NNss
f(aiLjS)=∑∑∑∑
L=1S=1i=1j=1
( aL- aL )2
(11)
where ajjs represents known coefficients of the unbalanced matrix whereas aj indicates coefficients
of the objective matrix. Minimization8 is carried out under the following constraints:
N N
(12)
(13)
∑∑ajS ∙XSS = ZiN (i, j = 1,2,-,5)
j=1 S=1
aijjS ≥0 (i,j=1,2,-,5 j,S=1,2,-,N)
where ZjN represents the national intermediate flows from sector i to sector j. System (12) imposes
that the sum of flows from sector i to sector j for all regions must equal the relevant national flows
whereas system (13) imposes non-negativity of coefficients9.
From the resulting balanced multiregional I-O table, there are calculated employment and income
multipliers used for impact analysis10 (Tabs. 3 and 4).
2.6 Modelling policy into the multiregional I-O model
Assessing impact from EU policy by a multiregional I-O model requires estimating regional
funds and distributing funds sectorally.
As regards regional allocation, there was used information from the Romanian Development Plan
2004-2006 (Romanian Ministry of Integration, 2003). The National Development Plan calculates for
every development region a complex index ( Ir ) , named “development index”, which is proposed to
allocate structural funds regionally. This index should reflect the disparities among regions and give
preference to underdeveloped regions in the process of distribution of resources. It is composed of
three parts: (a) a combination of per capita income and population reflecting the basic criteria for
“structural underemployment”; (b) a combination of unemployment rate and population highlighting
peculiar problems regarding employment; (c) a combination of basic transport and utilities
infrastructure highlighting the problems regarding the structural endowment.
From development indices, shares of allocations11 are calculated as: ( Ir∣Ii ). These shares were
applied to the national amounts to estimate regional funds for all policies considered. Tab. 5 shows
the allocation of national funds among the regions.
8 This problem of non-linear programming was codified and solved by an algorithm developed within GAMS.
9 Through the specification of further constraints, it is also possible to insert all available exogenous information, which
the analyst considers to be appropriate to improve the overall reliability of the multiregional I-O table.
10 From an analysis of multipliers, one can identify for every region the so-called key sectors i.e. sectors which can
stimulate economic growth in terms of income and employment in the regions under study by means of interrelationships
with the other sectors of both the region examined and the other regions. Identifying key sectors helps policy makers to select
sectors to which investments should be addressed in order to favour economic development.
11 Percentages of allocation are: 21.6 (NER), 13.6 (SER), 16.5 (SR), 11.8 (SWR), 8.6 (WR), 11.9 (NWR), 10.8 (CR),
5.2 (BR).
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