Indirect Effects - A Formal Definition and Degrees of Dependency as an Alternative to Technical Coefficients

The use of input-output analysis for the computation of secondary effects of final demand changes is well-known. These 'final demand effects' can be calculated using technical coefficients and the inverse of the Leontief matrix. This paper offers an alternative to the use of technical coefficients. Its goal is threefold. First of all degrees of dependency are defined and it is shown how they can be used to compute secondary effects. Their definition is based on an input-output table. Secondly the concept of secondary effects is extended to what is called indirect effects. These indirect effects are not only related to final demand but to total industry output. It is shown how these indirect effects can be calculated using technical coefficients or degrees of dependency. The method used is a variant of the so-called Hypothetical Extraction Methods. Double counting is avoided, as such the resulting multipliers are 'net multipliers'. It is formally demonstrated that technical coefficients and degrees of dependency give the same results when a recent input-output table is available. If this is not the case then the results are different. It is impossible to say which of the two estimates is better. Since technical coefficients are already broadly accepted, some examples are given to justify the use of degrees of dependency. Finally it is explained how the unavailability of an input-output table can be solved. Starting from the supply-use tables a 'quick and dirty method' to infer an input-output table is provided. This topic is justified by the fact that for Belgium input-output tables are only published for those years that are divisible by five, with a three year lag. A short empirical analysis, based on currently available data, shows that technical coefficients and degrees of dependency have comparable performance, with a slight advantage for the technical coefficients. This performance is measured relative to a 'right' result, being the indirect effects for the year 2000 computed using the now available input-output table for the year 2000. This result is called 'right' because it does not make any assumptions on stability of technical coefficients nor of degrees of dependency. The empirical analysis also compares the use of a recent supply-use table to the use of an old input-output table. Supply-use tables on average overestimate the 'right' result. They are however often closest to the 'right' result at the first level. Since these conclusions are based on limited data further analysis is required as more data becomes available.