Discussion Papr Sris CDP No 08/07 Illgal igration Enforcmnt and inimum Wag Gil S. Epstin and Odlia Hizlr Cntr for Rsarch and Analysis of igration Dpartmnt of Economics Univrsity Collg ondon Drayton Hous 30 Gordon Strt ondon WC1H 0AX
CRA Discussion Papr No 08/07 Illgal igration Enforcmnt and inimum Wag Gil S. Epstin and Odlia Hizlr (Cohn) Bar-Ilan Univrsity CRA ondon and IZA Bonn Bar-Ilan Univrsity Non-Tchnical Abstract This papr xamins th connction btwn illgal migration minimum wags and nforcmnt policy. W first xplor th mployrs dcision rgarding th mploymnt of illgal migrants in th prsnc of an ffctiv minimum wag. W show that th mployrs dcision dpnds on th wag gap btwn thos of th lgal and illgal workrs and on th pnalty for mploying illgal workrs. W considr th ffcts a chang in th minimum wag has on th mploymnt of illgal immigrants and local workrs. W conclud by considring th optimal migration policy taking into considration social wlfar issus. Kywords: illgal immigration migration policy minimum wag intrst groups. Cntr for Rsarch and Analysis of igration Dpartmnt of Economics Drayton Hous 30 Gordon Strt ondon WC1H 0AX Tlphon Numbr: +44 (0)0 7679 5888 Facsimil Numbr: +44 (0)0 7916 775
Illgal igration Enforcmnt and inimum Wag Gil S. Epstin 1 Bar-Ilan Univrsity CRA ondon and IZA Bonn and Odlia Hizlr (Cohn) Bar-Ilan Univrsity Abstract This papr xamins th connction btwn illgal migration minimum wags and nforcmnt policy. W first xplor th mployrs dcision rgarding th mploymnt of illgal migrants in th prsnc of an ffctiv minimum wag. W show that th mployrs dcision dpnds on th wag gap btwn thos of th lgal and illgal workrs and on th pnalty for mploying illgal workrs. W considr th ffcts a chang in th minimum wag has on th mploymnt of illgal immigrants and local workrs. W conclud by considring th optimal migration policy taking into considration social wlfar issus. Kywords: illgal immigration migration policy minimum wag intrst groups. 1 Corrsponding author. Dpartmnt of Economics Bar-Ilan Univrsity Ramat-Gan 5900 Isral mail: pstig@mail.biu.ac.il.
1. Introduction Illgal immigration is a vry hot social and conomic issu facing many tchnologically advancd countris. Dspit fforts to limit th numbr of immigrants allowd into ths countris th illgal immigrant stock is rising. It is difficult to accuratly stimat th numbr of illgal immigrants. At th bginning of 000 som OECD countris publishd official figurs of unauthorizd immigrants. In th USA stimats wr btwn 4 to 7 million 3 which is about 1.5% of th population. In Grc it was about 3% and in Italy about 0.5%. Th incrasing stock of illgal immigrants has turnd it into a cntral issu in numrous lctions throughout th Wstrn Hmisphr. Th ffct of lgal immigration on th host country s wlfar is controvrsial. Som studis found that th immigrants ar a bnfit to th local population and othrs claimd th opposit (s for xampl Brry and Soligo 1969; Rivra-Batiz 198 and Borjas 1995). Howvr it is widly blivd that illgal immigration is dtrimntal to th host country. This is bcaus th illgal immigrants impos additional costs by th ssnc of thir illgality in addition to th burdn imposd by thir illgality i.. th rplacmnt of local workrs. Th illgal immigrants tnd not to pay taxs and ar oftn involvd in clandstin activitis both as flons and as victims. Furthrmor thir xistnc srvs as a signal to th nativs that th govrnmnt dos not nforc th law or that illgality is accptabl thus causing thm to avoid paying taxs (s Epstin and Wiss 006). any articls discuss th govrnmnt s fforts to control illgal immigration (for xampl Ethir 1986; Chiswick 1988; Zimmrmann 1995; Djajic 1999; Gaytan- Frgoso and ahiri 000 and mor rcntly Guzman t al. 007). Efforts to rduc illgal immigration utiliz a numbr of instrumnts. Th main instrumnt is th allocation of rsourcs for apprhnding illgal immigrants. This is implmntd via bordr controls which block th ntry of undsirabl lmnts as wll as intrnal nforcmnt whrby such popl ar apprhndd and xplld from th country. Som countris also provid forign aid to th country of origin in ordr to rduc incom diffrntials and thus th incntiv to immigrat. An additional way to minimiz S http://www.ocdobsrvr.org/nws/fullstory.php/aid/190 3 S http://www.cis.org/topics/illgalimmigration.html 1
illgal immigration which has rcntly bcom vry common is to grant amnstis to illgal immigrants who hav bn in th country for an xtndd priod of tim. Th Immigration Rform and Control Act (IRCA) of 1986 in th U.S.A. rprsnts an attmpt to control illgal immigration by imposing fins on mployrs who hir unauthorizd workrs (s for xampl Cobb-Clark t al. 1995). Employrs who knowingly hir illgal alin workrs ar subjct to civil mony pnaltis of $50 to $000 pr workr for a first offns and $3000 to $10000 pr alin for a third offns 4. Wstrn Europ countris such Franc and Grmany also nactd mployr sanctions in th mid-1970s. In Franc Employrs ar liabl for pnaltis of up to 1000 tims minimum wag whil in Grmany th maximum fin is 5600$. In UK mployr sanctions xist sinc 1997 and th maximum fin is 8000$ pr illgal workr hird (artin and illr 000) A vast litratur xists on migration policy (s for xampl Bnhabib 1996 Baur t al 000) but only fw articls xamin th intraction btwn conomic and political procsss. Amgashi (004) studid a modl in which th numbr of immigrants allowd into a country is th outcom of a costly political lobbying procss btwn a firm and a union using th all-pay auction contst. Epstin and Nitzan (006) hav rcntly prsntd a modl for th ndognous dtrmination of quotas viwing th quota as th outcom of a two-stag political contst btwn two intrst groups i.. workrs and capital ownrs. Garcia (006) xplaind why th control of immigration may b a rlvant issu in lctions and dmonstratd that rightist partis hav an advantag of winning in countris whr immigration control is a rlvant issu in th lction. Grthr t al. (001) dtrmind th migration policy as rsult of th lctorat s prfrncs. Epstin and Hillman (003) prsntd migration policy implications of th fficincy wag stting. Although many studis dal with th issu of illgal immigration as mntiond abov thr ar almost no rfrncs to th mployrs dcision rgarding th numbr of lgal and illgal workrs. Th majority of ths studis simply assum that whn th xpctd pnalty facd by th mployr incrass th numbr of illgal immigrants 4 In som countris sanctions ar lss ffctiv at dtrring illgal ntry and mploymnt for svral rasons including among othrs allocation of fw rsourcs th sprad of fals documnts and insufficint coopration btwn govrnmnt agncis.
dcrass (s for xampl Epstin Hillman and Wiss 1999). In our study w considr th rlationship btwn th numbr of illgal immigrants and th mployr's bnfits (wag gap btwn lgal and illgal workrs) and costs of mploying thm (xpctd pnalty). W also xamin how a chang in th minimum wag affcts th illgal immigrants and th local workrs. Anothr purpos of this study is to xamin th optimal migration policy. Th low wag rqustd by forign workrs ncourags capital ownrs to mploy thm. Th policy makr may protct th unskilld workrs by stablishing a minimum wag law and allocating rsourcs to catch th non-complying mployrs (i.. mployrs who mploy illgal workrs). In our modl two intrst groups ar dirctly affctd by th migration policy: th capital ownrs who bnfit from illgal immigrants and th unskilld workrs who suffr from thm. Th public is affctd indirctly by illgal immigration. Th politician dtrmins th optimal policy by taking into account all th factors: th capital ownrs and th unskilld workrs utility th public intrst and th financing cost. This papr is organizd as follows. Th following sction prsnts th dcision facd by th illgal workrs and th mployrs. Sction 3 dtrmins th optimal nforcmnt budgt. Th last sction contains a brif summary and conclusion.. Th Employrs and th Workrs Dcisions Th mployr s dcision: Considr a small opn and comptitiv conomy whr th mployrs ar risk nutral and may mploy local unskilld workrs or forign workrs in rturn for a wag that is lowr than th quilibrium wag of a closd conomy. In ordr to protct ths workrs th govrnmnt stablishs a minimum wag w for all workrs. orovr immigration law forbids mploying forign workrs who lack mploymnt authorization. Th mployr s profits qual: (1) Π = VF( N) Nw E 3
Whr N is th numbr of unskilld workrs F( N ) is th production function which satisfis F '( N) > 0 F' '( N) < 0 and V is th product pric. Dnot th optimal numbr of unskilld workrs by N which satisfis: () VF '( N) = w Now w assum th following: 1. Th mployr may mploy illgal workrs I who ar prfct substituts for th lgal unskilld workrs.. Th wag for a forign illgal workr w I is lowr than th wag of a lgal workrs w (blow w will dtrmin th forign illgal workr's wag w I ). 3. Th mployr pays wags which ar lowr than th minimum wag only to th illgal immigrants. Th rason for this is that th illgal forign workrs ar afraid to complain about thir mployrs paying thm a low wag. Whn an illgal workr is apprhndd both th workr and th mployr ar affctd: th illgal workr is xplld from th country and sanctions against th mployr ar implmntd. In addition as sn blow th wag rqustd by forign workrs may b lowr significantly from th wag rqustd by local workr. Thrfor th illgal workrs ar hrwith calld illgal immigrants. 4. An mployr who mploys illgal immigrants may b dtctd and punishd with probability p. 5. Th policy makr can rgulat p by an nforcmnt budgt E i.. pe ( ) such that p ( E) p ( E) ' > 0 '' < 0. 6. Th pnalty for mploying illgal workrs dpnds on th numbr of illgal immigrants θ (I) such that θ ( 0) = 0 and θ '( I) > 0 θ ''( I) > 0. 5 orovr w assum that θ ''' ( 0) = 0. This assumption simplifis our calculations. Blow w show whr this assumption is usd and that it is not critical for our rsults. 5 Indd in a lot of countris th fin is constant for ach mploy but whn marginal production dcrass thn th apprhnsion of a workr incrass th costs to th mployr in a non-linar way. In addition th financial cost of th fin (for instanc th marginal intrst) incrass as th total fins incrass. 4
7. At th bginning of ach priod th mployr dcids on th numbr of lgal and illgal workrs to mploy. Th mployr s xpctd profit is givn by: (3) E( Π ) = VF( N) w Iw pθ ( I) s.t. (3 ) N = + I E I Th mployr dtrmins th optimal numbr of workrs and illgal immigrants. Thrfor th first-ordr-conditions for maximizing th profits ar 6 : (4) and (5) ( ) E Π E = VF '( N) w = 0 N ( ) E Π E = w w I pθ '( I) = 0 I W obtain that th wags will qual: (6.1) w = w + pθ '( I) and (6.) VF '( N) = w + pθ '( I) I I At quilibrium th marginal cost of mploying an illgal immigrant quals th wag of a lgal workr - th minimum wag w. Th mployr mploys illgal immigrants as long as th cost for mploying thm w + pθ '( I) is lowr or qual to th minimum wag. Aftrwards h continus to mploy lgal workrs as long as thir wag w is lowr or qual to th marginal valu of production VF '( N ). This rsult is supportd by Yaniv s (001) conclusions that th mployr rducs mploymnt to th I 6 Th scond-ordr conditions for maximum ar satisfid. 5
point whr th marginal valu of th production quals th minimum wag but th total numbr of workrs dosn t chang as a rsult of violating th migration law. mma 1: A positiv rlationship xists btwn th stock of mployd illgal immigrants and th lvl of minimum wag. Proof: Using th invrs function rul with quation (6.1) w obtain: (7) I 1 1 = = w dw pθ ''( I) di I As assumd abov θ ''( I) > 0 hnc > 0.! w Th illgal immigrants dcision: It is assumd that th wag in th dstination country is highr than th wag in th sourc country. Howvr th immigrant has an adjustmnt cost that stms from living in an unfamiliar nvironmnt (s for xampl Chiswick 1999). In addition to this cost th illgal immigrant is subjct to apprhnsion and dportation by th authoritis. If h is apprhndd h has additional th costs of lost wags and distrss. Th potntial immigrant will thrfor agr to immigrat illgally if th wag rcivd in th dstination country w H including th pnalty if h is apprhndd w I is highr than th wag in th sourc country λ p and th adjustmnt cost in th host country c. Th condition for illgal immigration can b writtn as follows: (8) w w + c pλ I H + Not that this condition is writtn for on priod. 7 7 For simplicity w ignor th on-tim moving cost. But it can b assumd that this cost is dividd ovr all th priods. 6
Th mployr pays th illgal immigrants th minimal wag that thy ar willing to accpt. Stting quation (8) into (5) givs: (9) p( E) = w w λ + θ ' H c ( I ) Equation (9) dtrmins th conditions for th optimal numbr of illgal immigrants I that ar mployd for a givn nforcmnt budgt E. t us xplain this quality by looking at figur 1 that rprsnts quation (9): th solid lin rprsnts th numbr of mployd workrs N whras th dashd lin rprsnts th numbr of lgal workrs (local and forign). Th gap btwn ths lins rprsnts th numbr of illgal workrs I. At point (a) th govrnmnt dos not allocat rsourcs against illgal immigration (i.. pe ( ) = 0) th mployrs mploy only illgal immigrants and thir numbr is highr than N th numbr of workrs whos marginal product valu quals th minimum wag (s quation ()). In ara (b) th probability of bing dtctd incrass and th numbr of illgal immigrants dcrass. Howvr th mployr continus to mploy only illgal immigrants and thir numbr is highr than N. In ara (c) th mployr mploys both lgal and illgal workrs such that th cost of mploying illgal workrs quals th cost of mploying lgal workrs i.. th minimum wag. Th numbr of all th workrs quals N. In ara (d) th probability of bing dtctd is so grat that th mployr complis with th law and mploys only lgal workrs. To summariz Proposition 1 (s figur 1): (a) If p = 0 thn N = I = N and = 0. Thrfor N satisfis: (10) VF '( N ) = w + c. H w wh c (b) If p (0 ) λ+ θ'( N ) thn N = I > N and = 0. Thrfor I satisfis: 7
(11) VF '( I ) = w + c + pλ + pθ '( I ). H w wh c w wh c (c) If p ( ) λ+ θ'( N ) λ+ θ'(0) thn N = N I ( N 0) and (0 N ). Thrfor I satisfis: (1) w = w + c+ pλ + pθ '( I ). H (d) If w wh c p > λ+ θ'(0) thn N N = = and I = 0. Thrfor satisfis: (13) VF '( ) = w. Proof: (a) From stting p = 0 in quations (8) and (6.1) w obtain w I = w H + c and w w > I ( w is constant) rspctivly. This mans that th cost of mploying an illgal immigrant is lowr than in th cas of p > 0 and than th wag for a lgal workr. Th mployr thrfor mploys only illgal workrs. From quation (6.) w obtain that th numbr of mployd workrs holds VF '( N ) = w + c = w. H I (b) From quations (8) and (6.1) it follows that th cost of mploying an illgal immigrant is highr than th cost of cas (a) but is still lowr than th wag for a lgal workr. Th mployr thus continus to mploy only illgal workrs. From quation (6.) togthr with (8) w obtain that th numbr of mployd illgal workrs holds VF '( I ) = w + c + pλ + pθ '( I ). H (c) From quations (6.1) (6.) and (8) it follows that VF '( N ) = w = w + pθ '( I ) I such that w I = w H + c+ pλ. This mans that th cost of mploying illgal immigrants quals th wag for lgal workrs and quals th marginal product. (d) From quation (6.1) it follows that th cost of mploying lgal workrs is highr than th wag for lgal immigrants i.. w < w + pθ '( I). Th mployr I 8
thrfor mploys only lgal workrs and thir numbr holds VF '( ) = w.! t us now focus on th cas of ara (c) undr which both illgal and lgal workrs ar mployd. In this cas th total numbr of workrs is idntical to th numbr of workrs that would b mployd if only lgal workrs ar mployd (d). 3. Optimal Policy t us firstly xamin how a chang in th minimum wag affcts th numbr of local workrs mployd. Th lgally mployd workrs consist of th lgal nativ workrs and th forign workrs F. W assum that th mployrs first mploy th local workrs and if thr is a surplus dmand for lgal workrs thn thy import forign workrs. Th numbr of local workrs is givn by: (14) = N F I. Figur dscribs th ffct of incrasing th minimum wag to w 1 > w on th optimal numbr of workrs N. From quation () and from th sign of th scond dn drivativ of F( N ) (i.. F''( N ) < 0) it follows that < 0. Thus th optimal dw numbr of workrs thus dcrass from N to N. w wh c It is also asy to s that th boundaris dscribd abov λ+ θ'( N ) and 1 w wh c w wh c mov to th right to and λ+ θ'(0) λ+ θ'( N ) 1 w wh c rspctivly. Hnc λ+ θ'(0) ara (b) th ara of mploying only illgal workrs xpands and ara (d) th ara of mploying only lgal workrs diminishs. This is supportd by lmma 1 which di statd that > 0. This mans that if th govrnmnt wants to prvnt th ris in th dw stock of illgal immigrants rsulting from th incras in th minimum wag it must allocat mor rsourcs to countract illgal immigration (moving to th right in figur 9
). An additional ffct of th ris in th minimum wag is dscribd as follows: th supply of local workrs who wish to work for th currnt wag incrass and th df numbr of lgal forignrs dcrass i.. < 0 (Th illgal immigrants and th dw local workrs rplac thm). A chang in th minimum wag affcts th numbr of lgal workrs and quals: (15) d dn di = dw dw dw Proposition : a. Raising th minimum wag dcrass th numbr of lgal workrs mployd if th wag is lowr than th quilibrium wag of a closd conomy. Th chang in th numbr of lgal workrs is gratr than th chang in th numbr of all workrs. b. Raising th minimum wag has an ambiguous ffct on th numbr of local lgal workrs mployd. Proof: d dn di a. = < 0 th HS th chang in th numbr of lgal workrs dw dw dw quals th chang in th numbr of all workrs plus th ngativ trm di dw b. Whn th minimum wag incrass th supply of local workrs incrass and thy rplac th lgal forign workrs. Howvr th total numbr of workrs diminishs and th numbr of illgal workrs riss. If th formr ffct is biggr than th lattr thn th numbr of local workrs incrass and vic vrsa if th d dn di df formr ffct is smallr than th lattr. = th two first dw dw dw dw 10
trms of RHS ar ngativ and th last trm is positiv. Thrfor it is impossibl to know th sign of d dw.! It should b notd that rcnt studis hav indd found zro or vn a positiv ffct of minimum wag on mploymnt in monopsony markts (Dickns t al. 1999). Howvr othr studis show that raising th minimum wag has a ngativ ffct on mploymnt (s Yaniv 001). Our modl diffrs from th xisting typ of modls in th litratur. 3.1 Th optimal nforcmnt budgt In our modl th politician dtrmins th optimal nforcmnt budgt. W assum that th politician wishs to maximiz social wlfar including th costs and bnfits of th unskilld workrs th capital ownrs and th conomic as wll as social costs as a rsult of illgal immigration. It should b notd that if th politician dtrmins th optimal minimum wag and th struggl btwn th unskilld workrs and th capital ownrs is ovr th minimum wag rathr than ovr th nforcmnt lvl our main rsults will not chang. 8 Whn th nforcmnt budgt incrass th capital ownrs rduc th numbr of illgal immigrants for two rasons: 1. th probability of bing dtctd and th xpctd pnalty incras.. Th wag rqustd by th illgal immigrants also incrass (s quation (8)). Hnc incrasing th nforcmnt budgt causs a dcras in th capital ownrs profits. Th main costs of th xistnc of illgal immigration ar displacmnt of th local unskilld workrs and a rduction in rcivd wags. It is thus clar that incrasing th nforcmnt budgt dcrass th numbr of immigrants staying in th host country th unmploymnt of local unskilld workrs dcrass and thir utility incrass. Th scondary costs ar causd by th ssnc of thir illgality. For xampl th undocumntd immigrants ar oftn involvd in clandstin activitis and ar usd 8 Sinc G G = whr G is th politician s objctiv function E is th nforcmnt w w E budgt and w is th minimum wag. 11
as signals to th public that th govrnmnt dos not nforc th law. Raising th rsourc allocation to nforc th immigration law i.. th nforcmnt budgt rducs th social cost but it has a pric th altrnativ us. This mans that ths rsourcs ar allocatd non-productiv activitis. Th unskilld workrs ar intrstd in raising th nforcmnt budgt whil th capital ownrs ar intrstd in rducing it. Th govrnmnt s objctiv function is rprsntd by: 9 (16) ( ) G = απ + 1 α Π βc( I) γe E Whr E is th nforcmnt budgt α is th workrs rlativ political strngth ( 0 α 1) < < Π is th local workrs arning 10 Π E is th profits of th capital ownrs as givn in quation (3) C is th social harm rsulting from th xistnc of illgal immigrants such that ( ) C 0 = 0 C'( I) > 0 C''( I) < 0 β and γ dnot th wights of this social harm and th nforcmnt budgt ( 0 βγ 1) can b rwrittn as: < < rspctivly. Equation (16) (17) ( ) G = α w + 1 α ( VF( N) w ( N I) Iw pθ( I)) βc( I) γe. I Th optimal nforcmnt budgt quals: 9 Anothr scnario is that th nforcmnt budgt is financd by th fins and taxs. Th public bars th tax burdn paying for th nforcmnt (lik Guzman t al. 007) and taks part in th struggl. Hnc th govrnmnt s objctiv function will b G = απ + βπ 1 α β U ( ) ( ) ( ) ( ) 0 E public ( ) st.. U = C I + t E public E = pθ I + t t Whr t is th tax th othr variabls ar similar to th papr s body. Th cor of th rsults dos not chang and will b providd on rqust. 10 W us th workrs wags and not th workrs surplus bcaus th dclard main goal of th minimum wag is to maximiz th total incom transfr to minimum wag workrs (Sobl 1999). Furthrmor th labor supply curv is unknown (xcpt for th fact that it incrass) and whn th workrs total wags incras - th workrs surplus also incrass. 1
(18) dg ( 1 ) I I w I p w w wi I ( I) p '( I) I = α + α θ θ de. I βc' ( I) γ = 0 Th rgulator facs a givn mployrs and illgal immigrants bhavior as discussd abov. Th diffrnc btwn th minimum wag and th illgal workrs wag at quilibrium quals th xpctd pnalty (s quation (6.1)): (19) pθ '( I) = w wi In addition from quation (8) it follows that: wi p (0) = λ E From stting quation (19) and (0) into (18) w obtain: (1) dg ( 1 ) I I p w w wi ( I ( I) ) ( w wi) I = α + α λ+ θ de I βc' ( I) γ = 0 Rarranging quation (1) givs us: dg p I = α w 1 α ( Iλ+ θ I ) βc' ( I) γ = 0 de () ( ) ( ) Hnc th optimal nforcmnt is givn by 11 : I P ( ) (3) α w βc' ( I) = γ + ( 1 α) Iλ+ θ( I) 11 It is assumd that th sufficint scond ordr conditions ar satisfid. 13
If thr ar local workrs willing to work at th minimum wag thn > 0. I P orovr w know that < 0 > 0 C'( I) > 0. 3. Comparativ static Suppos that an xognous chang in th minimum wag has takn plac. 1 t us now xamin how this chang affcts th optimal nforcmnt budgt. As shown abov raising th minimum wag dcrass th numbr of mployd workrs and incrass th numbr of illgal immigrants working in th host country. W also s that th ffct of raising th minimum wag for th local workrs mploymnt is not clar. Th unskilld workrs and th capital ownrs ar affctd by th migration policy and struggl in ordr to chang th nforcmnt budgt. Indd th capital ownrs suffr from th additional cost of illgal immigration and financ th nforcmnt. Howvr thir dirct bnfit from illgal immigration is highr. W can thrfor say that th unskilld workrs hav an intrst in a larg nforcmnt budgt whil th capital ownrs hav th opposit intrst. Dnot th optimal nforcmnt budgt (which satisfis (3)) by xamin how an xognous chang in th minimum wag affcts E. t us now E. To simplify w ignor C w E.13 It can b vrifid that: (4) w G (.) w = G (). By th scond ordr condition G (.) is assumd to b ngativ so: 1 Th changs in th minimum wag can b causd by a chang in th avrag wag whil th minimum wag is adjacnt to it or inflation occurs and th minimum wag is rodd or th govrnmnt is subjctd to political constraints to rais th minimum wag (s Sobl 1999). 13 Th ssnc of th rsults dos not chang - proof will b provid on rqust. 14
(5) ( ) G. sign = sign w w It is known that = ( w) and I = I( w ) hnc and ( λ θ( )) I + I I I = λ + θ'( I ) w w w w E = + w w. Hnc from quation () w obtain: w (6) (.) G p I I α w ( 1 α) = + λ + θ' ( I) w w w w From quation (9) and th quotint rul w obtain: (7) p = ( w wh c) θ ''( I) ( λ+ θ'( I) ) I Stting quation (7) into (6) givs: (8) ( ) G. ''( ) w w c θ I I I I = α + w + 1 α λ θ' + ( I) w w w w ( ) ( ) H ( λ+ θ'( I) ) Equation (8) can b writtn as: (9) ( ) G. w w c ''( I) θ I I = α + w + w w λ+ θ'( I) w ( 1 ) ( ) H α Stting quation (9) into (9) affords: 15
(30) (.) G I I = α + w + ( 1 α) pθ''( I) w w w Aftr stting quation (7) into (30) w obtain: (31) (.) G I = α w + + ( 1 α) w w Hnc by quation (4) and (31) it follows that: I w w (3) sign = sign α w + + ( 1 α) Th first trm in RHS dnots th ffct of a chang in th nforcmnt budgt on th unskilld workrs wags whras th scond trm dnots th ffct of a chang in th nforcmnt budgt on th capital ownrs profits. It is obvious that thr is a ngativ rlationship btwn th nforcmnt budgt and th capital ownrs profits (i.. I < 0 ). Howvr th ffct of a chang in th nforcmnt budgt on th unskilld workrs wags is ambiguous. In ordr to calculat th sign of w w distinguish btwn two cass: A) ocal workrs ar willing to work at th minimum wag As w s in figur 3.1 th mployr mploys local workrs but dos not nd to mploy lgal forign workrs i.. F = 0. If th govrnmnt raiss th nforcmnt budgt th stock of illgal immigrants dcrass and th numbr of local workrs incrass i.. > 0 > 0 (S appndix A). Th first componnt of RHS in w quation (3) is thrfor positiv and th scond is ngativ. 16
Proposition 3: Th ffct of changs in th minimum wag on th optimal nforcmnt budgt dpnds on th political strngth of th groups. If th workrs wight α is 1 highr than E < thn a positiv rlation xists btwn th optimal + w w nforcmnt budgt and th minimum wag. Whras if α < + w w thn a ngativ rlation xists btwn th optimal nforcmnt budgt and th minimum wag. Proof: S appndix B. Th intuition for this rsult is as follows: as statd in lmma 1 raising th minimum wag causs an incras in th illgal immigrants mployd in th host country. It is also clar that as th total numbr of workrs and th total production dcrass th xpctd pnalty incrass and th capital ownrs profits dcras (s appndix C). This is followd by an incras in th numbr of mployd illgal immigrants th unmploymnt among th local workrs incrass and thrfor th utility of th local workrs dcrass. If th workrs hav a high political strngth rlativ to th capital ownrs' thn th policy makr raiss th rsourc allocation against illgal migration with an incras in th minimum wag. Th rason for this is that incrasing th budgt nforcmnt prvnts an incras in th stock of illgal immigrants and possibl harm to th local workrs utility. Howvr if th capital ownrs hav strong political strngth th policy makr rducs th nforcmnt budgt with an incras in th minimum wag sinc incrasing th minimum wag dcrass th capital ownrs profits. Th politician wishs to rais or at last maintain th utility of th strong group and achivs this by rducing th nforcmnt budgt. 17
B) No local workrs ar willing to work at th minimum wag ook at figur 3.. In this cas th dmand for lgal workrs is highr than th local supply. Thus th mployr should mploy lgal forign workrs i.. F > 0. Raising th nforcmnt budgt rducs th stock of illgal workrs incrass th numbr of lgal forign workrs but dos not affct th numbr of mployd local workrs i.. = 0 and w = 0 (in this zon th chang in th minimum wag has no affct = 0 ). Stting = 0 = 0 w into quation (3) givs: de I = 1 < 0. dwm (33) sign sign ( α ) Thus Proposition 4: Whn th minimum wag incrass and thr ar no local workrs willing to work for this wag th policy makr dcrass th nforcmnt budgt. In this cas as a rsult of incrasing th minimum wag th utility of on group th capital ownrs dcrass whil th utility of th othr group th local workrs dos not chang (th illgal immigrants displac th lgal forign workrs but not th lgal local workrs). Th politician may incras th capital ownrs profits without harming th local workrs utility. Th politician thrfor rducs th nforcmnt budgt as long as thr is no harm in th local workrs mploymnt. Aftr that h bhavs as dscribd in cas (A). t us xamin how a chang in th strngth of on of th partis affcts th optimal nforcmnt budgt. In a way similar to (3) w obtain: de P ( ) 0 dα E E λ θ = + + >. (34) sign sign w I ( I ) 18
It is clar that incrasing th workrs rlativ political strngth raiss th nforcmnt budgt and vic vrsa if th capital ownrs rlativ political strngth incrass. It is intrsting to not that if = 0 thn th local workrs hav no incntiv to try to incras thir rlativ political strngth. 4. Conclusion W xamind two policy masurs dsignd to protct th unskilld workrs and th public: prvnting a dcras in wag by a minimum wag law and allocating rsourcs to nforc th immigration law. W hav focusd on th mployrs bhavior and on th consqunt migration policy. As opposd to studis assuming a ngativ rlationship btwn th nforcmnt budgt and th stock of illgal workrs w find th rlationship btwn th numbr of mployd illgal immigrants and th nforcmnt budgt: at low budgt lvls mployrs mploy only illgal workrs and thir numbr is highr than th total numbr of workrs at highr budgt lvls. At high budgt lvls th mployr complis with th immigration law and mploys only lgal workrs. In our story w considr a small opn conomy. Th mployr may mploy lgal workrs and ithr pay thm minimum wag or not. Howvr th mployr prfrs to discriminat against th forign workrs by paying thm a lowr wag than th local workrs bcaus thy ar in th country illgally and may b afraid to complain to th authoritis. Thus forign illgal workrs ar willing to work for a wag which is lowr than that of th nativ workrs wag and is highr than th wag thy would obtain in th hom country. Th first main issu discussd in th papr is th ffct of incrasing th minimum wag on th domstic workrs and th illgal workrs. Th xisting litratur dals in dtail with th subjct of th ffct of th minimum wag on mploymnt (s Dickns t al. 1999; Yaniv 001). Howvr thr is no rfrnc to th ffct on th various groups: illgal immigrants and local workrs. Our rsults show that incrasing th minimum wag may incras dcras or not chang th numbr of mployd local workrs but also raiss th stock of illgal immigrants working in th host country. This rsult supports th stablishd claim in th litratur that a positiv corrlation xists btwn th wag in th host country and th numbr of immigrants (lgal and illgal) (s Chiswick 1999; Hanson and Spilimbro 19
1999). Howvr in our modl th ris in th stock of illgal immigrants is causd by th incrasd mployrs dmand whil in th othrs th rason is hiddn in th incras in th immigrants supply which is triggrd by a wag diffrntial. Th scond main issu dals with th optimal nforcmnt budgt. Th politicians dtrmin th optimal nforcmnt budgt basd on th mployrs and th illgal immigrants bhavior which was xamind in th first part whil taking into considration th public intrst. Following Epstin and Nitzan (006) w assum two intrst groups: nativ unskilld workrs who ar harmd by th illgal immigration and th capital ownrs who bnfit from it. Finally w study th ffct of a chang in th minimum wag on th optimal nforcmnt budgt. W show that th rlationship btwn th optimal nforcmnt budgt and th minimum wag dpnds on th groups rlativ strngth. If th workrs union is strong thn incrasing th minimum wag incrass th optimal nforcmnt and vic vrsa if th capital ownrs ar th strong group. 0
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Figur 1. Th optimal total numbr of workrs and illgal workrs N (a) ( N = I N N = N N = = N (b) (c) (d) = 0 w wh c w wh c λ+ θ'( N ) λ+ θ'(0) p gnd: lgal workrs total workrs 3
Figur. Th ffct of incrasing th minimum wag N ( N N (b) = 0 (c) (d) 1 w wh c λ+ θ'( N ) 1 w wh c λ+ θ'(0) p gnd: lgal workrs total workrs 4
Figur 3.1 Thr ar local workrs willing to work for th minimum wag: w I N Figur 3. Thr ar no local workrs willing to work for th minimum wag: w F I N 5
Appndix A Proof that whn F = 0 thn > 0. Th intuition is as follows: Whn th w minimum wag riss mor local workrs wish to work unmploymnt among th local population incrass and th ffct of chang in th nforcmnt budgt on th mployd local workrs (i.. ) incrass. Th formal proof: If F = 0 thn = N I hnc N I (A.1) = N It is known that = 0 so from quation (A.1) w obtain (A.) I = E From quation (6.1) it follows that: w (A.3) = pθ ''( I) I Hnc (A.4) I = w pθ I 1 ''( ) From quation (A.4) it follows that P I θ'' ( I) + pθ''' ( I) I (A.5) = w pθ ''( I) ( ) Undr th abov assumptions [s assumption (5)] th third drivativ of th pnalty θ ''' ( I ) quals zro. This assumption simplifis mattrs. Altrnativly it can b assumd that pθ ''' ( I) Hnc I is vry small or quals zro. 6
(A.6) I w < 0 From quation (A.) togthr with (A.6) w obtain (A.7) w > 0. Appndix B Proof of proposition 3: I From stting = (s appndix A) into quation (31) w obtain: E sign sign = α w + ( α 1). Th sign of w w only if α > + w E < + w w 1 w w is positiv if and all th componnts of this xprssion ar positiv so. And vic vrsa if α < + w mployrs political strngth 1 α is high and sign < 0. w w thn th Appndix C Th ffct of raising th minimum wag on th capital ownrs profits: From quation (3) w obtain: ( ΠE ) N N I I I (C.1) = VF '( N) ( N I ) w wi p θ' ( I ) dw W w w w w From quation (6) w obtain: (C.) pθ '( I) = w wi and VF '( N) = w Substituting (C.) into (C.1) givs us: 7
( Π ) N N I I I I I dw W w w w w Equation (C.3) can b rwrittn as: E( E ) () Π = I N dw E (C.3) = w ( N I) w w ( w w ) It is clar that N > I hnc ( Π E ) < 0. dw 8