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Appendix F Methodology for regional economic impact analysis

At the centre of any input-output analysis is the input-output, or inter-industry transactions table. This quantifies in monetary terms the flows of goods and services between industries and sectors of the economy. The basic layout of such a matrix can be seen in Figure 7.

Figure 7. An input-output transactions table schematic

See figure at its full size.

There are five basic sectors in an input-output table.

Industries are production sectors, each of which purchases inputs from other sectors. Inputs to an industry are made up of the goods and services purchased from other industries (known as intermediate demand), or primary inputs, which includes everything a firm purchases but which is not classified as an intermediate input (such as wage and salary payments for the purchase of labour, firm profits that accrue to the owners of the firm, and tax payments to the government). Each industry's inputs can be read down the columns of the input output table. Each industry's outputs can be determined by reading along the rows, and the entire output of an industry flows either to one of the other industries, or to one of the final demand categories (see quadrant 2).

Quadrant 2 of the transactions table contains the final demand categories. Regardless of the level of industry aggregation, there are essentially six categories of final demand - residential household consumption, central government, local government, exports, inventories or stocks, and investment (or what economists call capital formation). If the output of an industry is not purchased by another industry, then it is to one of these six categories that industry output will flow. The second broad sector comprises households, who are the individuals and families residing in the economy under study. They appear once in the table as buyers of goods and services; that is, the residential household consumption column of the final demand section. They also show up a second time as sellers of labour in the primary inputs section of the table (ie quadrant 3) where there is a row representing the payments firms make to wage and salary earners. Households are also the owners of capital, receiving part of the firms' profits (gross operating surplus) represented by a row contained in quadrant 3. Some of it accrues to foreign owners of capital while some of it is kept by firms as retained earnings.

The third sector of the economy we consider is the government, which shows up as a final demander of goods and services that it 'purchases' on behalf of the community. It purchases them from the industry called government services. The government also appears in the primary inputs section of the table as the row entity (or rows) to which tax payments are made.

A fourth sector is the outside world, comprising all private economic activity located outside the region under study. This is represented in the transactions table as either imports or exports. Specifically, imports show up as a primary input while exports are a component of final demand.

The final sector in the input-output framework acknowledges is the role of capital. There are two categories of final demand that relate to capital; inventories and investment, which record flows not stocks of capital. The changes in stocks component of final demand may be negative if inventory levels have been allowed to run down during the period covered by the input-output table. Capital also features in the primary inputs section of the transactions matrix, as a row to which payments by firms accrue to the owners of capital (called gross operating surplus); and also in the primary input section by rows that account for depreciation charges (or consumption of fixed capital) and, sometimes, by a row for second-hand asset sales.

We have not yet mentioned quadrant 4. Sometimes primary inputs go straight into final demand without passing through the industry sector of the economy. Two typical examples of such transactions would be tax payments by households directly to the government; for example GST payments, and imports of capital equipment which would appear in the cell denoted by the imports row and the investment column.

F.1 Available input-output tables

Compiling a set of input-output accounts is a major undertaking. Most of the information in the accounts is obtained from surveys. The major inter-industry studies are carried out at a very detailed level - over 200 industry classifications and well over 400 commodities. However, for reasons of confidentiality the results are not published at this level of detail; nor very frequently. The latest inter-industry study published by Statistics New Zealand covers the year ended March 31, 1996.

In addition to the major inter-industry studies, Statistics New Zealand will periodically publish a less detailed set of accounts. While in the past they have done this at intervals of two or three years, in the future this might well be done annually. These 'interim' accounts are more current with respect to the values of industry output, household consumption, tax payments, and the like, but they continue to use information obtained from the major studies to depict input shares and production technologies.

Like its counterparts in other countries, Statistics New Zealand does not produce regional input-output accounts. There is a sizeable literature describing techniques for 'regionalising' a national table. The alternative to employing one of the regionalising techniques is to produce a regional table using survey data. Doing so is very expensive and time-consuming.

F.2 Economic multipliers

Impact analysis is one form of analysis often undertaken within the input-output framework, and requires the calculation of multipliers. A basic tenet of the input-output model is that the various components of final demand (ie. the columns in quadrant II - household consumption, exports, investment, etc) are considered to be exogenous (ie. given, or fixed). Hence, the question one asks when calculating multipliers is: what is the impact on, say, output or value added or employment following an exogenous increase in final demand for the output of the sector of interest? Such an increase might take the form of an increase in export demand, an injection of construction activity or a boost for local production. In other words, given a unit (say, $1 million) increase in final demand for industry j's output, what is the total direct and indirect impact once the economy has responded and settled in a new equilibrium? An output multiplier is simply the figure by which an initial change in output throughout the entire economy should be multiplied to calculate the total change in output resulting from that initial exogenous change (recall that final demand is an element of gross output).

Using the input-output framework, it is easy to see that for an industry to deliver an additional $1 million worth of final demand, that industry is required to directly increase its gross output by $1 million. But that is not the end of the story. To produce an additional $1 million of gross output in one sector, additional inputs to that sector are needed from other industries. And to produce the additional output required in these other industries, additional inputs are needed from yet other industries. And so it continues. This process is sometimes referred to as the initial and subsequent expenditure rounds. A new equilibrium is attained when the value of a new round of purchases does not change from the current round. The total additional output needed from all industries is the amount by which total gross output rises in response to an exogenous $1 million increase in final demand. (The exogenous increase is usually, although not necessarily, associated with a single sector).

While it is possible to compute multipliers for a wide range of economic variables, those of most interest are typically output, value added, employment, and import multipliers. Multipliers are computed on a sectoral basis. The output multiplier for the jth sector is the total change in gross output (or sales) of the entire economy divided by the initial change in output in sector j, where the initial change is nothing more than the exogenous increase in final demand. Income multipliers are defined slightly differently and reflect the total income change in the economy per unit of income generated in the jth sector, where the income change in the jth sector is a direct result of the exogenous increase in final demand of the jth sector. [Two technical points of clarification are warranted at this juncture. First, the input-output model assumes a linear production technology and thus input requirements increase in proportion to output. Compensation of employees is one such input. Second, we have adjusted the data in the input-output table so that compensation of employees captures payments to the self-employed, proprietors income, and dividend payments, as well as wage and salary payments. It is this adjusted value, net of taxes, that we refer to as household income when we compute income multipliers.] Value added multipliers are similar to those for income, but refer to the increase in value added generated throughout the economy as a result of increased output in the jth sector. Employment multipliers are similarly analogous to the income multipliers except that instead of income, they refer to the number of additional full-time equivalent employees utilised in the economy as a result of increased output in the jth sector.

There are two 'types' of each multiplier. Type I multipliers follow the intuition described above. They include the 'direct' effect on output in the industry which experiences an exogenous increase in demand and the 'indirect' effect resulting from the need for all other industries to produce more inputs for that industry. Type II multipliers include an additional effect, the so-called 'induced-income' effect. This arises because as firms produce more output, households receive more income (ie. workers receive wages, investors receive dividends, proprietors receive a return to their management skill, etc), which they in turn spend on food, cars, holidays, TVs and a range of other things. So total output in the industries that produce all these other goods also rises as final demand has increased. Hence, increased output means increased income for households which induces yet more consumption and therefore output, which creates additional income. Like the Type I multiplier, the Type II multiplier measures the impact at the point at which a new equilibrium is reached.

Type I multipliers are likely to understate the economic impact, because they exclude the induced-income effect. However, Type II multipliers are likely to overstate the impact, because the way the input-output model is constructed with linear production technology and inputs that increase in proportion to outputs, it understated input constraints and the likelihood that expansion in some sectors will divert trade from other sectors. The technique is unable to distinguish trade diverting from trade creation effects. Nevertheless, Type II multipliers are more informative of the full inter-sectoral consequences than Type I multipliers, so those used in the Waitaki regional analysis are Type II multipliers.

Multipliers have been calculated for output, value added and employment. Each has a similar interpretation: the multiplier is the ratio of the final impact on output, income or employment to the initial impact on output, income, or employment that results from a $1 million increase in demand for output from a particular industry. [The employment data comes from Statistics New Zealand's 1996 Census of Populations and Dwellings.]

So, for example, the employment multiplier for an industry is the total increase in employment in all industries divided by the initial increase in employment in the sector directly affected by a $1 million increase in demand for output. The Type I multiplier includes the 'direct' effect (which is the same as the initial impact) and the 'indirect' effect, which is the flow-on to industries that supply the first industry with inputs. The Type II multiplier includes both these effects plus the 'induced income' effect caused by increased demand for outputs from all industries by households who now have a higher income.

Multipliers are easy to interpret incorrectly. It is tempting, for example, when a particular sector's income multiplier has a value of 4 to interpret this as meaning that a $1 million increase in output in that sector causes a $4 million increase in income. This is incorrect. What an income multiplier of 4 means is that the final impact on income of a $1 million increase in output in that sector is four times the initial impact on income following that increase in output. The initial impact may be quite small and hence a small total impact can give rise to a large multiplier.

Note that the multipliers used in this analysis are presented below.

F.3 Derivation of multipliers

This section explains the use and derivation of IO multipliers. For convenience, the diagram of the structure of the IO table is repeated here.

Figure 8. The input-output table

See figure at its full size.

F.3.1 Type I and Type II multipliers

As noted above, Type I and Type II multipliers differ in the extent to which they fully capture economy-wide impacts of a sectoral change. Type II multipliers provide a more comprehensive measure of economic change. The derivation of Type II multipliers is essentially an extension of the Type I algebra; hence both Type I and Type II derivations are presented here.

The distinction between Type I and Type II multipliers is as follows:

Type I multipliers measure the direct and indirect effects of a change. In the instance of an output multiplier, the direct effect is the initial rise in output in the industry which is experiencing higher demand. The indirect effects result from the need to produce more inputs for that industry.
Type II multipliers include the direct and indirect effects, as well as the income-induced effect of a change. The initial direct and indirect effects result in higher employment, which in turn boosts household income, which increases demand, which lifts output, which then lifts employment further, and so on.

F.3.2 Derivation of Type I multipliers

Given an n-sector economy, the transactions matrix and the vectors of final demands and outputs can be represented as: [In theInter-industry Study1996, which forms the basis of the multiplier analysis contained in this report,n = 126.]

Z = f = x =

where:

z_ij = sector i sales to sector j

f_j = sector j sales to final demand

x_j = total sector j sales

The c-th row represents compensation of employees (i.e. payments for labour), and the c-th column is household consumption.

The relationship between the elements of these matrices is:

(1)

The technical coefficients (or direct input coefficients) of sector j are written:

(2)

which in matrix form is:

A =

Thus a_ij is the proportion of sector j's total output (the value of which is equivalent to the value of sector j's total input) and is made up of inputs from other sectors.

Given equation (1), sector i's sales can be rewritten and expressed in terms of technical coefficients as:

(3)