metadata: authors: 0: author: Ahsan,Md Nazmul
1: author: Emran,M. Shahe
2: author: Shilpi,Forhad J.
count: Indonesia
docna: 0: docna: The Rural-Urban Divide and Intergenerational
            Educational Mobility in a Developing Country : Theory and
            Evidence from Indonesia
docty: Policy Research Working Paper
subtopic: Educational Sciences,Education Finance,Economics of Education,Rural Labor Markets,Labor Markets,Macro-Fiscal Policy,Economic Adjustment and Lending,Public Finance Decentralization and
            Poverty Reduction,Public Sector Economics
teratopic: Macroeconomics and Economic Growth,Social Protections and Labor,Rural Development,Public Sector Development,Education
abstracts: cdata!: This paper provides an analysis of the
            rural-urban divide in intergenerational educational mobility
            in Indonesia with two distinguishing features. First, the
            estimating equations are derived from theory incorporating
            rural-urban differences in returns to education and school
            quality, and possible complementarity between parent’s
            education and financial investment. Second, the data are
            suitable for tackling the biases from sample truncation due
            to coresidency and omitted cognitive ability heterogeneity.
            The evidence rejects the workhorse linear intergenerational
            educational persistence equation in favor of a convex
            relation in rural and urban Indonesia. The rural-urban
            relative mobility curves cross, with the children of low
            educated fathers enjoying higher relative mobility in rural
            areas, while the pattern flips in favor of the urban
            children when the father has more than nine years of
            schooling. However, the rural children face lower absolute
            mobility across the whole distribution of father's
            schooling. Estimates from the investment equation suggest
            that, in urban areas, children~^!!^s peers are complementary
            to financial investment by parents, while the adult role
            models are substitutes. In contrast, separability holds in
            villages. Peers and role models are not responsible for the
            convexity in both rural and urban areas, suggesting more
            efficient investment by educated parents as a likely
            mechanism, as proposed by Becker et al. (2015, 2018). The
            theoretical relation between the intercepts of the mobility
            and investment equations helps in understand whether school
            quality is complementary to or a substitute for parental
            financial investment. This paper finds evidence of
            substitutability, implying that public investment to improve
            the quality of rural schools is desirable on both equity and
            efficiency grounds.
geo_reg_key: 517198,517191
repnme: repnme: The Rural-Urban Divide and
            Intergenerational Educational Mobility in a Developing
            Country : Theory and Evidence from Indonesia
display_title: The Rural-Urban Divide and
            Intergenerational Educational Mobility in a Developing
            Country : Theory and Evidence from Indonesia
listing_relative_url: /research/2020/11/32550156/rural-urban-divide-intergenerational-educational-mobility-developing-country-theory-evidence-indonesia
topicv3: Labor Markets m1326488 855,Government Expenditure m1326649 1112,Education m1327048 470,Private Education m1327271 1490,Returns to Education m1327513 2174
publishtoextweb_dt: 2020-11-03T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Social Protections and Labor,Rural Development,Public Sector Development,Education
origu: DEC-Sustainability & Infrastruct (DECSI)
no_of_pages: 54
author_keys: 0: author_key: 84831
model_extractions: Policy Research Working Paper 9464 The Rural-Urban Divide and Intergenerational Educational Mobility in a Developing Country Theory and Evidence from Indonesia _Md Nazmul Ahsan M. Shahe Emran Forhad Shilpi_ Development Economics Development Research Group November 2020
Policy Research Working Paper 9464

# **Abstract**

This paper provides an analysis of the rural-urban divide in intergenerational educational mobility in Indonesia with two distinguishing features. First, the estimating equations are derived from theory incorporating rural-urban differences in returns to education and school quality, and possible complementarity between parent’s education and financial investment. Second, the data are suitable for tackling the biases from sample truncation due to coresidency and omitted cognitive ability heterogeneity. The evidence rejects the workhorse linear intergenerational educational persistence equation in favor of a convex relation in rural and urban Indonesia. The rural-urban relative mobility curves cross, with the children of low educated fathers enjoying higher relative mobility in rural areas, while the pattern flips in favor of the urban children when the father has more than nine years of schooling. However, the rural children face lower absolute mobility across the whole distribution of father’s schooling. Estimates from the investment equation suggest that, in urban areas, children’s peers are complementary to financial investment by parents, while the adult role models are substitutes. In contrast, separability holds in villages. Peers and role models are not responsible for the convexity in both rural and urban areas, suggesting more efficient investment by educated parents as a likely mechanism, as proposed by Becker et al. (2015, 2018). The theoretical relation between the intercepts of the mobility and investment equations helps in understand whether school quality is complementary to or a substitute for parental financial investment. This paper finds evidence of substitutability, implying that public investment to improve the quality of rural schools is desirable on both equity and efficiency grounds.

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
# **The Rural-Urban Divide and Intergenerational Educational Mobility in a Developing Country: Theory and Evidence from Indonesia**

**Md Nazmul Ahsan**<sup>1</sup> Saint Louis University

**M. Shahe Emran** IPD, Columbia University

**Forhad Shilpi** World Bank

**Keywords:** Intergenerational Educational Mobility, Rural-Urban Divide, complementarity, Convexity, Returns to Education, School Quality, Peer and Role Model Effects, Coresidency, Sample Truncation, Ability Heterogeneity

**JEL Codes:** J62, O12

> 1We would like to thank Hanchen Jiang for helpful discussions. Emails for correspondence: ahsanm@slu.edu, shahe.emran.econ@gmail.com, fshilpi@worldbank.org. Standard disclaimers apply.
# **(1) Introduction**

Economic liberalization in the 1980s and 1990s resulted in increasing inequality in many developing countries (World Development Report 2006). Intra-country spatial inequality also increased in most cases, with an increasing gap in living standards between rural and urban households (Kanbur and Venables (2005)).<sup>2</sup> Using Demographic and Health Survey (DHS) data on 65 countries, Young (2013) finds that rural-urban inequality accounts for 40 percent of the mean country inequality and much of the cross-country variation. To what extent the observed inequality is due to the roots of intergenerational persistence in economic status is an important question for the policymakers. It is thus surprising that there is little research on the rural-urban differences in intergenerational mobility in developing countries. Most of the existing studies focus exclusively on urban areas, and a comparative analysis of rural vs. urban areas remains relatively unexplored.<sup>3</sup> We provide a theoretically grounded empirical analysis of the rural-urban divide in intergenerational educational mobility in Indonesia in the 1990s and 2000s.<sup>4</sup> Inequality in Indonesia increased dramatically over this period: the consumption Gini rose from 29.2 in the 1990s to 38.9 in the 2000s. There are important rural-urban differences: inequality is lower in the rural areas, and the rise in inequality from the 1990s to 2000s has also been less pronounced compared to the urban areas (Kanbur and Jhuang (2014)). A link between higher inequality and lower intergenerational mobility has been the focus of a growing literature on the Great Gatsby Curve (Corak (2013), Fan et al. (2020), Neidhofer et al. (2018)). Does the _higher_ level of inequality in the urban areas imply that there is a “rural bias” where urban children face _lower_ educational (and economic) mobility compared to

> 2In Indonesia, the rural-urban gap in per capita monthly household expenditure increased from 12,991 rupiahs in 1984 to 18,005 rupiahs in 1996 (deflated by food price deflator, see Friedman (2005)). The rural-urban divide has been the focus of a long literature in development economics, from Lewis model to Kuznet’s inverted-U process of inequality, to political economy analysis highlighting “urban bias” (Lipton (1975))) in public goods allocation and “price scissors” (Sah and Stiglitz (1987)) designed to extract surplus from the rural areas in the 1960s and 1970s.

> 3Among the few available studies, see Iversen et al. (2017) on rural-urban differences in occupational mobility, and Emran and Shilpi (2015), and Asher et al. (2018) on rural-urban educational mobility in India. However, the estimating equations in these studies are not derived from a theoretical model.

> 4The focus on education is motivated primarily by the role played by skill premium in rising inequality, and an emphasis on educational mobility as the key to tackling economic inequality (Goldin and Katz (2008), Stiglitz (2012), Autor (2014)).

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the rural children, as the logic of the Great Gatsby Curve seems to suggest?

The empirical analysis is based on the estimating equations derived from an extension of Becker et al. (2015)’s model to incorporate the rural-urban differences in returns to education and school quality. The close link between the theory and empirical work allows us to explore the economic mechanisms in a consistent manner which distinguishes this paper from much of the existing literature on intergenerational educational mobility in developing countries.<sup>5</sup> The returns to education are usually higher in the urban areas because the manufacturing and services activities are more skill intensive and may give rise to agglomeration externalities.<sup>6</sup> Similar to the classic analysis of Becker and Tomes (1986) and Solon (2004), higher returns to education for parents strengthen the impact of family background on children’s educational opportunities in our model. The recent evidence on Indonesia shows that the rural schools remain at a substantial disadvantage in terms of teacher quality, teacher absenteeism, and school infrastructure during our study period (see World Bank (2016), Echazarra and Readinger (2019)).<sup>7</sup> An important policy question in this regard is whether public investment in rural schools would be effective in improving intergenerational mobility. As discussed by Becker and Tomes (1986), and Becker et al. (2015), the equity and efficiency effects of public educational investment depend critically on whether it is complementary to or a substitute for private educational investment by parents, and understanding the nature of this interaction is an important goal of our study.

The theoretical model delivers a quadratic estimating equation for intergenerational mobility similar to that of Becker et al. (2015)), with the linear conditional expectation function (CEF) widely used in the current literature as a special case.<sup>8</sup> Following Becker et al. (2015, 2018), an important feature of the model is complementarity of parent’s ed-

> 5Our model is different from that of Becker et al. (2015) in terms of the nature of the credit market imperfections. Becker et al. (2015) assume that the poor parents pay a higher interest rate for educational loans, but they can borrow as much as needed. Following Becker and Tomes (1986) and Solon (2004), we assume that there is no credit market for financing education of children, and the parents pay from their own income. We believe that, in the context of developing countries, our assumption is more realistic.

> 6For evidence of higher skill intensity in urban Indonesia, see World-Bank (2016).

> 7In Indonesia, the roots of urban bias in school quality go back to the Dutch colonial policies that allocated most of the educational budget to urban schools catering to the children of elite Dutch and Chinese households, and the rural schools (desa schools) were neglected (Frankema (2014)).

8All of the published empirical studies on intergenerational educational mobility we are aware of estimate a linear conditional expectation function (CEF).

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ucation with financial investment in the education production function of children. This complementarity may reflect peer and role model effects in addition to more efficient investment by educated parents, and can give rise to a convex CEF. Unlike the standard linear model, relative mobility in our model depends on parent’s schooling level, and the urban and rural relative mobility curves can cross. The approach developed in this paper is of wider interest as it can be applied to household survey data from other developing countries.

For the empirical analysis, we take advantage of the rich household panel data from the Indonesia Family Life Survey (IFLS) to make progress on two major issues highlighted in the literature: (i) truncation bias due to coresident sample, and (ii) omitted variables bias due to ability heterogeneity. An important data constraint on the analysis of intergenerational mobility in developing countries is truncation bias caused by coresidency restrictions in defining household membership in surveys (see Emran et al. (2018)). The IFLS data do not suffer from any significant truncation as the survey collected information on nonresident parents of any household member older than 15.<sup>9</sup> A second important advantage of the IFLS 2014 data used in this paper is that good quality measures of cognitive ability are available which allows us to control for ability heterogeneity across children in the regressions. Our main analysis of intergenerational mobility is based on the 18-40 years old children in the 2014 wave of IFLS who went to school in the 1990s and 2000s. We use the earlier rounds of the panel data (1993, 1997, 2000, 2007) to understand the effects of parent’s education on financial investment in children’s schooling. Another important part of our empirical analysis is the estimates of returns to education at the household level in rural vs. urban areas.<sup>10</sup> The availability of 5 rounds of panel data on household consumption expenditure allows us to provide estimates for both the parental and children’s generations.

The main conclusions from the empirical analysis are as follows. First, the CEF is convex in both rural and urban Indonesia, rejecting the work-horse linear model used in the existing literature. The estimates of relative mobility show contrasting rural-urban pattern:

> 9For a discussion on the advantages of the IFLS data for studying intergenerational mobility in Indonesia, see Mazumder et al. (2019).

> 10The returns to education here relate to a household’s permanent income, not only the labor market returns in a given year as is the case in the Mincerian literature. See below the discussion in section (6.1).

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while the children from low educated households enjoy higher relative mobility in the rural areas, the pattern flips at the right tail of father’s education distribution, with 9 years of father’s schooling as the bifurcation point. The pattern of relative mobility is thus much more nuanced than the simple negative relation between inequality and mobility posited in the Great Gatsby Curve. The rural children, however, face lower absolute mobility across the distribution of parental schooling.<sup>11</sup> The evidence shows that returns to education measured in terms of household income are higher in the urban areas, and this is true for both the parent’s and children’s generations. Higher returns to education in the _parent’s generation_ seem to be an important factor underlying the observed higher intergenerational schooling persistence in the urban areas. The estimates of the intercepts of the mobility and investment equations provide strong evidence in favor of the hypothesis that parental investment is a substitute for school quality in Indonesia. This suggests that government expenditure to improve school quality in rural Indonesia is likely to be an effective policy tool on both equity and efficiency grounds.

Our analysis of the sources of convexity in the mobility CEF shows that peer effect is complementary to parental investment in the urban areas, but it is not responsible for generating the convexity in the mobility equation. In the rural areas, the interaction between peer effect and financial investment is not significant, suggesting separability. Better educated peers weaken the impact of family background on children’s educational attainment in both the urban and rural areas. The role models, in contrast, are substitutes of financial investment in the urban areas, and separable in the rural areas. Similar to the peer effect, better educated role models weaken the impact of father’s education on children’s schooling attainment, both in rural and urban areas. It is important to appreciate that the empirical conclusions discussed in this paper are unlikely to be driven by biases arising from heterogeneity in cognitive ability, as we control for quadratic effects of children’s cognitive ability in all the regressions.

The extended Becker-Tomes model provides an explanation for these contrasting effects of peers and role models in the investment vs. mobility equations where the degree of 11This is in sharp contrast to the conclusion one gets from the standard linear model. The estimates from the linear CEF implies that all rural children enjoy higher relative mobility.

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diminishing returns to financial investment in the education production function plays a critical role. The evidence that peer and role model effects do not generate the convexity in the mobility equation suggests more efficient investment by educated parents as a likely source of convexity as emphasized by Becker et al. (2015, 2018).

The rest of the paper is organized as follows. Section (2) provides a brief discussion on the related literature with a focus on work on developing countries, and on Indonesia in particular. Section (3) develops the extension of the Becker et al. (2015) model with selffinance constraint on financing children’s education and derives the estimating equations for intergenerational persistence and optimal parental investment. Section (4) discusses the data with a focus on the issues of sample truncation due to coresidency and the construction of a cognitive ability index using three measures of ability in IFLS 2014. The next section presents the estimates for the mobility equation. Section (6) is devoted to understanding the economic forces at work behind the rural-urban divide in educational mobility. Section (7) explores the role of peer and role model effects in the convexity of mobility equation. The paper concludes with a summary of the results and highlights the portability of the model and methods developed here to other developing country analysis.

# **(2) Related Literature**

The literature on intergenerational economic mobility in developed countries is vast, with fundamental theoretical and empirical contributions, from Becker-Tomes (1979, 1986), to Solon (1992), to Chetty et al. (2014) are some of the seminal studies. Most of the studies focus on intergenerational persistence in permanent income between father and son. An important finding from this literature is that rich panel data on income for many years from appropriate phases of the life-cycle are required to get credible estimates of intergenerational persistence in permanent income (Solon (1992), Mazumder (2005)). For excellent surveys of this literature see, Solon (1999), and Black and Devereux (2011).

The literature on developing countries is limited, with increasing interest in the last few years (see Iversen et al. (2019) and Emran and Shilpi (2019) for recent surveys). The required panel data on income are not available in most of the developing countries, and as a result, the focus of the literature has been on educational linkages across generations (see, 5
among others, Neidhofer et al. (2018), Azam and Bhatt (2015), Emran and Shilpi (2015), Hertz et al. (2008), Thomas (1996)). Among the few contributions on income mobility, see Fan et al. (2020) on China. The recent analysis of intergenerational occupational linkages in developing countries includes Bossuroy and Cogneau (2013), Emran and Sun (2015) and Emran and Shilpi (2011).

The literature on intergenerational mobility in Indonesia is small, with only a handful of studies available. We are aware of three studies on Indonesia that can be broadly classified as dealing with intergenerational issues in education, and all of them study the effects of the same policy experiment: a large scale school construction program in the 1970s, originally studied by Duflo (2001).<sup>12</sup> Hertz and Jayasundera (2007) analyze the effects on IGRC in schooling for the children, and find that the exposure to new schools weakened the intergenerational persistence for men, but not for women. In a recent paper, Mazumder et al. (2019) focus on the long-term effects of the program on the second generation children, i.e., children of those who benefited from the school construction when they were children themselves. Since most of these second generation children have not completed their schooling, it is difficult to estimate IGRC in schooling attainment. They thus focus on the academic performance of the children which would be correlated with the final educational attainment of a child. They show that the children of the mothers exposed to the large scale school construction in the 1970s had significant gains in school examination scores. But they do not find any effects of the fathers. In a related paper, Akresh et al. (2018) study the effects of school construction on the socioeconomic well-being of the first generation directly exposed to the program and the intergenerational effects on school attainment using the SUSENAS 2016 cross section data.

# **(3) Rural vs. Urban: A Model of Intergenerational Educational Mobility**

We consider an economy consisting of two-person households with the parent and a child. The parent of child _i_ has education level _Ei_<sup>_p_(yearsofschooling).FollowingSolon</sup>

> 12The main impact of the program was on the cohorts who went to school in the early 1970s.

6
(2004) and Becker et al. (2015, 2018), parent’s income is determined as follows: So the returns to education is _R_<sup>_pj_</sup> in the parental generation in location _j_ = _r, u_ , with _r_ for rural and _u_ for urban. We assume that the parents with zero year of schooling earns _Y_ 0<sup>_p>_0.Thefocushereisonhowthehouseholdpermanentincomechangeswiththe</sup> education of the parent _Ei_<sup>_p_.The“returnstoeducation”herethusrefertoahousehold’s</sup> permanent income, not an individual’s labor market income in the survey year which has been the focus of the Mincerian literature on returns to education.

The parent allocates income _Yi_<sup>_p_betweenownconsumption</sup><sup>_C_</sup> _i_<sup>_p_andinvestmentinthe</sup> child’s education _Ii_ . The budget constraint is: An important assumption in this specification of the budget constraint is that there is no credit market where the parents can borrow to finance children’s education. This is a plausible assumption in the context of developing countries where the student loan market (public or private) is underdeveloped or nonexistent (Chapman and Suryadarma (2013)).

Following Becker et al. (2015), we assume that the education production function exhibits the following features: (i) diminishing returns to financial investment, (ii) complementarity between the financial investment and parental education, (iii) the direct effect of parent’s education capturing the non-financial aspects such as role model effects, and (iv) a higher ability of a child has an additively separable impact and also is complementary to financial investment. We augment the specification to allow for possible effects of a child’s ability on the curvature of the production function with respect to the financial investment by the parents.

_Ei_<sup>_c_=</sup><sup>_δ_0+</sup><sup>_α_1</sup><sup>_φi−α_2(</sup><sup>_φi_)2 + (1 +</sup><sup>_ω_1</sup><sup>_φi_)</sup><sup>_δ_</sup> 1<sup>_jIi−_(1</sup><sup>_−ω_2</sup><sup>_φi_)</sup><sup>_δ_</sup> 2<sup>_jI_</sup> _i_<sup>2+</sup><sup>_δ_</sup> 5<sup>_jIiE_</sup> _i_<sup>_p_+</sup><sup>_δ_</sup> 3<sup>_jE_</sup> _i_<sup>_p−δ_</sup> 4<sup>_j_(</sup><sup>_E_</sup> _i_<sup>_p_)2(3)</sup> 7
where _φi_ is the cognitive ability of the child, and we assume that _δ_ 0 _, δ_ 1<sup>_j, δ_</sup> 3<sup>_j>_0and</sup> _δ_ 2<sup>_j, δ_</sup> 4<sup>_j, δ_</sup> 5<sup>_j≥_0.The last inequalities are weak to allow for the possibility that over the relevant</sup> range the education production function is approximately linear in financial investment. This specification allows for a flexible effect of a child’s ability on the educational outcome; a higher ability is complementary to financial investment we have _ω_ 1 _, ω_ 2 _>_ 0, increasing the linear coefficient by a multiplier (1 + _ω_ 1 _φi_ ) and also lowering the quadratic coefficient by (1 _− ω_ 2 _φi_ ).<sup>13</sup> The specification adopted by Becker et al. (2015) is nested in this formulation: they assume that _α_ 2 = _ω_ 2 = 0. The direct effect of parental education can be either concave or linear which represents nonfinancial aspects of parental influences on children’s education such as home tutoring and role model effect.<sup>14</sup> The intercept term ( _δ_ 0) captures the common factors irrespective of location and thus is not indexed by _j_ .

There are two major sources of differences in rural vs. urban areas: (1) the returns to education ( _R_<sup>_pj_</sup> in equation (1) above) may be different because of differences in occupational and economic structure. The rural areas are engaged predominantly in agricultural activities, although the share of non-farm activities has increased substantially in many countries including Indonesia in the last few decades. The existing evidence suggests that returns to education in agriculture is low, especially beyond secondary schooling (Kurosaki and Khan (2006)), Phillips (1994).<sup>15</sup> While returns to education in nonfarm occupations in villages are usually higher, they may still be lower than the returns to education in urban areas specializing in modern manufacturing and services activities. (2) The quality of schooling is likely to be different across rural vs. urban locations. The rural areas might be primarily served by government schools and (some) low-quality private schools (Febriana et al. (2018)). The costs incurred by the parents are much less for the public schools compared to the private schools, and, as a result, the role parent’s income can play may be more limited in this case.<sup>16</sup> The high-cost private schooling is likely to be much

> 13In this formulation, substitutability implies that _ω_ 1 _, ω_ 2 _<_ 0.

> 14Becker et al. (2015) are agnostic about whether the direct impact is concave or convex. We believe in the context of a developing country, it is perhaps more likely that it is concave.

> 15Based on a meta analysis, Phillips (1994) reports an yearly rate of return of 1.60 percent. Kurosaki and Khan (2006) find that returns fall sharply after primary schooling in rural Pakistan.

> 16According to the compulsory schooling law in Indonesia, schooling must be provided by government free of costs to every citizen. However, the compulsory education law allowed “voluntary contributions” by

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better developed in urban areas making the impact of parental income more important. To capture these differences in the supply side of the education provision, we allow for the effects of financial investment to vary with the quality of schools, denoted as _q_ , with a higher value implying a better quality. In particular we assume the following: It is important to note that we do not impose any a priori restrictions on the signs of the parameters _μ_ 1 and _μ_ 2. When parental investment is complementary to school quality, we have _μ_ 1 _>_ 0and _μ_ 2 _>_ 0, and in this case, a higher school quality (a higher _q_ ) increases the marginal effect of parental financial investment by increasing the magnitude of the linear coefficient _δ_ 1<sup>_j_andloweringthestrengthofdiminishingreturnsascapturedbythe</sup> quadratic coefficient _δ_ 2<sup>_j_.Incontrast,whenprivateinvestmentisasubstituteforschool</sup> quality, we have _μ_ 1 _<_ 0and _μ_ 2 _<_ 0. For example, if the quality of school instructions is low and parents need to hire private tutors, then we would expect that investments by parents are substitutes.<sup>17</sup> The income function for the children is: Again, the returns to education is location specific; when returns to education is lower in rural areas, we expect _R_<sup>_cu_</sup> _> R_<sup>_cr_</sup> .

The consumption sub-utility function of the parent is given by: the parents which, in practice, resulted in schools effectively charging some fees. However, the important point for our analysis is that the costs in public schools are much less. The observation that “free schooling” may not be really free is of wider relevance in developing countries. Emran et al. (2020a) show that, in Bangladesh, the poor parents end up paying bribes for admission into “free” public schools while the rich do not pay because of their higher bargaining power.

> 17When school quality is a substitute for parental investment, an increase in government expenditure on school quality (better teachers, books in the school library etc.) would increase investment on the children from the more credit-constrained disadvantaged households.

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

The parent’s optimization problem is (denoting the Lagrange multiplier on the budget constraint by _λ_ ): where _σ_ is the degree of parental altruism, and parents use production function (4) to estimate the expected income of children _E_ ( _Yi_<sup>_c_).</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 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_= 0)</sup><sup>_,_andthereisnocomplementarity(</sup><sup>_δ_5= 0).</sup>

# **(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 (8) above.

10
Since optimal investment _I_<sup>_∗_</sup> is a linear function of parental education _E_<sup>_p_</sup> , _E_<sup>_c∗_</sup> is a quadratic function of parental education _E_<sup>_p_</sup> even when _δ_ 4<sup>_j_=0,</sup><sup>_δ_</sup> 2<sup>_j_=0</sup><sup>_δ_</sup> 5<sup>_j_=0.</sup> The estimating equation for intergenerational persistence implied by equations (8) and (11) above is as follows: where

# **(3.3) Discussion**

The above model has three notable features. First, the coefficients on parental education depend on the ability of a child _φi_ when the marginal effect of investment is a function of the child’s ability. In this case, the standard OLS estimates of intergenerational persistence provide an average of the underlying heterogeneous effects. Most of the discussion on ability bias in the literature on intergenerational mobility in developing countries assumes that the unobserved ability enters the estimating equation in an additively separable way, but, to our knowledge, this assumption is not tested. Since we have good quality data on the ability of children, we are able to check whether the widely-used assumption that there is no significant interaction between ability and returns to investment is supported by data in Indonesia. Second, following Becker et al. (2015), the intergenerational persistence equation can be concave or convex. An important source of convexity in the model is the interaction effect between father’s education and financial investment. Becker et al. (2015, 2018) emphasize that the interaction effect captures the fact that educated parents are more efficient in choosing the right kind of investment in a complex education market. They also suggest that the interaction effect can arise from peer and role model effects. An important goal of our empirical analysis below is to understand the roles of these factors in any observed convexity in intergenerational schooling persistence, i.e., when _ψ_ 2<sup>_j>_0</sup><sup>_._Next</sup> we explore this question in more detail.

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# **(3.4) Peers and Role Models as the Sources of the Interaction Effect**

Spatial sorting is primarily responsible for peer and role model effects as the educated parents locate in better neighborhoods which exposes the children to better peers and role models. The peers are defined as a reference group of children defined in terms of an age band around a child’s age. Peers with higher academic aspiration may stimulate a positive competitive environment for children and induce a child to work hard and the parents to invest more in children’s education. More educated adults as role models can influence the children in a number of ways. First, they can influence a child’s preference and also make him/her more confident about own ability.<sup>18</sup> Second, adults with higher education than the parents of a child in the neighborhood may help the parents to choose more efficient investment in education. However, we emphasize that the effects of peers or (adult) role models may also be substitutes for private expenditure by the parents on children’s education. For example, when the higher educated adults in the neighborhood effectively become free home tutors to supplement the school instructions, it reduces the need for parents to spend money on professional private tutors (for evidence of such neighborhood tutoring by more educated adults in Indonesia, see Yulianti et al. (2019)).

When the convexity of the mobility CEF found in the data is due to factors other than the efficiency in investment choices by the parents, the specifications for both the investment equation (8) and mobility equation (12) changes. Denote the average education of the reference group _k_ by _E_<sup>_k_</sup> _,_ with _k_ = _g_ (peer group) and _k_ = _m_ (role models). We consider the following modified education production function that allows for direct effects of peers or role models in addition to any complementarity (or substitutability) with the financial investments made by the parents: The resulting investment equation is as follows (ignoring the _j_ superscript for simplicity)

> 18Durlauf (2000) defines role model as the influence of characteristics of older members on the preferences of younger members, and Manski (1993) and Streufert (2000) define it as the observations on older members whose choices reveal information relevant for the choices of the younger members. In this paper, we take a broader perspective that encompasses both of these definitions.

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: where Equation (16) has two important testable implications. First, the estimate of _θk_ is sufficient to test complementarity ( _δ_ 6<sup>_k>_0) vs.substitutability (</sup><sup>_δ_</sup> 6<sup>_k<_0) because the sign of</sup> _θk_ is same as the sign of _δ_ 6<sup>_k_.Second,themagnitudeoftheimpactofpeersandrolemodels</sup> should differ across rural and urban areas because of differences in returns to education in the children’s generation ( _R_<sup>_c_</sup> ). This follows from the observation that the sign of<sup>_∂θk_is</sup> _∂R_<sup>_c_</sup> the same as the sign of _δ_ 6<sup>_k_.</sup> The corresponding intergenerational persistence equation is given by: where An important insight is that it is possible to have a negative coefficient on the interaction of father’s education with the peer’s (role model’s) education even when both father’s education and peer’s (role model’s) education are complementary to financial investment, because we can have _ψ_ 3<sup>_k_=</sup><sup>_δ_5</sup><sup>_θk_+</sup><sup>_δ_</sup> 6<sup>_kθp−_2</sup><sup>_δ_2</sup><sup>_θkθp<_0evenif</sup><sup>_δ_5</sup><sup>_>_0and</sup><sup>_δ_</sup> 6<sup>_k>_0.Thus,</sup> we cannot rule out complementarity even when peers or role models reduce the impact of father’s education on children’s schooling attainment, i.e., when _ψ_ 3<sup>_k<_0.Thelitmustest</sup> for whether the peer or role model effect is due to complementarity is its impact on the financial investment: _θk >_ 0 implies that _δ_ 6<sup>_k>_0(seeequation(16)).Thedirecteffectsof</sup> peers as captured by the parameters _δ_ 7 , _δ_ 8 in the production function would show up in 13
the mobility estimates, with no impact in the investment equation.

# **(4) Measures of Mobility and Data**

# **(4.1) Measures of Relative and Absolute Mobility**

The most widely used measure of relative mobility in the current literature is the intergenerational regression coefficient (IGRC) which is estimated as the slope parameter of a linear CEF. When the CEF is not linear, relative mobility depends on the level of parental education. We estimate the intergenerational marginal effect (IGME) across the distribution of father’s education and plot these IGME lines for rural vs. urban samples. Denoting the OLS estimate of a parameter with a hat, the IGME is defined as follows (Emran et al. (2020)): where _IGMEk_ is the intergenerational marginal effect when the father has _k_ years of schooling. Thus, relative mobility is lower (higher) at higher levels of parental education when the CEF is convex (concave).

As a measure of absolute mobility, we use expected years of schooling conditional of father’s schooling, denoted as _ESk_ when the father has _k_ years of schooling: Absolute mobility thus depends on both the slope and the intercept estimates of the intergenerational persistence equation (12) above. This definition of absolute mobility is similar to the one adopted by Chetty et al. (2014). There is a different measure of absolute mobility used by many authors where the focus is on whether the children achieve more schooling than their parents. This alternative definition may, however, not be of appropriate for understanding intergenerational educational mobility in the context of developing countries where a significant proportion of parents have zero schooling (for more details on this point, please see Emran and Shilpi (2019)).

While the _IGMEk_ and _ESk_ estimates provide a more realistic picture of intergenerational mobility when the CEF is not linear, it might be useful to have a summary statistic 14
that can answer questions like is relative educational mobility higher or lower in the rural areas? To this end, we calculate weighted IGME (henceforth WIGME) and weighted ES (henceforth WES): where _πk_ is the proportion of children in our sample with father having _k_ years of schooling.

# **(4.2) Data and Variables**

We use panel data from the Indonesia Family Life Survey (IFLS) for our analysis of educational persistence across generations in rural and urban areas in Indonesia. The first wave of IFLS was fielded in 1993, and the second, third, fourth and fifth waves were fielded in 1997, 2000, 2007 and 2014, respectively. At the time of the first wave, 7,224 households were interviewed and it represented 83 % of the national population of Indonesia covering 13 of the 27 provinces (Frankenberg et al., 1995). In the subsequent waves, the sample size grew because others joined the sampled households either through marriage or births.

Our focus is on the children of 18-40 years age cohorts in IFLS 2014 wave. This is motivated by three factors. First, we are interested in intergenerational educational persistence in rural vs. urban Indonesia during the 1990s and 2000s, and most of the children in the 18-40 age cohorts went to school during this period. Second, we can use the earlier rounds of IFLS to estimate the investment equation (8) above for most of these age cohorts which allows us to understand the role played by economic forces such as returns to education and school quality in the observed rural-urban differences in intergenerational educational mobility. Third, only the 2014 wave contains data on Raven’s scores for all adults which is necessary for our analysis of the biases from unobserved ability heterogeneity.

Returns to education for parents determine the gradient of household permanent income with respect to educational differences across households. The existing literature on returns to education provides estimates of labor market returns, and may capture only a small part of household permanent income we are interested in. To address this issue, we take advantage of the panel data on consumption expenditure in the first 3 rounds to calculate 15
a measure of household permanent income in the parental generation, and we estimate returns to education equation (1) above using this measure of permanent income. For returns to education at the household level in children’s generation, we use the household expenditure data from the last two waves (2007 and 2014).

An important data issue for estimating intergenerational mobility is sample selection bias that arises from the fact that many of the existing household surveys such as LSMS and DHS include information on only those household members coresident at the time of the survey. The criteria used for household membership may vary, but when nonresident parents or children are not included in a survey, it can cause substantial biases in the estimates of intergenerational persistence in education. We utilize the household roster, nonresident parents module, and mothers’ marriage module to gather the education information on fathers and children. For details, please see the online appendix on data.

We use the Raven test scores and two memory tests to construct an index of cognitive ability. An advantage of these measures is that they do not require any knowledge of numeracy or literacy to do well in the tests. For a detailed discussion on the construction of the cognitive ability index, please see pp. 18-19 in section (5.1) below. Table 1 provides the summary statistics for our various estimation samples, separately for rural and urban areas. In our “mobility sample”(18-40 years old children in 2014 wave), the average education of rural fathers is 5.66 years, and 7.54 years for urban fathers. The rural children attain 9.05 years of schooling, while the urban children acquire more than a year more schooling at 10.18 years on average. The household income and education expenditure are expressed in the units of 10,000 rupiahs and are deflated by rural and urban average rice prices in each wave of the survey. In the education expenses sample (pooled 1993, 1997, 2000, 2007), the average educational expenditure by rural households is 0.64, and it is more than twice as high in the urban households at 1.51. The household average expenditures in the parental generation (using 1993, 1997, and 2000 waves) are 199.32 for rural areas, and 334.79 in the urban areas. The summary statistics thus provide a vivid picture of the rural-urban divide in Indonesia.

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# **(5) Empirical Evidence**

# **(5.1) Estimates of the Intergenerational Persistence Equations**

We begin with the estimates of the intergenerational educational persistence equation; Table 2 reports the estimates (please see the upper panel). The estimation sample includes the age cohorts 18-40 years in 2014. All the estimated standard errors reported in this paper are clustered at the primary sampling unit.

The first two columns report the estimates from a linear CEF. These estimates are useful as a benchmark comparable to other estimates available in the literature. With linearity a maintained assumption, the estimates suggest that the rural children enjoy higher relative mobility: the IGRC estimate is 0.38 in rural areas, while it is 0.43 in the urban areas (the difference is significant at the 1 percent level). This seems to contradict the perception that the children in rural areas face lower mobility. These conclusions, however, may not be valid if the maintained assumption of linearity is rejected by the data.

The estimates of the parameters of the quadratic CEF in equation (12) are reported in columns (4) and (5) of Table 2 for rural and urban areas respectively. The evidence shows that the null hypothesis of a linear CEF (i.e., _H_ 0 : _ψ_ 2 = 0) is rejected at the 1 percent level for both the rural and urban households. The coefficient on squared father’s schooling is _positive_ across rural and urban areas, implying that the CEF is convex, with the degree of convexity substantially higher in the rural areas (the quadratic coefficient is 100 percent larger in the rural areas and the difference is significant at the 5 percent level).<sup>19</sup> The fact that the CEF is much more convex in the rural areas suggests that the forces of complementarity may be stronger in the rural areas. The estimates also show that ( _i_ ) there is no significant difference in the intercept estimates, and ( _ii_ ) the linear coefficient is larger in the urban areas (i.e., _ψ_ 1<sup>_u>ψ_</sup> 1<sup>_r_),andtherural-urbandifferenceisstatistically</sup> significant at the 5 percent level.

As noted in section (2) above, with a quadratic CEF, relative mobility depends on the level of father’s education, and intergenerational marginal effects (IGMEs) provide a measure of relative mobility in this case. The estimated IGMEs (based on equation (18)) 19This is in contrast to the recent evidence on India presented by Emran et al. (2020b) which shows that the CEF is concave.

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for a number of focal points of father’s schooling distribution are reported in the lower panel of Table 2. The estimates show that the children born to fathers with low education (less than 9 years) have higher relative mobility in rural areas, but the pattern flips in favor of urban children for the households with higher educated fathers (more than 9 years of schooling). In contrast, expected years of schooling, a measure of absolute mobility, is consistently higher in urban areas across the whole distribution of father’s schooling, although the rural-urban differences are small at the tails of father’s schooling distribution. The estimates of relative and absolute mobility using the _IGMEk_ (equation (18)) and _ESk_ (equation (19)) as the relevant measures highlight important aspects of the ruralurban divide in intergenerational educational mobility missed by the standard linear model. Perhaps the key finding is that relative mobility rankings are opposite in the two tails of the father’s schooling distribution, in sharp contrast to the linear model that suggests higher relative mobility of rural children irrespective of father’s education level.

We provide estimates of weighted IGME (WIGME) and weighted ES (WES) as summary measures of intergenerational schooling mobility (see equations (20) above). The estimates of WIGME and WES are reported in the last row of Table 2. The estimated WIGME is 0.36 for the rural sample, and 0.42 for the urban sample. Having a father with one year more schooling thus translates into 0.36 year of additional schooling in the rural areas on average, and 0.42 year of additional schooling in the urban areas. The estimated WES are 9.07 (rural) and 10.18 (urban) implying that growing up in the rural areas results in the penalty of a one year less schooling for a child.

# **The Role of Cognitive Ability**

A central concern in the literature on intergenerational mobility is whether the observed persistence across generations in economic status is primarily a result of mechanical transmission of ability from parents to children, with little influence of the economic forces such as returns to education and school quality discussed in the theoretical model in section (2). The IFLS 2014 is especially suited to make some progress on this question in the context of a developing country because it collected high quality data on cognitive ability of children.

We construct a measure of cognitive ability of children as follows. First, we calculate the 18
first principal component of three measures of cognitive ability available in IFLS: Ravens test, and two memory tests. In the second step, we take out the differences in ability due to age differences (i.e., the Flynn effect) by regressing the first principal component on age and age squared and retrieve the residual from this regression. Third, we calculate the percentile rank of an individual in the distribution of the residual as the measure of ability. We include this percentile ability measure as our indicator of ability heterogeneity across children.

A simple but plausible approach to understand the importance and direction of ability bias in the estimates in Table 2 is to control for children’s cognitive ability (and its squared) in the regressions and check the sensitivity of the estimated parameters of interest. Recall that the theory allows for both additive separable and interaction effects of ability in the education production function. We thus employ a flexible specification of the intergenerational persistence equation where ability and its squared are interacted with both father’s education and its squared.<sup>20</sup> The estimates from this exercise are reported in the appendix Table A1: none of the interaction terms is significant at the 5 percent level, and this is true in both the rural and urban areas.<sup>21</sup> In contrast, the direct effects of ability and its squared are statistically significant at the 5 percent level in rural areas, while ability has a linear significant effect in urban areas. The coefficient of ability squared is negative in rural areas, suggesting that high ability children face diminishing returns in rural areas, but not in the urban areas. The magnitudes of both the linear and quadratic coefficients are larger in rural areas which indicate a stronger role for cognitive ability of children in villages where the quality of schools is likely to be poor.

The estimates of the linear and quadratic CEFs for intergenerational mobility with ability and its squared as controls are reported in Table 3. The standard linear CEF estimates in the first two columns of Table 3 show that the inclusion of the ability controls

> 20The education production function with ability heterogeneity in Becker et al. (2015) yields an estimating equation where ability enters quadratically and also there is interaction of ability with father’s education. In their specification, there is no interaction of ability with the squared father’s education. Another difference is that when the interaction of ability with father’s education is not significant, their specification implies that the effect of ability is linear. In the more flexible specification adopted here, we can have quadratic effect of ability even when the interaction effects are zero.

> 21Only 1 interaction term is significant at the 10 percent level.

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reduces the magnitudes of both the estimated slope and intercept which confirms that ability bias is positive, as widely argued in the literature. The effects of ability controls on the quadratic CEF estimates are as follows: (i) the intercept and linear coefficients are lower, and (ii) the estimated quadratic coefficient is not affected in a substantial way. More important for our analysis of rural-urban divide, the pattern of rural-urban differences in the estimated coefficients we found earlier in Table 2 without any ability controls remain intact: (i) there is no significant differences in the intercepts, (ii) the linear coefficient is larger in the urban areas, and (iii) the quadratic coefficient is smaller in the urban areas. The estimates of the relative and absolute mobility estimates in the lower panel also paint a picture largely consistent with what we found in Table 2 in the previous subsection.

# **(5.2) Estimates of the Investment Equation**

In the Becker-Tomes model, parent’s financial investment in education plays a prominent role in generating intergenerational persistence in economic status under the plausible assumption of imperfect credit markets. It is thus curious that none of the published studies on intergenerational educational mobility we are aware of provide estimates of the parameters of the investment equation (8) in section 2 above. To understand possible differences in the financial investment by parents in rural vs. urban areas, we estimate the following regression specification: where _D_<sup>_r_</sup> is the rural dummy taking on the value 1 for a household located in villages, and zero otherwise. The estimated parameters of equation (21) are related to the parameters in the investment equation (8) as follows: _θ_ 0<sup>_u_=</sup><sup>_ρ_0,</sup><sup>_θ_</sup> 1<sup>_u_=</sup><sup>_ρ_1,and</sup><sup>_θ_</sup> 0<sup>_r_=</sup><sup>_ρ_0+</sup><sup>_ρ_2,</sup> _θ_ 1<sup>_r_=</sup><sup>_ρ_1+</sup><sup>_ρ_3.</sup> We use the pooled sample from four earlier rounds of the IFLS panel data to estimate equation (21) above.<sup>22</sup> The estimates of the regression equation (21) are reported in Table 4; we report estimates from three specifications : the first column contains the estimates of equation (21) without any controls, the second column controls for the number of children in

> 22IFLS 2007 (wave 4), IFLS 2000 (wave 3), IFLS 1997 (wave 2) and IFLS 1993 (wave 1).

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a household, and the third column in addition controls for the ability index and its squared. The evidence is robust regarding the interaction of rural dummy with father’s education: it is consistently negative across the three specifications and statistically significant at the 1 percent level. The marginal effect of father’s education on the educational expenditure on a child is thus lower in the rural areas. The evidence on the intercept is also similar: the sign of the rural dummy is negative, and significant at the 1 percent level in all three specifications. As noted earlier the intercept term refers to the educational expenditure on the children of fathers with no schooling, and thus of special interest in our context as these households are likely to be the poorest. The evidence suggests that the education expenditure by the parents is lower in the rural areas across the whole distribution of father’s schooling.

# **(6) Understanding the Rural-Urban Divide: The Mechanisms**

The estimates of the investment equation and intergenerational persistence equations discussed above can be summarized in the following binary relations (using a hat to denote the OLS estimate of a parameter): An important economic mechanism through which intergenerational persistence in economic status operates is returns to education. If the extended Becker-Tomes model is a reasonable description of the mechanisms behind the differences in educational mobility in rural vs urban households, the differences in returns to education are expected to play an important role. As a first step to exploring the underlying economic forces at work, we thus estimate returns to education in the next subsection.

# **(6.1) Household-level Returns to Education**

As noted earlier in section (2), the concept of returns to education relevant here is 21
different from most of the available estimates in the literature, as we are interested in how household economic status vary with the education level of the father. Given that IFLS is a panel data set, we have household level income and consumption expenditure information for multiple rounds. To reduce the measurement error, we focus on the household consumption expenditure as a measure of economic status; it is widely-noted that expenditure suffers much less measurement error from transitory shocks because of consumption smoothing and thus is likely to be a more reliable indicator of a household’s economic status (see, for example, the discussion in Deaton (1997)).

The availability of 5 rounds of panel data allows us to provide estimates of returns to education for both the parental and children’s generations: we rely on the first three rounds (1993, 1997, 2000) for the father’s generation, and the last two rounds (2007 and 2014) for the children’s generation. For parents, we use the average of the 1993, 1997, and 2000 rounds of household expenditure (deflated by average rice price) data as a measure of household permanent income and estimate the income equation (equation (1) in the theoretical model in section (2)). The estimating equation for the fathers is given as follows: For the children, we take the average of the household expenditure in 2007 and 2014. The estimates are reported in Table 5. For parent’s generation, the intercepts are not different across rural and urban areas which can be interpreted as evidence that the rural-urban divide does not matter for the subset of households where the father has no schooling (about 5 percent of our sample). In contrast, the interaction of the rural dummy with the father’s education is negative and statistically significant at the 1 percent level. The evidence thus strongly suggests that returns to education at the household level was substantially lower in the rural areas. In terms of the parameters of the income equation (1) we have the following binary relations implied by the estimates in Table 5: _Y_<sup>ˆ</sup> 0<sup>_pr_</sup> = _Y_<sup>ˆ</sup> 0<sup>_pu_</sup> and ˆ ˆ _R_<sup>_pr_</sup> _< R_<sup>_pu_</sup> . The evidence on children’s generation also shows that the returns to education at the household level is substantially lower in the rural areas.

The lower returns to education in the rural areas affect intergenerational persistence in 22
economic status in three ways: (i) a lower returns for the rural parents improve relative educational mobility by reducing the sensitivity of parental investment, (ii) a lower returns for rural children has more complex effects through both the intercept and slope of the investment function, and (iii) lower returns results in double-squeeze on the income of rural residents; they not only get lower expected education conditional on father’s education, they also get lower income for a given level of education.

# **(6.2) School Quality and Parental Financial Investment: Are they Complementary or Substitutes?**

We develop an approach that relies on the estimates of the mobility intercepts _ψ_ ˆ0<sup>_r_=</sup><sup>_ψ_ˆ</sup> 0<sup>_u_</sup> � � along with with the evidence on the intercepts of the investment equation _θ_ ˆ0<sup>_r<θ_ˆ</sup> 0<sup>_u_</sup> . To � � see this, figure 1 plots the function _ψ_ 0<sup>_j_</sup> � _θ_ 0<sup>_j_</sup> � : Equation (25) above reflects the fact that we control for ability and ability squared in the regressions (Table 2), and the interactions of ability with financial investment are not significant in the empirical analysis (see online appendix Table A1). We draw two curves corresponding to the two levels of school quality ( _q_ 1 _> q_ 2), but which curve refers to higher quality depends on whether quality is a substitute of or complementary to parental financial investment. We also put a horizontal line to represent _ψ_<sup>ˆ</sup> 0<sup>_r_=</sup><sup>_ψ_ˆ</sup> 0<sup>_u._Now observe that if quality</sup> and financial investment are complementary, then the upper curve refers to the urban areas with higher quality, and this implies that the intercept of the investment equation must be smaller in the urban areas, which is rejected by the evidence. The evidence is consistent only with the case where parental investment and school quality are substitutes.

# **(6.3) Is Financial Investment Complementary to Parental Education?**

The evidence that _θ_<sup>ˆ</sup> 1<sup>_r<θ_ˆ</sup> 1<sup>_u_impliesthefollowinginequalityfromequation(10)above</sup> (again ignoring the interactions with ability given the evidence above): 23
The evidence on the returns to education in parental generation shows that _R_<sup>_pr_</sup> _< R_<sup>_pu_</sup> (Table 5) which is consistent with inequality (26). Lower returns to education for rural parents thus lead to a lower sensitivity of educational investment with respect to father’s education, improving relative mobility.

However, from the earlier analysis, we have two additional pieces of information. First, _δ_ 2<sup>_r< δ_</sup> 2<sup>_u_because school quality is lower in rural areas and parental investment is a substitute</sup> of school quality ( _μ_ 2 _<_ 0), and second, _R_<sup>ˆ</sup><sup>_cr_</sup> _< R_<sup>ˆ</sup><sup>_cu_</sup> (see Table 5). Lower returns to education for the children in the rural areas (i.e., _R_<sup>_cr_</sup> _< R_<sup>_cu_</sup> ) help satisfy inequality (26) if the following condition holds: _δ_ 5<sup>_j−_2</sup><sup>_δ_</sup> 2<sup>_jRpj>_0inboththeurban(</sup><sup>_j_=</sup><sup>_u_)andrural(</sup><sup>_j_=</sup><sup>_r_)areas.</sup> Because in this case, we have<sup>_∂θ_1</sup><sup>_>_0.</sup><sup>_Theinequalityδ_</sup> 5<sup>_j−_2</sup><sup>_δ_</sup> 2<sup>_jRpj>_0</sup><sup>_cannotbesatisfied_</sup> _∂R_<sup>_c_</sup> _if financial investment is a substitute of parental education, i.e., if δ_ 5 _<_ 0 _._ The inequality is satisfied only if they are complementary ( _δ_ 5 _>_ 0) and the strength of complementarity is strong enough. The evidence is thus consistent with complementarity between parental investment and father’s schooling in education production function as emphasized recently by Becker et al. (2015, 2018). In section (7) below, we discuss additional evidence in favor of the hypothesis that the convexity in the mobility equation is driven primarily by complementarity of parental education with financial investment arising from more efficient investment choices by higher educated parents.

# **(6.4) The Role of the Direct (non-financial) Effect of Parental Education**

The parameters of the mobility equation are determined not only by parent’s optimal financial investment, they also capture the direct effects of parents education. The estimates of the parameters of the mobility equation are thus especially useful in understanding the role played by nonfinancial channels of intergenerational educational persistence. The quadratic coefficients of the mobility equation reported in Tables 2 and 3 provide an example. The evidence that _ψ_<sup>ˆ</sup> 2<sup>_r>ψ_ˆ</sup> 2<sup>_u_impliesthefollowinginequalityfromequations(13)</sup> above: Since the estimates from the investment function shows that _θ_<sup>ˆ</sup> 1<sup>_r<θ_ˆ</sup> 1<sup>_u_,inequality(27)</sup> requires _δ_ 4<sup>_r< δ_</sup> 4<sup>_u_,and/or (</sup><sup>_δ_</sup> 5<sup>_r−δ_</sup> 2<sup>_rθ_</sup> 1<sup>_r_)</sup><sup>_>_(</sup><sup>_δ_</sup> 5<sup>_u−δ_</sup> 2<sup>_uθ_</sup> 1<sup>_u_).This last inequality is more likely to be</sup> 24
satisfied when _δ_ 5<sup>_r>δ_</sup> 5<sup>_u>_0,and</sup><sup>_δ_</sup> 2<sup>_r<δ_</sup> 2<sup>_u_.Thesetwoinequalitiesimplythatthestrength</sup> of complementarity is stronger in the rural areas, and that school quality is a substitute of parental financial investment.

However, note that we cannot increase _δ_ 5<sup>_r_indefinitelytosatisfy(27),becauseahigher</sup> _δ_ 5<sup>_r_impliesahigher</sup><sup>_θ_</sup> 1<sup>_r_andbeyondathresholdwewillviolatetheinequality</sup><sup>_θ_ˆ</sup> 1<sup>_r<θ_ˆ</sup> 1<sup>_u_.</sup> This suggests that the direct effect of parents might be less concave in the rural areas, i.e., _δ_ 4<sup>_r<δ_</sup> 4<sup>_u_.Theevidenceonthequadraticcoefficientsofthemobilityequationthus</sup> suggests that the stronger convexity observed in the rural areas is likely to reflect both a stronger complementarity between parental education and financial investment and a smaller diminishing returns to a better educated parent’s direct impact through channels such as home tutoring and role model effects. Since the schools are of lower quality in rural areas, the advantage of having a higher educated parent who can help and guide with academics is likely to be much more important.

# **(7) Sources of Convexity in the Mobility CEF: Are Neighborhood Peer and Role Model Effects Responsible?**

As discussed in the theory section (2), Becker et al. (2015, 2018) suggest that the main source of convexity in the intergenerational mobility equation is likely to be complementarity between the financial investment and parent’s education. However, the complementarity may also arise from other channels such as peer and role model effects. We provide evidence on the importance of these channels in explaining the convexity in the mobility equation observed in Indonesia.

# **(7.1) Peer Effect**

We define the peer group education _Ei_<sup>_g_as the average years of schooling of children in the</sup> _±_ 3 years age band of child _i_ in his/her district of birth.<sup>23</sup> The estimates of the investment equation (15) and intergenerational mobility equation (17) are reported in Table 6A and Table 6B respectively.

The results on the investment equation in the urban areas show that better educated peers have a positive and significant (at the 1 percent level) effect on the financial investment

> 23The conclusions do not depend on the exact age band used; estimates from an alternative definition based on _±_ 5 years age band are reported in the online appendix.

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made by the parents on children’s education ( _θg >_ 0), which from equation (16) implies complementarity: _δ_ 6<sup>_g>_0.In the rural areas, the estimated effect is positive but numerically</sup> small and not significant at the 10 percent level. The evidence thus cannot reject the null hypothesis that peer effect is separable from financial investment in the education production function in the rural areas, i.e., _δ_ 6<sup>_g_=0.24</sup> The conjecture that peer effect is complementary to financial investment in determining the educational investment thus seems to hold only in the urban areas.

The estimates for educational mobility (Table 6B) show that the interaction of father’s education with the peer’s education is _negative_ (i.e, _ψ_ 3<sup>_g<_0) in both rural and urban areas,</sup> suggesting that a _more educated peer group makes intergenerational persistence in schooling lower_ . This is possible when financial investment faces strong enough diminishing returns, i.e., _δ_ 2 is large enough to make _ψ_ 3<sup>_g_=</sup><sup>_δ_5</sup><sup>_θg_+</sup><sup>_δ_</sup> 6<sup>_gθp−_2</sup><sup>_δ_2</sup><sup>_θgθp<_0.Theearlierevidenceon</sup> school quality suggests that _δ_ 2<sup>_r< δ_</sup> 2<sup>_u_which in turn suggests that the magnitude of</sup><sup>_ψ_</sup> 3<sup>_g_should</sup> be smaller in rural areas. This is confirmed by the evidence in Table 6B.

When we include the controls for peer effects, the magnitude of the coefficient on squared father’s education in the mobility equation does not change in the rural sample, but is larger in the urban areas suggesting a stronger convexity.<sup>25</sup> The evidence thus does not support the idea that positive peer effect might be a driving force behind the observed convexity in the intergenerational mobility CEF.

# **(7.2) Role Models**

We next consider whether the adults other than parents as role models play a part in generating the observed convexity in the mobility equation. For this exercise, we define a reference group of adults in the _±_ 3 years of age band of father in a child’s birth district.<sup>26</sup> The average years of schooling of the top 50 percent of the schooling distribution of this adult reference group (denoted as _E_<sup>_m_</sup> ) serves as the indicator of role model effect. We

> 24The smaller magnitude of the peer effect on educational investment in the rural areas is consistent with the theory given that the returns to education for children are lower in villages (see equation (16) above). It follows from the observation that when _δ_ 6 _>_ 0 _,_ we have _∂R_<sup>_∂θkc>_0</sup><sup>_._</sup>

> 25The rural-urban difference in the degree of convexity observed earlier goes away in this specification.

> 26Again, the main conclusions are robust to alternative age bands: the estimates for age band _±_ 5 years are reported in the online appendix.

26
exclude the observations from the lower half of the schooling distribution to capture the idea that a higher achieving adult is more likely to be the role model a child looks up to and aspires to emulate.

The estimates for the investment equation in Table 7A show that the impact of role models on the educational expenditure is different from that of peers in the urban areas. The coefficient _θm_ is _negative_ and significant at the 1 percent level _; the role model effect is thus a substitute for educational expenditure made by parents in urban Indonesia, implying that δ_ 6<sup>_m<_0</sup><sup>_._In contrast, the evidence in the rural sample cannot reject the null hypothesis</sup> of separability in the education production function, similar to the evidence on peer effect discussed earlier.

The results on intergenerational mobility in Table 7B show that the interaction of role models with father’s education is negative and statistically significant both in rural (at the 5 percent level) and urban (at the 1 percent level) areas. The inclusion of the role model effects in the mobility equation, however, does not reduce the convexity with respect to father’s education.

# **(8) Conclusions**

We incorporate the rural-urban differences in returns to education and school quality in a Becker-Tomes model to study the rural-urban divide in intergenerational educational mobility in Indonesia. Following Becker et al. (2018), the model includes an interaction effect between parent’s education and financial investment in children’s schooling production function which can give rise to a convex CEF. Using household data free of the truncation bias due to coresidency restrictions in surveys, we find that the linear CEF widely used in the current literature is rejected in favor of a convex CEF, both in the rural and urban areas. The rural-urban relative mobility curves cross; while the children from less educated households enjoy higher relative mobility in rural areas, the pattern reverses for the higher educated households. The rural children face lower absolute mobility across the whole distribution of father’s education.

The evidence on the intercepts of the investment and mobility equations when interpreted in terms of the theory suggests that school quality is a substitute for parental invest27
ment in schooling. This is important evidence for government policy, as substitutability implies that public investment to improve the quality of rural schools is desirable on both equity and efficiency grounds. The evidence on the slopes of the investment equation suggests that better educated peers are complementary to financial investment in urban areas, but separable in the rural areas. While adult role models are substitutes of financial investment by parents in the urban sample, they are separable in the rural areas. Theory provides plausible explanations for these contrasting effects. Peer and role model effects weaken the impact of family background on educational attainment of children, and this is true in rural and urban samples. The peer and role model effects are not responsible for the convexity observed in the intergenerational mobility equation, indicating that the higher efficiency of educated parents in financial investment decisions might be important, as emphasized recently by Becker et al. (2018). The empirical results are robust to controlling for the heterogeneity in cognitive ability of children. The theoretical and empirical approaches developed in this paper are of wider interest, as they can be applied to other developing countries with household panel data.

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32
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# **Tables**

Table 1: Summary Statistics

|||Panel A: Mo|bility Samp|le|
|---|---|---|---|---|
||Rural (N|OB:10239)|Urban (N|OB: 5238)|
||Mean|SD|Mean|SD|
|Father’s Years of Education|5.66|3.49|7.54|3.76|
|Child Years of Education|9.05|3.22|10.18|3.38|
|Child Age|29.47|6.25|28.88|6.37|
|Child Raven Test Score|67.14|24.20|71.55|23.23|
|Child Memory Test 1|55.74|16.00|57.65|15.84|
|Child Memory Test 2|46.40|17.39|48.30|17.23|
||Panel|B: Education|al Expense|Sample|
||Rural (N|OB: 9797)|Urban (N|OB: 8530)|
||Mean|SD|Mean|SD|
|Average Monthly Expenses|0.64|1.77|1.51|2.82|
|Father Edu|5.31|3.67|7.48|3.95|
|Child Edu|9.47|3.12|10.82|3.32|
|Child Raven Test Score|69.73|23.28|76.11|21.39|
|Child Memory Test 1|56.36|15.53|59.50|15.29|
|Child Memory Test 2|47.19|17.03|50.34|16.52|
|Number of School Age Children|2.21|1.16|2.31|1.16|
||Pane|l C: Permane|nt Income|(Father)|
||Rural (N|OB: 2253 )|Urban (N|OB: 1740)|
||Mean|SD|Mean|SD|
|Permanent Income|199.32|139.53|334.79|258.47|
|Father’s Years of Education|523|362|743|376|
||.<br>Panel|.<br>D: Permanen|.<br>t Income (|.<br>Children)|
||Rural (N|OB: 2419)|Urban (|NOB: 977)|
||Mean|SD|Mean|SD|
|Permanent Income|208.93|149.75|269.39|227.92|
|Child’s Years of Education|8.38|3.49|10.02|3.65|

Notes: Author’s calculation based on the Indonesian Family Life Survey. In Panel A, Rural and Urban are defined based on location of birth. If the respondent was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. The sample in Panel A is based on the 18 to 40 years old in the fifth wave of the IFLS. In panel B, Rural and Urban are defined based on the location of the household in the survey. The summary statistics of Panel B are based on the merged sample of first four waves of the IFLS. Average monthly expense was calculated using the inflation adjusted educational expenditure of the first four waves. In Panel C, Rural and Urban are defined based on household location in the first wave (1993). Father’s permanent income was calculated using the inflation adjusted household consumption expenditure in first three waves (1993, 1997, and 2000). In panel D, Rural and Urban are defined based on location of birth (same as in Panel A). Children’s permanent income was calculated using the inflation adjusted household consumption expenditure in last two waves (2007, 2014). Inflation rates are calculated using the price of rice separately for rural and urban areas. The school expense and permanent incomes are expressed in 10,000 rupiahs.

33
Table 2: Intergenerational Persistence in Schooling in Indonesia

|||**LINE**|**AR CEF**|||**QUADR**|**ATIC CEF**||
|---|---|---|---|---|---|---|---|---|
||**Full**|**Rural (R)**|**Urban (U)**|**R–U**|**Full**|**Rural (R)**|**Urban (U)**|**R–U**|
|Father Edu<br>Father Edu Sq<br>Constant|0.412***<br>(0.011)<br>6.836***<br>(0.096)|0.384***<br>(0.012)<br>6.878***<br>(0.104)|0.429***<br>(0.014)<br>6.941***<br>(0.131)|-0.045***<br>(0.017)<br>-0.0627<br>(0.14)|0.267***<br>(0.025)<br>0.010***<br>(0.001)<br>7.214***<br>(0.114)|0.220***<br>(0.027)<br>0.012***<br>(0.002)<br>7.258***<br>(0.119)|0.334***<br>(0.040)<br>0.006***<br>(0.002)<br>7.249***<br>(0.183)|-0.114**<br>(0.045)<br>0.007***<br>(0.003)<br>0.0086<br>(0.18)|
|Observations|15477|10239|5238|15477|15477|10239|5238|15477|
|||**Estimates**|**of Relative a**|**nd Absolute**|**Mobility from**|**Quadratic C**|**EF**||
||**R**|**elative Mob**|**ility**||||**Absolute Mob**|**ility**|
||**Full**|**Rural(R)**|**Urban(U)**|||**Full**|**Rural(R)**|**Urban(U)**|
|**IGME0**|0.267|0.220|0.334||**ES0**|7.214|7.258|7.249|
|**IGME6**|0.387|0.364|0.406||**ES6**|9.176|9.01|9.469|
|**IGME9**|0.447|0.436|0.442||**ES9**|10.427|10.21|10.741|
|**IGME12**|0.507|0.508|0.478||**ES12**|11.858|11.626|12.121|
|**IGME16**|0.587|0.604|0.526||**ES16**|14.046|13.85|14.129|
|**Weighted IGME**|0.3937|0.3602|0.4209||**Weighted ES**|9.4305|9.049|10.1756|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). Rural and Urban are defined based on location of birth. If the respondent was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. Here, _IGMEk_ = _ψ_<sup>ˆ</sup> 1 _j_ + 2 ˆ _ψ_ 2 _jEkp_<sup>and</sup><sup>_ESk_=</sup><sup>_ψ_ˆ0</sup> _j_ + _ψ_ ˆ1 _jEkp_<sup>+</sup><sup>_ψ_ˆ2</sup> _j_ ( _Ekp_<sup>)2 where</sup><sup>_Ep_</sup> is father’s years of education.

34
Table 3: Intergenerational Persistence in Schooling in Indonesia (with Controls for Cognitive Ability)

|||**LINEA**|**R CEF**|||**QUADRA**|**TIC CEF**||
|---|---|---|---|---|---|---|---|---|
||**Full**|**Rural (R)**|**Urban (U)**|**R–U**|**Full**|**Rural (R)**|**Urban (U)**|**R–U**|
|Father Edu|0.378***|0.352***|0.395***|-0.043**|0.226***|0.184***|0.288***|-0.104**|
||(0.010)|(0.012)|(0.014)|(0.017)|(0.023)|(0.025)|(0.038)|(0.042)|
|Father Edu Sq|||||0.011***|0.013***|0.006***|0.006***|
||||||(0.001)|(0.002)|(0.002)|(0.002)|
|Constant|5.416***|5.346***|5.753***|-0.407**|5.789***|5.7246***|6.0720***|-0.347|
||(0.155)|(0.173)|(0.188)|(0.198)|(0.170)|(0.184)|(0.225)|(0.225)|
|Ability Index|0.464***|0.536***|0.322***||0.477***|0.542***|0.336***||
||(0.046)|(0.052)|(0.064)||(0.046)|(0.052)|(0.064)||
|Ability Index Sq|-0.021***|-0.028***|-0.007||-0.022***|-0.029***|-0.009||
||(0.004)|(0.004)|(0.006)||(0.004)|(0.004)|(0.006)||
|Observations|15477|10239|5238|15477|10239|10239|5238|15477|

||**Relative**|**Estimates**<br>**Mobility**|**of Relative and Ab**|**solute Mobility from**|**Quadratic**<br>**Absolute**|**CEF**<br>**Mobility**||
|---|---|---|---|---|---|---|---|
||**Full**|**Rural(R)**|**Urban(U)**||**Full**|**Rural(R)**|**Urban(U)**|
|**IGME0**|0.2262|0.1838|0.2880|**ES0**|5.7887|5.7246|6.0720|
|**IGME6**|0.3522|0.3362|0.366|**ES6**|7.5239|7.2846|8.034|
|**IGME9**|0.4152|0.4124|0.405|**ES9**|8.675|8.4075|9.1905|
|**IGME12**|0.4782|0.4886|0.444|**ES12**|10.0151|9.759|10.464|
|**IGME16**|0.5622|0.5902|0.496|**ES16**|12.0959|11.9166|12.344|
|**Weighted IGME**|0.3588|0.3275|0.3856|**Weighted ES**|7.7738|7.326|8.704|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). Rural and Urban are defined based on location of birth. If the respondent was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. Here, _IGMEk_ = _ψ_<sup>ˆ</sup> 1 _j_ + 2 ˆ _ψ_ 2 _jEkp_<sup>and</sup><sup>_ESk_=</sup><sup>_ψ_ˆ0</sup> _j_ + _ψ_ ˆ1 _jEkp_<sup>+</sup><sup>_ψ_ˆ2</sup> _j_ ( _Ekp_<sup>)2where</sup> _E_<sup>_p_</sup> is father’s years of education. Cognitive ability index is expressed in percentile; it is constructed taking the first principal component of Raven Test and two memory memory tests net of age and age square.

35
Table 4: Estimates of the Investment Equation

|Father’s Years of Education|0.124***|0.125***|0.120***|
|---|---|---|---|
||(0.010)|(0.010)|(0.010)|
|Rural (=1)|-0.195***|-0.196***|-0.179***|
||(0.068)|(0.068)|(0.068)|
|Father’s Years of Education_×_Rural|-0.074***|-0.074***|-0.074***|
||(0.011)|(0.011)|(0.011)|
|Number of School Age Children||-0.051***<br>(0.016)|-0.051***<br>(0.015)|
|Ability Index|||0.015<br>(0.023)|
|Ability Index Sq|||0.003<br>(0.002)|
|Constant|0.480***|0.560***|0.418***|
||(0.079)|(0.081)|(0.085)|
|R2|0.058|0.059|0.061|
|Observations|18327|18327|18327|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). The dependent variable is educational expenditure adjusting for inflation. Inflation rates are calculated using price of rice separately for rural and urban areas. All regressions include wave fixed effects. Rural and urban are defined based on location of household at the time of survey. Cognitive ability index is expressed in percentile; it is constructed taking the first principal component of Raven Test and two memory memory tests net of age and age square.

36
Table 5: Household-level Returns to Education for Father and Children

||**Father’s G**|**eneration**|**Children’s**|**Generation**|
|---|---|---|---|---|
|Years of Education|25.977***|25.581***|18.327***|18.934***|
||(2.146)|(2.086)|(2.665)|(2.685)|
|Rural (=1)|-1.882|8.019|15.654|19.741|
||(16.644)|(16.186)|(26.260)|(26.147)|
|Years of Education_×_Rural|-14.628***|-14.272***|-5.494*|-5.787*|
||(2.446)|(2.377)|(2.942)|(2.943)|
|Number of Working Age Adults||35.157***||12.029***|
|||(3.293)||(2.586)|
|Constant|141.880***|46.038***|85.695***|49.451*|
||(14.893)|(16.752)|(24.199)|(25.510)|
|Observations|3993|3993|3396|3396|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). Unit of observation is household in both father’s generation and children’s generation. If reported father year’s education varied within a household, an average of father’s years of education is taken. For column (1) and (2), the dependent variable is the inflation adjusted household expenditure in first three waves ( wave 1 (1993), wave 2 (1997), and wave 3 (2000), for column (3) and (4), the dependent variable is inflation adjusted household expenditure in last two waves (wave 4 (2007) and wave 5 (2014)). Inflation rates are calculated using price of rice separately for rural and urban areas. For father rural and urban are defined based on the location of household in 1993. The fathers income sample is restricted to fathers who are between 25 and 56 in 1993. In father’s sample, the number of working age adults is the total number of individuals who are between age 18 to 60 within the household in 1993. For children rural and urban defined based on the location of birth. If the child was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. The children sample is restricted to individuals who are 18 to 40 in 2007 and also a household head. In child’s sample, the number of working age adults is the total number of individuals who are between 18 to 60 within the household in 2007.

37
Table 6A: Effects of Peers on Financial Investment on Childrens Education

||**Rural (R)**|**Urban (U)**|**R–U**|**Rural (R)**|**Urban (U)**|**R–U**|
|---|---|---|---|---|---|---|
|Father Edu|0.048***|0.109***|-0.061***|0.049***|0.112***|-0.063***|
||(0.006)|(0.010)|(0.011)|(0.006)|(0.010)|(0.012)|
|Peer Edu|0.026|0.141***|-0.115**|0.026|0.135***|-0.110**|
||(0.023)|(0.046)|(0.050)|(0.022)|(0.045)|(0.050)|
|Number of School Age Children||||-0.022<br>(0.019)|-0.081***<br>(0.026)||
|Constant|0.059|-0.819*||-0.043|-0.812*||
||(0.206)|(0.448)||(0.203)|(0.444)||
|Includes Ability|No|No|No|Yes|Yes|Yes|
|Observations|9463|8311|17774|9463|8311|17774|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). The dependent variable is educational expenditure adjusting for inflation. Inflation rates are calculated using price of rice separately for rural and urban areas. A peer is someone who was born in the respondents district within _±_ 3 years of respondents birth. Rural and Urban are defined based on location of birth. If the respondent was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. Cognitive ability index is expressed in percentile; it is constructed taking the first principal component of Raven Test and two memory memory tests net of age and age square. Ability controls include cognitive ability index and its square.

Table 6B: Peer Effect and Intergenerational Educational Mobility

||**Rural (R)**|**Urban (U)**|**R–U**|**Rural (R)**|**Urban (U)**|**R–U**|
|---|---|---|---|---|---|---|
|Father Edu|0.325***|0.528***|-0.203**|0.307***|0.471***|-0.164|
||(0.064)|(0.089)|(0.101)|(0.063)|(0.087)|(0.100)|
|Father Edu Sq|0.013***|0.012***|0.001|0.013***|0.012***|0.001|
||(0.002)|(0.002)|(0.003)|(0.002)|(0.002)|(0.003)|
|Father Edu_×_Peer|-0.020***|-0.037***|0.017|-0.022***|-0.034***|0.012|
||(0.008)|(0.010)|(0.011)|(0.007)|(0.009)|(0.011)|
|Peer Edu|0.840***|0.753***|0.088|0.579***|0.650***|-0.071|
||(0.170)|(0.233)|(0.285)|(0.150)|(0.217)|(0.262)|
|Peer Edu Sq|0.003|0.014|-0.01|0.016*|0.014|0.002|
||(0.010)|(0.013)|(0.016)|(0.009)|(0.012)|(0.015)|
|Constant|-0.223|-0.684|0.461|-0.253|-0.76|0.298|
||(0.755)|(1.140)|(1.372)|(0.632)|(1.071)|(1.241)|
|Includes Ability|No|No|No|Yes|Yes|Yes|
|Observations|9907|5087|14994|9907|5087|14994|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). A peer is someone who was born in the respondents district within _±_ 3 years of respondents birth. Rural and Urban are defined based on location of birth. If the respondent was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. Cognitive ability index is expressed in percentile; it is constructed taking the first principal component of Raven Test and two memory memory tests net of age and age square. Ability controls include cognitive ability index and its square.

38
Table 7A: Effects of Role Model on Financial Investment on Childrens Education

||**Rural(R)**|**Urban(U)**|**R–U**|**Rural(R)**|**Urban(U)**|**R–U**|
|---|---|---|---|---|---|---|
|Father Edu|0.052***|0.124***|-0.072***|0.053***|0.126***|-0.073***|
||(0.006)|(0.012)|(0.013)|(0.006)|(0.012)|(0.013)|
|Role Model Edu|-0.009|-0.044***|0.036*|-0.009|-0.045***|0.036*|
||(0.014)|(0.015)|(0.021)|(0.013)|(0.015)|(0.020)|
|Number of School Age Children||||-0.021<br>(0.019)|-0.055*<br>(0.030)||
|Constant|0.365***|0.868***||0.255**|0.761***||
||(0.104)|(0.188)||(0.112)|(0.205)||
|Includes Ability|No|No|No|Yes|Yes|Yes|
|Observations|8485|7281|15766|8485|7281|15766|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). The dependent variable is educational expenditure adjusting for inflation. Inflation rates are calculated using price of rice separately for rural and urban areas. A peer is someone who was born in the respondents district within _±_ 3 years of respondents birth. Rural and Urban are defined based on location of birth. If the respondent was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. Cognitive ability index is expressed in percentile; it is constructed taking the first principal component of Raven Test and two memory memory tests net of age and age square. Ability controls include cognitive ability index and its square.

Table 7B: Role Models and Intergenerational Educational Mobility

||**Rural(R)**|**Urban(U)**|**R–U**|**Rural(R)**|**Urban(U)**|**R–U**|
|---|---|---|---|---|---|---|
|Father Edu|0.238***|0.384***|-0.146**|0.200***|0.351***|-0.151**|
||(0.039)|(0.056)|(0.063)|(0.037)|(0.053)|(0.060)|
|Father Edu Sq|0.015***|0.011***|0.005|0.016***|0.011***|0.005*|
||(0.002)|(0.002)|(0.003)|(0.002)|(0.002)|(0.003)|
|Father Edu_×_Role Model|-0.011**|-0.014***|0.003|-0.010**|-0.014***|0.004|
||(0.004)|(0.004)|(0.006)|(0.004)|(0.004)|(0.006)|
|Role Model Edu|0.229***|0.103|0.126|0.189***|0.104|0.085|
||(0.061)|(0.118)|(0.124)|(0.057)|(0.112)|(0.118)|
|Role Model Edu Sq|-0.004|0.002|-0.006|-0.003|0.002|-0.004|
||(0.004)|(0.005)|(0.006)|(0.003)|(0.005)|(0.006)|
|Constant|5.988***|6.389***|-0.401|4.722***|5.406***|-0.6836|
||(0.285)|(0.682)|(0.676)|(0.272)|(0.683)|(0 .671)|
|Includes Ability|No|No|No|Yes|Yes|Yes|
|Observations|8292|4111|12403|8292|4111|12403|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). A role model is someone who was born in the respondent’s district but is within _±_ 3 of respondent’s father age and belongs to top 50 percent education level within that age group of that district. Rural and Urban are defined based on location of birth. If the respondent was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. Cognitive ability index is expressed in percentile; it is constructed taking the first principal component of Raven Test and two memory memory tests net of age and age square. Ability controls include cognitive ability index and its square.

39
# **Online Data Appendix: Not for Publication**

The Indonesian Family Life Survey (IFLS) is an ongoing longitudinal survey. So far five waves have been fielded. The first wave was fielded in 1993, and the second, third, fourth and fifth waves were fielded in 1997, 2000, 2007 and 2014, respectively. At the time of the first wave, 7224 households were interviewed and it represented 83 % of the national population of Indonesia covering 13 out of the 27 provinces (Frankenberg et al., 1995). In the subsequent waves, the sample size grew because others joined the sampled households either through marriage and births. An appealing feature of the IFLS is its low-attrition rate (Strauss et al., 2016).

Below we provide detailed discussion and rationale on how we have obtained different variables from the IFLS data:

**Children Sample:** As noted in data section, our primary mobility sample is based on children who are 18 to 40 years old in 2014 (wave 5). We restrict the sample to 18 to 40 years old of the fifth wave for two reasons. First, these individuals were in school at some point during 1990s and 2000s. Therefore, we can use the previous waves to estimate the effects on schooling investment. Secondly, only in the fifth wave, the IFLS started to collect Raven Test scores a measure of “fluid intelligence” for all adults. Since we include cognitive ability in much of our analysis, we have chosen to use the fifth wave for our children sample.

**Child Years of Education:** In order to obtain the child years of education, we use two sources of data in the fifth wave of the IFLS: book 3A and roster. Book 3A has education information for anyone who is 15 years and older. If the 18 to 40-year-old household member do not have education reported in book 3A, we use the education reported in roster.

1
**Father’s Years of Education:** We use three sources to calculate father’s years of education. Below we discuss each source:

_Household roster:_ As noted above, the IFLS household roster reports education information of the household member. Moreover, the roster data also provides household member ID of father and mother of each child listed in the roster. Starting with the latest (fifth) wave, we check if the father has co-resided with children at any wave. If the father has co-resided with the children during the any wave, we obtain the education information from the latest wave in which the father has co-resided with the children.

_Non-resident parents module:_ For any household member who is 15 years and older, the IFLS asks about parental education if the parents are not residing in the same household. If the child did not co-reside with the father in any of the survey waves, we use this module to obtain father’s years of education. Using the panel ID, we identify the latest wave in which the children have reported parental education of non-resident parents and extract that education information.

_Mothers marriage module:_ Ideally, we should be able to find education information all fathers using the above two sources. But in some cases, the fathers’ education is missing because of non-response or the reported value exceed any meaningful years of schooling value. The IFLS asks all married women about their husband’s years of education if the husband is not residing in the household. If we unable to find father’s years of education using above two sources, we identify if the mother has co-resided with the child in any of the waves. If the mother co-resided with the child, we then use mother’s marriage module to obtain fathers’ schooling information.

Using all three sources, we are able to collect fathers’ education information for almost 90 percent of the sample.

2
**Children’s Birth Location:** For any household member who are 15 or older, the IFLS has information about the location types of birth: village, small town, or a big city. If the respondents were born in a village, we define the birth location as rural and otherwise, urban. The IFLS collects this information in all waves. For any respondent, we use the birth location in the latest wave in which the respondent reported his/her birth location type.

**Child Cognitive Ability:** We use the Raven test scores and two memory tests to construct the cognitive ability index. An advantage of these measures is that they do not require any knowledge of numeracy or literacy to do well in the tests. To arrive at the index, we first take the first principal component of the raven test scores and two memory tests. Then we regress that on age and age square. A critical issue is that cognition outcomes are positively correlated with age because of the Flynn effect. We, therefore, use residual of the regression as the cognitive ability index.

**Education Expenses:** The IFLS has separate education modules for children (age below 15) and adult (age equal to or above 15). The expense data includes all types of school-related expenses. We aggregate the expenses Using the Panel ID, we match individuals of our children sample (18 to 40 years old in wave 5) with their education expense data in the previous waves. The expenses are then adjusted for inflation taking 1993 as the base year; we obtain the yearly inflation of Indonesia from the World Bank web site.

In the investment sample, we also control for number of school age of children. To calculate the number of school children in wave, we first obtain the fathers’ ID from the roster. We then calculate how many other individuals in the education sample also listed as the same ID as the father. That number provides us with the number of school age children. Finally, in the investment sample, we also include whether the household is located in urban area or 3
rural area. In each wave, the household location information is available in book K. We match the household ID with the location information.

**Permanent income:** We use the household expenditures as a proxy for income, since income data often suffer from more measurement error than household expenditure. For the fathers’ generation, we use the average of household consumption expenditure of the first three waves, and the children’s generation, we the average of household consumption expenditure of the last two waves. Below we discuss in more details how we calculate the permanent income:

# **Fathers’ generation permanent income:**

For each of the first three waves, we first separately calculate the household expenditure. For each household member, the IFLS provides his/her relationship to household head. We identify the households in which the individuals of our children sample (18 to 40 years old in 2014) were listed as children or grandchildren in the any of the first three waves. We consider both children and grandchildren because these children may grow up in an extended family where the grandfather is household head. Using the household tracking id, we then merge the identified households with their total expenditures. We adjust for inflation by using yearly inflation data from the World bank web site taking 1993 as the base year. After this we merge the sample with fathers’ age information. We restrict the sample to fathers who are age 25 to 56 in 1993.

# **Children’s Generation Permanent Income:**

For each of the last two waves, we first calculate the household expenditure. Since we want to focus on children who are 25 to 56 years old in 2007, we extend the original children sample to this age group. We then identify children who are household heads in 2007. We wanted to make sure the chil4
dren are household heads because if the children are living with parents, we may falsely attribute the permanent income of children to parents. Then we merge the household expenditure of the fourth wave (2007) with the household expenditure of the fifth wave (2014) using the household tracking ID. We adjust inflation taking 1993 as the base year.

**Role model data:** The role model in our study are individuals who were born in the same district as the child and belong to the top 50 percent of education distribution of fathers’ reference age group. To calculate the role model education, we first needed to obtain fathers’ age. We check if the father has co-resided with children in any of waves. If we can find the father, we obtain the age from the household roster and convert that value to what his age would be in 2014. For the non-resident father, we obtain the age from the non-resident module. The IFLS asks age at death and year of death, if the father is not alive. Using this information, we calculate what would have been fathers’ age in 2014. We then obtain the birth district information of the children. Separately, next we use the roster data of each wave to obtain years of education and age of all individuals who are older than 22 at the time of the survey. We choose older than 22 because by age 22 the individuals would have completed their education. Then we convert the age of these individuals to the value it would be in 2014. Using the birth district information, we obtain the birth district of all the individuals in the roster. For any given age, we calculate the average of years of education of the top 50 percent achievers within the _±_ 3 ( _±_ 5 for robustness check) age group of a district. We then merge the district ID information and age information with the birth district ID and father age information of the data above.

**Peer Data:** We select individuals who are within _±_ 3 ( _±_ 5 for robustness check) of the age group of our children sample and born in the same district

5
as the children. First, we create a data where we include individuals who are 15 to 43 years old. We then obtain years of education and birth district information for these individuals. After that, we take the average years of education for _±_ 3 ( _±_ 5 for robustness check) of the age group for each district. We then restrict that sample to 18 to 40 years old and merge the sample to the original

# **References**

**Frankenberg, Elizabeth, Lynn A Karoly, Paul Gertler, Sulistinah Achmad, IGN Agung, Sri Harijati Hatmadji, and Paramita Sudharto** , “The 1993 Indonesian family life survey: Overview and field report,” 1995.

- **Strauss, John, Firman Witoelar, and Bondan Sikoki** , _The fifth wave of the Indonesia family life survey: overview and field report_ , Vol. 1, RAND Santa Monica, CA, 2016.

6
# **Online Appendix: Not for Publication**

Table A1: Education and Cognition Interaction

||**Ru**|**ral**|**Ur**|**ban**|
|---|---|---|---|---|
|Father Edu|0.333***|0.226***|0.408***|0.278**|
||(0.021)|(0.071)|(0.027)|(0.121)|
|Ability Index|0.524***|0.702***|0.333***|0.420*|
||(0.055)|(0.109)|(0.066)|(0.225)|
|Ability Index Sq|-0.029***|-0.046***|-0.007|-0.015|
||(0.004)|(0.010)|(0.006)|(0.022)|
|Father Edu_×_Ability Index|0.004|-0.044|-0.002|-0.003|
||(0.003)|(0.030)|(0.004)|(0.055)|
|Father Edu Sq||0.013**||0.011|
|||(0.006)||(0.007)|
|Father Edu_×_Ability Index Sq||0.005*||0.000|
|||(0.003)||(0.005)|
|Father Edu Sq_×_Ability Index||0.002||-0.001|
|||(0.002)||(0.003)|
|Father Edu Sq_×_Ability Index Sq||-0.000||0.000|
|||(0.000)||(0.000)|
|Constant|5.432***|5.510***|5.673***|5.889***|
||(0.201)|(0.282)|(0.237)|(0.490)|
|Observations|10239|10239|5238|5238|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). Rural and Urban are defined based on location of birth. If the respondent was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. Cognitive ability index is expressed in percentile; it is constructed taking the first principal component of Raven Test and two memory memory tests net of age and age square.

1
Table A2: Effects of Peers and Role Models on Financial Investment on Childrens Education

|Father Edu|0.115***<br>(0.012)|0.115***<br>(0.012)|0.117***<br>(0.012)|
|---|---|---|---|
|Peer Edu|0.159***|0.161***|0.155***|
||(0.051)|(0.051)|(0.050)|
|Role Model Edu|-0.066***|-0.067***|-0.066***|
||(0.017)|(0.017)|(0.017)|
|HH Rural (=1)|0.584|0.570|0.564|
||(0.486)|(0.486)|(0.479)|
|Father Edu_×_Rural|-0.063***|-0.063***|-0.063***|
||(0.013)|(0.013)|(0.013)|
|Peer Edu_×_Rural|-0.133**<br>(0.056)|-0.133**<br>(0.055)|-0.128**<br>(0.055)|
|Role Model Edu_×_Rural|0.053**|0.053**|0.052**|
||(0.022)|(0.022)|(0.022)|
|Number of School Age Children||-0.041**<br>(0.017)|-0.040**<br>(0.017)|
|Ability Index|||0.016<br>(0.026)|
|Ability Index Sq|||0.002<br>(0.003)|
|Constant|-0.416|-0.359|-0.484|
||(0.448)|(0.450)|(0.451)|
|Observations|15766|15766|15766|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). The dependent variable is educational expenditure adjusting for inflation. Inflation rates are calculated using price of rice separately for rural and urban areas. The peer and role model measures in Panel C are only based on district level. A peer is someone who was born in the respondents district within _±_ 3 years of respondents birth. A role model is someone who was born in the respondent’s district but is within _±_ 3 of respondent’s father age and belongs to top 50 percent education level within that age group of that district. All regressions include wave fixed effects. Rural and urban are defined based on location of household at the time of survey. Cognitive ability index is expressed in percentile; it is constructed taking the first principal component of Raven Test and two memory memory tests net of age and age square.

2
Table A3: Effects of Peers on Financial Investment on Childrens Education (Robustness): Alternative Definition of Peer Group: _±_ 5 Years Age Band

||**Rural (R)**|**Urban (U)**|**R–U**|**Rural (R)**|**Urban (U)**|**R–U**|
|---|---|---|---|---|---|---|
|Father Edu|0.049***|0.109***|-0.061***|0.050***|0.112***|-0.062***|
||(0.006)|(0.010)|(0.011)|(0.006)|(0.010)|(0.011)|
|Peer Edu|0.024|0.158***|-0.134***|0.023|0.153***|-0.130**|
||(0.023)|(0.046)|(0.051)|(0.022)|(0.046)|(0.051)|
|Number of School Age Children||||-0.021<br>(0.026)|-0.082***<br>(0.038)||
|Constant|0.082|-0.982**||-0.021|-0.979**||
||(0.211)|(0.445)||(0.204)|(0.445)||
|Includes Ability|No|No|No|Yes|Yes|Yes|
|Observations|9463|8311|17774|9463|8311|17774|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). The dependent variable is educational expenditure adjusting for inflation. Inflation rates are calculated using price of rice separately for rural and urban areas. A peer is someone who was born in the respondents district within _±_ 5 years of respondents birth. Rural and Urban are defined based on location of birth. If the respondent was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. Cognitive ability index is expressed in percentile; it is constructed taking the first principal component of Raven Test and two memory memory tests net of age and age square. Ability controls include cognitive ability index and its square.

3
Table A4: Peer Effect and Intergenerational Educational Mobility (Robustness): Alternative Definition of Peer Group: _±_ 5 Years Age Band

||**Rural(R)**|**Urban(U)**|**R–U**|**Rural(R)**|**Urban(U)**|**R–U**|
|---|---|---|---|---|---|---|
|Father Edu|0.309***|0.546***|-0.236**|0.295***|0.488***|-0.194*|
||(0.075)|(0.098)|(0.111)|(0.073)|(0.096)|(0.111)|
|Father Edu Sq|0.013***|0.012***|0.001|0.013***|0.012***|0.001|
||(0.002)|(0.002)|(0.003)|(0.002)|(0.002)|(0.003)|
|Father Edu_×_Peer|-0.018**|-0.039***|0.021*|-0.020**|-0.035***|0.015|
||(0.009)|(0.011)|(0.012)|(0.009)|(0.010)|(0.012)|
|Peer Edu|1.003***|0.621**|0.382|0.723***|0.507*|0.216|
||(0.206)|(0.298)|(0.340)|(0.187)|(0.278)|(0.315)|
|Peer Edu Sq|-0.006|0.02|-0.026|0.008|0.022|-0.013|
||(0.013)|(0.016)|(0.019)|(0.012)|(0.015)|(0.018)|
|Constant|-0.958|-0.039|-0.919|-0.918|-0.102|-0.816|
||(0.864)|(1.424)|(1.604)|(0.741)|(1.340)|(1.462)|
|Includes Ability|No|No|No|Yes|Yes|Yes|
|Observations|9907|5087|14994|9907|5087|14994|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). A peer is someone who was born in the respondents district within _±_ 5 years of respondents birth. Rural and Urban are defined based on location of birth. If the respondent was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. Cognitive ability index is expressed in percentile; it is constructed taking the first principal component of Raven Test and two memory memory tests net of age and age square. Ability controls include cognitive ability index and its square.

4
Table A5: Effects of Role Models on Financial Investment on Childrens Education (Robustness): Alternative Definition of Role Model: _±_ 5 Years Age Band

||**Rural (R)**|**Urban (U)**|**R–U**|**Rural (R)**|**Urban (U)**|**R–U**|
|---|---|---|---|---|---|---|
|Father Edu|0.054***|0.124***|-0.070***|0.055***|0.126***|-0.071***|
||(0.006)|(0.012)|(0.013)|(0.006)|(0.012)|(0.013)|
|Role Model Edu|-0.015|-0.039**|0.025|-0.015|-0.040**|0.025|
||(0.013)|(0.016)|(0.020)|(0.013)|(0.016)|(0.020)|
|Number of School Age Children||||-0.021<br>(0.019)|-0.054*<br>(0.030)|-0.054*<br>(0.030)|
|Constant|0.407***|0.829***||0.295***|0.713***||
||(0.105)|(0.190)||(0.112)|(0.208)||
|Includes Ability|No|No|No|Yes|Yes|Yes|
|Observations|8485|7281|15766|8485|7281|15766|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). The dependent variable is educational expenditure adjusting for inflation. Inflation rates are calculated using price of rice separately for rural and urban areas. A role model is someone who was born in the respondent’s district but is within _±_ 5 of respondent’s father age and belongs to top 50 percent education level within that age group of that district. Rural and Urban are defined based on location of birth. If the respondent was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. Cognitive ability index is expressed in percentile; it is constructed taking the first principal component of Raven Test and two memory memory tests net of age and age square. Ability controls include cognitive ability index and its square.

Table A6: Role Models and Intergenerational Educational Mobility (Robustness):: Alternative Definition of Role Model: _±_ 5 Years Age Band

||**Rural (R)**|**Urban (U)**|**R–U**|**Rural (R)**|**Urban (U)**|**R–U**|
|---|---|---|---|---|---|---|
|Father Edu|0.238***|0.384***|-0.146**|0.200***|0.351***|-0.151**|
||(0.039)|(0.056)|(0.063)|(0.037)|(0.053)|(0.060)|
|Father Edu Sq|0.015***|0.011***|0.005|0.016***|0.011***|0.005*|
||(0.002)|(0.002)|(0.003)|(0.002)|(0.002)|(0.003)|
|Father Edu * Role Model|-0.011**|-0.014***|0.003|-0.010**|-0.014***|0.004|
||(0.004)|(0.004)|(0.006)|(0.004)|(0.004)|(0.006)|
|Role Model Edu|0.229***|0.103|0.126|0.189***|0.104|0.085|
||(0.061)|(0.118)|(0.124)|(0.057)|(0.112)|(0.118)|
|Role Model Edu Sq|-0.004|0.002|-0.006|-0.003|0.002|-0.004|
||(0.004)|(0.005)|(0.006)|(0.003)|(0.005)|(0.006)|
|Constant|5.988***|6.389***|-0.4011|4.722***|5.406***|-0.684|
||(0.285)|(0.682)|(0.675)|(0.272)|(0.683)|(0.672)|
|Includes Ability|No|No|No|Yes|Yes|Yes|
|Observations|8292|4111|12403|8292|4111|12403|

Notes: Standard errors are clustered at the community level (*** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1). A role model is someone who was born in the respondent’s district but is within _±_ 5 of respondent’s father age and belongs to top 50 percent education level within that age group of that district. Rural and Urban are defined based on location of birth. If the respondent was born in a big city or town, it was considered as Urban, and if the respondent was born in a village, it was considered Rural. Cognitive ability index is expressed in percentile; it is constructed taking the first principal component of Raven Test and two memory memory tests net of age and age square. Ability controls include cognitive ability index and its square.

5