Case of Catfish

8/6/2019 Case of Catfish

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Media-Specific Returns to Generic Advertising:The Case of Catfish

Henry W. Kinnucan and Yuliang MiaoDepartment of Agricultural Economics and Rural Sociology, Auburn University,

Auburn, AL 36849-5406

ABSTRACT

A key decision faced by managers of generic advertising programs is the allocation of the budgetamong media (e.g., television, radio, print). In this article, the economics of media allocation are ad-dressed using catfish as a case study. The hypothesis that demand responds equally to all media wasrejected. Further analysis indicated that the media with relatively modest expenditures (newspapersand television) had no reliable effect on demand, which suggests that scale is important. Losses sus-tained from the apparently ineffectual media were more than offset by gains from the effective me-dia (magazines and radio), so that returns overall, net of opportunity cost, were positive. The histor-ical media allocation, however, was inefficient in the sense that a different media mix would haveresulted in greater industry profits. 1999 John Wiley & Sons, Inc.

1. INTRODUCTION

Farm groups in the United States now invest over $750 million per year on advertising and

other promotional activities designed to strengthen the demand for their products in do-

mestic and foreign markets (Forker & Ward, 1993). A key decision faced by the managers

of these programs is the allocation of the advertising budget among alternative media (tele-

vision, radio, print). Yet despite a growing literature on the economic impacts of generic ad-

vertising (Ferrero, Boon, Kaiser, & Forker 1996), the literature is virtually silent on the is-

sue of media allocation. The only known empirical research on media-specific responses

are the milk advertising studies by Capps and Schmitz (1991) and by Pritchett, Liu, and

Kaiser (1998). In a recent study, Kinnucan and Thomas (1997) develop normative decision

rules to guide fund allocation across media under a variety of market structures and policy

settings. The Kinnucan and Thomas study used catfish to illustrate the theory but did notdevelop a comprehensive set of estimates for the media-specific responses to generic ad-

vertising. Beyond these studies, virtually nothing is known about the relative profitability

of alternative media for generic advertisers.

The purpose of this research is to determine the relative profitability of alternative me-

dia for a generic advertising campaign financed by the US catfish industry. Catfish repre-

sents a useful case study in that the industry has used a variety of media, including televi-

sion, in its national campaign, despite a limited budget (about $2 million per year). This

case permits examining the potential effects of scale on media effectiveness. In addition,

the industry has been cooperative in releasing the advertising data, thus avoiding measure-

81

Agribusiness, Vol. 15, No. 1, 8199 (1999) 1999 John Wiley & Sons, Inc. CCC 0742-4477/99/010081-19


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ment-error problems associated with tracking data or other secondary sources (Kinnucan &

Belleza, 1991). Finally, the catfish advertising program has been the subject of several

econometric analyses since its inception in March 1987 (Kinnucan, Nelson, & Xiao, 1995;

Kinnucan & Venkateswaran, 1990; Zidack, Kinnucan, & Hatch, 1992). This replication per-

mits testing whether advertising responses are robust, a growing concern in the advertisingeffectiveness literature (Kinnucan, Xiao, Hsia, & Jackson, 1997).

The analysis proceeds by first describing the statistical model used to estimate the ad-

vertising effects. The estimation results are then presented and compared to estimates ob-

tained in previous studies. The econometric estimates of advertising and price responses are

then inserted into an economic model to determine profitability and to identify optimal

spending levels across the media. The final section summarizes the main findings.

2. STATISTICAL MODEL

2.1. SpecificationThe basic model is a two-equation system as follows:

Wholesale Demand Equation:

(1a)

Price-Markup Equation:

1n WPt* = d

0+ d

11n FP

t+ d

21nMW

t+ d

31n (INV

t1/Q

t1)+

t(1b)

where Qt* is the desired per capita consumption of catfish in time period t; WP

tis the av-

erage wholesale price of processed catfish;INCtis per capita disposable personal income;

Mtis the per capita US imports of processed catfish (a substitute for farm-raised US-origin

catfish); PPt

is the price of poultry; MCIt

is an index of food marketing costs (Dunham,

1995);Ditare quarterly dummy variables to indicate seasonality in catfish demand;ZG

jtis

cumulative generic advertising expenditures for catfish in magazines (G MAG), news-

papers (G NEWS), radio (G RAD) and television (G TV); WPt

* is the desired aver-

age wholesale price of processed catfish in time period t; FPtis the pond-bank price of live

catfish;MWtis the minimum-wage rate (line workers in catfish processing plants are paid

at or slightly above the minimum wage);INVt-1

is beginning-of-month processor invento-

ries; and utand v

tare random disturbance terms. All money-denominated variables in the

model (includingMCIt

and advertising expenditures) are deflated by the Consumer Price

Index for all items (19821984 100)a

Because quantity and price measurements for catfish are taken at the processor level, (1a)

is interpreted as a derived-demand relationship. Thus, for example, an isolated increase in

ln*

ln ln ln ln lnQ a a WP a INC a M a PP a MCI

b Di c ZMAG c ZNEWS

c ZRAD c ZTV u

t t t t t t

i ti

m j jt j

m j jt j

m j jt j

m j jt t j

= + + + + +

+ + +

+ + +

= = =

= =

0 1 2 3 4 5

3

1

112

222

332

442

82 KINNUCAN AND MIAO

aA reviewer suggested that advertising expenditures should be deflated by a media cost index rather than the

CPI, arguing that this would provide a better measure of the advertising quantity. Unfortunately no reliable me-


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MCIt, a proxy for retailerscost, is expected to decrease the demand for catfish at the whole-

sale level. Equation (1a) differs from Zidack, Kinnucan, and Hatchs (1992) demand equa-

tion in that poultry price is included to test whether poultry is a substitute for catfish. In ad-

dition, advertising is specified alternatively in linear ( 1) and square-root ( ) form

rather than logarithmic form to accommodate zero observations. The square-root form im-plies diminishing marginal returns (provided the advertising elasticity is less than 0.5), and

the linear form implies increasing returns. Although increasing returns in general are not to

be expected (Simon & Arndt, 1980), in the present case expenditures in some media (e.g.,

newsprint) are so low as to suggest that the industry may be in stage 1 of the sales re-

sponse function (Forker & Ward, 1993, pp. 5455).

Synergy among media is a commonly cited phenomenon (Confer, 1992; Prasad and Ring,

1976; Smith, 1991; Speetzen, 1990). The potential for one medium to enhance the effec-

tiveness of another is taken into account by equation (1a)s log-linear and log-square root

specifications of the sales-advertising relationship. This can be seen by noting that the sec-

ond-order cross derivative 2Qt*/ZG

jtZH

jt is positive for any two media G andH. Thus,

equation (1a) implicitly treats synergy among the media as a maintained hypothesis, pro-vided the respective advertising coefficients (the c

js) are significant and positive. (For a

thorough discussion of advertising complementarity and functional form, see Kinnucan &

Fearon, 1986, pp. 99101.)

Carryover is an issue because advertising takes at least three months for its full effect to

be realized (Clarke, 1976; Leone, 1995). In their analysis, Zidack, Kinnucan, and Hatch

(1992) used a Nerlovian specification that implies a geometrically-declining lag distribu-

tion. Here we model carryover using the polynomial inverse lag (PIL) technique developed

by Mitchell and Speaker (1986). The PIL is an infinite distributed lag that subsumes the

Nerlovian lag as a special case. It is similar to the Almon procedure in that lag weights fall

on a polynomial, but it does not require specification of the lag length or endpoint con-straints.

With the PIL, theZvariables in (1a) are computed using the formula:

(2)

whereAgti

is real total expenditures in medium G and mG

is the degree of the polynomi-

al for medium Gs lag distribution. To select the degree of the polynomial, we follow

Mitchell and Speaker (1986, p. 331) and conduct nested tests by successively dropping the

highest degree terms, starting with a sixth-degree polynomial (m1

m2

m3

m4

6).

The optimal degree is determined using Akaikes Information Criterion (AIC) (Greene,

1993, p. 515), the same criterion used by Capps, Seo, and Nichols (1997) in their study of

ZG AG i G MAG NEWS RAD TV

j m

jtt

t ij

i

= + =

=

=

1

01

2

/( ) , , , ;

, . . . , G

CATFISH 83

dia cost index exists on a monthly basis. Our attempt to use a quarterly index specific to each medium proved un-

satisfactory in that most of the estimated advertising effects were insignificant, which suggested that a quarterly

indices introduced measurement error. In response to a related comment by another reviewer, we also estimated

the model with advertising expenditures divided by population. In this case, the results were robust, i.e. statistical

inference was unaffected by deflation by population. Because advertising is a type of public good (my viewing an

ad does not diminish another persons ability to see the same ad), changes in the population should not affect ad-

vertising quantity. As a consequence, we believe total (not per capita) advertising expenditures is the conceptual-

ly correct specification.


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spaghetti sauce advertising. Because a hump-shaped distribution generally requires at least

a fourth-degree polynomial (Mitchell & Speaker, 1986, p. 331), a sixth-degree polynomi-

al provides sufficient flexibility to reflect a variety of lag patterns.

The price-transmission equation (1b) is similar to Zidack, Kinnucan, and Hatchs (1992)

except that it is expressed in double-log form because subsequent analysis by Nyankori(1991) suggested this form fits the data better than a linear form. The specification is con-

sistent with the mark-up model developed by Heien (1980). The markup model implicitly

assumes that changes in the marketing margin originate from isolated (and not simultane-

ous) shifts in farm supply or wholesale demand. The isolated-shift assumption, as noted by

Lyon and Thompson (1993), is most appropriate in applications involving short-interval

(e.g., monthly) data, as is the case here. Following French and King (1986), we included an

inventory variable in the empirical specification to test for price-setting behavior. That is,

given industry concentration (Kouka, 1995), processors may have the ability to set price

based on perceived supply and demand conditions and ending inventories, at least in the

short run.

Owing to the use of monthly data to estimate the model, attention needs to be given topotential delays in consumer and producer responses to economic stimuli. For example,

consumers response to a change in the price of catfish may take several months due to

habits. Similarly, processors may be slow to pass cost changes along to consumers due to

uncertainty about whether cost changes are transitory or permanent. In this study, inertia is

modeled using Nerloves partial-adjustment model:

Qt/Q

t1= (Q

t*/Q

t1) (0 1) (3a)

WPt/WP

t1= (WP

t*/WP

t1) (0 1) (3b)

where and are elasticities of adjustment (Nerlove, 1958, p. 309) that indicate the rate

at which Qtand WP

tapproach their respective long-run equilibrium values, Q

t* and WP

t*.

In this formulation, adjustment is immediate if 1 (static model) and proceeds at

an increasingly slow pace as the adjustment elasticities approach zero. Taking the logarithm

of (3) and substituting (1) yields the estimating equations:

(4a)

(4b)

The coefficients of (4b) are interpreted as short-run elasticities. The corresponding long-

run elasticities are obtained by dividing the short-run elasticities by (one minus the co-

efficient of the lagged dependent variable). A similar interpretation applies to (4a) except

for the advertising terms, in which case the long-run coefficients are computed from the lag

weights defined as follows (Mitchell & Speaker, 1986, p. 330):

ln ln ln ln( / )

( ) ln

WP d d FP d MW d INV Q

WP

t t t t t

t t

= + + +

+ +

0 1 2 3 1 1

11

ln ln ln ln ln ln

( )

Q a a WP a INC a M a PP a MCI

b Di c ZMAG c ZNEWS

c ZRAD c ZTV

t t t t t t

i ti

m j jt j

m j jt j

m

j jt j

m

j jt j

= + + + + +

+ + +

+ + +

= = =

= =

0 1 2 3 4 5

3

1

112

222

3

32

4

42 1

lnln Q ut t +1



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(5)

where wGi

is the lag weight (coefficient) for medium G corresponding to the t i lagged

advertising term. Note that the parameters in (5) are the coefficients of the advertising vari-ables in (4a) after purging the adjustment parameter .

Advertising elasticities are computed from (5) using the formula:

(6)

where G

= 1nQ/1nAG is the advertising elasticity for medium G corresponding to a time

horizon ofTmonths.

Whether generic advertising has any detectable effect on catfish demand is tested by

forming the hypothesis:

(7a)

(7b)

Hypothesis (7) represents a test of linear zero restrictions, which can be tested with a stan-

dard F statistic (Greene, 1993, pp. 194195).

2.2. Data and Estimation Procedure

The demand equation (4a) was estimated using 130 monthly observations for the periodJanuary 1987 through October 1997, the latest available data point for all the variables. The

first eight observations are dropped to minimize truncation error associated with the PIL

technique (Mitchell & Speaker, 1986; p. 331). An additional four observations is lost due

to nonavailability of a consistent monthly series for poultry prices prior to 1987. The price-

transmission equation (4b) was estimated with 141 observations (February 1986October

1997). The first observation is lost due to the lagged dependent variable. The sample peri-

od includes five years of strictly print-media advertising (19871991), four years of com-

bined print and electronic media advertising (1992 and 19951997), and one year of strict-

ly electronic-media advertising (1994). (The industry advertising program commenced

March 1987 and no advertising was done in 1993.)The price and quantity data through December 1994 were obtained from Tables 11, 12,

14 and 17 of USDAsAquaculture Situation and Outlook Report(1994) andAquaculture

Outlook(1995). The updated data through October 1997 were obtained from David Harvey,

USDA, ERS. Data for the minimum wage rate and the CPI were obtained from the Statis-

tical Abstract of the United States (1994) and the Bureau of Labor StatisticsDetailed CPI

Report (19861996). The data for the Food Marketing Cost Index were obtained from

Howard Elitzack, USDA, ERS. The data for personal disposable income and US population

were obtained from the BLSs Survey of Current Business (19861996). The advertising

data were obtained from Kimberly Johnson of The Richards Group, the industrys adver-

tising agency. The advertising data reflect actual, not projected or budgeted, expenditures.

H H not true.A N:

HmG

N Gjjc G MAG NEWS RAD TV : ( ), ( ), ( ), ( )= =

= 0 1 2 3 42

G Giiw AG= =

= 0 1( , )

w c i iGimG

Gjj

j= + =

= / ( ) ,1 02 . . . ,

CATFISH 85


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The model was estimated using GLS.b Unless indicated otherwise, significance is deter-

mined using two-tail ttests and Ftests and thep 0.05 probability level.

2.3. Demand Estimates

The optimal degree of the polynomials, based on the AIC, was mG

2 for magazines (G

1), newsprint (G 2) and radio (G 3) and m4

4 for television. Thus, the print me-

dia and radio exhibit a geometrically declining lag distribution, whereas television shows a

hump distribution.

Ftests indicate rejection of hypothesis (7a) at thep 0.039 level for the linear model (

1, or Model A in Table 1), and at thep 0.010 level for the square-root model ( ,

or Model B in Table 1). Moreover, the hypothesis that all the media elicit the same response

is rejected atp 0.040 in both models. Testing further, the joint hypothesis that print and

electronic media elicit identical responses is rejected atp 0.025. Thus, aggregating the

media is inappropriate for these data.

Regression diagnostics indicate that the demand equation is well specified in that the er-ror terms are normally distributed and there is no evidence of parameter instability (Table

2). The BreuschGodfrey test, an appropriate statistic for a model containing a lagged de-

pendent variable (Greene, 1993, p. 428), indicates serial correlation in Model A but not

Model B. This suggests that the linear model is misspecified and thus is dropped from fur-

ther consideration. The hypothesis of homoscedasticity is rejected decisively. Accordingly,

Model B was estimated by GLS using the NeweyWest correction for heteroscedasticity

(Eviews, 1994).

Estimation results overall are satisfactory in that most coefficients are significant and

have the expected signs (Table 3). The adjustedR2 of 0.920 and the preponderance of sig-

nificant coefficients indicate that the equation provides a good fit to the data and that mul-ticollinearity is not unduly affecting results. The lagged dependent variable is significant

and the estimated coefficient lies between zero and one, as required to satisfy stability con-

ditions.

The estimated long-run own-price elasticity, which is obtained by dividing the whole-

sale-price coefficient in (4a) by one minus the coefficient of the lagged dependent variable,

is 0.706. Comparing this estimate to Zidack, Kinnucan, and Hatchs (1992) estimate of

1.01 based on 19801989 data and to Kinnucan and Wineholts (1989) estimate of1.28

based on 1980-83 data suggests catfish demand is becoming less elastic over time. A Wald

test to determine whether the long-run price elasticity is equal to 1.0 produced a 2 val-

ue of 3.30, which is not large enough to reject the null at the 5% level. Thus, the hypothe-

sis that catfish demand at wholesale is unitary elastic cannot be rejected.The estimated long-run income elasticity is 1.58 and is significantly different from zero

(2 13.72), but not one (2 1.84). Estimates for the early 1980s found the income elas-

ticity to be negative (Kinnucan & Wineholt, 1989), and for the later 1980s to be zero (Zi-

dack, Kinnucan, & Hatch, 1992). This suggests that catfish has overcome its status as an

inferior good and may now be considered a normal (but not a superior) good.c


bTechnically, it would be preferable to estimate (4a) and (4b) as a system using 3SLS. However, this is not

straightforward in the presence of serial correlation and lagged dependent variables. Because preliminary analy-

sis showed little difference between 3SLS (without correction for serial correlation) and OLS estimators, we

opted for the single-equation GLS estimators. Zidack, Kinnucan, and Hatch (1992) adopt a similar approach to

estimation.cA reviewer questioned the size of the income elasticity, arguing on intuitive grounds that it is too large. To test


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The dummy variables are significant, which suggests that catfish demand is seasonal. Thecoefficients for the dummy variables are all positive, which indicates that catfish demand

is higher in the first three quarters compared to the fourth quarter. The largest coefficient is

for the first calendar quarter, as expected since the demand for all fish, including catfish,

generally increases during the Lenten period.

The marketing cost variable is significant and negative in sign, as expected. The long-

run elasticity is 2.73, which suggests that the demand for catfish at wholesale is quite sen-

sitive to marketing costs. The effect of imports, in contrast, is modest. Although the esti-

mated coefficient is significant, the long-run elasticity is a mere 0.015. This probably

reflects imports declining and modest market share (less than 2% of processor sales in the

1990s). The estimated cross-price elasticity with respect to poultry of 0.229 is not signifi-

cant at usual probability levels.d

The estimated coefficients for advertising, the key policy variable in this study, are sig-

nificant for all media except newsprint. For television, the hypothesis that the PIL coeffi-

cients sum to zero is rejected at the p 0.007 level (2 7.61). The insignificance of

newsprint may be due to the industrys infrequent use of this medium (restricted to three

months over the sample period).

Elasticities based on the estimated PIL coefficients, computed using equations (5) and

(6), are presented in Table 4 for lengths of run ranging from three to 72 months. These elas-

ticities are evaluated at mean data points for 199297, the last 6 years in the sample. Bear-

ing in mind that the PIL coefficient for newsprint is not significant, all the elasticities with

CATFISH 87

TABLE 1. FTests of Restrictions on Advertising Coefficients

Computed F-value Probability

Model A Model B Model A Model BHypothesis (H

N) ( 1) ( ) ( 1) ( )

All advertising coefficients are zero 2.306 2.971 0.0388 0.0099(c

12 c

22 c

32j2

4 c4j

0)a

All media have same effect 2.863 3.526 0.0399 0.0172(c

12 c

22 c

32j2

4 c4j

)

Print & electronic media have same effect 3.834 4.601 0.0245 0.0120(c

12 c

22and c

32j2

4 c4j

)

aThe first subscript (i ) is defined as follows: i 1 (magazines), i 2 (newspaper), i 3 (radio), and i 4

(television). The second subscriptj is the degree of the polynominal.

this, we included a trend term and a fish price variable to see if specification error might be causing the estimate

to be upward biased. Both variables were insignificant, and the estimated income elasticity in the augmented mod-

el, while retaining its significance, was increased. The estimated long-run price and income elasticities do not dif-

fer significantly from unity, which, in light of the weak substitution effects indicated in Table 3, is consistent with

the homogeneity condition. Perhaps the increasing portion of value-added products in the quantity measure

accounts for the secular increase in the income elasticity.dIndustry growth stalled in 1992, causing speculation that low salmon prices were eroding the demand for cat-

fish. As a partial test of this, we estimated the model with a general price index for all fish (a salmon-specific price

series was unavailable), and with a trend variable. Neither variable was significant, which suggests that other fac-

tors may be at work. One possibility is the rise in the real price of catfish at wholesale from $1.35 per pound in

January 1992 to $1.56 in January 1995, which suggests that the slowed growth is due to movements along the de-

mand curve rather than shifts in the curve. This interpretation is supported by the fact that industry growth resumed(albeit modestly) in 1995 as the real price declined to $1.51 in January 1996 and to $1.43 in January 1997.


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the exception of television are consistent with a priori expectations. Specifically, the 3-month elasticities differ little from the longer-run elasticities, which suggests rapid decay.

This is consistent with Clarkes finding that 95% of the cumulative effect of advertising for

frequently purchased, low-cost mature products occurs within 3 9 months of the initial ex-

penditure (see also Leone, 1995). Moreover, the elasticities themselves are modest, with the

long-run estimates ranging from 0.0204 for radio and 0.0244 for magazines to 0.0614 (in-

significant) for newsprint. These are well within the range reported in the literature (Fer-

rero et al., 1996).

The unexpected result is for television. The point estimate of the advertising elasticity

for all lengths of run is negative. The reason is that the first and third PIL coefficients are

negative and of sufficient size collectively to dominate the positive middle coefficient (see

Table 3). To determine whether this pattern is robust, alternative specifications were con-sidered, including a time-varying parameter specification to test for structural change in the

television advertising response. (Structural change was suspected because the advertising

agency adjusted the commercials over the sample period in an attempt to boost effective-

ness as measured by tracking data.) Nothing changed the pattern, including respecification

with a Nerlovian lag and alternative functional forms. Conversations with the advertising

agency revealed internal data that indicated a spike in catfish cookbook requests coincid-

ing with the television advertising. Attempts to incorporate these data into the model only

accentuated the pattern. Multicollinearity as a potential culprit was ruled out due to the rel-

atively low correlation (r2 0.40) among the media variables and the relatively large tra-

tios (2.79 or larger in absolute value) for the individual PIL coefficients.Further analysis revealed that the point estimates of the television elasticity are highly

sensitive to the numerical values of individual polynomial terms. Accordingly, a confidence


TABLE 2. Regression Diagnostics

Demand Equation

Model A Model BMarkup Equation

Test ( 1)a ( )a Model C Model Db

p - value

Serial Correlation:Breusch-Godfrey 0.0271 0.0601 0.0000 0.0000

Heteroscedasticity:White 0.0025 0.0040 0.0071 0.0166

Normality:Jarque-Bera 0.4254 0.3971 0.0381 0.1123

Parameter Stability:Ramsey RESET 1 0.3213 0.4118 0.6443 0.2434Ramsey RESET 2 c c 0.1757 0.4977

CUSUM 1d

1.000 1.000 0.8298 1.000CUSUM 2d 1.000 1.000 1.000 1.000

Note: Tests performed using the econometric packageEViews.a 1 and denote that advertising variables are expressed, respectively, in linear and square-root forms.bIncludes a binary variable to indicate structural change for the 19951997 period.cCould not be computed due to near singular matrix.dProportion of observations inside the 5% confidence band.


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interval for the elasticity was estimated using a bootstrap procedure. Specifically, the PIL

weights for television (see (5)) were computed using the stochastic equations:

w4i

=y/(i + 1)j i = 0,. . . , 72 (5a)

y = c42

+ c43

+ c44

+ s.e.(c42

)*NRND+ s.e.(c43

)NRND

+ s.e.(c44

)*NRND (5b)

where c4j

(j 2, 3, 4) are the estimated coefficients for ZTVj given in Table 3 divided by

one minus the estimated coefficient of the lagged dependent variable (to purge ); the s.e.

CATFISH 89

TABLE 3. GLS Estimates of Wholesale Demand and Price Markup Functions for Catfish,United States, 19861997 Monthly Data

Demand Equation Markup Equation

Variables Coefficient t-ratio Coefficient t-ratio

Constant 10.4167 4.27 2.699 9.54Q1 0.1788 12.14 Q2 0.0508 3.71 Q3 0.0590 4.35 Wholesale Pricea 0.4051 4.71

(0.706)b

Consumer Incomea 0.9060 3.52 (1.579)

Marketing Cost Indexa 1.5661 3.57 (2.730)

Catfish Importsa 0.0087 1.30 (0.015)

Poultry Pricea

0.1313 1.47 (0.229)Lagged quantitya 0.4264 10.52

ZMAG2 8.93E-05 2.58

ZNEWS2 9.18E-06 0.12

ZRAD2 0.000105 2.16

ZTV2 0.003519 3.09

ZTV3 0.011254 2.89

ZTV4 0.007891 2.79

Farm Pricea 0.4234 11.70(0.633)

Minimum Wage

a

0.0484 1.28(0.072)Processor Inventorya 0.0237 3.41

(0.035)Lagged Wholesale Pricea 0.3308 6.79D9597 0.0222 4.59t1

0.2793 2.92t2

0.3555 3.42

R2 0.920 0.982

AdjustedR2 0.910 0.981

F-statistic 87.556 1026.899

Prob(F-statistic) 0.000000 0.000000

Number of Observations 130 141 aExpressed in natural logarithms, see text equations (4a) and (4b).bNumber in parentheses is the long-run elasticity.


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are the corresponding standard errors; and NRND is a normal random variable with zeromean and unit variance. Values for NRND were obtained using the generator function for

the standard unit normal distribution inEViews. Equations (5) were substituted into (6) and

solved 2,000 times to generate a sample of 2,000 elasticity values. The mean elasticities

from this sample and corresponding standard deviation are reported in the last column of

Table 4. Although the bootstrapped point estimates are negative as before, the 95% confi-

dence intervals include zero. Thus, we conclude that the estimated television effect is un-

reliable and thus is treated as zero.

The insignificant effect for television is consistent with Kinnucan and Thomass (1997)

findings based on earlier data, which showed television and radio advertising, when com-

bined, to have a minuscule effect on catfish demand (long-run advertising elasticity of

0.00024, see Table 5). It is also consistent with the fact that the industry dropped televisionfrom its media mix in 1998 (Allen, 1998). Although some have questioned television ad-

vertisings ability to increase sales in general (e.g., Tellis and Weiss, 1995), our interpreta-

tion is that the catfish industrys media budget (about $2 million per year) was simply un-

equal to the task, i.e., scale effects are important for this medium.e

2.4. Markup Equation

Turning to the markup equation, testing based on the CUSUM test indicated parameter in-

stability in the original specification, with an apparent structural change occurring in late

1995. Accordingly, equation (4b) (Model C in Table 2) was augmented with a dummy vari-ableD9597that assumes the value of zero for the period prior to September 1995 and one

afterwards. The augmented model (Model D) passed the CUSUM tests and the JarqueBera

test for normality (Table 2). However, the model still showed evidence of both serial

correlation and heterocscedasticity. Accordingly, Model D was estimated with Whites het-

eroscedasticity correction and correction for first- and second-order serial correlation.

Estimation results are satisfactory in that the model has an adjusted R2 of 0.981 and


TABLE 4. Estimated Advertising Elasticities Based on PIL Coefficients

Television

Time Horizon Magazines Newspapera Radio Point Estimate Bootstrapped

3 months 0.02033 0.05121 0.01955 0.0790 0.0407(0.415)b

12 months 0.02338 0.05888 0.02021 0.1010 0.0814(0.415)

15 months 0.02396 0.06035 0.02029 0.1042 0.0982(0.412)

72 months 0.02437 0.06137 0.02038 0.1074 0.1098(0.412)

aNot statistically significant.bNumber in parentheses is the standard deviation from a bootstrapped sample of 2,000. See text for details.

eAn alternative hypothesis, suggested by a reviewer, is that the creative approach or strategic aspect of the tele-

vision campaign was faulty, not the medium per se. That is, perhaps with a different set of commercials, or a dif-

ferent target audience, television could be an effective medium for catfish. Although we admit this possibility, with

such a limited budget to mount a national campaign, and given the robustness of the estimated effects for maga-zine advertising (see Table 5), prudence would appear to dictate continuing the magazine campaign, especially

because the medium is underfunded to begin with.


11/19

coefficients are significant with the expected sign. The estimated coefficient of the lagged

dependent variable is between zero and one, as required to satisfy stability conditions.

The estimated coefficient for minimum wage is positive, as expected, and statisticallysignificant according to a one-tail test. However, the long-run elasticity is modest (0.072),

which suggests that increases in minimum wage rate have only a modest effect on the

wholesale price. The estimated coefficient for the processor inventory variable is negative,

meaning that inventory accumulation induces processors to lower the wholesale price,

ceteris paribus. However, the long-run elasticity for inventory is tiny (0.035), which

suggests that inventory plays a relatively minor role in processor pricing decisions. This is

consistent with Zidack et al.s findings.

The dummy variable to indicate structural change is highly significant (t-ratio of4.59)

and the estimated coefficient has a negative sign. This suggests a generalized lowering of

the farmwholesale price spread in the more recent period, perhaps due to economies of

scale associated with industry restructuring. The number of processing plants declined froma peak of 37 in 1990 to 25 in 1994 (Moore, 1994).

The estimated long-run price transmission elasticity, the parameter of key interest in this

study, is 0.63. This estimate is similar to Zidack, Kinnucan, and Hatchs (1992) estimate of

0.68, which suggests that the transmission elasticity is stable over time. Asummary of elas-

ticity estimates for catfish is provided in Table 5.

3. ECONOMIC ANALYSIS

3.1. Marginal Returns

Net marginal returns are measured using the following formulas developed by Kinnucan

and Thomas:

CATFISH 91

TABLE 5. Comparisons of Estimated Price, Income, Price-Transmission and AdvertisingElasticities for Catfish Across Studies

Price Income Price Trans. AdvertisingAuthor Time Period Elasticity Elasticity Elasticity Elasticity

Kinnucan & Wineholt 19801983 1.28 Negative 0.29 N.A.Kinnucan & June 1988 N.A. N.S. N.A. PositiveVenkateswaran (survey data)

Zidack, Kinnucan 19801989 1.01 N.S. 0.68 0.0075a

& HatchKinnucan (1995) 19861993 0.32 N.A. 0.41 0.0066b

Kinnucan & Thomasa 19861994 0.873 2.19 0.64 0.0093c

0.00024d

This Study 19871997 0.706 1.58 0.63 0.0244a

0.0000e

0.0204f

0.0000g

Note: N.A. not available or not applicable; N.S. means not significantaMagazines.bMagazines, newspapers, and radio combined.cMagazines and newspapers combined.dRadio and television combined.eNewsprint.fRadio.gTelevision.


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MRRGF = {(

GPfX)/[A

G( + )]} (8a)

MRRGV = {(

GPfX)/[A

G( + + (1))]} (8b)

whereMRRGF

andMRRGV

represent the marginal return for medium G under Leontief andCobbDouglas aggregate marketing technologies, respectively. A Leontief technology im-

plies that middlemen cannot substitute marketing inputs for the farm-based input in re-

sponse to an advertising-induced increase in the relative price of the farm-based input;

CobbDouglas technology implies that input substitution is possible and that the Hicks

Allen substitution elasticity () is unitary (Kinnucan, 1997). These two scenarios are as-

sumed to represent polar substitution possibilities in the catfish processing sector.

The G

in (8a) and (8b) are advertising elasticities corresponding to medium G (G

1,2,3, 4 for magazines, newspapers, radio, and television, respectively); Pf

is the farm price

of catfish;Xis farm quantity; AG

is advertising expenditure in the Gth medium; is the

farm-level supply elasticity; is the farm-wholesale price-transmission elasticity; is the

absolute value of the wholesale-level demand elasticity; and represents the producer in-cidence of the promotion levy. The catfish advertising program is funded by a voluntary as-

sessment on catfish feed, a portion of which is shifted to producers depending on the elas-

ticities of supply and demand for feed (Chang & Kinnucan, 1991). In this study, we assume

that incidence is bounded between 0.5 and 1.0, i.e., at least 50% of the assessment is shift-

ed from feed mills to producers.

Equations (8a) and (8b) assume competitive market clearing, an isolated market, and a

closed-economy with respect to the advertised good. Although the assumption of compet-

itive market clearing may be questioned due to industry concentration at the processor lev-

el (Kouka, 1995; Nyankori, 1991) and price bargaining at the farm level, it appears that mar-

ket power is too weak for market prices to deviate significantly from competitive levels forany length of time (Kinnucan, 1995). The assumption of an isolated market is justified in

that catfish represents such a tiny portion of total consumer expenditures, even in the fish

group, that spillover effects are apt to be minor.

Perhaps least defensible is the closed-economy assumption in that imports are a factor in

the catfish market. However, in recent years imports have declined to less than 2% of

processor sales (USDA, ERS, 1995). This fact, coupled with the fact that the US is a large-

nation trader with respect to catfish, suggests that imports can be safely treated as exoge-

nous.

Notice from (8a) and (8b) that marginal returns under either technology can be positive,

zero, or negative depending on the relative magnitude of the terms in braces and the inci-

dence parameter. For example, if the Gth medium is ineffectual, as appears to be the casefor newspapers and television, then

2

4 0 andMRR

GF MRR

GV (G 2,

4), which means producers suffer a marginal loss for these two media equal to the incidence

parameter.

Equations (8a) and (8b) represent the marginal rate of return (MRR) to the Gth medium,

i.e., the increase in net producer surplus associated with the lastdollar invested. The MRR

is not to be confused with the average rate of return (ARR), which measures the rate of re-

turn for every dollar invested. Because the MRR is always less than the ARR if advertising

expenditure is in the profitable range i.e., in stage 2 of the sales-response function, the

MRR provides a lower-boundestimate of the ARR.

Another important distinction is that (8a) and (8b) represent the netreturn, i.e., the mar-ginal return after subtracting the incremental advertising cost. It is not to be confused with



13/19

the gross rate of return, sometimes called the marginal benefitcost ratio (BCR), which

measures the rate of return before subtracting incremental advertising cost. Because BCRs

must exceed one (BCR 1) to indicate profitability, whereas MRRs need simply to exceed

zero (MRR 0), care must be taken when comparing advertising rates of return across

studies.Bearing in mind the foregoing assumptions and caveats, (8a) and (8b) were used to sim-

ulate the marginal returns to catfish advertising using the baseline values for price and

quantity and parameter values given in Table 6. The price of $0.728 per pound is the aver-

age nominal price received by catfish producers for the period 19921997, and the quanti-

ty of 2,759 million pounds is the total industry output of live catfish over this 6-year time

horizon. Thus, returns are to be interpreted as long run. However, to highlight the sensi-

tivity of results to supply response, two sets of simulations are provided, one with the sup-

ply elasticity set to zero, and another with the supply elasticity set to 0.73. These elastici-

ties correspond to Zidack, Kinnucan, and Hatchs (1992) short-run (12 month) and long-run

(32 months and beyond) estimates of supply response in the catfish industry.

The advertising elasticities for magazines and radio are set to their long-run (72-month)values given in Table 6. The elasticities for newspapers and television are set to zero, as the

estimates for these media are insignificant or unreliable.

The incidence parameter is set alternatively to 0.5 and 1.0. The latter value implies that

producers bear the full burden of the advertising levy, an extreme but conservative as-

sumption from the standpoint of benefit measurement.

For media showing a positive demand response (magazines and radio), marginal returns

are uniformly positive, indicating that advertising in these media was profitable for pro-

ducers (Table 7). That is, the increases in demand associated with magazine and radio ad-

vertising were of sufficient magnitude to compensate for cost. Magazines, the medium ac-

counting for the largest budget share (44%), generated marginal returns of between $22 and$27 in the short run to between $8.78 and $10.05 in the long run. The upper limits of these

ranges correspond to a fixed-proportions marketing technology scenario with 50% of the

advertising cost shared with feed mills.

CATFISH 93

TABLE 6. Model Parameters and Baseline Values, US Catfish Industry, 19921997

Item Definition Value

Pf

Farm price, dollars per pound 0.728

X Farm quantity, million liveweight pounds 2,759A

1Magazine advertising, million dollars 4.001

A2 Newspaper advertising, million dollars 0.229A

3Radio advertising, million dollars 1.893

A4

Television advertising, million dollars 3.032A

TTotal advertising, million dollars 9.155

1

Magazine elasticity 0.024732

Newspaper elasticity 0.000003

Radio elasticity 0.020384

Television elasticity 0.00000 Supply elasticity 0.73 Demand elasticity (absolute value) 0.71 Farm-wholesale price transmission elasticity 0.63 Input substitution elasticity 0.0, 1.0 Farmers share of advertising levy 0.50, 1.00 Opportunity cost of advertising funds 0.0, 0.05, 0.10, 0.20


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Marginal returns to radio advertising range from $33 to $48 in the short run to between

$14.75 and $17.87 in the long run. The higher marginal returns for radio advertising are due

to the lower investment level (21% of the budget), and not to greater consumer respon-

siveness to this medium, as the advertising elasticity for radio (0.0204) is smaller than for

magazines (0.0247). Because industry profits are maximized when marginal returns are

equated across media, the higher marginal returns for radio simply means that industry prof-

its would have been higher if relatively more funds had been spent on radio advertising andrelatively less on the other media, including magazines.

Newspaper and television advertising, which were ineffectual according to the econo-

metric results, generated negative returns equal to the degree of tax shifting. For example,

if tax shifting is complete so that feed mills pass the entire levy onto producers, the pro-

ducer loss is dollar for dollar and MRR 1.0. Conversely, if producers and feed mills

share equally in the levy, producer loss from newspaper and television advertising is limit-

ed to the producer cost share and MRR 0.5.

An overall measure of profitability can be developed by taking a weighted average of the

returns from each medium with weights corresponding to media budget shares. Thanks to

the large budget share for magazines (44%) and the high marginal returns to radio, gains

from these two media are sufficient to offset losses from newspaper and television, yield-ing a positive return for the total program (Table 7). The highest overall marginal return

($22) occurs when processing technology is fixed proportions, feed mills absorb half the

levy, and supply is fixed ( 0). If supply is upward sloping ( 0.73), and the other con-

ditions are held constant, the top return drops to $7.91, which underscores the importance

supply response. If producers bear all advertising costs and supply is upward sloping, net

returns decline to $7.41 under fixed proportions and to $6.53 under variable proportions,

smaller but still highly favorable rates of return.

Taking the range of estimates ($6.53$7.91) corresponding to 0.73, a best guess re-

turn for 19921997 can be obtained by taking the midpoint of this range, which is $7.22.

This means that the lastdollar invested in catfish advertising added $7.22 in net producersurplus at the farm level. For comparative purposes, Reberte, Schmit and Kaiser (1996) es-


TABLE 7. Media-Specific Returns Under Fixed- and Variable-Proportions ProcessingTechnology with Partial ( 0.50) and Full ( 1.00) Advertising Cost Shifting,U.S. Catfish Industry, 19921997

BudgetFixed Proportions Variable Proportions

Medium Share 0.5 1.0 0.5 1.0Short Run ( 0.0) Net Marginal ReturnMagazines 0.437 27.25 26.75 22.50 22.00Newspapers 0.025 0.50 1.00 0.50 1.00Radio 0.207 47.84 47.34 33.14 32.64Television 0.331 0.50 1.00 0.50 1.00Alla 1.000 21.63 21.13 16.51 16.01

Long Run ( 0.73)Magazines 0.437 10.05 9.55 9.28 8.78Newspapers 0.025 0.50 1.00 0.50 1.00Radio 0.207 17.87 17.37 15.25 14.75Television 0.331 0.50 1.00 0.50 1.00

Alla 1.000 7.91 7.41 7.03 6.53aBudget share weighted average of the marginal returns in preceding rows.


15/19

timate a net marginal return to national egg advertising of $3.69. Since the average return

is greater than the marginal return when spending is in the profitable range, this means that

advertising returned to catfish producers is at least7.22 times the total spent over the 6-year

period. Specifically, according to these estimates, the industrys advertising expenditure of

$9.2 million over the 6-year period 19921997 generated at least$66.4 million in net pro-ducer surplus. This is equivalent to an increase in the farm price of 2.4 cents per pound.

One reason that the marginal return is high is that the program is voluntary. Voluntary

programs encourage free riding, which undermines the industrys ability to fund the pro-

gram at the economic optimum. Since the marginal return by definition decreases to zero

as the advertising expenditure approaches the optimum, caution is required in comparing

marginal returns across industries, as the differing rates of return may merely reflect

differences in advertising intensity.

3.2. Optimal Expenditures

With an unlimited budget, optimal advertising in each medium occurs where marginalreturn equals opportunity cost, i.e.,

MRRG

= (9)

where is the interest rate that could be earned on the next best use of the advertising funds.

Substituting (8a) and (8b) into (9) and solving forAG

yields:

AGF= (

GPfX)/[ + )( + )] (10a)

AGV= (

GPfX)/[( + + (1 ))( + )] (10b)

where AGF and A

GV represent, respectively, the optimal expenditure in the Gth medium

under fixed and variable proportions.

To implement (10a) and (10b), the opportunity cost of advertising funds in this study is

assumed to have an upper bound of 0.20, which implies that the next-best use of the funds

CATFISH 95

TABLE 8. Optimal Advertising Expenditures By Medium for Alternative Valuesof the Opportunity Cost (), Incidence () and Technology () Parameters,U.S. Catfish Industry, 19921997

Magazines Radio

Item 0 1 0 1 0.50 Ratio of Optimal to Actuala

0.0 21.1 16.1 36.8 28.0 0.05 19.2 14.6 33.4 25.4 0.10 17.6 13.4 30.7 23.3 0.20 15.1 11.5 26.3 20.0

1.00 0.0 10.6 8.0 18.4 14.0 0.05 10.1 7.7 17.5 13.3 0.10 9.6 7.3 16.7 12.7 0.20 8.8 6.7 15.3 11.7

a

Simulations assume 0.71 and 0.73. Actual expenditures are given in Table 5. Optimal investment levelsfor newspaper and television are zero owing to insignificant or unreliable advertising elasticities for these media.


16/19

(e.g., public relations, export promotion, investment in the farm business) could fetch an

annual rate of return of at most 20%. For comparative purposes, simulations were also

performed with set to zero, 0.05 and 0.10.

Simulations of (10a) and (10b) indicate that investments in magazine and radio adver-

tising were suboptimal in that higher spending would have resulted in larger profit (Table8). The degree of underfunding is relatively insensitive to opportunity cost, but highly sen-

sitive to tax shifting and processing technology. However, even in the most conservative

scenario (opportunity cost is 20%, incidence is 100%, and processing technology is vari-

able proportions), to maximize profit the investment in magazines would need to be in-

creased by a factor of 6.7, and in radio by a factor of 11.7. Again, the large increase called

for in radio advertising is due to its relatively low base ($1.89 million) and the consequent

high marginal return. Investment increases of this magnitude would almost certainly cause

the advertising elasticities to decline. Thus, the indicated optima are properly interpreted as

upper-bound estimates. Owing to the unreliable or insignificant advertising elasticities for

television and newspapers, the optimal investment for these media is zero.

3.3 Optimal Media Allocation

Equations (10a) and (10b) indicate the optimal expenditure in the various media if unlim-

ited funds are available. In reality the funds are limited, so the best allocation occurs where

the marginal returns are equated. That is, for any two media KandL, industry profits are

maximized in a limited-budget situation when

MRRK

=MRRL

(11)

Substituting (8a) and (8b) into (11) and solving for advertising yields:

AK*/A

L* =

K/

L(12)

whereAK* andA

L* refer to expenditure levels in the Kth andLth medium that maximize

producer profits. Notice that all that matters in the allocation decision is the relative mag-

nitudes of the advertising elasticities. Structural information, such as the price responsive-

ness of producers and consumers, is irrelevant when choice is constrained.

Letting K 1 for magazine advertising andL 3 for radio advertising, the optimal ra-

tio of magazine to radio advertising is A1*/A

3* =

1/

3= 0.02473/0.02038 = 1.21, which

means that magazines should receive 1.2 times the investment as radio. The actual ratio of

magazine to radio advertising for 19921997 was 2.1:1. Thus, it appears that industry prof-its could have been higher if relatively more funds had been invested in radio advertising,

relatively less in magazine advertising, and nothing at all in newspaper and television.

4. CONCLUDING COMMENTS

A basic theme of this article is that farm-level returns to generic advertising depend not only

on the size of the demand shift associated with the advertising but also on structural ele-

ments such as supply response, processor technology, markup behavior, consumer sensi-

tivity to price, the advertising tax incidence, and opportunity cost. All of these factors

have to be taken into account simultaneously when determining whether generic advertis-ing is profitable, and in determining optimal investment levels.



17/19

A related theme is that consumer responses to generic advertising are likely to differ

across media. Testing for these differences, therefore, is an important step toward improved

advertising benefitcost analysis. In the case of catfish, the hypothesis that all media (mag-

azine, newspaper, radio, and television) elicit identical responses is rejected, which implies

that combining the media would have created a biased estimate of the demand shift. Theestimated media-specific effects, moreover, differed significantly, with magazines and

radio showing a positive response, newspaper no response, and television a negative (but

unreliable) response. Incorporating these results into an economic model, we found that pro-

ducer returns from the total advertising program were positive, but that a different media

mix would have resulted in larger profits.

As demonstrated in this case study, econometric analysis can serve as a useful adjunct to

other evaluation tools, such as agency tracking studies, in assessing media effectiveness and

in providing guidance for allocation decisions. In addition to providing scientific evidence

on what works in the campaign and what does not work, the econometric analysis yields,

as a byproduct, estimates of key economic parameters (e.g., price and advertising elastici-

ties) that govern advertising profitability and optimal investment decisions.Armed with this knowledge, promotion board managers can improve program perfor-

mance through the application of equimarginal principles from economic theory. In the case

of media allocation, this means allotting the fixed promotion budget among the media so

that the last dollar invested yields the same return across all the media. In terms of adver-

tising elasticities, this principle reduces to allocating the budget in proportion to the esti-

mated elasticities. For example, if consumers are equally responsive to all media, then the

budget should be allocated among the media equally. Alternatively, if the advertising elas-

ticity for mediumXis twice as large as for medium Y, then mediumXshould receive twice

the budget allocation as medium Y. These rules assume a fixed budget. If the budget is un-

limited, the allocation should be made so that the marginal return from each medium equalsthe opportunity cost of the total advertising program. Because opportunity cost, and indeed

the advertising elasticities themselves, are likely to differ across commodities, the optimal

media allocation ultimately must be determined on a case-by-case basis. Still, the methods

and principles elucidated in this study apply across all commodities and thus provide a gen-

eral framework for identifying the optimal media mix.

5. ACKNOWLEDGMENTS

Appreciation is expressed to Howard Elitzak, David Harvey, Kimberly Johnson, Max

Runge, and Hui Xiao for assistance with data collection; to Bill Allen of The Catfish Insti-

tute for making the advertising data available; and to Robert N. Nelson and four anonymousjournal reviewers for providing helpful comments on earlier drafts of the manuscript. Funds

supporting this research were provided in part by the National Institute for Commodity Pro-

motion and Research, Cornell University. Responsibility for final content, however, rests

strictly with the authors.

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Henry W. Kinnucan is a professor in the Department of Agricultural Economics and Rural Sociol-

ogy, Auburn University. He earned a M.S. and Ph.D. from the University of Minnesota. His current

research interests include agricultural marketing, benefitcost analysis, and generic advertising.

Yuliang Miao is a graduate research assistant in the Department of Agricultural Economics and Rur-

al Sociology, Auburn University. He earned a M.S. from the China Agricultural University. His cur-

rent research interests include demand analysis and generic advertising.

CATFISH 99

Case of Catfish

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