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11.481J / 1.284J / ESD.192J Analyzing and Accounting for Regional Economic Growth
Spring 2009
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Regional Input-Output Models
Xin Li
Reference: Karen R. Polenske. 1995. Leontief’s Spatial Economic
Analyses, Structural Change and Economic Dynamics 6: 309-318
Assumptions
• Constant returns to scale
• Homogeneous products with no joint
production
• Constant direct input (technology)
coefficient
• A demand-driven model
National input-output table
Purchasing industries
Gross National Income
Gross National Product
Producing industries
VA
m X m
FD
FD= final demands, including
• Personal consumption expenditures
• Gross private capital formation
• Net inventory change
• Net foreign exports
• Federal, state and local gov’t purchase
VA= Value added, including
• Wages and salaries
• Rent
• Depreciation
• Taxes etc.
m = number of industries
Balanced Regional Input-Output Tables
Purchasing industries
Import
Export from
to other other
regions regions
(+)
(-)
FD
Producing industries
Sum of each row =
sum of each column
mXm
mx1
mx1
Assumption:
Technology coefficients
differ by region
VA
Region 1
m = number of industries
Unbalanced Regional input-output Table
Purchasing industries
FD
Producing industries
• Sum of each row: total consumption
only by purchasers within the region.
mXm
• Sum of each column: total input
requirements of each industry,
regardless of the location of production.
• Sum of each row ≠ sum of each column
VA
m = number of industries
Region 1
Regional Input-Output Tables
‘Purchasing industries FD
VA
Producing industries
Producing industries
mxm
‘Purchasing industries FD
m x m
Region n
VA
Region 1
• For a regional table, the sums of
corresponding rows and columns will not
necessarily be equal.
• The difference is attributable to
interregional trade.
m = number of industries
n = number of regions
‘Purchasing industries
Producing industries
Region 2
VA
VA
Nation
FD
Region 1
1
Region 1
1
Region 2
m FD 1
Region n
m FD
1
Total
m FD 1
m FD
mxm
mxm
mxm
mxm
mxm
mxm
mxm
mxm
mxm
mxm
mxm
mxm
mxm
mxm
mxm
National
flow table
Total
output
Interregional Input-Output table
m
VA
1
Region 2
m
VA
1
m
VA
1
Total
m
VA
Total
input
Regional
IO tables
GNP
Region n
GNI
Figure by MIT OpenCourseWare, based on Polenske (1963).
Multiregional input-output tables—
trade matrices
‘Receiving region
Industry 1
Shipping region
Shipping region
n x n
‘Receiving region
n x n
Industry m
Receiving region
Industry 2
• Sum of each row: For a given industry,
total outflows from a region.
• Sum of each column: for a given
industry, total inflows into a region.
• Sum of each row ≠ sum of each column
• The difference is net foreign export
Shipping region
Assumption: Technology coefficients are
the same for all regions
m = number of industries
n = number of regions
n x n
Total
Commodity Flow Table
Receiving region
Shipping region
nXn
Foreign Foreign
export import Total
output
(+)
(-)
nx1
nx1
Regional Demand
Industry 1
n = number of regions
Industry 1
1
Industry 1
1
Industry 2
m FD 1
m FD
Industry m
1
Total
m FD 1
m FD
nxn
nxn
nxn
nxn
nxn
nxn
nxn
nxn
nxn
nxn
nxn
nxn
nxn
nxn
nxn
National
flow table
Total
output
Multiregional Input-Output table
m
VA
1
Industry 2
m
VA
1
m
VA
1
Total
m
VA
Total
input
Multiregional
IO tables
GNP
Industry m
GNI
Figure by MIT OpenCourseWare, based on Polenske (1963).