Identifying Optimal Sector Groupings with the Hypothetical Extraction Method

We formulate the problems of finding a key sector and a key group of sectors in the economy by the hypothetical extraction method (HEM), and derive their analytic solutions that are termed industries' factor worths. It is shown that the key group of k >= 2 sectors is, in general, different from the set of top k industries selected on the basis of the key sector problem, the issue which is totally ignored in the input-output (IO) linkage literature. Further, the related problems of finding a key region and a key group of regions in an interregional IO setting are discussed. We also examine how a change in an input coefficient affects the factor worth 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