Children Left Behind in China: The Role of School Fees

The barriers faced by Chinese rural-urban migrants to access social services, particularly education, in host cities could help explain why the majority of migrants choose to leave their children behind. This paper proposes a theoretical framework that allows for an explicit discussion of the link between school fees and the decision of migrant parents to bring their children to the city. The analysis instruments the endogenous school fees with unexpected shocks to the city's public education spending, and empirically tests the theoretical predictions. The findings suggest that higher fees deter migrant workers from bringing their children, especially their daughters; reduce the number of children they bring; and increase educational remittances to rural areas for the children left behind. Increases in school fees most affect vulnerable migrant workers, and are likely to have stronger impacts during an economic crisis. These findings hold for different model specifications and robustness checks.


Policy Research Working Paper 7881
This paper is a product of the Development Data Group and the Environment and Energy Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http:// econ.worldbank.org. The authors may be contacted at hdang@worldbank.org, yhuang5@worldbank.org and hselod@ worldbank.org.
The barriers faced by Chinese rural-urban migrants to access social services, particularly education, in host cities could help explain why the majority of migrants choose to leave their children behind. This paper proposes a theoretical framework that allows for an explicit discussion of the link between school fees and the decision of migrant parents to bring their children to the city. The analysis instruments the endogenous school fees with unexpected shocks to the city's public education spending, and empirically tests the theoretical predictions. The findings suggest that higher fees deter migrant workers from bringing their children, especially their daughters; reduce the number of children they bring; and increase educational remittances to rural areas for the children left behind. Increases in school fees most affect vulnerable migrant workers, and are likely to have stronger impacts during an economic crisis. These findings hold for different model specifications and robustness checks.

Introduction
It is not easy to reach a priori conclusions about the net impact of parental migration on the children that are left behind in rural areas. Parental migration helps increase household income, which can lead to more resources being invested in children's education, but it also entails parental absence, which can result in lack of the parental supervision or support much needed by children in their formative years. Which effect dominates can depend on a host of context-specific factors; for example, if the remittances sent by parents are not put to good use, parental migration would likely result in lower education outcomes for their left-behind children (LBCs hereafter). On the contrary, if LBCs are taken good care of by their guardian(s), improved household resources and parental social capital at the destination area may benefit them over the long term. Evidence actually exists for both the positive and negative effects of parental migration on LBCs in different countries. 1 A better understanding of the interwoven connections between parental migration and child migration thus seems as relevant to guiding policy advice as studying the effects of parental migration.
We make several conceptual and empirical contributions in this paper. Our conceptual contribution is to investigate the effects of school fees on migrant parents' decision over whether or not they should bring their children with them. We explicitly model in our theoretical framework the role that school fees play in the migrant household's utility maximization problem. To identify the causal impacts of school fees, we employ in our empirical analysis a novel instrument-unexpected shocks to public spending on education.
Our paper straddles two distinct literatures on developing countries: one related to education 1 For example, parental migration is found to have positive effects on children left behind in terms of more education and reduced child labor in Mexico (Alcaraz, Chiquiar, Salcedo, 2012) and in the Philippines (Yang, 2008), lower infant mortality rates and higher birth weights in Mexico (Hildebrandt and McKenzie, 2005), and better cognitive and nutrition outcomes in Nicaragua (Macours and Vakis, 2010). Other studies, on the contrary, find that parental migration has negative effects on child education in Mexico (McKenzie and Rapoport, 2011) and on child health in Tonga (Gibson et al, 2011). See Lall et al. (2006) for a detailed survey of internal migration in developing countries and Antman (2013) for a review of the literature on the impacts of migration on family members left behind. 3 policies and the other related to internal migration. To our knowledge, it is the first paper to shed light on the unique interaction between school fees and child migration. 2 On the empirical front, we offer an empirical analysis of household survey data from China, which is a most interesting case to analyze the links between migration and access to education.
Indeed, due to the hukou (household registration) system, migrant workers in China are only granted limited access, if any, to the subsidized education and other social services available to local city residents. This contributes to many migrants leaving their children behind when migrating to cities for work. As a result, more than one-fourth of all children in China age 0 to 17-amounting to almost 70 million children-are estimated to be left behind by their migrant parents (UNICEF, 2013). 3 The focus on China offers relevant insights into important policy issues as recent studies overwhelmingly point to the detrimental impacts of parental migration on LBCs on educational outcomes including enrollment (Wang, 2014), grade attainment (Meyerhoefer and Chen, 2011), standardized test scores (Zhang et al., 2014;Zhou, Murphy, and Tao, 2014), and health outcomes including overweight and underweight measures (de Brauw and Mu, 2011) and anxiety levels and self-esteem (Bai et al., 2016). In addition to having worse education and health outcomes, Meng and Yamauchi (2015) find that LBCs spend less time studying after school, receive fewer tutoring lessons outside school, and are more likely to be enrolled in 2 The literature so far has mostly focused on the impacts of school fees on enrollment. For China, Yi et al. (2015) find that an unconditional financial aid program (fee-reduction program) had small effects on upper secondary school enrollment for Grade 9 students, but no effects for Grade 7 students; Shi (2012) finds educational fee reductions to be matched by increased voluntary household educational spending. For South Africa, Selod and Zenou (2003) provide theoretical evidence that increased school fees prevent the poor from having access to better schools, and Borkum (2012) finds that the elimination of school fees in poor districts had small positive effects on secondary school enrollment. De Brauw and Giles (forthcoming) discuss the effects of reducing barriers to migration on urban employment opportunities and rural enrollment for middle school graduates in China. See also Dang and Rogers (2008) for a review on studies related to households sending their children to private tutoring (classes with extra fees) and Glewwe and Muralidharan (2016) for a recent review of other studies on education in developing countries. 4 lower-quality schools. 4 The LBC phenomenon has also attracted much attention from the media, which highlight the psychological costs of family separation that can potentially lead to suicides of left-behind children (see, for example, Xinhua news agency (2015) and The Economist (2015aEconomist ( , 2015bEconomist ( , 2016). Against this background, the Government of China has set a priority to make urbanization "more inclusive" for migrant workers and their families (World Bank and DRC, 2014).
We provide a framework of analysis that closely integrates theory and empirics. Both our theoretical and empirical evidence suggests that increases in school fees decrease the chance that migrant households bring their children to the city, the number of children they bring, as well as the likelihood that they bring a daughter given preferences for sons. These results especially hold for more vulnerable migrant workers and for those who place a lower value on non-schooling outcomes. Furthermore, the negative impacts of higher school fees may be amplified during an economic crisis. Our findings suggest that a 10 percent increase in median school fees results in a reduction of 2 percentage points (or 5 percent) in the probability that the migrant worker brings his children along, and 0.02 fewer children being brought along. 5 This paper is organized as follows: we start by providing an overview of the country background in the next section before presenting our theoretical model in Section 3 and the empirical model and the data in Section 4. We then discuss estimation results, various robustness checks, and the heterogeneity analysis in Section 5. We offer further analysis of related outcomes in Section 6 and conclude in Section 7. 4 These findings contrast with Chen et al. (2009) who reported evidence of the positive impacts of parental migration and Mu and de Brauw (2015) who found that parental migration has no significant effect on the height of children, but has positive effects on their weight. 5 These empirical results are obtained using the latest data available from a household survey specially designed for the study of internal migration in China (i.e., the 2008/09 RUMIC data), which we discuss in more detail in the next section. 6 in Section 4.2 and Appendix 2) provides information on household expenditures on various types of school fees faced by migrants and local residents in 15 cities across China. Figure 1 graphs the distribution of mean (total) school fees paid by migrant households, which ranges from 1,100 yuan in Bengbu (a city with a dominant food industry in the Northern Anhui province) to more than 4,500 yuan in Shenzhen (the fastest growing migrant receiving city in the South). 7 School fees as a share of migrant households' consumption range from 4 percent in Hangzhou to 25 percent in Shenzhen, and represent, on average, 10 percent of migrant household consumption. For local households (i.e., urban residents with a hukou), school fees represent on average 11 percent of their consumption. School fees can be further broken down into different components, with tuition fees representing 40 percent and 31 percent of total school fees for migrants and urban residents respectively. Figure 2 plots the shares of migrant households that bring school-age children with them against the median school fees at the city level. These two variables show a negative relationship, with a correlation coefficient of -0.28. 8 Tuition fees in rural areas were formally abolished by the central government in 2006, thus the urban school fees paid by migrant households represented additional education expenses to their budget (which they would not have to pay in rural areas). The central government announced the abolition of these fees in urban areas as well after 2008 (State Council, 2008), but in practice, migrant households still often have to pay various "hidden" school fees (Li, 2013;Lu and Zhou, 2013). Using the RUMiC survey, we estimate that migrant households received a school fee reduction of approximately 20 percent, but not 100 percent, in 2008 (Appendix 3, Table 3.4). 9 7 Unless stated otherwise, school fees are calculated from the sample of migrants with at least one child enrolled in a school in the city. One yuan was approximately equal to 0.14 US dollars in 2008 (World Bank, 2016). 8 This correlation is somewhat stronger at -0.44 for the mean school fees. We describe how we construct different measures of school fees in section 4.2. 9 Our estimates using the most recent household survey from China in 2012 (i.e., the China Family Panel Studies implemented by Peking University) also indicate that, four (six) years after the official abolition of school fees in urban (rural) areas, both urban and rural households still paid various school-related fees. See Figures 3.1a and 3.1b in Appendix 3 for more details. 7 This practice of charging school fees is likely to persist, particularly given the strong fiscal decentralization in the country, unless follow-up policy measures are implemented (such as interventions from the central government). Being the first study that attempts to offer rigorous quantitative evidence on the impacts of school fees on child migration in China, our research is relevant not just as an assessment of the impacts of existing policy practices, but also sheds useful light on potential policies accompanying child migration (e.g., whether the government should subsidize child migration to help better integrate migrant households in the city's economy). 10 We return to this discussion in the last section.

Theoretical Framework
We present in this section a framework to study how school fees can affect migration and schooling decisions, which can guide our subsequent empirical analysis.

General Setup
Let us consider a household that consists of a migrant worker and his (her) child, both of whom originate from a rural area ∈ 1, . . , . The worker must decide among three choices: (i) migrating alone to a city, (ii) migrating to a city with the child, or (iii) remaining in the rural area of origin with the child. In the rural area, the worker earns a real income . The child attends a free school and obtains human capital from attending that school. The child also obtains non-schooling outcomes associated with growing up in the rural area. This vector includes all outcomes affecting the future productivity and well-being of the child, such as, for instance, health outcomes. 11 There are K cities indexed by ∈ 1, . . , . Each city is characterized by a wage , a school fee , a schooling outcome , and non-schooling 8 outcomes associated with residence in the city. As cities offer better labor market outcomes and better schooling outcomes than rural areas, we assume that and for any city k. We also assume that , implying that paying for an urban school is within the affordable choice set of migrants. These assumptions on the cost and quality of urban schooling are supported by both qualitative and quantitative studies on China (see Chen and Feng, 2013;Goodburn, 2009;and Lai et al., 2014). The migration cost from rural area to city is denoted , . 12 We assume that the worker has a linear utility of the form , where is household disposable income, is the child's human capital, and the child's vector of non-schooling outcomes. , is a function which increases in both and the components of and captures the rate at which the child's schooling and non-schooling outcomes translate into expected future income and/or the parental valuation of the child's well-being from schooling and non-schooling outcomes. Note that we do not assume any particular specification for function g and allow for any level of complementarity between schooling and non-schooling outcomes. 13 Also note that our setting with a single school fee in each city is compatible with a more complex framework that would have migrants choose a school within a distribution of heterogeneous schools in each city that each produces different levels of human capital at different costs. 14 12 For simplicity and without any loss of generality, we assume that the cost for a household to migrate to a given city is the same whether or not the worker brings his child along with him. 13 For example, choosing a CES specification , ∝ 1 where W(.) is a welfare index associated with non-schooling outcomes would allow us to consider all cases from perfect substitutability to perfect complementarity depending on the value of . 14 To see this, assume that the distribution of schools in each city is represented by a continuum of schools producing human capital for , where is a concave education production function increasing in . It is easy to see that if the condition . 1 holds, parents who bring their children to city k will optimally choose the cheapest and lowest human capital producing school in the city. This condition is likely to hold if (i) financial inputs do not have a strong impact on the production of education or (ii) returns to 9 When deciding whether and where to migrate and whether to take his child with him, a worker from a rural area compares utilities in the following 2 1 possible situations where is the rural area of origin of worker ∈ 1, . . , . Equation (3) simply states that migrant workers in city maximized their utility by choosing city . Equation (3) also indicates that each individual's migrating decision depends on the wages, school fees and schooling and non-schooling outcomes in all possible destination areas as well on the migration costs between the rural area of origin and all possible destination areas. 15 In the following subsections, we investigate the role of migration costs and school fees on migrations and schooling decisions. We will use ∆ to represent the gain in child outcomes associated with residence in city k over residence in a rural area, which is defined as follows human capital are low (see, e.g., Li et al. (2012)). Under this condition, we can abstract from modeling withincity school choice. 15 Although our setting is very general, we do not account for general equilibrium effects and assume that wages, schooling and non-schooling outcomes are fixed in each city.

The one child model
Let us consider a worker originating from a rural area who considers moving to city 1.
To reduce the dimensionality of the problem, we assume that min , , , , , , max , . Under this case, which is likely to occur when migration costs to remote cities are high, the problem boils down to comparing three scenarios only: migrating to city 1 with the child, migrating to city 1 without the child, or remaining in the rural area with the child. 16 We have the following proposition regarding the impacts of school fees on the migrant worker's decision to bring his child along.

Proposition 1. School fees and family migration
The worker will migrate to the city if the wage gain net of migration costs is positive ( , 0). If migrating, the worker will take the child with him if the gain in child outcomes exceeds the urban school fee ( ∆ ). Proof: Appendix 1, Part A. 17 The intuition beyond Proposition 1 is straightforward. The condition for the migrant worker to bring his child with him simply indicates that the cost of education must be lower than the worker's valuation of his child's gain in schooling and non-schooling outcomes. In fact, the result can be restated by noticing that, for any given school fee and any school quality gap between the urban and the rural area, the migrant worker brings his child with him if nonschooling outcomes provide sufficient benefits in urban areas. This result naturally follows from Proposition 1 and is stated in the following corollary.

Corollary 1.1. Non-schooling outcomes and family migration
The greater non-schooling outcomes in urban areas, the more likely the migrant worker is to bring his child with him. Proof: Appendix 1, Part A.

The two children model
We now extend the model to the situation where the household has two children. 18 We further assume that the migrant worker may give different weights in his utility function to each child's education. This can occur if the worker has a boy and a girl and has gender preferences regarding investment in education (for instance, preferring to invest in boys rather than in girls), 19 or if there is gender discrimination in the labor market that results in lower incomes for female workers, rendering investments in female education less profitable. The utility function of the worker in the two children case (with a boy and a girl) is where, similar to equation (1), is the child's human capital and the non-schooling outcomes, with the subscript indexing either boys (b) or girls (g), and v is the function valuing children outcomes. For illustrative purposes, we can write out this utility function using the additive form , , , where g is the outcome valuation function as previously defined, and  and  reflect worker preferences or differing labor market outcomes of boys and girls with   . We assume that , , and only depend on where the children live. Hence, if the boy and the girl live in the same place, they will have the same schooling and non-schooling outcomes, but we allow the parental valuation of child well-being to differ for boys and girls.
We have the following proposition. Proposition 2 is an extended version of Proposition 1 and implies that a higher school fee can decrease the number of children brought by the migrant worker. It also implies that, given son preference, a higher school fee may induce migrant workers to bring with them their sons rather than their daughters.

School Fee Increases after Rural-Urban Migration
We now return to the one child model to focus more on the ideas and keep the derivations tractable. Consider the case where the worker already migrated to city 1 with his child and faces an (unanticipated) increase in the school fee from to . To characterize the response to the school fee increase, we need to compare the utilities under the following scenarios: the worker remains in city 1 with his child; the worker remains city 1 but sends his child back to the rural area; and the worker moves to another city with or without his child (the "next best" city, denoted city 2). 20 We have the following proposition.
where , is the migration (relocation) cost from city 1 to city 2, and ∆ and ∆ are defined by equation (4). i) If * , * * , * * * * , an increase in the school fee to will cause the worker to send his child back to the rural area if and only if * .
ii) If * , * * , * * * * * , an increase in the school fee to will cause the worker to relocate to city 2 with his child if and only if * * .
iii) If * , * * , * * * * * * , an increase in the school fee to will cause the worker to relocate to city 2 and send his child back to the rural area if and only if * * * . Proof: Appendix 1, Part A.
The key take-away message from Proposition 3 is that the migrant worker's decisions respond to school fees. Depending on how wages, schooling and non-schooling outcomes 13 compare between the two cities, and depending on the migration/relocation cost between the two cities, an increase in the urban school fee may result in the migrant worker sending the child back to the rural area (case (i)) or relocating to another city with or without the child (cases (ii) and (iii) respectively). It is easy to see that when the relocation cost is sufficiently large, both * * * and * * * * hold, so that case (i) prevails. We thus have the following corollary.

Corollary 3.1. School fee increases and relocation decisions
If relocation costs are sufficiently large, an increase in the school fee will only affect the decision to bring the child as the worker will remain in the city. Proof: Appendix 1, Part A.  (3), is likely to remain the same after the change in school fee, which supports the internal validity of our empirical results using post-migration data in destination areas.
Moreover, note that higher school fees may place vulnerable households (i.e., poorer households or households with precarious jobs or without health insurance) at a particular disadvantage. These households are likely to expect lower (non-)schooling outcomes in the city, and would thus benefit most from social protection policies. 21 The following corollary to Proposition 3 helps shed light on their response to higher school fees.

Corollary 3.2. School fees and vulnerable households
Vulnerable migrant households are more likely to respond to an increase in the school fee by sending their children back to the rural area. Proof: Appendix 1, Part A.
14 Finally, in the following corollary, we characterize how the relationship between urban school fees and child migration changes when macro-economic conditions affect the returns to education.

Corollary 3.3. School fees, child migration and economic crisis
Under an economic crisis, the gain from child migration is reduced and households are more likely to respond to an increase in the school fee by sending their children back to the rural area. Proof: Appendix 1, Part A.
In summary, our theoretical framework suggests that higher school fees decrease the probability that a migrant worker brings his children with him to the city (Propositions 1 and 3), the number of children he may bring, and the probability that he brings a daughter given possible preference for boys over girls (Proposition 2). These effects may be more pronounced for more vulnerable migrant workers (Corollary 3.2) and during an economic crisis (Corollary 3.3). Our framework also implies that, other things equal, the migrant worker brings his children along if he values non-schooling outcomes more (Corollary 1.1). Although we abstract from modeling remittances to rural areas, our framework is also compatible with the scenario where, faced with high urban school fees, the migrant worker decides to leave one or several children in the rural area and to send remittances to support these children. 22 We will discuss the data and estimation models in the next section before validating these theoretical predictions in the empirical analysis. 22 Remittances would occur to the extent that investing in left-behind children provides greater utility than own consumption in the city. Denoting the remittance to the rural area and , the valuation of children outcomes as a function of remittances, it is easy to see from the utility function (1) that, budget permitting, the migrant will increase his utility by remitting if , . Because of lower outcomes in rural compared to urban areas, the remittance must be less than the fees the household would have spent on urban education.

Empirical Model
We estimate the migrant worker's decision to bring his children along using the following region fixed effects model where is a dummy variable indicating whether the migrant worker (or the head) in household i in city k brings his children along, and is the school fees faced by household i in city k. Consistent with our theoretical predictions that a higher school fee induces the worker not to bring his children (Proposition 1), we expect the coefficient on school fees ( to be negative. The control variables represent the household head's characteristics such as age, gender, educational achievement, working status, original residence, and city-level characteristics including the growth rate of the student-teacher ratio and housing prices. The dummy variable indicates that the migrant worker originates from region j. 23 We estimate equation (7) using a linear probability model. 24 School fees, however, may be prone to measurement errors or potentially be correlated with some unobserved city-level characteristics that also affect the migrant worker's decision to bring his children. For instance, if a city is observed to have been able to offer lower school fees thanks to more resources being allocated to education spending, migrants may factor this fact into their decision. There may even be reverse causality if, say, the influx of migrant children turns out to exceed the capacity of schools in the city; in this case, the city government 23 Provinces with few out-migrants are collapsed with their neighboring provinces into regional dummy variables (e.g., in our estimation sample, because Gansu has 6 migrants, Qinghai 3 migrants, Shaanxi 12 migrants, Xinjiang 1 migrant, we created a northwestern province dummy for these four provinces). In the end, we constructed 8 regional dummy variables: central province (Chongqing, Henan, Hubei, Hunan, Sichuan), eastern province (Jiangsu, Shanghai), northwestern province (Gansu, Qinghai, Shaanxi, Xinjiang), northern province (Shandong, Heibei, Tianjin), northeastern province (Heilongjiang, Jilin, Liaoning), south central province (Anhui, Jiangxi), southeastern province (Guangdong, Fujian, Zhejiang), and southwestern province (Guangxi, Guizhou, Yunan). 24 We use the linear probability model for easier interpretation of the coefficients. Estimates using a probit model are similar and shown in Appendix 3. We provide robust standard errors clustered at the city level for all the regressions. See also Cameron and Miller (2015) for a discussion on various standard error correction procedures. 16 may raise fees to obtain more revenue. Given our theoretical predictions that a higher school fee has a negative impact on the migrant worker's decision to bring his children, these endogeneity issues would bias estimates upward toward zero. But the magnitude of this upward bias is clearly an empirical issue.
Therefore, we use an instrumental variable (IV) framework to identify the impacts of school fees and jointly estimate equation (7)  to 2006). This IV satisfies all the conditions of a good IV, that is relevance, exogeneity, and exclusion conditions. We start first with discussing the relevance condition.
As discussed earlier, the funding of the Chinese education system is strongly decentralized.
Households are required to pay tuition and miscellaneous fees to supplement school operating expenses, and these fees are set by the local government and schools. Although the Education Law stipulates that public education spending should grow faster than regular government revenues, in practice, local governments are not held accountable to meet specific spending targets. This leaves local governments the flexibility to make up for the shortfall in public spending with contributions from households. A recent study by Yuan and Zhang (2015) finds that increases in public education spending are associated with significant decreases in urban household spending on public school tuition.
This situation is particularly relevant to migrant households, for whom the negative association between local public education spending and school fees is likely to be stronger. furthermore, these fees are less regulated than tuition fees and may be adjusted according to school needs. Figure 3 plots city-level school fees against public education spending shocks.
To remove contemporaneousness issues, we use one-year lagged shocks rather than the current shocks as instrumental variable (i.e., the fees are in 2007 but the spending shocks are in 2006).
There is a clear positive relationship between school fees and lagged education spending shocks (with a correlation coefficient of 0.47). A natural explanation is that, if the local government overspent in the previous year, they tend to compensate for the current fiscal deficit by raising current-year school fees. 25 We now turn to discuss why the cyclical components of public education spending shocks are exogenous to the migrant households' decision to bring their children, and why these shocks only affect this decision through school fees. In China, households, and particularly migrant workers, have little power to influence local governments' decisions. Local budgeting is largely influenced by a few top local officials and does not involve local residents (Wang et al., 2012;Liu et al., 2015). Because these officials are appointed, evaluated, and promoted mostly based on local economic performance and tax revenues, they have strong incentives to allocate public resources to activities directly oriented toward these objectives, rather than to the provision of local public good-such as education-that would meet the needs of local residents (Xu, 2011).
A recent study (Tsai, 2016) also suggests that local public spending responds to political cycles, which are completely exogenous to the migrant workers' decision. 26 In addition, public education spending has traditionally been invisible to migrants-as local budgeting was not publicly disclosed until recently-and migrants are usually not interested nor informed about local public affairs. Consequently, even if we assumed that migrants could somehow predict the trend of local public education spending, the shocks to education spending would remain unexpected and unforeseeable. It thus seems reasonable to consider these shocks as exogenous in our empirical setting.
As for the exclusion restriction, the most viable mechanism through which shocks to public education spending could affect the migrant workers' decision to bring their children is increased school fees. As discussed above, the budgeting process appears so far removed from migrant households (and local households) that it is unlikely to affect these households directly.
Moreover, even if we generously allowed the one-year lagged shocks to education spending to affect other city-level characteristics that are directly related to the migrant households' decision-an example could be that the education budget surplus may lead to the recruitment of more teachers or the construction of new schools-such scenarios are typically multi-year projects. They would take much longer than the IV's short time span of one year to develop. Note that we control for the growth rate of student-teacher ratio in equations (7) and (8). 19 were covered in the government basic urban health-care insurance scheme, which does not cover migrant workers (Hu et al., 2008). Furthermore, migrant workers tend to underuse health services in their destination cities, as almost two-thirds of migrant workers who report illness do not visit a doctor (Gong et al., 2012). Another type of public spending-social protection spending-provides similar evidence. 28 In the 15 cities of our estimation sample, the correlation between social protection spending and public education spending shocks is almost 0 (i.e., -0.06). 29 Nevertheless, we employ two different strategies to provide additional layers of robustness checks on the exclusion restriction. First, we employ different model specifications that control for a number of variables in estimating equations (7) and (8) due to any reason. We describe this method and our implementation in more detail in Appendix 1, Part B.

Data Description and Construction of Variables
We bring together various data sources for the empirical analysis. Our main data set is the As another check, we also compute alternative measures of school fees based on urban residents' school expenditures in the same cities. The school fees that they pay can be viewed as another measure of school fees in the city (e.g., because of a different sampling frame for the urban households in the same city). 32 Thus, while the fees obtained from the migrant household sample vary for each migrant household, the fees obtained from the urban household 30 We do not explore the panel feature of the data set between 2008 and 2009 since despite substantial efforts to track individuals over time, the panel data suffer from exceptionally heavy attrition (58.4 percent). This is due to the mobile nature of migrant workers and the consequences of the financial crisis that hit China in 2009 (Akgüç, Giulietti, and Zimmermann 2013). An option is to construct synthetic panel data that can allow dynamic analysis (Dang et al., 2014), but we leave this for future research. 31 These fees include tuition, food and accommodation, remedial classes, other fees (e.g. school uniforms and so on) and "sponsorship fees/boarding fees/selecting school fees". Unless otherwise noted, all numbers are our estimates from the RUMiC survey. 32 Figure 1, however, reassuringly indicates that there is no systematic difference between school fees obtained from the rural household sample or the urban household sample. See also Carletto, Larrison, and Ozden (2014) for a detailed discussion on the construction of proper sampling frames for collecting migration data.

Estimation Results
We use three model specifications to estimate equation (7) (and equation (8)) for both comparison purposes and robustness checks. Specification 1 is the most parsimonious and only controls for the household head's characteristics (including age, gender, educational achievement). Specification 2 adds to Specification 1 the head's employment characteristics (including whether the head is working and whether the head is self-employed), a dummy variable indicating whether the head migrated within the same province, as well as dummy 24 variables indicating the industry the head works in. 34 Finally, Specification 3 adds to Specification 2 the city-level housing prices to proxy for living costs in the city. To further help with the comparison, we use two different estimates for school fees to estimate these three specifications: one using median school fees and the other using mean school fees (with fees measured on the natural logarithm scale). The regressions using median fees are our preferred specifications, since the median is likely less affected by outlier observations than the mean.
While the variables further added to Specification 1 can help increase the goodness-of-fit of the model, they are more likely to be endogenous to the migrant worker's decision (e.g., the migrant worker may decide to be self-employed or to migrate within the same province to take better care of his children). But if the estimation results are (qualitatively) similar for all three specifications, it would provide stronger evidence for the impacts of school fees. For this reason, although Specification 3 is our preferred specification, we also refer to the other specifications when interpreting the estimation results.
We provide in Table 2 the estimation results for equations (7) and (8) table to save space. These estimates for Specifications 1 and 2 using either the mean school fees (Table 2, columns 1 and 2) or the median school fees (Table 2, columns 4 and 5) point to a negative and statistically significant relationship between school fees and the migrant worker's decision to bring his children. Adding housing prices to the regression (columns 3 and 6) renders this relationship statistically insignificant but does not change the negative sign. This result is broadly consistent with our theoretical prediction that a higher school fee decreases the migrant worker's probability of bringing his children along (Proposition 1). However, as discussed 34 We have five industry dummy variables for the following sectors: manufacturing, construction, wholesale and retail trade, hotel and catering services, and an "other" sector. The first four sectors absorb about 80 percent of the migrants. We do not control for the head's income because of potential endogeneity issues (e.g., as households may jointly decide on the type of job they do and thus on the pay they get and whether to bring their children along). We will return to this issue later in the section on robustness checks. earlier, the non-IV estimates mask the true impacts of school fees since they are biased upward toward zero. Put differently, they should be considered as the lower bound estimates in absolute magnitude of the true impacts.
We then instrument school fees with the shocks to local governments' education spending and show the full estimation results in the upper part of Table 2. 35 The lowest value of the F statistics (from the first stage regression) is 8.3 (column 1) and is somewhat lower than the rule of thumb (F>10) suggested by Stock and Yogo (2005); however, all the other F statistics are above this threshold, suggesting that our instrument is a reasonably good instrument. 36 All the estimated coefficients on the school fees variables are still negative and now statistically significant at the 5 percent level or less. Furthermore, these coefficients are between two and three times larger in absolute magnitude than those from the non-IV regressions. This confirms the negative impacts of school fees on migrant workers' decisions to bring their children along, and supports our hypothesis that the non-IV estimates are biased upward toward zero. Since school fees are in natural logarithm, for small changes in school fees the magnitude of the impacts (semi-elasticity) can be read directly from the estimated coefficients. A 10 percent increase in school fees results in approximately between a 2 percentage point decrease (Table 2, column 3) to a 4 percentage point decrease (column 1) in the probability that the migrant worker brings his children along. 37 Given that 38 percent of migrant households bring their children with them to the city, these figures are equivalent to a 5 percent (=2/38) and 11 percent decrease respectively in the probability that the migrant worker brings his children along. These changes are slightly larger if we consider the impacts of mean school fees (columns 4 to 6). 35 The first-stage regression results are reported in Table 3.1 in Appendix 3. 36 Note that Stock and Yogo's rule of thumb applies to identically and independently distributed errors, whereas our estimates are obtained with robust standard errors. Our IV also passes the Anderson-Rubin test for weakinstruments (not shown), which is valid with robust standard errors. 37 An alternative interpretation is to estimate and plot the predicted probabilities at different levels of school fees; see Figure 4 for this approach. 26 Estimation results for the other control variables (columns 2, 3, 5, and 6) show the expected impacts on the migrant worker's decisions. In particular, if the migrant worker is self-employed or migrated to a city within his original province, he is more likely to bring his children along.
The first result may be explained by the fact that self-employment may give the migrant worker a more flexible work schedule that permits better care of children; the second result suggests that within-province migration may provide migrant children with better prospects, perhaps because of either lower migration costs or similar languages or cultural proximity (see Corollary 1.1). Surprisingly, the growth rate of the student-teacher ratio has a negative effect on the migrant worker's decision, but this result is not strongly statistically significant. 38 Table 3 shows the impacts of school fees on the number of children the migrant worker brings to the city. The estimated coefficients on school fees are negative and strongly statistically significant as predicted by our theoretical model (Proposition 2) apart from column (6) were the effect is only significant at the 10 percent level. A 10 percent increase in the median school fees (Table 3, column 3) would lead to 0.02 fewer children being brought along. Other coefficients largely remain in the same order of magnitude as those in Table 2 (not shown).
We then examine whether school fees result in gender discrimination against girls. Put differently, we want to know if, conditional on having at least one school-age girl, the migrant workers bring their sons instead of their daughters in response to an increase in school fees as predicted by our theoretical model (Proposition 2). For each migrant household having at least one daughter, we define a variable indicating girl "representativeness", which is the share of girls in the number of children brought along over the share of girls in the household's total number of children. If this variable is larger (smaller) than one, then girls are "over-presented" ("under-represented") as migrants. Estimation results restricted to the sample of migrants that have at least one daughter are shown in Table 4. 38 We have also estimated the reduced form of our model and obtained coefficients that are all significant. 27 All the estimated coefficients on school fees are negative, but only marginally statistically significant at the 10 percent level under columns (1) and (4). This result can thus provide some supportive, but not very strong, evidence for girl discrimination when school fees increase.
However, note that the weak significance may also result from the smaller sample size-which is less than half of that in Tables 2 and 3-when we restrict the estimation sample to migrant households with at least one school-age girl.

Robustness Checks
Our estimation results remain stable against different robustness checks. Overall, out of all the robustness checks in Table 5, only three (columns 4, 14, and 18) lose some negligible statistical significance, and become statistically significant at the 6 percent level. We discuss next the specific checks.

Alternative measures of school fees
To rule out the concerns that our results may be driven by how the school fee variable is defined, we examine below four different options to construct this variable and present the estimation results in Table 5. For comparison purposes, we show the same estimates from columns 3 and 6 of Table 2 in columns 1 and 2 of this table. First, instead of looking at total school fees (which consists of tuition fee, food and accommodation, remedial class, and other fees), we focus on its major component-the tuition fee. The rationale behind this is that schools uniformly charge tuition fees across the country, whereas the use of other fees may vary from city to city. Estimation results (Table 5, columns 3 and 4) are qualitatively similar to those under columns 1 and 2, even though they are unsurprisingly slightly smaller in magnitude.
Second, to allay the concern that the median or the mean fees may not be the best measure, again, qualitatively similar. Finally, instead of using the fees paid by migrant households, we use the fees paid by urban households in the same city. As discussed earlier, the school fees that they pay can offer another measure of the distribution of school fees in the city. We show estimates for both the median and mean total fees (columns 9 and 10) and the median and the mean tuition fees (columns 11 and 12), which are qualitatively similar even though smaller in magnitudes.

Public versus private schools
Since public schools are generally considered to have higher quality than private schools in urban China (see, e.g., Goodburn, 2009), to what extent could our results be affected by the mix of school supply in different cities? Besides this quality difference, there can be a cost difference between these two types of school as well (e.g., public schools can charge migrant households the additional school selection (Jie Du fee). As such, could migrant households consider sending their children to the higher-quality (and possibly more expensive) public schools or leave them behind, rather than choosing the (possibly less expensive) private schools?
To investigate this issue, we implement several robustness checks as follows. First, we compare the various fees between public schools and private schools measured at the city level, which turn out not to be statistically different (except for the higher Jie Du fee charged by public schools, but the difference for this fee is only significantly different at the 10 percent level; not shown). Second, we rerun the estimates in Table 2 after dropping all the migrant children that attend a private school in the destination cities. Estimation results (Table 3.2 in Appendix 3) are very similar to those in Table 2. Finally, we rerun the estimates in Table 2

Additional control variables and empirical modeling options
One concern is that the negative impacts of school fees could be caused by their correlation with migrant workers' income. We address this issue by controlling for income in the regressions (columns 13 and 14). Estimates are slightly smaller in magnitude, but still qualitatively similar. An alternative modeling option besides the linear probability model is the probit model. The latter may be more appropriate if predictions from the former do not fit well in the range [0, 1] or the variance of the error terms heavily depends on the estimated model coefficients. Estimation results using the IV probit model, however, provide similar results (see Table 3.3 in Appendix 3).

Alternative IV construction and method
We offer two additional ways to construct the IV. First, we apply the HP filter to generate shocks, and second, we use the total sum of the shocks in the past two years. Estimation results are displayed in columns 13 to 16, which provide qualitatively similar results. Second, Figure   4 plots the predicted probabilities (based on Models 1 and 3 in Table 2) Table 2 and control for public schools as a share of the total number of schools in the cities. Estimation results (not shown) remain very similar. 40 Since the predicted probabilities from Model 2 are rather similar to those from Model 3, we do not plot them to make the graph easier to read.

Vulnerable migrant households
We check whether our estimation results still hold for different groups of migrant households, particularly the vulnerable and disadvantaged groups (as predicted by Corollary 3.2). For this, we stratify the sample in various ways and estimate our main specification (column 3 from Table 3) on each subsample. Table 6 reports the impacts of the instrumented median school fee on the migrant worker's decision to bring the child for (some of) these subsamples.
We first stratify the sample by income, defining as poor those who fall in the lower half of the household income distribution, and non-poor the remaining households. shows that higher school fees indeed deter poor migrants from bringing their children with them. These results, however, do not hold for the non-poor group. We then stratify the sample by insurance (or social benefits) status, and find that the same results hold for the migrants who do not have any access to these benefits (row 2). 41 The impacts of school fees are statistically significant for households who migrated to noncoastal cities: Zhengzhou, Luoyang, Hefei, Bengbu, Chongqing, Wuhan and Chengdu (row 3).
For households that migrated to coastal cities (Guangzhou, Dongguan, Shenzhen, Shanghai, Nanjing, Wuxi, Hangzhou and Ningbo), the impacts are only significant after controlling for housing prices (not shown).
We then stratify the migrant workers sample into two groups according to their work status: those with a permanent (or long-term) contract (one year or more) and those with a short-term contract (less than one year) or without a contract (including the self-employed, family business helpers, part-timers, workers in a probationary period or interns, apprentices or hourly workers).
Migrant households with a short-term contract are affected by higher school fees (row 4), while those with a permanent or long-term contract are not (not shown).
Next, we divide the sample by two subjective indicators: whether the household head is planning to stay in the city for a long time, and whether the household head is depressed based on Center for Epidemiological Studies Depression Scale (CES-D10) questions. 42 Estimation results, however, are similar for these different groups, even though the depressed migrant workers appear to be more impacted by changes in school fees (with the estimated coefficients being larger than those in Table 3, column 3) (row 6).
We then compare the impacts for migrant households with more than one child and migrant households with only one child. The estimation results show that households with only one child (row 7) are more likely to be affected by school fees. Migrant households with both spouses in the city (row 8) or with only one spouse (not shown) are both sensitive to school fee changes. The same result holds for both employees (not shown) and the self-employed (row 9).
Overall, the estimation results in Table 6 suggest that the vulnerable groups (including the poor, the uninsured, those without permanent contracts, and to some extent, the depressed) are more sensitive to changes in school fees. These results are consistent with our theoretical results.

School fees and child migration during the economic crisis
Our theoretical results suggest that child migration would increase in response to the reduced school fees in 2009 (Propositions 1 and 3), but would decrease during the economic crisis in this same year (Corollary 3.3). Which effect would dominate child migration?
Estimation results using the 2009 wave of the RUMiC survey show that the non-IV estimates (Table 7, row 1) are negative, and are between 60 percent and twice larger in absolute magnitude than those for 2008 (bottom of Table 2). Since the upward biased non-IV estimates 42 We recode the answers to the questions about depression such that higher scores imply a more intense state of depression. We define a person as depressed if the summation of his/her scores is greater than 22. 32 provide lower bound estimates of the true impacts of school fees, this offers evidence that the negative effects of the economic crisis dominate the positive effects coming from a reduction in school fees. Furthermore, even though our IV is severely weakened for the crisis year (as discussed in section 4.2) and thus could only offer statistically significant estimates in two specifications (columns 1 and 4), the IV estimates have the expected negative sign and are two to three times larger than those of the non-IV estimates. These results concur with those for While this option allows us to employ a richer econometric model by controlling for the year and city (fixed) effects, it does not offer more insights into the crisis year as discussed above. Estimation results on the pooled data (not shown) nevertheless confirm that school fees have a negative and statistically significant impacts on child migration. 44 The Body Mass Index (BMI), a measure of tissue mass (muscle, fat and bone) in an individual, is computed as the ratio of weight (in kilograms) to squared height (in meters). Using WHO's guidelines, we consider that children with a BMI less than 18.5 and equal or greater than 25 are respectively underweight and overweight. 33 indicate that moving with parents is associated with greater height, even though the impact is marginally statistically significant at the 10 percent level. Moving with parents is associated with a lower probability of being overweight (column 3) but has no statistically significant correlation with being underweight (columns 2 and 4).

School Fees and Education Remittances
A migrant worker may leave his children behind and send remittances back home rather than bring his children to the city if school fees are unaffordable. As discussed earlier, this is the migrant worker's best response to higher school fees, since the remittances in this case would be less than the expenses that would have been required for the children in the city given the higher school fees (see footnote 20 in Section 3). We assess the impacts of the school fees on the educational remittances sent back home and provide estimation results in Table 9. Since about 45 percent of the household reported zero educational remittances, we resort to an IV-Tobit model to address the left-censoring issue. Estimation results suggest that the higher the school fees in urban areas, the more migrant households remit back home. A 10 percent increase in school fees results in an increase of between 241 and 304 yuan in the annual remittances (Table 9, columns 1 to 3). 45 This lends further support to our theoretical intuition that higher school fees prevent migrant workers from bringing their children with them to the city, and thus encourages them to send education remittances back home instead. However, greater remittances may not necessarily result in better outcomes for LBCs; as a recent study by Demurger and Wang (2016) points to a strong negative impact of remittances on education expenditures in remittances-receiving households. This suggests that leaving the children behind and sending remittances may not be the optimal decision for migrant workers.

Conclusion
We add to the literature by investigating a major constraint to parental migration-school fees-that affects their children's welfare. We provide new theoretical and empirical evidence that points to the harmful effects of increased school fees (across major cities in China) on migrant households' decisions over whether to bring with them their children, the number of children to bring, and the gender of the children they bring. Moving with parents could benefit migrant children with better health outcomes and lower risks of being overweight. These effects are robust to different measures of school fees as well as to different techniques used to construct the instrumental variable. Further heterogeneity analysis shows that vulnerable migrant households are more impacted by school fee changes, and the negative effects of higher school fees may possibly be larger during an economic crisis.
Our study is relevant to the Chinese context or any other country that is undergoing urban migration. Remarkably, China's growing rural-urban dualism creates social tensions and increasingly becomes a constraint for further labor-market integration, urbanization, and economic development. Even though the country has abolished school fees starting in late 2008, in practice, migrant households are still found to be obliged to pay various school-related fees.
Thus, our results can lend quantitative supportive evidence to the removal of school fees by the government, and similar policies aimed at improving migrants' access to public service irrespective of their place of residence (see, for example, Hu et al., 2008). Our findings also suggest that the central government may consider better targeted budget transfers to local governments that would specifically address migrant children's education. If inclusive urbanization is to be accomplished, local governments could focus on achieving social welfare objectives (in particular better access to education for migrants) besides purely economic objectives.  Note: Each column presents the results from separate IV regressions with different school fee measures and different independent variables, where the IV is the one-year lag of shocks to public education spending. The dependent variable is a dummy variable that equals 1 if there is at least one child living with the household head, and 0 otherwise. The first three columns ((1)-(3)) use the median school fees reported in the migrant household sample as a regressor, and the last three columns ((4)- (6)  Note: Each column presents the results from separate IV regressions with different school fee measures and different independent variables, where the IV is the one-year lag of shocks to public education spending. The dependent variable is the numbers of children living with their parents in the household. The first three columns ((1)-(3)) use the median school fees reported in the migrant household sample as a regressor, and the last three columns ((4)-(6)) use the mean school fees reported in the migrant household sample as a regressor. Different sets of control variables, which are similar to Table 2  Note: Each column presents the results from separate IV regressions with different school fee measures and different independent variables, where the IV is the one-year lag of shocks to public education spending. The dependent variable is girl representativeness -defined as girls as a share of the number of migrant children divided by girls as a share of the total number of children in the household. The first three columns ((1)-(3)) use the median school fees reported in the migrant household sample as a regressor, and the last three columns ((4)-(6)) use the mean school fees reported in the migrant household sample as a regressor. Different sets of control variables, which are similar to   (1)-(12) are defined as follows: Columns (1)-(2), log median and mean school fees (including tuition fees, food and accommodation, remedial classes, and other fees) reported in the migrant sample; Columns (3)-(4), log median and mean tuition fees reported in the migrant household sample; Columns (5)-(6), log 25 th percentile and 75 th percentile school fees reported in the migrant household sample; Columns (7)-(8), median and mean school fees (in thousand yuan) reported in the migrant household sample; Columns (9)-(10), log median and mean school fees reported in the urban household sample; Columns (11)-(12), log median and mean tuition fees reported in the urban household sample. Columns (13)-(20) use the same measures of school fees as in columns (1)-(2). In columns (13)-(14), household income per capita is included as a control variable. In Columns (15)-(16), social protection spending per capita at the city level is included as a control variable. In columns (17) (1), poor households are those who fall in the lower half of the household income distribution; In row (2), the insured are those who have access to at least one of the job-related insurances/benefits (unemployment insurance, pension insurance, work injury insurance, and housing fund); In row (3), hinterland migration is to non-coastal cities (Zhengzhou, Luoyang, Hefei, Bengbu, Chongqing, Wuhan and Chengdu); Row (4), short-term workers are those who are without permanent contracts and long-term contract (one year or more) as; In row (5), not likely to move characterizes household heads who plan to stay in the city forever; In row (6), we define depressed migrants based on Center for Epidemiological Studies Depression Scale (CES-D10) questions (see footnote in the text for more details); In row (7), we consider migrants with only one child (versus migrants with more than one child); In row (8), the focus is on migrants who are living with their spouses; Row (9) corresponds to self-employed migrants. Standard errors in parentheses are clustered at the city level. *** p<0.01, ** p<0.05, * p<0.   (1)-(3)) use the median school fees reported in the migrant household sample as a regressor, and the last three columns ((4)-(6)) use the mean school fees reported in the migrant household sample as a regressor. Different sets of control variables, which are similar to Table 2, are included under each column. Rsquared values are not reported, instead, root-mean-square error (RMSE), the sample standard deviation of the differences between the predicted values and observed values, is reported under each column. Standard errors in parentheses are clustered at the city level. Prob>chi2 is the p-value of the chi-square test of overall significance. F-statistics of the first stage regressions are also reported. *** p<0.01, ** p<0.05, * p<0.          (1)  12.924 Note: Each column presents the results from separate IV regressions with different school fee measures and different independent variables, where the IV is the one-year lag of shocks to public education spending. All migrant children that attend urban private schools are dropped. The dependent variable is a dummy variable that equals 1 if there is at least one child living with the household head is sent to urban public school, and 0 otherwise. The first three columns ((1)-(3)) use the median school fees reported in the migrant household sample as a regressor, and the last three columns ((4)-(6)) use the mean school fees reported in the migrant household sample as a regressor. Different sets of control variables are included in different columns. R-squared values are not reported, instead, root-mean-square error (RMSE), the sample standard deviation of the differences between the predicted values and observed values, is reported under each column. Standard errors in parentheses are clustered at the city level. Prob>chi2 is the p-value of the chi-square test of overall significance. F statistics of the first stage regressions are also reported. *** p<0.01, ** p<0.05, * p<0.  Note: Each column presents the marginal effects obtained from separate IV probit regressions with different school fee measures and different independent variables, where the IV is the one-year lag of shocks to public education spending. The dependent variable is a dummy variable that equals 1 if there is at least one child living with the household head, and 0 otherwise. The first three columns ((1)-(3)) use the median school fees reported in the migrant household sample as a regressor, and the last three columns ((4)-(6)) use the mean school fees reported in the migrant household sample as a regressor. Different sets of control variables are included in different columns. R-squared values are not reported, instead, root-mean-square error (RMSE), the sample standard deviation of the differences between the predicted values and observed values, is reported under each column. Standard errors in parentheses are clustered at the city level. Prob>chi2 is the p-value of the chi-square test of overall significance. *** p<0.01, ** p<0.05, * p<0.