The Theory of Superstardom: Evidence from Golf
Cox, Raymond A. K., Mitchell, John B., Michigan Academician
One of the most pervasive phenomena in modern society is that a relatively small number of people dominate the activities in which they are engaged and earn enormous amounts of income. Recently, rigorous economic analyses have been applied to this so-called "superstar phenomenon" in an attempt to identify the critical forces driving the phenomenon. Rosen (1981) and MacDonald (1988) suggest that the large earnings of superstars are driven by an allocative equilibrium, in which markets reward talented people with increasing returns to ability. Rosen argues that much of the superstar phenomenon can be explained by the convexity of sellers' revenue functions, since the convex revenue function implies that the distribution of rewards is more skewed than the distribution of talent (i.e., small differences in talent are magnified into disproportionate levels of success).
Rosen shows that the convexity of revenue functions and the extra skew it imparts to the distribution of earnings can be obtained by imperfect substitution (i.e., lesser talent is a poor substitute fur greater talent) among different sellers. Rosen also demonstrates that the joint consumption technology (i.e., a performer puts out more or less the same effort in front of audiences of ten or one thousand), combined with imperfect substitution, can explain the marked concentration of output of those who have the most talent. In a similar vein, MacDonald (1988) presents a dynamic version of Rosen's superstar model. 
On the other hand, Adler (1985) suggests that the principal force that drives the superstar phenomenon is certain consumer behavior rather than differential talents of individuals. Adler argues that the superstar phenomenon exists where consumption requires knowledge. He claims that the need to discuss with other knowledgeable individuals in order to become familiar with an artist's work as a prerequisite to the ultimate consumption (appreciation) of the artist's work is an essential element in understanding the phenomenon. Adler argues that consumers minimize the cost of searching for knowledgeable discussants by choosing the most popular artist. Adler suggests that consumers are better off patronizing the star when either (a) other artists are not cheaper by more than the savings in search costs; or (b) other artists are not sufficiently better than the star.
Another approach to the superstar phenomenon is Lotka's Law of scientific productivity. Originally it explained the bibliometric distribution of science authors and showed the concentration of success, suggesting a superstar phenomenon. Subsequently, it has been used to describe a variety of sociological, biological, and economic phenomena.
In order to test the empirical validity of the theory of superstar, Hamlen (1991) examined the relationship between talent (proxied by voice quality) and success (measured by record sales) in the popular music industry while controlling for other factors such as gender, race, the type of music, and the duration of career. Although empirical results show that consumers recognize quality, the estimated elasticity of record sales with respect to voice quality is less than unity, repudiating the implication of the Rosen-MacDonald theory of superstar.
Ehrenberg and Bognanno (1990) examined the incentive effects of the prize money in Professional Golf Association tournaments and found higher prize levels lead to better performances especially in the late rounds. In addition, higher prize money tournaments attracted better players. However, contrary empirical evidence is presented by Orszag (1994) showing that the level of prize money has an insignificant incentive effect on the golfer's score. Indications are that the difference in performance is primarily caused by the weather.
In this paper, we view the superstar phenomenon as an implication for the probabilistic mechanism by which golf tournaments are won. …