QUARTERLY JOURNAL OF ECONOMICS

THE

QUARTERLY JOURNAL

OF ECONOMICS

Vol. CV



August 1990



Issue 3

CUSTOMER RACIAL DISCRIMINATION IN THE MARKET

FOR MEMORABILIA: THE CASE OF BASEBALL*

CLARK NARDINELLI AND CURTIS SIMON

Because consumer discrimination can reduce productivity, it is often impossible

to tell whether differential productivity is the effect of discrimination or of

differential ability. Detailed data for the sports labor market make it possible to

separate consumer discrimination from ability. We use a unique approach to

determine whether the entertainment value of baseball players is related to their

race: we examine whether race directly affects the value of a player in the market for

baseball cards. In contrast

to studies that use salaries, there is no room for owner

or coworker discrimination. Our evidence supports the hypothesis of consumer

discrimination.

I. INTRODUCTION

Economists have long attempted to explain the persistent wage

gap between blacks and whites. The usual practice is to specify an

empirical model that relates earnings to individual characteristics,

such as education, training, experience, and age, in an attempt to

control for productivity differences across individuals. Remaining

differences in earnings between races are attributed to dis-

crimination.' If the residual wage gap between races is accepted as

evidence of racial discrimination in labor markets, the question

arises: what type of discrimination? Becker [1971] identified three

principal sources of discrimination: discrimination by employers,

* We acknowledge the helpful comments of William Dougan, Lawrence M.

Kahn, Raymond Sauer, John Warner, and an anonymous referee. We alone are

responsible for all errors and omissions.

1. For an exception see Kamalich and Polachek [1982]. For a criticism of

Polachek's approach, along with a reply, see Blau and Kahn [1985] and Kamalich

and Polachek [1985].

Technology.

The Quarterly Journal of Economics,

August 1990

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discrimination by fellow workers, and discrimination by consumers.

Employer discrimination, often discussed in the popular press, is

highly unlikely to persist in competitive labor markets. If workers

are mobile in the long run, self-sorting by workers will cause

coworker discrimination to disappear in the long run.

A more likely source of the continuing wage gap, then, is

consumer discrimination. Empirical studies indicate that such

discrimination exists. Yinger [1986] found that it led to racial

discrimination in Boston housing markets. The study of consumer

discrimination in labor markets, however, faces a serious problem:

consumer discrimination is difficult to measure. A key assumption

in Becker's model is that blacks and whites are equally productive.

Yet, consumer discrimination can directly reduce productivity,

making it impossible to tell whether differential productivity is the

effect of discrimination or of differential ability to do the job. For

example, if black realtors sell fewer houses than white realtors, is it

because black realtors know less about houses, or is it because house

buyers and sellers discriminate against blacks? Unless ability can

be measured, this question cannot be answered.

Although ability is nearly impossible to measure in most labor

markets, there is an important

exception: the sports labor market.

The appeal of sports for studies of discrimination is that it is

possible to separate consumer discrimination from ability to do the

work. Professional sports firms produce entertainment. The enter-

tainment value of a sport is directly related to players' abilities and

to the way consumers repond to those abilities. The detailed data on

individual athletic performance permit the separation of consumer

response from other measures of performance.

For example, in a recent study of the National Basketball

Arrow [1972] argued that nonconvexities in the cost of adjusting the firm's

labor force could cause wage differentials arising from employer or coworker

discrimination to persist in the long run. That is, if there is a capital cost associated

with the addition of a worker to the labor force, employers may try to avoid replacing

white workers by black workers (and vice versa). A recent study by Lindsay and

Maloney [1988] empirically tested for the existence of coworker discrimination

against women. They pointed out that the costs of sorting vary inversely with labor

market size. Their empirical tests gave no support to the coworker discrimination

hypothesis against females. Another possible source of discrimination is imperfect

information. If individual data (education, experience, and so on) do not communi-

cate productivity perfectly, information on race and sex may enable the employer to

predict productivity more precisely. If this is the case, otherwise identical individuals

of different race or sex may be paid differently. McCall [1972] and Spence [1973]

were among the first to develop models of statistical discrimination.

What is crucial, is that omitted variables that measure players' abilities be

uncorrelated with race. In most studies using data from other (nonsports) labor

markets, this is usually not the case. This issue will be addressed below in Section IV.

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Association, Kahn and Sherer [1988] find a 20 percent wage gap

between blacks and whites, holding constant measures of perfor-

mance. Kahn and Sherer reject employer or coworker discrimina-

tion as the source of the wage gap, because buy-outs by nondiscrim-

inators or segregation by firm should reduce these sources of

discrimination. Furthermore, Kahn and Sherer find strong circum-

stantial evidence that the wage gap results from customer discrimi-

nation: basketball attendance is strongly and positively related to

the proportion of team members who are white, holding constant

other factors.

Kahn and Sherer's evidence of consumer discrimination is

suggestive, but indirect. Other evidence, although casual, suggests

that discrimination indeed exists in the sports labor market. For

example, it is widely believed that white sports heroes receive far

more offers for endorsements than black sports heroes of equal

ability.'

In this paper we use an unusual approach to determine whether

the entertainment value of baseball players is related to their race.

Previous studies, such as that of Kahn and Sherer and recent work

on discrimination in baseball [Raimondo, 1983; Hill and Spellman,

1984], focus primarily on salaries. By contrast, we examine whether

race directly affects the entertainment value of a player in the

market for baseball cards. We ask whether a player's race affects the

price consumers pay for a given card. Advantages of studying this

market rather than players' salaries are as follows: (1) the data are

readily available; and (2) in contrast to players' contracts, which are

often complex documents containing performance clauses, the

prices of baseball cards are measured with comparatively little

error. In contrast to studies of salaries, the link between consumer

racial attitudes and the price of baseball cards is direct. There is no

room for owner or coworker discrimination.

II. THE BASEBALL CARD MARKET

The defining characteristic of collectors is a serious interest in

baseball. The market for baseball cards has long ceased to be the

domain solely of children. Most serious collectors are adults.

4. An unnamed individual quoted in a recent

Wall Street Journal

[October 18,

1988] argued that "black athletes must be more famous, more accomplished, and

more personable than their white counterparts to make it in the endorsement

business."

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Children have not bid the price of a near-mint 1952 Mickey Mantle

Topps baseball card to $6,000 and the price of a near-mint 1952

Willie Mays Topps baseball card to $900.

Although baseball cards

are still sold in bubble gum packages, they are also sold in large

packages, often as complete sets or as subsets. There are thousands

of full- and part-time dealers, clubs, and conventions.

Although some small regional price differences persist, the

market for used and new cards is national. Beckett's

Official 1989

Price Guide to Baseball Cards

has set the standard for price guides

in the hobby, and was therefore chosen as our source for prices.

The

supply of a particular card is a fixed quantity. In general, the older

the card, the rarer the card. For old cards this rarity is a combina-

tion of smaller initial production and greater deterioration of the

existing stock of cards. Indeed, it is difficult to find top-condition

cards for some years. For more recent cards the scarcity is primarily

caused by depreciation.

We analyze the determinants of the 1989 price of the complete

set of mint Topps baseball cards issued for individual players in

1970, as reported in the 1989 edition of Beckett's price guide.

Although four companies, Topps, Fleers, Donruss, and Score issued

full sets of cards in 1988, Topps had a virtual monopoly on bubble

gum cards from 1956 to 1980. Our need for an older card set (for

reasons discussed shortly) required the use of Topps cards. Before

we discuss the reasons why we chose the year 1970, we provide some

background information on the baseball card market.

The value of a player's card is determined largely by two

factors: (1) career performance; and (2) the scarcity of the card,

which is related to the age of the card and the number originally

printed. Art counts for very little.

A player's lifetime performance

is the primary determinant of the demand for a player's card. If the

differences in ability are sufficiently large, it is virtually certain that

the card featuring the better player is more valuable. Henry Aaron

(755 career home runs) is invariably more valuable than teammate

Hawk Taylor (16 career home runs). Older cards are scarcer, and

therefore more valuable. The player's performance in the year the

Our source for these prices was the Beckett [1989] price guide, described

below.

Other publications that serve the hobby include

Baseball Cards

and

Baseball

Card Price Guide Monthly.

The differences in prices between Beckett and these

other guides are small.

7. Artistic design affects the value of a card only to the extent that it affects card

longevity. For example, cards with colored borders (e.g., Topps, 1962 and 1971)

physically deteriorate more rapidly than others.

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RACIAL DISCRIMINATION AND BASEBALL CARDS

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card was issued is largely irrelevant. A 1957 Topps Willie Mays

($100) is more valuable than a 1965 Topps Willie Mays ($40)

because it is older and rarer, not because Mays had better years in

1956-1957 (71 home runs in the two years) than 1964-1965 (99

home runs).

We chose the year 1970 to avoid having to account for

differential information about young and old players. There is a

brisk speculative demand for the cards of young players because

dealers and collectors attempt to forecast the future superstars of

the game. A young, but promising, player will therefore often sell for

more than a better, but older, player who has already established a

level of performance below superstar level. By choosing 1970 cards,

we have no young players (as of 1989). Nearly all the players in the

sample were retired by 1988, and those who had not yet retired

(Sutton, Carlton) had already established their career performance

levels.

Cards before 1974 were issued in series, each of which was made

available to the public sequentially throughout the baseball season.

Because interest in baseball cards waned toward the end of the

season, Topps produced fewer cards for series later in the set. Cards

issued later in the season therefore sell at higher prices, other

things

equal.

A curious aspect of the market is the peculiar attraction of

certain players. All else the same, Mickey Mantle (who is not in our

sample) is always the most valuable card in a set. Other favorites

include Pete Rose and Carl Yastrzemski. Although it is not

surprising that such great players are highly regarded by card

collectors, it is surprising that they are so much more highly valued

than other great players. The 1963 Topps Stan Musial sells for

$35,

and the 1963 Topps Yastrzemski sells for $50. Yet, Musial is

considered much the greater player in 49 of the 50 states and most

foreign nations.

The value of a card issued in a particular year may be related to events in a

player's life in that year, such as winning the Most Valuable Player award. We have

not undertaken a systematic study of such effects, however, because career perfor-

mance explains most of the demand for a player's card.

Comparisons involving Mantle are even more striking. Even accounting for

relative scarcity, Mantle cards are

always

more valuable than those of any other

player—in some years his cards are more than double the price of the second most

valuable card. The Mantle phenomenon is probably related to his charisma. Mickey

Mantle, Pete Rose, and Reggie Jackson had it; Stan Musial, Henry Aaron, and

Warren Spahn did not. The charisma of players, which is not measurable by the

researcher, is one component of the error term.

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III. MEASURING PLAYER PERFORMANCE

The appeal of sports for tests of the discrimination hypothesis

is that performance is more easily measured than in other occupa-

tions. Baseball probably generates more data on performance than

any other sport.' Despite the wide array of useful and often

sophisticated measures, it is difficult to compare the performance of

different players. A long list of small factors affects a player's

numbers.

For example, ball parks have different dimensions and sur-

faces, not to mention aerodynamics, complicating comparisons

between players. A hitter who played his entire career in a pitcher's

park such as Los Angeles's Dodger Stadium will have lower

performance statistics than if he played in a hitter's park such as

Chicago's Wrigley Field. Park differences pose similar problems for

pitchers.' Although park adjustments have been devised, it is

infeasible for us to use them. Few players spend their entire career

in one park; individual players change clubs; and whole teams

commonly (in our sample) moved to new parks. Park adjustment

calculations would therefore be exceedingly time-consuming. An-

other reason we do not make the adjustment is more easily justified:

park illusion exists. Most followers of baseball truly believe that the

Boston Red Sox and the Chicago Cubs have consistently good

hitting, though often (especially in Chicago) the belief is pure park

illusion.' If we are studying consumer preferences, the unadjusted

numbers tell the story.

We also decided against putting in a variable for team location

or team performance. Players switch teams, and teams themselves

fluctuate in quality. Such differences will tend to wash out over

time. It is possible, however, that individuals who played in

10.

Although no one source includes all data of interest, the Macmillan

Baseball

Encyclopedia is

an extraordinary compendium of data;

The Sports Encyclopedia:

Baseball

is nearly as complete. Other important sources include the

Sporting News

Official Baseball Guide

and other

Sporting News

publications, the

Elias Baseball

Analyst, the

Great American Stat Book,

and publications of the Society for

American Baseball Research. Countless other publications, large and small, produce

an array of new and interesting numbers. For a survey of various statistical and other

sources, see Chapter 3 of Tomlinson [1987].

11.

The problem may be smaller, however, because many of their performance

measures (wins, losses, possibly strikeouts, and walks) are less likely to be affected by

the home park of the pitcher; both the home team and visiting team pitchers pitch

under the same conditions.

12. In 1970 the Los Angeles Dodgers and their opponents combined scored 625

runs in Dodger Stadium, but they and their opponents scored 807 runs in games

played away from Dodger Stadium. The Chicago Cubs and their opponents scored

865 runs in Wrigley Field, Chicago, but 620 runs away.

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postseason (playoff and World Series) games received greater

attention and therefore are in higher demand by collectors. We

therefore controlled for the number of postseason games played by

hitters and the number of postseason innings pitched by pitchers.

Comparisons over time are even more problematic, even when

performance according to the numbers is comparable. Consider two

players with seemingly comparable statistics: Ken Williams in 1922

(39 home runs, 159 runs-batted-in, .332 batting average, .627

slugging average) and Billy Williams in 1972 (37 home runs, 122

runs batted in, .333 batting average, .606 slugging average). Because

of numerous factors, including the trend of ballparks to become less

favorable to hitters, possible changes in the ball, and advances in

the "science" of pitching, Billy Williams faced much tougher

competition than did Ken Williams.

Although formulas have been

developed for comparing players of different eras, these formulas

use a single index approach.

Such adjustments do not serve our

purpose because—as explained below—we reject the single index

approach to measuring performance.

The problems that arise when comparing players from dif-

ferent eras are reduced by including in our sample only players

active in 1970. Index problems still arise-1955-1972 is not the

same as 1969-1986—but errors arising from this source should be

comparatively small. The most important problem that arises is

that, holding constant the number of cards originally printed, the

remaining stock of cards of players may differ systematically with a

player's age. If a young player had not yet established himself as a

star in 1970, collectors might not have saved as many of his cards as

those of an already established star. The then-young player's card

may now have a higher value than the older player, all else the same.

In preliminary regressions not reported below, we entered each

player's year of debut as a control variable. We expected year of

debut to positively affect the card price. Because there were no cases

in which debut year was either significant or caused our other

results to change materially, we dropped this variable from the

analysis.

Despite the errors in the measurement of player performance,

the estimates of the effect of race on card price will be unbiased as

13.

The league batting and slugging averages were .284 and .397 for Ken

Williams, but only .248 and .365 for Billy Williams.

14.

For example, the batting performance of two players in different years can

be compared by comparing the ratio of each player's average to the mean batting

average in that year.

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long as these errors are uncorrelated with race. None of the factors

discussed above should affect players of one race more than

another.

A wide variety of measures of performance can be used as

explanatory variables. Summary measures that attempt to rank

players by using a single number are computed from basic statistics

such as singles, doubles, triples, home runs, walks, and so on.

Because these indexes impose econometric restrictions that may be

rejected by the data, we rejected the single-index approach in favor

of entering each of the rudimentary statistics as explanatory

variables. This procedure allows the data to speak as to how card

collectors value a given measure of performance. The raw statistics

are collected from the Macmillan

Baseball Encyclopedia

(seventh

edition).

IV. EMPIRICAL FRAMEWORK

The Common Player

Although the price of baseball cards is related to the entertain-

ment value of a player, most baseball cards sell at what is called the

"common player"

price. The price of the common player is the

minimum value a card can take, and is unrelated to the performance

of the player. Even the worst player's card commands a positive

price because it has intrinsic value as a card.

As we mentioned earlier, card sets issued before 1974 were

issued in series throughout the baseball season. Later series, issued

when interest in baseball cards had waned, therefore tend to be

rarer and command higher prices. Table I shows the common player

prices and frequencies in our sample. Six series of cards were issued

in 1970. Common player prices range from $0.20 to $1.50. About 70

percent of the hitters and 80 percent of the pitchers sell at the

common player price, which introduces a censored dependent

variable problem. The next section shows how we correct for this

problem.

The Model

Assume that the utility that fans receive from a player's

lifetime performance,

is linearly related to a vector of the player's

characteristics,

(1)



= 11'X,

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RACIAL DISCRIMINATION AND BASEBALL CARDS

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TABLE I

PERCENT COMMON PLAYERS AND COMMON PLAYER PRICES (IN DOLLARS)

Number



Percent



Common



Maximum



Mean

Player



common



player



card



card



players



players



price



price



price

Hitters



1-132



72.1



0.20



18.00



0.538



133-263



73.1



0.25



35.00



1.095



264-459



64.5



0.30



18.00



0.813



460-546



64.7



0.35



18.00



1.221



547-633



65.9



0.60



75.00



3.210



634-720



71.7



1.50



75.00



4.054

Pitchers



1-132



78.0



0.20



2.50



0.328



133-263



83.7



0.25



11.00



0.721



264-459



81.0



0.30



25.00



0.852



460-546



75.0



0.35



4.50



0.639



547-633



79.3



0.60



1.50



1.062



634-720



85.7



1.50



45.00



3.160

Note.

Player ID is the Topps card number. The number of observations is smaller than the total number of

cards because many cards are not of individual players. Percent common players is the fraction of players who

sold at the common player price.

where the vector

includes both the player's performance and

race. We wish to determine whether V is significantly affected by

the player's race. It is not possible to observe

and so estimate (1)

directly. Although one alternative is to replace

with the player's

card price, there is no observable effect of player's performance on

card price for the players who sell at the common player price,

despite significant performance differences. Rather than conclude

that

is the same for these players, we assume that each card has a

positive intrinsic value, and that the value of the card is not related

to performance at low levels of performance.'

Let

be the log dollar price of a baseball card. We assume that

is equal to the sum of two independent components:

(2)

P = Pc + Pp,

where

is the log price of the common player and

is the

component of log price that is related to player performance and

15. Cards featuring minor players have intrinsic value for collectors who desire a

complete set and to collectors who specialize in acquiring all cards ever issued for a

particular team.

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Player Performance ( X )

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race characteristics. We estimate equation (1) by defining V as a

latent variable that is related to

in the following way:

(3)

= max [0,V].

Combining equations (2) and (3), we have

(4)

P = P

max [0,

IT].

The situation is illustrated in Figure I for the case of two series of

cards. Because different quantities of cards were printed in the two

series, their common player prices, P

and

Pa,

differ. At low

performance levels, V < 0, and cards sell at the minimum, common

player price

As performance rises, V increases at the rate

eventually, becoming positive, at which point

includes a positive

performance premium of

Otherwise identical players who are

issued as part of different series will sell for different prices equal to

the difference between P

and

Pa.

Rearranging equation (4) and substituting in equation (1) gives

(5)



P — P

max [0,

3'X ] .

Equation (5) can be estimated using the well-known tobit tech-

nique. The left-hand side is the adjusted log card price. The

right-hand side is a linear function of player characteristics.

The determination of the price of baseball cards differs for

pitchers and hitters. We begin with the hitters.

Card Price ( $)

Pc2

P= P

+ ,6X

Pc2 +

fl X

FIGURE I

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RACIAL DISCRIMINATION AND BASEBALL CARDS

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585

C. Hitters

We specified the following basic model:

(+)



(+)



(+)

(6)

P — P

= a

+ a

HITS +

DOUBLES +

TRIPLES

( +)



(+)

HOME RUNS +

WALKS

(+)



( -)

STOLEN BASES +

AT BATS

(-)



(+)

SEASONS +

POSTSEASON GAMES

(?)



(?)

BLACK +

HISPANIC

POSITION DUMMIES + error term.

Position dummies were entered for first base, second base, third

base, shortstop, and catcher; the omitted category was outfield.

Expected signs on the coefficients are shown in parentheses.

Summary statistics for hitters' statistics appear in Table II.

The estimated coefficients on race will be unbiased indicators

of consumer discrimination as long as the race variables are

uncorrelated with omitted variables that measure the athletic

prowess of the players. The variables included in equation (6)

include most variables considered to be important by fans and

analysts of baseball. We believe that it is unlikely that there are any

important omitted variables that are correlated with race.

Two omissions may provoke some controversy: runs scored and

runs-batted-in. These measures are redundant because players who

have many walks, singles, doubles, triples, and home runs will score

and bat in large numbers of runs. Runs-batted-in and runs scored

are highly correlated with singles, doubles, triples, and home runs.

Holding constant these other variables, more runs-batted-in and

runs scored indicate principally the quality of the hitters surround-

ing the player in the lineup. We did not, therefore, include those

variables in our basic measure of player quality.

16.

The expected signs on the position dummies are as follows: first base ( — );

second base ( + ); shortstop ( + ); third base ( + ); and catcher (+ ), all relative to the

omitted category, outfield. The position dummies partly measure the effect of

fielding ability. We lacked sufficient degrees of freedom to undertake a full analysis

of the contribution of fielding ability to card prices.

17.

Some observers believe that runs-batted-in are a good indicator of "clutch"

performance, and that players with large totals are those who come through in

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We estimated equation (6) using tobit, reported in column 1 of

Table III.' The coefficients all entered as expected. Players with

more hits, doubles, triples, and home runs sold for higher prices.

Holding hitting performance constant, the more at-bats or seasons

that it took to accomplish the feat, the lower the price of the card.

Stolen bases entered positively, but not significantly.'

We first estimated a version of equation (6) in which we

combined blacks and Hispanics into a single category, NON-

WHITE. The resulting tobit regression is reported in column 1 of

Table III. Approximating the normal distribution 4) with the sample

proportion of cards that sold for more than the common price (31.4

percent), its coefficient implied that nonwhites sold for about 10

percent less than whites of comparable ability.

It is noteworthy

that the differences in card prices due to race were in the same range

as racial differences in earnings found using variations of the log

earnings model.

When separate dummy variables were defined for blacks and

Hispanics, the results of the tobit model indicated that cards

featuring blacks sold for about 6.4 percent less, and Hispanics about

important situations. Performance in pressure situations often varies over a career

for any one

player. Career runs-batted-in is therefore unlikely to measure clutch

performance over a lifetime. Moreover, runs-batted-in is a function of opportunities

as much as of ability. Lou Gehrig set the American League record for runs-batted-in

in 1931 (184) partly because the man batting in front of him, Babe Ruth, reached

base safely 327 times. Although it is possible to measure the number of what Bill

James [1985, p. 308] calls victory-important runs-batted-in, we do not have such a

measure for our sample. And although our rudimentary measures of performance do

not record the importance of the player's contribution in the clutch, it is not clear

that clutch performance can be adequately defined or measured independently of

the other measures of performance. As an example, Reggie Jackson is often cited as a

great player in important games. Evidence offered to support this hypothesis is that

in 27 World Series games Jackson hit 10 home runs, batted in 24 runs, and compiled

batting and slugging averages of .357 and .755, well above his career performance

levels in the regular season. Consider, though, that in 45 League Championship

Series games, Jackson hit 6 home runs, batted in 20 runs, and compiled batting and

slugging averages of .227 and .380—all figures well below his career regular season

levels. The evidence that Jackson was a big-game player is mixed at best, and, to us,

unconvincing. Other anecdotal evidence that this or that player was better in

important situations is open to similar criticisms.

18.

Results for the tobit model also include SIGMA, the estimated standard

error of the regression.

19.

This coefficient is consistent with Pete Palmer's [Thorn and Palmer, 1984]

estimate of a relatively small contribution of stolen bases to runs scored. In

regressions with team runs as the dependent variable, a stolen base was approxi-

mately one fifth as productive as a home run. Furthermore, unsuccessful attempts to

steal have a negative coefficient about twice as large in absolute value as stolen bases.

The small coefficient on stolen bases may therefore also pick up the negative effect of

being caught stealing.

20. Note that coefficients in the tobit regression do not measure

(P –

)/ax,

but

awax.

Rather,

(P –

) /ax=

(3X)

awax,

where 1( ) is the value of the

cumulative normal distribution function, which is the probability that a player sells

for more than the common player price.

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RACIAL DISCRIMINATION AND BASEBALL CARDS



587

TABLE II

MEANS (STANDARD DEVIATIONS) OF VARIABLES FOR HI1

1 ERS

All

races



White



Hispanic



Black

Card price*

P - Pc



0.341



0.237



0.291



0.237

(0.826)



(0.669)



(0.769)



(0.669)

EXP

(P - P

)



3.45



2.67



2.77



6.06

(12.64)



(10.97)



(8.61)



(17.84)

STAR



0.314



0.271



0.229



0.487

Lifetime performance

SEASONS



6.9



6.2



7.5



8.7

(4.5)



(4.2)



(4.5)



(4.9)

AT BATS



3,598.0



3,079.7



4,034.7



4,778.0

(2754.8)



(2453.7)



(2810.5)



(3121.2)

HITS



943.7



780.4



1,092.4



1,308.6

(789.0)



(678.6)



(808.0)



(923.5)

DOUBLES



149.2



124.1



167.8



208.0

(133.1)



(116.0)



(134.0)



(156.7)

TRIPLES



26.4



19.7



32.4



41.2

(26.8)



(19.6)



(31.0)



(34.2)

HOME RUNS



94.8



77.5



71.6



157.5

(119.8)



(95.6)



(89.3)



(167.6)

WALKS



358.8



326.2



283.5



496.0

(329.3)



(307.4)



(222.7)



(401.0)

STOLEN BASES



58.8



27.1



82.0



133.1

(106.4)



(40.4)



(125.1)



(165.9)

Race

BLACK



0.227



0.000



0.000



1.000

HISPANIC



0.140



0.000



1.000



0.000

Obs.



344



218



*P - P

is the log card price minus the log price of the common player. EXP

(P - P

)

is the unlogged card

price divided by the price of the common player. STAR is the proportion of players with a card price greater than

the price of the common player, that is, with

P - P

> O.

17 percent less, than otherwise comparable white players. The null

hypothesis of equal coefficients could be rejected at about the 7

percent level using a log likelihood (chi-square) test, with a

chi-square of 3.38.

One worry with respect to the empirical findings in Table III is

the role of outliers. A glance at Table I indicates that several players

sell for tremendously high prices. The question arises whether

customer discrimination is pervasive throughout the ability distri-

bution or whether the results are driven largely by the superstar end

of the market. We therefore also estimated a probit model in which

the dependent variable was whether a player sold for more than the

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TABLE III

LOG PRICE TOBIT REGRESSIONS AND PROBIT REGRESSIONS FOR HITTERS

Dependent variable:*



P - P,



STAR

Estimation method



Tobit



Probit

(1)



(2)



(3)



(4)

NONWHITE



-0.3188



-0.8389

(2.4)



(2.8)

BLACK



-0.2029



-0.3892

(1.4)



(1.2)

HISPANIC



-0.5516



-2.0647

(2.9)



(3.8)

HITS



0.0030



0.0031



0.0066



0.0084

(4.5)



(4.7)



(2.9)



(3.4)

DOUBLES



0.0008



-0.0008



-0.0066



-0.0044

(0.5)



(0.4)



(1.1)



(0.7)

TRIPLES



0.0021



0.0016



0.0132



0.0134

(0.6)



(0.5)



(1.1)



(1.1)

HOME RUNS



0.0032



0.0030



0.0095



0.0084

(4.4)



(4.0)



(2.8)



(2.4)

WALKS



0.0004



0.0003



-0.0013



-0.0019

(1.2)



(0.9)



(1.2)



(1.7)

STOLEN BASES



0.0002



0.0000



0.0026



0.0018

(0.3)

(0.1)

(1.1)

-0.0004

-0.0012

(1.7) (1.8)

(1.7)

-0.1417

-0.1336

0.0872

(1.7)

(1.6)

(0.5)

0.0262

0.0515

(6.0)

(4.0)

0.0597

0.0693

0.1939

(0.4)

(0.5)

-0.0474

-0.0328 -0.2694

(0.2)

(0.6)

0.4496

0.4970

0.7988

(2.4)

(2.7)

(1.9)

-0.0839 -0.0699

-0.0203

(0.4) (0.4)

(0.0)

0.1402

0.1602

0.0670

(0.8)

(0.9)

(0.2)

-1.2845 -1.3116

- 2.0219

(6.3)

(6.4)

(5.3)

0.6445

0.6421

(14.8)

-421.95 -421.95

-224.05

-154.18

-152.49

-88.88

(0.7)

-0.0017

(2.2)

-0.0510

(0.3)

0.0538

(3.9)

0.1386

(0.4)

-0.2622

(0.5)

1.0389

(2.3)

0.0212

(0.0)

0.1439

(0.4)

-2.1714

(5.4)

-224.05

-83.06

AT BATS

SEASONS

POSTSEASON GAMES

First base

Second base

Third base

Shortstop

Catcher

CONSTANT

SIGMA**

Log likelihood

(Slopes = 0)

Log likelihood

Note.

334 observations. Asymptotic t-ratios are in parentheses.

*P - P

is the log card price minus the log price of the common player. STAR is the proportion of players

with a card price greater than the price of the common player, that is, with

P - P

**SIGMA is the estimated standard error of the regression.

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RACIAL DISCRIMINATION AND BASEBALL CARDS

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589

common price. The probit results cannot be driven simply by the

tremendous prices commanded by a couple of players. The explana-

tory variables were identical to those in equation (6).

The results are reported in columns 3 and 4 of Table III.

The

dependent variable was STAR, where STAR equals one if the

player's card sold for more than the common player price, and zero

otherwise. The regression with nonwhites combined into a single

category indicates that nonwhites sold for significantly less than

otherwise comparable white hitters. We next divided nonwhites

into blacks and Hispanics. The race coefficient for Hispanics was

significantly less than zero. Although the race coefficient for blacks

was negative, it was not significantly different from zero at conven-

tional levels of statistical significance

= 1.2).

It was, however,

easy to reject the null hypothesis of equal race coefficients at better

than the 1 percent level (chi-square = 11.64).

D. Pitchers

We specified the following equation for pitchers:

(+)



(-)



(+)

(7)



P — P

= 13

+ 13

WINS + /3

LOSSES + (3

SAVES

(+)

COMPLETE GAMES

(-)



(+)

EARNED RUNS + 13

STRIKEOUTS

(-)



(?)

WALKS + 13

INNINGS PITCHED

(-)



(+)

/39

HITS + 0

POSTSEASON INNINGS

(?)



(?)

BLACK + O

HISPANIC

error term.

Most of the expected signs are self-explanatory. INNINGS

PITCHED represents longevity. Although for a given level of

STRIKEOUTS and COMPLETE GAMES, more innings pitched

21.

Note that the estimated coefficients from this probit model are consistent

estimates of the coefficients of the tobit model up to a factor of proportionality. See

Maddala [1983, p. 159].

22.

The effect of race on the marginal probability of being a STAR is given by

Vi3„ where V is the density function of the standard normal distribution and

13,

is the

estimated race coefficient.

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590

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QUARTERLY JOURNAL OF ECONOMICS

implies a lower performance level, the opposite is true for WALKS,

HITS, and EARNED RUNS. The net effect of INNINGS PITCHED

is therefore ambiguous.

Summary statistics for pitchers appear in Table IV. As with

hitters, nonwhite pitchers had better overall statistics measured by

career wins, saves, earned runs, complete games, and strikeouts.

Nonwhites also pitched far more innings on average over the span of

their careers.

Tobit estimates of equation (7) are reported in Table V. The

TABLE IV

MEANS (STANDARD DEVIATIONS) OF VARIABLES FOR PITCHERS

All

races



White



Hispanic



Black

Card Price*

P - P

0.241



0.230



0.336



0.334

(0.692)



(0.680)



(0.770)



(0.831)

EXP (P -

)



2.28



2.29



2.23



2.30

(6.76)



(7.07)



(3.60)



(3.46)

STAR



0.193



0.188



0.308



0.154

Lifetime performance

WINS



82.9



79.1



99.7



126.8



(73.2)



(71.6)



(90.2)



(69.4)

LOSSES



77.2



75.0



81.2



109.2



(58.8)



(58.4)



(66.6)



(51.5)

SAVES



27.4



28.4



19.7



18.2



(46.8)



(48.7)



(28.4)



(25.3)

COMPLETE GAMES



45.1



40.9



70.5



85.9



(60.3)



(55.6)



(87.4)



(81.9)

HITS



1,318.6



1,271.9



1,490.9



1,890.1



(1,065.0)



(1,054.6)



(1,240.6)



(935.3)

EARNED RUNS



543.0



523.6



617.8



777.8



(420.7)



(415.3)



(503.5)



(309.9)

STRIKEOUTS



891.7



846.8



1,011.5



1,487.5



(796.2)



(776.0)



(892.9)



(828.6)

WALKS



490.9



470.7



545.8



741.9



(796.2)



(364.2)



(452.7)



(284.6)

INNINGS



1,415.7



1,360.6



1,609.4



2,100.5

PITCHED



(1,157.4)



(1,140.9)



(1,355.8)



(1,057.2)

Race

BLACK



0.056



0.000



0.000



1.000

HISPANIC



0.056



0.000



1.000



0.000

Obs.



233



207



*P - P

is the log card price minus the log price of the common player. EXP

(P - P

)

is the unlogged card

price divided by the price of the common player. STAR is the proportion of players with a card price greater than

the price of the common player, that is, with

P - P

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RACIAL DISCRIMINATION AND BASEBALL CARDS

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591

TABLE

LOG PRICE TOBIT REGRESSIONS

AND

PROBIT REGRESSIONS FOR PITCHERS

Dependent variable:*



P - P,



STAR

Estimation method



Tobit



Tobit



Probit



Probit

(1)



(2)



(3)



(4)

NONWHITE



-0.6848



-1.9097

(2.7)



(2.0)

BLACK



-0.822



-3.3976

(2.2)



(0.8)

HISPANIC



-0.592



-1.5605

(1.9)



(1.3)

WINS



0.02364



0.023



0.02762



0.02770

(2.7)



(2.7)



(1.2)



(1.2)

LOSSES



-0.00625



-0.0060



-0.01341



- 0.01388

(0.8)



(0.8)



(0.6)



(0.6)

SAVES



0.00832



0.0083



0.02054



0.01989

(4.8)



(4.7)



(3.1)



(3.0)

COMPLETE GAMES



0.00883



0.0088



0.04948



0.04821

(2.6)



(2.6)



(2.8)



(2.7)

HITS



-0.00047



-0.00044



0.00163



0.00189

(0.5)



(0.5)



(0.5)



(0.6)

EARNED RUNS



-0.00139



-0.0015



-0.00330



-0.00387

(0.9)



(1.0)



(0.7)



(0.8)

STRIKEOUTS



0.00006



0.00068



0.00010



0.00024

(0.2)



(0.3)



(0.1)



(0.2)

WALKS



0.00007



0.00068



0.00365



0.00356

(1.4)



(1.4)



(1.7)



(1.6)

INNINGS PITCHED



0.00007



0.00006



-0.00301



-0.00305

(0.1)



(0.0)



(0.8)



(0.8)

POSTSEASON INNINGS



0.00209



0.00216



0.01446



0.01422

(0.8)



(0.8)



(1.1)



(1.0)

CONSTANT



-2.1318



-2.126



-3.7673



-3.7066

(2.0)



(8.4)



(5.0)



(5.0)

SIGMA**



0.528

(9.5)

Log likelihood

(Slopes = 0)



-244.20



-244.20



-114.34



-114.34

Log likelihood



-55.60



-55.4



-33.73



-33.54

Note.

233

observations. Asymptotic t-ratios are in parentheses.

*P - P

is the log card price minus the log price of the common player. STAR is the proportion of players

with a card price greater than the price of the common player, that is, with

P - P

> O.

**SIGMA

is the estimated standard error of the regression.

estimated coefficients all had the expected signs, with the exception

of WALKS, which entered positively and marginally significantly.

The estimated coefficients on the race variables were all

negative. We look first at the results in column 1, where blacks and

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QUARTERLY JOURNAL OF ECONOMICS

Hispanics were combined into a single category, NONWHITE. The

results indicated that nonwhites sold for 13 percent less than

otherwise comparable whites, where we approximated (I) with the

sample mean (19 percent of pitchers sold for more than the common

price). The results in column 2 indicated that cards featuring blacks

sold for about 16 percent less, and those featuring Hispanics for

about 12 percent less, than otherwise comparable white pitchers'

cards. Despite the considerable differences in the point estimates of

the effect of race, a log likelihood test did not reject the null

hypothesis of equal race coefficients for blacks and Hispanics at

conventional levels of statistical significance.

To determine whether the negative effect of being black or

Hispanic existed throughout the ability distribution or only at the

superstar end of the market, we ran probit regressions for the

pitchers, where the dependent variable was STAR (which is equal

to one if a card sold for more than the common player price, and

zero otherwise). When blacks and Hispanics were combined into a

single category, NONWHITE, the estimated coefficient on NON-

WHITE was statistically significant at the 5 percent level

= 2.0).

When blacks and Hispanics were separated, the t-statistics on each

of the race variables were insignificant at conventional levels (0.8

and 1.3 for blacks and Hispanics). In contrast to hitters, statistically

significant differences in consumer attitudes toward black versus

Hispanic pitchers were visible only at the superstar end of the

market: we could not reject the null hypothesis of equal race

coefficients. The lack of statistical significance on the individual

probit race coefficients is not surprising, given that there were only

13 black and 13 Hispanic pitchers.

The effect of being nonwhite on the card price of pitchers was

somewhat greater than for hitters (13 percent versus 10 percent).

The stronger effect of race in the pitcher regression seems plausible.

The pitcher is central and the most visible player in a baseball

game. As Becker [1971] suggested, customer discrimination against

nonwhites should be greater, the greater the degree of personal

contact with customers. We suggest that discrimination may be

greater, the more visible the player.

V. COMPARISON WITH STUDIES OF SALARY DISCRIMINATION

There are few studies of salary discrimination in sports. The

most recent is Kahn and Sherer's [1988] careful study of profes-

sional basketball. They find that blacks were paid about 20 percent

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RACIAL DISCRIMINATION AND BASEBALL CARDS

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593

less than otherwise comparable white players. The evidence of

discrimination from previous studies of baseball salaries is mixed.

The most recent empirical analyses of baseball salaries found no

wage gap between whites and blacks [Raimondo, 1983; Hill and

Spellman, 1984]. By contrast, Scully's [1974] study found strong

evidence of discrimination in major league baseball for the late

1960s.

In results not reported here, we found that functional form and

the choice of explanatory variables may be important determinants

of the sign and significance of race variables in studies of discrimina-

tion. Because single index measures of player performance impose

econometric restrictions, they must be chosen with care.

In the

absence of strong theoretical reasons for imposing restrictions on

the importance of each component of performance, we thought that

it was preferable to "let the data speak." In the course of our

investigation, we found evidence, albeit indirect, that the restric-

tions imposed by the use of single-index measures of performance

may have contributed to others' failure to find discrimination

among hitters.

Future research is necessary to resolve this issue.

23.

Raimondo and Hill and Spellman concluded that the introduction of free

agency in baseball led to the difference between their results and Scully's; according

to them, free agency caused racial discrimination in baseball to vanish within a

decade. The implicit assumption in recent explanations for the disappearance of

racial discrimination in baseball is that salary differences were caused by employer

discrimination. Scully's earlier study, however, implied that consumer discrimina-

tion was the factor driving baseball players' salaries. Scully reported that, prior to

integration, "Baseball management was concerned that attendance would decline

with the introduction of Negro players" [p. 231]. Indeed, Scully found evidence that

fans discriminated according to player color: "an average of 1,969 fewer fans

attended] games pitched by blacks than those pitched by whites," despite the fact

that "black pitchers ha[d] significantly better pitching records than whites" [p. 233].

24.

Although Scully's study was based on only

107 observations, Raimondo and

Hill and Spellman had enough degrees of freedom to experiment with functional

forms using more basic measures of performance, at least for the hitters. Raimondo's

sample included 209 hitters, but only 34 pitchers. The sample of Hill and Spellman

contained 326 hitters and 190 pitchers. Scully measured fielders' offensive perfor-

mance by slugging average and batting average, alternatively. Hill and Spellman

used runs scored per year as the sole explanatory performance variable. Raimondo

used a player's lifetime batting average for infielders and slugging average combined

with a dummy indicator that assumed a value of 1 if a player had a career slugging

percentage below average and a career batting average above average, and zero

otherwise.

25. Certain indexes, such as SLUGGING AVERAGE and RUNS CREATED

PER SEASON, did a comparatively poor job of explaining variation in card prices

compared with the specifications reported here. We did find, however, two single-

index measures, TOTAL BASES and RUNS CREATED, that explained nearly as

much of the variation in card prices as did our unrestricted models in which each

component of performance entered separately, suggesting that the restrictions they

impose are minor and can be ignored. TOTAL BASES is defined as HITS +

DOUBLES + (2 x TRIPLES) + (3 x HOME RUNS). RUNS CREATED is defined

as [(HITS + WALKS) x TOTAL

BASES]/(AT BATS + WALKS). It is not surpris-

ing that these indexes performed nearly as well as our specification; they are basically

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594

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QUARTERLY JOURNAL OF ECONOMICS

VI. CONCLUSION

Our results indicate that consumer discrimination exists in the

market for baseball cards. Among hitters, the cards of nonwhites

sell for about 10 percent less than the cards of white players of

comparable ability, whereas among pitchers, there is a 13 percent

discount on nonwhites. We admit that this is a small market and

that baseball cards are not a commodity purchased by most

households.

Sports, however, are an important part of the enter-

tainment industry. The collector of baseball cards is part of the

larger group of sports fans and, if anything, is better informed than

the typical fan. We therefore believe that our results do have some

implications for the general problem of consumer discrimination.

The lack of personal contact in the market is also significant. Race

enters only as a picture on a piece of cardboard, and should,

therefore, have minimal effect. The absence of personal contact

should reduce the potential for consumer discrimination. That it

does not eliminate it may be our most important result.

Becker predicted that racial consumer discrimination would be

more likely in markets where personal contact is prevalent. In such

markets the effects of discrimination often cannot be

measured

separately from the pure capability of the worker. If such measure-

ments were possible, we believe that they would show that con-

sumer discrimination makes race a more important contributor to

the continuing wage gap than the studies of employer and coworker

discrimination imply.

DEPARTMENT OF ECONOMICS, CLEMSON UNIVERSITY

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