metadata: authors: 0: author: Dang, Hai-Anh
1: author: Rogers, Halsey
count: Vietnam
docna: 0: docna: The decision to invest in child quality over
            quantity : household size and household investment in
            education in Vietnam
docty: Policy Research Working Paper
theme: Child health
majtheme: Human development
subtopic: Health Care Services Industry,Reproductive Health,Educational Sciences,Family Planning Research,Inequality
teratopic: Health, Nutrition and Population,Education
abstracts: cdata!: During Vietnam's two decades of
            rapid economic growth, its fertility rate has fallen sharply
            at the same time that its educational attainment has risen
            rapidly -- macro trends that are consistent with the
            hypothesis of a quantity-quality tradeoff in child-rearing.
            This paper investigates whether the micro-level evidence
            supports the hypothesis that Vietnamese parents are in fact
            making a tradeoff between quantity and quality of children.
            The paper presents data on private tutoring -- a widespread
            education phenomenon in Vietnam -- as a new measure of
            household investment in children's quality combining it
            with traditional measures of household education
            investments. To assess the quantity-quality tradeoff, the
            paper instruments for family size using the distance to the
            nearest family planning center. IV estimation results based
            on data from the Vietnam Household Living Standards Surveys
            (VHLSSs) and other sources show that families do indeed
            invest less in the education of school-age children who have
            larger numbers of siblings. This effect holds for several
            different indicators of educational investment and is robust
            to different definitions of family size, identification
            strategies, and model specifications that control for
            community characteristics as well as the distance to the
            city center. Finally, estimation results suggest that
            tutoring may be a better measure of quality-oriented
            household investments in education than traditional measures
            like enrolment, which are arguably less nuanced and less household-driven.
geo_reg_key: 80475,80451,80471
repnme: repnme: The decision to invest in child quality
            over quantity : household size and household investment in
            education in Vietnam
display_title: The decision to invest in child
            quality over quantity : household size and household
            investment in education in Vietnam
listing_relative_url: /research/2013/06/18430518/decision-invest-child-quality-over-quantity-household-size-household-investment-education-vietnam
topicv3: Poverty m1326687 695,Education m1327048 470,Family Planning m1327501 1452,Contraceptives m1327726 1453,Health m1504661 3480
publishtoextweb_dt: 2013-06-01T00:00:00Z
historic_topic: Health, Nutrition and Population,Education
no_of_pages: 53
model_extractions: WPS6487 Policy Research Working Paper 6487 The Decision to Invest in Child Quality over Quantity Household Size and Household Investment in Education in Vietnam _Hai-Anh Dang Halsey Rogers_ The World Bank Development Research Group Poverty and Inequality Team & Human Development Network Education Unit June 2013
Policy Research Working Paper 6487

# **Abstract**

During Vietnam’s two decades of rapid economic growth, its fertility rate has fallen sharply at the same time that its educational attainment has risen rapidly— macro trends that are consistent with the hypothesis of a quantity-quality tradeoff in child-rearing. This paper investigates whether the micro-level evidence supports the hypothesis that Vietnamese parents are in fact making a tradeoff between quantity and quality of children. The paper presents data on private tutoring—a widespread education phenomenon in Vietnam—as a new measure of household investment in children’s quality combining it with traditional measures of household education investments. To assess the quantity-quality tradeoff, the paper instruments for family size using the distance to the nearest family planning center. IV estimation results based on data from the Vietnam Household Living Standards Surveys (VHLSSs) and other sources show that families do indeed invest less in the education of schoolage children who have larger numbers of siblings. This effect holds for several different indicators of educational investment and is robust to different definitions of family size, identification strategies, and model specifications that control for community characteristics as well as the distance to the city center. Finally, estimation results suggest that tutoring may be a better measure of qualityoriented household investments in education than traditional measures like enrolment, which are arguably less nuanced and less household-driven.

This paper is a joint product of the Poverty and Inequality Team, Development Research Group; and the Education Unit, Human Development Network. I. 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 or hrogers@ 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
**The Decision to Invest in Child Quality over Quantity:**

**Household Size and Household Investment in Education in Vietnam**

Hai-Anh Dang and Halsey Rogers<sup>*</sup> _JEL:_ I2, J1, O1 _Keywords:_ family size, fertility, quantity-quality tradeoff, tutoring, Vietnam, private schooling, education finance

* Dang (hdang@worldbank.org) and Rogers (hrogers@worldbank.org) are respectively Economist (Poverty and Inequality Unit, Development Research Group) and Lead Economist (Human Development Network) with the World Bank. We would like to thank Mark Bray, Miriam Bruhn, Hanan Jacoby, Shahidur Khandker, Stuti Khemani, David McKenzie, Cem Mete, Cong Pham, Paul Schultz, and colleagues participating in the World Bank’s Hewlett grant research program, and participants at the Population Association of America Meeting for helpful comments on earlier drafts of this paper. We would also like to thank the Hewlett Foundation for its generous support of this research (grant number 2005-6791). The findings and interpretations in this paper do not necessarily reflect the views of the World Bank or its Executive Directors.
# **1. Introduction**

Over the past four decades, there has been considerable study of the relationship between household choices on the quantity and quality of children, starting with the seminal studies by Becker (1960) and Becker and Lewis (1973). The hypothesis driving the literature is that parents make tradeoffs between the number of children they bear and the “quality” of those children, which is shorthand for the amount of investment that parents make in their children’s human capital. If this hypothesis is true, it has considerable implications for policies aimed at increasing economic growth and reducing poverty. For example, small family sizes and slow population growth would then be conducive to increased human capital and higher earnings (Angrist, Lavy, and Schlosser, 2010), as well as to economic development more broadly (de la Croix and Doepke, 2003; Moav, 2005).<sup>1</sup> Consequently, this can motivate policy makers to work on policies that assist couples to avoid unwanted births or to subsidize birth control (Schultz, 2008).

Our contributions to the literature in this paper are threefold. First, we investigate a new measure of household investment in their children, which is private tutoring—or extra classes—in mainstream subjects at schools that children are tested in. Private tutoring merits attention for several reasons. Private tutoring may be an especially good measure of a household’s decision to invest voluntarily in children’s human capital – compared with enrollment, for example, which may also reflect exogenous factors such as compulsory schooling laws. Put differently, private tutoring can represent the household’s (and student’s)

> 1 The empirical evidence on the correlation between household size and poverty appears inconclusive. For example, Lanjouw et al. (2004) argue that the common view that larger-sized households are poorer is sensitive to assumptions made about economies of scale in consumption.

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extra efforts to increase human capital.<sup>2</sup> Furthermore, private tutoring is now widespread in many countries, especially but not solely in East Asia,<sup>3</sup> and evidence indicates that it improves students’ academic performance in some countries, including Germany, Israel, Japan, and Vietnam (Dang and Rogers, 2008).<sup>4</sup> Finally, there has been considerable debate about tutoring among policymakers. One crucial question is whether widespread availability and use of private tutoring exacerbates or helps equalize social and income inequality (Bray, 2009; Bray and Lykins, 2012), a question that is relevant to both developing and developed countries.<sup>5</sup> Here, the link with demography is important: if use of tutoring is correlated with both smaller family size and higher family income, this heightens the risk that it could exacerbate inequality.

Second, more generally, we improve on previous studies by providing a rather comprehensive investigation of different aspects of household investment in private tutoring for each child (i.e., at the child level), most of which have not been used before. These include participation in tutoring, household monetary investment in tutoring, and time spent both in the short term (i.e., frequency of attending tutoring classes in one year) and in the long term (i.e., number of years attending tutoring classes) on tutoring. We also go one step

> 2 Bishop (2006) emphasizes the importance of student effort on learning, and a recent study by MacLeod and Urquiola (2012) finds that it is not simply more school choice but rather student effort that can enhance educational performance.

> 3 Private tutoring (or supplementary education) is a widespread phenomenon, found in countries as diverse economically and geographically as Cambodia, the Arab Republic of Egypt, Japan, Kenya, Romania, Singapore, the United States, and the United Kingdom. A recent survey of the prevalence of tutoring in 22 developed and developing countries finds that in most of these countries, 25–90 percent of students at various levels of education are receiving or recently received private tutoring, and spending by households on private tutoring even rivals public sector education expenditures in some countries such as the Republic of Korea and Turkey (Dang and Rogers, 2008).

> 4 Other recent studies that find tutoring to have positive on different measures of student academic performance include student test scores and academic performance in India (Banerjee et al., 2010) and the United States (Zimmer et al., 2010). But see also Zhang (2013) for recent evidence that tutoring may benefit only certain student groups in China.

5 For example, in a recent opinion piece in the New York Times on the widening inequality in the US, the Nobel laureate Joseph Stiglitz (2013) calls for more “...summer and extracurricular programs that enrich lowincome students’ skills” to help level the playing field between these students and their richer peers.

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further than just looking at household investment in tutoring by considering the situation where households can make a joint decision on whether to enroll their children in school and to send them to tutoring classes.

Third, we explore the hypothesized child quantity-quality tradeoff in the context of Vietnam, a country that has undergone rapid change in fertility and educational attainment. The total fertility rate decreased steadily from 6 births per woman in the 1970s to 4 births per woman in the late 1980s and to just under 2 births per woman currently (World Bank, 2012). And over the past two decades, the average number of years of schooling for the adult population has increased rapidly, from 4 in 1990 (Barro and Lee, 2012) to 6.6 in 1998 and 8.1 in 2010 (VLSS, 1998; VHLSS, 2010).<sup>6</sup> The Government of Vietnam has paid much attention to family planning and has promulgated policies over the past fifty years encouraging (and in the case of government employees, requiring) families to restrict their number of children to one or two, but to our knowledge, our study is the first to investigate rigorously the quantity-quality tradeoff in the context of Vietnam.

In this paper we focus on households’ investment in their children rather than children’s outcomes, because doing so may provide a more direct test of the quantity-quality tradeoff hypothesis (see, for example, Caceres-Delpiano (2006) and Rosenzweig and Zhang (2009) for a similar approach). In the context of Vietnam, private tutoring as a new measure of the households’ investment in the quality of their children appears more appropriate than traditional measures (such as education expenditures or private school attainment) for two reasons. First, Vietnam’s education system is mostly public with more or less uniform

> 6 Unless otherwise noted, all estimates from the Vietnam Living Standards Surveys (VLSSs) and Vietnam Household Living Standards Surveys (VHLSSs) are authors’ estimates.

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tuition, and second, the market for private tutoring is well-developed, with approximately 42 percent of children age 6-18 attending private tutoring in the past 12 months.

To identify the impacts of family size on household investment in private tutoring, we use as instrument the distance from the household’s commune<sup>7</sup> to the nearest family planning center. In contrast to instruments used in most previous studies, this instrumental variable allows us to study the effects of family size for families with one child or more. Our results provide considerable support for the quantity-quality tradeoff in the Vietnamese context, with quality measured by both the households’ financial investments in private tutoring and their general expenditures on education. Furthermore, the IV estimates of the impacts of family size are larger in magnitude than the uninstrumented results. These estimation results hold for several different measures of tutoring and are generally robust to different model specifications, identification strategies, and definitions of family size. In particular, each additional sibling reduces the household’s investments in a child’s schooling as measured through a variety of indicators: it reduces education expenditure and tutoring expenditure by 0.4 and 0.5 standard deviations, respectively; it decreases the child’s probability of being enrolled in tutoring by 32 percentage points; it reduces the child’s enrolment and tutoring index or tutoring attendance frequency by 0.34; and it cuts the average time spent on tutoring by 74 hours and 1.4 years of tutoring.

This paper has six sections. We provide a review of the literature in the next section, followed in Section 3 by the data description and a description of family planning policies and the private tutoring context in Vietnam. Sections 4 and 5 present our empirical framework and estimation results, and Section 6 concludes.

> 7 A commune in Vietnam is roughly equal to a town and is the third administratively largest level (i.e., below the province and district levels) and higher than the village level. There are approximately 9,100 communes in the country (GSO, 2012).

5
# **2. Empirical Literature:  Testing the Quantity-Quality Tradeoff**

Our paper straddles two strands of literature: the more established literature on the quantity-quality tradeoff, and a smaller but growing number of studies on private tutoring. We briefly review the most relevant studies in this section.

One central and empirical challenge among the first literature, on the hypothesized quantity-quality tradeoff, is to address the endogeneity of family size convincingly in the data, since unobserved factors can affect both fertility and child human development outcomes. Different instrumental variables have been used and include unplanned (multiple) births (Rosenzweig and Wolpin, 1980; Li, Zhang, and Zhu, 2008), the gender mix of children combined with parental sex preference (Angrist and Evans, 1998; Angrist, Lavy and Schlosser, 2010), and relaxation of government regulation on family size (Qian, 2013). Despite these (and other) studies, the stock of evidence on the quantity-quality tradeoff appears far from conclusive<sup>8</sup> ; furthermore, while these identification strategies are useful, they cannot be applied in all contexts.

In the quantity-quality tradeoff framework proposed by Becker and Lewis (1973), a reduction in the costs of maternity care leads to changes in the relative price of quality and quantity of children and in the amount that parents choose to invest in their children. While no studies on the quantity-quality tradeoff appear to have used this insight to construct instruments, several studies in labor economics use variables related to family planning as

> 8 For example, Angrist, Lavy and Schlosser (2010) find no tradeoff in Israel; Lee (2008) finds a weak tradeoff in Korea that gets stronger with more children. However, while Black, Devereux, and Salvanes (2005) found that controlling for birth order reduces the impacts of family size to almost zero for older Norwegian birth cohorts, they find the opposite holds for more recent birth cohorts (Black, Devereux, and Salvanes; 2010); in China, Li et al. (2008) find a negative impact of family size on children’s education but Qian (2013) finds that an additional child significantly increased school enrollment of first-born children for one-child families; and in Brazil, Ponczek and Souza (2012) find larger family size has a negative causal impact on education and positively related with girls’ and boys’ labor force participation, while Marteleto and de Souza (2012) find these impacts on adolescents’ schooling in Brazil have turned from positive to no effect and then negative during the 1977-2009 period. See also Steelman et al. (2002) and Schultz (2008) for recent reviews.

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instruments to identify the causal impacts of family size on female labor supply.<sup>9</sup> Instrumenting for fertility with state- and county-level indicators of abortion and family planning facilities and other variables, Klepinger, Lundberg, and Plotnick (1999) find that teenage childbearing has substantial negative effects on women’s human capital and future labor market opportunities in the US. Another US study by Bailey (2006) employs state-level variations in legislation on access to the contraceptive pill to instrument for fertility, and it also provides strong evidence for the impact of fertility on female labor force participation. More recently, Bloom et al. (2009) instrument for fertility with country-level abortion legislation in a panel of 97 countries over the period 1960–2000; they find that removing legal restrictions on abortion significantly reduces fertility and that a birth reduces a woman’s labor supply by almost 2 years during her reproductive life.

We follow a similar identification strategy and use the availability of family planning services, which can reduce the cost of maternity care as well as the cost of controlling the quantity of children in general, as our instrument in the context of Vietnam.<sup>10</sup> Specifically, in our test of the quantity-quality tradeoff hypothesis, we use the distance to the nearest family planning center at the commune level as an instrumental variable for the quantity of children.<sup>11</sup> Perhaps the greatest advantage of this instrument over other commonly used

> 9 Another thread of the quantity-quality tradeoff literature estimates the reduced-form impacts of family planning services instead (see, for example, Rosenzweig and Schultz (1985) and Joshi and Schultz (2013)). Recent studies that find that family planning-related variables have important impacts on fertility include DeGraff, Bilsborrow, and Guilkey (1997) for the Philippines, Miller (2010) for Columbia, and Portner, Beegle, and Christiaensen (2011) for Ethiopia.

> 10 See the working version of this paper (Dang and Rogers, 2013) for a simple theoretical framework motivating this approach. Throughout this paper, we follow the literature by using the term “quality” of children to refer to the amount of human capital invested in them.  Needless to say, this should not be taken as a value judgment about their worth as individuals.  As noted earlier, however, higher human capital is associated with a host of other desirable development outcomes, at both the individual and societal levels.

> 11 Distance to services is often used as an instrument in the literature. For example, distance to college is used to identify the returns to education (Card, 1995), distance to the tax registration office is used to identify the impact of tax registration on business profitability (McKenzie and Sakho, 2010), and distance to the origins of the virus is used to estimate the response of sexual behavior to HIV prevalence rates in Africa (Oster, 2012).

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instruments such as twins and sibling sex composition is that the family-planning instrument allows us to analyze the impacts of family size on all the children in the household (or the single child, if there is only one), while using either twins or children sex composition restricts analysis to a subset of these children.<sup>12</sup> Turning now to the second strand of literature, on private tutoring, few papers have investigated the correlation between household size and household educational investment in their children through private tutoring. To our knowledge, the exceptions are the two papers on Korea by Lee (2008) and Kang (2011), and the former touches only briefly on tutoring. Both these papers share the same identification strategy, in that they use the sex of the first-born child as an instrument for family size,<sup>13</sup> but the former implements this analysis at the household level, while the latter does so at the level of the child. Lee (2008) finds a negative impact of larger family size on household investment in education in general and tutoring in particular, but Kang (2011) finds these negative impacts to be significant only for girls.

> Gibson and McKenzie (2007) provide a related review of household surveys’ use of distances measured via global positioning systems (GPS).

> 12 Using twins as the instrument also requires a much larger estimation sample size; as a result, most previous studies that took this strategy have had to rely on population censuses.

> 13 The use of the sex of the first-born child as an IV has some limitations.  First, it requires the assumption of son preference—which appears to be a weak IV, so that Kang (2011) has to rely on bound analysis to identify bounds of impacts of family size in the case of boys. Second, the assumption of son preference in turn requires the assumption that parents do not abort girls at their first childbearing; if they do, the sex of the first-born child is clearly not valid as an exogenous instrument. This concern is especially relevant to Vietnam, which has one of the highest abortion rates in the world (Henshaw, Singh, and Haas, 1999). And finally, this identification approach may only work for families with more than one child; our study makes no such restriction on family size, investigating families with between one and seven children.

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# **3. Data Description, Family Planning and Tutoring in Vietnam**

## **3.1. Data description**

In this paper, we analyze data from three rounds (2002, 2006, and 2008) of the Vietnam Household Living Standards Surveys (VHLSS). These are nationally representative surveys similar to the LSMS-type (Living Standards Measurement Study) surveys supported by the World Bank in many developing countries. The VHLSSs are implemented by Vietnam’s General Statistical Office (GSO) with technical assistance from the World Bank and cover around 9,200 households in approximately 3,000 communes across the country in each round. The surveys provide detailed information on education, including data on tutoring expenditures, as well as information on household demographics and consumption. In addition to a module collecting data on household members, these surveys include a community module that collects data on community infrastructure and facilities such as distances to schools or family planning facilities. Starting from 2002, the VHLSSs are implemented biannually and collect more data for rotating themes for each survey round; for example, the theme for the 2006 round is educational activities. These surveys are widely used for education analysis by the government and the donor community in Vietnam.

For data on family planning facilities (and community characteristics), we use the 2002 round, since only this survey round collects data on the distance to family planning centers. Because this information is only available for rural communes, we restrict our analysis to rural households in Vietnam. The VHLSSs collect data on different households who reside mostly in the same communes, which allows us to match the commune information from the 2002 survey round to most of the households in the 2006 and 2008 survey rounds.<sup>14</sup>

> 14 This matching process is complicated by the fact that there were administrative changes resulting in changes to administrative commune codes between 2002, 2006, and 2008. For around 150 communes, we have to rely

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However, we focus on the 2006 round of the VHLSS for the outcome variables, since this round has the most detailed information on household investment in tutoring activities. We also supplement our analysis with data from another nationally representative survey (VHTS) focused on private tutoring that we fielded in 2008,<sup>15</sup> as well as data on teacher qualifications in the community from the primary school census (DFA) database.<sup>16</sup> Since most children start their first grade at 6 years old, we restrict our analysis to children who are between 6 and 18 years old.<sup>17</sup> To address concerns about grown-up children that have already moved away from home, we consider only children who are living at home and households where the total number of children born of the same mother is equal to the number of children living in the household. We define family size as consisting of children born of the same mother, but we also experiment with a more relaxed definition of family size that considers all children living together in the households, as well as other stricter definitions to be discussed later.

# **3.2. Overview of family planning in Vietnam**<sup>**18**</sup>

Vietnam’s family planning policy dates back to 1961, when the government encouraged families to have between two and three children, with the aim of decreasing the annual population growth rate from 3.5 percent to 2.5 percent. Due to the Vietnam War and a lack

> on both commune and district names (in addition to province and district codes) for matching. We can match 96 percent of all the communes in 2002 to those in 2006 and 2008 (i.e., we can match 2,808 communes out of 2,933 communes in 2002).

> 15 For details on this survey, see Dang and Glewwe (2009).  We collaborated on designing the survey with other researchers, including Paul Glewwe (University of Minnesota), Seema Jayachandran (Northwestern University), and Jeffrey Waite (World Bank). The survey was administered by Vietnam’s Government Statistics Office, using funding from the World Bank’s Research Support Budget and the Hewlett Foundation.

> 16 This database is initiated and maintained by World Bank-supported projects. For a brief description on the history and objectives for the primary school census database, see Attfield and Vu (2013).

> 17 We also experimented with other age ranges such as ages 10- 18 and 12- 18. Estimation results (available upon request) are qualitatively very similar and even more statistically significant than those for the age range 6- 18.

> 18 This section is mostly based on GDPFP (2011).

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of resources, however, this policy had limited success, with some basic family planning services provided in certain areas in the North of Vietnam. Following the unification of Vietnam in 1975, policymakers became concerned when population expanded more rapidly than the economy, and they responded by setting a goal of lowering population growth rates to less than 2 percent. To make this goal a reality, in 1988 the government adopted a policy restricting families to one to two children.

This policy has remained in effect until now. The highlights of this policy include the universal and free provision of contraceptives and abortion services, incentives for families, and strict penalties for families with more than two children. These penalties include fines, restrictions on promotion (or even demotions) for government employees, and denial of urban registration status. Vietnam’s approach to family planning policy closely follows that of one-child-per-family in China, but it is administered less rigorously (Goodkind, 1995). This lack of rigor contributes to our analysis of the quantity-quality tradeoff, in fact, by expanding the range of variation of family size.<sup>19</sup> An important administrative landmark for family planning—and one that is quite relevant to the discussion below of our instrument’s validity—was the establishment of the ministry-level National Council of Population and Family Planning (NCPFP) in 1984. By the late 1980s, the NCPFP had established administrative offices and staff down to the commune level to ensure their activities reach the whole population. Together with the official administrative apparatus, the NCPFP also built up a wide-reaching network of family

> 19 We attempted in an earlier draft to use households’ exposure to the two-child-per-family policy as an instrument since the strictness with which it is applied varies with certain characteristics that can be largely exogenous to the family.  However, it turned out that the policy was not implemented rigorously enough to make it a viable instrument.

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planning volunteers, both at the village level as in most government agencies, to promote family planning policies.<sup>20</sup>

# **3.3. Background on tutoring in Vietnam**

The current education system in Vietnam has three levels: primary, secondary, and tertiary (post-secondary). Primary education consists of grades 1 to 5, which is for children age 6 to 10. Secondary education is divided into lower secondary education, which consists of grades 6 to 9 (for children age 11 to 14), and upper secondary education, which consists of grades 10 to 12 (for children age 15 to 17). Vietnam has almost achieved universal primary education with 94 percent of Vietnamese children age 15-19 having completed primary education (VHLSS, 2006). High-stakes examinations are widely used in the education system for performance evaluation, and performance on the exams determines whether students can obtain secondary-school degrees and gain admission to colleges/universities. The strict rationing at the tertiary level results in strong competition among high school students, which helps fuel the demand for private tutoring.

Private tutoring is such a major feature of the Vietnamese educational landscape that it is hotly debated, both in the media and during the Minister of Education’s presentations to the National Assembly. Policymakers, educators, and parents fall into two main opinion camps—one arguing that private tutoring worsens educational outcomes and harms children, and the other that tutoring can improve the quality of education. The former group

> 20 In 2007, the NCPFP was merged into the Ministry of Health and renamed the General Department of Population and Family Planning (GDPFP).

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calls for a total ban on private tutoring, while the latter supports the (controlled) development of tutoring.<sup>21</sup> Table 1 lists the reasons that students take private tutoring classes, according to data from the VHTS. Tutoring classes are divided into two categories: tutoring classes organized by the student’s own school, and other tutoring classes. Across the two types of tutoring, the most important reason for taking tutoring is to prepare for examinations, which accounts for almost half of all responses (42-47 percent). Other commonly cited reasons given include to catch up with the class (13-14 percent), to acquire better skills for future employment (13 percent), and to pursue a subject that the student enjoys (6-11 percent). Other reasons, such as to get childcare, to compensate for poor-quality lessons in school, or to study subjects not taught in mainstream classes, account for a smaller proportion of all responses (3-6 percent each). The preeminence of exam preparation over other reasons for taking tutoring classes reflects the importance of examinations in the school system in Vietnam.<sup>22</sup> Richer households in Vietnam spend more on tutoring classes than do poorer households, as shown in Table 2. Currently about 40 percent (= 100 - 60.4) of households in Vietnam send their children to private lessons, and the majority of them (90 percent) spend between 1 percent and 5 percent of household expenditure on tutoring classes. The percentage of households with positive expenditures on tutoring classes is only 21 percent in the poorest (1<sup>st</sup> ) consumption quintile, but nearly doubles to 38 percent in the next richer quintile (2<sup>nd</sup> ) and hovers around 35 percent in the top three quintiles (3<sup>rd</sup> to 5<sup>th</sup> ). In terms of

> 21 See also Dang (2011 and forthcoming) for more detailed discussions of the private tutoring phenomenon in Vietnam.

> 22 For examining our hypothesis of the quantity-quality tradeoff, we are in fact assuming that sending children to tutoring classes are completely determined by parents.  If corrupt teachers force tutoring on their own students beyond parental control (see, e.g., Bray, 2009; Jayachandran, 2012), household investment in tutoring would not provide valid evidence for this tradeoff. However, the results in Table 1 suggest this concern is a minor one in the context of Vietnam.

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actual expenditure, the mean expenditure on tutoring classes by the wealthiest 20 percent of households is 15 times higher than expenditure by the poorest 20 percent of households. And more expenditure on tutoring is found to increase student grade point average (GPA) ranking in Vietnam, with a larger influence for lower secondary students (Dang, 2007, 2008).

Our calculation (not shown) using the 2006 VHLSS shows that the majority of children age 6-18 have at most three siblings, with 10 percent having no sibling, 48 percent having one sibling, 27 percent having two siblings, and 10 percent having three siblings; only five percent of these children have four siblings or more. Table 3 provides a first look at children age 6-18 that are currently enrolled in school that comprise our estimation sample, of whom 42 percent attended private tutoring in the past 12 months. They spent on average D 104,150 (equivalent to $US 6)<sup>23</sup> and 89 hours on these tutoring classes also in the past 12 months, and had attended tutoring for 1.9 years; for those that attended tutoring in the past 12 months, the corresponding expenditure and hours spent on tutoring are D 246,590 and 215 hours. These children have 1.6 siblings on average, are mostly in secondary school (58 percent), and live an average of 8.6 kilometers away from the nearest family planning center.

# **4. Empirical Framework**

## **4.1. Estimation equations**

Our empirical approach first tests for multivariate correlations between family size and the education-related dependent variables and then instruments for family size in these regressions. The basic estimation equations are for child j, j= 1,..,J in household I, i= 1,..,N

> 23 The exchange rate was D 15,994 for $US 1 in 2006 (World Bank, 2012).

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While we focus primarily on households’ investment in their children rather than the final educational outcomes of those children—which can be affected by other factors rather than household investment alone—we also look at the more traditional measures for comparison. Thus, for the first equation, the dependent variable Eij includes both traditional measures and new measures of household investment in tutoring. The traditional measures include school enrolment, educational expenditure, and completed years of schooling.<sup>24</sup> The new measures include attendance at private tutoring classes, a combined school enrollment/tutoring index (which takes a value of 2 if enrolled in both school and tutoring, 1 if school only, and 0 if neither), frequency of tutoring attendance (which takes a value of 2 if enrolled in tutoring during both school year and holidays, 1 if either school year or holidays, and 0 if neither), expenditure on tutoring,<sup>25</sup> and the number of hours in the past year and the number of years to date spent on tutoring. Of these measures, only tutoring attendance and expenditure appear to have been used in previous studies on tutoring.

Distance to the nearest family planning center ( _DisFam_ ) is a commune-level variable. Zij is a vector of child, household, community and school characteristics that include age, gender, school level, mother’s age,<sup>26</sup> mother’s age squared, gender of the household head, head’s years of schooling, ethnicity, household expenditure, and distances to the nearest primary and secondary schools. A variable indicating the number of years that remains before the last grade in the current school level is also added, since this variable was found to capture the increasing intensity of tutoring classes as students progress in school (Dang,

> 24 For children that are currently in school, completed years of schooling is right-censored since we do not observe the final years of schooling for these children. Thus for such children (and our estimation sample), this variable represents a lower-bound estimate only.

> 25 For easier interpretation of results and because of the large number of zero observations, in our preferred specification we do not transform variables such as expenditures and hours spent on tutoring to logarithmic scale. Estimation results with the transformed variables are similar, however, and coefficients are slightly more statistically significant.

> 26 There are more missing observations with father’s age so we omit this variable.

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2007), but this variable is left out in the regression for the enrollment/tutoring index since it applies only to children currently enrolled in school.

For easier interpretation of results, we estimate equation (1) for all the outcomes above (except for expenditure and hours spent on tutoring) using an OLS model, where results can be readily read off of the estimated coefficients. For expenditure and hours spent on tutoring,<sup>27</sup> we use a Tobit model instead since a large number of children have zero values for these variables and subsequently provide separate estimates for the marginal effects. Let Eij∗ be the latent variable that represents the household’s potential spending (or hours) on tutoring; we observe tutoring spending Eij only when this potential spending is larger than 0, and observe zero spending otherwise. The Tobit model has the form It should be noted that there are two main ways to interpret the marginal impacts of the explanatory variables in a Tobit model, depending on the outcomes of interest. If we are interested in looking at the marginal effects of family size (or other explanatory variables) on household propensity to spend on tutoring classes, we can just look at the estimated coefficients in Table 6. However, if we want to know the marginal effects on households’ actual (observed) spending, we should look at the marginal effects provided in Table 1.2.<sup>28</sup> While the former interpretation may be more relevant for forecasting the future, the latter is

> 27 While the number of years of tutoring can also be fitted in a Tobit model, we prefer to use the OLS model for better interpretation. Estimation results using an IV-Tobit provide very similar results.

> 28 For a survey on the Tobit model, see Amemiya (1984). The marginal impacts for household propensity to spend can be calculated as ∂E(Ei∂FamSize∗j|FamSizeii,Zij) = β, and the marginal impacts for household actual spending can ∂E(Eij|FamSizei,Zij) α+βFamSizei+γZij be calculated as ∂FamSizei = βΦ( σ ~~)~~ where we also assume εij~N(0, σ<sup>2</sup> ) as in the OLS models. See, for example, Greene (2012) for more discussion on the marginal effects with the Tobit model.

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more commonly used and focuses on household spending at present. For our purposes, we will use the latter interpretation of the marginal effects.

# **4.2. Distance to family planning center as instrument**

We then estimate equations (1) and (2) jointly in an IV model (with 2SLS or IV-Tobit accordingly), where family size is instrumented by the distance to the nearest family planning center. We believe this instrument is appropriate in the context of Vietnam because it meets the exogeneity, relevance, and exclusion restriction conditions. In this section, we consider these three criteria in turn.

A major exogeneity-related concern with using public programs, including placement of family planning centers, as instruments is that these programs may have been established in response to local demand (Rosenzweig and Wolpin, 1986). The evidence suggests, however, that such demand response is not an issue in Vietnam, where family planning services were already offered at the commune level and reached virtually the whole population by the late 1980s (Goodkind, 1995; GDPFP, 2011). While little data exist on the local conditions when family planning centers were set up, it is generally the case with most policy implementation in Vietnam that the central government sets the national policies but it is the local governments that ultimately decide exactly how these policies will be implemented.<sup>29</sup> Thus the establishment of family planning centers was most likely decided by local governments. In theory, this might cause us to suspect that it was primarily local demand that drove the placement of the centers. But in an analysis of a survey of local governments' family planning efforts in 15 provinces across Vietnam, San et al. (1999) find that effort strength is mostly driven by the quality of local governments’ leadership and implementation

> 29 Scornet (2001) observes that local governments’ strong autonomy in implementing family planning policies takes its root in the traditional decentralization of monarchical governments in the past.

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ability, rather than local conditions such as geographical terrain or the level of economic development.<sup>30</sup> Still, some variation of the location (and timing) of family planning center may stem from differences in local governments’ resources: communes with more resources might have been more likely to build a family planning center earlier. We argue, however, that once this channel is controlled for in the regressions (as proxied for by commune infrastructure in several model specifications we examine later), the location of the family planning center is exogenous to each household’s decision on number of children. While it is impossible to directly test for the instrument’s exogeneity, we use a three-pronged approach for extra precaution to ensure its validity. First, we use the distance to family planning centers in 2002 to instrument for the impacts of family size on household investments in education four years later, in 2006, which can help reduce any contemporaneous correlation between the former and the latter.

Second, as a check we will also restrict our analysis later to a sample where the family planning centers had already been established before the 1997 round of the household survey. If family planning centers were more likely to be first established in locations with stronger demand for family planning, older centers would be more effective in reducing family size and would consequently allow households to increase investment in their children’s education. Thus an analysis showing similar impacts of family size for the sample with older centers compared to those for the overall sample would provide evidence for the instrument’s exogeneity.<sup>31</sup>

> 30 San et al. (1999) also provide some evidence that their selected 15 provinces share many characteristics of the overall functioning of the national family planning program.

> 31 This check does not hold in the opposite direction since older centers may also be effective through other channels that are uncorrelated with endogeneity of location (e.g., longer existence simply increases the chances

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Finally, if it were true that family planning centers were more likely to be first established in locations where households have larger family size, assuming a negative relationship between family size and household investment in their children, we would expect this endogenous placement of these centers to weaken the impacts of the instrument and thus bias estimates upward toward zero. Thus our estimation results would provide conservative estimates in this case.<sup>32</sup> For relevance, our review of the literature from other countries suggests that access to family planning facilities is highly relevant to household decisions on family size. Previous studies for Vietnam using data from the 1997 Demographic and Health Survey offer similar findings that increased access to family planning services increases contraceptive use (Thang and Anh, 2002; Thang and Huong, 2003) and reduces unintended pregnancy (Le et al., 2004). Our estimates turn out to consistently show a strong and negative impact of the distance to family planning center on family size.

On the issue of the exclusion restriction, there may be concerns that family planning centers directly affect the investment in children by explicitly promoting the idea of a quantity-quality tradeoff. But given the presence of family planning workers in every commune (GDPFP, 2011) who can provide interested households with detailed information on the benefits of family planning, family planning centers mostly serve as facilities that provide options for restricting family size to the desired number of children. These centers

> families know about and use the services at these centers). Larger impacts for family size in the sample of older centers thus would not necessarily indicate violation of exogeneity.

> 32 An additional concern related to exogeneity is that families could have immigrated to their current commune, meaning that they were not necessarily constrained by the current distance to family planning center when making their decision on giving birth. However, this concern does not apply in our context:  we restrict our analysis to rural families only, and fewer than 3 percent of the total population over five years of age move within or to rural areas in Vietnam between 1994 and 1999 (Dang, Tacoli, and Hoang, 2003). Our tabulation of the 2006 VHLSS also shows that 98 percent of the population register their official residence _(hộ khẩu)_ in their current community.  Because Vietnam has a rigid household registration system under which it usually takes years for households to change their official registration after moving (see, for example, Hardy (2001), this finding indicates that few families have moved recently.

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focus on services related to providing contraceptives—such as insertion of intrauterine devices (IUDs), provision of condoms and oral contraceptives, menstrual regulation, and advice on family planning— as well as birth-related medical services and abortions (MOH, 2001). Thus access to family planning facilities should affect the educational outcomes of interest only through family size, which satisfies the exclusion restriction.

Another possible objection to the validity of the exclusion restriction is that the distance to the nearest family planning center may be correlated with unobserved commune characteristics that also affect household investment in their children. For example, more remote, less developed communes may also be farther away from any family planning center. In such cases, any negative impacts of household sizes on the outcome variables as instrumented by availability of family planning might be caused by the negative correlation between the general development level of the commune and these outcomes (e.g., poorer communes may spend less on their children’s tutoring classes).

We use two strategies to address this concern. The first is to consider a number of different specifications that test for the strength of this instrument as different commune characteristics are included in the regressions. If the instrument becomes weaker or loses its statistical significance, this means that it is strongly correlated with these commune characteristics (or other unobserved characteristics proxied for by these variables) and concerns about the exclusion restriction are justified. Our second strategy is to use an alternative identification that relies on the heteroskedasticity of the error terms (Lewbel, 2012) rather than a regular instrumental variable. Heteroskedasticity-based identification has been used for some time (see, e.g., King, Sentana and Wadhwani, 1994; Rigobon, 2003; Klein and Vella, 2010), and the idea for it dates back to Wright’s original instrument variables idea (Lewbel, 2012). The Lewbel identification approach has been applied in 20
various settings to examine the impacts of body weight on academic performance (Sabia, 2007), the effects of access to domestic and international markets on household consumption (Emran and Hou, 2013), and the effects of academic seniority on research productivity (Mishra and Smyth, 2013). Due to its reliance on higher moments, this identification strategy is less reliable than the standard IV approach (Lewbel, 2012), but it can provide a qualitative robustness check on our estimation results.

We show estimation results for the first strategy in Table 4, which tests for the strength of this instrument using several different specifications sequentially. (Full estimation results are shown in Table 1.1 in the Appendix.) Model 1, the most basic model, includes only the instrument and the regional dummy variables. Model 2 adds the children’s characteristics and their household characteristics, while Model 3 adds to Model 2 the distances to the nearest primary and secondary schools and includes the variables we use for the subsequent secondstage regressions. Model 4 then adds to Model 3 basic commune characteristics such as distances to the nearest paved road, public transportation, and the post office, which are expected to proxy for the general level of economic development of the commune.

Next, to net out any effects that access to community health care has on family size (for example, inadequate health care may reduce family size through high child mortality rates), Model 5 adds to Model 3 the distance to the nearest health facilities.

Given the low-technology production techniques typically used in agriculture, rural farming households in Vietnam have had to rely for the most part on manpower for their farm work, giving them an incentive to have more children. Furthermore, government employees may be subject to a stricter enforcement of the one-to-two children rule than are farming households. Thus, in the IV terminology (see, for example, Angrist and Pischke 21
(2009)), farming households may be the population subgroup that is affected differently by the distance to the family planning center than other population subgroups.

To address this issue, in Model 6 we add to Model 3 a variable indicating the share of the commune population working in agriculture. If this addition changes significantly the estimated coefficient on the instrument, this result would suggest that the estimated impact of the distance to the family planning center on family size in Model 3 is influenced by the farming-oriented occupation structure in the commune rather than the costs of family planning. Finally, Model 7 includes all the variables from Models 1 through 6.

The results in Table 4 show that the distance to family planning center has a positive and strongly statistically significant impact on family size, as expected.<sup>33</sup> Importantly, except in the case of Model 1 (which is clearly too simplistic), the magnitude of the estimated coefficient on the distance to the family planning center is almost identical in all the models at around 0.007; this magnitude indicates that a child living 10 kilometers further away from a family planning center would have 0.07 more siblings on average. The consistency of the point estimates suggests both the strong relevance and robustness of this instrument. Since most of the additional variables in Models 4 to 6 are statistically insignificant, to keep our models parsimonious, we will use the variables in Model 3 in subsequent regressions. In a later section on robustness analysis, we explore different specifications to further assess the validity of this instrument.

> 33 The t-statistics for Model 3 are equivalent to an F-statistic of 8.6, which is slightly below the value of 8.96 for a strong IV suggested by Stock and Yogo (2005). Note, however, that Stock and Yogo’s critical values rely on the assumption of independently and identically distributed (iid) errors, whereas our F-statistic is obtained from a cluster-robust regression that is robust to heteroskedastic errors. Without this cluster-robust option, the F- statistic for Model 3 is much higher at 22.6.

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# **5. Estimation Results**

## **5.1. Uninstrumented results on quantity and quality**

Table 5 provides estimation results for equation (1) as first-cut test of the quantityquality hypothesis with the marginal effects for the Tobit regressions provided in Table 1.2 in the Appendix. We control for several child, family, and community characteristics, as well as regional and urban dummies.

In each of these regressions, the coefficient on number of siblings is negative and highly statistically significant. These results are consistent with the quantity-quality tradeoff story: families that are raising fewer children invest more in the education of each child, even controlling for income and parental education. Controlling for other characteristics, each additional sibling is associated with a 0.1 standard deviation reduction (=66,390/745,710) reduction either in the expenditure on a child’s education or in expenditures on his or her tutoring (=24,498/ 465,350; Appendix Table 1.2), a decrease of 0.04 (or 4 percentage points) in his or her probability of being enrolled in tutoring, and a drop of 0.09 in the child’s enrolment and tutoring index or tutoring attendance frequency. Each additional sibling is also associated with the child losing a quarter of a year of schooling, and with the child spending 46 fewer hours and 0.23 fewer years on tutoring.

## **5.2. IV estimates**

The uninstrumented regression results in Table 5 provide evidence only for a correlational, not causal, relationship between family size and households’ investment in their children’s education. While these uninstrumented results are useful for a first look, they are biased given the endogeneity of family size. If some parents decide to choose fewer children and greater investment in each child, a smaller family size would be strongly 23
correlated with unobserved parental devotion to their children, thus biasing estimates upward (in absolute magnitude); however, the opposite holds if parents decide to choose both more children and greater investment in them at the same time. More generally, the mismeasured relationship between family size and household investment in uninstrumented regressions would mask the true relative price of quantity over quality and would provide biased estimates. The direction of bias appears to be an empirical issue and depends on parental heterogeneity of preference, which is indicated by our review of previous studies discussed earlier.

The instrumented regressions shown in Table 6 indicate that a quantity-quality tradeoff exists in Vietnam: all of the instrumented estimated coefficients on family size have the same sign (i.e., negative) as the uninstrumented coefficients but have much larger absolute magnitude. (For the marginal effects for the Tobit regressions, see Table 1.2 in the Appendix.) In some cases, the instrumented coefficients on number of siblings are from four (enrolment and tutoring attendance index) to seven times (tutoring expenditure or attendance) as large as their uninstrumented counterparts, and the instrumented coefficients are statistically significant in the case of six of the nine dependent variables.

Controlling for other characteristics, each additional sibling is now shown to result in much larger reductions in the investments in a child’s schooling: reductions in education expenditure and tutoring expenditure respectively by 0.4 standard deviations (or equivalently, a reduction of D 308,246) and 0.5 standard deviations (or a reduction of D 211,087, Appendix Table 1.2); a decrease of 32 percentage points in his or her probability of being enrolled in tutoring; and a drop of 0.34 in the child’s enrolment and tutoring index or tutoring attendance frequency. One more sibling also leads to the child spending 74 fewer 24
hours and 1.4 fewer years on tutoring, although the estimated coefficient on tutoring hours is no longer statistically significant.

Estimation results also indicate that, ceteris paribus, older children are less likely to enroll in school but more likely to attend tutoring, while boys are less likely either to enroll in school or attend tutoring.<sup>34</sup> Children that are farther from the last grade in their current school level are, as expected, less likely to have tutoring, but the coefficient on this variable is mostly statistically insignificant except in the case of tutoring hours. Older mothers and richer households invest more in their children’s tutoring, but the quadratic term on mothers’ age is negative, indicating that the marginal effect of age declines and eventually turns negative.

# **5.3. Robustness checks**

# _Standard IV estimates_

In the previous section (Table 4), we have provided evidence against the concern that distance to the nearest family planning center may be proxying for other important unobserved commune characteristics. However, we test for this possibility again by including as control variables in the equation of interest some commune-level variables such as commune infrastructure (Table 7, row 1) and the distance to health facilities (row 2). To address the concern that past land allocation rules may have given rural farming households an incentive to have more children, we also include the share of the commune population

> 34 If the distance to family center can also be used as the instrument for the number of male or female siblings, we could consider the number of brothers and sisters age 0-18 separately instead of family size. However, this instrument is statistically significant only in the first-stage regressions for the number of brothers, with qualitatively similar second-stage estimation results (not shown). While this result may indicate a degree of son preference in Vietnam, and it is consistent with previous studies (see, e.g., Phai et al., 1996; Belanger, 2002), it may also suggest sex-selective abortion at the same time. Deeper analysis for intra-household gender differences would require better (and more than one) instruments than currently available.  Thus we leave this to further research.

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working in agriculture (row 3) separately. We then include all three of those variables together (row 4). Since our estimation sample is restricted to rural households, to examine the hypothesis—albeit in an indirect way—that urban households spend more on tutoring, we also include the distance from the commune to the nearest major city in Vietnam (row 5).<sup>35</sup> Estimation results are qualitatively similar for almost all specifications. The exception is the model specification with all the commune infrastructure and distances variables (row 4); in that case, magnitudes are similar but the coefficients have less statistical significance. This is perhaps unsurprising: the model is over-fitted, with all the distance variables statistically insignificant in both the first-stage regressions (as shown in Table 1.1) and second-stage regressions (not shown).

Our previous study (Dang, 2007) shows that communes with higher levels of education spend more on tutoring and argues that this impact can come from both the demand side (e.g., children have peer pressure to study harder or beneficial interaction with well-educated adults) and the supply side (e.g., communities with higher educational levels may be able to supply more tutors). To check whether the levels of commune education can affect our results, we include in our equation of interest the share of the commune adult population with upper secondary education or higher (row 6). As a further check, using the primary school census (DFA) database, we calculate the commune-averaged shares of teachers with upper secondary education, upper secondary education plus two more years of additional training, two-year teacher training college education, four-year teacher training college education, and student-teacher ratios. These variables are expected to capture teacher and

> 35 These cities are Hanoi and Haiphong in northern Vietnam, Danang in central Vietnam, and Cantho and Ho Chi Minh in southern Vietnam. We also experiment with using the distance to the provincial city instead of the distance to these major cities and obtain similar, albeit slightly statistically weaker, results.

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school quality in the commune (row 7). Again, the estimation results are similar to those in our base specification.

While we have reduced some contemporaneous correlation between the distance to family planning center and household investment in their children by using values for the former in 2002 and the latter in 2006 in our regressions, this gap of four years may not be enough, given that household make their tutoring investments only when children at least 6 years old. That is, a family planning center built in 2002 will have had no impact on parents’ decision to give birth to the children that are at least 6 years old in 2006; any impact in this case will come through the household decision on the number of younger siblings for these children. To examine the impacts of family planning center on total family size, in row 8 we restrict our estimation sample to the cases where the family planning center was already operating by 1997, which reduces the estimation sample by more than half.<sup>36</sup> Our results are for the most part qualitatively similar, except that the effects on education and tutoring expenditure now lose their statistical significance (though they keep their negative signs), while the effects on hours and years spent on tutoring become even more statistically significant.

This result also provides more support for the exogeneity of distance to family planning center as instrument. As discussed in the previous section, the similarity in impacts of household size for the full sample and the sample with older family planning centers indicates that the locations of family planning centers are effectively independent of household size.

> 36 There is a number of missing observations for the year a family planning center was set up, and the distances to school variables are not significant in this specifications, thus we left them out for larger sample sizes and more accurate estimates.

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For communes without a family planning center, commune officials report to the best of their knowledge the distance to the nearest center. This could result in measurement errors, especially for communes that are far away from any such center. To address this bias, we drop the highest five percent of the distance to family planning center. Again, there are some changes within a broadly similar pattern of estimation results (row 9): the effects on education expenditure become statistically insignificant and the effects on tutoring and enrolment and tutoring attendance variables are now significant only at 10 percent; but on the other hand, the effects on completed years of schooling and tutoring hours become statistically significant, with a 5 percent significance level for tutoring hours.

# _Lewbel heteroskedasticity-based IV estimates_

We can rewrite equations (1) and (2) in a more general format, where the distance to family planning center is subsumed in the vector of variables X.

Our standard identification strategy using this IV in fact comes from the restriction that the coefficient on the distance to family planning center be zero in equation (4). However, Lewbel (2012) shows that, given the standard regularity condition on the data, we do not need to use this restriction for identification if the error terms are uncorrelated with the right-hand side variables and we can find a variable (or vector of variables) Z that is uncorrelated with the product of the two error terms, that is, cov(Z, εijηij)= 0. In other words, we can use (Z−Z̅)ηij as the instrument for family size in equation (4). Since the strength of the instrument is proportional to cov((Z−Z̅)ηij, ηij) or the degree of heteroskedasticity of ηij with respect to Z, Lewbel suggests that heteroskedasticity tests such 28
as the Breusch-Pagan test can be used to measure the strength of this instrument. In practice, Z can be a subset of X as long as Z is clearly exogenous.

We thus use the distance to family planning center as Z and provide estimation results in row 10 in Table 7. The Breusch-Pagan χ<sup>2</sup> (1) test values (not shown) hover around 270 and strongly reject the null of no heteroskedasticity. Interestingly, while the estimated coefficients on tutoring variables show both weaker and stronger statistical significance than the standard IV estimates—with tutoring attendance and expenditure losing their statistical significance while tutoring hours becomes marginally significant at the 10 percent level—two general education measures enrolment and completed years of schooling become strongly statistically significant at the 5 percent and 1 percent level respectively. The magnitudes for the estimates are much smaller than those for the standard IV estimates and are closer to OLS estimates (which is similar to the finding by Sabia (2007) using the National Longitudinal Study of Adolescent Health for the US).

As suggested by Lewbel (2012), these heteroskedasticity-based IV estimates rely on higher moments of the error terms and are less reliable than the standard IV estimates. But it is reassuring to see the qualitatively similar result that family size has negative impacts on household investment on their children’s education.

# **5.4. Further/ Heterogeneity analysis**

Estimation results thus far support the negative relationship between family size and household investment in their children’s education, in particular tutoring classes. This subsection delves deeper into this result, to investigate whether it holds up with different definitions of family size, inclusion of birth order and school quality variables, and a focus on younger cohorts, as well as whether the result might apply broadly or to only a subset of the population.

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_Different definitions of family size_ Could our estimation results be sensitive to how we define family size? We provide further analysis based on different definitions of family size in Table 8. First, we restrict the number of siblings to not more than three (in row 1), to test whether the main result is driven by unusually large family sizes. Second, we extend the definition of family size from the children born of the same mother to all the children living in an extended family (row 2), who can include cousins or distant relatives. While the former definition is more common, the latter definition would perhaps be more consistent with an altruistic model in which resources are shared within the extended family (see, for example, Alger and Weibull, 2010, and Winkelmann, 2011). An altruistic model may be an equally valid model in the context of Vietnam, where Confucian culture remains strong (Huu Ngoc, 1996; Tran, 2001). Third, we restrict the number of siblings to age 6-18 only (row 3), hypothesizing that the quantityquality tradeoff will be stronger in the case of children with school-age siblings, because households have to invest more in school-age children than in younger ones.

Our estimation results remain similar. In fact, estimates are both larger in magnitude and have slightly stronger statistical significance when we use the more general definition of family size (row 2) and restrict the analysis to school-age siblings (row 3).

# _Birth order_

Beyond the impacts of family size, the birth order of a child can also influence his or her parents’ resource allocation (see, for example, Steelman et al., 2002, for a review). Previous studies suggest that birth-order effects may come through several different channels, including household resources constraints (or allocation), biological factors, and cultural factors. Moreover, these effects are not necessarily uni-directional but can be in opposite directions. For example, first-born children may enjoy more parental time and investment 30
due to their unique timing position compared to their younger siblings—a hypothesis that is supported by recent evidence for the US (Price, 2008; de Haan, 2010)—but if parents’ earnings increase over the life cycle, the younger siblings may benefit more (Parish and Willis, 1993).<sup>37</sup> Similarly, while older children may arrive when their mothers are younger and healthier (Behrman, 1988), younger children may also be at an advantage because of their mothers’ accumulated experience in child-rearing.

Since birth order is closely related with family size (e.g., a child in a higher birth order is more likely to be in a larger family), we follow Ejrnaes and Portner (2004) and construct a <u>p−1</u> birth-order index that is purged of any family-size effect. This index is simply n−1, where p is the child’s birth order, and n the total number of children in the family. The Pearson correlation coefficient with family size decreases from 0.52 for birth order to 0.16 with this index, which indicates that family size effect is considerably netted out. We add this birthorder index to our equation of interest (row 4) and find that coefficients become larger (in absolute value) but somewhat statistically weaker, with the birth-order index being marginally statistically significant at the 10 percent level in the three outcomes related to tutoring attendance. However, note that we do not have census data, and thus the birth order we have is for those children that are currently living in the household, and the Ejrnaes and Portner birth order index effectively rules out households with only children. To address this latter concern, we then construct another birth order index suggested by Booth and Kee (2009), which is defined as p/((n+1)/2), but find very similar results for this new index.<sup>38</sup>

> 37 A recent study for Turkey by Dayioglu, Kirdar, and Tansel (2009) also find that middle-born children fare worse in term of school enrolment than their earlier- and later-born siblings.

> 38 Certain cultures, especially in Asia, may prefer sons over daughters, thus older sons may imaginably be more favored than their younger female siblings.  We also try interacting this birth-order index with the male variable but this interaction variable is not significant either.

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# _School quality_

We turn next to the role of school quality in influencing parents to send their children to tutoring lessons. As discussed above, only a small proportion of households in Vietnam cite poor school quality as the reason for enrolling their children in tutoring classes, but other studies suggest that inadequate schooling quality may be one of the main drivers of tutoring investment in other countries (Kim and Lee, 2010; Bray and Lykins, 2012). If this is true, we may find that children enrolled in high-quality schools do not attend tutoring classes as much as their less fortunate peers, and the negative impacts of family size may possibly not hold for this group of children. To examine this hypothesis, we restrict our estimation sample to children going to schools perceived by their parents as being of high quality, and we find estimation results for tutoring outcomes to be very similar, except that the impact of household size on education expenditure now loses its statistical significance (row 5).

Interestingly, the coefficient on completed years of schooling becomes strongly statistically significant (after being insignificant in all other specifications) for this subset of the parent population. While too much should not be read into this single specification, it may indicate that these parents are those who are most interested in their children’s education and thus are likely to be most aware of their decisions related to the tradeoff between the quantity and quality of their children.

# _Local Average Treatment Effects (LATE)_

Since IV estimates may refer to the unobserved subset of the population that reacts to distance to the family planning center—which is known as the LATE (see, for example, Imbens and Angrist, 1994; Angrist and Pischke, 2009)—one concern arises that our previous estimation results may apply only to these households, which may comprise a small share of the total. However, various estimation results presented in this paper indicate that a 32
substantial share of the population appears to be influenced by this IV. For example, distance to the family planning center remains statistically significant and has similar estimated coefficients even when the first-stage regressions control for various commune characteristics, including infrastructure and occupation (Table 1.1 in the Appendix). The IV impacts of family size on different outcomes remain similar (and are even stronger for certain outcomes) in the case of households with larger extended families (row 2, Table 8), households that perceive their children’s school as being of good quality (row 5, Table 8), and those that are better-off (that is, that belong to the richest three consumption quintiles—results not shown). A conservative estimate shows that together, these groups of households make up half or more of our estimation sample.

_Outcomes for younger cohorts in 2008_ Even if the quantity-quality tradeoff exists, it will not necessarily remain the same for different cohorts over time. Recent studies find that this tradeoff holds for younger but not older cohorts in Norway (Black, Devereux, and Salvanes, 2010), turns from positive to no effect and then negative during the 1977-2009 period in Brazil (Marteleto and de Souza, 2012), and changes from positive for older cohorts to negative for younger cohorts in urban areas in Indonesia (Maralani, 2008).

To investigate whether the same quantity-quality tradeoff applies to younger cohorts in the same age range (6-18) in Vietnam, we rerun the same regressions on available indicators in the 2008 round of the VHLSS.<sup>39</sup> While the 2008 data collect fewer variables on tutoring and include information only on tutoring expenditures, our estimation results on the available indicators provide broadly qualitatively similar results (row 6), except that the effect

> 39 As in a previous regression in Table 7, because the distances to school variables are not significant in this specification, we left them out to allow larger sample sizes and greater precision of estimates.

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on education expenditure is no longer statistically significant, while the effect on enrolment is statistically significant at the 10 percent level, and the effect on tutoring expenditure becomes stronger both in magnitude and statistical significance.

## **5.5. Other tutoring-related measures**

The regressions in Tables 6 through 8 consider absolute measures of household investment in tutoring only. An alternative is to focus on relative expenditures on tutoring, through scaling tutoring investment by more traditional measures of education investment, such as household education expenditure or children’s completed years of schooling. If household investment in tutoring is more sensitive to changes in family size than are other traditional measures, this would both strengthen the case of using tutoring as a new measure of household investment and would strengthen the robustness of our results. Table 9 tests this by estimating the impacts of family size on two share variables: tutoring expenditure over total education expenditure, and years of tutoring over completed years of schooling. The estimated coefficients are negative and statistically significant at the 10 percent and 5 percent levels, respectively, and indicate that one more sibling results in a decrease of 8 percentage points and 20 percentage points, respectively, in the two share variables.

# **6. Conclusion**

Using the distance to family planning center as the instrument to identify the impacts of family size on household investment, we find that families invest less in the education of school-age children who have larger numbers of siblings. The instrumented number of siblings has a strongly negative effect on education investment, and the estimated coefficient is much larger (in absolute value) than in the original uninstrumented regressions. This effect is robust across different indicators of educational investment—including the general 34
education expenditure on the child, frequency of tutoring attendance, and expenditure and hours spent on tutoring—as well as with different specifications and definitions of family size.

Our results provide evidence that parents in Vietnam are indeed making a child qualityquantity tradeoff. The results suggest further that by lowering the relative cost of child quality and encouraging families to invest in quality, the availability of family planning services has increased investment in education in Vietnam. Finally, the analysis suggests that, compared with traditional indicators like enrolment, data on tutoring may be a more illuminating indicator of parents’ willingness to invest in the quality of education of their children. Indeed, the hypothesized quantity-quality tradeoff appears much more strongly in the tutoring-based measures than in the simple enrollment decision, which may be a coarser indicator of the household’s desire to invest in human capital. These results suggest the need for more research into these quality-oriented measures of schooling investment, with a view to providing better empirical evidence on the quantity-quality tradeoff in other settings.

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