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Media substitution and economies of scale in advertising Barry J. Seldon a , *, R. Todd Jewell b , Daniel M. O’Brien a a

School of Social Sciences, University of Texas at Dallas, Richardson, TX 75083 -0688, USA b Department of Economics, University of North Texas, Denton, TX 76203 -3677, USA

Received 1 January 1998; received in revised form 1 December 1998; accepted 1 March 1999

Abstract Two important issues in the economics of advertising are media substitutability in generating sales and scale economies in advertising. If media are substitutes then partial bans, e.g., broadcast bans on cigarettes or alcoholic beverages, may be ineffective; and mergers among radio and TV firms, currently widespread in the U.S. and Mexico, are unlikely to result in market power in setting advertising rates. If there are scale diseconomies in advertising, concerns that advertising increases entry barriers may be unfounded. Using U.S. beer firm data over 1983:Q1–1993:Q4 for three media categories, we find evidence of high substitutability and diseconomies of scale. 2000 Elsevier Science B.V. All rights reserved. Keywords: Advertising; Economies of scale; Media substitution; Advertising bans; Beer JEL classification: L13; M37; D21

1. Introduction Two significant issues in the economics of advertising involve the substitutability of advertising media and the existence of scale economies in advertising.1 These * Corresponding author. Tel: 11-972-883-2043; fax: 11-972-883-2735. E-mail address: [email protected] (B.J. Seldon). 1 We are using the terminology ‘scale economies in advertising’ in the usual, but admittedly imprecise, way. As Waterson (1984, p. 134 and the associated footnote 8 on p. 219) states, ‘This is a very common terminology but is obviously slightly inaccurate; what we really mean is a range of output over which there are increasing returns to advertising expenditures.’ We discuss the concept further below. 0167-7187 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0167-7187( 99 )00010-7

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issues are important in understanding both firm behavior and the relative impact of the various advertising media. In addition, they are relevant to three separate public policy debates: the effectiveness of partial advertising bans; the effects of the current merger wave among radio and television firms; and the anticompetitive effects of advertising. In this paper, we explore these issues using a translog cost model which estimates the cost of advertising in various media in order to sell particular quantities of a good. We use quarterly data for U.S. beer firms over 1983 to 1993 and separate advertising into three media categories: print, television, and radio. While we analyze a particular market, our qualitative results may apply to many other markets. The beer industry is representative of industries which produce alcohol beverages; and the consumption of these beverages is central to current policy debates. Various public policies have been designed to reduce the negative effects of alcohol use, which include cirrhosis of the liver, drunk-driving fatalities, and alcohol-related crime. Policies such as alcohol taxation, minimum drinking age laws, and alcohol availability restrictions are designed to decrease the consumption of alcohol by increasing its price or by limiting access to alcohol beverages (Grossman et al., 1993; Wagenaar, 1993; Jewell and Brown, 1995). Another tack pursued to lower the consumption of alcohol involves advertising. For some time, public policies have been proposed which would either ban beer and wine advertising in the broadcast media (similar to the ban on cigarette advertising, see, e.g., Fritschler, 1989) or restrict alcohol advertising in all media, because many people believe that advertising increases market demand.2 Recent events reignited the alcohol advertising controversy in the U.S. In May 1996, Representative Joseph Kennedy II introduced legislation addressing the advertising of alcohol beverages. His proposal would require health warnings, eliminate tax deductions for advertising, limit print advertising to black and white text in many publications, and restrict most TV advertising to the hours between 10:00 p.m. and 7:00 a.m. A month later, despite this attack on alcohol advertising, Seagram initiated TV advertising in Texas. This broke with the tradition among

2 This contrasts with the alcohol industries’ claim that advertising merely redistributes market share and has no effect on total alcohol consumption. The connection between alcohol consumption and advertising has been investigated, but the results of these studies are mixed (for literature reviews, see Saffer, 1993; Smart, 1988). Smart (1988) reported that earlier studies found little effect of advertising on alcohol consumption and that advertising bans have little effect on alcohol sales. But the controversy continued in later publications. Saffer (1991) concluded that banning alcohol advertising would reduce consumption. Young (1993), however, reexamined Saffer’s data and found that advertising bans may in fact lead to increased alcohol consumption. On the other hand, Tremblay and Tremblay (1995) found that a beer firm’s advertising increases the firms’s inverse demand function and that there are positive spill-overs from rivals’ advertising. Because this is true for all beer firms, these results imply that advertising increases the market demand for beer; which in turn suggests that bans could reduce consumption. Lee and Tremblay (1992) suggested that, while advertising bans may reduce consumption, tax increases could be more effective.

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liquor producers of avoiding radio (and, later, TV) advertising since 1936, a tradition formalized in 1948 by the Distilled Spirits Council’s (DSC’s) ‘Code of Good Practice.’ Representative Kennedy responded by introducing another bill to ban liquor ads on TV and radio (Beatty, 1996a,b,c). Despite this attack, the DSC voted unanimously to follow Seagram in overturning the voluntary ban on TV and radio advertising (Beatty, 1996e). This provoked President Clinton to urge the Federal Communications Commission (FCC) to ban liquor advertising on TV (Associated Press, 1996). The Federal Trade Commission (FTC) acted first by opening an investigation of alcohol beverage advertising (including beer), while the FCC contemplated, but to date has not undertaken, a parallel investigation (Ingersoll, 1996). Instead, the FCC suggests that broadcasters refuse liquor ads (Pope, 1997). Most recently, the FTC forced two TV commercials, for Beck’s beer and premixed Kahlua White Russian cocktails, off the air (Beatty, 1998). However, the effectiveness of bans on TV and radio advertising remains an open question. It depends not only upon whether such bans reduce market consumption (as suggested for alcohol by Saffer (1991), and implied by the results of Tremblay and Tremblay (1995, 1997)), but also upon whether other media are close substitutes for broadcast advertising. If they are close substitutes, the partial ban on advertising proposed by Representative Kennedy and President Clinton may not be effective. In this paper, we consider the substitutability of advertising media by beer firms. While the results are important to a consideration of partial advertising bans on beer, they may also be suggestive for advertising bans on liquor, tobacco, or other products. If media are substitutable in the beer industry, we might expect media substitutability in other markets. There is yet another aspect of media substitutability that is important for public policy. With recent mergers among entertainment corporations, especially since the passage of the Telecommunications Act of 1996, concerns have been raised that market power might accrue to the owners of newly-merged television or radio stations that sell advertising spots (Beatty, 1996d). This, in fact, is the subject of ongoing research at the U.S. Department of Justice and the Mexican Federal ´ Federal de Competencia) and is an implicaCompetition Commission (Comision tion of recent research concerning substitutability at the FCC. If media substitutability is similar across markets, the results of this study will suggest whether concerns about market power are well grounded or if competitive pricing for advertising outlets are ensured by easy substitution into other media.3 While we use U.S. data in this study, the results may be generalizable to other countries.

3

Research at the FCC and the Mexican CFC has been discussed with one of the authors of this study in personal communications with economists at both Commissions. However, the current study is independent of their efforts and is more encompassing. For instance, FCC research considered substitutability between different types of TV advertising only (McCullough and Waldron, 1998).

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To address these issues, we apply the little-used, but appropriate, Berndt and Savin (1975) autocorrelation correction to a translog cost function. We explore media substitution by estimating Morishima elasticities, which Blackorby and Russell (1989) demonstrated to be preferable to the more conventional Allen elasticities. We uncover evidence suggesting that there are diseconomies of scale in advertising. In addition, we find the various media to be substitutable.

2. Media substitutability, advertising economies, and public policy We will estimate advertising economies of scale and substitution elasticities among advertising media using an advertising cost function, which is the (minimum) total cost of advertising when the firm uses several media to generate a particular level of sales. Assuming separability of the production function, which relates levels of production inputs to the level of output, and the advertising function, which relates the number of advertising messages in various media to the level of sales, we can employ Brown’s (1978) definition of scale economies in advertising (which is consistent with Waterson, 1984) as ‘a greater than proportional increase in quantity sold per given increase in units of advertising.’ This definition is common in the advertising literature, so our results will be conceptually comparable to previous results. Our substitution elasticities will indicate how media can be substituted to maintain sales. While this paper differs from most previous studies, two articles explore these issues in manners comparable to ours. Bresnahan (1984) estimated advertising cost models for two cases: a cross-industry study of six consumer goods and a single-industry study of beer producers. While he separated advertising by media, Bresnahan was concerned with economies of scale in advertising and substitution between retail services and advertising media. He did not address substitution among the media. Seldon and Jung (1993) considered the markets for advertising in four categories of media (print, radio, TV, and outdoor), in effect summing across all products in the U.S. economy. They did not estimate economies of scale. They found the different media to be fairly good substitutes. However, because they summed advertising in each medium across industries and because all industries do not advertise in all media, their results should only be taken as suggestive, as they acknowledged. This study differs from these previous efforts in focus, modeling, and data. While Bresnahan estimated only share equations for the beer industry, we simultaneously estimate a cost function and share equations and focus upon substitution elasticities among the various media. We also consider economies of scale, but in a manner which differs from Bresnahan’s approach; we discuss this below. In addition, Bresnahan’s estimates used annual data from 1967 to 1981, while our study considers more recent quarterly data. Our study differs from Seldon and Jung in two respects. First, we concentrate on the firm level in one industry. This affords insight concerning the substitutability of media in the sales

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of a particular good. It also permits a discussion of policy issues related to advertising in that industry. Second we use quarterly, instead of annual, data.4 Our use of quarterly advertising data, which distinguishes our study from most previous studies of advertising, is more critical than one might think. The use of annual advertising data when advertising effects upon demand depreciates in a shorter period may result in a temporal aggregation bias which seriously distorts estimated coefficients (Bass and Leone, 1983; Leone, 1995). And there is strong evidence that a year is too long a period. Boyd and Seldon (1990), Thomas (1989), and Seldon and Doroodian (1989), who used annual data, suggest that advertising effects depreciate within a year; while Ashley et al. (1980) and Leone (1995), who examined shorter periods, suggest that advertising effects may depreciate within a quarter. In fact, Leone points to evidence that advertising effects for frequently purchased grocery products are largely depreciated within six weeks. Because beer is frequently purchased, we use quarterly, rather than annual, data. We investigate advertising in the beer industry over the quarters 1983:Q1– 1993:Q4. Advertising messages are divided into three media categories: those which are visual (print); those which are audio (radio); and those which are audiovisual (TV). The print media include magazines, newspapers, and outdoor advertising. We estimate a firm-level translog advertising cost function associated with a given level of sales, with media share equations as side conditions. The results will indicate a potential response by firms to a partial advertising ban in the beer market. The results also will suggest whether the mergers of TV and radio companies threaten the competitive pricing of advertising. In addition, the results will provide information on economies of scale in advertising. If there are economies of scale in advertising and if the maintenance of high levels of advertising by market incumbents is credible in the face of entry, advertising scale economies may raise barriers to entry because entrants would either have to incur a higher unit cost for generating sales or enter the market at a larger advertising scale.5 Under these conditions, policies that discourage advertis4 There are still other studies of the beer industry that estimate substitution elasticities from a cost function which does not separate production and advertising costs, and where advertising is not separated by media (e.g., Tremblay, 1987). Our approach is similar to Bresnahan (1984), who noted that if the production cost and advertising cost functions are separable (which is perfectly reasonable) then one may consider the advertising cost function in isolation. This model is developed and further justified below. 5 We address advertising economies of scale, but there are several means through which advertising could conceivably be anticompetitive, including an incumbent investing in long-lived advertising. However, as discussed previously, recent research found that advertising depreciates rapidly, so this is unlikely. Advertising may also have procompetitive effects, such as allowing an entrant to advertise before entering a market. As an example of this, Gallo entered the wine cooler market with advance advertising for Bartles and Jaymes. For discussions of possible anticompetitive and procompetitive effects of advertising see Albion and Farris (1981), Ekelund and Saurman (1988), Hay and Morris (1991, pp. 142–148), Krouse (1990, pp. 498–501), McAuliffe (1987), Scherer and Ross (1990, pp. 406–407), Sutton (1991), and Waterson (1984, pp. 134–136 and 201–204).

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ing may encourage lower prices due to the threat of entry if higher prices are maintained. In addition, previous research (see, e.g., Eckard, 1991) suggests that, if advertising is persuasive rather than informative, higher levels of advertising are associated with lower levels of price competition. Thus, in markets with persuasive advertising, policies that discourage advertising may further encourage price competition.

3. The cost function We employ duality techniques most often applied to the production of goods and services. We assume that the firm produces and sells beer using different inputs for production than for advertising. A production function relates the levels of inputs to the level of output, while our advertising function relates advertising messages to sales. Advertising enables sales for at least one of two reasons. First, advertising informs consumers that the good, a brand of beer in our case, exists. Second, advertising may serve in a persuasive capacity, encouraging the consumer to try the brand. Because different inputs are used for production and advertising, the cost function for production and advertising is separable in the sense that we can specify a production cum advertising cost function # (W, P; Q) 5 G(W; Q) 1 C(P; Q) where W is a vector of prices of production inputs, P is a vector of prices of advertising messages in various media, G is the production cost function given that the firm wishes to produce Q units, and C is the advertising cost function given that the firm wishes to sell Q units. This allows us to concentrate on the firm’s advertising cost function, C(P; Q), which gives the cost of advertising required to sell Q units. An alternative reason for separating the advertising cost function from the production cost function was suggested by Seldon and Jung (1993). Production occurs prior to advertising in the sense that firms may plan their production and advertising simultaneously; however, once production has occurred, firms are free to reconsider advertising plans made during production. For instance, if inventories were accumulating unexpectedly, firms could increase the number of advertisements (e.g., by renting more billboard space) relative to anticipated levels.6 The prices of advertising messages in the P vector are exogenous to the model. These prices are assumed to be fixed by the markets for advertising messages, and beer advertising is a small fraction of all advertising in every medium. As Bresnahan (1984, pp. 139–140) pointed out, when we consider the costs of production and advertising as being separable, it makes sense to discuss economies

6

In this case, the quantity that the firm wishes to sell can be treated as a predetermined variable in the econometric estimation. We test this assumption below.

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of scale in advertising. That is, we can consider what happens to sales when we increase all advertising in the various media proportionately, as in Brown (1978), and not be concerned with simultaneously increasing all production inputs by the same proportion.7 The advertising cost minimization problem may be stated as: min C 5 AP such that Q 5 C (A) A

where C is the total cost of advertising, A is a row vector of advertising messages in various media, P is a column vector of the prices of messages in the media, and Q is the output that firms wish to sell.8 C (A) is a quasiconcave twice differentiable advertising function that relates the quantity that the firm wishes to sell to the number of advertising messages used in each medium. The minimization problem results in the firm’s cost function C 5 C(P; Q). We employ a flexible functional form, the translog model 9 ln Cf,t

5

a0 1 fq (ln Q f,t ) 1 (1 / 2)fqq (ln Q f,t )2

O a (ln P ) 1 (1 / 2) O O b (ln P )(ln P ) 1O g (ln Q )(ln P ) 1 u 1

i

i,t

ij

i

i

qi

f,t

i,t

j

i,t

j,t

(1)

f,c,t

i

where Pi,t is the price of advertising messages for medium i, j 5 p, v, r ( p5print, v5television, and r5radio); f is the firm index; t is the time index; and uf,c,t is an error term. By the symmetry of second-order coefficients, bij 5 bji By the form of Eq. (1) we assume, as did Caves et al. (1981), that parameters

7

This, of course, is a reversal of the usual economies of scale study which (1) ignores advertising and (2) considers what happens to output when all production inputs increase proportionately. For instance, Elzinga (1995, pp. 129–131) implicitly ignores advertising costs in his discussion of economies of scale in beer production while later in the article he discusses the marketing of beer. Even Sutton (1991), who considers advertising in great detail throughout much of the book, discusses economies of scale in production (in Appendix 13, entitled ‘Scale Economies in Brewing’) as separate from advertising. When Sutton considers the ‘rising trend in concentration’ in recent years in the U.S. market, he notes (p. 299) that ‘it can . . . be argued that the initial impetus [was] the changing degree of scale economies [in production] in the industry,’ but also that ’a central role . . . was played by the . . . escalation of advertising outlays.’ Still, Sutton does not directly address economies of scale in advertising, as we do in this paper. 8 The advertising function might be written more completely as C (A, A Q ) where A Q is the advertising of the firm’s rivals. We do not have data for all beer producers, so we are unable to construct A Q . As another alternative, we might write the function as C (A; 3 ) where 3 is a vector of prices of the goods being sold (or, alternatively, an average price for the firm’s products). We are unable to find firm-level price data. We explain how we treat this potential missing data problem below. A Hausman test supports our treatment. 9 Translog models are reviewed in Berndt (1991, pp. 469–487).

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are the same across firms. This is plausible in the case of advertising cost so long as all firms have access to the same advertising media, which they do, and so long as the inputs used to create the ads are hired in competitive markets, as they seem to be (Jung and Seldon, 1995). In fact, after obtaining the results reported below, we added firm dummy variables to the intercept of Eq. (1), as in Bresnahan (1984), but found little change in our results. The difference among firms seems to be reflected in size: a regression of ln Q f,t on firm dummies explained 95 percent of the variance.10 Therefore, the addition of firm dummies would induce multicollinearity. Moreover, if firms have access to the same media and create ads through competitive markets, including the dummies would cause the model to be misspecified. Taking the derivative of Eq. (1) with respect to ln Pi,t and applying Shephard’s Lemma yields the cost share equations for the media. They are:

O b (ln P ) 1 g (ln Q

Sf,i,t 5 ai 1

ij

j,t

qi

f,t

) 1 uf,i,t

(2)

j

for i, j 5 p, v, r where Sf,i,t 5 Pi,t A f,i,t /Cf,t ; A f,i,t is the number of messages in the ith medium; and uf,i,t is an error term. The cost function must be homogeneous of degree one in prices. This homogeneity condition requires the following restrictions:

O a 51 i

and

i

O b 5O b 5O g 5 0. ij

i

ij

j

(3)

qi

i

4. The data Our data cover the period 1983:Q1 through 1993:Q4, which contains 44 quarters. Monetary variables are deflated to 1982 dollars using the producer price index from the Economic Report of the President. The variables, their sources, and means and standard deviations for the different firms are presented in Table 1. Beer advertising data are from various issues of Competitive Media Reporting’s Ad $ Summary (Competitive Media Reporting, 1983–93). This publication reports

10

The estimated regression equation is ln Q f

5 1.24 (0.03)

1 1.71DA (0.04)

1 0.19DC (0.04)

2 1.50DG (0.07)

2 0.16DP (0.10)

1 0.31DS (0.05)

with R 2 5 0.95 where Dx is a dummy variable for firm x 5 A (Anheuser-Busch), C (Coors), G (Genessee), P (Pabst), and S (Strohs). The omitted firm is Heilman / Bond. Standard errors are in parentheses. In this regression, the intercept and four of five dummy variables are significant at better than the 1 percent level. The dummy for Pabst is significant at the 10 percent level.

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Table 1 The variables, their sources, and descriptive statistics Quarterly advertising expenditures and sales Variable, source, units

Firm

Mean

Standard deviation

Total advertising expenditures

Anheuser-Busch Coors Genessee Heilman / Bond Pabst Strohs Anheuser-Busch Coors Genessee Heilman / Bond Pabst Strohs Anheuser-Busch Coors Genessee Heilman / Bond Pabst Strohs Anheuser-Busch Coors Genessee Heilman / Bond Pabst Strohs Anheuser-Busch Coors Genessee Heilman / Bond Pabst Strohs

69 852.32 20 429.18 1312.63 4511.23 3550.59 9477.01 61 209.88 18 827.22 1192.96 3636.20 3355.34 8515.26 5402.70 1240.14 119.67 662.46 195.25 666.89 3239.73 361.81 0.00 213.11 0.00 294.86 19.34 4.22 0.77 3.53 2.95 4.85

14 396.35 7087.35 461.77 2851.42 1655.53 6123.33 12 401.69 6233.48 437.92 2645.00 1637.86 5978. 70 2046. 96 884. 50 72.25 574.54 111.21 601.03 2959.84 949.28 0.00 682.65 0.00 558.87 2.77 0.69 0.09 0.76 0.37 1.19

Price indexes Source and units

Medium

Mean

Standard deviation

Source: McCann-Erickson, Inc. Units: 1982-based Index

Television Print Radio

1.207 1.195 1.107

0.104 0.091 0.067

Source: Ad $ Summary Units: 1000s, 1982 dollars Advertising expenditures Television Source: Ad $ Summary Units: 1000s, 1982 dollars Advertising expenditures Print Source: Ad $ Summary Units: 1000s, 1982 dollars Advertising expenditures Radio Source: Ad $ Summary Units: 1000s, 1982 dollars Beer sales Source: Beverage Industry Units: millions of barrels

nominal advertising expenditures in the various media for the 1000 largest advertisers in the U.S. Thus, the beer firms in our data set are companies that sell national or large regional brands; namely Anheuser Busch, Coors, Genessee,

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Heilman / Bond, Pabst, and Strohs.11,12 In some quarters, data for some firms are not reported because their quarterly advertising expenditures fell sufficiently so they were not among the 1000 largest advertisers. Nevertheless, we collected 195 observations. Deflating advertising expenditures in the various media to 1982 dollars, we obtain Pi,t A f,i,t of Eq. (2). The Ad $ Summary also reports firms’ total advertising expenditures across media. Deflating these figures yields Cf,t of Eq. (1). In a few cases, the sum of a firm’s media expenditures does not equal a firm’s reported total expenditures. In these cases, we replace the reported total with the sums of the reported media expenditures because the reported total expenditures seemed to be out of line with the time series for the particular firms. McCann-Erickson, a New York City advertising agency, provided cost indexes for advertising messages, which we employ for prices (Pi,t ).13 We use their cost-per-thousand media indexes, which represent the media advertising cost for reaching a thousand-person audience. The cost indexes are based on 1982 prices and are constructed by dividing the total cost of advertising in the various media by the number of people (in thousands) exposed to the advertising. Hence, advertising messages are conceptually measured in units which reach 1000 people. From the less aggregated McCann-Erickson cost indexes, we calculate Divisia indexes for the costs of messages in print, television, and radio using the ratio of expenditures in particular media (summed across the firms) to aggregated advertising expenditures (summed across firms and media) as weights. Thus, all firms face the same prices for advertising in a given medium. For example, we calculate a cost index for print media from data for magazines, newspapers, and outdoor advertising. This captures all print media in which beer firms advertise.14 While an element in any of these index series is the nominal cost-per-thousand in year t divided by the nominal cost in 1982, the indexes still increase with inflation. To make these data compatible with the other monetary data, we deflate the indexes by the 1982-based producer price index. The resulting advertising price indexes for the different media are annual series. We create a quarterly series for each medium using cubic spline functions (Greene, 1993). This method joins cubic polynomials together to form a continuous time series with continuous first

11 The Beverage Producers Association reports that the firms in this list accounted for 73.6 percent of domestic beer sales in the U.S. in 1993. We exclude Miller, a subsidiary of Philip Morris, because we are unable to isolate beer advertising expenditures. We exclude imported beer because a reliable time series for sales is not available for the entire 11-year period. 12 Because our sample includes only large beer producers, our results may not be accurate for smaller firms. Data for smaller firms are not available. 13 McCann-Erickson Inc. supplies the advertising data that are published annually in the Statistical Abstract of the United States. The price data are available from the authors upon request. 14 Beer is not advertised through direct mail, a medium used for many other goods and services.

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and second derivatives. The method assures that the average of the created quarterly data in each year equals the observed price index for that year.15 To estimate the cost function, we need firm-level sales data (Q f,t ). Data for the quantity of beer (millions of barrels) sold by each firm in each year are available from various issues of Beverage Industry. These quantities are annual data and must be converted to quarterly data. Because advertising expenditures exhibit seasonality, we convert the sales data in a manner which preserves the seasonality of sales. The Beer Institute (1994) records total U.S. beer sales on a monthly basis over the years of our sample. We convert this series to a quarterly series by adding sales for each month of each quarter and then determine the percentage of annual sales (in 1982 dollars) for each quarter for every year of our sample. We then apply these seasonal percentages to the various firms’ annual sales to compute a quarterly sales series for each firm.

5. The econometric model To simplify notation, we hereafter drop the firm index f. We estimate Eqs. (1) and (2) subject to conditions (3) using Zellner’s iterated seemingly unrelated regressions (ITSUR). To avoid singularity of the covariance matrix, one share equation must be omitted. ITSUR produces coefficient estimates which are invariant with respect to the omitted equation (Zellner, 1962, 1963). We omit the radio advertising share equation, but we recover the parameters of this equation using restrictions given by Eqs. (3). We also estimate additional sets of equations to test certain restrictions on the cost function. These tests will suggest the appropriate functional form of the regression equations to use in further analysis. One restriction (gqi 5 0 for i 5 p, v, r) forces the advertising function C (A) to be homothetic, implying that the advertising cost function is separable in output and prices (Christensen and Greene, 1976). If this condition holds, we could write the cost function as C 5 C1 (Q)C2 (P). A second restriction forces the advertising function to be homogeneous. The homogeneity restriction is that gqi 5 0 (as before, since any homogeneous function is homothetic) and gqq 5 0, so that the elasticity of cost with respect to output is constant. If the advertising function is homogeneous and fq 5 1, there are constant returns to scale in advertising. Because advertising effects depreciate rapidly, probably within months, we assume that any effects of previous quarters’ advertising upon present sales are small enough to disregard. Thus, if any effect of past advertising actually exists, it

15

The software used to produce the quarterly series is the EXPAND procedure of SAS Version 6. For a more complete explanation, see SAS Institute (1988, pp. 261–277).

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is suppressed into the error terms of the model.16 This would create patterns in the time series of the error terms and can be treated, and corrected for, as autocorrelation using the method of Berndt and Savin (1975).17 Care must be taken when correcting for autocorrelation in the share equations. First, the lagged error term associated with one equation may affect other equations (see, e.g., Berndt, 1991, pp. 476–479). Second, we must ensure that the shares sum to one. Write the system of share equations as S t 5 G X t 1 U t ; t 5 2, 3 . . . , 44 where S t is the three-element matrix of media shares (including the share which will be excluded in the econometric estimation), G is the matrix of parameters of the system suggested by Eq. (2), X t is the vector of predetermined variables, and U t is the vector of error terms associated with the share equations. Now, in addition to ensuring homogeneity of the cost function, conditions (3) ensures that i G Xt 5 1, where i 5 (1 1 1). Therefore, in order to obtain the adding-up condition, all that remains is to ensure that u r,t 5 2 u p,t 2 u v,t . Let ri, j be the autocorrelation coefficient associated with the lagged error term of the share equation of the jth advertising medium as it affects the ith share equation. Following Berndt and Savin (1975), we specify our three-element vector U t as: u p,t rp, p 2 rp,r rp,v 2 rp,r u v,t 5 rv, p 2 rv,r rv,v 2 rv,r u r,t rr, p 2 rr,r rr,v 2 rr,r

343

np,t u p,t21 n u v,t 21 1 v,t nr,t

4F

G

34

where ni,t for i 5 p, v, r are well-behaved error terms. This may be done because, in order to assure that shares sum to one, each column of the original undifferenced autocorrelation matrix with element ri, j (where i, j 5 p, v, r) must sum to the same, but unknown, constant number. We cannot solve for ri, j , but there is no need to do so. The above discussion does not take into consideration the system of equations which includes the cost function, but the extension is straightforward. As Berndt and Savin (1975, p. 955) pointed out, the restrictions discussed above apply only to autocorrelation terms associated with share equations. When we include the cost function, each of the share equations includes the lagged error of the cost function, and the cost function includes lagged errors for the share equations taking into

16 Because of missing quarterly observations as discussed in the data section, any attempt to incorporate lagged advertising would reduce our sample size considerably. 17 Similarly, if the advertising function were more properly specified as in footnote 8, the effects of any missing variables will also be relegated to the error terms, requiring us to treat the error terms for autocorrelation.

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consideration the adding-up constraint. The error terms that are used in the econometric estimation are, then, u c,t 5 rc,c u c,t 21 1 ( rc, p 2 rc,r )u p,t 21 1 ( rc,v 2 rc,r )u v,t 21 1 nc,t

(4)

u p,t 5 rp,c u c,t 21 1 ( rp, p 2 rp,r )u p,t 21 1 ( rp,v 2 rp,r )u v,t 21 1 np,t

(5)

u v,t 5 rv,c u c,t21 1 ( rv, p 2 rv,r )u p,t 21 1 ( rv, p 2 rv,v )u v,t 21 1 nv,t

(6)

and

where the terms for the r -differences (viz., ri, j 2 ri,k ; i, j, k 5 c, p, v, r) are estimated as one parameter because we are not interested in, and cannot estimate, these r s individually. Eqs. (4), (5), and (6) are substituted directly into the cost Eq. (1) and the share Eqs. (2), and the system is estimated using nonlinear iterated seemingly unrelated regressions (NLITSUR). This nonlinear method allows us to estimate the model parameters (a s, b s, g s, and f s) and the autocorrelation parameters ( ri,c , i 5 c, p, v; and the r -differences) simultaneously. This is because, in the place of the lagged error terms in Eqs. (4)–(6), we substitute the difference between the lagged dependent variable and the right-hand-side function with lagged independent variables. Thus, the lagged error term for a share equation is

F O b (ln P

u i,t 21 5 Si,t 21 2 ai 1

ij

j,t 21

) 1 gqi (ln Q t 21 )

j

G

for i, j 5 p, v, r. The lagged error of the cost function is estimated similarly. This is superior to other methods, such as ITSUR combined with the iterated CochraneOrcutt autocorrelation correction, which can only approximate the more exact estimates we are able to obtain using NLITSUR. The autocorrelation coefficients are then subject to the same asymptotic t tests applied to the model parameters.18 Given the structure of Eqs. (4)–(6), we are able to use only observations for which lagged data are available. Thus, we lose some observations due to missing data for some firms for some quarters. Nevertheless, we retain a sample size of 177.

6. Estimation of the cost and share functions The results of the NLITSUR estimations for the system of equations with

18

Because the inclusion of a lagged error term necessitates inclusion of the lagged endogenous variable, it might seem that we could distinguish between short- and long-run elasticities as in partial adjustment models. However, the inclusion of a lagged error term does not impart any dynamics to the economic model. See Seldon and Bullard (1992) for clarification.

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autocorrelation (obtained by substituting Eqs. (4)–(6) into the cost and share equations given by (1) and (2)), and the systems of equations for the autocorrelated homothetic, homogeneous, and constant returns to scale (constant RTS) models are presented in Table 2.19 The significance of the majority of the autocorrelation coefficients indicate that our use of the Berndt-Savin correction is appropriate. All of the separate r s (v iz. rc,c , rp,c , and rv,c ) fall within the interval (21, 1), as we would expect, and the differenced r terms are plausible. For example, the estimates for ( rc,v 2 rc,r ), which are greater than one, could occur if rc,v were in the interval (0, 1) and rc,r were negative and of sufficient magnitude within the interval (21, 0). Before further considering the results reported in Table 2, we test the propriety of treating the quantity Q as exogenous rather than endogenous using a J test (Davidson and MacKinnon, 1981, 1993) applied to the general cost function. Denote our cost equation as ln Ct 5 g(X g,t , b ) 1 eg,t where the exogenous quantities are included with the other right-hand-side variables in the X g vector, the b vector includes the model and autocorrelation coefficients, and eg is an error term. This model yields the estimated cost function gˆ ; g(X g,t , bˆ g ). Denote an alternative cost function as ln Ct 5 h(X h,t , b ) 1 eh,t where the vector X h is the same as X g with the crucial exception that, in every instance, the exogenous quantity variable, ln Q, is replaced with an instrumental variable created by regressing ln Q on the other exogenous variables in the system as well as on firm dummies and real disposable income.20 This model yields the estimated cost function hˆ ; h(X h,t , bˆ h ). The J test then involves running the two regression equations ln Ct 5 (1 2 ah )g(X g,t , b ) 1 ah hˆ 1 egg,t and ln Ct 5 (1 2 ag )h(X h,t , b ) 1 ag gˆ 1 ehh,t separately. If ah is significant and ag is insignificant, then the model which uses the quantity instrument is the correct specification. Alternatively, if ah is insignificant while ag is significant, then the model which uses the exogenous

19 We used Newton’s method as the maximization procedure. The results reported in Table 2 appear to be the global maxima; when we initiated the coefficients at widely different values they converged to the same point. 20 A price variable for the final product is not included as a determinant of ln Q in this test under assumption that the product’s price is endogenous. However, we ran another J test where we included a market-level beer price index (firm-level prices are not available), and our results in that test were qualitatively the same as our results for the J test described below.

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Table 2 NLITSUR estimates of total cost and share function coefficients in the advertising cost model, 1983–1993 a Coefficients

a0 ap av ar bpp bpv bpr bvv bvr brr gqp gqv gqr fq fqq rc,c ( rc, p 2 rc,r ) ( rc,v 2 rc,r )

rp,c ( rp, p 2 rp,r ) ( rp,v 2 rp,r )

rv,c ( rv, p 2 r,r ) ( rv, p 2 rv,v )

General model 6.8361 d (1.5237) 0.1100 (0.2843)d 0.8540 (0.3302) 0.0361 (0.3690)c 20.2997 (0.1487) 20.1715 c (0.0748)d 0.4713 (0.1232)b 0.1984 (0.1417) 20.0269 (0.1481) 20.4443 d (0.1279)d 0.1337 (0.0294) 20.1417 d (0.0369) 0.0080 (0.0739)d 0.8549 (0.3046) 20.0945 (0.1341)d 0.6068 (0.0603) 20.5584 (0.5980)d 1.2217 (0.4944)d 20.0227 (0.0071)d 0.9111 (0.0670) 0.0472 (0.0590)d 0.0366 (0.0116)d 20.6826 (0.1234)d 0.2277 (0.0949)

Homothetic model 6.8776 d (0.2484)d 0.1240 (0.0206)d 0.8490 (0.0279) 0.0270 (0.1341) 20.0953 (0.1275) 20.1008 (0.0823)c 0.1961 (0.1078) 20.0582 (0.1334) 0.1590 (0.1477) 20.3551 d (0.1080) –

Homogeneous model 6.9518 d (0.2068)d 0.1236 (0.0206)d 0.8498 (0.0279)c 0.0266 (0.0145) 20.0888 (0.1268) 20.1009 (0.0821)c 0.1896 (0.1063) 20.0675 (0.1326)b 0.1684 (0.1068) 20.3580 d (0.1076) –

Constant RTS model 16.8747 d (5.4142) 20.6861 b (0.4537)d 2.1100 (0.6894) 20.4239 b (0.2656) 20.0492 (0.1220) 20.0993 (0.0809)b 0.1485 (0.1005) 20.0980 (0.1288)c 0.1973 (0.1048) 20.3457 d (0.1082) –

–

–

–

–

–

1.3704 d (0.2227) 20.0639 (0.1228)d 0.6144 (0.0612) 20.3951 (0.6511)c 1.0022 (0.4791)d 20.0299 (0.0073)d 0.7042 (0.0781)c 0.1154 (0.0578)d 0.0438 (0.0117)d 20.6086 (0.1269)c 0.1602 (0.0928)

– 1.2589 d (0.0735)

–

set equal to 1.0 –

0.6113 d (0.0611) 20.4066 (0.6518)c 1.0125 (0.4790)d 20.0307 (0.0073)d 0.7026 (0.0778)c 0.1184 (0.0576)d 0.0447 (0.0118)d 20.6081 (0.1266)c 0.1561 (0.0926)

0.7697 d (0.0523) 20.5792 (0.6953)d 1.4123 (0.4886)d 20.0394 (0.0063)d 0.6858 (0.0781)c 0.0967 (0.0557)d 0.0561 (0.0106)d 20.5979 (0.1275)c 0.1922 (0.0909)

Goodness of fit e 0.9984 0.9985 0.9985 0.9983 Degrees f of freedom 170.667 171.333 171.667 172.000 a Standard errors are in parentheses. The coefficient subscripts are p5print, v5television, r5radio, q5quantity to be sold, c5total cost. b Significant at the 10 percent level, one-tailed test. c Significant at the 5 percent level, one-tailed test. d Significant at the 1 percent level, one-tailed test. e The goodness-of-fit measure for the NLITSUR systems is McElroy’s (1977) R 2z . f Degrees of freedom are equal for all equations in each of the systems. Because parameters are shared across equations, degrees of freedom are allocated across equations and need not be integers. Typically, the degrees of freedom for the cost equations would be different from the degrees of freedom for the share equations; but in our case they happen to be equal.

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quantities is the correct specification.21 In our case, ah is estimated as 20.25 with a t ratio of 20.64 while ag is estimated as 1.04 with a t ratio of 12.07. Therefore, our treatment of quantities as exogenous is appropriate. We now return to the models of Table 2. We test the validity of the homothetic, homogeneous, and constant RTS models using the likelihood ratio statistic 2 2(ln l) 5 nhln[det(Vr ) / det(Vu )]j where det(Vr ) and det(Vu ) are determinants of the estimated n -error covariance matrices of the restricted and unrestricted systems. The null hypotheses (that the restrictions hold) are subject to a x 2 test because 2 2(ln l) | x 2 with degrees of freedom equal to the number of restrictions. The degrees of freedom for our tests of homotheticity, homogeneity, and constant RTS are 3, 1, and 1, with critical values of 7.815, 3.841, and 3.841 at the 5 percent significance levels. We calculate 2 2(ln l)55.491, 0.268, and 18.045 respectively. Therefore, the homothetic model is not rejected in favor of the general model, and the homogeneous model is not rejected in favor of the homothetic model. However, the constant RTS model is rejected in favor of the homogeneous model.22 These tests focus our attention on the homogeneous model. The model fits well: McElroy’s (1977) R 2z is 0.9985, and all but three model coefficients are significant at the 10 percent level or better. Further evidence of the performance of the homogeneous translog model is afforded by inspection of the fitted share equations. For every observation, the fitted shares fall in the interval (0, 1), as they should. In addition, the estimated cost function satisfies concavity with respect to advertising media prices for every observation.23 Finally, the fitted own-price elasticities of demand, developed below, are negative for every observation. All this lends support for the homogeneous translog model. As a final statistical test of the appropriateness of the homogeneous model we employ a Hausman (1978) specification test. Spencer and Berk (1981, p. 1079) point out that the Hausman test has a diffuse alternative hypothesis; it would reject the null hypothesis that the regression is correctly specified for a variety of reasons, including ‘omission of relevant explanatory variables, errors in variables, inappropriate aggregation over time, simultaneity, incorrect functional form.’ In the Hausman test, we compare our coefficients for the homogeneous model estimated using NLITSUR, as reported in Table 2, against coefficients of the same

21 It is also possible for both ah and ag to be either significant or insignificant; these possibilities are discussed in Davidson and MacKinnon (1981, 1993). 22 The hypothesis of constant RTS can also be tested directly from the homogeneous model. In that model, we estimate fq 5 1.2589. The t statistic for the null hypothesis that fq 2 1 5 0 is 3.52; so we reject the null hypothesis at the 1 percent significance level. 23 We checked concavity of the cost function with respect to advertising prices by calculating the three principal minors of the Hessian matrix characterized by the element ≠ 2 Ct / ≠Pj,t ≠Pk,t for each year. Concavity of the cost function requires that these principal minors alternate from non-positive to non-negative to non-positive.

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model estimated using nonlinear ordinary least squares (NLOLS). Under the null hypothesis of no misspecification, NLITSUR is consistent, asymptotically normal, and asymptotically efficient; while NLOLS will not be asymptotically efficient (Zellner, 1962, 1963; Zellner and Huang, 1962). Let bˆ I and bˆ O be the estimated column vectors from the NLITSUR and NLOLS regression systems, and let VˆI and VˆO be their covariance matrices. Then Hausman’s m statistic is m 5 ( bˆ I 2 bˆ O )9(VˆI 2 VˆO )21 ( bˆ I 2 bˆ O ) where m | x 2 with 16 degrees of freedom, the number of coefficients estimated directly in the system of equations. The null hypothesis that the model is correctly ˆ 5 15.6306 specified is not rejected if m is statistically insignificant. We calculate m which is insignificant at the 5 percent level (the critical value is 26.296) and even at the 10 percent level (with a critical value of 23.542). This supports the homogeneous model. Because of the fit and performance of the homogeneous translog model and because the model is supported by the Hausman test, calculations that follow will use coefficient estimates from this model.

7. Derivation of elasticities We are interested in substitutability among the advertising media. Uzawa (1962) showed that the Allen partial elasticities of substitution can be expressed as (see also Berndt and Wood, 1975)

s Aii 5 ( bii 1 S i2 2 Si ) /S i2 ; i 5 p, v, r

(7)

s Aij 5 ( bij 1 Si Sj ) /Si Sj ; i, j 5 p, v, r; i ± j

(8)

and

where (7) is the own-Allen and (8) is the cross-Allen elasticity. The Allen elasticities are symmetric, so s Aij 5 s Aji . An alternative asymmetrical measure of substitution originally developed by Morishima is related to the Allen elasticities (Blackorby and Russell, 1989).24 Let sM ij denote the Morishima elasticity. Then (Ball and Chambers, 1982)

24 Blackorby and Russell (1989) discussed why one should expect asymmetry in an elasticity of substitution. The elasticity of substitution measures the curvature along an isoquant when the ratio Pi /Pj varies due to a change in Pi . The direction of change is different when the ratio Pi /Pj varies due to a change in Pj , so we would expect the curvature to be different. Blackorby and Russell pointed out that the Morishima elasticities will be symmetric only in the case of CES production functions.

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A A sM i, j 5 p, v, r. ij 5 Sj (s ij 2 s jj );

(9)

If i 5 j then the Morishima elasticity is zero. Only off-diagonal elements in a Morishima matrix may be non-zero. The Allen elasticities also can be used to calculate the own- and cross-price elasticities (eii and eij ) of the derived demand for inputs (Berndt and Wood, 1975) because

eij 5 Sj s Aij ;

i 5 p, v, r.

(10)

Like the Morishima elasticities, the price elasticities are asymmetric because Si ± Sj in general. Chambers (1988, p. 95) argued that the Allen elasticity yields no information beyond that given by the cross-price elasticity of demand because the Allen elasticity is merely the cross-price elasticity divided by the factor share of cost. Blackorby and Russell (1989) argued even more strongly that the Allen elasticity is uninformative. In contrast, they demonstrated that the Morishima elasticity is a meaningful and informative measure of substitutability. We agree with Blackorby and Russell. Although we use Allen elasticities to calculate Morishima and price elasticities, we do not report Allen elasticities in this paper. We do, however, offer them to the reader upon request. We measure scale economies along the expansion path as suggested by Hanoch (1975). To calculate the scale elasticity, hS , we first calculate the cost elasticity, hC . The cost elasticity for the homogeneous model is simply 25

hC 5 ≠(ln C) / ≠(ln Q) 5 fq .

(11)

We define the scale elasticity as the inverse of (11), so

hS 5 ≠(ln Q) / ≠(ln C) 5 (hC )21

(12)

With this definition, hS . 1 implies economies of scale in advertising while hS , 1 implies diseconomies of scale in advertising.26

25 For the general model, the cost elasticity would be hC 5 ≠(ln C) / ≠(ln Q) 5 fq 1 fqq (ln Q) 1 o i gqi (ln Pi ) for i 5 p, v, r. In the homogeneous model, the coefficients associated with the variables ln Q and ln Pi are zero, so hC 5 fq 26 An alternative definition of the scale elasticity is j S 5 1 2 hC (Christensen and Greene, 1976). With this definition, j S . 0 implies scale economies and j S , 0 implies scale diseconomies. Neither definition offers advantages over the other; j S . 0 is equivalent to hS . 1 and j S , 0 is equivalent to hS , 1.

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8. Estimated substitution elasticities We calculate Morishima and price elasticities at two points. First, we calculate them at the means, as is common in the literature, because the translog cost function can be interpreted as a Taylor series expansion around the means of the variables and, as such, estimation at the means best approximates the true, but unknown, cost function. We also calculate the elasticities for our final observation, the fourth quarter of 1993, because this will better represent the present and, therefore, will be useful in considering the policy implications of actions taken in the near future. In fact, the two points yield similar results. All elasticities are estimated using the coefficients of the homogeneous model of Table 2 and fitted shares, which are functions of the coefficients and dependent variables, as suggested by Berndt (1991). Because the expected value of the lagged error term is zero, the fitted shares for the homogeneous model, where gqi 5 0, are

O bˆ (ln P );

Sˆi (P; aˆ i , bˆ i ) 5 aˆ i 1

ij

j

i, j 5 p, v, r,

j

where Pj are either mean prices or prices for 1993:Q4, P is the price vector, bi is the vector of b coefficients, and ˆ denotes estimates from the homogeneous model. From Eq. (9), the estimated Morishima elasticities of substitution can be written as ˆ ˆ ˆ i , bˆ i ) 2 bˆ jj /Sˆj (P; aˆ j , bˆ j ) 1 1 sˆ M ij 5 b ij /Si (P; a with variance ˆ ˆ ≠sˆ M (≠sˆ M ij / ≠a ij / ≠ b )

O (≠sˆ

M ij

ˆ T / ≠aˆ ≠sˆ M ij / ≠ b )

where aˆ 5 ( aˆ i aˆ j ), bˆ 5 ( bˆ i bˆ j ), o is the relevant portion of the variance– covariance matrix, and T is the transpose operator.27 Taking the square root of the variance, we then form the t ratio. Price elasticities of demand and their associated standard deviations are calculated in a similar fashion. Morishima elasticities are presented in Table 3. The Morishima elasticity s M ij measures the curvature of the isoquant when adjustments are made in inputs i and j in response to a change in the price ratio Pi /Pj due to an increase in the price Pi

27

Many translog studies incorrectly treat shares as fixed when estimating the variances of elasticities; they do not consider the effect of the parameters upon the shares. This results in biased estimates of the variances. In contrast, we estimate the variance as a Taylor series expansion. For a discussion of these issues, see Anderson and Thursby (1986).

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Table 3 Morishima elasticities of substitution a j5p

j5v

j5r

(A) Morishima elasticities at the mean values of independent variables i5p – 0.1612 (0.8620) i5v 1.6887 b – (1.2166) i5r 5.4099 c 4.2780 c (3.1260) (2.1758)

9.5267 d (3.6041) 7.9992 d (2.6664) –

(B) Morishima elasticities for the average firm, fourth quarter, 1993 i5p – 0.1049 (0.9579) i5v 1.7380 b – (1.2644) i5r 4.8528 b 3.7394 c (2.9598) (1.7319)

8.4873 d (3.0624) 6.8543 d (1.8779) –

a

Standard errors are in parentheses. Entries in the table are Morishima elasticities, s M ij , where rows denote the ith medium and columns denote the jth medium for i, j 5 p, v, r (print, television, radio). The own Morishima elasticity of substitution is not calculated for i 5 j. b Significant at the 10 percent level, one-tailed test. c Significant at the 5 percent level, one-tailed test. d Significant at the 1 percent level, one-tailed test.

(Blackorby and Russell, 1989, p. 885). As discussed previously, this will typically be different from the curvature moving in the other direction, when Pi /Pj changes due to an increase in the price Pj . For instance, consider the substitution between television and print media using the mean values of the variables. If the price of TV advertising increases, the estimate for s M vp in Table 3A (1.69, significant at the 10 percent level) indicates that firms are able to substitute print for TV relatively easily.28 On the other hand, as the price of print media advertising increases, the results in Table 3A suggest that substitution into TV is not so readily accomplished ( sˆ M pv 5 0.16 in Table 3A, and insignificantly greater than 0). This asymmetry may result from the fact that television accounts for 81 to 85 percent of fitted advertising expenses while print accounts for only 9 to 13 percent of these expenses. Therefore, because television is already heavily saturated relative to print, increases in the price of print advertising induce beer producers to substitute 28

As a basis of comparison, the simple elasticity of substitution for the two-input Cobb-Douglas production function is unity. Because the Cobb-Douglas function has a long history in economic analysis, it seems reasonable to use unity as a benchmark. Blackorby and Russell (1989) showed that, unlike the Allen elasticity, the Morishima elasticity is unity for two inputs that enter the production function in a Cobb-Douglas form. As the Morishima elasticity approaches infinity, the two inputs become perfect substitutes.

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more heavily into radio ( sˆ M pr 5 9.53 in Table 3A, significant at the 1 percent level). The results in Table 3B suggest similar conclusions for the fourth quarter of 1993. In general, Table 3A and B suggest that the media are fairly good substitutes. While our elasticity estimates are based on marginal changes in advertising, they may hold more generally. To the extent that this is true, it suggests two policy implications. First, partial bans may be ineffective because firms banned from advertising in some media may switch to other media as outlets for their advertising. This may be particularly relevant for broadcast bans because print advertising appears to be a fairly good substitute for both TV and radio advertising: in Table 3B, where substitution elasticities are calculated for our latest ˆM data, sˆ M vp and s rp are 1.74 and 4.85 and are significant at the 10 percent and 5 percent significance levels, respectively. Second, with respect to mergers in the television and radio media, antitrust agencies perhaps need not be too concerned that the owners of these media outlets will be able to significantly increase the price of advertising because advertisers could switch to print advertising. Similarly, if the price of TV advertising increased, firms can switch into radio ( sˆ M vr 5 6.85, significant at the 1 percent level); and if the price of radio advertising increased, firms can switch into TV ( sˆ M rv 5 3.74, significant at the 5 percent level). The highest substitution elasticity is from print into radio ( sˆ M pr 5 8.49, significant at the 1 percent level). Table 4 Price elasticities of demand a j5p

j5v

j5r

(A) Price elasticities at the mean values of the independent variables i5p 21.6994 b 20.0817 (1.1607) (1.1569) i5v 20.0107 20.2430 b (0.1593) (0.1595) i5r 3.7105 b 4.0350 b (2.6165) (2.6004)

1.7811 b (1.2453) 0.2537 b (0.1590) 27.7456 d (2.6192)

(B) Price elasticities for the average firm, fourth quarter, 1993 i5p 21.7557 b 20.1428 (1.2083) (1.2065) i5v 20.0177 20.2477 b (0.1584) (0.1692) i5r 3.0971 c 3.4918 c (1.8582) (1.8431)

1.8984 b (1.2129) 0.2654 c (0.1555) 26.5889 d (1.8591)

a

Standard errors are in parentheses. Entries in the table are price elasticities of demand, eij , where rows denote the ith medium and columns denote the jth medium for i, j 5 p, v, r (print, television, radio). Own-price elasticities are on the main diagonal. b Significant at the 10 percent level, one-tailed test. c Significant at the 5 percent level, one-tailed test. d Significant at the 1 percent level, one-tailed test.

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Estimates of price elasticities of demand ( eˆij ) for the mean of the observations and for the fourth quarter of 1993 are presented in Table 4. Estimated own-price elasticities of demand ( eˆii ) are shown along the main diagonals of Table 4A and B. As required by the law of demand, the own-price elasticities are all negative; and all are significant at the 10 percent level or better. At the relevant points on their demand functions, demand for television advertising is relatively inelastic, while demand for radio and print media are relatively elastic. The inelasticity of TV advertising demand implies that market power is not being exerted in the setting of TV ad rates, because firms with market power have incentive to price in the elastic portion of their demand curve. The relative elasticity of demand for print and radio may be due, in part, to the fact that they account for smaller portions of firms’ advertising budget. However, they also may be due, in part, to market power enjoyed by the firms that sell print and radio advertising space. Nevertheless, with the exception of the cross-price elasticities between TV and print, these elasticities support our findings discussed above that the media are substitutes, so that market power is probably not extreme among the suppliers of advertising space. Both cross-price elasticities involving TV and print are negative (in Table 4A, eˆvp 5 2 0.01 and eˆpv 5 2 0.08), but both are highly insignificant. If the true values were one standard deviation above these estimates, both would be positive (0.15 and 1.08); we cannot place much confidence in these estimates.

9. Economies of scale in advertising From Eq. (11), the cost elasticity, hC , is estimated by fq in the homogeneous model. It is the same for all observations and for the mean of the variables because this elasticity is constant. From Table 2, hˆ C is 1.2589 with a standard error of 0.0735, significant at the 1 percent level. The scale elasticity is hˆ S 5 ( hˆ C )21 5 0.7943 with standard error 0.0464, significant at the 1 percent level. This suggests diseconomies of scale in beer advertising, at least over the advertising levels of firms in our sample (see Table 1). This contradicts some earlier results such as Peles (1971) and Brown (1978); see also Krouse (1990, p. 500), Martin (1994, pp. 245–247), and Berndt (1991, p. 415). However, Thomas (1989) also found scale diseconomies in advertising for cigarettes and soft drinks. In addition, in an earlier study, Simon (1965) reported a preponderance of evidence for a number of different goods that ‘the first ad is the most efficient, and additional repetitions do less and less work.’ 29 Our finding of diseconomies of scale in beer advertising implies that large-scale advertising, such as the levels employed by firms in our sample, is not useful in building barriers to entry into the beer market.

29

Some studies (e.g., Tremblay, 1987) confound economies of scale in production with economies of scale in advertising, so we cannot compare our results to these studies.

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Diseconomies of scale are certainly plausible. It is reasonable, and eminently rational, that advertising efforts should first be made through media outlets that would reach the largest audiences (e.g., national magazines and radio and TV shows aired nationwide). Then, as advertising efforts increase, media with less ‘reach’ would be used (such as regional magazines and spot radio and TV markets). It follows that marginal audiences would diminish in size as advertising efforts increase. Finally, we compare our results to Bresnahan’s (1984). In the section of his study that used data for six industries, Bresnahan deemed his results concerning scale economies inconclusive because of the insignificance of proxy variables he used in place of quantity (time and four-firm concentration ratios). He stated (p. 147) that his evidence could support either increasing returns to scale or a lessening of diseconomies of scale over time. In the part of his study that considered beer, Bresnahan found some support for economies of scale. However, our results are not directly comparable to his because his methodo1ogy is different from ours. He regressed the advertising / sales ratio on a number of independent variables, including a price index for all advertising messages. He then arrived at his conclusion based upon the sign associated with the price index coefficient in three alternative specifications of the advertising / sales ratio. In contrast to Bresnahan, who acknowledged that his regressions to measure scale economies were somewhat ad hoc,30 we follow Hanoch (1975) by measuring the scale elasticity along the expansion path using parameters from the cost function.

10. Conclusion This study focused upon the substitutability of advertising media and advertising economies of scale using a translog model and firm-level data for beer manufacturers over the period 1983–1993. We estimated Morishima elasticities of substitution and price elasticities and found that all advertising media are substitutes in promoting sales. We found strong substitution possibilities from TV into both print and radio, from radio into both print and TV, and from print into radio. In addition, we found evidence of diseconomies of scale in advertising. Aside from academic interest, these two findings suggest three policy implications. First, recent events in the U.S. have refocused attention upon the possibility of a partial ban on alcohol advertising, both for liquor and for beer. A ban on TV and

30

Bresnahan (1984) regressed the advertising / sales ratio on ‘quantitative measures of the firm’s environment, but not on any choice variables of the firm’ (p. 154). He further stated, ‘[i]t is not obvious what the determinants of [advertising / sales] should be’ and presented three versions of the regression. In contrast, our approach allows the cost function to determine the scale elasticity.

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radio advertising could be effective in reducing alcohol-related problems if print media are not good substitutes for TV and radio. However, our results suggest that beer producers can substitute fairly easily into print advertising, so a partial ban may be ineffective if the effects are noticeable at all. To the extent that the implications of our results, which hold for marginal changes, are indicative of larger changes, beer producers probably would respond to a ban on TV and radio advertising by increasing advertising in printed media. The fact that U.S. liquor producers voluntarily avoided broadcast advertising from 1936 until the recent advertising campaign by Seagram supports this possibility: liquor producers evidently have viewed other advertising media as close substitutes for broadcast advertising. Moreover, our results support evidence from research on cigarette advertising that suggests that partial bans have not been highly effective in reducing cigarette consumption (Seldon and Doroodian, 1989).31 This implication may hold for goods other than alcohol and cigarettes. For instance, consider children’s toys. Restrictions on TV advertising directed at children may be ineffective because advertising appears in children’s publications. While we do not examine other markets, it is clear that the effectiveness of a partial ban in any market will be mitigated by media substitutability.32 Second, regulatory agencies in the U.S. and Mexico have been concerned that increased concentration in TV and radio markets may result in the ability of large TV and radio corporations to raise advertising rates. Our estimated own-price elasticities suggest that TV corporations currently lack market power in setting advertising rates, while print and radio media owners may have some market power. However, our estimated substitution elasticities suggest that such market power is, and is likely to remain, limited. More succinctly, the results of this study imply that mergers in the entertainment industry will not lead to significant market power in setting advertising rates. Third, economies of scale in advertising have implications for the ability of advertising to raise barriers to entry into the beer market. In contrast to concerns that economies of scale in advertising can insulate incumbent firms from the threat of entry, we find diseconomies of scale, at least in the range of advertising of firms in our sample. This suggests that large-scale advertising may not create a barrier to

31

An exception is a recent paper by Tremblay and Tremblay (1997). They present ‘weak evidence that television and radio are the most effective media for promoting [cigarette] sales’ (pp. 10–11). They also suggest that the broadcast advertising ban indirectly reduced consumption. Their statistical results suggest that the broadcast advertising ban increased market power among cigarette companies leading them to increase prices. In response to higher prices, consumers reduced consumption. 32 Media substitution may change the types of consumers who purchase a good. While this study shows that the firm may maintain sales with media substitution, the composition of consumers could be different. This issue is beyond the scope of this study.

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entry due to scale economies, at least into the beer market. This implication may hold for other markets as well.33 We offer one final word, with reference to substitution among, and relative effectiveness of, the various advertising media. This study suggests that sales can be maintained using different combinations of advertising media. Therefore, contrary to the claim of Marshall McLuhan (1964), it appears that the message is more important than the medium.

Acknowledgements The authors thank Robert Coen of McCann-Erickson for providing media cost data, Jane Darling of The University of Texas at Dallas Library for assistance in data collection, and Devon Herrick for research assistance. We thank Joseph E. Harrington, Jr., Wim P.M. Vijverberg, and an anonymous referee for constructive comments and suggestions. The usual disclaimer applies. Authorship is shared equally. An earlier version of this paper was presented at the 25th Annual Conference of the European Association for Research in Industrial Economics in Copenhagen, August 1998.

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