PROJECTION OF SUPPLY AND USE TABLES: METHODS AND THEIR EMPIRICAL ASSESSMENT

Abstract

We present eight existing projection methods and test their relative performance in estimating Supply and Use tables (SUTs) of the Netherlands and Spain. Some of the methods presented have received little attention in the literature, and some have been slightly revised to better deal with negative elements and preserve the signs of original matrix entries. We find that (G)RAS and the methods proposed by Harthoorn and van Dalen (1987) and Kuroda (1988) produce the best estimates for the data in question. Their relative success also suggests the stability of ratios of larger transactions.

Keywords:

• Supply
• Use
• Updating techniques

Acknowledgements

We gratefully acknowledge the financial support provided by the EU FP7 WIOD project. This project is funded by the European Commission, Research Directorate General as part of the Seventh Framework Programme, Theme 8: Socio-Economic Sciences and Humanities. Grant Agreement no: 225 281, www.wiod.org. This paper was partly written when the first author was on a short visit to the Organisation for Economic Co-operation and Development (OECD) in Paris. He thanks the staff of the Directorate for Science, Technology and Industry of the OECD for their hospitality. We also thank Manfred Lenzen (ESR Editor), two anonymous referees and participants in seminars at the OECD and University of Groningen for their comments and suggestions. The views expressed in this paper are those of the authors and do not necessarily represent those of the OECD.

Notes

¹ The Euro method was originally devised for updating SIOTs, but is also used in a SUT-setting, see a report prepared by Joerg Beutel to the European Commission (e.g., contract number 1508302007 FISC-D, April 2008). The method will be presented in detail in this paper.

² See Lahr and Mesnard (2004) for details on RAS (including its history), which also gives an extensive set of references on the topic.

³ It should be mentioned that KRAS (K for Konfliktfreies) as described by Lenzen et al., (2009) generalizes the GRAS method: (i) to constraints on arbitrary subsets of matrix elements, (ii) for non-unity coefficients, i.e. the restrictions for constraint coefficients can be different from 1 or -1, and (iii) for incorporating reliability and conflict of external data.

⁴ See McDougall (1999) for a detailed comparison of RAS and other entropy-theoretic methods, including the MSCE model of Golan et al. (1994), who argues that, in general, the RAS remains the preferable matrix balancing technique.

⁵ The three-stage RAS (TRAS) proposed by Gilchrist and St. Louis (1999) extends the original RAS by including additional information on individual cells, and row and column totals of a sub-matrix of the original table. In general, it has been found that the introduction of extra accurate exogenous information into RAS improves the resulting estimates. See, for example, de Mesnard and Miller (2006).

⁶ Updating SUTs rather than SIOTs in this paper loosely parallels the SUT-based regionalization methods proposed by Jackson (1998) and Lahr (2001a).

⁷ Notation commonly used in the input–output literature is employed as much as possible. Adopting usual conventions, matrices are given in bold capital letters; vectors in bold lower case letters; and scalars in italicized lower case letters. Vectors are columns by definition, thus row vectors are obtained by transposition, indicated by a prime. denotes the diagonal matrix with elements of vector x on its main diagonal and zero otherwise.

⁸ General remark applicable to all updating methods using benchmark (or base) tables: for interpolation, when benchmark tables are available for the beginning and end of the projection period, both should be used. Assume we need to project SUTs for k years between the start and ending periods of available SUTs. Then the benchmark data may be simply taken to be as the arithmetic average of both tables, e.g. . However, since in some cases k can be large, it is better to use some weighting scheme that gives more weight to the available data closer to the projection time . Therefore, for example, the variable ‘benchmark’ Supply matrix can be written as . This way structural change can be partially taken into account.

⁹ One of the referees criticizes this step of the EUKLEMS approach on the ground of internal inconsistency (this applies to the Euro method for similar reasons). This conceptual concern “… lies in the use of commodity output to modify what are fundamentally industry representations, and the reverse, the use of industry-based growth rates to adjust commodity values”. The implication of uniformly adjusting rows in the Use table in Equation 8 “is that industries are substituting inputs one for another simply in response to changes in commodity supply rather than changes in technology or even price … Given that values in industry columns of the use matrix or rows of the make matrix are related by fundamental technological/behavioural relationships, it seems more sensible in most cases to make adjustments to these tables on an industry basis rather than a commodity basis, with the most notable exception being an accounting for price changes, which act (more or less) uniformly on all purchasers.” Such an approach for forecasting Make and intermediate Use tables is taken in Jensen and Jackson (2010).

¹⁰ Note that steps in Equations 8–9 are similar to the first two steps in the RAS procedure. It is important to note that the final demand matrix excludes the column of changes in inventories and valuables, which is considered as a residual category in order to guarantee the consistency of SUTs. That is, this residual category is equal to the difference between total commodity supply at purchasers' prices, Equation 7, and the sum of uses by product in Equation 9.

¹¹ The resulting Use table, Equation 11, is consistent with the Supply matrix at basic prices in Equation 2, because the vectors of margins and taxes by product, Equation 6, are taken from the Supply table projection.

¹² The SUT variant of the Euro method has been reported by Joerg Beutel to the European Commission (e.g., contract number 150830-2007 FISC-D, April 2008).

¹³ The listed data requirements mean that the vectors of sectoral value-added, v _t , totals of final demand categories, y _t , and aggregate value of imports, m _t , need to be known.

¹⁴ For example, the row growth rates adjustment multipliers of domestic uses in iteration iter + 1 are the diagonal elements of the matrix for all iterations iter ≥ 2.

¹⁵ The details of the RAS procedure is thoroughly discussed in Miller and Blair (2009, Ch. 7), which also gives an extensive list of references on the topic.

¹⁶ It seems fair to use the original name of the method as a corrected RAS (CRAS, C for corrected) in order to give credit to Günlük-Şenesen and Bates (1988). However, now there is a CRAS (cell-corrected RAS) approach attributed to Minguez et al. (2009), hence we follow the current convention and use the term GRAS.

¹⁷ Introducing this function, Huang et al. (2008) call the method the ‘Improved GRAS'. We should, however, note that the result of this optimization gives exactly the same outcome as in Lenzen et al. (2007), who use instead. The only ‘problem’ with the last function is that for , i.e. when the initial matrix trivially satisfies the prescribed row and column sums, the function is negative, . Its modified version gives a function value equal to zero as it should be. However, this adjustment does not play any role in determining the optimal Z.

¹⁸ An equivalent closeness between the normalized squared differences and RAS outcomes have been already mentioned in Harrigan and Buchanan (1984, p. 341).

¹⁹ More mathematical details of this and followup methods can be found in Temurshoev et al. (2010).

²⁰ When , we set the corresponding element of MAPE, WAPE and SWAD to zero, and when , the corresponding entry of is nullified as well.

²¹ In the 2005 Use table, there was the third commodity Retail trade services without any use, but we did not take it away, since these services were provided to the households at the amount of 492 and 461 mlllion Euros for years 1995 and 2000, respectively. As a result, we add a small number (unity) in the corresponding cell in the 2005 Use table to make the programs ‘feasible’.

²² All the projections are implemented in MATLAB.

²³ In fact, Voas and Williamson (2001) use the overall sum of the elements of the estimated matrix, but in our setting the last is equal to the overall sum of the true matrix entries, since the row and column sums of the predicted and actual tables match.

²⁴ Recall that Harthoorn and van Dalen's method with the elements' relative confidences equal to the absolute values of the original entries ( in (36)) is nothing else than the INSD approach.

²⁵ This number decreased from 75 to 73 because we were not able to distinguish between Market and Non-market health services, and Market and Non-market recreational, cultural and sporting activities. This is because CNPA 96 products classification does not distinguish between non-profit institution serving households (NPISHs) and governmental services, which is the case for CNAE 93 industry classification.

²⁶ We are grateful to Jiemin Guo for this suggestion.