Introduction to Regional Input-Output Model

2007. 8. 21.

서울대학교 농경제사회학부

안 동 환

Introduction

Local Economic ImpactLocal industry changes

• Industry expansion, Industry contractionLocal microeconomic changes

• Firm relocation, Firm expansion, Firm closureLarge projects

• Construction projectsRegional multiplier analysis

The impacts of industrial changes on a regional economy, throughan 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• …

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.

Economic base model

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-(b-d)(1-t)].b-d : marginal propensity to consume locally produced good

Application: ΔY = Δ(a –c + I + G + X)/[1- (b–d)(1-t)]

Keynesian Regional Multiplier

Why Input-Output Analysis?

Macro Economics ?Micro Economics ?Structure of economy!!Industrial interdependence and interaction!!

The IO model is centered on the idea of inter-industry 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

Wages & Salaries

Households buy the output of business: final demand or Yi

BusinessesHouseholdsGoods & Services

Consumption Spending

LaborBusinesses

Businesses purchase from other businesses to produce their own goods / services: xij (output of industry i sold to industry j)

Households sell labor & other inputs to business as inputs to production

Household and Industry

Purchasing sectors

Final demand (Y)

C E

Total output

Z1c Z1E

Z2E

Selling sectors

Payment sectors

Z3E

L1 L2 L3 Lc LI LG LE CFactor inputs(value added)

KE

ME

E

Z2c

X1

X2

X3

I

G

E

Z3c

Kc

Mc

C

1 2 3 I G

1 Z11 Z12 Z13 Z1I Z1G

2 Z21 Z22 Z23 Z2I Z2G

3 Z31 Z32 Z33 Z3I Z3G

K1 K2 K3 KI KG

Imports M1 M2 M3 MI MG

Total outlay X1 X2 X3 I G

Transactions and National Accounts

X1 = Z11 + Z12 + … + Z1n + Y1X2 = Z21 + Z22 + … + Z2n + Y2… … … … … …

Xn = Zn1 + Zn2 + … + Znn + Yn

C: Personal consumption

I: Investment

G: Government expenditure

E: Export

Wage

Interest, land rent

Taxes

Production technology, production functionx = f(z) = Min {k1z1, k2z2, …, knzn}

Technical coefficientaij = zij / xj (i.e. xj = zij / ajj )

• aij : technical coefficient• zij : input flow from i to j• xj : output of j

zij = aij xj

Leontief technologyxj = Min {z1j/a1j, z2j/a2j, …, znj/anj}

No factor substitution

z2j

z1j

xj =1

xj =2

xj =3

Leontief Technology

X1 = a11X1 + a12X2 + … + a1nXn + Y1

X2 = a21X1 + a22X2 + … + a2nXn + Y2

… … … … … …Xn = an1X1 + an2X2 + … + annXn + Yn

1-a11 a12 … a1n X1 Y1

a21 1- a22 … a2n X2 Y2

… … … … … = …an1 an2 … 1-ann Xn Yn

(I-A)X = Y

Input-Output Model

X1 = Z11 + Z12 + … + Z1n + Y1X2 = Z21 + Z22 + … + Z2n + Y2

… … … … ……Xn = Zn1 + Zn2 + … + Znn + Yn

zij = aij xj

(I-A)X=Y or X = (I-A)-1 Y Input-Output Model

X: total output vectorY: final demand vector

• Household• Investment• Government• Export

A: technical coefficient (aij) matrixΔX = (I-A)-1ΔY How to use for impact analysis??

ΔY: change in final demandΔX: change in total output

Input-Output Model

Zij Purchases

Sales X1 X2 X3 Final consumers

Total Output

X1 - - 70 30 100X2 20 - 80 100 200X3 20 80 - 200 300Factor inputs 40 110 140 - 290

Imports 20 10 10 30 70

Total input 100 200 300 360 960

Making trade flow table (transaction table)

Example

aij = zij / xj Purchases

Sales X1 X2 X3 Final consumers

X1 - - 0.23 0.08

X2 0.20 - 0.27 0.28

X3 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

Making technical coefficients

Example

Example

Increase in final demand in sector X3 : 1000First round

Sector X1: 0.23*1000 =230 Sector X2: 0.27*1000 =270Sector X3:

Second roundSector X1: Sector X2: 230(X1)*0.2=46Sector X3: 230(X1)*0.2=46, 270(X2)*0.4=108

Third roundSector X1: 0.23*154(X3) =35Sector X2: 0.27*154(X3) =42, 0.4*46(X2)=18Sector X3:

Fourth roundSector X1:Sector X2: 0.2*35(X1) =7Sector X3: 0.2*35(X1) =7 , 0.4*60(X2)=24

Ripple effects….

X1 X2 X3

X1 - - 0.23

X2 0.20 - 0.27

X3 0.20 0.40 -

dZij Purchases

Sales X1 X2 X3 Final consumers

Total Output

X1 - - 282 - 282

X2 56 - 322 - 378

X3 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

Example

Input-Output Analysis

Economic impactsdirect impact change in final demandindirect impact change required for direct impactinduced impact change result from household expenditure change

Open vs. Closed Open : household exogenous Type IClosed : household endogenous Type II

Open (Type I) Model

A : n X nTotal impact = Direct impact + Indirect impact

aa1111 aa1212 …… aa1n1n

A = aA = a2121 aa2222 …… aa2n2n

…… …… …… ……aan1n1 aan2n2 …… aannnn

Closed (Type II) Model

AC : (n+1) X (n+1)

aa1111 aa1212 …… aa1n1n aa1,n+11,n+1

AAC = a= a2121 aa2222 …… aa2n2n aa2,n+12,n+1

…… …… …… …… ……aan1n1 aan2n2 …… aannnn aan,n+1n,n+1

aan+1,1n+1,1 aan+2,2n+2,2 …… aan+1,nn+1,n aa1,n+11,n+1

= A HC

HR h

Closed (Type II) Model

HR : household input coefficients to the original n sectors an+1,j = Zn+1,j / Xj

Zn+1,j : j sector’s purchases of labor an+1,j : the value of household services (labor) used per dollar’s worth of j’s output

HC : consumption coefficients from the original n sectors ai,n+1 = Zi,n+1 / Xi

Zi,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 AR

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 AR

regional supply percentages (or regional purchase coefficients)

Many region modelInterregional modelMultiregional model

Single region model

1. Survey interregional trade ZijRR :

Regional input coefficients ARR

2. Using national technical coefficients A:Regional technical coefficients AR

= P (Regional supply percentages or regional purchase coefficients; diagonalized) * A

Regional Input Coefficient

aijRR = zij

RR / XjR

aijLL = zij

LL / XjL

ij from i sector to j sectorRR from R region to R regionLL from L region to L region

ARR : regional input coefficient for RALL : regional input coefficient for L

∆XR = (I-ARR)-1 ∆YR

∆XL = (I-ALL)-1 ∆YL⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=LLLLLL

LLLLLL

LLLLLL

LL

aaaaaaaaa

A

333231

232221

131211

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)

pjR = (Xj

R – EjR) / (Xj

R – EjR + Mj

R)(Xj

R – EjR) : locally produced amount of good j

available in region R(Xj

R – EjR + Mj

R) : total amount of good j available in region R, either produced locally or imported

Regional Technical Coefficient

aijR = zij

·R / XjR

ij from i sector to j sector·R from all regions to R region

AR = PA XR = (I-PA)-1 YR

P: diagonal matrix created from pjR

∆XR = (I-PA)-1 ∆YR

Many Region Model

1. Interregional I-O model (IRIO)Survey interregional trade Zij

RR Regional input coefficients ARR

2. Multiregional I-O model (MRIO)Regional technical coefficient AR

• Interregional trade coefficient CiRL

• LQ aijRR = aij

N*LQiR if LQ <1

aijN if LQ>1

• RAS for updating AR

Non-survey technique

Interregional Model

region L R

region sector 1 2 3 1 2

1 Z11LL Z12

LL Z13LL Z11

LR Z12LR

2 Z21LL Z22

LL Z23LL Z21

LR Z22LR

3 Z31LL Z32

LL Z33LL Z31

LL Z32LL

1 Z11RL Z12

RL Z13RL Z11

RR Z12RR

2 Z21RL Z22

RL Z23RL Z21

RR Z22RRR

L

Interregional trade, flows of goods Interregional trade, flows of goods

Interregional ModelRegional input coefficient

aijLL = zij

LL / XjL

aijLR = zij

LR / XjR

aijRL = zij

RL / XjL

aijRR = zij

RR / XjR

• ij from i sector to j sector• LR from L region to R region

⎥⎥⎦

⎤

⎢⎢⎣

⎡= RRRL

LRLL

ZZZZ

Z

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=LLLLLL

LLLLLL

LLLLLL

LL

aaaaaaaaa

A

333231

232221

131211

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=LRLR

LRLR

LRLR

LR

aaaaaa

A

3231

2221

1211

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

= RLRLRL

RLRLRL

RL aaaaaa

A 232221

131211

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

= RRRR

RRRR

RR aaaa

A 2221

1211

Interregional Model

LLRLRLLLLLLL YZZZZZX 112111312111 +++++=

LRLRRLRLLLLLLLLLL YXaXaXaXaXaX 12121113131121111 2 +++++=

⎥⎥⎦

⎤

⎢⎢⎣

⎡=⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎥⎦

⎤⎢⎣

⎡R

L

R

L

RRRL

LRLL

YY

XX

AAAA

II0

0

Interregional trade coefficient

CiRL = zi

RL / TiL

TiL : total shipment of i into L from all of the

regionsCi

RL : the proportion of all of good i used in L that comes from R

Multiregional Model

⎥⎦

⎤⎢⎣

⎡= LL

LLL

aaaa

A2221

1211 ⎥⎦

⎤⎢⎣

⎡= RR

RRR

aaaa

A2221

1211

⎥⎦

⎤⎢⎣

⎡= LR

LRLR

cc

C2

1

00

⎥⎦

⎤⎢⎣

⎡= RR

RRRR

cc

C2

1

00

⎥⎦

⎤⎢⎣

⎡= LL

LLLL

cc

C2

1

00

⎥⎦

⎤⎢⎣

⎡= RL

RLRL

cc

C2

1

00

⎥⎦

⎤⎢⎣

⎡= R

L

AA

A0

0

⎥⎦

⎤⎢⎣

⎡=

RRRL

LRLL

CCCC

C

⎥⎦

⎤⎢⎣

⎡=

R

L

XX

X ⎥⎦

⎤⎢⎣

⎡=

R

L

YY

Y

Multiregional Model

RLRLLLRRLRLLLL YCYCXACXACI +=−− )(RRRLRLRRRRLLRL YCYCXACIXAC +=−+− )(

RLRLLLRRLRLLLLL YCYCXACXACX +++=RRRLRLRRRRLLRLR YCYCXACXACX +++=

CYXCAI =− )(

CYCAIX 1)( −−=