1. Input-output tables Robin Lynch
National Accounts in Practice – Advanced course
Luxembourg, 2-11 October 2018
THE CONTRACTOR IS ACTING UNDER A FRAMEWORK CONTRACT CONCLUDED WITH THE COMMISSION

2. ESA 2010 Input-output What are input-output tables?
They show the flow of goods and services in the economy, the relationship between producers and consumers, and the interdependence of businesses.
Their form is

3. ESA 2010 Input-output Use by Production Use by Final Demand Total
Products W f q
Primary inputs y

4. ESA 2010 Input-output
This simple picture shows no difference between business output and products – no “off-diagonal” production in the make matrix
No distribution margins or taxes
No foreign trade

5. ESA 2010 Input-output
Final demand is final consumption of households and government, and capital formation
Primary inputs are the factor incomes generated by the production process – compensation of employment, and operating surplus

6. ESA 2010 Input-output
In the diagram, W is a matrix showing the purchases by business (in the columns) of the sales of products produced (in the rows)
A typical entry is wij – the sales of the product in row i purchased by the business in column j
f is the final demand vector
q is the vector of total products produced
y is the row vector of primary inputs

7. ESA 2010 Input-output
We can describe the output of each business as the sales to other businesses (intermediate demand) and sales to final demand
q1 = w11 + w12 + w w1n + f1
q2 = w21 + w22 + w w2n + f2
qn = wn1 + wn2 + wn wnn + fn

8. ESA 2010 Input-output
These equations express the input-output relations in terms of flows
If we express the input structure of the use matrix in coefficient form, so that a11 represents the ratio of the sale of q1 to activity 1 as a proportion of the total inputs to activity 1 ( which in our simple example where industry output = products output), is equal to the total product sales of activity 1), we get

9. ESA 2010 Input-output
q1 = a11.q1 + a12.q2 +a13.q3 +a1n.qn + f1 q2 = a21.q1 + a22.q2 +a23.q3 +a2n.qn + f2 qn = an1.q1 + an2.q2 +an3.q3 +ann.qn + f1 In matrix notation, q = A . q + f

10. ESA 2010 Input-output
The equation represents domestic output (q) being made up of a linear combination of a set of demands for this output from other industries and final demand The demand from other industries is represented as a constant fraction of the output of each purchasing industry – represented by the coefficients aij
Rearranging the equation gives

11. ESA 2010 Input-output q = A . q + f q (I – A) = f Q = ( I – A )-1 . f
where ( I – A )-1 is known as the Leontief inverse

12. ESA 2010 Input-output
What are the benefits and drawbacks of using this relationship in economic analysis?

13. ESA 2010 Input-output
Benefit – we can examine the effect of changes in final demand on industry outputs, and the relative changes in value added amongst industries
Warning – input-output analysis in its original simple form is becoming less fashionable - see A Review of Input-Output Analysis Carl F. Christ, BEA 1955, and comments by Milton Friedman

14. ESA 2010 Input-output Drawbacks
Industries and products are not homogeneous and different technical production functions may exist within a NACE 4 digit activity heading (example of ropes)
The simple model assumes linear responses to demand change, and no substitution in the face of price change

15. ESA 2010 Input-output ESA 2010 paragraph 9.19 says
I-O tables enable analysis of second order and indirect effects of changes in e.g. labour costs, energy prices.

16. ESA 2010 Input-output
In order to examine the effect of domestic policy change on supply and demand, using Leontief inverse techniques, it is necessary to separate the use of imports from domestic supply of products
This can be achieved using commodity flow analysis of imported products, assigning the products to users through their codes and description in the international trade data

17. ESA 2010 Input-output
In practice, the make matrix shows that production of characteristic products is not identical in value with industrial production of the products
For example, own account construction will supply more “structures” than accounted for by the construction industry
So industry output (g) is less than product output (q)

18. ESA 2010 Input-output
This implies that the fundamental relation in the supply-use framework is not expressed in terms of product output q, but also uses the measure of industry output g in the equation
q = B . g + f
In order to solve this equation, we must transform either q into g, or g into q

19. ESA 2010 Input-output
It is possible to use the structure of the Make matrix together with simple assumptions about the nature of the relationship between q and g, to generate a symmetric form of the equation, either in q or g.

20. ESA 2010 Input-output The two assumptions
The commodity technology assumes that a product has the same production function no matter which industry produces it
The industry technology assumption assumes that all products produced by an industry have the same production function

21. ESA 2010 Input-output
Either assumption can apply depending on the industry and product, and so it also possible to use a hybrid assumption, combining the two assumptions depending on the industry / product transformation
Chapter 11 of the Eurostat Manual on Supply, Use and input-output tables gives more detail

22. ESA 2010 Input-output
Using the commodity technology assumption can cause negative entries in the symmetric tables
The industry technology does not
Given the inherent errors in the data, it is generally accepted that the industry technology can be used on its own avoiding the negative entry issue, and without significant loss of accuracy