methodology) is published by ISTAT on a monthly basis. It includes more than
100 goods and services and allows us to aggregate sub-categories of goods consis-
tently. This (chained) price index has been available at regional level since January
1999 and spans until December 2005, the last household survey currently available.
In addition, since the household survey was revised in 1996, we were obliged
to use the Italian household budget survey starting from 1997. However, to avoid
any restrictions on the time-dimension of the sample, we approximate a monthly
consumer price index at regional level for 1997 and 1998. ISTAT has also published
the price index for aggregate goods for each province starting from January 1996,
referring to the consumption habits of the members of households whose heads
are workers or white-collar workers in non-agricultural sectors. We matched the
monthly regional elementary price index with the households interviewed in a given
month and region, grouping them according to the categories of goods selected in
the demand system.
Figure 4 shows the graphs for aggregate budget shares wit , with seasonal adjust-
ments obtained by the X12 census procedure, highlighting the fact that at least some
of these shares may also appear non-stationary. This study confirms the systematic
evidence of non-stationary in the variables of the demand system (Ng, 1995; Lew-
bel, 1999; Attfield, 1997, 2004). But, as discussed in Lewbel and Ng (2005), because
budget shares must, by construction, lie between 0 and 1, they cannot remain non-
stationary forever. The small changes that take place from month to month imply
that budget share changes can therefore approximate a non-stationary process for a
long time, as is the case of budget shares in the Italian non-durable data.
Although the demographic and socio-economic samples seem to have some speci-
ficity, we extend the assumption that the variables of the demand system are non-
stationary because the patterns of the variables related to the subsamples are close
to those of the full sample and, as noted above, changes in the budget share sub-
samples are very small7 . We therefore proceed with the empirical analysis by testing
the cointegrating rank of system (5), as a test for identifying the long-run demand
system, irrespective of whether it is applied to the data of the whole population or
only to subsamples.
In order to confine the analysis of a demand system to non-durables and to
7Results of formal tests of non-stationarity with the FDFGLS test of Elliot, Rothenberg and Stock (1996) and
KPSS (Kwiatkowsky et al., 1992) for the full sample and subsamples are not presented here, but they are consistent
with the hypothesis that budget shares (and also prices and real expenditure) contain unit roots. Both estimations
and graphs of budget share subsample patterns are available upon request.
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