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PRAGUE ECONOMIC PAPERS, 1, 2006 l 29
SALES-ADVERTISING RELATIONSHIP: AN APPLICATION
OF PANEL DATA FROM THE GERMAN AUTOMOBILE IN-
DUSTRY
Petr MARIEL, Cristina LÓPEZ, Karmele FERNÁNDEZ*
Abstract
This paper uses panel data from the German car industry for the estimation of parameters of a demand equation applying different statistical methodologies and paying special at- tention to advertising variables. Two important conclusions can be drawn. First, advertising plays an important role in this market but its effectiveness depends on its form and type of message; and second, the marketing policy of a firm has to take into account the size of its cars.
Key words: principal components, classification, advertising
JEL Classification: C23, M
1. I n t r o d u c t i o n
This paper tries to explain the behaviour of the oligopolistic German car market
using panel data from the period 1993 – 1995 applying different statistical metho-
dologies. Our primary goal is to estimate a demand function faced by the individual
car producer including the effect of advertising. Many analyses state that adverti-
sing has a limited capacity to stimulate total market growth and cast doubt on its
effect in more objective tasks. We therefore seek to determine the role of adverti-
sing in this specific car market using Principal Component Analysis (PCA), Classi-
fication Analysis and Instrumental Variable Method applied to a panel data model.
We also try to relate our conclusions to existing literature. Murfin (1984) applies
the Almost Ideal Demand System (AIDS) of Deaton, Muellbauer (1980) to the mo-
delling of market share in the UK passenger car market. Most estimated effects in
his study on aggregate demand are shown to conceal considerable differences
between submarkets. This leads to a suggestion that the model could be improved
by taking into account the existence of market segmentation and heterogeneity of
car characteristics and by defining the more relevant price variables. Our conclusi-
*) Departamento de Econometría y Estadística, Universidad del País Vasco, Lehendakari Aguirre 83, E48015 BILBAO, Spain, e-mail: etpmaxxp@bs.ehu.es. **) Financial aid from Gobierno Vasco (PI-1999-46) and from UPV-EHU (UPV038.321-G55/98, UPV 00038.321-13503/2001 and UPV 00038.321-13631/2001) is gratefully acknowledged.
30 l PRAGUE ECONOMIC PAPERS, 1, 2006
ons support these results, and show big differences between submarkets for big,
medium and small cars. We also correct the offcial list prices for quality characteris-
tics by constructing hedonic prices. In a similar paper (see Pelsmacker, 1988) there
are used data from the Belgian car market in order to estimate a modified AIDS mo-
del. Pelsmacker also shows that segmentation of the car market and a more accu-
rate definition of the price variable improve the significance of the estimated coeffi-
cients. Moreover, he does not find marketing variables particularly relevant except
for a certain extent in one of four segments analyzed.
The paper is organized as follows. Section 2 presents data and some prelimina-
ry analysis needed for a correct estimation of the model using panel data. One of
these analyses presented in section 3 is a classification needed to define car clas-
ses and direct rivals for each class model. Section 4 discusses different estimation
procedures applied to our data and section 5 concludes.
2. D a t a , V a r i a b l e s a n d R e l a t e d I s s u e s
In order to estimate our empirical model we use the data from the seven produ-
cers with the largest market shares in the German automobile industry: BMW
(6. 9 %), Mercedes (9. 7 %), Opel (10. 1 %), Volkswagen (23. 6 %), Fiat (4. 9 %), Ford
(7 %) and Renault (5. 7 %)1). Given that for most car models (e.g. GOLF, ASTRA) and
submodels (e.g. GOLF GTI, GT, TDI) the advertising variable has a zero value we
formed three segments for each producer, which can be called “big”, “medium” and
“small” cars, to get more homogeneous data. This way we form 18 groups of the
biggest-selling types of cars in Germany. The data run from January 1993 to June
1995. Sales series are the number of cars sold each month, obtained from the " Re-
port of New Car Registration in Germany "2), which is a detailed report by car mo-
dels and manufacturers.
The advertising expenditure data3)^ are the observed number of pages (newspa-
pers, journals) minutes (TV, radio) and posters devoted to the advertising of each
car model under study, multiplied by the official (unknown to us) price of one page,
minute or poster. Therefore, all the series are valued in German marks and repre-
sent the cost of the advertising efforts of the competitors. In order to represent the
diminishing returns to scale, it is assumed that the advertising levels are the square
roots of the observed advertising efforts. This reduction could be because additio-
nal units of advertising do not reach the same number of potential buyers as the first
units did, or simply because the additional units are assigned to less efficient re-
sources (see Jorgensen, 1982, Erickson, 1992).
Prices are taken from the official publication Schwacke Liste , which contains
prices for every car model. Price variables for each car group are built up as a weigh-
ted index where the weight is formed using the number of cars sold and finally de-
flating those prices by the consumer price index4). Our original source for the price
variable ( Schwacke Liste ) contains data on cars made by German producers. In
order not to lose the remaining car models in our analysis we use the data publis-
hed in the magazine Automóvil published in Spain, which provides data on all the
car models in our database. These new prices are treated as former prices after
- Data corresponding to January 1993.
- Source: Zulassungen von fabrikneuen Personenkraftwagen in Deutschland nach Herstellern und Typgruppen, published by Kraftfahrt-Bundesamt.
- Source: Nielsen Werbeforschung S+P GmbH, Hamburg
- Source: CD-ROM International Financial Statistics, International Monetary Fund.
32 l PRAGUE ECONOMIC PAPERS, 1, 2006
A look at the original price variable reveals a lack of significant changes over time.
The quality adjustment of price changes can be more explicitly obtained by the con-
struction of a hedonic or quality-adjusted price definition. One of the standard pro-
cedures for correcting prices for quality is to estimate the relationship between a
product's price and its quality characteristics, which in our case may be car dimen-
sion, car capacity, horsepower, etc., by means of least squares regression analysis
and to define regression residuals as a measure of quality-adjusted price.
In our analysis we estimate a hedonic price function including the following qua-
lity regressors for each car: cm^3 , horsepower, length, width, height, trunk capacity,
weight, average fuel consumption, top speed and acceleration. A competitive mar-
ket with a continuum of characteristics would ensure that the hedonic price function
is linear (see Arguea, Hsiao, 1993) and is defined by:
Pi = d 0 + d 1 Char 1 i + d 2 Char 2 i + ... + d pCharpi + vi i = 1 , 2 ,..., n
where Charji is the j th characteristic of the i th group of cars (in our case p = 10 and
n = 18) and vi the error term or residual used as the regressor in the estimation of
car market demand.
Since we use a linear function, the coefficients of each characteristics are the
estimated shadow prices (see Arguea, Hsiao, 1993). Nevertheless, many of the co-
efficients are not statistically significant because many of the regressors seem to
measure the same attributes and they are highly collinear (see Table 1). Hence, in
practice, there is strong linear dependency and the problem of selecting a set of
variables, which are not highly correlated, is an empirical one.
A common procedure for reducing the number of variables in statistical explora-
tory studies is PCA (see Anderson, 1984). We therefore carry out a PCA for each
month (from January 1993 to June 1995), obtaining 30 analyses. We take the re-
sults of the first month of our data, and compare them to the results obtained using
data from other months in order to analyze possible technology variations.
We actually find no significant differences among these 30 PCA’s, which is an
expected result given the relatively stable development of our data over time. As
shown by Arguea, Hsiao (1993), the technical specification of the products would
show time trends if there were any technology variations.
Table 1 Correlation Matrix
CM PW LENG WIDTH HEIGHT CAPT WEIG CONS SPEED ACCEL CM 1. PW 0.93 1. LENG 0.93 0.83 1. WIDTH 0.88 0.80 0.87 1. HEIGHT 0.39 0.28 0.44 0.51 1. CAPT 0.70 0.56 0.89 0.74 0.52 1. WEIG 0.93 0.92 0.92 0.87 0.47 0.77 1. CONS 0.94 0.92 0.91 0.89 0.42 0.72 0.94 1. SPEED 0.89 0.94 0.85 0.87 0.40 0.65 0.92 0.90 1. ACCEL -0.74 -0.79 -0.70 -0.84 -0.35 -0.53 -0.75 -0.73 -0.90 1.
Source: Own elaboration based on data from the magazine Automóvil.
The goal of the principal component method is to find the linear combinations
with large variance formed by the original variables. In many exploratory studies a
way of reducing the number of variables to be treated is to discard the linear combi-
PRAGUE ECONOMIC PAPERS, 1, 2006 l 33
nations which have small variances and study only those with large variances. An
important point is that principal components may be inputs to a multiple regression
or cluster analysis (see Johnson, Wichern, 1988) which is a technique we apply in
our paper. Although all principal components are required to reproduce the total
system variability a number of k principal components usually replace the initial p
variables ( k < p ) in empirical applications.
Principal components are particular linear combinations of the p observed vari-
ables X 1 , X 2 , ... , Xp (car characteristics, so that p = 10) which are observed for n
individuals, in our case for n = 18 groups of cars. The observations of these vari-
ables can be placed in a matrix ( n × p denoted X , the elements of which are deno-
ted xij ). The linear combinations sought represent the selection of a new coordinate
system obtained by rotating the original system of variables. The new axes repre-
sent directions with maximum variability and provide a simpler and more parsimoni-
ous description of the covariance structure of the observed variables.
Table 2 presents obtained eigenvalues, percentages and cumulative percenta-
ges of projected variances. The stopping rule (that is how many components will be
retained and used in the posterior procedures) is subjective, since the number of
components retained is based on an arbitrarily determined criterion for the amount
of variation accounted for (see Dillon, Goldstein, 1984). But when factoring a corre-
lation matrix, statistical procedures no longer hold and the retained variance criteri-
on lacks clear meaning. Perhaps the most frequently used extraction approach is
the “root greater than one” criterion originally suggested by Kaiser (1958) which pro-
poses retaining those components whose eigenvalues are greater than one.
Table 2 Eigenvalues and Percentages of Projected Variances
Number Eigenvalue Percentage Cumulative percentage
1 7.9005 79.00 79. 2 0.9264 9.27 88. 3 0.5370 5.37 93. 4 0.3274 3.27 96. 5 0.1425 1.42 98. 6 0.0747 0.75 99. 7 0.0413 0.42 99. 8 0.0258 0.25 99. 9 0.0135 0.14 99. 10 0.0111 0.11 100.
Table 3 Coordinates and Variable-Factor Correlations (1 to 5 axes)
Coordinates, Var.-Fact. Correl.
Variables 1 2 3 4 5
CM -0.95 0.11 -0.09 0.16 0. PW -0.92 0.31 0.06 0.20 -0. LENG -0.95 -0.07 -0.26 -0.04 0. WIDTH -0.94 -0.05 0.09 -0.15 0. HEIGHT -0.51 -0.78 0.34 0.17 -0. CAPT -0.80 -0.37 -0.39 -0.25 -0. WEIG -0.97 0.02 -0.07 0.13 -0. CONS -0.96 0.07 -0.08 0.15 0. SPEED -0.95 0.17 0.17 -0.03 -0. ACCEL 0.84 -0.19 -0.38 0.33 0.
PRAGUE ECONOMIC PAPERS, 1, 2006 l 35
Each of the 18 groups usually brought together submodels (e.g. GTI, GT) of one
model (e.g. GOLF) and we used a simple denomination of big, medium and small
which does not necessarily mean that "big" of one producer is a direct competitor
of a “big” of another. In order to identify the direct competitors of each group of cars
we apply the following classification analysis. The results of this classification will
be used in our demand equation because not only own price and advertising but also
rivals' price and advertising will be used as explanatory variables.
3. C l a s s i f i c a t i o n
Starting from the PCA performed above we carry out a classification analysis,
using the variance criterion and following Ward’s method. The variance method is
based on Huygens’s decomposition (see Lebart et al., 1984), where the total inertia
of a set of points is equal to the sum of the intra inertia (inertia within clusters) and
the inter inertia (inertia between clusters). The higher the ratio of inter inertia to to-
tal inertia is, the more homogeneous the groups of rivals will be. First, we describe
the general procedure of this method applied to the original data X and subsequently
apply it to the scores of the first principal components.
We consider n individuals (18 groups of cars) which we have to classify as an
individual set of points in a space of p dimensions (10 characteristics or variables).
Each point xi of that set of points is a vector of 10 coordinates ( i th row of X ) and has
a mass mi equal to one. The total mass of the set of points is
Figure 2 Quality Characteristics of the 18 Groups of Cars on the Main Plane
Source: Own elaboration based on data from the magazine Automóvil.
36 l PRAGUE ECONOMIC PAPERS, 1, 2006
1
n i i
m m
=
= (^) å
The square of the Euclidean distance between the points xi and xk would be de-
noted as:
|| xi – xk || 2 = d^2 ( xi, xk )
The inertia of the set of points is defined as the quantity:
2 1
n Total i i i
I m x g
=
= (^) å - ,
where g is the overall center of gravity, that is ( (^) 1/ ) (^1)
n g^ =^ m (^) å i (^) = m xi i.
Huygens’s decomposition (see Lebart et al., 1984) displays an additive decom-
position of the quantity I into within-cluster and between cluster inertia as shown in
the following formula:
2 2 Total q q i i q q q i q
I m g g m x g
Î
= (^) å - + (^) åå -
where mi is the mass of each vector xi , mq is the mass of the q th class, that is
m q^ =^ å (^) i Î qmi. Finally,^ gq is the center of gravity of each subgroup created, that is
gq^ =^ 1/ mq (^) å i (^) Î qm xi i. Each subgroup is treated in the next stage as a new individual.
The criterion of aggregation based on variance consists of finding at each stage
one partition that minimizes the internal inertia (inertia within cluster) of each class,
and at the same time maximizes the inertia between clusters. The two values inclu-
ded in this criteria are defined as follows:
2
2
Interia within clusters:
Interia between clusters:
within i i q q i q
between q q q
I m x g
I m g g
Î
åå
å
The ratio between inter inertia and total inertia indicates the degree of homoge-
neity of the classes obtained. The closer to 1 the ratio Ibetween / ITotal is, the more ho-
mogeneous classes are formed.
Sometimes it is more efficient to obtain a classification using a limited number of
factors and that is why we take into account only the first three principal components,
which account for 93.64 % of the total inertia explained for our final classification. In
this case xi is formed by the first three scores zi which contain the principal compo-
nent. Starting from the hierarchical tree shown below, an adequate number of clas-
ses should be decided, so that these classes are as homogeneous as possible with
regard to the model of cars included in them. At the same time they must be as dif-
ferent from one other as possible. The dendogram (3) shows five quite homogene-
ous and intuitive classes obtained by the procedure described above.
- Class 1: Big BMW, Mercedes and Ford and Medium BMW.
- Class 2: Big Renault, Opel and Volkswagen.
- Class 3: Medium Mercedes and Ford.
- Class 4: Medium Renault, Fiat, Opel and Volkswagen.
- Class 5: Small Opel, Volkswagen, Ford, Renault and Fiat.
38 l PRAGUE ECONOMIC PAPERS, 1, 2006
4. E s t i m a t i o n R e s u l t s
After the computation of the hedonic prices and identification of the direct rivals
of each group of car by application of PCA and classification analysis, we can esti-
mate coefficients of the demand equation using a panel data model. We consider
an oligopolistic market made up of 18 differentiated groups of cars whose sales,
price and advertising variables are observed over 30 months from January 1993 to
June 1995. Sales of group i in time period t are denoted by salesit , advertising level
in newspapers and journals and on TV and radio by adsjournit and adsrtvit respecti-
vely, hedonic price by pricehedit , and finally radsjournit , radsrtvit and rpricehedit re-
present the advertising level and hedonic price established by the direct rivals which
have been fixed previously by the classification procedure. If there is more than one
direct rival in a class, we use a sample mean of all the remaining groups in the class.
We also include one exogenous macro-variable, namely the rate of interest, which
is denoted by rateintt which a priori could have an impact on sales. It is common
procedure in the relevant literature to include a macro-variable in this kind of mo-
dels.
Based on the articles of Pelsmacker (1988) and Murfin (1984) the demand func-
tion faced by firm i in period t is defined as:
salesit = b 1 adsrtvit + b 2 adsjournit + b 3 pricehedit + b 4 radsrtvit
+ b 5 radsjournit + b 6 rpricehedit + b 7 rateintt + m + a i + e it, (1)
i = 1 , 2 , ... , 18, t = 1 , 2 ... , 30
where a i is the individual effect ( 1
n å (^) i = a = i ) and^ e it^ is the error term. Model (1) al-
lows us to analyze the effect of own and rivals’ advertising and price on sales. Ba-
sic economic theory indicates that the sign of the coefficient of own price (b 3 ) is li-
kely to be negative and that of the rivals’ price (b 6 ) positive. The effect of advertising
is, however, not so straightforward. Own advertising should have a positive effect (b 1 ,
b 2 > 0) and the sign of b 4 and b 5 depends on the nature of advertising. Advertising
is cooperative (informative) if the effect of the rivals' advertising on own future and
discounted sales is positive. But advertising is predatory if this effect is negative (see
Figure 4 Class Projections on the Factorial Plane
Source: Own elaboration based on data from the magazine Automóvil.
PRAGUE ECONOMIC PAPERS, 1, 2006 l 39
Friedman, 1983, and Slade, 1995). Applying this rule to our static model (1) we can
say that advertising is cooperative if b 4 , b 5 > 0 and predatory if b 4 , b 5 < 0.
The question now is how to treat the individual effects, a i. Are they fixed or ran-
dom? The fixed effects model is a reasonable approach when we can be sure that
differences between units can be explained by parametric movements of the regres-
sion function. In our model, differences between units refer to differences between
groups of cars. The groups of cars analyzed cover almost 70 % of the market. They
are clearly defined and are not interchangeable. Hence, it is reasonable to assume
that we face a fixed effects model. Moreover, it also seems reasonable to assume
that individual effects, a i , of each group of cars must be represented by a paramet-
ric movement rather than assuming that they are a realization of a random variable.
Table 4 Ordinary Least Square Estimation (fixed effects model)
Parameter Estimation t Statistic
Adsrtv 0_._ 155 2_._ 17 * Adsjourn - 0_._ 047 - 0_._ 85 * Pricehed - 0_._ 035 - 1_._ 84 * Radsrtv 0_._ 070 0_._ 84 * Radsjourn 0_._ 085 1_._ 62 * Rpricehed - 0_._ 002 0_._ 07 * Rateint - 134_._ 344 - 1_._ 04 * Constant 6303_._ 173 3_._ 90 *
F (7 ; 515) = 2_._ 250 Prob > F = 0_._ 028 F test that all a i = 0: F (17,515) = 13_._ 200
* Significant at 5 %. Source: Own elaboration.
Assuming a i to be fixed, equation (1) can be treated as a classical regression
model (sometimes called Least Square Dummy Variable Model) and the Ordinary
Least Square Estimator (presented in Table 4) has a desirable properties. The ge-
neral conclusion is that the t statistics are very low, which may be due to the fact
that our panel is very “narrow” (only 18 groups of cars). If we pay attention to the
variables with the highest t statistics the following conclusions can be drawn.
Own advertising in TV and radio has a significant positive effect on sales. Howe-
ver, own advertising in journals and newspapers does not seem to have a major ef-
fect on sales. The effect of the own price variable is, as expected, negative and the
“rivals” variable has a very low t -statistic, which may be a consequence of complex
interactions between direct rivals in each class.
The next point to analyze is the dynamics we might face in our data. Car sales
usually behave cyclically, with each cycle usually lasting years. Dynamics can be
included in the model in different ways, but we consider the following two possibili-
ties.
1. If e it = ge it – 1 + eit in yit = b xit + a i + e it , then yit = b xit + a i +
( 1 )
e it
2. If yit = g yit – 1 + b xit + a i + e it , then yit =
( ) ( ) ( )
i
xit it
L L
b a
+ + e
PRAGUE ECONOMIC PAPERS, 1, 2006 l 41
We note that the coefficient of the lagged sales and its corresponding t -ratio are
very low, confirming our suspicion that the underlying dynamics is not high. The
remaining variables are not significant at 5% either which indicate a bad fit of this
dynamic model.
Finally, following the conclusions of Pelsmacker (1988), we segment the car mar-
ket and carry out an analysis of each submarket (small, medium and big cars) se-
parately. We present the final estimations based on a simple specification of a sta-
tic model with fixed effects because the previous estimations do not support strong
dynamic behaviour of our data.
Table 6 Estimation of the Fixed Effects Model Using Segmented Data
Small cars Medium cars Big cars
Parameter Estimation t Statistic Estimation t Statistic Estimation t Statistic
Adsrtv - 0_._ 043 - 0_._ 30 * 0_._ 239 2_._ 42 * 0_._ 187 1_._ 18 * Adsjourn 0_._ 001 0_._ 02 * - 0_._ 103 - 1_._ 22 * - 0_._ 080 - 0_._ 82 * Radsrtv 0_._ 153 0_._ 54 * 0_._ 253 1_._ 88 * - 0_._ 063 - 0_._ 53 * Radsjourn 0_._ 175 0_._ 88 * - 0_._ 084 - 0_._ 72 * 0_._ 099 1_._ 63 * Pricehed - 0_._ 109 - 2_._ 30 * - 0_._ 068 - 2_._ 97 * 0_._ 183 2_._ 34 * Rpricehed - 0_._ 235 - 1_._ 28 * 0_._ 073 - 2_._ 00 * 0_._ 142 1_._ 63 * Rateint 138_._ 602 0_._ 41 * - 509_._ 510 - 2_._ 68 * - 97_._ 837 - 0_._ 24 * Constant 3477_._ 408 0_._ 83 * 10973_._ 860 4_._ 57 * 6891_._ 190 1_._ 32 *
* Significant at 5%. Source: Own elaboration.
Table 6 presents the final estimations based on model (1) segmenting the mar-
ket into three submarkets for small, medium and big cars according to our previous
classification. As classes 2 and 3 contain few groups of cars we put together clas-
ses 2, 3 and 4 according to the dendogram (see Figure 3), obtaining three classes
called small, medium and big cars. Our results confirm the importance of the seg-
mentation of the market because the behaviour of consumers in the different mar-
kets seems to be completely different. This is a very important issue because pro-
ducers would have to choose different marketing strategies in each segment if their
marketing variables are to have the expected effect.
The only significant variable at 5% in the small cars market is own price. No
advertising variable is significant in this segment. The consumers in the segment are
usually young people looking for their first car and that is why the budget restriction
is decisive for them. Big advertising campaigns in this segment will probably not
have the expected reaction.
In the medium car segment we find many relevant variables: own price, rivals’
price, own advertising on radio and TV, interest rate and rivals’ advertising on radio
and TV is significant at 10%. The consumers in this segment pay attention to both
price and advertising. Therefore, marketing strategies can combine new advertising
messages with price changes to obtain the expected reaction. The consumers in this
segment usually have higher purchasing power than small car buyers, and can the-
refore react to advertising by purchasing a more expensive car if its characteristics
are more suitable for them. The budget restriction is not the only decisive rule for
them.
The own and rivals’ advertising variables in radio and TV have a positive effect.
Own price has the expected negative sign and a relatively high t statistic confirms
42 l PRAGUE ECONOMIC PAPERS, 1, 2006
its relative importance. We should highlight the positive coefficient of rivals’ adverti-
sing on radio and TV. It is very important to indicate that advertising in the market
analyzed is cooperative (informative). This may be quite a surprising result, given
that the car market is very competitive, but there are a lot of advertising messages
describing new technical innovations included in a new car. These innovations are
usually quickly offered by all direct rivals, so the messages can have an informative
effect.
The big cars market is really a very interesting segment. The only significant
variable here is own price, but with a positive sign. We know that buyers of these
expensive cars usually have no budget restrictions but they do not seem to pay much
attention to advertising either. Their behaviour is probably based on brand loyalty
and at first sight the positive sign on the price variable seems to contradict classical
economic theory, but there are many papers where this unexpected behaviour is
described. Owning or consuming certain goods (luxury cars) defines an individual's
position in a society or in particular subgroups of a society (see Rauscher, 1992).
This may result in unexpected results concerning demand.
5. C o n c l u s i o n s
We use panel data from the German car industry to estimate parameters of a
demand equation, paying special attention to advertising variables. We have found
out that advertising plays an important role in this market but its effectiveness de-
pends on its form and type of message. This is one of the conclusions stated by
Lambin (1976). The parameters estimated indicate that advertising in this competi-
tive market is informative in nature. This surprising conclusion is also found in Ma-
riel (1997) and can be explained by featuring of exhibitions of new car elements
(ABS, side bars) which inform customers of rival manufactures who buy cars with
similar characteristics.
The building of marketing models is not an easy task and there is a large stream
of marketing literature that deals with the effect of advertising and other marketing
mix on sales or market shares (see Hanssens, Parsons, Schultz, 2001; Leeflang,
Wittink, Wedel, Naert, 2000). Our model tries to find out new insights in the Market
Response Models (see Vakratsas, Ambler, 1999) stressing that for a rigorous ana-
lysis of the effect of advertising, different statistical methodologies should be applied
and the homogeneity of the analyzed products should be carefully analyzed. In or-
der not to waste resources and to conduct marketing campaigns adequately it is
necessary to take into account more homogeneous submarkets such as those pre-
sented in Table 6. Thereby, in our case, the marketing policy to be undertaken by a
firm must take into account the size of its cars.
All this issues can help to build standardized models which should be useful for
marketing management and senior executives (see Hanssens, Leeflang, Wittink,
R e f e r e n c e s
Anderson, T. (1984), An introduction to Multivariate Statistical Analysis , 2nd ed., New York: John Wiley & Sons. Arellano, M., Bond, S. (1991),“Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations.” Review of Economic Studies, 58, pp. 277-297. Arellano, M., Bover, O. (1990), “La econometría de datos de panel.” Investigaciones Económicas, pp. 3-45.
