Summary Measures of Interconnectedness for input-output Models

Abstract

The performance of six alternative measures of input-output model interconnectedness was tested on a set of fourteen empirical models for Australia, for the State of Queensland, and for subregions within Queensland. Such measures of interconnectedness could be analytically useful, along with the input-output models themselves, as descriptions of the nature of the modeled economies, as aids in model estimation, and perhaps as indications of the level of economic development. Since there is no generally accepted interconnectedness measure, the six tested measures could be judged only on their consistency of behavior and on the validity of their underlying logic. Accounting conventions and model aggregation both affected most of the measures. The results suggest that mean intermediate coefficient total per sector is the most generally useful interconnectedness measure.The concept of interconnectedness is implicit in input-output methodology. Such models are used to describe the relationships among the component sectors of an economy. Multipliers give numeric measure to the relation of a given sector to the total economy. Yet there has been only minimal attention given to holistic measures, summarizing the degree of interconnectedness of the entire modeled economy. Such measures of interconnectedness could be analytically useful, along with the inputoutput models themselves, as descriptions of the nature of the modeled economies, as aids in model estimation, and perhaps as indicators of the level of economic development.This paper will examine the performance of a number of potential measures of model interconnectedness as they are applied to a set of consistent input-output models for Australia, for the State of Queensland, and for a number of regions within Queensland.It is clear that various economies differ in degree of interconnectedness. In an economy characterized by high interconnection, a shock will be churned by successive rounds of intersectoral transactions, with the result of substantial changes in all other sectors. In a less interconnected economy, lack of intersectoral linkages means that the effects of a shock will be confined mainly to the directly impacted industry. The differences observed may be attributed to variations in degree of closure and differences in structure between economies. If an economy is relatively open, external trade will take the place of some potential linkages among endogenous sectors. For economies similar in degree of openness, one would still expect variations in interconnectedness due to structural differences; differences in what industries are important to each economy, and differences in the production technologies used. An empirical measure of interconnectedness could serve as a useful descriptive statistic, giving insight into the extent to which intersectoral linkages serve to transmit impacts throughout the sectors of an economy.

Assessing Economic Connectedness Degree of the Malaysian Economy: Input-Output Model Approach

“…This measure was suggested by HAMILTON and JENSEN (1983;p.56) as a relatively good descriptor of interconnectedness. It is calculated as the arithmetical average of the sums of the columns of the Leontief inverse.…”

“…Since, as is known from matrix algebra, the inverse of a matrix equals the adjoint divided by its determinant, one can expect that the smaller the denominator in this formula, the larger the elements of the inverse (HEAL, HUGHES and TARLING, 1974;p.87). It might expect that smaller determinants would be associated with inverse matrices having larger elements, with larger multipliers, and with a greater degree of interconnectedness (HAMILTON and JENSEN, 1983;p.58). Since the determinant depends only on the direct coefficients, it is also a technical measure.…”

“…The intermediate coefficients are the links of interconnections, and more links suggest greater interconnection. Thus the percentage of the intermediate coefficients which are non-zero is one crude measure of interconnectedness (HAMILTON and JENSEN, 1983;p.57). In the case of more highly interconnected models, the coefficients matrix, A, is likely to have fewer zero entries.…”

“…Most of these measures were proposed by authors in economics but there are some proposed by biologists, and have an ecological content (useful surveys of some of these measures are HAMILTON and JENSEN 1983, SZYRMER 1985, BASU and JOHNSON 1996, CAI and LEUNG 2004, and AMARAL et al 2007and 2008. It used the measures proposed by economist for Malaysian economic analysis.…”

“…In contrast, if a national economy has a large enclave industry, which exports most of its output, and relies mostly on imported inputs, then percentage intermediate transactions will detect this condition better than the technical measures, because it is the only measure which incorporates information about sector size. The only measure insensitive to aggregation is percentage intermediate transactions, which is probably best relegated to instances of extreme sector size imbalance (HAMILTON and JENSEN, 1983;p.65). The implication, of course, is that when comparing the interconnectedness of economies by means of one of these five measures, the measures should be based on table with a common level of aggregation.…”