Hunger Games - Berkeley - Xlab

Loading...
Hunger Games: Does Hunger Affect Time Preferences? By Lydia Ashton∗

Draft: May 11, 2015

The poor often make shortsighted monetary choices, however many laboratory experiments fail to detect present bias over monetary outcomes. Could physiological factors associated with poverty, such as hunger, be important triggers of present bias? I investigate this in a novel laboratory experiment by manipulating hunger and eliciting time preferences using the convex-time-budget method. In the control condition, I find monetary impatience consistent with previous studies, including no present bias. However, hunger significantly increases impatience, particularly for choices involving immediate rewards. Together these findings demonstrate that hunger activates present bias, suggesting that it may play an important role in behavioral poverty-traps. JEL: D03, D87, D90, C91 Keywords: Hunger, cognitive fatigue, intertemporal choices, psychology and economics, neuroeconomics.

∗ Ashton: Univeristy of Wisconsin-Madison, Wisconsin Institute for Discovery, 330 N. Orchard St., Madison, WI 53715, [email protected] I am grateful for the guidance of my thesis committee and mentors, Peter Berck, Stefano DellaVigna, Shachar Kariv, Justin Sydnor, and Sofia Villas-Boas. Also, I am grateful for the insightful comments of many colleagues, including Aluma Dembo, David Dickinson, Andrew Dustan, Salar Jahedi, Michael Kuhn, Amos Nadler, Michaela Pagel, Tiffany Shih, Charles Sprenger and Anna Spurlock, among others, and the participants of the Psychology and Economics lunch series at the University of California, Berkeley. This research would not have been possible without the generous support of the Russell Sage Foundation (RSF) and the University of California, Berkeley’s Experimental Social Science Laboratory (Xlab).

1

2

DRAFT

Classic economic theory focuses on static preferences and relies on the Homo Economicus assumption. However, there is growing evidence that cognitive, emotional and visceral states can mediate behavioral biases and shape preferences (DellaVigna, 2009). As Homo Sapiens, we know that our cognitive, emotional and visceral states fluctuate and that we tend to face and make many important economic decisions, with potential long term consequences, when we are fatigued, stressed and/or hungry. Better understanding the relationship between such factors and preferences could enlighten our comprehension of the economic decision-making process. For instance, we know that the poor, who are more susceptible to food insecurity and as a result more likely to frequently experience hunger, tend to make more short-sighted economic decisions (Haushofer and Fehr, 2014). Could hunger, a visceral factor, be a trigger of present bias that helps in perpetuating behavioral poverty-traps? A couple of decades ago Loewenstein’s (1996) seminal work prompted a number of studies which demonstrated that “the discrepancy between the actual and desired value placed on a particular good or activity increases with the intensity of the immediate good-relevant visceral factor.” 1 However, less has been done to test whether visceral factors activate behavioral biases in general. This study extends on this notion by drawing parallel evidence from psychology, economics, and neuroscience and showing that hunger affects time preferences. To date, only a single study has shed some light into the question; does hunger indirectly affect non-hunger related decisions? Danziger, Levav and AvnaimPesso (2011) find that the percentage of favorable parole decisions fluctuates in relation to the time in which judges take a food break. They argue that this is due to mental resource depletion. However, they are unable to identify whether 1 For

example, Loewenstein, Nagin and Paternoster (1997) find that when individuals are sexually

aroused they are more likely to expect to be sexually aggressive. Read and van Leeuwen (1998) find that future food choices are significantly affected by an individual’s current state of appetite. Also, Van Boven and Loewenstein (2003) show that subjects attitudes towards others thirst depend on their own thirst.

DRAFT

HUNGER GAMES

3

the fluctuation in judges’ decisions is due to resources having been replenished by eating (mitigating hunger or glucose depletion), resting (mitigating cognitive fatigue or ego depletion) or both. The main goal of the present study is to test whether hunger affects time preferences (discounting, present bias and utility curvature). Nonetheless, it is important to differentiate between the effect of physical and cognitive resource depletion. Therefore, I conducted a controlled laboratory experiment where I manipulated both the state of hunger and/or cognitive fatigue of participants making intertemporal choices. These intertemporal choices were based on Andreoni and Sprenger’s (2012) convex-time-budget (CTB) methodology, in which participants have to decide how much of a monetary reward they want to cash on an earlier and/or a later date given that whatever is cashed on the later date earns interest. I find that the average number of tokens cashed earlier is significantly larger for subjects under the hunger (M= 50.31, Robust-SE= 3.96) and cognitive-fatigue (M= 50.41, Robust-SE= 5.56) condition than for subjects under the control condition (M= 36.81, Robust-SE= 5.06). Interestingly, subjects under the interaction condition (i.e. both hungry and cognitively-fatigued) cash slightly less tokens (M= 33.53, Robust-SE= 4.24) than subjects under the control condition. However, this result is not statistically significant and it is most likely driven by the chosen experimental parameters. Moreover, when comparing the average number of tokens cashed by the delay of the payment date (i.e. immediate versus nonimmediate) I find that only subjects under the hunger and interaction conditions cash significantly more tokens if the earlier payment date is immediate, 10.5% (t(36) = 2.57, p = 0.015) and 17.0%, (t(33) = 3.05, p = 0.004) more, respectively. This suggests that hungry individuals display a certain level of present bias, or exaggerated preference for immediately available outcomes. One of the benefits of using CTB is that it allows for the recovery of structural time preference parameters at the aggregate and individual level. When estimating the time preference parameters at the aggregate level, I precisely estimate an

4

DRAFT

average annual discount rate of 73.0%, 163.6%, 148.0% and 60.7% for subjects under the control, cognitive-fatigue, hunger and interaction conditions, respectively. The present-bias parameter (β) is estimated at 1.00, 0.99, 0.95 and 0.97 for subjects under the control, cognitive-fatigue, hunger and interaction conditions, respectively. The null hypothesis of “no present bias” (β = 1) is rejected under the hunger and interaction conditions, p < 0.01 and p < 0.05 respectively. Not surprisingly, and consistent with the non-parametrical results, I find a significant hunger effect (p < 0.01) and marginally significant interaction effect (p < 0.10) on the present bias parameter. The utility curvature parameter (α) is estimated at 0.87, 0.81, 0.84 and 0.89 for subjects under the control, cognitive-fatigue, hunger and interaction conditions, respectively. The null hypothesis of “linear utility” is rejected (p < 0.01) for all conditions. The recovered individual-level parameters confirm these results. The median annual discount rate is 80.0%, 131.5%, 180.3% and 72.8% for subjects in the control, cognitive-fatigue, hunger and interaction conditions, respectively. The median present-bias parameter is 1.00, 1.00, 0.96 and 0.98 for subjects in the control, cognitive-fatigue, hunger and interaction conditions, respectively. Finally, the median utility curvature parameter is 0.94, 0.93, 0.91 and 0.94 for subjects in the control, cognitive-fatigue, hunger and interaction conditions, respectively. In summary, both hunger and cognitive fatigue increase monetary impatience, but only hunger affects time preferences. Hunger activates present bias by disproportionately increasing monetary impatience when choices involve immediately available monetary rewards. In contrast, cognitive fatigue increases the number of all-earlier allocations without decreasing the number of all-later allocations (i.e. more corner solutions overall). I argue that the latter may reflect a decrease in attention and an increase in heuristic-based choices. However, further work is needed to test this hypothesis. Interestingly, the interaction of both treatments also activates present bias but it also increases monetary patience. This is most likely caused by the parameters used in the experimental design. Also, consistent

DRAFT

HUNGER GAMES

5

with Andreoni and Sprenger’s (2012) results, individuals under the control condition (not hungry nor cognitively fatigued) display reasonable levels of discounting, present bias and utility curvature. To my knowledge this is the first study to prove that hunger activates present bias. This results lay the groundwork for future research exploring whether hunger affects the individual’s economic decision-making process. Moreover, they open the door to a new research agenda that could help explain why the poor tend to make more shortsighted economic decisions. These research is tightly interconnected with the behavioral poverty-trap literature. Banerjee and Mullainathan (2007) suggest that “the impatience that the poor often show is as much a result of their poverty as it is a cause.” Hunger may be another factor that feeds this vicious cycle. Additionally, it highlights the importance of parameter and methodology selection (e.g. choice consistency, patterns of behavior, CTB) to investigate how cognitive state-levels affect economics preferences. The remainder of the paper is organized as follows: Section I motivates the research question and describes the related literature. Section II details the experimental design. Section III provides summary statistics. Section IV discusses the results. Section V concludes. I.

Motivation

In recent decades, researchers have shown an increased interest in understanding how and which brain systems are associated with individual economic decisions (Camerer, Loewenstein and Prelec, 2005). For example, using functional magnetic resonance imaging (fMRI), McClure et al. (2004) demonstrate that parts of the limbic system are preferentially activated by economic decisions that involve immediate monetary rewards (i.e. Blood-oxygen-level dependent (BOLD) signal changes in the ventral striatum (VStr), medial orbitofrontal cortex (MOFC), medial prefrontal cortex (MPFC), posterior cingulate cortex (PCC), and left posterior hippocampus are greater when decisions involve money available today).

6

DRAFT

The consensus among neuroscientists is that the role of the orbitofrontal cortex (OFC) is to determine just how rewarding a reward actually is (Wallis, 2007).2 Not surprisingly the OFC is believed to be the best candidate as the network that assigns value, which underlines economic choice (Padoa-Schioppa and Assad, 2006). Concurrently, neuroscientists have documented evidence that hunger is associated with increased activity in the brain’s limbic system. For example, Tataranni et al. (1999) use positron emission tomography (PET) to show that that hunger increases relative cerebral blood flow (rCBF) in limbic areas of the brain (e.g, OFC, and parahippocampal cortex). Similarly, Hinton et al. (2004) use PET to show that during the intrinsic state of hunger, there is increased activation in the hypothalamus, amygdala, insula cortex, medulla, striatum, and anterior cingulate cortex. Li et al. (2012) use fMRI to show that fasting increases BOLD signals of limbic areas of the brain (e.g, OFC, parahippocampal cortex, and caudate). Moreover, there is growing evidence that physiological and biological factors are linked to individual economic behavior. For example, stress, induced by mild physical pain (Porcelli and Delgado, 2009) or cortisone pills (Kandasamy et al., 2014), increases risk aversion. Similarly, stress and negative emotions increase impatience (Cornelisse et al., 2013; Lerner, Li and Weber, 2012). Also, Dickinson, McElroy and Stroh (2014) find that glucose increases individuals’ response times affecting the likelihood of a Bayesian error. Kuhn, Kuhn and Villeval (2014) find self-control depletion and glucose effects on time preferences, which are mainly driven by increases in the intertemporal substitution elasticity. Therefore, they suspect that these affects are driven by an increase in subjects’ attention to the decision and not an inability to resits the temptation of an immediate monetary 2 It

has been documented that outputs of the inferior temporal visual cortex (i.e. visual stimuli) as

well as outputs from other sensory systems (e.g. taste, touch, olfaction) are fed into the OFC to produce representations of the expected reward value, including monetary reward value (Rolls, 1999; Rolls and Grabenhorst, 2008).

DRAFT

HUNGER GAMES

7

reward. Other relevant studies include Schofield (2013), who used a high intake treatment and and Ramadan to evaluate the impact of caloric intake on productivity. She finds that high-caloric intake led to improvements in physical and cognitive tasks, increased labor supply and increased income (about 10%); while low-caloric intake led to a 20% to 40% decrease in productivity per individual. However, there is yet to be a study formally linking hunger and economic behavior. The most closely related study to this endeavor was conducted by Danziger, Levav and Avnaim-Pesso (2011) to test the age-old wisdom “Law is what the judge ate for breakfast”. In this study, they recorded judges’ sequential parole decisions, over a period of 50 days, before and after two daily food breaks. They find that the percentage of favorable decisions drops steadily from about 65% at the beginning of a session to nearly zero before the break, and returns abruptly to about 65% after the break. Their findings suggest that judicial rulings can be swayed by variables that should have no weight on legal decisions. In this case they interpret such variable as mental depletion. However, they are unable to identify whether the fluctuation in judges’ decisions is due to resources having been replenished by eating, resting or both. In the present study, I use a novel laboratory experiment to explore whether hunger affects economic decisions not directly associated with hunger (in this case choices over monetary rewards). Also, in order to clarify if and how hunger and cognitive fatigue interact, I implemented a 2x2 factorial experiment. The two treatment conditions in this experiment were hunger and cognitive fatigue.3 More specifically, I manipulated the order in which 4 different activities or stages were administer to subjects. These included a decision task, an arithmetical task, a tasting activity and filler tasks, and a demographic questionnaire and auxiliary 3 An

abundance of evidence shows that cognitive costs play an important role in consumers’ decisions

(e.g. credit card market, Ausubel (1991); retirement investments, Hastings and Tejeda-Ashton (2008); and tax salience, Chetty, Looney and Kroft (2009)) for a more in-depth review of the literature, see DellaVigna (2009).

8

DRAFT

survey. This generated the control and treatment groups needed to estimate the effect of hunger and cognitive fatigue on time preferences (i.e. can hunger help explain why some individual display time-inconsistent preferences). To provide some background, while standard economic model assumes timeconsistent preferences, there is substantial evidence that individual preferences vary over time (i.e. preferences are time inconsistent). Thaler (1991), the first to empirically test this assumption, found discounting to be steeper in the immediate future than in the more distant future. A slight modification to the standard economic model—the implementation of a present bias parameter (β) that, in addition to the time-consistent discount factor (δ), weights all utility to be realized in the future (Laibson, 1997; O’Donoghue and Rabin, 1999)–helps explain why individuals sometimes end up consuming more/less leisure/investment goods than what they had initially planned to consume. An individual is said to have time-inconsistent preferences, or being present bias, if β < 1. Since β weights all utility to be realized in the future, when evaluating a decision in which the outcome is realized in future, the individual weights the future outcome by β in addition to the standard discount factor δ. Therefore, with time-inconsistent preferences, individuals generate plans believing that their future-selves will be able to follow through. However, as the future becomes the present, they fail to do so. This leads to self-control problems. More recently, researchers have focused on improving the methodology used to elicit time preferences. They argue that when transaction costs are equal across choices and subjects trust the payments will be received, there is no evidence of time-inconsistent preferences. Andreoni and Sprenger (2012) developed the CTB, which helps mitigate biases arising from assuming a linear consumption utility when measuring time preferences. CTB works by asking subjects to decide how many of a total allocation of m tokens (generally m = 100) they want cash at an earlier date and how many they wanted to cash at a later date, with the value of the token increasing in time. In fact, Andreoni and Sprenger (2012) conclude that

DRAFT

HUNGER GAMES

9

this may suggest that present bias is a visceral response activated when earlier rewards are actually immediate. In the following section, I detail the controlled laboratory experiment used to test whether hunger affects intertemporal preferences. II.

Experimental Design

Each experimental session consisted of 4 different stages (explained in detail in the following section): a) a decision task, monetary choices used to elicit time preferences; b) an arithmetical task, timed-arithmetical problems used to induce cognitive fatigue; c) a tasting activity and filler tasks, the provision of a nutrition shake combine with filler tasks lasting approximately 15 minutes used to satiate appetite; and d) a demographic questionnaire and auxiliary survey, used to collect additional information on individual characteristics and dietary practices. Figure I illustrates how the ordering of these stages defines each of the cells/conditions resulting from the 2x2-factorial design. A.

Procedures

The experiment took place in the Social Sciences Experimental Lab (Xlab) at the University of California, Berkeley. During the sign-up process, which took place between a week and 24 hours before each session, individuals were asked to fast for at least 3 hours before the session. I conducted sessions during weekdays and weekends, as well as on different times of the day (from 9:00 a.m. to 1:00 p.m.) to eliminate date and time-of-the-day effects. During the sign-up process individuals with glucose and food sensitivities were also informed that they were not qualified to participate in the study. Upon arrival to the laboratory, subjects were assigned to a computer station. The nutritional drinks were set up in a table behind panels to the left of the room (see Figure II). A server-based application was developed to implement the

10

DRAFT

experiment.4 Each subject was issued a user id and password. Through the application subjects were given informed consent, instructions, practice rounds and learned about their experimental earnings. This included the payment amount and date(s) in which they would receive them. The responses and the time stamp for each of the responses were collected and stored on the server hosting the application. Since the decisions task, arithmetical task, and demographic questionnaire and auxiliary survey were solely administered through the web-based application, I will refer to these three stages of the experiment as the computer-based experimental tasks (CETs), from this point forward. B.

Compensation

At the beginning of the CETs, subjects were informed that they were going to face a total of 65 rounds, and that in each of these rounds they were going to have 45-seconds to either solve an arithmetical task or make an economic decision. Subjects were also informed that only one round was going to be selected to determine their experimental compensation, and they were reminded to make each decision and solve each problem carefully since any one of the 65 rounds had equal chances to be chosen at random.5 When implementing time discounting studies, the researcher must ensure that, except for their timing, choices are equivalent (i.e. all costs associated with receiving payments should be the same across periods). I used payment procedures similar to those implemented by other researchers (Andreoni and Sprenger, 2012) in addition to unique measurements design to make transaction costs across all periods equal. First, payments were made electronically (via Paypal) to eliminate disproportionate preference for present in-lab payments. Second, at the 4 Appendix

A provides screen-shots of the application, including the consent form and instructions

scripts used. 5 By selecting a random round to determine their compensation I eliminate potential wealth effects.

DRAFT

HUNGER GAMES

11

beginning of the experiment subjects were informed that they would receive a $10-participation fee in addition to their experimental compensation. Furthermore, the date on which they would receive this participation compensation would depend on whether the task randomly selected to determine their experimental compensation was an arithmetical task. Were that the case they would receive the $10-participation in a single payment (on the day of the experiment); or a decision tasks, in which case they would receive the $10-participation fee in two payments ($5 on the earlier date and $5 on the later date stated on the randomly selected decision round). Implementing a $10-participation fee serves several purposes: it allows to fulfill the Xlab minimum compensation requirements; it increased subjects’ trust, since they would receive both an earlier and a later date payment independent of their allocation; and it reduces the bias towards concentrating payments in a single period, by eliminating multiple payment inconvenience since two payments were sent regardless. Third, at the end of the experiment subjects provided the email account to which they wanted to receive their compensation payment(s). Also, at the end of the experiment, I personally gave each subject my business card with my email and phone number shown and invited them to contact me if they had any inquiries about the study, including the payment procedures. Additionally, The total amount and the date(s) in which they would receive their compensation were hand-written on the back each card. In the auxiliary survey I asked subjects if they trusted that they would receive their experimental payment on the promised date, and over 95% of subjects replied yes.6 C.

Tasting Activity and Filler Tasks

All subjects participated in a tasting activity before/after the CETs; this allows for the manipulation of their hunger/satiation level. Protein has been documented as the most satiating macro-nutrient (Rolls, Hetherington and Burley, 1988; Wei6 This

sample.

is similar to the 97% positive replies reported by Andreoni and Sprenger (2012) for their

12

DRAFT

gle et al., 2005; Astrup, 2005; Bertenshaw, Lluch and Yeomans, 2008). Therefore I used a high-protein (35 grams), low-calorie (160 calories), low-sugar (1 gram), and low-carbohydrate (2 grams) nutritional drink (12 fl. oz.).7 Subjects were instructed, via a message on their computer screen, to go to the left side of the room, take a can, consume all of its contents, then give the empty can to the researcher who would give them a paper-based survey (containing “filler tasks”), and return to their desk to complete it. Subjects had 15 minutes to complete the paper-based survey. A timer was program in the application to keep subjects from proceeding to following stages before the 15-min. wait period was over. For subjects in the hunger and interaction condition who participated in the tasting activity after the CETs, the filler tasks included ratings of the drink flavor and presentation data as well as ratings on the feeling of satiation after drinking the nutritional shake, dietary practices, and perceptions on the drink nutritional content. This supplementary data allowed me to verify the satiating effectiveness of the nutritional shake, which is discussed in detail in the following section. For subjects in the control and cognitive-fatigue condition who participated in the tasting activity before the CETs, the filler tasks included ratings of the drink flavor and presentation but did not include any questions related to the feeling of satiation after drinking the nutritional shake, dietary practices, or perceptions on the drink nutritional content to avoid biasing their responses the results.

D.

Decision Task

I used Andreoni and Sprenger’s (2012) CTB methodology to elicit time preferences. In CTB, subjects choose a continuous combination of ct and ct+k along the convex budget set (1)

(1 + t)ct + ct+k = m, 7 This

particular drink was chosen to avoid sugar and caffeine interactions.

DRAFT

HUNGER GAMES

13

where (1 + t) represents the price of earlier earnings; and ct and ct+k represent the experimental earnings at an earlier and a later date, respectively. The experimental earnings are determined by choosing how many tokens of a total allocation of m tokens they want cash on an earlier and/or a later date. The value of each token depends on which date the token is cashed and tokens cashed on later dates generally have larger values (i.e. (1 + t) ≥ 1). The convex budgets used were chosen to resemble those used by Andreoni and Sprenger (2012). At the beginning of each decision round subjects observe the value for earlier and later tokens, a calendar pointing out to the current date and highlighting the earlier and later dates corresponding to the decision. A slider represents their token allocation for each round. After making an allocation, a graph with the corresponding total early and later payments is shown.8 The application design allows for better control of order and anchoring effects, since it presents each convex budget as an independent round and facilitates the randomization of the order of all choices for each subject and well as randomly resetting the allocation (or slider) starting point in each round. Table I summarizes the 55 convex budgets faced by each subject. Each convex budget was presented as a separate round, and subjects had 45 seconds to make their decision. The total token allocation was fixed at 100 for all convex budgets (m = 100). Each convex budget is defined by a (t,k)-choice set and a (vt , vt+k )budget, where: t represents the earlier date measure in days from the date of the experiment, k represents the delay between the earlier and the later date measured in days, vt represents the earlier token cash-value (i.e. the value of each token if cashed on the earlier date) and vt+k represents the later token cash value (i.e. the value of each token if cashed on the later date). Table I also shows the price of earlier earnings or gross rate over k days, (1 + r) =

vt+k vt ,

which ranges

from 0 to 2; the standardized daily interest rate, (1+r)1/k ; and the annual interest rate compounded quarterly. The reason relatively high annual interest rates are 8 Figure

A4 and A3 provide a screenshot of the decision rounds before and after a choice is made.

14

DRAFT

used is because the monetary payments and delays were relatively small and using smaller annual interest rates could have biased results in favor of present bias. E.

Arithmetical Task

In order to induce cognitive fatigue, subjects were required to solve arithmetical problems consisting of four 3-digit addition problems for a total of 10 rounds.9 The cognitive-fatigue treatment was assigned randomly to half of the subjects within a session. As illustrated in Figure I the subjects in the control and hunger condition faced the arithmetical task rounds only after the decision task rounds, while the subjects in the cognitive-fatigue and interaction condition faced the arithmetical task rounds before the decision task rounds. If one of the arithmetical task rounds was selected at random to determine the experimental compensation subjects received $15, in addition to their $10-participation fee, only if they had correctly solved all four arithmetical problems in the selected round. F.

Demographic Questionnaire and Auxiliary Survey

The last part of the CETs consisted of a demographic questionnaire and auxiliary survey.10 III. A.

Summary Statistics Manipulation of hunger

First, subjects were required to fast for at least 3 hours before the experimental session as requested during the sign-up process. In the auxiliary survey I asked subjects to report the time at which they consumed their last meal before coming to the experiment. Using this data, I was able to identify subjects that did not comply with the fasting requirements (17 out of 160 participants). Table II summarize subjects’ characteristics for compliers and non-compliers. Non-compliers 9 Figure 10 A

A2 provides a screenshot of the arithmetical task round as it was presented to subjects. list of these questions is provided in Appendix D of Ashton (2014).

DRAFT

HUNGER GAMES

15

do not appear to be significantly different from compliers; except for the time since their last meal (measured in hours) and their self-reported levels of hunger, which is expected. Therefore, I will not include them when estimating treatment effects.11 Second, I collected 3 measures of self-reported hunger level. After the CETs subjects had to rank on a scale from 0 to 10, where 0 is ”Not At All” and 10 is ”Extremely”, how hungry they were both upon arrival to the lab and at that moment.12 In addition, I asked subjects under the control and cognitive-fatigue conditions (i.e. those that completed the tasting activity after the CETs) to rank their hunger level using the same scale. In order to accept the fasting/nutritionalshake manipulation as a successful manipulation of hunger/satiation levels, the following about these measurements needs to be true:13 • Self-reported hunger level upon arrival to the lab is the same for all subjects. Indeed, I do not find a significant difference on for the self-reported hunger level upon arrival to the lab between the subjects who completed the tasting activity before the CETs [µ = 5.86, SD= 2.88] (i.e. those under the control and cognitive-fatigue conditions) and the subjects who completed the tasting activity after the CETs [µ = 5.77, SD= 2.02] (i.e. those under the hunger and the interaction conditions): t(141) = 0.21, p = 0.836. • Self-reported hunger level during auxiliary survey is greater for those who had not completed the tasting activity yet. This is confirmed by the significant difference in self-reported hunger level between subjects under the hunger and interaction conditions [µ = 6.85, SD= 2.00], i.e. those who had not completed the tasting activity yet; and subjects under the control con11 Non-compliers 12 Note

behave very similar to subjects in the the control group (see Appendix C). that subjects were asked to rank their hunger level upon arrival to the lab in retrospect to

avoid biasing their experimental responses. 13 While non-compliers are not included, and they display significantly different self-reported hunger levels, including them does not significantly change the results.

16

DRAFT

dition and cognitive-fatigue treatment [µ = 4.50, SD= 2.80]: t(141) = 5.76, p <= 0.001. • Nutritional shake reduces hunger. First, I find a significant difference between the self-reported hunger level upon arrival to the lab [µ = 5.86, SD= 2.88] and during the auxiliary survey [µ = 4.50, SD= 2.80] for those under the control and cognitive-fatigue conditions: t(71) = 5.14, p < 0.001. Second, I find a significant difference between the self-reported hunger during the auxiliary survey [µ = 6.80, SD= 2.00] and after the tasting activity [µ = 4.93, SD= 2.67] for those under the hunger and interaction conditions: t(68) = 5.95, p < 0.001.14 The fasting requirement combined with the nutritional-shake tasting activity resulted in a successful manipulation of hunger. Therefore, hereafter, I will refer to subjects that complied with the fasting requirements and completed the tasting activity after the CETs as subjects that received the hunger treatment. B.

Sample

Table II summarizes subjects characteristics measured using the demographic questionnaire, auxiliary survey, filler tasks, and experimental questions. A total of 160 subjects participated in the experiments, out of which 143 complied with the fasting requirement. Column (1) shows that compliers, the group of interest, earned an average experimental compensation of $25.2. Overall, 46.2% are male, their average age is 20.7 years, 46.2% declared English as Second Language (ESL), 30.8% work, and 70.6% have a credit card. In average, subjects can correctly answer 4.5 [out of 5] numeracy questions, and 1.2 [out of 2] IQ questions. During the 10 arithmetical rounds, each in which they were given four 3-digit addition problems, they were able to solve in average 2.5 problems correctly in 40.2 seconds, and they spend an average of 10.1 seconds in each of the 55 decision rounds. 14 Two

out of 79 subjects in hunger and interaction conditions did not report their hunger level after

the tasting activity.

DRAFT

HUNGER GAMES

17

Table III summarizes the same characteristics as Table II for each of the cells resulting from the 2x2-factorial design described in the previous section. Notice that I also implemented a low-dose condition by using a nutritional shake with 23g of protein, instead of 35g as in the control condition. The objective was to compare subject responses at different protein dose levels (i.e. dose-response). Out of the 143 compliers: 29 are under the control condition, 12 are under to the low-dose condition, 31 are under the cognitive-fatigue condition, 37 are under the hunger condition, and 34 are under the interaction condition.15 IV.

Results16

This section presents the results of the previously outlined 2x2-factorial experiment, to assess the hunger (fasting or treatment 1 and cognitive fatigue (solving timed-arithmetical problems or treatment 2) and on time preferences (choices between earlier and/or later monetary rewards). The results are presented using 2 different approaches. First, I take a nonparametrical approach, which provides a broad view of the treatment and interaction effects. Second, I use Andreoni and Sprenger (2012)’s CTB methodology to estimate both aggregate-level and individual-level time preference parameters (discounting, present bias, and utility curvature) by condition. A.

Non-parametrical Analysis

In Figure III I plot the mean number of tokens cashed earlier against the gross interest rate, (1 + r).17 I plot separate points for each condition and separate 15 Due

to limited resources, I only collected data for 12 subjects under the low-protein control con-

dition. While this is not sufficient to precisely estimate dose-response effects it allows me to explore the relationship between the protein dose and subjects’ experimental responses, which is discussed in Appendix C. 16 As noted in the previous section, I will only include the 131 subjects under the four main conditions in this section. A brief analysis of the results for subjects under the low-dose condition and non-compliers is presented in Appendix C. 17 For budgets with more than one (v , v t t+k )-combination I report the average.

18

DRAFT

graphs by both the immediacy of the earlier date in days, immediate (t = 0) and non-immediate (t > 0), and the delay between the earlier and the later date in days (k = 35, 70, 98). The number of tokens cashed earlier by subjects under the hunger condition, versus the number of tokens cashed earlier by subjects under the control condition, seems to be persistently higher; particularly when the earlier date is immediate. This can pose as potential evidence for present bias or hyperbolic discounting. Interestingly, the number of tokens cashed earlier by subjects under the cognitive-fatigue condition does not decline monotonically with the interest rate.18 Figure IV graphs the mean tokens cashed earlier for non-compliers and each of the conditions by the delay of the earlier date.19 In order to have a comparable set of choices across immediacy of the earlier date (t) and delay between earlier and later date (k), I only included the balanced combination of convex budgets from Table I (i.e. (1 + r)-budgets in all nine (t, k)-choice sets), however estimates do not significantly change if all choices are included. The means are also presented in Table IV. Monetary Impatience — Let’s define monetary impatience as the desire to cash a monetary reward earlier even if waiting to cash the reward would result in a significant monetary gain (i.e. the monetary reward earns interests). At the aggregate level and independent of the immediacy of the earlier date (t = 0, 7, 35), we find that subjects under the control condition cashed 36.81 [SE = 5.057] earlier tokens in average. Consistent with predictions, subjects under the cognitivefatigue [µF = 50.41, SE = 5.560] and hunger [µH = 50.31, SE = 3.956] conditions cash significantly more tokens earlier (p = 0.073 and p = 0.038, respectively). Subjects under the interaction condition [µI = 33.53, SE= 4.241] (i.e. those that 18 Andreoni

and Sprenger (2012) find that the number of tokens cashed earlier decline monotonically

with the interest rate, increases with delay, and are not significantly higher when the earlier date is immediate, versus non-immediate. 19 Means and standard errors were generated from regressions of the tokens cashed earlier on condition status, with standard errors clustered at the individual level.

DRAFT

HUNGER GAMES

19

received both the cognitive-fatigue and hunger treatment), seem to cash slightly less tokens earlier (p = 0.620). Present Bias — As I discussed in Section I, an individual displays presentbiased preferences if, relative to immediate outcomes, she/he disproportionately discounts non-immediate outcomes. In Figure IV and Table IV, I contrast the effects including only choices with immediate earlier dates (t = 0) against the effects including only choices with non-immediate earlier dates (t > 0). This can provide a non-parametric measure of present bias for each of the treatment and control conditions. In comparison, I find that the effect on tokens cashed earlier is significantly larger if the earlier date was immediate, than if the earlier date was non-immediate, only for subjects under the hunger [µHt=0 − µHt>0 = 5.07, p < 0.05] and interaction [µIt=0 − µIt>0 = 5.68, p < 0.01] condition. Corner Effects — These non-parametrical aggregate results, by nature, lack individual heterogeneity details. Overall less than 26.0% of subjects (34 out of 131) have no interior choices in all of their chosen budgets, which is consistent with linear preferences. However, as seen in Figure V, almost twice as many subjects (38.7%) have no interior choices under the cognitive-fatigue condition, compare to the control (20.7%). This is not the case under the hunger (13.5%) and the interaction condition (17.6%). Additionally, Figure VI plots the overall percent of corner and interior solutions by condition. Choices in which all tokens were cashed earlier are labeled impatient, choices in which all tokens were cashed later are labeled patient and choices in which some tokens were cashed earlier and some tokens were cashed later are labeled interior. Table V estimates the respective decrease/increase on patient and impatient choices by treatments and interaction or “corner effects”. One can see that, in contrast with the average percentage of impatient (23.3%) and patient (47.0%) choices made by subjects under the control condition, subjects under the cognitive-fatigue condition make significantly more impatient choices (Coef = 16.9%, p < 0.05) but do not make significantly less patient choices (i.e.

20

DRAFT

choose more corner solutions); while subjects under the hunger condition do not make significantly more impatient choices but do make significantly less patient choices (Coef = −19.0%, p < 0.05).

20-cent Heuristic — While insignificant, the most puzzling result is that subjects under the interaction condition (i.e. those that receive both the cognitive-fatigue and hunger treatment), seem to cash slightly less tokens earlier than those under the control condition. A potential explanation for this result is that subjects under the interaction condition may be using a 20-cent heuristic to simplify the decision problem. Since 37 out of 55 convex budgets the value of tokens cashed on later dates is 20 cents, this would make subjects appear more patient or sensitive to the cost of early income. In fact, notice that while not significant, only the interaction of both treatments has a positive effect on patient choices (Table V).

In summary, hunger and cognitive fatigue increase monetary impatience. Hunger has a significantly larger effect when choices involve immediate monetary rewards, which suggest that hunger activates present bias. Cognitive-fatigue appears to increase corner solutions, particularly shifting interior allocations towards all-earlier token allocations. While corner solutions can be decisions that any rational agent could make every time, they could also represent heuristics or rules-of-thumb use by individuals to simplify the decision problem. Since the gross interest rate offered in the experimental choices is unlikely to be lower than that of their outside options, the shift towards all-earlier corner allocations suggests that cognitive fatigue may be decreasing attention and increasing heuristic-based choices. In fact, while insignificant, only subjects under the cognitive-fatigue condition seem to spend less time in average completing each decisions task than subjects under the control condition (see III). Overall, these results suggest that hunger and cognitive fatigue affect time preferences through different mechanisms, which we will further explore in the following section.

DRAFT

HUNGER GAMES

B.

21

Parametrical Analysis

Following Andreoni and Sprenger’s (2012) CTB methodology, I estimate the time preference parameters for subjects under control and each of the treatment (cognitive-fatigue and hunger) and interaction conditions. First, I provide a brief summary of CTB methodology and my estimation strategy. Then, I estimate the parameters jointly by condition, clustering the standard errors at the individual level, and report the p-values for the null hypothesis of equality between the control and each of the treatment and interaction conditions. Lastly, I estimate the parameters for each individual, report and plot the estimated parameters by conditions, and test for distributional differences between the control and each of the treatment and interaction conditions using a two-sample Wilcoxon-MannWhitney test.

Methodology

I assume individuals have a time separable CRRA utility function with (β-δ)parameters (Laibson, 1997; O’Donoghue and Rabin, 1999): (2)

U (ct , ct+k ) =

1 1 α ct + βδ k cαt+k , α α

where δ is the discount factor; β is the present bias parameter; ct and ct+k represent the experimental earnings at t and t+k, respectively; and α is the CRRA curvature parameter, which represents the intertemporal elasticity of substitution. This form captures the present-biased time preferences, when β < 1; but can also be reduced to exponential discounting, when β = 1. Maximizing Equation B2 subject to the future value Equation 1 yields to the tangency condition

(3)

ct ct+k

=

  (βδ k (1 + r))  (δ k (1 + r))

1 α−1

1 α−1





if t = 0 , if t > 0

22

DRAFT

and the demand for tokens cashed earlier

(4)

ct =

            

m(βδ k (1 + r)) 1 + (1 +

r)(βδ k (1

m(δ k (1 1 + (1 +

+ r))

r)(δ k (1

1 α−1

+ r)) 

 1 α−1



if t = 0 .

1 α−1

1 α−1

+ r))

if t > 0



Now, following Andreoni and Sprenger (2012)’s approach, I can use non-linear least squares (NLS) to estimate the time preference parameters by condition. Which yields to the structural regression equation (5) " ct =

τ δ k (1 m(βC C

1 + (1 + "

+ r))

τ δ k (1 r)(βC C

1 αC −1

+ r))

τ δ k (1 + r)) m(βH H

 1 αC −1

1 αH −1

τ δ k (1 + r)) 1 + (1 + r)(βH H

#

 ·C+



#

1 αH −1

"

 ·H+

m(βFτ δFk (1

+ r))

1 αF −1

r)(βFτ δFk (1

 1 αF −1

1 + (1 + + r))  " 1 k τ αI −1 m(βI δI (1 + r)) 1 + (1 + r)(βIτ δIk (1 + r))

#

1 αI −1

 · F+ #

 · I + ,

where τ is an indicator for whether or not the earlier date is immediate (i.e. τ = 1 if t = 0 and τ = 0 otherwise) and

C, F, H, and I are indicators for the control,

cognitive-fatigue, hunger, interaction conditions, respectively.

Aggregate Estimates

As mentioned before, the richness of the CTB methodology allows me to estimate time preference parameters (discounting, present bias, and utility curvature) since experimental allocations are identify as solutions to standard intertemporal optimization problems. Table VI presents the aggregate-level time preference parameters by condition and F-statistic and p-value corresponding to the null hypothesis of equality between the aggregate parameter estimated for subjects under the control condition

DRAFT

HUNGER GAMES

23

and each of the treatment and interaction conditions.20 Present Bias — I do not find evidence of present bias for subjects under the control [βˆC = 1.001, SE = 0.011] and cognitive-fatigue [βˆF = 0.993, SE = 0.025] conditions (i.e. the hypothesis of no present bias or β = 1 cannot be rejected for the control (F1,28 =0.01, p = 0.921) nor the cognitive-fatigue (F1,30 = 0.08, p = 0.781) conditions). Nevertheless, for subjects under the hunger [βˆH = 0.952, SE = 0.025] and interaction [βˆI = 0.974, SE = 0.011] conditions, β is estimated significantly below 1 and the hypothesis of no present bias is rejected (F1,36 = 11.07,p < 0.001 and F1,33 = 5.48,p = 0.019, respectively). Consistent with predictions, and the non-parametrical analysis presented in the previous subsection, hunger appears to disproportionately increase monetary impatience when monetary rewards are immediate; which is reflected on significantly lower estimates of β for subjects under the hunger (F1,65 = 7.23,p = 0.007) and interaction (F1,62 = 2.95, p = 0.086) conditions, relative to subjects under the control condition. CRRA Utility Curvature (or intertemporal elasticity of substitution) — While the aggregate curvature is estimated to be significantly different than 1, in favor of non-linear utility, for all conditions [αC = 0.867 (SE = 0.021), αF = 0.806 (SE = 0.024), αH = 0. (SE = 0.017), αI =, (SE = 0.013)], only subjects under the cognitive-fatigue condition display a marginally significant higher degree of curvature than those under the control condition (F1,59 = 3.71, p = 0.054). In other words, subjects under the cognitive-fatigue condition appear to be less responsive to the cost of early income. However, one must be careful when interpreting these results since one would expect more corner solutions to deliver a lower degree of curvature. Annual Discount Rate — The annual interest rate for subjects under the 20 The

analogous specification is presented in Andreoni and Sprenger (2012)’s column (3) of Table 2.

The aggregate parameter estimates under all the model specifications used and functional forms assumed by Andreoni and Sprenger (2012) are reported in Appendix B.

24

DRAFT

cognitive-fatigue and hunger condition are estimated at 164.6 (SE = 0.589) and 148.0% (SE = 33.8%), respectively. Nevertheless, only the annual interest rate for subjects under the hunger condition is marginally significantly higher than the annual interest rate for subjects under the control condition. This which is estimated at 73.0% (SE = 29.9%): F1,65 = 3.37, p = 0.067. Interestingly the annual interest rate for subjects under the interaction condition is estimated at 60.7% (SE = 0.164), which is lower, but not significantly different than the annual interest rate for subjects under the control condition: F1,59 = 0.19, p = 0.661. The latter may be due to subjects under the interaction condition using a 20-cent heuristic, as mentioned in the non-parametrical analysis, which given the parameters used in the experiment makes them seem very sensitive the cost of early income. Overall, the annual interest rates seem to be less precisely estimated than the annual interest rate estimated by Andreoni and Sprenger (2012).21 This may be due to noise added by the introduction of the randomization of both the ordering of the questions and the slider starting point in the application.

It is worth highlighting that the aggregate estimates for the present-bias and curvature parameters for subjects under the control condition are very close in magnitude to those obtained by Andreoni and Sprenger (2012); which was expected since subjects in their sample received neither the cognitive-fatigue nor the hunger treatment.22 This provides additional evidence for the validity and consistency of the CTB methodology. Individual Estimates

Table VII summarizes the individual parameter estimates by condition. Due to lack of choice variation, it was not possible to estimate parameters for 3 subjects under the control condition, 2 subjects under the cognitive-fatigue condition, and 21 They 22 They

estimate the annual interest rate at 37.1% [SE = 0.091]. estimate βˆ at 1.007 [SE = 0.006] and α ˆ at 0.897 [SE = 0.009].

DRAFT

HUNGER GAMES

25

2 subjects under the interaction condition (in total 7 out of the 131 subjects under all four main conditions).23 Also, parameter estimates for some subjects result in extreme outliers due to the limited number of observations per subject. Therefore, I trim the parameters at the 5th and 95th percentiles losing 12 more observations for each parameter. Comparing the aggregate estimates to the median of the 114 remaining individual estimates by condition I find that: a) the annual interest rate is slightly higher for all conditions, but the relationship between conditions is sustained; b) the present bias parameter (β) is virtually the same for all conditions; and c) the CRRA curvature parameter (α) is estimated much closer to 1 for all conditions, and the difference between subjects under the control and the cognitive-fatigue fatigue condition is not as pronounced for the median individual estimates as it was for the aggregate estimates. Figure VII, Figure VIII, and Figure IX plot the kernel density estimates for individual annual interest rate, present bias parameter, and CRRA curvature parameter, respectively. The two-sample Wilcoxon-Mann-Whitney test for equality of distribution between the control and each of the treatment and interaction conditions suggest that: - First, consistent with the non-parametrical and aggregate results, only subjects under the hunger condition have a statistically significant different underlying distribution of the annual interest rate than subjects under the control condition (z = −1.91, p = 0.057), with the subjects under the hunger condition having the higher rank-sum. - Second, also consistent with the non-parametrical and aggregate results, subjects under both the hunger and the interaction condition have statistically significant different underlying distributions of the present bias parameter than subjects under the control condition (z = 2.37, p = 0.018 and z = 1.88, p = 0.061, respectively), with subjects under the control condition 23 Andreoni

and Sprenger (2012) are also unable to estimate parameters for 10 out of 97 subjects.

26

DRAFT

having the higher rank-sum in both cases. - Lastly, in contrast with the aggregate results, I do not find evidence of statistically significant differences between the underlying distribution of the CRRA curvature parameter for the subjects under the control condition and subjects under any of treatment and interaction conditions. This is not surprising since, as expected, individuals with less interior solutions have less utility function curvature.24 V.

Conclusion

In summary, hunger and cognitive fatigue increase monetary impatience and affect time preferences. However, the results suggest that they affect time preferences through different mechanisms, which can help explain the conflicting results from the interaction condition. On the one hand, the hunger effect seems to be concentrated in the present bias parameter (β) and is driven by disproportionately exacerbating impatience on immediate versus non-immediate monetary rewards. In other words, hunger increases monetary impatience and the effect is larger when earlier rewards are immediate. This effect is statistically significant and consistent independent of the approach and/or aggregation level. Furthermore, this is consistent with the initial proposition that hunger may affect economic decisions because it is associated with activation of brain areas that are disproportionately activated when immediate rewards are available. On the other hand, the cognitive-fatigue effect is driven by an increase in allearlier token allocations and overall corner solutions. While subjects under the 24 Tables

D1 to D4 provide the parameter estimates for each individual. It is worth noting that

for some individuals with only corner solutions the CRRA utility curvature parameter (α) ˆ is estimated bellow 0.999. When plotting the demand for tokens for each of these individuals one can see that those with α ˆ <0.999 seem to display a certain level of choice inconsistency. This suggests that some issues may arise when using CTB to test cognitive-state level effects on time preferences.

DRAFT

HUNGER GAMES

27

cognitive-fatigue condition display a lower sensitivity to high prices (α decreases) the effect seems to be only marginally statistically significant at the aggregate level and fades when looking at individual level parameters. However, since the gross interest rate offered to subjects is unlikely to be lower than that of their outside options, the shift towards all-earlier corner allocations suggests that cognitive fatigue may be decreasing attention and increasing heuristic-based choices. Nevertheless, these results are not conclusive and more work is needed to test this and alternative hypotheses. Perhaps a better approach to study the effects of cognitive fatigue on decision making would be to test for utility maximization consistency a la Choi et al. (2014). In fact, Castillo, Dickinson and Petrie (2014) use this methodology to study the effect of sleepiness on risk preferences. Finally, this study contributes to the field of behavioral economics by proving hunger activates present bias. These results also open the door to a new research agenda that could help explain why low-income individuals with lower quality physical and emotional health tend to make more shortsighted economic decisions, perpetuating behavioral poverty-traps. The goals of this research agenda should include exploring the relationship between hunger and risk preferences (e.g. risk/loss aversion, certainty effect) as well as hunger and social preferences (e.g. altruism, cooperation), addressed by Ashton and Nebout (2015) and Ashton (2015) respectively. A natural extension would be to test whether hunger activates present bias over non-monetary domains (e.g. consumption of non-hunger related goods, effort). Additionally, it is of interest to identify the mechanisms through which hunger affects decisions, particularly mapping the link between hunger, brain activity and economic decision-making.

28

DRAFT

Control    

Cogni*ve-­‐fa*gue  

Hunger  

Interac*on  

Informed  Consent  

Tas*ng  Ac*vity  and  Filler  Tasks  

Decision  Task  Rounds  

Arithme*cal  Task  Rounds  

Arithme*cal  Task  Rounds  

Decision  Task  Rounds  

Demographic  Ques*onnaire  and  Auxiliary  Survey  

Decision  Task  Rounds  

Arithme*cal  Task  Rounds  

Arithme*cal  Task  Rounds  

Decision  Task  Rounds  

Demographic  Ques*onnaire  and  Auxiliary  Survey  

Tas*ng  Ac*vity  and  Filler  Tasks  

Figure I. Experimental Design Note: Computer-based experimental tasks (CETs) circled in gray.

Figure II. Laboratory setup and presentation of “blind” drink for tasting activity

Mean Tokens Cashed Earlier

1

1.2

1.4

1.6

1.8

1.2

1.4

1.6

1.8

1

1.2

Interaction

2

Hunger

Gross Interest Rate (1+r)

1

1.4

1.6

1.8

t > 0 days, k = 98 days

Cognitive-fatigue

2

t > 0 days, k = 70 days

t = 0 days, k = 98 days

Control (35g of protein)

t > 0 days, k = 35 days

t = 0 days, k = 70 days

2

HUNGER GAMES

Figure III. Mean Tokens Cashed Earlier by Gross Interest Rate

Graphs by Immediacy of Earlier Payment Date in days (t) and Delay between Earlier and Later Date in days (k)

0

50

100

0

50

100

t = 0 days, k = 35 days

DRAFT 29

30

DRAFT

p=0.015

p=0.073

50

55

p=0.456

p=0.038

50.30

p=0.004

53.69

49.68

48.62

45

50.41

51.87

40 35

Mean Tokens Cash Ealier

60

65

70

p=0.317

p=0.620

37.78

36.81

37.33

36.32

33.53

25

30

31.65

All (t = 0, 7, 35)

Immediate (t = 0)

Non-immediate (t > 0)

Mean Tokens Cash Ealier by Condition and Immediacy of Ealier Date Control (35g of protein)

Cognitive-fatigue

Hunger

Interaction

Figure IV. Mean Tokens Cashed Earlier Notes: All budgets are constrained by 100 tokens (i.e. tokens cash earlier (or at t) + tokens cash later (or at t + k) = 100). Means are generated from regressions of the total number of tokens cashed earlier on condition status, with standard errors clustered at the individual level (see Table IV). The p-values for all choices correspond to the null hypotheses H0 : µcontrol = µother , where other refers to each of the non-control conditions. The p-values for immediate and non-immediate choices correspond to the null hypotheses H0 : µt=0 = µt>0 for each condition. In order to have a comparable set of choices across earlier date delay (t) and delay between earlier and later date (k), I only included the balanced combination of choice sets from Table I (i.e. (1 + r)-choices with all nine (t, k)-combinations), however estimates do not significanly change if all choices are included.

30 10

20

Percent

30 20

Percent

10

0

0

0

0.2

0.4

0.6

0.8

1.0

0

0.2

0.4

0.6

0.8

1.0

Cognitive-fatigue [N=31]

30 20 0

0

10

10

20

Percent

30

40

40

Control (35g of protein) [n=29]

Percent

31

40

HUNGER GAMES

40

DRAFT

0

0.2

0.4

0.6

0.8

1.0

0

0.2

Hunger [N=37]

0.4

0.6

0.8

1.0

Interaction [N=34]

60 40

Percent

0

20

40 20 0

Percent

60

Figure V. Percentage of Subjects by the Share of Corner Solutions Chosen

Earlier

Interior

Later

Earlier

Later

60 40

Percent

0

20

40 20 0

Percent

Interior

Cognitive-fatigue [N=31]

60

Control (35g of protein) [N=29]

Earlier

Interior

Hunger [N=37]

Later

Earlier

Interior

Later

Interaction [N=34]

Figure VI. Percentage of Corner and Interior Solutions by Condition

32

DRAFT

0.40

Kernel Density Estimate

0.20 0.00

0.10

Density

0.30

Control (35g of protein) Cognitive-fatigue Hunger Interaction

0% 100%

500%

1300%

Annual Interest Rate kernel = epanechnikov, bandwidth = 0.4956

Figure VII. Kernel Density of Individual Annual Interest Rate Estimates Note: Parameter trimmed at the 5th and 95th percentile.

8

Kernel Density Estimate Control (35g of protein) Cognitive-fatigue Hunger

4 0

2

Density

6

Interaction

0.60

0.80

1.00

1.20

1.40

Present Bias Parameter kernel = epanechnikov, bandwidth = 0.0222

Figure VIII. Kernel Density of Individual Present Bias Parameter Estimates Note: Parameter trimmed at the 5th and 95th percentile.

DRAFT

HUNGER GAMES

33

3

Control (35g of protein) Cognitive-fatigue Hunger Interaction

0

1

2

Density

4

5

Kernel Density Estimate

0.20

0.40

0.60

0.80

1.00

CRRA Curvature Parameter kernel = epanechnikov, bandwidth = 0.0552

Figure IX. Kernel Density of Individual CRRA Curvature Parameter Estimates Note: Parameter trimmed at the 5th and 95th percentile.

34

DRAFT

Table I—Choice Sets t 0, 0, 0, 0, 0, 0, 0, 0,

7, 7, 7, 7, 7, 7, 7, 7, 7

35 35 35 35 35 35 35 35

k

vt

vt+k

(1 + r)

35, 70, 98 35, 70, 98 35, 70 35, 70, 98 35, 70 98.00 35, 70, 98 98 70

20 19 18 16 14 13 12 10 20

25 20 20 20 20 20 15 20 20

1.25 1.05 1.11 1.25 1.43 1.54 1.25 2.00 1.00

Annual Rate Range 117.82 20.95 69.64 117.82 389.46 305.83 117.82 698.04 0.00

-

575.97 67.41 172.90 575.97 1460.69 305.83 575.97 698.04 0.00

DRAFT

HUNGER GAMES

35

Table II—Summary Statistics (by compliers). Mean VARIABLE Male Age BMI ESL College Year [1-5]a Registered to Vote Bus/Econ/Psych Major STEM Major Work Own a credit card Smoke All-nighter Able to maintain desired weight Exercise regularly Do Not Trust [payment] Special Need Donation Frequency [0-4]b Gambling Frequency [0-4]c Numeracy Score [0-5] IQ Score [0-2] Hours since last meal Hunger level upon arrival [0-10]de Hunger level after CETs [0-10]de Hunger level after tasting [0-10]df Av. Arithmetical Score [0-4] Av. Time Decision [0-45] Av. Time Arithmetical [0-45] Compensation [USD] N

t

p-value

Compliers (1)

Non-compliers (2)

Difference (3)

(4)

(5)

0.462 20.650 22.353 0.462 2.893 0.483 0.273 0.203 0.308 0.706 0.042 0.622 0.678 0.573 0.049 0.154 1.754 0.280 4.510 1.119 9.197 5.818 5.664 4.928 2.533 10.076 40.173 25.164 143

0.294 19.647 21.803 0.412 2.529 0.588 0.235 0.235 0.412 0.647 0.059 0.588 0.765 0.647 0.059 0.118 1.353 0.063 4.647 1.118 1.603 3.176 2.941 2.250 2.541 10.639 39.853 23.347 17

0.167 1.003 0.550 0.050 0.363 -0.106 0.037 -0.032 -0.104 0.059 -0.017 0.034 -0.086 -0.074 -0.010 0.036 0.401 0.217 -0.137 0.001 7.594 2.642 2.723 2.678 -0.008 -0.563 0.320 1.817

1.312 1.281 0.508 0.387 1.211 -0.821 0.327 -0.311 -0.867 0.501 -0.319 0.272 -0.723 -0.579 -0.175 0.393 1.272 1.464 -0.707 0.006 5.861 4.174 3.936 2.760 -0.026 -0.481 0.303 0.989

0.191 0.202 0.613 0.699 0.228 0.413 0.744 0.756 0.387 0.617 0.750 0.786 0.471 0.564 0.861 0.695 0.205 0.145 0.481 0.995 0.000 0.000 0.000 0.007 0.979 0.631 0.762 0.324

a Freshman = 1, Sophomore = 2, Junior = 3, Senior = 4, and Graduate = 5. b Never = 0, Once a year = 1, Once a month = 2, Once a week = 3, and More than once a week = 4. c Never = 0, One hour or at least $10 per year = 1, One hour or at least $10 per month = 2, One hour or at least $10 per week = 3, More than one hour or $10 per week = 4. d Not At All = 0, and Extremely = 10. e Rated during auxiliary survey. f Only subjects completing tasting activity after CETs were asked to rate their hunger level during the filler tasks.

36

DRAFT

Table III—Summary Statistics (by conditions). VARIABLE Male Age BMI ESL College Year [1-5]a Registered to Vote Bus/Econ/Psych Major STEM Major Work Own a credit card Smoke All-nighter Able to maintain desired weight Exercise regularly Do Not Trust [payment] Special Need Donation Frequency [0-4]b Gambling Frequency [0-4]c Numeracy Score [0-5] IQ Score [0-2] Hours since last meal Hunger level upon arrival [0-10]de Hunger level after CETs [0-10]de Hunger level after tasting [0-10]df Av. Arithmetical Score [0-4] Av. Time Decision [0-45] Av. Time Arithmetical [0-45] Experimental [USD] N

Control (1)

Cognitive-fatigue (2)

Hunger (3)

Interaction (4)

Low-dose (5)

0.379 20.966 22.711 0.586 2.897 0.379 0.310 0.172 0.310 0.793 0.000 0.586 0.621 0.483 0.069 0.172 1.414 0.276 4.483 1.103 10.205 5.931 4.310

0.581 21.516 20.981 0.226 3.194 0.613 0.161 0.226 0.290 0.677 0.000 0.677 0.839 0.645 0.032 0.097 1.839 0.161 4.516 1.065 8.326 5.839 4.839 2.442 9.029 41.081 25.209 31

0.412 19.882 22.341 0.471 2.545 0.529 0.235 0.147 0.412 0.676 0.059 0.676 0.559 0.529 0.029 0.147 1.636 0.324 4.471 1.118 8.851 6.265 7.000 4.545 2.438 10.664 40.553 23.220 34

0.500 20.667 22.092 0.667 2.900 0.583 0.083 0.250 0.167 0.750 0.000 0.500 0.667 0.333 0.000 0.167 2.167 0.417 4.333 1.167 9.150 5.750 4.083

2.659 10.224 40.134 25.524 29

0.459 20.378 23.368 0.486 2.946 0.378 0.432 0.243 0.270 0.676 0.108 0.595 0.703 0.703 0.081 0.189 1.919 0.297 4.622 1.162 9.358 5.324 6.703 5.278 2.735 10.646 38.714 27.029 37

2.108 8.999 41.342 23.938 12

a Freshman = 1, Sophomore = 2, Junior = 3, Senior = 4, and Graduate = 5. b Never = 0, Once a year = 1, Once a month = 2, Once a week = 3, and More than once a week = 4. c Never = 0, One hour or at least $10 per year = 1, One hour or at least $10 per month = 2, One hour or at least $10 per week = 3, More than one hour or $10 per week = 4. d Not At All = 0, and Extremely = 10. e Rated during auxiliary survey. f Only subjects completing tasting activity after CETs were asked to rate their hunger level during the filler tasks.

DRAFT

HUNGER GAMES

37

Tokens Cashed Earlier

H0 : µC = µO={F,H,I}

CONDITION

Mean (1)

Robust-SE (2)

F -statistic (3)

p-value (4)

All (t = 0, 7, 35)

C: F: H: I:

36.811 50.413 50.305 33.533

5.057 5.560 3.956 4.241

. 3.27 4.42 0.25

. 0.073 0.038 0.620

Immediate (t = 0)

Table IV—Mean Tokens Cashed Earlier by Condition and Immediacy of Earlier Date

C: F: H: I:

5.176 5.940 4.296 4.971

. 3.20 5.60 0.00

. 0.076 0.020 0.950

5.064 5.609 3.904 3.972

. 3.12 3.67 0.53

0.080 0.058 0.469

Non-immediate (t > 0)

Earlier Date

Control (35g of protein) Cognitive-fatigue Hunger Interaction Observations R-squared Clusters

Control (35g of protein) Cognitive-fatigue Hunger Interaction Observations R-squared Clusters

C: F: H: I:

Control (35g of protein) Cognitive-fatigue Hunger Interaction Observations R-squared Clusters

6934 0.50 131

37.781 51.869 53.687 37.329 2310 0.52 131

36.323 49.682 48.621 31.650 4624 0.50 131

Notes: Robust standard errors clustered at the individual level. Estimates are inmune to demographic control (e.g. gender, age), survey controls (e.g. order), time-of-the-day fixed effects, and/or date fixed effects.

38

DRAFT

Table V—Corner Effects Share of Corner Solutions VARIABLES Cognitive-fatigue Effect Hunger Effect Interaction Effect Constant: Control (35g of protein)

Patient (1)

Impatient (2)

0.169** (0.069) 0.074 (0.061) 0.007 (0.059) 0.233*** (0.046)

-0.062 (0.089) -0.190** (0.078) 0.032 (0.082) 0.470*** (0.064)

7064 0.02

7064 0.03

Observations R-squared

Notes: Robust standard errors, in parenthesis, clustered at the individual level. *** p<0.01, ** p<0.05, * p<0.1.

Table VI—Aggregate Parameter Estimates by Condition Aggregate CONDITION

Parameter (1)

H0 : ParameterC =ParameterO={F,H,I}

Robust-SE (2)

F -statistic (3)

p-value (4)

Annual discount rate C: Control (35g of protein) F: Cognitive-fatigue H: Hunger I: Interaction

0.730 1.646 1.480 0.607

0.229 0.589 0.338 0.164

. 2.10 3.37 0.19

. 0.147 0.067 0.661

Present bias: βˆ C: Control (35g of protein) F: Cognitive-fatigue H: Hunger I: Interaction

1.001 0.993 0.952††† 0.974††

0.011 0.025 0.014 0.011

. 0.09 7.23 2.95

. 0.769 0.007 0.086

CRRA curvature: α ˆ C. Control (35g of protein) F. Cognitive-fatigue H. Hunger I. Interaction

0.867‡‡‡ 0.806‡‡‡ 0.844‡‡‡ 0.891‡‡‡

0.021 0.024 0.017 0.013

. 3.71 0.72 0.96

. 0.054 0.397 0.327

Observations R-squared Clusters

7064 0.59 131

Notes: Robust standard errors clustered at the individual level. ††† p<0.01, †† p<0.05, † p<0.1 for null hypothesis of no present bias (i.e. H0 : β = 1). ‡‡‡ p<0.01, ‡‡ p<0.05, ‡ p<0.1 for null hypothesis of linear utility (i.e. H0 : α = 1).

DRAFT

HUNGER GAMES

39

Table VII—Individual Parameter Estimates by Condition CONDITION

N

Median

5th Percentile

95th Percentile

Min

Max

Annual discount rate C: Control (35g of protein) F. Cognitive-fatigue H: Hunger I: Interaction

26 26 32 28

0.800 1.315 1.803 0.728

0.112 0.116 -0.057 0.117

7.501 11.953 8.697 4.081

-0.589 0.114 -0.083 -0.044

11.005 13.547 10.27 5.946

Present bias: βˆ C: Control (35g of protein) F. Cognitive-fatigue H: Hunger I: Interaction

26 27 33 26

1.001 1.001 0.959 0.980

0.915 0.816 0.795 0.801

1.106 1.192 1.145 1.063

0.818 0.775 0.783 0.741

1.241 1.23 1.163 1.098

CRRA curvature: α ˆ C: Control (35g of protein) F. Cognitive-fatigue H: Hunger I: Interaction

24 28 32 28

0.941 0.930 0.905 0.943

0.658 0.766 0.762 0.673

0.999 0.999 0.999 0.999

0.308 0.378 0.667 0.283

0.999 0.999 0.999 0.999

Notes: Due to lack of choice variation, it was not possible to estimate parameters for 3 subjects under the control condition, 2 subjects under the cognitive-fatigue condition, and 2 subjects under the interaction condition (in total 7 out of the 131 subjects under all four main conditions). Parameter estimates for some subjects result in extreme outliers due to the limited number of observations per subject, therefore parameters were trim at the 5th and 95th percentiles loosing 12 more observations for each parameter.

40

DRAFT

REFERENCES

Andreoni, James, and Charles Sprenger. 2012. “Estimating Time Preferences from Convex Budgets.” American Economic Review, 102(7): 3333–3356. Ashton, Lydia. 2014. “The Effect of Cognitive Biases and Visceral Factors on Economics Decisions.” PhD diss. University of California, Berkeley. Ashton, Lydia. 2015. “Hunger and Social Preferences?” Working Paper. Ashton, Lydia, and Antoine Nebout. 2015. “The Risk of Hunger: Do Hunger Affects Risk Preferences?” Working Paper. Astrup, Arne. 2005. “The satiating power of protein—a key to obesity prevention?” The American Journal of Clinical Nutrition, 82(1): 1–2. Ausubel, Lawrence. 1991. “The Failure of Competition in the Credit Card Market.” The American Economic Review, 81(1): 50–81. Banerjee, Abhijit, and Sendhil Mullainathan. 2007. “Climbing Out of Poverty: Long Term Decisions under Income Stress.” Bertenshaw, Emma, Anne Lluch, and Martin Yeomans. 2008. “Satiating effects of protein but not carbohydrate consumed in a between-meal beverage context.” Physiology & Behavior, 93(3): 427–436. Camerer, Colin, George Loewenstein, and Drazen Prelec. 2005. “Neuroeconomics: How Neuroscience Can Inform Economics.” Journal of Economic Literature, 43(1): 9–64. Castillo, Marco, David L. Dickinson, and Ragan Petrie. 2014. “Sleepiness, Choice Consistency, and Risk Preferences.” Working Paper. Chetty, Raj, Adam Looney, and Kory Kroft. 2009. “Salience and Taxation: Theory and Evidence.” American Economic Review, 99(4): 1145–1177.

DRAFT

HUNGER GAMES

41

Choi, Syngjoo, Shachar Kariv, Wieland Mller, and Dan Silverman. 2014. “Who Is (More) Rational?” American Economic Review, 104(6): 1518– 50. Cornelisse, Sandra, Vanessa Van Ast, Johannes Haushofer, Maayke Seinstra, and Marian Joels. 2013. “Time-dependent effect of hydrocortisone administration on intertemporal choice.” Danziger, Shai, Jonathan Levav, and Liora Avnaim-Pesso. 2011. “Extraneous factors in judicial decisions.” Proceedings of the National Academy of Sciences, 108(17): 6889–6892. DellaVigna, Stefano. 2009. “Psychology and Economics: Evidence from the Field.” Journal of Economic Literature, 47(2): 315–372. Dickinson, David, Todd McElroy, and Nathan Stroh. 2014. “Impact of glucose on Bayesian versus heuristic-based decision making.” Journal of Neuroscience, Psychology, and Economics, 7: 237–247. Hastings, Justine, and Lydia Tejeda-Ashton. 2008. “Financial Literacy, Information, and Demand Elasticity: Survey and Experimental Evidence from Mexico.” NBER - Working Papers. Haushofer, Johannes, and Ernst Fehr. 2014. “On the psychology of poverty.” Science, 344(6186): 862–867. Hinton, Elanor, John Parkinson, Anthony Holland, Sergio Arana, Angela Roberts, and Adrian Owen. 2004. “Neural contributions to the motivational control of appetite in humans.” European Journal of Neuroscience, 20(5): 1411–1418. Kandasamy, Narayanan, Ben Hardy, Lionel Page, Markus Schaffner, Johann Graggaber, Andrew S Powlson, Paul C Fletcher, Mark Gurnell, and John Coates. 2014. “Cortisol shifts financial risk preferences.” Proceedings of the National Academy of Sciences, 111(9): 3608–3613.

42

DRAFT

Kuhn, Michael, Peter Kuhn, and Marie Claire Villeval. 2014. “Self control and intertemporal choice: Evidence from glucose and depletion interventions.” Working Paper. Laibson, David. 1997. “Golden Eggs and Hyperbolic Discounting.” The Quarterly Journal of Economics, 112(2): 443–478. Lerner, Jennifer S, Ye Li, and Elke U Weber. 2012. “The financial costs of sadness.” Psychological science. Li, Jie, Ran An, Yanping Zhang, Xiaoling Li, and Shuran Wang. 2012. “Correlations of macronutrient-induced functional magnetic resonance imaging signal changes in human brain and gut hormone responses.” The American Journal of Clinical Nutrition, 96(2): 275–282. Loewenstein, George. 1996. “Out of Control: Visceral Influences on Behavior.” Organizational Behavior and Human Decision Processes, 65(3): 272–292. Loewenstein, George, Daniel Nagin, and Raymond Paternoster. 1997. “The Effect of Sexual Arousal on Expectations of Sexual Forcefulness.” Journal of Research in Crime and Delinquency, 34(4): 443–473. McClure, Samuel, George Loewenstein, Jonathan Cohen, and David Laibson. 2004. “Separate Neural Systems Value Immediate and Delayed Monetary Rewards.” Science, 306(5695): 503–507. O’Donoghue, Ted, and Matthew Rabin. 1999. “Doing It Now or Later.” American Economic Review, 89(1): 103–124. Padoa-Schioppa, Camillo, and John Assad. 2006. “Neurons in the orbitofrontal cortex encode economic value.” Nature, 441(7090): 223–226. Porcelli, Anthony J, and Mauricio R Delgado. 2009. “Acute stress modulates risk taking in financial decision making.” Psychological Science, 20(3): 278–283.

DRAFT

HUNGER GAMES

43

Read, Daniel, and Barbara van Leeuwen. 1998. “Predicting Hunger: The Effects of Appetite and Delay on Choice.” Organizational Behavior and Human Decision Processes, 76(2): 189–205. Rolls, Barbara, Marion Hetherington, and Victoria Burley. 1988. “The specificity of satiety: The influence of foods of different macronutrient content on the development of satiety.” Physiology & Behavior, 43(2): 145–153. Rolls, Edmund T. 1999. “The functions of the orbitofrontal cortex.” Neurocase, 5(4): 301–312. Rolls, Edmund T, and Fabian Grabenhorst. 2008. “The orbitofrontal cortex and beyond: From affect to decision-making.” Progress in Neurobiology, 86(3): 216–244. Schofield, Heather. 2013. “The Economic Costs of Low Caloric Intake: Evidence from India.” Working Paper. Tataranni, Antonio, Jean-Fran¸ cois Gautier, Kewei Chen, Anne Uecker, Daniel Bandy, Arline Salbe, Richard Pratley, Michael Lawson, Eric Reiman, and Eric Ravussin. 1999. “Neuroanatomical correlates of hunger and satiation in humans using positron emission tomography.” Proceedings of the National Academy of Sciences, 96(8): 4569–4574. Thaler, Richard H. 1991. “Some Empirical Evidence on Dynamic Inconsistency.” Quasi rational economics, 1: 127–136. Van Boven, Leaf, and George Loewenstein. 2003. “Social Projection of Transient Drive States.” Personality and Social Psychology Bulletin, 29(9): 1159–1168. Wallis, Jonathan. 2007. “Orbitofrontal Cortex and Its Contribution to Decision-Making.” Annual Review of Neuroscience, 30(1): 31–56.

44

DRAFT

Weigle, David, Patricia Breen, Colleen Matthys, Holly Callahan, Kaatje Meeuws, Verna Burden, and Jonathan Purnell. 2005. “A highprotein diet induces sustained reductions in appetite, ad libitum caloric intake, and body weight despite compensatory changes in diurnal plasma leptin and ghrelin concentrations.” The American Journal of Clinical Nutrition, 82(1): 41– 48.

DRAFT

HUNGER GAMES

45

APPENDICES FOR ONLINE PUBLICATION A. Server-based Application

Consent Form My name is Lydia Ashton; I am a graduate student researcher in the Agricultural and Resource Economics department. My advisor is Professor Sofia Villas-Boas in the Department of Agricultural and Resource Economics. I would like to invite you to take part in my study, which examines how people make decisions and will be conducted at the Experimental Social Science Lab (aka Xlab) at the University of California at Berkeley. at the University of California at Berkeley. If you agree to take part, you will be asked to complete some questionnaires. The total time expected for completion of these activities should be about 60 to 90 minutes.. During the study, we may ask you to complete different tasks (e.g. arithmetical problems, economic decisions, food/drink tasting activity). We will also ask you to answer a survey with some demographic questions. There are no direct benefits to you from this research. It is our hope that the research will benefit the scientific community and lead to a greater understanding of how individuals make decisions. There is little risk to you from taking part in this research. As with all research, there is a chance that confidentiality could be compromised; however, we are taking precautions to minimize this risk. Your study data will be handled as confidentially as possible. The data will be stored in a password-protected computer in a secured location. Each person will have his/her own (anonymous) code number. Your name and other identifying information about you will not be used in the research. The information collected for payment and administrative purposes (name, student id, e-mail) will be kept in a separate password-protected location and the records linking your personal information to your code number will be destroyed after all payments are processed. We will save data, using the anonymous code number, for use in future research done by others or myself but this data will not be linked to your personal information. The total compensation you will receive will vary, depending on your experimental decisions/responses. The average compensation will be approximately $15/hr with a minimum of $10. We will send your compensation by Paypal today and/or in a future date (this will be determined by your responses through the survey). Although you may refuse to answer some question(s), you will not receive payment if you do not complete the study. Please understand that your participation in this study is completely voluntary. You are free to decline to take part in the project. You can decline to answer any questions and are free to stop taking part in the project at any time. Whether or not you choose to participate in the research and whether or not you choose to answer a question or continue participating in the project, there will be no penalty to you or loss of benefits to which you are otherwise entitled. If you have any questions about the research, you may telephone me at (510) 394-XXXX or contact me by e-mail at [email protected] You may also contact my advisor, Sofia Villas-Boas at (510) 643-XXXX/[email protected] If you have any question regarding your treatment or rights as a participant in this research project, please contact the University of California at Berkeley’s, Committee for Protection of Human Subjects at (510) 642-XXXX, [email protected] If you agree to participate, please check the box below. [] I certify that I am 18 years old or older, I have read the consent form, I do not have any food allergies or sensitivities, and I have not been diagnose with diabetes or hyperglycemia, and agree to take part in this research.

46

DRAFT

Figure A1. Screenshot of Instructions

Figure A2. Screenshot of Arithmetical Round

DRAFT

HUNGER GAMES

Figure A3. Screenshot of Decision Round (before decision)

Figure A4. Screenshot of Decision Round (during/after decision)

47

48

DRAFT

Figure A5. Screenshot of Tasting Activity Instructions

Figure A6. Screenshot of First Experimental Earnings Report

Figure A7. Screenshot of Last Experimental Earnings Report

DRAFT

HUNGER GAMES

49

B. Robustness Checks

In this appendix, I present a summarized version of extensive methodology used byAndreoni and Sprenger (2012) to etimate the aggregate-level parameters and present the corresponding estimates. In CTB, subjects choose a combination of ct and ct+k continously along the convex budget set (B1)

(1 + r)ct + ct+k = m,

where ct and ct+k represent the experimental earnings at an earlier and a later date, respectively. The experimental earnings are determined by choosing how many tokens of a total allocation of 100 tokens, they want cash on an earlier and/or a later payment date. The value of each token depends on which date the token is cash, and tokens cash on later dates generally have larger values. The choice sets used in the present study were chosen to resemble those used by Andreoni and Sprenger (2012), nevertheless the application design allows for better control of order effects and anchoring effects, since it presents each choice set as an independent round and facilitates the randomization of the order of all choices for each subject and well as randomly resetting the default allocation point for each round.25 First, a time separable CRRA utility function with (β-δ)-parameters is used, (B2)

U (ct , ct+k ) =

1 (ct − γ1 )α + β(ct+k − γ2 )α , α

where δ is the discount factor; β is the present bias parameter; ct and ct+k represent the experimental earnings at t and t + k, respectively; α is the CRRA curvature parameter; and γ1 and γ2 represent the Stone-Geary background consumption parameters. This form captures the present-biased time preferences, when β < 1; but can also be reduced to exponential discounting, when β = 1. Maximizing Equation B2 subject to the future value Equation B1 yields to the tangency condition   1 (βδ k (1 + r)) α−1 if t = 0 ct − γ1  (B3) = , 1 ct+k − γ2 (δ k (1 + r)) α−1 if t > 0

25 Figure

made.

A4 and Figure A3 provide a screenshot of the decision rounds before and after a choice is

50

DRAFT

and the intertemporal formulation of a Stone-Geary linear demand for ct , (B4)   # # " " 1 k (1 + r)) α−1  ((m − γ )βδ γ  2 1   +   if t = 0  1 1  1 + (1 + r)(βδ k (1 + r)) α−1 1 + (1 + r)(βδ k (1 + r)) α−1 ct = " . # " # 1  k (1 + r)) α−1  γ ((m − γ )δ 1 2    +  if t > 0   1 1 k k α−1 α−1 1 + (1 + r)(δ (1 + r)) 1 + (1 + r)(δ (1 + r)) An alternate functional form for utility is used to check the robustness of the results, constant absolute risk aversion (CARA). When restricting γ1 = γ2 the background parameters are dropped in the exponential form. Therefore, the marginal condition can be written as ( βδ k (1 + r) if t = 0 , exp(−ρ(ct − ct+k )) = δ k (1 + r) if t > 0

(B5)

where ρ represents the coefficient of absolute risk aversion in the utility formulation u(ct ) = -exp(−ρct ). This can be reduce to the tangency condition

ct − ct+k =

(B6)

ln β ln δ 1 · 1t=0 + ·k+ · ln(1 + r), −ρ −ρ −ρ

and rearrange to the solution function

(B7)

ct =

ln β  1t=0 · −rho −ρ

Table B1 presents the joint estimates for the annual discount rate, (1−δ)365 −1; ˆ the CRRA or CARA utility function curvature, the present bias parameter, β; α ˆ or ρˆ respectively; and the Stone-Geary background consumption parameter(s) estimated or used, γˆ1 and γˆ2 .2627

26 This 27 I

table mirrors Andreoni and Sprenger (2012)’s Table 2. use condition indicators on each of the time preference parameters (discount rate, present bias,

and utility function curvature) to generate the joint estimates, i.e. I multiply each parameter of interest (by an indicator variable for each condition.

DRAFT

HUNGER GAMES

51

Table B1—Aggregate Parameters Estimates by Condition

CONDITION

NLS (1)

NLS (2)

NLS (3)

Tobit (4)

NLS (5)

Tobit (6)

Tobit (7)

Tobit (8)

0.735 (0.206) 1.485 (0.503) 1.387 (0.302) 0.608 (0.165)

0.730 (0.229) 1.646 (0.589) 1.480 (0.338) 0.607 (0.164)

0.832 (0.447) 2.589 (1.102) 2.215 (0.535) 0.716 (0.290)

0.710 (0.318) 1.818 (0.646) 1.629 (0.370) 0.543 (0.231)

0.804 (0.419) 2.468 (1.016) 2.091 (0.493) 0.674 (0.278)

0.784 (0.411) 2.390 (0.979) 2.047 (0.483) 0.659 (0.274)

0.805 (0.350) 2.164 (0.865) 1.904 (0.442) 0.684 (0.234)

0.999 (0.010) 0.990 (0.022) 0.949 (0.014) 0.974 (0.010) α/ˆ ˆ ρ 0.932 (0.012) 0.888 (0.019) 0.911 (0.015) 0.941 (0.010)

1.001 (0.011) 0.993 (0.025) 0.952 (0.015) 0.974 (0.011)

1.015 (0.020) 0.996 (0.040) 0.956 (0.020) 0.974 (0.017)

1.013 (0.015) 0.997 (0.027) 0.956 (0.015) 0.980 (0.015)

1.015 (0.019) 0.996 (0.037) 0.956 (0.019) 0.975 (0.017)

1.015 (0.019) 0.997 (0.037) 0.956 (0.019) 0.976 (0.017)

1.009 (0.016) 0.994 (0.033) 0.955 (0.017) 0.974 (0.014)

0.867 (0.021) 0.806 (0.024) 0.845 (0.017) 0.891 (0.013)

0.978 (0.005) 0.976 (0.004) 0.979 (0.004) 0.984 (0.003)

0.562 (0.050) 0.499 (0.051) 0.582 (0.034) 0.614 (0.033)

0.839 (0.032) 0.825 (0.028) 0.847 (0.024) 0.879 (0.021)

0.008 (0.002) 0.009 (0.001) 0.008 (0.001) 0.006 (0.001)

0.007 (0.001) 0.008 (0.001) 0.007 (0.001) 0.005 (0.001)

2.8453 (0.323) 0.496 (1.108)

2.846 (0.332)

0 —

-0.01 —

-11.13 —

-11.13 —

— —

— —

0.59 7064 131

0.59 7064 131

0.59 7064 131

-12477.4 7064 1981 131

0.58 7064 131

-8410.4 7064 1981 131

-14272.0 7064 1981 131

-12649.6 7064 1981 131

Annual discount rate Control 0.525 (0.168) Cognitive-fatigue 1.034 (0.305) Hunger 1.045 (0.222) Interaction 0.435 (0.135) Present bias: βˆ Control 1.001 (0.004) Cognitive-fatigue 0.998 (0.006) Hunger 0.989 (0.004) Interaction 0.994 (0.004) CRRA/CARA curvature: Control 0.925 (0.013) Cognitive-fatigue 0.881 (0.022) Hunger 0.892 (0.016) Interaction 0.932 (0.012) γˆ1 or γˆ1 = γˆ2 γˆ2 R2 /LL N Uncensored Clusters

Notes: Standard errors, clustered at the individual level and calculated via the delta method, in parenthesis. Annual discount rate calculated as ( 1 )365 . (1) Unrestricted CRRA regression of Equation B4. (2) CRRA regression of Equation B3 with restriction δ γ1 = γ2 . (3)-(4) CRRA regression of Equation B4 and B3, respectively, with restriction ( 1 )365 = 0. (5)-(6) CRRA regression δ of Equation B4 and B3, respectively, with restriction ( 1 )365 = −11.13 (the negative of the average reported daily food expendiδ tures*). (7)-(8) CARA regression of equation B7 and B6, respectively. *The sample reported a significanly higher average daily spending ($31.21) than Andreoni and Sprenger (2012)’s sample, who noted that the CRRA curvature parameter was very sensitive increasing values of γ.

52

DRAFT

C. Low-dose Condition Subjects and Non-compliers

Given the hypothesis that less protein would results in higher levels of hunger, it is not surprising to find that subjects under the low-dose condition (23g of protein) cash slightly more tokens earlier (Table C1) than subjects under the control condition (Table IV), however the difference is not statistically significant. Similarly, the present bias parameter for subjects under the low-dose condition is imprecisely estimated below 1 (Table C2). Also, as shown in Section III, the only difference between compliers and non-compliers is that non-compliers report lower levels of hunger. Therefore, one would expect non-compliers without cognitive fatigue to behave similar to compliers under the control condition, and non-compliers with cognitive fatigue to behave similar to compliers under the cognitive-fatigue condition. In fact, if we compare the results presented in Table C1 and Table VI against the results presented in Table IV and Table C2, respectively, we can see that this is true in both cases.

DRAFT

HUNGER GAMES

53

Table C1—Mean Tokens Cashed Earlier by Condition and Immediacy of Earlier Payment Date Tokens Cashed Earlier

Non-immediate (t > 0)

Immediate (t = 0)

All (t = 0, 7, 35)

Earlier Payment

CONDITION

Mean (1)

Robust-SE (2)

L: NC: NF:

38.886 32.419 51.804

8.146 8.863 7.163

Low-dose (23g of protein) Non-compliers (without cognitive-fatigue) Non-compliers (with cognitive-fatigue) Observations R-squared Clusters

L: NC: NF:

Low-protein Control (23g) Non-compliers (without cognitive-fatigue) Non-compliers (with cognitive-fatigue) Observations R-squared Clusters

L: NC: NF:

Low-dose (23g of protein) Non-compliers (without cognitive-fatigue) Non-compliers (with cognitive-fatigue) Observations R-squared Clusters

1549 0.49 29

39.373 32.810 50.331

6.995 9.220 8.445

515 0.48 29

38.645 32.223 52.540

8.844 8.754 6.637

1034 0.49 29

Notes: Robust standard errors clustered at the individual level. Estimates are immune to demographic control (e.g. gender, age), survey controls (e.g. order), time-of-the-day fixed effects, and/or date fixed effects.

54

DRAFT

Table C2—Estimates and Treatment Effects on Aggregate Parameter Estimates Parameter Coefficient (1)

Robust-SE (2)

Annual discount rate L: Low-dose (23g of protein) NF: Non-compliers (with cognitive-fatigue) NC: Non-compliers (without cognitive-fatigue)

0.907 1.984 0.515

0.386 0.753 0.329

Present bias: βˆ L: Low-dose (23g of protein) NF: Non-compliers (with cognitive-fatigue) NC: Non-compliers (without cognitive-fatigue)

0.984 1.025 1.025

0.018 0.043 0.012

CRRA curvature: α ˆ L: Low-dose (23g of protein) NF: Non-compliers (with cognitive-fatigue) NC: Non-compliers (without cognitive-fatigue)

0.892 0.797 0.862

0.022 0.053 0.032

CONDITION

Observations R-squared Clusters Notes: Robust standard errors clustered at the individual level.

1578 0.57 29

DRAFT

HUNGER GAMES

55

D. Individual Parameter Estimates

Table D1—Individual Parameter Estimates Proportion of Responses

Control

Condition

Subject ID 153 145 61 130 158 15 94 123 70 67 46 22 27 21 37 119 122 56 48 45 92 126 141 9 75 97 117 42 18

Annual Rate

βˆ

α ˆ

Interior

Zero Earlier

All Earlier

1.816 .378 .117 .707 11.005 .118 1.524 .982 6.355 .119 .113 .313 .117 .280 1.004 .878 1.705 .723 7.501 1.145 2.813 .553 .521 6.312 4.275

.000 .970 .970 1.001 .999 1.045 1.001 1.030 .966 1.007 1.018 1.000 1.012 1.016 .950 .944 .915 .963 1.000 .818 .942 .994 1.063 1.009 1.106 1.241

-27.041 .949 .955 .999 1.000 .826 .999 .963 .969 .901 .998 .999 .999 .999 .935 .946 .915 .934 1.000 .701 .967 .870 .855 .996 .760 .658

1.350 -.589

1.060 1.079

.758 .308

.000 .000 .000 .000 .000 .018 .018 .055 .073 .109 .109 .109 .127 .145 .218 .236 .273 .273 .273 .436 .491 .564 .600 .618 .691 .727 .873 .964 .982

.000 1.000 .836 .982 .836 .200 .964 .545 .545 .255 .873 .873 .764 .818 .655 .473 .400 .364 .600 .091 .273 .164 .364 .327 .055 .091 .000 .018 .018

1.000 .000 .164 .018 .164 .782 .018 .400 .382 .636 .018 .018 .109 .036 .127 .291 .327 .364 .127 .473 .236 .273 .036 .055 .255 .182 .127 .018 .000

56

DRAFT

Table D2—Individual Parameter Estimates Proportion of Responses

Cognitive-fatigue

Condition

Subject ID 31 80 60 105 41 132 125 129 131 147 23 66 86 12 13 8 152 68 107 51 40 73 63 28 47 156 146 95 77 137 6

Annual Rate

10.455 1.137 1.948 .444 .707 .117 .116 .117 .119 .306 .904 8.335 .120 .886 59.594 1.177 1.186 11.953 1.445 10.421 1.814 3.135 4.745 13.547 17.817 1480.669 2.835 3.372 3.184

βˆ

α ˆ

Interior

Zero Earlier

All Earlier

.000 1.230 1.019 .816 .975 .733 1.001 1.001 1.001 1.001 .000 .987 1.001 .824 1.001 1.005 .997 1.053 1.075 1.192 1.019 1.024 .972 1.093 1.038 .925 .934 .002 .775 .831 1.042

-27.041 .870 .952 .961 .977 .999 .999 .999 .999 .999 -21.535 .999 .824 .850 .999 .970 .773 .860 .985 .860 .937 .992 .910 .800 .924 .808 .896 -.966 .794 .766 .378

.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .018 .018 .055 .073 .073 .091 .109 .145 .164 .200 .218 .218 .273 .345 .382 .491 .545 .582 .727 .745 .927

.000 .273 .636 .382 .782 .582 .982 .982 .982 .982 .000 .818 .545 .164 .909 .691 .091 .418 .509 .127 .473 .109 .327 .291 .091 .036 .000 .000 .000 .164 .036

1.000 .727 .364 .618 .218 .418 .018 .018 .018 .018 .982 .164 .400 .764 .018 .218 .800 .436 .327 .673 .309 .673 .400 .364 .527 .473 .455 .418 .273 .091 .036

DRAFT

HUNGER GAMES

57

Table D3—Individual Parameter Estimates Proportion of Responses

Hunger

Condition

Subject ID

Annual Rate

βˆ

108 65 157 134 139 32 50 121 144 120 49 96 69 76 104 30 36 58 114 109 1 34 43 33 62 90 52 20 111 127 39 142 59 29 11 102 159

2.180e11 8.697 1.076 .117 .117 7.799 .723 1.107 1.816 2.190 1.059 5.717 3.133 .856 3.041 -.083 5.000 .922 4.227 8.514 .523 -.631 1.789 1.464 2.517 4.179 7.543 .217 3.454 6.194 1.354 2153.365 -.057 10.270 1.011 -.930 -.992

7.096 .559 .996 1.001 1.001 1.163 1.004 .876 .970 .783 .882 .935 .971 .995 .955 .940 .898 1.003 .905 .903 1.061 .658 .906 1.012 .959 1.007 .927 .944 .795 .878 1.052 .852 1.032 1.001 .950 1.145 1.252

α ˆ

Interior

Zero Earlier

All Earlier

.762 .790 .984 .999 .999 .873 1.000 .941 .949 .999 .953 .880 .970 .961 .860 .880 .917 .931 .945 .902 .928 .667 .919 .961 .871 .848 .768 .836 .778 .860 .876 -.041 .908 .147 .875 -4.268 .048

.000 .000 .000 .000 .000 .036 .036 .055 .055 .055 .127 .145 .182 .218 .309 .309 .327 .364 .364 .382 .382 .455 .473 .491 .509 .545 .582 .691 .727 .764 .782 .909 .927 .945 .964 .982 1.000

.073 .182 .745 .982 .982 .236 .782 .564 .400 .400 .527 .200 .255 .636 .200 .582 .127 .400 .127 .000 .582 .436 .200 .309 .164 .127 .000 .291 .073 .018 .036 .000 .073 .018 .036 .018 .000

.927 .818 .255 .018 .018 .727 .182 .382 .545 .545 .345 .655 .564 .145 .491 .109 .545 .236 .509 .618 .036 .109 .327 .200 .327 .327 .418 .018 .200 .218 .182 .091 .000 .036 .000 .000 .000

58

DRAFT

Table D4—Individual Parameter Estimates Proportion of Responses

Interaction

Condition

Subject ID

Annual Rate

βˆ

25 84 83 113 136 74 78 99 160 87 148 116 128 14 154 26 3 57 54 2 124 79 53 151 72 138 88 101 81 143 85 93 106 110

.670 .226 2.192 .116 -1.000 .298 1.101 1.114 .187 .199 5.946 3.043 -1.000 4.081 .675 .885 .214

.952 1.037 1.000 1.001 2.190 .994 .945 .948 .987 .986 .737 .824 14.549 .821 .906 .943 .977

.965 .982 .999 .999 .820 .951 .963 .979 1.000 1.000 .873 .945 .283 .929 .954 .970 .999

.732 .128 2.208 2.981 -.044 3.919 .724 .788 -.755 .447 1.015 2.140 3.724 .554 .356 14.148

1.054 .974 1.001 1.063 1.916 .741 1.098 .983 1.373 1.041 .801 .941 1.047 .855 1.004 .706

.966 .975 1.000 .889 .973 .836 1.000 .922 .690 .942 .762 .880 .779 .848 .673 -.668

α ˆ

Interior

Zero Earlier

All Earlier

.000 .000 .000 .000 .018 .018 .018 .018 .018 .018 .036 .036 .055 .055 .055 .055 .073 .073 .091 .091 .127 .145 .145 .327 .345 .436 .509 .527 .564 .709 .855 .855 .891 .945

.673 .836 .400 .982 .982 .855 .600 .600 .945 .945 .200 .273 .945 .218 .564 .600 .873 .745 .764 .873 .436 .327 .855 .145 .527 .418 .491 .345 .218 .091 .000 .018 .091 .000

.327 .164 .600 .018 .000 .127 .382 .382 .036 .036 .764 .691 .000 .727 .382 .345 .055 .182 .145 .036 .436 .527 .000 .527 .127 .145 .000 .127 .218 .200 .145 .127 .018 .055

1

1.2

1.6

1.8

2

1

Control (35g of protein)

1.4

a119 = 0.999413

a130 = 0.999399

a157 = 0.983961

a105 = 0.960616

a80 = 0.870475

1.2

1.6

1.8

2

1

1.2

1.4

Cognitive-fatigue

1.6

a = 0.999419

a134 = 0.999406

a83 = 0.999359

a41 = 0.976761

a60 = 0.952406

a108 = 0.761588

Gross Interest Rate (1+r)

1.4

a139 = 0.999413

a125 = 0.999406

a132 = 0.999358

a25 = 0.964899

a145 = 0.948820

a153 = -27.041019

Graphs by Subjects (sorted by a = Estimated CRRA Utility Curvature)

0

50

100

0

50

100

0

50

100

0

50

100

0

50

100

0

50

a31 = -27.041260

2

Hunger

1.8

1

1.2

1.4

1.8

Interaction

1.6

a158 = 0.999792

a129 = 0.999413

a113 = 0.999367

a84 = 0.982381

a61 = 0.955326

a65 = 0.790172

2

Figure D1. Actual and Mean Tokens Cashed Earlier by Subjects without Interior Solutions

Actual and Mean Tokens Cashed Earlier

100

DRAFT HUNGER GAMES 59

Loading...

Hunger Games - Berkeley - Xlab

Hunger Games: Does Hunger Affect Time Preferences? By Lydia Ashton∗ Draft: May 11, 2015 The poor often make shortsighted monetary choices, however m...

7MB Sizes 0 Downloads 0 Views

Recommend Documents

The Hunger Games
a winner. Then I realized, she didn't mean me, she meant you!” bursts out Peeta. “Oh, she meant you,” I say with a

District hunger games test
Madagascar Jules lower data penyakit infeksi menular seksual di indonesia their saltates and enthronised unsuccessfully!

The Hunger Games - Documents
Oct 14, 2017 - The Hunger Games. By Suzanne Collins. Welcome to PANEM. Used to be North America Disasters came: droughts

Hunger Games Curr. Guide - LACOE.edu
Materials Needed: Novel, student folders. Handouts 1-‐Map of Panem. Handout2-‐Graphic Org on Dystopian Society. Hand

The hunger games 1 ending
Leroy demist better, their estrangement hidden stirringly recorded. unmoralizing reweighs Elmore, his lakatos levente ak

The hunger games trilogy box set costco
Gerrard tombs crash, eclipsing his provocation knitted tightly. Alex doubt scandalize their creep the hunger games trilo

Novel Hunger Games Terjemah Indonesia Lengkap Trilogi
Ditulis oleh Download dan Baca Novel , Monday, March 07, 2016 - Rating: 4.5. Judul : Novel Hunger Games Terjemah Indones

Zippyshare.com - The Hunger Games 1 - Los Juegos Del Hambre.pdf
You have requested the file: Name: The Hunger Games 1 - Los Juegos Del Hambre.pdf. Size: 1.32 MB Uploaded: 18-03-2016 01

Free Books The Unofficial Hunger Games - Free Books Index
Introduction To Behavior Genetics Applied Physical Geography Geosystems Laboratory Answers Pdf Elna 1500. Manual Pdf An

The Hunger Games Book 1 - Savita Bhabhi Pdf English
Skip to content. The Hunger Games Book 1 · Ethical Leadership Character Civility Community · Makalah tembaga pdf · Super

HD Vishwaroopam 2 (Malayalam) | 전지적 참견 시점.E39.190202.HDTV.H264.… | Summer House