Do consumer s tastes differ final 1.7. - HEC

D O C ONSUMER’ S T ASTES D IFFER?
2. Common Demand Model
The common demand model provides an informal analysis of the extent to which the estimates of the
individual country model differ across countries and will provide some preliminary evidence regarding
the similarity – or lack thereof – of consumers.
As the weighted mean of the income coefficients and of the income flexibility 6 are not too different
from their unweighted counterparts of model 1, it can be suspected that weights do not seem to play
a vital role.
A plotting of income coefficients and their weighted means and of income flexibility and its weighted
means give a clear result: among the 165 points in the 11 plots, all except 8 lie within the twostandard
error bands constructed using the root-mean-square- error (95% lie within the bands). This
finding points in the direction of similarity of consumers in the countries, as measured by the
coefficients i β and φ .
3. Formally Pooled Demand System
The third model directly includes the hypothesis of similar tastes as it specifies that the coefficients of
the demand equations, the demand parameters, are the same in all countries. The data is being
pooled to estimate a common system for all 15 countries, i.e.
commodities and c = 1,...,15 countries.
c
β i = i β
c
φ
=
φ
, with i = 1,...10
c
α
As the constant terms i take account of non-economic factors, they have a different status and
therefore Selvanathan allowed them to vary across countries. The error terms are assumed to be
normally distributed with zero means and independent over time and countries.
In other models, a comparison of data from individual countries was rather difficult, as it was
expressed in national currencies, being converted to a common currency, using prevailing exchange
rates or purchasing power parities. Selvanathan expresses prices, quantities and incomes in logarithmic
change-form. The changes are unit-free and therefore can be pooled internationally.
When running a likelihood ratio test, here testing the similarity of the individual-country estimates
(model 1) and their standard errors with this unrestricted model, the test confirms the similarity of the
pooled estimates and the weighted means.
The finding that ninety-five percent of the individual-country estimates lie within the two-standarderror
bands and that the pooled estimates are very close to the weighted means, implies that the
pooled estimates are not too different from those of the individual country model. Since additionally
the estimates from model 2 and 3 are not significantly different from one another, Selvanathan
concentrates on model 3.
A too high value for ✪² is obtained on the basis of the likelihood test, making it impossible to accept
the pooled model. This is a puzzling result, but Selvanathan suspects that the asymptotic test is not
performing satisfactorily, as it has also been found to be the case for homogeneity and symmetry
testing. As the author uses the hypothesis of preference independence, where goods do not interact
in the consumer’s utility function, the utility function is additive. In contrast to previous tests,
Selvanathan’s is distribution-free and does not rely on asymptotic theory. Therefore, the pooled model
does not need to be rejected due to the results of the likelihood ratio test.
4. Theil’s Cross-Country Demand System
The fourth model that Selvanathan uses to clarify consumer behaviour, is a model used by Theil (1987)
where countries play the role of time periods, so that now the unit of observation is countries,
whereas before it was years. Another major difference is that in his 30-country sample, only 9 of the
15 OECD countries included above are used.
When comparing this model’s estimates with the ones of the pooled model (3), hardly any similarities
are found. Nevertheless, one needs to be aware that the models are not strictly comparable, as on the
one hand, model 3 has constant terms, which allow for trend-like changes in tastes etc. and Theil’s
6 income flexibility = reciprocal of the income elasticity of the marginal utility of income
B EKE T INNEBERG 6
19 MARCH 2003