Difference between revisions of "Technical Coefficient Matrix"

Revision as of 15:43, 2 March 2022

Definition

A Technical Coefficient Matrix (also Technology Matrix, Direct Coefficients or Direct Requirements Matrix) is the collection of input-output coefficients . It is a central element of an Input-Output Model. It is derived by dividing the Input-Output Matrix (Z) by the vector of Total Output (x), thereby generating a normalized representation of economic structure that is independent of the units used to quantify exchanges (whether those are monetary or physical units). The input coefficients for all of the intermediate inputs and all value components add up to one (100%).

Formula

The technical coefficients matrxi is often in IO literature denoted as the $A$ matrix and it is given by multiplication of Z with the diagonalised and inverted industry output x:

\begin{align} A & = Z\hat{x}^{-1} \\ A_{ij} = \frac{Z_{ij}}{x_j} \end{align}

Issues and Challenges

“Accounting coefficient” would be a better term than “technical coefficient”, since what we have are monetary amounts and not quantities. However, the term “technical coefficient” is generally used.^[1]

References

↑ Understanding National Accounts F.Lequiller, D. Blades, OECD 2014

[1] Understanding National Accounts F.Lequiller, D. Blades, OECD 2014

[1]

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 == Definition ==
-A '''Technical Coefficient Matrix''' is the collection of all [[Input-Output Coefficient | input-output coefficients]] (also Technology Matrix, Direct Coefficients Matrix). It is the central element of an [[Input-Output Model]] (Also total inter-industry requirements). The input coefficients for all of the intermediate inputs and all value components add up to one (100%).
+A '''Technical Coefficient Matrix''' (also ''Technology Matrix'', ''Direct Coefficients'' or ''Direct Requirements Matrix'') is the collection of [[Input-Output Coefficient | input-output coefficients]] . It is a central element of an [[Input-Output Model]]. It is derived by dividing the [[Input-Output Matrix]] (Z) by the vector of [[Total Output]] (x), thereby generating a normalized representation of economic structure that is independent of the units used to quantify exchanges (whether those are monetary or physical units). The input coefficients for all of the intermediate inputs and all value components add up to one (100%).
 == Formula  ==
-It is often denoted as the <math>A</math> matrix
+The technical coefficients matrxi is often in IO literature denoted as the <math>A</math> matrix and it is given by multiplication of Z with the diagonalised and inverted industry output x:
+:<math>
+    \begin{align}
+        A & = Z\hat{x}^{-1} \\
+        A_{ij} = \frac{Z_{ij}}{x_j}
+    \end{align}
+</math>
 == Issues and Challenges ==