Effects of parental encouragement on their child's academic performance and poverty alleviation

Nakamura, Yui Article Effects of parental encouragement on their child's academic performance and poverty alleviation Review of Economic Analysis (REA) Provided in Cooperation with: International Centre for Economic Analysis (ICEA), Waterloo, Ontario Suggested Citation: Nakamura, Yui (2024) : Effects of parental encouragement on their child's academic performance and poverty alleviation, Review of Economic Analysis (REA), ISSN 1973-3909, International Centre for Economic Analysis (ICEA), Waterloo (Ontario), Vol. 16, Iss. 4, pp. 409-422, https://doi.org/10.15353/rea.v16i4.5240 This Version is available at: https://hdl.handle.net/10419/328172 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ Review of Economic Analysis 16 (2024) 409-422 1973-3909/2024409 409 www.RofEA.org Effects of Parental Encouragement on Their Child’s Academic Performance and Poverty Alleviation Empty 15 YUI NAKAMURA Faculty of Economics, Fukuoka University  Empty 15Empty 15 Parental encouragement improves a child’s academic performance, which reflects the individual accumulation of human capital and can prevent the child from becoming poor in the future. We provide a model to clarify the mechanism by which parental encouragement influences the child’s efforts by considering parental time preference, wages, and background. We find that parents who have a child with low innate ability, high wages, strong time preference, and were given little encouragement from their parents in the past hesitate to encourage their child and tend to give them assistance for survival. We also imply that the influence of parental encouragement to children’s academic performance is strong in early grades rather than in late grades. Moreover, we indicate that educational institutes such as schools and local governments can reduce parents’ time preference and provide information about opportunities that stimulate children's efforts at schools. These actions urge the parents who hesitated to encourage their children to begin to encourage them. Furthermore, these actions increase the effectiveness of parental encouragement and realize the child's efforts at school, which results in improving their wages in the labor market in the future. Empty 10 Keywords: encouragement, assistance, opportunity cost, time preference, poverty, school policy JEL Classifications: D61, I20, I28 1 Introduction According to the human capital theory proposed by Becker (1964), increasing accumulation of human capital improves individual wages in the labor market. Therefore, schoolteachers and parents support children to improve their academic performance, which reflects the level of individual human capital which can prevent them from becoming poor in the future. Numerous studies have shown the positive effects of parental involvement on children's performance. Parental involvement generally includes school-based activities such as attending parent-teacher conferences, home-based involvement like reading with children and discussing school activities and assignments, as well as resource-based involvement such as fiscal  Faculty of Economics. [email protected] © 2024 Yui Nakamura . Licensed under the Creative Commons Attribution - Noncommercial 4.0 Licence (http://creativecommons.org/licenses/by-nc/4.0/. Available at http://rofea.org. Review of Economic Analysis 16 (2024) 409-422 410 www.RofEA.org expenditures on private tutoring and school materials. Henderson and Mapp (2002) show that family support is effective in improving student's academic performance, attendance, and behavior, especially in middle and high schools. El Nolali et al. (2010) indicate that parental involvement declines children's problem behaviors and improves their social skills in elementary school. Hill and Craft (2003) explain the positive relationship between parental school involvement and students' school performance by focusing on ethnic variations. Chuha and Heckman (2008) focus on the sensitive periods of parental involvement in the development of cognitive and noncognitive skills, noting that the sensitive period for the former occurs earlier in the life cycle than for the latter. Dernbusch et al. (1987), Garg et al. (2005), and Newman et al. (2015) compare the results of students' academic performance by dividing parenting styles into authoritarian and permissive, and analyze the optimal parenting style. 1 Hill and Tyson (2009) and Sankaran et al. (2020) compare the impacts on children's academic performance among various parental involvements and show several parental involvements except help with homework are helpful to increase children's performance. Parental encouragement similarly involves parents investing their time in their child's education, but unlike parental involvement, it does not include resource-based involvement such as fiscal expenditures. For example, parents may recommend their children read books to gain knowledge or seek opportunities to communicate with someone who speaks a different language to understand the importance of learning foreign languages. Additionally, parents might encourage their children to engage in career experiences and emphasize the need to learn what is necessary at school to succeed in the labor market. Parents also praise their children's daily achievements and encourage them to explore their interests. Steinberg et al. (1992) and Gunderson et al. (2013) indicate the positive effects of parental encouragement on children's academic performance. Darolia and Wydick (2011) clarify that students who are given encouragement from their parents show more effort at school compared to students who are given assistance, such as money and cars. Fan (2001) implies that parents' encouragement for their children's education attainment has a positive impact on growth of children's academic performance. Although the impacts of parental involvement and parental encouragement have attracted much attention, few studies have focused on the amount of parental encouragement based on parents’ types as considering parents' time preferences and their backgrounds. Some parents have a strong time preference; that is, they consider the current situation to be more important than the future, whereas others have a weak time preference; that is, they consider things in the long term. Moreover, as Van Ijzendoorn (1992) and Belsky et al. (2009) show, parenting styles are transmitted from parents to their children. Some parents are familiar with ways to encourage 1 Altalib et al. (2013) classify parenting into four styles: authoritarian, authoritative, permissive, and democratic, and state that sociologists consider authoritative parenting to be the best in general. NAKAMURA Parental Encouragement and Academic Performance 411 www.RofEA.org their children because they were encouraged by their own parents in the past, and vice versa. These differences may generate various amounts of parental encouragement for their child as well as parenting styles, resulting in differences in children's efforts and their academic performance. In this study, we provide a model to clarify the types of parents whose encouragement affects children's efforts by considering the level of parents' time preferences and backgrounds. Moreover, we examine the effects of the differences in parents' wages because we assume that parents' utility includes their consumption, as well as their children's future incomes. 2 From the model, we find that parents who have a child with high innate ability, low wages, and weak time preferences, and who were given enough encouragement by their parents tend to encourage their child. On the contrary, parents who have a child with low innate ability, high wages, and strong time preferences, and who were given little encouragement by their parents in the past tend not to encourage their child. Next, we indicate some remedies for poverty alleviation by classifying the types of children based on the results from our model. Educational institutions such as schools and local governments can reduce parents' time preferences and increase the effectiveness of parental encouragement. These actions encourage parents to give their children optimal encouragement which can be a remedy for poverty alleviation. In the following section, we analyze a model that explains the relationship between parental encouragement and a child's effort to increase academic performance under perfect and imperfect information of a child's innate ability. In Section 3, we classify the types of parents and show their children's academic performance, which is based on their efforts. In Section 4, we classify the types of children and examine the optimal remedies for poverty alleviation in each case. Section 5 provides concluding remarks. 2 The Model 2.1 Perfect Information of a Child's Innate Ability To increase income, individuals must make an effort to increase their accumulation of human capital during childhood. We can observe the level of individual human capital based on their academic performance at school. Parental encouragement is effective in encouraging children to make efforts. The encouragement can act as a trigger to increase their children's motivation to study, efforts at school, accumulation of human capital, and future incomes. At the same time, encouragement consumes parents' time. Parents have to observe their children, check the 2 Some previous studies assume that parents are altruistic and that their utility does not include their consumption. Review of Economic Analysis 16 (2024) 409-422 412 www.RofEA.org available options to increase their motivation, and decide which kind of encouragement is optimal for their children. We propose a model based on Darolia and Wydick (2011) to clarify which types of parents tend to encourage their children to make efforts to increase their children's future incomes. 3 If the child's optimal effort is not significant enough to earn an income to survive, I, parents give them assistance, such as money, commodities, and cars. First, we consider the situation of perfect information about a child's innate ability. That is, each child knows their own innate ability as well as that of their parents. The utility function of child i is formed as: 𝑈𝑖𝑐= 𝛿𝑖𝐶(𝜃𝑖ln(𝑒𝑖)+𝑑𝑠𝑆𝑖)−𝑒𝑖 (1) where 𝛿𝑖𝐶 is the discount present value of a child's utility and 0<𝛿𝑖𝐶<1 is satisfied. When the child has a weak time preference, the discount rate is low while the discount present value is high and vice versa. 𝑒𝑖 is the level of child i's effort and ln(𝑒𝑖) is child i's academic performance. 𝜃𝑖 is a child's innate ability and 𝜃𝑖ln(𝑒𝑖) is a child's future income and 𝑑𝑠 is a dummy variable. 𝑆𝑖 is the amount of assistance provided by the parents. We are not considering the option that a child may avoid making an effort from the start just because they lack the income to live on, as long as their parents provide the amount of assistance. Parents can be assured of their child's abilities, and whether the child has made an effort or not can be monitored by their income. Therefore, by assuming that if the effort is lower than its optimal level, the parents' support will also be zero, the child will always make the optimal effort. When 𝜃𝑖ln (𝑒𝑖∗) ≥ 𝐼 is realized, parents do not give their child any assistance and d𝑠= 0 is satisfied. By contrast, when 𝜃𝑖ln(𝑒𝑖∗)< 𝐼 is realized, the parents give assistance to their child, I−𝜃𝑖ln(𝑒𝑖∗), and d𝑠= 1 is satisfied. Hence, 𝑆𝑖 is written as follows: 𝑆𝑖= 𝐼 −𝜃𝑖ln(𝑒𝑖) if 𝐼 −𝜃𝑖ln(𝑒𝑖)> 0 (2) 𝑆𝑖= 0 if 𝐼 −𝜃𝑖ln(𝑒𝑖)≤ 0 The derivation of (1) for 𝑒𝑖 is as follows: 𝜕𝑈𝑖𝑐 𝜕𝑒𝑖=𝛿𝑖 𝐶𝜃𝑖 𝑒𝑖−1 = 0 (3) 3 We introduce factors that affect the amount of encouragement, such as parents’ time preference, wages, and backgrounds. Moreover, we assume that parents include their own consumption in their utility, while Darolia and Wydick (2011) assume that parents are altruistic, and that their utility function incorporates their children’s utility and excludes their own consumption. NAKAMURA Parental Encouragement and Academic Performance 413 www.RofEA.org Therefore, the optimal effort level for child i, 𝑒𝑖∗, is the same as the discount present value of innate ability. In other words, 𝑒𝑖∗= 𝛿𝑖𝐶𝜃𝑖 is satisfied. Since the child's effort is decided based on the discount present value of their innate ability, parental encouragement is not effective in increasing their child's effort under perfect information. 2.2 Imperfect Information of a Child's Innate Ability In this section, we assume imperfect information about a child's innate ability. That is, a child does not know their own ability, whereas the parents do. Therefore, the child guesses it based on the amount of encouragement from their parents which determines the optimal level of effort. We classify the types of parents into nine groups, focusing on their backgrounds, time preferences, and wages, to clarify which type effectively increases children's future incomes. To simplify, we indicate that parents who were given enough encouragement from their parents to earn incomes to survive, I in the past, are EN, while parents who were not given enough encouragement to earn I and were given assistance to survive are AS. Next, we imply that parents who have strong time preferences are STP, whereas parents who have weak time preferences are WTP. Finally, we denote that parents whose wages are high are HW, and parents whose wages are low are LW. Table 1 is the classification of the types of parents. Parents who belong to Type 9 earn too little income to share their time for giving their children enough encouragement to realize the child's income to survive, I, regardless of their backgrounds and levels of time preference. We refer to these parents as LLW. The utility function of the parents j is represented as 𝑈𝑗𝑝= 𝛿𝑗𝑝(𝜃𝑖ln(𝑒𝑖)−𝑑𝑠𝐶𝑗𝑠)+𝑤𝑗(𝑇 −𝐸𝑗) (4) where 𝛿𝑗𝑝 is the discount present value of a parent’s utility and 0<𝛿𝑖𝐶<1 is satisfied. 𝐶𝑗𝑠 denotes the assistance cost. T is the parents' time in their lives, and 𝐸𝑗 is the hours of parents j 's encouragement for their child and 1<𝐸𝑗<T is satisfied. That is, 𝑇−𝐸𝑗 is the number of working hours. 4 A child makes an effort based on the amount of parental encouragement, which is denoted as E𝑗 𝐴𝑗, where 𝐴𝑗 is the effectiveness of encouragement and that 𝐴𝑗> 1 is satisfied. Therefore, 𝑒𝑖= 𝐸𝑗𝐴𝑗is satisfied, and (4) can be rewritten as: 4 Although there is time for household chores and leisure in real life, we omit them from the model because the main results are the same regardless of time. Review of Economic Analysis 16 (2024) 409-422 414 www.RofEA.org Table 1: The classification of the types of parents Type 1 Type 2 Type 3 Type 4 Type 5 Type 6 Type 7 Type 8 Type 9 EN WTP HW EN WTP LW AS WTP HW AS WTP LW EN STP HW EN STP LW AS STP HW AS STP LW LLW 𝑈𝑗𝑝= 𝛿𝑗𝑝(𝜃𝑖ln(E𝑗 𝐴𝑗)−𝑑𝑠𝐶𝑗𝑠)+𝑤𝑗(𝑇 −𝐸𝑗) (5) The value of 𝐴𝑗 is determined based on the parents' background. Parents who were given encouragement from their parents in the past are familiar with some options, features, and advantages of providing encouragement. Therefore, their value of 𝐴𝑗 is large and their encouragement effectively stimulates their child's effort. On the contrary, parents who were not given much encouragement from their parents in the past do not know their options well and their encouragement of their child becomes ineffective. Therefore, their value of 𝐴𝑗 is low. The child determines the optimal level of effort by guessing the value of 𝜃𝑖 as observing the amount of encouragement from their parents, E𝑗 𝐴𝑗. The derivation of (5) for 𝐸𝑗 is as follows: 𝜕𝑈𝑗 𝑝 𝜕𝐸𝑗=𝛿𝑗 𝑝𝜃𝑖𝐴𝑗 𝐸𝑗−𝑤𝑗= 0 (6) That is, we obtain the parents' optimal hours for encouragement as 𝐸𝑗∗=𝛿𝑗 𝑝𝜃𝑖𝐴𝑗 𝑊𝑗 (7) Each child guesses the own innate ability from the amount of encouragement shown by (7), when the child knows the parents' wages, background, and time preference and determines the optimal level of effort, 𝑒𝑖∗∗, where 𝑒𝑖∗∗ = 𝛿𝑖𝑐𝜃𝑖 is satisfied. From (5), when 𝑒𝑖∗∗ = 𝛿𝑖𝑐𝜃𝑖≥ 𝐸𝑗𝐴𝑗 is satisfied, optimal parental encouragement is efficient. In contrast, it becomes inefficient under 𝑒𝑖∗∗ = 𝛿𝑖𝑐𝜃𝑖< 𝐸𝑗𝐴𝑗, because some of the encouragement does not work. We notice that parental encouragement affects their children’s academic performance only when the children do not know their own innate ability. From this fact we obtain the following proposition. Proposition 1 Parental encouragement can affect their children’s academic performance in early grades rather than in late grades. NAKAMURA Parental Encouragement and Academic Performance 415 www.RofEA.org Proof. The children come to know their innate ability by some test results or report cards as the school year progresses. Therefore, the uncertainty of children’s innate ability decreases and a power of influence of parental encouragement diminishes in late grades. 5 3 Parental encouragement and child's effort From the (7), we obtain the following four propositions: Proposition 2 High-ability children tend to be given encouragement from their parents, whereas low-ability children tend not to be given encouragement. Proof. From (7), we obtain that the parents' hours for encouragement of their child, E𝑗, is the increasing function of the child's innate ability, θ𝑖. Therefore, high-ability children receive more encouragement from their parents, and vice versa. This result is the same as that proposed by Darolia and Wydick (2011). Regardless of the assumption that parents are altruistic or not, parents tend to encourage their children with high innate ability because children with high innate ability can increase their incomes more than children with low innate ability and realize the higher utility of their parents. Proposition 3 Parents with high wages (Types 1, 3, 5, and 7) hesitate to encourage their child, while parents with low wages (Types 2, 4, 6, and 8) tend to encourage their child. Proof. From (7), we obtain that the parents' hours for encouragement of their child, E𝑗, is the decreasing function of the parents' wage, w𝑗. Therefore, parents with high wages do not spend their time on encouragement compared with parents with low wages. Proposition 3 indicates that the opportunity costs of parents with high wages are large, and that they prefer working to encourage their child and vice versa. This result indicates that parental encouragement can alleviate the children's achievement gap based on the differences of parents' incomes. 6 This result may seem counterintuitive, as it suggests that children of higher-income parents are less likely to receive educational support from their parents. This considers the fact 5 Seror (2022) reveals that the use of television, smartphones, and tablets from early childhood hinders children's development, and emphasizes the need for parental encouragement from an early age instead. 6 Sankaran et al. (2020) imply the possibility that the reduction of educational inequality caused by the differences of parental levels of education can be realized through engaging in indirect within school parental involvement activities. Falk et al. (2021) also indicate that parental encouragement can have a positive effect on the economic preferences of children from families with low socioeconomic status, which could contribute to an increase in their future income. Review of Economic Analysis 16 (2024) 409-422 416 www.RofEA.org that even if parents are not directly involved in their children's education, they may provide support by paying for after-school tutoring or extracurricular activities. It is important to note that the definition of parent encouragement here refers to parents actively spending time engaging in their children's education. 7 Proposition 4 Parents with strong time preferences (Types 5, 6, 7,and 8) hesitate to give encouragement to their child, while parents with weak time preferences (Type 1, 2, 3, and 4) tend to give encouragement to their child. Proof. From (7), the parents' hours for encouragement of their child, E𝑗, is the increasing function of the parents' discount present value 𝛿𝑗𝑝. As the parents who have strong time preferences have a low value of 𝛿𝑗𝑝, they hesitate to devote their time to encouraging their child, while the value of 𝛿𝑗𝑝 for the parents who have weak time preferences is large and their hours for encouragement become longer. Proposition 4 indicates that parents who have weak time preferences suffer less from delayed effects of children's performance by their encouragement compared to parents who have strong time preferences. Proposition 5 Parents who had experience in obtaining encouragement from their parents (Types 1, 2, 5, and 6) spend a longer time encouraging their children, while parents who were not be encouraged by their parents (Type 3, 4, 7, and 8) spend a shorter time encouraging their children. Proof. From (7), we obtain that parents' hours for encouragement to their children, E𝑗, is the increasing function of the effectiveness of encouragement based on the parent's experience, A𝑗. Therefore, parents who were given encouragement from their parents in the past spend a longer time for encouragement compared to parents who were not. In this study, we consider that parents are not altruistic and care about their own incomes as well as their children's future incomes and focus on the opportunity costs of encouragement when the parents give encouragement to their children because these assumptions reflect real society. From these assumptions, we can conclude that parents' opportunity costs, time preferences, and backgrounds also affect the choice of parents, as Propositions 3, 4, and 5 suggest. These results imply that there is a possibility that children with low innate abilities and have parents with high income who have strong time preferences and did not get enough 7 Del Boca et al. (2014) indicate that parents spending time engaging in their children’s education is more effective for their cognitive development than financial expenditures, especially when the children are young.