Policy Research Working Paper 10074 What the Mean Measures of Mobility Miss Learning About Intergenerational Mobility from Conditional Variance Md. Nazmul Ahsan M. Shahe Emran Hanchen Jiang Forhad Shilpi Development Economics Development Research Group June 2022 Policy Research Working Paper 10074 Abstract To understand the role of family background in intergen- effects of family background on the conditional variance erational mobility, a large literature has focused on the along with the standard conditional mean effects. This conditional mean of children’s economic outcomes given paper derives risk-adjusted measures of relative and abso- parent’s economic status, while ignoring the information lute mobility by accounting for an estimate of the risk contained in conditional variance. This paper explores the premium for the conditional variance faced by a child. The effects of family background on the conditional variance estimates of risk-adjusted relative and absolute mobility of children’s outcomes in the context of intergenerational for China, India, and Indonesia suggest that the existing educational mobility using data from three large develop- evidence using the standard measures of mobility substan- ing countries (China, India, and Indonesia). The empirical tially underestimates the effects of family background on analysis uses exceptionally rich data free of sample trunca- children’s educational opportunities, and thus gives a false tion because of the nonresident children at the time of the impression of high educational mobility. The magnitude survey. Evidence from all three countries suggests a strong of underestimation is especially large for the children born influence of father’s education on the conditional variance into the most disadvantaged households where fathers have of children’s schooling. The analysis finds substantial het- no schooling, while it is negligible for the children of col- erogeneity across countries, gender, and geography (rural/ lege educated fathers. The standard (but partial) measures urban). Cohort-based estimates suggest that the effects of may lead to an incorrect ranking of regions and groups in father’s education on the conditional variance have changed terms of relative mobility. Compared to the risk-adjusted qualitatively; in some cases, a positive effect in the 1950s measures, the standard measures are likely to underesti- cohort turns into a substantial negative effect in the 1980s mate the gender gap and rural-urban gap in educational cohort. A methodology is developed to incorporate the opportunities. 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 What the Mean Measures of Mobility Miss: Learning About Intergenerational Mobility from Conditional Variance 1 Md. Nazmul Ahsan, Saint Louis University M. Shahe Emran, IPD, Columbia University Hanchen Jiang, University of North Texas Key Words:Conditional Variance, Family Background, Intergenerational Educational , Risk Adjusted Mobility Measures, China, India, Indonesia Mobility JEL Codes: I24, J62, O12 1 Emails for correspondence: nazmul.ahsan@slu.edu (Md. Nazmul Ahsan); shahe.emran.econ@gmail.com (M. Shahe Emran); Hanchen.Jiang@unt.edu (Hanchen Jiang); fshilpi@worldbank.org (Forhad Shilpi). We would like to thank Matthew Lindquist and Charlie Rafkin for valuable comments on an earlier draft. The standard disclaimers apply. (1) Introduction A large economic and sociological literature provides estimates of intergenerational persis- tence in economic status. A higher persistence across generations is interpreted as inequality of economic opportunities for children as their life chances are tied down closely to the so- cioeconomic status of their parents irrespective of their own choices and eort. The bulk of the measures used for understanding the transmission of economic status from one generation to the next are based on a conditional expectation function. The focus is on estimating the expected value of an indicator of socioeconomic status of children (e.g., permanent income, education ) conditional on parent's (usually father's) socioeconomic status (for surveys, see Solon (1999), Bjorklund and Salvanes (2011), Iversen et al. (2019), and Torche (2019)). This vast and growing literature largely neglects any information contained in the condi- 2 tional variance of children's economic outcomes. This is a reasonable approach under two conditions: (i) the conditional variance of the relevant economic outcome does not vary in any systematic way with parental economic status, geographic location, gender, race and ethnicity etc.; (ii) parents and children are approximately risk neutral. A large body of evidence ac- cumulated over many decades rejects risk neutrality, and strongly suggests an important role for risk aversion in economic choices under uncertainty (see, for example, Eeckhoudt et al. (2005)). There is no systematic evidence in the literature on the rst condition, but there are a variety of economic mechanisms that can make the conditional variance a function of parent's economic status and geographic location, for example. Conditional variance in chil- dren's schooling may vary across the households in a village because of their dierent abilities to cope with adverse weather shocks. With better access to credit and insurance markets, the highly educated (high income) households are better able to deal with negative shocks such as ood and drought without any disruption to children's education. In contrast, such a negative income shock may force the uneducated poor parents to take the children out of school and 2 Although largely ignored in the literature on intergenerational mobility, some studies in the related but distinct literature on inequality of opportunity (IOP) account for the fact that conditional variance is likely to depend on the circumstances a child is born into (see, for example, Bjorklund et al. (2012)). But their focus is very dierent. Please see the discussion in section 2 below. There is a small literature that exploits the information in conditional variance by estimating quantile regression models of intergenerational mobility. But the focus there is not on understanding the inuence of parental socioeconomic status on conditional variance of children's outcomes. Please see section 2 below for a detailed discussion. 1 send them for child labor. This adds an element of uncertainty (on top of ability dierences) for the children born into disadvantaged households, resulting in a higher conditional variance in completed schooling. The conditional variance of children's schooling attainment is likely to decline with the education of parents when such economic shocks (income or health shocks) are the primary sources behind the observed variance in the data. In this case, children born to higher educated parents not only have higher expected years of schooling (as found in numer- ous studies of intergenerational educational mobility), but also a lower variance in schooling attainment. Under the plausible assumption of risk aversion, this implies being born to higher educated parents brings double advantages for children part of which is ignored by the existing measures of intergenerational mobility. We analyze the relationship between family background and conditional variance of chil- dren's outcome in the context of intergenerational educational mobility. We make two con- tributions to the literature. First, using data from three large developing countries (China, India, and Indonesia, with 42 percent of world population in 2000 (2.56 billion)), we provide the rst empirical evidence that the conditional variance of children's schooling is system- 3 atically related to his/her family background as captured by father's education. Second, we develop a methodology that combines the eects of father's education on both the mean and conditional variance of children's schooling. We propose new measures of relative and absolute mobility that adjust the standard mean eects by the risk premium associated with the conditional variance in educational outcomes faced by children. With risk neutrality, our proposed measures reduce to the canonical measures of intergenerational educational mobility widely used in the current literature (see, for example, Hertz et al. (2008), Azam and Bhatt (2015), and Narayan et al. (2018)). But, under the more plausible assumption of risk aversion, the measures of mobility developed in this paper incorporate the eects of family background operating through conditional variance. For our empirical analysis, we use household survey data from China Family Panel Studies (CFPS) 2010, India Human Development Survey (IHDS) 2012, and Indonesia Family Life 3 We are not aware of any studies on intergenerational mobility that estimates the eects of parent's economic status on the conditional variance of children's economic outcomes. 2 4 Survey (IFLS) 2014. The estimates from the full sample (1950-1989 birth cohorts) suggest that the conditional variance in children's schooling declines with father's education in all three countries, thus conrming the conjecture that the children born to more educated fathers enjoy double advantages in the form of a lower variance in addition to a higher expected (mean) schooling attainment. We nd evidence of substantial heterogeneity across countries, geographic location (rural vs. urban), gender, and birth cohorts. Conditional variance in children's schooling is the highest in India (18.76) and the lowest in Indonesia (13.58), with China in between (16.83). The inuence of father's education on conditional variance of children's schooling follows a reverse cross-country pattern: Indonesia (-0.51), China (-0.48), and India (-0.38). Conditional variance is higher in the rural areas in a country, but the inuence of father's education on conditional variance is smaller in magnitude. The rural-urban dierence is specially striking in India where the estimate is negative and large (-0.77) in the urban sample but small and statistically not signicant (10 percent level) in the rural sample (-0.022). In contrast, the rural-urban dierence is small in China: -0.55 (urban) and -0.52 (rural). We also nd substantial gender dierences with a larger negative eect on sons. The gender dierences in India are the starkest: the estimated eect is negative in the sons sample, but positive 5 in the daughters sample. The results from cohort-based analysis suggest that the negative eect of father's education on conditional variance has become stronger over time in all three countries. In the rural and daughter's samples in India and Indonesia, the estimate turned 6 from positive in the 1950s cohort to a strong negative eect in the 1980s cohort. We check some alternative explanations for the observed relations between conditional variance in children's education and father's education. We provide evidence that functional 4 These surveys are chosen to ensure that the estimates are not biased because of sample truncation due to coresidency restrictions. It is well known that truncations biases the estimated variance downward (Cohen (1991)). Recent evidence suggests that coresidency causes substantial downward bias in the estimate of relative educational mobility as measured by IGRC; see Emran et al. (2018). 5 Government policies and social norms can make the relation between father's education and conditional variance of children's schooling positive. For example. gender based social norms such as son preference and Purdah may results in low conditional variance in low educated households as parents target a reference level of schooling for the daughters, and the girls' schooling attainment bunches around that reference point. This can also give rise to a positive eect in the conditional variance regression. Please see section 2 below. 6 This suggests that the positive eect in the full sample (1950-1989) found earlier for rural India and the daughters in India is driven by the earlier cohorts. 3 7 form mis-specication is not responsible for the observed relations. Taking advantage of data on cognitive ability in IFLS 2014 in Indonesia, we explore whether the estimated eect of father's education is largely due to omitted ability heterogeneity of children. We nd that the inclusion of quadratic controls for ability reduces the magnitude of the impact of father's education on conditional variance, but the estimates still remain substantial and statistically signicant at the 1 percent level. For relative mobility, the estimates of risk adjusted IGRC (RIGRC) suggest that the workhorse measure of relative mobility in the literature, IGRC, substantially underestimates the impact of family background. The estimates for the full sample (1950-1989 cohorts) suggest that the extent of underestimation on average is 26 percent in China, 41 percent in 8 India, and 10.4 percent in Indonesia. Accounting for the inuence of family background on conditional variance of schooling makes a dramatic dierence in the estimated relative and absolute mobility for the children 9 born to the most disadvantaged households (fathers with no schooling). RIGRC estimates from the full sample (1950-1989 birth cohorts) for this subgroup shows that the standard IGRC overestimates relative mobility by 37 percent in China, and by 63 percent and 28 percent in India and Indonesia respectively. In contrast, the gap between the RIGRC and IGRC estimates for the subgroup with college educated fathers is small. Absolute mobility is also substantially overestimated for the most disadvantaged subgroup without risk adjustments: conditional mean of years of schooling is overestimated by 48 percent in China, 127 percent in India, and 25 percent in Indonesia. Again, for absolute mobility of the children of college educated father, the risk adjustments does not make any substantial dierence. The upshot is that while the standard estimates of relative and absolute mobility seem to capture reasonably well 7 Based on recent evidence, we allow for a quadratic mobility CEF in place of a linear functional form (see Becker et al. (2015, 2018), Emran et al. (2021), Ahsan et al. (2021)). We nd that allowing for a quadratic CEF does not change the relation between the conditional variance in children's schooling and father's education in any signicant manner. 8 The smaller magnitude of underestimation in Indonesia despite a large inuence of father's education on the conditional variance noted earlier reects the fact that the ratio of the conditional variance to the conditional mean is much smaller. This ratio is important in determining the risk premium. Please see section (5) below. 9 Note that IGRC, the measure of relative mobility in the workhorse linear model, does not vary with father's education level. But the risk adjusted measure RIGRC varies across low and high educated households because of dierences in the conditional variance and the conditional mean. 4 the educational opportunities of children born to college educated fathers, a failure to account for the eects of family background on conditional variance vastly overstates the educational opportunities of the most disadvantaged children with father having no schooling. Ignoring the conditional variance can also lead to wrong conclusions in inter-group com- parisons. For example, In India, the urban and rural daughters appear to enjoy similar relative mobility according to the standard IGRC estimates (0.60 (urban) and 0.59 (rural)), but the RIGRC estimates reveal a substantial disadvantage faced by the rural daughters (0.92 (rural) and 0.79 (urban)). The estimates of both RIGRC and IGRC for decade wise birth cohorts show that the evolution of intergenerational educational mobility has been very dierent in China compared to India and Indonesia. China has become less mobile from the 1950s to the 1980s while mobility has improved monotonically from the 1950s to the 1980s in India and Indonesia, and the magnitude is substantial. While both measures pick the trend correctly, the standard IGRC substantially underestimates the improvements over time in India. The rest of the paper is organized as follows. The next section discusses the relevant conceptual issues with a focus on the economic mechanisms that can give rise to a negative or positive eect of father's education on the conditional variance of children's schooling, and lays out the estimating equations. Section (3) is devoted to a discussion of the surveys and data sets used for our analysis: CFPS 2014 (China), IHDS 2012 (India), and IFLS 2014 for Indonesia. These three surveys are dierent from many other household surveys available in developing countries as the samples do not suer from signicant truncation. This is important as truncation of a sample is expected to reduce the estimate variance. Section (4) reports the evidence on the conditional variance. In section (5), we develop a methodology for estimating relative mobility that takes into account both the conditional mean and conditional variance, and provide estimates of the risk adjusted relative mobility measure. The paper concludes with summary of the ndings and points out the central contributions of the paper to the literature. (2) Conceptual Issues and Estimating Equations The standard estimating equation for intergenerational educational mobility is: 5 Sic = α + βSip + εi ; E (εi ) = 0 (1) where Si is the years of schooling of child i and superscripts c and p stand for child and parents respectively. The focus of the analysis is the parameter β which is known as intergen- 10 erational regression coecient (IGRC, for short) in the literature. It is implicitly assumed that the variance of the error term εi does not depend on father's education in any system- atic way, and thus β alone adequately captures the inuence of family background. This assumption is valid when the error term captures primarily the variations in children's ability uncorrelated with father's education, and there are no market imperfections. In a model with perfect credit and insurance markets, the optimal investment in a child's education depends only on his/her ability, the family background is irrelevant. Under the plausible assumption that the conditional variance of children's (innate) cognitive ability does not depend on family background, there is no additional information in the conditional variance of schooling attain- ment that could be useful for understanding the impact of family background on educational opportunities of children. In a more realistic setting where the credit and insurance markets are imperfect (or miss- ing), we would expect that the conditional variance would reect the interactions of a child's ability with the credit constraint and risk coping strategies of a household. First, consider the implications of credit market imperfections in the absence of income or health shocks. We consider two types of credit market imperfections. In the rst case, the poor (less educated) households pay a higher interest rate but can borrow as much as they want for educational 11 investment (i.e., no quantitative credit rationing). In this case, the poor (less educated) parents invest less, given the ability of a child, because of a higher interest rate, but the in- vestment dierences across children from the same family (or similar family background where fathers have the same education) are determined solely by the ability dierences among the 10 Among many studies relying on this specication, please see Hertz et al. (2008) and Narayan et al. (2018) for cross country evidence, Azam and Bhatt (2015), Emran and Shilpi (2015) and Asher et al. (2018) on India, Knight et al. (2011), Golley and Kong (2013), and Emran and Sun (2015) on China. For recent surveys of this literature, see Iversen et al. (2019), Torche (2019), and Emran and Shilpi (2021). 11 This model of credit market imperfections is adopted by Becker et al. (2018) in their recent theoretical analysis of intergenerational mobility. 6 children. We thus expect lower average level of education for the children of less educated parents, but the conditional variance should not depend in any signicant way on father's education in this case. The second model of credit market imperfections focuses on the quan- titative credit rationing, a special case of which is self nancing by the parents (the case of missing credit market for investment in education). When the parents have limited investment funds, they might choose to invest in the most able child to maximize the expected income ? ( ). Since the probability of success is higher for a child with high cognitive ability, it may be optimal for the parents to reallocate investment funds from other children, specially when 12 returns to education are convex. Such investment choices would increase the variance of children's schooling in the less educated credit constrained families as the less able children's education level is depressed and the education level of the high ability child is pushed up. Negative income shocks can amplify the eects of a binding credit constraint, as the family may need to allocate the funds earmarked for education investment to buy food. It is not uncommon for one sibling to drop out of school in response to a negative shock to supplement family income through child labor, while the more promising sibling continues with his/her study. However, as emphasized by Behrman et al. (1982), equity concerns for a low ability child may dominate the income maximizing motive, leading to a compensating investment allocation where the low ability child gets a larger share of the educational investment. If compensating investment rather than the reinforcing investment is the overriding behaviorial response of parents facing scarcity, then we would expect lower conditional variance for the 13 children born to low educated fathers. Government policies and social norms can also aect the conditional variance of children's education. When government policies such as free and compulsory primary schooling are well designed and implemented, it ensures that the children from the poor socioeconomic background attain primary schooling irrespective of a child's ability. This will reduce the conditional variance in the poor households by eectively eliminating the lower tail of the counterfactual schooling distribution of children without any government policy interventions. 12 There is emerging evidence that returns to education function is convex in many developing countries. See Kingdon (2007) on India, and Fasih et al. (2012) for cross-country evidence. 13 There is a large sociological literature on reinforcing vs. compensating parental investments in children's education. But most of the literature focuses on the developed countries. See, for example, Conley (2004). 7 Merit based scholarships provided by schools or government programs on the other hand can relax the credit constraints only for the most able child in a poor family and thus increase the conditional variance by expanding the upper tail of educational attainment. Social norms can create reference points for the desired level of education of children which may vary signicantly by gender, specially in the older cohorts. For example, strong son pref- erence and Purdah may imply that girls in poor households go to school only if schooling is easily accessible and, more importantly, free. They drop out after primary schooling because secondary and higher schooling requires substantial private investments by the parents and the high schools may be far away. We might thus observe low conditional variance in the households with less educated parents because of bunching around primary schooling or other thresholds determined by social norms, particularly for daughters. The richer and more edu- cated households may invest substantially in daughter's education even with son preference, and their investment would be more closely aligned with the ability of a child irrespective of gender. The preceding discussion thus suggests that depending on government policy and so- cial norms, we may in fact observe an increasing conditional variance with father's education, specially for daughters in rural areas. To understand the potential inuence of family background as captured by father's edu- cation, we estimate the following equation for conditional variance: V (εi ) = θ0 + θ1 Sip + υi ; E (υi ) = 0 (2) We are not aware of any studies on intergenerational mobility that provide estimates of equation (2). In the related but distinct literature on inequality of opportunity that grew out of Roemer's seminal work (Roemer (1998), Roemer and Trannoy (2016)) , there are a number of studies that estimate equation (2); see, for example, Bjorklund et al. (2012) and Hederos et al. (2017) in the context of income mobility in Sweden. However, their focus is very dierent, they are interested in estimating a clean measure of eort in order to decompose the observed income of children into two parts: one due to the circumstances a child is born into, and the other due to a child's own eort. Similar to this paper, they recognize that the residual from a linear regression of children's education, for example, on a set of variables 8 dening the circumstances is not a clean measure of eort as it partly reects the eects of 14 family background. As measure of eort, they use the sterilized residual from the regression of the residual squared (the residual from the earlier stage) on circumstances. There is a small literature on intergenerational mobility that exploits the information in conditional variance using quantile regressions. See, for example, Grawe (2004) on the United States and Kishan (2018) on India. The focus in this approach on estimating dierent conditional mean functions corresponding to the quantiles of children's education. Grawe (2004) provides an interesting analysis of the pitfalls in relying on functional form of the CEF to learn about credit constraints in the context of income mobility. His analysis suggests that a quantile regression approach can be useful in understanding the existence of credit constraints. (3) Data and Variables We use the following household surveys for our empirical analysis: China Family Panel Studies (CFPS) for China, India Human Development Survey (IHDS) for India, and Indonesia Family Life Survey (IFLS) for Indonesia. These data sets are suitable for our analysis because they do not suer from any signicant sample truncation arising from coresidency restrictions commonly used to dene household membership in a survey. A truncated sample is likely to underestimate the conditional variance, for example when the data miss observations on highly educated children who left the natal house for college. The data for China come from the China Family Panel Study (CFPS) 2010 wave, which has a unique T-Table design that presents a complete family network, in which household members' education information is also available. For more detailed discussions about the unique advantage of CFPS in analyzing intergenerational mobility related questions, please see Fan, Yi ang Zhang (2021) and Emran, Jiang, Shilpi (2020). The data for India come from the India Human Development Survey (IHDS) 2012 wave. We follow Emran, Jiang, Shilpi (2021) closely, which updates and expands the sample of father-child pairs for years of schooling in India in two major ways compared to the earlier studies such as in Azam 14 The circumstances usually include parent's education, occupation, race, ethnicity, geographic location, and gender. 9 and Bhatt (2015) and Azam (2016). Our sample includes not only the non-resident fathers but also other non-resident family members, and non-resident children of household heads in particular. The data for Indonesia come from Indonesia Family Life Survey (IFLS) 2014 wave. IFLS's household roaster, nonresident parents module, and mother's marriage module allow us to construct father-children pairs whose education information is not subject to truncation bias. More details about the sample construction procedure, readers are referred to Ahsan, Emran, Shilpi (2021) and Mazumder et al. (2019). The summary statistics for our main estimation samples are reported in Table 1. We rst report the average years of schooling for both father and children in our full sample born between 1950 and 1989 across three countries respectively. The average years of schooling for fathers is 4.24 in China, 3.63 in India, and 6.21 in Indonesia. The average years of schooling for children is 7.52 in China, 6.50 in India, and 9.52 in Indonesia. Therefore, Indonesia has the best education outcome for both fathers and children among the three countries while India has the lowest mean education for both generations. We also report the summary statistics for our four main sub-samples: urban, rural, sons, and daughters in the following panels respectively. In each country, there is consistent rural- urban gap in education for both generations. Children in urban China and urban India have about 3 more years of schooling than children in rural areas, while the gap is smaller in Indonesia (2 years). All three countries exhibit dierent degree of gender gap in schooling among children: 1.3 years in China, 2.3 years in India, and 0.6 years in Indonesia. Gender gap in Indonesia is much smaller, consistent with a large literature showing that girls in Indonesia do not face any signicant disadvantages compared to the boys. (4) Evidence on Conditional Variance Estimates of equations (1) (conditional mean) and (2) (conditional variance) for our full estimation samples (1950-1990 birth cohorts) are reported in Table 2. The estimates for the mobility equation (1) are in odd columns and those for the conditional variance equation (2) are in even columns. The evidence is consistent across the three countries: conditional variance of children's schooling is a negative function of father's education. Estimates from the mobility 10 equation show that father's education has a substantial positive inuence on the expected schooling of children, consistent with a large literature that focuses solely on the mean eects. When considered together, the evidence on the mobility and conditional variance equations suggests that being born to a higher educated father is equivalent to winning an education lottery with higher mean (expected years of schooling) and a lower variance. There are some important cross-country heterogeneity: while father's impact on the expected education of children (IGRC) is the highest in India (0.62), the eect on conditional variance is the smallest (-0.38). The inuence of father's education on conditional variance is of comparable magnitude in China (-0.48) and Indonesia (-0.51), but the estimate for the mean schooling is much smaller in China (0.38) compared to that in Indonesia (0.48). (4.1) Heterogeneity: Rural vs. Urban, and Sons vs. Daughters The top panel of Table 3 reports the estimates of equations (1) and (2) separately for rural and urban samples. The evidence suggests striking rural/urban dierences which vary across countries. Conditional variance on average is higher in rural areas, although the rural-urban 15 gap is small in China. In India, the eects of father's education on conditional variance is large in urban sample (−0.77), but we cannot reject the null hypothesis of no inuence in the rural sample (−0.02). As we discuss below this null eect hides important gender dierences in the rural areas. The estimates are similar in magnitude across rural and urban areas in the case of China (−0.55 (urban) and −0.52 (rural)), and in Indonesia, the urban estimate is much larger ( −0.71 (urban) and −0.29 (rural)). The lower panel of Table 3 contains the estimates for the son's and daughter's samples. In India, the estimate for sons is negative, and large in magnitude (-0.93), but the estimate in the daughter's sample is positive and numerically much smaller (0.33) (both estimates are signicant at the 1 percent level). The evidence in Table 3 thus suggests that the idea that being born into a highly educated household confers you double dividends is valid only for the sons in India. However, the evidence below on the evolution of educational mobility across cohorts shows that this conclusion is valid only for the older cohorts (see below). In China, 15 The higher conditional variance in rural areas is consistent with the observation that the rural economy is more exposed to weather shocks and the credit and insurance markets are less developed. 11 higher education of a father lowers the conditional variance of schooling for both sons and daughters, but the magnitude of the impact is substantially larger for sons (-0.48 for sons, and -0.36 for daughters). The evidence is dierent in Indonesia: there is no signicant dierence 16 across gender. In the online appendix, we discuss the estimates for four subsamples dened by gender and rural/urban location of a child (see Table A.1 in the online appendix section OA.1). The evidence on India suggests that the rural daughters face very dierent educational prospects: the impact of father's education is positive and numerically large for this subgroup, while the eect is negative in the other three subgroups. The nding that the rural daughters are qualitatively dierent from the other three groups also holds in China: there is no signicant impact on conditional variance of rural daughter's schooling, while the eect is negative and signicant in the other three subgroups. (4.2) The Evolution of Conditional Variance: Evidence from Decade-wise Birth Cohorts Table 4 reports the estimates for equations (1) and (2) for decade-wise birth cohorts: 1950-1959, 1960-1969, 1970-1979, 1980-1989. The evidence shows interesting pattern in the evolution of the inuence of family background on conditional variance of children's schooling. If we focus only on the mean eect as is done in the existing literature, the evidence suggests that relative mobility has improved in India and Indonesia over time, while it has worsened in China. However, the impacts on the conditional variance shows a much stronger role of the family background in the recent decades which counteracts the improvements in the mean eects. In all three countries, the inuence of father's education on the conditional variance is negative and substantial in magnitude in the 1980s, suggesting that the children born to educated parents gain in terms of a much lower conditional variance, in additional to a higher conditional mean. There are dramatic dierences in the earlier cohorts across countries: the estimate is negative in China, positive in Indonesia, and a zero eect in India for the 1950s 16 The standard mean eects (see the IGRC estimates in the odd numbered columns of Table 3) show that the inuence of father's education is much higher for daughters in terms of the rst moment (expected years of schooling) in China. The gender advantages thus are opposite in terms of the mean vs. conditional variance eects. We discuss a simple summary measure of relative mobility that combines these two aspects in section 5 below. 12 cohort. The estimate turns negative and signicant in Indonesia in the 1960s, and in India a decade later in the 1970s. The inuence of family background on conditional variance has increased dramatically, and relative mobility is substantially overestimated in both countries in the recent decades if we ignore the impact on conditional variance. In section (5) below, we combine the conditional mean and conditional variance eects to provide risk adjusted relative and absolute mobility measures. The estimates disaggregated across gender and geography, and for dierent cohorts are reported in the online appendix Tables A.2, and A.3 (please see online appendix section OA.1). Again, the evidence suggests important heterogeneity across gender and rural-urban locations. The inuence of family background on conditional variance in early cohorts is negative in the urban and son's samples for India and China, but there is no signicant eect in Indonesia. It is positive and numerically substantial in the rural and daughters samples for India and Indonesia, but no signicant eect in China. The estimate turned negative in the 1980s even in the rural and daughters samples in all three countries. (4.3) Robustness Checks The evidence discussed above suggests that the conditional variance of children's school depends systematically on father's education, and there are substantial heterogeneity across countries, regions (rural/urban), gender, and cohorts. We rst check whether the observed patterns in conditional variance of children's schooling are primarily driven by functional form misspecication. As noted briey earlier, there is a growing theoretical and empirical literature that suggests that the intergenerational educational mobility equation is quadratic 17 (Becker et al. (2018) , Emran et al. (2020) ): Sic = α + βSip + δ (Sip )2 + ζi (3) If the true conditional expectation function is given by equation (3), but we estimate 17 Most of the studies on intergenerational income mobility use a specication linear in logs. Bratsberg et al. (2007) nds that it is convex in Norway, Denmark, and Finland, but closer to linear in the United States and the United Kingdom. However, Chetty et al. (2014) report evidence of a concave relation (see their Figure 1) in the United States, and a recent analysis by Mitnik et al. (2018) provides evidence that the income mobility equation is convex in the United States. 13 the linear equation (1), the error term is εi = δ (Sip )2 + ζi , and the conditional variance of εi is a function of father's education simply because of a misspecied functional form. To check this, we estimate the mobility equation (3) and the impact of father's education on the conditional variance dened in terms of ζi . The estimates for various samples are reported in Tables A.4-a.8 in the online appendix section OA.2. The evidence suggests strongly that the relations between family background and conditional variance of children's schooling uncovered in Tables 2-4 are not driven by functional form misspecication of the mobility CEF. The next question we address is whether the estimated impact of father's education largely reects the omitted cognitive ability heterogeneity of children. For this analysis, we take advantage of the IFLS-2014 survey in Indonesia which collected data on multiple indicators of cognitive ability of a child (measurement taken in 2014 when the children are adult): raven test scores and two memory tests. We construct an index of cognitive ability in two steps. First, we construct the rst principal component of the dierent measures of cognitive ability. In the second step, we regress the rst principal component on age and age squared of a child to take out the Flynn eect. The residual from this regression is our index of cognitive ability of a child. We control for the ability index and its squared in the regression for conditional variance in equation (2) above. The estimates for the full sample are reported in online appendix Table A.4 (see online appendix section OA.3). The main message that comes out is that the estimated eects of father's education on conditional variance of schooling of children are not driven by omitted ability heterogeneity. Even though ability controls reduce the estimated coecient, the inuence of father's education still remains substantial and statistically signicant at the 1 percent level. The estimates for other subsamples are available from the authors. (5) Combining the Mean and Conditional Variance Eects: New (and More Complete) Measures of Relative and Absolute Mobility The evidence presented above suggests strongly that it is important to understand the inuence of family background on the conditional variance in addition to the standard mean eects. In this section, we develop an approach that combines the mean and variance eects using standard results from the theory of decisions under uncertainty. 14 Assume a concave payo function (utility function) dened over the possible schooling outcomes of a child i, W (Sic ). Denote the expected schooling as E (Sic ), and i = Sic − E (Sic ). So we can rewrite W (Sic ) = W (E (Sic ) + i ). Using the intergenerational mobility equation (1) above, E (Sic ) = α + βSip , which implies W (Sic ) = W (α + βSip + i ). We have the following: EW (Sic ) = W (α + βSip − Πi ) (4) where Πi is the risk premium which depends on the variance of εi . Using second order Taylor series expansions around the conditional mean on both sides of equation (4), the risk premium can be approximately written as: 2 1 σi Πi R (5) 2 (α + βSip ) 2 where V ar(εi ) = σi , and R is the parameter of relative risk aversion in a CRRA util- ity/payo function (see, for example, Eeckhoudt et al. (2005)). Using equation (2) and de- noting an estimated parameter by a hat, we can have an estimate of the risk premium as below: ˆ ˆ p ˆi 1 θ0 + θ1 Si Π R (6) 2 α ˆ p ˆ + βS i Combining (4) and (6), we have:   ˆ1 S p ˆ0 + θ θ ˆ p−1 i EW (Sic ) W α ˆ + βS i R (7) 2 α ˆ ˆ + βS p i Since W (.) is a monotonically increasing function, the rankings remain the same if we use ˆ ˆ p ˆ p 1 θ0 + θ1 Si α ˆ+ βS i − R instead of the RHS of equation (7). 2 α ˆ p ˆ + βS i ˆ1 S p ˆ0 + θ θ ˆ p− 1 i ˆ + βS We propose measures of absolute and relative mobility based on α i R. 2 α ˆ p ˆ + βS i This has some important advantages compared to the measures of mobility based on equation 15 (7) above, as we will see below. Let ˆ ˆ p ˆ p 1 θ0 + θ1 Si Ψi (Sip ) =α ˆ+ βS i − R (8) 2 α ˆ p ˆ + βS i Ψi (Sip ) is our measure of absolute mobility for child i which shows the risk adjusted ex- pected years of schooling of children conditional on father's schooling (called RESi for short).18 The measure of relative mobility is:   ˆ0 + θ ˆ θ β ˆ1 S p ∂Ψ ˆ R ˆ1 − i RIGRCi = p = β − θ  (9) ∂Si 2 α ˆ ˆ + βS p α ˆ p ˆ + βS i i An important advantage of the measures of relative and absolute mobility in equations (8) and (9) is that they are readily comparable to the standard estimates of mobility (they are measured in the same units: years of schooling). A second important feature of the proposed measures is that they yield the standard measures of relative and absolute mobility currently used in the literature under risk neutrality. For example, consider the workhorse measure of relative educational mobility in the current literature called IGRC, estimated as the parameter β in equation (1). For the risk neutral case, we have R = 0, and relative mobility is equal to β (IGRC). Under risk aversion, the extent of underestimation when we omit the eects of family background on the conditional variance is given by the second term. It also important to appreciate some of the dierences between the standard measures and the risk-adjusted measures proposed here. Even though all the estimates of β as a measure of relative mobility we are aware of fall in the open interval (0, 1), the risk adjusted measures may not be contained in this interval. For example, when the ratio of conditional variance to conditional mean is large, the risk premium in equation (9) can be large enough 19 to make RIGRC estimate greater than 1. This implies that the conventional argument that 1−β can be interpreted as a measure of mobility (while β is a measure of intergenerational 18 This measure is similar to the other measures of absolute mobility based on the conditional mean function; see, for example, Chetty et al. (2014) in the context of intergenerational income mobility. 19 This, however, does not mean an explosive process, as the magnitude of RIGRC declines with father's education. 16 persistence) may not be useful in this context. We propose the inverse of RIGRC for such an 20 interpretation. To operationalize equations (8) and (9), we need an estimate of the CRRA coecient R. A substantial literature suggests that a CRRA utility function with risk aversion parameter of 1 is consistent with a variety of evidence (see, for example, Chetty (2006) on the United States, and Gendelman and Hernández-Murillo (2014) for cross country evidence including 21 many developing countries). We will thus set R=1 for our estimation below. Note that when the inuence of father's education on the conditional variance is negative (i.e., θ1 < 0), the second term in equation (9) is unambiguously positive, and the estimate of risk adjusted relative immobility is necessarily larger than the standard estimate. However, the term in brackets can be negative even when θ1 > 0, for example, when the conditional variance term ˆ1 S p ˆ0 + θ θ is large (more likely in rural areas subject to weather shocks to i agriculture). When comparing dierent groups, the risk adjusted estimates may be very dierent from the canonical IGRC estimates even if the impact of father's education on the conditional variance (i.e., ˆ1 ) is similar across groups, because of dierences in the magnitudes θ of ˆ0 θ across groups. (5.1) Estimates of Risk Adjusted Measures: Mobility across the Distribution of Father's Education The standard measure of relative mobility in the workhorse linear model given by the slope of the mobility equation, IGRC, does not vary across the distribution of father's schooling. In contrast, the RIGRC estimates from a linear mobility model vary with father's education level because the risk premium is dierent across dierent levels of parental education. As noted earlier, the risk premium depends on the ratio of conditional variance to conditional 20 Note that we use the linear mobility CEF as the default specication for the mobility equation because it is almost universally used in the existing studies on intergenerational educational mobility with a few recent exceptions. As noted earlier, recent evidence suggests that the mobility CEF is likely to be concave or convex in many cases. In such cases, relative mobility varies across the distribution without any risk adjustments, and one can nd that the marginal eect of father's education on children's schooling is larger than 1, especially in the lower tail (for concave CEF) or the upper tail (for convex CEF). Thus, in a nonlinear model, using the inverse of the marginal eect of father's schooling as a measure of mobility seems more appropriate. 21 While a CRRA coecient of 1 across countries helps understand the role played by the inuence of family background on conditional variance, one might prefer to use dierent estimates of the CRRA coecient for dierent countries when the focus is on interregional and intergroup dierences within the same country. 17 mean. Figures 1A (China), 1B (India), and 1C (Indonesia) present the graphs of the estimated conditional mean and conditional variance functions using the full sample (1950-1989). The graphs show that the ratio of conditional variance to conditional mean is large in the low educated households, and the ratio declines with father's education. This suggests that the risk premium at the lower end of the distribution is substantially higher, and we expect risk adjustments to substantially reduce the estimates of both relative mobility (RIGRC larger than the IGRC) and absolute mobility (RES lower than ES) of the most disadvantaged children. The estimates of the risk adjusted relative and absolute mobility for the full sample are reported in Table 5 along with the standard estimates for ease of comparison. Figures 2A (China), 2B (India), and 2C (Indonesia) present the graphs of RIGRC and IGRC estimates, and the corresponding estimates of absolute mobility (RES and ES) are in Figures 3A (China), 3B (India) and 3C (Indonesia). Consistent with the discussion above, the evidence conrms that accounting for risk reveals much worse educational opportunities for the children born to fathers with low or no education. The gap between the RIGRC and IGRC estimates is the largest for the children of fathers with no schooling, and the same is true for the gap between ES (expected years of schooling) and RES (risk adjusted expected years of schooling). For relative mobility, the canonical IGRC estimate underestimates the inuence of family background for this most disadvantaged subgroup of children by 41 percent in China, 63 percent in India, and 28 percent in Indonesia. A comparison of the RES estimates with the ES estimates (see Table 4) show that a failure to take into account the eects on conditional variance overestimates the expected years of schooling for this subgroup of children by 48 percent in China, and by about 26 percent in India and Indonesia. A second important conclusion that comes out of the evidence is that, for the children of college educated fathers, the standard estimates are reasonably close to the risk adjusted estimates. For example, the standard IGRC overestimates relative mobility of the children of college educated fathers by 6.2 percent and absolute mobility by 4.1 percent in India, and the corresponding numbers for Indonesia are 5.6 percent and 2.1 percent. The biases in the corresponding estimates for China are larger, but even then, the biases are about half of that found for the subgroup where fathers have no schooling. The evidence thus suggests that the failure to consider the 18 implications of family background for the second moment of data may not be as consequential for the children born into highly educated households. The estimates of the risk adjusted and standard measures of relative and absolute mobility across the distribution for rural vs. urban areas are reported in Table 6A for all three countries. The estimates of gender dierences are reported in Table 6B. The evidence suggests that the standard measures of mobility consistently overestimate the educational opportunities for the disadvantaged children (father with low education). The risk adjustments make a big dierence specially for the rural areas and the daughters. (5.2) Estimates of Risk Adjusted Measures: Relative Mobility across Countries, Regions, and Gender Since the risk adjusted relative mobility varies across the distribution, it does not provide us with a summary statistic such as IGRC which can be easily compared across countries, regions, and dierent social groups. For such comparisons, we calculate a weighted RIGRC using the proportion of children as weights. As a summary measure of relative mobility, weighted RIGRC may be specially useful for policymakers. The weighted RIGRC for various sub-samples dened by gender and geography (ru- ral/urban) are reported in the odd numbered columns in Table 7 for our main estimation sample of 1950-1989 birth cohorts. For ease of comparison, the corresponding canonical IGRC estimates are in the even numbered columns. The estimates show that the RIGRC estimates are uniformly larger than the corresponding IGRC estimates, and the dierence is substantial in magnitude. For example, the estimates for the aggregate sample in row 1 of Table 7 suggest that the magnitude of underestimation in the standard IGRC estimate is 26 percent in China, 41 percent in India and 10.4 in Indonesia. The cross-country rankings do not change when we use RIGRC instead of IGRC estimates. However, when comparing dierent subgroups (based on gender and geography), the rank- ings based on the weighted RIGRC may be dierent (compared to the rankings based on standard IGRC). For example, in India, the rural-urban gap in educational mobility seems negligible according to the standard IGRC estimates (a 4.6 percent higher estimate in rural areas), but the gap is much larger according to the weighted RIGRC estimates (20 percent 19 larger estimate in rural). Similarly, the standard IGRC estimates suggest no signicant gender gap in India, while the RIGRC estimates reveal a substantially lower relative mobility for the daughters. In India, the urban and rural daughters enjoy similar educational mobility accord- ing to the standard IGRC estimates with a slight advantage in favor of the rural daughters (a 2.9 percent higher IGRC estimate for urban daughters). But the weighted RIGRC estimates reveal a substantial disadvantage faced by the rural daughters (a 16.5 percent higher estimate for rural daughters). The estimates for decade wise birth cohorts show that the evolution of intergenerational educational mobility has been very dierent in China compared to India and Indonesia (see Table 8). China has become less mobile from the 1960s to the 1980s after experiencing a slight improvement from 1950s to 1960s. In contrast, the estimates of both weighted RIGRC and IGRC suggest that mobility has improved from the 1950s to the 1980s in India and Indonesia. While both measures pick the time trend correctly, the standard IGRC underestimates the improvements substantially, especially in India. (6) Conclusions A large literature on intergenerational mobility focuses on the eects of family background on the conditional mean of children's economic outcomes and ignores any information contained in the conditional variance. We provide evidence on three large developing countries (China, India, and Indonesia) that suggests a strong inuence of father's education on the conditional variance of children's schooling. We nd substantial heterogeneity across countries, gender, and geography (rural/urban). Cohort based estimates suggest that the eect of father's ed- ucation on the conditional variance has changed qualitatively, in some cases a positive eect in the 1950s cohort turning into a substantial negative eect in the 1980s cohort. The evidence on the eects of family background on the mean and conditional variance suggests that being born into a more educated father brings in double advantages for children in the form of a lower expected variance in schooling in addition to the standard higher ex- pected years of schooling. We develop a methodology to incorporate the inuence of family 20 background on the conditional variance along with the standard conditional mean estimates. Based on the standard results from the theory of decisions under uncertainty, we adjust the canonical measure of intergenerational relative and absolute mobility by an estimate of the risk premium associated with the conditional variance in schooling attainment faced by chil- dren. The risk premium is determined by the ratio of conditional variance to conditional mean along with the coecient of relative risk aversion. The estimates of the risk adjusted relative and absolute mobility for China, India and Indonesia suggest that the current prac- tice of ignoring the conditional variance results in substantial underestimation of the eects of family background on children's educational opportunities. More important, the magni- tude of underestimation in the standard measures is the largest for the most disadvantaged children born into households where fathers have no schooling. 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WIDER Working Paper Series 2019-88. 24 Table 1: Summary Statistics CHINA INDIA INDONESIA Mean SD Mean SD Mean SD Full Sample Father's Edu 4.124 4.370 3.633 4.540 6.213 3.854 Children’s Edu 7.521 4.430 6.501 5.168 9.524 4.154 Observations N=94159 N=86748 N=18356 Urban Father's Edu 5.089 4.662 5.233 5.035 7.717 4.023 Children’s Edu 9.376 4.173 8.446 5.048 10.836 3.876 Observations N=35308 N=31216 N=5919 Rural Father's Edu 3.546 4.078 2.734 3.962 5.497 3.554 Children’s Edu 6.408 4.202 5.408 4.907 8.899 4.136 Observations N=58851 N=55532 N=12437 Sons Father's Edu 4.086 4.373 3.689 4.495 6.177 3.839 Children’s Edu 8.169 4.143 7.557 4.972 9.822 4.022 Observations N=46791 N=46701 N=8558 Daughters Father's Edu 4.163 4.367 3.569 4.590 6.245 3.867 Children’s Edu 6.880 4.609 5.269 5.120 9.264 4.249 Observations N=47368 N=40047 N=9798 Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. 25 Table 2: Family background and Conditional Mean and Conditional Variance ( Full Sample Estimates) CHINA INDIA INDONESIA Yrs Sch. Res. Sq. Yrs. Sch. Res. Sq. Yrs. Sch. Res. Sq. Father's Edu 0.383*** -0.483*** 0.621*** -0.379*** 0.497*** -0.514*** (0.014) (0.036) (0.005) (0.028) (0.011) (0.052) Constant 5.943*** 18.823*** 4.244*** 20.134*** 6.437*** 16.784*** (0.152) (0.424) (0.043) (0.144) (0.113) (0.429) Observations 94,159 94,159 86,748 86,748 18356 18356 R-squared 0.142 0.009 0.298 0.006 0.212 0.011 ̅ Mean of 𝑌 7.521 16.83 6.501 18.76 9.523 13.587 Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. 26 Table 3: Heterogeneity Across Urban vs. Rural and Sons vs. Daughters CHINA INDIA INDONESIA Yrs Sch. Res. Sq. Yrs. Sch. Res. Sq. Yrs. Sch. Res. Sq. Urban Father’s Edu 0.356*** -0.548*** 0.563*** -0.772*** 0.468*** -0.707*** (0.013) (0.053) (0.007) (0.034) (0.016) (0.065) Constant 7.564*** 17.449*** 5.498*** 21.478*** 7.225*** 16.935*** (0.147) (0.586) (0.074) (0.250) (0.171) (0.598) Observations 35,308 35,308 31,216 31,216 5919 5919 R-squared 0.158 0.013 0.316 0.029 0.236 0.027 ̅ Mean of 𝑌 9.376 14.66 8.446 17.44 10.835 11.475 Rural Father’s Edu 0.321*** -0.524*** 0.589*** -0.022 0.467*** -0.294*** (0.014) (0.044) (0.007) (0.040) (0.012) (0.069) Constant 5.271*** 17.799*** 3.798*** 18.702*** 6.331*** 15.967*** (0.165) (0.342) (0.048) (0.177) (0.115) (0.516) Observations 58,851 58,851 55,532 55,532 12437 12437 R-squared 0.097 0.013 0.226 0.000 0.161 0.003 ̅ Mean of 𝑌 6.408 15.94 5.408 18.64 8.899 14.351 Sons Father’s Edu 0.329*** -0.476*** 0.595*** -0.927*** 0.461*** -0.522*** (0.014) (0.048) (0.006) (0.025) (0.013) (0.066) Constant 6.824*** 17.033*** 5.361*** 20.974*** 6.971*** 16.259*** (0.142) (0.547) (0.049) (0.165) (0.133) (0.516) Observations 46,791 46,791 46,701 46,701 8558 8558 R-squared 0.121 0.009 0.290 0.038 0.194 0.012 ̅ Mean of 𝑌 8.169 15.09 7.557 17.55 9.821 13.03 Daughters Father’s Edu 0.438*** -0.364*** 0.643*** 0.334*** 0.528*** -0.483*** (0.015) (0.052) (0.006) (0.040) (0.013) (0.061) Constant 5.057*** 19.099*** 2.974*** 16.306*** 5.964*** 16.892*** (0.174) (0.347) (0.048) (0.200) (0.123) (0.499) Observations 47,368 47,368 40,047 40,047 9798 9798 R-squared 0.172 0.006 0.332 0.004 0.231 0.010 ̅ Mean of 𝑌 6.880 17.58 5.269 17.50 9.263 13.875 Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) Each row uses a sub- sample of children who were born in the given birth cohort and the given category. 27 Table 4: Evolution Across Birth Cohorts CHINA INDIA INDONESIA Yrs Sch. Res. Sq. Yrs. Sch. Res. Sq. Yrs. Sch. Res. Sq. 1980-1989 0.420*** -0.766*** 0.551*** -0.644*** 0.424*** -0.478*** (0.034) (0.101) (0.007) (0.034) (0.013) (0.050) 1970-1979 0.398*** -0.445*** 0.582*** -0.294*** 0.492*** -0.299*** (0.021) (0.055) (0.007) (0.041) (0.015) (0.065) 1960-1969 0.292*** -0.435*** 0.650*** 0.053 0.586*** -0.328** (0.015) (0.046) (0.009) (0.056) (0.024) (0.139) 1950-1959 0.292*** -0.275*** 0.681*** 0.028 0.521*** 0.462** (0.017) (0.070) (0.011) (0.077) (0.036) (0.228) Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. 28 Table 5: Relative Mobility and Absolute Mobility (Full Sample) Risk Adjusted vs. Standard Estimates CHINA INDIA INDONESIA Linear Linear Linear RIGRC RES RIGRC RES RIGRC RES ES ES ES No Sch 0.525 4.359 5.943 1.013 1.872 4.244 0.637 5.134 6.437 (0.019) (0.195) (0.152) (0.011) (0.069) (0.043) (0.014) (0.140) (0.113) Primary 0.457 7.272 8.239 0.752 6.109 7.350 0.562 8.691 9.418 (0.019) (0.126) (0.111) (0.006) (0.042) (0.035) (0.012) (0.082) (0.075) Junior High 0.440 8.615 9.386 0.686 9.674 10.455 0.546 10.351 10.908 (0.015) (0.122) (0.111) (0.005) (0.047) (0.043) (0.012) (0.077) (0.072) Senior High 0.428 9.915 10.534 0.673 11.031 11.698 0.535 11.971 12.399 (0.015) (0.134) (0.125) (0.005) (0.053) (0.049) (0.011) (0.087) (0.083) College 0.417 11.604 12.064 0.660 13.028 13.561 0.525 14.089 14.386 (0.015) (0.168) (0.160) (0.005) (0.063) (0.060) (0.011) (0.114) (0.110) IGRC 0.383 0.621 0.497 (0.014) (0.005) (0.011) Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) The RIGRC refers to the Risk Adjusted IGRC. The RES refers to the Risk Adjusted Expected Schooling. The Linear ES refers to the Expected Schooling from a linear CEF mobility model. And the IGRC is the Intergenerational Regression Coefficient from a linear CEF mobility model. 29 Table 6A: Relative Mobility and Absolute Mobility Across Urban vs. Rural Areas CHINA INDIA INDONESIA Linear Linear Linear RIGRC RES RIGRC RES RIGRC RES ES ES ES Urban No Sch 0.446 6.411 7.564 0.833 3.545 5.498 0.593 6.053 7.225 (0.015) (0.174) (0.147) (0.012) (0.102) (0.074) (0.020) (0.203) (0.171) Primary 0.411 8.970 9.700 0.681 7.255 8.314 0.533 9.400 10.033 (0.014) (0.114) (0.104) (0.008) (0.060) (0.052) (0.017) (0.104) (0.096) Junior High 0.401 10.187 10.768 0.629 10.512 11.130 0.518 10.974 11.436 (0.013) (0.105) (0.099) (0.007) (0.052) (0.048) (0.017) (0.082) (0.078) Senior High 0.393 11.377 11.836 0.618 11.758 12.256 0.507 12.511 12.840 (0.013) (0.112) (0.107) (0.007) (0.056) (0.052) (0.016) (0.089) (0.086) College 0.385 12.933 13.260 0.605 13.591 13.946 0.498 14.521 14.712 (0.013) (0.139) (0.134) (0.007) (0.067) (0.064) (0.016) (0.130) (0.127) IGRC 0.356 0.563 0.468 (0.013) (0.007) (0.016) Rural No Sch 0.473 3.583 5.271 0.973 1.336 3.798 0.583 5.071 6.331 (0.021) (0.220) (0.165) (0.016) (0.082) (0.048) (0.016) (0.144) (0.115) Primary 0.402 6.177 7.195 0.711 5.362 6.741 0.523 8.357 9.134 (0.017) (0.121) (0.103) (0.009) (0.057) (0.046) (0.014) (0.090) (0.081) Junior High 0.384 7.355 8.157 0.648 8.730 9.685 0.509 9.903 10.536 (0.016) (0.102) (0.088) (0.008) (0.073) (0.065) (0.013) (0.092) (0.085) Senior High 0.372 8.488 9.119 0.636 10.013 10.862 0.500 11.416 11.937 (0.016) (0.106) (0.094) (0.008) (0.084) (0.076) (0.013) (0.110) (0.103) College 0.362 9.588 10.081 0.623 11.901 12.628 0.492 13.398 13.806 (0.015) (0.128) (0.117) (0.007) (0.101) (0.093) (0.013) (0.146) (0.139) IGRC 0.321 0.589 0.467 (0.014) (0.007) (0.012) Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) The RIGRC refers to the Risk Adjusted Intergenerational Regression Coefficient. The RES refers to the Risk Adjusted Expected Schooling. The Linear ES refers to the Expected Schooling from a linear CEF mobility model. And the IGRC is the Intergenerational Regression Coefficient from a linear CEF mobility model. 30 Table 6B: Relative Mobility and Absolute Mobility Across Sons vs. Daughters CHINA INDIA INDONESIA Linear Linear Linear RIGRC RES RIGRC RES RIGRC RES ES ES ES Sons No Sch 0.424 5.576 6.824 0.899 3.405 5.361 0.576 5.805 6.971 (0.018) (0.173) (0.142) (0.009) (0.069) (0.049) (0.017) (0.160) (0.133) Primary 0.387 7.994 8.800 0.721 7.358 8.338 0.520 9.066 9.740 (0.016) (0.108) (0.097) (0.007) (0.039) (0.034) (0.014) (0.092) (0.085) Junior High 0.376 9.137 9.788 0.664 10.798 11.315 0.506 10.605 11.124 (0.015) (0.106) (0.098) (0.006) (0.040) (0.038) (0.014) (0.086) (0.081) Senior High 0.367 10.251 10.776 0.651 12.112 12.506 0.497 12.109 12.509 (0.015) (0.122) (0.115) (0.006) (0.047) (0.045) (0.014) (0.100) (0.095) College 0.360 11.704 12.093 0.638 14.045 14.292 0.488 14.079 14.354 (0.015) (0.161) (0.154) (0.006) (0.059) (0.057) (0.013) (0.135) (0.130) IGRC 0.329 0.595 0.461 (0.014) (0.006) (0.013) Daughters No Sch 0.638 3.169 5.057 1.180 0.232 2.974 0.694 4.547 5.964 (0.024) (0.241) (0.174) (0.024) (0.099) (0.048) (0.018) (0.158) (0.123) Primary 0.524 6.585 7.685 0.767 4.737 6.189 0.599 8.369 9.134 (0.017) (0.155) (0.133) (0.009) (0.061) (0.048) (0.014) (0.085) (0.077) Junior High 0.501 8.120 8.999 0.697 8.360 9.405 0.580 10.135 10.720 (0.017) (0.147) (0.132) (0.007) (0.074) (0.065) (0.014) (0.082) (0.076) Senior High 0.486 9.599 10.313 0.685 9.741 10.691 0.567 11.854 12.305 (0.016) (0.157) (0.144) (0.007) (0.082) (0.074) (0.014) (0.098) (0.093) College 0.476 11.041 11.627 0.673 11.776 12.620 0.557 14.101 14.419 (0.016) (0.179) (0.168) (0.007) (0.097) (0.089) (0.013) (0.135) (0.130) IGRC 0.438 0.643 0.528 (0.015) (0.006) (0.013) Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) The RIGRC refers to the Risk Adjusted Intergenerational Regression Coefficient. The RES refers to the Risk Adjusted Expected Schooling. The Linear ES refers to the Expected Schooling from a linear CEF mobility model. And the IGRC is the Intergenerational Regression Coefficient from a linear CEF mobility model. 31 Table 7: Comparing Weighted Risk Adjusted IGRC to Canonical IGRC CHINA INDIA INDONESIA Weighted Canonical Weighted Canonical Weighted Canonical RIGRC IGRC RIGRC IGRC RIGRC IGRC All 0.484 0.383 0.876 0.621 0.568 0.497 Urban 0.420 0.356 0.721 0.563 0.527 0.468 Rural 0.436 0.321 0.863 0.589 0.532 0.467 Sons 0.402 0.329 0.800 0.595 0.524 0.461 Daughters 0.571 0.438 0.980 0.643 0.607 0.528 Urban Sons 0.351 0.312 0.651 0.524 0.498 0.443 Urban Daughters 0.486 0.402 0.791 0.597 0.551 0.489 Rural Sons 0.357 0.270 0.829 0.592 0.487 0.431 Rural Daughters 0.519 0.375 0.921 0.580 0.571 0.500 Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) The weights are the proportion of children at each level of father ’s education. Table 8: Evolution of Risk Adjusted IGRC by Birth Cohorts CHINA INDIA INDONESIA Weighted Canonical Weighted Canonical Weighted Canonical RIGRC IGRC RIGRC IGRC RIGRC IGRC 1980-1989 0.507 0.420 0.705 0.551 0.468 0.424 1970-1979 0.493 0.398 0.822 0.582 0.540 0.492 1960-1969 0.369 0.292 0.993 0.650 0.704 0.586 1950-1959 0.399 0.292 1.054 0.681 0.597 0.521 Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) Each row uses a sub- sample of children who were born in the given birth cohort. (3) (2) The weights are the proportion of children at each level of father’s education. 32 Table 9: Evolution of Risk Adjusted IGRC by Birth Cohorts Urban vs. Rural and Sons vs. Daughters CHINA INDIA INDONESIA Weighted Canonical Weighted Canonical Weighted Canonical RIGRC IGRC RIGRC IGRC RIGRC IGRC Urban 1980-1989 0.398 0.344 0.630 0.524 0.466 0.427 1970-1979 0.396 0.343 0.685 0.537 0.461 0.422 1960-1969 0.323 0.273 0.771 0.575 0.617 0.516 1950-1959 0.334 0.260 0.788 0.580 0.622 0.554 Rural 1980-1989 0.453 0.359 0.674 0.512 0.439 0.397 1970-1979 0.405 0.300 0.789 0.538 0.512 0.470 1960-1969 0.298 0.213 0.913 0.576 0.649 0.555 1950-1959 0.308 0.210 0.995 0.620 0.511 0.451 Sons 1980-1989 0.469 0.393 0.622 0.505 0.450 0.407 1970-1979 0.431 0.357 0.394 0.275 0.499 0.455 1960-1969 0.311 0.256 0.906 0.633 0.626 0.529 1950-1959 0.310 0.240 1.035 0.704 0.585 0.502 Daughters 1980-1989 0.543 0.447 0.783 0.585 0.482 0.438 1970-1979 0.553 0.439 0.913 0.605 0.580 0.529 1960-1969 0.425 0.326 1.105 0.653 0.758 0.626 1950-1959 0.499 0.349 1.275 0.620 0.612 0.555 Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) Each row uses a sub- sample of children who were born in the given birth cohort and the given category. (3) (2) The weights are the proportion of children at each level of father ’s education. 33 Figure 1. Conditional Mean and Variance of Child’s Schooling Against Father’s Schooling Panel A. China Panel B. India Panel C. Indonesia 34 Figure 2. Risk Adjusted and Linear Relative Mobility Panel A. China Panel B. India Panel C. Indonesia 35 Figure 3. Risk Adjusted and Linear Absolute Mobility Panel A. China Panel B. India Panel C. Indonesia 36 ONLINE APPENDIX: NOT FOR PUBLICATION OA1. Additional Results on Residual Squared Table A.1: Intersections of Geography and Gender CHINA INDIA INDONESIA Yrs Sch. Res. Sq. Yrs. Sch. Res. Sq. Yrs. Sch. Res. Sq. Urban Sons Father’s Edu 0.312*** -0.400*** 0.524*** -1.007*** 0.443*** -0.714*** (0.012) (0.062) (0.008) (0.035) (0.020) (0.096) Constant 8.152*** 15.510*** 6.456*** 20.780*** 7.640*** 16.389*** (0.131) (0.604) (0.084) (0.309) (0.208) (0.808) Observations 17,823 17,823 16,697 16,697 2649 2649 R-squared 0.136 0.007 0.307 0.058 0.224 0.028 ̅ Mean of 𝑌 9.732 13.48 9.264 15.39 11.043 10.902 Urban Daughters Father’s Edu 0.402*** -0.640*** 0.597*** -0.384*** 0.489*** -0.694*** (0.015) (0.059) (0.008) (0.049) (0.019) (0.075) Constant 6.956*** 18.774*** 4.463*** 20.284*** 6.884*** 17.225*** (0.180) (0.610) (0.085) (0.309) (0.190) (0.739) Observations 17,485 17,485 14,519 14,519 3270 3270 R-squared 0.184 0.018 0.336 0.007 0.247 0.026 ̅ Mean of 𝑌 9.013 15.50 7.504 18.33 10.667 11.851 Rural Sons Father’s Edu 0.270*** -0.631*** 0.592*** -0.793*** 0.431*** -0.323*** (0.016) (0.053) (0.008) (0.039) (0.015) (0.083) Constant 6.267*** 16.681*** 4.972*** 20.436*** 6.901*** 15.577*** (0.166) (0.551) (0.058) (0.199) (0.137) (0.596) Observations 28,968 28,968 30,004 30,004 5909 5909 R-squared 0.077 0.017 0.227 0.021 0.146 0.004 ̅ Mean of 𝑌 7.208 14.49 6.608 18.25 9.273 13.798 Rural Daughters Father’s Edu 0.375*** -0.275*** 0.580*** 0.793*** 0.500*** -0.231*** (0.014) (0.069) (0.009) (0.050) (0.017) (0.089) Constant 4.281*** 16.972*** 2.431*** 13.383*** 15.530*** 5.816*** (0.179) (0.212) (0.052) (0.227) (0.596) (0.134) Observations 29,883 29,883 25,528 25,528 6528 6528 R-squared 0.128 0.004 0.260 0.022 0.177 0.002 ̅ Mean of 𝑌 5.632 15.98 3.997 15.52 9.273 13.798 Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) Each row uses a sub- sample of children who were born in the given birth cohort and the given category. 37 Table A.2: Evolution by Birth Cohorts Across Urban vs. Rural and Sons vs. Daughters CHINA INDIA INDONESIA Yrs Sch. Res. Sq. Yrs. Sch. Res. Sq. Yrs. Sch. Res. Sq. Urban 1980-1989 0.344*** -0.845*** 0.524*** -0.841*** 0.427*** -0.561*** (0.027) (0.128) (0.010) (0.048) (0.018) (0.072) 1970-1979 0.343*** -0.550*** 0.537*** -0.658*** 0.422*** -0.476*** (0.019) (0.095) (0.010) (0.053) (0.023) (0.091) 1960-1969 0.273*** -0.465*** 0.575*** -0.634*** 0.516*** -0.957*** (0.014) (0.056) (0.012) (0.072) (0.039) (0.194) 1950-1959 0.260*** -0.521*** 0.580*** -0.690*** 0.554*** 0.243 (0.019) (0.091) (0.016) (0.100) (0.055) (0.287) Rural 1980-1989 0.359*** -0.787*** 0.512*** -0.456*** 0.397*** -0.384*** (0.038) (0.106) (0.009) (0.048) (0.015) (0.064) 1970-1979 0.300*** -0.549*** 0.538*** 0.051 0.470*** -0.086 (0.021) (0.060) (0.011) (0.059) (0.017) (0.091) 1960-1969 0.213*** -0.514*** 0.576*** 0.631*** 0.555*** 0.182 (0.015) (0.053) (0.014) (0.077) (0.031) (0.174) 1950-1959 0.210*** -0.115 0.620*** 0.584*** 0.451*** 0.589** (0.017) (0.079) (0.018) (0.112) (0.047) (0.287) Sons 1980-1989 0.393*** -0.774*** 0.505*** -0.860*** 0.407*** -0.485*** (0.033) (0.113) (0.008) (0.038) (0.017) (0.071) 1970-1979 0.357*** -0.493*** 0.548*** -0.956*** 0.455*** -0.306*** (0.022) (0.072) (0.009) (0.041) (0.019) (0.075) 1960-1969 0.256*** -0.394*** 0.633*** -0.785*** 0.529*** -0.528** (0.015) (0.058) (0.011) (0.057) (0.031) (0.210) 1950-1959 0.240*** -0.383*** 0.704*** -0.608*** 0.502*** 0.040 (0.017) (0.082) (0.013) (0.077) (0.056) (0.329) Daughters 1980-1989 0.447*** -0.724*** 0.585*** -0.262*** 0.438*** -0.473*** (0.036) (0.111) (0.009) (0.050) (0.016) (0.063) 1970-1979 0.439*** -0.315*** 0.605*** 0.470*** 0.529*** -0.263*** (0.022) (0.072) (0.010) (0.057) (0.018) (0.086) 1960-1969 0.326*** -0.388*** 0.653*** 0.984*** 0.626*** -0.049 (0.017) (0.062) (0.012) (0.074) (0.030) (0.171) 1950-1959 0.349*** 0.059 0.620*** 1.126*** 0.555*** 0.918*** (0.021) (0.110) (0.020) (0.119) (0.045) (0.256) 38 Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) Each row uses a sub- sample of children who were born in the given birth cohort and the given category. Table A.3: Evolution of Risk Adjusted IGRC by Birth Cohorts Across Geography and Gender CHINA INDIA INDONESIA Weighted Canonical Weighted Canonical Weighted Canonical RIGRC IGRC RIGRC IGRC RIGRC IGRC Urban Sons 1980-1989 0.385 0.330 0.585 0.499 0.462 0.421 1970-1979 0.362 0.315 0.618 0.500 0.459 0.417 1960-1969 0.288 0.251 0.687 0.528 0.551 0.458 1950-1959 0.250 0.210 0.736 0.565 0.541 0.521 Urban Daughters 1980-1989 0.415 0.359 0.668 0.540 0.469 0.432 1970-1979 0.434 0.373 0.741 0.566 0.463 0.427 1960-1969 0.356 0.294 0.840 0.609 0.659 0.556 1950-1959 0.428 0.312 0.917 0.581 0.689 0.586 Rural Sons 1980-1989 0.422 0.339 0.607 0.478 0.420 0.381 1970-1979 0.359 0.271 0.745 0.538 0.462 0.427 1960-1969 0.242 0.178 0.904 0.606 0.567 0.494 1950-1959 0.263 0.180 1.079 0.684 0.559 0.455 Rural Daughters 1980-1989 0.484 0.381 0.730 0.532 0.456 0.411 1970-1979 0.446 0.326 0.819 0.522 0.560 0.514 1960-1969 0.350 0.247 0.905 0.521 0.698 0.593 1950-1959 0.367 0.251 0.947 0.496 0.451 0.463 Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) Each row uses a sub- sample of children who were born in the given birth cohort and the given category. 39 OA2. Robustness Check: Linear vs. Quadratic CEF Model Table A.4: Full Sample Estimates with Linear CEF and Quadratic CEF CHINA INDIA INDONESIA Mobility CEF Linear Quadratic Linear Quadratic Linear Quadratic Specification Outcome Var Res. Sq. Res. Sq. Res. Sq. Res. Sq. Res. Sq. Res. Sq. Father's Edu -0.483*** -0.484*** -0.379*** -0.379*** -0.514*** -0.508*** (0.036) (0.037) (0.028) (0.028) (0.052) (0.052) Constant 18.823*** 18.821*** 20.134*** 20.099*** 16.784*** 16.728*** (0.424) (0.431) (0.144) (0.146) (0.429) (0.428) Observations 94,159 94,159 86,748 86,748 18356 18356 R-squared 0.009 0.009 0.006 0.005 0.011 0.011 ̅ Mean of 𝑌 16.83 16.83 18.76 18.72 13.587 13.569 Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. 40 Table A.5: Heterogeneity Across Urban vs. Rural and Sons vs. Daughters CHINA INDIA INDONESIA Mobility CEF Linear Quadratic Linear Quadratic Linear Quadratic Specification Outcome Var Res. Sq. Res. Sq. Res. Sq. Res. Sq. Res. Sq. Res. Sq. Urban Father’s Edu -0.548*** -0.546*** -0.772*** -0.773*** -0.707*** -0.707*** (0.053) (0.054) (0.034) (0.033) (0.065) (0.065) Constant 17.449*** 17.436*** 21.478*** 21.452*** 16.935*** 16.930*** (0.586) (0.593) (0.250) (0.251) (0.598) (0.599) Observations 35,308 35,308 31,216 31,216 5919 5919 R-squared 0.013 0.013 0.029 0.029 0.027 0.027 ̅ Mean of 𝑌 14.66 14.66 17.44 17.41 11.475 13.568 Rural Father’s Edu -0.524*** -0.528*** -0.022 -0.023 -0.294*** -0.294*** (0.044) (0.044) (0.040) (0.039) (0.069) (0.069) Constant 17.799*** 17.810*** 18.702*** 18.660*** 15.967*** 15.931*** (0.342) (0.339) (0.177) (0.178) (0.516) (0.515) Observations 58,851 58,851 55,532 55,532 12437 12437 R-squared 0.013 0.013 0.000 0.000 0.003 0.003 ̅ Mean of 𝑌 15.94 15.94 18.64 18.60 14.351 14.314 Sons Father’s Edu -0.476*** -0.478*** -0.927*** -0.934*** -0.522*** -0.516*** (0.048) (0.049) (0.025) (0.025) (0.066) (0.066) Constant 17.033*** 17.033*** 20.974*** 20.960*** 16.259*** 16.216*** (0.547) (0.554) (0.165) (0.166) (0.516) (0.514) Observations 46,791 46,791 46,701 46,701 8558 8558 R-squared 0.009 0.009 0.038 0.039 0.012 0.012 ̅ Mean of 𝑌 15.09 15.08 17.55 17.52 13.03 13.025 Daughters Father’s Edu -0.364*** -0.365*** 0.334*** 0.335*** -0.483*** -0.477*** (0.052) (0.052) (0.040) (0.040) (0.061) (0.061) Constant 19.099*** 19.095*** 16.306*** 16.296*** 16.892*** 16.824*** (0.347) (0.351) (0.200) (0.200) (0.499) (0.499) Observations 47,368 47,368 40,047 40,047 9798 9798 R-squared 0.006 0.006 0.004 0.004 0.010 0.010 ̅ Mean of 𝑌 17.58 17.58 17.50 17.49 13.875 13.846 Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) Each row uses a sub- sample of children who were born in the given birth cohort and the given category. 41 Table A.6: Intersections of Geography and Gender CHINA INDIA INDONESIA Mobility CEF Linear Quadratic Linear Quadratic Linear Quadratic Specification Outcome Var Res. Sq. Res. Sq. Res. Sq. Res. Sq. Res. Sq. Res. Sq. Urban Sons Father’s Edu -0.400*** -0.399*** -1.007*** -1.009*** -0.714*** -0.715*** (0.062) (0.063) (0.035) (0.035) (0.096) (0.096) Constant 15.510*** 15.498*** 20.780*** 20.778*** 16.389*** 16.393*** (0.604) (0.610) (0.309) (0.308) (0.808) (0.805) Observations 17,823 17,823 16,697 16,697 2649 2649 R-squared 0.007 0.007 0.058 0.058 0.028 0.028 ̅ Mean of 𝑌 13.48 13.47 15.39 15.38 10.902 10.901 Urban Daughters Father’s Edu -0.640*** -0.638*** -0.384*** -0.385*** -0.694*** -0.691*** (0.059) (0.060) (0.049) (0.049) (0.075) (0.076) Constant 18.774*** 18.761*** 20.284*** 20.268*** 17.225*** 17.196*** (0.610) (0.616) (0.309) (0.311) (0.739) (0.744) Observations 17,485 17,485 14,519 14,519 3270 3270 R-squared 0.018 0.018 0.007 0.007 0.026 0.026 ̅ Mean of 𝑌 15.50 15.50 18.33 18.31 11.851 11.845 Rural Sons Father’s Edu -0.631*** -0.633*** -0.793*** -0.805*** -0.323*** -0.319*** (0.053) (0.052) (0.039) (0.038) (0.083) (0.083) Constant 16.681*** 16.688*** 20.436*** 20.425*** 15.577*** 15.530*** (0.551) (0.547) (0.199) (0.200) (0.596) (0.596) Observations 28,968 28,968 30,004 30,004 5909 5909 R-squared 0.017 0.017 0.021 0.022 0.004 0.004 ̅ Mean of 𝑌 14.49 14.48 18.25 18.20 13.798 13.773 Rural Daughters Father’s Edu -0.275*** -0.281*** 0.793*** 0.793*** -0.231*** -0.237*** (0.069) (0.069) (0.050) (0.049) (0.089) (0.090) Constant 16.972*** 16.989*** 13.383*** 13.370*** 15.857*** 15.837*** (0.212) (0.211) (0.227) (0.227) (0.620) (0.620) Observations 29,883 29,883 25,528 25,528 6528 6528 R-squared 0.004 0.004 0.022 0.022 0.002 0.002 ̅ Mean of 𝑌 15.98 15.98 15.52 15.51 13.798 14.534 Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) Each row uses a sub- sample of children who were born in the given birth cohort and the given category. 42 Table A.7: Evolution of Mobility by Birth Cohorts CHINA INDIA INDONESIA Mobility CEF Linear Quadratic Linear Quadratic Linear Quadratic Specification Outcome Var Res. Sq. Res. Sq. Res. Sq. Res. Sq. Res. Sq. Res. Sq. 1980-1989 -0.766*** -0.772*** -0.644*** -0.644*** -0.478*** -0.478*** (0.101) (0.106) (0.034) (0.033) (0.050) (0.050) 1970-1979 -0.445*** -0.452*** -0.294*** -0.291*** -0.299*** -0.297*** (0.055) (0.056) (0.041) (0.041) (0.065) (0.065) 1960-1969 -0.435*** -0.441*** 0.053 0.061 -0.328** -0.324** (0.046) (0.047) (0.056) (0.054) (0.139) (0.139) 1950-1959 -0.275*** -0.281*** 0.028 0.022 0.462** 0.470** (0.070) (0.068) (0.077) (0.073) (0.228) (0.228) Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. 43 Table A.8: Evolution of Mobility by Birth Cohorts Across Urban vs. Rural and Sons vs. Daughters CHINA INDIA INDONESIA Mobility CEF Linear Quadratic Linear Quadratic Linear Quadratic Specification Outcome Var Res. Sq. Res. Sq. Res. Sq. Res. Sq. Res. Sq. Res. Sq. Urban 1980-1989 -0.845*** -0.846*** -0.841*** -0.843*** -0.561*** -0.561*** (0.128) (0.136) (0.048) (0.047) (0.072) (0.073) 1970-1979 -0.550*** -0.551*** -0.658*** -0.657*** -0.476*** -0.470*** (0.095) (0.099) (0.053) (0.053) (0.091) (0.090) 1960-1969 -0.465*** -0.470*** -0.634*** -0.631*** -0.957*** -0.957*** (0.056) (0.057) (0.072) (0.070) (0.194) (0.194) 1950-1959 -0.521*** -0.524*** -0.690*** -0.694*** 0.243 0.229 (0.091) (0.091) (0.100) (0.096) (0.287) (0.287) Rural 1980-1989 -0.787*** -0.787*** -0.456*** -0.458*** -0.384*** -0.386*** (0.106) (0.101) (0.048) (0.047) (0.064) (0.065) 1970-1979 -0.549*** -0.553*** 0.051 0.057 -0.086 -0.086 (0.060) (0.060) (0.059) (0.057) (0.091) (0.091) 1960-1969 -0.514*** -0.514*** 0.631*** 0.656*** 0.182 0.184 (0.053) (0.053) (0.077) (0.074) (0.174) (0.177) 1950-1959 -0.115 -0.150** 0.584*** 0.577*** 0.589** 0.594** (0.079) (0.075) (0.112) (0.105) (0.287) (0.287) Sons 1980-1989 -0.774*** -0.784*** -0.860*** -0.863*** -0.485*** -0.487*** (0.113) (0.119) (0.038) (0.038) (0.071) (0.072) 1970-1979 -0.493*** -0.500*** -0.956*** -0.957*** -0.306*** -0.303*** (0.072) (0.073) (0.041) (0.041) (0.075) (0.075) 1960-1969 -0.394*** -0.399*** -0.785*** -0.783*** -0.528** -0.532** (0.058) (0.058) (0.057) (0.056) (0.210) (0.209) 1950-1959 -0.383*** -0.388*** -0.608*** -0.630*** 0.040 0.059 (0.082) (0.080) (0.077) (0.072) (0.329) (0.331) Daughters 1980-1989 -0.724*** -0.728*** -0.262*** -0.262*** -0.473*** -0.469*** (0.111) (0.113) (0.050) (0.049) (0.063) (0.064) 1970-1979 -0.315*** -0.322*** 0.470*** 0.471*** -0.263*** -0.262*** (0.072) (0.073) (0.057) (0.057) (0.086) (0.086) 1960-1969 -0.388*** -0.396*** 0.984*** 0.986*** -0.049 -0.048 (0.062) (0.061) (0.074) (0.072) (0.171) (0.169) 1950-1959 0.059 0.051 1.126*** 1.121*** 0.918*** 0.919*** (0.110) (0.108) (0.119) (0.121) (0.256) (0.256) Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) Each row uses a sub- sample of children who were born in the given birth cohort and the given category. 44 OA3. Robustness Check: Control for Ability Table A.9 : Estimates with Ability Controls in Indonesia Yrs. Sch Res. Sq. Full Sample Father's Edu 0.497*** -0.420*** (0.011) (0.057) Constant 6.437*** 14.806*** (0.113) (0.452) R-squared 0.212 0.030 Observations 18356 18356 Urban Only Father's Edu 0.468*** 0.468*** (0.016) (0.016) Constant 7.225*** 7.225*** (0.171) (0.171) R-squared 0.236 0.236 Observations 5919 5919 Rural Only Father's Edu 0.467*** 0.467*** (0.012) (0.012) Constant 6.331*** 6.331*** (0.115) (0.115) R-squared 0.161 0.161 Observations 12437 12437 Sons Only Father's Edu 0.461*** 0.461*** (0.013) (0.013) Constant 6.971*** 6.971*** (0.133) (0.133) R-squared 0.194 0.194 Observations 8558 8558 Daughters Only Father's Edu 0.528*** 0.528*** (0.013) (0.013) Constant 5.964*** 5.964*** (0.123) (0.123) R-squared 0.231 0.231 Observations 9798 9798 Notes: (1) The data are from the IFLS 2014 round for Indonesia. The regression includes the cognitive ability index and its square. The cognitive ability index was constructed taking the first principal component of Raven test scores and two memory tests net of age and age square. 45 OA4. Estimated Relative and Absolute Mobility Table A.10: Relative Mobility and Absolute Mobility Across Sons vs. Daughters in Urban Area CHINA INDIA INDONESIA Linear Linear Linear RIGRC RES RIGRC RES RIGRC RES ES ES ES Urban Sons No Sch 0.373 7.200 8.152 0.733 4.847 6.456 0.552 6.568 7.640 (0.014) (0.151) (0.131) (0.012) (0.108) (0.084) (0.024) (0.243) (0.208) Primary 0.352 9.369 10.023 0.630 8.211 9.078 0.503 9.710 10.298 (0.013) (0.106) (0.098) (0.009) (0.061) (0.055) (0.021) (0.124) (0.116) Junior High 0.346 10.415 10.958 0.588 11.242 11.700 0.490 11.199 11.627 (0.013) (0.104) (0.098) (0.009) (0.050) (0.048) (0.021) (0.100) (0.095) Senior High 0.340 11.444 11.894 0.578 12.408 12.749 0.481 12.654 12.956 (0.013) (0.115) (0.109) (0.008) (0.056) (0.054) (0.021) (0.113) (0.108) College 0.335 12.795 13.142 0.567 14.124 14.322 0.472 14.559 14.728 (0.012) (0.144) (0.138) (0.008) (0.071) (0.069) (0.020) (0.166) (0.161) IGRC 0.312 0.524 0.443 (0.012) (0.008) (0.020) Urban Daughters No Sch 0.527 5.607 6.956 0.944 2.191 4.463 0.628 5.633 6.884 (0.019) (0.220) (0.180) (0.019) (0.133) (0.085) (0.024) (0.231) (0.190) Primary 0.471 8.574 9.371 0.722 6.216 7.449 0.557 9.150 9.816 (0.017) (0.134) (0.121) (0.010) (0.079) (0.067) (0.020) (0.110) (0.102) Junior High 0.456 9.963 10.578 0.661 9.646 10.434 0.540 10.795 11.281 (0.016) (0.118) (0.110) (0.009) (0.077) (0.070) (0.020) (0.088) (0.083) Senior High 0.446 11.315 11.785 0.648 10.954 11.628 0.529 12.398 12.747 (0.016) (0.122) (0.116) (0.009) (0.084) (0.077) (0.019) (0.103) (0.099) College 0.438 12.639 12.993 0.635 12.878 13.419 0.519 14.493 14.701 (0.016) (0.143) (0.137) (0.009) (0.099) (0.093) (0.019) (0.156) (0.153) IGRC 0.402 0.597 0.489 (0.015) (0.008) (0.019) Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) The RIGRC refers to the Risk Adjusted Intergenerational Marginal Effect. The RES refers to the Risk Adjusted Expected Schooling. The Linear ES refers to the Expected Schooling from a linear CEF mobility model. And the IGRC is the Intergenerational Regressional Coefficient from a linear CEF mobility model. 46 Table A11: Relative Mobility and Absolute Mobility Across Sons vs. Daughters in Rural Area CHINA INDIA INDONESIA Linear Linear Linear RIGRC RES RIGRC RES RIGRC RES ES ES ES Rural Sons No Sch 0.378 4.936 6.267 0.916 2.917 4.972 0.525 5.773 6.901 (0.021) (0.206) (0.166) (0.014) (0.084) (0.058) (0.019) (0.165) (0.137) Primary 0.338 7.071 7.889 0.719 6.894 7.932 0.481 8.770 9.489 (0.018) (0.105) (0.092) (0.009) (0.050) (0.043) (0.016) (0.100) (0.091) Junior High 0.326 8.067 8.699 0.660 10.318 10.892 0.470 10.195 10.783 (0.018) (0.087) (0.078) (0.008) (0.063) (0.058) (0.016) (0.102) (0.095) Senior High 0.317 9.031 9.510 0.647 11.624 12.076 0.462 11.592 12.076 (0.017) (0.101) (0.092) (0.008) (0.074) (0.070) (0.016) (0.123) (0.116) College 0.310 9.971 10.321 0.634 13.544 13.852 0.455 13.425 13.801 (0.017) (0.133) (0.126) (0.008) (0.093) (0.089) (0.015) (0.168) (0.160) IGRC 0.270 0.592 0.431 (0.016) (0.008) (0.015) Rural Daughters No Sch 0.580 2.299 4.281 1.073 -0.322 2.431 0.637 4.453 5.816 (0.028) (0.262) (0.179) (0.035) (0.119) (0.052) (0.023) (0.174) (0.134) Primary 0.463 5.355 6.529 0.682 3.703 5.330 0.559 7.993 8.814 (0.018) (0.155) (0.128) (0.013) (0.087) (0.065) (0.019) (0.097) (0.087) Junior High 0.439 6.705 7.652 0.623 6.934 8.229 0.543 9.645 10.312 (0.017) (0.141) (0.120) (0.011) (0.118) (0.100) (0.018) (0.108) (0.100) Senior High 0.423 7.997 8.776 0.613 8.169 9.388 0.533 11.258 11.811 (0.016) (0.146) (0.127) (0.011) (0.133) (0.116) (0.018) (0.140) (0.132) College 0.413 9.251 9.900 0.603 9.992 11.128 0.524 13.370 13.810 (0.016) (0.164) (0.147) (0.011) (0.158) (0.141) (0.018) (0.196) (0.187) IGRC 0.375 0.580 0.500 (0.014) (0.009) (0.017) Notes: (1) The data are from children who were born between 1950 and 1989 using the CFPS 2010 round for China, the IHDS 2012 round for India, and the IFLS 2014 round for Indonesia. (2) The RIGRC refers to the Risk Adjusted Intergenerational Marginal Effect. The RES refers to the Risk Adjusted Expected Schooling. The Linear ES refers to the Expected Schooling from a linear CEF mobility model. And the IGRC is the Intergenerational Regressional Coefficient from a linear CEF mobility model. 47