ESTIMATING PRICE ELASTICITIES OF
DEMAND FOR ALCOHOL AND TOBACCO
IN THE UK
James Collis
Magdalena Czubek
Surjinder Johal
27 May 2010
Abstract
UK duties on alcohol and tobacco generated almost £18 billion in exchequer revenues
in 2009-10. HM Revenue & Customs use own-price and cross-price elasticities to
analyse the effect of duty rate changes upon exchequer revenues. A duty rate increase
will have two opposing effects on tax revenues: increase revenues by levying more
duty per unit sold, but also reducing consumption through the resulting higher prices
as consumers substitute away to other products, and sometimes towards the
significant non-duty paid sector. The interplay between these effects is very important
for predicting exchequer revenues and informing policy debate.
Contact Details:
James.Collis@hmrc.gsi.gov.uk; Magdalena.Czubek@hmrc.gsi.gov.uk; Surjinder.Johal@hmrc.gsi.gov.uk.
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1
Introduction
Duty on alcohol and tobacco generated £9.0 billion and £8.9 billion respectively in
exchequer revenues in 2009-10. This is around 3%-4% of the total raised by HM
Revenue & Customs (HMRC).
HMRC uses own-price and cross-price elasticities to analyse the effect of duty rate
changes upon exchequer revenues. A duty rate increase will have two opposing effects
on tax revenues: increase revenues by levying more duty per unit sold, but also
reducing consumption through the resulting higher prices as consumers substitute
away to other products. There is also the possibility that consumers may opt to switch
to the non-duty paid sector both through legal (cross border shopping) and illegal
(smuggling and counterfeit) means. The size of the non-duty paid sector can be
significant. The latest estimates for cigarettes, for example, suggest the market share is
around 12%. The interplay between these different effects is very important for
predicting exchequer revenues and informing policy debate.
HMRC are primarily concerned with the elasticity of duty paid alcohol and tobacco
rather than consumption as a whole. This distinction is important because whilst the
consumption of these products is typically thought of as inelastic, particularly with
regard to their social habit or addiction properties, consumption from the duty paid
sector will be more elastic.
As well as overall revenue, HMRC are also interested in the substitutability across
different products and what that implies for duty rates. For example, for a number of
years in the 1990s, spirits duty was frozen whilst duty rates on beer and wine
increased; cider has typically been taxed less heavily than beer. When considering the
revenue effects of such policies, it is important to understand in what way changes in
the relative prices of different alcohols will affect sales and therefore tax revenues
from each type of alcohol.
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One of the main objectives in re–estimating the models are to ensure that our
elasticity estimates accurately reflect current market conditions. The evidence is that
estimated demand elasticities can be relatively unstable and can vary considerably
across studies. This variability may reflect actual changes in tastes but probably also
includes a stochastic element, particularly with regard to different data sets and nonlinearity and so on.
We are estimating elasticities separately for the alcohol and tobacco markets. This
paper outlines the different methodologies pursued to estimate demand for alcohol
and tobacco. Section 2 summarises some previous studies. Section 3 discusses a
cointegration technique using time series data. Sections 4 and 5 are based on the same
cross-section household expenditure dataset. The first uses a QUAIDS model whilst the
second employs a Tobit estimation.
2
Previous Studies
Alcohol
The last time that HMRC modelled alcohol demand was in the paper by Huang (2003).
That used a single equation dynamic error-correction model and applied it to data
from the Office for National Statistics (ONS). Four different equations were estimated:
beer in the off trade, beer in the on trade, spirits and wine.
Although the model has performed well it is clearly time that the estimations were
updated. In particular, there are a number of areas that we think need to be reconsidered. Firstly, the current model only considers the distinction between the on
and off trade for beer. Whilst it is arguable that the beer market is the one where the
distinction is most important, we would ideally like to make the separation for all
products. Secondly, there have been some significant changes in drinking habits, in
particular the growth of the markets for cider and the ready-to-drink category. Neither
of these was modelled in the previous study.
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Tobacco
The previous tobacco modelling exercise was carried out by Cullum and Pissarides
(2004). They used an Almost Ideal Demand System (AIDS) to look at the markets for
cigarettes and hand rolled tobacco (HRT). They also explicitly estimated the demand
for the duty-paid domestic market, the cross-border market and the illicit market. They
used data from ONS, HMRC and tobacco manufacturers.
At the time of this research there was considerable concern that prior models had not
captured the rapid rise in the growth of the non duty-paid sector. During the 1990s the
size of this sector grew from virtually zero to over 20% of the cigarettes market and
over 60% of the HRT market.
Arguably, this model has performed less well than the alcohol estimation. One of the
main reasons for this is that the size of the non duty-paid sector has declined in the
ensuing years. In 2000 HMRC introduced a new tobacco strategy to counter the
growth in the non duty-paid sector and it would appear that this has had a good
degree of success, though other factors (exchange rates, inflation only duty rises
amongst others) have also likely played a role. The elasticities estimated in the Cullum
and Pissarides study are probably on the high side in the current climate, where
receipts from tobacco have risen sharply in recent years.
Meta-Analysis
There are a large number of studies looking at alcohol and tobacco but, fortunately,
Gallet (2007) and Gallet and List (2003) have conducted extensive meta-analysis to
examine the differences across the literature. Gallet (2007) considers results from 132
international studies on alcohol from 1942 to 2002 to see how the price elasticity
varies across a range of different factors, including beverage type, functional form,
data type and estimation method. Each was compared to a simple baseline regression.
He found that:
 Beer was consistently more inelastic than other beverages (wine and
spirits).
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 Non-linear functional forms (AIDS, Rotterdam, semi-log) tended to produce
more inelastic elasticities than linear models.
 However, addiction models were not significantly different.
 There was no significant difference between time series data and panel
data.
 Compared to OLS, other estimation methods - two stage least squares
(2SLS) and three stage least squares (3SLS) produce more elastic price
elasticities.
 However, a single equation maximum likelihood estimation (MLE) tends to
result in more inelastic elasticities than OLS.
 Full information maximum likelihood (FIML), generalised least squares
(GLS) and generalised method of moments (GMM) were not significantly
different to OLS.
 The short run elasticity is more inelastic than the long run.
Gallet and List (2003) looks at tobacco research in a similar way, comparing different
studies to a baseline estimation, in this case a single equation, OLS, semi-log regression
with smoking consumption as the dependent variable. They look at 86 studies from
1933 to 2001. Again, their selection is not limited to the UK. The main findings were:
 Estimations based on AIDS specifications tend to produce more inelastic
elasticities than the baseline.
 The rational addition model tends to generate more inelastic elasticities
than the baseline; estimates from the myopic model are not significantly
different.
 The linear and double-log specifications are not significantly different to
the baseline.
 There is no significant difference between using time series and cross
section data.
 Neither 2SLS, 3SLS, FIML were significantly different to the OLS baseline.
GLS and MLE studies tended to produce more inelastic elasticities, though
the latter result is of marginal significance. GMM estimations tend to result
in more elastic elasticities.
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 The short run elasticity is more inelastic than the long run.
The results from these two meta-analyses are useful benchmarks when modelling
alcohol and tobacco. In particular, they are of value when we compare results across
the different approaches we have been exploring.
3
Approach 1: Cointegration
3.1
Data
Data on consumption is sourced from the ONS publication Consumer Trends. This
provides quarterly data on expenditure for each of the following:
 On-trade beer
 Off-trade beer
 On-trade spirits
 Off-trade spirits
 On-trade wine
 Off-trade wine
 Cigarettes
 Hand Rolled Tobacco
Pricing data for alcohol also comes from ONS, who make use of industry data. Tobacco
prices are direct from the manufacturers. The prices for smuggled and cross border
tobacco are estimated internally in HMRC.
For alcohol we separate on-trade (bought in pubs and restaurants) from off-trade
(bought in off-licenses and supermarkets). This is because the markets are distinct
from one another. For example, consumers may switch to drinking at home if prices in
pubs become too high. Real non-seasonally adjusted quarterly data is used. The
volume of sales and the average prices of individual types of beverages for the off
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trade are obtained from a continuous survey of retail outlets. Volumes are then
grossed up to align with clearances data from HMRC. The price data is used to estimate
current expenditure. Expenditure on alcohol in the on trade is estimated separately.
In addition, we also have data on household final consumption expenditure,
employment ratios, exchange rates and duty rates for each type of alcohol. The
household final consumption data is used as a proxy for income in the regressions. It is
also possible to use this data to transform our prices into relative prices to control for
the positive correlation between price and expenditure on any given good. An
alternative way to cope with this problem is to convert expenditures into volumes.
There are some weaknesses in the data set. Data on cider is not available. Wine
includes both cider and coolers, which ideally we would like to separate. Whilst the
alcohol expenditure data excludes cross-border shopping, it includes smuggled goods.
For tobacco, there is a separate data set for smuggled expenditure though cross
border shopping is not accounted for. We have internal HMRC data on smuggled and
cross border tobacco, spirits and beer. However, there is concern over the reliability of
some of this data.
For tobacco, the ONS Consumer Trends data includes consumption expenditure on
cigarettes and other tobacco products. Expenditure is split between UK duty paid and
smuggled. One of the weaknesses with the data is that the smuggling estimates are
probably an overestimate, since they do not fully take into account the recent
reduction measured by HMRC.
Pricing data comes from information provided by tobacco manufacturers. Most other
data: income, exchange rates, overseas travel numbers is also sourced from the ONS.
Tax information is held by HMRC.
For alcohol the dependent is available from 1970q1 up to 2009q4. However, we
believe that omitting some of the early data would likely give better results due to
changes in the market since the 1970s. For tobacco, the data on the dependent
variable is available from 1982q1.
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3.2
Methodology
The general model is described in the equation below. It is a straightforward
specification where consumption or expenditure is a function of own prices (Pi), prices
of other goods (Pj), income (Y), and a number of other explanatory variables (X). These
include the exchange rate, overseas travel numbers duty rates. Important dummies, D,
such as the 2007 smoking ban have also been included.
Cons i     i Pi    j Pj  Y    k X k  D
i j
k
As is commonly the case with time series data, many of our variables suffer from nonstationarity. This can cause spurious correlations between variables in our regressions
which do not reflect any true economic relationships. We use Augmented DickeyFuller tests along with simple data plots and correlograms which confirm our
suspicions of non-stationarity in the data. Further testing establishes that the data is
integrated of order one and therefore is stationary in first differences.
Modelling in differences overcomes many of the problems associated with nonstationary variables. However, this is done at the sacrifice of the long-term properties
of the model. In the long-run, the differences should be zero and hence the differences
approach looses the long-run relationship between the variables in the regression. In
order to keep both the short and long-run relationships in our model we follow the
two step Engel-Granger (EG) procedure for cointegration modelling.
The first step of this method is to model the long-run relationship in levels. We must
assume that this is a true long-run relationship to proceed with the EG method. Given
the weight of economic theory supporting the relationship between price and quantity
demanded of a good; this is a weak assumption. The t-statistics from the first stage
procedure should be taken as indicative at best, because the non-stationary variables
undermine the standard distributions. The residuals from this regression are then
tested for stationarity. If they are stationary, there is a cointegrating relationship and
we can proceed to the second stage. The second stage is to estimate the dynamic
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short-run relationship in differences. We use seasonal differences when there is strong
seasonality in the data; otherwise first differences are used. The short-run regression
includes the lagged residuals from the first step as the error correction term. Because
the variables used in the dynamic relationship are stationary, the results are no longer
spurious and the t-statistics can now be interpreted without bias. However the
explanatory power of a model on differences is not expected to be great.
The two-stage EG method may be less appropriate for modelling more than two
variables. With two variables there is a single long-run relationship which the EG
procedure estimates. However, with more than two variables, there are multiple
possibilities of the long-run relationship from which the EG procedure implicitly
assumes only one is correct. This A more robust alternative when modelling multiple
variables is the Johansen Vector Error Correction (VEC) procedure. This follows a
similar error correction process to the EG model but relaxes the implicit assumption on
the choice of the long-run relationship. As with the EG procedure, the Johansen VEC
model is only applicable to cointegrated variables. Although this approach was
specifically developed for use with systems of Vector Autoregression equations, it can
also be used as an auxiliary tool for the single equation EG procedure. If the Johansen
procedure indicates the existence of only one cointegrating vector, it can be regarded
as some confirmation of the single equation model to which EG method was applied.
3.3
Results
Due to data issues and availability the time series approach proved more appropriate
for tobacco rather than alcohol analysis. Therefore initial alcohol results are not
reported in this paper. For tobacco, this approach is the only one that has been
pursued. The model requires less complexity than alcohol because of the significant
difference in size between cigarettes and other tobacco products. In the first instance
we have only looked at the demand for cigarettes, which forms 90% of the UK tobacco
market. Table 1 below lists the two best long run relationships identified through data
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mining and cointegration testing. Both models have been estimated for two time
periods: 1982q1 to 2009q4 and 1984q1 to 2009q4. Initial observations show much
higher levels of cigarettes consumption followed by a sharp decline in 1984. The
shorter estimation period was used in order to avoid leverage and preserve the
number of degrees of freedom.
Table 1
Dependent
Independent
Model 1
Volume
Price
Price (HRT)
Expenditure
Visits
Trend
Smoking Ban
EU Single Market
Quarterly Dummies
Model 1a
Volume
Price
Price (HRT)
Expenditure
Visits
Trend
Smoking Ban
EU Single Market
Quarterly Dummies
Model 2
Volume
Price
Price (HRT)
Expenditure
Exchange rate
Trend
Smoking Ban
EU Single Market
Quarterly Dummies
Model 2a
Volume
Price
Price (HRT)
Expenditure
Exchange rate
Trend
Smoking Ban
EU Single Market
Quarterly Dummies
Dummy 1984
Dummy 1984
The second step of the Engle-Granger procedure is performed separately for each of
the four models and the final long run regression is established based on cointegration
results and residuals testing. Dynamic equations are estimated on first differences. In
order to prevent the loss of information available in the earlier years, as well as due to
the weak data reliability, illicit and cross border shopping variables have been excluded
from the final regression. Instead the impact of the non duty paid consumption
developments was approximated by other regressors like exchange rate, travel
numbers and overseas prices. This choice of variables was dictated by the fact that
falling travel numbers during recessions are expected to have negative implications for
the levels of cross border shopping and that, as shown by evidence, the tax gap
estimates have fallen alongside the exchange rate. Hence we expect declining
exchange rate to reduce both the demand for and supply of illicit product, since the
price differential between UK duty paid and non duty paid is lowered.
Tables A1 and A2 in the annex shows long run and short run results of the above
equations for both linear and semi-log specifications. Cointegration tests give
satisfactory results and the error correction terms are successfully identified. High
significance and negative sign of the lagged residuals in the short run regressions
ensure that the series adjust to the long run equilibriums.
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The elasticities that have been estimated are consistently lower than those of Cullum
and Pissarides. This supports the view that the demand for cigarettes has become less
elastic in the past six years. It also defies one of the main results from the meta
analysis that AIDS models tended to produce lower elasticities.
The alcohol model has a bit more complexity since we attempt to estimate all the
alcohol cross price elasticities. Given that this approach and data set is broadly similar
to that of Huang, it is not surprising that the results are not massively different. Own
price elasticities all have the correct sign though that for wine is not significant. As
predicted by the meta-analysis, beer is less elastic, spirits are more elastic. However,
some of the cross price elasticities are puzzling, particularly one or two instances
where the results suggest there is a sizeable complement effect. As this is not our
preferred model, the full results are not reported in this paper.
4
Approach 2: QUAIDS
The second approach we have pursued uses cross-section data in a quadratic almost
ideal demand system (QUAIDS). This approach was only used for alcohol due to
insufficient coverage of tobacco in cross-sections. The QUAIDS approach is
theoretically very appealing as it is a complete demand system and it is very efficient
because of the simultaneous estimation procedure. Another benefit is that the wider
data coverage allows us to explicitly model both cider and RTDs, as well as the on and
off trade for all beverages. It was also hoped that we might be able to get more
plausible cross-price effects,
4.1
Data
The data set used in this analysis is from the Expenditure and Food Survey (EFS) which
contains data on the price, quantity and value of alcohol bought/consumed across the
UK. The variables included in the data set are:
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 Alcohol:
 Beer and Lager (off trade)
 Spirits and Liqueurs (off trade)
 Wine from grape of other fruit (off trade)
 Fortified Wine (off trade)
 Ciders and Perry’s (off trade)
 Ready To Drink (off trade)
 Champagne and Sparkling Wine (off trade)
 Beer and Lager (on trade)
 Spirits and Liqueurs (on trade)
 Wine from grape or other fruit (on trade)
 Fortified Wine (on trade)
 Ciders and Perry’s (on trade)
 Ready To Drink (on trade)
 Champagne and Sparkling Wine (on trade)
 Round of Drinks (on trade)
Non-Alcohol:
 Gender
 Ethnicity
 Age
 Education
 Region
 Household composition
 Household size
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 Employment status
 Income
The EFS is an annual survey of around 7,000 randomly selected households in the
United Kingdom. It records the purchasing of a range of goods, via a diary system for
the individual over a two week period. In general, EFS records the amount of a good
bought, the price paid by the purchaser and the type of outlet where the purchase was
made. In terms of alcohol, it provides detailed information on all the categories we
require. In addition, the EFS also contains a substantial set of information on the
individuals’ characteristics.
There are two key draw backs to using the EFS data set. Firstly there is a fairly low
response rate (53% in 2008) which could lead to bias. Secondly, there is an apparent
over reporting of zero consumption of alcohol. Roughly 30% of households report no
alcohol consumption, double the usual estimate of 10%-15% of UK households that are
teetotal. As can be seen in table 5 in the annex, of those households that do consume
some alcohol, most consume only a few types; over half consume only one or two
drink types. Dealing with these zeros is a major obstacle to obtaining usable results.
4.2
Methodology
The first step is to consider an appropriate framework for specifying individual
preferences at the microeconomic level. The aim is to model a narrow set of nondurable commodities that are well recorded in micro data sets. Preferences are
characterised such that in each time period t, household h makes decisions about how
much to consume of these commodities subject to various household characteristics
and on the consumption levels of other goods.
For each household, we measure the share of expenditure on a given alcohol for each
household as
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
s ith   i   j  ij ln p jt   itj ln x th   hit ln x th
2
Where x th is real total expenditure; the  ih ,  ih and  ih parameters are allowed to vary
with household characteristics and other conditional characteristics; and ln P (p) is
defined as
K
ln P p    0    i ln p i 
i 1
1 K K
  ij ln pi ln p j
2 i 1 j 1
E.g. the share of expenditure on on-trade beer in a given period will be a function of:
 log of its own prices;
 logs of prices of other alcohols;
 log of total real household expenditure;
 log of total real household expenditure squared.
4.3
Results
Gallet’s meta-analysis suggests that both AIDS models and maximum likelihood
estimation tended to produce lower elasticities. However, our finding for the QUAIDS
approach produces higher elasticities. Also, unusually, the results suggest that wine,
rather than beer is more inelastic. For almost all the alcohols, the on trade is more
elastic than the off trade, which we would probably expect. All own price elasticities
have the expected signs; some cross price elasticities again suggest a degree of
complementarity. As this is not our preferred model, the full results are not reported
in this paper.
5
Approach 3: Tobit
The motivation for pursuing the Tobit model originated with the difficulties in dealing
with the large numbers of recorded zero consumption. Once again, this approach has
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only been used for alcohol. As the QUAIDS methodology suffered considerably from
the large degree of zero consumption reporting, and the time series approach did not
produce satisfactory results for as many alcohol types as we would like, the Tobit
approach for alcohol is the only one for which results are reported in this paper.
5.1
Data
The data set is the same household expenditure survey as is used for the QUAIDS
approach.
5.2
Methodology
With a large number of zeros reported in the data set, it is difficult to analyse the
interactions between consumption of different alcohol types when prices change.
Fitting a simple OLS regression is likely to yield biased and inconsistent results: the
slope being biased downward and the intercept biased upward. Reducing the dataset
to remove a number of the zero observations would not fully alleviate this problem
and would, in turn, entail a selection bias.
One method to cope with the problem of the zero observations is to employ Tobit
analysis (censored regressions). This method is essentially a hybrid of a binary choice
model, estimated using maximum likelihood, and a conventional regression. The basic
equation is the following:
Y* =
β1 + β2X + u
Y =
Y*
for Y* > YL
Y =
YL
for Y* ≤ YL
Where, for example, Y could be expenditure on beer and X the price of beer. The
binary choice element investigates why some households consume zero of a given
alcohol while others consume a positive amount. The conventional regression element
quantifies the relationship between the regressors for those with a positive demand
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for the alcohol in question. That is, it assesses how much a change in price affects
demand amongst households already consuming the alcohol.
Tobit analysis assumes that the error term, u, is homoskedastic and has a normal
distribution. If either of these assumptions is violated then the regression yields
inconsistent estimates. In the presence of heteroskedasticity, using consumption
shares (rather than levels) may be preferable (Amemiya [1984]). Atkinson et al [1990]
show that the assumption of normality can be relaxed by using what they term a
Gamma-Tobit Model as a generalisation of the standard Tobit approach.
A potential weakness of the Tobit model is that it assumes that the effects of the
independent variables are closely linked in both the binary choice decision and the
conventional regression. This may not necessarily be the case for alcohols. It is possible
to capture heterogeneity between the two elements of the Tobit regression by instead
conducting a Two-stage Heckman approach, with the first stage run as a Probit
regression. This is largely equivalent to a Tobit model but at the sacrifice of some
efficiency by moving to two-stages.
Tobit analysis is simpler to use than the QUAIDS approach, making experimentation
with the inclusion of extra variables, or use of sub-samples, more practical.
5.3
Results
Within the Tobit framework, it is possible to experiment with different functional
forms. For example, should we assume constant elasticities with a log-log function, or
is a linear model more realistic? We experiment with various functional forms. We
found the lin-log form to be most appealing both in terms of results, and through not
having to impose the assumption of constant elasticities.
For our dependent variable we have experimented with the use of volumes of alcohol
and expenditure shares, defined as expenditure on a given alcohol product as a
proportion of total household consumption expenditure. As shown table A9 in the
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appendix, using volume as the dependant variable yields very high elasticities which
appear unrealistic. Using logged volume, the elasticities are somewhat varied with
some higher and some lower than expected. Hence we prefer to use expenditure
shares as the dependent variable.
For our independent variables, we have the price of each of the ten alcohol categories
(lnpi and lnpj), total expenditure on alcohols (lnexp_alc), total expenditure on nonalcohol goods (lnexp_notalc), region (gor), socio-economic characteristics (socio) and
year (yr) and quarter (qtr) dummies. The time dummies control for time-specific
variations and allow the pooled cross-section dataset to be used. Hence our model is:
wci = lnpi + lnpj + lnexp_alcs +ln exp_notalcs + gor + socio +yr +qtr
The standard Tobit estimates will be inconsistent if the distribution of the residuals is
not normal or if they suffer from heteroskedasticity. If these problems are severe then
it may be necessary to extend the Tobit model to a more generalised form that allows
different distributions of the residuals (such as the Gamma-Tobit model discussed
previously). However if the violations of the standard Tobit assumptions are moderate,
then the Tobit estimates are likely to still be reasonably good. A simple plot is very
informative about the distribution of the residuals. Taking the example of on trade
beer, we can see below that the residuals appear to be largely normally distributed;
supporting the assumptions underlying the standard Tobit model.
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0
2
Density
4
6
Diagram 1: residuals from on trade beer Tobit regression
-.2
.2
0
.4
Fitted values
An informal test of the general appropriateness of the model is to estimate a Probit
model for the same binary choice element as the Tobit regression and compare the
results to those of Tobit. Dividing each coefficient form Tobit by the regression output
σ computes a comparable figure to the Probit estimates. The two sets of results will
never be identical because of sampling error, but the coefficients should not be
significantly different in sign if the model is well specified. Taking the example of on
trade beer once again, the results are shown in table 2 below. As can be the seen, the
coefficients for logged prices (note elasticities are not reported here for computational
convenience) always have the same sign when significant and their magnitudes are
always fairly similar. However, the coefficients for expenditure on non-alcoholic
products are opposite in sign. This result is slightly concerning however the variable in
question is not of primary importance for our analysis.
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Table 2: Tobit and Probit results for on trade beer
lnp
beer on
wine on
cider on
spirits on
RTDs on
beer off
wine off
cider off
spirits off
RTDs off
exp_notalc
exp_alc
on trade beer exp share
Probit
Tobit
coefficient beta/sigma
-0.89
-0.47
-0.26
-0.12
-0.14
-0.03
0.08
0.10
0.06
0.07
0.10
0.13
0.10
-0.57
0.45
0.62
As a further general check, we analyse the robustness of the estimates to the inclusion
of extra variables. If the coefficients (and resultant elasticities) change significantly
when adding or dropping variables then the model may be misspecified. We find that
our results are generally robust to including or dropping variables. For example, table
A8 in the appendix shows the results of dropping the expenditure on non-alcohol
goods variable, socio-economic characteristics or excluding RTDs from the regressions.
As can be seen, the elasticities change only slightly in each case. In particular, the
results are almost identical with and without RTDs.
Tobit allows us to compute elasticities for those households starting with positive
consumption from the complete population. It is likely that these households will be
more responsive to price changes than when considering the population as a whole,
which would include those that will not consume at any price. This is supported by our
results, given in table A6 of the appendix. The own price elasticities from this approach
all seem sensible, though they are, on the whole, slightly lower than the other two
approaches.
The results suggest that beer and wine are the least elastic while spirits and cider are
more elastic, again fairly sensible results. The relative elasticities of on and off trade
Page 19 of 30
PRELIMINARY AND INCOMPLETE
products are mixed. Beer and cider own-price elasticities are a bit less elastic in the on
trade; wine and spirits are a bit more elastic in the on trade; RTDs are very similar in
both. Of the three approaches, the Tobit also produces arguably the most plausible
cross-price elasticities. We would generally expect positive cross-price effects,
reflecting substitution between alcohols. This is the case for most of our drink types.
Where cross-price effects are negative, the complimentarity could plausibly be the
result of decisions being made at the household rather than individual level. For
example, if one household member likes wine and another likes beer, the household
decision to go out could depend on the prices of both alcohols. Where cross-price
elasticities are not reported, the results were insignificant at the 5% level.
6
Conclusions
We have used various data sources and methodological approaches in order to
estimate price elasticities of tobacco and alcohol demand in UK. The two markets
differ considerably in structure and underlying characteristics. The split between ontrade and off-trade alcohols is important as are various cross price elasticities for each
of the alcohol types. Tobacco market in turn is made up of cigarettes in 90% which
makes the cross-price effect less crucial.
Cointegration analysis of the tobacco time series data gave satisfactory and robust
results and the Engle-Granger approach has been accepted as the final model. Issues
characteristic to the cross-sectional alcohol data motivated the use of Tobit analysis
and indeed this model gave the most sensible and stable results.
Estimated cigarettes elasticities are consistently lower than those from the most
recent study (Cullum and Pissarides 2004). This supports the view that the demand for
cigarettes has become less elastic in the past six years.
Page 20 of 30
PRELIMINARY AND INCOMPLETE
The own price alcohol elasticities are sensible, though they tend to be slightly lower
than in the other approaches in this paper. Of the three alcohol approaches discussed
in this paper, the final Tobit model arguably produces the most plausible cross-price
elasticities.
Page 21 of 30
References
Amemiya, T. (1984), “Tobit Models: A Survey”, Journal of Econometrics, Volume 24, Issues 1-2, January-February 1984, pp. 3-61.
Atkinson, A.B., Gomulka, J. and Stern N.H. (1990), “Spending on Alcohol: Evidence from the Family Expenditure Survey 1970-1983”, The
Economic Journal, 100 (March), pp. 808-827.
Culum, P. and C. Pissarides (2004), “The Demand for Tobacco Products in the UK”, Government Economic Service Working Paper, No 150.
Gallett, C. (2007), “The Demand for Alcohol: A Meta-analysis of Elasticities”, The Australian Journal of Agricultural and Resource Economics, 51,
pp. 121–135.
Gallett, C. and List, J. (2003), “Cigarette Demand: A Meta-analysis of Elasticities”, Health Economics, pp. 821–835.
Huang, C-D. (2003), “Econometric Models of Alcohol Demand in the United Kingdom”, Government Economic Service Working Paper No. 140.
Yen, S.T. and Jensen, H.N. (1996), “Determinants of Household Expenditures on Alcohol”, The Journal of Consumer Affairs, Vol.30, No.1 pp.4867.
Page 22 of 30
PRELIMINARY AND INCOMPLETE
Annex
Table A.1 : Cigarettes: Long Run results
Time period
Specification
Own price
HRT price
Expenditure
Model 1
Model 1a
Model 2
Model 2a
1982q1 - 2009q4
1984q4 - 2009q4
1982q1 - 2009q4
1984q4 - 2009q4
Linear
Semi-Log
Linear
Semi-Log
Linear
-22.427 ***
0.873
0.305 ***
0.054
0.006
0.009
-0.065 ***
0.003
0.001 ***
0.000
0.000 *
0.000
-22.374 ***
0.879
0.307 ***
0.055
0.007
0.009
-0.065 ***
0.003
0.001 ***
0.000
0.000 *
0.000
0.000
0.000
-0.867
0.176
-14.894
3.642
-3.214
2.901
7.795
3.364
11.704
5.192
-14.894
3.642
729.618
30.312
-0.910
3.017
-0.939
0.037
0.000
0.000
-0.003
0.001
-0.072
0.013
0.006
0.010
0.036
0.012
0.042
0.018
6.678
0.108
0.010
0.011
0.054
0.011
-1.147
0.055
0.000
0.000
-0.884
0.176
-14.627
3.638
-2.408
2.970
9.041
3.473
12.414
5.414
710.956
31.567
0.000
0.000
-0.003
0.001
-0.071
0.013
0.007
0.011
0.039
0.013
0.045
0.020
6.683
0.116
Exchange rate
Visits
Trend
Smoking Ban
Q1
Q2
Q3
Constant
d84q1
European Single Market
Own price elasticity
*
***
***
**
**
***
***
*
***
***
**
**
***
***
Page 23 of 30
-0.875
3.014
-0.992
0.039
*
***
***
**
**
***
Semi-Log
Linear
Semi-Log
-21.967 ***
1.322
0.291 ***
0.067
0.002
0.009
17.323
16.423
-0.059 ***
0.005
0.001 **
0.000
0.000
0.000
0.128 **
0.057
-21.507 ***
1.334
0.276 ***
0.068
0.003
0.009
23.858
16.556
-0.058 ***
0.005
0.001 **
0.000
0.000
0.000
0.142 **
0.059
-1.028
0.195
-14.943
3.684
-2.600
2.904
3.502
2.594
2.890
1.952
724.212
30.920
-15.038
3.161
-1.918
3.056
-0.920
0.055
-0.004
0.001
-0.071
0.013
0.007
0.010
0.020
0.009
0.013
0.007
6.643
0.108
0.010
0.011
0.049
0.011
-1.041
0.081
-1.086
0.195
-14.512
3.668
-1.739
2.951
4.472
2.631
3.175
2.001
704.296
32.109
-0.004
0.001
-0.070
0.013
0.009
0.011
0.022
0.009
0.014
0.007
6.644
0.115
*
***
***
**
**
***
0.055 ***
0.011
-1.173
0.058
***
***
***
***
***
***
**
*
***
***
-2.007
3.039
-0.953
0.059
***
***
*
***
***
***
**
*
***
0.049 ***
0.011
-1.049
0.086
PRELIMINARY AND INCOMPLETE
Table A.2 : Cigarettes: Short Run results
Model 1
Model 1a
Model 2
Model 2a
Time period
1984q4 - 2009q4
1982q1 - 2009q4
1984q4 - 2009q4
Specification
Δ Own price
Δ HRT price
Δ Expenditure
1982q1 - 2009q4
Linear
Semi-Log
-16.642 ***
3.291
0.135
0.111
-0.023
0.018
Linear
Semi-Log
Linear
-0.029 ***
0.007
0.000
0.000
0.000
0.000
-15.130 ***
3.092
0.142
0.108
-0.021
0.018
-0.029 ***
0.007
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
-0.007
0.007
0.001
0.016
0.056
0.017
0.049
0.017
-0.027
0.013
-0.004
0.007
-0.006
0.007
-0.235
0.067
-0.510
0.000
0.000
0.009
0.051
-1.676
2.786
-0.234
7.111
23.890
7.720
19.702
7.935
-11.943
5.416
0.000
0.000
0.000
0.000
-0.008
0.007
0.002
0.017
0.063
0.018
0.055
0.019
-0.034
0.013
Δ Exchange rate
Δ Visits
Trend
Smoking Ban
Q1
Q2
Q3
Constant
d84q1
European Single Market
Error Correction Term
Own price elasticity
0.000
0.000
0.018
0.054
-2.177
2.919
-3.259
7.117
20.753
7.628
17.450
7.846
-8.877
5.582
-1.247
3.169
-0.937
2.966
-0.611
0.110
-0.697
*
**
**
***
**
**
**
**
**
Page 24 of 30
**
**
**
**
-0.802
2.805
-11.943 **
5.416
-0.671
Semi-Log
Linear
Semi-Log
-17.587 ***
2.946
0.228 **
0.100
-0.004
0.017
-54.894 *
28.658
-0.031 ***
0.007
0.001 **
0.000
0.000
0.000
-0.070
0.069
-15.594 ***
2.739
0.232 **
0.096
-0.001
0.017
-42.872
27.783
-0.032 ***
0.007
0.001 **
0.000
0.000
0.000
-0.046
0.073
0.046
0.050
-0.773
2.785
-3.751
6.231
6.434 **
2.016
1.955
1.813
-2.185
3.286
-1.423
2.963
-2.637
2.741
-0.809 ***
0.105
-0.736
0.000
0.000
-0.004
0.007
-0.009
0.015
0.013 **
0.005
0.004
0.004
-0.003
0.008
-0.004
0.007
-0.008
0.007
-0.349 ***
0.071
-0.553
0.036
0.047
-0.282
2.606
-1.678
6.127
7.022 ***
1.932
1.776
1.747
-3.963
2.867
0.000
0.000
-0.005
0.007
-0.011
0.016
0.014 **
0.005
0.003
0.005
-0.007
0.007
-2.487
2.554
-0.832 ***
0.094
-0.691
-0.007
0.007
-0.335 ***
0.073
-0.575
**
**
**
**
-0.006
0.007
-0.214 **
0.068
-0.521
PRELIMINARY AND INCOMPLETE
Table A.3 : Cigarettes: Long Run Post Estimation Tests
Model 1
Model 1a
Model 2
Model 2a
Time period
1984q4 - 2009q4
1982q1 - 2009q4
1984q4 - 2009q4
1982q1 - 2009q4
Specification
Linear
Residual Sum of Squares
Root Mean Sq. Error
Akaike ic.
Bayesian ic.
Residuals: white noise
Residuals: normality
Ommited variables
Autocorrelation: Durbin Watson
Autocorrelation: Breusch-Godfrey
Heteroscedastisity: Breusch-Pagan
Cointegration:ADF
Johansen Vector Error Correction rank
5165.0
7.2
768.9
798.8
74.4
2.1
4.9
1.2
15.8
0.4
-6.8
1.0
Semi-Log
***
**
***
**
Page 25 of 30
0.1
0.0
-518.4
-488.5
139.6 ***
0.8
54.7 ***
0.8
39.5 ***
0.0
-4.7
1.0
Linear
3828.6
6.4
692.1
721.2
92.8
1.5
9.2
1.4
7.7
2.9
-6.3
1.0
Semi-Log
***
***
**
*
*
0.1
0.0
-476.3
-449.8
130.8 ***
1.3
54.9 ***
0.8
39.6 ***
0.5
-4.6
1.0
Linear
4245.2
6.5
749.0
781.6
88.9
1.1
7.2
1.6
5.4
2.9
-8.3
1.0
Semi-Log
***
***
**
*
**
0.1
0.0
-518.7
-486.1
139.5 ***
4.3
53.3 ***
0.8
39.4 ***
0.1
-5.2
1.0
Linear
3882.5
6.5
693.6
722.7
70.1
6.8
7.6
1.5
6.8
4.4
-7.3
1.0
Semi-Log
**
**
***
**
**
**
0.1
0.0
-477.3
-448.3
151.6 ***
4.5
53.8 ***
0.8
40.0
0.8
-5.2 **
1.0
PRELIMINARY AND INCOMPLETE
Table A.4 : Cigarettes: Short Run Post Estimation Tests
Model 1
Model 1a
Model 2
Model 2a
Time period
1984q4 - 2009q4
1982q1 - 2009q4
1984q4 - 2009q4
Specification
Residual Sum of Squares
Root Mean Sq. Error
Akaike ic.
Bayesian ic.
Residuals: white noise
Residuals: normality
Ommited variables
Autocorrelation: Durbin Watson
Autocorrelation: Breusch-Godfrey
Heteroscedastisity: Breusch-Pagan
1982q1 - 2009q4
Linear
Semi-Log
Linear
Semi-Log
Linear
Semi-Log
Linear
4715.09732
6.9364
757.1428
792.3667
61.91
19.07
8.83
1.962753
0.01
37.1
0.024441693
0.01579
-593.7261
-558.5022
**
58.72
***
9.42
***
2.73
2.093907
0.858
***
12.82
3984.44482
6.581
698.2985
730.0
59.0
6.3
5.8
1.8
1.3
23.3
0.023346201
0.01593
-554.6388
-522.9
57.9
10.6
2.8
1.9
0.2
14.4
4146.83957
6.505
742.8878
778.1117
126.67
14.99
9.33
1.975811
0.004
36.81
0.023820839
0.01559
-596.5821
-561.3582
124.10
7.21
3.08
2.056645
0.376
13.65
3374.09671
6.056
681.0064
712.7391
100.1894
4.97
4.27
1.826054
1.161
15.03
Page 26 of 30
**
***
**
***
**
**
**
***
**
**
**
***
***
***
***
***
***
**
**
***
Semi-Log
0.022967
0.0158
-556.3404
-524.6077
***
123.41 ***
*
8.79 **
**
2.09
1.900416
0.011
***
14.57 ***
PRELIMINARY AND INCOMPLETE
Table A.5: Alcohol Cross Sectional Data
Number of households with share of alcohol
type consumption:
Alcohol Type
0
between 0 and 1
1
11,402
19,753
25,990
21,604
25,289
17,768
13,693
25,583
22,227
26,243
13,499
7,431
1,674
5,892
2,347
8,602
11,317
1,932
4,719
1,337
2,823
540
60
228
88
1,354
2,714
209
778
144
Number of types of
alcohol consumed
in household
Number of
Households
Cumulative
Cumulative
%
10
9
8
7
6
5
4
3
2
1
3
5
49
202
652
1,685
3,387
5,378
7,425
8,938
3
8
57
259
911
2,596
5,983
11,361
18,786
27,724
0.0%
0.0%
0.2%
0.9%
3.3%
9.4%
21.6%
41.0%
67.8%
100.0%
Beer on
Wine on
Cider on
Spirit on
RTD on
Beer off
Wine off
Cider off
Spirit off
RTD off
Page 27 of 30
PRELIMINARY AND INCOMPLETE
Table A.6: Alcohol Tobit Results: Own and Cross-Price Elasticities by Drink Type
expenditure share
beer on
wine on
price
cider on spirit on RTD on
beer off wine off cider off spirit off RTD off
beer on -0.571***
0.437***
0.224***
wine on -0.154*** -0.589*** -0.278*** -0.125*** -0.137* 0.098*** -0.060**
cider on
-0.920***
spirits on
-0.035*
-0.229** -0.996*** -0.501*** 0.117*** 0.186***
RTDs on
beer off
wine off
cider off
spirits off
RTDs off
exp_not_alc
exp_alc
0.122***
0.080**
0.161***
-0.688***
0.752***
0.219*
-0.858***
0.145**
0.365*** 0.300** 0.338***
-0.780*** 0.208***
0.138**
-0.316*** -0.204*** -0.355***
0.195** -0.346*
0.164***
0.152*
-0.109*
0.144*
0.128***
-0.200*** 0.209*** -0.469*** -0.304***
0.685*** 0.720*** 0.947*** 0.882*** 0.492*** 0.504***
Page 28 of 30
0.166**
-0.668***
-1.263***
-0.278*
-0.411***
0.382***
0.135***
0.162***
-0.816***
-0.508***
0.867***
0.165*
-0.548***
-0.421**
-0.882***
0.321***
PRELIMINARY AND INCOMPLETE
Table A.7: Alcohol Tobit
Model: Misspecification Check
lnp
beer on
wine on
cider on
spirits on
RTDs on
beer off
wine off
cider off
spirits off
RTDs off
exp_notalc
exp_alc
on trade beer exp share
Probit
Tobit
coefficient beta/sigma
-0.89
-0.47
-0.26
-0.12
-0.14
-0.03
0.08
0.10
0.06
0.07
0.10
0.13
0.10
-0.57
0.45
0.62
Page 29 of 30
PRELIMINARY AND INCOMPLETE
Table A.8:Alcohol Tobit Model: Robustness: Including and Dropping Variables
Regression
Own-Price Elasticities
beer on wine on cider on spirits on RTDs on beer off wine off cider off spirits off RTDs off
wc,lnp,exp_alc,exp_notalc,gor,socio
-0.571*** -0.589*** -0.920*** -0.996*** -0.858*** -0.780*** -0.355*** -1.263*** -0.816*** -0.882***
wc,lnp,exp_alc,gor,socio
-0.658*** -0.582*** -0.924*** -0.984*** -0.862*** -0.806*** -0.375*** -1.302*** -0.835*** -0.882***
wc,lnp,exp_alc,exp_notalc,gor
-0.529*** -0.580*** -0.918*** -1.013*** -0.867*** -0.792*** -0.278*** -1.242*** -0.817*** -0.898***
wc,lnp,exp_alc,exp_notalc,gor,no_rtds -0.573*** -0.589*** -0.919*** -0.995***
-0.779*** -0.353*** -1.269*** -0.816***
wc=weight of consumption of alcohol i; lnp=logged prices of alcohols; exp_alc=total alcohol exp; exp_notalc=total exp on other goods
gor= government office region; socio=socio economic characteristic; no_rtds=drops on and off trade rtds price variables
Note: all of these regression also include year and quarter dummies
Table A9:Alcohol - use of different dependent variables
Own-Price Elasticities
beer on wine on cider on spirits on RTDs on beer off wine off cider off spirits off RTDs off
wc,lnp,exp_alc,exp_notalc,gor,socio -0.571*** -0.589*** -0.920*** -0.996*** -0.858*** -0.780*** -0.355*** -1.263*** -0.816*** -0.882***
q,lnp,exp_alc,exp_notalc,gor, socio
-1.151*** -1.418*** -1.296*** -1.603*** -1.478*** -1.515*** -0.967*** -1.670*** -1.407*** -1.371***
lnq,lnp,exp_alc,exp_notalc,gor, socio -0.790*** -0.357*** -0.390*** -1.022*** -0.264*** -1.053*** -0.471*** -1.113*** -0.527*** -0.626***
wc=weight of consumption of alcohol i; lnp=logged prices of alcohols; exp_alc=total alcohol exp; exp_notalc=total exp on other goods; exp_all=total exp on all goods
gor= government office region; socio=socio economic characteristic; no_rtds=drops on and off trade rtds price variables
Note: all of these regression also include year and quarter dummies
Page 30 of 30