distance from the cross-sectional average11 , i.e.
1N
yit = in(1 + ∖ya - N∑yit|)∙ (10)
i=1
The first step is the Levin-Lin-Chu (LLC) PUR test. As discussed in section
3 this test takes into account differences between regions that are constant
over time, but does not consider differences in the speed of convergence. Still
it provides useful inference of whether the data exhibits a process of conver-
gence on average. Considering the full sample, for both measures of distance
from the benchmark this test cannot reject the null of no stationarity in the
series, leading us to conclude that there is no convergence in the Italian re-
gional system as a whole. Interestingly, however, when we make a partition
of the sample into two sub-groups (South and Centre-North), we observe a
substantial difference in the results obtained from the two measures of dis-
tance. The test of convergence on y concludes at the 5% critical level that
there is no convergence among the Southern regions (Basilicata, Calabria,
Campania, Molise, Puglia, Sardegna, Sicilia), and convergence among the
regions of the Centre-North (Emilia Romagna, Friuli V.G., Liguria, Lom-
bardia, Piemonte, Trentino A.A., Veneto, Lazio, Marche, Toscana, Umbria,
Abruzzo). Interestingly, this result is overturned when we consider y. As
a further check, we have refined the disaggregation of the grouping of re-
gions, dividing the Centre-North into Central (Lazio, Marche, Toscana, Um-
bria, Abruzzo), and Northern regions (Emilia Romagna, Friuli V.G., Liguria,
Lombardia, Piemonte, Trentino A.A., Veneto). Now the test concludes for
both measures that there is no convergence among Central regions (at the
5% critical level). The two measures, however, still yield different results for
the Northern sub-group. The LLC test on y shows that most of the con-
vergence picked up in the Centre-North grouping was coming through the
11The rationale may be that distinguishing between regions above and below the average,
as in the conventional measure, makes the two groups fall a priori on parts of the log
function with different slopes, the second does away with this distinction and treats both
groups of regions equally.
13
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