Your Favorite Anomalies

10 October 2006 at 9:22 am 4 comments

| Lasse Lien |

Anomalies are a key engine of scientific progress, so say Kuhn and Clayton Christensen, among others. Anomalies should accordingly be celebrated and distributed. In this spirit I offer what I consider to be a great example of an anomaly (and please submit your own favorites, or comment on the one below). This one is lifted from a recent AER paper by DellaVigna and Malmendier.

How do consumers choose from a menu of contracts? We analyze a novel dataset from three U.S. health clubs with information on both the contractual choice and the day-to-day attendance decisions of 7,752 members over three years. The observed consumer behavior is difficult to reconcile with standard preferences and beliefs. First, members who choose a contract with a flat monthly fee of over $70 attend on average 4.3 times per month. They pay a price per expected visit of more than $17, even though they could pay $10 per visit using a 10-visit pass. On average, these users forgo savings of $600 during their membership. Second, consumers who choose a monthly contract are 17 percent more likely to stay enrolled beyond one year than users committing for a year.

So is this an anomaly, or is it just me?

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4 Comments Add your own

  • 1. Bo's avatar Bo  |  10 October 2006 at 10:30 am

    Consumers who pay the flat fee are busy people and go for the “easy” solution – can you ever find your punch card when you need it? Busy people can only attend sporadically, however, enjoy the freedom and possibility of going at any time and money matters less for this group. In general, busy people often pay over price for goods..and may even know it! I suspect that at least a portion of this group may be “pro forma” members so they can tell their friends that they too are members of a health club. If we dare go one step further – how many of this group are men/women? How many are (rich) house wifes, who got the membership for social or other reasons etc.?

    The second one could probably be explained something like this: If you enroll on a monthly contract you are constantly reminded about your membership since you constantly have to renew it – the other group probably forget they enrolled along the way – that is we may expect a large subsample of this group to never show up after the first two-three months and thus never renew membership. This is a marketing issue: perhaps less marketing is directed toward the costumers that are enrolled for a year (i.e. they are forgotten by the center)?

    Is this really an anomaly? How do you define an anomaly in the scientific sense? One could argue, that since you are averaging the consumer behavior and looking at trends, this can hardly be an anomaly? Is it an anomaly that “homo sapiens” do not act like “homo economicus”?

  • 2. Lasse's avatar Lasse  |  11 October 2006 at 6:38 am

    Bo, let me first comment on what an anomaly is. Clearly what counts as an anomaly depends on which theories you believe in in the first place. To define an observation as a universal, objective anomaly, we would need a universally believed theory generating a universally believed prediction. This can occur in the natural sciences, but in the social sciences what should count as an anomaly will be more subjective and “local” to each theoretical tradition. So in this sense an anomaly to an economist, may in principle be a confirmation to an anthropologist (or someone from marketing).

    The anomaly in this case – in my opinion – is that a large literature on contract design assumes that consumers who choose between contracts have rational (or at least unbiased) expectations about their future consumption, and that they tend to choose the utility-maximizing contract given these beliefs. In the dataset I referred to, this seems to be grossly violated. This is not likely to be due to high complexity or uncertainty, since this is a rather simple decision.

    Now to your specific suggested explanations, which are good candidates, but if you had the same information I have you would probably doubt them. Busy people should not pay extra unless there is some compensating benefit. You suggest that flexibility is the compensating benefit. The problem with this that there is no extra flexibility from choosing the flat fee. You are in both cases free to work out at any time you would like, and you are supposed to register with a card at the center in both cases (which is how the dataset was generated), but even if you forget your card, the clerk can look you up in the database and register your attendance manually (so the dataset does not omit such cases). In sum the flexibility and the need to bring your punchcard is identical over the two contracts.
    The proforma membership explanation does probably not suffice either. The number of members with a flat fee that are inactive is less than 10%, while the share of members with a flat fee that would have been better off with a pay per visit contract is between 80% (monthly contracts) and 76% (annual contracts).
    Note also that the share of females is 46% and the average age is 31.8. So the median member is not an old, rich houswife :-)

  • 3. Yvonne's avatar Yvonne  |  11 October 2006 at 7:55 am

    I think the key to this anomaly could actually be he fact, that members who sign-up for the monthly contract attend the gym only 4.3 times a month. Obviously these are people who don’t work out very regularly. I think it is possible these members “rationally” choose the monthly flat rate to create an incentive to attend the gym at all and are aware of the fact that they pay extra to create this incentive. I am not sure, if it is really helpful to calculate the probability of members continuing the contract after one year (e.g. why one year, why not 1,5?) I’d be more interested in the average contract length in both groups. If the assumption with the 600 USD of foregone savings is correct, the average contract length for monthly-flat rate payers is actually only 19,9 months. (600 USD foregone savings / (4.3 * 7 USD).

  • 4. Lasse's avatar Lasse  |  12 October 2006 at 3:36 am

    I agree with you, Yvonne. The flat fee may be used as a commitment device, and the authors of the paper speculate in the same direction. However, they find that this is insufficient to explain other aspects of the data (which I did not include in the posting). At any rate, a major insight is that drawing inferences about prefrences from observed contract choices is far from straight forward.

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