Non-Linear Input-Output Models: Practicability and Potential

The conventional input-output model has been widely criticized, both justly and unjustly, for its limiting assumptions. One of these assumptions is homogeneity of degree one. This paper explores some approaches to minimize this limitation of traditional input-output analysis by removing the assumption of linear coefficients for the intermediate and household sectors. As is well documented in the literature, the household sector is the dominant component of multiplier effects in an input-output model, so using marginal income and expenditure coefficients for the household sector provides a more accurate estimate of the multiplier effects. A price model can then be utilized to estimate the relative changes in local to imported inputs. There are several implications arising from the use of this model, compared to the conventional input-output model. Firstly, while the output multipliers and impacts may not be significantly different between the two models, we would expect the income and employment impacts to be smaller in the marginal coefficient model. This is because many industries, especially those which are more capital intensive and can implement further productivity gains, can increase output, particularly in the short run, without corresponding proportional increases in employment and hence income payments. However, when price effects are incorporated into the model, the direction of change becomes less clear. Secondly, unlike the conventional input-output model in which the multiplier value is the same for all multiples of the initial shock, the multiplier values from the marginal coefficient model vary with the size of the initial impact. Thus larger changes in final demand will tend to be associated with smaller multipliers than small changes in final demand. Therefore, the differential impacts of the marginal coefficient model are not additive, unlike the conventional (linear) Leontief model and CGE model. While not attempting to be a substitute for a CGE model, the methods described in this paper could be used where construction of CGE models are impracticable due to cost and data considerations.