1. EUKLEMS 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

2. EUKLEMS UK 1995. Use table in purchasers prices

3. EUKLEMS Marcel Timmers June 23 2005 document: Interindustry Accounts in EUKLEMS Column sum of USE table, output in basic price, inputs in purchasers prices: Industry sum of Supply table, output in basic price: Or, inputs in basic prices:

4. EUKLEMS Marcel Timmers June 23 2005 document: Interindustry Accounts in EUKLEMS Row sum of USE table, in purchasers price: Commodity sum of Supply table, in purchasers price: Nominal GDP is sum of value added or sum of final demand:

5. EUKLEMS

7. Ingredients for interpolation from benchmarks: 1.Benchmarks on the same definitions 2.Time series for industry output, or commodity output, or both; VY(j,t) VY C (i,t) 3.Time series for final demand, C,I,G,X,M 4.Any other time series, e.g. value added by industry VK(j),VL(j); energy input by industry;

8. EUKLEMS 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: VY C = [S] (VY+TV+T) 2.2 If you have both, then they must be consistent: 2.3 Relation of the different price concepts:

9. EUKLEMS 3 From the National Accounts (C,I,G) derive the time series of VC it, VI it, VG it, VEX it, VM it 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: LC jt, OS jt, T O jt.

10. EUKLEMS

11. 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:

12. EUKLEMS 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 VX ij to change. 4. Methods to estimate new matrix. 4.1 RAS 4.2 Minimize objective function

13. EUKLEMS Method of minimizing some deviation function. 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 w ij may be set according to additional information about quality of (i,j) data.

14. EUKLEMS GAMS implementation of min sum of squares

15. EUKLEMS Implementing min sum of squares by using first- order conditions (Wilcoxen 1988 appendix E3) 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) Lagrangian:

16. EUKLEMS Method of rAs Iterate A ij, 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:

17. EUKLEMS Implementing RAS using metadata and Stata

18. EUKLEMS SAS RAS metadata example. Want E(gender,age,educ,occupation,sector) Have Etarget(gender,age,educ,occupation)

19. EUKLEMS Implementing RAS directly (not using Metadata)

20. EUKLEMS Implementing RAS directly; continued

21. EUKLEMS Example of effects of incompatiable row and column controls