Does Children’s Education Matter for Parents’ Healthand Cognition in Old Age? Evidence from China

Mingming MA∗†

November 7, 2017

Abstract

Intergenerational transmission of human capital from parents to offspring has been widely doc-umented. However, whether there are also upward spillovers from children to parents remainsunderstudied. This paper uses data from the China Health and Retirement Longitudinal Studyto estimate the causal impact of educational attainments of the highest educated adult child onvarious health and cognition outcomes of older adults. Identification is achieved by using theexposure of adult children to the compulsory education reform around 1986 in China and itsinteraction with enforcement intensity as instruments for children’s years of schooling. IV es-timation results using the baseline survey data demonstrate that increasing years of educationof adult children lead to higher level of cognitive functions of older adults. Parents with bettereducated children also have higher subjective survival expectations, improved lung functionand greater body weight. Dynamic model results for the follow-up sample indicate positiveand significant incremental effects of children’s education on cognitive abilities of older adultswhen baseline cognition is controlled for. Further evidence suggests that adult children’s ed-ucation might shape parental health in old age by providing social support, affecting parentalaccess to resources as well as influencing parental labor supply and psychological well-being.Keywords: CHARLS, Education, Health, Cognition, Upward spillover

∗3620 S. Vermont Ave. KAP 300, Los Angeles, CA 90089, USA, email: mingminm@usc.edu. I am very grateful tomy adviser John Strauss for his guidance and support. This paper has benefited substantially from comments providedby Jeff Nugent, Cheng Hsiao, Geert Ridder, Eileen Crimmins, Vittorio Bassi, my colleague Urvashi Jain and seminarparticipants at University of Southern California. All errors are my own.†Preliminary version. Please do not cite or circulate without the author’s permission.

1 Introduction

Social science literature has consistently found positive and robust relationships between educationand health (Baker et al., 2011). Compared with income, race, social rank and other individual so-cioeconomic characteristics, education has been shown to be one of the most important predictorsfor mortality and health (Cutler and Lleras-Muney, 2010). Over time, education plays an increas-ingly important role in explaining independently disparities in health, adding fuel to the interest ineducation as a policy instrument for enhancing population health (Montez and Friedman, 2015).Studies have also pointed out that the effects of education on health spill over to later generations.Grossman (2006) in a detailed review shows that individuals’ schooling is also the most importantcorrelate of the health of their children.

A natural question thus arises: is the interaction between parents and children in terms of edu-cation and health a downward stream from parents to children? Or, other than individuals’ own ed-ucation, does their children’s education also matter for their health and longevity, especially whenthey are old and dependent on familial support? Can policies aimed at improving educational at-tainment of one generation benefit not only the present and future (generations) but also the past(generations)? However, only a few recent studies have tried to test such hypothesis empirically(e.g. Lee, 2017; Lee et al., 2017; Yang et al., 2016; Torssander, 2013, 2014; Lundborg and Majlesi,2017; Zimmer et al., 2002, 2007; Kravdal, 2008; Friedman and Mare, 2014; Yahirun et al., 2016,2017; De Neve and Harling, 2017; De Neve and Fink, 2017). Whether there is indeed an upwardspillover effect from children’ education to parental health is still an open question and the impor-tance of such effect might be different in different contexts (De Neve and Kawachi, 2017).

Understanding the relationship and the causal pathways between children’s education and in-dividual old-age health might be especially important in developing countries where older adultsare more reliant on children and informal support due to strong family filiation and/or insufficientold-age security network. It might help identify the elderly people that are more susceptible topoor health and help design policy instruments by utilizing the benefit of intergenerational effectof socioeconomic status (Yahirun et al., 2016).

This paper contributes to the small but expanding literature on upward spillover effects ofchildren’s education on parental health by providing a causal analysis on older adults in an age-ing developing country (China). It extends the correlational studies of Lee (2017), Yang et al.(2016), Zimmer et al. (2002) and Zimmer et al. (2007) who have also studied Chinese elderly,and De Neve and Fink (2017) and Lundborg and Majlesi (2017), which conducted causal analysis.I employ an instrumental variables (IV) estimation method similar to Duflo (2001), Chou et al.(2010), Lundborg and Majlesi (2017), De Neve and Fink (2017) and Huang (2015) to identify theimpact of adult children’s schooling on health of older adults by exploiting the decentralized grad-

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ual implementation of compulsory education in China during the period from 1985 to 1991. Thereforms in compulsory education took place in different years across Chinese provinces and withineach province increased differentially the amount of formal education of different birth cohorts.Constructions of instruments for children’s education are based on the number of years exposed tocompulsory education of the highest educated child and its interaction with the regional averageyears of schooling before the compulsory schooling law enforcement (related to program inten-sity). I include in both stages birth year fixed effects, along with province or community fixedeffects and province-specific trends to control for cohort and regional heterogeneity in schoolinglevels and the different paths of the educational expansion across provinces. Robustness checkswere also conducted with regard to alternative instruments, further control of other social program-s, the instrumentation of education of older adults themselves and multiple hypotheses testing.

The second contribution of this paper is that a wide array of health and cognition outcomesare studied in order to offer a comprehensive analysis of the health effect of children’s educationon older adults. These measures are shown to be important predictors of old-age disability andmortality. I find that children’s education is significantly and positively correlated with health andcognition of Chinese elderly. Strong causal relations based on the IV estimations are found forcognitive abilities, expected survival, lung function and body weight.

Third, this paper adds to the work of Friedman and Mare (2014), Yahirun et al. (2017), Lee(2017), Lundborg and Majlesi (2017) and De Neve and Fink (2017), who shed light on the po-tential pathways through which children’s education influences health of parents in later life, byexplicitly discussing and testing the following possible mechanisms and pathways: social influenceon health behaviors, social support, access to resources, labor supply and psychological well-being.I find evidence for improved social support that parents received in the form of net monetary trans-fer from children, and increased parental access to resources such as general economic resources(measured by household expenditure), clean fuels (gas and electricity as apposed to solid fuel) andimproved sanitation (private in-house toilets). Parents with better educated children are more satis-fied with their lives and less likely to work in old age, implying that psychological well-being andleisure/labor supply of parents might also play a role in explaining the health effect of educationof children.

Last, this paper also estimates a dynamic model for health and cognition of older adults, whichcontrols for lagged baseline outcomes that are treated as endogenous. It offers evidence on thecausal incremental effect of children’s education on the short-run changes of health and cognition,which also re-inforces the correlation results found by Yahirun et al. (2017) and Zimmer et al.(2007). Using the two-year follow-up data, I show in the appendix that the baseline conclusion us-ing a static model still holds for most of the health outcomes. Furthermore, Lewbel IV estimationof the dynamic model reveals that given the baseline level of cognitive abilities, adult children’s

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education has incremental effects on the cognition, especially the episodic memory, of older adult-s. However, for other health measures of parents, children’s education does not seem to havesignificant incremental effects.

The rest of the paper is organized as follows. Section 2 reviews the related literature. Section3 outlines the possible channels through which the health of older adults may be linked to theeducation among their children. Section 4 introduces the institutional context and compulsoryeducation reform of China. Section 5 describes the data. Section 6 presents the baseline empiricalmodels, the identification strategy and reports baseline model results for health of older adults andthe underlying channels. Section 7 presents the dynamic model and the estimated results. Section8 discusses the robustness of the results. Section 9 concludes and discusses the paper.

2 Related Literature

The analysis of this paper builds upon several strands of economic research in human capital.The first related line of literature is the study of the effect of education on health whose theoreti-

cal foundation was provided by Grossman (1972, 1976) and Strauss and Thomas (2008). Empiricalevidence mounted that linked increased education to lower mortality (e.g., Elo and Preston, 1996;Lleras-Muney, 2005), healthier life styles (e.g., Cutler and Lleras-Muney, 2010), and improvedmorbidity indicators including self reported health, mental health, chronic conditions, functionallimitations and disabilities (e.g., Mackenbach et al., 2005, for European countries). Although it isstill an on-going debate whether such correlation is causal, recent reviews by Grossman (2006),Baker et al. (2011), and Cutler and Lleras-Muney (2012) have shown that at least part of it is.

The second strands of literature this paper relates to are the studies in the intergenerationaltransmission of human capital, social mobility and effects of family background on child out-comes. Past research has documented the positive influence of parental socioeconomic status onchildren’s early life health, education and economic outcomes (e.g., Thomas et al., 1990, 1991;Strauss and Thomas, 1995; Case et al., 2002; Currie and Moretti, 2003; Oreopoulos et al., 2006;Currie, 2009; Lundborg et al., 2014).

There is also a literature in economics on effects of peers on health. Empirical evidence hasshown that socioeconomic status, health and behaviors of social network members, such as spous-es, friends and siblings, are important in shaping an individual’s health and behaviors (e.g., Wilson,2002; Brown et al., 2014; Meyler et al., 2007; Monden et al., 2003; Fowler and Christakis, 2008;Altonji et al., 2017).

Last but not least, this paper belongs to the small strand of literature that studies the relationshipbetween later life health of older adults and the education of their children. Recent works havedemonstrated that children’s education level is important for their parents’ physical functioning

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(Zimmer et al., 2002; Yahirun et al., 2016, 2017), physiological dysregulation (Lee, 2017), depres-sive symptoms trajectories (Lee et al., 2017) and survival (Yang et al., 2016; Zimmer et al., 2007;Torssander, 2013, 2014; Lundborg and Majlesi, 2017; Friedman and Mare, 2014; Yahirun et al.,2017; Kravdal, 2008; De Neve and Harling, 2017; De Neve and Fink, 2017). Zimmer et al. (2007)and Lee (2017) in addition showed the importance of the education of the children on mortal-ity and biological functioning of older adults when controlling for socioeconomic and demo-graphic characteristics, and health at baseline. Furthermore, Zimmer et al. (2007) and Lee et al.(2017) find that children’s education seems to have stronger association than older adults’ owneducation with mortality1 and depressive symptoms2 of older adults in Taiwan, suggesting dif-ferential effects of education in the progression of health problems. Yahirun et al. (2017) alsomade use of panel data and their results imply a stronger relation of children’s education withlong-term survival of parents than with the short-term change in functional limitation that maybe more contingent on earlier life exposures. These studies cover both countries with developedold-age security networks, e.g., Sweden (Torssander, 2013, 2014; Lundborg and Majlesi, 2017),regions with limited public support, e.g., Africa (De Neve and Harling, 2017; De Neve and Fink,2017) and Mexico (Yahirun et al., 2016, 2017), countries with less filial obligation, e.g., the U-nited States (Friedman and Mare, 2014), societies where there are strong filial links, e.g., Taiwan(Zimmer et al., 2002, 2007), and societies with both insufficient public support network and strongfilial obligation, e.g., mainland China (Yang et al., 2016).

Though research in this area is growing rapidly, most of the aforementioned results are corre-lational evidence that are more econometrically challenged. Upward bias arises from the reversecausality problem that healthier parents are better able to invest in children’s schooling, and theomitted variable problem that unobserved genetic and/or environmental factors could lead to con-cordant levels of human capital of both parents and children. The use of sibling fixed effectsmodels as in Torssander (2013) can only partially control for the latter and not at all for the former.

Lundborg and Majlesi (2017) and De Neve and Fink (2017) are the only exceptions that es-timated the causal impact of children’s educational attainment on parents’ longevity by usingexposure to educational reforms in Sweden and Tanzania as instruments for years of schoolingof children respectively. Lundborg and Majlesi (2017) exploited changes in years of compulso-ry schooling from seven to nine that took effect at different points in time across municipalitiesin Sweden to construct an instrument for years of schooling of children in estimating the causaleffect of children’s education on parental survival, while controlling for state fixed effects andmunicipality-specific cohort trends. While Lundborg and Majlesi (2017) fail to find any causaleffect of children’s education on survival until 2013 of parents born between 1899 and 1941 on

1for those with severe diseases.2But the association decreases as older adults age.

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average, they do find some heterogeneity in the effects. Their results imply that the schooling ofdaughters affects survival of fathers and especially those from low socio-economic background.De Neve and Fink (2017), on the other hand, using data from a much poorer economy and lesseducated population, find positive impacts of schooling of children born after 1945 but older than15 years old on parental survival in 1988 or 2002 for both genders3.

As a missing piece of puzzle, the study of the effect of children’s SES or human capital onparents’ health builds upon and enriches the literature in development of human capital and itsspillover within networks, across generations and dimensions. Without taking into account the up-ward spillover of human capital from younger to older generations, the social benefit of educationand other programs that lead to human capital advancement will be underestimated and maybeeven misleading. It is also especially important to empirically estimate such spillover effect andthe various pathways through which it might work in different settings in order to understand whenand how the spillover is effective. This paper is therefore motivated to add to the limited empiricalcausal studies in this growing area of research with special focus on a developing and rapidly agingcountry, China.

3 Potential Mechanisms

Children’s education can relate to parents’ health in old age in multiple ways, as depicted in thediagram in Figure 1. Parents who are healthier have more resources and thus are better able to givebirth to healthier children and invest in their children’s education. Children who are healthier inearly life are also more likely to achieve higher levels of education in adulthood. It is also possiblethat genetic endowments or unobserved abilities give rise to both parents and offspring who arehealthier and better educated. Parents might also invest more in the education of their childrenin exchange for old age support due to informal contract incentive (Nugent, 1985). On the otherhand, children is part of the social network of parents, whose SES might have independent effecton parental health in old age (Berkman et al., 2000). Children’s education being an indispensablefamily resource could affect parental health in a number of behavioral processes: provision of so-cial support, access to resources, social influence which work through more proximate behavioraland psychological pathways.

3The authors pooled the data from two sources: United Republic of Tanzania Population Census 1988 and Popu-lation and Housing Census 2002.

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3.1 Social Support

Children’s socioeconomic status can directly affect type, frequency, intensity, and extent of sup-port provided to parents. Children with higher educational attainment are better able to provideinformational support to parents, including advice or information on health care services, becausethey have better health knowledge themselves (Torssander, 2013; Friedman and Mare, 2014). Onthe other hand, as more-educated children are more likely to have a full-time job with higher wagesand to migrate, it might be costlier for them to have frequent and intense in person contacts withparents such that the emotional support they provide might be less (Torssander, 2013). In China,for example, people with more schooling are also more likely to migrate (Zhao, 1997) and thepossibility of co-residence of parents with higher-educated children is lower than those with less e-ducated children (Lei et al., 2015). While living away from children is shown to constrain Chineseelderly receiving help on daily activities (Sun, 2002) and frequent visits (Lei et al., 2015), parentsreceive more net transfers from children who are living farther away and in whom they investedmore in schooling (Lei et al., 2015). Children with more schooling might also have better health,more skills and greater flexibility in their work schedule because of occupational prestige or morejob control (Fletcher and Frisvold, 2009) which could allow them to provide more care to theirill parents when needed (Friedman and Mare, 2014). Therefore, children with different educationlevels tend to provide different types of support with varying quality (Friedman and Mare, 2014),making the net impact of children’s education on parental health in old age less clear theoretically.

3.2 Social Influence

One’s social network plays a key role in forming health-related behaviors among its members.Education of one’s family members, including children, could have influence on individual atti-tudes toward health habits, such as smoking and excessive drinking, when the family as a wholeshare their health knowledge and values (Torssander, 2013). Additionally, children’s educationcould have indirect impact on their parents’ health outcome through their own behaviors. If thereis positive spillover effect of health behaviors from children to parents via peer pressure, socialinfluence or social comparison (Eisenberg et al., 2014; Card and Giuliano, 2013; Berkman et al.,2000), children with better health-related behaviors that result from more education could also helptheir parents adopt concordant lifestyles and affect their health in old age.

3.3 Access to Resources

Economic and environmental resources (risk factors) such as sanitation and clean fuel also playa significant role in shaping human health (Thomas et al., 1990; Lavy et al., 1996; Smith, 2007;

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Zhang et al., 2010). Social networks help distribute and transfer such resources to individuals whenprivate and public access is constrained. This pathway might be especially important in low incomesettings, like China, where old-age poverty measured by consumption is prevalent and householdair pollution from solid fuel use along with poor sanitation are leading risk factors for diseaseand remain major public health problems (Carlton et al., 2012; Zhang and Smith, 2007). Bettereducated children could improve parental health by financing and boosting parental expenditure,helping them get access to clean fuels and installing sanitation facilities at home.

3.4 Psychological Well-being

Other than micro-psychosocial and behavioral processes (Berkman et al., 2000), children’s educa-tion could affect parents’ health through more “proximate” pathways which might also be resultsof the previously discussed mechanisms. Steptoe et al. (2015) have shown that psychological well-being and health are closely related to each other for elderly people. Lower physiological stressand higher self-efficacy might lead to better health outcomes and the adoption of and adherence tohealth-promoting behaviors among older adults. (Perkins et al., 2008; Schneiderman et al., 2005;de Leon et al., 1996; Duncan and McAuley, 1993). Children that are more affluent in life becauseof higher educational attainment (Friedman and Mare, 2014; Torssander, 2013) are better able tosupport parents, protect parents from stressful events and raise parental psychological well-beingby reinforcing social class identification (Lee, 2017).

3.5 Labor Supply

A considerable share of older population in developing countries, especially in rural areas, con-tinues to work in very old age until physically incapacitated (Cameron and Cobb-Clark, 2008;Cai et al., 2012). Although it is less clear in the literature about the effect of retirement on healthof older people (van der Heide et al., 2013), it is possible that in developing countries, where olderpeople work out of necessity, retirement could have a beneficial impact on their health in old age.Cai et al. (2012) found that rural elderly with more educated household members and pensions areless likely to be working in China. Children’s socioeconomic status could affect parental healthin old age through affecting the labor supply of parents which could be substituted by informalold-age support (Cameron and Cobb-Clark, 2008).

3.6 Significance of Different Pathways

Torssander (2013), Friedman and Mare (2014), De Neve and Fink (2017), Yahirun et al. (2017),Lee (2017) and Lundborg and Majlesi (2017) have provided suggestive evidence on the potential

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pathways through which children’s education forms health of parents. De Neve and Fink (2017)show that children with higher education level are more likely to work, get married with bettereducated spouses, have a larger household size and have better access to basic utilities in Tanzania.Their results are based on information for households of children instead of their parents, andhence are only indirect evidence for the possible causal pathways. Lundborg and Majlesi (2017)find that for the Swedish population on average, children’s schooling has no significant impact onparental economic resources. However, they suggest that the positive effects of female schoolingon parental survival arise through improved health knowledge. Friedman and Mare (2014) findthat for U.S. elderly, the health effect of children’s schooling is more pronounced for deaths thatare linked to behavioral factors (chronic lower respiratory disease and lung cancer) which appearsto be explained by smoking and exercise behaviors of parents. Yahirun et al. (2017) find that forthe Mexican elderly, even after controlling for children’s financial status and their financial transferto parents, education of children is still strongly correlated with longevity which implies that othermediating factors might be important, such as spillovers of health knowledge and social influenceon behavior and values. Lee (2017) investigates the behavioral and psychological pathways thatlinked children’s education to parental biological functioning in Taiwan and finds that parentswith better educated children have higher level of psychological well-being and are more likely toengage in healthy behaviors.

As parent-child interactions and relationships vary across societies, it is less clear about therelative importance of mechanisms through which children and their educational attainment areworking to affect the health of parents in different settings. In poor countries where extended fam-ily structures and the pooling of resources as informal insurance are prevailing, mechanisms likefinancial support and access to resources might be more salient than in developed countries wherepublic support systems are more sufficient and upward net transfer is less common (Torssander,2013; Friedman and Mare, 2014).

4 Institutional Background

4.1 Demographic Transition, Aging and Old-Age Support in China

As one of the fastest growing economies in the world, China has experienced unprecedented de-mographic transition in the past thirty years. Not only is prominent the slowdown in its populationgrowth, but also is its changing population structure, which makes China an acceleratingly agingsociety, especially in the rural areas (Cai et al., 2012; Cai and Du, 2015).

Meanwhile, the inadequate pension system in China has led to persistent old-age poverty(Cai et al., 2012). The Chinese system of extended families, which is traditionally organized as

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a corporate unit by pooling economic resources and providing assistance to all family members(Zimmer et al., 2002), has been the major form of old-age security for Chinese elderly. Zhao et al.(2013b) showed that private transfers are critical for reducing consumption poverty rates of Chineseelderly households, especially in rural areas. Given the increase of life expectancy, the decreaseof family size along with rapid urbanization and migration process in China, the duty of old-agesupport has been placed increasingly on a smaller network of children who are better educated.Consequently, the socioeconomic status of children might play an increasingly important role inthe later life of Chinese elderly since there is little margin and trade-off available from the havinga larger extended family.

4.2 Compulsory Education Reform in China

There are huge gaps in educational opportunities and attainments across cohorts in China becauseof various education expansion endeavors after 1949. Less than 46% of the population born before1960 completed at least lower secondary education in China, while the number is 74% and 82% forcohorts born during 1961–1970 and 1971–1980 respectively (National Bureau of Statistics of China,2010). Such a situation could potentially make children’s social influence, provision of social sup-port and resources more efficient and valuable for parental old-age health (Zimmer et al., 2002,2007).

The present paper specifically exploits variations in compulsory education enforcement acrossChinese provinces as a natural experiment. With the economic reform and opening up of Chinain the 1980s, Chinese government started its first structural educational reform by announcing theDecision of The Central Committee of the Communist Party on Reform of China’s Educational

Structure (Ministry of Education, 1985). The reform aimed at the decentralization of free basiceducation and the implementation of nine-year compulsory education, which is composed of six-year primary education and three-year junior secondary education4, in the entire country (Tsang,1991; Ming, 1986). In addition to the the reform document, the Law on Nine-Year Compulsory

Education was passed and took effect on July 1, 19865. Table 1 lists the timing of the provinciallaw enforcement of the nine-year compulsory education and first birth cohorts affected. Based onthe information in Table 1, Figure 2 display the gradual and decentralized roll-out of the nine-yearcompulsory education graphically6. The first municipality to implement the nine-year compulsory

4After 1981, some regions adopted the “pilot” system with five-year primary education and four-year junior sec-ondary education which is much less prevalent than the 6+3 system.

5Other components include the development of vocational and technical education; and changing the student ad-mission and allocation of higher education graduates while increasing “decision-making power” or autonomy of highereducation institutions.

6The reform document actually provided guidelines for implementation levels and timetables for three tiers ofregions with different economic development levels on achieving the goal (Ming, 1986). Economically developed

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education was Shanghai which issued the provincial regulation on July 28, 1985, which becameeffective on September 1, 1985 even before the Law on Nine-year Compulsory Education waspassed in 1986. It was also one of the most developed coastal areas in China then and now. Gansuis one of the poorest provinces in China; it officially wrote compulsory education into provincialregulations that came into effect from the school year of 19917. The majority of provinces andmunicipalities make the age of compulsory education to be six to fifteen years old with excep-tions in certain poor regions where the eligible age can be set from seven to sixteen8. Becauseof the decentralization of basic education, local governments instituted the compulsory educationaccording to their own economic and educational resources which does not make the roll-out ofthe law implementation random. Table 1 also shows vast inter-province and rural-urban differencein educational attainment among cohorts that were ineligible to compulsory schooling9 (cohortsthat were one to five years older than the first compulsory education eligible cohorts). Such dif-ferences in economic developments could induce disparities in health of parents and education ofchildren. I control for the province (or community) level time-invariant heterogeneity to addressthe endogenous program roll-out (Rosenzweig and Wolpin, 1986), and allow for province-specificbirth cohort (of children) trends to capture any deviation from the national trend.

5 Data

5.1 CHARLS Data

I use data from the China Health and Retirement Longitudinal Study (CHARLS) for the analysisof this paper. CHARLS is one of the sister studies of Health and Retirement Study (HRS) ofthe United States and is designed to facilitate multidisciplinary research on population aging inChina. The national baseline CHARLS was conducted in 2011/2012 and is representative of theChinese population of age 45 and above, covering 450 random communities from 150 randomly

areas and cities (25% of the population) were set to make junior secondary education universal by 1990, followedby economically semi-developed townships and villages (50% of the population) by around 1995 after completingthe spread of primary education, while the last category, which consisted of economically under-developed areas(25% of the population), were supposed to take various steps in universalizing primary school education as economicdevelopment permits with support from the central government (Ming, 1986).

7Gansu provincial government issued a pilot regulation in 1985 to implement nine-year compulsory schoolingwithout success. Retrieved from http://fgk.chinalaw.gov.cn/article/dfgz/198510/19851090520158.shtml. Accessed onJan 14, 2017.

8The actual eligible age of compulsory education is not stated clearly in the Law on Nine-year Compulsory Edu-cation and most provincial regulations. However, the provision to the Law in 1992 explained that the age eligibilityshould be made by provincial governments and hence varied across provinces and regions within provinces.

9In the present paper, I will use compulsory education and compulsory schooling interchangeably. Exposure tocompulsory education (law) and or compulsory schooling (law) will also be used as the same measure. I will useabbreviation CS for compulsory schooling and CSL for compulsory schooling law.

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sampled counties from 28 Chinese provinces. Randomly selected age-eligible respondent and thespouse irrespective of age in one household were interviewed and the response rate was around85% for the national baseline (Zhao et al., 2013a,b). A wide array of information was collected:demographics, family information, health and functioning, health care and insurance, work andretirement, income, consumption and assets. The follow-up surveys happen every 2 years and theCHARLS wave 2 and 3 were fielded in 2013 and 2015, respectively, with a between wave life-history survey in 2014. This paper utilizes data from the national baseline and wave 2, which arepublicly available for all modules.

5.2 Measure of Children’s Education

Children’s education is measured in years of completed formal schooling which are based on thenumber of years “usually” taken to obtain a certain degree (Kemptner et al., 2011). Years of school-ing is then imputed from the information on the highest completed educational level, ranging from0 which means no completed formal schooling to 21 which equals the number of years to earn adoctoral degree10. In the entire CHARLS child sample before any sample restriction, 60% com-pleted lower secondary education (9 years) or above while only 28% of their parents have doneso. Children with parents living in rural communities have less education than children whoseparents live in urban areas. The difference between the two groups is around 2.4 years. There isalso gender gap in educational attainments of children. Female children have about 1 year less inschooling than male children.

On average, there are about 3.5 living children for each responding household in the unre-stricted data. Since it is not clear which child’s education is the most important for the parents(Zimmer et al., 2007) and it is not possible to include all children’s information in instrumentalvariables estimations, I chose the years of schooling of the highest educated child as the measureof children’s education, and hence extract his or her birth information to construct instruments11.When there was more than one highest educated children, I chose the birth information of the oldest

10In CHARLS, formal schooling is composed of elementary school (6 years), middle school (3 years), high school(3 years), vocational school (3 years), 2 or 3 year college/associate degree (2.5 years), 4 year college/bachelor’s degree(4 years), master’s degree (3 years) and doctoral degree (3 years). Measurement errors exist for calculating years ofschooling from the highest completed education level question in CHARLS because of (1) the regional difference(even within the same province) in number of years in elementary and middle school, either 6+3 or 5+4, and it isnot possible to know it from CHARLS (including community survey and life history survey). But as four-year lowersecondary education was introduced to pilot areas only around 1981, it affects only a small portion of the sample. Inaddition, according to MOE China, in 2016, more than 98% of students in lower secondary school study in three-yearmiddle school; (2) years in elementary school for dropouts not included; (3) additional years of education after thehighest completed degree not included. However, changing the number of years in elementary school and middleschool, or including the years in primary school and additional years after highest completed education do not alterthe finding in this paper.

11I experiment with different ways of constructing a single variable for children’s education, including among oldestchild, highest educated child/children and lowest educated child/children.

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one. Results from different measures of children’s education are very similar. I report only resultsusing the highest educated children’s information following Zimmer et al. (2007) who found thatthe association between parents’ mortality and highest educational level of all adult children is thestrongest among others. Results using other measures of children’s education are available uponrequest.

5.3 Birth Information of Children

In order to get the exposure of each highest educated child to the compulsory schooling policy, Iuse their birth year as well as birthplace information. As it is not possible to know where the childlived when they were subject to compulsory education, their birthplace serves as a better proxythan their current Hukou location or their first Hukou information which has more missing data.Of the children in the entire child sample, 94.2% were born in the same province of the currentresidence of their parents. Although the CHARLS baseline and wave 2 survey asked the birthprovince of children if they were not born in the province where their parents live, the coding ofthe province in the baseline is different from the primary sampling unit and the province list inthe appendix of the questionnaire and this information from wave 2 was not released to the public.Because of data limitations from both waves, I dropped children with unmatchable birth locationbecause they were born in a province/county different from parents’ current residing province orcounty which account for about 4.5% of the entire children sample. I also drop children withmissing birth location information which are another 1.2% of the unrestricted children sample.

5.4 Control Variables

Parental and Household Characteristics. I control for a set of variables of each parent that arefound to be highly correlated with health and cognition in old age, including gender, a set ofage dummies (5 year interval), years of schooling of their own, number of living children of theolder adults, height at baseline and childhood health status (Smith et al., 2012). I refrain fromadding more mediating factors that are endogenous such as household expenditure, labor supplyand living arrangements. Instead I treat them as left hand side variables. All control variablesare treated as exogenous including education of older adults. As a robustness check, I also reportresults from estimations where own education is instrumented in Appendix A. Table 2 summarizesthe descriptive statistics of those controls.

Child Characteristics. Besides years of schooling of the highest educated child, I control forchild’s gender, child’s birth cohort fixed effects and birth province fixed effects.

Regional Characteristics. As found by Smith et al. (2013) that the unmeasured communitycharacteristics of living had a significant effect on individual’s health and cognition in China, resi-

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dence information of the parent is controlled for in all estimations. Either province or communityfixed effects are included to control for any regional heterogeneity that are time invariant.12 WhenI include only province fixed effects, I also control for the average years of schooling of com-pulsory education ineligible cohorts in the province (which is also the birthplace of the highesteducated child), stratified by rural or urban area, as a measure for regional educational level be-fore compulsory schooling enforcement. When community fixed effects are included, the regionaleducational level before compulsory schooling enforcement is absorbed. A dummy variable thatequals one if the individual lives in a rural area is controlled for in specifications with provincefixed effects. Since all children in the analysis sample were born in the same province and countywhere the parents resided at the time of the survey, province and community fixed effects absorbchild’s birth-province fixed effects. As in Figure 3, there is potential heterogeneity in cohort trendsof years of schooling across provinces, which could result from differential economic and socialdevelopment, I control for provincial GDP per capita, number of doctors and hospital beds per10,000 population in the child’s birth year as well as province-specific linear trends of child birthcohort in both first and second stage.

5.5 Health and Cognition Outcomes

I studied a wide array of health and cognition related outcomes of Chinese older adults.Cognition. The first group of outcomes consists of two cognition measures: mental intact-

ness(MI) and episodic memory (EM). Mental intactness of the respondent is defined as the sumof correct answers to questions on the date, day of the week, season of the year (orientation), suc-cessive subtractions of 7 from 100 (numeracy) and picture re-drawing (Lei et al., 2012). Episodicmemory of the respondent is measured as the average score of immediate word recall and delayedword recall following McArdle et al. (2011). In CHARLS, respondents were asked to recall, bothimmediately and in 10 minutes, the same ten simple nouns that were read to them just once.

Health. I studied both subjective health measures, objective physical health outcomes measuredby trained nurses and mental health (depressive symptoms). The first subjective health measureis self-reported health based on a general health question in CHARLS with responses of 1 (verygood), 2 (good), 3 (fair), 4 (poor) and 5 (very poor). I take the actual Likert scale answer such thatsmaller values indicate better general health. Another subjective heath measure is based on theexpectation of survival to age 75 (80, 85, 90, 95, 100, 105, 110, 115) for respondents aged 64 orbelow (65-69, 70-74, 75-79, 80-84, 85-89, 90-94, 95-99, 100 and above) on a Likert scale from 1(almost certain) to 5 (almost impossible). A corresponding binary outcome is defined that equals1 if one has a low expectation (not very likely or impossible), or 0 otherwise. Objective physi-

12Results from estimations with county fixed effects are available upon request.

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cal health indicators include lung function, which is measured as average of peak expiratory flowreadings (L/min) and grip strength, which is the average of readings from the dominant hand mea-sured by dynamometer. Body mass index (BMI) and indicators of being underweight (BMI<18.5)and overweight (BMI≥25) are also included as outcomes of interest as they reflect nutritional sta-tus and risk-factors for health problems like diabetes and cardiovascular disease (Kemptner et al.,2011). Depressive symptoms are measured by the Center for Epidemiological Studies-Depression(CES-D) 10 question index of depression which ranges from 0 to 30.

5.6 Potential Channels

Furthermore, I explore the possible working pathways to parental health that children’s educationoperates on, including social influence on health behaviors, social support, access to resources,labor supply and psychological factor.

Social Influence. Effects of children’s education on health behaviors of parents, includingsmoking and drinking, are studied to investigate whether children influences parental health throughthe social influence pathway. Smoking and drinking status are considered as binary outcomes.Smoking (drinking) status equals 1 if the respondent smokes now (was drinking over last year).Frequency of smoking defined by number of cigarettes per day and frequency of drinking mea-sured by number of days per week the respondent drank last year are also checked to providefurther analysis in Appendix A.

Social Support. Frequency of contact with children–or number of days in a week childrenvisit or call, send text messages or mails/emails (co-residence with children accounts for 7 daysper week)–is the indicator of time transfer from children, which measures amount for emotionalsupport from children. Different types of contacts, either in-person or not-in-person, are studiedand measured by (1) number of days per week children visit and; (2) contact via phone, mails,text and emails13. Net annual amount of cash and in-kind transfer from children (in RMB) is themeasure of monetary or financial support provided by children. To rule out the influence fromoutliers, I trim the net transfer to exclude the top 1.5% and bottom 1.5%14.

Access to Resources. Economic resources, clean fuels and sanitation are considered to test thepathway of access to resources. Following Smith et al. (2012), I use per capita household expen-diture as an indicator of long-run economic resources as it has less measurement error than currentincome. Expenditure includes both food and non-food consumption in the past year. Parentalaccess to in-house flush-able toilets is a binary outcome variable, which measures the level of san-itation. In addition, whether parents used non-solid fuel (mainly gas and electricity) for cooking is

13Results for different types of time transfer are shown in Appendix A14The results are similar if I use other trimming criteria, e.g.,top and bottom 1%, 2% or 5%

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studied as another mediating factor that is important for population health in low-income settings(WHO, July).

Labor Supply and Psychological Well-being. Furthermore, I explore other proximate pathwaysthrough which children’s education could shape parental health, such as labor supply and psycho-logical well-being. Labor supply, which could be a result of social support and economic resourcesprovided by children, is a binary variable which equals 1 if the parent is currently working whichincludes farming and unpaid family work. For the psychological well-being of parents, I use a5-point scale life satisfaction measure with 1 being most satisfied and 5 being least satisfied andexamine whether parents with better educated children enjoy life more.

5.7 Sample and Descriptive Statistics

I restrict the sample to parents who are older than 40 at CHARLS baseline with highest educatedchild born between 1956 and 1991 such that the children under consideration are at least 20 yearsold in 2011 and more likely to have completed education15 while not too old to be without a livingparent. Different age and birth cohort restriction criteria have barely changed the main conclusionand results using different samples are available upon request. Wave 2 data on children’s infor-mation are used to complement the baseline analysis because of data limitations16. By doing so, Ikeep parents or parental households that were in both waves17.

Table 2 shows the summary statistics of health, cognition outcomes, pathway variables of par-ents, parental demographic variables, years of schooling of highest educated adult child and otherchild-level, household-level or regional control variables. For both the baseline and the follow-upsample, 52% of whom are female. More than 83% of them are married and 64% of them live inrural areas. The average age of parents is about 58 at baseline and 60 in the follow-up survey.Sample sizes vary for different outcomes of interest. It is worth noting that on average, more than30% of the parents are overweight and mean BMI is about 24 in the baseline sample, which isconsistent with the literature that consistently find old-age overweight being a prevalent problemin developing countries.

Average years of completed schooling are 4.6 years for parents and 10.5 years for their highesteducated children. Figure 3 shows that, in years of schooling among highest educated children not

15In practice, I could drop children who are still in school but this does not change our results.16Because of the design of the baseline survey, information of co-residing children and non-coresiding children

were asked in different modules. After careful scrutiny, basic information of many co-residing children were alsoasked in the module where they should not have been, which created duplications of children and a lot of missing datafor other co-residing children in that module. As a result, it is impossible to merge the information or append the twogroups to children to create a single child set accurately. In contrast, in wave 2, both types of children were askedin the same family information module and hence, this paper makes use of wave 2 child information instead of thebaseline.

17Sample selection problem will be discussed in Appendix B.

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eligible to compulsory education, there were slight positive cohort trends, which were basically“parallel” in high schooling areas and low schooling areas. In low schooling areas where theinitial schooling levels were lower than regional median, the trend in years of schooling amongcohorts that were partially affected by compulsory education is slightly more positive than that inhigh schooling areas where the initial schooling levels were higher than regional median. And thediscontinuity in years of schooling at the first compulsory education eligible cohorts is also moreconspicuous in low schooling areas. For cohorts which were completely eligible to the compulsoryeducation, children’s years of schooling flatten out18. It manifests that exposure to compulsoryeducation creates variation in children’s years of schooling, with higher potential gain more inyears of schooling in general for law-eligible cohorts from areas with lower educational attainmentof the law-ineligible cohorts. Hence the regional educational attainment and its interaction withthe the compulsory education exposure creates additional variations in the years of schooling ofchildren.

6 Baseline Model

6.1 Empirical Methods: IV/2SLS

Formally, a linear regression equation for baseline health and mediating factors is estimated asbelow:

Hijk0 = β0 + β1ChildEduijk + β3Controlijk + ChildCohortj + τk + λj + uijk (1)

where Hijk0 is the health and cognition outcome or the mediating factor of individual i livingin province j whose highest educated adult child was born in year k. ChildEduijk denotes theyears of schooling of the highest educated adult child of i. β1 is the parameter of interest whichmeasures the effect of increasing 1 year of schooling of the highest educated child on parentalhealth, cognition or mediating factors. Controlijk is a vector of other child, parental level so-ciodemographic characteristics, household characteristics and observed regional characteristics,including PreLawijh, h = {rural, urban}, which is the regional average educational attainmentof cohorts ineligible for compulsory schooling. It is calculated as the average years of schoolingof cohorts born five or less years before the first cohort affected by compulsory education in area

18A similar graph by provinces shows that for cohorts that were not affected by the compulsory schooling law, thetrend in their completed education level was rather flat or slightly upward sloping. For cohorts that were exposed tothe compulsory education, there was an upward trend in completed education level which is steeper in provinces withlower schooling level to begin with, in general. It also implies the heterogeneity of such trends in different areas. Forinstance, education expansion in provinces such as Anhui, Chongqing and Zhejiang is more aggressive than provincesin the Northeast. The graph is available upon request.

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h in province j. λj are the province fixed effects, which account for time invariant heterogeneityacross provinces. Models with county and community fixed effects are also estimated while onlythe results from province and community fixed effects are reported.19 τk are the child birth cohortfixed effects to capture the nonrandom birth of children and cohort heterogeneity in educational at-tainments. I also include the province-specific child birth cohort trends, ChildCohortj , to controlfor province-specific deviations from the common nationwide trend that is captured by the birthcohort dummies (Kemptner et al., 2011; Lundborg and Majlesi, 2017). Ideally, it would be betterif I could separately control for children’s birth-place fixed effects and parental residing provincefixed effects, but as we only include households whose children were born in the same place wheretheir parents currently live because of data limitations; those two fixed effects are actually the same(λj). As a matter of fact, children born elsewhere constitute less than 4.5% of the entire childrensample.

6.1.1 Identification

As has been discussed, ChildEduijk in Equation (1) is endogenous because of omitted variableand reversed causality problems, and hence OLS estimates are biased.

Natural experiments such as compulsory education laws and education expansion program-s have been widely used to address the endogeneity problem of schooling in studying the re-turn to education (e.g., Duflo, 2001; Kemptner et al., 2011; Huang, 2015; Lundborg and Majlesi,2017). Exposure or eligibility of individuals to such programs and/or its interaction with the pro-gram intensity are assumed to be correlated with educational attainment but uncorrelated with theunobserved omitted variables, and hence they serve as instruments for educational attainments(Chou et al., 2010).

Duflo (2001) made use of a primary school construction program in Indonesia between 1973-74 and 1978-79 and showed that individuals who entered school later gained more in schoolingand so did those from districts with greater program intensity. Because program intensity was de-termined by the pre-program supply of primary education on the district level that directly affectsthe educational opportunity of individuals, she defined the interaction between birth cohort andprogram intensity as the IV for years of schooling to estimate a wage equation for men in whichdistrict of birth fixed effects were controlled for. In a recent paper by Huang (2015) he first ex-ploited the variation in the different timing of compulsory education adoption across provinces inChina and generated a policy eligibility indicator for each birth cohort in different provinces asan IV for years of schooling. He then further explored the cross-province variation in the poten-tial increase in education from compulsory schooling policy as in Duflo (2001), by hypothesizing

19Results from models with county fixed effects are available upon request.

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that provinces with less nine-year schooling completion rate before the law enforcement shouldpotentially gain more from the law.

I follow the IV estimation method of Huang (2015). In addition, to measure the differential laweffectiveness or program intensity, I draw upon more detailed information on regional differencesin educational attainments in cohorts that were not eligible to compulsory education both acrossprovinces and between rural and urban areas within provinces as in Rawlings (2015). The highesteducated child’s education is instrumented using the variation in exposure to compulsory educationand its interaction with program intensity across birth-provinces. Formally, a first stage equationis estimated as follows:

ChildEduijk = α0+α1Expijk+α2ExpPreLawijk+α3Controlijk+ChildCohortj+tk+κj+eijk

(2)Whether the child was born at or after the first affected cohort in each province is a natural

instrument. However, as the variation in timing of law enforcement is limited, to introduce morevariations in the exposure of children to compulsory education born between the first (marginally)affected cohort (age 15 when the law took effect) and fully affected cohort (age less than 7 whenthe law took effect), I define the first instrument Expijk as

Expijk =

0, if ChildCohort < FirstCohortj;ChildCohort−FirstCohortj+1

10, if FirstCohortj ≤ ChildCohort ≤ FullCohortj;

1, if ChildCohort > FullCohortj.

which will range from 0 (for those age 16 or older at law enforcement) to 1 (for those age 6 oryounger at law enforcement). The linear extrapolation of the policy exposure variable is basedon the years of the child eligible for compulsory education, given the assumption that the moreyears of the child eligible for compulsory education, the larger the potential effect of the law.The left panel in Figure 4 shows the point estimates and confidence intervals of the effect ofcompulsory education on years of schooling of cohorts with different level of exposure. They arefrom a regression of years of schooling on indicators of years of compulsory education exposurewith birth cohort fixed effects, province fixed effects and province-specific trends. In comparisonwith cohorts not exposed to compulsory education, which is the omitted category, cohorts thatwere 12 years old or were exposed to compulsory education for three to four years when regionalregulations took effect have roughly one more year of schooling. Except for the first three groups,the effects of compulsory education law increase almost monotonically and linearly. Therefore, alinear function of law exposure could capture such pattern reasonably well. A formal first stageregression will be presented in section 6.2 to show the strength of the instruments used in thispaper. As a robustness check, I also present in Appendix A the results using indicator variables

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for each year of exposure as instruments instead of the linearly extrapolated law exposure. I didnot use indicators for each level of compulsory schooling exposure as the preferred instrumentsbecause of the resulting problem of “too many” weak instruments, which will be discussed in therobustness check section.

The graphs in the middle and on the right in Figure 4 illustrate the heterogeneous effects ofcompulsory schooling law by regional schooling levels before the law enforcement. For childrenthat were born in regions with average years of schooling less than the regional median amonglaw ineligible cohorts, the gain in years of schooling for each level of law exposure is higher thantheir counterparts in high schooling areas. Therefore, in addition to Expijk, I introduce anotherinstrument that is the interaction term of Expijk with the average years of schooling of cohorts in-eligible for compulsory schooling, PreLawijh, h = {rural, urban}. Following Duflo (2001) andHuang (2015), this specification allows for the compulsory education law to be more effective inincreasing schooling level in areas with lower educational attainments before the law enforcement.On basis of the province where the parents lived at the time of the survey (which is the same aschildren’s birth province) and whether it is in rural or urban communities, I calculate the secondinstrument as:

ExpPreLawijk = Expijk × PreLawijh, h = {rural, urban}

By adding the second instrument, I can test the exogeneity restriction using Hansen J statistics.All instrumental variable regression results reported in the main text employ both of the instru-ments. Standard errors are clustered at the province level since the implementation of compulsoryeducation was on province level. Results from using compulsory education exposure as the onlyinstrument are available upon request.

6.1.2 Threat to Identification

The identification of children’s education rests on the assumption that conditional on other co-variates and the fixed effects, variations in compulsory education exposure and its interaction withimplementation effectiveness affect health, cognition and other outcomes of parents only indirectlythrough children’s education. In other words, changes in education policies are independent of anyunobserved determinants of health in the second stage (Kemptner et al., 2011). This assumptionimplies that there are no social programs influencing the health of parents or omitted children’scharacteristics other than education underway that are also varying across regions and cohorts andcoincide with compulsory education enforcement. I will address the potential threat to validity ofcompulsory education exposure as instruments in four parts.

Firstly, investment in the social safety net had been largely neglected until the 2000s when

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major reforms in social security, including the minimum support reforms, the establishment ofNew Cooperative Medical Scheme and new Urban Residents Basic Medical Insurance in China,formally started (Daemmrich, 2013; Fan et al., 2011). For example, the New Cooperative MedicalScheme which replaces the rural Cooperative Medical Scheme (1950s-1980s) was piloted in threehundred counties in four pilot provinces in 2003 and then subsequently rolled out nationally withnearly universal (94.3%) coverage among the rural population in 2009. For urban workers, since1998 health insurance has been provided by the Urban Employee Basic Medical Insurance pro-gram. In 2007, the new Urban Residents Basic Medical Insurance started in 79 pilot cities to testcoverage of non-working urban residents, which subsequently expanded nationally20.

Secondly, while it seems unlikely for any major social policy or investment in social infrastruc-ture changes that varied across provinces to have affected individuals’ health directly as did thecompulsory education laws in 1980s, the provincial GDP per capita and health facilities measuredby number of doctors and hospital beds per 10,000 population from the birth year of the highesteducated child are included as covariates in all specifications to help control for concurrent invest-ment in social infrastructure. The province-specific cohort trends should also help capture effectsof other public policies which might be implemented together with the compulsory schooling law.

Thirdly, though it would be impossible to test or control for all concurrent or previous policychanges at regional level as argued by Huang (2015), Huang (2015) directly tested the extent towhich compulsory education increased the years of schooling and suggested that the positive as-sociation between education and the compulsory schooling eligibility and its interaction term withintensity result from compulsory education implementation rather than from other unobserved fac-tors. He also conducted a placebo test to support the exclusion restriction of the IVs by showing thecommon trend and absence of regression to the mean in education of individuals not affected bythe law. In this paper, I test the robustness of the main baseline results to the further control of oneconfounding policy: the One Child Policy which is a nationwide program with differential enforce-ment strictness across regions and time (Ebenstein, 2010). the One Child Policy is shown to haveaffected fertility, timing of birth, number of siblings, health, education, economic outcomes andmarriage market outcomes for children (e.g., Huang et al., 2016; Zhang, 2017). Since it became

20Other public expenditure in healthcare includes investment in better national disease prevention and surveillancesystem after the SARS outbreak of 2003. The central government allocated 2.9 billion RMB and additional fundingto help every province, city and county, especially the rural area, set up its own disease control and prevention center.The government has also implemented initiatives to control costs of healthcare by providing guidelines to restrictunnecessary prescriptions of doctors in 2004. Reforms are also undergoing since 2005 to develop hospital managementand organization and improve quality of health services. The government has set up ambitious plans to improve thenational health care infrastructure by 2010 with goals of five to eight pilot regional health care systems establishedby the end of 2006, covering digital services, integration with insurance, referral systems, electronic records, etc(Business Consulting Services, 2006). As part of the fiscal stimulus package of 2009, construction and renovation ofnew and existing facilities, and creation of an essential drug list and public hospital finance reform are also announced(Daemmrich, 2013).

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effective in the late 1970s, all children who were completely eligible to compulsory education werealso subject to One Child Policy, while some of children with partial exposure or no exposure werenot. I re-estimate the model by additionally controlling for provincial level strictness of the OneChild Policy measured by fines, bonus, and premium from Ebenstein (2010) to take into accountthe effects of One Child Policy that is not captured by province-specific trends and other fixedeffects.

Lastly, it is possible that the policy of compulsory education itself could affect children orhousehold characteristics that are related to parents’ old-age health. The instruments used in thispaper might be invalid if such children or household characteristics are unobserved. For example,children’s early life health predicts their health in adulthood, and hence affects their ability tosupport their parents. If it is directly affected by the policy of compulsory education, the exclusionassumption of the instruments will not hold. Though information of children’s early life healthwas not asked in CHARLS, Huang (2015) using other datasets from China found that compulsoryeducation law has not improved individual’s childhood health/nutritional status which is measuredby adult height. This finding lends more credibility to the identification strategy in this paper.

6.2 Basline Model Estimation Results

6.2.1 First Stage

Table 4 shows the first-stage results using the baseline estimation sample for mental intactness.First-stage results barely change for samples using different outcomes and hence are omitted.Columns (1) and (3) use only the linearly imputed law exposure measure as the excluded in-strument, while columns (2) and (4) add its interaction term with average years of schooling oflaw ineligible cohorts, as the second instrument. The first two columns control for province fixedeffects, the second two control for community fixed effects21. All columns control for child birthcohort fixed effects and province-specific linear birth cohort trends. Standard errors are clusteredat the province level in each column. Exposure to compulsory education is a strong predictor ofyears of schooling of the highest educated child’s, with all coefficients positive and significant atthe 1% level. All interaction terms are significantly negative, which implies the heterogeneity inthe impact of compulsory schooling law: children born in areas with lower education levels beforelaw enforcement gain more in years of schooling from the law. The weak identification test Fstatistics based on the KleibergenPaap rk statistic for the two excludable instruments in the over-identified specification are above 10 in the province fixed effects model, indicating the strength ofthe two instruments (Staiger and Stock, 1997). The weak identification test F statistic is around8.6 in community fixed effects model when the outcome of interest in the second stage is mental

21Results of county fixed effects models are available upon request.

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intactness. It is generally larger than 10 for other health outcome of interests in the second stage,while it tends to be smaller than 10 when sample size is greatly reduced for mechanism analysis.Because the strength of the two instruments varies in different samples and might result in weakinstrument problems in some specifications, for all second-stage results, I report the test statisticsor p values for under-identification test, weak-identification test and Anderson-Rubin F test on thejoint significance of endogenous variables22. If the null hypotheses of the tests are rejected, thereis more confidence in drawing a statistical inference from the IV estimates.

6.2.2 Cognition

Table 5 presents the estimated results for baseline cognitive functions of Chinese older adults. Forboth cognition measures, I first show simple OLS results and IV estimation results using two in-struments with province fixed effects controlled for. Then I report results from specifications withcommunity fixed effects. For either outcome, the OLS estimates with province and communityfixed effects are very similar. So is the case with IV regression results. The causal effects of oneyear increase of education are about a 0.4-point increase in the mental intactness score, which isabout four times of the size of OLS estimates, and a 0.2-point increase in the episodic memoryscore, which is about five times the size of OLS results. The estimated effects of children’s educa-tion are not sensitive to the control of community fixed effects, though there seems to be a declineof significance of coefficients. Instruments appear weaker in community fixed effects model forepisodic memory score because weak identification F statistic is smaller than 10. For all IV re-gressions and outcomes, under-identification is rejected and Anderson-Rubin F statistics show thatcoefficients of children’s education are significantly different from zero, robust to the weak instru-ment problem. Hansen J statistics are also consistent with the exclusion restrictions being satisfied.A comparison of the coefficients of children’s education and own education in OLS models impliesthat own education matters more for both cognition measures, but IV regression results show theopposite. The caveat in interpreting the coefficients for older adults’ own education is that they arebiased because they are endogenous in nature23.

The estimated causal effect of increase of one year of schooling of the highest educated child isabout 6% of the mental intactness score and the episodic memory score, given their averages being7.4 and 3.4, or about 0.11 standard deviation for both measures. In Huang (2015), which studied ayounger Chinese population, one additional year of schooling increased number of words recalled,which corresponds to the episodic memory, by 0.09 standard deviation, and mathematical calcu-lation ability, which is a component of the mental intactness index, by 0.16 standard deviation.

22Anderson-Rubin F test is robust to weak IV problem.23Results using Lewbel’s IV approach to instrument own education are reported in Appendix A, which show a

pattern similar to the traditional IV results, where own education is treated as exogenous.

22

Therefore, the estimated effects of children’s education on Chinese elderly’s cognitive abilities arecomparable to that of one’s own education but smaller than the estimated causal effects of owneducation from some developed countries. For example, in Banks and Mazzonna (2012) who usethe English Longitudinal Study on Ageing to study the effect of education on old age cognitiveabilities, the estimated causal effect of one additional year in school of one’s own education isabout an increase of 0.4–0.5 standard deviation for memory. The estimated effects of older adult-s’ own schooling on cognition from Table 5 are also smaller than what have been found in theaforementioned studies, though the effects can not be causally interpreted.

6.2.3 Subjective Health Measures

Table 6 reports results on subjective health measures of parents. An interesting pattern arises fromOLS results: The negative correlation of education of children with likelihood of low survivalexpectation is stronger than that of one’s own education level which is consistent with the findingsin Zimmer et al. (2007) using actual mortality data. Although a higher education level of adultchildren is correlated with both improved self-reported health and higher survival expectation,only the latter correlation is significant in the IV estimations. The estimated negative effects ofchildren’s education on the likelihood of low survival expectation are not sensitive to the levelof fixed effects that are controlled. While the OLS estimate for effect of one additional year ofchildren’s schooling is 0.9 percentage point, IV results show an 8.5-percentage-point decrease inthe likelihood of low survival expectation, which is about a 28% reduction in the likelihood ofhaving a low survival expectation. For all specifications, under-identification is rejected and thethe Anderson-Rubin F statistics show that effects of years of schooling of highest educated childon parental expected survival are significant. Hansen J statistics are consistent with exclusionrestrictions being satisfied.

6.2.4 Objective Physical Health

Lung function and grip strength. Table 7 shows estimated effects of child’s education the objectivemeasures of the physical health of parents: peak expiratory flow which measures lung function andgrip strength of the dominant hand. For peak flow, the estimated causal effect of the schooling ofthe highest educated child is positive and significant. The estimated coefficients of child educationare slightly larger when community fixed effects are controlled of. Generally speaking, the esti-mated effects of one year increase in children’s schooling on peak flow of parents are not sensitiveto different fixed effects, ranging from 19 to 22 L/min, which is about an 8% increase in peak flowover its baseline average. Table 7 shows no evidence of causal impacts of children’s education ongrip strength of parents in old age. For both outcomes, under-identifications are rejected for IV

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regressions with either province fixed effects or community fixed effects and Hansen J statisticsalso prove that exclusion restrictions are satisfied.

Body weight. Education of the highest educated child also has a significant and positive effecton parents’ body weight in old age. Children’s education seems matter more than older adults’own education for body weight, as evident from OLS estimates in Table 8. IV regression results inTable 8 show that with either province fixed effects or community fixed effects, one additional yearof schooling of the highest educated child leads to a 0.83-unit increase in BMI. Over-identificationtests are not rejected for any of the IV specifications according to Hansen J statistics. Furthermore,columns (6) and (8) of Table 8 show that one more year of schooling of the highest educatedchild leads to better nutrition status of parents, with a decrease of about 6 percentage points in theprobability of being underweight (BMI <18.5). The estimates are not sensitive to different fixedeffects controlled of. Column (10) and (12), on the other hand, report the effect of children’s yearsof schooling on the probability of parents being overweight (BMI ≥ 25). A substantial proportion(more than 30%) of individuals in the baseline sample are overweight, and columns (10) and(12) show that the probability of being overweight increases by about 6 percentage points witheach additional year of schooling of the highest educated child. However, the Anderson-Rubin Fstatistic in column (12) is not significant, though the magnitudes of estimated coefficients of theeducation of the highest educated child are similar in column (10) and (12). The positive effects ofchildren’s education on the probability of parents being overweight might be related to the fact thatpeople who are more affluent are more likely to be overweight and obese in developing countries.For a review on the association between obesity and socioeconomic status in developing countries,see Dinsa et al. (2012). As will be discussed shortly, parents with higher educated children havegreater household expenditure and more financial transfer from children which might translate intohigher body weight in older adults.

6.2.5 Mental Health

Table 9 shows estimated effects of children’s education on parents’ depressive symptoms, mea-sured by a CES-D 10-item index. Based on OLS results, education of children is negatively cor-related with CES-D score and seems to matter more for Chinese elderly’s mental well-being thantheir own education. However, I find no evidence for any causal impact of child’s education ondepressive symptoms of parents in old age, though the estimated coefficients remain negative.

6.2.6 Mechanism: Social Influence

Berkman et al. (2000) suggests that the social influence of children on parents could be an impor-tant pathway through which upward spillover happens. I test this hypothesis by estimating the

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impact of children’s education on health behaviors of parents, including smoking and drinking.Table A6 reports both OLS and IV estimation results using the baseline sample. Because onlyabout 6% of elderly women smoke in the sample of analysis, while more 57% of elderly men do, Ionly report results on smoking behaviors for men. Although men with higher educated children areless likely to smoke, as shown by OLS, IV estimation results fail to provide any significant causalestimates. For drinking behaviors, I do find significantly positive effect of children’s education onparents ever drinking in the past year: One additional year of schooling of the highest educatedchild increases the probability of drinking of parents by 4 to 6 percentage points. As moderatedrinking has been shown to be correlated with better old age cognitive functions in the medicineliterature (e.g., Lang et al., 2007), I also test whether children’s schooling influences the intensityof drinking of parents in Table A6. I find no significant effects of children’s education on numberof drinks per week (for both men and women) or number of cigarettes per day (for men). Drinkingis more prevalent among individuals with better educated children, but the intensity of drinkingdoes not seem to be affected by children’s education.

6.2.7 Mechanism: Social Support

Past research has found that for Chinese elderly, children’s educational level is associated with liv-ing arrangements, time and financial transfer within family (Lei et al., 2015). Table 11 shows thatat least some of the association is causal. For instance, IV estimates for the effect of children’s ed-ucation on time transfer or emotional support, which is measured by the frequency of contact withchildren, show that better educated children are not significantly related to reduced time transfer.

On average, children’s education does not have negative effects on the amount of emotionalsupport provided to parent. On the other hand, children with more education can provide theirparents with more financial support as shown in the last 4 columns in Table 11. One additionalyear of schooling of the highest educated child leads to a 518–578 RMB increase in the annualamount of net monetary transfer from children to parental household. These findings suggest thatchildren’s education significantly improves the financial support provided to their parents but doesnot significantly influence the amount of time transfer from children to parents.

6.2.8 Mechanism: Access to Resources

Access to resources was tested as a channel through which children’s education could influenceparents’ health, by examining parental household per capita expenditure, access to clean fuel (elec-tricity and gas) and private flush-able toilets. Table 12 shows the effect of children’s educationalattainment on those measures. Simple OLS results imply that household per capita expenditure andaccess to private flush-able toilets is correlated to children’s education, more than to their own edu-

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cation. The estimated causal effects on household expenditure of education of the highest educatedchild are sensitive to the choice of fixed effects. When only province fixed effects are included andboth instruments are used, the percentage increase in expenditure is about 14%, while it is only 5%when community fixed effects are included. As is consistent with Lei et al. (2015), such findingsimply the importance of controlling for community fixed effects. The effect of a one-year increasein children’s schooling was about an 8–9 percentage-point increase in the likelihood of householdhaving clean fuel, though Anderson-Rubin F statistics are insignificant (marginally). Access to im-proved sanitation is positively and causally related to the education of children, with the effect ofone additional year of schooling of the highest educated child being a 14.5–17.5 percentage-pointincrease in the probability of parents having access to flush-able in-house toilets. Anderson-RubinF statistics are not significant (at 10% level) in the IV regression with community fixed effects. Ingeneral, there are positive and significant causal effects of children’s education on parental accessto economic resources, clean fuels and sanitation, though the finding is not robust to the level offixed effects controlled for.

6.2.9 Mechanism: Other Proximate Pathways

I check whether children’s education also affects working status of parents. Table 13 and A8demonstrates that children’s education has a negative and significant impact on labor supply ofolder adults for both the entire sample and the rural households sample (in Appendix). IV re-gression estimates using the entire sample are significant: A one year increase in schooling of thehighest educated child reduces the likelihood of parents working by about 8 percentage points.Hansen J tests only marginally reject the assumption of over-identification, as their p values arevery close to 10%. This result is consistent with the hypothesis that children’s education has pos-itive effects on the health of older adults through decreasing the their need to work for incomeand consumption, rather than the reverse interpretation that children’s education keep older peoplehealthy so they are better able to work.

Table 13 also reports results for parental psychological well-being which is proxied by theevaluative subjective well-being measure: life satisfaction. Parents with better educated childrenare more satisfied with their life though the estimated coefficients for children’s education are notrobust according to Anderson-Rubin test.

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7 Dynamic Model

7.1 Empirical Methods: Lewbel’s IV Approach

The static model strives to explain the level effect of children’s education on tje health of theirparents in old age. Whether children’s education has any effect on the changes of health of par-ents is of interest as well. Conditional on the past health of parents, does children’s educationstill matter for the health and cognition of parents? Or in other words, does children’s educationhas incremental effects on parental health? This section provides some tentative answers to thisquestion. Following Zimmer et al. (2007), I estimate a dynamic model of health which follows anAR(1) process using the two-year follow-up data. A static model for the follow-up data is alsoestimated as a robustness check; the results are in Appendix A. A linear dynamic model of healthfor the follow-up sample is as follows:

Hijk1 = b0 + cHijk0 + b1ChildEduijk + b3Controlijk + ChildCohortj + hk + lj + wijk (3)

As baseline health is endogenous and related to children’s education, instruments are neededfor the lagged baseline health so that the incremental effects of children’s education are identifi-able. It is difficult to find external instruments for lagged health since it requires very restrictiveassumptions on them to affect only current health through lagged health. Therefore, I apply an in-strumental variable estimation method introduced by Lewbel (2012) which relies on heteroscedas-ticity of errors and higher moment conditions when traditional instruments are weak or exclusionrestriction conditions for traditional IVs are violated. Specifically, Lewbel-type instruments aregenerated as the product of heteroscedastic error terms, which are predicted from auxiliary regres-sions of the baseline health outcomes on only the exogenous independent variables, with the sub-set of demeaned exogenous variables. Heteroscedasticity in errors from the auxiliary regressionsis tested using the Breusch Pagan test and Sargan-Hansen test of overidentification are conductedfor the Lewbel IV regressions. (Appendix B describes the Lewbel IV approach in more detail.)Lewbel-type IVs are generated only for lagged health, not for years of schooling of the highesteducated adult child, so the results on the incremental effects of children’s education are not drivenby the use of generated instruments, which are unnecessary and in some cases reduce the powerof estimates for children’s education. The IV regression with Lewbel’s generated instruments areconducted using two-stage least squares method. The subset of exogenous variables used for in-strument construction includes age categories and respondent’s gender, which are exogenous andstrongly correlated with both past and current health of parents, as well as baseline height, which isa measure of childhood health and shown to be strongly related to later life health among Chineseelderly by Smith et al. (2012).

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By estimating the dynamic model, I provide suggestive evidence on the effects of children’seducation on the progression of parental health and cognition. With baseline health controlledof, which is arguably a sufficient statistic for the accumulated effects of children’s education onparents’ health, I can estimate the incremental or periodic effects of children’s education on thehealth of parentsI estimate a dynamic model instead of taking first differences of outcomes toavoid the magnification of measurement error. In addition, on basis of the data generation processof health in Appendix B, the dynamic model provides estimates for the incremental effects ofchildren’s education in a more direct manner, while the estimates for children’s education from thefirst difference equation can be interpreted as the persistent effects. For the detailed description ofthe data generating process, please see Appendix B.

An obvious limitation in the estimation strategy is that own education of older adults has beentreated as exogenous. This contradicts the fact that both education and health are endogenouslydetermined. With no credible external instruments, I therefore also apply Lewbel’s IV approach togenerate “internal” instruments for older adults’ own education for the main static as a robustnesscheck. For the dynamic models, I use the dynamic specification where parents’ education areinstrumented using Lewbel’s IV approach as the main specification, and the results where olderadults’ own education is treated as exogenous in the appendix.

A growing number of studies in economics have been utilizing Lewbel’s IV method in recen-t years, either as the main identification strategy when no valid external instruments are present(e.g., Brown, 2014; Banerjee et al., 2017), or as a complement to traditional IV estimation to pro-vide overidentification or robustness test for models that are just identified (e.g., Sabia, 2007;Belfield and Kelly, 2012; Emran and Hou, 2013; Mishra and Smyth, 2014; Islam and Smyth, 2015).To generate the Lewbel-type IVs for own education of older adults, I use parental age categories,gender and baseline height that are strongly correlated with years of schooling of older adult-s. Tow-stage least squares estimation results using Lewbel IV (for own education) and externalinstruments (for children’s education) are shown in Appendix A.

7.2 Dynamic Model Estimation Results

Taking advantage of the follow-up data, I show that most results found for the baseline sample alsohold for wave 2 sample. Table A1, A2, A3, A4, and A5 in Appendix A report the static modelresults using CHARLS wave 2 data. Static estimation results using the follow-up data are similarto the baseline results, though some of the IV estimates for children’s education are smaller andinsignificant for the follow-up sample.

I then estimate the dynamic models for the follow-up sample to study whether there is anyincremental effect of children’s education on parents’ health and cognition in old age. I report

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simple OLS estimates and Lewbel IV estimation results with generated instruments based on het-eroscedasticity in lagged baseline health or cognition.

Table 14 report estimation results for parents’ cognitive abilities in two years after the baseline.For the mental intactness index, the Lewbel IV estimate of the incremental effect of years ofschooling of highest educated child is insignificant in the province fixed effects model. Whencommunity fixed effects are controlled of, it is similar in magnitude to the Lewbel IV estimate inthe province fixed effects model. A similar pattern is found for episodic memory index, exceptthat the estimated causal impact of one additional year of schooling of the highest educated childis significant even in the community fixed effects model. Breusch-Pagan tests of homoscedasticityof auxiliary regressions are rejected for all Lewbel IV models. One general take-away from thedynamic estimation results for cognition is that in comparison with static model results, there isa smaller but significant incremental effect of children’s schooling on parents’ cognitive abilities,especially their episodic memory. Another finding worth mentioning is that the state dependenceof episodic memory (0.38–0.48) is smaller than mental intactness (0.69), and the coefficient of thebaseline episodic memory is not significant in Lewbel IV model with community fixed effects.In fact, the state dependency is relatively low in comparison with what people used to find in theliterature, even though I have not taken first differences to remove individual fixed effects.

As for the subjective health measures of older adults, there seems to be no significant incre-mental effect of children’s education (Table 15). I fail to find evidence for any incremental effectsof education of highest educated adult on objective health measures (Table 16), body weight (Table17) or depressive symptoms (Table 18). The lack of significant causal impacts of education of chil-dren on the progression of health outcomes and the decline of point estimates in magnitude suggestthat while children’s education matters for the level of health and cognition of parents in old age, itdoes not have significant impact on their changes or maintenance over a short period of time. Thisfinding is also consistent with Yahirun et al. (2017). However, all dynamic model results shouldbe interpreted with caution, as for most outcomes and specifications, the under-identification is notrejected though F statistics for weak-identification tests are above than 10 in most columns. Stud-ies of the long-term incremental effects of children’s education on parental health are warranted inthe future using longer-span panel data.

8 Robustness Checks

In this section, I test the sensitivity of the baseline results to the use of alternative instruments, thecontrol of the One Child Policy, the instrumentation of own education of older adults using LewbelIV approach and the adjustment for multiple hypotheses testing. I also test the sensitivity of thedynamic results to the instrumentation of older adults’ own education by showing the results when

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education of older adults themselves is not instrumented.Table A9 to Table A13 in Appendix A report results from estimations on health and cognition

of parents using indicator variables for each level of compulsory education exposure instead oflinearly imputed exposure and their interactions with regional average years of schooling of cohortsineligible to compulsory education as instruments. For all outcomes except for baseline bodyweight, the estimated effects of children’s education are similar to those that have been previouslyshown in Section 6.2. However, from results of Hansen J tests in regressions on the baseline mentalintactness, subjective survival expectation and CES-D 10 index, the over-identification assumptionis rejected. Another major problem with using indicators as instruments for years of schoolingof children is that the indicators seem to be weak as implied by the F statistics of the weak-identification test, most of which are well below the rule of thumb value of 10. Therefore, thealternative instruments are used only for robustness check, not in the main analysis.

Table A14 and Table A15 show that the baseline results are not sensitive to the further controlof exposure to the One Child Policy. But controlling for the One Child Policy reduces the value ofthe F statistics from first stage regressions which is consistent with the previous findings that theOne Child Policy has contributed to the increase of schooling in cohorts that were affected.

Table A16, Table A17, Table A18 and Table A19 show how sensitive the baseline and dynamicresults are to the instrumentation for older adults’ education using Lewbel’s approach (Lewbel,2012). Generally speaking, static model results based on the baseline sample still hold and someof the causal estimates from models with community fixed effects, that is, grip strength and CES-D10 index, become significant when I instrumented the education of older adults themselves. Fordynamic models results, I find that the incremental effect of children’s educaion remains significantfor parental episodic memory index when Lewbel IVs are not used for older adults’ education.Using Lewbel’s IV method to instrument parents’ own education leads insignificant estimates ofchildren’s education on parental mental intactness, as the comparison of Table A17 and Table 14shows.

I also test whether the baseline results are robust to the adjustment for multiple hypothesestesting using Simes (1986)’s method, since I assess the effects of children’s education on a widearray of health and cognition outcomes of older adults. I report results of hypothesis testing basedon critical p-values adjusted for multiple testing in Table A20. The estimated effects of children’seducation on baseline mental intactness, episodic memory, peak flow and body weight remainsignificant at the overall 5% significance level.

These four sensitivity analyses support the baseline or dynamic findings by showing that theyare robust to the control of other social programs, uses of instruments whose first stages are less re-strictive, additional instrumentation for own education of older adults, and adjustment for multipletesting.

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9 Conclusion and Discussion

A multiplicity of research in economics has shown that human capital transmits from older gen-erations to younger ones. However, less evidence is available on whether there is also significantupward spillover from children to parents (De Neve and Kawachi, 2017). Furthermore, as educa-tion is proven to be an important predictor of human health and longevity in a substantial body ofliterature, whether the education of younger generations also has significant and causal influenceson the health of older generations is an interesting question that the literature has neglected for themost part. That said, mounting research has been conducted recently, though most of the stud-ies are association studies that did not control for bias arising from omitted variables and reversecausality problems.

This paper reinforces and extends what existing works have found on the relation betweenparental health in later life and children’s education by providing a causal analysis on a rich set ofmeasures on health and cognition of Chinese elderly. The gradual roll-out of compulsory school-ing in the 1980s and early 1990s across Chinese provinces is used as a natural experiment toachieve identification of causation because the exposure to compulsory education creates exoge-nous variations in the schooling of children within the same province. IV estimation results showthat increasing years of education of adult children lead to substantial increase of the cognitivefunctions of parents including both episodic memory and mental intactness. Parents with better e-ducated children have greater body weight, higher subjective survival expectations and better lungfunction. In addition to its level effect, children’s education also seems to help older adults in termsof maintenance of cognitive functions, shown in results of the dynamic model. For Chinese elderly,improved financial support from children, better access to resources and sanitation as well as lesslabor supply and higher level of psychological well-being might explain why children’s educationcould shape parental health and cognition in later life.

Cognitive decline, lung function and body weight are important biomarkers for old-age healthand strong predictors of mortality (e.g., Mannino et al., 2003; Gale et al., 2006; Lee et al., 1993).The analysis on these biomarkers helps explain the relationship that existing literature has foundbetween children’s education and parental survival. Working pathways being social support andaccess to resources, rather than social influence of children on parental health behaviors, whichmight be more important in developed countries, is also consistent with the fact that parents relyon children for old-age support and the pooling of resources among family members is commonin developing countries. However, a formal mediation analysis is warranted to understand therelevant importance of different mechanisms in explaining the effect of education of children onparental health.

Although in this paper, I have not discussed the possible heterogeneity in the spillover ef-

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fects from children’s education to parents’ health, it is very likely that parents benefit differ-entially by their own schooling level (Friedman and Mare, 2014), gender or children’s gender(Lundborg and Majlesi, 2017). Furthermore, other than the potential mechanisms that have beenexamined in this paper, there could well be other mediating factors that link children’s educationwith parental health and survival. For example, education is also strongly associated with higherlevels of social capital or social engagement (Campbell, 2006) which is shown to be associatedwith health behaviors, self-rated health, survival (Lindstrom et al., 2001; Nieminen et al., 2013;Veenstra, 2000; Sirven and Debrand, 2008; Sundquist et al., 2004), and cognitive functioning andits decline among the elderly (Bielak, 2010; James et al., 2011) by providing an increased sense ofbelonging and attachment (Berkman et al., 2000), mutual trust (Hyyppa and Maki, 2003), stimu-lation, and resistance to depression (Glei et al., 2005). Although I have not been able to find anysignificant causal relation between parental social activity participation and children’s educationusing CHARLS data24, some heterogeneity might remain hidden.

Policy implications from the findings in this paper are twofold. First, The findings on theeffects of children’s education on parental health in old age re-emphasize the broader return orbenefits of both public and private investments in education. Second, as Friedman and Mare (2014)argued, policies targeting one generation of the family may spill over to previous and subsequentgenerations, and to the broader family unit. A broader network perspective including family andmultiple generations on health is warranted, in order to harness the value of social programs forhealth in the most efficient way. Education as a policy instrument targeted at one generation mightnot come at the expense of other generations or other social policies. Education policy on youngergenerations might complement policies in public support system, help reduce health disparities,and improve health of the entire population.

24Results are available upon request.

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Figures

Adult

ChildrenParent

Knowledge,

Behaviors,

Income,

Job flexibility,

Migration, etc.

Health

Social

Influence

Access to

Resources

Social

Support

Behaviors:

Health

Behaviors

Behaviors:

Labor Supply

Psychological

Factors

Unobserved Genetic

Endowment/Abilities

Childhood Health,

Investment

Spouse,

Friends, etc.

Based on the Social Network Theory of Health

Informal

Contract

Education

Figure 1: Linking Parents’ Health and Children’s Education, based on the Social Network Theoryof Health of Berkman et al. (2000)

41

Anhui

Beijing

Fujian

Gansu

Guangdong

Guangxi

Guizhou

Hainan

Hebei

Henan

Heilongjiang

Hubei

Hunan

Jilin

Jiangsu

Jiangxi

Liaoning

Inner Mongol

NingxiaQinghai

ShandongShanxi

Shaanxi

Shanghai

Sichuan

TaiwanTaiwanTaiwan

Tianjin

Xizang/Tibet

Xinjiang

Yunnan

ZhejiangChongqing

198519861987198819891991No data

Figure 2: Provincial Implementation of Compulsory Education

42

67

89

1011

1213

14

-12 -9 -6 -3 0 3 6 9 12 15 -12 -9 -6 -3 0 3 6 9 12 15

High Schooling Area Low Schooling Area

Cohort mean Left: fitted trend-ineligible cohortsMiddle: fitted trend-partially eligible cohorts Right: fitted trend-completely eligible cohorts

Mea

n Y

ears

of S

choo

ling

Age Difference with First CS Eligible Cohorts*

Source: CHARLS and author's own calculation.*Year of birth of the highest educated child minus year of birth of the the first CS eligible cohort in each province.

Figure 3: Effect of Compulsory Education on Completed Education Level by High/Low Schoolingareas

43

marginally~1 year

1~2 years

2~3 years

3~4 years

4~5 years

5~6 years

6~7 years

7~8 years

8~9 years

9+ years

-2 0 2 4 -2 0 2 4 -2 0 2 4

All Low Schooling Area High Schooling Area

Note: Point estimates and confidence intervals from regressions of years of schooling of the highesteducated child on indicators of compulsory education exposure, birth cohort fixed effects, provincefixed effects, province-specific trends and rural residence indicator using CHARLS data.

Figure 4: Effects of Exposure to Compuslory Education on Years of Schooling

44

Tables

Table 1: Implementation of Compulsory Education and Educational Attainments ofCohorts Ineligible to Compulsory Education

Province Law Effect Year First Eligible Birth Cohort Average Years of Schooling of Law Ineligible CohortsUrban Rural

Beijing 1986 1971 11.31 8.62Tianjin 1987 1972 10.30 7.92Hebei 1986 1971 9.92 8.25Shanxi 1986 1971 10.14 8.08Inner Mongolia 1989 1974 9.91 7.30Liaoning 1986 1971 10.20 7.88Jilin 1987 1972 10.21 7.38Heilongjiang 1986 1971 9.94 7.58Shanghai 1985 1970 9.93 8.03Jiangsu 1987 1972 9.75 8.21Zhejiang 1985 1970 8.63 7.25Anhui 1987 1972 9.14 7.20Fujian 1988 1973 8.68 7.01Jiangxi 1986 1971 9.60 6.86Shandong 1987 1972 9.80 7.84Henan 1987 1972 9.98 8.22Hubei 1987 1972 9.84 7.41Hunan 1991 1976 10.33 8.03Guangdong 1987 1972 9.41 7.77Guangxi 1991 1976 9.90 7.72Chongqing 1986 1971 9.35 6.87Sichuan 1986 1971 9.38 7.01Guizhou 1988 1973 8.58 4.86Yunnan 1987 1972 8.84 5.53Shaanxi 1987 1972 10.13 7.44Gansu 1991 1976 10.19 6.11Qinghai 1989 1974 9.68 4.52Xinjiang 1988 1973 10.03 7.23

Note: Implementation information is retrieved from China’s National People’s Congress and Chi-nese Laws and Regulations Information Database. Average years of schooling of law ineligiblecohorts is calculated by the author using 2000 population census data.

45

Table 2: Descriptive Statistics of Major Variables

Baseline Wave 2VARIABLES mean N sd mean N sd

Health and Cognition Measures:mental intactness score(0-11) 7.427 10,776 3.133 7.044 10,270 3.432episodic memory(0-10) 3.408 9,988 1.756 3.279 10,270 1.879self-report of health (very good=1,good,fair,poor,very poor=5) 3.044 10,808 0.889 2.998 10,174 0.932peak expiratory flow (average of 3 measurements) 266.3 10,290 112.8 266.4 7,696 114.0dominant hand grip strength (average of 2 measurements) 30.55 10,610 10.56 29.72 8,035 10.57CESD 10 score(0-30) 8.432 10,220 6.274 7.901 9,130 5.768body mass index=kg/m2 23.51 10,769 3.928 23.76 8,093 3.797BMI <18.5 0.0657 10,769 0.248 0.0605 8,093 0.239BMI ≥ 25 0.312 10,769 0.463 0.346 8,093 0.476low subjective survival expectation 0.296 9,373 0.457 0.328 7,925 0.469

Channels:ever drinks any alcohol last year 0.330 10,812 0.470# of drinks per week 1.601 9,422 4.101r smoke now 0.308 10,774 0.462# cigarettes/day 4.533 9,886 9.733# of d/w of contacting children per week(co-residence = 7) 4.139 10,704 2.325# of d/w of contacting children in person per week(co-residence = 7) 5.266 10,675 2.897# of d/w of contacting with children by phone/mail/text/email 1.982 8,492 2.379net monetary transfer from children 628.4 10,714 12,016log of per capita household expenditure last year 8.445 9,311 0.853access to clean fuel (gas, electricity) for cooking 0.412 10,699 0.492access to in-house flush-able toilets 0.329 10,773 0.470life satisfaction (completely=1,very,somewhat, not very, not at all=5) 2.939 9,732 0.699currently working 0.727 10,780 0.445

Demographics of Parents:age in years 58.51 10,811 9.043 60.42 10,480 8.996height in meters 1.581 10,812 0.0855bad childhood health 0.0727 10,812 0.260gender:female = 1 0.531 10,812 0.499own years of schooling 4.443 10,812 4.516marital status 10,812 10,480

married (%) 85.6 9,256.00 83.4 8,743.00married, sp abs (%) 4.3 462 4.7 489

widowed (%) 0.4 46 0.3 28 widoweddivorced (%) 0.6 65 0.5 57 single

separated (%) 9 977 11 1,157.00 singlenever married (%) 0.1 6 0.1 6 single

Child Characteristics:gender of the highest educated child 0.402 10,812 0.490years of schooling of the highest educated child 10.45 10,812 3.714exposure to CSL of the highest educated child 0.587 10,812 0.429birth year of the highest educated child 1,977 10,812 8.395Household Characteristics:lives in rural or urban 0.659 10,812 0.474 0.660 10,480 0.474number of living children 2.722 10,812 1.361 2.814 10,480 1.374

Regional Characteristics:average years of schooling of compulsory schooling ineligible cohorts 8.174 10,812 1.321# of beds per 10000 population in child’s birth year and province 17.79 10,812 8.449# of doctors per 10000 population in child’s birth year and province 10.59 10,812 4.929log of per capita provincial GDP in child’s birth year 5.931 10,812 0.750

46

Table 3: Distribution of Compulsory Education Exposure of Highest Educated Child

Age at CSL Implementation Years Exposed to CSL ChildExp % No.

6 and 6- 9 1 41.8 4,5177 8 to 9 0.9 4.3 4678 7 to 8 0.8 3.9 4269 6 to 7 0.7 4 43110 5 to 6 0.6 3.5 37411 4 to 5 0.5 3.4 37312 3 to 4 0.4 3.8 41013 2 to 3 0.3 3.1 33614 1 to 2 0.2 3.1 33015 Marginally to 1 0.1 2.7 29716 and 16+ 0 0 26.4 2,851Total 100 10,812

47

Table 4: First Stage Results for Years of Schooling of the Higest EducatedChild

(1) (2) (3) (4)MODELS First Stage: Education of Children(Years of Schooling)

Exposure to CSL 1.766*** 3.869*** 1.382*** 3.177***(0.485) (0.734) (0.490) (0.742)

Exposure PrelawEdu -0.264*** -0.225***(0.069) (0.069)

Own Education 0.239*** 0.239*** 0.194*** 0.195***(0.008) (0.008) (0.008) (0.008)

Observations 10,776 10,776 10,769 10,769Child Birth Year FE YES YES YES YESProv Birth Year Trend YES YES YES YESProvince FE YES YES NO NOCommunity FE NO NO YES YESF stat for Excludable IVs (weak Identification) 7.492 12.02 3.766 8.620

Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

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Table 5: Level Effects of Children’s Education on Baseline Cognition of Parents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV OLS IV OLS IV OLS IV

VARIABLES Baseline Mental Intactness Baseline Episodic Memory

Education of Children 0.107*** 0.423*** 0.102*** 0.477** 0.045*** 0.245*** 0.038*** 0.209**(0.006) (0.153) (0.007) (0.197) (0.006) (0.090) (0.005) (0.095)

Own Education 0.246*** 0.171*** 0.244*** 0.172*** 0.099*** 0.053** 0.093*** 0.060***(0.008) (0.034) (0.009) (0.037) (0.007) (0.021) (0.006) (0.018)

Observations 10,776 10,776 10,776 10,769 9,988 9,988 9,988 9,979Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 429 422 28 28 429 420Mean of Dependent Variable 7.427 7.427 7.427 7.427 3.408 3.408 3.408 3.408LM stat for underid. 10.17 10.34 11.48 10.98p-val of LM stat 0.00620 0.00568 0.00322 0.00413F stat for weak-id. 12.02 8.620 15.82 10.31Anderson-Rubin F stat 4.481 3.640 6.849 4.003p-val of AR F stat 0.0209 0.0399 0.00393 0.0300p-val of Hansen J stat 0.549 0.582 0.181 0.0499

1 Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.2 The LM version of the KleibergenPaap rk statistic tests whether the rank condition, or in other words,

requirement that all of the canonical correlations between endogenous variables and the instruments aresignicantly dierent from zero, are satisfied. The consequence of utilizing excluded instruments that areuncorrelated with the endogenous regressors is increased bias in the estimated IV coefficients. If one ormore of the canonical correlations is zero, the model is underidentied or unidentied. The rejection of thenull hypothesis implies full rank and identification.

3 A Wald F statistic based on the KleibergenPaap rk statistic (F stat for excludable IVs) for weak identificationtest. As Baum et al. (2007) suggests, I refer to the older “rule of thumb” of Staiger and Stock (1997), i.e.,to use 10 as the threshold for weak identication.

4 An F test version of Anderson-Rubin of joint significance of endogenous regressors which is robust to weakinstrument problems is used and p values of the F statistics are reported. When the instruments are onlyweakly related to the endogenous variables, 2SLS or IV estimates are biased and t tests are unreliable. Thenull hypothesis of Anderson-rubin test is that the endogenous variables are jointly zero, or H0 : β = 0,conditional on that the instruments are exclude-able. When instruments are irrelevant, Anderson-rubin testhas no power which makes this test robust to weak instruments problems. The F-statistic in the regression ofY −Xβ0 on Z where Y is the outcome of interest, X are the endogenous variables, Z are the instruments.

49

Table 6: Level Effects of Children’s Education on Baseline Subjective Health Measures ofParents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV OLS IV OLS IV OLS IV

VARIABLES Self Reported Health Low Subjective Survival Expectation

Education of Children -0.018*** -0.048 -0.017*** -0.059 -0.009*** -0.085** -0.008*** -0.085**(0.003) (0.045) (0.003) (0.051) (0.001) (0.041) (0.001) (0.039)

Own Education -0.011*** -0.004 -0.011*** -0.003 -0.008*** 0.010 -0.007*** 0.008(0.003) (0.012) (0.003) (0.011) (0.001) (0.010) (0.001) (0.008)

Observations 10,808 10,808 10,808 10,801 9,373 9,373 9,373 9,367Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 429 422 28 28 426 420Mean of Dependent Variable 3.044 3.044 3.044 3.044 0.296 0.296 0.296 0.296LM stat for underid. 10.33 10.60 9.360 9.667p-val of LM stat 0.00572 0.00499 0.00928 0.00796F stat for weak-id. 12.61 9.276 14.20 9.889Anderson-Rubin F stat 0.659 1.070 2.673 3.931p-val of AR F stat 0.525 0.357 0.0873 0.0317p-val of Hansen J stat 0.900 0.708 0.660 0.888

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

50

Table 7: Level Effects of Children’s Education on Baseline Physical Health of Parents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV OLS IV OLS IV OLS IV

VARIABLES Baseline Peak Flow Baseline Grip Strength

Education of Children 1.433*** 19.207*** 1.163*** 22.101*** 0.198*** 0.448 0.130*** 0.651(0.308) (7.252) (0.246) (8.399) (0.034) (0.400) (0.020) (0.478)

Own Education 2.329*** -1.870 1.808*** -2.272 0.124*** 0.065 0.123*** 0.023(0.371) (1.843) (0.264) (1.654) (0.030) (0.091) (0.019) (0.090)

Observations 10,290 10,290 10,290 10,283 10,610 10,610 10,610 10,603Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 426 419 28 28 427 420Mean of Dependent Variable 266.3 266.3 266.3 266.3 30.55 30.55 30.55 30.55LM stat for underid. 10.43 10.21 9.891 9.273p-val of LM stat 0.00545 0.00607 0.00712 0.00969F stat for weak-id. 12.88 8.475 11.29 7.554Anderson-Rubin F stat 6.071 5.681 1.160 1.371p-val of AR F stat 0.00665 0.00873 0.329 0.271p-val of Hansen J stat 0.407 0.659 0.636 0.877

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

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Table 8: Level Effects of Children’s Education on Baseline Body Weight of Parents

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)OLS IV OLS IV OLS IV OLS IV OLS IV OLS IV

VARIABLES Baseline BMI Baseline Underweight Baseline Overweight

Education of Children 0.076*** 0.826*** 0.064*** 0.829** -0.004*** -0.063** -0.003*** -0.059** 0.006*** 0.061*** 0.005*** 0.064**(0.014) (0.268) (0.010) (0.325) (0.001) (0.027) (0.001) (0.028) (0.002) (0.021) (0.002) (0.029)

Own Education 0.023** -0.156** 0.004 -0.144** -0.001 0.014** -0.000 0.011* 0.002 -0.012** 0.000 -0.011*(0.011) (0.062) (0.012) (0.062) (0.001) (0.007) (0.001) (0.006) (0.002) (0.005) (0.002) (0.006)

Observations 10,769 10,769 10,769 10,763 10,769 10,769 10,769 10,763 10,769 10,769 10,769 10,763Child Birth Year FE YES YES YES YES YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YES NO NO YES YESNumber of groups 28 28 428 422 28 28 428 422 28 28 428 422Mean of Dependent Variable 23.51 23.51 23.51 23.51 0.0657 0.0657 0.0657 0.0657 0.312 0.312 0.312 0.312LM stat for underid. 10.07 10.02 10.07 10.02 10.07 10.02p-val of LM stat 0.00652 0.00668 0.00652 0.00668 0.00652 0.00668F stat for weak-id. 12.41 8.916 12.41 8.916 12.41 8.916Anderson-Rubin F stat 7.271 3.145 6.346 4.183 3.106 1.784p-val of AR F stat 0.00298 0.0592 0.00551 0.0262 0.0611 0.187p-val of Hansen J stat 0.777 0.401 0.393 0.247 0.821 0.859

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

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Table 9: Level Effects of Children’s Education on Base-line Mental Health of Parents

(1) (2) (3) (4)OLS IV OLS IV

VARIABLES Baseline CESD 10 Score

Education of Children -0.155*** -0.267 -0.142*** -0.470(0.028) (0.350) (0.021) (0.472)

Own Education -0.134*** -0.108 -0.130*** -0.068(0.015) (0.085) (0.015) (0.093)

Observations 10,220 10,220 10,220 10,216Child Birth Year FE YES YES YES YESProv Birth Year Trend YES YES YES YESProvince FE YES YES NO NOCounty FE NO NO NO NOCommunity FE NO NO YES YESNumber of groups 28 28 426 422Mean of Dependent Variable 8.432 8.432 8.432 8.432LM stat for underid. 9.710 9.498p-val of LM stat 0.00779 0.00866F stat for weak-id. 10.29 6.961Anderson-Rubin F stat 0.377 1.010p-val of AR F stat 0.689 0.378p-val of Hansen J stat 0.605 0.242

Standard errors clustered at province level in parentheses. ***p < 0.01, ** p < 0.05, * p < 0.1.

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Table 10: Social Influence: Level Effects of Child’s Education on Baseline HealthBehaviors of Parents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV OLS IV OLS IV OLS IV

VARIABLES Whether Smoke now (men) Whether Drink last year

ChildEdu -0.012*** 0.046 -0.010*** 0.099 0.002 0.039* 0.002 0.059**(0.002) (0.066) (0.002) (0.106) (0.001) (0.020) (0.001) (0.024)

REdu -0.006*** -0.021 -0.006*** -0.031 0.001 -0.008 0.001 -0.009*(0.002) (0.017) (0.002) (0.025) (0.001) (0.005) (0.001) (0.005)

Observations 5,036 5,036 5,036 5,021 10,812 10,812 10,812 10,805Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 422 407 28 28 429 422Mean of Dependent Variable 0.590 0.590 0.590 0.590 0.330 0.330 0.330 0.330LM stat for underid. 6.877 6.213 10.32 10.50p-val of LM stat 0.0321 0.0448 0.00573 0.00524F stat for weak-id. 9.039 4.516 12.53 9.079Anderson-Rubin F stat 0.404 0.696 2.467 3.868p-val of AR F stat 0.672 0.507 0.104 0.0333p-val of Hansen J stat 0.748 0.739 0.276 0.502

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

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Table 11: Social Support: Level Effects of Child’s Education on Baseline Transfer of Time and Money from Children

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)OLS IV OLS IV OLS IV OLS IV OLS IV OLS IV

VARIABLES Frequency of Visits of Children: # d/w Frequency of Contacts of Children not in person: # d/w Net Annual Transfer Amount from Children: RMB

Education of Children -0.039*** 0.043 -0.045*** -0.124 0.040*** 0.204 0.020* 0.249 27.496** 508.294** 33.898*** 577.637**(0.013) (0.268) (0.013) (0.327) (0.012) (0.233) (0.010) (0.250) (11.673) (213.655) (11.963) (235.476)

Own Education -0.004 -0.027 -0.004 0.015 0.043*** -0.003 0.041*** -0.015 -10.771 -142.124** -7.282 -135.418**(0.010) (0.077) (0.010) (0.079) (0.012) (0.065) (0.014) (0.063) (6.570) (60.960) (7.480) (57.684)

Observations 6,547 6,547 6,547 6,533 5,210 5,210 5,210 5,193 6,377 6,377 6,377 6,363Child Birth Year FE YES YES YES YES YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YES YES YES YES YESProvince FE NO NO NO NO YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YES NO NO YES YESNumber of groups 28 28 429 415 28 28 423 406 28 28 429 415Mean of Dependent Variable 5.299 5.299 5.299 5.299 1.948 1.948 1.948 1.948 817.3 817.3 817.3 817.3LM stat for underid. 6.760 7.578 8.471 6.640 5.610 6.974p-val of LM stat 0.0341 0.0226 0.0145 0.0361 0.0605 0.0306F stat for weak-id. 8.498 6.878 10.06 7.235 7.151 6.794Anderson-Rubin F stat 1.695 0.591 5.541 5.194 8.033 7.730p-val of AR F stat 0.203 0.561 0.00963 0.0123 0.00183 0.00222p-val of Hansen J stat 0.203 0.291 0.0323 0.128 0.408 0.647

Standard errors clustered at province/county/community level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

55

Table 12: Access to Resources: Level Effects of Child’s Education on Baseline Access to Resources of Parents

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)OLS IV OLS IV OLS IV OLS IV OLS IV OLS IV

VARIABLES Log Per Capita Household Expenditure Access to Clean Fuel for Cooking Access to Flush-able In-house Toilets

ChildEdu 0.031*** 0.147* 0.023*** 0.062 0.012*** 0.079* 0.005** 0.093* 0.013*** 0.068* 0.005** 0.069**(0.003) (0.079) (0.003) (0.090) (0.002) (0.048) (0.002) (0.049) (0.002) (0.038) (0.002) (0.030)

REdu 0.023*** -0.009 0.021*** 0.011 0.013*** -0.005 0.009*** -0.013 0.008*** -0.007 0.005*** -0.011(0.003) (0.022) (0.003) (0.021) (0.002) (0.014) (0.001) (0.013) (0.002) (0.012) (0.001) (0.008)

Observations 5,652 5,652 5,652 5,640 6,562 6,562 6,562 6,549 6,608 6,608 6,608 6,596Child Birth Year FE YES YES YES YES YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YES NO NO YES YESNumber of groups 28 28 425 413 28 28 427 414 28 28 428 416Mean of Dependent Variable 8.439 8.439 8.439 8.439 0.419 0.419 0.419 0.419 0.332 0.332 0.332 0.332LM stat for underid. 7.356 7.305 7.477 8.660 7.342 8.219p-val of LM stat 0.0253 0.0259 0.0238 0.0132 0.0255 0.0164F stat for weak-id. 8.650 6.303 9.556 7.855 9.226 7.613Anderson-Rubin F stat 2.957 0.836 2.111 2.442 8.775 4.476p-val of AR F stat 0.0690 0.444 0.141 0.106 0.00116 0.0209p-val of Hansen J stat 0.331 0.390 0.686 0.775 0.223 0.960

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

56

Table 13: Other: Level Effects of Child’s Education on Baseline Labor Supply and Psycho-logical Well-being of Parents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV OLS IV OLS IV OLS IV

VARIABLES Whether Work Now Life Satisfaction (1-5)

Education of Children -0.004*** -0.076*** -0.001 -0.082** -0.015*** -0.086* -0.013*** -0.108*(0.001) (0.029) (0.001) (0.033) (0.003) (0.046) (0.004) (0.064)

Own Education -0.006*** 0.011 -0.003** 0.013** 0.002 0.018* 0.002 0.019(0.001) (0.007) (0.001) (0.006) (0.003) (0.011) (0.003) (0.013)

Observations 10,780 10,780 10,780 10,773 9,732 9,732 9,732 9,726Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 429 422 28 28 426 420Mean of Dependent Variable 0.727 0.727 0.727 0.727 2.939 2.939 2.939 2.939LM stat for underid. 10.27 10.35 10.55 10.36p-val of LM stat 0.00589 0.00566 0.00513 0.00563F stat for weak-id. 12.42 8.888 13.71 8.961Anderson-Rubin F stat 5.930 5.093 1.866 1.296p-val of AR F stat 0.00733 0.0133 0.174 0.290p-val of Hansen J stat 0.0982 0.0845 0.742 0.575

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

57

Table 14: Incremental Effects of Child’s Education on Wave 2 Cognition of Parents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV+Lewbel OLS IV+Lewbel OLS IV+Lewbel OLS IV+Lewbel

VARIABLES Wave 2 Mental Intactness Wave 2 Episodic Memory

Baseline 0.509*** 0.694*** 0.526*** 0.685*** 0.293*** 0.478*** 0.308*** 0.383***(0.014) (0.063) (0.012) (0.067) (0.010) (0.118) (0.010) (0.107)

Education of Children 0.078*** 0.140 0.072*** 0.141 0.036*** 0.125** 0.036*** 0.129**(0.011) (0.115) (0.010) (0.102) (0.006) (0.061) (0.006) (0.060)

Own Education 0.130*** -0.094* 0.126*** -0.069 0.079*** 0.023 0.080*** 0.037*(0.010) (0.051) (0.008) (0.046) (0.006) (0.021) (0.006) (0.021)

Observations 10,239 10,239 10,239 10,232 9,507 9,507 9,507 9,499Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 427 420 28 28 426 418Mean of Dependent Variable 7.052 7.052 7.052 7.052 3.340 3.340 3.340 3.340LM stat for underid. 21.74 19.45 18.99 23.51p-val of LM stat 0.244 0.365 0.392 0.172F stat for weak-id. 15.88 8.011 8.655 16.60Anderson-Rubin F stat 41.88 18.64 8.154 7.247p-val of AR F stat 0 5.62e-11 6.48e-07 2.17e-06p-val of Hansen J stat 0.620 0.499 0.755 0.673Breusch Pagan test p-val 1.20e-92 2.01e-48 1.39e-31 4.11e-25

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

58

Table 15: Incremental Effects of Child’s Education on Wave 2 Subjective Health Measures of Parents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV+Lewbel OLS IV 1+2 + Lewbel IV OLS IV+Lewbel OLS IV+Lewbel

VARIABLES Wave 2 Self Reported Health Wave 2 Low Subjective Survival Expectation

Baseline 0.420*** 0.488*** 0.411*** 0.438*** 0.393*** 0.051 0.385*** 0.017(0.012) (0.167) (0.012) (0.160) (0.019) (0.195) (0.020) (0.199)

Education of Children -0.010*** 0.001 -0.008** 0.003 -0.010*** -0.042 -0.008*** -0.040(0.003) (0.038) (0.003) (0.035) (0.002) (0.033) (0.002) (0.031)

Own Education -0.002 -0.009 -0.002 -0.006 -0.005*** -0.003 -0.004*** -0.001(0.002) (0.015) (0.002) (0.014) (0.001) (0.007) (0.001) (0.007)

Observations 10,170 10,170 10,170 10,163 7,071 7,071 7,071 7,062Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 427 420 28 28 424 415Mean of Dependent Variable 2.998 2.998 2.998 2.998 0.331 0.331 0.331 0.331LM stat for underid. 21.64 22.50 21.29 20.47p-val of LM stat 0.248 0.210 0.265 0.307F stat for weak-id. 6.895 5.606 18.05 15.30Anderson-Rubin F stat 2.845 2.508 16.06 21.48p-val of AR F stat 0.00605 0.0134 3.33e-10 0p-val of Hansen J stat 0.889 0.742 0.322 0.312Breusch Pagan test p-val 7.83e-23 1.34e-35 1.25e-15 1.45e-11

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

59

Table 16: Incremental Effects of Child’s Education on Wave 2 Physical Health of Parents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV+Lewbel OLS IV+Lewbel OLS IV+Lewbel OLS IV+Lewbel

VARIABLES Wave 2 Lung Function (Peak Flow) Wave 2 Grip Strength

Baseline 0.404*** 0.492*** 0.471*** 0.492*** 0.356*** 0.457*** 0.443*** 0.487***(0.028) (0.037) (0.024) (0.041) (0.030) (0.062) (0.025) (0.067)

Education of Children 1.431*** -1.574 1.374*** 3.302 0.101*** 0.691* 0.125*** 0.505(0.362) (3.512) (0.317) (3.249) (0.027) (0.383) (0.022) (0.429)

Own Education 0.838** 4.279** 0.748** 3.245** 0.080*** 0.008 0.047** 0.056(0.362) (2.118) (0.354) (1.636) (0.021) (0.103) (0.019) (0.118)

Observations 7,383 7,382 7,383 7,371 7,892 7,892 7,892 7,883Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 27 411 399 28 28 416 407Mean of Dependent Variable 268 268 268 268 29.74 29.74 29.74 29.74LM stat for underid. 18.35 21.46 21.34 20.37p-val of LM stat 0.433 0.257 0.263 0.312F stat for weak-id. 16.76 18.29 11.56 8.533Anderson-Rubin F stat 32.94 79.84 52.51 22.28p-val of AR F stat 0 0 0 0p-val of Hansen J stat 0.228 0.213 0.311 0.204Breusch Pagan test p-val 9.27e-89 8.60e-109 2.70e-111 1.20e-197

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

60

Table 17: Incremental Effects of Child’s Education on Wave 2 Body Weight of Parents

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)OLS IV+Lewbel OLS IV+Lewbel OLS IV+Lewbel OLS IV+Lewbel OLS IV+Lewbel OLS IV+Lewbel

VARIABLES Wave 2 BMI Wave 2 Underweight Wave 2 Overweight

Baseline 0.752*** 0.372*** 0.754*** 0.418*** 0.591*** 0.731*** 0.591*** 0.737*** 0.736*** 0.731*** 0.731*** 0.719***(0.029) (0.069) (0.028) (0.063) (0.022) (0.044) (0.021) (0.044) (0.010) (0.037) (0.010) (0.034)

Education of Children 0.019*** -0.133 0.013** -0.033 -0.001** -0.014 -0.001* -0.013 0.001 0.030*** 0.000 0.024(0.005) (0.190) (0.006) (0.183) (0.001) (0.017) (0.001) (0.021) (0.001) (0.011) (0.001) (0.016)

Own Education -0.000 -0.037 -0.004 -0.028 -0.000 0.002 -0.000 0.002 0.002** 0.001 0.001 0.002(0.005) (0.052) (0.004) (0.056) (0.000) (0.004) (0.000) (0.005) (0.001) (0.006) (0.001) (0.005)

Observations 8,057 8,057 8,057 8,050 8,057 8,057 8,057 8,050 8,057 8,057 8,057 8,050Child Birth Year FE YES YES YES YES YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NO YES YES NO NOCounty FE NO NO NO NO NO NO NO NO NO NO NO NOCommunity FE NO NO YES YES NO NO YES YES NO NO YES YESNumber of groups 28 28 417 410 28 28 417 410 28 28 417 410Mean of Dependent Variable 23.77 23.77 23.77 23.77 0.0604 0.0604 0.0604 0.0604 0.347 0.347 0.347 0.347LM stat for underid. 20.08 20.62 21.85 21.32 19.12 20.55p-val of LM stat 0.328 0.299 0.239 0.264 0.384 0.303F stat for weak-id. 10.08 9.308 11.32 5.069 17.29 7.414Anderson-Rubin F stat 14.09 47.60 117.2 42.83 18.83 18.65p-val of AR F stat 1.54e-09 0 0 0 5.00e-11 5.61e-11p-val of Hansen J stat 0.208 0.271 0.292 0.301 0.227 0.273Breusch Pagan test p-val 1.30e-119 0.00e+00 0.00e+00 0.00000e+00 1.66e-22 5.81e-03

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

61

Table 18: Incremental Effects of Child’s Education on Wave2 Mental Health (CESD 10) of Parents

(1) (2) (3) (4)OLS IV+Lewbel OLS IV+Lewbel

VARIABLES Wave 2 CESD 10 Score

Baseline 0.408*** 0.525*** 0.408*** 0.549***(0.013) (0.066) (0.013) (0.073)

Education of Children -0.111*** -0.199 -0.092*** -0.092(0.021) (0.253) (0.023) (0.225)

Own Education -0.029 0.141 -0.017 0.092(0.017) (0.127) (0.013) (0.129)

Observations 8,705 8,705 8,705 8,700Child Birth Year FE YES YES YES YESProv Birth Year Trend YES YES YES YESProvince FE YES YES NO NOCounty FE NO NO NO NOCommunity FE NO NO YES YESNumber of groups 28 28 425 420Mean of Dependent Variable 7.829 7.829 7.829 7.829LM stat for underid. 19.06 19.93p-val of LM stat 0.388 0.337F stat for weak-id. 7.146 10.60Anderson-Rubin F stat 44.62 29.68p-val of AR F stat 0 0p-val of Hansen J stat 0.842 0.660Breusch Pagan test p-val 3.88e-34 2.97e-46

Standard errors clustered at province level in parentheses. *** p <0.01, ** p < 0.05, * p < 0.1.

62

Appendix A

Table A1: Level Effects of Children’s Education on Wave 2 Cognition of Parents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV OLS IV OLS IV OLS IV

VARIABLES Wave 2 Mental Intactness Wave 2 Episodic Memory

Education of Children 0.131*** 0.454*** 0.124*** 0.483* 0.049*** 0.283*** 0.048*** 0.263**(0.011) (0.160) (0.010) (0.247) (0.005) (0.094) (0.005) (0.129)

Own Education 0.256*** 0.178*** 0.255*** 0.185*** 0.110*** 0.054** 0.109*** 0.067**(0.010) (0.041) (0.010) (0.048) (0.007) (0.026) (0.006) (0.028)

Observations 10,270 10,270 10,270 10,263 10,270 10,270 10,270 10,263Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 427 420 28 28 427 420LM stat for underid. 9.793 9.275 9.793 9.275p-val of LM stat 0.00747 0.00968 0.00747 0.00968F stat for weak-id. 10.66 7.103 10.66 7.103Anderson-Rubin F stat 4.667 2.164 6.465 3.884p-val of AR F stat 0.0182 0.134 0.00508 0.0329p-val of Hansen J stat 0.387 0.487 0.383 0.258

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

63

Table A2: Level Effects of Children’s Education on Wave 2 Subjective Health Measuresof Parents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV OLS IV OLS IV OLS IV

VARIABLES Wave 2 Self Reported Health Wave 2 Low Subjective Survival Expectation

Education of Children -0.018*** -0.046 -0.015*** -0.055 -0.014*** -0.097*** -0.012*** -0.102**(0.003) (0.057) (0.003) (0.065) (0.002) (0.032) (0.002) (0.050)

Own Education -0.007*** 0.000 -0.007*** 0.001 -0.008*** 0.012 -0.007*** 0.010(0.002) (0.014) (0.002) (0.013) (0.002) (0.008) (0.001) (0.010)

Observations 10,174 10,174 10,174 10,167 7,925 7,925 7,925 7,914Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 427 420 28 28 427 416LM stat for underid. 9.035 8.114 9.513 6.710p-val of LM stat 0.0109 0.0173 0.00859 0.0349F stat for weak-id. 9.907 6.369 11.15 5.100Anderson-Rubin F stat 0.753 0.682 4.506 2.492p-val of AR F stat 0.481 0.514 0.0205 0.102p-val of Hansen J stat 0.456 0.469 0.668 0.831

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

64

Table A3: Level Effects of Children’s Education on Wave 2 Physical Health of Par-ents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV OLS IV OLS IV OLS IV

VARIABLES Wave 2 Lung Functation (Peak Flow) Wave 2 Grip Strength

Education of Children 1.888*** 20.326 1.692*** 19.416 0.179*** 1.031 0.175*** 0.696(0.368) (12.509) (0.330) (15.647) (0.031) (0.761) (0.019) (1.207)

Own Education 1.835*** -2.731 1.654*** -1.862 0.114*** -0.096 0.095*** -0.009(0.364) (3.184) (0.377) (3.089) (0.025) (0.186) (0.021) (0.232)

Observations 7,696 7,695 7,696 7,685 8,035 8,035 8,035 8,026Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 27 414 403 28 28 418 409LM stat for underid. 4.966 3.111 4.827 2.253p-val of LM stat 0.0835 0.211 0.0895 0.324F stat for weak-id. 4.314 2.075 3.954 1.313Anderson-Rubin F stat 5.492 2.785 1.731 0.412p-val of AR F stat 0.0102 0.0802 0.196 0.667p-val of Hansen J stat 0.199 0.425 0.497 0.580

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

65

Table A4: Level Effects of Children’s Education on Wave 2 Body Weight of Parents

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)OLS IV OLS IV OLS IV OLS IV OLS IV OLS IV

VARIABLES Wave 2 BMI Wave 2 Underweight Wave 2 Overweight

Education of Children 0.082*** 0.559** 0.064*** 0.399 -0.003*** -0.045 -0.003*** -0.038 0.007*** 0.042 0.005*** 0.025(0.014) (0.219) (0.012) (0.362) (0.001) (0.039) (0.001) (0.051) (0.002) (0.035) (0.002) (0.055)

Own Education 0.014 -0.104** -0.001 -0.067 -0.001 0.009 -0.001 0.006 0.003 -0.006 0.001 -0.003(0.013) (0.051) (0.012) (0.071) (0.001) (0.010) (0.001) (0.010) (0.002) (0.009) (0.002) (0.011)

Observations 8,093 8,093 8,093 8,085 8,093 8,093 8,093 8,085 8,093 8,093 8,093 8,085Child Birth Year FE YES YES YES YES YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YES NO NO YES YESNumber of groups 28 28 418 410 28 28 418 410 28 28 418 410LM stat for underid. 4.753 2.564 4.753 2.564 4.753 2.564p-val of LM stat 0.0929 0.277 0.0929 0.277 0.0929 0.277F stat for weak-id. 4.161 1.680 4.161 1.680 4.161 1.680Anderson-Rubin F stat 3.806 1.632 1.674 0.702 0.973 0.772p-val of AR F stat 0.0350 0.214 0.206 0.505 0.391 0.472p-val of Hansen J stat 0.297 0.142 0.509 0.474 0.274 0.259

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

66

Table A5: Level Effects of Children’s Education onWave 2 Mental Health of Parents

(1) (2) (3) (4)OLS IV OLS IV

VARIABLES Wave 2 CESD 10 Score

Education of Children -0.166*** -0.285 -0.142*** -0.257(0.027) (0.596) (0.024) (0.708)

Own Education -0.091*** -0.063 -0.078*** -0.055(0.018) (0.149) (0.015) (0.146)

Observations 9,130 9,130 9,130 9,123Child Birth Year FE YES YES YES YESProv Birth Year Trend YES YES YES YESProvince FE YES YES NO NOCommunity FE NO NO YES YESNumber of groups 28 28 427 420LM stat for underid. 7.746 7.195p-val of LM stat 0.0208 0.0274F stat for weak-id. 5.945 4.205Anderson-Rubin F stat 0.814 0.117p-val of AR F stat 0.454 0.890p-val of Hansen J stat 0.272 0.692

Standard errors clustered at province level in parentheses.*** p < 0.01, ** p < 0.05, * p < 0.1.

67

Table A6: Level Effects of Children’s Education on Baseline Health Behaviors of Par-ents: Frequency

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV OLS IV OLS IV OLS IV

VARIABLES # of cigarettes per day (men) # drinks per week

Education of Children -0.226*** 0.871 -0.219*** 1.234 -0.012 0.201 0.004 0.370(0.069) (1.354) (0.075) (2.110) (0.011) (0.210) (0.015) (0.340)

Own Education -0.106* -0.387 -0.099* -0.438 -0.025** -0.075 -0.017* -0.087(0.054) (0.363) (0.054) (0.508) (0.010) (0.048) (0.010) (0.063)

Observations 4,300 4,300 4,300 4,279 9,422 9,422 9,422 9,410Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 420 399 28 28 429 417Mean of Dependent Variable 9.862 9.862 9.862 9.862 1.601 1.601 1.601 1.601LM stat for underid. 9.145 8.004 10.36 9.878p-val of LM stat 0.0103 0.0183 0.00564 0.00716F stat for weak-id. 13.31 7.252 10.41 8.155Anderson-Rubin F stat 0.243 0.192 1.207 1.113p-val of AR F stat 0.786 0.826 0.315 0.343p-val of Hansen J stat 0.771 0.917 0.427 0.650

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

68

Table A7: Level Effects of Children’s Education on Transfer of Time: One IV

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)OLS IV 1 IV 1+2 OLS IV 1 IV 1+2 OLS IV 1 IV 1+2 OLS IV 1 IV 1+2

VARIABLES Frequency of Visits of Children: # d/w Frequency of Contact with Children not in person: # d/w

Education of Children -0.039*** -0.197 0.043 -0.045*** -0.384 -0.124 0.040*** 0.580* 0.204 0.020* 0.578** 0.249(0.013) (0.398) (0.268) (0.013) (0.514) (0.327) (0.012) (0.307) (0.233) (0.010) (0.292) (0.250)

Own Education -0.004 0.040 -0.027 -0.004 0.078 0.015 0.043*** -0.109 -0.003 0.041*** -0.096 -0.015(0.010) (0.112) (0.077) (0.010) (0.122) (0.079) (0.012) (0.090) (0.065) (0.014) (0.077) (0.063)

Observations 6,547 6,547 6,547 6,547 6,533 6,533 5,210 5,210 5,210 5,210 5,193 5,193Child Birth Year FE YES YES YES YES YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YES YES YES YES YESProvince FE YES YES YES NO NO NO YES YES YES NO NO NOCommunity FE NO NO NO YES YES YES NO NO NO YES YES YESNumber of groups 28 28 28 429 415 415 28 28 28 423 406 406LM stat for underid. 3.126 6.760 2.237 7.578 3.672 8.471 2.800 6.640p-val of LM stat 0.0771 0.0341 0.135 0.0226 0.0553 0.0145 0.0942 0.0361F stat for weak-id. 7.458 8.498 3.732 6.878 7.100 10.06 4.630 7.235Anderson-Rubin F stat 0.243 1.695 0.637 0.591 8.781 5.541 9.943 5.194p-val of AR F stat 0.626 0.203 0.432 0.561 0.00629 0.00963 0.00393 0.0123p-val of Hansen J stat 0.203 0.291 0.0323 0.128

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

69

Table A8: Level Effects of Children’s Education onLabor Supply: Rural Sample

(1) (2) (3) (4)OLS IV 1+2 OLS IV 1+2

VARIABLES Whether work now (rural)

Education of Children -0.006*** -0.181** -0.003** -0.348(0.001) (0.085) (0.001) (0.225)

Own Education -0.005*** 0.040* -0.003** 0.075(0.002) (0.022) (0.001) (0.052)

Observations 5,053 5,053 5,053 5,037Child Birth Year FE YES YES YES YESProv Birth Year Trend YES YES YES YESProvince FE YES YES NO NOCounty FE NO NO NO NOCommunity FE NO NO YES YESNumber of groups 28 28 423 407LM stat for underid. 4.639 3.309p-val of LM stat 0.0983 0.191F stat for weak-id. 4.624 2.009Anderson-Rubin F stat 7.677 8.696p-val of AR F stat 0.00229 0.00122p-val of Hansen J stat 0.138 0.473

Standard errors clustered at province level in parentheses.*** p < 0.01, ** p < 0.05, * p < 0.1.

70

Table A9: Robustness with Alternative Instruments: Level Effects of Children’s Educa-tion on Baseline Cognition of Parents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV 1+2 OLS IV 1+2 OLS IV 1+2 OLS IV 1+2

VARIABLES Baseline Mental Intactness Baseline Episodic Memory

Education of Children 0.107*** 0.288*** 0.102*** 0.328*** 0.045*** 0.202*** 0.038*** 0.214***(0.006) (0.105) (0.007) (0.119) (0.006) (0.070) (0.005) (0.074)

Own Education 0.246*** 0.203*** 0.244*** 0.201*** 0.099*** 0.063*** 0.093*** 0.059***(0.008) (0.026) (0.009) (0.024) (0.007) (0.017) (0.006) (0.015)

Observations 10,776 10,776 10,776 10,769 9,988 9,988 9,988 9,979Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 429 422 28 28 429 420LM stat for underid. 55.94 42.46 53.69 44.20p-val of LM stat 2.97e-05 0.00241 6.43e-05 0.00142F stat for weak-id. 2.864 2.146 2.714 2.235Anderson-Rubin F stat 2.167 2.033 1.551 1.963p-val of AR F stat 0.00188 0.00418 0.0551 0.00628p-val of Hansen J stat 0.0214 0.0457 0.354 0.112

Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

71

Table A10: Robustness with Alternative Instruments: Level Effects of Children’s Educa-tion on Baseline Subjective Health Measures of Parents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV 1+2 OLS IV 1+2 OLS IV 1+2 OLS IV 1+2

VARIABLES Baseline Self Reported Health Baseline Low Subjective Survival Expectation

Education of Children -0.018*** -0.010 -0.017*** -0.037 -0.009*** -0.040** -0.008*** -0.048**(0.003) (0.033) (0.003) (0.039) (0.001) (0.019) (0.001) (0.021)

Own Education -0.011*** -0.013 -0.011*** -0.007 -0.008*** -0.001 -0.007*** 0.001(0.003) (0.008) (0.003) (0.008) (0.001) (0.005) (0.001) (0.004)

Observations 10,808 10,808 10,808 10,801 9,373 9,373 9,373 9,367Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 429 422 28 28 426 420LM stat for underid. 57.21 44.17 50.63 43.37p-val of LM stat 1.91e-05 0.00143 0.000180 0.00182F stat for weak-id. 2.930 2.234 2.602 2.200Anderson-Rubin F stat 0.804 0.788 2.288 1.646p-val of AR F stat 0.712 0.731 0.000888 0.0347p-val of Hansen J stat 0.665 0.755 0.0102 0.223

Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

72

Table A11: Robustness with Alternative Instruments: Level Effects of Children’s Educa-tion on Baseline Physical Health of Parents

(1) (2) (3) (4) (5) (6) (7) (8)OLS IV 1+2 OLS IV 1+2 OLS IV 1+2 OLS IV 1+2

VARIABLES Baseline Peak Flow Baseline Grip Strength

Education of Children 1.433*** 13.277*** 1.163*** 13.699*** 0.107*** 0.288*** 0.102*** 0.328***(0.308) (3.990) (0.246) (4.270) (0.006) (0.105) (0.007) (0.119)

Own Education 2.329*** -0.469 1.808*** -0.635 0.246*** 0.203*** 0.244*** 0.201***(0.371) (0.977) (0.264) (0.870) (0.008) (0.026) (0.009) (0.024)

Observations 10,290 10,290 10,290 10,283 10,776 10,776 10,776 10,769Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YESNumber of groups 28 28 426 419 28 28 429 422LM stat for underid. 56.55 43 55.94 42.46p-val of LM stat 2.40e-05 0.00204 2.97e-05 0.00241F stat for weak-id. 2.891 2.165 2.864 2.146Anderson-Rubin F stat 1.706 1.567 2.167 2.033p-val of AR F stat 0.0255 0.0512 0.00188 0.00418p-val of Hansen J stat 0.383 0.628 0.0214 0.0457

Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

73

Table A12: Robustness with Alternative Instruments: Level Effects of Children’s Education on Baseline Body Weight ofParents

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)OLS IV OLS IV OLS IV OLS IV OLS IV OLS IV

VARIABLES Baseline BMI Baseline Underweight Baseline Overweight

Education of Children 0.076*** 0.354** 0.064*** 0.287* -0.004*** -0.014 -0.003*** -0.005 0.006*** 0.026 0.005*** 0.027(0.014) (0.153) (0.010) (0.172) (0.001) (0.011) (0.001) (0.012) (0.002) (0.017) (0.002) (0.020)

Own Education 0.023** -0.043 0.004 -0.039 -0.001 0.002 -0.000 -0.000 0.002 -0.003 0.000 -0.004(0.011) (0.038) (0.012) (0.035) (0.001) (0.003) (0.001) (0.002) (0.002) (0.004) (0.002) (0.004)

Observations 10,769 10,769 10,769 10,763 10,769 10,769 10,769 10,763 10,769 10,769 10,769 10,763Child Birth Year FE YES YES YES YES YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YES YES YES YES YESProvince FE YES YES NO NO YES YES NO NO YES YES NO NOCommunity FE NO NO YES YES NO NO YES YES NO NO YES YESNumber of groups 28 28 428 422 28 28 428 422 28 28 428 422LM stat for underid. 56.54 42.13 56.54 42.13 56.54 42.13p-val of LM stat 2.41e-05 0.00266 2.41e-05 0.00266 2.41e-05 0.00266F stat for weak-id. 2.894 2.129 2.894 2.129 2.894 2.129Anderson-Rubin F stat 1.241 1.195 1.919 1.815 1.092 1.057p-val of AR F stat 0.209 0.247 0.00804 0.0143 0.350 0.390p-val of Hansen J stat 0.369 0.295 0.0110 0.0118 0.458 0.462

Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

74

Table A13: Robustness with Alternative Instruments:Level Effects of Children’s Education on BaselineMental Health (CESD 10) of Parents

(1) (2) (3) (4)OLS IV OLS IV

VARIABLES Baseline CESD 10 Score

Education of Children -0.155*** 0.129 -0.142*** -0.040(0.028) (0.254) (0.021) (0.281)

Own Education -0.134*** -0.201*** -0.130*** -0.150***(0.015) (0.062) (0.015) (0.056)

Observations 10,220 10,220 10,220 10,216Child Birth Year FE YES YES YES YESProv Birth Year Trend YES YES YES YESProvince FE YES YES NO NOCommunity FE NO NO YES YESNumber of groups 28 28 426 422LM stat for underid. 50.79 39.24p-val of LM stat 0.000171 0.00622F stat for weak-id. 2.605 1.992Anderson-Rubin F stat 1.877 1.421p-val of AR F stat 0.0102 0.100p-val of Hansen J stat 0.0114 0.0835

Robust standard errors in parentheses. *** p < 0.01, ** p <0.05, * p < 0.1.

75

Table A14: Robustness to Control of OCP: Level Effects of Children’s Education on Baseline Health and Cognition ofParents

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)IV

VARIABLES Baseline Mental Intactness Baseline Episodic Memory Baseline Peak Flow Baseline Grip Strength Baseline Low Expected Survival

Education of Children 0.436** 0.488** 0.239** 0.195* 20.817*** 24.242*** 0.483 0.731 -0.093* -0.089**(0.184) (0.232) (0.098) (0.102) (7.594) (9.386) (0.440) (0.544) (0.049) (0.046)

Own Education 0.168*** 0.170*** 0.054** 0.063*** -2.250 -2.688 0.057 0.007 0.012 0.009(0.041) (0.043) (0.023) (0.020) (1.935) (1.854) (0.101) (0.103) (0.012) (0.010)

Observations 10,776 10,769 9,988 9,979 10,290 10,283 10,610 10,603 9,373 9,367Child Birth Year FE YES YES YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YES YES YESProvince FE YES NO YES NO YES NO YES NO YES NOCommunity FE NO YES NO YES NO YES NO YES NO YESNumber of groups 28 422 28 420 28 419 28 420 28 420LM stat for underid. 9.643 9.357 11.21 10.20 10.08 9.545 9.255 8.138 8.386 8.545p-val of LM stat 0.00806 0.00929 0.00368 0.00611 0.00647 0.00846 0.00978 0.0171 0.0151 0.0139F stat for weak-id. 8.015 5.967 10.86 7.140 9.390 6.562 7.344 5.066 7.390 6.259Anderson-Rubin F stat 3.901 3.272 6.068 3.549 7.527 6.075 1.455 1.436 2.470 3.318p-val of AR F stat 0.0325 0.0534 0.00666 0.0428 0.00252 0.00663 0.251 0.255 0.103 0.0515p-val of Hansen J stat 0.460 0.507 0.189 0.0640 0.288 0.539 0.506 0.995 0.772 0.816

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

76

Table A15: Robustness to Control of OCP: Level Effects of Children’s Education onBaseline Body Weight and Depressive Symptoms of Parents

(1) (2) (3) (4) (5) (6) (7) (8)IV

VARIABLES Baseline BMI Baseline Underweight Baseline Overweight Baseline CESD

Education of Children 0.877*** 0.924** -0.070** -0.067** 0.064*** 0.069** -0.254 -0.475(0.313) (0.377) (0.031) (0.032) (0.024) (0.031) (0.377) (0.516)

Own Education -0.168** -0.163** 0.015* 0.012* -0.012** -0.012* -0.111 -0.067(0.073) (0.072) (0.008) (0.007) (0.006) (0.006) (0.091) (0.101)

Observations 10,769 10,763 10,769 10,763 10,769 10,763 10,220 10,216Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES NO YES NO YES NO YES NOCommunity FE NO YES NO YES NO YES NO YESNumber of groups 28 422 28 422 28 422 28 422LM stat for underid. 9.620 9.190 9.620 9.190 9.620 9.190 8.884 8.523p-val of LM stat 0.00815 0.0101 0.00815 0.0101 0.00815 0.0101 0.0118 0.0141F stat for weak-id. 8.394 6.294 8.394 6.294 8.394 6.294 6.662 5.127Anderson-Rubin F stat 5.675 3.054 6.544 4.420 2.978 1.863 0.376 1.180p-val of AR F stat 0.00876 0.0637 0.00482 0.0218 0.0678 0.175 0.690 0.323p-val of Hansen J stat 0.934 0.522 0.527 0.358 0.707 0.965 0.523 0.193

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

77

Table A16: Instrumenting Own Education: Level Effects of Children’s Education on Baseline Health and Cognitionof Parents

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)IV+Lewbel

VARIABLES Baseline Mental Intactness Baseline Episodic Memory Baseline Peak Flow Low Expected Survival Baseline Grip Strength

Education of Children 0.252*** 0.163*** 0.457*** 0.378** 17.929** 16.923** -0.068* -0.065** 0.179 0.878*(0.081) (0.062) (0.146) (0.161) (7.867) (7.604) (0.036) (0.030) (0.445) (0.456)

Own Education 0.130*** 0.123*** 0.180*** 0.147*** 3.485* 2.384 -0.001 0.002 -0.087 -0.055(0.035) (0.031) (0.044) (0.041) (1.883) (1.754) (0.009) (0.008) (0.156) (0.134)

Observations 9,988 9,979 10,776 10,769 10,290 10,283 9,373 9,367 10,610 10,603Child Birth Year FE YES YES YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YES YES YESProvince FE YES NO YES NO YES NO YES NO YES NOCommunity FE NO YES NO YES NO YES NO YES NO YESLM stat for underid. 14.16 14.23 13.50 14.12 13.40 12.74 12.35 12.89 13.79 14.77p-val of LM stat 0.0778 0.0761 0.0959 0.0786 0.0990 0.121 0.136 0.116 0.0875 0.0639F stat for weak-id. 4.560 5.413 4.337 5.656 3.754 4.119 3.651 4.889 5.445 7.953Anderson-Rubin F stat 2.569 5.149 1.657 2.069 4.191 3.310 2.084 2.635 1.163 4.645p-val of AR F stat 0.0279 0.000425 0.149 0.0698 0.00179 0.00758 0.0679 0.0248 0.357 0.000891p-val of Hansen J stat 0.323 0.165 0.696 0.546 0.471 0.389 0.359 0.388 0.583 0.429Breusch Pagan test p-val 2.13e-22 1.11e-25 4.96e-30 3.51e-33 1.54e-25 1.43000e-30 2.60e-20 5.26e-21 1.42e-28 2.68e-31

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

78

Table A17: Instrumenting Own Education: Level Effects of Children’s Education on Baseline Body Weightand Depressive Symptoms of Parents

(1) (2) (3) (4) (5) (6) (7) (8)IV+Lewbel

VARIABLES Baseline BMI Baseline Underweight Baseline Overweight Baseline CESD 10 Score

Education of Children 0.679** 0.523* -0.057*** -0.037** 0.046* 0.036 -0.474 -0.700**(0.278) (0.285) (0.021) (0.016) (0.025) (0.028) (0.304) (0.298)

Own Education 0.004 -0.046 -0.003 0.002 -0.001 -0.004 -0.224* -0.201*(0.093) (0.080) (0.007) (0.005) (0.007) (0.007) (0.127) (0.109)

Observations 10,769 10,763 10,769 10,763 10,769 10,763 10,220 10,216Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES NO YES NO YES NO YES NOCommunity FE NO YES NO YES NO YES NO YESLM stat for underid. 13.57 13.82 13.57 13.82 13.57 13.82 13.88 15p-val of LM stat 0.0936 0.0865 0.0936 0.0865 0.0936 0.0865 0.0850 0.0591F stat for weak-id. 4.543 5.809 4.543 5.809 4.543 5.809 3.270 5.247Anderson-Rubin F stat 2.142 1.766 4.426 3.280 1.250 1.801 1.478 1.429p-val of AR F stat 0.0610 0.122 0.00124 0.00798 0.308 0.114 0.206 0.225p-val of Hansen J stat 0.801 0.461 0.375 0.306 0.644 0.541 0.510 0.562Breusch Pagan test p-val 7.41000e-30 8.10000e-33 7.41000e-30 8.10000e-33 7.41000e-30 8.10000e-33 3.58000e-24 2.09000e-26

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

79

Table A18: Own Education as Exogenous: Incremental Effects of Children’s Education on Wave 2 Health and Cognitionof Parents

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)IV+Lewbel

VARIABLES Wave 2 Mental Intactness Wave 2 Episodic Memory Wave 2 Peak Flow Wave 2 Grip Strength Wave 2 Low Expected Survival

Baseline 0.579*** 0.593*** 0.478*** 0.383*** 0.508*** 0.505*** 0.469*** 0.503*** 0.004 -0.033(0.072) (0.080) (0.118) (0.107) (0.038) (0.039) (0.068) (0.076) (0.253) (0.245)

Education of Children 0.268** 0.269 0.125** 0.129** -5.625 -2.952 0.279 -0.025 -0.042 -0.023(0.130) (0.181) (0.061) (0.060) (4.176) (4.713) (0.691) (0.916) (0.055) (0.056)

Own Education 0.065** 0.070** 0.023 0.037* 2.295** 1.535* 0.016 0.068 -0.002 -0.006(0.031) (0.028) (0.021) (0.021) (1.069) (0.873) (0.157) (0.170) (0.011) (0.009)

Observations 10,239 10,232 9,507 9,499 7,382 7,371 7,892 7,883 7,071 7,062Child Birth Year FE YES YES YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YES YES YESProvince FE YES NO YES NO YES NO YES NO YES NOCommunity FE NO YES NO YES NO YES NO YES NO YESNumber of groups 28 420 28 418 27 399 28 407 28 415Mean of Dependent Variable 7.052 7.052 3.340 3.340 268 268 29.74 29.74 0.331 0.331LM stat for underid. 13.32 12.06 13.32 23.51 15.54 16.34 10.12 11.18 13.33 9.896p-val of LM stat 0.207 0.281 0.206 0.172 0.114 0.0903 0.430 0.343 0.206 0.450F stat for weak-id. 3.790 2.573 2.847 16.60 12.85 12.31 1.585 1.739 3.885 1.944Anderson-Rubin F stat 8.802 7.758 3.256 7.247 25.11 26.40 7.521 6.982 4.118 3.598p-val of AR F stat 2.25e-06 7.44e-06 0.00606 2.17e-06 0 0 9.91e-06 1.94e-05 0.00132 0.00325p-val of Hansen J stat 0.625 0.820 0.630 0.673 0.281 0.0735 0.461 0.871 0.121 0.152

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

80

Table A19: Own Education as Exogenous: Incremental Effects of Children’s Education onWave 2 Body Weight and Depressive Symptoms of Parents

(1) (2) (3) (4) (5) (6) (7) (8)Lewbel+IV

VARIABLES Wave 2 BMI Wave 2 Underweight Wave 2 Overweight Wave 2 CESD

Baseline 0.359*** 0.372*** 0.740*** 0.742*** 0.719*** 0.711*** 0.527*** 0.555***(0.077) (0.080) (0.047) (0.047) (0.040) (0.036) (0.070) (0.081)

Education of Children -0.355 -0.562 -0.004 -0.003 0.029** 0.020 -0.280 -0.195(0.341) (0.462) (0.028) (0.040) (0.015) (0.025) (0.303) (0.356)

Own Education 0.108 0.116 0.001 0.000 -0.005 -0.003 0.032 0.027(0.088) (0.093) (0.007) (0.008) (0.004) (0.005) (0.077) (0.074)

Observations 8,057 8,050 8,057 8,050 8,057 8,050 8,705 8,700Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES NO YES NO YES NO YES NOCommunity FE NO YES NO YES NO YES NO YESNumber of groups 28 410 28 410 28 410 28 420Mean of Dependent Variable 23.77 23.77 0.0604 0.0604 0.347 0.347 7.829 7.829LM stat for underid. 12.71 9.665 10.81 12.10 12.75 7.151 12.80 15.15p-val of LM stat 0.240 0.470 0.373 0.279 0.238 0.711 0.235 0.127F stat for weak-id. 2.739 1.320 2.049 2.970 4.353 0.827 2.918 4.231Anderson-Rubin F stat 4.918 5.431 45.25 34.27 7.687 9.613 20 9.986p-val of AR F stat 0.000358 0.000164 0 0 8.10e-06 9.49e-07 3.44e-10 6.49e-07p-val of Hansen J stat 0.299 0.393 0.412 0.489 0.125 0.207 0.635 0.713

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

81

Table A20: Robustness to Adjustment for Multiple Hypotheses Testing

Province FE Community FEBaseline Outcome P Value Corrected Critical P Value Overall Sig at 5%* P Value Corrected Critical P Value Overall Sig at 5%*

Mental Intactness 0.00572 0.015 1 0.0153 0.015 1Episodic Memory 0.00638 0.02 1 0.0273 0.025 1Self Reported Health 0.291 0.045 0 0.251 0.045 0Low Expected Survival 0.0388 0.035 0 0.0281 0.03 1Peak Flow 0.00808 0.025 1 0.0085 0.005 1Grip Strength 0.263 0.04 0 0.174 0.04 0CESD 10 Index 0.446 0.05 0 0.32 0.05 0BMI 0.00208 0.005 1 0.0108 0.01 1Underweight 0.0175 0.03 1 0.0322 0.035 1Overweight 0.004 0.01 1 0.0272 0.02 1

*Uncorrected overall significance level. Corrected critical p-values are based on adjustment method in Simes (1986).

82

Table A21: Robustness with Lewbel IV for Children’s Education: Level Effects of Children’s Edu-cation on Baseline Cognition and Health of Parents

(1) (2) (3) (4) (5) (6) (7) (8)IV+Lewbel

VARIABLES Baseline Mental Intactness Baseline Episodic Memory Baseline Peak Flow Baseline Low Subj. Survival

Education of Children 0.438*** 0.412*** 0.200*** 0.093 11.751*** 11.060** -0.032 -0.032(0.114) (0.120) (0.075) (0.065) (3.736) (4.756) (0.025) (0.024)

Own Education 0.167*** 0.184*** 0.063*** 0.082*** -0.109 -0.120 -0.003 -0.002(0.028) (0.025) (0.019) (0.014) (1.111) (0.968) (0.006) (0.005)

Observations 10,776 10,769 9,988 9,979 10,290 10,283 9,373 9,367Child Birth Year FE YES YES YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YES YES YESProvince FE YES NO YES NO YES NO YES NOCommunity FE NO YES NO YES NO YES NO YESLM stat for underid. 12.75 14.16 13.16 14.49 13.24 13.79 13.46 14.56p-val of LM stat 0.238 0.166 0.215 0.152 0.211 0.183 0.199 0.149F stat for weak-id. 5.438 3.856 5.481 4.471 5.043 3.865 12.45 7.360Anderson-Rubin F stat 7.031 7.111 6.451 3.686 3.377 4.897 1.288 1.296p-val of AR F stat 2.50e-05 2.26e-05 5.24e-05 0.00332 0.00568 0.000470 0.286 0.282p-val of Hansen J stat 0.741 0.805 0.154 0.235 0.730 0.475 0.715 0.792Breusch Pagan test p-val 3.88e-35 1.58e-72 1.66e-28 1.50e-61 2.79e-36 1.95e-76 2.24e-26 7.36e-51

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

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Table A22: Robustness with Lewbel IV for Children’s Education: LevelEffects of Children’s Education on Baseline Body Weight of Parents

(1) (2) (3) (4) (5) (6)IV+Lewbel

VARIABLES Baseline BMI Baseline Underweight Baseline Overweight

Education of Children 0.752*** 0.771*** -0.041*** -0.034** 0.057*** 0.064***(0.191) (0.211) (0.016) (0.015) (0.017) (0.021)

Own Education -0.138*** -0.133*** 0.008** 0.005* -0.011** -0.011**(0.049) (0.046) (0.004) (0.003) (0.004) (0.004)

Observations 10,769 10,763 10,769 10,763 10,769 10,763Child Birth Year FE YES YES YES YES YES YESProv Birth Year Trend YES YES YES YES YES YESProvince FE YES NO YES NO YES NOCommunity FE NO YES NO YES NO YESLM stat for underid. 12.37 13.60 12.37 13.60 12.37 13.60p-val of LM stat 0.261 0.192 0.261 0.192 0.261 0.192F stat for weak-id. 4.952 3.695 4.952 3.695 4.952 3.695Anderson-Rubin F stat 4.788 5.901 1.832 1.434 3.368 2.861p-val of AR F stat 0.000555 0.000110 0.103 0.219 0.00577 0.0144p-val of Hansen J stat 0.997 0.993 0.550 0.539 0.899 0.750Breusch Pagan test p-val 1.25e-35 4.56e-72 1.25e-35 4.56e-72 1.25e-35 4.56e-72

Standard errors clustered at province level in parentheses. *** p < 0.01, ** p < 0.05,* p < 0.1.

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Appendix B

Lewbel’s IV Approach Based on Heteroskedasticity

Lewbel (2012) introduces an instrumental variable estimation method for linear regression modelswith endogenous independent variables when there are no plausible external instruments availableor when traditional instruments are not sufficient. For a traditional IV estimation, the instrumentsmust satisfy three conditions at the same time: (1) being exogenous or orthogonal to the errorterm of the model, (2) being sufficiently correlated with the endogenous variables, and (3) beingexcludeable from the model such that it does not directly relate to outcome of interest. Whencondition (3) is violated, traditional IV estimation method is not valid and the model remains u-nidentified. Lewbel (2012) hence proposes to generate instruments that satisfy the three conditionsby having heteroskedasticity in errors and regressors orthogonal to the product of heteroskedasticerrors in structural models to achieve identification.

Generally, in a structural model without excludeable instruments as:

Y1 = X ′β1 + Y2γ1 + e1,

Y2 = X ′β2 + Y1γ2 + e2.

Lewbel (2012) shows that, under (1) heteroskedasicity, i.e., E(X, e2j) 6= 0, j = 1, 2, as well as(2) Cov(Z, e1e2) = 0, where Z is a subset of X , and (3) E(X, ej) = 0, j = 1, 2, the structuralparameters are identified. Instead of the exclusion restriction, heteroskedasicity in (1) that is afeature of many models and higher moment conditions in (2) are required. Lewbel (2012) notes thatthe assumptions can be approximately validated by a Breusch-Pagan type test of heteroskedasticity(scale-related) for (1) and Sargan-Hansen test of overidentification for (2).

In context of estimating a dynamic health production model with an endogenous lagged de-pendent variable as in Brown (2014), it is difficult to find any excludeable instruments that onlyindirectly relate to current health through past health without having to make very strong assump-tions. In light of this, Lewbel’s IV approach can help correct for the endogeneity bias arising fromlagged dependent variable with less restrictive assumptions that are standard in many econometricmodels according to Lewbel (2012). Therefore, Lewbel’s IV approach is applied to the dynamicmodel to supplement traditional IV estimation. Specifically, I have a triangular system:

H1 = X ′β1 + e1,

H2 = X ′β2 +H1γ2 + e2.

To empirically implement Lewbel’s IV estimation method, auxiliary regressions of the baseline

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health outcomes with only exogenous independent variables are conducted to generate residuals,e1, which are then tested against homoskedasticity. Instruments are constructed by multiplyingZ, a subset of mean-centered exogenous variables, with the residuals, i.e., (Z − Z)e1. It impliesthat zero mean condition of traditional IV is fulfilled as E((Z − Z)e1) = 0 because covariance ofe1 with Z is zero by construction. Lewbel (2012) type IVs are only generated for lagged health,not for years of schooling of highest educated adult child such that the results on the effect ofchildren’s education from Lewbel IV approach is not driven by the use of generated instruments25.Z includes age categories and respondent’s gender which are exogenous and strongly correlatedwith both past and current health of parents which is implied by the first stage. I also include inZ the baseline height which is a measure of childhood health and shown to be strongly related tolater life health among Chinese elderly by Smith et al. (2012) and confirmed by the first stage. Thegenerated instruments for lagged health as well as the external instruments for children’s years ofschooling are used to estimate the dynamic models using IV/2SLS method when both are treatedendogenous. Breusch-Pagan tests on residuals from auxiliary regressions and Hansen J test ofoveridentification of external and generated instruments are reported.

25Lewbel’s IV approach results when children’s education is also instrumented by generated instruments are avail-able upon request.

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Model Parental Health as an AR(1) Process

Assume H0 is the health endowment of older adults. Children’s education affects parental healthin a fashion as below:

H1 = αH0 + β1ChildEdu+ e1

H2 = αH1 + β2ChildEdu+ e2

Ht = αHt−1 + βtChildEdu+ et

where the health status of parents follows an AR(1) process. It assumes that lagged 1 periodhealth is a sufficient statistics for impacts of all past health inputs (Strauss and Thomas, 2008).Children’s education has a direct and periodic impact on parental health in each period which iscaptured by βt. The periodic effect, βt , is the incremental effect to be estimated in the dynamicmodel.

Also by iteration,

Ht = αtH0 + (αt−1β1 + αt−2β2 + ...+ αβt)ChildEdu+ (αt−1e1 + αt−2e2 + ...+ et) (4)

or, we have

Ht = at + btChildEdu+ ut (5)

Therefore, at time t, estimating equation (5) gives the level (cumulative) effect of children’seducation, bt, which is a weighted average of the periodic/incremental effect of children’s educationin the current and all previous periods.

By taking first difference of equation (4),

Ht+1 −Ht = at+1 − at + (bt+1 − bt)ChildEdu+ ut+1 − ut (6)

For simplicity, assume βt = β. Therefore, estimation of the first difference equation actuallygives the change in the level effects of children’s education, which is αtβ , instead of the incremen-tal effect β. They will be the same if α equals 1. However, as what I have shown in the dynamicmodel results, the state dependence is relative low and not close to 1, which implies that estimat-ing a first difference equation will not provide what is the main effect of interest in this paper.The change in the level effect , αtβ, can be also interpreted as the persistent effect of children’s

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education since it measures how the initial incremental effect persists into future time t.

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Sample Selection

As mentioned in the main text, I conducted the analysis on a relative balanced panel of parentswho or whose household responded to both the baseline survey and its first follow-up. Whilethe restriction of sample is due to data limitations on child information in the baseline, it couldresult in biased estimates for the health effects of children’s education if such sample selection isnot random and correlated with parents’ health and/or their children’s education. Although thereis no clear evidence as to the association between children’s education and attrition, it is verypossible that healthier parents are better able to survive to the follow-up survey (positive selectionon health); or it is possible that healthier parents to be able to move and therefore attrite (negativeselection on health). If there is positive selection on health, and the effect of children’s educationis stronger on parents with worse health, the sample selection might lead to underestimation forthe causal effects of children’s education, or vice versa, overestimation if the effect of children’seducation is stronger on parents with better effect. In theory, the direction of biases due to sampleselection is unclear.

To test whether there is selection on baseline health, I run an OLS regression of whether theparent remained in wave 2 on their baseline health measures that are found to be significantlyaffected by children’s education in the baseline static model, including mental intactness, episodicmemory, peak flow, low expected survival and BMI, as well as the same set of control variables asin the IV estimation model. Tests of joint significance on these health measures in both provincefixed effects model (F(4,27) = 0.63, p value = 0.6429) and community fixed effects model (F(4,27)= 1.82, p value = 0.1547) show that they are not jointly significant. Therefore, there seems nosevere sample selection on baseline health when one includes multiple health measures. Theseresults lend more credibility to the main results of this paper.

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