2  Input output tables[1]

Inter industry tables provide a summary of the industrial structure of an economy for a given year. They contain information on the values of flows of goods and services between industries and sectors of the economy.

All commodity and industry flows in the input output tables are recorded in nominal terms at basic prices. The basic price of a good or service is the amount receivable by the producer minus any tax payable and plus any subsidy receivable. The producer price is the amount receivable by the producer minus any deductible goods and services tax (GST) or value added tax (VAT) invoiced to the purchaser. The purchaser’s price is the amount paid by the purchaser, excluding any deductible GST or VAT in order to take delivery of a unit of a good or service. In the case of goods, the purchaser’s price includes any trade margins and transport charges paid by the purchaser. Both basic and producer prices exclude transport charges invoiced separately by the producer.

The focus of input output analysis tends to be on inter industry transactions or the industry by industry flow matrix. Table 1 provides an example of such a matrix.[2] It shows the New Zealand inter industry transaction table for 1995-96 at the 49-industry level. The rows of the inter industry transactions table describe the distribution of an industry’s output throughout the economy, while the columns describe the composition of inputs required by a particular industry to produce its output.

Rows 1 to 49 record how much each industry sells to other industries (columns 1 to 49) and final demand output (columns 51 to 57), where final demand (column 58) consists of household consumption (column 51), private non-profit final consumption (column 52), central and local government final consumption (columns 53 and 54), gross fixed capital formation (column 55), change in inventories (column 56) and exports (column 57). Column 50, labelled “total industry”, is the sum of intermediate products supplied by a particular industry.[3] The column labelled “total economy” (column 59) is the sum of total sales of intermediate and final demand products.

Columns 1 to 49 show how much each industry purchases from other industries (rows 1 to 49) and other inputs to production (rows 50 to 56). Compensation of employees (row 52), operating surplus (row 53), consumption of fixed capital (54), other taxes on production (row 55) and subsidies (row 56) add up to total value added at basic prices (row 59). Entries along the principal diagonal (row 1, column 1; row 2, column 2; … row 49, column 49) of the intermediate input flow matrix (grey shaded area) show the amount of intra industry trade.

Table 1 also shows the link between total use in basic prices (row 57) and purchaser’s prices (row 58).

From Table 1 gross domestic product (GDP) at market prices can be calculated. The sum of total use in purchaser’s prices of final demand ($M 120,388) less total economy imports ($M 26,641) is equal to GDP ($M 93,747). Alternatively, GDP can be calculated as total industry value added in basic prices ($M 84,120) plus total economy taxes on products ($M 9,626).

The inter industry transactions table shows the composition of supply and use by industries. It can be used to construct input output coefficients to assess inter industry linkages that take into account direct and indirect transactions.

The basic input output identity can be expressed as follows

(1)    x = Ax + f

where x = [x₁,...,x_N]^/ is the vector of gross output, N denotes the number of industries, f = [f₁,...,f_N]^/ is the vector of final demand and A=[a_ij] is the matrix of technical coefficients.[4] Technical or input coefficients record the inputs directly required from one industry in order to produce one unit value of output of another industry. They are calculated as follows

(2)    

where R = [r_ij] is the intermediate input flow matrix (shaded area in Table 1). Equation (1) thus states that gross output,X, is the sum of all intermediary output, Ax, and final demand, f.

Equation (1) can be solved for X to obtain

(3)    x = [I - A]^-1f

if [I - A] is non-singular and where I is the identity matrix.[5] The matrix [I - A]^-1 is called the inverted Leontief matrix or total requirement matrix. Total requirement coefficients show how much output is required directly and indirectly from each industry for every unit value of output produced for final use. The elements of [I - A]^-1 are denoted b_ij .

The inter industry transaction table and input output model are used to compare New Zealand’s production structure to that in other OECD countries. Comparator countries include: Australia, Belgium, Denmark, Finland, Germany, Norway and the United Kingdom. The choice of countries was based on the following criteria: (i) availability of inter industry transactions at basic prices, (ii) aggregated at around 50 industries, (iii) produced for the mid-1990. A fourth criterion was language. Table 2 summarises the data and sources.

The data should be reasonably comparable although there are differences. For example, in New Zealand bank service charges (or financial intermediation services indirectly measured) are allocated directly to industries and final use, and hence included in intermediate consumption. In Belgium, Denmark, Finland, Norway and the United Kingdom financial intermediation services indirectly measured are reported separately. Another example is the treatment of remuneration of working proprietors in small family companies. In New Zealand remuneration of working proprietors in small family companies is put to profit distribution (and not wages and salaries). The System of National Accounts does not provide guidance on such payments and it is unlikely that the New Zealand practice is followed by all comparator countries.

Table 2: Summary of data and sources