Intergenerational co-residence and schooling

The Journal of the Economics of Ageing 4 (2014) 8–23

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Full Length Article

Intergenerational co-residence and schooling q Anjini Kochar Stanford Center for International Development, Stanford University, United States

a r t i c l e

i n f o

Article history: Available online 4 November 2014 Keywords: Schooling Old age security Inter-generational co-residence

a b s t r a c t This paper investigates how parents’ expectations of co-residence with their children affects schooling outcomes. Using an overlapping generations model, the effect is shown to be ambiguous; it depends on how schooling affects life cycle income profiles. The empirical analysis utilizes household data that reports young parents’ expectations regarding residence in old age and also provides measures of schooling achievement for their children. Identification comes from interactions of demographic shocks that differentially affect the probability of co-residence with specific children with measures that affect the profitability of the inter-generational contract with children relative to an autarchic option whereby parents live alone but can still enter into consumption smoothing contracts with members of their extended family network. Through regressions that also condition on the total number of children, the ratio of sons to total children and household savings. I find that the expectation of co-residence with a child reduces the child’s attendance in school and schooling achievement. Ó 2014 Elsevier B.V. All rights reserved.

Introduction ‘‘There is ...an interesting question of why the demand for the schooling of children exists, given that it destroys a family structure of which the older generation has always approved and a family economy that brought them benefits in proportion to the number of children they had (Caldwell 1980)." This paper examines how the expectation of future co-residence affects parental investments in their children’s schooling. In economies with weakly developed financial markets, such as India, many households lack access to the financial instruments that enable saving to smooth consumption over the life cycle. Instead, co-residence with a child is the primary method of ensuring consumption requirements in old age. How does this contract affect the schooling and hence the wealth of future generations? The effect is generally perceived to be positive. Researchers have argued that old-age support is just one side of a reciprocal exchange system, whereby parents invest in the schooling of their children in anticipation of support in old age (Lillard and Willis, 1997). If imperfectly developed financial markets also imply lack of access to the credit necessary to finance educational investments, the inter-generational family unit can q This paper uses survey data collected as part of a larger study on schooling in the state of Karnataka, India. Data collection was generously funded by the William and Flora Hewlett Foundation. The author alone is responsible for the findings of this paper.

http://dx.doi.org/10.1016/j.jeoa.2014.09.009 2212-828X/Ó 2014 Elsevier B.V. All rights reserved.

substitute for formal markets, enabling implicit loans for schooling from parents to their young children, that, when subsequently repaid, support the consumption requirements of elderly parents. Others, however, note that collective or social institutions may enhance poverty because default remains a significant concern, even in social contracts (Greif, 1997). This may be particularly true of implicit intra-family contracts across generations; formal legal institutions are generally reluctant to intervene in intra-familial conflicts. Reducing the probability of default requires actions to enhance the value of the contract, and these may come at the cost of wealth enhancing investments. I apply these insights to an analysis of the effect of intergenerational co-residence on schooling, building on a theoretical literature that examines loan contracts between overlapping generations when commitment is not possible (Lambertini, 1998 and Azariadis and Lambertini, 2003). Theoretical work that utilizes a two-period model with incomes rising between the two periods generally suggests an unambiguous effect of children’s schooling on support for the elderly. In contrast, utilizing a model in which adults live three periods, I show that the effect of children’s schooling on the terms of the implicit intergenerational contract, and hence the welfare of the elderly, is ambiguous. This is because the demand for, and supply of, credit depends not on wealth, but on the profile of income over the life cycle. If schooling makes income more ‘‘hump shaped’’, then the probability of adherence to the inter-generational loan contract increases with schooling, since it increases the demand for old-age support. However, if schooling also increases incomes in old age, the need for the family

A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

contract is reduced, thereby increasing the likelihood of default by the child in question. In such cases, parents have a strong incentive to identify the child they will reside with at any early age and invest strategically in his education so as to reduce the probability of default. An empirical analysis of the effect of expectations of coresidence on schooling investments is rendered difficult by the possibility of reverse causation: Residential choices may be made after observing a child’s academic ability, so that it is schooling that determines co-residence rather than the other way around. Parents may identify the son with the least interest in schooling as their preferred child for co-residence in old-age, since he may be most likely to remain in rural areas and continue with traditional family occupations. Residential choices may also reflect other unobserved traits of children, including parental affinity for the child that could similarly generate biased estimates. I address these issues by using social norms relating to residential arrangements and data on extended family networks to identify the effect of parents’ expectations of co-residence with a specific child on investments in his or her schooling. The choice of co-residence is made by comparing the value of this contract to the autarchic option. This latter option, even though it implies residing alone with one’s spouse, still provides access to consumption smoothing through contracts with members of the extended family network in the same village. I construct a measure of the value of this network for lifecycle consumption smoothing, based on the age difference between the father and his brothers, and interact this with variables that determine the probability that parents would contract with the child in question. This probability reflects social norms that dictate that parents reside with a son, with the choice amongst sons reflecting the total number of sons. Typically, the oldest son moves out of the family residence on marriage, leaving parents to reside with the youngest son. Since this possibility is only available to parents with more than one son, those with just one son generally reside with their oldest, while parents with more than one son are more likely to reside with a younger son. Thus, the probability of old-age residence varies across children in the household, with an increase in the number of sons reducing the probability of parents’ residing with the oldest son but increasing that of co-residence with younger sons. Since the number of sons may be endogenous, I develop instruments based on variables that predict this number. Building on a literature that notes that the gender of the first child determines the number of children (and sons), and incorporating the variation in the probability of co-residence across children in the household, I use as an instrument the triple interactions of an indicator variable for whether the child is the oldest or younger son, an indicator variable for the gender of the first child and the age-difference measure of the value of the extended family network. The strength of the identification strategy stems from this triple interaction that allows the effect of the age of the father’s brother to vary across households depending on their demographic structure and, additionally, to vary across children within a household. To ensure that identification comes only from this triple interaction, all regressions include indicator variables for the oldest and youngest son, the age difference, and the gender of the first child. I also condition on a rich array of other variables that may be likely to confound results, including the number of the father’s brothers and sisters, and the land holdings of grandparents on both sides of the family. There are two primary concerns with this strategy. First, since the gender of the first child predicts both the number of children and the ratio of sons to this total number, the instruments may be correlated with these demographic outcomes, despite the fact

9

that the gender of the first child is included as an independent regressor. In turn, fertility choices of parents, or the number of children in the household, will directly affect schooling investments through a quality-quantity trade-off. Second, I assume that expectations of old-age residence affect the rate of return to investments in children’s schooling or, equivalently, the rate of return on implicit intergenerational credit contracts that enable long-term consumption smoothing over the life cycle. However, the demographic characteristics and information on extended family networks used as instruments may also determine current income and access to short-term credit markets, and hence the availability of funds to finance current consumption requirements, including schooling. To address the first concern, I extend the research documenting the demographic consequences of the gender of the first child, noting that the gender of the first two births has different implications for the number of sons and the total number of children. While I defer a detailed discussion to the body of this paper, this implies that indicator variables for four household types, distinguished by the gender of the first two births (son–son, son–daughter, daughter–son, daughter–daughter), satisfy the rank conditions to identify both the total number of sons as well as the total number of children. Using these four indicator variables, I estimate regressions that condition not just on expectations of co-residence, but also on the total number of children and on the proportion of sons, treating both as endogenous. I address the second concern, that the instruments predict access to short term consumption smoothing mechanisms rather than those that enable life-cycle smoothing, by further conditioning regressions on household’s current savings. This regression recognizes that current savings reflect current income and current credit constraints. Household savings are treated as endogenous, and are instrumented by baseline values of financial assets. Controlling for current credit constraints and income mitigates the possibility that estimates of expectations of old-age residence with the child reflect current credit constraints, rather than the demand for life cycle consumption smoothing. The empirical analysis uses household data from rural Karnataka state, in South India. The data set, part of a larger study on the determinants of schooling in the region, provides information on expected residential arrangements in old age of young parents who are currently investing in their children’s schooling. This is invaluable for several reasons. First, the data provide the ‘‘correct’’ independent variable of interest: it is only expectations of future residential patterns that can affect schooling investments at the time that they are made. Second, the availability of data at the time when schooling investments are being made provides ‘‘correct’’ measures of other relevant variables. Studies based on data on the current elderly and their adult children generally lack information on savings and school quality at the time that current adults were in school. The drawback of using data on households at the time of investing in their children’s schooling is that I cannot examine the effect of expectations of co-residence on completed schooling. Instead, I measure household investments in a child’s schooling by the proportion of school days that the child attended school in the 2012– 13 school year. Attendance data are from school administrative records. This is important, since it removes the need to rely on parent-provided measures of their investment in their children, such as reported hours of work or expenditures on private tuitions. I also provide results that examine the effect of expectations of old-age residence with the child on test scores for both language and mathematics, using tests that were independently designed and implemented for the purpose of this survey. The analysis of this paper reveals that school attendance is lowered by parent’s expectation of co-residence with a child. The

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A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

evidence thus suggests a reduced commitment to the schooling of the child parents expect to reside with him when elderly. The results are robust to controls for total number of children, the ratio of sons to total children, and household savings. The remainder of this paper is structured as follows. I start by discussing the related literature. This is followed by a description of the theoretical framework and a discussion of its implications for the effect of schooling on the profitability of the inter-generational contract. I then describe the data and the setting, and follow this with a section that outlines the empirical framework and the identification strategy. "Results" discusses the findings of this paper and the last section concludes.

Related literature This paper is related to several literatures, most obviously to research on the economic relationship between parents and children, the determinants of parental investment in the schooling of children and old-age support for the elderly, and on family and social exchange. Becker’s (1981) seminal work on the economic determinants of fertility and investments in children, emphasizing the costs and returns to parents, generated a rich literature explaining these investments as a consequence of parental need for old-age support (Nugent, 1985; Cain, 1982, 1983). Focusing explicitly on schooling, researchers have examined whether parents would invest efficiently in their children’s schooling, particularly in economies where young parents lack access to credit (Baland and Robinson, 2000). In the absence of such markets, it has been recognized that the intergenerational family unit can serve as an implicit credit market (Kotlikoff and Spivak, 1981; Lillard and Willis, 1997; Cox, 1990; Raut, 1990), reducing borrowing constraints of younger generations and serving the savings needs of older ones. While much of the earlier literature neglected concerns about default, justifying this by assuming two-sided altruism, recent work acknowledges the probability of default and discusses how exchange amongst overlapping generations of agents can be sustained through social norms that take the form of trigger strategies, conditioning future access to the intergenerational contract to current adherence to its terms (Kandori, 1992; Lambertini, 1998; Azariadis and Lambertini, 2003). Rangel (2003), for example, shows that even in the absence of parental altruism, parents will invest in children’s schooling (forward intergenerational goods) if old-age support from children (backward intergenerational goods) is conditional on investment in children’s schooling. Within a similar framework, Anderberg and Balestrino (2003) explore the determinants of parental investments in children’s schooling, when parents can finance these investments either through a family contract or through borrowing from formal credit markets at an exogenously specified interest rate. They allow schooling to increase incomes in just one (adult) period, and compare the rate of return to schooling across the two contracts. Because the probability of default generates borrowing constraints within the family contract, they show that, in equilibrium, the rate of return to schooling in this contract exceeds that obtained when parents borrow from formal markets, suggesting that family contracts are characterized by lower levels of schooling. In contrast, by allowing schooling to affect incomes at different stages of the life cycle, I show that the return parents get from children’s schooling within the system of family exchange is ambiguous, and is determined by how schooling affects life cycle income profiles. The empirical literature on the topic has primarily focused on transfers from non-resident children to their parents, examining

whether they increase with children’s schooling, in regressions that also control for (adult) children’s incomes (Lillard and Willis, 1997; Raut and Tran, 2005).1 Raut and Tran (2005) also examine the reverse relationship, regressing completed schooling on transfers from non-resident (adult) children to their parents. These studies generally take children’s schooling (or transfers, when examining the effect of transfers on schooling) as exogenous, ignoring the possibility that schooling investments and expectations of old-age support are jointly determined. If schooling is determined keeping expectations of old-age support in mind, then unobservable determinants of levels of support will directly influence schooling, generating biased coefficients. A related empirical literature examines the determinants of family residential arrangements and structures (Edmonds, Mammen and Miller, 2004; Manacorda and Moretti, 2006; Foster, 1993; Edlund and Rahman, 2005) and considers the effect of coresidence on a variety of outcomes, such as the labor supply of the (adult) son and daughter-in-law the parents reside with (Sasaki, 2002). Much of this literature instruments inter-generational co-residence by the birth order of the adult son in question, utilizing the prevailing norm of residence with the oldest son that prevails in many cultures. However, as previously noted, birth order is known to be a significant determinant of an individual’s education and health, and hence is also likely to be correlated with unobserved individual ability and preferences. As such, a father’s birth order may directly influence outcomes for his children and his wife, invalidating its use as an instrument. A final contribution of this paper is to the literature on social networks. Many have argued that membership in social networks, including the family, provides a substitute for absent or imperfectly functioning credit and insurance markets, and that they may also enable more efficient exchange (Nugent, 1990; Ben Porath, 1980). In Asia, it is widely believed that social norms which sustain family exchange reduce the need for the development of annuities markets and others that enable life cycle consumption smoothing. While it is also recognized that participation in such networks may come at a cost, there are few studies that investigate what these costs are, or their magnitude. The analysis of this paper provides evidence on this issue. Theoretical framework The primary objective of this section is to sketch a theoretical framework of household decision making that illustrates the ambiguous effect of schooling on the terms of an inter-generational loan contract between parents and their children and the factors that determine this relationship. The model applies specifically to conditions in developing economies such as India, in that it assumes that parents determine children’s schooling and that households lack access to formal financial instruments that enable consumption smoothing over the life cycle. Cultural norms dictate that choices regarding the schooling of children in India are generally made by parents, perhaps because the average years of completed schooling in the economy is still very low, at only 5.1 years (2013). This implies that decisions regarding the cessation of schooling are generally made when children are still economically dependent on parents. Similarly, the very limited use of formal financial markets in this economy, particularly by rural households, and for long term life cycle consumption smoothing,

1 While such transfers play an important role in many economies, particularly the East Asian economies, they are less important in the Indian context, where support for the elderly primarily takes the form of co-residential arrangements with adult children.

A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

justifies the second assumption.2 The model also ignores other factors that may affect the profitability of the inter-generational contract, such as variation across households in life expectancies.3 I start by assuming a single-child household so as to focus on the determinants of contractual terms between parents and the child in question. I subsequently extend this analysis to the more realistic context of multiple children households, and discuss the choice of which child to contract with as well as the effect of alternative informal arrangements with other family members on the terms of the contract. Though the framework of this section ignores parents’ fertility choices, this obviously importantly affects schooling outcomes and is taken into account in the empirical analysis of this paper. Though households lack access to formal financial instruments that enable life cycle consumption smoothing, this is still possible through loan contracts amongst units of different overlapping generations. The starting point of this analysis is the assumption that commitment to the intergenerational contract is not possible; children do not always provide for their elderly parents. I draw heavily on Lambertini’s (1998) analysis of loan contracts amongst overlapping generations, extending her analysis to the determination of parental investments in children’s schooling. I show that when commitment is not possible, the effect of the intergenerational contract on children’s schooling is ambiguous; it depends on the effect of schooling on the profile of life-cycle incomes.4

Intergenerational exchange and family structures As has been shown by Lambertini (1998), Azariadis and Lambertini (2003) and others, despite the inability to commit to the intergenerational contract, perfect information can enable consumption to be smoothed over the life cycle through trades between overlapping generations. Following default, assume that the debtor cannot lend in the inter-generational market, either because of social norms that disallow future trades or because the debtor’s assets can be seized following default. With perfect information on defaulters, lenders can then tailor the terms of the contract so that it is always in the borrower’s interest to voluntarily repay. One feature of this model is that these contracts are most likely to be observed in households with a high demand for consumption smoothing, with demand being determined by life cycle income profiles and by preferences (the inter-temporal elasticity of substitution). In particular, households with hump-shaped income profiles are likely to value inter-generational contracts more than those with relatively flat profiles. I apply this framework to the context of intergenerational exchange in the Indian economy, an economy in which financial 2 An earlier draft version of this paper extends the analysis to allow for a ‘‘storage’’ good that provides an alternative method of life cycle consumption smoothing. Even with such a good, households may opt for the inter-generational contract, if the interest rate on this contract, evaluated at a zero loan amount, exceeds the rate of return on the storage good. In this situation, the results of this section still apply. As the formal interest rate dominates, the profitability of the family as a means of long term consumption smoothing falls. In the intermediate case, where households are indifferent between the two contracts, the rate of return is unaffected by schooling. However, the fact that schooling affects the probability of default still ensures that schooling investments take this probability into account. Details of this extension are available from the author on request. 3 As noted by an anonymous referee, variation in life expectancy of parents would work analogously to default risk in affecting the expected yield on the intergenerational contract. 4 In contrast, when commitment is not an issue, intergenerational exchange will increase children’s schooling, assuming that the primary effect of schooling is to increase incomes in later stages of the life cycle (prime earning years and later), relative to early working years.

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instruments that enable life cycle consumption smoothing are still scarce, particularly in rural areas. The requirement of perfect information suggests that exchange will occur primarily amongst family members. I assume that these contracts exist within co-residential intergenerational family units, specifically within co-residential stem families, an inter-generational family unit featuring just one unit of each generation. In India, this unit is the dominant residential arrangement for the elderly. Surveys reveal that it constitutes approximately 83% of all stem, joint and joint-stem families (Caldwell et al., 1984),5 and that the majority of stem families feature the participation of 3–4 generations (Hashimoto, 1991). The preference for exchange within co-residential units has been explained by one of two factors. The first is that the intergenerational contract also enables the smoothing of labor services over the life cycle, given imperfect substitutability between family and hired labor, with older family members providing child care in return for labor services in old age (Asis et al., 1995). The lower transaction costs associated with co-residence would make this the preferred mode of exchange. While the theoretical framework of this paper takes the form of a loan contract between overlapping generations, it can easily be adapted to the case where members of different generations trade labor services, with the older generation providing support to young adults through supervision of their children, with this service being repaid by care provided by the younger generation to elderly parents. A second reason for embodying exchange within the co-residential unit is the importance of household public goods, such as kitchens, open space and certain household durables. Co-residence may be preferred since it lowers the cost of public goods (Rosenzweig and Wolpin, 1993; Kochar, 2000). Both these explanations undoubtedly contribute to the prevalence of inter-generational co-residence as the preferred means of exchange. Co-residence also provides a natural way to transfer a primary asset, the residential house, across generations in a way that is conducive to repayment being in the form of care and help for the elderly.

Inter-generational loan contracts without commitment Consider a pure exchange overlapping generations economy, where individuals live three adult periods: young adulthood, a period of middle age, and old age. As soon as children become adults (i.e., in the first adult period), they make their own independent consumption decisions, even though they may continue to reside with their elderly parents. Income is low in young adulthood, peaks when an individual is middle aged, and falls thereafter. Consumption requirements are highest in the first period of adulthood, when young adults are raising their own children and investing in their children’s human capital. Because of the difference between consumption and income profiles, individuals would like to borrow in young adulthood and to lend when middle aged, so as to smooth consumption over the life cycle. Let c be private consumption, b be the subjective discount factor, and let qt represent the cost of a unit investment in schooling (h).6 Rt+1 is defined as the gross yield on loan bt+1, Rt+1=(1 + rt+1) where r is the interest rate. I use superscripts to index generations and sub-scripts to index the stage of the individual’s life cycle. Assuming that an individual’s utility function is separable in consumption and the schooling of his children, a generation t individual 5 A joint family refers to married siblings living together, while a joint-stem family is one in which the parents live with multiple married children and grandchildren. 6 Alternatively, h could represent completed years of schooling, with a human capital production function relating h to investments in schooling including time spent at school, s. Budget constraint (3), below, would then replace ht+1 with s, with q representing the opportunity cost of time spent in school.

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A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

(one who reaches adulthood in period t) maximizes the following utility function when young:

U tt ¼

2   X   tþ1 bt u cttþs þ v h

t

b>0

ð1Þ

Both u(c) and v(h) are strictly increasing, concave and differentiable. Lifetime utility is maximized subject to the set of one-period constraints: t

bt ¼ 0 tþ1

t

¼ ytt þ btþ1 t

t

cttþ1 ¼ yttþ1  Rtþ1 btþ1  btþ2

tþ1

btþ2 ðRtþ1 ; Rtþ2 ; yt Þ ¼ btþ2 ðRtþ2 ; Rtþ3 ; ytþ1 Þ

ð11Þ



s¼0

ctt þ qt h

equation (8) for generation t + 1) with the supply from parents (Eq. (10), generation t).7 Thus, Rt+2 solves the equation:

 tþ1 tþ1 where yt ¼ fytt; yttþ1 ; yttþ2 g and ytþ1 ¼ ytþ1 tþ1 ; ytþ2 ; ytþ3 . This yields interest rates for each period that vary with the life cycle incomes of the contracting parties, but also of all past and previous genera  tions, Rtþ2 ¼ R yt ; ytþ1 ; ytþ2 ; . . . : . With incomes reflecting schooling t

ð2Þ

investments, yt ¼ yðh Þ, the interest rate function can in turn be expressed as a function of the schooling of different generations:

ð3Þ

Rtþ1 ¼ Rðh ; h

t

tþ1

;h

tþ2

ð12Þ

; . . .Þ

ð4Þ Schooling investments

t

cttþ2 ¼ yttþ2 þ Rtþ2 btþ2

ð5Þ

t

where btþ1 represents the loan taken by generation t individuals, repayable in period (t + 1) and other loan quantities are similarly defined. With hump shaped income, the optimal plan calls for an individual in generation t borrowing from his parents in period t, the first period of young adulthood, repaying this loan in period t t + 1, and simultaneously making loans to his child ðbtþ2 Þ. These loans are repaid by the child when the parent is old, in period (t + 2). As previously discussed, default implies the cessation of exchange with future generations. Since the inter-generational contract provides the only means of smoothing consumption across periods, borrowing and lending decisions (for individuals in families which have previously maintained the inter-generational contract) are therefore subject to the individual rationality constraints (IRCs):

      u cttþ1 þ bu cttþ2  u yttþ1 þ buðyttþ2 Þ

ð6Þ

  u cttþ2  uðyttþ2 Þ

ð7Þ

Let l1 be the Lagrange multiplier on constraint (6) and l2 be the t multiplier on (7). Then, the first order condition for btþ1 , the loan demanded by members of generation t from their parents, and t btþ2 , the loan supplied by members of generation to their son, are, respectively:

u0 ðctt Þ þ bRtþ1 u0 ðcttþ1 Þ þ l1 Rtþ1 u0 ðcttþ1 Þ ¼ 0

ð8Þ

u0 ðcttþ1 Þ þ bRtþ2 u0 ðcttþ2 Þ  l1 u0 ðcttþ1 Þ þ ðl1 b þ l2 ÞRtþ2 u0 ðcttþ2 Þ ¼ 0 ð9Þ A similar set of first order conditions apply to generation (t + 1), describing the demand for loans from this generation from their parents (members of generation t) and the supply to their offspring. With ‘‘hump’’ incomes that peak when the individual is middle-aged, the budget constraints (3–5) reveal that constraint (6) will be binding but constraint (7) will not. That is, in (8) and t (9), l1 > 0 but l2 = 0. With this, the first order condition for btþ1 is given by (8), so that IRCs reduce the demand for loans by young adults from their middle-age parents. However, middle-aged parents’ decisions regarding the amount of loan to supply to their chilt dren are unaffected by IRCs: The first order condition for btþ2 (Eq. (9)) reduces to the standard first order condition that obtains when commitment is not an issue:

u0 ðcttþ1 Þ ¼ bRtþ1 u0 ðcttþ2 Þ

ð10Þ

Interest rates in the ‘‘market’’ between family members of different generations are determined by an equilibrium condition that equates the demand for loans from the son (as given by

Parents make schooling investments strategically, taking into account the effect of schooling on loan interest rates. That is, optimal investment in schooling is solved for sequentially, by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling, and then working backwards to determine the optimal investment in a child’s human capital, taking into account the effect of schooling on interest rates. The first order condition for investments in a child’s human capital is given by:

v 0 ðhtþ1 Þ ¼ kt qt  ktþ2 bttþ2

@Rtþ2 @h

tþ1

ð1 þ l1 Þ

ð13Þ

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default, reflected in the Lagrange multiplier on the IRC (6), l1, affect the rate of return to investment in children’s schooling. In the absence of the intert

generational contract, that is, if btþ2 ¼ 0, parental investments in children’s schooling would be given by the familiar condition: v 0 ðhtþ1 Þ ¼ kt qt , and would reflect preferences, schooling costs and parental income. An inter-generational contract affects the parental rate of return on children’s schooling, either increasing it or tþ2 decreasing it, depending on the sign of @R . If this term is positive, @htþ1

parents will strategically over-invest in their children’s education relative to a pure consumption model. In contrast, if a child’s schooling reduces the rate of return on the inter-generational loan contract, then parents will under-invest in his schooling. tþ2 As shown in Appendix A, the sign of @R depends on the effect @htþ1 of schooling on second-stage adult incomes relative to third stage, and on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age. If schooling primarily increases second stage income, its effect is to make life cycle incomes more ‘‘hump shaped.’’ This in turn increases first period loan demand and hence the rate of return on the inter-generational loan. As a consequence, parents are likely to over-invest in their child’s schooling. Conversely, if schooling makes the profile of income over the life cycle less hump shaped, as is commonly believed, then it will reduce the demand for the inter-generational loan by children, lowering interest rates and so reducing investments in schooling. The same result holds if there is little difference in the effect of schooling on incomes in period 2 relative to period 3, but if the inter-generational contract 7 Azariadis and Lambertini (2003) discuss the conditions for an equilibrium to exist. They show that assumptions of hump-shaped endowment profiles, low rates of time preference and moderate inter-temporal elasticities of substitution generate a stationary non-autarkic equilibrium, even in the absence of commitment. However, the equilibrium is no longer unique and coexists with an unconstrained stationary equilibrium and an autarkic unconstrained one.

A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

is primarily valued for its effect on consumption in old-age. Eventually, however, the sign of this effect is an empirical issue. The autarchic option, multiple children and strategic investments This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their children’s schooling. While this framework assumes just one child, strategic investments in families with multiple children require parents to identify the child they expect to reside with at an early age. This section discusses determinants of this choice in the Indian context. In most Asian economies, there is a strong norm that dictates residence with a son. Though the choice of which son to live with varies with individual characteristics and circumstances (Caldwell et al., 1984), residence with the youngest son is the custom in many part of South India (Dharmalingam, 1994). Older sons move out of the parental residence and establish their own households as younger sons get married, leaving parents to reside, in their old age, with the youngest son. This, of course, can only occur in families with more than one son. In households with one or no sons, parents generally reside with the oldest son. As we substantiate in the next section using survey data, the fact that the majority of parents who reside with a child do so with their oldest son primarily reflects the large percentage of households who have just one son. A role for social norms in reducing default is easily accommodated in the theoretical framework of the previous section, by including an additive term in the utility function that reflects the additional utility from adherence to the social norm. The interest rate on the inter-generational contract between parents and children will then vary across children, not just because of variation in individual income profiles but also because of norms. This framework can also easily be extended to allow for the use of an extended family network for long-term consumption smoothing. While residence with brothers or other relatives is rare, the fact that brothers generally reside in the same village, in very close proximity, suggests that an extended network is available to participate in credit or labor-sharing arrangements. These include credit contracts that enable smoothing consumption over different stages of the life cycle, if a sufficient age difference exists between family members. The same theoretical framework of the previous section delivers an interest rate on the contract with extended family members, once again taking the probability of ^ f then comprises the default into question. This interest rate, R tþ2 autarchic interest rate. Comparing this rate to that from the inter-generational contract with children, parents would select co-residence with children when it represents the more profitable contract. Data and Setting Survey The data I use for this study comes from a survey of approximately 10,000 households in rural areas of the southern state of Karnataka. The study was designed to understand the determinants of schooling. The unit of administration for school planning purposes in the state is a cluster, a unit above the village, with each cluster covering an average of 15 villages. For the purposes of this study, 240 clusters were randomly chosen from across the study area (11 districts of the state). Within each cluster, an average of 1.5 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller), and, within each Gram Panchayat, two schools were surveyed (the largest and a randomly selected school). In each school, parents of

13

all children in 3rd grade in 2009–10 (henceforth referred to as ‘‘index’’ children) were interviewed. The analysis of this paper is based on a re-survey of approximately 9,000 households in the 2012–13 school year, when the index child was in 6th grade. In addition to a standard household survey, detailed data were collected in this round on expectations of old-age residence of current parents, as well as residential arrangements of the current generation of grand-parents. Parents who stated that they expected to reside, when old, with a child, were asked to identify the child they expected to reside with. For such households, ‘‘can’t say’’ was also provided as an option. Index children were tested in language and mathematics, using tests designed by an independent agency and implemented by the survey team. The tests were designed to assess student learning relative to the state-specific standards for grade 6. In addition to test scores, detailed data on the monthly attendance of the index child between June 2012 and February 2013, the date of the survey, were collected from schools. A school survey also provides information on the characteristics of the schools attended by the index child. The regression sample is based on data for the index child alone, since it is only for this child that we have data on attendance. Thus, it does not include data on all children in the household, but only on the one child who was in grade 6 in 2012–13. Residential arrangements and expectations Table 1 provides survey information on parents’ expectations of old age residence, by the number of sons. The data reveal that the majority of parents with one son expect to live, when old, with this son (60%). The percentage who expect to reside with the oldest son drops dramatically as the number of sons increase; only 11% of households with two sons, for example, expect to live with their oldest son. Of these households, 16% expect to live with a younger son, and a higher proportion (relative to households with just one son) also state uncertainty regarding old–age residential arrangements (44%). Thus, the dominance of the arrangement of residence with the oldest son, the expected arrangement for 33% of our survey households who expect to live with a child, reflects the fact that parents with just one son represent 42% of sample households. Table 2 provides information on the number of children and the number of sons by four household demographic types, distinguished by the gender of the first two births (son–son, son–daughter, daughter–son, daughter–daughter). The table confirms that son–son households have the most sons, while daughter–daughter households have the least. Correspondingly, parents whose first two children are daughters should be more likely to expect co-residence with their oldest son, while son–son households should reveal a greater preference for residence with other sons. This is supported in Table 3 that provides information on the child parents expect to reside with, amongst parents with at least two children who state that they expect to reside with a child when elderly. Of son–son households, 30% state that they expect to reside with their oldest son, while 36% reveal an expectation of co-residence with a younger son. Conversely, of daughter– daughter households, 51% state that they expect to reside with their oldest son. Tables 4 and 5 use data on the actual residential arrangements of the current generation of grandparents to evaluate whether realized residential patterns conform to these expectations. I use data on both sets of grandparents, the mother’s parents as well as the father’s. For ease in understanding, I refer to the grandparent’s generation as generation t1, and the current generation of parents as generation t. Classifying households into the same four demographic types, but now based on the gender of children of generation t1 (current grandparents), Table 4 reveals the same

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A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

Table 1 Parent’s expected residential arrangements in old age by number of sons. Residential arrangement

Alone Joint family Other relatives Can’t say With child Of which Oldest son Other son Daughter Can’t say which child Total

Number of sons

Total

0

1

2

3

4

14.96 (22.30) 0.56 (3.16) 0.19 (25.00) 53.81 (14.77) 30.48 (6.37)

7.41 (43.34) 1.20 (26.32) 0.05 (25.00) 22.78 (24.53) 68.56 (56.24)

5.32 (25.25) 3.28 (58.42) 0.09 (37.50) 49.96 (43.61) 41.35 (27.50)

5.46 (7.71) 1.69 (8.95) 0.10 (12.50) 52.78 (13.74) 39.98 (7.93)

4.07 (1.40) 2.44 (3.16) 0.00 (0.00) 52.85 (3.36) 40.65 (1.97)

7.23 (100.00) 1.93 (100.00) 0.08 (100.00) 39.25 (100.00) 51.52 (100.00)

0.00 (0.00) 0.00 (0.00) 12.23 (78.79) 18.25 (19.68) (100.00) (10.77)

65.76 (84.68) 0.00 (0.00) 0.29 (7.27) 2.52 (10.65) (100.00) (42.26)

11.42 (11.92) 15.82 (76.98) 0.50 (10.30) 13.61 (46.65) (100.00) (34.26)

9.23 (2.87) 12.20 (17.70) 0.50 (3.03) 18.06 (18.46) (100.00) (10.21)

6.91 (0.53) 15.04 (5.32) 0.41 (0.61) 18.29 (4.56) (100.00) (2.49)

32.81 (100.00) 7.04 (100.00) 1.67 (100.00) 9.99 (100.00) (100.00) (100.00)

Note: In each cell, the first number is the column percentage, while the second number is the row percentage. Households with more than 4 sons constitute 1.24% of total households and are not included in this table.

Table 2 Number of children, probability of third child and number of sons, by household type. Household type

Number of children

Proportion with >=3 children

Number of sons

Son–son

2.97 (1.27) 3.00 (1.21) 2.90 (1.12) 3.52 (1.30)

0.56 (0.50) 0.59 (0.50) 0.57 (0.50) 0.80 (0.40)

2.52 (0.86) 1.51 (0.79) 1.47 (0.72) 0.75 (0.77)

Son–daughter Daughter–son Daughter–daughter

Table 3 Parent’s expected residential arrangements by household demographic type (Sample: Parents with at least two children who expect to reside with a child). Household type (gender of first two children)

Son–son

Son–daughter

Daughter–son

Daughter–Daughter

Total

Of parents who expect to reside with children, expect to reside with Oldest son

Other son

Daughter

Can’t say

Total

298 (29.10) (9.19) 1081 (975.33) (33.34) 1069 (75.87) (32.97) 794 (62.67) (24.49) 3242 (63.14) (100.00)

350 (34.18) (48.41) 171 (11.92) (23.85) 144 (10.22) (20.08) 52 (4.10) (7.25) 717 (1396) (100.00)

11 (1.07) (6.63) 5 (0.35) (3.01) 11 (0.78) (6.63) 139 (10.97) (83.73) 166 (3.23) (100.00)

365 (35.64) (36.14) 178 (12.40) (17.62) 185 (13.13) (18.32) 282 (22.26) (27.92) 1010 (19.67) (100.00)

1024 (100.00) (19.94) 1435 (100.00) (27.95) 1409 (100.00) (27.44) 1267 (100.00) (24.67) 5135 (100.00) (100.00)

broad patterns of household type with the number of sons and the total number of children. Specifically, son–son households have more sons (an average of 3.4), while daughter–daughter households have fewer (1.55). As with expected residential arrangements of generation t, this difference in the number of sons translates into differences in residential patterns. For parents whose first two births were sons, the

preferred arrangement was co-residence with a younger son (50% of such households). Conversely, only 28% of daughter–daughter households reported residing with a younger son, with the most common arrangement being residence with the oldest son (35%). The relatively small percentage of generation (t1) parents who reported residing with their oldest son (36%) reflects higher fertility rates amongst this generation, and hence a smaller percentage

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A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23 Table 4 Grandparent’s generation (t1): Number of children, probability of third child and number of sons, by household type. Household type

Number of children

Proportion with >=3 children

Number of sons

Son–son (n = 7,985) Son–daughter (n = 5,007) Daughter–son (n = 4,342) Daughter–daughter (n = 5000)

4.82 (2.22) 4.58 (2.17) 4.59 (2.13) 5.06 (2.23)

0.89 (0.31) 0.85 (0.36) 0.86 (0.35) 0.93 (0.26)

3.40 (1.44) 2.27 (1.33) 2.32 (1.31) 1.55 (1.39)

Note: Sample includes both sets of grandparents

Table 5 Grandparent’s old age residence by household demographic type (Sample: grandparents with at least two children). Household type (gender of first two children)

Son–son

Son–daughter

Daughter–son

Daughter–Daughter

Total

Reside(d) with Alone

Oldest son

Other son

Other

Total

435 (6.04) (24.83) 387 (8.07) (22.09) 340 (8.16) (19.41) 590 (12.22) (33.68) 1752 (8.35) (100.00)

2,312 (32.10) (30.31) 2,072 (43.22) (27.17) 1,566 (37.60) (20.53) 1,677 (34.72) (21.99) 7627 (36.33) (100.00)

3,623 (50.30) (44.37) 1,635 (34.11) (20.02) 1,563 (37.53) (19.14) 1,344 (27.83) (16.46) 8165 (38.90) (100.00)

833 (11.56) (0.24) 700 (0.15) (0.20) 696 (0.17) (0.14) 219 (0.05) (0.06) 3,448 (0.16) (100.00)

7.203 (100.00) (34.31) 4,794 (100.00) (22.84) 4,165 (100.00) (19.84) 4,830 (100.00) (23.01) 20,992 (100.00) (100.00)

Note: Sample includes both sets of grandparents.

of parents who report having just one son (21%, compared to 41% in the current generation).8

alone are much more likely to own land (68% relative a sample average of 54%. The average land holding for such households (2.4 hectares) is also in excess of the average (1.8).

Summary statistics Summary statistics for the sample as a whole, as well as by parents’ expected residential arrangements when old, are in Table 6. School records reveal an average attendance rate of 88% of school days, with little variation in attendance across households distinguished by parental expectations regarding residential arrangements in old age. As in much of rural India, mean test scores are low, only 39% for both language and mathematics. Parents have an average of three children, with the number of children being least (2.8) for parents who expect to reside with their oldest son, and the most for those who expect to reside with a younger son or who cannot yet specify old-age residential arrangements. Supporting the evidence of the previous subsection, households in which parents expect to reside with their oldest sons typically have a low ratio of sons to total children (0.45), while those that expect to reside with younger sons have a much higher ratio (0.59). Parents that expect to reside with their oldest sons also typically have higher levels of parental education (5 years for fathers and 4 years for mothers, relative to sample averages of 4 and 3 respectively). Though the proportion of households that expect to reside with either an older or a younger son do not differ in terms of the proportion who own land, households that intend to live 8

A similar proportion of current parents (33%) report an expectation of residing with their oldest son, despite the greater number of households with just one son. This reflects the fact that 49% of households are uncertain about their residential arrangements, or about the child they expect to reside with.

Empirical Methodology The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established. This section takes up that task. I start by discussing the empirical framework. The next sub-secction discusses other factors that could generate a relationship between old-age residence and schooling, and hence the bias that exists in OLS regressions. The instruments used to implement an instrumental variable regression that identifies the causal effect of the inter-generational contract on schooling are discussed in Section ‘‘Summary statistics. I follow this with a discussion of the approach I take to allow for fertility choices and address the possibility that estimates may be biased because of this choice. I then address an additional empirical challenge, specifically the possibility that the results identify the effect of short-term credit constraints on households, rather than the demand for a long-term contract. The last two sections detail the estimating equation and describe the regression sample.

Framework The primary objective of the empirical analysis of this paper is to examine whether, and how, the schooling of a child is affected if parents expect to reside with him or her in old age. Let di be an indicator variable which equals 1 if parents expect to enter into

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A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

Table 6 Summary Statistics, Regression Sample. Variable

Full sample

For index child Parent’s expect to co-reside Prop. days attended Language score Mathematics score Household Total children Ratio sons Savings Father’s brothers SC/ST Father’s education Mother’s education Prop. own land Ag. Land Other School size Student–teacher ratio Village population Sample size

Expected old-age residential arrangement Alone

Oldest son

Other son

Cannot say

0.20 (0.40) 0.88 (0.12) 39.25 (19.77) 39.55 (18.49)

–

–

–

–

0.88 (0.11) 37.98 (19.22) 38.04 (16.44)

0.89 (0.12) 41.00 (20.05) 39.86 (18.37)

0.87 (0.12) 35.90 (0.00) 38.00 (17.83)

0.87 (0.12) 39.24 (20.07) 40.47 (19.46)

3.09 (1.23) 0.52 (0.30) 20,167 (48,571) 2.99 (1.55) 0.33 (0.47) 4.18 (4.42) 3.34 (3.88) 0.54 (0.50) 1.81 (3.02)

2.90 (1.02) 0.44 (0.32) 25,912 (49,067.92) 2.88 (1.50) 0.31 (0.46) 4.69 (4.81) 3.48 (4.05) 0.68 (0.47) 2.38 (3.38)

2.81 (1.07) 0.45 (0.20) 20,804 (58,990) 1.65 (1.47) 0.34 (0.47) 4.99 (4.44) 4.04 (4.02) 0.57 (0.50) 1.70 (2.54)

3.21 (1.22) 0.59 (0.26) 19,049 (33,026) 2.95 (1.50) 0.35 (0.48) 4.01 (4.46) 2.67 (3.63) 0.57 (0.50) 1.76 (2.94)

3.20 (1.29) 0.56 (43,403) 21,414 (43,403) 3.03 (1.61) 0.32 (0.46) 4.29 (4.41) 3.21 (3.81) 0.56 (0.50) 1.94 (2.92)

230.80 (134.44) 29.52 (10.14) 3398.65 (2881.19) 8,109

231.72 (142.37) 29.76 (9.55) 3616.36 (3836.21) 568

209.46 (125.55) 28.06 (9.57) 2994.54 (2328.13) 2,190

241.42 (133.22) 30.53 (10.49) 3672.49 (4058.27) 852

236.17 (133.84) 30.21 (10.68) 3036.42 (2351.55) 2,907

Note: The number of households in the last four columns, by expected residence in old age, ignore households that expect to live with daughters, other relatives or those who expect to live with a child but cannot identify the child. Standard deviations in parentheses.

a loan contract with child i, 0 otherwise. From the analysis of the previous section,

d¼1 0

if

Rtþ2 >¼

  u0 cttþ1 ; B ¼ 0 bu0 ðcttþ2 ; ;B ¼ 0Þ

ð14Þ

the expectation of co-residence, at the time when parents are investing in their children’s schooling, ei is likely unknown at the time these investments are being made. This suggests that Eðdi ei Þ ¼ 0, justifying identification through instrumental variables.

Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling, the first order condition for schooling investments (Eq. (13)) can be rewritten as:

 @Rtþ2 v 0 ðhtþ1 Þ ¼ kt qt  d ktþ2 bttþ2 tþ1 ð1 þ lÞ @h

ð15Þ

Taking a linear approximation, the estimating equation for years of schooling (hi) is:

hi ¼ ao þ a1i di þ X0i a2 þ ui

ð16Þ

bttþ2 @Rtþ2 Rtþ1 Rtþ2 @htþ1

where a1i ¼ ð1 þ lÞ, and Xi represents wealth and observed preference shifters that determine schooling. This is a standard random coefficient model with an endogenous regressor, di. Let E be the expectation operator, and let a1i ¼ Eða1i Þ þ e1i ;  i < 1; Eðei Þ ¼ 0. Then, (16) can be written as: Eða1i Þ ¼ a

 1i di þ X0i a2 þ ½ui þ di ei  hi ¼ ao þ a

ð17Þ

As noted by Heckman and Robb (1985), identification using instrumental variables would not be possible if the error term in (17) has a non-zero mean. However, as they note, since di reflects

Regression error term and bias in OLS regressions The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from Eq. (14) and (12). From (14), the probability of co-residence reflects the interest rate on the inter-generational loan account. Eq. (12) shows that this interest rate will, in turn, reflect the schooling attainment of all generations, including expectations of the schooling of the current generation of children. That is, expectations of co-residence and schooling investments in children are jointly determined. OLS estimates will suffer from reverse causation: It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son, instead of expectations of co-residence causing strategic investments in children’s schooling. If parents can infer their children’s ability at a young age, as is very likely, this ability, unobserved by the econometrician, will be a component of the regression error term. It will also be correlated with expectations of co-residence. Thus, any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables, and cannot be taken as indicative of a causal effect of co-residence on schooling attainment.

A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

Regression estimates may also be biased if parents prefer to reside with the child they have the greatest affinity to. If parents also tend to invest more in this child, then this will introduce a positive bias in OLS estimates of the effect of co-residence on schooling investments. If the ‘‘true’’ effect of co-residence on schooling is negative, this positive bias would generate insignificant effects of co-residence on schooling in OLS regressions. Identification of expectations of inter-generational co-residence While, as noted above, identification cannot be based on the interest rate on the inter-generational contract, Ritþ2 , it is possible to exploit both the factors that determine which child parents will contract with and the fact that the decision to enter into a contract with this child will be based on a comparison between the autarchic rate and the inter-generational rate. In doing so, I assume that ^ f Þ incorporates the probability of entering the autarchic rate, ðR tþ2 into an alternative contract with members of the extended family, specifically with the father’s brothers. Let di = 1 if the child is the oldest son. Then, from the analysis of the previous section, and from (14),

  Prðdi ¼ 1Þ ¼ di  Pr sons  1; Ritþ2 >¼ F^ftþ2 þ ð1  di Þ   ^f  Pr sons > 1; Ritþ2 >¼ R tþ2

ð18Þ

The probability that parents demand a contract with the oldest ^ tþ2 . In households son increases if he is the only son, and if Ritþ2  R with more sons, there is a greater probability that parents chose residence with younger sons, provided the inter-generational interest rate exceeds that from contracting with the father’s brothers. Since the value of contracting partners for smoothing consumption across different stages of the life cycle increases with the age difference between them, one component of the difference in the interest rates is the difference in age between the father and the child in question relative to that between the father and his brother. This latter difference is calculated as the difference in age between the father and his youngest brother, for households in which the father is the oldest brother, and between the father and his oldest brother in other households. Contrasting the age difference between the father and the child with that between brothers, the profitability of the inter-generational contract relative to that with brothers is given by the age difference between the father’s brother and the child. A larger age difference between the father and his brother may merely reflect the birth order of the father and the number of his brothers. To ensure that this is not the case, all regressions of this paper include the number of the father’s brothers (and sisters), as well as indicator variables that take the value 1 if the father is the oldest or the youngest brother. Turning to determinants of the number of sons, I initially predict this number using an indicator variable that takes the value 1 if the first birth in the household is a daughter (first_d). This strategy exploits son preference amongst Indian households. A preference for sons will generate ‘‘son preferring, differential stopping behavior’’, with parents continuing to have children until the targeted number of sons is born. Such behavior will increase the number of children in the family (Das, 1987) and suggests that the gender of the first child is likely to be a determinant both of family size and of the proportion of sons to total children (Jensen, 2003). Data from the 2005–06 National Fertility and Health Survey (NFHS) confirm a preference for sons in the state, though to a lesser degree than in other states, particularly those in North India. The percentage of women and men wanting more sons than daughters was 11.6% and 12.7% respectively, while the percentage of women

17

who want more daughters than sons is only 4.6%. The corresponding percentage of men who want more daughters than sons is 2.7%. Households in the state, however, also demonstrate a demand for at least one daughter, a characteristic common to most of the Indian economy (National Family and Health Survey 2005–06).9 At the national level, 74% of women and 65% of men want at least one daughter (77% of women and 70% of men want at least one son). My initial instrument set is therefore an interaction between a dummy variable for the oldest son, the indicator variable for the first child being a daughter (first_d), and the age difference between the father’s brother and the child in question (agediff; a similar set of interactions of first_d and agediff with a dummy indicator for other (younger) sons; and the interacted term first_d * agediff. This methodology would not be valid in regions where parents are able to ‘‘select’’ the gender of their child using available technology. There is, however, little evidence on this in the survey region. In contrast to earlier work on this topic, identification of expectations of parental co-residence is thus not based on the assumption that parents will co-reside with the oldest son but, instead, the recognition that this will occur only in households with few sons and for who the inter-generational contract is of greater value than a contract with brothers. The use of an interacted term for identification makes it possible to include a dummy indicator variable for the oldest son and for younger sons amongst the regressors, thereby accommodating a literature that argues that birth order affects schooling investments, perhaps because of differences in ability, parental preferences for children of specific birth orders, or credit constraints that change with the gender and age profile of children in the household (Ejrnæs and Pörtner, 2004; Behrman and Taubman, 1986; Willis and Parish, 1994; Garg and Morduch, 1998). Similarly, I also include first_d in the set of regressors. Since the event of the first-born child being a daughter predicts the ratio of sons and the total number of children, doing so allows this event to independently determine schooling investments through, for example, a quality-quantity trade-off (Becker et al., 1973).

Allowing for the number of children and the ratio of sons The primary concern with the identification strategy outlined above is that the instruments may still be picking up the effect of the effect of the demographic profile of the household, despite the fact that the triple interaction implies that the effect of household demographic characteristics on expectations of co-residence vary across children in the household and by the age difference between the child in question and the father’s brothers. The primary household demographic characteristics that affect schooling investments are the total number of children and the ratio of sons. To the extent that these variables predict future credit constraints, and under the assumption that the only source for long-term consumption smoothing contracts, other than autarky (and hence the extended family) is the inter-generational contract, the number of children and sons will affect schooling investments only through the probability of this contract. However, these variables could also affect current income and preferences. One way, of course, is through a classic quality-quantity tradeoff (Becker et al., 1973). Alternatively, many have argued that daughters can substitute for a mother’s time in home production, increasing household income by allowing mothers to increase their participation in the paid labor market. To address the concern that the instrument set also predicts the number of children and sons, I include these variables amongst the 9 This is generally ascribed to the Hindu religious obligation of Kanyadan, or the giving of a daughter in marriage, considered to be a sacred duty of all Hindus.

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A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

regressors, treating both as endogenous. This requires standard rank conditions for identification to be met. I do so by extending the literature that relates the number of children and the ratio of sons to the gender of the first birth, recognizing that, in the Indian context, the gender of the first two births provides the information necessary for the separate identification of these variables. Specifically, I exploit the difference in the correlation of the number of children and the number of sons, respectively, to the gender of the first two births. As revealed in Table 2, the total number of children does not statistically differ across son–son, son–daughter or daughter–son households. This is consistent with a demand for at least 1 daughter and a preference for sons. Thus, amongst the four household demographic types, the total number of children is higher only in daughter–daughter households. Conversely, the number of sons falls from son–son to son–daughter to daughter–son households, and is lowest in daughter–daughter households. Again, a preference for sons explains the difference in the number of sons between son–son, daughter–daughter and the remaining two household types. It does not suggest a difference in the number of sons between son–daughter and daughter–son households, and the data also suggest that the difference in the number of sons between these two types of households is small relative to the difference across other household types. This difference in correlation patterns between the number of children and the number of sons, respectively, and household types, provides the basis for a viable identification strategy: A variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of one that does so on the basis of the number of sons. Thus, regressions that include both rankings would satisfy the rank conditions for identification, making it possible to separately identify the effect of the number of sons and the total number of children. As in Angrist and Evans (1998), more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator variables generated by each pairing as separate instruments. This allows me to implement standard over-identification tests for these instruments, by including sub-sets of the indicator variables for demographic types amongst the regressors. In turn, this allows for alternative ways in which the gender composition of children can affect socio-economic outcomes. Specifically, it allows for the possibility that households in which a daughter is the first-born may be better off, perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis, 1994; Garg and Morduch, 1998). As in Angrist and Evans, a limitation of this approach is that the analysis is restricted to households with two or more children (84% of the total sample of households). Thus, results may only apply to households with two or more children. This qualification should be kept in mind in interpreting results. The second set of regressions I implement therefore replace first_d with a set of indicator variables based on the gender and birth order of the first two children (son–son, son–daughter, daughter–son, daughter–daughter), using these indicator variables to determine the ratio of sons and the total number of children. Correspondingly, I use interactions with these indicators, (oldest son * agediff * son–son, oldest son * agediff, dtr-dtr; a similar set of interactions with the indicator for younger sons, othson; and interactions of son–son and dtr-dtr with agediff) as the relevant instruments for inter-generational co-residence with the child in question.10

10 I restrict attention to interactions with son–son and daughter–daughter, given a lack of significant different in results that combine the remaining two categories into one.

Allowing for short-term credit constraints A final concern is whether the instrument set identifies the rate of return on the inter-generational family contract or that on informal short-term credit markets. From (15), with or without an inter-generational loan, schooling investments would still reflect current credit constraints that determine income at the time that parents are investing in a child’s schooling. The demographic variables and measures of extended family networks used as instruments may reflect access to short-term informal credit markets, rather than their effect on the probability of an inter-generational loan between parents and any specific child. To address this issue, I condition regressions on current household savings, building on research by MaCurdy (1983) and Blundell and Walker (1986). Household savings incorporate expectations of future income as well as current and future credit constraints, and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through current income or credit constraints, leaving expectations to affect schooling choices only through preferences or through the net returns to schooling. This approach, however, requires a treatment of the endogeneity of savings. Baseline assets are a natural instrument, and I accordingly predict household savings with the value of assets held by the household at the start of the current period. Assets used for this purpose should not, however, directly affect the value of time of household members (parents or children, since the labor market choices of all household members will directly affect schooling investments. Thus, land ownership or the value of agricultural land are unlikely to be valid instruments. Financial assets, however, are credible instruments. Accordingly, I instrument household savings by the value of initial bank accounts. Estimating equation The basic estimating equation for the educational outcome of child i in household j and village k is:

    E educijk ¼ ao þ a1 E resijk þ a2 first djk þ a3 oldest sonijk þ a4 oth sonijk þ a5 ageijk þ a6 agediffijk þ a7 fath agejk þ X 0ij a8 þ Z 0ij a9 þ T 0k a10 þ uijk

ð19Þ

In this equation, educ is the schooling outcome being considered (attendance days, language and mathematics test scores). E(Res) is an indicator variable that takes the value 1 if parents state that they expect to reside with the child in question, 0 otherwise. First_d is a dummy variable that takes the value 1 if the oldest child in the household is a daughter, oldest_son takes the value 1 if the child in question is the oldest son, and oth_son is an indicator variable for younger sons. The set of age variables included in the regression measures the age of the child (age), the age of the father (father_age), and the difference in age between the father’s brother and the child (agediff). Since age is included as a separate regressor, including agediff is equivalent to including the father’s brother’s age. E(res) is instrumented using the following set of interacted variable: oldest_son * first_d * agediff, oth_son * first_d * agediff, first_d * agediff. The regression also includes other individual regressors (X), specifically, an indicator variables for the oldest daughter in the household. Additional parental and household characteristics (Z) include the number of the father’s brothers and sisters, indicator variables for whether the father is the oldest or the youngest brother, mother and father’s education, an indicator variable for ownership of agricultural land, the amount of land owned, the amount of land owned by the fathers parents and by the mothers

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A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

parents. This rich vector of household characteristics ensures that the age difference between the child and the father’s brother, a component of the instrument set, does not reflect characteristics of the father that may independently affect outcomes, such as the father’s birth order or the number of his siblings. School and village level variables (T) are the student teacher ratio in the school attended by the index child, village population and the number of village households. The first extension of this basic regression replaces first_d, both as an independent regressor and in the instrument set, with sonson (first and second births are sons) and dtr-dtr (first and second births are daughters). A second extension includes kids and rsons, the total number of children in the household and the ratio of sons to total children, treating both as endogenous. This regression expands the instrument set to include son–son, son-dtr, and dtrdtr, on the assumption that these variables affect schooling only through their effect on expectations regarding co-residence, number of children, or the ratio of sons. As previously explained, I also report results from a set of auxiliary regressions that implement over-identification tests on this set of demographic indicators. The final regression of the paper includes household savings, expanding the set of instruments to include the value of inventories and bank assets. Regression sample As previously noted, the sample is restricted to the 84% of households with at least two children, and to households in which each father had at least one brother. The final regression sample is 7,628 children.

Results OLS and IV regressions, using information on the first birth Table 7 provides OLS estimates from regressions of the proportion of school days attended on parental expectations of co-residence with the child in question, as well as a set of IV regressions. The IV regressions use simple demographic characteristics for identification, to highlight the difference in the empirical methodology of this paper relative to others in the literature. The first IV regression uses an indicator variable for the oldest son as an instrument, replicating a research that identifies old-age residence based on this indicator. The first stage regression for this specification is in the preceding column, and attests to the significance of the indicator variable for the oldest son in explaining expectations of co-residence with the child in question. The second IV regression uses the first of the empirical methodologies discussed in this paper, basing identification on a triple interaction between indicators for the oldest son, the gender of the first birth, and the age difference of the father’s brother and the child in question. Again, results from the first stage regression for this specification are in the column preceding the IV results. The OLS estimates reveal an insignificant effect of expectations of co-residence on the proportion of school days attended by the child in question. Similarly, IV estimates that use an indicator variable for the oldest son as an instrument for expectations of co-residence also generate an insignificant effect on attendance. In contrast, the last IV regression based on the triple interaction suggests that expectations of co-residence reduce investments in the child’s schooling. The effect is statistically significant at the 5% level.

Table 7 First Stage and IV Regressions, proportion of school days attended. OLS

Instrument: oldest son indicator

Instruments: expanded set

First stage

IV

First stage

IV

0.002 (0.004)

–

0.001 (0.008)

–

0.10* (0.04)

Instruments Oldest son * first_d * agediff

–

–

–

–

Other son * first_d * agediff

–

–

–

First_d * agediff

–

–

–

0.004* (0.001) 0.001 (0.001) 0.0004 (0.001)

0.001 (0.004) 0.01* (0.004) 0.001 (0.003) 0.02* (0.003) 0.0003 (0.0003) 0.0001 (0.0003) 0.001 (0.005) 0.01* (0.003) 0.001 (0.001) 12.54 (0.00) –

0.413* (0.015) 0.123* (0.014) 0.053* (0.009) 0.003 (0.01) 0.001 (0.001) 0.001 (0.001) 0.007 (0.013) 0.001 (0.01) 0.004 (0.004) 46.92 (0.00) –

–

0.34* (0.02) 0.10* (0.01) 0.01 (0.03) 0.002 (0.01) 0.0017 (0.0011) 0.0003 (0.001) 0.002 (0.01) 0.002 (0.01) 0.004 (0.004) 40.60 (0.00) 10.85 (0.00)

0.04* (0.02) 0.00003 (0.01) 0.004 (0.004) 0.02* (0.003) 0.0003 (0.0003) 0.0002 (0.0004) 0.0001 (0.005) 0.01* (0.003) 0.0001 (0.002) 237.40 (0.00) –

Expect to reside with child

Other regressors Oldest son Other son First_d Age Age difference (father’s brother–child) Father’s age Father is oldest brother Father is youngest brother Father’s brothers (number) Regression F / Wald v2(Prob > F, v2) F test on instruments

0.012* (0.003) 0.001 (0.003) 0.02* (0.003) 0.0003 (0.0003) 0.0001 (0.0003) 0.001 (0.005) 0.01* (0.003) 0.001 (0.001) 250.67 (0.00) –

– –

Note: Sample size is 7628. Standard errors, clustered at the level of the village, in parentheses. Additional regressors: caste, mother and father’s education, agricultural land, father and mother’s parents land, school student teacher ratio, village population and households. * Significant at 5% level.

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A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

The first stage regression results reveals that a larger age difference between the father’s brother and the child reduces the probability of co-residence. This supports the hypothesis that, conditioning on the father’s age, an increase in the father’s brother age increases the profitability of contracting with the brother, and hence reduces the value of the inter-generational contract with the child. The regression results also suggest that households with fewer sons (indicated by the indicator variable first_d) reduces the probability of co-residence, but that this effect is smaller in households with a larger age difference between the father’s brother and the child, households who may be better able to contract with brothers for the purpose of life cycle consumption smoothing. However, many of these variables are statistically insignificant, raising questions regarding identification. I therefore turn to regression results that also condition on the total number of children and the ratio of sons to children. Incorporating fertility choices As discussed in the previous section, identification of these additional demographic outcomes is achieved by expanding the set of regressors to include indicator variables of the gender and order of the first two births. Correspondingly, the interacted variables that constitute the instrument set similarly replace first_d with these indicators.

Results from first stage regressions on expectations of co-residence, but also on the number of children and the ratio of sons, are reported in Table 8. F statistics on the joint explanatory power of the set of instruments, reported at the bottom of this table, confirm their statistical significance. The first column suggest that the probability of co-residence is again larger for oldest sons. As before, the probability of co-residence is greater in households in which the oldest son is likely to be the only son (dtr-dtr households), with an increase in the age difference between the father’s brother and the child in question reducing this probability. Conversely, households with a large number of sons (son–son households) are less likely to observe co-residence, and again the magnitude of this effect is reduced as the profitability of contracting with brothers increases. For oldest sons, as predicted, the probability that parents expect to co-reside with him is lower in households with many sons. Table 9 provides results from IV regressions. The first column presents results from a regression that includes the total number of children and the ratio of sons. The second column includes household savings, instrumenting this by the value of the household’s bank accounts. Results from language and mathematics test scores are presented in the last two columns. All regressions reveal a negative effect of co-residence on schooling outcomes, with the effect on attendance being statistically significant at the 5% level. The negative effect of co-residence on language test scores is also statistically significant, but at a 10%

Table 8 First stage regressions, expanded instrument set.

Instruments Oldest son * son–son * agediff Oldest son * dtr-dtr * agediff Other son * son–son * agediff Other son * dtr-dtr * agediff Son–son * agediff Dtr-dtr * agediff Son–son Son-dtr Dtr-dtr Other regressors Oldest son Other son Age Age difference (father’s brother and child) Father is oldest brother Father is youngest brother Father’s brothers (number) Regression F F test on instruments

Expect to reside

Number of Kids

Ratio sons

0.01* (0.001) 0.001 (0.001) 0.002* (0.0008) 0.003* (0.001) 0.002+ (0.001) 0.001 (0.001) 0.09* (0.04) 0.017 (0.012) 0.04 (0.04)

0.03* (0.004) 0.01* (0.002) 0.04* (0.004) 0.03* (0.01) 0.04* (0.01) 0.001 (0.001) 0.41* (0.16) 0.002 (0.04) 0.47* (0.19)

0.01* (0.0004) 0.004* (0.0003) 0.002* (0.0003) 0.004* (0.0005) 0.003* (0.001) 0.001+ (0.0006) 0.30* (0.02) 0.001 (0.004) 0.28* (0.02)

0.49* (0.02) 0.15* (0.02) 0.002 (0.01) 0.0003 (0.001) 0.0002 (0.01) 0.001 (0.01) 0.004 (0.004) 39.19 (0.00) 25.70 (0.00)

0.26* (0.04) 0.64* (0.07) 0.03 (0.03) 0.01 (0.01) 0.12* (0.05) 0.06 (0.04) 0.06* (0.02) 55.63 (0.00) 57.05 (0.00)

0.04* (0.004) 0.18* (0.01) 0.01* (0.003) 0.0004 (0.0004) 0.00002 (0.001) 0.0001 (0.005) 0.00002 (0.001) 687.97 (0.00) 1089.35 (0.00)

Note: Standard errors, clustered at the level of the village, in parentheses. Additional regressors are listed in the note to Table 7. * Significant at 5% level. + Significant at 10% level.

21

A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23 Table 9 IV regressions, expanded instrument set. Variables Endogenous regressors Parents expect to reside with this child Total children Ratio sons Savings Other regressors Oldest son Other son Age Age difference Father’s age Father is oldest brother Father is youngest brother Father’s brothers Wald v2

Attendance

Attendance

Language

Mathematics

0.07* (0.02) 0.01* (0.005) 0.03+ (0.01) –

0.06* (0.02) 0.01* (0.006) 0.02 (0.01) 0.0002 (0.0002)

7.72+ (4.09) 1.36 (1.00) 3.67+ (2.06) 0.09* (0.03)

4.70 (4.13) 1.03 (1.02) 1.98 (2.09) 0.09* (0.03)

0.03* (0.01) 0.01 (0.01) 0.02* (0.003) 0.0004 (0.0003) 0.001 (0.0004) 0.001 (0.01) 0.01* (0.003) 0.0005 (0.005) 241.24 (0.00)

0.02* (0.01) 0.002 (0.01) 0.02* (0.004) 0.0003 (0.0003) 0.001 (0.0004) 0.001 (0.005) 0.01* (0.004) 0.00003 (0.002) 216.10 (0.00)

1.06 (2.11) 3.20 (1.48) 0.14 (0.59) 0.04 (0.06) 0.22* (0.08) 0.49 (0.77) 0.56 (0.64) 0.34 (0.23) 328.60 (0.00)

0.45 (2.12) 0.41 (1.40) 0.98 (0.77) -0.02 (0.05) 0.07 (0.08) 1.22+ (0.74) 0.35 (0.62) 0.46 (0.28) 53.64 (0.00)

Note: Standard errors, clustered at the level of the village, in parentheses. Additional regressors are listed in the note to Table 7. * Significant at 5% level. + Significant at 10% level.

level of significance. The effect on mathematics scores, though negative, is smaller in magnitude and not statistically significant.11 The estimates from the first regression, evaluated at the mean values of the variables, suggests that a 10% increase in the probability of co-residence reduces the proportion of school days attended by 0.16%. This estimate is reduced marginally in regressions that include household savings, to 0.13%. This reduction supports the hypothesis that demographic variables also help predict current constraints and income, and the necessity of allowing for this, particularly in regressions on test scores. The estimates for language and mathematics test scores suggest that a 10% increase in the probability of co-residence reduces language test scores by 0.4% and mathematics scores by 0.2%. The results also reveal that the total number of children reduces attendance, suggestive of a quality-quantity tradeoff. The coefficient of the ratio of sons to total children is also negative, but not statistically significant. A similar trade-off between quality and quantity is suggested in the regressions on language test scores. Standard over-identification tests on the indicator variables for son–son, son-dtr and dtr-dtr, presented in Table 10, confirm their validity as instruments: F tests for these variables, when included in pairs as independent regressors, confirm their joint insignificance. That is, the regressions suggest that the gender and birth order of the first two births affects schooling investments only through their effects on the set of endogenous variables. Even removing these variables from the set of instruments, expectations of co-residence have a negative effect on attendance, though the effect is smaller in magnitude and not statistically significant when the indicator variable dtr-dtr is not included in the instrument set. For comparison, Table 11 provides similar estimates from OLS regressions. This comparison suggests that the bias in regressions 11 In general, there is much lower explanatory power for the regression on mathematics test scores, reflecting the greater variability in these scores.

on both attendance and test scores from ignoring the endogeneity of expectations of co-residence is positive, in that the coefficient on expected co-residence in OLS regressions is smaller in magnitude and very close to zero. As previously discussed, one reason for this could be that parents are most likely to cite the son they have the greatest affinity with as the one they expect to reside within old age. Controlling for observed covariates, they might then also be expected to favor this child in schooling and other investments. Conclusion The question of how familial systems of support endure, and their effect on family outcomes, has long been of interest to researchers. This paper examines one such system: the dependence of elderly parents on their children for support in old age, and, specifically, the expectation that they will reside with their adult children. It has long been assumed that this is one factor explaining son preference in countries such as India, and hence observed high fertility rates. And, though such arrangements are widely believed to affect parental investments in their children’s schooling, different theoretical models deliver different predictions regarding the sign of this effect. This paper first develops a theoretical framework that suggests that, allowing for the probability of default on inter-generational contracts, parental dependence on children for old age support has an ambiguous effect on their schooling; it depends on how schooling affects life cycle income profiles. The empirical analysis explores the effect of parents’ child-specific expectations of co-residence on schooling attendance and test scores, treating expectations of co-residence as endogenous. I identify the effect of expectations of co-residence by building on the theoretical prediction that they reflect the difference in the interest rate on the inter-generational loan relative to that obtained in autarky, as well as the variation in probabilities of

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A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

Table 10 Over-identification tests, dependent variable: Attendance. Endogenous regressors

(1)

Parents expect to reside with this child Total children Ratio sons Savings Other regressors Son–son Son–daughter Daughter–daughter Oldest son Other son

Age Age difference Father’s age Father is oldest brother Father is youngest brother Father’s brothers Wald v2 Over-identification test F

(2) *

–0.06 (0.03) 0.01+ (0.006) 0.02 (0.018) 0.0002 (0.0002)

0.04 (0.034) 0.013* (0.006) 0.001 (0.02) 0.0002 (0.0001)

0.002 (0.008) 0.002 (0.004) –

–

0.02+ (0.013) 0.003 (0.01)

0.003 (0.004) 0.009 (0.009) 0.012 (0.018) 0.005 (0.01)

0.02* (0.004) 0.0003 (0.0003) 0.001 (0.0004) 0.001 (0.005) 0.01* (0.004) 0.0001 (0.002) 221. (0.00) 0.20 (0.90)

0.02* (0.004) 0.0004 (0.0003) 0.001+ (0.0004) 0.001 (0.005) 0.01* (0.004) 1.9 e6 (0.002) 225.74 (0.00) 1.24 (0.54)

Note: Standard errors, clustered at the level of the village, in parentheses. Additional regressors are listed in the note to Table 7. * Significant at 5% level. + Significant at 10% level. Table 11 OLS regressions. Variables Parents expect to reside with this child Total children Ratio sons Savings Oldest son Other son Age Age difference Father’s age Father is oldest brother Father is youngest brother Father’s brothers Regression F

co-residence with different children. The latter reflects the birth order of different sons but also, importantly, the number of sons in the household. Predicting this by the gender of the first two children, I use triple interactions for indicators of oldest (and youngest) sons, indicators for the gender ordering of the first two births, and measures of the profitability of the inter-generational contract based on the age of the father’s brother and the child as identifying variables. The identification strategy is enabled by a rich data set that provides data not just on the household in question, but on schooling outcomes for the index child, and information on the demographic characteristics of the father’s siblings. I address concerns that the demographic outcomes that are incorporated in identifying variables directly predict the total number of children and the number of sons, variables that in turn are likely to independently affect schooling outcomes, by implementing regressions that include these variables. I also report results that allow for the possibility that expectations of future co-residence affect savings not because they enable consumption smoothing over the life cycle but because the set of instruments may also predict current credit constraints and income. As is always the case in the case of instrumental variables, the results of this paper are conditional on the validity of the instrument set. Under the assumption that the exclusion restriction holds, the empirical analysis of this paper supports the hypothesis that expectations of old-age support reduce investments in children’s schooling. It thus suggests that the lack of formal markets that provide long-term consumption smoothing, and the consequent need to rely on children for the same, comes at a cost. Though social arrangements enable households to overcome market failures, they do so by reducing investments in children’s schooling and hence the incomes of future generations. Appendix A Proof of Proposition 1. I ignore any effect of schooling on first stage income.12 First, consider the case when schooling only increases second stage income (yt+2). Under the assumption that incomes increase monotonically with schooling, the sign of

Attendance 0.003 (0.004) 0.01* (0.002) 0.005 (0.006) 0.00002 (0.00001) 0.002 (0.004) 0.01* (0.005) 0.02* (0.004) 0.0004 (0.0003) 0.0005 (0.0004) 0.0004 (0.005) 0.012* (0.003) 0.0004 (0.001) 10.55 (0.00)

Language 2.00* (0.91) 0.77* (0.34) 1.34 (1.23) 0.004 (0.02) 3.66* (0.81) 4.90* (1.01) 0.39 (0.59) 0.03 (0.06) 0.18* (0.07) 0.45 (0.74) 0.59 (0.63) 0.31 (0.22) 14.62 (0.00)

Mathematics 0.96 (0.97) 0.30 (0.38) 0.65 (1.21) 0.007 (0.02) 0.79 (0.85) 1.47 (0.95) 1.21 (0.77) 0.02 (0.05) 0.003 (0.06) 1.06 (0.72) 0.32 (0.62) 0.38 (0.26) 2.01 (0.004)

Note: Standard errors, clustered at the level of the village, in parentheses. Additional regressors are listed in the note to Table 7. * Significant at 5% level.

therefore determined by that of

@Rtþ2 tþ1 , @ytþ2

@Rtþ2 @htþ1

is

in turn given by the equilibrium

condition (11). Differentiating (11):

dRtþ2 tþ1 dytþ2

@btþ1 tþ2

¼

@ytþ1 tþ2 @bttþ2 @Rtþ2

ðA1Þ

@btþ1

 @Rtþ2 tþ2

Eq. (A1) results because the son’s peak earnings ðytþ1 tþ2 Þ do not t

directly influence the father’s loan supply decision ðbtþ2 Þ. Thus, the numerator on the right hand side of (14) comprises only the effect of the son’s income on the loan he demands from his father tþ1

when he is young ðbtþ2 Þ. Under standard regularity conditions, the denominator of (A1) is positive. Therefore, the sign of hence

dRtþ2 dhtþ1

dRtþ2 dytþ1 tþ2

, and

, will be positive if the son’s demand for loans increases

with his income when middle-aged. Suppressing the super-script for generation t for notational t tþ1 simplicity (so that btþ1 ¼ btþ1 ¼ btþ2 , the effect of incomes on loan demands, and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by:

12 Even if schooling did increase first stage income, due to the likelihood of default, changes in first stage income have no effect on young adults’ demand for loans from their parents. Intuitively, the inability to enforce the contract implies binding credit constraints on first period loan demands. Conversely, changes in second period income (and consumption) affect the probability of default and hence the constraint itself.

A. Kochar / The Journal of the Economics of Ageing 4 (2014) 8–23

@btþ1 Rtþ1 u0 ðctþ1 Þ ½½u00 ðctþ1 Þ þ bu00 ðctþ2 ÞR2tþ2 ½u0 ðctþ1 Þ  u0 ðcatþ1 Þ ¼ @ytþ1 j Aj ðA2Þ 13

catþ1

where ¼ ytþ1 is autarkic consumption and |A|<0. Since l2=0, u(ct+2) > u(yt+2). This inequality, in conjunction with l1 > 0, implies that u(ct+1) < u(yt+1), because (6) is now a strict   inequality. Consequently, u0 ðctþ1 Þ > u0 ytþ1 , which in turn implies that

@btþ1 @ytþ1

> 0. Thus, schooling increases the interest rate on loans

between (adult) children and their parents. Now allow schooling to also increase third-stage income. With this,

dRtþ2 tþ1

dh

@ytþ1 @btþ1 tþ2 tþ2

tþ1 @ytþ1 @Rtþ2 @ytþ1 @Rtþ2 @ytþ3 tþ2 ¼ tþ1 þ tþ1 ¼ tþ2 tþ1 tþ1 @ytþ2 @h @ytþ3 @h

tþ1 @btþ1 @ytþ3

@htþ1

tþ2 þ @ytþ1

@bttþ2 @Rtþ2

@btþ1 tþ2 @Rtþ2

tþ3



@htþ1

ðA3Þ

In turn, and once again ignoring generational subscripts,

i

 i @btþ1 Rtþ1 u0 ðctþ1 Þ h h 00  u ðctþ1 Þþbu00 ðctþ2 ÞR2tþ2 u0 ðctþ2 Þu0 catþ2 ¼ @ytþ2 j Aj ðA4Þ As before,

catþ2

¼ ytþ2 is autarkic consumption in old age. Since  

l2=0, u(ct+2) > u(yt+2), and. u0 ðctþ2 Þ > u0 ytþ2 which in turn implies that

@btþ1 @ytþ2

< 0. Thus, while schooling induced increases in second

stage income increase interest rates, similar increases in third stage incomes lower interest rates. Allowing for schooling to increase both second and third stage incomes, the overall effect on interest rates is given by:

dRtþ2 tþ1

dh

" ¼M

tþ1

0   @ytþ1

0   @ytþ1 tþ2 tþ3 0 a u ðctþ2 Þ  u0 catþ2 þ u ð c Þ  u c tþ3 tþ3 tþ1 tþ1 @h @h

#

ðA5Þ where

M tþ1 ¼

ii Rtþ2 u0 ðctþ2 Þ h h 00  u ðctþ2 Þ þ bu00 ðctþ3 ÞR2tþ3 j Aj

tþ2 Thus, the sign of dR depends on whether the value of the interdhtþ1 generational contract, relative to autarky, is greater in the second or third stage of the life cycle, and on the schooling gradients in these two stages. h

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13

jAj ¼ Rtþ1 u0 ðctþ1 Þ½bu0 ðctþ1 Þu00 ðctþ1 ÞRtþ1 Rtþ2  bu00 ðctþ2 Þu0 ðctþ1 ÞRtþ1 R2tþ2  < 0

23

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