Department of Economics

Working Paper

What can bookies teach us about pari-mutuel wagering

reform? Applying Australian lessons to the U.S.

Charles C. Moul Miami University

Joseph M. G. Keller

dunnhumby

August 2011

Working Paper # - 2011-01

What can bookies teach us about pari-mutuel wagering

reform? Applying Australian lessons to the U.S.∗

Charles C. Moul† Joseph M. G. Keller‡

August 2011

Abstract

We consider a policy reform relaxing price controls in American pari-mutuel wager-

ing on horse racing by examining bookie behavior in Australia’s fixed-odds gambling

sector. Descriptive regressions indicate that bookie takeouts (the effective prices of

races) vary substantially and systematically with race characteristics, though in some-

times counterintuitive ways. Estimates of an explicitly reduced form model of bookie

takeout, however, qualitatively match both intuition and prior findings in the litera-

ture. Calibration using these estimates suggests that regulatory reform that permits

racecourses to alter takeout across races would increase variable profit by 3-6%.

Keywords: regulatory reform, gambling, horse racing

JEL codes: D22, L5, L83

Markets all over the world are subject to strict price regulation, and deregulation in those

areas could presumably increase welfare markedly. Unfortunately, the stringent regulations

themselves often prevent the observable variation that would permit empirical analysis to

gauge the potential welfare benefits from deregulation. One such example is American pari-

mutuel wagering on horse racing. This gambling, in which the racetrack takes a percentage

of money wagered (the take-out rate or takeout) and then returns the remainder to winning

bettors, is regulated at the state level and typically involves the takeout being set at a

particular level for different types of wagers. There have been several recent attempts to learn

the responsiveness of bettors to this takeout rate with temporary (Laurel Park, MD, 2007) or

∗This paper is based in part on Keller’s 2010 Master’s exit paper from Miami University. We thank

Max Kaftal for excellent research assistance (in particular for seeking out the data), Tim Ryan (CEO of the

Australian Bookmakers Association) for giving it to him, and Ryan Ruddy for additional research support.

We also thank our many Australian acquaintances with first-hand racetrack experience for sharing their field

research.†Corresponding author: Miami University Farmer School of Business, Department of Economics, Oxford,

OH 45056, USA. Tel: 513-529-2867. E-mail: moulcc@muohio.edu‡dunnhumby, Email: jmgkeller@gmail.com

1

permanent (Hialeah, FL, 2010; Tioga Downs, NY, 2010) reductions, but results have thus far

been inconclusive.1 Such regulatory changes and experiments did not permit racetracks to

engage in price discrimination by actively adjusting the takeout across races. Bettor demand

may be such that varying takeout across races, rather than simply selecting a fixed level of

takeout, is another important margin of deregulation. Schmalensee (1981) admittedly shows

that price discrimination by a monopolist that does not increase quantity sold will increase

revenues but decrease welfare. Because states typically levy excise taxes on wagering, though,

shifting to taxes on cumulative takeout and allowing such price discrimination would increase

tax revenues and may allow the reduction of more egregiously welfare-harming taxes. It is

therefore possible that welfare would rise from such a policy change. Both regulatory issues

of takeout level and variability have been prominent in industry suggestions (NRTA Player

Panel Recommendations, 2004). Furthermore, the industry’s ongoing financial troubles from

increased gambling competition and the recent recession have focused both regulators and

racetracks on ways to improve the industry’s viability.

We have no data from U.S. racetracks and such regulatory changes, but we instead

observe bookies from Australian fixed-odds thoroughbred horse race wagering. Bookies in

this context set the takeout implicitly by selecting the level of odds on the field of horses,

and their behavior therefore may be indicative of what a profit-maximizing racetrack would

do if permitted to set and vary its own takeout. Such a comparison hinges on the similarity

between bettors in the two countries. Australians appear to gamble substantially more than

Americans, with Australian per capita losses at least triple those in the U.S.2 This gap,

though, presumably stems at least in part from the comparatively easy access to gambling

in Australia rather than radically different consumer preferences. Moreover, the countries’

common heritages and other resemblances suggest that the comparison may be apt. To the

extent that Australian and American bettors share preferences over race characteristics and

disutility on money spent, our results can shed light on the revenue and welfare impacts for

certain U.S. reforms.

Previous researchers have used variation in takeout rates and amounts wagered to es-

timate price-elasticities for U.S. pari-mutuel gambling (Gruen, 1976; Suits, 1979; Mobilia,

1993; Thalheimer and Ali, 1998; Gramm et al., 2007). These studies have generally found

1Laurel Park halved its takeouts across the board for ten days in August 2007. Hialeah Park lowered its

takeout to 12% for all bet-types in October 2010. Tioga Downs reduced all its takeouts to the state minima

(15% for win/place/show bets) for the 2010 season and maintained those lower levels for the 2011 season.2"The world’s 10 biggest gambling nations - including Canada", Vancouver Sun, 7/11/2011, data taken

from H2 Gambling Capital.

2

that takeout rates are higher than the revenue-maximizing level, with point estimates of

own-takeout elasticities ranging from -1.6 to -3. To our knowledge, no studies have consid-

ered how race characteristics themselves can affect these price-elasticities. This is exactly

the information that the estimates of our reduced form model provide. When combined with

plausible estimates of own-price demand parameters, these estimates allow for the identifica-

tion of the full set of structural parameters and can therefore predict the impacts of different

policy recommendations. We need race-level characteristics to employ this analysis, and we

lean heavily on Coffey and Maloney (2010, henceforth CM) to do so. While that paper uses

data from Churchill Downs (KY) in 1994 to distinguish the incentive effect from selection in

explaining the correlation between performance and reward, it also includes regression results

that show the impact of race characteristics on the amount of money wagered, known in the

U.S. as handle and in Australia as turnover. CM find that handle increases in field size (i.e.,

number of horses) and purse and decreases in dispersion of horse-talent. It is those regres-

sion results (with CM’s summary statistics) that we will combine with the Kentucky-specific

price elasticity estimate from Thalheimer and Ali (1998) in our calibration exercise.

While we build on the above literature, our research is superficially most similar to the

work of Shin (1993) in that we both use the bookmaker’s implied takeout as the dependent

variable and employ race characteristics such as size of field and dispersion of horse-talent as

explanatory variables. Shin (1993), though, frames his empirical exercise as identifying the

prevalence of insider trading, which he posits is the cause of the recurrently observed favorite-

longshot bias in which favorites are underbet and longshots are overbet.3 Our approach, on

the other hand, begins with descriptive regressions and then turns to estimating a reduced

form model that is explicitly derived from a structural model. While the estimates from

the descriptive regression are more useful for predicting the equilibrium impacts of race

characteristics on takeout, the reduced form estimates illuminate the mechanisms by which

those impacts arise.

We begin by showing the extent of variation in our observed bookie takeout rates. Even on

the same day and at the same racetrack, the sample standard deviation for takeout is three

percentage points (compared to a mean of seventeen percentage points). Our descriptive

3Broadly speaking, bookies in Shin’s model protect themselves from bettors with inside information on

longshots by offering less favorable odds on those horses than objective probabilities would suggest. Cain et

al. (2003) provide additional empirical support consistent with the thesis. Working against the primacy of

this interpretation, recent research has looked to explain the observed longshot bias in pari-mutuel gambling

as the result of bettor misperception (Sobel and Raines, 2003; Snowberg and Wolfers, 2010) or sequential

information release (Ottaviani and Sorenson, 2009).

3

results linking bookie takeout rates with race characteristics are generally as expected, in

that these takeouts are higher for races with more ex ante even fields, for races with larger

fields, and for late-day races. The inclusion of a race’s purse (prize money to top finishers)

as a proxy for a race’s unobserved prestige and quality, though, yields a surprising result:

observed takeouts are lower for higher purse races. As we find no anecdotal support for the

idea that competition is greater for these races, this apparent demand anomaly is analogous

to the common observation that many items go on sale during periods of high demand.

Explanations for this curious pricing pattern have often centered on an item being a loss-

leader (e.g., Chevalier et al., 2003), but Nevo and Hatzitaskos (2005) offer a novel if more

prosaic explanation that we follow. If high demand periods are characterized not only by

an outward shift of demand but also by an increase in demand elasticity, then firms with

market power may respond to the increased elasticity by lowering markups. Likewise, if

higher purse races attract more elastic bettors, then profit maximizing bookies will respond

by lowering their implied takeout rates.4 The structural model from which we derive our

reduced form model allows for just this sort of demand rotation. The resulting estimates

indicate that the model reconciles the observed negative correlation of purse and takeout

with the expectation that bettor demand should be higher for higher purse races by letting

the slope of the bookie’s residual demand become flatter.

The reduced form parameter estimates are insufficient to conduct any policy experiments,

as most estimates are only identified up to scale. We return to our originally posited rep-

resentative bettor and calibrate the price-disutility parameter from a previously estimated

own-take elasticity for Kentucky and average race characteristics from Churchill Downs,

thereby identifying all parameters of the structural model. Using these parameters, we back

out what bookie variable profits and welfare would have been under hypothetical regulatory

regimes. These results indicate that restricting Australian bookies to common takeout rates

(instead of the observed variable rates) would have reduced bookie variable profits by 3-6%.

This compares to the 7.7% increase in variable profits that our preferred elasticity measure

suggests would occur if Kentucky regulators reduced racecourse takeout for win bets from

16% to 14%.

We next lay out the institutions of pari-mutuel wagering on horseracing in the U.S.

and the hybrid wagering of Australia that allows both pari-mutuel and fixed-odds bets. A

simple model links a bookie’s observed odds to the implied takeout rate, which becomes our

4This can be rationalized by the presence of a core group of price-insensitive bettors (addicts) whose

influence is lessened when more price-sensitive bettors (tourists) attend higher visibility races.

4

primary variable of interest. We introduce our model of a representative bettor’s demand for

horserace wagering and consider the equilibrium supply-side relationships between implied

takeout rates and race characteristics. After discussing the data, we estimate descriptive and

reduced form regressions, and we close with a discussion of our results from the calibration

exercise.

1 Background

1.1 Institutions: American and Australian

Horse race gambling in the U.S. uses the pari-mutuel format exclusively.5 Takeout rates in

the US tend to be set directly by state government or by the state’s regulatory body over

gambling, though some states offer racetracks limited discretion.6 As of 2008, takeout for

win bets ranged from California’s 15.4% to Arizona’s 20% (HANA 2008). Kentucky, the

state which gives us the race characteristics for our calibration exercise, had a relatively low

takeout rate of 16% for win bets. Takeouts for exotic bets on multi-horse outcomes (e.g.,

exacta, quinella, Pick 6) are also regulated and tend to be several percentage points higher

(e.g., Churchill Downs has a takeout of 19% for those non-simple bets). Most states have

excise taxes on handle. For a sense of the magnitudes of handles and the related taxes,

Churchill Downs in the 2009 season had about $649M in handle on which it paid about

$20M in tax.7

In the pari-mutuel format, bettors make wagers on horses in the time leading up to the

race, but, as posted odds are preliminary, these wagers are for an unspecified price. Payouts

are based on final odds and depend on how the handle is distributed across the field of horses

at race time. For simple bets (such as the win-bets that we observe in our Australian data),

the racetrack subtracts a percentage equal to the takeout and then returns the remaining

money to the bettors who placed wagers on the winning horse proportionally to the amounts

wagered. Odds for any given race are therefore determined entirely by how bettors decide

to wager. These wagers can be made at the racetrack or at off-track betting facilities.8

5After gambling was prohibited in almost all American states in the early 20th century, racetrack-operated

pari-mutuel wagering on horse races was reintroduced in many revenue-starved states during the Depression,

with the new condition that excise taxes were placed on handle.6New York, for example, mandates minimum takeout rates of 15% for win/place/show bets, though it

appears that only Tioga Downs since its recent reduction is presently at those minima.7Churchill Downs 2009 annual report, p. 48.8The Interstate Horseracing Act of 1978 (Public Law 95-515) stipulates that off-track betting facilities

are subject to the same regulations regarding takeout as the racetracks themselves and that such facilities

5

Fixed odds gambling in horse racing (as can be found in Australia, Ireland, the United

Kingdom, and several other countries) differs from pari-mutuel wagering in several ways. The

most prominent distinction is the existence of the bookmaker, an individual who is actively

setting odds. As the format’s name implies, odds offered to a bettor are fixed, though these

odds may be changed for subsequent bettors. Foremost to this analysis, the takeout (the

expected percentage of the last dollar bet that is kept by the bookie) is implicitly determined

by the set of odds chosen by the bookmaker and thus can vary across time, racetracks and

races.

Australia, like its Imperial kin, allows gambling using both a fixed odds format and a

pari-mutuel format. There are 379 racetracks in Australia, though only 17 are considered

large. Major racetracks in the same city rarely operate on the same day.9 While Saturday

races tend to draw the largest crowds, Wednesday and Friday (midweek) races are also held.

A number of independent bookmakers (typically 20-40) at these racecourses compete for

bettor business against one another, against the on-site pari-mutuel system, and against

all off-site gambling options. Each bookmaker should be thought of as a three-person team

consisting of the bookie, the penciler (who records odds), and the ledger (who records bettors’

wagers). Depending on the state, the pari-mutuel system is either state-run or operated

under substantial regulation by a for-profit firm. The pari-mutuel takeout rate in New South

Wales (Sydney) and Victoria (Melbourne) varies by bet type; the pari-mutuel takeout rate

for straight win bets is 14.5% in both cities. Pari-mutuel takeout in Queensland (Brisbane)

is regulated differently in that the blended takeout (weighted average of simple and exotic

bet takeouts) cannot exceed 16% over a twelve-month period and no takeout rate can exceed

25%.

The horses that are slated to race are known in advance of race day. Opening odds from

the bookmakers are posted approximately 30 minutes before race time, and changes to these

odds are periodically made prior to the posting of the official starting prices. As shown in

McAlvanah and Moul (2011), the takeouts implied by these fixed odds start out relatively

high (∼30%) and tend to fall as the race approaches. This decline occurs as the risk to thebookie of a bettor with inside information falls and as the value to the bettor of fixed odds

wagers relative to pari-mutuel wagers becomes smaller. In the data and throughout this

paper, a wager’s gross odds is the amount for each dollar wagered that is returned to the

bettor in the event of his horse winning. For example, a $1 wager on a winning horse with

be at least 60 miles from the nearest racetrack.9In our sample, two racetracks in the same city are open on only 2 of our 241 Saturdays.

6

listed odds of 4 would pay back $4 (the original $1 plus the $3 of winnings). The price of a

wager is the reciprocal of those odds, and so the above wager would have a price of 0.25.

Two commonly used measures of bookies’ profit potential are the margin and takeout.10

The margin is defined as the amount of a marginal dollar wagered that is retained by the

bookie as a proportion of the amount returned to bettors. The takeout is defined as the

amount of a marginal dollar wagered that is retained by the bookie as a fraction of the total

amount wagered. For example, a 25% margin corresponds to the bookie retaining 20% of

the total amount wagered as takeout and paying out 80%. The connecting formulae between

margin and takeout are thus = +1

and = 1− . Both the margin and takeout should

be weakly positive, else there exists an arbitrage opportunity. While bookie margin has

instructive parallels with Arrow-Debreu prices that sum to more than one as bookies impose

the equivalent of a tax, we prefer the implied takeout in order to facilitate comparisons with

the competing and American pari-mutuel regimes. All of our empirical results are robust to

employing bookie margin instead of implied takeout rates as the dependent variable.

1.2 Transforming observed odds into implied takeout

We now detail assumptions under which the bookmaker’s expected takeout for a race can

be constructed from a set of observed odds. We assume that bettors obtain sufficiently high

recreational utility from gambling as to always wager on a race and that they decide on

which horse to bet on the basis of the expected monetary payoff, assuming risk neutrality.

Our model of bettors is thus a special case of Ottaviani and Sorensen (2010) without private

bettor information so that bettors share common beliefs about race outcomes. Imperfectly

competitive bookmakers set odds , the gross payout to a winner of a $1 wager on horse k

winning the race. Let denote the bookie’s subjective probability of horse k winning the

race. The expected takeout on horse k is thus = 1 − . In expectation, the bookie

retains of every dollar wagered on horse k and pays out . Let denote a bettor’s

subjective probability of horse winning the race. Bettor equilibrium conditions imply that a

bettor is indifferent between a wager on any two horses: = ∀ . These conditionsalso correspond to the bookie maintaining a balanced book, where the bookie is guaranteed

a riskless return. When combined with the fact that subjective probabilities sum to one

(P

= 1), our system contains K equations for K horses. For a given set of observed odds

10An alternative term for the margin is the overround, and alternative, more colorful terms for the takeout

are the juice, the vig (short for vigorish), the edge, and the house edge.

7

in equilibrium, one can uniquely determine the bettor subjective probabilities: =11

.

Note that the converse is not true, as bettor subjective probabilities do not correspond to

a unique set of odds. Bettor subjective probabilities determine only the ratio of odds; for

example, 12=

21, and 1

2=

31for a three-horse race. The bookie has the capacity to fix

the magnitude of the odds for any one horse and thus implicitly the takeout for the race.

Consider the following simple three-horse race example. Substituting =1−

into the

consumer indifference conditions yields(1−1)1(1−2)2 =

21and

(1−1)1(1−3)3 =

31, which simplifies

to 1−11−2 =

1221

and 1−11−3 =

1331. As before, we have more unknowns than equations, and

horse-level takeouts are not uniquely identified by the subjective probabilities. Without

loss of generality, assume the bookie sets the odds on horse 1 and thus determines 1. The

consumer indifference conditions then imply that 2 = 1−(1−1)2112and 3 = 1−(1−1)3113

.

These equations indicate that a bookie maintaining a balanced book cannot set individual

horse-level takeouts independently of each other, due to the inter-linking of odds imposed

by the bettor equilibrium conditions. The expected race-level takeout would thus appear to

depend on , , and for all k.

The expected race takeout is then the sum of individual horse-level takeouts, weighted

by each horse’s fraction of the total amount wagered. In the general case in which bookie

and bettor subjective probabilities may not coincide, we follow the pari-mutuel system and

assume that the fraction wagered on a particular horse coincides with bettor subjective

probability for that horse, so that =P

. Substituting = 1 − and our prior

expression for equilibrium subjective probabilities as the relative share of summed reciprocal

odds yields the formula for takeout:

=X

µ1P 1

¶(1− ) =

µ1P

1

¶X

µ1

−

¶= 1−

µ1P

1

¶(1)

Alternatively, the race-margin is given by

=X

1

− 1 (2)

Intuitively, the extent to which the reciprocal gross odds (i.e., the wagers’ prices) sum to

greater than one signifies bookie’s expected profit margin.

We now link the race takeout (and implicitly the margin) to the bookmaker’s presumed

objective function of expected profits. Let Λ denote the number of dollars wagered on horse

k, and let denote the total amount wagered on a race with a bookmaker. The expected

profit for the race will then be () =P

Λ. Using the prior assumption that the amount

8

of money wagered on a particular horse as a share of the total amount wagered coincides with

bettor subjective probability on that horse (i.e., Λ= ), then () =

P = ∗ .

If the total amount wagered depends on the takeout so that ( ), then the bookie chooses

the level of odds and implicitly the takeout to maximize ( ) ∗ . The bookie’s problem isthus analogous to a revenue-maximizing firm facing a downward-sloping demand curve.

2 Model

We begin by considering the most general case of our bookie’s profit-maximization problem.

Bookmakers choose their margin (and implicitly their takeouts) to maximize their expected

profits conditional on having a balanced book. Letting denote the relevant residual demand

for win bets, the first order condition for the profit maximization problem is

()

= +

= 0 (3)

If race characteristics are exogenous to the bookmaker, then appealing to the Implicit

Function Theorem yields the comparative statics of race characteristics on bookmaker take

at the optimum.

= −

+ 2

2+ 2

2

(4)

The denominator is negative by necessity to ensure a maximum. The sign of (that is, the

sign of a coefficient in our descriptive regressions) then depends on the sign of + 2

.

If the impact of on the slope of the demand of betting is insignificant (i.e., 2

≈ 0),then descriptive estimates

will be the same sign as the impact of race characteristics on

the amount of money wagered . If, however, changes in affect the slope of the demand

curve (i.e., 2

6= 0), may not mimic

in sign.

We posit a representative bettor who has a linear demand for race-time win-bets.11 Let

denote this demand in AUD$ wagered in racetrack i, race k, and period t:

= + − (1 + + ) + (5)

In the above, denotes race takeout (the price of wagering on the race). denotes a

matrix of race characteristics that shift demand, and (a subset of ) denotes a matrix of

characteristics that rotate demand. We allow for two unobserved disturbances ( and ); the

11Limiting our discussion to race-time bets matches the fact that we observe race-time odds and minimizes

the distinction between pari-mutuel and fixed-odds wagers for our cross-country comparison.

9

former captures ex ante determined characteristics that may influence the number and quality

of horses in the field, and the latter captures ex post characteristics. Respective examples for

the two are the race’s prestige and weather on the day of the race. This framework introduces

the obvious concern of omitted variable bias, as higher prestige races may generate larger

and more even fields and the econometrician would then be unable to distinguish bettors’

preferences on the race’s prestige from other observed race characteristics. While bettors

are unlikely to care directly about a race’s purse, purse and prestige are presumably highly

positively correlated. We therefore address this concern by using race-purse as a proxy

for race-prestige ( = ) and henceforth subsume purse into our and

matrices.

The aggregated demands for win-bets can be found bymultiplying this representative con-

sumer’s demand by some fraction of racetrack i’s market population for period t¡()

¢.

Let denote this aggregated demand:

=

¡()

¢− ¡()¢ (1 + ) +¡()

¢(6)

As Louisville has a single major thoroughbred racecourse (Churchill Downs) which only

permits pari-mutuel betting and has no off-track betting facilities nearby, we assume that

= 1 in that case. This demand specification is exactly our endgoal for that market,

and we will employ it when calibrating against the Thalheimer and Ali (1998) own-take

elasticity estimate and the CM summary statistics. Australian betting and its consequent

demand estimates differ in that bettor demand in Australia is divided between pari-mutuel

wagering and fixed-odds wagering and between on-track and off-track wagering. Using data

from the Australian Racing Book (2008) and assuming that tracks do not serve as same-day

competitors to each other, we set = 0084.12

We will further assume that our observed bookmaker at racecourse i in period t is one

of bookies. As the summary statistics will show, the observed bookie takeouts are quite

similar to the pari-mutuel takeouts for the racetrack’s state for Sydney and Melbourne and

higher than the pari-mutuel takeout in Brisbane. When combined with the observation that

racetracks have many (at least 20 and up to 45) bookies, this suggests that bookies engage in

(perhaps tacit) collusion rather than imperfect competition.13 We estimated our model under

12Australian Racing Fact Book 2007/08, pp. 66, Table 86: equals the ratio of summed 2002-07 bookmak-

ers on course totals to sum of comparable total wagering. While it would have been preferable to specify a

model that permitted substitution among the different betting alternatives, we lacked the data to implement

such a model in any meaningful way.13The tourist trap model of Diamond (1971) could also rationalize this result, though the bookies being

10

the differing assumptions of perfect cartel behavior and symmetric Cournot behavior, and

the levels of demand that would rationalize observed takeouts under the Cournot assumption

were implausible (e.g., each bookie-team capturing AUD$72,000 in a eight-race Saturday).

This is driven by observed bookie takeouts being so close to the pari-mutuel takeout and

the assumption that pari-mutuel takeout is either at or above the revenue-maximizing level.

We therefore maintain the hypothesis that our sampled bookie is part of a cartel and limit

our theoretical discussion to that case. The bookie’s residual demand is thus his share of

the market demand.

Our demand specification in (6) then implies inverse demand of

=

µ

1 +

¶µ

¶+

(1 + )−µ

1

() (1 + )

¶ (7)

Our bookie maximizes revenue by setting odds that imply a takeout of

∗ =

µ

1 +

¶µ

2

¶+

2 (1 + )=

µ

1 +

¶µ1

2

¶ + (8)

This is the standard result of revenue-maximization under linear demand, where a monop-

olist will optimally choose a price equal to half of demand’s vertical intercept (choke-price).

Our reduced form can therefore identify the structural parameters that are interacted with

takeout (i.e., demand rotating s) but demand shifting s are identified only up to scale:

=

. Note that neither the population-weighting parameter nor the population variable

appears in this pricing equation; they will arise only in our cross-country calibration exer-

cise. Residuals will be heteroskedastic by construction, and robust standard errors will be

required.

3 Data

The data set, courtesy of the Australian Bookmakers Association, includes near-complete

fixed odds betting information from Saturday races from November 2, 2002, to August

4, 2007, at nine Australian tracks.14 These racetracks lie in three different markets and

states–four in Sydney, New SouthWales; three in Melbourne, Victoria; and two in Brisbane,

Queensland. Odds are taken from a sampled bookie for each racecourse and day. The

data originally contained 5,213 racing starts. Six races were dropped because of apparently

in such close proximity at the racetrack makes a search cost explanation unlikely.14The data did not include eight Saturdays, five of which occurred from November 2002 through January

2003. We thus observe 96.8% of Saturday races between November 2, 2002 and August 4, 2007.

11

erroneous data (for example, all horses having the same odds). Another 190 races were

dropped because they included late scratches.15 The remaining 5,017 observations were then

matched with the races’ total purse value where possible.16 Because purse data were not

available for all races, the final data set includes 4,661 observations. This contrasts favorably

with the sample sizes employed by Shin (1993) and Cain et al. (2003) which respectively

had 136 and a maximum of 1430 observations. Other than purse data being less available

in Victoria than New South Wales and Queensland (82% vs. 97% and 98%), the race

characteristics when purse was and was not observed are similar.

For each race, we observe the date, racetrack, size of field, ordinal placement of race

(e.g., second of day), purse value, and the starting (i.e., final) odds on horses from the sam-

pled bookie. The starting odds were used to calculate bettors’ subjective probabilities, the

bookmaker’s takeout, and various measures of dispersion in the field (e.g., Gini coefficients,

variance of subjective probabilities, entropy). While all dispersion measures yielded similar

results, we will focus on the variance of the logged subjective probabilities (VarLP) as this

is the best match to CM which we use for our later calibration exercise. We operationalize

the race’s ordinal placement by creating an indicator variable Late that equals 1 if the race

is the eighth of the day or later. As late-day races are often the most publicized of the day,

we found that this variable sufficiently captured that form of intraday variation. Finally, we

include a week-based time trend over the sample to capture any secular changes in demand.

Table 1 reports summary statistics for the full Australian sample and broken down by

market, as well as CM’s 1994 sample.17 Of primary interest is the bookie takeouts. Takeouts

differ markedly in levels across markets, with Sydney bookies retaining 13.6% of money

wagered, Brisbane bookies retaining 21.7%, and Melbourne bookies in between with 15.8%.

We have no compelling explanation for the elevated Brisbane takeouts, though it seems

likely to be related to anecdotal observations that Brisbane bettors are largely domestic

Australians while Sydney and Melbourne tracks receive more wagering from potentially

more price-sensitive southeast Asian bettors. There is substantial variation in takeouts

across markets, but over four-fifths of the variation within markets occurs in races on the

same day at the same track. To the extent that weather is relatively constant within a day,

15Late scratches occur when horses drop out of races after bookmakers publish opening odds but prior to

the start of the race. McAlvanah and Moul (2011) consider how this sort of late change to the field might

lead to deviation from our profit-maximization assumption.16Purse values were obtained from Racing Information Services Australia (RISA), Racing New South

Wales, and Queensland Racing.17CM do not restrict themselves to Saturday races, but they do limit their data set to races that pay out

to four places. As the Kentucky Derby in 1994 paid out to five places, it was excluded from their sample.

12

this strongly suggests that race characteristics play an important role in the takeouts that

bookies set.

We deflate purse to 1994 US $ to facilitate comparisons with the Louisville data.18 Races

at Melbourne and Sydney racetracks offer substantially higher purses than those held at

Brisbane or Louisville tracks, but Brisbane’s average purse is comparable to that of Louisville.

All Australian markets show higher variance in purse than Louisville, though this is lessened

somewhat when the 1994 Kentucky Derby (excluded from CM) is included. Australian races

tend to have larger fields with more variation than the observed Louisville races; this is

driven in large part by the fact that Australian racetracks have a number of fields with at

least 20 horses, while the Louisville sample’s maximum field size is 12. Ex ante dispersion of

the field varies markedly across the three Australian markets, and the Louisville races show

comparable dispersion.

Table 2 presents simple correlations among the observed variables of interest and means

conditioning on a race’s ordinal placement for the entire Australian sample and broken

down by market. Perhaps the most striking figures are the large and positive correlation

coefficients between field size and take. While consistent with Shin’s story of insider trading,

they could also reflect bettor demand for races with more horses (as found in CM) or field

size capturing unobserved race-quality measures. The negative correlation between take and

purse for Melbourne is superficially counterintuitive and appears to run against the results

of CM.19 Even when that correlation is positive, it is of a smaller magnitude than one might

expect. Variable means that condition on whether a race is late in the day indicate that late

races have higher takeouts, larger fields, and (weakly) less dispersion of horse-ability. While

late races have larger purses in Melbourne, data surprisingly indicate that late races have

smaller purses in Brisbane and Sydney.

4 Results

4.1 Empirics

Table 3 displays the descriptive results and t-statistics when takeout is regressed on various

race characteristics. These estimates should be interpreted as the equilibrium impact of the

18The exchange rate in 1994 and 2002-07 was similar and relatively stable at US $0.74 to AU $1. We use

US-CPI data to adjust for inflation.19The negative correlation between purse and takeout for the entire sample is primarily driven by the

fact that Brisbane has low purses and high takeouts while Melbourne and Sydney have high purses and low

takeouts.

13

characteristic on bookie takeout. Given the widely differing levels of takeout across markets,

we include market fixed effects for the full sample, and we also consider market-specific

regressions. Preliminary estimates indicated an increasing and concave relationship between

takeout and field size that was well accommodated by including field size in logs, and so we

proceed using that transformation.

All estimates indicate that takeout falls with purse (though insignificant in the Sydney

regression) and field dispersion (though insignificant in Brisbane regression) and rises with

field size and being late in the day. The time trend polynomial estimates imply that takeout

falls early in the sample, stabilizes and then falls again toward the sample’s end, though

these transition points vary across markets.

We highlight two points from these descriptive regressions. First, coefficients appear to

differ enough across markets to warrant market-specific, rather than pooled, regressions going

forward. Second, with the exception of the negative impact of purse on takeout, these results

are largely consistent with the extant literature. CM find on-site pari-mutuel handle to be

increasing in field size and decreasing in field dispersion. As stated above, Shin (1993) and

the related papers have already documented the positive relationship between field size and

takeout. The purse coefficient, however, stands out. In addition to being counterintuitive, it

appears to contradict our primary purpose for its inclusion, namely that it serves as a proxy

for unobserved (to the econometrician) ex ante race quality. It is this apparent paradox

and the potential resolution proposed by Nevo and Hatzitaskos (2005) that motivates our

particular structural model and its reduced form.

We display our estimates for the reduced form model in Table 4. As discussed above,

our maintained hypothesis is that the observed bookie is part of a bookmaker-cartel, and

so our linear demand implies that the observed takeout is simply one-half of the market

demand’s vertical intercept (i.e., choke price).20 The prior descriptive regressions are merely

special cases of the reduced form in which = 0 for all variables. The nonlinear least

squares estimates for Brisbane and Melbourne reconcile our prior expectations and purse’s

descriptive impact on demand. In both markets, increases in purse shift demand outward

but also increase price sensitivity. Melbourne’s estimates especially showcase the value of the

reduced form model. Those estimates show that, while purse’s net impact is a combination

of countervailing forces (outward shift and more price sensitive), field size’s net impact is

a combination of two forces working in the same direction (outward shift and less price

20Identification of -parameters comes from second-order effects and interactions that were not explored

in the prior simple descriptive results.

14

sensitive). While not shown, when is set to zero in the Brisbane regression, is

positive and highly significant (t-stat ≈ 16).Estimates using Sydney races, though, are less satisfactory. While not significant, es-

timates indicate that increasing purse shifts demand inward and makes bettors less price

sensitive. The latter results could be rationalized, but the former runs counter to both intu-

ition and the results of CM. It is unclear why our model would accommodate Melbourne so

readily and yet struggle with Sydney, even though they both represent high-visibility, high-

quality gambling markets. For our purposes, these results imply that a representative bettor

inferred from Sydney bookie takeouts will be irreconcilable with our Louisville situation. We

therefore focus our calibration exercises on the Brisbane and Melbourne estimates.

4.2 Calibration exercise

We begin by inferring the price-disutility parameter from Louisville’s observed population,

sample means from CM, the Kentucky-specific own-take elasticity of Thalheimer and Ali

(1998), and the -parameters of our reduced form model after deflating purses to 1994 USD.

The linearity of our structural model implies that own-take elasticity (evaluated at sample

means) is

= ∗ ¡− ¡1 + ¢¢ ∗µ

¶(9)

so is calibrated as b = µ −1 + b

¶µ

¶µ1

¶(10)

In addition to the estimates from Table 4, we use a 1994 Louisville population of 676,404,

Thalheimer and Ali’s estimate of = -1.85, the state takeout for win bets of 0.16, and sample

means as found in Table 1.21

Table 5 displays the parameter values that result when using the Brisbane and Mel-

bourne reduced form estimates (3.24 and 3.36, respectively). Given the small Louisville

sample means and comparable estimates of , it is not surprising that the markets’ implied

s are so similar. We then use each value for to compute per capita handle for each of

our observed races. Results suggest that Melbourne’s per capita money wagered is about

double that of Louisville and that Brisbane’s is even greater. This is consistent with other

data showing Australians’ pronounced propensity to gamble, even compared to a U.S. city

21This Louisville population is a linear extrapolation of the 1990 and 2000 Census observations of the

Louisville consolidated city-county.

15

where wagering is relatively easy. Interacting these per capita values with the city popu-

lations using on-track bookies yields the average amount wagered with bookies each race.

Multiplying those aggregate amounts by the implied takeout gives a measure of aggregate

cumulative takeout (variable profit) by race. To the extent that bookies fail to achieve our

profit-maximizing ideal, this figure is an overstatement, but it may also be understated as

bookies capture rents on bets well before racetime. We then compute a rough measure of

per-bookie variable profit by dividing this aggregate figure by the typical number of bookies,

finding that the average three-person bookie-team in Brisbane earns $940 per race and the

average Melbourne bookie-team $900 per race. Over our sample’s complete years (2003-06),

these figures suggest that a Brisbane bookie-team who worked every Saturday race for a year

at one of the racetracks would earn a gross income of about $170,000, from which associated

expenses and track fees would have to be paid. Melbourne racetracks have races on fewer

days, and a comparable bookie-team would earn a gross income of about $100,000. These

implied figures seem somewhat high for three individuals, but, without information on the

fees that bookies must pay in order to be on-site, it is difficult to gauge the extent of the

overstatement.

Our recovered structural parameters also enable us to consider how their implied impacts

compare to the elasticity estimates of CM. Table 5 displays CM’s 95% confidence intervals

for purse elasticity, field size elasticity, and dispersion hemi-elasticity. Neither Brisbane’s

estimates nor Melbourne’s estimates match especially well, as both imply purse effects well

below and field size effects well above those of CM. For both elasticities, however, Brisbane

is much closer to Louisville than Melbourne is. On the dispersion measure, Brisbane’s

implication is within the confidence interval while Melbourne’s is not. When combined with

the fact that the variation in the Louisville sample is most similar to that of the Brisbane

sample, we cautiously judge that implications from the Brisbane estimates are likely to have

more relevance for our Louisville question.

Levels and elasticities are interesting side-tests, but our primary concern is the predicted

impact of allowing a U.S. pari-mutuel racetrack the flexibility to vary its takeout across

races.22 We address this by considering the converse question of what would happen if our

bookmaker cartel were restricted to charge the fixed profit-maximizing takeout

=1

2∗P

( + )P (1 + )

(11)

22These percentage impacts are therefore generally robust to any proportional overstatements that the

prior figures may display.

16

We compare the outcomes under this counterfactual to the previously inferred outcomes

under perfectly variable takeouts. The implication of these results is then the change that

would result if constant pari-mutuel takeouts were already set at the unit-elastic level.

Our first counterfactual considers the comparison between all tracks in a market facing a

common fixed takeout, and the second considers the case of when each track may have its own

fixed takeout. Consistent with Schmalensee (1981), moving from a fixed to variable takeout

in either market raises cumulative takeout, substantially decreases consumer surplus, and

marginally decreases welfare.23 There appears to be minimal heterogeneity across racetracks

that would lead to markedly different outcomes under the two counterfactual scenarios.

Brisbane impacts are uniformly smaller (in absolute value) than Melbourne’s, and, given our

prior arguments, we will focus on the Brisbane predictions. Allowing flexible takeouts raises

cumulative takeout by 3%, lowers consumer surplus by over 8%, and lowers welfare by 1%.

To put those figures into context, the Thalheimer and Ali (1998) elasticity estimate of -1.85

implies that dropping Kentucky’s takeout for win bets from 16% to 14% would raise handle

by 23.1% and cumulative takeout by 7.7%.

Similar to other states, the state of Kentucky levies an excise tax on handle on live races

of 3.5% (1.5%) for large (small) tracks, where $1.2M of daily average handle is the size-

threshold (KRS 138.510). Our linear functional form implies that moving from a fixed to

variable takeout will have no impact on cumulative handle, and so the current excise tax

regime would yield no gains to the state from a reform that increases takeout flexibility.

If, however, Kentucky were to tax cumulative takeout instead of handle, then some of the

gains would go to the state government where they could displace or prevent other taxes

with higher negative welfare consequences. Given the presently fixed takeouts, this change is

largely semantic, in that the 3.5% excise tax on a large track’s money wagered is equivalent

to a 21.875% tax on cumulative takeout on simple win/place/show bets.

5 Conclusions

While bookies have no role in pari-mutuel wagering in the U.S., we have provided a model

to link our Australian estimates to potential reforms of the American horse racing industry.

Our estimates highlight the value of the incorporation of theory into empirical work and also

provide more support for the idea that many observations that appear paradoxical within a

23Our linear functional form implies that moving from a fixed to variable takeout will have no impact on

handle.

17

model of perfect competition can be readily reconciled in a model that allows market power.

Finally, our estimates give some idea of the impacts that would follow reform that grant

racetracks flexibility in setting takeouts.

Economists are broadly interested in cases when deregulation might improve welfare,

and pari-mutuel wagers on horse racing, while a small industry, illustrates how cross-country

study may provide critical empirical variation to achieve answers to relevant questions. Given

the possibility that proposed flexibility would lower consumer surplus and even welfare, we

hesitate to advocate too strongly for it. Nevertheless, the American horse racing industry is

in a sufficiently parlous state that a proposal that may increase track profits and viability

as well as government coffers without reducing welfare is worth some consideration.

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18

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19

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[25] Tioga Downs, Announcement: “NY Board approves Tioga

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ing+Canada/5084481/story.html

20

Table 1: Summary Statistics of Australian (2002‐07) and Louisville/Churchill Downs (1994) data

    ‐‐ Louisville data from Coffey and Maloney (2010), Table 1a

All‐AUS Brisbane Melbourne Sydney Louisville

# Tracks/Races 9/4661 2/1672 3/1261 4/1728 1/566

Pari‐mutuel TOb‐‐‐ ~16%/25%c

14.5% 14.5% 16%

Implied bookie TObmean 17.12% 21.74% 15.84% 13.59% ‐‐‐

std‐all 5.28% 3.87% 4.04% 3.79% ‐‐‐

std‐by track 3.87% 3.86% 3.99% 3.78% ‐‐‐

std‐by track‐yr 3.71% 3.72% 3.86% 3.61% ‐‐‐

std‐by track‐day 3.23% 3.22% 3.24% 3.24% ‐‐‐

Betting poold mean ‐‐‐ ‐‐‐ ‐‐‐ ‐‐‐ 153,410

std ‐‐‐ ‐‐‐ ‐‐‐ ‐‐‐ 110,410

Pursed mean 54,460 29,829 71,724 65,695 28,748

std 116,370 45,477 132,543 144,191 26,122

min 11,525 13,648 13,130 11,525 7,320

max 1,881,251 612,002 1,792,082 1,881,251 233,950

Field Size mean 11.0 11.9 11.0 10.2 10

std 2.9 2.9 2.8 2.7 2

min 4 5 4 4 4

max 21 20 21 20 12

VarLPe mean 0.90 0.79 0.67 1.16 1.01

std 0.52 0.37 0.35 0.62 0.38

min 0.022 0.035 0.077 0.022 0.09

max 4.96 2.67 2.91 4.96 2.28

Latef mean 0.15 0.12 0.16 0.17 ‐‐‐

a Louisville dataset excludes 1994 Kentucky Derby. If Derby (Purse=$500,000, Field Size = 14 with 11 unique win‐bets, VarLP = 0.344) 

  included, Purse's mean and standard deviation rise to $29,579 and $32,743, but other variables' means and standard deviations are 

  essentially unchanged.  

b All takeouts apply to win‐bets.

c Pari‐mutuel blended takeouts in Brisbane cannot exceed 16% over 12‐month period and cannot exceed 25% for any bet‐type.d Betting pool and all purses in 1994 US $ (multiply by 1.637 for 2002 AUS $)e VarLP=Var(ln()) where  is bettor subjective probability implied by observed oddsf Late is indicator for race being eighth or later in day

Table 2: Correlations and conditional meansa

All markets (n=4661)

Take Purse Field Size VarLP Trend Late=0 Late=1

Take 1.00 ‐0.09 0.55 ‐0.25 ‐0.10 Take 16.79% 18.98%

Purse ‐0.09 1.00 0.14 0.12 0.01 Purse 0.090 0.084

Field Size 0.55 0.14 1.00 ‐0.07 0.02 Field Size 10.8 12.6

VarLP ‐0.25 0.12 ‐0.07 1.00 0.08 VarLP 0.90 0.85

Trend ‐0.10 0.01 0.02 0.08 1.00

Brisbane (n=1672)

Take Purse Field Size VarLP Trend Late=0 Late=1

Take 1.00 0.02 0.38 ‐0.04 ‐0.08 Take 21.46% 23.79%

Purse 0.02 1.00 0.32 0.12 0.10 Purse 0.050 0.040

Field Size 0.38 0.32 1.00 0.06 0.10 Field Size 11.8 13.2

VarLP ‐0.04 0.12 0.06 1.00 ‐0.04 VarLP 0.79 0.79

Trend ‐0.08 0.10 0.10 ‐0.04 1.00

Melbourne (n=1261)

Take Purse Field Size VarLP Trend Late=0 Late=1

Take 1.00 ‐0.07 0.55 ‐0.16 ‐0.18 Take 15.47% 17.79%

Purse ‐0.07 1.00 0.17 0.16 0.00 Purse 0.115 0.128

Field Size 0.55 0.17 1.00 0.03 ‐0.03 Field Size 10.7 12.5

VarLP ‐0.16 0.16 0.03 1.00 0.16 VarLP 0.68 0.62

Trend ‐0.18 0.00 ‐0.03 0.16 1.00

Sydney (n=1728)

Take Purse Field Size VarLP Trend Late=0 Late=1

Take 1.00 0.08 0.68 ‐0.19 ‐0.15 Take 12.99% 16.48%

Purse 0.08 1.00 0.19 0.10 ‐0.02 Purse 0.112 0.085

Field Size 0.68 0.19 1.00 ‐0.04 ‐0.02 Field Size 9.7 12.3

VarLP ‐0.19 0.10 ‐0.04 1.00 0.12 VarLP 1.18 1.05

Trend ‐0.15 ‐0.02 ‐0.02 0.12 1.00

a Purses in 2002 AUS $Ms, implied take on win‐bets, VarLP=Var(ln()) where  is bettor subjective probability implied by 

  observed odds, Late is indicator for race being eighth or later in day

Table 3: Descriptive regressions (OLS) on implied win‐bet takeout T (in percentage points)a 

Sample         All‐AUS       Brisbane    Melbourne        Sydney

#Tracks/Races         9/4661          2/1672        3/1261          4/1728

E(T)         17.12%          21.74%        15.84%         13.59%

b /t/ b /t/ b /t/ b /t/

Purse ‐1.13 2.38* ‐3.21 3.64** ‐2.68 6.40** ‐0.18 0.60

ln(FS) 7.73 22.41** 6.28 17.12** 8.41 24.56** 8.39 25.50**

VarLP ‐0.88 7.02** ‐0.32 1.37 ‐1.19 5.12** ‐0.87 9.52**

Late? 1.28 8.22** 1.53 6.03** 0.87 3.95** 1.32 6.57**

Trend ‐8.72 7.31** ‐8.91 5.56** ‐3.89 2.45* ‐12.58 10.39**

Trend2 7.34 7.85** 7.98 5.77** 4.80 3.50** 9.15 8.85**

Trend3

‐1.89 8.51** ‐2.10 6.05** ‐1.62 4.67** ‐2.02 7.80**

Intercept ‐‐‐ 9.35 10.00** ‐1.92 1.92 ‐0.01 0.02

R2        0.6538        0.2172         0.4116        0.5382

a Results using all markets employ market fixed effects; purse deflated to 2002 AUS $Ms; Trend reflects number of  weeks since

  start of sample (divided by 100); all t‐statistics reflect White correction and those using all‐market  sample also reflect  clustering

  at the racetrack level and use of Student t distribution; * and ** indicate 95% and 99% levels of significance

Table 4: Reduced Form estimates (NLLS) on implied win‐bet takeout T (in percentage points)a 

            B = Pop*(X ‐ (1+Z)T + ) Structural demand            T* = (X/(1+Z))(1/2) + U, where  = / Profit‐maximizing takeout

Sample            Brisbane         Melbourne             Sydney

#Tracks/Races              2/1672             3/1261              4/1728

E(T*)              21.74%             15.84%              13.59%

b /t/ b /t/ b /t/

Purse 0.85 3.20** 0.66 4.53** ‐0.043 1.67

ln(FS) ‐0.100 1.72 ‐0.110 3.17** ‐0.193 9.73**

Purse 31.32 3.98** 12.55 10.62** ‐1.76 1.02

ln(FS) 5.73 0.89 10.55 2.84** 4.31 1.65

VarLP ‐0.53 1.09 ‐2.06 4.01** ‐0.93 3.88**

Late? 2.34 2.83** 1.30 2.71** 1.29 2.27*

Trend ‐14.20 3.37** ‐5.91 1.76** ‐13.47 4.39**

Trend2 12.78 3.40** 7.48 2.49* 9.78 4.11**

Trend3 ‐3.37 3.45** ‐2.54 3.17** ‐2.16 3.81**

Intercept 23.48 3.51** 2.08 0.43 11.13 3.76**

R2             0.2180             0.4172             0.5464

a Reduced form assumes bookmakers acting as cartel; purse deflated to 2002 AUS $Ms; Trend reflects number of  weeks since

  start of sample (divided by 100); all t‐statistics reflect White correction; * and ** indicate 95% and 99% levels of significance

  

Table 5: Calibration results

  Reduced form model re‐estimated using purse in 1994 US $Ms and with Take in percentage

            T* = (X/(1+Z))(1/2) + U, where  = / Profit‐maximizing takeout

            B = Pop*(X ‐ (1+Z)T + ) Structural demand

  Matched against Thalheimer & Ali's (1998) KY‐specific own‐take elasticity  = ‐1.85           ‐1.85 =  = Pop*(‐(1+Z))*(T/B), so  = (‐/(1+Z))*(1/T)*(B/Pop)

 Louisville Brisbane Melbourne

‐‐‐ 3.24 3.36

Louisville observations/Australian implications for win bets  (in 1994 US $)a

Per capita $ wagered 0.23 0.56 0.43

Total $ wagered 153,410 84,010 134,750

Total $ retained 24,546 18,798 22,545

  Per‐bookie $ retainedb‐‐‐ 940 902

Retention rate 16% 22.38% 16.73%

Louisville s from 1994 (Pop = 676404), 95% confidence intervalsc

Purse [0.270, 0.431] 0.119 0.014

Field Size [0.226, 0.574] 1.046 1.826

VarLP [‐0.227, ‐0.043] ‐0.076 ‐0.307

Counterfactuals from takeout flexibility around optimal retention rate

  Case 1: All tracks in market face same and constant takeout rate over entire sample

% change in cumulative takeout 3.17% 6.61%

% change in consumer surplus ‐8.37% ‐15.57%

% change in welfare ‐0.98% ‐1.97%

  Case 2: Each track faces constant takeout rate over entire sample

% change in cumulative takeout 3.17% 6.39%

% change in consumer surplus ‐8.36% ‐15.15%

% change in welfare ‐0.98% ‐1.91%

a Louisville money wagered is total amount wagered with Churchill Downs, Australian money wagered is implied amount 

  wagered with on‐site bookmakers b Assumes 20 (25) bookmakers in each of Brisbane (Melbourne) racetracks  c Estimates taken from Coffey and Maloney (2010), Table 3. VarLP parameter is hemi‐elasticity.