Projecting supply and use tables: new variants and fair comparisons

ABSTRACT

We have introduced in this paper new variants of two methods for projecting Supply and Use Tables that are based on a distance minimisation approach (SUT-RAS) and the Leontief model (SUT-EURO). We have also compared them under similar and comparable exogenous information, i.e.: with and without exogenous industry output, and with explicit consideration of taxes less subsidies on products. We have conducted an empirical assessment of all of these methods against a set of annual tables between 2000 and 2005 for Austria, Belgium, Spain and Italy. From the empirical assessment, we obtained three main conclusions: (a) the use of extra information (i.e. industry output) generally improves projected estimates in both methods; (b) whenever industry output is available, the SUT-RAS method should be used and otherwise the SUT-EURO should be used instead; and (c) the total industry output is best estimated by the SUT-EURO method when this is not available.

KEYWORDS:

• SUT-EURO
• SUT-RAS
• updating
• projection
• supply and use tables

Acknowledgements

We gratefully acknowledge EUROSTAT and the Austrian, Belgian, Italian and Spanish National Statistics Offices for having provided us with their annual estimations for SUTs at basic prices. The results shown here would have not been possible without such information. We also thank the editor and four anonymous referees for their valuable comments and suggestions. The views expressed herein are those of the authors and do not necessarily reflect an official position of the European Commission.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 For the European Union (EU), according to the European Transmission programme (Annex B of the Council Regulation (EU) No 549/2013 of the European Parliament and of the Council of 21 May 2013) data delivery of SUIOTs should take place 36 months after the reference period.

2 The KRAS method is a generalization of the GRAS method, suitable for cases where exogenous information is conflicting (cfr. Gallego and Lenzen, 2009). When exogenous information is not conflicting, reliability weights are set to one (i.e. all the information available is given the same reliability) and constraints coefficients are 1 or −1, the KRAS method is equivalent to the GRAS method.

3 To our knowledge, only Temurshoev et al. (2011) stated in a footnote (p. 880) a way to include TLS in the SUT-RAS method but without distinguishing between domestic and import uses.

4 Matrices and vectors are given in bold upper (X) and lower case (x), respectively. Scalars are expressed in italics and lower case (x). Vectors are defined by default by column so row vectors are defined by means of the transposition sign (prime) x’. $\mathit{\iota }$ stands for a vector with all elements equal to one. $\stackrel{\mathbf{ˆ}}{\mathit{x}}$ denotes a diagonal matrix with the elements of vector $\mathbf{x}$ placed on its main diagonal and zero otherwise (off-diagonal elements). Subscripts may denote the year or the valuation concept (basic prices, b; purchasers’ prices, p).

5 This is denoted by superscripts in matrices and vectors. Domestic uses are denoted with superscript d and imported uses with superscript m.

6 Our aim is to stick as much as possible to the original SUT-EURO method rather than creating a new model by means of assuming other alternatives such as, for instance, the stability of the product mix instead of the market share.

7 Other options could have been possible, however, according to Eurostat (2008, p. 316), Model D (fixed product sales structures) is favoured against the assumption of fixed industry sales structures which seems to be rather unrealistic. This is also the choice of several European Union countries that compile industry-by-industry SIOTs (Rueda-Cantuche, 2011, p. 26)

8 $\mathbf{O}$ and $\mathbf{0}$ are null matrices and vectors with adequate dimensions.

9 More details on the pros and cons of different measures of goodness of fit can be found in Knudsen and Fotheringham (1986), Makridakis (1993), Butterfield and Mules (1980) and Hyndman and Koehler (2006).

10 An IS = 1 implies that a perfect and direct linear correlation between $X$ and $\tilde{X}$ exists. This is the case when $X=\tilde{X}$ , a perfect match. However, some kind of systematic errors (linear shifts such as $\tilde{X}=X+a$ , or scale transformations $\tilde{X}=a\cdot X$ ) could also lead to an IS = 1. So, for practical purposes, the interpretation of this indicator should be done carefully, since a very good fit could be due to some kind of systematic errors instead of a good fit.

11 Without loss of generality, we do not show the results for the other indicators because they do not provide any new additional information and/or conclusion. All the results are available in a specific Appendix where all the results, figures and tables provided in this article can be reproduced and checked by the reader.

12 For the SUT-EURO method, this is clear because every element of the use table is rescaled by positive column and row factors. As for the supply table, this is also true given the fact that the Supply Table is computed preserving the base-year market shares multiplied by the consistently estimated output by product. The demonstration for the SUT-RAS method can be found in Temurshoev and Timmer (2011, p. 868).