1. The Input-Output table of Saudi Arabia
Dr. Imtithal AL-Thumairi

2. purpose provide an overview on
Data sources
Methodology
Used/ will be used for modeling Saudi economic using I/O table.

3. The Input-Output table of Saudi Arabia
Background
Schematic Diagram for the I/O table for SA
I/O partial matrices and equations
The data used for the updating procedure
The main data sources
The RAS approach to I/O updating
RAS 1997
I/O table for 1997: comments
Updating and estimating a new I-O table/ SAM for Saudi Arabia 2002
A Cross- Entropy Model
Types of information
RAS & CE

4. Background
Saudi’s first I/O table published by the ministry of planning in 1976 which used as a ten by ten matrix by (Aljiffory, 1983).
Dean Schreiner updated the table of 1976 to the year of 1981 and extended it into an eleven by eleven matrix, this table was used by (Tawi, 1989).
Imtithal Althumairi updated the table of 1981 to the year of The table used to find out the economic impact of the accession of the kingdom of Saudi Arabia to the World Trade Organization (Althumairi,2000).
The updated table of 1997 by (Althumairi,2000) has been used by later academic researchers such as ( Albqami, 2001).

5. Schematic Diagram for the Input-Output table for Saudi Arabia (1997)
1 2 …j…n
Total Intermediate Demand
C G I CHS E I
Total final demand
Total output 1 2 . i n
Interindustry Transactions +
Structure of Final Demand =
Total
Receipts
Total Intermediate cost
Labor
Capital
Indirect Tax
Value added
Other final demand
Total value added
Total cost of production
(total input)
Gross output

6. Input-output partial matrices and equations

7. Transaction matrix The most important part of the I/O table
Square matrix, Rows=Columns
Rows
Final demand
Intermediate demand
Columns
Intermediate requirements
Primary inputs or requirements
Wi=Σxij…(1)
Uj= Σxij…(2)
Wi: intermediate demand (i)
Uj: intermediate requirements(j)
Xij:value of goods and services of sector (i) used by sector (j)

8. Final demand matrix Final consumption Private consumption Cp
Government consumption Cg
Final demand for capital accumulation
Final demand for private capital accumulation Ip
Change in stocks Ch
Final demand for government capital formation Ig
Final demand for Exports E
Fi= Xi- Σxij…(3)
Fi= Cip + Cig +Chi +Iip +Iig +Ei …(4)

9. Value Added Matrix
Total value added = Total production – intermediate inputs
Vi = Xj – Uj …(5)
Taking imports into account:
Vi = Xj – (Uj + Mj) …(6)
Vi = Mj + Wj + Pj + Tj – Sj …(7)
Wj: wages
Tj: indirect taxes
Sj: subsidies

10. Leontife I/O Model Gross output = intermediate demand + final demand
Xi = ΣX ij + Fi …(8)
Gross output = intermediate requirements + primary requirements
Xj = Σxij + Vj …(9)
From (8) & (9)
Xi = Xj Total Row = Total Column
∑Vj = ∑Fi
X = AX + F …(10)
A: technical coefficients matrix
A = aij aij = Xij/ Xj
X – AX = F
( I – A ) X = F
X = ( I – A ) –1 F … (11)
( I – A ) –1 : Leontief Inverse Total Technical Coefficients Matrix

11. The data used for the updating procedure
I/O table 1981
National Accounts Aggregates(1997)
Private consumption
Government consumption
Gross Fixed capital formation
Stock changes
Exports
Imports
GDP at market prices
Sectoral value added and Intermediate consumption

12. The main data sources
Saudi Arabia Monetary Agency (SAMA). Annual report
Ministry of Finance and National Economy. National Accounts of Saudi Arabia
Ministry of planning. Development plans and achievements of the development plans.
Other sources

13. The RAS approach to I/O updating
Updating an I/O matrix when we have new information on the row & column sums, but do not have new information on the input-output flows.
The problem is to find a new I/O coefficient matrix A*, that is in some sense ( close) to an existing coefficient matrix A`, but yield a I/O transactions matrix with the new row and column sums.
That is, RAS approach to solving this problem is to generate a new matrix A* from the old matrix A` by means of (biproportional) row and column operations: aij* = ri aij`sj
Or, in matrix terms:
A* = r^ A` s^
Where the hat indicates a diagonal matrix of elements ri and sj

14. RAS 1997
X1997=(I- A1981) -1. F1997 …(1) X1997: Gross Output 1997 (I-A1981) –1: Leonetif Inverse 1981 F1997: Final Demand Column X1997 – F1997 = S1997 …(2) X1997 – V1997 = R1997 …(3) S1997 : Intermediate Demand Column 1997 R1997 : Intermediate requirement Row 1997 V1997 : Sectoral Value Added 1997 By (2) and (3): R A1981. S1997 = A1997 …(4)

15. I/O table for 1997
A look at the coefficient matrix and its inverse reveals the lack of strong linkage except in few cases.
The most important sector, of course, is Mining and Quarrying, the bulk of which is exported and serves as the engine of growth of the economy as a whole.
48%linkage with Manufacturing Sector
Manufacturing Sector has strong linkage with most of sectors.
19.9%with Agriculture Sector
36%with Construction Sector
15%with Trade and Services Sectors
14%with Electricity, Gas and Water Sector
13% with Transport Sector
Apart from these two, the rest of the economy, linkage is quite poor.
Zero. (Column 1, Row 9)
Agricultural Sector not buying any Services, or Services Sector not selling to Agricultural. Not realistic.
This depends on the procedure of building I/O by Planning Ministry.
INDUSTRY. INDUSTRY
COMMODITY. COMMODITY
INDUSTRY. COMMODITY which in this case can be justify.

16. Updating and Estimating a new I-O table/ SAM for Saudi Arabia 2002

17. Current work
Updating of the I/O table with the most recent national accounts (2002)
Building of the Social Accounting Matrix (SAM)

18. The updating and estimating methods
A Cross-Entropy Model for Matrix Balancing
When the information for 2002 is imposed on the 1997 I/O table, all sector accounts are out of balance( as would be expected).
An estimation approach is needed to generate a balanced I/O table
The underlying philosophy of entropy estimation is to use all, and only the information available for the problem at hand.
It is technique for solving undetermined estimation problems, that has been applied to the estimation of I/O tables and SAM
Our I/O table balancing problem is undetermined because the number of cells in the table( the unknowns which are to be estimated) far exceed the number of constraints that can be imposed.

19. Types of information
Priors. I/O table from an earlier year provides information about the new coefficients. The approach is to estimate a new set of coefficients (close) to the prior, using new information to update the priors.
Moment constraints. The most common kind of information to have is data on some or all of the row and column sums of the new I/O. while the RAS procedure is based on knowing all row and column sums, it is only one of several possible sources of information in CE estimation.
Economic aggregates. In addition to row and column sums, one often has additional knowledge about the new I-O/SAM. For example, aggregate national accounts data may be available for various macro aggregates such as value added, consumption, investment, government, exports, and imports. There also may be information about some of the SAM accounts, such as government receipts and expenditures. This information can be summarized as additional linear adding-up constraints on various elements of the I-O/SAM.
Inequality constraints. While one may not have exact knowledge about values for various aggregates, including row and column sums, it may be possible to put bounds on some of these aggregates.
Zeros. In the RAS method, the row and column operations guarantee that the updated I-O/SAM will contain zeros wherever the original SAM had zeros, and non-zero elements otherwise. Such constraints are also easily incorporated in the CE approach by constraining I-O/SAM entries to be zero in the estimation problem. However, it is also straightforward in the CE approach to allow zero elements in the prior to become non-zero in the estimated I-O/SAM and vice versa.

20. Updating: RAS and CE
The CE approach provides a flexible and powerful method for estimating I-O/ SAM when dealing with inconsistent data. Inconsistent can arise from
Measurement errors
Incompatible data sources
Or lack of data
The method represents a considerable extension and generalization of the standard RAS method, which assumes that one start from a consistent prior I-O/SAM and has knowledge only about new row and column totals.
The CE framework allows a wide range of prior information to be used efficiently in estimation.
Drawing on information theory, CE approach is efficient in that it uses all available information, but only that information-no assumed information is injected into the estimation procedure.
The prior information can be in a variety of forms, including linear and nonlinear inequalities, errors in equations, and measurement error.