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as a measure of relative fan loyalty, and the results conform to anecdotal evidence as to which teams have the best fans in the National Football League.

Depken / FAN LOYALTY IN JOURNAL PROFESSIONAL OF SPORTS SPORTS ECONOMICS / August 2001

Research Notes

Fan Loyalty in Professional Sports An Extension to the National Football League CRAIG A. DEPKEN II University of Texas at Arlington

Using the stochastic frontier framework, estimates of relative fan loyalty in professional football for 1990 to 1997 are estimated. The traditional inefficiency score is reinterpreted as a measure of relative fan loyalty, and the results conform to anecdotal evidence as to which teams have the best fans in the National Football League. The decision of whether to relocate a professional football franchise is related to fan loyalty and other explanatory variables. It is found that a relatively low level of fan loyalty is a motivating factor in the decision to relocate a franchise to a new host city.

In a recent issue of the Journal of Sports Economics, estimates of relative fan loy-

alty in Major League Baseball were presented. This comment extends the methodology to the National Football League (NFL) and investigates how fan loyalty influences the decision to relocate a franchise. Anecdotal evidence suggests that professional team owners are not only concerned about publicly provided stadiums, but also the strength of the underlying fan base in their host city. Several professional baseball and football franchises have initiated fan loyalty programs very similar to frequent flyer programs. In 1999, the Portland Pythons, an indoor soccer franchise, threatened relocation if “an adequate number of ticket pledges for next season [was] not received” (Nolen, 1999, p. D2). The NFL franchise relocation guidelines specify that any proposed franchise relocation would consider “the extent to which fan loyalty and support for the team has been demonstrated during the team’s tenure in the existing community” (NFL, 1991). What motivates some owners to relocate their franchises when others choose not to? Several professional football teams have relocated in recent years: the Oakland

AUTHOR’S NOTE: The author thanks an anonymous referee for helpful comments. The usual caveat applies. JOURNAL OF SPORTS ECONOMICS, Vol. 2 No. 3, August 2001 © 2001 Sage Publications

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Raiders to Los Angeles in 1982 and then back to Oakland in 1995; the Los Angeles Rams to St. Louis in 1995; the Houston Oilers to Tennessee in 1997; and perhaps most famously, the Cleveland Browns to Baltimore in 1995 (and subsequently renamed the Ravens). This article presents evidence that franchise relocation in professional football is not just about stadium issues, but also about relatively weak fan bases compared with other (actual) host cities. The strength of a team’s fan base, hereafter referred to as fan loyalty, is estimated using the stochastic frontier framework in the context of a demand structure. The findings provide evidence that teams relocate when their relative fan loyalty is low. Following Depken (2000), a panel of data describing all 34 NFL teams for the years 1990 to 1998 is used in the estimation process.1 The transformation function, slightly modified from the baseball study, is of standard Cobb-Douglas form:2  k b  1 ATTi = C ∏ X ij j  exp( ei )   .  li   j =1 

(1)

When transformed by taking logs of both sides, Equation 1 yields k

ln ATTi = ln C + ∑ b j ln X ij + ei* ,

(2)

j =1

where C is a constant term identical to every team, the βj are parameters to be estimated, and ε*i = εi – ln(γi) is a composite error term common to the stochastic frontier literature. Equation 2 is estimated, and the resulting coefficients are interpreted as attendance elasticities. In the estimation, I employ the maximum likelihood estimator (MLE) of the stochastic frontier literature, assuming the fan loyalty measure γi is distributed half-normal. The explanatory variables used in this study are consistent with those in other studies (for a review, see Rascher, 1995) and are listed in Table 1, along with descriptive statistics for the entire sample.3 However, a few explanatory variables are unique to this study and merit extra discussion. The price of a ticket (PAVE) is the average price of tickets actually purchased during the season, as calculated by total gate revenues divided by total attendance. As mentioned by Salant (1992), Noll (1974), and Siegfried and Eisenberg (1980), this is a more accurate measure of ticket price because it measures the average price of the tickets actually sold, not the average price of all seats available in the stadium. The quality of the team is measured by the winning percentage of the current and previous year. However, to account for other team quality issues not reflected directly in the team’s winning percentage, the total player cost (PLAYERC) is included as an explanatory variable. If teams set real wages equal to marginal product, then a higher overall payroll should indicate a higher level of marginal product, holding prices constant.4 Therefore, one would expect a nonnegative estimated coefficient on team payroll.

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TABLE 1: Variables, Definitions, and Descriptive Statistics Variable ATT PAVE FRAGE STAGE CITYAGE CITYPOP CITYINC WIN LAGWIN YR91 YR92 YR93 YR94 YR95 YR96 YR97 CAP PLAYC

Description

M

SD

Home game attendance 475,980.70 80,303.77 Average ticket price ($) 37.11 13.19 Age of franchise 38.61 15.45 Age of stadium 26.05 15.96 Year in host city 34.02 18.95 MSA population 3,464,123.21 2,435,187.14 City income ($) 24,590.50 4,531.29 Current year’s win % 498.94 184.65 Previous year’s win % 500.32 183.02 1991 dummy variable 0.12 0.32 1992 dummy variable 0.12 0.32 1993 dummy variable 0.12 0.32 1994 dummy variable 0.12 0.32 1995 dummy variable 0.12 0.32 1996 dummy variable 0.13 0.33 1997 dummy variable 0.13 0.33 Stadium capacity 69,939.36 8,754.97 Player salaries (millions $) 38.05 11.95

Min

Max

224,221.00 635,889.00 19.75 97.67 1.00 76.00 0.00 73.00 0.00 76.00 194,594.00 9,087,015.00 16,560.00 43,641.00 63.00 875.00 63.00 875.00 0.00 1.00 0.00 1.00 0.00 1.00 0.00 1.00 0.00 1.00 0.00 1.00 0.00 1.00 56,454.00 101,574.00 13.10 66.80

NOTE: MSA = Metropolitan Statistical Area.

The model is estimated first via OLS for comparison reasons and then via MLE (see Depken, 2000). Estimation results and their associated standard errors are reported in Table 2. The similarity of the OLS and MLE estimates is not surprising in that both methods yield consistent estimates. The results of the estimation confirm the expectation that variables that significantly affect the demand for other sports franchises also affect the demand for professional football franchises. Most of the estimated parameters are statistically significant, with a few notable exceptions, and have the expected signs. The estimated price elasticity of demand is –0.581, which is in keeping with other studies of professional sports demand. It is interesting that the age of a franchise (FRAGE) does not have a statistically significant impact on the demand for a given team. However, the older a stadium is (STAGE), the less attendance a team receives, ceteris paribus. This is in keeping with common claims by team owners that newer stadiums are required to augment attendance. Although it may be that older stadiums have less capacity, the model controls for seating capacity. Therefore, the negative influence of stadium age on attendance might represent the lack of desirable amenities such as food courts, better viewing angles, and so forth. This intuition is supported by Wakefield and Sloan (1995). The longer a team has resided in its host city (CITYAGE), the greater the attendance a team enjoys. This may reflect an accumulation of good will toward the team based on team history within the host city. Given the insignificance of the franchise age, one might expect multicollinearity between these two variables. However, the

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TABLE 2: Estimation Results From Ordinary Least Squares (OLS) and Maximum Likelihood Unrestricted Model OLS Variable INTERCEPT LNPAVE LNFRAGE LNSTAGE LNCITYAGE LNCITYPOP LNCITYINC LNWIN LNLAGWIN YR91 YR92 YR93 YR94 YR95 YR96 YR97 LNCAP LNPLAYC σ λ R2 Log-L Log-L test

Coefficient 7.890*** –0.615*** –0.004 –0.034*** 0.019 –0.009 0.240*** 0.102*** 0.089*** –0.103*** –0.104*** –0.100*** –0.054 0.044 0.129*** 0.301*** 0.328*** 0.076 .— .— 0.653

Restricted Model

Maximum Likelihood

Maximum Likelihood

SE

Coefficient

SE

Coefficient

SE

1.120 0.091 0.022 0.010 0.016 0.009 0.060 0.016 0.022 0.033 0.037 0.043 0.044 0.060 0.076 0.075 0.077 0.051

7.611*** –0.581*** –0.003 –0.033*** 0.017*** –0.0109 0.239*** 0.103*** 0.085*** –0.0926*** –0.094*** –0.093 –0.047 0.047 0.129** 0.290*** 0.357*** 0.065 7.592*** 1.116*** .— 188.964

1.309 0.056 0.017 0.011 0.007 0.014 0.090 0.017 0.014 0.037 0.046 0.060 0.057 0.065 0.070 0.076 0.074 0.073 0.867 0.488

6.070*** –0.397*** .— –0.034*** 0.015*** .— 0.245*** 0.107*** 0.083*** –0.051*** –0.041 .— .— .— 0.103*** 0.220*** 0.438*** .— 6.440*** –1.734*** .— 178.187 0.117

1.028 0.049 0.009 0.007 0.065 0.016 0.012 0.024 0.027

0.029 0.041 0.063 0.606 0.576

NOTE: N = 228. Dependent variable is the log of annual attendance. For variable definitions, see Table 1. **Significant at the .10 level. ***Significant at the .05 level.

correlation between the logs of the two variables is only 0.57. This may indicate that attendance for a given franchise is based on the accumulated goodwill within a given host city rather than the overall history of the franchise. This is a potential concern for team owners who might choose to relocate a franchise to another host city. The population of the host city has a statistically insignificant effect on attendance, perhaps because the majority of host cities have a large suburban area. The population figures used in this study account for the population of the Metropolitan Statistical Area (MSA) that the team resides in, and the population reasonably included in the geographic market of a given franchise might well be understated by this measure. Unfortunately, no better consistent measure of population is available for all teams and all years in the sample.5 The income of a team’s MSA has a positive and statistically significant effect on team attendance. The estimated income elasticity of demand is 0.239, indicating

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that football is a normal good, although income effects are rather small. This is also in keeping with the findings in other sports studies. Specific to football, the fact that the average ticket price is approximately $37.00 may already price those consumers most sensitive to income changes out of the market. Current and recent-past performance of the team (WIN and LAGWIN, respectively) have a positive and statistically significant impact on current season attendance. As would be expected, current season winning percentage has a greater effect on attendance than the team’s performance the previous year. The time dummy variables (YR91 to YR97) indicate that, relative to attendance in 1990, the NFL suffered attendance decreases through 1994; however, the estimated parameters for 1993 to 1995 are statistically insignificant. Attendance then increased, relative to 1990, in 1996 and 1997. This increase might have been caused by an increased interest in the league by the expansion of the NFL by two teams, Jacksonville and Carolina. The final two parameters estimated also take the expected signs. Increased stadium capacity does translate to an increase in attendance. A 1% increase in stadium capacity led to a 0.357% increase in actual attendance. The increase in player expenditures, however, did not have a statistically significant effect on team attendance, although the estimated parameter does take the expected sign. This is perhaps because the NFL has a team salary cap, unlike professional baseball, that limits the ability for team owners to purchase a winner. Because the majority of teams are at or near the salary cap in a given year, the variation in aggregate team salaries is relatively low. At the suggestion of an anonymous referee, the insignificant variables were discarded, the model was reestimated, and the fan loyalty measures were recalculated. Results are reported in Table 2 as the restricted model. A log-likelihood test reveals that we cannot reject the hypothesis that all the insignificant variables in the unrestricted model are jointly equal to zero. Upon reestimating the model, the signs and magnitudes of the remaining variables stayed the same. Having estimated the overall demand for the NFL, it is possible to address the issue of fan loyalty. The resultant error structure from the MLE procedure is a composite error term. One component is a standard-normal disturbance, which accounts for white noise impacts on a particular team’s attendance such as weather, other activities available in a given host city, the strength of a team’s home schedule, and so forth. The second component is one-sided, modeled as a half-normal disturbance term. This one-sided error term accommodates a relative measure of fan loyalty. The first two columns of Table 3 list the average fan loyalty measures for the teams in the NFL during the time span of 1990 to 1997 using the unrestricted and restricted models. The fan loyalty index is created using the Jondrow, Knox Lovell, Materov, and Schmidt (1983) measure and, in keeping with their approach, the arithmetic average is taken during the time period of the study. The fan loyalty mea-

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TABLE 3: Relative Fan Loyalty Rankings for 1990 to 1997 Team Rank Unrestricted Restricted 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

1 4 3 2 5 7 9 8 6 11 15 10 14 12 13 16 17 20 22 21 18 25 26 28 30 24 23 27 19 31 29 32 33 34

Team Name

a

Fan Loyalty (1/

Baltimore Ravens Carolina Panthers Buffalo Bills Cleveland Browns Denver Broncos Philadelphia Eagles Dallas Cowboys Jacksonville Jaguars St. Louis Rams Cincinnati Bengals Oakland Raiders Kansas City Chiefs Chicago Bears Miami Dolphins New York Giants New York Jets Washington Redskins New England Patriots Pittsburgh Steelers New Orleans Saints Indianapolis Colts Houston Oilers San Diego Chargers San Francisco 49ers Los Angeles Rams Seattle Seahawks Detroit Lions Minnesota Vikings Green Bay Packers Arizona Cardinals Tampa Bay Buccaneers Atlanta Falcons Los Angeles Raiders Tennessee Titans

1.10712 1.07210 1.06827 1.06683 1.06173 1.06043 1.05785 1.05704 1.05559 1.05053 1.04907 1.04898 1.04894 1.04790 1.04730 1.04723 1.04233 1.04050 1.03871 1.03756 1.03743 1.03665 1.03664 1.03539 1.03519 1.03512 1.03453 1.03422 1.03383 1.03380 1.03198 1.03135 1.02500 1.01557

i)

Relocation (after 1990) From Cleveland in 1996

To Baltimore in 1996

From Los Angeles in 1995 From Los Angeles in 1995

To Tennessee in 1997

To St. Louis in 1995

To Oakland in 1995 From Houston in 1997

a. Based on an unrestricted model.

sures are strikingly in keeping with claims by NFL fans and commentators as to which teams have the strongest fan base. The Baltimore Ravens enjoy the greatest fan loyalty in this study, with the Carolina Panthers, Buffalo Bills, Cleveland Browns, and Denver Broncos rounding out the top five teams. The five worst teams in terms of fan loyalty during the sample span were the Arizona Cardinals, Tampa Bay Buccaneers, Atlanta Falcons, Los Angeles Raiders, and Tennessee Oilers (recently renamed the Titans). The relative

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fan loyalty measures are rather robust to several different model specifications, thus offering some confidence on the approximate relative rankings of the teams. Considering the differences between the unrestricted and restricted models, the vast majority of the teams did not experience a dramatic change in their relative ranking in fan loyalty. The sole exception is the Green Bay Packers, who jump from a ranking of 29 to 19, most likely caused by the exclusion of host city population from the model.6 Rankings based on the restricted model are reported in Table 3. After dividing the teams into thirds and comparing the team rankings between the two specifications, 10 of the top 11 teams and 10 of the bottom 11 teams remain the same. Further confidence can be placed on the relative measures by looking at the actions taken by several team owners during the past decade. The Browns left Cleveland even as the city of Cleveland was prepared to spend $125 million in renovating their stadium (Shuster, 1995). The move was so controversial that the Senate Judiciary Committee held hearings on the issue in November 1995. The fans in Cleveland were so outraged by the move that lawsuits were filed to annul the relocation (“Cleveland Fights Modell,” 1995). As the suits failed, many decried the move as foolish on the part of the team ownership. However, the relocation of the Browns to Baltimore resulted in a relatively stronger fan base and, in the end, a new, publicly financed stadium. As seen in Table 3, Cleveland fans were ranked 4th in relative strength among the various host cities in the league. Other host cities that experienced franchises leaving, Houston (ranked 22nd) and Los Angeles (ranked 33rd for the Raiders and 25th for the Rams), recently applied for new NFL franchises. The NFL subsequently offered new franchises to Cleveland (who began play in the 1999 to 2000 season) and Houston (to begin play during the 2002 to 2003 season). Both of these expansion decisions seem appropriate. Cleveland and Houston rank higher in terms of fan base strength than Los Angeles, although Los Angeles is the largest population concentration without an NFL franchise. Further implications can be gleaned from the relative fan loyalty measures. In addition to the Cleveland Browns’ relocation to Baltimore, the other teams that relocated all improved their relative fan base. The Los Angeles Raiders relocated to their original host city of Oakland, California, improving their relative fan base from 33 of 34 to the 11th strongest fan base. Likewise, the Los Angeles Rams relocated to St. Louis, trading the Los Angeles fan base (25th of 34) for the 9th strongest fan base in the sample. Finally, the Houston Oilers relocated to Tennessee amidst claims by team owners that the fan base in Houston was too weak. Indeed, Houston’s fan base was ranked 22nd out of 34 host cities in the sample. The subsequent decline in the Oilers fan base, trading the 22nd strongest fan base for the 34th strongest, is rather easily explained. The Tennessee Oilers played their first season in Memphis, Tennessee. However, their actual host city is Nashville, Tennessee. The residents of Memphis, unhappy with the decision to ulti-

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TABLE 4: Probit Estimation Variable Unrestricted model Intercept Fan loyalty STAGE CITYAGE N = 228 Predicted = 98.24% Psuedo R2 = 0.387 Restricted model Intercept Fan loyalty STAGE CITYAGE N = 228 Predicted = 98.24% Psuedo R2 = 0.286

Estimate

SE

dP/dX (move = 0)

83.315*** –85.122*** 0.044*** 0.024*

38.496 38.124 0.018 0.016

–2.357 2.408 –0.001 –0.000

43.782* –46.623* 0.038*** 0.020

25.542 25.496 0.015 0.016

–1.417 1.509 –0.001 –0.000

NOTE: Dependent variable is team moving = 1. *Significant at the .15 level. ***Significant at the .05 level.

mately locate the team in Nashville, expressed their displeasure by not attending the games played in Memphis. Although casual empiricism indicates than fan loyalty measures tend to correlate with team relocations, it is possible to implement a statistical test of this hypothesis. Accordingly, yearly team relocation decisions are related, in a probit framework, to the year-specific fan loyalty measure, the length of time the team has been in the city, and the physical age of the stadium.7 Table 4 reports the results of estimation using the restricted and unrestricted fan loyalty measures.8 Team relocation is coded using a dummy variable that takes a value of one if a team relocated to a new host city between seasons and zero otherwise. Not surprisingly, the probit results indicate that fan loyalty has a statistically significant impact on the decision to relocate; estimates have the expected signs, and most are statistically significant. Table 4 also reports the marginal impacts of the three explanatory variables on the decision to relocate. The model accurately predicts the outcome of a team relocation decision 98% of the time.9 The results confirm the intuition provided by Root (1994) on firm location decisions. Firms should relocate when there is a benefit on the revenue or the cost side of the profit relationship. Although it is still open to debate whether professional sports franchises are profit maximizers, there is little doubt that teams are operated at least as profit earners. As such, team owners must be concerned with the cost and revenue sides of the profit relationship of their team. If a team can relocate to a stronger fan base, then the impact is beneficial on the revenue side. This is because, ceteris paribus, a team can have a lower quality and

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higher price combination than it would have been able to extract in its previous host city. This can enhance the profit of the relocated franchise; the empirical results confirm that relative fan base is a part of the calculus in determining team relocation. Team owners often threaten relocation if a new stadium is not provided by the host city or if a potential host city has already promised a new venue. Although some teams actually do relocate after such threats, the evidence provided in this article suggests that team owners also choose to relocate because of the relative weakness of their fan base.10 This is also rather intuitive. Team owners typically know what their costs will be for a given season. Player salaries are, for the most part, determined before the beginning of the season. Furthermore, in general, stadium expenditures are also predetermined. Therefore, the most important random element of a team’s profit relation is revenue. Although season ticket sales provide a predetermined level of revenue, the number of marginal ticket sales is the source of the randomness in team revenues. A team owner desires the strongest fan base possible to weather random influences on his or her team’s competitiveness. Random impacts to a team’s competitiveness, such as player injuries, opponent competitiveness, or overall team synergies, cause a team owner to prefer a fan base that attends games at a level greater than predicted by the quality-price relationship alone. NOTES 1. The sample is larger than the number of teams at any given time because of team relocation. Thus, the Los Angeles Rams are considered a different team than the St. Louis Rams. 2. In this instance, I include the team-specific fan loyalty measure in an inverse fashion. This facilitates an easier interpretation of the fan loyalty metric. In particular, the resulting fan loyalty estimates show, in percentage terms, how much more attendance individual teams receive above that predicted by the model and the two-sided error component. 3. Team revenue figures were obtained from various issues of the Financial World and Forbes Magazine, macroeconomic figures from the Census Bureau, and team productivity from the National Football League (NFL) and various issues of the Dallas Morning News. 4. The NFL does have a salary cap that is binding for most teams. This lack of variance in team-level player costs would lead one to expect this parameter estimate to be insignificant. 5. The insignificance of population in the current study is at odds with results from other studies, but may not be too surprising in light of the high number of sellouts in the NFL. However, the result is robust to various specifications of the model. A dummy variable for multiple teams in one host city was negative and statistically significant, but otherwise did not alter the results presented here. 6. The Green Bay Metropolitan Statistical Area (MSA) is the smallest of all NFL host cities, with a sample-span average population of 205,639. 7. An anonymous referee suggests that an identification problem may exist in the interpretation of the coefficient on stadium age if stadium renovations influence franchise relocation decisions. This identification problem is not addressed in this study, but would be an interesting focus of future research.

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8. The inclusion of the fan loyalty index as an explanatory variable introduces the generatedregressors problem. Although the resultant estimates are biased, they are consistent (Greene, 2000). Furthermore, the reported standard errors are asymptotically consistent. 9. Various other explanatory variables, such as population, income, and historical team performance, were used in alternative model formulations. However, these variables were insignificant in explaining team relocation decisions. 10. Indeed, 2 days after Art Modell, owner of the Cleveland Browns, announced the relocation of his franchise to Baltimore, Cleveland overwhelming voted to allocate $175 million to renovate the stadium. However, the proposed renovation did not keep the Browns in Cleveland.

REFERENCES Cleveland fights Modell over lease; City hopes judge will prevent move. (1995, November 11). Cincinnati Post, p. D5. Depken, C. A. II. (2000). Fan loyalty and stadium funding in professional baseball. Journal of Sports Economics, 1, 124-138. Greene, W. (2000). Econometric analysis (4th ed.). Englewood Cliffs, NJ: Prentice Hall. Jondrow, J., Knox Lovell, C. A., Materov, I. S., & Schmidt, P. (1983). On the estimation of technical efficiency in the stochastic production frontier model. Journal of Econometrics, 19, 233-238. National Football League. (1991). NFL franchise relocation rules. NFL Constitution, Article 8.5. Nolen, J. (1999, October 25). Pythons win; Team threatens move. Portland Oregonian, p. D2. Noll, R. G. (1974). Attendance and price setting. In R. G. Noll (Ed.), Government and the sports business (pp. 115-157). Washington, DC: Brookings Institution. Rascher, D. (1995). Sports and economics: Literature review and research ideas. Unpublished manuscript, UC Berkeley. Root, F. R. (1994). International trade and investment (7th ed.). Cincinnati, OH: South-Western. Salant, D. J. (1992). Price setting in professional team sports. In P. M. Sommers (Ed.), Diamonds are forever: The business of baseball (pp. 77-90). Washington, DC: Brookings Institution. Shuster, R. (1995, November 10). Congress reacts. USA Today, p. C1. Siegfried, J. J., & Eisenberg, J. D. (1980). The demand for minor league baseball. Atlantic Economic Journal, 8, 59-69. Wakefield, K. L., & Sloan, H. J. (1995). The effects of team loyalty and selected stadium factors on spectator attendance. Journal of Sport Management, 9, 153-172.

Craig A. Depken II is an assistant professor of economics at the University of Texas at Arlington. His main research interests are applied microeconomics and applied industrial organization, including sports economics and the economics of advertising.

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