THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE

DEPARTMENT OF ECONOMICS

THE STADIUM SUBSIDY GAME

ALEXANDER ELLIS SPRING 2020

A thesis submitted in partial fulfillment of the requirements for baccalaureate degrees in Mathematics and Economics with honors in Economics.

Reviewed and approved* by the following:

Peter Newberry Assistant Professor of Economics Thesis Supervisor

Russell Chuderewicz Teaching Professor of Economics Honors Adviser

* Electronic approvals are on file. i

ABSTRACT

This thesis analyzes the strategic situation that allows sports teams in the US to secure large subsidies from cities. Using a simple league model and a two-period subsidy auction model, the paper establishes conditions under which a league will strategically leave viable cities open to extract greater subsidies in the future. That finding is then compared with historical subsidy data for NFL, MLB, NBA, and NHL teams1. To that end, historical data on the largest open markets in each of the Big Four leagues was compiled independently for this paper.

However, a regression of subsidies on open market size fails to provide evidence of the relationship predicted by the league and subsidy auction model. Additionally, linear regression shows that metropolitan population explains at most half of the variation in team revenues, contrary to the league model’s assumption that revenues are determined entirely by metro population.

1 NFL, MLB, NBA, and NHL refer to the National Football League, Major League Baseball, National Basketball Association, and National Hockey League, respectively. ii

TABLE OF CONTENTS

LIST OF TABLES ...... iii

LIST OF FIGURES ...... iv

ACKNOWLEDGEMENTS ...... v

Chapter 1 Introduction ...... 1

Chapter 2 Literature Review ...... 3

Models of Leagues and Subsidies ...... 3 Contingent Valuation Studies ...... 6

Chapter 3 League Model ...... 9

Multiple Teams per City ...... 9 Talent, Revenue, and Profit ...... 10 Social Value ...... 15

Chapter 4 Stadium Subsidy Game Model ...... 16

General Two-Period Model ...... 17 Two-Period Model: Numerical Example ...... 20 Comparative Statics: 훼, 휆 ...... 23

Chapter 5 Comparison to Data ...... 26

League Model vs Revenue & Profit Data ...... 26 Contingent Valuation: Case Studies ...... 31 Testing Subsidy Data ...... 33

Chapter 6 Conclusion ...... 35

Appendix A Verification of Four Properties of 휎(푗, 푛)...... 37

Appendix B Derivations under Revenue Sharing ...... 39

Appendix C Deriving the Social Value Constant “c” ...... 41

Appendix D Regression Output: Revenue vs Metro Population ...... 42

Appendix E Historical Subsidy & Vacant City Data ...... 44

Appendix F Regression Output: Subsidy vs. Time, Avg Vacant City...... 50 iii

BIBLIOGRAPHY ...... 52

iv

LIST OF TABLES

Table 1. Profits by Team, Time Period ...... 17

Table 2. Case 1: League’s Offers in Period 2 by Team 1 Location Decision ...... 18

Table 3. Case 2: League’s Offers in Period 2 by Team 1 Location Decision ...... 19

Table 4. Case 3: League’s Offers in Period 2 by Team 1’s Location Decision ...... 20

Table 5. Meaning and Value of Constants ...... 20

Table 6. Single Team Values for Each City ...... 21

Table 7. Case 1: League’s Period 2 Offers by Team 1 Location Decision ...... 22

Table 8. Case 2: League’s Period 2 Offers by Team 1 Location Decision ...... 22

Table 9. Case 3: League’s Period 2 Offers by Team 1 Location Decision ...... 23

Table 10. Period 1 City Choice vs 훼, 휆 ...... 24

Table 11. Regression of Revenue on Metro Population ...... 30

Table 12. NHL Revenue Regressed on Metro Population and Southern Binary Variable ...... 30

Table 13. Results of Subsidies Regressed on Avg Vacant City, Time ...... 34

v

LIST OF FIGURES

Figure 1. NFL, MLB Team Revenues & Profits, 2018-19 ...... 27

Figure 2. NBA, NHL Team Revenues & Profits, 2018-19 ...... 28

vi

ACKNOWLEDGEMENTS

Thank you to Peter Newberry and James Tybout for helping me through the process of writing this thesis. You have both given me a better understanding of economics and the research process, and I hope to continue improving as a researcher over the next several years.

I would also like to thank all the students in ECON 489M who gave suggestions for improving this paper. I enjoyed our thesis class – especially before we had to move online – and

I hope at least a few of my suggestions were helpful for you as well.

Finally, thank you to my parents and my dog, Layla, for enduring my late-night thesis work while at home this semester.

1

Chapter 1

Introduction

Since 2000, US taxpayers have spent at least $16.7 billion2 to subsidize sports stadiums for the Big Four sports leagues (the NFL, MLB, NBA, and NHL), despite those leagues taking in a combined $38 billion in revenue – and keeping $8 billion in profits – in 2019 alone (Forbes)3.

Cities are often forced to offer teams enticing deals to avoid losing them to other cities; those deals often include property tax exemptions, below-market leases, stadium naming rights, and hundreds of millions of dollars in public money for stadium construction. In this paper, I will investigate the competition between cities that produces such large subsidies for sports teams, and I aim to explain teams’ location decisions. In particular, I will seek to establish conditions under which leagues strategically leave large cities open to extract subsidies in the future.

Stadium subsidies are a compelling topic because they do not appear to make economic sense. The most common claim made to justify these subsidies – namely, that sports teams make a sufficient economic impact to repay their cities – is unsupported by the literature (Baade,

1996). Though stadiums may have some impact on a city’s economy, that impact is quite small compared to the size of the city’s economy and is also mitigated by a crowding-out effect; rather than exclusively attracting new economic activity to the city, sporting events often take business away from other local establishments. The intangible value of teams to fans both within the city and outside it is considerably larger, though that value cannot be easily captured by the city paying the subsidy (Noll & Zimbalist, 1997).

2 $16.7 billion is the sum of subsidy figures from various sources, including Marquette’s NSLI (2015). 3 I calculated revenue and profit by summing the numbers published separately by Forbes for each league. 2 Though the economic results of subsidies are worth discussing, an even more interesting question is why cities commit to paying subsidies. The first and most obvious answer is that cities want to keep their teams where they are. US sports teams are privately owned franchises whose owners will move their teams to more profitable cities if the opportunity arises. For example, Brooklyn Dodgers owner Walter O’Malley infamously moved his team to Los Angeles in 1957 after being denied his preferred stadium location in Brooklyn. Though O’Malley’s decision was economically sound, the people of Brooklyn were understandably outraged, and they focused that rage at him rather than at the unelected official who denied his development request (Brownell, 2018).

Today, however, funding decisions fall to elected officials who would certainly bear the brunt of their voters’ outrage in such situations. Indeed, though team movement is relatively rare, the threat of relocation looms over many stadium deals; when used credibly, a threat to move can generate public outcry and force even larger concessions from lawmakers. The potential strength of that threat makes it an essential part of the strategic situation that leads to today’s multi- million dollar stadium subsidies.

I will represent this strategic situation with a subsidy auction model similar to Slattery’s

(2019), and I will find revenue and profit functions from a league model similar to the one developed by Owen (2003). I will also expand on Owen’s league model by allowing for multiple teams to locate in the same city and by calculating teams’ optimal talent decisions, revenues, and profits after taking revenue sharing into account. After analyzing the comparative statics of a two-period subsidy auction model, I will compare its theoretical expectations to the results of cases in which teams have relocated or received stadium subsidies. 3 Chapter 2

Literature Review

The literature regarding models of sports leagues and stadium subsidies is most relevant to this paper. I will also review two contingent valuation studies that give some insight into the social value of sports teams; in fact, further contingent valuation studies would provide invaluable data to test this paper’s central models.

Models of Leagues and Subsidies

The stadium subsidy game can be modeled in a few different ways. One way is to approach the problem of expansion from the league’s perspective. According to Buchanan’s classical club theory, the league with complete revenue sharing will expand up to the point where average profit per franchise is maximized (Vrooman, 1997). Vrooman builds on Buchanan’s club theory by introducing the proportion of shared revenue as an explicit parameter – which I will use in my league model – and incorporating the possibility of “stadium extortion” from available markets. He finds that any equilibrium of NFL franchises is unstable because the franchises can extract more value by relocating to new cities that are willing to pay for new stadiums.

Alternatively, a public choice model can be used to analyze the situation from the city’s perspective, modeling the city’s decision as a referendum. Though I will not use that approach in this paper, the political considerations of stadium subsidies are certainly worth studying. Porter and Thomas (2010) develop such a model that considers the effort each citizen will expend for or against a subsidy in a referendum. The effort exerted by each voter is modeled as a function of 4 the net benefit they derive from the stadium subsidy, and the net benefit of voter 푖 is expressed as a function of the total subsidy 푆 in the following equation:

푁퐵푖(푆) = 푉푖 + 퐶푆푖(푃̅) − 푡푖푆, where 푉푖 is any value from the team not associated with consumption, 푃̅ is the average ticket price, and 푡푖 is the proportion of city tax revenue accounted for by voter 푖. The subsidy the city can provide is then found by maximizing the total subsidy under the constraint that public support outweighs public opposition. As it turns out, the pro-subsidy side outspends the opposition in every single referendum (Brown & Paul, 2002).

Porter’s public choice model implies a principle of location invariance, stating that subsidies generally do not alter a team’s location decision. The reasoning behind this principle is that the value of a market depends largely on the city’s population size, which is also highly correlated with the maximum subsidy the city can provide for a stadium. Porter did note that the principle may not hold in all cases due to transaction costs in winning referendums, and it would seem that there are significant transaction costs in moving between cities as well.

Porter’s conclusion of location invariance raises the question of how subsidies can be economically justified. The most common political justification for stadium subsidies is that sports teams make economic impacts that in effect repay their cities, but that idea has been thoroughly rejected by the literature (Siegfried & Zimbalist, 2000). As stated in the introduction, the impact that stadiums have on a city’s economy is quite small compared to the size of the city’s economy and is tempered by a crowding-out effect. The intangible value of teams to fans both within the city and outside it is considerably larger and merits closer investigation (Noll &

Zimbalist, 1997). 5 Indeed, social value of sports teams may be a determining factor in the subsidies paid to them by cities. It is also at the center of a league model developed by Owen (2003), which I will adapt for use in this paper. In his model, Owen considers cities of size 휎1, 휎2, … , 휎푛, where city size decreases as 푛 increases, which have corresponding social values 푉푖 and profit potentials 휋푖.

In particular, 푉푖 is the value a team provides to city 푖 by locating there, and 휋푖 is the profit a team can make after locating in city 푖. Cities are then willing to provide subsidies up to 푉푖 to attract teams, providing a maximum profit of 휋푖 + 푉푖 to teams looking to locate in city 푖. Importantly, this creates the threat point of 휋푛+1 + 푉푛+1, which is the profit that the largest city without a team can provide; during negotiations with its home city, a team can confidently threaten to leave for city 푛 + 1 unless city 푖 agrees to a subsidy of (휋푛+1 + 푉푛+1) − 휋푖.

Owen’s model makes the assumptions that only one team will locate in each city and that those teams will fill the largest cities available. Furthermore, his model implies that a free entry league would lead to a multi-tier system whereby big- and small-market teams – which his model associates with top-level and lower-level talent – would become functionally segregated into different circuits. That system sounds quite similar to promotion and relegation, which is used by many soccer leagues in the world; at least in England, that system results in many, many teams being concentrated in the largest city, London. It seems to me, therefore, that his model should allow for multiple teams in the same city; indeed, I will allow for multiple teams per city in this paper, despite fixing the number of teams in a league and not considering free entry.

The stadium game itself can be modeled as an auction for teams, as I will do in this paper. In a study of subsidies paid to various types of businesses by states and counties, Slattery

(2019) found that subsidies change firms’ location decisions quite often and can be welfare improving as well. One major difference is that she assumes large firms’ entry will cause 6 medium firms to follow them in an agglomeration effect, which likely does not occur to the same extent in professional sports.

Slattery uses an English outcry auction, as I will in this paper. In the first stage of the game, a firm announces its intention to expand to a new location. Next, states bid up to their valuation of the firm. In the final stage, the firm selects the location that has the largest sum of expected profit and subsidy bid. As a result, welfare increases when the firm locates in a state that values the firm more; however, the firm captures the entire welfare increase.

In the case of business subsidies, policymakers state that their main objective is to create jobs. However, Slattery found a very weak relationship between the number of direct jobs created and the size of the subsidy given to firms; either firms are being compensated for indirect job creation or there are other factors at work. She also notes that subsidies will only be welfare improving if states specifically aim to compensate firms for positive spillovers, rather than attracting them for political purposes. That concern also applies to sports subsidies; politicians may overspend on stadium subsidies to keep their city’s team to help their re-election prospects.

However, such political considerations are beyond the scope of my model in this paper.

Contingent Valuation Studies

One such situation where a city’s politicians were threatened by a team took place in

Minnesota this past decade. A years-long fight ended in 2012 when the Minnesota legislature passed a bill to commit funds to a new stadium for their NFL team, the Minnesota Vikings – but not before Fenn and Crooker (2009) could carry out a contingent valuation method (CVM) study. The study took advantage of the situation to estimate the willingness to pay (WTP) of 7 Minnesota residents to keep the Vikings under credible threat of relocation. In this situation,

WTP is equivalent to the welfare contribution of the Vikings franchise to Minnesota households.

The study found that the Vikings were worth between $445.3 million and $1.5713 billion to the households of Minnesota.

Fenn and Crooker conducted their survey during the off-season to mitigate biases from recent victories or defeats, asking participants in a yes/no format whether they would be willing to pay $5, $10, $25, or $100 to finance a new stadium. They sent half of the surveys to households in the Minneapolis-St. Paul metropolitan area, and the other half to rural areas in the state. Importantly for the design of the study, they found a significant positive correlation between a belief that the Vikings would relocate without a new stadium and willingness to pay the subsidy; that backs up the researchers’ claims that CVM studies are most effective when the participants perceive the situation to be real, which in this case is the relocation threat.

Furthermore, the survey responses indicate that the Vikings act as a public good; many respondents indicated that they read about the team frequently, talked about their games, were a

“die-hard fan,” or would have less fun in their lives if the team left (Fenn & Crooker, 2009). The point estimate of the team’s value, at about $775 million, is above the reported public funding amount of $498 million for the stadium (Stadiums of Pro Football, 2019). Though the true public cost may be higher than the nominal $498 million, this study shows that the social value of a team is a significant source of value that can justify stadium subsidies in some cases.

An earlier CVM study of the Pittsburgh Penguins reached similar conclusions, though it was done at a less opportune time and arrived at a lower figure. The valuation study was conducted for Pittsburgh’s NHL team following the city’s decision to build separate stadiums for baseball and football, replacing the multipurpose Three Rivers Stadium (Groothius, Johnson, & 8 Whitehead, 2004). Though the Penguins would later ask for a new arena, the survey was conducted in 2000, immediately after the team was purchased by a consortium that was dedicated to keeping it in Pittsburgh.

The survey asked whether participants would be willing to pay $1, $5, $10, or $25 to keep the Penguins in Pittsburgh and concluded that citywide WTP was between $23.5 million and $66 million (in 2000 US dollars). The respondents also indicated that they perceived the team as a source of civic pride for the city. Though the team appears to act as a public good and some respondents are willing to pay higher taxes to support it, those taxes would be insufficient to fund a new arena. As Fenn and Crooker (2009) suggest, this result may be due to a lack of perceived relocation threat.

9 Chapter 3

League Model

My league model is adapted from the one introduced by Owen (2003), with added allowances for multiple teams per city and revenue sharing. I also simplify the revenue function, which removes a few parameters from the model. Additionally, subsidies are determined through an auction, which will be modeled as an English open-outcry auction.

Multiple Teams per City

Consider a finite set of cities in which city 푖 has a metropolitan population of 휎푖. In this paper, I will treat cities and metropolitan areas synonymously. Metro population will act as a proxy for all factors other than ticket prices that affect demand; in practice, other important factors may include the median income of city 푖 and the preferences of city 푖’s residents.

Now, let us consider a case in which a second team locates in the same city as an established team. This event has implications for the demand for tickets to both teams’ games: the demand for the established team will shift to the left because some fans will become more interested in the new team. The demand for the second team will be lower than if it had the whole city to itself because many sports fans will remain loyal only to the first team.

I will define the effective population for each team 푘 in city 푖 to be proportional to 휎푖,

1 where 휎푖 is the metropolitan population of city 푖. In particular, let 휎푘(푗푘, 푛푖) = 휎푖 ⋅ , where √푗푘푛푖

th team 푘 is the 푗푘 earliest team to locate in city 푖, out of 푛푖 total teams in the city. For example, of the two MLB teams currently in New York City, the Yankees were the earlier to enter; for them,

푗푘 = 1 and 푛푖 = 2. Note that the choice of 휎푘(푗푘, 푛푖) accounts for teams being imperfect 10 휎푖 substitutes. If perfect substitutability of teams were assumed, the simpler function 휎푘(푛푖) = 푛푖 would suffice. The properties of each of these functions are demonstrated in Appendix A.

However, it turns out that this choice does make a difference in the final analysis, so I will use

1 휎푘(푗푘, 푛푖) = 휎푖 ⋅ . √푗푘푛푖

Talent, Revenue, and Profit

Having defined a market size variable for each team in each city, I will proceed to formulate the revenue a team can earn from playing there. Once team 푘 locates in city 푖, its owner knows the population 휎푘 available to it and can estimate the resulting demand curve. That knowledge allows the team to choose the level of talent and ticket prices that maximize profits, given the available talent pool. In fact, the team might not act quite like a monopolist when setting ticket prices (Porter & Thomas, 2010), but that is not an important feature of the model in this paper. Additionally, let 푁 denote the number of teams in the league.

The revenue that team 푘 earns will be increasing in effective metro population (휎푘), the

푡 ratio of team 푘’s talent to the average talent in the league ( 푘), and the average talent of the 푡̅ league (푡)̅ . Since 푡 ̅ has an ambiguous effect on revenue, it can be left out of the model, with the result that revenue depends only on metro population (휎푘) and team 푘’s talent (푡푘). Ticket prices can be left out as well; since it is assumed that the team is setting prices to maximize profits in this model, the other two parameters fully define revenue and profit. Let us specify the function

훼 훽 to be 푅푘 = 푐푅휎푘 푡푘 , where 훼, 훽 ∈ (0,1) and 푐푅 is a constant of proportionality. In practice, 푐푅 will be set according to the values of 훼 and 훽, since those parameters would otherwise have a 11 dramatic effect on the scale of revenues for all teams. The revenue function implies that metro population and talent each have decreasing marginal returns.

In practice, professional sports leagues implement revenue sharing between franchises.

Though revenue sharing mechanisms vary between leagues, this model will use the post-sharing

1 revenue function 푅푠 = (1 − 푠) ⋅ 푅 + 푠 ⋅ 푅̅, where 푅̅ = ∑푁 (푅 ) is the average revenue of the 푘 푘 푁 푘=1 푘 league. Importantly, the extent of revenue sharing impacts each team’s optimal talent level as well as their resulting revenues and profits. Additionally, it may put the league’s interests at odds with teams’ interests in situations such as franchise relocation.

Teams’ payroll expenses will be assumed to be proportional to their talent levels, giving us 퐶푘 = 푤 ⋅ 푡푘 + 푐푘, where 푤 is a constant wage rate and 푐푘 represents fixed costs such as stadium investments. Since 푐푘 is constant with respect to 푡푘, it will be ignored in the analysis below. We will start by writing the team’s profit maximization equation and then solve for the

푠 optimal talent level. That optimal talent level will allow us to solve for 푅푘(푡푘) and 휋푘(푡푘).

First, however, let us derive the version with no revenue sharing; the expressions involving revenue sharing will be quite messy. The profit maximization problem for team 푘 without revenue sharing is as follows:

max 휋푘 = 푅푘(푡푘) − 퐶푘(푡푘) 푡푘

푑휋 훽푐 휎훼 푘 = 푅 푘 − 푤 = 0 푑푡 1−훽 푡푘

1 훽 ⋅ 푐 ⋅ 휎훼 1−훽 푡∗ = [ 푅 푘 ] . 푘 푤

∗ Having solved for the optimal level of talent (푡푘), we can substitute it into the revenue equation to find the revenue for team 푘: 12 훼 ∗훽 푅푘 = 푐푅휎푘 푡푘

훽 훽 ⋅ 푐 ⋅ 휎훼 1−훽 = 푐 휎훼 [ 푅 푘 ] 푅 푘 푤

1 훽훽 ⋅ 푐 ⋅ 휎훼 1−훽 푤 = [ 푅 푘 ] = ⋅ 푡∗. 푤훽 훽 푘

∗ Similarly, substituting 푡푘 into the profit equation gives us the following:

∗ ∗ 휋푘 = 푅푘(푡푘) − 퐶푘(푡푘) 푤 = ⋅ 푡∗ − 푤 ⋅ 푡∗ 훽 푘 푘

푤(1 − 훽) = ⋅ 푡∗ 훽 푘

= (1 − 훽) ⋅ 푅푘.

Remember that the above results assume no revenue sharing, i.e. 푠 = 0. Now we will find the same expressions under the general case for revenue sharing, 0 ≤ 푠 ≤ 1. Full derivations for the expressions under revenue sharing can be found in Appendix B, but we will show minimal derivation, along with the results, in the main text of the paper.

푠 max 휋푘 = 푅푘(푡푘) − 퐶푘(푡푘) 푡푘

휕휋 휕푅 휕푅̅ 0 = 푘 = (1 − 푠) 푘 + 푠 − 푤 휕푡푘 휕푡푘 휕푡푘

1 훼 1 훽 ⋅ 푐 ⋅ 휎 1−훽 푠 1−훽 푡∗ = [ 푅 푘 ] ⋅ [(1 − 푠) + ] . 푘 푤 푁

This result gives the general solution for any extent of revenue sharing, 0 ≤ 푠 ≤ 1. Note

1 푠 that the proportional factor introduced by revenue sharing, [(1 − 푠) + ]1−훽, decreases as 푠 푁 13 1 1 increases; it takes its maximum value of 1 at 푠 = 0 and its minimum value of ( )1−훽 at 푠 = 1. 푁

Therefore, one consequence of the model is that teams will tend to hire less talent as the extent of revenue sharing in a league increases. However, the model assumes team owners only care about profits; under that assumption, winning has no benefit to the owner apart from bringing in greater pre-sharing revenues. Additionally, it is assumed that 푁, the optimal number of teams, is fixed; in reality, the number of teams is affected by the extent of revenue sharing (Vrooman, 1997).

The optimal level of talent found above increases with market size (휎푘) and decreases with respect to the wage rate (푤); this result makes sense intuitively, since revenue increases

∗ with market size and cost increases with the wage rate. Now, the optimal level of talent (푡푘) can be substituted into the revenue equation to find the revenue for team 푘. See Appendix B for the full derivation.

1 훽 훽 훼 1−훽 훽 ⋅ 푐 ⋅ 휎 푠 1−훽 푅 = [ 푅 푘 ] ⋅ [(1 − 푠) + ] . 푘 푤훽 푁

푁 푠 1 푅 = (1 − 푠) ⋅ 푅 + 푠 ⋅ 푅̅, where 푅̅ = ∑ 푅 ′. 푘 푘 푁 푘 푘′=1

푁 푠 −훼 훼 푅푠 = 푅 ⋅ [(1 − 푠) + ⋅ 휎1−훽 ⋅ ∑ 휎1−훽]. 푘 푘 푁 푘 푘′ 푘′=1

We can similarly find profits under revenue sharing (휋푘).

푠 ∗ 휋푘 = 푅푘 − 푡푘 ⋅ 푤

푠 −1 = 푅푠 − 푅 ⋅ 훽 ⋅ ((1 − 푠) + ) 푘 푘 푁 14 푁 푠 −훼 훼 푠 = 푅 ⋅ [((1 − 푠) + ⋅ 휎1−훽 ⋅ ∑ 휎1−훽) − 훽 ⋅ ((1 − 푠) + )]. 푘 푁 푘 푘′ 푁 푘′=1

It turns out that the profit 휋푘 under revenue sharing is proportional to the team’s pre- sharing revenue, 푅푘, just as we found in the case without revenue sharing. However, the constant multiplying 푅푘 has become quite ugly and depends on 푠, 푁, 훼, 훽, and the ratios of other teams’ city sizes to 휎푘.

푤 푠 −1 Additionally, the revenue derivation shows that 푅 = 푡 ⋅ ⋅ ((1 − 푠) + ) . We can 푘 푘 훽 푁 rearrange the terms from that equation to find the players’ revenue share:

푤 ⋅ 푡 푠 푘 = 훽 ((1 − 푠) + ) 푅푘 푁

Note that the expression on the right-hand side is constant; that is, it does not rely on any team- specific variables. As a result, this expression for players’ revenue share is the same for every team (before revenue sharing). Since revenue sharing does not change the total revenue of the league, it applies to the entire league as well.

This equation tells us that the players’ revenue share increases with 훽. Indeed, as talent

∗ plays a larger role in team 푘’s revenue function, 푡푘 will increase and the overall wages paid to players will increase as well. The equation also implies that extensive revenue sharing will lead to low revenue shares for players; this conclusion relies on the assumption that owners care about profits but not about winning. Additionally, the presence of players’ unions is beyond the scope of this model; in reality, players may demand a revenue share far larger than this equation gives us. Indeed, the equation above represents the league-optimal result.

15 Social Value

Now the quantities relevant to teams have been solved in terms of the parameters specified at the beginning of the model section. However, a city should only care about the social value that the team provides, 푉푘. In addition to providing a product that people are willing to pay for, teams provide a public good for fans in their host cities and beyond. Indeed, that public good reaches fans across the country, and in practice, stadium subsidies come from states and the federal government as well as from cities.

According to contingent valuation methods (CVM) studies done by Fenn & Crooker

(2009) and Groothius et al. (2004), the social value of a professional sports team may be on the order of hundreds of millions of dollars. That value is high enough to potentially justify the hundreds of millions of dollars that some cities spend on stadium subsidies. Since no other value provided by sports teams approaches that level, we may infer that cities are paying subsidies to these teams to compensate them for the public good they are providing to the city’s residents.

From that reasoning, cities would be willing to spend up to the social value of the team, 푉푘, on stadium subsidies if it is necessary to do so to prevent the team’s relocation.

The social value 푉푘 should intuitively be increasing in market size (휎푘) and talent level

(푡푘). Since these factors are both present in the revenue function 푅푘, let us assume that social value is proportional to a team’s pre-sharing revenue: 푉푘 = 휆 ⋅ 푅푘. Recall that the model established a proportional relationship between a team’s revenue and its profit. There is a similar relationship between a team’s revenue and its social value to the city, which implies that the profit a team earns in a city is linearly related to the social value it provides to that city.

Therefore, the cities that provide the largest profit potential are also able to provide the largest subsidies to teams. 16 Chapter 4

Stadium Subsidy Game Model

The league model’s results for revenue, profit, and social value can now be used in a model of a league’s extortion of subsidies. When a team or league wants a subsidy for a new stadium, it does not need to negotiate with its host city one-on-one. It can effectively hold an auction between multiple cities to get them to bid against each other.

I will model this auction as an English outcry auction because cities typically make public offers and have the chance to raise their subsidy bids until the team decides where to locate. Let us take the Raiders’ recent relocation from Oakland to Las Vegas as an example. In

October 2016, the Nevada Senate passed a bill allocating $750 million for an NFL stadium

(Associated Press, 2016). In early 2017, the city of Oakland publicly made a last-minute pitch that included a $600 million hedge fund investment but no public funding (Stites, 2019). Having considered these offers, the Raiders chose to move to Las Vegas and the NFL voted in favor of the move in March 2017.

In this auction format, the winning city should pay just enough to beat its closest competitor, and the winning offer is the one that maximizes profits and subsidies (rather than simply being the highest subsidy offer). Additionally, in this paper, I will assume that the league controls its teams’ movements completely. As a result, the league will choose the offer that maximizes leaguewide profits and subsidies. This is a rather strong assumption; in reality, leagues’ control of team relocation is limited to veto power. 17 General Two-Period Model

Beyond that single-stage auction model, let us form a two-period model to describe the movement of franchises. Consider a model of a small league with three cities available for two teams. The cities have sizes 휎1, 휎2, 휎3 such that 휎2 = 푎휎1 and 휎3 = 푏휎1, with 휎1 ≥ 휎2 ≥ 휎3.

Suppose team 1 is already located in city 1, the largest city.

In period 1, the league chooses a city for team 2. In period 2, the league will hold a subsidy auction for team 1 with the three cities acting as bidders. We will attempt to find the location decision in period 1 that maximizes total leaguewide profits. Those profits are shown in

Table 1 for each team and split up by time period. Profits from ticket sales are denoted by 휋 and subsidies are denoted by 푆. Let us assume that each time period is sufficiently long for profits over that time to be on a similar scale as the social value of a team to its city.

Table 1. Profits by Team, Time Period

Period 1 (t=1) Period 2 (t=2) Total 휋 휋 + 푆 휋 + 휋 + 푆 Team 1 11 12 12 11 12 12

Team 2 휋21 휋22 휋21 + 휋22

Let us derive these values for each of three cases, which represent team 2’s three possible location decisions in period 1. Also, let 휋(휎) denote the profit a team can earn from a city with effective metro population 휎, and let 푃2 denote the league’s combined profit in period 2.

To start, we will define 푉푖 to be the value of a team to city 푖 when it is the only team present. That allows us to express a team’s value to city 푖 as 푐푉푖 in the cases below, where 푐 is determined by the number of teams in city 푖. If there are multiple teams, the city values them less for two reasons: first, they bring in less revenue 푅푘 and value is proportional to revenue; and second, if one team leaves a city that had multiple teams, the remaining teams will become more 18 valuable following that departure. Therefore, the appropriate value to use is the change in the total value of a city’s teams after the team in question leaves the city. That calculation gives us the constant 푐. The three cases of team 2’s decision are below.

Case 1. Team 2 locates in city 1 (which is already occupied by team 1).

휎 In this specific case, team 1’s profit in period 1 is decreased to 휋 ( 1). Now the league √2

has the following potential profits values in period 2:

Table 2. Case 1: League’s Offers in Period 2 by Team 1 Location Decision

City 1 City 2 City 3 League 휎1 휎1 휋 ( ) + 휋 ( ) 휋(휎 ) + 휋(휎 ) 휋(휎 ) + 휋(휎 ) Profits √2 2 1 2 1 3 Team 1 푐푉 푉 푉 Value 1 2 3

휎1 휎1 휋(휎1) + 휋(휎2) 휋(휎1) + 휋(휎3) Total Offer 휋 ( ) + 휋 ( ) + 푐푉1 √2 2 + 푉2 + 푉3

훼 훼 1 1 Here, 푐 = ( )1−훽 + ( )1−훽 − 1. See Appendix C for derivation. √2 2

Let us first define each team’s period 1 profits:

휎 • 휋 = 휋 ( 1) 21 2

휎 • 휋 = 휋 ( 1) 11 √2

We need to figure out which cities are making the largest and second-largest offers, and

all we know a priori is that city 3’s offer is less than city 2’s, since profit and value are

proportional to city size. This leaves a few if statements:

i. If City 1’s offer > City 2’s offer:

휎1 휎1 푃2 = max {휋 ( ) + 휋 ( ) , 휋(휎1) + 휋(휎2) + 푉2} √2 2 19 ii. Else if City 1’s offer > City 3’s offer:

휎1 휎1 푃2 = max {휋(휎1) + 휋(휎2), 휋 ( ) + 휋 ( ) + 푐 ⋅ 푉1} √2 2

iii. Else:

푃2 = max {휋(휎1) + 휋(휎2), 휋(휎1) + 휋(휎3) + 푉3}

Case 2. Team 2 locates in city 2.

Now the league the following potential profits and values in period 2:

Table 3. Case 2: League’s Offers in Period 2 by Team 1 Location Decision

City 1 City 2 City 3 League 휎2 휎2 휋(휎 ) + 휋(휎 ) 휋 ( ) + 휋 ( ) 휋(휎 ) + 휋(휎 ) Profit 1 2 √2 2 2 3 Team 1 푉 푐푉 푉 Value 1 2 3 휎 휎 Total Offer 휋(휎1) + 휋(휎2) 2 2 휋(휎2) + 휋(휎3) 휋 ( ) + 휋 ( ) + 푐푉2 + 푉1 √2 2 + 푉3

Here, 푐 takes the same value as in case 1; the value of adding a second team is the same

as the value of keeping a team when the city has two. In this case, we know that city 1’s

offer is highest; we just have to figure out the ordering of the other cities’ offers.

• 휋21 = 휋(휎2)

• 휋11 = 휋(휎1)

• Conditional statements:

i. If City 2’s offer > City 3’s offer:

휎2 휎2 푃2 = max {휋(휎1) + 휋(휎2), 휋 ( ) + 휋 ( ) + 푐푉2} √2 2

ii. Otherwise:

푃2 = max{휋(휎1) + 휋(휎2), 휋(휎2) + 휋(휎3) + 푉3} 20 Case 3. Team 2 locates in city 3.

Now the league has the following potential profits and values in period 2:

Table 4. Case 3: League’s Offers in Period 2 by Team 1’s Location Decision

City 1 City 2 City 3 League -- 휋(휎 ) + 휋(휎 ) 휋(휎 ) + 휋(휎 ) Profit 1 3 2 3 Team 1 -- 푉 푉 Value 1 2

Total Offer 휋(휎1) + 휋(휎3) + 푉1 휋(휎2) + 휋(휎3) + 푉2 --

Here we do not need to calculate the values in city 3 because they are clearly less than

those in both city 1 and city 2. We also have no conditional statements.

• 휋21 = 휋(휎3)

• 휋11 = 휋(휎1)

• 푃2 = π(σ3) + max{휋(휎1), 휋(휎2) + 푉2}

Two-Period Model: Numerical Example

To make this model more illustrative, let us assume a set of values for the constants 훼, 훽,

푐푅, 푤, 휆, and 푐푘. Additionally, we’ll use 푁 = 2 (two teams). The assumed values and meanings of the constants are given in Table 5:

Table 5. Meaning and Value of Constants

Constant(s) Chosen Value Meaning 훼, 훽 0.4, 0.6 marginal returns to revenue of city size and talent, respectively 4 푐푅 2.5 × 10 proportionality constant in revenue function 푤 106 wage rate paid to talent 휆 1 ratio of a team’s value to its revenue (i.e. 푉 = 휆 ⋅ 푅) 7 푐푘 5 × 10 fixed costs in team 푘’s profit function 푎, 푏 0.7,0.5 ratio of 휎2 to 휎1 and 휎3 to 휎1, respectively 21 As it turns out, the metro population ratio of 10 to 7 to 5 is essentially the ratio between New

York, L.A., and Chicago. Using the Table 5 values, we can simplify the following formulas:

1 1 훽 ⋅ 푐 ⋅ 휎훼 1−훽 0.6 ⋅ 2.5 × 104 1−0.6 푡∗ = [ 푅 푘 ] = (휎0.4 ⋅ ) = 2.76 × 10−5 ⋅ 휎 푘 푤 푘 106 푘

푤 106 푅 = ⋅ 푡∗ = ⋅ 푡∗ = 45.9 ⋅ 휎 푘 훽 푘 0.6 푘 푘

7 휋푘 = (1 − 훽) ⋅ 푅푘 − 푐푘 = 0.4 ⋅ 푅푘 − 푐푘 = 4.3 ⋅ 휎푘 − 5 × 10 .

푉푘 = 휆 ⋅ 푅푘 = 1 ⋅ 푅푘 = 45.9 ⋅ 휎푘

훼 훼 1 1−훽 1 1−훽 푐 = ( ) + ( ) − 1 = 0.2071 √2 2

Let us choose a value for 휎1, which will then determine the other city sizes. For example:

휎1 = 10 million, σ2 = 7 million, σ3 = 5 million

Here is the talent, revenue, profit, and value for each city if occupied by just one team:

Table 6. Single Team Values for Each City

∗ 푡 푅푘 (mil) 휋푘 (mil) 푉푖 (mil) City 1 276 459 134 459 City 2 193 322 79 322 City 3 138 230 42 230

Now let us go through the cases again with actual numbers.

Case 1. Team 2 locates in city 1 (which is already occupied by team 1).

휎 In this specific case, team 1’s profit in period 1 is decreased to 휋 ( 1) from 휋(휎 ). That √2 1

is, 휋11 decreases to $80 million from $134 million. The league has the following

potential profits and values in period 2 (in millions USD): 22 Table 7. Case 1: League’s Period 2 Offers by Team 1 Location Decision

City 1 City 2 City 3 League 122 212 176 Profit

Value 푐 ⋅ 푉1 = 95 322 230 Total Offer 217 534 406

Note that city 2 and city 3 make the greatest offers. With that information, we can proceed to define 휋11, 휋22, and 푃2:

• 휋11 = 80, 휋21 = 42

• Since city 3’s offer is better than city 2’s:

푃2 = max{212, 406} = 406.

Thus the total profit in this case is 80 + 42 + 406 = 528 million dollars.

Case 2. Team 2 locates in city 2.

Now the league has the following potential profits and values in period 2:

Table 8. Case 2: League’s Period 2 Offers by Team 1 Location Decision

City 1 City 2 City 3 League 212 55 120 Profit

Value 459 푐푉2 = 67 230 Total Offer 672 122 350

Note that city 1 and city 3 make the best offers.

• 휋11 = 134, 휋21 = 79

• Since city 1’s offer is better than city 3’s:

푃2 = max{212, 350} = 350

In this case, the total profit is 134 + 79 + 350 = 563 million dollars. 23 Case 3. Team 2 locates in city 3.

Now the league has the following potential profits and values in period 2:

Table 9. Case 3: League’s Period 2 Offers by Team 1 Location Decision

City 1 City 2 City 3 League -- 176 120 Profit Value 459 321 -- Total Offer 635 442 --

Here we do not need to calculate the values in city 3 because they are clearly less than

those in both city 1 and city 2.

• 휋11 = 134, 휋21 = 42

• 푃2 = max{176, 442} = 442

The total profit is 134 + 42 + 442 = 618 million dollars.

In this example, the league maximizes profits by locating team 2 in city 3 and then threatening to move team 1 to city 2 (but leaving it in city 1). The league can extort a larger subsidy from city 1 by using this strategy, and that difference makes up for the loss of profits for team 2. Let us explore how that might change as the parameters 훼 and 휆 are varied.

Comparative Statics: 휶, 흀

The parameters 훼 and 훽 are each restricted to the [0,1] domain; furthermore, they should satisfy the condition that cities prefer having two teams to having one. The preceding analysis

훼 훼 1 1 provides the formula 푐 = ( )1−훽 + ( )1−훽 − 1. When 푐 > 0, a city views a second team as √2 2 24 contributing positive social value; that condition can be solved as a function of 훼 and 훽, giving us the equation 훽 > 1 − .72훼. As a result, for 훽 = 0.6, it is required that 훼 < 0.555.

The values of 훼 and 휆 represent the returns to city size and the ratio of social value to a team’s revenue, respectively. Let us see how the league’s period 1 location decision changes as these parameters vary. Under the conditions in the preceding numerical example, with city size ratios 10: 7: 5, the league will choose city 3 in its period 1 location decision under most reasonable circumstances. City size ratios of 10: 4: 2 (e.g. the ratio of New York: Dallas: Seattle) will be used instead to produce more variety in the results, which are shown in Table 10 below.

Table 10. Period 1 City Choice vs 휶, 흀

휆 = .2 휆 = .5 휆 = 1 휆 = 1.5 휆 = 2 훼 = 0.20 1 1 1 1 3 훼 = 0.35 2 1 1 1 3 훼 = 0.40 2 2 1 3 3 훼 = 0.45 2 2 2 3 3 훼 = 0.55 2 2 2 2 3

Before characterizing the results from the table, let us briefly explore the logic behind each city choice. The city 3 choice sacrifices period 1 profits for high period 2 subsidies. The city 2 choice sacrifices period 2 subsidies for high period 1 profits. The city 1 choice, like the city 3 choice, sacrifices period 1 profits for high period 2 subsidies. However, its potential for period 2 subsidies is somewhat limited because team 1’s value to city 1 is less sensitive to increases in 휆 (due to team 2’s presence).

As Table 10 shows, city 3 is chosen more often when 휆 is high, which translates to social values – and therefore subsidies – being large relative to profits. City 2 is chosen more often when 훼 is high and 휆 is low, which leads profits to be large relative to subsidies and gives 25 effective city size a higher weight in determining profits. In that scenario, choosing city 2 – which means having the first team in city 1 and the second in city 2 – significantly increases leaguewide profits in period 1. Finally, city 1 is more attractive when 훼 is low and 휆 is close to 1.

As 휆 increases, the city 3 choice becomes more attractive because its period 2 subsidy is more responsive to 휆; as 휆 decreases and 훼 increases, the city 2 choice’s advantage in period 1 profits is magnified.

The cities’ surplus is maximized when the league chooses city 2 (as long as city 2 is at least 15 percent as large as city 1). There is a separate reason for each time period: in period 1, social value is maximized when teams are located in the two largest cities; in period 2, subsidies are lower when the two largest cities are already occupied. The results in Table 10 show that the league is more likely to make the socially optimal location decision when there is a stronger relationship between city size and profits (i.e. a high value of 훼) and when revenue and profits are large relative to social value (i.e. a low value of 휆).

As the number of cities in the model is expanded, it should be socially optimal for teams to fill the largest cities available; as smaller and smaller cities are added, the socially optimal placement of teams should eventually include multiple teams in the largest cities. Though I will not formally extend the two-period model to larger numbers of cities and teams in this paper, future researchers may wish to do so. It may also be beneficial to include more time periods in the model and use empirical analyses to estimate its parameter values.

26 Chapter 5

Comparison to Data

In this section, I will compare the league model and subsidy auction model to data from the NFL, MLB, NBA, and NHL. Specifically, I will compare the league model’s prediction of revenues and profits to the values estimated for each league’s 2018-19 season. Furthermore, I will take a brief look at contingent valuation studies and discuss their implications for the relationship between teams’ revenues, their social value to cities, and the subsidies cities give them in our model. Finally, I will analyze how the subsidies given to teams in each league change with respect to the distribution of vacant cities. If the league model and auction model are both correct, there should be a positive correlation between the two.

League Model vs Revenue & Profit Data

The league model predicts team revenues and profits based solely on a league’s revenue sharing arrangement and team city sizes, which allows us to look at its predictions for the NFL,

MLB, NBA, and NHL during the 2018-19 season. I should note, however, that all four leagues – and the NFL in particular with its massive TV deals – violate the model’s assumption that all revenue is generated locally. Each league’s revenue and profit data comes from Forbes (2019,

2020abc), and metro population data for this section comes from the Census Bureau (US Census

Bureau, 2020) and the website City Population (City Population, 2020).

The following figures show the model’s predictions along with 2018-19 data for each league. The model uses revenue sharing proportions of 60 percent for the NFL (Bloom, 2014),

50 percent for the MLB (Baseball Reference, 2019), 48 percent for the NBA (Pearce, 2012), and 27 18 percent for the NHL (Mirtle, 2018). Additionally, the proportionality constant 푐푅 was set for each league to match the average of predicted revenues with the actual mean team revenue.

Fixed costs were set at $150 million per team for the NFL based on Green Bay Packers financial disclosures (Gough, 2019a) (Gough, 2019b). I set fixed costs at $100 million for the MLB and

NBA and $50 million for the NHL, though there is no available data for those leagues. In each figure, the black dots represent teams and the blue line represents the model’s estimates.

Figure 1. NFL, MLB Team Revenues & Profits, 2018-19

28 Figure 2. NBA, NHL Team Revenues & Profits, 2018-19

Additionally, the model estimates player revenue shares of 0.25 in the NFL, 0.31 in the

NBA, 0.32 in the MLB, and 0.50 in the NHL; those estimates are dictated by the revenue sharing proportion of each league and the constant 훽. In reality, player revenue shares are much higher and are often dictated by collective bargaining agreements. The NFL guarantees players at least

48 percent share of revenue, which will increase to 48.5 percent under a 17-game regular season; 29 the NBA requires that the player share of revenue fall between 49 and 51 percent; and the NHL guarantees an even 50/50 split. Only the MLB does not specify a minimum player revenue share

(Manuel, 2020). Its player split has historically oscillated around 50 percent, but it dipped to 41 percent during the 2018 season (Rymer, 2019).

The disparity in revenue share between the model and reality can be explained by players’ bargaining power, leaguewide benefits of high talent levels, and owners’ incentives to win as well as make profits. Specifically, the model assumes that the wage level is fixed and that teams are free to choose the profit-maximizing level of talent. Furthermore, its estimate of the profit-maximizing talent level is too low because the model doesn’t account for the leaguewide benefits of high overall talent. If these leagues failed to secure the most talented players in their sport and pay them adequately, new leagues would threaten their market share. Finally, the model assumption that teams maximize profits but not wins means that as revenue sharing increases, optimal talent levels decrease dramatically.

The shortcomings in predicting talent and wage levels explain why the model’s profit predictions are generally too high: the difference is made up by money that should be going to players. The figures also show that city size has limited predictive power of teams’ revenues and profits. Though city size has some effect on revenue and profit, competitive success is largely determined by other factors and in turn affects team revenues.

The model indicates that revenue is proportional to metro population, and that prediction can be tested with simple linear regression. The results for each league are in the table below, along with the significance indicators produced in the R output. The regressions demonstrate that metro population is a significant predictor of team revenue in each league except for the NFL.

Furthermore, the R2 values are quite high in the MLB and NBA; in those leagues, about half of 30 variation in team revenues is explained by their city’s metro population. However, the model assumes that metro population explains 100 percent of the variation in revenues as well as team talent levels. Full regression output is in Appendix D.

Table 11. Regression of Revenue on Metro Population

NFL MLB NBA NHL 훽 coefficient 10.1 27.5 13.6 8.11 p-value 0.07 1.4e-5 (***)4 3.8e-5 (***) 0.002 (**) R2 value 0.10 0.50 0.46 0.28

Let us explore at least one additional factor that could explain team revenues. Since hockey’s popularity is concentrated in northern cities and especially in Canada, I will introduce a binary variable southern to denote teams that play in southern cities and see what effect it has on the R2 value of the NHL regression.

Table 12. NHL Revenue Regressed on Metro Population and Southern Binary Variable

훽 coefficient Std. Error p-value R2 value metro population 8.34 2.23 8.3e-3 (***) 0.40 southern -30.7 13.1 0.026 (*)

As Table 2 shows, the addition of southern increased the R2 value and made metro population more highly significant in the regression. However, most of the variability in team revenue remains unexplained – for the NHL and the other leagues as well. Some of that variability is due to local demand and could theoretically be explained by a more complicated league model; the rest can be attributed to the business acumen of team owners and managers, the performance of players, and random noise.

4 As in R, 1.4e-5 is used to denote 1.4 × 10−5. 31 Contingent Valuation: Case Studies

As described in the literature review, Fenn & Crooker (2009) carried out a contingent valuation study to estimate the social value of the Minnesota Vikings when the team was threatening to leave Minnesota. Their study estimated that the Vikings contributed $774.2 million in welfare to Minnesota households, with their 95 percent confidence interval stretching from $445.3 million to $1.571 billion.

Three years later, the Vikings secured $348 million from the state of Minnesota and $150 million from the city of Minneapolis (Stadiums of Pro Football, 2019), making for a total of

$498 million in up-front public funding. That nearly $500 million subsidy is on the scale of the social value the Vikings provide to the state of Minnesota. According to our model, lawmakers would only pay that large a subsidy if they were competing with another city to retain the team.

Indeed, immediately after voting to allocate public funds toward building the Vikings’ new stadium in 2012, a Minnesota state senator said that the possibility of the team moving to

Los Angeles influenced her decision (Markazi, 2012). At the time, there were two potential ownership groups in Los Angeles, and one had already gotten the city council to approve plans for a new $1.1 billion downtown stadium. However, the extent of public funding for the stadium in LA was never made clear.

In this case, the competitive pressure put on Minnesota lawmakers is consistent with the subsidy auction model. However, they paid much more than was required to beat out their closest competitor, seemingly contrary to model assumptions. Indeed, it is possible that the lawmakers’ incentives did not align with the city’s best interest or that they simply made a bad strategic decision. However, since the English outcry auction is not strategyproof, this type of outcome is also possible under the assumptions of the model. For example, consider the case in 32 which a low initial offer by Minnesota induces Los Angeles to make a serious offer, starting a bidding war and potentially increasing L.A.'s willingness to pay a large subsidy. That eventuality exposes Minnesota to the risk of paying a greater subsidy or even losing the team. By making a jump bid at the beginning of the subsidy auction, lawmakers reduced that risk considerably.

An earlier contingent valuation study of the Pittsburgh Penguins was carried out by

Johnson, Groothuis, & Whitehead (2004). They sent out a survey in 2000, shortly after a local consortium headed by former Penguins player Mario Lemieux bought the franchise, and concluded that the total willingness to pay (WTP) to keep the Penguins in Pittsburgh was between $23.5 million and $66 million (in 2000 US dollars).

Fenn & Crooker (2009) argue that there was not a credible relocation threat at that time of the survey, which may have contributed to the relatively low estimate. Johnson et al. were also very careful to produce a conservative upper bound; for example, they treated all unreturned surveys and all answers of “unsure” as being equivalent to “no” and therefore a WTP of $0.

Taking those two factors into consideration, the true value of the Penguins franchise is likely above the upper bound of $66 million.

The Penguins did secure the promise of a new arena in 2007 after threatening to move to

Kansas City, where they reportedly could have played in a new $276 million arena for free (CBC

Sports, 2007). Pittsburgh’s PPG Paints Arena required $15.5 million in up-front public funding plus $7.5 million annually from a state economic development fund backed by slot machine revenues5 (Munsey & Suppes, 2017). The present value of those funds in 2008 would have been approximately $118 million, using a 6 percent discount rate. It appears that the total subsidy was

5 As was often the case for this section, it took an exhaustive search to find an accurate characterization of public funding for the arena. The Marquette database listed the public funding for PPG Paints Arena as $0, which was contradicted by various news reports. The involvement of casinos in this case was also a complicating factor. 33 again on the same scale as the team’s social value, though the relationship between the two figures is unclear, due to the conservative upper bound used by Johnson et al.

Testing Subsidy Data

Stadium subsidy numbers for this section were drawn from data compiled by Judith

Grant Long (2005) and by Marquette’s National Sports Law Institute (2015). Long’s data accounts for all costs, including lost property taxes and ongoing maintenance costs; it is not clear whether the Marquette data does the same. For both sets of data, I accounted for inflation to put all subsidy amounts in terms of 2020 US dollars. I attempted to find the year that funding was secured for each stadium, but in many cases, I used the year that construction started because that data was more readily available. Metropolitan population data comes from Macrotrends

(Macrotrends LLC, 2020).

To test the relationship between the distribution of vacant cities and subsidy size, I collected data on the largest three empty locations for each league for every year going back to the 1950s. I then calculated my independent variable of interest (avg), which is the average metropolitan population of the three largest empty markets, and adjusted those values to account for general population increase over time. Full tables of this population and subsidy data for each of the Big Four leagues can be found in Appendix E. In the regression, I included both avg and time, where time is equal to the number of years since the first observation in the dataset, to account for time dependence in the subsidy data. The results are in Table 13 below, and the full output is in Appendix F. 34 Table 13. Results of Subsidies Regressed on Avg Vacant City, Time

NFL MLB NBA NHL avg coefficient 8.29 84.5 -28.3 -3.90 time coefficient 8.20 8.23 8.06 2.41 avg p-value 0.70 0.50 0.65 0.95 time p-value 0.002 (**) 0.083 (.) 0.023 (*) 0.27 R2 value 0.35 0.10 0.31 0.04

Subsidies appear to be increasing over time in the NFL and NBA, and the time coefficient is remarkably similar across the NFL, MLB, and NBA, despite the MLB having a marginal p-value. Unfortunately, the variable avg is not a significant predictor of subsidy size.

This result indicates that at least one of the assumptions linking metro population to revenue, revenue to social value, and social value to subsidies is faulty. It was already shown that revenue depends somewhat on metro population, although less so than the model assumed. The links involving social value are more difficult to test, but I suspect that both are at least as weak as the link from metro population to revenue. It may be possible to test the auction subsidy model in other ways, but it is difficult without many contingent valuation studies to provide social value data directly.

35 Chapter 6

Conclusion

This paper’s main contribution is the two-period subsidy auction model. From that model, I found conditions under which a league would want to fill the largest cities available and when it would prefer to leave a large city open. Since the model allowed for multiple teams per city, I was able to find conditions for the league to put two teams in the largest market as well.

However, the auction model would become far simpler with the assumption that cities could accept only one team at a time. That assumption would allow the subsidy auction to be conducted with respect to the individual team’s profits rather than leaguewide profits, which would make the model scale to larger numbers of teams far more easily.

The data comparison section makes clear that my league model is very simplistic.

Though the league model is not the major focus of this paper, researchers who pursue these topics in the future may want to incorporate the following elements: an incentive for owners to win in addition to maximizing profits; an upward adjustment to talent levels caused by labor negotiation and league reputation; and consideration of non-local revenue sources such as national TV deals. Additionally, the parameters 훼 and 훽 could be estimated from data.

The data also made clear that there is no relationship between subsidy size and the size of the largest available markets in a given league. However, as I described in the previous section, that does not mean that the auction model is entirely wrong; the issue is likely that there are too many tenuous links between city size and subsidy size, and legitimate aspects of the model may be obscured as a result. Indeed, individual cases imply that subsidies are motivated by a city’s fear of losing its team, which is one of the foundations of the subsidy auction model. Instead, this 36 result reinforces the conclusion that the model is overly simplistic; it is assuming that everything relevant about a city can be extrapolated from the size of its metro population.

That assumption fails quite often in specific cases. For example, Los Angeles’s metro population is over five times the size of Las Vegas’s. According to the model, a team could earn more revenue and have a greater social value in Los Angeles than in Vegas, which in turn would motivate Los Angeles to offer enough of a subsidy to attract any team interested in relocating.

However, Los Angeles did not make any concrete offer to the Vikings when they threatened to relocate in 2012, whereas Las Vegas promised $750 million in 2017 to lure the Raiders away from Oakland. In this case, it seems clear that a football team is more valuable to Las Vegas than to Los Angeles, perhaps precisely because Las Vegas is a smaller city with fewer sports teams.

The number of other sports teams in a city is an example of a demand shifter that is left out of this paper’s league model.

The most promising direction for future research lies in the two-period model, which could be generalized to arbitrarily many time periods, teams, and cities. Furthermore, an ambitious theoretical treatment could model relocation patterns over a continuous time domain, making assumptions about how the social value of a franchise and willingness of a city to pay subsidies changes over time. Alternatively, further empirical studies could be devised to test the subsidy auction model’s assumptions and findings. For example, a comparison of subsidy sizes between cases where a team does or does not make a credible relocation threat would be a direct way of testing whether cities are truly bidding against one another.

37 Appendix A

Verification of Four Properties of 흈(풋, 풏).

(1) 휎푘( 푗 = 1, 푛 = 1) = 휎푖.

(2) 휎푘(푗, 푛) is decreasing in 푗, 푛:

1 3 휕휎푘(푗,푛) 1 − − = − 휎 푛 2푗 2 < 0, 휕푗 2 푖

3 1 휕휎푘(푗,푛) 1 − − = − 휎 푛 2푗 2 < 0. 휕푛 2 푖

(3) 휎푘(푗, 푛) decreases in 푗, 푛 at a decreasing rate:

2 1 5 휕 휎푘(푗,푛) 3 − − = 휎 푛 2푗 2 > 0, 휕푗2 4 푖

2 5 1 휕 휎푘(푗,푛) 3 − − = 휎 푛 2푗 2 > 0. 휕푛2 4 푖

′ Since the first and second derivatives have opposite signs, the decrease in 휎푖 with

respect to 푗 and 푛 becomes less dramatic as 푗 and 푛 increase.

(4) The sum of the effective populations available to all teams converges as the

number of teams increases:

푛

lim ∑ 휎푘(푗, 푛) 푛→∞ 푗=1

푛 1 = 휎푖 ⋅ lim ∑ 푛→∞ 푗푛 푗=1 √

1 ( ) 2 퐻푛 = 휎푖 ⋅ lim 푛→∞ √푛

38 1 2 ( ) 2 √(퐻푛 ) = 휎푖 ⋅ lim 푛→∞ 푛

1 2 ( ) 2 √ (퐻푛 ) = 휎푖 ⋅ lim 푛→∞ 푛

1 2 ( ) 푑 2 (퐻푛 ) √ 푑푛 = 휎푖 ⋅ lim 푛→∞ 푑푛 푑푛

1 3 ( ) ( ) 3 −퐻 2 (퐻 2 − 휁 ( )) √ 푛 푛 2 = 휎푖 ⋅ lim 푛→∞ 1

= 휎푖 ⋅ √4

= 2휎푖

(∙) Note: 휁(∙) is the Riemann zeta function; 퐻푛 represents the generalized harmonic numbers.

39

Appendix B

Derivations under Revenue Sharing

∗ 1. Solving for optimal talent, 푡푘.

푠 argmax 휋푘 = 푅푘(푡푘) − 퐶푘(푡푘) 푡푘

푑휋 휕푅 휕푅̅ 0 = 푘 = (1 − 푠) 푘 + 푠 − 푤 푑푡 휕푡푘 휕푡푘

훽푐 휎훼 훽푐 휎훼 ( ) 푅 푘 푅 푘 = 1 − 푠 ⋅ 1−훽 + 푠 ⋅ 1−훽 − 푤 푡푘 푡푘 ⋅ 푁

훽푐 휎훼 푠 → 푤 = 푅 푘 ⋅ [(1 − 푠) + ] 1−훽 푁 푡푘

1 훼 1 훽푐 휎 1−훽 푠 1−훽 → 푡∗ = [ 푅 푘 ] ⋅ [(1 − 푠) + ] . 푘 푤 푁

푠 ∗ 2. Finding post-sharing revenue (푅푘), given 푡푘.

훼 ∗훽 푅푘 = 푐푅휎푘 푡푘

훽 훼 훽 훽푐 휎 1−훽 푠 1−훽 = 푐 휎훼 [ 푅 푘 ] ⋅ [(1 − 푠) + ] 푅 푘 푤 푁

1 훽 훽 훼 1−훽 훽 ⋅ 푐 ⋅ 휎 푠 1−훽 = [ 푅 푘 ] ⋅ [(1 − 푠) + ] 푤훽 푁

푤 푠 −1 = 푡∗ ⋅ ⋅ [(1 − 푠) + ] . 푘 훽 푁

푁 푠 1 → 푅 = (1 − 푠) ⋅ 푅 + 푠 ⋅ 푅̅, where 푅̅ = ∑ 푅 ′ 푘 푘 푁 푘 푘′=1 40 푁 훽 훽 훼 1−훽 1 훼 훽푐푅휎푘′ 푠 1−훽 → 푅̅ = ⋅ ∑ [휎 ′ ⋅ [ ] ⋅ [(1 − 푠) + ] ] 푁 푘 푤 푁 푘′=1

훽 훽 푁 훼 1 훽푐 1−훽 푠 1−훽 = ⋅ [ 푅] ⋅ [(1 − 푠) + ] ⋅ ∑ 휎1−훽 푁 푤 푁 푘′ 푘′=1

1 훽 푁 훽 1−훽 훼 1 훽 푐 푠 1−훽 = [ 푅] ⋅ [(1 − 푠) + ] ⋅ ∑ 휎1−훽 푁 푤훽 푁 푘′ 푘′=1

−훼 1−훽 푁 훼 푅푘 ⋅ 휎 = 푘 ⋅ ∑ 휎1−훽 . 푁 푘′ 푘′=1

Thus we have the following once we substitute in the expression for 푅̅:

푁 푠 −훼 훼 푅푠 = 푅 ⋅ [(1 − 푠) + ⋅ 휎1−훽 ⋅ ∑ 휎1−훽]. 푘 푘 푁 푘 푘′ 푘′=1

3. Finding post-sharing profit, 휋푘.

푠 ∗ 휋푘 = 푅푘 − 푡푘 ⋅ 푤.

푤 푠 −1 We now replace 푡∗, using the fact that 푅 = 푡∗ ⋅ ⋅ [(1 − 푠) + ] : 푘 푘 푘 훽 푁 푠 휋 = 푅푠 − 푅 ⋅ 훽 ⋅ [(1 − 푠) + ] 푘 푘 푘 푁

푠 And we can factor 푅푘 out of 푅푘 by using the expression from (2):

푁 푠 −훼 훼 푠 휋 = 푅 ⋅ [((1 − 푠) + ⋅ 휎1−훽 ⋅ ∑ 휎1−훽) − 훽 ⋅ ((1 − 푠) + )]. 푘 푘 푁 푘 푘′ 푁 푘′=1

41

Appendix C

Deriving the Social Value Constant “c”

To find the social value of the second team in a city, we need to find the difference between the value of a single team in the city and the combined value of two teams. Let us denote the value of a single team by 푉(1) and the combined value of two teams by 푉(2).

푐 ⋅ 푉(1) = 푉(2) − 푉(1)

푉(2) − 푉(1) → 푐 = 푉(1) 휎 휎 휆 ⋅ [푅 ( ) + 푅 ( )] − 휆 ⋅ 푅(휎) 2 2 = √ 휆 ⋅ 푅(휎)

휎 푅 ( ) 휎 2 푅 ( ) = √ + 2 − 1 푅(휎) 푅(휎)

훼 휎 1−훽 훼 ( ) 휎 1−훽 √2 (2) = 훼 + 훼 − 1 휎1−훽 휎1−훽

훼 훼 1 1−훽 1 1−훽 = ( ) + ( ) − 1 √2 2

42

Appendix D

Regression Output: Revenue vs Metro Population

Here is the R output from the regressions of revenue on metro population.

NFL:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 381.848 29.388 12.993 7.46e-14 *** pop 10.072 5.409 1.862 0.0724 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 91.84 on 30 degrees of freedom Multiple R-squared: 0.1036, Adjusted R-squared: 0.07375 F-statistic: 3.468 on 1 and 30 DF, p-value: 0.07238

MLB:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 209.501 29.417 7.122 9.49e-08 *** pop 27.463 5.222 5.259 1.37e-05 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 76.24 on 28 degrees of freedom Multiple R-squared: 0.4969, Adjusted R-squared: 0.479 F-statistic: 27.66 on 1 and 28 DF, p-value: 1.365e-05

NBA:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 226.976 15.727 14.432 1.71e-14 *** pop 13.626 2.787 4.889 3.75e-05 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 46.04 on 28 degrees of freedom Multiple R-squared: 0.4605, Adjusted R-squared: 0.4413 F-statistic: 23.9 on 1 and 28 DF, p-value: 3.755e-05

43 NHL:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 128.616 12.338 10.424 2.55e-11 *** pop 8.111 2.391 3.393 0.00202 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 36.54 on 29 degrees of freedom Multiple R-squared: 0.2842, Adjusted R-squared: 0.2595 F-statistic: 11.51 on 1 and 29 DF, p-value: 0.002017

NHL including southern variable:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 137.535 12.091 11.375 5.2e-12 *** pop 8.335 2.226 3.745 0.00083 *** cities$Southern -30.686 13.074 -2.347 0.02623 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 34 on 28 degrees of freedom Multiple R-squared: 0.4019, Adjusted R-squared: 0.3591 F-statistic: 9.406 on 2 and 28 DF, p-value: 0.0007504

44

Appendix E

Historical Subsidy & Vacant City Data

Each table will show stadium subsidy data along with the largest vacant cities at the time:

“Avg” is the time-adjusted average of the listed cities’ metro populations in the given year.

However, the individual population columns for each city are not time-adjusted. The “Subsidy” column is in 2020 USD.

NFL:

Year Stadium Subsidy Avg City 1 Pop1 City 2 Pop2 City 3 Pop3 2017 Allegiant Stadium 799 3.80 Toronto 6.0 San Diego 3.2 St. Louis 2.2 Mercedes-Benz 2013 Stadium 688 6.91 Los Angeles 12.3 Toronto 5.7 Portland 1.9 2012 US Bank Stadium 589 7.12 Los Angeles 12.2 Toronto 6.2 Portland 1.9 2012 New Era Field 154 7.12 Los Angeles 12.2 Toronto 6.2 Portland 1.9 2004 AT&T Stadium 489 5.78 Los Angeles 11.9 Portland 1.7 San Jose 1.6 2004 Lucas Oil Stadium 866 5.78 Los Angeles 11.9 Portland 1.7 San Jose 1.6 State Farm 2003 Stadium 494 5.84 Los Angeles 11.9 Portland 1.7 San Jose 1.6 Lincoln Financial 2001 Field 300 5.87 Los Angeles 11.8 Portland 1.6 San Jose 1.6 2001 Soldier Field 610 5.87 Los Angeles 11.8 Portland 1.6 San Jose 1.6 2000 NRG Stadium 360 6.80 Los Angeles 11.8 Houston 3.8 Portland 1.6 1998 Heinz Field 395 6.78 Los Angeles 11.6 Houston 3.6 San Jose 1.5 1998 Mile High 421 6.78 Los Angeles 11.6 Houston 3.6 San Jose 1.5 Ralph Wilson 1998 Stadium 348 6.78 Los Angeles 11.6 Houston 3.6 San Jose 1.5 1997 CenturyLink Field 482 5.97 Los Angeles 11.5 San Jose 1.5 Portland 1.5 Qualcomm 1997 Stadium 243 5.97 Los Angeles 11.5 San Jose 1.5 Portland 1.5 1996 Ford Field 413 5.96 Los Angeles 11.4 San Jose 1.5 Portland 1.4 Paul Brown 1996 Stadium 844 5.96 Los Angeles 11.4 San Jose 1.5 Portland 1.4 1996 Titans Coliseum 430 5.96 Los Angeles 11.4 San Jose 1.5 Portland 1.4 Raymond James 1996 Stadium 329 5.96 Los Angeles 11.4 San Jose 1.5 Portland 1.4 1996 Ravens Stadium 529 5.96 Los Angeles 11.4 San Jose 1.5 Portland 1.4 45 1995 Browns Stadium 484 2.07 Baltimore 2 San Jose 1.5 Portland 1.4 1995 Oakland Coliseum 308 2.07 Baltimore 2 San Jose 1.5 Portland 1.4 1994 FedEx Field 147 2.27 St. Louis 2 Baltimore 1.9 San Jose 1.4 1994 Ericsson Stadium 252 2.27 St. Louis 2 Baltimore 1.9 San Jose 1.4 1993 ALLTEL Stadium 302 2.30 St. Louis 2 Baltimore 1.9 San Jose 1.4 Edward Jones 1992 Dome 550 2.33 St. Louis 2 Baltimore 1.9 San Jose 1.4 1989 Georgia Dome 480 2.33 St. Louis 1.9 Baltimore 1.8 San Jose 1.4 Pro Player 1985 Stadium 139 2.32 Baltimore 1.8 Phoenix 1.7 San Jose 1.3 1979 Metrodome -156 1.99 Phoenix 1.4 San Jose 1.2 Milwaukee 1.2 Pontiac 1973 Silverdome 139 2.19 Seattle 1.6 Milwaukee 1.2 San Jose 1.1 1971 Giants Stadium 171 2.19 Seattle 1.6 Milwaukee 1.2 San Jose 1 1970 Foxboro Stadium 3 2.28 Seattle 1.6 Milwaukee 1.3 San Jose 1 Arrowhead 1967 Stadium 181 2.16 Seattle 1.4 Milwaukee 1.2 San Jose 0.9 1967 Texas Stadium 169 2.16 Seattle 1.4 Milwaukee 1.2 San Jose 0.9 Louisiana 1966 Superdome 824 2.14 Seattle 1.4 Milwaukee 1.2 San Jose 0.8 1964 Veterans Stadium 134 2.09 Seattle 1.3 Milwaukee 1.2 San Jose 0.7 1958 Candlestick Park 73 2.97 St. Louis 1.6 Dallas 1.3 Milwaukee 1.1 1958 Sun Devil Stadium 26 2.97 St. Louis 1.6 Dallas 1.3 Milwaukee 1.1 1956 Lambeau Field 63 2.98 St. Louis 1.6 Dallas 1.2 Milwaukee 1

MLB:

Year Stadium Subsidy Avg City 1 Pop1 City 2 Pop2 City 3 Pop3 2016 Globe Life Field 707 2.77 Montreal 4.10 Las Vegas 2.12 Riverside 2.10 2014 Truist Park 466 2.73 Montreal 4.04 Riverside 1.99 Portland 1.98 2009 Marlins Park 492 2.70 Montreal 3.85 Portland 1.83 Riverside 1.76 2007 Target Field 514 2.68 Montreal 3.77 Portland 1.77 Riverside 1.68 2006 Yankee Stadium 1188 2.67 Montreal 3.73 Portland 1.75 Riverside 1.63 2006 Citi Field 422 2.67 Montreal 3.73 Portland 1.75 Riverside 1.63 2006 Nationals Park 737 2.67 Montreal 3.73 Portland 1.75 Riverside 1.63 Citizens Bank 2001 Park 257 2.79 Washington 3.83 Portland 1.61 San Jose 1.55 Great American 2000 Ball Park 396 2.79 Washington 3.77 Portland 1.59 San Jose 1.54 2000 Petco Park 286 2.79 Washington 3.77 Portland 1.59 San Jose 1.54 1998 PNC Park 442 2.77 Washington 3.65 San Jose 1.51 Portland 1.50 46 1997 Comerica Park 168 3.40 Washington 3.60 Phoenix 2.63 Tampa Bay 1.85 Qualcomm 1997 Stadium 243 3.40 Washington 3.60 Phoenix 2.63 Tampa Bay 1.85 1996 Miller Park 636 3.37 Washington 3.54 Phoenix 2.53 Tampa Bay 1.82 Minute Maid 1996 Park 364 3.37 Washington 3.54 Phoenix 2.53 Tampa Bay 1.82 Pacific Bell 1996 Park 207 3.37 Washington 3.54 Phoenix 2.53 Tampa Bay 1.82 1996 SafeCo Field 806 3.37 Washington 3.54 Phoenix 2.53 Tampa Bay 1.82 Edison Intl. 1996 Field 90 3.37 Washington 3.54 Phoenix 2.53 Tampa Bay 1.82 Oakland 1995 Coliseum 308 3.34 Washington 3.48 Phoenix 2.44 Tampa Bay 1.78 Bank One 1994 Ballpark 114 3.31 Washington 3.43 Phoenix 2.35 Tampa Bay 1.75 1993 Turner Field 139 3.28 Washington 3.38 Phoenix 2.26 Tampa Bay 1.72 1992 Coors Field 430 4.23 Miami 3.88 Washington 3.31 Phoenix 2.18 Ballpark at 1991 Arlington 363 4.18 Miami 3.79 Washington 3.25 Phoenix 2.10 1990 Jacobs Field 523 4.14 Miami 3.70 Washington 3.19 Phoenix 2.03 1989 Oriole Park 284 4.10 Miami 3.61 Washington 3.12 Phoenix 1.95 1989 New Comiskey 432 4.10 Miami 3.61 Washington 3.12 Phoenix 1.95 1986 Tropicana Field 468 3.97 Miami 3.36 Washington 2.95 Phoenix 1.76 1986 SkyDome 512 3.94 Miami 3.36 Washington 2.89 Phoenix 1.76 Pro Player 1985 Stadium 139 3.92 Miami 3.28 Washington 2.89 Phoenix 1.70 1979 Metrodome -156 3.61 Miami 2.69 Washington 2.65 Phoenix 1.36 Olympic Stad. 1973 (Montreal) 1373 4.22 Toronto 2.70 Washington 2.49 Miami 2.14 Old Yankee 1971 Stadium 392 3.92 Toronto 2.63 Dallas 2.07 Miami 1.96 1968 Kauffman Field 230 4.21 Montreal 2.56 Toronto 2.34 Dallas 1.90 1968 Cinergy Field 376 4.21 Montreal 2.56 Toronto 2.34 Dallas 1.90 Veterans 1964 Stadium 134 3.96 Montreal 2.31 Toronto 2.02 Dallas 1.66 1964 Busch Stadium 140 3.96 Montreal 2.31 Toronto 2.02 Dallas 1.66 1961 Shea Stadium 168 3.78 Montreal 2.12 Toronto 1.83 Dallas 1.50 1958 Dodger Stadium 96 3.51 Montreal 1.87 Toronto 1.58 Dallas 1.31

47 NBA:

Year Arena Subsidy Avg City 1 Pop1 City 2 Pop2 City 3 Pop3 2017 Chase Center 0 3.55 Montreal 4.138 Seattle 3.339 San Diego 3.18 2016 Fiserv Forum 364 3.56 Montreal 4.104 Seattle 3.299 San Diego 3.148 Little Caesars 2014 Arena 437 3.58 Montreal 4.037 Seattle 3.22 San Diego 3.086 2014 Golden 1 Center 325 3.58 Montreal 4.037 Seattle 3.22 San Diego 3.086 2010 Barclays Center 768 3.62 Montreal 3.897 Seattle 3.069 San Diego 2.964 2008 Amway Center 612 3.35 Montreal 3.812 San Diego 2.905 Tampa Bay 2.25 2003 Spectrum Center 379 3.36 Montreal 3.564 San Diego 2.763 St. Louis 2.101 2002 FedEx Forum 302 3.37 Montreal 3.511 San Diego 2.735 St. Louis 2.094 2001 Toyota Center 295 3.39 Montreal 3.458 San Diego 2.708 St. Louis 2.087 2000 AT&T Center 214 3.41 Montreal 3.429 San Diego 2.681 St. Louis 2.079 Chesapeake 1999 Energy Arena 130 3.43 Montreal 3.404 San Diego 2.648 St. Louis 2.067 American 1998 Airlines Arena 321 3.45 Montreal 3.379 San Diego 2.614 St. Louis 2.054 Conseco 1997 Fieldhouse 306 3.47 Montreal 3.354 San Diego 2.58 St. Louis 2.041 American Air. 1997 Arena (Miami) 217 3.47 Montreal 3.354 San Diego 2.58 St. Louis 2.041 1997 Philips Arena 233 3.47 Montreal 3.354 San Diego 2.58 St. Louis 2.041 1997 Pepsi Center 89 3.47 Montreal 3.354 San Diego 2.58 St. Louis 2.041 1997 Staples Center 281 3.47 Montreal 3.354 San Diego 2.58 St. Louis 2.041 Air Canada 1997 Center 36 3.47 Montreal 3.354 San Diego 2.58 St. Louis 2.041 1996 Oakland Arena 136 3.49 Montreal 3.33 San Diego 2.547 St. Louis 2.027 1995 MCI Center 222 3.52 Montreal 3.305 San Diego 2.514 St. Louis 2.014 First Union 1994 Center 166 4.50 Toronto 4.122 Montreal 3.282 San Diego 2.482 1994 Key Arena 153 4.50 Toronto 4.122 Montreal 3.282 San Diego 2.482 1993 Rose Garden 140 4.51 Toronto 4.048 Montreal 3.258 San Diego 2.45 1993 TD Garden 122 4.51 Toronto 4.048 Montreal 3.258 San Diego 2.45 General Moters 1993 Place 36 4.51 Toronto 4.048 Montreal 3.258 San Diego 2.45 1992 Gund Arena 290 4.52 Toronto 3.976 Montreal 3.234 San Diego 2.418 1992 United Center 87 4.52 Toronto 3.976 Montreal 3.234 San Diego 2.418 San Antonio 1990 Dome 386 4.52 Toronto 3.807 Montreal 3.154 San Diego 2.356 America West 1990 Arena 112 4.52 Toronto 3.807 Montreal 3.154 San Diego 2.356 1990 Delta Center 115 4.52 Toronto 3.807 Montreal 3.154 San Diego 2.356 Madison Square 1989 Garden 112 4.49 Toronto 3.71 Montreal 3.095 San Diego 2.293 48 1988 Target Center 211 4.45 Toronto 3.616 Montreal 3.038 San Diego 2.22 TD Waterhouse 1987 Center 241 4.41 Toronto 3.524 Montreal 2.981 San Diego 2.15 Charlotte 1986 Coliseum 111 4.38 Toronto 3.434 Montreal 2.926 San Diego 2.082 Palace of 1986 Auburn Hills 36 4.38 Toronto 3.434 Montreal 2.926 San Diego 2.082 1986 Bradley Center 74 4.38 Toronto 3.434 Montreal 2.926 San Diego 2.082 1986 Arco Arena 51 4.38 Toronto 3.434 Montreal 2.926 San Diego 2.082 Continental 1979 Airlines Arena 93 4.87 Toronto 2.956 Montreal 2.818 Miami 2.69 1973 Compaq Center 50 4.72 Montreal 2.77 Toronto 2.7 Dallas 2.15

NHL:

Year Arena Subsidy Avg City 1 Pop1 City 2 Pop2 City 3 Pop3 Little Caesars 2014 Arena 437 4.47 Houston 5.52 Atlanta 4.66 Seattle 3.22 2014 T-Mobile Arena 0 4.47 Houston 5.52 Atlanta 4.66 Seattle 3.22 2014 Rogers Place 456 4.47 Houston 5.52 Atlanta 4.66 Seattle 3.22 2010 Barclays Center 768 3.89 Houston 4.98 Seattle 3.07 San Diego 2.96 PPG Paints 2008 Arena 22 3.87 Houston 4.73 Seattle 3.00 San Diego 2.91 Prudential 2005 Center 306 3.83 Houston 4.38 Seattle 2.89 San Diego 2.82 2003 Bell MTS Place 59 3.81 Houston 4.16 Seattle 2.82 San Diego 2.76 Gila River 2002 Arena 175 3.80 Houston 4.05 Seattle 2.79 San Diego 2.74 American Air. 1998 Arena 321 3.84 Houston 3.64 Atlanta 2.78 Seattle 2.61 Nationwide 1998 Arena 90 3.84 Houston 3.64 Atlanta 2.78 Seattle 2.61 Xcel Energy 1998 Center 120 3.84 Houston 3.64 Atlanta 2.78 Seattle 2.61 Raleigh Sports 1997 Arena 243 3.80 Houston 3.54 Atlanta 2.65 San Diego 2.58 1997 Philips Arena 233 3.80 Houston 3.54 Atlanta 2.65 San Diego 2.58 1997 Pepsi Center 89 3.80 Houston 3.54 Atlanta 2.65 San Diego 2.58 1997 Staples Center 281 3.80 Houston 3.54 Atlanta 2.65 San Diego 2.58 Air Canada 1997 Center 36 3.80 Houston 3.54 Atlanta 2.65 San Diego 2.58 Office Depot San 1996 Arena 397 3.76 Houston 3.45 Diego 2.55 Atlanta 2.53 Gaylord Ent. San 1995 Center 239 3.73 Houston 3.35 Diego 2.51 Seattle 2.45 49 San 1995 MCI Center 222 3.73 Houston 3.35 Diego 2.51 Seattle 2.45 San 1994 HSBC Arena 188 3.72 Houston 3.26 Diego 2.48 Seattle 2.40 Le Centre San 1994 Molson 36 3.72 Houston 3.26 Diego 2.48 Seattle 2.40 San 1994 Corel Center 44 3.72 Houston 3.26 Diego 2.48 Seattle 2.40 San 1994 Ice Palace 243 3.72 Houston 3.26 Diego 2.48 Seattle 2.40 First Union San 1994 Center 166 3.72 Houston 3.26 Diego 2.48 Seattle 2.40 San 1993 Fleet Center 122 3.70 Houston 3.17 Diego 2.45 Seattle 2.35 General Motors San 1993 Place 36 3.70 Houston 3.17 Diego 2.45 Seattle 2.35 1992 Kiel Center 156 4.89 Miami 3.88 Dallas 3.39 Houston 3.09 1992 United Center 87 4.89 Miami 3.88 Dallas 3.39 Houston 3.09 Arrowhead 1991 Pond 105 4.84 Miami 3.79 Dallas 3.30 Houston 3.00 1991 San Jose Arena 312 4.84 Miami 3.79 Dallas 3.30 Houston 3.00 America West 1990 Arena 112 4.80 Miami 3.70 Dallas 3.22 Houston 2.92 Madison Square 1989 Garden 112 4.76 Miami 3.61 Dallas 3.14 Houston 2.86 Pengrowth 1981 Saddledome 260 4.43 Miami 2.90 Dallas 2.53 Houston 2.47 Continental Air. 1979 Arena 93 4.30 Miami 2.69 Dallas 2.42 Houston 2.35 1977 Joe Louis Arena 120 4.17 Miami 2.49 Dallas 2.32 Houston 2.18 1972 Skyreach Center 261 4.22 Washington 2.42 Dallas 2.11 Miami 2.05 Nassau Vets. 1970 Mem. Col. 184 4.09 Washington 2.28 Dallas 2.03 Miami 1.87 1958 Civic Arena 261 3.55 Washington 1.54 Baltimore 1.37 Dallas 1.31

50

Appendix F

Regression Output: Subsidy vs. Time, Avg Vacant City

The R output of subsidy regressed on time, avg is below. The variable avg is equal to the time-adjusted average of the largest three markets that were vacant at the time of the subsidy.

Output for NFL and MLB is on this page, and output for NBA and NHL is on the following page. In the output, avg appears as “x” and time appears as “t.”

NFL:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 37.708 89.133 0.423 0.67477 x 8.292 21.147 0.392 0.69728 t 8.197 2.521 3.252 0.00249 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 205.4 on 36 degrees of freedom Multiple R-squared: 0.348, Adjusted R-squared: 0.3117 F-statistic: 9.606 on 2 and 36 DF, p-value: 0.0004538

MLB:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -191.765 560.844 -0.342 0.7345 x 84.501 123.569 0.684 0.4986 t 8.232 4.606 1.787 0.0826 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 284.7 on 35 degrees of freedom (1 observation deleted due to missingness) Multiple R-squared: 0.1044, Adjusted R-squared: 0.05326 F-statistic: 2.041 on 2 and 35 DF, p-value: 0.1451

51 NBA:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -4.712 360.255 -0.013 0.9896 x -28.302 61.828 -0.458 0.6499 t 8.064 3.387 2.381 0.0227 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 137.6 on 36 degrees of freedom Multiple R-squared: 0.3093, Adjusted R-squared: 0.2709 F-statistic: 8.06 on 2 and 36 DF, p-value: 0.00128

NHL:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 116.567 258.984 0.450 0.655 x -3.904 59.625 -0.065 0.948 t 2.406 2.123 1.133 0.265

Residual standard error: 151.9 on 35 degrees of freedom (1 observation deleted due to missingness) Multiple R-squared: 0.03564, Adjusted R-squared: -0.01946 F-statistic: 0.6468 on 2 and 35 DF, p-value: 0.5298

52 BIBLIOGRAPHY

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ACADEMIC VITA

Alex Ellis EDUCATION Penn State University | Schreyer Honors College University Park, PA Eberly College of Science Aug 2016 – May 2020 Majors: Math & Economics (Minors: Statistics & Physics)

EXPERIENCE

Undergraduate Grader – Penn State University, University Park, PA Fall 2017; 2019 • Did grading work for Econ 102, Econ 402, Math 484, & Math 486 Computational Math REU – Penn State University, University Park, PA May – June 2019 • Worked with Dr. Ryan Murray to find optimal parameters for a supervised learning algorithm IES Berlin Summer Internship Program – Berlin, Germany May – July 2018 • Internship at Humboldt Institute for Internet and Society (HIIG) o Ranking Digital Rights: made linked spreadsheets for internet, telecom firm evaluations o Elephant in the Lab science blog: reviewed literature and contacted contributors for the topic of ethics in science; improved the blog’s system for categorizing articles • IES culture class and German language class Summer Research: Statistics – Penn State College of Medicine in Hershey May – Aug 2017 • Compared the robustness of the SAS procedures LOGISTIC and GLIMMIX, working with Dr. Vernon Chinchilli; found procedures to be similarly robust and presented at poster session RELEVANT AWARDS, COURSES, & SKILLS

Awards • Valedictorian at Cedar Crest High School (graduating class of 370 students) June 2016 • H. Freeman Stecker Award from Penn State Math Department April 2019 Selected Courses • Econ 302H, 489M – Honors Intermediate Micro, Honors Thesis • Math 312H, 486 – Honors Real Analysis, Game Theory • Stat 415, 463 – Mathematical Statistics, Time Series Analysis Skills • Experience with Python, Mathematica, MATLAB, LaTeX, and Excel o Exposure to R, Stata, Minitab, and SAS • German (intermediate level) – studied four years in high school + two semesters in college

ACTIVITIES

Quiz Bowl – have competed since 2010, currently at Penn State President, Penn State Quiz Bowl 2019-20 • As president: run practices and meetings, set teams for tournaments, contact other schools • In general: learn as much as possible, help run tournaments, write questions occasionally Treasurer; Vice President (Penn State Quiz Bowl) 2017-18; 2018-19 Tennis – have played since 2015 Member, Penn State Tennis Club 2016-20