Search and O shoring in the Presence of Animal Spirits

Transcription

1 Search and O shoring in the Presence of Anima Spirits Devashish Mitra Priya Ranjan Syracuse University University of Caifornia - Irvine Abstract: In this paper, we introduce two sources of unempoyment in a two-factor genera equiibrium mode: search frictions and fairness considerations. We nd that a binding fairwage constraint increases the unskied unempoyment rate and can at the same time ead to a higher unempoyment rate for skied workers, as compared to an equiibrium where fairness considerations are absent or non-binding. Starting from a constrained equiibrium, an increase in the fairness parameter eads to increases in both skied and unskied unempoyment. The wage of unskied workers increases but the wage of skied workers decreases. Next we aow for o shoring of unskied jobs in our mode, and we nd that, as a resut, it becomes more ikey that the fair-wage constraint binds. O shoring of unskied jobs aways eads to an increase in skied wage, a decrease in skied unempoyment and an increase in unskied unempoyment. The presence of fairness considerations increases the adverse impact of o shoring on unskied unempoyment. The unskied wage can increase or decrease as a resut of o shoring. Key words: Fair wages, unempoyment, strategic e ect, o shoring JEL Cassi cation Codes: E24, F6, F4 Introduction Akerof and Shier (2009) in their recent book expain the importance of paying attention to anima spirits in understanding how economies behave. By anima spirits, they mean the thought patterns that animate peope s ideas and feeings. Akerof and Shier ook at various aspects of anima spirits that impact economic decision making. According to them, fairness is one such aspect (other aspects are con dence, corruption and antisocia behavior, money iusion etc.) and is the aspect of anima spirits that can ead to unempoyment. They discuss in detai how our sense of fairness resuts, up to a imit, in a positive reationship between the e ort we, as workers, put in and the wage we receive reative to what we beieve is fair, and how in turn, that can resut in the empoyer setting a wage above what cears the market. Obviousy, this resuts in unempoyment. There is now a whoe strand in the unempoyment iterature, foowing Akerof and Yeen (990), that focuses on such fairness or fair-wage considerations. It is, however, important to point out that in addition to fair-wage modes, macroeconomists use a wide variety of other modes to expain the existence of unempoyment. Prominent among them are minimum-wage modes, insider-outsider abor union modes,

2 modes based on impicit contracts, search-unempoyment modes and e ciency wages. In a fair-wage mode with skied and unskied workers, the fairness constraint usuay binds for unskied workers and is never binding for skied workers (as ong as a skied worker makes more than an unskied worker). Thus, the mode generates zero unempoyment for skied workers and a positive rate of unempoyment for unskied workers. Whie surveys of managers and workers, socioogica studies of work environments, rm-eve studies of pay structures, experiments, personne management textbooks etc. provide a weath of evidence supporting the assumption or idea of a fair-wage (see for instance Akerof and Yeen (990), Bewey (2005) and Howitt (2002) for a survey of the evidence), the prediction of a fair-wage mode, with skied and unskied abor, that skied unempoyment is zero is not very reaistic. According to the OECD Empoyment Outook (2007), whie the unempoyment rate in the US in 2006 for peope with ess than secondary education was roughy 9 percent, it was 5 percent and 2.6 percent for peope with upper secondary and tertiary education, respectivey. The EU unempoyment rates for the same year for the same three categories were 3, 7 and 4 percent respectivey. Thus, in addition to unskied unempoyment, skied unempoyment can be quite substantia. In order to generate positive unempoyment rates for both categories of workers and at the same time take the strong evidence in favor of the fair-wage hypothesis seriousy, we incorporate this hypothesis into a search mode of unempoyment. 2 Another reason for combining the two di erent strands of the unempoyment iterature is Soow s (980) insight that unempoyment in the rea word is caused by di erent sources. Moreover, we show that the two aternative sources of unempoyment we focus on, namey search frictions and the fair-wage constraint do not ead to additivey separabe e ects but actuay interact with each other in important and interesting ways to produce outcomes when the economy is hit by di erent shocks. To iustrate this point, we perform comparative statics with respect to the fairness parameter (that measures the society s preference for fairness) and the economy s stock of skied abor, and ook at the impact of o shoring. By combining search frictions with fair-wage concerns, we obtain severa new resuts. One of the resuts, which we nd quite interesting, is that introducing fairness considerations in a search mode eads not ony to an increase in the unempoyment of unskied workers, a group for whom the fair-wage constraint is binding, but can aso possiby ead to an increase in the unempoyment of skied workers, a group for whom the In fact, the fair-wage mode can be viewed as a kind of e ciency wage mode. 2 There is a very we-deveoped iterature in macroeconomics on the search theory of unempoyment. See Pissarides (2000) for an exceent and comprehensive treatment. In addition to the vast macroeconomic iterature on search unempoyment in a cosed economy, it is important to note that there aso exists a iterature on search induced unempoyment in an open economy (e.g. Davidson, Martin and Matusz (999), Davidson and Matusz (2004), Moore and Ranjan (2005), Hepman and Itskhoki (2007)). 2

3 fair-wage constraint is not binding. The intuition here can be expained as foows. Introducing fairness considerations (or increasing the preference for fairness) resuting in a binding fair-wage constraint makes it more expensive to hire unskied workers, and therefore, ess jobs are created for unskied workers eading to increased unempoyment of unskied workers. Since the number of unskied workers empoyed is now ower, given the compementarity between the two types of workers in production, we get a reduction in the margina product of skied workers. This reduces the demand for skied workers as we, uness it is o set by the strategic e ect (expained beow) which causes increased hiring of skied workers. Hence, their market tightness and wage rate may go down and we then aso get an increase in their unempoyment. Introducing a fairness ( fair-wage ) constraint resuts in a net strategic e ect in the wage and empoyment decision of rms, identi ed by Stoe and Zweibe (996), even if it is absent in net terms in the unconstrained mode. The strategic e ect in our set up can be expained as foows. In search modes, wage is positivey reated to the market tightness, which aso impies that the abor cost (wage pus recruitment cost) is positivey reated to market tightness. Therefore, the fairness constraint is ikey to bind when the ratio of market tightness for skied to unskied abor is high. A rm correcty anticipating a binding fair-wage constraint has an incentive to increase the reative empoyment of skied workers to reduce their margina product to, in turn, reduce the wage obtained through wage bargaining. Therefore, this strategic e ect causes the empoyment of skied workers (reative to unskied) to be higher than it woud be in its absence. In the unconstrained case (where there is no fairness constraint or the constraint does not bind), the "strategic e ects" of the reative empoyment of skied abor on skied and unskied wage rates are in opposite directions and cance each other out in the determination of the wage bi. In the constrained case, there is aways a non-zero net "strategic e ect" uness the production function is such that the margina product of skied workers is independent of the number of skied workers empoyed (as in the case of Leontief production function). When the strategic e ect is weak or absent, a binding fairness constraint eads to an increase in skied unempoyment, aong with the increase in unskied unempoyment. For a margina increase in the degree of fairness (when the fair-wage constraint is binding), the strategic e ect is of the second order, and hence, there is aways an increase in the skied unempoyment as we. Since the unempoyment rate and wage of skied workers move in opposite directions, the skied wage decreases, however, the unskied wage increases due to increased concern for fairness. What this impies is that when we compare two countries with di erent degrees of concern for fairness, we expect the country with a greater concern for fairness not ony to have a higher unempoyment for unskied workers, but aso to have a higher unempoyment for skied workers. The unempoyment gures we provided earier show that unempoyment rates are higher for Europe reative to the US for a educationa attainment categories of workers. This is consistent with our mode s prediction that an increase in the fairness parameter eads to higher unempoyment for both types of workers 3

4 since, based on survey evidence of attitudes to poverty and income, one can argue that socia norms of fairness are stronger in Europe than in the US. According to cacuations by Aesina and Gaeser (2005), based on data from the Word Vaues Survey for the years , whie ony 29 percent of the responders from the US beieve that the poor are trapped in poverty, about 60 percent of the European responders beieve this to be the case. Furthermore, ony 30 percent in the US beieve that uck determines income, whie 54 percent in the EU beieve in uck being a determinant. Aesina and Gaeser aso nd that 60 percent of the Americans surveyed beieve that the poor are azy, whie ony 26 percent of the EU nationas surveyed beieve so. 3 Finay, using the Internationa Socia Survey Program (ISSP) surveys of pubic opinion, Osberg and Smeeding (2006) nd in the case of the US ess concern for eveing up at the bottom of the distribution than in other nations. That is, there is ess concern for raising the income of the poor reative to the mean income in the US than in other countries. Next, we nd that introducing fairness considerations in a search mode of unempoyment aso eads to the possibiity of mutipe equiibria. As discussed earier, the fair-wage constraint binds if the market for skied abor is tight reative to the market for unskied abor. If rms expect the ratio of market tightness of skied to unskied to be high and therefore the fair-wage constraint to bind, they wi end up hiring more skied workers reative to unskied workers due to the strategic e ect discussed earier. This, in turn, wi make the reative market tightness for skied workers higher creating a sef-fu ing prophecy. We nd that the possibiity of mutipe equiibria exists for intermediate eves skied-to-unskied abor endowment ratios. Thus, the impication here is that, in this intermediate range of ski abundance, countries with identica preference for fairness and with identica reative factor endowments can have di erent wages and unempoyment rates. Looking at the impact of a reduction in ski endowment on unempoyment, we nd that the presence of a fair-wage constraint (in addition to search) ampi es the adverse e ect on unskied unempoyment. That is, the increase in unskied unempoyment is arger as a consequence of a decrease in ski endowment when the fair-wage constraint is binding. Therefore, the fair-wage constraint makes the impact of a decrease in ski endowment on unskied unempoyment worse. Finay, we ook at the impact of o shoring on unempoyment and wages in the presence of fairness considerations and search frictions. Both in the presence and absence of fairness considerations (with search frictions present in both cases), o shoring of unskied jobs increases skied wage, reduces skied unempoyment and increases unskied unempoyment. The reason is that the input produced by foreign abor in the 3 Aesina and Angeetos (2005) point to the fact that whie the pre-tax inequaity is much higher in the US than in Europe (Gini coe cient of 38.5 as opposed to 29.), the redistributive poicies are much more extensive and the tax structure much more progressive in the atter. They argue that "the di erence in poitica support for redistribution appears, rather, to re ect a di erence in socia perceptions regarding the fairness of market outcomes and the underying sources of income inequaity." 4

5 mode is a substitute for domestic unskied abor, and through this competitive e ect, o shoring reduces the tightness in the unskied abor market. Thus, the cost of hiring domestic unskied abor aso goes down. Due to the compementarity between skied abor and the production input of domestic unskied abor (or that produced by foreign abor), we get an increase in the demand for skied abor and increase in skied-abor market tightness. The presence of fairness considerations makes the impact of this kind of o shoring on unskied unempoyment worse because in addition to the reduced market tightness in the unskied abor market coming from the direct competitive pressure from the substitutabe input produced by foreign abor, there is an indirect upward pressure on unskied wages coming from the fact that o shoring can convert a non-binding fairness constraint into a binding one. This can make the impact of o shoring on the unskied wage ambiguous. In fact, if the fair-wage constraint is binding before and after o shoring, contrary to genera perceptions, we wi get an increase in the unskied wage as a resut of o shoring (as skied and unskied wage wi be moving in the same direction). Finay, the fair-wage constraint aso a ects the amount of o shoring in equiibrium. We get more o shoring in the presence of fair-wage considerations. Aso, the extent of o shoring increases as the society s preference for fairness increases. Looking at reated iterature, Kreickemeier and Neson (2006) extend the Akerof and Yeen (990) mode to a two-sector setting to study the impact of internationa trade and technoogy shocks on unempoyment and reative wages. 4 They show that trade between US and Europe, with the preference for fairness being greater in the atter, eads to reduction in wage inequaity and increase in unempoyment in the US and increase in wage inequaity and reduction in unempoyment in Europe. They aso anayze how trade with the newy industriaizing countries (NICs) a ects wage inequaity and unempoyment di erenty in these two regions. Cahuc and Zyberberg (2004) (in subsection 2.6 of Chapter 0 of their book) compare the Ango-Saxon abor market with the European abor market. Whie search frictions with skied and unskied workers are incorporated in both these types of markets, the European abor market aso has an endogenous minimum wage for unskied workers that is proportiona to the skied wage, i.e., notions of fairness and equaity are incorporated into the determination of the minimum wage. This is very simiar to the concept of the fair wage that we use in this paper. However, the focus of Cahuc and Zyberberg (2004) is imited to a comparison of the e ects of ski-biased technoogica change on the two types of abor in the two abor markets. They assume that each type of abor speci cay produces excusivey a particuar intermediate good in an industry devoted to such production, and then there is a na good industry where the two intermediate goods are combined to produce the na good. By separating the two types of workers to work in di erent rms in di erent sectors, Cahuc and Zyberberg abstract from what we ca in our paper strategic e ect and as a 4 See aso Age and Lundborg (995). 5

6 resut do not have the "mutipe-equiibria" case that we nd. As we, the vast empirica iterature on the fair-wage hypothesis suggests that whie the notion of "fair wage" can be based on wage comparisons across occupations and ski types, it is hardy ever based on comparisons across sectors. To keep the comparison between skied and unskied wages in the same industry to arrive at the fair wage, both types of workers in our mode are empoyed in the same rm. This feature gives rise to the cross-factor strategic e ect (in addition to the own strategic e ect ) in our mode, which means that not ony can the empoyment eve of one type of workers a ect the negotiated wage of that worker type, it can aso a ect the negotiated wage of the other kind of workers. This is taken into account in both the rm s maximization probem and the wage negotiation process. In addition, the empoyment of both types of workers by the rms aows us to study the impications of o shoring of the job done by one type of workers. Cahuc and Zyberberg do not ook at o shoring to which we devote a substantia part of our paper. Finay, we perform severa di erent types of comparative static exercises, incuding anaysis of shocks that move us from a situation of nonbinding to binding "fair-wage" constraint. Another recent reated paper is Grossman and Hepman (2008). In that paper, the utiity derived by a worker is increasing in her own wage but decreasing in the average wage of the rm. This utiity has to be above a threshod for the participation constraint of the worker to be satis ed. Thus, under certain conditions, Grossman and Hepman are abe to get an equiibrium where in some rms, a arge number of unskied workers (reative to the number of skied workers) work at a very ow wage ( rm-eve average wage is ow) and in others, a sma number of unskied workers work at very high wages ( rm-eve average wage is high). Since the e ect of own wage and average rm wage are in opposite directions in the worker s utiity function, the two types of rms resut in the same eve of worker utiity. There is no unempoyment in the Grossman-Hepman mode since workers can be empoyed at very ow wages as ong as the average wage in the rm is ow. In order to get rid of ine ciencies caused by jeaousies or fairness considerations, rms o shore the work of unskied workers in their mode. The assumption driving this resut is that for a mutinationa rm, ony the average rm wage for operations carried out within the domestic boundaries of a country enters the domestic worker s utiity function. Again, there is no unempoyment of any kind in this case. A resut in the Grossman-Hepman paper that is simiar to ours is the direct positive reationship between the strength of the preference for fair wages and the extent of o shoring, even though the motivation for o shoring in our mode is very di erent from theirs. Before ending the introduction, we woud ike to reiterate and substantiate our earier caim that the e ects of shocks on wages and unempoyment rates in our mode are not additivey separabe into e ects that one woud see in a pure fair-wage mode and a pure search mode. 5 By incorporating search frictions 5 Whie the pure fair-wage mode is worked out in the appendix, the unconstrained case in the main text is nothing but a pure search mode. 6

7 in a fair-wage mode of unempoyment, not ony do we triviay generate skied unempoyment, but more substantivey, identify another margin of adjustment to shocks in the form skied unempoyment or market tightness for skied workers. In a pure fair wage mode, the margins of adjustment are skied wage and unskied unempoyment, therefore, the impact of shocks on unskied unempoyment may be exaggerated and the impact on skied unempoyment understated. For exampe, starting from an equiibrium where the fairness constraint binds, an increase in the preference for fairness has no impact on the skied unempoyment in the pure fair-wage mode, but skied unempoyment increases unambiguousy in the hybrid (fair wage pus search frictions) mode. Looking at the o shoring of jobs done by unskied abor, we nd that o shoring can ead to compete unempoyment of unskied workers in a pure fair-wage mode because skied wage rises and consequenty fair wage rises to a eve that makes it unpro tabe for rms to empoy unskied workers. However, in our hybrid mode, skied wage does not rise as much because a part of adjustment takes pace through a tightening of skied abor market, resuting in ower skied unempoyment. Thus, the increase in skied wage, and hence, in the fair wage is ess, which aeviates the impact of o shoring on unskied unempoyment. 2 The Mode 2. The Goods Market The economy comprises three types of agents: S skied workers, L unskied workers, and a arge number of entrepreneurs. Entrepreneurs have access to technoogy to produce a na good, Z, using skied and unskied abor. The production function for the na good Z, which is constant returns to scae, is given by Z = F (" s s; " ) () where s and ; respectivey, are the numbers of skied and unskied workers empoyed, and " s and " are the e orts undertaken by the two types of workers which depend on the fairness considerations as discussed beow. We aso assume that the na good, Z; is the numeraire. 2.2 The Labor Market Our description of abor market is a combination of a static version of Pissarides (2000) (aong the ines of Hepman and Itskhoki (2007)) and Akerof and Yeen (990). Entrepreneurs must post vacancies to hire skied and unskied workers to undertake production. Once a vacancy is matched with a worker, she is hired to work for that rm (entrepreneur). Each worker has one unit of abor to devote to market activities, however, workers choose their e ort at work, "; where " 2 (0; ]: Foowing Kreickemeier and Neson (2006) 7

8 we postuate the foowing instantaneous utiity function for a worker of type-i: G(C i ; " i ) = g(c i ) + 4" i (2) where C i is the consumption of the na good by the worker of type-i and 4" i j" i " n i j is the degree of norm vioation for a worker of type-i: The e ort norm of worker of type-i is determined by " n i = min( w i wi ; ) (3) where w i denotes the fair wage for a worker of type-i and w i is the actua wage paid: From the utiity function in (2) it is obvious that once a worker s wage is set, she aways chooses " i = " n i to maximize utiity. Therefore, (3) above impies that workers provide the norma eve of e ort, which is set to, if they receive at east their fair wage. The abor markets for both skied and unskied are characterized by a matching technoogy that depends on the number of searchers (size of the abor force) and the number of job vacancies. Pissarides (2000) describes the empirica support for a constant returns to scae matching function, which is what we use in this paper. Let u i denote the unempoyment rate of factor i, i the vacancy rate (i.e., the number of vacancies divided by the abor force), S the economy s endowment of skied abor, and L the endowment of unskied abor. Since the mode is static where a workers search for a job, and a fraction u i of workers of type-i is matched, i is aso the measure of market tightness. Then, we write the number of matches for each factor as constant-returns-to-scae functions as foows: De ne m s M(sS;S) S M( s S; S) = M( s ; )S (4) M( L; L) = M( ; )L (5) = M( s ; ) and m M( L;L) L = M( ; ) as the matching rates for the two factors, where m 0 ( i ) > 0. De ne q( i ) mi i : The constant returns to matching impies q 0 ( i ) < 0: With this notation, the probabiity of nding a job for a searcher of type- i is i q( i ), and the probabiity of ing up a vacant job is q( i ). The former is an increasing function of market tightness, and the atter is a decreasing function of market tightness. The number of vacancies that a rm needs to create for it to expect to create one job at the end of the matching process is q( i) : For a arge rm, by the aw of arge numbers the actua ratio of vacancies to jobs (matches) created wi be q( i) : We wi restrict attention to the case where skied workers woud never prefer to search for an unskied job, even if that were possibe. 6 Note once again that the mode is static (one-period). The unempoyment 6 This can be done by imposing reasonabe restrictions on the parameters of production and matching functions and on the reative factor endowments of skied and unskied abor. 8

9 rate for each factor is given by: u i = m i = i q( i ) (6) An entrepreneur posting vacancies must pay a recruitment cost of c i (i = s; ) units of the na good per vacancy posted. Since a rm needs to post q( i) empoyed equas vacancies to create one job, the vacancy cost per worker c i q( i) : Once a job is ed, the entrepreneur receives the vaue of the margina product of that factor ess the factora wage, w i, where the wage is denoted in units of the na good. We sove the entrepreneur s probem in two stages. In the rst stage, empoyment and the number of vacancies are chosen, anticipating the wages as functions of skied and unskied empoyment (determined through bargaining in the second stage) correcty. Then given the empoyment eves chosen in the rst stage, the wage rate is determined by a process of bargaining between the entrepreneur and the worker, aong the ines of Stoe and Zweibe (996). A worker and her empoyer bargain with each other taking into account the impact of the worker s possibe exit on wages of other empoyees. In other words, we aow the possibiity of renegotiation of the empoyer with other empoyees if bargaining fais with any empoyee, and this feature is competey factored into the bargaining process. 7 The discussion above impies that our overa equiibrium concept is one of subgame perfect equiibrium which is soved using backward induction. That is, taking as given the empoyment chosen in the rst stage, in the second stage the wages are determined through a process of simutaneous Stoe-Zweibe bargaining between the rm and the workers. Anticipating the second stage wage as a function of empoyment, the rm optimay chooses empoyment in the rst stage. Next, aong the ines of Akerof and Yeen (990), we show in the appendix that a rm never pays a wage ess than the fair wage, therefore, workers aways work at fu e ort, and there is no oss of generaity in assuming the production function given in () to be Z = F (s; ) (7) With the fair-wage constraint never binding for skied workers (as shown ater), the entrepreneur soves the foowing probem in the rst stage correcty anticipating the wages paid in the second stage of skied and unskied empoyment. MaxF (s; ) w s (s; )s Maxfw (s; ); w g s; q( s ) s c q( ) (8) Beow we describe the wage determination in two cases: when the fairness constraint does not bind and when it does bind. 7 A specia case of this, where the worker and empoyer have equa bargaining weights, exacty bois down to the Shapey vaue soution to a cooperative, mutiatera bargaining probem. 9

10 2.3 Wage Determination 2.3. Unconstrained case The rst-order conditions for the optima choices of s and are given by [F (s; )] w s [F 2 (s; )] w = = q( s ) c q( ) where subscripts and 2 denote partia derivatives of the production function with respect to the rst and second arguments, respectivey. Denote the expressions on the :h:s in the above two equations by J i ; i = s; ; where J i is the surpus of the rm from hiring the margina worker of type-i: Assuming unempoyment bene t to be zero, the bargaining weight of a worker to be ; the bargained wage for a worker of type-i is obtained as foows. w b i = arg max w i w i J i As mentioned earier, a worker and her empoyer bargain with each other taking into account the impact of the worker s possibe exit on wages of other empoyees. In other words, we aow the possibiity of renegotiation of the empoyer with other empoyees if bargaining fais with any empoyee, and this feature is competey factored into the bargaining process. Using (9), (0), the rst-order conditions of the above maximization probem yieds the foowing expressions for wages for the two types of workers. w s = [F (s; ) w = [F 2 (s; ) (9) ] (3) The above is a system of di erentia equations, where each worker s bargained wage is a fraction of the surpus she creates in the form of her margina product pus the reduction in the wage bi (or minus the increase in the wage bi) of the existing workers through her empoyment (reative to the situation where she exits and wages with other workers are renegotiated). As seen from the above di erentia equations, there are own as we as cross e ects of skied and unskied empoyment on wages. It is important to note here that if w s and w are homogeneous of degree zero in s and ; the two rst-order conditions above resut in the zero-pro t condition for the rm being satis ed: 8 Taking this as an important hint in nding the soution to the above set of di erentia equations, we write w s and w as functions of s=: Denote s= by t: Given that F (s; ) is CRS, we can write F (s; ) = F (t; ): Denote F (t; ) by f(t) and it foows that F (s; ) = f 0 (t) and F 2 (s; ) = f(t) tf 0 (t): 8 Mutipying (9) by s and (0) by and adding we get F (s; ) = (w s+ cs q )s+(w s( s) + c q ( ) Therefore, the zero pro t condition hods @ of degree zero in s and @ws )+( +s @s = 0, which aways hods if if ws and w are homogeneous 0

11 In the appendix we show that the soutions to (2) and (3), namey bargained wage rates in the second (bargaining) stage for any reative skied empoyment, t set in the rst (prior) stage- are given by Lemma : w s (t) = f 0 (t); w (t) = (f(t) tf 0 (t)) That is, the wages are simpy a fraction of the respective margina products of abor. This is despite the presence of the strategic e ect mentioned in the introduction which are captured by ; for i; j = s; in the rst-order conditions (9) and (0). For captures the e ect of hiring an additiona skied worker on skied wage. If hiring an additiona skied worker owers their margina product it wi reduce the Nash bargained wage that rms have to pay to skied workers. Therefore, the vaue of a skied job to the rm woud exceed the margina product of skied abor due to this e ect. However, an additiona skied worker aso increases the margina product of unskied workers which woud ead to an increase in the unskied > 0); eading to a reduced vaue of a skied job for the rm. For a constant returns to scae production function, these two strategic e ects cance out in the determination of the wage bi. Thus, the surpus that is shared between the worker and the rm is the worker s margina product and it is shared according to their bargaining weights Constrained Case Suppose the fair wage is w ; and the rm expects it to be the unskied wage in the second stage. Assuming that w, determined in genera equiibrium, is taken by the rm parametricay (as given), the rst-order conditions for the empoyment choice in the rst stage become f 0 (t) w s f(t) tf 0 (t) w = = q( s ) c q( ) The vaue of an extra skied worker for a rm is given by the :h:s of (4). As in the unconstrained case, if w s is homogeneous of degree zero in s and ; the two rst-order conditions above resut in the zero-pro t condition for the rm being satis ed: We thus write w s as a function of t = s=: Using Nash bargaining, as in the unconstrained case, the wage of a skied worker is given by the foowing di erentia equation The soution to the above di erentia equation is given by (4) (5) w s (t) = [f 0 (t) tw 0 s(t)] (6) w s (t) = t Z t In the case of Cobb-Dougas production function given by 0 x f 0 (x)dx (7) s F = ( ) (8)

12 the skied wage given in (7) takes the foowing simpe form w s (t) = f 0 (t) (9) where ( ). Since > ; it impies that the skied wage is a greater fraction of the margina product of skied workers in the constrained case than in the unconstrained case. This happens because of the strategic e ect mentioned earier. Since the fair wage of unskied workers is determined outside the rm, an additiona skied worker does not increase the wage of unskied workers giving rise ony to the positive strategic e ect of reducing the wage for a empoyed skied workers in the rm. Therefore, the vaue of a skied job exceeds the margina product of skied abor, which is re ected in the skied wage being a higher fraction of margina product of skied abor in the case of Cobb-Dougas production function. For anaytica tractabiity and to obtain cosed form soutions, in rest of the paper we make the foowing assumption. Assumption : The production function for the na good is of the Cobb-Dougas form given in (8) and hence f(t) = t ( ) : Having determined wages in the constrained and unconstrained cases, we next sove for the equiibria in the two cases. 3 Autarky Equiibrium 3. Unconstrained case It is shown in the appendix that the rst-order conditions (9), (0), and emma impy Lemma 2: w s (t) = f 0 (t) = q( ; w s) (t) = (f(t) tf 0 (t)) = c q( ) : The above reationships are determined by the fact that the surpus from a job-i in equiibrium equas the hiring cost of c i q( i) : Since the rms take i as given, emma 2 provides us with two expressions for the reative demand t d for a rm, both of which must be true in equiibrium. Dividing one expression by the other we get the foowing expression for the reative demand t d as a function of s and : f 0 (t d ) f(t d ) t d f 0 (t d ) = q( ) c q( s ) Using the functiona form for f(t) given in Assumption, the above can be written as t d = c q( s ) q( ) To obtain cosed form soutions, we assume that the matching function is aso of Cobb-Dougas form given as foows. Assumption 2: m( i ) = k( i ) and hence q( i ) = k( i ) : (20) 2

13 Under the above assumption, the reative demand is decreasing in s : This is shown using a downward soping curve denoted by RLD u in Figure in ( s ; s ) space. This is intuitive as the reative cost of empoying skied abor (reative to unskied) is increasing in its reative market tightness. Having obtained an expression for reative demand, next we derive an expression for the reative suppy of two types of abor. Denoting the economy s endowments of skied and unskied abor by S and L respectivey, the reative suppy (avaiabe for empoyment) is given by S( t s = S sq( s ) L q( ) = S L s us) L( u ) ; which using (6) becomes (2) where the ast equaity foows from the functiona form for the matching function given in Assumption 2. The above is ceary increasing in s : In other words, because the reative empoyment rate is increasing in the reative market tightness of skied abor (through the Beveridge curve reationship between the unempoyment rate and abor market tightness), the reative suppy of skied abor avaiabe for empoyment is aso increasing in its reative market tightness. The intersection of the downward soping reative demand with the upward soping reative suppy determines the autarky equiibrium in the unconstrained case as shown in Figure. The unconstrained equiibrium s and t are given by s c L = ( )S ; t = c ( ) L (22) S The corresponding equiibrium vaues of w s ; w, s ; and are obtained as foows. As mentioned earier, when both (9) and (0) are satis ed, rms make zero pro ts. From the two expressions in emma 2, which are derived from the two rst-order conditions (9) and (0), we get the foowing zero pro t condition cs q( s ) c = (23) q( ) The above simpy states that to maintain zero pro ts in equiibrium, an increase in s must be associated with a decrease in ; and vice-versa. This negative reationship between s ; and is potted in Figure 2 and denoted by ZP C u. Once we know the equiibrium s from (22); we can determine the equiibrium vaues of s ; and from ZP C u ; and the corresponding w i from emma 2. Denote the unconstrained equiibrium wage and market tightness variabes by w u ; wu s ; u ; u s. 3.2 Constrained case The fair-wage constraint in our mode arises from socia norms about the maximum permissibe wage inequaity. Akerof and Yeen (990) mode fair wage for type-i as a inear combination of the wage of the other type and the market cearing wage for type-i: Given the search friction and wage bargaining, there is no market cearing wage in our framework. In principe, we coud use the unconstrained bargained wage in 3

14 pace of the market cearing wage, that is we coud use a fair-wage speci cation as foows. w = w s + ( )w u (24) where w u is the unconstrained equiibrium fair wage. Without oss of generaity, and to simpify the exposition consideraby, we assume that our fair wage, w ; takes the foowing simpe form Assumption 3: w = w s Now, there are two possibiities: either the fair-wage constraint does not bind (w u bind. Therefore, the expression for the unskied wage is given by > w u s ) or it does w = Maxfw u ; w g where w is the equiibrium skied wage in the case where the wage of unskied workers is constrained to be equa to its fair wage. 9 When the fair-wage constraint binds, the constrained reative demand as a function of s foows. Re-write (4) and (5) using (6) and (9) as is derived as Dividing (25) by (26) we get w s (t) = f 0 (t) = q( s ) f(t) tf 0 (t) + t 2 w 0 s(t) = f(t) tf 0 (t) = w + c q( ) f 0 (t) f(t) tf 0 (t) = which upon using the functiona form of f(t) yieds q( s) c q( ) w + c q( ) ) t d = (w + ( ) cs q( s) (25) (26) (27) (28) The above is the reative demand for a rm taking w ; ; and s as given. Comparing the above reative demand with the one in the unconstrained case given in (20) note that for any given and s ; the constrained reative demand for skied abor is higher. This is due to the strategic e ect mentioned earier. Hiring an extra skied worker owers the wages of a skied workers, and therefore, rms have an incentive to hire more skied workers than in the unconstrained case. Aso, hiring an additiona unskied worker increases the skied wage, therefore, rms want to reduce the hiring of unskied workers. Both these e ects tend to increase the reative demand for skied workers in the constrained case. 9 We can aso have exacty the same fair-wage constraint for skied workers in terms of the unskied wage. However, as ong as the skied wage is greater than unskied wage (which is assumed to be true throughout by choice of parameters), it is obvious that the constraint is never binding for skied workers. 4

15 If the fair wage w were exogenous, say a poicy determined minimum wage, then we woud use (2) and (28) to determine the equiibrium vaues of ; and s : Using the fair wage speci ed in assumption 3, the equation for the reative demand becomes t d = (w s(t) + ( ) cs c q( ) ) q( s) (29) To obtain a simpi ed expression for reative demand, we use the foowing emma which is proved in the appendix. Lemma 3: w s (t) = q( s) hods even in the constrained case. The reason that the expression for the skied wage as function of s is unchanged from the expression in emma 2 for the unconstrained case is the foowing. Nash bargaining impies that the skied wage, w s equas J s; where J s is the surpus of the rm from hiring the margina skied worker. Note from (9) and (4) that, for any given market tightness that the rms and workers take as given, the interaction between a rm and its workers it decides to hire (through its empoyment decision and wage bargaining) aways resuts in an outcome in which J s must equa the recruitment cost of hiring an additiona worker, Using emma 3 to substitute out w s (t) in (29) we get t d = ( ) + c q( s ) q( ) q( s) : The reative demand above is decreasing in s : Comparing (20) and (30) it is easy to see that the constrained reative demand RLD c in Figure 2 ies to the right of the unconstrained demand RLD u when the constraint is binding. The reative suppy curve, which is an increasing function of s ; remains unchanged. Therefore, the equiibrium vaues of s to the unconstrained case. (30) and t are higher in the constrained case (with the constraint binding) compared To obtain the equiibrium vaues of ; s ; and w s in the constrained case, we again make use of the two rst-order conditions (25) and (26) to eiminate t to get our zero pro t condition in terms of and s given by ( ) cs q( s ) cs q( s ) + c = (3) q( ) The above is again a negative reationship between ; and s ; which yieds equiibrium vaues of ; and s for an equiibrium s : It is shown in the appendix that, in the range of s for which the constraint is binding, the curve representing (3) ies to the eft of (23) in Figure 2. Intuitivey, for any and s satisfying (23), the introduction of a binding fairness constraint increases the cost of hiring unskied abor without a ecting the cost of hiring skied abor. Therefore, rms start making osses. To restore zero pro ts, must be ower for each s and vice-versa. Beow we derive the range of s in which the constraint is binding. 5

16 3.3 When does the constraint bind? The constraint binds when w u < w u s : From emma 2 the constraint binds if which upon using q() = k c q( u ) < q( u s ) from assumption 2 becomes u s c > u Thus, the reative demand curve with the possibiity of the fair-wage constraint becomes the one denoted by RLD c in Figure which has two segments, one for vaues of s greater than c ; and the other for vaues beow it which corresponds to the unconstrained reative demand curve. Given the shape of the reative demand curve with fair-wage constraint, it is possibe to get mutipe equiibria. To see this, suppose the reative suppy curve is one denoted by RLS 0 in Figure. Now, if the society did not have any concern for fairness, then the equiibrium woud be at e 3 : However, fairness concerns cause a stepward shift in the reative demand curve making e 4 a candidate for equiibrium as we. That is, both e 3 and e 4 are possibe equiibria when fairness considerations are present. The intuition for mutipe equiibria here is the foowing. Since the reative cost of abor (wage pus recruitment cost) is positivey reated to the reative market tightness, the fair-wage constraint binds if s is high. If rms expect s to be high and therefore the fair-wage constraint to bind, they wi end up hiring more skied workers reative to unskied workers due to the strategic e ect discussed earier. This, in turn, wi make the reative market tightness for skied workers higher creating a sef-fu ing prophecy. Simiary, if s is expected to be ow, the fair-wage constraint is then not expected to bind, the reative demand for skied abor is ower, which in turn eads to a ow s outcome. (32) and thus, an e ectivey unconstrained As seen from Figure, we have mutipe possibe expectations regarding s ; when reative suppy is in the intermediate range, which happens ony when the reative endowment of skied abor is in the intermediate range. In other words, if the reative endowment of skied abor is very high (ow), which the rms know, they wi expect the reative market tightness of skied abor to be aways ow (high). Using (22) which gives the vaue of unconstrained equiibrium s ; the condition (32) can be written as c ( )S > (33) L Therefore, if the condition above is satis ed, the constraint binds, and the equiibrium must be obtained using the constrained reative demand curve. For exampe, in the case where c = ; L = 2S; = = :5; must be greater than :7 for the constraint to bind. In Figure 2, if s is greater than a threshod vaue, the fair-wage constraint binds and for such vaues the zero pro t curve under the binding constraint, ZP C c is to the eft of the unconstrained one, ZP C u : 6

17 3.4 Comparing constrained and unconstrained equiibria Let us compare the autarky equiibrium in the absence of fairness considerations given by point e in Figure with the constrained autarky equiibrium given by point e 2 : Since the equiibrium s is higher in the constrained case, Figure 2 impies a ower and consequenty a higher unempoyment rate of unskied in the constrained case. Since the impact on s is ambiguous, the impact on skied unempoyment and skied wage is ambiguous. Since the impact on skied wage is ambiguous, the impact on unskied wage is ambiguous as we. It is shown in the appendix (section 6.6) that in the absence of the strategic e ect, there is an increase in skied unempoyment as we. In the absence of the strategic e ect, a binding fairness constraint has two e ects on the demand for skied abor. Firsty, since unskied abor becomes more expensive, rms substitute skied abor for unskied abor. Secondy, given the compementarity between skied and unskied abor, ower empoyment of unskied abor reduces the margina product of skied abor and hence reduces the demand for skied abor. It is shown that, for an individua rm there is an increase in the reative demand for skied abor at each s compared to the unconstrained case. However, at the aggregate eve, the increased ratio of skied to unskied empoyment resuts in a ower margina product of skied abor and consequenty a ower market tightness for skied abor. Lower market tightness for skied abor impies ower skied wage and higher skied unempoyment. Given that the the ratio of skied to unskied unempoyment is higher, the margina product of unskied abor is higher. With a ower recruitment cost per unskied worker due to a ower market tightness in the constrained equiibrium, this higher margina product impies a higher unskied wage. The resut is summarized beow. Proposition : In a constrained equiibrium where w w u ; unskied unempoyment is higher and skied unempoyment (and skied wage) may be higher or ower compared to an unconstrained equiibrium. If the strategic e ect in empoyment choice is absent (as is the case with a Leontief production function), then skied unempoyment is higher as we and whie skied wage is ower, the unskied wage is higher. The proposition above highights the importance of the strategic e ect in determining the impact of fair-wage considerations on skied unempoyment. When the constraint is binding, the possibiity of paying a ower wage to skied workers in the second stage ( rst stage empoyment choice determines margina product, and hence wage through wage bargaining in the second stage) induces rms to hire more skied workers (and fewer unskied workers) in the rst stage which reduces skied unempoyment (and increases unskied unempoyment). The strength of the strategic e ect depends on the easticity of substitution between the two factors of production. In the extreme case of zero easticity of substitution (Leontief production function) the strategic e ect is zero as we (See appendix). 7

18 3.5 Comparative statics with respect to Let us assume that the economy is at a constrained equiibrium, i.e., the reative suppy curve in Figure intersects the fair-wage reative demand curve in its upper right-hand downward soping part (that ies above the cut-o vaue of s at which the fairness constraint binds). An increase in impies a rightward shift in the upper right-hand segment of the reative demand for skied abor from (30). Aso, from (32), it impies a reduction in the cut-o vaue of s at which the fairness constraint binds. Since the reative suppy remains unchanged, an increase in increases the equiibrium vaues of s and t: Since the corresponding part of the zero-pro t curve shifts to the eft in Figure 2 (and the ray through the origin indicating the threshod vaue of s rotates cockwise), there is an unambiguous decrease in. An increase in t impies from (25) a decrease in s as we. Decreases in w s ; s ; and impy from (3) (and from our de nition of the fair unskied wage) that the unskied wage must rise. Reca that decreases in s and wi reduce the cost of recruiting both types of workers, and since the skied wage decines, the unskied wage must increase to restore the zero pro t condition. Therefore, we get the foowing resut. Proposition 2: Starting from a constrained equiibrium, an increase in the fairness parameter eads to increases in both skied and unskied unempoyment. Skied wage fas and unskied wage rises. Whie a comparison of unconstrained and constrained equiibria yieds ambiguous resuts on the skied unempoyment as mentioned in proposition, proposition 2 shows that any increase in, starting from a constrained equiibrium, eads to an unambiguous increase in skied unempoyment. As discussed in proposition, in the absence of the strategic e ect, a move from unconstrained to constrained equiibrium eads to an increase in skied unempoyment. However, the strategic e ect confounds this by providing increased incentive to hire skied workers. Starting from a constrained equiibrium, for an incrementa increase in the strategic e ect is of the second order (the e ect is present in the initia and na equiibrium, both of which are constrained and so at east partiay get canceed out when ooking at the di erence between the two situations), and hence skied unempoyment increases. 3.6 Change in the reative endowment of skied abor It is easy to see from the discussion of autarky equiibrium in the constrained and unconstrained cases that an increase in the reative endowment of skied abor rotates the reative suppy curve to the right in Figure. This eads to a decrease in the equiibrium s : From Figure 2, a decrease in s impies a decrease in s and an increase in : Therefore, skied unempoyment increases and unskied unempoyment decreases in both cases. In the unconstrained case it aso eads to a decrease in wage inequaity. Since wage inequaity is xed at in the constrained case, there is no change in wage inequaity as a resut of increased reative endowment of skied abor. 8

19 Next, note from (33) that an increase in S L makes it ess ikey that the constraint binds. Therefore, it is possibe that an increase in S L makes a binding constraint non-binding. This is shown in Figure when the there is a rightward shift in the reative suppy curve from RLS to RLS 00 : In this case, there is a decrease in wage inequaity because the wage inequaity decreases from (33). to the inverse of the expression on the r.h.s of To compare the e ects of reative endowment changes in the presence and absence of fairness considerations and to keep the initia equiibrium the same under both situations for a fair comparison, et us consider the reverse case of a reduction in S L : In the presence of fairness considerations, et us assume that the fairwage constraint does not bind initiay, which gives us the same equiibrium as when there are no fairness considerations at a. The impact on unempoyment can be anayzed using Figures and 2. In Figure, the initia reative suppy curve is RLS 00 and therefore, the intersection with the reative demand curve is in the unconstrained part at e 5, irrespective of whether we have fairness considerations or not: After the reduction in S L the reative suppy curve moves from RLS00 to RLS: Now, there is a greater increase in the equiibrium s under fairness considerations since this reduction now makes the fair-wage condition bind. In Figure 2, the zero pro t curve now is the one corresponding to the constrained case whose reevant portion now ies to the eft of the unconstrained one. Therefore, under fairness considerations, there is a arger reduction in ; but the impact on s becomes ambiguous. In other words, the increase in unskied unempoyment is magni ed by the fact that this decrease in the skied abor force makes the fair-wage constraint binding. 4 Impact of o shoring For o shoring to be possibe, rms have to be abe to fragment their production in such a way that semi- nished output, whose production ony requires the appication of unskied abor, can be produced in another country (South) and then imported back to be combined with skied abor at home to produce the na product. To keep things simpe, we assume that one unit of this semi- nished good is a perfect substitute for a unit of domestic unskied abor. We assume the price of imported input incusive of the search and trade costs as xed, which is equivaent to a sma country assumption. (This assumption is reasonabe if we beieve that the South has arge quantities of unskied abor and that xed abor productivity in a arge subsistence, numeraire sector there xes their unskied wage.) Suppose the unit cost (faced at home) of o shored input is p m : Let the amount of this input imported be denoted by m: As far as the timing of o shoring is concerned, we assume that the quantity of o shored input is chosen in the rst stage aong with skied abor. This assumption may be coser in spirit to the o shoring of services, whie the assumption of freey adjustabe input wi be coser to the case of imported intermediate good. Later we wi note the impication of aowing 9