2.1. Son or daughter

When a father is the only adult male in the household, he might be the optimal and only candidate for migration trips: N _ft ≤ 1. His migration trip increases the consumption of family members, but leaves females and young children unprotected at home (P _t = 0). Since fathers’ future migration durations do not differ by the sex of under-age children [Li (Reference Li2016)],Footnote ¹ it is reasonable to believe that fathers’ candidacy for migration trips, candidate constraints, and utility maximization problems might be influenced by the number of young children, which is predetermined in the model, but not the sex of them. When the disutility caused by no anchor at home (P _t = 0) is high, a father may stay in Mexico.

However, having an adult son provides an additional candidate for migration trips or the anchor position at home, loosening the original candidate constraint and increasing the maximized household utility if a different maximization solution is achieved. For example, with a son, rather than a daughter, households without migrants before might be willing to send a migrant, either the son or the father, when the son reaches adulthood. After the father retires from the labor market, a family without an adult son does not have any candidate for migration: N _ft = 0. With an adult son, the retired father can act as the anchor at home and send the son to the US, N _ft ≤ 1.

Specifically, as a couple plans to have their only child around age 25: time t = 0, when the child reaches adulthood, such as 14 years later (t = 14), the candidate constraint after year t = 14 becomes N _f,t≥14 ≤ 2 if the child is a son, and remains unchanged as N _f,t≥14 ≤ 1 if it is a daughter, while the utility maximization problem keeps the same as $U = \sum _{t = 1}^{T} u( c_{1t},\; \, c_{2t},\; \, c_{3t},\; \, {\mathbb 1}{( P_{t} = 1) })$ subject to $\sum _{i = 1}^{3} c_{it} = W_{ht}\times ( NA_{t}-N_{ft}) + W_{ft}\times N_{ft}$. The trade-off between collecting W _ft − W _ht and satisfying P _t = 1 faced by a father is broken by having an adult son. If at the time t = 30, the father retires (or simply no longer wants to make the temporary migration to the US) and can only act as the anchor at home, the candidate constraint will become N _f,t≥30 ≤ 1 if the child is a son, while become N _f,t≥30 = 0 if it is a daughter. Therefore, an adult son, being his father's substitute to a degree, can either serve as the anchor at home to encourage the father's longer US durations or travel to the US himself to collect the wage differential. When sex-selective abortion is a choice at low costs, a son would be preferred to a daughter. Longer previous migration experiences of the father enlarging the wage differential (W _ft > W _ht) may facilitate future migration trips of candidates for migration and thus the utility increase brought by an adult son compared to an adult daughter.

2.2. One son or two sons

Generally, having more sons loosens the candidate constraint by changing not only the choice of the migrants but also the number of migrants. However, temporary Mexican migrants generally travel alone to the US [Donato et al. (Reference Donato, Wagner and Patterson2008), Li (Reference Li2016)].Footnote ² Budget constraints and upfront migration costs may not allow households to send out multiple migrants at the same time. When migrants, either sons or fathers, travel alone without company all the time in the model, as long as there is one adult son in the household, additional brothers may not change the utility maximization problem greatly. In an example that a couple wants a firstborn around age 25 (t = 0) and a second-born round age 30 (t = 5), they may need to determine the sex of both children. When two children are sons, the second son might migrate but not act as the anchor at home if his father or elder brother migrates, suggesting that he may share fewer of his father's responsibilities or duties than the firstborn son does. The eldest son, who reaches adulthood earlier than his brothers, is more likely to migrate when the father acts as the anchor or take the anchor position when the father stays abroad. In other words, conditional on having a son in household, the possible marginal increase in maximized utility by having a boy as a second son is small if the home country wage rates do not differ too much by sex. The firstborn son brings the biggest marginal increase in household utility.

2.3. First son being the first child

Making the firstborn son the firstborn child increases the probability of having a son as the firstborn, increasing the maximized household utility, especially for those with migration experiences. In the example above, when the couple wants different sex of two children, the first son born at t = 0 with a younger sister born, say, at t = 5 weakens the anchor candidate constraint earlier than the first son born at t = 5 with an elder sister born at t = 0. The former case suggests a longer time period for a loosened constraint. When the father ceases migrating at t = 30, the loosened candidate constraint can be N _{f,14≤t≤30} ≤ 2 when the first son is born at t = 0, while N _{f,19≤t≤30} ≤ 2 when the first son is born at t = 5.

Though resources in families tilt toward sons in Mexico already [Durand and Massey (Reference Durand and Massey2004)], having a son as the first child provides the child with a larger amount of investments, including parental time and possibly material resources, since firstborn children usually receive larger marginal investments than their younger siblings [Binder (Reference Binder1998), Price (Reference Price2008)]. Firstborn sons of lower birth order receiving larger investments may suggest higher marginal utility caused by their candidacy for migration and the anchor position, especially when wage differential in two countries is larger for people who receive more investments. The above analysis also implies that the son preference would diminish with higher order births.

The magnitude of possible increases in household utility resulting from the first child being a son might not be small. Because of the pregnancy time with the first child, the second opportunity of having a son will be about one year later. An abortion could end at least one year's wait. An eager family counting on the eldest son to share some responsibilities of the father in the future may see a potential increase in wealth by at least one year's wage differential between two countries when migration decision is at the margin but father would not travel with no male adult at home.

Females are assumed to stay in Mexico in the model above. If they also move to the US and the whole household settles down north of the border, both fathers and sons take migration trips while there is always an anchor at home (P _t = 1). When females act as tied movers, sons, compared to daughters, are more likely to find better jobs in the US due to Mexican women's low labor force participation rate and the US labor market's historical demand for Mexican male labor [Donato (Reference Donato1994)]. The increases in utility are even larger for having a son, rather than a daughter, as the firstborn if females with jobs in Mexico could not find a job in the US.

The above arguments mainly indicate that a son as the firstborn child substitutes for his father when they are separated and shares more of his father's responsibilities. Whether the existence of an adult son enlarges fathers’ future migration durations remains unclear. On the one hand, with an adult son staying at home, fathers may stay longer in the host country to accumulate wealth due to the lower psychic costs. On the other hand, as the adult son migrates, fathers may stay at home as the anchor. Furthermore, the migration experiences of fathers and sons may facilitate future migration trips of each other. However, from the perspective of gender of first (eldest) child, under either situation, a son, compared to a daughter, gives higher household utility.

2.4. Limitations

In addition to the economic perspectives, migration assimilation may also encourage migrants to prefer that the firstborn is a boy. As Americans have a preference for “first a son and second a daughter” [Markle and Nam (Reference Markle and Nam1971), Westoff and Rindfuss (Reference Westoff and Rindfuss1974), Markle and Wait (Reference Markle and Wait1976)], migrants who enter the US at earlier ages and stay longer may adapt to this value of American society more easily.

Manipulating the sex of the first child may not be easy unless people are able to circumvent the law on abortion in Mexico. Women travel to Mexico City, the only state where abortion is available on request since 2007, to get legal abortions [Senderowicz et al. (Reference Senderowicz, Sanhueza and Langer2016)]. At the same time, illegal abortions are common but not well recorded [Guillaume et al. (Reference Guillaume, Rossier and Reeve2018)]. Planning the sex of the firstborn seems more common than the sex of higher-order births because Mexican women who do not have children or have only one child are more likely to have an abortion [Guillaume et al. (Reference Guillaume, Rossier and Reeve2018)]. Focusing on the sex of the first child sheds light on the abortions in Mexico.

The main arguments above presume that number of total children is predetermined before couples decide on the sex of their first children. However, son preference could create fertility stopping rules and change couples’ desired sex ratios [Kishore and Spears (Reference Kishore and Spears2014), Jayachandran (Reference Jayachandran2017)]. Migrants who accumulated wealth in the host country while lack family time in Mexico may also have different fertility choices than non-migrants. Whether the numbers of sons and daughters are affected by fathers’ migration experiences is another research question. Furthermore, fathers’ migration experiences may also affect the timing of giving birth to children.

4.1. Ordinary least squares

Table 3 presents the relationship between fathers’ US duration and the sex of their firstborn children by applying Ordinary Least Squares (OLS) to equation (4). Columns (1) and (2), which control for different fixed effects, show that an additional year in the US is associated with an increase in the probability of having a son as the firstborn by 0.5 percentage point. With two years in the US, the probability of having a boy as the firstborn for an average migrant is 53%, a 2% increase in that probability for non-migrants, 52%. Compared to aborted boys, about 65 more girls were lost for migrants in the sample. As for the 1.13 million Mexico-born males aged from 15 to 24 years in the US estimated by the 2000 US census, two years of them in the US are associated with about 11 thousands fewer girls born. Controlling for fathers’ marital status and locations in column (3) does not change the magnitude or significance of the coefficient on US duration greatly. The birth country of the children is also controlled for in column (3). Its insignificant coefficient suggests that the possible movements of pregnant women are not significantly associated with the sex of the fetus. A subsample limiting to children born in Mexico gives similar coefficients on US duration.

Table 3. The relationship between fathers’ migration durations and sex of first children (MMP)

Sample: fathers with their first children born after they age 16.

Dependent variable: dichotomous variable = unity for boys and zero for girls.

Independent variable: US duration.

***Significant at 0.01, **significant at 0.05 level, *significant at 0.1 level.

Errors are clustered at community level.

Across specifications in Table 3, R ² values are small. Coefficients on all variables, except for US duration, are either insignificant or barely significant, suggesting that the sex of children is generally random if there is no sex-selective abortion. Though US durations imply human capital acquisition and wealth accumulation, human capital captured by education is not significantly associated with the sex of the first child.Footnote ⁹ The significant coefficients on US duration distinguishing it from other variables may suggest two hypotheses. First, other than human capital, fathers’ migration experiences may build networks and other social capital in the US, which can not be easily obtained by solely education or wealth. Those networks and social capital may facilitate future migration trips of family members, especially males. Sons, compared to daughters, are more likely to encourage the households to take advantage of those resources in the US. Second, migrants might be self-selected on unobservables, such as possible son preference. Limiting the samples to migrants, who are defined as those with migration experiences before the interview, Appendix Table A1 still shows that the coefficients on US duration have higher significance levels than the coefficients on other variables. These migrant samples do not fully solve the self-selection issue, since the lengths of US durations could be correlated with unobservables.

In fact, facilitated future migration trips mentioned above suggest an influx of wealth, the value of which varies by the sex of the firstborn child. As education also encourages a wealth increase in the labor market which is dominated by males, just like migration, educated fathers with established resources in the labor market may want a son to continue collecting returns on those recourses. This may explain why coefficients on years of schooling in Table 3 column (4) and Appendix Table A1 are marginally significant.

The insignificant coefficients on the migration experience of fathers’ relatives or wives in Table 3 columns (4) and (5) emphasize the specialty of father's migration experience. In fact, though not shown in this paper, a sample consisting of female household heads also shows no significant coefficients on mothers’ US durations. As women seldom migrate for economic reasons, their previous US durations may not provide economic opportunities for future migration trips. The small mean value and variation of wife's US duration in Table 3 and a much smaller sample size of female household heads do not allow me to find a clear relationship between mothers’ US duration and the sex of their first child.

4.2. Instrumental variable

Estimating equation (4) eliminates reverse causality because we use the fathers’ migration experience before knowing the sex of the fetus. The main problem hurting the causal interpretation of the estimation is the selection issue, as people with different lengths of US durations might be different in unobservable characteristics. In fact, a Durbin–Wu–Hausman test rejects the hypothesis that US duration is exogenous at 10% level. Therefore, an instrumental variable (IV) analysis is applied.

In the literature on Mexico–US migration, some studies use the distance to the destinations based on the Mexican railroad networks several decades ago to instrument household migration behaviors [Alcaraz et al. (Reference Alcaraz, Chiquiar and Salcedo2012), Pfutze (Reference Pfutze2012)]. In this paper, distance to the US is largely captured by community FE and state FE. Therefore, as Alcaraz et al. (Reference Alcaraz, Chiquiar and Salcedo2012) claim that variables measuring past migration rates may serve as good instruments for current migration flows, I follow Hanson and Woodruff (Reference Hanson and Woodruff2003) and construct an IV based on the historical migration flows of neighbors in the same community. On the one hand, larger historical migration flows imply not only stronger networks and better job opportunities in the US but also lower migration costs [Winters et al. (Reference Winters, De Janvry and Sadoulet2001), Munshi (Reference Munshi2003), McKenzie and Rapoport (Reference McKenzie and Rapoport2010)]. Those community networks may affect individuals’ migration intentions and migration durations in the US. On the other hand, it is reasonable to believe that neighbors’ previous migration trips do not directly affect individuals’ fertility decisions or possible sex preference over children, as Table 3 suggests that even the migration experiences of relatives, including fathers of household heads, show no significant association with the sex of the first child.

Specifically, the IV in this paper is the proportion of migrants, who stayed or migrated to the US, among all other household heads in the community c five years before the endogenous variable US Duration _i,c,s,t−2 is measured: Migrant Neighbor _i,c,t−7. It is expected to be positively associated with individuals’ US durations.

Therefore, the first stage of the IV estimation is

(5)$$\eqalign{ US \; Duration_{i, c, s, t-2} =&\eta_{0} + \eta_{1} Migrant \; Neighbor _{i, c, t-7} + \eta_{2} X_{i, c, s, t} + \eta_{3} COM_{c, d} + \alpha_{t} \cr & + \beta_{s} + \gamma_{c} + \epsilon_{i, c, s, t},\;} $$

and the second stage is

(6)$$G_{i,c, s, t} = \kappa_{0} + \kappa_{1} \hat{US \; Duration_{i, c, s, t-2}} + \kappa_{2} X_{i, c, s, t} + \kappa_{3} COM_{c, d} + \alpha_{t} + \beta_{s} + \gamma_{c} + u_{i, c, s, t},\; $$

where $\hat {US \; Duration_{i, c, s, t-2}}$ is the fitted value from equation (5). Robustness checks using proportions of migrant neighbors in different years, such as t–3, t–4, t–5, t–6, and t–8, give consistent results.

It is possible that information and remittances sent back by migrant neighbors could reshape the development of the community, which may influence individuals’ fertility decisions. Controlling for rich economy-related characteristics at community-decade level (COM _c,d) and community fixed effects (γ_c) as shown in equation (6) relieves the concern.

Table 4 shows the IV results.Footnote ¹⁰ In the first stage, as expected, with more migrant neighbors in the past, the household heads are more likely to stay longer in the US. F values and Kleibergen–Paap F statistics for all specifications reject the weak instrument hypothesis.Footnote ¹¹ In the second stage, one more year in the US leads to an increase in the probability of having a boy as the firstborn by about 3 percentage points in columns (1)–(3). An average migrant spends two years in the US, which could increase the probability of having a boy as the firstborn from 52%, the random probability, to 58%. The coefficients on US duration are slightly larger in columns (3)–(5), which controlled for variables related to household heads’ marital status, locations, and other members’ migration experiences. The marginally significantly positive coefficients on years of schooling may be due to sons’ greater labor market participation and higher expected earnings.

Table 4. Fathers’ migration durations lead to son preference for the firstborn - IV analysis (MMP)

Dependent variable: dichotomous variable = 1 for boys; 0 for girls.

Independent variable: US duration.

Sample: fathers with their first children born after they age 16.

Errors are clustered at community level.

***Significant at 0.01, **significant at 0.05 level, *significant at 0.1 level.

4.3. Robustness checks

Though fathers’ previous migration experiences give them some son preference regarding their first child, their future migration trips after the births of first children should not have any impact on the sex of those first children. Including variables indicating fathers’ migration durations after knowing the sex of their first child in regressions confirms that. Specifically, two variables are used. One is fathers’ migration durations occurred between year t + 3 and the survey year: US duration (future). Migration experiences in years t + 1 and t + 2 are not counted because fathers may stay in Mexico when their children are infants. But they are counted in the alternative variable: US duration (rest) = total US duration before interview minus US Duration _i,c,s,t−2.Footnote ¹² These two variables are added in Table 5 columns (1) and (2), respectively.

Table 5. Robustness checks for fathers’ future migration durations and placebo tests before 1957 (MMP)

Dependent variable: dichotomous variable = 1 for boys; 0 for girls.

Independent variable: US duration.

Sample (columns (1)–(2)): fathers with their first child born after they age 16.

Sample (column (3)): fathers with their first child born before 1957.

Errors are clustered at community level.

***Significant at 0.01, **significant at 0.05 level,

*significant at 0.1 level.

Holding US Duration _i,c,s,t−2 constant, Table 5 columns (1) and (2) show insignificant coefficients on both US duration (future) and US duration (rest) in the first and second panel where OLS and IV estimation results are displayed, respectively.Footnote ¹³ Limiting the samples to those migrant fathers, Appendix Table A2 gives consistent results.

In addition, a placebo test is constructed based on the fact that detecting prenatal sex is impossible before the technology was first reported in the year 1956, and it would have taken time for the technology to be adopted in Mexico. Limiting my sample to all fathers having their first child before the year 1957, the sex of the children should be random even if migrants have a preference for sons. Summary statistics for this sample are shown in Appendix Table A3. Table 5 column (3) reports both the OLS and IV estimation results for this sample. Though the sample sizes are much smaller, the sex of children before the invention of prenatal sex discernment technologies seems random as no coefficients in the first panel columns (3) are significant. The insignificant coefficient on US duration is only about half of the coefficients on the same variable from the OLS results shown in Table 3. The second panel using IV estimation gives similar results, but the IV is a weak one probably due to the small sample size and small variation of the IV.Footnote ¹⁴ Consistent results can be found for migrant samples in Appendix Table A2, but the sample sizes are even smaller.

Furthermore, I use the data from the MxFLS to test the hypothesis. Without community-decade characteristics, weighted OLS regression controlling for state FE, year FE, and community FE gives consistent results in Table 6: the coefficient on US duration in column (2) is significantly positive and has a magnitude closer to the MMP coefficients from IV regressions in Table 4. Unweighted results reported in column (1) show insignificant coefficients which may due to the small sample size and the small number of migrants. An IV analysis is not shown because of the weak instrument issue possibly resulting from the small variation in the instrument variable.

Table 6. The relationship between fathers’ migration durations and sex of first children (MxFLS)

Data Source: the MxFLS

Sample: fathers with their first children in households.

Dependent variable: dichotomous variable = unity for boys and zero for girls.

Independent variable: US duration.

***Significant at 0.01, **significant at 0.05 level, *significant at 0.1 level.

Errors are clustered at individual level.

Other robustness checks include (1) Fathers’ migration experiences may affect the total number of children wanted by a family. Controlling for the total number of children or the number of sons and daughters at the survey time and repeating the analyses above give consistent results. Appendix Table A4 uses the panel data for the number of children by sex and their fathers’ previous migration experiences and shows that they are not significantly associated with each other after controlling for individual FE and year FE. If migration experiences also cause fertility declines, securing a son as soon as possible may also be the reason for migrants’ higher probability of having sons as firstborn children. (2) Using fathers’ migration durations before marriage to replace US Duration _i,c,s,t−2 gives consistent results. (3) When migrants are defined as people with positive values for US Duration _i,c,s,t−2, the migrant sample gives a smaller sample size but consistent results.

1. (4) As sex-selective abortions are suggested, a boy fetus is more likely to be kept compared to a girl fetus. Unfortunately, abortions, especially illegal ones, are usually not clearly recorded, let alone the sex of the aborted fetuses. To explore how sex-selective abortions are related to illegal behaviors, Appendix Table A5 column (1) divides the US duration in equation (4) into legal US duration and illegal US duration; column (2) limits the sample to children who were born before year 2007; column (3) limits the sample to household heads whose wives have no trips to the US or Mexico city: have to adopt illegal abortions if wanted. Appendix Table A5 column (1) shows that the influences of fathers’ US durations do not differ by the legality of migration trips. Columns (2) and (3) suggest that when legal abortion is not available, the effects of fathers’ US duration on the sex of firstborn children still exist.

4.4. Birth order of the first son

Migrants’ higher probability of having sons as the firstborn child suggests their higher intentions to make their first sons the firstborn child especially when they plan to start parenthood at a certain age. This section aims to show some evidence of migrants moving down the birth order of their first sons and support the theoretical arguments in section 2.3.

Conditional on having at least one son in the household, the natural probability of the first son being the firstborn child varies by the total number of children in the family as listed in the first panel in Appendix Table A7. Focusing on households with at least one son, the frequencies of migrants having their first sons being the first children are higher than the natural probabilities as shown in Figure 1(a), while non-migrants show frequencies closer to the natural probabilities.Footnote ¹⁵ While in samples consisting of fathers with at least one daughter, migrants’ frequencies of having the first daughter being the firstborn child are generally lower than those for non-migrants and the natural probabilities.

Fig. 1. Probability and frequency of the first son or daughter being the firstborn child. This figure shows the comparison between the natural probability of having the first son (daughter) being the first child and the frequency of fathers having their first son (daughter) as the firstborn. Figures (a) and (b) limit to fathers with at least one son or daughter ever born to them before the interview, respectively. For example, in a family with two children and at least one son, the frequency of the first son being the first child is 0.6832 as shown in figure (a), which is higher than the natural probability (0.6711) as shown in Appendix Table A7. Non-migrants show frequencies that are closer to the natural probability. Figure (b) shows migrants’ lower frequency of having the first daughter being the first child than that of non-migrants and the natural probability. Samples with more than 5 children are not shown because of the small sample sizes, (a) first son is the firstborn, (b) first daughter is the firstborn.

Migrants’ higher probabilities of making the first sons their firstborn child can also be found in Table 7 where I limit samples to fathers with at least one son ever born to them after they age 16 and link their previous migration experiences to the birth order of their first sons. Specifically, I replace the dependent variable in the OLS estimation equation (4) and IV estimation equation (6) with F _i,c,s,t, a dichotomous variable which equals unity if father i's first son, who is born in year t, is the first child and zero if the first son is of higher birth order. This tests whether fathers’ migration experiences increase the probability of the first son being the firstborn child. Both the OLS and IV results in Table 7 columns (1)–(3) show that fathers’ additional year in the US increases the probability of having the first son as the firstborn child by about 3 percentage points.

Table 7. The probability of the first son or daughter being the firstborn child (selected coefficients)

Samples (1)–(4): fathers with at least one son ever born to them. Samples (4)–(8): fathers with at least one daughter ever born to them.

Samples (5) and (8): limit the sample to fathers with their first sons or daughters born before year 1957. Dependent variable: dichotomous variable = unity for the first son (daughter) being the firstborn, zero otherwise. Errors are clustered at community level. ***Significant at 0.01, **significant at 0.05 level, *significant at 0.1 level.

Repeating the estimations but focusing on fathers with at least one daughter, the coefficients on US duration from IV estimations are all negative, though insignificant, in columns (5)–(7). Columns (4) and (8) provide robustness checks focusing on fathers who have their first son or daughter born to them before year 1957 and finds insignificant coefficients on US duration.

5.1. Assimilation

If Mexican migrants assimilate into the “first a son and second a daughter” preference of Americans, those who travel earlier in life may have stronger incentives to make the firstborn a boy, holding migrants’ US experiences before the births of children the same. Ost and Dziadula (Reference Ost and Dziadula2016) find that Asian immigrants exhibit a fertility pattern quite close to that of US natives only if they arrive in the US as children. However, most migrants in the MMP travel as adults for economic reasons, making it difficult to test for gender biased assimilation if it only happens to young migrants.Footnote ¹⁶ In addition, as males dominant migration flow, most mothers do not travel, the effects of assimilation for mothers are limited and depend on how fathers are empowered in the family.

One possible way to test assimilation is to see whether the second children of migrants are more likely to be daughters, though undergoing an abortion to choose the sex of the second child seems uncommon. Focusing on the fathers with at least two children and regressing the sex of the second child on fathers’ previous migration durations, both the OLS and IV estimations in Table 8 show that fathers’ migration durations have no significant effects on the sex of the second children. Summary statistics for the sample consisting of fathers with at least two children are presented in Appendix Table A6.Footnote ¹⁷ Specifically, Table 8 columns (1), (3), and (5) use fathers’ US durations two years before the birth of the second child, while columns (2), (4), and (6) use fathers’ US durations two years before the birth of the first child. When the first child is a son in columns (3) and (4), fathers’ US durations have no significant coefficients in both the OLS panel and the IV panel. Similar results can be found for the sample consisting of fathers having a daughter as their first child in columns (5) and (6), but the IV analysis shows a weak instrument variable problem.

Table 8. Fathers’ migration experience and the sex of their second children (MMP)

Data source: the MMP

Sample (columns (1)–(2)): fathers with at least two children.

Sample (columns (3)–(4)): fathers with two children and the first children are boys.

Sample (columns (5)–(6)): fathers with two children and the first children are girls.

Dependent variable: dichotomous variable (sex of the second child) = unity for boy and zero for girl.

Independent variable (columns (1), (3), (5)): US duration (birth year of the second child −2).

Independent variable (columns (2), (4), (6)): US duration (birth year of the first child −2).

Birth year FE, state FE, community FE, and community-decade characteristics are controlled for.

Errors are clustered at community level.

***Significant at 0.01, **significant at 0.05 level, *significant at 0.1 level.

In fact, as demonstrated in Figure 2, regressing the sex of children of different birth orders on fathers’ US durations shows that only the sex of the firstborn children is significantly associated with fathers’ US durations. Plots in Figure 2(a) show the coefficients and their confidence intervals on US Duration _i,c,s,t−2 when replacing the dependent variable in equation (4) with the sex of children of different birth orders. Figure 2(b) displays results controlling for the sex of elder siblings. Figure 2(c) uses fathers’ US durations two years before the births of the first child, while Figure 2(d) uses fathers’ US durations before their first marriages to replace US Duration _i,c,s,t−2 in equation (4). Dependent variables are dichotomous variables indicating whether children of different birth order are sons.Footnote ¹⁸ The IV estimation results for children with birth order lower than 5 are shown in Figure 3, presenting consistent results. The instrument variable becomes a weak one when the birth order is higher than 4 probably due to the decreasing sample size.

Fig. 2. Coefficients on US duration (OLS) vs. birth order. Plots show the coefficients and their confidence intervals on US duration related variables when replacing the dependent variable in equation (4) with the sex of children of different birth order. The dependent variables are the dichotomous variables indicating sons of different birth order. Independent variables are US Duration _i,c,s,t−2 in figures (a) and (b), fathers’ US durations two years before the births of the first children in figure (c), and fathers’ US durations before their first marriages in figure (d), (a) US duration (t–2), (b) US duration (t–2) (sex of children), (c) US duration (t–2) before first child, (d) US duration before first marriage.

Fig. 3. Coefficients on US duration (IV) vs. birth order. Plots show the coefficients and their confidence intervals on US duration related variables when replacing the dependent variable in equation (6) with the sex of children of different birth order. The dependent variables are the dichotomous variables indicating sons of different birth order. Independent variables are US Duration _i,c,s,t−2 in figures (a) and (b), fathers’ US durations two years before the births of the first children in figure (c), and fathers’ US durations before their first marriages in figure (d), (a) US duration (t–2) (IV), (b) US duration (t–2) (sex of children) (IV), (c) US duration (t–2) before first child (IV), (d) US duration before first marriage (IV).

As the sex of children of higher birth order is not affected by fathers’ migration durations, this paper does not find evidence for migrants’ assimilation to the “first a son and second a daughter” preference. At the same time, a hypothesis that migration causes biologic changes and then affects the sex of children can be rejected, otherwise the sex of other children should not remain natural. Parents using abortions to delay parenthood as mentioned by Guillaume et al. (Reference Guillaume, Rossier and Reeve2018) could be one of the reasons why only the sex of the first child is affected. Other explanations may relate to the difference between sons who are the firstborns and other children, including daughters as the firstborns and sons of higher birth order. The section below aims to show that sons who are the firstborn are less likely to travel with their fathers than other children, suggesting that they substitute more of their fathers’ roles and responsibilities.

5.2. Comparison between children

First, focusing on the household migration behaviors, I compare fathers with firstborn children being sons and fathers with firstborn children being daughters to see whether sons, compared to daughters, are more likely to substitute for fathers’ responsibilities. Table 9 first panel column (1) is limited to fathers with their first children older than age 20 at the interview. The dependent variable is fathers’ US durations that occurred after their first children are 14 years’ old. The independent variables include a dichotomous variable indicating a son as the firstborn, firstborn child's US duration occurred after age 14, and the interaction term between them. Fathers’ previous US experiences, other demographic characteristics in the survey year, children's birth year FE, and community FE are controlled for. Errors are clustered at the community level. Summary statistics of this sample and other samples in Tables 9 and 10 are displayed in Appendix Table A8. The aim of this regression is to see whether the effects of the first child's migration behavior on fathers’ migration behavior differ by the sex of the children.Footnote ¹⁹

Table 9. Comparison between first son and first daughter

Data source: the MMP

Sample (first panel): male household heads with at least one child.

Sample (second panel): male household heads with at least one son and one daughter.

Dependent variable (first panel): fathers’ US durations after their first child ages 14.

Dependent variable (second panel): fathers’ US durations after both children age 14.

Independent variables: children's US duration after they age 14.

Wealth indicators, community FE, and birth year of each child FE are controlled for.

Errors are clustered at community level.

***Significant at 0.01, **significant at 0.05 level, *significant at 0.1 level.

Table 10. Comparison between first son and second son

Data source: the MMP

Sample (1st panel): male household heads with two sons, one is the first born child.

Sample (second panel): male household heads with at least two sons.

Dependent variable (1st panel): fathers’ US durations after their second son ages 14.

Dependent variable (2nd panel): fathers’ US durations after sons age 14.

Independent variables: children's US durations after they age 14.

Wealth indicators, community FE, and birth year of each child FE are controlled for.

Errors are clustered at community level.

***Significant at 0.01, **significant at 0.05 level, *significant at 0.1 level.

Table 9 first panel column (1) shows that when children migrate, fathers are more likely to migrate. Migration trips of family members may facilitate each others’ movements to the US. The negative coefficient on the interaction term between children's US durations and the sex dichotomous variable suggests that if the firstborn is a son, the positive association between two generations’ migration experiences decreases. First panel column (2) and column (3) divide the dependent variable in column (1) into fathers’ US durations traveling with their adult firstborns and the remaining US durations. As shown in Appendix Table A8, fathers’ US durations in the company of the first child are much shorter than of the remaining children. The positive correlation between the US durations of the firstborns and fathers’ US durations with a child is larger for daughters, as the coefficient on the interaction term in column (2) is significantly negative. Holding children's migration duration constant, daughters are more likely to travel with their fathers, compared to sons. This is also reflected in column (3) as the coefficient on the interaction term in column (3) is positive. Though Li (Reference Li2016) mentions that the number of adult children increases fathers’ US durations in Mexico, it seems that this relationship does not differ by the sex of adult children, at least the firstborn children as shown in column (1). However, the sex of the first child influences how much time fathers spend alone in the US. Sons, compared to daughters, as the firstborns are more likely to stay at home if fathers migrate to the US, suggesting that they substitute more for fathers’ responsibilities. This is consistent with Mexican traditional gender divisions that men usually control and protect the family more than women [Donato et al. (Reference Donato, Wagner and Patterson2008)].

Table 9 second panel includes all fathers with at least one adult son and one adult daughter at the interview to show that first sons, compared to first daughters in the same family, are more likely to be separated from their fathers if fathers travel. The dependent variable is fathers’ US durations occurred after their first sons and first daughters over age 14 in column (1), fathers’ US durations traveling with their first sons in column (2), and fathers’ US durations traveling with their first daughters in column (3).Footnote ²⁰ The coefficient on the daughters’ US duration in column (3) is larger than the coefficient on sons’ US durations in column (2), suggesting that first daughters, compared to first sons, are more likely to travel with fathers.

Table 10 aims to show the comparison between first sons and second sons. Table 10 first panel limits to fathers with sons as the firstborn children and the second sons older than age 14 at the survey time. The dependent variable is fathers’ US durations occurred after both sons age 14 in column (1), and fathers’ US durations traveling with the first and second sons after both sons age 14 in columns (2) and (3), respectively. Independent variables are US durations of each son as an adult. Compared to the first sons who are also the firstborn children in this sample, the second sons are more likely to travel with fathers, as the coefficient on second sons’ US duration in column (3) is larger than the coefficient on first sons’ US duration in column (2). A similar conclusion can be drawn by limiting the sample to fathers with at least two sons older than age 14 at the survey time. It is still true that the second sons, compared to the first sons, are more likely to travel with fathers. In other words, fathers are more likely to separate from their first sons when they travel.

The causal relationship between sons’ migration durations and fathers’ migration durations depends on how households maximize utility. Tables 9 and 10 just show that sons as the firstborn children provide less company to their migrating fathers than sons of higher birth order and daughters as the firstborns do, though causal links are not established here. This supports the above arguments that sons as the firstborn are more likely to substitute for fathers and share more of fathers’ responsibilities than other children do. This difference between sons as the firstborns and other cases may explain why migrants develop son preference. The longer fathers stay in the US, the more households benefit from sons as the firstborn substituting for fathers.