Academic journal article
*European Research Studies*

# The Effect of Sector Loss on the Internal Structure of Regional Economies

## Article excerpt

1. Introduction

Input--Output models are being employed quite widely in the analysis of economic growth. Generally these models assume that certain forces will remain relatively unchanged as others act upon the economy, but this is never actually the case. It should be useful, therefore, to examine the impact upon the structure of the model of selected changes under conditions where all other forces are held constant. So, the main goal of this paper will be the investigation of the impact upon the internal structure of the regional economies of the complete loss of an industrial sector. This impact will be isolated by simply pulling the row and column representing each of the several sectors from the matrix and reinvested to develop new multipliers. Starting with a summary of the earlier extraction methods we will apply it to the case of regionalized Greek economy. Next we will provide a statistical analysis of the results. Finally some conclusions will be proffered.

2. Review of Literature

This study provides a useful framework to examine various kinds of possible "hypothetical extraction" linkages measures. The idea was to try to quantify how much an economy's total output would change if a particular sector was loss. The method of extraction originally conceived by Paelinck, de Caevel, end Degueldre (1965) and later employed by Strassert (1968), Schultz (1976, 1977), Meller and Marfan (1981), Milana (1985), and Hemler (1991). A complete recapitulation for extraction methods as well as their properties and their economic interpretation, can be found in Miller and Lahr (2001). In accordance to the literature a measure of the relative importance of any particular sector in an economy is found by extracting that sector.

3. Methodology

The basic balance equation of Leontief's model is, x = [(I - A).sup.-1] y so, it may be assumed that one sector is extracted from the economy. Extraction of the jth sector for example, means that the jth row column of input matrix A are deleted (not replaced by zero).

Thus the equation can be rewritten as:

[bar.x](j) = [[I-[bar.A](j)].sup.-1] [bar.y] (j) (1)

Where [bar.A] (j) is a (n-1) input matrix by deleting jth sector from A, also [bar.x](j) and [bar.y](j) are (n-1) dimensions vectors corresponding to output vector x and final demand vector y, respectively.

If y and [bar.y](j) is given, the results [bar.x](j) should be less than x, [bar.x](j) < [x.sub.i]

Thus, the sum of the differential between the output vector x excluding jth element and [bar.x](k) can measure linkage effect of the extracted sector j on total output. Cella (1984) decomposed the matrix A and defined a total linkage effect of each sector and then identified into backward linkage and forward linkage.

Accordingly, the basic balance equation of Leontief s model, X = A x+y, may be rewritten as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

The sectors of the economy can be divided into one category that consists of the sectors that are to be extracted from the economy and category two that encompasses all the other sectors of the economy.

If the extracted sectors do not sell or buy any intermediate products to or from the other sectors of the economy ([A.sub.11] and [A.sub.21] are equal to zero), then the above equation can be rewritten as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Where [[bar.x].sub.1] and [[bar.x].sub.2] are the output vectors after extraction. So, the solution equations of the extracted outputs may be obtained as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

The total linkage effect (TL) can be defined as:

TL = e'(x - [bar.x]) (5)

Where [bar.x] demotes the output column vector of all sectors after the sector loss, e is a column summation vector (that is [e.sub.i] = 1 for all i). …