On the Joint Consumption and Labour Supply Effects of Migration on those Left Behind

Abstract Previous literature has investigated the effect of migration on remaining household members’ consumption or labour supply, but has rarely examined them jointly. When migration increases consumption but reduces leisure time, one needs a specific framework to draw a conclusion about the overall impact on welfare. I propose such a new approach and test its theoretical implications using household panel data from rural Mexico. The results reveal that adjusting for leisure costs reduces the net welfare gain of migration by one fourth relative to what the consumption gain would suggest.


Introduction
Worldwide, one in seven people migrate out of their region of origin, most often leaving the rest of the family behind. While migrants may realise important income gains when moving, the question arises whether household members left behind also benefit. In fact, although non-migrants may benefit from remittance inflows, the local earnings and time inputs of the migrants are lost. As the next section will show, previous literature has developed into two separate branches which examine different factors of non-migrants' welfare. A first traditional strand of research focuses on the consumption effects of migration while a second recent strand concentrates on the labour supply effects. Existing evidence suggests that migration has opposite effects: migration can increase nonmigrants' consumption but may also reduce leisure time. These seemingly conflicting results call for a unified framework in order to draw a conclusion about the overall welfare impact of migration. This paper is the first to propose such a new approach in which the utility of consumption and the disutility of labour are both taken into account.
Whenever non-migrants increase their labour supply in response to the migration of a household member, they generate an additional income which can be used for consumption. Such an increase in consumption due to higher labour supply must, however, not be confused with a welfare gainas most previous studies dosince it comes at the expense of leisure time. To address this issue, I propose a welfare metric which includes leisure costs into the evaluation of the welfare impact of migration. The principle of this metric is to translate the leisure costs into consumption terms by estimating the extra consumption produced by the longer working time, and then remove these costs from the total consumption gain of migration.
Using survey data from rural Mexico, I first document that migration to the United States increases the remaining households' consumption by 20 per cent, equivalent to 180 pesos a month, but also increases their labour supply in farm work by about 1.4 hours a week. I then provide an average migration in Bangladesh induced increases in food and non-food expenditures of the origin household by 30-35 per cent (see also Mergo, 2016 for results in Ethiopia).

Labour supply studies
Another recent strand of research examines the labour supply effects of migration. Many studies find that migration causes household members left behindespecially femalesto increase their labour supply in farm work or in other unpaid family work (self-employment). This finding has been shown in many different contexts, such as China (Chang, Yuan Dong, & MacPhail, 2011;Démurger & Li, 2013;Mu & van de Walle, 2011), Albania (Mendola & Carletto, 2012), or Egypt (Binzel & Assaad, 2011). More generally, the literature has been concerned with various factors of non-migrants' wellbeing, such as health or educationfor an overview see Antman (2013). In particular in Mexico, evidence suggests that remaining Mexican children attend less school and increase work hours in response to a parental migration (Antman, 2011;McKenzie & Rapoport, 2011). Yang (2008) is one of the only studies to examine simultaneously both the consumption and labour supply effects of remittances. The author uncovers positive effects of overseas migrants' remittances on Philippine households' hours in self-employment and investment in entrepreneurial activity (as well as in education) while finding negligible impacts on current consumption. Yet, the theoretical implications for the welfare of those left behind are not fully explored. Also, the effects of remittances are not necessarily informative about the overall impacts of migration. 3 This paper contributes to fill this gap.

Intra-household sharing
Finally, this paper relates to the literature examining how the gains of migration are shared within the family. A growing body of literature has shown that transnational households are not immune to noncooperative behaviours due to acute information asymmetries arising between family members separated over long distances. Findings in Ambler (2015) and Seshan and Zubrickas (2015) suggest that migrants may take strategic advantage of these information asymmetries to send a lower amount of remittances. In the context of rural Mexico, I find that international migration largely benefits those staying behind. This result is more in line with the theory of Stark and Bloom (1985), which views migration as a cooperative and mutually-beneficial contract between the migrant and the rest of the family.

A stylised model of migration
In this section, I develop a stylised model to gain insights into how migration decisionstaken to increase the household welfareshould affect the consumption and time allocation of those left behind.

Framework
Formally, I assume that the family maximises a Bergson-Samuelson joint welfare function θU 2 þ ð1 À θÞU 1 , with 0 < θ < 1 the Pareto weight. For each i ¼ 1; 2, individual utility U i is a concave function of individual consumption c i and leisure l i , which are complementary inputs in the utility (U i c i l i ! 0). Each family member allocates his time endowment T i between on-farm work L F i , off-farm wage work L O i , and leisure l i . Family members' labour is remunerated at different fixed wage rates w 1 and w 2 in the local labour market. 4 Family members' labour supplies are perfect substitutes in the farm production F, which exhibits diminishing marginal productivity of labour (F 0 ð0Þ ¼ þ1; F 0 ðLÞ > 0; F 00 ðLÞ < 0). Other inputs such as land or capital are supposed to be fixed. 5 Joint consumption and labour effects of migration 131 Let member 1 be the potential migrant and w US 1 the foreign wage rate. If he migrates, member 1 can no longer work in the family farm at the origin. Let C be the monetary costs of migration (for example travel, housing, and job search at destination) and let π ¼ C w US 1 L US 1 be the costs expressed in foreign earnings-equivalent units (0 < π < 1), with L US 1 member 1's working hours at destination. π represents the fraction of foreign earnings that are forgone to meet migration costs, which I assume to be constant. In addition to monetary costs, the separation of family members also entails psychological costs δ > 0, which I suppose are additive in the family utility. To decide whether member 1 migrates, the household compares his indirect utilities with and without migration. The household optimisation process can be expressed as a utility maximisation in the following two labour regimes: with w Ã 1 ¼ ð1 À πÞw US 1 the foreign wage net of migration costs. The time constraints are L F i þ L O i T i , for i ¼ 1; 2. I assume that family members supply at least one unit of labour, that is L F i þ L O i > 0. The Pareto weight θ reflects the relative bargaining power of the family members. In this setting, θ is constant and exogenous, which ensures that migration decisions are beneficial for the non-migrant member. This hypothesis will be tested in the data in the next sections. If migration were to reduce the bargaining power of the non-migrant member, he would possibly be worse-off after migration.

Income effect through remittances
To simplify the exposition of the income effect of migration, let me consider a landless household who only derives income from wage-earning labour (F ¼ 0). 6 The maximisation of the utility of landless families can then be attained by a two-stage budgeting: in the first stage, household fulltime income is allocated between members; and in the second stage, each individual independently maximises his utility with respect to his own budget constraint. Let R ¼ w 1 L 1 À c 1 denote the net transfer of member 1 to member 2, which represents migrant's remittances if member 1 migrates. Subsequently, the programme max θU 2 þ ð1 À θÞU 1 s:t: with the optimal R such that θU 2 c 2 ðR; w 2 Þ ¼ ð1 À θÞU 1 c 1 ðR; w 1 Þ. Differentiating the last equation gives: @U 1 c 1 @R Because utilities are concave and leisure and consumption are complementary, it can be shown that @R @w 1 > 0: the intra-household transfer increases with the wage rate of member 1. In this unitary model of the family, member 1 shares any earnings gain with the other member 2 (corollary of income pooling). Since migration only occurs if the wage abroad is higher than the wage at home (w Ã 1 > w 1 ), this implies that the migrant remits at least his initial net contribution to the household income (Rðw Ã 1 Þ > Rðw 1 Þ). Migration thus increases the unearned income accruing to the non-migrant, raising his reservation wage. Since off-farm wages remain unaffected by migration, the non-migrant reduces his wage work in the labour market. The consumption of the non-migrant also unambiguously increases, as well as his utility.

Substitution effect and farm labour
Let me now introduce farm production. To fix ideas, I assume that member 1's wage is higher than member 2's, that is that w 2 ¼ αw 1 with 0 < α < 1. The predictions essentially remain the same in the opposite case (see Supplementary Materials). The farm always demands a positive amount of labour input. Since family members are substitutes in the farm although member 1's off-farm wage is higher, efficiency requires that member 2 specialises in farming. Figure 1 shows the optimal labour participation choices of member 1 depending on his wage and the marginal productivity of farm labour. When his wage w 1 is lower than the marginal productivity of the farm Ω, member 1 only works in the farm. When his wage is sufficiently high (w 1 > Ω), member 1 starts participating in the local labour market and the household equalises the return of farm and off-farm work, that is F 0 ðL F Þ ¼ w 1 . A marginal increase in member 1's wage reduces the total family labour devoted to the farm, given that it is now more efficient to reallocate labour to offfarm work. This reallocation increases the household income which is pooled within the family. Member 1 migrates and leaves the farm when the foreign wage w Ã 1 is sufficiently high. Since the earnings gains of migration are shared between the family members, member 2 does not need to completely replace the migrant's farm labour. Due to this income effect, the total family labour in the farm declines.
The marginal productivity of member 2's farm labour rises when member 1who initially worked in the farmmigrates. Due to this substitution effect, which has the opposite influence of the income effect, the impact of migration on the non-migrant's farm labour remains ambiguous. However, migration does not entail any substitution effect when the migrant does not work in the farm initially. In this case, the non-migrant's farm labour should decrease with migration. It may also remain constant if the non-migrant initially participates in both farm and off-farm work. 7

Testable predictions
In summary, the theoretical model generates the following five predictions, necessarily implied by migration decisions taken to increase non-migrants' welfare: (1) The migrants' remittances should exceed the forgone net income contribution to the origin household; (2) Members left behind should reduce their labour in off-farm wage-earning jobs; (3) Non-migrants' consumption should increase; (4) The total family labour devoted to the farm should decrease with migration; (5) Non-migrants' farm labour should increase more (or decrease less) when the migrant initially worked in the farm relative to when he did not. These predictions will be tested by estimating the effect of migration on non-migrants' consumption and time allocation using an empirical model developed in the next section.

Measuring the welfare gain
The migration of a farmer may cause non-migrants to increase their labour supply in the farm. The consumption gain generated by the additional hours spent in the farm does not represent a welfare gain because it comes at the expense of leisure time. In order to take into account the leisure costs, I propose a welfare metric that translates these costs into consumption terms, that is into the amount of consumption that non-migrants would have forgone if they had not increased their working hours.

Joint consumption and labour effects of migration 133
Formally, noting ðc o 2 ; , o 2 Þ, the consumption and leisure at the non-migration optimum, and ðc m 2 ; , m 2 Þ, the ones at the migration optimum, the welfare metric is defined by the value of consumption Δ ? c such as: The first condition means that Δ ? c measures the consumption increase that would generate the same welfare gain of migration, holding non-migrants' leisure constant. The second condition means that, conversely, Δ ? c is the drop in consumption that would generate the same welfare loss caused by return migration. The individual utility U 2 being a concave function, Δ ? c can be bounded by above by c m ðc m 2 ; , m 2 Þ. 8 Given that, at each optimum, the marginal rate of substitution between leisure and consumption is equal to the marginal product of the non-migrant's labour Ω e 2 (for e ¼ o; m), the welfare gain can be bounded by Figure 1. Marginal productivity of farm labour and member 1's wage. Notes: Ω is the marginal product of farm labour when member 1 works in the farm only. Ω 2 is the marginal product of member 2's farm labour when he is the only farmer. Ω 2 increases with w 1 and w 1 is the (unique) intersection of Ω 2 with the 45°line. Furthermore, "w 1 ! w 1 , Ω 2 ðw 1 Þ < w 1 . When w 1 < Ω, member 1 only works in the farm and F 0 ðL F Þ ¼ Ω. When Ω < w 1 < w 1 , member 1 works both off-farm and in the farm and F 0 ðL F Þ ¼ w 1 . When w 1 < w 1 , member 1 stops working in the farm and F 0 ðL F Þ ¼ Ω 2 ðw 1 Þ. When member 2's wage w 2 > Ω 2 ðw 1 Þ, member 2 works both off-farm and in the farm and F 0 ðL F Þ ¼ w 2 .
with L o 2 and L m 2 the labour supply of the non-migrant at each optimum. When migration does not affect the marginal return of non-migrant's labour, that is Ω m 2 ¼ Ω o 2 ; Ω 2 , the welfare gain Δ ? c simply amounts to c m 2 À c o 2 À ðL m 2 À L o 2 Þ Ã Ω 2 , that is the total consumption gain c m 2 À c o 2 minus the consumption generated by the labour supply adjustment L m 2 À L o 2 .
3.6. The role of liquidity constraints The model's assumption that farm inputs other than labour are fixed is not in line with the view of migration as a household strategy to alleviate liquidity constraints on the purchase of new inputs in the farm, or investment constraints on new technologies or new activities (Stark & Bloom, 1985;Taylor & Lopez-Feldman, 2010;Woodruff & Zenteno, 2007). If remittances help loosen liquidity (or risk) contraints, the new inputs or technologies may contribute to increase the marginal returns to labour among the remaining households, which would add to the welfare gain of migration, beyond and above the mechanical productivity effect caused by the out-migration of a farmer (that is the substitution effect). Non-migrants may work harder to complement the new inputs, and so much harder that they exceed the loss of the migrant's farm labour. This would result in a net increase in the total household labour devoted to the farm, which would be in contradiction with the model's prediction (4). Therefore, the model offers a good empirical test of whether farm inputs remain fixed or whether migration loosens liquidity constraints on farm investments: if the total household farm labour were found to increase with migration, this would offer supporting evidence in favour of the alleviation of liquidity constraints. Another issue arises if the income gains from the increased investment take time to materialise. In the presence of liquidity constraints, migrant households may forgo some consumption in the shortrun in order to finance farm investments, and reinvest any profits into growing their farm. Their income and welfare would then increase in the long-run, at the expense of their short-term welfare.

The Mexican Family Life Survey
I use the Mexican Family Life Survey (MxFLS), which is a longitudinal household survey representative at the national and regional level. The baseline survey was conducted from April to July 2002 and covered approximately 3,700 households residing in 93 different rural municipalitiesdefined as municipalities with fewer than 15,000 inhabitants. The second round of the survey began in mid-2005 and was completed in 2006, with a 95 per cent re-contact rate at the household level. If an individual interviewed in the previous round is not found in the same household of origin, resident members of the household are asked about the location and date of departure of this individual. Therefore, even if they could not be individually re-contacted, all international migrants can be identified from the household roster. All sorts of migration to the United States can be observed, either legal or illegal, temporary or permanent. For the rest of the empirical analysis, I exclude singleperson households, as well as households in which no individual is within the age range of migrating (that is 12-43 years old). In fact, these households are extremely unlikely to send migrants by 2005. 9 The Appendix provides a detailed overview of the way we construct the outcome variables (consumption and labour supply), as well as the explanatory variables. Table A1 in the Appendix provides descriptive statistics of the sample of 2,642 households used in this study. Among those, 293 households (11%) sent at least one member to the United States between the two surveys rounds, that is between 2002 and 2005. Among the sample of 8,152 individuals older than 15, 330 migrate to the United States during that period (4%) and leave behind 753 non-migrant household members (9%). Table A1 shows how the initial characteristics of households in 2002 differ between households with and without migrants (see Appendix for details). Also, Table A2 reports the variation in some household characteristics between 2002 and 2005, and Joint consumption and labour effects of migration 135 shows that both the consumption and labour supply of migrant-sending households increase significantly more relative to other households.

Empirical specification
To estimate how a household member's migration to the United States affects the labour supply and other outcomes of the non-migrants left behind, I estimate the following regression of outcome measure Y ihpt for individual i in household h residing in municipality p at time t: where MigUS ht is a binary equal to 1 if household h has at least one member currently living in the United States at time t, and zero otherwise. The vector of individual fixed effects η i captures observed and unobserved time-invariant heterogeneity at the individual level. μ p is a vector of fixed effects indicating the municipality of residence and λ t is a vector of year fixed effects. The interaction of year and municipal fixed effects λ t Ã μ p controls for municipal-specific time-varying shocks. The interaction λ t Ã X ih α controls for shocks or time trends that are specific to individuals and households with certain exogenous characteristics X ih , determined prior to migration. Since the MxFLS panel data only contains two roundsone in 2002 and the other in 2005 -Equation (5) can be first-differenced over time to obtain the following difference-in-differences regression: where the operator Δ indicates first-difference over time. The change in the household's migration status ΔMigUS h is a binary variable taking the value of one if a household member out-migrates to the United States between 2002 and 2005, and zero otherwise. 10 Included in the vector X ih are premigration exogenous characteristics measured in 2002: individual age, sex and education, the household size, the number of children and elderly persons in the household, the highest education attained in the household, a quadric form of wealth index, and the amount of public transfers. To account for different time trends between households with and without migration networks or past migration experience in the United States, the vector X ih includes two additional binary variables: one indicating whether the household has extended family living in the United States in 2002 and the other equal to 1 if a former United States returnee lives in the household in 2002. Finally, I cluster the standard errors at the household level to allow for correlations of the error terms Δε ih within households. When the outcome of interest is measured at the household levelfor example consumption per capita -I collapse the data by household and include only household-level characteristics in the controls. In this specification, the reference group effectively contains individuals left behind by family members migrating internally within Mexico. Whether or not I include the internal migration status of the household in the controls of Equation (6) does not significantly alter the estimated impacts of international migration to the United States.

Causal identification
The principal threat to the identification of the causal impact of migration in Equation (6) is the possibility of time-varying shocks to the household that affect both migration decisions and labour allocation (or other outcomes of interest). To address this concern, the regression includes a rich set of municipality-year fixed effects. Since municipalities are small geographical areas in rural Mexico, these fixed effects control for unobserved shocks at a very local level, such as labour demand and agricultural or weather shocks.
However, it is possible that within municipalities, household-specific shocks constitute another source of endogeneity varying over time. For example, it could still be the case that due to a negative shock to household income, the family is compelled to send a migrant abroad and reallocate its labour supply at the origin. I examine whether this problem is likely to bias the results by using data on shocks reported by the household head. I investigate whether shocks incurred by the household between the two survey rounds influence the decision to send a migrant to the United States during the same period. As shown in Table 1, I find that none of the five types of shocksdeath or illness of a household member, job loss (or business failure), crop loss or property loss (house, animal, business)significantly affect migration decisions between 2002 and 2005. Additionally, I explore whether shocks occurring before the baseline survey could influence migration in the subsequent years, thereby causing an artificially low (or high) initial outcome for households with future migrants. Table 1 shows that shocks between 1998 and 2002 have no significant effect on migration in the following years, which tends to rule out the possibility of a 'Ashenfelter dip' type of bias.
One criticism of this approach is that it relies on self-reported data and that unobserved timevarying factors could still invalidate the parallel-trend assumption necessary for identification. To address this problem, I examine whether pre-migration time trends in outcomes are similar between households with and without United States migrants. Because the MxFLS only provides two rounds, I draw upon the Mexican Labor Force Survey (ENOE), which follows each household for five consecutive quarters (with a rotating panel structure) and keep only rural municipalities in the years 2005, 2006, and 2007. Figure S1 (Supplementary Materials) shows that the average differences in labour supply (in various activities) between households with and without United States migrants remain stable over time across the four quarters preceding migration. A formal test of parallel time trends before migration cannot be rejected (Table S7). Accordingly, the inclusion of municipalityyear fixed effects, combined with evidence that the timing of migration is quasi-random, suggests that a causal interpretation of the estimates is plausible.

Results
5.1. Evidence of welfare gain 5.1.1. Consumption gain. I first examine the effects of migration on non-durable consumption expenditure per adult equivalent among the remaining household members at the origin. Table 2 shows that United States migration generates a significant increase in food and non-food consumption between 2002 and 2005. In line with the prediction (3) of the model, total consumption increases by about 180 pesos per household member per month in migrant-sending households, representing an increase of more than 20 per cent relative to households without migrants. 11 Because this increase in non-durable consumption could potentially be financed by cutting down savings or selling durable assets, I also examine how migration affects the ownership of some household durable goods and assets.  Table 3 presents estimates of the effect of United States migration on the labour supply of non-migrant individuals older than 15. I find that United States migration significantly increases labour force participation by 4.3 percentage points among those left behind. This effect is entirely driven by the increase in the participation in self-employed activities by 5.6 percentage points, which represents a 28.2 per cent increase in the probability to work in selfemployment with respect to the non-migrant households' average. Non-migrants spend 1.80 more hours per week in self-employed work, and particularly in the household farm where they work 1.38 additional hours on average. Non-migrants could also replace migrant's lost labour by hiring non-family workers in the farm. Table S5 (Supplementary Materials) shows that migration is not significantly (nor sizeably) correlated with variation in the number of non-family workers on the land or in non-agricultural business.   Joint consumption and labour effects of migration 139 5.1.3. Overall effect on welfare. Given that migration increases non-migrants' consumption but also reduces their leisure time, one needs a specific framework to draw a conclusion about the overall welfare impact. This is precisely the issue that the welfare metric Δ ? c addresses by including the leisure costs in the estimation of the welfare impact of migration (Section 3.5). Δ ? c can be bounded by above by c m 2 À c o 2 À ðL m 2 À L o 2 Þ Ã Ω o 2 and by below by c m 2 À c o 2 À ðL m 2 À L o 2 Þ Ã Ω m 2 , where c m 2 À c o 2 and L m 2 À L o 2 respectively represent the consumption and labour supply effect of migration. Since migration seems to affect no other types of work than self-employment in the farm, ðL m 2 À L o 2 Þ Ã Ω e 2 comes down to the the extra farm income generated by the additional hours worked in the farm for e ¼ o; m. The householdspecific marginal productivity of farm labour (Ω e 2 ) is unobserved and difficult to estimate, but can be easily bounded using the distribution of the hourly wages paid in the agricultural sector. Noting w agri and w agri , the upper and lower limit of the wage distribution, the average welfare effect of migration can be delimited by E½c m The third column of Table 2 and the fifth one of Table 3 respectively provides the average effect on consumption (pesos per month) and on farm labour (hours per week). We thus obtain:  (7) where weekly hours are multiplied by four to obtain a welfare impact in terms of pesos per month. Figure 2 shows how the lower bound of E½Δ ? c varies with the value of w agri and the upper bound with w agri : To proxy for w agri , I use the 90th percentile of the agricultural hourly wage distribution obtained from the 2000 Mexican census. Using this proxy, I find a lower bound of the average welfare effect of 104.9 pesos per month, which is statistically significant at a 5 per cent level. Using the 10th percentile of the wage distribution to proxy for w agri , I find an upper bound of 162.8 pesos per month, also statistically significant at a 5 per cent level. 12 Two conclusions can be made. First, there is a significantly positive welfare gain of migration, even when the leisure costs of farm labour are accounted for. This gain is still sizeable and represents an increase of at least 12 per cent in consumption terms relative to the average among non-migrant households. Second, the upper bound of the welfare gain is still 10 per cent lower than the pure consumption gain. When migration barely affects the farm's marginal productivity (that is Ω m 2 % Ω o 2 ), the welfare impact can be approximated by E½Δ ?  Table 4 shows that, among those households without farm nor business, migration significantly increases consumption by about 243 pesos a month. Non-migrants reduce their work in non-agricultural jobs by 3.2 hours a week, which decreases their earnings by about 227 pesos per month (second column) and which is in line with the prediction (2) of the model (income effect). Had they maintained their labour supplyand thus their earningsconstant, nonmigrants could have consumed up to 227 + 243 = 471 additional pesos, which is precisely what the welfare impact E½Δ ? c measures in the third column. Non-migrants prefer instead to substitute consumption with more leisure, which means that the welfare gain of migration is even higher than what the consumption gain suggests.
I now explore the mechanisms through which migration benefits those left behind.

Evidence of income effect
5.2.1. Remittances. I first examine whether the migrants' remittances compensate for the forgone income contribution to the origin household. One distinctive feature of the MxFLS is that it tracked all 2002 baseline respondents who migrated to the United States between the two survey rounds (Teruel, Arenas, & Rubalcava, 2012). 13 The descriptive statistics provided by Farfan et al. (2013) suggest that 65 per cent of MxFLS migrants remit, and those who remit send on average 3340$ during the year prior to the interview, which implies that families of migrants staying behind receive 1800 pesos a month on average. 14 Had they not migrated, migrants would have contributed to the household income. In 2002, 65 per cent of the migrants initially participate in the labour force and earn a monthly wage of about 2300 pesos on average. Assuming equal consumption among members of the same household, migrants consume on average 735 pesos, which means that their net contribution to the household income amounts to 0:65 Ã 2300 À 735 ¼ 760 pesos a month. Thus, on average, the migrants' remittances of 1800 pesos seem to exceed their forgone local income contribution by about 1000 pesos, which is in line with prediction (1) of the model. The MxFLS also collects data on private transfers that each respondent receives from his non-coresident family living either in Mexico or abroad. The first column of Table 5 shows that nonmigrants are 6 per cent more likely to receive transfers as a result of United States migration. I also examine the effect on the household non-labour income calculated as the difference between consumption expenditures and total labour income realised at the origin, derived from selfemployment or wages. As the second column of Table 5 suggests, United States migration is associated with an increase in the household non-labour income by about 1700 pesos a month, which is similar to the average amount of remittances that migrants declare remitting. Joint consumption and labour effects of migration 141 5.2.2. Total labour input in the farm. The model predicts that, due the income effect, the total labour input in household production, which includes both the migrant's and the non-migrants' labour, should decline. To test this, I measure the total labour input either by the number of self-   (1)  employed workers, or by summing up individual hours across all household members. Although estimates are not strongly significant, columns 3, 4, and 5 of Table 5 suggest that United States migration tends to decrease the total labour input in self-employed work, as well as in farm work. This reveals that, despite the fact that they work more in household production, non-migrants do not completely offset the loss of the migrant's labour. This finding is consistent with prediction (4) of model.

Evidence of substitution effect
I now explore the second mechanism through which migration benefits those left behind, namely the productivity effect. First of all, since there is evidence that migration generates a net income gain, the finding that non-migrants increase their farm labour (as shown in Table 3) can only be explained, in theory, by an increase in the marginal productivity of agricultural labour. In order to provide further evidence that migration increases the marginal productivity of nonmigrants' labour in self-employed activities, I investigate the heterogeneity of the migration impacts depending on whether the migrant worked in self-employed activities prior to departure. Table 6 shows that the effect of migration on non-migrants' self-employed labour is more positive when the migrant initially worked in the family production relative to when he did not. 15 When the migrant initially helped in household production (40% of migrants do so), non-migrants are 10 per cent more likely to participate in self-employment relative to when the migrant did not.
The third and fourth columns replicate the same analysis by examining the differential impact according to whether the migrant worked on the family farm. Among the group of households initially engaged in farming, 45 per cent of migrants participated in farm work before leaving. I find that when a farmer migrates, the remaining members are 21 per cent more likely to engage in Table 6. Evidence of productivity effect among households with self-employed activity  (1) and (2), the sample is restricted to non-migrant individuals living in households initially engaged in self-employment in 2002. In columns (3) and (4) agricultural tasks relative to when a non-farmer migrates. These findings provide direct evidence in favour of the substitution effect highlighted in the model, in line with prediction (5). Another possible alternative explanation of these results is related to childcare and other domestic tasks. Since one potential childcare provider is absent after migration, the remaining family members may tend to shift labour towards types of self-employment that are more compatible with childcare. Using time use data, I find no significant effects of United States migration on non-migrants' hours spent in caring for children and elders, or on hours devoted to domestic tasks (Table S6 in Supplementary Materials).
It could also be that the farm production requires a fixed and lumpy amount of work: for example, a farmer cannot milk half a cow. These indivisibilities in agricultural production could result in a less efficient use of non-migrants' time relative to an alternative occupation. However, Table 5 suggests that non-migrants' farm work does not completely offset the loss of the migrant's labour, which is inconsistent with the idea that the household needs to devote a fixed amount of labour in order to keep the farm.

Liquidity constraints and long-term welfare
Is the uncovered welfare gain of migration driven by the alleviation of liquidity constraints on productivity-enhancing investments in the farm? The finding that total household labour devoted to the farm decreases with migration does not support this view, and is more consistent with the model's assumption that farm inputs (other than labour) remain fixed (see Section 3.6). To further explore this issue, I examine the effect of migration on the use of new farm inputs such as fertilisers, pesticides, improved seeds, tractor, or yoke, separately for 'poor' and 'rich' households, defined as those with initial consumption per capita below or above the median (in 2002). Panel A of Table S1 (Supplementary Materials) shows that migration has no significant impact on the use of farm inputs between 2002 and 2005. Therefore, the welfare gain of migration does not seem to be driven by new investments in the farm, at least in the short-run.
Given that farm inputs are generally lumpy investments, households may need time to save and gather the resources necessary to acquire them. Using the third round of the MxFLS survey conducted in 2009, Panel B of Table S1 (Supplementary Materials) shows that, in the longer-run (that is between 2002 and 2009) migration significantly increases the use of improved seeds, pesticides, and other farm inputs such as tractor or yoke. This result is entirely driven by the impact on 'poor' households, while I find no effect among 'rich' households. Given that liquidity constraints are more likely to bind for 'poor' than for 'rich' households, these results indicate that migration helps loosen liquidity constraints on farm investments, but only in the long-run, that is at least four years after migration (in line with Taylor & Lopez-Feldman, 2010). The fact the consumption gains of remaining households persist over time and do not vanish by 2009 (Table S2 in Supplementary Materials) suggests that the farm investments may have generated enough returns to buffer the drop in remittances income caused by the 2008 US Great Recession. 16 Migrant households may therefore save resources and forgo some consumption in the short-run in order to finance farm investments and increase income and welfare in the longer-run. If migrant households make such intertemporal trade-offs between present and future consumption, the short-term welfare effect of migration may underestimate the longer-term effect. Another reason why the short-and long-term effect could differ is the possibility that migration reduces investments in human capital among the remaining households (McKenzie & Rapoport, 2011). I do not yet find evidence in support of this channel when examining the educational attainment and labour supply of teenagers and young adults left behind (Tables S3 and S.4 in Supplementary Materials).

Conclusion
Using panel data from rural Mexico and controlling for time-invariant individual heterogeneity, this paper documents that migration to the United States increases non-migrants' consumption but also reduce their leisure time. These opposite effects, also evidenced by previous studies, call for a unified framework in order to draw a conclusion about the overall welfare impact of migration on those left behind. I propose such a new approach which takes into account not only the consumption gain of migrationthe traditional focus of the literaturebut also the leisure costs. The main result of the paper uncovers that adjusting for leisure costs reduces the welfare gain by one fourth (and at least 10%) relative to what the consumption gain would suggest.
In the short-run, that is within the two to three years following migration, the net welfare gain of migration remains sizeable in the Mexican context (a 12-18% increase in consumption terms) and seems to be caused by the combination of an income effectdriven by the migrant's remittancesand a productivity effectdriven by the out-migration of a farmer in a context of diminishing marginal productivity of agricultural labour. In the long-run, the evaluation of the welfare effect of migration might be further complicated by liquidity constraints on farm investments that remittances can help alleviate. Migrant households may forgo some consumption in the short-run in order to finance farm investments whose returns may only materialise in the long-run. If so, the short-term welfare effect of migration may underestimate the longer-term effect.
While my empirical findings concern the Mexican context, I believe the methodological contribution of this paper offers broader lessons for other migration studies. First, consumption changes are not equivalent to welfare changes, either because they may result from endogenous labour supply adjustments at the cost of leisure, or because they may reflect intertemporal trade-offs between present and future welfare. Second, labour supply effects are not necessarily informative about welfare changes either, because migration may increase the productivity of farm labour for those left behind. Since the opportunity cost of leisure may rise with migration, an increase in non-migrant' labour may not represent a welfare loss. 5. The setting of the model builds on standard agricultural household models (Taylor & Adelman, 2003). The model assumes that the household does not hire non-family workers in the farm. This assumption does not modify the crucial predictions, as I show in an extended version of the model presented in the Supplementary Materials. 6. The predictions of the model remain the same when farm production is introduced (for a formal proof, refer to the Supplementary Materials). 7. This can happen because for member 2, every infra-marginal unit of farm labour is more valuable than wage labour (F 0 ðL F 2 Þ ¼ w 2 and F 00 < 0). Due to the income effect of migration, member 2 first reduces the type of labour whose marginal product is the lowest, that is wage labour. If the income effect is not sufficiently high, member 2 only reduces his off-farm work and holds constant his farm labour. 8. The concavity of U 2 implies that for all consumption-leisure vectors x and y: ÑU 2 ðyÞ Á ðy À xÞ U 2 ðyÞ À U 2 ðxÞ ÑU 2 ðxÞ Á ðy À xÞ with ÑU 2 the gradient vector of U 2 . 9. This drops about 16 per cent of the sample. My main results are robust to retaining them in the analysis. 10. In theory, ΔMigUS h can take three values: +1 if a member out-migrates, 0 if there is no change and −1 if a former United States migrant returns to the household of origin. In practice, extremely few cases of return migration to the same origin household are observed in the data (fewer than 20 households, that is 0.7% of the sample). 11. I find that the results are robust to using different adult equivalent scales. In particular, using C N θ as the dependent variable, with C the total household expenditure and N the household size, I obtain very similar estimates of the migration impact for θ ranging from 0.5 to 1. 12. I test the robustness of the bounds to the use of two alternative data sources to proxy for w agri and w agri , namely the MxFLS survey and the Mexican Labor Force Survey (ENOE). As shown in Figure S2 and Table S9 in the Supplementary Materials, I find that wages are slightly higher in the MxFLS and ENOE data relative to the 2000 Census. Using the 90th percentile of the ENOE (or the MxFLS) as a proxy for w agri generates a lower bound of the welfare gain of 94.83 pesos that is still statistically significant at a 10 per cent level. 13. Individual-level data from the migrant's interviews in the United States has not been publicly released and my request to access this data was declined. 14. On average, migrant households receive remittances inflows of 0:65 Ã 3340=12 ¼ 181 dollars a month, or 1801 pesos a month (using OECD exchange rate data). 15. I restrict the analysis to households where at least one member is engaged in self-employed activities in 2002 for the following reason. In households in which the migrant is initially self-employed, non-migrants can possibly work in the family production together with the migrant. By contrast, the group of households in which the migrant is not initially selfemployed may include landless households without any means of production. Given that the presence of such landless households without any farm or business may generate bias in the estimation, I restrict the sample to households initially engaged in self-employed activities. 16. Using the third round of the MxFLS, I find in Table S2  ORCID Elie Murard http://orcid.org/0000-0003-3950-4532 their own production in the following way: 'In the past 7 days, what was the total value of […] that the household was given as a gift, as a payment, or that obtained from its crops, animals, or business?'. For non-food times, the question is the following: 'In the past 3 months, which was the total value of […] that the household produced for its own consumption, used from its business, or received as a payment or gift?'. I then convert consumption at the household level into consumption at the individual level by dividing total expenditure by the same equivalence scale as Attanasio and Székely (2004) used in Mexico. Initially proposed by Contreras (1996), this adult equivalence scale takes into account economies of scale and different needs of different age groups. This scale gives a weight of 1.2 to the first adult, 0.8 to individuals 11 years of age or older, 0.4 to children aged five to 10 and 0.3 to children under the age of five. I finally deflate all nominal values by using the CPI and convert them into 2002 values. Finally, when using a continuous dependent variable representing an amount of pesos, I trim the estimation sample by dropping observations with values above the 99th percentile and below the first percentile. The trimming of the data avoids the results being driven by extreme outliers. The MxFLS also asks each individual older than 15 the amount of private transfers (in cash or kind) that he receives from his non-co-resident family: either his parents, siblings, or children. Although no specific question is asked about remittances, private transfers should include them in principle.

A2. Definition of explanatory variables
The MxFLS also collects information on public transfers (for example pensions, Progresa, Procampo), household assets (for example financial savings, livestock, and land), and household durable goods (for example vehicle, electronic appliances). Following the methodology of Filmer and Pritchett (2001) and McKenzie (2005), I construct a wealth index using principal component analysis with data on household assets and durable goods, as well as data on dwelling conditions and access to public utilities. Table A1 reports the average initial characteristics of households in 2002, by migration status. Households that send migrants are significantly larger in size, have lower consumption and income per capita, rely more on private transfers from the extended family, and have more networks in the United States relative to households without migrants. Panel B indicates that migrant individuals are typically young males around 23 years old. The initial labour allocation across activities is quite similar between households with and without migrants: around 50 per cent of individuals participate in the labour force, with 20 per cent working in non-agricultural jobs, 10 per cent in agricultural jobs, and 20 per cent in self-employed activities. Around 15 per cent of individuals work in the family farm, while 19 per cent of the future migrants do so prior to departure. Table A2 reports the variation in household consumption and labour supply between 2002 and 2005 by migration status. The consumption of migrant-sending households increase significantly more between 2002 and 2005 relative to that of households without migrants. Individuals left behind by a United States migrant also increase their labour force participation significantly more between 2002 and 2005 relative to members of nonmigrant households. The difference in average participation is especially pronounced for self-employed work (+5%). : stars indicate that the difference in mean between households with and without migrants is statistically significant with significance level: *p < 0:10; **p < 0:05.