ST
where E is employment vector and Y is labour income vector. E = I ej I is the employment inverse
S
matrix where
is an employment
es = bs .-L. ; bSτ is an element of (I-A) and Es XT
ij ij X T ij ii
coefficient, which expresses the number of employees of region s per one output unit of sector 1 in
region T. Y = ∣hS ɔ
is the labour income inverse matrix where h1sT
1j
Ys
= ' XT^ and YS /X1T is a labour
income coefficient, expressing the amount of income paid to workers of region s per one output unit
of sector 1 in region T.
2.2 Der1v1ng the mult1reg1onal I-O matr1x: a three-stage est1mat1on method
To construct a multiregional matrix, it is necessary to have at disposal much information, which
involve both intraregional flows among sectors and interregional flows. Since collecting information
by survey is costly, indirect techniques reducing need for data have been introduced over time
(Chenery, 1953; Moses, 1955; Leontief and Strout, 1963; Polenske, 1970).
In the case of a bi-regional I-O model, the Round’s interregional approach (Round, 1972; 1978;
1983) can be a straightforward solution. This approach allows deriving both interregional imports and
exports and offers a higher degree of internal consistency than single region applications3. A problem
associated to this technique is that there is no obvious extension of the approach to multiregional
input-output tables involving three or more regions (Hewings and Janson, 1980). In this research, we
tried to extend the Round’s approach to production of multiregional models implementing that within
an integrated procedure. The technique proposed is a three-stage est1mat1on method. Stage 1 provides
the application of a location quotient technique to estimate the intersectoral flows within a given
region (input coefficient matrix) and imports of the region from the rest of the country (total trade
coefficient matrix). In stage 2, a gravity model is used to allocate total imports of a given region
among the other regions (trade coefficients matrices). Finally, stage 3 provides the application of an
optimization technique to reconcile discrepancies within the multiregional I-O table and the
calculation of multipliers. The first two stages are repeated recursively as many times as is the number
of the regions under study. In next paragraphs, the three stages are described in more detail.
2.3 stage 1: est1mat1ng 1nput and total trade coeff1c1ents matr1ces
In this stage, a preliminary estimate of input and total trade coefficients is obtained using a
location quotient technique. Within the location approach, several methods can be included, such as:
simple location quotient, purchases-only location quotient, West’s location quotient, cross industry
location quotient, symmetric cross industry location quotient, semilogarithmic quotient and Flegg’s
location quotient (West, 1980; Miller and Blair, 1985; Flegg et al., 1995; Flegg and Webber, 1996a,
1996b, 1997; Oude Wansink and Maks, 1997).
The Flegg’s location quotient (FLQ) has been designed to overcome some theoretical drawbacks
related to traditional location quotients. Of the properties which a regionalization method should
incorporates (Round, 1978), the FLQ, different from other location quotients, takes account of all the
three properties: importance of selling sectors, importance of purchasing sectors and size of the region.
Moreover, recent empirical evidence (Flegg and Webber, 2000) has shown that the FLQ outperforms
traditional location quotients in reproducing survey-based models.
3 Round proposed a two-stage estimation method based on SLQ for deriving the regional requirement coefficients. The
first stage involves a preliminary estimation of intraregional and interregional flows using location quotients. Consider two
regions R and s. The location quotient approach establishes that if q1Rj ≥ 1 , then region R is supposed to be self-sufficient
and the surplus is exported. In the case of one region, this amount is undefined. However, in a closed system with two
regions, if q1Rj ≥ 1 , there results that q1sj < 1 . It signifies that region s will import goods and services by an amount of
(1 - q1sj )r1jN, where r1jN represents the national technological coefficient. This quantity is supposed to be imports from the
other region (imports from abroad are therefore excluded) and consequently exports from region R . The second stage
involves the adjustment of initial estimates to conform them to known vectors of intermediate output.