Directory UMM :Data Elmu:jurnal:A:Agricultural Economics:Vol22.Issue2.Mar2000:
Agricultural Economics 22 (2000) 147±162
Modeling the demand for alcoholic beverages and
advertising speci®cations
EÂric LarivieÁrea, Bruno Larueb,*, Jim Chalfantc
b
a
Agrifood and Agriculture, Sainte-Foy, Que., Canada G1K 7P4
Â
Centre de Recherche en Economie Agroalimentaire (CREÂA) DeÂpartement d'EÂconomie Agroalimentaire Universite Laval,
Sainte-Foy, Que., Canada G1K 7P4
c
Department of Agricultural and Resource Economics, University of California at Davis, Davis CA, USA
Received 18 March 1998; received in revised form 20 August 1999; accepted 15 September 1999
Abstract
In this paper, the demand for beer, wine, spirits and soft drinks in Ontario is modeled in two parts: an equation is speci®ed
to endogenize group expenditures and a demand system is set up to allocate budgeted group expenditures across types of
beverages. Advertising is allowed to in¯uence both the level of group expenditures and its allocation. Three popular
advertising speci®cations are compared using the J-test and the likelihood dominance criterion. Even though all three
speci®cations ®tted well according to standard criteria, the calculated expenditure, price and advertising elasticities were
sensitive to the manner with which advertising is speci®ed. This clearly highlights the need to rely on a sound criterion to
identify a dominant speci®cation. From the identi®ed dominant speci®cation, we found that advertising has very subtle effects
on expenditures on alcoholic beverages (group and individual beverages). Thus, advertising is not effective in enlarging
markets and this suggests that ®rms (especially breweries) use advertising to compete in zero-sum market share games. From a
public policy perspective, our results are comforting but future research should investigate whether the neutral effect of
advertising on aggregated expenditures hide substantial offsetting changes in the drinking habits of individuals. # 2000
Elsevier Science B.V. All rights reserved.
1. Introduction
The consumption of alcoholic beverages has been a
public concern for decades. As a result, policymakers
have designed regulations to internalize the negative
consumption externalities affecting public safety (i.e.,
drunk driving), public health (i.e., liver cirrhosis) and
*
Corresponding author. Tel.: 1-418-656-2131 ext 5098; fax:
1-418-656-7821.
E-mail address: bruno.larue@eac.ulaval.ca (B. Larue).
labor productivity without loosing sight of the substantial contribution of consumption taxes on government revenues. Advertising is a major preoccupation
of regulators in most countries. In some cases, there is
or has been an outright ban on advertising while in
others the restrictions are designed to censor the
content of the ads or limit the range of media outlets
through which the ads can be shown.
The literature on the effects of advertising of the
consumption of alcoholic beverages can be classi®ed
into two groups. The ®rst one addresses the psycho-
0169-5150/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 9 - 5 1 5 0 ( 9 9 ) 0 0 0 4 4 - 4
148
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
logical and sociological aspects of the ads about
alcoholic beverages and how they end up in¯uencing
individual consumption.1 Our study falls in the second
group since it is concerned with the effects of advertising on aggregate consumption. Our objective is
threefold. First, we assess how different speci®cations
of advertising effects in¯uence the size and signs of
estimated elasticities and determine whether a speci®cation dominates the others. Second, we investigate
the effect of advertising on the level of expenditures on
alcoholic beverages as well as the effect of advertising
on the allocation of these expenditures between beer,
wine, spirits and soft drinks. As such, this constitutes
an extension of what is known in some circles as the
Galbraithian hypothesis.2 Finally, we estimate price
and expenditure elasticities to characterize the
demand for alcoholic beverages and soft drinks in
Ontario, Canada.
In order to achieve these objectives, we constructed
a model in which group expenditure and budget shares
for different types of alcoholic beverages and soft
drinks are endogenized. Group expenditure is modeled as a function of prices, per capita income, advertising, demography and trigonometric variables to
account for seasonality. To facilitate comparisons with
previous studies, we chose dynamic versions of the
LA/AIDS model to explain variations in budget
shares. Three model speci®cations differentiated by
the manner with which advertising effects are incorporated were estimated. Bayesian techniques were
used to insure that the estimated elasticities were
consistent with the concavity and monotonicity conditions. We applied the J-test and the Likelihood
Dominance Criterion (LDC) developed by Pollak
and Wales (1991) to identify dominant advertising
speci®cations for the group expenditure and budget
shares sub-models. We found that advertising is not
effective in enlarging markets and this suggests that
®rms (especially breweries) use advertising to compete in zero-sum games. From a public policy perspective, our results are comforting but future research
should investigate whether the neutral effect of advertising on aggregated expenditures hide potentially
perverse offsetting changes in the drinking habits of
individuals.
The rest of the paper is organized as follows. The
next section presents an overview of the literature on
the demand for alcoholic beverages with an emphasis
on the role of advertising in explaining the demand for
beer, wine and spirits. This is followed by a discussion
about methodology and data. Empirical ®ndings are
presented in the fourth section while the last section
dwells on the modeling and policy implications.
1.1. The consumption of alcoholic beverages and
advertising: some ambiguities and some recurring
results
1
Typically, these studies rely on narrowly defined samples but
allow for a broad range of factors which along advertising can
influence consumption. For example, Strickland (1982) reviewed
700 ads (TV and magazines) and argued that the content of the ads
is less important than the influence of family and friends in
explaining the level of consumption. Strickland (1983) used the TV
watching habits of students to determine their exposure to
advertising of alcoholic beverages. A very weak correlation was
established between advertising and consumption but only after age
and race were accounted for. Again, the attitude of friends and
parents were much more influential than publicity which was also
found to be orthogonal to the proxies used to characterize abuse. In
contrast, Adlaf and Kohn (1989) found a direct link between
advertising and consumption and an indirect link between
advertising and abusive consumption. However, they too found
that the attitude of family and friends has a stronger influence than
advertising.
2
The Galbraithian hypothesis can be traced back to Galbraith
(1967) who asserted that advertising can have a powerful influence
on the distribution of expenditures between broadly defined
product groups. For a more detailed discussion, the interested
reader is referred to Duffy (1991).
Several economists have studied the demand for
alcoholic beverages but only a subset have attempted
to estimate the effect of advertising. Table 1 provides a
non-exhaustive but insightful list of studies on the
demand for alcoholic beverages and some of their
elasticities. A glance at these results reveals that
expenditure and own-price elasticities vary considerably from one study to another. Expenditure elasticities for beer, wine and spirits range from ÿ0.83 to
1.94, ÿ0.01 to 2.10 and 0.46 to 2.66, respectively. The
ranges for the own-price elasticities for the same
products are: 0.26 to ÿ0.89, ÿ0.43 to ÿ1.89, ÿ0.37
to ÿ1.88. The lack of consensus across studies extends
to qualitative results about the nature of the relationships between alcoholic beverages (i.e., complements
versus substitutes).
Studies that incorporate advertising as an explanatory variable have reported low and often negative
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
149
Table 1
Summary of previous studies on the demand for alcoholic beverages
Authors and country
Income elasticities
Own price elasticities
Beer
Wine
Spirits
Beer
Wine
Spirits
Hogarty and Elzinga, 1972 (United States)
Johnson and Oksanen, 1974
Johnson and Oksanen, 1977 (Canada)
Duffy, 1982 (UK)
Clements and Johnson, 1983 (Australia)
0.43
0.04
0.00
0.49
0.80
n.a
ÿ0.01
0.04
1.50
0.75
n.a.
0.23
0.11
1.65
1.91
ÿ0.89
ÿ0.23
ÿ0.27
ÿ0.17
ÿ0.36
n.a.
ÿ0.50
ÿ0.67
ÿ1.14
ÿ0.43
n.a.
ÿ0.91
ÿ1.14
ÿ0.84
ÿ0.74
Tsolakis et al., 1983 (Australia)
Short run
Long run
0.46
0.39
0.88
2.81
n.a.
n.a.
ÿ0.23
ÿ0.20
ÿ0.43
ÿ1.35
n.a.
n.a.
Fuss and Waverman, 1987 (Canada)
Short run
Long run
Quek, 1988 (Canada)
Alley et al., 1989 (British-Columbia: Canada)
Heien and Pompelli, 1989 (United States)
0.39
0.52
0.44
ÿ0.03
1.94
0.54
0.70
1.26
0.21
2.10
0.83
1.05
0.95
0.46
2.66
ÿ0.27
ÿ0.32
ÿ0.16
ÿ0.11
ÿ0.84
ÿ0.76
ÿ0.76
ÿ0.66
ÿ0.75
ÿ0.55
ÿ0.81
ÿ0.83
ÿ0.66
ÿ1.88
ÿ0.50
Johnson et al., 1992 (Canada)
Short run
Long run
0.38
0.27
0.97
2.19
0.92
1.02
ÿ0.26
ÿ0.14
ÿ0.88
ÿ1.17
ÿ0.63
ÿ0.37
Tegene, 1990 (United States)
With structural change
Without structural change
0.50
0.83
0.66
0.69
1.72
1.80
ÿ0.72
ÿ0.80
0.10
ÿ1.10
ÿ1.20
ÿ0.76
n.a.
0.5±1.3
n.a.
n.a.
ÿ0.7±1.9
A
n.a.
0.6±1.5
n.a.
n.a.
ÿ0.8±1.4
n.a.
0.08
0.11
0.48
n.a.
n.a.
2.02
n.a.
n.a.
1.83
ÿ0.54
ÿ0.72
ÿ0.24
n.a.
n.a.
ÿ0.55
n.a.
n.a.
ÿ0.56
n.a.
n.a.
ÿ1.72
n.a.
0.26
n.a.
Advertising elasticities
n.a.
n.a.
Wine
Spirits
ÿ0.044
0.019
Larue et al., 1991 (Ontario: Canada)
wine differentiated by color and origin
(local vs foreign)
wine differentiated by country of origin
Tremblay and Lee, 1992 (United States)
Short run
Long run
Selvanathan, 1995 (UK)
Gallet and List, 1998 (United States)
1964±73
1983±92
Johnson and Oksanen, 1974 (Canada)
Johnson and Oksanen, 1977 (Canada)
Duffy, 1982 (UK)
Fuss and Waverman, 1987 (Canada)
ÿ0.26
n.a.
ÿ0.83
n.a
Cross-price effects
Complements
Substitutes
Beer
beer/wine
beer/spiritsa
beer/spirits
n.a.
beer/wine
wine/beer
wine/spiritsa
wine/beer
n.a.
beer/winea
beer/spiritsa
wine/spiritsa
Quek, 1988 (Canada)
Alley et al., 1989 (British-Columbia: Canada)
beer/spriritsa
wine/spiritsa
beer/winea
beer/spiritsa
wine/spiritsa
n.a.
0.017
n.a.
wine/spiritsa
wine/beera
n.a.
n.a.
n.a.
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
150
Table 1 (Continued )
Authors and country
Income elasticities
Beer
Heien and Pompelli, 1989 (United States)
Own price elasticities
Wine
Spirits
a
beer/wine
beer/spiritsa
wine/spiritsa
Tegene, 1990 (United States)
Without structural change
With structural change
Beer
Wine
Spirits
ÿ0.217
ÿ0.266
0.002±0.022
0.09
0.16
0.07
n.a.
n.a.
n.a.
n.a.
beer/winea
beer/spiritsa
wine/spiritsa
0.282
Larue et al., 1996 (Canada)
Tremblay and Lee, 1992 (United States)
Selvanathan, 1995 (UK)
Gallet and List, 1998 (United States)
a
Canadian with french with most
most others
other wines
beer/spirits
beer/spiritsa
beer/winea
wine/spiritsa
beer/wine
beer/wine
1983±92
1964±73
n.a.
A permutation yields the same qualitative result (e.g., beer/spirits vs. spirits/beer) n.a.: not applicable.
advertising elasticities.3 The lack of support for large
positive advertising effects is robust to differences in
methodology, time periods and geographical areas.
For example, Ogborne and Smart (1975) were puzzled
by the fact that beer sales actually rose through a ban
on beer advertising in Manitoba during the 1980s. In
order to isolate the effects of advertising (or lack of) on
beer sales from other factors, they estimated a singleequation econometric model. They concluded that
advertising had no effect.4 Simpson et al. (1985)
compared per capita consumption of alcoholic beverages of a sample of countries with complete or
partial bans on the advertising of alcoholic beverages
(Norway, Finland, Hungary and Denmark) to a sample
of countries without restrictions (Australia and Japan).
They found no signi®cant differences and argued that
other variables were likely to have a much stronger
in¯uence on consumption than advertising. Wilcox
(1985) analyzed the impact of a restriction that made it
illegal to convey price information in beer ads in
Michigan. With data prior, during and after the
3
Negative own-advertising elasticities are common and not only
in studies about alcoholic beverages. For example, Green et al.
(1991) report negative elasticities for dried fruits generic advertising that are robust across advertising specifications.
4
This study did not control for the publicity originating from
neighboring provinces and US states.
`experiment', he demonstrated that the restriction of
price advertising did not affect beer sales. In contrast,
Ornstein and Hanssens (1985) argued that price information, and hence beer ads, may have an indirect
effect on beer sales through the negative effect of the
ads on prices.5 However, the publicity variable in their
model turned out to be statistically insigni®cant. Duffy
(1982) analyzed the effect of advertising on the consumption of beer, wine and spirits between 1963 and
1978 in England. OLS and 3SLS estimation results
showed that advertising had no effect on sales. Duffy
(1983) tried to capture the effect of advertising within
beverage types by introducing ®ner product de®nitions (i.e., eight categories of wine and spirits). It was
concluded that advertising had very small effects on
budget shares and no effect on the amount spent on all
alcoholic beverages. Tegene (1990) used Kalman
®lters to address the issue of structural change in
the computations of elasticities. Indeed, he found
structural changes in the demands for beer, wine
and spirits but failed to identify a signi®cant relationship between advertising and demand. Motivated by
5
Price advertising need not lead to price reductions. In fact, in an
oligopoly setting, it is well-known that price advertising and
policies of not being `undercut' facilitate collusion. The intuition is
that a firm has no incentive to lower prices if it is certain that other
firms will match any price cut.
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
the same purpose, Gallet and List (1998) used a gradual
switching model to show that the demand for beer in the
United States had become an inferior good insensitive to
price changes.Tremblay and Lee (1992)investigated the
effects of advertising on beer sales in the US for the
period 1953±1983.Again,advertisingfailed toin¯uence
total sales but might have had an effect on the market
shares of various brands.
2. Methodology and data
Our methodology is based on the hypothesis that
advertising can alter both the size and the allocation of
monthly expenditures on alcoholic beverages and soft
drinks. As in Fuss and Waverman (1987) and Heien
and Pick (1991), the structure of our model can be
decomposed into two sub-models. The ®rst one endogenizes expenditures on alcoholic beverages and soft
drinks. It is assumed that individuals allocate their
income between this group of beverages and an
aggregate good. The second sub-model is a conditional AIDS demand system that allocates the expenditures derived from the ®rst sub-model between beer,
wine, spirits and soft drinks.6
6
Our modeling strategy assumes that the utility function is
weakly separable. This allows the utility function to be partitioned
into at least two subsets, say one including alcoholic and soft drinks
beverages and another one for all other goods. In this instance, the
demand for a good in a particular subset can be expressed as a
function of the prices of the goods in that subset and the level of
expenditure spent on those goods (Pollak and Wales, 1992, p. 47).
The prices of goods belonging to the other subset and the level of
expenditure spent on all subsets influence the demand for a good in
a given subset only through the level of expenditure allocated to the
given subset. Weak separability is not a sufficient condition for
treating expenditures on a given subset as exogenous (Lafrance,
1991). Hence, the estimation of conditional demand systems should
endogenize subset expenditures. The estimation of subset expenditures and budget shares equations is often done in the context of a
two-stage budgeting process which imposes stronger restrictions on
preferences. This is so because one needs to worry about the
conditions under which an aggregate price index (for the goods in a
subset say the alcoholic beverages and soft drinks) can be used.
Strong price aggregation is consistent with utility maximizing
behavior if and only if the sub-utility functions are of either the
Generalized Gorman Polar Form (GGPF) or a homothetic form.
Unfortunately, homothetic weak separability translates into unitary
conditional expenditures elasticities (Moschini and Green, 1994).
In this study, the class of preferences for the beverage subset is the
price-independent generalized log-linear or PIGLOG form which is
GGPF (Deaton and Muellbauer, 1980). Two-stage budgeting using
151
The ®rst sub-model is speci®ed as a single equation
with the log of per capita expenditure on alcoholic
beverages and soft drinks as the dependent variable:
(1)
ln x f PSTONE; PNA; ; Y; POP; g AI ; Z
Pn
where x i1 Pi Qi , Pi is the deflated price of
beverage i, Qi is the per capita quantity consumed
of beverage i, PSTONE is the Stone price index, PNA is
a price index for non-alcoholic beverages, Y is real per
capita income, POP is the proportion of the population
of age 15 and above, g(Ai) are functions of per capita
advertising expenditure on beverages i 1,...,n, and Z
is a set of variables internalizing seasonal effects.
Nominal variables were deflated by a beverage price
index for Ontario.
Advertising can be modeled in different ways.
Common functional forms for g(Ai) encountered in
the literature include the lag transformation speci®cation LkAi (e.g., Duffy, 1982, 1983; Clements and
Johnson, 1983; Goddard, 1988; Tremblay and Lee,
1992)7 and Kinnucan's structural heterogeneity speci®cation Ait (e.g., Kinnucan and Venkateswaran,
1994), where L is the lag operator and t is a time
trend. Polynomial Distributed Lag (PDL) schemes are
also commonly used (e.g., Thompson, 1978; Ward and
Dixon, 1989). In our empirical analysis, a PDL
scheme of degree 2 with end-points restrictions was
compared to the other two advertising speci®cations.
We relied on non-nested tests,8 diagnostics checks and
the plausibility of the derived elasticities to rank the
GGPF is also generally restrictive because it requires the utility
function to be additive in the sub-utility functions. However, when
there are only two sub-utility functions, strong price aggregation
and two-stage budgeting does not imply unreasonable restrictions
on the form of the utility function (Gorman, 1959; Fuss and
Waverman, 1987). Edgerton (1997) argues that multistage budgeting can nevertheless generate `reasonably' accurate results under
rather usual conditions.
7
The setting of k is arbitrary even though indicators like AIC or
FPE and studies like Clarke's (Clarke, 1976) can help narrow down
the range of plausible values. In our tests, k 2 worked best. A
generalization to choosing a specific k is to construct a weighted
average of lagged advertising levels as in Rickertsen et al. (1995).
In this case, appropriate lag length and weights must be chosen.
8
In the context of single equation models, several non-nested
tests have been developed in the early 1980s. In this instance, we
relied on the well known J-test. For a thorough review of this test
and alternative ones, see Davidson and MacKinnon (1993) (pp.
381±388).
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
152
speci®cations. Kinnucan's structural heterogeneity
outperformed the other speci®cations and it was
retained. Regarding the modeling of seasonal effects,
two competing alternatives were compared (dummy
variables versus trigonometric functions). Using the
same criteria as for the selection of the advertising
speci®cation, it was found that the trigonometric
functions outperformed the seasonal dummies.
The functional form for the conditional demand
system is the linear version of the Almost Ideal
Demand System commonly known as LA/AIDS. Several arguments can be presented to justify this choice.
First, several studies on alcoholic beverages have used
the AIDS model (e.g., Fuss and Waverman, 1987;
Alley et al., 1989; Heien and Pompelli, 1989; Larue
et al., 1991) and relying on the same functional form
makes for `cleaner' comparisons. Secondly, the AIDS
functional form is (locally) ¯exible, it is easy to
estimate, especially in its linear version and it fared
very well in a recent comparative study (Green et al.,
1995). Finally, Alston et al. (1994) have demonstrated
that LA/AIDS provides accurate estimates of elasticities when the true data generating process is AIDS.
We augmented the speci®cation of the standard LA/
AIDS model with habit formation variables (lagged
quantities Qjtÿ12), a time trend (t), trigonometric
variables to captures seasonal effects and advertising
variables. The estimated budget shares can be represented as follows:
w i ai
n
X
gij lnPj bi ln
j1
n
X
Oij Qjtÿ12
j1
ji t mi
n
x X
Fij g Ajt
pc j1
6
X
kcik cos fk ksik sin fk
k1
(2)
where fk 2pk, k 1,...,6, Pj is the price of beverage
j, x is the level of expenditure estimated in Eq. (1), pc is
a normalized Stone price index9 and gAjt captures
advertising effects as in Eq. (1). For theoretical con-
9
As argued by Moschini (1995), the Stone price index is not
invariant to the choice of measurement units in prices and
quantities and this influences the approximation properties of the
model. To remedy this problem, prices are divided by their mean
before being used to construct the Stone price index. This
normalization does not affect the computations of elasticities.
sistency and to reduce the number of parameters to be
estimated, it is common to impose additivity, symmetry and homogeneity restrictions. A sufficient condition for the expenditureP
shares to be homogenous of
degree zero in prices is: nj1 gij 0, 8i. Symmetric
changes in compensated demand functions can be
imposed
by settingP
gij gji, 8i 6 j. Additivity requires
Pn
n
i1 ai 1 and
i1 bi 0. These conditions are
trivially satisfied for a model with n goods when the
estimation is carried out on a subset of n ÿ 1 independent equations. The parameters of the dropped
equation are then computed from the restrictions
and the estimated parameters of the n ÿ 1 expenditure
shares.
In studies using the AIDS or LA/AIDS functional
forms, it is common to test whether concavity and
monotonicity conditions are respected. The concavity
property of the expenditure function insures that substitution possibilities lessen the impact of price
increases on expenditures while monotonicity maintains budget shares in the {0,1} domain. The concavity
and monotonicity conditions cannot be easily imposed
because they involve inequality restrictions. For
instance, concavity imposes negative semi-de®niteness on the Slutsky matrix for all observations. As in
Chalfant et al. (1991) and Tif®n and Aguiar (1995), we
used a Bayesian framework and, more speci®cally
Monte Carlo integration and Importance Sampling, to
insure that the parameters used to compute elasticities
are consistent with the concavity and monotonicity
conditions.10
Conditional short term elasticities were computed
according to the LA/AIDS formulae found in Alston
et al. (1994). Assuming as in Chalfant (1987) that
@P*/@ln Pj wj, it can be shown that the expenditure
and Marshallian own and cross price elasticities are
Zi 1
Zij
bi
;
wi
gij
wj
ÿ bi
wi
wi
Zii ÿ1
gii
ÿ bi ;
wi
(3)
10
The implementation is thoroughly described in Chalfant et al.
(1991). A classical alternative to imposing curvature conditions has
been proposed by Moschini (1998) and Ryan and Wales (1998).
Though more cumbersome, the Bayesian framework has the
advantage of providing an estimate of the probability that the
restrictions hold.
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
where the wi's are the estimated budget shares. The
formulae for the Hicksian/compensated and substitution elasticities are
Zij wj sij Zij wj Zi ;
sij 1
gij
;
wi wj
sii 1
8i 6 j;
gii
1
ÿ ;
2
wi wi
(4)
As in Goddard (1988) and Duffy (1982), the formula for the advertising elasticity is
Fij
(5)
ADij
wi
Conditional short term elasticities are static measures that do not take into account habit formation.
Adjusting for the dynamics yields the following conditional long run expenditures and Marshallian elasticities:
bi wi
;
wi ÿ Oi Qi
gij ÿ bi wj
Zij
wi ÿ Oi Qi
Zi
Zii
gii ÿ wi ÿ bi wi
;
wi ÿ Oi Qi
(6)
where Oi is a coefficient associated with habit formation and Qi is the mean of per capita consumption for
beverage i. Hicksian and substitution elasticities can
be derived through the Slutsky equation. Conditional
long run advertising elasticities are computed according to the formula below:
ADij
Fij
wi ÿ Oi Qi
(7)
Finally, total elasticities that combine both estimation
stages can be computed (e.g., Edgerton, 1997). These
elasticities are useful because they take into account
that a change in an exogenous variable will affect the
budget shares of each type of alcoholic beverages
as well as the overall budget spent on alcoholic
beverages. Total price, income and advertising
elasticities are computed according to the following
formulae:
ZTij Zij wi Zi by ;
ADTij ADij Zi Ayj ;
ZTi Zi by ;
share for beverage i, by is the income coefficient
from the first sub-model and Ayj is the advertising
coefficient for beverage j in the group expenditure
sub-model.
A critical step in the implementation of the Bayesian framework is the generation of the parameter
estimates and the variance-covariance matrix that are
used in the generation of antithetic replications. We
attempted an FIML estimation of both sub-models
with homogeneity and symmetry imposed. Even
though convergence was achieved, less than 0.1%
of the 10000 replications generated from the estimated
coef®cients and the variance-covariance matrix were
consistent with the monotonicity and concavity conditions. As a result, we chose to estimate the submodels separately. The ®rst sub-model was estimated
with OLS and the second sub-model was estimated
with the ITSUR estimator. Prior to the estimation, we
checked the stationarity property of the variables in
the model with the Augmented Dickey±Fuller test.
The results led us to reject the null of non-stationarity
and to estimate both sub-models in levels.11
The monthly data series for this study cover a period
starting in May of 1979 and ending in April of 1987.
Data about quantities consumed and expenditures on
wine, spirits and beer were provided by the Liquor
Control Board of Ontario and Brewers Retail. The data
on advertising expenditures comes from Ambler
Research and Elliot Research. These two ®rms graciously made available to us their compilations of
advertising expenditures. The advertising expenditures were aggregated over all media.
Fig. 1 illustrates the evolution of per capita consumption of beer, wine, spirits and soft drinks in
Ontario between 1979 and 1987. Among alcoholic
beverages, beer is the product with the highest per
capita consumption with 6 l/person/year or about six
times the per capita consumption of wine and spirits.
Consumption trends for all beverages are ¯at over the
entire sample period. However, there appears to be
seasonal deviations around the trends. The seasonal
pattern for beer consumption is characterized by peeks
11
(8)
where Zij and Zi are the conditional Marshallian
price and expenditures elasticities, wi is the budget
153
Because of obvious seasonal effects, the specification of the
ADF tests included seasonal dummy variables. Because they are of
the same order as the constant term, these nonstochastic regressors
do not affect the asymptotic distributions of the test statictics
(Davidson and MacKinnon, 1993, p. 705).
154
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
Fig. 1. Ontario per capita consumption.
in the summer and around Christmas. As an indication
of the magnitudes of the seasonal variations, per capita
beer consumption typically falls under 2 l in February
to rise to roughly 8 l in July. The seasonal pattern for
per capita soft drinks consumption is very similar to
the one for beer. In contrast, per capita consumption of
wine and spirits slowly rise in the spring and summer
months before `jumping' to a peak in December.
Fig. 2 shows the trends in per capita expenditures on
advertising for beer, wine and spirits. As for per capita
consumption, beer leads the other alcoholic beverages.
Unlike the per capita consumption series, the long
term trends in advertising are not ¯at and exhibit rather
modest seasonal variations. Per capita advertising
expenditure for beer gradually rose between 1979
and 1984 and fell thereafter (reaching a peak of
$0.058 in September of 1984). Per capita advertising
expenditures on wine and spirits peeked much earlier
than beer and have been declining throughout most of
the sample period. The decline in per capita advertising expenditures is most pronounced for spirits ($0.04
in April of 1981 versus $0.015 in April of 1987).
3. The results
The estimation results of the dominant speci®cation
of the ®rst sub-model are presented in Table 2. To
avoid coef®cients with wrong signs and implausible
elasticities, we augmented the speci®cation of Eq. (1)
with: (i) a lagged dependent variable to allow for
dynamic expenditure adjustments and (ii) a non-alcoholic beverages price index. This version of the ®rst
sub-model, like its competitors with different advertising speci®cations, ®tted very well as indicated by
the high adjusted R2 and the magnitude of most t
statistics. As expected the trigonometric variables
introduced to internalize the seasonal variations in
expenditures on alcoholic and soft drinks beverages
are highly signi®cant. The Stone price index
(PSTONE) has a coef®cient of 0.59 which suggests
that the demand for the alcoholic and soft drinks
beverages aggregate is inelastic. Expenditures on
alcoholic and soft drinks beverages are unaffected
by changes in per capita income as indicated by the
small and insigni®cant per capita income (Y) coef®-
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
155
Fig. 2. Ontario per capita expenditures on advertising.
cient. It is unclear whether the lack of signi®cance is
real or an artifact stemming from the relatively short
period covered by our monthly series. The coef®cients
for beer and spirits advertising are positive but insigni®cant but the ones for wine and soft drinks are
statistically signi®cant and respectively negative and
positive. In short, advertising has a rather weak effect
on the level of expenditures allocated to alcoholic
beverages. The negative sign on the POP coef®cient
means that expenditures on alcoholic and soft drinks
beverages falls as the population gets older. This
con®rms that changes of life styles over the life cycle
of individual consumers contribute to the shrinkage of
the market for alcoholic beverages.
The results from the application of the LDC criterion to three LA/AIDS sub-models provided a clear
ranking about the three competing advertising speci®cations (see Footnote 10 about the mechanics). The
Polynomial Distributed Lag (PDL) was identi®ed as
the dominant one. Kinnucan's structural heterogeneity
and the lag transformation speci®cations ranked second and third. The estimation results for the dominant
speci®cation are presented in Table 3. A large proportion of the coef®cient are signi®cant and the standard
measures of ®t are good (i.e., system's R2: 0.99; R2s for
the beer, spirits, and wine equations are: 0.82, 0.91,
0.92). The habit formation coef®cients for wine and
spirits are signi®cant and therefore support the
hypothesis that consumers gradually develop a taste
for wine and spirits. This phenomenon is not observed
for a more homogenous product like (Canadian) beer.
The own and cross advertising coef®cients are signi®cant, an outcome that suggests that advertising
effects need not be limited to brand switching within
narrowly de®ned product categories. The imposition
of the inequality restrictions slightly altered the magnitude of the coef®cients but did not provoke sign
reversals. However the importance of inequality
restrictions should not be underestimated as will
become evident in our discussion of the elasticities
below.
Table 4 compares results from the three advertising
speci®cations in he LA/AIDS sub-model. In some
respects, the three speci®cations appear equivalent.
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
156
Table 2
Estimation results from the per capita expenditure sub±modela
Parametersb
Coefficients
t-statistics
Constant
PSTONE
Abeer
Aspirits
Awine
Asoft±drinks
ln xtÿ1
POP
Aapple±juice
Atomato±juice
Y
PNA
cos 1
sin 1
cos 2
sin 2
cos 3
cos 4
sin 4
cos 5
sin 5
cos 6
12.4182
0.5902
0.0018
0.0007
ÿ0.0103
0.0026
ÿ0.2314
ÿ0.000001
0.0001
ÿ0.0001
0.0983
0.4435
ÿ0.1075
0.1478
ÿ0.0600
0.1043
0.1025
ÿ0.0317
ÿ0.0582
ÿ0.0320
0.0509
0.0262
2.09
1.72
1.07
0.21
ÿ2.71
1.67
ÿ3.19
ÿ1.90
0.61
ÿ0.41
0.17
1.47
ÿ4.38
14.99
ÿ7.43
9.11
13.47
ÿ4.34
ÿ8.99
ÿ4.99
6.95
5.72
a
R2 0.98; R2 adjusted 0.97; DW 2.07.
Advertising was specified according to Kinnucan's structural
hetereogeneity hypothesis.
b
For example, the concavity and monotonicity conditions hold with probabilities varying from 23 to 27%
across advertising speci®cations. Similarly, the results
regarding the substitutability between beer and spirits
and beer and soft drinks, the complementarity between
beer and wine and the positive sign of the advertising
elasticity for spirits are robust across advertising
speci®cations. We can also be con®dent about the
positioning of the conditional short run expenditure
elasticities relative to the unit reference. These results
and historical simulations do not provide sharp contrasts between different advertising speci®cations.
According to the reported probabilities, we can be
con®dent that the conditional expenditure elasticity
for beer is the only one in excess of one. Divergence in
results is found in the advertising elasticities. The
results for the PDL speci®cation and its related but
less general Lag Transformation counterpart contrast
with the results from the Structural Heterogeneity
speci®cation. The probability of a negative ownadvertising elasticity is 0.98 for the PDL speci®cation
and only 0.07 for the Structural Heterogeneity model.
The reported probabilities clearly support the Galbraithian hypothesis about the importance of cross
advertising effects. In the PDL model, advertising
expenditures on soft drinks and spirits have a negative
in¯uence on beer consumption but advertising on beer
and soft drinks tend to boost consumption of spirits.
For wine, the probabilities are not high enough to
warrant strong conclusions about cross advertising
effects.
Table 5 also illustrates differences across speci®cations. The magnitude of the advertising elasticities
vary considerably from one speci®cation to another
and sign reversals are observed for all beverages
except spirits. The long run elasticities consistent with
concavity and monotonicity for beer and wine computed from the PDL and lag transformation models are
negative. This phenomenon is not surprising since the
presence of negative advertising elasticities is well
documented in the literature. Saffer (1997) attributes
this phenomenon to a S-shaped `industry-level alcohol
advertising response function'. At high levels of
advertising like the ones observed in North American
markets, the response function is ¯at and could have a
negative slope. Obviously, this does not apply to
spirits with total long run elasticities ranging from
0.225 to 0.361. Spirits have the highest own-advertising elasticity across model speci®cations.
Table 6 shows that the total own-price elasticities
for spirits and wine are essentially unitary across
speci®cations. In contrast, the elasticities for beer
and soft drinks vary widely but they remain within
the boundaries implicitly de®ned by Table 1. The beer
elasticities range from ÿ0.59 to ÿ1.05 while for soft
drinks they span the {ÿ0.22, ÿ0.79} interval. This
evidence clearly shows that advertising speci®cations
can signi®cantly affect advertising and other elasticities! The magnitude of the elasticities, especially for
the more heavily taxed spirits and wine, suggest that
the government would not increase its revenues
through further tax increases.
The long run conditional expenditure elasticities
reported in Table 7 are all close to unity except for soft
drinks. These long run elasticities are more plausible
than their short run counterparts reported in Table 4.
The elasticity for beer is under unity and smaller than
the elasticities for wine and spirits which exceed unity.
The total income elasticities are low for all beverages
and thus con®rm that increases in revenue do not lead
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
157
Table 3
Estimation results of the LA/AIDS sub-model (based on 10000 replications)
Parameters
Estimates
(w/o ineq. restr.)
abeer
tbeer
ADbeerÿbeer
ADbeer±spirits
ADbeer±wine
ADbeer±SD
Qbeer
gbeer±beer
gbeer±spirits
gbeer±wine
gbeer±SDc
bbeer
cos 1
sin 1
cos 2
sin 2
cos 3
sin 3
cos 4
sin 4
cos 5
sin 5
cos 6
sin 6
aspirits
tspirits
ADspirits±beer
ADspirits±spirits
ADspirits±wine
ADspirits±SD
Qspirits
gspirits±beer
gspirits±spirits
gspirits±wine
gspirits±SD
bspirits
0.42167
ÿ0.00005
ÿ0.00209
ÿ0.00425
0.00761
ÿ0.00333
ÿ0.00392
0.09631
ÿ0.02521
ÿ0.07466
0.00356
0.00014
0.00412
0.05251
ÿ0.01513
0.00286
ÿ0.00529
ÿ0.00150
0.00208
0.00995
ÿ0.00676
ÿ0.00023
0.00217
0.00685
0.12180
ÿ0.01643
0.00213
0.00330
ÿ0.00541
0.00152
0.04771
ÿ0.02521
0.06282
0.06766
ÿ0.10527
ÿ0.00015
(0.223)a
(0.017)
(0.001)
(0.002)
(0.003)
(0.002)
(0.004)
(0.103)
(0.082)
(0.025)
(0.053)
(0.000)
(0.006)
(0.007)
(0.005)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.003)
(0.005)
(0.220)
(0.014)
(0.001)
(0.002)
(0.003)
(0.001)
(0.024)
(0.082)
(0.078)
(0.024)
(0.047)
(0.000)
Estimates
(w. ineq. restr.)
0.41256
0.00048
ÿ0.00212
ÿ0.00424
0.00762
ÿ0.00331
ÿ0.00399
0.09211
ÿ0.02185
ÿ0.07394
0.00368
0.00014
0.00421
0.05273
ÿ0.01512
0.00273
ÿ0.00523
ÿ0.00143
0.00218
0.00999
ÿ0.00667
ÿ0.00026
0.00216
0.00687
0.12791
ÿ0.01678
0.00214
0.00332
ÿ0.05439
0.00153
0.04812
ÿ0.02185
0.06062
0.06704
ÿ0.10581
ÿ0.00015
(0.004)b
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.001)
(0.001)
(0.001)
(0.000)
(0.001)
(0.020)
(0.259)
(2.082)
(±)
(±)
(0.006)
(±)
(±)
(±)
(±)
(±)
(±)
(±)
(±)
(±)
(0.006)
(±)
(0.020)
(0.020)
(±)
(0.020)
(0.002)
(0.001)
(0.002)
(0.000)
Parameters
Estimates
(w/o ineq. restr.)
Estimates
(w. ineq. restr.)
cos 1
sin 1
cos 2
sin 2
cos 3
sin 3
cos 4
sin 4
cos 5
sin 5
cos 6
sin 6
awine
twine
ADwine±beer
ADwine±spirits
ADwine±wine
ADwine±SD
Qwine
gwine±beer
gwine±spirits
gwine±wine
gwine±SD
bwine
cos 1
sin 1
cos 2
sin 2
cos 3
sin 3
cos 4
sin 4
cos 5
sin 5
cos 6
sin 6
ÿ0.01113
ÿ0.04573
0.01096
0.00425
0.01349
ÿ0.00799
ÿ0.00556
ÿ0.01252
ÿ0.00342
0.00743
0.00006
ÿ0.00711
ÿ0.08538
0.00651
0.00019
0.00064
ÿ0.00089
0.00032
0.01766
ÿ0.07466
0.06766
0.01529
ÿ0.00829
ÿ0.00003
ÿ0.00214
ÿ0.01542
0.00374
0.00189
0.00399
ÿ0.00108
ÿ0.00190
ÿ0.00404
ÿ0.00208
0.00379
0.00104
ÿ0.00267
ÿ0.01129
ÿ0.04578
0.01096
0.00432
0.01348
ÿ0.00797
ÿ0.00566
ÿ0.01255
ÿ0.00347
0.00752
0.00006
ÿ0.00711
ÿ0.08369
0.00646
0.00019
0.00064
ÿ0.00089
0.00032
0.01777
ÿ0.07394
0.06704
0.01513
ÿ0.00822
ÿ0.00003
ÿ0.00215
ÿ0.01544
0.00374
0.00191
0.00400
ÿ0.00107
ÿ0.00194
ÿ0.00403
ÿ0.00209
0.00381
0.00104
ÿ0.00266
(0.004)
(0.004)
(0.004)
(0.003)
(0.003)
(0.004)
(0.004)
(0.003)
(0.003)
(0.004)
(0.002)
(0.004)
(0.068)
(0.004)
(0.000)
(0.001)
(0.001)
(0.000)
(0.009)
(0.025)
(0.240)
(0.009)
(0.016)
(0.000)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.000)
(0.001)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.002)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.002)
(0.001)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
a
Numbers in parentheses are standard deviations.
Numbers in brackets are numerical standard errors (NSE).
c
SD: soft drinks; The coefficients of the soft drinks equation were derived from the addivity condition.
b
to drastic consumption changes. Conditional Hicksian
elasticities are reported in Table 8. All own-price
elasticities are smaller than one in absolute values
which implies inelastic compensated demands. The
pairs beer/wine and spirits/soft drinks are complements while all other pairs of beverages exhibit substitution relations. Differences between short run and
long run elasticities are minor in comparison to the
differences observed between elasticities computed
with and without the inequality restrictions. Dynamics
are unimportant for beer but matter a little for wine
and spirits.
Conditional Marshallian elasticities are reported in
Table 9. All beverages are price inelastic both in the
short run and in the long run. However, the long
run own-price elasticities for spirits and wine are
close to unity. For beer, the cross-price elasticities
are small except for wine. A glance at the probabilities
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
158
Table 4
Posterior Probabilities about conditional short run elasticities from the three LA/AIDS sub-modelsa
Restrictions
PDL
Struc. Het.
Lag Trans.
Restrictions
PDL
Struc. Het.
Lag Trans.
Concavity and Monotonicity
sbeer±spirits > 0
sbeer±wine < 0
sbeer±SD > 0
sspirits±wine > 0
sspirits±SD < 0
swine±SD > 0
ADbeer±beer < 0
ADspirits±spirit > 0
ADwine±wine < 0
ADSD±SD > 0
ADbeer±spirits < 0
ADbeer±wine > 0
ADbeer±SD < 0
ADspirits±beer > 0
ADspirits±wine < 0
ADspirits±SD > 0
ADwine±beer > 0
ADwine±spirits > 0
ADwine±SD > 0
ADSD±beer < 0
ADSD±spirits > 0
ADSD±wine < 0
Zbeer > 1
Zspirits < 1
Zwine < 1
0.2496
1.00
0.95
0.96
1.00
0.57
0.99
0.98
0.98
0.88
0.92
0.99
0.99
0.98
0.99
0.98
0.86
0.83
0.91
0.76
0.62
0.65
0.79
0.96
0.98
0.94
0.2398
1.00
0.90
0.94
1.00
0.70
0.95
0.07
0.96
0.41
0.40
0.93
0.81
0.93
0.02
0.83
0.97
0.32
0.72
0.49
0.29
0.51
0.60
0.96
0.97
0.91
0.2714
1.00
0.74
0.91
0.99
0.55
0.95
0.77
0.92
0.74
0.88
0.92
0.95
0.88
0.93
0.94
0.65
0.32
0.75
0.51
0.79
0.53
0.62
0.83
0.90
0.79
ZSD < 1
Zbeerÿspirits < 0
Zbeerÿwine < 0
ZbeerÿSD < 0
Zspiritsÿbeer < 0
Zspiritsÿwine < 0
ZspiritsÿSD < 0
Zwineÿbeer < 0
Zwineÿspirits < 0
ZwineÿSD < 0
ZSDÿbeer < 0
ZSDÿspirits < 0
ZSDÿwine < 0
ZSD:ÿspirits < 0
Zbeer±wine < 0
Zbeer±SD < 0
Zspirits±beer < 0
Zspirits±wine < 0
Zspirits±SD < 0
Zwine±beer < 0
Zwine±spirits < 0
Zwine±SD < 0
ZSD±beer < 0
ZSD±spirits < 0
ZSD±wine < 0
±
0.72
1.00
0.95
0.96
1.00
1.00
0.57
0.95
1.00
0.99
0.96
0.57
0.99
0.41
0.99
0.45
0.41
0.99
0.99
0.99
0.99
0.68
0.45
0.99
0.69
±
0.61
1.00
0.90
0.94
1.00
1.00
0.70
0.90
1.00
0.95
0.94
0.70
0.95
0.34
0.98
0.61
0.34
0.97
0.90
0.98
0.97
0.61
0.61
0.90
0.60
±
0.66
1.00
0.74
0.92
1.00
0.99
0.54
0.74
0.99
0.95
0.92
0.54
0.95
0.19
0.95
0.52
0.19
0.95
0.95
0.95
0.95
0.77
0.52
0.95
0.77
±
a
s: Allen±Uzawa elasticities of substitution, AD: advertising elasticities, Zi: expenditures elasticities, Zij : Hicksian elasticities, Zii:
Marshallian elasticities, SD: soft drinks. Except for the probability about the concavity and monotonicity conditions, all other probabilities are
computed from the truncated posterior distribution consistent with concavity and monotonicity.
Table 5
Conditional and total advertising elasticities from the three LA/AIDS sub-model specifications and the dominant group expenditures submodela
Beer
Short run (w/o ineq. restr.)
PDL
Struc. Het.
Lag Trans.
ÿ0.008
ÿ0.006
0.254
0.256
ÿ0.079
ÿ0.077
Spirits
Wine
SD
.
Beer
Short run (w. ineq. restr.)
0.010
0.011
0.215
0.252
0.281
0.282
ÿ0.008
ÿ0.018
0.014
0.004
ÿ0.129
ÿ0.139
0.006
0.009
ÿ0.018
ÿ0.015
0.152
0.155
PDL
Long run (w/o ineq. restr.)
PDL
Struc. Het.
Lag Trans.
a
ÿ0.273
ÿ0.271
0.254
0.256
ÿ0.084
ÿ0.082
Struc. Het.
Lag Trans.
ÿ0.009
ÿ0.007
0.228
0.230
ÿ0.125
ÿ0.123
Spirits
Wine
SD
0.009
0.010
0.242
0.243
0.222
0.223
ÿ0.007
ÿ0.017
0.007
ÿ0.003
ÿ0.103
ÿ0.113
0.007
0.010
ÿ0.027
ÿ0.024
0.210
0.213
0.360
0.361
0.241
0.242
0.224
0.225
ÿ0.260
ÿ0.271
0.007
ÿ0.005
ÿ0.105
ÿ0.116
0.099.100
0.100
ÿ0.027
ÿ0.026
0.286
0.289
Long run (w. ineq. restr.)
0.392
0.393
0.215
0.216
0.283
0.284
ÿ0.296
0.307
0.014
0.002
ÿ0.130
ÿ0.141
0.093
0.094
ÿ0.016
ÿ0.013
0.172
0.175
PDL
Struc.Het.
Lag Trans.
ÿ0.287
ÿ0.285
0.228
0.230
ÿ0.129
ÿ0.127
Total income elasticities appear right below conditional expenditure elasticities SD: soft drinks.
Table 6
Long run Marshallian total price elasticities for all three advertising specifications
Beer
Beer
Spirits
Wine
SD
Spirits
Wine
Soft drinks
PDL
Struc.
Het.
Lag
Trans
PDL
Struc.
Het.
Lag
Trans
PDL
Struc.
Het.
Lag
Trans
PDL
Struc.
Het.
Lag
Trans
ÿ0.59
ÿ0.04
ÿ0.64
0.02
ÿ0.89
0.15
0.57
0.14
ÿ1.05
0.25
0.38
0.12
ÿ0.05
ÿ0.88
0.64
ÿ0.15
0.15
ÿ1.12
0.51
ÿ0.15
0.29
ÿ1.07
0.39
ÿ0.23
ÿ0.24
0.23
ÿ0.96
ÿ0.01
ÿ0.19
0.20
ÿ1.01
0.00
ÿ0.14
0.17
ÿ0.92
0.01
0.04
ÿ0.31
ÿ0.06
ÿ0.22
0.09
ÿ0.15
ÿ0.01
ÿ0.49
0.03
ÿ0.22
ÿ0.07
ÿ0.79
Table 7
Long run conditional expenditure and total income elasticities associated with the dominant model specification
Cond. exp. (w/o ineq. restr.)
Cond. exp. (w. ineq. restr.)
a
Beer
Spirit
Wine
SD
0.933
1.100
1.108
Total income (w/o ineq.restr.)
0.092
0.108
a
0.109
Beer
Spirit
Wine
SD
0.422
0.925
1.110
1.114
0.404
0.041
Total income (w. ineq.restr.)
0.091
0.109
0.110
0.040
SD: soft drinks.
Table 8
Conditional Hicksian elasticities from the PDL LA/AIDS sub-model
Short run (w/o ineq. restr.)
Short run (w. ineq. restr.)
Elasticities
Beer
Spirit
Wine
SD
Elasticities
Beer
Spirit
Wine
SD
Beer
Spirits
Wine
Soft drinks
ÿ0.382
0.204
ÿ0.330
0.285
0.262
ÿ0.475
0.894
ÿ0.062
ÿ0.150
0.317
ÿ0.751
0.089
0.271
ÿ0.046
0.187
ÿ0.313
beer
spirits
wine
soft drinks
ÿ0.552
0.324
ÿ0.242
0.259
0.416
ÿ0.602
0.795
ÿ0.004
ÿ0.110
0.282
ÿ0.780
0.108
0.247
ÿ0.003
0.227
ÿ0.364
Long run (w/o ineq. restr.)
Long run (w. ineq. restr.)
Elasticities
Beer
Spirit
Wine
SD
Elasticities
Beer
Spirit
Wine
SD
Beer
Spirits
Wine
Soft drinks
ÿ0.347
0.229
ÿ0.364
0.126
0.237
ÿ0.527
0.988
ÿ0.023
ÿ0.142
0.348
ÿ0.833
0.037
0.252
ÿ0.049
0.209
ÿ0.140
beer
spirits
wine
soft drinks
ÿ0.507
0.361
ÿ0.269
0.105
0.382
ÿ0.671
0.885
ÿ0.003
ÿ0.101
0.312
ÿ0.871
0.046
0.226
ÿ0.003
0.254
ÿ0.154
Table 9
Conditional Marshallian elasticities from the PDL LA/AIDS sub-model
Short run (w/o ineq. restr.)
Short run (w. ineq. restr.)
Elasticities
Beer
Spirit
Wine
SD
Elasticities
Beer
Spirit
Wine
SD
Beer
Spirits
Wine
Soft drinks
ÿ0.654
ÿ0.067
ÿ0.601
0.014
ÿ0.087
ÿ0.823
0.546
ÿ0.410
ÿ0.273
0.193
ÿ0.874
ÿ0.034
0.013
ÿ0.303
ÿ0.071
ÿ0.570
beer
spirits
wine
soft drinks
ÿ0.660
ÿ0.063
ÿ0.600
0.014
ÿ0.081
ÿ0.826
0.544
ÿ0.411
ÿ0.273
0.193
ÿ0.877
ÿ0.032
0.013
ÿ0.304
ÿ0.067
ÿ0.572
Long run (w/o ineq. restr.)
Long run (w. ineq. restr.)
Elasticities
Beer
Spirit
Wine
SD
Elasticities
Beer
Spirit
Wine
SD
Beer
Spirits
Wine
Soft drinks
ÿ0.600
ÿ0.070
ÿ0.664
0.012
ÿ0.088
ÿ0.910
0.602
ÿ0.169
ÿ0.257
0.212
ÿ0.969
ÿ0.015
0.011
ÿ0.333
ÿ0.076
ÿ0.249
beer
spirits
wine
soft drinks
ÿ0.613
ÿ0.069
ÿ0.669
0.006
ÿ0.075
ÿ0.917
0.606
ÿ0.166
ÿ0.254
0.214
ÿ0.977
ÿ0.013
0.012
ÿ0.337
ÿ0.074
ÿ0.231
160
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
in Table 4 con®rms that beer and wine are complements. From Tables 4 and 9, we can infer that like wine
and beer, spirits and soft drinks are complements for
each other. As expected, spirits are substitutes for
wines and vice versa.
3.1. Modeling and policy implications
There exists a large body of literature in demand
analysis that demonstrates that the choice of a functional form has a strong incidence on calculated
elasticities. In this paper we presented empirical evidence which suggests that `®ner' speci®cation issues
matter as well. We focused on the speci®cation of
advertising in demand analysis holding the choice of a
functional form constant. Three popular speci®cations
were compared. They all performed well (in terms of
estimation and simulation) but they produced wideranging price and advertising elasticities. We believe
that practitioners are often confronted to dif®cult
model selection decisions and this is why a criterion
like that of Pollak and Wales (1991) Likelihood
Dominance Criterion is likely to become an indispensable instrument in the practi
Modeling the demand for alcoholic beverages and
advertising speci®cations
EÂric LarivieÁrea, Bruno Larueb,*, Jim Chalfantc
b
a
Agrifood and Agriculture, Sainte-Foy, Que., Canada G1K 7P4
Â
Centre de Recherche en Economie Agroalimentaire (CREÂA) DeÂpartement d'EÂconomie Agroalimentaire Universite Laval,
Sainte-Foy, Que., Canada G1K 7P4
c
Department of Agricultural and Resource Economics, University of California at Davis, Davis CA, USA
Received 18 March 1998; received in revised form 20 August 1999; accepted 15 September 1999
Abstract
In this paper, the demand for beer, wine, spirits and soft drinks in Ontario is modeled in two parts: an equation is speci®ed
to endogenize group expenditures and a demand system is set up to allocate budgeted group expenditures across types of
beverages. Advertising is allowed to in¯uence both the level of group expenditures and its allocation. Three popular
advertising speci®cations are compared using the J-test and the likelihood dominance criterion. Even though all three
speci®cations ®tted well according to standard criteria, the calculated expenditure, price and advertising elasticities were
sensitive to the manner with which advertising is speci®ed. This clearly highlights the need to rely on a sound criterion to
identify a dominant speci®cation. From the identi®ed dominant speci®cation, we found that advertising has very subtle effects
on expenditures on alcoholic beverages (group and individual beverages). Thus, advertising is not effective in enlarging
markets and this suggests that ®rms (especially breweries) use advertising to compete in zero-sum market share games. From a
public policy perspective, our results are comforting but future research should investigate whether the neutral effect of
advertising on aggregated expenditures hide substantial offsetting changes in the drinking habits of individuals. # 2000
Elsevier Science B.V. All rights reserved.
1. Introduction
The consumption of alcoholic beverages has been a
public concern for decades. As a result, policymakers
have designed regulations to internalize the negative
consumption externalities affecting public safety (i.e.,
drunk driving), public health (i.e., liver cirrhosis) and
*
Corresponding author. Tel.: 1-418-656-2131 ext 5098; fax:
1-418-656-7821.
E-mail address: bruno.larue@eac.ulaval.ca (B. Larue).
labor productivity without loosing sight of the substantial contribution of consumption taxes on government revenues. Advertising is a major preoccupation
of regulators in most countries. In some cases, there is
or has been an outright ban on advertising while in
others the restrictions are designed to censor the
content of the ads or limit the range of media outlets
through which the ads can be shown.
The literature on the effects of advertising of the
consumption of alcoholic beverages can be classi®ed
into two groups. The ®rst one addresses the psycho-
0169-5150/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 9 - 5 1 5 0 ( 9 9 ) 0 0 0 4 4 - 4
148
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
logical and sociological aspects of the ads about
alcoholic beverages and how they end up in¯uencing
individual consumption.1 Our study falls in the second
group since it is concerned with the effects of advertising on aggregate consumption. Our objective is
threefold. First, we assess how different speci®cations
of advertising effects in¯uence the size and signs of
estimated elasticities and determine whether a speci®cation dominates the others. Second, we investigate
the effect of advertising on the level of expenditures on
alcoholic beverages as well as the effect of advertising
on the allocation of these expenditures between beer,
wine, spirits and soft drinks. As such, this constitutes
an extension of what is known in some circles as the
Galbraithian hypothesis.2 Finally, we estimate price
and expenditure elasticities to characterize the
demand for alcoholic beverages and soft drinks in
Ontario, Canada.
In order to achieve these objectives, we constructed
a model in which group expenditure and budget shares
for different types of alcoholic beverages and soft
drinks are endogenized. Group expenditure is modeled as a function of prices, per capita income, advertising, demography and trigonometric variables to
account for seasonality. To facilitate comparisons with
previous studies, we chose dynamic versions of the
LA/AIDS model to explain variations in budget
shares. Three model speci®cations differentiated by
the manner with which advertising effects are incorporated were estimated. Bayesian techniques were
used to insure that the estimated elasticities were
consistent with the concavity and monotonicity conditions. We applied the J-test and the Likelihood
Dominance Criterion (LDC) developed by Pollak
and Wales (1991) to identify dominant advertising
speci®cations for the group expenditure and budget
shares sub-models. We found that advertising is not
effective in enlarging markets and this suggests that
®rms (especially breweries) use advertising to compete in zero-sum games. From a public policy perspective, our results are comforting but future research
should investigate whether the neutral effect of advertising on aggregated expenditures hide potentially
perverse offsetting changes in the drinking habits of
individuals.
The rest of the paper is organized as follows. The
next section presents an overview of the literature on
the demand for alcoholic beverages with an emphasis
on the role of advertising in explaining the demand for
beer, wine and spirits. This is followed by a discussion
about methodology and data. Empirical ®ndings are
presented in the fourth section while the last section
dwells on the modeling and policy implications.
1.1. The consumption of alcoholic beverages and
advertising: some ambiguities and some recurring
results
1
Typically, these studies rely on narrowly defined samples but
allow for a broad range of factors which along advertising can
influence consumption. For example, Strickland (1982) reviewed
700 ads (TV and magazines) and argued that the content of the ads
is less important than the influence of family and friends in
explaining the level of consumption. Strickland (1983) used the TV
watching habits of students to determine their exposure to
advertising of alcoholic beverages. A very weak correlation was
established between advertising and consumption but only after age
and race were accounted for. Again, the attitude of friends and
parents were much more influential than publicity which was also
found to be orthogonal to the proxies used to characterize abuse. In
contrast, Adlaf and Kohn (1989) found a direct link between
advertising and consumption and an indirect link between
advertising and abusive consumption. However, they too found
that the attitude of family and friends has a stronger influence than
advertising.
2
The Galbraithian hypothesis can be traced back to Galbraith
(1967) who asserted that advertising can have a powerful influence
on the distribution of expenditures between broadly defined
product groups. For a more detailed discussion, the interested
reader is referred to Duffy (1991).
Several economists have studied the demand for
alcoholic beverages but only a subset have attempted
to estimate the effect of advertising. Table 1 provides a
non-exhaustive but insightful list of studies on the
demand for alcoholic beverages and some of their
elasticities. A glance at these results reveals that
expenditure and own-price elasticities vary considerably from one study to another. Expenditure elasticities for beer, wine and spirits range from ÿ0.83 to
1.94, ÿ0.01 to 2.10 and 0.46 to 2.66, respectively. The
ranges for the own-price elasticities for the same
products are: 0.26 to ÿ0.89, ÿ0.43 to ÿ1.89, ÿ0.37
to ÿ1.88. The lack of consensus across studies extends
to qualitative results about the nature of the relationships between alcoholic beverages (i.e., complements
versus substitutes).
Studies that incorporate advertising as an explanatory variable have reported low and often negative
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
149
Table 1
Summary of previous studies on the demand for alcoholic beverages
Authors and country
Income elasticities
Own price elasticities
Beer
Wine
Spirits
Beer
Wine
Spirits
Hogarty and Elzinga, 1972 (United States)
Johnson and Oksanen, 1974
Johnson and Oksanen, 1977 (Canada)
Duffy, 1982 (UK)
Clements and Johnson, 1983 (Australia)
0.43
0.04
0.00
0.49
0.80
n.a
ÿ0.01
0.04
1.50
0.75
n.a.
0.23
0.11
1.65
1.91
ÿ0.89
ÿ0.23
ÿ0.27
ÿ0.17
ÿ0.36
n.a.
ÿ0.50
ÿ0.67
ÿ1.14
ÿ0.43
n.a.
ÿ0.91
ÿ1.14
ÿ0.84
ÿ0.74
Tsolakis et al., 1983 (Australia)
Short run
Long run
0.46
0.39
0.88
2.81
n.a.
n.a.
ÿ0.23
ÿ0.20
ÿ0.43
ÿ1.35
n.a.
n.a.
Fuss and Waverman, 1987 (Canada)
Short run
Long run
Quek, 1988 (Canada)
Alley et al., 1989 (British-Columbia: Canada)
Heien and Pompelli, 1989 (United States)
0.39
0.52
0.44
ÿ0.03
1.94
0.54
0.70
1.26
0.21
2.10
0.83
1.05
0.95
0.46
2.66
ÿ0.27
ÿ0.32
ÿ0.16
ÿ0.11
ÿ0.84
ÿ0.76
ÿ0.76
ÿ0.66
ÿ0.75
ÿ0.55
ÿ0.81
ÿ0.83
ÿ0.66
ÿ1.88
ÿ0.50
Johnson et al., 1992 (Canada)
Short run
Long run
0.38
0.27
0.97
2.19
0.92
1.02
ÿ0.26
ÿ0.14
ÿ0.88
ÿ1.17
ÿ0.63
ÿ0.37
Tegene, 1990 (United States)
With structural change
Without structural change
0.50
0.83
0.66
0.69
1.72
1.80
ÿ0.72
ÿ0.80
0.10
ÿ1.10
ÿ1.20
ÿ0.76
n.a.
0.5±1.3
n.a.
n.a.
ÿ0.7±1.9
A
n.a.
0.6±1.5
n.a.
n.a.
ÿ0.8±1.4
n.a.
0.08
0.11
0.48
n.a.
n.a.
2.02
n.a.
n.a.
1.83
ÿ0.54
ÿ0.72
ÿ0.24
n.a.
n.a.
ÿ0.55
n.a.
n.a.
ÿ0.56
n.a.
n.a.
ÿ1.72
n.a.
0.26
n.a.
Advertising elasticities
n.a.
n.a.
Wine
Spirits
ÿ0.044
0.019
Larue et al., 1991 (Ontario: Canada)
wine differentiated by color and origin
(local vs foreign)
wine differentiated by country of origin
Tremblay and Lee, 1992 (United States)
Short run
Long run
Selvanathan, 1995 (UK)
Gallet and List, 1998 (United States)
1964±73
1983±92
Johnson and Oksanen, 1974 (Canada)
Johnson and Oksanen, 1977 (Canada)
Duffy, 1982 (UK)
Fuss and Waverman, 1987 (Canada)
ÿ0.26
n.a.
ÿ0.83
n.a
Cross-price effects
Complements
Substitutes
Beer
beer/wine
beer/spiritsa
beer/spirits
n.a.
beer/wine
wine/beer
wine/spiritsa
wine/beer
n.a.
beer/winea
beer/spiritsa
wine/spiritsa
Quek, 1988 (Canada)
Alley et al., 1989 (British-Columbia: Canada)
beer/spriritsa
wine/spiritsa
beer/winea
beer/spiritsa
wine/spiritsa
n.a.
0.017
n.a.
wine/spiritsa
wine/beera
n.a.
n.a.
n.a.
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
150
Table 1 (Continued )
Authors and country
Income elasticities
Beer
Heien and Pompelli, 1989 (United States)
Own price elasticities
Wine
Spirits
a
beer/wine
beer/spiritsa
wine/spiritsa
Tegene, 1990 (United States)
Without structural change
With structural change
Beer
Wine
Spirits
ÿ0.217
ÿ0.266
0.002±0.022
0.09
0.16
0.07
n.a.
n.a.
n.a.
n.a.
beer/winea
beer/spiritsa
wine/spiritsa
0.282
Larue et al., 1996 (Canada)
Tremblay and Lee, 1992 (United States)
Selvanathan, 1995 (UK)
Gallet and List, 1998 (United States)
a
Canadian with french with most
most others
other wines
beer/spirits
beer/spiritsa
beer/winea
wine/spiritsa
beer/wine
beer/wine
1983±92
1964±73
n.a.
A permutation yields the same qualitative result (e.g., beer/spirits vs. spirits/beer) n.a.: not applicable.
advertising elasticities.3 The lack of support for large
positive advertising effects is robust to differences in
methodology, time periods and geographical areas.
For example, Ogborne and Smart (1975) were puzzled
by the fact that beer sales actually rose through a ban
on beer advertising in Manitoba during the 1980s. In
order to isolate the effects of advertising (or lack of) on
beer sales from other factors, they estimated a singleequation econometric model. They concluded that
advertising had no effect.4 Simpson et al. (1985)
compared per capita consumption of alcoholic beverages of a sample of countries with complete or
partial bans on the advertising of alcoholic beverages
(Norway, Finland, Hungary and Denmark) to a sample
of countries without restrictions (Australia and Japan).
They found no signi®cant differences and argued that
other variables were likely to have a much stronger
in¯uence on consumption than advertising. Wilcox
(1985) analyzed the impact of a restriction that made it
illegal to convey price information in beer ads in
Michigan. With data prior, during and after the
3
Negative own-advertising elasticities are common and not only
in studies about alcoholic beverages. For example, Green et al.
(1991) report negative elasticities for dried fruits generic advertising that are robust across advertising specifications.
4
This study did not control for the publicity originating from
neighboring provinces and US states.
`experiment', he demonstrated that the restriction of
price advertising did not affect beer sales. In contrast,
Ornstein and Hanssens (1985) argued that price information, and hence beer ads, may have an indirect
effect on beer sales through the negative effect of the
ads on prices.5 However, the publicity variable in their
model turned out to be statistically insigni®cant. Duffy
(1982) analyzed the effect of advertising on the consumption of beer, wine and spirits between 1963 and
1978 in England. OLS and 3SLS estimation results
showed that advertising had no effect on sales. Duffy
(1983) tried to capture the effect of advertising within
beverage types by introducing ®ner product de®nitions (i.e., eight categories of wine and spirits). It was
concluded that advertising had very small effects on
budget shares and no effect on the amount spent on all
alcoholic beverages. Tegene (1990) used Kalman
®lters to address the issue of structural change in
the computations of elasticities. Indeed, he found
structural changes in the demands for beer, wine
and spirits but failed to identify a signi®cant relationship between advertising and demand. Motivated by
5
Price advertising need not lead to price reductions. In fact, in an
oligopoly setting, it is well-known that price advertising and
policies of not being `undercut' facilitate collusion. The intuition is
that a firm has no incentive to lower prices if it is certain that other
firms will match any price cut.
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
the same purpose, Gallet and List (1998) used a gradual
switching model to show that the demand for beer in the
United States had become an inferior good insensitive to
price changes.Tremblay and Lee (1992)investigated the
effects of advertising on beer sales in the US for the
period 1953±1983.Again,advertisingfailed toin¯uence
total sales but might have had an effect on the market
shares of various brands.
2. Methodology and data
Our methodology is based on the hypothesis that
advertising can alter both the size and the allocation of
monthly expenditures on alcoholic beverages and soft
drinks. As in Fuss and Waverman (1987) and Heien
and Pick (1991), the structure of our model can be
decomposed into two sub-models. The ®rst one endogenizes expenditures on alcoholic beverages and soft
drinks. It is assumed that individuals allocate their
income between this group of beverages and an
aggregate good. The second sub-model is a conditional AIDS demand system that allocates the expenditures derived from the ®rst sub-model between beer,
wine, spirits and soft drinks.6
6
Our modeling strategy assumes that the utility function is
weakly separable. This allows the utility function to be partitioned
into at least two subsets, say one including alcoholic and soft drinks
beverages and another one for all other goods. In this instance, the
demand for a good in a particular subset can be expressed as a
function of the prices of the goods in that subset and the level of
expenditure spent on those goods (Pollak and Wales, 1992, p. 47).
The prices of goods belonging to the other subset and the level of
expenditure spent on all subsets influence the demand for a good in
a given subset only through the level of expenditure allocated to the
given subset. Weak separability is not a sufficient condition for
treating expenditures on a given subset as exogenous (Lafrance,
1991). Hence, the estimation of conditional demand systems should
endogenize subset expenditures. The estimation of subset expenditures and budget shares equations is often done in the context of a
two-stage budgeting process which imposes stronger restrictions on
preferences. This is so because one needs to worry about the
conditions under which an aggregate price index (for the goods in a
subset say the alcoholic beverages and soft drinks) can be used.
Strong price aggregation is consistent with utility maximizing
behavior if and only if the sub-utility functions are of either the
Generalized Gorman Polar Form (GGPF) or a homothetic form.
Unfortunately, homothetic weak separability translates into unitary
conditional expenditures elasticities (Moschini and Green, 1994).
In this study, the class of preferences for the beverage subset is the
price-independent generalized log-linear or PIGLOG form which is
GGPF (Deaton and Muellbauer, 1980). Two-stage budgeting using
151
The ®rst sub-model is speci®ed as a single equation
with the log of per capita expenditure on alcoholic
beverages and soft drinks as the dependent variable:
(1)
ln x f PSTONE; PNA; ; Y; POP; g AI ; Z
Pn
where x i1 Pi Qi , Pi is the deflated price of
beverage i, Qi is the per capita quantity consumed
of beverage i, PSTONE is the Stone price index, PNA is
a price index for non-alcoholic beverages, Y is real per
capita income, POP is the proportion of the population
of age 15 and above, g(Ai) are functions of per capita
advertising expenditure on beverages i 1,...,n, and Z
is a set of variables internalizing seasonal effects.
Nominal variables were deflated by a beverage price
index for Ontario.
Advertising can be modeled in different ways.
Common functional forms for g(Ai) encountered in
the literature include the lag transformation speci®cation LkAi (e.g., Duffy, 1982, 1983; Clements and
Johnson, 1983; Goddard, 1988; Tremblay and Lee,
1992)7 and Kinnucan's structural heterogeneity speci®cation Ait (e.g., Kinnucan and Venkateswaran,
1994), where L is the lag operator and t is a time
trend. Polynomial Distributed Lag (PDL) schemes are
also commonly used (e.g., Thompson, 1978; Ward and
Dixon, 1989). In our empirical analysis, a PDL
scheme of degree 2 with end-points restrictions was
compared to the other two advertising speci®cations.
We relied on non-nested tests,8 diagnostics checks and
the plausibility of the derived elasticities to rank the
GGPF is also generally restrictive because it requires the utility
function to be additive in the sub-utility functions. However, when
there are only two sub-utility functions, strong price aggregation
and two-stage budgeting does not imply unreasonable restrictions
on the form of the utility function (Gorman, 1959; Fuss and
Waverman, 1987). Edgerton (1997) argues that multistage budgeting can nevertheless generate `reasonably' accurate results under
rather usual conditions.
7
The setting of k is arbitrary even though indicators like AIC or
FPE and studies like Clarke's (Clarke, 1976) can help narrow down
the range of plausible values. In our tests, k 2 worked best. A
generalization to choosing a specific k is to construct a weighted
average of lagged advertising levels as in Rickertsen et al. (1995).
In this case, appropriate lag length and weights must be chosen.
8
In the context of single equation models, several non-nested
tests have been developed in the early 1980s. In this instance, we
relied on the well known J-test. For a thorough review of this test
and alternative ones, see Davidson and MacKinnon (1993) (pp.
381±388).
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
152
speci®cations. Kinnucan's structural heterogeneity
outperformed the other speci®cations and it was
retained. Regarding the modeling of seasonal effects,
two competing alternatives were compared (dummy
variables versus trigonometric functions). Using the
same criteria as for the selection of the advertising
speci®cation, it was found that the trigonometric
functions outperformed the seasonal dummies.
The functional form for the conditional demand
system is the linear version of the Almost Ideal
Demand System commonly known as LA/AIDS. Several arguments can be presented to justify this choice.
First, several studies on alcoholic beverages have used
the AIDS model (e.g., Fuss and Waverman, 1987;
Alley et al., 1989; Heien and Pompelli, 1989; Larue
et al., 1991) and relying on the same functional form
makes for `cleaner' comparisons. Secondly, the AIDS
functional form is (locally) ¯exible, it is easy to
estimate, especially in its linear version and it fared
very well in a recent comparative study (Green et al.,
1995). Finally, Alston et al. (1994) have demonstrated
that LA/AIDS provides accurate estimates of elasticities when the true data generating process is AIDS.
We augmented the speci®cation of the standard LA/
AIDS model with habit formation variables (lagged
quantities Qjtÿ12), a time trend (t), trigonometric
variables to captures seasonal effects and advertising
variables. The estimated budget shares can be represented as follows:
w i ai
n
X
gij lnPj bi ln
j1
n
X
Oij Qjtÿ12
j1
ji t mi
n
x X
Fij g Ajt
pc j1
6
X
kcik cos fk ksik sin fk
k1
(2)
where fk 2pk, k 1,...,6, Pj is the price of beverage
j, x is the level of expenditure estimated in Eq. (1), pc is
a normalized Stone price index9 and gAjt captures
advertising effects as in Eq. (1). For theoretical con-
9
As argued by Moschini (1995), the Stone price index is not
invariant to the choice of measurement units in prices and
quantities and this influences the approximation properties of the
model. To remedy this problem, prices are divided by their mean
before being used to construct the Stone price index. This
normalization does not affect the computations of elasticities.
sistency and to reduce the number of parameters to be
estimated, it is common to impose additivity, symmetry and homogeneity restrictions. A sufficient condition for the expenditureP
shares to be homogenous of
degree zero in prices is: nj1 gij 0, 8i. Symmetric
changes in compensated demand functions can be
imposed
by settingP
gij gji, 8i 6 j. Additivity requires
Pn
n
i1 ai 1 and
i1 bi 0. These conditions are
trivially satisfied for a model with n goods when the
estimation is carried out on a subset of n ÿ 1 independent equations. The parameters of the dropped
equation are then computed from the restrictions
and the estimated parameters of the n ÿ 1 expenditure
shares.
In studies using the AIDS or LA/AIDS functional
forms, it is common to test whether concavity and
monotonicity conditions are respected. The concavity
property of the expenditure function insures that substitution possibilities lessen the impact of price
increases on expenditures while monotonicity maintains budget shares in the {0,1} domain. The concavity
and monotonicity conditions cannot be easily imposed
because they involve inequality restrictions. For
instance, concavity imposes negative semi-de®niteness on the Slutsky matrix for all observations. As in
Chalfant et al. (1991) and Tif®n and Aguiar (1995), we
used a Bayesian framework and, more speci®cally
Monte Carlo integration and Importance Sampling, to
insure that the parameters used to compute elasticities
are consistent with the concavity and monotonicity
conditions.10
Conditional short term elasticities were computed
according to the LA/AIDS formulae found in Alston
et al. (1994). Assuming as in Chalfant (1987) that
@P*/@ln Pj wj, it can be shown that the expenditure
and Marshallian own and cross price elasticities are
Zi 1
Zij
bi
;
wi
gij
wj
ÿ bi
wi
wi
Zii ÿ1
gii
ÿ bi ;
wi
(3)
10
The implementation is thoroughly described in Chalfant et al.
(1991). A classical alternative to imposing curvature conditions has
been proposed by Moschini (1998) and Ryan and Wales (1998).
Though more cumbersome, the Bayesian framework has the
advantage of providing an estimate of the probability that the
restrictions hold.
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
where the wi's are the estimated budget shares. The
formulae for the Hicksian/compensated and substitution elasticities are
Zij wj sij Zij wj Zi ;
sij 1
gij
;
wi wj
sii 1
8i 6 j;
gii
1
ÿ ;
2
wi wi
(4)
As in Goddard (1988) and Duffy (1982), the formula for the advertising elasticity is
Fij
(5)
ADij
wi
Conditional short term elasticities are static measures that do not take into account habit formation.
Adjusting for the dynamics yields the following conditional long run expenditures and Marshallian elasticities:
bi wi
;
wi ÿ Oi Qi
gij ÿ bi wj
Zij
wi ÿ Oi Qi
Zi
Zii
gii ÿ wi ÿ bi wi
;
wi ÿ Oi Qi
(6)
where Oi is a coefficient associated with habit formation and Qi is the mean of per capita consumption for
beverage i. Hicksian and substitution elasticities can
be derived through the Slutsky equation. Conditional
long run advertising elasticities are computed according to the formula below:
ADij
Fij
wi ÿ Oi Qi
(7)
Finally, total elasticities that combine both estimation
stages can be computed (e.g., Edgerton, 1997). These
elasticities are useful because they take into account
that a change in an exogenous variable will affect the
budget shares of each type of alcoholic beverages
as well as the overall budget spent on alcoholic
beverages. Total price, income and advertising
elasticities are computed according to the following
formulae:
ZTij Zij wi Zi by ;
ADTij ADij Zi Ayj ;
ZTi Zi by ;
share for beverage i, by is the income coefficient
from the first sub-model and Ayj is the advertising
coefficient for beverage j in the group expenditure
sub-model.
A critical step in the implementation of the Bayesian framework is the generation of the parameter
estimates and the variance-covariance matrix that are
used in the generation of antithetic replications. We
attempted an FIML estimation of both sub-models
with homogeneity and symmetry imposed. Even
though convergence was achieved, less than 0.1%
of the 10000 replications generated from the estimated
coef®cients and the variance-covariance matrix were
consistent with the monotonicity and concavity conditions. As a result, we chose to estimate the submodels separately. The ®rst sub-model was estimated
with OLS and the second sub-model was estimated
with the ITSUR estimator. Prior to the estimation, we
checked the stationarity property of the variables in
the model with the Augmented Dickey±Fuller test.
The results led us to reject the null of non-stationarity
and to estimate both sub-models in levels.11
The monthly data series for this study cover a period
starting in May of 1979 and ending in April of 1987.
Data about quantities consumed and expenditures on
wine, spirits and beer were provided by the Liquor
Control Board of Ontario and Brewers Retail. The data
on advertising expenditures comes from Ambler
Research and Elliot Research. These two ®rms graciously made available to us their compilations of
advertising expenditures. The advertising expenditures were aggregated over all media.
Fig. 1 illustrates the evolution of per capita consumption of beer, wine, spirits and soft drinks in
Ontario between 1979 and 1987. Among alcoholic
beverages, beer is the product with the highest per
capita consumption with 6 l/person/year or about six
times the per capita consumption of wine and spirits.
Consumption trends for all beverages are ¯at over the
entire sample period. However, there appears to be
seasonal deviations around the trends. The seasonal
pattern for beer consumption is characterized by peeks
11
(8)
where Zij and Zi are the conditional Marshallian
price and expenditures elasticities, wi is the budget
153
Because of obvious seasonal effects, the specification of the
ADF tests included seasonal dummy variables. Because they are of
the same order as the constant term, these nonstochastic regressors
do not affect the asymptotic distributions of the test statictics
(Davidson and MacKinnon, 1993, p. 705).
154
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
Fig. 1. Ontario per capita consumption.
in the summer and around Christmas. As an indication
of the magnitudes of the seasonal variations, per capita
beer consumption typically falls under 2 l in February
to rise to roughly 8 l in July. The seasonal pattern for
per capita soft drinks consumption is very similar to
the one for beer. In contrast, per capita consumption of
wine and spirits slowly rise in the spring and summer
months before `jumping' to a peak in December.
Fig. 2 shows the trends in per capita expenditures on
advertising for beer, wine and spirits. As for per capita
consumption, beer leads the other alcoholic beverages.
Unlike the per capita consumption series, the long
term trends in advertising are not ¯at and exhibit rather
modest seasonal variations. Per capita advertising
expenditure for beer gradually rose between 1979
and 1984 and fell thereafter (reaching a peak of
$0.058 in September of 1984). Per capita advertising
expenditures on wine and spirits peeked much earlier
than beer and have been declining throughout most of
the sample period. The decline in per capita advertising expenditures is most pronounced for spirits ($0.04
in April of 1981 versus $0.015 in April of 1987).
3. The results
The estimation results of the dominant speci®cation
of the ®rst sub-model are presented in Table 2. To
avoid coef®cients with wrong signs and implausible
elasticities, we augmented the speci®cation of Eq. (1)
with: (i) a lagged dependent variable to allow for
dynamic expenditure adjustments and (ii) a non-alcoholic beverages price index. This version of the ®rst
sub-model, like its competitors with different advertising speci®cations, ®tted very well as indicated by
the high adjusted R2 and the magnitude of most t
statistics. As expected the trigonometric variables
introduced to internalize the seasonal variations in
expenditures on alcoholic and soft drinks beverages
are highly signi®cant. The Stone price index
(PSTONE) has a coef®cient of 0.59 which suggests
that the demand for the alcoholic and soft drinks
beverages aggregate is inelastic. Expenditures on
alcoholic and soft drinks beverages are unaffected
by changes in per capita income as indicated by the
small and insigni®cant per capita income (Y) coef®-
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
155
Fig. 2. Ontario per capita expenditures on advertising.
cient. It is unclear whether the lack of signi®cance is
real or an artifact stemming from the relatively short
period covered by our monthly series. The coef®cients
for beer and spirits advertising are positive but insigni®cant but the ones for wine and soft drinks are
statistically signi®cant and respectively negative and
positive. In short, advertising has a rather weak effect
on the level of expenditures allocated to alcoholic
beverages. The negative sign on the POP coef®cient
means that expenditures on alcoholic and soft drinks
beverages falls as the population gets older. This
con®rms that changes of life styles over the life cycle
of individual consumers contribute to the shrinkage of
the market for alcoholic beverages.
The results from the application of the LDC criterion to three LA/AIDS sub-models provided a clear
ranking about the three competing advertising speci®cations (see Footnote 10 about the mechanics). The
Polynomial Distributed Lag (PDL) was identi®ed as
the dominant one. Kinnucan's structural heterogeneity
and the lag transformation speci®cations ranked second and third. The estimation results for the dominant
speci®cation are presented in Table 3. A large proportion of the coef®cient are signi®cant and the standard
measures of ®t are good (i.e., system's R2: 0.99; R2s for
the beer, spirits, and wine equations are: 0.82, 0.91,
0.92). The habit formation coef®cients for wine and
spirits are signi®cant and therefore support the
hypothesis that consumers gradually develop a taste
for wine and spirits. This phenomenon is not observed
for a more homogenous product like (Canadian) beer.
The own and cross advertising coef®cients are signi®cant, an outcome that suggests that advertising
effects need not be limited to brand switching within
narrowly de®ned product categories. The imposition
of the inequality restrictions slightly altered the magnitude of the coef®cients but did not provoke sign
reversals. However the importance of inequality
restrictions should not be underestimated as will
become evident in our discussion of the elasticities
below.
Table 4 compares results from the three advertising
speci®cations in he LA/AIDS sub-model. In some
respects, the three speci®cations appear equivalent.
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
156
Table 2
Estimation results from the per capita expenditure sub±modela
Parametersb
Coefficients
t-statistics
Constant
PSTONE
Abeer
Aspirits
Awine
Asoft±drinks
ln xtÿ1
POP
Aapple±juice
Atomato±juice
Y
PNA
cos 1
sin 1
cos 2
sin 2
cos 3
cos 4
sin 4
cos 5
sin 5
cos 6
12.4182
0.5902
0.0018
0.0007
ÿ0.0103
0.0026
ÿ0.2314
ÿ0.000001
0.0001
ÿ0.0001
0.0983
0.4435
ÿ0.1075
0.1478
ÿ0.0600
0.1043
0.1025
ÿ0.0317
ÿ0.0582
ÿ0.0320
0.0509
0.0262
2.09
1.72
1.07
0.21
ÿ2.71
1.67
ÿ3.19
ÿ1.90
0.61
ÿ0.41
0.17
1.47
ÿ4.38
14.99
ÿ7.43
9.11
13.47
ÿ4.34
ÿ8.99
ÿ4.99
6.95
5.72
a
R2 0.98; R2 adjusted 0.97; DW 2.07.
Advertising was specified according to Kinnucan's structural
hetereogeneity hypothesis.
b
For example, the concavity and monotonicity conditions hold with probabilities varying from 23 to 27%
across advertising speci®cations. Similarly, the results
regarding the substitutability between beer and spirits
and beer and soft drinks, the complementarity between
beer and wine and the positive sign of the advertising
elasticity for spirits are robust across advertising
speci®cations. We can also be con®dent about the
positioning of the conditional short run expenditure
elasticities relative to the unit reference. These results
and historical simulations do not provide sharp contrasts between different advertising speci®cations.
According to the reported probabilities, we can be
con®dent that the conditional expenditure elasticity
for beer is the only one in excess of one. Divergence in
results is found in the advertising elasticities. The
results for the PDL speci®cation and its related but
less general Lag Transformation counterpart contrast
with the results from the Structural Heterogeneity
speci®cation. The probability of a negative ownadvertising elasticity is 0.98 for the PDL speci®cation
and only 0.07 for the Structural Heterogeneity model.
The reported probabilities clearly support the Galbraithian hypothesis about the importance of cross
advertising effects. In the PDL model, advertising
expenditures on soft drinks and spirits have a negative
in¯uence on beer consumption but advertising on beer
and soft drinks tend to boost consumption of spirits.
For wine, the probabilities are not high enough to
warrant strong conclusions about cross advertising
effects.
Table 5 also illustrates differences across speci®cations. The magnitude of the advertising elasticities
vary considerably from one speci®cation to another
and sign reversals are observed for all beverages
except spirits. The long run elasticities consistent with
concavity and monotonicity for beer and wine computed from the PDL and lag transformation models are
negative. This phenomenon is not surprising since the
presence of negative advertising elasticities is well
documented in the literature. Saffer (1997) attributes
this phenomenon to a S-shaped `industry-level alcohol
advertising response function'. At high levels of
advertising like the ones observed in North American
markets, the response function is ¯at and could have a
negative slope. Obviously, this does not apply to
spirits with total long run elasticities ranging from
0.225 to 0.361. Spirits have the highest own-advertising elasticity across model speci®cations.
Table 6 shows that the total own-price elasticities
for spirits and wine are essentially unitary across
speci®cations. In contrast, the elasticities for beer
and soft drinks vary widely but they remain within
the boundaries implicitly de®ned by Table 1. The beer
elasticities range from ÿ0.59 to ÿ1.05 while for soft
drinks they span the {ÿ0.22, ÿ0.79} interval. This
evidence clearly shows that advertising speci®cations
can signi®cantly affect advertising and other elasticities! The magnitude of the elasticities, especially for
the more heavily taxed spirits and wine, suggest that
the government would not increase its revenues
through further tax increases.
The long run conditional expenditure elasticities
reported in Table 7 are all close to unity except for soft
drinks. These long run elasticities are more plausible
than their short run counterparts reported in Table 4.
The elasticity for beer is under unity and smaller than
the elasticities for wine and spirits which exceed unity.
The total income elasticities are low for all beverages
and thus con®rm that increases in revenue do not lead
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
157
Table 3
Estimation results of the LA/AIDS sub-model (based on 10000 replications)
Parameters
Estimates
(w/o ineq. restr.)
abeer
tbeer
ADbeerÿbeer
ADbeer±spirits
ADbeer±wine
ADbeer±SD
Qbeer
gbeer±beer
gbeer±spirits
gbeer±wine
gbeer±SDc
bbeer
cos 1
sin 1
cos 2
sin 2
cos 3
sin 3
cos 4
sin 4
cos 5
sin 5
cos 6
sin 6
aspirits
tspirits
ADspirits±beer
ADspirits±spirits
ADspirits±wine
ADspirits±SD
Qspirits
gspirits±beer
gspirits±spirits
gspirits±wine
gspirits±SD
bspirits
0.42167
ÿ0.00005
ÿ0.00209
ÿ0.00425
0.00761
ÿ0.00333
ÿ0.00392
0.09631
ÿ0.02521
ÿ0.07466
0.00356
0.00014
0.00412
0.05251
ÿ0.01513
0.00286
ÿ0.00529
ÿ0.00150
0.00208
0.00995
ÿ0.00676
ÿ0.00023
0.00217
0.00685
0.12180
ÿ0.01643
0.00213
0.00330
ÿ0.00541
0.00152
0.04771
ÿ0.02521
0.06282
0.06766
ÿ0.10527
ÿ0.00015
(0.223)a
(0.017)
(0.001)
(0.002)
(0.003)
(0.002)
(0.004)
(0.103)
(0.082)
(0.025)
(0.053)
(0.000)
(0.006)
(0.007)
(0.005)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.003)
(0.005)
(0.220)
(0.014)
(0.001)
(0.002)
(0.003)
(0.001)
(0.024)
(0.082)
(0.078)
(0.024)
(0.047)
(0.000)
Estimates
(w. ineq. restr.)
0.41256
0.00048
ÿ0.00212
ÿ0.00424
0.00762
ÿ0.00331
ÿ0.00399
0.09211
ÿ0.02185
ÿ0.07394
0.00368
0.00014
0.00421
0.05273
ÿ0.01512
0.00273
ÿ0.00523
ÿ0.00143
0.00218
0.00999
ÿ0.00667
ÿ0.00026
0.00216
0.00687
0.12791
ÿ0.01678
0.00214
0.00332
ÿ0.05439
0.00153
0.04812
ÿ0.02185
0.06062
0.06704
ÿ0.10581
ÿ0.00015
(0.004)b
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.001)
(0.001)
(0.001)
(0.000)
(0.001)
(0.020)
(0.259)
(2.082)
(±)
(±)
(0.006)
(±)
(±)
(±)
(±)
(±)
(±)
(±)
(±)
(±)
(0.006)
(±)
(0.020)
(0.020)
(±)
(0.020)
(0.002)
(0.001)
(0.002)
(0.000)
Parameters
Estimates
(w/o ineq. restr.)
Estimates
(w. ineq. restr.)
cos 1
sin 1
cos 2
sin 2
cos 3
sin 3
cos 4
sin 4
cos 5
sin 5
cos 6
sin 6
awine
twine
ADwine±beer
ADwine±spirits
ADwine±wine
ADwine±SD
Qwine
gwine±beer
gwine±spirits
gwine±wine
gwine±SD
bwine
cos 1
sin 1
cos 2
sin 2
cos 3
sin 3
cos 4
sin 4
cos 5
sin 5
cos 6
sin 6
ÿ0.01113
ÿ0.04573
0.01096
0.00425
0.01349
ÿ0.00799
ÿ0.00556
ÿ0.01252
ÿ0.00342
0.00743
0.00006
ÿ0.00711
ÿ0.08538
0.00651
0.00019
0.00064
ÿ0.00089
0.00032
0.01766
ÿ0.07466
0.06766
0.01529
ÿ0.00829
ÿ0.00003
ÿ0.00214
ÿ0.01542
0.00374
0.00189
0.00399
ÿ0.00108
ÿ0.00190
ÿ0.00404
ÿ0.00208
0.00379
0.00104
ÿ0.00267
ÿ0.01129
ÿ0.04578
0.01096
0.00432
0.01348
ÿ0.00797
ÿ0.00566
ÿ0.01255
ÿ0.00347
0.00752
0.00006
ÿ0.00711
ÿ0.08369
0.00646
0.00019
0.00064
ÿ0.00089
0.00032
0.01777
ÿ0.07394
0.06704
0.01513
ÿ0.00822
ÿ0.00003
ÿ0.00215
ÿ0.01544
0.00374
0.00191
0.00400
ÿ0.00107
ÿ0.00194
ÿ0.00403
ÿ0.00209
0.00381
0.00104
ÿ0.00266
(0.004)
(0.004)
(0.004)
(0.003)
(0.003)
(0.004)
(0.004)
(0.003)
(0.003)
(0.004)
(0.002)
(0.004)
(0.068)
(0.004)
(0.000)
(0.001)
(0.001)
(0.000)
(0.009)
(0.025)
(0.240)
(0.009)
(0.016)
(0.000)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.000)
(0.001)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.002)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.002)
(0.001)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
a
Numbers in parentheses are standard deviations.
Numbers in brackets are numerical standard errors (NSE).
c
SD: soft drinks; The coefficients of the soft drinks equation were derived from the addivity condition.
b
to drastic consumption changes. Conditional Hicksian
elasticities are reported in Table 8. All own-price
elasticities are smaller than one in absolute values
which implies inelastic compensated demands. The
pairs beer/wine and spirits/soft drinks are complements while all other pairs of beverages exhibit substitution relations. Differences between short run and
long run elasticities are minor in comparison to the
differences observed between elasticities computed
with and without the inequality restrictions. Dynamics
are unimportant for beer but matter a little for wine
and spirits.
Conditional Marshallian elasticities are reported in
Table 9. All beverages are price inelastic both in the
short run and in the long run. However, the long
run own-price elasticities for spirits and wine are
close to unity. For beer, the cross-price elasticities
are small except for wine. A glance at the probabilities
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
158
Table 4
Posterior Probabilities about conditional short run elasticities from the three LA/AIDS sub-modelsa
Restrictions
PDL
Struc. Het.
Lag Trans.
Restrictions
PDL
Struc. Het.
Lag Trans.
Concavity and Monotonicity
sbeer±spirits > 0
sbeer±wine < 0
sbeer±SD > 0
sspirits±wine > 0
sspirits±SD < 0
swine±SD > 0
ADbeer±beer < 0
ADspirits±spirit > 0
ADwine±wine < 0
ADSD±SD > 0
ADbeer±spirits < 0
ADbeer±wine > 0
ADbeer±SD < 0
ADspirits±beer > 0
ADspirits±wine < 0
ADspirits±SD > 0
ADwine±beer > 0
ADwine±spirits > 0
ADwine±SD > 0
ADSD±beer < 0
ADSD±spirits > 0
ADSD±wine < 0
Zbeer > 1
Zspirits < 1
Zwine < 1
0.2496
1.00
0.95
0.96
1.00
0.57
0.99
0.98
0.98
0.88
0.92
0.99
0.99
0.98
0.99
0.98
0.86
0.83
0.91
0.76
0.62
0.65
0.79
0.96
0.98
0.94
0.2398
1.00
0.90
0.94
1.00
0.70
0.95
0.07
0.96
0.41
0.40
0.93
0.81
0.93
0.02
0.83
0.97
0.32
0.72
0.49
0.29
0.51
0.60
0.96
0.97
0.91
0.2714
1.00
0.74
0.91
0.99
0.55
0.95
0.77
0.92
0.74
0.88
0.92
0.95
0.88
0.93
0.94
0.65
0.32
0.75
0.51
0.79
0.53
0.62
0.83
0.90
0.79
ZSD < 1
Zbeerÿspirits < 0
Zbeerÿwine < 0
ZbeerÿSD < 0
Zspiritsÿbeer < 0
Zspiritsÿwine < 0
ZspiritsÿSD < 0
Zwineÿbeer < 0
Zwineÿspirits < 0
ZwineÿSD < 0
ZSDÿbeer < 0
ZSDÿspirits < 0
ZSDÿwine < 0
ZSD:ÿspirits < 0
Zbeer±wine < 0
Zbeer±SD < 0
Zspirits±beer < 0
Zspirits±wine < 0
Zspirits±SD < 0
Zwine±beer < 0
Zwine±spirits < 0
Zwine±SD < 0
ZSD±beer < 0
ZSD±spirits < 0
ZSD±wine < 0
±
0.72
1.00
0.95
0.96
1.00
1.00
0.57
0.95
1.00
0.99
0.96
0.57
0.99
0.41
0.99
0.45
0.41
0.99
0.99
0.99
0.99
0.68
0.45
0.99
0.69
±
0.61
1.00
0.90
0.94
1.00
1.00
0.70
0.90
1.00
0.95
0.94
0.70
0.95
0.34
0.98
0.61
0.34
0.97
0.90
0.98
0.97
0.61
0.61
0.90
0.60
±
0.66
1.00
0.74
0.92
1.00
0.99
0.54
0.74
0.99
0.95
0.92
0.54
0.95
0.19
0.95
0.52
0.19
0.95
0.95
0.95
0.95
0.77
0.52
0.95
0.77
±
a
s: Allen±Uzawa elasticities of substitution, AD: advertising elasticities, Zi: expenditures elasticities, Zij : Hicksian elasticities, Zii:
Marshallian elasticities, SD: soft drinks. Except for the probability about the concavity and monotonicity conditions, all other probabilities are
computed from the truncated posterior distribution consistent with concavity and monotonicity.
Table 5
Conditional and total advertising elasticities from the three LA/AIDS sub-model specifications and the dominant group expenditures submodela
Beer
Short run (w/o ineq. restr.)
PDL
Struc. Het.
Lag Trans.
ÿ0.008
ÿ0.006
0.254
0.256
ÿ0.079
ÿ0.077
Spirits
Wine
SD
.
Beer
Short run (w. ineq. restr.)
0.010
0.011
0.215
0.252
0.281
0.282
ÿ0.008
ÿ0.018
0.014
0.004
ÿ0.129
ÿ0.139
0.006
0.009
ÿ0.018
ÿ0.015
0.152
0.155
PDL
Long run (w/o ineq. restr.)
PDL
Struc. Het.
Lag Trans.
a
ÿ0.273
ÿ0.271
0.254
0.256
ÿ0.084
ÿ0.082
Struc. Het.
Lag Trans.
ÿ0.009
ÿ0.007
0.228
0.230
ÿ0.125
ÿ0.123
Spirits
Wine
SD
0.009
0.010
0.242
0.243
0.222
0.223
ÿ0.007
ÿ0.017
0.007
ÿ0.003
ÿ0.103
ÿ0.113
0.007
0.010
ÿ0.027
ÿ0.024
0.210
0.213
0.360
0.361
0.241
0.242
0.224
0.225
ÿ0.260
ÿ0.271
0.007
ÿ0.005
ÿ0.105
ÿ0.116
0.099.100
0.100
ÿ0.027
ÿ0.026
0.286
0.289
Long run (w. ineq. restr.)
0.392
0.393
0.215
0.216
0.283
0.284
ÿ0.296
0.307
0.014
0.002
ÿ0.130
ÿ0.141
0.093
0.094
ÿ0.016
ÿ0.013
0.172
0.175
PDL
Struc.Het.
Lag Trans.
ÿ0.287
ÿ0.285
0.228
0.230
ÿ0.129
ÿ0.127
Total income elasticities appear right below conditional expenditure elasticities SD: soft drinks.
Table 6
Long run Marshallian total price elasticities for all three advertising specifications
Beer
Beer
Spirits
Wine
SD
Spirits
Wine
Soft drinks
PDL
Struc.
Het.
Lag
Trans
PDL
Struc.
Het.
Lag
Trans
PDL
Struc.
Het.
Lag
Trans
PDL
Struc.
Het.
Lag
Trans
ÿ0.59
ÿ0.04
ÿ0.64
0.02
ÿ0.89
0.15
0.57
0.14
ÿ1.05
0.25
0.38
0.12
ÿ0.05
ÿ0.88
0.64
ÿ0.15
0.15
ÿ1.12
0.51
ÿ0.15
0.29
ÿ1.07
0.39
ÿ0.23
ÿ0.24
0.23
ÿ0.96
ÿ0.01
ÿ0.19
0.20
ÿ1.01
0.00
ÿ0.14
0.17
ÿ0.92
0.01
0.04
ÿ0.31
ÿ0.06
ÿ0.22
0.09
ÿ0.15
ÿ0.01
ÿ0.49
0.03
ÿ0.22
ÿ0.07
ÿ0.79
Table 7
Long run conditional expenditure and total income elasticities associated with the dominant model specification
Cond. exp. (w/o ineq. restr.)
Cond. exp. (w. ineq. restr.)
a
Beer
Spirit
Wine
SD
0.933
1.100
1.108
Total income (w/o ineq.restr.)
0.092
0.108
a
0.109
Beer
Spirit
Wine
SD
0.422
0.925
1.110
1.114
0.404
0.041
Total income (w. ineq.restr.)
0.091
0.109
0.110
0.040
SD: soft drinks.
Table 8
Conditional Hicksian elasticities from the PDL LA/AIDS sub-model
Short run (w/o ineq. restr.)
Short run (w. ineq. restr.)
Elasticities
Beer
Spirit
Wine
SD
Elasticities
Beer
Spirit
Wine
SD
Beer
Spirits
Wine
Soft drinks
ÿ0.382
0.204
ÿ0.330
0.285
0.262
ÿ0.475
0.894
ÿ0.062
ÿ0.150
0.317
ÿ0.751
0.089
0.271
ÿ0.046
0.187
ÿ0.313
beer
spirits
wine
soft drinks
ÿ0.552
0.324
ÿ0.242
0.259
0.416
ÿ0.602
0.795
ÿ0.004
ÿ0.110
0.282
ÿ0.780
0.108
0.247
ÿ0.003
0.227
ÿ0.364
Long run (w/o ineq. restr.)
Long run (w. ineq. restr.)
Elasticities
Beer
Spirit
Wine
SD
Elasticities
Beer
Spirit
Wine
SD
Beer
Spirits
Wine
Soft drinks
ÿ0.347
0.229
ÿ0.364
0.126
0.237
ÿ0.527
0.988
ÿ0.023
ÿ0.142
0.348
ÿ0.833
0.037
0.252
ÿ0.049
0.209
ÿ0.140
beer
spirits
wine
soft drinks
ÿ0.507
0.361
ÿ0.269
0.105
0.382
ÿ0.671
0.885
ÿ0.003
ÿ0.101
0.312
ÿ0.871
0.046
0.226
ÿ0.003
0.254
ÿ0.154
Table 9
Conditional Marshallian elasticities from the PDL LA/AIDS sub-model
Short run (w/o ineq. restr.)
Short run (w. ineq. restr.)
Elasticities
Beer
Spirit
Wine
SD
Elasticities
Beer
Spirit
Wine
SD
Beer
Spirits
Wine
Soft drinks
ÿ0.654
ÿ0.067
ÿ0.601
0.014
ÿ0.087
ÿ0.823
0.546
ÿ0.410
ÿ0.273
0.193
ÿ0.874
ÿ0.034
0.013
ÿ0.303
ÿ0.071
ÿ0.570
beer
spirits
wine
soft drinks
ÿ0.660
ÿ0.063
ÿ0.600
0.014
ÿ0.081
ÿ0.826
0.544
ÿ0.411
ÿ0.273
0.193
ÿ0.877
ÿ0.032
0.013
ÿ0.304
ÿ0.067
ÿ0.572
Long run (w/o ineq. restr.)
Long run (w. ineq. restr.)
Elasticities
Beer
Spirit
Wine
SD
Elasticities
Beer
Spirit
Wine
SD
Beer
Spirits
Wine
Soft drinks
ÿ0.600
ÿ0.070
ÿ0.664
0.012
ÿ0.088
ÿ0.910
0.602
ÿ0.169
ÿ0.257
0.212
ÿ0.969
ÿ0.015
0.011
ÿ0.333
ÿ0.076
ÿ0.249
beer
spirits
wine
soft drinks
ÿ0.613
ÿ0.069
ÿ0.669
0.006
ÿ0.075
ÿ0.917
0.606
ÿ0.166
ÿ0.254
0.214
ÿ0.977
ÿ0.013
0.012
ÿ0.337
ÿ0.074
ÿ0.231
160
EÂ. LarivieÁre et al. / Agricultural Economics 22 (2000) 147±162
in Table 4 con®rms that beer and wine are complements. From Tables 4 and 9, we can infer that like wine
and beer, spirits and soft drinks are complements for
each other. As expected, spirits are substitutes for
wines and vice versa.
3.1. Modeling and policy implications
There exists a large body of literature in demand
analysis that demonstrates that the choice of a functional form has a strong incidence on calculated
elasticities. In this paper we presented empirical evidence which suggests that `®ner' speci®cation issues
matter as well. We focused on the speci®cation of
advertising in demand analysis holding the choice of a
functional form constant. Three popular speci®cations
were compared. They all performed well (in terms of
estimation and simulation) but they produced wideranging price and advertising elasticities. We believe
that practitioners are often confronted to dif®cult
model selection decisions and this is why a criterion
like that of Pollak and Wales (1991) Likelihood
Dominance Criterion is likely to become an indispensable instrument in the practi