Connecting commitment to self-control problems: Evidence from a weight loss challenge

Transcription

1 Connecting commitment to self-control problems: Evidence from a weight loss challenge Séverine Toussaert New York University March, 2016 Abstract In the context of a weight loss challenge, I use the menu choice approach of Gul and Pesendorfer (2001) to provide new insights on the link between commitment demand and self-control problems. First, I study commitment demand to eat healthy by eliciting participants preferences over a set of lunch reimbursement options, which differed in their food coverage. Using information on the entire ordering, I develop menu preference measures of temptation and validate them with survey data. Finally, I investigate whether temptation revealed through menu choice can predict self-control problems in an other domain: commitment to self-set goals pertaining to exercise and participation in the challenge. I find strong evidence of a demand for commitment driven by temptation. First, close to 50% of participants strictly preferred a coverage that excludes the foods they rated as most tempting and unhealthy. Second, temptation revealed through menu choice not only predicts a higher likelihood of commitment to self-set goals but also a lower likelihood of achieving them. The elicitation of menu preferences therefore offers a promising venue for measuring self-control problems. JEL Classification Numbers: C93, D03, I12. Key Words: Commitment, temptation, flexibility, self-control, experiment. Acknowledgments: I feel greatly indebted to my advisors Guillaume Fréchette and David Cesarini as well as to my former colleague Sevgi Yüksel for their support and continuous feedback in the development of this project. I thank Yves Le Yaouanq for his careful reading of the paper. I also thank seminar participants at NYU and Amsterdam as well as participants at the 2014 North American ESA Conference for their useful comments. Finally, I would like to acknowledge the enthusiasm and interest of the manager of the NYU wellness services, Christine Gould, without whom this project would have never seen light. Contact: st1445@nyu.edu.

2 1. Introduction Commitment behavior is at the heart of economic theories of temptation (Laibson (1997), O Donoghue and Rabin (1999), Gul and Pesendorfer (2001), Fudenberg and Levine (2006)). While standard decision makers always weakly prefer larger choice sets, individuals aware of their self-control problems may choose to constrain their future choices at a cost to themselves. This behavioral implication of temptation has been widely tested, both in the lab and in the field, by studying the take-up of a specific commitment device. Examples of such devices are illiquid accounts designed to increase savings (Ashraf et al. (2006), John (2015), Beshears et al. (2015)), deadlines to reduce procrastination on an effort task (Ariely and Wertenbroch (2002), Bisin and Hyndman (2014)) or deposit contracts with financial penalties for smoking or failing to exercise (Giné et al. (2010), Royer et al. (2015), stickk.com). Despite the wealth of studies, there is only limited evidence of a demand for commitment motivated by temptation concerns. First, commitment take-up is often low, mostly in the range of 10%-35%. 1 Second, even when individuals choose commitment, it is not clear whether temptation is the driving factor. 2 For instance, take-up might be due to signaling concerns or experimenter demand effects if subjects perceive commitment to a specific behavior as the choice that is expected of them (Exley and Naecker (2016)). Alternatively, they might adopt the device simply to try out a new feature or product that is proposed to them (Chow and Acland (2011)). Because most studies only allow individuals to restrict their choice set in a specific way, little can be learned from decisions to take up commitment or not. In this paper, I conduct a field experiment with participants in a weight loss challenge to gather new insights on the link between commitment demand and self-control problems. I study participants commitment decisions to lose weight through nutrition, exercise and active participation in the challenge. My main contribution is methodological. To study temptation, I follow the revealed preference approach of Gul and Pesendorfer (2001) (henceforth GP) and construct an environment of menu choice. In the GP model, the decision maker s preferences not only depend on final consumption but also on the menu from which this consumption is taken. Commitment is defined as a preference for a smaller menu 1 For instance, the take-up rate of the deposit contract proposed by Giné et al. (2010) is 11%, while it is 28% in Ashraf et al. (2006). Royer et al. (2015) report a 12% enrollment rate in their exercise commitment contract, while Kaur et al. (2015) report a 35% take-up rate of their work contract. In the lab, Augenblick et al. (2015) find that less than 10% of subjects are willing to pay even $0.25 to constrain their effort choices. Two notable exceptions are Milkman et al. (2014) who find that 61% of students are willing to pay to access audio novels only when exercising at the gym, and Schilbach (2015) who finds that over 50% of his study participants demand commitment to increase their sobriety. 2 While a few studies find a positive relation between commitment demand and some measure of present bias (Ashraf et al. (2006), Kaur et al. (2015), John (2015), Augenblick et al. (2015)), other studies find no relation or a negative relation (Sadoff et al. (2015), Toussaert (2015)). 2

3 and the decision maker is revealed to be tempted by an option if he strictly prefers a menu that excludes it. I implement the menu choice approach in the context of a lunch reimbursement program. During the challenge, participants had a chance to be reimbursed for all their lunch meals over the period of one month. The menus were reimbursement options that systematically differed in the range of foods covered by the reimbursement. Instead of offering participants to select one reimbursement option, I elicit their preference ordering over the full set of options and implement their preferences using an incentive-compatible procedure. This rich dataset allows me to take a more agnostic and comprehensive approach to measuring temptation. First, I allow for any degree of commitment, from commitment to a single food category to complete flexibility. Secondly, I allow commitment to target any food category, without taking a stance as to what may constitute a temptation for the individual. With this dataset, I test whether there is a demand for commitment to eating healthy (or less unhealthy) and study how it depends on the nature and the number of available food options. I then develop revealed preference measures of temptation, which solely rely on the structure of participants menu preferences, and validate these measures using survey data. Finally, I investigate whether these menu preference measures can predict self-control problems in an other domain: commitment to self-set goals pertaining to exercise and participation in the challenge. At the start of the challenge, participants were offered to receive their payment for the study only contingent on the achievement of self-set attendance goals. I test whether temptation revealed through menu choice is predictive of goal setting and goal achievement. I find strong evidence of a demand for commitment motivated by self-control problems. First, while the largest coverage guaranteed maximal reimbursement, only a third of respondents strictly preferred this option. In contrast, close to 50% of respondents strictly preferred options that exclude the food category they rated as most tempting and unhealthy. Furthermore, temptation by the most unhealthy foods is not only widespread, it is also structurally consistent with temptation in the GP model and with their main axiom, Set Betweenness. Finally, temptation revealed through menu choice is a strong predictor of participants likelihood to set attendance goals and achieve them. On the one hand, participants with a stronger preference for excluding unhealthy foods from their coverage are more likely to commit to an attendance goal. On the other hand, they are less likely to follow through and achieve the goals they set. Therefore the elicitation of menu preferences offers a promising venue for measuring the importance of self-control problems. The rest of this paper proceeds as follows. Section 2 describes the weight loss challenge and study design. Section 3 studies temptation through menu preferences in the lunch reimbursement program. Section 4 presents survey evidence that validates these menu preference measures of temptation and tests their power in predicting other commitment behaviors. 3

4 Section 5 concludes. Supplementary material is available in an Online Appendix (hereafter, OA ). 2. Study Design 2.1. Description of the weight loss challenge The study was conducted with participants in an eight-week weight loss challenge organized every year since 2011 by the wellness services of New York University (NYU). Only NYU faculty and staff members are eligible to participate. The data concerns the 2014 edition, which took place over the months of March and April. The basic rules of the challenge were inspired from the American TV show The Biggest Loser : the contestant who loses the highest percentage of body mass over the challenge period wins a grand prize. Contestants were required to participate in an initial weigh-in on Week 1 of the challenge, which determined their reference weight. Three follow-up weigh-ins were scheduled during the challenge but only the final weigh-in on Week 8 was required in order to be considered for the grand prize. All weigh-ins were conducted at a private gym club near NYU. To encourage participants to attend the follow-up weigh-ins, the top loser between any two weigh-ins received a small prize. The final winners (one male and one female) were the participants who lost the highest percentage of their reference weight at the end of the challenge. In addition to the weigh-ins, participants could sign up for many activities and events to help them stay on track during the challenge. First, participants were offered free access to the gym facilities during the first month of the challenge. Interested participants received a gym badge during the first weigh-in, which they were required to scan every time they wished to access the facilities. Secondly, participants could sign up for any of four wellness events (two nutrition seminars and two exercise classes) scheduled by the wellness services during the challenge. Participants received regular reminders about these events, which were advertised at the start of the challenge Recruitment procedures and structure of the study Participants were recruited for the experiment at the first weigh-in. The experiment was advertised as an online study on improving health through exercise and nutrition conducted in collaboration with the wellness services. Participants were told that for completing a two-part survey, they could receive a $20 gift card as well as the chance to be reimbursed 3 See OA for more specific details about the challenge rules and procedures. 4

5 for their lunch meals during the month of April. Interested participants were asked to complete an online consent form, the link to which was printed on flyers and on a weight booklet. The study was composed of two online surveys completed during the first week of the challenge and after the final week. 4 Eligibility for the full incentives was contingent on having completed the entire study ($10 for partial completion). Overall, 193 participants were present at the first weigh-in and 117 signed up for the study. Among those 117 participants, 113 completed the first survey and 87 also completed the second survey. 5 Table 1: Timeline and content of the study Online Survey Data Collection Period Survey Content Part 1: Basic socio-demographics Survey 1 March 4th through Questions about the challenge N = 113 March 11th, 2014 Part 2: Goal setting Part 3: Reimbursement program Challenge and personal performance evaluation Survey 2 April 29th through Follow-up questions on Survey 1 (Part 2 & 3) N = 87 May 6th, 2014 Intertemporal choice tasks Self-Control measures of Ameriks et al. (2007) Table 1 summarizes the structure of the study. Survey 1 had three main components. The first part gathered data on basic socio-demographics, past participation in the challenge and expectations of weight loss, physical activity and obstacles to success. The second part studied commitment demand through goal setting by offering participants to receive their payment for the study only contingent on the achievement of self-set attendance goals (Section 4.2). The third part of the survey studied participants commitment demand to eat healthy through a lunch reimbursement program offered during the second month of the challenge. Participants were asked to rank various reimbursement options, which systematically differed in the range of foods covered by the reimbursement. The elicitation and implementation procedures are discussed in Section 3.1. After having submitted their ranking, participants answered a set of questions related to their food habits and were asked to rate food items in terms of their healthiness and attractiveness (Section 4.1). The aim of Survey 2 was threefold. The first objective was to gather information about respondents evaluation of their participation in the challenge and to identify barriers to 4 For logistical reasons, completion of the second survey was delayed by one week relative to the initial announcement. There is no evidence that this delay affected respondents behavior or responses. 5 In addition, one respondent only partially completed the second survey and is excluded from the analysis of Survey 2 answers. 5

6 attendance and success. The second aim was to understand respondents Survey 1 decisions to constrain their future choices through goal setting and the reimbursement program. The final objective was to assess whether respondents commitment decisions in the challenge correlate with standard measures of self-control problems used in the literature. I focused on two such measures: (i) present bias over time-dated monetary rewards measured through a Multiple Price List mechanism; (ii) the self-control measures developed by Ameriks et al. (2007), which rely on survey answers to an hypothetical intertemporal consumption problem; see OA for an analysis of these measures and their relationship to commitment decisions Sample characteristics Appendix Table 5 presents summary statistics about the subject pool. Surveyed participants were 79% female and more educated than the general population. About 30% had previously participated in the challenge. On average, participants entered the challenge with the goal of losing 14.3 lbs (1.8 lbs per week), or about 7.7% of their body weight. These ambitious numbers do not vary significantly with gender or prior participation in the program. Although the study did not gather data on the BMI of respondents, the large majority of participants were overweight at the start of the challenge: the average starting weight was lbs for male participants (min: max: 253.6) and lbs for female participants (min: max: 312.2). These averages are above the US national average of lbs for males and lbs for females and much beyond the ideal body weight of lbs for males and lbs for females. 7 Furthermore, more than 80% of survey respondents reported having attempted at least one diet over the last 10 years, and among those, about 20% had attempted at least 10 diets (min: 1 - max: 25). The population under study is therefore greatly concerned with losing weight and struggling to achieve this goal. 3. Commitment in the reimbursement program 3.1. Description of the program and preference elicitation I used the approach of menu choice to study participants commitment demand to eat healthy in the context of a lunch reimbursement program. Respondents who completed the first 6 The link between commitment demand and those two standard measures of self-control problems is at best weak; however, attrition between the two surveys does not allow to draw strong conclusions. 7 Source: Anthropometric Reference Data for Children and Adults: United States, The Ideal Body Weight (IBW) was computed using the formula IBW M = 50kg + 2.3*(height(in)-60) for males and IBW F = 45.5kg + 2.3*(height(in)-60) for females, for the US average height of 69.3in for males and 63.8in for females. 6

7 survey could enter a lottery with a 10% chance of being reimbursed for all their lunch meals over the second month of the challenge. 8 Participants were asked for their preferences over various reimbursement options, which differed in the range of lunch items covered by the program. The reimbursement could cover one, two or all three categories listed in Table 2. 9 Table 2: Lunch Categories Green Category G - salads (regular, kale, quinoa), soups (veggie, noodle) - natural fruits and low-fat yogurt - water (spring or sparkling) Orange Category O - sandwiches (bagels, wraps, baguette, club, hot sandwiches) - cereal bars, fruit bars or trail mix - fruit juice Red Category R - burgers, pizzas or fried foods (French fries, chicken wings, barbecue) - pastries (cookies, cakes, muffins, donuts, croissants) - soda I elicited participants weak preference ordering over the set of reimbursement options M := {G, O, R, GO, GR, OR, GOR}. Formally, each option can be seen as a menu of reimbursable foods; for instance, G is the singleton menu {G} that commits a respondent to be reimbursed only for green foods, while GOR is the most flexible menu {G, O, R} that allows to be reimbursed for all lunch categories. The full preference ordering over M was elicited using an incentive compatible procedure. Respondents were asked to assign a rank number between 1 and 7 to each of the 7 reimbursement options and could express indifferences by assigning the same rank to several options. To elicit a truthful report of the entire ordering, participants were told that their reimbursement option would be determined through a lottery assigning higher odds to higher ranked options. 10 To incentivize 8 Reimbursement per respondent was capped at 20 meals and $15 per meal. The exact reimbursement period was 04/01/14-04/28/14. To be reimbursed, respondents were required to provide detailed lunch receipts. In order to encourage all respondents to participate in the program, the winners were announced only after the challenge was over. Despite the interest for the program, only 17% of respondents ended up providing lunch receipts, mainly due to the implied logistical costs; data on the submitted receipts is available upon request. 9 The instructions emphasized that the various options only differed in the range of foods covered by the reimbursement; otherwise, the terms of reimbursement were identical. Without being more explicit, it was also mentioned that being reimbursed only for a certain category of foods could provide an incentive to eat more of these foods and less of the foods not covered by the reimbursement. See OA for the instructions. 10 The exact odds were (0.35, 0.3, 0.2, 0.1, 0.03, 0.02, 0) where 0.35 = P{rank 1} and 0 = P{rank 7}. 7

8 a respondent to truthfully express an indifference, the ranking procedure made it easier to report indifferences than strict rankings: participants first selected all the options they wished to assign rank 1 and then proceeded iteratively to assign all other ranks until the list of options was empty. The 7 options appeared listed in a random order so as to control for order effects. Participants were individually informed by of the reimbursement option assigned to them upon completion of Survey Identification of temptation through menu preferences This rich dataset of menu preferences allows to gather new insights regarding the source, the strength and the structure of an individual s temptation, as explained below. The idea of using menu choice to elicit temptation was first introduced by Gul and Pesendorfer (2001) and subsequently extended in several directions (see Lipman and Pesendorfer (2013) for a review). To model temptation, GP consider a two-period expected utility model in which the decision maker (henceforth, DM) first chooses from a set of menus and then makes a choice from the selected menu at some later (unmodeled) stage. Their primitive is a preference relation on a set M of menus (of lotteries) on which they impose, besides the usual assumptions, a new behavioral axiom called Set Betweenness. 11 This axiom states that for any two menus M and M, M M implies M M M M This relaxation of the standard framework allows to capture the behavior of a tempted DM. To illustrate, consider an individual who would ex ante prefer to eat green foods rather than the more unhealthy red foods, {G} {R}. A standard DM free of temptation (ST D) evaluates a menu by its best element(s) and is unaffected by the presence of dominated options, implying {G} {G, R} {R}. On the other hand, a DM who is tempted by unhealthy foods would prefer to restrict his access to R than to be facing the choice between G and R at the time of ordering, {G} {G, R}. More generally, say that option m is a temptation in menu M if M\{m} M. In addition, say that m is globally tempting in M if M\{m} M for all M M such that m M. For instance, R is a global temptation for an individual if he would prefer to exclude red foods from any reimbursement option. Options assigned the same rank received in expectation the same chances of being selected. For instance, if three options were assigned rank 1, then which option was drawn with probability 0.35, 0.3 and 0.2 was determined at random. Information about the specific odds was accessible to participants. 11 is required to be a complete and transitive relation that satisfies the standard expected utility axioms of Continuity and Independence adapted to a menu choice setting. In the present context, completeness and transitivity follow directly from the rank ordering procedure, while Continuity and Independence are treated as maintained assumptions. Note that incentive comptability of the elicitation procedure relies on the Independence assumption. 8

9 In the GP model, there are two reasons why a tempted DM may prefer to commit to G. First, the DM may predict that he will give in to R if offered the choice and therefore assign the same value to {R} and {G, R}, that is, {G} {G, R} {R}. In this case, R is revealed to be an overwhelming temptation for the DM. Alternatively, he may anticipate to exert selfcontrol and resist R, which makes {G, R} more valuable than {R} i.e. {G} {G, R} {R}. Here R is revealed to be a resistible temptation. More generally, say that the DM (i) has Self-Control at two sets (M, M ) if M M implies M M M M (GP-SC ) and (ii) has no No Self-Control at (M, M ) if M M implies M M M M (GP-NSC ). 12 GP show that in the standard lottery framework of menu choice, imposing Set Betweenness on leads to the following self-control representation V GP (M) := max [u(x) + v(x)] max v(y) x M y M The commitment utility u measures the normative preferences of the agent i.e. when committed to a singleton choice so that temptation concerns are absent. The temptation utility v measures the temptation value of an alternative and max y M v(y) v(x) is the self-control cost of choosing x over the most tempting alternative in M. When choosing from M, the DM chooses as if he maximized the compromise utility u + v. The restrictions of Set Betweenness on choice data exclude two interesting phenomena. First, the DM cannot exhibit a strict Preference for Flexibility (FLEX ) at any two choice sets M and M, that is, M M M M. As a consequence, GP cannot capture an agent who may have a preference for diversity or may feel uncertain about his future tastes, an idea originally motivated by Kreps (1979). Secondly, Set Betweenness has a strong implication for the structure of temptation: the cost of self-control only depends on the most tempting alternative in the menu, and not on the number of temptations. As a result, Set Betweenness ignores Cumulative Temptation effects, which may be modeled by the ordering M M M M (CT ). 13 Alternatively, the ranking M M M M may reflect the agent s aversion to guilt when choosing something from M in M M while the choice to act virtuously (by selecting something from M) was also available (see Kopylov (2012)). 12 One should note that the ordering M M M M can also be rationalized by random indulgence (Dekel and Lipman (2012)) i.e. the DM prefers commitment because he expects to give in to temptation with positive probability and to have no temptation otherwise. Since random indulgence and costly self-control as two equally plausible interpretations of the data, I use the abbreviation GP-SC solely to refer to the fact that Strict Set Betweenness was originally introduced by Gul and Pesendorfer (2001). 13 To illustrate this point, consider the following example drawn from Dekel et al. (2009): let b denote broccoli, c chocolate and p potato chips and note that the preference ordering {b} {b, c} {b, p} {b, c, p} violates Set Betweenness; however, this ranking seems natural for a dieting agent if having to resist two temptations is strictly harder than resisting only one. 9

10 The analysis of participants preferences over reimbursement options performed in the next section will therefore center around three properties of temptation: Source: When participants prefer a restricted coverage, what food category tends to be excluded? This question about the source of temptation can be asked because the elicitation procedure imposes a priori no restrictions on when commitment demand should arise. Strength: What lunch categories appear as robust temptations in the sense of being classified as globally tempting? More generally, comparing two nested options, how often would a participant prefer the option that excludes a given food category from the coverage? Structure: When commitment is strictly preferred, what form does it take? This question refers to the structure of temptation as either satisfying Set Betweenness (GP-SC or GP-NSC ) or allowing for cumulative effects (CT ) Findings Below I analyze individual rank orderings in the reimbursement program to study the extent to which preferences exhibit temptation. Before doing so, Table 3 shows the percentage of participants who expressed a strict preference ordering relative to those who expressed some indifferences ( ). Table 3: Distribution of preference orderings Number of steps to Actual sample Benchmark 1 Benchmark 2 Coarseness of the complete ordering % (N) % % preference ordering (2) < < full indifference (0) (3) (4) (7) (4) (93) strict preference % (freq.) of indifferences 4.3 (103/2373) Notes: With M =7, there are ( 7 2) = 21 binary comparisons between reimbursement options per individual. Summing over N = 113, the total number of binary comparisons is therefore 2373 in the actual sample. 10

11 Given the iterative elicitation procedure, participants with a strict preference ordering completed their ranking in 7 steps, while those who were fully indifferent took only one step to complete their ranking. More than 80% of respondents gave a strict ordering of the 7 options. Among those who expressed indifferences, 30% assigned rank 1 to three reimbursement options and a different rank to each of the remaining options; this is the most common pattern, corresponding to 6 of the 7 participants who completed their ranking in 5 steps (see OA for the distribution of indifferences). Table 3 also reports the corresponding distribution of orderings for two benchmarks against which the actual distribution will be compared: Benchmark 1 (B1 ): random draw with replacement of 1M orderings from the set P of all possible weak orderings of M = 7 options. Each ordering is treated as equally likely. 14 Benchmark 2 (B2 ): random draw with replacement of 1M orderings from P with 82.3% of strict orderings (drawn from P ) and 17.7% of weak orderings (drawn from P \ ). The relative proportion of strict versus weak orderings is chosen to match the one observed in the actual sample. Figure 1 shows the mean rank (1-7) assigned to each reimbursement option; for comparison, mean ranks for both benchmarks (3.1 for B1 and 3.8 for B2) are also reported. The full rank distributions are reported in the OA. Option GO is by far the most popular option followed by GOR and G; these 3 options all perform significantly better on average than the other 4 options (p < 0.001, two-sided t-tests) and than predictions under the two benchmarks (except for G relative to B1). As would be expected from individuals trying to lose weight, OR and R are the least popular options and perform significantly worse relative to the two benchmarks. Options O and GR appear to be more neutral options, with respectively 60% and 72% of respondents assigning them rank 3, 4 or 5. Table 4 shows the proportion of times G, GO and GOR were strictly preferred to any other option. Almost one third of respondents expressed a strict preference for GO, while 15% of respondents strictly preferred to restrict their choice to G. Therefore, close to 50% of people expressed a desire for commitment to eating healthy by excluding R from the reimbursement coverage, while keeping G. At the same time, about 32% of respondents selected GOR as their unique rank 1 option. Together, these findings highlight a tension between commitment and flexibility and suggest that commitment take-up may be limited if it requires the individual to greatly restrict his choice set. Removing GO from the set of 14 It can be verified that allowing for indifferences, there are 47,293 different orderings of 7 options, among which 7! (= 5040) are strict orderings. 11

12 Figure 1: Mean rank assigned to each reimbursement option mean rank B2 B1 2.6 G O R GO GR OR GOR options, only 32% of respondents would strictly prefer to commit to G, a take-up rate for commitment closer to previous findings in the literature where commitment rarely presents different levels of flexibility. Table 4: Distribution of top choices Top option(s) Actual sample B1 p-value B2 p-value % (N) % % Option G 15.0 (17) Option GO 32.7 (37) 9.9 < < Option GOR 31.9 (36) 9.9 < < Other option 6.2 (7) 39.5 < < No unique top 14.2 (16) 30.7 < Total 100 (113) Notes: No unique top refers to participants who assigned rank 1 to several options. Reported p-values are the result of a binomial test that the observed frequency is equal to the frequency of benchmark B1 (B2). Information on the full preference ordering of each participant allows to further investigate 12

13 (i) the source, (ii) the strength and (iii) the structure of temptation. To study (i) and (ii), define the following Global Temptation Index for food category m {G, O, R} GT m = M m 1 {M\{m} M} where M m = {M M m M and M {m}}. For instance, M R = {GR, OR, GOR} and GT R {0, 1, 2, 3} measures the number of times a given respondent strictly preferred to eliminate category R from a reimbursement option that includes it. Therefore GT m measures the strength or robustness of an individual s temptation for m; in particular, GT m = 3 implies that m is globally tempting in M. Figure 2 shows the distribution of the Global Temptation Index for each lunch category as well as the distribution that would be observed under both benchmarks. Figure 2: Temptation value of G, O and R foods % of respondents G foods O foods Index value Index value R foods Benchmarks (any option) B1 B Index value Index value Notes: For each category m {G, O, R}, Index value refers to the value of the Global Temptation Index GT m = M m 1 {M\{m} M} {0, 1, 2, 3}. Red foods appear to be tempting for a large majority of participants and globally tempting for 46% of respondents. Unsurprisingly, green foods are not revealed to be a temptation 13

14 (GT G = 0 for 73% of respondents). More surprisingly, O is also never revealed to be tempting (GT O = 0) for 64% of respondents. Below I show that temptation by m as measured by participants preference for a coverage that excludes m is consistent with their subjective assessment of how tempting m is. Yet, very partial information on the preference ordering over M - such as information on the choice between G and GOR - would not be sufficient to infer the source of temptation and its strength. I now study the structure of temptation by assessing the performance of the Set Betweenness axiom in predicting the choice data. To this end, I look at all comparisons between any two non-nested reimbursement options, which makes 9 pairwise comparisons in total. 15 Following the discussion of Section 3.2, I consider five types of menu preferences depending on how the individual ranks the union of any two menus M and M : 1- Standard (STD): M M implies M M M M 2- Flexibility-loving (FLEX ): M M implies M M M M 3- GP with no self-control (GP-NSC ): M M implies M M M M 4- GP with self-control (GP-SC ): M M implies M M M M 5- Cumulative Temptation (CT ): M M implies M M M M Remember that while 1, 3 and 4 are consistent with Set Betweenness, 2 and 5 are not. Furthermore, only 3, 4 and 5 are consistent with temptation. Figure 3 shows the proportion of respondents who behaved according to each of these 5 categories for the most frequent binary choices (see Appendix Table 6 for a complete breakdown). There are four main findings. First, due to the low percentage of expressed indifferences, the fraction of choices satisfying STD or GP-NSC is very low. Second, a large percentage of respondents behaved either according to FLEX or GP-SC in each of these binary choices. For instance, about 67% of those who ranked G strictly above O also ranked GO strictly above these two menus, thus favoring flexibility. On the other hand, 69% of those who ranked G strictly above R also placed GR strictly in between. Third, commitment is mostly consistent with the strict form of Set Betweenness (GP-SC ), rather than with a cumulative temptation interpretation (CT ). Finally, whether commitment or flexibility prevails depends on the presence or absence of R in the menus being compared. When either both menus contain R or both exclude R, a majority of participants prefer flexibility. On the other hand, participants who strictly prefer a menu that does not contain R to a menu that contains R tend to favor commitment (GP-SC or CT ). Thus commitment is essentially motivated by a willingness to exclude R from the set of options, which is consistent with R being a 15 Comparisons between one menu and a proper subset of it are excluded from the analysis since the implications of Set Betweenness are trivial in this case. 14

15 Figure 3: Distribution of menu preferences in bilaterial comparisons % of respondents G > O O > R G > R G > OR O > GR GO > R GO > GR GO > OR GR > OR STD FLEX GP-SC GP-NSC CT Notes: Distribution of menu types for the most frequent preferences over two options (M, M ); see Appendix Table 6 for the least frequent preferences. For instance, the number 66.7% on the first bar means that among the respondents who ranked G strictly above O (G O), 66.7% had the F LEX ordering GO G O. tempting alternative for most participants. Flexibility is instead favored when respondents face a trade-off between G and O, all else constant. 16 Aggregating over all binary comparisons, I finally construct an index for each food category m {G, O, R}, which measures how frequently a given respondent exhibits a temptation for m in the form of GP-SC, the strict version of Set Betweenness. For this purpose, let M m = {M M \ {GOR} m M} and M m = {M M \ {GOR} m / M}. Then the Strict Set Betweenness Index for food category m is computed as SSB m = P m 1 {M M M M } where P m = {(M, M ) M m M m M M and M M}. For example, P R = {(G, R), (O, R), (G, OR), (GO, R), (O, GR), (GO, GR), (GO, OR)} and SSB R {0, 1,..., 7} 16 This observation also holds for the least frequent binary choices. For instance, only 18.5% of the 27 respondents who strictly preferred O to G put GO strictly in between. As another example, only 12% of the 50 participants who placed GR strictly above O also put GOR strictly in between. See Table 6 in the Appendix. 15

16 measures the number of times R is revealed to be a resistible temptation à la GP. The distribution of the Strict Set Betweenness Index for each food category is reported in the Appendix together with the distributions generated under both benchmarks. Consistent with the previous analysis, green and orange foods are almost never revealed to be temptations à la GP since SSB G and SSB O are equal to 0 or 1 for respectively 93% and 83% of respondents. On the other hand, R is widely revealed to be a GP temptation as SSB R takes a value of 5 or higher for close to 40% of respondents and 83% of those for whom R is globally tempting. 4. Discussion: Linking commitment to self-control The last section showed strong evidence of a demand for commitment through a lunch reimbursement program. While GOR was the option that maximized meal reimbursement by imposing no restrictions, only 32% of participants strictly favored this option. When a restricted coverage was instead strictly preferred, the modal preference was for only excluding the most unhealthy foods from the coverage. In particular, R was revealed to be a strong temptation for participants, while this was not the case of O. Finally, temptation by R is not only widespread, it is also structurally consistent with temptation in the menu choice model of Gul and Pesendorfer (2001) and with their main axiom, Set Betweenness. Together these findings suggest that research on the elicitation of menu preferences may offer a promising venue for measuring temptation in real life settings. In this section, I test whether temptation revealed through menu choice is in line with participants perceptions of what is tempting (4.1) and study its power to predict self-control problems in other choice contexts (4.2) Survey validation of menu preference measures of temptation The fact that a respondent chose to exclude R from his reimbursement coverage could a priori reflect other concerns than the one of avoiding temptations. Respondents could have simply excluded unattractive foods which are never part of their diet, and are therefore irrelevant to their choice of reimbursement coverage. At the same time, unfrequent consumption of red foods per se does not mean absence of temptation, if a respondent usually resists alternatives he craves. 17 The question is therefore whether a significant fraction of commitment choices can be explained by food tastes rather than by temptation concerns. To investigate this issue, I use the data collected in Surveys 1 & 2 about subjective perceptions of the various food alternatives, reported consumption frequencies for each lunch category and respondents 17 This is a major implication of the GP model: even agents who would resist temptation in the absence of restrictions might prefer to be committed ex ante. For instance, someone who always orders salads when other alternatives are available on the menu could be better off if the menu exclusively offered salads. 16

17 comments about their favorite reimbursement coverage. All sources of data support the hypothesis that commitment to a large extent reflects the temptation to eat unhealthy. The first source of evidence pertains to participants subjective perception of each lunch category. After having submitted their ranking, respondents were asked to rate a list of food items, belonging to one of the 3 lunch categories, in terms of (i) how healthy and (ii) how tempting they considered this item (1-7 scale). 18. Each lunch category was then assigned a Health (resp. Temptation) Score computed as the respondent s mean rating for (i) (resp. (ii)) over all food items of that category. Figure 4 Panel A shows the average Health and Temptation scores for the entire sample (N = 113), while Appendix Table 7 presents a breakdown by menu preferences (top choice and value of GT R ). Figure 4: Subjective evaluation of G, O and R and consumption patterns (a) Health and Temptation Scores (b) Actual versus Ideal Consumption Freq Health Score G O R Temptation Score G O R Actual Ideal Notes: The Health (Temptation) Score measures on a 1-7 scale the average health (temptation) value of each lunch category. Actual (Ideal) Consumption Freq. refers to the proportion of time a respondent consumed since the beginning of the year (should consume) a food item from category G (resp. O and R). N = 113 for Panel A and 87 for Panel B. Respondents ratings of the various food items are consistent with R being a tempting but unhealthy category relative to G and O. First, respondents unambiguously perceive G as the healthiest category and R as the most unhealthy, with O being moderately healthy. Second, while O was not rated as more tempting than G, respondents assigned a significantly higher temptation value to R than to both G and O. Furthermore, the Health and Temptation Scores of G, O and R do not significantly differ based on respondents ranking of the various reimbursement options. The ratings of participants whose top choice was one of the two most 18 These food items were: salad, soup, yogurt and fruit (category G); cold sandwich, hot sandwich and cereal bar/trail mix (category O); burger, pizza, fried food and pastry (category R) 17

18 popular options (GO or GOR) are very similar; in particular, R is rated as significantly more tempting than G and O in both cases (p < 0.05 in all comparisons). 19 Participants were also asked to report on a scale (i) how often they had each food item for lunch since the beginning of the year (Survey 1) and (ii) how often they thought they should consume each item (Survey 2). Figure 4 Panel B shows the actual and ideal consumption shares of each lunch category in a respondent s diet (N = 87), while Appendix Table 7 presents a breakdown by menu preferences. 20 In the GP model, one can think of actual consumption as maximizing u + v and ideal consumption as maximizing u. Food j is therefore tempting if s u+v (j) > s u (j) where s w (j) is the consumption share of food j that maximizes utility w {u + v, u}. Consistent with R being a temptation, there is a positive and significant gap between respondents actual and ideal consumption share of red foods ( s u+v (R) s u (R) = 8.3 ppts, p < 0.001). For orange foods, the gap is also positive but much smaller (4.0 ppts, p = 0.049), and both its sign and its size significantly vary depending on the menu preferences of respondents. The size of the gap for green foods also significantly differs across menu preferences; as expected, this gap is negative (-12.4 ppts, p < 0.001). In contrast, the gap for R is very similar across all preference categories, as is actual consumption. In other words, those who prefer to eliminate R from the coverage include red foods in their diet at about the same frequency as those who do not and show the same desire to reduce their consumption share of red foods. The last source of evidence concerns respondents explanations of their ranking. In Survey 2, respondents were asked to explain why they chose or did not choose to assign rank 1 to the most flexible option GOR. Out of 87 respondents, 69 provided motivated answers, which form the basis of the analysis. 21 Among those who preferred a restricted coverage, 52% explicitly mentioned that they wanted to be motivated to eat healthier and/or discouraged to eat O or R foods. Another 38% explained that they ranked the options based on their current consumption habits, most often specifying that they essentially eat green foods and/or rarely eat red foods. The remaining 10% mentioned a desire not to be reimbursed for unhealthy foods or to eat healthy, without being more specific. However, for these last two categories, information about respondents food tastes allows to discard the hypothesis that preference for a restricted coverage is orthogonal to temptation. Participants were asked to indicate the 5 food items they craved the most; not surprisingly, all respondents who strictly preferred 19 Interestingly, the respondents who strictly prefer GO give a significantly higher health rating to orange foods than those who strictly prefer G (p = 0.08 on a two-sided t-test); this suggests that those who prefer to commit to GO do not perceive O as a bad category that needs to be discarded. 20 For comparison, reported means for actual consumption are taken over the subsample of participants who also replied to Survey 2 regarding their ideal consumption; results are fairly similar for the entire sample. 21 See OA. The 18 remaining respondents either did not respond to the question, mentioned that they did not remember the ranking procedure/were not sure of their choice, or answered something unrelated to the question. The entire set of comments is available from the author upon request. 18

19 G or GO mentioned at least one craving that belonged to category R. 22 Together, these results support the hypothesis that commitment to a restricted choice set is taken as an incentive mechanism to shift consumption away from foods perceived as tempting but unhealthy Predictive power of menu preference measures of temptation The previous discussion suggests that preference for commitment in the reimbursement program reveals participants temptation for unhealthy foods. In this section, I investigate whether temptation revealed through menu choice can predict self-control problems in an other domain: commitment to self-set goals pertaining to exercise and participation in the challenge. Below I present data on goal setting and goal achievement before studying their link with the menu preference measures of temptation developed in Section Description of the commitment contract and goal setting In Survey 1, participants were offered to receive their payment for the study (a $20 gift card) only contingent on the achievement of self-set attendance goals. These goals belonged to three categories: number of gym visits (during a 4 week period), number of follow-up weighins (out of 3) and number of wellness events (out of 4). Participants could set attendance goals in none, one or multiple categories and were informed that their attendance would be verified at the end of the challenge (see instructions in the OA). In this context, goals may act as a self-disciplining device for participants who expect their motivation and effort to drop during the challenge. Figure 5 shows the take-up rate of commitment to one or multiple goals as well as the distribution of goals by category. Commitment demand is high: despite the absence of any financial reward for reaching their goals, about 65% of respondents committed to at least one goal, and 73% of them committed to multiple goals. The selected targets were non trivial. Among the 55 respondents who set a gym attendance goal, the mean target was about 9 visits (2.25 visits per week). Attending the weigh-ins was the most popular goal: 62% (70/113) of participants chose to commit to at least one weigh-in, with about half of them setting the goal to attend all follow-up weigh-ins. On the other hand, only 21% (24/113) chose to commit to attending a wellness event. 22 The most common food items were pastries (8), chocolate (7), pizza (6) and potato chips/fries (5). 19

20 Figure 5: Distribution of goals number of gym visits number of weigh-ins % of respondents (0,5] (5,10] (10,15] (15,20] % of respondents number of wellness events total number of goals % of respondents % of respondents Attendance Data Data regarding attendance of the weigh-ins and the wellness events was collected through the wellness services of NYU. The gym attendance data comes from two different sources. First, the gym provided data on the number of times a participant scanned his or her gym badge, a requirement to access the facilities. However, the system retrieved only 69 of the 113 names. 23 Furthermore, the number of scans is only a proxy for gym attendance because participants could have checked in without exercising, as could have been the case on weighin days. Therefore, most respondents were also asked to report their gym attendance. 24 Among the 44 participants for whom the data could not be retrieved, 20 had set a gym attendance goal. These participants received their gift card provided they had achieved their other goals, which was only the case of 9 of them. Gym reports were collected after payments were announced, which should have lowered incentives to misreport. When data from both sources was available, the final estimate was taken to be the minimum between the 23 Participants with and without retrieved gym attendance do not significantly differ in terms of observable characteristics, except for their previous experience with the challenge and the gym facilities; see OA. 24 Respondents were not contacted when the system recorded zero visits or when there was no conflict with a weigh-in date. 20