Price Elasticity Estimates for Cigarette Demand in Vietnam
Patrick Eozenou∗ and Burke Fishburn†
This Version: November 2007
In this paper, we analyze a complete demand system to estimate the price elasticity for cigarette demand in
Vietnam. Following Deaton (1990), we build a spatial panel using cross sectional household survey data. We
consider a model of simultaneous choice of quantity and quality. This allows us to exploit unit values from
cigarette consumption in order to disentangle quality choice from exogenous price variations. We then rely on
spatial variations in prices and quantities demanded to estimate an Almost Ideal Demand System. The estimated
price elasticity for cigarette demand is centered around -0.53, which is in line with previous empirical studies for
JEL Classiﬁcation: D12, H31, I12, O23
Keywords: Price elasticity, Cigarette Demand, Taxation, Consumption, Vietnam.
∗European University Institute, Economics Department, Villa San Paolo, Via Della Piazzuola 43, 50133 Florence, Italy;
†World Health Organization and Center for Disease Control; ﬁshburnb@wpro.who.int.
Cigarette smoking is a major global public health problem. By 2030, and if current trends are maintained, it is
expected to be the highest cause of death worldwide, accounting for more than 10 million deaths per year 1.
Vietnam is an unfortunate example of this trend. The World Health Organization (WHO)2 evaluated that 10%
of the Vietnamese alive today will die prematurely from disease related to tobacco use, and half of them will die
in their productive middle age. Smoking prevalence among Vietnamese men is among the highest in the world.
Tobacco control is already a concern for the Vietnamese authorities. The ministry of health, together with other
ministries and mass organizations have started taking comprehensive steps to curb the tobacco epidemic. In August
2000, the Prime Minister signed a governmental resolution on National Tobacco Control Policy and established
the National Tobacco Control Program. The national policy and program is steered by the Vietnamese Committee
on Smoking and Health (Vinacosh), chaired by the Minister for Health. The national policy addresses both supply
and demand-side strategies.
Evidence from countries of all income levels suggest that price increases on cigarettes are highly effective in
reducing demand. Higher taxes induce some smokers to quit and prevent other individuals from starting. They also
reduce the number of ex-smokers who return to cigarettes and reduce consumption among continuing smokers. On
average, a price rise of 10 percent on a pack of cigarettes would be expected to reduce the demand for cigarettes
by about 4 percent in high-income countries and by about 8 percent in low- and middle-income countries, where
lower incomes tend to make people more responsive to price changes Prabhat and Chaloupka (2000). Children and
adolescents are also more responsive to price rises than older adults, so this intervention would have a signiﬁcant
impact on them.
In order to anticipate the impact of taxation on the level of cigarette consumption for Vietnamese households,
we want to estimate the price elasticity of the demand. Ideally, one would like to use time-series data, to estimate
the reaction of the demand when prices change over time. However, accurate time-series data are often missing
for developing countries. One alternative is use cross-sectional data and exploit spatial price variations instead of
time variations to estimate a price elasticity. Such methodology has been developed by Angus Deaton3 in order to
estimate demand elasticities from Living Standards Measurement Surveys (LSMS). In this paper, we follow this
In section 2 we present the Almost Ideal Demand System (following Deaton and Muellbauer (1980)) and
2Vietnam Steering Committee on Smoking and Health, Ministry of Health. Government Resolution on National Tobacco Control Policy
2000-2010, Medical Publishing House, 2000.
3Deaton (1988, 1990, 1997), and Deaton and Grimard (1992).
a theoretical framework for the use of spatial prices variations together with a model for the choice of quality.
Section 3 describes the empirical procedure to estimate our demand system. Finally, in section 3, we describe the
data and present our estimation results.
An Almost Ideal Demand System (AIDS)
One advantage of using household survey data over aggregate data is that it is possible to estimate a system of
demands, accounting for different kinds of goods purchased, instead of a single demand equation. The estimation
of a single demand equation may give a wrong picture of consumption patterns because substitution and comple-
mentarity effects between different kinds of commodities are discarded. Another advantage of the demand system
approach is that it is more consistent with standard microeconomic theory. In practice many different demand
systems have been examined4.
The Almost Ideal Demand System (AIDS) is one of the most popular approach because of its generality and
because it satisﬁes many properties of standard utility functions. Starting from a speciﬁc class of preferences
which allows exact aggregation over consumers (PIGLOG class), Deaton and Muellbauer (1980) derive demand
functions which express budget shares (ωi) as functions of prices (pi for good i and P for the price index) and
ωi = αi +
γij log pj + βi (x/P )
To ensure that (1) represents a standard system of demands, the following three conditions are imposed:
αi = 1 ;
γij = 1 ;
βi = 0
γij = 0
4The ”Linear Expenditure Systems” (Stone, 1954), the ”Rotterdam System” (Theil, 1965), the ”Translog System” (Christensen et al., 1975),
or the ”Almost Ideal Demand System” (Deaton and Muellbauer, 1980).
(2) ensures that budget shares add up to total expenditures, (3) that demands are homogenous of degree 0 in
prices and (4) that the Slutsky matrix is symmetric.
One advantage when we use budget shares is that zero consumptions can be taken into account, contrarily to
the case where the demand equation is expressed in a logarithmic form. This is an interesting feature in our case
since we are interested in the effect of price variations among all the population, and not only among smokers.
However, we are still confronted with two important shortcomings with our data. The ﬁrst concern is the
cross section nature of the data. The VLSS has been conducted in 1993 and 1998 and it does not give sufﬁcient
longitudinal variation for our purpose. The second problem is that we do not observe truly exogenous prices for
the considered goods. Instead we observe unit values (ratio of expenditures on quantities purchased). Unit values
cannot be considered as true exogenous prices to the extent that they also reﬂect a choice of quality. High quality
items, or bundles that are composed with a large share of high quality items, will have higher unit prices. There-
fore, unit values are also choice variables, at least to some extent. Indeed, unit values give a mixed information
combining the inﬂuence of the exogenous price with the choice of quality from the household. We can reasonably
expect unit values to be positively correlated with income, to the extent that better-off households will tend to
consume higher-quality goods. Moreover, changes in prices are also expected to induce changes in the choice of
quality for any given household. Hence, we are exposed to simultaneity bias if we use unit values given by the
survey as true market prices.
Spatial Price Variations
Deaton (1988, 1990, 1997), and Deaton and Grimard (1992) propose a methodology which overcomes both short-
comings. The basic idea behind this methodology is to combine the transversal structure of the survey with a model
for the simultaneous choice of quality and quantity. The VLSS is structured by clusters which represent villages.
In each village, approximately 15 households are interviewed (table 1 give an idea of the structure of the survey).
Therefore, we can build a transversal panel with the two dimensions given by the villages and by the households.
The methodology relies on a two-steps procedure. In a ﬁrst stage, within-cluster variations are used to estimate
demand equations and unit values equations. Following this approach, we can disentangle the effect of exogenous
market prices, which are assumed to be constant within villages, from the determinants of the choice of quality.
In a second stage, between-clusters variations are used to estimate the spatial price elasticity for cigarette demand.
Relying on spatial price-variations can be reasonably justiﬁed in the case of developing countries if markets are
not perfectly integrated (because of high transport costs due to weak infrastructures for example).
A model for the simultaneous choice of quantity and quality
We want ﬁrst to deﬁne quality so that unit values are given by the prices multiplied by quality so that total expen-
ditures can be expressed as the product of quality, quantity and prices. Quality must be thought of as a property
of an aggregate bundle of different commodities. Consider a bundle of meat for example, composed of, say, beef,
chicken and duck, where beef is the most expensive item. Each item of the bundle is considered as a perfectly
homogenous good, and the highest quality bundle is the one where the proportion of beef is the highest.
More formally, write the group G quantity index QG as
QG = kG.qG
where qG is a vector of consumption levels for each item in the bundle G and kG is a vector used to aggregate
incommensurate items (it can be a calory based measure for example, or simply a vector of ones if quantities are
reported as weights).
Since each commodity within the bundle is assumed to be a perfectly homogenous good, commodity prices
contain no quality effects and we can write the price vector corresponding to the quantity vector qG as
pG = πG.p0G
where πG is a scalar measure of the level of prices in the group G, and p0 is a reference price vector.
In our analysis, we treat the π′s as varying from one village to another, and we assume that relative prices
within a given bundle are approximately constant across villages. Therefore with (6) we can express varying prices
while keeping ﬁxed the structure of prices within a group of commodities.
We can now deﬁne xG as
xG = pG.qG = QG.(pG.qG/kG.qG) = QG.πG.(p0G.qG/kG.qG)
The quality index ξG can then be deﬁned such that total expenditures are expressed as the product of quantity,
price and quality
ln xG = ln QG + ln πG + ln ξG
ξG = p0G.qG/kG.qG
which means that given a reference price vector p0 , quality depends only on the composition of demand within
the commodity group.
Now that quality is deﬁned, consider a multi-good model where the representative agent’s utility is separable
in each of the M commodity groups. This can be written as:
U = V [u1, ..., uG, ..., uM ] = V [ν1(q1), ..., νG(qG), ..., νM (qM )]
where each sub-utility uG has standard properties. The agent maximizes each νG(qG) subject to the amount xG
spent on the commodity group G. For this problem, we can deﬁne the cost function cG(uG, qG) as the minimum
amount of expenses needed to reach utility uG when facing prices pG. Since the agent maximizes utility, we can
xG = cG(uG, qG)
The commodity group quality ξG is implicitly deﬁned so that we can express the utility from group G con-
sumption as the product of quantity and quality,
cG(uG, p0G) = ξG.QG
The price index πG can then be expressed as the ratio of costs at actual prices to costs at reference prices,
cG(uG, p0 )
so that as in (8) we have
xG = QG.πG.ξG
In this case, group utility UG can then be expressed as a monotone increasing function of quality and quantity.
Therefore, overall utility is given by
u = V ∗(ζ1Q1, ..., ζ1GQG, ..., ζM QM )
and this overall utility is maximized subject to
This maximization problem will yield the following demand functions:
ζGQG = gG(x, π1, ..., πG, ..., πM )
Now, we want to establish a formal link between the price elasticity of quality with the usual price and quantity
elasticities. When preferences are separable over a commodity group, the maximization problem gives rise to the
following demand sub-group demand functions:
qG = fG(xG, pG) = fG(xG/πG, p0G)
where the second equality comes from (6) and from the fact that demand functions are homogenous of degree
zero. Since the reference price is held constant, demand functions depend only on the ratio of group expenditures
on group prices xG/πG. Given (9) and (18), we can now write
G = ζG(p0
G, qG, kG) = ζG(qG) = ζG(
) = ζ
G(ln xG − ln πG)
∂ ln ζG
∂ ln ζ
∂ ln x
G − 1)
∂ ln πG
∂ ln xG ∂ ln πG
The term between brackets is the elasticity of the demand QG with respect to its own price πG, i.e εp = ∂ ln QG ,
∂ ln πG
and the ﬁrst term on the right hand side, ∂ ln ζG , is an elasticity of quality with respect to the group expenditure.
∂ ln xG
Now, if we combine (7) and (9), we can write the unit value νG as νG = πG.ζG, or
ln νG = ln πG + ln ζG
∂ ln νG
∂ ln ζ
= 1 +
∂ ln πG
∂ ln πG
Hence, the price elasticity of the unit value is equal to one plus the price elasticity of the quality index. There-
fore, if quality does not respond to price changes, then unit values will evolve in the same proportion as prices. As
a result, it is possible to use the unit values as proxies for the true market prices.
The model is composed of two equations: a demand equation inspired from the AIDS of (Deaton and Muellbauer,
1980), and a unit value equation which comes from (Prais and Houthakker, 1955). For any good G, we have the
following two equations (23) and (24) for household h in village (cluster) c:
wGhc = α0G + β0G ln xhc + γ0G.zhc +
θGJ ln πJc + fGc + u0Ghc
ln νGhc = α1G + β1G ln xhc + γ1G.zhc +
ψGJ ln πJc + u1Ghc
The demand system has J goods, J = 1, ..., G, ..., M . Both the budget share (23) and the unit value (24)
depend on total income x, on a vector of household characteristics z and on market prices π. The error term in
(23) is composed of two terms: one village-speciﬁc effect fc in order to control for unobservable characteristics
which are speciﬁc to villages (e.g taste variables which are not accounted for by prices or by observable household
characteristics), and a random component u0
which is assumed to be normally distributed with zero mean.
We cannot estimate (23) and (24) as such because the true market prices are not observed. However, it is
possible to estimate the non-price parameters consistently if we assume that market prices are invariant within
villages so that they are included in the village ﬁxed effect. This hypothesis of cluster level invariance of market
prices seems reasonable since most villages only have one market. In this case, (23) and (24) can be estimated
with the variables expressed in deviation from their mean, which removes the village-speciﬁc variables from the
The income (total expenditures) elasticities are given by ∂ ln wG = β0G = β0 /w
∂ ln x
∂ ln x
G for the budget share equation,
and by ∂ ln νG = β1 for the quality index equation5. Now differentiating ln w
∂ ln x
G with respect to ln x, we have that
∂ ln wG
G = ε
∂ ln x
x + β1
G − 1
5If ν = p.ζ, then ∂ ln ζ/∂ ln x = ∂ ln ν/∂ ln x.
where εx is the income elasticity of demand6. Rearranging (25) gives us an analytical expression for the income
elasticity of demand based on the estimated parameters (for any good G):
εx = β0/w + (1 − β1)
Similarly, differentiating ln wG with respect to ln π gives the direct and cross price elasticities for the budget
∂ ln wG/∂ ln π = εp + ψGJ = θGJ /wG
Hence, for any good G:
εp = (θ/w) − ψ
With this speciﬁcation, the income and price elasticity of demand will vary according to the level of wG. We
will compute our estimates at mean budget shares (across households within villages).
We must now examine how to recover the coefﬁcients of the price variables, namely ψ and θ. To obtain ψ, ﬁrst
write the total expenditure elasticity of quality using the chain rule as
∂ ln ξ
∂ ln ξ
∂ ln x
β1 = ∂ ln ν
G/∂ ln x =
∂ ln x
∂ ln xG ∂ ln x
The last term of the expression is the total expenditure elasticity of the group εx. If we combine (29) and (20),
∂ ln ξG
= β1. p
∂ ln πG
where εp is the price elasticity of demand. Moreover, since the elasticity of the unit value with respect to price
is given by (22), we ﬁnd ψ as a function of the estimated parameters with
ψ = 1 + β1. p
Now if we substitute (26) and (28) into (31) and rearrange, we obtain
β1(w − θ)
ψ = 1 −
β0 + w
ψ and θ cannot be recovered directly from the data because market prices are not observed. However, we can
6This is because w = (v.q)/x ⇒ ln w = ln v + ln q − ln x ⇒ ∂ ln w/∂ ln x = ∂ ln v/∂ ln x + ∂ ln q/∂ ln x − 1
ﬁnd a consistent estimate of the ratio φ = θ . Given (32), we can write
1 + (w − φ)ς
β0 + w(1 − β1)
Therefore, if we can derive a consistent estimate of φ, knowing ¯
wG, β0 and β1, it is possible to compute the
total expenditure elasticity of demand εx. From there, one can get θ and then ψ using (31).
The intuition to derive a consistent estimate of φ is ﬁrst to use (24) to rewrite ln πJc as a function of the
logarithm of the unit value, of total expenditures, household characteristics and the error term. Then we can plug
this expression into (23) in order to obtain a linear relationship between the budget share, the logarithm of the
unit value and the other control variables. As a result, the coefﬁcient of the logarithm of the unit value will be φ,
which will be consistently estimated with a standard error-in-variable estimator (in order to account for potential
correlation between the error terms of the two equations u0 and u1 ).
The idea of the (Deaton, 1990) procedure is to use within-village variation in a ﬁrst stage in order to estimate
(23) and (24). The results from this ﬁrst stage yields an estimate of the mean value of exogenous prices at village
level by using the mean value of the estimated unit values purged from the effect of income and household char-
acteristics. Then, in a second stage, these price estimates are used to derive a price elasticity for demand, which is
estimated across villages using between-villages variations.
In the ﬁrst stage of the estimation procedure, we use the information available at village level. Equations (23) and
(24) are estimated with variables expressed in deviation from their village mean. This yields ˆ
and the residuals ˆ
e0 , ˆ
e1 which are used to estimate the variances and covariances of u0 and u1 . With these
estimated parameters, and using (26), we can derive the total expenditure elasticity of demand ˆ
εx evaluated at mean
value of budget shares across households within villages.
Now deﬁne the following two variables:
hc − ˆ
β0 ln xhc − ˆ