R E F E R E N C E O N L Y
UNIVERSITY OF LONDON THESIS
D e g re e Y e a r N a m e of A uthor CA.
C O P Y R IG H T
This is a th e sis a c c e p te d for a Higher D e g ree of th e University of London. It is an unpublished typescript a nd th e copyright is held by th e author. All p e r s o n s consulting th e th e sis m u st re a d a n d a b id e by th e Copyright Declaration below.
C O P Y R IG H T D E C L A R A T IO N
I re c o g n ise th a t th e copyright of th e a b o v e -d e s c rib e d th e s is re s ts with th e author and that no quotation from it or information derived from it m a y b e published without the prior written c o n s e n t of th e author.
L O A N S
T h e s e s m ay not b e lent to individuals, but the S e n a t e H o u se Library m ay lend a copy to a p p ro ved libraries within th e United Kingdom, for consultation solely on the p re m is e s of th o s e libraries. Application should b e m a d e to: Inter-Library Loans, S e n a t e H o u se Library, S e n a t e H ouse, Malet Street, London W C 1 E 7HU.
R E P R O D U C T IO N
University of London t h e s e s m ay not be re p ro d u c ed without explicit written perm ission from th e S e n a t e H o u se Library. Enquiries should b e a d d r e s s e d to the T h e s e s Section of th e Library. R egulations concerning reproduction vary according to th e d a te of a c c e p t a n c e of th e th e sis a nd a re listed below a s guidelines.
A. Before 1962. P erm issio n gran ted only upon th e prior written c o n s e n t of the author. (The S e n a t e H o u se Library will provide a d d r e s s e s w h e re possible). B. 1 9 6 2 - 1974. In m a n y c a s e s th e author h a s a g r e e d to permit copying upon
completion of a Copyright Declaration.
C. 1975 - 1988. Most t h e s e s m ay b e copied upon completion of a Copyright Declaration.
D. 1989 o nw ard s. Most t h e s e s m ay be copied.
This thesis comes within category D.
This copy h a s b e e n d e p o sited in th e Library of O This copy h a s b e e n d e p o sited in
Malet Street, London W C 1E 7HU.
Border enforcement, aid and migration
Manuela Angelucci
A D is s e rta tio n s u b m itte d to th e D e p a rtm e n t of E conom ics in p a r tia l fulfilm ent of th e req u irem e n ts for th e degree of
Doctor of Philosophy
University College London
L ondon 2004
UMI Number: U591801
All rights reserved
INFO RM A TIO N TO ALL U SER S
The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion.
Dissertation Publishing
UMI U591801
Published by ProQuest LLC 2013. Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC.
All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code.
ProQuest LLC
A b stra ct
This thesis addresses the issue of policy effects on domestic and international m igration, considering in particular the case of Mexican m igration. The first essay investigates the effect of U.S. border enforcement on the net flow of Mexican undocum ented m igration. Such effect is theoretically ambiguous, given th a t increases in border controls deter prospective m igrants from cross ing the border illegally, b u t lengthen the U.S. perm anence of current ones. It estim ates border enforcem ent’s net im pact on m igration inflow using a sample of potential and current illegal m igrants. U.S. border enforcement significantly reduces the net flow of undocum ented m igration. However, the reduction in net flow is more th an half the size of the decrease in inflow.
T he second essay models th e short and m edium -run im pact of aid on m igration, considering alternatively the effect of unconditional and condi tional cash transfers to financially constrained households. D a ta from the evaluation of a M exican development program , Progresa, are used to esti m ate the effect of th e grant on m igration. The empirical analysis shows th a t the program is associated w ith an increase in international m igration, which is also a positive function of the potential transfer size. Conditional grants in the form of secondary school subsidies reduce the short-term m igration probability. Progresa does not seem to increase m edium -term m igration.
The final chapter reviews the approaches employed to estim ate T reat m ent on the Treated Effects (TTEs) using experim ental d a ta in the presence of non-compliers. It discusses the types of param eters th a t can be identified using the Progresa data. It uncovers new param eters th a t have not been estim ated so far, based on the fact th a t a group of eligible households did not receive the program transfer in the initial stages of its im plem entation. It proposes alternative estim ating procedures to identify counterfactuals in the presence of non-compliers for users of the Progresa data. It complements the theoretical p a rt w ith an empirical application by estim ating th e effect of Progresa on school enrolment.
C on ten ts
1 I n tr o d u c tio n 12
1.1 U.S. border enforcement and the net flow of Mexican illegal
m i g r a t i o n ... 13
1.2 Aid and m igration: an analysis of the im pact of Progresa on the tim ing and size of Mexican m i g r a t i o n ... 15
1.3 E stim ation of treatm en t on the treated effects using the ex perim ental sample of P ro g re s a 16 1.4 Conclusion ... 17 2 U .S . B o r d e r E n fo r c e m e n t and th e N e t Inflow o f M e x ic a n Ille g a l M ig r a tio n 19 2.1 I n tro d u c tio n ... 19 2.2 L iterature r e v i e w ... 22 2.3 T he d a ta ... 24
2.4 A m odel of repeat m ig ra tio n ... 31
2.4.1 D eterrent e f f e c t ... 34
2.4.2 O ptim al m igration d u r a t i o n ... 37
2.5 Em pirical specification and estim ation issues... 38
2.5.1 E stim ating the likelihood of m igrating illegally . . . . 39
2.5.2 E stim ating the likelihood of returning from an illegal m i g r a t i o n ... 44
2.6 R e s u lts ... 46
2.6.2 P robability of returning from an illegal m igration . . . 50
2.6.3 Survey design and sensitivity a n a l y s i s ... 55
2.7 Interpretation and policy i m p lic a tio n s ... 58
2.8 C o n c lu s io n s ... 63
3 A id a n d M ig ra tio n : a n a n a ly sis o f th e im p a c t o f P r o g r e sa o n th e tim in g a n d siz e o f la b o u r m ig r a tio n 66 3.1 In tro d u c tio n ... 66
3.2 Aid and m igration: theoretical c o n s id e ra tio n s ... 69
3.2.1 Effect of an unconditional t r a n s f e r ... 71
3.2.2 Effect of a conditional t r a n s f e r ... 73
3.3 The Progresa d a t a ... 78
3.4 Econom etric a n a ly s is ... 81
3.4.1 Estim able p a r a m e t e r s ... 81
3.4.2 Program effect: specification and identification . . . . 82
3.4.3 Does the random ization work? Pre-program means . . 86
3.5 Aid and m igration: r e s u lts ... 90
3.5.1 Average program effect on m ig r a tio n ... 91
3.5.2 Heterogeneous treatm en t effects... 95
3.5.3 M edium -term m ig r a ti o n ...104
3.6 C o n c lu s io n s ...106
3.7 Appendix: variables creation ...108
4 A n o te o n th e id e n tific a tio n o f c o u n te rfa c tu a ls in th e e x p e r im e n ta l sa m p le o f P r o g r e sa 112 4.1 In tro d u c tio n ... 112
4.2 S tandard estim ation of T T E s with non-compliers or dropouts 114 4.3 E stim ation of T T E s in P r o g r e s a ... 116
4.3.1 1997 p o o r ... 121
4.3.2 Densificado p o o r ... 122
4.3.3 ’’Im m igrants” ... 125
4.3.5 Economic relevance of the estimable param eters . . . 130 4.4 An application: th e effect of Progresa on school enrolm ent . . 132
4.4.1 M ean difference in enrolm ent rates for all sample sub groups ... 134 4.4.2 Double-differenced effect of Progresa on school enrol
m ent by sample su b -g ro u p ...139 4.4.3 T he effect of poverty on enrolm ent for 1997 poor and
tre a te d densificados ...146 4.5 Conclusion ...149 4.6 A p p e n d i x ... 150
List o f Tables
2.1 Descriptive statistics of the variables used, November 1998
d a ta ... 25
2.2 Probability of illegal m igration, static m o d e l... 48
2.3 Probability of illegal m igration, lag and lead of b p ... 49
2.4 Effect of a m arginal increase in current enforcement on the likelihood of m igrating i ll e g a l ly ... 51
2.5 Probability of returning from an illegal m igration, static model 52 2.6 Probability of returning from an illegal m igration, lag and lead of bp m o d e l ... 54
2.7 Effect of a m arginal increase in current enforcement on the likelihood of returning from a m i g r a t i o n ... 55
2.8 m ean apprehensions and proportion arrested at least once for Mexican- and U.S.-based interviewees, 1972-1993 ... 58
2.9 estim ated im pact of average annual border enforcement growth on illegal Mexican m igration flow, 1972-1993 ... 61
3.1 Inter-tem poral schooling and m igration d e c is io n s ... 75
3.2 Sample size of s u b - g r o u p s ... 80
3.3 Pre-program m ean m igration le v e ls ... 88
3.4 Pre-program m igration differences for various percentiles . . . 89
3.5 Pre-program m igration difference for various household types 90 3.6 1998 and 1999 average m igration le v e ls... 92
3.7 1998 individual m igration difference for various household types 94 3.8 1999 m igration difference for various household t y p e s ... 94
3.9 M arginal effects of program components - individual-level 1998 d a t a ... 96 3.10 M arginal effects of program components - household-level 1998
d a t a ... 97 3.11 M arginal effects of program components - individual-level 1999
d a t a ... 99 3.12 M arginal effects of program components - household-level 1999
d a t a ... 100 3.13 M arginal effects of program components - 1998 ... 101 3.14 M arginal effects of program components - 1999 ... 102 3.15 Average m igration rate of 1999 secondary schoolchildren . . . 106 3.16 Average pre-program potential grant size (at 1999 values) and
grant composition ... 110 4.1 Household categories by village type (absolute values and per
centages), November 1998 d a t a ... 117 4.2 Poor households in treated villages by treatm ent status, Novem
ber 1998 d a t a ...119 4.3 M eans and p-values of differences, 1998 d a t a ... 127 4.4 Enrolm ent, attendance, child labour and shock rates for
non-compliers and beneficiaries...129 4.5 Household characteristics by g r o u p ... 131 4.6 Difference in enrollment rates by age group, year and gender 135 4.7 Double-difference program effect on enrollment rates by age
group, year and g e n d e r ...143 4.8 T T E s of Progresa on school enrolm ent of 1997 poor ... 145 4.9 Effect of household poverty level on the likelihood of being
enrolled, m arginal e ffe c ts ... 148 4.10 Mean comparison of individual and household-level variables,
1997 d a t a ... 152 4.11 Mean comparison of household-level variables, 1997 d a ta . . . 153 4.12 M ean enrolm ent by age groups, all c h i l d r e n ... 161
4.13 M ean enrolm ent by age groups, m a l e s ... 162 4.14 M ean enrolm ent by age groups, f e m a l e s ...163
List o f F igures
2.1 Border P atrol - million linewatch hours ... 27 2.2 U.S. hourly private sector wage in 1990 pesos (left) and Mex
ican real m anufacturing hourly wage index (1990=100) . . . . 28 2.3 Mean annual m igration (as proportion of potential m igrant
p o p u l a t io n ) ... 29 2.4 Annual returns from illegal m igrations (as proportion of
U.S.-resident Mexican undocum ented population) ... 30 2.5 Drugs Enforcement A dm inistration budget, 1990 million USD 42 2.6 average apprehensions for Mexico and US-based interviewees 57 2.7 proportion apprehended at least once - Mexico and US-based
in te rv ie w e e s... 57 2.8 comparison of various estim ates of illegal m igration inflow (in
thousands) ... 60 4.1 Densificados - distribution of village m arginalization index
A ck n ow led gem en ts
It is a tru th universally acknowledged th a t this thesis would have not been w ritten w ithout the help, guidance and support of the following people and institutions, to which I am m ost grateful.
F irst of all I would like to th an k my supervisors, Orazio A ttanasio and Costas Meghir. Among other things, they tried to provide me w ith a set of theoretical and empirical tools to identify, develop and test interesting research ideas and to teach me how to analyse them critically and concisely.
M any UCL faculty members, IFS staff members and PhD students pro vided excellent comments to my papers, in particular Sami Berlinski, Richard Blundell, Pedro Carneiro, Andrew Chesher, Marco Cozzi, Giacomo De Giorgi, E m la Fitzsimons, Mario Fiorini, Antonio Guarino, Nicola Pavoni and C ristina Santos, whom I thank also for the ’’technical assistance” , b ut especially for her support.
Jeff Sm ith has been my ’’honorary” supervisor. Not only did I learn much from his lectures and presentations and from our conversations; he also showed an enorm ous degree of support during the job m arket and through out my (few) career choices. Most of all, he has been the living proof th a t also economists can be fun and decent hum an beings. I am m ost indebted to him.
Gian Luigi Albano is single-handedly responsible for my m aterial and psychological survival during the last 12 months. I th an k him for the many nights he fed me when coming home late, for shedding light on the many shades and the m any sides of several economic issues, b u t prim arily for our illum inating dialogues on life, the universe and everything. I also thank him for his patience, his care and for reading innumerable drafts of my papers.
I took my first steps in the realm of economics while working with Saul E strin and M ario N uti a t London Business School. I saw for the first tim e how a research idea is conceived and a paper is developed; I did my very first presentation a t the Bureau for Economic Analysis in Moscow.
hum an behaviour, poetry and music with Adam Szeidl, with whom I also shared the excitem ent and difficulties of the job m arket, as well as a couple of ” Hu Bazmeg” .
Several institutions supported me financially: the Italian N ational Re search Council (CNR), th e Centre for Economics Studies ”Luigi Einaudi” , the Royal Economic Society and the University of Rome La Sapienza, which provided me w ith a research grant to complete the th ird chapter of this thesis under the supervision of M arina Capparucci.
I would also like to th an k the people I m et in these last few years, and of course the ” old guard” ; the friends who helped me stay sane and rem inded me th a t there is a life beyond the PhD . Listing names is unnecessary: they know who they are and how much they m ean to me.
Finally, I would like to th an k my family: those who supported me silently and those who talked too much. The ones who never visited and those who would never leave. My younger cousins, who, after meeting their first economist, whispered ’’Now we know why she hasn’t got m arried yet!” . They may not understand w hat I am doing, but they are always there for me.
D ecla ra tio n
1. No p a rt of this thesis has been presented to any University for any degree.
C h ap ter 1
In trod u ction
The first two chapters of this thesis study the im pact th a t different policies have on both international and domestic m igration. In particular, the ques tions I try to answer are whether enforcing the border of the destination country reduces the net flow of illegal imm igration from the country of ori gin; w hether there are alternative means to achieve this objective, and, in particular, how aid program s affects current and future domestic and inter national m igration. The final p a rt of my thesis deals with the estim ation of treatm en t on the tre a te d effects (TTEs) in the experim ental d a ta set used in the second chapter. I present a new set of identifying assum ptions, differ ent from the ones norm ally m ade by the users of these data, and I uncover several new param eters th a t have clear policy relevance.
The focus of th e empirical analysis is on Mexican m igration because of its interesting features. Mexico is a country where both domestic and in ternational labour m igration occurs. Given the geographic proximity and the large wage differential, alm ost all international m igrants are directed to the U nited States. T he bulk of Mexican m igration to the U.S. is illegal and composed of highly mobile tem porary movers, who may m igrate several tim es over the life cycle. T he size of the phenomenon is considerable: ac cording to the U.S. Im m igration and N aturalization Service, some 5 million undocum ented Mexicans lived in the United States in 2000, 69 percent of
the overall illegal population. Nevertheless, the theoretical conclusions can be easily extended to different sets of countries.
1.1
U .S . b ord er en fo rcem en t and th e n et flow o f
M ex ica n illeg a l m igration
Especially since the mid 1980s, the U.S. government has been exerting con siderable effort to discourage illegal immigration. The 1986 Im m igration Reform and Control Act has introduced employer’s sanctions for hiring u n docum ented workers and devoted more resources to the apprehension of aliens. T he tougher enforcement has resulted in substantial increases in border patrol. Aliens apprehended trying to cross the southern U.S. border are in m ost cases not prosecuted, given the high associated adm inistrative costs. They are instead driven back to the Mexican side of the border, from which they normally soon a tte m p t re-entry.
To date, there is a small but growing literature th a t tries to evaluate the effect on border enforcement on the inflow of illegal m igration. However, these studies suffer from two lim itations: first, they try to infer the deterrent effect of border controls on prospective m igrants by looking at changes in border apprehensions. T he relationship between the latter and the size of m igration is not straightforw ard, because of the possibility of repeated border-crossing atte m p ts w ithin a single trip. Moreover, in order to assess the policy im pact on the size of the undocum ented U.S. residents, one has to understand how the behaviour of current illegal m igrants is affected by changes in border enforcement. Tougher policing of the border translates in higher m igration costs. Higher costs may reduce the num ber of people entering the United States illegally, but at the same tim e it is likely to lengthen m igration spells, because it takes longer to reap a positive return from the trip. Also, if undocum ented m igrants who are currently in the U.S. anticipate future tougher enforcement, they may increase the duration of the current m igration knowing th a t future trips will be more costly. Since higher
border policing reduces b oth the inflow and the outflow of illegal m igration, its effect on m igration net inflow, hence stock, is ambiguous and it depends on the size of potential and current undocum ented m igrant populations and on how sensitive to changes of border patrol each group’s behaviour is.
The empirical analysis estim ates the effect th a t changes in the intensity of border enforcement between 1972 and 1993 have on both the U.S. inflow and outflow of illegal M exican m igrants modelling individual transitions be tween two states: potential and current illegal m igrant. The estim ations are undertaken using a unique d a ta set th a t merges aggregate border enforce m ent linewatch d a ta w ith inform ation on a sample of illegal potential and de facto m igrants from the Mexican M igration Project. The shortcomings associated w ith the particular design of the survey are extensively discussed. T he econometric model accounts for the endogeneity of border controls using Drugs Enforcement A dm inistration budget as instrum ental variable. Af ter com puting the size of the illegal undocum ented inflow, the estim ated m arginal effects are used to measure the effect of a m arginal change in en forcement on the num ber of individuals who are respectively deterred from m igrating illegally and from returning to Mexico from an undocum ented U.S. m igration. I show th a t the deterrent effect is small but significant, in line w ith the existing literature. W hen the outflow effect is included as well, the size of the net im pact is still positive, but halved. Hence, estim ates of the effectiveness of border patrol based on its reduction in inflow are grossly overestim ating its tru e effect. I provide back-of-the envelope measures of the m arginal cost of reducing the stock of m igration by one person, which am ounts to a few hundred dollars. Furtherm ore, an additional cost of this policy is its contribution to the creation of a more perm anent undocum ented resident population.
1.2
A id and m igration : an a n a ly sis o f th e im p act
o f P ro g r esa on th e tim in g and size o f M ex ica n
m igration
In the current analysis I study the im pact of aid policies on current and future domestic and international m igration. In particular, I consider the effects of an unconditional transfer and of a conditional schooling subsidy. Transfers to prospective m igrants reduce the economic disparities between home and the destination location, lowering the incentives to leave. How ever, if individuals or households are credit constrained, the grants may be used to finance new m igrations. The latte r fact may have sizeable effects, given th a t the imperfection of capital m arkets is one acute problem faced by indigent families in developing and middle-income countries. The con ditional transfer th a t requires recipients to stay in the home country may reduce m igration in the short-term . Nevertheless, individuals may revert to m igrating once the subsidy ends. Future m igration levels may even be higher th an in the zero-aid scenario, if recipients save in order to fund future trips.
A development policy th a t has all the aforementioned features is Pro gresa, a program th a t targets poor Mexican rural households. Among the various com ponents of the program , there are a (smaller) unconditional nu trition support grant, and then some (cumulatively larger) transfers condi tional upon attendance of the last four grades of prim ary school and first three grades of secondary school, all paid bi-monthly. The subsidy to pri m ary school attendance is roughly equivalent to an unconditional transfer, since prim ary school enrolm ent is very high. The secondary school grant ” conditionality” constraint is instead binding for the m ajority of potential recipients, as secondary school enrolm ent is much lower.
The effect of aid policies on m igration is estim ated by using the d a ta collected for the evaluation of Progresa, whose characteristics are discussed below. The m ain findings in this chapter support the hypothesis th a t credit
constraints lim it m igration: indeed, unconditional transfers are associated w ith increased international m igration, partly due to new trips being fi nanced or to households substituting (cheaper but w ith low-yielding) do mestic m igration for (costlier but with a higher benefit) international one. At the same tim e, grants to secondary school attendance are associated with a reduction in m igration.
1.3
E stim a tio n o f tr e a tm e n t on th e tr e a te d effects
u sin g th e ex p e r im e n ta l sam p le o f P ro g resa
This chapter deals with the estim ation of treatm ent on the treated effects (TTEs) using the Progresa data. Progresa is an aid program implemented in Mexico, aimed at fostering education, health and nutrition among poor households. The d a ta collected for its evaluation consists of 506 villages, 186 of which are random ized out. Poor residents of these villages are not adm in istered the program m e until 2000. All households are classified into poor and non-poor according to th e information collected in the pre-program me Septem ber 1997 census of Progresa localities. All residents of both control and treatm en t villages are then interviewed at biannual intervals. Detailed d a ta are collected on health, consumption, income and employment, edu cation and m igration a t least in one of the two annual surveys. W ith a sample size ranging between 22,000 and 25,000 households in both control and treatm en t villages, complete coverage of all locality residents, a panel of up to five waves, of which one or two prior to the im plem entation of the program me, and the exogenous variation induced by the random ization, the Progresa d a ta have a ttrac ted the attention of scholars and researchers.
One flaw of this d a ta set is th a t counterfactuals for a large sub-group of eligible households in treatm ent communities could not be identified. This has norm ally resulted into the exclusion of p a rt of the available data, which are simply om itted from the analysis. The contribution of the current ex ercise consists of recognizing th a t this group is composed by four different
subsets; suggesting ways to identify counterfactuals for three of these sub sets; presenting alternative hypotheses to identify T T E s in the presence of non-compliers; providing an empirical application by estim ating T T E s on school enrolm ent for all subsets of households.
The subgroup of households for which a counterfactual could not be identified can be divided into the following categories:
- ’’True” beneficiaries, i.e. households who are eligible to participate to the program , and receive th e treatm ent, provided th a t they comply w ith its requirem ents.
- S tandard non-compliers, th a t is households who, although eligible, de cide not to participate to the program . The standard approach to estim ate T T E s in th e presence of non-compliers consists of either making some hy potheses on the likely program effect on this group, or finding exclusions restrictions to identify a valid set of counterfactuals in the control group.
- ’’Forgotten” households who, despite their eligibility to the program , are excluded from it because of adm inistrative errors. These households know they belong to the treatm ent group but do not receive any subsidies, irrespective of their compliance with the program rules.
- Households who begin being recorded in the surveys after the program begins, hence who are not included in the program although they have the required characteristics to be included in the treatm ent group (i.e. they are classified as poor).
I discuss the relevance of the estim able param eters, and suggest possible applications.
1.4
C on clu sion
This thesis seeks to contribute to the m igration literature by assessing the im pacts of two existing and popular policies on both international and do mestic Mexican m igration. It is a first step towards a com parative eval uation of the effectiveness of the policies, as well as an attem p t to focus on the indirect effects th a t aid program s to developing countries may have.
T he methodological contribution is very specific, because it regards one particular sample. Nevertheless, it is hopefully going to provide w ith new param eters th a t will enable researchers to answer a richer set of questions.
C h apter 2
U .S . B order E nforcem ent
and th e N e t Inflow o f
M exican Illegal M igration
2.1
In tr o d u ctio n
This paper studies the relationship between illegal imm igration to the United States and the enforcement of its borders. Border enforcement has been a cornerstone of U.S. im m igration policy, especially since the second half of the 1980s. U nderstanding the impact of border controls on the flow of illegal Mexican m igration is of prim ary im portance for several reasons. First, Mexican nationals accounts for 69 percent of the total unauthorized resident population of the U nited States. Second, most illegal Mexican entries occur through the southern U.S. border. T hird, undocum ented Mexican m igrants tend to be very mobile and to undertake m ultiple U.S. trips over the life cycle. D onato et al. (1992), for instance, show th a t m igrating at least once increases the likelihood of undertaking future migrations.
The undocum ented resident population of Mexican nationality has grown from 1.1 millions in 1980 to 2 millions in 1990 and 4.8 in 2000 (U.S. Census, Im m igration and N aturalization Service), with an average annual growth of
90,000 units in the 1980s and 280,000 ones in the 1990s. At the same time, the intensity of border enforcement has nearly trebled between the early 1970s and the m id 1990s. T he allocated resources to border patrol have been growing steadily especially since the 1986 Im m igration Reform and Control Act. In 2002, the im m igration enforcement appropriation totalled two billion dollars.
The large growth in undocum ented m igration despite the higher expen diture in border controls questions the effectiveness of such policy. I argue th a t tight border controls may have perverse effects on the net flow of il legal m igration because they influence the behaviour of both prospective and current m igrants: while enforcement increases may deter prospective m igrants from crossing the border illegally, the optim al U.S. perm anence of current ones may be lengthier because of the higher costs of future m igra tions. This effect may be of a relevant m agnitude, given the large size and the high m obility of such group (see Massey and Singer (1995) for estim ates of annual inflow and outflow of U.S.-based Mexican m igrants.). If tougher border enforcement lengthens m igration duration by raising its cost, patrol of the border m ight, to some extent, indirectly encourage the form ation of a more perm anent undocum ented resident community.
This fact provides an additional explanation for the disproportionate resources allocated to border versus interior enforcement. If the effectiveness of border patrol is m easured by its reduction in undocum ented entries only, neglecting its im pact on the outflow of m igrants, the resulting estim ate will overstate border enforcem ent’s tru e effect on m igration net inflow. This causes a larger th an optim al resource allocation to border controls.
Although there is awareness of these issues both a t the theoretical and anecdotal level, the existing literature has focussed almost entirely on border enforcem ent’s im pact of m igration inflow only, neglecting to assess its effect on the outflow of illegal m igrants. I suspect this is partially due to the scarcity of d a ta on undocum ented migrations.
on the net inflow of illegal Mexican m igrants, contributing to the existing literature in several ways. F irst, it proves how the im pact of border patrol on m igration net flow is theoretically ambiguous, and how optim al enforcement is a function of the stock of th e U.S. undocum ented resident population.
Second, it presents a model where m ultiple m igrations over the life cycle are the optim al choice of utility maximizing rational agents with complete information. To my knowledge, m ultiple m igrations have been explained as the consequence of shocks or of imperfect information. I show th a t if absence from home entails a positive cost th a t increases over time, repeated, short term m igrations may maximize inter-tem poral utility even in the presence of a sunk cost of m igration. This setting perm its us to endogenise m igration duration.
Third, it provides direct estim ates of the effect of border enforcement on the net inflow of undocum ented Mexican m igrants. This is the first paper in which such estim ates are provided. This is achieved by merging border enforcement inform ation w ith individual-level d a ta on undocum ented m igra tion from the Mexican M igration P roject (MMP71). Hence, it is possible to test border controls’ effects on both the likelihood and the duration of ille gal migrations. The obtained estim ates are consistent w ith the theoretical predictions. Border enforcement has a significant deterrent effect, as it dis courages prospective m igrants from attem pting an illegal trip to the U nited States. At the same tim e, it lengthens the U.S. perm anence of current mi grants. My favourite set of estim ates reveals th a t a m arginal increase in border controls is associated w ith a significant reduction in the net inflow of undocum ented Mexican m igrants between 1972 and 1993. The net effect is roughly half the size of the inflow reduction. Hence, assessing the effective ness of border enforcement by analysing its deterrent effect only provides a gross overestim ates of its true impact
Fourth, it considers how the survey design and the d a ta structure may affect the estim ation of the param eter of interest. This analysis, which may be relevant in different applications, has to my knowledge never been
undertaken before, despite the wide use of the MMP71 sample.
The paper is organized as follows. Section 2 reviews the existing lit erature. Section 3 describes the d a ta used. Section 4 derives testable hy potheses on the im pact of border enforcement on both inflow and outflow of undocum ented m igrants using a dynamic model of illegal m igration with heterogenous costs. Section 5 illustrates the empirical specification and the related estim ation and identification issues. Section 6 presents the results from the econometric analysis. It further discusses how the sample design m ay bias the estim ates of the border controls coefficient. Section 7 uses the estim ated param eter of interest and calculates the size of the undocu m ented illegal m igration to com pute border p atro l’s net effect on the size of undocum ented m igration, highlighting some policy implications. Section 8 concludes.
2.2
L itera tu re review
There is a growing literature trying to understand the relationship between illegal m igration and border enforcement. However, the effects of border controls on m igration net flow are scarcely known. In my opinion, there are a conceptual and a practical reason for the scarcity of information on the im pact of border enforcement.
The m ain practical problem faced by this literature regards the difficulty of m easuring directly the volume of flow and stock of illegal m igration.1 Records of aggregate apprehensions are available. However, only tentative inference can be m ade to estim ate the m agnitude of the illegal m igration volume from this series, hence the im pact of border patrol: in fact, under current U.S. m igration law, the same individual may be arrested several tim es while trying to cross the border. If an apprehended illegal alien agrees on a voluntary departure, th a t person is simply driven back to the Mexican
1Warren and Passel (1987) use U.S. Census data to estim ate the stock of undocu mented aliens. M assey and Singer (1995) obtain estim ates of individual probability of apprehension to assess the m agnitude of the net flow of illegal migration.
side of the border. Thus num ber of arrests does not clearly represents the volume of apprehended m igrants.2 Borjas et a l (1991) look at the relation between apprehensions and expenditure for border enforcement. Bean et
al. (1990) assess the im pact of the 1986 Im m igration Reform and Control Act. Espenshade (1994) tests the deterrent effect of the probability of bor der apprehension on the inflow of undocum ented m igration. Hanson and Spilimbergo (1999), estim ate the elasticity of apprehensions with respect to border enforcement from a reduced-form aggregate apprehension function. Davila et al (2001) estim ate the short and long-run deterrent effect of border controls.
On the conceptual side, the existing empirical literature has not fully acknowledged the necessity of considering enforcement’s im pact on m igra tio n ’s net flow, and has rather concentrated solely on the inflow, although there is increasing awareness of the link between m igration costs and dura tion. All the aforementioned papers are concerned w ith the estim ation of the m igration inflow effect of border controls. Instead, no m ention is made of the fact th a t rising m igration costs may lengthen current illegal m igrants’ optim al m igration duration. This fact is illustrated in Hill’s (1987) model of individual m igration, where it is shown th a t higher enforcement may reduce the num ber of m igrations while increasing their length. More recently, Cor nelius (2001) m entions the possibility th a t higher m igration costs may result in lower m obility for undocum ented individuals, once they have reached the destination country. T he same point is made in a recent survey by The Economist (2002).
A notable exception in the empirical literature is constituted by the work of Kossoudji (1992), who uses a sample of repeated illegal Mexican m igrants to assess the effect of past apprehension on current m igration frequency and
2Espenshade (1995b) estim ates the relationship between aggregate attem pts and appre hensions using a repeated trials model of illegal migration and presents a way of obtaining estim ates of the flow o f undocumented aliens by observing the fraction o f repeated ap prehensions of the sam e individuals. However, collection of this piece of information has been discontinued since the late 1980s.
duration. However, the d a ta set she uses does not perm it to distinguish interior from border apprehension. Furtherm ore, being a sample of sole m igrants, it does not perm it to estim ate the deterrent effect of enforcement (i.e. the size of the individuals discouraged from attem pting to m igrate by the high level of controls).
A branch of the literature questions the policy effectiveness on differ ent grounds from the one m ade above. Advocates of interior enforcement suspect th a t inspections to firms in undocum ented labour-intensive sectors might prove more successful in the eradication of illegal m igration. The very rationale of border controls is challenged by a work by Hanson and Spilimbergo (2001). Their paper suggests th a t border enforcement may be the product of conflicting interests, as it is relaxed when the dem and for illegal labour is high. Davila et al. (1999) argue th a t the disproportionate resource allocation favouring border versus interior enforcement is consistent w ith budget-m aximizing behaviour, rather th an with trying to minimize the stock of illegal U.S. residents.
As regards m igration and individual heterogeneity, theories range from positive m igrant self-selection in unobservables because of m otivational rea sons to negative one, when m igrations take place from a country with a wide income distribution (such as Mexico) to a less unequal one (Borjas (1987)). As concerns m igration duration, the extremes of the spectrum of existing theories are target earning behaviour, which postulates an inverse relation ship between labour m arket skills and length of stay in the host country, and demand-side selection in skills, according to which unsuccessful m igrants are forced to leave before successful ones.
2.3
T h e d a ta
Table 2.1 describes the d a ta used, providing their means and standard de viations for the period of interest.
The d a ta used come from several different sources: border enforcement and aggregate apprehension d a ta are from unpublished records of the Immi
gration and N eutralization Service (INS), the D epartm ent of Justice agency managing border enforcement. U.S. wage and unemployment d a ta are from the Bureau of Labor Statistics. Mexican unemployment rate is from World Economic Outlook (W EO) data. The other Mexican macroeconomic vari ables used are from the Mexican National Statistical In stitu te (IN EG I).3 Hanson and Spilimbergo (1999b) describe both enforcement and macroeco nomic d a ta in great detail.
Table 2.1: Descriptive statistics of the variables used, November 1998 data.
1972-1993
Name Mean St. Dev. Description
Linewatch hours 2.15 0.51 Million annual hours of border control Illegal migrations 0.037 0.188 Proportion undertaken illegal migrations R eturns 0.546 0.497 Proportion of returns from illegal migrations US unemployment 6.84 1.30 U.S. unemployment rate
US wage in pesos 29.53 5.86 U.S. real hourly wage rate in the private sector, 1990 pesos
MX wage index 1.09 0.16 Mexican real hourly manufacturing wage index, production (1990=1)
D EA budget 495.25 241.91 Drugs Enforcement A gency real budget, 1990 million dollars
Legalizations 25.95 43.86 Annual MMP71 Mexican legalizations Apprehension 540.54 216.09 annual INS border apprehensions (xlOOO)
In the MMP71 sample, a panel is created from individual retrospective inform ation collected from 71 communities in 13 different Mexican states between 1987 and 1998. Every year a num ber of different Mexican com m unities (normally 5) are selected in such a way as to represent a range of diverse characteristics (size, ethnic composition, location and economy). In each of them , a random ly drawn sample of 200 households is interviewed between December and January.4 Heads of household are asked about their
3W ith the exception of the devaluation rate, which is from aggregate MMP71 data. 4In these months migrants tend to return home for Christmas.
m igratory experience and their labour history. Interviewees include individ uals with past spells of m igration (both legal and illegal ones) as well as others who never m igrated. Each year, a series of U.S.-based non-random follow-up interviews are undertaken in the summer months, using snowball sampling5. This much smaller group is discarded from the analysis because it is selected through a non-probabilistic sampling methodology, although Massey and Zenteno (1999) analyze the quality of the data, and conclude th a t they are generally a representative source of information on Mexico- U.S. m igration. Further details about the study design can be found in Massey (1987). Valid cases are selected by looking a t individual age and physically able to m igrate: people aged outside the 16 and 55 interval and receiving a disability pension during the recall period are excluded from the valid sample.67 The upper cut-off year is 1993, because the available d a ta for the last five years of the sample (1994 to 1998) consist of too few obser vations to be included. In such way an unbalanced person-year panel with both entries and exits is obtained.
Since individuals are interviewed in Mexico, I only observe complete spells of m igration, and I do not have information on current m igrants. The excluded individuals may not be a random sub-set of the illegal m igrant population. The issue of the potential non-randomness in the sample and its im plications regarding the bias in the estim ates of the effect of enforce m ent on the probability of both m igrating illegally and returning from an undocum ented m igration will be discussed in detail in the next section.
After the described arb itrary truncations, two groups are formed. One is composed by 9,990 individuals and 143,851 person-year units, observed when they are in Mexico until an illegal m igration takes place. Observed m igrations are recorded by a variable th a t takes the value of zero whenever
5A m ethod whereby interview subjects are indicated by previous interviewees. 6The results from the econometric specification are robust to the inclusion or exclusion of women, who are much more unlikely to migrate. Roughly 25 percent of males from the valid sam ple migrate illegally, versus 6 percent of women.
the individual is in Mexico, and of one when the individual m igrates to the United States. All subsequent years spent in the U.S.A. are recorded as missing. A bout 85% of the sample never m igrates in the observed years, with a m aximum of 22 m igrations being undertaken. Mean m igration for the whole sample is 0.59, while average num ber of m igrations for those who m igrate is 2.49.
T he other group consists of 2,316 m igrants (and 8,986 person-year units) who stay in the U nited States a t least once. In this case, the interest is on the likelihood of returning from a m igration. Hence, a variable records with a zero each year spent in the U.S.A., taking instead the value of one in the year the m igrant returns home. The variable is missing for all years spent in Mexico between interm ediate migrations.
As regards aggregate data, border enforcement’s upward sloping trend (measured along the whole U.S. Mexico border) and its higher steepness in the second half of the 1970s and since 1986 can be noticed in Figure 2.1.
3.4 -3.2 -2.8 -I 2.4 -2.2 -c (Q C o e 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 year
Figure 2.1: Border P atrol - million linewatch hours
Average intensity of border controls between 1986 and 1993 is 20% higher th an the 1977-1985 one as a consequence of the implem entation of the 1986 Im m igration Reform and Control Act (IRCA). Indeed, one of the A ct’s var ious m easures to curb illegal im m igration is the increase in border policing8, 8Border patrol budget, which has been increasing continuously since 1986, does not
together w ith sanctions for the employment of undocum ented labour and with an am nesty to legalize a large group of current illegal U.S. residents. The im plem entation of IRCA is partly a reaction to the increased m igration incentives caused by the economic and financial crisis th a t hit Mexico in the early 1980s. W ith high inflation levels eroding the purchasing power of wages9 and periodic peso devaluations, more individuals are induced to seek jobs illegally in the U nited States.
135 132 129 126 123 120 117 114 111 10S 105 102 96 93 90 87 42 40 38 36 34 32 30 28 26 24 22 1972 1974 1976 1!
Figure 2.2: U.S. hourly private sector wage in 1990 pesos (left) and Mexican real m anufacturing hourly wage index (1990=100)
Figure 2.2 shows the change in the peso value of both U.S. and Mexican wages caused by the high inflation and by the currency devaluations both during and before the Mexican crisis. W ith higher expected benefits from m igration, a higher enforcement level is required to discourage individuals from making an illegal U.S. trip.
reflect the 1988 sharp linewatch hours decrease. One possibility is th at funds might have been allocated to other enforcement-related activities.
9Mexican real minimum wage decreases by 74% in the first half of the 1980s (Hanson and Spilimbergo, 1999).
.045 -.043 -.041 -c o .039 -ra o> I n .037 -.035 -S .033 -a> o> ra .031 -.029 -c .027 -.025 -.023 .0 2 1 -1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 year
Figure 2.3: M ean annual m igration (as proportion of potential m igrant pop ulation)
The im pact of the Mexican economic crisis on incentives to m igrate is also noticeable in Figure 2.3, where average annual m igration is expressed as proportion of overall population of potential m igrants. Although the size and growth rate of the underlying population is unknown10, the proportion of individuals who m igrate nearly doubles between 1972 and 1986, with a peak in 1985-1986, when rum ors of the incoming amnesty cause a rush to the United States. The rising m igration trend reverses from 1986. P a rt of this effect is supposedly a consequence of the IRCA amnesty granted to more th a n two million U.S.-based illegal Mexicans migrants: a large group of individuals simply switch from illegal to legal s ta tu s.11 The improvement of the Mexican economic conditions, the toughening of border enforcement and the introduction of employer’s sanctions are expected to be further de term inants of the trend reversal. Figure 2.4 shows average annual returns from illegal m igrations (expressed as proportion of U.S.-resident Mexican
10W ith a positive growth rate of the Mexican population and a deterioration of low-income household living standards during the 1980s, the number of potential illegal mi grants is expected to rise, unless outbalanced by legalizations.
n INS estim ates a total of 2,600,000 Mexican legalizations (Statistical Handbook on U.S. Hispanics, 1992), while Bratsberg (1995) reports nearly 2,200,000 ones.
undocum ented population). The pre-IRCA upward sloping p a rt is consis ten t with the hypothesis of an increase in short-term tem porary m igration, favoured by lower individual apprehension probability brought by a rising m igration volume and a roughly constant border enforcement.
.66 - .65 - .64 - .63 - .62 - .61 -E o .59 - .58 - .57 - .56 - .55 - .54 - .53 - .52 - .51 -E 3 £ c ra .49 - .48 -1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 year
Figure 2.4: Annual returns from illegal m igrations (as proportion of U.S.- resident Mexican undocum ented population)
The sharp decrease in 1986 and 1987, which coincides w ith the rise in border patrol activities, is probably exacerbated by the lower m obility of am nesty applicants (as well as by the tighter border controls). In fact, it is likely th a t am nesty applicants refrain from returning to Mexico while waiting for their legalization application to be processed, i.e. approxim ately between 1986 and 1988.12 The last 5 years do not show a clear trend in returns from illegal migrations. Average returns are now proportionally higher th an pre-IRCA ones.
Two measures of wages are available: for the U.S.A., average hourly m in imum and private sector wages; an index of average production m anufac turing hourly wage, or m onthly average minimum wage for Mexico. On the one hand m inimum wages seem to be more appropriate, since repeated mi
12This result is obtained sum ming the 12-month interval allowed to apply for the legal ization and further few months for the authorization to be granted to the year of IRCA im plem entation (1986).
grations regard m ainly unskilled individuals: average education level for the population of potential m igrants is 5.1 years, whereas Hanson and Spilim- bergo (1999b) report th a t m ean school years for individuals employed in m anufacturing in Mexico was 8.1 in 1990. Moreover, low-skilled, illegal m igrants are likely to be offered low wages. On the other hand, though, minimum wages are consistently associated with a higher degree of multi- collinearity in the regressions.13 For this reason, U.S. private-sector wage and Mexican m anufacturing wage index are instead used. Their trends are not too dissimilar from their respective minimum wages.
2.4
A m o d el o f rep ea t m igration
This section models m ultiple m igration choices of heterogeneous agents. The model is used to understand how the decisions of m igrating illegally and of returning from a m igration are affected by border controls, and to derive the testable hypotheses and the appropriate econometric specification. In addition, it sheds light on how the survey design may bias the estim ates of the param eters of interest.
W hile it is understood why people m igrate (Sjaastad (1962)) and why it may be optim al to retu rn to the home country even given the higher foreign wage (see, for instance, Borjas and Bratsberg (1996), Stark et al. (1997) and D ustm ann (2003)), less is known about repeated m igration. Since moving is costly, it is not clear why individuals may refer multiple, short-term ed m igrations to a single, longer one. M ultiple m igrations have been linked by the literature to imperfect inform ation or shocks (Da Vanzo (1983)). In my view, however, repeated m igrations over the life cycle can arise also as the optim al decision of agents w ith complete information. Given the vast scale of Mexican m igration to the U nited States and the existence of m igration networks, it is believed th a t access to information is relatively easy and
13A nalysis of the correlations betw een both sets of wages and the other variables used in the econometric model show that the multicollinearity arising from the use of minimum wages cannot be directly related to any pairwise correlation.
costless.
Two m ain determ inants of repeated Mexican m igrations over the life cycle are: labour dem and and costly absence. The former explains th e exis tence of cyclical m igration pattern s as the consequence of seasonal changes in labour demand. One obvious example is the increased dem and for agri cultural workers during harvest time, or the one for hotel staff during peak season. The latter, instead, is based upon the concept th a t being away from home has a positive cost. This can be thought of as absentees’ positive likelihood of losing claims on current and future ownership of family assets (such as land and properties) increasing w ith tim e spent abroad, or as indi viduals being homesick. The longer the absence, the looser the tie w ith the family members left behind. Such hypothesis is consistent with the alter native views of rem ittances being used as a means to retain a tie w ith the household in the home country, or being a m anifestation of altruism . The hypothesis th a t tim e away from home may be costly is consistent w ith the observed evidence from the MMP71 data: the likelihood of returning from a m igration is ceteris paribus higher for parents and m arried m igrants, and is increasing w ith the num ber of children and hectares of land owned.
The current model of repeated m igration is based on the latter hypoth esis. W hile further research on the issue is clearly needed, I believe th a t the model sketched here captures some existing features of Mexican repeat m igration. In any case, the implications of the model regarding the effect of border enforcement on the intensity and duration of illegal m igration could have been equally derived from a wide class of alternative determ inants of multiple m igrations.
An additional feature of this model is th a t it endogenises m igration du ration. Hill (1987) models m ultiple m igration over the life cycle assuming th a t m igration duration if fixed.
I assume th a t m igration costs are heterogeneous. This may arise because of different reasons. Individuals may be endowed with different levels of abil ity to cross the border, or they may have access to private information. The
d a ta provide evidence of heterogeneity in border-crossing ability. The num ber of observed apprehensions within a single trip in fact varies considerably, ranging between 0 and 15, although 78 percent of m igrants manage to cross the border a t first attem p t, and 16 percent w ith up to three. Alternatively, individuals may face varying degrees of financial constraint, hence financing similar trips may entail different costs. Finally, costs may vary because of distance from the border and different levels of community-specific network effects. Modelling alternative sources of heterogeneity, such as differences in labour m arket-related skills, results into different types of individuals being selected in and out of m igration. Nevertheless, the im pact of border controls on their net inflow in the U.S. would be the same irrespective of the type of heterogeneity (in sign, if not in m agnitude).
Assume a continuum of potential illegal m igrants with heterogeneous mi gration costs deriving from different ability endowments. Agents tre a t wages and border enforcement (bp) as given. There is no uncertainty. Assume the existence of a utility function representing individual preferences. Such func tion depends on consumption (c > 0) and on the fraction of tim e spent in the host country (t ) and it is assumed to be continuously twice differentiable, additively decomposable both in consumption and tim e and over time. In dividuals choose the optim al m igration duration in both periods given the positive wage differential between U.S. and Mexican wages (w u s > w M X),
the strictly concave disutility from staying away from home (u t14 < 0 and
Vtt < 0 )? their appetite for consumption (u c > 0 and ucc < 0)15, and the sunk cost associated with the illegal m igration (Me)- The latter is a pos itive function of border enforcement (bp), Mcbp > 0, and a negative one
(Mca < 0) of an individual-specific param eter (a E (0,1)) capturing hetero geneity in costs, a varies continuously among the agents. This param eter will be from now on referred to as ability in crossing the border. I assume capital m arket perfection, r is the interest rate paid on savings (S) and (3
14Partial derivatives are sub-indexed w ith respect to the argument, hence d v / d t = v t .
15 The assum ptions on the utility function ensure that the agents’ optim ization problem has a maximum.
is the inter-tem poral discount factor. T he m axim ization problem is:
max c i >c2lS ,ti€ [0 )l],t2e[0,l]
U(ci,C2, t i , t2,S ; a ) = u ( c \(ti, 5, a) , t\)-\-/3u(c2(t2, S, a) , £2)
where
t i w ^ + (1 - t 1) w f IX - M c {bpi,a)1[tl>0} - S
t2W%S + (1 - t 2) w ? x - M c (bp2,a ) 1{t2>Q.tl<1} + (1 + r ) S
w,US > wM X
Given the param eters of the model, different ability endowments will be associated w ith varying optim al m igration durations, including t\ = = 0 and perm anent migrations. In the current analysis, however, I restrict the valid solutions to include only return m igrants, i.e. t£ € [0,1) and G [0,1).
The model could be easily extended to allow for future m igration costs being a negative function of past m igrations or for agents being unable to borrow. The conclusions reached would be unaffected, although the m agni tude of the m igrant flows would differ.
2.4.1 D eterren t effect
Given preferences, wages, some continuous ability distribution and enforce ment, agent with different ability levels will choose a different combination
16The second-order condition matrix is negative semi-definite.
The first-order conditions16 for m igrants in both periods, i.e. individuals for whom t\ > 0 and t£ > 0, are:
of current and future m igrations. Individuals whose ability level exceeds a certain threshold (a > ah) will m igrate in both periods. Those w ith a sufficiently low ability (a < a1) will never migrate. The im pact of changes in m igration costs on the inflow of m igration can be studied by observing how the ability threshold levels change due to higher enforcement. If I prove th a t the values of the existing thresholds are augmented by a m arginal increase in border controls, then I have shown th a t higher enforcement is associated w ith a lower m igration inflow.
Agents’ behaviour cannot be predicted w ithout assuming an explicit form of the utility function or w ithout making restrictions on the range of values taken by the param eters of the model. Indeed, the model is such th a t agents choose in each period whether to m igrate or not, and for how long. Using H and M to indicate home stay and m igration, there will be four possible outcomes: H H , H M , M H, M M and various ability threshold for individuals indifferent between alternative inter-tem poral choices. There are six potential thresholds (the six possible pairwise combinations of the four different outcomes). Only a sub-set of them will be valid, depending on the values of the param eters and on the type of utility function.
I may illustrate the im pact of higher m igration costs on the ability thresh olds by performing com parative statics exercises for all possible cases. I believe th a t this is unnecessary, given th a t higher m igration costs will in no circum stance result in higher aggregate migration. Since the effect of tighter enforcement on im m igration is not ambiguous, I prefer to choose one specific case to illustrate this point formally.
I consider the case in which the values of wages and enforcement are identical in both periods and {3(1 + r) = 1. In such case, optim al m igration duration will be the same in both periods (t^ = ££) and there will be no savings. Since the two periods are identical, agents will either m igrate op tim ally in both periods or stay always in Mexico. Hence, there is a unique ability threshold (i.e. ah = a1 = aT). Consider the agent indifferent between
m igrating in both periods and not m igrating in either
M M ( a T ) - H H ( a T ) = 0 (2.1)
In this scenario, any current or future increases in border controls will induce the agent to favour the zero m igration outcome. Formally, I can com pute the sign of the enforcement effect on ability threshold (aT) from (2.1) using the implicit function and the envelope theorems:
daT . ( u c* (d M c /d b p i) \
dbpi 9 ^ (uc* + Puc*) { p M c / d a ) ) > °
daT . ( (3uc*(dM c/dbp2) \
dbp2 Slgn ( («c. + 0 u ci) (d M c / d a ) ) >
The effect of a current enforcement increase is larger than the one of a future cost rise because of discounting. Perm anent enforcement increases will result in a more m arked rise in the ability threshold.
W hile the simple case presented above is sufficient to make my point, more realistic assum ptions on variation in costs and benefit of m igration and in inter-tem poral preferences will result in agents w ith varying ability endowments being indifferent between alternative options. Such alternatives may imply different responses to current or future enforcement changes. All possible cases show th a t higher enforcement is associated with positive (or at m ost non-negative) changes in the minimum level of ability required to migrate.
One case worth m entioning is when the anticipation of higher future costs of m igration results in m igrations being undertaken in period one rather th a n in period two. Consider the individual who is indifferent between m igrating once, irrespective of when the m igration occurs: M H — H M = 0. This individual will be induced to m igrate in the first period by a m arginal increase in future m igration costs. The reverse is true in case of an increase in current enforcement levels.
2.4.2 O p tim al m igration duration
Unlike the m igration decision, optim al m igration duration is a function of both current and future enforcement level. W hile higher levels of border controls deter some prospective m igrants to attem p t to reach the United States, reducing the inflow of illegal m igration, the average m igration du ration of current m igrants will increase, given the higher m igration costs. Com parative statics shows th a t the optim al m igration length is a positive function of both current and future levels of border enforcement:
= sign ( - ( 1 + r )u c*c*(uc*c*ut*q - 2uc*c*A2)) > 0 (2.2) = sign [f3uclclut*t* + w | c*A2(2 + r ) ) > 0 (2.3) where A indicates the wage differential.17 These results are intuitive: the higher the costs of m igrating, the longer the tim e th a t m ust be spent abroad to reap positive returns from the m igration. Changes in border enforcement influence the behaviour of current illegal m igrants as well. Indeed, m igration duration is also a positive function of future m igration costs. Com parative statics shows th a t for individuals who m igrate in both periods, a m arginal increase in future enforcement levels will increase optim al current m igration duration. This means th a t, while prospective m igrants may be deterred from m igrating by an increase in border patrol, current ones will lengthen the duration of their present m igration spell. In practice, given the large stock of undocum ented resident U.S. m igrants, the latter effect may be of a relevant size.
Equations (2.2) and (2.3) are particularly interesting, given the objective of the current exercise, because they show how increases in border policing, although reducing the inflow of undocum ented m igration, extend the length of perm anence in the United States for those who decide to m igrate and for current illegal m igrants.
17I also assumed that wage differentials are identical in the two period. This simplifies the notation w ithout changing the signs of the partial derivatives.
To summarize, modelling the effect of border enforcement on choice and duration of repeated tem porary undocum ented m igrations shows how the former has a deterrent effect: higher enforcement levels correspond to fewer m igrations. However, rising m igration costs affect also the length of the perm anence in the receiving count
