Basic analytical tool-kit for input-output tables with multiple related outputs: Applications to physical input-output tables with disposals to nature

Physical Input-Output Tables (PIOTs) are a powerful accounting framework since they trace simultaneously all physical flows of the economy, including goods and emission. However, there is no IO model able to operate them and, thus, they cannot be used for analytical purposes - only descriptive. A series of papers suggested different methods to operate them but without clearly identifying a IO model matching the specificities of PIOTs (Hubacek and Giljum 2003; Giljum and Hubacek 2004; Suh 2004; Giljum, Hubacek, and Sun 2004; Dietzenbacher 2005; Dietzenbacher et al. 2009; Xu and Zhang 2009). This paper aims to develop an output-driven and an input-driven IO model to operate PIOTs, which would constitute the basic analytical tool-kit to analyse such tables. First, section 2 compares the operation of the traditional Input-Output Tables (IOTs) with PIOTs. It identifies a new type of table - a multiple related outputs IOT - that matches the specificities of a PIOT: it has several outputs (goods and emissions) and one of the outputs - the emissions - is related to the total sectoral throughput by the technology of production. Then, it is shown that the related output causes traditional output-driven IO models such as the Leontief one to underestimate the total outputs. Then, section 3 devises a new IO model by assuming a linear relationship between the related outputs (emissions) and the total throughput (total output or input); consequently, the related outputs such as the emissions can be endogenised in the structure of production and, thus, the model can be driven with final goods alone. Section 3.2 generalises the model for any number of multiple related outputs and shows how to operate a PIOT with five types of simultaneous emissions. Then, section 3.3 shows that Suh's (2004) method is in fact a change of total output units that transforms the PIOT - a multiple related outputs IOT - into a single output IOT that can then be operated with traditional IO models. For completeness, section 4 examines the use of input-driven models with multiple related output tables and finds that no special modification of the input-driven model is required. Thus, this paper provides the theoretical background to analyse PIOTs and any other multiple related outputs IOTs. It is expected that this new model will revive the momentum in PIOT development and analysis which had been lost because of the lack of robust analytical tools.