Faculty of Economics and Business
How do health club users choose from a
menu of contracts? An empirical analysis
of time-inconsistent behavior
By Marina Svetachov Student number: 6071171
Master Thesis
Table of Contents
1. Introduction ... 2
2. DellaVigna’s and Malmendier’s model and findings ... 5
3. Data and descriptive statistics ... 10
4. Methodology and hypotheses ... 12
5. Results ... 15
6. Conclusion and discussion ... 25
7. Reference list ... 29
Appendix I ... 30
1. Introduction
This thesis evaluates the contract choice of health club users; in particular to what extend health club users minimize their costs of attendance and how they learn from their behavior over time. I replicate the study of DellaVigna and Malmendier (2004, 2006) (henceforth DM) in which they use data from three health clubs in de US to test whether the health club users make choices according to a standard model of contract choice. DM define the standard model assuming health club users have immediate costs, delayed benefits, rational expectations and time-consistent preferences. I use a novel dataset from the gym of the University of Amsterdam containing contract choice and attendance behavior to examine to what extend consumer behavior is in line with this standard model.
It is interesting to analyze consumers’ choice of gym contracts. If users do not exhibit behavior in line with DM’s model, it can indicate that consumers exhibit nonstandard preferences. In turn, this challenges the assumption of a rational agent, which forms the base of a large class of economic theory. According to DM the most plausible explanation for nonstandard behavior of health club users is (naïve) time-inconsistency. Time-inconsistent agents have a hyperbolic discounting function; their discount rate is not stable over time and therefore they make choices that are not optimal for their future self. This can lead for agents to systematically overestimate their future self-efficiency and procrastinate a costly task. For example, students unwillingly procrastinate studying for exams (Wong, 2008) and consumers procrastinate saving (Thaler & Benartzi, 2004).
Understanding the time-inconsistent preferences of users facing a menu of contracts is interesting for several reasons. Contracts commit consumers to experience some benefit and/or cost. Consumers that are aware of their time-inconsistency (sophisticated) can increase their expected utility by committing to a contract. For example, DM argue that sophisticated time-inconsistent health club users may subscribe to a contract to commit themselves to going to the gym, even though paying per visit would be cheaper. On the other hand, firms may exploit consumers that are not aware of their time-inconsistency. For example, DM argue that some health club users are (partially) naïve, unaware of their time-inconsistency, and thus do not cancel their costly contract even though they do not attend. Likewise, Shui and Ausubel (2005) show that consumers on the credit card market choose the less beneficial contract for their borrowing behavior and do not switch to the better contract. Eliaz and Spiegler (2006) confirm in their theoretical model that firms can extract large profits from naïve time-inconsistent agents.
There is evidence of nonstandard behavior of health club users. Charness and Gneezy (2009) show that health club users are unaware of the habits they can form after a number of attendances. In their experiment they give monetary incentives to health club users if they attend the gym sufficiently during the intervention period. Subsequently, they observe a persistent increased attendance after the intervention, which points towards habit formation. According to Charness and Gneezy (2009) health club users who are aware of their future benefits but have trouble to attend the gym in the present, should commit themselves to going to the gym, e.g. by subscribing to a contract and thus having a zero monetary marginal cost of attendance. Acland and Levy (2011) performed a similar experiment but in addition measured users’ prior expectations of future attendance and beliefs about their ability to form habits. From their results they argue that health club users are not fully aware of their ability to form a habit. However users do over predict their future attendance. Both the unawareness of the ability to form a habit and the overestimation of future attendance can lead to low present attendance.
Royer, Stehr and Sydnor (2012) did a similar experiment with financial incentives and in addition measured the take-up and effect of commitment devices offered after the intervention. After the intervention, half of the group received the offer to commit to exercising by putting money at stake. If they exercised in the two months after the intervention, they kept their money and otherwise it was donated to charity. The financial incentives increased gym attendance overall but, in contrast to Charness and Gneezy (2009) and Acland and Levy (2011), they found little habit formation in the months thereafter in the group that was not offered the commitment device. However, the average attendance in the subsequent months in the group that was offered the commitment device was higher compared to the control group. The interesting finding in this study is that people voluntarily chose to commit themselves to exercising; 22 percent amongst the employees who at least had exercised once during the intervention with financial incentives accepted the commit device. This suggests that users are aware of their time-inconsistent preferences and wish to commit themselves to increase future utility. These studies shows that people do no fully maximize the present value of the flow of future utilities, and that some are aware of their inability to do so.
panel data on contractual choice and attendance. They find that, in line with the standard model, there is selective exit (users learn over time) and users with high initial attendance sort in annual contracts. However, they find more evidence of nonstandard behavior: consumers choose contracts that do not maximize their utility. For example, consumers choose a flat-rate contract and pay more than the price they would pay per visit, foregoing a saving of $600 during their membership. Moreover, monthly members are 17% percent more likely to stay enrolled one year later than annual members. This is unexpected as monthly members have a higher fee per month but the advantage to quit any month. Finally, DM find that users delay their cancelation too long. Besides time-inconsistency, DM consider multiple alternative explanations for this behavior, such as having transaction costs when paying per visit or the benefits of having a membership. However, they argue that the best fitting explanation for this behavior is that consumers exhibit time-inconsistent preferences with naiveté and they overestimate their future self-control.
To the best of my knowledge, DM are the only ones who have studied the behavior of health club customers concerning contract choice using a longitudinal panel data on contractual choice and attendance. In order to understand whether their results are also valid in other settings, I replicate their study. I use a dataset from the gym of the University of Amsterdam containing contract choice and attendance behavior to examine to what extend consumer behavior is nonstandard in this context. There are some differences between the health clubs DM studied and the University Gym, which might lead to different results.
There are five main differences between DM’s sample and my sample. First, in contrast to DM’s sample, the population I study consists mainly of students and university/college staff. Second, the University Gym has three price categories for fitness contracts that vary greatly in price: for students, for university/college staff and for all other customers. This segmentation allows an analysis on the behavior between different groups. Third, all contracts end automatically and thus, in contrast to DM’s sample, there are no cancellation costs. Fourth, the choice of contracts is larger for the health club I study and thus users can sort better at enrollment to the contract that suits their preferences best. Lastly, the saving in monthly fee a user makes by committing to a longer-term contract is larger in my sample; i.e. the year contract is more attractive to paying per visit in my sample compared to DM’s sample.
This thesis contributes to the literature on how users choose when facing a menu of contracts when there are immediate costs and delayed benefits. Similar to DM’s results, the
results of this study show evidence of time-inconsistent agents and selective exit (learning) over time. However, in contrast to DM, initial enrollment in a contract with longer duration correlates with renewal probability 15 and 27 months later. Moreover, there is no evidence that users with higher initial attendance sort into contracts with a longer duration. This suggests that users do not sort at enrollment solely on their expectations of their monthly attendance, but also (or more so) on their expectations of how many months they wish to attend the health club. The results have implications for a profit-maximizing firms’ optimal contract and for policy makers stimulating physical exercise.
The remainder of this paper is organized as follows. Section 2 describes DM’s study and their outcome. Section 3 describes the data I use, section 4 the methodology and section 5 presents the results. Finally, section 6 summarizes and discusses the results.
2. DellaVigna’s and Malmendier’s model and findings
As this paper replicates DM’s study, I will extensively discuss their study in this section. First I give a summary of their sample, the contractual menu the consumers in their sample face and how the dataset is structured. Next, I provide the model they use for consumer behavior, followed by the predictions they make from this model accompanied with their findings.
Data and sample construction
DM collected a panel dataset from three health clubs containing data on users’ contractual choices and attendance from April 1997 to July 2000/2001. In addition, the dataset contained information on the (subsidized) price paid for the contracts and the memberships type (student, corporate, family). The health clubs offer users three types of contracts: a monthly and annual contract with an initiation fee but no fee per visit, and a pay-per-visit option. Health club 1 and 2 have approximately the same fees, health club 3 has slightly lower fees. The following summarizes the contractual menu:
• The monthly contract has a fee between $70 (discounted fee) and $85 and noncorporate users pay a fee ranging from $0 (during promotions) to $150. Corporate users are subsidized and thus pay a lower fee, ranging between $19 and $65, and pay no initiation fee. Health club 3 has a monthly fee from $13 to $52 and an initiation fee of a maximum of $50. A monthly contract can be cancelled in person at the health club or in writing. If it
• The fee for an annual contract is ten times the fee for a monthly contract. The initiation fee is the same as for a monthly contract. The annual contract ends automatically; users have to sign up again to stay enrolled.
• The clubs offer two ways for paying per visit, either by paying $12 for club 1 and 2 and $10 for club 3 or by purchasing a 10-ticket pass for $100 in club 1 and 2 and $80 in club 3. DM consider purchasing a 10-ticket pass as paying per visit.
DM analyses focus on enrollment spells which start when an individual (re)enrolls and ends when an individual quits. After dropping members with data inconsistencies and members who had a free or seasonal membership before enrolling (to limit to first time users), the sample contained 7752 individuals and 8273 enrollments spells. DM focus on the first enrollment spell for each individual – thus 7752 enrollment spells. Of these individuals 89 percent initially chose a monthly contract; health club members seldom change the type of contract enrolled in. DM restrict some analyses to a sample of unsubsidized health club members, consisting of 1070 individuals.
Model
Health club users in DM’s sample can choose to pay per visit, subscribe for a monthly contract (renewed automatically) or a year contract (ends automatically). DM summarize this contractual menu using four variables: (T’, L’, p’, k’).
𝑇’ = contractual duration in days
𝐿’ = lump sum fee for contractual duration 𝑝’ = price per visit
𝑘 ’ = transaction cost for switching to a pay-per-visit contract
Agents with a contract pay a lump sum fee (𝐿’ > 0) and have no additional cost per visit (𝑝’ = 0) for 𝑇’ period of days. Agents that pay per visit pay no lump sum fee (𝐿’ = 0) and a constant price per visit (𝑝’ > 0). Consumers with a monthly contract have a transaction cost of 𝑘’ > 0 for switching to a pay-per-visit contract as they need to actively end their monthly contract. The model does not allow for agents to have liquidity constraints.
After agents have chosen a contract they can attend the health club and incur an immediate cost 𝑐 at time 𝑡 and receive a benefit 𝑏 at time 𝑡 + 1. The cost 𝑐 represents the effort cost of going to the gym and 𝑏 represents the delayed net present value of future health
benefits. The effort cost is uncertain ex ante and individuals differ in their probability ex ante of either being a low cost or a high cost type.
When choosing a contract, agents will maximize the sum of all future utilities. The following function captures the present value of a flow of (future) utilities for time 𝑠:
𝑢!+ 𝛽 𝛿!!!𝑢! !
!!!!!
The discount factor for one period is 𝛿 and 𝛽 captures the time-(in)consistency of an agent. If 𝛽 = 1, then this is a consistent individual. If 𝛽 < 1, this agent exhibits time-inconsistency; the discount factor between the present and the next period is smaller than the discount factor between two adjacent periods in the future.
Agents have beliefs about their 𝛽, with is denoted by 𝛽. If 𝛽 = 𝛽 = 1 This is an exponential agent, a time-consistent agent who is aware of it
If 𝛽 = 𝛽 < 1 This is a sophisticated agent, a time-inconsistent agent who is aware of it
If 𝛽 = 1 and 𝛽 < 1 This is a naïve agent, a time-inconsistent agent who believes it’s fully time-consistent
If 𝛽 < 𝛽 < 1 This is a partially naïve agent, a time-inconsistent agent who it not fully aware of its time-inconsistency.
DM do not consider 𝛽 < 𝛽 as this would imply that an agent would belief to be more inconsistent than it is. DM argue that experimental evidence shows that a naïve
time-inconsistent agent (𝛽 > 𝛽) is the most plausible alternative to the ‘regular’ exponential agent.
Predictions from the standard model and empirical findings
DM take the time-consistent agent as the null hypothesis, as this agent is most encountered in economic models. What follows are the predictions stemming from this standard model and the empirical findings.
Prediction 1) The expected price per attendance under a contract should be equal or lower to the price of paying for one visit.
𝐿
𝐸 𝑣 ∗ 𝑎 𝑇 ≤ 𝑝
𝐸 𝑣 represents the expected visits during period T and 𝑎 𝑇 is the discount factor to adjust for having to pay a contract up front. This adjustment factor is assumed to be (close to) zero.
Finding 1)
The prediction does not hold: users with a monthly contract and an annual contract pay on average a price per average attendance higher than the price per visit. In addition the share of users who would have been better off ex-post by paying per visit is 80 percent in the monthly contract and 76 percent in the annual contract.
Prediction 2) The average initial attendance of annual members should be higher than the average initial attendance of monthly members.
The underlying assumption is that a user who expects to have a low cost 𝑐 and thus be a high attender should go for a year contract. Users that are have a higher probability of having a high cost 𝑐 for attendance will not want to make a commitment for a year and thus should go for a monthly contract.
Finding 2)
The prediction holds: the average initial attendance of annual members is 10 percent higher than the average initial attendance of monthly members.
Prediction 3) The average forecast of attendance should equal actual attendance
The underlying assumption is that users have rational expectations of their attendance. DM base the average forecast of attendance on the results of a survey.
Finding 3)
The prediction does not hold: the average forecasted number of attendances is higher than the actual average number of attendances observed.
Prediction 4) Low attenders under the monthly contract delay cancellation for at most a few days
The underlying assumption is that the cancelations costs are low compared to the savings from canceling a monthly contract.
Finding 5)
The prediction does not hold: the average contract delay period is 2.31 months.
Prediction 5) The survival probability after one and after two years is higher for agents who initially chose the annual contract than for agents who initially chose the monthly contract. The underlying assumption is similar to the one of prediction 2: agents sort at enrollment and agents with a low cost will go for an annual contract.
Finding 6)
The prediction does not hold: the survival probability for monthly members is higher than the survival probability for annual members.
Prediction 6: Among users initially enrolled in an annual contract, the expected attendance in the second year among stayers is higher than the expected attendance in the first year for the initial group.
Prediction 7: Among users initially enrolled in a monthly contract, the expected attendance among stayers should increase from month to month.
The underlying assumption for both predictions is that users learn over time about their cost of attending and selective exits will occur.
Findings 6 & 7)
The predictions hold: the average attendance among stayers increases for monthly members and for annual members.
DM (2006) argue that their results point towards a (partially) naïve time-inconsistent agent. The agent must be time-inconsistent as the price for paying per visit is lower than the ex-post average price per visit of users with a contract. Furthermore, the agent must be (partially) naïve as the cancelation delay would otherwise not be this long (2.31 months). A sophisticated agent would cancel quickly if it knew it would not attend at all anymore.
3. Data and descriptive statistics
This section describes the menu of contracts consumers face in my sample, how the dataset was constructed and provides summary statistics.
I have a collected a dataset from the university sports center. The sports center offers a wide menu of sport and gym contracts. In this study I focus on gym contracts only. There are three price categories: students, employees and all others. All contracts end when the contract period is over; no contract is renewed automatically. The contract period is either a year, six months, three months or a month. The gym introduced the month contract in July 2013. There are three main different types of contracts: a contract that allows unlimited visits (regular contract), a contract that allows 1 visit per week and a contract that allows unlimited visits in off-peak hours. As the number of contracts that allow 1 visit a week (646 first enrollment contracts) or only visits in off-peak hours (171 first enrollments contracts) is small, I focus my analyses on gym users enrolled in a regular contract. Table 1 summarizes the contracts and contract fees for the three categories over time.
Table 1. Contract menu and prices
2010 - 2012 2012 - 2013 2013 - 2014 Cat 1 Cat 2 Cat 3 Cat 1 Cat 2 Cat 3 Cat 1 Cat 2 Cat 3 Year 140 231.50 470 147 243 470 154 255 479
Half year 104 174 273 109 182.50 273 112. 187 273
Three month 63.50 104 142 66.50 109 142 70 110 146
Month NA NA NA NA NA NA 27 41 54
10-ticket pass 57.50 81 101 57.50 81 101 52.50 78.50 100.50
Notes: Each cell reports the price in euros for the different categories and type of contracts over time for each
year. The year starts in September and end in August. The price is applicable to the month in which they enroll in the contract, even though the contract may continue in next year’s pricing period. Category 1 consists of students, category 2 of employees of the university/college of Amsterdam and category 3 of all other members. All memberships, except the 10-ticket pass, allow for unlimited visits within the enrollment period.
The dataset consists of three parts:
1) A list of all fitness contracts starting between August 2009 and May 2014. Each contract has a unique contract number, is linked to an individual id, and has specified the type of contract and the beginning and end date. As attendance is only observed from August 2010, the sample is restricted to contracts with a begin date in or after this month. From the whole dataset I have inferred whether a contract was the first of an individual or not. I considered all fitness related contracts including contracts mixed with non-fitness elements, promotional contracts and 10-visit passes. However, as there was no data before August 2009, this should be regarded as a proxy. For most of the analyses I restrict the sample to first enrollment contracts (10503 contracts) as first users can be compared better to each other as they have all not yet learned from experience. I use a wider sample (18,761 contracts) for analyses focusing on renewal decisions.
2) All (attempted) attendances through entrance gates of members who have a fitness related contract are recorded from August 2010 to May 2014. Each successful attendance is registered under a contract number. However, some attendances have no contract number but an error indicated something went wrong, e.g. the contract was no longer valid or the entrance gate malfunctioned. I assumed that each individual with an active fitness contract that made an attempt to enter an entrance gate has paid a visit to the gym. This assumption may overestimate the attendance. However, there might also be instances where attendance is under recorded, e.g. due to accidentally open or malfunctioning entrance gates.
3) Background information on each individual: birthdate, gender, type of student and price category. The birthdate is slightly inaccurate. Individuals who have not enrolled in a contract for some time (37.84 percent), have their birthdate set at 16 or 17 of June. However, the year of birth is correct.
All data was matched and formed into a longitudinal dataset with monthly observations from August 2010 until the end of April 2014. The start and end date of a contract, and the date of the attendances was standardized so that each contract would begin on the first day of the month it enrolled in and end on the last day of a month. The following contracts were excluded from the dataset: contracts with zero attendances (331 contracts), contracts with non-fitness elements (258 contracts), contracts that either were too long or too short (259 contracts), contracts with an overlapping period of a month or longer (42 contracts) and irregular contracts for certain smaller groups (1151 contracts). In addition also
promotional contracts were excluded (1017 contracts), expect for testing hypothesis 2 (Table 6).
Table 2 summarizes the whole dataset. All statistics are based on contracts that ended before the end of the sample period. Table 1 in the appendix summarizes the dataset restricted to first enrollments.
Table 2. Summary statistics
Total Cat 1 Cat 2 Cat 3
Total number of contracts in sample 18761 13347 3883 1531 Proportion of contracts held by females 0.475 0.509 0.423 0.306 (0.499) (0.500) (0.494) (0.461) Average age at beginning of contract 25.88 22.87 33.71 32.35
(8.020) (3.573) (10.91) (9.929) Average monthly attendance per contract in whole
sample
3.791 3.535 4.038 5.402 (3.120) (2.966) (2.952) (4.145) Average monthly attendance in:
Year contract 3.268 3.041 3.821 4.315
(2.757) (2.648) (2.893) (3.282)
N = 9999 N = 7291 N = 2383 N = 325
Half year contract 3.626 3.550 3.714 4.141
(2.776) (2.778) (2.641) (3.083)
N = 2734 N = 1961 N = 581 N = 192
Three months contract 4.452 4.138 4.600 5.651 (3.330) (3.081) (2.999) -4.244
N = 5430 N = 3725 N = 834 N = 873
One month contract 7.299 7.119 6.824 8.057
(4.639) (4.638) (3.870) (5.000)
N = 596 N = 370 N = 85 N = 141
Notes: This first half of the table reports the average age and proportion of contracts of females in the sample.
The second half reports the average attendance per month for the whole sample and per contract type. Only contracts included that ended before the end of the sample period. Category 1 consists of students, category 2 of employees of the university/college in Amsterdam and category 3 of all other members. Refer to Table 1 in the appendix for summary statistics restricted to first contracts of users. Standard deviations in parentheses. The number of observations is denoted by N.
4. Methodology and hypotheses
Similar to DM, I use a dataset of users’ contract choices and behavior to determine whether individuals’ behavior is in line with the standard model. In this section I provide the hypotheses I will test. To be able to compare my results to DM, I closely follow their
reasoning and method of estimation. However, as my data and gym contracts differ from the sample that DM use, some predictions and estimation techniques differ. Moreover, in line with DM, I do not allow agents to be liquidity constraint because the price of a contract for students and employees is relatively low. Moreover, students can lend money from the government at a low interest rate to overcome this liquidity constraint. Users in category 3 have a higher price but can opt to pay a monthly fixed fee during the contract period for a small additional charge.
Testing for time-inconsistency and rational expectations.
Hypothesis 1) The expected average price per attendance under the chosen contract should be lower than the expected average price per attendance under any alternative.
This hypothesis tests whether users have rational expectations. As users have uncertain effort costs, the expected attendance is also uncertain. Under the assumption of rational expectations, they should on average make the right choice.
I examine whether users have rational expectations or are time-inconsistent in several ways. First, to be consistent with DM, I follow their method by calculating the expected price per attendance and comparing this to paying per visit. They take the ratio of the average sample price and average sample attendance as a proxy for the expected price per attendance. However, this approach does not incorporate that individuals have different expectations of their effort costs and will choose a contract accordingly. Thus, I will also examine the ratio of the price and average attendance per contract per individual. As the average of this ratio is influenced by outliers, I will examine the distribution by looking at the percentage of people being better off by paying per visit. Next, I extend the analysis to include combinations of contracts and paying per visit as an alternative. Finally I look at the percentage of people that make a suboptimal choice in their second enrollment; especially whether people who made a suboptimal choice in their first enrollment do it again. As I assume that users learn their effort cost after one enrollment, making a suboptimal choice twice points towards time-inconsistency and a rejection of rational expectations.
Testing for sorting at enrollment
Hypothesis 2) The initial attendance of users with a yearly contract is higher compared to users enrolled in a six month contract; the initial attendance of users with a six month contract is higher compared to users enrolled in a three month contract.
This hypothesis tests whether users sort at enrollment given their effort costs. DM assume that users with a probability of being a high-cost type will choose a short-term contract as they are not willing to make a long-term commitment. Although it is plausible that high-cost types will prefer a short-term contract, they might not enroll in it as the price per month is higher compared to longer-term contracts. In addition, there might be users not willing to make a long-term commitment for other reasons than being a high-cost type, e.g. they might move to another place or do other physical activity in certain months. As other reasons than having a high probability of being a high-cost type may have no correlation with expected attendance, the group of users considering a short-term contract does not only constitute high-cost types. As the price per month for short-term contract is higher than for long-term contracts, only users that expect to be low-cost type will enroll and high-cost type might not enroll at all. Thus, there is reason to believe that the group having a short-term contract consists of low-cost types who have chosen the short-term contract as it fits their expectations of the amount of months they wish to attend the gym better.
As there are two opposite forces that influence sorting and expected initial attendance, comparing initial attendance of users in different contracts will explain little about their sorting behavior. However, my data allows me to examine a group of users that face a menu of contracts with the same price per month irrespectively of duration, and thus eliminate the selective exit of low-cost types due to costly short-term contracts. This group consists of first year students that enrolled in September 2013 in a promotional contract. These promotional contracts all cost € 9.90 per month and have a commitment of three months, six months or a year.
To be consistent with DM, I will first examine whether hypothesis 2 holds for the initial attendance of regular contracts, and then examine how the results differ for the promotional contract.
Hypothesis 3) Survival probability after 12 or 24 months is higher for annual members than for 3 or 6 months members.
This hypothesis also tests sorting at enrollment. The underlying assumption is similar to the assumption underlying hypothesis 2. Users with high attendance expectations will enroll in a contract with a longer duration. In addition, users that want to make a long-term commitment for other reasons, also have a higher probability of enrolling again for the same reasons. Moreover, studies (Acland & Levy, 2011; Charness & Gneezy, 2009) have shown that gym users (unknowably) form habits in the long run. Thus, members with a longer duration of enrollment are more likely to form a habit of going to the gym and enrolling again.
Testing for selective exit
Hypothesis 4): The average attendance among stayers should increase in each additional contract.
This hypothesis tests for selective exit. The underlying assumption is that users who experienced high attendance should renew their contract. Other users should either quit or switch to paying per visit.
5. Results
Hypothesis 1) The expected average price per attendance under the chosen contract should be lower than the expected average price per attendance under any alternative.
As there are many alternative combinations of contracts and paying per visit for a given period of time, I restrict my analysis to the three most common groups of alternatives to a contract that can result in a lower ex-post price for first time users. First I follow DM by considering paying per visit as an alternative (Table 3). Next, I include any combination of a shorter contract and paying per visit (Table 4). The third way a user can be better off is by having a six month or year contract instead of two sequentially three month of six month contracts (Table 4). Subsequently, I also consider users in their second enrollment who make a suboptimal choice (Table 5).
I use the price of a 10-ticket pass as a reference point for paying per visit. The gym does have a day ticket, but it was introduced in July 2013 and thus not a relevant reference
as the 10 tickets are valid up to a half year and thus I assume a user will use all 10 tickets in a half year. Especially when considering the second alternative to a contract (a shorter contract in combination with paying per visit) the assumption of a user using all 10 tickets in a half year is weak. It is however the only alternative for users enrolled in a contract prior to July 2013 for paying per visit instead of paying a flat fee rate. The price for one visit in a 10-ticket pass differs between years and surprisingly is lower at the end of the sample period. For attendees in category 1 the price per visit is between € 5.25 and € 5.75, for attendees in category 2 between € 7.85 and € 8.10 and for category 3 between € 10.50 and € 11.
The sample was restricted to only include (the proxy for) first enrollments. Attendees in their second or later enrollment will have learned what their costs and benefits are for attending and therefore considering all contracts would bias the average attendance upwards.
The first alternative was examined by considering the average price per average attendance over all contracts and the average price per attendance per individual per contract. Table 3 summarizes the results. The average price per average attendance is lower than the pay per visit price for all contracts, except the half year contract for category 2 and category 3. However, this ratio, which is also reported by DM, is not the most meaningful estimator as it does not incorporate that users have different expectations of their effort costs. The lower part of Table 3 shows the average price per attendance of individual contracts. This measure shows what percentage of users would have been better off in terms of money spent by paying per visit. For year, half year and three month contracts around 50 to 70 percent of the users would have been better off paying per visit. For monthly contracts, this percentage is around 70 percent.
P ri ce p er a ve ra ge a tte nd an ce fo r fir st co ntr ac t co nt ra ct : Ye ar H al f ye ar 3 M ont hs Mo nt h Ye ar H al f ye ar 3 M ont hs Mo nt h Ye ar H al f ye ar 3 M ont hs Mo nt h at io ns : 4364 1284 2280 152 902 312 443 27 165 101 400 73 2. 679 3. 353 3. 983 6. 638 3. 153 3. 509 4. 390 7. 333 3. 926 3. 670 4. 890 7. 890 (0 .0 36 3) (0 .0 76 0) (0 .0 62 9) (0 .3 37 ) (0 .0 89 2) (0 .1 53 ) (0 .1 36 ) (0 .9 70 ) (0 .2 74 ) (0 .2 81 ) (0 .1 83 ) (0 .5 50 ) 11. 80 17. 60 21. 60 27 19. 43 29. 46 35. 02 41 39. 17 45. 17 47. 40 54 (0 .0 04 41 ) (0 .0 18 7) (0 .0 20 8) (0 ) (0 .0 19 4) (0 .0 48 6) (0 .0 60 9) (0 ) (0 ) (0 .1 87 ) (0 .0 40 1) (0 ) 4. 40 5. 25 5. 42 4. 07 6. 16 8. 40 7. 98 5. 59 9. 98 12. 31 9. 69 6. 84 P erc en til e 10t h 2. 00 2. 57 2. 65 2. 25 2. 83 4. 14 4. 00 3. 11 4. 20 6. 50 5. 04 3. 98 20t h 2. 80 3. 30 3. 53 2. 88 3. 92 5. 44 5. 36 3. 73 6. 44 8. 13 6. 45 4. 50 30t h 3. 68 4. 33 4. 54 3. 38 4. 82 6. 69 6. 42 5. 42 8. 55 9. 97 8. 35 5. 01 40t h 4. 67 5. 20 5. 54 3. 99 5. 94 8. 29 7. 43 5. 86 10. 68 11. 80 10. 14 5. 76 me di an 6. 09 6. 50 6. 65 4. 50 7. 47 10. 24 8. 67 5. 86 13. 82 13. 00 11. 83 6. 75 60t h 7. 78 8. 38 7. 94 5. 40 10. 56 13. 04 11. 56 6. 83 18. 08 17. 29 14. 20 8. 23 70t h 10. 00 10. 90 10. 58 6. 75 14. 47 17. 40 14. 86 8. 20 23. 50 23. 58 17. 75 10. 80 80t h 14. 70 15. 57 14. 00 9. 00 23. 15 24. 86 20. 80 11. 62 33. 57 39. 00 23. 67 18. 00 90t h 28. 00 27. 25 21. 17 13. 50 38. 58 36. 50 27. 40 20. 50 55. 49 91. 00 47. 33 27. 00 e ab ov e pa rt re po rt s th e av er ag e m on th ly a tt en da nc e an d pr ic e of m em be rs d ur in g th e gi ve n co nt ra ct p er io d. S ta nd ar d er ro rs in p ar en th es es . Th e th ird ro w re po rt s th e ra tio o f t he on th ly a tt en da nc e an d pr ic e. Th e se co nd p ar t r ep or ts th e di st rib ut io n of in di vi du al s' a ve ra ge p ric e pe r a tt en da nc e. P er ce nt ile s un de rli ne d in b et w ee n w he re a 1 0-tic ke t p as s c he ape r opt ion - f or c at egor y 1 thi s is be tw ee n € 5. 25 a nd € 5. 75 , f or c at egor y 2 be tw ee n € 7. 85 a nd € 8. 10 a nd for c at egor y 3 be tw ee n € 10 .5 0 and € 11 . I f onl y one va lue is d, thi s is a ppr ox im at el y the va lue w he re a 1 0-tic ke t pa ss be com es the c he ape r opt ion. C at egor y 1 cons is ts of s tude nt s, c at egor y 2 of e m pl oye es of the uni ve rs ity/ col le ge in m a nd c at eg or y 3 of a ll ot he r m em be rs Sa m pl e: F irs t e nro llm en t c on tra ct s en di ng in s am pl e pe rio d m on th ly p ric e ge p ric e pe r av era ge ce pric e an ce tra ct Ca te go ry 1 Ca te go ry 2 Ca te go ry 3 m on th ly a tte nd an ce
The second alternative was examined by calculating the percentage of users better off with any combination of a shorter contract and paying per visit. Table 4 shows the results. The above part of Table 4 examines the percentage of people initially enrolled in a year, six or three month contract and whether they would be better off with any other combination in that time period. The results show that the percentage of users who would be better off with any other alternative increases with 10 to 20 percentage points compared to only considering paying per visit as an alternative.
The second part of the table examines users who subsequently enrolled in a three month or a six month contract. These users are better off by respectively enrolling in a six month and year contract.
Table 4. Percentages of users making suboptimal choices in their first enrollment
Sample: First enrollment contracts
Total Category 1 Category 2 Category 3 Percentage with a year contract - better off with
an alternative
60.74% 61.59% 54% 74%
(51.22 %) (51.72 %) (46.90 %) (61.82 %)
N = 5431 N = 4364 N = 902 N = 165
Percentage with a six month contract - better off with an alternative
71.95% 71.42% 71.47% 80.20% (58.52 %) (56.93 %) (61.22 %) (70.30 %)
N = 1697 N = 1284 N = 312 N = 101
Percentage with a three month contract - better off with an alternative
59.49% 60.13% 54.63% 61.25%
N = 3123 N = 2280 N = 443 N = 400
Percentage of users with two adjacent six month contracts - better off with a year contract
3.18% 2.41% 5.77% 4.95%
N = 1697 N = 1284 N = 312 N = 101
Percentage of users with two adjacent three month contracts - better off with a six month contract
8.87% 7.19% 10.16% 17%
N = 3123 N = 2280 N = 443 N = 400
Notes: The first part of the table reports the percentage of users better off with any combination of a shorter
contract and paying per visit during the given contract period. Percentages of users better off if they exclusively paid per visit in parentheses. The second part reports the percentage of users that subsequently enrolled in two six (three) month contracts but would be better off with a year (six) month contract. Category 1 consists of students, category 2 of employees of the university/college in Amsterdam and category 3 of all other members. The number of observations is denoted by N.
To understand whether users make suboptimal choices twice, I examine users’ second enrollment. I first consider all users in their second enrollment and next the group of users that made a suboptimal choice in their first enrollment. The first group – all users in their second enrollment – consists of users that have any experience in this health club before (with data from August 2009). This also includes having had a 10-ticket pass. I define having
made a suboptimal choice in two ways: being better off with any alternative in a contract period (broader definition) and being better off by paying per visit (narrow definition). Table 5 shows the results. Of the users that made a suboptimal choice in their first enrollment, more than 73 percent makes a suboptimal choice again (using the narrow and broad definition). Of all users in their second enrollment, still a high percentage of the users makes a suboptimal choice 45.61 % (narrow definition) to 51.36% (broad definition).
Table 5. Percentages of users making suboptimal choices in their second enrollment
Total Category 1 Category 2 Category 3 Percentage of users in second enrollment - better
off with an alternative
51.36% 52.83% 45.03% 58.12%
N = 4813 N = 3316 N = 1146 N = 351
Percentage of users in second enrollment - who made a suboptimal choice in their first enrollment - better off with an alternative contract choice
73.53% 71.68% 76.96% 81.54%
N = 1311 N = 964 N = 217 N = 130
Percentage of users in second enrollment - better off with paying per visit
45.61% 46.17% 41.36% 54.13%
N = 4813 N = 3316 N = 1146 N = 351
Percentage of users in second enrollment - who were better of paying per visit in their first enrollment - better off with paying per visit
74.88% 74.12% 77.59% 75.68%
N = 609 N = 456 N = 116 N = 37
Notes: The first part of the table reports the percentage of users better off with any combination of a shorter
contract and paying per visit in their second enrollment; the first row of percentages examines all second enrollments and for the second row the sample is restricted to users who made a suboptimal choice in their first enrollment. The second part of the table reports the percentage of users better off with paying per visit in their second enrollment; the first row of percentages examines all second enrollments and the second row only those who made were better off by paying per visit in their first enrollment. Category 1 consists of students, category 2 of employees of the university/college in Amsterdam and category 3 of all other members. The number of observations is denoted by N.
The empirical analysis of users’ attendance shows that there is reason to believe expectations are not rational and/or users are time-inconsistent. Although the average price per average attendance is below the price per visit, more than 50 percent of the users would be better off paying per visit. When considering more alternatives to a contract, the percentage rises with 10 to 20 percentage points. Finally, the analysis of users’ second enrollment shows that some users do not learn from their first enrollment. The finding that more than 73 percent of the
an alternative contract and/or paying per visit, also gives reason to believe that expectations are not rational and/or preferences are time-inconsistent.
Hypothesis 2) The initial attendance of users with a yearly contract is higher compared to users enrolled in a six month contract; the initial attendance of users with a six month contract is higher compared to users enrolled in a three month contract.
To test the above hypothesis, the sample was restricted to (the proxy for) first enrollments. Only initial attendance is considered to be able to compare attendance with the three month contract. Table 6 reports the average monthly attendance in the first, second and third month of users’ first three month, six month or year contract. The results show no clear pattern of increasing attendance as the contract period increases.
Table 6. Initial monthly attendance
Sample: First enrollments contracts
Category 1 Category 2 Category 3
Month 1 Month 3 Month 3 Month 1 Month 2 Month 3 Month 1 Month 2 Month 3 Year contract 5.109 3.621 3.242 5.536 3.91 3.693 6.553 4.645 4.528 (0.0501) (0.049) (0.0479) (0.116) (0.107) (0.108) (0.314) (0.295) (0.295) N = 5297 N = 5297 N = 5297 N =1083 N = 1083 N =1083 N = 197 N = 197 N = 197 Half year contract 5.249 3.895 3.664 5.597 4.025 3.634 5.829 4.324 3.867 (0.098) (0.102) (0.105) (0.191) (0.189) (0.193) (0.349) (0.338) (0.379) N = 1395 N = 1395 N = 1395 N = 325 N = 325 N = 325 N = 105 N = 105 N = 105 Three month contract 5.528 3.728 2.693 6.124 4.056 3.018 6.695 4.45 3.525 (0.0754) (0.0751) (0.0722) (0.169) (0.172) (0.152) (0.216) (0.21) (0.208) N = 2280 N = 2280 N = 2280 N = 444 N = 444 N = 444 N = 400 N = 400 N = 400
Notes: Monthly average attendance reported among users in given month and contract reported. Standard errors in parentheses.
Category 1 consists of students, category 2 of employees of the university/college in Amsterdam and category 3 of all other members. The number of observations is denoted by N.
Table 7 summarizes the initial average attendance of users with a promotional contract. As the promotional contract has a flat monthly fee regardless of the duration, users sort by choosing their preferred duration. The results in Table 7 show no clear increasing pattern of attendance as the contract period increases. Thus, there is no reason to believe that users with a higher probability of having a high effort cost sort into short-term contracts.
Table 7. Initial monthly attendance of users with a promotional contract
Sample: First enrollments contracts
Month 1 Month 2 Month 3
Year contract
5.041 4.302 3.502 (0.172) (0.169) (0.165)
N = 566 N = 566 N = 566
Half year contract
4.699 3.555 2.914 (0.23) (0.202) (0.204)
N = 292 N = 292 N = 292
Three month contract
5.937 4.528 3.208 (0.363) (0.35) (0.324)
N = 159 N = 159 N = 159
Notes: Monthly average attendance reported among category 1
users, students, in given month and contract reported. Standard errors in parentheses. The promotional contracts were all € 9.90 per month, irrespective of the duration. Only first year bachelor students were eligible. The number of observations is denoted by N.
Hypothesis 3) Survival probability after 12 or 24 months is higher for annual members than for 3 or 6 months members.
To test this hypothesis, the probability of being enrolled in the 15th month and 27th month
after first enrollment is compared between users in different type of first contracts. I report marginal effects from a probit analysis. Table 8 summarizes the results.
Table 8. Probit of renewal decision
Sample: All contracts
Enrollment in 15th month Enrollment in 27th month No controls Controls + time dummies No controls Controls + time dummies Year contract 0.0906*** 0.0834*** 0.108*** 0.103*** (0.0112) (0.0117) (0.0117) (0.0122)
Half year contract 0.0287* 0.0185 0.0302* 0.0207
(0.0163) (0.0165) (0.0179) (0.0179) Category 2 0.126*** 0.130*** (0.0169) (0.0182) Category 3 0.0207 -0.00783 (0.0231) (0.0232) Female -0.0533*** -0.0435*** (0.00979) (0.0101) Age -0.00247*** -0.00285*** (0.000878) (0.000880)
Time dummies No Yes No Yes
Baseline renewal probability 3 month contract
0.234 0.225 0.131 0.119
Observations N = 8815 N = 8815 N = 6223 N = 6223
Notes: Coefficients of a probit regression with marginal effects reported. Year contract, half year
contract, category 2, category 3 and female are dummy variables. The time dummies consist of dummies for the year and month of the beginning of the first contract. The coefficients represent the difference in probability of being enrolled in the 15th or 27th month in response to a discrete change of a dummy variable or an infinitesimal change in a continuous variable. Standard errors in
parentheses. ***, ** and * denote significance at 1%, 5% and 10% respectively.
The coefficients for year contract and half year contract capture the difference in probability of being enrolled in the 15th or 27th month between users initially enrolled in a year or half year contract and users initially enrolled in a three month contract. The survival probability in the 15th month for a user initially enrolled in a year contract is 8.34 percentage points higher than the survival baseline probability of 22.5 percent of a user enrolled in a three month contract, if controlling for observed heterogeneity. The difference in survival probabilities in the 27th month of users initially enrolled in a year contract and a three month contract increases to a difference of 10.3 percentage point. As the overall survival rate decreases for the 27th month for all users, the survival probability for users initially enrolled in an annual contract is almost twice as large as the survival probability of 11.9 percent of users initially enrolled in a three month contract.
The hypothesis is confirmed: survival probability of members initially enrolled in annual contracts is higher than the survival probability of members initially enrolled in half year or three month contracts. Thus, members sort at enrollment. However, the reason for sorting might not be that annual members expect to have a high attendance (as Table 7 shows). It is more likely that annual members expect to attend for a longer period of time for reasons unrelated to monthly attendance and thus are more likely to enroll in another contract.
Hypothesis 4): The average attendance among stayers should increase in each additional contract.
I test this hypothesis by examining if the average attendance of all users increases in each additional enrollment. Table 9 reports the average attendance per contract per enrollment per category. In all categories average attendance per contract increases as the number of enrollment increases. In Table 10, the hypothesis is tested formally using a linear regression with control variables for observed heterogeneity such as the type of contract. The coefficient of the number of enrollment is significant and large: average monthly attendance increases by 0.459 (p < 0.01) per month among users enrolled in each additional contract. The hypothesis is confirmed; the average attendance among stayers increases in each additional contract.
Table 9. Monthly average attendance per contract per enrollment Sample: All contracts
All categories Category 1 Category 2 Category 3
1st enrollment 3.400 3.228 3.612 4.800 (2.902) (2.772) (2.869) (3.810) N = 10503 N = 8080 N = 1684 N = 739 2nd enrollment 3.847 3.627 4.049 5.177 (2.902) (2.772) (2.869) (3.810) N = 10503 N = 8080 N = 1684 N = 739 3rd enrollment 4.509 4.299 4.571 5.730 (3.227) (3.187) (3.001) (3.915) N = 2046 N = 1242 N = 623 N = 181 4th enrollment 4.913 4.778 4.705 6.240 (3.382) (3.329) (3.120) (4.147) N = 810 N = 412 N = 308 N = 90 5th enrollment 6.083 6.009 4.838 7.438 (4.448) (4.511) (3.296) (4.985) N = 207 N = 98 N = 54 N = 55 6th enrollment 7.072 7.230 6.304 7.370 (4.542) (5.147) (3.181) (4.378) N = 93 N = 46 N = 20 N = 27 7th enrollment 8.305 9.314 5.882 9.300 (5.333) (5.678) (2.826) (6.246) N = 58 N = 26 N = 17 N = 15 8th enrollment 8.592 9.083 6.792 9.442 (5.617) (6.622) (2.706) (6.195) N = 30 N = 12 N = 8 N = 10 9th enrollment 9.108 10.119 6.667 9.407 (7.350) (8.902) (4.064) (7.662) N =20 N = 7 N = 4 N = 9 10th enrollment 9.152 6.778 9.667 10.095 (6.445) (4.764) (7.600) N = 11 N = 3 N = 1 N = 7
Notes: The average monthly attendance during a contract per enrollment per category
reported. The enrollments represent the number of contract a user is enrolled in, irrespective of the length of a contract. Category 1 consists of students, category 2 of employees of the university/college in Amsterdam and category 3 of all other
members. Standard deviations in parentheses. The number of observations is denoted by N.
Table 10. Effect of number of enrollment on average monthly attendance
Sample: All contracts No controls Controls Number of enrollment 0.617*** 0.459*** (0.0198) (0.0195) Category 2 0.468*** (0.0636) Category 3 0.997*** (0.0861) Age -0.0138*** (0.00330) Female -1.086*** (0.0428)
Contract dummies No Yes
Constant 2.721*** 3.214***
(0.0409) (0.0885)
Observations 18,761 18,761
R-squared 0.049 0.145
Notes: The coefficients reported come from an OLS regression with the average
monthly attendance during a contract period as dependent variable. Category 2, category 3 and female are dummy variables. The contract dummies consist of a dummy for the type of contract (year, half year, 3 month or one month). Standard errors in parentheses. ***, ** and * denote significance at 1%, 5% and 10% respectively.
6. Conclusion and discussion
In this thesis I replicated DM’s study on bounded rationality of health club users choosing from a menu of contracts. To be consistent with DM’s approach, I tested similar hypotheses with the null hypothesis inferred from a standard model of contract choice with rational agents.
In contrast to DM, I do not find convincing evidence that the average price per average attendance is higher than the price for paying per visit. However, I do find that more than 50 percent of the health club users make a suboptimal choice and some users make suboptimal choices twice; I conclude that this points towards time-inconsistency. DM argue that the users in their sample exhibit (partially) naïve time-inconsistency as the cancelation lags are too long for sophisticated agents. As contracts end automatically in my sample, I
argued that if a user is better off by paying per visit it must be (partially) naïve as paying-per-visit can be done upfront with a 10-ticket pass, especially in the case of a half year or a three month contract. Thus, fully sophisticated agents should have chosen a 10-ticket pass as a commitment device. However, the marginal monetary cost of attending with a 10-ticket pass is not zero as under a regular contract, but is equal to the opportunity cost of attending another time and using the ticket. Moreover, sophisticated users might also prefer a contract of longer duration to commit for a longer period of time. Therefore, this does not present convincing evidence of the presence of naïve time-inconsistent preferences.
In contrast to DM, I do not find that the initial attendance of health club users in a longer contract period is higher compared to users enrolled in a shorter contract. I am able to test this on users with the same monthly rate for contracts with different durations, and therefore exclude the sorting effect a higher monthly fee for shorter contract normally brings with it. Also for these users, there is no evidence of higher initial attendance among users with a contract of longer duration. Therefore there is no reason to believe that users with a high probability of having a high effort cost sort into short-term contracts.
In line with the standard model but in contrast with DM, I find that survival probability of members initially enrolled in annual contracts is higher than the survival probability of members initially enrolled in half year or three month contracts. Thus, members sort at enrollment. However, as shown above, the reason for sorting might not be that annual members expect to have low effort costs. It is more likely that annual members sort at enrollment because they expect to attend for a longer period of time for reasons unrelated to monthly attendance and thus are more likely to enroll in another contract. Another explanation is that users with an annual contract are more likely to develop a habit of exercising and thus enrolling in another contract. Finally, DM’s results could stem from the automatically renewal of the monthly contract, making it more likely for (naïve time-inconsistent) users with an automatically renewed monthly contract to stay enrolled.
Finally, my results regarding the selective exit of users are in line with DM. The average attendance among stayers increases in each additional contract. From this, I argue that users with a low prior attendance choose to not enroll again and vice versa. Thus, users learn from their past experience.
To conclude, this thesis contributes to the literature on nonstandard preferences of health club users by examining a novel dataset of gym users’ contract choices and attendance over time. It challenges some of DM’s assumptions and findings. First of all, it challenges
DM assumption that people sort into contracts according to being a high or a low cost type. I find that users that choose a contract with a short duration do not attend less frequently than users that sort into a contract of longer duration. Second, my finding that users with a contract of longer duration are more likely to stay enrolled is in contrast with DM’s results. These contrasting results indicate that sorting at enrollment and renewal decisions are more complex than DM’s model suggest.
This study also contributes to the understanding of time-inconsistent preferences of health club users. By validating that more than 50 percent of the health club users make a sub-optimal choice, more evidence is provided that consumers might exhibit time-inconsistent preferences. Moreover, the finding that the average price per average attendance is below the price for paying per visit, gives rise to some questions. How do consumers choose from a menu of contract in which benefits and costs have a skewed distribution? Do they take this into account and only measure their expectations of personal costs?
The results have implications for a profit-maximizing firms’ optimal contract and for policy makers stimulating physical exercise. However, one of the limitations of this study is that it sheds little light on the distribution of sophisticated and (partially) naïve agents. More research on this should distinguish these two types of time-inconsistent agents.
The distinction between sophisticated and naïve time-inconsistent agents is of interest for firms as the profit-maximizing contract will differ among the type of agents. DM demonstrate that in a market place with naïve time-inconsistent agents and where consumers have immediate costs and delayed benefits, firms maximize their profit by offering contracts with automatic renewal and below marginal cost pricing. However, a profit maximizing contract for sophisticated agents most probably has different characteristics, e.g. it can incorporate commit devices to attract these (new) customers. Some research has emerged regarding commit devices. Milkman, Minson and Volpp (2013) found that when gym visits were bundled with tempting and otherwise inaccessible audio novels, gym attendance increased. Moreover, they show that there is a willingness to pay for such a commitment device. This is in line with Royer, Stehr and Sydnor (2012) findings that show that some people are willing to put money at stake to commit to exercising. Some health clubs1 have adopted commitment devices, e.g. by lowering the monthly fee if users attend more frequently. However, there is no research on what features a profit-maximizing contract for sophisticated agents exhibits.
Furthermore, understanding consumers’ behavior in the health club industry and making a distinction between sophisticated and (partially) naïve agents can help policy makers stimulate physical exercise. For example, public policy may subsidize commitment devices to increase participation of sophisticated agents or give monetary incentives to new members in order to stimulate habit formation.
7. Reference list
Acland, D., & Levy, M. (2011). Habit formation, naiveté, and projection bias in gym attendance. Working paper.
Charness, G., & Gneezy, U. (2009). Incentives to exercise. Econometrica,77(3), 909-931. DellaVigna, S., & Malmendier, U. (2004). Contract design and self-control: Theory and
evidence. The Quarterly Journal of Economics, 119(2), 353-402.
DellaVigna, S., & Malmendier, U. (2006). Paying not to go to the gym. The American
Economic Review, 694-719.
Eliaz, K., & Spiegler, R. (2006). Contracting with diversely naive agents. The Review of Economic Studies, 73(3), 689-714.
Milkman, K. L., Minson, J. A., & Volpp, K. G. (2013). Holding the Hunger Games hostage at the gym: An evaluation of temptation bundling. Management Science, 60(2), 283-299. Royer, H., Stehr, M. F., & Sydnor, J. R. (2012). Incentives, Commitments and Habit
Formation in Exercise: Evidence from a Field Experiment with Workers at a Fortune-500 Company (No. w18580). National Bureau of Economic Research.
Shui, H., & Ausubel, L. M. (2004). Time inconsistency in the credit card market(Doctoral dissertation, University of Maryland).
Simon, H. A. (1972). Theories of bounded rationality. Decision and organization, 1, 161-176. Thaler, R. H., & Benartzi, S. (2004). Save More Tomorrow: Using behavioral economics to
increase employee saving. Journal of political Economy, 112(S1), S164-S187.
Wong, W. K. (2008). How much time-inconsistency is there and does it matter? Evidence on self-awareness, size, and effects. Journal of Economic Behavior &
Appendix I
Table 1. Summary statistics – first enrollment contracts
Total Cat 1 Cat 2 Cat 3
Total number of first enrollment contracts in sample 10503 8080 1684 739 Proportion of contracts held by females 0.513 0.539 0.456 0.359
(0.500) (0.499) (0.498) (0.480) Average age at beginning of contract 24.61 22.39 32.04 31.88
(6.888) (3.433) (9.673) (10.01) Average monthly attendance per contract for first
enrollments
3.401 3.228 3.612 4.806 (2.902) (2.773) (2.869) (3.810) Average monthly attendance in:
Year contract 2.794 2.678 3.153 3.908
(2.498) (2.398) (2.680) (3.506)
N = 5429 N = 4364 N = 902 N = 165
Half year contract 3.401 3.353 3.509 3.670
(2.726) (2.723) (2.706) (2.825)
N = 1697 N = 1284 N = 312 N = 101
Three months contract 4.157 3.983 4.390 4.890
(3.091) (3.003) (2.859) (3.662)
N = 3123 N = 2280 N = 443 N = 400
One month contract 7.075 6.638 7.333 7.890
(4.433) (4.154) (5.038) (4.695)
N = 252 N = 152 N = 27 N = 73
Notes: The first half of the table reports the average age and proportion of contracts of females in the sample.
The second half reports the average attendance per month for the whole sample and per contract type. Only first enrollment contracts included that ended before the end of the sample period. Category 1 consists of students, category 2 of employees of the university/college in Amsterdam and category 3 of all other members. Standard deviations in parentheses. The number of observations is denoted by N.
