A Puncher's Chance: Expected Gain and Risk Taking in a Market For

A Puncher’s Chance: Expected Gain and Risk Taking in a

Market for Superstars∗

Jordan Roulleau-Pasdeloup National University of Singapore

July 4, 2019

Abstract

Do policies that decrease potential earnings at the top of the income distribution induce agents to alter their risk-taking behavior? To answer this question I collect data on Mixed Martial Arts leagues. I exploit the fact that one league introduced such a policy, while its counterpart did not. Using a standard Difference-in-Differences analysis, I find that fighters in the league that implemented the policy take significantly less risks after its inception. On top of being statistically significant, the effect is also economically significant : the decrease in frequency of risk-taking ranges from 7% to 22% in the treatment group.

JEL Classiﬁcation: D31, D81, H00

Keywords: Inequality, Risk, Difference-in-Differences

∗I would like to thank Anissa Ouasti and Célia Aouadj for excellent research assistance. Financial support from EconGlobe and and HEC Research Fund is gratefully acknowledged. I thank Johannes C.Buggle, Mathieu Coutte- nier, Sophie Hatte, Seyhun Orcan Sakalli, and seminar participants at HEC Lausanne and the National University of Singapore. 1 Introduction

The rise in income and wealth inequality over the last few decades has been heavily documented (Piketty & Saez(2003), Atkinson et al.(2011) and more recently Alvaredo et al.(2017)).

An important feature of this rise is that it has been fast, especially in the United States. In a recent contribution, Gabaix et al.(2015) show that a standard random growth model is not able to replicate such a fast increase in top income inequality. Modiﬁcations of the random growth process to include "superstar" effects help the model achieve a faster transition to a higher level of inequality. Another feature of the recent rise in income inequality is that it sparked an intense debate about potential ways to curb this fast rise in inequality. Most of the debates have centered around using taxes to achieve this goal (Piketty et al.(2014), Scheuer & Werning

(2017)).

The question that arises naturally is the following : if such policies to curb income inequality are going to be carried out, what are going to be their effects? If we consider market for superstars, risk taking will be a relevant margin. Take entrepreneurs for example. Starting a business is a risky venture by itself, so we want to know whether higher top income or corporate tax rates will deter would-be entrepreneurs to take the ﬁrst step.

The goal of this paper is to estimate the causal effect of a policy that compresses earnings inequality —especially at the top —on risk taking behavior in a market for superstars. Pro- fessional athletes leagues ﬁt the description of a market for superstars in that a few talented athletes usually end up reaping most of the pecuniary rewards. I focus here on one type of sport in particular : Mixed Martial Arts. There are two important reasons to do so. First, in contrast with sports such as football, baseball or basketball, there does not exist a particular league with an entrenched monopoly. In Mixed Martial Arts, there are basically two leagues that compete with one another : The Ultimate Fighting Championship (UFC) and Bellator.

Second, in mid-July 2015, the UFC introduced a new earnings policy that had the effect to reduce earnings inequality, especially at the top : lower-tier ﬁghters’ earnings increased mod- estly, while top earners took a heavy hit. In contrast, Bellator did not introduce any new policy during the same period.

To clarify the notion of risk-taking that I recover from the data, I lay out a simple model

1 in which agents with different risk aversion have to choose between two actions : one with a stochastic payoff and one with known payoff. The model makes clear predictions regarding the share of agents that choose the risky (i.e with stochastic payoff) action. A decrease in incomes at the top of the distribution should decrease the average amount of risk-taking.

Moreover, the effect is likely to be different across agents. In particular, agents in the bottom of the income distribution should be mostly affected by their modest increase in income and should be more willing to take on risk after the policy. I then collect a unique dataset to study these effects.

The dataset consists in ﬁght outcomes over the period 2009 to early 2018. I run a standard

Difference-in-Differences analysis to gauge the effects of the policy. I do not have access to data on actual risk-taking during a given fight, so I use the way in which the fight ends (submission or (T)KO versus judges decision) as a proxy. I find that the probability that fights are

finished before going to the judges decreases significantly for the treatment group after the policy. Moreover, the effect is economically significant : using my preferred specification, the

95% interval for the decrease in probability ranges from 7% to 22%. Under the hypothesis that increased risk taking most likely leads to a ﬁght ending before going to the judges scorecards, this shows that the policy had the causal effect to decrease risk taking in this particular setup.

I also ﬁnd evidence that this decrease is more pronounced for higher-earners. In particular, as predicted by the model, the effect is (i) strongest for higher-earners (ii) dampened but still signiﬁcant for the middle of the distribution and (iii) reversed for individuals at the low end of the distribution. Since these latter are not likely to be affected by the decrease in top income but rather by the modest increase in their (relatively low) income, the model predicts that they should be more willing to take on more risks.

A potential threat to identification is that the UFC introduced a new doping control policy alongside the sponsorship policy. As such, it could well be that the decrease in the probability of fights finishing before the distance is due to the fact that now fighters are more reluctant to use Performance Enhancing Drugs (PEDs) and thus have subpar performances as a result. I gather data for the number of random controls per fighter/quarter after mid-2015 to control for this. What I find is that the stricter anti-doping policy actually had the opposite effect :

ﬁghters that have been controlled more times tend to exhibit more ﬁnishes via losses. This is

2 the exact opposite of what is needed to explain the previous results. Therefore, it is reasonable to conclude that the decrease in the proxy for risky strategies in the treatment group is mostly due to the sponsorship policy and its effect on expected earnings.

All in all, I ﬁnd that this policy had a causal, overall negative effect on risk-taking. This begs for the following questions: what about external validity? Do we learn something useful from this particular setup? Since the market that I analyze is a market for superstars in which risk plays an important factor, it can be compared to entrepreneurship. Entry into entrepreneurship is a risky decision, but with potential rewards that can be very large for successful ones.

In this respect, this paper provides evidence that a policy enacted which has the effect to decrease potential earnings at the top signiﬁcantly decreases risk-seeking behavior. Therefore, the ﬁndings in this paper indicate that higher top income/wealth tax rates might decrease the entry into entrepreneurship.

1.1 Related Literature

This paper is closely related to studies of entrepreneurship and its determinants. In particular,

Olds(2014, 2016) studies the effect of more generous safety nets for entrepreneurs and ﬁnds that this has a positive effect on entry into entrepreneurship. In a related and recent contribution Hombert et al.(2014) also ﬁnd that a French reform to provide more generous downside insurance increased entry into entrepreneurship. Cullen & Gordon(2007) and Djankov et al.

(2010) show that higher corporate tax rates usually correlate with lower business formation.

The data that I will study in this paper allows me to go beyond and estimate the causal impact of a policy that decreases top incomes on risk taking. There is also a sizable literature that studies entrepreneurship and the access to capital —see Holtz-Eakin et al.(1994), Buera(2009) and Bianchi & Bobba(2013) among others.

This paper is also related to recent applied papers that analyze the drivers of risk-taking behavior. In the context of tournaments, Genakos & Pagliero(2012) ﬁnd that revealing information on relative performance induces individuals trailing just behind the interim leaders to take greater risks. Using data for World War II pilots, Ager et al.(2017) ﬁnd that status competition increases risk-taking. Finally, using data from Ice Hockey Chong & Restrepo(2017)

3 ﬁnd that having to wear protective gear increases risky behavior. Using data from the NFL,

Lehman & Hahn(2013) look at the effect of momentum on risk taking. Finally, papers looking at the nexus between compensation structure and risk-taking within one organization includes

Hu et al.(2011), while Ederer & Manso(2013) look at innovation.

The paper is structured as follows. In Section2, I lay develop a simple model of risk taking that will guide the empirical analysis. In Section3 I describe the speciﬁc background surround- ing the data that will be used, as well as the policy change. In Section4, I present the empirical results. In Section5, I show that stronger drug testing cannot explain the results reported in

Section4. Finally, I conclude in Section6.

2 A Simple Model of Risk

In this Section, I lay out a simple model of risk1 based on Pratt(1964). I use this model to deﬁne in a precise way what object I set out to estimate using the novel dataset.

Consider a continuum of individuals indexed over the interval [r r]. Each individual r has a utility fonction deﬁned over income x : U(x). The utility function is twice differentiable and features constant relative risk aversion.2 Individual r is characterized by a degree of relative 00 0 risk aversion r = −x ·U (x)/U (x). Consider two individuals indexed by r1 > r2: in this case, individual r1 is more risk averse than r2.

Each individual has a choice between two actions : the ﬁrst one has a known payoff of w. The second one pays off y with probability p and 0 with probability 1 − p. In each case, the individual has an endowment e. To simplify the exposition, I assume that the payoffs are exogenous and verify p · y > w. Given the payoffs, the goal is to characterize the distribution of individuals who will choose the safe decision with known payoff and those who will choose the risky decision with stochastic payoff. Assuming for simplicity that each individual lives

1For a survey of the rich literature focusing on risk and choice, see Gollier et al.(2013) and the references therein. 2To use the terminology in Pratt(1964), the proportional risk aversion is constant, whereas the absolute risk aversion is decreasing.

4 for one period, individual r will choose the risky action if and only if

p ·U(y + e) + (1 − p) ·U(e) > U(e + w). (1)

Theorem 1 in Pratt(1964) guarantees that there is a unique w(r∗) such that equation (1) holds with equality. For individual r∗, w(r∗) is just enough to compensate his/her aversion towards the risky action. An individual r < r∗ is less risk averse and thus for him w(r∗) is too low

: he/she will choose the risky action. Consequently, the cumulative distribution function of individuals that choose the risky action is G(r∗) ≡ P(r ≤ r∗).

Observe that the payoffs cover the interval [e, y + e]. The policy that I will study in the remainder of the paper consists in (i) a sizable decrease in y coupled with (ii) a comparatively modest increase in e. Given that the decrease in y dominates the increase in e, it is clear that the payoff distribution compresses. The main question that I set out to answer is : what will this imply for overall risk taking decisions?

Let us denote n = G(r∗) as the share of individuals that choose the risky action. From equation (1), it is clear that a decrease in y will decrease n: the payoff associated with the risky action decreases while the one associated with the safe action remains unchanged. On the other hand, the effect of an increase in e is not so straightforward. Theorem 2 in Pratt(1964) proves that w(r∗) is a decreasing function of e : wealthier individuals will exhibit a higher propensity towards risk since the bad outcome with large marginal utility is comparatively less likely for a large e —see also Bianchi & Bobba(2013). Putting it all together, the impact of the policy can be computed as

∂n ∂n dn(y, e) = dy + de ∂y ∂e ∂r∗ ∂r∗ = g(r∗) dy + g(r∗) de ∂y ∂e ∂r∗ ∂r∗ = g(r∗) dy + de . ∂y ∂e

Given that both g(r∗) and the partial derivatives are positive and that the decrease in y dominates the increase in e, the share of individuals that choose the risky action is likely to decrease.

Again, a compressed distribution can be the result of higher top income taxes (decrease in y) coupled with a weakly higher safety net (modest increase in e). In the next Sections, I will

5 analyze a novel dataset to test this prediction. It should be noted that this is consistent with the correlations reported in Cullen & Gordon(2007) and Djankov et al.(2010). The data that I will study in this paper is a step forward in that it will shed light on the causal effect of lower top incomes and risk taking behavior.

This prediction is about an aggregate outcome. Indeed, the only dimension of heterogene- ity is through risk aversion here. However, if in reality top income tax rates are increased this will likely not affect the whole income distribution. For example, an increase in the top tax rate will likely affect more the behavior of a student fresh out of, say, a computer science masters program than that of someone working a low-paid job in retail. Assume that the latter has a maximum attainable income of y. Then, provided that

∂r∗ −1 ∂r∗ −dy ≤ de ∂y ∂e the effect of the increase in e of magnitude de dominates and n should increase after the policy.

In other words, there is a subset of individuals for which the effective decrease −dy will be negligible. At the end of the day, for this subset of individuals the model predicts that the fraction choosing the risky action should increase. The data that I will analyze throughout the paper can provide evidence on this. Note also that this prediction aligns well with the empirical evidence reported in Olds(2014, 2016).

Before delving into the speciﬁc setup that concerns this paper, there is again a parallel to be drawn between this setup and the issue of entrepreneurship decisions. In their seminal paper, Kihlstrom & Laffont(1979) use a general equilibrium version of the model just laid out to analyze how attitudes towards risk shape entrepreneurship decisions. Following this, several papers have used this framework to ask related questions; a recent example of which is Bianchi & Bobba(2013) who studies a variant with ﬁnancial frictions. Therefore, the analysis carried out in this paper potentially provides useful evidence about the potential impact of tax policies on attitudes towards risk.

6 3 Some Background : The Sport and the Policy Change

3.1 The Sport

As its name indicates, the sport of MMA is a blend of many styles of martial arts. A typical

MMA competition/event comprises a number of ﬁghts between two opponents. It usually takes place in a cage at the center of the arena. In the early days of the sport, the ﬁghts were basically advertised as having very few rules. This generated a backlash from both politicians and the general public. As a result, the sport is now characterized by a comprehensive set of rules.3

According to the latter, each regular ﬁght (i.e a ﬁght in which there is no title on the line or that is not the main event) is set for three 5-minute rounds. For a championship/main event

fight, the standard duration is five 5-minute rounds. The fight can end in three different ways

: (1) one of the contestants suffers a (technical) Knock Out or (2) Submission. If none of these happens, then (3) the win/lose/draw decision is given by three judges sitting at ringside. In my empirical analysis, I will use the fact that options (1) and (2) —especially (1)—reﬂect riskier strategies by the contestants.

There exists many competing leagues of MMA. The biggest two that I will reference throughout the paper are named Bellator and Ultimate Fighting Championship (henceforth UFC).

Fighters in these leagues are usually considered to be independent contractors and not em- ployees. As such, they are free to get their own sponsors : a typical fighter wears a pair of shorts with sponsors stitched on them. Also, during fight announcements while both fighters are in the cage, they usually display a banner with sponsors on it. While this is still the case for Bellator fighters, this changed abruptly for UFC fighters in May-July 2015.

3.2 The Policy

In December 2014, it was (unexpectedly) announced that, after July 2015, UFC ﬁghters would not be able to have their own sponsors (and the money that came with it, naturally). Instead,

3These are regrouped in the so-called Uniﬁed Rules and other Important Regulations of Mixed Martial Arts, accessible at: http://media.ufc.tv//discover-ufc/Unified_Rules_MMA.pdf

7 Figure 1: Search results for UFC Reebok deal (Google Trends)

they would be only allowed to wear ofﬁcial sponsors of the UFC, such as Reebok and Monster

Energy Drink. This stipulation holds during fight week, meaning that if a fighter is scheduled to fight on a saturday night he/she can only wear official sponsors during the week. For most

ﬁghters, this is when they get their peak exposure. To illustrate the timing of the policy, I plot in Figure1 results of search for the words Reebok UFC deal in Google Trends.

That deal (which was basically forced upon the ﬁghters without any discussion, thereby generating a lot of protests ) came with sponsorship money of its own. More speciﬁcally, each

ﬁghter would be awarded a certain ﬁxed amount based on different characteristics. These amounts where disclosed in May 2015 (hence the spike in searches in Figure1) and are de- scribed in Table1 (in nominal US$)

This has to be contrasted with the previous situation, in which each ﬁghter had to fend for himself to ﬁnd sponsorship money. The result of this was that sponsorship payouts were

8 Table 1: Reebok Sponsorhip Payouts for UFC Fighters

Characteristics payout 1 to 5 fights under company $ 2500 6 to 10 fights under company $ 5000 11 to 15 fights under company $ 10000 16 to 20 fights under company $ 15000 20 + fights under company $ 15000 Title Challenger $ 30000 Champion $ 40000 known4 to be rather unequally distributed : superstars would land sponsors with big brands such as NIKE (UFC fighter Jon Jones for example) or BURGER KING (UFC fighter Anderson

Silva for example), to cite only two salient examples. As a result, top fighters now earn most likely significantly less than before (6-figure sponsorship payouts for superstars were not un- usual), while lower-tier fighters (i) do not have to search for sponsors and (ii) likely earn more than what they would on their own. The overall effect is that potential sponsorship earnings are more concentrated than before : lower-tier fighters can expect more compensation even if they lose the fight, while top stars can expect their compensation to decrease drastically.

3.3 The Data

3.3.1 Treatment Variable

While important, sponsorship money is only one part of fighter compensation. Usually, fighters get a fixed amount to fight on a particular occasion.5 Under UFC rules, if a fighter has an exceptional performance, he/she can receive a one-time bonus of $50 000. With this in mind, I have collected data on fighter payout before and after the Reebok deal.6 For each event, earnings display a power law behavior : most of the earnings accrue to a few selected fighters, while the rest earn significantly less.7

4There does not exist publicly available data on this, only reported anecdotes from fighters themselves. 5The usual pay structure comprises two distinct amounts : show money that is guaranteed as long as the fighter makes it to the ring on fight night and a win bonus. As the name suggests, fighters only get the second one if they win their fight. 6These amounts are public when MMA events are held in U.S. states that require this, such as Nevada. For events that are held in other states or overseas, I rely on the computations of MMA journalist Jeff Fox that runs a database publicly available on http://thesportsdaily.com/mma-manifesto/. In a nutshell, when a fighter competes enough in locations that require salaries to be made public, we can interpolate the earnings in locations that do not. 7See Gabaix(2009) as well as Gabaix et al.(2015).

9 Figure 2: Measure of Inequality : 2015-2016 0 -.05 -.1 -.15 Difference between Coefficients -.2 01jul2015 01oct2015 01jan2016 01apr2016 01jul2016

Assuming that earning follow a power law8 with exponent ζ, the lower this exponent, the more unequal the distribution is. Accordingly, I plot in Figure2 the difference in the estimated

ζˆ with and without taking Reebok payouts into account. I normalize it so that a negative value for this difference means less inequality. By construction, this difference is exactly 0 before the policy.

From this Figure, one can see that the new policy made earning less unequal for every event after July 2015. This is the main treatment that I will analyze in this paper. I will use the

Bellator league as a control group since they did not implement such a policy. Unfortunately, the UFC also introduced increased drug testing under the guidance of the U.S. Anti-Doping

Agency (henceforth USADA) at the same time. I also collect data for doping controls per

ﬁghter/quarter9 and study this in Section5.

8More formally, I assume that, for earnings E, P(E > x) = k · x−ζ , where k is a constant and ζ > 0. 9The data is publicly available at https://ufc.usada.org/testing/results/athlete-test-history/.

10 3.3.2 Dependant Variable and Controls

The main dependant variable for the empirical analysis will be the outcome of a ﬁght. Using R,

I have scraped this data off Wikipedia webpages. The dataset contains every UFC and Bellator

ﬁght during the 2009-early 2018 period. I then construct a dummy that equals 1 for each possible outcome. To get a sense of what this variable looks like, I plot in Figure3 the quarterly average of this dummy for each league for a 10-quarter window around the treatment.10 One can see from Figure3 that there is a break in the treatment group (UFC) at the moment of treatment : the share of Finishes drops.

For the control group, there seems to be a slight downward break as well. This is actually reassuring as we could expect that it would trend upward after the treatment. Since I will carry out a Differences in Differences analysis, an implicit assumption is the Stable unit treatment value assumption (SUTVA). Let’s assume that all the sponsorship money that is not allowed in the UFC after the treatment flows into Bellator. Then this would generate higher expected gains in the control group and higher risk taking in this group. This would be materialized through a higher number of finishes post-treatment and lead the empirical analysis to over- estimate the true effect. Judging from Figure3, this does not seem to be the case. As a matter of fact, to the best of my knowledge there is no evidence of sponsorship money flowing massively in the control group.

I then gather data to control for individual characteristics. For each ﬁgh in the dataset I collect data on (i) physical properties (gender, weight class) of both ﬁghters and (ii) spot on the card.11

I report summary statistics for these data and break it down in terms of leagues in Table2.

One can see from Table2 that the percent of male fighters is large and not significantly different across the two leagues. On the other hand, fighters tend to be slightly heavier in the UFC than in Bellator. Also, the average number of fights on a given card is significantly lower for the

UFC. 10This choice is dictated by the fact that I have exactly 10 quarters of data after the treatment. 11By default, the main event of the night is the first spot. Subsequent fights are usually deemed less important and get less attention/coverage as the spot on the card increases. For example, the 13th fight on the card will most likely not air directly on TV.

11 Figure 3: Quarterly Average of Finish Dummy .7 .6 .5 .4 .3 -10 -5 0 5 10 Quarter_

(mean) Finish_UFC (mean) Finish_Bel

Table 2: Summary Statistics

UFC Bellator P-value Weight (pounds) 169.9 167.7 0.08 Gender (% male) .94 .95 0.79 Average # of ﬁghts 6.25 7.09 .00

12 4 Empirical Analysis

The unit of observation in the empirical analysis will be a ﬁght. The main hypothesis is that

fights in the treatment group after the policy are more likely to end in a way that is suggestive of riskier strategies. Therefore, my baseline dependant variable will be a dummy that equals 1 if the fight ends by (T)KO or Submission.12 To study this, I estimate the following specification:

1 = + + + 1 · 1 + {Finish} f ot At Bo γX f ot δ {After Policy}t {UFC}o υ f ot, (2)

where At collects both time fixed-effects and organization-specific time trends, Bo is an organization fixed effect and X f ot is a vector of controls for fight f that happens under organization o during quarter t. The main coefficient of interest here is δ. If fighters take less risks in the treated group after the policy compared to the control group, we would expect δ < 0. I cluster the standard errors across organization-quarter pairs.13 I estimate this using OLS first. Since the dependant variable is a dummy, predicted values from the OLS can potentially fall outside the [0, 1] interval.14 Therefore, I also report the results with a logistic specification in the

Appendix. That being said, I report the estimation results15 of equation (2) in Table3.

Table 3: Difference-in-Differences OLS estimates

1Finish (1) (2) (3) (4) (5) After Treatment x UFC −.09∗∗∗ −.099∗∗∗ −.099∗∗∗ −.088∗∗∗ −.12∗∗∗ (.024) (.025) (.025) (.025) (.027) Gender .12∗∗∗ .12∗∗∗ .13∗∗∗ .16∗∗∗ (.025) (.024) (.03) (.04) Spot .001 .001 .004 (.003) (.003) (.003) Weight Class .001 .001 (.002) (.002) PPV Events Yes Yes Yes Yes No # Clusters 63 63 63 63 62 # Observations 5,029 5,029 5,029 4,736 3,358 Note : * p<0.1, ** p<0.05, *** p<0.01. Standard errors are reported in parentheses.

Several results emerge from Table3. First, the policy has a significantly negative effect on the probability that fights in the UFC end up with a finish compared to the ones under the

12I will study other outcomes throughout the paper, in which case the change in dependant variable will be highlighted. 13See Bertrand et al.(2004) for a review of clustering in these kind of setups. 14 This is not the case here: using the baseline speciﬁcation, predicted values for 1Finish fall in the interval [.058, .485]. In addition, there are very few variables in the lower tail since the 5% percentile is roughly .158. 15Data and codes to reproduce these ﬁndings can be downloaded here.

13 Bellator banner. As ﬁnishes result from riskier strategies, I interpret this ﬁnding as a negative causal effect of the policy on risk-taking by those affected. This suggests that the correlations reported in Cullen & Gordon(2007) and Djankov et al.(2010) are likely to be more than just correlations.

Above and beyond that, I find that male fighters seem to employ riskier strategies on average. On the other hand, at first glance both the placement on the card and and weight class do not seem to have any impact on the fight going the distance or not.

Finally, in specification (5) I exclude Pay Per View Events. Held exclusively by the UFC,16 these are not accessible through cable channels. One needs to pay a fixed amount to watch those. Importantly, some fighters get a percentage of the number of PPV buys after the event.

This can represent a sizable amount of money and might change the incentives for ﬁghters competing in these events. Since these are runs exclusively by the UFC, it seems reasonable to exclude them in order to make incentives more comparable across treatment/control groups.

In addition, one would expect that if these are kept in the sample they might dampen the effect of the policy on the treatment group : while the potential for earnings are diminished, for these special events it is still possible to earn a massive paycheck. As a result, the coefﬁcient on the treatment variable is much higher when those events are excluded.

To dig a bit deeper, I will now differentiate between the two ways a fight can be ended before the distance : (T)KO and submission. If both fighters are on the ground and the one in dominant position (most likely on top) attempts a submission, the worst that can happen is to loose position : both fighters end up on their feet again. If one attempts a big punch to score a

(T)KO, the worst that can happen is if he/she gets countered and suffer a (T)KO him/her-self.

It follows that of these two ways to end a ﬁght, one is intrinsically riskier than the other. With this in mind, I will ﬁrst run the same difference-in-differences analysis, but with (T)KO as a dependent variable. I report the results for this estimation in Table4.

From Table4, one can see that the policy had a signiﬁcantly negative causal effect on a

ﬁght ending via (T)KO. The magnitude is very similar to the one I obtain with 1Finish as a dependent variable, showing that the results of the latter are most likely driven by (T)KOs.

16Bellator only has 2 over the 8 years of my sample, while the UFC usually hosts a dozen a year.

14 Table 4: Difference-in-Differences OLS estimates : (T)KO

1TKO (1) (2) (3) (4) (5) After Treatment x UFC −.07∗∗ −.084∗∗∗ −.083∗∗∗ −.1∗∗∗ −.15∗∗∗ (.028) (.028) (.028) (.028) (.039) Gender .13∗∗∗ .13∗∗∗ .18∗∗∗ .21∗∗∗ (.023) (.022) (.032) (.04) Spot −.006∗∗ .005∗ .004 (.002) (.003) (.003) Weight Class .003∗∗ .004∗∗ (.001) (.002) PPV Events Yes Yes Yes Yes No # Clusters 63 63 63 63 62 # Observations 5,029 5,029 5,029 4,736 3,358 Note : * p<0.1, ** p<0.05, *** p<0.01. Standard errors are reported in parentheses.

For specification (5), the 95% confidence interval of δ is estimated to be [−.226, −0.069] so that the effect is economically significant. When I use 1Submission as a dependent variable, I get a coefficient that is (i) statistically non-significant and (ii) economically much less significant with δˆSub = .026 at best.

This is consistent with the fact that attempting a submission does not carry as much risk as attempting to end the fight via (T)KO. Indeed, because it is not very risky, a compressed earnings distribution does not have much influence on its occurrence. Since attempting to win the fight via (T)KO is very risky, it responds strongly to expected earnings.

Evidently, this is clearly not what a sports promotion such as the UFC wants. They want their fighters to put on exciting fights so that, next time around, more and more people will either (i) buy the PPV or (ii) tune-in en masse during broadcasts on Cable TV so that they can earn more in advertising money. It has been noticed recently that fighters have been more cautious. One salient case is fighters that are the champions of their respective weight category.

They stand to loose a very large amount of money per ﬁght if they loose their title —see Table1.

A recent example involves T.Woodley, UFC Welterweight champion. He had two notoriously lackluster performances in defending is title against S.Thompson and D.Maia. Here is what

UFC president D.White had to say about it:

“Who wants to pay to see Tyron Woodley fight again? He’s an absolute physical specimen and could’ve finished the fight any time he wanted. But, you know, he didn’t want to take the

risks. You take no risks, you get no rewards.”

15 Dana White, UFC President

To see whether the observed decrease in risk taking is driven by a particular subset of individuals in my data set, I now include new variables that interact characteristics with the policy variable. I report these results in Table5. One can see from Table5 that, expect for the

Spot on the card, the interaction terms are statistically insignificant. Therefore, the results do not seem to be driven by fighters exhibiting particular characteristics. Nonetheless, the effect of the treatment seems to be driven by the place on the card. According to the estimate, bumping a fight from the 11th spot of the card (close to the last) to the main event (first spot) decreases the probability of a (T)KO for the treatment group of 13% after the policy. Accordingly, I study in more detail whether the treatment has heterogeneous effects depending on fighter’s placement on the card.

Table 5: Difference-in-Differences OLS estimates : Interactions

1Finish (1) (2) (3) After Treatment x UFC −.18∗∗∗ −.03 −.12∗∗ (.05) (.04) (.04) After Treatment x UFC x Gender .06 (.06) After Treatment x UFC x Spot −.013∗∗∗ (.005) After Treatment x UFC x Weight .00 (.003) PPV Events No No No # Clusters 62 62 62 # Observations 3358 3358 3358 Note : * p<0.1, ** p<0.05, *** p<0.01. Standard errors are reported in parentheses.

4.1 Heterogeneous Treatment Effect

The previous result is linked with the discussion (see Section2) about the potentially different effects of the policy across agents. The spot on the card can be used as a proxy to differentiate between upper-tier and lower-tier athletes. Usually, those that end up on the top spots are the ones that have the highest earnings —pre- or post-treatment. Conversely, the ﬁghters on the undercard of the events have the lowest earnings. Therefore, an individual in the former group is likely to be affected by the decrease in maximum earnings; an individual in the latter group will most likely be affected only through the increase in "safety net" —Reebok sponsorship money here.

16 To test this prediction, I will run separate regressions for three groups in my sample : lower, middle and upper tier. All three groups comprise roughly one thousand observations. The upper tier corresponds to fights on spots 1 to 4: those are the ones with the most exposure and include the main/co-main events. All of these fights include recognizable names and are aired on cable TV. The middle-tier group fights include those on spots 5 to 8; they are also aired on cable TV but include less recognizable names. Finally, the lower-tier group includes the rest of the fights. Often, these fights stream on Facebook live and have very little visibility.17 The results are reported in Table6

Table 6: Difference-in-Differences OLS estimates : Finish

Spot 1 − 4 5 − 8 9 − 16 After Treatment x UFC −.24∗∗∗ −.2∗∗ .12∗∗ (.06) (.08) (.06) PPV Events No No No # Clusters 62 62 62 # Observations 1217 1045 1063 Note : * p<0.1, ** p<0.05, *** p<0.01. Standard errors are reported in parentheses.

Three main ﬁndings emerge from Table6. First, consistent with the model laid out in

Section2 the effect is stronger for upper-tier fighters. This is expected as these fighters are the ones which will likely be among the most affected by the decrease in top income. In addition, they will not be affected by the increase in safety net income. Second, the middle-tier fighters also decrease their risk-taking behavior, although to a lesser extent than upper-tier fighters.

Third, lower-tier ﬁghters exhibit an opposite effect: they increase risk-taking after the policy.

Through the lenses of the model, these ﬁghters will likely be more affected by increased safety net income rather than by the decrease in top income. Again, this is in line with the results reported in Olds(2014, 2016).

4.2 Dynamic Effect of the Treatment

Regarding these results, two remarks are in order. First, I have estimated the overall causal impact of the treatment and we might wonder weather the treatment had dynamic effects or

17Using a different dataset (see Section5), I find that the spot on the card is highly correlated with total earnings with a coefficient of correlation of −0.4111. I also find that it has good predictive power. Regressing total earnings on various controls and comparing the R2 with and without Spot included in the controls yields a R2 that increases from .16 to .24.

17 Figure 4: Dynamic Treatment : (T)KO .1 0 -.1 -.2 Estimated Coefficient -.3 -.4 -5 0 5 10 Quarters after treatment

Coeff lo95/up95

not. Second, as can be seen from Figure1 the treatment was effective in July 2015 but was announced in December 2014. Therefore, we might wonder whether the announcement itself might have had an effect on risk taking. Indeed, since the announcement essentially unveils that returns from risk-taking will be lower in the future agents have an incentive to take more risks now, when it actually pays off. To see whether that is the case in the data, I estimate a dynamic treatment effect18 and plot the results in Figure4, with the associated 95% conﬁdence bands.

From Figure4, one can see ﬁrst that the effects of the treatment seem to build up over time. Second, there seems to be some intertemporal substitution in risk-taking as (T)KO ﬁn- ishes increase slightly before the treatment takes effect. This anticipation effect is even more pronounced if I include PPV events as well —see Appendix Figure A.6. Since there is some substitution going on, the natural question is what is substituted for?

From Appendix Figure A.7, it seems that (T)KOs increase at the expense of Submission

18I use the speciﬁcation without PPV events (I get the same results with PPV events) as the incentives are potentially different for those events.

18 Figure 5: Dynamic Treatment : Decision .3 .2 .1 Estimated Coefficient 0 -.1 -5 0 5 10 Quarters after treatment

Coeff lo95/up95

ﬁnishes. These are inherently less risky so it is natural to switch from submission to (T)KO attempts. This does not seem to happen after the treatment however : from Figure5, one can see that decisions pick up the slack. Now that it pays less to be noticed, it seems that altogether safer strategies are employed.

All in all, it seems that the policy had a negative effect insofar as it has decreased the proportion of ﬁnishes and in particular (T)KOs. As it has been alluded to before, the UFC also put in place a stronger anti-doping stance at the same time. This can potentially explain the decrease in ﬁnishes that has been documented here so I turn to this issue now.

5 The Anti-Doping Policy

A potential threat to my interpretation of the results is the following : the UFC also enacted a tougher drug testing policy under the guidance of the United States Anti Doping Agency

(USADA). Before July 2015, ﬁghters were usually tested by the State Athletic Commissions in

19 which they were supposed to fight. After, they would all have to enroll into the USADA testing pool and be subject to random testing in and out of competition, whether they were booked for a fight or not. As a result, it could be that increased drug testing deterred cheaters to take performance enhancing drugs. Since their performance is now potentially subpar because they are "clean", we might see less fights ending via finishes. That could potentially explain the negative effect that I find after July 2015, so that it has nothing to do with earnings.

I will show that this is not the case. I collect a new dataset with individual information for each fighter. Since this dataset has been collected by hand, its scope is much narrower: it covers only one and a half year before and after the policy. As stated before, I use USADA’s website and collect data on the number of random drug tests for each fighter/quarter. To get a proxy for individual ability, I also collect data on betting odds from a betting website.19 I gather two types of betting odds : (1) the odds that the fighter wins and (2) the odds that the

fighter wins with a finish. I also use various sources to collect data on the country of origin for each fighter.

To see whether USADA drug tests can explain the decrease in ﬁnishes, I concentrate on the post-treatment part of the sample. I regress the Finish/(T)KO dummy on the set of controls and the number of random drug test within the quarter. Importantly, from the perspective of the

ﬁghter the drug test cannot be anticipated. Therefore, for all intents and purposes this variable can be considered as exogenous and the OLS/Logistic estimate should recover the causal effect of increased drug testing. Since I only have one league and three quarters, I cluster standard errors at the quarter-weight class level.20 I show the results of this experiments in Table7.

Table 7: OLS & Logistic estimates : USADA

1TKO 1Submission All Win Loss All Win Loss OLS .05∗∗ .12 .03∗∗ .01 .01 .00 (.024) (.015) (.014) (.02) (.01) (.01) Logistic 1.21 1.07 1.23∗∗ 1.07 1.06 1.04 (.14) (.11) (.12) (.15) (.13) (.2) PPV No No No No No No # Clusters 36 36 36 36 36 36 # Observations 593 593 593 593 593 593 Note : * p<0.1, ** p<0.05, *** p<0.01. Standard errors are reported in parentheses.

From Table7, one can see that the effect of increased drug testing under USADA (i) is

19The data on betting odds can be accessed at https://www.bestfightodds.com/. 20I get similar results with robust standard errors.

20 rather small and (ii) goes mostly trough (T)KO losses. It seems that ﬁghters used to cheat somewhat before and now that they are under tighter scrutiny, they perform worse than they did. Finally, as for the policy studied before submission ﬁnishes do not seem to be affected.

The same results emerge using a logistic model. Importantly, this policy has the opposite effect of the treatment studied earlier. If anything, the introduction of tighter drug control has had the effect to increase the propensity of risky strategies. It is then reasonable to argue that the effect found earlier might under-estimate the true negative effect as the presence of USADA drug testing plays a mitigating role.

6 Conclusion

The recent tax reform(s) in the United States have sparked an intense debate. These reforms have been criticized as a gift to top-earners while the middle of the distribution stood to gain much less. Relatively absent from the debate is how policies that decrease potential earnings at the top might have an effect through risk taking.

Using data from a market for superstars, I ﬁnd that such policies have a causal and sig- niﬁcantly negative effect on the occurrence of risky strategies. Outside of this narrow setup, one might think of entrepreneurship as a quite risky endeavor. Translated to this market, my results indicate that an increase in top-income/wealth taxes might have a negative effect on the decision to become an entrepreneur.

21 References

Ager, P., Bursztyn, L., & Voth, H.-J. (2017). Killer Incentives: Status Competition and Pilot Perfor-

mance during World War II. CEPR Discussion Papers 11751, C.E.P.R. Discussion Papers.

Alvaredo, F., Chancel, L., Piketty, T., Saez, E., & Zucman, G. (2017). Global Inequality Dynam-

ics: New Findings from WID.world. American Economic Review, 107(5), 404–409.

Atkinson, A. B., Piketty, T., & Saez, E. (2011). Top Incomes in the Long Run of History. Journal

of Economic Literature, 49(1), 3–71.

Bertrand, M., Duﬂo, E., & Mullainathan, S. (2004). How Much Should We Trust Differences-

In-Differences Estimates? The Quarterly Journal of Economics, 119(1), 249–275.

Bianchi, M. & Bobba, M. (2013). Liquidity, Risk, and Occupational Choices. Review of Economic

Studies, 80(2), 491–511.

Buera, F. (2009). A dynamic model of entrepreneurship with borrowing constraints: theory

and evidence. Annals of Finance, 5(3), 443–464.

Chong, A. & Restrepo, P. (2017). Regulatory protective measures and risky behavior: Evidence

from ice hockey. Journal of Public Economics, 151(C), 1–11.

Cullen, J. B. & Gordon, R. H. (2007). Taxes and entrepreneurial risk-taking: Theory and evi-

dence for the u.s. Journal of Public Economics, 91(7), 1479 – 1505.

Djankov, S., Ganser, T., McLiesh, C., Ramalho, R., & Shleifer, A. (2010). The Effect of Corporate

Taxes on Investment and Entrepreneurship. American Economic Journal: Macroeconomics, 2(3),

31–64.

Ederer, F. & Manso, G. (2013). Is pay for performance detrimental to innovation? Management

Science, 59(7), 1496–1513.

Gabaix, X. (2009). Power Laws in Economics and Finance. Annual Review of Economics, 1(1),

255–294.

Gabaix, X., Lasry, J.-M., Lions, P.-L., & Moll, B. (2015). The Dynamics of Inequality. CEPR Dis-

cussion Papers 11028, C.E.P.R. Discussion Papers.

22 Genakos, C. & Pagliero, M. (2012). Interim Rank, Risk Taking, and Performance in Dynamic

Tournaments. Journal of Political Economy, 120(4), 782–813.

Gollier, C., Hammitt, J., & Treich, N. (2013). Risk and choice: A research saga. Journal of Risk

and Uncertainty, 47(2), 129–145.

Holtz-Eakin, D., Joulfaian, D., & Rosen, H. S. (1994). Sticking It Out: Entrepreneurial Survival

and Liquidity Constraints. Journal of Political Economy, 102(1), 53–75.

Hombert, J., Schoar, A., Sraer, D., & Thesmar, D. (2014). Can Unemployment Insurance Spur En-

trepreneurial Activity? NBER Working Papers 20717, National Bureau of Economic Research,

Inc.

Hu, P., Kale, J. R., Pagani, M., & Subramanian, A. (2011). Fund ﬂows, performance, managerial

career concerns, and risk taking. Management Science, 57(4), 628–646.

Kihlstrom, R. E. & Laffont, J.-J. (1979). A General Equilibrium Entrepreneurial Theory of Firm

Formation Based on Risk Aversion. Journal of Political Economy, 87(4), 719–748.

Lehman, D. W. & Hahn, J. (2013). Momentum and organizational risk taking: Evidence from

the national football league. Management Science, 59(4), 852–868.

Olds, G. (2014). Entrepreneurship and Public Health Insurance. Working papers, Harvard Business

School.

Olds, G. (2016). Food Stamp Entrepreneurs. Working papers, Harvard Business School.

Piketty, T. & Saez, E. (2003). Income Inequality in the United States, 1913 1998. The Quarterly

Journal of Economics, 118(1), 1–41.

Piketty, T., Saez, E., & Stantcheva, S. (2014). Optimal Taxation of Top Labor Incomes: A Tale of

Three Elasticities. American Economic Journal: Economic Policy, 6(1), 230–271.

Pratt, J. W. (1964). Risk Aversion in the Small and in the Large. Econometrica, 32(1/2), 122–136.

Scheuer, F. & Werning, I. (2017). The Taxation of Superstars. The Quarterly Journal of Economics,

132(1), 211–270.

23 A Additional Tables and Figures

Table 8: Difference-in-Differences Logistic estimates : Finish

1Finish (1) (2) (3) (4) (5) After Treatment x UFC .68∗∗∗ .66∗∗∗ .66∗∗∗ .69∗∗∗ .60∗∗∗ (.07) (.07) (.07) (.07) (.07) Gender 1.61∗∗∗ 1.61∗∗∗ 1.69∗∗∗ 1.97∗∗∗ (.16) (.16) (.22) (.31) Spot 1 1 1.02 (.01) (.01) (.01) Weight Class 1 1 (.01) (.01) PPV Events Yes Yes Yes Yes No # Clusters 63 63 63 63 62 # Observations 5,029 5,029 5,029 4,736 3,358 Note : * p<0.1, ** p<0.05, *** p<0.01. Standard errors are reported in parentheses.

Table 9: Difference-in-Differences Logistic estimates : TKO

1TKO (1) (2) (3) (4) (5) After Treatment x UFC .7∗∗∗ .67∗∗∗ .67∗∗∗ .62∗∗∗ .49∗∗∗ (.09) (.09) (.09) (.08) (.1) Gender 1.99∗∗∗ 2∗∗∗ 2.52∗∗∗ 2.92∗∗∗ (.27) (.27) (.45) (.62) Spot .97∗∗ .98∗ .98 (.01) (.01) (.013) Weight Class 1.01∗∗ 1.02∗∗ (.01) (.01) PPV Events Yes Yes Yes Yes No # Clusters 63 63 63 63 62 # Observations 5,029 5,029 5,029 4,736 3,358 Note : * p<0.1, ** p<0.05, *** p<0.01. Standard errors are reported in parentheses.

24 Table 10: Difference-in-Differences OLS estimates : Submission

1Submission (1) (2) (3) (4) (5) After Treatment x UFC −.016 −.016 −.017 −.012 −.026 (.03) (.03) (.03) (.03) (.036) Gender −.15 −.17 −.05∗ −.44 (.023) (.023) (.028) (.035) Spot .007∗∗∗ .006∗∗∗ .008∗∗∗ (.002) (.002) (.002) Weight Class −.002∗ −.003∗∗ (.001) (.001) PPV Events Yes Yes Yes Yes No # Clusters 63 63 63 63 62 # Observations 5,029 5,029 5,029 4,736 3,358 Note : * p<0.1, ** p<0.05, *** p<0.01. Standard errors are reported in parentheses.

Table 11: Difference-in-Differences Logistic estimates : Submission

1Submission (1) (2) (3) (4) (5) After Treatment x UFC .92 .93 .91 1.07 1.13 (.15) (.15) (.15) (.19) (.2) Gender .91 .92 .72∗ .77 (.12) (.15) (.12) (.16) Spot 1.04∗∗∗ 1.04∗∗∗ 1.04∗∗∗ (.01) (.01) (.01) Weight Class .99∗ .98∗ (.01) (.001) PPV Events Yes Yes Yes Yes No # Clusters 63 63 63 63 62 # Observations 5,029 5,029 5,029 4,736 3,358 Note : * p<0.1, ** p<0.05, *** p<0.01. Standard errors are reported in parentheses.

25 Figure A.6: Dynamic Treatment : (T)KO .2 .1 0 -.1 Estimated Coefficient -.2 -.3 -5 0 5 10 Quarters after treatment

Coeff lo95/up95

Figure A.7: Dynamic Treatment : Submission .2 .1 0 -.1 Estimated Coefficient -.2

-5 0 5 10 Quarters after treatment

Coeff lo95/up95