A multi-regional generalized RAS updating technique

Abstract

We present an extension of the generalized RAS (GRAS) technique to a multi-regional (MR) or multi-national setting. The framework is applicable to updating/regionalizing/balancing any partitioned matrix that needs to conform to new row sums, column sums and additional non-overlapping aggregation constraints. The technique, which we refer to as MR-GRAS, also handles non-exhaustive constraints, in which case the missing values are endogenously generated in the updating process. We derive the closed-form solution of MR-GRAS, propose a simple iterative algorithm for its computation, and discuss the main analytical properties of the method as well as the normalization and interpretation of MR-GRAS multipliers. From a wide range of possible MR-GRAS applications, several updating frameworks of national and interregional supply and use tables are examined.

The multidimensional nD‐GRAS method: Applications for the projection of multiregional input–output frameworks and valuation matrices

“…Oosterhaven et al (1986) introduced a method for estimating an interregional input-output system in a bi-dimensional RAS set-up where the regional cells must add up to a national figure. The approach followed by Oosterhaven et al (1986) is similar to the multiregional GRAS (MR-GRAS) method developed by Temursho, Oosterhaven, and Cardenete (2020). Both methods constitute a bi-dimensional set-up where the additional national constraint provides a sort of third dimension.…”

“…In principle, the approaches of Oosterhaven et al (1986) and Temursho, Oosterhaven, and Cardenete (2020) are not a real three-dimensional approach because the authors use a bi-dimensional set-up with constraints over these two dimensions, hence, the third dimension is not taken into account as such. Nonetheless, by introducing this additional set of restrictions, the methods of Oosterhaven et al (1986) and Temursho, Oosterhaven, and Cardenete (2020) produce a three-dimensional solution.…”

“…In the MR‐GRAS method, the third set of linear restrictions operates across any non‐overlapping subsets of elements in the multiregional IOT that must add up to a given total. As Temursho, Oosterhaven, and Cardenete (2020) show, this approach can be adapted for updating inter‐national/regional or global SUTs, where the third dimension constraint is introduced for the interregional blocks add up to a given figure. The MR‐GRAS approach has been extensively used for the creation of a baseline scenario called PIRAMID 4 for the 2018 Global Energy and Climate Outlook (Rey Los Santos et al, 2018; Temursho, Cardenete, et al, 2020) in the projection of national IOTs in a multiregional context for future years, ensuring the consistency of the projections with National Accounts.…”

Internal multi-portfolio rebalancing processes: Linking resource allocation models and biproportional matrix techniques to portfolio management

“…More recently, the literature has broadened these biproportional studies to consider when different information is known or unknown. For instance if one or more entries of the matrix A are known or include negative elements, as in the GRAS algorithm from Junius and Oosterhaven [28] and its extensions detailed in Huang et al [22], or one or more entries of the column or row totals p j , a i are unknown, as in Temursho et al [55]. See also Miller and Blair [41,§ 7.4.1] or [56,Ch.…”

Raising the bar (18)

“…Generally, survey and non-survey methods are used to construct so-called intraregional input-output models from their national counterpart. Spatial Economic Analysis has published several papers dealing with this problem using ever more advanced and sophisticated methods (most recently Temursho et al (2021), Jahn et al (2020) and Pereira-López et al ( 2020)). As in the previous paper, this model reflects the notion that regions should not be treated as independent entities and that statistical information about nearby regions should be given a higher weight than that of remote regions.…”