metadata: authors: 0: author: Dang,Hai-Anh H.
1: author: Huang,Yang
2: author: Selod,Harris
count: China
docna: 0: docna: Children left behind in China : the role of
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docty: Policy Research Working Paper
subtopic: Economics of Education,Education Finance,Educational Sciences,Employment and Unemployment,Public Sector Economics,Public Financial Management,Public Finance Decentralization and
            Poverty Reduction,Access of Poor to Social Services,Disability,Economic Assistance,Services & Transfers to Poor
teratopic: Education,Public Sector Development,Social Protections and Labor,Macroeconomics and Economic Growth,Poverty Reduction
abstracts: cdata!: 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.
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repnme: repnme: Children left behind in China : the role of
            school fees
display_title: Children left behind in China : the
            role of school fees
listing_relative_url: /research/2016/11/26917401/children-left-behind-china-role-school-fees
topicv3: Public Finance Management m1326316 716,Education m1327048 470,Social Assistance m1327201 1466,User Fees in Education m1327515 1493,Migrant Workers m1504032 2729
publishtoextweb_dt: 2016-11-07T00:00:00Z
historic_topic: Education,Public Sector Development,Social Protections and Labor,Macroeconomics and Economic Growth,Poverty Reduction
no_of_pages: 63
author_keys: 0: author_key: 747967
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2: author_key: 750638
model_extractions: WPS7881 Policy Research Working Paper 7881

# Children Left Behind in China The Role of School Fees

_Hai-Anh Dang Yang Huang Harris Selod_ Development Data Group & Development Research Group Environment and Energy Team November 2016
Policy Research Working Paper 7881

# **Abstract**

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.

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 Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Children Left Behind in China: The Role of School Fees**<sup></sup>

Hai-Anh Dang,<sup>±</sup> Yang Huang,<sup></sup> Harris Selod<sup></sup>

**Key Words:** child migration, school fees, public education spending, urbanization, China **JEL Codes:** I22, J61, O15

> * We are grateful to Marc Gurgand, John Giles, Carine Milcent, Steven Brakman, Hillary Caruthers, Yi Chen, Elena Glinskaya, Tiago Freire, Laurent Gobillon, Thierry Magnac, David McKenzie, Scott Rozelle, Ruixin Wang, Jeffrey Zax and participants at the Conference on Urban Development in China (Suzhou) and the 7<sup>th</sup> International Symposium on Human Capital and Labor Markets (Beijing) for comments on earlier drafts.

> ± Hai-Anh Dang, Survey Unit, Development Data Group, World Bank and Vietnam’s Academy of Social Sciences. Email: <u>hdang@worldbank.org.</u>

>  Yang Huang, Human Development and Public Services Team, Development Research Group, World Bank and Paris School of Economics. Email: <u>yhuang5@worldbank.org.</u>

>  Harris Selod, Energy and Environment Team, Development Research Group, World Bank. Email: <u>hselod@worldbank.org.</u>
# **1. 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.<sup>1</sup> 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.

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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.<sup>2</sup> 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).<sup>3</sup> 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.

> 3 This number of left-behind children is slightly more than the total population of a country the size of France or the UK. Also note that migrant workers play a major role in the Chinese economy and account for 44 percent of total urban employment (World Bank and DRC, 2014).

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lower-quality schools.<sup>4</sup> 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 (2015a, 2015b, 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.<sup>5</sup> 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.

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# **2. Overview of Education and School Fees**

Confucian values that strongly encourage education have historically played a key role in Chinese parents’ decision to enroll children in schools. The advent in 1986 of the ‘Law of Compulsory Education’ made school enrollment mandatory for all children age 6 and above and required all children to attend school for a minimum of 9 years. Grassroots enforcement and monitoring of this law by urban resident committees or rural village councils (the smallest administrative units in China) has helped rank the country among those with the highest school enrollment rates. The gross enrollment rate at the primary and secondary school levels reached 108 percent and 96 percent respectively in 2013 (UNESCO, 2016).

Universal compulsory education, however, does not fully alleviate the burden of school fees for families. The education system’s finance is highly decentralized in China, leading to subnational governments bearing most of the costs of public education spending (approximately 95 percent) and the central government funding the rest (World Bank and DRC, 2014). These challenges gave rise to school fees as an important source of revenue for local governments’ public education budget. These school fees are often collected by the local government (through schools) and then transferred back to each school, with the specific amounts being determined in negotiations between the former and the latter. Notably, migrant households are often asked to pay extra school fees, the exact amounts of which vary from city to city (see, e.g., Yuan, (2010)).<sup>6</sup> No official data exist on school fees, but these can be estimated from household education expenditures. The Rural-Urban Migration in China (RUMiC) data set (discussed in more detail

> 6 Despite the repeated calls to give migrant children equal treatment, many public schools in China continue to impose higher tuition fees or other fees on migrant children, often with local government approval (World Bank and DRC, 2014). There are at least two main reasons for this. First, compulsory education for migrant children is supposed to be financed by the sub-national governments of migrant-sending areas rather than the sub-national governments of migrant-receiving areas. The latter lack motivation to finance the education of migrant children, and often have inadequate resources to do so given their already heavy fiscal responsibilities (Shen, Zhao and Zou 2014). Second, subnational governments tend to allocate public resources to activities related to short-term economic performance rather than to local public goods such as compulsory education (Shen, Zhao and Zou, 2014; Xu, 2011; Yuan and Zhang, 2015).

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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).<sup>7</sup> 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.<sup>8</sup> 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).<sup>9</sup>

> 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.

6
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).<sup>10</sup> We return to this discussion in the last section.

# **3. 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.

# **3.1. 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 �<sup>�</sup> . The child attends a free school and obtains human capital �<sup>�</sup> from attending that school. The child also obtains non-schooling outcomes �<sup>�</sup> 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.<sup>11</sup> There are K cities indexed by � ∈ �1, . . , ��. Each city � is characterized by a wage ���, a school fee ��, a schooling outcome ���, and non-schooling

> 10 Reviewing numerous studies on migration policies, McKenzie and Yang (2015) observe that the importance of obtaining rigorous evidence to evaluate policies cannot be overemphasized.

> 11 We assume that all rural areas provide the same wage, schooling and non-schooling outcomes.

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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 ��,�.<sup>12</sup> 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.<sup>13</sup> 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.<sup>14</sup>

> 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

8
j 2K +1 Vinee = wk — mx — fe + gH, XD) if migrating with the child to a city k, for k € {1,...,K} Vin = we — mx + g(H®, X®) if migrating to a city k without the child, for k € {1,...,K} (2) VR = w* + g(H®, X®*) if staying in the rural area J k k J k k Vix = max{V;°, Vien} k J k Sy = {ilk = argmax{{ Vithrer’ VR} i@ i€ {1,..,} i€ {1,..,} <!-- Start of picture text --> k<br><!-- End of picture text --> c= G(Ag Xx) — GH", X*)
# **3.2. Migration and the Decision to Bring the Children**

# **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 ��<sup>�</sup> �,�����. 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.<sup>16</sup> 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 (_ ��� � �<sup>�</sup> ���,� �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 _._<sup>17</sup> 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 _._

> 16 We analyze the more general case of several potential destination areas in Appendix 1, Lemma 1.

> 17 In our framework, parental migration is strictly motivated by labor market outcomes (see Stark 1991). Under a simple condition (see Appendix 1), we rule out the unlikely case where the worker's only incentive to migrate would be to improve his child's outcomes in spite of an otherwise net income loss from migration.

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# **The two children model**

We now extend the model to the situation where the household has two children.<sup>18</sup> 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),<sup>19</sup> 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. School fees and selection in children migration**

_If migrating, the worker takes both children with him if the school fee is sufficiently low (_ �� � ��∆� _). He leaves both children behind if the school fee is sufficiently high (_ �� ���∆� _). He only takes the boy with him in the intermediate case (_ ��∆���� ���∆� _)._ **Proof:** Appendix 1, Part A _._

> 18 The model is easily generalizable to more than two children. Very few households, however, have more than two children in China, hence our focus on one child or two children for the discussion.

> 19 See, for example, Chen et al., (2013) and Ebenstein (2011) for recent studies on son preference in China.

11
<!-- Start of picture text --> fh fteh<br><!-- End of picture text --> = Ay — Ag + (wy — wy’) + (fg +12) f fi =4A,+fi(wy =Ay—wy) +m, TM4,2 1 minhminh fiofifiofi s=hs=h h>hh>h__ fi hi_ minh fiofi s=h hi7 h>h_ 1 2
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 _._ Corollary 3.1 is relevant in the case of China and helps explain that, given prohibitive relocation costs across Chinese cities, migrants typically do not relocate after migrating to a city (see, for example, Chen et al., 2010). Put differently, under Corollary 3.1, ��, the set of migrants in city 1 defined in equation (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.<sup>21</sup> 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 _._

> 21 Households with lower education levels, for example, may not know how to access information about the city’s services and, thus may not have access to these services.

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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.<sup>22</sup> 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.

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# **4. Empirical Model**

# **4.1. 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_ .<sup>23</sup> We estimate equation (7) using a linear probability model.<sup>24</sup> 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.

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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) and the following first-stage equation for the year 2007 �����,���� �����������,���� ��′��� ��� ���� (8) where the instrumental variable ������,���� is the lagged cyclical component of public education spending in 2006 (i.e., obtained after detrending city education spending from 2002 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. Since the funding of school does not follow migration (World Bank and DRC, 2014), the education of migrant children is only partially funded by the local government in the destination area. Migrant children are required to pay extra fees on top of the regular fees; 16
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.<sup>25</sup> 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.<sup>26</sup> 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

> 25 Due to mean reversion, our positive correlation between current school fees and lagged education spending shocks is consistent with Yuan and Zhang’s (2015) negative correlation found for current school fees and _current_ education spending shocks. In other contexts, including the European Union, public spending shocks are found to result in budget deficits (Beetsma and Giuliodri, 2011); see also Ramey (2011) for a recent review of related studies.

> 26 Tsai (2016) shows that two years prior to the National Congress of the Communist Party (NCCP), politicians are likely to shift public spending toward capital expenditures, such as innovation funds and capital construction, and away from current expenditures, such as agricultural subsidies, social expenditures and government administration.

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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. Furthermore, in the context of China, information about these projects may even take longer to percolate to migrant households and subsequently affect their decision.<sup>27</sup> Still, it could be argued that if unexpected shocks to public education spending are somehow correlated with other types of social welfare spending such as spending on health or security, and if such social welfare spending can help improve the non-schooling outcomes for migrant workers’ children, these shocks may also affect child migration through this channel. This would result in biased estimates. This argument, however, is unlikely to hold since, as discussed earlier, migrant households generally have limited access to (and little information about) social services in urban areas. Consequently, increases (or decreases) in other types of public spending would likely have little effect on their decision over child migration. The area of health care furnishes a good illustration. In 2006, only 28 percent of the urban population

> 27 Note that we control for the growth rate of student-teacher ratio in equations (7) and (8).

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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.<sup>28</sup> 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).<sup>29</sup> 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). These include the migrant worker’s (household head’s) demographics, employment, and dummy variables indicating his work industry, province of origin, and whether he migrates within the same province. If somehow there is a reason to believe that the city-level shocks to public education spending can have differential effects on different occupations and migrant workers coming from different locations, these variables can help net out such effects. Furthermore, we explicitly control for social protection spending in a robustness check. If the estimated coefficient on school fees does not lose its statistical significance (or change significantly) when social protection spending is included, this would provide supportive evidence for the validity of the exclusion restriction. Second, we apply a bounding method recently developed by Chernozhukov, Lee, and Rosen (2013) that does not require the exclusion restriction. This second strategy, in fact, generally allows for the violation of the exclusion restriction to occur

> 28 Social protection spending is defined in the China City Statistical Yearbooks as being composed of social security benefits, employment subsidies, and unemployment grants. 29 This result is consistent with the fact that migrant workers generally have no access to other social welfare benefits—which are closely tied with residence status—such as social security, housing, transportation, and medical benefits (Wang and Zuo, 1999; Wong et al., 2007; Song et al., 2008; World Bank and DRC, 2014).

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due to any reason. We describe this method and our implementation in more detail in Appendix 1, Part B.

# **4.2. Data Description and Construction of Variables**

We bring together various data sources for the empirical analysis. Our main data set is the Rural-Urban Migration in China (RUMiC) survey, which consists of three independent modules: a migrant household module, an urban household module, and a rural household module. It collects rich data on the socioeconomic characteristics of rural-urban migrants and their left-behind children, including information on co-residence status, schooling status, and household expenditures on various types of school fees for their children. We restrict our sample to households that have at least one school-age child (age 6-16) as we focus on the impacts of school fees on child migration. This leaves us with a working sample of 1,349 households. We provide a more detailed description of this survey and other data sources in Appendix 2.

While we analyze two rounds of the RUMiC data set, we focus in this paper on the 2008 (first) round for two main reasons. First, as discussed earlier, local governments typically relied on raising revenues through school fees before 2008 to compensate for the lack of funding transfer from the central government to pay for the education of migrant children. The abolition of school fees in 2008 resulted in local governments being no longer able to collect revenues this way, at least in theory. Thus there could be (almost) no correlation between schools fees and budget deficits, which violates the relevance condition of our IV for 2009. Second, the linkage between shocks to public education spending and school fees is also likely to be weakened during an economic crisis. This is because local governments would typically be constrained by competing spending priorities in such times, thus would unlikely have total discretion over their education budget. For example, they might not be able to spend the surplus from the education budget generated in the previous year on education in the following year, 20
which prevents them from lowering school fees.<sup>30</sup> Our theoretical results (Corollary 3.3), however, suggest that migrant households’ decision on child migration may be more affected by school fees during a crisis; thus our use of the 2009 round will be limited to supplementary analysis.

There are challenges with measuring school fees. First, the administrative measures of citylevel school fees are not available; second, even if these data were available, it is impossible to predict the counterfactual school fees that migrant households who left their children behind would have paid if they had taken them along. For these reasons, we compute the mean and the median of migrant households’ per child expenditures on all school-related fees as measures of the school fees faced by migrant households.<sup>31</sup> To reduce endogeneity concerns with school fees, we exclude each household before implementing this calculation (i.e., for each migrant household, the mean (median) is based on the expenditures of all the migrant households in the sample except theirs). For robustness checks, in addition to the mean (median), we also compute alternative measures such as the 25<sup>th</sup> percentile and the 75<sup>th</sup> percentile of the household education expenditures.

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).<sup>32</sup> 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.

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sample are, by construction, the same for all migrant households in a given city. Both measures provide estimates of the average school fees that each migrant household is (exogenously) faced with when migrating to the city.

Yet, these school fee measures may still be endogenous at the city level if unobserved citylevel events occur that affect both a city’s school fees and its migrant workers’ decisions regarding child migration. As discussed earlier in the presentation of the empirical model, we address this issue by instrumenting school fees with the one-year lag of unexpected shocks to the city government’s education spending. We gathered the historical city-level education spending as a share of local public spending in the 15 cities (metropolitan areas) covered by RUMiC 2008 for the period 2002-2007 from the China City Statistical Yearbooks. For each city, using different detrending techniques (i.e., Hodrick-Prescott (HP) filter and linear filter), we decomposed the time series records into a trend component and a cyclical component.

We constructed a measure for the trend in city education services with the growth rate of the student-teacher ratio in 2007 based on the number of students and teachers in metropolitan areas in 2006 and in 2007 using the China City Statistical Yearbooks. As a proxy for migration distance between the original and the destination areas, we constructed a dummy variable that equals 1 if the migrant household is from a rural area within the same province and equals 0 if the migrant household is from another province. Since city-level Consumer Price Index data are not available for China, we proxy for living costs with city-level housing prices in 2007 from the China Urban Life and Price Yearbook 2008.

Table 1 shows the summary statistics for household and city characteristics. The average age of household heads in our sample is 36.7, with around one-fourth (26 percent) of households being female-headed. About half of all household heads are primary school graduates and less than one-third (29 percent) of them hold a junior high school diploma or higher. 38 percent of migrant households bring their children with them to the city, and a 22
migrant household has on average 0.46 migrant children; out of these households, 7 percent bringing two children or more, and less than half (43 percent) of the migrant children are girls (not shown). About two-thirds of migrant households have both spouses living together, and more than half (57 percent) of the migrant households are from the same province (suggesting that within-province migration costs are lower; see Appendix 1, Lemma 1). About half (47 percent) of the migrant households currently live in coastal cities. Almost all (97 percent) of all household heads are employed and slightly more than one-third (36 percent) are selfemployed. Only one-third of all household heads have a long-term work contract. The average annual education remittance migrant households sent back home in 2007 was 1,100 yuan, amounting to about 5 percent of a migrant household’s annual income. Overall, the studentteacher ratio in 2007 did not change much compared with that in 2006, even though the change was larger (up to 7 percent) in some cities. Lastly, the average housing price in 2007 was about 5,600 yuan per square meter in these 15 cities, with the price in the most expensive city being about 6 times greater than in the least expensive city.<sup>33</sup>

# **5. Impacts of School Fees**

# **5.1. 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

> 33 The sample for the 2009 round is somewhat different from the 2008 round. For example, households are less likely to bring their children to the city but have slightly more income per capita, and more household heads are female (Appendix 3, Table 3.4).

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variables indicating the industry the head works in.<sup>34</sup> 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) using the linear probability model, where the non-IV estimates are shown at the bottom of the 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.

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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.<sup>35</sup> 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.<sup>36</sup> 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.<sup>37</sup> 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.

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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.<sup>38</sup> 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.

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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.

# **5.2. 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, we consider other measures such as the 25<sup>th</sup> and the 75<sup>th</sup> percentiles of the distribution of school expenses. These percentiles provide further checks against the possibility that outliers may possibly dominate the distribution of school fees and affect the results. Estimates shown under 27
columns 5 and 6 are qualitatively similar to those under columns 1 and 2, and are even slightly larger in magnitude. Third, instead of converting the school fees into logarithmic form, we consider them in units of thousand yuan. Estimation results shown under columns 7 and 8 are, 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 but focus only on the sample of migrant children that currently live in the cities, and convert the dependent 28
variable to a dummy variable that respectively equals 1 or 0 if the migrant child attends a public school or a private school. This regression can help us detect whether school fees can have an impact on the type of schools in the cities that migrant children attend; estimation results, however, indicate that the estimated coefficients on schools fees are not statistically significant (not shown).<sup>39</sup>

# _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) that the migrant worker brings his children and their upper bounds and lower bounds based on the Chernozhukov et al. (2013) method against the median school fees. The predicted probabilities reassuringly fall within the bounds.<sup>40</sup>

> 39 Yet, as a further check, we re-estimate 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.

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# **5.3. Heterogeneity Analysis**

_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. Table 6 (row 1) 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).<sup>41</sup> 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).

> 41 For each migrant worker, RUMiC records the enrollment status of four major social insurances/benefits: unemployment insurance, pension insurance, work injury insurance, and housing fund ( _San Xian Yi Jin_ ), which are mandated by the Social Insurance Law. We define a migrant worker as insured if he/she has access to at least one of these insurances/benefits.

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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.<sup>42</sup> 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.

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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 Table 2.<sup>43</sup>

# **6. Further Analysis of Related Outcomes**

# **6.1. Health Outcomes for Migrant Children**

Our theoretical model predicts that children brought along by migrant households may have better health outcomes (Corollary 1.1). This result is strongly supported by most, if not all, of the recent studies on China as discussed earlier. We re-examine this result with the RUMiC data, and investigate whether moving with parents impacts children's height, their body mass index (BMI) and the underweight/overweight status.<sup>44</sup> We regress these child health outcomes on a dummy variable indicating whether the child is living in the city with the migrant household, controlling for children’s and the household heads’ characteristics. The endogenous variable here is the child migration dummy variable and the IV is the public education spending shocks (the first-stage regression in this case is the reduced form regression). Unlike the previous regressions that were run at the household level, we run these regressions at the individual level for all the school-age children in the sample. Estimation results (Table 8)

> 43 Since we do not have data on migrants’ province of original residence for 2009, we do not control for these dummy variables. An alternative modeling option is to pool the 2008 and 2009 rounds of the RUMiC for analysis. 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.

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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).

# **6.2. 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 IVTobit 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).<sup>45</sup> 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.

> 45 We include the remittances used for education-related expenditures including tuition fees, food and accommodation, remedial class, and other fees. Other interesting results in Table 9 indicate that older household heads send more remittances back home, while those who are self-employed and within-province migrants send less remittances, and that educational achievement does not have any impact on remittances.

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# **7. 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.

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