demetrix
 
   

Method

I/O analysis

I/O analysis in its modern form was developed by Vassilii Leontief in the 1930es. He used it to analyse the US economy. Since then, the I/O framework has been extended and transferred to many other application domains (like environmental analyses).

Basics of input-output analysis provides a brief introduction into the I/O methodology. Basics of Input-Output Analysis in Matrix Form presents the same stuff, but in a more compact (and more useful) matrix notation.

Technical coefficients

Technical coefficients tell you, how much output of each sector of the economy, is necessary to produce one unit of the produce of another sector.

Consider the following figure.

Aggregated technology matrix of the US economy of 1958

The red column states that in order to produce one unit of good FM, you need 0.0040 units of good FN, 0.2950 units of good FM, 0.1730 units of good BM etc.

Technical coefficients tell you the direct effect of a change in final output. Thus, if final demand for good FM increases by 1 unit, demand for good BM will increase by 0.1730 units, demand for good BN will increase by 0.0370 units etc.

However, technical coefficients do not tell you indirect effects of a change in final demand.

Direct and indirect effects

If final demand changes, this leads to a change in the inter-industry demand. This is the direct (or first-order) effect of a final demand chage.

Imagine, the final demand for some good increases. This leads to increase in inter-industry demand for several other goods, which are required to produce the good, final demand for which increased.

Now, in order to satisfy the increased inter-industry demand, more intermediate goods have to be produced. In order to produce them, one needs more goods, and thus the demand increases again.

These changes in intermediate demand are called indirect effects (or n-th order effects, with n > 1)

Direct effects are reflected by technical coefficients.

Interdependence coefficients

Interdependence coefficients reflect indirect effects of a change in final demand. Interdependence coefficients can also be interpreted as the extent, to which one sector of the economy is dependent upon other sectors.

Software

In order to make the experiments with I/O data, we used following software:

  • excel2maxima - a tool for converting Microsoft(R) Excel(tm) files into Maxima readable form
  • Maxima - a computer algebra system, which we use for matrix operations
  • OpenOffice.org - open-source office suite, using which one can manipulate Microsoft(R) Excel(tm) files
  • numericalio-0.3.zip - Maxima functions, using which it is possible to export matrices to CSV

Sample data sets

We've prepared some sample datasets for experimenting with I/O tables. They are described in the next part of this document.