University of Wisconsin-Madison Department of Agricultural & Applied Economics

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1 University of Wisconsin-Madison Department of Agricultural & Applied Economics Staff Paper No. 587 February 2018 Endogenous Selection, Migration & Occupation Outcomes for Rural Southern Mexicans By Esteban J. Quiñones and Bradford L. Barham AGRICULTURAL & APPLIED ECONOMICS STAFF PAPER SERIES Copyright 2018 Esteban J. Quiñones & Bradford L. Barham. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies.

2 Endogenous Selection, Migration & Occupation Outcomes for Rural Southern Mexicans Esteban J. Quiñones & Bradford L. Barham February 2018 University of Wisconsin-Madison, Department of Agricultural & Applied Economics; Center for Demography & Ecology & Abstract: This article integrates theory on migration and labor outcomes including attention to network effects and a novel econometric design to explicitly account for the selection-based dimensions of these endogenous relationships. We use a Mixed Nonlinear Endogenous Switching Regression to test the causal hypothesis that migration within Mexico and to the US affects occupation outcomes while also probing the role of endogenous selection. The dataset from Southern rural Mexico contains detailed information on migration, return migration, and occupation outcomes for working-age females and males. Our empirical findings are consistent with previous research that demonstrate heterogeneity in migration selection processes and gendered patterns of community migration networks and labor market outcomes. The value of an endogenous switching approach is highlighted by hypothesis tests that reveal outcomes that cannot be recovered in a standard two-stage sample selection estimation. The first is the negative and statistically significant evidence of endogeneity of migration and occupation for both females and males driven by unobserved heterogeneity, perhaps associated with nonpecuniary motives such as family reunification efforts. The other is unambiguous causal evidence that occupational outcomes are positively influenced by both migration and return migration, especially for females. On average, migration and return migration increase the probability of upward occupational mobility by 55 to 62% for females and 44 to 21% for males. Keywords: gender, migration, occupation, selection, and southern Mexico Acknowledgements: This research was also supported by training grant T32 HD and core grant P2C HD047873, awarded to the Center for Demography and Ecology at the University of Wisconsin-Madison by the Eunice Kennedy Shriver National Institute of Child Health and Human Development, as well as the University of Wisconsin-Madison Science and Medicine Graduate Research Scholars Program. We thank Stephen Boucher, Michael Carter, Brian Gould, Jenna Nobles, Dan Phaneuf, Christopher Woodruff, and participants of the 2016 Population Association of America Annual Meetings and the 2017 Midwest International Economic Development Conference, for their insightful comments.

3 I. Introduction Domestic and international migration have been essential components of livelihood strategies for rural Mexican households in response to persistent poverty and high levels of inequality (Chiquiar and Hanson, 2005; Hanson and McIntosh, 2010; McKenzie and Rapoport, 2007, 2010). As the New Economics of Labor Migration literature explores, rural households shift investment decisions towards migration based on resource constraints, market imperfections, networks, risk and shock coping strategies, and differential access to opportunities (Stark and Bloom, 1985; Rozelle, Taylor and de Brauw, 1999; Munshi 2003; Barham, Callenes, Gitter, Lewis, and Weber, 2011). Since the 1980s, migration choices in Mexico have also been significantly affected by major economic and policy shifts including stabilization and adjustment programs (Lustig, 2000), liberalization of trade and foreign investment (Hanson and Harrison, 1998), reforms of rural property rights and agrarian programs (de Janvry et al. 2015; Gordillo et al., 2015), economic crises, and social programs (Angelucci, 2015). In other words, rural migration is a complex phenomenon driven by a multitude of individual, household, community, and economywide factors that give rise to heterogeneity in terms of who migrates, why they migrate, where they go, what they experience, and whom else they can help. Occupation prospects for migrants and return migrants are critical drivers of migration choices and the subsequent welfare effects on individuals and their households and sending communities (Sjaastad, 1962, Munshi, 2003; Bertoli et al 2013; and Kaestner and Malamud, 2014). However, only a handful of migration studies directly examine the domestic (within Mexico) and international (primarily to the United States US) labor outcomes associated with migration (and return migration) for working-age populations from specific sending communities (Jasso and Rosenzweig, 1995; Akresh, 2006, 2008). Most studies focus only on earnings rather than occupation and compare migrant and nonmigrant populations (but omit return migrant considerations) using selection-based models or, sometimes, ignoring selection altogether. One practical reason for this knowledge gap is the difficulty in tracking migrants over time as they move back and forth between sending communities and international or domestic labor market destinations. For example, the household data associated with the evaluation of Progresa/Oportunidades does not include labor occupation outcomes for migrants, only total remittance inflows. In a strictly empirical sense, this article contributes to the literature with household data from southern Mexico that documents occupational outcomes of migrants and return migrants for a random sample of rural households and individuals and provides a unique platform for evaluating migration, return migration, and occupation outcomes jointly. More fundamentally, this article addresses a methodological issue in the migration and occupation literature related to how to model the endogenous selection process associated with these intertwined choices. Previous research has demonstrated the necessity of incorporating the inherent selection process associated with migration in order to avoid biased estimates of both migration decisions and multi-stage estimations of other key welfare outcomes (Borjas, 1987; Barham and Boucher, 1998; Chiquiar and Hanson, 2007; Mirsha, 2007; McKenzie and Rapoport, 2010; Bertoli et al. 2013, Kaestner and Malamud, 2014). None of these multi-stage estimations incorporate selectivity beyond including a selection correction term in a Heckman-style sample selection model. As such, they do not allow for explicit examination of the impact of the actual migration choice on the labor outcome of interest. In contrast, this study jointly incorporates the endogenous 1

4 migration choice and a sample selection term into the migration occupation analysis by using a non-linear endogenous-switching regression framework to support identification of both effects. This estimation strategy was developed by Rabe-Hesketh, Skrondal, and Pickles (2004, 2005) along with Miranda and Rabe-Hesketh (2006). It has been applied in the health economics literature by Bratti and Miranda (2010, 2011). This article extends its application to the migration occupation literature, and in the process arguably provides deeper insights into pecuniary and non-pecuniary factors shaping migration-occupation outcomes within Mexico and in the US. The theoretical foundation builds on a standard Roy Model of migration and occupation selection consistent with several recent studies (e.g. Chiquiar and Hanson, 2008; McKenzie and Rapoport, 2010) that include the role of networks in mediating migration decisions. Then, the theory is linked directly to an econometric design and empirical strategy that explore the endogenous selection aspects of migration, return migration, and occupational attainment. Unlike previous efforts, our approach allows for hypothesis testing regarding both the causal effects of observed migration and selection on occupation outcomes. The results provide nuanced interpretations on these measures that are not recoverable from previous estimation strategies. A secondary contribution is the extent to which we examine the occupation outcomes of migrants and return migrants; the extant literature rarely considers return migration and, to an even lesser degree examines, the occupation outcomes of both migrants and return migrants relative to non-migrants. Typically, only one is feasible due to data limitations, which leaves an incomplete understanding of the role that migration plays in determining the full range of labor market outcomes for working age people. There are two obvious advantages to explicitly assessing both migration and return migration. Most importantly, examining return migrants and their occupational outcomes distinctly from non-migrants overcomes the potential to otherwise lump them into the non-migrant category when comparing the impacts of migration on current occupation (or earnings) outcomes in the home community. Second, developing a clearer understanding of the occupational changes associated with migration (and return migration), separately for females and males, holds the potential for contributing to a better understanding of how labor markets work differently for them. Importantly, our methodology also sheds light on unobserved non-pecuniary motives (like family reunification) that might drive return migration choices and are likely under-emphasized in the literature, as demonstrated by Gibson and McKenzie (2011). In sum, this study explores the occupational outcomes of working-age females and males from southern Mexico during a period of dynamic change defined by increased labor mobility, state-led social protection, and human capital accumulation in a setting where migration is crucial for supporting household welfare. It addresses issues of endogeneity and selection head on (detection, correction and interpretation) on the basis of an integrated theoretical and econometric framework for both migrants and return migrants, and develops a set of hypotheses that relate migration to occupational outcomes in the community and beyond. Our core findings are as follows: First, the importance of measuring and controlling for selectivity of migration in an endogenous switching model on occupational outcomes is shown to matter empirically for both genders in some similar and heterogeneous ways. In particular, we find evidence of negative endogenous selection of migration (return migration) and occupation outcomes 2

5 for both females and males driven by unobserved heterogeneity, perhaps associated with family reunification efforts or other non-pecuniary motives instead of primarily economic motives. Second, having accounted for this selection we find unambiguous causal evidence that female occupational outcomes are positively influenced by both migration and return migration, ranging from an increased average likelihood of upward occupational mobility of 55 to 62%. Evidence regarding males is similarly positive for male migrants with an average marginal probability of 44%, but is weaker for male return migrants with an average marginal probability of 21% and inconsistent statistical significance across occupation categories. While the magnitude of the increased likelihood of upward occupational attainment as a result of migration and return migration varies across the occupation ladder, the positive effect persists across occupation categories, especially for females Third, migration within Mexico is more clearly linked to occupational mobility of migrants who have left the origin community, while migration to the US has more ambiguous and potentially dampening effects on occupational mobility of the rural migrant, especially for males who frequently migrate from agricultural work in their home communities to agricultural work in the US. 1 Fourth, while human capital characteristics and household endowments that are typically important in explaining occupational mobility e.g. education and wealth play a predictable role in enhancing female occupational mobility, this relationship appears to be stronger for women than for men (Lewis Valentine et al., 2017; Curran and Rivero-Fuentes, 2003). Finally, although the positive effects of return migration on occupational mobility exhibit similarities to those of migration, they are also more difficult to interpret perhaps because of the idiosyncratic (or unobservable) factors shaping return decisions and ensuing occupational outcomes. This is potentially suggestive of stronger non-pecuniary motives associated with return migration. The rest of this manuscript follows a familiar sequence. Section II reviews the literature on migration, selection, and occupation, and highlights our proposed contribution. Section III presents the theoretical model and hypotheses, while Section IV describes the econometric approach and identification strategy. Section V introduces the data, study context, and descriptive evidence. Section VI presents the empirical results and Section VII discusses the implications of our efforts. II. Related Literature Early economic research on labor market outcomes of Mexican migrant populations in the US focused on the effects of assimilation on the performance and wellbeing of both migrant and native populations. Drawing on 1970 US Census data, Chiswick (1977) found that while foreign parentage was associated with a small increase in earnings, this was not the case for Mexican-Americans with foreign parent, who experienced an 18% earnings deficit. Based on the same source of data, Chiswick (1978) showed that while immigrant earnings at the time of arrival were lower than those of the native population, they grew faster as immigrants built US labor market experience. 1 Ideally, it would also be possible to disaggregate this analysis by migration destination, namely, within Mexico versus the U.S., to tease out this pattern. Unfortunately, this is not feasible with our data because of a lack of sufficient observations in each occupation category for female and male migrants, return migrants, and non-migrants across locations. 3

6 Borjas (1985, 1987) analyzed US Census data from 1970 and 1980 to show that the growth in earnings for immigrants was overstated in cross-sectional analyses. He subsequently argues that this was due to a decline in the quality of immigrant cohorts over time. Although this explanation has not typically been corroborated (Lalonde and Topel, 1991; Duleep and Regets, 1992, 1997a,1997b; Chiswick, 1999; Chiquiar and Hanson, 2005; Mirsha, 2007; McKenzie and Rapoport, 2010), his work did serve to highlight the critical role of selection in migration and hence labor market outcomes. Most of the subsequent attention to selectivity concerns in the migration and labor market literature has been applied to migration and earnings comparisons rather than to migration and occupation outcomes. Perhaps the one major exception to that characterization is the article by Jasso and Rosenzweig (1995), where they compare occupation outcomes for employment-preference and family-preference migrants in a study of occupation mobility for legal immigrants in the Immigration- Naturalization Cohort (INC) dataset. Their finding of no significant differences between these groups may be explained by migrant-quality screening on the part of the receiving families living in the US, as well as their existing access to social and employment networks. Meanwhile, drawing on data from the 1989 and 1992 Legalized Population Surveys (LPS), Powers, Seltzer, and Shi (1998), as well as Powers and Seltzer (1998), describe a pattern of substantial upward mobility in terms of earnings and labor outcomes for undocumented Mexican migrants who became legal permanent residents in the US. They also find that this upward trajectory was typically slow, strongest prior to legalization, and often limited to men working in select industries. More recently, Akresh (2006, 2008) explored the relationship between migration and labor market outcomes in the US with longitudinal data from the New Immigrants Survey Pilot (NIS-P, 1996 cohort) and the ensuing New Immigrant Survey (NIS, 2003 cohort). Akresh s work focuses on the occupation trajectories of legal migrants over time as they assimilate and receive green cards. Within this subset of migrants, she finds evidence of considerable occupation downgrading, particularly among the high-skilled migrants from Latin America and the Caribbean (LAC) motivated by family reunification (2006). For a larger sample of legal migrants in the US, Akresh (2008) demonstrates that legal migrants in the US experienced a U-shaped pattern of occupational change over time (i.e., downgrading following by recovery), similar to what Chiswick, Lee, and Miller (2003, 2005) found in Australian data. Akresh attributes the bulk of this recovery to the accumulation of US labor market experience. Oddly enough, neither the studies by Akresh and Chiswick nor the vast majority of the aforementioned research (with the notable exceptions of Jasso and Rosenzweig, as well as Munshi) explicitly address selection and endogeneity issues, which are inherent in migration and complicate analysis of occupation outcomes due to the bias they introduce. 2 In addition to the selection results presented by Chiquiar and Hanson (2005) and McKenzie and Rapoport (2010), Kaestner and Malamud (2014) confirm the salience of selection in the migration process, particularly with respect to age, gender, education, and origin location, but not cognitive ability and health. Thus, this paper s focus on occupational outcomes in a model that explicitly addresses both the endogenous and selection properties 2 Akresh (2006) does test for the robustness of ordinary least squares (OLS) estimates via instrumental variable two-stage least squares (IV-TSLS) approach designed to address endogeneity, though the results are not presented and the exclusion restriction is not credibly satisfied. 4

7 of migration is a first. It is also worth highlighting some recent efforts to examine occupational mobility among return migrants. Conceivably, migrants who accumulate financial and human capital while abroad are better positioned to attain superior labor market outcomes at home (in terms of occupations or earnings), which may result in positive productivity spillover effects (Carletto and Kilic, 2011). However, analyses of return migration are especially complicated as they not only require dealing with the endogenous selection involved in who chooses to migrate in the first place, but also the selection process in which migrants decide to return instead of staying abroad. This multi-stage, non-random process of intensified endogenous selection can be referred to as compound-selection. 3 On top of compound-selection, much like the study of migrants abroad, survey data rarely includes a satisfactory counterfactual (or comparison) group. As a result, the number of studies comparing the labor market outcomes of return migrants relative to non-migrants is limited. Co, Gang, and Yun (2000) offer one example using panel data from Hungary where they find that female return migrants experienced a considerable earnings premium (40%) relative to non-migrant women; no earnings premium was observed for male return migrants. Based on a cross section of data from Egypt, Wahba (2007) finds a sizable wage gap in favor of return migrants as compared to non-migrants (roughly 40% higher). De Vreyer, Gubert, and Robilliard (2010) demonstrate that a sizable wage premium existed for migrants returning from OECD countries to seven West African capital cities with a cross-section of data from , but not those returning from elsewhere. Drawing on 2000 census data from Mexico and US, Lancuesta (2010) concludes that return migrants enjoyed a 11% wage premium, though he noted that this was simply a reflection of the positive selection involved in the initial decision to migrate and posits that self-selection in return migration was not influential. In Albania, Carletto and Kilic (2011) demonstrate that previous migration increased the probability of experiencing occupation upgrading upon return, based on a cross-section of data from 2005, particularly when the experience abroad took place in Italy instead of Greece. 4 In 2013, Reinhold and Thom (2013) demonstrate a wage premium of 5% for migrants returning to Mexico from the US based on MMP data from (as well as other sources). Wahba (2015) recently revisited her work on Egypt from 2007 to show that earnings of return migrants were 16% higher than those for non-migrants, but that failing to control for compound-selection overstated the earnings gap by more than double. 5 Wahba s 2015 study, in particular, highlights the need to confront the selection dynamics in return migration decisions. Finally, Gibson and McKenzie (2011) examine migration 3 Various forms of compound-selection may be modeled. Although doing so would be unwieldy, one could consider the following five dimensions of compound-selection: (i) individuals decisions to migrate, (ii) households decisions to migrate entirely, (iii) individuals decisions to return, (iv) individuals lengths of migration, and, finally, (v) individuals decisions to engage the labor market. 4 Carletto and Kilic aim to control for compound-selection with and instrumental variable (IV) approach. They include (i) instruments measuring Italian and Greek language proficiency to predict migration and (ii) an instrument measuring the number of children age zero to five in the origin household at the source location (at the time of return or no return) to predict return migration. We adopt a similar approach to implicitly address compound selection when analyzing return migration. 5 Wahba (2015) strives to control for compound-selection in terms of: (i) individuals decisions to migrate, (ii) individuals decisions to return, (iii) individuals decisions to engage the labor market, and (iv) individuals occupation choices. Wahba refers to this as quadruple selection. 5

8 and return migration among the best and the brightest from three Pacific Island countries and utilize a mix of stated and revealed preference data to illustrate the importance of nonpecuniary factors (related to job, family, and community satisfaction) in shaping choices. As summarized above, most previous research find a positive association between migration and labor market outcomes, especially over time. Furthermore, the body of research points to substantial heterogeneity in migration-occupation outcomes mediated by gender, migration motivation, location of migration, access to networks, length of journey, and so forth. However, most studies treat gender as sub-sample heterogeneity that can t quite be avoided, if at all, as opposed to a crucial determinant or a basis for separate estimations. Lastly, these studies indicate that the influence of selection is persistent, widespread, and far-reaching. As a result, explicitly addressing endogenous selection dynamics, is not merely an analytical refinement, but rather is crucial to obtain unbiased and precise estimates for females and males. We set forth next to offer a theoretical and econometric framework that addresses these issues explicitly, taking advantage of a dataset that although cross-sectional includes historical information on migration episodes and timing as well as current information on occupational outcomes for all household members whether they are present or away from their home communities. We use individual and household information to incorporate the types of explanatory factors that inform the New Economics of Migration literature. Consistent with previous research, we use community migration rates to account for network factors and to provide exclusion restrictions for the initial migration (first) stage regressions. While these variables may be subject to critique, they are not strictly necessary to identify the model, because the non-linearity of the econometric structure is technically sufficient the community migration rates, which reflect the theory, therefore primarily serve to improve identification. We account for selectivity concerns through an innovative Heckman-like two-stage migration and occupation framework, namely a Mixed Non- Linear Endogenous Switching Regression. We then exploit this estimation procedure to examine the direct causal impacts of individual migration choices and experiences while also controlling for endogenous selection associated with migration and occupation. These features extend the extant literature, but as a proviso we note that we do not explicitly incorporate compound selection processes in the return migration analysis. III. Theory III.a. Model Modeling the relationship between migration decisions and occupation outcomes requires an approach that explicitly features the presence of selection the non-random, unobservable, and endogenous process by which migrants with specific ability, ambition, and personality attributes self-select into migration. Roy s Model (1951) on the distribution of earnings over occupations provides a natural foundation for this exercise. Borjas (1987, 1991) applies the Roy Model to establish the conditions under which positive or negative selection are plausible, zeroing in on (i) the distribution of returns to skills in origin and receiving countries and (ii) the correlation of returns to skills over origin and receiving countries, as the influential mechanisms. 6 6 According to Borjas, positive selection will be observed when the receiving country has a wider income distribution than the origin country and there is a strong positive correlation between returns to skills across the two countries. On the other hand, negative selection will be observed when the origin country has a wider 6

9 Chiquiar and Hanson (2005) extend and enrich Borjas and Roy s contributions by modeling the migration and labor market outcomes while allowing migration costs to vary. In particular, they introduce the possibility that migration costs may be negatively correlated with skill or earnings to demonstrate that in some cases negative selection may actually be reversed (positive). Following Chiquiar and Hanson s approach, McKenzie and Rapoport (2010) further extend the model by incorporating the size of community migration networks, which have been shown to mediate the costs of migration (Massey, Goldring, and Durand, 1994; Munshi, 2003; and Cuecuecha, 2005), as a means to flesh out the heterogeneity in selection dynamics across the size of community migration networks and education levels. We build on the McKenzie and Rapoport (2010) approach, which emphasizes the roles of selection on observables and network size in arbitrating migration decisions and labor market outcomes. With that framework in mind, we also account explicitly for the influence of unobservable traits like ambition and ability. Consider the following wage equation for an individual (female or male):, (1) where w0 represents the (natural log) of the wage in an origin community in southern Mexico (subscript 0) in equation 1. This consists of the base return to labor in the absence of education (μ>0), the return to observable characteristics such as schooling ( >0), and the returns to unobserved characteristics including ambition or ability ( ). The analogous equations in the US (subscript 1) are presented in equation 2:. (2) Minimum wages are higher in the US so while returns to observable characteristics like school for the potential migrant are greater in Mexico so. 7 These assumptions are supported by Chiquiar and Hanson (2005), Cuechuecha (2005), and McKenzie and Rapoport (2010). The cost of migration can be represented in equation 3 by ( ), which is a function of an individual s observable characteristics, unobserved traits, as well as the size of the community migration network that the individual has access to. (3) Migration costs are assumed to be decreasing in observable characteristics like education, unobservable characteristics like ambition, and the size of the community migration network, such that. It is convenient to express migration costs in terms of the number of labor hours needed to cover the cost of migrating from southern Mexico to the US (i.e., time equivalent units), represented by in equation 4. Furthermore, time equivalent costs are also decreasing in education, ambition, and network size. For income distribution than in the potential host country and there exists a strong positive correlation between returns to skills across the two countries. Though insightful, these results do not necessarily hold when the assumption that costs are constant is relaxed. 7 Within Mexico, this relationship is likely to differ for earnings in domestic migration destinations (d) relative to origin communities and in the US. For instance, minimum wages may not differ substantially within Mexico ( ) while returns to observable education may be highest in domestic migration destinations ( ). 7

10 instance, a hyper-driven individual of high ability with an above average education and access to a larger migration network incurs a reduced migration cost and earns a higher wage in southern Mexico, thereby doubly reducing time equivalent costs. The following is distinct from Borjas formulation where time equivalent costs are assumed to be a constant:. (4) We express (natural log of) time equivalent costs ( ), which retain the aforementioned qualities of ( ), as follows:. 8 (5) An individual in southern Mexico applies the following decision rule when determining whether or not to migrate in order to maximize utility (equation 6). (6) Equation 6 is a valid approximation when wages ( ) are conceived of as the present value of a flow of future earnings, i.e. is small. Hence, the migration decision can be described accordingly in equations 7 and 8 for individual i:, (7). (8) In words, the migration decision rule states that if the net return of migrating, formulated as the wage abroad ( ) less the time equivalent cost of migrating ( ), is greater than the wage at the origin location ( ), the individual will migrate ( ). Otherwise, the individual finds the wage in southern Mexico to be advantageous and chooses not to migrate ( ). An individual can only pursue one wage and location at a time, eliminating the possibility of observing the counterfactual migration and wage outcome. 9 Thus, labor market outcomes for migrants, net of migration costs, can be expressed as: and labor market outcomes of non-migrants can be expressed as:, (9). (10) It is straightforward to consider how this data generation process may vary by gender (i.e., adding a g subscript throughout, in the simplest representation). For starters, even if we hold minimum wages constant for men and women, it is likely that the returns to observed characteristics like schooling and unobserved traits including ambition and ability differ substantially. As a result, wages will necessarily vary by gender. The costs of migrating are likely to differ for men and women as well. In particular, the cost of migrating, which is decreasing in the size of the community migration network, may be more responsive to the size of the community migration network for men or for women 8 Hence, time equivalent costs can also be written as, where. 9 Additional details of the model, including proofs, are fleshed out by Chiquiar and Hanson (2005) and McKenzie and Rapoport (2010). Having adopted a similar approach for this study, these details are not reprised herein in the interests of brevity. 8

11 depending on the destinations involved; not to mention the gender composition of the network. Even without taking into account gender- differentiated social costs associated with migration, it is easy to see how the decision to migrate can differ substantially by gender as a result of disparities in wages and costs. As such, gender is likely associated with distinct migration and labor market landscapes, as well as different migration and selection dynamics. 10 One aspect where this is particularly salient is the presence of gendered community migration networks, which imply substantially different costs and distinct selection on observables and unobservable for females and males. Although we do not extend our theoretic model to explicitly accommodate for gender heterogeneity, it is clear that exploring migration and occupation experiences of the population as a whole, instead of disaggregated by gender, is likely to obscure underlying and potentially rich and explanatory variation. III.b. Application & Implications This conceptualization of migration can be depicted graphically, as presented in Figure 1, which describes the (natural log of) wage profiles net of migration costs associated with observable characteristics. 11 In other words, Figure 1 describes equation 9 (conditional on equation 7) and equation 10 (conditional on equation 8) for migrants and non-migrants, respectively. The minimum wage that individuals can earn in an origin community in southern Mexico ( ) is represented by the diagonal (red) line. Migration is associated with a concave increasing net wage profile ( ), which is depicted by the solid (black) curve. Note that the inter-location minimum wage differential is not high enough to motivate individuals with exceedingly high migration costs (due to a lack of schooling, ability and motivation, or access to migration networks) to migrate. 12 Figure 1 illustrates that higher net wage profiles are associated with higher schooling, the key observable characteristic ( ) driving labor market outcomes in all (potential) locations. However, given the different shapes of wage profiles one can also see that migration is governed by lower and upper thresholds ( and ), each of which can be directly related to observable education levels. Additionally, as McKenzie and Rapoport (2010) point out, wage profiles are increasing in network size ( ), which shifts the solid curved and dotted steep lines upward through reductions in the cost of migration. Ambition and ability, i.e., unobservable characteristics ( ), also shift wage profiles upward in all (potential) locations. This feature is integral to our econometric strategy, which we describe in the next section. Thus, in this model it is apparent that shifts in net wage profiles, whether they be due to observable characteristics, network size, or unobservable traits, have bearing on the thresholds mediating the migration decisions. If we take to represent years of schooling, then the x-axis can be thought of as characterizing the range of education outcomes, which is instructive for assessing the selection with respect to observables that is inherent in the migration-labor relationship. For instance, in the case of international migration, negative, positive, and neutral (intermediate) selection of migrants from southern Mexico with respect to observable characteristics is determined by the distribution of observed schooling outcomes, as 10 Consistent with Jasso and Rosenzweig (1982), Lindstrom and Massey (1994), Duleep and Regets (1997a; 1997b), and Akresh (2008). 11 This visual exposition is adapted from McKenzie and Rapoport (2010). 12 Put explicitly:. 9

12 described by Chiquiar and Hanson (2005) and expanded upon by McKenzie and Rapoport (2010). In short, where the support and mass of the schooling distribution lies relative to lower and upper thresholds determines the type of selection on observables inherent in the labor migration process. 13 Fortunately, selection on observables can be accounted for in many studies, as information on the age and schooling of a (potential) migrant is readily available in individual level data. Figure 1: Net Wage Profile Trajectories & Thresholds The same cannot be said for unobserved yet influential traits ( ) like ability and ambition or objectives for migration, which may be indicative of an individual s type (i.e., low vs. high). However, the novel econometric approach that we adopt, which is described in the following section, also allows us to characterize the selection on unobservables 13 Negative selection takes place when the support of the observable characteristic distribution, take schooling for example, only overlaps with the upper migration threshold (i.e., the point where it is no longer profitable to migrate at high education levels). Then it is only advantageous for individuals with lower schooling to migrate. Positive selection takes place when the support of the schooling distribution only overlaps with the lower migration threshold (i.e., where it becomes profitable to migrate at low education levels); then it is only advantageous for individuals with higher schooling to migrate. Neutral (intermediate) selection takes place when the support of the schooling distribution overlaps with both the lower and upper migration thresholds ( and ); then it is only advantageous for individuals with intermediate schooling levels to migrate. Given a distribution of observable characteristics, McKenzie and Rapoport (2010) show that the type of selection can be heterogeneous, varying according to community migration network size and the interaction of those networks with levels of observable characteristics. The growth of a community migration network serves to reduce the costs of migration, which has the effect of lowering the aforementioned bottom migration threshold and increasing the upper migration threshold. As a result, more individuals at the low and high ends of the education distribution find it advantageous to migrate. In other words, the region of the schooling distribution where it is profitable to migrate becomes larger. 10

13 underlying the migration-labor outcome process. To the extent that observed characteristics ( ) and unobserved traits ( ) are (strongly) correlated ( ), accounting for factors like schooling may be sufficient to characterize and control for underlying selection processes. Under such circumstances, unobserved attributes ( ) merely have a modest influence or strictly contribute to a further intensified overall selection process. If, on the other hand, this is not the case, it will be advantageous to explicitly account for the role of unobservable traits ( ) mediating migration decisions and related labor market outcomes, particularly if migration and labor market outcomes are commonly correlated with unobservable characteristics. This is because selection on unobservables ( ) is likely to operate through two channels: (i) as direct selection on unobservables ( ) with respect to the distribution of ability, ambition, or more broadly type, not to mention reasons for migrating, as well as (ii) indirectly through shifts in migration thresholds associated with education or other observables ( ). As such, effort to carefully account for and characterize the negative, positive, or neutral (intermediate) nature of selection on unobservables, particularly when studying a phenomenon like migration where traits like ambition, ability, and family relationships are thought to be important, is warranted. This theoretical model is presented with both domestic and international migration in mind. It could be extended to distinguish between the two, but we do not as the qualitative implications of the model do not change. The model can also be extended to apply to cases of (voluntary) return migration, where an individual weighs whether or not utility will be maximized by remaining in the destination location or returning to the origin community. One important caveat for this model is that it does not account for forced return migration (or migration, in dire cases), which is a realistic consideration for many migrants. Labor market outcomes are ideally measured by a combination of employment status, wage ( ), net wage ( ), and overall earnings information, occupational attainment, working conditions, as well as job specific skill requirements. In this case, primary occupation status ( ) is the best measure of labor market outcomes available in our migration rich data. Accordingly, we adapt equations 9 and 10 for occupation ( ) conditional on migration equations 7 and 8, respectively. Although it is intuitive that a superior occupation should correlate with increased earnings, it is not necessarily straightforward to classify occupations; plus, income may not always correlate directly with occupation status. 14 Despite this caveat, occupation status clearly influences a broad range of outcomes including wages, earning, educational attainment, health status, and overall welfare. This research is, therefore, predicated upon the argument that the aforementioned theoretical model applies to occupational attainment without requiring any qualitative changes. Given this backdrop, we offer several hypotheses related to the migration choice and the relationship between migration and occupational outcomes. Previous studies and our model show that migration is positively selected for education and possibly unobservable factors. H1: we hypothesize that these observable selection outcomes may be stronger for females than for males, especially in the case of US migration, where males often migrate for low skills jobs including agricultural work. H2: with respect to return 14 Details of how occupation outcomes are indicative of wages are discussed in various other sections, particularly Section IV on the Econometric Strategy and Section V on Data and Descriptive Statistics. 11

14 migration, the effect of selection is less clear, though it is reasonable to expect that positive selection on unobservables could be lower than for migration or even possibly reversed if individuals are returning to resume family or community responsibilities rather than for occupational advance. H3: in terms of migration s impact on outcomes, we hypothesize positive causal effects in general for both genders, though again the strong potential for males to migrate to the US for agricultural work (lower on the occupational ladder) might reduce the strength of that positive casual effect. H4: controlling for unobservables, we expect return migration to exhibit a positive or perhaps ambiguous influence on occupation outcomes, because many return migrants will have more experience and skills to offer upon return but may face limited opportunities for that expression in their home community. IV. Econometric Strategy This section describes our empirical strategy for estimating the direct impact of migration and return migration on labor market outcomes in a manner that also explicitly accounts for selection (detection, correction and interpretation). We start by explicitly linking the theoretical Roy model with the familiar Heckman, two-stage approach that features a first stage model of the migration decision and a second-stage selectioncontrolled model of occupational outcomes. Occupational outcomes are categorical and ordered, which makes the second stage estimation non-linear. Because occupation is an outcome that we observe for all adults in the sample, whether they stayed in their village or migrated elsewhere, we can exploit both the full-observability of occupation outcomes and the non-linear specification to adopt an endogenous switching specification. This framework allows inclusion of both the selection coefficient on the migration outcome in the first stage and the observed endogenous switching migration outcome in the second stage. Recent health economics research (Bratti and Miranda, 2010, 2011) has deployed this strategy to examine the impacts of education on preventive behavior, specifically smoking intensity conditional on higher education attainment. Our application of this specification to the migration-occupation nexus is new, and it permits a deeper exploration of the role of migration and selection in labor market outcomes. IV.a. Heckman Selection & Endogenous Switching Methods In cases where selection is both inherent and influential in determining labor market outcomes, it is useful to specify a two-stage model. This is the case for both Heckman Selection and Endogenous Switching regressions. In the case of a classic Heckman procedure, the selection variable is observed for all observations while the outcome of interest is only observed for those who select in. In this framework, the selection variable is migration ( ) and the outcome of interest is the occupation outcome ( ) for individuals who migrated ( ). With an Endogenous Switching Regression (ESR) this setup is extended to include individuals who do not select in ( ) in parallel second stage equations as occupation outcomes ( ) are observed irrespective of migration; the first stage is unchanged. The ESR is an extension of the well-known Heckman sample selection technique (1978, 1979) that corrects for sample selection bias. Seminal presentations of ESRs include Amemiya (1973), Lee, (1978), Lee and Trost (1978), and Maddala (1983) Though far less popular than Heckman sample selection models, ESRs are not uncommon in agricultural and development economics literature. Examples include, van der Gaag and Vijverberg, (1988), Fuglie and Bosch, (1995), Barham and Boucher, (1998), Carter and Olinto, (2003), Marenya and Barrett (2009a, 2009b), 12

15 Consider the following exposition where equation 11 is the first stage or endogenous switching stage, which corresponds to equations 7 and 8 in the theoretic model, while equation 12 is the second stage focused on the occupation outcome of interest:, (11). (12) is a vector of individual characteristics mediating migration and labor market outcomes (such as age or experience and schooling); this represents the observable characteristics that serve as common influences of migration and labor market outcomes. Additionally, is a vector of household characteristics representing the economic unit s productive endowment (land and labor), access to capital, and engagement in income generating activities (agricultural and non-agricultural). A vector of indicator variables ( ) are incorporated to account for any systematic effects of age cohorts (subscript a) and states (subscript s) on migration outcomes., which is unique to equation 11, is a vector of historical community based measures to improve identification these are discussed in more detail in the next sub-section. is a vector of household and community-level measures characterizing the occupation landscape, which is distinctive to equation 12. This includes measures of household participation in local institutions and social programs, such as Oportunidades, that mediate occupation outcomes ( ), net of the factors that influence both migration decisions and labor market outcomes. The residual terms and, which are assumed to be normally distributed, represent unobserved factors that influence migration choices and occupation outcomes, respectively. If there is correlation between these unobserved factors, such as ability and ambition, then the error terms in equation 11 and 12 ( and ) will be correlated:. (13) Under these circumstances, standard econometric techniques yield biased results. However, as Heckman (1978) demonstrated, under normality it is feasible to correct for selection by incorporating the correlation between the residuals ( ) and the estimated inverse Mills ratio ( ) in the second stage for the selected sample; in effect, takes the place of in equation Comparable selection correction procedures are also at the heart of ESR models, where the endogenous switching that takes place between regimes is akin to non-random selection or sorting, whether the statistical models involve a traditional two-stage approach or simultaneous maximum likelihood optimization. While this enables consistent estimation of how individual characteristics mediating migration and labor market ( ) as well as the household and community-level descriptors of migration ( ) influence occupation outcomes, it does not allow us to directly test the effect of migration ( ) on occupation outcomes ( ). That is, measures of household participation in migration or community migration propensities can only partially and indirectly describe how individual migration decisions influence individual Taylor and Lopez-Feldman, (2010), Bratti and Miranda (2010, 2011), Floro and Swain (2013), and Abdulai and Huffman (2014). 16 The estimated inverse Mills ratio is, where is the standard error of the residual in the second stage occupation equation (13). Alternatively, the inverse Mills ratio can be thought of as being a function of the linear prediction of first stage, i.e. the predicted probability of migration. 13

16 occupation outcomes. In order to accomplish this, one of the main objectives of this paper, we turn to a related non-linear ESR method from the health economics literature. In addition to correcting for endogenous selection, this method also facilitates the consistent estimation of the (switching) migration variable ( ), which is the outcome in the switching first-stage and the regressor of interest in the second-stage occupation equation. The full details of this approach are discussed below. IV.b. Mixed Nonlinear Endogenous Switching Regression The Mixed Nonlinear Endogenous Switching Regression (MN-ESR) framework allows us to correct for endogenous selection, in a similar fashion to Heckman and conventional ESR techniques. Additionally, it enables us to directly test the impact of the endogenous migration switching term ( ) on the occupation outcome of interest ( ). As noted above, classic Heckman and ESR methods do not allow for the estimation of the selection or endogenous switching term. The MN-ESR method was developed by Rabe-Hesketh, Skrondal, and Pickles (2004 & 2005) for mixed response (also known as mixed level) frameworks to deliver consistent results for binary, ordinal, or Poisson ESRs via maximum likelihood estimation when responses are estimated jointly. These, and other related models, are commonly known as Generalized Linear Latent and Mixed Models (GLLAMMs). The details of the empirical strategy presented below closely follow the exposition by Miranda and Rabe- Hesketh (2006). We begin by reviewing the details of the migration switching stage, which is analogous to both the migration decision rule in our theoretical model (equations 7 and 8) and the first-stage of a conventional two-step estimation procedure (equation 11); the formulation below is identical to equation 11, but is reprised for the convenience of the reader. Although the MN-ESR estimation is solved simultaneously, instead of in stages, it remains convenient to think of the equations in stages or moments. The migration decision rule is the first moment of the MN-ESR and can be specified as a Probit for all observations at the individual level (subscript i). Equation 14 then serves as the migration switchingstage of the ESR that distinguishes between distinct migration regimes:. (14) In addition to the aforementioned observable individual characteristics ( ), household characteristics ( ), age cohort and state controls ( ), equation 14 also includes a community-level measures ( ) to improve identification. Instruments are not formally required to identify the model (Heckman, 1978; Wilde, 2000; Miranda and Rabe- Hesketh, 2006), but are preferred to avoid tenuous identification (Keane, 1992). 17 A valid exclusion restriction should be correlated with the potentially endogenous independent variable of interest (i.e., current migration status) while being uncorrelated with the dependent outcome variable of interest (i.e., occupational attainment). The first exclusion measure is a historical community-level variable of individual migration experiences. It is calculated as the number of individuals who have ever migrated over the total number of individuals surveyed in the community. 18 The second measure interacts the aforementioned historical community migration variable with the number of 17 The associated exclusion restriction can be expressed accordingly:. 18 The following measure is constructed for each community: 14