Local & Regional Economic Analysis
Lecture 2b - Introduction to
econometric &
input-output models
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
1
Local & Regional Economic Analysis
RALE – Lecture 2b
Last session Multipliers & output models
This session: Econometric & I-O models
Aims

To examine regional econometric models

Introduce the concept of the I-O approach.

Review selection of studies, look at the limitations &
review extensions
Objectives




Be familiar with regional econometric models.
Awareness of the I-O methodology.
Ability to access a range of studies & be conversant with
the limitations
To have an awareness of improvements that have been
made.
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
2
Local & Regional Economic Analysis
Econometric models
Multiplier models estimate changes in TOTAL regional
income and employment they do not detail the effects of
alternative policies - so there is a need to use something
else
Requirements of econometric models
 Detailed enough to provide info on a wide range of data.
 Need to be able to model for different spatial areas.
 Models need to be “internally consistent”
What are they?
“An interdependent set of equations. Each equation
determines the numerical value of one regional variable.
Right hand side consists of both endogenous and
exogenous variables e.g. tax, birth and death rates etc.”
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
3
Local & Regional Economic Analysis
Regional econometric model (Conceptual)
Region’s
productivity
Competitiveness of
region’s exports
World demand
for goods and
services
Output of
export sector
Population of
working age
Net Migration
Supply of labour
Participation rate
Adapted from Armstrong
and Taylor (2000) pp 32
Regional
unemployment
Regional wage
level
Regional
employment
Wages &
salaries
Transfer
payments
Non-export
sector
Regional income
Taxes
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
4
Local & Regional Economic Analysis
Evaluation of Rival Regional Econometric Models



Hunt (et al) found little or no consistency across the results
Differences only explained by detailed analysis of the model’s
underlying structures, the data sets used, derivation of regional
data and treatment of regional and sector productivity.
They suggest modellers may be attempting to model the
impossible - lack of differentiated data on MPC.
Follow up study of stand alone models Liverpool-Cardiff and
Cambridge Econometrics Local Economy Forecasting Model




L-C model subjected to academic scrutiny the LEFM has not.
The LEFM is much more disaggregated than the L-C model
The L-C model is supply-side driven the LEFM is demand driven.
The L-C is based on a system of inter-linked equations whereas
the LEFM has an input-output approach as its’ underlying
philosophy.
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
5
Local & Regional Economic Analysis
The Input- Output concept
labour
Imports
Raw
materials
Semi
finished
products
output
 Basis of approach is that production of an OUTPUT
requires INPUTS .
 The input- output linkages are recorded in a
“transactions” or “flows” matrix which records all
payments TO and FROM a sector within a year.
 Works on basis of double-entry book keeping, so that
Gross Outputs must equate to Gross Inputs.
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
6
Local & Regional Economic Analysis
Transaction Tables
 Main UK Input-Output table uses a 123 sector model but a
simpler version can be used. Simpler versions used to
demonstrate the concept e.g. 3 sectors.
 Cells in columns = purchases that a sector makes (inputs)
 Cells in Rows = Sales of Products from sector (outputs)
Columns
show
purchase
of inputs
Input 100
Rows show sale
of outputs
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
Output 100
7
Local & Regional Economic Analysis
The Transaction Table
Inputs purchased by
Agri.
Manu.
Services
Output
produced by
Agriculture
Manufacturing
Services
Payments for
Household
services
Government
Services
Imports into
region
Gross inputs
H’holds
Final demand sectors
Gov.
Exports
Investt
Gross
output
20 (0.2)
20 (0.2)
0 (0)
40 (0.2)
20 (0.1)
40 (0.2)
0 (0)
10 (0.1)
10 (0.1)
20
75
25
0
10
20
20
55
5
0
10
0
100
200
100
40 (0.4)
70 (0.7)
5
0
0
0
160
5 (0.05)
0
0
0
0
30
10 (0.1)
45
(0.225)
15
(0.075)
40 (0.2)
5 (0.05)
0
0
0
5
60
100
200
100
125
30
80
15
650
10 (0.1)
() = technical coefficients
GDP = C+G+I+(X-M) = 125+(30-30)+15+(80-60) = 160
Adapted from Armstrong and Taylor (2000) pp 39
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
8
Local & Regional Economic Analysis
Two Ways to construct the Transactions Matrix
 The DOMESTIC flow & The TOTAL flows approaches
Inputs purchased by
Final demand sectors
Agriculture
M anufacturing
Services
Households
Government
Exports
Investment
Gross
output
Output produced by
Agriculture
M anufacturing
Services
20 (0.2)
20 (0.2)
0 (0)
40 (0.2)
20 (0.1)
40 (0.2)
0 (0)
10 (0.1)
10 (0.1)
20
75
25
0
10
20
20
55
5
0
10
0
100
200
100
Payments for
Household services
Government Services
Imports into region
40 (0.4)
10 (0.1)
10 (0.1)
45 (0.225)
15 (0.075)
40 (0.2)
70 (0.7)
5 (0.05)
5 (0.05)
5
0
0
0
0
0
0
0
0
0
0
5
160
30
60
100
200
100
125
30
80
15
650
Gross inputs
() = technical coefficients
-10
-40
-5
KEY ASSUMPTIONS:
Production Technology is in fixed proportions therefore if
demand doubles inputs will have to double.
There are no constraints on productive capacity thus the
supply of factor inputs is perfectly elastic
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
9
Local & Regional Economic Analysis
Technical Coefficients

The Technical Coefficients allow us to estimate the effect of a
change in final demand.
 TC = the flow of output from industry i to industry j divided
by the gross output of industry j.
 The matrix of technical coefficients allows us to see the
effect of an increase in final demand throughout the whole
system.
 If Agricultural demand increases by £10 then it will require
Inputs pu rcha sed by
additional input of:
A griculture
M anufacturing
Agriculture
0.2*£10 = £2
O utput produced by
A griculture
20 (0.2)
40 (0.2)
Manufacturing 0.2*£10 = £2
M anufacturing
20 (0.2)
20 (0.1)
Services
0.0*£10 = £0
Services
0 (0)
40 (0.2)
Households
0.4*£10 = £4
P aym ents for
H ousehold services
40 (0.4)
45 (0.225)
Government
0.1*£10 = £1
G overnment Services
10 (0.1)
15 (0.075)
Im ports into region
10 (0.1)
40 (0.2)
Imports
0.1*£10 = £1
G ross inputs
() = technical coefficients
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
100
200
Services
0 (0)
10 (0.1)
10 (0.1)
70 (0.7)
5 (0.05)
5 (0.05)
100
10
H ouseh
Local & Regional Economic Analysis
The Process
In itia l in c re a s e in d e m a n d fo r a g ric u ltu ra l
g o o d s b y £ 1 0 ra is e s a g ric u ltu ra l o u tp u t b y £ 1 0
10
A g ric u ltu re (A )
0 .2 *1 0 = 2
A;
0 .2 *2 = 0 .4
A;
0 .0 8
M;
0 .0 8
S e rv ic e s (S )
0 .0 *1 0 = 0
M a n u fa c tu rin g (M )
0 .2 *1 0 = 2
M;
S;
0 .2 *2 = 0 .4 0 .0 *2 = 0
A;
0 .2 *2 = 0 .4
S;
0
A;
M;
S;
0 .0 8 0 .0 4 0 .0 8
A;
0 .0 8
M;
0 .0 8
S;
0 .2 *2 = 0 .4
M;
0 .1 *2 = 0 .2
S;
0
A;
0
M;
0 .0 4
S;
0 .0 4
A;
M;
S;
0 .0 4 0 .0 2 0 .0 4
In je c tio n
A =10
F irs t ro u n d
A = 2,
M = 2
S e c o n d R o u n d A = 0 .8 , M = 0 .6 ,
S = 0 .4
T h ird R o u n d
A = 0 .2 8 , M = 0 .0 2 6 , S = 0 .1 6
Adapted from Armstrong and Taylor (1993) pp 38
Agriculture
Manufacturing
Services
Total
Multiplier
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
13.26
3.02
0.67
16.95
1.69
11
Local & Regional Economic Analysis
The inverse Matrix
1
0
0
0
1
0
0
0
1
-
0.2
0.2
0
0.2
0.1
0.1
0
0.2
0.1
Identity matrix
=
A matrix
0.8
-0.2
0
-0.2
0.9
-0.1
0
-0.2
0.9
1- A matrix
Invert the Matrix
1.326
0.302
0.034
0.302
1.208
0.134
0.067
0.268
1.141
Matrix of multipliers
1- A-1 matrix
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
12
Local & Regional Economic Analysis
Summarising changes in demand


To summarise the effect of a change in demand, multipliers
are used - there are 2 types TYPE 1 & TYPE 2
TYPE 1 multipliers treat the household sector as exogenous
Direct  Indirect
•
Direct
The key to calculating multipliers is the matrix
of multipliers (I-A)-1 and the row of household
coefficients
Type 1 Matrix of multipliers
Agriculture Manufacturing
Agriculture
1.326
0.302
Manufacturing
0.302
1.208
Services
0.067
0.268
Output Multipliers
1.695
1.779
Agriculture Manufacturing
Household coefficient
0.400
0.225
Household income multiplier
1.613
2.580
HH  inc  mult
 (1 . 326
Services
0.034
0.134
1.141
1.309
Services
0.700
1.203
* 0 . 4 ); ( 0 . 302 * 0 . 225 ); ( 0 . 067 * 0 . 7 )
 1 . 613
0 .4
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
13
Local & Regional Economic Analysis

TYPE 2 multipliers treat the household sector as endogenous
A  Output  1 . 74  1 . 13  0 . 48
Direct
 Indirect
Direct
 induced
A  HH  inc .  1 . 33 / 0 . 40
Type 2 Matrix of multipliers
Agriculture Manufacturing
Agriculture
1.7417
0.6766
Manufacturing
1.1344
1.9571
Services
0.4833
0.6430
Households
1.3319
1.1985
Sectoral output multipliers
3.3595
3.2767
Agriculture Manufacturing
Household coefficient
0.400
0.225
Household income multiplier
3.330
5.327

Services
0.5770
1.2210
1.6843
1.7389
3.4824
Services
0.700
2.484
Households
0.6452
1.2903
0.6452
2.0645
Commentators suggest that the Type 2 multipliers
overestimate the scale of additional spending because it
assumes all additional income is spent
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
14
Local & Regional Economic Analysis
Applications of input-output analysis
 Often used to study island economies ( they are relatively
self-contained) see Lewis & McNicholl for study of the
Shetlands.
 Harris, Urban Studies Vol. 34 No.4 pp 605-626 looks at the
University of Portsmouth, contains a discussion about the
merits of using the partial survey method and type 1 & 2
multipliers.
 Hill looks at the effect of overseas students on the Welsh
economy.
 Bishop et al. look at the impact of the naval base at
Plymouth and its impact on the economy of Devon and
Cornwall.
 Clark & Grainger, et al Portsmouth Naval Base4
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
15
Local & Regional Economic Analysis
Strengths





Shows the supply chain linkages
Captures the full system effects
The methodology is transparent
Produces more detailed sectoral results
Applicable to scenario (what if) analysis
Weaknesses






Availability and reliability of data
Production techniques are assumed fixed
Import propensities may chane
Changes in industry linkages
Assumption of constant returns
Assumption of no supply constraints
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
16
Local & Regional Economic Analysis
New directions
 To get over the problem of fixed technology and excess
supply the I - O model is expanded to include a supply-side
and is linked to an econometric model
 This allows for price & quality adjustments to be incorporated
 Time dimension allows adjustment of output/labour ratio and
changes in consumption patterns
Advantages
 The sectoral diversity of I-O is maintained and the dynamic,
price responsiveness and forecasting abilities of the EC
model are captured.
 See Integrated Econometric and I-O models – Issues and
Opportunities by Rey (2000) (Papers in Regional Science Vol.
79 pp271 – 292)
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
17
Local & Regional Economic Analysis
Integration of Input – Output and regional econometric models
F in a l d e m a n d fo r
re g io n ’s o u tp u t
R e g io n a l
o u tp u t
In v e rs e m a trix
(in p u t-o u tp u t m o d e l)
D e m a n d fo r
re g io n ’s la b o u r
S u p p ly o f
la b o u r
R e g io n a l
e m p lo y m e n t
U n e m p lo y m e n t
R e g io n a l
h o u s e h o ld in c o m e
R e g io n a l
w a g e le v e l
Net
m ig ra tio n
P a rtic ip a tio n
ra te
R e g io n a l d e m a n d
fo r c o n s u m e r g o o d s
In teg ra tin g th e in p u t-o u tp u t m o d e l in to th e e c o n o m e tric m o d e l
S o u rc e: A rm s tro n g an d Ta y lo r (2 0 0 0) R e g io n a l E c o n o m ics a n d P o lic y
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
18
Local & Regional Economic Analysis
Summary econometric and Input - Output modelling
 More complex relationships can be modelled by using econometric
models – problem which model to use.
 More robust than economic base or Keynesian multipliers
 Transparent Interaction between a region's industries
 More precise tool for forecasting exogenous shocks.
 Used in a wide range of studies and seen as reliable
 Problems restrictive assumptions and data availability
 Integration with econometric models improves performance in the
short-run and creates a “dynamic” model
 Next week: Regional growth disparities - the
Neoclassical and Keynesian perspectives
Regional and Local Economics (RALE) Lecture
slides – Lecture 2b
19