Developmental trajectories of delay discounting from childhood to young adulthood: longitudinal associations and test-retest reliability

Abstract

Delay discounting (DD) indexes an individual’s preference for smaller immediate rewards over larger delayed rewards, and is considered a form of cognitive impulsivity. Cross-sectional studies have demonstrated that DD peaks in adolescence; longitudinal studies are needed to validate this putative developmental trend, and to determine whether DD assesses a temporary state, or reflects a more stable behavioral trait. In this study, 140 individuals aged 9–23 completed a delay discounting (DD) task and cognitive battery at baseline and every-two years thereafter, yielding five assessments over approximately 10 years. Models fit with the inverse effect of age best approximated the longitudinal trajectory of two DD measures, hyperbolic discounting ($\text{log}[k]$) and area under the indifference-point curve (AUC). Discounting of future rewards increased rapidly from childhood to adolescence and appeared to plateau in late adolescence for both models of DD. Participants with greater verbal intelligence and working memory displayed reduced DD across the duration of the study, suggesting a functional interrelationship between these domains and DD from early adolescence to adulthood. Furthermore, AUC demonstrated good to excellent reliability across assessment points that was superior to $\text{log}(k)$, with both measures demonstrating acceptable stability once participants reached late adolescence. The developmental trajectories of DD we observed from childhood through young adulthood suggest that DD may index cognitive control more than reward sensitivity, and that despite modest developmental changes with maturation, AUC may be conceptualized as a trait variable related to cognitive control vs impulsivity.

1. Introduction

Adolescence is a developmental period marked by pronounced changes in both physical and cognitive capabilities. Relative to children, adolescents display improved self-regulation, working memory, and abstract thinking; they also demonstrate improved coordination between affective and cognitive processes (Steinberg, 2005). Nonetheless, adolescence is also a period of heightened vulnerability and increased mortality (Cunningham et al., 2018). The dual systems model (Casey et al., 2011; Steinberg, 2010) posits that mismatches in the maturational timing of subcortically-mediated functions associated with reward processing (i.e., reward system) versus prefrontally mediated functions underlying cognitive control (i.e., cognitive control system), lead to heightened reward sensitivity as well as behavioral impulsivity. Developmentally, an inverted U-shaped or quadratic trajectory characterizes the development of the reward system, which is hypothesized to peak in adolescence, while the cognitive control system develops steadily from adolescence through adulthood (i.e., approximates a linear function across development; Almy et al., 2018; Steinberg, 2010; Urošević et al., 2012), or perhaps stabilizes in adolescence (i.e., approximates an inverse trajectory across development; Luna, 2009; Luna & Wright, 2016). These dynamics predict that in early-to-mid adolescence, reward strivings outpace capacities for regulatory control, potentially biasing individuals toward maladaptive decision-making (Luciana & Collins, 2012).

An important aspect of goal-directed behavior is the ability to consider the relative value of proximal versus distal rewards in present decision-making. Preferences for immediate/proximal as opposed to delayed/distal rewards could, under some conditions, reflect cognitive impulsivity (Zisner & Beauchaine, 2016). Individuals with greater cognitive impulsivity are more vulnerable to externalizing psychopathology including substance use disorders (Ersche et al., 2010), attention-deficit hyperactivity disorder (ADHD), conduct disorder, and antisocial personality disorder (Beauchaine et al., 2017). Additionally, cognitive impulsivity predicts the development of maladaptive and risky behaviors (Pearson et al., 2013), and is robustly linked to the initiation of pathological substance use during adolescence (Mitchell & Potenza, 2014).

An example of a laboratory paradigm that indexes cognitive impulsivity is the temporal delay discounting (DD) task. Though the structure and stimuli vary across studies, the general procedure involves asking individuals to choose between smaller immediate versus larger delayed hypothetical rewards. These selections are then examined to quantify the point at which the subjective value of smaller proximal (i.e., immediate) and larger distal (i.e., temporally delayed) rewards are equated, termed the indifference point (Odum, 2011a). An individual’s discounting tendencies can be inferred by plotting indifference points against each delay interval. Steeper temporal discounting of hypothetical rewards is associated with substance misuse across a number of drugs (Bailey et al., 2020; Odum et al., 2020). Critically, a greater preference for immediate rewards predicts diminished engagement of the executive/cognitive control network, as examined by functional magnetic resonance research (fMRI), in adolescents; impairments in this network are implicated in adolescent substance misuse (Stanger et al., 2013). Further, greater temporal discounting partially mediates the association between risky-decision making and substance misuse (Kim-Spoon et al., 2019), predicts maladaptive health behaviors such as medication adherence and diet quality in individuals at risk for developing diabetes, and influences health safety decisions implicated in risk perception (e.g., the choice to wear a seatbelt; Daugherty & Brase, 2010; Epstein et al., 2021). Taken together, greater DD is associated with maladaptive behaviors—and predicts worse functional outcomes (Bickel et al., 2011)—during adolescence.

These associations raise the question of how DD can be understood as a developmental phenomenon as opposed to a stable behavioral trait. If DD markedly changes with adolescent development, then a heightened tendency toward cognitive impulsivity may represent an age-related vulnerability factor that predisposes individuals to decisions predicated on attaining immediate rewards. On the other hand, if DD reflects a stable trait that is invariant across development, then vulnerable individuals (e.g., Jones et al., 2017) could be identified earlier in childhood, and prevention efforts could be directed in a personalized manner. Determining the behavioral stability of DD during the developmental transition from adolescence to adulthood would help clarify the cognitive and behavioral phenomena underlying DD (Parsons et al., 2019), and whether DD is a stable individual trait, or a context dependent behavior (i.e., state-like; Odum, 2011b; Peters & Büchel, 2011) that changes with development. Both mechanisms may characterize adolescence.

Cognitive impulsivity inferred through DD paradigms appears to change, albeit modestly, with adolescent development. Cross-sectional analyses of individuals aged 8 to 30 show age-related declines in discounting of future hypothetical rewards (Olson et al., 2007). Achterberg and colleagues studied 254 participants, aged 8 to 25, who completed a DD task at two time points, separated by approximately-two years. Cross sectional associations between age and the delay AUC were moderate (r = 0.207 for time 1 and r = 0.201 for Time 2: Achterberg et al., 2016). Large sample studies, such as the National Consortium on Alcohol and Neurodevelopment in Adolescence (NCANDA) have found that age, ethnicity, and SES (but not sex) impact delay discounting performance (Sullivan et al., 2016). Among 692 adolescents, aged 12 to 21 years, age accounted for 9 % of the variance in delay discounting performance. Another large study of 935 individuals aged 10 to 30 years observed that adolescents demonstrate greater DD than both children and adults, suggesting that discounting behaviors may peak in adolescence (Steinberg et al., 2009). Longitudinal studies are needed to validate these putative developmental trajectories (Thomas et al., 2009), and to formulate theoretical models of how DD changes across development (Collins, 2006).

DD is robustly associated with other functions, including general intelligence (Kirby & Marakovic, 1996). It appears that verbal intelligence (Olson et al., 2007; Richards et al., 1999), but not nonverbal intelligence (Shamosh et al., 2008) is directly linked to DD. Likewise, discounting appears to be related to specific aspects of working memory and other executive processes (Shamosh et al., 2008; Wesley & Bickel, 2014); those with better developed working memory and executive skills demonstrate decreased discounting behavior (Hinson et al., 2003). Indeed, increased rates of discounting observed in individuals with externalizing psychopathology may be partially accounted for by weaknesses in working memory capacity (Finn et al., 2015). Likewise, greater DD coupled with weaknesses in working memory may index a hyperactive reward system and a hypoactive executive control system that interact to predict the initiation of compulsive drug-taking in rats (Belin et al., 2008), or early drug use and subsequent progression to substance use disorders in adolescents (Khurana et al., 2017). Longitudinal analyses measuring the associations between working memory and DD from childhood through young adulthood could clarify how maturational changes in executive systems influences the concurrent maturation of DD behaviors.

A number of demographic factors appear to influence the degree of DD. Evidence for gender differences in DD are mixed, with some studies demonstrating that males discount more than females (Kirby & Marakovic, 1996; Steinberg et al., 2009), some demonstrating more discounting in females (Reimers et al., 2009), and others reporting no gender differences (Anokhin et al., 2015; Martínez-Loredo et al., 2017). Notably, discounting behaviors are influenced by sociocultural factors (Sheffer et al., 2016). Reduced socioeconomic status (SES; Bickel et al., 2016), and lower parental education (Sweitzer et al., 2013), are associated with preferences for smaller immediate/proximal rewards. Thus, resource scarcity and environmental instability may alter choice behaviors in DD paradigms. Accordingly, in historically marginalized communities, and/or economically disadvantaged populations, discounting behaviors would not reflect cognitive impulsivity, and instead represent an adaptive economic strategy (Oshri et al., 2019).

While there has been an explosion in DD research in the last decade, relatively few studies have employed longitudinal methods. In a recent meta-analysis of studies that employed experimental methods to reduce DD rates, only 10 of 92 studies employed a longitudinal approach. Moreover, only five of these studies assessed DD at three or more time points (Rung & Madden, 2018). Relatively few other studies have examined DD behaviors across time (c.f. Achterberg et al., 2016; Anokhin et al., 2015; Kim-Spoon et al., 2019; Lee et al., 2017; Martínez-Loredo et al., 2017). In general, longitudinal studies of decision-making that extend beyond two time points and utilize sophisticated longitudinal modeling techniques are rare (Almy et al., 2018), obviating accurate estimates of within-subject change across time (King et al., 2018).

The most oft-used function for quantifying the relationship between delays and indifference points is the hyperbolic function. The hyperbolic function yields a single parameter $k$ that represents the rate at which a hypothetical reward decreases in value as a function of the delay to its receipt, as represented in the following equation:

$$\mathbf{\text{V}}=\mathbf{\text{A}}/(1+\mathit{k}\mathbf{\text{D}})$$ (1)

This equation describes how the present subjective value (V) of a reward of amount (A) decreases as a function of delay (D) to receiving said reward. The free parameter $k$ represents the rate of DD, with higher $k$ representing greater discounting of temporal rewards (Madden et al., 2003; Mazur, 1987). Generally, given the highly skewed nature of empirical distributions of $k$, the parameter is typically log-transformed (represented as $\text{log}(k)$) to conduct parametric statistics (Yoon et al., 2017).

An alternative approach is to calculate the combined area under the curve (AUC) after plotting subjective reward against the relative delay (e.g., Myerson et al., 2001). AUC is calculated as follows:

$$\mathbf{\text{AUC}}=(\mathbf{\text{D}}2-\mathbf{\text{D}}1)\left(\frac{\mathbf{\text{V}}1+\mathbf{\text{V}}2}{2}\right)$$ (2)

As indicted, the trapezoidal area results from multiplying the base (i.e., difference between respective delay D1 and D2) by the height (i.e., the average of temporally adjacent indifference points V1 and V2; Myerson et al., 2001). A 2011 meta -analysis of delay discounting found that 70 % of studies employed $\text{log}(k)$, while roughly 14 % employed AUC (MacKillop et al., 2011). Within more recent meta-analyses, the majority of contributing studies have likewise used the hyperbolic model to derive $\text{log}(k)$, while AUC was the 2nd most used metric (Amlung et al., 2019; Rung & Madden, 2018; Weinsztok et al., 2021). Developmental studies (e.g., Martínez-Loredo et al., 2017) have used both.

There are several tradeoffs in the decision to use AUC versus $\text{log}(k)$. Given that AUC is calculated by fitting straight lines between observed indifference points, it does not assume a latent smoothly varying discounting function. Furthermore, the $k$ parameter is dependent on assumptions inherent in Samuelson’s (1937) discounting utility model, including: 1) disparate motives underlying preferences in intertemporal choice can be condensed into the discounting rate; and 2) that individuals consider the present intertemporal choice as part of a larger consumption set (i.e., individuals integrate new alternatives with existing plans; Frederick et al., 2002). In contrast, AUC is theoretically neutral (Myerson et al., 2001). There are potential drawbacks to AUC as well, with recent reports suggesting that AUC is not entirely atheoretical (given it is at least partially reliant on time-constancy assumptions implicit in systematic DD; Gilroy & Hantula, 2018), and it may exhibit greater positive skew compared to $\text{log}(k)$ when examining populations of steep discounters, such as those with substance use disorders (Yoon et al., 2017, 2018). Comparing the long-term stability of these models would help researchers decide which measure is most appropriate for longitudinal studies (Hedge et al., 2018). Likewise, examining the relative influence of practice effects on these models is necessary to determine the influence of true developmental change in cognition on the theoretical assumptions implicit in the models (Kurth-Nelson et al., 2012; Scharfen et al., 2018).

There are a number of other models by which to examine delay discounting beyond the nonparametric AUC, and the parametric $\text{log}(k)$. Indeed, in 2012, Doyle surveyed over 20 models (Doyle, 2012), with Dai and Busemeyer fitting 57 different models to experimental data (Dai & Busemeyer, 2014). Attribute-wise models posit that participants weigh each option based on where it falls along the delay and reward attribute (Cheng & Gonzalez-Vallejo, 2016; Dai & Busemeyer, 2014), or use heuristics to compare the relative or absolute differences along these attributes (Marzilli Ericson et al., 2015). Others have used the drift diffusion model to demonstrate that individuals vary in their propensity (bias) to choose immediate rewards (Zhao et al., 2019), and to glean novel insights into the cognitive and neural mechanisms underlying intertemporal choice (Peters & Büchel, 2011; Peters & D’Esposito, 2020; Rodriguez et al., 2015). Due to the large number of potential models by which to examine DD, the question of which model(s) to employ on a given dataset is an important question. The vast majority of studies of DD have used either the single-parameter hyperbolic model (i.e., $k$) or AUC, as evidenced by numerous meta-analyses of DD (Amlung et al., 2019; MacKillop et al., 2011; Rung & Madden, 2018; Weinsztok et al., 2021). Crucially—and most relevant to the present work—longitudinal studies of adolescent development have also used these models (Achterberg et al., 2016; Audrain-McGovern et al., 2009; Khurana et al., 2013, 2017; Kim-Spoon et al., 2019). Likewise, seminal studies of child development (Kirby et al., 2005; Steinberg, 2010; Steinberg et al., 2009), and more recent experimental studies examining DD in children and adolescents (Burns et al., 2021, 2022; Yu et al., 2021) have also used AUC or $k$. While the single-parameter hyperbolic model is not without its limitations, the $k$ parameter is directly interpretable as a metric of impulsivity (van den Bos & McClure, 2013). Given the emphasis of this prior work, and to allow comparability with these prior findings, the present work examines the longitudinal developmental trajectories of log($k$) and AUC to increase the relevance of findings within the broader DD research contexts, and to remain contiguous with the child and adolescent development literatures. Because we assume that children and adults do not make intertemporal choices using the same cognitive processes, a broadly interpretable index of cognitive impulsivity (i.e., $k$ or AUC) is most appropriate to model neurodevelopmental changes in this construct from childhood to young adulthood.

Accordingly, the current study investigates age-related changes in discounting behavior during adolescence and early adulthood, while comparing the psychometric properties of the natural log-transformed $k$, henceforth referred to as $\text{log}(k)$, and AUC as indices of DD. Additionally, to examine the influence of time perception on the development of DD, we include a supplemental analysis of Ebert and Prelec’s Constant Sensitivity Model (CS; Ebert & Prelec, 2007). Previous reports have cross-sectionally examined AUC values for DD across adolescence (Olson et al., 2007, 2009). Here we expand that analysis to a completed five-wave longitudinal data set (conducted from 2004 to 2016). We assessed whether the developmental trajectories of AUC and $\text{log}(k)$ approximated a quadratic curve with steeper discounting manifested during adolescence followed by relatively decreased discounting in young adulthood, as shown in research adolescent reward sensitivity (c.f., Achterberg et al., 2016; Steinberg et al., 2009), or a linear or inverse function of age, as reported for executive function measures (Almy et al., 2018; Luciana et al., 2005; Luna et al., 2004). The former would suggest that the developmental trajectory of DD behavior follows that of measures linked to reward system processes—hypothesized to follow a U-shaped trajectory and to peak in adolescence—whereas the latter would suggest that DD behavior approximates a similar trajectory to measures that tap executive abilities comprising the cognitive control system. To further investigate the overlap of DD and executive function, we examine the relative contribution of working memory indices to the developmental trajectories of DD (in light of strong experimental evidence of associations between these impulsivity measures Bickel et al., 2011; Shamosh et al., 2008; Wesley & Bickel, 2014; Finn et al., 2015), as well as an estimate of verbal IQ as a covariate of interest (Olson et al., 2007). Regarding psychometric aims, we examine the stability of inter-individual differences of discounting behaviors from late childhood to young adulthood to determine if temporal discounting of hypothetical rewards emerges as a behavioral trait during this period of development (Odum, 2011b). We assume that adolescents are unlikely to make economic decisions in precisely the same way as adults (Borges et al., 2016), leading to variations in the shape of the indifference-point curve over time that decreases the reliability of hyperbolic curve fitting, relative to the integration of the indifference-point curve itself (regardless of the shape of the curve). Accordingly, we expect AUC to be more reliable than $\text{log}(k)$ as the primary DD measure in tests of our developmental hypotheses.

2. Methods

2.1. Participants

The longitudinal study was approved by the University of Minnesota human participants committee (protocol 0405 M59982) and incorporated a cohort sequential design. Participants were recruited between 2004 and 2006 from a community database of research volunteers maintained by the Institute of Child Development at the University of Minnesota. Baseline data collection commenced in November 2004; wave 2 began in February 2007; wave 3 began in August 2009; wave 4 began in February 2012, and wave 5 began in June 2014. Each wave (with the exception of wave 3) took 2–3 years to complete. Thus, the bulk of data collection occurred across an approximate 10-year period (i.e., ~10-year) for each participant, depending on when they completed each subsequent wave. Participants ranged in age from 9 to 23 years at baseline, and were invited to complete four subsequent assessments, spaced approximately-two years apart. For minors, families were recruited through a community database maintained by the University of Minnesota. When their child was born, parents throughout the metro area indicated an interest in participating in University-sponsored research, allowing adolescents to be identified within the database. Additionally, invitation postcards were mailed to nonacademic University employees who might be parents. Young adults (aged 18 + ) were recruited through community postings. A phone screening followed by an in-person clinical assessment (Kaufman et al., 1997) determined study eligibility. Exclusion criteria included a history of neurological or psychiatric disorders, preterm birth, or other birth complications, current or past substance abuse or dependence, significant head injury, learning disabilities, psychoactive drug use, and non-native English speaking.

At baseline, 197 individuals were enrolled, and 140 individuals (69 %) completed the DD task (i.e., it was added partway through the baseline assessment). Participant demographics are presented in Table 1. In total, 185 participants completed the delay discounting task across all five waves. Of these 185, 156 completed at least two waves (29 participants only had one data point for discounting data), with participants completing the discounting task an average of 3.15 times.

Table 1.

Participant Demographics.

Demographic	N = 197
Mean BL Age	16.39
(SD)	(4.09)
BL Age Range	9–23
Percent Female	39
Ethnicity (%)
white	85
Black	1.5
Asian and Pacific Islander	4.1
Hispanic	1.5
Other†	4.6
Mean BL Maternal Years of Education	15.64
(SD)	(2.0)
Mean BL Paternal Years of Education	16.33
(SD)	(2.85)
Mean Waves Completed	3.38
(SD)	(1.41)
Mean Income	99,497
(SD)	(75,844)
Mean FSIQ	115.9
(SD)	(10.74)
Participants with available DD Data	185
Mean Number of DD Task	3.15
Completions (SD)	1.33

Note. BL = baseline/year 0 of study. SD = standard deviation. Age is presented in years.

^†Includes individuals with multiple racial identities.

2.1.1. Delay discounting task (Richards et al., 1999)

The delay-discounting task has been described previously (Olson et al., 2007, 2009) and was programmed in E-Prime (Psychology Software Tools; https://www.psnet.com). On each trial, participants chose between $10 available after a delay or a smaller amount of money available immediately (i.e., “Would you rather have $2 now or $10 in 30 days?”). Discounting was assessed at six delays (1, 2, 10, 30, 180, and 365 days). The immediate amount was determined by an adjusting-amount procedure (Richards et al., 1999) involving random selection within a fixed interval that depended on previous choices and ultimately converged on an indifference point (equal frequencies of choosing immediate vs delayed amounts, i.e., no clear choice preference) for each delay interval. The amount of immediate certain money was randomly selected for each participant, and adjusted across the successive trials presented to participants on the computer screen until an amount was reached that was equivalent to a delayed (delay trials) $10 reward (determined by the participant’s previous choices during the task). Participants were informed that at the end of the task, the computer would select one trial randomly and they would receive the chosen outcome for that trial. For pragmatic reasons this selection was constrained to select from trials in which participants chose the smaller immediate amount of money, resulting in an additional payment at the time of study participation. At the first three data collection waves, the task also included a probability discounting condition; baseline results for those data were reported elsewhere (Olson et al., 2007, 2009), and are not included in the current analysis. Table 2 displays the number of participants who completed DD at each assessment wave, information about the number of trials completed by participants at each wave, and the percentage of trials on which participants chose the delayed and immediate rewards. Fig. 1 shows the distribution of AUC and $\text{log}(k)$ values based on the number of times participants completed the delay discounting task.

Table 2.

Delay Discounting Data At Each Assessment Wave.

Study Wave and Year (2004–2014)	$N$	Percentage of Subject Responses Choosing Delayed Reward	Percentage of Subject Responses Choosing Immediate Reward	Range of Trials Completed	Average # of Trials Completed	Median # of Trials Completed
Baseline (2004–2007)	140	59.9 %	40.1 %	[50 – 114]	83.4	84.0
Wave 2 (2007–2009)	164	62.9 %	37.1 %	[48 – 116]	84.6	86.0
Wave 3 (2009–2010)	79	65.3 %	34.7 %	[48 – 113]	83.4	84.0
Wave 4 (2012–2014)	99	65.6 %	34.4 %	[41 – 146]	89.7	87.0
Wave 5 (2014–2016)	101	64.0 %	36.0 %	[38 – 156]	89.0	88.0
Average across Waves	120	63.5 %	36.5 %	[45 – 129]	86.0	85.8

Note. Wave 3 was not budgeted within the award that supported the work. The attrition between Waves 2 and 3 is due to resource limitations, not to participants’ willingness to contribute data.

Fig. 1. Distribution of Delay Discounting Data.

Fig. 1. Distributions of delay discounting data based on the number of times participants competed the delay discounting task. The green diamond represents the mean of discounting across participants, while the black line in the center of the boxplots represents the median. A). Participants’ AUC values as a function of the number of times they completed the discounting task. B). Participants’ $\text{log}(k)$ values as a function of the number of times they completed the task. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Indifference points were established for each participant at each interval and were plotted against time (at time = 0, the subjective value of $10 was assumed to be $10 for all participants and verified using catch trials). AUC was calculated using the trapezoidal method (Myerson et al., 2001; Olson et al., 2007, 2009). Hyperbolic discounting rate ($k$) values were produced by fitting Mazur’s one parameter model to participants’ trial-level data (i.e., choice of delayed vs immediate reward on each trial) using MATLAB (R2019b) code for estimating temporal discounting functions via maximum likelihood (Lau, 2013), which were subsequently log transformed (using the natural logarithm) to yield $\text{log}(k)$ values. As a supplemental exploratory analysis, we also examined Ebert And Prelec’s Constant Sensitivity Model using the Bayesian Delay Discounting Toolbox (Vincent, 2016). The methods and findings for these analyses can be found in the Supplementary Materials.

To examine the effects of non-systematic discounting, Johnson & Bickel’s (2008) algorithm was applied to the data. Discounting was categorized as non-systematic if either of the following criteria were met: 1) any indifference point (starting with the second delay) was greater than the preceding indifference point by more than $2 (i.e., 20 % of the delayed reward); and 2) the indifference point for the longest delay (365 days) represented less than $1 of discounting (i.e., a temporal discounting rate of<10 % at the maximal temporal delay interval used in our task). Given our goal to determine the developmental trajectory of discounting behaviors from childhood to young adulthood, eliminating non-systematic discounters might increase the risk of failing to detect valid developmental changes. In fact, exclusion of non-systematic data did not significantly alter the results of the present study, which are reported for the full sample (see Supplementary Materials for results from analyses based on a subsample with non-systematic discounters excluded).

2.1.2. Vocabulary and Digit Span

Participants completed the Wechsler Abbreviated Scale of Intelligence (WASI; Wechsler, 1999) Matrix Reasoning and Vocabulary subtests at each assessment wave. Given previously-reported findings of associations between DD and verbal intelligence, we examined associations between age-normed $T$-scores from the WASI Vocabulary subtest and DD. Participants also completed the Digit Span subtest of the Wechsler Adult Intelligence Scale-Third Edition (Wechsler, 1997). Summed raw scores for forward and backward digit spans were used to assess associations between working memory and DD (Bickel et al., 2011; Shamosh et al., 2008).

2.2. Analysis plan

Mixed effects models (nlme package, R version 4.0.2; Bates et al., 2020) were used to model the developmental trajectories of the DD measures and covariates of interest (Fitzmaurice et al., 2012). Data from the current study adhered to assumptions of these models (Almy et al., 2018; Heitjan & Basu, 1996). Visual inspection of the residuals of the fixed and random effects demonstrated that the model residuals did not deviate from assumptions of normality or heteroskedasticity. Five main models were compared to select an appropriate unadjusted model (i.e., modeling age effects without covariates of interest) to determine if age-related changes in DD measures were best approximated by a linear, quadratic, cubic, inverse, or inverse quadratic function. By examining various linear and non-linear functions, we sought to determine it if age-related changes in DD increase at a constant rate across development (i.e., linear; Casey et al., 2011), plateau in adolescence (i.e., asymptotic, operationalized by an inverse function of age; Luna et al., 2021), or reach a peak or trough in adolescence (i.e., approximate a quadratic curve; Hallquist et al., 2018). Cubic models were included to determine if the magnitude of change differs as a function of age (e.g. in the transition from childhood to adolescence, or adolescence to young adulthood etc.; Ferguson et al., 2021). Random effects of age were added incrementally to each main model to determine whether there was important variation among participants in the rate of change in addition to overall level. We used a heterogeneous first-order autoregressive covariance structure to model the error variance within-participants. This structure is more flexible for individuals with missing data (e.g., if a participant missed wave 2 but returned for all other assessments; Singer & Willett, 2003), and yields less biased estimates of model parameters in longitudinal data (Jahng & Wood, 2017). The Bayesian Information Criterion (BIC; Schwarz, 1978) and Akaike Information Criterion (AIC; Akaike, 1974) values were used to select the best-fitting model. In cases where there was disagreement between AIC and BIC, a likelihood ratio test was used. We employed orthogonal polynomials when examining the effects of age in order to reduce multicollinearity between linear, quadratic and cubic effects of age (Smith & Sasaki, 1979). Table 3 displays the BIC and AIC values, and the weight of evidence for these information criteria, for mixed effects models fit with the various age effects (10 total including the null model).

Table 3.

Comparison of Bayesian Information Criterion (BIC), Weight of Evidence for BIC (bWeight), Akaike Information Criterion (AIC), and Weight of Evidence for AIC (aWeight) for Unadjusted Models of DD Performance Metrics.

Overall Performance Model: AUC	BIC	bWeight	AIC	aWeight
1. Null model (intercept only)	67.0	<0.001	49.5	<0.001
2. Linear effect of age and random effect of intercept	48.7	0.002	27.1	0.001
3. Linear effect of age and random effects of intercept and age	61.4	<0.001	31.1	<0.001
4. Quadratic and linear effects of age and random effect of intercept	42.5	0.054	16.6	0.223
5. Quadratic and linear effects of age and random effects of intercept and age	71.1	<0.001	23.5	0.007
6. Cubic, quadratic and linear effects of age and random effect of intercept	48.4	0.003	18.1	0.105
7. Inverse effect of Age and random effect of intercept	36.9	0.901	15.3	0.427
8. Inverse effect of age and random effect of intercept and slope	49.2	0.002	18.9	0.069
9. Inverse and inverse quadratic effects of age and random effect of intercept	43.2	0.038	17.3	0.157
10. Inverse and inverse quadratic effects of age and random effect of intercept and slope	70.2	<0.001	22.6	0.011
Overall Performance Model: $\text{log}(k)$	BIC	bWeight	AIC	aWeight
1. Null model (intercept only)	2489	<0.001	2472	<0.001
2. Linear effect of age and random effect of intercept	2370	0.01	2348	0.007
3. Linear effect of age and random effects of intercept and age	2382	<0.001	2352	0.14
4. Quadratic and linear effects of age and random effect of intercept	2368	0.03	2342	0.001
5. Quadratic and linear effects of age and random effects of intercept and age	2396	<0.001	2349	0.006
6. Cubic, quadratic and linear effects of age and random effect of intercept	2373	0.002	2343	0.09
7. Inverse effect of Age and random effect of intercept	2361	0.91	2340	0.50
8. Inverse effect of age and random effect of intercept and slope	2966	0.03	2943	0.07
9. Inverse and inverse quadratic effects of age and random effect of intercept	2367	0.04	2341	0.19
10. Inverse and inverse quadratic effects of age and random effect of intercept and slope	2398	<0.001	2351	0.002

Note. Bolded font indicates best-fitting model for the criterion.

Age-related changes in time-varying covariates were also assessed using mixed-effects models. Covariates of interest in adjusted models included: 1) $T$-scores on the WASI Vocabulary subtest; 2) overall digit span raw scores (i.e., digits forward and backward total scores, summed); and 3) overall experience with the task (grand mean-centered as used in previous longitudinal analyses;Almy et al., 2018) in order to assess the potential confounds between retest gains (i.e., practice effects) and true age effects in the present longitudinal design (Hoffman et al., 2011). This method of correction has been shown to dissociate retest effects from true change in cognitive performance over time (Racine et al., 2018). The influence of gender was modeled as described below. SES indices were modeled as well.

Four models were tested to observe the effects of covariates on DD performance. The first model was the best-fitting unadjusted model (i.e., intercept and age effect). A second model added Vocabulary, total score on Digit Spans, and the task experience variable, which is described below. The third model examined whether experience with the task varied as a function of age (i.e., the interaction between age and experience). A fourth model added interactions with Vocabulary and age as well as total Digit Spans and age to Model 3 to assess whether the effects of these covariates on performance varied as a function of age. The best approximating unadjusted models were compared against models fit with the fixed effect of gender, and the interaction between age and gender.

For both the best approximating unadjusted (i.e., age effects only) and adjusted models (i.e., models with inclusion of covariates), visual inspection of residual plots did not reveal any obvious deviations from homoscedasticity or normality. To increase the precision of model coefficients, we performed 1000 semi-parametric bootstrap replications in both unadjusted and adjusted models (lmeresampler R package version 0.1.1; Loy & Steele, 2020) to yield corresponding 95 % confidence intervals and standard errors. The semi-parametric approach has less stringent assumptions than the parametric approach (Leeuw & Meijer, 2008), with simulation studies suggesting it may yield the most precise estimates in studies where participants have different number of observations (Thai et al., 2013). Moreover, it has been shown to reduce bias in linear mixed effects model coefficients (Carpenter et al., 2003).

Retest stability of discounting behaviors was calculated using the intraclass correlation coefficient (ICC) function in the psych package (R package version 2.0.12; Revelle, 2022). Per Shrout and Fleiss (1979), ICC_(3,1) was calculated where the subscript “3″ denotes case three (i.e., a two-way mixed effects model) with “1” denoting that the reliability is calculated using a single measurement. ICC_(3,1) is the most appropriate ICC to establish test–retest stability in longitudinal data (Koo & Li, 2016; Mcgraw & Wong, 1996). The ICC_(3,1) function utilizes mixed effects models that are robust to cases of missing data in the calculation of retest stability and avoids issues apparent in test–retest correlation such as a failure to detect systematic changes in mean levels of responding (Hays et al., 1993). ICC was calculated across all five assessment waves, as well as between each assessment wave and the subsequent one (e.g., baseline to wave 2, wave 3 to wave 4 etc.). We also calculated ~ 10-year stability (across all five assessment waves), ~8-year (waves 2–5) and ~ 6-year (waves 3–5) stability to explore whether DD stabilizes as participants age. Likewise, to further validate test–retest stability of DD measures, we calculated the test–retest correlation (using Pearson correlation coefficients) between assessment waves to complement ICC values. While ICC is often employed for test–retest reliability, it more susceptible to systematic error that may be introduced due to developmental change, or practice effects (Anokhin et al., 2022). Data and relevant R code is available upon request from the corresponding author.

2.3. Constant sensitivity model

Though we are primarily interested in AUC and $\text{log}(k)$ as indices of discounting, to maximize the viability of measuring DD in our study incorporating a cohort sequential design (Burns et al., 2020), and to examine the role of time perception on adolescent DD, we include a supplemental exploratory analysis using non-hierarchical Bayesian estimation (Vincent, 2016) of Ebert and Prelec’s Contrast Sensitivity Model (CS; Ebert & Prelec, 2007; see Supplementary Materials). This CS model includes a measure of time sensitivity (i.e., the impact of near vs far delays on the subjective value of a given reward), while Bayesian techniques allow for robust estimation of DD at the trial- and participant-levels (Ahn et al., 2017) that are available through a number of open-source toolboxes (Ahn et al., 2021; Vincent, 2016). The use of open-source materials enhances opportunities for replication and validation in future studies (Hawkins et al., 2018; Klapwijk et al., 2021). We note that the results from these expanded analyses agree with our broader conclusions about the developmental trajectory of DD, consistent with previous work that has compared the hyperbolic model to other models of DD using Bayesian estimation (Kvam et al., 2021).

3. Results

3.1. Developmental trajectories of delay discounting

AUC.

In predicting the developmental trajectory of AUC, the best-fitting unadjusted model included the inverse effect of age with a random effect of intercept (Table 4). Tangent lines at ages 10, 15, 20, 25 and 30 along the inverse curve (Fig. 2) demonstrate that as age increased, the slope of the inverse function decreased. In other words, as age increased, the magnitude of change in AUC decreased. Notably, discounting behaviors decreased steeply from childhood to adolescence: the slope of the tangent line decreased from 0.06 at age 10, to.02 at age 20; by age 25 the slope was 0.009 (roughly 1 % of the total range of AUC values).

Table 4.

Comparison of Best-Fitting Adjusted Model with Unadjusted Model of DD Performance (AUC).

Model Coefficient	Unadjusted Model	Final Model
Intercept	0.95 [0.86, 1.04]*	0.46 [0.22, 0.72]*
(SE)	(0.05)	(0.13)
Age−1	−6.32 [−7.8, −4.73]*	−4.13 [−5.89, −2.33]*
(SE)	(0.78)	(0.91)
Vocabulary	-	0.004 [0.001, 0.007]*
(SE)		(0.002)
Digit Span Total	-	0.007 [0.002, 0.01]*
(SE)		(0.003)
Experience	-	0.019 [−0.001, 0.04]
(SE)		(0.01)
Variance Components
Random Effects	0.027	0.026
Fixed Effects	0.009	0.011
Residual	0.048	0.046
Model Fit
Marginal R2 (Fixed Effects Only)	0.11	0.13
Conditional R2 (Fixed and Random Effects)	0.43	0.44
BIC	36.91	37.73
AIC	15.28	3.18
Log-likelihood	−2.64	6.41

Note. Vocabulary = $T$-Score on Vocabulary subtest of WASI, Digit Span Total = combined number digits forward and digits backward. Model coefficients are estimates obtained from 1000 semi-parametric bootstrap replications, with corresponding 95 % confidence intervals (95 % CI) and standard error (SE). Bolded text indicates superior fit indices when comparing unadjusted and final models.

^*Denotes that the 95 % CI does not contain zero.

Fig. 2. Developmental Trajectory of AUC.

Fig. 2. DD (AUC) performance for all participants (solid black dots and lines) during the study. The solid green line represents the predicted values of AUC from the best-fitting unadjusted model (i.e., the inverse effect of age; the yellow band represents the 95% confidence interval of the predicted values). The dashed lines represent the tangent line (i.e., first order derivative of the model) at each associated age (dashed vertical lines). The legend above displays the slope and intercept of the tangent lines at corresponding age. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

$$\text{log}(k).$$

In predicting the developmental trajectory of $\text{log}(\text{k})$, the best-fitting unadjusted model included the inverse effect of age with random effects of intercept (Table 4). In predicting the developmental trajectory of $\text{log}(\text{k})$, the best-fitting unadjusted model included the inverse effect of age with random effects of intercept (Table 4). As with AUC, the convergence of both AIC and BIC suggests that the inverse effect of age best approximated developmental changes in $\text{log}(k)$. (Fig. 3). Likewise, tangent lines at ages 10, 15, 20, 25 and 30 along the inverse curve demonstrated that as age increased, the slope of the inverse function became less steeply negative—as age increased the magnitude of change in $\text{log}(k)$ decreased. The slope of the tangent line increased from −0.440 at age 10 to −0.110 by age 20; the slope increased to −0.070 by age 25 (less than one percent of the total range of $\text{log}(k)$ values). Taken together, the results indicated that developmental change in DD behavior, as indexed by both $\text{log}(k)$ and AUC, the most used metric in developmental studies, stabilized by late adolescence/ early adulthood.

Fig. 3. Developmental Trajectory of $\text{log}(k)$.

Fig. 2. DD ($\text{log}(k)$) performance for all participants (solid black dots and lines) during the study. The solid green line represents the predicted values of $\text{log}(k)$ from the best-fitting unadjusted model (i.e., the inverse effect of age i.e., the inverse effect of age) with the yellow band around this line reflecting the 95% confidence interval around predicted values. The dashed lines represent the tangent line (i.e., first order derivative of the model) at each associated age (dashed vertical lines). The legend above displays the slope and intercept of the tangent lines at corresponding age. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

3.2. Predictors of delay discounting

3.2.1. Gender and sociodemographic status

When gender as a categorical covariate was added to unadjusted models for AUC and $\text{log}(k)$, there was not a significant fixed effect of gender (AUC: F_1,166 = 0.30, p =.58; $\text{log}(\text{k})$: F_1,159 = 0.27, p =.60) or an interaction between age effects and gender (AUC: F_1,316 = 0.20, p =.66; $\text{log}(k)$: F_1,307 = 0.78, p =.38). Gender was therefore not included as a categorical covariate in adjusted models.

Participants reported relatively high average family incomes and parental education (see Table 1). An index of SES computed from a mean standard score of parental education and family income at baseline (Kim-Spoon et al., 2019) was not significantly associated with either $\text{log}(k)$ (r(457) = −0.04, p =.342) or AUC (r(450) = 0.03, p =.46) across the duration of the study. Furthermore, when this index of SES was included as a covariate to the best-approximating unadjusted models, there was no effect of the index on AUC (F_1,267 = 0.10, p =.65) nor $\text{log}(k)$ (F_1,248 = 0.32, p =.57). This index of SES was therefore not included as a categorical covariate in best-approximating unadjusted models.

3.2.2. Cohort effects

Given the cohort sequential design of this study, we examined whether there were cohort effects by including the initial age of participants (i.e., age at baseline) as an additional covariate within the best approximating unadjusted models for $\text{log}(k)$ and AUC using methods outlined by Galbraith and colleagues (2017). There was no effect of baseline age on $\text{log}(k)$ (F_1,166 = 2.26, p = 16), and a non-significant interaction between a participant’s age at baseline and the inverse effect of age (F_1,359 = 0.24, p =.63)., suggesting the longitudinal trajectory of participants’ discounting behaviors did not vary as a function of baseline age. Likewise, there was no effect of baseline age on AUC (F_1,166 = 1.65, p =.20), nor a significant interaction between baseline age and the inverse effect of age (F_1,359 = 1.23, p =.36),. Taken together, these analyses provide evidence that the observed longitudinal trajectories of DD are not related to differences in DD across cohorts.

3.2.3. Predictors of AUC

When comparing the best-fitting unadjusted models to various adjusted models, a model fit with covariates and no interactions best approximated the data (Table 4). As with the unadjusted model, the inverse effect of age was a negative predictor of AUC, indicating that as age increased, the magnitude of change in AUC decreased, though the magnitude of this effect was reduced in the adjusted model. In addition, both Vocabulary and total score on Digit Spans were positive predictors of AUC, i.e., as scores increased, discounting of future rewards decreased. There were no significant effects of prior task exposure on AUC.

3.2.4. Predictors of $\text{log}(\text{k})$

The best approximating adjusted model for $\text{log}(\text{k})$ was a model fit with covariates and the interaction between age and overall experience with the task (Table 5), with the relative influence of these retest gains on $\text{log}(k)$ displayed in Supplementary Fig. 2. Simple slopes analyses indicated that the relationship between the inverse effect of age and $\text{log}(k)$ was significant when individuals had less experience (i.e., one standard deviation below the mean experience; t(340) = 3.74, p <.001) and average experience (i.e., mean level of experience with the task; t(340) = 2.30, p <.02). Thus, there was no observed association between the inverse effect of age for those with above average experience (i.e., one standard deviation above mean). Vocabulary and total digit span scores were significant negative predictors of $\text{log}(\text{k})$, i.e., as scores increased, discounting of future rewards decreased (as with AUC).

Table 5.

Comparison of Best-Fitting Adjusted Model with Unadjusted Model of DD Performance ($\text{log}(\text{k})$).

Model Coefficient	Unadjusted Model	Final Model
Intercept	−1.96 [−1.54, −7.17]	−1.96 [−3.63, −0.34]*
(SE)	(0.35)	(0.84)
Age−1	43.8 [32.2, 56.2]*	-
(SE)	(6.14)	-
Age × Experience	-	−7.17 [−10.2, −4.19]*
(SE)		(1.45)
Vocabulary	-	−0.04 [−0.06, −0.001]*
(SE)		(0.01)
Digit Span		−0.07 [−0.12, −0.02]*
(SE)		(0.02)
Variance
Random Effects	1.23	1.13
Fixed Effects	0.46	0.48
Residuals	3.54	3.56
Model Fit
Marginal R2 (Fixed Effects Only)	0.088	0.093
Conditional R2 (Fixed and Random Effects)	0.32	0.31
AIC	2339	2271
BIC	2361	2301
Log-likelihood	−1165	−1128

Note. Vocabulary = $T$-Score on Vocabulary subtest of WASI, Digit Span Total = combined number of digits forward and digits backward. Model coefficients are estimates obtained from 1000 semi-parametric bootstrap replications, with corresponding 95 % confidence intervals and standard error (SE). Bolded text indicates superior fit indices when comparing unadjusted and final models.

^*Denotes that the 95 % CI does not contain zero.

3.2.5. Retest stability of delay discounting

The retest stability (i.e., ICC_(3,1)) of AUC and $\text{log}(k)$ across assessment points is presented in Table 6. Given the range and distribution of DD indices differs (e.g., AUC is limited from 0 to 1), we transformed participants’ DD indices into z-scores. The use of z-scores adjusts for individual differences in development (Faust et al., 1999), makes scores more comparable over time (Gonzalez Casanova et al., 2021), adjusts ICC for missing values in the data (Courrieu & Rey, 2011), and more directly relates to Cicchetti’s standards of test–retest reliability (Cicchetti, 2016). Using standardized scores, the ~ 10-year stability of AUC was 0.62, 95 % CI [0.56, 0.68]), which represents fair-to-good reliability based on the 95 % CI (Cicchetti 1994, 2016). The ~ 10-year stability of $\text{log}(k)$ was 0.51, 95 % CI [0.44, 0.58]), representing fair reliability. Given the rapid developmental change that was observed between baseline and wave 2 (see Fig. 1 and Fig. 2), that may have decreased reliability of DD, we examined the ~ 6-year stability (i.e., waves 2 to 4) of AUC and $\text{log}(k)$ to examine whether DD becomes more stable in older participants. The ~ 6-year stability of AUC was 0.75, 95 % CI [0.69, 0.80], while the ~ 6-year stability of $\text{log}(k)$ was 0.68, 95 % CI [0.62, 0.74], suggesting that DD becomes stable in late adolescence and early adulthood.

Table 6.

Longitudinal Stability of Delay Discounting Parameters.

Assessment Waves	Variable	ICC(3,1) (full sample)	Mean (SD)	Correlation Coefficient (Pearson’s $r$)
All (~10-year)	AUC	0.62 [0.57, 0.67]	0.62 (0.29)	-
All (~10-year)	$\text{log}(k)$	0.52 [0.46, 0.58]	−5.5 (2.30)	-
Wave 2 – Wave 5 (~8-year)	AUC	0.71 [0.66, 0.75]	0.65 (0.27)	-
Wave 2 – Wave 5 (~8-year)	$\text{log}(k)$	0.61 [0.56, 0.67]	−5.69 (2.22)	-
Wave 3 – Wave 5 (~6-year)	AUC	0.75 [0.70, 0.79]	0.69 (0.26)	-
Wave 3 – Wave 5 (~6-year)	$\text{log}(k)$	0.71 [0.65, 0.75]	−5.98 (2.21)	-
Baseline -Wave 2	AUC	0.42 [0.26, 0.56]	0.55 (0.29)	0.48
Baseline - Wave 2	$\text{log}(k)$	0.45 [0.28, 0.58]	−5.0 (2.23)	0.54
Wave 2 - Wave 3	AUC	0.72 [0.60, 0.80]	0.61 (0.28)	0.76
Wave 2 - Wave 3	$\text{log}(k)$	0.63 [0.46, 0.74]	−5.4 (2.15)	0.64
Wave 3 - Wave 4	AUC	0.70 [0.55, 0.81]	0.69 (0.26)	0.72
Wave 3 - Wave 4	$\text{log}(k)$	0.63 [0.43, 0.75]	−5.94 (2.26)	0.66
Wave 4 - Wave 5	AUC	0.62 [0.46, 0.73]	0.70 (0.26)	0.75
Wave 4 - Wave 5	$\text{log}(k)$	0.65 [0.52, 0.76]	−6.04 (2.25)	0.73

Note. Bold indicates p <.05 for Pearson’s r.. Per the standards of Cicchetti (2016), test–retest reliability is poor for ICC values<0.40, fair for values between 0.40 and 0.59, good for values between 0.60 and 0.74, and excellent for values between 0.75 and 1.0.

The overall ~ 10-year retest stability of $a$ (0.54, 95 % CI [0.33 – 0.47] was superior to $\text{log}(k)$, but not AUC. Generally, however, $\text{log}(k)$ demonstrated superior reliability between assessment waves, and greater 6- (0.61 vs 0.55) and ~ 6-year reliability (0.71 vs 0.60; see Supplementary 11). Finally, time sensitivity ($b$) was the least reliable DD parameter (~10-year stability of 0.28, 95 % CI [0.21 – 0.35]).

3.2.6. Constant sensitivity model

In predicting the developmental trajectory of DD indexed via the Constant Sensitivity Model, the natural log transformed $a$ parameter (i.e., impatience), which is comparable to $\text{log}(k)$ was best approximated by the inverse effect of age. In contrast, b (i.e., time sensitivity) was best approximated by the linear effect of age (see Supplementary Table 8). These results provide further evidence that DD stabilized by late adolescence/ early adulthood in the current sample, whereas time sensitivity appeared to decrease steadily as a function of age, such that individuals become less sensitive to time (i.e., increased discounting of near future and decreased discounting of the far future).

3.2.7. Predictors of a

When comparing the best-fitting unadjusted models to various adjusted models, a model fit with covariates and no interactions best approximated the data (see Supplementary Table 9). As with $\text{log}(k)$ and AUC, working memory and digit span were negative significant predictors of $a$. Additionally, $a$ appears susceptible to practice effects, as experience was a significant negative predictor of $a$.

4. Discussion

The present report examined longitudinal changes during adolescence and early adulthood in temporal discounting behaviors. Within the developmental literature, there has been some debate about whether temporal discounting tasks based on hypothetical decisions should be construed as measures of reward sensitivity, or whether they are similar to other decontextualized measures of executive control. While the ability to forgo immediate gains in favor of longer-term goals undoubtedly involves integration across both processes, it is useful to understand how the development of discounting behaviors compares to the development of other aspects of higher order cognition (Crone, 2016). Our findings suggest that the developmental trajectory of delay discounting (i.e., inverse effect of age) is similar to the development of inhibitory control (Luna, 2009; Marek et al., 2015), hypothesized within the dual systems framework (Casey et al., 2008) to reflect activity within a system that limits imprudent impulses. Indeed, the ability to allocate cognitive resources to limit the subjective discounting of delayed rewards reaches adult levels in late adolescence, consistent with prior work demonstrating that inhibitory control matures more slowly than reward sensitivity as individuals transition from adolescence to adulthood (Hallquist et al., 2018). In addition, discounting of future rewards was negatively predicted by performance on the Vocabulary and Digit Span subtests, suggesting that individuals with greater verbal intelligence and working memory capacity are better able to allocate cognitive resources to maximize future rewards (at least in the context of hypothetical decision-making).

In contrast, incentive motivation—facilitated by dopaminergic activity in the reward system that increases motivation to pursue rewards (Luciana et al., 2012)—and the driven-dual systems model (Luna & Wright, 2016), hypothesizes that this reward system is approximated by a quadratic trajectory that peaks in adolescence. We did not observe a vertex in adolescence indicative of a peak in discounting of future rewards, suggesting that performance on the task does not resemble this hypothesized development of the reward system (e.g., Steinberg et al., 2010; Luna & Wright, 2016) or incentive motivational processes (e.g. Luciana et al., 2012). Achterberg and colleagues (2016) demonstrated that the quadratic effect of age best approximated the developmental trajectory of discounting behaviors as indexed by AUC. However, in their longitudinal analyses of DD, which included two assessment waves in a sample of 299 participants aged 8–25, they did not include the inverse effect of age in model comparisons. The present results are nonetheless consistent with their conclusion that temporal reward discounting increases rapidly during early adolescence, and appears to plateau by late adolescence/early adulthood. Our findings that an inverse function of age best approximates the developmental trajectory of DD behaviors constitutes a novel contribution to the extant literature.

It appears that there is a rapid increase in the ability to make decisions that delay time to reward receipt from childhood to early adolescence, which then subsequently stabilizes into early adulthood. In this regard, temporal reward discounting behavior would seem to resemble, in its developmental course, executive functions such as working memory (Luciana et al., 2005), planning (Luciana et al., 2009), motivated decision-making (Almy et al., 2018), and inhibitory control (Luna et al., 2004), all of which show the same accelerated slope of development from late childhood to mid-adolescence. Early-to-mid-adolescence would seem to represent a vulnerability period when inclinations toward cognitive impulsivity might bias behavior toward maladaptive decision-making. These developmental changes were apparent in our longitudinal analyses using both integration of observed indifference points (AUC) and fitting of a theory-driven hyperbolic curve to the data ($\text{log}(k)$).

An exploratory analysis using Ebert and Prelec’s CS model further supports our findings that DD follows an inverse trajectory from childhood through young adulthood. Likewise, it validates our findings that working memory and verbal intelligence are negative predictors of DD (see Supplementary Table 9). These analyses also add to our understanding of the development of time perception—it increases steadily from childhood through young adulthood, consistent with traditional dual-systems models that posit the executive system increases gradually during this same period (Steinberg, 2010). This increase suggests that as participants age, they are less sensitive to time (i.e., more time-insensitive), and are better able to allocate cognitive resources to focus on the immediate future (Gilovich et al., 2002), consistent with prior studies demonstrating that greater cognitive resources are related to time-insensitivity (Ebert, 2001; Ebert & Prelec, 2007).

Interestingly, our observed developmental findings are broadly consistent with the literature regarding animal models of DD. For instance, the ability to forego a smaller more immediate reward evident in a number of primate species (Beran, 2021), with evidence suggesting this ability is reflective of increased self-control across species (Miller et al., 2019). In rats, DD appears to decline as a function of age, working memory and cognitive flexibility, consistent with our findings. Furthermore, recent work has demonstrated that DD has trait- and state-like characteristics in rodent models of DD (Haynes et al., 2021).

Regarding predictors of DD, we have previously reported associations between higher verbal intelligence and reduced discounting (Olson et al., 2007) as have others (Shamosh et al., 2008), and the present work extends those results by demonstrating that these associations endure longitudinally. Our finding that relatively higher working memory capacity predicts reduced discounting is consistent with previous studies documenting working memory training reduces discounting behaviors in substance use disorders (Wesley & Bickel, 2014). Our longitudinal analyses suggest that working memory capacity also predicts the developmental trajectory of DD. Given research indicating that greater working memory capacity is associated with normative development of prefrontally-guided functions that proceeds into the early 20 s (Simmonds et al., 2017), our observation of increasing self-regulation as shown in reduced temporal reward discounting may represent another facet of the same underlying neurodevelopmental processes during adolescence and early adulthood.

When comparing AUC to $\text{log}(k)$ as a measure of DD, AUC appeared to be relatively insensitive to practice effects, while overall experience with the task moderated the observed association between the inverse effect of age and $\text{log}(\text{k})$. AUC also demonstrated greater retest stability over the five assessments. Together, these psychometric findings suggest that AUC may be a more suitable measure than $\text{log}(k)$ for longitudinally assessing developmental trajectories of DD behavior from adolescence into adulthood.

To our knowledge, this is the first study to compare a ~ 10-year longitudinal developmental trajectory of AUC and $\text{log}(k)$ as measures of DD. Two prior studies have compared these metrics in cross-sectional samples. In the first, the authors reported that $\text{log}(k)$ more reliably differentiated among smokers, individuals with ADHD and healthy controls (Mitchell et al., 2015). The second study (Yoon et al., 2017) extended the results of the first, and demonstrated that in a sample of participants with steep discounting curves, i.e., non-treatment-seeking stimulant-drug dependent individuals, the distribution of AUC values was as highly skewed as the $\text{log}(k)$ distribution, which typically, is not observed in studies of DD in normative samples. Accordingly, Yoon et al. (2017) recommended using multiple indices of DD and careful checking of psychometric properties of AUC when steep discounting is observed. Though AUC was left-skewed (Fig. 1), examination of LME model residuals of both fixed and random effects demonstrated that models met all relevant assumptions (i.e., residuals were normally distributed), and this skew is easily tolerated by LMEs (Arnau et al., 2013; Fitzmaurice et al., 2012). Furthermore, in our five-datapoint longitudinal analysis, we found that $\text{log}(k)$, but not AUC, was sensitive to practice effects approximated by the best-fitting adjusted models. Moreover, there was an interaction between the inverse effect of age and overall experience that partially obscured the $\text{log}(k)$-based developmental trajectory of DD, and suggested that in some age ranges processes other than hyperbolic discounting may have had an impact on $\text{log}(k)$ values. Compared to AUC, $\text{log}(k)$ values demonstrated reduced longitudinal retest stability.

Retest stability is critically important to reproducibility of longitudinal findings (Downing, 2004), as well as for assessment of traits such as behavioral inhibition vs impulsivity (Roberts, 2009), given that reliability sets the upper bounds around which individual differences can be detected. Similarly, Martínez-Loredo et al (2017) assessed the one-year reliability and temporal stability of discounting behavior, quantified using both AUC and $\text{log}(k)$, in 1375 12–1 ~ 6-year-olds, finding good stability (ICC for AUC = 0.68; for $\text{log}(k)$ = 0.70) and good internal consistency reliability (α = 0.90). Findings were similar when inconsistent discounters were excluded. Anokhin, Golosheykin, and Mulligan (2015) assessed two cohorts of adolescents, aged 16 and 18, each of whom were tested two years apart. Retest correlations for DD AUC were significant for both cohorts: ICCs = 0.67 and 0.76, respectively, and Pearson correlations were similar in magnitudes to those reported by Achterberg et al. (2016). Both Martinez-Lopez et al., (2017) and Anokhin et al. (2015) found modest but significant effects of time (d = 0.25 in Anokhin et al.), suggesting that age-related declines in cognitive impulsivity occur against a backdrop of highly stable DD performance that reflects trait variations. Our findings concur with those conclusions.

Our findings that AUC demonstrates greater stability, and is likewise less susceptible to practice effects than $\text{log}(k)$, warrant consideration. First, we note that $\text{log}(k)$ was derived using trial-level data rather than the indifference points, as is typically done (Richards et al., 1999). We used trial-level data to more robustly model participant-level data (Bailey et al., 2021). It is unlikely that deriving $\text{log}(k)$ using the indifference points would have substantively changed our results, given previous finding that $\text{log}(k)$—derived using indifference points—demonstrated reduced reliability relative to AUC (Anokhin et al., 2015b; Martínez-Loredo et al., 2017; Odum, 2011b). One possible explanation for greater reliability of AUC relative to $\text{log}(k)$ is due to the fact that the delayed reward was relatively small in magnitude (i.e., 10 dollars)—smaller amounts tend to be discounted more steeply (Green et al., 1997). Responses that steeply discount delayed rewards—alternatively conceptualized as tolerating the delay in the present sample—may have restricted the range of participants’ AUC values (Odum, 2011b). In other words, a given AUC could theoretically exist for a number of different indifference points in the present sample, and this consistency would not be reflected by the hyperbolic discounting rate (i.e, $\text{log}(k)$). However, reliabilities were calculated from z-scored variables, which would reduce the expected effect of these absolute differences in the ranges of these variables on the observed reliabilities. Furthermore, exclusion of non-systematic discounters (see Supplementary Table 5) would reduce the number of AUC values that were close to the maximum value of one (indicative of always choosing the delayed reward of $10). However, after adjusting for non-systematic responses, the overall reliability (i.e., ~10-year) of AUC was still greater than $\text{log}(k)$ (0.62 vs 0.52 respectively), as were the ~ 8-year (0.71 vs 0.61) and ~ 6-year (0.75 vs 0.71) reliabilities. These observed ~ 6-year reliabilities demonstrate that by the time participants reached middle adolescence, both AUC and $\text{log}(k)$ were highly stable.

Another possibility is that the atheoretical, nonparametric approach captured by AUC does not include equation type-dependent error (Harrison & McKay, 2012), thereby reducing systematic error that results from fitting a hyperbolic function to a participants’ discounting data. This would be consistent with previous work demonstrating that AUC has greater reliability (Anokhin et al., 2015; Beck & Triplett, 2009; Ohmura et al., 2006). Likewise, this systematic error may have decreased over time given that DD stabilizes in late adolescence and early adulthood; this decrease would be greatest in individuals that had more experience with the task, and could account for why practice effects contribute to best approximate $\text{log}(k)$, but not AUC. Using more modern Bayesian estimation techniques to yield more accurate estimates of subject level data lead to improved ~ 10-year reliability for the $a$ parameter, 0.54 for $a$ vs 0.52 for $\text{log}(k)$, which was still not as reliable as AUC, and was also susceptible to practice effects. This finding is consistent with the latter interpretation that fitting participants’ DD behavior to a theoretical model introduces systematic error that reduces the reliabilities. Thus, though there are limitations to the use of AUC, we contend that it may better model the tendency of individuals to discount future rewards across a variety of outcomes, and that this general tendency better accounts for response consistency that is typical of personality traits (Odum, 2011b; Roberts, 2009) because it is free from errors that arise due to constraining DD behavior to a particular theoretical model.

Cognitive impulsivity, as measured by the delay discounting task, may index broad trait domains such as Conscientiousness (McCrae & Costa, 2003) and Constraint (Tellegen & Waller, 2008) as well as narrower traits of disinhibition or impulsivity (Moreira & Barbosa, 2019). The stability of DD behaviors in the present study—particularly AUC—is consistent with a number of studies demonstrating rank-order stability of personality from childhood to adulthood. in spite of marked developmental change that occurs during this period (Caspi & Shiner, 2007; Shiner et al., 2012). Our findings that DD became highly stable (i.e., 0.75 for AUC and 0.68 for $\text{log}(k)$) during the final three waves of our longitudinal study is generally consistent with the cumulative continuity principle, wherein a trait becomes more stable as a function of increasing age (Roberts et al., 2008; Syed et al., 2020). Because DD of monetary rewards indexed by AUC is positively associated with other forms of discounting, e.g food and alcohol, and steep discounting is associated with disinhibitory psychopathology (Odum, 2011b), the DD task likely reflects trait-level variation in cognitive control processes. If tendencies toward steep reward discounting were identified in childhood or early adolescence, it may be possible to reduce impulsive decision-making and associated problem behaviors through early intervention strategies (Rung & Madden, 2018).

5. Limitations and future directions

The present work is not without limitations. First, the results based on our sample of moderate-to-high SES individuals cannot be generalized to individuals who reside in resource-scarce environments—particularly BIPOC communities that have been historically disenfranchised—where unreliability of resources can render choosing of immediately available rewards advantageous rather than reflective of cognitive impulsivity. Within our sample, an index of SES adapted in part from the work of Kim-Spoon and colleagues (2019) was not associated with DD, nor was it a significant longitudinal predictor of DD. Nonetheless, it is important to note that these findings may not generalize to the full population. Future work should examine how SES factors influences DD behaviors; an examination of ethnic and SES factors in large-scale studies such as the ABCD study (Luciana et al., 2018) would seemingly be an ideal means through which to test these effects.

Participant attrition and subsequent missing data, particularly at the third assessment wave, which was initiated during a funding lapse, is another limitation of the present work. Additionally, the amount of available data for DD performance and covariates in the tails of the age-ranges of individuals in the sample (e.g., 9- and ~ 10-year-olds, 30 years of age and older) was lower than the data for the middle adolescent ages, potentially introducing bias into the models. However, when we excluded participants that fell within these age extremes (approximately 20 % of observations within the models), the inverse effect of age was still the best approximating model for both AUC and $\text{log}(k)$ (see Supplementary Table 6). Coupled with the fact that removing the influence of non-systematic discounters did not change the best-approximating unadjusted model, or substantively influence longitudinal covariate selection for the best-approximating adjusted models, the stability of the findings after removing the tails of the age distribution strongly suggests that DD behaviors exhibit an inverse developmental trajectory from early adolescence to adulthood. Finally, we used a Heterogeneous First-Order Autoregressive process to model error variance within-participants that is ideal for modeling changes in individual performance over time (Pusponegoro et al., 2017), and employed a semi-parametric bootstrap that leads to consistent, bias-corrected parameter estimates, standard error and confidence intervals (Carpenter et al., 2003), increasing the robustness of our reported modeling results.

In the context of models of DD, we acknowledge that there are certainly other models with which to examine intertemporal choice. For example, a number of studies have compared attribute-wise, as opposed to alternative-wise, mechanisms in the context of intertemporal choices (Cheng & Gonzalez-Vallejo, 2016; Dai & Busemeyer, 2014). These models are also able to account for the subadditivity—an interval effect where a future reward is discounted more steeply if a delay is considered at a shorter period than as a whole—and superadditivity (the opposite effect; Scholten et al., 2014; Scholten & Read, 2006, 2010). Given the DD task we used in the present study did not vary along the time attribute (i.e., receipt of immediate reward was always framed as receiving the reward “now”), nor the reward attribute (i.e., the amount of the delayed reward was held constant at 10 dollars Richards et al., 1999), our study design is not well-suited to examine how these attributes influence decision making related to longitudinal change in intertemporal preferences. Future work should utilize tasks that vary along these attributes to examine how participants’ intertemporal preferences change as a function of the reward and time attributes, and whether this pattern of intertemporal choice (i.e., whether individuals make decisions along these attributes) emerges in adolescence. Attribute wise models may be particularly relevant to questions related to greater risk-taking in adolescence given recent work demonstrating that attribute-wise models may be better suited to predicting substance use than traditional models of DD (Kvam et al., 2021).

Finally, though we have utilized AUC in the present analyses to remain contiguous with the developmental literature, we note that there are other forms of AUC to consider. These include AUC_log—where delays are transformed using log base-10 scaling—and AUC_ord, where the delays are ordinally transformed to integers with even scaling. These changes can help adjust for the systematically uneven contributions of indifference points to calculate the conventional AUC (Borges et al., 2016). These measures are particularly relevant when AUC is highly skewed (Yoon et al., 2017), and may have greater psychometric properties relative to traditional AUC (Borges et al., 2016; Yoon et al., 2018). However, we note that our observed AUC already has good to excellent reliability (Cicchetti, 2016b). Future work should examine longitudinal changes in AUC_ord relative to AUC; a comparison to this nontheoretical approach to attribute-wise models could be particularly fruitful.

6. Conclusions

In conclusion, this study demonstrated that self-regulation as reflected by reduced discounting of future hypothetical rewards increased markedly during the early-to-mid-adolescent period before leveling off thereafter into early adulthood. Furthermore, greater verbal intelligence and working memory capacity were longitudinally associated with DD, suggesting a functional inter-relationship between these domains and DD from early adolescence to adulthood, possibly with overlapping neural substrates. The present report also extends and supports previous work suggesting that AUC as an index of DD behavior is stable over time and may be conceptualized as a trait variable (Odum, 2011b). This has implications for how we conceptualize developmental changes in cognitive impulsivity indexed by intertemporal delay discounting from childhood to young adulthood. The DD task may represent a valuabl assessment tool for targeted interventions designed to reduce or prevent behavioral problems associated with deficiencies in executive control.

Data Availability Statement

Although adolescent participants and their parents provided consent and, where relevant, assent to participate in the study, participants did not consent to public data sharing. For questions about the data or to explore collaborative opportunities, please contact Monica Luciana (lucia003@umn.edu).

Data availability

The authors do not have permission to share data.