Rainfall and self-selection patterns in Mexico-US migration

This article studies the role of rainfall in determining the education composition of Mexi-co-US migration. Emphasizing the relationship between rainfall and migration costs, a revised Roy model indicates that rainfall affects selection on education through not only households’ liquidity constraints but also the comparisons between changes in migration costs and wage differentials at different levels of education. With retrospective data on the migration history of male Mexicans, the empirical analysis shows that the inverted U-shaped relationship between migration probabilities and education is less dispersed with a higher vertex when rainfall decreases, suggesting higher migration costs and reinforced self-selection patterns. The impacts of rainfall on selection and education are stronger for the migrant stock than for migration flows. Studying how rainfall influences migrants’ return decisions provides consistent results.


Introduction
With large semi-arid areas, Mexico has a long history of drought. Its primary crop, which is maize, mainly grows on rain-fed land, and this characteristic leads to a high dependence on rainfall for agriculture. Given the fact that about 30% of male workers worked in the agricultural sector in the 1990s, Mexican household income is sensitive to precipitation anomalies historically. In drought, migration is one of the coping strategies. Literature finds that rainfall deficits increase the propensity of Mexicans to migrate to the United States, especially for farmers or rural residents in dry Mexican states (Munshi, 2003;Feng et al., 2010;Hunter et al., 2013;Fishman and Li, 2017). This drought-driven migration appears to relate low educational attainments to "climate refugees." However, the real role of rainfall in determining the skill or education composition of migration flows has not been fully explored yet.
Studying whether Mexican migrants to the United States are composed of more highly educated individuals has important political and economic implications for both countries.
The existing literature, nevertheless, offers conflicting findings regarding migration selection on education. Ambrosini and Peri (2012) and Moraga (2011) have found that Mexican migrants have less schooling than non-migrants, supporting the negative migration selection when the home country has more dispersed income distribution (Borjas, 1987). In contrast, Mishra (2007) found a positive selection on education, which is consistent with Chiswick's (1999) model, which argues that high migration costs impede the migration movements of lowskill workers. Furthermore, Moraga (2011) also provided evidence for migrants' lower wages, compared to non-migrants in Mexico, challenging Chiquiar and Hanson (2005)  McKenzie and Rapoport (2010) explicitly provided one of the explanations for the absence of consensus on the direction of migration selection. They indicated that the selection on education tends to be positive or neutral in Mexican communities with weak networks in the US, but negative in communities with strong networks. Different data sets of communities yield different conclusions on selection. In addition to networks in communities, other potential determinants of selection include economic conditions, migrants' networks at the household level, and border enforcement, as Orrenius and Zavodny (2005) displayed their significant influences on the skill level of illegal Mexican migrants to the US.
If "climate refugees" are less educated than other migrants as people may think, then rainfall affects migration selection as well. Data sets with different time lengths and geographic/ atmospheric characteristics lead to different answers to the direction of selection.
Thinking of wage differentials between countries netting migration costs as demonstrated by Sjaastad (1962), conditions of insufficient rainfall, for example, drought, may hurt the income of Mexicans; people without liquidity constraints are more likely to migrate to the US due to larger wage differentials, while those who cannot afford upfront migration costs have to stay in Mexico. If less-educated people face tighter constraints in liquidity or ability as suggested by Angelucci (2015), drought-driven migration may not lead to higher possibilities of negative selection. This article demonstrates that the effects of rainfall on wage or income differentials and on migration costs differ by Mexicans' educational attainments, resulting in changes in the selection on education.
Studies have suggested that decreases in rainfall lower the income of Mexicans differently at education levels. Poorly educated people are more likely to take agricultural jobs and are more vulnerable to climatic fluctuations. This results in more severe inequality in Mexico when rainfall decreases, although drought may negatively impact both crop income and non-farm income (Gathmann, 2008;Dell et al., 2014;Hunter et al., 2013;Fishman and Li, 2017).
However, relatively little is known about the possible effects of rainfall on migration costs.
Rainfall may affect migration costs, including upfront monetary costs that may impede the movements of poorly educated people who cannot afford them. When decreases in rainfall lead to larger wage differentials and drive more Mexicans to migrate to the US as stated in Munshi (2003), there may be a higher and stronger demand for migration-related services, such as using coyotes, taking transportations, utilizing networks in the US, and borrowing to cover corresponding expenditures. In this article, a theoretical analysis of the seemly constant supply of other migration-related services suggests a negative relationship between rainfall and migration costs. This is verified by empirical evidence on higher coyote (smuggler) prices, more difficulties in border crossing, and lower chances of using networks in drier years.
Considering the changes in wage differentials and migration costs caused by different rainfall levels, this article uses the models in Roy (1951), Borjas (1987), and Cattaneo and Peri (2016) to study the effects of rainfall on migration selection. Wage differentials net of migration costs determine migration decisions at different education levels. When individuals are indifferent between staying in Mexico and traveling to the US, the threshold levels of education for migration decisions can be derived. Rainfall affects these thresholds through liquidity constraints as well as the comparisons between changes in wage differentials and migration costs, thus influencing the selection on education.
Empirically, using retrospective data on male Mexicans' migration history from the Mexican Migration Project (MMP), the author finds that individuals from the middle of education distribution are more likely to be migrants, when compared to those from the tails of education distribution, suggesting intermediate selection. Lower rainfall levels reinforce this selection because the inverted U-shaped relationship between migration probabilities and education is less dispersed with a higher vertex when rainfall decreases. The least educated people without a primary school diploma lower their probabilities to migrate to the US in drier years because higher migration costs give them tighter liquidity constraints. Another possible explanation is that the increases in migration costs are larger than the increases in wage differentials or the decreases in income in Mexico in drier years, thus making migration less profitable. This latter explanation works better for the declined migration probabilities of most educated people with a college degree, whose income is less vulnerable to lower rainfall levels and whose wealth releases them from liquidity constraints. Opposite changes in migration probabilities are found in the case of people with some years of schooling, especially those who attended middle school and high school. Given their higher migration probabilities in drier years, if liquidity constraints are not binding, it is highly likely that they encounter larger changes in wage differentials than in migration costs. The role played by rainfall deficits in reinforcing original migration selection is more substantial for the migrant stock than for migration flows, supporting higher migration costs with lower rainfall levels. Analysis of return decisions of migrants in the US provides consistent results.
The structure of this article is as follows. In Section 2, the theoretical model underlying the effect of rainfall on migration selection is demonstrated. Section 3 provides a brief description of the MMP data and presents empirical strategies. Section 4 displays the main results showing how selection changes with rainfall. Robustness checks are also discussed. Section 5 concludes the article.

Climate shock and selection
The literature views the migration decision as an investment to maximize migrants' lifetime utility or earnings. Lower migration costs and larger wage differentials between the home and host countries imply higher migration intentions (Sjaastad, 1962;Borjas, 1987;Chiswick, 1999).
Taking into account considerations of climate change, Cattaneo and Peri (2016) also extend Roy's model to indicate that higher temperatures, which negatively influence agricultural productivity, increase migration rates in middle-income economies while reducing migration rates in poor countries. The primary reason is that poor countries are facing binding liquidity constraints. Though they focus on migration rates in countries with different levels of wealth, a revised model sharing the spirit and allowing for changes in migration costs can be applied to examine how rainfall affects the migration propensity of people with different educational attainments.

Roy's model
Consider an individual living in the home country, Mexico, and deciding whether to migrate to the host country, the US. Suppose his labor market performance depends on his skills (education levels). The wage equations in Mexico (subscript 0) and the US (subscript 1) can be written as follows.
where w i (i = 0,1) is the wage, µ > 0 denotes the wage level with no schooling, δ > 0 is the return to schooling, s. The wage level with no schooling is higher in the US while Mexico has a higher return to schooling; thus I the author assumes µ 1 > µ 0 and δ 0 > δ 1 (Chiquiar and Hanson, 2005; McKenzie and Rapoport, 2010).
Earnings in Mexico are assumed to be affected by rainfall in Mexico through wage level with no schooling, µ, and return to schooling, δ, therefore, Eq. (1) becomes ln(w 0 ) = µ 0 (R)+δ 0 (R)s, where R denotes rainfall in Mexico that the individual experiences.
The author assumes ∂µ 0 /∂R > 0: decreases in rainfall hurt the income of people with no schooling. Without well-developed insurance markets, uneducated people suffer a monetary loss in drought due to lower crop yield and impaired non-farm income. Furthermore, a higher return to schooling in drier years is assumed: ∂δ 0 /∂R < 0. People who are more educated may self-select into job positions which are less vulnerable to natural disasters and diversify their income packages to avoid substantial losses arising which arise from climate fluctuations. 1

Migration costs
When regional rainfall in Mexico has no effects on migrants' income in the US, an individual in Mexico will migrate to the US if where C denotes migration costs. Migration costs in time equivalent units, π = C/w 0 , are assumed to decrease with schooling (Chiswick, 1999;Chiquiar and Hanson, 2005;McKenzie and Rapoport, 2010). Without enough money, either from savings or credits, to pay for the upfront migration costs, Mexicans are not able to afford the migration trip even if condition (3) above is satisfied.
Migration costs mainly include upfront costs, such as transportation costs and coyote (smuggler) prices, and other costs, such as seeking help from networks and finding lodgings in the US. How rainfall influences these migration costs depends on its impacts on both the demand and supply in the market. In drier years, the lower-income of Mexicans suggests larger wage differentials and therefore stronger demand for migration services. More potential migrants and their higher willingness to pay for the movement lead to a higher and steeper downward sloping demand curve.
However, the manner by which the supplies of different migration costs change is ambiguous. The supplies of transportation services and existing networks in the US seem not to be affected by rainfall in the short run, since international train or flight services do not change greatly while networks in the US are mainly determined by historical migration.
Stronger demand for them in drought may lead to higher prices of these services. Section 4 empirically shows that migrants traveling in drier years are less likely to contact and lodge from relatives in the US, implying not only higher monetary costs but also higher psychological costs. Besides, though the changes in the supply of coyote services are not clear, Section 4 also provides some evidence on higher coyote costs for illegal migrants who face lower rainfall levels.
Therefore, migration costs, C, are assumed to increase in drier years, yielding where μ π > 0, γ 1 > 0, γ 2 > 0. For simplicity, the effects of rainfall on migration costs are assumed to be identical across education levels. However, these effects would be larger for those who are less educated, since less-educated people are willing to pay more for the migration trips due to their larger changes in wage differentials in drought.

Decision and selection
If the values of s satisfy then individuals with s years of schooling are indifferent between staying in Mexico and migrating to the US. Viewing migration as an investment, the author sets Mexicans with educational attainment around s L may have high migration costs especially when p is sensitive to education levels. If migration costs and their dependency on education (γ 1 ) are large enough to make (δ 1 − δ 0 + πγ 1 ) > 0, more years of schooling give larger net benefits from migration, which is consistent with positive selection around s L . Under these circumstances, it is very likely that ∂s/∂R < 0 when rainfall causes larger changes in migration cost (πγ 2 ) than in income in Mexico, in other words, ∆ < 0. s L moves to the right in drier years as shown in Figure 1(a). The effects of decreased rainfall on selection through higher migration costs outweigh the effects occasioned through lower Mexican income; then therefore, only those people who have more educated educational credentials with years of schooling greater than ′ s L will stick to their original decision because of their larger net benefits from migration.
However, people with education levels between s L and ′ s L change their decision because they lack enough adequate net benefits from migration to offset the negative effects of larger changes in migration costs than in income in Mexico. If income in Mexico is more sensitive to rainfall than migration costs, having ∆ > 0 and ∂s/∂R > 0, s L moves to the left in drier years as shown in Figure 1  with education levels between s L and s″ L may prefer and be able to make a migration trip in normal years, while in drier years they have to stay in Mexico because of higher upfront migration costs.
Similar reasoning can be applied to people with educational attainment around s U , where a negative selection pattern is demonstrated. Their low migration costs suggest a high possibility that (δ 1 − δ 0 + πγ 1 ) < 0. It is very likely that income in Mexico for them is not significantly affected by rainfall, especially when |∂µ 0 /∂R| > |∂δ 0 /∂R|. Then, ∆ ≈ −πγ 2 < 0 and ∂s/∂R > 0.
Decreases in rainfall only bring higher migration costs, then s U moves to the left in drier years as shown in Figure 1(a), as more years of schooling imply lower net benefits from migration.
When rainfall has larger effects on income in Mexico than on migration costs, ∆ tends to be positive and ∂s/∂R tends to be negative. s U may move to the right in drier years as shown in  if we hold s U unchanged. The gap in average education levels can be either enlarged or narrowed.
Therefore, using person-year unbalanced panels, the author examines whether the effects of rainfall on migration probabilities differ by education levels. To provide more solid analysis, two separate samples for movement decision and migration status are used for the regression below α β γ ϕ = + − + − × + − + + + + Mi c s y Rs y Ei y Ei y Rs y Xi y As By Cc ei c s y , , , where M i,c,s,y denotes movement decision or migration status in year y of individual i who is interviewed in community c and resides in state s in year y. Empirically, movement decision refers to the question of whether any actual migration trip to the US, longer than 1 month, in year y is made conditional on no migration experience in year y-1. If yes, then this dichotomous variable, M i,c,s,y , is equal to unity; zero otherwise. Therefore, tourism trips are not regarded as migration experience. Since return trips are not clearly recorded in the MMP, the condition of no US experience in year y-1 is set to distinguish migration trips to the US from return trips to Mexico. 5 In the corresponding sample, except for traveling years in which migrants move to the US, migrants' years in the US have been dropped for not experiencing rainfall in Mexico. However, these years imply migrants' preference for staying in the US. To include them in the analysis, a second sample and a differently defined dependent variable, migration status, is used. Employing individuals' annual location information provided by the MMP and regarding location choices as migration status decisions, the dichotomous dependent variable, M i,c,s,y , is set equal to unity if the individual spends at least 1 month in the US in year y, zero otherwise. The corresponding sample for migration status includes all years of individuals no matter where they stay and how frequently they travel.
The movement decision sample focuses on migration flows, while the migration status sample focuses on the migrant stock in the US. Both of them are worth studying. The difference between these two samples is mainly migrants' years in the US, except for their traveling years.
Conditional on staying in the US already, migrants make their location decisions without considering upfront migration costs. Therefore, switching from the movement decision sample to the migration status sample, the effects of rainfall through upfront migration costs should be smaller. As discussed above, rainfall may decrease savings to cover upfront migration costs or increase those costs. If migration costs never change, then lower rainfall levels strengthen liquidity constraints only through savings. In the migration status sample, more observations are not troubled by upfront migration costs or liquidity constraints; thus, the negative rainfall-driven effects of migration costs for poorly educated people on their migration decisions should be smaller than that in the movement decision sample. If rainfall deficits increase migration costs, especially those costs after arriving in the US, the rainfall-driven effects of migration costs should be larger in the migration status sample. In other words, migrants who are in the US and sensitive to migration costs may increase their return propensity in drier years if the costs of return trips to Mexico are trivial.
Though two definitions of dependent variables and two samples are used, independent variables are the same. E i,y−1 denotes education-related variables. Generally, the author has years of schooling and its squared term in year y−1. In specifications that the author groups people based on their years of schooling, E i,y−1 presents different educational categories. Coefficients on E i,y−1 explain the relationship between migration probability and education, suggesting a selection pattern in migration. (2017), R s,y is the rainfall in the main agricultural season, spring-summer season, in year y in the individual's home state s in Mexico, measured in 100 mm units. 6 5 The MMP does not record migrants' return trips to Mexico as clearly as their migration trips to the US. Using individuals' location information in each life year makes it difficult to define migrants returning years. If migrants stay in the US in year y-1 but make a new migration trip to the US in year y, it is very likely that migrants firstly return to Mexico in year y and then travel to the US again in the same year. Therefore, with the condition of no US experience in year y-1, when migrants make new migration trips to the US every year continuously, those years are dropped in the corresponding sample. 6 Mexico's main agricultural outcome, Maize, has two major agricultural seasons: Spring-Summer (78.5% of total production) and Autumn-Winter (21.5%) (Secretariat of Agriculture, Livestock, Rural Development, Fisheries and Food (SAGARPA) 2008). The Spring-Summer season includes (i) planting period (April-June), (ii) growing period (July-August), and (iii) maturation and harvesting period (September-November).

Following Fishman and Li
The annual seasonal rainfall data from 1941 to 2012 at the state level are from the MMP and Comisin Nacional del Agua (Conagua). 7 Although the effects of rainfall may last years, the author follows the literature and focuses exclusively on the effects in the short run (Feng et al., 2010;Cattaneo and Peri, 2016;Nawrotzki et al., 2013). In the robustness checks, controlling for rainfall in previous years yields consistent results. In line with Orrenius and Zavodny (2005) and Cattaneo and Peri (2016), the interaction term between education and rainfall, E i,y−1 × R s,y , illustrates how the effects of rainfall on migration decision change with years of schooling and how rainfall shapes the relationship between migration probability and education.    No school (0)

Return decisions
Many migrants may return to Mexico or transit back and forth across the Mexico-US border. Analysis of return decisions of migrants who already stay in the US should provide some information on changes in wage differentials and migration costs other than upfront costs as rainfall changes.
To study migrants' return decisions, the author replaces the dependent variable in Eq. (7) with a dichotomous variable for migrants' return trips to Mexico  4 Results

Migration costs
Before presenting the relationship between selection on schooling and rainfall, the author studies the increasing migration costs in drier years as given in Tables 3 and 4. Using limited data in the MMP on migration costs, Table 3 displays a strong negative correlation between rainfall and illegal migration costs; Table 4 suggests fewer benefits from networks in the US and tighter liquidity constraints in years with lower rainfall levels. Table 3 include (1) (4) and (5)  Considering the possible effects of rainfall on exchange rates, using coyote costs in pesos give consistent results. either. Furthermore, the negative effects of rainfall on migration costs might be smaller for people with more years of schooling, although the positive coefficient on the interaction term between School and Rainfall in column (3) is barely significant.

Illegal migration costs in
Conducting a similar analysis in the second panel in Table 3, the dependent variable is changed to a dichotomous variable for the most common cross sector for illegal crossings. It is set at unity if migrants choose Tijuana in Baja California del Norte to cross the border, zero

otherwise. 11 Regressions of this choice of sectors for illegal trips on rainfall (R s,y ) in columns
(1)- (3) show that illegal migrants are more likely to switch to unfavorable sectors as rainfall decreases, although only column (3) presents a significant coefficient. Since crossing in remote or unpopular areas requires more time and higher payments to coyotes (Gathmann, 2008), illegal migrants may face extra costs in drier years, supporting the results in the first panel in a degree. People may argue that rainfall may influence migrants' intentions for illegal trips and using coyotes. However, the first panels of Tables A1 and A2 in Appendix show that on average the effects of rainfall on the probability of choosing to be illegal or hiring a coyote are not significant. 12 Furthermore, focusing on migrants' interactions with their connections or relatives, Table 4 also suggests higher migration costs in drier years for both legal and illegal migrants.
The dependent variables in columns (1)-(3) are dichotomous variables for lodging from relatives during their stays, contacting relatives in the US, and receiving financial help for their US trips, respectively. Regressing them on rainfall in Mexico, columns (1) and (2)  However, the author admits that it is difficult to identify a solid relationship between migration costs and rainfall in the absence of availability of more detailed data on total migration costs, including money spent on legitimate procedures and transportation. If total migration costs, rather than just coyote costs in illegal migration trips, increase by 7% as rainfall decreases by one standard deviation as shown in Table 3, migration trips become less profitable and more difficult if liquidity constraints bind. Therefore, the costs channel through which rainfall affects migration decision and selection cannot be ignored.

Rainfall and selection
Regarding the relationship between rainfall and selection on schooling, Eq. (7) has been fitted to the MMP data. Results are reported in Table 5. The first three columns are from the movement decision (travel) sample, while the remaining three columns are from the migration status (in the US) sample. 14 In column (1) of Table 5, the inverted-U-shaped relationship between migration probability and years of schooling suggests that migrants are more likely to be from the middle of the 11 About 40% of illegal crossings in the sample took place in Tijuana. In addition, migrants usually would not change their cross sectors within a year. 12 Table A1 and A2 in Appendix focus on migrants' choices, while the statement holds even if we include all nonmigrants in the sample. 13 In the MMP, about 90% of migrants with financial help report that friends, relatives, and community members are the sources, while the rest of them receive help from employers or banks. 14 Unweighted specifications are used because sample weights are at the community level, while community FE are controlled for. Weighted regressions give consistent results.  (2). Graphically presenting these results in Figure 2 The selection on education in a normal year with average rainfall level tends to be intermediate toward negative since the inverted-U shape shows higher migration probability for relatively poor people. When rainfall decreases, the less dispersed curve indicates increased migration probabilities of people with about 5-12 years of schooling, but decreased migration probabilities of others.
Column (3) of Table 5   Setting the values of all control variables to zero and ignoring the constant terms, these figures show the expected migration probabilities versus individuals' years of schooling based on coefficients in Table 5. (a) and (b) are from the movement decision (Travel) sample and the migration status (in the US) sample, respectively. The inverted U curves in droughts are sharper with higher vertexes than curves in normal years. Facing droughts, people with about 5-13 years of schooling increase their migration probabilities, while people with years of schooling fewer than 5 years or more than 15 years decrease their probabilities of migrating migration becomes less attractive to them, they may give it up voluntarily. When the opposite happens, tighter liquidity constraints should be the main factor impeding their movement. If migration costs, including upfront costs, are not affected by rainfall, only declines in savings could lead to the reinforced positive selection on education among those identified as poorly educated people, as shown in Table 5, and Figures 2 and 3. However, if we believe that rainfall in the spring does not affect Mexicans' savings, which are largely likely to have been accumulated in previous years, in Table 5, higher upfront costs as shown in Table 3 are the only reason for tighter liquidity constraints as shown in column (3) of Table 3.

Figure 3
The relationship between educational attainments and migration probabilities changes with rainfall. Points on the solid line represent the coefficients on educational categories based on the migration regression results in Table 5. Points on the dashed line represent the changed coefficients on educational categories caused by a decrease in rainfall (439 mm). Both (a) and (b) show an inverted U relationship between migration probabilities and educational attainments. When rainfall decreases, people in categories Middle and High have higher probabilities to travel to or stay in the US, while people in categories No school, Primary, and Grad reveal lower migration probabilities.
In addition, given the fact that people in the Middle and High categories are more likely to migrate in drier years, we know that at least some people have larger increases in wage differentials than increases in migration costs. Besides, liquidity constraints are not hindering their movement.
As for people who are highly educated, such as those with graduate degrees, their lower migration propensities in drier years may mainly result from higher migration costs, especially those do not decline as education levels increase since their income in Mexico may not be sensitive to rainfall. Another possible explanation is that their income in Mexico may increase as rainfall decreases since the prices of unskilled labor may decline.
Using the migration status sample to study people's location choices every year, columns (3)-(5) of Table 5  Assuming other migration costs do not change by rainfall, in drier years at least those poorly educated migrants in the US should have stronger intentions to stay and present smaller gaps between lines for the migration status sample. However, this contradicts the fact that larger gaps between lines in Figures 2 and 3, implying their higher return rate. A good explanation is that migration costs, other than upfront costs, increase as rainfall decreases. It is quite possible that upfront costs only make up a small portion of total migration costs, while the rest are more sensitive to rainfall.
Migrants in the US who are from the High category prefer to stay in the US when there is a reduction in rainfall probably because they benefit more from migration as rainfall decreases.
People in this category display higher incentives to migrate as rainfall decreases in the movement decision sample. As upfront costs being absent, the trend is stronger due to smaller changes in migration costs for migrants in the US than migrants traveling with upfront costs.
The comparison between results from those two samples for people with graduate degrees is unclear because of their small proportion in samples. Migrants in the US increasing their intention to return in drier years may reflect that upfront costs are not significant compared to other costs, such as money and time on searching jobs.
The analysis mentioned above shows that the intermediate selection pattern is reinforced when rainfall decreases. Furthermore, this is more obvious for the migrant stock than migration flows, suggesting higher migration costs as rainfall decreases. The return analysis mentioned in Section 4.3 uses migrants' years in the US and provides supporting results. Table 6 presents how migrants' return decisions are determined by rainfall levels in Mexico.

Return
Two definitions for migrants' returns and corresponding samples are used as mentioned in the data section. They give consistent results. In columns (1) and (3), coefficients on School, School Squared, and their interaction terms with Rainfall have expected signs, which are the opposite of the signs of coefficients in the migration decision regressions in Table 5. Figure 4 uses two Table 6 Return decision varies with rainfall by schooling (selected coefficients).

Dependent variable Return (leave) Return (arrive)
( lines to display the relationship between return decisions and years of schooling at different rainfall levels. In a normal year with an average rainfall level (791 mm), migrants with fewer years of schooling are more likely to return. However, in a drier year, migrants with about 4-12 years of schooling tend to stay, while migrants with no years of schooling (Figure 4(b)) or more than 12 years of schooling are more likely to return to Mexico. Columns (2) and (4) of Table 6 confirm that by using different educational categories. The original selection on education in return migration is also reinforced in drier years.

Robustness
The following robustness checks provide consistent results, though some of the result tables are not reported in the present article.
Mexicans who work in the agriculture sector may be more sensitive to rainfall. Controlling for the occupational dichotomous variable, Agriculture, and dropping observations without a job does not bring about any significant change in results. Agricultural workers may experience larger changes in wage differentials as well as migration costs when rainfall levels change. Distinguishing agricultural workers from nonagricultural workers, Tables A4 and A5 in Appendix show how rainfall affects migration selection on education in those subsamples, respectively. 16 Both tables show reinforced migration selection patterns on education in drier years.
Rainfall in previous years may have continuous effects on later migration decisions. Controlling for rainfall in previous years, for example, comparison of rainfall in the last year with rainfall during the preceding 8 years, provides consistent results.
Applying the Cox proportional hazard model to conduct migration duration analysis, Table A6 in Appendix indicates that migrating in drier years results in longer durations of stay in the US. This is consistent with higher migration costs as rainfall decreases.
16 The corresponding summary statistics are shown in Table A3 in Appendix.

Figure 4
The relationship between years of schooling and return probabilities changes with rainfall.

(a) Column (1) -Return (Leave) sample (b) Column (3) -Return (Arrive) sample
Setting the values of all control variables to zero and ignoring the constant terms, these figures show the expected or predicted return probabilities versus individuals' years of schooling based on coefficients in Table 6. Facing droughts, migrants with some years of schooling lower their return probabilities, while the least educated migrants and the most educated migrants increase their probabilities of return to Mexico.
Since the MMP asks respondents about their migration history to get retrospective data, recall errors may bias results. Limiting the author's samples within the most recent 10 years, or 5 years, or from years after 1987 when Immigration Reform and Control Act (IRCA) was in the act in the US, regressions provide highly consistent results.
One may be concerned about the possible causal effects of rainfall on education, though most of the people in the sample finish their education, owing to the fact that the average years of schooling is about 5. Using the main samples and regressing years of schooling (E i,y−1 ) on rainfall (R s,y ), Table A7 in Appendix shows that rainfall levels in the current year have no significant effects on education levels in the previous year when individual characteristics and different types of FE are controlled according to different specifications. In addition, limiting the study to people with a job or people whose ages are above 6 years combined with their years of schooling creates subsamples consisting of individuals who barely change their education levels. Employing those subsamples and repeating the empirical analysis give consistent results.

Conclusion and discussion
To summarize, a revised Roy model demonstrates that the relationship between rainfall and selection on education is determined by household liquidity constraints and the comparisons between changes in migration costs and wage differentials caused by rainfall fluctuations. People from different educational attainment groups respond differently when faced with climate shocks. Employing retrospective data on Mexican individuals' US migration history, which is provided by the MMP, the inverted U-shaped relationship between migration probability and years of schooling becomes less dispersed with a higher vertex when rainfall levels fall.
Specifically, faced with insufficient rainfall, those people who are least educated, with less than 5 years of schooling, have lower migration probabilities, probably due to their tighter household liquidity constraints. Focusing on coyote costs, difficulties of illegal crossings, and utilizing networks in the US, higher migration costs in drier years result in those tighter liquidity constraints. Comparing the increases in both wage differentials and migration costs, in drier years highly educated people with more than 15 years of schooling decrease their migration probabilities, while people from the middle spectrum of education distribution increase their migration probabilities. Declines in rainfall levels reinforce the original selection pattern with a stronger effect for migrant stock than migration flows. Return analysis for migrants in the US supports the conclusion mentioned above.
Though changes in wage differentials and migration costs determine the direction of selection on education, empirical estimation of the effects of rainfall on them is difficult, since panel data on individuals' earnings in both countries and migration costs of all migration trips are required. In addition, regarding the reasons for liquidity constraints, it is not easy to distinguish the effects of savings from those of upfront migration costs unless more detailed information is available on both. With limited data, studying the effects of rainfall on selection still provides some information.

A.1 Migration behavior
Tables A1 and A2 in Appendix explore how rainfall affects migration behavior related indicators.
In Table A1 in Appendix, the sample includes all migrants' trips (traveling years) to the US.
Dependent variables for columns (1)-(3) are dichotomous variables for being illegal migrants,  Table A2 in Appendix limits the sample to illegal trips verifies that. In the second panel in Table A1 in Appendix, the interaction terms between School and Rainfall suggest that less-educated people in drier years are more likely to be illegal, use coyote, and cross alone. This conclusion would not affect the migration costs analysis in the article since education is controlled for in regression. However, it is not clear whether those behaviors are associated with higher migration costs.
Columns (4)-(6) of Table A1 in Appendix study the relationship between rainfall and family members' migration experience to see whether lower rainfall levels encourage better-connected migrants to move, because with parents or siblings migrated before, migrants may have more information and connections in the US and therefore lower migration costs.
Results show that lower rainfall levels drive migrants with no migrating parents to travel to the US. In other words, migrants who travel in drier years have higher migration costs.

A.2 Duration analysis
The author applies the Cox proportional hazard model to examine the effects of rainfall in migrants' traveling years to study migrants' durations in the US. Income effects of larger wage  (2016), the author provides a brief explanation for the Cox proportional hazard model employed to study durations of all migration trips to the US.
The hazard function that depends on a vector of explanatory variables Z with unknown coefficients β is factored as where h(t) is the base hazard function. The possibility of return is allowed to vary with exogenous variables Z which include R and X in Eq. (7)  This is consistent with the hypothesis of higher migration costs in the drier year, since migrants may want to stay longer in the US to recoup the costs associated with migration. Columns (2) and (3) of Table A6 in Appendix explore how the inverted U function of migrants' durations and their years of schooling changes with rainfall. In column (3), traveling in drier years, migrants from category Primary will stay longer in the US, while other migrants, especially those from category Grad, may return sooner.   Standard errors for coefficients, rather than hazard ratios, are reported in parentheses. Stars signify the following: ***significant at 0.01, **significant at 0.05 level, and *significant at 0.1 level.

Table A7
The insignificant effects of rainfall on years of schooling.