ALTERNATIVE APPROACHES TO MODELLING ZERO EXPENDITURE: AN APPLICATION TO SPANISH DEMAND FOR TOBACCO*
| Date | 01 August 1996 |
| Author | Jaume García,José M. Labeaga |
| Published date | 01 August 1996 |
| DOI | http://doi.org/10.1111/j.1468-0084.1996.mp58003004.x |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 58,3(1996)
0305-9049
ALTERNATIVE APPROACHES TO
MODELLING ZERO EXPENDITURE: AN
APPLICATION TO SPANISH DEMAND FOR
TOBACCO *
Jaume García and José M Labeaga
I. INTRODUCTION
Tobacco demand has been a matter of major concern in recent years for
several reasons. One of them consists of developing suitable models that
deal with the important percentage of zeros arising in microeconomic
data sets where information is available at a highly dissagregated level.
Since proposals by Cragg (1971), alternatives to univariate Tobit type
models have been widely used and applied to tobacco demand by several
authors with different purposes (for instance, Atkinson et al. (1984),
Deaton and Irish (1984), Jones (1989) and Fry and Pashardes (1994)).
The other strand of literature based on social, health and fiscal grounds
has also contributed to the proliferation of papers that attempt to model
the consumption of a good in which habit plays a key role.
Zero observations may arise for three main reasons. First, in survey
data with short recording periods the purchase policy of the household
could generate a large percentage of zero consumption (infrequency).
Second, tobacco may not be a good for some households because they are
non-smokers (abstention). Third, although households contain potential
smokers they may not afford the good at current income and prices
(corner solution). The main aim of this study is to estimate a tobacco
demand equation for Spain emphasizing the use of double-hurdle models.
We are interested in analysing the distinction between abstentions and
corner solutions,1 and how relaxing specification and distributional
assumptions affect the income and price elasticities. We also test restric-
tions embodied in different specifications.
*We would like to thank Manuel Arellano, Richard Blundell, Ignacio Mauleón, Clemente
Polo, José L. Raymond, Jumana Saleheen, Amparo Sancho, participants at the Sixth World
Congress of the Econometric Society and an anonymous referee for their useful comments.
Financial support was provided by CYCIT Ns. PB89-0309 and BP92-1036-0O2-01, Fundación
BBV and a grant of the Bank of Spain. All remaining errors are our own.
'In the case of tobacco, infrequency has been shown to be a minor problem in a descrip-
tive study of Spanish surveys by López (1993).
489
© Blackweil Publishers 1996. Published by Blackwell Publishers, 108 Cowley Road, Oxford 0X4 1JF,
UK & 238 Main Street, Cambridge, MA 02142, USA.
490 BULLETIN
Tobit, P-Tobit and first hurdle dominance models are shown to be
restrictive and the data confirms the existence of separate individual
decisions, on participation and consumption. We also propose to estimate
a dependent version of a double-hurdle model, although we find inde-
pendence is not a restrictive assumption once additional powers of total
expenditure are included in the specification of the second hurdle.
Another interesting feature of our results is the reduction in the elastici-
ties when moving from univariate to bivariate models.
The outline of the paper is as follows: in Section II the statistical
models are described and an overview of testing alternative specifications
and distributional assumptions are presented. The data and results of this
cross-section study together with an evaluation of the income and price
elasticities are reported in Section III. The paper ends with a summary of
the main conclusions.
IL ALTERNATIVE SPECIFICATIONS, RELATIONSHIPS AND HYPOTHESIS
TESTING
Our main concern throughout this paper will be the estimation of a
tobacco demand equation for Spain using cross-section data from the
EPF. Following previous empirical evidence, we emphasize the use of
double-hurdle models when analysing individual decisions regarding
consumption of this good. This approach allows us jointly to model, first,
why one decides to be a smoker and second, the quantity one decides to
consume.2 Univariate models only allow a differentiation between zeros
and positives but not among the reasons generating the former.
Let us suppose that from the individual utility optimization problem we
derive an equation that relates tobacco consumption to the explanatory
variables through the following demand function and an observability
rule.3
y7=ß'X,+c (1)
J*fZ+v (2)
where y7 is the value which corresponds to the latent variable (notional
demand), J7 is a non-observable indicator which determines whether the
individual j is a smoker or not (discrete preference parameter), X, and Z
are vectors of conditioning factors (economic and socio-demographic
characteristics of individual j and t and y are non-observable random
variables.
2This double-hurdle approach and its name is due to Cragg (1971). There are numerous
applications not only to tobacco demand as mentioned, but also to alcoholic beverages or
clothing demand as Deaton and Irish (1984), Blundell and Meghir (1987) or Atkinson et al.
(1989), and to labour supply as Blundell and Meghir (1987) or Blundell et aL (1987), for
instance.an interesting treatment of this kind of problem see Pudney (1989) and references
therein.
© Blackwell Publishers 1996.
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