International Openness, Insecurity, and ImplicitContracts.

John McLaren and Andrew NewmanUniversity of Virginia and University College, London

June, 2001Note: This is extremely preliminary and incomplete!! This is a

conference draft: Please do not quote without the authors’permission.

1 Abstract.

We construct two simple models of the e¤ect of increased in-ternational openness on risk bearing in an environment in whichthe only risk-sharing institutions are self-enforcing agreements. Weshow how increased openness can weaken long-term relationships,and hence risk sharing, by increasing the e¤ectiveness of the mar-ket, much as some critics of globalization have argued. However, theharm thereby done is tempered by the fact that in order to have sucha negative indirect e¤ect, openness must have a direct e¤ect that re-duces risk. It is shown that if the market is either highly e¤ectiveor highly ine¤ective, globalization cannot provide a net increase inindividual risk-bearing.

2 Introduction.

When trade economists study the e¤ect of economic openness on the welfare ofworkers and on income distribution, the focus usually rests on how trade changesthe average wage paid to various categories of worker. For example, muchwork has tested for “Stolper-Samuelson” e¤ects, under which a rich country onopening up to trade would see in increase in the wages paid to higher-skilledworkers and a fall in the wages to unskilled workers (see Slaughter (1998) for

1

a survey). However, when non-economists argue that globalization has largesocial costs, they often argue something more subtle: That increased opennessadds to increased risk or insecurity for individual workers, by breaking downexisting relationships.1

This paper explores that possibility. We construct two simple modelsof risk-bearing in environments in which complete contracts are unavailablefor informational reasons. In this envrironment, the only way for agents toshare risk is to develop a long-run relationship with another agent in which thetwo promise to help each other out when one is su¤ering from bad luck. Thisarrangement is enforceable only through the threat that if one reneges, he or shewill lose the bene…t of the trust on which the relationship was founded, and willneed to su¤er the whims of the market and search for a new partner. However,the process of globalization makes the market work better, and by breakingdown barriers makes it easier to …nd a new partner. This makes the loss ofone’s current relationship less frightening, and thus weakens risk-sharing. Thus,in a well-de…ned sense, globalization does indeed weaken domestic institutionsfor risk bearing, and this is an indirect cost of the process that needs to bereckoned.

However, it also is a cost that will not arise unless globalization providesa direct bene…t in risk reduction. The analysis shows how ambiguous thewelfare e¤ects are once these two e¤ects are taken into account. It does this…rst in a pure endowment economy model, in which the results can be obtainedsimply at the expense of some lost richness; and in an economy with productivematching, which is more technically di¢cult but allows for additional issues tobe discussed.

The models are highly abstract but are intended to serve as a metaphor forimportant real-world risk sharing institutions, most notably long-term implicitemployment contracts. A number of researchers have argued that long-termrelationships in labor markets have been eroded in recent years, and debated thepossible reasons (see Farber 1997). Bertrand (1998) argues that US evidencesupports the claim that implicit labor contracts have been broken down byinternational competition, as …rms in import-a¤ected industries no longer shieldtheir workers from spot-market wage ‡uctuations. A journalistic account of abroad erosion of the importance of long-term relationships in Japan in the faceof international competition is found in Kristof (1997).

In order to address these questions, we have borrowed ideas from variousstrands of theory. The theory of implicit contracts was considerably advancedby MacLeod and Malcomson (1989), and is the focus of Baker et. al. (1994).Coate and Ravallion (1993) study risk-sharing arrangements through long-runrelationships. The idea that a rise in the e¢ciency of the market can harmexchange appears in some form in MacLeod and Malcomson (1989) and Baker

1 Copious citations of this view can be found in the popular press. For example, NicholasD. Kristof, New York Times, July 15, 1997, describes a perception that local relationshipsthroughout Japan are breaking up under pressure of globalization, and Linda Diebel, TorontoStar, Aprill 11, 2001, cites activists who blame trade openness for increased insecurity forworkers.

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et. al. (1997), and is a focus of Kranton (1996), from which this paper derivessome inspiration. However, none of the ideas in this literature appear to havemade their way into the trade literature.

On the other hand, a provocative monograph, Rodrik (1997), argues thatglobalization does make economic life riskier for most workers, and on that basisargues for corrective action by government. The main economic mechanism de-scribed in that work is the increase elasticity of demand for labor in a globalizedeconomy. In a closed economy, a negative productivity shock in sector i woulddrive down the marginal product of labor there, tending to depress i-workers’wages; but it would also drive up the price of i output, raising the marginalvalue product of labor and providing a cushion for those wages. However, ifthe country becomes part of a large world market in which it has no in‡uenceover prices, that cushion disappears. We would argue that the Rodrik analysisis suggestive, but seriously incomplete. A …rst reason is that in most respectsaggregate risk would seem to be diminished, not increased, by trade, as long assupply and demand shocks are not perfectly correlated across countries. Themain reason, however, is that it assumes that there are no domestic institutionsfor sharing risk (in particular between employers and employees); that despiterisk aversion, only spot markets are permitted to operate. This is not merelya simplifying assumption, but essential to the logic. A more persuasive argu-ment would be to consider imperfect risk institutions and ask how they respondto the globalized environment. In this respect, the current paper is similar inspirit to Dixit’s (1989) criticism of existing writing on trade and insurance; thatliterature had mostly assumed away risk markets by …at, while Dixit showedthat allowing for imperfect risk markets instead could dramatically change theconclusions.

The following section analyses the simplest model, which is a pure endowment-exchange economy. The following section analyses the more di¢cult but richerproduction-matching economy.

3 A Pure Exchange Model.

Consider an economy with two countries, A and B, in each of which there isa continuum of agents of measure 1. Each agent in each period receives anendowment of a non-storable, homogeneous consumption good. Each period,the quantity the agent receives is "H with probability ¼ and "L with probability(1¡¼), where "H > "L and ¼ 2 (0; 1) are constants. Time is discrete, measuredin periods indexed from t = 0 to 1. Each agent has a strictly concave von-Neumann-Morgenstern utility function ¹ and a common discount factor ¯ 2(0; 1).

Clearly, there are gains from risk sharing and one would expect to seemutual insurance contracts if they are feasible. However, contracting is limited

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by two factors. First, the endowment an agent receives in a given period is ob-servable only by that agent and another agent who is in the same location. Atmost two agents can be in the same location at one time, so this compromisesthe enforceability of risk-sharing contracts. Second, agents can communicateand thus agree on risk-sharing arrangements only if they are in the same loca-tion, and they can …nd themselves at the same location only through a processof random search. This prevents ex ante contracts involving more than twoparticipants.

The searching works as follows. Once per period, any agent i can withprobability Á identify the location of one other agent, say j, in which case heor she also learns the nationality of that agent and whether or not the agentis already sharing a location (and hence risk) with another. (The letter ‘Á’stands for ‘…nd.’) Agent j simultaneously learns the same about agent i (andany agent learns about at most one other agent in each period). The searchis equally likely to identify an agent in either country. If agent j is alreadysharing risk with another or is unavailable for reasons of nationality (this willbe discussed below), then the search has been unsuccessful, but otherwise, i canimmediately move to j’s location and begin a risk-sharing relationship with jthere.2

When two agents get together to form an agreement on risk sharing, theyunderstand that since they cannot write binding contracts, they must agree ona scheme that will be subgame-perfect. Thus, as in Malcomson and Macleod(1984), the partners agree to the optimal subgame-perfect equilibrium at themoment they meet (we will often call these ‘self-enforcing agreements,’ as inthat paper). This agreement will typically use the ‘grim’ punishment of ex-clusion from the relationship as an enforcement mechanism, if the incentive-compatibility constraint binds; in practice, this means that if ever a partnerreneges on the agreement, the other partner will from that point never trusthim/her again, and both partners will need to search for a new partner to at-tain risk sharing again. (Of course, this is not renegotiation-proof; an extensionto renegotiation-proofness would be of interest, but is beyond the scope of thisdraft. We doubt that it would change the basic message.)

We also assume that for any existing partnership, in each period, there is a…xed probability, (1 ¡ ½), that the partnership will be dissolved for exogenousreasons (the letter ‘½’ stands of the probability that the partners will be ableto remain together). One might think of this as the case in which one partnermust move for personal reasons, for example. This is helpful to our argumentbecause it avoids the situation in which all agents wind up in relationships inthe steady state; as will become apparent, this would eliminate any scope fordiscussing the role of globalization.

A key assumption concerns what happens when a searcher …nds a potentialpartner who is in the other country. In order to put the idea of globalization

2 This is a very arti…cial search technology, and has been used here because it seems tobe the simplest way to introduce a market-thickness e¤ect into the model. Other, moresophisticated matching technologies, such as that used in Kranton (1996), could be used todeliver the same results at the expense of more complication.

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into sharp focus, we assume that before globalization, one is not allowed to crossthe border, so search that identi…es a potential partner in the other country isunsuccessful. On the other hand, after globalization, any agent is free to moveacross the border at will, so that partnerships with foreigners are just as easyto form as with compatriots.

A …nal feature of relationships is that they can impose a kind of pychic costif the two agents do not get along well. This is determined by a random variable· drawn from a distribution with cdf G, density g, and support [¡·; ·], where· > 0 is a constant; the realized utility of a person in a relationship in a givenperiod is then equal to the utility ¹ of that period’s consumption minus the valueof · for that relationship. (The letter · stands for ‘cost.’) The interpretation isthat · gives the per-period disutility (if positive) or utility (if negative) to stayingtogether for that particular pair of agents, based on non-pecuniary factors suchas personality. This variable is realized once per relationship, and is iid acrossrelationships. The reason for introducing this variable is that for some portionsof the parameter space, if there is no such element of personality (equivalently,if · = 0), then no equilibrium exists, but an equilibrium does exist for a smallpostitive ·. We assume that g(·) > 0 for j·j < ·. In addition, we assume thatif one is in a relationship currently, in order to …nd out what one’s level of ·would be with a given other potential partner, one must (irrevocably) break o¤the current relationship and move to the same location as the potential partner.Thus, as · ! 0, it becomes extremely unattactive to search merely in order to…nd a relationship with a better ·. Initially, we will assume that · = 0, becausethe model is simpler when that is true, although an equilibrium does not existfor all parameter values; subsequently, we will assume that · > 0, in which casewe will be interested in what happens as · ! 0.

The sequence of events within each period is as follows. (i) Agents withina relationship learn whether they are to be separated exogenously or not. (ii)Agents without a partner search, and learn whether or not they will identifya new potential (and currently unmatched) partner in this period. (iii) Wherean agent has identi…ed a new potential partner and the two are in the samelocation, the psychic cost, ·, of their match is realized and becomes known toboth partners. (iv) Then negotiations occur between the two new potentialpartners over the new partnership. (v) This period’s endowment for each agentis revealed. Within a partnership, this is immediately common knowledge.(vi) Each partner chooses to surrender a fraction µ 2 [0; 1] of her output to herpartner (this is the form that risk-sharing takes). (vi) Consumption occurs; ineach period this is equal to the agent’s output plus net transfers received fromthe agent’s partner.

3.1 Risk-sharing agreements.

Assume for the time being that · = 0. In each period, within the partnershipbetween i and j, there are four possible endowment outcomes: Both partnershave large endowments; both have small endowments; i has a large endowmentand j has a small one; and vice versa. Clearly, risk sharing requires action

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only in the latter two, and clearly the relevant action will be for the partnerwith the large endowment to give some up it up to the partner with the smallerendowment. Thus, the agreement can be characterised by the fraction, µ, ofthe large endowment surrendered by the agent who receives it to the agent withthe small endowment. (It is straightforward to verify that there is no generalityto be gained by allowing for payments in both directions.)

Consider a pair of agents negotiating a new relationship. If the incentivecompatibility constraint implied by the subgame perfect requirement did notbind, then they would agree to perfect insurance, with µ = µopt ´ ("H¡"L)=2"H .This is the value of µ at which consumption of the two partners is equalized.The case of interest, however, will be the case in which the incentive compati-bility constraint does bind, so that insurance falls short of the …rst-best. Thatconstraint is:

¹("H) ¡ ¹((1 ¡ µ)"H) · ¯[V C(µ) ¡ V S], (1)

where V C is the payo¤ from being in the risk-sharing relationship (the ‘C’stands for ‘cooperation’) and V S is the payo¤ from being without a relationship(the ‘S’ stands for ‘search’). Note that V C depends on the value of µ chosenwithin the relationship in question, while V S does not, but rather dependson the level of risk-sharing available in any future relationships the partnersmight have with other agents. The left-hand side is the instantaneous bene…tto the well-endowed partner from reneging on the risk-sharing promise (or the‘temptation to cheat’), and the right-hand side is the cost in ostracism of doingso (or the ‘punishment’).

As mentioned above, for the time being we assume that · = 0. The valueof being in the current relationship, then, follows:

V C = ½(¹c + ¯V C) + (1 ¡ ½)V s,

where

¹C(µ) ´ ¼2¹("H) + (1 ¡ ¼)2¹("L) + (1 ¡ ¼)¼[¹((1 ¡ µ)"H) + ¹(µ"H + "L)]

is the per-period expected utility of an agent in a relationship with sharingparameter µ. The last two terms denote, respectively, the ex post utility of ahigh-endowment partner whose partner has a low endowment, and vice versa.This enables us to write the incentive compatibility constraint as:

¹("H) ¡ ¹((1 ¡ µ)"H) · ¯½

1 ¡ ¯½(¹C(µ) ¡ (1 ¡ ¯)V S). (2)

Note that by the concavity of ¹, the temptation to cheat, measured on theleft hand side, is a strictly convex function of the risk sharing parameter µ chosenby the partners, and that the punishment, as measured on the right hand side,is a strictly concave function of µ. The latter attains a maximum at µ = µopt.

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3.2 Steady state calculations.

We focus on steady states, which simpli…es the analysis in two important way.First, analysis of equilibrium requires us to keep track of the number of peoplesearching for partners, because this determines how easy it is for anyone out ofa relationship to …nd a new one. Second, it is necessary to compute payo¤sto any agent in a relationship as well as any agent out of one. Either of thesewould be an order of magnitude more di¢cult outside of a steady state.

Initially, we will do all of these calculations for the post-globalization sit-uation. It will then be straightforward to see how things are di¤erent beforeglobalization.

First, we analyse the number of agents searching. Denote the fraction ofthe total population searching by ¾S (where ¾ stands for ‘share’ and S standsfor ‘search’). The fraction of agents without partners who remain withoutpartners next period is equal to the fraction who are unable to …nd any otheragent, (1¡Á), plus the fraction who identify another agent who turns out to havea partner already, Á(1 ¡ ¾S). The fraction of agents with partners who will bewithout partners next period is equal to the fraction who lose their relationshipsexogenously and who fail to …nd a new one in their search this period, in otherwords, (1 ¡ ½) times the probabiliy that an agent without a partner …nds a newpartner. Thus, the steady state fraction of the population without partnerssatis…es the following equation:

¾S =¡¾S + (1 ¡ ¾S)(1 ¡ ½)

¢(1 ¡ Á + Á(1 ¡ ¾S)). (3)

The right-hand side of this equation is quadratic in ¾S, with one zero for¾S < 0 and another zero where ¾S = 1=Á > 1. Between those zeroes, the righthand side is positive. Thus, (3) has one negative root and one positive root lessthan one; the latter is the steady state value of ¾S. This is depicted in Figure 1,where the parabola indicates the right-hand side expression. Further, since anincrease in Á shifts the parabola down everywhere, ¾S is a decreasing functionof Á. A last point is that taking the total derivative of (3) with respect to Á andrearranging terms, it is easy to see that ¾ + Á(d¾=dÁ) = d(¾Á)=dÁ > 0. Thiscan be summarized thus:

Proposition 1 There is a unique steady state value of ¾S. It is decreasing inÁ, with an elasticity less than one in absolute value.

Essentially, an improvement in search technology makes it easier to …nd apartner and escape the state of autarchy, reducing the number of searchers inthe long run. The …nding on the elasticity will be important later in analyzingincentives.

Second, we analyze the value of being in a relationship and being withoutone. First, de…ne:

¹S ´ ¼¹("H) + (1 ¡ ¼)¹("L),

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the per-period expected utility of an agent without a partner. An agent witha partner will lose the relationship with probability (1 ¡ ½).

Consider an agent in a relationship with sharing parameter µ, who alsounderstands that in any future relationship with di¤erent partners the sharingparameter would be the same. In any given periond, this agent will lose therelationship with probability ½. If this occurs, that agent will become a searcher,and receive the same payo¤ as any other searcher. With probability (1¡½), theagent will remain in the relationship. Thus, in a steady state, such an agent’spayo¤ will follow:

V C = (1 ¡ ½)V S + ½(¹C(µ) + ¯V C).

An agent who is searching, on the other hand, will succesfully obtain arelationship if he or she …nds another agent who is not currently in a relationship.This occurs with probability Á¾S, implying that such an agent’s payo¤ mustfollow:

V S = Á¾S(¹C + ¯vC) + (1 ¡ Á¾S)(¹S + ¯vS).

Note that for any given value of µ, these two equations de…ne a pair of linearequations in V C and V S. These are readily solved, yielding the following.

Proposition 2 For given parameters and a given value of µ, the steady-statevalues V S and V C are uniquely de…ned by their two laws of motion. Thus,holding other parameters constant, we can write V S(µ; Á) and V C(µ; Á). Forµ 2 (0; µopt], these are both increasing in µ, and V C(µ; Á) > V S(µ; Á). Further,taking into account the e¤ect of a change in Á on the steady-state value of ¾S,both V S(µ; Á) and V C(µ; Á) are increasing in Á for µ 2 (0; µopt].

Proof. The solution is:

V S(µ; Á) =Á¾S¹C(µ) + (1 ¡ ¯½)(1 ¡ Á¾S)¹S

(1 ¡ ¯)(1 ¡ ¯½(1 ¡ Á¾S));

V C(µ; Á) =(Á¾S + ½(1 ¡ ¯)(1 ¡ Á¾S))¹C(µ) + (1 ¡ ½)(1 ¡ Á¾S)¹S

(1 ¡ ¯)(1 ¡ ¯½(1 ¡ Á¾S)).

It is seen readily that (1 ¡ ¯)V S(µ; Á) and (1 ¡ ¯)V C(µ; Á) are both weightedaverages of ¹C(µ) and ¹S. The weight on ¹C(µ) in the expression for V C exceedsthe corresponding weight in the expression for V S, and since ¹C(µ) strictlyexceeds ¹S(µ) in the range µ 2 (0; µopt), we must have V C(µ; Á) > V S(µ; Á) inthat range as well. Further, since ¹C(µ) is strictly increasing in that range,both V S(µ; Á) and V C(µ; Á) are as well. Finally, since by Proposition 1 anincrease in Á will increase the steady-state value of Á¾S, an increase in Á willincrease the weight on ¹C(µ) in both expressions, which in the indicated rangemust increase their values.

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where A = ¯½(1¡¯½)¼(1 ¡ ¼). Note that, regardless of functional form, µcrit does

not depend on Á.An equilibrium will exist if the eµ curve of Figure 3 crosses the 45-degree line,

which will be true if and only if P (µcrit; µcrit; Á) ¡ T (µcrit) ¸ 0. Noting thatan increase in Á, by Proposition 2, will shift the P curve down for any µ, thuslowering the maximum eµ sustainable for any given µ, we see that the increasein Á shifts the µ curve of Figure 3 to the left. As a result, although condition(4) can be shown to imply that an equilibrium will exist for low values of Á, itmay not for high values. Now, bringing in the small amount of noise providedby the psychic costs · of personality mismatch, we can remove this problem.

Thus, henceforth we will assume that · > 0. Once we do so, we need toexpand the de…nition of equilibrium. For a given ·, an equilibrium is a functioneµ(¢) : [¡·; ·] 7¡! [0; 1] such that if a pair with cooperation cost · are attemptingto negotiate a cooperative arrangement, and if they anticipate that any futurearrangement either partner may have with future partners will be governed bythe function eµ(¢), then their best sustainable level of cooperation will also bedescribed by µ = eµ(·). We will be interested in the limit of such equilibria as· ! 0.3

Two observations allow us to simplify the analysis when we let · ! 0.First, it is possible that a certain fraction of agents who attempt to negotiatea cooperative arrangement will be unable to commit to cooperation, becausetheir P curve has been shifted down by the negative realization of · and nowlies everywhere below their T curve. For these agents, eµ(·) = 0. The set ofpairs of agents for whom this is true is now an additional endogenous variable.Of course, the set of agents that are able to commit to cooperation are thosefor whom · is less than or equal to some threshhold value, say ·¤. The set isthus completely characterised by the fraction ® = G(·¤) of new pairs that areable to commit to cooperation. (The letter ‘®’ stands for ‘able to commit.’)Second, the range of the portion of eµ(¢) that has positive values will converge toa constant. Thus, in studying the limit of equilibria as · ! 0, we need to focuson only a value of ® and µ. (More formally, we seek a value of ® and µ such that

for any sequence ·i ! 0, there is a corresponding sequence of equilibria eµi(¢)

such that eµi(¢) 7¡! µ uniformly and the fraction of the set of · with eµi

(·) > 0converges to ®.)

It is easy to see that these modi…cations to the model do not change mattersat all in the limit if an equilibrium exists with · = 0. However, when nosuch equilibrium exists, allowing for this small bit of noise now guarantees theexistence of an equilibrium, if · is small enough. The essential point is that, if

3 This discussion supposes that it is never advantageous for a partner in a functioningrelationship to dissolve the relationship in order to begin a new one with a lower ·. Thisis valid for two reasons. First, recall that we are assuming that one cannot discover the ·one would experience with a potential partner without separating from one’s current partner…rst. Second, note that in the limit all values of · will be close to zero, but the expectedutility bene…t to being in a relationship will be a positive number that does not vanish in thelimit. These two features guarantee that as the limit is approached, no one will ever dissolvea functioning relationship in order to pursue a lower value of ·.

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the fraction ® of pairs who are able to commit drops below unity, then the e¤ectis isomorphic to a drop in Á. We can de…ne eÁ = ®Á as the e¤ective value of Á,and note that if ® is less than unity in the steady state, all of the steady stateanalysis (beginning with Proposition 1) goes through unchanged after replacingÁ by eÁ everywhere. Thus, heuristically, allowing ® to fall shifts the eµ curvein Figure 3 to the right, restoring equilibrium, at the same time shifting theP (eµ; µ; Á) curve of Figure 2 back up until it is approximately tangent to the Tcurve, leaving it either slightly above or slightly below the point of tangency sothat exactly a fraction ® of pairs of agents who are negotiating will be able tocommit to cooperation.

To see the argument more precisely, …x a value of · > 0. Suppose thatP (µcrit; µcrit; Á) ¡ T (µcrit) < 0, so that there would have been no equilibriumwith · = 0. Now, focus on the class of eµ(·) functions constructed in thefollowing way. Each function in the class is indexed by a value ·¤ 2 [¡·; ·], sowe will write it as eµ(·; ·¤). For a given ·¤, de…ne P ¤(µ; ·; ·¤) for any µ and· by P ¤(µ; ·; ·¤) = ¯½

1¡¯½(¹C(µcrit) ¡ B ¡ ·), where B is such that T (µcrit) =¯½

1¡¯½ (¹C(µcrit) ¡ B ¡ ·¤). Then set eµ(·; ·¤) for · · ·¤ equal to the highest

level of µ not exceeding µopt such that T (µ) · P ¤(µ; ·; ·¤) (note that this implieseµ(·¤; ·¤) = µcrit), and set eµ(·) equal to zero for · > ·¤. Any equilibrium eµfunction would have to be in this class.

Now, suppose that a given pair of agents are attempting to negotiate acooperative agreement, and they both anticipate that any future cooperationeither partner might have with any future partner would be characterized byeµ(·; ·¤). Then, one can compute their anticpated value to searching and hencethe analogue to the ‘punishment’ curve of Figure 2, and thus for any givenvalue of the · in their current relationship, one can compute the µ that theywould choose. Thus, a given anticipated future eµ(·; ·¤) curve induces a currenteµ(·; ·¤) curve. Any anticipated value of ·¤ that would induce current partnersto choose the same value would be an equilibrium. Next, note that an increase inthe anticipated ·¤ results in an improvement in the anticipated distribution of µby …rst order stochastic dominance, so a higher anticipated value of ·¤ increasesthe value to searching, thereby shifting the punishment curve down and thusleading to a reduction in the induced ·¤. This dependence of the induced ·¤

on the anticipated ·¤ is continuous, because all of the e¤ects of the anticipated·¤ on future expected utilities are continuous. Further, if the anticipated ·¤

equals ·, the induced current ·¤ will be equal to ¡·, provided that · is smallenough (since P (µcrit; µcrit; Á)¡T (µcrit) < 0), while if the anticipated ·¤ equals¡·, the induced current ·¤ will be equal to ·, provided that · is small enough(by (4)). Thus, in between there is a unique equilibrium ·¤, and hence anequilibrium value of ® = G(·¤).

Taking the limit as · ! 0, we see that this always yields a value of ® justequal to the level required to make P (µ; µcrit; Á) tangent to T (µ); furthermore,since eµ(·¤; ·¤) = µcrit at all times, the range of positive values of µ converge tothe single value µ = µcrit.

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This is summarized in the following proposition.

Proposition 3 If P (µcrit; µcrit; Á) ¡ T (µcrit) ¸ 0, then the limit of equilibriaas · ! 0 is the unique solution to eµ(µ) = µ with ® = 1, and is just the sameas the equilibrium with · = 0. If P (µcrit; µcrit; Á) ¡ T (µcrit) < 0, then thelimit of equilibria as · ! 0 has µ = µcrit and a value of ® < 1 such thatP (µcrit; µcrit; ®Á) ¡ T (µcrit) = 0.

The comparative statics implied by this analysis are summarized in Figure4. For Á below a critical level, marked as Ácrit, increases in Á worsen the degreeof cooperation as re‡ected in the decrease in µ, but they increase the fractionof people who are in relationships, as re‡ected in the decline in ¾S. However,everyone who …nds a potential partner succeeds in committing to cooperation,as re‡ected in the fact that ® = 1. Past that critical value of Á, the fraction ofpairs who can commit to cooperation declines so that ®Á is a constant, and sothe fraction of the population who are in a relationship is also constant, as is µ,which remains equal to µcrit.

This has all been discussed under the assumption that the system is in the‘post-globalization’ situation. It is now straightforward to see how all of thisis di¤erent in the pre-globalization situation. In that world, everything is thesame except that when one searches for a new partner, there is a …fty-percentchance that the agent one …nds through the search will be a foreigner, and thusunavailable as a partner. Thus, everything in these calculations is unchangedexcept that all of the probabilities of a successful search are cut in half. Thus,replacing Á in these equations with Á=2 will give the pre-globalization steadystate.

3.4 The equilibrium, before and after globalization.

We can now turn to the normative analysis of globalization. First, in theevent that Á ¸ Ácrit, globalization changes neither µ nor the fraction of thepopulation ¾S who are not in a functioning relationship. Thus, globalizationhas no e¤ect on welfare at all. In the event that Á < Ácrit, on the otherhand, globalization strictly lowers µ and ¾S. Thus, globalization has weakenedall agents’ ability to protect themselves against risk, in the sense that the oneavailable risk-sharing institution – the long-run bilateral relationship – has beenweakend.

However, it is immediate that the e¤ect of all of this on overall risk is am-biguous. The reason is that the mechanism through which the partnershipshave been weakened, namely the increased ease of …nding a new partner whenone is without one, consitutes a prima facie reduction in risk. The globalizationhas a direct risk-reducing e¤ect, together with an indirect risk-enhancing e¤ect,and the net e¤ect of these two is unclear.

This can be made clearer using Lorenz curves, because changes in risk inthis economy are isomorphic to changes the degree of horizontal inequality. To

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see why, …rst consider the realized sum of payo¤s of all agents in, for example,country A, which is given by: Z 1

j=0

1Xt=0

¯¹(cj;t)dj, (5)

where ci;t denotes the consumption of worker j 2 [0; 1] in period t. Since we arefocussing on steady states, and since the aggregate behaviour of the economyat each date will be identical due to the fact that the endowments are iid andand there is a continuum of aggents, this expression is equal to:

1

(1 ¡ ¯)

Z 1

j=0

¹(cj;0)dj.

Thus, all that we need to know about the lifetime risk faced by agents in theeconomy together is revealed by a one-period snapshot of the population. Fur-ther, since the average endowment, and hence the average consumption, is un-a¤ected by globalization, the Lorenz curve in any one period tells us all thatwe need to know about that. The Lorenz curve for this economy is depicted inFigure 5.

Recall that the value measured on the horizontal axis of the diagram is thecumulative fraction of the population, and the value measure on the verticalaxis is the cumulative fraction of consumption, so that for example a point onthe Lorenz curve one …fth of the way from the left-hand axis to the right-handaxis represents the share of consumption enjoyed by the poorest one …fth of thepopulation. Recall as well that a shift upward in the Lorenz curve representsan unambiguous reduction in inequality and vice versa, while for any pair ofeconomies whose Lorenz curves cross, the two cannot be ranked unambiguouslyby inequality (see Atkinson (1971) for a classic analysis).

For this discussion, assume that Á < Ácrit to focus on the case in whichglobalization does have an e¤ect. The Lorenz curve for this economy withoutglobalization is represented as the piecewise linear curve acegi. There are fourdistinct groups in the population, as distinguished by their level of consumption:There are agents without partners, some of whom have large endowments andsome of whom have small; and there are agents with partners, some of whomhave large endowments and some of whom have small. For example, the fractionwho are not in relationships and who have small endowments are the poorestgroup; they number ¾G(1 ¡ ¼), and the consumption level of each is simply theendowment, "L. Thus, their share of total consumption is equal to ¾G(1 ¡¼)"L=", where " is the economy-wide average endowment. This is point c in the…gure.

Note that the slope of ac is the ratio of the typical unpartnered, low-endowment agent’s consumption to the economywide average consumption, andthat this is una¤ected by globalization. A parallel argument holds for the slopeof gi. On the other hand, globalization certainly will lower the fraction ¾S ofthe population without partners. Therefore, with globalization, point c will

13

slide leftward along the ray ac, to a point like b; and point g will slide rightwardalong the ray gi, to a point like h. If the share parameter µ for risk-sharingagreements were to be unchanged by globalization, then the new Lorenz curvewould be abdhi4, which is everywhere above the old curve, indicating lower in-equality and risk. This is the direct e¤ect of globalization: By making it easierto …nd a partner, it lowers the inherent riskiness of economic life.

However, as indicated, the share parameter µ will indeed change due to glob-alization, and this will add to riskiness by creating inequality within relation-ships. What this will do is to slide point d of the new Lorenz curve downward.It is possible that it will be driven downward su¢ciently that the new Lorenzcurve will dip down below the old one, as illustrated with curve abfhi ; but it isnot possible that the new Lorenz curve will be everywhere the old one.

There remains the question of the net e¤ect of globalization on expectedutility. It can be seen readily that in the steady state, aggregate welfare (5)will be equal to:

¾S¹S + (1 ¡ ¾S)¹C(µ)

1 ¡ ¯.

Globalization will lower ¾S, providing a prima facie bene…cial e¤ect, but lowerµ, thus providing an indirect negative e¤ect, unless Á ¸ Ácrit, in which casethere is no e¤ect. One point is obvious: Welfare has its minimum at Á = 0,in which case ¾S = 1 and so welfare equals ¹S, and welfare will be strictlyabove this level whenever ¾S 6= 1 and µ 6= 0; therefore, for su¢ciently smallÁ, globalization must be bene…cial. Thus, we …nd that for either very highor very low values of Á, globalization cannot increase provide a net increase inindividual risk-bearing. Whether or not it is possible in intermediate cases is aquestion on which we are still working.

4 A Production Model.

[This model is still in progress. The analysis is parallel to the previous one,but more complicated.Here is what we have so far.] The preceding model hasdeveloped the main issues fairly simply but has (at least) two major defectsif our commentary is to address the issues raised at the outset. The …rst isthat by eliminating the possibility that agents might search for new productiveopportunities, we have closed o¤ the possibility that the right-hand tail of theincome distribution might be fattened by globalization (note that in Figure 3,both tails are thinned out by the change). The second is that the rate at whichpartnerships break up is the same regardless of globalization, and so we cannotaddress the possibility that turnover rises, or that employment becomes moretemporary, as a result of the change in the environment. Both are widely held

4 The segment bd is parallel to ce, as is dh to eg.

14

popular perceptions in some quaters about what increased openness does, andare part and parcel with some arguments about the costs of economic progress,and so it would be desirable to have a richer model that can incorporate them.We construct such a model here, by allowing for the possibility that partnershipshave not only a risk-sharing aspect, but a productive function as well, and thatsome partnerships are more productive than others do to variation in matchquality.

In such a model, a new kind of risk emerges: the possibility that one maybe ‘dumped’ by one’s partner when that partern …nds a new partner who is abetter match for his or her particular talents. In principle, this may bring aboutsubstantial welfare costs in a world in which contracting is limited.

Consider an economy with two countries, A and B, in each of which there isa continuum of agents of measure 1. Two agents must meet in order to produceoutput, which is homogeneous and non-storable. An agent can produce withat most one other agent at a time. An agent who is currently producing withanother will be called ‘employed,’ and an agent who is not currently producingwith another will be called ‘unemployed.’ Time is discrete, measured in periodsindexed from t = 0 to 1.

If an agent has produced with another in the previous period, say thatthose two agents are ‘partners.’ An agent can search at the beginning of eachperiod for a partner. This is costless, and can be done whether the agentcurrently has a partner or not. Each time an agent searches, with probabilityÁ 2 (0; 1) she will locate another agent, randomly selected from the generalpopulation (employed as well as unemployed), who then becomes a potentialnew partner. It is necessary for an agent to locate another in this way beforethey can communicate.

All agents are ex ante identical, but ex post not all matches are equallyproductive. When two agents produce together, the output they realize willbe given by ! units of output per period, where ! = e! if they are both fromthe same country and ! = e! ¡ K if they are from di¤erent countries, where e!is a random variable realized once in the lifetime of any pair of agents, and isunchanging thereafter, and K is a cost of doing business across borders. Thevariable e! is distributed iid across agents, and its realization can be observed byeither agent in a potential partnership immediately when they …nd each otherthrough search. The variable e! measures the ‘match quality’ of this particularpair of agents together. The parameter K can be thought of as capturing thecost of adapting to di¤erent regulations; communications costs; costs of trans-portation of inputs and production output; and outright trade impediments.

By contrast, any unemployed agent receives an endowment of y per period.There is risk within each relationship, because the output of ! per period is

not distributed evenly within the relationship. In particular, in each period onemember (the ‘lucky’ member) of the partnership receives ¸! units of productionand the other (the ‘unlucky’ member) receives (1¡¸)! units, where ¸ 2 (1=2; 1)is a parameter indicating the importance of luck. Regardless of the history, ineach period each agent in a partnership is equally likely to be the lucky member.Importantly, which member is the lucky one in any given period is observed by

15

then permanently dissolved. At this time an agent who has an existing partnerand who has found a potential new partner has the option of relocating to thelocation of that new partner, which is a necessary condition for establishing anew partnership with that new partner. (v) After any such relocations, wherean agent has moved to the location of a new potential partner, negotiations oc-cur between the two new potential partners over the new partnership. (vi) Theidentity of this period’s lucky partners is revealed. (vii) Each partner choosesto surrender a fraction µ 2 [0; 1] of her output to her partner (this is the formthat risk-sharing takes). (viii) Consumption occurs; in each period this is equalto the agent’s output plus net transfers received from the agent’s partner.

4.1 Symmetric equilibria.

Equilibria of the type of model described above can be very complicated, partlybecause of the potential for renegotiation many times within each relationship.If agents i and j are partners, for example, and i …nds an attractive alternativepartner, if j then o¤ers i a better deal in order to persuade her not to dissolvethe partnership and i accepts, then the relationship between i and j becomesasymetric, and will generally remain so after i’s alternative partner has vanishedfrom the scene. In equilibrium, then, there would be a distribution of payo¤sacross the population, in which agents in apparently the same situation willreceive di¤erent payo¤s because of the e¤ect of past opportunities. Even if theequilibrium is ex ante symmetric, it would not be ex post symmetric.

Such e¤ects are certiainly of interest, but in order to preserve the simplicity ofthe model and make the trade-o¤s of interest clear, we will focus on a portion ofthe parameter space in which ex post symmetric equilibria exist. In order for thisto be the case, it must be an equilibrium for an agent with an existing partnerwho has discovered an alternative partner either to reject a partnership withthe newcomer as no more attractive than the status quo, and thus irrelevant, orto leave. In order to ensure that this is consistent with equilibrium, we imposethree parameter restrictions.

First, we assume that the variable e! is drawn from a two-point distribution,with low value !B (for ‘bad match’) attained with probability (1 ¡ ¼) and highvalue !G (for ‘good match’) attained with probability ¼.

Second, we focus on only two values for the cost, K, of producing in aninternational partnership. Consider the ‘pre-globalization’ value of K to be avalue large enough that international partnerships are not viable: K > !H .Then under ‘globalization,’ we set the value of K to zero. This way, we need toconsider, e¤ectively, only two values of ! either with or without globalization.

Third, we need to assume that if agent i is in a partnership with j, withwhom the match is bad (! = !B), and then i comes across a potential newpartner k with whom his match would be good (! = !G), then i cannot bepersuaded to stay with j by any credible promise that j might make. Thissays that the highest expected present discounted value of utility that i couldreceive in any subgame-perfect equilibrium of the game between i and j is less

17

than the utility i would get in the best symmetric subgame-perfect equilibriumin the game between i and k. To make this more precise, consider the bestsubgame-perfect equilibrium for i in the partnership between i and j, and forany s = 0; 1; : : : 1 let V ¤(s) and V ¤¤(s) denote the present discounted valueof expected utility, for i and j respectively, evaluated at the (s + 1)’th periodof that equilibrium path on into the future. (Thus, V ¤(0) indicates the payo¤from the …rst period on, or the payo¤ from the whole equilibrium path.) Letthe payo¤ in the best symmetric equilibrium in a good match be V G. We thenwant:

V G > V ¤(0).

We can put some bounds on V ¤(0). Consider the incentive compatibilityconstraint on j in the …rst period of the equilibrium that most favors i, assumingthat j is the lucky member that period:

U(¸!B) + ±V U · U(¸!B(1 ¡ µL)) + ±½V ¤¤(1) + ±(1 ¡ ½)V U ,

where µL is the fraction of i’s output that she delivers to j given that she islucky, and V U is the payo¤ to an unemployed person. Similarly, the incentivecompatibility constraint in the event that i is not lucky is:5

U((1 ¡ ¸)!B) + ±V U · U((1 ¡ ¸)!B(1 ¡ µN)) + ±½V ¤¤(1) + ±(1 ¡ ½)V U ,

where µN

is the fraction of i’s output that she delivers to j given that she isnot lucky. Clearly, the larger is V ¤¤(1), then the larger is the (µL; µN) pair

that will satisfy these conditions. Denote by µ(v) = (µL

(v); µN

(v)) the highest

(µL; µN) pair to satisfy these two conditions if V ¤¤(1) = v. Note that both µL

and µN

are strictly increasing, strictly concave functions. We know that

V ¤(0)

= [U((¸ + µN(1 ¡ ¸))!B) + U(((1 ¡ ¸) + µL¸)!B)]=2

+±½V ¤(1) + ±(1 ¡ ½)V U

· [U((¸ + µN

(V ¤(0))(1 ¡ ¸))!B) + U(((1 ¡ ¸) + µL

(V ¤(0))¸)!B)]=2

+±½V ¤(0) + ±(1 ¡ ½)V U

As a result:

V ¤(0) · ª(V ¤(0)),

5 We assume for this discussion that in the …rst period of the best subgame perfect equilib-rium that is most favorabe to j, i would make a payment to j regardless of which partner islucky in that period. Given this, it is straightforward to see that without loss of generalitywe can assume that j makes no payment to i. The possibility that which partner makes thepayment to the other depends on which is lucky can be examined in a parallel manner.

18

where

ª(v) ´ f[U((¸ + µN

(V ¤(0))(1 ¡ ¸))!B) + U((1 ¡ ¸) + µL

(V ¤(0))¸)!B)]=2

+±(1 ¡ ½)V Ug=(1 ¡ ±½).

The function ª is increasing and strictly concave function, and lies weaklyabove the 45± line at v = V ¤(0). Therefore, there are at most two values ofv, at which v = ª(v), and the larger must be greater than or equal to V ¤(0).Call this value V max. This value provides an upper bound to the true value ofV ¤(0). The su¢cient condition required is then, simply, that V G > V max. Thiscan be checked readily for any given set of parameters.

With our focus on ex post symmetric equilibria, we can then denote thepayo¤s to all agents succinctly. Let V U denote the expected present discountedutility of an unemployed agent and let V (!) denote that for an employed agentwhose match quality is !, measured at the beginning of the period before thesearch stage.

References[1] Baker, George; Robert Gibbons; and Kevin J. Murphy (1994). “Subjective

Performance Measures in Optimal Incentive Contracts.” Quarterly Journalof Economics 109:4 (November), pp. 1125-56.

[2] Baker, George; Robert Gibbons; and Kevin J. Murphy (1997). “ImplicitContracts and the Theory of the Firm.” National Bureau of EconomicResearch Working Paper: 6177 (September).

[3] Bertrand, Marianne (1998). “From the Invisible Handshake to the InvisibleHand? How Import Competition Changes the Employment Relationship.”Princeton Industrial Relations Section Working Paper 410 (December).

[4] Coate, Stephen and Martin Ravallion (1993). “Reciprocity without Com-mitment: Characterization and Performance of Informal Insurance Ar-rangements.” Journal of Development Economics 40:1 (February), pp. 1-24.

[5] Dixit, Avinash K. (1987). “Trade and Insurance with Moral Hazard.” Jour-nal of International Economics 23:3/4 (November), pp. 201-20

[6] Farber, Henry S. “The Changing Face of Job Loss in the United States,1981-1995”. Brookings Papers on Economic Activity (Microeconomics1997), pp. 55-128.

[7] Kranton, Rachel E. (1996). “Reciprocal Exchange: A Self-Sustaining Sys-tem.” American Economic Review 86:4 (September), pp. 830-51.

[8] Kristof, Nicholas D. (1997). “Real Capitalism Breaks Japan’s Old Rules.”New York Times, July 15.

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[9] MacLeod, W. Bentley and James M. Malcomson (1989). “Implicit Con-tracts, Incentive Compatibility, and Involuntary Unemployment. Econo-metrica 57:2 (1989), pp. 447-80.

[10] MacLeod, W. Bentley and James M. Malcomson (1993). “Investments,Holdup, and the Form of Market Contracts American Economic Review83:4 (September), pp. 811-37.

[11] Rodrik, Dani (1997). Has Globalization Gone Too Far? Washington, DC.:Institute for International Economics.

[12] Slaughter, Matthew J. (1998). “International Trade and Labor-Market Out-comes,” Economic Journal, 108:450 (September), pp. 1452-1462.

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Figure 1: The Determination of the Steady-State Number of Searchers: Endowment Model.

450

1 1/φσS

θ~

P(θ,θ;φ)~ _

T(θ)~

Figure 2: The optimal choice of θ, given θ._~

θopt

θ ∗

Figure3: Construction of the Equilibrium.

θ(θ)~ _

θcrit

45O

θ_

Figure 4: Comparative statics.

φ

α

σ sφ

φ

θ

1

1

θ opt

critθ

critφ

Figure 5: Income distribution effects of globalization.

Cumulative fraction of population.

Cum

ulat

ive

frac

tion

of c

onsu

mpt

ion.

(1−π)σ S 1−πσ Sa

b c

de

f

g

h

i

(1−π)

}}

}}

(1−σ )(1−π)(ε +θε )/ε_

S L H

(1−σ )π(1−θ)ε /εS H _

_πσ ε /εS H

S L(1−π)σ ε /ε_