metadata: authors: 0: author: Emran,M. Shahe
1: author: Jiang,Hanchen
2: author: Shilpi,Forhad J.
count: China,India
docna: 0: docna: Gender Bias and Intergenerational
            Educational Mobility : Theory and Evidence from China and India
docty: Policy Research Working Paper
subtopic: Educational Sciences,Gender and Development,Economics of Education,Rural Labor Markets,Labor Markets,Inequality
teratopic: Gender,Education,Rural Development,Social Protections and Labor,Poverty Reduction
abstracts: cdata!: This paper incorporates gender bias
            against girls in the family, school and labor market in a
            model of intergenerational persistence in schooling where
            parents self-finance children's education because of
            credit market imperfections. Parents may underestimate a
            girl's ability, expect lower returns, and assign lower
            weights to their welfare (“pure son preference”). The model
            delivers the widely used linear conditional expectation
            function under constant returns and separability but
            generates an irrelevance result: parental bias does not
            affect relative mobility. With diminishing returns and
            complementarity, the conditional expectation function can be
            concave or convex, and parental bias affects both relative
            and absolute mobility. This paper tests these predictions in
            India and China using data not subject to coresidency bias.
            The evidence rejects the linear conditional expectation
            function in rural and urban India in favor of a concave
            relation. Girls in India face lower mobility irrespective of
            location when born to fathers with low schooling, but the
            gender gap closes when the father is college educated. In
            China, the conditional expectation function is convex for
            sons in urban areas, but linear in all other cases. The
            convexity supports the complementarity hypothesis of Becker
            et al. (2018) for the urban sons and leads to gender
            divergence in relative mobility for the children of highly
            educated fathers. In urban China, and urban and rural India,
            the mechanisms are underestimation of the ability of girls
            and unfavorable school environment. There is some evidence
            of pure son preference in rural India. The girls in rural
            China do not face bias in financial investment by parents,
            but they still face lower mobility when born to uneducated
            parents. Gender barriers in rural schools seem to be the
            primary mechanism.
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repnme: repnme: Gender Bias and Intergenerational
            Educational Mobility : Theory and Evidence from China and India
display_title: Gender Bias and Intergenerational
            Educational Mobility : Theory and Evidence from China and India
listing_relative_url: /research/2020/05/32045790/gender-bias-intergenerational-educational-mobility-theory-evidence-china-india
topicv3: Inequality under Law m1326002 925,Labor Markets m1326488 855,Education m1327048 470,Returns to Education m1327513 2174,Gender m1327621 615
publishtoextweb_dt: 2020-05-18T00:00:00Z
historic_topic: Gender,Education,Rural Development,Social Protections and Labor,Poverty Reduction
origu: DECRG: Environment & Energy (DECEE)
no_of_pages: 85
author_keys: 0: author_key: 1469904
1: author_key: 84831
model_extractions: Policy Research Working Paper 9250

# Gender Bias and Intergenerational Educational Mobility Theory and Evidence from China and India

_M. Shahe Emran Hanchen Jiang Forhad Shilpi_ Development Economics Development Research Group May 2020
Policy Research Working Paper 9250

# **Abstract**

This paper incorporates gender bias against girls in the - family, school and labor market in a model of intergener ational persistence in schooling where parents self-finance children’s education because of credit market imperfections. Parents may underestimate a girl’s ability, expect lower returns, and assign lower weights to their welfare (“pure son preference”). The model delivers the widely used linear conditional expectation function under constant returns and separability but generates an irrelevance result: parental bias does not affect relative mobility. With diminishing returns and complementarity, the conditional expectation function can be concave or convex, and parental bias affects both relative and absolute mobility. This paper tests these predictions in India and China using data not subject to coresidency bias. The evidence rejects the linear conditional expectation function in rural and urban India in favor of a concave relation. Girls in India face lower mobility irrespective of location when born to fathers with low schooling, but the gender gap closes when the father is college educated. In China, the conditional expectation function is convex for sons in urban areas, but linear in all other cases. The convexity supports the complementarity hypothesis of Becker et al. (2018) for the urban sons and leads to gender divergence in relative mobility for the children of highly educated fathers. In urban China, and urban and rural India, the mechanisms are underestimation of the ability of girls and unfavorable school environment. There is some evidence of pure son preference in rural India. The girls in rural China do not face bias in financial investment by parents, but they still face lower mobility when born to uneducated parents. Gender barriers in rural schools seem to be the primary mechanism.

This paper is a product of the Development Research Group, Development Economics. 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://www.worldbank.org/prwp. The authors may be contacted at fshilpi@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
# **Gender Bias and Intergenerational Educational Mobility: Theory and Evidence from China and India**

**M. Shahe Emran**<sup>1</sup> IPD, Columbia University

**Hanchen Jiang** Johns Hopkins University

**Forhad Shilpi** World Bank

**Key Words:** Gender Bias, Intergenerational Mobility, Education, Becker-Tomes Model, Complementarity, Son Preference, India, China, Coresidency Bias

**JEL Codes:** I24, J62, J16, O20

> 1Email for correspondence: shahe.emran.econ@gmail.com. fshilpi@worldbank.org. hjiang15@jhu.edu. We would like to thank Mehtabul Azam for helpful discussions on India, Yi Fan for help with CFPS data, and participants at the WALES 2020 conference at GWU for comments on an earlier draft. The standard disclaimers apply.
# **(1) Introduction**

Gender bias against girls in developing countries has been the focus of a large and growing economic and sociological literature. Son preference, selective abortion, genital mutilation, mobility, and social restrictions such as Purdah are widely noted. There is a broad consensus that education is a key policy instrument for tackling gender disparity and socioeconomic inequality (see, for example, Stiglitz (2012), Duflo (2012), Jayachandran (2015)). This paper provides an analysis of the gender gap in education in China and India from the perspective of intergenerational mobility.<sup>2</sup> Most of the studies of intergenerational mobility, both in developed and developing countries, focus on the father-son linkage, and research on women in general and on gender bias in particular remains scant.<sup>3</sup> Many existing studies on intergenerational mobility, especially in developing countries, lack a well-articulated theoretical foundation. As emphasized recently by Mogstad (2017), it is thus difficult to interpret the estimates, or understand the underlying economic mechanisms. We develop a model of intergenerational educational persistence in the tradition of Becker and Tomes (1986) that captures different sources of gender bias against girls in the family, the school, and the labor market. The sources of gender bias in the family are: (i) biased estimate of academic ability, (ii) lower weight to the welfare of a daughter compared to that of a son (we call it “pure son preference”), and (iii) lower expected returns from a daughter’s education. The expected returns may in part reflect biases in the labor market. These factors affect the financial investment in education of the daughters, but the daughters may also face bias in non-financial aspects such as home tutoring.<sup>4</sup> Moreover, unfavorable school environment, for example, the absence of bathrooms for girls, can result in dropouts when a girl reaches puberty.

> 2In most developing countries, girls have historically lagged behind boys in educational attainment. However, there is evidence that the gender gap in schooling attainment may be narrowing over time. Reverse gender gap has emerged in Latin America in educational attainment (Grant and Behrman (2010)).

> 3Among the few available contributions on intergenerational mobility of daughters, see Chadwick and Solon (2002) on United States, Azam (2016) on India, and Torche (2015b) on Mexico. But they do not study the effects of gender bias. For a discussion on gender and intergenerational mobility with a focus on persistence in gender attitude and labor market participation, see Luke (2019). For evidence on intergenerational transmission of gender attitudes in India, see Dhar et al. (2019).

> 4A better educated parent may act as a more effective home tutor, but son preference may mean that priority (and more attention) is given to sons.

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The conditional expectation function (CEF) of children’s education given parental education is assumed to be linear in all of the existing studies on intergenerational educational mobility we are aware of.<sup>5</sup> In a Becker-Tomes model with self-financing constraint, a linear and additively separable education production function delivers a linear estimating equation for intergenerational educational persistence.<sup>6</sup> This “linear model” of intergenerational educational mobility, however, yields strong predictions: parental bias against girls in financial investment does not affect relative mobility; the effects of parental gender bias are captured solely by the intercept of the regression function. Although the linear estimating equation has been the workhorse in the current literature, the sharp implications of the linear model for gender bias in intergenerational educational mobility have not been noted before, to the best of our knowledge.

When the education production function exhibits diminishing returns, the estimating equation for intergenerational educational mobility is concave in parental schooling, assuming that the separability holds.<sup>7</sup> However, separability may not be an appropriate assumption, especially in urban areas with developed education markets. As noted by Becker et al. (2015), the better educated parents may reap higher marginal returns from financial investment because they are more-efficient in such investment decision making in a complex education market, thus parental education is likely to be complementary to financial investment in such a context. This complementarity, when strong enough, can more than offset the diminishing returns in the education production function making the intergenerational educational persistence equation convex. In contrast to the linear model,

> 5Functional form assumptions are usually not tested in much of the literature on intergenerational mobility, both in the developed and developing countries. For an important recent exception see the discussion in Chetty et al. (2014) on the instability of the log-linear model of intergenerational income mobility in the United States.

> 6This, in particular, implies that (i) there are constant returns to financial investment in education, and (ii) the financial investment and the direct effects of parental education are separable.

> 7To our knowledge, the quadratic intergenerational educational persistence equation was first derived by Becker et al. (2015). Their set-up is different from ours in terms of modeling the credit constraint. They assume that low income parents pay a higher interest rate, but can borrow as much as they want given the interest rate. We assume that parents cannot borrow from the credit market to finance educational investment and thus use part of their income for such investment. The credit market model we adopt is similar to Becker (1991). Given that the education loan markets are practically non-existent for most of the parents in India and China, we believe this is an appropriate modeling choice. Becker et al. (2015) do not explore gender differences in intergenerational mobility.

2
parental gender bias affects both relative and absolute mobility when diminishing returns and/or complementarity are important.

A credible empirical analysis of the above ideas, however, depends critically on the quality of the data available.<sup>8</sup> Most of the existing household surveys use coresidency criteria to define household membership and thus miss children from the sample in a nonrandom fashion. This results in truncation bias in the estimates of widely used measures of intergenerational mobility such as the intergenerational regression coefficient (IGRC). As reported by Emran et al. (2018), the truncation bias due to coresidency can vary significantly across gender and countries, making it doubly hazardous to rely on the coresident sample for a comparative study of gender bias in China and India. We take advantage of rich household surveys from China and India that do not suffer from coresidency bias for our analysis. Since the theory yields interesting predictions regarding the effects of gender bias on educational investment, our empirical analysis estimates both the intergenerational persistence equation (using IHDS 2012 for India, and CFPS 2016 for China) and the investment equation (using IHDS 2005 and NSS1995 for India, and CFPS 2010 for China).

The main conclusions from the empirical analysis are as follows. In India, the intergenerational mobility equation is _concave_ irrespective of gender and geographic location, rejecting the almost universally used linear specification in the existing literature. The concavity suggests that the complementarity between financial investment and parental education emphasized recently by Becker et al. (2018) may not be important in India. There are strong diminishing returns to both financial investment and parental direct inputs in education for girls in rural India. Girls face significantly lower relative and absolute mobility when the father is uneducated, but the gender difference becomes negligible when the father is college educated.<sup>9</sup> The relative magnitudes of the estimated parameters of the 8A large literature on intergenerational income mobility in the context of developed countries emphasizes the attenuation bias in the intergenerational income elasticity estimates due to measurement error in yearly income data. See, for example, the seminal analysis by Solon (1992). Measurement error is likely to be less of a concern in education data (Deaton (1987)).

> 9If one relies on the linear CEF estimates, s _/_ he would miss the gender convergence at the right tail of the father’s schooling distribution.

3
investment and mobility equations across gender are combined with substantial evidence of higher returns to education for girls in urban and rural India to sort out the mechanisms. The evidence suggests that parents systematically underestimate the academic ability of daughters, and girls also face disadvantages in school. There is evidence of pure son preference in rural India.

In urban China, the CEF is _convex_ for sons, while we cannot reject linearity for daughters. The evidence of convexity for sons is interesting, providing the first evidence in favor of the complementarity hypothesis of Becker et al. (2015, 2018) in the context of a developing country. Similar to urban India, daughters of uneducated fathers face significantly lower mobility, in terms of both absolute and relative measures. There is evidence of gender convergence in absolute mobility for the most educated households, but, unlike urban India, there is a widening gender gap in relative mobility at the right tail of the father’s schooling distribution. The main mechanisms at work are, however, similar to those in urban India noted above.

The results on rural China are different: the evidence is largely consistent with a linear model with no significant diminishing returns or complementarity. The IGRC estimate is larger for girls, while the intercept is lower. Girls face lower expected years of schooling when the fathers have less than 14 years of schooling, but the advantage flips in the households with higher schooling of fathers. The estimates of educational investment show that girls consistently enjoy an advantage. The constraints girls face in school is a major factor behind the observed pattern of the estimates, but the evidence cannot reject the null hypothesis of no parental bias. An important advantage of the approach developed in this paper is that the inferences regarding the nature of gender bias and its implications for intergenerational educational mobility pertain to the whole population of interest, not a subset as is usually the case with estimates based on an instrumental variables approach or a regression discontinuity design.

The rest of this paper is organized as follows. In section 2, we develop a theoretical model in the tradition of Becker and Tomes (1986) that incorporates gender bias in both financial investment and nonfinancial inputs by parents, and also gender bias in the labor 4
market (returns to education) and school. The next section provides a discussion on the data sets used for the empirical analysis. Section 4 reports and discusses the estimates of the investment and mobility equations for the urban households, along with an analysis of how the estimated parameters can help sort out the mechanisms driving the observed pattern of educational investment and intergenerational mobility. Section (5) then discusses the corresponding results for the rural households. Section (6) concludes with a summary of the main findings and the methodological contributions of the paper.

# **(2) Related Literature**

The literature on intergenerational mobility in developed countries is well-developed, with many fundamental theoretical and empirical contributions. For excellent surveys of the literature, please see Solon (1999), Black and Devereux (2011), and Bjorklund and Salvanes (2011). The focus of this literature has been on intergenerational (permanent) income persistence, and a lot of effort has been devoted to understanding the biases that arise from measurement error and life-cycle effects. Also, most of the studies deal with father-son linkages, and, as noted above, research on women, and in particular on gender bias is lacking.

In contrast, research on intergenerational economic mobility in developing countries remains relatively neglected. This partly reflects the data constraints. Good quality income data for long enough time periods to calculate permanent income remain rare. As a result, the focus of the research on developing countries has been on intergenerational educational persistence. For a discussion on the methodological challenges and data constraints in research on intergenerational mobility in developing countries, see Emran and Shilpi (2019). Recent surveys of this literature include Iversen et al. (2019), Behrman (2019) and Torche (2019). For cross-country evidence, please see Hertz et al. (2008), Narayan et al. (2018) and Bhalotra and Rawlings (2013). The recent studies on India include Azam and Bhatt (2015), Azam (2016), Emran and Shilpi (2015), Asher et al. (2018), Maitra and Sharma (2010), and Ahsan and Chatterjee (2017). On intergenerational mobility in China, see, among others, Fan et al. (2019), Golley and Kong (2013), Emran and Sun (2015), Gong et al. (2012), Park and Zou (2017), and Knight et al. (2011). Most of the studies on India 5
and China focus on intergenerational schooling persistence based on a linear CEF, but none of them derives the estimating equation from theory.

# **(3) Sons vs. Daughters: A Model of Gender Bias in Intergenerational Educational Mobility**

The economy consists of households with a parent and a child (son denoted by _s_ ) or daughter (denoted by _d_ ). The parent of child _i_ has schooling _Hi_<sup>_p_.Giventheeducation</sup> level, the parent’s income is determined as follows (similar to the specification adopted by Solon (2004), and Becker et al. (2015)): Since our empirical work focuses on father’s education because of data constraints, in what follows, we couch the discussion in terms of father as the parent. The income determination equation assumes that the fathers with zero year of schooling earn _Y_ 0<sup>_p>_0,</sup> and the return to education is _R_<sup>_p_</sup> in the parental generation.<sup>10</sup> The assumption that _Y_ 0<sup>_p>_0</sup> reflects our empirical context where 15-40 percent of fathers have zero year of schooling, but all the households report positive income.

The father allocates his income _Yi_<sup>_p_to own consumption</sup><sup>_C_</sup> _i_<sup>_p_and investment in the child’s</sup> education _Ii_ , thus the budget constraint is The budget constraint assumes that there is no credit market where the father can borrow to finance children’s education, thus has to pay from his own income. As noted earlier, this is a plausible assumption in the context of developing countries where the student loan market (public or private) is underdeveloped or nonexistent.

Following Becker et al. (2015), we assume that the education production function exhibits three features: (i) diminishing returns to financial investment, (ii) complementarity between the financial investment, and parental education (iii) the direct effect of parent’s

> 10We ignore the gender differences in parental income, as our empirical analysis focuses on the effects of father’s education due to substantial missing observations on mother’s education.

6
education capturing non-financial aspects such as “cultural capital”: where _j_ = _s, d_ is the gender index ( _s_ for son, and _d_ for daughter). We assume that _δ_ 0 _, δ_ 1<sup>_j, δ_</sup> 3<sup>_j>_0and</sup><sup>_δ_</sup> 2<sup>_j, δ_</sup> 4<sup>_j, δ_</sup> 5<sup>_j≥_0.Thelastinequalitiesareweaktoallowforthepossibility</sup> that over the relevant range the education production function is approximately linear. The direct effect of parental education can be concave or linear. The direct effect captures nonfinancial aspects of parental influences including home tutoring and role model effects as noted before.<sup>11</sup> When the complementarity effect is ignorable, we have _δ_ 5<sup>_j_= 0</sup><sup>_._The intercept</sup> term ( _δ_<sup>0</sup> ) captures the common family and school factors that affect a child’s education irrespective of gender and thus is not indexed by _j_ . The slope parameters determining the effects of financial investment are specified as below: where _q_ denotes the institutional quality such as schools, and _φ_ is the ability of a child. The specifications in (4) imply that higher ability and better school quality increase the marginal returns to educational investment by both increasing the linear coefficient _δi_<sup>_j_and</sup> by reducing the degree of diminishing returns through a lower _δ_ 2<sup>_j_.Notethattheability</sup> parameter in the production function is not gender-specific, but the institutional quality depends on gender because of factors such as role model effects of female teachers, school policy on gender bias and its enforcement, and the availability of appropriate infrastructure such as separate restrooms for women, which becomes an important factor for girls, especially after puberty (see the discussion by Adukia (2017) in the context of India). When there are few or no female teachers and no restroom in the school, we would expect _q_<sup>_d_</sup> _< q_<sup>_s_</sup> _._ The assumption that ability is not indexed by gender reflects substantial evidence that cognitive ability does not depend on the gender of a child in a systematic manner,

> 11These are part of the family endowment transmission across generations in Becker and Tomes (1979), Becker and Tomes (1986), and Becker (1991).

7
# _ceteris paribus_ .

But it is important to appreciate the distinction between the true ability of a child _φ_ and a parent’s estimate of a child’s ability denoted as _φ_<sup> ̃</sup><sup>_j_</sup> . The investment choices of parents are determined by the estimated ability _φ_<sup> ̃</sup><sup>_j_</sup> , and given an investment level, the actual educational attainment is determined by the true ability of a child _φ_ . In societies where son preference is strong, it is likely that the parents would overestimate a son’s ability and underestimate a daughter’s ability, implying that _φ_<sup> ̃</sup><sup>_s_</sup> _> φ > φ_<sup> ̃</sup><sup>_d_</sup> .<sup>12</sup> The expected schooling (denoted as _H_<sup> ̃</sup><sup>_c_</sup> ) for a given level of financial investment can be written as: where _δ_<sup> ̃</sup> 1<sup>_j_=</sup> _δ_ 1<sup>0+</sup><sup>_γ_1</sup><sup>_qj_+</sup><sup>_γ_2</sup><sup>_φ_ ̃</sup><sup>_j_�</sup> and _δ_<sup> ̃</sup> 2<sup>_j_=</sup> _δ_ 2<sup>0</sup><sup>_−ω_1</sup><sup>_qj−ω_2</sup><sup>_φ_ ̃</sup><sup>_j_�</sup> In contrast to the true � � production function (3), ability is gender specific in equation (5), with _j_ = _s, d_ . The income function for the children is: The returns to education are gender specific; when return to education is lower for girls, we expect _R_<sup>_cs_</sup> _> R_<sup>_cd_</sup> . There is substantial evidence that returns to education in the labor market may be higher for women. In their extensive cross-country study, Psacharopoulos and Patrinos (2018) find that, in about 66 percent cases, returns to education in the labor market are higher for women. Higher returns for girls are also observed in India and China during the 1980s and 1990s (see, for example, the estimates reported by Bargain et al. (2009)).<sup>13</sup> Pitt et al. (2012), and Rosenzweig and Zhang (2013) suggest that the higher

> 12If gender bias in the household is strong enough to systematically discriminate against girls in food and medical care, especially in the early years of a child’s life, girls may end up with lower academic ability. There is evidence that the development of a child’s brain is significantly affected by socioeconomic conditions (Noble et al. (2015). In this case, the inequality above will reflect both the actual differences in cognitive ability generated by gender bias, and also biased estimate given a certain level of cognitive ability.

> 13The estimated coefficients for the higher secondary schooling in 2002-2004 from the Mincer equation are: 1.09 (women, India), 0.55 (men, India), 0.51 (women, China), and 0.26 (men, China) (see Table A3 in Bargain et al. (2009)). They use CHIP data from China and NSS data for India. Their estimates are at the national level, they do not present separate estimates for rural and urban areas. We discuss the

8
returns to education for girls reflect women’s comparative advantage in skill-intensive occupations as opposed to brawn-intensive occupations and structural change in the economy in favor skill-intensive occupations. However, the evidence also consistently shows that there is a substantial gender wage-gap against the women due to the fact that _Y_ 0<sup>_cd_</sup> _< Y_ 0<sup>_cs_</sup> in most of the cases. It is well-known in the literature that return to education plays a prominent role in intergenerational educational persistence (Becker (1991), Solon (1999), Solon (2004)). As we will see below, in contrast, the intercept _Y_ 0<sup>_cj_</sup> matters much less.<sup>14</sup> For the main analysis of the mechanisms underlying intergenerational persistence in schooling, we assume that the parents are aware of the fact that the labor market returns are higher for girls. We are not aware of any studies on eliciting parental belief about returns to education for sons vs. daughters in our study countries.<sup>15</sup> In fact, data on what parents state (which may differ from the true belief) when asked about relative returns to education in a survey are also not available in the major data sets we are aware of in India (such as NSS, IHDS, REDS, NHSF) and China (CHIP, CFPS, CHNS). The only data set we are aware of is the Gansu Survey of Children and Families in China. An analysis of the Gansu survey shows that about 55 percent of mothers disagree that returns to education (in terms of higher income) are higher for sons. We also explore the implications of the alternative assumption where parents believe that the returns to education are lower for girls notwithstanding the evidence noted above. This alternative assumption, however, leads to implausible conclusions, as we discuss below in the context of urban India in section (4.1). The consumption sub-utility function of the parent is given by: available evidence on rural and urban areas below which is consistent with the national-level results of Bargain et al. (2009).

> 14This refers to educational mobility; the wage gap clearly has important implications for income and poverty.

> 15In a widely-cited study, Jensen (2010) shows that parents in the Dominican Republic underestimate the returns to education, but he does not analyze possible gender differences in parental belief. In a related study in the context of India, Jensen (2012) finds that women’s education responds positively to labor market opportunities, providing a basis for the argument that labor market returns are important for parental decisions regarding women’s education in India.

9
# **(3.1) Optimal Educational Investment**

The parent’s optimization problem is (denoting the Lagrange multiplier on the budget constraint by _λ_ ): where _σ_<sup>_j_</sup> is the degree of parental altruism, and son preference implies that _σ_<sup>_s_</sup> _> σ_<sup>_d_</sup> , and parents use production function (5) to estimate the expected income of children _E_ � _Yi_<sup>_cj_</sup> �. The order conditions are: Using the first order conditions and equations (1) and (2) above, we solve for the optimal investment in a child’s education as a function of parental education: where It is important to note some of the implications of equations (11) and (12) which are not well-appreciated in the current literature where linearity is a maintained assumption. As we discuss below, the intergenerational mobility equation is necessarily linear when the education production function is linear ( _δ_ 2<sup>_j_=</sup><sup>_δ_</sup> 4<sup>_j_=</sup><sup>_δ_</sup> 5<sup>_j_=0).Inthiscase,genderbiasin</sup> the form of pure son preference _(i.e., σ_<sup>_d_</sup> _< σ_<sup>_s_</sup> _)_ , lower returns to education for girls _(i.e., R_<sup>_cd_</sup> _< R_<sup>_cs_</sup> _)_ , low estimate of academic ability of girls _(i.e., φ_<sup> ̃</sup><sup>_d_</sup> _< φ_<sup> ̃</sup><sup>_s_</sup> _)_ , and bias against girls in schools _(i.e., q_<sup>_d_</sup> _< q_<sup>_s_</sup> _)_ implies that _θ_ 0<sup>_d<θ_</sup> 0<sup>_s_,but</sup><sup>_θ_</sup> 1<sup>_d_=</sup><sup>_θ_</sup> 1<sup>_s._Theresultthatsuchgender</sup> 10
bias does not affect the slope parameter is especially striking, and suggests that we should be careful in interpreting the evidence from the investment equation (10) above. Without the benefit of the theory, most researchers would interpret the finding that the data do not reject _θ_ 1<sup>_d_=</sup><sup>_θ_</sup> 1<sup>_s_asevidenceagainstgenderbiasineducationalexpenditure.Thisis</sup> compounded by the fact that the focus of the analysis usually is on the slope parameter, and many studies do not report the intercept estimates which should be the focus of an analysis of gender bias if the linear model is correct.

# **(3.2) Intergenerational Persistence in Education**

The optimal education of a child can be written as follows: where _I_<sup>_∗_</sup> is given by equation (10) above.

Since optimal investment _I_<sup>_∗_</sup> is a linear function of parental education _H_<sup>_p_</sup> , _H_<sup>_cj∗_</sup> is a quadratic function of parental education _H_<sup>_p_</sup> even when _δ_ 4<sup>_j_= 0and</sup><sup>_δ_</sup> 5<sup>_j_= 0.Theestimating</sup> equation for intergenerational persistence implied by equation (10) and (13) above is as follows: where

# **(3.3) Sorting Out the Mechanisms**

A comparison of the two estimating equations (investment equation (10) and mobility equation (14)) above shows that the parental gender bias in ability estimate and pure son preference are reflected in the parameters of the investment equation, while the estimated mobility parameters are useful in understanding the role played by biases in the direct impact of parents on children’s education. As we will see below in the empirical analysis section, both in India and China, the evidence, in general, suggests an important role for the 11
bias arising from direct (nonfinancial) impact of parents through, for example, homework help and role model effects.

The estimated parameters from the investment equation (10) and the mobility equation (14) provide us 5 binary relations, which impose restrictions on the potential explanations, and help sort out the existence and mechanisms of gender bias when combined with information on gender differences in returns to education.<sup>16</sup> In particular, combining information about returns to education with the estimated _intercepts_ of the investment equation can help infer whether the parents underestimate a girl’s ability and whether girls face constraints in school. This can be seen by considering the intercept as a function of returns to education, i.e., the function _θ_ 0<sup>_j_(</sup><sup>_Rcj_).Itiseasytocheckthat</sup><sup>_θ_</sup> 0<sup>_d_=</sup><sup>_θ_</sup> 0<sup>_s<_0when</sup> _R_<sup>_cd_</sup> = _R_<sup>_cs_</sup> = 0, implying that the intercept of the function _θ_ 0<sup>_j_(</sup><sup>_Rcj_)isnegativeanddoes</sup> not depend on the gender of a child. As we discuss in the online appendix, _θ_ 0<sup>_j_(</sup><sup>_Rcj_)is</sup> an increasing function of returns to schooling, i.e.,<sup>_∂θ_</sup> 0<sup>_j>_0withahorizontalasymptote</sup> equal to _δ_ ̃1<sup>_j_</sup> . More importantly, if _θ_ 0<sup>_j>_0,theslope</sup> _∂R_<sup>_∂θcj_</sup> 0<sup>_j_ishigherwhentheparentshave</sup> 2 _δ_<sup> ̃</sup> 2<sup>_j_</sup> _∂R_<sup>_cj_</sup> higher estimate of a child’s ability, and/or when the school environment is favorable, i,e, _∂R∂_<sup>_cj_2</sup> _θ∂_ 0<sup>_j_</sup> _φ_<sup> ̃</sup><sup>_j>_0,and</sup> _∂R∂_<sup>_cj_2</sup> _θ∂q_ 0<sup>_jj>_0.17Theconditionthat</sup><sup>_θ_</sup> 0<sup>_j>_0issatisfiedinallthecases</sup> we consider below in India and China. The upshot of the above discussion is that when we plot two functions _θ_ 0<sup>_j_(</sup><sup>_Rcj_)fordifferentabilityandschoolquality,thecurvecorresponding</sup> to higher ability estimate and better school must lie above the other curve at each positive value of returns to schooling (see Figures F1.IU and F1.IR below).

When we superimpose the estimates of the intercepts and returns to education in this graph, we can infer whether the upper curve refers to the sons or daughters. For illustration, we consider two cases in (i) Figure F1.IU: _θ_<sup>ˆ</sup> 0<sup>_d_=</sup><sup>_θ_ˆ</sup> 0<sup>_s_,and(ii)FigureF1.IR:</sup><sup>_θ_ˆ</sup> 0<sup>_d<θ_ˆ</sup> 0<sup>_s_.For</sup> brevity, we discuss Figure F1.IU in more detail, and leave Figure F1.IR to the readers. In Figure F1.IU, the _θ_<sup>ˆ</sup> 0<sup>_d_=</sup><sup>_θ_ˆ</sup> 0<sup>_s_curve is drawn as a horizontal line, and it is clear that the returns</sup>

> 16It is important to appreciate that the inference about the mechanisms refer to the whole population of interest, rather than a subset.

17 <u>0</u> The effects of pure son preference on (<sup>_∂θj_),however,arenotunambiguouswithoutadditionalre-</sup> _∂R_<sup>_cj_</sup> strictions on the curvature of the consumption sub-utility function ( _α_ 2).

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to education corresponding to the higher _θ_<sup>ˆ</sup> 0 curve must be lower. As discussed in some detail above, returns to education are lower for sons in both India and China which implies that the upper curve must refer to the sons. This implies that if the estimated intercepts of the investment equation do not vary across gender, then the evidence would imply that the parents underestimate a girl’s cognitive ability, and/or the girls face significant genderspecific constraints in school.

# **(3.4) Discussion**

Many existing studies on intergenerational educational mobility in developing countries share two features. First, all of the published empirical studies on intergenerational educational mobility we are aware of use a linear intergenerational persistence equation. Second, the implicit theoretical model assumes that the primary source of intergenerational link in educational attainment is financial investment by parents in children’s schooling, with special emphasis on the roles of credit constraint and returns to education. Although a primary focus of Becker-Tomes (1979, 1986) model was the implications of optimal parental financial investment on children’s education for intergenerational transmission of inequality, they also emphasized the link across generations due to factors such as cultural capital of a family. Following Becker et al. (2015, 2018), the cultural capital is represented by the direct effect of father’s education on son’s schooling.

The theoretical analysis above clarifies the assumptions implicit in the linear CEF used almost universally in the empirical literature on intergenerational educational mobility. A linear intergenerational persistence equation implies that _ψ_ 2<sup>_j_=</sup><sup>_θ_</sup> 1<sup>_j_</sup> � _δ_ 5<sup>_j−δ_</sup> 2<sup>_jθ_</sup> 1<sup>_j_</sup> � _− δ_ 4<sup>_j_= 0.We</sup> have _ψ_ 2<sup>_j_= 0 when there are no diminishing returns or complementarity in the human capital</sup> production function; i.e., _δ_ 5<sup>_j_=</sup><sup>_δ_</sup> 2<sup>_j_=</sup><sup>_δ_</sup> 4<sup>_j_=0.Wecallthisthe“linearmodel”,astheCEF</sup> is _necessarily_ linear in this case. It is easy to check that in the linear model, parental bias against girls irrespective of the form it takes does not affect relative mobility (as measured by intergenerational regression coefficient IGRC), its effects are captured by the intercept of the linear CEF alone. However, we can also have a linear CEF as a special case of the more general quadratic model; this happens when, as a matter of chance, the convexity due to complementarity approximately cancels out the diminishing returns. When estimating 13
intergenerational schooling persistence, significant differences in the IGRCs for sons and daughters ( _ψ_<sup>ˆ</sup> 1<sup>_d_=</sup><sup>_ψ_ˆ</sup> 1<sup>_s_)should,ingeneral,beinterpretedasevidencethattheunderlying</sup> model is likely to be quadratic, even though the CEF is approximately linear. If the evidence does not reject a linear CEF ( _ψ_<sup>ˆ</sup> 2 = 0), one would be more confident that this reflects an underlying linear model when the evidence from the investment equation also does not reject constant returns and separability, implying _θ_ 1<sup>_d_=</sup><sup>_θ_</sup> 1<sup>_s_.Itisunlikelytohave</sup> _δ_ 5<sup>_j>_0;</sup><sup>_δ_</sup> 2<sup>_j>_0andthenthedifferentparametervaluestoaligninawaytosatisfy</sup><sup>_θ_</sup> 1<sup>_d_=</sup><sup>_θ_</sup> 1<sup>_s_</sup> along with the conditions that _ψ_ 2<sup>_j_= 0for</sup><sup>_j_=</sup><sup>_d, s_.18</sup> When data reject the linear CEF in favor of a quadratic CEF, we do not have a constant relative mobility measure like IGRC; the marginal effect of father’s education varies across the education distribution. We call it “intergenerational marginal effect” or IGME for short: . In the empirical analysis, we will provide estimates of IGME at focal points of father’s education distribution: no schooling, primary (5 years in India, and 6 years in China), secondary (9 years in China and 10 years in India), and college (16 years of schooling). We denote the marginal effect for the children born to parents with no schooling as _IGME_ 0, and so on. As a measure of absolute mobility, we provide estimates of expected years of schooling conditional on father’s schooling at these focal points of father’s schooling distribution.<sup>19</sup> The expected years of schooling for the children born to parents with no schooling is denoted as _ES_ 0, and so on. The fathers with no schooling is an important group for our analysis, as the proportion is substantial in our data set, especially in India, and, more important, these are likely to be the poorest of the households.

> 18Note that even with constant returns and no complementarity, we can get _ψ_ 1 _d_<sup>=</sup><sup>_ψ_</sup> 1<sup>_s_ifgirlsface</sup> significant constraints in the schools.

> 19This definition of absolute mobility is similar to that of Chetty et al. (2014), although the interpretation is somewhat different when the CEF is not linear. There is a different concept of absolute mobility adopted by many authors where the focus is on whether a child attains higher education than his/her parents. For a discussion of the limitations of this concept in empirical application to developing countries where 20-40 percent fathers have no schooling, please see Emran and Shilpi (2019). Equally important, we are not aware of any economic model that yields this alternative empirical specification of absolute mobility.

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# **(4) Data**

# **(4.1) Data for China: CFPS (2016, 2010)**

The data for estimating the intergenerational mobility of education in China come from the China Family Panel Study (CFPS)- 2016 wave. In order to match children-parents pairs irrespective of residency status at the time of the survey, we take advantage of the Family Member Module, which has an innovative T-Tables design feature. As discussed in Xie and Hu (2014), the T-Tables in CFPS consist of three tables - T1, T2, and T3. Table T1 (on family members living together) and Table T2 (on immediate relatives not living together) record the basic socio-demographic characteristics of every family member and her immediate relatives (parents, children and spouses) who are not living with them. Table T2 (on relations) identifies the relations of all the family members and the corresponding relations between T1 and T3 members. Therefore, three tables jointly present a complete family network, and most importantly, allow us to avoid truncation of the sample.

More specifically, in order to identify all the children-fathers pairs, we take the following steps. For each individual currently living in the family, own education and father’s education are directly available in the Family Member module irrespective of whether the father is coresident at the time of the survey. This subsumes two cases involving three generations. (i) If such an individual is the household head (or head’s spouse) who lives in the family, their parents are matched, irrespective of whether they are co-resident or not. (ii) If such an individual is household head’s (or head’s spouse’s) child, who lives in the family, the child’s parents are of course matched, i.e. they are household head and head’s spouse. However, step 1 misses the following case: if household head’s (or head’s spouse’s) child is currently living outside. An important advantage of the CFPS survey is that it collected data on such nonresident children. In the second step, we include these nonresident children in the sample. Our estimation sample thus includes both the nonresident parents of household head and spouse, and also their nonresident children.

The summary statistics for various estimation samples are reported in Table T1.U for the urban households and Table T1.R for the rural households; the upper panel in each table corresponds to China, and the bottom panel to India. For China, the main estimation 15
sample for the analysis of intergenerational mobility consists of children 18-35 years of age in 2016, and the estimation samples for the investment equation are 6-22 and 8-23 years in the 2010 round of the panel. This age range is chosen so that the age cohorts in the investment equation have substantial overlap with the age cohorts in the mobility analysis. In CFPS-2016 for the 18-35 age cohorts, the mean schooling of fathers is 7.65 in the sons sub-sample and 7.67 in the daughters sub-sample in the urban areas according to Table T1.U. The average schooling of sons is 11.17 years, and 11.18 years for daughters. However, there is a gender gap in the average schooling attainment in rural China: 9.2 (sons) years and 8.7 (daughters) (see Table T1.R, upper panel). The average education expenditure is _higher for daughters_ in the urban estimation samples, but favors the sons in the rural samples.

# **(4.2) Data for India: IHDS (2012, 2005) and NSS (1995)**

The data for estimating the intergenerational mobility of education in India come from the India Human Development Survey (IHDS)-2012. The construction of matched children and parents pairs are slightly different between sons and daughters. To generate matched son-father pairs, we follow Azam and Bhatt (2015) closely (see the Table 8 in Azam and Bhatt (2015)). The only difference is that we are using wave 2 (2012) while Azam and Bhatt (2015) use wave 1 (2005) of IHDS panel data. For all household heads, their father’s education information is available directly in the household module, irrespective of a father’s residency status at the time of the survey. The comparison between our sample using IHDS2012 to Azam and Bhatt’s sample using IHDS-2005 is documented in the online appendix Table A1.S. To generate matched daughter-father pairs, we follow Azam (2016) closely (see the Table 1 in Azam (2016)). Since Azam (2016) also use IHDS-2012 data, we can compare our sample precisely, as shown in the online appendix Table A1.D.

The summary statistics for our various estimation samples for IHDS-2012 (for intergenerational mobility estimation), and IHDS-2005 and NSS-1995 (for estimation of the investment equation) are reported in the lower panels of Tables T1.U (for the urban plus rural sample), T1.R (for rural sample). The mean education of fathers in urban areas is 6.64 years in the sons sub-sample, and 6.44 years in the daughters sub-sample of the main 16
estimation sample for intergenerational mobility (18-35 year old children in 2012). The average schooling is 10 years for sons and 9.36 for daughters. In the rural sample, the average education of fathers is much lower; 3.90 years (sons sub-sample) and 3.83 (daughters subsample). The gender gap in average schooling is also much more pronounced in the rural areas; 8.13 years (sons) vs. 6.24 years (daughters). The average educational expenditure in IHDS-2005 is higher for sons and it is true irrespective of geographic location and for both the estimation samples (6-22 year old) and (8-23 year old). The bias in educational expenditure against girls is also observed in the NSS-1995 data.

# **(5) Empirical Results**

The empirical estimates of the mobility and investment equations discussed below report robust standard errors. However, we also estimate the standard errors clustering at different levels: district and state levels for India, and county (only for investment) and province levels for China. We cannot cluster the standard errors at the county level for the mobility estimates for China, as the county location is not available for the non-resident members of a household. The estimated clustered standard errors are reported in the online appendix. All the main conclusions based on the robust standard errors, however, remain intact when we use clustered standard errors instead. If and when clustering makes a difference in inference, we will note that in the following discussion.

# **(5.I) Intergenerational Mobility in India: Evidence and Interpretations (5.I.1) Urban India**

The estimates of the effects of father’s schooling on children’s schooling in urban India are reported in the upper panel of Table T2.IU.<sup>20</sup> The first two columns contain the evidence from a linear CEF which provides estimates comparable to the existing literature where linearity is a maintained assumption. The IGRC estimate is higher for the daughters, suggesting that the daughters face significantly lower relative mobility in urban India.

Although almost all of the existing studies on India focus primarily (or exclusively) on relative mobility, it has been emphasized in the recent literature that inter-group analysis of

> 20The table numbers are indexed by country and location. For example, T2.IU stands for Table 2 for the Indian Urban sample, and so on.

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intergenerational mobility based solely on relative mobility can be misleading, as different groups may be converging to different steady states defined in part by the intercept term (Hertz (2005), Mazumder (2014), Torche (2015a), Emran et al. (2020), Emran and Shilpi (2019)). The estimates for the linear CEF show that the intercept for the daughters is lower. The daughters attain lower education than the sons when the father has less than 16 years of schooling, but the gender advantage flips in favor of girls for the children of the fathers with higher education.

The estimates from a linear CEF provide suggestive evidence in favor of the widelyheld notion of strong gender bias against girls in India. However, the evidence rejects the assumption of linearity; the estimates of the quadratic term in columns (4) (for sons) and (5) (for daughters) in Table T2.IU are negative and statistically significant at the 1 percent level. The quadratic coefficient is numerically larger for the daughters, but the difference is not statistically significant at the 10 percent level. Consistent with the econometric evidence, the nonparametric LOWESS plots of son’s and daughter’s schooling against father’s schooling in urban India suggest a concave relation (see Figure F2.IU). The evidence that the CEF is concave implies that we cannot reject the null hypothesis: _δ_ 5 = 0, suggesting the absence of any significant complementarity between father’s education and investment in urban India.

The estimated quadratic CEFs using the coefficients in Table T2.IU are plotted in Figure F3.IU and show that the expected schooling attainment conditional on father’s education is higher for sons, except at the right tail of the distribution of father’s schooling. As a measure of absolute mobility, we report estimated expected years of schooling conditional on a father having 0, 5, 10 and 16 years of schooling in the bottom panel of Table T2.IU. The daughters born to low educated fathers face significant disadvantage in term of expected schooling attainment (the _ES_ 0 estimates are: 5.8 (daughters) vs. 6.8 (sons)), but there is no gender difference when the father has college education (the _ES_ 16 estimate is 13.8 for both daughters and sons).<sup>21</sup> For relative mobility, the estimated _IGMEs_ in the bottom panel of Table T2.IU show

> 21The _ES_ 0 estimates refer to the children of fathers with zero years of schooling. The proportion of fathers with zero schooling in urban India is 24 percent in our data.

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that the persistence is much stronger for the girls born to fathers with low education ( _IGME_ 0 estimates are: 0.65 (daughters) vs. 0.55 (sons)), but, again, the gender difference becomes negligible when the father has college or more education: ( _IGME_ 16 estimates are: 0.33 (sons) vs. 0.35 (daughters)). Please see Figure F4.IU. The evidence on absolute and relative mobility thus favors the idea that gender difference in educational attainment may primarily be a product of low education (and thus low permanent income) of parents. This also brings into focus the incorrect conclusions from the standard linear CEF that the daughters face less relative mobility throughout the parental schooling distribution. A researcher focused exclusively on the linear CEF would completely miss the gender convergence in relative mobility at the right tail of father’s schooling distribution.

# **Sources of Gender Bias**

The extended Becker-Tomes model in section (2) above highlights parental educational investment as a major mechanism through which inequality persists across generations. Thus, it is informative to look first at the estimates of the investment equation to understand the economic mechanisms at play. The estimates of _θ_ 0 and _θ_ 1 for urban India are reported in Table T3.IU, using IHDS 2005 and NSS 1995 data. We report estimates for two age groups of children for each data set to ensure robustness of the conclusions.<sup>22</sup> The evidence suggests strongly that _θ_<sup>ˆ</sup> 1<sup>_d<θ_ˆ</sup> 1<sup>_s_;theinteractionoffather’seducationwith</sup> the daughter dummy is negative across the board, and is statistically significant at the 10 percent or lower level in 7 out of 8 cases.<sup>23</sup> The estimates for the intercept shows a contrasting picture: the daughter dummy is _not_ statistically significant at the 10 percent level in 6 out of 8 cases. The evidence cannot reject the null hypothesis that _θ_<sup>ˆ</sup> 0<sup>_d_=</sup><sup>_θ_ˆ</sup> 0<sup>_s_.</sup>

> 22We also used other age groups for estimating the investment equation. The conclusions reached in this paper are robust to such alternative age samples.

> 23This is consistent with the existing evidence on gender bias against girls in educational expenditure in India (see Kingdon (2007), Azam and Kingdon (2013)). Azam and Kingdon (2013) find significant pro-male bias for the 10 years or older children, using the IHDS 2005 data. They point out that the focus on educational expenditure misses substantial gender bias against girls in terms of schooling continuation decisions. When gender bias manifests as early drop-out of daughters from school, this is captured by lower educational attainment in our data. Datta and Kingdon (2019) use 1995 and 2014 NSS data and find that the role played by gender bias in educational expenditure (the intensive margin) has increased substantially over time in India. _Note, however, that the existing evidence while suggestive does not provide estimates of the effects of father’s education on children’s educational expenditure, which is the focus of the investment equation in intergenerational mobility analysis._

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The estimates for the educational investment equation and the quadratic intergenerational persistence equation can be summarized as the following binary relations (denoting an estimated parameter with a hat): These binary relations impose restrictions on plausible explanations for the observed differences between the sons and the daughters. We combine these with the evidence on gender differences in returns to education to understand the role played by different forms of gender bias discussed in the theoretical section.

# **Interpreting the Evidence: The Investment Equation**

As noted earlier, the evidence on functional form fails to reject the null hypothesis that _δ_ 5 = 0 in urban India, and we trace out the implications of the binary relations in (16) above with this restriction imposed. However, some of important conclusions regarding the mechanisms of gender bias discussed below hold irrespective of whether _δ_ 5 = 0. Using equation (12) from the theoretical model, _θ_<sup>ˆ</sup> 1<sup>_d<θ_ˆ</sup> 1<sup>_s_impliesthefollowinginequality:</sup> A substantial body of evidence suggests that, in urban India, the returns to education in the labor market are higher for daughters, especially at the secondary and higher secondary levels (see Duraisamy (2002), Aslam et al. (2010)).<sup>24</sup> For a summary of the available

> 24However, there is also substantial evidence that educated women, especially married women, withdraw from the labor market and devote to home production such as child care and home tutoring (Afridi et al. (2018)). This may partly reflect the fact that there is a significant gender wage gap against women in the labor market, even though the Mincerian returns are higher, reflecting a low intercept for women. Moreover, the expected returns to education for daughters _R_<sup>_cd_</sup> capture both labor market and non-market returns (expressed in shadow prices), including the returns in the marriage market, and from home production, for example, in the form of higher quality grand children. If educated women withdraw from the labor market even though the returns are higher than those of men, it implies that the shadow returns from

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estimates of returns to education in urban India, please see the first two columns of Table T4.I. We focus on the returns to education at secondary (10 years of schooling) and higher secondary (12 years of schooling) levels, given that the average education in urban India in our data set is 9.93 years for the sons, and 9.43 years for the daughters.<sup>25</sup> Since _R_<sup>_cd_</sup> _> R_<sup>_cs_</sup> , inequality (17) is satisfied even if we assume that _δ_<sup> ̃</sup> 2<sup>_dσd_=</sup><sup>_δ_ ̃</sup> 2<sup>_sσs_.Clearly,thislastequalityis</sup> consistent with no gender bias by the parents.

Turning to the intercept estimates from the investment equation, the theory implies the following relation: An immediate observation is that it is not possible to satisfy (18) if there are no gender biases (i.e, if _δ_<sup> ̃</sup> 1<sup>_d_=</sup><sup>_δ_ ̃</sup> 1<sup>_s_,</sup><sup>_δ_ ̃</sup> 2<sup>_d_=</sup><sup>_δ_ ̃</sup> 2<sup>_s_,and</sup><sup>_σd_=</sup><sup>_σs_),because</sup><sup>_Rcd> Rcs_.</sup> The fact that there is no significant difference in the intercepts implies that urban India corresponds to the case depicted in Figure F1.IU in section 2.3 above. An inspection of Figure F1.IU shows that the returns to education must be smaller for the curve with higher ( _φ_<sup> ̃</sup><sup>_j_</sup> _unexpected_<sup>_′′_</sup> _inmath_ ) and ( _q_<sup>_j_</sup> ). Since the returns to education is smaller for the sons (see Table T4.I), the higher curve must refer to the sons, implying that the parents have systematically higher ability estimates for the sons, and/or the girls face substantial hurdles in the schools. It is important to note that these conclusions hold irrespective of the value of _δ_ 5.

The above analysis of the mechanisms of gender bias in the observed educational investment in urban India is based on the assumption that the parents are aware of the fact that returns to education are, in fact, higher for the daughters. One might wonder what are the implications of the alternative assumption that, despite the evidence, the parents believe that the returns from education are lower for daughters. If _R_<sup>_cd_</sup> _< R_<sup>_cs_</sup> , then an

> non-market sources are even higher. Thus the expected total returns for women are likely to be higher than that suggested by the estimates of labor market returns.

> 25Most of the estimates of returns to education in India are based on NSS data, which do not provide years of schooling information, only the highest completed level (primary, secondary etc).

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analysis based on Figure 3.IU suggests the following conclusions: (i) parents believe that the daughters have more academic ability, and (ii) the daughters enjoy a more favorable school environment. When we combine these with the evidence above that _θ_<sup>ˆ</sup> 1<sup>_d>θ_ˆ</sup> 1<sup>_s_,weget</sup> the conclusion that the parents must hold pure daughter preference. All these conclusions seem implausible given the accumulated evidence on gender bias against girls in India in the economics and sociology literature.

The discussion above suggests that the evidence on the functional form of the mobility equation, returns to education, and the investment equation taken together cannot reject the following joint null hypothesis: (i) complementarity between financial investment and father’s education is not important in urban India, i.e., _δ_ 5 = 0, (ii) parents systematically underestimate the ability of daughters, and (iii) the daughters face unfavorable school environment. In what follows, we confront the estimates from the mobility equation to check whether this set of null hypotheses is sufficient to explain the pattern of the inequalities in (15) above.

# **Learning about Gender Bias: The Intergenerational Mobility Equation**

We begin with the estimates of the quadratic coefficients. When interpreted in terms of the theoretical analysis of section (2.2) above, _ψ_<sup>ˆ</sup> 2<sup>_d_=</sup><sup>_ψ_ˆ</sup> 2<sup>_s_impliesthefollowing:</sup> From the estimates of the investment equation, we know that _θ_<sup>ˆ</sup> 1<sup>_d<θ_ˆ</sup> 1<sup>_s_,whichimplies</sup> that equation (19) cannot be satisfied without some form of bias against daughters that works through either _δ_ 2 and/or _δ_ 4. It is important to recognize that _δ_ 2 and _δ_ 4 are the parameters of the “true” production function, and thus do not depend on parental bias, but are affected by bias in the school. However, unfavorable school environment found earlier does not help satisfy equation (19). This follows from the observation that, starting at no bias, i.e., � _q_<sup>_d_</sup> = _q_<sup>_s_</sup> = _q_ �, a lower school quality for the girls � _q_<sup>_d_</sup> _< q_ � reduces the value ˆ 2 ˆ 2 of _δ_ 2<sup>_d_</sup> _θ_ 1<sup>_d_</sup> , while a higher school quality for the boys ( _q_<sup>_s_</sup> _> q_ ) increases _δ_ 2<sup>_s_</sup> _θ_ 1<sup>_s_</sup> . The � � � � upshot of the above discussion is that, to satisfy equation (19), we need gender bias in the form of _δ_ 4<sup>_d>δ_</sup> 4<sup>_s_,implyingthatthediminishingreturnstothedirecteffectoffather’s</sup> 22
education are stronger for daughters. Recalling that the evidence earlier also suggests stronger diminishing returns to financial investment for daughters, the daughters in urban India thus seem to face stronger diminishing returns at double margins.

We next turn to the implications of the inequality _ψ_<sup>ˆ</sup> 1<sup>_d>ψ_ˆ</sup> 1<sup>_s_.Fromthetheoryinsection</sup> (2.2), this inequality implies the following (with _δ_ 5 = 0): According to the educational investment estimates discussed above, _θ_<sup>ˆ</sup> 1<sup>_d<θ_ˆ</sup> 1<sup>_s_and</sup><sup>_θ_ˆ</sup> 0<sup>_d_=</sup><sup>_θ_ˆ</sup> 0<sup>_s_.</sup> Again, it is important to keep in mind that _δ_ 1<sup>_d_and</sup><sup>_δ_</sup> 2<sup>_d_are parameters of the true production</sup> function. The evidence on the investment equation discussed above shows that the girls face unfavorable school environment, i.e., _q_<sup>_d_</sup> _< q_<sup>_s_</sup> , implying that _δ_ 1<sup>_d< δ_</sup> 1<sup>_s_and</sup><sup>_δ_</sup> 2<sup>_d> δ_</sup> 2<sup>_s_.This</sup> implies that _θ_<sup>ˆ</sup> 1<sup>_d_</sup> _δ_ 1<sup>_d−_2</sup><sup>_δ_</sup> 2<sup>_dθ_ˆ</sup> 0<sup>_d_</sup> _< θ_<sup>ˆ</sup> 1<sup>_s_</sup> _δ_ 1<sup>_s−_2</sup><sup>_δ_</sup> 2<sup>_sθ_ˆ</sup> 0<sup>_s_</sup> _._ It is thus necessary to have _δ_ 3<sup>_d>δ_</sup> 3<sup>_s_for</sup> � � � � inequality (20) to hold. When considered along with the evidence earlier that _δ_ 4<sup>_d> δ_</sup> 4<sup>_s_,this</sup> suggests that the _marginal direct effect_ of father’s education � _δ_ 3<sup>_j−_2</sup><sup>_δ_</sup> 4<sup>_jHp_�</sup> is higher for the daughters of fathers with low education, but lower when father’s education is high enough. Since _θ_<sup>ˆ</sup> 0<sup>_d_=</sup><sup>_θ_ˆ</sup> 0<sup>_s_, the inequality of intercepts of the mobility equation, i.e.,</sup><sup>_ψ_ˆ</sup> 0<sup>_d<ψ_ˆ</sup> 0<sup>_s_implies</sup> the following (denote the common value by _θ_<sup>ˆ</sup> 0<sup>_c_):</sup> It is easy to check that bias in the school against girls found earlier i.e., � _q_<sup>_d_</sup> _< q_<sup>_s_�</sup> _,_ is necessary and sufficient for inequality (21) to hold.

# **(5.I.2) Rural India**

The estimates of intergenerational persistence in schooling in rural India are reported in Table T2.IR. The pattern of estimates from the linear CEF is similar to that in urban India; the IGRC estimate is larger for the daughters implying lower relative mobility, while the intercept is smaller. A comparison with the estimates for urban India shows that the IGRC estimates do not vary significantly across rural vs. urban areas, but the intercept for girls in rural areas is substantially lower. Also, the difference in the intercepts between sons 23
and daughters is larger in rural areas, a 50 percent higher intercept for the sons, compared to only a 16 percent higher intercept in the urban areas. Although useful as a benchmark comparable to the existing estimates in the literature, these preliminary estimates are, however, contingent on the maintained assumption that the CEF is linear.

The estimates from the quadratic specification for rural India show that the coefficient of the quadratic term is statistically significant at the 1 percent level, for both the sons and the daughters, providing clear evidence that the null hypothesis of a linear CEF is rejected. The estimated quadratic coefficient is negative, suggesting that both the CEFs are concave, similar to what we observed in urban India (see also the Lowess plots in Figure F2.IR). However, there is an important gender difference between the urban and rural India; the degree of concavity is similar for sons irrespective of location (the estimate of the quadratic coefficient is -0.007 in both rural and urban samples), but the quadratic coefficient is substantially larger in magnitude for daughters in rural areas. In fact, the null hypothesis of equality of quadratic coefficients can be rejected in rural India at the 1 percent level, indicating that the girls face especially strong forces of diminishing returns in the villages.

The estimates of mobility in the bottom panel of Table T2.IR show that the girls face lower mobility, both in terms of absolute and relative measures, when they are born to low educated parents. The expected years of schooling remains consistently lower for girls, even when the father has college education; a girl growing up in rural India can expect a year less schooling on average. For the lowest educated households, the gender gap is almost 2 years of expected schooling. The estimates of relative mobility show that the intergenerational persistence is substantially higher for the daughters born into households with low educated fathers (compare the _IGME_ 0 estimate of 0.52 (sons) with 0.64 (daughters)).<sup>26</sup> The gender difference in _IGME_ , however, becomes negligible for the households with highly educated fathers (college educated). Please see Figure F4.IR.

# **Sources of Gender Bias in Rural India**

The estimates of the parameters of the educational investment in Table T3.IR show that

> 26About 40 percent of fathers in rural India in our data have zero schooling.

24
the daughters receive significantly less educational investment in rural India; the daughter dummy is negative and statistically significant at the 10 percent or lower levels, implying that _θ_<sup>ˆ</sup> 0<sup>_d<θ_ˆ</sup> 0<sup>_s_.Theevidenceisrobustacrossalternativedatasets(IHDS2005andNSS</sup> 1995) and consistent with existing evidence in the context of India (Azam and Kingdon (2013)).<sup>27</sup> The evidence on the marginal effect of father’s higher education in Table T3.IR also suggests a smaller effect for girls; the interaction of the daughter dummy with father’s schooling is negative, and significant at the 10 percent level in 5 out of 8 cases. However, the evidence is weaker than that in urban India, because only one of the estimates is significant at the 5 percent level, and the magnitude of the interaction effect is also smaller.<sup>28</sup> Moreover, the interaction is significant only in 4 cases when we use standard errors clustered at the district level (see Table A3.IR in online appendix).

Putting together the estimates of investment equation with those from the intergenerational mobility equation, we have the following binary relations in rural India: Since the CEF is concave for both sons and daughters, we cannot reject the null hypothesis that _δ_ 5 = 0. In what follows, the discussion assumes that this restriction holds.

# **Implications of the Investment Equation Estimates**

We first consider the evidence on the slope of the investment function. Given the uncertainty regarding the evidence discussed above ( _θ_<sup>ˆ</sup> 1<sup>_d_≦</sup><sup>_θ_ˆ</sup> 1<sup>_s_), the inference regarding gender bias</sup> depends critically on one’s interpretation. If one interprets the evidence as a lower slope for the girls (i.e., _θ_<sup>ˆ</sup> 1<sup>_d<θ_ˆ</sup> 1<sup>_s_),thenwehaveexactlythesameresultsasinurbanIndia,andas</sup>

> 27Azam and Kingdon (2013) show that the gender bias against girls in education expenditure is larger in rural areas in India. We, however, restate the caveat that the existing evidence does not relate to the question of how educational expenditure varies with the education of a father.

> 28In urban India, the interaction effect is significant at the 1 percent level in 2 cases, and at the 5 percent level in 4 cases.

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noted before, the slope estimates are consistent with no parental bias because returns to education are higher for girls (see Table T4.I for the evidence on returns to education in rural India).<sup>29</sup> In contrast, if the conclusion is that there is no strong evidence of difference in the marginal effect of father’s education across gender of children, then we have _θ_<sup>ˆ</sup> 1<sup>_d_=</sup><sup>_θ_ˆ</sup> 1<sup>_s_.</sup> This, in turn, implies _δ_<sup> ̃</sup> 2<sup>_dσdRcd_=</sup><sup>_δ_ ̃</sup> 2<sup>_sσsRcs_.Since</sup><sup>_Rcd>Rcs_,wemusthave</sup><sup>_δ_ ̃</sup> 2<sup>_dσd<δ_ ̃</sup> 2<sup>_sσs_.</sup> Observe that if parents underestimate a girls ability, we have _δ_<sup> ̃</sup> 2<sup>_d>δ_ ̃</sup> 2<sup>_s_,andwecanhave</sup> ̃ _δ_ 2<sup>_dσd<δ_ ̃</sup> 2<sup>_sσs_onlyifthereispuresonpreference,i.e.,</sup><sup>_σd<σs_.Wediscussbelowthatthe</sup> evidence on the intercepts is consistent with parents underestimating a daughter’s academic ability.

_R_<sup>_cd_</sup> _> R_<sup>_cs_</sup> when combined with _θ_<sup>ˆ</sup> 0<sup>_d<θ_ˆ</sup> 0<sup>_s_provideevidenceconsistentwithparentsun-</sup> derestimating ability of a daughter, and girls facing constraints in the school. This case is depicted in Figure F1.IR in section 2.3 above. An inspection of the graph makes it clear that it is not possible have _θ_<sup>ˆ</sup> 0<sup>_d<θ_ˆ</sup> 0<sup>_s_with</sup><sup>_Rcd>Rcs_,iftheuppercurveinFigureF1.IR</sup> refers to the daughters. The evidence is consistent with only the case where the upper curve refers to sons, implying gender bias against girls in the form of lower ability estimate and/or unfavorable school environment.<sup>30</sup>

# **Implications of the Intergenerational Mobility Estimates**

With _δ_ 5 = 0 _,_ the evidence that _ψ_ ˆ2 _d > ψ_ ˆ2 _s_ implies the following inequality: _δ_ 2 _d θ_ ˆ1<sup>_d_</sup> 2 + ��� ��� ��� ��� � � ˆ 2 _δ_ 4<sup>_d>δ_</sup> 2<sup>_s_</sup> _θ_ 1<sup>_s_</sup> + _δ_ 4<sup>_s_.Fromtheestimatesoftheinvestmentequationandthediscussion</sup> � � above, we know that _δ_ 2<sup>_d>δ_</sup> 2<sup>_s_becauseoftheconstraintsgirlsfaceintheschool.Sincethe</sup> case with _θ_<sup>ˆ</sup> 1<sup>_d<θ_ˆ</sup> 1<sup>_s_wasdiscussedatlengthforurbanIndia,herewefocusonthecasewhen</sup> _θ_ ˆ1<sup>_d_=</sup><sup>_θ_ˆ</sup> 1<sup>_s_.Inthiscase,theinequalityaboveissatisfiedwithoutimposinganyrestrictionson</sup> the relative magnitudes of the parameters _δ_ 4<sup>_d_and</sup><sup>_δ_</sup> 4<sup>_s_.Similarly,itiseasytocheckthatthe</sup> inequality _ψ_<sup>ˆ</sup> 1<sup>_d>ψ_ˆ</sup> 1<sup>_s_alsoisnotusefultosortouttheroleofdifferentmechanismsofgender</sup> bias.<sup>31</sup> Since _θ_<sup>ˆ</sup> 0<sup>_d<θ_ˆ</sup> 0<sup>_s_and</sup><sup>_δ_</sup> 2<sup>_d> δ_</sup> 2<sup>_s_,asufficientconditionfor</sup><sup>_ψ_ˆ</sup> 0<sup>_d<ψ_ˆ</sup> 0<sup>_s_toholdisthat</sup><sup>_δ_</sup> 1<sup>_s> δ_</sup> 1<sup>_d_</sup>

> 29Again, if we assume that the parents are not aware of the fact that returns are higher for girls, and believe the opposite, then the evidence from the investment equation implies implausible conclusions such as parents have pure daughter preference in rural India.

> 30If the parents believe that the returns to education are in fact lower for girls, then it implies that the parents underestimate the ability of boys, and also that boys face gender-based constraints in the school.

> 31This follows from the observation that _θ_ 0 _d_<sup>_θ_</sup> 1<sup>_d< θ_</sup> 0<sup>_sθ_</sup> 1<sup>_s_but</sup><sup>_δ_</sup> 2<sup>_d> δ_</sup> 2<sup>_s._</sup>

26
but it is not necessary. From the evidence in the immediately preceding section, we know that � _q_<sup>_d_</sup> _< q_<sup>_s_�</sup> which implies _δ_ 1<sup>_s> δ_</sup> 1<sup>_d_.</sup>

# **(5.C) Intergenerational Mobility in China: Evidence and Interpretations**

# **(5.C.1) Urban China**

The estimates of the effects of father’s schooling on children’s schooling in urban China are reported in Table T2.CU. The estimates for the linear CEF show that, similar to urban India, the intercept is lower for girls but the IGRC estimate is larger. With linearity a maintained assumption, the evidence thus suggests that the girls face lower relative mobility in urban China, but the expected level of schooling is, in fact, higher for girls when father’s education is higher than 7 years of schooling.

The evidence on the null hypothesis of a linear CEF shows that it is a good approximation for the daughters in urban China, but not for the sons. The estimates in Table T2.CU show that, for sons, the quadratic term is statistically significant at the 1 percent level, and perhaps more strikingly, it bears a _positive_ sign, implying that the CEF of sons’ schooling is _convex_ . The convexity is also apparent in the Lowess plot (please see Figure F2.CU). The evidence on functional form in urban China is thus different from the concave CEF found earlier in urban India. The estimated convex CEF using the coefficients in Table T2.CU for sons is plotted in Figure F3.CU along with the linear CEF for the daughters. The CEF plots show very different pattern of mobility when compared to the urban India case; the sons born to fathers at the tails of the schooling distribution enjoy higher expected years of schooling, while the daughters have a slight advantage in the middle of the distribution. This is reflected in the absolute mobility estimates in the bottom panel of Table T2.CU.

The relative mobility estimates in the bottom panel of Table T2.CU show a large gender difference in terms of magnitude. The intergenerational persistence is very low for the sons born to fathers with no schooling (0.09), but the daughters face much higher persistence (0.35). The pattern flips when the fathers have more than 9 years of schooling (junior secondary). The IGME estimate for sons is 0.56 when the father has college education (16 years schooling), while IGME remains the same (0.35) for daughters given the linear CEF. Please see Figure F4.CU. This is in sharp contrast to urban India where the gender 27
difference in educational persistence becomes negligible for the most educated parents.

# **Sources of Gender in Urban China**

To understand the role played by parental financial investment in children’s education, we utilize the data from the first round of the CFPS survey (2010) to estimate the parameters of the investment equation (i.e., equation (10) above) in Table T3.CU and test the equality of the coefficients across gender. The evidence in Table T3.CU is clear that parental financial investment in schooling does not depend on the gender of a child; we cannot reject the null hypothesis that _θ_ 0<sup>_d_=</sup><sup>_θ_</sup> 0<sup>_s_and</sup><sup>_θ_</sup> 1<sup>_d_=</sup><sup>_θ_</sup> 1<sup>_s._Theseconclusionsareconsistent</sup> with the other existing evidence (see, for example, Tsui and Rich (2002)).

The estimates of the parameters of the investment function and the estimates of the mobility equation discussed above can be summarized in the following binary relations for sons vs. daughters: We first look at the implications of the evidence on the functional form of the intergenerational schooling persistence regressions. The evidence of convexity in the case of sons (i.e., _ψ_<sup>ˆ</sup> 2<sup>_s>_0) implies that we can reject the null hypothesis of</sup><sup>_δ_</sup> 5<sup>_s_= 0 in favor of</sup><sup>_δ_</sup> 5<sup>_s>_0</sup><sup>_._This</sup> is interesting evidence for the Becker et al. (2015, 2018) hypothesis that higher educated fathers are more efficient in financial investment in education.<sup>32</sup> The linearity of the CEF for the daughters, however, cannot be interpreted as evidence in favor of the linear model. With _δ_ 5<sup>_s>_0,itisdifficulttosatisfy</sup><sup>_θ_ˆ</sup> 1<sup>_d_=</sup><sup>_θ_ˆ</sup> 1<sup>_s_if</sup><sup>_δ_</sup> 5<sup>_d_= 0.</sup>

# **Learning from the Investment Equation**

Two pieces of evidence in urban China are similar to that in urban India: (i) the returns to education are higher for girls (see Table T4.C), and (ii) _θ_<sup>ˆ</sup> 0<sup>_d_=</sup><sup>_θ_ˆ</sup> 0<sup>_s_.Asdiscussedinsection</sup>

> 32 We are not aware of any other analysis of intergenerational educational persistence that provides such evidence in favor of the Becker et al. (2015, 2018) convexity hypothesis in a developing country.

28
(4.1) above, these together imply that parents underestimate a daughter’s academic ability ̃ ̃ _φ_<sup>_d_</sup> _< φ_<sup>_s_�</sup> , and the daughter’s also face disadvantages in the school � _q_<sup>_d_</sup> _< q_<sup>_s_�</sup> .<sup>33</sup> � However, the evidence that _θ_<sup>ˆ</sup> 1<sup>_d_=</sup><sup>_θ_ˆ</sup> 1<sup>_s_does not add to our understanding without bringing</sup> in additional restrictions imposed by the estimates of the parameters of the intergenerational mobility equation. This is because, in contrast to urban India, the evidence on functional form of the CEFs reject the null hypothesis that _δ_ 5 = 0.<sup>34</sup> So we turn to the evidence from the intergenerational mobility equation below to see if that helps narrow down the possible explanations.

**Learning from the Intergenerational Mobility Equation** Since _θ_<sup>ˆ</sup> 1<sup>_d_=</sup><sup>_θ_ˆ</sup> 1<sup>_s_,theevidencethat</sup><sup>_ψ_ˆ</sup> 2<sup>_d<ψ_ˆ</sup> 2<sup>_s_impliesthefollowinginequality(denotingthe</sup> common value of _θ_ 1<sup>_j_by</sup><sup>_θ_</sup> 1<sup>_c_):</sup>

Now, note that � _q_<sup>_d_</sup> _< q_<sup>_s_�</sup> imply that � _δ_ 2<sup>_d−δ_</sup> 2<sup>_s_</sup> � _>_ 0, and from the functional form evidence we know that � _δ_ 5<sup>_s−δ_</sup> 5<sup>_d_</sup> � _>_ 0. So a sufficient condition for inequality (24) to be valid is that � _δ_ 4<sup>_s−δ_</sup> 4<sup>_d_</sup> � _≤_ 0 _,_ but it is not necessary. This is in contrast to the evidence on urban India where it is necessary that � _δ_ 4<sup>_s−δ_</sup> 4<sup>_d_</sup> � _<_ 0 _._ Next, we consider the evidence _ψ_<sup>ˆ</sup> 1<sup>_d>ψ_ˆ</sup> 1<sup>_s_whichimpliesthefollowinginequalitywhen</sup> combined with the evidence that _θ_<sup>ˆ</sup> 1<sup>_d_=</sup><sup>_θ_ˆ</sup> 1<sup>_s_and</sup><sup>_θ_ˆ</sup> 0<sup>_d_=</sup><sup>_θ_ˆ</sup> 0<sup>_s_:</sup> A necessary condition for inequality (25) to be satisfied is that _δ_ 3<sup>_d>δ_</sup> 3<sup>_s_becausewhen</sup> � _q_<sup>_d_</sup> _< q_<sup>_s_�</sup> we have � _δ_ 1<sup>_s−δ_</sup> 1<sup>_d_</sup> � _>_ 0 and � _δ_ 2<sup>_d−δ_</sup> 2<sup>_s_</sup> � _>_ 0. This is similar to what we found earlier for urban India.<sup>35</sup>

> 33The implication of the alternative assumption about parental belief regarding returns to education are also the same.

> 34Note that with _δ_ 5 _>_ 0, we cannot sign the slope of the _θ_ ˆ1<sup>_j_(</sup><sup>_Rcj_)function.</sup>

> 35But, unlike urban India, we cannot determine whether the _marginal direct effect_ of father’s education _δ_ 3<sup>_j−_2</sup><sup>_δ_</sup> 4<sup>_jHp_�</sup> is higher for daughters with low educated fathers because the evidence does not pin down � the sign of � _δ_ 4<sup>_s−δ_</sup> 4<sup>_d_</sup> � in the case of urban China.

29
Finally, the inequality of the intercepts of the mobility regressions implies the following for urban China: This is similar to what we had before for urban India, and as noted earlier, inequality (26) is satisfied when the daughters face gender-based constraints at the school, i.e., � _q_<sup>_d_</sup> _< q_<sup>_s_�</sup> .

# **(5.C.2) Rural China**

The estimates for intergenerational persistence in schooling in rural China are presented in Table T2.CR. The first striking thing to notice is that the evidence on the functional form cannot reject the null hypothesis of linearity for both the sons and the daughters; this is in contrast to the other three cases we considered above in sections (4.1), (4.2) and (5.1). However, note that the linear CEF estimates show substantial difference in the IGRC of sons and daughters; the daughters face higher intergenerational persistence in schooling. As discussed in section (2.3) above, the estimated CEF can be approximately linear even if the underlying model is a quadratic one. Following the discussion in section (2.1), we can check the plausibility of the linear model with evidence from the investment equation: by testing whether the null hypothesis that _θ_ 1<sup>_d_=</sup><sup>_θ_</sup> 1<sup>_s_isrejectedbythedata.Theevidenceonthe</sup> investment equation parameters in Table T3.CR suggests that the null hypothesis cannot be rejected at the 5 percent level. This is also consistent with other available evidence on the lack of any significant gender differences in educational investment in the economic and sociology literature on rural China (Hannum et al. (2009)). Taken together, the evidence from the investment and mobility equations thus suggests that the linear model provides a plausible characterization of the data in rural China.

Given a linear CEF, the estimate of relative mobility does not vary across the distribution of parental schooling (Figure F4.CR): the IGRC is 0.27 for sons, and 0.33 for daughters, suggesting much lower relative mobility for the daughters. The estimate of absolute mobility, on the other hand, depends on the level of parental schooling. The estimated absolute mobility (expected years of schooling) in the lower panel of Table T2.CR shows that the daughters are at a disadvantage when the father’s schooling is less than 13 years, but the 30
advantage flips when the father has college education. This implies that, even though the girls face stronger intergenerational persistence across the board, they in fact leave the boys behind in terms of schooling attainment when the father is sufficiently well-educated. The estimated CEFs are plotted in Figure F3.CR.

# **Mechanisms of Gender Bias: Interpretations**

When the correct model is, in fact, linear (no significant diminishing returns or complementarity), then the only mechanism that can lead to different relative mobility (IGRCs) for sons vs. daughters is gender-specific constraints in school. The estimates on relative mobility (IGRC) in Table T2.CR thus imply that an important source of gender bias against girls in rural China is unfavorable school environment.

However, with a linear model, the theory also implies that the effects of parental or labor market bias would be reflected in the intercept estimates of the investment and mobility equations. The estimates of the intercept of the investment equation in Table T3.CR show that _θ_<sup>ˆ</sup> 0<sup>_d>θ_ˆ</sup> 0<sup>_s_.Combinedwiththeevidencethat</sup><sup>_θ_ˆ</sup> 1<sup>_d_=</sup><sup>_θ_ˆ</sup> 1<sup>_s_,theestimatesoftheinvestment</sup> equation thus suggest no gender bias against girls in rural China, if anything financial investment favors the daughters.<sup>36</sup> _θ_ ˆ0<sup>_d>θ_ˆ</sup> 0<sup>_s_impliesthefollowinginequality:</sup><sup>_δ_ ̃</sup> 1<sup>_dσdRcd>δ_ ̃</sup> 1<sup>_sσsRcs_.TableT4.Cprovidesa</sup> summary of the available estimates of returns to education in rural China showing evidence in favor of _R_<sup>_cd_</sup> _> R_<sup>_cs_</sup> .<sup>37</sup> These two inequalities are, however, consistent with a variety of hypothesis about parental attitude towards sons vs. daughters and do not help us narrow down the explanations.

The intercept estimates of the mobility equation shows that _ψ_<sup>ˆ</sup> 0<sup>_d<ψ_ˆ</sup> 0<sup>_s_,whichimplies</sup> _δ_ 1<sup>_dθ_</sup> 0<sup>_d<δ_</sup> 1<sup>_sθ_</sup> 0<sup>_s_.Since</sup><sup>_θ_</sup> 0<sup>_d>θ_</sup> 0<sup>_s_,thisimpliesthat</sup><sup>_δ_</sup> 1<sup>_d<δ_</sup> 1<sup>_s._Thislastinequalityholdswhen</sup> the girls face constraints in the school. Thus, the only conclusion we can reach is that the girls in rural China face significant bias in the schools, but do not find any evidence that the parents discriminate against girls when choosing educational investment. This 36This is consistent with other available evidence. See, for example, Hannum et al. (2009). 37The available estimates of returns to education for rural China suggest that the returns were very low during the early period of economic liberalization (deBrauw and Rozelle (2008), Meng (1998)), but the more recent evidence shows increasing returns to education with higher returns for girls (see, for example, Ren and Miller (2012)).

31
last conclusion, in fact, is consistent with in-depth case studies reported by Hannum et al. (2009).

# **(6) Robustness Checks**

The empirical results on intergenerational mobility discussed so far are based on the sample of 18-35 years age cohorts of children in the survey year. To check robustness of the findings, we also estimated the mobility equation (14) in section (2) for alternative age ranges. The estimates for the age cohorts 18-30 years are reported in the online appendix; please see the Tables A2.IU.B, A2.IR.B, A2.CU.B, and A2.CR.B. The main conclusions regarding gender differences in intergenerational educational mobility remain intact.

We also check whether the conclusions are partly due to the effects of gender bias working through endogeneous fertility choices. To this end, we estimate the mobility equation using only the sub-sample of the first-born child, as the gender of the first born is usually not determined by parental preference. The CFPS survey on China is suitable for such an analysis. But we are unable to implement this for IHDS data in India, as the IHDS survey does not contain the information on the birth-order of the household head and spouse. The estimates based on the first-born sample for urban and rural China are reported in online appendix Tables A2.CU.C and A2.CR.C respectively for the 18-35 age cohorts; the main conclusions discussed in the text above are again robust. The estimates from the first=born sub-sample of the 18-30 age cohorts also support the main conclusions.

# **(7) Concluding Comments**

This paper provides a theoretical and empirical analysis of the implications of gender bias against girls for intergenerational educational mobility in developing countries. We develop a Becker-Tomes model where the parents self-finance children’s schooling because of credit market imperfections, and the girls may face bias in the family, the school, and the labor market. The model yields a linear conditional expectation function (CEF) under the assumptions of constant returns and separable education production function but delivers sharp predictions: parental bias against girls is irrelevant for relative mobility and for the marginal impact of parent’s education on investment in schooling. The effects of parental bias are captured by the intercepts of the investment and mobility equations, which are 32
usually not the focus in the existing literature relying on a linear estimating equation. When the education production function exhibits diminishing returns to financial investment and complementarity between parents’ direct impact and financial investment as proposed by Becker et al. (2015, 2018), the CEF can be concave or convex depending on the strength of complementarity. With quadratic CEF, parental gender bias affects both relative and absolute mobility.

We take advantage of rich household survey data from China and India to test the above ideas. The data sets used (IHDS for India and CFPS for China) do not suffer from sample truncation due to coresidency restrictions common in household surveys in developing countries. Our estimates are thus free of severe truncation bias reported recently by Emran et al. (2018) because of coresidency restrictions. The evidence shows interesting cross-country and rural-urban differences. The CEF is concave in India irrespective of gender and location. In contrast, the CEF is convex for sons, but linear for daughters in urban China. In rural China, the CEF is linear for both sons and daughters. The evidence on functional form suggests that children face diminishing returns India, and girls in rural India face diminishing returns both in financial investment and parental direct inputs to schooling. The convexity observed in urban China for sons supports the complementarity hypothesis of Becker et al. (2018).

Girls face lower relative and absolute mobility in India when the father has low education, but there is gender convergence at the right tail of the parental schooling distribution. The relative magnitudes of the estimated parameters of the investment and mobility equations across gender when combined with the evidence of higher returns to education for girls help us sort out possible explanations for the observed pattern of mobility. The evidence on rural and urban India is consistent with the hypothesis that parents systematically underestimate the academic ability of girls, and girls also face significant bias in school. The same mechanisms can also explain the evidence in urban China, but, in rural China, the evidence indicates constraints in the school as the main mechanism at work and fails to reject the null hypothesis of no parental bias. There is some evidence that pure son preference plays a role in educational persistence in rural India.

33
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39
# **Figure F1.IU**

<!-- Start of picture text --> Sons<br>θ0(R c )<br>Daughters<br>θ0(R cs )<br>=<br>θ0(R cd )<br>R c<br>R cs R cd<br><!-- End of picture text -->
<!-- Start of picture text --> 89 (R*)<br>| Sons<br>oo oe —7<br>|<br>|<br>| Daughters<br>|<br>Op (RS) |<br>|<br>|<br>8p (R°) |<br>RS<br>Re pea<br><!-- End of picture text -->
# **Table T1.U: SUMMARY STATISTICS (URBAN SAMPLES)**

||**F**|**ull**|**Sons**|**Daughters**|
|---|---|---|---|---|
||**Mean**|**SD**|**Mean**<br>**SD**|**Mean**<br>**SD**|
||||**CHINA**||
|CFPS2016 (18-35)|N=6|433|N=3192|N=3241|
|Father's Sch.|7.66|4.27|7.65<br>4.32|7.67<br>4.23|
|Children's Sch.|11.17|3.88|11.17<br>3.85|11.18<br>3.9|
|CFPS2016 (18-30)|N=4|435|N=2230|N=2205|
|Father's Sch.|7.8|4.2|7.8<br>4.23|7.79<br>4.17|
|Children's Sch.|11.27|3.77|11.23<br>3.73|11.31<br>3.8|
|CFPS2010 (6-22)|N=2|784|N=1425|N=1359|
|Father's Sch.|9.35|4|9.24<br>4|9.48<br>4|
|Educ. Exp.|3178.11|4760.34|3014.98<br>4761.47|3349.16<br>4754.89|
|No. of Children|1.2|0.72|1.18<br>0.67|1.21<br>0.76|
|CFPS2010 (8-23)|N=2|435|N=1251|N=1184|
|Father's Sch.|9.28|3.99|9.17<br>4.02|9.39<br>3.95|
|Educ. Exp.|3261.35|4990.48|3101.34<br>5093.39|3430.41<br>4875.83|
|No. of Children|1.17|0.75|1.15<br>0.69|1.19<br>0.8|
||||**INDIA**||
|IHDS2012(18-35)|N=1|8519|N=9449|N=9070|
|Father's Sch.|6.54|5.05|6.64<br>4.96|6.44<br>5.14|
|Children's Sch.|9.69|4.52|10.01<br>4.2|9.36<br>4.8|
|IHDS2012(18-30)|N=1|4140|N=7314|N=6826|
|Father's Sch.|6.81|5|6.9<br>4.89|6.72<br>5.1|
|Children's Sch.|10|4.35|10.2<br>4.06|9.78<br>4.63|
|IHDS2005 (6-22)|N=1|3086|N=6917|N=6169|
|Father's Sch.|8.55|4.68|8.52<br>4.71|8.59<br>4.65|
|Educ. Exp.|3798.29|5349.04|4060.57<br>5657.13|3504.2<br>4965|
||241|143|236<br>143|246<br>143|
|No. of Children|.|.|.<br>.|.<br>.|
|IHDS2005 (8-23)|N=1|1051|N=5883|N=5168|
|Father's Sch.|8.58|4.68|8.54<br>4.7|8.61<br>4.66|
|Educ. Exp.|4082.12|5721.06|4368.01<br>6025.75|3756.67<br>5335.11|
|No. of Children|2.42|1.46|2.35<br>1.46|2.5<br>1.46|
|NSS1995 (6-13)|N=1|8689|N=10071|N=8618|
|Father's Sch.|5.09|2.46|5.03<br>2.47|5.16<br>2.43|
|<br>Educ. Exp.|1101.84|1237.90|1145.16<br>1293.68|1051.22<br>1167.40|
|No. of Children|2.67|1.11|2.61<br>1.10|2.73<br>1.13|
|NSS1995 (6-18)|N=2|7819|N=15152|N=12667|
|Father's Sch.|5.24|2.44|5.16<br>2.46|5.33<br>2.42|
|Educ. Exp.|1338.27|1529.59|1382.00<br>1588.18|1285.96<br>1454.75|
|No. ofChildren|2.67|1.14|2.60<br>1.12|2.75<br>1.17|

Notes: CFPS stands for China Family Panel Survey, IHDS stands for Indian Human Development Survey, and NSS stands for National Sample Survey.
# **Table T1.R: SUMMARY STATISTICS (RURAL SAMPLES)**

||**Fu**|**ll**|**Sons**|**Daughters**|
|---|---|---|---|---|
||**Mean**|**SD**|**Mean**<br>**SD**|**Mean**<br>**SD**|
||||**CHINA**||
|CFPS2016 (18-35)|N=8|040|N=3955|N=4085|
|Father's Sch.|5.9|4.27|5.93<br>4.29|5.88<br>4.26|
|Children's Sch.|8.96|4.08|9.2<br>3.91|8.74<br>4.23|
|CFPS2016 (18-30)|N=5|647|N=2833|N=2814|
|Father's Sch.|6.01|4.16|6.11<br>4.17|5.91<br>4.15|
|Children's Sch.|9.4|3.93|9.53<br>3.75|9.26<br>4.1|
|CFPS2010 (6-22)|N=4|326|N=2224|N=2102|
|Father's Sch.|6.44|3.88|6.45<br>3.9|6.42<br>3.87|
|Educ. Exp.|1301.35|2386.63|1328.64<br>2535.81|1272.48<br>2218.14|
|No. of Children|1.63|0.93|1.57<br>0.9|1.7<br>0.97|
|CFPS2010 (8-23)|N=3|632|N=1843|N=1789|
|Father's Sch.|6.4|3.9|6.43<br>3.88|6.37<br>3.91|
|Educ. Exp.|1432.85|2593.57|1449.28<br>2710.91|1415.92<br>2467.5|
|No. of Children|1.62|0.96|1.52<br>0.9|1.72<br>1|
||||**INDIA**||
|IHDS2012(18-35)|N=3|3979|N=16957|N=17022|
|Father's Sch.|3.87|4.41|3.9<br>4.32|3.83<br>4.49|
|Children's Sch.|7.18|4.71|8.13<br>4.36|6.24<br>4.86|
|IHDS2012(18-30)|N=2|5903|N=12946|N=12957|
|Father's Sch.|4.08|4.46|4.12<br>4.37|4.04<br>4.54|
|Children's Sch.|7.61|4.59|8.43<br>4.21|6.8<br>4.8|
|IHDS2005 (6-22)|N=2|3058|N=12631|N=10427|
|Father's Sch.|5.58|4.58|5.47<br>4.61|5.71<br>4.55|
|Educ. Exp.|1489.73|3110.61|1613.94<br>3440.39|1339.27<br>2649.23|
||287|153|279<br>151|297<br>155|
|No. of Children|.|.|.<br>.|.<br>.|
|IHDS2005 (8-23)|N=1|9002|N=10514|N=8488|
|Father's Sch.|5.59|4.56|5.47<br>4.6|5.74<br>4.52|
|Educ. Exp.|1667.11|3469.9|1802.6<br>3836.22|1499.27<br>2945.42|
|<br>No. of Children|2.91|1.55|2.8<br>1.53|3.03<br>1.55|
|NSS1995 (6-13)|N=2|6668|N=15819|N=10849|
|Father's Sch.|3.31|2.08|3.18<br>2.06|3.50<br>2.10|
|Educ. Exp.|386.44|477.52|398.38<br>484.29|369.03<br>466.95|
|No. of Children|2.47|1.06|2.37<br>1.04|2.61<br>1.07|
|NSS1995 (6-18)|N=3|7155|N=23172|N=13983|
|Father's Sch.|3.36|2.10|3.21<br>2.08|3.59<br>2.12|
|Educ. Exp.|543.89|655.29|568.55<br>677.05|503.02<br>615.41|
|No. ofChildren|2.45|1.10|2.35<br>1.08|2.63<br>1.11|

Notes: CFPS stands for China Family Panel Survey, IHDS stands for Indian Human Development Survey, and NSS stands for National Sample Survey.
**Table T2.IU: Intergenerational Persistence in Schooling in Urban India**

|||**LINEAR CEF**||**QU**|**ADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft.|**0.46*****|**0.52*****|**0.066*****|**0.55*****|**0.65*****|**0.094*****|
||(0.0074)|(0.0080)|(0.011)|(0.023)|(0.025)|(0.034)|
|Quadratic Coefft.||||**-0.0070*****|**-0.0093*****|**-0.0022**|
|||||(0.0014)|(0.0016)|(0.0022)|
|Intercept|**6.96*****|**5.97*****|**-0.99*****|**6.81*****|**5.80*****|**-1.00*****|
||(0.071)|(0.075)|(0.10)|(0.085)|(0.086)|(0.12)|
|No. Observations|9449|9070|18519|9449|9070|18519|
|||**Estimates**|**of Mobility**|**fromQuadr**|**atic CEF**||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|6.81|5.80||**_IGME0 _**|0.55|0.65|
|**_ES5 _**|9.39|8.82||**_IGME5 _**|0.485|0.556|
|**_ES10_**|11.61|11.37||**_IGME10_**|0.414|0.464|
|**_ES16_**|13.82|13.82||**_IGME16_**|0.330|0.353|

Notes: (1) The data used are IHDS 2012 with children aged 18-35. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,5,10,16. (4) Robust standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1.
**Table T3.IU:  Father's Education and  Educational Expenditure on Children**

|||**URBAN**<br>**IHDS**<br>|**INDIA**<br>**2005**<br>||
|---|---|---|---|---|
||**(6-22) Yea**|**rs Children**|**(8-23) Yea**|**rs Children**|
|Father's Sch.|384.4***|338.7***|403.9***|348.0***|
||(14.9)|(14.40)|(17.4)|(16.9)|
|**Father's Sch. * Daughter**|**-34.00***|**-37.50***|**-36.5**|**-40.2***|
|**Dummy**|**(20.5)**|**(20.3)**|**(23.9)**|**(23.5)**|
|**Daughter Dummy**|**-290.2*****|**-189.9**|**-325.1****|**-174.3**|
||(136.9)|(138.7)|(164.4)|(162.9)|
|Intercept|784.8***|2763.50***|917.3***|3220.7***|
||(105.1)|(148)|(124.9)|(175.6)|
|No. of Children||-673.1***||-777.7***|
|||(36.0)||(41.9)|
|No. Observations|13086|13086|11051|11051|
|||**NSS**<br>|**1995**<br>||
||**(6-18) Yea**|**rs Children**|**(8-18) Yea**|**rs Children**|
|Father's Sch.|108.4***|108.4***|110.4***|110.9***|
||(2.817)|(2.817)|(3.070)|(3.039)|
|**Father's Sch. * Daughter**|**-11.3*****|**-11.3*****|**-11.2*****|**-11.2*****|
|**Dummy**|(3.906)|(3.906)|(4.295)|(4.238)|
|**Daughter Dummy**|**-39.4**|**-39.4**|**-41.6**|**-11.1**|
||(26.12)|(26.12)|(29.00)|(29.03)|
|Intercept|505.9***|505.9***|543.6***|1004.0***|
||(17.95)|(17.95)|(19.75)|(26.13)|
|No. of Children||||-178.0***<br>(7.963)|
|No. Observations|27810|27810|24443|24443|

Notes: (1) The data used are IHDS 2005 and NSS 1995 respectively. (2) Robust standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1.
**Table T2.IR: Intergenerational Persistence in Schooling in Rural India**

|||**LINEARCEF**||**QU**|**ADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft|**0.45*****|**0.52*****|**0.075*****|**0.52*****|**0.64*****|**0.12*****|
||(0.0064)|(0.0071)|(0.0095)|(0.019)|(0.021)|(0.028)|
|Quadratic Coefft.||||**-0.0070*****|**-0.011*****|**-0.0070*****|
|||||(0.0014)|(0.0018)|(0.0014)|
|Intercept|**6.39*****|**4.24*****|**-2.14*****|**6.32*****|**4.16*****|**-2.16*****|
||(0.044)|(0.043)|(0.062)|(0.048)|(0.046)|(0.066)|
|No. Observations|16957|17022|33979|16957|17022|33979|
|||**Estimate**|**s of Mobility**|**fromQuadra**|**tic CEF**||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|6.32|4.16||**_IGME0 _**|0.52|0.64|
|**_ES5 _**|8.75|7.09||**_IGME5 _**|0.454|0.533|
|**_ES10_**|10.82|9.46||**_IGME10_**|0.384|0.426|
|**_ES16_**|12.85|11.58||**_IGME16_**|0.300|0.298|

Notes: (1) The data used are IHDS 2012 with children aged 18-35. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,5,10,16. (4) Robust standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1.
**Table T3.IR:  Father's Education and Educational Expenditure on Children**

|||**RURAL**<br>**IHDS**<br>|**INDIA**<br>**2005**<br>||
|---|---|---|---|---|
||**(6-22) Year**<br>|**s Children**<br>|**(8-23) Year**<br>|**s Children**<br>|
|Father's Sch.|153.9***|145.4***|169.2***|158.7***|
||(9.08)|(8.77)|(11.0)|(10.6)|
|**Father's Sch. * Daughter**|**-22.8****|**-21.9***|**-24.0***|**-22.4**|
|**Dummy**|**(11.4)**|**(11.3)**|**(13.9)**|**(13.7)**|
|**Daughter Dummy**|**-182.5*****|**-137.1*****|**-211.0*****|**-134.0****|
||(43.5)|(43.7)|(52.3)|(52.7)|
|Intercept|772.3***|1585.4***|877.6***|1949.3***|
||(33.3)|(54.7)|(39.8)|(67.9)|
|No. of Children||-274.4***||-361.9***|
|||(17.2)||(21.8)|
|No. Observations|23058|23058|19002|19002|
|||**NSS**<br>|**1995**<br>||
||**(6-18) Year**|**s Children**|**(8-18) Year**|**s Children**|
|Father's Sch.|35.2***|35.2***|36.5***|37.5***|
||(1.425)|(1.425)|(1.535)|(1.567)|
|**Father's Sch. * Daughter**|**-3.7***|**-3.7***|**-3.4**|**-3.5**|
|**Dummy**|(2.083)|(2.083)|(2.285)|(2.281)|
|**Daughter Dummy**|**-74.1*****|**-74.1*****|**-65.2*****|**-58.5*****|
||(8.694)|(8.694)|(9.700)|(9.729)|
|Intercept|426.9***|426.9***|461.0***|507.7***|
||(5.420)|(5.420)|(5.882)|(9.728)|
|No. of Children||||-21.6***<br>(3.749)|
|No. Observations|37144|37144|32499|32499|

Notes: (1) The data used are IHDS 2005 and NSS 1995 respectively. (2) Robust standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1.
**Table T2.CU: Intergenerational Persistence in Schooling in Urban China**

|||**LINEARCEF**||**QU**|**ADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft.|**0.29*****|**0.35*****|**0.061*****|**0.093****|**0.32*****|**0.22*****|
||(0.016)|(0.016)|(0.023)|(0.045)|(0.045)|(0.063)|
|Quadratic Coefft.||||**0.015*****|**0.0023**|**-0.012*****|
|||||(0.0029)|(0.0029)|(0.0041)|
|Intercept|**8.97*****|**8.51*****|**-0.46****|**9.33*****|**8.57*****|**-0.76*****|
||(0.15)|(0.15)|(0.21)|(0.18)|(0.18)|(0.25)|
|No. Observations|3192|3241|6433|3192|3241|6433|
|||**Estimate**<br>|**s of Mobility**|**fromQuadra**|**tic CEF**<br>||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|9.33|8.51||**_IGME0 _**|0.093|0.35|
|**_ES6 _**|10.43|10.61||**_IGME6 _**|0.268|0.35|
|**_ES9_**|11.38|11.66||**_IGME9 _**|0.354|0.35|
|**_ES16_**|14.66|14.11||**_IGME16_**|0.558|0.35|

Notes: (1) The data used are CFPS 2016 with children aged 18-35. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,6,9,16. (4) Robust standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1.
**Table T3.CU:  Father's Education and Educational Expenditure on Children**

|||**URBAN**<br>**CFPS**<br>|**CHINA**<br>**2010**<br>||
|---|---|---|---|---|
||**(6-22) Yea**|**rs Children**|**(8-23) Yea**|**rs Children**|
|Father's Sch.|236.9***|162.8***|225.4***|138.3***|
||(35.0)|(34.1)|(32.9)|(30.5)|
|**Father's Sch. * Daughter**|**36.8**|**18.6**|**27.5**|**13.5**|
|**Dummy**|(48.2)|(46.9)|(49.2)|(47.4)|
|**Daughter Dummy**|**-71.2**|**181.1**|**22.4**|**267.5**|
||(400.2)|(386.8)|(413.7)|(397.5)|
|Intercept|827.4***|4137.0***|1034.3***|4592.9***|
||(278.8)|(337.8)|(264.5)|(330.1)|
|No. of Children||-2222.0***||-2401.2***|
|||(132.7)||(154.4)|
|No. Observations|2784|2784|2435|2435|

Notes: (1) The data used are CFPS 2010. (2) Robust standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1.
**Table T2.CR: Intergenerational Persistence in Schooling in Rural China**

|||**LINEARCEF**||**QU**|**ADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
|||**Dahters**|||**Dahters**||
||**Sons (S)**|**ug**<br>**(D)**|**D-S**|**Sons (S)**|**ug**<br>**(D)**|**D-S**|
|Linear Coefft|**0.27*****|**0.33*****|**0.062*****|**0.27*****|**0.38*****|**0.11***|
||(0.015)|(0.015)|(0.021)|(0.042)|(0.045)|(0.061)|
|Quadratic Coefft.||||**-0.00025**|**-0.0047**|**-0.0045**|
|||||(0.0035)|(0.0037)|(0.0051)|
|Intercept|**7.59*****|**6.78*****|**-0.81*****|**7.59*****|**6.73*****|**-0.86*****|
||(0.11)|(0.12)|(0.17)|(0.12)|(0.13)|(0.18)|
|No. Observations|3955|4085|8040|3955|4085|8040|
|||**Estimate**<br>|**s of Mobilit**|**y fromQuadra**|**tic CEF**<br>||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|7.59|6.78||**_IGRC_**|0.27|0.33|
|**_ES5 _**|9.21|8.76|||||
|**_ES10_**|10.02|9.75|||||
|**_ES16_**|11.91|12.06|||||

Notes: (1) The data used are CFPS 2016 with children aged 18-35. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,6,9,16. (4) Robust standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1.
**Table T3.CR:  Father's Education and Educational Expenditure on Children**

|||**RURAL**<br>**CFPS**<br>|**CHINA**<br>**2010**<br>||
|---|---|---|---|---|
||**6-22 Yea**|**r Children**|**8-23 Yea**|**r Children**|
|Father's Sch.|105.5***|79.6***|115.7***|85.6***|
||(12.8)|(12.1)|(15.0)|(14.0)|
|**Father's Sch. * Daughter**|**-31.8***|**-31.2***|**-21.7**|**-21.7**|
|**Dummy**|**(17.3)**|**(16.6)**|**(20.9)**|**(20.0)**|
|**Daughter Dummy**|**151.6**|**240.3****|**111.2**|**275.2****|
||(103.1)|(100.6)|(120.7)|(117.1)|
|Intercept|648.0***|1939.7***|705.7***|2173.6***|
||(71.0)|(117.9)|(83.3)|(132.7)|
|No. of Children||-716.8***||-838.0***|
|||(49.7)||(56.8)|
|No. Observations|4326|4326|3632|3632|

Notes: (1) The data used are CFPS 2010. (2) Robust standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1.
**Table 4.I: Returns to Education Estimates for India**

||**URB**|**AN (U)**|**RUR**|**AL (R)**|**ALL**<br>**(R**|**INDIA**<br>**+U)**||
|---|---|---|---|---|---|---|---|
||**Men**|**Women**|**Men**|**Women**|**Men**|**Women**|**Year**|
|||**SEC**|**ONDAR**|**Y**||||
|Duraisamy (2002)|14.7|32.4|17.9|34.1|||1993/94|
|Kingdon (1998)|4.9|13.4|||||1995|
|Kanjilal et al. (2017)|74.1|91.9|||||2011/12|
|Bargain et al. (2009)|||||24|64|1987/88|
|Bargain et al. (2009)|||||28|64|1993/95|
|Bargain et al. (2009)|||||25|41|2002/04|
|||**HIGHER**|**SECON**|**DARY**||||
|Duraisamy (2002)|10.1|12.9|8.4|11|||1993/94|
|Kanjilal et al. (2017)|108|123|101.4|124.3|||2011/12|
|Kingdon (1998)|17.6|20.8||||||
|Bargain et al. (2009)|||||64|124|1987/88|
|Bargain et al. (2009)|||||60|136|1993/95|
|Bargain et al. (2009)|||||55|109|2002/04|
|||**C**|**OLLEGE**|||||
|Duraisamy (2002)|13.2|9.3|11.6|10.1|||1993/94|
|Kanjilal et al. (2017)|150.9|153.6|141|146.9|||2011/12|
|Kingdon (1998)|18|8.9||||||
|Bargain et al. (2009)|||||111|174|1987/88|
|Bargain et al. (2009)|||||108|175|1993/95|
|Bargain et al. (2009)|||||121|170|2002/04|

Note: The complete references for the studies cited are in the online appendix.
**Table 4.C: Returns to Education Estimates for China**

|**Mincerian Re**|**turns t**<br>|**o Years of**<br>|**Schooling**<br>||
|---|---|---|---|---|
||**URB**|**AN (U)**|**RURAL (R)**||
||**Men**|**Women**|**Men**<br>**Women**|**Year**|
|Jamison, D., & Van der Gaag, J. (1987)|4.5|5.5||1985|
|Xie, Y., & Hannum, E. (1996)|2.2|4.4||1988/1989|
|Johnson, E. N., & Chow, G. C. (1997)|2.78|4.46|2.95<br>4.82|1988/1989|
|Liu, Z. (1998)|2.39|3.31||1988/1989|
|Meng, X. (1998)|||1.1<br>2.2|1986/1987|
|Maurer‐Fazio, M. (1999)|3.74|4.94||1991/1992|
|Li, H. (2003)|4.3|6.9||1995/196|
|Bishop, J.., Luo, F., Wang, F. (2005)|3.56|4.43||1995/1996|
|Zhang, J., Zhao, Y., Park, A., Song, X.<br>(2005)|2.9|5.2||1988|
|Zhang, J., Zhao, Y., Park, A., Song, X.<br>(2005)|8.4|13.2||2001|
|Hauser, S. M., & Xie, Y. (2005)|3.6|7.4||1995/1996|
|Ren, W., & Miller, P. W. (2012)|||3.81<br>7.18|2006|
|Chen, Q., Xu, J., Zhao, J., & Zhang, B.<br>(2017)|||6.8|2004|
|Xiao, S., & Asadullah, M. N(2018)|7.1|9||2010|
|**SECONDARY(**|**Estimat**|**es for All**|**China(R+U))**||
|||**Men**|**Women**||
|Bargain et al. (2009)||3|15|1987/88|
|Bargain et al.(2009)||11|25|2002/04|
|**HIGHER SECONDAR**|**Y(Esti**|**mates are f**|**or All China(R+U))**||
|||**Men**|**Women**||
|Bargain et al. (2009)||9|26|1987/88|
|Bargain et al.(2009)||26|51|2002/04|
||**COLL**|**EGE**|||
||**R**|**ural**|**All China**<br>**(R+U)**||
||**Men**|**Women**|**Men**<br>**Women**||
|Gustafsson, B and Li, S (2000)|8.9|10.2||1988/1989|
|Gustafsson, B and Li, S (2000)|15.5|20.8||1995/1996|
|Bargain et al. (2009)|||24<br>42|1987/88|
|Bargain et al. (2009)|||54<br>84|2002/04|
|Wang, L. (2012)|21.1|27||1995/1996|
|Wang, L.(2012)|48.2|56.6||2002/2003|

Note: Full citations are provided in the online appendix.
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## **Online Appendix to: Gender Bias and Intergenerational Educational Mobility: Theory and Evidence from China and India**

## **M. Shahe Emran**

IPD, Columbia University

## **Hanchen Jiang**

Johns Hopkins University

**Forhad Shilpi** World Bank

# **NOT FOR PUBLICATION**

# **Omitted Proofs for the Results on Urban India in Section (2.3)**

(1) Using equation (11) in the text, we have the following: where _χ_<sup>_j_</sup> 0<sup>=</sup><sup>_α_2+</sup><sup>_δ_</sup> 2<sup>_jσjRcj_andthelastinequalityabovefollowsfromtheobservation</sup> that 2 _α_ 2 _Y_ 0<sup>_p_+ 2 ̃</sup><sup>_δ_</sup> 1<sup>_jσjRcj−α_1</sup> _>_ 0 when _θ_ 0<sup>_j>_0whichisinfactthecaseforboth</sup><sup>_j_=</sup><sup>_s, d_</sup> ( ) according to the empirical evidence reported in the text. Thus, a higher estimate of ability by parents would result in a higher slope of the curve at each point.

Since at _R_<sup>_cj_</sup> = 0, the value of _θ_ 0<sup>_j_does not depend on the ability of a child,the curve for</sup> a higher ability estimate, ceteris paribus, lies above the curve for a lower ability estimate at all positive values of returns to schooling for children.

(2) For a higher school quality, we have the following (again, using equation (11) in the main text): (3) The claim that the effects of pure son preference on the slope is not unambiguous follows from the result below: The above expression cannot be signed because we do not know the sign of ( _α_ 2 _− δ_<sup> ̃</sup> 2<sup>_jσjRcj_)</sup> .
## **Papers Cited on Returns to Education in India and China in Tables T4.I and T4.C in the main Text**

## **Papers Cited on Returns to Education in China**

Jamison and Van der Gaag (1987), Xie and Hannum (1996), Johnson and Chow (1997), Liu (1998), Meng and Kidd (1997), Maurer-Fazio (1999), Li (2003), Bishop et al. (2005), Zhang et al. (2005), Asadullah and Xiao (2020), Hauser and Xie (2005), Ren and Miller (2012), Bargain et al. (2009), Wang (2012), Gustafsson and Li (2000).

## **Papers Cited on Returns to Education in India**

Duraisamy (2002), Bargain et al. (2009), Kingdon (1998), Kanjilal-Bhaduri and Pastore (2018).

# **References**

- Asadullah, M. N. and Xiao, S. (2020). The changing pattern of wage returns to education in post-reform china. _Structural Change and Economic Dynamics_ , 53:137–148.

- Bargain, O., Bhaumik, S. K., Chakrabarty, M., and Zhao, Z. (2009). Earnings Differences Between Chinese And Indian Wage Earners, 19872004. _Review of Income and Wealth_ , 55:562–587.

- Bishop, J. A., Luo, F., and Wang, F. (2005). Economic transition, gender bias, and the distribution of earnings in china. _Economics of Transition_ , 13(2):239–259.

- Duraisamy, P. (2002). Changes in returns to education in India, 1983-94: by gender, agecohort and location. _Economics of Education Review_ , 21(6):609–622.

- Gustafsson, B. and Li, S. (2000). Economic transformation and the gender earnings gap in urban china. _Journal of Population Economics_ , 13(2):305–329.

- Hauser, S. M. and Xie, Y. (2005). Temporal and regional variation in earnings inequality: Urban china in transition between 1988 and 1995. _Social Science Research_ , 34(1):44–79.

- Jamison, D. T. and Van der Gaag, J. (1987). Education and earnings in the people’s republic of china. _Economics of Education Review_ , 6(2):161–166.

- Johnson, E. N. and Chow, G. C. (1997). Rates of return to schooling in china. _Pacific Economic Review_ , 2(2):101–113.

- Kanjilal-Bhaduri, S. and Pastore, F. (2018). Returns to Education and Female Participation Nexus: Evidence from India. _The Indian Journal of Labour Economics_ , 61(3):515–536.

- Kingdon, G. G. (1998). Does the labour market explain lower female schooling in India? _Journal of Development Studies_ , 35(1):39–65.

- Li, H. (2003). Economic transition and returns to education in china. _Economics of education review_ , 22(3):317–328.

- Liu, Z. (1998). Earnings, education, and economic reforms in urban china. _Economic Development and Cultural Change_ , 46(4):697–725.

- Maurer-Fazio, M. (1999). Earnings and education in china’s transition to a market economy survey evidence from 1989 and 1992. _China Economic Review_ , 10(1):17–40.
- Meng, X. and Kidd, M. P. (1997). Labor market reform and the changing structure of wage determination in china’s state sector during the 1980s. _Journal of Comparative Economics_ , 25(3):403–421.

- Ren, W. and Miller, P. W. (2012). Gender differentials in the payoff to schooling in rural china. _Journal of Development Studies_ , 48(1):133–150.

- Wang, L. (2012). Economic transition and college premium in urban china. _China Economic Review_ , 23(2):238–252.

- Xie, Y. and Hannum, E. (1996). Regional variation in earnings inequality in reform-era urban china. _American Journal of Sociology_ , 101(4):950–992.

- Zhang, J., Zhao, Y., Park, A., Song, X., et al. (2005). Economic returns to schooling in urban china, 1988 to 2001. _Journal of Comparative Economics_ , 33(4):730–752.
# **<u>Table A1.S: Construction of Matched Sons-Fathers in India</u>**

|||**IHDS Wave 1**<br>**Azam (2015)**|**IHDS Wave 2**|
|---|---|---|---|
|Total Num of Individuals<br>Surveyed in IHDS||215,784|204,569|
|Total Num of Men in 20-65<br>Age Group||58,194|56,883|
|Education Information<br>Missing (dropped)||325|232|
|Identification through<br>coresidence only|Father identified if coresidence is<br>used|19,556|19,629|
||percentage of male aged 20-65 who<br>can be potentially matched using<br>coresidence|33.60%|34.508%|
|Panel A. Total Number of<br>Men (20-65 age group) with<br>Education Information|Identification of Father|||
||a) Individual is head of household|34,069|31,780|
||b) Individual who are not household<br>heads, however, whose father is<br>living in the household|18,056|18,325|
||c) Individual is neither head of the<br>household, nor his father is living in<br>the household (no father<br>identification is provided)|4,029|1,905|
||d1) Individual is head's father<br>(dropped, father cannot be<br>identified)|591||
||d2) Individual's father cannot be<br>identified (dropped)|1,124||
|Total number of men (20-65<br>age group) whose father is<br>identified: a) + b) + c)||56,154|52,010|
|Percentage of men (20-65 age<br>group, panel A) whose fathers<br>are identified||96.494%|91.433%|

Notes: Column 1-3 are directly obtained from Table 8 in Azam (2015) using IHDS 2005 while column 4 is based on authors’ own calculation using IHDS 2012.
# **Table A1.D. Construction of Matched Daughters-Fathers in India**

||**IHDS Wave 2**<br>**Azam (2016)**|**IHDS Wave 2**|
|---|---|---|
|Total Surveyed women in age 20-49|45,319|45,319|
|Total Surveyed women in age 20-49, with non-missing<br>education information|45,276|45,276|
|Father's Edu from household co-resident|4,416|4,957|
|Father's edu from Women's Module|34,290|34,290|
|Total Women whose father's Edu is available|38,706|39,247|
|% of surveyed women for whom father's Edu is<br>available|85.49%|86.68%|

Notes: Column 1-2 are directly obtained from Table 1 in Azam (2016) using IHDS 2012 while column 3 is based on authors’ own calculation using IHDS 2012.
# **Table A2.IU.A: Intergenerational Persistence in Schooling in Urban India -** **<u>(18 35 Years Age Cohorts)</u>**

|||**LINEAR CEF**||**Q **|**UADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|D-S|**Sons (S)**|**Daughters**<br>**(D)**|D-S|
|Linear Coefft.|0.46|0.52|0.066|0.55|0.65|0.094|
||(0.0074)***|(0.0080)***|(0.011)***|(0.023)***|(0.025)***|(0.034)***|
||[0.012]***|[0.013]***|[0.013]***|[0.035]***|[0.036]***|[0.039]***|
||{0.024}***|{0.022}***|{0.017}***|{0.046}***|{0.037}***|{0.043}***|
|Quadratic Coefft.||||-0.0070|-0.0093|-0.0022|
|||||(0.0014)***|(0.0016)***|(0.0022)|
|||||[0.0022]***|[0.0022]***|[0.0025]|
|||||{0.0022}***|{0.0025}***|{0.0025}|
|Intercept|6.96|5.97|-0.99|6.81|5.80|-1.00|
||(0.071)***|(0.075)***|(0.10)***|(0.085)***|(0.086)***|(0.12)***|
||[0.14]***|[0.17]***|[0.13]***|[0.15]***|[0.17]***|[0.13]***|
||{0.34}***|{0.37}***|{0.17}***|{0.35}***|{0.35}***|{0.17}***|
|No. Observation|9449|9070|18519|9449|9070|18519|
|||**Mobil**|**ity Estimates f**|**romQuadratic**|**CEF**||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0_**|6.81|5.80||**_IGME0_**|0.55|0.65|
|**_ES5_**|9.39|8.82||**_IGME5_**|0.485|0.556|
|**_ES10_**|11.61|11.37||**_IGME10_**|0.414|0.464|
|**_ES16_**|13.82|13.82||**_IGME16_**|0.330|0.353|

Notes: (1) The data used are IHDS 2012 with children aged 18-35. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,5,10,16. (4) Robust standard errors in parentheses; standard errors clustered at district-level in square brackets; standard errors clustered at state-level in braces; *** p<0.01, ** p<0.05, * p<0.1.
# **Table A2.IU.B: Intergenerational Persistence in Schooling in Urban India -** **<u>(18 30 Years Age Cohorts)</u>**

|||**LINEAR CEF**||**Q **|**UADRATIC CE**|**F**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|D-S|**Sons (S)**|**Daughters**<br>**(D)**|D-S|
|Linear Coefft.|0.44|0.50|0.06|0.53|0.62|0.084|
||(0.0085)***|(0.0091)***|(0.012)***|(0.027)***|(0.029)***|(0.039)**|
||[0.014]***|[0.014]***|[0.016]***|[0.040]***|[0.038]***|[0.041]**|
||{0.029}***|{0.026}***|{0.016}***|{0.059}***|{0.038}***|{0.039}**|
|Quadratic Coefft.||||-0.0069|-0.0088|-0.0019|
|||||(0.0016)***|(0.0018)***|(0.0024)|
|||||[0.0025]***|[0.0023]***|[0.0026]|
|||||{0.0027}**|{0.0025}***|{0.0024}|
|Intercept|7.18|6.45|-0.74|7.02|6.27|-0.75|
||(0.082)***|(0.089)***|(0.12)***|(0.10)***|(0.10)***|(0.14)***|
||[0.17]***|[0.19]***|[0.14]***|[0.18]***|[0.19]***|[0.15]***|
||{0.40}***|{0.42}***|{0.16}***|{0.43}***|{0.40}***|{0.16}***|
|No. Observation|7314|6826|14140|7314|6826|14140|
|||**Mobil**|**ity Estimates f**|**romQuadratic**|**CEF**||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0_**|7.02|6.27||**_IGME0_**|0.53|0.62|
|**_ES5_**|9.50|9.15||**_IGME5_**|0.463|0.528|
|**_ES10_**|11.63|11.59||**_IGME10_**|0.394|0.441|
|**_ES16_**|13.73|13.94||**_IGME16_**|0.312|0.335|

Notes: (1) The data used are IHDS 2012 with children aged 18-30. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,5,10,16. (4) Robust standard errors in parentheses; standard errors clustered at district-level in square brackets; standard errors clustered at state-level in braces; *** p<0.01, ** p<0.05, * p<0.1.
**Table A2.CU.A: Intergenerational Persistence in Schooling in Urban China -** **<u>(18 35 Years Age Cohorts)</u>**

|||**LINEAR CEF**||**Q**|**UADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft.|0.29|0.35|0.061|0.093|0.32|0.22|
||(0.016)***|(0.016)***|(0.023)***|(0.045)**|(0.045)***|(0.063)***|
||[0.027]***|[0.020]***|[0.025]**|[0.063]|[0.060]***|[0.074]***|
|Quadratic Coefft.||||0.015|0.0023|-0.012|
|||||(0.0029)***|(0.0029)|(0.0041)***|
|||||[0.0034]***|[0.0037]|[0.0049]**|
|Intercept|8.97|8.51|-0.46|9.33|8.57|-0.76|
||(0.15)***|(0.15)***|(0.21)**|(0.18)***|(0.18)***|(0.25)***|
||[0.20]***|[0.27]***|[0.274]*|[0.25]***|[0.30]***|[0.31]**|
|No. Observations|3192|3241|6433|3192|3241|6433|
|||**Estima**|**tes of Mobility**|**from Quadrati**|**c CEF**||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|9.33|8.51||**_IGME0 _**|0.093|0.35|
|**_ES6 _**|10.43|10.61||**_IGME6 _**|0.268|0.35|
|**_ES9_**|11.38|11.66||**_IGME9 _**|0.354|0.35|
|**_ES16_**|14.66|14.11||**_IGME16_**|0.558|0.35|

Notes: (1) The data used are CFPS 2016 with children aged 18-35. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling, (3) ESK is expected schooling when father has K years of schooling. K=0,6,9,16. (4) Robust standard errors in parentheses; standard errors clustered at province-level in square brackets; *** p<0.01, ** p<0.05, * p<0.1.
**Table A2.CU.B: Intergenerational Persistence in Schooling in Urban China -** **<u>(18 30 Years Age Cohorts)</u>**

|||**LINEAR CEF**||**Q**|**UADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft.|0.26|0.35|0.089|0.067|0.34|0.28|
||(0.019)***|(0.020)***|(0.027)***|(0.052)|(0.055)***|(0.076)***|
||[0.025]***|[0.024]***|[0.028]***|[0.052]|[0.077]***|[0.075]***|
|Quadratic Coefft.||||0.014|0.00048|-0.014|
|||||(0.0034)***|(0.0034)|(0.0048)***|
|||||[0.0030]***|[0.0045]|[0.0049]***|
|Intercept|9.19|8.58|-0.61|9.59|8.6|-0.99|
||(0.17)***|(0.18)***|(0.25)**|(0.21)***|(0.23)***|(0.31)***|
||[0.20]***|[0.28]***|[0.33]*|[0.23]***|[0.36]***|[0.38]**|
|No. Observations|2230|2205|4435|2230|2205|4435|
|||**Estima**|**tes of Mobility**|**from Quadrati**|**c CEF**||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|9.59|8.58||**_IGME0 _**|0.067|0.35|
|**_ES6 _**|10.50|10.68||**_IGME6 _**|0.237|0.35|
|**_ES9_**|11.33|11.73||**_IGME9 _**|0.322|0.35|
|**_ES16_**|14.25|14.18||**_IGME16_**|0.521|0.35|

Notes: (1) The data used are CFPS 2016 with children aged 18-30. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling, (3) ESK is expected schooling when father has K years of schooling. K=0,6,9,16. (4) Robust standard errors in parentheses; standard errors clustered at province-level in square brackets; *** p<0.01, ** p<0.05, * p<0.1.
**Table A2.IR.A: Intergenerational Persistence in Schooling in Rural India -** **<u>(18 35 Years Age Cohorts)</u>**

|||**LINEAR CEF**<br>||**QU**|**ADRATIC C**<br>|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft.|0.45<br>(0.0064)***|0.52<br>(0.0071)***|0.075<br>(0.0095)***|0.52<br>(0.019)***|0.64<br>(0.021)***|0.12<br>(0.028)***|
||[0.011]***|[0.012]***|[0.012]***|[0.027]***|[0.030]***|[0.033]***|
||{0.017}***|{0.025}***|{0.024}***|{0.031}***|{0.053}***|{0.044}***|
|Quadratic Coefft.||||-0.007|-0.011|-0.007|
|||||(0.0014)***|(0.0018)***|(0.0014)***|
|||||[0.0019]***|[0.0022]***|[0.0019]***|
|||||{0.0020}***|{0.0034}***|{0.0020}***|
|Intercept|6.38|4.24|-2.14|6.32|4.16|-2.14|
||(0.044)***|(0.043)***|(0.062)***|(0.048)***|(0.046)***|(0.062)***|
||[0.12]***|[0.14]***|[0.097]***|[0.12]***|[0.14]***|[0.0097]***|
||{0.25}***|{0.38}***|{0.21}***|{0.25}***|{0.37}***|{0.21}***|
|No. Observations|16957|17022|33979|16957|17022|33979|
|||**Estima**|**tes of Mobility**|**from Quadrati**|**c CEF**||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|6.32|4.16||**_IGME0 _**|0.52|0.64|
|**_ES5 _**|8.75|7.09||**_IGME5 _**|0.454|0.533|
|**_ES10_**|10.82|9.46||**_IGME10_**|0.384|0.426|
|**_ES16_**|12.85|11.58||**_IGME16_**|0.300|0.298|

Notes: (1) The data used are IHDS 2012 with children aged 18-35. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,5,10,16. (4) Robust standard errors in parentheses; standard errors clustered at district-level in square brackets; standard errors clustered at statelevel in braces; *** p<0.01, ** p<0.05, * p<0.1.
**Table A2.IR.B: Intergenerational Persistence in Schooling in Rural India -** **<u>(18 30 Years Age Cohorts)</u>**

|||**LINEAR CEF**<br>||**QU**|**ADRATIC C**<br>|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft.|0.42<br>(0.0071)***|0.51<br>(0.0079)***|0.083<br>(0.011)***|0.49<br>(0.021)***|0.63<br>(0.023)***|0.14<br>(0.031)***|
||[0.011]***|[0.013]***|[0.012]***|[0.028]***|[0.032]***|[0.034]***|
||{0.017}***|{0.027}***|{0.023}***|{0.033}***|{0.054}***|{0.0020}***|
|Quadratic Coefft.||||-0.0061|-0.011|-0.0051|
|||||(0.0016)***|(0.0019)***|(0.0025)**|
|||||[0.0019]***|[0.0023]***|[0.0025]**|
|||||{0.0020}***|{0.0033}***|{0.0025}*|
|Intercept|6.69|4.76|-1.93|6.63|4.67|-1.96|
||(0.050)***|(0.051)***|(0.072)***|(0.055)***|(0.054)***|(0.077)***|
||[0.12]***|[0.15]***|[0.11]***|[0.13]***|[0.16]***|[0.11]***|
||{0.26}***|{0.42}***|{0.23}***|{0.27}***|{0.41}***|{0.23}***|
|No. Observations|12946|12959|25903|12946|12959|25903|
|||**Estima**|**tes of Mobility**|**from Quadrat**|**ic CEF**||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|6.63|4.67||**_IGME0 _**|0.49|0.63|
|**_ES5 _**|8.93|7.55||**_IGME5 _**|0.429|0.518|
|**_ES10_**|10.92|9.87||**_IGME10_**|0.369|0.407|
|**_ES16_**|12.91|11.93||**_IGME16_**|0.296|0.272|

Notes: (1) The data used are IHDS 2012 with children aged 18-30. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,5,10,16. (4) Robust standard errors in parentheses; standard errors clustered at district-level in square brackets; standard errors clustered at statelevel in braces; *** p<0.01, ** p<0.05, * p<0.1.
**Table A2.CR.A: Intergenerational Persistence in Schooling in Rural China -** **<u>(18 35 Years Age Cohorts)</u>**

|||**LINEAR CEF**||**QU**|**ADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft.|0.27|0.33|0.062|0.27|0.38|0.11|
||(0.015)***|(0.015)***|(0.021)***|(0.042)***|(0.045)***|(0.061)*|
||[0.040]***|[0.045]***|[0.025]**|[0.096]***|[0.11]***|[0.062]*|
|Quadratic Coefft.||||-0.00025|-0.0047|-0.0045|
|||||(0.0035)|(0.0037)|(0.0051)|
|||||[0.0058]|[0.0075]|[0.0050]|
|Intercept|7.59|6.78|-0.81|7.59|6.73|-0.86|
||(0.11)***|(0.12)***|(0.17)***|(0.12)***|(0.13)***|(0.18)***|
||[0.36]***|[0.42]***|[0.32]**|[0.40]***|[0.48]***|[0.33]**|
|No. Observations|3955|4085|8040|3955|4085|8040|
|||**Estima**<br>|**tes of Mobility**|**from Quadrati**|**c CEF**<br>||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|7.59|6.78||**_IGRC_**|0.27|0.33|
|**_ES6 _**|9.21|8.76|||||
|**_ES9_**|10.02|9.75|||||
|**_ES16_**|11.91|12.06|||||

Notes: (1) The data used are CFPS 2016 with children aged 18-35. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,6,9,16. (4) Robust standard errors in parentheses; standard errors clustered at province-level in square brackets; *** p<0.01, ** p<0.05, * p<0.1.
**Table A2.CR.B: Intergenerational Persistence in Schooling in Rural China -** **<u>(18 30 Years Age Cohorts)</u>**

|||**LINEAR CEF**||**QU**|**ADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft.|0.27|0.32|0.054|0.27|0.38|0.11|
||(0.017)***|(0.019)***|(0.025)**|(0.048)***|(0.053)***|(0.071)|
||[0.039]***|[0.049]***|[0.028]*|[0.10]**|[0.12]***|[0.051]**|
|Quadratic Coefft.||||-0.00047|-0.0056|-0.0052|
|||||(0.0039)|(0.0043)|(0.0058)|
|||||[0.0067]|[0.0075]|[0.0037]|
|Intercept|7.91|7.37|-0.54|7.90|7.31|-0.60***|
||(0.13)***|(0.15)***|(0.20)***|(0.14)***|(0.16)***|(0.22)|
||[0.34]***|[0.41]***|[0.27]*|[0.38]***|[0.47]***|[0.26]*|
|No. Observations|2833|2814|5647|2833|2814|5647|
|||**Estima**<br>|**tes of Mobility**|**from Quadrat**|**ic CEF**<br>||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|7.91|7.37||**_IGRC_**|0.27|0.32|
|**_ES6 _**|9.53|9.29|||||
|**_ES9_**|10.34|10.25|||||
|**_ES16_**|12.23|12.49|||||

Notes: (1) The data used are CFPS 2016 with children aged 18-30. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,6,9,16. (4) Robust standard errors in parentheses; standard errors clustered at province-level in square brackets; *** p<0.01, ** p<0.05, * p<0.1.
**Table A2.CU.C: Intergenerational Persistence in Schooling in Urban China - -** **<u>(18 35 Years Age Cohorts. First born Sample)</u>**

|||**LINEAR CEF**||**Q**|**UADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft.|0.28|0.36|0.083|0.11|0.34|0.24|
||(0.019)***|(0.018)***|(0.026)***|(0.053)**|(0.051)***|(0.074)***|
||[0.024]***|(0.021)***|[0.027]***|[0.067]|[0.066]***|[0.079]***|
|Quadratic Coefft.||||0.013|0.0015|-0.011|
|||||(0.0033)***|(0.0032)|(0.0046)**|
|||||[0.0037]***|[0.0040]|[0.0053]**|
|Intercept|9.26|8.47|-0.79|9.62|8.51|-1.11|
||(0.18)***|(0.17)***|(0.25)***|(0.22)***|(0.21)***|(0.30)***|
||[0.21]***|[0.30]***|[0.29]***|[0.28]***|[0.34]***|[0.33]***|
|No. Observations|2428|2617|5045|2428|2617|5045|
|||**Estima**<br>|**tes of Mobility**|**from Quadrati**|**c CEF**<br>||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|9.62|8.47||**_IGME0 _**|0.12|0.36|
|**_ES6 _**|10.75|10.63||**_IGME6 _**|0.257|0.36|
|**_ES9_**|11.66|11.71||**_IGME9 _**|0.333|0.36|
|**_ES16_**|14.71|14.23||**_IGME16_**|0.51|0.36|

Notes: (1) The data used are CFPS 2016 with first-born children aged 18-35. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,6,9,16. (4) Robust standard errors in parentheses; standard errors clustered at province-level in square brackets; *** p<0.01, ** p<0.05, * p<0.1.
**Table A2.CU.D: Intergenerational Persistence in Schooling in Urban China - -** **<u>(18 30 Years Age Cohorts. First born Sample)</u>**

|||**LINEAR CEF**||**Q**|**UADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft.|0.25|0.37|0.12|0.072|0.4|0.33|
||(0.022)***|(0.023)***|(0.032)***|(0.062)|(0.065)***|(0.090)***|
||[0.025]***|(0.026)***|[0.030]***|[0.066]|[0.089]***|[0.088]***|
|Quadratic Coefft.||||0.013|-0.0018|-0.014|
|||||(0.0038)***|(0.0039)|(0.0054)**|
|||||[0.0039]***|[0.0053]|[0.0059]**|
|Intercept|9.53|8.45|-1.07|9.93|8.4|-1.53|
||(0.21)***|(0.22)***|(0.30)***|(0.26)***|(0.28)***|(0.38)***|
||[0.22]***|[0.30]***|[0.34]***|[0.30]***|[0.41]***|[0.40]***|
|No. Observations|1668|1748|3416|1668|1748|3416|
|||**Estima**|**tes of Mobility**|**from Quadrati**|**c CEF**||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|9.93|8.45||**_IGME0 _**|0.12|0.37|
|**_ES6 _**|10.83|10.67||**_IGME6 _**|0.222|0.37|
|**_ES9_**|11.63|11.78||**_IGME9 _**|0.298|0.37|
|**_ES16_**|14.41|14.37||**_IGME16_**|0.474|0.37|

Notes: (1) The data used are CFPS 2016 with first-born children aged 18-30. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,6,9,16. (4) Robust standard errors in parentheses; standard errors clustered at province-level in square brackets; *** p<0.01, ** p<0.05, * p<0.1.
**Table A2.CR.C: Intergenerational Persistence in Schooling in Rural China - -** **<u>(18 35 Years Age Cohorts. First born Sample)</u>**

|||**LINEAR CEF**||**Q**|**UADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft|0.26|0.33|0.069|0.25|0.33|0.08|
||(0.019)***|(0.019)***|(0.027)**|(0.055)***|(0.019)***|(0.078)|
||[0.036]***|[0.046]***|[0.023]***|[0.097]**|[0.046]***|[0.074]|
|Quadratic Coefft.||||0.00031|-0.00071|-0.001|
|||||(0.0044)|(0.0047)|(0.0064)|
|||||[0.0060]|[0.0073]|[0.0067]|
|Intercept|7.72|6.85|-0.86|7.72|6.84|-0.88|
||(0.15)***|(0.15)***|(0.21)***|(0.17)***|(0.17)***|(0.24)***|
||[0.31]***|[0.41]***|[0.27]***|[0.36]***|[0.47]***|[0.29]***|
|No. Observations|2444|2772|5216|2444|2772|5216|
|||**Estima**<br>|**tes of Mobility**|**from Quadrat**|**ic CEF**<br>||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|7.72|6.85||**_IGRC_**|0.26|0.33|
|**_ES6 _**|9.28|8.83|||||
|**_ES9_**|10.06|9.82|||||
|**_ES16_**|11.88|12.13|||||

Notes: (1) The data used are CFPS 2016 with first-born children aged 18-35. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling. (3) ESK is expected schooling when father has K years of schooling. K=0,6,9,16. (4) Robust standard errors in parentheses; standard errors clustered at province-level in square brackets; *** p<0.01, ** p<0.05, * p<0.1.
**Table A2.CR.D: Intergenerational Persistence in Schooling in Rural China - -** **<u>(18 30 Years Age Cohorts. First born Sample)</u>**

|||**LINEAR CEF**||**QU**|**ADRATIC C**|**EF**|
|---|---|---|---|---|---|---|
||**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|**Sons (S)**|**Daughters**<br>**(D)**|**D-S**|
|Linear Coefft|0.25|0.32|0.073|0.2|0.32|0.12|
||(0.022)***|(0.024)***|(0.032)**|(0.062)***|(0.065)***|(0.090)|
||[0.030]***|[0.044]***|[0.031]***|[0.091]**|[0.098]***|[0.055]|
|Quadratic Coefft.||||0.0043|0.00048|-0.0039|
|||||(0.0050)|(0.0052)|(0.0072)|
|||||[0.0063]|[0.0060]|[0.0042]|
|Intercept|8.11|7.43|-0.68|8.16|7.43|-0.73|
||(0.17)***|(0.18)***|(0.25)***|(0.19)***|(0.20)***|(0.28)***|
||[0.25]***|[0.34]***|[0.24]***|[0.30]***|[0.40]***|[0.24]***|
|No. Observations|1732|1888|3620|1732|1888|3620|
|||**Estima**<br>|**tes of Mobility**|**from Quadrati**|**c CEF**<br>||
||**Absolute**|**Mobility**|||**Relative**|**Mobility**|
||**Sons**|**Daughters**|||**Sons**|**Daughters**|
|**_ES0 _**|8.11|7.43||**_IGRC_**|0.25|0.32|
|**_ES6 _**|9.61|9.35|||||
|**_ES9_**|10.36|10.31|||||
|**_ES16_**|12.11|12.55|||||

Notes: (1) The data used are CFPS 2016 with first-born children aged 18-30. (2) IGMEK is Intergenerational Marginal effect when father has K years of schooling, (3) ESK is expected schooling when father has K years of schooling. K=0,6,9,16. (4) Robust standard errors in parentheses; standard errors clustered at province-level in square brackets; *** p<0.01, ** p<0.05, * p<0.1.
**Table A3.IU:  Father's Education and  Educational Expenditure on Children**

|||**URBAN**<br>**IHDS**|**INDIA**<br>**2005**||
|---|---|---|---|---|
||**(6-22) Year**|**s Children**|**(8-23) Year**|**s Children**|
|Father's Sch.|384.4|338.7|403.9|348|
||(14.9)***|(14.40)***|(17.4)***|(16.9)***|
||[22.2]***|[20.4]***|[24.1]***|[22.6]***|
||{28.2}***|{26.4}***|{30.9}***|{28.8}***|
|Father's Sch. * Daughter|-34.0|-37.5|-36.5|-40.2|
|Dummy|(20.5)*|(20.3)*|(23.9)|(23.5)*|
||[19.0]*|[18.4]**|[21.9]*|[21.1]*|
||{18.7}*|{16.7}**|{23.9}|{19.6}**|
|Daughter Dummy|-290.2|-189.9|-325.1|-174.3|
||(136.9)***|(138.7)|(164.4)**|(162.9)|
||[125.0]**|[118.9]|[144.0]**|[138.6]|
||{142.2}*|{123.9}|{171.0}*|{148.0}|
|Intercept|784.8|2763.5|917.3|3220.7|
||(105.1)***|(148)***|(124.9)***|(175.6)***|
||[157.5]***|[271.2]***|[185.7]***|[332.3]***|
||{223.2}***|{279.4}***|{255.2}***|{338.3}***|
|No. of Children||-673.1||-777.7|
|||(36.0)***||(41.9)***|
|||[75.9]***||[88.8]***|
|||{83.1}***||{99.8}***|
|No. Observations|13086|13086|11051|11051|
|||**NSS**<br>|**1995**<br>||
||**(6-18) Year**|**s Children**|**(8-18) Year**|**s Children**|
|Father's Sch.|108.4|108.6|110.4|110.9|
||(2.817)***|(2.789)***|(3.070)***|(3.039)***|
||[7.819]***|[7.467]***|[7.436]***|[7.021]***|
||{7.898}***|{7.735}***|{7.781}***|{7.644}***|
|Father's Sch. * Daughter|-11.3|-11.5|-11.2|-11.2|
|Dummy|(3.906)***|(3.860)***|(4.295)***|(4.238)***|
||[2.766]***|[2.788]***|[3.114]***|[3.121]***|
||{4.559}**|{4.497}**|{4.682}**|{4.616}**|
|Daughter Dummy|-39.4|-14.3|-41.55|-11.14|
||(26.12)|(26.15)|(29.00)|(29.03)|
||[16.95]***|[17.48]|[21.47]|[22.19]|
||{26.77}|{29.61}|{30.19}|{33.90}|
|Intercept|505.9|923.0|543.6|1004.0|
||(17.95)***|(23.74)***|(19.75)***|(26.13)***|
|---|---|---|---|---|
||[22.78]***|[54.14]***|[23.99]***|[57.27]***|
||{43.75}***|{79.43}***|{44.32}***|{85.89}***|
|No. of Children||-161.1||-178.0|
|||(7.164)***||(7.963)***|
|||[19.38]***||[19.83]***|
|||{22.93}***||{24.72}***|
|No. Observations|27810|27810|24443|24443|

Notes: (1) The data used are IHDS 2005 and NSS 1995 respectively. (2) Robust standard errors in parentheses; standard errors clustered at district-level in square brackets; standard errors clustered at state-level in braces; *** p<0.01, ** p<0.05, * p<0.1.
**Table A3.CU:  Father's Education and Educational Expenditure on Children**

|||**URBAN**<br>**CFPS**<br>|**CHINA**<br>**2010**<br>||
|---|---|---|---|---|
||**(6-22) Yea**|**rs Children**|**(8-23) Yea**|**rs Children**|
|Father's Sch.|236.9|162.8|225.4|138.3|
||(35.0)***|(34.1)***|(32.9)***|(30.5)***|
||[38.7]***|[36.0]***|[39.1]***|[33.9]***|
||{63.9}***|{47.5}***|{72.6}***|{56.4}**|
|Father's Sch. * Daughter|36.8|18.6|27.5|13.5|
|Dummy|(48.2)|(46.9)|(49.2)|(47.4)|
||[39.2]|[39.6]|[38.6]|[38.9]|
||{31.9}|{31.5}|{24.4}|{27.9}|
|Daughter Dummy|-71.2|181.1|22.4|267.5|
||(400.2)|(386.8)|(413.7)|(397.5)|
||[327.1]|[348.5]|[334.6]|[364.5]|
||{275.1}|{305.8}|{252.7}|{318.8}|
|Intercept|827.4|4137.0|1034.3|4592.9|
||(278.8)***|(337.8)***|(264.5)***|(330.1)***|
||[300.0]***|[397.1]***|[295.5]***|[401.7]***|
||{316.8}**|{436.8}***|{292.6}***|{488.9}***|
|No. of Children||-2222.0||-2401.2|
|||(132.7)***||(154.4)***|
|||[211.3]***||[233.4]***|
|||{366.3}***||{412.4}***|
|No. Observations|2784|2784|2435|2435|

Notes: (1) The data used are CFPS 2010. (2) Robust standard errors in parentheses; standard errors clustered at county-level in square brackets; standard errors clustered at province-level in braces; *** p<0.01, ** p<0.05, * p<0.1.
**Table A3.IR:  Father's Education and Educational Expenditure on Children**

|||**RURAL**<br>**IHDS**|**INDIA**<br>**2005**||
|---|---|---|---|---|
||**(6-22) Year**|**s Children**|**(8-23) Year**|**s Children**|
|Father's Sch.|153.9|145.4|169.2|158.7|
||(9.08)***|(8.77)***|(11.0)***|(10.6)***|
||[16.3]***|[15.5]***|[19.8]***|[18.5]***|
||{23.5}***|{21.5}***|{262.4}***|{23.8}***|
|Father's Sch. * Daughter|-22.8|-21.9|-24.0|-22.4|
|Dummy|(11.4)**|(11.3)*|(13.9)*|(13.7)|
||[13.0]*|[12.8]*|[15.4]|[15.1]|
||{8.69}**|{9.11}**|{9.63}**|{10.3}**|
|Daughter Dummy|-182.5|-137.1|-211.0|-134.0|
||(43.5)***|(43.7)***|(52.3)***|(52.7)**|
||[47.7]***|[49.1]***|[58.6]***|[60.9]**|
||{38.1}***|{42.5}***|{48.5}***|{56.7}**|
|Intercept|772.3|1585.4|877.6|1949.3|
||(33.3)***|(54.7)***|(39.8)***|(67.9)***|
||[60.9]***|[101.5]***|[69.7]***|[125.9]***|
||{106.3}***|{214.7}***|{118.4}***|{256.0}***|
|No. of Children||-274.4||-361.9|
|||(17.2)***||(21.8)***|
|||[32.4]***||[42.4]***|
|||{52.7}***||{65.7}***|
|No. Observations|23058|23058|19002|19002|
|||**NSS**<br>|**1995**<br>||
||**(6-18) Year**|**s Children**|**(8-18) Year**|**s Children**|
|Father's Sch.|35.2|36.0|36.5|37.5|
||(1.425)***|(1.453)***|(1.535)***|(1.567)***|
||[2.444]***|[2.408]***|[2.501]***|[2.477]***|
||{4.779}***|{4.739}***|{4.678}***|{4.647}***|
|Father's Sch. * Daughter|-3.7|-3.8|-3.4|-3.5|
|Dummy|(2.083)*|(2.081)*|(2.285)|(2.281)|
||[2.115]*|[2.094]*|[2.236]|[2.210]|
||{2.097}*|{2.068}*|{2.100}|{2.053}*|
|Daughter Dummy|-74.1|-69.2|-65.2|-58.5|
||(8.694)***|(8.719)***|(9.700)***|(9.729)***|
||[9.920]***|[9.122]***|[9.454]***|[8.760]***|
||{13.59}***|{13.40}***|{15.46}***|{15.11}***|
|Intercept|426.9|463.7|461.0|507.7|
||(5.420)***|(8.892)***|(5.882)***|(9.728)***|
|---|---|---|---|---|
||[13.84]***|[14.70]***|[14.66]***|[16.35]***|
||{31.18}***|{43.40}***|{32.70}***|{45.84}***|
|No. of Children||-17.0||-21.6|
|||(3.393)***||(3.749)***|
|||[7.615]||[7.554]***|
|||{16.69}||{17.29}|
|No. Observations|37144|37144|32499|32499|

Notes: (1) The data used are IHDS 2005 and NSS 1995 respectively. (2) Robust standard errors in parentheses; standard errors clustered at district-level in square brackets; standard errors clustered at state-level in braces; *** p<0.01, ** p<0.05, * p<0.1.
**Table A3.CR:  Father's Education and Educational Expenditure on Children**

|||**RURAL**<br>**CFPS**<br>|**CHINA**<br>**2010**<br>||
|---|---|---|---|---|
||**(6-22) Yea**|**rs Children**|**(8-23) Yea**|**rs Children**|
|Father's Sch.|105.5|79.6|115.7|85.6|
||(12.8)***|(12.1)***|(15.0)***|(14.0)***|
||[15.3]***|[14.1]***|[17.5]***|[15.6]***|
||{18.7}***|{15.3}***|{20.7}***|{14.8}***|
|Father's Sch. * Daughter|-31.8|-31.2|-21.7|-21.7|
|Dummy|(17.3)*|(16.6)*|(20.9)|(20.0)|
||[18.9]*|[17.8]*|[21.6]|[19.8]|
||{21.0}|{16.9}*|{23.2}|{16.5}|
|Daughter Dummy|151.6|240.3|111.2|275.2|
||(103.1)|(100.6)**|(120.7)|(117.1)**|
||[116.9]|[110.3]**|[132.5]|[121.1]**|
||{147.9}|{126.6}*|{168.4}|{135.9}*|
|Intercept|648.0|1939.7|705.7|2173.6|
||(71.0)***|(117.9)***|(83.3)***|(132.7)***|
||[88.1]***|[171.4]***|[100.0]***|[186.5]***|
||{86.4}***|{229.6}***|{87.9}***|{246.5}***|
|No. of Children||-716.8||-838.0|
|||(49.7)***||(56.8)***|
|||[87.2]***||[100.1]***|
|||{123.2}***||{141.5}***|
|No. Observations|4326|4326|3632|3632|

Notes: (1) The data used are CFPS 2010. (2) Robust standard errors in parentheses; standard errors clustered at county-level in square brackets; standard errors clustered at province-level in braces; *** p<0.01, ** p<0.05, * p<0.1.