O shoring, Unemployment, and Welfare with Risk Averse Workers. Priya Ranjan University of California - Irvine

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1 O shoring, Unemployment, an Welfare with Risk Averse Workers Priya Ranjan University of California - Irvine pranjan@ui.eu Current Draft Deember, 03 Abstrat This paper stuies the welfare an poliy impliations of o shoring when risk averse workers fae the risk of unemployment. If o shore inputs an be easily substitute for omesti workers, then o shoring reues wages an inreases unemployment. In this situation, in the absene of any government intervention o shoring not only reues the welfare of workers but oul reue aggregate welfare as well if workers are highly risk averse an the markets for insurane against unemployment risk are missing. In aition to unemployment insurane, the role of employment protetion poliies- severane payments an aministrative ost of ring -in proteting workers against the averse onsequenes of globalization is stuie. An aministrative ost of ring reues job estrution, however it ens up reuing the welfare of workers. Manate severane payments an unemployment insurane an both protet workers against the averse e ets of o shoring an have the potential to make o shoring aggregate welfare improving. When unemployment arises ue to both job estrution an mathing fritions, a ombination of severane payments an unemployment bene ts is a better poliy to shiel workers from the averse onsequenes of o shoring than either of them alone. Keywors: o shoring, unemployment, enogenous job estrution, severane payments, unemployment bene ts JEL Coes: F6, F66, F68 0 I woul like thank the seminar paripants at the Universities of Calgary, Munih, Linz, an Gabriel Felbermayr an Dalia Marin for useful omments.

2 Introution While eonomists have evote a lot of attention to the impat of various aspets of globalization on wage an inome inequality, the poliymakers an the publi at large have been more onerne with the impliations of globalization for jobs (both quantity an quality). This has given rise to a reent surge in works stuying the impliations of globalization for jobs. The empirial literature using atasets from various ountries an inustries ns mixe results. Dutt, Mitra, an Ranjan (009) n trae liberalization to be assoiate with lower unemployment at longer intervals in a ross-ountry stuy, however, there is a spike in unemployment in the immeiate aftermath of trae liberalization. A reent in uential stuy by Autor, Dorn, an Hanson (forthoming, AER) ns that the inrease ompetition from Chinese imports has inrease unemployment in the loal U.S. labor markets an explains about one quarter of the ontemporaneous aggregate eline in the U.S. manufaturing employment. Gorg (0) provies a survey of the empirial literature on o shoring an unemployment an ns a iverse set of results: o shoring a ets employment aversely in some inustries/ountries an positively in others. Given the possibility of globalization inreasing unemployment, at least in the short to meium run, a serious isussion of poliies relate to this issue is warrante whih is the subjet of this paper. We fous on a partiular aspet of globalization- o shoring- whih has been inreasing in importane in reent times. By o shoring we mean the fragmentation an reloation of a part of proution proess abroa unertaken both within the rm bounary an outsie the rm bounary. We onstrut a theoretial moel with risk averse workers whih is a key eparture from the stanar moels of globalization an labor market. In our moel a single goo is proue using omesti labor an o shore inputs with a onstant elastiity of substitution proution funtion. While all workers are ex ante iential, the math spei proutivity is ranom, an it is not worthwhile for rms to keep very low proutivity mathes. Wage etermination follows the ompetitive searh traition of Moen (997), an Aemoglu an Shimer (999) where rms post a wage to attrat workers. In this set up, it is shown that the impat of o shoring on the labor market an welfare ruially epens on the elastiity of substitution between omesti labor an o shore inputs. If there is su ient omplementarity between omesti labor an o shore inputs, then o shoring not only improves the welfare of workers by lowering unemployment an inreasing wages but inreases aggregate welfare as well. On the other han, if o shore inputs an be easily substitute for omesti labor then workers

3 are aversely a ete by o shoring: unemployment inreases an wages erease. In the latter ase, there is an inrease in inequality in the istribution of inome sine pro ts rise an wages fall. More importantly, if workers are su iently risk averse, then o shoring not only reues the welfare of workers, but reues aggregate welfare as well. Therefore, in the absene of any instruments for reistribution or soial protetion, there woul be a ase for restriting o shoring to inrease aggregate welfare. The potential welfare loss from o shoring is a onsequene of the risk aversion of workers. If instea, workers are risk neutral then irrespetive of the elastiity of substitution between omesti labor an o shore inputs, o shoring always inreases aggregate welfare. Risk aversion of workers an missing market for insurane against labor inome risk reates a role for soial protetion. While soial protetion refers to safety nets of various kins, in this paper we restrit it to mean soial insurane programs that enable iniviuals to negotiate labor market risk. The main reason for the existene of suh programs in market eonomies is that the market for private insurane against inome risk is missing for various reasons. Soial protetion programs protet workers from shoks irrespetive of whether the shok originates within a ountry or has its origins abroa. However, proviing protetion against external shoks aquires saliene ue to politial eonomy reasons. We stuy the roles of unemployment insurane (UI) an employment protetion (EP) legislation in proteting workers against the possible averse onsequenes of o shoring. Both UI an EP are ommon in evelope ountries, but EP seems to be more ommon in eveloping ountries probably beause setting up UI programs requires onsierable aministrative expertise. For example, uring the East Asian risis of the late 990s, South Korea was the only ountry that ha any kin of unemployment insurane, but all East Asian ountries ha employment protetion poliies in plae. Not only were there restritions on ring, but rms were require to make severane payments upon ismissal as well. Our theoretial preition that o shoring an inrease unemployment in some inustries an reue them in others is onsistent with the iverse empirial nings summarize in Gorg (0). A more iret eviene is provie in Harrison an MMillan (0). Using ata on the U.S. multinationals, they n that when the tasks performe by the subsiiary of a multinational are omplementary to the tasks performe at home, o shoring leas to more job reation in the Unite States; however, o shoring auses job losses when the tasks performe in the subsiiary are substitutes for the tasks performe at home. see Mitra an Ranjan (0) for etails. 3

4 While the role of unemployment insurane as an instrument of soial protetion is relatively well known, it is less lear how some elements of employment protetion programs an at as an instrument of soial protetion an hene an play a ruial role in proteting workers against the potentially averse onsequenes of globalization. Employment protetion refers to a host of manatory restritions pertaining to the separation of workers from rms. The two key elements of employment protetion are severane payments whih is a transfer from rms to workers an an aministrative ost borne by employers whih oes not arue to employees iretly. Fousing on the ase where o shoring aversely a ets workers (high elastiity of substitution between omesti labor an o shore inputs), it is shown that severane payments have the potential to o set the averse welfare e ets of o shoring on workers. More preisely, when the ost of o shoring goes own a level of severane payments that keeps the welfare of workers unhange, allows the aggregate welfare to be higher than before the erease in the ost of o shoring. Therefore, severane payments an be use as a poliy tool to ompensate the workers an make o shoring potentially Pareto improving. As well, the greater the erease in the ost of o shoring the larger is the inrease in severane payments require to keep the welfare of workers unhange implying an expansion in the role of the welfare state with further globalization. We also stuy the welfare impliations of o shoring when severane payments are always set at the soially optimal level. It is shown that the soially optimal level of severane payments fully insure workers against labor market risk. However, o shoring an reue the welfare of workers as well as aggregate welfare even if severane payments are always set at soially optimal level. The reason is that there are two istortions in the moel: one arising from a lak of insurane an the other from a lak of instrument for reistribution. While severane payments orret the istortion from lak of insurane, when o shoring reistributes inome from workers to pro t owners it auses welfare losses by aggravating soial inequality. It is shown that if a su iently large share of pro ts is istribute to workers, then o shoring inreases both the welfare of workers as well as aggregate welfare in the presene of optimal severane payments. Looking at the pure aministrative ost omponent of employment protetion, it is shown that an inrease in this ost reues job estrution by rms an thereby reues unemployment, however, it ens up reuing the welfare of workers. Therefore, this omponent of the stanar employment protetion program protets employment but fails to improve the welfare of workers. What this suggests 4

5 is that not all omponents of employment protetion are equal in terms of their welfare impliations an insight that may be relevant for empirial work. Empirial work on the subjet lumps together all elements of employment protetion in onstruting an aggregate inex of employment protetion. An alternative poliy to insure workers is publily provie unemployment bene ts whih is like a self insurane program where employe workers pay a payroll tax to fun the unemployment bene ts. Comparing optimal severane payments with optimal unemployment bene ts, we n that the former leas to greater aggregate welfare. Intuitively, sine workers are risk averse an rms are risk neutral, optimal risk sharing requires rms to bear the risk. Sine severane payments allow rms to bear the risk while unemployment bene ts are a form of self insurane for workers, the former yiels greater aggregate welfare. The baseline moel isusse above abstrats from mathing fritions to fous on job estrution an severane payments. As a result, unemployment is etermine solely by job estrution whih is not onsistent with reality. In reality, an in the workhorse Pissaries (000) moel, the pool of unemploye in any perio onsists of workers who fail to math an those whose jobs have been terminate. To apture this aitional soure of unemployment, we exten the moel to inorporate mathing fritions. Now the ajustment in response to o shoring takes plae through both less job reation an greater job estrution. In partiular, when omesti labor an be easily substitute by o shore inputs, o shoring inreases unemployment by inreasing job estrution as well as reuing job reation. The latter happens through a reution in the market tightness. Looking at poliies in the extene moel, sine severane payments are targete towars re workers, they annot be use to insure workers who fail to math. However, unemployment bene ts an be use to insure unmathe workers. In this setting, a poliy that uses a ombination of severane payments an unemployment bene ts is a better tool for insuring workers than just unemployment bene ts. That is, severane payments an omplement unemployment bene ts when unemployment is ause by both job estrution an mathing fritions.. Relate Literature While muh work in labor/maro eonomis fouses on the aministrative ost aspet of employment protetion, Pissaries (00) onstruts a moel to highlight the insurane motive for severane payments. In his setting, rms an provie insurane to workers through severane payments. Essentially, 5

6 rms reue the wages of employe workers an make a payment to them when the workers are re. Now, if rms an o this, then there won t be a nee for government intervention. However, there are reasons why rms may not be willing or able to o er insurane through severane payments. One possible reason is wage rigiity as highlighte in a moel by Garibali an Violante (005). Note that in orer for rms to o er insurane through severane payments, they shoul have the ability to reue the wages of employe workers. However, wage rigiity may prevent them from oing so. Alternatively, severane payments rely on a ontrat that a rm has to enter into with the workers whereby workers agree to a lower wage so that they an get severane payments when they are re. However, a rm may renege on its severane payments obligations later. In this ase, a worker may be fore to take the efaulting rm to the ourt. Getting the ontrat enfore may be ostly for an iniviual worker. A legislation requiring severane payments may be easier to enfore than an iniviual ontrat. There is a large literature on globalization an labor markets using searh moels of unemployment. While muh of this literature uses a ynami framework, Keushnigg an Ribi (009) an Helpman an Itskhoki (00) showe that the key insights an be as easily generate using a stati framework, whih is the approah taken in the present paper as well. Helpman an Itskhoki (00) also provie an extension where they stuy the role of ring ost in a setting where rms re an exogenous fration of mathe workers. This extension is loser to our set up, however, in our ase the fration re is enogenous. Also, sine workers are risk neutral in Helpman an Itskhoki (00), ring ost oes not have the insurane role whih is a key feature of our moel. Our proution struture with heterogeneous math spei proutivity of workers is similar to Helpman, Itskhoki an Reing (00). In their moel rms have to sreen the mathe workers after bearing a ost to n out if the proutivity of workers is above a uto. Workers below the uto are not hire. Given rm heterogeneity, more proutive rms sreen more whih leas to i erent rms having workers with i erent average proutivities resulting in i erent wages. This set up allows them to stuy the impliations of globalization for wage inequality. Sine our aim is to erive poliy impliations when the ost of o shoring ereases, we reate a simpler framework with homogeneous rms where the math spei proutivities are observe ostlessly an rms retain only workers above the pre-annoue level of proutivity an all the retaine workers are pai the same wage. Given our aim to stuy o shoring, our proution funtion also inlues an input whih is o shore, an omesti labor an o shore inputs are ombine using a CES proution funtion. 6

7 While most of the reent papers on labor market impliations of globalization use moels with risk neutral workers thereby obviating the nee for soial protetion, there is an oler literature in international trae ealing with risk averse agents. For example, Dixit an Rob (994) show how trae may be inferior to autarky in the presene of missing insurane markets when iniviuals are risk averse. Due to missing insurane markets, the eentralize solution i ers from the planner s problem an hene trae an be inferior to autarky or even a tari equilibrium an be inferior to autarky. This is similar in spirit to our result esribe earlier that when omesti labor is a goo substitute for o shore inputs, o shoring an reue aggregate welfare. However, they o not isuss the role of soial protetion in proteting workers. Among other relate papers, Braner an Spener (994), Feenstra an Lewis (994), an Davison an Matusz (006) stuy various poliies to ompensate the workers who lose from trae. However, workers are risk neutral in these papers. Closer to our approah is the paper by Breher an Chauhuri (994) whih examines the issue of Pareto superiority of free trae over autarky through Dixit-Norman ompensation shemes when there is unemployment in the eonomy ause by e ieny wage onsierations an unemploye workers get an unemployment ompensation. In this setting, workers who beome unemploye ue to trae an be fully ompensate for their losses only if unemployment bene ts beome equal to the wages. However, in this ase, no e ort will be unertaken by any worker, an hene output will beome zero. Therefore, fully ompensating workers who lose their jobs is not feasible. Even though this paper has unemployment as well as unemployment ompensation, workers are risk neutral an hene the insurane motive for unemployment bene ts is not present. The paper most losely relate to our work is Keushnigg an Ribi (009), whih to the best of our knowlege is the only paper to stuy the poliy impliations of o shoring in a moel with searh fritions an risk averse workers. Our moel i ers from their moel in several respets. While they assume omesti labor an o shore inputs to be perfet substitutes, we work with a CES proution funtion whih allows us to stuy ases when o shore inputs are omplementary to omesti labor as in the seminal paper by Grossman an Rossi-Hansberg (008) where this raises the possibility of wages inreasing for workers whose jobs are o shore. In fat, we get a uto value of the elastiity of substitution parameter suh that if the elastiity of substitution is higher than the uto then the workers are hurt by o shoring, but gain otherwise. Aitionally, while in Keushnigg an Ribi (009) unemployment arises solely beause some workers are unmathe, in our baseline moel unemploy- 7

8 ment arises solely from the ring of workers while in the extension unemployment arises ue to both mathing fritions an enogenous job estrution. As well, while Keushnigg an Ribi (009) fous on unemployment bene ts, we fous on employment protetion poliies as an alternative way to provie soial protetion, an in this sense the two papers are omplementary. More substantively, we show that if unemployment arises solely ue to job estrution then severane payments an be a superior tool for insuring workers than unemployment bene ts. When unemployment arises ue to both job estrution an unmathe workers, a poliy that ombines severane payments an unemployment bene ts an be superior to unemployment bene ts only. In the next setion we present the baseline moel without searh fritions. Setion 3 stuies the impliations of o shoring for labor market an welfare an onuts the poliy analysis. Setion 4 presents the extension with searh fritions. Setion 5 provies onluing remarks. The Moel The proution funtion is given by Z = A((L e ) + M ) ; 0 < < () where L e is the omesti labor in e ieny units an M enotes foreign proue inputs. aptures the elastiity of substitution between omesti labor an foreign proue inputs an aptures the iminishing returns an is useful in making the rm size eterminate. Also, there is a ontinuum of omesti rms of unit mass so there is no istintion between a rm level variable an an eonomy level variable. Workers are iential ex ante but their math spei proutivity, enote by, is rawn from a istribution G(). In the benhmark moel we assume the mathing to be fritionless an later we exten the moel to allow for mathing fritions. One the math spei proutivity of a worker is reveale, the rm an eie whether to retain the worker or re them. There are two osts of ring workers: f t is the aministrative ost while f w is the manate severane payment that goes to re workers. If rms use a uto rule whereby they retain workers with proutivity above an re others, then the average proutivity of retaine workers is Z G() () G( ) 8

9 If they hire L h workers then they retain ( e ieny units that is use in proution is G( )) L h of them, an hene the amount of labor in L e = ( G( )) L h = L; (3) where L is the number of workers retaine by the rm. The above implies that rms fae a quantityquality trae-o in the hiring of workers. To proue a given level of output, they an go for higher quality an lower quantity or vie-versa. Sine ring is ostly, higher quality omes at a higher ost. Denote the aggregate pro t of rms by : The total number of workers in the eonomy is enote by L: A fration t [0; ] of the pro ts oul go to workers where t oul either be base on their ownership of rms or it oul be an instrument of reistributive taxation by the government. Therefore, eah worker has a possible non-wage inome given by = t L (4) In the benhmark ase we are going to assume t = 0, that is, workers o not get any share of pro ts an hene = 0: Later while isussing poliy we will isuss the ase of t > 0: Workers are risk averse. Their utility funtion is given by U(x); U 0 > 0; U 00 < 0 (5) where x is their inome in a partiular state: employe or unemploye. Sine all workers are mathe in the baseline moel an some are retaine while others are re, the inome of workers when they are retaine is x = w + ; where w is the wage an is their share of pro ts, while the inome when they are re is x = f w +z + where z is the value of leisure/home proution, an f w is the severane payment. Firms post wages an ring rates to attrat workers. Denote the wage rate poste by rm-i by w i an the uto proutivity by i : Workers iret their appliations to the rm whose (w i ; i ) pair gives them the highest expete utility. Suppose W is the highest utility that a worker an expet from a job at another rm. Now, in orer to attrat workers, (w i ; i ) must satisfy ( G( i )U(w i + ) + G( i )U(f w + z + ) W (6) E etively, for any ring rate that the rm posts, (6) etermines the wage that the rm has to o er. 3 If a rm wants to raise the average proutivity of its workfore by being more seletive (higher i ) then 3 Note that this way of moeling labor market is similar in spirit to the ompetitive searh framework of Moen (997) 9

10 it will have to o er higher wages. Even though looking at (6) one gets the impression that rms an hoose i erent pairs of (w; ) to satisfy (6), it an be shown from the rm s maximization exerise that all rms en up posting the same wage rate 4. Therefore, in the analysis below we rop the rm subsript i: Given the above esription of the moel, one an raise the question that why on t the rm an the worker renegotiate wages one the math spei proutivity is realize as happens in the stanar Mortensen-Pissaries (994) set up after the realization of a shok. One way to justify our set up woul be to assume that rms get a noisy signal of a worker s math spei proutivity as in Helpman, Itskhoki, an Reing (00). That is, if a rm hooses a uto ; it only knows whether the worker s proutivity is above or below : In Helpman, Itskhoki, an Reing (00) if rms inur a sreening ost of ( ) they learn whether the worker s proutivity is above or below ; where 0 ( ) > 0. Sine their aim is to erive wage heterogeneity in a moel with rm heterogeneity, this is an essential omponent of their moel. We work with a representative rm moel, an sine there are alreay osts assoiate with ring workers isusse above, the introution of sreening ost just as to those osts an oes not hange our qualitative results. Therefore, our set up an be thought of as one where ( ) = 0. Denote the per unit prie of the importe/o shore input by : Now, rms perform the following pro t maximization exerise. subjet to the onstraint Max A( L L;M;w; + M ) wl G( ) G( ) (f w + f t ) L M ( G( ))U(w + ) + G( )U(f w + z + ) W (7) an Aemoglu an Shimer (999) where rms post wages an workers iret their searh. The i erene is that in the ompetitive searh framework rms post wages, whih for a given W etermines the length of the queue, q i; an onsequently how fast the vaany is lle. That is, a rm is hoosing a pair (w i; q i) to ensure that the worker gets a utility of W; while in our framework the rm hooses (w i; i) to ensure that the worker gets a utility of W: 4 This an be aomplishe by noting that the wage rate an be expresse as a funtion of W an in the rm s maximization exerise. Sine eah rm takes W as given, it ens up hoosing the same ; whih implies the same wage rate. 0

11 Using % to enote the Lagrangian multiplier on the onstraint above, the rst orer onitions for the above maximization are given by L : A( L + M ) L G( ) = w + G( ) (f w + f t ) (8) M : A( L + M ) M = (9) w : L + %( G( ))U 0 (w + ) = 0 (0) : A G( ) ( L +M ) L = (f w + f t ) L ( G( )) +%U((w +) U(f w +z +)) () Intuitively, the l.h.s of (8) is the marginal prout of an aitional retaine worker while the r.h.s is the expete ost of a retaine worker: wage plus the separation ost (for eah retaine worker the rm hires G( ) workers, a fration G( ) of whom is re resulting in a separation ost of G( ) G( ) (f w + f t )): Similarly, the l.h.s of () is the bene t of a higher, whih for a given L results in higher average proutivity of these workers. The r.h.s is the ost of a higher resulting from greater separation G( ost pai to workers who are not retaine (for eah retaine worker, the number re is ) G( ; an ) g( inrease in inreases the number of workers re per retaine worker by ) :) an higher ( G( )) wages to satisfy the wage onstraint beause the probability of getting re is higher whih must be o set by a higher wage. The last omponent is relate to the risk aversion of workers. The greater the risk aversion, the greater the ost in terms of meeting the reservation wage of workers. Also, while f w an f t a et the ost of an extra retaine worker symmetrially, they have i erent e ets on the etermination of : While an inrease in f t makes going for higher more expensive, an inrease in f w has two opposing e ets: The separation ost pai by the rms inreases but the reservation wage onstraint is relaxe. The latter arises ue to the insurane role of severane payments an therefore is stronger the more risk averse the worker. Sine all workers are mathe, the number employe simply equals the number re an therefore, the aggregate labor market equilibrium onition is given by Upon using () the expression for aggregate pro ts is given by L = L( G( )) () = A( ( G( ))L + M ) w( G( ))L G( ) (f w + f t ) L M: (3)

12 Therefore, is given by = t A( ( G( ))L + M ) w( G( ))L G( ) (f w + f t ) L M : (4) L The 6 equations (8)-(), () an (4) etermine w; L; M; ; % an : It is shown in the appenix that using (8)-() an () we an obtain the following two key equations in w an whih are useful for proving the existene of equilibrium as well as omparative statis. (fw + f t ) w = G( ) G( ) + (5) A( +! ( ) ) L ( G( ) ) = w ( G( )) + G( ) (f w + f t ) (6) where we use the following ompat notation. In rest of the paper we make the following two funtional form assumptions for analytial tratability. U(w + ) U(f w + z + ) U 0 (w + ) ;! w + G() G( ) (f w + f t ) Assumption : G() is Uniformly istribute over [0; ]: This is a stanar istributional assumption in the literature on enogenous job estrution (e.g. Mortensen an Pissaries (994)). 5 Assumption : Utility funtion U(x) is of CRRA type, that is x U 00 (x) U 0 (x) is onstant. The existene of equilibrium for the baseline ase of t = 0 is prove in the appenix. In the analysis below the efault is the t = 0 ase unless iniate otherwise. 3 O shoring, Unemployment an Welfare Now we are reay to analyze the impat of o shoring on the labor market, the welfare of workers, an aggregate welfare. The impat of o shoring is going to be apture by a erease in the ost of o shore inputs, : The following proposition is easily prove in the appenix. 5 All the analytial an numerial results in the paper have been erive for Pareto istribution as well. They are available upon request.

13 Proposition : A reution in the ost of o shoring inreases wages an reues unemployment if < ; leaves them unhange if =, an reues wages an inreases unemployment if > : Intuitively, a erease in has two e ets on the eman for omesti labor. Sine o shore inputs are heaper now, rms substitute away from omesti labor. However, there is a proutivity e et arising from the inrease usage of o shore inputs. That is, the inrease usage of o shore inputs inreases the marginal prout of omesti labor. For > the substitution e et ominates, an hene the eman for omesti labor ereases. As rms reue their eman for omesti labor, the expete rewar of labor, W; ereases. This erease in W allows rms to raise : More mehanially, at the aggregate level the amount of labor employe in e ieny units is L e = ( ) L: Therefore, the only way the amount of labor employe in e ieny units an erease is through an inrease in : as The measure of welfare of workers is simply W whih for uniform istribution of an be written W = ( )U(w + ) + U(f w + z + ): (7) Aggregate welfare is given simply by the sum of welfares of workers an pro t owners: SW = + LW The expressions for the impat of o shoring on the welfare of workers an aggregate welfare for the ase of t = 0 (erive in the appenix) are given by W + LW = U 0 (w) ( ) w = (U 0 (w) )L ( ) w (8) M (9) Before isussing the welfare impliations of o shoring further for the ase of risk averse workers, it is useful to note the results for the ase of risk neutral workers: U(w) = w. The following result is easily veri e from (8), (9), an proposition. Proposition : When workers are risk neutral, o shoring inreases workers welfare if < ; leaves it unhange if = ; an reues it otherwise. However, o shoring always inreases aggregate welfare. The result above shows that if there are no istortions in the eonomy arising from either the risk aversion of workers or reistributive onsierations, then o shoring, whih is like a positive proutivity 3

14 shok, is welfare improving for the eonomy as a whole. Going bak to the ase of risk averse workers, there are two relevant ases for the welfare impliations of o shoring. Case : < ) w < 0 an > 0: In this ase, o shoring inreases the welfare of workers as well as aggregate welfare as long as U 0 (w) > : In aition to the iret proutivity enhaning bene ts of o shoring, it interats with the two istortions present in a positive way. If U 0 (w) >, then a shift of inome in favor of workers is welfare improving. Therefore, o shoring inue rise in wage an eline in shifts inome away from pro ts towars workers. This reistributive e et is welfare improving beause workers are poorer than pro t owners (U 0 (w) > ): O shoring also inreases the welfare of risk averse workers by mitigating the risk through a erease in : Case : > ) w > 0; < 0; an < 0: Sine U 0 (w) > ; the reistribution of inome away from workers an towars pro ts is welfare reuing. Also, the o shoring inue inrease in is ba for workers beause the probability of low inome state is rising. This e et is stronger the more risk averse the worker. If the insurane market was omplete, this averse e et through a rise in woul be absent. The pro ts inrease unambiguously. Therefore, the impat on aggregate welfare is theoretially ambiguous. Numerial simulations reveal that when the egree of risk aversion is high, aggregate welfare ereases as the ost of o shoring ereases. Figures an provie numerial examples. Both gures are base on a CRRA utility funtion of the type U(x) = x where is the oe ient of risk aversion. In gure = :5 (low risk aversion) an in gure = 3 (high risk aversion): In both ases as the ost of o shoring ereases unemployment ( ) inreases ( gures a an a) an wages erease ( gures b an b) an onsequently the welfare of workers ereases ( gures an ). The i erene is in aggregate welfare. While in panel aggregate welfare inreases when the egree of risk aversion is low, in panel aggregate welfare ereases with a higher egree of risk aversion. 6 Sine wages erease an pro ts inrease, the inequality in the istribution of inome as measure by pro ts to wage inome also rises. The results erive above are summarize in the proposition below. 6 In all gures the numbers for welfare are negative. The negative sign is not obvious in the gures beause of the onversion from powerpoint to pf. 4

15 Proposition 3: When < ; o shoring reues unemployment an inreases wages, thereby, inreasing the welfare of workers as well as the aggregate welfare. When > ; not only oes the welfare of workers erease but the aggregate welfare an erease as well. In the latter ase, there is an inrease in inequality in the istribution of inome as well sine pro ts rise an wages erease. It follows from proposition 3 that there may be a ase for reating obstales to o shoring if no other poliy interventions are available. Sine o shoring ereases the welfare of workers an possibly aggregate welfare when > ; our isussion of various poliies below fouses on this ase. 3. Change in the aministrative ost of ring The rst poliy that we onsier is the hange in the aministrative ost of ring. Sine o shoring inreases unemployment in the relevant ase ( > ); it is tempting to argue that an inrease in the aministrative ost of ring an inrease the welfare of workers by reuing unemployment. We show below that even though an inrease in f t is likely to reue unemployment, it ens up reuing the welfare of workers. The following lemma summarizes the impat of o shoring on wages an unemployment. Lemma : An inrease in f t reues wages an is likely to reue unemployment for reasonable parameter values. Intuitively, at the rm level an inrease in f t inues rms to lower the proutivity uto beause ring workers is ostlier. For a given W, if they go for lower they an satisfy the worker s outsie option onstraint with a lower w. Therefore, at the rm level, for a given W; there is a erease in w an : As rms reue, the amount of labor employe by rms inreases whih puts a ownwar pressure on the rewar of labor re ete in W: The erease in W has a feebak e et on the rms hoies of w an : A lower W implies that rms an satisfy the onstraint with a higher or a lower w: Therefore, the feebak e et on w is in the same iretion as the original e et of an inrease in f t ; however, the feebak e et on is in the opposite iretion, reating the theoretial ambiguity. For reasonable parameter values 7 the iret e et on ominates the feebak general equilibrium e et, leaing to a erease in : A lower implies less job estrution an lower unemployment at 7 A su ient onition for to be ereasing in f t is < +. 5

16 the aggregate level. That is, in the equilibrium with higher ring osts the amount of labor employe by rms inreases. The impat of a hange f t on the welfare of workers is given by W f t = ( )U 0 (w) w f t (U(w) U(f w + z)) f t Lemma implies that the impat of an inrease in f t on the welfare of workers is ambiguous beause workers gain from a lower but lose from a lower wage. However, a little bit of algebra shows that the wage e et always ominates an therefore, an inrease in f t reues the welfare of workers. This gives us an important result. Proposition 4: An inrease in the aministrative ost of ring ereases wages an is likely to erease unemployment by reuing job estrution. However, it unambiguously reues the welfare of workers. With risk averse workers, the level of ring is sub-optimal in our set up. Inrease aministrative buren of ring makes it ostlier for rms to re, therefore, it worsens the existing istortion an ens up making the workers worse o. That is, this is a poliy whih is going to hurt the intene bene iaries. Therefore, greater aministrative buren of ring annot be use to shiel workers from the averse onsequenes of o shoring. 3. Change in Severane Payments Before stuying the impat of a hange in f w when workers are risk averse, it is useful to stuy the impat of a hange in f w when workers are risk neutral. The following lemma is easily prove in the appenix. Lemma : When workers are risk neutral, an inrease in severane payments has no impat on unemployment. Firms ajust wages by an amount that leaves the welfare of workers as well as pro ts unhange. The above neutrality result of severane payments in the risk neutral worker ase is important in unerstaning its role in proviing insurane an istinguishing it from unemployment bene ts. Intuitively, in the absene of insurane nees for risk neutral workers, severane payments just make ring more ostly for rms, whih the rms o set by lowering wages, thereby leaving the rate of ring an worker welfare unhange. 6

17 Moving to the ase of risk averse workers, we obtain the following results on the impat of a hange in f w : Lemma 3: When workers are risk averse, an inrease in severane payments inreases job estrution ( ) but has a non-monotoni e et on wages. When workers are risk averse an the market for insurane against labor inome risk is missing, it is ostly for rms to re workers. Sine severane payments provie insurane to workers, it allows rms to go for higher quality workers by hoosing a higher : The impat on wages is theoretially ambiguous but numerial simulations reveal the following pattern. Starting from no severane payments, an inrease in severane payments inreases wages initially, but beyon a point wages start ereasing. The reason is the general equilibrium e et of an inrease in inue by the inrease in f w. The lower employment of workers at the aggregate level implies higher W given iminishing returns to labor. The higher W; in turn, requires higher wages when f w is low, but at higher levels of f w rms an a or to pay lower wages an still meet the reservation utility of workers. In all ases, however, the welfare of workers, W; inreases. It is this feature of severane payments that makes it a aniate for a poliy to protet workers against the possible averse e ets of o shoring. 3.. Severane payments in response to o shoring Suppose the level of severane payments is sub-optimal to begin with. The question is an an inrease in severane payments allow o shoring to inrease aggregate welfare without reuing the welfare of workers. That is, an severane payments be use to soften the blow of o shoring on workers without ausing aggregate welfare losses. From (7) note that the hange in the welfare of workers in response to o shoring an hange in severane payments is W = ( )U 0 (w)w + U 0 (f w + z)f w (U(w) U(f w + z)) (0) Sine at f w = 0 o shoring auses a erease in welfare (when > ), to ompensate the losses of workers we must have f w > 0: The level of f w that keeps the worker welfare unhange in response to an o shoring shok is obtaine by setting W = 0 above an is given by f w = ( + ') ( ( )w) () 7

18 where = U(w) ' w z fw w : U(fw+z) U 0 (w) sine = 0 an using linear approximation U 0 (f w+z) U 0 (w) What is the impat of this hange in f w on pro ts? erive in the appenix, note that ( + ') where From the expression for hange in pro ts = L ( ( )w) Lf w M () Using () in () we get = 'Lf w M (3) Sine f w > 0; the ompensating hange in f w in response to a erease in inreases pro ts. That is, a ompensating inrease in severane payments leaves pro ts higher than before the hange in : Therefore, the aggregate welfare ( + LW ) is higher as well. This gives us the following result. Proposition 5: When o shoring auses welfare losses for workers ( > ) an inrease in severane payments that keeps the welfare of workers unhange allows the pro ts to be higher than the pre-o shoring pro ts. The above result is also veri e numerially. An example is inlue in gure 3 whih is onstrute for the ase of = 3: As shown in gure, a erease in the o shoring ost leas to a erease in aggregate welfare in this ase. Figure 3 is onstrute by setting f w suh that the welfare of workers is hel onstant at the initial value of = :5. Again, a reution in o shoring ost inreases unemployment as shown in gure 3a. Figure 3b shows that the level of severane payments require to keep the welfare of workers onstant inreases as ereases. Figure 3 shows that the pro ts still inrease as ereases, an most importantly, gure 3 shows that the aggregate welfare inreases as ereases. This shoul be ontraste with gure where the aggregate welfare ereases as ereases. Therefore, an inrease in severane payments o sets the losses of workers from o shoring without making pro t owners worse o. This obviously leas to an inrease in aggregate welfare. Therefore, if severane payments are sub-optimal to begin with, an inrease in severane payments is a way to reistribute some of the gains of o shoring to workers when they lose from it. 8

19 3.3 Optimal Severane payment an o shoring We are going to talk about the role of reistribution in this setion, therefore, we erive results for t 0 an onsequently, 0. Sine workers are risk averse while pro t owners are risk neutral, the optimal severane payment in the moel (both from the worker s point of view an the aggregate welfare point of view) is full insurane for any given level of o shoring ost. The following lemma is prove formally in the appenix. Lemma 4 : For all t [0; ]; the level of severane payments that maximizes the welfare of workers as well as aggregate welfare is full insurane given by f w = w z: Reall that proposition was prove for the ase of t = 0: We oul not prove it analytially for t > 0: However, when > ; we an prove the following useful lemma. Lemma 5: For all t [0; ]; w > 0 when > : That is, irrespetive of the level of t; a erease in the ost of o shoring reues wages when o shore inputs an be easily substitute for omesti workers. Now, the impat of o shoring on the welfare of workers when severane payments are optimally hosen is given by (shown in appenix) W = U 0 (w + ) ( t) t M L is the hange in wage with respet to hange holing severane payments onstant.8 It follows from lemma 5 that W > 0 for t = 0 an > : That is, if workers o not get any share of pro ts, then o shoring reues their welfare in the relevant ase even if severane payments are hosen to maximize their welfare. The impat of o shoring on aggregate welfare in the presene of optimal severane payments is given by ( t) + LW = U 0 (w + ) L( M( + t U 0 (w + ) ) (5) Therefore, when t = 0 an U 0 (w + ) >, o shoring an reue aggregate welfare as well. This gives us the following result. 8 We are using partial erivative here beause f w is an enogenous variable in the present ase. + f w w is same as in lemma 5 beause lemma 5 was erive for the ase of exogenous fw: w = 9

20 Proposition 6: When > ; even when severane payments are optimally hosen, o shoring reues the welfare of workers an an reue aggregate welfare as well. The aggregate welfare loss in this ase arises purely beause of the averse istributional e ets of o shoring. The reason that even in the presene of soially optimal severane payments, o shoring oes not neessarily improve welfare is beause the eonomy has two istortions. While the optimal severane payment aresses the istortion arising from lak of insurane, it annot aress the istortion arising from istributional issues. To learly see the role of reistribution, note from (4) that if all pro ts are reistribute to workers (t = ); then o shoring is neessarily welfare improving in the presene of optimal severane payments. In fat, we on t nee all pro ts to be istribute to workers. From (4) verify that there exists a level of t w suh that if t > t w ; then workers gain from o shoring in the presene of optimal severane payment. The level of t w is given by t w = + M L (0; ) (6) As well, verify from (5) that there exists a t sw suh that if t > t sw ; then o shoring inreases aggregate welfare where t sw = M L(U 0 (w+) ) + M L Visual inspetion of (6) an (7) suggests that t w > t sw ; however, the r.h.s in both the expressions also epens on the level of t: Therefore, we annot laim that t w > t sw : However, we verify numerially that inee t w > t sw : That is, the share of pro ts going to workers that makes o shoring aggregate welfare improving is smaller than the one that makes o shoring worker welfare improving. A su iently high t alleviates the welfare loss from inequality in the istribution of inome, an therefore ensures that o shoring is welfare improving. The results above were erive for the ase of > ( t) + L W in summarize below. > 0: It is easy to verify from (4) an (5) < 0 then W (7) < 0 an < 0 irrespetive of the value of t: Therefore, the results are true for any an are Proposition 7: When severane payments are optimally hosen an workers get a su iently large share of pro ts, o shoring improves workers welfare an aggregate welfare irrespetive of the elastiity of substitution between omesti workers an o shore inputs. 0

21 3.4 Other Poliies 3.4. Unemployment bene ts While we have fouse on severane payments in this paper whih are pai by rms, it is also possible to insure workers against labor market risk through publily provie unemployment bene ts. Countries use i erent methos to fun unemployment bene ts. In most ases it is fune by ontributions from both employers an employees with some exeptions. In Ielan, Italy an the U.S. only employers ontribute while in Luxembourg only employees ontribute. Below we isuss two alternative ases epening on the naning of unemployment bene ts. Case I: unemployment bene ts nane by a tax on rms Suppose unemployment bene ts are nane by a tax on employers, as is the ase in the U.S. Suppose the unemployment bene ts are set at b per worker, an the government requires rms to ontribute exatly b per worker re by the rm. Then the unemployment bene t of this kin is exatly like the severane payment in our moel. However, in pratie, the amount that rms ontribute in the U.S. is only imperfetly relate to the number of workers they re in whih ase they are not going to fully internalize the ost of ring. Also, the experiene rating base funing of unemployment bene ts in the U.S. is an exeption rather than the rule. Case II: unemployment bene ts nane by a tax on workers The tax on workers oul either be a lump sum tax pai by both employe an unemploye workers as in Aemoglu an Shimer (999) or it oul be a payroll tax on only employe workers as in Keushnigg an Ribi (009). In the former ase, the onstraint faing the rms is given by ( )U(w ) + U(b + z ) W (8) where = b is the balane buget onition. In the latter ase, the onstraint faing rms is given by where = b. ( )U(w ) + U(b + z) W (9) The key equations for the etermination of key enogenous variables are given in the appenix. It is also veri e from the key equations that when unemployment bene ts are hosen optimally, the equilibrium labor market outomes are inepenent of the moe of funing unemployment bene ts.

22 Given this, in the omparison of severane payments with unemployment bene ts, we fous on the ase where unemployment bene ts are pai by a payroll tax as in Keushnigg an Ribi (009). It is lear that both unemployment bene ts an severane payments an be use to insure workers against labor market risk. The question is whih poliy is better. We attempt to answer this by omparing aggregate welfare uner optimal unemployment bene ts an optimal severane payments. Sine eriving analytial result is har, we provie numerial examples. Figure 4 is onstrute to ompare the outomes for aggregate welfare maximizing unemployment bene ts with optimal severane payments. Figure 4a shows that unemployment is higher uner unemployment bene ts (re line) than uner severane payments (blak line). In gure 4b the vertial axis is the ratio of the onsumption in unemployment state to the onsumption in employment state. There is full insurane uner severane payments as shown in the ratio of by the blak line. The re line showing the ratio for unemployment bene ts is always less than one showing inomplete insurane. Figures 4 an 4 show the worker welfare an the aggregate welfare, respetively. The blak line for severane payments is always above the re line for unemployment bene ts in both gures. That is, both the worker welfare an the aggregate welfare are higher with optimal severane payments than with optimal unemployment bene ts. Intuitively, both unemployment bene ts an severane payments reue the ost of ring workers for rms leaing to greater ring in both ases. However, in the ase of severane payments, the ost is borne by the rm itself, while in the ase of unemployment insurane workers are bearing the ost (an iniviual rm treats an b in (8) an (9) as given). As a result, there is greater ring in the ase of unemployment insurane whih leas to lower welfare. More generally, sine workers are risk averse while rms are risk neutral, the optimal risk sharing arrangement involves rms bearing the risk. Severane payments allow rms to bear the risk while unemployment insurane makes workers bear the risk. Therefore, the former yiels greater aggregate welfare than the latter. Therefore, if unemployment is ause by job estrution, then severane payments an be a better tool for insuring workers than unemployment insurane. Note, however, that severane payments annot be use to insure workers when unemployment is ause by the failure of a worker to math. In the next setion we exten the moel to inlue mathing fritions an let unemployment be etermine by both enogenous job estrution an mathing fritions. In this ase there is a role for both severane payments an unemployment bene ts.

23 4 Extension With Searh Fritions Suppose that there is a ost of posting vaanies an there are mathing fritions as in the stanara Pissaries (000) moel. Denote the ost of posting a vaany by : Assume a onstant returns to sale mathing funtion suh that the probability of a vaany being lle is ; while the probability of an appliant ning a job is where 0 < < an is the market tightness e ne as the ratio of the number of vaanies to the number of workers searhing for a job. Sine the probability of a vaany being lle is that it ens up with L h =, if a rm posts v vaanies, using the law of large numbers we an say v mathe workers. Therefore, a rm wanting to be mathe with L L h workers must post h vaanies. Given the uniform istribution of math-spei proutivity, if a rm hooses a proutivity uto of, it res ( ) of mathe workers an therefore, retains L = ( )L h = ( ) v workers. Therefore, a rm wanting to retain L workers must post v = L ( ) vaanies. The rm s maximization problem is given by Max L;M;w; ; ( A( ( + )L + M ) wl (f w + f t ) L M ) L ( ) subjet to the onstraint (( )U(w) + U(f w + z)) + U(z) W (30) The aggregate labor market onstraint is given by L = ( )L Therefore, the fration of workers who are unemploye is given by u = + That is, there are two soures of unemployment now: workers who o not get mathe an those who get mathe but are re ( ). The key equations for this ase are erive in the appenix. The key i erene in the results is that now o shoring a ets unemployment an welfare through both job reation an job estrution. That is, in aition to hanging o shoring also a ets : Figures 5 an 6 illustrate the impat of o shoring for the ase of high elastiity of substitution between omesti labor an o shore inputs 3