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

data is available. Hence, we have adapted the growth accounting methodology
(Solow, 1957) in order to obtain the regional series for the period beginning
1970 and ending in 2001. This approach starts from a conventional Cobb-
Douglas production function with constant returns of scale:

Y = K^1-α(AL)^α,

where Y is value added at constant prices, K is the stock of physical capital, L
is labour measured in standard units, and A is the technical progress, which is
assumed to be labour-augmenting (or Harrod neutral). Perfect competition
is assumed in the inputs market. In this methodology, the main problem is to
define a reasonable value for the labour income share (α). In many papers,
this parameter is assumed to be a fixed value of 0.07 both over time and
across units. Hence, the possibility of different regional economic structures
is not taken into account. In order to overcome this criticism, particularly
binding in our case, we have obtained an estimate of as the ratio between
labour costs and added value:¹⁰

wL
^α = Y ^,

where w is the per capita income of employed workers, L is the overall number
of workers (employed and self-employed) measured in standard unit, and Y
is the added value. This allows us to have labour income shares which vary
both over time and across units. Figure 1 shows that each region had a
different structural change over time. Indeed, while in 1970 the average α
across units is 0.7, it becomes 0.6 in 2001. This result is coherent with the
hypothesis of a change in the structure of the economy. From equation (6),
we can obtain the value of the regional TFP:

1-α

A=TFP=[( Y )∕μ K ) *]•            (7)

¹⁰Felli, Gerli and Piacentino (2004) used this measure of the income labour share pa-
rameter of Italian regions for the first time.

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