Free Riders or Easy Riders?: an Examination of the Voluntary Provision of Public Radio Authors(s): Eric J. Brunner Source: Public Choice, Vol. 97, No. 4 (1998), pp. 587-604 Published by: Springer Stable URL: http://www.jstor.org/stable/30024449 Accessed: 28-03-2016 15:30 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

Springer is collaborating with JSTOR to digitize, preserve and extend access to Public Choice

http://www.jstor.org

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

Public Choice 97: 587-604, 1998.

@ 1998 Kluwer Academic Publishers. Printed in the Netherlands.

Free riders or easy riders?: An examination of the voluntary

provision of public radio

ERIC J. BRUNNER*

Department of Economics, San Diego State University, San Diego, CA 92182, U.S.A.

Accepted 12 June 1996

Abstract. This paper tests the widely accepted hypothesis that when a pure public good is

voluntarily provided incentives to free ride increase with the number of individuals consum-

ing the good. Specifically, I use unique data on the number of listeners and contributors to

public radio to test two hypotheses. First I test whether the proportion of contributors falls as

group size increases and second I test whether contributions per contributor falls as group size

increases. I find that increases in group size result in significantly more free riding. However,

I also find that group size has no effect on contributions per contributor.

1. Introduction

Economic theory hypothesizes that when a pure public good is voluntarily

provided incentives to free ride increase with the number of individuals con-

suming the good. As group size increases, and aggregate provision rises, each

individual perceives their own contribution as having little or no effect on the

total provided by the rest of the group. Consequently, it is in the self interest of

each individual to understate his or her true preferences by reducing or with-

holding their own contribution (Samuelson, 1954; Olson, 1965; Buchanan,

1968). Despite wide-spread acceptance of this hypothesis, evidence from em-

pirical studies fails to support it.' For example, Lipford (1995), using data on

church congregations ranging from 7 to 3,294 members, found no significant

relationship between congregation size and contributions per member. Even

more surprising, in a recent experimental study, Isaac, Walker, and Williams

(1994) found that an increase in group size from 4 to 100 subjects resulted in

significantly less free riding.

This paper uses unique data on total voluntary contributions to individual

public radio stations and the number of individuals who contribute and listen

to each of these stations to provide new econometric evidence on the rela-

tionship between free riding and group size. Prior studies have focused on

* Thanks go to Edward Funkhouser, Nick Ronan, Perry Shapiro, Jon Sonstelie and Charles

Stuart for helpful comments. All errors are mine.

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

587

588

the relationship between group size and average contributions. However, av-

erage contributions may decrease as group size increases for two reasons.

First, individuals may "easy ride", that is, they may still contribute but con-

tribute less as group size increases. Alternatively, the proportion of the group

contributing may decrease while contributions per contributor remain con-

stant. This study is unique in that I examine the effect group size has on both

the proportion of contributors and contributions per contributor.

Public radio provides an ideal framework within which to examine the

relationship between group size and the provision of a pure public good. First,

public radio is non-rival in consumption; any number of individuals can listen

to public radio broadcasts without affecting the utility of other listeners. The

empirical results obtained in this study, therefore, are not affected by con-

gestion. Furthermore, given the current state of technology it is impossible to

exclude people from consuming the good; any individual within the broadcast

range of a station may listen without paying.

I find that increases in group size result in significantly more free riding.

Specifically, the proportion of listeners contributing to public radio decreases

as the number of listeners increases. However, I also find no significant re-

lationship between contributions per contributor and group size. Thus, as

Bergstrom, Blume, and Varian (1986), suggest, "adjustments at the 'extensive

margin' - the decision of whether or not to become a contributor - are at least

as important as adjustments on the 'intensive margin' - the decision of how

much to contribute".1

2. Theories of voluntary provision and the free-rider hypothesis

The hypothesis that incentives to free ride increase with group size is derived

from the pure public-goods model or, as it is commonly referred to, the pure

altruist model of voluntary provision. The primary assumption is that indi-

viduals care only about the total provision of a public good and not their own

contribution per se. Several authors have questioned the generality of results

derived from this model. For example, Sugden (1982) and Andreoni (1990)

argue that the prediction of extensive free riding derived from the pure altru-

ist model is inconsistent with the observation that a large proportion of the

population contribute to charities such as the United Way and the American

Cancer Society.

A number of theoretical papers have developed alternative models of vol-

untary provision which address this criticism. Most notably, Andreoni (1989,

1990) introduced what he refers to as the impure altruist model. This model

assumes individuals care about the total provision of the public good but also

receive some private benefit, a "warm glow", from contributing. Hence, in the

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

589

impure altruist model an individual's utility function is:

Ui = Ui(xi, gi, G) (1)

where xi is individual i's private good consumption, gi is individual i's con-

tribution to the public good, and G = Egi is the total provision of the public

good.2

The utility function in (1) nests two competing models as special cases,

namely the pure altruist model and the pure egoist model. In the pure al-

truist model, Ui = Ui(xi,G), implying individuals care only about the total

provision of the public good. Alternatively, in the pure egoist model, Ui =

Ui(xi,gi), implying individuals care only about the warm glow they receive

from contributing and view their own contribution as a purely private good.

Each of these models yields a different prediction about the pervasiveness of

free riding.

In the pure altruist model, Andreoni (1988) proves that as group size

grows infinitely large the proportion of the group contributing to the pub-

lic good decreases to zero. Furthermore, Fries, Golding and Romano (1991)

and Andreoni (1988) prove that as group size increases average contribu-

tions decrease to zero while total contributions increase to a finite positive

value. Underlying these results is the assumption that individuals treat the

contributions of others as a perfect substitute for their own contribution. Con-

sequently, as group size increases, individuals become less likely to contribute

themselves and more likely to rely on the contributions of others.

In the pure egoist model, which has been used extensively in the literature

to estimate price and income elasticities of charitable contributions, the total

supply of the public good does not enter the individual's utility function. An

individual's desired contribution is therefore independent of the contributions

made by others and hence individuals have no incentive to free ride. The pure

egoist model therefore predicts that the proportion of a group contributing to

a public good is independent of the number of contributors.

Because the impure altruist model incorporates both the egoist and altruist

motives of voluntary contributions, the prevalence of free riding depends on

the relative strength of each of these motives. If individuals are motivated to

contribute primarily by altruism, free riding will be pervasive. On the other

hand, if individuals are motivated primarily by egoism, free riding will be

minimal.

The focus in this study is on the effect group size has on the proportion

contributing, however, other variables affect the proportion contributing as

well. For example, the inequality of income has played a key role in the

theory of voluntary contributions. In the context of the pure altruist model,

Bergstrom, Blume, and Varian (1986) demonstrated that when individuals

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

590

have identical preferences but different incomes, the larger the dispersion of

income, the smaller the proportion of the population contributing. Thus, the

pure altruist model predicts an inverse relationship between the proportion

of listeners contributing to public radio and the dispersion of income among

listeners.

The pure altruist model also predicts an inverse relationship between the

level of government support for public radio and the proportion of listeners

contributing. Because individuals treat government contributions as a perfect

substitute for their own contribution, as government contributions increase,

incentives to free ride also increase.

Changes in the rate at which contributions are subsidized or changes in the

average income of the group also affect the proportion of the group contribut-

ing in the pure altruist model. Specifically, it can be shown that the proportion

of the group that contributes will tend to be smaller as either the subsidy rate

increases or the average income decreases.3 A proof of the first proposition

can be found in Andreoni and Bergstrom (1993) while a proof of the second

proposition is available upon request.

Thus far, the effect of changes in the inequality of the income distribution,

the average income of listeners, the level of government support, and the rate

at which contributions are subsidized has been discussed within the context

of the pure altruist model. However, as Andreoni (1990) notes, when some

individuals do not contribute, the comparative statics of the impure altruist

model carry over exactly from the pure altruist model. Thus, all the predic-

tions derived from the pure altruist model for these variables carry over to the

impure altruist model.

With the exception of the effect subsidies have on the proportion of lis-

teners contributing all the comparative statics discussed above also hold for

the pure egoist model. For example, if individuals have identical preferences

but different incomes and if private contributions are a normal good, there

exists a critical income level such that only individuals with incomes above

the critical level choose to contribute. Thus, suppose the dispersion of income

among listeners is increased by transferring income from a poorer contributor

to a richer one. If the income transfer reduces the poorer contributor's income

below the critical income level, the proportion contributing will decrease.

Similarly, an increase in tax financed government contributions will tend to

decrease the proportion of listeners contributing through its effect on dispos-

able income. On the other hand, an increase in the average income of listeners

will tend to increase the proportion contributing since it increases the number

of listeners with income above the critical income level. However, because the

income and substitution effects of a tax financed increase in the subsidy rate

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

591

work in opposite directions, an increase in the subsidy rate has an ambiguous

effect on the proportion of listeners contributing.

Finally, in all three models, the pervasiveness of free riding depends on

the heterogeneity of preferences. Specifically, as McGuire (1974), Bergstrom,

Blume, and Varian (1986) and Andreoni (1988) demonstrate, the proportion

of the group that contributes will tend to be smaller the larger the dispersion

of preferences.

3. The data

To distinguish between alternative models of voluntary provision, this paper

makes use of unique data on the number of listeners and the number of

contributors to public radio stations located across the United States. The

Radio Research Consortium and the Arbitron Company provided data on

the number of public radio listeners. The data consist of observations on

the estimated number of different individuals who listened to a public radio

station during Arbitron's Spring 1987 survey. The sample consists entirely

of stations affiliated with National Public Radio (NPR). This sample was

then merged with data, provided by the Corporation for Public Broadcasting

(CPB), on the number of individuals contributing to each of these stations

in 1986. Finally, the 1990 Census provided the population characteristics of

each station's listening area.

The Census does not report population characteristics by listening area,

of course, so I approximated listening areas by metropolitan statistical areas

(MSA's). The majority of stations were located in or near an MSA. If a station

was located more than 50 miles from the nearest MSA, the listening area was

defined to be the city or town in which the station was located. In localities

containing more than one public radio station, the number of listeners and

number of contributors were defined to be the total number of listeners and

contributors within the locality.

The CPB also provided data on the amount of government support each

station received in 1986. Government support is composed of two categories;

federal support, which consists primarily of CPB funding, and state and local

support. Federal support consists of a fixed base grant which is the same for

all stations and a matching grant which is based on the share of total non-

federal income each station receives. Since this matching grant reduces the

effective price of contributing to a public radio station by an equal amount

in all localities, matching federal support can be omitted from the empirical

analysis. However, even though all stations received the same base grant,

non-matching federal aid will differ across localities because some localities

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

592

contain more than one station. Non-matching federal aid, therefore, must be

included in the empirical analysis.

State and local funding consists of the sum of all state and local gov-

ernment support as well as the support stations received from universities

or colleges. Unfortunately, very little information is available on the nature

of state and local funding. Specifically, it is impossible to determine which

stations, if any, received matching grants from these sources. The empirical

analysis which follows assumes taht all state and local support is composed of

non-matching grants.4 Total government support was therefore defined as the

sum of all non-matching federal aid and state and local support in a locality.

To measure the distribution of income among listeners the Gini Coeffi-

cient was calculated using the 25 household income categories in the 1990

Census.5 This measure has two desirable properties. First, it is mean inde-

pendent, providing a means of separating the effect of changing total in-

come from the effect of dispersing that income. Furthermore, it is invariant to

proportionate differences in population size. Hence, the effect of changing

the number of listeners can be separated from the effect of changing the

dispersion of income among listeners.

Because contributions to public radio are tax deductible the subsidy an

individual receives for contributing depends on his marginal tax rate and

hence his income. Since individuals with different incomes may face different

subsidy rates, what is needed is the average subsidy rate for public radio

listeners. To obtain this measure, income data from NPR's 1986 study, "Pub-

lic Radio Listeners: Supporters and Nonsupporters" was used. This survey

asked 6,448 public radio listeners across the United States to which one of 12

income intervals they belonged. This information was then used to calculate

a nation-wide estimate of the percentage of listeners with incomes in each of

these intervals. The average subsidy rate of listeners in each state was then

calculated as follows:

Ss = (tf + ts)IN

where Ss is the average subsidy rate of listeners in state s, (tf + ts) is a vector

of the combined federal and state marginal tax rates corresponding to each

of the 12 income intervals and IN is a weighting vector of the nation-wide

percentage of listeners in each of these intervals.6 Tax rates differ across

states so individuals with identical incomes but different states of residence

are likely to have different marginal tax rates and therefore different sub-

sidy rates. Interstate variation in tax rates therefore provides the necessary

exogenous variation in subsidy rates.

Eight stations were dropped from the initial sample because they did not

raise funds from the public. These stations were prohibited from fund-raising

because of specific state statutes or local ordinances. For example, some pub-

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

593

Table 1. Summary statistics.

Mean SD

Total number of listeners 77,414 132,137

Total number of contributors 7,049 10,932

Proportion contributing 0.11 0.08

Gini coefficient 0.43 0.02

Government support 306,327 424,406

Average subsidy rate 0.37 0.02

Average income 37,000 5,306

Percent college degree or higher 22.10 5.73

Average age (25 plus) 47.29 1.89

Number of observations = 142

lic radio stations located on state or private universities were prohibited from

fund-raising by the univerisities that owned them.

Table 1 presents summary statistics for the variables used in the study. On

average, there were 77,414 public radio listeners in each locality in 1986.

The large standard deviation indicates that the number of listeners varied

substantially across localities. For example, the largest locality in the sample

contained close to a million listeners while the smallest locality contained just

3,500 listeners. Furthermore, note that on average only 11 percent of listeners

contribute to public radio.

4. Results

With the data outlined above, the following log-linear model was estimated:

InContj = Po + PlllnListj + P2Ij + P3lnMj + ,4lnSj (2)

+P5lnGovj + 6Colj + 7Agej + 'j,

where j indexes localities, Cont is the total number of contributors to public

radio, List is the number of public radio listeners, I is the Gini index, M is av-

erage income, S is the average subsidy rate, Gov is the amount of government

support for public radio, Col is the percentage of individuals with a college

education or higher, Age is the average age of individuals 25 years or older,

and " is a random disturbance term.7

If the proportion of listeners contributing to public radio is independent of

the number of listeners, as the pure egoist model predicts, P1 should equal

one. To see this, note that, abstracting from the variables other than the num-

ber of listeners in equation (2), the pure egoist model implies Cont/List = f0.

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

594

Table 2. Parameter estimates - Log-linear specification.

Coefficient

(SD)

Regressor (Coefficient) Regressor (Coefficient)

Log listeners (1i)* 0.849 Log gov't support (05) -0.016

(0.056) (0.022)

Gini coefficient (02)* -5.04 Percent college (O6)* 0.020

(2.39) (0.010)

Log mean income (03) 0.065 Average age (07) 0.007

(0.441) (0.023)

Log subsidy rate (04) 0.993 Constant 1.12

(0.711) (4.72)

R-square 0.77

Number of observations 142

* Indicates coefficient is significant at 5% level or better.

Taking logs and rearranging terms yields InCont = Info + InList, thus im-

plying that the coefficient on InList should equal one. If the proportion of

listeners contributing to public radio decreases as the number of listeners

increases, however, f1 should be positive but less than one. The hypothesis

that the proportion of listeners contributing falls as the number of listeners

increases can therefore be tested using a nested test of the form:

Ho : 1= 1

HI : l <1

Regression results are reported in Table 2. Graphical inspection of the raw

data revealed greater variation in the number of contributors in localities with

a large number of listeners than in localities with relatively few listeners.

Although taking logs removed most of this heterogeneity, White's covariance

estimator was employed to ensure that the estimated standard errors were

consistent.8 Table 2 contains these corrected standard errors.

Based on the results of the t-test, ,I = 1, the null hypothesis that the

proportion of listeners contributing to public radio is independent of the num-

ber of listeners was rejected at the 1 percent level or better. The pure egoist

model of voluntary provision, therefore, was not supported empirically. Fur-

thermore, this result supports the hypothesis that as the number of listeners

increases the proportion of listeners contributing decreases.9'10

It is well known that when regressors are measured with error their co-

efficients will be biased toward zero. Thus, it is possible that i1 was found

to be significantly less than one simply because the number of listeners in a

locality was measured with error. To test this hypothesis, I used the number

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

595

of households in each locality as an instrument for the number of listeners

and re-estimated the model. When this was done, the estimate of /1 actually

fell to .752. However, there was no statistically significant difference between

this estimate of fi and the estimate of f1 reported in Table 2. Furthermore,

for the instrumental variables regression, the null hypothesis that B1 = 1 could

once again be rejected at the 1 percent level or better.

In Section 3 I noted that very little information is available on the nature

of state and local government support. If some of this support is in the form of

matching grants, government support and private contributions are simultane-

ously determined. As a result, estimates of the effect government support have

on the proportion of listeners contributing will suffer from simultaneity bias.

To check if this possibility had a significant impact of the results I excluded

government support in equation 2 and re-estimated the model. This had no

effect on the estimated coefficients of the remaining variables.

4.1. Specification and functional form

A number of tests for correct functional form were also conducted. First, the

sample was sorted into three subgroups on the basis of the number of lis-

teners (<20,000, 20,000-60,000 and >60,000) and separate regressions were

estimated for each group. With these sub-samples, there was no statistically

significant difference between the estimated coefficients.

Second, to test if the proportion of listeners contributing continually de-

creased as the number of listeners increased, the regression equation was

extended to include a quadratic term in log listeners. This corresponds to

a more general model which allows the proportion of listeners contributing

to be a U-shaped function of the number of listeners. The coefficient of this

quadratic term, however, was insignificant. Thus, the hypothesis that the pro-

portion of listeners contributing continually declined over the range of the

data could not be rejected.

Third, previous experimental studies have been careful to separate "pure"

group size effects from other group size effects that also change the incentives

individuals face to contribute. For example, if there are economies to scale

in supplying public radio, listeners located in densely populated or urban-

ized areas might be asked to contribute less than listeners located in more

sparsely populated areas. As a consequence, in densely populated areas, a

higher proportion of listeners may contribute. Similarly, localities with large

populations are likely to have a larger number of commercial stations which

offer services that compete with public radio. Listeners located in localities

with large populations, therefore, may place a lower value on the services

provided by public radio and hence be less likely to contribute. To control

for these strategic group size effects the regression equation was extended to

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

596

Table 3. Extended regression results.

Coefficient

(SD)

Regressor (Coefficient) Regressor (Coefficient)

Log listeners (1 )* 0.84 FM stations (fi8) 0.004

(0.07) (0.010)

Gini coefficient (02) -1.12 Percent urban (O9)* -0.010

(3.24) (0.004)

Log mean income (03) 0.56 Pop. density (o10)** 0.0002

(0.47) (0.0001)

Log subsidy rate (04) 0.90 Percent black ( 11)* -0.013

(0.76) (0.006)

Log gov. support (05) -0.017 Percent hispanic (p12) -0.006

(0.020) (0.006)

Percent college (06) 0.009 Constant -2.56

(0.010) (4.69)

Average age (07) -0.037

(0.032)

R-square 0.79

* Indicates coefficient if significant at 5% level.

**Indicates coefficient if significant at 10% level.

include an additional set of control variables. In particular, for each locality,

I constructed measures of the population density and the percentage of the

population living in urbanized areas from the 1990 Census." Furthermore, I

used the 1987 Broadcasting Cable Listing Yearbook to obtain a control for

the number of competing FM stations in each locality. Finally, I also added

the percent of the population black and the percent Hispanic to the regression

to further control for differences across localities in tastes and preferences.

Results from the extended regression are reported in Table 3. The results

are quantitatively and qualitatively similar to those reported in Table 2. In

particular, although some of the additional control variables are significant

(the coefficients on percent urban, population density and percent black),

their inclusion has no significant effect on the point estimate of f~1. The null

hypothesis that fi1 = 1 is once again rejected at the 5% level or better.

Finally, the sensitivity of the results to the specification of the number of

listeners and number of contributors in a locality was examined. First, the

log-linear and linear models were re-estimated using data on the number of

listeners and the number of contributors to individual stations. In this specifi-

cation, the unit of observation is the individual station and hence observations

on the number of listeners and the number of contributors in localities with

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

597

more than one station were not aggregated. The results obtained using this

specification were virtually identical to those reported in Table 2.12

Second, the results reported in Table 2 are based upon estimates of the total

number of listeners in a locality that are adjusted for the fact that some indi-

viduals listen to more than one station. Specifically, if an individual listens to

more than one station he is only counted once. On the other hand, the number

of contributors was defined simply as the sum of the number of contributors in

a locality. Research conducted by NPR suggests that, on average, 21 percent

of contributors contribute to more than one public radio station. Thus, it is

possible that the total number of listeners might be understood in localities

with more than one station. To check if this had a significant impact on the

results, the log-linear and linear models were re-estimated using data on the

total number of listeners which was not adjusted for the possibility that some

individuals might listen to more than one station. The results obtained using

this specification were also virtually identical to those reported in Table 2.

5. Group size and average contributions

Previous empirical studies which examine the effect of group size on the

provision of a pure public good have focused on the relationship between

average contributions and group size. However, as I noted in the introduction,

average contributions may fall either because individuals "easy ride" - they

still contribute but contribute less as group size increases - or because indi-

viduals become true free riders and contribute nothing at all. To demonstrate

this, let G denote total contributions to public radio, Cont denote the number

of contributors to public radio and List denote the number of listeners. The

log of contributions per listener (average contributions) can be written as:

log Gt = log Gt +log Gt.

(3)

Taking the derivative of log(G/List) with respect to logList yields:

alog (G) = alog + alog(Cnt (4)

Equation 4 reveals that the overall effect of an increase in group size on

average contributions can be decomposed into two separate effects. The first

term on the right hand side of 4 encompasses easy riding. It is the effect an

increase in group size has on contributions per contributor. The second term

on the right hand side of 4 encompasses free riding. It is the effect an increase

in group size has on the proportion of the group that contributes.

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

598

Table 4. Parameter estimates - Log-linear specification.

Coefficient

(SD)

Dependent variable: Contributions per contributor

Regressor (Coefficient) Regressor (Coefficient)

Log listeners (Pi) 0.009 Log gov't support (05) -0.016

(0.03) (0.013)

Gini coefficient (02) 1.80 Percent college (f6) -0.007

(1.24) (0.006)

Log mean income (03) 0.339 Average age (07) 0.004

(0.294) (0.015)

Log subsidy rate (04) -0.440 Constant -0.915

(0.382) (3.34)

R-square 0.07 Number of observations 142

Thus far, I have concentrated on estimating the second term. The point es-

timate of P1 reported in Table 2 suggests that the effect of an increase in group

size on the proportion of the group that contributes, 1-P 1, is approximately

-0.15. To estimate the first term, I used data, provided by the CPB, on total

contributions in each locality. Specifically, I replaced the dependent variable,

the log of the number of contributors, in (2) with the log of contributions per

contributor and re-estimated the model.

Regression results are reported in Table 4.13 Note that the estimate of P1 is

close to zero and statistically insigificant. This suggests that although average

contributions fall as the number of listeners increases, contributions per con-

tributor do not. The observed decrease in average contributions, therefore,

is the result of a decrease in the proportion of listeners contributing and

not a result of a decrease in contributions per contributor. Hence, as group

size increases, individuals appear to become true free riders rather than easy

riders.

6. Pure or impure altruism?

The results reported in Table 2 can also be used to predict just how pervasive

free riding is likely to be in localities with different numbers of listeners. In

Figure 1, the predicted proportion of listeners contributing to public radio,

denoted PCONT, is plotted as a function of the number of listeners.14 As

the graph illustrates, although the proportion of listeners contributing does

decrease as the number of listeners increases, the magnitude of this effect

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

599

PCONT

0 136

0.063

3,500 1,000,000

UISTENERS

Figure 1. Predicted proportion of listeners contributing.

is relatively small. For example, as the number of listeners increases from

3,500 to 1,000,000 the predicted proportion of listeners contributing falls

from 0.136 to 0.063. This implies that a 28,471 percent increase in the number

of listeners leads to only a 54 percent decline in the proportion of listen-

ers contributing. Are these results consistent with the pure altruist model of

voluntary provision?

Andreoni (1988) conducted simulations based on the pure altruist model

which provide an answer to this question. Specifically, Andreoni assumed a

Cobb-Douglas utility function of the form Ui = xil-aGG in these simulations.

The parameter a is then the slope of the contribution function. Furthermore,

a density function fitted to 1980 Census data on the distribution of income in

the United States was used. The pure altruist model was then solved for the

expected proportion of individuals contributing under various assumptions

about a and group size.

The Cobb-Douglas utility function used in these simulations implies an

income elasticity of unity. Kingma (1989), using surveys data on individual

contributions to public radio, estimates the income elasticity for contributions

to public radio to be 0.99. Furthermore, when Kingma subdivides the sample

into three income groups, (<$20,000, $20,000-$35,000 >$35,000) there was

no statistically significant difference between the estimated income effects.

Assuming a Cobb-Douglas utility function, therefore, appears appropriate for

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

600

Table 5. Simulation results for pure altru-

ist model.

Proportion of group contributing

a Group size = 20 Group size = 200

.1 0.033 0.003

.2 0.060 0.007

.3 0.090 0.015

.4 0.129 0.021

.5 0.116 0.029

.6 0.210 0.037

.7 0.281 0.06

public radio. For comparison with the results obtained in this paper, some of

these simulation results are reported in Table 5.

The simulation results reported in Table 5 suggest that, for any realistic

values of the parameters used to calibrate the model, the proportion of a group

contributing quickly falls toward zero as group size increases. For example,

even if listeners were to contribute half of every dollar to public radio (0c = .5),

for groups as small as 200 listeners the pure altruist model predicts that

the proportion of listeners contributing will be less than 3 percent. On the

other hand, the empirical results obtained in this study predict that even for

groups of a million individuals, the proportion of listeners contributing will

be greater than 6 percent. Furthermore, results obtained in empirical studies

which estimate linear contribution functions suggest that any reasonable para-

meterization of the model should include a value of ca that is substantially less

than 0.1. For example, Reece and Zieschang (1985), using data on individual

contributions obtained from the Consumer Expenditure Survey, estimate ca to

be .0342. When this value of a is used in the simulations the pure altruist

model predicts that, for groups of size similar to be those found in this study

(3,500 individuals or more), the proportion of listeners contributing will be

zero. Thus, although the results reported in Table 2 provide strong support

for the hypothesis that increases in group size reduce the proportion of the

group contributing, they do not support the pure altruist model of voluntary

provision.

One possible explanation for these results is that listeners care about the

quality of public radio but also receive a warm glow from contributing. This

corresponds to the more general impure altruist model of voluntary provision.

Recall that in this model the pervasiveness of free riding depends on the

relative importance of altruism and warm glow in motivating individuals to

contribute. The small magnitude of the group size effect found in this study,

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

601

therefore, suggests that the egoist or warm glow motive for contributing plays

an important role in mitigating individual incentives to free ride.

7. Conclusions and caveats

The main finding in this study is that individuals do free ride on the con-

tributions of others. Specifically, the proportion of listeners contributing to

public radio decreases as the number of listeners increases. The robustness

of this result is indicated by its invariance to a number of different model

specifications. However, the results obtained in this study also indicate that

as group size increases, contributions per contributor remain constant. Com-

bined, these results imply that as group size increases individuals become true

free riders rather than easy riders. In a recent empirical study, Smith, Kehoe,

and Cremer (1995) reach a similar conclusion. Based on the results obtained

using survey data on individual contributions to a rural health facility, the

authors conclude that, "Once the free ridership problem (paying no share)

was overcome, easy riding (paying less than one's fair share) appeared to be

less likely".

Finally, while the results obtained in this study provide strong support

for the hypothesis that incentives to free ride increase with group size, they

also indicate that free riding is not as pervasive as the pure altruist model

predicts. This suggests that the correct model of voluntary provision is the

impure altruist model in which individuals care about the total provision of

the public good but also receive a warm glow from contributing. However,

let me note that this conclusion is still tenuous. Specifically, although the

results indicate that free riding is not as pervasive as the pure public goods

model predicts, it is impossible to ascertain if this finding is the result of

warm glow, as suggested above, or institutional features not captured in the

model. For example, it is possible that stations with larger audiences have

more effective fund-raising strategies or simply spend more on fundraising.

This in turn might explain why localities with large listener bases receive

contributions from a higher proportion of listeners than the pure public-goods

model predicts.

Notes

1. An exception is a study conducted by Goetze, Glover, and Biswas (1993). They found that

an increase in the number of public television viewers resulted in a significant reduction

in average contributions per viewer.

2. Similar models have been developed by Margolis (1982), Sugden (1982, 1984), Comes

and Sandler (1984), Schiff (1985) and Steinberg (1987).

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

602

3. Andreoni and Bergstrom (1993) demonstrate that when contributions are subsidized and

the goverment funds the subsidy with a head tax, small changes in the subsidy rate will

have no effect on total contributions and therefore no effect on the proportion of indi-

viduals contributing. However, large changes in the subsidy rate affect the supply of the

public good. Specifically, if the government pays for the subsidy by taxing any individual

an amount greater than what he would have contributed in the absence of a subsidy, total

contributions will increase and the proportion contributing will decrease.

4. If some of this support is in the form of matching grants, estimates of the effect gov-

ernment contributions have on the proportion of listeners contributing will suffer from

simultaneous-equations bias. I address this issue in detail later in the paper.

5. The mean of each income interval was assumed to be located at the midpoints in making

these calculations except for the open ended interval at the top, for which information on

mean income was available. Furthermore, adjustments were made using a Pareto curve

for the open ended, top income interval. A detailed description of how these indexes were

calculated is available from the author upon request.

6. Some states do not allow individuals to deduct charitable contributions. For these states,

only the federal marginal tax rates were used to calculate the average subsidy rate.

7. The variables Col and Age are included in the regression to control for the heterogeneity

for preferences. Using other measures of heterogeneity such as the percent of individuals

40 years old or older or the coefficient of variation for educational attainment or age has

no effect on the results reported.

8. A number of tests for heteroscedasticity were performed. The chi-square statistic for

White's test was 16.0. The 95 percent critical value for this statistic is 23.7. The F statistic

for the Goldfeld-Quant test, obtained by sorting the sample by the number of listeners,

was 1.43. The 95 percent critical value for this statistic is 1.51.

9. Since income is known to be positively correlated with both education and age (the simple

correlation coefficients between income and percent college and income and average age

in the sample are, 0.39 and 0.24 respectively) the insignificant coefficient on income could

be a result of multicollinearity. When these variables are dropped from the regression

income becomes significant at the 10 percent level.

10. To examine the robustness of the results reported in Table 2, the model was also estimated

using the following linear specification:

Cont

= 00 + 1iListj + I21j + fi3Mj + 04Sj + -5Govj + -6Colj + fi7AgeJ + -j

Listj

The results obtained using this specification were qualitatively similar to those reported

in Table 2. In the linear specification, the pure egoist model predicts P1 should be zero.

The point estimate of 01 obtained, however, was negative and statistically significant at

the one percent level or better suggesting that as the number of listeners increases the

proportion of listeners contributing decreases. Results are available upon request.

11. Percent urban was calculated by dividing the number of individuals living in census de-

fined urban areas by the total populations (those living in census defined urban, nonurban,

farm and nonfarm areas). Similarly, population density was calculated by dividing the

total number of individuals 25 years old or older by the total land area of a locality

(measured in square kilometers). A second measure of population density, the number

of households per square kilometer, was also calculated. Both measures yielded similar

regression results.

12. The results obtained using this specification were both qualitatively and quantitatively

similar to those reported in Table 2. In fact, the point estimate of f1 obtained using this

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

603

specification was nearly identical to the point estimate of f1 reported in Table 2. Results

are available upon request.

13. The model was also estimated without controls for the percent college and average age.

This had no significant effect on the results reported in Table 4. In particular, the coeffi-

cient on average income remained insignificant. Furthermore, the regression was extended

to include the additional set of control variables discussed previously. The results obtained

using this specification were nearly identical to those reported in Table 4. These results

are available upon request.

14. Figure 1 is based on the results obtained using the log-linear specification. A similar

relationship between the predicted proportion of listeners contributing and the numbers

of listeners is obtained when the results obtained using the linear specification are used.

The primary difference is that the function plotted in Figure 1 is not as smooth when the

linear specification is used. It tends to cycle (rise and fall) around the function plotted in

Figure 1.

The variable, PCONT was calculated in the following manner. First, the results shown in

Table 2 were used to predict the logarithm of the number of contributors by holding all

regressors, other than the log of the number of listeners, at their means. Second, letting

XB denote this predicted value, the proportion of listeners contributing was calculated as,

PCONT = exB/Number of listeners.

References

Andreoni, J. (1988). Privately goods in a large economy: The limits of altruism. Journal of

Public Economics 35: 57-73.

Andreoni, J. (1989). Giving with impure altruism: Applications to charity and Ricardian

equivalence. Journal of Political Economy 97: 1447-1458.

Andreoni, J. (1990). Impure altruism and donations to public goods: A theory of warm-glow

giving. The Economic Journal 100: 464-477.

Andreoni J. and Bergstrom, T. (1993). Do government subsidies increase the private supply of

public goods? Manuscript. University of Wisconsin, Madison.

Bergstrom, T.C., Blume, L. and Hal Varian, H. (1986). On the private provision of public

goods. Journal of Public Economics 29: 25-49.

Buchanan, J.M. (1968). The demand and supply of public goods. Chicago: Rand McNally.

Clotfelter, C.T. (1985), Federal tax policy and charitable giving. Chicago, IL: University of

Chicago Press.

Cornes, R. and Sandler, T. (1984). Easy riders, joint production, and public goods. Economic

Journal 94: 580-598.

Fries, T., Golding, E. and Romano, R. (1991). Private provision of public goods and the failure

of the neutrality property in large finite economics. International Economic Review 32:

147-157.

Goetze, L., Glover, T.E. and Biswas, B. (1993). The effects of group size and income on

contributions to the corporation for public broadcasting. Public Choice 77: 407-414.

Hochman, H.M. and Rodgers, J.D. (1973). Utility interdependence and income transfers

through charity. In K.E. Boulding (Ed.), Belmont: Transfers in an Urbanized Economy.

Isaac, R.M., Walker, J.M. and Williams, A.W. (1994). Group size and the voluntary provision

of public goods. Journal of Public Economics 54: 1-36.

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms

604

Kingma, B.R. (1989). An accurate measurement of the crowd-out effect, income effect, and

price effect for charitable contributions. Journal of Political Economy 97: 1197-1207.

Lipford, J. (1995). Group size and the free-rider hypothesis: An examination of new evidence

from churches. Public Choice 83: 291-303.

Margolis, H. (1982). Selfishness, altruism and rationality. Cambridge, MA: Cambridge

University Press.

McGuire, M. (1974). Group size, group homogeneity, and the aggregate provision of pure

public goods under Cournot behavior. Public Choice 18: 107-126.

Olson, M. (1965). The logic of collective action. Cambridge, MA: Harvard University Press.

Reece, W.S. and Zieschang, K. (1985). Consistent estimation of the impact of tax deductibility

on the level of charitable contributions. Econometrica 53: 271-293.

Samuelson, P.A. (1954). The pure theory of public expenditure. Review of Economics and

Statistica 36: 387-390.

Schiff, J. (1985). Does government spending crowd out charitable contributions? National Tax

Journal 38: 535-546.

Smith, V., Kehoe, M. and Cremer, M. (1995). The private provision of public goods: Altruism

and voluntary giving. Journal of Public Economics 58: 107-126.

Steinberg, R. (1987). Voluntary donations and public expenditures in a federalist system.

American Economic Review 77: 24-36.

Sugden, R. (1982). On the economics of philanthropy. Economic Journal 92: 341-350.

Sugden, R. (1984). Reciprocity: The supply of public goods through voluntary contributions.

Economic Journal 94: 772-787.

White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test

for heteroskedasticity. Econometrica 48: 817-838.

This content downloaded from 137.99.216.203 on Mon, 28 Mar 2016 15:30:58 UTC All use subject to http://about.jstor.org/terms