Introduction to Regional Input-Output Model

Introduction to Regional
Input-Output Model
2007. 8. 21.
서울대학교 농경제사회학부
안동환

Introduction
Local Economic Impact
• Local industry changes
• Industry expansion, Industry contraction
• Local microeconomic changes
• Firm relocation, Firm expansion, Firm closure
• Large projects
• Construction projects
Regional multiplier analysis
• The impacts of industrial changes on a regional economy, through
an assessment of the linkages between firms and factor inputs.
• The regional trade patterns
• The regional industrial structure
• Approaches
• Economic Base Model
• Keynesian Multiplier
• Input-Output Model
• …

Economic base model
Total employment (T) = Basic (B) + non Basic (N)
• basic sector Industries whose markets are national or
global (export-base industry).
• non-basic sector Industries that sells almost of all their
output to local consumers.
The performance of non-basic sector is determined by
the performance of the local economy as a whole.
N = nT (n = the strength or sensitivity of the linkage between
the local economy, T and the locally oriented activities, N)
T = B + nT (T/B = 1/(1-n) : economic base multiplier)
Application: ΔT = [1/(1-n)]ΔB the increase in total
employment generated by an increase in export (basic
sector) employment.

Keynesian Regional Multiplier
Income = Aggregate Demand
Y = C (Consumption) + I (Investment) + G (Gov. Exp.)
+ X (Export) – M (Import)
• C=a+bY, M=c+dY
Y = a + b(1-t)Y + I + G + X – c – d(1-t)Y
Y = (a – c + I + G + X) / [1 – (b - d)(1-t)]
Keynesian multiplier k=1/[(1-(b-d)(1-t)]
• An exogenous increase in I of $1 will increase Y by k=1/[1-(bd)(1-t)].
• b-d : marginal propensity to consume locally produced good
Application:
ΔY = Δ(a –c + I + G + X)/[1- (b–d)(1-t)]

Macro Economics ?
Micro Economics ?
Structure of economy!!
Why Input-Output Analysis?
Industrial interdependence and interaction!!
• The IO model is centered on the idea of interindustry
transactions, that is industries use
the products of other industries to produce
their own products.
Quesnay, 1758; Walras, 1874; Leontief, 1936
(Nobel Prize in 1973).

Inter-industry Transactions
Outputs from one industry become inputs to
another.
• e.g. Automobile producers use steel, glass,
rubber, and plastic products to produce
automobiles.
• When you buy a car, you affect the demand for
glass, plastic, steel, etc.
• e.g. Policy increasing the demand for cars vs.
the demand for housing

Household and Industry
Households buy the output of
Consumption Spending
business: final demand or Y i
Households
Goods & Services
Labor
Businesses
Businesses
Wages & Salaries
Households sell labor & other inputs
to business as inputs to production
Businesses purchase from other
businesses to produce their own
goods / services: x ij (output of
industry i sold to industry j)

Transactions and National Accounts
Selling
sectors
Purchasing
sectors
Final demand (Y)
1 2 3 C I G
Z 1c
E
Total
output
1 Z 11
Z 12
Z 13
Z 1I
Z 1G
Z 1E
X 1
2 Z 21
Z 22
Z 23
Z 2c
Z 2I
Z 2G
Z 2E
X 2
C: Personal consumption
I: Investment
G: Government expenditure
E: Export
3 Z 31
Z 32
Z 33
Z 3c
Z 3I
Z 3G
Z 3E
X 3
Payment
sectors
Factor
inputs
(value
added)
L 1
L 2
L 3
L c
L I
L G
L E
C
K 1
K 2
K 3
K c
K I
K G
Imports M 1
M 2
M 3
M c
M I
M G
K E
M E
I
G
Total outlay X 1
X 2
X 3
C I G
E
E
Wage
Interest, land rent
Taxes
X 1 = Z 11 + Z 12 + … + Z 1n + Y 1
X 2 = Z 21 + Z 22 + … + Z 2n + Y 2
… … … … … …
X n = Z n1 + Z n2 + … + Z nn + Y n

Production technology, production
function
x = f(z) = Min {k 1 z 1 , k 2 z 2 , …, k n z n }
Leontief Technology
z 2j
Technical coefficient
• a ij = z ij / x j (i.e. x j = z ij / a jj )
• a ij : technical coefficient
• z ij : input flow from i to j
• x j : output of j
• z ij = a ij x j
x j
=3
x j
=2
x j
=1
z 1j
Leontief technology
x j = Min {z 1j /a 1j , z 2j /a 2j , …, z nj /a nj }
No factor substitution

Input-Output Model
X 1
= a 11
X 1
+ a 12
X 2
+ … + a 1n
X n
+ Y 1
X 2
= a 21
X 1
+ a 22
X 2
+ … + a 2n
X n
+ Y 2
… … … … … …
X n
= a n1
X 1
+ a n2
X 2
+ … + a nn
X n
+ Y n
X 1
= Z 11
+ Z 12
+ … + Z 1n
+ Y 1
X 2
= Z 21
+ Z 22
+ … + Z 2n
+ Y 2
… … … … …
…
X n
= Z n1
+ Z n2
+ … + Z nn
+ Y n
z ij
= a ij
x j
1-a 11
a 12 … a 1n X 1
Y 1
a 21
1- a 22
… a 2n X 2
Y 2
… … … … … = …
a n1
a n2
… 1-a nn X n
Y n
(I-A)X = Y

Input-Output Model
(I-A)X=Y or X = (I-A) -1 Y Input-Output Model
• X: total output vector
• Y: final demand vector
• Household
• Investment
• Government
• Export
• A: technical coefficient (a ij
) matrix
ΔX = (I-A) -1 ΔY How to use for impact analysis??
• ΔY: change in final demand
• ΔX: change in total output

Z ij
Purchases
Example
Making trade flow table (transaction table)
Sales X 1 X 2 X 3 Final
consumers
Total
Output
X 1 - - 70 30 100
X 2 20 - 80 100 200
X 3 20 80 - 200 300
Factor inputs 40 110 140 - 290
Imports 20 10 10 30 70
Total input 100 200 300 360
960

Making technical coefficients
Example
a ij = z ij / x j
Purchases
Sales X 1 X 2 X 3 Final consumers
X 1 - - 0.23 0.08
X 2 0.20 - 0.27 0.28
X 3 0.20 0.40 - 0.56
Factor inputs 0.40 0.55 0.47 -
Imports 0.20 0.50 0.03 0.08
Total input 1.00 1.00 1.00 1.00

Example
Increase in final demand in sector X3 : 1000
First round
• Sector X 1 : 0.23*1000 =230
• Sector X 2 : 0.27*1000 =270
• Sector X 3 :
Second round
• Sector X 1 :
• Sector X 2 : 230(X 1 )*0.2=46
• Sector X 3 : 230(X 1 )*0.2=46, 270(X 2 )*0.4=108
Third round
• Sector X1: 0.23*154(X 3 ) =35
• Sector X2: 0.27*154(X 3 ) =42, 0.4*46(X 2 )=18
• Sector X3:
Fourth round
• Sector X1:
• Sector X2: 0.2*35(X 1 ) =7
• Sector X3: 0.2*35(X 1 ) =7 , 0.4*60(X 2 )=24
Ripple effects….
X 1 X 2 X 3
X 1 - - 0.23
X 2 0.20 - 0.27
X 3 0.20 0.40 -

Example
dZ ij
Purchases
Sales X 1 X 2 X 3 Final
consumers
Total Output
X 1 - - 282 - 282
X 2 56 - 322 - 378
X 3 56 151 - 1000 1207
Factor inputs 113 207 563 -
Imports 56 19 40 -
Total input 282 378 1207 1000 1867
Multiplier = 1867/1000 = 1.867

Economic impacts
Input-Output Analysis
• direct impact change in final demand
• indirect impact change required for direct
impact
• induced impact change result from
household expenditure change
Open vs. Closed
• Open : household exogenous Type I
• Closed : household endogenous Type II

A : n X n
Open (Type I) Model
Total impact = Direct impact + Indirect
impact
a 11 a 12 … a 1n
A = a 21 a 22 … a 2n
… … … …
a n1
a n2 … a nn

Closed (Type II) Model
A C : (n+1) X (n+1)
a 11 a 12 … a 1n
A C = a 21 a 22 … a 2n
a 1,n+1
a 2,n+1
… … … … …
a n1
a n+1,1
a n2 … a nn
a n+2,2 … a n+1,n
a n,n+1
a 1,n+1
= A H C
H R
h

Closed (Type II) Model
H R : household input coefficients to the original n
sectors a n+1,j = Z n+1,j / X j
• Z n+1,j
: j sector’s purchases of labor
• a n+1,j
: the value of household services (labor)
used per dollar’s worth of j’s output
H C : consumption coefficients from the original n
sectors a i,n+1 = Z i,n+1 / X i
• Z i,n+1
: the value of sector i’s sales to
households
Total impact = Direct impact + Indirect impact +
Induced impact

Limitations of Input-Output Model
Requirement for regional data : transactions
Stability of input coefficients
Constant returns to scale
Constant multipliers
No price effects

Regional Input-Output Model
National Model vs. Regional Model
Single-region vs. Multi-region Model
Data and Steps

Regional Coefficient
National technical coefficient A is available.
For regional model, we need a regional
matrix showing inputs from firms in the
region to production in that region.
• Regional technical coefficient A R
Although the technology in region R is the
same as in the nation, national technical
coefficient A must be modified so as to
indicate only the inputs of locally produced
goods in local production.

Single region vs. Many region model
Single region model
• regional technical coefficients A R
• regional supply percentages (or regional
purchase coefficients)
Many region model
• Interregional model
• Multiregional model

Single region model
1. Survey interregional trade Z ij
RR
:
Regional input coefficients A RR
2. Using national technical coefficients A:
Regional technical coefficients A R
= P (Regional supply percentages or regional
purchase coefficients; diagonalized) * A

a
RR
ij = z
RR
ij / X
R
j
a
LL
ij = z
LL
ij / X
L
j
• ij from i sector to j sector
• RR from R region to R region
• LL from L region to L region
Regional Input Coefficient
A RR : regional input coefficient for R
A LL : regional input coefficient for L
∆X R = (I-A RR ) -1 ∆Y R
∆X L = (I-A LL ) -1 ∆Y L
A
LL
=
⎡a
⎢
⎢a
⎢
⎣a
LL
11
LL
21
LL
31
a
a
a
LL
12
LL
22
LL
32
a
a
a
LL
13
LL
23
LL
33
⎤
⎥ ⎥⎥ ⎦

Regional supply percentages
the percentage of the total required outputs
from each sector that could be expected to
originate within the region (or RPC: Regional
Purchase Coefficient)
p jR = (X jR –E jR ) / (X jR –E jR + M jR )
• (X jR
–E jR
) : locally produced amount of good j
available in region R
• (X jR
–E jR
+ M jR
) : total amount of good j
available in region R, either produced locally
or imported

Regional Technical Coefficient
a ijR = z ij·R
/ X j
R
• ij from i sector to j sector
• ·R from all regions to R region
A R = PA X R = (I-PA) -1 Y R
• P: diagonal matrix created from p j
R
∆X R = (I-PA) -1 ∆Y R

1. Interregional I-O model (IRIO)
Many Region Model
• Survey interregional trade Z ij
RR
Regional
input coefficients A RR
2. Multiregional I-O model (MRIO)
• Regional technical coefficient A R
• Interregional trade coefficient C i
RL
• LQ a ij RR = a ij N *LQ i R if LQ 1
• RAS for updating A R
• Non-survey technique

Interregional Model
Interregional trade, flows of goods
region L R
region sector 1 2 3 1 2
1 Z 11
LL
Z 12
LL
Z 13
LL
Z 11
LR
Z 12
LR
L
2 Z 21
LL
Z 22
LL
Z 23
LL
Z 21
LR
Z 22
LR
3 Z 31
LL
Z 32
LL
Z 33
LL
Z 31
LL
Z 32
LL
R
RL
1 Z 11
RL
2 Z 21
RL
Z 12
RL
Z 22
RL
Z 13
RL
Z 23
RR
Z 11
RR
Z 21
RR
Z 12
RR
Z 22

Regional input coefficient
• a ij
LL
= z ij
LL
/ X j
L
• a ij
LR
= z ij
LR
/ X j
R
• a ij
RL
= z ij
RL
/ X j
L
• a ij
RR
= z ij
RR
/ X j
R
• ij from i sector to j sector
• LR from L region to R region
A
LL
⎡a
⎢
= ⎢a
⎢
⎣
a
⎡a
⎢
= ⎢a
⎢
⎣
LL
11
LL
21
LL
31
a
a
a
a
LL
12
LL
22
LL
32
Interregional Model
a
a
a
a
LL
13
LL
23
LL
33
RL
11
RL
12
RL
13
RL RL RL RL
A
21
a22
a23
⎤
⎥
⎥
⎥
⎦
⎤
⎥
⎥
⎥
⎦
Z
A
⎡Z
LL
Z
LR⎤
= ⎢ ⎥
RL RR
⎢⎣
Z Z ⎥⎦
LR
⎡a
⎢
= ⎢a
⎢
⎣a
⎡a
⎢
= ⎢a
⎢
⎣
LR
11
LR
21
LR
31
a
a
a
a
LR
12
LR
22
LR
32
RR RR
11 12
RR RR RR
A
21
a22
⎤
⎥
⎥
⎥
⎦
⎤
⎥
⎥
⎥
⎦

Interregional Model
L
LR
LR
LL
LL
LL
L
Y
Z
Z
Z
Z
Z
X 1
12
11
13
12
11
1 +
+
+
+
+
=
L
R
LR
R
LR
L
LL
L
LL
L
LL
L
Y
X
a
X
a
X
a
X
a
X
a
X 1
2
12
1
11
3
13
1
12
1
11
1 2 +
+
+
+
+
=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎥ −
⎦
⎤
⎢
⎣
⎡
R
L
R
L
RR
RL
LR
LL
Y
Y
X
X
A
A
A
A
I
I
0
0

Interregional trade coefficient
C i
RL
= z i
RL
/ T i
L
• T iL
: total shipment of i into L from all of the
regions
• C i
RL
: the proportion of all of good i used in L
that comes from R

Multiregional Model
⎥
⎦
⎤
⎢
⎣
⎡
= L
L
L
L
L
a
a
a
a
A
22
21
12
11
⎥
⎦
⎤
⎢
⎣
⎡
= R
R
R
R
R
a
a
a
a
A
22
21
12
11
⎥
⎦
⎤
⎢
⎣
⎡
= LR
LR
LR
c
c
C
2
1
0
0
⎥
⎦
⎤
⎢
⎣
⎡
= RR
RR
RR
c
c
C
2
1
0
0
⎥
⎦
⎤
⎢
⎣
⎡
= LL
LL
LL
c
c
C
2
1
0
0
⎥
⎦
⎤
⎢
⎣
⎡
= RL
RL
RL
c
c
C
2
1
0
0
⎥
⎦
⎤
⎢
⎣
⎡
= R
L
A
A
A
0
0
⎥
⎦
⎤
⎢
⎣
⎡
= RR
RL
LR
LL
C
C
C
C
C
⎥
⎦
⎤
⎢
⎣
⎡
= R
L
X
X
X
⎥ ⎦ ⎤
⎢
⎣
⎡
= R
L
Y
Y
Y

Multiregional Model
R
LR
L
LL
R
R
LR
L
L
LL
Y
C
Y
C
X
A
C
X
A
C
I +
=
−
− )
(
R
RR
L
RL
R
R
RR
L
L
RL
Y
C
Y
C
X
A
C
I
X
A
C +
=
−
+
− )
(
R
LR
L
LL
R
R
LR
L
L
LL
L
Y
C
Y
C
X
A
C
X
A
C
X +
+
+
=
R
RR
L
RL
R
R
RR
L
L
RL
R
Y
C
Y
C
X
A
C
X
A
C
X +
+
+
=
CY
X
CA
I =
− )
(
CY
CA
I
X
1
)
(
−
−
=