Borrowing Constraints, Migrant Selection,
and the Dynamics of Return and Repeat Migration
Joseph-Simon Görlach∗
March 22, 2016
Work in Progress
Please click here for the latest version.
Abstract
This paper analyzes the impact of an exogenous change in household incomes in
a migrant’s sending country on migration duration, the incidence of repeat migration and migrant selection. Higher incomes raise the opportunity cost of residing
abroad, but also help facilitate a costly migration if households are borrowing constrained. To disentangle these mechanisms and to evaluate the effects of income
changes on return and re-migration choices, I formulate a dynamic life cycle model
of consumption, employment, emigration, return and repeat migration. Households
may borrow up to an endogenous limit that gives higher-income households better
access to credit. Given unobserved heterogeneity in productivity and the preference for migrating, identification of this income dependence of borrowing limits
requires exogenous variation in income. I thus exploit a policy experiment that
randomly allocated cash transfers in Mexico. I find that an increase in income in
Mexico reduces migration duration, but increases both the average number of trips
per migrant and the responsiveness to economic conditions. The effect on return
migration makes immigrants staying at the destination more positively selected,
which has important implications for the assessment from a U.S. perspective of
migrations that have been induced by higher incomes in Mexico.
JEL codes: J61, O15, F22, D31
Keywords: Migration, Borrowing, Income, Selection
∗
Department of Economics, University College London and Centre for Research and Analysis of
Migration; e-mail: joseph-simon.gorlach.09@ucl.ac.uk. I am grateful to my advisors Christian Dustmann
and Jérôme Adda for their feedback and support. I also greatly benefited from discussions with James
Albrecht, Joseph Altonji, Orazio Attanasio, Mariacristina De Nardi, Aureo de Paula, Jan Eeckhout,
Rebecca Lessem, Suphanit Piyapromdee, Imran Rasul, Mark Rosenzweig, Uta Schönberg and Michela
Tincani, as well as participants of the joint CReAM/UCL, Norwegian School of Economics and University
of Warwick Workshop on Topics in Labor Economics, participants at the Oxford Development Economics
Workshop, the NEUDC conference at Brown, the Econometric Society’s European Winter Meeting
at Bocconi and at various seminars at UCL. I acknowledge funding from the NORFACE program on
migration.
1
1
Introduction
The impact of immigration on a destination country, its labor market and the fiscal system depends on the size and composition of the immigrant population. These in turn are
determined by the dynamics of return and repeat migration, and the length of time different immigrants choose to stay in the destination country. These choices are influenced
by factors that determine the affordability of a migration, with potentially important
consequences of rising wealth levels in many traditional migrant sending countries for
migrant selection and—ultimately—the effects of immigration on receiving countries.
This paper evaluates the effect of a rise in household income in a migrant’s country
of origin on return and re-migration when households are borrowing constrained. To
assess likely implications for the receiving country, it further investigates the dynamics
of compositional change within an immigrant population through the selection induced
by return and repeat migration.1
One focus of this paper is on the monetary cost of migration, which is a major, though
usually unobserved determinant of migrant behavior. Part of this cost may have to be
paid in advance and prevent many migrations that would be welfare improving for the
respective individuals. Prohibitive migration costs are an often-cited argument in the
literature for lower than expected emigration rates of individuals at the lower end of
the earnings distribution despite presumably high returns from migration for low-skilled
workers (Chiquiar and Hanson, 2005; McKenzie and Rapoport, 2010; Grogger and Hanson, 2011; Belot and Hatton, 2012; Dustmann and Okatenko, 2014). The extent to which
wealth constraints are binding depends on a potential migrant’s income and on the ability to borrow. Hence, policies that increase incomes in migrant sending countries or ease
credit constraints will—apart from increasing the opportunity cost of emigration—also
help overcome migration constraints. Therefore, the overall effect of a rise in household
income on migration decisions is ambiguous. Provided exogenous variation in income,
a reduced form identifies the net effect of an increase in this opportunity cost and a
relaxation of financial constraints, but cannot disentangle these two mechanisms.
A distinction between the two components however can be achieved by putting some
structure on the choices and constraints faced by individuals. To this end, I formulate
a dynamic life cycle model of saving decisions, and both individual and family location
choices. This allows me to study not only the channels through which an income shock
affects emigration, but also the effect on the intensive margin of migration duration, as
1
The analysis focuses on the empirically important case of Mexico-U.S. migration, where repeat
migration is a common phenomenon. The American Community Survey estimates 11.7 million Mexicans
reside in the U.S. (U.S. Census Bureau, 2012), which makes it the worldwide largest bilateral migrant
population.
2
well as the proportion of individuals migrating repeatedly and the selection of return and
repeat migrants.
Since assets and debt levels are rarely observed both before and after migration costs
have been covered, identification of the monetary cost of migration relies on observed
emigrations conditional on previously held assets and income. This requires the analyst
to specify the extent to which households have access to credit: If households can borrow
up to some unknown limit to cover part of the cost of migration, it is unclear whether an
observed migration has been facilitated by low migration costs or by a generous borrowing
limit. Hence, information on realized migrations alone cannot identify both the cost
of migration and the unobserved limit to debt that a household can hold. Existing
studies have therefore assumed that individuals have no access to credit (see Rendon and
Cuecuecha, 2010; Thom, 2010; Nakajima, 2014).
While this assumption may be a plausible simplification for those at the very bottom
of the income distribution, it is violated for a considerable part of the Mexican population,
as I will illustrate below. Such income dependence implies an endogeneity of borrowing
limits with respect to income that makes the identification of credit access in a model like
the one used here, where earnings and migration choices are affected by unobserved factors, challenging. Whereas in a simpler model without individual heterogeneity, observed
covariation between income and borrowing could be used to pin down credit constraints
that depend on income, this provides little information on the structural relation between
income and credit access in a model where unobserved individual productivity may be
related to the preference for migrating. For instance, if one motive for taking up credit
is to finance a migration, a positive correlation between credit take-up and income could
either be due to better access to loans by high-income households (which is the relation
that needs to be identified), or due to a higher demand for credit to finance migrations,
arising from a lower attachment to the country of origin and a stronger preference for
moving to the U.S. Similarly, unobserved factors like English language knowledge that
enhance earnings in Mexico and access to loans, may at the same time be correlated
with the preference for moving to the U.S. and thus the demand for credit. Hence, an
observed joint distribution of income, borrowing and migration could be generated by different combinations of income dependent borrowing limits and correlations in unobserved
heterogeneity.
To achieve identification of households’ access to credit, I use truly exogenous variation in income from the randomized introduction of the Mexican cash transfer program
PROGRESA together with information on differences in loan take-up by households in
treatment and control communities. While exogenous cash transfers from the program do
affect both borrowing and the probability to emigrate, the identifying assumption I make
3
is that the randomization of the program is uncorrelated with unobserved preferences
for moving to the U.S. Hence, whereas standard survey covariation between income and
borrowing can identify the income dependence of credit limits under the restriction of
orthogonality between individual productivity and preferences, the effect of randomized
variation in income from the experiment on borrowing allows such identification without
restrictions on unobserved heterogeneity. As such, the policy experiment breaks the contaminating link between income and other factors that determine the desire to emigrate
and thus the demand for credit. The treatment effect of cash transfers from the program
on household borrowing is used as an additional moment in the structural estimation
of the model, which together with observed migrations allows a joint identification of
migration costs and debt limits.
A further novelty of the model developed here is that it is the first within the structural migration literature to consider the role of aggregate seasonal fluctuations in labor
demand for the timing of migration decisions. The prospect of higher earnings is one of
the most important motives for individuals to migrate, and this prospect depends on employment probabilities in the destination country. A large share of Mexican immigrants
works in the U.S. agricultural sector or in construction, where employment is strongly
seasonal, which translates into seasonality in the desire to migrate. To account for this,
the model allows for seasonal variation in employment transitions. This is important, as
some migrations do not take place in winter if individuals know that the probability of
receiving a job offer in the U.S. is low. A decreasing marginal utility of wealth implies
that this reduction in migrations is not fully compensated by higher job offer probabilities
in the U.S. during summer. A model without this seasonal fluctuation falsely attributes
lower overall migration rates to high migration costs.
I estimate the model using data from the Mexican Family Life Survey, the U.S. Survey
of Income and Program Participation, the Mexican Migration Project and PROGRESA’s
evaluation survey. I explicitly address the non-representativeness of some of the survey
populations, as well as the asymptotics of a simulated minimum distance estimator under
different sample sizes. I then use the model to evaluate dynamic effects of higher Mexican incomes both on compositional changes in the immigrant population due to selective
immigration and return migration, as well as the behavioral changes in the length of stay
and the frequency of migrations by previous migrants. I find that an increase in household income in Mexico reduces the time immigrants stay in the U.S., but that contrary
to a model without financial constraints the distribution of the number of migrations is
shifted towards a larger number of trips per migrant. A 10 percent increase in Mexican
incomes is predicted to raise the average number of trips undertaken by Mexican U.S.
migrants by more than 6 percent, net of compositional changes. Important for selection,
4
I find that return migration becomes more responsive to economic outcomes in the host
country as origin incomes increase. These higher incomes reinforce the already negative
selection of returning migrants, implying that over time, the U.S. is left with an increasingly positive selection of stayers among an initial immigrant cohort. This compositional
change leads to 6 percent higher average earnings within the population of Mexican immigrants in the U.S. Both the responsiveness in migrations to economic outcomes and
the selection of stayers is important for an assessment of immigration from a receiving
country’s perspective.2 These results also suggest that while much of the literature on
selective return migration has focused on effects of host country outcomes (e.g. Hu, 2000;
Dustmann, 2003; Lubotsky, 2007), economic conditions in a migrant’s country of origin
may have to be taken into account more strongly in future research.
My work is related to a paper by Lessem (2013), who among other things studies the
effect of wages at origin on emigration rates, migration duration and the average number
of trips using a life cycle model of Mexico-U.S. migration. While her focus is on the impact
of varying degrees of border enforcement, she also uses her model to evaluate effects of a
change in Mexican incomes, however abstracting from monetary migration costs and thus
financial constraints. In her model, a rise in the opportunity cost of migrating through
an increase in Mexican wages therefore mechanically predicts a reduction in Mexican
emigration as well as a decrease in the average length of stay and the number of trips
per migrant. My results show that some of these conclusions reverse when financial
constraints are accounted for.
The paper also is related to reduced form studies that estimate the effect of an income shock on the probability of emigration. In the context of Mexico-U.S. migration,
Angelucci (2015) finds that an exogenous increase in incomes from PROGRESA transfers
raises emigration rates by about 50 percent.3 While such analysis identifies the net effect
of a decrease in the relative attractiveness of migrating to the U.S. and of a relaxation
of financial constraints, it cannot disentangle these two effects. It also cannot identify
the cost of migration, which is an inherent part of the financial constraint, and which
prevents individuals at the lower end of the wealth distribution from migrating, nor the
dynamic effects on return and re-migration choices that result from the income shock.
By introducing exogenous variation of the type used in the reduced form literature
2
A wider discussion of the implications of temporary migrants’ behavior for migrant sending and
receiving countries is provided in Dustmann and Görlach (2016).
3
See Stecklov et al. (2005) and Rubalcava and Teruel (2006) for similar analyses in this context. Using
cross-state variation in a public works program in India, Imbert and Papp (2015) on the other hand find
a negative effect of participation in the program on urban migration. For international migration from
Indonesia, Bazzi (2014) uses rainfall and commodity price shocks to evaluate determinants of emigration.
In line with the existence of credit constraints, he finds a positive effect of income shocks on emigration
from villages with relatively more small landholders. See Clemens (2014) for a survey of this literature.
5
to the analysis of migration dynamics based on structurally estimated life cycle models,
this paper also contributes to the growing literature that combines structural estimation
with experimental variation. While some studies use policy reforms or a randomized
treatment of sub-populations to examine the external validity of a structural model that
has been estimated on the non-treated sample (e.g. Lise et al., 2005; Todd and Wolpin,
2006; Kaboski and Townsend, 2011), exogenous variation can alternatively be used for
identification of model parameters that are not well identified using observational survey
covariations alone. This is the approach taken here, where identification of the income
dependence of debt limits requires information on borrowing in response to exogenous
variation in incomes that can be credibly separated from heterogeneous preferences. The
randomized experiment, thus, is used to allow a more flexible specification of the structural model’s assumptions on access to credit, increasing its credibility. On the other
hand, the structural model increases the scope of evaluation of the policy experiment,
in particular toward a more dynamic analysis of return and repeat migration, and a
disentangling of different underlying mechanisms. In this respect, I build on Attanasio
et al. (2012), who use the randomized introduction of PROGRESA to analyze education
choices in Mexico. Another recent example from a different context is the paper by Adda
et al. (2014), who use an equilibrium model to evaluate the effect on non-drug-related
crime of a counterfactual expansion of a south London experiment depenalizing cannabis
possession to the entire city.
The next section presents the model on which my results are based, before describing
in Section 3 the data sources used, with a number of descriptive statistics providing
further detail on the context considered. In Section 4, I discuss identification of the
model’s parameters and produce estimates of the treatment effect of randomized cash
transfers on household borrowing, which provide the additional moments required to
identify endogenous debt constraints in the structural estimation. Also in that section, I
discuss issues arising in the combination of multiple data sources, as is required for the
estimation of my model. In Section 5, estimation results are reported and the dynamic
implications of higher sending country incomes evaluated.
2
Model
The model is chosen to reflect emigration, return migration and re-migration decisions
of household heads and dependent family members under financial constraints, as well
as their asset accumulation and loan take-up. The model’s main purpose is to provide
a framework in which the effect of origin country incomes on migration dynamics under
borrowing constraints can be evaluated. To the best of my knowledge, it is the first model
6
to be used to identify monetary migration costs taking into account that households may
have access to credit to cover part of this cost. To make the model applicable to the
Mexico-U.S. context where many Mexican migrant workers take up jobs in the U.S.
agricultural sector or in construction, the model further is the first to consider the role of
aggregate seasonal variation in labor demand.4 This section describes the primitives of
the model, including agents’ information set and choices, state variable transitions and
the timing of choices, and finally the dynamic specification of the model. Additional
specification details can be found in Appendix A.
State variables. A household head i at time t makes decisions based on age ait ,
employment status eit ∈ {working (w), not working (nw)}, on whether there are dependent
members fit = {0, 1}, on current household head and family location
family
f
lit ≡ lit , lit ∈ {M X, U S}2 , legal status in the U.S. δit ∈ {0, 1}, total U.S. experience
XitU S , the accumulated stock of assets Ait , and current season st ∈ {summer, winter}.
Furthermore, decisions are based on information known by the agent, but unobserved
by the econometrician. This includes the unobserved productivity in different locations,
αi ≡ αiM X , αiU S , preferences πi towards the home country, and transitory shocks to
earnings and locational preference, summarized in Υit ≡ (vitl , εlit ). The vector Ωit =
ait , eit , fit , lit , δit , XitU S , Ait , st , αi , πi , Υit collects the state variables observed by an agent
at time t, though some of this information is revealed sequentially within the period, as
will be detailed below. In the estimation, a period is taken to be six months.
Family, legal status and location. At the beginning of each period, it is determined
whether an individual gains or loses dependent family, with state dependent transition
rates pf (Ωit ). Also at the beginning of the period, individuals learn about their U.S.
legal status. Transitions rates pδ (Ωit ) for an individual’s legal status vary with age and
employment status. The timing in the model is such that after family size and legal
status are known, household members choose a location. It is assumed that when there
is dependent family, families make consumption and location decisions in agreement, so
that choices maximize household welfare.5 This can result, however, in no one, all, or just
the household head migrating. In data from the Mexican Migration Project (see Section
3), the probability of a spouse migrating while the household head stays in Mexico is
only about 4 percent of the reverse. I thus exclude the possibility that dependent family
resides in the U.S. while the household head is in Mexico. To further save on computation
4
29% of Mexicans in my Mexican Migration Project sample (more on this below) report having worked
in agriculture during their last trip to the U.S., with another 15% in construction.
5
As this is a unitary household model focusing on migration behavior of male Mexican household
heads, I will refer to household heads and individuals interchangeably.
7
time, I assume that all family members share the same legal status in the United States.
For married migrants sampled by the Mexican Migration Project this is true in 93 percent
of cases. Individuals choosing to migrate face a monetary cost, which varies by age and
whether an immigrant holds a U.S. visa, and which may be different for the household
head and other family.
Employment and earnings. I focus on the extensive margin of employment and
assume that individuals either work full time or do not work, with job offers arriving
at a rate λw (Ωit ), and jobs being lost at a rate λnw (Ωit ), each depending on individual
characteristics such as age and time spent in either of the two countries, but also on
seasonally varying aggregate demand for workers. If working, log monthly earnings in
location l ∈ {M X, U S} are given by
log yitl = αil + f l (ait , XitU S ) + vitl
where f M X (·) is a function of age, while f U S (·) also is a function of the U.S. experience an
individual has accumulated up to time t.6 Idiosyncratic shocks to wages, vitl , are assumed
to be independent and identically distributed across time and individuals, with mean zero
and location specific variance σv2l . Individuals retire at age aret and from then until the
(known) end of life receive retirement benefits y ret (Ωit ). See Appendix A for details on
the exact specification of λw (Ωit ), λnw (Ωit ), f l (ait , XitU S ) and y ret (Ωit ).
Budget constraint. The driving motives for temporary migration in the model are
financial wealth accumulation for an increase in future consumption and the buffering of
employment and wage fluctuations, and the response to preference shocks. For a given
location l, I assume a standard intertemporal budget constraint augmented by migration
cost C(Ωit ) for household heads and C f (Ωit ) for the remaining family to relate future
assets Ait+1 to income yitl , the current stock of assets Ait , and consumption cit ,
Ait+1 = (1 + rA )Ait + y(Ωit ) − cit
−1[lit−1 = M X ∩ lit = U S]C(Ωit )
f
−1[lit−1
= M X ∩ litf = U S]C f (Ωit ),
(1)
where the real interest rate rA depends on whether a household holds debt, so that Ait < 0.
At the beginning of working life, the stock of assets of household i is assumed to equal
Ai0 = Ã0 exp(αiM X ). To abstract from the decision of where to hold accumulated savings,
6
Since location is chosen endogenously, returns to U.S. experience after a return to Mexico cannot
be identified in my data separately from a correlation between productivity αiM X and the preference for
being in the U.S., see also the discussion on identification in Section 4.1
8
I assume that interest rates are identical in Mexico and the United States. In order to
take into account differences in currency purchasing power, however, the stock of assets
is adjusted by real exchange rate x if individuals (re-)migrate. When a household head is
in Mexico, the household may choose to borrow up to some limit B(E[yitM X ], Ωit ) in order
to smooth consumption or to finance a migration.7 Motivated by evidence presented in
Section 3, I let this limit vary by (expected) income. I further assume that borrowing
constraints become tighter towards the end of life, enforcing a repayment of debt during
retirement (see Appendix A for details). Hence, assets are constrained by
Ait ≥ min{−B(E[yitM X ], Ωit ), (1 + rA )Ait−1 }
at all times,
(2)
i.e. apart from temporal variation in income that drives B(E[yitM X ], Ωit ) below debt levels
inherited from the previous period, B(E[yitM X ], Ωit ) is the credit constraint. Equations
(1) and (2) summarize the identification problem when both borrowing constraint B and
migration cost C are unknown, and the level of assets just after a migration has been
paid for, Ait+1 , is unobserved. This typically is the case and leaves it unclear, whether
an observed migration has been facilitated by a C that is low enough to be covered by
cash on hand, (1 + rA )Ait + y(Ωit ), or whether migration costs are in fact higher, while
B > 0 and households can borrow to partly pay for the migration.
Preferences. Individuals derive utility from consumption, family and locational amenities. For individuals residing in the U.S. who have dependent family, utility flows are
further adjusted by where this family resides. With these features in mind, per period
utility is specified as
uit = φlf
fit
cφitc πil + εlit ,
f
f
where φlf = φl6f=l if families are spatially separated, and φlf = φl=l
if not. In addition to
f
heterogeneous time-constant location preferences πil , households face transitory preference
shocks εlit that are assumed to be additive and independently extreme value distributed.8
As only relative utility flows in the two locations are identified, πiM X is normalized to
one, so that πiU S becomes the marginal utility from consumption in the U.S. relative
to marginal utility from consumption in Mexico.9 I further assume that uit goes to
7
Evidence by Banerjee and Munshi (2004) and Laszlo and Santor (2009) suggests that weaker network
structures at the destination are likely to limit credit access relative to the origin.
8
Shocks ε have cdf P (ε ≤ x) = exp(− exp(−x/sε (ait ))), where sε (ait ) is an estimated spread parameter, specified as a linear function of age. Additivity of ε in the utility function, independence and
extreme value distribution imply that the location choice probabilities take a logistic form, with value
functions in the home and host country as arguments (Rust, 1987).
9
An alternative explanation for migration rates that fall short of fully eliminating persistent wage
differences across locations is the existence of insurance networks in an individual’s home community,
9
minus infinity for cit < 0, which prevents individuals for whom (1 + r)Ait + y(Ωit ) +
B(E[yitM X ], Ωit ) < C(Ωit ), i.e. cash on hand plus the maximum obtainable credit does not
cover the migration cost, from migrating.
Welfare. After family and legal status are revealed, the location of both the household head and of dependent family members has been chosen, and individuals know the
job offers and income available to them, consumption is chosen to maximize household
welfare. The dynamic problem for these choices is given by the Bellman equation
V (Ωit ) = max uit (cit , Ωit ) + βEt [V (Ωit+1 )] ,
cit ,lit
where β discounts future utility streams and Et [·] is the expectations operator given the
information available at time t. Individuals live until age aend , with V (Ωit |ait = aend ) = 0.
3
Data and Descriptives
To estimate the model, data from different sources are needed, as identification of the
full set of parameters requires information on individuals’ choices and outcomes for nonmigrants and return migrants in Mexico, for both temporary and permanent Mexican
immigrants in the U.S., and of course on migration behavior itself. In addition, given a
potential correlation between unobserved heterogeneity in location preferences and productivity, credible identification of the income dependence of access to credit requires
information on borrowing and variation in income that can be separated from the preference for a costly migration. Hence, I further use information from the randomized
introduction of PROGRESA cash transfers (more on this below) as a truly exogenous
variation in income, and data on its effect on borrowing. This section introduces the data
sources used and provides some descriptive statistics. Estimates of the aforementioned
treatment effect of a cash transfer program on borrowing are shown in Section 4.1 where
identification of the various groups of model parameters is discussed.
Mexican Migration Project (MMP). A major challenge to empirical migration research in a context where migrants may choose to move back and forth is the lack of
datasets that track individuals across international borders. Existing analyses of repeat
migration thus rely almost exclusively on retrospective information about migration hiswhich are weakend in case of a migration (see e.g. the recent paper by Munshi and Rosenzweig, 2016).
In contrast to location specific utility flows from consumption, the existence of insurance networks alone,
however, cannot rationalize temporary emigration.
10
tories from the Mexican Migration Project.10 Between 1982 and 2013, the MMP has
surveyed 22,894 households in 143 communities in Mexico. The main advantage for the
purpose of this paper is its complete retrospective life histories, which contain detailed
information on employment, family status and migrations for each household head and
spouse. MMP data are most suited to assess the duration of completed migrations, the
documentation used, the incidence of repeat migrations and their correlation with individual characteristics. Besides annual information on whether an individual has been to
the U.S., the MMP data also report the length of stay, so that separate migrations in
consecutive years can be identified. This allows an analysis of seasonal migration, which
so far has been prominently absent from the structural econometric migration literature.
I explore this further below. Figure 1a displays the distribution of the number of completed migrations made by Mexican men who have reached age 65 or older, and are thus
likely to have completed their total lifetime number of trips. In this sample of former U.S.
migrants, 60 percent report having been to the U.S. more than once, among whom about
two thirds have migrated more than twice. Figure 1b shows the distribution of duration
of the most recent migration. Although there is much variation in migration duration, a
considerable proportion, 38 percent, has returned within one year after emigration.
Figure 1: Number of migrations and migration durations.
Source: MMP 143. Figure 1a shows the distribution of the number of migrations made per returned
migrant by the end of working life. The distribution is based on the MMP cross-sectional files, restricting
the sample to Mexican-born non-tertiary educated males aged 65 or older at the time of the survey. Figure
1b, showing the distribution of migration duration, refers to the last trip to the U.S. by Mexican-born
non-tertiary educated males aged 16-64 at the time of the survey.
For the main analysis, I restrict the sample to the years 1996-2007. The reason for
this is twofold: first, a series of policy changes since the Immigration and Control Act
10
mmp.opr.princeton.edu; Deléchat (2001); Colussi (2003); Thom (2010); Lessem (2013) and Nakajima
(2014, 2015) all use the MMP as their main data source.
11
(IRCA) of 1986 gradually tightened control of the U.S. southern border, culminating in
the Illegal Immigration Reform and Immigrant Responsibility Act of 1996. Each of these
reforms, which include some more local measures, such as Operation Hold-the-Line in
1993 and Operation Gatekeeper in 1994, expanded border control (see e.g. Gathmann,
2008, for details). I do not intend to model these shifts in the environment faced by
Mexican migrants. Second, the focus on post-1996 data avoids contamination of my
results by the peso crisis of December 1994 and the most abrupt economic woes that
followed (see e.g. Sachs et al., 1996). I further exclude individuals who were born in the
U.S. and may thus have a stronger attachment to the United States. Lastly, I restrict
attention to male household heads aged 16-64 without tertiary education.11 I do, however,
use information on migrations of household heads’ spouses to identify model parameters
relating to dependent family members’ residence location. The same restrictions apply
to moments generated from the other datasets discussed below. This leaves a relatively
homogeneous sample to which the model of Section 2 is applied.
While the MMP is a valuable source on migration experiences, there are a number of
shortcomings. First, it is relatively weak on asset information. Data on assets, however
are essential for the estimation of a model of international migration, where emigration
is restricted by financial constraints. Moreover, the MMP is a representative data source
only within the communities surveyed, while the communities themselves are a nonrandom selection of all Mexican localities. Although the population in these communities
presumably is representative for a large share of the Mexican population, a number of
authors criticize its bias toward communities with a strong history of sending migrants to
the United States (Orrenius and Zavodny, 2005; Hanson, 2006; McKenzie and Rapoport,
2007; Fernández-Huertas Moraga, 2011). I explicitly address this non-randomness in the
estimation as explained in Section 4.2.
Mexican Family Life Survey (MxFLS). Due to the above-mentioned shortcomings,
moments from the MMP are supplemented with information from the Mexican Family
Life Survey,12 which is a representative household survey conducted in 2002, with followups in 2005-06 and 2009-12, and of which I use the first two waves. In addition to detailed
household and individual characteristics, including income, debt and savings, the MxFLS
reports whether and where individuals are thinking of migrating in the future. Based
on this information, the MxFLS data support the earlier assertion that emigration is
particularly desirable for Mexicans at the lower end of the income distribution. Figure
2 shows that Mexicans who express the wish to move to the U.S. are disproportionately
11
In the MMP data, and given the other restrictions, less than 10 percent of individuals are tertiary
educated.
12
http://www.ennvih-mxfls.org.
12
drawn from the lower tail of the income distribution, with a significant difference of about
14.97 percent in mean incomes, conditional on age, gender, years of schooling, occupation
and year observed.
Figure 2: Log annual income in Mexico and
the wish to move to the United States.
Source: Mexican Family Life Survey, 2002, 2005.
Log annual income is denoted in purchasing power
adjusted USD, deflated to 2005. The sample includes
individuals aged 16-64. The density is computed using an Epanechnikov kernel with 3/4 of the optimal
bandwidth to prevent oversmoothing.
Important for the purpose of this paper, the MxFLS inquires about asset and debt
holdings. In the presence of positive migration costs, wealth constraints have been highlighted as an important factor in migration decisions and migrant selection (Chiquiar and
Hanson, 2005; Belot and Hatton, 2012; McKenzie and Rapoport, 2010; Grogger and Hanson, 2011; Dustmann and Okatenko, 2014). Such constraints may serve as an explanation
of lower observed emigration rates from the bottom of the income distribution than would
be expected given the often lower spread and higher level of this distribution in destination countries. An underlying assumption is that individuals face borrowing constraints
that are too tight to finance a migration. Indeed, existing dynamic structural migration
models which allow for asset accumulation (Rendon and Cuecuecha, 2010; Thom, 2010;
Nakajima, 2014) assume that individuals cannot borrow at all. Contrasting this, almost
one fifth of the working age population surveyed by the MxFLS reports to hold some, if
only modest, amounts of debt.
This of course does not imply that there are no binding borrowing constraints. Given
the evidence, however, these are likely to be at non-zero levels of debt. Angelucci (2015)
argues that access to credit and borrowing limits are likely related to income, including
any anticipated governmental transfers that can be used as collateral. A positive relation
13
between debt and income is supported by Figure 3. The left panel shows the cumulative
distribution of debt held separately for above and below median income individuals. At
the mean, the difference in debt levels is strongly significant, with high income individuals
holding more than twice as much debt than individuals with incomes below the median.
The same strongly positive relation is depicted in the right panel of the same figure,
which plots (log) debt against (log) incomes. This pattern motivates the more flexible
specification of debt limits in the model of Section 2.
Figure 3: Distribution of debt levels by income.
Source: Mexican Family Life Survey, 2002, 2005. Debt is calculated as negative net assets (in purchasing
power adjusted USD). Figure 3a includes zeros to illustrate the fraction holding debt. Means and 95%
confidence intervals are computed for positive debt levels (negative net assets) only. Figure 3b plots log
debt levels against log annual earnings, and a fitted local polynomial regression line with 95% confidence
interval, excluding the top and bottom 0.5% of observations. Both samples include non-tertiary educated
male household heads aged 16-64.
Survey of Income and Program Participation (SIPP). A second shortcoming of
the MMP is that—as it surveys households in Mexico—long-term Mexican emigrants are
not covered. To assess the evolution of employment and wages for these individuals, I use
data from the Survey of Income and Program Participation.13 The SIPP is a short panel
survey, the advantage of which over other and possibly longer U.S. panel surveys is its
large sample size that allows a separate analysis of Mexican immigrants. In addition, the
SIPP provides monthly information suitable to assess the relevance of seasonal variation.
As Figure 4a suggests, seasonality in employment rates is indeed prevalent. In fact,
fluctuations in U.S. labor demand can be expected to be stronger, as seasonal variation
in labor supply due to migration is likely to be pro-cyclical.
13
http://www.census.gov/sipp
14
This is supported by data on monthly apprehensions during 1999-2007 provided by
the U.S. Border Patrol, which suggest an approximately twice as high number of apprehensions at the U.S. southern border during the summer months than in winter (Figure
4b). To the extent that this reflects a larger immigrant stock in summer, such increased
labor supply indeed confirms that seasonal variation in labor demand is actually stronger
than apparent from the seasonal employment profile depicted in Figure 4a. To take
this important feature of Mexico-U.S. migration into account, the model in Section 2
allows job offer and job loss probabilities to vary by season. In line with my restriction
of the MMP sample, I use the three slightly overlapping but unconnected SIPP panels
1996-2001, 2001-2004 and 2004-2007.
Figure 4: Seasonality.
Sources: (a) SIPP, 1996-2007; (b) U.S. Border Patrol, 1999-2007. The graphs show seasonality in (a) the
share among non-tertiary educated Mexican-born male household heads aged 16-64 residing in the U.S.
who worked for at least one week during the respective month, and (b) average monthly apprehensions
at the U.S. southern border. Vertical lines show the 95% confidence intervals.
The main variables used from each of these three data sources are listed in Table 1.
Panel (a), which summarizes the MMP variables, separately displays means and standard
deviations in different reference populations: for the MMP’s retrospective life history files
and for an individual’s most recent migration to the U.S. Further, the top most panel
distinguishes between moments of the entire sample population, and of (retrospective)
observation points in the U.S. The first entry shows the strong migration history of
communities sampled by the MMP, with 8.6 percent of the individuals sampled spending
at least part of a given year in the U.S. This high propensity to migrate contributes
toward many individuals from these communities departing for the U.S. without legal
documentation. The fraction of 37.7 percent of relatively low-income MMP immigrants
residing in the U.S. legally is likely lower than the share among all Mexican immigrants.14
14
Passel (2005) estimates the 47% of Mexicans in the U.S. to have legal permits, see Hanson (2006)
15
While most moments describing employment transitions in the U.S. are computed from
SIPP data, I use covariation of employment transitions and legal status from the MMP
to pin down the effect of having legal documentation on job finding and job loss rates in
the U.S. A comparison with employment rates from the SIPP data at the end of the table
shows virtually no difference across the two samples in this respect. Migration duration
and the amount saved refer to an individual’s most recent migration spell. Savings in
this case include remittances made for the purpose of saving throughout the migration
spell and the total amount of savings accumulated and repatriated at return. As shown
earlier in Figure 3a, close to one fifth of the Mexican population report having negative
net assets, with (positive) debt levels averaging around 500 USD. Immigrants surveyed
by the SIPP have been to the U.S. on average for close to 17 years. This is considerably
more than the average migration duration of just five years for the exclusively temporary
migrants covered by the MMP, and highlights the importance of using a data source that
includes permanent migrants as well. Finally, average earnings in the U.S. of Mexicans
who select into migration are about 2 log points higher than average earnings in Mexico,
suggesting an on average strong economic incentive for U.S. migrations.15
PROGRESA evaluation data. In order to identify how access to credit varies with
income when migration costs are unobserved and preferences for the U.S. may be correlated with unobserved earnings factors, so that the demand for credit varies across
income groups as well, I use evaluation data for the Mexican Programa de Educación,
Salud, y Alimenación (PROGRESA, later called Oportunidades, now Prospera).16 In
May 1998, PROGRESA started handing out conditional cash transfers in a randomized
group of 320 “treated” communities. To evaluate the program, household data in both
this treatment group and in a control group of 186 communities, where the program was
introduced in November 1999, were collected. Eligibility of families was determined by
a pre-program survey in 1997, based on a multi-dimensional marginalization measure.17
The pre-program sample allows for a comparison of prior outcomes of households in program and control localities. Information on loan take-up is not available for 1997. Instead,
Table 2 lists differences between a number of wealth proxies and other household characteristics. Overall, this comparison suggests small and statistically insignificant differences
for a detailed account of unauthorized Mexican immigration to the United States.
15
Hanson (2006) reports differences in average wages of Mexicans in the U.S. and in Mexico based on
the respective Censuses in 2000. Depending on age and education, this difference amounts to 97%-490%
of wages in Mexico.
16
Programa de Educación (2012)
17
See Skoufias et al. (1999) for details. Similar to the MMP sample, households eligible for PROGRESA
are not representative of the Mexican population, which will be taken into account in the estimation, as
explained in Section 4.2.
16
Table 1: Summary statistics for the three main data sources used.
(a) Mexican Migration Project (MMP)
Life history files
Full sample
Variable
Is in the U.S.
Number of trips∗
X U S (in years)∗
Individuals
population
Mean
Std. dev.
0.086
0.281
2.177
2.495
5.621
6.348
If in the U.S.
Variable
Mean
Legal status
0.377
Working
0.900
Family in the U.S.
0.266
(given head is)
10,202
Std. dev.
0.485
0.300
0.442
1,366
Cross-sectional files, last U.S. migration
Variable
Migration duration (in years)
Total amount saved (in USD)
Individuals
Mean
4.878
5393.124
Standard deviation
6.598
4636.865
1,835
(b) Mexican Family Life Survey (MxFLS)
Variable
Mean
Age
42.276
Has dependent family
0.941
Working, Oct-Mar
0.907
Working, Apr-Sept
0.885
Log annual earnings (in USD, PPP adj.)
8.253
Net assets (in USD, PPP adj.)
1067.702
Has debt
0.187
Amount of debt (in USD, PPP adj.)
502.828
Individuals
5,810
Standard deviation
11.474
0.235
0.290
0.319
0.992
14209.370
0.390
1773.736
(c) Survey of Income and Program Participation (SIPP)
Variable
Mean
Standard deviation
Age
38.732
10.046
Years since immigration
16.903
9.617
Working, Oct-Mar
0.887
0.294
Working, Apr-Sept
0.901
0.272
Log annual earnings (in USD)
10.228
0.773
Individuals
1,447
MMP, 1996-2007; MxFLS, 2002, 2005; SIPP, 1996-2007. In each case, the sample includes non-tertiary educated
male household heads aged 16-64. SIPP statistics on age, years since immigration and earnings are based on
the March survey, thus the number of observations are annual rather than monthly. Individuals are considered
working in a given half-year if this is the case in at least 4 months. Monetary values are deflated to 2005, and
adjusted by purchasing power parities if referring to Mexico.
∗ Conditional on ever having been to the U.S.
in these dimensions.18
Starting in 1998, eligible families in program communities received scholarships for
each child aged 8 to 21 who attended school in one of the last four grades of primary,
or the first three grades of secondary school. Judging from school attendance rates in
control communities, the transfer was in fact unconditional for low-income families with
children up to age 14, of whom over 97 percent attended school in the absence of the
program. For the estimation, I thus restrict attention to these families. Amounts paid
vary by grade attended and gender of the child as displayed in the left graph of Figure 5.
This randomized introduction of the program induces exogenous variation in incomes and
allows the construction of the additional moments needed to identify income dependent
18
See also Behrman and Todd (1999) for an extensive evaluation of the PROGRESA randomization.
17
Table 2: Comparison of pre-treatment household wealth proxies in program and control communities.
Control mean
age of HH head
40.320
literate HH head
0.744
HH head works
0.947
hours worked
42.134
hourly wage (in pesos)
3.450
no. of rooms
1.640
land owned (in hectares)
1.902
Observations
2450
Difference between
treatment and control
−0.164
(0.220)
−0.007
(.011)
−0.010
(0.006)
0.125
(0.395)
−0.081
(0.069)
−0.003
(0.024)
−0.054
(0.099)
6596
PROGRESA evaluation data, 1997. Column 1 lists mean outcomes for the control
sample, while column 2 shows the difference between program and control observations
before introduction of the program, with standard errors in parentheses.
borrowing limits and thus migration costs. The data show that loans taken out by eligible
families in program localities during the 6 months leading up to November 1998, when
evaluation data were collected, are on average higher than in control localities.
Figure 5: PROGRESA’s monthly cash transfers (1998, 2nd term) and loans taken during
the last 6 months.
Sources: Schultz (2004) and PROGRESA, November 1998. Figure 5a depicts monthly cash transfers by
PROGRESA by gender of the child and grade attended. Figure 5b shows the distribution of log amounts
of loans taken within the previous 6 months by treatment status. The sample includes male heads aged
16-64 of eligible households with children aged 8-14 attending school. The density is computed using an
Epanechnikov kernel with 3/4 of the optimal bandwidth to prevent oversmoothing.
Figure 5b depicts the conditional density of the log amount of these recent loans in the
two groups of locations, and when discussing model identification in Section 4, I provide
18
point estimates of the treatment effect of randomized transfers from the program on loan
take-up, which serves as an additional moment in the structural estimation.
4
Estimation
The model in Section 2 can be solved by backward induction, and the choice functions
obtained are used to simulate migration and consumption behavior of a sample of individuals the moments of which can be compared to those observed in the Mexican and
U.S. data. I estimate the 101 parameters of the model by minimizing the distance of 210
moments computed from model simulations to their empirical counterparts in the four
datasets used. As I combine different data sources, which all have different sample sizes
and partly represent different populations, a number of important issues arise, which are
discussed in Section 4.2. First, however, I discuss identification of the model parameters,
with further details provided in Appendix B.
4.1
Identification
Most parameters are identified from static or dynamic conditional data moments that
can be obtained through auxiliary regressions, and which—apart from selection that is
modeled explicitly—are relatively direct counterparts to the respective parameters. For
instance, to identify parameters governing transitions in family status (pf (Ω)), legal status
(pδ (Ω)) and employment (λe (Ω)), I match coefficients from OLS regressions of observed
transitions in these outcomes on observed state variables that are arguments of these
functions. Note, however, that due to the endogenous selection of individuals into the
Mexican and U.S. samples, these parameters cannot simply be pre-estimated outside the
model. Similarly, to identify parameters from the earnings function (the mean level of
productivity αil , parameters in f l (ait , XitU S ) and the variance σv2l of transitory shocks), I
regress log earnings of workers in Mexico on age indicators, and log earnings of Mexican
workers in the U.S. on indicators of age and U.S. experience.19
Unobserved heterogeneity in productivity αil around its mean is identified by quantiles
of within-individual mean earnings residuals from these regressions. The distribution of
relative preferences for being in the U.S., πiU S , is pinned down by the distribution of U.S.
19
The joint distribution of earnings (over two waves) and past migration experience in the MxFLS do
not allow a separate identification of returns in Mexican earnings to having been to the U.S. from selection
in migration choices that are due to a correlation between productivity and the relative preference for
the U.S. The literature so far has been ambiguous about whether there are returns to a temporary U.S.
migration for Mexican workers: while Reinhold and Thom (2013) do find small positive returns, Lacuesta
(2010) argues that observed earnings differences between Mexican non-migrants and returnees are likely
the result of selective emigration.
19
experience, as well as by coefficients from an auxiliary regression of past U.S. migration on
quantiles of within-individual mean earnings residual for individuals working in Mexico
from the above regressions, and coefficients from a regression of staying in the U.S. for
another period on mean earnings residual quantiles in the United States. These latter
two sets of moments also link the dimensions of unobserved heterogeneity in the model.
The average number of trips per migrant by age, in turn, is informative for the spread
parameter of transitory shocks to locational preferences, sε (ait ).
The adjustment of utility flows if having family and by where this family resides,
φlf , is identified from covariation of assets or debt with having family, and with where
dependent family members reside. The parameter relating productivity to the initial
stock of assets, Ã0 , and risk aversion, 1 − φc , are identified by the level and the evolution
of savings over the life cycle.
Given asset accumulation and access to credit, migration cost parameters are identified
from observed migrations conditional on observed state variables. More specifically, the
coefficients from regressions of indicators for household heads and spouses making a new
trip to the U.S. on age and legal status are informative for migration costs C(Ωit ) and
C f (Ωit ) for documented and undocumented individuals at different ages.
Identification of these cost parameters here crucially depends on migrants’ access to
credit. Under unobserved borrowing constraints, observed migrations only identify a
combination of migration costs and borrowing limits, so that identification also requires
information on borrowing. In addition, the model allows for access to credit to depend on
income. Given that high income individuals also may have a high preference for migrating
to the U.S. and, hence, a potentially higher demand for credit to finance migrations, this
debt limit cannot be identified from survey covariation of debt and income alone. Such
covariation would be sufficient to identify the income dependence of borrowing limits in
a simpler model that abstracts from correlated unobserved heterogeneity in dimension
that determine both income and the demand for credit. The more realistic model used
here, however, does not impose such a restriction. Hence, correlations observed between
income and the propensity to migrate, and between income and borrowing in principle
can be generated by different combinations of the structural correlation in the unobserved
heterogeneity dimensions and of migrants’ access to credit. In addition to the above moments, I thus use the effect on borrowing of an exogenous variation in incomes induced
by the randomized introduction of PROGRESA, a cash transfer program detailed in Section 3, under the assumption that this randomized policy is uncorrelated with individual
preferences. The average treatment effect of being covered by the program,
AT E = E[loani |1treated
= 1] − E[loani |1treated
= 0],
i
i
20
is identified by α1 in an OLS regression of the form
loani = α0 + α1 1treated
+ γ 0 xi + ui ,
i
(3)
where the sample is restricted to eligible households with children in the relevant age
range attending school, and xi includes a full set of age indicators for the male household
head, as well as his employment and marital status. To proxy for pre-program wealth,
I further include indicators for the number of rooms and the amount of land owned by
the household. Table 2 above lists the pre-program differences in these variables. While
the randomized introduction of the program guarantees consistency, inclusion of these
controls reduces the residual and increases precision of the point estimates. Table 3
shows the results of this estimation. In this sample of fairly poor households, the mean
monthly transfer amount of 260.32 pesos (51.14 PPP adjusted USD) corresponds to 27.8
percent of household heads’ average earnings in control villages. This sizeable exogenous
variation in income helps to pin down the income dependence of borrowing limits. While
I do not find evidence for an increase in the extensive margin of credit take-up (column
1), the average level of recent (positive) loans increases by 0.38 log points or 63.72 PPP
adjusted USD.
After the introduction of a state variable indicating whether an individual is from a
treated community of origin or a control community, these are moments the model can
generate and that will be used in the structural estimation below. The model’s estimation by matching simulated to observed moments does not actually require a consistent
estimate α̂1 , as (3) only serves as an auxiliary regression. The importance rather lies with
the income variation being unrelated to location preferences. The model then implies,
for a given set of parameters, a distribution of incomes and a corresponding demand for
credit. To the extent that for some individuals this demand exceeds the (unobserved)
borrowing constraint, i.e. that the constraint is binding, the covariation of income and
observed borrowing captured by α̂1 identifies the borrowing limit.20
The full set of moments and their role in identification are listed in Appendix B.
4.2
Data Combination
Two important issues arise when combining different data sources for the structural
estimation of the model parameters: first, the datasets used here have different target
populations, and two (the MMP data and the PROGRESA evaluation sample) are not
representative for my population of interest, i.e. the population of non-tertiary educated
male Mexican household heads. Second, all four datasets have different sample sizes and
20
Adda and Eaton (1998) use a similar strategy to identify constraints to sovereign debt.
21
Table 3: Average treatment effect of the program on
loans taken during the previous 6 months.
1treated
Observations
loan> 0
0.00170
(0.00436)
6490
log(loan amount in USD)
0.380
(0.192)∗∗
186
PROGRESA evaluation data, November 1998. The sample includes eligible male household heads aged 16-64. Dependent variable: loans taken
within past 6 months. ATE identified by OLS, controlling for age (full
set of indicators), employment status, marital status, number of rooms
(indicators for 1, ...9, 10+ rooms), land owned (indicators for 1, ..., 9,
10+ hectares) in both regressions.
Heteroskedasticity robust standard errors in parentheses; ∗∗ p < 0.05.
thus provide moments of different precision. I address these concerns in turn.
4.2.1
Representativeness
Both communities sampled by the Mexican Migration Project and by PROGRESA are
predominantly rural, low-income villages. The model presented in Section 2, however, was
chosen as a description of the entire population of Mexican-born male household heads
without tertiary education, as are—conditional on the respective location of residence—
the moments generated from the two other data sources used.
The dimensions along which the samples differ are not clear a priori. The higher
poverty level among households covered by PROGRESA, however, is the most obvious
deviation from representativeness, while the main recurrent critique against the MMP in
the literature is its bias toward communities with a strong history of sending migrants to
the United States (Orrenius and Zavodny, 2005; Hanson, 2006; McKenzie and Rapoport,
2007; Fernández-Huertas Moraga, 2011). Some of these authors maintain that while the
MMP might not be a good representation of the Mexican population as a whole, it probably is a good approximation of the population of Mexican migrant sending households.
Given that interviews take place in Mexico, however, the latter certainly is a relief only
to the extent that the emigration and return migration process is modeled. To further
address the oversampling of migrant sending households by the MMP and different income levels across the sampled populations, I allow for different weights of the unobserved
heterogeneity types in the model.
The estimation approximates heterogeneity in the population by allowing for T discrete types τ of simulated individuals, each of which is associated with a 3-tuple of
preference for the U.S. (π U S ), productivity in Mexico (αM X ) and productivity in the U.S.
(αU S ). The value of each of these components and the weights ωτ assigned to each type
with unobserved characteristics {πτU S , ατM X , ατU S }, τ ∈ {1, ..., T }, are estimated based on
the combination of residual quantiles from auxiliary regressions of earnings and location
22
on observed state variables as explained above in Section 4.1.
To allow both for a higher propensity to migrate conditional on observables and
for lower productivity levels in rural communities, I estimate separate sets of weights
{ω1M M P , ..., ωTM M P } and {ω1P ROGRESA , ..., ωTP ROGRESA } used in the construction of simulated moments that have their empirical counterparts in the MMP and PROGRESA
samples, respectively. Suppose, for instance, that stronger migrant networks from MMP
communities reduce the utility cost of residing in the U.S., and that log earnings conditional on observables are lower in these locations. Then types with a higher preference
for the U.S. πτU S and lower productivity in Mexico ατM X would receive a higher weight in
simulated moments that are to be matched with empirical moments from the MMP data
than in moments from the nationally representative Mexican Family Life Survey. Note,
that this not only allows for different productivity or preference levels across samples, but
leaves the entire joint distribution of the three dimensions of unobserved heterogeneity
unrestricted allowing, for example, also for different levels of inequality across samples.
As explained above, differences in the propensity to migrate and earnings levels are
likely the most important concerns and are addressed by these multi-dimensional weights.
Exogenous differences (i.e. differences unexplained by the model) along other dimensions
are possible of course, though a simple comparison of sample moments from the four
sources is barely informative about this. As an example, lower unemployment rates
in the MxFLS sample, where earnings are higher than in PROGRESA villages may—
rather than reflecting a fundamental difference in local labor demand—result from better
affordability of migration costs, so that after a job loss emigration is a viable option, while
unemployed individuals in PROGRESA villages who cannot afford emigration stay and
are counted as unemployed. While this is a pure selection issue, other mechanisms are
also captured by the model. Employment rates may vary across samples, for instance,
also due to differences in past U.S. experience, which will affect employment transition
probabilities after a return to Mexico. Such effects are modeled explicitly and hence do
not require any re-weighting.
4.2.2
Different Sample Sizes
A further concern arises irrespective of the representativeness of the samples used. All
four datasets in my analysis have different sample sizes and thus tend to yield moments of
different precision. If all data moments needed for identification were observed from the
same source with sample size N , Gourieroux et al.’s (1993) indirect inference estimator
√
would converge at a rate N . My estimation matches simulated moments to empirical
counterparts from four samples ς ∈ {M M P, M xF LS, SIP P, P ROGRESA} of different
sizes Nς . While consistency of the simulated minimum distance estimator is unaffected
23
by the use of multiple samples, the derivation of the asymptotic distribution requires an
assumption on the rate at which these samples increase.
In line with Angrist and Krueger (1992) and Arellano and Meghir (1992), who derive
the asymptotics of a two sample instrumental variables estimator in a situation where
identification requires moment conditions from two independent data sources,21 assume
that sample sizes increase at proportional rates, and let simulated sample sizes Nςs increase
at a rate such that
lim (Nς /Nςs ) = nς ,
Nς →∞
Nςs →∞
with 0 < nς < ∞. The simulated minimum distance estimator θ̂ for a vector of pa0
rameters θ minimizes criterion Γ(ϑ) = D(ϑ)0 W D(ϑ) = md − ms (ϑ) W md − ms (ϑ) ,
where D(ϑ) = md − ms (ϑ) is the difference between a vector of observed data moments
md and the corresponding moments ms (ϑ) simulated from the model with structural
parameters ϑ, and W is a weighting matrix. Importantly, the observed moment vector may be a collection of moments calculated from different data samples, such that
md = (mdM M P mdM xF LS mdSIP P mdP ROGRESA )0 . The moments used in this paper are
OLS estimates of coefficients in linear auxiliary models, and are thus asymptotically normally distributed. Given this, and under the additional assumption listed in Appendix
C,
√
d
N (θ̂ − θ) −→ N 0,
−1
∂D0
∂D
(θ̂)W 0 (θ̂)
∂ϑ
∂ϑ
∂D0
∂Dς
(θ̂)
N (1 + nς ) ς (θ̂)Wς var(mdς )Wς
∂ϑ
∂ϑ0
ς
−1 !
∂D
∂D0
(θ̂)W 0 (θ̂)
,
∂ϑ
∂ϑ
!
X
with Dς (θ̂) = mdς − msς (θ̂), and where Wς are blocks on the diagonal of the weighting
matrix W , with one block of weights for the moments from each sample ς. I provide a
derivation of this result as well as the assumptions required in Appendix C.
21
See also Ridder and Moffitt (2007) for an extensive survey on data combination.
24
5
5.1
Results
Model Fit
The model was chosen to mirror migration choices in a context where many migrants
choose to return and possibly re-migrate at a later stage. The left panel of Figure 6a
displays the distribution of the number of migrations undertaken up until the time individuals were surveyed by the Mexican Migration Project.22 For comparison, the right
panel of Figure 6a shows the same distribution in the population simulated by the model.
Similarly, Figure 6b shows the empirical and simulated distributions of cumulative U.S.
experience, that is the time in the U.S. that may have been accumulated over several
trips, while Figure 7 shows the model fit for the conditional distributions of the time
continuously spent in the U.S. by legal status. Note that in the structural estimation
only means of these outcomes are targeted rather than the full distributions. Overall, I
conclude that although the distribution of cumulative U.S. experience predicted by the
model is somewhat too compressed, with too many individuals predicted to have been to
the U.S. for between 5 and 10 years, the model replicates well the prevalence of migration temporariness and repeat migrations. Appendix B lists the full set of observed and
simulated moments used in the structural estimation.
Figure 6: Model fit: Number of migrations and cumulative U.S. experience.
Distributions of (a) the number of migrations in the MMP data at the time of the survey and the
corresponding distribution in the population simulated by the model; and (b) cumulative U.S. experience
in the MMP data and the simulated sample. Model predictions are based on 20,000 simulated individuals,
drawing from the MMP’s age distribution at the time of the survey and using estimated weights used in
the construction of moments with empirical counterparts in the MMP.
22
Note that this is weakly less than the total number of migrations during an individual’s life cycle,
which Figure 1 attempted to capture by restricting the sample to individuals aged 65 or older.
25
Figure 7: Model fit: Migration duration by legal status.
Distributions of the number of migrations in the MMP at the time of the survey and the corresponding
distribution in the population simulated by the model for (a) immigrants with a U.S. visa; and (b)
for undocumented immigrants. Model predictions are based on 20,000 simulated individuals, drawing
from the MMP’s age distribution at the time of the survey and using estimated weights used in the
construction of moments with empirical counterparts in the MMP.
5.2
Estimates
The model has 101 estimated parameters. I focus here on a subset, in particular on
estimates describing preferences, migration costs and access to credit. A full list of the
structural parameter estimates is provided in Tables 17-23 in Appendix D.
Preferences. Utility in the model is derived from consumption, family status and family location, as well as from locational amenities that may be valued differently across
individuals. Everything else equal, individuals tend to derive slightly higher utility from
being in Mexico, with an average utility loss of 6 percent from migrating (π Ui S = 0.97),
though with considerable heterogeneity across individual types (see Table 4).23 The estimate of φc indicates a decreasing marginal utility of consumption. Per period utility flows
are adjusted by whether an individual has dependent family members, and by whether
f
f
they reside in the same location. An estimate of φl=l
(φl6f=l ) larger (smaller) than one
f
means that individuals derive positive utility (suffer a utility loss) from having family if
this family resides in the same (a different) location. Estimates suggest that individuals who have family that does not migrate are—at equal consumption flows—more than
23
The estimated weights for the four types are (0.167, 0.101, 0.487, 0.245) in the representative data
sources (MxFLS and SIPP), (0.000, 0.236, 0.279, 0.485) for the MMP sample, and (0.082, 0.714, 0.205,
0.000) for the PROGRESA sample. This yields a higher mean relative preference for being in the U.S. of
1.07 among household heads in MMP communities, and a lower one of 0.76 in the PROGRESA sample.
The correlation betweeen πiU S and log earnings heterogeneity in Mexico, αiM X , is 0.77, that with log
earnings heterogeneity in the U.S., αiU S , is -0.78.
26
three times better off if staying with their family in Mexico than if migrating.
Table 4: Structural estimates of preference, borrowing constraint and
migration cost parameters.
Parameter
c
l
Preferences: uit = φlf πil cφ
it + εit
preference of type 1 for the U.S. (π1U S )
preference of type 2 for the U.S. (π2U S )
preference of type 3 for the U.S. (π3U S )
preference of type 4 for the U.S. (π4U S )
returns to consumption (φc )
Point estimate
0.640
0.721
0.956
1.315
0.627
f
effect of spatial separation from family (φl6f=l )
Standard error
(0.050)
(0.010)
(0.014)
(0.024)
(0.002)
0.161
(0.008)
3.295
(0.037)
Borrowing limit: B(E[yit ], Ωit ) = min {b0 + by E[yit ], ·}
intercept (b0 )
8.632
effect of biannual income (by )
0.702
(7.256)
(0.004)
Migration cost: C(Ωit ) = mc0 + gC (ageit ) + coyote
intercept (mc0 )
4952.948
effect of age at age ≤ 30
12.906
effect of age at 30 < age ≤ 50
57.665
effect of age at age > 50
110.577
coyote
775.357
(84.604)
(2.251)
(1.965)
(0.013)
(27.993)
f
effect of family in same location (φfl=l )
Model parameters characterising preferences, access to credit and migration costs estimated by
simulated minimum distance estimation based on 20,000 simulated individuals × 50 years × 2
seasons. See Section 4.2.2 for details on the computation of standard errors.
Borrowing limit. Apart from a debt limit that becomes tighter towards the end of life
and ensures repayment, households face a constraint to the maximum amount of debt
they can hold that is related to their current predicted income (see Appendix A for more
detail). This part of the constraint, which is specified as a linear function of predicted
income, is estimated to be the binding constraint in most cases. Given the low estimate
of the intercept b0 , the estimate of by implies that households have credit access to about
70 percent of their half yearly or 35 percent of their annual income.
Migration costs. The monetary cost of migration depends on age and may be different
for household heads and other family members, with an extra cost for border crossings
without a U.S. permit. The cost of migration is estimated, for instance, to equal 5.340
USD for 30-year-old household heads with a U.S. visa, and an additional 775 USD for
undocumented immigrants. This estimate of the cost for a “coyote” turns out to be very
close to the mean of 774 USD reported by former undocumented migrants in my MMP
sample. This is particularly reassuring given that I do not use this information in the
structural estimation. My estimates compare to 8,900 USD for undocumented migrants
estimated by Thom (2010) for the year 2000 using a model where other family members’
migration is not explicitly considered; the estimate of 8,900 USD potentially includes
27
migration costs for other family members. For a sample of mostly, but not exclusively,
undocumented migrants, Nakajima (2015) estimates the cost of migration per person to
be 10,900 USD, which is assumed to be equal for wives joining their husbands in the U.S.
Note that the models used vary across several margins, some of which suggest an overestimation and others an underestimation of the cost of migration. The assumption of zero
access to credit tends to reduce migration cost estimates, while for instance abstracting
from seasonality in labor demand increases this estimate as long as this seasonality is
stronger in the sectors employing Mexicans in the U.S. than employment seasonality in
Mexico. Similarly, additional costs for family migration are, if not modeled explicitly,
picked up by this parameter.
5.3
Policy Simulation
Higher incomes at origin. I use the estimated model to analyze the effect of higher
origin country incomes on migration dynamics. While identification of short-run net
effects of income on emigration can be achieved by reduced form estimations if an exogenous variation in income can be exploited, an investigation of subsequent choices, for
example whether and when to return, requires a more structural approach. Given that
many Mexican migrants stay in the U.S. only temporarily, it is a priori unclear whether a
positive effect on the propensity to emigrate implies a one-to-one increase in the stock of
migrants residing in the U.S. Furthermore, the selection of both immigrants and return
migrants is likely to respond to changes in economic conditions at the origin. I thus
use the model to investigate how flexibly migrants respond to economic outcomes, and
whether policies that relax financial constraints in the country of origin induce changes in
migration durations, repeated migrations undertaken and the selection in terms of labor
market outcomes.
As discussed earlier, a rise in household income has at least two counteracting effects
on the propensity of individuals to emigrate: While staying becomes relatively more
attractive as incomes and thus the opportunity cost of migration rise, a higher income
may help to overcome binding liquidity constraints and facilitate emigration to a still
higher paying destination, or one where an individual desires to move to for non-economic
reasons. Existing evidence points toward a positive net effect in many contexts (e.g. Bazzi,
2014; Angelucci, 2015). Beyond this extensive margin, however, an increase in income also
affects migration on the intensive margin of migration duration, as well as the propensity
of individuals to move back and forth repeatedly, and the selection of those who return.
Figure 1 illustrated that repeat migration is a common phenomenon between Mexico
and the U.S. In the model used here, repeated migrations are driven by changes in
any of the time varying state variables. For instance, an immigrant in the U.S. who
28
has accumulated sufficient savings may find it worthwhile—given expectations about
employment and other outcomes—to return and enjoy a higher utility from consumption
in Mexico where other family members live. If later on that returnee loses a job and reemployment probabilities in Mexico are relatively low, a re-migration may be the optimal
choice. Similarly, shocks to preferences, wages, family or legal status may trigger repeated
migrations. As with the first migration undertaken, however, individuals are prevented
from re-migrating if their cash on hand plus the debt limit does not cover the monetary
cost of a migration.
An increase in sending country incomes makes migrations more affordable. Hence,
apart from increasing the appeal of spending time in the origin country, such a change
enhances the capacity of individuals to adjust to changing personal and economic conditions, including employment opportunities. For instance, immigrants in the U.S. losing
a job will be less reluctant to return to Mexico, knowing that a re-migration the following spring, when more jobs will be on offer, is affordable. Figure 8, which shows
the distribution of the number of migrations, illustrates this for an increase in Mexican
incomes by 10 and 20 percent, and separately for (a) all migrations under each of the
respective scenarios, and (b) for only those individuals who migrate at least once under
either regime, hence eliminating compositional changes by looking at the same group of
individuals throughout. At baseline, without any transfers, the average number of migrations throughout an individual’s working life and conditional on having ever migrated
is about 1.5.24
Figure 8: Effect of higher origin country incomes on repeated migrations.
Number of migrations under different income levels in Mexico, considering (a) all individuals with at
least one migration under the respective scenario, and (b) individuals with at least one migration in
either of the cases considered. Model prediction based on 20,000 simulated individuals.
An increase in incomes by 10 percent shifts the distribution of the number of trips
outward, increasing the average number of migrations by about 3.9 percent. Part of
the behavioral change among individuals who would have migrated under both scenarios
24
Note that this does not correspond to the distribution displayed in Figure 1a, which is drawn from
the non-representative MMP data, and is conditional on migrants having returned.
29
is obscured by compositional changes as additional individuals can afford to migrate
and others may prefer to stay in Mexico if incomes are higher. To abstract from these
selection issues, the right-hand graph shows the change in the distribution of the number
of migrations only for those who are predicted to migrate at least once in either case.
The purely behavioral change in response to a 10 percent increase in incomes in Mexico is
predicted to lead to an average increase in the number of trips per migrant of 6.1 percent.
This shows that rather than by compositional changes, the effect is driven by the response
of individuals who would have migrated even in the absence of the program (Figure 8b),
while compositional changes partly offset this shift in the distribution (Figure 8a). A
closer look by income groups reveals that this increase in repeat migration is driven by
migrants in the middle of the income distribution, of whom many are on the margin of
being able to finance their desired migrations. Immigrants in the second tercile of the
income distribution raise their number of trips by 12.4 percent. Lower-income migrants,
who often are still constrained even under 10 percent higher incomes, and higher-income
migrants, who are less restricted by financial constraints to start with, each only migrate
1.7 percent more frequently.
A rise in expected incomes at origin not only raises the opportunity cost of staying
abroad in terms of origin income forgone, but the value of being in the country of origin
is boosted further because individuals know that the future option of emigrating will be
more easily affordable if desired. Both these channels are likely to shorten migration
durations among immigrants in the U.S. From a host country’s perspective this is important, given that a stronger concern to policy makers than the number of migrations
undertaken usually is the stock of immigrants residing in the country. The left-hand
graph of Figure 9 shows the survival rates of immigrants in the U.S., that is, the fraction of initial arrivals left in the country by years since immigration. Whereas the solid
curve represents the survival rate at baseline, the dashed profile shows the reduction in
migration durations when incomes in Mexico increase by 10 percent, which shortens the
average length of completed migrations by one year, or 19 percent.25 Again, the figure
shows the composite effect of a behavioral change among individuals who are predicted
to migrate in either case and of compositional changes. Figure 9b shows the change in
survival rates only for those who are predicted to migrate under either scenario, with the
effect on migration durations becoming still stronger. The reason for the lower survival
rates (and the seemingly smaller effect of higher incomes in Mexico) for the full migrant
population at baseline (Figure 9a) is that it includes some migrants with a relatively
strong preference for Mexico who under low Mexican incomes tend to stay only for a
25
The overall effect on the Mexican population residing in the U.S. at a given point in time is negative
(-4.8 percent), though I show at the end of this section that in line with other studies the effect on the
flow of immigrants is positive for low-income individuals.
30
short period in the U.S., while prefering not to migrate at all when incomes in Mexico
are higher.
Figure 9: Fraction left in the U.S.
Survival rates in the U.S. under different income levels in Mexico of (a) all Mexican immigrants, (b) Mexicans who would have migrated under both income levels. Model prediction based on 20,000 simulated
individuals.
With many migrants returning, a relevant question from a host country’s perspective
is how responsive out-migration decisions by immigrants are to economic outcomes, and
hence how those who stay at the destination are selected. While policymakers will be
less interested in location choices that are driven merely by individual preferences, there
may be an interest in how immigrants react to labor market shocks, and in particular
whether immigrants stay in the country during unemployment spells. The responsiveness
of migration decisions to employment at destination is of particular relevance in the
Mexico-U.S. context, where a large proportion of Mexicans work in the U.S. agricultural
and construction industries, in which labor demand varies strongly across season and job
offers are distributed very unevenly over the year. Figure 10 shows the annual fraction of
immigrants that the model predicts to return the following period by employment status.
The figure suggests that at baseline the probability to return is higher for unemployed
immigrants. The model further predicts that an increase in incomes not only shortens
migration duration and raises return migration rates, but it does so much more among
immigrants who have lost their job in the host country. This is because the higher wealth
level helps immigrants to better respond to economic shocks, and prevents unemployed
immigrants from staying in a host country merely on the basis that they will be less likely
to re-migrate if desired in the future.
The other important dimension of migrant selection is individual productivity. A
large part of the early microeconometric migration literature has been concerned with the
estimation of immigrants’ earning profiles (Chiswick, 1978; Long, 1980; Borjas, 1985), and
a number of later studies explicitly consider contexts where some immigrants stay only
temporarily (Hu, 2000; Lubotsky, 2007; see Dustmann and Görlach, 2015, for a critical
31
Figure 10: Effect of higher origin country
incomes on return decisions of unemployed
immigrants.
Annual return migration rates of Mexican immigrants in the U.S. by employment status under different income levels in Mexico. Model prediction
based on 20,000 simulated individuals.
review of this literature). The long-standing interest in this topic can be explained by
the various concerns about immigration, such as the fiscal contribution of immigrants
or increased labor market competition with certain groups of native-born workers, an
analysis of which requires an understanding of immigrant career paths. The above model
allows an evaluation of both Mexican immigrant and out-migrant selection to and from
the U.S. in terms of individual productivity when migration from Mexico is constrained
by monetary costs. Similar to the increased responsiveness of migration to employment
outcomes in the U.S., higher incomes in Mexico make migrants react more strongly to
the wage payoff from being in the U.S., but also affects various types of immigrants in
different ways.
Under higher origin incomes, immigration increases most strongly among the least
productive group of workers, depressing the average of immigrant wages at arrival. However, as many of these migrants cannot afford to bring their families with them, they
suffer a disproportional utility loss from residing in the U.S., so return migration rates
are high for this group of workers. In addition, the length of stay of these low-skilled
migrants is most strongly affected by a change in origin incomes, so return migration
responds strongly to a rise in the opportunity cost of staying abroad. Immigration also
increases among workers at the middle and the upper part of the skill distribution. These
immigrants are more likely to bring their family with them and become longer-term immigrants. Hence, the U.S. tends to retain immigrants with above average productivity.
This implies that those of an initial arrival cohort staying at the destination become
increasingly positively selected on productivity as time passes. Figure 11 displays immigrant earnings profiles in the U.S. by time since the last immigration for different origin
32
country incomes. The graph suggests that 10 percent higher incomes in Mexico lead to
about 6 percent lower average earnings at arrival, while negatively selected outmigration
reverses this gap after about two years.26 The net effect of lower initial average earnings
and higher average earnings by long-term immigrants is ambiguous. The last row in Table
5 shows mean log annual earnings at baseline as well as under 10 percent higher Mexican
incomes, indicating that the overall effect on the selection of the immigrant population
residing in the U.S. is positive. The model predicts that 10 percent higher incomes in
Mexico lead to an about 6 percent higher average in immigrant earnings .
Figure 11: Effect of higher origin country incomes on
migrant selection in terms of earnings.
Mean annual earnings of Mexican immigrants in the U.S. by
time since last immigration under different income levels in
Mexico. Model prediction based on 20,000 simulated individuals.
The effect of a 10 percent rise in household incomes in Mexico is summarized in Table
5, which lists outcomes at the baseline, as well as under the higher income level. The first
two rows show the change in repeat migration and migration duration, corresponding to
the patterns illustrated in Figures 8 and 9. In order to disentangle the negative effect on
emigration due to a rise in the opportunity cost of migration when incomes at home are
higher, and the positive effect due to a relaxation of financial constraints, rows 3 and 4 of
Table 5 contrast the fall in the fraction of Mexicans who would prefer to emigrate to the
U.S. in any given year, and the reduction in the share among them who are prevented
from actually migrating because their assets, income and maximum debt level are too low
to cover the cost of migration. The resulting annual emigration rates are shown in row 5.
It is only this net effect of higher income at the origin on emigration that is identified in
26
Note that neither the “baseline” nor the counterfactual profiles show the returns to time spent in the
U.S., but that the comparably steep slope is partially driven by negatively selected out-migrants under
all three scenarios.
33
reduced form estimations. The model thus suggests an income elasticity of emigration of
approximately 0.6 (≈ (1.53 − 1.44)/1.44 · 10). I relate this to comparable reduced form
estimates in more detail at the end of this section.
Table 5: Effect of higher incomes in the origin country.
(1) Mean Number of trips per migrant
(2) Mean migration duration∗ (in years)
(3) Fraction that would like to emigrate∗∗
in summer
in winter
(4) Fraction constrained∗∗
(5) Fraction actually emigrating∗∗
(6) Mean log ann. earnings in the U.S.
(in log USD)
baseline
1.504
6.390
13.40%
10.33%
9.81%
89.28%
1.44%
9.626
10% higher origin incomes
1.562
5.249
11.92%
9.03%
8.57%
87.18%
1.53%
9.685
Effects predicted by the model, based on 20,000 simulated individuals.
∗ of completed migrations
∗∗ annual fractions: shares of those who want to emigrate/are constrained (among
those who want to emigrate)/actually emigrate at least once per year.
Motivated by the observation that more than 40 percent of former migrants surveyed
by the Mexican Migration Project report having worked in the U.S. agricultural or construction sectors, the model takes into account seasonality in aggregate labor demand.
Since the values of being in Mexico or in the U.S. are non-linear functions of income,
seasonality in choices does not average out to choices that would be predicted by a model
which abstracts from seasonality. Hence, this is an important aspect in modeling migration decisions which so far has been absent from the structural migration literature. The
seasonality in (expected) employment in the U.S. translates into a seasonality in migrations, in line with the indirect evidence on apprehensions along the U.S. southern border
in Figure 4b. This is because prospective migrants anticipate employment probabilities
in the U.S., so that the desire to emigrate is higher during summer months.
The previous analysis has focused on migrant selection and the responsiveness to
employment shocks which, given the sectors many Mexican immigrants work in, is likely
of concern to U.S. policymakers. In light of the temporary nature of many migrations
and the better capacity to accumulate savings in the U.S., an interesting question from a
Mexican perspective is whether a cash transfer program that raises incomes in Mexico can
raise domestic demand over and above the aggregate transfer amount paid by facilitating
migrations that would not have taken place otherwise. For simplicity I simulate a scheme
that pays out an annual lump sum to all households whose head resides in Mexico. While
some migrants induced by such a program may stay for very long or even permanently and
consume most of their wealth in the U.S.—including assets that have been accumulated
in Mexico prior to migration—others may return with a stock of assets larger than what
they owned before emigrating. To evaluate the effect on aggregate expenditure in Mexico,
34
Figure 12 compares average discounted cumulative transfer amounts paid under different
schemes to the rise in average discounted cumulative consumption by individuals residing
in Mexico, where each period’s consumption is calculated as cash on hand minus next
period’s (discounted) assets and migration costs in case an individual emigrates. The
difference between bars for each policy shows that repatriated savings, indeed, make up
easily for forgone domestic consumption by long-term emigrants.
Figure 12: Effect of income subsidies on expenditure
in Mexico.
Discounted cumulative cost of a cash transfer program and discounted cumulative consumption in Mexico. Model prediction
based on 20,000 simulated individuals.
Access to credit. A relaxation of debt constraints has similar effects to an increase
in Mexican incomes: prospective migrants are less likely to be wealth constrained, and—
anticipating this—immigrants in the U.S. are also more flexible in their location choice.
On the other hand, staying in Mexico becomes more attractive as better access to credit
makes negative labor market shocks less painful. The model suggests that in 89 percent
of cases, Mexicans who would choose to move to the U.S. are prevented from doing so
because they cannot cover migration costs. To illustrate the effect of access to credit on
the prevalence of binding wealth constraints, Figure 13 displays the share of would-bemigrants in a given period who are constrained under different (counterfactual) limits to
the maximum amount of loans they can access to finance a migration.27 The mean debt
limit predicted by the model is 631 USD, and the figure shows that starting from current
levels, better access to credit has a modest effect on the fraction of potential migrants
who can actually afford to migrate. The simulation suggests a potentially strong effect
27
In contrast to the estimated model, where debt limits vary by age and potential income, this counterfactual simulation for simplicity assumes equal access to credit for all.
35
of a development of capital markets in Mexico on emigration. For instance, an increase
in the debt limit from 1,000 to 1,500 USD (PPP adj.) is predicted to reduce the fraction
of would-be-migrants who are prevented from migrating due to borrowing constraints by
about 7 percent.
Figure 13: Access to credit for financing migrations.
Fraction of constrained Mexicans among those who desire to
migrate to the U.S. by the amount of migration costs that can
be covered by credit. In contrast to the estimated model, this
counterfactual simulation assumes equal access to credit irrespective of individuals’ earnings potential. Model prediction
based on 20,000 simulated individuals.
Emigration. The focus of this paper is on choices taken after an initial emigration has
taken place, the analysis of which requires a dynamic model of the kind I use. Nevertheless, this estimated model also makes predictions about the rate of emigration from
Mexico to the U.S., which other studies have looked at. The most directly comparable estimates are those by Angelucci (2015), who evaluates the average treatment effect
of PROGRESA on the propensity to emigrate in a linear probability model. As the
treatment effect on emigration is not used in the estimation of the structural model in
Section 2, a comparison to her estimate may serve as an additional credibility check
of the model. To match Angelucci’s estimation as closely as possible, I draw from the
simulated sample individuals with dependent family from the age distribution of eligible
households’ heads in the PROGRESA evaluation data and use the estimated unobserved
heterogeneity weights for this sample (see Section 4.2). I further restrict attention to
under 40-year-olds in line with her sample restriction. Figure 14 shows the percentage
point increase in emigration by age group that is induced by an increase in incomes
corresponding to the PROGRESA transfers. For comparison, the figure also shows the
36
corresponding estimate and 95 percent confidence interval reported by Angelucci. On
average, the effect predicted by my model is well within her confidence bounds.
Figure 14: Comparison to effect of PROGRESA on
emigration to the U.S. estimated by Angelucci (2015).
Percentage point change in emigration rates due to a 600 USD
(PPP adjusted) increase in incomes in Mexico, corresponding
to the average amount received by households eligible for PROGRESA transfer, by heads of eligible households by age group.
Model prediction based on 20,000 simulated individuals.
The differentiation by age group reveals both a strong variation and an interesting
non-monotonicity over the life cycle. Emigration is particularly attractive for younger
workers: the difference in employment probabilities between the U.S. and Mexico is
largest among young workers and among workers close to retirement. At the same time,
migration costs are estimated to be lowest for the youngest. Taken together, the desire
to emigrate is especially strong among younger Mexicans, who however are also likely to
be wealth constrained, as they have not yet accumulated a large stock of assets and often
lack access to credit. In particular among the over-proportionally poor households eligible
for PROGRESA, the transfers are often still not sufficient for young household heads to
overcome these constraints. Thus, while the desire to emigrate may be large for young
Mexicans, the effect of the transfers on emigration is in fact strongest for individuals in
their early 30s, when a larger mass of prospective migrants is on the margin of being
able to afford a migration. For older Mexicans, on the other hand, attachment to the
origin and higher migration costs are more likely to discourage a migration irrespective
of transfer receipts.
37
6
Conclusion
Understanding return and repeat migration, and the selection they involve is essential
for an assessment of immigration. One important determinant of migration is the income
level in a migrant’s country of origin, which affects both the desire and the ability of
individuals to migrate. Importantly, a change in sending country incomes not only has
a short-term effect on the probability to emigrate, but also affects the more dynamic
aspects of migration, like the duration of stay at a destination, the propensity to migrate
back and forth repeatedly, and the selection of both return and re-migrants. Any of these
effects depends on the prevalence of financial constraints and whether individuals can
borrow in order to finance a migration.
This is the first paper to evaluate the effect of a change in incomes in a migrant
sending country on return and repeat migration under financial constraints. I further
relate the selection in return migration to economic condition in the migrant’s country
of origin taking into account migration dynamics that may lead to multiple migration
spells. The explicit consideration of a migrant’s ability to cover part of the monetary cost
of migration by loans is an important contribution to the empirical migration literature,
which so far has estimated migration costs under the assumption of zero borrowing.
To identify the model’s parameters, I use a combination of panel and cross-sectional
datasets that provide individual and household level information in Mexico and in the
U.S., including randomized variation in income induced by a policy experiment. This
truly exogenous variation allows the identification of income dependent borrowing limits
in a context where the preference for migration and thus the demand for credit may be
related to an individual’s earnings capacity. My results suggest that access to credit and
hence the ability to migrate is indeed strongly related to household income.
One prediction of the model is that the number of trips per migrant increases as
financial constraints at the origin are relaxed and migrants are better able to respond
to economic shocks. This contrasts with the prediction of models that abstract from
asset accumulation and financial constraints. Alternative explanations for a rise in repeat migration include initial information constraints about earning opportunities at the
destination that are reduced after a first migration has been undertaken. This is the
mechanism suggested in the recent paper by Bryan et al. (2014), who find a higher probability of consecutive rural-urban migrations in Bangladesh after the cost of an initial
trip has been covered. While I consider a relaxation of financial constraints a plausible
explanation in the Mexico-U.S. context, where income differentials are known to be large,
a definitive separation of the two mechanisms is an interesting avenue for future research.
Also in contrast to models abstracting from financial constraints, the prediction by the
38
model estimated in this paper that the overall emigration rate rises with origin incomes
is well in line with previous reduced form estimations.
The economic literature on temporary migration largely has focused on the effects of
economic outcomes in the host country on the decision to return. This paper suggests
that besides host country outcomes, economic conditions in a migrant’s country of origin
may have to be taken more strongly into account in future analyses of migrant behavior.
Furthermore, my findings that the selection of immigrants staying in the U.S. for longer
becomes more positive as origin country incomes increase imply that events in migrant
sending countries play an important role also for the impact of immigration on the host
country population. In particular, policies that raise incomes in the origin country are
thus likely to translate into a higher average fiscal contribution to the host economy by
an increasingly positively selected population of long-term immigrants. This is in stark
contrast with simpler static models, where in the presence of financial constraints, a rise
in origin incomes unambiuously leads to a more negatively selected immigrant population.
From a sending country’s perspective my results predict that such higher incomes may
well lead to a more than proportional increase in domestic consumption expenditure due
to repatriated savings of new emigrants who are likely to leave only temporarily.
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43
APPENDIX
A
Model Specification
The below details specifications of model components from Section 2, including the values
of parameters that are calibrated using outside information.
Functional form specifications. The probability of gaining dependent family is assumed to be given by
pf =1 (Ωit |fit−1 = 0) = Φ ψ0f + + gf =1 (ait ) ,
where Φ() denotes the standard normal cumulative distribution function, and gf =1 (ait ) is a
f+
f+
piecewise linear function of age with nodes at 30 and 50 years, and slopes ψa≤30
, ψ30<a≤50
f+
and ψa>50
. Similarly, the probability of losing dependent family is given by another
transformed piecewise linear function of age,
pf =0 (Ωit |fit−1 = 1) = Φ ψ0f − + gf =0 (ait ) ,
f−
f−
f−
and ψa>50
.
, ψ30<a≤50
where gf =0 (ait ) again has nodes at 30 and 50 years, and slopes ψa≤30
The probabilities of obtaining or losing a U.S. legal permit are assumed to be
pδ=1 (Ωit |δit−1 = 0) = Φ ψ0δ+ + gδ=1 (ait ) + ψeδ1 eit
and
pδ=0 (Ωit |δit−1 = 1) = Φ ψ0δ− + gδ=0 (ait ) + ψeδ0 eit ,
respectively, where again gδ=1 (ait ) and gδ=0 (ait ) are piecewise linear functions with nodes
at 30 and 50 years of age, and correspondingly denoted slope parameters. Finally, when
an individual is in Mexico, jobs are assumed to be found and lost with probabilities
w,M X
1[XitU S > 0]
λw (Ωit |eit−1 = nw, lit = M X) = Φ ψ0w,M X + gw,M X (ait ) + ψX
!
+ψsw,M X 1[sit = summer]
44
and
nw,M X
λnw (Ωit |eit−1 = w, lit = M X) = Φ ψ0nw,M X + gnw,M X (ait ) + ψX
1[XitU S > 0]
!
+ψsnw,M X 1[sit
= summer] ,
and when having migrated to the U.S. with probabilities
w,U S
λw (Ωit |eit−1 = nw, lit U S) = Φ ψ0w,U S + gw,U S (ait ) + ψX
Xit
!
+ψsw,U S 1[sit = summer] +
ψδw,U S 1[δit
= 1]
and
nw,U S
λnw (Ωit |eit−1 = w, lit = U S) = Φ ψ0nw,U S + gnw,U S (ait ) + ψX
Xit
!
+ψsnw,U S 1[sit = summer] + ψδnw,U S 1[δit = 1] ,
with linear splines gw,M X (ait ), gw,M X (ait ), gw,U S (ait ) and gw,U S (ait ) that all have nodes at
30 and 50 years of age, and correspondingly denoted slope parameters.
The location specific function relating age and U.S. experience to earnings is given by
y,M X
f M X (ait , XitU S ) = gay,M X (ait ) + ψX
1[XitU S > 0]
when an individual works in Mexico, and by
y,U S
f U S (ait , XitU S ) = gay,U S (ait ) + gX
(XitU S )
when working in the United States, with the piecewise linear functions ga,M X (ait ) and
ga,U S (ait ) having nodes at 20, 25, 35 and 50 years of age, and gX,U S (XitU S ) has nodes at
5 and 10 years of U.S. experience.
Migration costs are a function of age and may be different for household heads and
for the remaining family. They further include an extra cost Ccoyote if a household has
no legal permit to enter the U.S. The age specific part is specified as a piecewise linear
function of age, with nodes at 30 and 50 years of age, separately for heads and dependent
family.
45
Retirement benefits. Individuals are assumed to live until age aend = 75, which
corresponds to life expectancy in Mexico at the middle of my sample period in 2002
(World Bank, 2015). Retirement schemes in Mexico and in the U.S. are approximated
based on OECD (2007) data as follows: individuals retire at age aret = 65, with benefits
y ret (Ωit ) corresponding to a net replacement rate in Mexico of 37.9 percent (55.3 percent
in the U.S.) of potential earnings at age 64. If a migrant retires in the U.S., the retirement
benefits are a weighted average between Mexican entitlements and benefits from the U.S.,
with the weight toward U.S. benefits being the fraction of working life spent in the U.S.,
X U S /(65 − 16).
Interest rates and time preference. The biannual real interest on positive asset
holdings is set to rA≥0 = 0.02, while the real lending interest rate is set to rA<0 =
rA≥0 + 0.034, based on information from the World Bank’s (2015) World Development
Indicators. The biannual discount factor β is assumed to equal 1/(1 + rA≥0 ).
Borrowing limit. Households with a working age head can take up credit. They are
assumed to face two constraints to the maximum amount of debt, B(E[yitM X ], Ωit ), they
can hold: a debt limit that depends on retirement benefits (used as collateral) and which
becomes tighter towards the end of life to ensure full debt repayment, and one that
captures better access to credit by high-income households and is a linear function of
expected earnings, E[yit ], so that for ait < aret ,
!)
(
aend −aret +1
1
−
(1
+
r
)
A<0
.
B(E[yit ], Ωit ) = min b0 + by E[yit ], y ret (Ωit )
−rA<0
46
B
Moments Used for Identification
Identification and model fit are discussed in Sections 4.1 and 5.1, respectively. This
appendix provides further details. Table 6 lists the model parameters to be estimated
and the identifying moments more systematically. Figure 15 illustrates the fit to the
marginal distributions of the three dimensions of unobserved heterogeneity. It should be
noted that the model features four ex-ante heterogeneous types of individuals, and hence
has a hard time matching all ten targeted deciles of these distributions. Tables 7-14 list
the full set of empirical moments used in the estimation together with their simulated
counterparts and standard deviation.
Parameters
λe (Ω)
f l (a, X U S )
l
σu
pf (Ω)
pδ (Ω)
φlf
Ã0 , φc
sε (a)
C(Ω)
C f (Ω)
B(a, E[y M X ])
pdf of αli , πi
MMP weights
PROGRESA
weights
Identifying moments
fraction working, season last worked, and transitions into and out of employment by age, legal status, location, having been to the U.S. and season
log earnings by age, location and U.S. experience
standard deviation of log earnings residuals
transitions to and from having dependent family if being in Mexico by age
transitions to and from having U.S. visa by age, employment status and having
previously been to the U.S. with legal documentation
stock of assets/debt if in Mexico by family status and family location by age
stock of assets/debt if in Mexico by age, and annual savings and remittances
if in the U.S. by age, U.S. experience and employment status
number of U.S. migrations by age
annual fraction of household heads migrating to the U.S. by age and legal status
annual fraction of spouses migrating to the U.S. by age and legal status
loan amount taken within the past six months by age and randomized income
shock treatment
mean log earnings by location and quantiles of within-individual mean log
earnings residual by location,
having been to the U.S. by quantiles of mean log earnings residual in Mexico,
leaving the U.S. by quantiles of mean log earnings residual quantiles in the U.S.
fraction residing in the U.S. and quantiles of within-individual mean residual
from regression of location on age
quantiles of within-individual mean log earnings in Mexico
Table 6: Identification of model parameters
47
Dataset
MMP, MxFLS, SIPP
MxFLS, SIPP
MxFLS, SIPP
MxFLS
MMP
MxFLS, MMP
MxFLS, MMP
MMP
MMP
MMP
PROGRESA
MxFLS, SIPP
MMP
PROGRESA
Figure 15: Model fit: Unobserved heterogeneity
Model fit for the three dimensions of unobserved heterogeneity: The upper two panels
compare deciles of within-individual mean residuals from the auxiliary earnings regressions that identify f l (a, X U S ) in Mexico and in the U.S., i.e. a regression of log annual
earnings in Mexico on age indicators and an indicator of having been in the U.S. from
the MxFLS, and a regression of log annual earnings in the U.S. on indicators for age and
years since immigration. The bottom panel shows the fit for deciles of within-individual
mean residuals from a regression of an indicator for being in the U.S. in a given year on
age indicators from the MMP data.
48
Table 7: Migration outcomes by age.
Moment
share in U.S.
share in U.S.
share in U.S.
share in U.S.
share in U.S.
at
at
at
at
at
16 ≤ a < 25
25 ≤ a < 35
35 ≤ a < 45
45 ≤ a < 55
55 ≤ a < 65
Data
0.091
0.075
0.047
0.030
0.014
Std. err.
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
Simulation
0.088
0.064
0.030
0.018
0.020
share
share
share
share
share
in
in
in
in
in
U.S.
U.S.
U.S.
U.S.
U.S.
0.906
0.855
0.847
0.850
0.846
(0.008)
(0.006)
(0.007)
(0.011)
(0.020)
0.885
0.856
0.818
0.864
0.956
0.220
0.513
0.536
0.482
0.587
(0.016)
(0.011)
(0.011)
(0.012)
(0.015)
0.117
0.293
0.421
0.485
0.532
0.184
0.099
0.077
0.135
0.162
(0.016)
(0.009)
(0.010)
(0.015)
(0.027)
0.323
0.439
0.283
0.330
0.523
Regression of head migrating to the U.S. on:
1[16 ≤ age < 25]
0.042
1[25 ≤ age < 35]
0.036
1[35 ≤ age < 45]
0.019
1[45 ≤ age < 55]
0.008
1[55 ≤ age < 65]
−0.010
1[legal]
0.178
(0.002)
(0.001)
(0.001)
(0.001)
(0.002)
(0.003)
0.023
0.013
0.011
0.004
0.001
−0.001
Regression of spouse migrating to the U.S. on:
1[16 ≤ age < 25]
0.044
1[25 ≤ age < 35]
0.028
1[35 ≤ age < 45]
0.018
1[45 ≤ age < 55]
0.033
1[55 ≤ age < 65]
0.074
(0.010)
(0.005)
(0.006)
(0.009)
(0.015)
0.011
0.010
0.003
0.002
0.003
of
of
of
of
of
number
number
number
number
number
share
share
share
share
share
year
year
year
year
year
of
of
of
of
of
with
with
with
with
with
trips
trips
trips
trips
trips
by
by
by
by
by
family
family
family
family
family
at
at
at
at
at
16 ≤ a < 25
25 ≤ a < 35
35 ≤ a < 45
45 ≤ a < 55
55 ≤ a < 65
16 ≤ a < 25
25 ≤ a < 35
35 ≤ a < 45
45 ≤ a < 55
55 ≤ a < 65
in
in
in
in
in
U.S.
U.S.
U.S.
U.S.
U.S.
at
at
at
at
at
16 ≤ a < 25
25 ≤ a < 35
35 ≤ a < 45
45 ≤ a < 55
55 ≤ a < 65
Data moments obtained from the MMP. Simulation based on 20,000 individuals × 50 years × 2 seasons.
49
Table 8: Family and legal status transitions.
Moment
Data
Std. err.
Transition to having family (MxFLS):
1[16 ≤ age < 25]
0.429
(0.179)
1[25 ≤ age < 35]
0.553
(0.077)
1[35 ≤ age < 45]
0.372
(0.072)
1[45 ≤ age < 55]
0.269
(0.066)
1[55 ≤ age < 65]
0.283
(0.061)
Transition to not having family (MxFLS):
1[16 ≤ age < 25]
0.053
(0.024)
1[25 ≤ age < 35]
0.007
(0.005)
1[35 ≤ age < 45]
0.013
(0.004)
1[45 ≤ age < 55]
0.026
(0.004)
1[55 ≤ age < 65]
0.043
(0.005)
Simulation
0.719
0.736
0.228
0.043
0.042
0.005
0.001
0.001
0.004
0.029
Regression of transition to having a U.S. visa (MMP) on:
1[16 ≤ age < 25]
0.012
(0.024)
0.032
1[25 ≤ age < 35]
0.284
(0.022)
0.087
1[35 ≤ age < 45]
0.433
(0.023)
0.249
1[45 ≤ age < 55]
0.526
(0.023)
0.600
1[55 ≤ age < 65]
0.514
(0.024)
0.501
1[working]
0.369
(0.022)
0.030
Regression of transition to not having a U.S. visa (MMP) on:
1[16 ≤ age < 25]
0.020
(0.012)
0.014
1[25 ≤ age < 35]
0.015
(0.010)
0.011
1[35 ≤ age < 45]
0.009
(0.010)
0.010
1[45 ≤ age < 55]
0.002
(0.010)
0.008
1[55 ≤ age < 65]
0.002
(0.014)
0.009
1[working]
−0.002
(0.009)
−0.008
Data moments obtained from the MMP and the MxFLS as indicated.
Simulation based on 20,000 individuals × 50 years × 2 seasons.
50
Table 9: Employment in Mexico.
Moment
Data
Std. err.
Regression of working in Mexico on:
1[summer]
−0.018
(0.014)
1[16 ≤ age < 25]
0.946
(0.020)
1[25 ≤ age < 35]
0.956
(0.015)
1[35 ≤ age < 45]
0.948
(0.015)
1[45 ≤ age < 55]
0.898
(0.015)
1[55 ≤ age < 65]
0.770
(0.016)
Simulation
−0.004
0.863
0.866
0.826
0.751
0.593
Regression of season last worked∗ in Mexico on:
1[summer]
−0.637
(0.185)
−0.649
1[16 ≤ age < 25]
0.689
(0.208)
0.813
1[25 ≤ age < 35]
0.660
(0.195)
0.827
1[35 ≤ age < 45]
0.770
(0.207)
0.822
1[45 ≤ age < 55]
0.882
(0.190)
0.823
1[55 ≤ age < 65]
0.769
(0.190)
0.832
Regression of transition into work in Mexico on:
1[16 ≤ age < 25]
1.000
(0.335)
1.013
1[25 ≤ age < 35]
0.795
(0.087)
1.092
1[35 ≤ age < 45]
0.768
(0.066)
1.044
1[45 ≤ age < 55]
0.611
(0.057)
0.969
1[55 ≤ age < 65]
0.487
(0.046)
0.791
1[been in U.S.]
0.079
(0.108)
−0.162
Regression of transition out of work in Mexico on:
1[16 ≤ age < 25]
0.034
(0.055)
0.003
1[25 ≤ age < 35]
0.053
(0.013)
−0.006
1[35 ≤ age < 45]
0.057
(0.010)
0.007
1[45 ≤ age < 55]
0.080
(0.010)
0.056
1[55 ≤ age < 65]
0.160
(0.012)
0.183
1[been in U.S.]
0.036
(0.023)
0.087
* Dependent variable is an indicator taking value 1 if the last season
an individual has worked (excluding the current one). Data moments
obtained from the MxFLS. Simulation based on 20,000 individuals × 50
years × 2 seasons.
51
Table 10: Employment in the U.S.
Moment
Data
Std. err.
Regression of working in the U.S. (MMP) on:
1[legal]
−0.003
(0.013)
U.S. experience
0.001
(0.001)
constant
0.886
(0.007)
Simulation
−0.021
0.005
0.936
Regression of fraction of year worked in the U.S. (MMP) on:
1[legal]
−0.186
(0.010)
−0.037
U.S. experience
0.011
(0.001)
0.012
constant
0.855
(0.006)
0.829
Regression of transition into work in the
1[16 ≤ age < 25 ∩ winter]
0.500
1[25 ≤ age < 35 ∩ winter]
0.500
1[35 ≤ age < 45 ∩ winter]
0.308
1[45 ≤ age < 55 ∩ winter]
0.145
1[55 ≤ age < 65 ∩ winter]
0.034
1[16 ≤ age < 25 ∩ summer]
0.000
1[25 ≤ age < 35 ∩ summer]
0.157
1[35 ≤ age < 45 ∩ summer]
0.152
1[45 ≤ age < 55 ∩ summer]
0.075
1[55 ≤ age < 65 ∩ summer]
0.052
Regression of transition out of
1[16 ≤ age < 25 ∩ winter]
1[25 ≤ age < 35 ∩ winter]
1[35 ≤ age < 45 ∩ winter]
1[45 ≤ age < 55 ∩ winter]
1[55 ≤ age < 65 ∩ winter]
1[16 ≤ age < 25 ∩ summer]
1[25 ≤ age < 35 ∩ summer]
1[35 ≤ age < 45 ∩ summer]
1[45 ≤ age < 55 ∩ summer]
1[55 ≤ age < 65 ∩ summer]
U.S. (SIPP) on:
(0.115)
0.257
(0.048)
0.246
(0.052)
0.225
(0.044)
0.294
(0.035)
0.120
(0.145)
0.621
(0.046)
0.566
(0.048)
0.559
(0.036)
0.633
(0.030)
0.259
work in the U.S. (SIPP) on:
0.023
(0.013)
0.090
0.023
(0.004)
0.058
0.023
(0.004)
0.011
0.022
(0.005)
0.005
0.085
(0.008)
0.002
0.005
(0.009)
0.054
0.004
(0.003)
0.037
0.004
(0.003)
0.007
0.008
(0.004)
0.003
0.009
(0.008)
0.002
Data moments obtained from the MMP and the SIPP as indicated. Simulation based on 20,000 individuals × 50 years × 2 seasons.
52
Table 11: Earnings.
Moment
Data
Std. err.
Simulation
Regression of log annual earnings in Mexico (MxFLS) on:
1[16 ≤ age ≤ 20]
7.885
(0.093)
7.001
1[20 < age ≤ 25]
8.307
(0.045)
7.831
1[25 < age ≤ 30]
8.333
(0.032)
8.198
1[30 < age ≤ 35]
8.347
(0.029)
8.500
1[35 < age ≤ 40]
8.340
(0.028)
8.528
1[40 < age ≤ 45]
8.317
(0.029)
8.370
1[45 < age ≤ 50]
8.236
(0.031)
8.208
1[50 < age ≤ 55]
8.160
(0.035)
8.010
1[55 < age ≤ 60]
8.026
(0.039)
7.768
1[60 < age < 65]
7.933
(0.053)
7.536
standard deviation of residual
0.984
(0.023)
0.976
Regression of log annual earnings in the U.S. (SIPP) on:
1[16 ≤ age ≤ 20]
10.047
(0.135)
8.645
1[20 < age ≤ 25]
9.969
(0.058)
9.092
1[25 < age ≤ 30]
10.004
(0.052)
8.986
1[30 < age ≤ 35]
10.022
(0.052)
9.650
1[35 < age ≤ 40]
9.934
(0.056)
10.042
1[40 < age ≤ 45]
10.141
(0.057)
10.135
1[45 < age ≤ 50]
10.254
(0.062)
10.355
1[50 < age ≤ 55]
10.076
(0.066)
10.425
1[55 < age ≤ 60]
9.954
(0.077)
10.462
1[60 < age < 65]
9.520
(0.114)
10.515
1[5 ≤ U.S. experience < 10]
0.060
(0.054)
0.341
1[10 ≤ U.S. experience < 15]
0.149
(0.054)
0.032
1[15 ≤ U.S. experience]
0.285
(0.050)
−0.543
standard deviation of residual
0.747
(0.015)
0.796
Data moments obtained from the MxFLS and the SIPP as indicated.
Simulation based on 20,000 individuals × 50 years × 2 seasons.
Table 12: Assets and debt.
Moment
Data
Regression of log assets (MxFLS) on:
1[16 ≤ age < 25]
5.214
1[25 ≤ age < 35]
6.324
1[35 ≤ age < 45]
6.838
1[45 ≤ age < 55]
6.986
1[55 ≤ age < 65]
7.057
1[f amily]
0.000
Regression of log debt (MxFLS) on:
1[16 ≤ age < 25]
1[25 ≤ age < 35]
1[35 ≤ age < 45]
1[45 ≤ age < 55]
1[55 ≤ age < 65]
1[f amily]
4.202
4.437
4.656
4.626
4.612
0.026
Std. err.
Simulation
(0.190)
(0.174)
(0.173)
(0.172)
(0.173)
(0.168)
7.966
8.659
8.800
8.576
7.926
−0.409
(0.220)
(0.186)
(0.181)
(0.186)
(0.193)
(0.175)
5.720
5.957
5.926
5.892
5.464
0.181
Regression of log loan take-up during last 6 months (PROGRESA) on:
1[age > 40]
0.593
(0.288)
−0.524
1[PROGRESA treated]
0.349
(0.222)
0.342
1[age > 40 ∩ PROGRESA treated] −0.471
(0.354)
−0.219
constant
4.384
(0.168)
5.948
Data moments obtained from the MxFLS and PROGRESA as indicated.
Simulation based on 20,000 individuals × 50 years × 2 seasons.
53
Table 13: Unobserved heterogeneity.
Moment
Within-individual mean earnings
1. dec of mean earn res in MX
2. dec of mean earn res in MX
3. dec of mean earn res in MX
4. dec of mean earn res in MX
5. dec of mean earn res in MX
6. dec of mean earn res in MX
7. dec of mean earn res in MX
8. dec of mean earn res in MX
9. dec of mean earn res in MX
10. dec of mean earn res in MX
Data
Std. err.
Simulation
residual in Mexico (MxFLS):
−1.768
(0.012)
−1.934
−0.774
(0.012)
−0.558
−0.424
(0.012)
−0.154
−0.192
(0.012)
−0.107
−0.007
(0.012)
−0.059
0.168
(0.012)
0.114
0.329
(0.012)
0.585
0.505
(0.012)
0.652
0.719
(0.012)
0.699
1.341
(0.012)
0.764
Within-individual mean earnings
1. dec of mean earn res in US
2. dec of mean earn res in US
3. dec of mean earn res in US
4. dec of mean earn res in US
5. dec of mean earn res in US
6. dec of mean earn res in US
7. dec of mean earn res in US
8. dec of mean earn res in US
9. dec of mean earn res in US
10. dec of mean earn res in US
residual in the U.S. (SIPP):
−1.336
(0.012)
−1.224
−0.638
(0.012)
−0.500
−0.369
(0.012)
−0.332
−0.188
(0.012)
−0.219
−0.025
(0.012)
−0.142
0.114
(0.012)
0.051
0.241
(0.012)
0.445
0.408
(0.012)
0.549
0.629
(0.012)
0.621
1.046
(0.012)
0.719
Fraction having been to the U.S. (MxFLS):
1. dec of mean earn res in MX
0.068
2. dec of mean earn res in MX
0.063
3. dec of mean earn res in MX
0.045
4. dec of mean earn res in MX
0.059
5. dec of mean earn res in MX
0.042
6. dec of mean earn res in MX
0.045
7. dec of mean earn res in MX
0.044
8. dec of mean earn res in MX
0.067
9. dec of mean earn res in MX
0.053
10. dec of mean earn res in MX
0.045
(0.007)
(0.007)
(0.007)
(0.007)
(0.007)
(0.007)
(0.007)
(0.008)
(0.007)
(0.008)
0.021
0.076
0.047
0.061
0.054
0.212
0.322
0.265
0.270
0.312
Fraction staying in the U.S. for at least 1 more years (SIPP):
1. dec of mean earn res in US
0.555
(0.026)
0.884
2. dec of mean earn res in US
0.622
(0.026)
0.918
3. dec of mean earn res in US
0.599
(0.026)
0.954
4. dec of mean earn res in US
0.630
(0.026)
0.976
5. dec of mean earn res in US
0.598
(0.026)
0.981
6. dec of mean earn res in US
0.639
(0.026)
0.979
7. dec of mean earn res in US
0.637
(0.026)
0.996
8. dec of mean earn res in US
0.634
(0.026)
0.998
9. dec of mean earn res in US
0.640
(0.026)
0.999
10. dec of mean earn res in US
0.643
(0.026)
0.999
Data moments obtained from the MxFLS and the SIPP as indicated.
Simulation based on 20,000 individuals × 50 years × 2 seasons.
54
Table 14: Non-representative weights.
Moment
U.S. migration in the MMP:
1. res dec of being in US—age
2. res dec of being in US—age
3. res dec of being in US—age
4. res dec of being in US—age
5. res dec of being in US—age
6. res dec of being in US—age
7. res dec of being in US—age
8. res dec of being in US—age
9. res dec of being in US—age
10. res dec of being in US—age
Earnings in PROGRESA:
1. earnings decile in PROGRESA
2. earnings decile in PROGRESA
3. earnings decile in PROGRESA
4. earnings decile in PROGRESA
5. earnings decile in PROGRESA
6. earnings decile in PROGRESA
7. earnings decile in PROGRESA
8. earnings decile in PROGRESA
9. earnings decile in PROGRESA
10. earnings decile in PROGRESA
Data
Std. err.
Simulation
−0.087
−0.077
−0.066
−0.052
−0.043
−0.036
−0.028
−0.017
0.063
0.395
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
−0.081
−0.073
−0.064
−0.057
−0.052
−0.047
−0.044
−0.018
0.070
0.381
6.374
7.186
7.578
7.813
7.975
8.171
8.360
8.412
8.568
9.176
(0.010)
(0.010)
(0.009)
(0.011)
(0.010)
(0.009)
(0.009)
(0.056)
(0.010)
(0.011)
6.374
7.265
7.473
7.785
7.978
8.140
8.205
8.473
8.681
8.972
Data moments obtained from the MMP and PROGRESA as indicated.
Simulation based on 20,000 individuals × 50 years × 2 seasons.
55
C
Asymptotic Distribution of the Simulated Minimum Distance Estimator with Multiple Samples
The following derivation of the asymptotic distribution of the estimator used in this
paper extends results by Gourieroux et al. (1993) for the simulated minimum distance
estimator with one data source to the case where identification requires moments from
multiple datasets.28 The following assumptions need to be made:
Assumption 1. The different samples used are drawn independently. This implies that
any cross-sample moments are zero and most plausible weighting matrices W , including
the efficient ones, will be block diagonal, with a block Wς for each set of moments derived
from the same dataset ς.
Assumption 2. The criterion function to be minimized, Γ(ϑ) = D(ϑ)0 W D(ϑ) =
0
md − ms (ϑ) W md − ms (ϑ) , is differentiable and attains its global minimum at the
true parameter vector θ.
(θ) has full rank, which ensures identification of parameters θ
Assumption 3. ∂D(ϑ)
∂ϑ0
through the moments in D(ϑ).
Assumption 4. The moments targeted, md , are aymptotically normally distributed.
Assumption 5. Sample sizes Nς of the datasets used increase at a proportional rate
lim (Nς /N ) = λς ,
Nς →∞
N →∞
with N =
P
Nς and 0 < λς < ∞. This ensures that none of the samples is irrelevant
ς
relative to the others.
Assumption 6. Simulated sample sizes Nςs increase at a rate such that
lim (Nς /Nςs ) = nς ,
Nς →∞
Nςs →∞
with 0 < nς < ∞.
28
The derivation is similar to that of the properties the two sample IV estimator by Angrist and
Krueger (1992) and Arellano and Meghir (1992). Also related is the discussion by Singleton (2006) of
GMM estimation with time series data of unequal length.
56
Then, by the first order conditions for a minimum of the criterion function at the
parameter estimate θ̂,
∂Γ
∂ms0
(θ̂) = −2
(θ̂)W md − ms (θ̂) = 0,
∂ϑ
∂ϑ
or
∂D0
(θ̂)W D(θ̂) = 0.
∂ϑ
By the mean value theorem, for some θ̄ between θ̂ and θ,
D(θ̂) = D(θ) +
∂D
(θ̄) · (θ̂ − θ).
∂ϑ0
Substituting into the first order condition yields
θ̂ − θ = −
−1
∂D
∂D0
∂D0
(θ̂)W 0 (θ̄)
(θ̂)W D(θ).
∂ϑ
∂ϑ
∂ϑ
If the observed moment vector md consists of moments from several independently drawn
samples ς, and W is block diagonal as described above, Γ(ϑ) can be written as a sum
of the contributions to the criterion by the moments of each sample. Hence, by the first
order conditions,
X ∂Dς0
∂D0
d
s
d
s
0=E
(θ̂)W m − m (θ) =
E
(θ̂)Wς mς − mς (θ) ,
∂ϑ
∂ϑ
ς
where mdς and msς (θ) are vectors of observed and simulated moments from sample ς. So
one can write
h ∂D0
i
∂D0
X√
√ ∂D0
ς
ς
N
(θ̂)W D(θ) =
N
(θ̂)Wς mdς − E
(θ̂)Wς mdς
∂ϑ
∂ϑ
∂ϑ
ς
−
!
h ∂D0
i
ς
ς
(θ̂)Wς msς (θ) − E
(θ̂)Wς msς (θ)
.
∂ϑ
∂ϑ
∂D0
Then, under assumptions 4-6, this yields the asymptotic distribution for θ̂,
√
d
N (θ̂ − θ) −→ N 0,
∂D0
∂D
(θ̂)W 0 (θ̂)
∂ϑ
∂ϑ
−1
!
∂Dς0
∂D
ς
·
(θ̂)Wς var(mdς )Wς
(θ̂)
N (1 + nς )
0
∂ϑ
∂ϑ
ς
−1 !
0
∂D
∂D
·
(θ̂)W 0 (θ̂)
.
∂ϑ
∂ϑ
X
57
D
Structural Estimates
This appendix lists the full set of structural parameters estimated. I group these into
parameters governing family status transitions, legal status transitions, employment transitions in Mexico, employment transitions in the U.S., earnings in Mexico, earnings in
the U.S., preferences, migration costs, and the initial stock of assets and debt limits.
Table 15: Structural estimates of
family status transition parameters.
Parameter
ψ0f +
ψ0f −
f+
ψa≤30
Point estimate
−0.840
−1.570
−0.001
Standard error
(0.023)
(0.088)
(0.001)
f+
ψ30<a≤50
−0.084
(0.090)
f+
ψa>50
f−
ψa≤30
0.014
−0.067
(0.415)
(0.003)
0.019
(0.008)
f−
ψa>50
0.077
(0.033)
f−
ψ30<a≤50
Estimation by simulated minimum distance estimation, standard errors in parentheses.
Table 16: Structural estimates of legal status transition parameters.
Parameter
ψ0δ+
ψ0δ−
ψeδ+
ψeδ−
δ+
ψa≤30
δ+
ψ30<a≤50
δ+
ψa>50
δ−
ψa≤30
δ−
ψ30<a≤50
δ−
ψa>50
Point estimate
−3.063
−1.404
0.575
−2.712
0.033
0.076
−0.012
−0.024
−0.029
0.041
Standard error
(0.100)
(0.468)
(0.085)
(0.000)
(0.003)
(0.011)
(0.146)
(0.014)
(0.138)
(0.273)
Estimation by simulated minimum distance estimation, standard errors in parentheses.
58
Table 17: Structural estimates of
employment transition parameter
for Mexico.
Parameter
ψ0w,M X
ψ0nw,M X
ψsw,M X
ψsnw,M X
w,M X
ψX
nw,M X
ψX
w,M X
ψa≤25
nw,M X
ψa≤25
Point estimate
−1.537
−0.835
0.002
0.003
−0.725
−0.025
0.167
Standard error
(0.030)
(0.016)
(0.016)
(0.003)
(0.026)
(0.037)
(0.002)
−0.009
(0.001)
w,M X
ψ25<a≤40
−0.094
(0.002)
0.011
(0.001)
w,M X
ψ40<a≤55
−0.051
(0.002)
0.019
(0.003)
w,M X
ψa>55
nw,M X
ψa>55
−0.069
0.041
(0.017)
(0.009)
nw,M X
ψ25<a≤40
nw,M X
ψ40<a≤55
Estimation by simulated minimum distance estimation, standard errors in parentheses.
Table 18: Structural estimates of
employment transition parameters
in the U.S.
Parameter
ψ0w,U S
ψ0nw,U S
ψsw,U S
ψsnw,U S
w,U S
ψX
nw,U S
ψX
ψδw,U S
ψδnw,U S
w,U S
ψa≤25
nw,U S
ψa≤25
w,U S
ψ25<a≤40
Point estimate
−1.395
−3.978
0.896
−0.093
0.004
0.028
−0.022
0.021
−0.005
−0.019
Standard error
(0.024)
(1.906)
(0.015)
(0.872)
(0.001)
(0.013)
(0.035)
(5.583)
(0.000)
(0.119)
−0.009
(0.004)
nw,U S
ψ25<a≤40
0.011
(0.123)
0.020
(0.002)
nw,U S
ψ40<a≤55
0.011
(0.127)
−0.256
0.033
(0.140)
(0.040)
w,U S
ψ40<a≤55
w,U S
ψa>55
nw,U S
ψa>55
Estimation by simulated minimum distance estimation, standard errors in parentheses.
59
Table 19: Structural estimates of
earnings function parameters in
Mexico.
Parameter
X
αM
i
y,M X
ψa≤20
y,M X
ψ20<a≤25
y,M X
ψ25<a≤35
y,M X
ψ35<a≤50
y,M X
ψ50<a
MX
σu
Point estimate
3.733
0.193
0.162
Standard error
(0.021)
(0.001)
(0.002)
0.004
(0.001)
−0.028
(0.001)
−0.038
0.361
(0.002)
(0.011)
Estimation by simulated minimum distance estimation, standard errors in parentheses.
Table 20: Structural estimates of
earnings function parameters in the
U.S.
Parameter
S
αU
i
y,U S
ψx≤5
y,U S
ψ5<x≤10
y,U S
ψx>10
y,U S
ψa≤20
y,U S
ψ20<a≤25
y,U S
ψ25<a≤35
y,U S
ψ35<a≤50
y,U S
ψ50<a
U
σu S
Point estimate
7.263
0.143
Standard error
(0.073)
(0.004)
0.044
(0.002)
0.035
0.090
(0.001)
(0.001)
−0.112
(0.003)
−0.067
(0.002)
−0.051
(0.002)
−0.029
0.344
(0.005)
(0.010)
Estimation by simulated minimum distance estimation, standard errors in parentheses.
Table 21: Structural estimates of
preference parameters.
Parameter
S
πU
i
φc
φl6f=l
f
φl=l
f
sε0
sεa
f
Point estimate
0.968
0.627
Standard error
(0.008)
(0.002)
0.161
(0.008)
3.295
378.090
−1.434
(0.037)
(5.839)
(0.424)
Estimation by simulated minimum distance estimation, standard errors in parentheses.
60
Table 22: Structural estimates of
migration cost parameters.
Parameter
mc0
mca≤30
mc30<a≤50
mca>50
mcf0
mcfa≤30
Point estimate
4952.948
12.906
57.665
110.577
13090.514
15.673
Standard error
(84.604)
(2.251)
(1.965)
(0.013)
(1.420)
(0.000)
mcf30<a≤50
161.568
(52.790)
mcfa>50
Ccoyote
130.750
775.357
(0.000)
(27.993)
Estimation by simulated minimum distance estimation, standard errors in parentheses.
Table 23: Structural estimates of
borrowing constraint and initial
stock of assets parameters.
Parameter
B0
By
A0
Point estimate
8.632
0.702
26.530
Standard error
(7.256)
(0.004)
(0.724)
Estimation by simulated minimum distance estimation, standard errors in parentheses.
61