The existence and persistence of a winner's curse: new evidence from the (baseball) field.

• Author: Burger, John D.

1. Introduction

   In controlled experiments, bidders at auction often fall prey to a winner's curse, failing to consider factors conducive to overbidding and thus earning disappointing or even negative returns. What is more, this curse appears to be persistent, disappearing slowly (if at all) when experiments are structured to allow subjects to learn from past auction outcomes and modify their bidding behavior. (1)

   Evidence of a winner's curse in naturally occurring markets is less common because of data availability problems and is less robust because there are often alternative explanations for apparent overbidding. For example, Capen, Clapp, and Campbell (1971) found overbidding and low returns on federal auctions of offshore oil leases, but Hendricks and Porter (1988) concluded that the pattern of bids on such leases was consistent with rational behavior in the presence of asymmetric information. In the corporate takeover market, the suggestion by Roll (1986) that hubris causes acquiring firms to ignore curse considerations and overpay for target firms has been supported by Varaiya (1988), but in the market for initial public offerings of common stock there is evidence that investors are aware of a curse and compensate for it (Koh and Walter 1989; Levis 1990).

   Some of the field evidence on overbidding comes from the baseball labor market, where detailed performance data enable accurate ex post evaluations of returns on player contracts. The first such study, by Cassing and Douglas (1980), concluded that the majority of free agent players signed in the late 1970s (2) yielded negative returns for teams--specifically, that these players were paid 20% more than their estimated marginal revenue products (MRPs). Followup studies have muddied the waters a bit. Evidence consistent with a curse has come from Zimbalist (1992, p. 128), who claimed that free agents' salaries exceeded their MRPs by as much as 40% during the late 1980s, and Kahn (1993, p. 163), who interpreted free agents' increased contract duration as an indication of supracompetitive compensation. On the other hand, Sommers and Quinton (1982), Raimondo (1983), and MacDonald and Reynolds (1994) concluded that free agents' salaries generally were commensurate with their MRPs rather than significantly above them. Despite this apparent empirical draw, it is common to name the baseball labor market as one afflicted by a winner's curse in textbook discussions of the topic and in surveys of the theoretical and empirical literature on it. (3)

   Even if all the evidence from the baseball labor market pointed to the same conclusion, however, it would be desirable to revisit this issue because of recent advances in both the precision with which individual output in this market can be measured and the methods by which that output is valued. Baseball statistics have long been part of the appeal of the game for fans and tools for decision makers, and in recent years the data available for performance analysis have been improved significantly. In valuing players, it is no longer necessary to rely on rough approximations of individual players' marginal products (often based on regressions that correlated team success with a few summary measures of hitting or pitching efficiency (4)), as many early studies of free agents' salaries did. What is more, recent research on pay and performance in the industry makes clear that attaching value to individual players' output is more complex than previously thought. In particular, the finding by Burger and Walters (2003) and Solow and Krautmann (2007) that players' MRPs are affected by the size of the market in which they play--and not uniform across teams, as is commonly assumed means that prior judgments about overbidding may be erroneous because they are based on comparisons of players' salaries to misestimated MRPs. (5)

   These advances suggest another important reason to evaluate the bidding for baseball free agents: Even if there are signs of a curse in free agency's early days, it is possible that experience or improvements in the tools used in formulating bids may lead to better decisions over time. The sport's free agent market has been in operation for three decades and the bidding organizations have been constant over that period (though, of course, many executives within those organizations have come and gone), providing a wonderful opportunity to assess whether those who fall prey to a curse learn to avoid it or not; nevertheless, the question of persistence of a winner's curse in baseball has never been addressed properly. (6)

   Accordingly, in this study we both revisit the era from which the earlier evidence of a curse arose and examine a more recent cohort of free agents to learn whether bidder behavior has changed over time. Although we do not find the sort of gross overbidding (i.e., negative average returns) claimed in some prior studies, we do find evidence that bidders in the late 1970s systematically failed to properly adjust their bids in accord with available information, especially about risk. Further--and somewhat surprisingly (7)--the passage of decades has not eliminated these errors, which remain for a large sample of free agent contracts signed in the late 1990s and recently concluded. These findings highlight the difficulty of making efficient decisions in a competitive, high-stakes environment when the elements influencing an asset's value are many, complex, and volatile. Our results are broadly consistent with experimental evidence on bounded rationality and should prove of interest not just to labor and sports economists but to all those interested in the burgeoning fields of behavioral economics and finance.

2. Methodology

   Tests for Average Realized Returns

   In a full-information, competitive equilibrium, a profit-maximizing team ought to pay a player a wage (w) no more than his expected MRP, which equals his expected marginal physical product times its value in the team's market. In an auction setting, efficient bidders will adjust their estimates of a good's expected value in light of signals from the market--for example, the number of bidders and/or measures of the variance in their valuations. Given the practical difficulties of modeling bidders' expectations-formation process and the lack of data about signals available to them during this process, it is customary to perform an ex post examination of winning bids as a basic, "first-pass" test of their efficiency. In effect, if bidders are avoiding systematic errors in forming their expectations about an asset's value and/or in adjusting their bids for risk and uncertainty, a necessary (though not sufficient) condition for efficient bidding is that, on average, w [less than or equal to] realized MRP and average realized returns [greater than or equal to] zero.

   The method commonly used to measure a player's MRP originated with Scully (1974), though subsequent research has greatly refined its precision. (8) The process involves two steps: (i) econometrically estimating the relationship between a team's output of wins (which may be a proxy for the quality of the spectacle fans are consuming) and its revenue, in order to obtain the marginal revenue associated with each extra win and (ii) multiplying this marginal win value (MWV) by the player's marginal output of wins.

   As noted earlier, recent research by Burger and Waiters (2003) and Solow and Krautmann (2007) has shown that MWVs are a positive function of the size of a team's particular market-that is, market size affects both the intercept and slope of a team's revenue function, so a given level of individual output will have greater value in large markets than in small ones. The failure to recognize this fact is a major deficiency of earlier studies of overbidding in baseball; almost all, therefore, are based on estimated MRPs, which are erroneous--likely too small for players signed by large-market teams and too large for players on small-market teams. The direction of any bias in results is unclear and will depend on whether a particular year's auction involves disproportionate participation by large- or small-market teams. What is more, ignoring the effect of market size on players' MRPs means that prior researchers have overlooked an important question related to the rationality of bidders: Do they properly adjust their bids for this source of variation in value?

   Accordingly, we have estimated team-specific revenue functions and MWVs for the early 1980s and the late 1990s. (For a detailed discussion of the sources and any limitations of the data employed throughout this study, see the Appendix.) We employ the former (in section 3) to reassess returns on contracts in the first few years of the free agency system in the late 1970s; the latter are used (in section 4) to gauge returns on free agent contracts that were signed prior to the 1998 and 1999 seasons, and that all have run their course.

   For both eras, we used pooled time-series and cross-sectional data to estimate the requisite team revenue functions. For the early 1980s regressions, the dependent variable was total revenue for team i in year t; in the later period, when revenue sharing led to different slopes for teams' total and locally generated revenue functions, the dependent variable was local revenue. For both eras, the independent variables of prime interest (given the need for market-specific MWVs) were [POP.sub.it], the population in team i's consolidated metropolitan statistical area (CMSA) (9) in year t; [WINS.sub.it], team i's win total in year t; and [POPWINS.sub.it], an interaction term, population times wins for team i in year t. We also included two control variables: a dummy variable indicating whether a team played in a stadium constructed within a decade of year t (since enhanced facilities commonly shift the revenue function), and a stadium age variable to allow for decay in the stadium's effect on...