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EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks -Necessary input -simple RAS method -minimizing deviations methods. UK 1995. Use table in purchaser’s prices.

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EUKLEMS, Groningen, 15 Sept 2005

Workshop: Inter Industry Accounts, WP1

Mun Ho

KSG, Harvard University

Interpolation of IO Tables from benchmarks

-Necessary input

-simple RAS method

-minimizing deviations methods



Marcel Timmer’s June 23 2005 document:

Interindustry Accounts in EUKLEMS

Column sum of USE table, output in basic price, inputs in purchaser’s prices:

Or, inputs in basic prices:

Industry sum of Supply table, output in basic price:


Marcel Timmer’s June 23 2005 document:

Interindustry Accounts in EUKLEMS

Row sum of USE table, in purchaser’s price:

Commodity sum of Supply table, in purchaser’s price:

Nominal GDP is sum of value added or sum of final demand:


Ingredients for interpolation from benchmarks:

  • Benchmarks on the same definitions

  • Time series for industry output, or commodity output, or both; VY(j,t) VYC(i,t)

  • Time series for final demand, C,I,G,X,M

  • Any other time series, e.g. value added by industry VK(j),VL(j); energy input by industry;


2 time series data on industry output commodity output
2 Time series data on industry output, commodity output

2.1 If you have industry output, but not commodity, then first get it using an assumed Supply table:

VYC = [S] (VY+TV+T)

2.2 If you have both, then they must be consistent:

2.3 Relation of the different price concepts:


3 From the National Accounts (C,I,G) derive the time series of VCit , VIit,VGit, VEXit, VMit for as many different commodities as possible. This involves linking National a/c categories to IO categories via bridge tables.

4 From the National a/c derive the value added components by industry: LCjt, OSjt, TOjt.


Interpolating the use table
Interpolating the USE table

Denote the benchmark USE table for years 0 and T, and the time series for the column and row totals:

1) Initial guess, or target, of USE table for t:

perhaps including

2) Find USE(t) such that:


3 In the interpolation process we can allow everything to change, or, keep some items fixed.

E.g. keep value added and CIGXM fixed and only allow VXij to change.

4. Methods to estimate new matrix.

4.1 RAS

4.2 Minimize objective function


Method of minimizing some deviation function. change, or, keep some items fixed.

E.g. sum of squared deviations of shares.

e.g. where value added and final demand are assumed to be correct

Subject to:

where weights wij may be set according to additional information about quality of (i,j) data.


GAMS implementation of “min sum of squares” change, or, keep some items fixed.


Implementing “min sum of squares” by using first-order conditions (Wilcoxen 1988 appendix E3)

Lagrangian:

C(j) = column control total; R(i) = row control total

First order conditions:

which is a linear system in λ and μ and solved immediately by inverting a matrix (i.e. no iterations to optimize)


Method of rAs conditions (Wilcoxen 1988 appendix E3)

Iterate Aij, by alternately scaling the columns and rows to the column and row control totals.

Start with

Scale the columns, j:

Scale the rows, i:

Repeat until converged:


Implementing RAS using metadata and Stata conditions (Wilcoxen 1988 appendix E3)


SAS RAS metadata example. conditions (Wilcoxen 1988 appendix E3)

Want E(gender,age,educ,occupation,sector)

Have Etarget(gender,age,educ,occupation)


Implementing RAS directly (not using Metadata) conditions (Wilcoxen 1988 appendix E3)


Implementing RAS directly; continued conditions (Wilcoxen 1988 appendix E3)


Example of effects of incompatiable row and column controls conditions (Wilcoxen 1988 appendix E3)


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