In double columns.Includes bibliographical references

Johansson, Johny K.

Redinger, Robert

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A path analysis model of the advertising-sales relationship / 201

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Faculty Working Papers
A PATH ANALYSIS MODEL OF THE
ADVERTISING -SALES RELATIONSHIP
Johny K. Johansson
and
Robert Redinger
#201
I
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign

FACULTY WORKING PAPERS
College of Commerce and Business Administration
University of Illinois at Urbana -Champaign
August 26, 1074
A PATH ANALYSIS MODEL OF THE
ADVERTISING -SALES RELATIONSHIP
Johny K. Johansson
and
Robert Redinger
#201
:-
:
J
A PATH ANALYSIS MODF.L OF THE ADVERTISING-SALES RELATIONSHIP
Johny K. Johansson, University of Illinois
Robert Redingcr (student). University of Illinois
ABSTRACT
On the basis of the most commonly used mechanism link-
ing advertising and sales— the so-called hierarchy of
effects paradigm— the usual multiple equation modeis
are contrasted with a path analysis model. The path
analysis approach takes causal lags explicitly into
account, and allows for direct effects as well as
indirect effects—channeled through an intermediate
variable—of advertising upon sales. This is espe-
cially valuable for a correct representation of tne
hierarchy of effects framework as is shown in an
empirical example
.
INTRODUCTION
Several approaches to the measurement of the strength
of the advertising and sales relationship have been
presented in the literature. The earliest efforts
took the form of single equation regression models,
with some explanatory variables, such as season,
introduced in addition to advertising. An improvement
over this simple approach was the introduction of
explicit distributed lags, on the basis that there are
theoretical reasons to assume that advertising has
effects that extend over time. The latest development
is the use of recursive and simultaneous equation
models which take into account the fact that advertis-
ing decision rules often incorporate sales as one
determinant.
Another approach, so far not tried in advertising-sales
research, is path analysis. Developed in sociology
for the analysis of complex interrelationships between
explanatory and dependent variables, its aim is the
exact, portrayal of the causal links and their strength
between the various variables. Since one of the basic
mechanisms proposed as a mediator between advertising
and sales— the so-called hierarchy of effects
paradigm—comprines such a system of complex interre-
lationships, it seems appropriate to apply the path
analysis approach to the disentangling of the causal
links connecting advertising to sales.
After a presentation of the fundamentals of path
analysis, the paper compares the technique briefly
with the more common techniques in advertising
research. Then an empirical application to advertis-
ing's effect upon market share (as a proxy for sales)
and the linkages in the hierarchy is presented.
THE PATH ANALYSIS MODEL
The Basic Model
Several excellent presentations of the basic pith
analysis model exists in the literature. Thus,
although no application has yet to our knowledge boon
made to the advertising effects issue, only a bri<_f
overview of the model will be fi^n here. It La drawn
mainly from Van do. Ccer [6] who also lists thf basic
references.
Assume we have a set of four variables, x^, 1*1,2,3,
and y. Our theory tells us that x^ and X2 are inde-
pendent of the other two variables and of each other.
Similarly, our a priori notion is that X3 is determined
by x^ and :<2, and in turn determines y. The y values,
however, are also directly dependent upon xj_. Thus, we
have the following two-equation system
x
3
- b 3lXl + b 32
x
2
+ e
3
y " VX1 + by3X3 + ey
(1)
(2)
where the relations are assumed to be linear, the
intercept terms vanish on the assumption that we use
standardized variables, and the e's represent equation
error terms. Let us now interpret these errors as
occurring because of unobserved or "latent" determining
factors u3 and uv , respectively. Then the system can
be written
x = b x. + b x + b„ u,
3 31 1 32 2 3u 3
y b ,x, + b _x, + b u
' yl 1 y3 3 yu y
(3)
(4)
The u's are assumed independent of each other and of x^
and *2*
The basic problem in path analysis is to find the
weights b which describe the causal "paths" from the
determining factors to the "dependent" or "endogeneous"
variable y. The solution starts with the computation
of the simple correlation coefficients (the r's)
between all the variables. With the variables stan-
dardized we recognize that the variance of, say y, can
be written
V(y) = yy (5)
and the expectation of cros3-product terms becomes, for
example
,
COV(y, Xl ) =» y Xl = r , (6)
where the variables are represented as observation vec-
tors of order n.
If we now premultiply equation (3) by x3 we get
1
"
b
31
r
31
+ b
32
r
32
+ b
3u
r
3u
13)
Then premultiplyinf, by x^ we have
r
13 "
b
31
+ b
32
r
l2
and finally by x<> we derive
'23 b 3i
r
2l +
b 32"
(7)
(8)
(9)
We have rhen three equations for our desired b's—but
since also r^ is unknown, one more relationship is
necessary in order to derive the e3timate3. This last
equation is generated bv a preraultiplication of (3i by
113, which gives
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r, - b, . (10)3u 3u
This last relation eliminates one unknown, and the
three equations can be solved tor the three b's.
In a similar fashion the estimates for the second
relation (4) can be derived. Since the principles an"
thtf same, no further discussion will be presented
here. The interested reader is referred to the Van de
Geer reference [6j.
although it should properly be viewed as different sim-
ple lags for different measures. In the application of
the path analysis presented below, a polynomial distri-
buted lag approach is followed rather than the usual
Koyck model [5]. In the estimation runs made to choose
the appropriate lag, some efforts were made to account
for such simple lags, but no conclusive evidence
emerged supporting i leir existence. Since the majority
of the literature in the area supports a distributed
lag approach, we followed their stance for the present
paper.
Relationship to Other Techniques
A brief account of the relations between path analysis
and other techniques will be of interest in evaluating
the potential of oath analysis. Clearly, the approach
provides much stronger a priori specification as com-
pared to many other multivariate techniques. Accord-
ingly, it is closer to econometric techniques than to
much of behavioral statistics. The model encompassed
by equations (1) and (2) can clearly be seer, as a
recursive system, estimable by the usual least squares
techniques. The difference between path analysis and
recursive systems is in fact small, and consists
mainly of the more explicit consideration of indirect
effects upon an endogeneous variable offered by the
path analysis. For example, the linkage between y and
x? might seem nonexistent if only equation (2) is
evaluated, whereas the indirect effect of X2 via x-j
might in fact be great—in path analysis, the total
impect of an earlier variable upon a later one is
simply determined by a summation of the separated
indirect and direct effects. Tnus, the effect of x^
upon y in system (3) and (4) is computed as byj +
by3*b3i. Again, however, the recursive system con-
tains the same basic information, althcuph not as
cle rly articulated.
.The path analysis does not allow two-way causal direc-
tions between endogeneous variables. The causation
can flow from one endogeneous variable to the next,
and, over time, there can be feedback from one to the
other, but contemporaneous loops are ruled cut. For
this reason, path analysis offers no help with simul-
taneous systems. As i.^. well known, the simultaneity
is often a reasonable approximation of the advertising-
sales relationship [1] and where that is the case path
analysis is inappropriate. The problem hinges ulti-
mately on the specification or the ''error" terms or
"unobserved" variables and is thus connected with the
identification problem. No exhaustive treatment can
be given here, but the rtle of Identifying predeter-
mined variables should be pointed out. In the path
analysis model, it suffices often to have ere single
exogeneous variable which will guide the whole system.
When the appropriate model is Pinuitaneous, several
exogeneous variables are needed to identify the separ-
ate causal relations. The interested reader is
referred to Blaiock's treatment [2].
Since much research into the advertising-sales rela-
tionship has utilized a distributed lag approach, a
brief comment is warranted. The appropriateness of a
distributed lag model is in most respects independent
of which of the earlier models are chosen. It is only
when the distributed lag affects Lhe causal links in
the system that care has to bo exercised. Thus, for
example, it might be that advertising has an immediate
effect upon customers awareness, and after some time
will affect other cognitive structures, such as HkinR,
and after some further time has pan ,:d it will finally
reach purchase behavior. Such a process
—
partially
Incorporated Into ti.e so-caLlou hierarchy—of-effects
paradigm [3]~mlght appear as a distributed lag effect
AN EMPIRICAL APPLICATION
The Data
An empirical application of the path analysis model to
the advertising-sales relationship is presented here.
The data used come from [4] where an extensive discus-
sion of the original source can be found. In brief,
monthly observations of total brand advertising (in
dollars) and repeated survey data on the brands are
available. The 9urvey questions were directed to about
600 product users--the product used here is hair
spray—and covered their brand awareness, liking, and
preferences, as well as brand trial, last and repeat
purchases. From the response frequencies we derived
the different indicators as sample proportions of heavy
users. The variables used, besides advertising , are
the proportion of heavy users aware of the brand, the
proportion liking it, the proportion rating the brand
higher than or as high as any other brand (acceptance),
the proportion rating the brand higher than any other
brand ( preferenc e) , and the proportion buying the brand
last time (purchase ) . This last measure standi for a
type of "market share among heavy users" variable in
this particular application, and represents our sales
measure. Thirteen monthly data points were available
for each brand.
Tne Models
The path analysis ap roach was used to formulate two
alternative causal structures linking the variables.
In both, advertising was seen as exogeneous, not
determined by the other variables, including purchases.
This assumption was based upon the short time span
involved, allowing no feedback into Che next period's
advertising decision making. The hierarchy variables,
excepting purchases, were all seen as simultaneously
determined, since the survey questionnaire literally
forced such simultaneity (by directing all questions
about the hierarchy variables to the present situation).
Purchase, on the other hand, was seen as determined by
lagged hierarchical variables, since the "present" pur-
chase in fact was the one made last time. To acco
for the possibility of a feedback from purchase to Che
hierarchy, one alternative model incorporated the last
period's purchases as a predetermined variable in addi-
tion to the advertising.
The lagged effects of advertising were incorporated by
using polynomial distributed lags. The particular form
of the lag was chosen after several alternatives had
been tried [4]. It incorporated two constraints,
effectively setting the impact of advertising to ?
after five periods. With the constraints, the ad\<
tistng variable became simply a moving average of live
periods, with weights 1.0, 8/5, 9/5, 8/5, and 1.0. T.ie
maximum impact from advertising occurs accordingly in
period t-2, or two months after insertion.

In addition to the two path analysis models, two
recursive models incorporating a similar causal struc-
ture vhlfiQ. estimated for comparison. Two brands were
run, one relatively new and another well established.
The models and the results are presented in Figures 1
end 2.
?13
P14
p15
p16
'17
P 25
?26
p27
p 34
PA5
p46
p47
p56
p57
p67
r13
p 14
P15
P16
P17
p25
p26
P27
p34
P45
p46
p47
p56
p57
P67
FIGURE 1
HIDDEN MAGIC
I II III IV
.933 .933 .933 .933
-.066 -.078 -.066 -.089
.148 .149 .118 .113
.512 .227 .603 .118
.781 1.22 1.808 1.12
.142 .133
1.053 .625
.295 .928
1.023 1.035 1.023 1.10
.844 .842 .743 .756
.035 .753 -.093 .681
.557 .697 .947 .779
-.189 -.206 -.765 -.595
1.942 -1.745 -2.631
-2.379
,489 .476
FIGURE 2
VO-5
.198 .202
I II III IV
.441 .441 .441 .441
-.058 -.074 -.058 -.088
-.255 -.255 -.263 -.266
.341 .371 .545 .375
.803 .845 .776 .887
.145 .107
-.531 -.026
-.532 -.262
.760 .796 .760 .496
.924 .924 .794 .844
.358 .358 1.002 .372
.669 .504 1.867 .651
.270 .270 .316 .276
-.199 -.201 -.828 -.146
-.670 -.664 -.971 -.670
KEY
Subscripts
1 = Advertising (-fc)
2 Purchase (fc - 1}
3 Awareness (-fc)
4 - Like (-fc)
5 Acceptance (-fc.)
6 * Preference (-fc)
7 = Purchase (fc + 1)
(p 13> for example, la path from advertising to
awareness, i.e., the effect of advertising on
awareness.)
I « Path Analysis w/o P(-t - 1)
II * Recursive w/o P(-fc - 1)
III = Path Analysis w P(-fc - 1)
XV « Recursive w P(-fc - I)
The Results
In analyzing the results, let us first compare the
path analysis models with the recursive formulations.
As would have been expected, both approaches yield
similar results in the early stages of the hierarchy
—
here the advantages of the path analysis make little
difference. Proceeding towards the purchase variable,
j
however,, we can see how the separation of causal
influences possible in the path analysis approach
yields added insights into the working of the hierar-
chy. For example, In Figure 1 it seems that advertis-
ing affects liking slightly negatively, but when the
indirect effect through awareness is accounted for in
1 the path analysis, the net effect is positive. Slmi-
.
larly, the small negative effect of acceptance on pur-
chase is counterbalanced by the positive influence via
;
preference.
Comparing the path analysis runs for the two different
•brands, some interesting features emerge. For the
newly introduced brand (Figure 1), the effect of adver-
tising upon awareness is much stronger than for the
well established brand (Figure 2). On the other hand,
the relationship visavis purchase is the opposite, with
, the established brand showing a stronger positive
effect* With the exception of the preference-to-
purchase link, the established brand exhibits a gener-
ally stronger advertising effect in the later stages of
the hierarchy, with the new brand showing the greater
effect early. This would seem to indicate that as a
brand becomes established in a market, advertising can
be directed more effectively towards purchase related
output, whereas for a new brand the advertising will
have to focus upon earlier stages in the hierarchy.
The preference-to-purchase link seems to go against
this very plausible picture, however, since it is
slightly negative for the established brand and strong-
ly positive for the new brand. The explanation here
might be that for the established brand preferences
have been quite firmly developed, and changes in pur-
chases will occur quite independently of preferences.
The small negative impact might come about through deal
offers of the brand which might temporarily increase pur-
chases but lead to slightly negative preference reac-
tions among loyal customers. The new brand, however,
will attract purchases continuously from the pioneer
customers who develop a preference for the brand, and
these customers might in addition generate favorable
word-of-mouth communication.

This interpretation of the preference discrepancies is
supported by the differences between the two brands
when the effect of - lagged purchases is incorporated.
Thus, the established brand shows a negative relation-
ship between lagged purchases and preferences, as well
as a weak negative relationship between past and pre-
sent purchases. For the new brand, both of those rela-
tionships are strongly positive-.
CONCLUSION
Although there are other interesting results depicted
in Figures 1 and 2, the main findings quoted should be
sufficient to indicate the potential of path analysis
in the analysis of the advertising and sales relation-
ship. If the aim of such an analysis is the axplor-
ation of possible causal relationships, the specifica-
tion approach followed in path analysis seems very
logical and relatively easy to carry out. Using path
analysis as a complement to simultaneous systems where
the relationships are uni-directional in any one time
period would seam to offer more insights into the
causal mechanism than the usual recursive modeling
; approach.
i
REFERENCES
] Bass, Frank M., "A Simultaneous Equation Regres-
sion Study of Advertising and Sales of Cigar-
ettes." Journal of Marketing Research , 6
(August, 1969), pp. 307-14.
^2] Blalock, Herbert M. , Theory Construction: From
Verbal to Mathematical Formulations (Englewood
Cliffs, New Jersey: Prentice-Hall, Inc., 1969).
(33 Engel, James F., David T. Kollat, and Roger D.
Blackwell, Consumer Behavior (New York: Holt*
Rinehart and Winston, 1973).
[4] Johansson, Johny K, 5 "Returns to Scale in Media
Advertising." Unpublished Doctoral Dissertation.
University of California, 1972.
[5] Palda, Kristlan S., The Measurement o f Cumulative
Advertising Effe cts (Englewood Cliffs, New
Jersey: Prentice-Hall, Inc., 1963).
f63 Van de Geer, John P., Introduction to Mul tivar-
iate Analysis for the Social Sciences (San
Francisco; W. H. Freeman and Co., 1971).





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A path analysis model of the advertising-sales relationship / 201

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