Measuring the Accountability of Advertising Expenses in the Presence of Sales Cost Inefficiency and Marketing Spillovers

Transcription

1 Univerity of Nebraka - Lincoln DigitalCommon@Univerity of Nebraka - Lincoln Preentation, Working Paper, and Gray Literature: Agricultural Economic Agricultural Economic Department October 2005 Meauring the Accountability of Advertiing Expene in the Preence of Sale Cot Inefficiency and Marketing Spillover Kontantino Giannaka Department of Agricultural Economic, Univerity of Nebraka-Lincoln, Lincoln, Nebraka, USA, kgiannaka2@unl.edu Gianni Karagianni Univerity of Macedonia, Greece Vangeli Tzouveleka Univerity of Crete, Greece Follow thi and additional work at: Part of the Agricultural and Reource Economic Common Giannaka, Kontantino; Karagianni, Gianni; and Tzouveleka, Vangeli, "Meauring the Accountability of Advertiing Expene in the Preence of Sale Cot Inefficiency and Marketing Spillover" (2005). Preentation, Working Paper, and Gray Literature: Agricultural Economic Thi Article i brought to you for free and open acce by the Agricultural Economic Department at DigitalCommon@Univerity of Nebraka - Lincoln. It ha been accepted for incluion in Preentation, Working Paper, and Gray Literature: Agricultural Economic by an authorized adminitrator of DigitalCommon@Univerity of Nebraka - Lincoln.

2 Meauring the Accountability of Advertiing Expene in the Preence of Sale Cot Inefficiency and Marketing Spillover Kontantino Giannaka (Dept of Agricultural Economic, Univerity of Nebraka-Lincoln, USA) Gianni Karagianni (Dept of Economic, Univerity of Macedonia, Greece) Vangeli Tzouveleka (Dept of Economic, Univerity of Crete, Greece) Correponding Author: Kontantino Giannaka Profeor and Co-Director Center for Agricultural & Food Indutrial Organization Department of Agricultural Economic Univerity of Nebraka-Lincoln 216 H.C. Filley Hall Phone: (402) Lincoln NE Fax: (402) U.S.A. The author wih to thank the participant of the 5 th Conference on Reearch in Economic Theory and Econometric (CRETE) and Rolf Färe for their ueful comment and uggetion that materially improved the paper. The uual caveat apply. Thi reearch ha been partly upported by a Marie Curie Tranfer of Knowledge Fellowhip of the European Community' Sixth Framework Programme under contract number MTKD-CT , and by funding from the General Secretariat of Greece under the reearch project PENED 2005.

3 Meauring the Accountability of Advertiing Expene in the Preence of Sale Cot Inefficiency and Marketing Spillover Abtract Thi paper develop a tractable theoretical framework for analyzing the ubtitutability between different advertiing media, the extent of marketing pillover in the market, the allocative efficiency of advertiing pending, and the ource of total advertiing productivity and ale growth. Maintaining the eparability aumption between ale and production technology, the propoed methodology relie on cot-function decompoition of total factor productivity and the duality between input ditance and cot function. Utilizing a flexible Tranlog advertiing ditance function, the methodology i applied to the advertiing activity of meat proceing firm in Greece during the period Scale economie in advertiing expene turn out to be an important ource of total advertiing productivity change in the Greek meat proceing ector. Advertiing pillover are ignificant contributing to total advertiing productivity oberved. Our analyi alo indicate that improvement in (technical and allocative) advertiing efficiency are more important mean of enhancing firm return than improvement in advertiing technique. Keyword: Advertiing productivity, advertiing direct ditance function, media ubtitutability, proceed meat indutry, Greece. JEL Code: D24, L25, L66, M37. Introduction Advertiing (peruaive or informative) i a critical element of buine conduct affecting conumer valuation of advertied good, market tructure, firm profitability and ocial welfare. It require ignificant reource a well a kill in determining the appropriate meage and the media ued to communicate them. It ha received coniderable attention in the economic literature with the main focu being either on the market and welfare effect of different advertiing trategie or on empirically etimating tructural model (i.e., ale or advertiing cot function) aimed to characterize marketing technology and the effectivene of marketing effort. Thi trand of advertiing literature, uing tructural model, ha been baed on the eparability aumption between marketing and production technologie initiated by Brown (1978), Wateron (1984) and - 1 -

4 Brenahan (1984). In thee empirical model three important iue have been conidered o far: firt, the ubtitutability of advertiing media (e.g., Seldon and Jung, 1993; McCullough and Waldon, 1998; Seldon et al., 2000; Silk et al., 2002); econd, the role of cale economie in advertiing (e.g., Seldon et al., 2000); and third, the degree of advertiing efficiency (e.g., Luo and Donthu, 2001; 2005; Fare et al., 2004; Vardanyan and Tremblay, 2006). The interet in media ubtitutability and the role of return to cale tem from the quetion regarding three eparate public policy debate: firt, the effectivene of partial advertiing media ban; econd, the effect of merger wave among radio, televiion and printed media firm and; third, the anticompetitive effect of advertiing. Firm banned from uing one advertiing medium could maintain a contant level of ale by increaing their ue of another advertiing medium if the latter i ubtitutable for the former. A a reult, intermedia ubtitutability tend to limit the effectivene of partial advertiing ban but complementary relation may alo be expected ince firm often ue more than one cla of media in a given campaign (Silk et al., 2002). All thee are about the flexibility of advertiing mix in attaining a given level of ale. 1 On the other hand, the recent merger wave among entertainment corporation worldwide raie important concern with regard to the market power accrue to the owner of merged broadcating and printed media firm that ell advertiing pot (Slade, 1998; Bue and Ryman, 2005). Competitive pricing of advertiing outlet (i.e., TV, radio, printed media) i enured by eay of ubtitution between advertiing media. If, however, broadcating or printed media firm are merged, then the eaine of media ubtitutability acro market, will reult in increaed advertiing pot price and therefore in detetorating conumer welfare. Apart of that, advertiing expene are conidered a a key determinant of the barrier to entry in a market and, therefore, an important determinant of market tructure. Comanor and Wilon (1969) were among the firt to argue that advertiing affect the height of barrier to entry through the exitence of cale economie. In the preence of uch economie, potential entrant face an additional (unk) capital requirement, which can deter entry and therefore decreae competition in the market

5 While the determination of effective marketing campaign (i.e., trategie that can achieve certain firm objective) i certainly neceary for the ucceful performance of a firm, uch a determination i not ufficient a key iue i the identification of thoe effective advertiing campaign that are alo efficient, i.e., they can achieve the firm objective at minimum cot. High level of advertiing inefficiency, plague buine and frutrate manager a inefficient advertiing pending and miallocated reource reult in lower profit margin and obtacle firm utainable growth. Several author recently conidered that advertiing expene might not be a efficient a it ha been recognized in generating ale (e.g., Smith and Park, 1992; Luo and Donthu, 2001, 2005; Färe et al., 2004; Vardanyan and Tremblay, 2006). Technical efficiency of advertiing i certainly important, but it i not the ole determinant of advertiing efficiency. Another but cloely related iue that ha not been conidered previouly i on whether the choice in advertiing mix i in accordance with the oberved price for meage in the variou media type, in firm attempt to attain a given level of ale with the minimum poible cot. Thi i about allocative inefficiency in advertiing and how it may affect competitivene by increaing unnecearily the cot of advertiing compared to rival firm. With the benefit of advertiing varying between different advertiing media (Becker and Murphy, 1983; Tirole, 1988; Yiannaka et al., 2002; Färe et al., 2004), 2 the identification of the allocative efficient advertiing mix can be a challenging propoition. Nerlove and Arrow (1962) and Grabowki (1970) argued that while the advertiing to ale ratio varie acro firm and indutrie, individual firm tend to allocate a nearly fixed ratio over time which, in turn, ugget that firm may be engaged in a rule of thumb deciion making when faced with uncertaintie regarding the allocation of advertiing expene. Thi i particularly true in highly protected ector and oligopolitic market where government intervention and imperfect competition create major impediment to the efficient allocation of reource (Fulginiti and Perrin, 1993). However, media allocation i a critical dimenion of advertiing deciion making, and it ha even been uggeted that it i more important than advertiing pending deciion (Doyle and Saunder, 1990). Our tudy alo attempt to complement exiting literature by offering an evaluative tool for a brand' budget allocation deciion over - 3 -

6 time. A uggeted by pat tudie, different media may exhibit different long-term effectivene, uggeting that budget allocation plan have long-term implication. However, marketing effort in practice are often driven by hort-term profit maximization goal or by competitive reaction (Dekimpe and Hanen, 1995; Yoo and Mandhachitara, 2003). A a reult, budget allocation deciion may not be formulated baed on their long-term potential. Allocative i one of the component of cot inefficiency conidered by Luo and Donhu (2001, 2005), Färe et al., (2004) and Vardanyan and Tremblay (2006), and it indicate how correctly firm are able to tranmit price ignal into their input choice. One of the contribution of the preent paper i to bring allocative inefficiency explicitly in the empirical analyi of the advertiing proce by examining it relative importance compared to technical inefficiency. The econd contribution i to empirically quantify the advertiing pillover among firm, that i, the effect of the marketing effort of one firm on the marketing effectivene of other firm within the ame market (Metwally, 1975; Friedman, 1983; Sheldon et al., 2000; Yiannaka et al., 2002; Bagwell, 2005). 3 Empirical tudie reveal that advertiing pillover are ignificant particularly in market where non-cooperative behavior occur between firm (e.g., Tremblay and Polaky, 2001). The magnitude and the direction of thee pillover depend on the extent to which competing product are homogeneou with imilar characteritic, the tage of market development and the kind of advertiing meage. On the other hand, advertiing pillover are unlikely to be ignificant in market where product have very different characteritic and where conumer have a trong loyalty to a particular brand (Ackerberg, 2001). 4 In addition, advertiing pillover are not preent in a monopoly market or in market where producer cooperate in their marketing effort (Liu and Forker, 1988). However, in cae that firm are producing a homogeneou product advertiing pillover are preent and affecting the demand for all brand and at the ame time individual advertiing expene. The former i the ale effect of advertiing pillover aociated with the change in individual firm ale, wherea the latter i the generic effect related with the change in individual advertiing expene. Thee pillover may well be affected by the extent of advertiing meage in each particular market. Thi crowding-out effect may affect both poitive or negative individual marketing expene. For intance in market with homogeneou - 4 -

7 product, if firm are not cooperating and heavily advertie their product, the effect of pillover may turn to be negative due to high level of advertiing expene undertaken by rival which increae the cot of promotion. Finally, the pillover effect may alo depend on the maturity tage of the market (maturity effect). In later tage, when the market matured, advertiing may become predatory creating negative pillover. 5 The net pillover effect i cae pecific and depend on the direction of each one of thee four different effect. The third contribution of the preent paper i to relate allocative inefficiency and advertiing pillover with the previouly analyzed iue of cale economie and cot inefficiency in order to provide a more comprehenive picture of performance evaluation baed on the notion of total advertiing productivity (TAP) growth. Recently, Rut et al., (2004) pinpoint concern about the productivity of advertiing and ale promotion expenditure. In particular, to rebuild confidence in advertiing and marketing invetment, they ugget the urgent need to how how marketing add to hareholder value, a the perceived lack of accountability ha undermined marketing credibility, threatened marketing tanding in the firm, and even threatened marketing exitence a a ditinct capability within the firm. For the advertiing proce TAP refer to the increae in ale that cannot be accounted by the oberved increae in the number of advertiing meage in variou media. It may be due to change in advertiing technology per e, to cale economie in advertiing, to improvement in technical and allocative efficiency and, to the net advertiing pillover effect. The empirical quetion i to etimate the relative importance of each of thee ource of ale growth and then to ue thi information to propoe appropriate meaure for improving advertiing effectivene. The objective of thi paper i to addre thee iue developing a tractable approach for analyzing empirically the marketing proce and advertiing effectivene Maintaining the eparability aumption between ale and production technology, the propoed approach relie on the theoretical framework developed by Karagianni et al., (2004) which i adapted in an advertiing cot function etting. Utilizing a flexible advertiing ditance function, the developed methodology i then applied to the advertiing activity of meat proceing firm in Greece during the period

8 The ret of the paper i tructured a follow. Section 2 preent the theoretical framework of analyi. Section 3 dicue the empirical model and the etimation procedure. Section 4 preent the data and the empirical reult. Section 5 conclude. 2. Theoretical Framework Following Seldon et al., (2000) and Färe et al., (2004) we may ditinguih between two type of procee that take place within each production unit: the pure production proce via which conventional input (i.e., labor, material, capital) are converted to output, and the ale promotion proce via which conumer are either informed about the exitence and characteritic of a good or brand or peruaded to buy the product for real or imagined benefit mainly through advertiing. Given thi ditinction, the firm total cot i compried of two eparable element, the cot of conventional factor of production and that of advertiing, i.e., p where { 1 h } production, { 1 k} ( p ) = ( p ) + ( ) C T y,, x r,t C p y, t C y, x r,t w w w w (1) p p H w i the vector of price of the H conventional factor of w,,w R ++ w i the vector of K advertiing media price, y i the w,,w R K ++ total firm produce, and t i an index of time. r x i the total advertiing expene of firm rival that affect cot of ale. In addition, a uggeted by Seldon and Jung (1993), firm may not plan imultaneouly their production and advertiing deciion. In other word, firm may want to build or deplete their inventorie during the period under conideration and, therefore, the quantitie in the production and ale cot function may r be different, i.e., C ( y, w x,t) and p p p C ( y, t) w with y and p y being firm ale and production volume in period t, repectively. Therefore, we can ditinguih between production and advertiing cot by defining two different underlying technologie for production and ale. Concentrating on ale, we may define an advertiing technology et decribing all poible media combination, conditional on advertiing expene of the firm rival that are able to generate a given level of ale a: 6-6 -

9 {( ) } T y, x x R K,y R,x r R, x can produce y (2) Then for any given T, the advertiing or ale function ( x r ) R K f x,t : + R+ that relate the advertiing expene with firm total ale i defined by: where { 1 k} f () x,,x R K ++ { } ( ) ( ) r r f x x,t max y x x,t T (3) y x i the vector of advertiing media utilized to promote ale, i i a quaiconcave twice differentiable function, x r are the total advertiing expene of the firm rival and, t i a time index reflecting change in advertiing effectivene in the different media due to change in advertiing technique. Equivalently the advertiing/ale technology may be repreented by the following advertiing requirement et: { } ( ) ( ) L y x r,t y f x r,t x x (4) Uing the advertiing media correpondence et above, the advertiing technology can alo be repreented by the (direct) advertiing ditance function 7 ( ) M r K D y, x x,t : R + R+ R+ + + ( ) 0 ( ) ( ) R + (Färe and Primont, 1995, p. 19): 8 { δ δ + } M r r D y, x x,t up > x L y x,t y R (5) Ultimately, we may define the (direct) advertiing cot function a the olution of the following optimization problem (Balk, 1998, p. 26): { } { w x M ( x r ) 1w 0} ( ) w w x x ( ) C y, x,t min L y t,x r r x min D y, t,x, x (6) - 7 -

10 Uing the advertiing cot function above the advertiing cot efficiency can then be defined a: where ( ) r CE y,, x,t ( w ) r C y, x,t w x (7) C C i the oberved total cot of media mix and CE ( y,, x r,t) 0< w x 1. Advertiing cot efficiency i independent of media price caling and ha a clear cot r interpretation with 1 CE ( y,, x,t) w x reflecting the percentage reduction in total ale cot if cot inefficiency i eliminated (Kopp, 1981). 9 Taking the logarithm of each ide of (7) and totally differentiating with repect to time yield: i ( ) = ε ( ) + ( ) w x w w w i r y r r CE y,, x,t y, x,t y y, x,t where 10 y ( ) ( ) r r ε y, x,t = C y, x,t y i t ( w ) ( w ) i r x r r r + ε y, x,t x +C y, x,t C w w i the ale cot elaticity, ( y, x,t) C r x ( y, x,t) Sr x r r ε w = w i the pillover effect of rival advertiing expene on firm total advertiing cot, ( r ) ( y, x,t = C y, x r,t w ) (8) w w i the vector of optimum media cot hare, and t ( r ) ( -C y, x,t = C r t y, x,t) w w i the rate of cot diminution of advertiing media. Taking the logarithm of the oberved ale cot, i.e., C = w x, and totally differentiating it with repect to time yield: i i i C x w = + (9) Subtituting (9) into (8) reult in: i ( ) = ε ( ) + ( ) i CE y, w, x r x,t y y, w r x,t y y, w r x,t w t ( ) ( ) i i i x r r r r + ε y, w x,t x +C y, w x,t - x - w (10) - 8 -

11 Uing the conventional Diviia index meaure of total advertiing productivity i i i S (TAP) growth of firm ale, i.e., TAP = y x, the relation (10) can be rewritten a: t { 1 ε ( )} ( ) i i i y y y, x r,t y C y x w, w x r,t = + i { } ( ) i ( ) ( ) r x r r r r ε y, w x,t x + y, w x,t w + CE y, w, x x,t (11) Following Farrell (1957), advertiing cot efficiency can be decompoed a ( w x ) ITE ( y, x Sr,t) IAE ( y,, x Sr Sr x w x,t), with ITE ( y, x x,t) Sr CE y,, x,t = = ( x ) 1 and ( w x ) = ( x ) ( w ) M Sr D y, x,t { } IAE y,, x,t D y, x,t C y, x,t C Sr M Sr Sr are, repectively, the medium oriented meaure of advertiing technical and allocative efficiency. By definition, both meaure lie within the ( 01, ] interval, are independent of media price caling, and have an analogou to CE cot-aving interpretation. Taking it time rate of change and ubtituting it into (11), we get the final ale growth decompoition formula a: { 1 ε ( )} ( ) { } = + + i i i i y r r y x y, w x,t y y, w x,t w ize effect advertiing cale effect medium price adjutment effect i r x r r ε ( y, w x,t) x i i ( ) ( ) ( ) t r C y, x,t ITE y, x r,t IAE y w + x +, w, x x r,t adverti in g pillover effect technical change effect adverti in g TE effect adverti in g AE effect (12) The firt term in (12) capture the contribution of aggregate advertiing media growth on ale change over time (ize effect). 11 The more effective i an advertiing medium, the higher it contribution to the ize effect. The econd term meaure the relative contribution of cale economie in advertiing to the growth of ale (cale y r effect). Thi term vanihe under contant return to cale a ε ( y, w x,t) = 1, while it i poitive (negative) under increaing (decreaing) return to cale, a long a firm total ale increae, and vice vera. The third term in (12) i the medium price adjutment effect. 12 The exitence of thi term indicate that the aggregate meaure of media-mix i - 9 -

12 biaed in the preence of advertiing allocative inefficiency (Bauer, 1990). Under advertiing allocative efficiency, the media price adjutment effect i equal to zero a ( r y, x,t) = w. Otherwie, it magnitude i inverely related to the degree of advertiing allocative inefficiency. The medium price adjutment effect i alo equal to zero when advertiing media price change at the ame rate. The fourth term capture the advertiing pillover effect, the impact that rival advertiing expene may have on firm total advertiing productivity level. It i zero in the abence of marketing pillover and under a flexible pecification of the advertiing technology can be further decompoed into the four effect identified in the introductory ection. The fifth term refer to the dual rate of technical change in firm ale technology (cot diminution), which i poitive (negative) under progreive (regreive) technical change. The lat two term in (12) are poitive (negative) a advertiing technical and allocative efficiency increae (decreae) over time. Note that there i no a priori reaon for both type of advertiing efficiency to increae or decreae imultaneouly (Schmidt and Lovell, 1980) nor that their relative contribution hould be of equal importance for TAP growth. More importantly, what really matter in TAP growth decompoition analyi i not the degree of advertiing efficiency itelf, but it improvement over time. That i, even at low level of advertiing cot efficiency, ale gain may be achieved by improving either technical or allocative efficiency, or both. However, it eem difficult to achieve ubtantial rate of ale growth at very high level of technical and/or allocative advertiing efficiency. The next tep concern the recovery of all factor in (12) from a advertiing-ditance function, through it duality with the ale cot function. For doing o we have modified the framework developed by Karagianni et al., (2004) for the cae of advertiing technology. The Lagrangean multiplier and the firt-order condition of the minimization problem in (6) are given, repectively, a: and { } M r (, ) = + 1 D ( y, x,t) Λ x ξ w x ξ x (13) ( ) w = ξ D y, x x,t (14) M r x

13 ( ) M r 1 D y, x x,t (15) where ξ i the Lagrangean multiplier. Uing the firt-order condition and the linear homogeneity of the advertiing-ditance function in x, it can be hown (ee Färe and Primont, 1995, p. 52) that ( r ) ( ξ y, x,t = C y, x r,t) w w. In addition, by applying the envelope theorem the following relation can be obtained (Färe and Primont, 1995, p. 51): and ( ) = ξ( ) y ( ) C y, w x,t y, w x,t D y, x x,t (16) r r M r y ( ) = ξ ( ) r x ( ) C y, w x,t y, w x,t D y, x x,t (17) r r M r r x ( ) ( ) w = x w (18) r r C y, x,t y, x,t w ( ) = ξ( ) t ( ) C y, w x,t y, w x,t D y, x x,t (19) r r M r t Uing (16), the firt-order condition, and ( r ) ( ξ y, x,t = C y, x r,t) al., (1986) have hown that: ( y, x,t) D y ( y, x,t) w w, Färe et y r M r ε w = x (20) which provide the relationhip for recovering the cale effect in (12) directly from the advertiing ditance function. On the other hand, uing (19), the firt-order condition, and ( y, x r,t r ) C ( y, x,t ) ξ w = w, Atkinon and Cornwell (1998) have hown that: ( ) t ( ) C y, w x,t = D y, x x,t (21) r M r t which relate the cot diminution with the primal rate of technical change in advertiing technique through the medium-ditance function. Finally, uing (17), the firt-order condition and ( r ) ( ξ y, x,t = C y, x r,t) w w it can be hown that:

14 ( y, x,t) D r x ( y, x,t) r x r M r ε w = x (22) Meaurement of advertiing allocative efficiency require knowledge of either the r minimum advertiing cot C ( y, x,t) ( r y, x,t) w or the cot minimizing media vector x w. Karagianni et al., (2004) have developed a procedure for deriving the latter by uing the dual Shephard lemma ( C y, x r,t) M D ( y w = w, x x r,t x ) w r denote the vector of virtual media price and C ( y, w x,t), where the minimum hadow ale cot of the oberved media mix (Färe and Grokopf, 1990). 13 Then, by definition, virtual and market media price coincide at the (oberved) advertiing cot minimizing media-mix and, conequently, ( r ) ( C y, x,t = C y, x r,t) r that w = C ( y, w x,t) D M r x ( y, x x,t ) w w. Thi, in turn, implie. Karagianni et al., (2004) have hown that thi ytem of equation can be olved for the cot minimizing medium ratio ( j 1 ) x x a long a the underlying technology i known and the virtual price of one advertiing medium (i.e., the firt) coincide with it market price. 14 Uing thee ratio, the relation ( w ) 2 r C y, x,t x x k = w 1 + w2 w + + k (23) x1 x1 x1 can be ued to compute allocative advertiing efficiency a: ( w x ) r IAE y,, x,t where 1 1 ( x = x y, w x r,t) ( x ) ( w ) M r r D y, x,t C y, x,t = = w x r C ( y, w x,t) x 1 ( x ) x w x 1 M r D y, x,t (24). Finally, the ale cot-minimizing media hare required to compute the third term in (12) can alo be obtained from relation (23) a:

15 r ( y, w x,t) ( x x1 ) w = C y, x,t x ( w ) r 1 (25) with the cot-minimizing hare for the firt advertiing medium computed reidually uing the adding-up property. 3. Empirical Model and Etimation Procedure Quantitative meaure of technical and allocative advertiing efficiency can be obtained by econometrically etimating a advertiing ditance function. Thi i feaible with only advertiing and ale quantity data, and the ue of a ingle-equation etimation procedure ince the advertiing ditance function i agnotic with repect to the economic motivation of deciion-maker. In the preent tudy, the tranlog function i ued to approximate the underlying advertiing ditance function a a more flexible repreentation in the ene that it allow for ubtitution poibilitie without retrictive aumption about the hape of the technological relationhip. Auming that panel data are available, the tranlog advertiing ditance function with k media and exogenou factor uch a technical change and rival advertiing expenditure i given by (Lovell et al., 1994; Grokopf et al., 1997; Coelli and Perelman, 1999): 1 1 ln D y, ;t,x t t ln y ln y ln y ln x 2 ( ) ( ) 2 r x 0 K M it = α + ζt + ζtt + α it + α it + δk it kit 2 2 k = 1 1 +ζ ln y ln x ln x ln x ln x t K K K K t it + βk kit + βkj kit jit + ζtk kit k= 1 2 k= 1 j= 1 k= 1 r 1 r r r r +θo ln xit + θoo ln xit + θo ln xit ln yit + θok ln xit ln xkit + θot ln xit t 2 ( ) 2 K k 1 = (26) where, i = 12,,,N are the production unit and t = 12,,,T are the time period. The required regularity condition include homogeneity of degree one in advertiing media and ymmetry (of the cro term and thu the Heian matrix). Thee imply the following retriction on the parameter of (26):

16 K K K K K β = 1, β = δ = ζ = θ = 0 and βkj = β jk (27) k kj kj τk οk k = 1 k=1 k=1 k=1 k=1 Note that the homogeneity retriction can alo be impoed by dividing the left-hand ide and all advertiing media quantitie on the right-hand ide of (26) by the quantity of any advertiing medium ued a numeraire (ee Lovell et al., (1994)). Given linear homogeneity in advertiing expene, to obtain an etimable form of r the advertiing ditance function, firt rewrite (26) a ln x jit = ln f ( y, x x j x,t) ( x ), where j i the numeraire medium and ( f y, x r j x,t) ln D y, x,t M r it x i the right-hand ide of (26) after dividing all advertiing media with the j th medium ued a numeraire. Since there are no obervation for ln D and given that M ( D y, x x r,t) 1 M it it and M ( ln D y, x x r,t) 0 it a tochatic frontier framework:, the following relationhip may be ued to tranlate (26) into ( ) ln D y, x x,t = u (28) M r it where u it i an one-ided, non-negative error term repreenting the tochatic hortfall of the i th firm from it ale frontier due to the exitence of advertiing technical inefficiency. Then, the tochatic advertiing ditance function model may be written a: ( ) r jit j it it it ln x = ln f y, x x x,t + v u (29) where v it depict a ymmetric and normally ditributed error term (i.e., tatitical noie), repreenting a combination of thoe factor that cannot be controlled by firm, omitted explanatory variable, and meaurement error in the dependent variable. It i alo aumed that v it and u it are ditributed independently of each other. Note that the temporal pattern of technical efficiency i important in (12) a it i the change in advertiing technical efficiency over time rather than the degree of technical efficiency that matter. In thi context, Battee and Coelli (1992) formulation i adopted to model the temporal pattern of medium technical inefficiency a:

17 it { η ( ) } u = exp t T u (30) i where η capture the temporal variation of individual technical efficiency rating, and [ 12 ] t,,,t. 15 If the parameter η i poitive (negative), technical efficiency tend to improve (deteriorate) over time. If η = 0, advertiing technical efficiency i timeinvariant, and it doe not contribute to advertiing productivity change. After ubtituting (30) into (29) the reulting model i etimated by a ingleequation etimation procedure uing the ML method. The variance parameter of the likelihood function are etimated in term of σ = σ + σ and γ = σ σ, where the γ- parameter ha a value between zero and one. The cloer i the etimated value of the γ- parameter to one, the higher the probability of the advertiing technical inefficiency effect to be ignificant in the tochatic frontier model. Firm-pecific etimate of advertiing technical efficiency are obtained directly from the etimated mean and variance of u it. Specifically, v u u it ( ) 1 it (31) ITE = exp u which i predicted uing the conditional expectation of exp( u it ) given it ( vit uit ) ε. 16 After etimating the underlying advertiing ditance function, the advertiing cale elaticity i calculated uing (20) a: K y r ε = α + α lnyit + δk lnxkit + ζ tt+ θo lnxit (32) k = 1 The hypothei of contant return to cale can be teted by impoing the neceary retriction aociated with the linear homogeneity of the advertiing ditance function with repect to ale. If thi hypothei cannot be rejected, the underlying ale technology exhibit contant return to cale and the econd term in (12) vanihe. On the other hand, by uing (21), the dual and the primal rate of technical change are related to each other a follow:

18 K t r Cit = ζt + ζttt + ζtk ln xkit + ζt ln yit + θot ln xit (33) k = 1 The hypothei of zero technical change can be teted by impoing the retriction that ζ = ζ = ζ = ζ = θ = If the hypothei of zero technical change cannot be t tt tk t to k rejected, the fourth term in (12) become equal to zero, and technical change ha no effect on TAP change. Then uing (22) the marketing pillover effect may be calculated from (26) a: K r x r it = o + oo it + o it + ok kit + ot k = 1 ε θ θ ln x θ ln y θ ln x θ t (34) r where, the firt two term in (34) ( i.e., θo θooln xit ) + contitute the generic effect of marketing pillover that i the extent that rival advertiing expene affect firm cot of ale, the third term ( i.e., o ln yit ) θ i the ale pillover effect capturing the extent that i rival advertiing expene affect firm total ale, the fourth term ( i.e., θok ln xkit ) the crowding-out effect capturing the extent that rival advertiing expene affect firm media choice and the lat term ( i.e., t) θ i the maturity effect capturing the tage of market development and it impact on firm cot of ale. The preence of marketing pillover effect can be tatitically examined by impoing the retriction θ = θ = θ = θ = θ = 0 in the parameter of (26). o oo o ok ot k By manipulating the dual Shephard lemma for the tranlog advertiing ditance function, evaluating them for the ale cot minimizing medium vector, and taking ratio reult in: ot x K jit r 0 βk + βkjln + δkln yit + ζ ktt + θkoln xit kit x kit j 1 x = 1it = K 1it 1it jit r β1+ β1j ln + δ 1ln yit + ζ1 tt + θ1 oln x it j = 2 x 1it w w x x (35) After few manipulation (35) may be written a:

19 K w kit r exp ( λjit ) βk + βkjλjit + δk ln y it + ζkt t + θko ln x it = w1 it j = 2 K r 1+ 1j jit + 1 it + 1t + 1o it j = 2 = β β λ δ ln y ζ t θ ln x (36) where ( jit ln x jit x1 it ) λ =. Thi i a ytem of n-1 non-linear equation becaue of the exponential term on the left hand-ide of (36) and it ha no cloed form olution. In principle it can be olved to obtain ( jit 1it ) x x for j=2,,k in term of the oberved media price, the oberved ale, the index of technical change, and the etimated advertiing technology parameter. Karagianni et al., (2005) have provided an approximate baed on ( ) 1 Λ = exp z + z. In thi cae, (36) may be rewritten a: jit jit jit K w kit r βk + βkjλjit + δk ln yit + ζktt + θko ln xit = w1 it j = 2 K r 1+ 1j jit + 1 it + 1t + 1o it j = 2 = β β Λ δ ln y ζ t θ lnx (37) The advantage of thi approximation i that the ytem of equation become linear and can be olved uing tandard technique. 18 Then, thee cot minimizing advertiing media ratio are ubtituted into (23) and then into (24) to derive firm-pecific etimate of advertiing allocative efficiency. Uing the dual Shephard lemma and the obtained virtual price we can evaluate the extent of over- or under- utilization of advertiing expene by comparing virtual with oberved media hare a: ( ) y,w x,t MU lnmu ln y,w x,t ln r k r k = k = k( ) k k (38) Value greater than unity (zero) indicate under-utilization of the k th advertiing medium, wherea value le than one (zero) over-utilization. Further, uing virtual price we can evaluate the lope of the ioquant at the oberved media mix i.e., the marginal rate of technical ubtitution, a follow:

20 MRTS ( x ) ( x ) D y, x,t M r k kj = M r j D y, x,t (39) where the ubcript refer to partial derivative of the advertiing ditance function. If the advertiing technology atifie all regularity condition, the MRTS kj will increae a the ratio of advertiing media fall becaue increaed ue of one medium alone occur at higher opportunity cot. Thi require the normalization of (39) by the oberved media mix (Grokopf et al., 1995b), i.e., Sub = MRTS (40) kj kj x j xk for all k j which i the ratio of marginal rate of technical ubtitution (or relative opportunity cot) to relative media mix, i.e., normalized MRTS kj. Value of Sub kj greater (le) than unity reflect relative difficulty (eae) in ubtitution between media k and j. Following Blackorby and Ruell (1989), Grokopf et al., (1995b) and Sharma (2002), the Morihima indirect advertiing elaticitie of ubtitution can be computed from the advertiing ditance function a: ( x ) ( x ) ( x ) ( x ) σ = D y, x,t D y, x,t D y, x,t D y, x,t M r M r M kj kk kj xk x M r k M r j k (41) M Media j and k are Morihima ubtitute if σ > 0 and Morihima complement if σ < 0. Following Blackorby and Ruell (1989), the percentage change in the relative M kj hare of media k and j induced by a given percentage change in their relative price due to a change in the price of medium j i equal to ( 1 σ M kj ) kj. Thu, for a given increae in the price of the j th M medium, the relative hare of medium j decreae if σ > 1 and M increae if σ < 1. In addition, the Allen elaticitie of advertiing ubtitution can be kj obtained in term of the advertiing ditance function a: kj

21 ( x ) kj ( x ) ( x ) j ( x ) M r M r D y, x,t D y, x,t A kj M r M r σ = D y, x,t D y, x,t k (42) which, in contrat with Morihima, are ymmetric Data and Empirical Reult The data ued in thi paper are firm level data on ale and diaggregated advertiing expenditure for all firm that operated ytematically in the Greek meat proceing ector during the period Sytematically operating firm are defined a thoe whoe balance heet are publihed annually by ICAP Hella SA that provide individual annual balance heet data for all manufacturing ector in Greece. Sample participant account for mot of the indutry production (96.5 per cent in 1997) 20 and are the one who advertied their product during the tudy period. The panel data et ued in the analyi i unbalanced due to late entrie and early exit from the market. The number of ytematically operating firm varied between 22 in 1983 and 34 in the period 1989 to Data on total firm ale were obtained from ICAP Hella SA ( ), while thoe for advertiing expene from Nielen Hella ( ). The data on advertiing indicate that total advertiing expene almot tripled between 1983 and 1997 in real 1983 price. On average, approximately 80 percent of the indutry' advertiing wa carried out by even of the bigget firm of the ector. Variation in the ranking of the top four firm in term of advertiing budget indicate competition in advertiing among firm of the ector. Media ued in proceed meat advertiing included televiion, radio, magazine and newpaper with the televiion being the favored medium for firm of the indutry. Total televiion advertiing expenditure wa greater than the aggregate of the three other media for the whole tudy period. A decreae in televiion hare during the lat year benefited other media, epecially radio, which wa a remarkably well-utilized medium for the leading advertier of the ector. The high utilization of both magazine and newpaper by the ytematic advertier in the ector hould alo be noted. The even firm that advertied conitently accounted, on average, for 90 percent of print media expenditure, and about 70 percent of total magazine and newpaper advertiing wa carried out each year by the four firm with the larget advertiing budget. The latter

22 obervation may be conitent with the argument that for high-quality firm with the incentive to reveal their product uperior quality, print media and epecially newpaper are the mot appropriate and, therefore, favorite advertiing media (Tirole, 1988). A brief ummary tatitic of the variable ued in the analyi i preented in Table 1. Televiion advertiing expene were ued a the numeraire medium in impoing the linear homogeneity in media retriction. To avoid problem aociated with unit of meaurement, all variable included in the tochatic medium-ditance function were converted into indice. The bai for normalization wa the firm with the mallet deviation of it ale and advertiing expene level from the ample mean. The etimated parameter of the tranlog advertiing ditance function are preented in Table 2. According to the etimated parameter, the tranlog advertiing ditance function i found, at the point of approximation, to be non-increaing in ale and nondecreaing in advertiing media. Alo, at the point of approximation, the Heian matrix of the firt- and econd-order partial derivative with repect to advertiing media i found to be negative definite and that with repect to ale to be poitive definite. Thee indicate the concavity and convexity of the underlying advertiing ditance function with repect to media and ale, repectively. The logarithm of the likelihood function indicate a atifactory fit for the particular functional form. The ratio parameter, γ, i ignificant at the 1 per cent level implying that firm-pecific advertiing technical inefficiency i important in explaining the total variability of realized ale. Obviouly, the remained unexplained portion i due to meaurement error and mipecification problem from factor that have not been included in the tochatic advertiing ditance function. The tatitical ignificance of modeling advertiing technology i examined uing the likelihood ratio tet. 21 Several hypothee are conidered for different model pecification and the reult are preented in Table 3. It i evident that the average advertiing ditance function doe not adequately repreent the tructure of Greek meat proceing firm in the ample. The null hypothei that γ = μ = η = 0 i rejected at the 5 per cent level of ignificance indicating that the advertiing technical inefficiency i in fact preent. Moreover, Schmidt and Lin (1984) tet for the kewne of the compoed error term alo confirm the exitence of advertiing technical inefficiency. 22 Thi indicate that the majority of Greek meat

23 proceing firm in the ample operate below their tochatic advertiing frontier. Thu, a ignificant part of ale variability among firm i explained by the exiting difference in their degree of advertiing technical inefficiency. In addition, the hypothei that μ = η = 0 i alo rejected at the 5 per cent level of ignificance indicating that the tochatic frontier cannot be reduced to the Aigner et al., (1977) model, where advertiing technical efficiency core i time-invariant following a half-normal ditribution. Thi i alo true for time-varying advertiing technical efficiencie a the hypothei that μ = 0 i alo rejected. Finally, the hypothei that advertiing technical inefficiency i timeinvariant, η = 0, i alo rejected at the ame level of ignificance. The hypothee of no technical change (i.e., ζ = ζ = ζ = 0 ) and Hick-neutral t tt tj j technical change (i.e., ζ tj = 0 j ) are rejected at the 5 per cent ignificance level indicating that technical change ha been a ignificant ource of total advertiing productivity growth in the Greek meat proceing indutry and it hould be taken into account in equation (12). The neutral component of technical change i found to be progreive at a contant rate a the etimate for the parameter ζ t and ζ tt are both negative and tatitically ignificant at the 5 per cent ignificance level (ee Table 2). Regarding technological biae, technical change i found to be print media-uing and televiion-aving, but radio-neutral (a the relevant etimated parameter i not tatitically different from zero). On the other hand, the null hypothei of a linearly homogeneou production technology i alo rejected at the 5% ignificance level, indicating noncontant return to cale. Thu, the advertiing cale effect i a ignificant ource of productivity growth and hould be taken into account in equation (12). According to our empirical reult, production wa characteried by increaing return to advertiing cale, with average cale parameter of during the period An implication of thi reult i that large-cale advertiing undertaken by meat proceor ha been a barrier to entry into the Greek proceed meat market. Thi reult i in line with previou evidence reported in the literature (Pele, 1971; Brown, 1978) although recently Seldon et al., (2000) found contradictory evidence in the US brewery ector. Increaing return to advertiing cale alo imply that advertiing expenditure have not grown beyond the potential capabilitie of the ale technology. Even though

24 the average advertiing expenditure were le than the advertiing expenditure that maximize the ray average productivity, the continued increae in average advertiing expenditure reulted in return to cale following a declining trend over time. The relevant point etimate of return to media cale fell from in 1983 to in The marketing pillover effect are important in modelling advertiing technology of Greek proceed meat firm. Statitical teting reject the hypothei of zero marketing pillover at the 5% ignificance level (ee Table 3). Further, examining the individual tatitical ignificance of the relevant parameter reported in Table 2, it reveal that all four pillover effect identified herein are preent affecting the advertiing cot function of Greek proceed meat firm. Uing thee parameter etimate the eparate marketing pillover effect calculated uing (34) were found to be for the generic effect, for crowding-out effect, for ale effect and for maturity effect. Thee figure mean firt, that advertiing expene in the market are affecting negatively the individual cot of ale implying a low degree of product differentiation in the market. Given the nature of the ector which heavily advertied newly developed proceed meat product during the year of urvey, implie that generic advertiing effect reulted in the increae for the demand of thee newly developed product that affected negatively the individual advertiing expene. Thi i alo evident from the ale effect which i alo poitive. However, thee poitive pillover are leened from the extenive advertiing campaign from all firm in the market that force increaed individual advertiing expene in order to maintain market hare. Finally, the maturity effect wa found to be poitive (i.e., increaing advertiing cot) a market expand confirming previou finding reported in the literature. Thee marketing pillover once are preent are important factor explaining total advertiing productivity and hould be taken into account in (12). Uing the parameter etimate of the advertiing ditance function and the relation (39) to (42), we have calculated normalized and non-normalized marginal rate of technical ubtitution a well a the Morihima and Allen elaticitie of ubtitution of all media pair. 23 Summary tatitic of thoe calculation for the whole period are preented in Table 4. The highet MRTS are thoe between televiion and the other two advertiing media. The ame pattern remain when the MRTS are normalized by the

25 oberved media-mix (ee Sub in Table 3). In general, there i an eae of ubtitution between TV and radio or print media. Looking at the individual point etimate, large firm with high market hare exhibit higher MRTS value implying that larger firm are better able to adjut their media-mix in repone to change in their repective hadow price. Turning to the Morihima and Allen elaticitie of ubtitution (alo preented in Table 4), we find ome intereting difference acro media type. Recall that negative value of the Allen elaticitie imply that the two media are ubtitute, wherea poitive value imply the two media are complement. 24 Hence, according to the relevant point etimate, televiion advertiing meage are complementary to both print and radio meage, while radio and print meage appear to be ubtitute. Although the Morihima elaticitie of ubtitution do not alway have the ame ign with the Allen, the reult reported in Table 4 are rather imilar. 25 Table 4 reveal that the etimated Morihima elaticitie of ubtitution between televiion and radio meage and between radio and televiion meage are poitive and tatitically ignificant at the 5 per cent level. Hence, televiion and radio meage are Morihima ubtitute irrepective of whether the price of radio or the price of televiion meage rie. Moreover, it hold that σ M TVR < σ M RTV a the average etimate over firm and time are and , repectively. Thi implie that when the price of televiion meage rie there i an increae in the radio to televiion meage ratio which i greater than the increae in the televiion to radio meage that occur when the price of radio meage rie. For example, an one per cent increae in the price of televiion meage caue the radio over televiion meage ratio to change by per cent while a one per cent increae in the price of radio meage caue the televiion over radio meage ratio to rie by per cent. On the other hand, televiion and print meage a well a print and televiion meage are Morihima complement a the correponding point etimate are negative in both cae. Finally, radio and print meage exhibit negative elaticity value implying Morihima complementarily. However, in all cae ubtitutability i weak among televiion and the other two media type implying that, if the price of TV broadcating meage increae, there i a relatively low opportunity for ubtitution

26 The etimated advertiing technical efficiency uing relation (31) wa found to be per cent during the period (ee Table 5). Thu, on the average, a per cent decreae in total advertiing cot could have been achieved during thi period, without altering the total ale, ale technology, and media ue. The vat majority of the firm in the ample (76.5 per cent) have conitently achieved core of technical efficiency greater than 70 per cent. On the other hand, there are 8 firm in the Greek meat proceing indutry that are faced with ignificant advertiing technical inefficiency problem a their repective core are below 60 per cent. However, the portion of firm with low advertiing technical efficiency problem ha been decreaed over the period analyzed. In general, during the period, advertiing technical efficiency tended to increae a the etimated parameter η t wa poitive and tatitical ignificant. Specifically, advertiing technical efficiency increaed from per cent in 1983 to per cent in 1997, implying that it contribution to ale growth wa poitive during the ame period. The average annual rate of increae in advertiing technical efficiency wa calculated to be 0.34 per cent. Mean advertiing allocative efficiency wa found to be higher than the correponding technical efficiency during the period analyzed (ee Table 5). Thi indicate that Greek meat proceing firm were more ucceful in allocating their advertiing expene to the different media than in achieving the maximum attainable ale for given advertiing expene. Specifically, mean advertiing allocative efficiency wa found to be per cent ranging from a minimum of per cent to a maximum of per cent. Thi average value implie that, in light of the prevailing price for advertiing media, a per cent reduction in cot of ale would be poible by mean of further re-allocation of media-mix for any given level of firm ale. The majority of Greek meat proceing firm (21 firm) have conitently achieved core of advertiing allocative efficiency above 80 per cent. In addition, thi portion tended to increae ince Generally peaking, advertiing allocative efficiency increaed at a higher rate than advertiing technical efficiency during the period. In particular, advertiing allocative efficiency ha been increaing at an average annual rate of 0.76 per cent and ha contributed poitively to both total advertiing productivity (TAP) and ale growth