Immigration Policy and Counterterrorism

Transcription

1 Iigration Policy and Counterterroris Subhayu Bandyopadhyay a ederal Reserve Bank of St. Louis, and IZA, Bonn odd Sandler b University of exas at Dallas April 2011 Abstract A terrorist group, based in a developing (host) country, draws unskilled and skilled labor fro the productive sector to conduct attacks at hoe and abroad. he host nation chooses proactive countereasures, while accounting for the terrorist capaign. Moreover, a targeted developed nation decides its optial ix of iigration quotas and defensive counterterroris actions. Even though proactive easures in the host country ay not curb terroris at hoe, it ay still be advantageous in ters of national incoe. Increases in the unskilled iigration quota augent terroris against the developed country; increases in the skilled iigration quota ay or ay not raise terroris against the developed country. When the developed country assues a leadership role, it strategically augents its terroris defenses and reduces its unskilled iigration quota to induce ore proactive easures in the host country. he influence of leadership on the skilled iigration quota is ore nuanced. Keywords: ransnational terroris, iigration, counterterroris policy, developing country, externalities JEL codes: 22, O10, D74 a Research Division, ederal Reserve Bank of St. Louis, PO Box 442, St. Louis, MO E-ail: bandyopadhyay@stls.frb.org; el: ; ax: b Corresponding author. School of Econoic, Political & Policy Sciences, University of exas at Dallas, 800 W. Capbell Rd., Richardson, X E-ail: tsandler@utdallas.edu; el: ; ax: Sandler s research was funded, in part, by the US Departent of oeland Security (DS) through the Center for Risk and Econoic Analysis of erroris Events (CREAE) at the University of Southern California, grant nuber 2010-S-061-RE0001. Any opinions, findings, and conclusions or recoendations are solely those of the authors and do not necessarily reflect the view of the ederal Reserve Bank of St. Louis, the ederal Reserve Syste, DS, or CREAE.

2 Iigration Policy and Counterterroris 1. Introduction Ever since the unprecedented terrorist attacks on Septeber 11, 2001 (henceforth 9/11), econoists have focused on yriad aspects of terroris including its ipact on growth (Bloberg et al. 2004; Gaibulloev and Sandler 2008, 2011), developent (Keefer and Loayza 2008), stock arkets (Chen and Sies 2004), and counterterroris policy (Bandyopadhyay and Sandler 2011). Econoists and political scientists applied gae-theoretic tools to investigate the practice of counterterroris against both hoegrown doestic terroris and transnational terroris (see, e.g., Arce and Sandler 2005; Bapat 2006, 2011; Landes 1978; Sandler et al. 1983). Soe contributions investigated the deand side in ters of the nuber and location of terrorist incidents (e.g., Sandler and Siqueira 2006; Siqueira and Sandler 2007), while other studies exained the supply side in ters of the roots of terroris (e.g., Abadie 2006; Krueger and Maleckova 2003; Piazza 2006, 2011). Krueger and Laitin (2008) investigated both sides of terroris by analyzing what deterines whether a nation is a source or a target of transnational terroris (see, also, Bloberg et al. 2009). Another strand of the terroris literature relates to international trade and foreign direct investent (e.g., Bandyopadhyay et al. 2011a; Enders and Sandler 1996; Nitsch and Schuacher 2004). he findings and ethodology of this literature are nicely suarized by Mirza and Verdier (2008). In general, terroris can curb trade and capital flows owing to heightened costs and risks. Despite these contributions, there is no paper that forally connects iigration policy to the supply of terroris in a gae-theoretic general equilibriu context. his is an iportant oission because an exclusive focus on the standard ters-of-trade effects of iigration policy

3 2 ay result in isleading policy recoendations. 1 he purpose of this paper is to fill this void by integrating iigration and counterterroris policies in a strategic general equilibriu fraework. We show that terroris-related costs and/or benefits, along with ters-of-trade effects, are required when deterining an optial iigration policy. here is a sall eerging epirical literature that coes to vastly divergent conclusions about the relationship between iigration and transnational terroris. In particular, studies that focused on known transnational terrorists showed that any were iigrants (e.g., Leiken and Brooke 2006), while a study that looked at iigrants in general did not find a significant relationship between iigration and terroris (Dreher and Gassebner 2010). Based on the World Values Survey on attitudes, ischer (2011) found that iigrants are ore likely than natives to support the application of terroris. hese ixed epirical results indicate that a theoretical analysis of the relationship between terroris and iigration quotas iposed on the potential source country for terrorists ay enlighten not only policyakers, but also epirical researchers. his is especially true in our theoretical fraework, which has counterterroris easures as choice variables in the target and source countries. In our theoretical fraework, a transnational terrorist organization, based in a developing country, draws unskilled and skilled labor fro the productive sector to attack targets at hoe and abroad. hese two types of laborers join the terrorist group when their anticipated gain exceeds that in the productive sector; this decision is influenced by wages and counterterrorisinduced risks of failure. he ideal factor proportions differ between attacks at hoe and abroad. itting targets abroad in a developed country, such as the United States or rance, requires a greater proportion of skilled to unskilled labor, copared with hitting targets at hoe. his 1 In this context, ters-of-trade effect refers to the wages of skilled or unskilled iigrants that the developed nation has to pay. A fall in the iigrant s wage is a ters-of-trade gain for the developed nation.

4 3 follows because attacks abroad require ore coplex logistics, language skills, reduced infrastructure, and traversing borders. Given that attacks abroad are ore skill-intensive than hoe attacks, we analyze the effects of counterterroris policy as well as iigration policy on the supply of terroris and on the national incoe of the two countries. he source country applies proactive easures to annihilate the resident terrorists, while the targeted developed country relies on defensive easures to deflect attacks abroad. As such, there are eleents of positive and negative international externalities. Our theoretical construct is descriptive of transnational terroris in the post-cold War era during which terrorist groups e.g., al-qaida, al-qaida in the Arabian Peninsula, Lashkar-e-aiba, and Jeaah Islaiyah take refuge in developing countries (e.g., Pakistan, Yeen, and Indonesia), while attacking host and developed countries interests at hoe and abroad. Given the diverse types of agents in our odel (i.e., terrorist recruits, terrorist group, source country, and developed country) and the alternative policy instruents, the tradeoffs are subtle and coplex. Aong other results, we find that the developed country s defensive efforts deflect attacks back to the source country. Proactive easures against the terrorists in the source or host country ay or ay not reduce attacks abroad depending on a critical unskilled to skilled labor threshold. When this threshold is high, the terrorist group reduces unskill-intensive terroris rapidly at hoe in response to proactive easures, thereby shifting ore of its resources to attacks abroad. he opposite is true when this threshold is relatively sall. Larger unskilled iigration quotas raise terroris in the developed country as terroris is reduced in the source country as unskilled workers eigrate. An increase in skilled iigration quotas need not raise terroris in the developed country despite skill-intensive terroris on its soil owing to opposing forces. Even when a proactive capaign in the source country results in ore terroris, it ay be advantageous as the productive sector recaptures ore labor, thereby

5 4 raising incoe. he developed country ay gain fro assuing a leadership role in choosing its defensive easures and iigration quotas by inducing ore proactive countereasures in the source country. Such easures safeguard the developed country a positive externality. he reainder of the paper contains four sections. Section 2 displays the proble of the terrorist group and its volunteers as they respond to the two countries policy choices. In Section 3, the source or foreign country s proactive choice is analyzed. his is followed in Section 4 by an analysis of the defensive and iigration choices in the developed (hoe) country under two scenarios: (i) siultaneous policy choices in the two countries, and (ii) a leadership role for the developed country. Concluding rearks are contained in Section he terrorist organization erroris is the preeditated use or threat to use violence by individuals or subnational groups in order to obtain a political or social objective through intiidation of a large audience beyond that of the iediate victis (Enders and Sandler 2011). erroris is transnational when an incident in one country involves perpetrators, victis, institutions, governents, or citizens of another country e.g., 9/11 skyjackings. In recent years, transnational terrorist groups often locate their base in a developing country fro which they can attack Western interests at hoe or abroad. hus, Yeen, Lebanon, Soalia, Syria, Pakistan, Morocco, Algeria, Afghanistan, and other developing countries have been the base for any notorious terrorist groups (offan 2006; Mickolus 2008). he underlying gae has two to three stages. In the first variant, the two governents choose their counterterroris and iigration policies in the first stage, and the terrorist group decides its terrorist capaign in the second stage. In the second variant, the developed country decides its counterterroris and iigration policies in the first stage, followed by the

6 5 developing country picking its proactive countereasures in the second stage. inally, the terrorist group allocates its attacks at hoe and abroad in the third stage. We solve both gaes backwards beginning with terrorist group s decision in the final stage. he terrorist organization derives benefit fro attacking targets in both the host developing nation (say, ) and the developed nation (say, ). Along the lines of Mirza and Verdier (2008) and Bandyopadhyay et al. (2011b), the terrorist group s utility function is where * V p p p, (1) j is the terrorists preference for attacking nation j (=, ); success of a planned attack in nation j; in nation. 2 In (1), * is terroris daage in ; and j p is the probability of is terroris daage is s terroris daage fro an attack in, so that developed countries interests can be hit at hoe or abroad. his accords with reality e.g., very few attacks on US interests occur on US soil in recent years (Enders and Sandler 2011). As in Bandyopadhyay et al. (2011b), we assue that terror daage for in is 3, (2) where is a paraeter easuring the extent of s foreign interests in. he probability of success of a planned attack against is lowered by its defensive actions, e, although at a diinishing rate, i.e., 2 We assue that both econoies produce the sae single good, which serves as the nueraire in this odel. Also, the developed nation is assued to have superior technology, which contributes to its factor returns being strictly larger than the corresponding factor returns in the developing nation. his international factor price difference is possible (in equilibriu) because factor obility is controlled by iigration quotas iposed by the developed nation. 3 We note a few things. irst, we assue that has no foreign interests in, so that attacks in are attacks against alone. owever, has foreign interests in that ay be subject to terroris attacks. In principle, attacks in against s or s interests ay be separate. Also, these attack technologies ay be distinct, with different skill intensities. If this is the case, then there are three skill intensities, a high skill intensity for attacks in, an interediate skill intensity for attacks against in, and a low skill intensity for attacks against. Although this structure is reasonable, it is analytically intractable in this general equilibriu setup. he coproise that we use is that an attack against has a collateral daage coponent for, which is weighted by its foreign interests in. or exaple, if the United States has extensive foreign interests in Pakistan, then US interests are ore likely to be targeted in Pakistan than in the United States by Pakistan-based groups.

7 6, p e 0, and p e 0 p p e. (3) errorist attacks targeted in a developed nation fro foreign bases require a higher degree of sophistication and are produced using a ore skill-intensive technology. owever, both types of terroris require a ix of unskilled and skilled labor and exhibit constant returns to scale (CRS). he terroris production functions in and are: 4 t t L, S and (4a) t t L, S, (4b) respectively, where tj tj L ( S ) is unskilled (skilled) labor used by the terrorists to attack targets in nation j. A natural question is how is the terroris that is produced by a developing nation s resources delivered in the developed nation? Although cyber-attacks can be delivered reotely, ore traditional terrorist attacks necessitate soe physical presence in the target nation. his ay require participation by iigrants and/or tourists in the developed nation. or tourist perpetrators, soeone ay acquire a teporary visa, visit the country, and carry out the attack without any local help, so that iigrants are not involved. If, in contrast, the terrorist group s attack is facilitated by an existing iigrant pool, then the effective terroris (i.e., * ) in the developed nation depends on a sypathetic pool of skilled and unskilled iigrants. A siple way to odel this is as follows: 4 j hese are standard CRS production functions with positive arginal products i, negative second-order partials J j ( ii 0 ), and positive cross partials ( ix 0, i x). We also assue without loss of generality that producing tj t t tj L terroris directed against is ore skill-intensive (i.e., l l, where l, j, ). Unless specified tj S otherwise, we will use the convention that for any function f x1, x2,.. x n, fi is the partial derivative of f with respect to its i th arguent, and fij the partial derivative of fi with respect to the j th arguent.

8 7 * t t A A A, L, S, A 0, A 0, and A 0, (5) where and are unskilled and skilled iigrant pools, respectively, in the developed nation. he partials of A are non-negative because the presence of ore skilled or unskilled iigrants potentially iproves the delivery capability for terroris in. Using Eqs. (1)-(5), we express the terrorist group s expected utility as:, A, p e V, and p. (6) Let the unskilled (skilled) labor supply be inelastically given for at L ( S ). We assue that s skilled and unskilled wages are sufficiently large relative to their counterparts in, such that given an option to eigrate to, a labor unit (skilled or unskilled) will choose to do so. hus, the iigration levels and equal the iigration quotas for unskilled and skilled iigration chosen by. he unskilled and skilled labor force in net of eigrants are L, and S, respectively. u Each unit of unskilled labor has a certain level of radical beliefs, paraeterized by, which eans that if they succeed in working for the terrorist organization they get a utility u equivalent to units of the nueraire good. Even though units of unskilled labor are hoogeneous as inputs in terroris or in producing goods, they differ in their radical beliefs. he distribution of such beliefs is given by the following probability density and cuulative distribution functions, respectively: u u u x, u. (7) X x d All unskilled labor units in earn u w fro the productive sector, which equals the arginal product of unskilled labor in producing goods. When they volunteer for the terrorist

9 8 organization, they know that there is a chance that they ay not be able to serve effectively. or exaple, they ay be killed or incarcerated before being able to take part in an attack. hey are assued to succeed in providing their services to the terrorist organization with a probability, which is a declining function of proactive effort undertaken by the host governent. Assuing diinishing returns in the use of such offensive action, we have, 0, and 0. (8) An unskilled labor unit stays in the productive sector if its wage exceeds it expected arginal return fro being a terrorist: u u u u w w. (9) Eq. (9) describes a argin that is siilar to ones used in odels of equilibriu igration, where a igrant equates the expected return fro igrating to that of the status quo. 5 Consider the decision faced by an illegal iigrant (e.g., Ethier 1986). If, say, soeone stays hoe in Mexico, s/he earns a Mexican wage with certainty. When, however, s/he attepts to igrate illegally to the United States, s/he ay be caught and returned hoe after soe penalties are iposed; or s/he ay cross successfully and earn a higher wage. he higher the probability of detection at the border and the greater the penalty, the less likely is the individual to igrate. he analogy here is that higher proactive effort reduces the anticipated probability of success for a laborer conteplating a ove to the terrorist sector. he associated deterrence effect of proaction provides a ore favorable allocation of labor for the productive sector, thereby bolstering national incoe. hus, the argin, described in (9), is critical and endogenous to 5 he legal iigration quotas discussed in this paper are not based on an internal equilibriu relationship. hey arise fro a corner solution where the igrant s ex ante return fro eigrating exceeds the return that can be obtained fro staying back. owever, because iigration is controlled by quotas, this wedge in the returns is sustained in equilibriu.

10 9 policy choices. Based on Eq. (7) and (9), the fraction of unskilled labor force that stays in the productive sector is u w X. hus, 1 XL labor units volunteer for the terrorist organization, of which a fraction succeeds in providing their services in terrorist attacks. hus, the unskilled labor pool Siilarly, let L for the terrorist organization is u w L 1 X L L, w,, L u s s, s g, and G. (10), be the radicalization paraeter, the probability density function, and the cuulative distribution function for skilled labor, respectively. herefore, the skilled-labor pool for the terrorist organization is s w S 1 G S S, w,, S s. (11) he terrorist organization axiizes its utility [Eq. (6)], given its supply of skilled and unskilled labor [Eqs. (10) and (11)]. he constrained optiization proble for the terrorist organization is Max,, L,,, V L S L S L w L L L t t t t u t t, s,, t t S S w S S S, (12) where L and S are the Lagrangian ultipliers associated with the unskilled and skilled labor constraints, respectively. he first-order conditions (OCs) yield the unskilled and skilled labor used by the terrorist organization in attacks at hoe and abroad and also the shadow prices (i.e., the optial values of L and S ) of these resources for the terrorist organization. Denoting the

11 10 vector of paraeters faced by the terrorist organization by, we have tj, tj tj S S tj L L, j, ; i, i L, S, where i u s,,,, w, w,, L, S. (13) Substituting (13) into (12), we have the envelope function interests: * * u s V V w w L S * V :, ;,,,,,,. (14) Using the envelope theore, we obtain the supply of terroris aied at s and s * 1, ;,, u, s,,, V w w L S and (15a) * 2, ;,, u, s,,, V w w L S. (15b) It is easy to show that * V is convex and hoogeneous of degree one in and. 6 Proposition 1: A rise in s counterterroris defense effort ( e ) reduces terroris against it while raising the terroris directed at. Proof Based on the OCs of the optiization proble, it is easy to show that 7 0V 0. (16) * 11 Given that Ap e, we have * Ap 0 A 0. (17) e e e 6 * V is siilar to the revenue function used in dual odels of trade (see Dixit and Noran 1980). he proofs of convexity and hoogeneity are standard and are available fro the authors on request. 7 Proof is in the Appendix.

12 11 Because zero in and * * V is hoogeneous to degree one, the first-order partial V 1 is hoogeneous of degree. Using Euler s theore and (16), we get * * * * * * 0V11 V12 V12 V11 0V12 V21 0. (18a) Eq. (18a) iplies that e Ap 0. (18b) Eqs. (17) and (18b) establish the proposition. Proposition 1 confirs the terroris reduction versus terroris deflection consequence of defensive easures that dates back to Lapan and Sandler (1988) (see also Bandyopadhyay and Sandler 2011; Bier et al. 2007; Intriligator 2010; Sandler and Siqueira 2006). his proposition shows that a general equilibriu fraework preserves this result. s defensive actions reduce the likelihood of successful terrorist incidents in, thereby deflecting the back to the source country. Although s hoeland is now safer for its actions, its interest can still be hit abroad e.g., attacks against US people or property in Pakistan. hus, country ust weigh these losses against the gains fro reduced attacks on its hoeland when coing up with an optial defense policy (see Section 4). oeland attacks are typically ore daaging than foreign attacks on its interests. Recent epirical studies showed a arked shift in terrorist attacks fro developed to developing countries following 9/11-otivated security increases (Enders and Sandler 2006, 2011). Developed countries interests were ore frequently targeted abroad. We now turn our attention to the effects of proactive policies in the country hosting the terrorists. he effect of a rise in proactive easures on is

13 12 * V1 V *. (19) Using the envelope property of * V and (12), we obtain V L * L S S. (20) Differentiating (10) and (11), respectively, yields L xw L L X u 1 0 and s S gw S S G 1 0. (21) Eq. (21) shows that proactive effort ust reduce both the unskilled and the skilled labor resources of the terrorist group for two reasons. irst, a rise in proactive effort depletes the group s labor resources for a given labor allocation between the productive and terrorist sectors. Second, as proaction rises, the ex ante return fro joining the terrorist organization ust fall [Eq. (9) above], so that fewer laborers becoe terrorists. his effect copleents the direct effect of proaction, leading to fewer terrorists. Substituting (21) into (20) and differentiating (20), we obtain * V L S L S. (22) In the Appendix, we show that L l t 11 0 t S l and (23) ro Eq. (12), is the arginal return of for the terrorist organization. A rise in this return akes the terrorists produce relatively ore of this type of terroris, so that expands, thus requiring ore skilled relative to unskilled labor. o supply these additional resources,

14 13 terrorists ust contract unskill-intensive, which releases relatively ore unskilled labor. he result is an excess supply of unskilled labor and an excess deand of skilled labor, which leads to a fall in the shadow price of unskilled labor (i.e., L ) and a rise in the shadow price of skilled labor (i.e., S ). Using (19)-(23), we find that the sign of on this abiguity. is abiguous. Proposition 2 throws light Proposition 2: A sall rise in s proactive effort will reduce terroris in if and only if l t exceeds a critical level l 0. his critical level depends on the initial proactive level, s iigration quotas, s factor endowents and factor prices, and the probability density functions x and g. erroris in will fall if and only if l t is less than the critical value l 0. It is not, however, possible for terroris to rise in both nations. Proof Using (19)-(23), we show in the Appendix that * 0 A 0 if and only if t l 0 l, where u 0 L 1 L X xw 0 l l,, w, w,, L, S s S S 1G gw u s. (24) Analogously, we can show that 0 if and only if t l 0 l. (25) ro the terrorist organization s OCs, terroris labor intensities are entirely deterined by and. Depending on the values of and, we can have different possibilities. We can

15 14 rule out the possibility that both * and are positive, because it requires that t l 0 l and t l 0 l in violation of the assued factor intensity ranking l l. Based on (24) and (25), t t three cases are possible: Case 1: * 0, 0, if t l 0 l, t l 0 l. Case 2: * 0, 0, if t l 0 l, t l 0 l. Case 3: * 0, 0, if t 0 t l l l. Cases 1 through 3 establish the proposition. ro (21), we know that a rise in proactive effort reduces both the skilled and unskilled labor resources of the terrorist group; however, this does not iply that terroris ust fall in both nations. o explain why, we focus on Case 1. Eq. (24) indicates that l 0 is the relative rate at which proaction reduces the terrorist group s unskilled copared with its skilled labor resources. Consider a situation where herefore, l 0 is arbitrarily large and ust exceed both S tends to zero, while L is nonzero and finite. t l and l t. Now, consider a rise in proactive effort. his rise reduces the terrorist organization s unskilled resources, but has a negligible effect on its skilled resources (because S 0 ). his relative scarcity of unskilled labor akes the terrorist group scale back unskill-intensive, which sheds soe skilled labor in the process. If this excess supply of skilled labor is exactly offset by the reduction in skilled resources due to proaction, then there is no uneployent of skilled resources. owever, given that the agnitude of S is arbitrarily sall, the excess supply of skilled labor cannot be

16 15 neutralized. he only way for these resources to be fully utilized is to transfer the to the production of production of. Consequently, at an optiu, the terrorist organization ust scale up its, which then raises the volue of terror redistribution of labor happens in Case 2. * experienced by. he opposite erroris ust fall in both nations only in the interediate case (Case 3), where l 0 lies between the two labor intensities l t and l t. In this case, proaction s daaging effects on skilled and unskilled labor resources of the terrorist organization are ore balanced relative to either Case 1 (where unskilled labor suffers ore) or Case 2 (where skilled labor suffers ore). In Case 3, as unskilled labor resources decline, the terrorist group scales back, releasing soe skilled labor. his excess supply of skilled labor is ore than offset by the decline in skilled labor due to proaction (i.e., labor, which is resolved by scaling down S is sufficiently large). he result is a shortage of skilled. hus, the terrorist group s ability to circuvent s countereasures through a change in the ix of terroris is ore liited. Proposition 3: A rise in the terrorist group s target preference for raises An increase in the unskilled iigration quota raises skilled iigration quota ay or ay not raise Proof he proof is in the Appendix. * * and and reduces. * and lowers. A rise in the. A greater target preference for akes the terrorists devote ore of their resources to attacking, which leaves fewer resources for attacks on. hus, when terrorists fixate on, * rises and falls. he effect of iigration quotas is ore coplicated. When

17 16 increases, it raises A and akes it easier to deliver terroris in. his creates a greater incentive for the terrorist group to perpetrate terroris in. he net supply of unskilled labor in (i.e., L ) is also reduced, which decreases the relative supply of unskilled labor for the terrorist group [see Eq. (10)]. his then results in a rise in the supply of skill-intensive terror * and a reduction in the supply of unskill-intensive terroris. Both the terroris-delivery facilitation and the factor-intensity effect suggest that a rise in unskilled iigration ust augent terroris in and reduce it in. When, however, we consider the skilled iigration quota, we encounter two opposing effects. On the one hand, a greater pool of skilled iigrants facilitates terroris delivery in, which tends to raise * and reduce. On the other hand, a reduction in the relative availability of skilled laborers due to eigration in reduces S [see Eq. (11)], which liits skill-intensive * and augents unskill-intensive of an increase in the skilled iigration quota on both * and is abiguous.. hus, the net effect 3. he foreign (source) governent In stage 2, s governent decides its proactive easures against the resident terrorist group. We assue that produces a single good, where Q, using the following CRS production function: Q L, S, (26) L and S are unskilled and skilled labor used in the production of this good. Recalling that X is the share of unskilled labor engaged in productive activity in, we have 8 and, siilarly, L L X, (27a) 8 We assue that eigration is neutral in ters of affecting the probability distributions of radicalization in s population of skilled and unskilled labor. hus a reduction of the unskilled (skilled) labor pool through eigration does not affect the fraction X (G).

18 S S G. (27b) s national incoe, including the earnings of its eigrants and net of terroris daage,, and counterterroris spending, is where, Y L X S G w u w s u w and s w 17, (28) are the unskilled and skilled wage rates, respectively, in. In (28), the price of proactive easures is noralized to be 1. We assue that s CRS production function is: Q L, S. (29) Accounting for the iigrants in s labor pool, we obtain L L and S S. (30) he wage rates in the two nations reflect their respective arginal products. Suppressing the factor endowents in the functional fors, we have: 1,1, w s 2 i,1 w s i, w u 1 i,1 w u i w i w i u u w s 2 i,1 w s i, where, and i L S i, and u w L X i i,,. (31) s w S G Eq. (31) reflects that hoogeneity of degree one of the production functions in both nations akes the arginal products and, hence, the factor returns deterined entirely by the j unskilled labor intensity i j,. In equilibriu, the unskilled labor intensities reflect the

19 18 relative abundance of the unskilled labor available in the two nations for productive activities. Clearly, iigration affects this abundance by aking ore labor available to at the expense of country. or exaple, a rise in unskilled iigration raises the unskilled labor intensity in and reduces it in. his then reduces the arginal product of unskilled labor and its wage in. In contrast, a rise in s unskilled labor intensity raises its arginal product of skilled labor and, hence, its skilled wage. or the sae reasons, eigration fro ust ove its wages in exactly the opposite direction. inally, proactive effort can affect the wages in but not in. Wages in are unaffected because i is entirely deterined by the iigration quotas and s existing labor stocks, so that proaction has no direct effect on it. In contrast, increased proactive easures deplete both types of labor in [see Eq. (21)], possibly changing i and wages in. When, however, proaction reduces the availability of skilled and unskilled labor in the sae proportion, their relative abundance in is unchanged, so that s wages are unaffected. his issue is addressed below. Country takes s iigration quotas ( and ) as given when choosing its nationalincoe-axiizing proactive effort. 9 In light of (31), this fixes i and, hence, the skilled and unskilled wages in in ters of s decision aking. Differentiating (28), we obtain the OC for s incoe-axiizing proactive effort: Y Y ; e,, 1 L X 2 S G 10. (32a) Eq. (32a) iplicitly defines s Nash reaction function as e,,. (32b) Differentiating the distribution function X yields: 9 his is consistent with two scenarios: and siultaneously choosing their incoe-axiizing policies; and choosing its policy at an earlier stage copared to. We analyze both scenarios.

20 19 u X x w i w 2 i In the Appendix, we show that u. (33) i 0 X if and only if G, X u dln X G, u d ln s dln G, (34) s d ln where X G and are the elasticity of the distribution functions X and G with respect to the u s respective radicalization paraeters and, respectively. he intuition behind (34) is straightforward. Proactive easures reduce the returns fro joining the terrorist group for both skilled and unskilled volunteers [see Eqs. (9)-(11)]. hus, the proportions of skilled and unskilled labor (i.e., G and X, respectively) that join the productive sector ust both rise. If X exceeds G, the proportion X rises faster than the proportion G. In the light of (31) this suggests that i ust rise. If the elasticities are equal (as in the specific functional fors for the probability distributions we use below), X and G rise at the sae rate, and i does not change. Consequently, wages in do not change. or siplicity, we henceforth assue that the probability density functions x and g are independently, identically, and uniforly distributed with supports zero and, such that 10 x 1 g and X G Using (35) and the definitions of. (35) X and G fro (34), we get 1 0. (36) X G i Using (36) in (33), we have: 10 We show in (36) below that this assuption allows us to focus on the siplest of the three possible cases in (34), X which is G. Most of the tradeoffs faced by the governents then coe out cleanly. While it is possible to X analyze the other two cases (i.e., G X, and G ), we choose not to do so in this paper, both for clarity of exposition and space considerations.

21 20 u X w x 0 2. (37a) Siilarly, we get: s G w g 0 2. (37b) Proposition 4: Nation chooses its proactive response to reduce its terroris daages and also to benefit fro bringing ore of its resources fro the terrorist sector into the productive sector. Even when proactive efforts raise terroris in, the governent ay still choose to eploy it. Proof Using (31), we can write (32a) as u X s G w L w S 1. (38) he proposition is established fro (38) in light of (37a), (37b), and Proposition 2. A positive X in (37a) reflects the rise in the proportion of productive unskilled labor in as greater proactive easures dissuade soe potential terrorist volunteers. he ensuing rise in output in is captured by the first ter of (38). Siilarly, the second ter in (38) reflects the corresponding rise in output fro the return of skilled labor to productive activities. Based on Proposition 2, proactive effort ay, however, increase. Even then, national incoe ay increase as long as the first two ters in (38) doinate (starting fro 0 ). his is a general equilibriu result, novel to this literature. his finding indicates that the deterrence effect, which keeps ore of the population away fro terroris, ay be an iportant deterinant of national-incoe-axiizing counterterroris policy. It can rationalize the apparently

22 21 counterintuitive behavior of governents that continue to engage in proactive counterterroris policies, despite a rise in terrorist attacks due to such policies. Such attacks are known as backlash steing fro counterterroris-induced grievances (Bloo 2005; Rosendorff and Sandler 2004; Siqueira and Sandler 2007). 4. he developed country s governent policy choices Based on (29)-(31), s national incoe, net of iigrant earnings, terroris daages, and counterterroris expenditure, is 11 * Y L, S w u w s p e e, (39a) where the price of defensive effort is noralized at 1. Using (2) and (5), we have Y L, S w u w s p e A, e. (39b) We consider two scenarios for s choice of its national-incoe-axiizing cobination of defense and iigration policies. irst, we analyze the (Nash) case where oves siultaneously with in the first stage. Second, we analyze a Stackelberg gae where chooses its policy one stage earlier copared with, so that we have a three-stage gae. 4.1 Nash equilibriu We have already described the policy choice rule for where it assues s policies to be given when choosing its incoe-axiizing proactive level. Under the Nash assuption, takes as given while choosing its incoe-axiizing policy variables. he resulting equilibriu is a Nash policy equilibriu. Using (31), we can differentiate (39b) to obtain s OCs for defense 11 Oitting iigrant incoes fro the host nation s objective function is a debatable issue. owever, for lack of an unabiguously superior alternative, this approach is standard and is used widely in the trade-iigration literature (e.g., see Ethier 1986).

23 22 and iigration quota choices as: Y A p Ap 10, (40a) e e e u Y w i p A A 0 u Y w i p A A 0, and (40b). (40c) Proposition 5: Defensive countereasures are chosen to balance terroris-reducing benefits in with terroris-deflecting costs and defense costs. If the unskilled labor intensity of the iigrant pool (i.e., / ) is larger than the corresponding intensity in production i, then unskilled iigration confers ters-of-trade benefits that ust be weighed against costs fro increased terroris. If / exceeds i, skilled iigration confers ters-of-trade losses that ust be weighed against potential gains fro terroris reduction for. Proof he proof is provided in the Appendix. ere we discuss the intuition behind Proposition 5 by focusing on each of the three policy choices separately. or given levels of the iigration quotas, we see that i, u w, and s w are all fixed see (31). hus, defense cannot affect the first three ters on the right-hand side of (39b). Its effect on s national incoe is through the expected terroris daages in and and fro its budgetary cost. Using Proposition 1, we know that defense reduces terroris in and raises

24 23 terroris in. hus, at an optiu, the benefit fro terroris reduction at hoe has to be balanced against the daages on s foreign interests in, as well as against the direct budgetary cost of defense. Eq. (40a) provides this optial choice rule. he influences on s decision regarding the unskilled labor quota is captured in (40b). Using Eq. (31), we can see that u w i his fall in unskilled wage benefits (hurts) depending on whether i is negative (positive). his is best understood by first considering the case where there are no skilled iigrants in (i.e., 0 ). In this case, the first ter on the right-hand u w side of (40b) equals 0. his is siply the gain in s national incoe fro having to pay less to the infraarginal units of unskilled iigrants when the arginal iigrant reduces the wages for the existing unskilled laborers. Now, consider the presence of an existing pool of skilled iigrants (i.e., 0 ). he fall in the unskilled wage due to unskilled s u w w iigration drives up the skilled wage ie.., i 0. hus, ore has to be paid to the skilled iigrant pool i.e., s w w. his loss for and the gain u i fro having to pay less to the unskilled iigrant pool are suarized by the first right-hand side ter in Eq. (40b). If the unskilled labor intensity of the iigrant pool (i.e., / ) is larger than the corresponding intensity in production i incoe., then these influences raise s national he effect of unskilled iigration on terroris in is captured by the second ter on the right-hand side of Eq. (40b). Analyzing this ter, we can show that a rise in ust raise the

25 24 effective terroris * in. here are several reasons for this, of which the ones related to terroris facilitation in and resource reallocation for the terrorist organization had been discussed in Proposition 3. An additional effect derives fro changes in s wage rates. ro (31), a rise in ust reduce the unskilled labor intensity in s productive sector and, consequently, raise u w and lower s w. his draws ore unskilled labor out of terroris and ore skilled labor into terroris. he decline in the relative supply of unskilled labor for the terrorist group akes it produce ore of the skill-intensive terroris We know fro Proposition 3 that the factor allocation effects lead to a fall in the unskillintensive *.. In addition, the wage changes discussed above also draws ore skilled labor into terroris. his tends to reduce, which benefits if it has extensive foreign interests. Eq. (40b) suggests that in the presence of terroris, the ter-of-trade effects as well as the terrorisrelated costs (or benefits) ust be appropriately evaluated to design unskilled iigration policy. he general equilibriu analysis highlights that there is a coplex interplay of argins. inally, we turn to an analysis of the skilled iigration quota on s incoe. In light of the preceding discussion, it is easy to see that a rise in the skilled iigration quota s reduces w and raises u w. owever, unlike the case discussed above, if / exceeds i, then s national incoe falls due to the ters-of-trade effect. his follows because loses ore fro paying higher wages to unskilled iigrants than it gains fro reduced payents to the relatively sall group of skilled iigrants. We know fro Proposition 3 that a rise in ay or ay not reduce * because of opposing terroris-facilitation and resource-reallocation effects. An additional effect not contained in Proposition 3 is at work here. he unskilled labor intensity i ust be larger when is raised, which tends to raise s w and reduce u w. ollowing the sae logic as in the case of

26 25 unskilled iigration, this causes resource reallocation in which tends to reduce. Because terroris facilitation in tends to raise effects. he final ipact on * and * and reduce * and raise, there are opposing is abiguous without further inforation on the paraeters deterining the relative strength of these opposing effects. 4.2 Stackelberg equilibriu his subsection describes the Stackelberg equilibriu in which chooses its policy one stage ahead of, so that the underlying gae has three stages. o copare the Stackelberg equilibriu with the Nash equilibriu, we need the slope of s Nash policy reaction function at the Nash equilibriu. Analysis of this slope is intractable for the general forulation. herefore, we analyze the special case of A, 1 (i.e., where iigrants have no role in facilitating terroris) to throw ore light on this issue. Lea: or A, 1and t 0 t l l l, s incoe-axiizing proactive level is increasing in s defense choice. 12 his proactive response is negatively related to s choice of unskilled iigration quota. he proactive level ay either rise or fall in response to an increase in the skilled iigration quota. he direction of this response critically depends on the relative strength of the quota s effects on productive resource allocation and terroris in. Proof: We show in the Appendix that: 12 t 0 t 0 he range l l l corresponds to Case 3 in Proposition 2. If l lies outside this range, one of the two types of terroris ust be scaled up. As we explain below, the strategic copleentarity of defense and proactive easures depends on how factor intensities change due to defense, and also on how proaction affects the level of terroris. When both types of terroris are reduced by proaction, these two effects copleent each other. When proaction raises one kind of terroris, while reducing the other, we have opposing effects and the pattern of strategic copleentarity (or substitutability) is not clear.

27 26 e N 0 ; 0. Also, 0 if and only if N where Z is the su of the first two ters in (38), and N. Z, Consider the effect of defense on the net arginal benefit of s proactive response, where the latter is defined in (38). or given and iigration quotas ( and ), Eq. (31) indicates that skill intensities and skilled and unskilled wages in both nations are fixed. hus, the first two ters in (38) cannot be affected by defensive easures in. owever, the third ter in (38), which easures the arginal reduction in terroris in coing fro s proactive easures, is aplified by s actions to deflect ore attacks to. s increased defense creates an incentive for to engage in greater proactive easures. his happens because a rise in defense reduces as is fortified. he labor intensity of l t ust fall because 0. Next consider the effect of s proactive easures. If it reduces labor is released by decline in of unskill-intensive that can be redeployed for (see Proposition 2), unskilled. Because s defense reduces l t, a unit due to s proactive effort releases less unskilled labor, which liits the expansion. he net effect is a sharper decline in due to its proactive effort. his positive effect of s defense on the effectiveness of s proactive response induces s governent to choose a higher proactive response (i.e., 0 ). e Unskilled eigration reduces the size of the unskilled labor pool in [i.e., L As a result, proaction s arginal benefit fro raising the fraction of laborers entering the ]. productive pool (in ) is reduced [see the first ter in (38)]. here are other effects working through changes in wages. hese cancel out under the assued unifor probability

28 27 distributions. inally, we have another effect working through terroris-related daages. When L is saller, the unskilled labor pool for the terrorist organization is also saller [see (10)]. As a result, proaction s daaging effect on this labor pool is reduced [i.e., L is saller], so that proaction is not very effective in reducing unskilled-labor intensive. he lower effectiveness of proaction for a larger level of tends to reduce the incoe-axiizing level of proaction i.e., 0. Skilled iigration has two opposing effects on the arginal benefit of s proactive easures. irst, a larger reduces the skilled labor pool in, thereby reducing the arginal benefit of proaction captured by the second ter in (38). Second, as in the case of in the preceding paragraph, a larger skilled iigration quota reduces the absolute value of proaction s effect on the skilled labor pool [see S in (21)]. A saller reduction in the skilled labor pool iplies a saller rise in, which increases the net arginal benefit of s counterterroris easures. Without further inforation, we cannot say which of these two aforeentioned effects doinate. herefore, the effect of on s incoe-axiizing proactive level is abiguous. o analyze the Stackelberg equilibriu, we write (39b) as Y Y e,,,. (41a) Using (32b), we can rewrite (41a) to represent the payoff of fro being a Stackelberg leader, as where quotas are L Y Y e,,, e,,, (41b) L Y is s payoff function. he OCs for the choice of defense and the iigration

29 28 L Y Y Y 0, (42a) e e e L Y Y Y 0, and (42b) hence, L Y Y Y 0. (42c) Eq. (31) indicates that, for given e, and, i is given and is not affected by ; u w and s w and ) with respect to, we obtain cannot be directly affected by. By differentiating (39b) (for given e, Y p 0, (43) owing to Case 3 in Proposition 2 where 0 l l l, so that both and decline with proactive easures. Eq. (43) suggests that increased proactive effort of leads to an unabiguous incoe gain for, because it reduces s daages both at hoe and abroad. If we evaluate the arginal leadership payoffs at the Nash equilibriu, then the first ter on the right-hand side of (42a) through (42c), respectively, is zero. Using the Lea above, we have 0, 0, while the sign of e N N N is abiguous. hus, assuing that 0 l l l, we have L Y Y e e N N 0, (44a) L Y Y N N 0, and (44b)

30 29 L Y Y N N 0 if and only if 0. (44c) N In the light of Eq. (43), it is clear that gains fro a policy that can spur s proactive effort. Given that the Lea establishes that s defense and s proaction are strategic copleents, a sall rise in s defensive effort ust raise s proactive effort. his, in turn, raises s national incoe. Eq. (44a) captures this effect; Eqs. (44b) and (44c) follow a siilar logic. Proposition 6: Assuing that A, 1 and 0 l l l, s leadership choice of defensive action exceed the Nash level, while its choice of the unskilled iigration quota ust be lower than the Nash level. s choice of the skilled iigration quota is lower than the Nash level if and only if Z. Proof L Y Eqs. (44a) and (44b) show that 0 e N L Y and 0. his suggests that e should be N raised and should be reduced at the Nash equilibriu to raise the Stackelberg payoff towards its axiu. 13 Using the Lea, we know that 0 N if and only if Z. In this L Y case, (44c) establishes that 0. In turn, this suggests that the leadership skilled N iigration quota ust be lower than the Nash level if Z. 13 We have to assue here that the cross effect of on the arginal benefit of defense and vice versa does not outweigh the first-order effects we highlight here.

31 30 At the Nash equilibriu, assues that s proaction is not affected by s policies. owever, under leadership, knows that a rise in its hoeland defense will induce to engage in greater attacks on its resident terrorists. If 0 l l l, greater proaction reduces terrorist attacks against both at hoe and in. hese benefits propt to behave strategically by raising its defensive easures to spur s proactive efforts. he arguent for reducing the unskilled iigration quota at the Stackelberg equilibriu is siilar, since it raises terroris in. he skilled iigration quota will be raised or lowered depending on whether raises or reduces proaction, respectively. he condition that is critical in deterining the direction of change of the skilled iigration quota is outlined in Proposition Concluding rearks Iigration and counterterroris policies are both central concerns confronting the United States and any other targeted developed countries. Moreover, consistent with our odel, nuerous transnational terrorist groups have taken up residency in developing countries with liited capabilities to root out the groups. his paper is the first gae-theoretic general equilibriu analysis that investigates the interrelationship between iigration quotas and the choice between defensive countereasures in the developed country and proactive easures in the (source) developing country. Even though the analysis is coplex and abiguous in places, there are any iportant and unabiguous insights. irst, developed countries gain fro deflecting attacks back to the source country despite their own interests in the latter. Second, proactive easures against a resident terrorist group need not reduce terroris at hoe and abroad. his is a novel result that hinges on labor-intensity considerations in the productive and terrorist sectors at hoe and abroad. In contrast, the literature views such proactive easures as necessarily reducing