1 Introduction

Self-control is viewed in economics and other disciplines as a key individual characteristic responsible for effective self-regulation and personal goal attainment (Moffitt et al., Reference Moffitt, Arseneault, Belsky, Dickson, Hancox, Harrington, Houts, Poulton, Roberts, Ross, Sears, Murray Thomson and Caspi2011). Lack of self-control is thought to explain suboptimal choices and outcomes in many life domains, including financial decision making, health, and education. Given the importance of self-control, this individual trait is widely studied theoretically and empirically in many different fields (Duckworth et al., Reference Duckworth, Milkman and Laibson2018).

In the economics literature, researchers usually model problems of self-control through time-inconsistent preferences that predict choices such as planning to go on a diet starting next week but not going on the diet when next week arrives. Two well-known models that can capture such behaviours are the hyperbolic (Loewenstein & Prelec, Reference Loewenstein and Prelec1992) and quasi-hyperbolic (Laibson, Reference Laibson1997) discount models. The latter model has attractive analytical features that have contributed to its popularity in economics (Frederick et al., Reference Frederick, Loewenstein and O’Donoghue2002), and for this reason we focus on it in our paper. The underlying assumption of the model is that agents have a “present bias” toward current consumption, as the values of all future rewards are downweighed relative to rewards in the present (in addition to the standard exponential discounting of delayed rewards). Economists have applied quasi-hyperbolic discounting theoretically and empirically to explain problematic behaviours across a wide variety of domains such as financial decision making (Laibson et al., Reference Laibson, Repetto and Tobacman1998), health behaviours (DellaVigna & Malmendier, Reference DellaVigna and Malmendier2006; Gruber & Kőszegi, Reference Gruber and Köszegi2001; Schilbach, Reference Schilbach2019), and work effort (Augenblick et al., Reference Augenblick, Niederle and Sprenger2015; Kaur et al., Reference Kaur, Kremer and Mullainathan2015).

In stark contrast to these diverse domains of application, most experimental research aimed at quantifying present bias has focused on a single specific reward type, namely money, and on samples from developed countries, in particular students at research universities. Further, most studies have used a cross-sectional design, which is not a true test of time inconsistency (Halevy, Reference Halevy2015; Read et al., Reference Read, Frederick and Airoldi2012).Footnote ¹ Only a longitudinal design permits a test of inconsistent planning, the key prediction of the quasi-hyperbolic model (O’Donoghue & Rabin, Reference O’Donoghue and Rabin1999). In this paper, we address each of these shortcomings that have characterised much of the existing literature. We next expand upon each of these points in turn.

In this paper, we estimate and compare time preferences for money, healthy foods, and unhealthy foods. We thus contribute to the literature by identifying the shape of time preferences for food rewards. While the quasi-hyperbolic model has been applied to explain behaviour across a variety of domains, several recent experimental studies find no present bias for money (Andersen et al., Reference Andersen, Harrison, Lau and Rutström2014; Andreoni & Sprenger, Reference Andreoni and Sprenger2012a; Andreoni et al., Reference Andreoni, Kuhn and Sprenger2015; Augenblick et al., Reference Augenblick, Niederle and Sprenger2015). An influential interpretation of these findings (Cohen et al., Reference Cohen, Ericson, Laibson and White2020) holds that experiments using money will fail to detect present bias if subjects engage in arbitrage: if subjects integrate experimental earnings with borrowing and savings opportunities outside the experiment, they will simply switch from sooner to later payment at the market interest rate, revealing linear utility and no present bias.

Clearly, to shed light on this issue it is necessary to compare present bias for monetary and non-monetary rewards. Augenblick et al. (Reference Augenblick, Niederle and Sprenger2015) compare present bias for money and real effort, finding present bias for effort but not money. In their experiment, choices over effort (which is aversive) may be interpreted as revealing preferences toward leisure (a reward) if it is assumed that time not spent working for the experimenters is instead devoted to the consumption of leisure. However, since it is only the effort choice that is elicited and controlled for in the experiment, it is possible that this effort instead displaces another aversive use of time—such as domestic work, study, or an outside form of market employment—as opposed to leisure. This, in effect, is the real effort analogue to the potential confound of arbitrage in experiments using money. While previous studies (discussed next) have compared impatience and risk preference for monetary and direct consumption rewards, ours is the first to do so for present bias.Footnote ² For now, we point out that if present bias is real but confounded by arbitrage in experiments using money, then we would expect to find present bias for food but not money. We return to the issue of arbitrage in the discussion.

With regard to other economic preferences, it has been found that people tend to be less patient (as distinct from present biased) for primary rewards than for money (Estle et al., Reference Estle, Green, Myerson and Holt2007; Odum & Rainaud, Reference Odum and Rainaud2003; Reuben et al., Reference Reuben, Sapienza and Zingales2010; Tsukayama & Duckworth, Reference Tsukayama and Duckworth2010; Ubfal, Reference Ubfal2016) but that risk preferences estimated for money and food rewards are essentially the same (Levy & Glimcher, Reference Levy and Glimcher2012).Footnote ³ These contrasting results highlight the importance of studying the consistency of preferences across domains separately for each economic preference. Moreover, within the domain of foods, unhealthy foods may be more tempting, triggering more present bias. It is thus also important to compare time preferences between healthy and unhealthy food.

A key feature of this paper is our sample of 697 relatively poor adolescents in China. Most previous studies have focused on the so called WEIRD subject pool (Henrich et al., Reference Henrich, Heine and Norenzayan2010). WEIRD refers to samples drawn from populations that are Western, Educated, Industrialised, Rich and Democratic. One reason why carefully designed studies do not find present bias for money may simply be that the participants, having been admitted into top universities, did not have serious self-control problems to begin with.Footnote ⁴ Indeed, several recent studies provide evidence that participants from developing countries show present bias for money (Balakrishnan et al., Reference Balakrishnan, Haushofer and Jakiela2020; Banerji et al., Reference Banerji, Goto, Ishizaki, Kurosaki, Lal, Paul and Tsuda2018; Clot & Stanton, Reference Clot and Stanton2014; Giné et al., Reference Giné, Goldberg, Silverman and Yang2018; Janssens et al., Reference Janssens, Kramer and Swart2017). Aycinena et al., (Reference Aycinena, Blazsek, Rentschler and Sprenger2020) find impatience for money and a preference to smooth payments over time in a sample of low-income Guatemalans, but do not find present bias. There is also evidence that certain clinical populations (e.g. prescription drug program enrolees and diabetes patients) show present bias for money (Abaluck et al., Reference Abaluck, Gruber and Swanson2018; Mørkbak et al., Reference Mørkbak, Gyrd-Hansen and Kjær2017). Our paper contributes to the still relatively limited evidence on the time preferences of non-WEIRD samples.

Our subjects differ not only on each of the dimensions of the WEIRD samples, but also in their age. Self-control established early in life is critical to personal development, yet few studies to date have estimated time preferences in children and adolescents.Footnote ⁵ Research in psychology has shown that poor self-control in childhood is associated with a range of damaging behaviours, for example cigarette smoking. Moreover, children with greater self-control are significantly more likely to be from socioeconomically advantaged families (Moffitt et al., Reference Moffitt, Poulton and Caspi2013).

To identify present bias we conduct a longitudinal experiment in schools. Halevy (Reference Halevy2015) distinguishes three properties of standard preferences over temporal payments relative to a dated collection of such preferences. Stationarity implies that the ranking of two temporal payments at time t depends only on the difference between the two payments and their relative delay. The standard cross-sectional design is a test of this property. Time invariance implies that preferences are not a function of calendar time. Time consistency requires that the ranking of temporal payments does not change as the evaluation perspective changes from t to t’. Only a true longitudinal design can test for this property. Halevy (Reference Halevy2015) finds that people can be time inconsistent and have stationary preferences at the same time, implying that the results of a cross-sectional design may be misleading.

Finally, conducting our experiment in school allows us to avoid selection into the study as well as attrition from it. Further, with access to administrative data from schools, we test the ability of our experimental measures to predict field outcomes such as academic performance.

697 Chinese high-school students participated in a five-week, incentivised longitudinal experiment using a modified version of the Convex Time Budget design (Andreoni & Sprenger, Reference Andreoni and Sprenger2012a) to elicit individual preferences for three reward types: money, healthy food and unhealthy food. Subjects faced the same set of decisions, featuring the same reward amounts delivered on the same dates, at two points in time. In the first session, all choices involved rewards to be received at two dates in the future, while in the second session the sooner rewards were available today. Our design also incorporates a test of rationality in the form of violations of the Generalised Axiom of Revealed Preference (GARP). We conducted our experiment during regular class time and all 697 subjects completed both sessions, resulting in zero attrition.

We highlight several key findings. First, we provide the first estimates of present bias for consumption rewards. At the median, averaging over all trials, our subjects choose to receive 2% more food on the sooner payment date when the decision is made on that day than when it is made in advance. Our structural estimate of $\beta$ for a representative agent is 0.69 for healthy food and for unhealthy food it is 0.71 (both are significantly less than one, but not significantly different from one another). Food consumption is highly consequential for people’s health. Focusing on the amount consumed in the moment, a representative agent who has a healthy $BMI=21$ and who participates in our experiment every week would become overweight in 4 years.

In contrast to some recent literature, we also find strong present bias for money. At the median, subjects choose to receive 4% more money on the sooner payment date when the decision is made on that day than when it is made in advance. Our structural estimate of $\beta$ for a representative agent is 0.65 for money (also significantly less than one, as well as significantly different from our estimates for food).

Next, in contrast to previous findings in the domain of risk, we find differences in the curvature of utility between monetary and primary rewards. For money, we confirm recent findings in the time preference literature that instantaneous utility is at best only mildly concave (Abdellaoui et al., Reference Abdellaoui, Bleichrodt, L’Haridon and Paraschiv2013; Andreoni & Sprenger, Reference Andreoni and Sprenger2012a; Cheung, Reference Cheung2020). However, for both healthy and unhealthy foods we find strong evidence of concave utility (implying a preference to spread rewards evenly over time), more in line with conventional findings in the domain of risk.

At an individual level, we find significantly positive and moderate correlations between individual measures of present bias for all reward type pairs [ $\rho \in (0.47,0.60)]$ , as well as between individual measures of impatience [ $\rho \in (0.59,0.66)]$ . We find even stronger correlations for a measure of the preference to smooth consumption over time [ $\rho \in (0.81,0.85)]$ .Footnote ⁶ Together, these findings imply that conventional choices over money are moderately predictive of choices for food.

Finally, we find that our experimental measures of time preferences for both monetary and dietary rewards are predictive of subjects’ field behaviours. Adolescents who make less patient choices for any reward type are more likely to drink alcohol and have lower grades. Moreover, those who are more present biased for money and healthy food are more likely to drink alcohol and have lower grades.

The paper proceeds as follows: Sect. 2 describes our experimental design, Sect. 3 explains our empirical approach, Sect. 4 presents the results, and Sect. 5 provides a discussion of our findings.

2 Experimental design

2.2 Task

Our experimental task is an extension of the convex time budget (CTB) design of Andreoni and Sprenger (Reference Andreoni and Sprenger2012a), which allows us to estimate subjects’ utility and discounting parameters using data from a single task. To simplify this task, we implement a discrete version of the CTB based upon Andreoni et al. (Reference Andreoni, Kuhn and Sprenger2015).

Following the CTB framework, we provide options that allocate amounts of a reward between two payment dates subject to a future-value budget constraint:

$\left(1,+,r\right)\times c_t+c_{t+k}=70,$

where $c_t$ denotes the amount of reward received at the sooner payment date $t$ , $c_{t+k}$ denotes the amount of reward received at the later payment date $t+k$ , and $r$ denotes the simple interest rate between the two dates. Between trials, we systematically vary the interest rate $r$ keeping the future value of the endowment fixed at 70. The back-end delay $k$ was always equal to three weeks.

Figure 1A shows a sample budget with an interest rate of 0%. In that case, regardless of which bundle a subject chooses, the amounts received on the two dates always sum to 70. To discretise this choice, we offer six evenly spaced options (shown as dots in Fig. 1A) along the budget line that a subject can choose from. There were always six options in every trial to keep choice difficulty constant. We exclude corner bundles [i.e. ${(c}_t,0)$ and $(0,c_{t+k})$ ] from the choice set, as previous studies find that subjects who consistently choose corner bundles generate issues for structural estimation (Harrison et al., Reference Harrison, Lau and Rutström2013). Another advantage of this procedure is that by forcing subjects to receive payments on both dates, we equalise transaction costs without the use of a show-up fee.

Fig. 1 Experimental design. A: Budget constraint with 0% interest rate. The six dots on the budget line indicate bundles available to the chooser. B: Decision screen for the 0% interest rate trial. Each row represents one bundle. On the left is the amount received on the sooner date and on the right is the later date. Dots represent the quantity of a reward to be received on that date. The six bundles are presented in random order for each participant

Figure 1B shows the corresponding decision screen for the 0% interest rate trial. As well as stating the amounts of a reward that are available on each payment date, we also visualise these quantities to facilitate comparison of the alternatives. The order of presentation of the six options on the screen was randomised for each subject, and the subject chose their most preferred bundle by clicking on it.

The other simple interest rates we use are − 9%, 11%, 25%, 43%, 67% and 100% (see Fig. 2A for these seven budget sets). As the interest rate varies, a subject’s choices trace out a price expansion path in terms of sooner and later rewards, with the optimal choices depending upon both utility curvature and discounting parameters.

Fig. 2 Budget constraints

We further enrich this framework by adding an additional seven decisions to allow for a test of the consistency of subjects’ choices with the Generalised Axiom of Revealed Preference (Varian, Reference Varian1982), as recommended by Chakraborty et al. (Reference Chakraborty, Calford, Fenig and Halevy2017). We derive these additional choice sets from a present-value budget constraint:

$c_t+\frac{1}{1+r}\times c_{t+k}=56,$

and in these trials we vary the interest rate while holding the present value of the endowment fixed at 56. The interest rates $r$ for these additional trials are − 13%, 0%, 13%, 25%, 38%, 50%, and 63%. Figure 2B shows the complete set of budgets used in our design. The two sets of budget lines intersect one another, allowing us to count the number of times a subject’s choices violate GARP. The maximum number of GARP violations in this task is 91, while a random chooser would be expected to commit 12 violations. Note also that the trial with a 25% interest rate is presented twice (with other trials interleaved in between), allowing us to check for the consistency of subjects’ choices when making the same decision twice.Footnote ⁷

2.3 Timeline

Figure 3 shows the timeline of our five-week longitudinal experiment. In the first session in week one, subjects were presented with decisions where the sooner payment is in one week’s time (hence in week two) and the later payment is in four weeks’ time (hence in week five). In the second session in week two, the same subjects made the same sets of decisions over bundles of rewards received in weeks two and five, where the sooner payment is now available today.Footnote ⁸ This longitudinal design identifies dynamic inconsistency by comparing initial allocations in week one (when all rewards are in the future) with subsequent allocations in week two (when the sooner reward is in the present). In each school, all sessions were conducted at the same time of day and on the same day of the week to keep other variables such as hunger constant; for logistical reasons, the timing of the sessions differed slightly between schools. Before making their decisions in week one, subjects were told that they would be making decisions again in week two, and that one out of all their decisions would be randomly selected at the end of session two to be realised for payment. In the third session which took place in week five, subjects did not make any decisions and only received rewards. The experiment dates were between 25 February and 29 March 2019. Over this period, there were no public holidays, school vacations or examinations.

Fig. 3 Timeline of the experiment

After completing their decisions, subjects filled out a questionnaire which included demographic characteristics (in the first session) as well as current hunger and fatigue level,Footnote ⁹ and appetite ratings (in both sessions); see Online Appendix 2 for an English translation of these questionnaires.

3 Empirical approach

We next outline two approaches we adopt to measure subjects’ time preferences and utility curvature. Our first approach is to use descriptive measures of time preference and preference for smoothness that are based on simple proportions of rewards allocated to sooner versus later payment dates. These descriptive measures provide evidence on the behaviours we are interested in without needing to commit to specific structural assumptions. However, since descriptive measures cannot always cleanly distinguish between parameters, our second approach is to impose a quasi-hyperbolic discounted utility model (Laibson, Reference Laibson1997) and jointly estimate three parameters: the discount factor $\delta$ , present bias $\beta$ , and utility curvature $\alpha$ . We find that these two approaches yield broadly consistent results.

3.1 Descriptive measures

3.1.1 Impatience

To investigate subjects’ impatience, without confounding it with present bias, we consider decisions made in the first session (week one) which result in bundles of rewards received in weeks two and five. Since all rewards are received in the future, present bias does not play any role. Subjects who select a bundle with a larger proportion of rewards allocated to the sooner payment date (week two) relative to the later date (week five) can be classified as more impatient (equivalently less patient).

Let $c_{i,j}$ be the amount of a reward that a subject would receive in week i based on a decision made in week j. We define impatience for each of the 14 week one decisions ( $Impatienc{e}_k,k\in \left[1,14\right]$ ) for a given reward type as the proportion of the reward allocated to week two relative to the total amount of rewards in the chosen bundle, when the choice is made in week one:

$Impatienc{e}_k=\frac{c_{2,1}}{c_{2,1}+c_{5,1}}$

Then, for each reward type separately, to measure an individual’s impatience we take the average of $Impatienc{e}_k$ for that reward type over all 14 decisionsFootnote ¹⁰:

$Impatience=\frac{1}{14}\sum _{k=1}^{14}Impatienc{e}_k$

By construction, this measure is bounded between zero (most patient) and one (most impatient), although in practice because we removed corner bundles from the choice sets the measure cannot go all the way to these limits in our design.

3.1.2 Present bias

Present bias occurs when an individual allocates a larger proportion of a reward to the sooner date when the sooner payment is immediate relative to when it is delayed, other things equal. To construct a descriptive measure of present bias, we first compare an individual decision made in week two when the sooner payment is today to the same decision made in week one when the sooner payment is delayed. We thus define present bias for a given decision scenario ( $Presentbia{s}_k,k\in \left(1,14\right)$ ) as the difference in the proportion of the reward allocated to week two when making a choice in week two compared to when making the same choice in week one:

$Presentbia{s}_k=\frac{c_{2,2}}{c_{2,2}+c_{5,2}}-\frac{c_{2,1}}{c_{2,1}+c_{5,1}}$

Then, for each reward type separately, to measure an individual’s present bias we take the average of $Presentbia{s}_k$ for that reward type over all 14 decision scenarios:

$Presentbias=\frac{1}{14}\sum _{k=1}^{14}Presentbia{s}_k$

By construction, this measure is bounded between negative one (most future biased) and one (most present biased). Again, because we removed corner bundles from our choice sets, the measure does not go all the way to these limits in our design.

3.1.3 Preference for smoothness

In addition to their time preferences, a subject’s choices in the experiment depend on the strength of their preference to smooth payoffs over time, as captured by the curvature of the utility function in a discounted utility model. A subject who has highly concave utility for a reward will have a strong preference for more mixed (temporally balanced) bundles, while one who has near-linear utility will tend to choose more extreme bundles near the corners of the budget set. To construct a descriptive measure of preference for smoothness, for a given decision trial ( $k\in \left(1,28\right)$ ), we calculate the difference between the sum of the amounts of a reward allocated to both dates and the absolute difference in those amounts, normalised by the sum of the amounts:

$Smoot{h}_k=\frac{\left(c_1+c_2\right)-\left(\left(c_1-c_2\right)\right)}{c_1+c_2}$

where $c_1$ represents the amount of a reward allocated to the sooner date and $c_2$ represents the amount of a reward allocated to the later date.

In the limiting case of a corner solution (where one of the $c$ s is zero), the numerator collapses to zero and so $Smoot{h}_k$ goes to zero. At the opposite extreme of perfect smoothing (such that $c_1=c_2$ ), it is the absolute difference term that collapses to zero and so $Smoot{h}_k$ goes to one.

Then, for each reward type separately, to measure an individual’s preference for smoothness we take the average of $Smoot{h}_k$ for that reward type over all 28 decision scenariosFootnote ¹¹:

$Smooth=\frac{1}{28}\sum _{k=1}^{28}Smoot{h}_k$

By construction, this measure is bounded between zero (no preference for smoothing) and one (maximum preference for smoothing), although in practice it does not go to these limits because we removed the corner bundles in our design.

3.2 Structural model

To conduct a parametric estimation of the discount factor, present bias, and utility curvature we assume a $\mathrm{CRRA}$ utility function and quasi-hyperbolic discount function (Laibson, Reference Laibson1997; O’Donoghue & Rabin, Reference O’Donoghue and Rabin1999). The instantaneous utility from experimental payments, $c$ , is:

(1) $u\left(c\right)=\left(\begin{array}{cc}\frac{c^{1-\alpha }}{1-\alpha }& \alpha \ne 1\\ lnc& \alpha =1\end{array}\right)$

The parameter $\alpha$ is $\mathrm{CRRA}$ utility curvature, where $\alpha =0$ indicates linear utility, and $\alpha >0$ ( $\alpha <0$ ) indicates concave (convex) utility. With a quasi-hyperbolic discount function, the intertemporal utility from experimental payments $c_t$ received at date $t$ , and $c_{t+k}$ received at date $t+k$ , is:

(2) $U_t\left(c_t,c_{t+k}\right)=u\left(c_t\right)+{\beta }^{1_{t=0}}{\delta }^{k}u\left(c_{t+k}\right)$

The parameter $\beta$ captures present bias. When $\beta =1$ , the discount function is exponential and there is no present bias, while $\beta <1$ indicates present bias. The variable $1_{t=0}$ is an indicator of whether the sooner payment date, $t$ , is immediate. The parameter $\delta$ is the weekly discount factor.

Given the discrete nature of the choice sets in our design, we estimate this model using multinomial logit (MNL) regression (Cheung, Reference Cheung2015; Harrison et al., Reference Harrison, Lau and Rutström2013) which compares the discounted utility of a subject’s chosen bundle to that of each of the available alternatives. Conditional on candidate values of the parameters being estimated, we use Eqs. (1) and (2) to compute the discounted utility of each of the six alternative bundles. Then, given the bundle chosen by the subject, the multinomial logit probability of the observed choice is given by:

$Pr\left(\mathrm{choice}\right)=\frac{e^{U^{\ast }/s}}{e^{U_1/s}+e^{U_2/s}+\dots +e^{U_6/s}},$

where $U^{\ast }$ represents the utility of the chosen bundle, $s$ is a “noise” parameter, and $U_i(i\in \left(1,,,6\right))$ represents the utilities of the six bundles in each trial. The estimates of $\alpha ,\beta$ and $\delta$ are chosen to maximise the log-likelihood of the observed choices, with standard errors clustered at the level of the subject.

We report representative agent models for each reward type, estimated in STATA using both the MNL procedure as well as the nonlinear least squares (NLS) estimation technique used by Andreoni and Sprenger (Reference Andreoni and Sprenger2012a) for continuous CTB data. Unless noted, our conclusions are qualitatively the same using either estimation procedure. In addition, we report the summary statistics of individual-level MNL models estimated in MATLAB for each subject and reward type. For individuals with extreme choice patterns exhibiting little variance, individual estimation is unreliable. Since we set bounds on the individual estimates for each parameter, this problem expresses itself as one or more parameter estimates running to the bounds.Footnote ¹² Despite this issue, we report results using individual estimates for all subjects, for two important reasons. First, this ensures consistency with our reporting of results using individual descriptive measures. Second, it allows us to evaluate the in- and out-of-sample prediction performance of our estimates under worst-case conditions. This confirms that even where our individual point estimates are not reasonable, they are nonetheless in line with our subjects’ behaviour. As a result, these boundary estimates do not adversely affect our ability to correctly predict subjects’ choices in Sect. 4.3 below (see Online Appendix 5 for details).