Input-Output Matrix

Definition

The Industry Transaction Matrix (o Transactions Table) is the fundamental quantitative information used in Input-Output Analysis. It concerns the flow of products from each industrial sector (considered as a producer) to each of the sectors, itself and others (considered as consumers).

Usage

This basic information from which an input–output model is developed is contained in an interindustry transactions table. The rows of such a table describe the distribution of a producer’s output throughout the economy. The columns describe the composition of inputs required by a particular industry to produce its output.

The Matrix is of fundamental importance and may underpin alternative possible input-output models.

Formula

• Usually denoted as Z, if there are n sectors in an economy the matrix reads:

$\begin{align} Z & = \begin{pmatrix} Z_{11} & Z_{12} & \cdots & Z_{1n} \\ Z_{21} & Z_{22} & \cdots & Z_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ Z_{n1} & Z_{n2} & \cdots & Z_{nn} \end{pmatrix} \end{align}$