Evidence of Adverse Selection from Thoroughbred Wagering.

Wimmer, Bradley S.

Brian Chezum [*]

Bradley S. Wimmer [+]

Previous research has shown the thoroughbred sales market to be affected by adverse selection. In the market, sellers who race as well as breed thoroughbreds will choose to keep thoroughbreds when their estimated private values exceed expected sales prices. The presence of asymmetric information leads these sellers to sell their low-quality horses and keep their best for racing. We extend the analysis by examining how bettors use similar information when wagering on thoroughbred races. We show, using a sample of two-year-old maiden races, that homebreds (those horses kept by their breeders for racing) are favored over otherwise similar nonhomebreds.

1. Introduction

In his Lemons Market example, Akerloff (1970) shows that some mutually beneficial trades will not occur when sellers have private information about the quality of goods. Essentially, a buyer's best estimate of the quality of any seller's good is the market average, and sellers of high-quality goods may not enter the market. Although there is little dispute over the theoretical underpinnings of Akerloff's Lemons Market, relatively few empirical studies present evidence illustrating this outcome. Some examples are Greenwald and Glasspiegel (1983), Gibbons and Katz (1991), Genesove (1993), and Chezum and Wimmer (1997).

These papers relate data on prices with distinguishing characteristics of sellers to show that sellers with "adverse" characteristics receive lower prices. For example, Chezum and Wimmer, examining the thoroughbred yearling sales market, show that prices commanded by sellers who also race thoroughbreds are lower than prices commanded by sellers who sell all of their thoroughbreds. Intuitively, breeders will take a thoroughbred to market when the expected market price exceeds the value they would receive from retaining the animal. If private information is important and costly to transmit, prices for thoroughbreds sold by racing-intensive breeders will be lower than those received for similar thoroughbreds sold by breeders who do not race. [1]

This paper extends this intuition by examining how bettors evaluate two-year-old thoroughbreds when they reach the track. If breeders adversely select the horses they sell, a horse retained by a breeder should be of a higher average quality. If betting markets are efficient, a finding that bettors expect homebreds (horses retained by their breeders) to outperform horses that were sold indicates that adverse selection is present in the market for thoroughbreds.

Studies of betting markets have found that bettors predict the outcome of horse races (and other sporting events), relatively accurately. [2] These studies show that bettors are able to aggregate disparate pieces of information efficiently. Use of betting information therefore provides an opportunity to examine how markets incorporate information on breeders' decisions to keep or sell thoroughbreds in settings other than a sale. Such a test of adverse selection is relatively unique to the literature because it does not rely on sales data to determine whether adverse selection is present in a market. [3] The use of race data allows us to compare the quality of goods retained by their producers with that of those offered for sale.

This prediction is clarified in section 2. Section 3 describes the data used to test our prediction and the empirical strategy. Using data from a set of races run by two-year-old Thoroughbreds conducted at the Keeneland and Saratoga racecourses in the summer and fall of 1995, we find that homebreds are favored over otherwise similar nonhomebreds as reflected by the post-time odds of a race.

2. Thoroughbred Sales Markets and Betting Behavior

In the thoroughbred industry, owners obtain thoroughbreds for racing by purchasing them privately, at auction, or through their own breeding operations. [4] In turn, breeders may be classified as one of three types: those who sell all of their thoroughbreds, those who race all of their thoroughbreds, and those who both sell and race thoroughbreds. Breeders who keep a portion of their crop are expected to use private information to determine which thoroughbreds they keep to race.

In the time before breeders take their thoroughbreds to market, they observe how their horses respond to other thoroughbreds, have access to their horses' complete medical histories, and are generally able to identify their thoroughbreds' temperaments. Although these factors do not predict future on-track success perfectly, they do give the seller an informational advantage over buyers. At thoroughbred auctions, information on a thoroughbred's breeding is available and buyers are allowed to inspect thoroughbreds prior to the sale. However, buyers do not have access to the information that the seller possesses. Because buyers do not have perfect information, sales prices reflect the average quality of thoroughbreds offered for sale with similar breeding and visual characteristics.

Sellers who also race are expected to use private information to determine which thoroughbreds to take to market. As in the standard lemons model, the presence of bad thoroughbreds forces the average price down, and the highest quality yearlings are likely to exit the market. If buyers know this, they expect the average quality to decline and, as in Akerloff (1970), the market may collapse. Genesove (1993) examines a model in which buyers and sellers have identical tastes but sellers are capacity constrained so that some thoroughbreds are sold for reasons other than adverse selection. The presence of capacity constraints generates an equilibrium with positive prices because buyers do not know whether a seller is selling a thoroughbred because it is capacity constrained or because the horse is being adversely selected. In this model, price reflects the average quality traded, and sellers take their lowest quality horses to market to ease their capacity constraints. This may describe the thoroughbred industry because participants who race are limited in their capacity to maintain a large stable. [5]

When horses reach the racetrack, they race for a portion of a purse that is typically funded through pari-mutuel wagering. [6] Consumers bet on the order of finish. Simple bets are those for win, place, and show (first, second, and third, respectively). A bettor receives a payoff when the horse on which he wagered finishes in the wagered position or better. For example, a show bet will pay if the horse finishes first, second, or third [7] Each wager type has its own pool, which is the sum of money bet on all horses for each type of wager. Payoffs are based on the relative proportion of money bet in the appropriate pool on each horse in the race. These payoffs are indicated by the odds. As the relative amount bet on a horse increases, the odds and subsequent payoffs fall.

Bettors analyze available information to predict how the horses entered in a race will finish. This process is referred to as handicapping. The object of handicapping is to allocate available funds in a way that maximizes expected returns. [8] The question of interest is how bettors use information on whether a horse was sold before it reached the track when making their wagers. This information, as well as other relevant handicapping information, is published in The Daily Racing Form. [9]

If bettors know that breeders may keep some of their yearlings, and that breeders are more likely to sell horses from the lower end of the distribution, they should expect thoroughbreds being raced by their breeder to be of higher average quality and a test for adverse selection arises. Specifically, bettors should favor thoroughbreds that are kept by their breeder over otherwise similar thoroughbreds.

More formally, presume that horses in a race are drawn from a quality distribution F(q), on the interval ([q.sub.L],[q.sub.H]) here q indexes quality (L indicating low quality). Higher-quality horses are more likely to win races. With no other information, the best estimate of a horse's quality is the mean quality from the known distribution. If bettors know a horse is a homebred, they also know that the breeder has chosen to race, rather than sell, the horse. If thoroughbreds taken to auction are adversely selected, the signal that the horse is a homebred indicates that it is drawn from the top of the distribution. That is to say, homebreds are drawn from the interval ([q.sup.*],[q.sub.H]), where [q.sup.*] [greater than] [q.sub.L]. [10] Bettors should favor homebreds over otherwise similar nonhomebreds.

It is worth noting that a breeder may race a particular horse for many reasons. Some breeders will keep a portion of their female horses because they are inputs in the future breeding process. Also, a breeder may be "stuck" with a horse because it was ill at the time of a sale. [11] The weight put on the homebred characteristic may be discounted if such information is available to bettors.

3. Data and Empirical Strategy

We test our hypothesis by examining data on two-year-old maiden races conducted during the summer and fall of 1995 at the Saratoga and Keeneland racecourses. [12] We examine two-year-old maiden races to highlight the differences that might exist in bettors' perceptions based on the distinction that a horse is or is not a homebred. We define a homebred as a horse that has at least one entity listed as both its breeder and owner at the time of the race. The variable "Homebred" is set equal to one when this condition is met and is set equal to zero otherwise.

A maiden race is a race restricted to thoroughbreds that have not yet won a race. The majority of horses in two-year-old maiden races have few or no previous starts because thoroughbreds do not begin racing until their two-year-old season. Generally, two-year-old maidens are randomly allocated to races based on a nomination process. Owners nominate their maiden two-year-olds to races for an upcoming meet. From this pool of eligible two-year-olds, horses are drawn into particular races several days prior to the race. In the meets studied, most nominations are made well in advance of the races. [13]

In maiden races, bettors have limited information about the on-track performance of horses. For the problem examined here, this is advantageous because as horses start in more races, information about their on-track ability is revealed. If a horse's on-track ability is correlated with being a homebred, the homebred variable may become less important statistically. [14]

Posttime odds are used to measure the attitudes of bettors toward each horse in our sample. The most prominent piece of information displayed at the track prior to each race is the odds. The current win odds are displayed and updated in one-minute intervals, following the most recent race until the horses reach the starting gate. The odds are calculated as follows:

odds = (1 - t)/[P.sub.k] - 1,

where [P.sub.k] is the proportion of the total win pool bet on horse k, and t is the takeout or parimutuel tax. As more dollars are bet on a particular horse, the odds fall. Lower odds indicate that bettors find it relatively more likely that a horse will win the race. At the time the horses reach the starting gate, the betting windows are closed and the final race odds are calculated. These posttime odds are published for each race and are the measure of odds we use in this study.

We model the speed of a racehorse as being equal to [y.sub.ir] = [X.sub.ir][beta] + [[epsilon].sub.ir], where x is a vector of covariates, [beta] is the corresponding vector of coefficients, [epsilon] is the random error term, i indexes the horse, and i indexes the race. [15] Horse i will win race r if for each j [not equal to] i, [y.sub.i] [greater than] [y.sub.i]. Assuming the error terms are independent extreme value random variables, the probability that horse i wins a race is given by [e.sup.[x.sub.i][beta]]/([[[sigma].sup.m].sub.j=1] [e.sup.[x.sub.j][beta]]), where j indexes all the horses included in a race.

This model leads naturally to a fixed-effects regression model. Setting the probability that a horse will win a race equal to (1 - t)/(l + odds), the betting public's expected probability that a horse will win a race, and manipulating, gives the fixed-effects model

In([odds.sub.ir] +1) = [d.sub.r] + [x.sub.ir][beta],

where i indexes each horse in race r and [d.sub.r] is a set of dummy variables to capture fixed race effects.

We also examine a rank-ordered logit specification. Several studies have shown that the odds may not reflect the true probability that a horse will win a race. [16] The basic result is that long shots (horses with a low true probability of winning a race) are overbet. Bettors perceive the probability that a long shot will win a race to be higher than it actually is. Similarly, the true probability of favorites winning a race is lower than bettors predict, or they are underbet. This favorite--long-shot bias suggests that the odds may not properly aggregate the information on the relative quality of the horses entered in a particular race, although their predicted rankings are, on average, accurate. The noise introduced by this bias is reduced in the rank-ordered logit model.

Beggs, Cardell, and Hausman (1981; BCH) show that if the probability of choice i being favored over choice j is independent of the other choices available, the probability of an observed ranking, 1 [greater than] 2 [greater than] ... [greater than] m, is the product of the conditional probabilities of choices from successively restricted subsets. This gives the following likelihood function for a set of observations:

L = [[[pi].sup.n].sub.r=1] ([e.sup.[x.sub.1][beta]]/[[[sigma].sup.m].sub.i=1] [e.sup.[x.sub.i][beta]] . [e.sup.[x.sub.2][beta]]/[[[sigma].sup.m].sub.i=2] [e.sup.[x.sub.i][beta]] ... [e.sup.[x.sub.m-1][beta]]/[[[sigma].sup.m].sub.i=m-1] [e.sup.[x.sub.i][beta]]),

where r = 1, ..., n indexes each race, and i = 1, ..., m indexes the horses in each race by rank, where i = 1 indicates the horse is the favorite in the race. This specification improves over an ordinary logit specification because it contains information on the entire ranking rather

than estimating only the probability that one horse is favored over all others. Additionally, this specification accounts for within-race effects.

Hausman and Ruud (1987) note that people are likely to use more care when differentiating between top choices compared to the less favored alternatives. Intuitively, bettors paint a clearer picture among the favorites, but random factors become more important for lower-ranked options. To account for these difficulties, Hausman and Ruud modify the BCH likelihood function by restricting the model to include only the top P ranks. This specification is given by

L = [[[pi].sup.n].sub.r=1] ([e.sup.[x.sub.1][beta]]/[[[sigma].sup.m].sub.i=1] [e.sup.[x.sub.i][beta]] . [e.sup.[x.sub.2][beta]]/[[[sigma].sup.m].sub.i=2] [e.sup.[x.sub.i][beta]] ... [e.sup.[x.sub.p][beta]]/[[[sigma].sup.m].sub.i=p] [e.sup.[x.sub.i][beta]]),

where P is the number of ranks used to estimate the model. This is essentially a weighted maximum likelihood technique, where the weight on the first P ranks is 1, and zero on the remainder. We estimate both full-rank and partial-rank logit specifications along with the fixed-effects model discussed above.

The data on the control variables and information regarding the name of the breeder, owner, and trainer of each horse in our sample were collected from various issues of The Daily Racing Form (henceforth The Form) and the American Produce Records. For each race, The Form lists the conditions of the race and the "past performances" of all horses entered. [17] The past performances include information on the horse's name, its sire (father) and dam (mother), the names of the breeder and owner of the horse, the trainer, the horse's career record (number of starts, record in starts, and money earnings), the horse's most recent performances, and the results of recent workouts. We collected information from each of these components to capture the information available to bettors.

Posttime odds, post position, and jockey were taken from the charts for each race. The charts for the races in our sample were obtained from The Lexington Herald-Leader for the Keeneland races and from The Form for the Saratoga races. Our sample includes 389 horses drawn from 39 horse races. The sample includes all two-year-old maiden races run during the Saratoga and Keeneland fall meetings that had at least two homebreds or at least two nonhomebreds entered.

To measure the ability of the jockeys, we include the variable Jockey Winning Percentage. Jockey Winning Percentage is equal to each jockey's 1994 winning percentage (number of wins divided by number of starts). An increase in Jockey Winning Percentage indicates that a jockey of relatively high skill is riding the horse and should therefore be looked at more favorably by bettors. Thus, Jockey Winning Percentage should be inversely related to its odds and positively related to the probability that the horse will be among the race favorites. The race favorite has the lowest odds among the horses in the race. In the rank-ordered logit model, variables that are positively correlated with the probability that a horse will be among the race favorites will have a positive coefficient. To keep the analysis consistent, we use the negative of the natural logarithm of (odds + 1) in the fixed-effect model.

The Form includes information on recent workouts, which indicates how a horse is performing. A common workout listing is

* Oct 1 Kee 5f fst :[58.sup.2] B 1/23.

This line shows that the horse worked five furlongs on October 1 at Keeneland. [18] The track was fast. The workout was completed in a time of 58 and 2/5 seconds. The B is a comment that the horse was breezing or moving easily. The fraction indicates that this was the day's fastest time of the 23 horses that worked this distance at Keeneland on October 1. The solid black dot at the front of a workout line indicates that the work was a bullet, or the fastest five-furlong work at Keeneland that day.

To incorporate information contained in the work line, we include the number of listed works (Works), the number of bullets in the previous three works (Bullets), and the relative ranking of a horse's last work (Workrank). As Works increase, we argue that the trainer has made greater efforts to prepare the horse for the race. A bullet workout indicates that a horse is training well. We expect Works and Bullets to be positively related to the probability that a horse will be among the race favorites. Finally, a higher Workrank indicates the last workout was relatively poor, and we expect to see an inverse relationship between Workrank and the public's view that a horse will win.

The variable Month is defined to be equal to one if the horse was born in January, two if February, and so on. The more recently a horse was born, the larger the value of this variable. We include the variable Month to capture the effect of a horse's age and expect horses born more recently to be relatively more immature. We expect a negative correlation between Month and the probability that a horse will win.

On a regular basis, The Form publishes a list of sires that have shown a propensity to beget horses that win as two-year olds. The variable Outstanding Juvenile Sire is set equal to one if a horse's sire appears on this list, and zero otherwise. We expect Outstanding Juvenile Sire to increase the probability that a horse is among the race favorites. We also include a variable New Sire, which is set to one if the sire's first crop of two-year olds is currently racing. This variable is included to control for the inability of these sires to appear on the published juvenile sire list and the surrounding uncertainty regarding the sire's potential.

To control for the past racing performance of each horse, we include the variables Percent in the Money, which is defined as the ratio of top-three finishes (in the money) to the number of races a particular horse has started. In maiden races (races for horses that have not previously won), there is some indication that the horse may soon win if it has previously been in the money. We expect Percent in the Money to be positively related to the public's perception that a horse will win. We also include the variable First Start, defined as one if the horse is a first-time starter, and zero otherwise. Because horses making their first start lack experience, we expect the public to look upon these horses less favorably than experienced horses.

We include Trainer Winning Percentage and Trainer Zero to account for the quality of the horse's trainer. Trainer Winning Percentage is equal to a trainer's number of wins in 1994 divided by the number of starters in 1994. An increase in Trainer Winning Percentage indicates that a conditioner of relatively higher skill trains the horse and therefore should be looked at more favorably by bettors. Conditioners who had a zero winning percentage in 1994 train a portion of the horses in our sample. These are predominantly trainers that earned less than $50,000 in 1994. We include the variable Trainer Zero to account for these observations and expect this to decrease the likelihood that a horse will be among the race favorites.

As noted above, the sample includes races for colts (young male horses) and races for fillies (young female horses). In the sample, there are 203 male horses, and among these, 32 have been gelded (or neutered). Geldings have no residual value in breeding. Breeders and owners will therefore prefer not to geld a horse unless there is a compelling reason to do so. Generally, the factors that lead to a horse being gelded are negative signs regarding a horse's performance. For example, horses are typically gelded when they are extremely aggressive and difficult to train. We include the variable Gelding and expect it be inversely related to the public's perception that a horse will win a race.

In the presence of adverse selection, market mechanisms should evolve to correct market inefficiencies that may arise. Several auction houses, most notably Keeneland, conduct sales where the horses offered for sale must qualify by passing an inspection. [19] If the auction house is able to certify that all of the yearlings offered in a sale exceed some cutoff, the average quality, and thus price, in the sale will increase. The distribution of horses sold in a certified sale is therefore truncated in a fashion similar to homebreds. Information regarding the sale in which a horse is sold is published widely in industry journals and in the American Produce Records. Bettors are therefore likely to know which horses were sold in certified sales. We include the variable Select to control for this and expect it to be positively related to the probability that it will be among the race favorites.

Finally, we include a variable Pick, which is set equal to one if The Form's handicappers have indicated that a horse is one of their top three choices in a race, and zero otherwise. In every edition of The Form, four handicappers give their top three choices for each race on the day's program. The Form uses a simple formula to aggregate the picks and publishes the consensus view. While the experts will use the information provided to bettors in The Form, they are also likely to use information that is observable to bettors but not to the econometrician. For example, The Form's handicappers may use information on how a particular horse is behaving in its morning workouts, whether it is having trouble handling starting gates or if it has a tendency to get nervous when around other horses. We expect the betting public to use the consensus picks, or information that is correlated with them, when handicapping a race and expect this variable to positively relate to the likelihood that a horse will be among the race favorites. [20]

Horses may be coupled for wagering purposes. This occurs when a particular trainer trains two or more horses in a race and, in most jurisdictions, have common ownership. Coupled horses are treated as a single entry for wagering purposes. When two or more horses are coupled, a bet on this entry will pay off if any of the horses in the coupling finish in the wagered position or better Our sample contains 13 coupled horses from six races (approximately 3% of our sample). Dropping these observations from our sample will not affect the public's ranking of horses and will, therefore, have little effect on the rank-ordered logit model. We also drop these observations from the fixed-effects model. [21]

Summary statistics for the control variables are presented in Table 1. The table presents the results for the full sample, broken down by Homebred and Nonhomebred and by the Keeneland and Saratoga races. The sample consists of 389 horses, 165 homebreds and 224 nonhomebreds. In the Keeneland races, 191 horses that ran in 17 races are included in our sample. From the table, we see that the mean of Posttime Odds are only slightly lower for homebreds. The control variables are similar between the homebred and nonhomebred portions of the sample. We observe that homebreds are slightly older and are less likely to be from a new sire.

The means for Keeneland and Saratoga show that fields are larger at Keeneland and, thus, have higher mean odds. Keeneland entries have a higher Percent in the Money and are less likely to be first-time starters. This last finding is consistent with the fact that Keeneland's meet follows Saratoga's.

4. Results

Table 2 presents the results of our empirical analysis. [22] In the table, column 1 presents the results for fixed-effects model, and column 2 for the partial-rank-ordered logit model including three ranks. Column 3 presents the partial-rank model using the top four ranks, and column 4 presents the results for the full-rank logit. [23]

Estimated coefficients for the control variables are generally as expected. In all of the specifications, we see that the coefficients for Jockey Winning Percentage, Workrank, Percent in the Money, Trainer's Winning Percentage, Pick, and Select are statistically significant and of the expected signs. In addition, the variables Works and Bullets are significant in the fixed-effects model, Trainer Zero is significant in the top three partial-rank logit, First Start is significant in the top four partial-rank logit, and Works, Bullets, and Outstanding Juvenile Sire are significant in the full-rank logit.

The results for our variable of interest, Homebred, are as predicted. In all four specifications, it is statistically significant (although only at the 10% level in the full-rank model) and has the predicted sign. In the rank-ordered logit models, the significance of the Homebred variable is greatest in the partial-rank specifications. This may indicate that the difference between homebreds and nonhomebreds is most important when bettors are choosing between top-ranked horses. [24] These results indicate that the signal provided by Homebred is important for determining the betting patterns of two-year-old maiden races. [25]

In general, our results are consistent with the notion that bettors favor homebreds over otherwise similar nonhomebreds when examining two-year-old maiden races. The implication of these results is that bettors recognize that horses racing as homebreds are drawn from a distribution that is truncated from below. It appears that based on bettors' perceptions, asymmetric information leads racing breeders to keep their best thoroughbreds and adversely select the horses they choose to sell. [26]

5. Conclusions

In this paper, we hypothesize that horses raced as homebreds will be favored over otherwise similar nonhomebreds. A homebred is defined as a horse being raced by its breeder. All breeders have the option of selling horses without racing them. Those breeders who both race and sell thoroughbreds, because of informational asymmetries, are likely to sell their low-quality horses. It follows that horses raced as homebreds are drawn from a quality distribution that is truncated from below and have an expected quality that is higher than the expected quality of otherwise similar nonhomebreds. Betting markets, which have been shown to be relatively efficient, provide a natural setting to examine the consequences of asymmetric information in this market. If the act of keeping (or selling) a thoroughbred is based on private information, bettors should favor homebreds over otherwise similar nonhomebreds.

We test this prediction using a sample of 39 two-year-old maiden races conducted at the Keeneland and Saratoga racecourses in the summer and fall of 1995. We find evidence consistent with our predictions. Fixed-effects regressions of the natural log of post-time odds, controlling for characteristics of the race and the individual horses, show that homebreds, on average, have lower odds. Similarly, rank-ordered logit regressions show that homebreds tend to be favored over otherwise similar nonhomebreds. The evidence suggests that adverse selection is present in the market for thoroughbreds but may be less severe at the top end of the market where independent agents certify the quality of horses.

This study suggests that further work is needed to understand the effect asymmetric information has on markets. In particular, it may be reasonable to conclude that problems of asymmetric information are less problematic at the top end of markets because information may be more valuable and the market will provide mechanisms to correct for any inefficiency that may arise. The gain from providing information or developing institutional arrangements to alleviate problems of asymmetric information is likely to be greater as the value of items being sold increases. Other possible extensions include conducting a study that examines older horses to see if the "homebred effect" persists throughout a horse's career. Finally, an examination of differences in lifetime earnings between homebreds and nonhomebreds as well as a comparison of horses sold at different sales would provide more conclusive evidence of the presence of adverse selection.

(*.) Department of Economics, St. Lawrence University, Canton, NY 13617, USA; E-mail chezum@stlawu.edu, corresponding author.

(+.) Department of Economics, University of Nevada Las Vegas, Las Vegas, NV 89154-6005, USA; E-mail wimmer@ccmail.nevada.edu.

We would like to thank John Garen, David Richardson, Seungmook Choi, and an anonymous referee for helpful advice. All mistakes are the fault of the authors.

Received July 1997; accepted June 1999.

(1.) Chezum and Wimmer (1997) show that breeders who also race, receive, on average, lower prices at thoroughbred yearling sales than breeders who take all of their thoroughbreds to market.

(2.) While bettors accurately estimate the order of finish, there is evidence that favorites are underbet and long shots are overbet (see, e.g., Sauer [1998] for a recent survey).

(3.) Bond (1982) compares the maintenance records of trucks acquired new with those acquired used and finds no significant differences. Bond's work is comparable to this study.

(4.) An interesting question, which is beyond the scope of this paper, is the extent to which racers will vertically integrate into the breeding end of the business.

(5.) Alternatively, Wilson (1980) examines the case where buyers and sellers have different preferences for the goods being sold to generate an adverse-selection result. In the context of the example presented here, buyers and sellers have some preference for racing thoroughbreds. Presumably, some buyers have a preference that exceeds sellers' preferences for racing. Wilson shows that in such a model, a positive-price equilibrium exists. (Wilson also examines the possibility of multiple equilibria and different market arrangements.) In this equilibrium, sellers will keep their highest quality thoroughbreds, selling from the lower end of the distribution.

(6.) Pari-mutuel wagering is the process where the odds are determined by the relative amount of money bet on each horse after accounting for the amount of money taken out of the betting pool. A portion of this "takeout" is used to fund racetrack operations and purses, with the remainder going to state and local governments.

(7.) Additional wagers are also available. These "exotic" wagers include bets where the bettor must pick the top two (an exacta) or top three finishers (a trifecta) in the correct order to earn a payoff.

(8.) Maximizing returns should approximate the objectives of utility maximization if the bettor's utility is a function of the payoffs and cashing tickets. Golec and Tamarkin (1998) argue that bettor utility functions depend not only on expected returns but also on the skewness of returns. They argue that this may explain the observed long-shot bias.

(9.) The Daily Racing Form is a daily newspaper that publishes information regarding the horses entered in the races at several racetracks across the country. It is available at the track on the afternoon prior to the racing day.

(10.) Nonhomebreds may be one of two types. A nonhomebred may have been sold by a breeder that does not race, selling all of his thoroughbreds, or may come from a breeder that both sells and races thoroughbreds. We assume that bettors may not have access to this information and implicitly assume that the expected quality is taken over the entire distribution for both types.

(11.) Several of the homebreds in our sample were actually sold at auction, but the original breeder retained ownership or a share of ownership in the horse. This may happen for several reasons. First, the horse may have failed a veterinarian's exam following the sale and was returned to the breeder. This might be a case where you could argue that the seller is "stuck" with a horse. Alternatively, breeders may approach buyers following the sale and attempt to buy a share of the horse.

(12.) The Saratoga meet is run during late July and August, and Keeneland meets in October.

(13.) For claiming and allowance races, horses are sorted into quality categories. In general, horses in a claiming race are of lower quality. Additionally, allowance races have conditions that define which horses are eligible for the race. Thus, the draw of horses is much less random in allowance and other races than in two-year-old maiden races.

(14.) The underlying notion is that the importance of the homebred variable will evaporate as a horse establishes a racing record. Farber and Gibbons (1996)--examining the relationship between education, experience, and wages--suggest that this result may not hold.

(15.) We would like to thank an anonymous referee for pointing out this model and the specifications that follow.

(16.) For studies that find this result, see Griffith (1949; 1961), Hoerl and Fallin (1974), Ali (1977), and Golec and Tamarkin (1998). A recent survey of these results can be found in Sauer (1998).

(17.) The conditions define the length of the race, the quality of the race, and the size of the purse.

(18.) A furlong is equal to one-eighth of a mile.

(19.) For a more complete discussion of certification in this market, see Wimmer and Chezum (1998).

(20.) In addition to the results reported, we ran several specifications that did not include the Pick variable. These results were generally consistent with those reported.

(21.) In other specifications not reported here, the likelihood function in the rank-ordered logit model was corrected to account for the joint probability of coupled horses winning the race. In the fixed-effects model, we ran a specification that included a qualitative variable to account for coupled horses. Results from both specifications are qualitatively similar to those reported below.

(22.) The regression presented in column one is based on proportions data and is therefore heteroskedastic. The results reported are corrected for this as in Greene (1993, pp. 653-5), using the number of horses entered in the race to account for differences in the size of the total purse.

(23.) Because bettors typically only wager on the top three finishers, use of the top three ranks is a natural specification in this setting. Evidence from Hoerl and Fallin (1974) indicate that the majority of money is bet on the top three or four ranked horses. Additionally, the decrease in the predicted and actual probabilities of winning as rankings increase (where a ranking of one indicates a horse is the favorite) is much greater between the first several rankings than the differences for horses whose odds indicate they are looked upon less favorably by bettors. This suggests that favored horses are likely to be ranked more accurately than are lower ranked horses.

(24.) Chi-square tests to determine whether there is a statistically significant difference between the full- and partial-rank-ordered logits yielded teat statistics of 26.88 and 23.58 for the top three and top four specifications. The critical value for a chi-square distribution with 15 degrees of freedom is 24.996, allowing us to reject the null hypothesis that the full-rank specification yields the same estimates as the partial-rank specifications in the case of the three-rank model. This suggests that bettors pay closer attention to the top ranks, or random factors play a larger role when differentiating between long shots. Hausman and Ruud (1987) suggest a technique to control for heteroskedasticity in this model. This specification was examined and showed no improvement over the partial-rank specification.

(25.) In addition to rank-ordered logits based on the ranking of odds, specifications using the actual position of finish as the dependent variable were estimated. In general, these regressions produced weaker results than those found using odds to rank the horses. Using the same specification as in the log odds regressions, only Percent in the Money and Trainer Winning Percent were statistically significant and of the expected sign. Homebred received the expected sign but was not statistically significant. These mixed results are likely due to the noise inherent in the running of a horse race. We expect that a larger sample of races might yield more favorable results. Several specifications yielded more favorable results but included covariates not readily available to the public. Discussion of these factors is beyond the scope of this paper.

(26.) Chezum and Wimmer (1997), using a continuous variable, show that sellers that race more receive lower prices for otherwise similar thoroughbred yearlings at auction. We included such variables in several unreported specifications, but the data suggest this information is too fine for bettors to perceive and were not statistically significant.

References

Akerloff, George A. 1970. The market for 'Lemons': Quality uncertainty and the marker mechanism. Quarterly Journal of Economics 84:488-500.

Ali, Mukhtar M. 1977. Probability and utility estimates for racetrack bettors. Journal of Political Economy 83:803-15. Beggs, S., S. Cardell, and J. Hausman. 1981. Assessing the potential demand for electric cars. Journal of Econometrics 16:1-19.

Bond, Eric W. 1982. A direct test of the "Lemons" model: The market for used pickup trucks. American Economic Review 72:836-40.

Chezum, Brian, and Bradley S. Wimmer. 1997. Roses or Lemons: Adverse selection in the market for thoroughbred yearlings. Review of Economics and Statistics 79:521-6.

Farber, Henry S., and Robert Gibbons. 1996. Learning and wage dynamics. Quarterly Journal of Economics 116:1007-47.

Genesove, David. 1993. Adverse selection in the wholesale used car market. Journal of Political Economy 101:644-65.

Gibbons, Robert, and Lawrence T. Katz. 1991. Layoffs and Lemons. Journal of Labor Economics 9:351-80.

Golec, Joseph, and Maurry Tamarkin. 1998. Bettors love skewness, not risk at the horse track. Journal of Political Economy 106:205-25.

Greene, William H. 1993. Econometric Analysis. 2nd edition. New York: Macmillan Publishing Company.

Greenwald, Bruce C., and Robert R. Glasspiegel. 1983. Adverse selection in the market for slaves: New Orleans, 1830-1860. Quarterly Journal of Economics 98:479-99.

Griffith, Richard M. 1949. Odds adjustments by American horse-racing bettors. American Journal of Psychology 62:290-4.

Griffith, Richard M. 1961. A footnote on horse race betting. Transactions Kentucky Academy of Science 22:78-81.

Hausman, Jerry A., and Paul A. Ruud. 1987. Specifying and testing econometric models for rank-ordered data. Journal of Econometrics 34:83-107.

Hoerl, Arthur E., and Herbert K. Fallin, 1974. Reliability of subjective evaluations in a high incentive situation. Journal of the Royal Statistical Society 137:227-30.

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The Daily Racing Form. 1995. Various issues, July-August.

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Wilson, Charles. 1980. The nature of equilibrium in markets with adverse selection. Bell Journal of Economics 11:108-30.

Wimmer, Bradley, and Brian Chezum. 1998. The effects of certification in a lemon's market. Unpublished paper, University of Nevada-Las Vegas.

 Descriptive Statistics (Standard Deviations in Parentheses)
 Full Sample Homebreds Nonhomebreds Keeneland Saratoga
Posttime odds 21.950 21.347 22.395 26.444 17.615
 (23.11) (22.39) (23.66) (26.58) (18.22)
Homebred 0.4242 0.4293 0.4192
 (0.495) (0.496) (0.495)
Jockey winning 0.1455 0.1430 0.1474 0.1328 0.1579
 Percentage (0.051) (0.051) (0.050) (0.052) (0.047)
Works 6.303 6.406 6.227 6.094 6.505
 (2.39) (2.35) (2.43) (2.78) (1.95)
Bullets 0.2519 0.2424 0.2589 0.2984 0.2071
 (0.511) (0.496) (0.523) (0.552) (0.465)
Workrank 0.4729 0.5055 0.4489 0.4604 0.4851
 (0.286) (0.281) (0.287) (0.293) (0.279)
Month 3.244 3.097 3.353 3.325 3.167
 (1.25) (1.31) (1.19) (1.25) (1.24)
Outstanding 0.1748 0.1697 0.1786 0.1937 0.1566
 juvenile sire (0.380) (0.377) (0.384) (0.396) (0.364)
New sire 0.0925 0.0424 0.1295 0.1152 0.0707
 (0.290) (0.202) (0.336) (0.320) (0.257)
Percent in the 0.1733 0.1841 0.1655 0.1812 0.1659
 money (0.339) (0.347) (0.333) (0.333) (0.344)
First start 0.4319 0.4182 0.4420 0.3508 0.5101
 (0.496) (0.495) (0.498) (0.478) (0.501)
Trainer's 0.1333 0.1346 0.1324 0.1301 0.1365
 winning (0.068) (0.073) (0.064) (0.074) (0.061)
 percentage
Trainer zero 0.1028 0.1030 0.1027 0.1675 0.0404
 (0.304) (0.305) (0.304) (0.374) (0.197)
Gelding 0.0823 0.0848 0.0804 0.0733 0.0909
 (0.275) (0.280) (0.272) (0.261) (0.288)
Pick 0.2725 0.2545 0.2857 0.2565 0.2879
 (0.446) (0.437) (0.453) (0.438) (0.454)
Select 0.1311 0.0242 0.2098 0.1414 0.1212
 (0.338) (0.154) (0.408) (0.349) (0.327)
Observations 389 165 224 191 198
 Results for Fixed-Effects and Rank-Ordered Logit
 Models (t and z Statistics in Parentheses)
 Fixed Top Three Top Four
 Effects Ranks Ranks
Homebred 0.1783 [**] 0.6530 [***] 0.4770 [**]
 (2.39) (2.60) (2.210)
Jockey winning 4.7229 [***] 9.3057 [***] 8.5601 [***]
 percentage (6.14) (3.66) (3.86)
Works 0.0435 [**] 0.0859 0.0701
 (2.36) (1.35) (1.36)
Bullets 0.1619 [**] 0.2091 0.2460
 (2.23) (0.85) (1.19)
Workrank -0.4299 [***] -0.8434 [*] -1.1821 [***]
 (3.14) (1.78) (2.90)
Month -0.0046 0.0116 0.0195
 (0.16) (0.13) (0.24)
Outstanding juvenile 0.1072 -0.0935 0.1909
 sire (1.15) (0.31) (0.73)
New sire -0.0520 -0.4232 -0.0306
 (0.40) (0.97) (0.09)
Percent in the money 1.0067 [***] 2.3760 [***] 2.3581 [***]
 (8.84) (6.18) (6.91)
First start 0.0895 0.5556 0.5880 [**]
 (0.90) (1.55) (2.04)
Trainer's winning 3.0742 [***] 9.3394 [***] 9.3697 [***]
 percentage (4.23) (3.72) (3.91)
Trainer zero 0.0772 1.3079 [**] 0.8536
 (0.43) (2.05) (1.52)
Gelding -0.0772 -0.2531 -0.0046
 (0.53) (0.52) (0.01)
 Full Rank
Homebred 0.2120 [*]
 (1.62)
Jockey winning 6.8675 [***]
 percentage (4.42)
Works 0.0547 [*]
 (1.72)
Bullets 0.2520 [*]
 (1.78)
Workrank -0.9252 [***]
 (3.45)
Month 0.0150
 (0.27)
Outstanding juvenile 0.4781 [**]
 sire (2.44)
New sire -0.0055
 (0.02)
Percent in the money 2.0112 [***]
 (7.80)
First start 0.1564
 (0.92)
Trainer's winning 5.2968 [***]
 percentage (3.62)
Trainer zero 0.1183
 (0.39)
Gelding -0.2398
 (0.89)
Pick 0.7656 [***] 1.5096 [***] 1.5329 [***] 1.2592 [***]
 (9.61) (6.10) (7.22) (7.37)
Select 0.3657 [***] 0.6637 [*] 0.6690 [**] 0.4378 [**]
 (3.57) (1.91) (2.25) (2.06)
Constant -4.3961 [***]
 (20.480)
Log likelihood -169.073 -227.512 -489.888
[R.sup.2] 0.6566
(*.)Significant at the 10% level.
(**.)Significant at the 5% level.
(***.)Significant at the 1% level.