Trade Liberalization, Unemployment, and Inequality with Endogenous Job Destruction

Transcription

1 Trade Lberalzaton, Unemployment, and Inequalty wth Endogenous Job Destructon Prya Ranjan Unversty of Calforna - Irvne 35 SSPA, Irvne, CA Phone: ; Fax: emal: pranjan@uc.edu Abstract In a two sector extenson of the Mortensen-Pssardes model of endogenous job destructon, t s shown that trade lberalzaton ncreases both job creaton and job destructon n the mport competng sector and reduces them n the export sector. Snce trade lberalzaton ncreases unemployment n the mport competng sector and reduces t n the export sector, the mpact on economywde unemployment s ambguous. Whle job destructon ncreases upon mpact n the mport competng sector, there s no mmedate decrease n job destructon n the export sector leadng to short term spkes n the net job destructon and unemployment rates n response to trade lberalzaton. Trade lberalzaton ncreases ntersectoral wage nequalty, however, ntra-sectoral wage nequalty ncreases n the export sector but decreases n the mport competng sector. Fnally, a more generous unemployment bene t ncreases the responsveness of job destructon to trade lberalzaton. Key words: trade lberalzaton, job destructon, unemployment, wage nequalty JEL Class caton Codes: F6

2 Introducton The man worry of people concerned wth the adverse e ect of trade lberalzaton on jobs s that t leads to job destructon. However, much theoretcal work n the lterature on trade and unemployment uses models where job destructon s exogenous. In these models trade lberalzaton changes the ncentves for job creaton leavng the ncentve for job destructon una ected. Therefore, the rate of job destructon s unchanged. Ths s contrary to not only popular percepton, but emprcal work on job ows as well. Ths paper ams to ll ths gap n the lterature by analyzng the mpact of trade lberalzaton on unemployment and job ows n a model where job destructon s endogenous a la Mortensen and Pssardes (994). It constructs a two sector general equlbrum model wth search generated unemployment and endogenous job destructon. All new jobs are created at maxmum productvty but the job spec c productvty s subject to an dosyncratc shock whch can lower job productvty. If the productvty falls below a cuto then the job s destroyed. Trade lberalzaton reduces the relatve prce of the mport competng good and ncreases the relatve prce of the export good. Ths leads to a decrease n the value of a job n the mport competng sector and an ncrease n the value of a job n the export sector. Ths n turn ncreases the cuto level of productvty below whch jobs are destroyed n the mport competng sector and decreases the cuto n the export sector. The result s an ncrease n the rate of job destructon n the mport competng sector and a decrease n the rate of job destructon n the export sector. Snce the rates of job creaton and destructon are equalzed n steady state, the rate of job creaton ncreases n the mport competng sector and decreases n the export sector. Even though the steady state results are symmetrcally opposte n the two sectors, the mpact e ects are asymmetrc. A lot of jobs n the mport competng sector become unvable and are destroyed mmedately. The opposte happens n the export sector. That s, a lot of lower productvty jobs whch were not vable to begn wth survve now. However, snce these lower productvty jobs were not vable earler, they do not exst at the tme of trade lberalzaton. These jobs appear and survve n the X sector only n the medum run. Ths asymmetry can lead 2

3 to short term spkes n job destructon and unemployment n response to trade lberalzaton. Next, the paper looks at the mpact of trade lberalzaton on wage nequalty. Snce wages are determned through Nash barganng and there s renegotaton of wages followng changes n job productvty, the model exhbts ntra and ntersectoral wage nequalty. It s shown that the ntersectoral wage nequalty ncreases upon trade lberalzaton. As far as ntra-sectoral wage nequalty s concerned, t ncreases n the export sector and decreases n the mport competng sector. The paper also studes how generous unemployment bene ts a ect job ows and unemployment n the open economy. It nds that generous unemployment bene ts ncrease the responsveness of the rate of job destructon and unemployment to trade lberalzaton. The results of the model are consstent wth the emprcal work descrbed below. In a recent paper studyng the relatonshp between job ows and trade costs, Grozard et al. (20) nd that a reducton n the ndustry trade cost sgn cantly reduces job creaton and sgn cantly ncreases job destructon. Moreover, the e ect on job destructon s larger than the e ect on job creaton. Dutt, Mtra and Ranjan (2009), usng cross-country data on trade polcy and unemployment, nd that unemployment and trade openness are negatvely related. Usng panel data, they nd an unemployment-ncreasng short-run mpact of trade lberalzaton, followed by an unemployment-reducng e ect leadng to the new steady state. Even though ths paper does not look at job creaton and job destructon separately, the result on the d erental responses of trade lberalzaton n the short and long runs can be explaned usng our endogenous job destructon framework. Our results are also consstent wth the results n Hasan et al. (forthcomng), whch, usng state level varaton n the exposure to trade lberalzaton across Indan states, nds some weak evdence that the mmedate short-run e ect of a tar reducton s to ncrease unemployment pror to reducton to a lower steady-state unemployment rate. Whle our model studes the e ect of trade lberalzaton on job ows, one could use the two sector set up to study the mpact of real exchange rate changes on job ows n the traded and nontraded sectors. Snce exchange rate apprecatons ncrease the relatve prce of non-traded goods, the mpact on the traded sector would be smlar to the mpact on the mport competng sector 3

4 n our framework. Snce manufacturng produces traded goods, one would expect the mpact of exchange rate apprecaton on manufacturng to be smlar to that on the mport competng sector n our theoretcal framework. Klen, Schuh, and Trest (2003) study the mpact of real exchange rate changes on job ows n the U.S. manufacturng ndustres from 974 to 993. Ther key ndng s that movements n trend real exchange rates sgn cantly a ect both job creaton and destructon n the same drecton and by smlar magntudes, thus they have large allocaton e ects but no e ect on net employment growth. In contrast, an apprecaton of the cyclcal component of real exchange rates ncreases job destructon but has lttle e ect on job creaton, thus t reduces net employment growth but has no other allocaton e ects. Also related s a recent paper by Moser, Urban, and dmauro (200) whch studes the mpact of real exchange rate changes on job ows usng a sample of establshment-level data from Germany. They nd evdence of net job losses n response to a real exchange rate apprecaton. Ther most nterestng ndng s that the bulk of adjustment n response to a real exchange rate apprecaton occurs through less job creaton than ncreased job destructon. They attrbute ths to rgd labor regulatons that make job destructon costly for rms. The paper s also related to the burgeonng theoretcal lterature on search generated unemployment n open economes. In a seres of papers spannng over two decades Carl Davdson and Steven Matusz have studed the mplcatons of ntroducng unemployment arsng from labor market frctons n trade models. The man focus of ther work, as dscussed n Davdson and Matusz (2004), has been the role of e cency n job search, the rate of job destructon and the rate of job turnover n the determnaton of comparatve advantage. Among more recent works, Moore and Ranjan (2005) show how trade lberalzaton n a skll-abundant country can reduce the unemployment of sklled workers and ncrease the unemployment of unsklled workers. Skll-based technologcal change on the other hand, can reduce the unemployment of unsklled workers. Helpman and Itskhok (200) use an mperfectly compettve set up wth heterogeneous rms to look at how gans from trade and comparatve advantage depend on labor market rgdtes, and how labor-market polces n a country a ect ts tradng partner. Felbermayr, Prat and Schmerer (20) ncorporate 4

5 search unemployment n a one sector model wth rm heterogenety to study the mplcatons of a blateral reducton n trade cost on unemployment. Mtra and Ranjan (200) study the mpact of o shorng n a two sector model where some jobs n one of the two sectors can be o shored whle all the jobs n the other sector must reman onshore. In all these papers the rate of job destructon s exogenous, however. Therefore, trade lberalzaton a ects unemployment through changes n job creaton only. The plan of the rest of the paper as follows. The next secton descrbes the two sector search model wth endogenous job destructon. Secton 3 studes the mplcatons of trade lberalzaton and also studes how unemployment bene ts a ect the responsveness of job ows and unemployment to trade lberalzaton. Secton 4 concludes. 2 The Model 2. Product Market There s a sngle non-tradable nal good Z whch s produced usng two potentally tradable nputs X and Y: The producton functon for Z s gven below. Z AX Y ( ) () Gven the prces p x ; and p y ; of nputs, the unt cost for producng Z s gven as follows. c(p x ; p y ) A (p x) (p y ) (2) The market for good Z as well as the nputs X and Y s perfectly compettve. Snce Z s chosen as the numerare, p z ; and therefore, c(p x ; p y ) ; or A (p x) (p y ) (3) The relatve demand for the two nputs can be wrtten as a functon of the relatve prce as 5

6 follows. X d Y d ( )p y (4) p x 2.2 Labor Market Our descrpton of labor market adapts the endogenous job destructon model of Mortensen and Pssardes (994) to a two sector settng. To produce ether X or Y, a rm needs to open job vacances and hre workers. Let L be the total number of workers who look for a job n sector : We are mplctly assumng that workers are not moble across sectors. Ths may be a good descrpton of the labor market n the presence of hgh moblty cost. Allowng the workers to move costlessly across sectors wll convert t nto a Rcardan model because then e ectvely there wll be a sngle factor of producton. In ths case, trade lberalzaton wll wpe out the sector wth comparatve dsadvantage. Snce we want to capture the mpact of trade lberalzaton on job creaton and job destructon n the mport competng sector, we make the assumpton of no worker moblty. Also, we thnk that n the short to medum run, workers face hgh moblty costs whch s the approprate tme frame for ths knd of model and therefore, there s no loss of generalty n assumng no worker moblty across sectors. In the long run, workers are lkely to be moble across sectors, therefore, the model and the results n the paper should be consdered to be vald n a "medum run" scenaro. Alternatvely, the workers n the two sectors can be thought of as d erent types of labor such as sklled labor and unsklled labor. De ne v u as the measure of market tghtness n sector ; where v L s the total number of vacances n sector and u L s the number of unemployed workers searchng for jobs n sector. The probablty of a vacancy lled s q( ) m(v ;u ) v where m(v ; u ) s a constant returns to scale matchng functon. Snce m(v ; u ) s constant returns to scale, q 0 ( ) < 0: The probablty of an unemployed worker ndng a job s m(v ;u ) u q( ) whch s ncreasng n : The productvty of a job s denoted by t wth support [0; ] and a dstrbuton functon denoted by G(t): All jobs are See Mtra and Ranjan (200) for a search and o shorng model wth varyng degrees of moblty costs. 6

7 created at the full productvty of : That s, a new job n ether sector produces one unt of output. A job n sector- s ht wth an dosyncratc shock that leads to a change n the job productvty. s the Posson arrval rate of the shock. If the job productvty falls below a reservaton productvty R (to be determned endogenously) the job s destroyed mmedately. Denote the asset values of an occuped job n sector- wth productvty t for a rm and for a worker by J (t) and W (t); respectvely. Denote the wage for a job n sector wth productvty t by w (t): Denotng the rate of dscount by r; the expresson for J (t) s gven by Z rj (t) p t w (t) + J (s)dg(s) J (t) (5) R Denotng the asset value of an unemployed worker n sector- by U ; the expresson for W (t) s gven by Z rw (t) w (t) + W (s)dg(s) + G(R )U W (t) (6) R Denotng the unemployment bene t ncludng the value of lesure by b; the asset value of an unemployed worker n sector- s ru b + q( )[W () U ] (7) Note that snce all jobs are created at the full productvty of, W () s the value of a new job for a worker. The wage rate, w (t); s such that the surplus from the job s dvded accordng to the barganng shares. Assume that the barganng weght of workers s : Denote the asset value of a vacant job n sector- by V : Now, the total surplus from a job s J (t) V + W (t) U : Generalzed Nash barganng mples that the worker gets a fracton of the surplus. W (t) U [J (t) + W (t) V U ] (8) Denote the cost of postng a vacancy n sector- n terms of good- by c : In a two sector model t s not obvous whether the cost of postng a vacancy should be n terms of the sectoral output 7

8 or the numerare good. In fact, one can make an argument that modelng the recrutment cost n terms of the numerare s more realstc. For example, f you want to post job vacances to hre workers for a textle mll, you are more lkely to pay the vacancy costs (recrutment or hrng cost) such as cost of job advertsement, payng a recruter/head-hunter n terms of the nal good rather than n terms of the textles that your mll wll produce. In the present model t turns out that modelng the recrutment cost n terms of the sectoral output makes the model slghtly more tractable. Therefore, we decde to make ths assumpton n the paper. In an optonal appendx avalable upon request t s shown that the qualtatve results are unchanged when the recrutment cost s n terms of the numerare. Snce all jobs are created at the maxmum productvty t, the expected pro t from a vacancy n sector- s rv p c + q( )[J () V ] (9) Assumng no entry barrer n the postng of vacancy mples all rent from vacances s dsspated: V 0: Therefore, the above mples that the value of a new job sats es J () p c q( ) (0) The expresson for wage can be derved as follows. Use (8) and (0) to re-wrte (7) above as ru b + p c () To derve an expresson for wage, multply (6) by ( from the former and use (8) and () to get ) and (5) by and subtract the latter w (t) ( )b + p (t + c ) (2) That s, the wage s ncreasng n the productvty of a job n addton to beng ncreasng n the market tghtness parameter, ; and the unemployment bene t, b: The latter two mprove the barganng poston of the worker and hence hs wage. A change n the productvty, on the other hand, a ects the rent avalable from the job and hence the wage. Therefore, the model 8

9 exhbts heterogenety n wages among dentcal workers. It s worth contrastng ths result wth those obtaned n models wth heterogeneous rms (e.g. Felbermayr et al. (20)) where dentcal wage s pad by heterogeneous rms. In those models, rms hre many workers and the value of the margnal worker for the rm s equal to the expected recrutment cost for the worker. Snce the recrutment cost s dentcal for all rms, the value of a margnal worker s equalzed among heterogeneous rms. An mplcaton of Nash barganng over wages s that the surplus of worker s a scalar multple of the surplus of rms from the margnal worker. Therefore, the equalty of the surplus from the margnal worker across rms mples the equalty of wages as well. In our set up wth sngle worker rms, all rms wthn a sector pay dentcal wages to a worker when the worker s hred. Ths s because the value of a new job s equated to the expected recrutment cost as can be seen clearly from (0). However, for exstng workers (0) does not apply and the wages are renegotated to re ect the current productvty whch determnes the rent to be shared between the worker and the rm. Next, we derve job creaton and job destructon equatons so that we can solve for R and as functons of p : Note that n order for a job to be destroyed, the rm s surplus from the job must be zero. Snce the rm s share of the surplus s a fracton ( ); the overall surplus must be zero as well. That s, J (R ) ( )(J (R) + W (R ) U ) 0: Therefore, W (R ) U 0 as well or W (R ) U. For t > R ; W (t) > U ; and hence the worker s better o stayng employed, whle for t < R ; W (t) < U ; and hence the worker would want to qut as well. To derve the job creaton curve, substtute the expresson for wage gven n (2) nto (5) to get Z (r + )J (t) ( )(p t b) p c + J (s)dg(s) (3) R Snce J (R ) 0; the above mples Z J (s)dg(s) p c ( )(p R b) (4) R Therefore, (3) can be wrtten as (r + )J (t) ( )p (t R ) (5) 9

10 Next, note that the job creaton condton (0) can be wrtten usng (5) as ( )( R ) (r + ) c q( ) (6) The left hand sde of the above expresson s the gan from a new job, whle the rght hand sde s the expected recrutment cost. An ncrease n mples hgher recrutment cost and hence requres a lower R for the job creaton to be vable. That s, the jobs should last longer. Alternatvely, a hgher R mples a greater probablty of job destructon G(R ); and therefore, recrutment costs should be low as well whch requres a lower : Therefore, n (; R) space, the curve representng (6) s downward slopng. To get a smple expresson for the job destructon condton, substtute (5) nto (3) to get (r + )J (t) ( )(p t b) p c + ( )p r + Now, the job destructon condton J (R ) 0 can be wrtten as Z R (s R )dg(s) (7) R b p c + Z (s R )dg(s) 0 (8) r + R It can be ver ed that the l.h.s of (8) s ncreasng n R and decreasng n : Intutvely, a hgher mples stronger barganng poston of workers, and therefore, reservaton productvty must be hgher for rms to break even or margnal jobs are destroyed. Therefore, the curve above s upward slopng n (; R) space. R : The two equatons (6) and (8) determne the two key endogenous varables of nterest: and The unemployment rate n sector- evolves accordng to The above mples that n steady-state ( : u 0) u s gven by : u G(R )( u ) q( )u (9) u G(R ) G(R ) + q( ) (20) 0

11 2.3 Measures of Inequalty We de ne our measure of ntra-sectoral nequalty as the rato of the top wage to the bottom wage: w () w (R ): If the workers n the two sectors are d erent, then ths can be vewed as a measure of wthn group nequalty. Usng the wage equaton (2) ths measure can be wrtten as! w () w (R ) ( )b + p ( + c ) ( )b + p (R + c ) (2) We can also construct a measure of ntersectoral wage nequalty by computng the rato of the average wages n the two sectors as follows. De ne w to be the average wage n sector- where w s the total wage bll n sector-, denoted by W B ; dvded by the number of employed: ( u )L : The equaton for the evoluton of the total wage bll s as follows. Z : W B q( )u L w () + ( u )L R w(s)dg(s) W B (22) The rst term above s the wage bll from the new jobs created at full productvty. The second term s the wage bll from the exstng jobs whch are ht by a shock and survve and the last term s the loss n wage bll due to the change n the productvty of jobs resultng from the dosyncratc shock. Therefore, the wage bll n steady state ( W B 0) s gven by And, the average wage s gven by : W B Z q( )u L w () + ( u )L w(s)dg(s) (23) R w Z q( )u w () + w(s)dg(s) (24) ( u ) R Upon usng the expresson for u from (20) the above becomes Our measure of ntersectoral wage nequalty s gong to be wx w y : Z w G(R )w () + w(s)dg(s) R (25)

12 2.4 Impact of a sectoral prce change on unemployment and nequalty Let us rst work out the mplcatons of an ncrease n p on R and : It s easy to verfy from (6) and (8) that whle the job creaton curve remans unchanged, the job destructon curve shfts to the rght because margnal jobs become vable now as rms have to pay less to workers due to a decrease n the outsde opportunty of workers ( b p decreases). Therefore, an ncrease n p leads to an ncrease n and a decrease n R : Snce an ncrease n p leads to an ncrease n and a decrease n R ; t can be ver ed from (20) that t must lead to a decrease n u as well. An ncrease n the sectoral prce p a ects wage nequalty through three channels. Frst, there s a drect e ect workng to ncrease nequalty because the value of a job at full productvty ncreases more than the value at the cuto productvty R ; whle the unemployment bene t s the same for all workers and does not depend on job productvty. Second, a decrease n the cuto productvty R ncreases nequalty. Fnally, an ncrease n tends to reduce nequalty because the barganng postons of all workers ncreases by the same magntude. Therefore, the mpact of an ncrease n p on! s theoretcally ambguous. To resolve the ambguty, we assume a Cobb-Douglas matchng functon of the form below. Assumpton : M(v L ; u L ) m (v L ) (u L ) It s shown n the appendx that under assumpton a su cent condton for d! > 0 s p ( c ) < ( )b: Ths condton s easly sats ed for reasonable parameter values used n the search lterature. As mentoned n the numercal example later, a reasonable value of n the lterature s 0:5: For ths value of the nequalty n the su cency condton s sats ed rrespectve of the values of b; ; and p as long as c < whch s very reasonable gven the estmates of c and n the lterature. Therefore, t s reasonable to expect! to be ncreasng n p. 2

13 2.5 General Equlbrum The model can be solved as follows. Start wth a relatve prce px p y : Obtan p x and p y n terms of the numerare nal good from (3). Now, obtan the correspondng R and from (6) and (8). Then, obtan the unemployment rate u from (20). Next, the total output of good- can be computed as follows. Denote the total amount of labor avalable for employment n good- by L : The amount of labor employed n sector- s ( u )L : Denote the output per unt of labor force n the two sectors by x and y; respectvely. That s: x XL x ; y YL y : The equaton for the evoluton of the sectoral output per unt of labor force s gven below. Z : q( )u + ( u ) sdg(s) ; x; y (26) R The rst term above s the output resultng from new matches whch are created at full e cency. The second term s the output of the exstng jobs that are ht by a shock and survve. The last term s the output that s lost due to the arrval of the dosyncratc shock. In steady state : 0; therefore, Z q( ) u + ( u ) sdg(s); x; y (27) R Next, note from (9) that n steady-state q( )u must equal G(R )( be wrtten as u ): Therefore, (27) can Z ( u ) G(R ) + sdg(s) ; x; y (28) R Thus, we can wrte the relatve output of good-x at relatve prce px p y h X s Y ( u x )(G(R x ) + R R x sdg(s)) L x h ( u y )(G(R y ) + R (29) R y sdg(s)) L y Next, we establsh that the relatve supply above s ncreasng n the relatve prce px p y : An ncrease n px p y mples an ncrease n p x and a decrease n p y : Ths n turn mples that u x and R x decrease whle u y and R y ncrease. Whle changes n u rase the relatve supply of X; the mpact of changes n R s ambguous. To get ntuton for the ambguty, note from (28) that decreases n as 3

14 u and R ncrease the output from exstng jobs (( u ) R R sdg(s)); but they have an ambguous e ect on the output from new jobs (( u )G(R )): To resolve the ambguty n the response of relatve supply to the relatve prce, we make the followng functonal form assumpton whch s also useful n dervng some later results. Assumpton 2 : t Unform[0; ] Under the above functonal form assumpton ( u ) R ( R 2 ) + 2 (30) Therefore, d R ( R 2 ) + du + ( u )( R ) dr (3) 2 As well, usng assumpton for the matchng functon, the expressons for job creaton (6) and job destructon (8) can be wrtten as ( )( R ) (r + ) c (32) m r R + R 2 r + r + 2 Usng the above two t s shown n the appendx that c + 2(r + ) b (33) p d 2R ( R ) 2 ( ) > (<) 0 ff u > (<) (( R )( ) + R )(R (2 R ) + ) (R ) (34) Numercal smulatons usng the standard values of parameters taken from the search lterature 2 suggest that d > 0. 2 In the numercal example below r :0033, (monthly rate of dscount) corresponds to 4% annual rate of nterest; :5; :5; :035 (montly job destructon rate); m :64 (scale parameter n the matchng functon); these parameters are taken from Felbermayr et al. (20). 4

15 Numercal example : r :0033; :035; m :64; :5; :5; b :7; c :4 Wth these parameter values, the ntal wage turns out to be 0:98 when the prce s set at : Therefore, the unemployment bene t and home producton s roughly 75% of the ntal wage and the recrutment cost s roughly 40% of the ntal wage, whch s broadly consstent wth the lterature (example, Delacrox (2006)). Also, these parameters lead to reasonable values of the market tghtness varable, ; of 0:65; and the unemployment rate of 6%: For these parameters, u s always greater than (R) de ned n (34) for any value of p and therefore, d > 0: Small perturbatons of the parameters above leave the result ntact. Therefore, we acknowledge the theoretcal possblty of d < 0, but assume d > 0 n rest of the paper: E ectvely, we are assumng that the output e ect from exstng jobs domnates the output e ect from the new jobs n response to an ncrease n p : In ths case we get an upward slopng relatve supply curve. Gven the downward slopng relatve demand n (4), we get a unque equlbrum n autarky. What are the determnants of the pattern of comparatve advantage n the model? One obvous determnant of comparatve advantage s the relatve endowment of the two types of workers: Lx L y : The greater the Lx L y the greater the relatve supply of X and hence the lower the relatve prce of X: Therefore, a country wth a greater Lx L y wll have a comparatve advantage n X: In addton, t s possble for parameters lke b; c ; m ; ; etc. to d er across sectors and countres and gve rse to comparatve advantage. We refer the reader to Davdson, Martn, and Matusz (999) for a rch dscusson of the determnants of pattern of comparatve advantage n a search model of ths type. 3 Trade lberalzaton Suppose the economy has a comparatve advantage n producng nput X: That s, the autarky relatve prce px p y s less than the world prce. In ths case, trade lberalzaton wll lead to an ncrease n the relatve prce of good X: Ths mples from (3) that p x ncreases and p y decreases. 5

16 Below we study the mpact of these changes n the nput prces on the job creaton, job destructon and unemployment n the two sectors. It can be ver ed from (6) and (8) that an ncrease n p x leads to an ncrease n x and a decrease n R x : A decrease n p y leads to a decrease n y and an ncrease n R y : It s clear from (20) that u x decreases and u y ncreases. Therefore, the mpact of trade lberalzaton on aggregate unemployment s ambguous. Whle the result on steady state unemployment s smlar to those obtaned n a model wth exogenous job destructon, we obtan nterestng results on job ows below whch are absent n models wth exogenous job destructon. 3. Impact of trade lberalzaton on job creaton and job destructon De ne job destructon rate as the rato of total job destructon to employment: G(R )( u )L ( u )L G(R ): Smlarly, the rate of job creaton s equal to the number of matches over employment: q( )u u The dscusson earler mples that there s an ncrease n the rate of job destructon n the Y sector due to mport competton. Now, n steady-state ths also mples an ncrease n the rate of job creaton snce the two are equal. Therefore, trade lberalzaton leads to ncreases n the rates of job creaton and job destructon n the Y sector and decreases n the rates of job creaton and job destructon n the X sector. The result s summarzed n the proposton below. Proposton Trade lberalzaton ncreases job ows n the mport competng sector and reduces job ows n the export sector. The result above s consstent wth the ndngs of Grozard et al. (20) where a reducton n the trade cost n an ndustry leads to greater job destructon for the ndustry. If one nterpreted the two sectors as tradable and non-tradable sectors, then the model would mply an ncrease n job destructon n the traded sector n response to an apprecaton of the real exchange rate. Ths 6

17 s consstent wth the evdence n Klen et al. (2003) that exchange rate apprecaton s assocated wth ncreased job destructon n the manufacturng ndustres n the U.S. Snce much of the lterature on trade and unemployment uses models wth exogenous job destructon we can contrast our result wth that n the exogenous job destructon model as follows. The exogenous job destructon model s a specal case of our model where R : Note that, by de nton ths also mples G(R ) : Therefore, the rate of job destructon s dentcally equal to : Thus, trade lberalzaton has no e ect on job destructon n ether sector. 3.. Transton Dynamcs Snce the equatons determnng R and ; (6) and (8), do not depend on the unemployment rate, R and jump to ther new steady-state values nstantaneously n response to trade lberalzaton. However, the unemployment rate adjusts gradually. Denote the pre-lberalzaton values of the endogenous varables wth a superscrpt 0 and the post-lberalzaton values wth a superscrpt : We assume that rms can destroy jobs costlessly and therefore, the job destructon condton J (R ) 0 always holds (even outsde steady-state). We prove the followng result below. Proposton 2 Durng transton from the pre-lberalzaton steady-state to the post-lberalzaton steady-state, the rate of job destructon exceeds the rate of job creaton n the mport competng sector whle the rate of job creaton exceeds the rate of job destructon n the export sector. Proof: As shown earler, u 0 y < u y: As well, y G(Ry) y q( y )u y ; snce n steady-state u y the rate of job destructon must equal the rate of job creaton. Therefore, y G(Ry) > yq( y)u 0 y u 0 y u 0 x < u x:qed for u 0 y < u y: By a smlar argument t follows that x G(R x) > xq( x)u 0 x u 0 x for What s even more nterestng s the mpact e ect of trade lberalzaton. Snce the rate of job destructon jumps up to y G(R y); on mpact a fracton y [G(R y) G(R 0 y)] of extra jobs are destroyed n the Y sector mmedately: That s, all the jobs wth productvty t 2 (R 0 y; R y) were 7

18 vable before lberalzaton, however, now they must be destroyed. In the X sector the rate of job destructon goes down from x G(R 0 x) to x G(R x): However, ths has no mmedate e ect because there are no jobs wth productvty t 2 (R x; R 0 x) n the X sector at the tme of trade lberalzaton that can survve now. Thus, on mpact the rate of job destructon does not decrease n the X sector. Therefore, there s an asymmetry n the mpact e ect of trade lberalzaton on the two sectors. Whle a fracton y [G(R y) G(R 0 y)] of jobs are destroyed n the Y sector mmedately leadng to a large ncrease n unemployment upon mpact, there s no commensurate decrease n job destructon n the X sector mmedately upon trade lberalzaton. The lower rate of job destructon n the X sector wll show up n the medum run when jobs wth t 2 (R x; R 0 x) wll survve. The mpact e ect on the rate of unemployment s as follows. u 0 y u 0 y + : u y u 0 y + y G(R y)( u 0 y) yq( y)u 0 y > u 0 y (35) Note from the expresson for u 0 y that f u 0 y > u y; then there s overshootng of unemployment. That s, the unemployment rate jumps up and then decreases gradually to ts new steady state. Therefore, t s possble for the unemployment rate to shoot up n the mport competng sector n response to trade lberalzaton and then come down gradually. The results on the mpact e ect of trade lberalzaton are consstent wth some stylzed facts whch are hard to reconcle wth the model of exogenous job destructon. For example, Dutt, Mtra and Ranjan (2009) nd that trade lberalzaton leads to short term spkes n unemployment followed by long-run declnes. The short term spke n unemployment can be explaned usng the asymmetrc responses of the two sectors above wth regard to job destructon. In the model wth exogenous job destructon, all the adjustment n the jobs takes place through job creaton. Therefore, durng transton from pre-lberalzaton steady-state to post-lberalzaton steady-state, the rate of job destructon wll reman unchanged, but the rate of job creaton wll slow down to a rate below the rate of job destructon n the mport competng sector. In steadystate the rate of job creaton wll go back to the autarky level. The opposte wll happen n the export sector. Snce all the acton takes place through job creaton, one cannot get an asymmetrc 8

19 response across the two sectors ether. Before endng ths secton, t s worth pontng out another nterestng mplcaton of trade lberalzaton n a model wth endogenous job destructon. Snce the productvty cuto ncreases n the mport competng sector, trade lberalzaton ncreases the productvty of the mport competng sector. Ths s smlar to the selecton e ect of globalzaton operatng n the Meltz type heterogeneous rm models due to a xed cost of tradng. It arses n the current framework due to labor market frctons. 3.2 Trade Lberalzaton and Wage Inequalty Gven the dscusson of the mpact of sectoral prce, p ; on the ntra-sectoral wage nequalty,! ; n the prevous secton, t s straghtforward to study the mpact of trade lberalzaton on!. Snce trade lberalzaton leads to an ncrease n p x and a decrease n p y ; t also leads to an ncrease n! x and a decrease n! y. In other words, n the short to medum run, trade lberalzaton leads to an ncrease n the wthn group nequalty among workers employed n the export sector and a decrease n the wthn group nequalty among workers employed n the mport competng sector. Gven our functonal form assumpton 2, the measure of ntersectoral wage nequalty de ned earler can be wrtten as w x R R xw x () + R x w x (s)ds w y R y w y () + R (36) R y w y (s)ds Snce w (s) s ncreasng n p as s easly ver ed from (2), w x (s) ncreases and w y (s) decreases upon trade lberalzaton. Ths would tend to ncrease the ntersectoral wage nequalty. However, R x decreases and R y ncreases. The decrease n R x decreases the rst term n the numerator but ncreases the second term. Smlarly, an ncrease n R y ncreases the rst term, but decreases the second term. Therefore, the only force that works aganst an ncrease n ntersectoral wage nequalty s the mpact of a change n R on the rst terms n both the numerator and the denomnator. Intutvely, a decrease n R x mples less job destructon and consequently less job creaton as well n the X sector. A lower job creaton n steady state mples smaller number of jobs 9

20 at full productvty whch serves to lower the average wage. The opposte happens n the Y sector. However, ths e ect by tself cannot outwegh the other e ects tendng to rase ntersectoral wage nequalty. It s shown n the appendx that a su cent condton for ntersectoral wage nequalty to ncrease s Note that snce d because dr c + (R + R2 2 ) + p c d + p ( R ) dr > 0 (37) > 0; the only negatve term on the l.h.s of the nequalty above s the last term < 0: Ths captures the e ect on average wage arsng from lower job creaton. However, the last term by tself s unlkely to outwegh the rst three terms. In fact, f c > ( )( R ) 2 ; then, as shown n the appendx, the sum of last two terms s postve whch s su cent for the above nequalty to be true. The condton c > ( )( R ) 2 s easly sats ed n the numercal smulatons wth reasonable parameter values. Therefore, we conclude that the ntersectoral wage nequalty s lkely to ncrease upon trade lberalzaton. 3.3 Impact of unemployment bene ts on job ows and unemployment n the open economy In ths secton we study how generous unemployment bene ts nteract wth trade lberalzaton. In partcular, whether a generous unemployment bene t ampl es or moderates the mpact of trade lberalzaton on unemployment. Takng the total dervatve of equatons (32) and (33) wth respect to b obtan ( ) dr (r + ) (r + R ) dr c d r + c m ( ) d (38) p (39) To reduce notatonal clutter, de ne De nton: (R ; ) ((r + R ) + m 20

21 Now, (38) and (39) mply Therefore, dr (R ; ) dr r + (40) p r + p (R ; ) > 0; d ( )m dr (r + )c ( ) < 0 (4) Takng the total dervatve of the expresson for unemployment n (20) wth respect to b we obtan du u ( u )( R dr d ) > 0 (42) That s, a hgher unemployment bene t mples greater rate of job destructon, lower market tghtness and a hgher unemployment rate. Agan, t s worth pontng out that n a model wth exogenous job destructon, the mpact of unemployment bene t on job ows works only through job creaton. An ncrease n unemployment bene t wll reduce job creaton resultng n a lower market tghtness and hgher unemployment. The steady state rates of job creaton and job destructon are left una ected. Next, we study how unemployment bene t a ects the mpact of trade on the rate of job destructon and unemployment. Use the followng de nton: De nton: " R p p dr R ; " b b d It s shown n the appendx that d" R p " R p R + (R ; ) + b (R ; ) R m (R ; )( R )( ) 2 " Rp (43) That s, the sgn of d" R p s theoretcally ambguous. However, numercal smulatons wth the parameter values n the neghborhood of those n numercal example con rm that d" R p < 0: Numercal Example 2: r :0033; :035; m :64; :5; :5; b :7; c :4; for p ; then d" R p :5 and t asymptotes towards zero for hgher values of p : For lower values of p t s a larger negatve number. For example, for p :75; d" R p :5: 2

22 Snce " R p s negatve, d" R p < 0 mples that an ncrease n b ncreases the magntude of " R p : That s, an ncrease n b ncreases the responsveness of R to trade lberalzaton. Therefore, other thngs equal, a more generous unemployment bene t s lkely to amplfy the e ect of trade lberalzaton on job destructon. It s also shown n the appendx that d" p R d" R p R ( R ) 2 ( ) " dr R p (44) Agan, the sgn of the dervatve above s theoretcally ambguous. However, f d" R p n the numercal smulatons, then d" p < 0 as found > 0: That s, a more generous unemployment bene t ncreases the responsveness of the market tghtness to trade lberalzaton. Next, t s shown n the appendx that d" R p < 0 also mples d( du ) < 0: Snce du < 0; t mples that a more generous unemployment bene t ncreases the responsveness of unemployment to trade lberalzaton as well. Note agan that compared to the model wth exogenous job destructon where changes n unemployment bene ts a ect unemployment only through job creaton (see for example, Moore and Ranjan (2005)), here they have an mpact on job destructon as well. Therefore, the responsveness of job ows as well as the rate of unemployment to trade lberalzaton s larger when the unemployment bene t s more generous. Even though a more generous unemployment bene t ncreases the responsveness of unemployment as well as job ows to trade lberalzaton, ths cannot be an argument aganst havng a more generous unemployment bene t n an open economy. To arrve at a normatve concluson about unemployment bene ts, one wll have to ntroduce rsk averson n the household utlty functon because the key motvaton behnd unemployment bene ts s to nsure households aganst labor market rsk arsng from unemployment. We leave ths exercse for future research. 22

23 4 Conclusons Ths paper has shown how studyng trade lberalzaton n a model of endogenous job destructon can provde results on job ows and unemployment consstent wth the recent emprcal work. It was shown that trade lberalzaton ncreases both job creaton and job destructon n the mport competng sector and reduces them n the export sector. Snce trade lberalzaton also ncreases unemployment n the mport competng sector and reduces t n the export sector, the mpact on economywde unemployment s ambguous. More nterestngly, trade lberalzaton also has an asymmetrc mpact e ect on the two sectors. Whle there s a lot of job destructon n the mport competng sector upon mpact, the reducton n job destructon n the export sector takes e ect only n the medum run. Ths can lead to short term spkes n the net job destructon and unemployment rates n response to trade lberalzaton. The paper also shows how trade lberalzaton could lead to an ncrease n the wthn group wage nequalty n the export sector and a decrease n the wthn group wage nequalty n the mport competng sector. The ntersectoral wage nequalty s lkely to ncreases as well as a consequence of trade lberalzaton. Fnally, t was shown that a more generous unemployment bene t ncreases the responsveness of job destructon to trade lberalzaton. Before endng the paper, t should be noted that the framework can also be used to study the mplcatons of other labor market regulatons such as more strngent rng restrctons on job ows and unemployment n the open economy. Snce unemployment bene ts and rng restrctons are two alternatve nstruments used to protect workers aganst the volatlty n the labor market, t would be a useful exercse to study the mplcatons of rng restrctons as well. To prevent the paper from becomng too cumbersome, ths s left for future research. 23

24 Acknowledgement: I would lke to thank an anonymous referee for very useful comments. 24

25 References [] Davdson, C., Martn, L., & Matusz, S. (999). Trade and Search Generated Unemployment. Journal of Internatonal Economcs, 48, [2] Davdson, C., & Matusz, S. (2004). Internatonal trade and labor markets. Kalamazoo, Mchgan: WE Upjohn Insttute of Employment Research. [3] Delacrox, A. (2006). A Multsectoral matchng model of unons. Journal of Monetary Economcs, 53, [4] Dutt, P., Mtra, D., & Ranjan, P. (2009). Internatonal Trade and Unemployment: Theory and Cross-Natonal Evdence. Journal of Internatonal Economcs, 78(), [5] Felbermayr, G., Prat, J., & Schmerer, H. (20). Globalzaton and Labor Market Outcomes: Wage Barganng, Search Frctons, and Frm Heterogenety. Journal of Economc Theory, 46(), [6] Grozard, J.L., Ranjan, P., & Rodr guez-l opez, J.A. (20). O shorng and Job Flows, mmeo, UC-Irvne. [7] Hasan, R., Mtra, D., Ranjan, P., & Ahsan, R. (forthcomng). Trade Lberalzaton and Unemployment: Theory and Evdence from Inda. Journal of Development Economcs. [8] Helpman, E., & Itskhok, O.(200). Labor Market Rgdtes, Trade and Unemployment. Revew of Economc Studes, 77 (3), [9] Klen, M. W., Schuh, S., & Trest, R.K. (2003). Job Creaton, Job Destructon, and the Real Exchange Rate. Journal of Internatonal Economcs, 59(2), [0] Mtra, D., & Ranjan, P. (200). O shorng and Unemployment: The Role of Search Frctons Labor Moblty. Journal of Internatonal Economcs, 8(2),

26 [] Moore, M., & Ranjan, P. (2005). Globalzaton vs skll based techncal change: Implcatons for unemployment and wage nequalty. Economc Journal, 5 (503), [2] Mortensen, D.T., & Pssardes, C. (994). Job Creaton and Job Destructon n the Theory of Unemployment. Revew of Economc Studes, 6(3), [3] Moser, C., Urban, D., & d Mauro, B.W. (200). Internatonal Compettveness, Job Creaton and Job Destructon An Establshment-Level Study of German Job Flows. Journal of Internatonal Economcs, 80(2), [4] Pssardes, C.A. (2000). Equlbrum Unemployment Theory. ( 2nd ed.). Cambrdge, Mass: MIT Press. 26

27 5 Appendx 5. Impact of an ncrease n p on wage nequalty From (2) n the text obtan the expresson for d!, whch after cancelng terms can be wrtten as d! ( )b( R) 2 p 2 c ( R ) d dr (( )b + p ( + c )) p (( )b + p (R + c )) 2 (45) From (6) and (8) n the text obtan ( ) dr c ( (r + ) m (r + G(R)) dr c d b r + p 2 ) d (46) The above two mply that d ( )m dr (r + )c ( ) dr ; dr ( )( R ) p 2 b(r + ) (47) (r + G(R ) + m ( ) where the last expresson for d d n d! above to get s obtaned upon usng (6). Next, substtute the expresson for d! ( )b( R) + p p ( c ) ( )b dr (( )b + p (R + c )) 2 (48) Therefore, a su cent condton for d! > 0 s p ( c ) ( )b < Impact of an ncrease n p on sectoral output Take the total dervatves of (32) and (33) n the text wth respect to p to obtan ( ) dr c ( (r + ) m (r + R ) dr c d b r + p 2 ) d (49) (50) 27

28 Usng the de nton, (R ; ) ((r + R ) + m ; already de ned n the text, wrte (R ; ) dr b r + p 2 (5) or dr b(r + ) p 2 (R ; ) < 0; d ( )m dr > 0 (52) (r + )c ( ) Gven assumpton regardng the functonal forms, the expresson for unemployment n (20) becomes R u R + m Next, take the dervatve of the expresson for unemployment n (20) to get (53) du u ( u )( R dr d ) < 0 (54) Next, usng (54), re-wrte (3) n the text as d R ( R 2 ) + u ( 2 u )( dr + ( )m dr )+( u )( R ) dr (55) R (r + )c ( ) Next, usng (49) re-wrte (55) as d ( u ) dr ( 2R R )( ( R )( ) + R ) )u ( R ) ( R )R ( ) (56) Snce dr partcular, < 0; the sgn of d depends on the sgn of the term n the square bracket n (56). In d 2R ( R ) 2 ( ) > (<)0 f u > (<) (( R )( ) + R )(R (2 R ) + ) (R ) (57) 5.3 Impact of trade lberalzaton on ntersectoral wage nequalty Upon usng the expresson for w (t) from (2), the ntersectoral wage rato can be wrtten as 28

29 w x ( )b + p xc x x + p x (R x + R2 x w y ( )b + p y c y y + p y (R y + R2 y Note from above that t s enough to show that p c + p (R + the dervatve of p c + p (R + c + (R + R2 2 ) wth respect to p obtan R2 2 ) + p c d + p ( 2 ) 2 ) (58) R2 2 ) s ncreasng n p. Takng R ) dr (59) Re-wrte the above as c + (R + R2 2 ) c ( )( R ) dr ( R ) p (60) Therefore, snce dr c > ( )( R ) 2. < 0; a su cent condton for wx w y to ncrease upon trade lberalzaton s 5.4 Impact of generous unemployment bene t n the open economy From (5) above obtan " R p b(r + ) p R (R ; ) " R b (6) where the last equalty can be ver ed from the expresson for dr gven n the text n (42). Therefore, d" R R Usng (49) the above can be re-wrtten as R dr R p (62) d" R p " R p p + ( (r + )c ( R dr (63) Next, note from (6) R p (R ; ) + R " R R (R ; ) > R p m " R (R ; )( ) > 0 (64) 29

30 Usng (64) n (63), and makng use of the fact that " R p " R b we get "! d" R p " R p + (R ; ) + R R m ( )m b (R ; ) (R ; ) ( ) 2 (r + )c " R p # (65) Next, usng (32) n the text, re-wrte the above as d" R p " R p b Next, we nd out d" p : Usng (52) above obtan (R ; ) + R + (R ; ) R m (R ; )( R )( ) 2 " Rp (66) " R p c (r + )( ) " p m ( )R (67) Upon usng (32), the above can be wrtten as " p R ( R )( ) " R p (68) Therefore, d" p R d" R p ( R )( ) Next, usng the expresson for unemployment n (53) obtan ( )( R ) 2 " dr R p (69) du u ( u ) R ( + p ( R )( ) )" R p < 0 (70) Therefore, d( du ) ( R 2u )( + ( R )( ) )" du R p + ( u ) ( R ) 2 ( ) " dr R p +( R u )( + ( R )( ) )d" R p (7) The sgn of the dervatve above s ambguous, however, when d" R p < 0; the dervatve above s negatve under the reasonable assumpton that u < 2 because all 3 terms are negatve. 30