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A gravity model analysis of the demand for mass communications
Regional Science and Urban Economics 6 (1976) 289-308.0
North-Holland
A GRAVIl’Y MODEL ANALYSIS OF THE DEMAND FOR MASS COMMUNICATIONS* Yale M. BRAUNSTEIN New York University, New York, NY 10003, USA Received January 1976 The gravity model specification is shown to be applicable to a study of the demand for a mass communication medium. The data are taken from newspaper circulations in the San Francisco metropolitan area. The demand equations have properties different from those for either private communication or travel demands.
1. Introduction Gravity models are well known and have been used for a variety of empirical analyses including studies of the demand for transportation services and for communications. In these analyses the interaction (e.g., communication or travel) between two localities was hypothesized to be proportional to socioeconomic characteristics of the localities and inversely proportional to the distance separating them. Simple tests have also been conducted by Zipf and his students to show that an elementary gravity model can explain the circulations of newspapers [Zipf (1948)], the number of radio stations per city [Boland (1948)] and the number of periodicals published per city [Conant and Davis (194&)]. The gravity model approach was also used by Seneca and Cicchetti (1969) to measure the demand for private point-to-point communications. This paper will examine the use of a gravity model to estimate the demand for mass communications, particularly the circulation pattern of daily newspapers. It will then explore the modifications in the gravity model required by the one-way nature of mass communications. Within the last few years Neidercorn and Bechdolt (1969, 1970, 1972) have provided a theoretical basis for the gravity model. They have shown that utility theory using a characteristics approach derived from the works of Lancaster (1965, 1966) can provide an economic rationale for the gravity formulation. The equations that are estimated in this analysts of demand contain as explanatory variables both the demographic and distance measures that are standard *James Rosse, Michael Spence, and William Baumol made several contributions versions of this paper. The author alone is responsible for any remaining errors.
to earlier
290
Y.hf. Braunstein,A gravity model analysis
in gravity models and mleasures of characteristics of each of the modes. This approach is comparable to the abstract mode approach to transportation demands first developed by Quandt and Baumol (I 966). The next section will describe the estimating procedure, sources of data, and results. In section 3 we shall contrast our results using a model of the demand for mass communications with the results from models of the demands for travel and for private communications. Sections 4 and 5 will interpret our findings in light of other studies of mass communications and present conclusions, respectively. 2. The gravity model: Estimation and results The circulation patterns of the daily newspapers of the San Francisco bay area were quantified and tested to see if they are consistant with what would be predicted by a gravity model. Using the ‘gravity’ analogy, the circulation of a newspaper in a specific commtunity is taken to be proportional both to the population of that community (pi) and to the population (or some other measure of socio-economic activity) of the home city of the newspaper (Pi). The circulation is assumed inversely proportional to the distance between the community snd the place of publication (UJ. Other determinants of the circulation may be characteristics specific to the newspaper (the AJ and the number of different newspapers (or other mass media) available in the community (NJ. The relationship describing such a model takes the form
where the subscripts 1”refer to the newspaper and its city of publication and the subscriptsj refer to the community where the newspaper is purchased and read. (We are considering only home-delivered daily newspapers.) A major advantage of gravity model formulation is that it can be tested by means of a multiple linear regression using only a logarithmic transformation of the data. The program chosen for this computation was BMD 02R of BMD Biomedical Computer Programs.’ This is a stepwise multiple regression routine that includes or deletes explanatory variables by calculating the effect each variabIe would have on the overall F-ratio of the regression equation. The circulation data came from the 1970 ‘Audit Reports’ compiled by the Audit Bureau of Circulation (1970) for the fourteen audited daiIy newspapers in the six central counties of the San Francisco bay area. The population data used were the number of households and median family income from the 1970 ‘Dixon (1971).
Y.M. Braunstein, A grauity model analysis
291
Census of Population. The distances were measured using highway mileage by the most direct route. As another descriptor of socio-economic activity, the level of retail sales in 1967 was collected for each of the fourteen home cities.2 Additional data were sought for each of the newspapers. Since each had a newsstand price of tsn cents and a home-delivered price that was mostly determined by the number of issues per week, information other than price had to be used to describe the particular newspaper. One characteristic is the time of publication; distinctions were made between morning edtions, afternoon editions, and those papers that had two editions per day. This last category was broadened to include the San Jose Mercury and News and the San Francisco C/zronicle and Examiner. The San Jose newspapers are both published by Ridder Publications and have combined editorial, news, and business departments. There is a joint operating agreement between the Chronicle ar.d Examiner, and although they have separate editorial and news operations and separate ‘publishers’, their advertising and circulation functions are combined. In each case, the rate structure makes it unlikely that an advertiser would purchase space in only one edition rather than both. And in each case there are few homes that receive both editions, although this is more true with the San Jose newspapers than of the San Francisco ones. Another descriptor of the individual newspapers is the number of national wire services to which they subscribe. The San Francisccl, Oakland, and San Jose newspapers view themselves as regional or metropclitan newspapers rather than local newspapers. A dummy variable was used to indicate this regional-local dichotomy. Additional dummy variables were used to indicate if the sales were in the home city of another newspaper in the survey and to distinguish cities and counties outside the six-county bay area from those inside the area. To determine the effects of having many newspapers serving the same city or county, a variable was constructed to represent the number of newspapers that serve a given area. The sample consisted of 234 cases for which all the data described above could be collected. Each city was counted as many times as there were different newspapers with sales of at least twenty-five in that city. Because the number of households and the retail sales in the newspapers’ home cities had a simple correlation coefficient of 0.983, and in order to avoid problems of multicollinearity, these rxplanatory variables, which may be proxies for the coverage of the newspapers, were not allowed to enter the same estimating equation. The following notational system was used to describe the different variables: Cl, = average daily circulation (in thousands) of newspaper i in cityj; Pr = households (in thousands) in cityj (or countyj for distant locations); distance (in miles) from home city of newspaper i to cityj (or county,& Dij
=
2A further description of the data sources and the problems in data collectior is in Braunstein (1975).
Y. hf. Braunstein, A gravity motiel analysis
292
= households (in thpusancis) in home city of newspaper i; annual retail sales (in hundred millions of dollars) of home city of si newspaper i; = median family income in city i ( Yj for cityj) ; yi wi = number of wire services lsubscribed to by newspaper i; = dummy variable equal to 1 if newspaper publishes evening editions only; ei equals 0 otherwise; ?IIi = dummy variable equal to 1 if newspaper publishes morning editions only; equals 0 otherwise; 4 = number of different newspapers serving cityj.
pi
-=
The stepwise structure of the computation permits the equations to be as simple as one taking the circullation of newspaper i in any city to be a function only of the population of that city (C, = APil) or to be a more complex relationship with additional explanatory variables. The results of the computations are presented in table 1, where each column presents the results of a different regression. The numbers in the cells are the coefficients of the variables included in each of the regressions and the corresponding values of the t-statistics (in parenthesis). The dependent variable in each case was log Cij, and a blank cell indicates that explanatory variable (the row) was not included in the specific equation (the column). At the bottom of each column are the coefficient of correlation (I?) and the value of the F-statistic. The reflession equations are identified by a two-digit number. The first number indicates whether the size of the home city of each newspaper is measured by number of households (1) or volume of retail sales (2). The second digit is the number of explanatory variables that have entered the regression. Because the population of the city in which the sales occur and the distance from that city to the home city of the newspaper were the first variables to enter, equations 2-l and 2-2 are the same as l-l and l-2 and therefore are not shown in table 1. Before examining the explanatory variables that were significant in explaining the circulation data and their coefficients, it is interesting to look at the nondemographic variables that did not enter any of the regression equations. As part of the stepwise nature of the computer program that was utilized, an F-statistic - ‘F to enter’ - is calculated for each of the variables that is not in the regression equation at each step. The value of the F-statistic provides information to test the null hypothesis: Explanatory variable X, does not add significantly to the regression of Y on XI, . . ., X,_ 1 (the variables that have entered previously). 3 As explained above, a dummy variable was used for the San Francisco and San Jose newspapers since each city has morning and afternoon newspapers 3Efrcm,jymson (1960, p. 101).
Y.M. Braunstein, A gravity model analysis
293
published under separate names although there is either a joint operating agreement (in the San Francisco case) or a single publisher. If the dummy variable had entered the regression equation and if its coefficient were positive and significant, there would be an indication that the notion of single day-long newspaper was not an appropriate one. As soon as the regression equations included the variables representing the size of the home city (as a proxy for the newspapers’ coverage), the value of the ‘F to enter’ of the *day-long’ dummy variable was no longer significant. Therefore the null hypothesis cannot be Table 1 Results of regressions on 1970 newspaper data. Regression Variable
1-l
1-2
Constant
-1.36
log PJ
0.81 (12.6)
log Du
--
l-3
l-4
l-5
2-3
2-4
-1.81
- 1.25
-1.86
- 0.03
-0.08
0.77 (12.9)
0.72 (13.8)
0.73 (14.01)
0.72 (14.0)
0.71 (13.8)
0.72 (14.1)
0.72 (14.1)
- 0.48 (6.04)
- 0.92 (10.67)
- 0.93 (10.9:
-0.97 (11.41)
- 0.92 (11.1)
-0.95 (11.49)
-0.98 (11.68)
0.11
0.68 (8.59)
log Pf
0.45 (3.66)
0.57 (4.59)
0.82 (9.29) 0.49 (2.44)
0.45 (2.56)
1.13 (3.79) 0.74 (2.87)
et
-0.62 (1.75)
m
R F
0.07
0.39 (3.14)
log & log W
2-5
0.6369 158.35
0.6977 109.52
0.7820 12Q.66
0.7882 93.91
0.7365 79.14
0.7917 128.75
0.7979 100.92
0.8009 81.57
rejected, and one can conclude that the San Francisco and San Jose newspapers may be properly viewed as single day-long newspapers comparable in nature to the other daily newspapers of the bay area. The values of the ‘F to enter’ at the fifth step of this dummy variable are shown in table 2. None of the dummy variables other than those: representing time of publication had an ‘F to enter’ greater than 1.30 (most were less than 1.OO)by the fifth step and therefore the null hypothesis that they did not add significantly to the regression of daily circulation on the set of e:8cplanatory variables that had entered cannot be rejected. Thus there was no significant difference between the
Y.M. Braunstein, A gravity model analysis
294
cases where the paper considered itself regional rather than local in nature, where the sales were in the home city of another newspaper rather than not, or where the sales were inside or outside the bay area. The values of the ‘F to enter’ for these dummy variables are also presented in table 2. The first column shows the results for the regression with population data representing the size of the home cities, and the second column is for the regression in which retail sales data are used. The variable (Ni) that measured the number of different newspapers serving a given area also was not significant in explaining the circulation data. The Table 2 Values of the ‘F to enter’ of dummy variables that had not entered by the fifth step. -Dummy variable
l-5
Regression 2-5 .-
‘Day-long’ publication Regional newspaper Home city of another newspaper ’ City outside bay area
0.0059 1.2783 0.6593 0.7866
0.3583 0.1281 0.7183 0.6033
meaning of this variable has received considerable attention from Quandt and Baumol(1966) : The presence of the variable N has one discdvantage - it implies that travel demand will be affected by the availability of ‘irrelevant modes’ -modes that would not even be considered by the class of travelers in question. It also makes the calculation dependent on fineness of classification whether, e.g., we consider local and express trains to constitute one mode or two. (p I7n). Ceteris paribus, we would expect total travel volume to be an increasing function of the range and density of alternatives and volume traveled by any one mode a decreasing function of the density of alternatives. (p. 21) Tn the regression equations that did contain NJ, it had a negative coefficient as ,would be expected. However, in each of these cases, the null hypothesis that the true coefficient was not different from zero can not be rejected. An example would be equation 2-7, the one with the least number of variables that also contained Nj, log C, = -0*51-0.57mi+0*74 lOgP]+O.28 log Yj (1.62) (13.75) (1.12) -0.92 log 0,+0.56 (9.78)
log Si+O.41 log W~-O.ZO log Njs (4.41) (2.28) (0.88)
Y.M. Braunstein, A gravity model analysis
29.5
The corresponding values of the t-statistics are shown in parentheses below the coefficient estimates. In the eight regression equations which contained explanatory variables having significant coefficients (table I), the variables entered in a predictable order: (I) the number of households in the city in which sales occurred (city to city j, (3) the number of households or volume of retail sales in the home city, (4) the number of wire services to which newspaper su‘clscribed, and (5) the dummy variables reflecting either morning or evening publication. As soon as three independent variables - the sizes of the two cities and the disiance between them-had entered, the coefficient of the logarithm of the distance ranged from -0.92 to -0.97. The standard errors of this coefficient in these regression equations varied between 0.083 and 0.086. These results provide information for a test of the following hypothesis: The true coefficient of the variable log D, [logarithm of distance of home city (i) to city of sales ti)l is - 1.0; that is, after the anti-logarithms are taken, the true exponent of distance is - 1-O.The test of this hypothesis at the 95 percent significance level is a standard one (using the most restrictive standard error), P(accept flZ = - 1.O) =
@(!Z!Z)-@(
ZZP2)
9
where Kis the limit of the critical region, and 0.95 = :.
@($$$)-B(-~~~mo) or +I.96
K = -0.837,
= z,
- 1.163.
Since the estimated coefficients range from -0.92 to -0.97, all are within the critical region and the hypothesis that the true value is - 1.Ocannot be rejected. This agrees with the more elementary results of Zipf (1948) in his pioneer newspaper study. Additional interpretations of the results are possible and are also rather encouraging: (1) The estimated coefficients of the population of city j(P,) are highly significant in every regression, have the expected sign, and range from 0.71 to 0.82. (2) As a measure of the size of the home cities i, the volume of retail sales (SJ has slightly more significant coefficients than number of households (PJ, although in every regression that either appears, each has significant explanatory power. (3) The number of wire services to which a newspaper subscribes (Wi) is a E
296
Y. M. Braunstein, A gravity model analysis
significant explanatory variable. However, because of the presence of multicollinearity, the estimates of the coefficients are uncertain. The wire services variable has high partial correlation coefficients of 0.839 with the number of households in the home city and 0.794 with the volume of retail sales. The large drop in the values of the t-statistics of the coefficients of the home city size variables when IV, enters is a further demonstration of the multicollinearity. This drop is less in the case with the retail sales variable as would be expected by the slightly lower partial correlation coefficient between IV, and S1 than between IV, and Pi. Therefore it is likely that the coefficients in equations 2-4 and 2-5 have a higher precision than those in l-4 and 1-5. For the estimated equations to be demand equations, it is necessary for the consumers to be reacting to the characteristics of the firm rather than vice versa. The assumption of best industry practice in the choice of inputs is sufficient to permit a demand estimation. There is a possibility that the equation is misspecified and that some of the variables are proxies for a set of other, missing variables. The study by Rosse (1966) included measures of advertising content, news content, and a measure of quality in the circulation demand equation. For the newspapers included in this study, detailed information of that type is rare and incomplete. In the most recent study of this nature, Rivers and Rubin (1971) developed partial data for newspapers in the San Francisco bay area. They compared the space and location given by five of the newspapers in this study to six different national news items. They also presented a discussion on the quality of the news coverage and the variety of opinion columns in seven of the newspapers. A similar analysis of the coverage of foreign news by the metropolitan dailies was also presented [Rivers and Rubin (1971, pp. 164-165, 168-169)]. (The definition of different newspapers’ used by Rivers and Rubin varies from that of this study in that they counted the San Francisco Chronicle and San Francisco Examiner as separate papers.) The number of wire services subscribed to by each newspaper may in fact be a crude proxy for the quality of that newspaper. It is also known that the total content of a newspaper varies proportionally with the circulation and the size ofthehomecommunity;seeBagdikian(1971,pp. 119-120): Smaller papers are smaller in three ways: in number of pages per issue, in total papers printed per day, and in the number of different editions issued each day. The smaller paper is in a smaller community with fewer local advertisers and attracts fewer national advertisers. Since the volume of advertising determines the number of pages in American papers, small advertising volume results in a low number of pageq. There are fewer papers printed daily because its community has fewer households that might buy the paper. And it issues fewer editions because the area of its coverage has
Y.M. Braunstein, A gravity model ana(vsis
297
fewer neighborhood and governmental units, so that it is possible to provide their news and advertising information in one standard edition a day. The area covered by a larger paper encompasses massive retail establishments typical of a metropolis and so needs more pages to carry ads. The same area is densely populated, with thousands of governmental units and citizen organizations. Suburbs at one edge of the city will have little interest in news from suburbs at the opposite edge, so each will receive its own area edition, The possibility of misspecification brings into further question the reliability of the estimators of the two variables describing the size of the home city (Pi and SJ and the wire services variable ( WJ. Among the attributes that may actually be influencing demand are the volume of local news and the quantity of information on local retailers and the goods and services offered for sale, both of which are highly correlated with Pi and SI. An additional reason why the estimate of the coefficient of the retail sales variab1.e (SJ is more significant than that of the number of households (PJ may be that the information conveyed by the advertising content is useful to the reader. Rosse (1966, p. 54) found that a ceterisparibus increase in advertising lineage results in an increase in the demand for subscriptions. However it should be noted that the estimators of the coefficients of the other variables (especially D, and Pi) have no specification bias because these variables are not correlated with the possibly misspecified variables [Theif (1957)J. The partial correlation coefficients are shown in table 3. Those variables that did not have significant explanatory power are shown in table 4, along with their estimated coefficients and t-statistics. The equation that was the source of these statistics was, in each case, the one that contained the fewest variables in addition to the one cited. Results are shown both for the set of equations that used number of houseb.olds (set 1) and the set that used retail sales (set 2) to measure the size of the home cities of the newspapers. In each case but one, the estimated coefficient had the sign to be expected a priori. Cities with higher median family income ( Yj) purchase more of a particular newspaper. The meaning of N,, number of different newspapers sold in a given community, has already been described. And from the signs of the coefficients of the dummy variables, we can conclude that: (1) if there was a residential community that was equi-distant from two cities, one with a regional newspaper and one with a suburban newspaper, more households in the residential community would buy the regional newspaper than would buy the suburban newspaper; (2) other factors being equal, one newspaper would sell !ewer copies in a city that was the home of another newspaper as compared to a city that had no newspaper of its own ; and (3) sales would be lower in a city outside the six-county bay area than in a city of comparable size and distance from the newspaper within the bay area.
Y.M. Braunstein, A gravity model analysis
298
The variable Yi , the median family income of the home city of the newspaper did not have the expected positive sign. A possible explanation of the negative coefficient is that the movement of wealthy and middle class families to the suburbs has left the major cities - the homes of the regional newspapers - with a generally lower income structure. This, plus the fact that the area chosen for the income data was just the immediate home city and not entire area in which the paper circulated, leads to the seemingly anomolous result. Table 3 Selecteii partial correlation coefficients.
logPl log s, 108 w
0.587 0.565 0.528
0.034 0.054 - 0.008
Table 4 Coetlicients and l&a&tics of explanatory variables not statistically significant.’ Equation set 1
Equation set 2
Variable
Coefkient
t
Coefficient
yJ
0.29 - 0.98
1.16 0.95
0.23
-0.13 0.49 -0.17 -0.24
0.50 1.13 0.98 1.00
-0.20 0.16 -0.17 -0.14
Yl NJ
Regional newspaper Home city of auothcr newspaper City outside bay area
1 0.96
n.e. 0.88 0.53 0.83 0.61
*Taken from equation with least number of explanatory variables that contained the specified variable. n.e. = not estimated.
When anti-logarithms of both sides of the regression equations are taken, the equations are transformed back into the usual gravity model formulation. The exact results for equations 1-5 and 2-5 are, respectively,
where
Al = 0.16 if morning paper (or day-long), = 0.33 if evening paper;
Y. M. Braunstein, A gravity model analysis
299
where A2
=
0.58 if morning paper,
= 0.07 if evening paper (or day-long). We have discussed the meaning of the exponents of the distance variable (p. 295). The significance of the exponents of the population variables will be explored in section 3. In section 4 we shall examine our estimates of the exponent of the wire services variable to see if they are consistent with the results of other researchers. 3. The asymmetry of the competition between suburban and metropolitan newspapers
The broadcast nature of mass communications results in the asymmetry of the exponents of the population variables. This contrasts with the interaction between the populations of two citres in the gravity models generally used in studies of transportation or of private communications. In these cases the population exponents are equal because the model had been designed to apply to cases that Aibit ‘round-trip’ or ‘two-way’ properties and therefore a symmetry between origin and destination. The asymmetry in mass communications will be shown to be manifest in both. the circulation patterns and the advertising sales and rates. Using the Quandt and Baumol (1966) study of travel between pairs of California cities, we find that there is no statistically significant difference between the calculated exponents of the variables representing the populations at the origin and the destination (see table 5). In other words, the number of trips by air from San Francisco to Los Angeles, for example, is approximately equal to the number of trips in the opposite direction between the two cities. Table 5 shows the exponents of the population variables Pi and Pj estimated by Quandt and Baumol for their seven regression equations. We wish to test the null hypothesis that the true values of the exponents of the populations at the origin and at the destination are equal. The t-statistics for each of the comparisons were calculated, and, in each case, were less than the value of the cumulative t-statistic at the 0.975 level with the appropriate (2~ - 2 = 94) degrees of freedom (I = 1.99). Therefore, the null hypothesis of equality of the exponents cannot be rejected at the 95 percent significance level. The study of telegraphic communications by Seneca and Cicchetti (1969) exhibits similar properties. They examined intra-state messages between cities within California and within New York. In four of their twelve equations, they explicitly assumed the exponents of the population variables to be equal. In two other equations, they estimated the exponents for the origin and destination
1.14
1.14 1.12
0.95
0.94 0.92
0.91 0.93
0.23 0.19
0.20 0.22
0.13
Difference
(4)
: Quandt and Eaumol(l966);
1.08
Expontnr of P,
Regression equation
‘Sources: Columns 1,2,3,7,8
(3) Exponent OfP,
(2)
(1)
columns 4,5,6:
0.144 0.154
0.216 0.196
0.186
(5) Average s.e.
Average Income/P income
avail. of car at j
Y0 % empl. in white mfg.collar
Deposits/P
Irlcome/P
Income/P
(3) Other demographic variables
(7) Weights of population
calculated from columns 2 and 3 and respective f-statistics.
1.603 1.230
0.926 1.122
0.699
t
(6)
Table 5 ‘l’ests of equality of exponents of population variables - Quandt and Baumol study of travel demands.”
.
P
,$
f
”
ea s‘ P 3 S
Y.M. Braunstein, A gravity model analysis
301
popu1ation variables separately. (In the remaining six equations, eitner the populations were weighted differently or other demographic measures, such as number of business firms, were used, or both.) For these two, the l-statistics testing the null hypothesis of equality of the exponents were calculated as above. The results are shown in table 6. Again, the null hypothesis cannot be rejected in these two cases at the 95 percent significance level. In the case of mass communication, however, the interaction is asymetrical. Although there may be some audience feedback, it is of a different sort and is! transmitted by a different medium. This ‘unidirectional’ nature of the messages carried by the mass media manifests itself in the circulation data. For example, newspaper A in large city A generally sells many more copies in neighboring suburb B than suburban newspaper B sells in city A. To limit the effects of this asymmetry on the estimation of the gravity model for newspaper circulation it was necessary to use the requirement that there be sales of at least twenty-five copies for a particular newspaper in a given city for that paper-city pair to be included. From the results of the regression equations, the three cases that included the populations of the home cities of the newspapers in addition to the populations of the receiving cities as explanatory variables were analyzed in the same manner as the gravity models of Quandt and Baumol (1966) and Seneca and Cicchetti (1969). As shown in table 7, the exponents of the population variables were significantly different and the null hypothesis rejected in the two cases that also included as explanatory variables the number of wire services describing the newspapers. In the one equation that was the simple gravity model of the form C’ij = A#‘Y~/D$ (equation 1-3) without any other explanatory variables, the hypothesis of equality of the exponents b, and b2 could not be rejected statistically. But even this case supports the view that mass communications do not possess the symmetry with respect to the origin and the destination that is exhibited by the travel and private communications studies. The only regression equations that are strictly comparable to the newspaper regressions are Quandt and Baumol’s regression equations 5, 6, and 7. In these regressions, the populations are unweighted, and the only other explanatory variables describe the mode or the medium or arc: averages of characteristics of the origin and the destination. Quandt and Baumol (1966, p. 25) believe that their regression equation 7 is the most plausible of the forms of the relationships they tested: Regression 7 from which the bank deposit, percent white collar, percent manufacturing and car availability variables were omitted seems best not only on the grounds that it yields the smallest unexplained residual (although not the highest F-value) but also on the grounds that the coefficients Of Pi and Pi are the same, which is what we would expect on a priori grounds.
0.4939
0.4049
1
2 0.0208
0.0182
Table 7
- 0.423
0.810
I
Income/P
IncomefP
Weights of population
calculated from columns 2 and 3 and
Average s.e.
Seneca and Cicchetti (1969), columns 4,5,6:
-0.0088
0.0147
Difference
0.68 0.45 0.38
l-3 l-4 l-5 0.04 0.28 0.33
Difference
OfP,
0.72 0.73 0.71
(4)
( .q Exponent
0.066 0.088 0.088
rs) A VXl-&G s.e.
0.066 3.182b 3.771b
t
(6)
variables Distance Distance, no. of wire services Distance, no. of wire services, time of publ.
Other explanatory
(7)
aSollrces: Columns 1,2, 3,7: table 1, supra, colums 4,5, 6: calculated from cohunns 2 and 3 and respective I-stat&i% bSignificant at 99 percent level.
(2) Exponent of P,
(1) Regression equation
Tests of equality of exponents of population variables - 1970 newspaper circulation regressions.*
aSources: Columns 1,2,3,7: respective t-statistics.
0.4792
OfP,
0.4137
Exponent OfP,
Exponent
Regression equation
_
Table 6 Tests of equality of exponents of population variables - Seneca and Cicchetti study of telegraphic communicatioils.’
8 g k’
1 Iz jl a b f3 “s’ k 3 $ b
$ T
.____-_ _--..-T__T_ - --~--
vantage if there are a [lowing quotation of But in our equation Z-3, this equality or’ the estimated &rates this point. See obtain simply because of the lack of symmetry between the o of mass communications, Lvea higher cost to the This asymmetry in the circulation patterns between tlte than metropolitan metropolitan newspapers is widely recognized in the n cost could be a signiindustry. It is matched by a similar asymmetry in the neting with the metromarket. Generally the metropolitan newspaper has a highapartment stores which advertising, but, because of its larger circulation, the metro1 a lower price per reader. This is often quoted in terms oft and compare it to the cost of one line of advertising reaching one million readers. (basic per line prices), circulations, and milline rates for SC’ ~~~~~~r~~~~?$y papers are shown in table 8. Ither’s home area. The the advertising linage Table 8 ,?~aiZy&uiew and the Comparisonof advertisingrates, San Francisco bay area nc Y. M. Braunstein, A gravity model analysis
Newspaper San Francisco Chronicle and Examiner Oakland Tribune San Mateo Times Hayward Daiiy Review
Ad rate $2.80 0.77 0.34 0.25
Circulation 682,899 209,449 44,758 35,802
*Sources: Ad rate - ENor and Publisher International Yearbook Audit Reports(1970). 303 The higher cost per reader for the advertiser in the sub place the suburban papers at a severe competitive disadl significant number of multi-outlet advertisers. The fol coefficients does not San Francisco Chronicle publisher Charles Theiriot illusrigin and destinations Tile Newspaper Preservation Act (1969, p. 345) : te suburban and the While it is generally true that suburban newspapers ha newspaper publishing advertiser per reader and thus a higher milline ra ewspaper advertising newspapers, I would assume that this discrepancy in r price for one line of cant factor when the suburban newspaper is compr Jolitan newspaper has politan newspaper for the retail advertising of large de he ‘milline rate’ - the are headquartered in the central city. The advertising rates To quantify this asymmetry in the advertising market everal bay area newsasymmetry in the circulation market, the circulations and were analyzed for one of the suburban newspapers and metropolitan daily, both in their home area and in the o data are the 1970 a.verage daily circulation figures and :wspapers, 1970.” from the week of October 22-28, 1973 for the Hayward Milline rate
4.10 3.68 7.60 K011
Y.M. Braunstein, A gravity model analysis
304
Oakland Tribune. The Tribune is the only one of the three large city newspaper firms in our sample publishing one newspaper per day - an evening paper. The Reuiew is also an evening newspaper. The circulation data are taken from the 1970 ABC Audit Reports; the adversiting data are from exhibits prepared by the Hayward Daily Review.4 In comparing tables 9, 10 and 11 one can see that the suburban newspaper (the Review) sells Iess than one and one-half percent of its daily circulation, or its Table 9 Competition between the Hayward Daily Review and the Oakland Tribune for circulation, 1970.”
Newspaper Ha-ward Dad’ Review Oakland Tribune
Circulation in Hayward area
Total circulation 35,802
Circulation in Oakland
27,080
209,449
‘Source: ARC Audit Reports (1970). Table 10 Competition between the Hayward DaiZy Reoiew and the Oakland Tdbune for classified advertising, week of October 22-28, 1972.”
Newspaper
Total lines
Lines r riginating from Hayward area
Lines originating from Oakland area
,Hayward Daily Review
125,802
123,802
Oakland Tribune
194,068
1694 (1.3O%I 122,918 (63.3 %)
*Classified ads were assigned to areas on basis of telephone nonmessage unit exchanges. Inc., et al. (1973).
Source: Defendants’exhibit EEE-4, Knutson et a!. versus Daily Review,
classified advertising linsge, in the neighboring larger city, while the metropolitan newspaper (the Tribune) selis approximately one-half as many subscriptions, or classified lines, in the neighboring suburb as it does in its home city. The data for retail advertising are not quite comparable, but nevertheless they exhibit the same pattern. The existence of mr ltiple outlet advertisers causes an accounting problem; in table 11, those advertisements coming from firms with outlets in ‘Defendants exhibits EEE2
Y.M. Braunstein, A gravity model emalysis
305
both Hayward and Oakland (or in Hayward and in any other city) are counted in the ‘accounts with Hayward outlets’ column. The phenomenon that we observe is competition that occur in layers -the suburban newspapers compete with each other only at the fringes of each paper’s circulation area and compete with the ‘satellite’ city newspapers throughout the suburban area. In turn, the satellite city papers compete with each other at the fringe and face competition from the major metropolitan/regional daily throughout their circulation area. It is interesting to note which of the suburban newspapers have significantly overlapping circulation areas; all reflect common ownership. The Hayward, Livermore, and Fremont-Newark newspapers in southern Alameda County are Table 11
Competitionbetween the Hayward Daily Review and the Oakland Tribune for retail advertising, week of October 22-28,1973.’
Newspaper
Total retail adv. inches
Adv. inches from accounts with Hayward outlets
Hayward Daily Review
13,221
Oakland Tribune
25,900
13,169 (99.6 %) 14,963
Balance of retail adv. inches
(57.8 “4
‘Retail advertising inches includes run-of-press retail advertising only; pre-printed inserts are excluded. Source: Defendants* exhibit EELL, Knutson et al. versus Daily Review, Inc., et al. (1973).
all owned and published by Floyd Sparks. The Hayward DaiZy Review is an evening paper; the Livermore Herald and the Fremont-Newark Argus are morning newspapers. Similarly, two of the overlapping newspapers between San Francisco and San Jose, the Redwood City Tribune and the Palo Alto Times have a common owner, Peninsula Newspapers, Inc. The remaining competition between two of the suburban newspapers for a heavily populated area is between the Berkeley Gazette and the Richmond Independent. These papers have recently announced plans to combine some of their operations. The concept that the normal gravity interaction is interrupted when reaching a larger city is similar to a hypothesis of Stouffer (1957) that the interaction is inversely proportional to the number of intervening opportunities as opposed to a measure of distance. It may be that our relationship should be partially reformulated in the following way: The interaction is inversely proportional to the distance between the home city of the newspaper and the location of the potential subscriber; if a locality with greater population than the home city of
306
X M. Bramstein, A gravity
modelamulyds
the newspaper intervenes, there is no further interaction from localities more distant in that direction.
with the newspaper
4, Comgarison with other studies of mass communications The estimated coefficienrs in a regression linear in logs are partial elasticities; i.e., each is an estimate of the percentage change in circulation due to a one percent change in that explanatory variable, ceteris paribus. Other researchers, using different samples, have independently obtained estimates of some of these elasticities. It would be interesting and useful at this point to see if the various results are consistent. For example, equations l-4,2-4, and 2-5 indicate that those newspapers that subscribe to a second wire service (a 100 percent increase) would find their circulation increased by approximately 40 to 50 percent if nothing else were to change. While other factors certainly play some role, the two-wire service papers (Rerkeley, Hayward, Oakland, Palo Alto, Richmond, and San Rafael) are generally of a higher qua!ity than those with one wire service (Antioch, Concord, Fremom-Newark, Livermore, and Redwood City) and our results are therefore consistent with those of Rosse in which quality had a significant positive explanatory power in the demand for subscriptions. The measure of quality used by Rosse was editorial cost per news inch published. He estimated the partial elasticity of circulation with respect to the quality measure to be approximately 0.01 [Rosse (1966, p. 55)]. It would probably be misleading to push this comparison further by attempting to convert the number of wire services into editorial cost per rrews inch for two reasons. Fist, the amount a wire service charges a given newspaper is negotiated, and second, Rosse’s (1966, p. 89) sample consisted of data from 59 Mid-Western newspapers, generally non-metropolitan in nature, during years from 1958 to 1964. Rosse (1966, p. 25) also obtained an estimate for the partial elasticity of circulation with respect to the number of households in an adjusted version of the Audit Bureau’s Retail Trade Zone for each newspaper. This elasticity was approximately 0.33 [Rcsse (1966, p. 55)]. Solving his reduced-form equations to allow for interaction between the advertising and circulation markets gives a partial elasticity of 1.31. Neither of these estimates are inconsistent with the estimates of from 0.71 to 0.82 that we obtained above. Again, there is the disparity of the samples, but more important, the elasticity after interaction of 1.31 in Rosse’s results is based on ceteris paribus considerations that would never obtain -- e.g., advertising rates generally increase as circulation increases as shown in table 8. The final comparison of our regression results is based on the lack of significance of the dummy variable used to dichotomize the sample into ‘day-long’ newspapers and newspapers with either a morning or an evening edition. We found that this dummy variable that would have segregated the two Ridder newspapers in San Jose and the newspapers published under the joint operating
Y.M. Bramstein, A gravity modelmdysir
307
agreement in San Francisco from the other newspapers was not statistically signiiicant. This result from the circulation market data is entirely consistent with the results obtained by Owen (1970) in examining advertising market data. Owen (1970, p. 84) found that ‘agency firms [those operating under joint agreements] do not charge significantly different prices than monopoly firms [those with no other daily newspaper in their home city].’ His results were based upon 1969 data obtained from twenty-two agency firms, twenty-two monopoly firms, and twenty-four firms each publishing in a city with one other daily newspaper. 5. conclusions The following conclusions, therefore, can be drawn about the usefulness of the gravity model in analyzing the demand for mass communications media: (1) The gravity formulation is an appropriate one for daiiy newspapers; a gravity model that includes measures of abstract characterisfics provides additional inforrmation to the elementary models of %pf and others that showed sales simply proportional to population divided by distance. [Zipf (1948), Conant and Davis (1948)]. (2) The measures of certain partial elasticities of demand obtained from such a gravity model are not inconsistent with comparable elasticities obtained by other researchers using other methods. (3) The gravity formulation permits statistical tests of hypotheses. The results of such tests (i.e., the exponent of the distance variable equals minus one, the dummy segregating the ‘day-long’ newspapers from the others is not significant) agree with the results of different tests generated by others examining these questions. (4) Unlike the gravity models used in the analysis of transportation and of private communications, the gravity model in this study of mass communications has different coefficients for the two population variables. This is a result of the asymmetrical nature of mass communications. (5) The competition between a metropolitan daily newspaper and a suburban competitor exhibits similar properties on both the circuIation and the advertising markets, In each market, the sales of the metropolitan newspaper in a neighboring large suburb might be one-half or more of the sales in its home city, while the suburban newspaper sells no more than an amount equal to one or two percent of its home city sales in the adjoining large city. References Audit Bureau of Circulations, 1970, Audit Reports for San Fran&co bay area daily newspapers (Chicago, IL). Bagdikian, B.H., 1971, The information machines: Their impact on men and the media (Harper and Row, New York).
308
Y.M. Braunstein, A gravity model analysis
Boland, J.P., 1948, On the number and sizes of radio stations in relation to the populations of their cities, Sociomeuy 11,ll l-l 16. Braunstein, Y.M., 1975, Dynamics of inter- and intra-media competition: Effects of technological and demographic change, unpublished Ph.D. dissertation (Stanford University, Stanford, CA). Conant, J.M. and A.Y. Davis, 1948,A measurement of the number and diversity of periodicals in 92 American cities, Sociometry 1,117-l 20. Dixon, W.J., ed., 1971, BMD Biomedical Computer Programs (University of California Press, Berkeley, CA). E,’ “qymsen,M.A., 1960, Multiple regression analysis, in: A. Ralston and H.S. Wilf, eds., Mathematical methods for digital computers (Wiley, New York). International Yearbook, Editor and Publisher, 1970. Knutson et al. versus Daily Review, Inc., et al., 1973,Case C-73-1354(CBR) (N.D. Cal). Lancaster, K.J., 1965, Change and innovation in the technology of consumption, Papers and Proceediny of the American Economic Association 86,14-23. Lancaster, K.J., 1966, A new approach to consumer theory, Journal of Political Economy 14, 132-157. Niedercorn, J.H. and B.V. Bechdolt, Jr., 1969, An economic derivation of the ‘gravity law’ of spatial interaction, Journal of Regional Science 9,273. Niedercom, J.H. and B.V. Bechdolt, Jr., 1971,A further reply and a reformulation, Journal of Regional Science 12,127. Niedercom, J.H. and B.V. Bechdolt, Jr., 1970, Reply, Journal of Regional Science 10,407-410. Owen, I?., 1970,Price effects of mergers, Memorandum No. 96, Workshop in the economics of the press, Research Center in Economic Growth mimeo. (Stanford University, Stanford, CA). Quandt, R.E. and W.J. Baumol, 1966,The demand for abstract transportation modes: Theory and measurement, Journal of Regional Science 6,13-26. Rivers, W.K..end D.M. Rubin, 1971, A region’s press: Anatomy of newspapers in the San Fran&cc bay area (Institute of Government Studies, University of California, Berkeley, CA). Rosse, J.N., 1966, Daily newspapers, monopolistic competition and economies of scale, unpublished Ph.D. dissertation (University of Minnesota, Minneapolis, MN). Rosse, J.N., 1967, Daily newspapers, monopolistic competition and economies of scale, American Economic Review 57,522-533. Seneca, J.J. and C.J. Cicchetti, 1969,A gravity model analysis of the demand for public communication, Journal of Regional kience 9,459-78. Stouffer, S.A., 1957, Intervening opportunities: A theory relating mobility and distance, American Sociological Review 25,269280. The& H., 1957, Specification errors and the estimation of economic relationships, Review of the International Statistical Institute 25,41-S 1c United States Bureau of the Census, 1970,Census of Population. United States Senate, Committee on the Judiciary, 1969, The Newspaper Preservation Act, Hearings before the Subcommittee on Antitrust and Monopoly -9lst Congress, 1st Session, June 12,13, and 20. zipf, G.K., 1948,On the number ,circulation, sizes, and the probable purchasers of newspapers, American Journal of Psychology 61,83-92.
North-Holland
A GRAVIl’Y MODEL ANALYSIS OF THE DEMAND FOR MASS COMMUNICATIONS* Yale M. BRAUNSTEIN New York University, New York, NY 10003, USA Received January 1976 The gravity model specification is shown to be applicable to a study of the demand for a mass communication medium. The data are taken from newspaper circulations in the San Francisco metropolitan area. The demand equations have properties different from those for either private communication or travel demands.
1. Introduction Gravity models are well known and have been used for a variety of empirical analyses including studies of the demand for transportation services and for communications. In these analyses the interaction (e.g., communication or travel) between two localities was hypothesized to be proportional to socioeconomic characteristics of the localities and inversely proportional to the distance separating them. Simple tests have also been conducted by Zipf and his students to show that an elementary gravity model can explain the circulations of newspapers [Zipf (1948)], the number of radio stations per city [Boland (1948)] and the number of periodicals published per city [Conant and Davis (194&)]. The gravity model approach was also used by Seneca and Cicchetti (1969) to measure the demand for private point-to-point communications. This paper will examine the use of a gravity model to estimate the demand for mass communications, particularly the circulation pattern of daily newspapers. It will then explore the modifications in the gravity model required by the one-way nature of mass communications. Within the last few years Neidercorn and Bechdolt (1969, 1970, 1972) have provided a theoretical basis for the gravity model. They have shown that utility theory using a characteristics approach derived from the works of Lancaster (1965, 1966) can provide an economic rationale for the gravity formulation. The equations that are estimated in this analysts of demand contain as explanatory variables both the demographic and distance measures that are standard *James Rosse, Michael Spence, and William Baumol made several contributions versions of this paper. The author alone is responsible for any remaining errors.
to earlier
290
Y.hf. Braunstein,A gravity model analysis
in gravity models and mleasures of characteristics of each of the modes. This approach is comparable to the abstract mode approach to transportation demands first developed by Quandt and Baumol (I 966). The next section will describe the estimating procedure, sources of data, and results. In section 3 we shall contrast our results using a model of the demand for mass communications with the results from models of the demands for travel and for private communications. Sections 4 and 5 will interpret our findings in light of other studies of mass communications and present conclusions, respectively. 2. The gravity model: Estimation and results The circulation patterns of the daily newspapers of the San Francisco bay area were quantified and tested to see if they are consistant with what would be predicted by a gravity model. Using the ‘gravity’ analogy, the circulation of a newspaper in a specific commtunity is taken to be proportional both to the population of that community (pi) and to the population (or some other measure of socio-economic activity) of the home city of the newspaper (Pi). The circulation is assumed inversely proportional to the distance between the community snd the place of publication (UJ. Other determinants of the circulation may be characteristics specific to the newspaper (the AJ and the number of different newspapers (or other mass media) available in the community (NJ. The relationship describing such a model takes the form
where the subscripts 1”refer to the newspaper and its city of publication and the subscriptsj refer to the community where the newspaper is purchased and read. (We are considering only home-delivered daily newspapers.) A major advantage of gravity model formulation is that it can be tested by means of a multiple linear regression using only a logarithmic transformation of the data. The program chosen for this computation was BMD 02R of BMD Biomedical Computer Programs.’ This is a stepwise multiple regression routine that includes or deletes explanatory variables by calculating the effect each variabIe would have on the overall F-ratio of the regression equation. The circulation data came from the 1970 ‘Audit Reports’ compiled by the Audit Bureau of Circulation (1970) for the fourteen audited daiIy newspapers in the six central counties of the San Francisco bay area. The population data used were the number of households and median family income from the 1970 ‘Dixon (1971).
Y.M. Braunstein, A grauity model analysis
291
Census of Population. The distances were measured using highway mileage by the most direct route. As another descriptor of socio-economic activity, the level of retail sales in 1967 was collected for each of the fourteen home cities.2 Additional data were sought for each of the newspapers. Since each had a newsstand price of tsn cents and a home-delivered price that was mostly determined by the number of issues per week, information other than price had to be used to describe the particular newspaper. One characteristic is the time of publication; distinctions were made between morning edtions, afternoon editions, and those papers that had two editions per day. This last category was broadened to include the San Jose Mercury and News and the San Francisco C/zronicle and Examiner. The San Jose newspapers are both published by Ridder Publications and have combined editorial, news, and business departments. There is a joint operating agreement between the Chronicle ar.d Examiner, and although they have separate editorial and news operations and separate ‘publishers’, their advertising and circulation functions are combined. In each case, the rate structure makes it unlikely that an advertiser would purchase space in only one edition rather than both. And in each case there are few homes that receive both editions, although this is more true with the San Jose newspapers than of the San Francisco ones. Another descriptor of the individual newspapers is the number of national wire services to which they subscribe. The San Francisccl, Oakland, and San Jose newspapers view themselves as regional or metropclitan newspapers rather than local newspapers. A dummy variable was used to indicate this regional-local dichotomy. Additional dummy variables were used to indicate if the sales were in the home city of another newspaper in the survey and to distinguish cities and counties outside the six-county bay area from those inside the area. To determine the effects of having many newspapers serving the same city or county, a variable was constructed to represent the number of newspapers that serve a given area. The sample consisted of 234 cases for which all the data described above could be collected. Each city was counted as many times as there were different newspapers with sales of at least twenty-five in that city. Because the number of households and the retail sales in the newspapers’ home cities had a simple correlation coefficient of 0.983, and in order to avoid problems of multicollinearity, these rxplanatory variables, which may be proxies for the coverage of the newspapers, were not allowed to enter the same estimating equation. The following notational system was used to describe the different variables: Cl, = average daily circulation (in thousands) of newspaper i in cityj; Pr = households (in thousands) in cityj (or countyj for distant locations); distance (in miles) from home city of newspaper i to cityj (or county,& Dij
=
2A further description of the data sources and the problems in data collectior is in Braunstein (1975).
Y. hf. Braunstein, A gravity motiel analysis
292
= households (in thpusancis) in home city of newspaper i; annual retail sales (in hundred millions of dollars) of home city of si newspaper i; = median family income in city i ( Yj for cityj) ; yi wi = number of wire services lsubscribed to by newspaper i; = dummy variable equal to 1 if newspaper publishes evening editions only; ei equals 0 otherwise; ?IIi = dummy variable equal to 1 if newspaper publishes morning editions only; equals 0 otherwise; 4 = number of different newspapers serving cityj.
pi
-=
The stepwise structure of the computation permits the equations to be as simple as one taking the circullation of newspaper i in any city to be a function only of the population of that city (C, = APil) or to be a more complex relationship with additional explanatory variables. The results of the computations are presented in table 1, where each column presents the results of a different regression. The numbers in the cells are the coefficients of the variables included in each of the regressions and the corresponding values of the t-statistics (in parenthesis). The dependent variable in each case was log Cij, and a blank cell indicates that explanatory variable (the row) was not included in the specific equation (the column). At the bottom of each column are the coefficient of correlation (I?) and the value of the F-statistic. The reflession equations are identified by a two-digit number. The first number indicates whether the size of the home city of each newspaper is measured by number of households (1) or volume of retail sales (2). The second digit is the number of explanatory variables that have entered the regression. Because the population of the city in which the sales occur and the distance from that city to the home city of the newspaper were the first variables to enter, equations 2-l and 2-2 are the same as l-l and l-2 and therefore are not shown in table 1. Before examining the explanatory variables that were significant in explaining the circulation data and their coefficients, it is interesting to look at the nondemographic variables that did not enter any of the regression equations. As part of the stepwise nature of the computer program that was utilized, an F-statistic - ‘F to enter’ - is calculated for each of the variables that is not in the regression equation at each step. The value of the F-statistic provides information to test the null hypothesis: Explanatory variable X, does not add significantly to the regression of Y on XI, . . ., X,_ 1 (the variables that have entered previously). 3 As explained above, a dummy variable was used for the San Francisco and San Jose newspapers since each city has morning and afternoon newspapers 3Efrcm,jymson (1960, p. 101).
Y.M. Braunstein, A gravity model analysis
293
published under separate names although there is either a joint operating agreement (in the San Francisco case) or a single publisher. If the dummy variable had entered the regression equation and if its coefficient were positive and significant, there would be an indication that the notion of single day-long newspaper was not an appropriate one. As soon as the regression equations included the variables representing the size of the home city (as a proxy for the newspapers’ coverage), the value of the ‘F to enter’ of the *day-long’ dummy variable was no longer significant. Therefore the null hypothesis cannot be Table 1 Results of regressions on 1970 newspaper data. Regression Variable
1-l
1-2
Constant
-1.36
log PJ
0.81 (12.6)
log Du
--
l-3
l-4
l-5
2-3
2-4
-1.81
- 1.25
-1.86
- 0.03
-0.08
0.77 (12.9)
0.72 (13.8)
0.73 (14.01)
0.72 (14.0)
0.71 (13.8)
0.72 (14.1)
0.72 (14.1)
- 0.48 (6.04)
- 0.92 (10.67)
- 0.93 (10.9:
-0.97 (11.41)
- 0.92 (11.1)
-0.95 (11.49)
-0.98 (11.68)
0.11
0.68 (8.59)
log Pf
0.45 (3.66)
0.57 (4.59)
0.82 (9.29) 0.49 (2.44)
0.45 (2.56)
1.13 (3.79) 0.74 (2.87)
et
-0.62 (1.75)
m
R F
0.07
0.39 (3.14)
log & log W
2-5
0.6369 158.35
0.6977 109.52
0.7820 12Q.66
0.7882 93.91
0.7365 79.14
0.7917 128.75
0.7979 100.92
0.8009 81.57
rejected, and one can conclude that the San Francisco and San Jose newspapers may be properly viewed as single day-long newspapers comparable in nature to the other daily newspapers of the bay area. The values of the ‘F to enter’ at the fifth step of this dummy variable are shown in table 2. None of the dummy variables other than those: representing time of publication had an ‘F to enter’ greater than 1.30 (most were less than 1.OO)by the fifth step and therefore the null hypothesis that they did not add significantly to the regression of daily circulation on the set of e:8cplanatory variables that had entered cannot be rejected. Thus there was no significant difference between the
Y.M. Braunstein, A gravity model analysis
294
cases where the paper considered itself regional rather than local in nature, where the sales were in the home city of another newspaper rather than not, or where the sales were inside or outside the bay area. The values of the ‘F to enter’ for these dummy variables are also presented in table 2. The first column shows the results for the regression with population data representing the size of the home cities, and the second column is for the regression in which retail sales data are used. The variable (Ni) that measured the number of different newspapers serving a given area also was not significant in explaining the circulation data. The Table 2 Values of the ‘F to enter’ of dummy variables that had not entered by the fifth step. -Dummy variable
l-5
Regression 2-5 .-
‘Day-long’ publication Regional newspaper Home city of another newspaper ’ City outside bay area
0.0059 1.2783 0.6593 0.7866
0.3583 0.1281 0.7183 0.6033
meaning of this variable has received considerable attention from Quandt and Baumol(1966) : The presence of the variable N has one discdvantage - it implies that travel demand will be affected by the availability of ‘irrelevant modes’ -modes that would not even be considered by the class of travelers in question. It also makes the calculation dependent on fineness of classification whether, e.g., we consider local and express trains to constitute one mode or two. (p I7n). Ceteris paribus, we would expect total travel volume to be an increasing function of the range and density of alternatives and volume traveled by any one mode a decreasing function of the density of alternatives. (p. 21) Tn the regression equations that did contain NJ, it had a negative coefficient as ,would be expected. However, in each of these cases, the null hypothesis that the true coefficient was not different from zero can not be rejected. An example would be equation 2-7, the one with the least number of variables that also contained Nj, log C, = -0*51-0.57mi+0*74 lOgP]+O.28 log Yj (1.62) (13.75) (1.12) -0.92 log 0,+0.56 (9.78)
log Si+O.41 log W~-O.ZO log Njs (4.41) (2.28) (0.88)
Y.M. Braunstein, A gravity model analysis
29.5
The corresponding values of the t-statistics are shown in parentheses below the coefficient estimates. In the eight regression equations which contained explanatory variables having significant coefficients (table I), the variables entered in a predictable order: (I) the number of households in the city in which sales occurred (city to city j, (3) the number of households or volume of retail sales in the home city, (4) the number of wire services to which newspaper su‘clscribed, and (5) the dummy variables reflecting either morning or evening publication. As soon as three independent variables - the sizes of the two cities and the disiance between them-had entered, the coefficient of the logarithm of the distance ranged from -0.92 to -0.97. The standard errors of this coefficient in these regression equations varied between 0.083 and 0.086. These results provide information for a test of the following hypothesis: The true coefficient of the variable log D, [logarithm of distance of home city (i) to city of sales ti)l is - 1.0; that is, after the anti-logarithms are taken, the true exponent of distance is - 1-O.The test of this hypothesis at the 95 percent significance level is a standard one (using the most restrictive standard error), P(accept flZ = - 1.O) =
@(!Z!Z)-@(
ZZP2)
9
where Kis the limit of the critical region, and 0.95 = :.
@($$$)-B(-~~~mo) or +I.96
K = -0.837,
= z,
- 1.163.
Since the estimated coefficients range from -0.92 to -0.97, all are within the critical region and the hypothesis that the true value is - 1.Ocannot be rejected. This agrees with the more elementary results of Zipf (1948) in his pioneer newspaper study. Additional interpretations of the results are possible and are also rather encouraging: (1) The estimated coefficients of the population of city j(P,) are highly significant in every regression, have the expected sign, and range from 0.71 to 0.82. (2) As a measure of the size of the home cities i, the volume of retail sales (SJ has slightly more significant coefficients than number of households (PJ, although in every regression that either appears, each has significant explanatory power. (3) The number of wire services to which a newspaper subscribes (Wi) is a E
296
Y. M. Braunstein, A gravity model analysis
significant explanatory variable. However, because of the presence of multicollinearity, the estimates of the coefficients are uncertain. The wire services variable has high partial correlation coefficients of 0.839 with the number of households in the home city and 0.794 with the volume of retail sales. The large drop in the values of the t-statistics of the coefficients of the home city size variables when IV, enters is a further demonstration of the multicollinearity. This drop is less in the case with the retail sales variable as would be expected by the slightly lower partial correlation coefficient between IV, and S1 than between IV, and Pi. Therefore it is likely that the coefficients in equations 2-4 and 2-5 have a higher precision than those in l-4 and 1-5. For the estimated equations to be demand equations, it is necessary for the consumers to be reacting to the characteristics of the firm rather than vice versa. The assumption of best industry practice in the choice of inputs is sufficient to permit a demand estimation. There is a possibility that the equation is misspecified and that some of the variables are proxies for a set of other, missing variables. The study by Rosse (1966) included measures of advertising content, news content, and a measure of quality in the circulation demand equation. For the newspapers included in this study, detailed information of that type is rare and incomplete. In the most recent study of this nature, Rivers and Rubin (1971) developed partial data for newspapers in the San Francisco bay area. They compared the space and location given by five of the newspapers in this study to six different national news items. They also presented a discussion on the quality of the news coverage and the variety of opinion columns in seven of the newspapers. A similar analysis of the coverage of foreign news by the metropolitan dailies was also presented [Rivers and Rubin (1971, pp. 164-165, 168-169)]. (The definition of different newspapers’ used by Rivers and Rubin varies from that of this study in that they counted the San Francisco Chronicle and San Francisco Examiner as separate papers.) The number of wire services subscribed to by each newspaper may in fact be a crude proxy for the quality of that newspaper. It is also known that the total content of a newspaper varies proportionally with the circulation and the size ofthehomecommunity;seeBagdikian(1971,pp. 119-120): Smaller papers are smaller in three ways: in number of pages per issue, in total papers printed per day, and in the number of different editions issued each day. The smaller paper is in a smaller community with fewer local advertisers and attracts fewer national advertisers. Since the volume of advertising determines the number of pages in American papers, small advertising volume results in a low number of pageq. There are fewer papers printed daily because its community has fewer households that might buy the paper. And it issues fewer editions because the area of its coverage has
Y.M. Braunstein, A gravity model ana(vsis
297
fewer neighborhood and governmental units, so that it is possible to provide their news and advertising information in one standard edition a day. The area covered by a larger paper encompasses massive retail establishments typical of a metropolis and so needs more pages to carry ads. The same area is densely populated, with thousands of governmental units and citizen organizations. Suburbs at one edge of the city will have little interest in news from suburbs at the opposite edge, so each will receive its own area edition, The possibility of misspecification brings into further question the reliability of the estimators of the two variables describing the size of the home city (Pi and SJ and the wire services variable ( WJ. Among the attributes that may actually be influencing demand are the volume of local news and the quantity of information on local retailers and the goods and services offered for sale, both of which are highly correlated with Pi and SI. An additional reason why the estimate of the coefficient of the retail sales variab1.e (SJ is more significant than that of the number of households (PJ may be that the information conveyed by the advertising content is useful to the reader. Rosse (1966, p. 54) found that a ceterisparibus increase in advertising lineage results in an increase in the demand for subscriptions. However it should be noted that the estimators of the coefficients of the other variables (especially D, and Pi) have no specification bias because these variables are not correlated with the possibly misspecified variables [Theif (1957)J. The partial correlation coefficients are shown in table 3. Those variables that did not have significant explanatory power are shown in table 4, along with their estimated coefficients and t-statistics. The equation that was the source of these statistics was, in each case, the one that contained the fewest variables in addition to the one cited. Results are shown both for the set of equations that used number of houseb.olds (set 1) and the set that used retail sales (set 2) to measure the size of the home cities of the newspapers. In each case but one, the estimated coefficient had the sign to be expected a priori. Cities with higher median family income ( Yj) purchase more of a particular newspaper. The meaning of N,, number of different newspapers sold in a given community, has already been described. And from the signs of the coefficients of the dummy variables, we can conclude that: (1) if there was a residential community that was equi-distant from two cities, one with a regional newspaper and one with a suburban newspaper, more households in the residential community would buy the regional newspaper than would buy the suburban newspaper; (2) other factors being equal, one newspaper would sell !ewer copies in a city that was the home of another newspaper as compared to a city that had no newspaper of its own ; and (3) sales would be lower in a city outside the six-county bay area than in a city of comparable size and distance from the newspaper within the bay area.
Y.M. Braunstein, A gravity model analysis
298
The variable Yi , the median family income of the home city of the newspaper did not have the expected positive sign. A possible explanation of the negative coefficient is that the movement of wealthy and middle class families to the suburbs has left the major cities - the homes of the regional newspapers - with a generally lower income structure. This, plus the fact that the area chosen for the income data was just the immediate home city and not entire area in which the paper circulated, leads to the seemingly anomolous result. Table 3 Selecteii partial correlation coefficients.
logPl log s, 108 w
0.587 0.565 0.528
0.034 0.054 - 0.008
Table 4 Coetlicients and l&a&tics of explanatory variables not statistically significant.’ Equation set 1
Equation set 2
Variable
Coefkient
t
Coefficient
yJ
0.29 - 0.98
1.16 0.95
0.23
-0.13 0.49 -0.17 -0.24
0.50 1.13 0.98 1.00
-0.20 0.16 -0.17 -0.14
Yl NJ
Regional newspaper Home city of auothcr newspaper City outside bay area
1 0.96
n.e. 0.88 0.53 0.83 0.61
*Taken from equation with least number of explanatory variables that contained the specified variable. n.e. = not estimated.
When anti-logarithms of both sides of the regression equations are taken, the equations are transformed back into the usual gravity model formulation. The exact results for equations 1-5 and 2-5 are, respectively,
where
Al = 0.16 if morning paper (or day-long), = 0.33 if evening paper;
Y. M. Braunstein, A gravity model analysis
299
where A2
=
0.58 if morning paper,
= 0.07 if evening paper (or day-long). We have discussed the meaning of the exponents of the distance variable (p. 295). The significance of the exponents of the population variables will be explored in section 3. In section 4 we shall examine our estimates of the exponent of the wire services variable to see if they are consistent with the results of other researchers. 3. The asymmetry of the competition between suburban and metropolitan newspapers
The broadcast nature of mass communications results in the asymmetry of the exponents of the population variables. This contrasts with the interaction between the populations of two citres in the gravity models generally used in studies of transportation or of private communications. In these cases the population exponents are equal because the model had been designed to apply to cases that Aibit ‘round-trip’ or ‘two-way’ properties and therefore a symmetry between origin and destination. The asymmetry in mass communications will be shown to be manifest in both. the circulation patterns and the advertising sales and rates. Using the Quandt and Baumol (1966) study of travel between pairs of California cities, we find that there is no statistically significant difference between the calculated exponents of the variables representing the populations at the origin and the destination (see table 5). In other words, the number of trips by air from San Francisco to Los Angeles, for example, is approximately equal to the number of trips in the opposite direction between the two cities. Table 5 shows the exponents of the population variables Pi and Pj estimated by Quandt and Baumol for their seven regression equations. We wish to test the null hypothesis that the true values of the exponents of the populations at the origin and at the destination are equal. The t-statistics for each of the comparisons were calculated, and, in each case, were less than the value of the cumulative t-statistic at the 0.975 level with the appropriate (2~ - 2 = 94) degrees of freedom (I = 1.99). Therefore, the null hypothesis of equality of the exponents cannot be rejected at the 95 percent significance level. The study of telegraphic communications by Seneca and Cicchetti (1969) exhibits similar properties. They examined intra-state messages between cities within California and within New York. In four of their twelve equations, they explicitly assumed the exponents of the population variables to be equal. In two other equations, they estimated the exponents for the origin and destination
1.14
1.14 1.12
0.95
0.94 0.92
0.91 0.93
0.23 0.19
0.20 0.22
0.13
Difference
(4)
: Quandt and Eaumol(l966);
1.08
Expontnr of P,
Regression equation
‘Sources: Columns 1,2,3,7,8
(3) Exponent OfP,
(2)
(1)
columns 4,5,6:
0.144 0.154
0.216 0.196
0.186
(5) Average s.e.
Average Income/P income
avail. of car at j
Y0 % empl. in white mfg.collar
Deposits/P
Irlcome/P
Income/P
(3) Other demographic variables
(7) Weights of population
calculated from columns 2 and 3 and respective f-statistics.
1.603 1.230
0.926 1.122
0.699
t
(6)
Table 5 ‘l’ests of equality of exponents of population variables - Quandt and Baumol study of travel demands.”
.
P
,$
f
”
ea s‘ P 3 S
Y.M. Braunstein, A gravity model analysis
301
popu1ation variables separately. (In the remaining six equations, eitner the populations were weighted differently or other demographic measures, such as number of business firms, were used, or both.) For these two, the l-statistics testing the null hypothesis of equality of the exponents were calculated as above. The results are shown in table 6. Again, the null hypothesis cannot be rejected in these two cases at the 95 percent significance level. In the case of mass communication, however, the interaction is asymetrical. Although there may be some audience feedback, it is of a different sort and is! transmitted by a different medium. This ‘unidirectional’ nature of the messages carried by the mass media manifests itself in the circulation data. For example, newspaper A in large city A generally sells many more copies in neighboring suburb B than suburban newspaper B sells in city A. To limit the effects of this asymmetry on the estimation of the gravity model for newspaper circulation it was necessary to use the requirement that there be sales of at least twenty-five copies for a particular newspaper in a given city for that paper-city pair to be included. From the results of the regression equations, the three cases that included the populations of the home cities of the newspapers in addition to the populations of the receiving cities as explanatory variables were analyzed in the same manner as the gravity models of Quandt and Baumol (1966) and Seneca and Cicchetti (1969). As shown in table 7, the exponents of the population variables were significantly different and the null hypothesis rejected in the two cases that also included as explanatory variables the number of wire services describing the newspapers. In the one equation that was the simple gravity model of the form C’ij = A#‘Y~/D$ (equation 1-3) without any other explanatory variables, the hypothesis of equality of the exponents b, and b2 could not be rejected statistically. But even this case supports the view that mass communications do not possess the symmetry with respect to the origin and the destination that is exhibited by the travel and private communications studies. The only regression equations that are strictly comparable to the newspaper regressions are Quandt and Baumol’s regression equations 5, 6, and 7. In these regressions, the populations are unweighted, and the only other explanatory variables describe the mode or the medium or arc: averages of characteristics of the origin and the destination. Quandt and Baumol (1966, p. 25) believe that their regression equation 7 is the most plausible of the forms of the relationships they tested: Regression 7 from which the bank deposit, percent white collar, percent manufacturing and car availability variables were omitted seems best not only on the grounds that it yields the smallest unexplained residual (although not the highest F-value) but also on the grounds that the coefficients Of Pi and Pi are the same, which is what we would expect on a priori grounds.
0.4939
0.4049
1
2 0.0208
0.0182
Table 7
- 0.423
0.810
I
Income/P
IncomefP
Weights of population
calculated from columns 2 and 3 and
Average s.e.
Seneca and Cicchetti (1969), columns 4,5,6:
-0.0088
0.0147
Difference
0.68 0.45 0.38
l-3 l-4 l-5 0.04 0.28 0.33
Difference
OfP,
0.72 0.73 0.71
(4)
( .q Exponent
0.066 0.088 0.088
rs) A VXl-&G s.e.
0.066 3.182b 3.771b
t
(6)
variables Distance Distance, no. of wire services Distance, no. of wire services, time of publ.
Other explanatory
(7)
aSollrces: Columns 1,2, 3,7: table 1, supra, colums 4,5, 6: calculated from cohunns 2 and 3 and respective I-stat&i% bSignificant at 99 percent level.
(2) Exponent of P,
(1) Regression equation
Tests of equality of exponents of population variables - 1970 newspaper circulation regressions.*
aSources: Columns 1,2,3,7: respective t-statistics.
0.4792
OfP,
0.4137
Exponent OfP,
Exponent
Regression equation
_
Table 6 Tests of equality of exponents of population variables - Seneca and Cicchetti study of telegraphic communicatioils.’
8 g k’
1 Iz jl a b f3 “s’ k 3 $ b
$ T
.____-_ _--..-T__T_ - --~--
vantage if there are a [lowing quotation of But in our equation Z-3, this equality or’ the estimated &rates this point. See obtain simply because of the lack of symmetry between the o of mass communications, Lvea higher cost to the This asymmetry in the circulation patterns between tlte than metropolitan metropolitan newspapers is widely recognized in the n cost could be a signiindustry. It is matched by a similar asymmetry in the neting with the metromarket. Generally the metropolitan newspaper has a highapartment stores which advertising, but, because of its larger circulation, the metro1 a lower price per reader. This is often quoted in terms oft and compare it to the cost of one line of advertising reaching one million readers. (basic per line prices), circulations, and milline rates for SC’ ~~~~~~r~~~~?$y papers are shown in table 8. Ither’s home area. The the advertising linage Table 8 ,?~aiZy&uiew and the Comparisonof advertisingrates, San Francisco bay area nc Y. M. Braunstein, A gravity model analysis
Newspaper San Francisco Chronicle and Examiner Oakland Tribune San Mateo Times Hayward Daiiy Review
Ad rate $2.80 0.77 0.34 0.25
Circulation 682,899 209,449 44,758 35,802
*Sources: Ad rate - ENor and Publisher International Yearbook Audit Reports(1970). 303 The higher cost per reader for the advertiser in the sub place the suburban papers at a severe competitive disadl significant number of multi-outlet advertisers. The fol coefficients does not San Francisco Chronicle publisher Charles Theiriot illusrigin and destinations Tile Newspaper Preservation Act (1969, p. 345) : te suburban and the While it is generally true that suburban newspapers ha newspaper publishing advertiser per reader and thus a higher milline ra ewspaper advertising newspapers, I would assume that this discrepancy in r price for one line of cant factor when the suburban newspaper is compr Jolitan newspaper has politan newspaper for the retail advertising of large de he ‘milline rate’ - the are headquartered in the central city. The advertising rates To quantify this asymmetry in the advertising market everal bay area newsasymmetry in the circulation market, the circulations and were analyzed for one of the suburban newspapers and metropolitan daily, both in their home area and in the o data are the 1970 a.verage daily circulation figures and :wspapers, 1970.” from the week of October 22-28, 1973 for the Hayward Milline rate
4.10 3.68 7.60 K011
Y.M. Braunstein, A gravity model analysis
304
Oakland Tribune. The Tribune is the only one of the three large city newspaper firms in our sample publishing one newspaper per day - an evening paper. The Reuiew is also an evening newspaper. The circulation data are taken from the 1970 ABC Audit Reports; the adversiting data are from exhibits prepared by the Hayward Daily Review.4 In comparing tables 9, 10 and 11 one can see that the suburban newspaper (the Review) sells Iess than one and one-half percent of its daily circulation, or its Table 9 Competition between the Hayward Daily Review and the Oakland Tribune for circulation, 1970.”
Newspaper Ha-ward Dad’ Review Oakland Tribune
Circulation in Hayward area
Total circulation 35,802
Circulation in Oakland
27,080
209,449
‘Source: ARC Audit Reports (1970). Table 10 Competition between the Hayward DaiZy Reoiew and the Oakland Tdbune for classified advertising, week of October 22-28, 1972.”
Newspaper
Total lines
Lines r riginating from Hayward area
Lines originating from Oakland area
,Hayward Daily Review
125,802
123,802
Oakland Tribune
194,068
1694 (1.3O%I 122,918 (63.3 %)
*Classified ads were assigned to areas on basis of telephone nonmessage unit exchanges. Inc., et al. (1973).
Source: Defendants’exhibit EEE-4, Knutson et a!. versus Daily Review,
classified advertising linsge, in the neighboring larger city, while the metropolitan newspaper (the Tribune) selis approximately one-half as many subscriptions, or classified lines, in the neighboring suburb as it does in its home city. The data for retail advertising are not quite comparable, but nevertheless they exhibit the same pattern. The existence of mr ltiple outlet advertisers causes an accounting problem; in table 11, those advertisements coming from firms with outlets in ‘Defendants exhibits EEE2
Y.M. Braunstein, A gravity model emalysis
305
both Hayward and Oakland (or in Hayward and in any other city) are counted in the ‘accounts with Hayward outlets’ column. The phenomenon that we observe is competition that occur in layers -the suburban newspapers compete with each other only at the fringes of each paper’s circulation area and compete with the ‘satellite’ city newspapers throughout the suburban area. In turn, the satellite city papers compete with each other at the fringe and face competition from the major metropolitan/regional daily throughout their circulation area. It is interesting to note which of the suburban newspapers have significantly overlapping circulation areas; all reflect common ownership. The Hayward, Livermore, and Fremont-Newark newspapers in southern Alameda County are Table 11
Competitionbetween the Hayward Daily Review and the Oakland Tribune for retail advertising, week of October 22-28,1973.’
Newspaper
Total retail adv. inches
Adv. inches from accounts with Hayward outlets
Hayward Daily Review
13,221
Oakland Tribune
25,900
13,169 (99.6 %) 14,963
Balance of retail adv. inches
(57.8 “4
‘Retail advertising inches includes run-of-press retail advertising only; pre-printed inserts are excluded. Source: Defendants* exhibit EELL, Knutson et al. versus Daily Review, Inc., et al. (1973).
all owned and published by Floyd Sparks. The Hayward DaiZy Review is an evening paper; the Livermore Herald and the Fremont-Newark Argus are morning newspapers. Similarly, two of the overlapping newspapers between San Francisco and San Jose, the Redwood City Tribune and the Palo Alto Times have a common owner, Peninsula Newspapers, Inc. The remaining competition between two of the suburban newspapers for a heavily populated area is between the Berkeley Gazette and the Richmond Independent. These papers have recently announced plans to combine some of their operations. The concept that the normal gravity interaction is interrupted when reaching a larger city is similar to a hypothesis of Stouffer (1957) that the interaction is inversely proportional to the number of intervening opportunities as opposed to a measure of distance. It may be that our relationship should be partially reformulated in the following way: The interaction is inversely proportional to the distance between the home city of the newspaper and the location of the potential subscriber; if a locality with greater population than the home city of
306
X M. Bramstein, A gravity
modelamulyds
the newspaper intervenes, there is no further interaction from localities more distant in that direction.
with the newspaper
4, Comgarison with other studies of mass communications The estimated coefficienrs in a regression linear in logs are partial elasticities; i.e., each is an estimate of the percentage change in circulation due to a one percent change in that explanatory variable, ceteris paribus. Other researchers, using different samples, have independently obtained estimates of some of these elasticities. It would be interesting and useful at this point to see if the various results are consistent. For example, equations l-4,2-4, and 2-5 indicate that those newspapers that subscribe to a second wire service (a 100 percent increase) would find their circulation increased by approximately 40 to 50 percent if nothing else were to change. While other factors certainly play some role, the two-wire service papers (Rerkeley, Hayward, Oakland, Palo Alto, Richmond, and San Rafael) are generally of a higher qua!ity than those with one wire service (Antioch, Concord, Fremom-Newark, Livermore, and Redwood City) and our results are therefore consistent with those of Rosse in which quality had a significant positive explanatory power in the demand for subscriptions. The measure of quality used by Rosse was editorial cost per news inch published. He estimated the partial elasticity of circulation with respect to the quality measure to be approximately 0.01 [Rosse (1966, p. 55)]. It would probably be misleading to push this comparison further by attempting to convert the number of wire services into editorial cost per rrews inch for two reasons. Fist, the amount a wire service charges a given newspaper is negotiated, and second, Rosse’s (1966, p. 89) sample consisted of data from 59 Mid-Western newspapers, generally non-metropolitan in nature, during years from 1958 to 1964. Rosse (1966, p. 25) also obtained an estimate for the partial elasticity of circulation with respect to the number of households in an adjusted version of the Audit Bureau’s Retail Trade Zone for each newspaper. This elasticity was approximately 0.33 [Rcsse (1966, p. 55)]. Solving his reduced-form equations to allow for interaction between the advertising and circulation markets gives a partial elasticity of 1.31. Neither of these estimates are inconsistent with the estimates of from 0.71 to 0.82 that we obtained above. Again, there is the disparity of the samples, but more important, the elasticity after interaction of 1.31 in Rosse’s results is based on ceteris paribus considerations that would never obtain -- e.g., advertising rates generally increase as circulation increases as shown in table 8. The final comparison of our regression results is based on the lack of significance of the dummy variable used to dichotomize the sample into ‘day-long’ newspapers and newspapers with either a morning or an evening edition. We found that this dummy variable that would have segregated the two Ridder newspapers in San Jose and the newspapers published under the joint operating
Y.M. Bramstein, A gravity modelmdysir
307
agreement in San Francisco from the other newspapers was not statistically signiiicant. This result from the circulation market data is entirely consistent with the results obtained by Owen (1970) in examining advertising market data. Owen (1970, p. 84) found that ‘agency firms [those operating under joint agreements] do not charge significantly different prices than monopoly firms [those with no other daily newspaper in their home city].’ His results were based upon 1969 data obtained from twenty-two agency firms, twenty-two monopoly firms, and twenty-four firms each publishing in a city with one other daily newspaper. 5. conclusions The following conclusions, therefore, can be drawn about the usefulness of the gravity model in analyzing the demand for mass communications media: (1) The gravity formulation is an appropriate one for daiiy newspapers; a gravity model that includes measures of abstract characterisfics provides additional inforrmation to the elementary models of %pf and others that showed sales simply proportional to population divided by distance. [Zipf (1948), Conant and Davis (1948)]. (2) The measures of certain partial elasticities of demand obtained from such a gravity model are not inconsistent with comparable elasticities obtained by other researchers using other methods. (3) The gravity formulation permits statistical tests of hypotheses. The results of such tests (i.e., the exponent of the distance variable equals minus one, the dummy segregating the ‘day-long’ newspapers from the others is not significant) agree with the results of different tests generated by others examining these questions. (4) Unlike the gravity models used in the analysis of transportation and of private communications, the gravity model in this study of mass communications has different coefficients for the two population variables. This is a result of the asymmetrical nature of mass communications. (5) The competition between a metropolitan daily newspaper and a suburban competitor exhibits similar properties on both the circuIation and the advertising markets, In each market, the sales of the metropolitan newspaper in a neighboring large suburb might be one-half or more of the sales in its home city, while the suburban newspaper sells no more than an amount equal to one or two percent of its home city sales in the adjoining large city. References Audit Bureau of Circulations, 1970, Audit Reports for San Fran&co bay area daily newspapers (Chicago, IL). Bagdikian, B.H., 1971, The information machines: Their impact on men and the media (Harper and Row, New York).
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Y.M. Braunstein, A gravity model analysis
Boland, J.P., 1948, On the number and sizes of radio stations in relation to the populations of their cities, Sociomeuy 11,ll l-l 16. Braunstein, Y.M., 1975, Dynamics of inter- and intra-media competition: Effects of technological and demographic change, unpublished Ph.D. dissertation (Stanford University, Stanford, CA). Conant, J.M. and A.Y. Davis, 1948,A measurement of the number and diversity of periodicals in 92 American cities, Sociometry 1,117-l 20. Dixon, W.J., ed., 1971, BMD Biomedical Computer Programs (University of California Press, Berkeley, CA). E,’ “qymsen,M.A., 1960, Multiple regression analysis, in: A. Ralston and H.S. Wilf, eds., Mathematical methods for digital computers (Wiley, New York). International Yearbook, Editor and Publisher, 1970. Knutson et al. versus Daily Review, Inc., et al., 1973,Case C-73-1354(CBR) (N.D. Cal). Lancaster, K.J., 1965, Change and innovation in the technology of consumption, Papers and Proceediny of the American Economic Association 86,14-23. Lancaster, K.J., 1966, A new approach to consumer theory, Journal of Political Economy 14, 132-157. Niedercorn, J.H. and B.V. Bechdolt, Jr., 1969, An economic derivation of the ‘gravity law’ of spatial interaction, Journal of Regional Science 9,273. Niedercom, J.H. and B.V. Bechdolt, Jr., 1971,A further reply and a reformulation, Journal of Regional Science 12,127. Niedercom, J.H. and B.V. Bechdolt, Jr., 1970, Reply, Journal of Regional Science 10,407-410. Owen, I?., 1970,Price effects of mergers, Memorandum No. 96, Workshop in the economics of the press, Research Center in Economic Growth mimeo. (Stanford University, Stanford, CA). Quandt, R.E. and W.J. Baumol, 1966,The demand for abstract transportation modes: Theory and measurement, Journal of Regional Science 6,13-26. Rivers, W.K..end D.M. Rubin, 1971, A region’s press: Anatomy of newspapers in the San Fran&cc bay area (Institute of Government Studies, University of California, Berkeley, CA). Rosse, J.N., 1966, Daily newspapers, monopolistic competition and economies of scale, unpublished Ph.D. dissertation (University of Minnesota, Minneapolis, MN). Rosse, J.N., 1967, Daily newspapers, monopolistic competition and economies of scale, American Economic Review 57,522-533. Seneca, J.J. and C.J. Cicchetti, 1969,A gravity model analysis of the demand for public communication, Journal of Regional kience 9,459-78. Stouffer, S.A., 1957, Intervening opportunities: A theory relating mobility and distance, American Sociological Review 25,269280. The& H., 1957, Specification errors and the estimation of economic relationships, Review of the International Statistical Institute 25,41-S 1c United States Bureau of the Census, 1970,Census of Population. United States Senate, Committee on the Judiciary, 1969, The Newspaper Preservation Act, Hearings before the Subcommittee on Antitrust and Monopoly -9lst Congress, 1st Session, June 12,13, and 20. zipf, G.K., 1948,On the number ,circulation, sizes, and the probable purchasers of newspapers, American Journal of Psychology 61,83-92.