Supply Driven Input-Output

The supply driven I-O was first formulated by Ghosh (1958). The Ghosh Model (or sales- coefficient or allocation model) is designed to trace the economic implications of changes in the final payments sector. It is made by examining the ‘bottleneck’ effects according to the changes in the final payments sectors (Park, 2007). Thus, the model assumes that there is no unused capacity and that all resources are scarce except for one sector. The sales-coefficient model is described in Equation 2.8, which corresponds to the direct requirements of the standard model (Equation 2.2).

i ij ij x X

b  / ( 2.8)

ij

b ₌ sales coefficient of sector i to sector j = proportion of sales of sector i to sector j ij

x ₌ sales of sector i to sector j

i

X = total sales (output) of sector i

Equation 2.8 shows the foundation of the allocation model, based on a direct output coefficient matrix or sales coefficient matrix. This is the total opposite of the standard Leontief Model, which is built upon a direct-input coefficient matrix and is demand oriented.

The allocation model can be partitioned into unconstrained sectors (not subjective to scarcity constraints), represented by the subscript r, and constrained sectors, represented by the subscript s, as shown in Equations 2.9.

       rr rs sr ss B B B B B ( 2.9)

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where:

B = nn matrix of sales coefficients bij

n_{= r}_{s, for} r and s smaller than n (rn and sn)

sr

B = (sr)matrix containing elements from the first s _{columns and the last} r rows of the

B matrix, representing the sales coefficients of outputs by the s _{unconstrained} industries of the r constrained industries inputs;

rs

B = (rs)matrix containing elements from the last r columns and the first s _{rows of the}

B matrix, representing the sales coefficients of outputs by the r constrained industries of inputs to the s unconstrained industries;

ss

B = (ss) matrix containing the elements from the first s _{rows and the first} s _columns of the B matrix, representing the sales coefficients between the s _{unconstrained} industries;

Given the final payments of the unconstrained sectors, the new outputs of the unconstrained sectors can be determined by Equation 2.10. Similarly, given a value of outputs for the constrained sector, the final payments of the constrained sector can be determined by Equation 2.11. 1 ) )( (     r rs s ss s X B V I B X ( 2.10) sr s rr r r X I B X B V  (  ) ( 2.11) where: r X = )

(r -element row vector 1r with elements Xs through Xr; representing total input

of the constrained industry;

s X =

)

(s -element row vector with elements X1 through Xs; representing total input of

unconstrained industries;

r

V = row vector of final payments of the r constrained industries; s

V = row vector of final payments of the s unconstrained industries;

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The model assumes that final demand changes do not affect the sales coefficients because the coefficients are fixed: output distribution patterns in an economic system are stable or output coefficients are fixed. It means that if output of sector i is doubled, then the sales from i to the other sectors will also be doubled. Additional assumptions are i) unchanged vector of final payments for the unconstrained sectors; ii) altered vector of final payments for the constrained sector; and iii) perfect substitutability between factors.

The model also presupposes a monopolistic or a centrally planned economy approach. It considers the best feasible combination of the unconstrained (non-scarce) sector based on the rest of the scarce resources with respect to a welfare function (Ghosh, 1964). This is a reasonable approach for analysing oil shocks. While the oil market is an oligopoly with competitive elements, the monopolistic characteristics prevail, such as price controlling (Cohen, 2007), and it is not easy to find alternative suppliers of oil in the short run. The model ultimately considers how the forward inter-industry allocation processes work. This suggests that not necessarily value-added factors have to rise to increase total outputs, if the expected final demands are to satisfy the minimum requirements (Park, 2007).

An important debate about the supply driven I-O model is related to its stability. Oosterhaven (1988, 1989, 1996) stresses that the way the model is formulated implies that input factors might be combined without any technological relationship. He concluded that this model is implausible and should not be used. However, Davar (2005) states that the model might be plausible in practice. In addition, Dietzenbacher (1997) says that the allocation model is an absolute price model equivalent to the Leontief price I-O model. His interpretation of the model is that it is not a quantity model, which limits the applicability of the model as an impact analysis tool. These contradictory conclusions indicate the need to further analyse the applicability of the model, and that resolving the dilemma might not be a simple task.

Park (2007) facilitates the applicability of the supply driven I-O model by presenting four main conditions for correctly using it:

 Monopoly;

 Scarcity of factors;

 Short period; and

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Park suggests that if the case study meets these four criteria, then the supply driven I-O can be applied. However, the model still needs to be applied with care and the results should not be used in major decisions, but only for descriptive analyses (2007). While, this model appeared to be promising due to its initial assumptions, it is unclear whether it is reliable to use this model or not. Thus, it was decided to find another method to analyze the impacts of supply constraints. The alternative was the supply constrained or mixed I-O model.