A Generalized Hypothetical Extraction Analysis

We explicitly formulate (optimization) problems of finding a key sector and a key group of sectors within the framework of a hypothetical extraction method (HEM), and derive their solutions in terms of simple measures termed industries' factor worths. It is shown that the top k >= 2 sectors with the largest total contributions to some factor, in general, do not constitute the key group of k sectors, the issue which is totally ignored in the input-output linkage literature. The link to the fields of influence approach is discovered, which gives an alternative economic interpretation for the HEM problems in terms of sectors' input self-dependencies. Further, we examine how a change in an input coefficient affects the importance of an industry. The key group problem is applied to the Australian economy for factors of water use, CO2 emissions, and generation of profits and wages.