migrant smuggling when exploitation is private information

Migrant smuggling when exploitationis private information

Yuji Tamura School of Economics, La Trobe University

Abstract. This study contributes to the small theoretical literature on human smugglingby assuming for the first time asymmetric information in analysis. The assumption raisesthe possibility of an adverse selection equilibrium where only exploitative smugglers areemployed at a low fee even though migrants are willing to pay non-exploitative smugglersa high fee. More important, I find that improved inland apprehension of migrants mayincrease the incidence of migrant exploitation while failing to decrease smuggling attempts.Furthermore, improved border apprehension of migrants and smugglers may not affectthe market at all. JEL classification: F22, D82

Contrebande d’immigrants quand l’information a propos de l’exploitation est privee.Cette etude contribue au corpus restreint de litterature theorique sur la contrebanded’immigrants en developpant une analyse pour le cas ou il y a information asymetrique.Le postulat souleve la possibilite d’un equilibre de selection adverse ou les contrebandierssont engages a un taux de remuneration faible meme si les immigrants sont prets a payerdes frais eleves a des contrebandiers qui ne sont pas des exploiteurs. Plus important, unmecanisme ameliore d’interception des immigrants illegaux a la frontiere peut accroıtrel’incidence de l’exploitation des immigrants sans diminuer les tentatives de contrebande.De plus, un mecanisme ameliore d’interception des immigrants et des contrebandiers a lafrontiere peut fort bien ne pas affecter ce marche du tout.

I am also affiliated with the ANU Centre for Economic Policy Research. This article is based ona chapter in my PhD thesis. I received useful comments from Ben Lockwood, Ian Preston, TomRenstrom, Richard Cornes, Tim Hatton, Jeff Williamson, Jeff Round, Uwe Dulleck, NormanIreland, Sajal Lahiri, Kieron Meagher, Lana Friesen, Nutt Thampanishvong, Beverly Lapham,Yvette Kirby, an anonymous referee, and participants of seminars at Warwick, Linz,Queensland, and ANU, the Eleventh Spring Meeting of Young Economists at Universidad deSevilla, and UNU-WIDER Conference ‘Fragile States—Fragile Groups’. I am grateful forfinancial support from the Department of Economics at Warwick University, and the Institutefor International Integration Studies at Trinity College Dublin. All remaining errors are mine.Email: [email protected]

Canadian Journal of Economics / Revue canadienne d’Economique, Vol. 46, No. 4November / novembre 2013. Printed in Canada / Imprime au Canada

0008-4085 / 13 / 1463–1479 / C© Canadian Economics Association

1464 Y. Tamura

1. Introduction

In this article, I introduce asymmetric information to Tamura’s (2010) model ofthe migrant smuggling market where smugglers are heterogeneous in terms of thecapacity to exploit smuggled labour. The economic literature on this market is stilltiny, both theoretically (Friebel and Guriev 2006; Tamura 2010) and empirically(Gathmann 2008; Omar Mahmoud and Trebesch 2010).1 The theoretical expo-sitions have so far assumed complete and perfect information. However, there isevidence that suggests that potential users of smugglers face uncertainty regard-ing the risk of exploitation by their smugglers (Omar Mahmoud and Trebesch2010; UNODC 2011). Hence my purpose is to analyze a model by assuming thatpotential migrants are informationally disadvantaged in this market.

In Tamura (2010), workers wishing to migrate are randomly matched withsmugglers. Each smuggler then proposes a price of an illegal border crossing.The matched worker may or may not accept the proposal. If the worker accepts,he or she must obey the smuggler’s instructions so that a successful border cross-ing can be achieved. This gives the smuggler a chance to use the client’s labourunfairly at the destination. However, smugglers differ in their capacities to exploitsmuggled labour, and hence not all smugglers utilize the opportunity to exploit.2

His analysis suggests that destination countries may prefer to improve the appre-hension of smugglers and their clients at the border rather than inland, althougheither one of these anti-smuggling measures would reduce the incidence of mi-grant exploitation. The reason is that improved border apprehension decreasesthe incidence of smuggling attempts by causing existing exploitative smugglersto become unemployable. Improved inland apprehension, on the other hand,either maintains or even increases people smuggling by inducing exploitative andunemployed smugglers to take up non-exploitative smuggling.

In this paper, I change the informational assumption and examine the casewhere smugglers’ capacities to exploit smuggled labour are private information.The introduction of this type of asymmetric information is justifiable becausesurveys of victims of human trafficking indicate that potential users of smugglersface uncertainty regarding the risk of post-migration exploitation by their smug-glers (UNODC 2011, 6-7, 43-4). Furthermore, Omar Mahmoud and Trebesch(2010) provide some microeconometric evidence that suggests that the incidenceof exploitation may be reduced by promoting the awareness of exploitation riskamong potential migrants.

My analysis shows that the market equilibrium may be characterized by ad-verse selection a la Akerlof (1970), though not necessarily. Adverse selection inthis market’s context is the situation where only exploitative smugglers are hired,even though potential migrants are willing to pay a higher-than-market fee to

1 Friebel and Guriev (2013) summarize and compare the insights provided by the few existingstudies.

2 In both Friebel and Guriev (2006) and Tamura (2010), only one side of the market ischaracterized by heterogeneity. In the former, potential migrants are heterogeneous.

Migrant smuggling when exploitation is private information 1465

smugglers who do not exploit migrants and non-exploitative smugglers are will-ing to smuggle at that higher fee. I find that anti-illegal migration efforts tendto result in an adverse selection equilibrium where all smuggled migrants areexploited. Although this may be a concern in terms of the welfare of smuggledpeople, a move to an adverse selection equilibrium implies a fall in the numberof smuggling attempts and hence might be desired by destination countries. Onthe other hand, anti-exploitation efforts tend to result in a full employment equi-librium, although they do discourage post-smuggling exploitation: they convertexploitative smugglers into non-exploitative ones but do not make smugglersunemployable.

More important, I find that an insufficient improvement in one of the anti-illegal migration measures – namely, inland apprehension of smuggled migrants –may increase the incidence of migrant exploitation without reducing the numberof smuggling attempts. In other words, a half-hearted effort to improve inlandapprehension of smuggled migrants is not only ineffective in terms of reducingmigrant smuggling but also harmful to smuggled migrants. This result suggeststhat destination countries may unintendedly increase migrant exploitation whenthe market is characterized by asymmetric information. Furthermore, I find thatimproved border apprehension affects neither the employment nor the exploita-tion decisions of smugglers when the apprehesion rate is not made sufficientlyhigh. This is also different from the symmetric information case, where even amarginal improvement can decrease smuggling by making exploitative smugglersunemployable.

The next section presents the model. Section 3 examines policy implications.Section 4 concludes.

2. Model

In this section, I modify Tamura’s (2010) model to introduce asymmetric infor-mation. I use the same notations to facilitate a comparison. For self-containment,I reproduce several key equations presented in that article. However, accompa-nying notes and caveats are omitted, as the reader can find them in that article.The reader who is familiar with Tamura (2010) may skip to subsection 2.2,where expected post-migration exploitation is introduced to the utility functionof each potential migrant as a consequence of assuming asymmetric information.However, note that subsection 2.1 presents two thresholds (4) and (8) that are dif-ferent from (12) and (13) in Tamura (2010), owing to the different informationalassumption.

In the migrant smuggling market, smugglers are the sellers, and workers arethe buyers. Two countries exist: the home country and the destination country.A smuggler is a smuggling organization, operating across the two countries. Allworkers are legal residents of the home country. The earnings per unit of workers’labour are exogenously given, and they are higher in the destination country than

1466 Y. Tamura

in the home country. Workers may therefore wish to migrate to the destinationcountry. However, a worker cannot migrate except by hiring a smuggler. Eachsmuggler has an identical capacity to smuggle: it is normalized to one worker.On the other hand, smugglers differ in the capacity to exploit smuggled labourin the destination country. Workers are identical and are not wealth constrainedin financing clandestine migration. All workers and smugglers are risk neutral.There are at least as many workers as smugglers in the market. The measure ofsmugglers is normalized to 1. Events take place in the following order.

1) Each smuggler is randomly matched with a worker in the home country.2) In each pair, the smuggler proposes to the worker a fee for smuggling.3) The worker either hires or does not hire the smuggler at the proposed fee.

A. If the worker does not hire the smuggler, the match breaks.B. If the worker hires the smuggler, the latter attempts to smuggle the former.

The worker is required to obey the smuggler during smuggling.i. If the border crossing is unsuccessful, the worker pays nothing, and the

match breaks.ii. If the border crossing is successful, the worker pays the proposed fee.

After receiving the fee, the smuggler may continue to restrict the free-dom of the worker for exploitation.

a. If not exploited, the worker becomes free to sell all labour.b. If exploited, the worker can sell the labour net of exploitation when

released.

Thus, matched smugglers and workers play an ultimatum game.Policy implications will be derived through the following parameters whose

values the destination country can choose: p > 0, the fixed penalty for smug-gling; q > 0, the constant marginal penalty for exploitation; βi ∈ (0, 1), the givenprobability of border apprehension of player i ∈ {M, S}, where M labels migrantand S smuggler; and λi ∈ (0, 1), the given probability of inland apprehension.The four apprehension probabilities are independent of each other.

2.1. SmugglersLet k ∈ [0, 1] denote the exogenously given capacity of a smuggler to exploit thesmuggled client’s labour net of exploitation costs. Let �(k) be a smooth, non-degenerate distribution function and φ(k) > 0 ∀ k ∈ [0, 1] be the correspondingdensity function. Each worker is endowed with one unit of labour that can gen-erate y > 0 in the destination country. Accordingly, if exploitation takes place,the smuggler appropriates ky and the client’s gain is (1 − k)y.

Suppose that the migrant paid a smuggling fee, f , after a successful bordercrossing. The type-k smuggler’s expected profit from the post-smuggling exploita-tion is

π (f |k) = (1 − λS)(1 − λM)ky − λS[f + p + (1 − λM)kq], (1)


where the second term implies that the total penalty is increasing in the feereceived.

The type-k smuggler exploits the client if π (f |k) > 0. Each smuggler’s ex-ploitation decision is indicated by

e(f |k) ={

1 if π (f |k) > 0

0 otherwise.(2)

The exploitation decision condition can be rewritten as

f < f (k) = (1 − λM)(

1 − λS

λSy − q

)k − p, (3)

where f (k) is the type-k smuggler’s exploitation decision threshold fee. It impliesthat, if y > qλS/(1 − λS) holds, smugglers with higher exploitation capacitiesare more likely to exploit their clients for a given fee. The exploitation decisioncondition can also be rewritten as

k > k(f ) = f + p

(1 − λM)(

1 − λS

λSy − q

) , (4)

where k(f ) is the exploitation decision threshold capacity at a given fee. Smug-glers with k ∈ [0, k(f )] can commit to non-exploitative smuggling at f, while theothers with k ∈ (k(f ), 1] cannot.

The success of a border crossing is uncertain at the pre-smuggling stage. Hence,the type-k smuggler’s expected profit from smuggling is

π (f |k) = (1 − βS)(1 − βM)[f + π (f |k)e(f |k)] − βSp − c, (5)

where c > 0 denotes the sum of smuggling costs. The type-k smuggler requiresπ (f |k) > π to smuggle a worker, where π > 0 denotes the alternative profit avail-able to any smuggler. If a smuggler decides not to exploit the client, that is, ifπ (f |k) ≤ 0, then the requirement can be rewritten as

f > f ≡ βSp + c + π

(1 − βS)(1 − βM). (6)

The threshold fee, f , is independent of the capacity type and is hence any smug-gler’s reservation value of non-exploitative smuggling. If f is not greater than that,no smuggler makes a positive expected profit from non-exploitative smuggling.

1468 Y. Tamura

If a smuggler exploits the client after successful smuggling, that is, if π (f |k) >

0, then the requirement, π (f |k) > π , becomes

f > f (k) = f + λSp1 − λS

− (1 − λM)(

y − λS

1 − λSq)

k, (7)

where f (k) is the type-k smuggler’s reservation value of exploitative smuggling.It suggests that if y > qλS/(1 − λS) holds, the higher the exploitation capacity asmuggler has, the lower the reservation value of the exploitative service. In otherwords, an exploiting smuggler with a high k can operate at a low fee. Inequality(7) can be rewritten as

k > k(f ) =f + p − f − f

λS

(1 − λM)(

1 − λS

λSy − q

) , (8)

which suggests that smugglers with k ∈ (k(f ), 1] make a positive expected profitfrom exploitative smuggling at a given fee if hired. Note that thresholds (4) and(8) together imply

k(f ) � k(f ) ⇔ f � f . (9)

2.2. WorkersEach worker is endowed with one unit of labour which is supplied inelastically ineither the home or the destination country. Returns to a unit of labour is 0 andy > 0 in the home and destination countries, respectively. If apprehended at theborder or inland, the worker is sent back to the home country without paying apenalty for illegal migration.

The exploitation capacity of each smuggler is private information, and po-tential migrants cannot observe the k of any specific smuggler. A successfullysmuggled worker’s expected utility after paying the fee is

u(f ) = [1 − (1 − λS)κ(f )](1 − λM)y, (10)

where κ(f ) denotes the expected exploitation that was formed when the fee wasproposed. When information is complete and perfect, ke(f |k) enters instead.

At the pre-migration stage, a worker’s expected utility from hiring a smuggler is

u(f ) = (1 − βS)(1 − βM)[u(f ) − f ]. (11)


A worker hires the matched smuggler if u(f ) ≥ 0 or, equivalently,

f ≤ u(f ). (12)

Thus, u(f ) is every worker’s reservation value of smuggling services.

2.3. EquilibriumI now characterize the perfect Bayesian equilibrium of this model. Let f ◦ ≡ (1 −λM)y, the maximum fee which every worker is willing to pay for non-exploitativesmuggling, as condition (12) suggests. Accordingly, λSf ◦ is the maximum fee thatevery worker is willing to pay for the most exploitative smuggling. Tamura (2010)characterizes the subgame perfect Nash equilibrium under the assumption thatboth f (1) > f ◦ and λSf ◦ > f (1) hold. For ease of comparison, I also assume thatthese two inequalities initially hold. The first inequality means that, as implied byinequality (3), f ◦ is not sufficiently large to motivate the type-1 smuggler to giveup post-smuggling exploitation, which in turn suggests that the type-1 smugglerwill always exploit the client if hired. The second inequality means that, as impliedby inequality (7), λSf ◦ is sufficiently large for the type-1 smuggler to supply themost exploitative smuggling, which in turn suggests that the type-1 smuggler is infact hired unless the expected exploitation unreasonably exceeds one. As statedin Tamura (2010, lemmas 3 and 4), the second inequality also implies f ◦ > f ;that is, the worker’s reservation value of non-exploitative smuggling exceeds thesmuggler’s. Finally, inequalities (3), (4), (7), (8), and Tamura (2010, lemma 2)imply that both k(f ) and k(f ) are less than one for f ∈ (f (1), f (1)) when f (1) > f ◦

and λSf ◦ > f (1) hold.I assume that, prior to listening to a fee proposal, each matched worker has

a belief about the type of the matched smuggler according to the distribution ofsmugglers across different capacities.3 That is, the prior belief that the probabilityof the matched smuggler being of type k is simply φ(k) ∈ (0, 1). When making adecision, each matched worker knows the fee proposal by the matched smuggleronly and does not know the fee proposals in the other matches. Once the matchedsmuggler proposes a fee, the belief is updated to μ(k|f ) ∈ [0, 1].

I assume that workers believe that any particular f can be proposed by allsmugglers who can make a positive expected profit if workers accept it. This as-sumption is reasonable because, as Tamura (2010, lemma 1) suggests, the expectedprofit of every smuggler is strictly increasing in the fee. In other words, workersare aware that smugglers have an incentive to masquerade as less exploitativethan they actually are in order to receive a fee higher than what workers wouldbe willing to pay if the exploitation capacity is not private information.

3 This assumption may not be overly unrealistic if, for example, workers are aware of humantrafficking incidents because of rumours in their communities and the media.

1470 Y. Tamura

Accordingly, if the proposed fee is greater than f ,

μ(k| f > f

) = φ(k) ∀ k ∈ [0, 1], (13)

because all smugglers can make a positive expected profit at any f > f . Inequality(6) suggests that all smugglers can make a positive expected profit from non-exploitative smuggling at such a fee. Inequality (4) suggests that all smugglers withk ≤ k(f ) can commit to non-exploitative smuggling at any f > f . By inequality(8) and relation (9), all smugglers with k > k(f ) can make a positive expectedprofit from exploitative smuggling and are unable to commit to non-exploitativesmuggling at any f ∈ (f , f (k)).

If the proposed fee is greater than f (1) but does not exceed f , inequality (6) im-plies that no smuggler can make a positive expected profit from non-exploitativesmuggling. Inequalities (4) and (8) and relation (9) suggest that smugglers withk ∈ (k(f ), k(f )] cannot make a positive expected profit from exploitative smug-gling, either. However, smugglers with k > k(f ) can make a positive expectedprofit from exploitative smuggling. Hence, workers believe that an f ∈ (f (1), f ] isproposed by smugglers with k > k(f ) only; that is,

μ(k| f ∈ ( f (1), f ]) =

⎧⎪⎨⎪⎩

0 for k ∈ [0, k( f )]φ(k)

1 − ∫ k( f )0 φ(k)dk

for k ∈ (k( f ), 1]. (14)

Finally, if the proposed fee does not exceed f (1), then no smuggler can make apositive expected profit from either exploitative or non-exploitative smuggling.Therefore,

μ(k| f ≤ f (1)) = 0 ∀ k ∈ [0, 1]. (15)

The expected exploitation at a given fee is

κ( f ) =∫ 1

0μ(k| f )ke( f |k)dk. (16)

LEMMA 1. Suppose f (1) > f ◦ and λSf ◦ > f (1). The expected exploitation is thendecreasing in f over ( f (1), f (1)) and is continuous except at f .

Proof. The expected exploitation for f > f is

κ( f | f > f ) =∫ 1

0φ(k)kdk −

∫ k( f )

0φ(k)kdk. (17)


Since function (4) implies dk( f )/df > 0, we have dκ( f | f ∈ ( f , f (1)))/df < 0.The expected exploitation for f ∈ ( f (1), f ] is

κ( f | f ∈ ( f (1), f ]) =∫ 1

0 φ(k)kdk − ∫ k( f )0 φ(k)kdk

1 − �(k( f )). (18)

Function (8) implies dk( f )/df < 0, and the denominator in expression (18) in-creases more than the numerator as k( f ) decreases, because k ∈ [0, 1]. Therefore,dκ( f | f ∈ ( f (1), f ])/df < 0. The discontinuity at f is due to the discrete changein μ(k| f ) for k ≤ k( f ) at f ; that is, μ(k| f > f ) = φ(k) > 0 but μ(k| f ) = 0 ∀k ∈ [0, k( f )], where k( f ) = k( f ). Q.E.D.

Accordingly, function (10) suggests that the expected post-migration payoff toeach worker is increasing in the fee over ( f (1), f (1)). Note that κ( f | f ≥ f (1)) = 0because all smugglers can commit to non-exploitative smuggling at an f ≥ f (1);that is, by Tamura (2010, lemma 1), e( f |k) = 0 ∀ k ∈ [0, 1] if f ≥ f (1).

Since condition (12) suggests that workers accept any fee that ensures thema non-negative expected utility, Tamura (2010, lemma 1) suggests that everysmuggler will propose

f = [1 − (1 − λS)κ( f )] f ◦ (19)

if a positive expected profit is guaranteed by this fee. If this fee causes a non-positive expected profit, the smuggler will not propose it but will propose anyfee at which the expected profit is positive if hired. Such a fee is too high forthe worker to accept and allows the proposing smuggler to avoid supplyingnon-profit-making smuggling.

At this point, the reader might question the reasonableness of the worker’sbelief. Why do workers believe that an f can be proposed by all smugglers who canmake a positive expected profit at the fee when the f in question is greater thanu( f )? Shouldn’t workers anticipate that smugglers know such a fee is rejected?Therefore, should workers not realize that the smugglers making such a proposalare trying to avoid being hired? Should workers not then become aware that thesmugglers who can make a positive expected profit at u( f ) do not propose any feehigher than that because they desire to be hired? In other words, should workersnot regard a fee higher than u( f ) as a signal that the proposing smuggler is theone who is adversely affected in the market and hence deserves the high fee beingproposed?

Workers do know that the smugglers who can make a positive expected profitat u( f ) do not propose a fee higher than that. They also know that the smugglerswho cannot make a positive expected profit at u( f ) will propose a fee higher thanthat in order to avoid being hired. However, if workers regard the high fee as asignal for less exploitative smuggling that deserves the high fee and will accept it,the smugglers who can make a positive expected profit at u( f ) will also propose

1472 Y. Tamura

the high fee, as Tamura (2010, lemma 1) suggests. Thus, the high fee is not acredible signal for less exploitative smuggling. Therefore, it is in the worker’s bestinterests to believe that an f can be proposed by all smugglers who can make apositive expected profit if workers accept it even if the f in question is greaterthan u( f ).

LEMMA 2. Suppose both f (1) > f ◦ and λSf ◦ > f (1). Then, there exists at leastone f ∈ [λS f ◦, f ◦) that satisfies equation (19) if either

i) u( f + ε) ≥ f + ε with an arbitrarily small ε > 0,ii) u(λS f ◦) > λS f ◦ and u( f ) ≤ f , or

iii) u(λS f ◦) = λS f ◦.

Proof. First, since κ( f ) ∈ [0, 1], equation (19) does not hold for any f /∈[λS f ◦, f ◦]. Second, f (1) > f ◦ and λS f ◦ > f (1) imply κ( f ◦) > 0; that is, therealways is at least one exploitative smuggler who can make a positive expectedprofit at f ◦ by assumption; see Tamura (2010, lemma 3). Hence, u( f ◦) < f ◦.Third, from lemma 1, we know that u( f ) is increasing in f ∈ [λS f ◦, f ◦] and con-tinuous except at f . (i) The weak inequality ensures that at least one u( f ) = fexists over ( f , f ◦). (ii) The gap between λS f ◦ and f (1) is large enough to allowsome smugglers with k < 1 to make a positive expected profit from exploitativesmuggling at λS f ◦; that is, λS f ◦ > f (k) for these type-k < 1 smugglers. In such acase, u(λS f ◦) > λS f ◦. Hence, u( f ) ≤ f ensures that at least one u( f ) = f existsover (λS f ◦, f ]. (iii) The gap between λS f ◦ and f (1) is so small that any smug-gler other than type-1 cannot make a positive expected profit from exploitativesmuggling at λS f ◦. Q.E.D.

The conditions (i) and (ii) may hold simultaneously. In such a case, there areat least two fees that meet equation (19) over (λS f ◦, f ◦). The conditions (i) and(iii) may also hold simultaneously. However, it is obvious that the conditions (ii)and (iii) cannot hold simultaneously.

Note that the conditions in lemma 2 are sufficient but not necessary for theexistence of an f ∈ [λS f ◦, f ◦) that satisfies equation (19). For example, even ifu( f + ε) < f + ε, there may exist some f ∈ ( f + ε, f ◦) at which equation (19)is met, depending on �(k). This can happen if many smugglers switch fromexploitative to non-exploitative smuggling as soon as f is gradually increasedfrom f + ε, and the number of switching smugglers becomes very small soonafterwards. In such a situation, u( f ) cuts the 45-degree line twice over ( f + ε, f ◦),as f increases in the ( f, u( f )) space: the first from below and the second fromabove (see, e.g., Wilson 1980).

PROPOSITION 1. Suppose both f (1) > f ◦ and λS f ◦ > f (1).

i) If at least one u( f ) = f ∈ ( f , f ◦) exists, then we have a unique pooling equi-librium where all smugglers propose

f ≡ max{f : f = u( f ) ∈ ( f , f ◦)} (20)


and are hired. Smugglers with k ≤ k( f ) do not exploit their clients, while theothers with k > k( f ) do.

ii) Suppose f = u( f ) ∀ f ∈ ( f , f ◦) so that case (i) does not apply. If at least oneu( f ) = f ∈ [λS f ◦, f ] exists, then we have partially pooling equilibria where allsmugglers with k > k( f ′) propose

f ′ ≡ max{ f : f = u( f ) ∈ [λS f ◦, f ]}, (21)

are hired, and exploit their clients. Smugglers with k ∈ (k( f ′), k( f ′)] proposeany f > f (k) and are not hired. Smugglers with k ≤ k( f ′) propose any f > fand are also not hired.

Proof. (i) If equation (19) holds over ( f , f ◦), Tamura (2010, lemma 1) suggeststhat every smuggler maximizes the expected profit by proposing f , whetheror not equation (19) holds over [λS f ◦, f ]. (ii) If equation (19) does not holdover ( f , f ◦), but it does over [λS f ◦, f ], Tamura (2010, lemma 1) suggests thatevery smugglers with k ∈ (k( f ′), 1] maximizes the expected profit by proposingf ′. Smugglers with k ∈ (k( f ′), k( f ′)] propose any f > f (k) in order to avoid loss-making smuggling. Smugglers with k ≤ k( f ′) propose any f > f also in order toavoid being hired.4 Q.E.D.

Proposition 1(ii) suggests that the equilibrium might be characterized by ad-verse selection a la Akerlof (1970): only exploitative smugglers are hired at f ′, andall non-exploitative smugglers are driven out of the market even though migrantsare willing to pay f ◦ to hire non-exploitative smugglers and non-exploitativesmugglers are willing to be hired at that fee. Note that non-exploitative smug-glers are not able to signal the nature of their services by proposing an f > f ′,because workers believe that any particular f can be proposed by all smugglerswho can make a positive expected profit if workers accept it. Signalling a laSpence (1973, 1974) is not available either, for the model does not contain acostly investment opportunity, which some smugglers may use to indicate theircapacity to exploit.

Before examining policy implications, let us compare the equilibrium with theone characterized by Tamura (2010, proposition 1), who assumes that k is notprivate information.

PROPOSITION 2. Suppose both f (1) > f ◦ and λS f ◦ > f (1) . Then, both equilibriummeasure and proportion of employed non-exploitative smugglers are smaller withunobservable k than with observable k.

Proof. Inequality (4) indicates that smugglers with k ∈ [0, k( f )] are non-exploitative if hired. As Tamura (2010, proposition 1) shows, they propose f ◦

4 Alternatively, smugglers with k ≤ k( f ′) can also propose any f > f ′, knowing that it will not beaccepted anyway.

1474 Y. Tamura

and are hired in equilibrium when k is observable. Since f < f ◦, we have k( f ) <

k( f ◦). Besides, all non-exploitative smugglers are not hired in case (ii) of propo-sition 1, whereas there are always employed non-exploitative smugglers when k isobservable. Q.E.D.

As Tamura (2010, lemma 1) suggests, a type-k smuggler maximizes the ex-pected profit by proposing f ◦ if f (k) < f ◦ and the exploitation capacity is observ-able to the matched worker. However, when the worker cannot observe the ex-ploitation capacity, the fee this smuggler can charge is reduced by the existence ofother smugglers for whom f (k) ≥ f ◦ holds. Some smugglers for whom f (k) < f ◦

holds then end up providing exploitative smuggling, because the reduced fee isnot greater than f (k) but still exceeds f (k) for them. As a consequence, whenthe exploitation capacity is private information, more workers are exploited inthe market where all smugglers are employed: compare proposition 1(i) withTamura (2010, proposition 1). This means that although the pooling equilibriumfee under asymmetric information, f , is based on the average exploitation, it islower than the average of the symmetric-information equilibrium fees.

When not all smugglers are hired in the market, as in proposition 1(ii), somemay argue that the non-observability of the exploitation capacity is not necessar-ily bad. This is because the asymmetric information shrinks the market by makingall non-exploitative smugglers unemployed. Note that, since k( f ′) > k( f ◦), theequilibrium measure of employed exploitative smugglers is also smaller withunobservable k than with observable k.

3. Policy implications

I now examine the ceteris paribus effects of policy measures on the marketequilibrium.5 For illustrative purposes, I suppose that the market is initiallycharacterized by proposition 1(i). That is, there initially exists a unique poolingequilibrium where all smugglers propose an identical fee f ∈ ( f , f ◦) and arehired: some are exploitative, and the others non-exploitative.

PROPOSITION 3. Suppose f (1) > f ◦, λS f ◦ > f (1), and ∃u( f ) = f ∈ ( f , f ◦) initially.i) The equilibrium measure of employed non-exploitative smugglers is increasing

in the penalty for exploitation (q) and the probability of inland apprehensionof smugglers (λS) until it reaches unity. The equilibrium measure of employedexploitative smugglers is decreasing in q and λS by the same quantity until itreaches zero.

ii) The equilibrium measure of employed non-exploitative smugglers is initiallyincreasing in the penalty for smuggling (p), but subsequently drops to zero iffurther increasing p leads to u( f ) = f ∀ ( f , f ◦] . The equilibrium measure ofemployed exploitative smugglers is decreasing in p until it reaches zero.

5 An alternative, diagrammatic presentation of the same comparative statics is given in Tamura(2011, section 3).


iii) The equilibrium measure of employed non-exploitative smugglers is decreasingin the probability of inland apprehension of smuggled workers (λM) until itreaches zero. The equilibrium measure of employed exploitative smugglers isinitially increasing in λM , but is subsequently decreasing in it until it reacheszero if further increasing λM leads to u( f ) = f ∀ ( f , f ◦].

iv) Both equilibrium measures of employed non-exploitative and exploitativesmugglers are initially unaffected by the probabilities of border apprehen-sion of smugglers (βS) and migrating workers (βM), but subsequently themeasure of the former drops to zero and that of the latter is decreasing in theprobabilities until it reaches zero if further increasing in these probabilitiesleads to u( f ) = f ∀ ( f , f ◦].

Proof. (i) Expressions (4), (17), and (10) imply ∂ k/∂q, ∂ k/∂λS > 0, dκ(k(q))/dq,

dκ(k(λS))/dλS < 0, and du(κ(k(q)))/dq, du(λS, κ(k(λS)))/dλS > 0. To continueto hold (19), f must increase because du(κ(k( f )))/df ∈ (0, 1). Thus, f and krise. Expression (6) implies that neither q nor λS affects f . f ◦ is also unaffectedby them. (ii) Expressions (4), (17), and (10) imply ∂ k/∂p > 0, dκ(k(p))/dp < 0,and du(κ(k(p)))/dp > 0. To keep (19) maintained, f must increase becausedu(κ(k( f )))/df ∈ (0, 1) . Thus, f and k rise. However, expressions (3), (6), and(7) imply ∂ f /∂p, df (p, f (p), k)/dp > 0 and ∂ f (k)/∂p < 0. Therefore, further in-creasing p may result in u( f ) = f ∀ ( f , f ◦). If so, (6) is violated, and all non-exploitative smugglers become unemployed. Expressions (8), (18), and (10) thenimply ∂ k/∂p > 0, dκ(k(p))/dp > 0, and du(κ(k(p)))/dp < 0. To maintain (19), fmust decrease because du(κ(k( f )))/df ∈ (0, 1). Thus, f ′ falls, and k rises. (iii) Ex-pressions (4) and (17) imply ∂ k/∂λM > 0 and dκ(k(λM))/dλM < 0. Expression(10) implies

dudλM

= (1 − λS)yφ(k)k2 − [1 − (1 − λS)κ]y,

where the second term is the direct impact of λM on the post-migration payoff,and the first term is the indirect impact via the expected exploitation. This canbe rewritten as

dudλM

= [(1 − λS)(φ(k)k2 + κ) − 1

]y,

where the first term in the square brackets is less than one. Hencedu(λM, κ(k(λM)))/dλM < 0. To continue to hold (19), f must fall becausedu(κ(k( f )))/df ∈ (0, 1). Thus, f and k decrease. Further increasing λM may re-sult in u( f ) = f ∀ ( f , f ◦). If so, (6) is violated, and all non-exploitative smugglersbecome unemployed. Expressions (8), (18), and (10) then imply ∂ k/∂λM > 0,dκ(k(λM))/dλM > 0, and du(λM, κ(k(λM)))/dλM < 0. To maintain (19), f mustdecrease because du(κ(k( f )))/df ∈ (0, 1). Thus, f ′ falls, and k rises. (iv) Expres-sion (4) implies that neither βS nor βM affects k, which in turn suggests f remains

1476 Y. Tamura

the same. However, expressions (6) and (7) imply ∂ f /∂βi, df ( f (βi), k)/dβi > 0.Hence, further increasing βi may result in u( f ) = f ∀ ( f , f ◦). If so, (6) is vi-olated, and all non-exploitative smugglers become unemployed. Expressions(8), (18), and (10) then imply dk( f (βi))/dβi > 0, dκ(k( f (βi)))/dβi > 0, anddu(κ(k( f (βi))))/dβi < 0. To continue to hold (19), f must decrease becausedu(κ(k( f )))/df ∈ (0, 1). Thus, f ′ falls, and k rises. Q.E.D.

Proposition 3(i) indicates that the effects of the penalty for exploitation andthe inland apprehension of smugglers are qualitatively the same as those un-der complete and perfect information (Tamura 2010, proposition 2(i)); that is,the proportion of exploitative smugglers is reduced while full employment ismaintained even if unlimited resources are available. The difference is, of course,that, under asymmetric information with the initial equilibrium characterized byproposition 1(i), there is a unique smuggling fee that continues to rise to reachf ◦ as q or λS, or both, increases. The intuition behind this result is that these twopolicy measures do not affect the profitability of non-exploitative smuggling, asf ◦ − f > 0 is unaffected.6 Hence, initially exploitative smugglers simply switchto non-exploitative smuggling, as q and λS reduce the profitability of exploita-tive smuggling. It should be noted that, although the average exploitation permigrant is falling as q or λS increases, the small number of those who unluckilyhire exploitative smugglers suffer a large ex post loss from migration becausethese smugglers are endowed with the highest exploitation capacities while theequilibrium fee is relatively high.

The remaining parts of the proposition show that the effects of the otherfour policy measures depend on the informational assumption. Proposition3(ii) indicates that the effect of the penalty for smuggling is qualitatively sim-ilar to, but not the same as, the one under complete and perfect informa-tion (Tamura 2010, proposition 2(ii)). The equilibrium measure of employednon-exploitative smugglers is increasing in p as long as non-exploitative smug-gling is profitable. This conversion of initially exploitative smugglers into non-exploitative ones is also found under symmetric information. However, sincenon-exploitative smugglers are unable to charge as much as f ◦ when k is privateinformation, all non-exploitative smugglers could drop out of the market be-fore all exploitative smugglers do so. This possibility of adverse selection causedby making the penalty for smuggling severer does not arise under symmetricinformation.

Proposition 3(iii) shows that the effect of the inland apprehension of smuggledworkers is very different from the one under complete and perfect information(Tamura 2010, proposition 2(ii)). Here, improved inland apprehension of mi-grants initially converts non-exploitative smugglers into exploitative smugglers,

6 However, the profitability of non-exploitative smuggling is negatively affected by inlandapprehension if the probability of being apprehended inland is assumed positive fornon-exploitative smugglers. In this case, a sufficient improvement in inland apprehension caneliminate the market.


while the opposite is true under symmetric information. The reason is that, aslong as the fee is high enough to maintain full employment, λM has not only adirect negative effect on the profitability of exploitative smuggling (as in thecase of symmetric information) but also an indirect negative effect on the prof-itability of both exploitative and non-exploitative smuggling via a fall in the fee(as migrants’ reservation fee is lowered; see the proof). The overall effect is thatmore smugglers find exploitative smuggling more profitable than non-exploitativesmuggling. This result signals the importance of the impact of asymmetric in-formation because, in this model, non-exploitative smuggling remains profitableunder symmetric information even when exploitative smuggling becomes unprof-itable for the most exploitative smuggler (Tamura 2010, proof of proposition 2).

Proposition 3(iv) indicates that border apprehension probabilities do not affectthe profitability of exploitation for each smuggler unless they are large enoughto make non-exploitative smuggling unprofitable. Any profit from exploitation isconditional on a successful border crossing, and the exploitation decision is madegiven a successful border crossing. Therefore, the exploitation decision does notdepend on border apprehension probabilities under full employment. In short,improved border apprehension may maintain the status quo under asymmet-ric information, whereas it reduces smuggling by making initially exploitativesuppliers unemployable under complete and perfect information (Tamura 2010,proposition 2(iii)) when limited resources are available.

4. Conclusion

In this article, I have extended Tamura’s (2010) analysis of the migrant smugglingmarket by assuming that smugglers’ exploitation capacities are private informa-tion. Policy implications do not depend on the informational assumption whenthe destination country has sufficient resources. That is, anti-illegal migrationefforts can eliminate the migrant smuggling market, whereas anti-exploitationefforts cannot. In reality, available resources are never unlimited. When commit-table resources are limited, a worker’s ability to observe the exploitation capacityof the matched smuggler does make a difference to policy implications.

First, increased anti-illegal migration efforts tend to result in an adverse selec-tion equilibrium where all smuggled migrants are exploited more or less, whichmay be a concern to those who care about the welfare of migrants regardlessof their legal status. However, an adverse selection equilibrium is not necessarilya bad outcome for destination countries that desire to stop migrant smuggling,as it implies a fall in the number of smuggling attempts via unemploymentof smugglers with low exploitation capacities. The equilibrium outcome undercomplete and perfect information differs: increased anti-illegal migration effortsmake exploitative smuggling unprofitable first, and initially exploitative smug-glers become either non-exploitative (in the case of increased penalty for smug-gling or improved inland apprehension of smuggled migrants) or unemployed

1478 Y. Tamura

(in the case of improved border apprehension of smugglers or migrants). Thisimplies that a reduction in informational asymmetry between smugglers andpotential migrants decreases the incidence of migrant exploitation.

Second, when workers cannot observe the exploitation capacity of their smug-glers, improved inland apprehension of smuggled migrants may have an unin-tended consequence of increasing the incidence of migrant exploitation, at thesame time failing to reduce the number of smuggling attempts. This happenswhen the impact of this apprehension improvement on the workers’ reservationvalue of smuggling is so weak that the equilibrium moves not from a poolingto a partially pooling one but to a new pooling one where every smuggler re-mains employed. The resulting fee reduction does, however, induce some initiallynon-exploitative smugglers to become exploitative, as exploitation becomes prof-itable for them. In this sense, a half-hearted effort to improve inland apprehensionof smuggled migrants is not only ineffective in terms of reducing migrant smug-gling but also harmful to smuggled migrants. Hence, inland apprehension ofsmuggled migrants is a policy parameter that requires careful consideration ifdestination countries wish to avoid exacerbating the exploitation risk faced byusers of smugglers.

Finally, improved border apprehension does not affect either the employmentor the exploitation decisions of smugglers when the improvement is marginal.The status quo is maintained unless the improvement is significant enough tolower the market fee to a level at which non-exploitative smuggling is unprof-itable, resulting in an adverse selection equilibrium. Under complete and perfectinformation, migrant smuggling is better fought at the border than inland. Butwhen exploitation capacities are private information, a small investment in bordercontrol may turn out to be a mere waste of resources.

The literature would significantly benefit from dynamic analysis of the market.Descriptive evidence suggests that potential migrants often make use of socialnetworks in their search for reliable smugglers. Therefore, a more realistic modelwill explicitly include the process of transmitting user experiences to future users,which will in turn generate reputations of smugglers over time. Such an extensionis likely to relax some of the unrealistic assumptions in the current study. Forexample, there are cases where a migrating worker must pay before a border cross-ing, and the smuggler provides border-crossing services even if post-smugglingexploitation is unprofitable. The current model does not allow for such a sit-uation. But it is likely to arise in a dynamic model where reputation matters.Moreover, dynamic analysis will allow smugglers with different reputations tocharge different fees because of the transition of the market away from asym-metric information even though exploitation capacities do not become perfectlyobservable to users of smugglers.


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