Why Do Financially Illiterate Students Perceive Lower Education Returns? Evidence From a Survey in Rural China

This paper studies how students’ financial literacy affects their perceptions of returns to schooling and consequently their schooling decisions. We first propose a model of human capital accumulation where financially illiterate students exhibit a cognitive bias of “ironing heuristic.” With this decision heuristic, students tend to linearize the relationship between educational investments and future earnings, resulting in underestimated returns to education and inadequate study efforts. Using survey data from four rural middle schools in Southwest China, we then find a positive correlation between financial literacy and students’ perceived returns to education. In particular, the estimate of students’ perceived earnings function shows that its curvature significantly increases with students’ financial knowledge of compound interest, supporting the assumption in the theory. Our findings suggest that promoting students’ financial literacy may be an effective policy to motivate students to learn at school, especially in poor rural areas. JEL: I26, G53 (Financial Literacy), D91, J24


Introduction
It is well known that students' perceptions of educational benefits and costs exert a considerable influence on their schooling decisions.Many studies have found that a biased perception of the returns to education can contribute to the lack of motivation to study (e.g., Attanasio & Kaufmann, 2014;Jensen, 2010).One possible remedy for such a misperception is to provide target students (and their parents) with a range of tailored information, including that of schooling costs, financial aid opportunities, and future earnings.There has been a fast-growing literature on this important informational intervention policy (e.g., Damgaard & Nielsen, 2018;Lavecchia et al., 2016).
However, the evidence on the effectiveness of informational interventions remains mixed so far in the literature.Positive evidence is reported in, for example, Nguyen (2013), Jensen (2010), Wiswall and Zafar (2015), McGuigan et al. (2016), and Peter and Zambre (2017).On the other hand, many experimental studies in both developing and developed countries have found no statistically significant effects of informational interventions on school enrollment or completion.For instance, Busso et al. (2017) provided twelfth-grade students in Chile with information about financial aid and the returns to specific career-school programs, but this intervention did not affect the extensive margin of enrollment.Kerr et al. (2020) found no significant impact on the postsecondary education enrollment in Finland from informing high school graduates of the earning distribution and employment rates for different post-secondary degrees.Fryer (2016) examined an intervention in the United States by sending middle school students daily text messages with information about financial and non-financial benefits of education.He found a positive effect on the awareness of benefits but no effects on state test scores or student study efforts at least in the short term.Similar findings for the United States are reported in Hastings et al. (2015) and Carrell and Sacerdote (2017).
This raises the crucial issue that this paper seeks to address: why do students lack the motivation to study even when they are aware of educational costs and benefits?Our study first applies the concept of financial literacy to provide a possible explanation of why informational interventions are sometimes ineffective.
The key component in our theory is that if students (or their parents) are financially illiterate, then even if they are fully informed of the costs and benefits of schooling, they are still subject to a cognitive bias, the ''ironing heuristic,'' when they estimate the returns to education.As we will review in detail in Section ''The ironing heuristic and financial illiteracy,'' this ironing heuristic, as introduced in Liebman and Zeckhauser (2004), is well documented in the behavioral economics literature.Its essential idea is that people tend to linearize complex non-linear schedules and regard the average rate as the marginal rate in decision-making.In our context, the relationship between the costs and returns of an educational investment is typically non-linear (Kail & Ferrer, 2007;Murre, 2014).Under the ironing heuristic, students mistakenly believe that the marginal payoff of their study efforts is given by the average payoff.They will then underestimate the return to schooling, especially when the actual marginal return rate is increasing (i.e., when the educational investment is in the most beneficial phase).Due to this misperception, students will make insufficient study efforts, diluting the potential benefit from informational interventions.We formalize this idea in a two-period model of human capital investment.
Moreover, the paper provides empirical evidence that students' financial literacy indeed influences their perceptions of returns to education.We conducted a survey among four junior high schools in a state poverty county in Southwest China.Based on the survey data, our analysis shows that financially literate students are more likely to agree that investing in education will increase their future earnings.These students also expect higher monthly incomes in the future.In particular, students who are less skilled in compound interest have a perceived earnings curve with a smaller curvature.This is consistent with our assumption that financially illiterate students are more prone to the ironing heuristic and tend to linearize the marginal rate of returns to education.In addition, we find that not all financial knowledge has the same impact on students' perceptions of returns to schooling.Although knowledge of compound interest enhances one's expectation of educational returns as well as future earnings, knowledge of inflation, for example, has no such an effect.This paper is also motivated by the issue of high dropouts in remote and poverty-stricken areas in China.These areas include, for example, Bijie city in Guizhou province, Nujiang of the Lisu Autonomous Prefecture in Yunnan Province, and Liangshan Yi Autonomous Prefecture in Sichuan Province.(See, e.g., http://www.gov.cn/zhengce/2017-09/05/content_5222840.htm for discussions on school dropouts in these areas.)Despite the requirements of 9-year compulsory education and relevant policies that provide financial assistance to underprivileged students, independent surveys have reported that the school dropout rate remains high, especially in poor rural areas.For instance, based on eight surveys covering 24,931 students in four provinces, Shi et al. (2015) showed that the three-year cumulative dropout rate in grades 7 through 9 ranged from 17.6% to 31%.Using data from an annual survey of rural households in more than 100 villages across 30 provinces, Liu and Rozelle (2020) suggested that the dropout rate from junior high schools reached 14% overall and was especially high in some of the poorest areas.Similar evidence has been provided by H. Yi et al. (2012), Mo et al. (2013), H. Yi et al. (2015), Chang et al. (2016), Gao et al. (2019), andW. Yi (2021).Our research suggests that on top of providing financial aid, improving students' (and perhaps also their parents') financial literacy can be an effective complementary approach to encouraging students to stay at school.
Our paper also contributes to the growing literature on how financial literacy affects decision-making.Existing research finds supporting evidence that financial literacy helps, for example, household financial sophistication, personal portfolio investment, and accumulation of wealth (Bongini et al., 2015;Lusardi & Mitchell, 2014;Xu & Zia, 2012).However, there is little research on the impact of financial literacy on educational investment.To the best of our knowledge, this paper is the first to address this issue and examine how financial literacy influences an individual's perception of educational returns and schooling decisions.
The remainder of this paper is organized as follows.Section ''Theoretical Background'' presents a two-period model of human capital investment and formalizes the idea of how the ironing heuristic can lead to suboptimal educational investments.Section ''Data and Variables'' describes our data sources and provides descriptive statistics of the main variables.Section ''Empirical Results'' reports the empirical results on the relationship between financial literacy and the perception of returns to education.Section ''Mechanism: Financial Literacy and Ironing Heuristic'' explores a possible underlying mechanism based on the ironing heuristic.Section ''Conclusions and Policy Implications'' concludes and discusses the possible policy implications of our research.

Theoretical Background
This section studies a two-period model of human capital investment.Our main assumption is that when a student is financially illiterate, she will be subject to the ''ironing'' heuristic when she makes her study effort choice.We will give a detailed discussion of the literature on the ironing heuristic after presenting the model.

The Model
Consider a student who lives for two periods.She derives utility u(c i ) in period i = 1, 2 if her consumption in that period is c i The utility function u(c i ) is assumed to be twice continuously differentiable, strictly increasing and concave.Let b be her discount factor.
In the first period, the student attends school with a fixed amount of allowance y 1 from her parents to cover the non-tuition expenses in that period.She has two choices to make: her consumption c 1 (in which case her savings will be y 1 À c 1 , and her study effort e.).(More broadly, we interpret e as a joint product of the length of her schooling, which is determined by whether and when to drop out of school, and how hard she studies while she is in school.)When her effort choice is e, she will possess human capital f e ð Þ when she leaves school and joins the labor market in the second period.Here f e ð Þ is referred to as the function of human capital formation.We assume that f 0 ð Þ = 0 and f 0 e ð Þ.0, that is, the student's human capital increases with her study effort.Denote by v e ð Þ the student's effort cost function, and it is assumed to be twice continuously differentiable, strictly increasing and convex.
Following the literature on learning curves starting from Mazur and Hastie (1978), we assume that the human capital formation function f e ð Þ is S-shaped, that is, it is first convex and then concave as illustrated in Figure 1 below.It captures the idea that human capital accumulation has a stage of increasing returns in the beginning, followed by a phase of decreasing returns.Mazur and Hastie (1978) first proposed the concept of S-shaped learning curves.They also provide psychological experiment evidence that an accumulation model with S-shaped learning curves predicts better than the negative exponential growth model of learning process.This concept has been supported by many subsequent works such as Kail and Ferrer (2007), Leibowitz et al. (2010), andMurre (2014).In our context, S-shaped learning curves well capture the realistic learning pattern that students accumulate knowledge and skills at an increasing speed in the beginning (e.g., because the basic knowledge is relatively easy to learn but is very useful for their future jobs), but then enter a slow-down phase (e.g., because the knowledge becomes more advanced and so harder to learn).
In the second period, the student graduates from school (or drops out of school) and enters the labor market.When her accumulated human capital from the first period is f e ð Þ, we assume that she makes an income y 2 = f e ð Þw in the second period, where w is the market wage rate (for per unit of human capital).After receiving her income, the student makes her consumption choice c 2 .Since w does not play a critical role in our analysis, we henceforth normalize it to 1.
The student aims to maximize her lifetime utility by choosing her consumption in each period and her study effort level, subject to budget constraints: Where y 2 = f e ð Þ and r is the interest rate for the firstperiod savings.To deliver our main message in the most transparent way, we further simplify our model by assuming the allowance from the parents is so limited that it is impossible to save money in the first period (i.e., c 1 = y 1 ).(This is a plausible assumption for students in the poor rural areas in China.)Then the student's problem is simply to maximize by choosing her study effort in the first period.As a benchmark, suppose first that the student is perfectly rational and accurately understands the function of human capital formation f e ð Þ.Then the optimal study effort e Ã is determined by the first-order condition where the left-hand side is the marginal cost of making an effort, and the right-hand side is the (discounted) marginal utility in the second period from making an additional effort in the first period.Note that the first-order condition is also sufficient for the optimal solution if the objective function ( 1) is concave in e, that is, if This condition is satisfied for the concave part of the function of human capital formation, and it is also satisfied for the convex part if the cost function v e ð Þ is sufficiently convex.For simplicity, we henceforth assume the objective function is concave.

The Ironing Heuristic and Financial Illiteracy
People tend to simplify complicated decision problems by resorting to decision heuristics (e.g., Berthet, 2022;Stanovich, 2003).In our context, the non-linear human capital formation function f e ð Þ is not easy for all students (or their parents) to understand and take into account when they make decisions about investment in human capital.Instead of calculating the margin return to study effort from the actual f e ð Þ, students, especially those who are financially illiterate, may linearize the relationship between efforts and human capital accumulation and use the ''average'' rate to simplify their decisions.This decision heuristic is called the ''ironing'' heuristic, a cognitive bias well documented in the behavioral economics literature.Liebman and Zeckhauser (2004) define the ''ironing'' heuristic as a misperception of complex nonlinear payoff schedules such as pricing schedules, tax schemes, and welfare systems.It arises when a decision-maker perceives the slope of a line segment between the origin and a point on a nonlinear schedule as her average incentive.For example, when facing a progressive tax schedule, a taxpayer may linearize it and use the average income tax rate to decide her optimal effort in earning income.This ironing heuristic has been widely observed in empirical research on income taxes (de Bartolome, 1995;Feldman et al., 2016;Liebman & Zeckhauser, 2004;Rees-Jones & Taubinsky, 2020).For example, Rees-Jones and Taubinsky (2020) find that the ironing heuristic is prevalent among taxpayers, with about 43% of them ironing.A special case of the ironing heuristic is the so-called ''exponential growth bias'' in financial decision-making (Almenberg & Gerdes, 2012;Levy & Tasoff, 2016; C. R. Mckenzie & Liersch, 2019;Stango & Zinman, 2009).It accounts for people's tendency to linearize exponential functions.For example, Almenberg and Gerdes (2012) and C. R. Mckenzie and Liersch (2019) find that, without a proper understanding of compound interest, participants in their experiments are prone to believe that savings grow linearly and hence underestimate the exponential growth of lifetime earnings.This suggests that the tendency to adopt the ironing heuristic is correlated with a lack of financial literacy.
Although we are not aware of any direct evidence of the ironing heuristic in educational investment decisions, the extensive evidence from other contexts suggests that adopting this heuristic in scenarios involving non-linear payoff schedules is a general tendency in the population, especially among people with poor financial literacy.Consequently, in this paper we assume that financially illiterate students exhibit the ironing heuristic when choosing their study efforts.More specifically, we assume that a financially illiterate student makes a linear estimate of the marginal return to study effort: , where e Ã is the optimal effort choice made by a perfectly rational student.(One possible justification for observing the optimal choice is that schools may advise students to act optimally by showing them the future income they could earn if they made the optimal effort now.)Given this misperception, the student expects a future income y 2 = ke if she chooses an effort level of e. Then the first-order condition of the utility maximization problem becomes where ẽ denotes the ''optimal'' effort choice under the ironing heuristic.Figure 2 below illustrates how the ironing heuristic works.Ray k a is the linear relationship perceived by a financially illiterate student after observing the outcome Þ is the only tangent point between a ray from the origin and the S-shaped function of human capital formation; at that point Þ , the student will underestimate (overestimate) the marginal return of study effort if e Ã \e 0 (e Ã .e 0 ).

Insufficient Effort Choice
We now compare e Ã the optimal study effort by a perfectly rational student with sufficient financial literacy, with ẽ, the study effort chosen by a student with poor financial literacy.Using ( 2) and (3), we get Recall that when a student with low financial literacy observes e Ã , she infers a constant marginal return to Then we have the following result: Proposition 1.Compared to a student with sufficient financial literacy, a financially illiterate student chooses a lower level of study effort (i.e., ẽ\e Ã ) if and only if she observes e Ã \e 0 .
Proof.Consider first the case when the student observes e Ã \e 0 .Suppose in contrast ẽ.e Ã .Then we must have , given e Ã \e 0 .Hence, the left-hand side of condition ( 5) is strictly less than 1, while the righthand side is strictly greater than 1.This is a contradiction.A similar logic implies ẽ.e Ã if the student observes e Ã .e 0 .Q.E.D.This result is simply because when e Ã \e 0 , compared with a student with sufficient financial knowledge, a financially illiterate student underestimates the marginal effect of study effort on her future income.While when e Ã .e 0 , the student overestimates that effect.
Since this paper focuses on students from povertystricken regions, presumably they face a sufficiently high marginal cost of making effort (or staying at school).As a result, it makes more sense to assume that their optimal study effort e Ã is below e 0 .That is, their study effort choice, even if they are rational, is likely to be at the phase of increasing returns.This, together with Proposition 1, implies that relative to financially literate students, financially illiterate students are inclined to perceive a lower marginal return to education and expect a lower income in the future.As a result, even when fully informed of the costs and benefits of education, they still tend to exert less study effort.
We therefore have the following hypotheses for students in poor rural areas: Hypothesis 1. Students with lower financial literacy expect a smaller impact of educational attainment on their future earnings.Hypothesis 2. Students with lower financial literacy expect a lower monthly income in the future.From the next section, these two hypotheses will be tested by using survey data from four junior high schools in a county in Southwest China.

Data
The data in our empirical analysis was collected from a hybrid questionnaire survey conducted online-offline in July 2018 at M County of Southwest China, as part of the Peking University Caitong EconEdu for Kids Program.This voluntary program offers free short-term courses on financial knowledge in rural schools, with the aim of improving rural children's financial literacy.The project is concerned with the educational quality in rural regions of western China.Many of these regions are characterized by poor environmental conditions and traffic inconvenience.Compared with the eastern and central regions of China, these regions in western China have slower economic growth and thus make relatively low investments in compulsory education.As a result, the issue of high dropouts becomes concerning, especially in poor rural areas.Children from low-income families or left-behind children in these areas are more likely to lack study motivation.
Located in an autonomous prefecture of Yunnan Province, M County is one of the nationally designated poor counties, with the highest poverty rate in the autonomous prefecture and a large outflow of migrant workers.Over 90% of the area of M County is mountainous and 85% of the population lives in rural areas.According to the data from M County Government, the per capita net income of rural residents was less than 1,600 dollars in 2017.Forty-two percent of the low-wage workers in M County work downtown or outside the county, leaving their children behind.Figure 3 shows the per capita income and the average middle school enrollment rate in each county of the autonomous prefecture.Both indexes are relatively low in M County compared to other counties.In this sense, M County is a good representative sample of the poor rural areas in question.On the other hand, M County has been experiencing high dropouts from middle schools.Specifically, the average graduation rate of the eight rural middle schools in the county was 86.7% in 2017, which was 3.6 percentage points and 8.2 percentage points lower than the autonomous prefecture and the country, respectively.
The project team randomly chose four out of the eight rural junior high schools in M County (see Figure 4 for the locations of these four schools).The 43 surveyed classes were determined by cluster sampling to reduce inter-group differences, and the survey was conducted under the guidance of IT instructors.We trained the instructors to fully understand the questions and  procedures before assigning them to the classes.In the classrooms, they guided the students to complete the online questionnaire within 40 min using computers.Students were allowed to seek help from the instructors if they had difficulty understanding the survey questions.After the students completed the questionnaire, all the responses were submitted to the online survey platform.This combination of online and offline procedures helped to ensure the efficiency and quality of the data collection.
The survey collected 1,737 valid responses in total.Among the respondents, 43.7% were in grade 7, 43.29% in grade 8, and 13.01% in grade 9; males account for 52.6%, and left-behind children account for 17.5%.The average age in the sample was 15 years.Their parents had an average of 7 years of schooling, merely beyond the 6 years of primary education.This dataset contains a broad range of data items relating to (1) basic personal information and family background; (2) the understanding of financial information on government subsidy policies in compulsory education; (3) financial knowledge measured by the understanding of compound interest, inflation, and personal financing; (4) financial behaviors in terms of budget planning and saving; and (5) perceptions of costs and returns to education, measured by the self-assessed opportunity cost of attending school, expected future earnings, preference of savings for further education, and attitude toward educational returns.

Descriptive Statistics
Variables Indicating Financial Literacy.Financial knowledge is the core measure of financial literacy.This paper examines a student's financial knowledge of basic financial concepts such as compound interest, inflation, and personal financing.In the questionnaire, three questions are designed for the respondents to calculate compound interest, estimate their purchase power when prices increase at the same rate as the allowance from parents, and choose appropriate ways to ''make money with money.''The respondent is then scored on a 100-point scale according to the answers.The weighted average score k_score is used to measure the respondents' financial knowledge.As shown in Table 1, the average score is approximately 52 points, suggesting that these students' financial knowledge is limited.
Dependent Variables.This paper examines the relationship between a student's financial literacy and the perceptions of educational returns.We employ two variables to represent different aspects of the student's perceptions: the recognition of education returns and the expected monthly earnings over the following twenty years.Based on these variables, we can then investigate how well a student's financial literacy explains the variation in their understanding of the returns to education.
Recognition of education returns is the belief that one's future earnings increase with the educational attainment.68.11% of respondents agree that earnings can increase with education level.To further investigate the effect of financial literacy, this study also examines the link between financial literacy and the belief that hard work changes one's life.The latter is measured by a dummy variable which takes the value of 1 if the respondent agrees that working hard can improve the family's socioeconomic status, 0 otherwise.Our data show that 86.70% of respondents believe that working hard can reduce poverty, while 59% of respondents agree that they can benefit from both education and working hard.
We use the expected monthly earnings in 10 years' time to quantify students' expectations of their future income.As a reference, the questionnaire provides information on the average monthly salary by education level.The responses of the interviewed students are shown in Figure 3(a).About 25% of respondents expect themselves to earn 4,000 renminbi (RMB) per month in 10 years.
Control Variables.The basic control variables are selected according to three categories: personal characteristics, family background, and the student's financial status.Besides, students' understanding of the government's subsidy policies on compulsory education and their risk attitude are included.We also control for students' math scores to mitigate the potential endogeneity bias caused by unobserved cognitive factors that are correlated with financial literacy.Furthermore, we take into account school-level fixed effects to separate the variation in students' perception of the returns to education due to schools' education quality, management styles, among other factors.The summary statistics are presented in Table 1.
Among the respondents, 52.6% are male.Most of the respondents are in seventh and eighth grades, and 16.6% are the only child in the family.As for family backgrounds, the average years of education of the more-educated parent in the household are 7.6 years, slightly more than 6 years of primary education.Students' personal disposable income mainly comes from the allowance provided by parents.With the top and bottom 1% outliers removed from the sample, students' monthly allowance averages 193.25 RMB.The amount of monthly allowance, to a great extent, reflects family economic conditions and varies considerably among students, with the maximum reaching 4,000 RMB while the minimum of less than 1 RMB.The balance of monthly allowance is 40.37 RMB on average and is also notably different among students, with the maximum of 2,025 RMB and minimum of less than 0.10 RMB.In the regressions, we take the logarithm of both students' monthly allowance and allowance balance.
A student's understanding of the subsidy information is indicated by the extent to which they comprehend the government subsidy policies in compulsory education.The Chinese government has carried out several widespread subsidy programs in rural compulsory education to support rural education and narrow the discrepancy between urban and rural education.The programs which target rural students mainly include a general subsidy for needy students, student nutrition and meal subsidy, and subsidy for boarding expenses.All the schools in our sample are subsidized and supported by national rural education subsidy programs.Also, subsidy policies are the primary source of public financial information that rural students can access daily.Our survey has six questions that query whether they know about the subsidy policies mentioned above, the rates of student subsidies, and the recipients of subsidies.Each question is scored out of 50 points, and the total score is used to represent the student's understanding of financial information.According to Table 1, students seem to have achieved a relatively high comprehension of student subsidies, averaging 42 points.
A student's risk attitude is measured by their choice between a certain reward (''earning a certain 1,000 RMB'') and a risky lottery game (''flipping a coin and receiving 2,000 RMB if it comes up heads or nothing if tails'').The mean value of risk_attitude indicates that more than half of the respondents are risk-averse.
Both a student's financial literacy and their subjective evaluation of the cost-benefit of education may be influenced by their cognitive ability.However, cognitive ability cannot be directly observed or measured.This will cause the problem of correlation between the error term and the explanatory variables, leading to inaccurate estimation of coefficients.To address this potential endogeneity concern, we use students' math scores in the most recent exam as a proxy for their cognitive ability.The average score is 68 out of 120 points.
Figure 5 illustrates the distribution of students' expected monthly earnings, financial literacy score, monthly allowance, and balance of monthly allowance.

Financial Literacy and Recognition of the Returns to Education
In examining how well financial literacy explains the variation in students' recognition of returns to education, we use stu_income as the dependent variable.It is a dummy variable that takes the value of 1 when the respondent agrees that schooling increases future earnings and 0 otherwise.We apply a binary logit model to do the estimation: where P stu income i = 1 ð Þcorresponds to the possibility of student i agreeing that education can increase one's earnings; a is the coefficient on the score of financial knowledge; Y is the matrix of control variables, and b is the corresponding coefficient vector.Columns (1) to (5) in Table 2 provide the regression results by gradually adding control variables.In the regressions, financial knowledge is measured by standardized scores.In column (6), the sample is truncated at 1% of students with the highest monthly allowance and monthly allowance balance for regression.In Column (7), the financial knowledge score is standardized with the means and variances at the school level.The indicator of financial knowledge enters significantly positive at the 5% level in regression (5) when we take all control variables into consideration and at the 10% level in regressions ( 6) and (7).These results all support that gaining financial knowledge is positively associated with students' recognition of schooling returns, in line with Hypothesis 1 that financially illiterate students tend to underestimate the effect of educational attainment on their future earnings.
By contrast, the understanding of subsidy policies has no correlation with students' recognition of the returns to education.This result suggests that a complete understanding of subsidy information might induce students to estimate a lower cost of schooling but may not necessarily help them improve their recognition of the benefits of education.Students with higher math scores, which we assume indicates higher cognitive ability, are significantly more likely to agree that education increases future earnings; this shows that students' higher cognitive ability may help them better understand human capital accumulation and more positively recognize returns to education.Compared with non-left-behind children, left-behind children are less likely to agree on the benefits of education, which may reflect the negative impact of the absence of parents' involvement on adolescent educational variables, as suggested by D. McKenzie and Rapoport (2011) and Zhou et al. (2014).
All the other variables do not appear to have significant correlations with the dependent variable after we control for the school fixed effect.Among them, the insignificant effect of parents' higher education level is inconsistent with existing studies.According to Coleman (1988), parents' educational levels positively affect their children's educational outcomes.However, Coleman also points out that such a positive influence requires a benign parent-child relationship to act as an ''incubator.''In fact, when adolescents start to change their beliefs about parental authority to impose rules and restrictions, they are likely to exhibit ''psychological reactance'' and defy their parents (Donnell et al., 2001;Van Petegem et al., 2015).Parents with higher levels of education tend to advocate the importance of schooling because of their higher expectations for their children (Davis-Keen, 2005;Wang et al., 2016).This may lead their children to have more negative attitudes toward school, resulting in an insignificant correlation between parents' educational levels and students' recognition of educational returns.Moreover, neither the allowance nor the balance of allowance is significantly correlated with students' recognition of education benefits.This may be because the balance of allowance is too low to stimulate the demand for financial knowledge.The recognition of education returns does not seem to vary by gender or among students with and without siblings.

Financial Literacy and Expected Monthly Earnings
We propose the following multivariable linear regression model to examine the impact of students' financial literacy on their expected monthly salaries over the next 20 years: The survey asked students about their expected monthly earnings by offering choices of six income ranges ranging from ''less than 3,000 RMB'' to ''more than 20,000 RMB'' as illustrated in Figure 3(a).Therefore, we apply Tobit regression to estimate the correlation between financial knowledge and expected monthly salaries.The vector of control variable X in equation ( 7) is almost the same as X in equation ( 6), except the former includes the student's self-assessed opportunity cost of attending school instead of working, measured by the threshold monthly salary that just induces the student to quit school for paid work.(The details and meaning of the variable ''self-assessed study cost'' are further discussed in Section ''Mechanism: Financial Literacy and Ironing Heuristic.'')The variable ''self-assessed study cost'' reflects how much effort a student is willing to devote to studying.Intuitively, the higher the cost the student would like to pay for schooling, the higher her expectations for future earnings.Columns (1) to ( 4) in Table 3 present the Tobit regression results with different sets of control variables.In Columns ( 5) and ( 6), ''selfassessed schooling cost'' is controlled for, and in column (6), students' financial knowledge score is standardized at the school level.
The estimated coefficients of financial knowledge are significantly positive in all six specifications.With all the control variables and school fix effect included in specifications ( 5) and ( 6), the coefficient remains statistically significant at the 5% significance level.This indicates that the expected monthly earnings increase with the level of financial knowledge.A rise of one standard deviation of the scored financial knowledge, ceteris paribus, significantly corresponds to an increase of nearly 400 RMB in the expected monthly earnings.This finding supports the theoretical assertion in Section ''Theoretical Background'' and justifies Hypothesis 2 that students with higher financial literacy generally expect better wage prospects.
Although teenagers may disagree with their parents about the value judgment of education benefits due to their adolescent rebellious psychology, they still subconsciously refer to their parents' income level when they are thinking about the question of their expected future earnings.Therefore, the higher their parents' education level, the higher their expected income, which may lead to a significant positive correlation between parents' education level and children's expected monthly income.Similar to the regression results for recognition of the benefits of education, monthly allowance, balance of monthly allowance, and the knowledge of subsidy policy do not have a significant correlation with students' expected monthly income.
Male students' expected monthly earnings are significantly higher, which may be related to the wage difference between genders observed by students.Compared with the risk-averse students, the students with risk preference have significantly higher expected monthly income.Because education investment has certain risks (Levhari & Weiss, 1974;Weiss, 1972), students with risk preference are more willing to take risks and obtain high returns to educational investment.
In Columns ( 5) and ( 6), the effect of the financial knowledge becomes slightly smaller in magnitude with the self-assessed study cost included in the regression, statistically significant at the 5% level.The result implies that those students with a stronger willingness to pay for schooling usually have higher expectations for their education returns, which is consistent with a standard investment model.

Potential Endogeneity Problem
In Tables 2 and 3, we include various variables such as students' financial status, personal characteristics, and parents' education level.We also control for school fixed effects in the regressions.However, there are some unobserved factors, such as students' study motivation, IQ, and family economic status, which may affect both the students' perception of educational benefits and their level of financial literacy.This could result in endogeneity bias.In this section, we perform instrumental variable estimations to further investigate the impact of financial knowledge.
We construct two instrumental variables for financial knowledge.One instrument is the average financial knowledge score on class level.The other is the monthly expenditure gap, calculated as the self-reported expenditure minus the difference between the monthly allowance and the monthly allowance balance.According to the survey data, the average gap of monthly expenditure is considerably high, reaching 264 RMB, which indicates that the rural teenagers are poor in financial management.Both the Sargan test for exogeneity of the instruments and the F test for weak instruments suggest that the two instrumental variables are valid.
Table 4 reports the IV regression results.The p values of Anderson-Rubin test for the exogeneity of financial knowledge in Columns (2), (3), (5), and ( 6) are all less than 10%, implying that there might be endogeneity bias in the previous estimates.Nevertheless, the IV estimation results strongly support that students' financial knowledge can help enhance their recognition of education returns and increase their expected monthly earnings.
Moreover, IV estimates are greater than OLS, Probit, and Tobit estimates.

Further Discussions on Financial Literacy
We conduct additional regressions to establish the robustness of the results presented in Tables 2 and 3. We first ''decompose'' the financial knowledge score; then we add variables related to financial decisions to the regressions.The positive correlations found in the previous sections prove robust to a number of alternative specifications.
Detailed Financial Knowledge.As discussed in Section ''Data and Variables,'' financial knowledge score is a weighted average score of a student's knowledge about compound interest, inflation, and money management.In this section, we investigate the impact of each of these scores and standardize the scores for the convenience of comparison.A student's knowledge about subsidy policies is also standardized in the regression.Specifications (1) and (2) in Table 5 present the new regression results.The score of compound interest positively correlates with the dependent variables, while no significant correlation exists between a student's knowledge of inflation and the dependent variables.Students with better understanding of personal finance are significantly more likely to agree that education increases personal income.However, there is no significant correlation between a student's understanding of personal finance and their expected future monthly income.
These findings confirm what our theoretical model and hypotheses predict.Indeed, compound interest is a typical example of non-linearity, as it involves the nonlinear relationship between the interest rate and the amount of money accumulated at the end of a period.It corresponds to a special case of the ironing heuristic, namely the exponential growth bias in financial decisionmaking as discussed in Section ''Theoretical  2 and 3. * and *** indicate 5% and 1% level of significance, respectively.
Table 5. Regressions on Detailed Financial Knowledge.
Regression method Background.''Students with insufficient financial knowledge particularly in compound interest are more likely to evaluate the complicated non-linear payoff schedules by simply linearizing it.This heuristic bias would drive them to perceive the average payoff to their study efforts as the marginal payoff at the convex phase of human capital formation, resulting in an underestimation of returns to education.Whereas the other two aspects of financial knowledge, namely the understanding of inflation and financial investment, are in fact less relevant in the context of the non-linear relationship.As such, students who are financially illiterate in these two aspects are less affected by the ironing heuristic.In light of these findings, we expect that different aspects of financial knowledge could have different effects on a student's perception of returns to education.This provides a policy implication that informational interventions should distinguish behavioral biases that are caused by different aspects of financial illiteracy.
Financial Behavior.Although financial knowledge is the core of financial literacy, it does not cover the whole story.In addition to the understanding of financial concepts and risks, financial literacy also involves the skills, motivation, and self-efficacy to apply such knowledge to make effective decisions in various financial contexts (OECD, 2017).Therefore, we also need to consider financial behavior which is an essential part of financial literacy.It involves the actions a student does or does not take in a specific situation to secure her financial future.Specifically, we examine the financial behavior from two aspects: how often she makes budget plans and whether she made savings recently.According to our survey, 38.11% of respondents make monthly budget plans, while 11.86% do not.Statistics also show that 70.29% of the respondents have savings.
We include these financial behaviors in our model.Regression results of specifications (3) and (4) in Table 5 provide evidence that planning and saving behaviors have no significant correlation with students' recognition of the returns to education or their expected future earnings.Specifications ( 5) and ( 6) take into account the detailed financial knowledge and the two aspects of financial behavior.There are no apparent changes in the correlations between these variables and dependent variables.In brief, our empirical findings hold in various robustness checks.

Mechanism: Financial Literacy and Ironing Heuristic
Ironing Heuristic in a Perceived Earnings Curve The previous section shows the positive impact of students' financial knowledge on their recognition of returns to education and their expected future earnings.Further investigation, however, is needed to elucidate the mechanism underlying such correlations.As discussed in the theoretical framework in Section ''Theoretical Background,'' financially illiterate students are likely to draw on their observations of the real world to linearize the relationship between educational inputs and future earnings.In this section we will provide further evidence to justify the mechanism of this ironing heuristic that our model proposes.
We use a student's self-assessed opportunity cost of staying at school (instead of working) to measure the efforts she wants to devote to studying.The higher the wage level that attracts a student to leave school to work, the greater the opportunity cost for her.In our sample, the average of this opportunity cost is 5,721.93RMB.The vast majority of the respondents (31.09% of the sample) opt for a monthly rate of 10,000 RMB or more, while 27.46% of the respondents choose 3,000 RMB.Provided with a monthly rate as low as 1,000 RMB, 8% of the respondents are still willing to drop out of school for paid work.
We then specify a linear earnings curve that a student with poor financial knowledge perceives as follows: where cost is the student's self-assessed opportunity cost of schooling.Meanwhile, we specify a nonlinear earnings curve for a financially literate student where a .0. The term cost a captures the nonlinear relationship between schooling costs and benefits at the teenagers' early education stage.We incorporate equations ( 8) and ( 9) into a single equation by adding a cross term k score Á cost a as follows: Equation (10) implies that the coverture of the quadric function for earnings varies with students' financial literacy, so the sign and size of its coefficient l reflect the heterogeneity of the ironing heuristic among students with different financial literacy levels.A positive l indicates that students' nonlinear thinking ability increases, or their ironing heuristic decreases, with their financial literacy.To ensure that expected earnings increase with financial literacy, a is set equal to 3/2 in the regressions.

Ironing Heuristic Due to Financial Illiteracy
Table 6 presents the regression results for equation (10).Columns (3) to (8) use scores on each question on financial literacy to substitute the total score.The control variables are the same as in Table 2.Only the coefficient on the cross term score of compound interest with cost 3=2 remains positive at the 5% significance level in all specifications.Due to the collinearity between cost and cost 3=2 , the estimate of g 2 is not significant, but the estimate of g 3 keeps significant in all regression specifications.The significantly positive estimate of d in column (3) and (4) suggests that students who are more skilled in calculating compound interest have a higher degree of curvature in their education cost-benefit curve estimation.In contrast, less proficient students tend to linearize the relationship between education costs and benefits and have a stronger ironing heuristic cognitive bias.As our theoretical model predicts, such a bias leads students to underestimate the rate of returns to education at their early school stage.
Several studies have offered evidence that the cognitive bias related to exponential growth or compound interest might affect an individual's decision-making process.Existing experimental research shows that exponential growth bias, which is defined as a tendency to linearize exponential functions and is similar to the ''ironing'' heuristic bias, is negatively correlated with an individual's financial literacy and household financial outcomes (Almenberg & Gerdes, 2012; C. R. Mckenzie & Liersch, 2019;Stango & Zinman, 2009).From a field experiment conducted in rural China, Song (2020) finds that explaining the concept of compound interest to rural households increases their pension contributions by roughly 40%.The regression results in Table 6 provide evidence that students' financial knowledge of compound interest shapes their perceptions of the future value of educational investment, especially their perceptions of the increasing growth rate at the early stage of human capital accumulation.
It is worth noting that the influence of (possibly heterogeneous) discounting is ignored in the theoretical analysis, and surveyed students did not carry out any discounting calculations.Theoretically, compound interest defines the future value of wealth as an exponential growth function of the interest rate.Compared with simple interest, it emphasizes the nonlinear relationship between the present value and future value.In our model, human capital accumulates with study effort non-linearly.Therefore, the future earnings increase with schooling year non-linearly.Students lacking compound interest knowledge would tend to linearize the above relationships and then get a lower perceived educational return.As a result, the knowledge of compound interest and the curvature of the estimated education cost-benefit curve positively correlates.The intuition behind this phenomenon is exponential growth bias, but such a correlation does not rely on discounting.
As for the survey, we provided information on the average monthly salary by educational level as a reference, and students could match their expected schooling level with monetary gain, which actually reflects students' planning for future educational outcomes.In the process of students answering the questionnaire, they did not carry out any discounting calculations.Therefore, the results in Table 6 clearly demonstrate that students with better knowledge of compound interest usually have a better understanding of nonlinear relationships and thus have more optimistic expectations of educational outcomes resulting from learning input, which corresponds to higher earnings expectations.

Conclusions and Policy Implications
Young people's lack of motivation to study, especially among developing economies, has been the subject of much discussion.In China, nine-year compulsory education is provided for free.Moreover, direct financial aid is offered to poor youths to ease their burden of educational costs.Yet the opinion of ''schooling is useless'' prevails widely among students in some regions.Meanwhile, poor rural areas have been experiencing high dropouts, especially from junior high schools.One reason could be students' biased perceptions of returns to education.And to address these challenges, policy interventions have been utilized to provide students with detailed information about educational costs and benefits.However, plenty of evidence suggests that such informational interventions are not always effective.
From the perspective of behavioral biases, our study explores possible explanations by investigating the role of financial literacy in determining one's perceptions of returns to education.The approach of this paper is twofold.We first provide a theoretical analysis of a twoperiod model of human capital investment.An important assumption is that students with insufficient financial literacy tend to exhibit a cognitive bias, the ''ironing heuristic.''Under the ironing heuristic, people are prone to linearizing complex non-linear payoff schedules.Consequently, they regard the average rate of the payoff schedule as the marginal rate.In our context, financially illiterate students tend to linearize the nonlinear human capital formation.As a result, they mistakenly perceive the average payoff to their study efforts as the marginal payoff, especially when the educational investment is in the most beneficial phase.This leads to students' underestimation of the marginal return to education and thus insufficient investment in education.These theoretical results suggest two hypotheses that, with lower financial literacy, students would perceive a smaller influence from education on future earnings and also expect lower monetary returns to schooling.
We then proceed to provide empirical evidence of the effect of financial literacy, using survey data from four rural junior secondary schools in Southwest China.The outcome of interest is the perception of returns to schooling.To test the two hypotheses, there are clear rationales for measuring the outcome variable in the following two dimensions: an individual's awareness of educational benefits and her expected labor market payoffs.Our empirical analysis is laid out as follows.First, our baseline estimations indicate significantly positive correlations between financial literacy and the perception of educational returns, consistent with the two hypotheses.That is, financially illiterate students are more likely to underestimate the impact of educational attainment on monetary returns to schooling; and these students generally expect lower future earnings.Second, these results hold in various robustness checks and are also supported by the IV estimations.In particular, students with poor knowledge of compound interest are found to perceive lower returns to education, which is in line with our theoretical assumption that poor financial literacy is associated with linearization bias.Last but not least, the estimate of students' perceived earnings curve indicates that the relationship between the quadratic term of schooling costs and students' perceived benefits varies with the understanding of compound interest.This finding indicates that the more students learn about compound interest, the higher the degree of curvature of their perceived earnings curve and the less ironing heuristics they hold.
In conclusion, both our theoretical and empirical analyses suggest that financial illiteracy biases impair students' understanding of returns to education.These findings have two practical implications for more effective interventions in information and more suitable financial education programs in rural areas.First, the traditional informational intervention has been limited to the information about educational costs and benefits, without considering whether rural students understand the information before they make schooling decisions.Therefore, it is necessary to provide them with learning programs focusing on financial knowledge, especially knowledge of non-linearity such as compound interest calculation.By helping them better understand the nonlinear characteristics of human capital accumulation, such financial education programs could reduce their ''ironing'' heuristic cognitive bias and, as a result, motivate them to devote more efforts to schooling.Second, since there is little demand for financial service among rural students, they can hardly foresee any benefit from learning financial knowledge.Therefore, it is crucial to design other financial education curricula that could improve rural students' ability in terms of goal setting, self-control, delayed gratification, etc.In the short run, rural students will derive much benefit from these programs which, in the long run, can eventually contribute to reducing poverty in rural regions.

Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figure 2 .
Figure 2. Ironing Heuristic in estimating the relationship between efforts and incomes. e

Figure 3 .
Figure 3. Per capita income and average middle school enrollment rate in each county of the autonomous prefecture.Note.Horizontal axis is the per capita income ranking (from the lowest to the highest).

Figure 4 .
Figure 4. Map of surveyed area.Note.The map of China shows the location of Yunnan Province.The map of Yunnan Province shows administrative divisions at the county level.The map of M County shows the locations of four schools.

Figure 5 .
Figure 5. Distribution of variables: (a) expected return of education, (b) score of financial literacy, (c) monthly allowance, and (d) allowance balance.

Table 2 .
Financial Literacy and Recognition of Returns to Education.

Table 3 .
Financial Literacy and Expected Monthly Earnings.
Note.Standard errors in parentheses.Control variables are the same as in Tables

Table 6 .
Financial Knowledge and Earnings Curve.