Manajemen | Fakultas Ekonomi Universitas Maritim Raja Ali Haji 768.full

Steffen Reinhold is an assistant professor at the University of Mannheim, Fellow at the Munich Center for the Economics of Aging (MEA), and a research fellow at the Danish National Centre for Social Research. Kevin Thom is an assistant professor at New York University. This paper draws on and replaces the MEA Discussion Paper 182–2009 “Temporary Migration and Skill Upgrading: Evidence from Mexican Migrants.” The code for replicating the data and results is available upon request. The current correspond-ing e- mail is kevin.thom@nyu.edu. The authors thank Robert Moffi tt, Tiemen Woutersen, Paul Romer, Jennifer Hunt, Martin Salm, Govert Bijwaard, and Christina Gathmann for helpful comments on this and the previous version of this paper. Also, they are grateful for the feedback offered by seminar participants at the Institute for Research on Poverty Summer Research Workshop, the CUNY Graduate Center, Oregon State University, the University of Mannheim, CERGE- EI, the meetings of the International Economic Association, the meetings of the Society of Labor Economists, and the meetings of the Verein für Socialpo-litik. Finally, they would like to acknowledge the excellent research assistance of Jacob Bastian and Nicole Hildebrandt.

[Submitted August 2011; accepted September 2012]

SSN 022 166X E ISSN 1548 8004 8 2013 2 by the Board of Regents of the University of Wisconsin System T H E J O U R N A L O F H U M A N R E S O U R C E S • 48 • 3

the Mexican Labor Market

Steffen Reinhold

Kevin Thom

A B S T R A C T

We present a theoretical and empirical analysis of the relationship between U.S. migration experience and earnings in the Mexican labor market. We use our model to analyze the effects of self- selection and endogeneity on OLS estimates of the return to migration experience in the Mexican labor market. Under plausible assumptions, OLS estimates provide a lower bound on the true average return to migration experience among return migrants. Using Mexican Migration Project (MMP) data, we fi nd a return to migration experience of about 2.2 percent per year. Our estimates are robust to the inclusion of proxies for unobserved skill. A comparison with patterns in the 1995 Mexican Population and Dwelling Count suggests that our results are robust across data sets and are driven by a relationship between migration experience and wages, not hours worked. We also explore the plausibility of multiple mechanisms that could explain this relationship. We fi nd the most evidence for the theory that individuals are acquiring occupation- specifi c work experience in the United States. The return to a year of occupation- specifi c migration experience is estimated to be as high as 8.7 percent for some occupations.

I. Introduction

This paper investigates the relationship between migration experience and earnings among return migrants in the Mexican labor market. Our analysis com-plements a growing literature assessing the effects of out- migration on the economies of migrant- sending countries. Two main concerns dominate research on this topic: the consequences of skilled migration (the “brain drain”) and the effects of remittances1_. However, if migration is temporary and migrants eventually return home, then out- migration might have an additional effect by upgrading the skills and raising the earn-ings of return migrants. We develop a theoretical model of return migration and skill upgrading to guide the interpretation of our empirical results. In particular, the model provides conditions under which OLS regression estimates provide a lower bound on the average causal effect of migration experience for migrants. We further explore the nature of skill upgrading by considering several mechanisms that might mediate this relationship including occupation- specifi c learning, knowledge spillovers in large urban areas, the acquisition of English skills, and legal status during migration.

We use data from the Mexican Migration Project (MMP) and the Population and Dwelling Count (1995) to document the relationship between past U.S. migration experience and the labor market earnings of return migrants in Mexico. Our baseline speci_fi cation suggests that each additional year of migration experience is associated with an increase in earnings of approximately 2.2 percent, everything else equal. We fi nd that the return to migration experience is at least twice as high as the return to age in the Mexican labor market at nearly every point in the life cycle.

A natural concern is that the observed relationship between earnings and migra-tion experience refl ects the self- selection of high- ability or high- skill individuals into return migration, or the endogeneity of length- of- stay in the United States. To assess the likelihood and consequences of such biases, we develop a model of temporary mi-gration with heterogeneity in ability or skill. Under plausible assumptions, the model suggests that our empirical estimates may understate the true effect of migration ex-perience on earnings. Furthermore, the model shows that extensive margin selection (where return migrants are placed in the skill distribution) does not bias OLS results once a dummy for any migration experience is included. Rather, the OLS estimates suffer from bias only if unobserved components of skill are correlated with accumu-lated migration experience within the group of return migrants.

Instrumental variables techniques and fi xed effects methods are two common strat-egies for addressing this kind of endogeneity. In an earlier working paper, we used macroeconomic shocks in the United States to instrument for accumulated migration experience, and estimated a very large return (around 9 percent) to migration experi-ence. However, the instruments were weak in many specifi cations and quite sensitive to the inclusion or exclusion of age controls. Furthermore, one might be concerned that U.S. macro shocks are correlated with Mexican macro shocks, and thus cannot be credibly excluded from the earnings equation. In the absence of credible instruments, one could address this question with panel data. Unfortunately, existing Mexican panel

1. See Docquier and Rapoport (2009) for a review of recent literature on the positive and negative conse-quences of skilled migration for human capital accumulation in sending countries. Rapoport and Docquier (2006) provide a survey of recent work on the economics of remittances.

data sets do not contain suffi cient information on return migrants to be useful.2 _While panel data with earnings observations before and after migration are not available, we can observe wage data from the United States for the migrants in our sample to con-struct a control for ability and unobserved skill. When we add this control to our basic specifi cation, our estimates are very close to the baseline. We argue that this exercise provides evidence against the proposition that the relationship between migration ex-perience and earnings is being driven by correlation between migration exex-perience and permanent unobserved skill.

Another contribution of the paper is to compare results on the returns to migra-tion experience across both the MMP and the Populamigra-tion and Dwelling Count Survey (PDC). While the MMP provides superior information on migration histories, the MMP only includes data on Mexican income (not wages). However, the PDC reports hours data that allow us to construct wage rates. When using comparable regressors and samples, we _fi nd very similar results in both the MMP and the PDC. Furthermore, the analysis using the PDC wage data reveals that our results primarily refl ect a rela-tionship between migration experience and wages, not experience and hours worked. The paper also contributes to the literature on migration and human capital accu-mulation by suggesting and empirically testing some possible explanations for the ex-istence of a return to migration experience. We fi nd evidence that occupation- specifi c job experience accounts for much of this return. The return to migration experience is largest for migrants who worked in occupations in the United States that match their current occupation in Mexico. Indeed, the return to a year of this kind of job- relevant migration experience is estimated to be a little less than 4.8 percent in the whole sample, and as high as 8.7 percent when restricting the sample to unskilled manufacturing workers. It is noteworthy that our basic estimate of the return to a year of job- relevant migration experience is nearly as large as our estimate of the return to education in our baseline specifi cations.

Another mechanism that could explain our results is the effect of exposure to urban labor markets. As documented by Glaeser and Mare (2001) and others, it could be the case that experience in large urban labor markets is more valuable than experience elsewhere because of greater knowledge spillovers that might occur in cities. The rich migration information available in the MMP allows us to test whether the return to migration experience is actually a return to urban labor market experience in the United States. However, we do not _fi nd evidence that urban migration experience is more valuable than nonurban experience.

We also test whether the return to migration experience is related to the acquisition of English skills. Data limitations prevent us from drawing fi rm conclusions here, but controlling for English ability does not substantially reduce the return to migration experience. This suggests that English language acquisition does not explain much of the relationship between migration experience and earnings. However, we do _fi nd that the return to migration experience is higher for those with some English skills. This is consistent with the idea that individuals who can more easily communicate while abroad might be better able to absorb skills while working.

2. For example, we attempted to use the Mexican Family Life Survey’s 2002 and 2005 waves to explore this question. This yielded a very small sample of individuals with nonmissing Mexican income data in 2002 and 2005 that accumulated migration experience between the two waves.

Just as English skills might allow migrants to interact more freely in U.S. labor mar-kets, one’s legal status while a migrant might also shape the opportunities that one has to accumulate skills while abroad. We fi nd evidence of a greater return to documented migration experience, and a greater propensity for documented migrants to acquire job- relevant work experience appears to drive this result.

II. Literature on Return Migration

and Skill Upgrading

There is a large literature on the determinants and effects of migration, and Mexican migration in particular. Hanson (2006) offers a comprehensive survey of the work on Mexico. Much of this literature addresses the selection of migrants observed in the United States. While our empirical work does not directly engage this issue, later we will place our results in the context of that literature (see the appendix). Rather, here we restrict our attention to the theoretical and empirical work on return migration and skill upgrading.

A number of studies, including Borjas and Bratsberg (1996), Dustmann and Weiss (2007), and Dustmann, Fadlon, and Weiss (2011), develop theoretical models of tem-porary migration in which migrants acquire additional skills while working abroad that are rewarded in the home country. If the return to such skill is suffi ciently high, then this mechanism provides an incentive for individuals to return home. As Domingues Dos Santos and Postel- Vinay (2003) argue, this effect of temporary migration may help to expand a source country’s human capital stock and increase its rate of eco-nomic growth. Mayr and Peri (2009) further link this mechanism to the literature on the “brain gain” by developing a model of return migration, skill upgrading, and endogenous schooling to analyze the conditions under which temporary migration opportunities can raise the education level of a sending country.

While there is an existing empirical literature on temporary migration and skill up-grading, it tends to focus on the European experience. De Coulon and Piracha (2005) analyze data from Albanian workers and fi nd that the return migrants in their sample are negatively selected on the basis of premigration earnings, but experience a wage premium as a result of temporary migration. Using Hungarian data, Co, Gang, and Yun (2000) conclude that time spent abroad improves the labor market performance of female migrants, but not the performance of male migrants. Barrett and O’Connell (2001) and Barrett and Goggin (2010) also _fi nd a premium for return migrants in Ireland.

While the high volume of recent intra- European migration certainly justi_fi es the attention paid to temporary migration and skill upgrading in Europe, relatively little research assesses the skill- upgrading hypothesis in the context of Mexican migration to the United States. Beginning with the Bracero guest worker program (1942–64), Mexico- U.S. migration has been distinguished by a high propensity for return migra-tion (Massey, Durand, and Malone 2003). Although much has been written on the development impact of migrants’ remittances in Mexico3_{, the possibility of skill} up-grading on the part of return migrants has not received much attention. The MMP 3. For examples, see Woodruff and Zenteno (2007) and Durand, Parrado, and Massey. (1996).

data contain very rich information about migration experience over the life cycle, which is valuable in exploring the return to migration experience. Zahniser and Green-wood (1998) use an early version of the MMP with fewer observations dominated by high- migration communities and _fi nd a large positive return to migration experience. Alternately, using data from the 2000 Mexican census, Lacuesta (2010) fi nds that migrants tend to earn about 7–10 percent higher wages than nonmigrants upon return-ing. However, Lacuesta does not fi nd that wages grow with experience, and interprets this as evidence that the return migrant premium re_fl ects self- selection rather than skill upgrading. While the Census data has the advantage of being nationally representative, it only provides data on the duration of the last trip to the United States taken within the last fi ve years. We fi nd that these data limitations have substantial consequences for the estimation of returns to migration experience when we censor the MMP data in a similar way.

III. A Simple Model of Temporary Migration

Our empirical analysis centers on OLS regressions of Mexican earn-ings on accumulated migration experience. A natural concern is that the self- selection of return migrants and the endogeneity of accumulated migration experience bias the OLS estimates of a return to migration experience. Here we present a simple theoreti-cal model to help guide the interpretation of the observed relationship between earn-ings and migration experience given this concern. We argue below that the primary challenge to interpreting the results of such a regression comes not from extensive margin selection (how return migrants compare to nonmigrants in terms of unobserved skill), but rather from intensive margin selection (how migration experience is cor-related with unobserved skill within the group of return migrants). Under plausible parameterizations, the model predicts that total accumulated migration experience should be negatively correlated with skill conditional on migration. This implies that OLS regression coef_fi cients will represent a lower bound on the true causal effect of migration experience on income. The model considered here builds on the temporary migration models of Dustmann (2003) and Dustmann and Weiss (2007).

Consider the following environment. There are two countries: the home country (h), and the foreign country (f). Individuals are endowed with a unit of continuous time, and they start life in the home country. An individual can only migrate at time t = 0, and chooses some fraction of time τ to spend in the foreign country. If the individual chooses τ = 1, then the individual is a permanent migrant. If the individual chooses 0 < τ < 1, the individual is a temporary migrant and returns home after τ units of time. Note that this model restricts immigrants to taking at most one migratory trip to the United States. In reality, many Mexican migrants engage in patterns of repeated circular migration involving multiple trips to the United States (see Massey, Durand, and Malone 2003; Thom 2010; Rendon and Cuecuecha 2010). While the assumption of a one- trip structure is needed to keep the theoretical analysis tractable, the model presented here can be thought of as an approximation to a more general multiple- trip model in which individuals choose the overall fraction of time that they spend abroad.

We assume that individuals differ in their level of permanent skill, s_i. We assume that this refl ects anything responsible for permanent differences in the productivity of

workers including innate ability and skills accumulated before migration. For the pur-poses of the model, s_i can be thought of as subsuming several components of skill, some of which will be observed in the data (such as schooling), and some of which will be unobserved. Skill is randomly distributed in the population, and we will allow some of the model parameters to depend on skill. We assume that wage rates in the home and foreign countries depend both on skill and on the amount of migration ex-perience that has been accumulated up to time t: w_c = w_c(s_i,τ_t) for c = h, f. There is an international wage gap, so w_f – w_h > 0. Furthermore, we assume that wages are in-creasing in both skill and migration experience in both countries: (∂w_c/∂s) > 0, (∂w_c /∂τ) > 0.

We allow the relationship between wages and migration experience to depend on baseline skill, and the nature of this dependence is theoretically ambiguous: (∂2_w

c /∂τ∂s)P0. For example, consider the return to migration experience in the home country. It could be the case that less- skilled workers gain more from such ex-perience. This could occur if the job opportunities for migrants in the foreign country are skewed toward low- skilled occupations. Experience as a cab driver is unlikely to be useful for a migrant who is qualifi ed to work as an engineer in his home country. Additionally, work experience in the foreign country might serve a remedial function if it provides low- skilled workers with opportunities to gain skills that only more- skilled workers can gain at home. For example, if more advanced capital equipment in construction or manufacturing is scarce at home and only more- skilled workers are able to gain experience using it, then low- skilled workers might have more chances to gain such experience by working abroad. Alternately, the return to migration experi-ence might be higher for more- skilled workers if jobs in the foreign country provide learning opportunities that are only useful for the skilled. A physician, engineer, or Ph.D. trained academic from a developing country might pro_fi t tremendously from the interactions with similar workers in a high- income country.

Given this wage structure, individuals choose an optimal duration of stay in the foreign country and a life- time consumption profi le, where we assume that the instan-taneous utility from consumption is given by u(c_t) = log(c_t). Migration enables higher consumption over the life cycle, but there exists a tradeoff because living abroad in-curs disutility of η per unit of time. In addition, if an individual migrates, he or she must pay a fi xed migration cost of λ(s_i). As argued by Chiquiar and Hanson (2005), the costs of migration might be lower for high- ability people if such individuals are more capable or ambitious. If there is a correlation between baseline skill and the cost of migration, we would thus expect it to be negative: (∂λ /∂s) < 0.

Given these assumptions, the individual’s decision problem becomes:

τ,_ct

max _{V =}

0 1

∫

log(c_t)e−δt_dt−

0

τ

∫

ηe−δt_dt s.t.

0 1

∫

c_te−rt_{dt =}

0

τ

∫

w_fe−rt_dt+

τ

1

∫

w_he−rt_{dt− λ1(τ> 0)} 0≤ τ ≤1

For simplicity, we follow Dustmann (2003) and assume that individuals do not discount future utility, and that the individuals can freely borrow and save at a real in-terest rate of 0 (δ = r = 0). In such an environment, consumption is fi xed at a constant

rate, c, over the life cycle. Furthermore, we also assume that wages in both countries have the following log- linear form:

(1) log(w_c(s_i,τ)) = γ₀c_(s i)+ γ1

cτ₊ γ

2

cτs i. Where γ₀c_(s

i) is an increasing function of si. We refer to the derivative of log- wages

with respect to migration experience as the return to migration experience. This is given by γ₁c₊ γ

2

c_{s for the wages of someone with baseline skill level s in country c.} Under these particular assumptions, the individual’s decision problem becomes: (2) max

τ log(c)− ητ

s.t.c = 1 γ1

f _{+ γ}

2

f_s[wf(s,τ)− wf(s, 0)]+ wh(s,τ)(1− τ)− λ(s)1(τ > 0).

The First Order Condition for an interior solution implies (∂c/∂τ)− ηc = 0. Implicit differentiation of this condition allows us to derive the relationship between optimal migration duration and baseline skill:

(3) ∂τ* ∂s =−

∂wf ∂s −

∂w_h ∂s ⎛

⎝⎜

⎞

⎠⎟ +(1− τ*) ∂2_w

h ∂s∂τ− η ∂

c ∂s ∂wf

∂τ − 2 ∂wh

∂τ ⎛

⎝⎜

⎞

⎠⎟ +(1− τ*) ∂2_w

h ∂τ2 − η ∂

c ∂τ ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥

A set of plausible assumptions on the model parameters allows us to predict that the sign of this partial derivative should be negative. First note that the derivative of con-sumption with respect to baseline skill is positive for everyone ((∂c/∂s) > 0) as long as migration costs do not increase with skill. Also, lifetime consumption should be increasing in τ for anyone who migrates ((∂c/∂τ) > 0 evaluated at τ*), or otherwise τ* is not optimal. These conditions allow us to sign the terms involving η (disutility of staying in the foreign country) as negative.

Neglecting the second order terms for a moment, ∂τ/∂s will be negative at the optimum if these two (suffi cient) conditions are satisfi ed. The fi rst condition is that [(∂w_f /∂s) – (∂w_h/∂s)] < 0 at the optimal duration, making the numerator of

Equa-tion 3 negative. Since s includes both observed and unobserved components of an in-dividual’s skill, it is dif_fi cult to verify that this condition holds on the basis of existing empirical evidence. However, the condition does seems to hold for the case of Mexico if one looks at important observable components of skill, such as schooling.4 _For ex-ample, hourly wage calculations presented in Hanson (2006) suggest that the US- Mexico wage gap is generally declining with education, at least for individuals with less than 16 years of schooling. Evidence for an international earnings gap that de-clines with skill is also found by Ambrosini and Peri (2012) .

The second condition is that the denominator of Equation 3 must be negative. Under the assumption that the optimal migration duration is small (approximately zero), the following condition ensures that the denominator of Equation 3 will be negative for an individual of skill s:

(4) (γ₁f _+γ

2

f_{s) <} 1+θ θ ⎡ ⎣⎢

⎤ ⎦⎥(γ1

h_+γ

2

h_s)+ (θ −1)2 θ

Here θ= (w_f /w_h) > 1. A full derivation of this condition is offered in the appendix. This condition essentially requires that the return to migration experience in the United States not be too much larger than the return to migration experience in Mexico. In-deed, for plausible parameter values, this will only be violated for extremely high rates of return to migration experience in the United States.5

In the model presented here, optimal migration duration is negatively associated with skill. The primary reason for this is that more- skilled individuals are assumed to face a smaller international wage gap. The opportunity cost of spending time abroad is higher for these individuals, and so they choose shorter durations. Under some al-ternate assumptions, this result becomes ambiguous. For example, if the disutility of spending time abroad is lower for more- skilled individuals ((∂η/∂s) < 0), then it will not be possible to sign ∂τ* /∂s with the assumptions made here.

We have also neglected the second- order terms in Equation 3. The prediction that our model makes about the sign of ∂τ* /∂s would become ambiguous if there are large increasing returns to U.S. labor market experience in Mexico ((∂2_w

h/∂τ

2_{) > 0} and large). In addition, we have to consider the cross- derivative (∂2_w

h/∂s∂τ*) = w_h(s,τ)(γ₂h₊₍₍γ

0

h₎′₊γ

2

hτ₎₍γ

1

h₊γ

2

h_{s)). If there are large complementarities between skill} and U.S. labor experience (if γ₂h _{> 0 and large), then this could make sign of ∂τ* /∂s} ambiguous as more- skilled workers would have an extra incentive to extend their stay. Note that this also implies that return migrants will be positively selected from the set of migrants, a pattern consistent with the empirical results of Ambrosini and Peri (2012) and Biavaschi (2010).

We proceed by assuming that wages are log- linear in their arguments, and that the parameters are such that (∂τ* /∂s) < 0 for an interior solution. In the population indi-viduals will choose to stay home, become permanent migrants, or become temporary migrants depending on their initial skill level. Figure 1 provides some numerical ex-amples that highlight how the optimal migration duration varies with baseline skill, which is drawn from the interval [0,1]. Panel A assumes some reasonable parameters that generate a pattern of behavior that is broadly consistent with the features of Mex-ican migration. Nonmigrants are drawn from both the lower and upper ends of the skill distribution. At the lower end, there is some group of individuals that either cannot afford to migrate (so lifetime resources under migration are negative), or who can af-ford to migrate but are better off not paying the cost of migration. At the upper end, there is a group of individuals that do not have a wage incentive to migrate since the international wage gap is declining in skill. For those who migrate temporarily, the 5. To give some sense of the strictness of this condition, consider males aged 23-27 with fi ve to eight years of education, a group with one of the highest migration rates in Mexico. The calculations in Hanson (2006) indicate that the US-Mexico wage ratio for this group is equal to θ = (8.19 / 1.80) = 4.55. In this case, the condition in Equation 4 requires γf_{(s) < 1.2γ}h_{(s) + 2.77. Thus, this condition requires that the return to}

migra-tion experience in the United States not be very much greater than the returns in Mexico. Suppose that the return to migration experience is 2 percent per year in Mexico. Since τ represents a fraction of a working lifetime, a hypothetical 2 percent return in Mexico per year of migration experience corresponds to γh _{= 1}

assuming a 50 year working life. In order for the condition in Equation 4 to hold in this scenario, it would need to be true that γf _{< 3.97, or that the return to migration experience be less than 8 percent per year in the}

United States. The suffi cient condition presented here is only violated if there are extremely large returns to migration experience in the United States.

amount of time spent abroad will vary negatively with skill as long as our maintained assumptions hold. There will generally be skill bounds S and S such that only indi-viduals with baseline skill levels in the interval _s∈[S,S] will _fi nd it optimal to mi-grate. The skill threshold S* further separates the group of migrants who permanently migrate from those that temporarily migrate. Panel B shows what happens to behavior if the returns to migration experience are shut down in both countries. Although this change in parameters induces fewer individuals to migrate, the same basic qualitative patterns present in Panel A continue to hold.

Panels C and D further highlight scenarios in which violations of our assumptions can result in a positive relationship between migration durations and baseline skill.

0 0.5 1

Baseline Skill

Optimal Migration Duration

0 0.5 1

(C) γh > 0 and large 2

(A) Baseline Scenario (B) No Returns to Experience

(D) η is declining in skill

0 0.5 1

Baseline Skill

Optimal Migration Duration

0 0.5 1

S S S 0 0.5 1

Baseline Skill

Optimal Migration Duration

0 0.5 1

S S S

0 0.5 1

Baseline Skill

Optimal Migration Duration

0 0.5 1

Figure 1

Numerical Examples of the Model Solution

Note: Unless otherwise noted, wages are parameterized as follows: w_h(s,τ) = exp(1.5 + 2s + 0.4τ), and w_f(s,τ) = exp(3.5 + 0.2s + 0.4τ). This generates an international wage gap that decline with skill, with foreign wages being about six to seven times home wages at low levels of skill, about three times home wages at intermedi-ate levels, and about 1.15 times homes wages at high levels. It is assumed that monetary migration costs are declining in skill: λ(s) = exp(3.91 − 5s). The disutility of being away from home is set at η = 1. In Panel B, returns to migration experience both at home and abroad are set to 0. In Panel C, it is assumed that the returns to migration experience at home are increasing in skill, so that w_h(s,τ) = exp(1.5 + 2s + 4sτ). Additionally, the disutility of being abroad is increased in this example to η = 2, and migration costs are increased to λ(s) = exp(4.61 − 5s). In Panel D, it is assumed that η is declining in skill, so that η(s) = exp(1.61 − 3.25s). Ad-ditionally, migration costs are lowered in this panel so that λ(s) = exp(3.69 − 5s).

Panel C describes a scenario in which the return to migration experience at home rises steeply with baseline skill. In this scenario, more- skilled individuals have an incentive to make longer temporary trips abroad. Likewise, if the disutility of spending time abroad is negatively related to skill, then the more- skilled will be observed completing longer stays abroad. Such a scenario is depicted in Panel D.

IV. Implications for Relationships in the Data

Consider a cohort of individuals who behave according to the model presented here, and suppose that we have cross- sectional data on this cohort at age t back in the home country. In this cross- section, we observe nonmigrants with skill levels in the set: S

nm = {si|si < Sorsi> S}. We also observe the temporary migrants who have returned by age t. Let s(⋅) represent the inverse of the optimal duration func-tion. Then the return migrants that we observe in the data have skill levels that fall on the interval S _{= [s(}⋅_{),S], and optimal migration durations that fall on the interval} T = [τ*(S),t]. Let M refer to the set of migrants returning by age t.

Suppose that we observe the log of earnings, y_i = log(w_h,i), where the true data generating process is given by the following log- linear specifi cation:

(5) y_i =γ₀h₊γ

0s h_s

i+ γ1

hτ i+γ2

h_s iτi

For simplicity, we ignore covariates and suppose that all skill is unobserved. Then such a data generating process will leave us with observations of log- earnings, and migration durations for those individuals that migrate. A natural empirical strategy to learn about the relationship between migration experience and earnings is to regress log- earnings on a dummy for any migration experience and a measure of migration experience (which is zero for nonmigrants):

(6) y_i =δ₀+δ

11(τi> 0)+δ2τi+ui

Where τ_i is the optimal migration duration chosen by individual i (we suppress the star notation here), and u_i is an error term. What do the OLS estimates identify in this case? The point estimates of the parameters in Equation 6 can be decomposed into the fol-lowing summary statistics of observables and unobservables (See the appendix for a derivation):6

(7) δˆ₀ = (y_i|_τ i=0)

(8) δˆ₁= (y_i|_i∈M)−(yi|τi=0)−(τi|i∈M)ˆδ2

(9) δˆ₂= γ₁h_{+ γ}

2

h_(s i|i∈M)

Avg. effect for return migs.

.

+γ

0s

h Cov(si,τi|i∈M)) Var(τi |i∈M)

Negative

+γ

2

h(τi|i∈M)Cov(si,τi|i∈M) Var(τi|i∈M)

Sign depends on γ₂h

6. Here (yi|i∈M) indicates the sample mean of y conditional on being a migrant. Similarly, Cov(si,τi|i∈M) indicates the sample covariance of skill and the optimal migration duration.

We can now give an interpretation to the OLS coeffi cients in this simple regression model. The coef_fi cient on U.S. migration experience, δˆ₂, has three parts. The _fi rst part refl ects the true average causal effect of U.S. labor market experience on wages in Mexico for return migrants, our main parameter of interest. The average effect on re-turn migrants could be higher or lower than the average effect for the whole population, depending on the sign of γ₂h _{and the pattern of extensive margin selection into return} migration. If there is negative to intermediate selection into return migration relative to the whole population (which is consistent with our _fi ndings and those of the previous literature), and if γ₂h _{> 0, then the true average return for the migrants in the sample will} be less than the population average. If this pattern of selection holds and γ₂h _{< 0, then} the average return for migrants will be greater than the population average.

The second and third terms in Equation 9 introduce bias in the OLS estimate of the average return to migration experience. Rearranging, we see that the bias- inducing terms equal (γ₀h_{s+ γ}

2

h_τ

i|i∈M)(Cov(si,τi|i∈M) /Var(τi |i∈M)). Given our assump-tions on the parameters, (Cov(s_i,τ_i|i∈M) /Var(τ_i |i∈M)) < 0 so the sign of the bias will depend on the sign of (γ₀h_{s+ γ}

2

h_τ

i| i∈M). This represents the average partial

derivative of log- earnings with respect to skill among return migrants, holding migra-tion duramigra-tions _fi xed. Intuitively, the relationship between skill and wages should be positive (even fi xing migration durations), making the OLS bias negative. However, if there is a suf_fi ciently large degree of negative complementarity between skill and mi-gration experience (γ₂h _{< 0 and large), then this average could be negative and the OLS} bias could be positive. Suppose that skill in the model were perfectly measured by observed years of education. Then we could get positive bias only if the coeffi cient on the interaction between education and migration experience were greater in magnitude than (1 / τ) times the coeffi cient on schooling itself. In later empirical results, we will fi nd that the estimated coef_fi cient on the interaction is far lower than this threshold value.

Furthermore, if we make the assumption that there is no heterogeneity in the return to migration experience, we get:

(10) δˆ₂= γ₁h_+γ

0s

h Cov(si,τi|i∈M) Var(τi|i∈M)

which indicates a negative bias. Our conclusion is that the endogeneity of τ is likely to bias the OLS estimate of δ₂ downward relative to γ₁h_{. Under the assumptions made} here, the model predicts that δˆ₂ will provide a lower bound for the true average effect of migration experience on the earnings of return migrants.

An important point related to the estimation of Equation 6 is that the return to mi-gration experience is identifi ed entirely from comparisons between return migrants. Indeed, the computation of δˆ₂ does not involve any data on nonmigrants when other covariates are excluded from the regression. When both a dummy variable for any migration experience 1(τ > 0), and the continuous experience measure τ are included, the coeffi cient on the dummy variable absorbs the difference in earnings due to the selectivity of migrants, since it is estimated by the difference in mean earnings be-tween return migrants and nonmigrants (adjusting for estimated returns to migration). The coef_fi cient on τ is still potentially biased, but only because migrants with different levels of skill choose different migration durations. Migrants could be selected from any portion of the skill distribution. They could be less- skilled or more- skilled, on average, than nonmigrants. However, as long as more- skilled migrants choose shorter trips, this generates a downward bias in the OLS estimate of γ₁h_{. In this sense, the bias}

does not result from the selectivity of return migrants, but from the endogeneity of accumulated migration experience.

V. Data and Descriptive Statistics

The Mexican Migration Project (MMP) is a collaborative research project based at the Princeton University and the University of Guadalajara.7 _{The data} collected by the MMP present researchers with the unique opportunity to observe earnings for particular individuals along with detailed migration histories. Each year, the MMP selects a group of Mexican communities and surveys a random sample of the households in each location. The MMP survey collects demographic and economic data on households and individuals, with a particular emphasis on migration experi-ence. The survey also requests a detailed, self- reported life history from household heads recording some economic, demographic, and migration variables for every year in their lives. These life histories record whether an individual migrated in a given year, how many months an individual spent in the United States, and what documents, if any, were used to migrate.

Our sample consists of male household heads aged 18–65 who were surveyed during the years 1987–2009, and who were in Mexico at the time of the interview. The MMP asks each household head to report his or her current occupation, and their income in Mexico. Although the income variable is reported at different rates (weekly, biweekly, monthly), we convert all income measures to monthly values throughout the paper. In order to interpret the income variable as a measure of earn-ings we only consider those individuals who are currently employed, and who are not self- employed and do not own a business. After imposing these restrictions, and dropping those individuals with missing values for important regressors, we also trim the data by dropping individuals in the top and bottom 1 percent of the monthly earnings distribution, and those return migrants in the top 1 percent of the migra-tion experience distribumigra-tion (where migramigra-tion experience is measured in years). After making these restrictions, our full sample consists of 6,200 men. For the descriptive statistics and throughout the paper, we de_fl ate earnings using CPI indices for Mexico and the United States (2000 base year) taken from the IMF’s International Financial Statistics series. The appendix provides a more thorough description of the data and the sample selection criteria.

We present summary statistics of log earnings and important characteristics of migrants and nonmigrants in Table 1. The fi rst pair of columns displays statistics for the full sample of individuals interviewed while in Mexico. This includes non-migrants and return non-migrants, but excludes individuals who have migrated but have not returned to Mexico. The average age for the full Mexican sample is about 40, and the average level of education is about 6.8 years. Most individuals are married (89 percent). A substantial fraction of individuals have some experience migrating to the United States (28.0 percent). The average log of real monthly earnings is about 8, while the average real monthly earnings in levels is roughly 3,596 pesos per month.

The second pair of columns reports summary statistics for nonmigrants, while the 7. See the MMP website at mmp.opr.princeton.edu

last pair of columns reports summary statistics for return migrants. Return migrants tend to be less educated, with an average number of years of education (5.54) that is more than a year and a half lower than the average education level of nonmigrants (7.29). This pattern is consistent the idea that return migrants are negatively selected compared to nonmigrants. The average earnings of return migrants is about 5 percent lower than the average earnings of nonmigrants.

Table 1 also presents some summary statistics related to the migration experience of return migrants. About 91 percent of return migrants have some experience as an undocumented migrant, while only 20 percent have any documented migration experi-ence. The migrants in our sample are thus predominantly engaging in undocumented migration. The average return migrant has accumulated about 2.63 years of experience in the United States, with about 2.18 years of undocumented migration experience, and about 0.45 years of documented experience.

The model presented in Section II suggests that if skill is negatively correlated with the Mexico- US wage gap but unrelated to other model parameters, then un-der quite general conditions there should be a negative relationship between skill and the accumulated migration experience of return migrants. Such a negative correlation would induce a downward bias in the OLS estimate of the return to a year of migration experience. To test this implication of the theory, we examine the relationship between education (an observable component of skill) and the accumulated migration experience of return migrants in Table 2. We are implicitly assuming that the pattern of correlation between observables and migration expe-rience is informative about the correlation between unobservables and migration experience. In Column 1, we regress migration experience on education and other controls. The point estimate suggests a weak negative relationship between educa-Table 1

Summary statistics

Entire Sample Nonmigrants Return Migrants

Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard Deviation

Age 40.44 11.53 40.30 11.60 40.80 11.32

Education 6.81 4.77 7.29 4.92 5.54 4.10

Married 0.89 0.31 0.87 0.33 0.93 0.25

Log earnings 8.00 0.59 8.02 0.58 7.97 0.62

Ever migrant 0.28 0.45

Ever undocumented 0.91 0.28

Ever documented 0.20 0.40

USExp 2.63 3.18

Undocumented experience 2.18 2.69

Documented experience 0.45 1.60

tion and migration experience. A one- year increase in education is associated with a decline in accumulated migration experience of –0.024 years. This relationship is not statistically signifi cant. To explore this a bit further, we add a quadratic term in education as a regressor in Column 2. Neither education coef_fi cient is precisely estimated, but the point estimates suggest a nonmonotonic relationship, with migration experience rising with education up to about _fi ve years, and there-after declining. For very low levels of education it thus appears that accumulated migration experience is positively associated with migration experience. However, we emphasize that this appears to hold only at the lowest levels of education. In Column 3 of Table 2, we restrict the sample to those with at least three years of ed-ucation, a group containing about 75 percent of the migrants in our main sample. In this subpopulation, there is a statistically signi_fi cant, negative relationship between education and accumulated migration experience. An additional year of education here is associated with a reduction in accumulated migration experience of about 0.0562 years.

The prediction of a negative relationship between migration experience and edu-cation weakly holds in the entire sample, and holds with much greater strength for the mass of individuals with three or more years of education. At the very least, we certainly do not fi nd clear evidence of a positive relationship between education and migration experience. Even the negative correlations that we _fi nd are rather small in magnitude, suggesting that the endogeneity of accumulated migration experience probably explains little of any correlation between migration experience and Mexican income.

Table 2

Migration Experience and Education

(1) (2) (3)

Age 0.202*** 0.210*** 0.224***

(0.055) (0.055) (0.069)

Age2 –0.226*** –0.229*** –0.243***

(0.068) (0.068) (0.089)

Educ –0.024 0.082 –0.056*

(0.032) (0.102) (0.031)

Educ2 _–0.007

(0.005)

Married –0.352 –0.360 –0.817

(0.619) (0.609) (0.759)

Sample Complete Complete Educ ≥ 3

Observations 1,673 1,673 1,262

R2 _{0.128 0.130 0.165}

Note: Stars signify the following: *** signifi cant at the 0.01 level, ** signifi cant at the 0.05 level, * signifi cant at the 0.1 level. Standard errors are reported in parentheses. All specifi cations include MMP community ef-fects which subsume time efef-fects.

VI. Empirical Results

A. Basic Patterns

Table 3 presents OLS estimates of the relationship between the log of monthly earn-ings in Mexico and U.S. migration experience. Each column adds an additional set of controls. Unless otherwise specifi ed, all regressions throughout the paper will include MMP community _fi xed effects that subsume calendar year effects. All regressions also make use of the sampling weights provided by the MMP. The main regressor of inter-est measures the number of years of migration experience (USExp). A dummy for any migration experience (US) is also included, and this absorbs the average difference in earnings between migrants and nonmigrants that is not accounted for by observables including the years of migration experience. Column 1 presents results when the only additional controls are Age and Age2 _{/ 100. The estimate of the coef}

fi cient on US sug-gests that the average migrant earns about 9.6 percent less in Mexico than the average nonmigrant. As demonstrated in Section I, the coef_fi cient on this variable partially refl ects the difference in the average skill level of return migrants and nonmigrants,

Table 3

Basic Regressions (Monthly Earnings)

(1) (2) (3) (4) (5)

USExp 0.020*** 0.022*** 0.022*** 0.024*** 0.038***

(0.008) (0.007) (0.007) (0.007) (0.013)

US –0.096*** –0.053** –0.055** –0.043* –0.082**

(0.028) (0.026) (0.026) (0.026) (0.042)

Age 0.045*** 0.040*** 0.039*** 0.032*** 0.039***

(0.005) (0.005) (0.005) (0.005) (0.005)

Age2 _{/ 100 –0.058*** –0.044*** –0.043*** –0.036*** –0.043***}

(0.006) (0.006) (0.006) (0.006) (0.006)

Educ 0.054*** 0.054*** 0.032*** 0.054***

(0.002) (0.002) (0.003) (0.002)

Married 0.049* 0.046* 0.048*

(0.026) (0.025) (0.026)

EducXUS 0.006

(0.005)

EducXUSExp –0.003*

(0.002)

Occupation dummies N N N Y Y

Observations 6,200 6,200 6,200 6,200 6,200

R2 _{0.238 0.372 0.372 0.436 0.373}

Note: Stars signify the following: *** signifi cant at the 0.01 level, ** signifi cant at the 0.05 level, * signifi cant at the 0.1 level. Standard errors are reported in parentheses. All specifi cations include MMP community effects, which subsume time effects.

and thus the selectivity of return migrants. The coeffi cient on years of migration ex-perience, USExp, is about 0.020 and highly signi_fi cant, suggesting that the return to a year in the United States (above any beyond the increase in age or general experience), is about 2 percent. This implies that the total return to a year of migration experience is more than double the return to age for all but the youngest individuals. Since ac-cumulated migration experience is negatively correlated with education within our group of return migrants, we would expect this OLS estimate to be biased downward if experience is also negatively correlated with unobserved skill. Given the assumptions made earlier, our theoretical model also predicts this pattern of bias, and thus suggests interpreting 2 percent as a lower bound.

The successive columns of Table 3 introduce additional explanatory variables to the basic regression that are likely to be correlated with unobserved skill. Column 2 adds years of education, which we expect to be highly correlated with unobserved skill. After introducing education, the coef_fi cient on the US dummy is cut nearly in half, refl ecting (on average) negative selection of return migrants relative to nonmigrants. The coef_fi cient on USExp rises slightly to 0.022, which is consistent with the theo-retical prediction of a negative correlation between optimal migration duration and unobserved skill. Overall, our results suggests patterns of selection into migration and return migration that are quite consistent with previous studies, especially Kaestner and Malamud (2010) and Fernández- Huertas Moraga (2011). The appendix offers a detailed discussion of how the patterns of selection that we fi nd in the data compare to those found in the existing literature.

Columns 3–4 add further controls for marriage and occupation (dummies), respec-tively. Looking across the _fi rst four columns of Table 3, one notices that the coef_fi cient on the US dummy in general falls as we add more and more controls that might be correlated with unobserved skill. This is expected, since in theory the coef_fi cient on US should be directly related to the average skill difference between return migrants and nonmigrants. However, the estimate coef_fi cient on USExp tends to rise as we add more controls. This is consistent with negative correlation between accumulated migration ex-perience and unobserved components of skill. When occupation _fi xed effects are added in Column 4, we estimate a return to migration experience of about 2.4 percent per year.

Looking across the speci_fi cations reported in Columns 1–4, the stability of the estimated coeffi cient on USExp is noteworthy. The coeffi cient rises, but not drasti-cally, with the inclusion of important controls that are likely to be correlated with the unobserved determinants of earnings. Thus, while USExp is endogenous, the results presented here suggest that the effects of endogeneity bias on our basic estimates may be limited. Since occupation is in part an outcome of education and work experience, we prefer a speci_fi cation that does not include occupational dummies. We thus take 0.022 as our baseline estimate of the return to migration experience above and beyond the return to age. There appears to be an economically substantial relationship between migration experience and earnings in the Mexican labor market.

Column 5 of Table 3 also adds an interaction between years of education and the two migration experience variables, US and USExp. Adding the interactions boosts the estimated coef_fi cient on USExp to 0.038, and there is a negative estimated coef_fi cient of −0.003 on the interaction between years of education and USExp. Less educated individuals appear to gain more from a year of U.S. migration experience than those

with more education.8 _{This is an interesting pattern in its own right, but it also suggests} that it is reasonable to assume, as we did earlier, that the return to migration experience does not signifi cantly increase with skill.

B. Results with U.S. Wage Data

If we had access to panel data on wages or income in Mexico before and after migra-tion to the United States, we could use tradimigra-tional _fi xed- effects methods to control for permanent unobserved components of skill. While the MMP data does not contain repeated observations of earnings in Mexico, we do observe data on the hourly wage rates that migrants earn on their last trip to the United States.9 _{We assume that wages} re_fl ect worker skill plus shocks to productivity in the United States. One can therefore use the wage in the United States as a noisy measure of skill, and include this in Mexi-can income regressions as a control for unobserved skill.

Although we could directly include the U.S. wage in the Mexican income regres-sions, we would like to try to reduce some of the noise in this measure of skill by elim-inating variation from observable shocks. To do this, we fi rst regress an individual’s last U.S. wage on a set of controls, and then add the U.S. wage residual as a regressor to our basic Mexican earnings specifi cation. For a subsample of return migrants, we observe complete data on the hourly wage rate and other control variables related to the last trip to the United States. We discuss the construction of this sample in the appendix. After dropping the top and bottom 1 percent of U.S. wage observations, we are left with 1,240 return migrants with U.S. wage data. In the fi rst column of Table 4, we report the results of regressing the real hourly wage rate in the United States on age, the square of age, education, accumulated migration experience, as well as dum-mies for year, U.S. state, interactions between year and U.S. state, and an individual’s community of origin in Mexico. All of these variables refl ect characteristics at the time of the last migration. While the coef_fi cient estimates from this regression are not of interest by themselves, we extract the residual from this regression as a measure of unobserved skill. In the next column of Table 4, we reestimate our basic Mexican earnings regression using only the 1,240 return migrants with U.S. wage data. Since we are restricting ourselves to migrants in this subsample, we drop the US dummy variable. With this smaller subsample of migrants, we estimate a return to U.S. migra-tion experience of about 2.3 percent, which is very close to the estimate obtained in the baseline specifi cation and reported in Column 3 of Table 3. In Column 3 of Table 4, we directly add the log of the real wage from the last migratory trip as a control. The coeffi cient on the log wage is small and imprecisely estimated, consistent with the idea 8. Earlier, we found that the negative relationship between education and migration experience was strongest for educated migrants. Indeed, for those with less than three years of education, there appears to be a positive relationship between education and migration experience. Thus, an alternate interpretation of the results in Column 5 is that the interaction term captures not heterogeneity in returns, but rather changes in the correla-tion between USExp and the unobserved components of income across education groups. However, when we restrict the sample to those with three years of education or more, we get very similar point estimates and again fi nd a decline in the return to migration experience as education rises.

9. The MMP asks individuals about the wages earned on the fi rst and last trips to the United States. We use the wage data for the last trip in this exercise for two reasons. First, we have many fewer missing observations for the last trip. Secondly, one might be concerned about recall error when asking retrospective questions about a number as specifi c as a wage rate. Using more recent wage data might lessen such error.

that the log wage by itself is a very noisy measure of underlying skill. In Column 4, we add the normalized U.S. wage residual (residual divided by the standard deviation of residuals) to the Mexican earnings speci_fi cation. The coef_fi cient on the U.S. wage residual suggests that a one standard deviation increase in the U.S. wage residual is associated with a 3.8 percent increase in earnings back in Mexico, and this estimate is signifi cant at the 0.10 level. This relationship suggests that the U.S. wage does contain information about an individual’s level of skill that is not captured by our observables. Crucially, when the U.S. wage residual is added, the coeffi cient on U.S. migration experience is virtually identical to the estimate in the previous column. If endogeneity were driving our results, we would expect the coeffi cient on years of migration experi-ence to drop substantially with the inclusion of a the U.S. wage residual as a control. This exercise provides some evidence against the claim that selection and endogeneity bias are driving our main results.

C. Comparison with the Population and Dwelling Count

Two further concerns naturally present themselves related to the empirical speci_fi ca-tions in Tables 3–4. First, it might be the case that the communities selected by the Table 4

Regressions with U.S. Wage Residual

Dependent variable

(1) Wage (U.S.)

(2) Earnings (Mexico)

(3) Earnings (Mexico)

(4) Earnings (Mexico)

USExp 0.015** 0.023*** 0.023*** 0.023***

(0.007) (0.009) (0.009) (0.009)

Age –0.024* 0.048*** 0.048*** 0.047***

(0.013) (0.014) (0.014) (0.014)

Age2 0.033* –0.054*** –0.054*** –0.054***

(0.018) (0.016) (0.016) (0.016)

Educ 0.022*** 0.046*** 0.045*** 0.046***

(0.006) (0.006) (0.006) (0.006)

Married 0.099* 0.153** 0.153** 0.156**

(0.056) (0.073) (0.074) (0.074)

U.S. wage (log) 0.012

(0.051)

U.S. wage residual 0.038*

(0.022)

Observations 1,240 1,240 1,240 1,240

R2 _{0.538 0.350 0.350 0.352}

Note: Stars signify the following: *** signifi cant at the 0.01 level, ** signifi cant at the 0.05 level, * signifi cant at the 0.1 level. Standard Errors are reported in parentheses. All specifi cations include MMP community ef-fects which subsume survey time efef-fects. In Column 1, we also include a full set of U.S. state and year efef-fects for the last migration, along with their interactions.

MMP are not generally representative of Mexico, or even of the states in which they are located. Secondly, the MMP is only able to provide data on monthly labor market earnings and not hourly wage rates. Thus, we might be concerned that the estimates presented in Table 3 do not reveal much about the effect of migration experience on productivity (as measured through wages), but rather refl ect a combination of the effect of migration on wages and hours worked. To assess these concerns, and more generally test the robustness of the fi ndings, we compare the patterns found here with those present in the 1995 Population and Dwelling Count.

The 1995 Population and Dwelling Count (hereafter abbreviated PDC) is a nation-ally representative survey that contains some questions on the amount of time that return migrants spent abroad before returning to Mexico.10 _{We defi ne our main PDC} sample by applying the same sample selection criteria used for the MMP sample. Specifi cally, we restrict our attention to male household heads, aged 18–65, who are employed and do not own a business. We would like to restrict the PDC sample so that it covers similar communities as those in the MMP. To do this, we initially restrict the PDC sample to only include those individuals that live in the same State- Community Size cells as those represented in the MMP.11

Table 5 presents summary statistics related to the PDC sample. While the detailed life- histories in the MMP allow us to construct a measure of total lifetime migration experience, the PDC contains a more limited set of migration questions. The PDC survey asks respondents if they have previously resided in a different location, and then asks individuals how long they resided in that previous location. We count as return migrants those individuals that indicate previously residing in the U.S., and we measure USExp in the PDC as the duration of stay in the previous location. It is note-worthy that there are substantially fewer return migrants in the PDC than in the MMP. While about 28 percent of the MMP sample has some past migration experience, only about 5 percent of individuals in the PDC are classifi ed as return migrants. Some of this gap is due to the fact that the PDC asks about the place of last residence, which could be a domestic location. Thus, if people move around in Mexico after returning from a trip to the United States, they will not be counted as return migrants. In the MMP sample, we can observe whether such internal migration takes place. Classifying post- return internal movers as nonmigrants reduces the fraction of return migrants in the MMP sample to about 22 percent.

Using the measure of US and USExp available in the PDC, we replicate our ba-sic regression in Column 1 of Table 6. The estimated coeffi cient on USExp is 0.015, which is imprecisely estimated and smaller than our baseline estimate of 0.022 from the MMP. Furthermore, the coeffi cient on the US dummy is now very close to zero, whereas it was negative in the MMP speci_fi cations. However, it may be inappropriate to directly compare the PDC estimates with those of Table 3, because the PDC and the MMP use distinct measures of migration experience. While we observe total migration experience in the MMP, we only observe migration experience accumulated on the last U.S. trip in the PDC. Furthermore, the PDC classi_fi es internal movers as nonmigrants. 10. The PDC is administered by the Mexican statistical agency INEGI (Instituto Nacional de Estadística y Geografía). We use the version made available by IPUMS International (Minnesota Population Center 2011) 11. In both the MMP and the PDC, we observe the Mexican state that an individual lives in as well as the size of their community. In the PDC, we observe a categorical variable that indicates the following com-munity sizes: < 2,500; 2,500−14,999; 15,000−19,999; 20,000−99,999; ≥ 100,000.

In Column 2 of Table 6, we estimate our basic specifi cation with MMP data, but now we impose the two kinds of measurement error that are present in the PDC’s USExp variable on our preferred measure in the MMP. That is, we only consider experience form the last trip, and we code internal movers as nonmigrants. When we do this, we get results that are quite consistent with those from the PDC data. The estimated coef_fi cient on USExp is smaller and insigni_fi cant (0.011), and the coef_fi cient on US is very close to zero. The measurement error present in the PDC’s measure of migration experience thus seems to decrease the precision of estimated coef_fi cient on experience, and perhaps induce a downward bias. The lack of precision could also be due to the smaller number of return migrants in the PDC sample relative to the MMP sample. If the MMP data is any guide, then the 0.015 estimate is probably a lower bound of the return to migration experience in the PDC data.

In Column 3 of Table 6, we expand our PDC sample to include all of Mexico. In this sample, we estimate a return to migration experience of 2.3 percent which is sta-tistically signifi cant at the 0.05 level. Again, this may be a lower bound on the return to migration experience given the presence of measurement error described above. Nevertheless, it is interesting that we get a return to migration experience here that is very similar in magnitude to our basic MMP estimate of 2.2 percent. In Column 4, we try to assess whether this relationship between migration experience and earnings is still present when we look at the log hourly wage as the dependent variable. Here we estimate a return of about 1.9 percent that is imprecisely estimated. Some of the im-precision in the wage speci_fi cation could be due to noisy hours and income measures for those individual who are more marginal participants in the labor force. In Columns 5–6, we repeat this exercise but now restrict the PDC sample to those working at least 20 hours. Here we estimate a return to migration experience of 2.5 percent when income is the dependent variable, and 2.1 percent when the wage is the dependent variable. Both coeffi cient estimates are signifi cant at the 0.10 level or higher. Thus, it appears that most of the relationship between income and migration experience in the PDC data is coming through wages.

Table 5

Summary statistics—Population and Dwelling Count Survey

Entire Sample Return Migrants

Mean

Standard

Deviation Mean

Standard Deviation

Age 37.10 10.53 35.98 9.74

Education 7.30 4.81 6.72 4.32

Married 0.80 0.40 0.84 0.36

Monthly earnings 3232.95 2860.90 3252.16 3009.78

Return migrant 0.05 0.22

USExp (last trip) 1.82 2.36

T

he

J

ourna

l of H

um

an Re

sourc

es

Table 6

Comparison with the Population and Dwelling Count

(1) (2) (3) (4) (5) (6)

Dependent variable Earnings Earnings Earnings Hourly Wage Earnings Hourly Wage

Data source PDC MMP PDC PDC PDC PDC

Regions MMP MMP All All All All

Hours restriction None None None None ≥ 20 ≥ 20

USExp 0.015 0.011 0.023** 0.019 0.025** 0.021*

(0.011) (0.009) (0.011) (0.012) (0.011) (0.013)

US 0.000 0.007 –0.025 –0.011 –0.033 –0.005

(0.036) (0.027) (0.037) (0.040) (0.038) (0.039)

Age 0.038*** 0.040*** 0.037*** 0.039*** 0.037*** 0.039***

(0.004) (0.005) (0.003) (0.004) (0.003) (0.004)

Age2 –0.039*** –0.044*** –0.037*** –0.037*** –0.037*** –0.037***

(0.005) (0.006) (0.004) (0.005) (0.004) (0.005)

Educ 0.076*** 0.054*** 0.080*** 0.088*** 0.080*** 0.089***

(0.002) (0.002) (0.001) (0.002) (0.001) (0.002)

Married 0.051*** 0.046* 0.061*** 0.049*** 0.055*** 0.055***

(0.017) (0.026) (0.013) (0.015) (0.013) (0.014)

Observations 10,570 6,200 25,280 25,190 24,709 24,619

R2 _{0.526 0.369 0.500 0.464 0.506 0.488}

Note: Stars signify the following: *** signifi cant at the 0.01 level, ** signifi cant at the 0.05 level, * signifi cant at the 0.1 level. Standard errors are reported in parentheses. All specifi cations include MMP community effects, which subsume survey time effects.

One caveat to this exercise is that the PDC and the MMP samples cover differ-ent time periods. This raises the possibility that the results from the MMP and the PDC may not be comparable because of changes over time in the relationship be-tween migration experience and earnings. Whereas the PDC data represent a single cross- section from 1995, the MMP data come from survey waves throughout the in-terval 1987–2009. One could imagine restricting the comparison to MMP data from 1995, but since only a small number of communities are surveyed in each year, and community characteristics change over time, the resulting sample would be quite small and would be representative of very few communities. Without richer data, it is dif_fi cult to learn more about such time trends.

Although the different sampling frames and migration questions in the MMP and PDC make precise comparisons dif_fi cult, the exercises performed here suggest that the two data sets provide reasonably consistent evidence on the relationship between migration experience and income. Measuring experience only in terms of the last trip seems to decrease the precision of estimates and lower the estimated returns to migra-tion experience. In the larger namigra-tionally representative PDC sample, we get a return to migration experience that is comparable to our baseline MMP estimate, and in the presence of measurement error, this may be a lower bound on the average return.

D. Mechanisms 1. Relevant Experience

Our hypothesis is that the return to migration experience observed in the data refl ects a causal effect of migration experience on earnings, and not primarily a correlation between migration and unobserved characteristics that infl uence earnings. In the fol-lowing sections, we propose some mechanisms that might be generating or mediating such an effect, and test for empirical evidence on their presence. There are several possible reasons why a causal relationship might exist between migration experience and Mexican earnings. One of the most basic explanations is that individuals learn skills while working in the United States that are useful in the Mexican labor market. These skills could be occupation- specifi c (such as working with occupation- specifi c machinery), or they could be more general, such as English skills that might be useful in a wide variety of occupations and industries.12 _{Alternately, the process of} success-fully migrating and returning might make an individual more confi dent and motivated, increasing their productivity in a wide variety of tasks. Other stories, such as the role that migration might play in signaling quality to potential employers, could also be operative.

One advantage of the MMP data is that they provide a self- reported occupation for every year that an individual works, whether in Mexico or the United States. If human capital is strictly occupation- specifi c, then migration experience should only positively affect an individual’s productivity in Mexico if that individual worked in the same occupation in both the United States and Mexico. In order to test this, we construct a new measure of experience, which we call relevant experience. This is the total number of years that an individual spent in the United States working in an oc-12. Zahniser and Greenwood (1998) consider the possibility that there might be a higher return to migration experience if migrants had occupations in the United States that match their current Mexican occupations.

Reinhold and Thom 815

tion into migration out of Mexico (ii) positive selection among migrants into return migration. Thus, our evidence is consistent with much of the literature on the selection of migrants to the United States.

4. U.S. Wage Sample

The pers128 fi le contains responses to some detailed questions about an individual’s last trip to the United States. Speci_fi cally, questions are asked that allow the MMP to calculate an hourly wage on the last trip. In order to create a subsample that contains both a clean measurement of both income in Mexico and an hourly wage in the United States, we restrict ourselves to migrants in our main sample with nonmissing data on their wage in the United States, and nonmissing data about their education level at the time of their last trip to the United States. An individual’s level of education, their state of residence, and their occupation on the last trip are calculated as those values reported for the last year of the last trip in the life128 fi le. We exclude individuals if they report that their primary occupation on the last migration was either unemploy-ment or activity associated with being out of the labor force. Previously accumulated migration experience is a regressor in the U.S. wage equation. This is constructed from the life128 fi le by adding up the total number of years spent in the United States before the start of the last trip. After making these restrictions, we also trim the top and bottom 1 percent of the U.S. wage observations to create our fi nal U.S. wage sample.

Appendix A4

Additional Descriptive Statistics

Table A2

Summary statistics—Occupations and Relevant Experience

Mean

Standard Deviation N

Current occupation: agriculture 0.25 0.43 6,200

Current occupation: manufacturing (supervisors) 0.02 0.15 6,200 Current occupation: manufacturing (skilled) 0.21 0.41 6,200 Current occupation: manufacturing (operatives) 0.02 0.13 6,200 Current occupation: manufacturing (unskilled) 0.12 0.32 6,200

Current occupation: transportation 0.08 0.26 6,200

Current occupation: sales workers 0.05 0.23 6,200

Current occupation: service workers 0.03 0.18 6,200

Current occupation: other 0.21 0.41 6,200

RelevantExp (migrants only) 0.94 2.27 1,478

USExp- RelevantExp (migrants only) 1.79 2.70 1,478 (USExp- RelevantExp) > 0 (migrants only) 0.74 0.44 1,478

T

he

J

ourna

l of H

um

an Re

sourc

es

Table A3

Summary Statistics—Sample with Self- employment

Entire Sample Wage Workers

Self- Employed

(but not Entre.) Entrepreneurs

Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard Deviation

Age 41.16 11.39 40.46 11.53 42.65 11.00 44.00 10.16

Education 7.04 4.78 6.81 4.78 7.49 4.85 8.04 4.32

Log earnings 8.07 0.63 8.01 0.6 8.18 0.68 8.43 0.63

Ever migrant 0.28 0.45 0.28 0.45 0.31 0.46 0.24 0.43

USExp. (return migrants) 2.93 3.58 2.71 3.38 3.3 4.05 4.17 3.52

Self- employed 0.28 0.45

Entrepreneur 0.06 0.24

Total observations 8,536 6,238 1,815 483

Reinhold and Thom 817

Appendix A5

Robustness Exercises

In Table A4, we present some alternate specifi cations that test the robustness of our fi ndings to the inclusion of alternate control variables or speci_fi cations. Throughout the paper, we have included a quadratic in Age as a control for general work experi-ence. This allows one to interpret the coef_fi cient on U.S. migration experience as the return to migration experience above and beyond a return to experience in Mexico. Alternately, we could use the MMP data to directly measure Mexican labor market experience and include this instead of age. In Column 1, we add a quadratic in this measure (MexExp) instead of the age controls. Here we estimate a return to migra-tion experience of about 2.7 percent, which is substantially higher than our baseline estimate in Column 3 of Table 3. This is due to the fact that the coef_fi cient on USExp no longer measures an extra return to a year in the United States, but rather the total return. A year of Mexican Experience is found to have a return of a little less than 2 percent at most levels of experience, and this declines as the overall level of ence increases. Just as we can use the MMP data to calculate Mexican work experi-ence, we can also use it to calculate job- relevant Mexican experience. In Column 2, we revisit our speci_fi cation testing the importance of relevant experience (dropping the “Other” occupations), and now adding a quadratic in MexExp, and also including a variable measuring relevant Mexican working experience, in addition to the measure of relevant U.S. migration experience. Our estimates for the coeffi cients on migration experience and relevant migration experience are quite similar to those found in Table 7, suggesting that our basic results are robust to the use of Mexican work experience as a control instead of age. Interestingly, we _fi nd no evidence of an extra return to relevant Mexican work experience above and beyond the return to a generic year of Mexican work experience. This is a stark _fi nding, but one that is consistent with the idea that Mexican labor markets over the period of our sample were not providing the same kinds of opportunities for skill upgrading as could be found in the United States.

In Columns 3–4, we further test the robustness of the results to including alternate regressors. In Column 3, we try to add _fi ner controls for skill. Instead of adding a quadratic in age and a continuous measure of education, we discretize education into a categorical variable taking six possible levels (0–2 years, 3–5, 6–8, 9–12, 13–15, 16+), and we interact dummies for these categories with a quadratic in age. Adding this level of detail in our basic skill measurements results in an estimate of the coef-fi cient on migration experience of 0.023, which is slightly higher than our baseline estimate. In Column 4, we test to see if the presence of migration networks at the community level might be altering the return to migration experience. Specifi cally, we use the community- level MMP data to create a community migration rate for men, and interact this with migration experience (the main effect of migration networks is absorbed by the community _fi xed effects). It appears that there is a slightly smaller return to experience for those individuals from high- migration communities, but the coef_fi cient on the interaction term is not statistically signi_fi cant.

Table A4

Robustness Exercises

Specifi cation

(1) Mexican Experience

(2) Mexican Experience

(3) Age- Education

(4) Community

Mig Rate

USExp 0.027*** 0.018** 0.023*** 0.026*

(0.007) (0.007) (0.007) (0.015)

USExpxMigRate –0.009

(0.031)

RelevantExp 0.031**

(0.013)

US –0.061** –0.054* –0.050* –0.067

(0.026) (0.028) (0.026) (0.055)

USxMigRate 0.029

(0.139)

MexExp 0.017*** 0.013***

(0.003) (0.003)

MexExp2 –0.028*** –0.021***

(0.005) (0.005)

RelevantMexExp –0.000

(0.001)

Age 0.003 0.039***

(0.011) (0.005)

Age2 –0.009 –0.043***

(0.012) (0.006)

MigRate

Educ 0.055*** 0.027*** 0.054***

(0.002) (0.003) (0.002)

Married 0.060** 0.051* 0.053** 0.049*

(0.025) (0.028) (0.025) (0.026)

Observations 6,200 4,999 6,200 6,200

R2 _{0.367 0.355 0.377 0.372}

Note: Stars signify the following: *** signifi cant at the 0.01 level, ** signifi cant at the 0.05 level, * signifi cant at the 0.1 level. Standard Errors are reported in parentheses. All columns contain controls for education, mar-riage, and MMP community effects which subsume survey time effects.

Reinhold and Thom 819

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