Financial Illiteracy and Pension Contributions: A Field Experiment on Compound Interest in China

Abstract

The inadequacy of retirement savings in the United States is a common, and at times controversial, theme in the literature (Venti and Wise 1997; Lusardi 1999; Lusardi and Mitchell 2011; Scholz, Seshadri, and Khitatrakun 2006). Two strands of literature seek to explain this phenomenon. One, which focuses on the lack of information and financial sophistication, stresses the importance of financial literacy and financial education; the other attributes undersaving to self-control problems and procrastination.¹

This paper follows the first strand. Financial illiteracy is widespread in the world and is correlated with poor decision-making, even when the consequences are as significant as they are for retirement savings and home equity loans (Agarwal et al. 2009; Gerardi, Goette, and Meier 2013; Lusardi and Mitchell 2014; Agarwal and Mazumder 2013; Goda et al. 2015; Stango, Yoong, and Zinman 2017). I focus on one concrete definition of financial illiteracy: misunderstanding compound interest. Understanding compound interest is especially important to retirement savings decisions due to long investment horizons. Does such a misunderstanding influence pension contributions? Can pension contributions be improved by explaining the concept of compound interest to potential pension contributors?

I designed a field experiment to evaluate whether misunderstanding compound interest is partially responsible for low pension contributions in rural China. I randomly assigned more than 1,000 Chinese households to 1 of 3 groups: the Control group, the Calculation group, and the Education group. In the control group, I visited households, explained the pension contract, and conducted a survey about their socioeconomic background. In the calculation treatment, I also calculated respondents’ expected pension benefit levels after age 60 if they contributed at various levels starting at age 30. In the education treatment, I asked respondents questions about compound interest, explained the correct answers, taught them the basic concept of compound interest, and performed the same calculations used in the calculation treatment. The education treatment tests whether I can correct individual bias about compound interest through consumer learning. Comparison of the calculation treatment and the education treatment tests whether providing information or improving understanding increases pension contributions. I collaborated with a local government to provide the interventions before participants chose their contributions for that year, and then collected administrative data on their actual pension contributions from the local government.

I find that 56% of rural households in the sample told us they do not know the answer to the simplest compound interest question (after repeated prompting), and 73% of those who answered the question underestimated compound interest. The experiment reveals that the education treatment increased the contribution for that year by 49–53 RMB, resulting in an increase of 40% relative to the average contribution of 133 RMB in the control group.

Why does teaching compound interest increase pension contributions? One possible channel is a better understanding of compound interest, so that subjects can apply the principle to their own choices. Another is learning the benefits of a pension in general, which suggests that providing retirement income projection should have equivalent effects. To distinguish these channels, I study the heterogeneous effect with respect to initial knowledge about compound interest, compare the effects between the education group and the calculation group, and analyze the treatment effects on the understanding of compound interest.

I find that the treatment effect of the education group is larger for those who underestimate compound interest than for those who overestimate compound interest. Moreover, simply performing the calculations and explaining the benefits increased the contribution by 20–25 RMB, an increase of 15%–19% relative to the control group. This effect is significantly smaller than the effect of the education treatment. The treatment effects of the education and calculation groups are similar for those who are around age 30, but differ as age increases: the treatment effect of the calculation group is lower than that of the education group for those who are around ages 40 to 50. In addition, I measured financial literacy in a post-intervention survey, and found that financial education can help people improve their understanding of compound interest. These results suggest that learning the benefits of a pension in general is unlikely to explain the overall treatment effects. In contrast, explaining compound interest is likely to increase people’ ability to link the calculation of benefits to their own choices, and thus increase pension contributions.

I further exploit the experimental variation and structurally estimate a life cycle model in which subjects underestimate compound interest. I combine both the survey data and actual pension contributions from the experimental data to estimate risk aversion parameters, time preferences parameters, and parameters of underestimating compound interest. Estimates show that households underestimate compound interest in both the control group and the education group. The estimated bias in the education group is much smaller than that in the control group, which is consistent with the reduced form results that the education treatment helps to reduce the underestimation of compound interest.

Finally, I use the estimated parameters to simulate the impact of several counterfactual policies on pension contributions. Simulation results show that, while both increasing the subsidy and financial education help to increase pension contributions, financial education about compound interest is more effective than increasing the existing subsidy by 100%. Based on the counterfactual simulation, I can calculate the lifetime utility for each individual and analyze the welfare effect. I show that the education treatment increases the lifetime utility by 8.6% compared to the control group, and the lifetime utility increases by 10.0% if the misunderstanding of compound interest is eliminated.

This paper makes several contributions. First, it contributes to the literature on financial literacy and financial education.² My main innovation is to study a concrete definition of financial literacy: understanding compound interest. I provide financial education on a specific aspect of financial literacy, and link understanding of compound interest with actual pension savings. In a recent field experiment, Goda, Manchester, and Sojourner (2014) show that sending retirement-income projections in a printed brochure increases individual contributions to voluntary retirement plans in the United States. In particular, the calculation group in this paper is similar to Goda, Manchester, and Sojourner (2014) key interventions, and my results are similar; what differs is that I connect this response to a concrete aspect of financial literacy. I add the education group and show that teaching compound interest has a larger effect than projecting income. I also measure the understanding of compound interest so that I can identify consumer bias and the mechanisms by which my interventions can increase individual contributions; this design enables us to identify individual utility functions and, in turn, generate hypotheses for other household finance decisions, such as borrowing (Stango and Zinman 2009) and life cycle consumption (Levy and Tasoff 2016).

Second, I bridge the gap between my theoretical framework and experimental results by structural estimation of individual preference and welfare analysis of the financial education provided. Previous research on financial education focuses on identifying which interventions change financial decisions; few focus on whether the intervention affects underlying structural parameters or changes individual decisions toward the decisions implied by economic models, and thus improves welfare. In this paper, I combine a field experiment with structural estimation based on a benchmark life cycle model, and test whether the intervention changes individual decisions toward the decisions implied by the benchmark model. I exploit the experimental variation and quantify the treatment effects by estimating the parameters of underestimating compound interest in both the control group and the education group. The results are consistent with the reduced form results that the intervention reduces the misunderstanding of compound interest.

Third, the results contribute to the literature on consumer bias and pension savings. Prior research suggests that many people do not save enough voluntarily to maximize their lifetime utility (Barr and Diamond 2008). Low savings for retirement can be driven by behavioral factors, such as procrastination (Choi et al. 2002; Thaler and Benartzi 2004), defaults (Madrian and Shea 2001; Beshears et al. 2008), or how information and choices are framed (Choi et al. 2012; Beshears et al. 2013). Misunderstanding compound interest is another plausible explanation for low pension contributions, yet it has not drawn much attention in this literature. I build on previous studies that analyze the relationship between misunderstanding compound interest and saving decisions using laboratory experiments (Eisenstein and Hoch 2007; McKenzie and Liersch 2019) or observational data (Lusardi and Mitchell 2007b). My approach goes further by using a field experiment to identify a causal relationship between misunderstanding compound interest and actual pension contributions. In addition, the psychology and economics literatures have documented many individual biases, but whether these biases can be lessened is rarely explored. I show that I can improve consumers’ financial decisions by correcting their erroneous understanding of compound interest through consumer education.

1. The New Rural Social Pension Insurance Program

In 2009, the Chinese government introduced the New Rural Social Pension Insurance Program (NRSPIP), which is a voluntary defined contribution plan that is highly subsidized by the central and local governments. Farmers aged 16 or older who are not students and are not enrolled in an urban pension plan are eligible for the program. An individual’s pension fund account comprises the person’s contributions and government subsidies. In the county I study, subjects can choose 1 of 5 annual contribution levels: 100, 200, 300, 400, or 500 RMB, which range from 2% to 8% of the county’s 2009 rural annual per capita net income. Table 1 shows the match contributions made by the Chinese government as subsidies.

All individual contributions and government subsidies are deposited in the individual’s account. The interest rate is the 1-year base rate according to the People’s Bank of China (China’s central bank), which is 2.5% as of 2011. When the central bank changes the base rate, the pension plan’s interest rate adjusts accordingly. Interest is compounded yearly.

The new pension plans are highly subsidized by the central and local governments.⁴ As an illustration, consider a farmer who is 30 years old and contributes the minimum amount (100 RMB) each year for 15 years. Assuming the interest rate is 2.5%, after age 60 the farmer is supposed to receive 1,259 RMB per year, of which about 82% comes from the government subsidy and its interest. If the farmer contributes 500 RMB, approximately 56% would come from the government subsidy. The new pension plan not only has high subsidies, but also has high returns compared to a standard certificate of deposit (CD) from a bank. For a person aged 45, the return on contributing the maximum amount (500 RMB) is about 500 base points higher than the return on a CD (see Online Appendix Table B1).

The pension program has several notable features. First, individual account balances are not forfeited at death. If pensioners die sooner than 139 months after age 60, their heirs will receive a lump sum payment that equals the remaining balance in the individual account minus the government subsidies. If pensioners live more than 139 months after age 60, they will still receive a monthly pension as an annuity until death. Second, participants may stop contributing for a few years and make up for the missed contributions later; they would only lose the subsidies for the years that they did not make contribution. Third, partial withdrawal is not allowed. They can withdraw all of their savings under the following conditions: migration, change from a rural hukou to an urban hukou, or enrollment in an urban pension plan.⁵ In any case, withdrawing all one’s money would result in the loss of all the subsidies one was receiving.

2. Theoretical Framework

To model the income uncertainty, I adopt Gourinchas and Parker (2002) formulation and decompose the labor income into a permanent component, |$P_t$|⁠, and a transitory component, |$U_t$|⁠: |$Y_t=P_tU_t$| and |$P_t=G_tP_{t-1}N_t$|⁠. The transitory shocks, |$U_t$|⁠, are independently and identically lognormally distributed, |$lnU_t \sim N(0, \sigma_u^2)$|⁠. The log of the permanent component of income, |$lnP_t$|⁠, evolves as a random walk with age-specific expected income growth, |$lnG_t$|⁠. Shocks to the permanent component of income, |$N_t$|⁠, are independently and identically lognormally distributed, |$lnN_t \sim N(0, \sigma_u^2)$|⁠.

Figure A2 compares distributions of actual contribution and calibrated contribution levels. The left-hand side shows that around 90% of rural households chose the lowest contribution level, and the right-hand side shows the benchmark model’s prediction. The benchmark model captures some aspects well: most people participate in the program. However, it captures other aspects poorly: people save more in the calibration than what I observe in practice.

Next, I bootstrap the confidence interval of the calibrated contribution levels. To account for the correlation within each village, I use block bootstrap with each village as a block. I find that the mean of the contribution level is 225 RMB, with a 95% bootstrapped confidence interval [215 RMB, 236 RMB]. The average actual contribution level is 104 RMB. Therefore, these calibration results suggest that rural households should contribute more to their pension plans.

Given that the per capita balance of savings deposits in rural China in 2010 is about 8,765 RMB (Almanac of China’s Finance and Banking 2011), and the return on pensions is much higher than that on savings deposits (Table B1), why do rural households decline to allocate more savings to their high-return pension plans? One possibility is that people underestimate compound interest. Evidence suggests that people tend to linearize exponential functions when assessing them intuitively (Eisenstein and Hoch 2007; Stango and Zinman 2009; McKenzie and Liersch 2019; Levy and Tasoff 2016). For savings, such an error implies a systematic tendency to underestimate interest accrued in the future, in which case people will underestimate the value of saving.

I introduce a structural parameter in the utility function to measure the degree of underestimation. Consider the individual who underestimates compound interest with the following form: |$f(i,t,\theta)=(1+r)^{(1-\theta)t}$|⁠. |$\theta$| measures the degree of underestimation of compound interest: Unbiased consumers have |$\theta=0$| and correctly predict compound interest, while those with |$0<\theta<1$| underestimate it. A higher |$\theta$| indicates greater underestimation of compound interest. Perceived future values are then calculated using |$FV=PV \cdot f(i,t,\theta)$|⁠. I incorporate underestimation of compound interest into the life cycle consumption model. Based on the experimental design and treatment effects, I structurally estimate the degree of underestimation and conduct counterfactual simulations in Section 6.

3. Experimental Design and Survey Data

The standard practice by which rural pensions are offered involves two steps: registration and payment. In step 1, county coordinators hire village coordinators to visit households in person to deliver information about the pension plan. Households then decide whether they would like to participate in the plan and, if so, at what level they will contribute. In step 2, households pay the given amount to village coordinators within 1 month. County coordinators then collect the list of participants and their contributions from village coordinators and administrate individual accounts for all participants with the banks.

I collaborated with a county government in Shaanxi province during the registration period for the rural pension plan. The county launched the rural pension plan in 2010, and many residents made their first contributions in the same year. In 2011, 14 villages from the sample county were randomly selected as experimental sites. In these sample villages, instead of village coordinators calling on households, a research team visited them in step 1 and followed a protocol similar to that used by village coordinators in villages not included in the sample. I asked households to choose a contribution level, and provide their information to the village coordinators. In step 2, they pay the given amount to village coordinators within the next month. I collected administrative data from village coordinators after the households had made their contributions in 2011; the data include name, gender, age, village, and the contribution levels for both 2010 (baseline data) and 2011 (experimental data).

The procedures above have two advantages. First, this study takes place in a naturally occurring environment: I build on the infrastructure of the government and offer the same pension plan the government would offer in any case. Key changes are that participants are given a chance to participate in a survey, in addition to making a choice about their contribution level. Farmers are familiar with the logistics of separate registration and payment, because such procedures are typical in this area; also, local representatives had visited them the previous year to explain the pension program. Second, because I collected data about participants’ actual contribution levels, I was able to test the impact of explaining compound interest on actual pension contributions.⁶

Figure 1 presents the experimental design. Randomization of intervention was conducted at the household level. Households were randomly assigned to 1 of 3 groups: the Control group, the Calculation group, or the Education group. Assignment of treatment was determined by the order of interviews for each enumerator, and the order of interviews was determined by the location of households along village roads. Enumerators were assigned to different roads in the villages and conducted door-to-door visits from the beginning of the road to the end under the guidance of village coordinators. For example, the first household on the road was assigned to the control group, the second to the calculation group, the third to the education group, and the fourth to the control group to begin the cycle again. The assignment rule, which was the same for all enumerators, helped to control for village fixed effects and enumerator fixed effects.

Figure 1

Experimental design

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In the control group, enumerators gave households a flyer about the pension plan and went over information about the contract. Households were then asked to fill out the short survey about their age, education, wealth, family members, risk attitudes, time preferences, and financial literacy. At the end of the visit, enumerators asked households to state their contribution decision. Households were informed that their decisions would be passed to local village coordinators, who would later collect the contributions based on registration in the program.

In the calculation group, enumerators followed the same procedure as the control group, but before administering the survey about preference, they calculated the expected pension benefits after age 60 if households contributed at various levels beginning at age 30. Table 1, panel B, provides the expected benefits. Enumerators went over the benefits at each contribution level with households and explained the range of differences; the purpose was to inform households of the explicit benefit amount at each contribution level without explaining the concept of compound interest. Comparing the control group and the calculation group will suggest whether explaining the benefits in general can increase participation and contribution levels in pension plans.

In the education group, the enumerators followed the same procedure for the control group, but then asked questions about compound interest, explained the concept, and provided the calculated benefit for each contribution level before administering the survey about preference. I asked three compound interest questions during the intervention, one of which is adapted from Eisenstein and Hoch (2007):

You deposit 100 RMB as a certificate of deposit this year at a constant interest rate of 9% per year. Interest is compounded annually. How much money could you receive in 30 years? (1) Less than 300, (2) 300–500, (3) 500–1,000, (4) 1,000–1,500, or (5) more than 1,500?

Regardless of the participant’s answers, the enumerator furnished the correct answer: 1,327 RMB (option 4). The enumerator then briefly explained the basic concept of compound interest in a manner similar to Eisenstein and Hoch (2007): “Compound interest means that when interest is earned, it is left in the account. In future years, interest accumulates on the full amount that is in the account, so you earn interest on the interest as well as on the original principal amount.”

Table 3, panel A, provides the other two questions. Enumerators varied the interest rate (9% and 2.5%) and the number of years before receiving the benefits (30 years and 15 years) so that households would have a better understanding of compound interest. The purpose of this approach is, first, to document whether households underestimate the value of savings from compound interest, and second, to explain compound interest in order to debias them. Note that the questions asked are complex, and I am simply aiming to crudely measure subjects’ understanding of compound interest. I also calculated expected benefits after age 60, which are the same for the calculation group.

In summary, the calculation treatment provides households with information about the expected benefits at each contribution level. The education treatment asks households to estimate interest, explains compound interest, and provides information about its benefits.

Risk attitudes and time preferences were elicited using the questions outlined in Online Appendix Table A2.⁷ These will help us to calibrate the life cycle model and conduct structural estimation. I also asked five questions to measure numeracy and financial literacy (Table 3, panel B, provides these questions, which were adopted from Banks, O’Dea, and Oldfiel 2010, Lusardi and Mitchell 2007a, Eisenstein and Hoch 2007, and Cole et al. 2012). As described previously, the survey about preference, which includes questions about financial literacy, was administered after the interventions in the education and calculation groups. I used a between-subject design based on random assignment. Comparison of the education group with the other groups allows us to test whether education changes financial literacy.⁸

Table 2 presents summary statistics for the different groups. I visited a total of 1,330 households; of these, 177 did not answer the door, 32 declined to participate in this study, and 17 households were not eligible but were mistakenly surveyed. Therefore, the sample contains 1,104 surveys. The overall nonresponse rate was 17.0%; differences in nonresponse rates between groups are not statistically significant. The sample county launched the rural pension plan in 2010 (baseline), before my interventions in 2011. The take-up rate in 2010 was 93%, and the average contribution was 104 RMB (which includes those who did not participate), so most households participated in the pension plans but chose the lowest contribution level. The last column shows the p-values for the Wald test of equal means of the three groups. Most control variables are balanced between different treatment groups.

Table 3 presents results for financial literacy. More than half answered question 4 correctly, which suggests that they have a basic understanding of inflation and purchasing power. Thirteen percent answered question 2 correctly, and 5.6% answered question 3 correctly, which suggests that most subjects have a poor understanding of compound interest.

4. Empirical Results

In this section, I first show that rural households underestimate the value of savings with compound interest, then demonstrate that financial education about compound interest can increase households’ contribution levels. I also analyze possible channels for the effects of financial education about compound interest on pension contributions.

4.1 Misunderstanding of compound interest

I measure misunderstanding of compound interest using the compound interest question A that preceded the intervention in the education group. Figure 2 shows responses to the question.

Figure 2

Response to compound interest question

This figure shows the distribution of responses to the compound interest rate question before intervention. I asked subjects the following question: You deposit 100 RMB as a certificate of deposit this year at a constant interest rate of 9% per year. Interest is compounded annually. How much money could you receive in 30 years? (1) Less than 300, (2) 300–500, (3) 500–1,000, (4) 1,000–1,500, or (5) more than 1,500? 1, 2, 3, underestimate; 4, correct; 5, overestimate.

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Of 369 households in the education group, 201 could not answer the question. Figure 2 includes only the 155 households that answered the question. The correct answer is 1,327 RMB (option 4). Eighteen percent chose the correct answer, and 73% chose options 1, 2, or 3; these can be characterized as underestimating the value of compound interest. A further 9% chose option 5, which can be characterized as overestimating the value of compound interest. From Figure 2, I see that rural households underestimate the value of savings with compound interest. Although the compound interest questions are different, the results are consistent with those of Lusardi and Mitchell (2007b), who find that only 18% of subjects in the Health and Retirement Study answered the compound interest question correctly.

Online Appendix Figure A1 shows responses to compound interest questions B and C. For question B, 26% underestimated the value of compound interest. For question C, 59% underestimated the value of compound interest. Responses to all three compound interest questions suggest that a significant portion of rural households underestimate compound interest, even at a relatively low interest rate of 2.5%.

4.2 Impact of education on pension contributions

Figure 3, panel A, shows that almost all the households in the three groups participated in the pension plan and that there is no significant treatment effect. Figure 3, panel B, shows the treatment effect on contributions. In the control group, the average contribution is 133 RMB. In the calculation group, the average contribution increases to 156 RMB. In the education group, the average contribution increases to 182 RMB. These results suggest that both the education treatment and the calculation treatment increase contribution levels, but that the education treatment is more effective.

Figure 3

Treatment effects

Panel A shows the treatment effect on take-up of pension plans. In the control group, take-up is 98.4%. In the calculation group, take-up is 98.1%. In the education group, take-up is 98.6%. This suggests that almost all the households in the three groups participate in the pension plans. Panel B shows the treatment effect on contributions to pension plans.

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Figure 4 shows the distribution of contribution levels for different groups. Contribution level 1 corresponds to 100 RMB contributions, and contribution levels 2 to 5 range from 200 RMB to 500 RMB. After the intervention, most subjects still contribute 100 RMB in the pension. In the education group, however, more subjects contribute 300 RMB and 500 RMB relative to the other two groups.

Figure 4

Distributions of contribution levels

This figure shows the distribution of contribution levels for different groups. Contribution level 1 corresponds to 100 RMB, and levels 2 to 5 correspond to 200 RMB to 500 RMB.

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In Column 1, the dependent variable is individual take-up after intervention. There is no evidence of a treatment effect on take-up. This could potentially be due to a high participation rate. In Column 2, the dependent variable is the individual contribution level after intervention. Variables on the right-hand side are treatment indicators, socioeconomic variables, and the fixed effects of natural villages and enumerators. The education treatment increases the contribution by 53 RMB—an increase of 40% relative to the average contribution of 133 RMB in the control group—and is significant at the 1% level. The effect of the calculation treatment (25.22) is positive and statistically significant at the 1% level. The impact of the education treatment is greater than that of the calculation treatment, and the Wald test shows that it is significant at the 1% level. In Column 3, the dependent variable is changes in individual contribution level from 2010 to 2011, and I run the same regression from Column 2. Coefficients are of similar magnitude and have the same direction as those in Column 2. In Column 4, I study the heterogeneous effect with respect to the baseline contribution in 2010. Coefficients of the interaction between treatment indicators and baseline contribution are not significantly different from zero. This suggests that treatment effects are similar across different initial contributions. Online Appendix B3 reports the robustness analysis and shows that the main results in Table 4 are robust to different specifications.

To bridge the gap between the theoretical framework and empirical results, I calculate the degree to which these treatment effects can explain the gap between the control group and the level implied by the benchmark model. I find that the treatment effect accounts for 55% of the gap between the control group and the benchmark model prediction, with a 95% bootstrap confidence interval [31%, 77%]. This suggests that my interventions reduce the gap between actual decisions and the level implied by the benchmark model.

To study the long-run effect, I also collect the new administrative data for pension contributions in the year 2018 and merge the administrative data with the existing data set. The administrative data includes information about name, gender, age, village, and the contribution levels in the year 2018. Equation (3) estimates the long-run effect. I find that the pension contribution in the education treatment is still 45 RMB larger than that in the control group and is significant at the 1% level. The difference between the calculation treatment and the control group is 21 RMB and statistically significant at the 5% level. Only 9% of participants change their pension contribution in the long run. This is likely due to inertia when choosing their pension plans (Madrian and Shea 2001). These results suggest that the long-run effect is similar to the short-run effect in Table 4, and the effect on contribution persists over time.

In sum, the education treatment increases the contribution by 49–53 RMB, resulting in an increase of around 37%–40% relative to the average contribution of 133 RMB in the control group.¹⁰ The effect on contribution persists over time. This suggests that the financial education has a positive and significant effect on retirement savings for rural households.

4.3 Possible channels

For these findings to inform theory, more information is needed to analyze the mechanisms through which this effect could work. Possible explanations include: (1) learning the expected benefits of pensions through a better understanding of compound interest and (2) learning the expected benefits of pensions in general. Grasping the difference between the two channels is important: it will help us understand the factors involved in pension contributions and design better interventions to improve decisions about household retirement savings. Moreover, understanding individual bias about compound interest has important implications in other household finance decisions, such as life cycle consumption (Levy and Tasoff 2016). The experiment is designed to distinguish between these mechanisms.

4.3.1 Learning the concept of compound interest

People may underestimate the value of savings from compound interest, and thus contribute less to their pension plans. Financial education might increase household contribution levels by helping households correct their erroneous understanding of compound interest. If learning about the concept of compound interest can explain the treatment effects, I should have several predictions. First, the treatment effects should depend on the initial understanding of compound interest: those who overestimate compound interest should have smaller treatment effects compared to those who underestimate compound interest. Second, I should observe that the education treatment has larger effects than the calculation treatment, because the only difference between these two groups is that the education treatment explains compound interest. Third, the education treatment should increase their understanding of compound interest, but should have no effect on other financial literacy questions.

I first analyze heterogeneous treatment effects. In Table 4, Column 5, I study the heterogeneous treatment effects based on the initial understanding of compound interest. The measurement of compound interest in the calculation group is affected by the intervention, so I restrict my sample to the control group and the education group only. I create five indicators based on the participant’s choice on question A before the treatment in the education group or question 3 in the control group. These indicators measure subjects’ initial understanding of compound interest, because subjects do not receive any treatment before answering the questions.

I find that the effect of the education treatment is 56 RMB for those who were unable to provide an answer to the compound interest question. However, the treatment effect is 78 RMB smaller if they overestimate compound interest. The effect of the interaction term is significant at the 1% level. In fact, those who overestimate compound interest reduce their contributions by about 22 RMB after the education treatment, though this is not statistically significant (p = .42). The treatment effect is 30 RMB if they correctly estimate compound interest (p = .54), and 70 RMB for those who have the lowest range of estimation (p = .06). Although the treatment effect is not monotonic as participants underestimate more, the pattern is clear: the treatment effect is larger for those who underestimate compound interest than for those who overestimate compound interest. Hence, the evidence is consistent with understanding the concept of compound interest.

Second, I study the comparison between the education group and the calculation group. There could be two explanations for the different treatment effects between the education and calculation groups. First, explaining why the benefit is large might increase the credibility of the described benefits. Second, the education treatment might increase the ability to link the described benefits of beginning to contribute at age 30 to their own choices. In the calculation treatment, I calculated participants’ expected pension benefit levels if they contributed at various levels starting from age 30. As such, those who are around 30 can learn the expected benefits directly from the calculation treatment. Those who are closer to 40 or 50, however, only learn the expected benefit for participants who begin at age 30 and, as a result, must link those benefits to their own choices. Therefore, the second explanation has two predictions: (1) the calculation treatment should have similar treatment effects as the education treatment for those around age 30, because teaching compound interest does not provide more information about the expected benefit; (2) the calculation treatment should have lower treatment effects than the education treatment when age increases, because teaching compound interest increases subjects’ ability to link the described benefits at age 30 to their own choices. Then I can use the treatment effects for different ages to distinguish these two hypotheses. Figure 5 shows the treatment effects of the education and calculation groups for different ages. In Figure 5, panel A, the dependent variable is the individual level contribution. In Figure 5, panel B, the dependent variable is the change in the individual’s contribution level.

Figure 5

Treatment effects by age

Panel A shows treatment effects for the education and calculation groups by age group. The dependent variable is individual level contribution. The horizontal axis represents four age groups. The vertical axis is the treatment effects. I report one standard error for each coefficient. Panel B shows the treatment effects for the education and calculation groups by age groups. The dependent variable is change in individual level contribution. The horizontal axis represents four age groups. The vertical axis is treatment effects.

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I find that the treatment effects of the education and calculation groups are similar for those who are around age 30, but differ when age increases. The treatment effect of the calculation group is lower than that of the education group for those who are around ages 40, 50, and 60.

Table 5, panel A, reports the results for the four age groups. In Column 1, the dependent variable is the individual-level contribution. For those who are around age 30, the difference between the treatment effects of the education and calculation groups is 11 RMB and is insignificant. The differences are 15, 42, and 44 RMB for those who are around age 40, 50, and 60, respectively. The difference is significant at the 5% level for those who are around age 50, and it is close to marginally significant for those who are around age 60 (p = .1179). In Column 2, the dependent variable is the change in individual-level contribution. The results are similar to Column 1. Differences between the treatment effects of the education and calculation groups are significant at least at the 5% level for those who are around ages 50 to 60. Table 5, panel B, also analyzes the results for two age groups to check robustness, and results are similar to panel A. Differences between the treatment effects of the education and calculation groups are 37–41 RMB for those who are between ages 40 and 60, and are significant at the 1% level.

I also investigate the qualitative explanation for participants’ contribution decisions using the same specification in Table 5. I find that the likelihood of subjects basing their contribution decisions on learning the benefits of compound interest is greater in the education group than in the calculation group for older subjects (see Online Appendix B3 for details).

Third, I study the impact of my interventions on the understanding of compound interest. Figure 6 shows the responses to the compound interest question (question 3) after the intervention in different groups. I only include the 369 households that answered the question. The correct answer is 574 RMB, which is option 4. One can clearly see that rural households underestimate the value of savings from compound interest after the intervention. Although underestimation of compound interest persists after the intervention, there are fewer extremely wrong answers (option 1) and more correct answers (option 4) in the education group than in the other groups.

Figure 6

Response to compound interest question

This figure shows the distribution of responses to the compound interest question after intervention. I asked subjects the following question: You deposit 100 RMB as a certificate of deposit this year at a constant interest rate of 6% per year. Interest is compounded annually. How much money could you receive in 30 years? (1) Less than 300, (2) 300–400, (3) 400–500, (4) 500–600, or (5) more than 600? Figures only include those who answered the question and exclude those who did not know. 1, 2, 3, underestimate; 4, correct; 5, overestimate.

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To estimate the treatment effect on financial literacy, I follow the specification in Equation 1 and change the dependent variable to financial literacy. I use absolute distance to the correct answer to measure financial literacy. Absolute distance measures how close the respondents’ answers are to the correct one, even when they are incorrect. This can help to measure the magnitude of misunderstanding of compound interest. I take the negative sign of the measure so that the higher the measure, the better the understanding of compound interest. Table 2, panel B, reports summary statistics.

Table 6 presents results. I run a seemingly unrelated regression (SUR) with five financial literacy questions. In Columns 1 to 5, the dependent variables are the absolute distance between the chosen answer and the correct answer for questions 1 to 5 (which are shown in Table 3), normalized by the standard deviation of the control group. Because the information in the education treatment includes only compound interest, I predict that the education treatment increases understanding of compound interest but has no effect on numeracy questions or inflation questions. I find that the effects of education on the financial literacy questions are all positive, but most are not significant. The only exception is question 3, the compound interest question. In Column 3, the effect is positive and significant at the 5% level. Therefore, education reduces the distance from the correct answer by about one-sixth of a standard deviation; this demonstrates that financial education increases people’s understanding of compound interest.¹¹ Robustness checks suggest that other measures of financial literacy show similar results (Online Appendix B.4 provides a complete description of the measurement of absolute distance and robustness checks).

To illustrate the impact of the intervention on overall financial literacy, I follow Kling, Liebman, and Katz (2007) and construct average standardized treatment effects. In Columns 6 to 8, I report average standardized treatment effects on three combinations of questions. In Column 6, I report average standardized treatment effects on questions 2 and 3, both of which are compound interest questions. The effect of financial education is positive and significant at the 5% level. In Column 7, I report average standardized treatment effects on questions 1, 4, and 5, which are unrelated to compound interest. The effect of financial education is positive but not significant. In Column 8, I report average standardized treatment effects on all questions, which is positive and significant at the 10% level. This suggests that financial education has a positive and significant effect on overall financial literacy, and especially on the understanding of compound interest.

In sum, I find that the treatment effect of the education group is larger for those who underestimate compound interest than for those who overestimate compound interest. I also find that the treatment effect of the education group is greater than that of the calculation group for older subjects. The likelihood of subjects basing their contribution decisions on learning the benefits of compound interest is greater in the education group than in the calculation group for older subjects. These results support the notion that the different treatment effects of the education and calculation groups are likely due to participants’ ability to link the benefit to their own choices. Moreover, although rural households underestimate compound interest and contribute less to pension plans, education about compound interest can improve people’s understanding of compound interest. Therefore, these results demonstrate that the understanding of compound interest is the main channel for the treatment effects.

4.3.2 Alternative explanations for treatment effects

An alternative explanation is that learning the benefits of a pension in general can fully explain the effect of the education treatment, because the education group also provides benefit calculation. As discussed in Table 4, the impact of the education treatment is greater than the calculation treatment, and it is significant at the 1% level. The difference between these two interventions indicates that households acquire information about compound interest during the education. Thus, learning the benefits of a pension cannot fully explain the treatment effect of the education group.

Another concern is that enumerators could have put more effort into just persuading households in the treatment groups to contribute more to the pension plan, without explaining the compound interest. However, stronger persuasion is unlikely to explain the better understanding of compound interest after the education treatment. Moreover, there are no incentives for enumerators when participants contribute either more or less. Enumerators are instructed that the contribution is voluntary and that they should not push participants to contribute more or less.

Another explanation is that enumerators provide a more intensive treatment when they perceive that participants are more biased. This is consistent with the finding that the treatment effect is larger for those who underestimate compound interest. To test this explanation, I study the enumerators’ efforts when they interact with participants with different degrees of bias. Although I do not have a direct measure of treatment effort for the education group, I have some suggestive evidence to show this is unlikely to be true. First, the main prediction of enumerators’ biased treatment is that enumerators should spend more time explaining the question to more biased participants. I use the number of minutes enumerators required to administer the survey as a proxy for effort and find that the average time is 28–30 minutes for those with a different initial understanding of compound interest in the education group. Thus, there is no evidence that enumerators’ biased treatment can explain the larger effects of more biased participants. Moreover, enumerators were asked to follow the instructions and provide similar treatment intensity to those in the education group, in order to minimize any effect from enumerators.

5. Structural Estimation

The experiment demonstrates that the education treatment increases both understanding of compound interest and pension contributions. In this section, I bridge the gap between the theoretical framework and experimental results by formally estimating risk aversion parameters, time preferences parameters, and parameters of underestimating compound interest in a life cycle model. The experimental design has two advantages to conduct the structural estimation with a life cycle model. First, I have experimental variation in financial education, which allows us to identify the parameters in different treatment groups. Second, I use survey questions to elicit preferences and combine these data with actual pension contributions (Ameriks et al. 2011; Koijen, Nieuwerburgh, and Yogo 2016). Thus, I can jointly estimate preference and allow for individual heterogeneity in these parameters.

I use both survey data and actual pension contributions from the experimental data to estimate risk aversion parameters, time preference parameters, and parameters of underestimating compound interest, and Table 7 reports the results. The measurement of compound interest in the calculation group is affected by the intervention, so I restrict my sample to the control group and the education group only. I estimate two specifications. In specification 1, I attempt to recover the values of four key preference parameters: the coefficient of relative risk aversion, |$\rho$|⁠; the discount factor, |$\beta$|⁠; the magnitude of underestimating compound interest in the control group, |$\theta_1$|⁠; and the magnitude of underestimating compound interest in the education group, |$\theta_2$|⁠. The estimation is based on twenty-five moment conditions: five from risk attitude questions, six from time preference questions, twelve from compound interest questions, one from actual pension contributions in the control group, and one from actual pension contributions in the education group (see Online Appendix A.4 for calculations about moment conditions). The parameter estimates, |$\hat{\Theta}=(\hat{\rho},\hat{\beta},\hat{\theta_1},\hat{\theta_2})$| , minimize the generalized distance of the sample moments from zero.