Southern regions, but also among themselves.
3 Econometric Methodology
The traditional approach to testing for convergence consists of applying Or-
dinary Least Squares (OLS) to a regression of the average growth rate of per
capita output over a specified period, ∆yn , on the initial level of per capita
output, yn0 , after controlling for a number of cross-country permanent dif-
ferences, xn, i.e.
δ Уп = α + βyn 0 + δxn + tn, (2)
where tn is the usual country-specific random disturbance. Clearly, for con-
vergence to have taken place over the period under consideration, a negative
sign is expected on the coefficient of the initial level of per capita output,
i.e. economies starting from a lower income grow more quickly than those
starting from a higher income. This testing procedure is usually applied on
a large number of cross-sections in order to get sufficient variation from the
data.
However, Evans (1996) shows that OLS provides biased estimates ofβ and
δ', if tn is correlated with yn0, unless ynt — yt is a stationary process and the
cross-country differences are permanent, i.e. they do not vary over time5 . If
these conditions are met, the N economies are said to converge, and inferences
on the heteroskedastic-consistent t-ratio of β and F-ratio of δ of eq. (2) are
valid. However, two further issues have to be considered. Firstly, technology
differs widely across countries (or regions). Secondly, the assumption that
all the economies have identical first-order autoregressive properties relies
on the unlikely assumption that the set of variables x is able to control for
all differences. These two assumptions imply that the traditional approach
is valid only if the economies considered are homogeneous. Final criticism
to the conventional approach is that it throws away all of the time series
5Hence, they are uncorrelated with en.