Under-investment of Parents in China in
Their Children’s College Education
Jerry(Jiyuan) Wang
∗Department of EEF, University of Groningen
July 31, 2016
Abstract
This paper tries to answer the question why many parents in China do not invest in their children’s college education. The theoretical framework adopted in the paper is the two-period setting proposed in Raut and Tran (2005) who assume the parents decide to invest in their children’s education in the first period and the children decide to transfer money to their parents in old age due to two-sided altruism. The framework consists of two types of models: “the parents as dictator” model and “the children have bargaining power” model. However, the models cannot explain why many parents do not invest in their children’s college education. Therefore we extend the model and propose three candidate reasons for the corner solutions of the children’s college education at household levels. Firstly, the corner solutions might be caused by the absence of altruism from the parents or the children. Secondly, it could be the reason that the fixed costs of sending children to college is substantial. Thirdly, the parents might be liquidity constrained in their earlier ages so that they cannot support their children to finish the study. By using the CHARLS (China Health and Retirement Longitudinal Study) 2013 data set which has a more precise measure of college educational investment than the one in Raut and Tran (2005), we test the three reasons above. Evidence shows that: firstly, similar to Raut and Tran (2005),“the children have bargaining power” model is empirically supported. Secondly, the reasons of absence of altruism and the existence of fixed costs are plausible in explaining the corner solutions while no clear evidence supports the reason of liquidity constraint.
Keywords: Two-sided Altruism; Fixed Costs; Liquidity Constraint ; Household behaviour; China Health and Retirement Longitudinal Study
JEL classification: C35, D12, J14
∗I gratefully acknowledges my supervisors, prof. Dr. Rob Alessie and Dr. Viola Angelini, for their
1
Introduction
Human capital investment is thought to be a strategically important element laying founda-tion for economic growth and improving the welfare of a nafounda-tion. As for households, investing in human capital on the new generation by the old one might also enhance the welfare of a household, see Schultz (1961). The mechanism behind this investment behaviour has been intensely studied in Laferr`ere and Wolff (2006). The motivation of the investment could be explained in two respects. Human capital investment on children, as a candidate financial instrument, acts actively in a household’s portfolio decision. As its name implies, human capital investment, as an investment instrument, yields future profits, therefore parents in the household have incentive for children’s human capital investment, see Cigno (1993). Oliveira (2015), for instance, shows that the parents’ old-age support is strongly affected by fertility decisions, which means that the children are regarded as sources of transfers and care-taking. Alternatively, investment behaviour originates from the parents’ altruism. Intuitively, the parents care for their children’s well-being, and investment on education is a way to increase the children’s future earnings and life satisfaction, see Becker (1974). Some parents could be at the two extrema, i.e. purely motivated by the financial property of the human capital investment or purely motivated by their altruism, while most of the parents stay in between, i.e. they have both altruistic and strategic concerns.
The role of human capital investment has an impact on public securities choices, i.e. the future return on human capital investment crowds out the public transfers (see Barro (1974)). Therefore, it can be reasoned that the private transfers, generated by the human capital investment, will dominate the position of public transfers, for example pension, in those economies lacking public transfers, see Cai et al. (2006). Hence households in devel-oping countries might care more about the children’s human capital investment. Moreover, educational investment is thought to be one of the most profitable instruments compared to other financial instruments. For example, in Figure 11, data from US reveals this
ad-vantageous investment channel. Compared to other instruments, investing on education brings much higher rate of return. However, it is important to further investigate the rate
1Data Source: http://www.hamiltonproject.org/charts/returns_to_education_compared_to_
of returns on education in developing countries, especially in China. Zhang et al. (2005) show that the rate of returns to education in China was influenced by the institutinal re-forms and they obtain an estimate that the returns change from 4 % in 1988 to 10.2 % in 2001 in which most of the rise after 1992 attributes to the increase of the retuns in higher education. The estimated rate of returns in Li and Luo (2004) is 15%, which is much higher than other estimates in previous literature. All the estimates of rate of returns reveal the fact that human capital investment, especially higher education investment, has the rate of returns which other financial instruments cannot achieve.
Figure 1: Returns to Education Compared to Other Investment
Compared with the dramatic growth rate of overall human capital stock in other countries, China shows substantially low tertiary education stock and growth. Given the fact that China has a large proportion of population which is not covered by the public pension, the human capital investmenst should have been comparatively larger. Even if neglecting the Cultural Revolution period (1966-1976) when the Chinese education system was sus-pended, there is still small positive growth, even negative growth of college education in China in the following decades. Therefore, it is of interest to learn what happened when individuals were making choices in China. Were the school drop-outs for direct working so tempting that the college education is undervalued? Or the individuals in an economy were so poor that, even though the investment is profitable, they were liquidity constrained? Or the investors, i.e. parents, were not altruistic at all, such that they outweighed the private savings and just gave up investing?
Table 1: The Tertiary Average Years of Schooling Across Countries
Stock Growth Country Name 1970 1975 1980 1985 1990 1995 2000 2005 2010 1970-1975 1975-1980 1980-1985 1985-1990 1990-1995 1995-2000 2000-2005 2005-2010 China 0.34 0.37 0.4 0.61 0.82 1.33 1.89 1.88 1.79 0.03 0.03 0.21 0.21 0.51 0.56 -0.01 -0.09 Japan 2.58 4.29 6.19 8.09 9.77 11.04 12.56 14.1 15.18 1.71 1.9 1.9 1.68 1.27 1.52 1.54 1.08 Korea 2.19 2.64 3.52 4.85 6.27 8.42 11.68 13.72 19.36 0.45 0.88 1.33 1.42 2.15 3.26 2.04 5.64 India 0.53 0.68 0.93 1.29 1.66 2.42 3.15 3.49 3.89 0.15 0.25 0.36 0.37 0.76 0.73 0.34 0.4 Vietnam 0.32 0.38 0.42 0.74 1 1.36 1.8 2.4 2.82 0.06 0.04 0.32 0.26 0.36 0.44 0.6 0.42 Singapore 0.85 1.13 1.38 1.4 1.27 4.49 7.24 8.07 17.67 0.28 0.25 0.02 -0.13 3.22 2.75 0.83 9.6 Indonesia 0.13 0.2 0.22 0.54 0.76 0.9 1.01 1.89 2.81 0.07 0.02 0.32 0.22 0.14 0.11 0.88 0.92 United States 9.49 11.86 13.48 16.24 18.6 18.98 21.01 21.9 24.35 2.37 1.62 2.76 2.36 0.38 2.03 0.89 2.45 Germany 1.46 2.71 3.69 4.5 6.03 7.33 8.29 8.62 10.57 1.25 0.98 0.81 1.53 1.3 0.96 0.33 1.95 Brazil 0.93 2.18 1.92 2.13 2.36 2.66 3.02 3.27 4.71 1.25 -0.26 0.21 0.23 0.3 0.36 0.25 1.44 Pakistan 0.6 0.72 0.85 0.98 1.13 2.1 3.19 2.87 2.86 0.12 0.13 0.13 0.15 0.97 1.09 -0.32 -0.01 Data is collected from World Bank database: Education Statistics: Education Attainment. Series Name: Barro-Lee: Average years of tertiary schooling.
absence of altruism, the existence of fixed costs and the liquidity constraint faced by the parents. Empirically, we employ a novel data set, CHARLS (China Health and Retirement Longitudinal Study), to test the models. In this data set, a more precise measure of human capital investment is employed, i.e. the exact amount the parents have invested on their children’s college education, compared to the measure employed in Raut and Tran (2005) which is the children’s educational attainment using the Indonesian Family Life Survey (IFLS) data .
The rest of the paper is organized as follows: we first summarize the literature on this topic in section 2. Then the theoretical aspects are covered in section 3. In section 4 we propose our econometric implementation strategy. In section 5 we show our estimation results; then we conclude the paper in section 6.
2
Literature Review
children transfer money to their parents in old age. The reciprocity, or two-sided altru-ism in some literature, for instance, is more preferable since it has more realistic feature (Bergstrom (1989)) and delineates complete intergenerational relationship (Cox and Stark (1996)). However, diversified altruistic patterns exist because of many reasons, such as culture, social norms, community organizations, see Cox and Stark (1996).
countries might reveal some compensating effect of the transfers from the intergenerational relationship in the world with less developed institutions, and Raut and Tran (2005) is a good example. For the case of China, Oliveira (2015) conducts research on whether the fertility decisions affect the inter-generational transfers employing CHARLS data set. The research shows that the number of children affects the intergenerational transfers substantially revealing the importance of the role of parents’ expectation on children’s support. However, the paper does not discuss what drives the children to make transfer decisions. The discussion continues and in this paper we employ the framework of Raut and Tran (2005), detouring the discussion merely on whether altruism induces transfers per se, instead, to test more alternative ways to explain why many households do not invest on children’s college education.
induces the sub-optimal investment on children’s human capital, suggested by Barham et al. (1995). Smilar arguement can be found in Cox (1990) and Keane and Wolpin (2001).
Combination between the altruism and human capital investment provides a route to understand this mechanism. We are going to justify not only the roles of absence of altruism and the liquidity constraint, but also the role of fixed costs faced by the parents on being devoid of the human capital investment on children.
3
Theoretical Models
3.1
Basic models
The models are based on Raut and Tran (2005), which study the two-sided altruism in a two-period context. Basically, two kinds of agents are involved: the parents and the children. Each parent’s utility function is
u(cp1) + β[u(cp2) + γpu(ck2)], (1)
where cp1 and cp2 are the consumption levels of the parents in the first and the second
period, respectively. The altruistic parent cares for the child’s well-being by augmenting the child’s utility u(ck2) in hers, where the parents’ altruism is parsimoniously captured in
a single parameter γp. The felicity function of the parent in the first period is u(cp1) and β
is the time discount factor, with 0 < β < 1. Here we assume not only the linearity, but also the homogeneity of the utility functions of parent and children across periods. In addition, the utility over consumption is assumed to be of logarithm form, i.e. u(x) = α ln(x), where α is the preference parameter.
Similarly, each altruistic child has the utility
u(ck2) + γku(cp2), (2)
where γk is the child’s altruism. Same to Raut and Tran (2005), we assume that γp is
increasing with the number of children while γk is decreasing with the number of children.
The parent can invest in the child’s human capital with the amount T1 in the first
period and in the second period, the child can transfer T2 to the parent for her old-age
consumption. The adult children earn income Ek2 which is a function of the investment
T1 and the child’s talent τ2 and this function obeys the rule of diminishing rate of return3.
The parent earns Ep1 and Ep2 in each period respectively.
The parent has n children and in the first period she has to choose how much to consume cp1 (or save s) and how much to invest in the human capital of her children nT1. Then the
parent faces the following budget constraints:
cp1+ nT1+ s = Ep1 (3) cp2 = (1 + r)s + nT2+ Ep2, (4) or cp1+ cp2 1 + r = Ep1+ Ep2 1 + r + nT2 1 + r − nT1 ≡ Υ(T1, T2), (5)
while the budget constraint of each child is
ck2 = Ek2(T1, τ ) − T2. (6)
From Equation (3) it can be seen that fertility decision is assumed to be exogeous and in Equation (4) we also assume that the parents have no bequest motives.
In addition, the parents might face a liquidity constraint at the first period s = Ep1− nT1− cp1,
where the private saving s cannot be negative. It means that the parents cannot borrow money from the future. We will assume the liquidity constraint not binding for simplicity for the moment, but we will investigate into the case where liquidity constraint is binding in depth in section 3.5.
As Raut and Tran (2005) do, we consider two cases: the one in which the parent has all the bargaining power and the one in which children are granted some bargaining power in the second period.
3.1.1 Parent as dictator
In the first model, the child has no bargaining power, and the parent decides the whole pack-age (T1, T2, s), or equivalently, (T1, T2, cp1, cp2). Then the optimization problem becomes
maximizing Equation (1) under restrictions (5) and (6) and the participation constraint of the child:
u(Ek2(T1, τ ) − T2) + γku(cp2) ≥ u(Ek2(0, τ )) + γku(cop2), (7)
where co
p2 is the consumption level that the parent would choose if she did not make the
educational transfer (T1) to her child. Raut and Tran (2005) assume that the parent’s and
the children’s altruism is high enough to keep (7) not binding, while this argument deserves explicit elaboration, as we will show in section 3.3. Regarding T2, the paper permits it to
be negative.
We first study the basic case where the child’s participation constraint and liquidity constraint are not binding and the parent is altruistic. Since in this model, the children have no bargaining power so if the children’s participation constraint is not binding, then whether children are altruistic or not (γk = 0 or γk> 0) does not change the predictions of
the model. We first derive the optimal demand return of human capital investment which can be seen in Equation (8), whose full derivations of the model are presented in Appendix A.1 and in this case:
∂Ek2(T1, τ )
∂T1
= (1 + r). (8)
This result means that the parent claims, in optimum, the return of human capital invest-ment must be equal to the market interest rate. Actually this result is commonly accepted since if the marginal rate of return on human capital investment (or the social rate of hu-man capital investment) is equal to the market rate, then the market is in equilibrium as no arbitrage is profitable any more, see Barham et al. (1995) for example.
In addition, we can obtain the optimal transfer decision T2:
T2∗ = 1 1 + αβγp Ek2+ (1 + r)αβγp 1 + αβγp T1− (1 + r)αβγp (1 + αβγp) · " Ep1+1+rEp2 n # , (9)
bargaining power. The positive sign of the children’s income on the transfer decision implies that the higher income of the children, the more transfers the parents will claim from them; and the more altruistic the parents are, the less transfer the parents will claim since they care more about the children’s consumption. Therefore, this term can be regarded as the pure effects of altruism. The second term in Equation (9) is the combination of altruistic and strategic concerns. The more human capital investment the parents made enables the parents to claim more on future transfers; and the more altruistic the parents are, the larger the coefficient is, hence the larger the increase of the transfer ex post is, given an extra unit of human capital investment ex ante. Intuitively, if the parents are more altruistic, they will value more the human capital investment on their children. The final term reveals that the more wealthy the parents are, the less the parents will ask from their children.
All the results discussed above are under the assumption that the parent is more or less altruistic such that she will invest certain amount to keep the children’s participation constraint not binding. If the parent is not altruistic at all (γp = 0), then the participation
constraint of the children will be binding, and we will discuss this case in section 3.3.
3.1.2 Child with Bargaining Power
In this model, we grant children some bargaining power in period 2 and therefore the par-ticipation constraint is not relevant. This implies that the optimization problem becomes a sequential optimization problem and the detailed derivations are summarized in Appendix A.2. The parent maximizes (1) with respect to T1, cp1 and cp2, and the children maximize
(2) with respect to T2, and implicitly ck2. Similar to the first model, we can obtain the
marginal rate of return on human capital investment in Equation (10) ∂Ek2(T1, τ )
∂T1
= 1 + r γpγk
, (10)
Because of imperfect altruism (0 < γp < 1 and 0 < γk < 1), this optimal demand of return
T1 T2 Ek2(T1, τ ) −Ek2(0, τ ) O ∂Ek2 ∂T1∗ = (1 + r) ∂Ek2 ∂T∗∗ 1 = (1+r) γpγk Ek2(T1∗, τ ) − Ek2(0, τ ) T1∗ T1∗∗ Ek2(T1∗∗, τ ) − Ek2(0, τ ) U nder − Investment
Figure 2: Parent’s Expected of Rate of Returns on Human Capital Investment only due to the imperfect altruism from children, but also due to the parents’ imperfect altruism. To see this, keeping γp unchanged, suppose γk decreases, we will find the
invest-ment is still less than T1∗but larger than T1∗∗. There are two things which should be noticed. Firstly, the earnings function in Figure 2 follows the law of diminishing rate of return, so that the rate of investment return are declining as investment increases. Secondly, the rate of return at point O should be a finite number instead of infinity such that corner solutions are allowed. We will discuss this issue in detail in the next section.
Regarding γpγk, Raut and Tran (2005) argue that γpγkis monotonically increasing with
respect to the number of children. This argument is somewhat arbitrary thus we will try a more flexible form to allow for the nonlinear relationship between γpγk and the number of
children. More precisely, we assume that the increase of the altruism from parents are faster than the decrease of the altruism from children when the number of children in the family is less than a certain amount. That is to say, if the number of children in a family is small and the next child is born, the increase of the parents’ altruism is larger than the decrease of the children’s altruism; if the number of children is large and the next child is born, the increase of parents’ altruism is smaller than the decrease of the children’s altruism. Technically, the first derivative of γpγk w.r.t. the number of children is positive when the
larger than n∗. For those households with fewer children, the increasing proportion brought by γp dominates the decreasing proportion through γk , while for those households with
more children, the decreasing proportion through γk dominates the increasing proportion
brought by γp. We will test this hypothesis in the empirical section.
Following a similar procedure, we can obtain the transfer Equation (11):
T2∗ = γk αβ + γk Ek2+ (1 + r)αβ γk+ αβ T1− (1 + r)αβ γk+ αβ "E p1+ E1+rp2 n # , (11)
where, contrary to the first model, the decision has only to do with the children’s altruism γk and does not depend on parental altruism γp. This implies that the power of the parents
has been weaken and they can only intervene through human capital investment decisions. Similar to the first model, we can find that: firstly, the higher the income of the children, the more money will be transferred to their parents; while the more altruistic the children are, the larger the coefficient of Ek2 is, which is contrary to the first model. Secondly, the
similar aspect to the first model is that the higher the human capital investment is, the higher transfers will be; while the difference is that the more altruistic the children are, the lower the coefficient is. This is because the children play the major role in deciding the transfers in this model. Thirdly, also similar to the first model, the wealthier the parents are, the less will be transferred. But the difference is that this time it is the children who evaluate the wealth profiles of the parents, not the parents themselves.
Before we dive into the exploration of the failures of human capital investment, it is worthwhile to first clarify the earnings function, which yields the supply side of the rate of return on human capital investment.
3.2
Earnings function of E
k2Raut and Tran (2005) have made the strong assumption that the first derivative of Ek2
with respect to T1 follows the Inada conditions. This assumption is too strong to survive
human capital investment has the following properties: lim T1→0 ∂Ek2(T1, τ ) ∂T1 = ∞ lim T1→∞ ∂Ek2(T1, τ ) ∂T1 = 0,
which implies no corner solutions should exist for T1 in the first model4, because if the
parent invested nothing, she would get an infinitely larger rate of return if she could have invested a bit more. Therefore, corner solutions should not occur. Intuitively, it does not fit the reality, which simply shows that many individuals actually invest nothing on human capital. Therefore, it is more plausible to have an earning function that can encompass corner solutions, while still following the law of decreasing marginal rate of returns. Raut and Tran (2005) do not take that into account partially because they use the children’s educational attainment as a proxy for the human capital investment. However, it becomes a problem when we consider more precise proxies such as the exact amount of investment. Without loss of generality, we assume that the earnings of the children is of double logarithmic form over T1 and the children’s talent is introduced linearly in to the earnings
function, i.e.
ln(Ek2) = E0+ a ln(1 + T1) + bτ, (12)
where E0 is the naturally endowed income, representing the income a child would get if he
have received no education and is under the smallest intellectual level, i.e. τ = 0. It can be seen that the corner solutions of human capital investment are allowed in this specification. In addition, to maintain the concavity of the earnings function over T1, the value of a
should be within 0 and 1. The positive sign before the last term represents that the higher talent of children yields higher income.
Based on this specification, we have the marginal return of human capital investment as ∂Ek2(T1, τ ) ∂T1 = aEk2 1 + T1 , (13)
thus when T1 is 0, the marginal return of human capital investment is related to the
income and no longer goes to infinity. Equating the supply side and the demand side of
4In the second model, the conditions need not to be specified when γ
p= γk= 0, as we will show in the
this investment, i.e. Equation (13) and (8) or (10), we have aEk2 1 + T1 = (1 + r) (14) in model 1 and aEk2 1 + T1 = 1 + r γpγk (15) in model 2. Based on this, we can test which model is preferable through testing the significance of the number of children in Equation (14) and (15), since γpγk is a function
of the number of children.
In the following three sections, we will examine the corner solutions. We first examine the case where altruism is absent. As a by-product, it produces the models with single-sided altruism or non-altruism and we can genralize the models, encompassing the models such as Cox (1987) and Alessie et al. (2014). Secondly we introduce the fixed costs, and finally we discuss the case with liquidity constraint.
3.3
Absence of Altruism
The results (8) - (11) are under rather strict assumptions. The first assumption the models make is the strictly positive property of the altruistic parameters, i.e. γkand γp. Under this
assumption, it is understandable that the parents and the children care about each other’s well-being then, as the models predict, the parents invest on their children’s human capital and the children transfer money to their parent at later stages. However, arguably, those kind of behaviors might also occur because of strategic motives of parents, as argued by Cox (1987) and Alessie et al. (2014). That is to say, the parents invest on children’s human capital because this investment yields future revenue, and the transfer decisions made by the children could either come from the dictator parents or be the results of bargaining. Therefore, as Raut and Tran (2005) want to justify, the investment and transfer happen only because there is reciprocity or just a pure loan contract “signed” by the parents and their children.
failure of human capital investment on children the parents should be blamed, or both characters should be responsible for those undesired results. We study in detail this issue by investigating through the two different models, i.e. the “parent as dictator” model and the “children have bargaining power” model. Within each model, we solve the models where certain characters are not altruistic at all. All the model solving details are shown in the Appendix B.
For the first model, as Raut and Tran (2005) argues, when the parents are non-altruistic, they will not invest at all and will take all the income of their children, which leads to the binding of children’s participation constraint, then the children’s altruism makes a differ-ence. While if the parents are altruistic, the altruism of the children is not important since the parents decide the whole package and they will not leave their children in desperation because of their altruism. The only case to be dealt with by the parents is to optimize the problem and, simultaneously, to keep her children from escaping. Therefore, if assuming γp > 0 and γk = 0, the solutions are exactly the same as Equation (8) and (9). Now suppose
only the parents are non-altruistic and the children are altruistic (γp = 0 and γk > 0), the
claimed rate of return on human capital investment is, still, ∂Ek2(T1, τ )
∂T1
= (1 + r) (16)
but the transfer decision is
lnEk2o − ln(Ek2− T2) = γk " ln αβΥ(1 + r) − lnco p2 # , (17)
where Ek2o = Ek2(0, τ ). Equation (16) implies that even if the participation constraint is
binding, the parent claims the human capital investment on children as much as the market rate. While Equation (17) is nonlinear, it provides a frontier such that at this frontier, the children would be indifferet between violating the contract made by the parent and not violating, from the parents’ point of view.
It would be more illuminating if we simplified this case by looking at the case where γk = 0 as well. In this scenario the optimal rate of return does not change but the transfer
T1 T2 Ek2(T1, τ ) T2 = T1(1 + r) −Ek2(0, τ ) O ∂Ek2 ∂T1∗ = (1 + r) Ek2(T1∗, τ ) − Ek2(0, τ ) T1∗ Choice Set
Figure 3: Transfer Decision in the Absence of Both Sides Altruism
found in Appendix B.2. In Figure 3, the best case for the parents now is to have the transfer equal to Ek2, but when they do like this, the participation constraint of the children will be
binding so they must choose an amount smaller than this. The worst case for the parents is the T1(1 + r) because if the future revenue is under this amount, it would be better to
invest on other instruments in the financial markets to get an profit of rT1 since the market
rate is defined as r. Therefore, the parents must choose in between. ∂Ek2(T1, τ )
∂T1
= (1 + r) (18)
Ek2(T1, τ ) − Ek2(0, τ ) > T2 > T1(1 + r) (19)
This result is different from the argument by Raut and Tran (2005) as they directly state that, when the children’s participation constraint is binding, T2 will become T1(1 + r),
while we show a feasible interval for investment. In addition, they obtain the result only when the parents are non-altruistic, while in our results, both children and parents are responsible for this, i.e. γp = γk = 0.
Another interesting result is that if the children are also non-altruistic, the parent experiences a consumption-smoothing pattern, as cp2 = β(1 + r)cp1, the same to the case
non-altruistic (participation constraint binding) and the children are altruistic, the parent will consume more, i.e. cp2 = β(1+r)cp1+θγk(1+r)cp1, where θ is the Lagrangian multiplier
of the participation constraint. This can be explained by the fact that the selfish parent happens to have nice children, and the tolerance level of the children is higher than those selfish children, which grants the parent more consumption in the second period.
Now we turn to the second model. In this model, the children decide the transfer amount to their parents. Therefore, it is a sequential Stackelberg game, and the whole derivations are given in Appendix B. When neither the parents nor the children are altruistic, i.e. γp = γk = 0, the amount of human capital investment and the transfer are both zero. This
is intuitive because this is a one-shot game, and the cold-hearted child would just keep his utility maximized and transfer nothing to his parent. In addition, the parent perfectly predicts this situation and decides to invest nothing in the first place. The prediction can be verified through the corner solutions of both T1 and T2, which will be discussed in the
empirical section. Similarly we can solve the case where only the child becomes altruistic and the parent is still cold-hearted, then the investment is still zero, but because of the child’s altruism, the parent receives some amount when she is old:
T2∗ = γk αβ + γk Ek2+ (1 + r)αβ γk+ αβ T1− (1 + r)αβ (γk+ αβ)n h Ep1+ Ep2 1 + r i , (20)
which is exactly the same as Equation (11).
Conversely, if the parent is altruistic while the child is not, then the old-age transfer decision is zero while the human capital investment is positive and the corresponding rate of return is ∂Ek2 ∂T1 = n(1 + r) γp ck2 cp2 , (21)
3.4
Existence of Fixed Costs
Now we introduce fixed costs in the parent’s budget constraint. The fixed costs mean that when the parent starts to invest on her children’s human capital, extra monetary costs would accompany. For instance, the parents have to provide better living conditions, transportation from home to school, and other material payments to ensure the children’s study. In addition, in some developing countries, sending children to school also yields numerous opportunity costs since the children would have been sources of household income if they directly went to work. Just as Jacoby (1995) argues, those children from wealthy families or with less opportunity costs of attending school will attend full-time for their entire educational careers. Therefore, the opportunity costs are valued with highest priority by most of the households. In the following modifications of the models employed above we will take these costs into account.
Hence, modified from Equation (5), the parent faces the budget constraint cp1+ cp2 1 + r + nT1 = Ep1+ Ep2 1 + r + nT2 1 + r − nC (22)
if she invests, where C is the fixed costs. Alternatively, she faces the budget constraint cp1+ cp2 1 + r = Ep1+ Ep2 1 + r + nT2 1 + r (23)
if she does NOT invest. cp1+ cp2
1+r and nT1 in model 1 (cp1 and nT1 in model 2) can be
regarded as two goods5, which can be shown in Figure 4. The solid line is the budget
constraint faced by the parent if she invests. V1, V2 and V3 are the imaginary indifference
curves that with different size of fixed cost concerned6.
To illustrate the effect of fixed costs, we first compare the points E and C. The two points are on the same indifference curve thus providing the same utility for the parent. Then the parent could be indifferent between investing or not, since at point E, the disutility brought out by fixed costs, i.e. C, is compensated by overall utility caused by altruism,
5Obviously, both goods are scaled to unit prices, so that the indirect utility functions will not be explicit
functions of prices any more.
6Arguably, the figure is problematic since the costs directly affect budget constraint merely. However,
i.e. E. Now suppose the costs are slightly higher, then the utiliy of not transferring, i.e. D, is higher than the utility of transferring, i.e. E. Therefore the parent will never invest. On the contrary, suppose the costs are slightly lower, the utility at B are lower than the utility at E, then the parent will definitely invest (or transfer).
Hence, the existence of fixed costs complicates this problem by allowing non-convex budget sets, see Hausman (1980). However, it now is merely two models, which could be distinguished if we solve them separately (For detailed derivations see Appendix C). Analogous to the basic model, the optimal transfer decisions are such that:
∂Ek2(T1, τ ) ∂T1 |T∗ 1 = (1 + r) (24) T2∗ = 1 1 + αβγp Ek2+ (1 + r)αβγp 1 + αβγp T1− (1 + r)αβγp (1 + αβγp) · n · Ep1+ Ep2 1 + r − nC , (25) if the parent invests in model 1. However, normally if we have neither proxies nor instru-ments to represent C, then this model cannot be identified, hence we cannot justify the existence of fixed costs, i.e. the opportunity costs of going to work directly. Nevertheless, we can still justify the fixed costs through the potential income of the children. To explain this, we assume that the opportunity costs of letting children go to school dominates other costs.
The potential income of each child can be defined as income of the child in the absence of a transfer from the parents, from Equation (12), when T1 = 0 we obtain:
ln(Epotential) ≡ ln(Ek2)|T1=0 = E0+ bτ, (26) where Epotential is exactly Ek2(0, τ ) in Equation (7), and the fixed costs are the opportunity
costs of getting transfer from children if they went to work directly:
C ≡ T2p = Epotential− cpk2, (27)
where cpk2 and T2p represent the child’s consumption and the transfer decision in the case where his parent did not invest at all. We first solve (1) in model 1 with restrictions (5), (6) and (22), then we have
Then by plugging Equation (28) into (22), and solving the model again, we have, T2∗ =h 1 1 + αβγp i Ek2+ h(1 + r)αβγp 1 + αβγp i T1+ h (1 + r)α2βγp (α + βγp)(1 + αβγp)n i Epotential−δ1 " Ep1+ Ep2 1 + r # , (29) where δ1 = h(1+r)αβγ p (1+αβγp)·n 1 + βγp(1+r) α+βγp i .
For model 2, it may become more complex since the corner solutions of T1 might also
be the result of the absence of altruism. However, since the motives for investing nothing might be the results of interaction of many causes, it is feasible to assume altruistic parent and children in this particular scenario. Then by solving the analogy of model 2, we have
C = γk αβ + γk Epotential− αβ(1 + r) n(αβ + γk) h Ep1+ Ep2 1 + r i (30) T2∗ =h γk αβ + γk i Ek2+ h(1 + r)αβ γk+ αβ i T1+ nγk αβ + γk (1 + r)αβ (γk+ αβ)n Epotential− δ2 " Ep1+ Ep2 1 + r # , (31) where δ2 = (1+r)αβ (γk+αβ)n 1 + (αβ+γαβ(1+r) k) .
The intuition of the positive sign of potential income is as follows: the parents make decisions ex ante taking not only the investment amount T1, but also the opportunity costs
into account if the children work directly. This consideration increases the relative price of the human capital and the larger the potential income is, the greater the fixed costs would be. “Compared to those parents who did not invest ex post, my parents must have made a braver decision”, the children who have received the investment might think. In addition, the more the potential income was, and the children transfer more not only because of altruism, but also because they are wealthier due to this investment.
Therefore, we can test the existence of fixed costs by testing the significance of the potential income in the transfer equations in either model.
3.5
Liquidity Constraint Binding
nT1 cp1+ cp2 1+r V1 V2 V3 A B C D E
Figure 4: Parent’s Choice with Fixed Costs
In previous research, for example Cox (1990), the liquidity constrained children receive transfers from their parents, however this is only true in developed economies since it has strong assumption that the parents are not liquidity constrained so that they can lend to their children. In developing countries, however, the parents might be liquidity constrained. In the following modifications of the models, we assume the parents are liquidity constrained.
Keeping other elements unchanged, we now add an extra liquidity constraint to the optimization problem:
s = Ep1− cp1− T1 ≥ 0, (32)
and its corresponding Lagrangian multiplier is denoted as µ. By solving the model again and whose detailed derivations can be found in Appendix D, we observe further under-investment on children’s human capital, namely
In addition, the transfer decisions T2 change as well. They are as follows: T2∗ = − β(1 + r) + (1 + r) + B (γp − 1)[β(1 + r) + B] − (1 + r) Ek2+ γp(1 + r)[β(1 + r) + B] n[(γp− 1)(β(1 + r) + B) − (1 + r)] (Ep1+ Ep2 1 + r−nT1) (35)
in model 1 where B = nβ(1 + r)[∂Ek2(T1,τ )
∂T1 − (1 + r)] and T2∗ = −1−γβ(1 + r) + A + (1 + r)) k γk (β(1 + r) + A − (1 + r)) Ek2+ (1 + r)(β(1 + r) + A) n(β(1 + r) + A)(1 − γk) − nγk(1 + r) (Ep1+ Ep2 1 + r−nT1) (36)
in model 2 where A = nβγpγk[∂Ek2∂T(T1,τ )
1 −
(1+r)
γpγk]. Both B and A are the rate of return gaps representing the premiums that the parents face when they encounter liquidity constraints. In specific, if the liquidity constraint was not binding for the parents, they would invest certain amount of money to keep the rate of return at (1 + r) or (1+r)γ
pγk. However, once the parents were liquidity constrained, they had to reduce the amount of investment to satisfy the consumption and saving plans, therefore the corresponding rate of returns higher than (1+r) or (1+r)γ
pγk and the gaps are the differences between the returns of the case with liquidity constraint and the one without liquidity constraint. It can be verified that if the gaps are zero, the results can be simplified to Equations (9) and (11).
The general idea is that, because of liquidity constraint, the parents are neither inclined to invest nor to consume at their earlier ages, which implies that the liquidity binding problems is also a cause for the absence of human capital investment. The challenge behind the results is the infeasibility of empirical testing on those results. Since it is difficult to justify the liquidity constraint through equations on T2 in this case, we will make use of
the extension on T1 instead.
As it shows in Equation (33) and (34), whichever model we choose, the marginal rate of return is always higher than the cases with no liquidity constraints. According to Equation (14) and (15), we can employ the following specifications:
aEk2 1 + T1 = (1 + r) + ck2µ αβγp(1 + r) (37) aEk2 1 + T1 = (1 + r) γpγk + cp2µ nαβγpγk . (38) Since ck2µ αβγp(1+r) and cp2µ
For convenience of the later empirical analysis, the summary of all the theoretical pre-dictions are listed in Table 10, Appendix E.
4
Empirical Analysis
4.1
Data and Descriptive Statistics
4.1.1 Data
The data set we use is the second wave of CHARLS (China Health and Retirement Longi-tudinal Study), namely the wave 2013. In this wave, 10,029 households with a head aged 45 and above participated, including 18,605 individuals. Compared to the first wave, this follow-up data is up-to-date and adds several important questions.
The sample is organized as the pair form of the main respondents and their children, and those households without children are not included in the sample. That is to say, we construct a child-level data set where each observation is a main respondent-child pair. The main variables in question are the human capital investment, old-age transfers, household wealth, parental income and the children’s current income. The human capital investment is obtained by asking the main respondent how much (s)he and his(her) spouse have invested on their child’s college education for each child in this household. The children less than 23 years old or still at school are not included in the sample since their parents might still be investing in their education. Alternatively, we have the children’s schooling to proxy the human capital investment, as Raut and Tran (2005) do. The old-age transfers are based on the question how much the couple received, in money or in kind, regularly or not regularly, from each of their children in the last year. Another possible and interesting alternative proxy for this variable is from the question asking the main respondents what they would like to rely on when they are old: children, pension or savings. We construct a dummy which is equal to one if the main respondents choose the children option, zero otherwise. The chidlren’s income is obtained by directly asking the parents how much each of their children earned last year.
and the pension income, but also the net farming (in a general sense, including fishing, forestry and livestock) income and net income from self-owned business. In addition, we also calculate household net financial wealth variable which subtracts the debt excluding the mortgage from the gross wealth terms as an important control variable. This wealth variable does neither contain durable goods nor housing. The reason why we exclude housing is that, for the generation in study, most of their houses are allocated by the government and they did not purchase them. The children’s income is directly obtained through the question that how much do each of them earn currently.
Worth noticing, we drop the observations less than 0.1% of the sample size who have extraordinary amounts in annual transfers, earnings or human capital investment men-tioned above. More precisely, more than 10,000,000 China yuans which is circa 1,525,553 US dollars are dropped. In addition, several social-economic variables are also constructed, and they are the numbers of children from both the main respondents and the children, their gender, the household registration types (Hukou)7, the marriage statuses of the main
respondents and their children, the ages of the individuals and the cohort dummies. We drop those observations which appears with unrealistic values, for example the age of the child is larger than his (her) father (mother).
Our final sample includes 23,551 observations and the descriptive statistics for all the variables included in our analysis are reported in Table 3.
4.1.2 Descriptive Statistics
Firstly, we observe the corner solutions of both human capital investment and old-age transfers in Table 2. It can be found that both transfers and investment variables have substantial corner solutions and it is more serious in the human capital investment case. The upper panel contains the observations where the children have no college education at all, and of course it can be seen that human capital investment is zero, which demonstrates the validity of the data. In the lower panel, children with higher education are included,
7Hukou is a special institution arrangement proposed to identify the origins of households. In general
and we can also find non-trivial number of corner solutions. This table is linked to the macro evidence we show in the introduction section.
Table 2: Tabulation of Corner Solutions of T1 and T2
Have College Education Observations Transfer(T2) No Transfer Total
Human Capital Investment(T1) 0 0 0
No No Human Capital Investment 16135 4415 20550
Total 16135 4415 20550
Have College Education Observations Transfer(T2) No Transfer Total
Human Capital Investment(T1) 1490 879 2369
Yes No Human Capital Investment 423 209 632
Total 1913 1088 3001
Table 3: Descriptive Statistics
VARIABLES N Mean S.D. Min Max Quartile 1 Median Quartile 3
Age of Parent 23,551 65.13 10.86 32 99 57 65 73
Num. Children of Parent 23,551 3.500 1.604 1 16 2 3 4
Depend on Child 23,551 0.624 0.484 0 1 0 1 1
Married Parent 23,551 0.751 0.432 0 1 1 1 1
Female Parent 23,551 0.527 0.499 0 1 0 1 1
Hukou Status of Parent 23,551 0.197 0.397 0 1 0 0 0
Parent’s Schooling 23,551 4.586 4.286 0 23 0 4 9
Age of Child 23,551 38.91 9.540 23 83 31 38 45
Female Child 23,551 0.468 0.499 0 1 0 0 1
Child’s Schooling 23,551 8.481 4.226 0 23 6 9 12
Num. Children of Child 23,551 1.511 1.273 0 20 1 1 2
Hukou Status of Child 23,551 0.243 0.429 0 1 0 0 0
Marriage Status of Child 23,551 1 0 1 1 1 1 1
Work Experience 23,551 24.43 11.43 0 69 15 24 33
Positive Human Capital Investment 2,369 5.140 4.822 1.00e-04 100 3 4.500 6 Positive Transfer from Children 18,048 0.494 1.192 1.00e-04 51.50 0.100 0.230 0.540
Household Income 23,551 1.409 3.130 0 92 0.0660 0.229 1.760
Household Net Wealth 23,551 0.525 12.03 -49.98 710 0 0.0500 0.517
Income of Child 23,551 2.451 3.393 0 30 0 1.500 3.500
Log Income of Child 23,551 0.119 1.371 -1.609 3.401 -1.609 0.405 1.253
Log Potential Income(EA) 23,551 0.114 0.299 -1.523 0.814 -0.0112 0.152 0.318 Log Potential Income(HC) 23,551 0.0708 0.236 -1.832 0.726 -0.0367 0.0747 0.231
1 All the monetary amounts are expressed in 10000 China yuan.
4.2
Econometric Implementation
The econometric implementation of this paper follows a logical sequence, as shown in Figure 5. The aim of the strategy employed is twofold. Our first objective is to discriminate between the “parent as a dictator” model and the “children have bargaining power” model. Since, in general, we cannot distinguish the two models through T2 given by Equation (9)
and (11), we, instead, can use the difference between T1 in two models, i.e. Equation (14)
and (15) with the help of earnings function. Given the empirically supported model, our second objective is to justify whether the corner solutions of T1 are caused by fixed costs,
Estimate Earnings Function (12) Select Model Using T1between (14) and (15)
Use T2to Estimate Unrestricted Model (9) or (11)
Causes of Corner Solutions
Fixed Costs (29) or (31) Absence of Altruism Liquidity Constraint (37) or (38) Predicted Potential Income (26)
Figure 5: Estimation Framework
know where the corner solutions originate from, or even whether all of them exist, and the three candidate reasons are not mutually exclusive, thus we cannot accept one through rejecting the other. We will first employ linear regression models for (14) and (15) to test the T1 equations. We then test the results produced by liquidity constraint, fixed costs and
absence of altruism one-by-one.
Suppose the first model is supported, then Equation (9) is the unrestricted model on T2. Results (17) and (19)(on T2) are the cases when altruism is absent. Equation (29) (on
T2) is the case when fixed costs exist, and Equation (37)(on T1) represent the case when
liquidity constraint is binding.
Suppose the second model is supported, then Equation (11) is the unrestricted model on T2. We can compare the corner solutions of T1 and T2 to see whose altruism is more
likely to be absent since the second model predicts many corner solutions, see Table 2. As for the fixed costs, we have Equation (31). Equation (38) (on T1) can be used to test the
existence of liquidity constraint.
The detailed specification of each empirical model depends on the cases mentioned and we, estimate earnings function (including predicting potential earnings) and T1 equations
(14) and (15) by using linear models, and we estimate T2 using Tobit models and two-part
4.3
Children’s Earnings Function
As argued before, the specification of children’s earnings function is crucial since both the specification of T1 function and the prediction of potential income rely heavily on it.
Therefore, we first estimate the earnings function using two different measures of human capital investment, i.e. the amount invested by the parents in their college education and the children’s years of college schooling. The empirical earnings function is of the following form:
ln(Ek) = E0+ α1· exp + α2· exp2+ a · ln(1 + T1) + b · T alent + 1, 1 ∼ N (0, σ2HH), (39)
where E0is the naturally endowed income without any talent or education, T1 is the human
capital or the schooling measure, exp is the working experience and we employ the schooling of the head of the households to proxy for the children’s talent. The estimation methods employed is the standard ordinary least square estimator with standard errors clustered at the household level HH.
Then we can predict the potential income as the income that the child would earn if no human capital had been invested, namely
ln(Epotential) = ˆE0+ ˆα1exp + ˆα2exp2+ ˆbT alent (40)
4.4
Model Selection and Liquidity Constraint
Based on the specification of children’s earnings function, we can now test which model, “parent as dictator” or “children have bargaining power”, is supported by the data. Ac-cording to Equation (14) and (15), the empirical human capital investment equation can be written as ˆ aEk 1 + T1 = β0 + β1T alent + Zβ20 + β3N oC + β4N oC2+ 2, 2 ∼ N (0, σ2HH). (41) where aEˆ k
the product of the parent and the child’s altruism is a bell-shaped curve on the number of children. The null hypothesis of the joint test is that both β3 and β4 are zero. If the null
hypothesis is rejected, then the second model and the hump-shaped relationship between investment and the number of children is supported; while if the null hypothesis is not rejected, but if one of the parameter estimates is significant from zero, then the second model is supported but the hump-shaped relationship is not supported; if both the null hypothesis of the joint test and the single parameter none-zero hypothesis are not rejected, then the first model is preferred.
As noted in the theoretical section, it would be convenient to justify the liquidity con-straint case through T1 estimation. Raut and Tran (2005) argue that this can be found
through introducing the parents’ permanent income into empirical equations, however, it is somewhat not feasible. We only have information on current income, which means the permanent income must be approximated or instrumented through some wealth variables. However, since the information we have on either current income or current wealth status is too limited to approximate the permanent income, we will consider alternative ways to test the liquidity constraint.
Empirically, there are many studies that test for liquidity constrants. The most popular method introduced by Zeldes (1989) tries to test the liquidity constraints by splitting the sample according to whether wealth is larger than two times current income. There also exist many other methods dealing with this issue. For example, Jacoby (1995) splits the sample based on the reported credit market activities instead of wealth profiles. Runkle (1991) splits the sample either using whether the households own the house or not, or based on the value of the housing assets compared with current income. Johnson and Li (2010) employ the debt-payment-to-income ratio to split the sample. But splitting the sample is not the only manner to deal with liquidity constraints. Jappelli et al. (1998) employ regime switching regression models and the information on whether the person has been denied credit to estimate the liquidity constraint problems instead of using the methods of splitting samples. Garcia et al. (1997) also follow the similar approach. However, those variants of Zeldes (1989) require the data one employs has extra information on the capital market participation history, and most of the time, those information is not approachable8.
It is also infeasible to directly apply Zeldes’s rule of spilting the sample since the current wealth and income profiles are far from the reality several decades ago. In our case we are interested in whether the parents were liquidity constrained in the past, when deciding whether and how much to invest in the education of their children.
Therefore, we step back and try to find some indicators which can proxy better for the liquidity constraint in the past. Actually, due to historical reasons, the housing registration type (Hukou) can be regarded as a good indicator whether certain households were liquidity constrained or not. The Hukou status of each individual is determined once (s)he was born and it is difficult to change. The long-last dual economic system in China discriminates the urban citizens from the rural ones. In rural areas, the only commodity that produces income is food, and those food products are low value-added hence the household income of rural families are little, never to say valuable collateral such as commercial housing or vehicles. The situations were much better for urban citizens. In addition, since the process of changing the registration type is rather restricted such that few households can achieve. Therefore, employing this indicator is much reliable than other criteria. We split the sample based on whether the household registration type is non-agricultural. If yes, we treat it as non-liquidity constrained, otherwise not. And the urban households have less probabilities to be liquidity constrained. Finally, as shown in (37) and (38), after comparing the estimated constants of different subsamples, i.e.
∆ = β0U rban− β0Rural. (42)
We can justify whether those liquidity constrained households failed to invest on children’s human capital because of being poor. The estimation method is also OLS with clustered standard errors at the household level.
4.5
Old-age Transfers T
2, Potential Income and Absence of
Al-truism
T2 is a function of parents’ permanent income, children’s current income and the human
capital investment amount T1. Regardless of the difference in coefficients between the two
equations, the empirical specifications are the same. We will use the current household income to proxy for the parents’ permanent income, although it might suffer from the measurement error problem. Therefore, we will control for the household net wealth to reduce the bias brought about by the measurement error. The model to be estimated is shown as follows: T2∗ = δ0+ δ1T1− δ2 HHIncome N oc + δ3Ek+ 3, 3 ∼ N (0, σ 2 HH), (43)
and HHIncome represents Ep1+
Ep2
1+r.
As argued before, each household might have faced fixed costs when making human capital investment decisions. The justification of this guess can be tested through the significance of the parameter estimate of the potential income in Equation(29) or (31), i.e.
T2∗ = δ0 + δ1T1− δ2
HHIncome
N oc + δ3Ek+ δ4Epotential+ 4, 4 ∼ N (0, σ
2
HH), (44)
where Epotential represents the potential income. So we will focus on the significance of the
estimate of δ4.
Since T2 is censored, Tobit estimator will be employed first. However, Tobit model
as-sumes the coefficients of both participation equation and the amount equation to be same, which is too strong, two-part models loosens this assumption by allowing for different co-efficients of participation equation from amount equation and the new-added participation equation is
P (T1 > 0) = γ0+ γ1T alent + Zγ20 + γ3N oC + γ4N oC2+ 5, 5 ∼ N (0, 1), (45)
whose variance is restricted to 1 in two-part models.
different from zero in the participation equation but not significantly different from zero in amount equation.
Under all specifications of T2 above, both parents and children are assumed to be
altruistic. The last possible cause of the failure of human capital investment could come from the absence of altruism from either side. The complicated aspect of this part is, dissimilar to binding liquidity constraint and fixed costs, the specifications differ a lot between “the parent as dictator model” and “the children has bargaining power model”. For the first model, we can test the absence of altruism using Equations (17) and (19). For the second model, we just need to analyze the corner solutions and see which side’s altruism is more likely to be absent.
5
Results
5.1
Earnings Function and Potential Income
The estimation results of the children’s earnings (39) can be seen in Table 4. The basic statistic of calculated working experience can be seen in the 14th row of Table 3. Columns (1) shows the OLS estimates on logrithmic earnings function using years of schooling as the measure of T1 while columns (2) is the OLS estimates using the human capital investment
amount as the measure of T1. We find that the parameter estimates of ln(1 + T1) in either
column is positive and smaller than 1 which shows the concavity of the earnings function over T1. The estimates can be interpreted as the elasticities. For example, in column
(2), one unit change of human capital investment is associated with 30% increase of the earnings. In addition, the children’s talent significantly affects the children’s earnings. The earnings on the working experience is inverted U-shaped. The calculated optimal working experience is around 22.9 (in column (1)) or 23.2 (in column (2)) years based on some calculations.
The predicted logrithmic potential incomes based on model (1) and (2) in Table 4 are shown in the last two lines of Table 3, and they show less diffuse patterns than the ac-tual distribution of logrithmic income in row 209. We have adopted two ways predicting
Table 4: Children’s Earnings Function
(1) (2) VARIABLES Log Income of Child Constant -0.429*** -0.462*** (0.0575) (0.0572) Work Experience 0.0383*** 0.0411*** (0.00397) (0.00400) Experience Squared -0.000836*** -0.000884*** (6.93e-05) (7.00e-05) Parent’s Schooling(Talent) 0.0357*** 0.0374*** (0.00336) (0.00338) Ln(1+Schooling) 0.422*** (0.0338) Ln(1+Human Capital) 0.302*** (0.0224) Observations 23,551 23,551 R-squared 0.048 0.047 lnL -40274 -40291
Note: *** p<0.01, ** p<0.05, * p<0.1. Clustered Robust Standard Errors are at Household Level in Parentheses. Column (1) is the OLS estimation of chilren’s earnings function using human capital investment amount as the measure of T1, while
column (2) is the OLS regression of children’s eanings function using years of college schooling as the measure of T1. the potential income: one using human capital amount (HC) and another using educa-tional attainment (EA) namely schooling based on Equation (40). Later on this predicted logrithmic potential income will be introduced to test the existence of fixed costs.
5.2
Investment T
1and Liquidity Constrained Parents
The OLS estimates of Equation can be found in Table 5. The ratios used as the dependent variables are calculated from aEˆ k2
1+T1 using the estimates of a in Table 4. The first column is the estimates obtained from the model using years of schooling as the measure of T1 and
the second column makes use of human capital investment as the measure. The estimates are similar in two columns.
The most important results the models show are that the number of children and its squared term enter the equation significantly. We pose a joint test on the estimates of the two variables, and the evidence rejects the null hypothesis that both coefficients of the two variables are zero, in both columns of Table 5. Therefore the evidence supports the “children has bargaining power” model, showing that the altruism of both parents and children increases the demand of expected rate of return on human capital investment, inducing the under-investment of human capital. As argued before, the product of both sides’ altruism is a nonlinear function of the number of children. Since the ratio ˆaEk2
1+T1 is decreasing in this product of altruism, the joint altruism is thus first increasing then decreasing over the number of children, and the maximum is around 6 under some calculations based on column (1) column (2). If we assume, as Raut and Tran do, the parent’s altruism is increasing while the children’s is decreasing in the number of children, then we find when the number of children is less than 6, the parent’s increasing altruism dominate the children’s decreasing, and the children’s decreasing altruism take the dominate position after the 6th baby is born.
Table 6 show the results of liquidity constraint cases. The first two column employ the ratio concerning the years of schooling as the measure of T1 and the rest two column employ
the human capital investment as the measure of T1. The liquidity constraint, hinders the
parents to invest sufficiently on children’s human capital. To see this, we estimate the coefficients between the liquidity non-constrained households and the constrained ones, and the sample splitting strategy is based on whether the household registration type is the agricultural one or the non-agricultural one, as mentioned in the previous section.
statis-Table 5: Model Selection Using αEk2
1+T1
(1) (2)
VARIABLES Ratio Using Schooling Ratio Using Human Capital
Age of Child 0.00514*** 0.00838*** (0.000775) (0.00112) Parent Age 55-60 0.0577*** 0.0898*** (0.0169) (0.0240) Parent Age 60-65 0.0776*** 0.131*** (0.0177) (0.0253) Parent Age 65-70 0.0282 0.0735*** (0.0194) (0.0284) Parent Age 70-75 -0.00894 0.0353 (0.0229) (0.0337) Parent Age 75 Older -0.0694*** -0.0513
(0.0260) (0.0386) Female Child 0.00749 0.0116 (0.00775) (0.0116) Female Parent -0.0766*** -0.0965*** (0.0117) (0.0175) Household Income 0.0236*** 0.0344*** (0.00319) (0.00448) Parent’s Schooling(Talent) 0.00675*** 0.00875*** (0.00155) (0.00237) Num. Child. of Parent -0.0416*** -0.0538***
(0.0124) (0.0196) Num. Child. Squared 0.00368** 0.00482**
(0.00146) (0.00237) Constant 0.312*** 0.347*** (0.0339) (0.0501) Observations 23,551 23,551 R-squared 0.034 0.031 lnL -21479 -30603
Joint Test of Num. Child. and Squared F(2,9110)=6.83 F(2,9110)=4.95
P-Value 0.0011 0.0071
Note: *** p<0.01, ** p<0.05, * p<0.1. Clustered robust standard errors are at household level in parentheses. Column (1) is the OLS regression on the ratio αEk2
1+T1 using human capital investment amount as the measure of T1, while column (2) is
the OLS regression on the ratio αEk2
tic of 0.94 in column (1-2), F statistic of 0.00 in column (3-4) without enough information rejecting the null hypothesis that two constants are close. This empirical result shows that the liquidity constraint might not be a powerful cause for the under-investment of children’s college education.
5.3
Old-age Transfers T
2, Fixed Costs and Absence of Altruism
The T1 estimation underpins the second model which allows the children to have bargaining
power as they become financially independent and dominant. The old-age transfers deci-sions from children thus can be empirically tested. First of all, we show the results of the unrestricted model namely Equation (11) in Table 7. The term HouseholdIncome/N oC in Table 7 means the household income divided by the number of children. From the co-efficient estimates, we find that the transfer decision models are empirically supported in various model specifications. The general results across all columns imply that the larger the HouseholdIncome/N oC is, the less extra attention from the children’s perspective on parents’ well-being will be, hence the less the children will transfer. In addition, the in-crease of the income of the children will motivate the children to transfer more to their parents suggested by all columns of Table 7. However, the human capital investment en-ters insignificantly in the Tobit model (column (3-4)) and the participation decisions of two-part model (column (4)). Nevertheless the marginal effects of human capital invest-ment on unconditional means are positive in column (6) which supports the theory. The difference between the result from the Tobit model and the two-part model is reflected on the substantial difference of the log-likelihoods. The two-part model is with much higher log-likelihood than the Tobit one, implying that the two-part model is preferable. More-over, we also employ the dummy whether depending on children as the dependent variable in columns (1) and (2). The signs of HouseholdIncome/N oC and the children’s income follow the theory, but the signs of T1 is insignificant and mixed since the human capital
investment enters the equation positively while the years of schooling enters negatively. It could be the reason that the dummy is not a precise measure of T2 such that the estimates
are biased with some unobservable heterogeneities.
Table 6: Liquidity Constraint
(1) (2) (3) (4)
Ratio Using Schooling Ratio Using Human Capital VARIABLES Constrained Not Constrained Constrained Not Constrained
Age of Child 0.00465*** 0.00643*** 0.00722*** 0.0109*** (0.000843) (0.00188) (0.00121) (0.00281) Parent Age 55-60 0.0534*** 0.0978*** 0.0770*** 0.174*** (0.0191) (0.0371) (0.0267) (0.0557) Parent Age 60-65 0.0672*** 0.151*** 0.103*** 0.281*** (0.0193) (0.0454) (0.0270) (0.0695) Parent Age 65-70 0.0261 0.0710 0.0541* 0.195*** (0.0220) (0.0440) (0.0313) (0.0714) Parent Age 70-75 -0.00100 0.0123 0.0160 0.171** (0.0261) (0.0519) (0.0371) (0.0837)
Parent Age 75 Older -0.0720** -0.0307 -0.0926** 0.120
(0.0293) (0.0600) (0.0418) (0.0985) Female Child 0.00325 0.0315 0.00510 0.0423 (0.00832) (0.0194) (0.0120) (0.0313) Female Parent -0.0762*** -0.0619** -0.106*** -0.0472 (0.0131) (0.0263) (0.0186) (0.0442) Household Income 0.0215*** 0.0277*** 0.0284*** 0.0417*** (0.00368) (0.00638) (0.00489) (0.00831) Parent’s Schooling(Talent) 0.00593*** 0.0112*** 0.00506** 0.0187*** (0.00171) (0.00360) (0.00242) (0.00578) Num. Children of Parent -0.0515*** -0.0131 -0.0611*** -0.0260
(0.0143) (0.0217) (0.0219) (0.0368)
Num. Children of Parent Squared 0.00379** 0.00410* 0.00443* 0.00684 (0.00167) (0.00233) (0.00257) (0.00432) Constant 0.375*** 0.0511 0.472*** -0.127 (0.0384) (0.0775) (0.0563) (0.119) Observations 18,922 4,629 18,922 4,629 R-squared 0.026 0.060 0.021 0.061 lnL -16946 -4477 -23799 -6624
Chow F-Test F(1,9110) = 0.94 P-Value=0.3329 F(1,9110) = 0.00 P-Value=0.9589
Note: *** p<0.01, ** p<0.05, * p<0.1. Clustered robust standard errors are at household level in parentheses. Column (1) and (2) contain the OLS estimates using schooling as the measure of T1on liquidity constrained sample and not constraint
one, respectively. Column (3) and (4) contain the OLS estimates using human capital investment as the measure of T1 on
liquidity constrained sample and not constraint one, respectively.
in the two-part model (column (5-6)), the older the parents are, the more likely the children will make the transfers while if the children indeed will transfer, the older their parents become, the less they will transfer. Again in column (4-6), we also find that, on averge, the female children transfer more to their parents than the male children. In column (1), (2) and (5), the children from rural areas, with agricultural household registration type, transfer less than those from urban areas. Moreover, the higher educational attainment the parents have, the less likely they will accept the transfer from their children, while the more transfer they will receive if they indeed obtain the transfer from column (5) and (6). Then we test the existence of fixed costs and the results are shown in Table 8 and 9. In all specifications of Table 8, the T1 is measured by the human capital investment and the
potential income is also calculated based on the Equation (44) considering human capital as the measure of T1, while the all specifications of Table 9 are based on the children’s
educational attainment. Compared with Tobit models, two-part models are with higher log-likelihoods, therefore we mainly focus on the two-part models in the two tables and the Tobit model is presented for references. As predicted by the theoretical parts, if the parents let their children directly participate in the labor market because they witnessed the future revenue, i.e. the potential income, of doing this is higher than the revenue if they invested in their children’s education, the transfer decisions will be affected by this potential income. We find that the potential income enters into the participation decisions significantly but not significantly in amount decisions, as column (4-5) of both Table 8 and Table 9 show. This implies that the potential income only matters when individuals are making decisions on whether to take the college education, but if they have made the decisions to take this education, potential income no longer matters. However, the evidence from the models considering the indicator of depending on children as dependent variable is unclear, as column (1) in both tables show.
Table 7: Marginal Effects on T2 Unrestricted Equations
(1) (2) (3) (4) (5) (6) Tobit on Transfer Two-part on Transfer VARIABLES Probit DependOnChild Probit DependOnChild P (transf er > 0|x) E(transf er|x) P (transf er > 0|x) E(transf er|x) Age of Parent -0.00160** -0.00162** 0.000190 0.00106 0.0146*** 0.00191*** (0.000696) (0.000695) (0.000325) (0.00175) (0.00235) (0.000536) Child Age 30-35 -0.00982 -0.0105 0.0105*** 0.0586*** 0.307*** 0.0687*** (0.0110) (0.0110) (0.00306) (0.0179) (0.0332) (0.0163) Child Age 35-40 -0.0360*** -0.0376*** 0.0218*** 0.121*** 0.476*** 0.136*** (0.0138) (0.0138) (0.00539) (0.0235) (0.0443) (0.0173) Child Age 40-45 -0.0572*** -0.0593*** 0.0206*** 0.115*** 0.572*** 0.174*** (0.0160) (0.0161) (0.00535) (0.0253) (0.0521) (0.0180) Child Age Above 45 -0.0816*** -0.0836*** 0.0188*** 0.105*** 0.467*** 0.185*** (0.0183) (0.0184) (0.00482) (0.0260) (0.0582) (0.0190) Female Child -0.0226*** -0.0230*** 0.00399** 0.0222** 0.177*** 0.0310*** (0.00573) (0.00581) (0.00176) (0.00997) (0.0194) (0.00883) Female Parent 0.0241** 0.0243** 0.00362 0.0201 0.000263 0.0319*** (0.0110) (0.0110) (0.00530) (0.0286) (0.0346) (0.00827) Parent’s Schooling -0.0139*** -0.0137*** 0.00183* 0.0102** -0.0126*** 0.0107*** (0.00143) (0.00144) (0.000963) (0.00478) (0.00450) (0.000986) Num. Children of Child 0.0286*** 0.0283*** -0.00112 -0.00621 0.0501*** -0.00287
(0.00390) (0.00390) (0.00126) (0.00688) (0.0157) (0.00378) Hukou Status of Child -0.230*** -0.228*** 0.00784* 0.0436* -0.193*** 0.0600*** (0.0108) (0.0110) (0.00439) (0.0245) (0.0364) (0.0103) Household Net Wealth -0.00207* -0.00206* 0.000725** 0.00403*** 0.00195 0.00186***
(0.00122) (0.00121) (0.000298) (0.00148) (0.00139) (0.000383) Household Income/NoC -0.0643*** -0.0641*** -0.00242 -0.0134 -0.127*** -0.0352*** (0.00937) (0.00935) (0.00342) (0.0199) (0.0169) (0.00453) Income of Child 0.00676*** 0.00694*** 0.00818*** 0.0455*** 0.0503*** 0.0332*** (0.00126) (0.00126) (0.00191) (0.00700) (0.00528) (0.00156) Human Capital Investment 0.00172 0.000253 0.00140 -0.00804 0.0100*** (0.00166) (0.00117) (0.00655) (0.00516) (0.00247) Child’s Schooling -0.000396
(0.00123)
Observations 23,551 23,551 23,551 23,551 23,551 23,551 lnL -13619 -13620 -61398 -11432 -41494
Note: *** p<0.01, ** p<0.05, * p<0.1. Clustered robust standard errors are at household level in parentheses. Column (1-2) contain the marginal effects using the dummy of “whether a household member would like to rely on children” as dependent variable. In specific, column (1) employs human capital investment as the measure of T1 while column employs
the child’s years of schooling as the measure of T1. Column (3) and (4) are the marginal effects of participation equation and
