Sectoral specialisation in the EU a macroeconomic perspective

gross growth rates of a Paasche and a Laspeyres
index, whereas in Luxembourg and Sweden
they are calculated just on the basis of the
Laspeyres index. To take the United States as an
example, the formula used is the following:

n

∑ Pi(t - 1)Qi(t)

i=1

n

∑ Pi(t - 1)Qi(t -1)

i=1

Where Q_i is the output of sector i and P_i is the
price of the good produced by sector i. As
shown, the price weights constantly move with
t, so the growth rate of the chain aggregate will
be the same as that of the fixed-weight
aggregate only if relative prices do not change.
If they do, then chain aggregates will grow
faster after the fixed-weight base year and
fixed-weight aggregates will grow faster before
the base year.

The main drawback of using chain-weighted
indices is that aggregate GDP can no longer be
interpreted as the sum of its various sub-
components because the price deflators differ
among the series. The size of the error depends
on the size of the relative price changes between
the sectors that were added up, which might
also be affected by the length of the time series
and the particular time period chosen.

4.2 ANNEX 2: METHODOLOGY

4.2.1 INDICATORS FOR SECTORAL

SPECIALISATION AND RE-ALLOCATION

4.2.1.1 SECTORAL SPECIALISATION AND
CONCENTRATION

Sectoral specialisation is measured by the
Krugman index, which is defined as follows:

K_k (t )=∑∣v√(* ) - P(t )

where V¹_k (t) is the share of sector i in country
k at time t based on gross value added at
constant prices, and V¹ (t) is the share of
sector i in the European union less country i.

The concentration index (also called the Balassa
index⁵⁴) is defined as follows:

^χ'k ^(t) / ^χ_k ^(t)
Xeu ^(t)/ ^Xeu ^(t)

where χ¹_k (t ) is gross value added in constant
prices in country kand sector i, and X¹_eu (t) is
gross value added in constant prices in the EU
and sector i.

4.2.1.2 SECTORAL RE-ALLOCATION AND THE
LILIEN INDICATOR

In order to measure the speed of sectoral re-
allocation of employment, the Lilien⁵⁵ indicator
was used. The Lilien indicator is defined as
employment in sector i.

4.2.1.3 THE SHIFT-SHARE ANALYSIS

A shift-share analysis decomposes the
aggregate growth rate into the weighted growth
rates of its individual components and the
change that has taken place between
components. Formally, the method for
aggregate labour productivity growth applied
here was as follows:
where P_i is labour productivity in sector i, S_i is
the employment share in sector i and a bar
denotes a two-period average. The first term
(intra effect) is the contribution from
productivity growth within individual
industries (weighted by the share of these

54 After B. Balassa (1965), “Trade liberalization and ‘revealed’
comparative advantage”, The Manchester School of Economic
and Social Sciences, no 33, pp. 99-123.

55 D. M. Lilien (1982), “Sectoral Shifts and Cyclical
Unemployment”, Journal of Political Economy, no 90/4, pp. 777-
793.

ECB

Occasional Paper No. 19

July 2004

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