Convergence in TFP among Italian Regions - Panel Unit Roots with Heterogeneity and Cross Sectional Dependence

auto-regressive coefficient. This essentially means assuming that all series in
the panel exhibit the same degree of mean-reversion. Although it is plausible
to assume that all series may converge on average, the restriction that all
converge at the same speed may be binding.

In this paper we are particularly interested in the issue of heterogene-
ity because differences in the economic structure across Italian regions are
sizeable and this can have relevant implications for empirical modelling.

Firstly, we are interested in whether the rate of convergence across re-
gions is of a similar magnitude. And consequently, whether we can group
particular regions in terms of rates of convergence or all regions converge
at the same pace. In addition, since the work of Robertson and Symons
(1992) and Pesaran and Smith (1995), it has been noted in the literature
that Fixed Effects (FE) estimation is potentially inconsistent when using dy-
namic equations under cross sectional heterogeneity. In contrast, an average
panel estimator, such as the Mean Group (MG) estimator,⁶ will provide con-
sistent estimates of the average of the parameters from dynamic regressions
although these estimates will be inefficient since we are not fully utilising all
the potential advantages of poolability in the panel. We use the Hausman
test statistic to explicitly examine panel poolability in what follows. The
Hausman test can be used to compare the estimated coefficients from FE
and RCM, hence whether bias is important for FE due to heterogeneity and
therefore whether we can pool coefficients and groups in a single panel. As
suggested by Pesaran, Smith and Im (1996) the test statistic, distributed as
a χ² (k), has a null hypothesis of homogeneity, when FE estimates are equal
to RCM estimates, and an alternative of heterogeneity. Where θ is a (k x 1)
vector of FE estimates and θ is a (k x 1) vector of RCM estimates under the
null of homogeneity. The test statistic is of the form

(θ - θ)0[V(θ) - V(θ)]-¹(θ - θ) ~ _χ²(k)                   (5)

⁶See Pesaran and Smith (1995) or Swamy’s Random Coefficient Model (RCM)

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