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Goals as reference points in marathon running: A novel test of reference dependence

Abstract

In a large-scale field study of marathon runners, we test whether goals act as reference points in shaping the valuation of outcomes. Theories of reference-dependent preferences, such as Prospect Theory, imply that outcomes that are just below or just above a reference point are evaluated differently. Consistent with the Prospect Theory value function, we find that satisfaction as a function of relative performance (the difference between a runner’s finishing time goal and her actual finishing time) exhibits loss aversion and diminishing sensitivity in both predictions of and actual experienced satisfaction. However, in contrast to Prospect Theory, we observe that loss aversion is partially driven by a discontinuity or jump at the reference point. In addition, we find that a runner’s time goal as well as their previous marathon times simultaneously impact runner satisfaction, providing support for the impact of multiple reference points on satisfaction.

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Notes

  1. Although we use reference-dependent preferences and Prospect Theory interchangeably, our investigation only considers the distortion of outcomes, not the nonlinear treatment of probabilities modeled by Prospect Theory (e.g., Wu and Gonzalez 1996; Prelec 1998).

  2. Some recent papers have used a combination of archival and survey data of marathoners to study the effect of round numbers on performance (Allen et al. 2017), optimism on performance (Krawczyk and Wilamowski 2017) and the relationship between performance and goal attainability (Burdina et al. 2017).

  3. The proposition that goals serve as reference points has broader implications. Heath et al. (1999b) proposed that goals also influence effort provision, an account supported by Sackett et al. (2015), Allen et al. (2017), and Corgnet et al. (2015).

  4. In the Electronic supplementary material, Section ?? A.3.9, we also present evidence that loss aversion is present and of similar magnitude for both experienced and inexperienced marathoners, also contrary to List (2003).

  5. Additional details and analyses are found in the Electronic supplementary material.

  6. Throughout, we assume that v(0) = 0.

  7. For rhetorical simplicity, we ignore the complication of a nonlinear probability weighting function (see Schmidt and Zank 2005).

  8. For instance, while Diecidue et al. (2015) found no support for an aspiration level at zero in a study on risky choice, both their data and those of Zeisberger et al. (2012) suggest heterogeneity in aspiration levels that may mask the ability to detest a jump at an aspiration level.

  9. The marathons surveyed were Boston (2008), Chicago (2007-2009), Grandma’s (2008), Los Angeles (2008), Marine Corps (2007-2009), New York City (2007), Portland (2007), Rock ‘n’ Roll San Diego (2008), and Twin Cities (2007-2009).

  10. http://www.marathonguide.com/Features/Articles/2007RecapOverview.cfm. Referenced on January 5, 2018.

  11. We created weighted averages by weighting the relevant statistics by the proportion of our sample in each marathon. For example, 18.4% of our participants ran the 2009 Marine Corps Marathon. To compute the weighted average finishing time, we multiplied the finishing time for all runners in the 2009 Marine Corps Marathon (281.23 minutes) by 18.4%, repeated this process for the other 14 marathons, and summed the 15 products.

  12. Of course, there is no obvious way to make satisfaction ratings incentive-compatible. Nevertheless, most studies of well-being use self-reports of happiness and satisfaction (cf. Schwarz and Strack 1999).

  13. The chip time is used as a qualifying time for “elite” races such as the Boston Marathon. However, clock time is the time generally used for determining prize money and other awards.

  14. Precise finishing times are not provided to protect the anonymity of our participants.

  15. Although a comparison of n− 10n− 20 to p+ 20p+ 10 reveals significant loss aversion (χ2(1) = 14.83, p < .001), a comparison of n− 1n− 10 to p+ 10p+ 1 does not (χ2(1) = 0.57, p = .45). In the Electronic supplementary material, Section ?? A.3.10, we present two alternative analyses: a parametric analysis using paired t-tests and an ordered logit analysis using piecewise polynomials, as in Section 5.2.

  16. For any combination of predictors, the ordered logit model produces a probability distribution for each of the 7 satisfaction levels. We can thus plot expected satisfaction for any level of relative performance. When we employ control variables such as dummy variables for a specific marathon, the control variables are set at their mean levels.

  17. The power function is the most commonly-used parametric form for estimating the Prospect Theory value function (e.g., Abdellaoui et al. 2007 and Wu and Gonzalez 1996). It has a single parameter governing curvature and a single parameter indexing loss aversion when the power parameter for gains and losses coincides. However, parametric forms such as the power function cannot be readily incorporated within ordered logit models.

  18. The smoothing spline has a single parameter, which determines the tradeoff between the curve’s smoothness and its closeness to the data. This parameter can be chosen subjectively or determined analytically by leave-one-out cross-validation, the approach taken here. Additional discussion of smoothing splines is found in Green and Silverman (1993) and Wang (2011).

  19. Our bootstrap validation involves drawing a bootstrap sample with replacement from the original sample, then fitting the model to be validated to the bootstrap sample. That fitted model was then applied to the original sample, and Somers’ d, a measure of the association between predicted probabilities and observed responses, was compared against that obtained by fitting the model directly to the original sample. This provided an estimate of the bias due to overfitting, also called the model’s “optimism.” This process was repeated 1000 times, and the average optimism was subtracted from the index of accuracy from the original sample, producing an overfitting-corrected estimate (Harrell 2010).

  20. In the proportional odds model, the inference is independent of the reference category, i.e., the effect of an increase in variable k on the log odds of Pr(Yj) is the same for any level of the response variable, j.

  21. Both of these questions, while important, pose empirical challenges. For example, focalism might produce differences in prediction and experience (Wilson et al. 2000). In prediction, marathon runners could focus on how falling short or exceeding a goal influences their satisfaction and ignore other factors (such as the weather, injuries, etc.) that also likely affect satisfaction. Focalism, therefore, could result in differences in loss aversion, as predicted by Kermer et al. (2006) or merely a more compressed relationship between satisfaction and relative performance in experience. In addition, asking a participant for multiple predictions of satisfaction might highlight the difference between gains and losses (e.g., McGraw et al. 2010).

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We thank the Editor, an anonymous reviewer, and attendees at various conferences and universities for useful comments.

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Markle, A., Wu, G., White, R. et al. Goals as reference points in marathon running: A novel test of reference dependence. J Risk Uncertain 56, 19–50 (2018). https://doi.org/10.1007/s11166-018-9271-9

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Keywords

  • Reference dependence
  • Prospect Theory
  • Loss aversion
  • Goals
  • Satisfaction

JEL Classification

  • C93 D03