The Absolute and Relative Joint Stability
of Input-Output Production and
CHIA-YON CHEN and ADAM ROSE
An important variant of the standard input-output model has been developed by Ghosh ( 1958). In contrast to the fixed input requirements of the Leontief Production function, Ghosh's allocation function approach calls for fixed output, or sales, distributions across sectors. Rather than a demand-driven model with fixed coefficients in relation to column sums, the new formulation is a supply-driven model with fixed coefficients in relation to row sums. Applications of the allocation model have been numerous. One set deals with the direct and indirect impacts of natural resource supply shortages (see Davis and Salkin 1984; Giarratani, 1976). Another set of applications pertains to the calculation of Hirschman ( 1958) concept of forward linkages (see Bulmer- Thomas, 1982, Jones, 1976). Yet another pertains to the formulation of multiregional input-output models (see Bon, 1984, 1988).
The conceptual soundness of the allocation function approach in several contexts has been supported by Ghosh ( 1958) characterization of the behavior of monopolies and planned economics as dominated by supply considerations. Empirical support for the use of the model emanates from studies that have shown allocation coefficients to be as stable over time as are production coefficients (see Augustinovics, 1970, Bon, 1986; Giarratani, 1981).
This chapter addresses a remaining concern of the legitimacy of the allocation model -- what we refer to as the joint stability of the production and allocation versions of the I-O model. This concern emanates from the fact that an I-O system cannot be operated with both production and allocation coefficients simultaneously fixed, except for the most trivial cases. Stated another way, when using the allocation model does the constancy of allocation functions implicitly result in production coefficient changes that are unreasonable? Will the results of a simulation of the impacts of, say, an oil embargo help yield a meaningful distribution of the burden of the ensuing oil shortage, but at the same time possibly call for oil input substitutions that are technologically or economically infeasible? The aforementioned empirical tests shed little light on this question because they provide no theoretical linkage