Is Tiger Woods Loss Averse? 2011 PDF

American Economic Review 101 (February 2011): 129–157 http://www.aeaweb.org/articles.php?doi=10.1257/aer.101.1.129 Is Tiger Woods Loss Averse? Persistent Bias in the Face of Experience, Competition, and High Stakes By Devin G. P...

American Economic Review 101 (February 2011): 129–157 http://www.aeaweb.org/articles.php?doi=10.1257/aer.101.1.129 Is Tiger Woods Loss Averse? Persistent Bias in the Face of Experience, Competition, and High Stakes By Devin G. Pope and Maurice E. Schweitzer* Although experimental studies have documented systematic decision errors, many leading scholars believe that experience, competition, and large stakes will reliably extinguish biases. We test for the pres- ence of a fundamental bias, loss aversion, in a high-stakes context: professional golfers’ performance on the PGA Tour. Golf provides a natural setting to test for loss aversion because golfers are rewarded for the total number of strokes they take during a tournament, yet each individual hole has a salient reference point, par. We analyze over 2.5 million putts using precise laser measurements and find evidence that even the best golfers—including Tiger Woods—show evidence of loss aversion. (JEL D03, D81, L83) A substantial literature has identified systematic ways in which individuals vio- late standard economic assumptions (see Colin F. Camerer, George Loewenstein, and Matthew Rabin 2004). This literature includes both laboratory and field studies (for reviews, see Camerer 2000; Camerer, Loewenstein, and Rabin 2003; Stefano DellaVigna 2009). In spite of the extant literature documenting behavioral biases, many scholars— including some who have documented behavioral biases—remain skeptical of the claim that biases persist in markets (e.g., John A. List 2003, Steven D. Levitt and List 2008, Sergiu Hart 2005).1 Critics of the decision bias literature believe that biases are likely to be extinguished by competition, large stakes, and experience. Levitt and List (2008) summarize their concern with the bias literature: “Perhaps the greatest challenge facing behavioral economics is demonstrating its applicability in the real world. In nearly every instance, the strongest empirical evidence in favor of behavioral anomalies emerges from the lab. Yet, there are many reasons to suspect that these laboratory findings might fail to generalize to real markets.” * Pope: University of Chicago, 5807 Woodlawn Ave., Chicago, IL 60637 (e-mail: devin.pope@chicagobooth. edu); Schweitzer: The Wharton School, University of Pennsylvania, 3730 Walnut Street #566, Philadelphia, PA 19104 (e-mail: [email protected]). We thank Bob Batt for excellent research support and Ken Lovell and Mike Vitti at the PGA TOUR for help with ShotLink data access. We also thank David Abrams, Nick Barberis, Gerard Cachon, Colin Camerer, Stefano DellaVigna, Kirk Doran, Peter Fishman, Adam Galinsky, John Hershey, Daniel Kahneman, Bruce Kothmann, Kory Kroft, Howard Kunreuther, Rob Letzler, Steve Levitt, Cade Massey, Arden Pope, Jaren Pope, Uri Simonsohn, Justin Sydnor, Richard Thaler, Jeremy Tobacman, Maisy Wong, Justin Wolfers, and seminar participants at Carnegie Mellon, the Federal Trade Commission, and The Wharton School for helpful comments and suggestions. We are also grateful to the Wharton Sports Business Initiative for generous funding. All errors are our own. 1 Despite the fact that List has argued that behavioral biases can be mitigated by economic markets, he has been very open to behavioral work in general (e.g., List 2002; Michael Haigh and List 2005). 129 130 THE AMERICAN ECONOMIC REVIEW FEBRUARY 2011 In this paper, we examine field evidence of loss aversion, a fundamental bias and a key component of Prospect Theory (Daniel Kahneman and Amos Tversky 1979). We consider a market with high stakes and experienced agents: The PGA Tour. The PGA Tour brings professional golfers together to play in a series of Tournaments each year. In each Tournament, golfers attempt to minimize the total number of shots they take across 72 holes. We focus our attention on putts, the final shots players take to complete a hole. We compare putts golfers attempted for par (the typical number of shots professional golfers take to complete a hole) to putts golfers attempted for scores different from par, such as birdie (one shot less than par). Our sample includes more than 2.5 million putts with laser measurements of initial and final ball placement (x, y, z coordinates). This is an ideal setting to test for loss aver- sion. Though golfers should care only about their overall Tournament score, golfers may be influenced by the salient, but normatively irrelevant, reference point of par when they attempt putts. In contrast to the normative account, we find that golfers are significantly influ- enced by the reference point of par. When golfers are “under par” (e.g., shoot a “birdie” putt that would earn them a score one stroke under par or shoot an “eagle” putt that would earn them a score two strokes under par) they are significantly less accurate than when they attempt otherwise similar putts for par or are “over par” (e.g., shoot a “bogey” putt that would earn them a score one stroke over par or shoot a “double bogey” putt that would earn them a score two strokes over par). Though we analyze each of these types of putts, most of the putts in our data involve birdie and par putts, and we summarize our results with respect to these putts. For exam- ple, on average, golfers make their birdie putts approximately 2 percentage points less often than they make comparable par putts. This finding is consistent with loss aversion; players invest more focus when putting for par to avoid encoding a loss. Beyond controlling for distance, consider and rule out several competing expla- nations for this finding. First, prior to hitting a par putt, players may have learned something about the green (by having already attempted a birdie putt). Second, birdie putts may start from a more precarious position on the green than par putts due to a longer approach shot. Third, player or Tournament-specific differences may bias our results. Using detailed data, we are able to rule out competing explanations with control methods and matching estimators. For example, we can match par and birdie putts attempted within one inch of each other on the exact same hole in the same Tournament. We are also able to rule out other psychological explanations. For example, we consider whether or not players become more nervous or overconfident when they shoot birdie putts relative to par putts. Our finding, that golfers are less accurate when attempting birdie putts than par putts, is moderated by Tournament round. The accuracy gap between par and birdie putts is largest in the first round of the Tournament (first 18 holes) and is less than half as large in the fourth round of the Tournament (last 18 holes). This finding dem- onstrates that the accuracy gap between par and birdie putts is neither automatic nor immutable. Consistent with our loss aversion account, early in the Tournament, the reference point of par is likely to be very salient; later in the Tournament, alterna- tive reference points, such as the scores of competitors, are likely to become salient. We also find evidence to support an additional prediction of Prospect Theory: a risk shift. Prospect Theory predicts that economic agents will be more risk averse in VOL. 101 NO. 1 POPE AND SCHWEITZER: IS TIGER WOODS LOSS AVERSE? 131 the gain domain than they are in the loss domain. If professional golfers use par as a reference point, they should be more cautious when putting for birdie (in the gain domain for a specific hole) than when putting for par. Specifically, conditional on missing a putt, we find that golfers hit birdie putts less hard than they hit par putts and are more likely to leave birdie putts short of the hole than par putts. In graphi- cal analysis, we demonstrate that players sacrifice success when putting for birdie to avoid difficult follow-up putts. This pattern of results is consistent with Prospect Theory and decreases expected profits. Recent theoretical work has conceptualized expectations as reference points (Botond K​ o​ ˝ szegi and Rabin 2006). Little prior work, however, has directly tested this theory (see Vincent P. Crawford and Juanjuan Meng 2008 and Kirk Doran 2008 for exceptions). In our data, we test for endogenous reference points by considering performance on holes in which players should expect to score either higher or lower than par. Our findings provide evidence consistent with K​ o​˝ szegi and Rabin’s (2006) prediction and suggest that expectations influence reference point adoption. In short, our findings demonstrate that loss aversion persists in a market setting with intense competition, large stakes, and very experienced agents. Even the best golfers—including Tiger Woods—exhibit loss aversion. We organize the paper in the following way: In Section I, we provide background information about loss aversion and professional golf. In Section II, we develop a conceptual framework to understand how loss aversion influences golf performance. In Section III, we describe the data and present our empirical strategy. We report our results and rule out competing explanations in Section IV, and we conclude with a discussion of our findings and their broader implications in Section V. I. Background on Loss Aversion and Golf A. Prospect Theory and Loss Aversion Rather than make consistent decisions over final wealth states, Kahneman and Tversky (1979) postulate that economic agents evaluate decisions in isolation with respect to a salient reference point. In Prospect Theory, Kahneman and Tversky (1979) propose a reference-dependent theory of choice in which economic agents value gains differently than they value losses in two key ways. First, economic agents value losses more than they value commensurate gains (loss aversion); the “value function” is kinked at the reference point with a steeper gradient for losses than for gains. Second, economic agents are risk seeking in losses and risk averse in gains (risk shift); the utility function is convex in the loss domain and concave in the gain domain. This model of reference dependent preferences has profound implications. If individuals segregate related decisions, they may choose different outcomes. For example, loss aversion and the risk shift may cause an individual to reject a series of small gambles with positive expected return but accept the aggregated gamble. Shlomo Benartzi and Richard H. Thaler (1995) studied this problem in the domain of retirement saving. Benartzi and Thaler (1995) found that people who evaluated their portfolios frequently (and made a series of related decisions) made different hypothetical choices than did people who evaluated their portfolios infrequently. 132 THE AMERICAN ECONOMIC REVIEW FEBRUARY 2011 Daniel Read, Loewenstein, and Rabin (1999) studied the issue of segregating deci- sions explicitly and coined the term “narrow bracketing” to describe how individu- als segregate or bracket related decisions. Loss aversion has been documented in many laboratory settings (e.g., Thaler et al. 1997; Uri Gneezy and Jan Potters 1997) and in several field settings (see David Genesove and Christopher Mayer 2001; Camerer et al. 1997; Ernst Fehr and Lorenz Goette 2007; Terrence Odean 1998, and Alex Mas 2006). Some scholars, however, have found evidence to suggest that experience and large stakes may eliminate deci- sion errors (List 2003, 2004). Our paper makes an important contribution to the literature by documenting loss aversion in a competitive field setting, with large stakes, and very experienced agents. Our paper is also atypical in that we have an unusually large amount of sta- tistical power and a well-defined reference point. In addition, we are able to directly test for evidence of small-scale risk aversion and whether or not reference points change based upon expectations (K​ o​˝ szegi and Rabin 2006). B. Professional Golf We analyze decisions made by professional golfers playing in the PGA Tour.2 The PGA Tour is a collection of Tournaments (40–50 each year) in which professional golfers (approximately 150 per Tournament) compete. In each Tournament, golfers play 18 holes of golf on each of four consecutive days (four “rounds”). After the second round, golfers with a score that places them in the bottom third are elimi- nated from the Tournament. All of the remaining players compete in the final two rounds and share the total purse for the Tournament (in 2008 the average purse for each Tournament was approximately $5 million). The distribution of payments is highly convex; for example, the winner typically earns 18 percent of the purse. In golf, players begin by placing a ball on a wooden tee and hitting (or “driving”) the ball towards a hole. The players typically end each hole by putting, attempt- ing a short shot on the well-manicured patch of grass (the “green”) near the hole. Each player’s score is the sum total of his strokes, or hits, across all 72 holes in the Tournament.3 The player with the lowest score wins the Tournament. For historical reasons, each hole is assigned a value or “par.” On PGA Tour courses, each hole has a par value equal to 3, 4, or 5. The par value represents the number of strokes that professional golfers often require to finish a hole, and both common golfer parlance and score cards represent performance on each hole with respect to par. Golfers who complete a hole one or two strokes under par have shot a “birdie” or “eagle,” respectively. Golfers who complete a hole equal to par have shot par. Golfers who complete a hole one or two strokes over par have shot a “bogey” or “double bogey,” respectively. On scorecards, golfers draw a circle for holes they shot under par and a square for holes they shot over par. Scores relative to par are 2 Golf has been used as the context of several papers in economics including Ronald G. Ehrenberg and Michael L. Bognanno (1990), Christopher Cotton and Joseph Price (2006), Jennifer Brown (2007), and Jonathan Guryan, Kory Kroft, and Matthew J. Notowidigdo (2009). 3 This scoring method is called “stroke play” or “medal play” which is by far the most popular method of scor- ing in professional golf. However, other scoring systems such as “match play” do exist. Our data consists only of Tournaments that were scored using stroke play. VOL. 101 NO. 1 POPE AND SCHWEITZER: IS TIGER WOODS LOSS AVERSE? 133 also quite salient because broadcasters and reporters will often refer to a golfer’s score on different holes relative to par. Although it is only performance across the 72 holes that matters, we postulate that par for individual holes will serve as a salient reference point and influence performance. II. Conceptual Framework We develop a simple conceptual framework to describe the influence that loss aversion may have on putting. When golfers attempt a putt, they can either make the putt and earn a score of Δx, or miss the putt. For simplicity, we start by assuming that if a golfer misses his first putt, he makes his following putt and earns a score of Δx − 1. In this framework, Δx represents the number of strokes (either positive or negative) from par. We consider the probability of making a putt to be a function of effort, which is endogenously set by the golfer, and other observable putt characteristics. Specifically, (1) Pr (make putt) = f (e, z) + ε, where e represents the amount of effort exerted, z represents a vector of other putt characteristics (e.g., putt distance), and ε is random noise. We assume that f ′ w.r.t. e ≥ 0 and f ″ w.r.t. e ≤ 0 indicating that additional effort weakly increases the probability of making a putt and that f (*) is weakly concave in effort. In our formulation, we consider the possibility that golfers do not consistently deliver their maximum effort for each putt. Golfers may devote different amounts of effort to their putts throughout the Tournament. This conceptualization is consistent with previous work, which has found that rather than playing consistently across every hole, golfers’ performance varies according to the incentives they face (Brown 2007; Ehrenberg and Bognanno 1990).4 For each putt, golfers derive the following utility: (2) U = ( f (e, z) + ε) V (Δ x) + (1 − f (e, z) − ε) V (Δ x − 1) − cost(e). Each golfer’s utility is equal to the values placed on making and missing the putt weighted by their probabilities and subtracting the cost of effort, which we assume to be strictly increasing (cost′(e) > 0) and convex (cost″(e) < 0). Incorporating loss aversion (Kahneman and Tversky 1979), we represent the value function V(∙) as (3) V (Δ x) = ​    { λΔx Δ x ​  ​if Δ x ≥ 0  ​ if Δx < 0, where λ ≥ 1 is the degree of loss aversion. This value function is a simple version (without diminishing sensitivity in gains or losses) of the value function described 4 This is also consistent with evidence from other sports that suggests that players/teams adjust their effort levels when psychologically discouraged (e.g., Chaim Fershtman and Gneezy 2007) or psychologically motivated (e.g., Jonah Berger and Pope 2009). 134 THE AMERICAN ECONOMIC REVIEW FEBRUARY 2011 9:78;! V(∆x) (Eagle-Birdie) V9:>134'=