A Short Note On RAS Method
Advances in Management & Applied Economics, vol. 3, no.4, 2013, 133-137ISSN: 1792-7544 (print version), 1792-7552(online)Scienpress Ltd, 2013A Short Note on RAS MethodBui Trinh1 and Nguyen Viet Phong2AbstractFor many researchers around the world, the applications of the RAS method can say inboth easy way and difficult way. In our study, we would like to bring to readers the RASmethod, and in the best way to understand in balancing the Supply-Use tables or InputOutput tables in the usual procedure. This work becomes easier if there is an effectivesoftware to do it automatically for all the balancing necessary steps in the usual way.JEL classification numbers: I32, I31, C43.Keywords: RAS method, Supply-Use tables, Input-Output tables, correct row total,correct column total.1 IntroductionAlmost countries compile input-output table or supply and use tables. However, this is notthe case as many of the entries are only estimated, and need to be balanced eithermanually or by an automatic procedure. Addition, they also want to update supply and usetables and input-output table, so The RAS method is the most widely known andcommonly used automatic procedure. This appendix shows a worked example on how theRAS method is used for balancing an S.U.T or I.O.T. Some experts believe that the RASmethod is named after the economist Richard Stone (1919–1991), who, among his otherachievements, co-authored the 1968 SNA together with Abraham Aidenof. His full namewas John Richard Nicholas Stone. He did not have “A” as his middle initial so there mustbe another explanation for RAS. This paper is tried in order to explain clearly thisapproach and be easy for practically it.12Corresponding author, National Account Department of Vietnam.Vietnam General Statistics Office.Article Info: Received : February 2, 2013. Revised : March 31, 2013.Published online : July 1, 2013
134Bui Trinh and Nguyen Viet Phong2 Preliminary NotesThe main target of RAS method is for balancing the columns and rows of input – outputor supply and use tables when updating or revising these tables. The basic equations arecycle sometimes depend to the gap level. These equations were described as follow:XCnew(tn). XCnew(tn-1).XCnew(t1).A.XRnew(t1) XRnew(tn-1). XRnew(tn) Anew(1)Where:XCnew(ti) is new vector of gross output follow column of round ti timeA is coefficient matrix of direct inputXRnew(ti) is new vector of gross output follow row of round ti timeThese equations can do interaction easy by software or do directly by excel very quicklyand easily.3 Case StudyThe basic data in Appendix Table 1 is a simple matrix of domestic production showingthree commodities and three kinds of industries. The margin totals are assumed to beknown accurately while the internal entries have been estimated from various less reliablesources. The task is to revise the less reliable internal entries so that they agree with thecorrect margin totals. The RAS adjustment can be seen as an iterative process in whichcolumns and rows (or rows and columns) are successively forced to add up to the correctmargin totals and the Balancing value of rows and columns become zero (0).Table 1: Matrix of Domestic ProductionSectorsSector 1Sector 2Sector 3ColumnTotalsCorrectColumnTotalsBalancingSector 1Sector 2Sector tRowBalancingTotals75.04.982.01.9125.05.2Table 2 presents the matrix A to be reallocated by Correct Row Totals first time withformula as yield: ARnew(t1) XCnew(t1).AIn this case, for the example with the first row and the first column (The old value is 21.2)The new value would be 22.7 after reallocation, and22.7 21.2 / 70.1 * 75
A Short Note on RAS Method135This procedure is used for other value of rows until the balancing Rows become 0.Table 2: First Iteration: Recalculating the Column Totals (XCnew(t1).A - First Round)CorrectRowSectorsSector 1 Sector 2 Sector 3RowBalancingTotalsTotalsSector 122.731.021.375.075.00.0Sector 29.250.022.982.082.00.0Sector 352.064.98.1125.0125.00.0Column Totals83.9145.952.3Correct Column85.0150.045.0TotalsBalancing1.14.1-7.3Table 3 shows the matrix A recalculated the column totals:XCnew(t1).A.XRnew(t1)For the example of the first column with the balancing column value is 1.1The old value of the first row and first column is 22.7The new value of the first row and first column would be 23.0 after reallocation, and23.0 22.7 / 83.9 * 85Table 3: Second Iteration: Recalculating the Column Totals (second Round)CorrectRowSectorsSector 1 Sector 2 Sector 3RowBalancingTotalsTotalsSector 123.031.918.373.275.01.8Sector 29.351.419.780.482.01.6Sector 352.766.87.0126.4125.0-1.4Column Totals85.0150.045.0Correct ColumnTotals85.0150.045.0Balancing0.00.00.0After that, we copy value from table 3 (from sector 1 to sector 3) and paste special againinto table 1. In this case we have to put about 7 times for balancing with correct columnvectors and correct row vectors become 0. This result is showed in table 4.
136Bui Trinh and Nguyen Viet PhongTable 4: The result after practice RAS methodCropsManufacturesServicesColumn TotalsCorrect otals75.082.0125.0Balancing000With the big difference between the total value (Row Totals and Column Totals) and theadjustment value (Correct Row Totals and Correct Column Totals), the manual methods"COPY and PASTE" value the iteration may make mistakes, and may take for sometimes.A software can be easily wrote based on equation (1). With the help of the software, thisprocedure becomes very easily and quickly, even this iteration is 7 times or 7 milliontimes.If this software can be designed based on Excel, the maximum rows number is more than1 million rows and the maximum columns number is more than 16 thousand columns andabsolutely appropriate for balancing and updating Supply-Use tables or Output-Outputtables.The users just define and input the data for:- The number of rows and columns;- The Correct Row Totals value and the Correct Column Total value;Then, the software would do the balancing procedure automatically.References[1][2][3][4][5]Asian Development Bank (ADB). Supply and Use Tables for Selected Economies inAsia and the Pacific. Manila, (December, 2012).McDougall, R.A. Entropy Theory and RAS are Friends. GTAP Working Paper No.6, (1999).Shannon, C.E. “A mathematical theory of information.” Bell System TechnicalJournal, 27, pp. 379-423, (1948).Studies in Methods Series F, No. 74. Handbook of Input–Output Table Compilationand, Analysis. New York. (1999).Though, Munching, The RAS Approach in Updating Input-Output Matrices : AnInstrumental Variable Interpretation and Analysis of Structural Change, EconomicSystems Research, Vol. 10, No. 1,pp63-79, (1998).
A Short Note on RAS Method137AppendixThe flowchart describes how the software processes all steps in balancing the Supply-Usetable or Input-Output table:BEGINStep 1. Defining the A matrix(Number of rows and Number of Columns)(1) # (2)or(3) # (4)Step 2. Inputting the A matrix(Values for Aij)Step 3. Inputting the Row Totals & Correct Row TotalsInputting the Column Totals & Correct Column TotalsStep 5. Checking the SUM of Column Totals (1) & and SUM of Row Totals (2)Checking the SUM of Correct Column Totals (3) & and SUM of Correct Row Totals (4)Step 6. Calculating the balancing value for rows & columnsBalancingvaluesnot equalto 0(1) (2)and(3) (4)Step 7. Calculating the new value for each Aij(Balancing the rows)Step 8. Calculating the new value for each Aij(Balancing the columns)Step 9. Recalculating the new balancing value for rows & columnsBalancingvaluesequal toStep 10. Making the new Supply-Use table or Input-Output table0END
tables and input-output table, so The RAS method is the most widely known and commonly used automatic procedure. This appendix shows a worked example on how the RAS method is used for balancing an S.U.T or I.O.T. Some experts believe that the RAS method is named after the econ
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cancer (Table 1), though H-Ras itself is rarely one of them. Although these numbers are, by now, painfully familiar, they underscore major gaps in our knowledge of Ras biology. Most obviously, we do not understand why K-Ras mutation is much more frequent in human cancer than N-Ras or H-Ras, even
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