The rectangular sector-by-technology model: not every economy produces every product and some products may rely on several technologies simultaneously

This paper identifies a fundamental challenge in the development of input-output databases of the world economy intended for analysis of alternative scenarios with a model of the world economy. Primary data sources for individual economies generally do not use the same sectoral classification schemes, in part for lack of coordination and also because not all economies produce all goods. In addition, some economies produce a given good simultaneously using several technologies, sometimes quite distinct in terms of factor requirements and cost structures, information that can and should be retained for scenario analysis. To accommodate the relevant information in a way that is both precise and parsimonious, we introduce rectangular input-output matrices and a modeling framework for analyzing them. This framework extends an existing input-output/linear programming model, the rectangular choice-of-technology (RCOT) model, and integrates it into an existing input-output/linear programming model of the world economy, the World Trade Model (WTM). The desirable properties of the resulting WTM/RCOT model are illustrated through a numerical example. This formulation requires that a criterion be specified to choose among available options, and we discuss some alternative criteria. Square input-output matrices and their inverses are only a special case of this more general formulation, and we show how moving to the rectangular formulation expands the types of questions that input-output analysts are able to address.