Political instability and illegal immigration

J Popul Econ (1995) 8:23-33 --Journal of _Population ¢onom cs © Springer-Verlag1995 Political instability and illegal immigration* Jose Edgardo L. Campos 1 and Donald Lien 2 1Country Economics Department, World Bank, Washington, DC 20433, USA 2Economics Department, University of Kansas, Lawrence, KS 66045, USA Received February 10, 1993 / Accepted February 7, 1994 Abstract. Economic theory suggests that transnational migration results from the push-pull effect of wage differentials between host and source countries. In this paper, we argue that political instability exacerbates the migration flow, with greater instability leading to relatively larger flows. We conclude then that an optimal solution to the illegal immigration problem requires proper coordination of immigration and foreign policies by the host country. A narrow preoccupation with tougher immigration laws is wasteful and may be marginally effective. 1. Introduction Illegal immigration has always been a problem for developed countries. The problem has been particularly severe for the United States, especially in the last fifteen years, see Corwin (1984). There have been different explanations for this phenomenon but perhaps the most well known is the push-pull theory [for an interesting alternative ~ see Stark (1984) and Stark and Taylor (1989)]. Proponents of the theory argue that individuals in source countries are induced to emigrate to host countries because of sheer poverty and/or the lack of employment opportunities in their countries (push factors) and are in turn attracted to the better living standards in the receiving countries - wages are substantially higher and job opportunities much better (pull factors). Put simply, the wage differential between source and receiving countries induces emigration from the former to the latter. * The authors wish to acknowledgean anonymousreferee for very helpful comments and suggestions. The research of Donald Lien is, in part, supported by a grant from The University of Kansas, GRF 3281-XX-0038. 1 Thistheory suggests relative deprivation as a possible cause of out-migration. In other words, the push-pull factors arise not only from intercommunity comparison (such as between the host and source countries) but also from intracommunity comparisons within the source country. 24 J. E.L. Campos and D. Lien Table 1. Total number of deportable aliens Years 1961 1966 197l 1976- 1965 1970 1975 1980 Arrested Average per Year 467261 1141095 3136788 5184710 93 500 228200 627340 1036900 Source: Immigration & Naturalization Service, US Department of Justice, Annual Report 1979, Table 30 The theory would be a good if not sufficient explanation except that it seems to disregard any impact that political instability (in source countries) may have on the migration process. This seems at odds with trends in the 70's and early 80's. Since the 70's, illegal migration to the United States has been rising at an alarming rate. Table I gives an indication of this. During the 60's about 1.6 million deportable aliens were arrested; during the 70's this number increased to 8.3 million. The annual averages give an even better picture, increasing from 93 500 to a little over a million. At about the same time, quite a few source countries were (and still are) experiencing serious political problems - the Philippines (Mercado 1986), Nicaragua (Wynia 1984a, Weber 1981), and E1 Salvador (Wynia 1984b, Stephens 1981), to name a few. It seems quite possible then that the sudden upsurge in illegal migration is related to the political difficulties of these countries. In this paper, we present a simple version o f the push-pull theory modified to account for political instability. We then use the resulting model to characterize an optimal solution to the illegal immigration problem. ~ 2. Political instability and the push-pull theory To simplify matters, let us assume there is one source country and one host or receiving country. Now consider a representative individual in a source country who must decide whether or not to migrate to a host country. Let Ws be the wage rate in the source country and Wr the rate in the receiving country. The individual would migrate if u(Wr) exceeded u(Ws) where u(. ) is his utility function. However, because of the possibility of being unemployed (in either country), he is faced with some uncertainty about the actual wage rates. He must decide then on the basis o f his expectations about these rates. That is, he migrates if Eu(Wr) is greater than Eu(Ws) where E "represents" his expectations based on unemployment rates in each country. Let us assume that his utility function is quadratic with respect to money (wage). 3 Then his decision criteria is equivalent to ~s - (2/2) as <//r-- (2/2) a r , (1) 2 A solution is optimal with respect to a given decision criterion. In this paper, we assume a specific criterion, that of minimizing a combination of the budget and the entry of aliens. 3 Alternatively, one can assume a constant risk aversion utility function coupled with wage as a normal random variable. For other justifications (see Epstein 1985). Political instability and illegal immigration 25 where p is the mean wage, a the standard deviation in the wage, and ;~ the individual's risk aversion index. 4 For a risk neutral individual (2 = 0), migration occurs when the expected wage in the source country is less than that in the receiving country ( U s < / a t ) . A risk averse individual migrates only when the difference in expected wages is large enough to overcome the possible increase in wage income risk. For the general case the uncertainty is greater in the receiving country for a possible immigrant, resulting greater wage income risk: q r > a s . Consequently a more risk individual (with larger 2) requires larger expected wage differences to migrate. Individuals in the source country will have an incentive to move to the host country if on average they expect a higher utility by doing so. This bias however may be intensified or weakened by non-monetary considerations. To capture this phenomenon, we will assume that inhabitants of the source country can be distributed along a non-monetary bias scale with h representing the bias level of an individual and G ( h ) its cumulative distribution function. 5 More precisely, we assume that the utility an individual may derive from moving to the host country is weighted by h. Hence, he migrates if /t s - (2/2) a s < h [fir -- (2/2) a t ] • (2) If h is less than 1, then non-monetary considerations reduce his monetary bias to migrate; if h exceeds 1, then non-monetary and monetary considerations supplement each other. Because of institutional rigidities, wages in the two countries will normally fail to adjust, i.e. inequality (2) will generally hold. Thus, to reduce migration, the host country may impose entry (legal) restrictions whose effect is to reduce the wage a potential migrant expects to receive and to increase its wtriability. That is, let k represent the level of restrictions. Then, /# = llr(k ) and o"r = ar(k ) with ~tr<O and ar>O. Thus, for any choice of k there will be some h* such that /us - (2/2) a s = h * [I.tr(k ) - 0~/2) ar (k)l • (3) All those individuals with h larger than h * will thus migrate and those with h less than or equal to h * will stay. The former will find migrating relatively less risky, 4 It may be the case that the decision-making unit is the family and not the individual. Bhattacharyya (1985) and Lucas and Stark (1985) provide empirical support for the case of rural-to-urban migrations. Presumably, it is also applicable to transnational migration. A n d if so, then the risk faced by any family member is reduced, i.e. "portfolio diversification" a m o n g family members reduces his income variance. Consequently, the risk aversion index it is reduced (but still non-negative). In any case, the model is not qualitatively affected. 5 The adoption of a non-monetary bias is commonplace in Kwok and Leland (1982), Lien (1987), Katz and Stark (1987), and Darvish-Lecker and K a h a n a (1992). All these articles assume individuals in the source country receive different wage scales due to different skill levels or abilities; DarvishLecker and K a h a n a (1992) also allows different financial resources. Yet they impose identical bias on every individual. This article is the first to consider different bias factors a m o n g individuals. The conclusions remain qualitatively unchanged when we consider the case of different skill levels. Herein the framework is somewhat similar to Darvish-Lecker and Kahana (1992) in that two factors interact to determine the migration outcome. While their paper considers linear, additive interaction between skill level and financial resources, the bias scale and skill level create a complex interaction in making migration decision within our framework. J. E.L. Campos and D. Lien 26 while the latter will find it more risky. In other words, [ 1 - G(h*)] of the total population will migrate. Let us assume that (3) represents the status quo. Now suppose for some reason or another political problems arise in the source country. This would affect the mean wage and/or the variability in wage that a potential migrant could make if he stays. Political instability tends to deter any new investments, foreign or local, and depending on its severity, to drive away existing firms. Hence, it reduces the prospects of finding work, raises the possibility o f being unemployed for long periods, and most likely lowers wages. This implies (3) will cease to be satisfied. More precisely, let i be the index of political instability with ie[0, co ]. Then ~ts = Ps(i), os = as(i), p~<0, and a ; > 0 . And, assuming i = 0 is the status quo, for any i > 0 , ps(i)- (2/2)as(i) <h * ~r(k ) - (2/2 )ar(k )] . (3 a) Inequality (3 a) implies that migration will increase if the source country experiences political difficulties. Those individuals with biases higher than (h * - e ) , e > 0, will now be induced to migrate; the greater i, the larger e will be and so the greater the migration outflow. This result is consistent with our earlier observation that political problems in some source countries coincided with stepped up illegal migration to the United States. 6 If it wants to reduce if not prevent further entry, the host country will have to make entry more restrictive - raise k - or help stabilize the source country say through foreign aid. 7 Both options require the use of funds. The host country must therefore decide how to allocate funds between these options. In the next section, we establish the optimality conditions to this decision problem. 6 Note that we are not arguing that political instability leads directly to emigration but that it induces migration because o f its impact on wage expectations and wage variabilities. Also note that the discount or bias factor h for each individual could be related to the instability index i; in particular, (dh/di) > 0. This is probably correct. However, we have chosen not to incorporate it into the model. In the model, we characterize the number o f ilIegal aliens by G (h), the distribution function of h when aggregating over the whole population. Introducing the aforementioned relationship would make the function dependent on i, i.e. G (h; i). Thus, when i changes, the whole distribution function shifts in such a way that G (h; i 1) Stochastically dominates G (h;/2) whenever i 1> i2. Analytically, this formulation causes great difficulty. Besides, the relationship may in fact strengthen our results (see Footnote 1 i). 7 We are assuming that foreign aid can in fact be disbursed in a way that will help the source country resolve its political problems. We interpret foreign aid as the cost o f assisting the source country with its problems. Hence, the selective relaxation o f trade restrictions would be considered aid under our definition. Morris and Mayio (1982), Portes (1983), Hofstetter (1984), Pastor (1983), Bach (i983) suggest ways in which aid can be used to alleviate proverty, foster rural development, and reduce income inequities and implicitly the consequential instability these cause (see for instance Sandos and Cross 1981). Political instability and illegal immigration 27 3. On the optimal allocation of funds The objective of the host country is to minimize entry of migrants with the use of as little funds as possible, s, 9 Let M be the budget allotted for this purpose and V(M, 1 - G ( h ) ) the host country's objective function. Then, OV/OM<O and 8 V/OG > 0. The exact functional form of V(., • ) specifies the trade-off between the two goals (of minimizing entry of migrants and minimizing funds allocated) from the host country's viewpoint. Now let M t be the portion of the budget allocated for foreign aid and M 2 for increased restrictions (M = M 1+M2). For simplicity, assume initially that M1 = M2 = 0 so that Eq. (2) represents the status quo. The host country's problem then amounts to solving, Problem (1) Max (M1,M2,h) V(Mt+M2,I-G(h)) subject to: las(i(MO )-OU2 )C~s(i(M1) ) = h Lur(k(Mz) )-Ot/2 )~rr(k(M2) )l Mt->O, M2>--O. To solve Problem (1), we will use a two stage procedure. First, we will fix h and maximize V with respect to M 1 and M2 = M - M 1 . The solution dictates the optimal budget allocation in control of a fixed number of immigrants (i.e., 1 - G ( h ) ) . This problem requires no specification of the functional form of V(., • ). However, to determine the optimal number of immigrants, the functional form of V must be well specified. More precisely, since OV/OM< 0 Problem (1) is equivalent to solving Problem (2) Max ( - M ) (M,Ma) subject to: l~s(i(Mt) )-Oc/2 )as(i(Mt) ) = h LUr(k(M-Mt ) ) - ( ~ / 2 )~r(R(M-M1) )] Mt>_O, M-Mt>_O . 8 It m a y be the case that immigrants benefit the host country as some scholars have argued about illegal aliens in the United States (see for example Roback 1981, Chiswick 1985). Here we are implicitly assuming the opposite. Optimality must therefore be interpreted within the strict confines of the host country's decision criterion - minimizing immigration. A different criterion would likely imply a different set of optimality conditions. 9 In our model, we assume individuals are endowed with equal skill levels or abilities. The immigration flow is then characterized by the number of immigrants - the quantity aspect of immigration problems. To account for the quality aspect, we need to modify the assumption by allowing individuals to have different skill levels. Thereafter, any immigration policy will affect not only the quantity but also the quality of immigrants. 28 J.E.L. Campos and D. Lien Forming the Lagrangean, we get L = -M+P[ps-(2/2)as-h#r+h(A/2)ar]+qlM 1+ q 2 ( M - M 1 ) . T h e resulting first order conditions are then - 1+p[-h#r+h(2/2)a'~]k'+q2 = 0 ; (4a) P[P'si'-(2/2)a'si'+hM'rk'-h(2/2)Cr'rk']+qt-qz = 0 ; (4b) #s-(2/2)as-h(Pr-(,~/2)CZr) = 0 ; (4c) MI>-O, ql>-O, qlM~ = O, M-MI>-O, q2>-O, q 2 ( M - M I ) = 0 . (4d) To guarantee that the solution to ( 4 a ) - ( 4 d ) is a maximizing point, we have to consider the second order condition. T h a t is, the bordered Hessian associated with P r o b l e m (2) must be positive. U n d e r some appropriate assumptions, L e m m a 1 ensures that the second order condition is satisfied. l_emma 1. Let ~ts = (PsOi), 6 s = (#sOi), ~l r ---- (#rOk), and #r = (at °k) with % " be- ing the composite function operator. Also, let f = #s-(2/2)~r s and Suppose that ( f " - h ~ " ) < O, then det (1) 2 Vh ) > O where De Vh is the bordered Hessian for the maximization problem (i.e., Problem (2)). = ~tr -- ( 2 / 2 ) # r. Proof." See Appendix. Essentially f ' denotes the marginal expected utility p r o d u c e d by additional foreign aid; ~ ' the marginal expected utility induced by additional funds allocated toward increased restrictions. 10 It can be easily shown that f ' > 0 and ~ ' < 0 , i.e., /~s^'= #s i ' > 0 , #s = a'si'<O,/~r = / - t r k ' < 0 and ar~'= ark'>O. Hence, f " - h ~ " < O means that the change in marginal expected utility induced by additional funds for tighter i m m i g r a t i o n laws is greater t h a n ( l / h ) times the change in marginal expected utility p r o d u c e d by additional foreign aid. We are now ready to state o u r results. First, we consider the n o n o p t i m a l i t y o f no foreign aid. P r o p o s i t i o n I shows that, under some assumptions, the o p t i m a l foreign aid must be nonzero. Proposition 1. For any fixed h with /~s(i(O))-(~/2)Crs(i(O))-h[Pr(k(O))(A/2)ar(k(O))]<O, if Ii'(0)1 is sufficiently large, then M~'>O where ( M * M T ) solves Problem (2). Proof." See Appendix. T h e first a s s u m p t i o n states that, for the relevant h selected by the host country, if the c o u n t r y does nothing (i.e., no funds allocated for foreign aid or restricl0 While/~s and/i s have the same nominal meaning, they have differnt mathematical properties. More precisely,/2s specifies the dependence of the expected wage in the source country on political instability (i.e., Msis a function of i); on the other hand,/is specifies the dependence of the expected wage in the source country on the amount of foreign aid (i.e.,/is is a function of M~). Similar interpretation applies to J/r and/~r (and so forth). Political instability and illegal immigration 29 tion of immigration policy), then those persons with a bias scale equal to or smaller but sufficiently close to h will all migrate. Consequently, the objective of allowing only 1 - G ( h ) illegal immigrants cannot be achieved. The assumption [i' (0) I be sufficiently large is in fact stronger than what is needed. However, it has a nice interpretation: the first dose of foreign aid must have a relatively huge impact on the political instability of the source country. This is to be expected if the situation in the country is unstable enough to have a measurable impact on economic conditions but not too unstable to be beyond help - in other words, a situation that is not too late to rectify. Given these two assumptions, we conclude that the host country must allocate some funds for aid to attain the goal of deterring 1 - G(h) illegal immigrants. Note that since Ii'(0)] is sufficiently large, the marginal benefit of allocating some funds to aid is large, making it optimal to provide some aid, i.e., MT > 0.11 Now, with fixed h, at the optimal solution to (4a)-(4d), all individuals with biases less than or equal to h will be kept out of the host country. Those with higher biases, however, will still find the host country attractive. Thus, to prevent more people from entering illegally, the host country must choose a larger h. To achieve this, certainly more funds must be provided. The interesting question however is, how these additional funds are allocated. Proposition 2 then provides the answer. Proposition 2. Let Mf, M*-Mf>O. Then under the hypothesis of Lemma 1, (i) OM*/Oh>O; (ii) aM?/Oh>__Oif ~,~,"-(~')2>__O. Proof." See Appendix. Note first that nonzero M~ is ensured by Proposition 1 under appropriate assumptions; similar assumptions can be constructed to ensure that M22= M - M 1 is positive. To understand Proposition (2), note that ( ~ (~')) >__0 (_< 0) if and only if (log ~) is convex (concave). Since ~ depends only on /~r and 8r, then the shape of log g will depend heavily on the response of employers in the host country to increasingly restrictive policies. If employers are cooperative, then increases in M2 will lead to progressively decreasing expected utility (wages) for potential illegal aliens, i.e., log ~ is likely to be concave. Thus, we would expect the government to allocate more and more of its budget to tightening immigration policies and less and less to foreign aid, i.e., (OMt/Oh) < 0. On the other hand, if employers are uncooperative, the restraining effect of further increases in M2 on expected utility will become progressively smaller i.e., log g is likely to be convex. Consequently, we would expect (OM~/Oh) > 0. That is, to further reduce the influx of illegal aliens, more funds will have to be allocated to aid. 11 As mentioned earlier, h and i may be positively related (see Footnote 6). This actually strengthens our results, i.e. foreign aid is a necessary component of the solution to the illegal alien problem. The reason is as follows: an additional dollar allocated to foreign aid will not only increase the expected utility of a potential illegal alien if he remains at h o m e - the term (tts-0~/2)crs) - but will reduce his bias in favor of migrating to the host country and hence the term (h ~r-O~/2)Crr]; therefore, the additional dollar leads to an even greater reduction in the flow of illegal aliens at the margin which then leads to a rise in the marginal utility of the government (OV/OM1)rises; consequently, more of the fixed budget will be allocated to aid. J. E. L. Campos and D. Lien 30 As a special case, assume 2 = 0 (i.e., risk neutrality) and ~r(M2) -- c exp (aMz) with c > 0 and a < 0 . Then, (8 2 (log ~ ) / S M 2) = 0 and so (SM~/Sh) = 0. That is, the optimal amount of foreign aid is independent of h. In this case, to prevent more aliens from entering illegally, more money should be spent on tightening and implementing immigration laws. This, of course, is a highly special case. In general, we would expect OM~/Oh>O or OM~/Oh < 0 depending upon the attitude of firms. We now turn to characterizing for the optimal h. The solution to Problem (2) yiels functions M~ = M ~ ( h ) and M~ = M ~ ( h ) = M * ( h ) - M ~ ( h ) . Plugging these into V(., ") and solving P r o b l e m ( l ) would yield the optimal h. Mathematically, the optimal h, h*, satisfies _0 v a s._t , ,¢h~ _, 0M 8h ov.oo(h):o, ON (5) Oh where N = 1 - G ( h ) ; provided the second order condition is satisfied. 12 That is, an increased h requires that more funds be spent. This yields a utility loss to the source country. On the other hand, it also implies fewer illegal aliens which results in a utility gain. Equation (3) then states that the optimal h must balance these two forces. 4. Concluding remarks and some extensions Over the years, the Unites States government has become increasingly concerned with the illegal alien problem. Although good estimates are hard to come by, many experts agree that their number has increased substantially in the last ten years or so. Our model suggests that the political problems experienced by some source countries during this period may have contributed significantly to steppedup migration. More importantly, it suggests further that, if the United States is bent on deterring further entry, then it cannot do so efficiently by simply creating newer, more restrictive rules. Minimizing entry requires a two-pronged approach - increased restrictiveness and a channeling of properly targeted aid. More precisely, it requires a coordination of immigration and foreign policy initiatives. Furthermore, if firms in the United States respond unenthusiastically to increased government regulations, more emphasis should be put on the latter. The conclusions are derived under the assumption of a representative individual. Nonetheless, they remain intact by allowing different individuals to have different skill levels or abilities. Appendix I provides detailed analyses. As noted earlier, our model applies to a single source country. However, it can conceivably be extended into a multisource country case by introducing a proximity parameter and incorporating secondary effects of aid allocations. The farther a source country is from the host country, ceteris paribus, the costlier it is for an individual in the former to move to the latter. This will help explain how foreign aid should be allocated across the different source countries. The closer (farther) a country is, the more (less) aid the host country is likely to provide. For 12 The second order condition requires (82V/OM2)'(OM*(h)/Sh)2-(O2V/ON2)'(OG(h)/Oh)2+ (0V/OM)"(O2M* (h)/0h 2) _ (8P/ON)"(O2G (h)/Oh) < 0 when evaluated at the solution to Eq. (5). 31 Political instability and illegal immigration countries sufficiently far away, perhaps no aid would be necessary; the new rules applicable to all source countries plus the moving cost may be sufficient to deter or at least to minimize entry from these countries. Aid to a single source country generates a secondary effect. Improved conditions in a single source country (resulting from aid) may attract illegal migrants from poorer source countries to that country. These migrants could then acquire better labors skills and thus would be better equipped to move into the host country. Thus, increased aid to a single source country, ceteris paribus, may indirectly increase the flow of illegal aliens from other source countries. A multi-source country model must account for this. Appendix Proof of Lemma 1 The bordered Hessian associated with Problem (2) is -phi" h~" D2 Vh = phi" -h~' 0 1 f"-h~" o ~ -~ -h~,' 0 0 0 0 0 ql 0 1 0 - q2 0 0 1 q2 Therefore, we have det ( 0 2 Vh)= (h~') 2 [ q 2 + q 1 - 0 ? " - h ~ " ) ] > 0 since qi, qz >-0 and f " - h~" < 0 by assumption. Proof of Proposition 1 Let f(M1) = Ps-(Xl2)as and g ( M - M 1 ) = pr-(Xl2)ar. From (4c) we get, dM M~= =-{O[f-hg]/OMl} dMl M~ ODC-hg]/OM Now, given our assumptions on/~;, a'r, and k', the denominator must be positive ' i' and profor any M~'. Suppose M~' = 0 then given our assumptions on a~, crs, vided I i' (0) I is sufficiently large then the numerator is negative at M~' = 0. But then this means M cannot be minimized, i.e., (dM/dM1)<O at M~' = 0. This is a contradiction. Proof of Proposition 2 Since M~', M * - M ~ > 0, the last two constraints associated with Problem (2) can be excluded. Therefore the new Lagrangean is L = - M + p L~-()L/2)~-h(l?tr-()~/2)6"~)] . J. E. L. Campos and D. Lien 32 The first order conditions are thus, -1-phi' =0 ; f +h~' = 0 ; f - h ~ = o. Total differentiation yields the following system, -phg" I hg" -hg' phg" -hg' dM (f"-h~,") o aM1 0 0 dp p~, = dh -~' Now let A = - ( h ~ " ) 2 ( f " - h ~ '') which is positive by hypothesis. Upon using Cramer's rule on the above equation system, we get OM*/Oh = (1/A )h~,~,'(f"-h~") . Since g'<0, A > 0 , f " - h g " < O , OM*/Oh must be positive. On the other hand, ÜM"?/Oh = - O / A ) h2 ~, ' (g ~,"-(~') 2) . Thus OMt/Oh>_O if and only if ~ " - ( ~ ' ) 2 _ > 0 since A > 0 and ~ ' < 0 . References Bach R (1983) Emigration from the Spanish-speaking Carribbean. In: Kritz MM (ed) US immigration and refuge e policy. 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