ESTIMATION OF SYMMETRIC INPUT–OUTPUT TABLES: AN EXTENSION TO BOHLIN AND WIDELL

Abstract

This paper presents two optimisation models for use in the production of symmetric input–output tables (SIOTs) based on data contained within supply-use tables (SUTs). The first model produces commodity-by-commodity SIOTs derived from the selection of appropriate technology assumptions, while the second produces industry-by-industry SIOTs derived through the selection of appropriate sales structure assumptions. Both models address the problem of negative coefficients and also permit the use of rectangular SUTs as base input data. Additionally, this paper explores the development of a ‘comprehensive model’ enabling production of both commodity-by-commodity and industry-by-industry SIOTs that are conceptually and mathematically consistent.

Keywords:

• Input–output model
• Technology assumptions
• Sales structure assumptions
• Optimisation

Acknowledgements

The authors would like to thank Robbie Andrew (Landcare Research Ltd) for his valuable input during the conception stages of this paper. The authors are also indebted to the New Zealand Ministry of Agriculture and Forestry and the Foundation for Research, Science and Technology's Cross Departmental Research Pool (CDRP) for financial assistance (Contract No. 0908-01). Additionally, it is noted that Nicola Smith has been funded through a Bright Futures Scholarship (Contract Number MAUX06024). Finally, the authors would like to thank the two anonymous referees for their valuable comments.

Notes

¹ A primary reason for the production of negative coefficients is heterogeneity in the underlying data. In practice, such heterogeneity is unavoidable due to the need to aggregate a vast range of economic activities and products into a set of industry and commodity groups. For a further discussion of negative coefficients arising in relation to the generation of SIOTs, reference can be made to Almon (1970), Steenge (1990) and Miller and Blair (2009).

² Although note that ten Raa and Rueda-Cantuche (2007) put forward evidence that the commodity and industry technology models are just two particular cases of a more generalised form.

³ Reference can be made to Stahmer (1985) and Viet (1994) for a discussion of the different methods for constructing input–output tables and the associated consequences and limitations of each method.

⁴ In fact, due to limitations associated with the ITA assumption, ten Raa et al. (1984) chose to apply the by-product technology model, rather than the ITA, to commodities classified as by-products.

⁵ These applications are sometimes also referred to as ‘partial life-cycle assessments’.

⁶ As the focus of this application is on comparing technical coefficients derived for the intermediate demand components of the input–output tables, Equations 6, 12 and 14 have been used to derive the three models rather than Equations 7, 13 and 15. The variables specifying primary demands by receiving industry and output commodity (i.e. the p _jk s) and final demands by commodity consumed and supplying industry (i.e. the f _il s) are simply estimated exogenously. For each industry, primary inputs are allocated to commodity outputs on a pro rata basis according to the proportion that each commodity makes up of the industry's total supply. Similarly, final demands by commodity are allocated to supplying industries according to each industry's share of the total supply of that commodity.