Appendix 2 - Total direct, indirect, and induced economic impact

In this appendix we provide the model results that include the inducted impact, i.e. the respending of households in the economy. Given our discussion above, these estimates may be considered an upper bound of the international student expenditures.

An input-output model, like any model, is an approximation to reality. It is built on assumptions that are never fully realized in the real world. While most analysts are well aware of the limitations of any I-O model it may be helpful to the general reader to review these limitations.

Input-output lacks an explicit time dimension

An input-output system provides a snapshot of an economy for a period of time (usually a one-year period). If the economy is in disequilibrium, all future uses of the tables and the related impact models will reflect the structural implications of the typical year.

Multiplier effects do occur over time. However, the impact models associated with input-output systems imply that the multiplier effects are virtually instantaneous. There is some evidence to show that the multiplier effects take from two or three years to move through an economy.

Sensitivity to relative price changes

Relative prices between commodities will change from the base year of model construction to the period in which the model is used. Therefore, the analysis of projects via input-output analysis in the future will reflect one set of relative prices, while the direct requirements coefficients in the tables reflect the relative prices of the base year. If the relative price changes are not accounted for, future data supplied to the impact model will produce "incorrect" impact results.

Constant technology

As mentioned earlier, the input-output system is a static model. However, times change and so do the technologies used. To mitigate this limitation, most input-output systems are updated on a periodic basis. Such an update picks up any technology changes in the economy. Between updates no changes in technology are assumed. The 2017, 2018 report uses Statistics Canada’s 2016 input/output model.

Constant returns to scale

Input-output systems assume constant returns to scale; that is, all inputs change in the same proportion as any change in an industry's output. This assumption implies that even for one dollar increase in sales, the model will show impacts on wages, salaries and employment associated with the multiplier effects. However, common sense tells us that this is not true. Such a small increase would not necessarily cause, especially in the short run, generation of a commensurate increase in wages or employment. However, in the long run, it can be assumed that even a small increase in final demand will produce the multiplier effects estimated by an input-output system.

In the short run, industries can draw on inventories, use their labour more efficiently, etc. to increase output with limited impact effects. However, if the new level of final demand is maintained, the firms in the long run will move back to their historical steady-state level of utilization of factors of production. In the long run, increases in, say household income due to increases in final demand will reflect the technical coefficients' relationship between income and output modelled in the input-output system.

No supply constraints

Input-output systems assume that whatever is demanded by industries as inputs can be supplied. They assume no productive capability constraints. This problem is not significant when there is excess capacity in an economy. However, when economies are operating at or near capacity, this limitation is important. The multipliers for an economy near capacity will be underestimated. This is because increased final demand will require new capital investment whose own direct and multiplier effects are not captured within the standard input-output system.

Fixed consumption patterns

The consumption patterns that result in households respending multipliers are assumed to be fixed and linear. As Canadians become "better off" they redirect real growth in income to savings and luxury consumption. Because the input-output system is static, it does not model the effect of non-linear patterns in household consumption (as real income increase) within its multiplier estimates. This problem is partially overcome by regularly updating input-output systems.

Conclusion

Although the list of limitations may appear long, a similar or longer list is associated with almost any form of economic analysis. The limitations occur in different areas in other analytical tools. No one economic model is expected to provide the comprehensive "answer". Economic analysis techniques should be used in a complementary fashion to appreciate the full scope of a problem. In a very real sense, then, quantitative economic models should be used to examine the structural implications of changes in an economy and should not be treated as providing "the" answer.