Download L11-IO-table

Lecture 11: Input-output table:
making of and analysis with
Advanced Macroeconomics
M.Sc. Programme in Environmental and
Natural Resource Economics
1/2007
Content
• Basic concepts– Rationale
– Uses
•
•
•
•
Mathematical structure
Construction
Link with national income account
Analysis with I-O table
consumption
production
income
The circular flow of income-in an
economy
Basic concepts
• Rationale
– Something to link up all the elemetns of the
economy-production/income/expenditure
• Uses- something to help analyse scenarios
– Predicting the future
– Predicting impacts of changes in exogenous
variables-
Mathematical structure
• A matrix format-row and column
• Row for disposal, sale from i to joutput
• Column for use, purchase by j from i
input
• Matrix algebra reduces notation
• Balance between row and column totals,
hence account
Mathematical structure(2)
3 sectors-1=agriculture, 2=manufacturing, 3=service
Each selling and buying from each other
Also some final consumption of output
Production requires both primary and intermediate inputs
So, how does the balance look?
sector
Ag
Man. Serv.
Total
Final
demand
Ag.
X11
X12 X13
f1
X1
Manuf.
X21
X22 X23
f2
X2
Serv.
X31
X32 X33
f3
X3
Labour
L1
L2
L3
total
X1
X2
X3
Can you write the equations out? In matrix form?
Mathematical structure(3)
The equation(s) system is:
By row:
X1 = X11+X12+X13 +f1
X2 = X21 + X22+X23 +f2
X3 = X31 + X32 +X33 +f3
By column:
Can you try?
What about the matrix form?
Mathematical structure(4)
The matrix form needs some more symbols.
Let aij = Xij/Xj
Then, rewrite the equation by row as:
Xi = Saij*XJ + fi, for i =1,2,3
In matrix form, it is
X = AX + F
See how much simpler it is!!!
Mathematical structure (5)
Then what?
Solve the equation, at least simplify—
(I-A)X = F
Then,
X = (I-A) –1 F
So, if we know F and A,
we can also know X
Link with national accounts
• National accounts: Production-income-expenditures
• Where are they in the I-O Table?
• Production-gross output (IO) vs. value added (NA)-so, has
to deduct intermediate inputs from gross output
• Income-as share of primary inputs (IO) and functional
incomes (NA)
• Expenditures –same in IO and NA
• Advantage of IO – having all three at the same time
Construction
•
•
•
•
•
Data requirement
Sector classification
Control totals
Flows between sectors
Balancing act between row and column
totals
• Updating with RAS-this is for the advanced
student only!!
Examples:
Sector classification: in 1998 IO table, 180x180 sectors,
but can be reduced. See Convertor table
Agriculture:from 001 to
16 x 16 Sectors
001Agriculture (001-029)
26 x 26 Sectors
001Crops (001-017, 024)
58 x 58 Sectors
001Paddy (001)
002Maize (002)
003Cassava (004)
004Beans and Nuts (006)
005Vegetables and Fruits (007-008)
006Sugarcane (009)
007Rubber (Latex) (016)
008Other Crops (003, 005, 010-015,017, 024)
Example:
Row/column/cell entry at different prices
001 001
9678269
9678269
0
0
2564
337
024 001
10712840
10712840
0
0
0
0
025 001
5280
5280
1264
0
240
0
027 001
10230
10230
1618
1117
341
0
074 001
67650
67650
1600
246
610
0
078 001
12540
12540
976
1015
196
0
079 001
1155
1155
97
157
21
0
085 001
17410618
17410618
2532964
1597516
1239893
10931814
Analysis
• What kind of questions to ask?
• Eg. Multiplier effect of increased
autonomous expenditure
• Mathematically,
DX = (I-A) –1 DF
• Eg. Effect of price changes
• Analysis by column!!
Application: Tourism
• What is the effect of SARS on tourism and
GDP?
• What do you need to know in order to
analyse this question?
• Given Tourism IOtable
Coral reef TOURISM
• Tourism IO table
• Change in visitor numberfall in tourist
expenditure
• Multiplier effect on GDP
• Use the tables provided in file
TourismIO.xls