Land Endowment and Parental Educational Investment in Rural China

Abstract

Education is fundamental to enhancing the quality of life and ensuring social and economic progress. However, the divisive economic structure separating urban and rural areas in China led to insufficient educational investment in rural China, and trapped farmers’ children in the agricultural sector. Land is one major asset of rural households, and can generate income or be mortgaged for credit used for educational investment. This study explored the relationship between land endowment and parental educational investment of rural households, from both theoretical and empirical perspectives, breaking down the effect of land endowment into two different components for the better promotion of educational investment. Based on data from a 2018 survey in Jiangxi Province, where rural education investment is severely restricted by the level of economic development, this study shows that the income and wealth effects of land endowment exists, and both increase the probability of educational investment. The wealth effect dominates the income effect when the households managed large-scale land or owned more land with contract rights. However, when the land endowment was less than a threshold of 3.85 mu, the wealth effect was replaced by the substitution effect, which conversely restrained educational investment for small-scale farmers in rural China. These findings highlight the importance of large-scale farmland as a mortgageable, or income-generating, asset in stimulating educational investment. Therefore, China should continue adhering to reform through the market-oriented land transfer system, with the government actively playing a role in ensuring the stability of land transfer and the security of land management rights, and increasing productivity for a high agricultural income to achieve sustainable educational investment.

1. Introduction

In the 1960s, with the rise of human capital theory in economics and the development of growth theory, the economic function of education received increasing attention [1]. Investment in education increased rapidly in some developing nations, as a pathway to increase economic growth and raise personal incomes, most notably in Africa and East Asia, resulting in an “education explosion.” China was no exception. China has made great progress in its compulsory education and higher education goals, but there still remains a considerable gap between achievements in urban and rural education. The overall education level remains low in rural regions, which is not conducive to high-level human capital accumulation (HCA), and hinders economic expansion. To solve insufficient rural HCA, besides the government’s public educational investment at the macro-level, parent’s educational investment (PEI) at the micro-level is also critical to improve the education of rural children. Many studies show that PEI influences children’s academic performance [2,3]. Children from families with relatively high educational investments tend to have a better educational performance, a higher likelihood of attending college, and a greater rate of finishing college [4,5].

In recent years, many scholars have explored educational investments from the perspective of educational decision-making, focusing on the effects of socio-economic status (e.g., household income) and demographic traits [6,7,8]. Given that land is one of the major income-generating assets in rural areas, some studies have delved into the impact of land endowment on families’ decision-making regarding education. Yang and Xu found that land endowment influences educational decisions in rural areas [9]. The land endowment and educational investment model indicates that when returns on educational investment are uncertain, farmers with more initial land endowment are more willing to invest in their children. Overall, land endowment influences PEI for children in two potential ways: the income effect and the wealth effect. First, income generated from agricultural production and management reduces the budget constraint for investing in children’s education, thus, producing an income effect. Second, farmland with a higher asset value allows households to spend more on children’s education than they otherwise would, either by withdrawing credit from assets or by saving less in other forms. Farmland value in China has risen in recent years, due to a series of market-oriented reforms in terms of land tenure security, farmland rental markets, and formal credit markets.

Much of the literature documents the income and wealth effects on household consumption, and several empirical investigations support a long-running relationship between consumption, income, and wealth, based on the aggregated national accounts data of different countries. However, to the best of the authors’ knowledge, there is no study to date that investigates these two effects on educational investment, in particular, in rural China. How does household educational investment respond to income and wealth correlated to land assets? Farm income could be invested or spent. Unlike consumption, an investment can be regarded as renunciation (postponement) of immediate satisfaction of wants. Therefore, there is no guarantee that a higher income will actually increase investment in children’s education. In addition, there needs to be quantitative evidence that the wealth effect of land endowment on education investment exists. Despite an increase in the value of farmland, financial institutions may not regard farmland as good collateral under the current institutional arrangement. In rural China, revenue from agricultural production is relatively low, and farm size is generally small for most farmers. The credit from the value of land may be so trivial as not to drive an increase in children’s education for smallholder farmers. The heterogeneity of household land endowment necessarily implies considerable heterogeneity in the response of household education investment. Therefore, there may exist a threshold of land endowment that changes the response towards education investment.

The objectives of this study were two-fold. First, this study examined whether income and wealth effects of land endowment on household educational investment exist, and investigated which effect is dominant. Second, this study derived the threshold and identified response heterogeneity among households. Based on this analysis, we further discussed the potential direction of land policy reform instrumental to household educational investment in rural China. The Chinese government has been actively promoting the reforms of rural agricultural land to improve farm productivity and output growth. The land security policy reform, and the emergence of the land rental market, significantly influenced the income level and the value of rural lands, and consequently changed farmers’ incentives for educational investment. In policy discussion, we drew attention to the implications of these reforms on educational investment, and the necessary change to promote further investment.

The remainder of the paper is organized as follows. The next section develops a theoretical model to examine both the income and wealth effects of land endowment on educational investment. The subsequent section presents a description of the data and estimation procedure, followed by the estimation results and robustness check. The heterogeneity of the effects is also tested for two groups of households, based on the identified threshold of land endowment. The final section presents the conclusions and discusses policy implications.

2. Materials and Methods

2.1. Theoretical Model

We developed a human capital investment model to derive the effect of land endowment on educational investment. Instead of setting up a fairly general model, we simplified the model of Glewwe and Jacoby [10], and adapted it to fit within the context of rural household decisions. We assume that rural households are capable of investing in education and farm capital assets. The investment in education accumulates human capital by sending children to school, purchasing school supplies, paying for before/after school programs, etc. Together, these inputs accumulated human capital according to

$$H_{t+1}=H_{t}G\left(I_{et}\right)$$

(1)

where $H_t$ is human capital at the period t, $I_{et}$ is the investment in education, and G is the function that transforms the investment into human capital, which relies on factors such as school quality, and the ability and motivation of the child. Investment in farm capital assets adjusted production in response to the changing market and regulatory conditions; farming is not a highly capital-intensive business in rural China. However, more and more households have adopted equipment and machinery technology to improve production efficiency. Capital was acquired by undertaking aggregate investment at rate $I_{kt}$, and capital stock depreciated at a time-varying proportional rate ${\delta }_t$, thus, the capital stock evolved as follows:

$$K_{t+1}=\left(1-{\delta }_t\right)K_t+I_{kt}$$

(2)

The investment expenditure was only sourced from current farm net revenue if households do not participate in the credit market. For simplification, we assumed that neither adults nor children worked in the labor market. (Note that if adults participated in the labor market, non-farm income could be used for investment in education or capital assets). The farm net revenue function was based on agricultural production with inputs of capital, labor, and land.

$$R_t=F\left(K_t,L_t,A_t\right)$$

(3)

where $L_t$ is the labor, and $A_t$ is the land endowment. Therefore, the budget constraint is

$$F\left(K_t,L_t,A_t\right)=I_{et}+I_{kt}+c_t$$

(4)

where $c_t$ is current consumption.

The maximization of family utility was the basic criterion of family behavior. We assumed that education is not only an investment product but also a consumption product. Under certain circumstances, parents used the income to purchase food for consumption, and also invested in their children’s education and capital assets; utility was maximized when the distribution between consumption and investment improved the lives of everyone in the family. We assumed that households maximized the expected lifetime utility subject to budget constraint (4), that is

$$\mathrm{Max}\left\{E_0\left[{\displaystyle \sum }_{t=0}^T{\theta }^{t}U\left(c_t,l_t,I_{et}\right)\right]\right\}$$

(5)

where $U$ is the current period household utility, defined as a concave function of consumption $c_t$; $l_t$ is the leisure ($l_t=1-L_t)$; $\theta$ is the subjective discount factor; and $E_0$ is the expectation operator with respect to information available for the household at time zero. The first-order conditions for an interior solution to this problem are

$$U_c\left(t\right)={\lambda }_t$$

(6)

$$U_l\left(t\right)={\lambda }_t{F}_L\left(t\right)$$

(7)

$$U_{I_e}\left(t\right)+{\mu }_t{G}_{I_e}\left(t\right)={\lambda }_t,$$

(8)

where ${\lambda }_t$ and ${\mu }_t$ are the shadow values of physical capital and human capital, respectively, scaled by the discount factor $\theta$. This system of equations can be solved to yield an optimal educational investment function of the form

$$I_{et}^{*}=I^{*}\left({\lambda }_t,{\mu }_t,F_L\left(t\right)\right)$$

(9)

Now we can trace through the potential effect of land endowment on educational investment by differentiating Equation (9) with respect to $A_t$, which yields

$$\frac{\partial I_{et}^{ *}}{\partial A_t}=\frac{\partial I{ }^{*}}{\partial F_L\left(t\right)}·\frac{\partial F_L\left(t\right)}{\partial A_t}+\frac{\partial I{ }^{*}}{\partial {\lambda }_t}·\frac{\partial {\lambda }_t}{\partial A_t}$$

(10)

The above formula shows the income and wealth effects of land endowment. We looked at the first term of the right-hand side of Equation (10), reflecting the income effect, composed of two parts. One part is the response of educational investment to the value of the marginal product of labor, and the other is the response of the value of the marginal product of labor to land endowment. The latter is positive, which means that an increase in land endowment improves the marginal product of labor, because of the higher scale of return. The former is also positive. If we take $F_L\left(t\right)$ as the shadow wage of labor, a higher wage rate generated more income, which relaxed the budget constraint for investment behavior.

The wealth effect is played through the shadow value ${\lambda }_t$. When cultivated land acts as financial collateral for a loan, allowing households to apply for loans from a bank, the household had more financial resources available. Whether or not households participate in the credit market, the availability of more resources implied a fall of the shadow price of physical assets, that is $\frac{\partial {\lambda }_t}{\partial A_t}$ < 0. Additionally, $\frac{\partial I{ }^{*}}{\partial {\lambda }_t}$ is proved negative by Glewwe and Jacoby through a transformation

$$\frac{\partial \mathit{I}{ }^{*}}{\partial \log \left({\mathit{\lambda }}_{\mathit{t}}\right)}=\left[-\frac{\partial \mathit{I}{ }^{*}}{\partial \log \left(\mathit{c}{ }^{*}\right)}\right]·\left[-\frac{\partial \log \left({\mathit{c}}^{ *}\right)}{\partial \log \left({\mathit{\lambda }}_{\mathit{t}}\right)}\right]$$

(11)

where the response of educational investment to the shadow price of assets is proportional to the response of educational investment to the total consumption, and where the constant of proportionality is the shadow price of elasticity of consumption (the elasticity is positive under the assumption of the normality of consumption [10]). In an empirical work with household survey data from Vietnam, Glewwe and Jacoby found a positive and significant relationship between ${\mathit{I}}^{*}$ and ${\mathit{c}}^{*}$, that is $\frac{\partial \mathit{I}{ }^{*}}{\partial \log \left({\mathit{c}}^{ *}\right)}$ > 0.

The above theoretical analysis confirmed that it is possible for the income and wealth effects of land endowment on educational investment to exist at the same time. However, if the land is not eligible to use as collateral for a loan/credit, due to, for example, low income-generating capacity or because it is too fragmented (e.g., $\frac{\partial {\mathit{\lambda }}_{\mathit{t}}}{\partial {\mathit{A}}_{\mathit{t}}}$ = 0), the wealth effect is trivial or insignificant. To verify the derivation results, we performed an empirical analysis.

2.2. Data

We obtained the data from the joint household survey conducted by the College of Modern Agriculture at Peking University, and the Institute of Rural Revitalization Strategies in Jiangxi Province, China. Jiangxi province in China was selected as the study area for two reasons. First, Jiangxi province, located in Central China (Figure 1), is a major grain producing province with a low per capita area of cultivated land because nearly half of the total population (45 million) are rural residents [11]. Land transferring is important in promoting the cultivated land large-scale operation in the province. Second, Jiangxi Province is a large agricultural province with a relatively low economic development, which has limited the investment level of education and human capital accumulation in the province. Insufficient investment in rural family education, and an over reliance on government financial appropriations, are the typical characteristics of education investment in Jiangxi province. Therefore, it is relevant and essential to study the investment in education in Jiangxi province.

The 2018 survey entailed a stratified sampling strategy designed to collect data from a random sample of 1080 households in Jiangxi Province, China. We randomly selected 12 counties, allocating 3 townships per county, 3 participating villages per township, and 10 households per village. We arrived at 806 observations after excluding samples that lacked educational information. While the survey covered a wide range of information, given our research objectives, we used only the following data: (1) demographic traits of household parents and children; (2) household educational investment; (3) detailed information concerning landownership, land transfers, and land rents; and (4) income sources (e.g., agricultural income and non-agricultural income).

To test the impact of land endowments on rural parents’ investment in their children’s education, we set educational investment as the dependent variable. In China, there are two types of educational expenses for families: in-school and out-of-school. Tuition is free during the first nine years of compulsory education, so there are no significant differences in in-school tuition among students from different backgrounds [12]. After-school tutoring, which is important in improving an individual student’s development and academic performance, is not free [13]. Hence, we focused on decisions related to out-of-school expenses. Due to increased incomes, rural households can pay cash for their children to be enrolled in an after-school program, attend a private tutoring class, or even have a family member (usually the mother) accompany their children to school to aid in classwork; in rural China, families, often mothers, prefer performing their role in supervising their children’s classwork and attempt to provide a desirable learning environment. This is also called parental involvement. As educational investment, parental involvement has significant benefits for the enhancement of students’ learning outcomes. We aggregated this into educational investment because parents invest additional resources and a significant amount of time with their child providing learning support. We used three questions to gauge the level of rural families’ educational investments in their children: (1) ‘Does the child attend a private tutoring class?’; (2) ‘Does the child take any extracurricular classes?’; and (3) ‘Is there a family member who accompanies the child to school?’ If any one of the above questions was answered with ‘yes’, the investment in education was assigned a value of 1, otherwise a value of zero was assigned. As

Table 1. Variable definition and descriptive statistics.

Variables	Definition	Mean	SD
Educational investment	Whether parents invest in children’s education (0 = no; 1 = yes)	0.28	0.45
Land endowment	Acreage of land managed/operated by family (Chinese mu)	5.76	10.68
Agricultural income	Annual household agricultural income (RMB)	3900.35	50,555.01
Gender	Gender of the child (0 = male; 1 = female)	0.49	0.50
Child Age	Age of the child (years)	15.30	4.29
Family Size	Total members of rural household	5.80	1.84
Number of children	Total number of children in the family	1.67	1.13
Non-agricultural income	Annual household non-agricultural income (RMB)	54,997.27	61,626.25
Parent education	Parents’ schooling years (years)	6.54	3.31
Parent age	Parents’ age (years)	59.25	11.15
Hukou	Type of household registration for parents (0 = agricultural; 1 = non-agricultural)	0.31	0.46
Health	Health level of parents (1 = very healthy; 2 = relatively healthy; 3 = average; 4 = relatively unhealthy; 5 = very unhealthy)	2.41	1.10
Awareness	Parents’ perception of the usefulness of education (1 = very useful; 2 = relatively useful; 3 = average; 4 = relatively useless; 5 = very useless)	1.17	0.46
Willingness	Whether parents are willing to work in agriculture (0 = no; 1 = yes)	0.54	0.50

shows, only 28% of sampled households invested in children’s education, suggesting that the current education investment has great potential to increase.

We used household land endowment and agricultural income as the major independent variables; the unit of household land endowment used was Chinese mu. Land endowment was defined as land management scale, referring to land that has been transferred to a household after deducting land that has been transferred out, and adding land that has been transferred in. Table 1 shows that the average land endowment of the surveyed farmers was 5.76 mu (the per capita land area was 0.28 mu), below the world average. A rural family’s income accrues from both agricultural and non-agricultural work. The income effect of land endowment on educational investment was mediated by agricultural income. Non-agricultural income was also included in order to avoid exaggerating the income effect. In the sample, households’ agricultural income had a high variation, and their non-agricultural income significantly exceeded the agricultural income level.

2.3. Empirical Model

Following the work of Judd and Kenny [14], we used the method of stepwise regression analysis to verify the income and wealth effects of land endowment on educational investment. The specifications of the three models are as follows:

$$\mathrm{M}1:Invest={\beta }_{10}+{\beta }_{11}log\left(Land\right)+{\beta }_{12}Contro{l}_1+{\mu }_1$$

(12)

$$\mathrm{M}2:Log\left(A\_income\right)={\beta }_{20}+{\beta }_{21}log\left(Land\right)+{\beta }_{22}Contro{l}_2+{\mu }_2$$

$$\mathrm{M}3:Invest={\beta }_{30}+{\beta }_{31}log\left(Land\right)+{\beta }_{32}log\left(A\_income\right)+{\beta }_{33}Contro{l}_3+{\mu }_3$$

where $Invest$ represents parental educational investment for children; $A\_income$ denotes a household’s agricultural income; $Land$ is land endowment or land managed size; $\beta$ is the parameters to be estimated; $Control$ is a vector of control variables; and u is random terms. We gradually tested the regression coefficients in a sequence according to Equations (12)–(14). The test steps are as follows: (1) test coefficient ${\beta }_{11}$ in Equation (12) (i.e., the total effect of land endowment on educational investment); (2) test coefficient ${\beta }_{21}$ in Equation (13) (i.e., the relationship between land endowment and the mediating variable [household’s agricultural income]); and (3) after controlling for the mediating variable A-income, test coefficients ${\beta }_{31}$ and ${\beta }_{32}$ in Equation (14). If ${\beta }_{32}$ is significant, the income effect exists, while the wealth effect exists if ${\beta }_{31}$ is significant.

Control variables were included in the model to reduce possible errors of missing variables. We classed the control variables into three broad categories of factors: child demographics, family characteristics, and parental demographics. Child demographics included gender and age. Traditionally, males have more access to educational resources than females in China. [14]. However, national reforms in China in the past decades have reduced gender inequality in education in order to give females more access to educational resources. In addition, as children grow older, parents’ educational investment changes accordingly.

Family characteristics include family size, number of children, and non-agricultural income. Lazear revealed that family size has a negative impact on PEI [15]. Rosenzweig and Zhang found that the number of children has a significant, negative impact on children’s educational investment [16]. According to the theory of resource dilution [17], parental resources are finite; as the number of children in the family increases, the resources earmarked for any one child necessarily declines, implying that as the number of children increases, the educational investment allocated for each child decreases. High-income parents teach their skills to their children, and invest in their children’s education for future benefits. Eckstein and Wolpin found that the less parents earn, the more likely their children are to drop out of school [18]. Non-agricultural income is an important component of family income and can be used as a proxy for family economic status. Ye and Zhao found that parents’ educational investment for their children increases with off-farm employment [19].

Parental demographics include parents’ ages, education, hukou (individual household registration), health status, perception of the usefulness of education (awareness of education), and willingness to continue working in agriculture in the future (willingness). Parental demographics were represented mainly by fathers’ demographics. Parents play a crucial role in their child’s education decisions. Studies have demonstrated that a higher parental education level indicates greater PEI [20]. Lloyd et al. analyzed the characteristics of the school enrollment of Pakistani children and found that the education level of parents affect the school enrollment ratio [21]. Further, parents’ hukou plays an important role in their children’s growth [22]. Parents facing health risks may increase household spending on health, and crowd out other types of household consumption and expenditure, thus lowering the investment in children’s education. Finally, education awareness and less willingness to work in agriculture increased PEI. Table 1 presents these variable definitions and the corresponding descriptive statistics. In M1 and M3, all these variables are controlled while in M2 the demographics of children, hukou, awareness of education, and willingness to work in agriculture are excluded from the control variables because they are not expected to affect agricultural income.

2.4. Threshold Regression

The effect of land endowment on PEI may depend on land endowment itself. As far as the income effect is concerned, only if the scale of managed land exceeded the “threshold value”, was agricultural income generated from farming spent on educational investment. Otherwise, it was spent on meeting other more fundamental demands, e.g., consumption. We used Hansen’s threshold regression to identify whether there exists a threshold value of land endowment that differentiate the effects. This regression was applied to M2 to estimate this threshold, or cut-off value, since a large coefficient of land endowment in M2 suggests a high agricultural income, which may trigger the income to be spent on educational investment. To test the threshold effect, M2 is changed to

$$\begin{array}{cc}\hfill Log\left(A\_income\right)& ={\beta }_{20}+{\beta }_{21}^{0}log\left(Land\right)I(log\left(Land\right)\hfill \\ & <\gamma )+{\beta }_{21}^{1}log\left(Land\right)I(log\left(Land\right)>\gamma )+{\beta }_{22}Contro{l}_2+{\mu }_2\hfill \end{array}$$

(13)

where $I(·)$ is the indicator function, l$og\left(Land\right)$ is taken as the threshold variable, and $\gamma$ is the threshold value. After obtaining the parameter estimate of threshold regression, it was necessary to verify the existence of the threshold effect. The null hypothesis of no threshold effect in the model, that is ${\beta }_{21}^0={\beta }_{21}^1$, was tested through the likelihood ratio test proposed in Hansen [23].

3. Results

Determinants of PEI

We begin the discussion with the aggregate effect of land endowment on PEI. Generally, land endowment is assumed to be exogenous to educational investment. However, educational investment decisions may affect a land transfer decision due to the budget constraint, and subsequently affect land management scale. To tease out the validity of our results, we used the endogeneity test to consider the extent to which land endowment and educational investment were jointly determined. The average land area of other farmers in the village was used as the instrumental variable. Due to the “herd effect”, the land operated by other farmers directly affects the farming size of the subject household, but does not have a direct impact on the PEI, which guarantees the exogeneity of the instrumental variable. We applied the endogeneity test of Smith and Blundell to a probit-type regression model (Smith and Blundell showed that an efficient test for endogeneity of right-hand side variables can be obtained by including residuals from a reduced-form equation for the suspected endogenous variable as regressors and then testing their statistical significance [24]). The Wald test statistic of exogeneity of instrumented variable is 0.36, not significant at the 0.05 level. Hence, we cannot reject the null hypothesis of no endogeneity. No endogeneity has two possible explanations. First, land transfer in the study area was not prevalent, meaning that the educational investment decision is independent of a land transfer decision. Second, the family member most often accompanying students to school is the wife of the household. In rural China, females mainly perform housework, so even spending time with their children at school does not seriously affect land management. A standard probit regression was applied to M1 and M3.

The estimation results of M1, M2, and M3 are presented in

Table 2. Regression Results.

Variables	M1	M2	M3
Log(Land)	0.096 ***	1.425 ***	0.063 ***
	(0.018)	(0.112)	(0.019)
Log(A_income)			0.018 ***
			(0.005)
Gender	0.039		0.042
	(0.032)		(0.032)
Child’s age	−0.021 ***		−0.021 ***
	(0.005)		(0.004)
Family size	0.010	−0.094	0.013
	(0.013)	(0.083)	(0.013)
Number of children	−0.042 *	0.023	−0.045 **
	(0.023)	(0.131)	(0.023)
Log(Non-agricultural income)	0.029 ***	0.013	0.029 ***
	(0.005)	(0.025)	(0.005)
Parent education	0.019 ***	0.051	0.019 ***
	(0.005)	(0.035)	(0.005)
Parent age	0.003 *	0.010	0.003 *
	(0.002)	(0.011)	(0.002)
Hukou	0.022		0.027
	(0.035)		(0.035)
Health	0.015	0.030	0.014
	(0.015)	(0.102)	(0.015)
Awareness	0.034		0.041
	(0.036)		(0.036)
Willingness	−0.091 **		−0.083 **
	(0.036)		(0.036)

Notes: (1) The coefficients of M1 and M3 are average marginal effects, while the coefficients of M2 are regression coefficients; (2) the values in parentheses are standard errors; and (3) ***, **, and * indicate that the estimated coefficients are significant at the levels of 1%, 5%, and 10%, respectively.

, and column 2 shows the determinants of educational investment, including the aggregate effect of land endowment, on PEI. The marginal effect of land endowment is 0.096 and statistically significant at the 0.01 level, showing that for every 1% increase in land endowment acreage, the probability of parents investing in their children increases by 9.6%. The result suggests that at least one of either income or wealth effects plays a positive role in promoting educational investment. Given that the income effect is more fundamental than the other, we expect this is due to the income effect. In the earlier study, Deininger and Jin did not find that land endowment had a systematic impact on the level of education obtained by the offspring in a household [25]. One possible explanation is that the effect of agricultural income on PEI depends on the overall income level. Parents do not invest in children’s education when the overall incomes are low and they are credit constrained.

A child’s gender does not have a negative impact on PEI. The gender difference in the number of years in education was great in rural China two decades ago. For example, Deininger and Jin found that there was a strong bias against girls receiving education in a combined village and household survey conducted in three of China’s poorest provinces in 2001 [24]. However, with reforms in social and economic development, gender inequality has reduced in rural China. In particular, the education expansion policy and the promotion of lasting gender equality in the last decades have contributed to China’s rebalance of education equality between genders. Unlike gender, a child’s age has a significant and negative effect on PEI. When the child is one year younger, on average the probability of PEI increases by 2.1%. Parents are willing to spend on/invest in out-of-school programs or private tutoring for their children when children are younger, because these programs help their children gain a competitive advantage in the early stages of education and build confidence to confront the fierce competition in the senior stage. Another possibility is that younger children are not self-disciplined or able to take care of themselves in school, and therefore, need a family member to help or supervise them in learning.

The effect of family size on PEI is not significant, which is not in alignment with Lazear [15], who revealed the negative influence of family size on education investment. One explanation of the different finding is that the effect of family size might be captured by the number of children, which shows a significant and negative effect on PEI. When a family has more children, the allocation of resources to each child is reduced according to the dilution effect theory [26]. The probability of PEI declines by 4.2% with one more child in the family. In contrast, Lee estimated that per-child investment is 74.6% for families with two children, and 57.6% in families with three children, compared to families with only one child [27]. The share of non-agricultural income in family income has increased dramatically and become an important source of household investment in, e.g., agricultural capital and children’s education. As expected, non-agricultural income is positively related to PEI, and the coefficient is significant at the 1% level. A 1% increase of non-agricultural income results in an increase of 2.9% in the probability of PEI.

The results in Table 2 also show that parents’ education and age have a statistically significant effect on PEI. One additional year of schooling in the education of a parent increases the PEI by 1.9%. The importance of parental education on children’s education in China is also supported by other studies [28]. Educated parents generally hold more favorable attitudes towards, and place a high value on, education. Therefore, they are more willing to invest in their children’s education. In addition, parents’ age is positively correlated with PEI, which differs from Chung and Choe [29], who found that as the mother’s age increases, spending for children’s private and after-school education decreases. In addition to these factors, this study suggests that hukou, the health status of the parents, and awareness of the value of education, have no significant influence on PEI. The effect of hukou is insignificant, in part due to the reforms of the hukou system, which relaxed the hukou restrictions and freed labor migration to some extent. Parents with health risks might not reduce PEI, possibly because the New Rural Cooperative Medical Scheme (NRCMS), implemented in China since 2003, has greatly reduced medical payments, and did not crowd out the expenditure given to education. Finally, as expected, willingness to work in the agriculture has a negative and significant effect.

Model 2 (M2) examined the elasticity of agricultural income with respect to land endowment. The land endowment parameter was estimated at 1.425, indicating an agricultural income increase of 1.425% for every 1% increase in land endowment. The increasing returns of scale in agricultural production might have happened due to the current land allocation not being optimized. Although a land transfer system is conductive to achieving economies of scale in China to some extent, a lower magnitude of farmland tenure security, the absence of complete rental rights, and imperfect labor migration prevents the maximization of land utilization.

The standard probit regression was also applied to M3 in testing whether there is the wealth effect after controlling for the mediating variable of agricultural income. Parameter estimates indicated a significant and positive effect of agricultural income on PEI, which corroborates the income effect, that is, land endowment promotes educational investment through generating income that allows households to relax the budget. This is consistent with earlier findings by Berlinschi, Swinnen, and van Herck [30], who analyzed the impact of agricultural income on investments in education and agricultural employment. After the income effect is controlled, the effect of land endowment is still positive and significant, which confirms the existence of the wealth effect. The coefficient estimate of land endowment indicates that the wealth effect accounts for slightly more than half (0.063/0.096 ≈ 66%) of the total effect. The finding that the wealth effect is greater than the income effect emphasizes the importance of land assets in access to credit in rural financing.

4. Discussion

4.1. Robustness Check

It is well known that the “three rights separation” reform in China divided farmland property rights into collective ownership rights, contract rights, and management rights. Contract rights are to possess and use contracted land, and also to collect rent from tenants, while land management rights are derived from land contract rights and can be transferred between households. In order to analyze the robustness of the previous results, and to study potential differences of impact between managed/operated land and “owned” land (land ownership rights in China belong to collective organizations permanently; due to a term of land contract rights usually lasting 30 years, we claimed rural households have contract rights of land to “own” the land), we conducted a robustness check. In M1, M2, and M3, land endowment is replaced by land owned by the household. The estimation results are presented in

Table 3. Results of the robustness test using owned land.

Variables	M1	M2	M3
Log(Land)	0.101 ***	1.054 ***	0.077 ***
	(0.024)	(0.170)	(0.025)
Log(A_income)			0.022 ***
			(0.005)
Gender	0.042		0.045
	(0.032)		(0.032)
Child’s age	−0.020 ***		−0.021 ***
	(0.004)		(0.005)
Family size	0.009	−0.123	0.013
	(0.013)	(0.090)	(0.013)
Number of children	−0.049 **	−0.059	−0.050 **
	(0.023)	(0.140)	(0.023)
Log(Non-agricultural income)	0.029 ***	0.008	0.029 ***
	(0.005)	(0.027)	(0.005)
Parent education	0.019 ***	0.044	0.018 ***
	(0.005)	(0.037)	(0.005)
Parent age	0.002	−0.001	0.002
	(0.002)	(0.012)	(0.002)
Hukou	0.036		0.040
	(0.036)		(0.036)
Health	0.019	0.070	0.017
	(0.015)	(0.120)	(0.015)
Awareness	0.046		0.053
	(0.035)		(0.036)
Willingness	−0.044		−0.054
	(0.034)		(0.034)

Notes: (1) The coefficients of M1 and M3 are average marginal effects, while the coefficients of M2 are regression coefficients; (2) the values in parentheses are standard errors; and (3) *** and **indicate that the estimated coefficients are significant at the levels of 1% and 5%respectively.

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As expected, the acreage of owned land has a significant, positive impact on rural families’ educational investment. Every 1% increase in the acreage of land owned increases the probability of PEIs by 10.1%, higher than the effect of managed land. Parameter estimates and significance level of other variables have little difference. The results in M2 show that the elasticity of agricultural income with respect to owned land is 1.054, lower than that with respect to managed land. Given the average acreage of land owned is comparable to that of managed land, the above result implies that the land transfer system has improved the unit land output. As many studies testify, land transfer expands the production scale and promotes new technologies, therefore helping to improve land production efficiency [31].

Likewise, income and wealth effects of owned land on educational investment are both apparent. An interesting finding is that the wealth effect (76% of the total effect) is higher than in the baseline case. The change of the wealth effect can be explained by the difference in management rights from land transfer and contract rights. Although management rights, from either land transfer or contract rights, are eligible as collateral for the credit, transferred land management rights are characteristic of several disadvantages. First, the agreed term of a land transfer contract is relatively shorter and less stable, negatively affecting the loan amount; second, a breach of the land transfer contract and the insecurity of land tenure reduce the quality of land transfer and correspondingly the mortgageable value of the land. In sum, land transferred from others has a smaller wealth effect, resulting in the lower aggregate effect of land endowment on educational investment.

4.2. Threshold Effect Analysis

The point estimate of the one threshold of log(Land) shows that the threshold is 1.579, equivalent to 3.85 mu. The null hypothesis of no threshold against the alternative of one threshold is rejected using the likelihood ratio test proposed by Hansen [24]. This threshold separates households into two different groups: those with no more than of 3.85 mu land, and those with an amount of land greater than 3.85 mu. The former concentrates 453 observations, while the latter has 353 observations. The regression parameter estimates and their standard errors of variables of interest are presented in

Table 4. The heterogenous effects of land endowment on educational investment.

Variables	When Acreage of Land ≤ 3.85 mu			When Acreage of Land > 3.85 mu
	M1	M2	M3	M1	M2	M3
Log(Land)	−0.074 **	0.596 ***	−0.088 ***	0.229 ***	1.357 ***	0.206 ***
	(0.035)	(0.159)	(0.035)	(0.047)	(0.368)	(0.048)
Log(A_income)			0.018 **			0.019 ***
			(0.009)			(0.007)
Obs.	453	453	453	353	353	353

Notes: (1) The coefficients of M1 and M3 are average marginal effects, while the coefficients of M2 are regression coefficients; (2) the values in parentheses are standard errors; and (3) *** and ** indicate that the estimated coefficients are significant at the levels of 1% and 5% respectively.

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As expected, all estimates have the expected sign and are statistically significant in the group with more land. In this group, the coefficient of land endowment in M3 is greater in magnitude compared to the baseline, indicating a higher wealth effect. Combined with the unchanged income effect, the aggregate effect of land endowment is realized at a higher rate. One possible explanation is that the asset value of large-scale land endows households with not only mortgageable land, but also access to other financial opportunities, which intensifies the wealth effect.

In sharp contrast, the coefficient of land endowment in M3 in the group with less land is negative, and statistically different zero. Yang and Xu call this effect the substitution effect [9], which works in the opposite direction of the wealth effect. When the scale of land is too small for technical improvement and the adoption of machinery, agricultural efficiency is relatively low, and more labor needs to be devoted to agricultural production. Therefore, on the one hand, extra labor to accompany children in school cannot be saved; on the other hand, parents have the motivation to keep children in the rural labor force and reduce spending on education. In addition, small-scaled land may be not eligible for a mortgage loan due to the deficient income-generating capacity, which results in no wealth effect. Although the income effect still exists, reflected in the expected positive and significant sign for agricultural income in M3, the substitution effect of land on educational investment dominates the income effect among small-scale households, pushing the net effect to be negative. As Yang and Xu indicate, this substitution effect may distort the allocation of land and labor [9]. Given that small land holdings per farm household are prevalent in China, (for example, the households with small-scale land in this study account for 56% of the total examined), it is important for policy makers to recognize the negative consequences of the substitution effect and pursue policies to mitigate, or even eliminate, this effect.

5. Conclusions and Policy Implications

Parents’ educational investment in children is an important component of human capital accumulation, and can help children achieve better educational outcomes, and subsequently, higher income in the labor market. The deficiency of PEI in rural China may trap farmers’ children in the agricultural sector, and inhibit labor migration or the land transfer needed for better resource allocation. This paper studied the relationship between land endowment and the educational investment of rural households, from both theoretical and empirical points of view, and split the effect of land endowment into two different components for the better promotion of educational investment. This study shows that the income and wealth effects of land endowment exist, and both increase the probability of educational investment. The wealth effect dominates the income effect for households with more “owned” land, or with large-scale land. However, when land endowment is less than a threshold, the wealth effect is replaced by the substitution effect, which, on the contrary, restrains educational investment.

The conclusions above point out the relevant policy implications. First, policymakers should boost the development of moderate-scale land operations, through the acceleration of land transfer among farmers. A small-scale operation is always accompanied by a low efficiency of labor and land input. Rural households tend to devote so much manual labor to agricultural production that they are less willing to send children to work in cities. When labor cannot be released from the agriculture, land transfer is limited, leading to a failure in the small-scale farming transformation for a rural community as a whole. Driven by the substitution effect, the overall educational investment always stays at a low level. To break this vicious cycle, policymakers should promote scaling up farming operations through institutional innovation in land transfer, e.g., improving the land rental markets to reduce transaction costs, and policy support to speed up land consolidation. Large farms are more efficient than their small counterparts, and have a higher income elasticity, as evidenced in the study, which also increases the income effect of land endowment. More importantly, the wealth effect emerges alongside large-scale land because the income-generating capacity of the land also makes it eligible for a mortgage loan, given that the loan amount available for mortgaged land is limited.

Second, land transfer quality should be improved to increase the wealth effect of transferred land. Although land management rights are eligible as collateral for a mortgage loan, the wealth effect of managed land is smaller than that of “owned” land. One reason is that the transfer of land management rights is accompanied by a series of problems, which depreciates the value of transferred land management rights in the credit market. The major problem is the instability of management rights caused by the breaking of land transfer contracts. Farmers’ weak legal awareness, the high cost of resorting to law, and the characteristics of social relationships in rural China result in no binding force of contract or the insecurity of transferred land tenure. Therefore, institutional and policy intervention are needed to address this common phenomenon. Measures recommended for stabilizing land management rights include (a) setting up a third party to monitor the execution of the land transfer contract, and establish a punishment mechanism to restrain the breach behavior; (b) deploying nonprofit programs to provide low-cost or free legal services in rural areas; and (c) increasing farmers’ legal knowledge and awareness through public legal education programs, etc. It is worth noting that irregular land reallocation in rural China caused an instability and uncertainty regarding management rights for both transferred land and “owned” land, crippling the wealth effect of land endowment. A mechanism should be designed to reduce the frequency of land reallocation.

Third, in order to increase the income effect, it is necessary to improve the farming productivity of small-scale farms. Small-scale operations have dominated in the rural economy for a long time, and will continue to do so. However, even for households with less land, we found that an additional increase of agricultural income was used for educational investment. Although it is very challenging to improve farming productivity for small-scale operations, identifying the drivers of productivity and weighing their significance are vital for effective policy making. A China-specific model is needed for the development of the machine service hiring market, which makes mechanical farm operations available for small-scale farmers. In addition to this, more institutional arrangements, such as cooperatives, that help improve the agricultural income of small households, should also be encouraged by the government.