montorng costs mples dfferent ages for ex ante dentcal orkers, leadng to a precse and ntutve defnton of good jobs as those that pay above the economy de average age. As n Meltz (2003), trade lberalzaton n our model has a poerful effcency-enhancng selecton effect, th the loest margnal cost frms expandng and less productve frms contractng or extng. Unlke n Meltz, here all jobs pay the same and all orkers beneft from lberalzaton, trade lberalzaton n our model has dramatcally dfferent effects on the elfare of ndvdual orkers. In a move from autarky to free trade, and controllng for frm productvty, trade destroys only good jobs. The number of bad jobs expands and ths occurs most sharply for the orst jobs. Under the same experment, effcency s enhanced and the typcal prce falls. These are not conflctng effects; they are actually alternatve descrptons of the same phenomenon. The model also suggests there are lkely to be aggregate employment effects arsng from thn-ndustry re-allocaton. Whle not mandated by the model, there are good emprcal reasons to beleve that the net effect of lberalzaton ll be to rase the average age relatve to the loest age n the economy. Ths occurs through selecton effects that leave the relatve age offered by any ndvdual frm unchanged. If trade does rase ths average age, though, t also tghtens the ncentve constrants on shrkng. In the ne steady state, the hgher average age makes job loss less dauntng, and equlbrum unemployment must be hgher to nsure effort. The second best nature of our model mples that aggregate ncome gans from lberalzaton are not certan, although they lkely reman a central case. Trade n our model has a strong tendency to ncrease varety, loer prces, and shft producton toard more effcent frms. Hoever t also has a strong tendency to threaten hat orkers consder good jobs and could contrbute to a rse n structural unemployment. There are to recent papers that also consder unemployment and job loss n a Meltztype model of heterogeneous frms. Egger and Kreckemeer (2006) ntegrate Meltz (2003) th the far age model of Akerlof and Yellen (990). Frm-level ages n ther model are a eghted average of frm productvty and an unemployment-adjusted average age. Unemployment arses because the far age constrant prevents ages from fully adjustng to nsure full employment. Whle trade lberalzaton may cost jobs n ther model, t does so only at the least productve frms offerng the loest ages. Hence ther model does not offer a sense n 2

5 hch trade may threaten good jobs at good ages. Janak (2006) ntegrates Meltz (2003) th a Pssardes (2000) large frm search model to sho that trade ntegraton rases equlbrum unemployment. Hoever, ths specfc result, and even the exstence and unqueness of equlbrum n Janak s model, requre mplausble restrctons on the substtutablty of products, so that equlbrum markups must be bounded belo by 00 percent. An earler lterature, ncludng Copeland (989), Brecher (992) and Hoon (200) consders the mplcatons of effcency ages n trade models. None of these papers consders the channels e consder n the current paper, and n partcular they rule out the sort of ntrandustry reallocatons that seem to be mportant n practce and that are the focus of Meltz (2003). The paper by Matusz (996), hch analyzes effcency ages n a Krugman-style model of ntrandustry trade, s the most relevant to our project, and e dscuss Matusz model further belo. Secton II of our paper lays out our labor market model of effcency ages hen montorng costs dffer across frms. Ths labor market s merged th the Meltz (2003) model of heterogeneous frms n Secton III and IV. Our results about the effects of trade lberalzaton on ages, jobs, unemployment, and economy-de effcency are presented n Secton V and VI. II. Unemployment, Effcency Wages, and the Frm A. Shapro-Stgltz th Heterogeneous Frm Level Montorng In consderng employment relatons, e follo the effcency age model of Shapro and Stgltz (984), amendng ths as needed to mesh th the frm-based model of Meltz (2003). In the Shapro and Stgltz model, frms can montor orker effort only mperfectly. Workers dstaste for effort tempts them to shrk, and they are deterred n equlbrum by the possblty that ther shrkng ll be dscovered and they ll be fred. Unemployment perssts n equlbrum because the age that frms offer s too hgh to clear the labor market. Unemployment s bad nes for orkers, and truly nvoluntary, n the sense that employed orkers are ex ante dentcal to the unemployed yet have hgher utlty. The market falure s that orkers cannot credbly commt to effort at less than the gong age. Our model has all these features, th the crucal dfference that frms dffer n ther ablty to detect shrkng. 3

6 There s a large lterature that tests varous aspects of the Shapro-Stgltz and other effcency age models, but there s no paper that drectly tests the predcton that montorng ablty and hgh ages are substtute means to elct effort. There are a number of papers, ncludng Groshen and Krueger (990), Rebtzer (995), and Nagn, Rebtzer, Sanders and Taylor (2002) that use exogenous varaton n montorng ntensty to confrm that effort does ndeed ncrease n montorng ntensty 2. There s also a lterature that documents ndustry age dfferentals (for example, Krueger and Summers (988)). Such dfferentals have no drect connecton to effcency age theory, but they are consstent th labor rents of the sort that obtan n the equlbrum of the Shapro-Stgltz model. We assume that utlty s addtvely separable n consumpton and effort. Utlty from consumpton s gven by a standard CES aggregate of dfferentated goods, hch has an assocated deal prce ndex P that s developed n Secton IV belo. Dsutlty from effort s measured n the same unts as the age. Ths mples that a household th ncome has ndrect utlty gven by: e (.) u = P An mplcaton of ths specfcaton s that real prce declnes due to technologcal progress or ncreases n varety, etc. do not lead to a change n the dsutlty of effort relatve to the utlty of consumpton 3. Ths s the assumpton made mplctly by Shapro and Stgltz (984), although the ssue of trends n the relatve cost of effort dd not arse n ther steady-state, one-good settng. The orker ho s employed ll need to make a dscrete decson to supply a unt of effort or to shrk and supply effort 0. For smplcty, e normalze the age (or other benefts) receved by the unemployed to zero. Workers are rsk neutral and dscount the future at rate r > 0. Workers lose ther job only f they are caught shrkng or f the frm des, and frm death happens at the exogenous rate δ. Frms montor orkers for shrkng and m s an nverse measure of the frm s montorng effectveness. Hence f orkers at frm ere to shrk, they ould face a probablty m of 2 We have also observed a postve relatonshp beteen montorng ntensty and homeork effort by resdent adolescents. We beleve that such an effect s ell-knon to other parents. 3 In the absence of such a specfcaton, secular progress ould be assocated th a secular declne n unemployment, hch s counterfactual (see Romer (2006), Chapter 0). 4

7 detecton, th a penalty of beng fred and spendng a perod n unemployment before fndng a ne job. We mpose the techncal condton that [, m m0 ), here the loer bound m0 δ s the maxmally effectve montorng of any frm. 4 Workers at frm have fundamental asset equatons that reflect ther status as shrkers or non-shrkers. Let S N V E and V E be the expected lfetme utlty respectvely of shrkers and nonshrkers at frm. Let VU be the expected lfetme utlty of a orker currently unemployed (notng that ths s ndependent of any frm because unemployed orkers are unattached). Then the fundamental asset equatons for employed non-shrkers and shrkers respectvely are: N N (.2) rve = ( e) + δ ( VU VE ) S S (.3) rve = + ( δ + m )( VU VE ) These consst of the flo beneft, ( e) or respectvely, plus an expected captal loss n the case of a shft to unemployment, here these terms dffer because shrkers face a hgher probablty of a move to unemployment due to the frm s montorng m for shrkng. Ths departs from the conventonal Shapro-Stgltz frameork n allong for frm specfcty n montorng ablty, the age, and the value of employment. Frm recognzes the ncentve to shrk. Hence n lght of these ncentves and ts on montorng ablty, t chooses a age suffcent to nduce employees to ork rather than shrk. Ths requres thatv N E V S E, a non-shrkng constrant hch frms ll choose to meet th equalty. Solvng for the non-shrkng age constrant at frm, e fnd: (.4) = rv + e+ ( r+ δ ) em U Equaton (.4) s the frm-level equvalent of the Shapro-Stgltz no-shrkng constrant. Frst, note that snce V U s common to all frms, ages ll vary across frms only due to montorng ablty and that equlbrum ages are n a one-to-one ncreasng relaton th a frm s dffculty n montorng. Second, note also that ths s a notonal age. That s, ths s the 4 Ths nsures that the nstantaneous probablty of job loss arsng from all sources does not exceed unty. 5

8 age requred of a frm th montorng ablty m f t s to elct effort, and s ell defned although n equlbrum not all frms ll survve. Snce all actve frms ll meet the no-shrkng constrant n equlbrum, e can defne the value of beng employed at frm by substtutng the no-shrkng age back nto our defnton of N V E to yeld: (.5) VE = VU + em Ths equaton s ntutve. Rearrangng, e see that ( ) m V V = e, or equvalently E U that the probablty of beng caught shrkng tmes the captal loss assocated th ths should just compensate for the cost of effort. As the frm s ablty to montor orkers deterorates (hgher m ), ever hgher age rates are requred to nduce effort. Moreover, snce ths reflects the requred no-shrkng age choce of any frm, the unemployed ll alays fnd t advantageous to accept the frst job offered. B. The No-Shrkng Constrant and Aggregaton We have derved n Equaton (.4) a lnk beteen the frm s no-shrkng age, varous parameters of the model, ncludng the frm s montorng ablty, and the flo benefts of beng unemployed, rv U. The unemployed orker does not kno ex ante from hch frm an offer ll arrve. Hence consderaton of the flo benefts of beng unemployed requres aggregaton, to hch e no turn. Later e ll address n detal ho employment levels at ndvdual frms are determned; for no e smply assume that the relevant dstrbuton s knon to all n the economy. Let f ( ), then, be the equlbrum densty of employed orkers at frm, hence recevng age. These are the eghts that ll be appled n calculatng averages for the benefts of beng employed, for ages, and for montorng ablty of frms. Let VE be the average lfetme utlty of an employed non-shrker. Expected job tenure doesn t vary across frms snce n equlbrum no one shrks, so job loss happens only at the common exogenous rate δ as frm death. Hence e have ( ) V V f d. E E Correspondngly, the average age ll be: 6

9 ( ) f d And the average montorng ablty of frms s: m m f ( ) d We are no ready to consder the flo benefts of beng unemployed. Snce unemployed orkers here receve a zero age, the flo benefts consst entrely of the expected captal gan from re-employment. Let a be the nstantaneous probablty of re-employment of an unemployed orker. Then the fundamental asset equaton for an unemployed orker s: ( ) rv = a V V U E U From equaton (.5), and takng averages, e have that: ( ) V V = em E U so that substtutng ths n e fnd: (.6) rv = a ( em) U The nstantaneous probablty of re-employment of an unemployed orker, a, can be examned n terms of the steady state, hch requres that flos nto and out of unemployment be equal. Let L be the total sze of the labor force and let U be the total number of unemployed. In equlbrum separatons happen at rate δ. Then the steady state mposes that: (.7) au = δ ( L U ) U Substtutng (.8) nto (.6) and defnng the unemployment rate to be u, e fnd that L u rvu = δ em u Ths allos us to elmnate the term u = e+ δ em+ ( r+ δ) em u We can use ths to calculate the average age: u = e+ δ em+ ( r+ δ) em u rv U from Equaton (.4), and gves us: 7

10 In order to keep ths consstent th the Meltz (2003) model, e ll consder ths for the lmtng case n hch r 0. 5 Hence the last to equatons become: u = e + δ em + δem, and u u δ e = e+ δ em+ δem= e+ m u u ( ) e u Solvng the second of these for m =, and substtutng ths nto the frst, e δ e fnally arrve at a smple equaton relatng the age pad by a frm to the aggregate unemployment rate, the average age, and the frm-specfc montorng cost: (.9) ( )( ) = e+ u e + δ em Equaton (.9) shos that the no shrkng age of the frm s ncreasng n the cost of effort e, the frm-specfc montorng cost m, and decreasng n the unemployment rate u, as one mght expect from Shapro and Stgltz. But the frm age s ncreasng n the economyde average age, an effect Shapro and Stgltz couldn t separately dentfy. Ths also foreshados a tradeoff beteen smultaneous ncreases n and u that leave be dscussed further belo. The loest feasble no-shrkng age, montorng. In ths case, m m0 unaffected, to L, arses n the case of the maxmally effectve =, and so e ( u)( e) δ em0 L = + +. Because dentcal orkers ll receve dfferent ages, e cannot follo Meltz n choosng labor as the numérare. Instead, e choose as our numérare labor employed at tasks n hch they earn the age on offer at frms th the maxmally effectve montorng technology. Hence L, hch n turn mples: (.0) ( δ m ) e ( u)( e) = Moreover, th ths choce of numérare, e can re-rte Equaton (.9) as: (.) = + δ e( m m ) 0 5 We have developed the key expressons here for the case of r > 0, as n Shapro and Stgltz (984), and as the setup requres. Of course, e can see drectly that the lmts for the relevant expressons exst as r 0. We choose ths path snce the effects of r here are purely conventonal, but the Meltz (2003) model s developed n a context 8

11 Equaton (.) s extremely mportant. The foregong has only assumed that there s some equlbrum dstrbuton of ages, f ( ). From ths e have no been able to derve an exact relaton beteen the prmtve dstrbuton of m and the notonal dstrbuton of ages that must hold n the no-shrkng equlbrum. Wage dfferences for dentcal orkers arse only f there are montorng dfferences across frms and the magntude of these age dfferences rses proportonately th the montorng gap tself, the exogenous job separaton rate δ, and the level of effort e requred to be productve. Returnng to the age equaton for the numérare, Equaton (.0), and solvng for the lnk beteen the unemployment rate and the average age consstent th non-shrkng, e fnd: +δ em0 (.2) u = e It s straghtforard to sho that the no-shrkng unemployment rate for the relevant case s postve, ncreasng, and concave n the average age. 6 Unemployment n ths model s nvoluntary n precsely the same ay as Shapro-Stgltz. Equaton (.2) hghlghts a crucal dfference, though, beteen the standard Shapro- Stgltz frameork and the present approach. In the standard Shapro-Stgltz model, all frms are dentcal, hence t s mpossble to separately dentfy the effect of the frm s on age and the economy s average age on ncentves to shrk and equlbrum unemployment. Ther aggregate no-shrkng condton, then, shos the total effect of a smultaneous rse n the frm and average here the source of frm dscountng s lmted to the nstantaneous frm death rate δ. Effectvely, takng lmts at ths pont just rds us of a nusance parameter. 6 Wth the maxmally effectve montorng age at unty, the average age cannot be loer, so the numerator n Equaton (.2) s postve. Note that > e or at least some of the orkers ould shrk (contrary to assumpton), so the denomnator s also postve. These to facts combned mply that equlbrum unemployment must be postve. Employment s feasble,.e. u <, henever the effort cost of beng productve s not too hgh relatve to the product of the effectve dscount factor from exogenous job separatons tmes the probablty of beng detected hen shrkng at the maxmally effectve montorng frms, or du e( +δ m0 ) = d e 2 ( ) 2 ( e( m0 )) 3 ( ) +δ 2 du = 2 d e e < m e δ 0. We also see that, hch s postve under the same condtons that make employment feasble. Further, s negatve under the same condtons. Whle a rse n the average age rases the equlbrum unemployment rate, the senstvty of the unemployment rate to movements n average ages s greatest 9

12 age, and shos that ths age rse reduces equlbrum unemployment along the no-shrkng constrant. It ould be smple to conclude that th effcency ages a rse n prevalng ages nevtably reduces equlbrum unemployment. Ths ould, though, be ncorrect. Our equaton (.9) shos that, as n Shapro and Stgltz, there s a negatve relaton beteen the frm s on age and the level of requred unemployment consstent th no shrkng. But equaton (.2) shos, by contrast, that there s a postve relaton beteen the average age and the equlbrum no-shrkng unemployment rate. The contrast s smple to understand. A fall n the unemployment rate on ts on alays makes shrkng more attractve. For the no-shrkng constrant to be met eakly requres somethng that makes shrkng less attractve. At the frm level, the fall n the unemployment rate requres a rse n the frm s age to prevent shrkng, hence unemployment and the frm s age have an nverse relaton. When consderng the average age, though, a drop n the unemployment rate that makes shrkng more temptng must be met th a drop n the average age to make shrkng less temptng, snce the average age s the age a fred orker receves hen eventually re-employed. Thus, hle the unemployment rate and the frm s on age are negatvely related, the unemployment rate and the average age must be postvely related. Ths contrast ll be key to our results belo. In our model, the average age ll be able to move through frm selecton effects even hen the age s constant among all actve frms. When these selecton effects lead the average age to rse, unemployment ll have to rse as ell. Let us take stock of hat ths secton has acheved. We have derved a smple relaton beteen the unemployment rate and the average age consstent th a no-shrkng equlbrum. We have also derved a smple relaton beteen the equlbrum no-shrkng age offered at ndvdual frms and exogenous frm-level montorng ablty. These ll be crucal n developng our model of the product market. Shapro and Stgltz closed ther model th a neoclasscal labor demand approach featurng dentcal compettve frms (even f the frms recognzed the bndng nature of the noshrkng constrant). We ll go on no to develop a monopolstcally compettve product hen average ages are relatvely lo. We ll focus precsely on these cases for hch equlbrum unemployment u 0,. s ( ) 0

13 market as the bass for our model of labor demand, one that ll feature frm heterogenety not only n productvty, as n Meltz, but also n montorng ablty. III. Lnks Beteen The Models of Heterogenety n Productvty and Montorng In ths secton e develop a varant of the heterogeneous frm model of Meltz (2003) and sho ho to lnk t to the heterogeneous effcency ages model based on Shapro and Stgltz (984) that e derved n Secton II. We frst dscuss the hgh level lnks beteen the models and then derve the key elements formally. Equlbrum n a standard Meltz model may be analyzed n three parts structure, scale, and the lnk beteen the to. By the equlbrum structure, e mean the prce, quantty, age bll, and profts for each frm per unt mass of frms. In the Meltz frameork, and for gven parameters, ths s fully determned by the dstrbuton of margnal costs across frms. And n Meltz s on model, the varaton n margnal costs across frms s fully descrbed by the varaton n frm physcal productvty n margnal cost, ndexed by ϕ. By equlbrum scale n a Meltz model, e mean the mass M of frms of each type that s requred to nsure equlbrum n the labor market. Gven Meltz s assumpton of compettve labor markets, ths determnes the mass M from full employment of the labor force L gven the economy s structure. Fnally, the lnk beteen structure and scale comes from the labor demand per unt mass mpled by the equlbrum structure of the economy. Ths s gven by the total revenue per unt mass dvded by the average age, here both are defned to nclude entry, fxed, and margnal costs. Ths takes a partcularly smple form n Meltz, here all frms pay a common compettve age, taken as the numérare, and so labor demand per unt mass s smply equal to revenue for ths mass. Turnng to our model, equlbrum structure s also fully determned by the dstrbuton of margnal costs across frms. Hoever margnal costs n our model vary across frms not only due to varaton n frm level productvty, ϕ, but also due to frm-specfc no-shrkng ages margnal cost actvtes. Indeed frm margnal costs ll be gven as the rato of these to, Our measure of nverse margnal costs (productvty) s then defned as z n ϕ. ϕ. Ths allos us

14 to use Meltz s results on the determnaton of the economy s structure as a functon of the dstrbuton of margnal costs thout modfcaton, here these are no ndexed by z. Equlbrum scale of the economy also dffers from Meltz. It stll features adjustment of the mass of frms M to ensure labor market equlbrum. Hoever labor market equlbrum no requres ths mass to adjust so that total labor demand equals the total labor force adjusted for the unemployment rate u. From our frm-based effcency age model, the unemployment rate u s n a one-to-one relaton th the average age. And the average age s tself determned by the structure of the economy. The lnk beteen the structure and scale of the economy also vares from that of Meltz. As before, ths lnk comes from labor demand per unt mass mpled by the equlbrum structure of the economy. Agan, ths s gven by total revenue per unt mass dvded by the average age, both defned to nclude entry, fxed, and margnal costs. Hoever, because e no longer have compettve factor markets, the average age departs from unty. Hence e have to take the total revenue and average age, as determned by the equlbrum structure of the economy, and convert these nto the mpled labor demand per unt mass of frms. The total mass of frms then adjusts to attan labor market equlbrum, hch here requres that that total employment s consstent th the unemployment rate requred for non-shrkng gven ths same average age. In sum, just a fe elements serve to lnk the models. To follo the Meltz frameork, all frm varaton n costs must affect only margnal costs. Hence e assume all frms have common montorng and pay a common age f n all fxed cost actvtes. For convenence, e assume that these fxed cost actvtes have the maxmally effectve montorng, hch from Secton II mples f. Hence frm level varaton n montorng ll affect only ages n margnal cost actvtes, gvng rse to margnal costs z =. These frm level margnal costs, combned th ϕ the dstrbuton of frm types, determne the structure of the economy. Ths structure, agan n combnaton th the dstrbuton of frm types, determnes the average age. The average age, n combnaton th results from Secton II, determnes the unemployment rate u as ell as the labor demand per unt mass of frms. And these n turn determne the equlbrum mass of frms n the economy, hence the full equlbrum. We turn no to sho these results more formally. 2

15 IV. The Product Market A. The Consumer s Problem Preferences over goods are dentcal and homothetc, hence can be represented by those of a representatve consumer. The representatve consumer s problem s dentcal to that n Dxt and Stgltz (977) and Meltz (2003). Consumers allocate expendtures across avalable varetes to: We also have Mn E= pqd ( ) ( ) () ρ st.. q ρ d = U 0 < ρ <, and σ =. ρ These delver demand curves for product of the form: σ p () q () = Q P here Q U and P s an aggregate prce ndex gven by () σ σ P= p d The demand curve above s a key nput to the producer s problem. B. The Producer s Problem Frms face a sequence of problems. There s an unbounded mass of potental frms. In the frst stage, a mass M of frms ll enter, pay a fxed entry cost of f e, and receve nformaton about ther type. Here a frm s type s represented by the par (, m ) ϕ coverng both productvty and montorng ablty n varable costs. We sa above n equaton (.) that there s a smple relaton beteen equlbrum no-shrkng ages and montorng, gven by δ e( m m0 ) Ths means that the frm can mmedately translate the productvty-montorng dra (, m ) a productvty-age dra ( ϕ, ) = +. ϕ to. As t turns out, the frm s ndvdual choces are affected only 3

16 by the rato z ϕ to analyze market equlbrum., although e ll be nterested n examnng ϕ and separately n order Here z can be thought of equvalently as age-adjusted productvty n margnal cost or as the nverse margnal cost for frm. Havng learned ts type z, frm ll produce f ts varable profts cover ts per perod fxed costs f ; otherse t ll ext before producng. In hat follos, e ork from the ndvdual frm problem and aggregate up. C. The Indvdual Frm We consder no the problem of an ndvdual frm that has already sunk the cost f e to learn ts type z. Physcal labor requrements n frm z follo Meltz: qz ( ) ( z, ϕ) = f + ϕ Note that frm level physcal labor demand requres knoledge of ϕ (not only z ), so must be recovered to establsh labor market equlbrum once the structure of the economy (ncludng the age bll for a frm of type z ) s determned. As e noted, our use of the Meltz approach requres that the only locus of frm level varaton s n margnal costs. Hence e assume that the frm pays a age f for labor employed n ts fxed costs and a age for labor employed n ts varable costs. A partcular frm thus faces a demand curve as defned n the consumer s problem above and chooses output to maxmze profts, q q π = p q f = p q f z ϕ The frst order condtons yeld the famlar prce as a markup on margnal cost: pz ( ) = = ρϕ ρz Prces and maxmzed profts vary across frms only because of varaton n z. That s, frms th a common nverse margnal cost z may be payng dfferent ages, hch are offset by productvty dfferences, but they charge the same prce, ll produce the same quantty, and 4

17 have the same revenue and profts. Hence e ll drop the subscrpt henceforth except as necessary to clarfy lmts of ntegraton. D. Aggregaton We have seen that the combnaton of a prmtve dstrbuton on (, m) equlbrum from the labor market, e can derve the jont dstrbuton for ( ϕ, ) ϕ and the. Knoledge of ths jont dstrbuton allos us as ell to calculate the dstrbuton of nverse margnal costs ϕ z th cumulatve dstrbuton functon Gz ( ) Pr[ Z z] and densty gz. ( ) The full equlbrum ll feature a cutoff level of nverse margnal cost, z, such that frms th z< z ext mmedately upon learnng of ther dra. Gven gz, ( ) e can also defne the equlbrum densty of actve frms: ( ) g z µ ( z) =, z z, G z ( ) ) If there s a mass M of frms, then the number of them at any gven nverse margnal cost z s Mg( z, ) and the number of those that survve and produce s M µ ( z). The defnton of the CES prce ndex gves σ P= p( z) Mµ ( z) dz σ ( ) µ ( ) σ z σ σ = M p z z dz z = M σ p here p s mplctly defned n the last step. As usual n ths type of model, holdng the densty of frms fxed, the prce level s decreasng n the number of frms, hch s the love-of-varety effect. Substtutng n ( ) ( ρ ) p z σ σ p ρ z µ ( z) dz z = z gves σ = = ρz 5

18 here, makng the dependence of z on z explct, σ z ( z ) = z µ ( z) dz σ z Ths last varable, z, s a measure of aggregate nverse margnal costs and plays a key role n the determnaton of equlbrum n the product market. E. The Margnal Frm and Equlbrum Structure of the Economy Equlbrum structure n an autarkc Meltz economy s determned by the soluton of to relatons beteen average profts π and the margnal cost of the margnal entrant z. The frst of these to relatons s a free entry condton (FE), hch asserts that from an unbounded set of ex ante dentcal frms, a suffcent mass enters so that the average profts from entry equal the fxed cost of entry. Wrtten n these terms, the FE condton s: π G( z ) = fe δ For a gven margnal entrant G z s the ex ante probablty of successful entry, z, ( ) π the per-perod average profts for successful entrants, and the factor that yelds expected δ value hen the stochastc ext rate for successful frms s δ. Solvng, e have: δ f π ( z ) = e (FE) G z ( ) Ths formulaton ponts at the path to soluton, hch s to lnk average profts to the margnal entrant. The frst step dras on the aggregate measure of nverse margnal cost z ( z ), from above. The second step s to sho that total profts can be rtten as Mπ ( z) Π=, so that average profts are: Π π ( z ) = π ( z ( z) ) =. M The proof follos Meltz and s omtted here. The second of the to key relatons s the zero cutoff productvty (ZCP), hch requres that the frms th the hghest margnal costs that actually produce should have varable profts 6

19 equal to the per-perod fxed cost, or π V ( z) = f. To convert ths to a form amenable to the smple determnaton of equlbrum va π as a functon of z requres only a fe more steps. V rz ( ) Generally, varable profts for an actve frm are gven by π ( z) =, and the revenue σ for ths frm s gven by r( z) [ ρ ] R P z σ =. Ratos of varable profts are equal to the rato of revenues and depend only on the rato of nverse margnal costs, so that e can rte V π z = σ V ( z ) π ( z ) 2 z2 for any actve and 2 z z. Recallng that π ( z) profts π, e can rte ths out for nverse margnal costs z and z as σ zz () rz () π = f z. If e further defne σ rz () cutoff productvty has σ π = fk() z (ZCP) s equal to average σ zz () kz () = z, and recall that the zero = f, e can mpose ths condton by requrng: The remander of the dervaton follos Meltz and s omtted. The Free Entry and Zero Cutoff Productvty condtons defne to relatons n π and z and can be solved for equlbrum values as n Meltz. The equlbrum exsts and s unque under the same condtons. The equlbrum z completely determnes the structure of the economy. We no need to go on to recover the average age, determne the assocated unemployment rate consstent th no-shrkng, and thus determne the mass of frms that provdes for equlbrum n the labor market. F. Labor Supply and Demand The labor force n our model s dvded nto four elements: U the unemployed L e L f L V orkers n fxed entry cost sector orkers n per-perod fxed cost actvtes orkers n varable cost actvtes The aggregate labor force constrant s 7

20 L= U + Le + Lf + LV For entry, e need to consder the steady state. The number of ne entrants every perod s a fracton of the ncumbents hch s exactly equal to the number of frm deaths, δ M labor devoted to ne entry n steady state s: L e = δ Mf e The physcal levels of employment n fxed cost s smply Lf = Mf. Thus For the varable cost actvty, e no have to make precse the dstncton beteen ages and physcal margnal productvty. It s the latter that gves employment n each frm. The complexty arses because frms th a gven z (and hence a gven level of output) may have an nfnte number of physcal productvtes ϕ. Physcal varable labor demand for frm s gven by dstrbuton of (, ) qz ( ) ( z, ϕ ) =. From the jont ϕ V ϕ and the equlbrum z e can construct the equlbrum jont dstrbuton represented by the densty ψ ( ϕ, z ). Wth the mass of frms M and ths jont densty, total employment n varable costs s gven by: qz ( ) V = ψϕ ϕ z z L M (, z ) ddz We can no rte the labor market clearng condton n quantty terms as: qz ( ) ( u) L = M δ fe + f + ψ( ϕ, z) ddz ϕ z z Note that for a gven unemployment rate u (hence average age ), the mass of frms M s drectly proportonal to the labor force sze L and employment ( u) L. G. Average Wages No e turn to determnng average ages. Multplyng each frm s employment of labor n varable cost varable cost as qz ( ) V ( z, ϕ ) = by the frm-specfc age gves the frm s age bll n ϕ 8

21 σ ( ) = [ ρ] z q z z Q P σ hch allos us to conclude that aggregate payments to labor n varable cost are z hch, usng becomes σ σ σ σ σ σ [ ρ ] µ ( ) = [ ρ ] µ ( ) = [ ρ] M z Q P z dz MQ P z z dz MQ P z ρ σ ρ ( ), ( ) Q= M q z P= M z, q( z) z M z To get total payments to labor e add employment n fxed and entry cost actvtes, here the age s one. Thus aggregate payments to labor are ( ) q z M δ fe + f + z so the average age s ( ) M q z = δ fe + f + ( u) L z H. Equlbrum n the Labor Market Wth the structure of the economy determned by z n Secton IV.E., e no have three equatons n three unknons, u,, and M. From Secton IV.F, the physcal labor market clearng condton: qz ( ) ( u) L = M δ fe + f + ψ( ϕ, z) ddz ϕ z z From Secton IV.G, e fnd that the average age satsfes: ( ) M q z = δ fe + f + ( u) L z And from Secton II, the no-shrkng constrant requres: +δ em0 u = e 9

22 We can substtute the frst of these equatons nto the second to solve for. We then substtute nto the no-shrkng constrant to get u, and solve for M by substtutng back nto the secton IV.G equaton for. Ths completes the soluton of the model. V. Autarky to Free Trade n To Specal Cases We have developed a general model that ntegrates the Meltz model of heterogenety n frm productvty th a Shapro-Stgltz model amended to allo for heterogenety n frm montorng abltes. We have shon that the structure of the economy s somorphc to that n Meltz and a functon of frm margnal costs mc = =, hch depend on frm varaton n ϕ z both ages and productvty. Before turnng to examne the consequences of trade lberalzaton n the general case, t ll prove useful to consder to specal cases, each of hch shuts don one of the to nfluences on margnal costs. A. The Meltz-Type Model Our frst specal case s hat e term a Meltz-type model. Margnal costs are assumed to vary th heterogenety n frm productvty, but e assume that all frms have the same montorng ablty, hch for convenence e assume are at the maxmal attanable level. Wth, e have mc = =, as n Meltz. Fgures A and B llustrate results famlar from ϕ z Meltz, here n the (, ϕ ) space, all frms le on the lne. In autarky, frms hose margnal costs are hgher than mc a (productvty loer than ϕ a ) ext thout producng. In a move from autarky to free trade steady states, the hghest margnal cost (loest productvty) frms mc, mc ) ext; the next loer margnal cost frms mc, ) a mcx contract; the next loer margnal cost frms mc,, x mc π ) succeed n exportng, although ther profts fall; and fnally the loest margnal cost frms, mc mc π, become super-exporters and rase ther profts. Homogeneous labor and a common montorng technology mply that nomnal ages are unchanged. Stll, the economy acheves hgher productvty through the elmnaton or contracton of hgh margnal cost frms to the beneft of lo margnal cost frms. And orkers ll be better off as a result of the avalablty of cheap mported varetes and through a possble 20

23 ncrease n varety avalable locally. Interestngly, the fact that the average age does not change mples that nether ll there be a change n the unemployment rate (see Equaton (.2)). Wthn the context of our model, ths justfes Meltz n havng put asde ssues of aggregate unemployment, snce f the only source of heterogenety n frm margnal costs s frm-level productvty, then unemployment, hle t does exst, does not change n the move from autarky to free trade 7. The Meltz model has many great features. But ts constrant that all ages for all orkers are dentcal makes t mpossble to make sense of publc concerns that trade destroys good jobs no job s any better than any other. And the fact that there are aggregate gans from lberalzaton combned th the homogenety of jobs suggests that all orkers ll beneft, at least eventually, from such a lberalzaton. Ths makes t hard to make sense of orker concern about trade and suggests the need for a rcher model n hch there s a clear sense of some jobs beng better than others. 8 B. Frm-Level Varaton Only n Wages A second specal case arses hen e abstract from heterogenety n frm productvty and allo only for heterogenety n frm montorng, hence n ages. For ths case, e set ϕ and thus have mc = =. Hence n ths case, e can speak synonymously of margnal costs z or ages. Note also that the fact that dentcal orkers receve dfferent ages at dfferent frms means that orkers perceve some jobs as beng better than others. Fgures 2A and 2B llustrate the relevant cases n autarky and n a move from autarky to free trade. In the fgures, all frms n the (, ϕ ) space le on the ϕ = lne at ages. Exactly as n the prevous case, n autarky frms th hgh margnal costs ext before producng. Hoever, snce all frms no have the same productvty, varaton n margnal costs arses only due to dfferences n the ages that must be pad. Hence frms n autarky hose poor montorng technology ould requre ages > mc ext before producng. a 7 Ths result contrasts th Matusz (996), here trade lberalzaton n a monopolstc competton model reduces unemployment. The key to the dfference s that n Matusz specfcaton an equlbrum ncrease n varety reduces the ncentve to shrk. Our specfcaton of utlty neutralzes ths effect, for reasons dscussed n secton II.A 8 As noted by Kletzer (200), mport-related job losses are often assocated th extended spells of unemployment and substantal declnes n ages hen re-employed. 2

24 Ths model also provdes a frst opportunty to make sense of the publc percepton that free trade destroys good jobs at good ages. In a move from autarky to free trade, the hghest age frms n exstence, those th ages (, a, ext and all the hgh age jobs at these frms are destroyed. The exstng frms that offer the next hghest ages, those th (, x contract and dsmss some of ther orkers. As e head don n the age dstrbuton to relatvely lo payng jobs, those th ages n the range ( π, x, frms expand employment to reach ne export markets, but even ths export success s nsuffcent to rase ther total profts. Employment expands most sharply at the frms offerng the loest ages, those n the range, π. And t s only these last frms, the ones offerng the loest ages and ho become super-exporters, ho actually have ther profts rse as a result of lberalzaton. Indeed, the proft gans to these frms offerng the loest ages exceed the combned proft losses to all other frms, ncludng those forced to ext. Snce the output response s greater at frms offerng loer and loer ages, e can be sure that the average age falls n the move from autarky to free trade. One compensaton n ths case s that the aggregate unemployment rate ll for ths reason fall. All orkers ll also beneft from the loer prces and possbly ncreased varety arsng from trade. Hoever, th a loer average age, and all of the hghest payng jobs elmnated from the economy, there are lkely to be many orkers ho see themselves as orse off on account of lberalzaton. Ths model n hch the only source of varaton n margnal costs s due to frm dfferences n ages has the great mert that t presents a very stark artculaton of the publc concerns that trade destroys good jobs at good ages. In ths model, t does. If e constran all frms to have a common technology, then those that pay the hghest ages are at rsk of ext or contracton n the move from autarky to free trade. Trade destroys the best jobs. Nevertheless, there are good reasons to beleve that ths model n hch all varaton n frm level margnal costs s due to dfferences n ages s at best ncomplete. Most pontedly, t ould have the mplcaton that hgh age frms are also small and unproftable frms. The data contradct ths (Idson and O, 999). Lke the Meltz model, hch alloed margnal costs to vary only th frm productvty, ths model n hch margnal costs vary only due to frm level age dfferences has mportant shortcomngs. We ll no turn to the general model, hch 22

25 allos for margnal costs to vary for both reasons to see that e can address the concerns that arse n the to specal cases. VI. Trade Lberalzaton n the General Case Ths secton ll consder the consequences for frms and orkers of trade lberalzaton n our general model. Sectons VI.A. and VI.B. consder ths n detal for the case of a move from autarky to free trade. In Secton VI.C., e ll dscuss t lberalzaton n economes that are already partally open. We dvde our dscusson of a move from autarky to free trade nto to peces. The frst ll consder the case of a lberalzaton that affects the structure of the economy, but not ts scale. As dscussed above, the lnk n our model beteen structure and scale s the average age relatve to the maxmally effectve montorng age, through the mpact of ths average age on the equlbrum unemployment rate. Dependng on the prmtve dstrbuton of productvty and montorng ( ϕ, m ), our model s consstent th ether a rse or fall n ths average age th lberalzaton. As a base case, e begn by assumng that lberalzaton has no mpact on ths average age. Ths mples that the structure of the economy ll change, but not ts scale, as the unchanged average age neutralzes any mpact on aggregate employment. Once the analyss of a change n structure s complete, e go on to consder ho e ould need to amend the conclusons of that analyss once e allo for changes n scale as ell. The analyss n ths secton, n formal terms, s comparatve steady state analyss. A complete analyss of the tme path of adjustment ould be requred to make defntve statements about elfare and poltcal economy. That s beyond the scope of ths paper. Nonetheless, the basc nature of the adjustments requred along the path to the ne steady state does emerge from our model. We beleve that ths provdes a poerful heurstc for understandng the forces at ork n dentfyng nners and losers, hence also n understandng the poltcal economy of lberalzaton. A. Changes n Structure Only We consder here the specal case n hch our economes move from autarky to free trade, but n hch the average age relatve to the maxmally effectve montorng age s unchanged. Wth an unchanged average age, aggregate employment s unchanged. Ths mples 23

26 that the analyss of the structure of frms prce and output decsons n the product market, as ell as proft, entry and ext, ll be precsely as n Meltz, so long as e use our on measure of nverse margnal cost, gven by z. Here, though, orkers have attachments to specfc frms because of rents created by dfferences at the frm level n ages. We can use Fgures 3A and 3B to thnk about the comparson of autarky and free trade as t affects profts of frms and employment of orkers. The loest feasble age s the maxmal montorng age and equals one by choce of numérare. In Fgure 3A, the ray labeled ndcates the hghest level of margnal cost consstent th zero post-entry profts, and thus defnes the cutoff for actve frms. Frms th loer margnal costs are to the southeast of the mc a ray, and frm sze s monotoncally decreasng n margnal cost. An mplcaton s that even f montorng ablty and physcal productvty are ex ante uncorrelated, there ll be an ex post correlaton beteen productvty and ages, because only hgh productvty frms can afford to stay n busness hle payng hgh ages. If ex ante montorng costs and productvty are postvely correlated, our model offers a potental explanaton for the frm sze-age premum: hghly productve frms are lkely to have hgher montorng costs and consequently pay hgher ages. As long as the hgh ages don t completely offset hgh productvty, hgh age frms ll also be bg frms on average (ths conjecture as also made by Bulo and Summers (986)). Our model s qute consstent th the Idson and O (999) explanaton for the frm sze-age premum. Idson and O dsmss the effcency age model on theoretcal grounds and clam n ther ttle that Workers are more productve n large frms hch s hy they are pad more. Wth an ex ante correlaton beteen montorng costs and productvty, effcency ages and productvty are complementary rather than substtute explanatons for the frm sze-age premum. The mpact of the shft n comparatve steady states from autarky to trade, llustrated n Fgure 3B, gves rse to three addtonal crtcal values n nverse margnal costs. The frst s mc, the margnal entrant under free trade. Next s mc a mc x, the margnal exporter. Fnally s mc π, the hghest margnal cost for hch a frm sees ts profts rse th free trade. Accordngly, these boundares defne Regons I to IV n the fgure. The mpact of trade on frms profts and output s straghtforard. All frms n Regon I ext th trade, so ther profts and output fall to zero. Frms n Regons II and III also see a 24

27 declne n profts. For frms n Regon II, the entry of foregn frms nto ther home market reduces ther domestc demand and profts, yet leaves them ncapable of fndng a suffcent foregn market to justfy the fxed costs of exportng. Output for these frms declnes. It s notable that frms n Regon III suffer a declne n profts n spte of the fact that they not only survve n the domestc market but also fnd a foregn market for ther products; the losses n the home market are not fully compensated by the ne profts n the export market. Total output for these frms expands and so the declne n profts s attached to the fxed cost of enterng the export market. Only the largest frms, those n Regon IV, fnd that ther profts rse th trade. Notably, frms can fnd ther ay nto Regon IV ether by ther nherent productvty or by effectve montorng of orkers, hch allos them to elct effort at lo ages. The analyss of the mpact on orkers s only slghtly more complex. We have set asde untl the next subsecton any mpact of trade on the average age and equlbrum unemployment. The age of a orker ho mantans employment at a specfc frm s determned by the frm specfc montorng technology and parameters of the model, so s unaffected by trade lberalzaton (see Equaton (.)). Ths leaves only to channels for trade to affect orkers. The frst, as n Meltz, s that lberalzaton loers the typcal prce and may rase total varety of products avalable to orkers qua consumers. Ths benefts all orkers and should be consdered as a potental offset to losses ncurred by some orkers. The second channel for trade to affect orkers here s va changes n employment, hch s most drectly related to the fate of frms n the output market. We have already seen that frms n Regon I ext the market, hence all orkers at these frms lose ther jobs. Frms n Regon II contract ther output, hence orkers at these frms may be seen as facng a probablty of job loss related to the degree of contracton. Frms n Regons III and IV expand employment suffcently n the ne steady state to provde precsely the same number of ne jobs as those lost va frngs among frms n Regons I and II. Workers at frms n Regons III and IV should expect to be unambguously better off th the move from autarky to free trade. The frms there are expandng output, so should have no unusual layoffs. And they enjoy gans from loer typcal prces and possbly ncreased varety. The stuaton s more ntrcate for orkers ntally th frms n Regons I and II. As noted, on one sde are the common varety and prce gans from lberalzaton. On the other sde 25