A Note on the Gras Method

Abstract

The GRAS method as presented by Junius and Oosterhaven [Junius, T. and J. Oosterhaven (2003) The Solution of Updating or Regionalizing a Matrix with Both Positive and Negative Elements. Economic Systems Research, 15,[87][88][89][90][91][92][93][94][95][96] assumes that every row and every column of a matrix to be balanced has at least one positive element. This might not necessarily be true in practice, in particular, when dealing with large-scale input-ouput tables, supply and use tables, social accounting matrices, or, for that matter, any other matrix. In this short note we relax this assumption and make available our MATLAB program for anyone interested in matrix GRASing. The same issue arises in the presentations of the KRAS method [Lenzen, M., B. Gallego and R. Wood (2009) Matrix Balancing Under Conflicting Information. Economic Systems Research, 21, and the SUT-RAS method [Temurshoev, U. and M.P. Timmer (2011) Joint Estimation of Supply and Use Tables. Papers in Regional Science, 90, 863-882], which should be accordingly accounted for in their empirical applications.

A Non-Sign-Preserving Ras Variant

“…However, given that RAS variants are in widespread use, we take a pragmatic view and do not question RAS's appropriateness in this paper. In this sense, our contribution is similar to that by Temurshoev et al (2013), who in their Equations 9a and 9b propose a mathematical solution to a particular problem in GRAS, which is one of the cases listed in our Table 1. Like the proposal by Temurshoev et al (2013), our modification to RAS is purely mechanical and is not based on any economic theory.…”

“…In this sense, our contribution is similar to that by Temurshoev et al (2013), who in their Equations 9a and 9b propose a mathematical solution to a particular problem in GRAS, which is one of the cases listed in our Table 1. Like the proposal by Temurshoev et al (2013), our modification to RAS is purely mechanical and is not based on any economic theory. We suggest a mathematical strategy that will repair a particular shortcoming, and thus at least avoids unrealistic outcomes in particular situations.…”

“…Column 7 specifies a scaler that will achieve the desired iterate of a listed in the final Column 8. Note that the final two cases are equivalent to Equations 9a and 9b in Temurshoev et al (2013). Note by editor Bart Los: This table existed in its present form in the original submission dating back to 2011.…”

“…Note by editor Bart Los: This table existed in its present form in the original submission dating back to 2011. Temurshoev et al (2013) was first submitted in 2012. The present manuscript was published after Temurshoev et al (2013) as a consequence of delays in its evaluation and processing.…”

Income, Economic Structure and Trade: Impacts on Recent Water Use Trends in the European Union

“…As we are comparing and explaining water use in 1995 and 2009, the MRIO table for 2009 is deflated and expressed in 1995 constant dollars. Following the approach developed by Junius and Oosterhaven [29] and improved by Lenzen et al and Temurshoev et al [30,31], we apply the Generalized RAS (GRAS) adjustment to obtain a balanced MRIO table. Data on the water used per country and sector have been taken from the Environmental Accounts of the WIOD [32] for the period 1995-2009.…”