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## Multipliers

If there is an increase in final use for a particular industry output, we can assume that there will be an increase in the output of that industry, as producers react to meet the increased use; this is the direct effect. As these producers increase their output, there will also be an increase in use on their suppliers and so on down the supply chain; this is the indirect effect. As a result of the direct and indirect effects the level of household income throughout the economy will increase as a result of increased employment. A proportion of this increased income will be re-spent on final goods and services: this is the induced effect. The ability to quantify these multiplier effects is important as it allows economic impact analyses to be carried out on the Scottish economy.

Type I and Type II multipliers are presented in the downloads section of this website. In summary, Type I multipliers sum together direct and indirect effects while Type II multipliers also include induced effects.

## Definitions of Multipliers and Effects:

###### Output Multipliers

The output multiplier for an industry is expressed as the ratio of direct and indirect (and induced if Type II multipliers are used) output changes to the direct output change due to a unit increase in final use. So that multiplying a change in final use (direct impact) for an individual industry's output by that industry's Type I output multiplier will generate an estimate of direct + indirect impacts upon output throughout the Scottish economy.

###### Employment Multipliers

The employment multiplier, expressed as full time equivalent or FTE, is the ratio of direct plus indirect (plus induced if Type II multipliers are used) employment changes to the direct employment change.  In other words, if you have the change in FTE employment for the industry the employment multiplier can be used to calculate the change in FTE employment for the economy as a whole.

###### Employment Effects

Employment effects show the direct plus indirect (plus induced if Type II multipliers are used) employment change to the direct output change due to a unit increase in final use. In other words, if you have the change in output for the industry the employment effect can be used to calculate the change in FTE employment for the economy as a whole.

###### Income (or Compensation of Employees) Multipliers

The income multiplier, expressed as compensation of employees (CoE) wage income only, excluding mixed income, is the ratio of direct plus indirect (plus induced if Type II multipliers are used) income changes to the direct income change. In other words, if you have the change in CoE for the industry the Income multiplier can be used to calculate the change in CoE for the economy as a whole.

###### Income (or Compensation of Employees) Effects

These show the direct plus indirect (plus induced if Type II multipliers are used) income change to the direct output change due to a unit increase in final use. In other words, if you have the change in output for the industry the income effect can be used to calculate the change in CoE for the economy as a whole.

###### GVA Multipliers

The GVA multiplier is expressed as the ratio of the direct and indirect (and induced if Type II multipliers are used) GVA changes to the direct GVA change. In other words, if you have the change in GVA for the industry the GVA multiplier can be used to calculate the change in GVA for the economy as a whole.

###### GVA Effects

The GVA effect is expressed as the direct and indirect (and induced if Type II multipliers are used) GVA changes to the direct output change, due to a unit increase in final use. In other words, if you have the change in output for the industry the GVA effect can be used to calculate the change in GVA for the economy as a whole.

A more detailed explanation of multipliers and their use can be found in this paper for the Input-Output Expert User Group.

## Example 1 - Use of employment multipliers: the effect of a company opening or closing

Multipliers can be used to look at the impact of a specific event on the Scottish economy - for example a company opening or closing. To illustrate this, a hypothetical opening of a company in the "Publishing services" industry, employing 100 people on a full-time basis is considered.

In assessing the impact of this new company we estimate:

• effects on suppliers of the company
• effects on the economy due to an increase in the spending of employees

This is achieved by employing the appropriate multipliers for the type of industry concerned. For the illustrative example, the multipliers used will be for the "58 - Publishing services" Input-Output group.

###### Effects on Suppliers (Indirect Employment Effect)

Multiplying the direct increase in jobs by the "Publishing services" Type I employment multiplier gives: 100 x 1.2 = 120 direct and indirect full-time equivalent jobs. Subtracting the initial direct job increase gives the additional indirect number of jobs supported throughout the Scottish economy as 20 (full-time equivalent).

###### Effect of increased Household Expenditure (Induced Employment Effect)

In addition to the effect of increased employment, we would expect to see an increase in household expenditure among the people who have gained employment through both the direct and indirect employment effects. This is the induced effect and is estimated using the Type II multipliers.

Multiplying the direct increase in jobs by the "Publishing services" Type II employment multiplier gives: 100 x 1.4 = 140 direct, indirect and induced jobs. As we have already calculated a direct and indirect increase in employment of 120 (FTE), we estimate that 20 further jobs will be supported as a result of this induced demand.

## Example 2 - Estimating the effects of a change in final demand

The above example used an estimate of jobs supported directly in one industry to estimate the numbers of jobs supported indirectly and through induced use throughout the economy. However, the direct impacts upon an industry are often presented in monetary terms, i.e. increased exports or a change in Government spending. The following example uses the hypothetical scenario of an additional £5 million of exports to the Rest of the World by the "Manufacture of other metals and castings" industry.

###### The effect on output (using Output Multipliers)

The direct impact upon "24.4-5 - Man. of Other basic metals and castings" will be a requirement to increase its total output by £5 million to meet this additional final use, this is the direct effect. To estimate the indirect effect on this industry's suppliers, we multiply the direct impact (£5m) by the Type I output multiplier for this industry (1.4) giving a total of direct plus indirect impacts of £7 million. Similar to the example above, we would expect the direct and indirect increases in output to lead to increased employment in the affected industries and subsequently to an increase in household consumption. Multiplying the direct impact (£5m) by the Type II output multiplier (1.5) gives £7.5 million of increased output (direct, indirect and induced effects).

###### The effect on employment (using Employment Effects)

The direct change in output can be also be used to estimate the effect upon employment in Scotland. Multiplying the direct output change by the Type I employment effect for this industry gives an estimate of the direct + indirect employment changes resulting from this additional output: £5m x 5.5 gives approximately 28 full-time equivalent jobs supported directly and indirectly throughout the Scottish economy. The direct, indirect and induced employment change can be estimated using the Type II employment effects.

###### The effect on compensation of employees (using Income Effects)

If employment were to rise, we would expect to see an associated rise in compensation of employees (wage income) as these new posts are filled. The Income effects estimate the effect of the direct change in output upon compensation of employees in Scotland. Multiplying the direct output change by the Type I Income effect for this industry gives an estimate of the direct + indirect income changes resulting from this additional output: £5m x 0.3 = £1.5 million of additional compensation of employees income supported directly and indirectly. The direct, indirect and induced wage income change can be estimated using the Type II employment effects.