Appendix F Methodology for regional economic impact analysis continued
F.3.2 Derivation of Type I multipliers contined
Output multipliers
Re-expressing equation (8) in expanded format gives:
From this it can be seen that the economy-wide impact of fj* is:
(9)
For fj* = 1, xj* reduces to:
(10)
xj* is the (Type I) output multiplier: that is, how much does economy-wide output have to increase to meet a $1 increase in final demand for the output of sector j.
Value added multipliers
In principle these are calculated in the same way as for output multipliers; the distinction is that changes in sectoral output arising from a change in final demand are scaled by each sector's value added input coefficient (ie the ratio of value added to total inputs).
The value added input coefficients are calculated using the sum of the compensation of employees, the operating surplus and net indirect tax rows of the input-output table. We shall denote this sum as zvaj. In a manner similar to that used to derive the direct input coefficients in equation (2), the value added input coefficients are:
(11)
By using this to scale the impact of changes in output we have:
(12)
This is the (Type I) value added multiplier. Its interpretation is: how much will economy-wide value added increase, above the initial increase in sector j's value added payments, given an increase in final demand of sector j's output of $1.
Employment multipliers
These are calculated as for the income multipliers, but rather than use compensation of employees to scale the output effects we have used the ratio of full-time equivalent (FTE) jobs to output by sector. This employment ratio is:
(15)
Using this in our multiplier calculation gives:
(16)
F.3.3 Derivation of Type II multipliers
In the calculations above, the matrix elements are restricted to those within the nxn confines of the transactions matrix of the inter-industry table. However, this effectively excludes the impact of changes in household income arising from additional final demand, since household income and consumption is outside of the nxn matrix. Type II multipliers address this issue by expanding the nxn matrix to include household consumption and compensation of employees. Households are effectively treated as another production sector in Type II multiplier analysis, producing labour services and demanding consumption goods and services.
The technical coefficients for the household row and column are:
(17)
(18)
where:
acj= the labour coefficient for sector j
aic= the 'household consumption' coefficient.
In equation (18), xCrepresents household disposable income. For the analysis contained in this report we calculated household disposable income as the sum of:
- compensation of employees (from the input-output tables)
- self-employed earnings (derived from Statistics New Zealand's Institutional Sector Accounts)
- dividends (derived from Statistics New Zealand's Institutional Sector Accounts)
and then subtracted tax from that sum using an average personal income tax rate derived from the Institutional Sector Accounts. Note that both self-employed earnings and dividends are reflected in the operating surplus row of the input-output table.
