Digital Financial Literacy and Hyperbolic Discounting: Evidence from Japanese Investors

Abstract

This study investigates the relationship between digital financial literacy (DFL) and hyperbolic discounting among 104,993 active securities account holders in Japan. As digital financial services expand rapidly, individuals increasingly require not only traditional financial knowledge but also the capacity to understand digital platforms, evaluate online financial information, and manage emerging technological risks. Using data from the 2025 wave of the Survey on Life and Money, hyperbolic discounting is measured through intertemporal monetary choice scenarios, while DFL is constructed as a multidimensional index encompassing digital knowledge, financial knowledge, service awareness, attitudes, behaviors, practical capability, and protection against digital fraud. Probit regression results reveal a statistically significant negative association between DFL and hyperbolic discounting, indicating that individuals with stronger digital financial competencies are less likely to exhibit hyperbolic discounting. Attitudinal components of DFL exhibit the strongest effects, suggesting that internalized financial beliefs may play a more decisive role than technical knowledge in promoting time-consistent decision-making. Subsample analyses further highlight gender-differentiated patterns in demographic and economic influences on present bias. These findings contribute to behavioral finance by integrating digital capability into intertemporal choice research and provide policy-relevant implications for designing comprehensive financial education and digital literacy initiatives in increasingly digitalized financial environments.

1. Introduction

The widespread expansion of digital financial services has profoundly transformed the ways in which individuals make financial decisions (Gomber et al. 2017; Arner et al. 2020; Choung et al. 2023). Online brokerage accounts, mobile trading applications, digital payment systems, and algorithm-driven financial interfaces have become integral to everyday financial behavior (Philippas and Avdoulas 2020; Thakor 2020). In such environments, individuals are increasingly required not only to understand basic financial concepts but also to deal with digital platforms, evaluate digitally presented information, and shield themselves from online financial risks (Morgan et al. 2019; Lyons and Kass-Hanna 2021; Lusardi and Mitchell 2023). These developments raise important questions about whether traditional measures of financial knowledge alone are sufficient to explain behavioral outcomes in modern financial contexts (Carlin et al. 2017; Lyons and Kass-Hanna 2021).

A growing body of behavioral economics research has documented that individuals often display time-inconsistent preferences, commonly referred to as hyperbolic discounting, in which immediate rewards are disproportionately favored over larger delayed rewards (Bawalle et al. 2024; Zhang 2016; Frederick et al. 2002; O’Donoghue and Rabin 1999; Meier and Sprenger 2010; Laibson 1997). Such present-biased behavior has been linked to suboptimal financial outcomes, including insufficient saving and impulsive consumption (Meier and Sprenger 2010; Gathergood and Weber 2017; Angeletos et al. 2001; Lim et al. 2014). In our previous work, we demonstrated that greater financial knowledge is linked to a reduced probability of displaying hyperbolic discounting behavior, suggesting that a consistent negative association between financial knowledge and present-biased decision-making (Katauke et al. 2023; Bawalle et al. 2024). However, financial knowledge as defined traditionally, primarily captures numeracy and conceptual understanding (Lusardi and Mitchell 2011, 2014) and may not fully reflect the competencies required in increasingly digitalized financial environments (Fernandes et al. 2014; Morgan et al. 2019; Lyons and Kass-Hanna 2021).

Digital financial literacy (DFL) extends beyond conventional financial knowledge by encompassing a broader set of skills and attitudes, including understanding of digital financial products, operational skills for digital interfaces, informed choices in technology-based financial situations, and defensive awareness against internet-based fraud (Morgan et al. 2019; Liu et al. 2021; Lyons and Kass-Hanna 2021; Amnas et al. 2024; Ogunola et al. 2024; Nguyen et al. 2024; Lal et al. 2025; Amarsanaa et al. 2025). While recent studies have shown that DFL is linked to financial well-being and life satisfaction (Prasad et al. 2018; Setiawan et al. 2022; Potrich et al. 2015; Choung et al. 2023), its relationship with intertemporal decision-making remains underexplored. In particular, it is unclear whether DFL can mitigate hyperbolic discounting in a manner similar to, or distinct from, traditional financial knowledge (Henager and Cude 2016; Xiao and Porto 2017). This study fills this gap by investigating the relationship between digital financial literacy and hyperbolic discounting based on a large-scale survey of Japanese investors. Building on our prior findings regarding financial knowledge, we extend the analysis to a digital finance framework and investigate whether broader digital competencies are linked to time-consistent financial decision-making. In particular, the study aims to address the following research questions:

RQ1: Is DFL linked to a lower probability of exhibiting hyperbolic discounting?

RQ2: Which components of DFL are most strongly related to hyperbolic discounting behavior?

By elucidating how digital financial literacy influences intertemporal preferences, this study advances the behavioral finance literature and offers policy-relevant implications for developing financial education and digital literacy initiatives in an increasingly digitalized financial environment.

2. Data and Methods

2.1. Data

This study utilizes data from the 2025 wave of the “Survey on Life and Money,” implemented through a collaboration between Rakuten Securities, Japan’s leading online brokerage firm, and the Kadoya Laboratory at Hiroshima University. The survey targeted respondents aged 18 and above who maintained active securities accounts and had visited the Rakuten Securities web address minimum of one time over the preceding twelve months. In this study, an “active” account refers to an account holder who logged into the Rakuten Securities platform at least once during the previous twelve months. The definition focuses on platform engagement rather than trading activity because the survey was administered through the brokerage’s online interface. Data were collected over the period spanning January to February 2025, gathering extensive demographic, economic, and psychological information. Several participants had taken part in previous survey waves during November–December 2022 and 2023. For these respondents, we incorporated previously collected data on digital financial literacy competencies and risk aversion perspective. Following standard data quality procedures, cases with incomplete data on the primary variables of interest were excluded, yielding an analytical sample of 104,993 individuals.

2.2. Variables

2.2.1. Dependent Variable

We examine hyperbolic discounting as the primary dependent construct, defined as a present-biased preference that leads individuals to choose smaller immediate rewards instead of larger delayed ones, even when delay would be economically preferable. (Thaler 1981; Ikeda et al. 2010). To capture present-biased tendencies, the study employed two hypothetical intertemporal choice situations that compared preferences for monetary gains across various delay periods, following established procedures from Kang and Ikeda (2013) and Ikeda et al. (2010). Respondents were presented with two versions of the following question: “Consider a situation in which you may receive a sum of money either after a short period (Option A) or after a longer period (Option B), where the two options involve different monetary values. Which option would you prefer?” These scenarios assessed time preferences by evaluating delay durations. Specifically, the first scenario (question 1) offered a choice between 2-day and 9-day delays (DR1), whereas the second scenario (question 2) compared 90-day and 97-day delays (DR2). Within each scenario, respondents evaluated eight combinations featuring progressively hypothetical larger monetary rewards from combination 1 to combination 8. Each scenario consisted of eight combinations in which the delayed reward increased progressively while the earlier reward remained fixed. The switching point is defined as the first combination where the respondent switches their preference from the earlier reward to the delayed reward. The implied interest rate corresponding to this switching point is then used to compute the discount rate for each delay horizon. Drawing on the frameworks of O’Donoghue and Rabin (1999) and Laibson (1997), this two-horizon switching-point methodology enables the detection of declining discount rates between short and long delays, characteristic of hyperbolic rather than exponential discounting. Hyperbolic discounting was measured by calculating the discount rate at each scenario’s switching point—defined as the point at which respondents switched from choosing option A to option B (Kang and Ikeda 2013; Ikeda et al. 2010; Fukuda et al. 2022). Using the implied interest rates at respondents’ switching points, we calculated discount rates for each scenario (DR1 and DR2) and then generated a binary measure of hyperbolic discounting, coded as 1 when the short-horizon rate (DR1) surpassed the long-horizon rate (DR2), and 0 otherwise. This methodology aligns with approaches employed in earlier research (Zhang 2016; Fukuda et al. 2022; Katauke et al. 2023; Bawalle et al. 2024) for operationalizing hyperbolic discounting.

2.2.2. Independent Variables

We employed DFL as our primary independent variable, measured using the framework developed by Lal et al. (2025) and Lyons and Kass-Hanna (2021). The DFL construct encompasses five overarching dimensions and eight sub-dimensions. Our study focused on the eight sub-dimensions: (1) Digital Literacy, (2) Digital Financial Services related awareness (DFS), (3) Positive Financial Attitudes and Behaviors related awareness, (4) DFS related practical Know-How, (5) Positive Financial Attitude, (6) Positive Financial Behavior, (7) Safeguard from Digital frauds, and (8) Financial knowledge (literacy).

Within the measurement framework, financial knowledge was assessed in line with the approaches proposed by Lusardi and Mitchell (2008) and the OECD (2024), using items related to simple interest, inflation, and risk diversification. Each correct response received a score of 1, while incorrect or “I don’t know” answers were coded as 0, yielding a possible range from 0 to 3. The other seven components of digital financial literacy were measured on five-point Likert scales ranging from 1 (“strongly disagree”) to 5 (“strongly agree”), drawing on established instruments from previous studies (Choung et al. 2023; Lal et al. 2025). Scores for each sub-dimension were obtained by averaging the corresponding item responses.

The final composite DFL was computed by summing the eight standardized sub-dimension scores. This standardized composite score serves as our primary independent variable, representing respondents’ overall digital financial literacy across knowledge, practical skills, awareness, decision-making competencies, and self-protection behaviors. This comprehensive measurement approach aims to capture the multifaceted nature of digital financial competencies while maintaining psychometric rigor through validated reliability, demonstrated structural validity, and appropriate standardization procedures. Complete DFL methodological approach and assessment questions are available in the study of Lal et al. (2025).

To isolate the influence of DFL on hyperbolic discounting and address potential confounding factors, we included three categories of control variables, demographic factors (gender, age, education, marital status & children), economic factors (employment, household income & household assets), and a psychological factor (risk aversion) (Holt and Laury 2002; Dohmen et al. 2011).

Table 1. Variable definitions.

Variables	Definitions
Dependent Variable
Hyperbolic discounting	A binary indicator is assigned a value of 1 if DR1 is greater than DR2, and 0 otherwise.
Independent Variable
DFL Index	A continuous measure derived from the summed average scores of eight components reflecting digital knowledge, financial knowledge, awareness of digital financial services, understanding of beneficial financial attitudes and behaviors, operational proficiency in digital financial services, constructive financial attitudes and behaviors, and protection from online financial frauds.
Male	A binary indicator is assigned a value of 1 if the responder is male, and 0 otherwise
Age	A continuous variable of respondents’ age
Age squared	A continuous variable of the square of the respondent’s age
Marital Status	A binary indicator is assigned a value of 1 if the respondent is married, and 0 otherwise
Number of children	A binary indicator is assigned a value of 1 if the respondent has a child, and 0 otherwise
Education Year	A binary indicator is assigned a value of 1 if the respondent has at least a university degree, and 0 otherwise
Employment	A binary indicator is assigned a value of 1 if the respondent is employed, and 0 otherwise
Household income	A continuous indicator reflecting the participant’s self-reported annual income, expressed in Japanese yen for 2025
Log of household income	The natural log transformation of the participant’s self-reported annual earnings in Japanese yen for the year 2025.
Household assets	A continuous indicator reflecting the participant’s self-reported household financial asset balance, expressed in Japanese yen for 2025
Log of household assets	The natural log transformation of the participant’s self-reported financial asset balance in Japanese yen for the year 2025.
Risk aversion	A continuous indicator based on the reported chance that the respondent would take an umbrella during rainfall, serving as a proxy for risk-averse behavior. Although experimental methods such as lottery-based tasks are often used to measure risk preferences, such approaches are difficult to implement in large-scale surveys involving more than 100,000 respondents. Therefore, consistent with previous survey-based studies, we employ this proxy measure to capture precautionary behavior under uncertainty.

presents the definitions and measurements of all variables.

2.3. Descriptive Statistics

Table 2. Descriptive Statistics.

Variable	Mean (Percentage)	Standard Deviation	Minimum	Maximum
Dependent Variable
Hyperbolic_discounting	0.127	0.333	0	1
Independent Variables
** DFL	29.93	4.725	7	36
Male	0.643	0.479	0	1
Age	44.98	11.87	18	90
Age_sq	2164	1114	324	8100
Age group	1.719	0.649	1	3
Marital status	0.662	0.473	0	1
Child(ren)	1.086	1.103	0	12
Education	15.20	2.054	9	21
Fulltime_employment	0.707	0.455	0	1
Household_Income	7,766,275	4,249,673	1,000,000	20,000,000
Log_Hincome	15.70	0.610	13.82	16.81
Household asset	21,490,000	25,340,000	25,000,00	100,000,000
Log_Hasset	16.28	1.104	14.73	18.42
Risk aversion	0.534	0.235	0	1
Observations	104,993

** Raw average scores before standardization.

shows the descriptive statistics for the key variables included in the analysis. Our sample comprises 104,993 respondents, providing substantial statistical power for examining the relationship between DFL and hyperbolic discounting (HD). The findings indicate that about 13% of respondents display hyperbolic discounting behavior. On average, respondents scored 29.93 out of 36 on digital financial literacy, though scores varied widely from 7 to 36. Most participants are male (64%), with a mean age of 45 years and an age range extending from 18 to 90 years. Most respondents are married (66%), employed (71%), and have approximately one child. Educational attainment averages 15 years, corresponding roughly to post-secondary education. Household income demonstrates substantial variation, averaging JPY 7,766,275, while household assets average JPY 21,490,000; both show large differences across families. Respondents also show moderate levels of risk aversion average score of 0.534.

We further conducted a preliminary examination of hyperbolic discounting patterns across major demographic characteristics like age, gender, marital status, and employment status. The data reveal significant variations across these population groups. Males demonstrate notably higher rates of present bias (13.49%) compared to females (11.36%). Married respondents exhibit higher hyperbolic discounting (13.12%) than their unmarried counterparts (11.94%), despite the expectation that married couples engage in more long-term planning. Employment status shows expected results, with unemployed respondents displaying higher present bias (13.51%) than employed respondents (12.40%). Age shows the most pronounced pattern: hyperbolic discounting remains relatively low among respondents under 40 (11.62%), increases moderately for those aged 40–65 (12.61%), and rises sharply among respondents over 65 (17.17%). The demographic distribution of hyperbolic discounting is reported in

Table 3. Distribution of Hyperbolic discounting by demographic patterns.

Hyperbolic Discounting	Gender		Married		Employment		Age
	Female	Male	Not Married	Married	Not Employed	Employed	<40	40–65	65>
0	33,271	58,362	31,225	60,408	26,606	65,027	36,236	45,880	9517
	88.64%	86.51%	88.06%	86.88%	86.49%	87.60%	88.38%	87.39%	82.83%
1	4262	9098	4235	9125	4156	9204	4765	6622	1973
	11.36%	13.49%	11.94%	13.12%	13.51%	12.40%	11.62%	12.61%	17.17%
Total	37,533	67,460	35,460	69,533	30,762	74,231	41,001	52,502	11,490
	100%	100%	100%	100%	100%	100%	100%	100%	100%
	t = −9.9357 ***		t = −5.4280 ***		t = 4.5916 ***		F = 125.34 ***

*** indicates significance level at 1%.

.

2.4. Methods

To address RQ1 and RQ2 regarding the association between DFL and hyperbolic discounting, we employ the following empirical strategy. First, hyperbolic discounting describes the phenomenon where people value rewards differently depending on when they are received. In standard economic theory, time-consistent preferences are typically modeled using exponential discounting (Samuelson 1937), as given in Equation (1).

$$\mathrm{V}\left(\mathrm{A},\mathrm{t}\right)=\mathrm{A}.{\mathsf{\delta }}^{\mathrm{t}}$$

(1)

where V denotes the present value of receiving reward A at time t, while the discount rate δ reflects the constant proportional reduction in value associated with each additional delay. However, evidence from psychology and behavioral economics indicates that certain individuals display time-inconsistent preferences, a phenomenon widely known as hyperbolic discounting. In this case, individuals tend to discount near-term rewards more heavily than rewards in the distant future, deviating from the constant discounting assumption implied by exponential discounting (Story et al. 2014; Green and Myerson 1996). The discount function for hyperbolic discounters is expressed as:

$$\mathrm{V}\left(\mathrm{A},\mathrm{t}\right)=\mathrm{A}.{\displaystyle \frac{1}{1+\mathrm{k}.\mathrm{t}}}$$

(2)

where $(\mathrm{k}$) represents the parameter that determines the rate at which value is discounted over time.

Second, based on the constructed binary indicator, participants are classified into hyperbolic discounters or non-hyperbolic discounters and a probit model is employed to analyze this binary outcome. To evaluate the association between hyperbolic discounting and DFL, we estimated the following empirical models:

$${\mathrm{Y}}_{\mathrm{i}}=\mathrm{f}({\mathrm{D}\mathrm{F}\mathrm{L}}_{\mathrm{i}}{,\mathrm{X}}_{\mathrm{i}},{\mathsf{\epsilon }}_{\mathrm{i}})$$

(3)

where ${\mathrm{Y}}_{\mathrm{i}}$ is the hyperbolic discounting behavior of the i respondent, ${\mathrm{D}\mathrm{F}\mathrm{L}}_{\mathrm{i}}$ represents the score of digital financial literacy, ${\mathrm{X}}_{\mathrm{i}}$ is, a vector of demographic and socioeconomic characteristics, and ${\mathsf{\epsilon }}_{\mathrm{i}}$ is the error term. We included three categories of control variables: demographic (gender, age, education, marital status, and children), economic (employment status, household income, and household assets), and behavioral (risk aversion), yielding four models for our study. In the equations presented below, β₀ shows the intercept, β₁–β₁₁ denote the estimated coefficients, and ε_i is the error term. The full models are as follows:

$$\begin{array}{cc}\hfill Hyperbolic {discounting}_i& \\ & \hfill ={\beta }_0+{\beta }_1{DFL}_i+{\epsilon }_i\end{array}$$

(4)

$$\begin{array}{cc}\hfill Hyperbolic {discounting}_i& \\ & ={\beta }_0+{\beta }_1{DFL}_i+{\beta }_2{Male}_i+{\beta }_3{Age}_i\hfill \\ & + {\beta }_4{Age square}_i+{\beta }_5{Marital Status}_i\hfill \\ & + {\beta }_6{Children}_i+{\beta }_7{Education}_i + {\epsilon }_i\hfill \end{array}$$

(5)

$$\begin{array}{cc}\hfill Hyperbolic {discounting}_i& \\ & ={\beta }_0+{\beta }_1{DFL}_i+{\beta }_2{Male}_i+{\beta }_3{Age}_i\hfill \\ & + {\beta }_4{Age square}_i+{\beta }_5{Marital Status}_i\hfill \\ & + {\beta }_6{Children}_i+{\beta }_7{Education}_i+{\beta }_8{Employment}_i\hfill \\ & + {\beta }_9{Log of Income}_i+{\beta }_{10}{Log of Assets}_i + {\epsilon }_i\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill Hyperbolic {discounting}_i& \\ & ={\beta }_0+{\beta }_1{DFL}_i+{\beta }_2{Male}_i+{\beta }_3{Age}_i\hfill \\ & + {\beta }_4{Age square}_i+{\beta }_5{Marital Status}_i\hfill \\ & + {\beta }_6{Children}_i+{\beta }_7{Education}_i+{\beta }_8{Employment}_i\hfill \\ & + {\beta }_9{Log of Income}_i+{\beta }_{10}{Log of Assets}_i\hfill \\ & + {\beta }_{11}{Risk Aversion}_i + {\epsilon }_i\hfill \end{array}$$

(7)

We calculated the coefficient of correlation and variance inflation factors (VIFs) to check for multicollinearity. Almost all the variables exhibited low intercorrelations (r < 0.6) (

Table A2. Pairwise Correlations Test.

Variables	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
(1) Hyperbolic Disc	1.000
(2) DFLindex	−0.035	1.000
(3) Male	0.031	0.054	1.000
(4) Age	0.043	−0.003	0.169	1.000
(5) Age_sq	0.047	−0.005	0.169	0.989	1.000
(6) Marital_Status	0.017	−0.002	0.072	0.211	0.192	1.000
(7) Children	0.022	−0.043	0.045	0.344	0.326	0.519	1.000
(8) Education	0.008	0.127	0.116	−0.123	−0.115	0.043	−0.065	1.000
(9) Employment	−0.015	0.043	0.228	−0.309	−0.333	−0.004	−0.062	0.167	1.000
(10) Log_Hincome	−0.001	0.138	0.086	−0.003	−0.038	0.417	0.222	0.219	0.350	1.000
(11) Log_Hasset	0.007	0.187	0.113	0.346	0.337	0.146	0.086	0.198	−0.046	0.359	1.000
(12) Risk_Aversion	0.004	0.004	0.057	0.108	0.113	−0.006	−0.019	0.078	−0.018	0.020	0.107	1.000

), consistent with thresholds suggested by Dormann et al. (2013) suggest that correlation coefficients below 0.6 indicate a low risk of multicollinearity in regression analyses. However, as expected, Age and Age-squared demonstrated high correlation (r = 0.989), yielding individual VIF values of 50.19 and 50.38, respectively, and contributing to a mean VIF of 10.25 (

Table A1. Variance Inflation Factor (VIF) Test.

Variable	VIF	1/VIF
Age_Square	50.38	0.020
Age	50.19	0.020
Log_Hincome	1.77	0.564
Marital_Status	1.61	0.620
Children	1.52	0.658
Employment	1.46	0.685
Log_Hasset	1.46	0.686
Male	1.16	0.865
Education	1.15	0.869
DFL	1.06	0.945
Risk Aversion	1.03	0.971
Mean VIF	10.25

). While this exceeds the conventional threshold of 10, the elevated VIF is anticipated and acceptable given that Age-squared is a mathematical transformation of Age, creating structural rather than problematic multicollinearity (Allison 2012). Excluding this polynomial term, the remaining variables showed acceptable VIF values below 2, supporting the reliability of our empirical findings.

3. Results

This section presents results addressing RQ1 by evaluating overall relationship between DFL and hyperbolic discounting, followed by analyses of heterogeneity across demographic groups and DFL components corresponding to RQ2. We constructed four models in our analysis: Model 1 includes only the DFL variable, establishing the baseline effect. Model 2 adds demographic controls (age, gender, marital status, children, and education). Model 3 incorporates socioeconomic factors (employment status, household assets, and household income). Model 4, our preferred model, includes a psychological variable (risk aversion), providing the most comprehensive specification.

3.1. Main Results

Table 4. Probit regression results.

	Hyperbolic Discounting
Variable	Model 1	Model 2	Model 3	Model 4
DFL	−0.0094 ***	−0.0101 ***	−0.0099 ***	−0.0100 ***
	(0.0008)	(0.0008)	(0.0009)	(0.0009)
Male		0.0860 ***	0.0876 ***	0.0879 ***
		(0.0113)	(0.0113)	(0.0113)
Age		−0.0143 ***	−0.0146 ***	−0.0146 ***
		(0.0028)	(0.0029)	(0.0029)
Age_sq		0.0002 ***	0.0002 ***	0.0002 ***
		(0.0000)	(0.0000)	(0.0000)
Marital_Status		0.0198	0.0123	0.0122
		(0.0124)	(0.0134)	(0.0134)
Children		0.0095 *	0.0080	0.0078
		(0.0055)	(0.0055)	(0.0055)
Education		0.0112 ***	0.0118 ***	0.0120 ***
		(0.0025)	(0.0026)	(0.0026)
Fulltime		−0.0216 *	−0.0305 **	−0.0304 **
		(0.0124)	(0.0132)	(0.0132)
Log_Hincome			0.0218 **	0.0219 **
			(0.0108)	(0.0108)
Log_Hasset			−0.0137 **	−0.0135 **
			(0.0054)	(0.0054)
Risk_Aversion				−0.0210
				(0.0211)
Constant	−1.1412 ***	−1.1759 ***	−1.2955 ***	−1.2919 ***
	(0.0049)	(0.0761)	(0.1548)	(0.1548)
Observations	104,993	104,993	104,993	104,993
Pseudo R2	0.0016	0.0060	0.0061	0.0061
Log likelihood	−39,951.1200	−39,776.6394	−39,772.6664	−39,772.1871

*, **, and *** indicate significance level at 10%, 5%, and 1%, respectively.

shows the results of the association of DFL with hyperbolic discounting. To facilitate interpretation of the probit coefficients, we also estimate marginal effects for the preferred specification (Model 4). The marginal effects, presented in

Table 5. Marginal effects from probit model.

	Hyperbolic Discounting
Variable	Model 4
DFL Index	−0.0021 ***
	(0.0002)
Male	0.0182 ***
	(0.0023)
Age	−0.0030 ***
	(0.0006)
Age Squared	0.0000 ***
	(0.0000)
Marital Status	0.0025
	(0.0028)
Children	0.0016
	(0.0011)
Education Year	0.0025 ***
	(0.0005)
Fulltime Employment	−0.0063 **
	(0.0027)
Log of Household Income	0.0045 **
	(0.0022)
Log of Household Assets	−0.0028 **
	(0.0011)
Risk Aversion	−0.0043
	(0.0044)
Observations	104,993

** and *** indicate significance level at 5% and 1%, respectively.

, indicate that a one-unit increase in the DFL index is associated with a 0.21-percentage-point decrease in the probability of exhibiting hyperbolic discounting (ME = −0.0021, p < 0.01). Our findings indicate that DFL is negatively associated with hyperbolic discounting across all four models, indicating that higher DFL is associated with a lower probability of hyperbolic discounting. Among demographic factors, being male is associated with a higher probability of hyperbolic discounting, while age shows a nonlinear relationship with present bias, initially decreasing before increasing again at advanced ages (Age Squared). Education years unexpectedly demonstrate a positive association with hyperbolic discounting, while marital status shows no significant relationship, and the number of children exhibits a weak positive association in Model 2 only. This pattern suggests that formal education and digital financial literacy capture distinct dimensions of intertemporal decision-making rather than serving as substitutes. Regarding economic factors, full-time employment is negatively associated with present bias at 10% significance in Model 2 and 5% level of significance in Models 3 & 4. Household income shows a positive association with hyperbolic discounting at 5% level of significance in Models 3 & 4, and household assets exhibit a negative relationship at 5% level of significance in Models 3 & 4. Risk aversion shows no significant relationship with hyperbolic discounting, suggesting that time and risk preferences operate as distinct psychological constructs.

3.2. Subsample Analysis Results

We performed a subsample analysis to explore whether the association between digital financial literacy (DFL) and hyperbolic discounting differs by gender and age. As reported in

Table 6. Probit regression results for subsamples.

	Gender		Age
	(1)	(2)	(3)	(4)	(5)
Variable	Male Model	Female Model	Under 40	40–60	Over 60
DFL	−0.0102 ***	−0.0095 ***	−0.0137 ***	−0.0076 ***	−0.0032
	(0.0010)	(0.0016)	(0.0013)	(0.0013)	(0.0026)
Male	-	-	0.0949 ***	0.0859 ***	0.0215
			(0.0172)	(0.0167)	(0.0370)
Age	−0.0141 ***	−0.0155 ***	−0.0627 ***	−0.0544 **	0.1160 *
	(0.0036)	(0.0053)	(0.0211)	(0.0243)	(0.0699)
Age Squared	0.0002 ***	0.0002 ***	0.0010 ***	0.0006 **	−0.0008
	(0.0000)	(0.0001)	(0.0003)	(0.0002)	(0.0005)
Marital Status	0.0338 **	−0.0158	0.0160	0.0070	0.0438
	(0.0168)	(0.0231)	(0.0224)	(0.0192)	(0.0398)
Children	0.0128 *	−0.0049	0.0042	0.0062	0.0105
	(0.0068)	(0.0096)	(0.0108)	(0.0073)	(0.0143)
Education Year	0.0129 ***	0.0088 *	0.0048	0.0168 ***	0.0098
	(0.0030)	(0.0050)	(0.0045)	(0.0035)	(0.0071)
Fulltime Employment	−0.0623 ***	−0.0106	−0.0347	−0.0197	−0.0236
	(0.0186)	(0.0199)	(0.0228)	(0.0184)	(0.0360)
Log of Household Income	0.0224 *	0.0345 *	0.0363 *	0.0210	0.0187
	(0.0134)	(0.0189)	(0.0198)	(0.0154)	(0.0247)
Log of Household Assets	−0.0103	−0.0223 **	−0.0189 *	−0.0159 **	−0.0195
	(0.0065)	(0.0099)	(0.0101)	(0.0074)	(0.0138)
Risk Aversion	0.0095	−0.0974 **	0.0031	−0.0618 **	0.0530
	(0.0250)	(0.0396)	(0.0348)	(0.0296)	(0.0618)
Constant	−1.2718 ***	−1.2631 ***	−0.5775	−0.3090	−5.2356 **
	(0.1916)	(0.2720)	(0.4152)	(0.6361)	(2.4186)
Observations	67,460	37,533	41,001	52,502	11,490
Pseudo R-squared	0.00557	0.00416	0.00568	0.00325	0.00151
Log likelihood	−26,534	−13,227	−14,649	−19,832	−5261

*, **, and *** indicate significance level at 10%, 5%, and 1%, respectively.

, DFL exhibits a negative and statistically significant relationship with hyperbolic discounting for both males (β = −0.0102, p < 0.01) and females (β = −0.0095, p < 0.01), with a marginally stronger effect observed among males. Marital status shows a positive association with present bias for males (β = 0.0338, p < 0.05) but not for females, whereas employment status is strongly negatively related for males (β = −0.0623, p < 0.01) and insignificant for females. These patterns indicate gender-specific mechanisms through which demographic and economic characteristics shape intertemporal preferences. In terms of age, the protective effect of DFL against hyperbolic discounting varies substantially across age groups, showing the strongest relationship among individuals under 40 (β = −0.0137, p < 0.01), a moderate effect for those aged 40–60 (β = −0.0076, p < 0.01). In contrast, among individuals aged over 60, the estimated association becomes statistically indistinguishable from zero (β = −0.0032, p > 0.1), suggesting a potential age-related boundary condition for the relevance of DFL in later-life intertemporal decision-making. Education demonstrates a significant positive association with hyperbolic discounting only in the 40–60 age group (β = 0.0168, p < 0.01).

3.3. DFL Subdimension Component Analysis Results

Table 7. DFL Components probit regression results.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Variable	Digital Literacy	Awareness of DFS	Awareness of Positive FAB	Practical Know-How of DFS	Positive Financial Attitudes	Positive Financial Behaviours	Self-Protection	Financial Literacy
Digital Literacy	−0.0394 ***
	(0.00481)
Awareness of DFS		−0.0429 ***
		(0.00475)
Awareness of Positive Financial Attitudes and Behaviors			−0.0707 ***
			(0.00466)
Practical Know-How of DFS				−0.0181 ***
				(0.00499)
Positive Financial Attitude					−0.0633 ***
					(0.00487)
Positive Financial Behavior						−0.0485 ***
						(0.00487)
Self-Protection from Digital Scams							−0.0260 ***
							(0.00503)
Financial Literacy (Knowledge)								−0.0165 ***
								(0.00528)
Male	0.0820 ***	0.0819 ***	0.0734 ***	0.0863 ***	0.0793 ***	0.0851 ***	0.0898 ***	0.0901 ***
	(0.0113)	(0.0113)	(0.0113)	(0.0113)	(0.0113)	(0.0113)	(0.0114)	(0.0115)
Age	−0.0138 ***	−0.0139 ***	−0.0152 ***	−0.0147 ***	−0.0161 ***	−0.0151 ***	−0.0153 ***	−0.0145 ***
	(0.00288)	(0.00288)	(0.00288)	(0.00287)	(0.00288)	(0.00288)	(0.00288)	(0.00288)
Age_Squared	0.000203 ***	0.000205 ***	0.000219 ***	0.000212 ***	0.000225 ***	0.000218 ***	0.000218 ***	0.000211 ***
	(3.03 × 10−5)	(3.03 × 10−5)	(3.03 × 10−5)	(3.03 × 10−5)	(3.03 × 10−5)	(3.03 × 10−5)	(3.03 × 10−5)	(3.03 × 10−5)
Marital_Status	0.0148	0.0135	0.0138	0.0155	0.0136	0.0159	0.0159	0.0164
	(0.0133)	(0.0133)	(0.0133)	(0.0134)	(0.0134)	(0.0134)	(0.0134)	(0.0133)
Children	0.00906	0.00859	0.00918 *	0.00943 *	0.00905	0.00890	0.00913 *	0.00984 *
	(0.00551)	(0.00551)	(0.00551)	(0.00552)	(0.00551)	(0.00551)	(0.00552)	(0.00551)
Education	0.0109 ***	0.0111 ***	0.0115 ***	0.0105 ***	0.0113 ***	0.0104 ***	0.0104 ***	0.0109 ***
	(0.00256)	(0.00256)	(0.00256)	(0.00256)	(0.00256)	(0.00256)	(0.00256)	(0.00258)
Fulltime Employment	−0.0292 **	−0.0297 **	−0.0285 **	−0.0289 **	−0.0302 **	−0.0293 **	−0.0291 **	−0.0278 **
	(0.0132)	(0.0132)	(0.0132)	(0.0132)	(0.0132)	(0.0132)	(0.0132)	(0.0132)
Log of Household_Income	0.0170	0.0189 *	0.0196 *	0.0154	0.0187 *	0.0166	0.0158	0.0136
	(0.0108)	(0.0108)	(0.0108)	(0.0108)	(0.0108)	(0.0108)	(0.0108)	(0.0108)
Log of Household_Assets	−0.0204 ***	−0.0190 ***	−0.0140 ***	−0.0198 ***	−0.0107 **	−0.0189 ***	−0.0184 ***	−0.0190 ***
	(0.00535)	(0.00536)	(0.00538)	(0.00538)	(0.00541)	(0.00536)	(0.00539)	(0.00542)
Risk Aversion	−0.0212	−0.0223	−0.0214	−0.0155	−0.0178	−0.0145	−0.0146	−0.0139
	(0.0211)	(0.0212)	(0.0211)	(0.0212)	(0.0212)	(0.0212)	(0.0212)	(0.0211)
Constant	−1.103 ***	−1.161 ***	−1.229 ***	−1.070 ***	−1.241 ***	−1.096 ***	−1.082 ***	−1.072 ***
	(0.154)	(0.154)	(0.153)	(0.155)	(0.154)	(0.153)	(0.154)	(0.155)
Observations	104,993	104,993	104,993	104,993	104,993	104,993	104,993	104,993

*, **, and *** indicate significance level at 10%, 5%, and 1%, respectively.

shows the DFL component analysis results, revealing that all eight subdimensions of DFL are significantly associated with reduced hyperbolic discounting among Japanese account holders at Rakuten Securities. Each component is estimated in a separate specification rather than simultaneously in a single model. This approach is adopted because the composite DFL index is constructed as the standardized sum of these components, and including all components simultaneously could introduce conceptual overlap and potential multicollinearity. The composite specification using the aggregated DFL index is therefore presented in Table 4, while Table 7 isolates the association of each component individually with hyperbolic discounting. The specific effects of each subdimension are as follows:

Strongest Associations—Attitudinal Components: Among the examined dimensions, awareness of beneficial financial attitudes and behaviors exhibits the largest negative association with hyperbolic discounting (β = −0.0707, p < 0.01), with positive financial attitudes showing a similarly strong effect (β = −0.0633, p < 0.01). This pattern suggests that heightened recognition of prudent financial conduct, together with the internalization of positive financial outlooks, is linked to markedly lower present bias.

Moderate Associations—Knowledge and Behavioral Components: Positive financial behavior (β = −0.0485, p < 0.01), awareness of digital financial services (β = −0.0429, p < 0.01), and digital literacy (β = −0.0394, p < 0.01) show stronger negative associations with hyperbolic discounting compared to traditional financial knowledge (β = −0.0165, p < 0.01), indicating that familiarity with modern digital financial tools and engagement in sound financial practices relate more strongly to reduced present bias than conventional financial education. Among protective factors, self-protection from digital scams demonstrates a moderate relationship (β = −0.0260, p < 0.01).

Weakest Association—Technical Proficiency: Practical know-how of DFS exhibits the weakest relationship with hyperbolic discounting (β = −0.0181, p < 0.01), closely followed by traditional financial literacy (β = −0.0165, p < 0.01). This suggests that technical skills and basic financial knowledge alone, without accompanying attitudes or broader behavioral awareness, show limited association with reduced present bias.

In summary, this comprehensive analysis reveals that awareness and positive financial attitudes show substantially stronger associations with lower present bias than technical skills or traditional financial literacy.

A one-unit increase in the DFL index is associated with a 0.21-percentage-point decrease (ME = −0.0021, p < 0.01) in the probability of hyperbolic discounting. This indicates that individuals with higher digital financial literacy are less likely to be classified as exhibiting hyperbolic discounting. While the effect size appears modest, it remains statistically meaningful given the large sample size and the wide distribution of DFL scores. Thus, the DFL index is consistently associated with a lower probability of hyperbolic discounting, with gender showing one of the strongest demographic associations.

4. Discussion

4.1. Digital Financial Literacy (DFL) and Hyperbolic Discounting

We analyzed the association between DFL and hyperbolic discounting through a comprehensive survey of Japanese account holders at Rakuten Securities. Our findings revealed a robust negative linkage between DFL and present bias, indicating that higher DFL is associated with a lower probability of hyperbolic discounting. This relationship remains statistically significant across all four models, suggesting that individuals with higher levels of digital financial literacy are less likely to exhibit hyperbolic discounting. These results align with emerging research documenting the beneficial influence of digital financial competencies on financial decision-making (Morgan et al. 2019; Lyons and Kass-Hanna 2021; Choung et al. 2023).

The magnitude of the DFL effect, while modest, carries practical significance given the widespread prevalence of hyperbolic discounting and its demonstrated consequences for wealth accumulation (Meier and Sprenger 2010; Barber and Odean 2013). Although the pseudo-R-squared values appear relatively small, such magnitudes are common in cross-sectional behavioral studies examining individual financial decision-making. Intertemporal preferences are shaped by numerous psychological and contextual factors that cannot be fully observed in survey datasets. Therefore, the primary objective of the present analysis is not predictive accuracy but identifying statistically meaningful associations between digital financial literacy and present-biased behavior. Previous research has established that even small reductions in present bias can substantially improve long-term financial outcomes through enhanced retirement contributions, reduced premature withdrawals, and improved portfolio discipline (Benartzi and Thaler 2007; Bradford et al. 2017).

4.2. Demographic Factors and Time Preferences

Gender appears as a significant determinant, with males demonstrating notably greater present bias than females, in line with prior studies highlighting gender-based differences in financial decision-making and intertemporal preferences (Meier and Sprenger 2010; Dohmen et al. 2011; Setiawan et al. 2022; Choung et al. 2023; Lal et al. 2025). However, DFL maintains protective effects for both genders, with slightly stronger associations among males.

Age demonstrated the most pronounced demographic pattern, exhibiting a nonlinear relationship with hyperbolic discounting. Present bias remains relatively stable through middle age before increasing sharply among individuals over 65. Critically, the protective effect of DFL varies substantially across age groups, showing the strongest relationship among younger individuals (under 40), diminishing among middle-aged individuals (40–60), and becoming non-significant among older individuals (over 65). Younger individuals may benefit more from DFL because they face longer investment horizons where digital tools for projecting compound growth prove particularly valuable (Lusardi et al. 2017).

The positive relationship between education and hyperbolic discounting emerged as a counterintuitive finding. Previous research has generally documented a negative relationship between educational attainment and present bias (Frederick 2005). However, our findings may reflect sample-specific characteristics, as our respondents comprise active securities account holders at Rakuten Securities, representing a financially engaged population where educational differences may operate differently than in general populations.

4.3. Socioeconomics and Psychological Factors

Employment status demonstrated expected associations, with full-time employment reducing hyperbolic discounting. This likely reflects multiple mechanisms, as employed individuals experience regular income flows that reduce immediate financial pressures and benefit from employer-sponsored retirement programs that facilitate long-term planning (Shah et al. 2012). The stronger employment effects among males align with traditional gender roles in labor force participation, though these patterns may evolve as labor markets transform.

Household income and assets exhibited contrasting relationships with present bias. Higher household income unexpectedly associates with increased hyperbolic discounting, while greater household assets reduce it. These divergent patterns suggest important distinctions between income flows and accumulated wealth in shaping time preferences (Shah et al. 2012; Mullainathan and Shafir 2013). Asset accumulation might reflect successful past application of patient time preferences, creating reinforcing feedback loops between wealth and reduced present bias (Mullainathan and Shafir 2013).

The absence of significant relationships between risk aversion and hyperbolic discounting provided valuable evidence that time preferences and risk preferences represent distinct psychological constructs (Andersen et al. 2008), suggesting that interventions targeting present bias need not simultaneously address risk attitudes.

4.4. Digital Financial Literacy Subdimension Components

Our findings revealed that attitudinal components of DFL exerted the strongest influence on reducing hyperbolic discounting, with awareness of positive financial attitudes and behaviors and positive financial attitudes showing the most substantial associations. This aligns with research demonstrating that financial attitudes mediate the relationship between literacy and behavior (Xiao and Porto 2017; Ajzen 1991). The prominence of attitudinal factors suggests that internalized beliefs about financial planning may be more influential than technical knowledge in promoting time-consistent preferences, consistent with the theory of planned behavior (Ajzen 1991).

Digital competencies, including positive financial behavior, awareness of DFS, and digital literacy, demonstrated stronger associations with reduced hyperbolic discounting in this sample than traditional financial knowledge. This finding supports recent evidence that DFL may outperform conventional financial knowledge in predicting certain financial outcomes (Prasad et al. 2018). The superior performance of digital literacy may reflect modern platforms’ behavioral nudges and visualization tools that make future consequences more salient (Karlan et al. 2016; Soman and Zhao 2011).

Most strikingly, practical know-how showed limited association with hyperbolic discounting, suggesting technical proficiency alone is insufficient without accompanying attitudes or behavioral awareness. This pattern echoes findings that skills-based interventions show limited effectiveness without addressing underlying preferences and motivations (Fernandes et al. 2014; Kaiser and Menkhoff 2017). The findings highlight the need for comprehensive digital financial education initiatives that emphasize the development of financial attitudes in addition to technical skills.

Our findings have demonstrated that DFL components, particularly awareness of digital financial services and digital literacy, show stronger associations with reduced hyperbolic discounting than traditional financial knowledge. This pattern aligns with Bawalle et al.’s (2024) findings that behavioral and attitudinal components surpass pure financial knowledge in mitigating hyperbolic discounting. The superiority of DFL suggests that in increasingly digitalized financial environments, competencies beyond conventional financial education, including awareness of digital tools, positive financial attitudes, and behavioral engagement, are more critical for promoting time-consistent decision-making (Prasad et al. 2018). These results underscore the need for comprehensive financial education programs that prioritize digital competencies and attitudinal development alongside traditional financial knowledge.

4.5. Practical Implications

From a practical perspective, these findings carry significant implications for financial institutions. Financial institutions should prioritize DFL interventions, emphasizing attitudinal development and awareness cultivation rather than focusing exclusively on technical training. The age-dependent effectiveness of DFL suggests that interventions should be tailored to different demographic groups, with younger individuals appearing particularly responsive to DFL-based interventions.

Platform designers should recognize that effective behavioral architecture requires users with adequate DFL to benefit fully, incorporating embedded educational content that develops competencies while facilitating positive behaviors.

4.6. Limitations and Future Research

Several limitations should be acknowledged when interpreting the findings of this study. Our sample comprises active securities account holders at a single financial institution, limiting generalizability. The cross-sectional nature of the study restricts the ability to draw causal conclusions. Furthermore, the explanatory power of the empirical models remains limited, reflecting the complexity of individual intertemporal preferences and the presence of unobserved behavioral factors. Future investigations should employ longitudinal or experimental designs to more rigorously examine causal links among digital financial literacy, present bias, and behavioral outcomes. Finally, the rapid evolution of digital financial services means that the specific competencies comprising DFL continue changing, requiring ongoing research.

5. Conclusions

This study investigated the association between digital financial literacy and hyperbolic discounting using data from 104,993 active securities account holders in Japan. Our findings demonstrated that higher DFL is associated with a lower probability of hyperbolic discounting, with this relationship persisting after controlling for demographic, socioeconomic, and psychological factors. The protective effect of DFL proved strongest among younger individuals, moderate among middle-aged individuals, and non-significant among older individuals. Component analysis revealed that attitudinal dimensions demonstrated substantially stronger associations with reduced present bias than technical skills or traditional financial knowledge.

The study offers significant contributions to the existing literature. First, we provide the first rigorous empirical examination directly linking DFL to hyperbolic discount rates using validated intertemporal choice measurements. Second, we identify specific mechanisms through which DFL influences time preferences by analyzing the differential effects of eight distinct DFL components. Third, our comprehensive subsample analyses identify which demographic groups respond most strongly to DFL, enabling more effective targeting of educational programs and platform features.

The findings also carry policy and practical implications. Japanese financial institutions should expand DFL programs, emphasizing attitudinal development rather than focusing exclusively on technical training. Institutions should implement age-targeted interventions, recognizing the differential effectiveness of DFL across life stages, with younger individuals representing particularly receptive audiences. Platform designers should integrate behavioral architecture with embedded DFL development, incorporating progressive educational content. Regulatory bodies should consider incorporating DFL standards into investor protection frameworks, and industry collaborations should develop standardized DFL assessment tools and curricula.

Overall, this research fills an important gap at the intersection of behavioral finance and financial technology. By demonstrating that DFL can reduce hyperbolic discounting and by identifying which specific components matter most, we provide actionable pathways for interventions that could substantially improve investment outcomes and long-term financial security for millions of investors navigating increasingly digital financial landscapes.