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
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).
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).
Additional details and analyses are found in the Electronic supplementary material.
Throughout, we assume that v(0) = 0.
For rhetorical simplicity, we ignore the complication of a nonlinear probability weighting function (see Schmidt and Zank 2005).
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).
http://www.marathonguide.com/Features/Articles/2007RecapOverview.cfm. Referenced on January 5, 2018.
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.
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).
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.
Precise finishing times are not provided to protect the anonymity of our participants.
Although a comparison of n− 10 − n− 20 to p+ 20 − p+ 10 reveals significant loss aversion (χ2(1) = 14.83, p < .001), a comparison of n− 1 − n− 10 to p+ 10 − p+ 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.
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.
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.
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).
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).
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(Y ≥ j) is the same for any level of the response variable, j.
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).
References
Abdellaoui, M. (2000). Parameter-free elicitation of utility and probability weighting functions. Management Science, 46(11), 1497–1512.
Abdellaoui, M., Bleichrodt, H., & & Paraschiv, C. (2007). Loss aversion under prospect theory: A parameter-free measurement. Management Science, 53(10), 1659–1674.
Abeler, J., Falk, A., Goette, L., & & Huffman, D. (2011). Reference points and effort provision. American Economic Review, 101(2), 470–492.
Allen, E.J., Dechow, P.M., Pope, D.G., & & Wu, G. (2017). Reference-dependent preferences: Evidence from marathon runners. Management Science, 63(6), 1657–1672.
Arkes, H.R., Hirshleifer, D., Jiang, D., & & Lim, S. (2008). Reference point adaptation: Tests in the domain of security trading. Organizational Behavior and Human Decision Processes, 105(1), 67–81.
Atkinson, J.W. (1957). Motivational determinants of risk-taking behavior. Psychological Review, 64(6p1), 359.
Austen, I. (2001). You clocked what? For marathon runners, it’s gun vs. chip. The New York Times.
Baillon, A., Bleichrodt, H., & & Spinu, V. (2017). Searching for the reference point. Working paper.
Barberis, N.C. (2013). Thirty years of prospect theory in economics: A review and assessment. Journal of Economic Perspectives, 27(1), 173–195.
Barberis, N., & Xiong, W. (2009). What drives the disposition effect? An analysis of a long-standing preference-based explanation. Journal of Finance, 64(2), 751–784.
Bartling, B., Brandes, L., & & Schunk, D. (2015). Expectations as reference points: Field evidence from professional soccer. Management Science, 61(11), 2446–2461.
Baucells, M., Weber, M., & & Welfens, F. (2011). Reference-point formation and updating. Management Science, 57(3), 506–519.
Benartzi, S., & Thaler, R.H. (1995). Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics, 110(1), 73–92.
Bentham, J. (1789). An introduction to the principles of morals and legislation. Oxford: Clarendon Press.
Booij, A.S., & Van de Kuilen, G. (2009). A parameter-free analysis of the utility of money for the general population under prospect theory. Journal of Economic Psychology, 30(4), 651–666.
Boyce, C.J., Wood, A.M., Banks, J., Clark, A.E., & & Brown, G.D. (2013). Money, well-being, and loss aversion does an income loss have a greater effect on well-being than an equivalent income gain?. Psychological Science, 24(12), 2557–2562.
Briesch, R.A., Krishnamurthi, L., Mazumdar, T., & & Raj, S.P. (1997). A comparative analysis of reference price models. Journal of Consumer Research, 24 (2), 202–214.
Burdina, M., Hiller, R.S., & & Metz, N.E. (2017). Goal attainability and performance: Evidence from Boston marathon qualifying standards. Journal of Economic Psychology, 58(1), 77–88.
Camerer, C. (2005). Three cheers – psychological, theoretical, empirical – for loss aversion. Journal of Marketing Research, 42(2), 129–133.
Camerer, C., Babcock, L., Loewenstein, G., & & Thaler, R. (1997). Labor supply of New York City cabdrivers: One day at a time. Quarterly Journal of Economics, 112(2), 407–441.
Carter, S., & McBride, M. (2013). Experienced utility versus decision utility: Putting the ‘s’ in satisfaction. Journal of Socio-Economics, 42, 13–23.
Clark, D., Gill, D., Prowse, V., & & Rush, M. (2017). Using goals to motivate college students: Theory and evidence from field experiments. IZA Discussion Papers. No. 10283.
Corgnet, B., Gómez-Miñambres, J., & & Hernán-Gonzales, R. (2015). Goal setting and monetary incentives: When large stakes are not enough. Management Science, 61(12), 2926–2944.
Crawford, V.P., & Meng, J. (2011). New York City cab drivers’ labor supply revisited: Reference-dependent preferences with rational expectations targets for hours and income. American Economic Review, 101(5), 1912–1932.
Curtin, R., Presser, S., & & Singer, E. (2000). The effects of response rate changes on the index of consumer sentiment. Public Opinion Quarterly, 64(4), 413–428.
Diecidue, E., & van de Ven, J. (2008). Aspiration level, probability of success and failure, and expected utility. International Economic Review, 49(2), 683–700.
Diecidue, E., Levy, M., & & van de Ven, J. (2015). No aspiration to win? An experimental test of the aspiration level model. Journal of Risk and Uncertainty, 51 (3), 245–266.
Draper, N.R., & Smith, H. (1966). Applied regression analysis. New York: Wiley.
Ericson, K.M.M., & Fuster, A. (2011). Expectations as endowments: Evidence on reference-dependent preferences from exchange and valuation experiments. Quarterly Journal of Economics, 126(4), 1879–1907.
Farber, H.S. (2005). Is tomorrow another day? The labor supply of New York City cab drivers. Journal of Political Economy, 113(1), 46–82.
Farber, H.S. (2008). Reference-dependent preferences and labor supply: The case of New York City taxi drivers. American Economic Review, 98(3), 1069–1082.
Fehr, E., & Goette, L. (2007). Do workers work more if wages are high? Evidence from a randomized field experiment. American Economic Review, 97(1), 298–317.
Fehr, E., Hart, O.D., & & Zehnder, C. (2011). How do informal agreements and renegotiation shape contractual reference points? National Bureau of Economic Research Working Paper No. 17545.
Frey, B., & Stutzer, A. (2002). The economics of happiness. World Economics, 3(1), 25–41.
Fryer Jr., R.G., Levitt, S.D., List, J., & & Sadoff, S. (2012). Enhancing the efficacy of teacher incentives through loss aversion: A field experiment. Natonal Bureau of Economic Research Working Paper 18237.
Gächter, S., Johnson, E.J., & & Herrmann, A. (2007). Individual-level loss aversion in riskless and risky choices. IZA Discussion Paper no. 2961. Technical report.
Genesove, D., & Mayer, C. (2001). Loss aversion and seller behavior: Evidence from the housing market. The Quarterly Journal of Economics, 116(4), 1233–1260.
Gilbert, D.T., Pinel, E.C., Wilson, T.D., Blumberg, S.J., & & Wheatley, T.P. (1998). Immune neglect: A source of durability bias in affective forecasting. Journal of Personality and Social Psychology, 75(3), 617–638.
Goldstein, E.R. (2011). The anatomy of influence. Chronicle of Higher Education, 58(13), B6–B10.
Green, P.J., & Silverman, B.W. (1993). Nonparametric regression and generalized linear models: A roughness penalty approach. Boca Raton: CRC Press.
Harrell, F.E. (2010). Regression modeling strategies: With applications to linear models, logistic regression, and survival analysis. New York: Springer.
Hart, O., & Moore, J. (2008). Contracts as reference points. The Quarterly Journal of Economics, 123(1), 1–48.
Hastie, R., & Dawes, R.M. (2001). Rational choice in an uncertain world: The psychology of judgment and decision making. Thousand Oaks: SAGE.
Heath, C., Huddart, S., & & Lang, M. (1999a). Psychological factors and stock option exercise. Quarterly Journal of Economics, 114(2), 601–627.
Heath, C., Larrick, R.P., & & Wu, G. (1999b). Goals as reference points. Cognitive Psychology, 38(1), 79–109.
Higdon, H. (2011). Marathon: The ultimate training guide. Emmaus: Rodale.
Ho, T.-H., & Zhang, J. (2008). Designing pricing contracts for boundedly rational customers: Does the framing of the fixed fee matter? Management Science, 54(4), 686–700.
Hsiaw, A. (2013). Goal-setting and self-control. Journal of Economic Theory, 148(2), 601–626.
Kahneman, D. (1992). Reference points, anchors, norms, and mixed feelings. Organizational Behavior and Human Decision Processes, 51(2), 296–312.
Kahneman, D. (1999). Objective happiness. In Kahneman, D.E., Diener, E.E., & & Schwarz, N.E. (Eds.) Well-being: The Foundations of Hedonic Psychology (pp. 3–25). New York: Russell Sage Foundation.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–291.
Kahneman, D., & Snell, J.S. (1990). Predicting utility (pp. 295–310). Chicago: University of Chicago Press.
Kahneman, D., & Lovallo, D. (1993). Timid choices and bold forecasts: A cognitive perspective on risk taking. Management Science, 39(1), 17–31.
Kahneman, D., Knetsch, J.L., & & Thaler, R.H. (1990). Experimental tests of the endowment effect and the Coase Theorem. Journal of Political Economy, 98(6), 1325–1348.
Kahneman, D., Fredrickson, B.L., Schreiber, C.A., & & Redelmeier, D.A. (1993). When more pain is preferred to less: Adding a better end. Psychological Science, 4(6), 401–405.
Kahneman, D., Wakker, P.P., & & Sarin, R. (1997). Back to Bentham? Explorations of experienced utility. Quarterly Journal of Economics, 112(2), 375–406.
Kermer, D.A., Driver-Linn, E., Wilson, T.D., & & Gilbert, D.T. (2006). Loss aversion is an affective forecasting error. Psychological Science, 17(8), 649–653.
Köbberling, V., & Wakker, P.P. (2005). An index of loss aversion. Journal of Economic Theory, 122(1), 119–131.
Kőszegi, B., & Rabin, M. (2006). A model of reference-dependent preferences. Quarterly Journal of Economics, 121(4), 1133–1165.
Kőszegi, B., & Rabin, M. (2007). Reference-dependent risk attitudes. American Economic Review, 97(4), 1047–1073.
Krawczyk, M., & Wilamowski, M. (2017). Are we all overconfident in the long run? Evidence from one million marathon participants. Journal of Behavioral Decision Making, 30(3), 719–830.
Larsen, J.T., McGraw, A.P., Mellers, B.A., & & Cacioppo, J.T. (2004). The agony of victory and thrill of defeat: Mixed emotional reactions to disappointing wins and relieving losses. Psychological Science, 15(5), 325–330.
List, J.A. (2003). Does market experience eliminate market anomalies? Quarterly Journal of Economics, 118(1), 41–71.
Locke, E.A., & Latham, G.P. (2006). New directions in goal-setting theory. Current Directions in Psychological Science, 15(5), 265–268.
Loewenstein, G., & Adler, D. (1995). A bias in the prediction of tastes. Economic Journal, 105(431), 929–937.
Long, J.S., & Freese, J. (2014). Regression models for categorical dependent variables using Stata. College Station: Stata Press.
Lopes, L.L. (1987). Between hope and fear: The psychology of risk. Advances in Experimental Social Psychology, 20, 255–295.
Lopes, L.L., & Oden, G.C. (1999). The role of aspiration level in risky choice: A comparison of cumulative prospect theory and SP/A theory. Journal of Mathematical Psychology, 43(2), 286–313.
March, J.G., & Shapira, Z. (1992). Variable risk preferences and the focus of attention. Psychological Review, 99(1), 172–183.
Mas, A. (2006). Pay, reference points, and police performance. Quarterly Journal of Economics, 121(3), 783–821.
McGraw, A.P., Larsen, J.T., Kahneman, D., & & Schkade, D. (2010). Comparing gains and losses. Psychological Science, 21(10), 1438–1445.
Mento, A.J., Locke, E.A., & & Klein, H.J. (1992). Relationship of goal level to valence and instrumentality. Journal of Applied Psychology, 77(4), 395–405.
Ockenfels, A., Sliwka, D., & & Werner, P. (2014). Bonus payments and reference point violations. Management Science, 61(7), 1496–1513.
Odean, T. (1998). Are investors reluctant to realize their losses? Journal of Finance, 53(5), 1775–1798.
Oettinger, G.S. (1999). An empirical analysis of the daily labor supply of stadium vendors. Journal of Political Economy, 107(2), 360–392.
Ordóñez, L.D. (1998). The effect of correlation between price and quality on consumer choice. Organizational Behavior and Human Decision Processes, 75(3), 258–273.
Ordóñez, L.D., Connolly, T., & & Coughlan, R. (2000). Multiple reference points in satisfaction and fairness assessment. Journal of Behavioral Decision Making, 13(3), 329–344.
Payne, J.W. (2005). It is whether you win or lose: The importance of the overall probabilities of winning or losing in risky choice. Journal of Risk and Uncertainty, 30 (1), 5–19.
Pope, D., & Simonsohn, U. (2011). Round numbers as goals evidence from baseball, SAT takers, and the lab. Psychological Science, 22(1), 71–79.
Pope, D.G., & Schweitzer, M.E. (2011). Is Tiger Woods loss averse? Persistent bias in the face of experience, competition, and high stakes. American Economic Review, 101(1), 129–157.
Post, T., & van den Assem, M.J. (2008). Deal or no deal? Decision making under risk in a large-payoff game show. American Economic Review, 98(1), 38–71.
Prelec, D. (1998). The probability weighting function. Econometrica, 66(3), 497–528.
Rabin, M. (2000). Risk aversion and expected-utility theory: A calibration theorem. Econometrica, 68(5), 1281–1292.
Sackett, A.M., Wu, G., White, R.J., & & Markle, A.B. (2015). Harnessing optimism: How eliciting goals improves performance. Working paper.
Samuelson, W., & Zeckhauser, R. (1988). Status quo bias in decision making. Journal of Risk and Uncertainty, 1(1), 7–59.
Schmidt, U., & Zank, H. (2005). What is loss aversion? Journal of Risk and Uncertainty, 30(2), 157–167.
Schneider, S.L., & Lopes, L.L. (1986). Reflection in preferences under risk: Who and when may suggest why. Journal of Experimental Psychology: Human Perception and Performance, 12(4), 535–548.
Schwarz, N., & Strack, F. (1999). Reports of subjective well-being: Judgmental processes and their methodological implications (pp. 61–84). New York: Russell Sage Foundation.
Scitovsky, T. (1976). The joyless economy: An inquiry into human satisfaction and consumer dissatisfaction. Oxford: Oxford University Press.
Shefrin, H., & Statman, M. (1985). The disposition to sell winners too early and ride losers too long: Theory and evidence. Journal of Finance, 40(3), 777–790.
Sullivan, K., & Kida, T. (1995). The effect of multiple reference points and prior gains and losses on managers’ risky decision making. Organizational Behavior and Human Decision Processes, 64(1), 76–83.
Tovar, P. (2009). The effects of loss aversion on trade policy: Theory and evidence. Journal of International Economics, 78(1), 154–167.
Tversky, A., & Kahneman, D. (1991). Loss aversion in riskless choice: A reference-dependent model. Quarterly Journal of Economics, 106(4), 1039–1061.
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297–323.
Wang, Y. (2011). Smoothing splines: Methods and applications. CRC Monographs on Statistics & Applied Probability. UK: Chapman and Hall.
Wang, X.T., & Johnson, J.G. (2012). A tri-reference point theory of decision making under risk. Journal of Experimental Psychology: General, 141(4), 743–756.
Weingarten, E., Bhatia, S., & & Mellers, B. (2016). Multiple goals as reference points. Working paper.
Wilson, T.D., & Gilbert, D.T. (2003). Affective forecasting. Advances in Experimental Social Psychology, 35, 345–411.
Wilson, T.D., Wheatley, T., Meyers, J.M., Gilbert, D.T., & & Axsom, D. (2000). Focalism: A source of durability bias in affective forecasting. Journal of Personality and Social Psychology, 78(5), 821–836.
Winer, R.S. (1986). A reference price model of brand choice for frequently purchased products. Journal of Consumer Research, 13(2), 250–256.
Wu, G., & Gonzalez, R. (1996). Curvature of the probability weighting function. Management Science, 42(12), 1676–1690.
Wu, G., & Markle, A.B. (2008). An empirical test of gain-loss separability in prospect theory. Management Science, 54(7), 1322–1335.
Zeisberger, S., Langer, T., & & Weber, M. (2012). Why does myopia decrease the willingness to invest? Is it myopic loss aversion or myopic loss probability aversion? Theory and Decision, 72(1), 35–50.
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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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DOI: https://doi.org/10.1007/s11166-018-9271-9