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1 Journal of International Econoics 84 (2011) Contents lists available at ScienceDirect Journal of International Econoics journal hoepage: Good jobs, bad jobs, and trade liberalization Donald R. Davis a,, Jaes Harrigan b,1 a Colubia University and NBER b University of Virginian and NBER article info abstract Article history: Received 23 January 2009 Received in revised for 11 February 2011 Accepted 11 March 2011 Available online 21 March 2011 Keywords: Trade liberalization Good jobs Fir heterogeneity Uneployent How do labor arkets adjust to trade liberalization? Leading odels of intraindustry trade (Krugan (1981), Melitz (2003)) assue hoogeneous workers and full eployent, and thus predict that all workers win fro trade liberalization, a conclusion at odds with the public debate. Our paper develops a new odel that erges Melitz (2003) with Shapiro and Stiglitz (1984), so also links product arket churning to labor arket churning. orkers care about their jobs because the odel features aggregate uneployent and jobs that pay different wages to identical workers. Siulations show that, for reasonable paraeter values, as any as one-fourth of existing good jobs (those with above average wage) ay be destroyed in a liberalization. This is true even as the odel shows inial ipact on aggregate uneployent and quite substantial aggregate gains fro trade Elsevier B.V. All rights reserved. 1. Introduction How do labor arkets adjust to trade liberalization? Three points otivate our approach to this question. The first is epirical. Most of trade is intra-industry trade and recent experience of large liberalizations suggests that the greater part of adjustent is likewise reallocation within rather than between industries. The second is a point of analysis. Recent theoretical advances that ephasize the role of fir heterogeneity and product arket churning also underscore the iportance of considering labor arket churning in trade liberalization episodes. The third otivation is again epirical. hile job rents appear to be ore odest than they appeared in soe early studies, they reain substantial for soe workers and this could be a source of resistance to trade refor. e develop a odel that integrates these eleents. Building on Melitz (2003), our odel is focused on within industry reallocation, and so is relevant for the bulk of trade and the nature of the ost significant trade refors. Linking Melitz (2003) fir heterogeneity with Shapiro and Stiglitz (1984) efficiency wages at the fir level, Much of this paper was written while Davis was visiting, and Harrigan was eployed by, the Federal Reserve Bank of New York. The views expressed in this paper are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve Syste. The authors are grateful to Elhanan Helpan and Oleg Itskhoki for very helpful coents on an early version of this paper, and to seinar participants at Colubia, Fordha, Harvard, Princeton, Yale and the NBER. Corresponding author at: Departent of Econoics, Colubia University, New York, NY 10027, United States. E-ail addresses: drdavis@colubia.edu (D.R. Davis), jaes.harrigan@virginia.edu (J. Harrigan). 1 Departent of Econoics, University of Virginia, Charlottesville, VA 22904, United States. there is equilibriu uneployent and jobs have fir specific rents attached, these rents iplying that workers distinguish between good and bad jobs. Selection effects now depend both on fir physical productivities and fir wages. Since our odel also features the product arket churning of Melitz, it likewise features labor arket churning. However, unlike in Melitz, job rents and the existence of uneployent ean that workers care about job loss, particularly the loss of good jobs. e go on to develop a siulation of this econoy, with key paraeters chosen where possible to atch existing epirical estiates, and study liberalization episodes that constitute transitions to Anderson and Van incoop's (2003) preferred estiate of actual level of trade integration as well as the case corresponding to the reoval of all trade barriers. Trade raises aggregate real incoe substantially, and the level of uneployent is at plausible agnitudes and is little affected by liberalization. However there is considerable product and labor arket churning. ith the reoval of all border barriers, trade leads to the gross destruction of up to onefourth of all good (above average wage) jobs. Our approach builds on a sustained dialog about the consequences of trade liberalization for labor arkets. Traditional coparative advantage odels highlight the potential disruptiveness of trade liberalization, which would require inter-industry reallocation of labor. Krugan Dixit Stiglitz type odels, by contrast, ephasized that the gains fro international exchange of varieties could exist with literally zero re-allocation of labor. The epirical literature is at odds with both hypotheses. Instead, actual trade liberalizations are associated with considerable labor re-allocation, but this takes place priarily within rather than between industries. This observation accords well with the heterogeneous fir paradig of Melitz, in which product arket churning of firs has as a consequence labor arket churning of jobs. However, the Melitz /$ see front atter 2011 Elsevier B.V. All rights reserved. doi: /j.jinteco

2 D.R. Davis, J. Harrigan / Journal of International Econoics 84 (2011) odel fares less well in another diension. Key characteristics of the labor arket in Melitz include the hoogeneity of workers and jobs. All workers are the sae, all jobs are the sae, and there is full eployent. Hence, while there is a churning of jobs, workers do not care about the churning per se, but just enjoy the gains available to all workers. This would be a world in which trade liberalization is uncontroversial, quite unlike the world in which we actually reside. Our paper is one aong a set that ai to reconsider the labor arket side of trade liberalization. Related papers include Egger and Kreickeeier (2009), Helpan and Itskhoki (2010), Helpan et al. (2010), and Felberayr, et al. (2008). The central essage of our paper is siple. The new heterogeneous fir odels place essentially all of the weight of gains fro trade on the efficiency effects of fir selection. The consequent product arket churning has a counterpart in labor arket churning. If there is uneployent and if, in addition, soe jobs carry epirically relevant rents, then the presence of aggregate gains does not preclude the existence of distributional conflicts between the eployed and the uneployed and between workers with good and bad jobs. In contrast to the first generation odels of intra-industry exchange, in the new odels such distributional conflict is to be expected. 2. Uneployent, efficiency wages, and the fir 2.1. Shapiro Stiglitz with heterogeneous fir level onitoring and iceberg effort costs In considering eployent relations, we follow the efficiency wage odel of Shapiro and Stiglitz (1984), aending this as needed to esh with the fir-based odel of Melitz (2003). In the Shapiro and Stiglitz odel, firs can onitor worker effort only iperfectly. orkers' distaste for effort tepts the to shirk, and they are deterred in equilibriu by the possibility that their shirking will be discovered and they will be fired. Uneployent persists in equilibriu because the wage that firs offer is too high to clear the labor arket. Uneployent is bad news for workers, and truly involuntary, in the sense that eployed workers are ex ante identical to the uneployed yet have higher utility. The arket failure is that workers cannot credibly coit to effort at less than the going wage. Our odel has all these features, with the crucial difference that firs differ in their ability to detect shirking. There is a large literature that tests various aspects of the Shapiro Stiglitz and other efficiency wage odels, but there is no paper that directly tests the prediction that onitoring ability and high wages are substitute eans to elicit effort. There are a nuber of papers, including Groshen and Krueger (1990), Rebitzer (1995), and Nagin et al. (2002) that use exogenous variation in onitoring intensity to confir that effort does indeed increase in onitoring intensity. 2 There is also a literature that docuents industry wage differentials (for exaple, Krueger and Suers (1988)). Such differentials have no direct connection to efficiency wage theory, but they are consistent with labor rents of the sort that obtain in the equilibriu of the Shapiro Stiglitz odel. orkers are infinitely lived, risk neutral, and discount the future at rate r. Subject to an interteporal budget constraint, they axiize: " # E Uw ð t ; e t Þ exp½ rtšdt : ð1þ 0 The real wage for a worker at fir i is w i = i P,where i is the noinal wage at fir i and P is the aggregate price index (developed below). 2 e have also observed a positive relationship between onitoring intensity and hoework effort by resident adolescents. e believe that such an effect is well-known to other parents. Depending on the eployent and effort status of a worker, utility takes the following fors: Uw; ð eþ = w if the worker shirks Uw; ð eþ = w ; e e N 1 if the worker exerts effort: U = 0 if the worker is uneployed Here the cost of effort e is odeled as an iceberg cost that shrinks the perceived real wage of the worker, although of course not shrinking the noinal wage paid by firs and received by workers (both of which treat the aggregate price index P as given). 3 orkers lose their job only if the fir dies or they are caught shirking. Fir death happens at an exogenous rate δ. e assue that no fir onitors effort perfectly. If workers at fir i were to shirk, they would face a hazard i ð0; Šof detection, where reflects the onitoring ability of the fir ost proficient at onitoring. If detected shirking, workers face the penalty of being fired and spending tie in uneployent before finding a new job. orkers at fir i have fundaental asset equations that reflect their status as shirkers or non-shirkers. Let V S Ei and V N Ei be the expected lifetie utility respectively of shirkers and non-shirkers currently eployed at fir i. Let V U be the expected lifetie utility of a worker currently uneployed (noting that this is independent of any fir because uneployed workers are unattached). Then the fundaental asset equations for eployed non-shirkers and shirkers respectively are: rv N Ei = w i e + δ V U V N Ei rv S Ei = w i + ðδ + i ð2þ Þ V U V S Ei : ð3þ These consist of the flow real wage benefits, (w i /e) or w i respectively, plus an expected capital loss in case of a shift to uneployent, where the instantaneous probabilities differ because shirkers face a higher likelihood of a ove to uneployent due to fir i's onitoring i for shirking. This departs fro the conventional Shapiro Stiglitz fraework in allowing for fir specificity in onitoring ability, the wage, and the value of eployent at a particular fir. Fir i recognizes the incentive to shirk. Hence in light of these incentives and its own onitoring ability, it chooses a wage sufficient to induce eployees to work rather than shirk. This requires: V N Ei V S Ei: The fir chooses to eet this non-shirking constraint with equality (so V N Ei =V S Ei =V Ei ). e can solve this for the fir-level equivalent of the Shapiro Stiglitz no-shirking constraint: w i = rv U where ˆ ˆ i = i ðe 1Þðr + δþ i e i ð4þ and ˆ i i N 0: ð5þ Since V U is independent of fir identity, wages will vary across firs only due to onitoring ability and equilibriu wages decline 3 The iceberg cost of effort, U=w/e, departs fro the traditional Shapiro Stiglitz forulation of the cost of effort as U=w e. This responds to the critique by Roer (2006) that the conventional forulation would give rise to a secular trend in uneployent. A consequence is that the aggregate price index P is siply a scale variable in Eq. (1). Moreover, changes in P, for exaple due to trade liberalization, will not directly affect the balance of incentives to work or shirk, since it affects the proportionately (cf. Matusz (1996)). The new forulation also has the iportant consequence for us, developed below, that the ranking of firs by arginal cost is a function only of fir-specific paraeters, hence invariant to the liberalization episodes we consider.

3 28 D.R. Davis, J. Harrigan / Journal of International Econoics 84 (2011) with iproveents in onitoring. Note as well that this is a notional wage. That is, this is the wage required of a fir with onitoring ability i if it is to elicit effort, and is well defined although in equilibriu not all firs will survive. 4 These allow us to have a precise definition of the utility cost of job loss for a worker at fir i: V Ei V U = ð i = i Þ e 1 : ð6þ P e This is always positive, which eans job loss is costly to workers and that uneployent is truly involuntary. Moreover, the utility cost of job loss varies across firs, being high where the wage distortion ( i / i ) is high. e can also return to the fir-specific real wages in Eq. (5) and consider it for any two firs A and B. Taking ratios, we find that: w A = ˆ B = A : w B ˆ A B That is, the fir-specific real and noinal wages are in a constant ratio that depends inversely on the fir-level relative onitoring abilities as well as coon paraeters. ith fir level physical arginal productivities also constant (as developed below), we arrive at the conclusion that relative arginal costs across firs will be constant. That is, firs can be ordered according to their arginal costs even before we have developed other eleents of the equilibriu. Assue that there is soe fir type with the best available onitoring technology, given by 1 = b. e will choose the wage paid at the best onitoring fir as our nuéraire, so that the noinal wage 1 1. Using Eq. (7), this gives rise to a notional noinal wage schedule i = i½ ðe 1Þðr + δþš ½ i ðe 1Þðr + δþš which is greater than one for i ð0; Þ and decreasing in i. Firs pay a wage preiu relative to that of the fir with the best onitoring technology, a preiu that decreases as their onitoring iproves. Although the noinal wage schedule is fixed, real wages of course are free to ove with changes in the aggregate price index P. This noinal wage schedule will play a central role when we turn to the Melitz side of our odel Aggregation The next step is to connect wages to uneployent. For this we need an equilibriu density of the wages paid by active firs f(), to be derived later, and which will be coon knowledge in the econoy. Given this equilibriu density, we can calculate EV ð Ei Þ = e 1 e P 1 E i i or, establishing notation, + V U V E V U = e 1 P 1 ; e where V E EV ð Ei Þ; The average wage distortion follows. ð7þ ð8þ E i : ð9þ i will play a crucial role in what 4 Eq. (5) requires the paraeter restriction: i /(r+δ)n(e 1). The left-hand side is the hazard rate of detection relative to the discounted hazard of losing your job anyway. This ust exceed the utility penalty of effort. As long as workers are patient, exogenous job loss isn't too likely, or effort isn't too costly, this restriction will be satisfied. e are now ready to consider the flow benefits of being uneployed. Since uneployed workers receive no incoe, the flow benefits consist entirely of the expected capital gain fro reeployent. Let b be the instantaneous probability of re-eployent of an uneployed worker. Then the fundaental asset equation for an uneployed worker is: rv U = bv ð E V U Þ: ð10þ e can substitute Eq. (9) into Eq. (10) to get rv U = b! e 1 P 1 : ð11þ e The hazard rate of re-eployent of an uneployed worker, b,can be exained in ters of the steady state, which requires that flows into and out of uneployent be equal. Let L be the total size of the labor force and let U be the total nuber of uneployed. In equilibriu separations happen at rate δ. Then the steady state iposes that: bu = δðl UÞ or, defining the uneployent rate u U/L, b = δ 1 u u Substituting Eq. (12) into Eq. (11) gives rv U = δ 1 u u e 1 e P 1! ð12þ : ð13þ Substituting Eq. (13) into the individual fir's no-shirking constraint (5). efind: i = δðe 1Þ 1 u : ð14þ e ˆ i u This no-shirking constraint is a key link between the acro variables u and (/)*. e now focus on Eq. (14) for the best onitoring fir 1, whose noinal wage serves as nuéraire. Setting 1 =1 and inserting ˆ 1 with 1 =, this iplies: 2 3 A 1 u = where A 1 δðe 1Þ is a constant e ˆ 1+A 1 1 ð15þ so the uneployent rate is strictly between 0 and 1, as required. Eq. (15) is central to the acro side of our odel. Consider this first for a given wage distortion (/)*. Uneployent is then increasing in both the death rate of jobs δ as well as the utility cost of effort e. Each shifts the balance of benefits against effort, the first because expected job tenure declines and the second because the utility derived fro non-shirking eployent declines. e can also look at Eq. (15) for given A 1,sofocusingon(/)*. Fro the Shapiro Stiglitz side of our odel, the average wage distortion ust be coputed across all active jobs. As in Helpan et al. (2010),weabstract fro wage distortions in the fixed costs, here by assuing that onitoring costs in these activities are coon at all firs and for siplicity setting this equal to those of the best onitoring activity, i.e., so the associated wage is unity. Looking inside any single fir, all fixed cost activities have a wage distortion of ð1 = Þ, while arginal cost activities have a wage distortion of ( i / i ). As we show in the next section, in response to trade liberalization there will be two sources of changes in the average wage

4 D.R. Davis, J. Harrigan / Journal of International Econoics 84 (2011) distortion. The first is within the fir, due to the fact that the ix of fixed and arginal activities changes. The second is the redistribution of these activities across firs, as soe expand output to reach new arkets, others contract and serve only the doestic arket, while others exit, in addition to the fact that the steady state ass of entry will adjust. Fro Eq. (9), the capital gain associated with oving out of uneployent rises with the average wage distortion (/)*. In this case, uneployent becoes less daunting and effort will be forthcoing only if there is a higher uneployent rate u, which explains the positive association of these variables in Eq. (15). The developent to this point has assued that workers discount the future at rate rn0. hen we turn to integrating our labor arket odel with the Melitz odel, we will take the liiting case where r 0, to be consistent with his assuption that firs do not discount the future. By inspection of Eqs. (8) and (15), focusing on this liiting case has no iplications for the key results of this section. In suary, we have developed a Shapiro Stiglitz odel with heterogeneity in fir onitoring and iceberg costs of effort. This odel yields two key relations that carry over to the Melitz side of our odel. The first is a schedule of noinal wages relative to that paid by the ost proficient onitoring fir. This pins down fir arginal costs. A second key acro relation is between the no-shirking uneployent rate and the average fir distortion, defined as the eployent-weighted average ratio of the noinal fir wage to its onitoring ability. That ratio eerges endogenously fro the Melitz side of the odel and so deterines the equilibriu uneployent rate. 3. The product arket 3.1. The consuer's proble Preferences over goods are identical and hoothetic. The representative consuer allocates expenditures to: MinE = pðþqi i ðþdi h i 1ρ s:t: qðþ i ρ di = V: e also have 0 b ρ b 1; and σ = 1 1 ρ. These deliver deand curves for product i of the for: qi ðþ= pi ðþ σ Q P where Q V and P is an aggregate price index given by h i P = pðþ i 1 σ 1 1 σ di : ð16þ The associated revenues for the producer of an individual variety fro this consuer are: ri ðþ= RP σ 1 pi ðþ 1 σ : ð17þ These revenues depend both on aggregate values, RP σ 1, as well as the fir choice of p(i) The producer's proble Firs face a sequence of probles. There is an unbounded ass of potential firs. In the first stage, a ass M e of firs will enter, pay a fixed entry cost of f e, and receive inforation about their type. Here a fir's type is represented by the pair (φ i, i ) covering both productivity and onitoring ability in variable costs. e saw above in Eq. (8) that there is a siple relation between equilibriu no-shirking wages and onitoring. This eans that the fir can iediately translate the productivity-onitoring draw (φ i, i ) to a productivitynoinal-wage draw (φ i, i ). In Melitz (2003), it is productivity φ that deterines fir perforance. e show below that the deterinant of perforance in our odel is productivity adjusted for the firspecific wage, which we denote as z i =φ i / i. Here z i can be thought of equivalently as the inverse arginal cost for fir i. e consider now the proble of an individual fir that has already sunk the cost f e to learn its inverse arginal cost z i. Having learned its z i, fir i will produce if its variable profits cover its per period fixed costs f; otherwise it will exit before producing. Physical labor requireents in fir z i follow Melitz: lz ð i ; φ i Þ = f + qz ð iþ : ð18þ φ i Note that fir level physical labor deand requires knowledge of φ i (not only z i ), so ust be recovered to establish labor arket equilibriu once the structure of the econoy (including the wage bill for a fir of type z i ) is deterined. Costs also depend on the wages paid to workers in fixed cost activities. Our focus on the Melitz approach requires that the only locus of fir level variation is in arginal costs. Hence we assue that the fir pays a wage f 1 for labor eployed in any of its fixed costs and a wage i for labor eployed in its variable costs. 5 For given acro variables, a particular fir i thus faces a deand curve as defined in the consuer's proble above and chooses output to axiize profits, q π i = p i q i i i f = p φ i q i q i f = r iðz i Þ f : ð19þ i z i σ The first order conditions yield the failiar price as a arkup on arginal cost: pz ð i Þ = i = 1 : ρφ i ρz i Prices and axiized profits vary across firs only because of variation in z i.thatis,firs with a coon inverse arginal cost z ay be paying different noinal wages, and eploying different aounts of labor, but they charge the sae price, will produce the sae quantity, and have the sae revenue, wage bill, and profits. Hence we will drop the subscript i henceforth except as necessary to clarify liits of integration or when it is necessary to specify physical labor deand The arginal fir and equilibriu structure of the econoy The cobination of a priitive distribution on (φ, ) and the equilibriu noinal wage fro the labor arket in Eq. (8) allows us to derive the joint distribution for (φ, ). Knowledge of this joint distribution allows us as well to calculate the distribution of inverse arginal costs z with cuulative distribution function GðÞ Pr z ½Z zš and density g(z). The full equilibriu will feature a cutoff level of inverse arginal cost, z*, such that firs with zbz* exit iediately upon learning of their draw. Given g(z), we can also define the equilibriu density of active firs: μðþ= z gz ðþ 1 Gðz Þ ; z z ; : 5 This asyetry between wages paid in fixed and arginal costs is for analytical convenience only, and is directly analogous to Melitz's assuption that firs differ only in their arginal and not their fixed costs. An alternative odeling choice would be to specify a second, constant returns sector, and have fixed costs paid in units of that sector, as for exaple in Helpan, Itskhoki and Redding (2010).

5 30 D.R. Davis, J. Harrigan / Journal of International Econoics 84 (2011) Equilibriu structure in an autarkic Melitz econoy is deterined by the solution of two relations between average profits π and the wage-adjusted productivity of the arginal entrant z*. The first of these two relations is a free entry condition (FE), which asserts that fro an unbounded set of ex ante identical firs, a sufficient ass enters so that the average profits fro entry equal the fixed cost of entry. The FE condition is essentially identical to that of Melitz: πðz Þ = δf e 1 Gðz Þ ðzcpþ: ðfeþ The second key relation is the Zero Cutoff Productivity (ZCP), which defines the arginal active fir: πðz Þ = rz ð Þ f =0: ðzcpþ σ As in Melitz, the intersection of the FE and the ZCP curves deterines the equilibriu arginal entrant z*. The equilibriu exists and is unique under the sae conditions. 4. General equilibriu The equilibriu z* copletely deterines the structure of the econoy, including output, revenue, eployent, and profit for each fir. e now need to go on to recover the average wage distortion, deterine the associated uneployent rate consistent with noshirking, and thus deterine the ass of firs that provides for equilibriu in the labor arket Uneployent and labor arket equilibriu e showed in Eq. (15) that the uneployent rate is an increasing function of the average wage distortion. In coputing the average wage distortion, we account for the fact that workers in fixed cost activities are paid a wage of 1, while workers in variable cost activities are paid a wage given by Eq. (8).EployentinactivefirsisgivenbyEq. (18). Letψ(i z*) denote the density of active firs, where i=(φ, ) identifies a fir type. This density depends on the priitive joint density of (φ, )aswellasthecutoff z* deterined in the previous section. The eployent-weighted average wage distortion in the econoy per unit ass of active firsisthen = δ 1 Gðz Þ f e + f + qi ðþ i ðþ φðþ i i ðþ ψ ijz di: ð20þ Plugging Eq. (20) into Eq. (15) delivers the equilibriu uneployent rate. ith the uneployent rate deterined, the equilibriu ass of firs M is deterined by setting eployed labor equal to labor deand, δ ð1 uþl = M 1 Gðz Þ f e + f + qi ðþ φðþ i ψ ijz di : ð21þ The ass of active firs plus their prices allows us to establish the aggregate price index P as in Melitz. Aggregate incoe equals total wages and likewise equals total spending. 6 This copletes the specification of our odel. 6 Unlike in Melitz, noinal national incoe is not siply equal to the size of the labor force Trade and selection effects In this section, we describe eleents of the trading equilibriu that will be relevant for the discussions in subsequent sections. As before, key eleents of equilibriu will be deterined by the intersection of two curves. The first is the free entry curve, which is defined so that ex ante profits are zero, hence ties each potential cutoff z with an expected profit level π. This curve is entirely unchanged in a ove fro autarky to costly trade. The second is the Zero Cutoff Productivity (ZCP) curve which lies above the autarky ZCP curve for the sae reasons as in Melitz. This iplies that the equilibriu cutoff z* ust rise. That is, our odel will feature the sae kind of selection effects as in Melitz and for exactly the sae reason i.e. the new opportunities available to exporters and the new pressures fro iport copetition. Given z*, the cutoff for exporting z x is also found as in Melitz. ith these cutoffs, we can calculate the new (/)*, hence also deterine the uneployent rate. ith these in hand, we can return to recover all other variables in the trading equilibriu Monitoring, productivity, and the size-wage correlation Unlike Melitz (2003), our odel features two diensions of rando heterogeneity across firs, productivity φ and onitoring ability, and so far we have ade no assuptions about the ex ante correlation between the. Heterogeneity in delivers heterogeneity in wages through Eq. (8), which deterines each fir's inverse arginal cost z=φ/. Fir size (easured by sales) in our odel is a onotonic function of z, which iplies that for a given φ that highwage firs will be saller. This is at variance with the data, which instead shows a positive correlation between wages and fir size (see Brown and Medoff (1989), Idson and Oi (1999) and Manning (2003), aong others). Since the size-wage correlation is an iportant epirical aspect of fir heterogeneity, here we provide soe discussion of how it fits into our fraework. In our odel, even if the ex ante correlation between φ and is zero, the Melitz-style selection effects will tend to induce an ex post positive correlation between φ and. This is because copetition will force the exit of high arginal cost firs, i.e. those with high but low φ. Thus a positive size-wage correlation is possible in our odel even with no ex ante correlation between φ and. However, in our nuerical siulations below it turns out that a sall negative ex ante correlation between productivity and onitoring ability is needed to get the siulated size-wage correlation to atch the epirical evidence. Thus while we do not odel the deterinants of onitoring at the fir level, it is worth looking ore closely at the issue. Mehta (1998) provides an account of the size-wage distribution that, while not developed in the context of the Melitz odel, nonetheless eshes quite naturally with it. Mehta ephasizes the crucial role of hierarchy in production, so he distinguishes anagers fro workers. Managers have two tasks. One is to onitor the effort of workers and the other is to engage in coordination of workers in ways that raise productivity. Large firs pair anagers with increasing nubers of workers. This increased span of control for the anager leads the anager to substitute higher wages for onitoring as a way to elicit effort. hile odeling of this trade-off is beyond the scope of our paper, we can easily think of the anager in the Melitz context as the residual claiant to profits at the fir. Thus, in reduced for, the approach of Mehta is captured in the assuption in soe of the nuerical exercises below that onitoring efficiency is inversely related to productivity. Helpan et al. (2010) also provide a odel of heterogeneous firs that in equilibriu has a positive fir size-wage correlation. hile their labor arket echanis is quite different fro ours, the otivation of their production structure that gives rise to the fir size-wage correlation is quite siilar to Mehta's and ours: anagerial tie is a fixed factor, so anagers supervise each worker less intensively in larger organizations.

6 D.R. Davis, J. Harrigan / Journal of International Econoics 84 (2011) Trade liberalization This section will consider the consequences for firs and workers of trade liberalization in our odel. e divide our discussion of a ove fro autarky to freer trade into two pieces. The first will consider the case of a liberalization that affects the structure of the econoy, i.e. the equilibriu arginal cost cutoff, but not its scale, i.e. the average wage distortion, (/)*, which deterines the equilibriu uneployent rate. Depending on the priitive distribution of productivity and onitoring (φ, ), our odel is consistent with either a rise or fall in this average wage distortion with liberalization. As a base case, we begin by assuing that liberalization has no ipact on this average wage distortion. This iplies that the structure of the econoy will change, but not its scale. Once the analysis of a change in structure is coplete, we go on to consider how we would need to aend the conclusions of that analysis once we allow for changes in scale as well. Theanalysisinthissection,inforalters,iscoparativesteady state analysis. A coplete analysis of the tie path of adjustent would be required to ake definitive stateents about welfare and political econoy. That is beyond the scope of this paper. Nonetheless, the basic nature of the adjustents required along the path to the new steady state does eerge fro our odel. e believe that this provides a powerful heuristic for understanding the forces at work in identifying winners and losers, hence also in understanding the political econoy of liberalization Changes in structure only e consider here the special case in which our econoies ove fro autarky to freer trade, but in which the average wage distortion, hence also aggregate eployent, is unchanged. This iplies that the analysis of the structure of firs' price and output decisions in the product arket, as well as profit, entry and exit, will be precisely as in Melitz, so long as we use our own easure of inverse arginal cost, given by z. Here, though, workers have attachents to specific firs because of rents created by differences at the fir level in wages. e can use Fig. 1 to think about the coparison of autarky and freer trade as it affects profits of firs and eployent of workers. The lowest feasible wage is that associated with the best onitoring fir and equals one by choice of nuéraire. A ray fro the origin is also a 1 0 i I * c a Exit II * c Contract III c x Export IV Profit c π Fig. 1. Autarky to freer trade. The ove fro autarky to free trade changes the arginal firs fro those with arginal costs c a *toc*. This leads to exit of the high arginal cost firs in Region I; contraction of the next highest arginal cost firs in Region II; and expansion of low arginal cost firs in Regions III and IV as they enter new export arkets. Profits drop to zero in Region I firs and decline for firs in Regions II and III. The RegionIII firs experiencetheprofit decline inspite oftheirsuccess inexporting the loss of local arket share and the fixed costs of exporting are not copensated by the new profits in the foreign arket. Only the super-exporting firs in Region IV experience higher profits. Job loss occurs wherever output contracts, naely in Regions I and II. ϕ i constant arginal cost curve. The ray labeled c a * indicates the highest level of arginal cost consistent with zero post-entry profits in autarky, and thus defines the cutoff for active firs. Firs with lower arginal costs are to the southeast of the c a *ray,andfir size is onotonically decreasing in arginal cost. The ipact of the shift in coparative steady states fro autarky to trade gives rise to three additional critical values in inverse arginal costs. The first is c*, the arginal entrant under freer trade. Next is c x, the arginal exporter. Finally is c π, the highest arginal cost for which a fir sees its profits rise with freer trade. Accordingly, these boundaries define Regions I to IV in the figure. The ipact of trade on firs' profits and output is straightforward. All firs in Region I exit with trade, so their profits and output fall to zero. Firs in Regions II and III also see a decline in profits. For firs in Region II, the entry of foreign firs into their hoe arket reduces their doestic deand and profits, yet leaves the incapable of finding a sufficient foreign arket to justify the fixed costs of exporting. Output for these firs declines. It is notable that firs in Region III suffer a decline in profits in spite of the fact that they not only survive in the doestic arket but also find a foreign arket for their products; the losses in the hoe arket are not fully copensated by the new profits in the export arket. Total output for these firs expands and so the decline in profits is attached to the fixed cost of entering the export arket. Only the largest firs, those in Region IV, find that their profits rise with trade. Notably, firs can find their way into Region IV either by their inherent productivity or by effective onitoring of workers, which allows the to elicit effort at low wages. The analysis of the ipact on workers is only slightly ore coplex. e have set aside until the next subsection any ipact of trade on the average wage distortion and equilibriu uneployent. The noinal wage of a worker who aintains eployent at a specific fir is deterined by the fir specific onitoring technology and paraeters of the odel, so is unaffected by trade liberalization. This leaves only two channels for trade to affect workers. The first, as in Melitz, is that liberalization lowers the typical price and ay raise total variety of products available to workers qua consuers. This benefits all workers and should be considered as a potential offset to losses incurred by soe workers. The second channel for trade to affect workers here is via changes in eployent, which is ost directly related to the fate of firs in the output arket. e have already seen that firs in Region I exit the arket, hence all workers at these firs lose their jobs. Firs in Region II contract their output, hence workers at these firs ay be seen as facing a probability of job loss related to the degree of contraction. Firs in Regions III and IV expand eployent sufficiently in the new steady state to provide precisely the sae nuber of new jobs as those lost via firings aong firs in Regions I and II. orkers at firs in Regions III and IV should expect to be unabiguously better off with the ove fro autarky to freer trade. The firs there are expanding output, so should have no unusual layoffs. They also enjoy gains fro lower average prices and possibly increased variety. The situation is ore intricate for workers initially with firs in Regions I and II. As noted, on one side are the coon price index gains fro liberalization. On the other side is the certainty (Region I) or probability (Region II) of job loss. In the odel workers ust pass through a period of uneployent before finding new eployent. Since workers always prefer to be eployed rather than uneployed, this is a cost. The agnitude of the cost of a job loss is higher the higher the initial wage. hile we don't have an explicit odel of the transition between steady states, trade liberalization creates a great deal of turnover while costing zero net jobs. This should be good news for those currently uneployed, who are happy to accept any job on offer and suddenly find a lot of hiring going on, even though the transition would require ore people to pass through uneployent. This analysis also provides a window on the debate over whether trade liberalization threatens good jobs. A precise way to state the

7 32 D.R. Davis, J. Harrigan / Journal of International Econoics 84 (2011) consequences for jobs here is that liberalization destroys jobs with high arginal costs of production. Soeties these are low wage jobs with very low productivity; soeties they are high wage jobs with productivity that ay be high but is not quite high enough to secure the jobs. However, there is another fro a worker's perspective, quite natural way to interpret the consequences of the shocks. This is to hold fixed the type of fir, indexed by its productivity φ, and copare what happens to different types of jobs at coparable firs defined in this way. Fig. 2 provides a siple window on this way of looking at the world. To the previous diagra, Fig. 2 adds the average wage in autarky, a,anda specific productivity level φ 0, which for illustrative purposes was chosen to intersect the average wage line at the boundary of Regions II and III. Perhaps the siplest definition of a good job in autarky is one that pays a wage above the average, i.e. a N a. Holding productivity fixed at φ 0,we see that trade threatens all and only good jobs. Controlling for fir productivity φ 0, the highest paying jobs are those in Region I all of which are lost in the opening to trade. The next highest paying jobs are those in Region II soe but not all of which will be lost to trade. Controlling for productivity, only the lowest paying jobs survive the opening to trade. Indeed, trade leads to an expansion of these jobs and ost sharply aong the lowest paying of these (those along φ 0 in Region IV). e see that the public perception that trade destroys good jobs at good wages does have foundation in the context of this odel. Soe workers who in autarky would enjoy high wages will find that a ove to freer trade eliinates their jobs. Indeed, if we condition on productivity, trade always destroys the best jobs. Having acknowledged this, it is also crucial to understand the liits of this way of thinking. Yes, trade will eliinate soe of what workers perceive as good jobs, and conditioning on productivity, trade always destroys the best jobs. Yet this is perfectly consistent with the possibility that trade will siultaneously expand the nuber of high wage jobs sufficiently that the average wage will rise. Indeed, we will argue below why we think this is the noral case. The net gain for specificworkersand for workers as a whole will then need to account for changes in prices and variety, which will typically be additional sources of gain, as well as for changes in aggregate uneployent. Moreover, in this odel, all incoe Good Jobs Bad Jobs i 0 a 1 Contract Export Profit Fig. 2. A conditional threat to good jobs at good wages. A good job ay be defined as one that pays ore than the average wage in autarky. For illustrative purposes, consider a productivity level φ 0 that corresponds to the point at which the average autarky wage curve crosses the boundary between Regions II and III. Conditional on productivity level φ 0, the highest wages on offer are at jobs in Region I firs; all of these good jobs are destroyed in the ove fro autarky to free trade. The next highest wages are on offer at jobs in Region II firs; soe of these jobs are lost as output contracts. The Region III jobs expand, but these are bad jobs. The sharpest expansion of jobs occurs at the Region IV firs offering the worst jobs. These Region IV firs offering the worst jobs are also the only ones who increase profits in the ove fro autarky to free trade. Conditional on this productivity level, trade destroys only good jobs and expands only bad jobs. ϕ 0 I Exit II III IV ϕ i accrues to labor. Good jobs are naturally very attractive to those who have the; however, the associated inefficiencies cost labor as a whole Changes in structure and scale In the previous section, we abstracted fro the possibility that liberalization ay affect the average wage distortion, hence uneployent, so we turn to this now. The fir level wage distortion, ( i / i ), is a constant, and so unaffected by liberalization. The average wage distortion across all firs is affected by the redistribution of output (including exit) across fir types that ay have different levels of distortions. At any arginal cost, indexed by z, there exist firs with different wage distortions. hile we can ake specific predictions about which firs will exit according to the ordering by z, it is not possible to say whether the average wage distortion will rise or fall with liberalization without knowledge of the full joint distribution of (ϕ, ). 7 In short, (/)* is a function of z*,butitneednotbeonotonic The average wage distortion, acro effects, and the new steady state The acro iplications of changes in the average wage distortion coe directly fro our heterogeneous fir odel of efficiency wages: a rise in the average wage distortion raises equilibriu uneployent. Fro Eq. (15), we recall that u = A 1 = 1+A 1.As " # discussed in Section 2.2., a rise in the average wage distortion, through fir selection effects, raises the expected capital gain fro oving between uneployent and eployent, so akes uneployent less daunting, requiring a rise in the structural uneployent rate to aintain the balance of incentives to elicit effort. This rise in uneployent relative to the case of no change in the average wage distortion changes the scale of the econoy, but not its structure. Because of the general second best nature of the econoy, we cannot rule out that with a sufficient rise in the uneployent rate, total real incoe ay decline with liberalization, although we would consider this an unusual case. Siilarly, even as the average price of products declines, there can be a rise in the econoy's price index because the rise in uneployent causes a decline in the total ass of varieties available in the arket. The fact that the possibility of absolute losses ight arise in a odel with factor arket distortions would not be surprising, although such an outcoe in the world sees unlikely. The rise in uneployent anticipated with the ove fro autarky to freer trade reduces the steady state ass of firs of each type relative to the previous case in which eployent was unchanged. In principle, asufficiently sharp rise in the average wage distortion, accopanied with a sharp rise in the required uneployent rate, could lead to a reduction of the presence even of the ost productive export fir types in the new steady state and a loss in total eployent there. 8 7 Unfortunately even knowledge of oveents in the average noinal wage would not suffice to deterine the qualitative change in the average wage distortion, as they need not be onotonically related. 8 hile the present paper develops only coparative steady states, it would be interesting to study transition dynaics for the case in which the rise in the average wage distortion, hence also the uneployent rate, in the new steady state requires a saller ass even of the highly productive fir types. e conjecture that in this case the transition will feature overshooting of both the average wage and the uneployent rate along the path to the new steady state. The logic is siple. Apart fro exogenous fir deaths, fir exits only arise when expected present discounted profits are negative. But fir profits are onotonically decreasing in arginal costs. Hence if the crowding of the arket by the excess prevalence of low arginal cost firs during the transition relative to the steady state leads to exit, this exit will be aong the highest arginal cost (sall) firs. But if indeed these sall firs are on average also the low wage distortion firs, then this change in coposition will lead the average wage distortion to be higher in the transition than in the steady state. All else equal, the rise in the average wage distortion also requires a higher uneployent rate to insure effort, since the no-shirking constraints have to hold at all ties. Our conjecture, then, is that both the average wage distortion and uneployent will overshoot inthetransition to thenew steady state. Confiring this conjecture is beyondthe scope of the present paper.

8 D.R. Davis, J. Harrigan / Journal of International Econoics 84 (2011) Political econoy The ain thrust of the political econoy for coparative steady states fro the view of firs can be understood through exaination of Fig. 1. As before, the ove fro autarky to freer trade divides the space into four key regions in ters of arginal costs. All firs with cnc π, i.e. those in Regions I, II, and III, lose profits as a result of the ove of coparative steady states fro autarky to freer trade. Only the largest firs, those with cbc π gain. Hence a ove fro autarky to freer trade should be supported only by the largest firs. Turning to workers, we start with several general observations. Trade always serves to lower the typical price and ay raise the total (local and iported) nuber of varieties available in the arket to consuers. Hence typically the price index will fall in the ove fro autarky to freer trade, which is a gain to all workers. Selection effects fro liberalization ay also alter the distribution of types of jobs in the econoy. e have to treat distinctly three separate concepts, naely the average wage distortion, (/)*, the average noinal wage, *, and the general equilibriu ipact on the average real incoe of workers. As we have noted, the uneployent rate is linked directly to the average wage distortion. e have seen at the fir level that a good job, i.e. one that pays a high wage (relatively) is one where this distortion is high. Yet when the average rises, uneployent rises, which is costly directly due to lost output and also due to associated loss of variety. hile the average noinal wage in the econoy sees likely to be positively associated with the average wage distortion, close exaination reveals that this connection is not a necessary one. Still, we ay expect that (/)* and * ay typically ove together, which would in such cases suggest a tradeoff between high uneployent and high average wages in the typical job. It is worth keeping in ind, though, that good jobs coe at a price. Here all incoe accrues to workers, so that average real incoe to workers is axiized exactly when total real incoe is axiized. The distortions that give rise to good jobs here lower aggregate real incoe and so also lower the average real incoe of workers. There are also iportant distributional effects job loss will fall particularly heavily on soe. Since firs in Region I exit and those in Region II contract output, all workers in Region I firs lose their jobs and soe in Region II firs lose their jobs as well. It is interesting to observe that although firs in Region III lose profits with the liberalization, workers there do not lose jobs, and so should have no reason to oppose liberalization on this basis. 6. Nuerical analysis Our odel offers a rich set of predictions for how labor arkets adjust to trade liberalization. In this section we siulate the odel, using a calibration approach that identifies key paraeters fro the data and fro previous estiates. The siulations establish the agnitude of effects identified in the odel. 9 Previewing our nuerical results, trade liberalization leads to little change in the uneployent rate, a rise in aggregate real incoe, and treendous churning in the labor arket, with the gross loss of as any as one-fourth of good jobs. The nuerical version of our odel requires specification of the ex ante joint distribution of productivity and wages, as well as values for the other odel paraeters such as fixed and variable trade costs, fixed and sunk entry costs, and the elasticity of substitution. The following sections explain our choices for these paraeters in detail The wage distribution In specifying the distribution of productivity and wages, we are guided by the large epirical literature on the fir size and wage 9 All calculations were perfored in Matheatica, and the progras are available on request. distributions. This literature alost invariably odels wages as log noral, and the fir size distribution as Pareto, so we do the sae. A key paraeter in our odel is the dispersion of wage rents. As discussed in our Introduction, Krueger and Suers (1988), aong others, argued that large easured industry wage differentials were evidence of labor rents, while Murphy and Topel (1987) and others argued that unobserved heterogeneity in workers' arginal products was responsible for industry wage differentials. A siilar dispute arises in interpreting the well-docuented correlation between fir size and wages (e.g. Brown and Medoff (1989), Idson and Oi (1999), Manning (2003, Chapter 4)). To resolve this dispute requires inforation on worker and fir characteristics, as well as enough job switchers to be able to reliably identify what coponent of a worker's wage is due to her inherent productivity and what coponent is due to the fir where she works. Abowd et al. (1999) assebled data (a panel of French workers and firs fro 1976 to 1987) that can answer this question. Their conclusion is that the person effect is uch ore iportant than the fir effect : Virtually all of the inter-industry wage differential is explained by the variation in average individual heterogeneity across sectors. Person effects, and not fir effects, for the basis for ost of the inter-industrial salary structure. (Abowd et al., 1999, pg. 253) hile this result can reasonably be interpreted as vindication for the view that labor rents are saller than Krueger and Suers ay have thought, virtually all does not ean all. In their Table IV, iddle panel, Abowd et al. report their estiate of the standard deviation of the fir effect on log French wages as In our odel the fir effect corresponds to wage variation due to variation in onitoring ability across firs, so we paraeterize the arginal distribution of wages F w (w) as being log noral with a standard deviation of The productivity distribution and elasticity of substitution Following any authors, we odel the ex ante arginal distribution of unit labor requireents a (where a=φ 1 ) as a Pareto distribution with shape paraeter κ and upper bound α. The Melitz (2003) odel can be solved analytically with this distribution (Baldwin 2005), a set of results that we will refer to here as the Pareto Melitz odel. Although our odel has no analytic solution, the Pareto Melitz odel proves very useful in guiding our choices for five paraeters: the Pareto shape paraeter κ, the elasticity of substitution σ, the sunk cost of entry f e, the fixed cost of production f, and the fixed cost of exporting f x. Solution of the Pareto Melitz odel requires that κnσ 1N0. In choosing κ and σ to satisfy these restrictions, we follow two strategies. The first relies on the literature on the fir size distribution, which generally finds values for κ that are not uch bigger than one. For exaple, Corcos et al. (2009) estiate that κ ranges between 1.8 and 2.5 across industries and European countries in 2000, with the larger industries having values close to Taking this value for κ constrains us to a very low value of σ=2, despite the fact that ost estiates of σ exceed 2 (for exaple, Harrigan (1993) estiates σ to be between 5 and 12, while Broda and einstein (2006) find edian values of σ greater than 2). Our second approach to choosing κ and σ follows Ghironi and Melitz (2005). They use the analysis of 1992 U.S. plant level data by Bernard et al. (2003) to calibrate their version of the Pareto Melitz 10 e are referring here to Abowd et al.'s paraeter ψ. The estiate is for en, for woen. The saple standard deviations of log wages are and for en and woen respectively, so the ratios of the standard deviation of the fir effect to the standard deviation of log wage are 0.13 and 0.12 for en and woen respectively. 11 These nubers coe fro Table 7 in Corcos et al. (2009).

9 34 D.R. Davis, J. Harrigan / Journal of International Econoics 84 (2011) odel, which iplies κ=3.4, σ=3.8 (see Ghironi and Melitz (2005) for details). This choice of paraeters allows for a ore realistic choice of σ, although κ=3.4 is substantially higher than what is found by Corcos et al. Thus there is an uncofortable tension between the atheatical requireents of the odel and the epirical evidence, regardless of the choice of κ and σ. e report results using both cases below. The Pareto upper bound paraeter α is a noralization, set to 10 for nuerical reasons Variable and fixed trade costs Our easures of variable trade costs coe fro the influential survey by Anderson and van incoop (2004). Using U.S. and other data sources, the authors report that ad valore equivalent trade costs are about 74%, which reflects the cobined influence of border costs of 44% and transport costs (including the tie cost of goods in transit) of 21%. Thus in our siulations, we take τ=1.74 as our easure of variable trade costs in the ove fro autarky to trade. e also report siulations that set all border barriers to zero, which iplies τ=1.21. The difference between τ=1.74 and τ=1.21 is thus a easure of the effect of the reoval of all border barriers. Turning to the choice of fixed costs, in the Pareto Melitz odel the entry and export choices depend respectively on the fixed cost ratios f/f e and f x /f. To calibrate f x /f, we use the result that the share of exporting plants is τ κ ½f x =f Š1 σ. κ This share was 0.21 for U.S. plants in 1992, and the corresponding share for French firs in 2000 was 0.22 (see Bernard et al. and Corcos et al. respectively for these nubers). Setting τ=1.74, we back out f x /f to atch The Pareto Melitz odel also delivers an expression for the share of firs that enter once they have paid the sunk cost f e, and this share depends on f/f e. However, there is no epirical counterpart to firs that do not enter, so there is no oent which we can use to back out an estiate of f/f e. e rather uncofortably choose f/f e =0.2, which guarantees an interior solution given all of our other paraeter values. Fortunately, wide variation in the choice of f/f e has alost no effect on our results Paraeters of the efficiency wage odel ith wages given by draws fro the distribution F w (w), the associated values of onitoring costs are given by inverting Eq. (8). To guide our choice of the reaining paraeters of the efficiency wage odel, we work with Eq. (15), which gives the equilibriu uneployent rate. Along with the average distortion, the deterinants of the equilibriu uneployent rate are the exogenous fir death rate δ, the utility cost of effort e, and the upper bound on onitoring efficiency. Following Bernard et al. and Corcos et al., we set δ=0.1 to atch the annual hazard rate for U.S. plant exit. e choose e and together so that the equilibriu uneployent rate is reasonable for an OECD country, which leads us to e= and = Joint distribution of wages and productivity ith the arginal distributions for wages and productivity fixed by the considerations described above, it reains to odel the joint distribution. e do so using the Ali Mikhail Haq copula, which specifies the joint cdf of wages w and unit labor requireents a as a function of the arginal cdfs and a paraeter θ, a sall ex ante correlation between productivity and wages of 0.144, and an ex post positive correlation between fir size and wages in equilibriu which is in line with the evidence discussed in section 6.1 above. For ore on copulas and sapling fro the above joint cdf, see Nelsen (2006). e also siulate our odel for a zero ex ante correlation between wages and productivity, θ= Nuerical results Table 1 provides the results of our nuerical siulations. Each colun copares autarky to restricted trade, covering both high (τ=1.74) and low (τ=1.21) trade cost cases. The top panel has σ=κ=2, and the botto top panel has σ=3.8, κ=3.4. Focusing on the first colun of nubers, the oveent fro autarky to current levels of trade costs (τ=1.74) raises real GDP by 12%, an effect which cobines an 18% iproveent in aggregate productivity with a decline in variety of 6%. The nuber of active firs is only 78% of the autarky level, an illustration of the powerful survival of the fittest echanis in the Melitz odel. Turning to the eleents that are new to our odel, the uneployent rate of 7% doesn't budge when the econoy opens up. orkers who aintain their old jobs see their real wages increase by 11% due to the fall in the price level, but any workers do lose their jobs: 15% of good jobs (jobs with above average wages in autarky) are lost, while 19% of bad jobs are eliinated. Thus while the average worker is uch better off than under autarky, there is a substantial reallocation of job rents. The effects of further reductions in trade costs are even larger: real GDP is 24% higher than under autarky, but ore than a fifth of autarky good jobs are eliinated. Our baseline paraeterization includes a sall ex ante correlation of between wages and productivity, which leads to a size-wage correlation of 0.05 with current levels of trade costs, in line with the evidence reported in Manning (2003) discussed above. 12 e odify this assuption in the second two coluns of Panel A, and with the exception of the size wage correlation which is now very sall and negative, our results about the aggregate and distributional effects of trade liberalization are virtually unchanged. The only notable difference is that job losses are now a bit ore heavily concentrated in good jobs, since these high-wage jobs are less likely to be at highly productive firs than in the baseline paraeterization. Thesecondpanelofthetabletellsuch the sae story, except that all the effects of liberalization are quite a bit saller. For exaple, in the ove fro autarky to current levels of trade costs, only 5% of good jobs are lost as opposed to 15% in our baseline. Uneployent in this panel is 10 or 11%,whichissoewhathighbyU.S.standardsbutveryuchinlinewith levels in France and elsewhere in Europe (recall that any of our paraeters are drawn fro French and other European data). The intuition for why larger values of σ and κ lead to saller effects of liberalization is that firs have both less arket power (larger σ) and a ore skewed productivity distribution (larger κ) than when σ and κ are sall, so that there are fewer sall, inefficient firs in autarky. Thus the selection effects of trade liberalization that are at the heart of the Melitz odel are less powerful. Fig. 3 illustrates the eployent effects of liberalization in our siulation. For the purpose of understanding Fig. 3 it is useful to think of each dot as representing an active fir in autarky, although strictly speaking the dots are draws fro a continuous joint distribution. 13 The firs that expand eployent are exporters, and the dispersion Fw; ð aþ = F w ðwþf a ðaþ 1 θð1 F w ðwþþð1 F a ðaþþ ; θ 1; ½ 1Þ: The degree of association between w and a is governed by θ, with independence corresponding to θ=0. e set θ= 0.9, which iplies 12 e refer here to Manning's Table 4.2, pg. 87, which reports that the estiated elasticity of wages with respect to eployer size is anywhere between and An estiate of 0.04 sees to be preferred. 13 For aesthetic reasons, Fig. 3 is constructed by drawing 5000 ties fro F(w,a), rather than the ore nuerically accurate saple of 20,000 draws used to construct Table 1. Paraeters are those used in the first colun in Table 1.

10 D.R. Davis, J. Harrigan / Journal of International Econoics 84 (2011) Table 1 Siulations of the odel for high and low trade costs. Panel A: σ=2, κ=2 High trade costs Low trade costs High trade costs Low trade costs Ex ante ρ(productivity,wage)n 0 Ex ante ρ(productivity,wage) =0 Trade relative to autarky values Real GDP Productivity Active local firs Price index Uneployent rate Levels Share of exporters Autarky uneploy Trade uneployent Autarky ρ(size,age) Trade ρ(size,age) Share of jobs lost in ove to trade Good jobs Bad jobs Panel B: σ=3.8, κ=3.4 High trade costs Low trade costs High trade costs Low trade costs Ex ante ρ(productivity,wage) N 0 Ex ante ρ(productivity,wage)=0 Trade relative to autarky values Real GDP Productivity Active local firs Price index Uneployent rate Levels Share of exporters Autarky uneploy Trade uneployent Autarky ρ(size,age) Trade ρ(size,age) Share of jobs lost in ove to trade Good jobs Bad jobs The high and low trade costs respectively are τ=1.74 and τ=1.21. The notation ρ(.,.) indicates the correlation coefficient. The ex ante correlation between productivity and the wage is in coluns 1 and 2 (the two cases correspond to θ= 0.9 and θ=0 respectively). All other paraeters identical across cases, with the exception of the export fixed cost f X, which is chosen to generate a share of exporters =0.215 when τ=1.74 (resulting in f X =1.24 in Panel A and f X =0.75 in Panel B). Siulation coputed using 20,000 draws fro ex ante joint distribution of wages and productivity. Coon paraeter values are Ex ante standard deviation of σ 0.06 log wages Scale paraeter on Pareto α 10 distribution Utility cost of effort e Upper bound onitoring 2000 hazard rate Exogenous fir death hazard δ 0.1 rate Fixed entry cost f e 5 Fixed production cost f 1 of this cloud reflects the long, thin upper tail of the Pareto productivity distribution. The cluster of firs just to the left of the vertical axis are firs that survive the opening to trade but do not export: instead, they shed workers in the face of iport copetition. Finally, the cluster of firs to the far left shut down and layoff their labor force when trade opens up. The key essage illustrated by the figure is that workers with the sae wages can suffer very dissiilar fates: their fir can shut down, contract, or expand (possibly a lot) when the econoy opens to trade. A related essage is that aong the three categories of firs (those that exit, iport copeting, and exporters) there is great heterogeneity in wages. 7. Conclusions How do labor arkets adjust to trade liberalization? The experience of ajor trade liberalizations underscores the iportance of intra-industry reallocations. First generation odels of intra-industry liberalization, based on Krugan (1981), ephasize that such integration will be sooth: no fir goes out of business, no worker loses a job, and welfare rises for everyone as the price index falls owing to variety gains. In such a world, liberalization should coand universal approval. Of course, trade liberalization in reality reains highly controversial, with overwheling ajorities in the United States saying that it costs jobs and lowers wages.

11 36 D.R. Davis, J. Harrigan / Journal of International Econoics 84 (2011) wages vs. change in eployent wage eployent Fig. 3. Each dot represents a fir active in autarky, its' wage, and the eployent response when trade costs fall fro τ= to τ=1.74 for σ =κ=2,θ= 0.09 (the case corresponding to the first colun of Panel A in Table 1). The set of points to the far left are firs that shut down when trade opens up, the set of firs just left of the vertical axis are firs that survive but do not export, while the dots to the right represent exporters. The scale on the horizontal axis is arbitrary, but the relative agnitudes are eaningful. A new generation of intra-industry trade odels, based on Melitz (2003), provides an opening to ake sense of these facts. In a benchark case for the new odels, the Krugan variety gains disappear entirely, even though consuers value variety. All of the gains coe through the product arket churning that expands output at high productivity firs and leads low productivity firs to contract or exit. Our innovation is to link this product arket churning to labor arket churning, while giving workers a reason to care about their jobs. e do this by erging the Melitz odel with a variant of the Shapiro Stiglitz odel of efficiency wages. In this odel, workers care about job loss for two reasons. First, and in contrast to Melitz, there is involuntary uneployent, so job loss ay give rise to a spell without work or wages. Second, different jobs pay different wages to identical workers, so that a worker with a particularly good job (high wage) ay reasonably fear that displaceent fro that job will result in eventual reeployent only at a lower wage. Of course, idiosyncratically high wages at a job, all else equal, also ake that job ore vulnerable in the face of liberalization. Hence this also helps us to ake sense of public concerns of trade costing jobs and lowering wages. e develop a siulation of our odel based on the best available paraeter estiates. e find quite substantial aggregate gains in our siulations. hile uneployent exists in our odel, it is little affected by liberalization. However, there is a treendous aount of labor arket churning. In one experient, up to one-fourth of all good (above average wage) jobs are destroyed. Given best estiates of the agnitude of the fir-specific coponent of wages, this could lead any to lose as a result of liberalization. In short, we have developed a odel of intra-industry exchange in which the cobination of labor arket churning and job specific rents can ake sense of public concerns that trade costs jobs and lowers wages. The odel explains this in a context that continues to feature large aggregate gains coon in intra-industry odels. 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