Hedonc Prce Analyss of Thoroughbred Broodmares n Foal Agrcultural Economcs Staff Paper # 460 June 2006 Kelly M. Stoeppel and Legh J. Maynard Unversty of Kentucky Department of Agrcultural Economcs 400 Charles E. Barnhart Bldg. Lexngton, KY 40546 0276 Phone: 859 257 5762 Fax: 859 323 1913 http://www.uky.edu/ag/agecon/ Legh Maynard may be contacted by e mal at: lmaynard@uky.edu. Ths publcaton has not been revewed by an offcal departmental commttee. The deas presented and the postons taken are solely those of the author(s) and do not represent the offcal poston of the Department of Agrcultural Economcs, the College of Agrculture, or The Unversty of Kentucky. Questons should be drected to the author(s).
Staff Paper No. 460 June 2006 Hedonc Prce Analyss of Thoroughbred Broodmares n Foal by Kelly M. Stoeppel and Legh J. Maynard Kelly Stoeppel and Legh Maynard are, respectvely, a former undergraduate student and assocate professor n the Department of Agrcultural Economcs at the Unversty of Kentucky. Senor authorshp s shared. Staff papers are publshed wthout formal revew. Vews expressed are those of the authors and do not necessarly reflect the vew of the Unversty of Kentucky, the Agrcultural Experment Staton, or the Cooperatve Extenson Servce.
Hedonc Prce Analyss of Thoroughbred Broodmares n Foal Abstract Thoroughbred broodmares are the foundaton of a successful racng operaton. Ths study estmated the mpact of breedng, racng, genetc, and market characterstcs on broodmare aucton prces. Data represent 298 broodmares n foal that were sold n Keeneland s 2005 sale. Prces were most responsve to the sre s stud fee and the broodmare s age, wth pronounced day-of-sale effects. Overall valuaton structure appeared smlar to Nebergs results usng 1996 data. Out-of-sample forecasts were far superor to nave forecasts, but were not accurate enough to use n solaton from other decson ads such as vsual nspecton of the horse. Key Words: broodmare, Thoroughbred horses, hedonc prce analyss, forecastng 1
Introducton In 2004, horses contrbuted over $100 bllon and 1.4 mllon jobs to the U.S. economy (The Jockey Club, 2006). Thoroughbreds contrbuted over 33% of the economc mpact, even though they represent only 14% of the horse populaton. Wth over a mllon Thoroughbreds and half of them nvolved n the racng ndustry, the buyng and sellng of Thoroughbreds can have a substantal mpact on some local economes, especally n Kentucky where the majorty of Thoroughbred horses are owned. Wth so much money rdng on Thoroughbreds, quanttatve evdence about ther prce determnants may be drectly useful to ndustry partcpants, and ndrectly helpful for economc development n some locales. Broodmares are the foundaton of a racehorse breedng program, and they represent a substantal captal nvestment. To date, the only econometrc analyss of broodmare prce determnants appears to be Nebergs (2001), who performed a hedonc prce analyss on data from the 1996 Keeneland November broodmare sale. Margnal values and prce flexbltes were estmated for breedng, racng, genetc, and market characterstcs. Nebergs cautoned that hs results were only applcable to 1996, however, because the data were generated early n a perod of prolonged prce recovery. Broodmare prces are generally much hgher now, and one would expect margnal values to follow sut. Whether the relatve mportance of broodmare prce determnants has evolved n the last decade s a testable hypothess. The objectves of ths study were to update estmates of broodmare attrbute margnal values and prce flexbltes, to determne f the overall structure of broodmare valuaton s approxmately stable despte changng economc condtons, to focus on prce determnants of broodmares n foal as opposed to barren broodmares, and to test whether a hedonc prcng 2
model forecasts suffcently well out-of-sample to be a useful tool for broodmare buyers and sellers. The analyss was performed usng data from the 2005 Keeneland November breedng stock sale, the largest broodmare sale n the world. Background Thoroughbred broodmares are dfferentated products that brng a dfferent prce for each horse dependng upon the perceved value of the broodmare. Lancaster (1966) developed a theoretcal model n whch consumers purchase goods delverng a utltymaxmzng bundle of attrbutes, subject to a budgent constrant. Thus, a product prce functon exsts contanng measurable product attrbutes as arguments (Rosen, 1974). Ladd and Martn (1976) developed ths theme n the context of demand for agrcultural nputs, whle Martn and Suvannunt (1976) focused on consumer goods. Both demand-sde and supply-sde models produce an equaton explanng prce as a functon of qualty and quantty of characterstcs assocated wth the product (Schroeder, Espnosa, and Goodwn, 1992). Many studes examned agrcultural products usng hedonc prcng models. Buccola and Izuka (1997) created a varant of a hedonc prcng model that establshed values for each of the characterstcs of mlk and tested whether producers responded to the market value of proten n ther management decsons. Krstofersson and Rckertsen (2004) estmated characterstc demand for qualty n Icelandc fshng auctons by usng a random coeffcent model. Schroeder, Espnosa, and Goodwn (1992) explaned prce varaton n purebred dary bulls by examnng the hertable producton and offsprng physcal trats that affectng the prce of bull semen. Schroeder, Jones, and Ncholas (1989) studed the prce of feeder pgs 3
and the varous characterstcs that dscounted the prce over tme. Hedonc prcng models have also been appled to the equne ndustres, wth the most emphass on Thoroughbred yearlngs. Chezum and Wmmer (2001) tested whether there s adverse selecton n Thoroughbred yearlng actons when some sellers both bred and raced Thoroughbreds. A hedonc prcng model was used to prce each sgnfcant characterstc exhbted by the yearlng, and the expected value of the yearlng was compared to the actual prce. Vckner and Koch (2001) evaluated yearlng characterstcs and establshed margnal values of each explanatory varable n ther model. Nebergs and Thalhemer (1997) created a hedonc prcng model that ncorporated both prce expectatons and market restrants to estmate supply and demand n the Thoroughbred yearlng market. Purse wnnngs were found to be the most sgnfcant varable mpactng prce. Commer s (2000) nformal study of factors affectng Thoroughbred yearlng sale prces suggested that the most salent factors were the qualty of the sre, the qualty of dam, foalng date, whether the foal was nomnated for the Breeders cup, where the foal was born, and where the yearlng was sold. Taylor et al. (2004) examned the prce determnants of show qualty Quarter Horses, fndng that genetc and physcal trats, ndvdual performance, and performance of the offsprng all affected the prce of the Quarter Horse. Vercken de Vreuschman (2005) was the only study to nclude conformaton as an explanatory varable n a Thoroughbred yearlng hedonc prcng model. Conformaton was represented as a dummy varable based on an ndustry expert s opnon about the sutablty of each horse s physcal structure for racng. Despte the subjectve nature of judgng 4
conformaton, the varable was statstcally and economcally sgnfcant n the model, suggestng that nformed vsual nspecton may be necessarly for complete model specfcaton. Buzby and Jessup (1994) dentfed the effects of macroeconomc varables on Thoroughbred yearlng prce and found that yearlng-specfc varables were the most sgnfcant, but other varables such as tax and nterest rates were prce determnants. Smlarly, Karungu, Reed, and Tvedt (1993) found evdence that exchange rates and tax law changes mpacted Thoroughbred yearlng prces. The mportance of the broodmare n the producton of qualty racehorses was shown by Laughln (1934) when he establshed that the majorty of characterstcs that make a horse successful on the track are nherted from ts parents. Hedonc prcng n regonal Thoroughbred markets contrbuted to the fndng that the dam plays a role n the prcng of yearlngs (Robbns and Kennedy, 2001). The success of the broodmare s prevous progeny was a stronger determnant of prce than the performance of the broodmare herself. Nebergs (2001) was, to our knowledge, the only study applyng hedonc prcng to Thoroughbred broodmares. He categorzed attrbutes as breedng, racng, genetc, and market factors, used data from the Keeneland broodmare sales, and estmated margnal values and prce flexbltes for each of the explanatory varables. The results suggested that the most mportant factors were the number of races the broodmare had won and the number of races the broodmare s exstng foals won. 5
Hedonc Prcng Model The mantaned assumpton of the followng hedonc prcng model s that the prce of a broodmare n foal s a functon of attrbutes sgnalng the future racng performance of her foals. The dependent varable s the prce (or a transformaton of prce) for whch the broodmare sold at aucton. To facltate comparson, we follow Nebergs (2001) categorzaton of ndependent varables nto breedng, racng, genetc, and marketng factors. Breedng factors nclude the racng performance of a mare s exstng foals, and measures of the sre s qualty. The mare s racng record sgnals heredtable expectatons of her foals racng performance. Genetc factors refer manly to the mare s placement on the spectrum of speed and stamna. In ths study, marketng factors consst of the day on whch the mare was auctoned durng the 12-day sale. The specfc varables collected for ths study appear n Table 1, and are descrbed n order of appearance below. < TABLE 1 ABOUT HERE > The age of the mare n years reflects her potental future earnngs from producng more foals. The younger the mare, the more foals she s capable of producng, suggestng that age negatvely nfluences prce. For the broodmares that already have foals of racng age, the performance of these foals s an ndcator of the racng success of the mare s future foals. The number of other foals that the broodmare has produced can ndcate how easly bred the mare s, but t can also correlate hghly wth age. Because purse wnnngs are the easest way to judge the qualty of a racehorse, total foal earnngs reveals the success of the mare s prevous foals, wth all earnngs converted nto U.S. dollars usng March 2006 exchange rates. The number of races the broodmare s foals have won, and average earnngs per foal, are 6
alternatve gudes to expected success of future foals on the racetrack. The qualty of the broodmare s sre and the sre bred to the broodmare are expected to be mportant characterstcs n determnng the prce of the broodmare. The dollar amount of the sre s stud fee s a measure of the market s valuaton of the stallon s genetcs. One would expect hgher stud fees to be correlated wth hgher-value foals, thus ncreasng the value of the broodmare carryng the foal. One mght also expect a postve relatonshp between broodmare prce and the number of foals sred by the stallon to whch she was bred. Each year, The Blood-Horse comples a Leadng Sres lst of the top 150 stallons ranked by that year s foal earnngs. An ndex called expected foal s sre value was created to compare the stallons to whom the broodmares were bred. The formula for the ndex (EFSV) s one plus the number of stakes wnners sred by the stallon (SW), multpled by an ndex of earnngs by a stallon s progeny relatve to the average of all runners (AE), multpled by an ndex of earnngs by a stallon s progeny relatve to the average of other stallons progeny from the same mares (COMP), dvded by the rankng on the leadng sres lst (R). That s, EFSV = 1 + SW * AE * COMP / R. If a stallon dd not appear on the leadng sres lst, t was assgned a value of one. The constructon of the ndex allows natural logs to be taken. Nebergs (2001) used a smlar ndex to measure sre qualty, and each component of the ndex s provded n the Leadng Sres lst. An analogous ndex called expected mare s sre value was calculated for each broodmare s sre, usng data contaned n the 2005 Leadng Broodmare Sres lst. The broodmare s racng hstory ndcates her capablty as a racehorse, whch s expected to be partally heredtable. The broodmare s total earnngs are one measure of 7
success on the racetrack. Her racng record can also be measured wth separate varables for the number of races the mare won, placed, and showed. Three measures of each broodmare s genetc attrbutes were collected. The dosage ndex s a computaton of the projected speed and stamna of a horse based upon the dosage values of the stallons n the horse s pedgree. The hgher the dosage ndex, the more lkely the horse s to be a sprnter, whle low dosage values suggest better stamna. The center of dstrbuton s an alternatve scorng system usng the same pedgree nformaton, wth hgher values also suggestng better performance n shorter races. The Genetc Strength Value s a mult-attrbute measure of pedgree performance extendng fve generatons back (Pedgree Onlne, 2006). Hgher values ndcate greater lkelhood of wnnng hgher-class races. Unlke dosage and the center of dstrbuton, the genetc strength value ncorporates nformaton about the mares n a horse s pedgree. The day of the sale on whch a broodmare s sold may affect the prce of the mare even holdng all other attrbutes constant. Hgher qualty mares are scheduled for sale early n the sale, but the varables descrbed above should control for many of the breedng, racng, and genetc attrbutes that justfy prce varaton. If there are sgnfcant day of sale effects, t mples ether that the other varables do not adequately capture the broodmares qualtes, or that prce vares systematcally by day regardless of broodmare attrbutes. Buyer fatgue and the percepton that the most valuable horses have already been sold are potental causes of prce declnes as the sale wears on. About three quarters of the auctoned broodmares were pregnant ( n foal ) at the tme of the 2005 sale. Seven of the nne breedng varables lsted n Table 1 are zero vectors for 8
barren broodmares,.e., those that were not pregnant. Thus, t s nether practcal nor vald to model the two types of broodmares usng the same regresson, and we focus on broodmares n foal. The emphass on mares n foal deserves dscusson, because t dverges from Nebergs (2001), who assgned stud fee values of zero to barren broodmares, argung that a zero value reflected the expected value of a nonexstent foal. Put another way, barren mares were treated as f they had been bred to sres so undesrable that ther stud fees were zero. Nebergs approach mplctly assumed that the margnal mpact of the stud fee (and all other varables) on broodmare prce was the same for barren mares and mares n foal. Ths assumpton mght not be vald, because one would not expect buyers to weght mssng nformaton about a varable as heavly as an observed zero value for that varable. As Nebergs hmself explaned, barren mares are dscounted not because ther foals nhert nferor characterstcs (whch would be the case f the sre truly had a zero stud fee), but rather because of delayed earnngs, hgher costs, and rsk of reproductve dffculty. Thus, we expect the data generatng process for a hedonc prcng model of barren mares vs. mares n foal to be suffcently dfferent that the two types of horses should not be combned n the same dataset. The Box-Cox transformaton was used to select a specfc functonal form. The dependent varable Prce was transformed as follows (Box and Cox, 1964): λ ( Prce) 1 ( λ ) when λ 0 Prce = λ. ln( Prce) when λ = 0 The parameter λ was allowed to vary from -2.0 to +2.0 by ncrements of 0.1, and for each of 9
these values the transformed dependent varable was regressed on the ndependent varables. The transformaton returnng the hghest log-lkelhood value was λ = 0.0, whch corresponds wth a dependent varable of ln(prce) and a sem-log functonal form. Nebergs (2001) also found the sem-log form to be most approprate. Broodmare prces are postvely skewed so that the mean far exceeds the medan, but as Fgure 1 shows, broodmare prces are approxmately log-normally dstrbuted. < FIGURE 1 ABOUT HERE > Severe multcollnearty (as suggested by varance nflaton factors exceedng 10) occurred when multple racng and genetc characterstcs were ncluded n the model. Based on contrbuton to adjusted R 2, the mare s center of dstrbuton was selected to represent genetc characterstcs, and total mare earnngs was selected to represent racng characterstcs. Four breedng characterstcs (age, stud fee, expected mare s sre value, and total foal earnngs) could be retaned n the model wthout producng severe multcollnearty. Explanatory power (as measured by adjusted R 2 ) was markedly hgher when the stud fee and expected mare s sre value were logged. In many cases, total foal earnngs were zero, so ths varable could not be logged, but a quadratc term was ncluded to allow a nonlnear relatonshp wth the log of prce. Accordngly, the estmated emprcal model was as follows: ln( Prce) = β + β Age + β TotalFoalEarnngs + β ( TotalFoalEarnngs) + β ln( Expected Mare' s SreValue) + β ln( Stud Fee) + β Total Mare Earnngs 4 7 0 + β Center of 1 2 Dstrbuton + β Day 2 +... + β Day12 + ε. 8 Margnal values and prce flexblty estmates are more meanngful than the 5 3 18 6 2 10
parameter estmates alone. The margnal value of a varable s the change n broodmare prce gven a one-unt ncrease n the ndependent varable. Formulas used to calculate margnal values for a gven varable x are as follows, where overbars denote sample means of contnuous varables and sample means of all contnuous varables: xβ e equals the predcted broodmare prce on Day 1 of the sale at the Prce = e x Prce = e x xβ Prce e β = x x Prce xβ = ( e x x xβ xβ β ( β + 2β x ) = 1) ( e xβ x = 0) f x not logged, wth no quadratc term f x not logged, wth quadratc term f x s logged f x s bnary. Prce flexbltes represent the percentage change n broodmare prce gven a one percent ncrease n an ndependent varable, and were calculated for each contnuous varable usng the followng formulas: ln Prce = β x ln x ln Prce = ( β + 2β x ln x ln Prce = β ln x ) x f f f x not logged, wth no quadratc term x not logged, wth quadratc term x s logged. Msspecfcaton testng was performed usng the jont condtonal mean and jont condtonal varance tests suggested by McGurk, Drscoll, and Alwang (1993). Indvdual tests mantan the possbly unreasonable assumpton that all other econometrc assumptons are not volated, whereas jont tests lmt the number of such assumptons. The jont 11
condtonal mean test regresses estmated resduals aganst all of the ndependent varables n the orgnal model, plus a tme trend (to test parameter stablty), squared and cubed ftted values (.e., a RESET test of functonal form), and lagged resduals (to test seral ndependence). If the regresson s jontly statstcally sgnfcant, the ndvdual test parameters can be examned to dentfy the lkely source of volaton. The jont condtonal varance test regresses squared resduals aganst an ntercept, a tme trend (to test varance stablty), squared ftted values (to test statc homoskedastcty), and lagged squared resduals (to test for ARCH errors). The normalty of the resduals was tested separately usng four common normalty tests, and multcollnearty was tested usng the rule of thumb that varance nflaton factors exceedng 10 ndcate severe multcollnearty. Snce the purpose of ths study s to assst future buyers and sellers of broodmares, t s not only mportant for the model to have acceptable n-sample explanatory power, t must also have acceptable out-of-sample predctve power. Usng numbers randomly generated from a unform dstrbuton, fve subsamples of 20 observatons were drawn from the full sample of broodmares n foal. In each case, the model was re-estmated usng only the n-sample observatons. The resultng parameter estmates were then used to predct sale prces for the out-of-sample broodmares. Thel s U-statstc was used to evaluate performance for each of the fve out-of-sample forecasts: 12
20 2 (ln P ˆ ln P ) = 1 U =. 20 2 (ln P ln P) = 1 Thel s U compares the root mean squared errors of the model forecast to those from a nave forecast. In ths case the most reasonable nave forecast appeared to be the mean of the nsample broodmare prces. A rato of zero mples a perfect forecast, whle a rato of one mples that the model performs no better than the nave forecast, and ratos greater than one mply that the model performs even worse than the nave forecast. Data The Keeneland November Breedng Stock Sale s the largest sale of Thoroughbred broodmares n the world. To facltate the sale of the 4,477 broodmares n the 2005 November Breedng Stock Sale, Keeneland produced a sales catalog descrbng each horse. Data obtaned from the sales catalog consst of the mare s age n years, whether the mare was n foal at the tme of the sale, the number of foals the mare had prevously and the foals total earnngs, the number of races won by the mare s foals, the number of races n whch the mare herself won, placed, and showed, the mare s total earnngs, and the day (1-12) on whch the mare was sold. Each broodmare s sale prce was obtaned from the Keeneland 2005 November Breedng Stock Sales results (Keeneland, 2006). Data on 2005 stud fees were obtaned from the Stallon Regster publshed by The Blood-Horse. Data regardng sres were collected from The Blood-Horse 2005 Leadng Sres lst and the 2005 Leadng Broodmare Sres lst. The dosage ndex, center of dstrbuton, and genetc strength value varables were acqured from Pedgree Onlne s Thoroughbred Database. 13
Of the 4,477 horses regstered for the sale, bddng on many horses dd not meet the seller s reserve prce, and other horses were pulled from the sale, resultng n 2,400 sales. Complete data were collected on 409 randomly selected broodmares, of whch 298 were n foal and therefore retaned for analyss. Summary statstcs appear n Table 1. The average broodmare prce was almost $170,000, wth prces rangng from $1,700 to $3,700,000. The average stud fee was almost $42,000 wth a range from $1,250 to $500,000. The average mare was 9 years old, and had produced an average of 2.76 foals that had won an average of 2.43 races and earned over $73,000. The broodmares themselves had won an average of 2.22 races and earned over $82,000. Broodmare earnngs ranged from $0 to $1.15 mllon. Results Table 2 shows no evdence of sgnfcant econometrc volatons. An F-test faled to reject the jont hypothess of zero values for the parameter stablty, functonal form, and seral dependence parameters n the jont condtonal mean test, and none of the ndvdual parameters were sgnfcant. Smlarly, the jont condtonal varance regresson was not sgnfcant, and nether were any of the ndvdual parameters. The null hypothess of normally-dstrbuted resduals could not be rejected, and the maxmum varance nflaton factor of 9.49 suggested an absence of severe multcollnearty. < TABLE 2 ABOUT HERE > Table 3 presents the parameter estmates, margnal values, and prce flexbltes. The adjusted R 2 was 0.83, whch s smlar to the 0.74 value found by Nebergs (2001). The 14
dfference s due to our study s focus on broodmares n foal. Out of curosty, we estmated a model usng the full sample ncludng barren mares, and also found an adjusted R 2 of 0.74. < TABLE 3 ABOUT HERE > All of the parameters except Day2, Day3, Day4, and Center of Dstrbuton were statstcally sgnfcant at the 1% level, Day4 was sgnfcant at the 10% level, and all but Day2 had the expected sgn. Moreover, most of the ndependent varables appear to be economcally sgnfcant. Each addtonal year that a broodmare ages reduced her value by an average of almost $14,000, holdng all else constant. At the mean, each addtonal dollar won by a mare s foals ncreased the mare s value by 18 cents, on average. Lkewse, each addtonal dollar won by the mare herself ncreased her value by an average of 20 cents. Even holdng other breedng, racng, and genetc factors constant, the day on whch a broodmare was sold strongly affected her sale prce. The margnal values of the day of sale parameters generally followed the same ncreasngly negatve pattern observed n Nebergs results, but the magntudes were much larger, consstent wth substantal nflaton n broodmare prces between 1996 and 2005. Prce flexblty estmates were hgher n absolute value than those estmated by Nebergs (2001), and the expected reason s that our parameter estmates were not nfluenced by barren mares wth zero values for several varables. Varables that returned hgher absolute flexbltes ncluded age (-1.13 vs. -0.86), total foal earnngs (0.12 vs. 0.08), expected mare s sre value (0.15 vs. 0.05), and total mare earnngs (0.15 vs. 0.10). A major dfference between our results and those of Nebergs s that our focus on broodmares n foal suggests a much stronger role for the stud fee n broodmare valuaton. We found that an 15
addtonal dollar of stud fee rased the broodmare s value by $1.79 (vs. Nebergs $0.37), wth a prce flexblty of 0.69 (vs. Nebergs 0.21). After randomly drawng each set of 20 out-of-sample observatons, the model was reestmated usng the remanng 278 n-sample observatons. Ths process was repeated fve tmes, and the parameter estmate vectors were generally robust across samples. Out-ofsample prce forecasts were generated from the n-sample parameter estmates, and the followng Thel s U-statstcs were calculated for the fve out-of-sample data sets: 0.40, 0.34, 0.52, 0.40, 0.50, wth lower values ndcatng better forecastng performance. All fve U- statstcs were less than one and ndcate much better performance than the nave forecast. Fgure 2 provdes a vsual representaton of forecastng performance n the best-performng scenaro. Even n ths scenaro, however, after takng ant-logs of the forecasts, the mean absolute percentage error was 51 percent. < FIGURE 2 ABOUT HERE > Conclusons In conversatons wth Thoroughbred ndustry partcpants, t s not unusual to hear the opnon that valuaton of horses cannot be reduced to a mathematcal formula. In the case of broodmares n foal, over 80 percent of varaton n aucton prces can n fact be explaned by a regresson model, at least wthn the sample evaluated here. The model was exceptonally well-behaved statstcally, and both the sgns and the magntudes of the parameters were consstent wth reasonable expectatons. As a descrpton of typcal broodmare valuaton, the model appears qute adequate. We ntended ths study to be an updated companon to Nebergs (2001) that buyers 16
and sellers would fnd useful. Nebergs was concerned that hs 1996 results mght not be applcable to future years because of unusual ndustry condtons at the tme, but except for nflaton and dfferences attrbutable to modelng choces, the basc structure of broodmare valuaton appears stable over tme. Most of our prce flexbltes were only modestly hgher n absolute value than Nebergs, perhaps because we dd not nclude barren mares n our dataset and assgn zero values to foal-related varables. Our results, however, suggest much greater mportance of the stud fee as a broodmare prce determnant. Not only s the prce flexblty of 0.69 much hgher than Nebergs 0.21, we estmated a margnal value of $1.79 vs. Nebergs $0.37. Ths s relevant for broodmare sellers because t suggests that addtonal money spent breedng a mare to a hgher-qualty stallon wll be more than recouped when the mare s sold. Forecastng performance, however, s the true measure of how useful hedonc prcng models are for agrbusness purposes. In ths study, Thel s U-statstcs suggested that the regresson model was much superor to a nave forecast, but mean absolute error percentages exceedng 50 percent are too hgh to justfy relyng only on the model as a gude to strategc decsons. It s not uncommon for regresson models wth good n-sample explanatory power to show unacceptably low out-of-sample forecastng ablty. Sometmes models wth fewer ndependent varables are superor forecastng tools because they are more robust, but forecastng performance only worsened when we omtted varables from our model. A useful topc for future research would be to calculate Thel s U aganst forecasts made by an ndustry expert, as opposed to nave forecasts. One possble outcome s that, gven only the quanttatve data avalable for ths study, an expert could not outperform the 17
regresson model. If he or she were able to do so, t would suggest that the model reported here s severely msspecfed, despte ts exemplary performance n the battery of msspecfcaton tests. An alternatve outcome s that an expert could only outperform the model by havng access to addtonal nformaton, perhaps ncludng a vsual nspecton of the broodmare s conformaton, as suggested by Vercken de Vreuschman s (2005) results. 18
References The Blood-Horse. Stallon Regster Onlne. Blood-Horse Publcatons, accessed March 2006 at http://www.stallonregster.com/. The Blood-Horse. 2005 Leadng Sres. Blood-Horse Publcatons, accessed March 2006 at http://breedng.bloodhorse.com/srelsts/natonal05/leadng_sre.asp. The Blood-Horse. 2005 Leadng Broodmare Sres. Blood-Horse Publcatons, accessed March 2006 at http://breedng.bloodhorse.com/srelsts/natonal05/broodmare1.asp. Box, G.E.P. and D.R. Cox. An Analyss of Transformatons. Journal of the Royal Statstcal Socety. Seres B (Methodologcal) 26,2 (1964): 211-252. Buzby, J. and E. Jessup. The Relatve Impact of Macroeconomc and Yearlng-Specfc Varables n Determnng Thoroughbred Yearlng Prce. Appled Economcs. 26 (1997): 1-8. Buccola, S. and Y. Izuka. Hedonc Cost Models and the Prcng of Mlk Components. Amercan Journal of Agrcultural Economcs. 79 (1997): 452-462. Chezum, B. and B. Wmmer. Roses or Lemons: Adverse Selecton n the Market for Thoroughbred Yearlngs. The Revew of Economcs and Statstcs. 79 (1997): 521-526. Commer, M. Prce Factors and Sales Trends Affectng the Md-Atlantc Thoroughbred Market. Maryland Cooperatve Extenson. Fact Sheet 665: (2000). The Jockey Club. 2006 Onlne Fact Book. New York: The Jockey Club. accessed March 2006 at http://www.jockeyclub.com/factbook.asp. Karungu, P., M. Reed and D. Tvedt. Macroeconomc Factors and the Thoroughbred Industry. Journal of Agrcultural and Appled Economcs. 25 (1993):165-173. Keeneland Assocaton, Inc. 2005 November Breedng Stock Sales Catalog. Lexngton, Kentucky. 2005. Keeneland Assocaton, Inc. Keeneland Sales Results: 2005 November Breedng Stock Sale. Lexngton, Kentucky. accessed March 2006 at http://www.keeneland.com/lvesales/ showsale.asp?saled =200603. Krstofersson, D. and K. Rckertsen. Effcent Estmates of Hedonc Inverse Input Demand Systems. Amercan Journal of Agrcultural Economcs 86 (2001): 1127-1137. Ladd, G. and M. Martn. Prces and Demand for Input Characterstcs. Amercan Journal of Agrcultural Economcs 58 (1976) 21-30. 19
Ladd G. and V. Suvannunt. A Model of Consumer Good Characterstcs. Amercan Journal of Agrcultural Economcs 58 (1976) 504-510. Lancaster, K.J. A New Approach to Consumer Theory. Journal of Poltcal Economy 74 (1966): 132-157. Laughln, H. Racng Capacty of the Thoroughbred. Scentfc Monthly 38 (1934):310-321. McGurk, A.M., P. Drscoll, and J. Alwang. Msspecfcaton Testng: A Comprehensve Approach. Amercan Journal of Agrcultural Economcs 75 (1993): 1044-1055. Nebergs, S. A Hedonc Prce Analyss of Thoroughbred Broodmare Characterstcs. Agrbusness 17 (2001): 299-314. Nebergs, S. and R. Thalhemer. Prce Expectatons and Supply Response n the Thoroughbred Yearlng Market. Journal of Agrcultural and Appled Economcs 29 (1997): 419-435. Pedgree Onlne. Thoroughbred Database. Pearl Technologes, Carlsbad, Calforna. accessed March 2006 at http://www.pedgreequery.com/. Robbns, M. and P. Kennedy. Buyer Behavor n a Regonal Thoroughbred Yearlng Market. Appled Economcs 33 (2001): 969-977. Rosen, S. Hedonc Prces and Implct Markets: Product Dfferentaton n Pure Competton. Journal of Poltcal Economy 82,1 (1974): 34-55. Schroeder, T., J. M. Jones, and D. A. Nchols. Analyss of Feeder Pg Aucton Prce Dfferentals. North Central Journal of Agrcultural Economcs 11 (1989): 253-263. Schroeder, T., J. Espnosa, and B. Goodwn. The Value of Genetc Trats n Purebred Dary Bull Servces. Revew of Agrcultural Economcs 14 (1992): 215-226. Taylor, M.R., K.C. Dhuyvetter, T.L. Kastens, M. Doutht, and T.L. Marsh. Prce Determnants of Show Qualty Quarter Horses. presented at the annual Western Agrcultural Economcs Assocaton meetngs, Honolulu, Hawa, 2004. Vercken de Vreuschman, C.A. Are Pnhooked Yearlngs Dfferent? A Hedonc Prcng Analyss of Yearlngs at the Select Auctons. unpublshed masters thess, Department of Agrcultural Economcs, Unversty of Kentucky, 2005. Vckner, S. and S. Koch. Hedonc Prcng, Informaton and the Market for Thoroughbred Yearlngs. Journal of Agrbusness 19,2 (2001): 173-189. 20
Table 1. Varables, Expected Sgns on Parameters, and Descrptve Statstcs Varable (N = 298) Exp. sgn Mean Std. Dev. Mn. Max. Dependent Varable Prce ($) n/a 169,735.23 358,986.22 1,700.00 3,700,000.00 Breedng Characterstcs Age (years) - 9.01 3.94 1.00 20.00 # of Foals out of Mare - 2.76 2.95 0.00 14.00 Total Foal Earnngs ($) + 73,326.91 252,358.02 0.00 3,599,843.00 # of Foal Wns + 2.43 5.02 0.00 33.00 Avg. Earnngs per Foal ($) + 10,404.06 30,198.83 0.00 359,984.30 Expected Mare's Sre Value + 25.57 133.01 1.00 1,025.91 Stud Fee ($) + 41,970.64 61,895.67 1,250.00 500,000.00 # of Foals by Sre + 168.72 263.13 0.00 1,583.00 Expected Foal's Sre Value + 13.15 59.24 1.00 492.34 Racng Characterstcs # Races Mare Won + 2.22 2.95 0.00 18.00 # Races Mare Placed + 1.86 2.48 0.00 15.00 # Races Mare Showed + 1.69 2.25 0.00 14.00 Total Mare Earnngs ($) + 82,469.60 145,266.74 0.00 1,150,410.00 Genetc Characterstcs Mare s Dosage Index? 2.85 2.05 0.33 23.00 Mare s Center of Dstrbuton? 0.68 0.36-1.00 1.83 Mare s Genetc Strength Value + 65.62 7.49 44.57 79.41 Note: Independent varables nclude day of sale (11 bnary varables for Day 2 Day 12), expected to have negatve parameters. The randomly drawn sample s approxmately unformly dstrbuted across days, rangng from 6.0% on Day 7 and Day 10 to 9.7% on Day 5. 21
Table 2. Msspecfcaton Test Results Jont Condtonal Mean Test Test value Pr > Crtcal Value Stablty of β -0.91 0.36 Seral dependence -1.25 0.21 Functonal Form (RESET2) 0.38 0.71 Functonal Form (RESET3) -0.35 0.73 Jont test 0.61 0.66 Jont Condtonal Varance Test Stablty of σ 2 0.35 0.73 ARCH errors 0.34 0.73 Heteroskedastcty -0.51 0.61 Jont test 1.27 0.29 Normalty of Resduals Tests Shapro-Wlk 0.99 0.20 Kolmogorov-Smrnov 0.05 0.13 Cramer-von Mses 0.07 >0.25 Anderson-Darlng 0.51 0.20 Multcollnearty: Max. Varance Inflaton Factor = 9.49 < 10 22
Table 3. Parameter Estmates, Margnal Values, and Prce Flexbltes Varable Parameter Estmate Margnal Value Prce Flexblty Intercept 5.31 *** a (0.74) b Age -0.13 *** -13,695.45-1.13 (0.02) Total Foal Earnngs 1.72E-06 *** 0.18 0.12 (4.57E-7) (Total Foal Earnngs) 2-4.00E-13 *** (1.32E-13) ln(expected Mare's Sre Value) 0.15 *** 8.52 0.15 (0.03) ln(stud Fee) 0.69 *** 1.79 0.69 (0.06) Total Mare Earnngs 1.86E-06 *** 0.20 0.15 (2.85E-7) Center of Dstrbuton 0.15 16,602.78 0.10 (0.11) Day 2 0.08 9,261.85 (0.17) Day 3-0.22-21,929.46 (0.17) Day 4-0.38 * -33,962.23 (0.20) Day 5-0.82 *** -61,268.72 (0.18) Day 6-0.58 *** -48,034.58 (0.20) Day 7-0.98 *** -68,027.41 (0.22) Day 8-1.07 *** -71,511.15 (0.21) Day 9-1.03 *** -70,163.09 (0.22) Day 10-1.22 *** -76,808.58 (0.24) Day 11-1.39 *** -82,054.70 (0.24) Day 12-1.56 *** -86,078.74 (0.24) Adjusted R 2 0.83 a *, **, and *** denote statstcal sgnfcance at the.10,.05, and.01 levels, respectvely b standard errors n parentheses 23
Fgure 1. Broodmare Prces are Approxmately Log-Normally Dstrbuted* 40 35 30 Frequency 25 20 15 10 5 0 7.4 8.2 9.0 9.7 10.5 11.2 12.0 12.8 13.5 ln(prce) * null hypothess of normalty not rejected at.10 level by Cramer-von Mses and Anderson- Darlng tests, and not rejected at.05 level by Shapro-Wlk and Kolmogorov-Smrnov tests 24
Fgure 2. Example of Out-of-Sample Forecastng Performance, Thel s U = 0.34 14 ln(forecasted Prce) 13 12 11 10 9 8 8 9 10 11 12 13 14 ln(actual Prce) 25