Statistical Training and Research Center
Research and Information Technology Division
Multiplier Analysis for Major Industries of the Philippines
By Input-Output Approach
Madeline D. Cabauatan
September 2013
Multiplier Analysis for Major Industries in the Philippines
by Input-Output1
Madeline B. Dumaua2
Abstract
This study utilized a non-competitive type of Input-Output table where each
cell element explicitly distinguishes the domestically-produced from the imported to
quantify correctly the impact of final demand on the various economic variables. The
paper seeks to construct a non-competitive or domestic type of IO tables wherein the
import content of each IO transaction is netted out. Using the constructed noncompetitive or domestic type of IO tables, domestic multipliers were re-estimated for
the major industries.
Key Words: multiplier analysis, input-output
1.
Introduction
One of the 2009 In-House Researches of the Statistical Research and
Training Center (SRTC) is on “Input-Output Multiplier Analysis for Major Industries in
the Philippines.” The study provides information on the impact of the different sectors
in the country’s economy in terms of output, income and employment through the
method called input-output multiplier analysis. The 2000 Input-Output Accounts of the
Philippines (IO Accounts) using the 11x11 matrix is the most recently published
tables by the National Statistical Coordination Board (NSCB) primarily used in doing
the analysis for all 11 major industries. These are agriculture, fishery and forestry;
mining and quarrying; manufacturing; construction; electricity, gas, and water;
transportation, storage and communication; wholesale and retail trade; finance; real
estate; private services; and government services.
This study utilized a competitive type of IO table wherein each cell element
does not explicitly distinguish the domestically-produced from the imported.
Nonetheless, it is important to quantify correctly the impact of final demand on the
various economic variables.
This project paper seeks to construct a non-competitive or domestic type of
IO tables wherein the import content of each IO transaction is netted out. Using the
constructed non-competitive or domestic type of IO tables, domestic multipliers will
be re-estimated for the major industries.
2.
Objectives of the Study
The study aims to measure the economic effects of the major industry groups
using non-competitive type of IO tables.
1
One of the in-house research undertakings of the Research and Information Technology Division
(RITD) of the Statistical Research and Training Center (SRTC) of the National Economic and
Development Authority (NEDA)
2
Statistician III, Research and Information Technology Division (RITD) of the Statistical Research and
Training Center (SRTC) of the National Economic and Development Authority (NEDA)
Specifically, the study aims to:
1. Generate non-competitive IO tables;
2. Estimate non-competitive multipliers for major industries; and
3. Evaluate and compare the multipliers using the 1994 IO Account of the
Philippines.
3.
Significance of the Study
In economics, the multiplier effect refers to the idea that the initial amount of
money invested by government leads to an even greater increase in national income.
In other words, an initial change in aggregate demand causes a change in aggregate
output of the economy that is multiple of the initial. This measures the degree to
which various businesses and households in an economy are interrelated. This
measure the impact of a given external change, such as new investment, export
expansion, startup of a new businesses, on total economic activity in a given
community or country, through the respending of new dollars within that economy.
The multiplier has been used to justify government spending or taxation relief that
will stimulate aggregate demand. Many governments consider spending/tax break as
instruments to stimulate aggregate demand. This is usually implemented during a
period of recession or economic uncertainty. The money invested by a government is
believed to create more jobs, which in turn will mean more spending that further fuel
activities in various sectors of the economy.
The idea is that the net increase in disposable income by different stakeholders
throughout the economy will be greater than the original investment. As this happens,
government can increase the gross domestic product by an amount that is greater
than an increase in the amount it spends relative to the amount it collects in taxes.
Multiplier focuses on the relationship between spending and consumption. It is
also referred as expenditure multiplier. The concept holds that a spending, whether
initiated by the government, corporations or households, will trigger the national
income. Expenditure multiplier does not differentiate between consumption and
investment spending.
Examples of multipliers include I-O multipliers which are derived from I-O tables
and show the impact of spending in certain industry on various economic variable
including GDP, employment, output and wages and salaries, etc.
4.
Limitations of the Study (Taken from the Phase I of the Study)
The paper makes use of the 2000 Input-Output tables from the National
Statistical Coordination Board (NSCB). It only uses I-O multiplier analysis in
estimating multipliers. While I-O multipliers can be a rich source of information, they
also have some limitations. These include:
 I-O models treat all inputs as complements and exclude substitutes implying that
increases in the demand for one input will only lead to demand increases for
other inputs. TheI-O model does not consider price-adjusting behavior or
substitution effects.
 Because the model is entirely open, there is no scarcity of resources. The
economy is assumed to have limitless amounts of all the inputs it requires.
 I-O models produce a snapshot of the economy at a given point in time.
Structural changes in the economy over time will reduce the validity of results
produced by I-O models.
 Analysis based on I-O models does not explicitly consider alternatives and tends
to show only benefits of expenditures while ignoring costs.
 The impacts considered through the I-O model are short-term and at the margin:
there is no consideration of whether the economy has the capacity to incorporate
the changes and whether changes in production are sustainable or cost
competitive.
Given these limitations, I-O multipliers can still provide a useful, but rough, initial
indication of the economic impact of changes in spending in different industries.
5.
Data and Methodology (5.2 to 5.5 was taken from the Phase I of the
Study)
This study was primarily carried out based on the 2000 Input-Output Accounts of
the Philippines (I-O Accounts), the most recently published tables by the National
Statistical Coordination Board (NSCB). In order to assess the economic effect of all
major industries in the whole economy, the Input-Output Multiplier Analysis was
used. The major industry groups used in the study include the following:
For the employment multiplier analysis, data for the total number of persons
employed in each industry was taken from the 2000 Census of Philippine Business
and Industry (CPBI) of the National Statistics Office (NSO) while data for the Gross
Value-Added (GVA) was taken from 2000 Economic Accounts of the NSCB.
Table 1. Major Industry Groups
Major Industry Groups
Code
01
Agriculture, Fishery and Forestry
02
Mining and Quarrying
03
Manufacturing
04
Construction
05
Electricity, Gas and Water
06
Transportation, Storage and Communication
07
Wholesale and Retail Trade
08
Finance
09
Real Estate
10
Private Services
11
Government Services
5.1 Computation of the Imports Table
The step by step procedure in generating imports table is described below:
Since the imports table is not readily available (from the NSCB IO accounts),
we can proceed to estimate the Leontief inverse using the following equation:
^
-1
[I - ( I - M ) A]
where
I = identity matrix
A = given matrix of input coefficients of the competitive type
^
M = diagonal matrix of import coefficients M, where Mi = mi/TDDi where mi is
import value of commodity i and TDDi is total domestic demand of commodity i, equal
to Total Intermediate Demand + PCE + GCE + GFCF + CI.
The need to construct an imports table is therefore imperative, which, when
subtracted from the given competitive table, gives the desired non-competitive table.
After constructing non-competitive or domestic type of IO table, multiplier will
be estimated using the Input-Output Multiplier Analysis. The resulting multipliers
using the above inverse equation would be comparatively much lower than those you
have calculated based on the competitive type, due to the fact that developing
economies such as the Philippines are highly dependent on imports. The multiplier
estimates will then be evaluated using the 1994 IO tables.
5.2 Computation of Final Demand-to-Output Multiplier
The step by step procedure in generating Final Demand-to-Output multiplier
analysis is described below:
1. Get the column elements of the inverse matrix for all major industries.
2. Multiply the column elements by the impact variable to get the specific impact
on each industry.
3. Get the total of the column elements of the inverse matrix for all major
industries.
4. Multiply the total column elements by the impact variable to get the impact on
the entire economy.
5.3 Output-to-Output Multiplier
The step by step procedure in generating Output-to-Output multiplier analysis is
described below:
1.
2.
3.
4.
Obtain the IO inverse matrix for all major industries.
Divide each column by its diagonal element.
Get the column sums of the output-to-output inverse matrix.
The column sums are the output-to-output multipliers for each industry.
5.4 Household Income Multiplier
The step by step procedure in generating Household Income multiplier analysis
is described below:
1. Get the household income coefficients of all the major industries in the
economy by dividing the compensation of employees by the total input of the
corresponding industry.
2. Multiply the column elements of the inverse matrix of all major industries by all
the household income coefficients.
3. Add all the products to get the household income multiplier.
5.5 Employment Multiplier
The step by step procedure in generating employment multiplier analysis is
described below:
1. Get employment coefficients of all industries in the economy by calculating the
employment in each industry and dividing it by gross value-added (GVA). Data
for the total number of persons employed in each industry was taken from the
2000 Census of Philippine Business and Industry (CPBI) of the National
Statistics Office (NSO). Data for GVA was taken from 2000 Economic
Accounts of the NSCB.
2. After getting the employment coefficients, get the employment multiplier.
Employment multiplier is computed by multiplying employment coefficient with
inverse matrix. This gives the individual effects of construction for each
industry. If we sum up the multipliers, this somehow gives an effect of the
construction industry in the economy.
3. In doing simulation, i.e., government increases construction output by One (1)
Billion, multiply the 1billion increase to each employment multiplier where the
result will provide possible additional jobs in every industry creating a
corresponding effect in the whole.
4. These multipliers are additional jobs aside from the existing employment in the
construction. In other words, the multiplier analysis assumes that from start to
finish, these additional employments were generated already, or in place. The
IO multiplier analysis cannot determine whether these additional jobs happened
before, during or after the construction stages.
6.
Results and Discussion
6.1 Domestic Leontiff inverse matrix table (11x11);
A
001
002
003
004
005
006
007
008
009
010
011
I
001
002
003
004
005
006
007
008
009
010
011
001
002
003
004
005
006
007
008
009
010
011
0.073492
0.128658
0.001442
0.009436
0.004109
0.007871
0.008327
0.000450
0.015121
-
0.001152
0.010544
0.166565
0.012820
0.054563
0.013570
0.007067
0.017586
0.001469
0.075733
-
0.110724
0.049351
0.325457
0.000328
0.020755
0.007419
0.079705
0.006934
0.001166
0.006894
-
0.000051
0.026103
0.281395
0.006012
0.002403
0.091256
0.012285
0.016171
0.006807
0.020671
-
0.000002
0.067531
0.107465
0.001264
0.076233
0.010301
0.019861
0.001854
0.000025
0.022485
-
0.000499
0.000043
0.332158
0.001087
0.004359
0.025246
0.010093
0.031503
0.009095
0.043880
-
0.017633
0.006233
0.139461
0.000189
0.004775
0.112957
0.001311
0.033851
0.006068
0.015676
-
0.070215
0.003431
0.014969
0.058366
0.001243
0.000189
0.030629
0.165253
-
0.000478
0.023452
0.008631
0.001493
0.003274
0.001083
0.031538
0.000831
0.034258
-
0.025954
0.000229
0.256633
0.028610
0.014391
0.010170
0.022915
0.008599
0.099281
-
0.007491
0.000038
0.106284
0.025061
0.012296
0.020925
0.004606
0.030286
0.008584
0.061208
-
007
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
1.000000
0.000000
0.000000
0.000000
0.000000
008
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
1.000000
0.000000
0.000000
0.000000
009
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
1.000000
0.000000
0.000000
010
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
1.000000
0.000000
001
1.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
002
0.000000
1.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
003
0.000000
0.000000
1.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
004
0.000000
0.000000
0.000000
1.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
005
0.000000
0.000000
0.000000
0.000000
1.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
006
0.000000
0.000000
0.000000
0.000000
0.000000
1.000000
0.000000
0.000000
0.000000
0.000000
0.000000
011
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
1.000000
^
001
0.0496594
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
M
001
002
003
004
005
006
007
008
009
010
011
^
(I-M )
001
002
003
004
005
006
007
008
009
010
011
002
0.000000
0.8332607
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
001
0.950341
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
003
0.000000
0.000000
0.4318817
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
002
0.000000
0.166739
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
004
0.000000
0.000000
0.000000
0.0188613
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
003
0.000000
0.000000
0.568118
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
005
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
004
0.000000
0.000000
0.000000
0.981139
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
006
0.000000
0.000000
0.000000
0.000000
0.000000
0.2389964
0.000000
0.000000
0.000000
0.000000
0.000000
005
0.000000
0.000000
0.000000
0.000000
1.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
007
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.0147748
0.000000
0.000000
0.000000
0.000000
006
0.000000
0.000000
0.000000
0.000000
0.000000
0.761004
0.000000
0.000000
0.000000
0.000000
0.000000
008
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.0866049
0.000000
0.000000
0.000000
007
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.985225
0.000000
0.000000
0.000000
0.000000
009
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
008
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.913395
0.000000
0.000000
0.000000
010
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.1491339
0.000000
009
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
1.000000
0.000000
0.000000
011
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.0018032
010
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.850866
0.000000
011
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.998197
^
(I-M )A
001
002
003
004
005
006
007
008
009
010
011
001
0.0698422
0
0.0730931
0.0014151
0.0094363
0.003127
0.0077543
0.0076056
0.0004503
0.0128659
0
002
0.0010946
0.001758
0.0946287
0.0125785
0.0545625
0.0103268
0.0069624
0.0160631
0.0014692
0.0644389
0
003
0.105226
0.0082287
0.1848979
0.0003218
0.0207555
0.0056459
0.0785278
0.0063337
0.0011665
0.0058657
0
004
4.873E-05
0.0043524
0.1598656
0.0058984
0.0024029
0.0694459
0.0121034
0.0147701
0.0068074
0.0175886
0
005
1.623E-06
0.0112601
0.0610528
0.0012398
0.076233
0.0078388
0.0195679
0.0016938
2.453E-05
0.019132
0
006
0.0004741
7.172E-06
0.1887048
0.0010666
0.0043591
0.0192123
0.0099441
0.0287751
0.0090952
0.0373362
0
007
0.0167574
0.0010392
0.0792301
0.0001854
0.0047748
0.0859604
0.0012911
0.0309194
0.0060677
0.0133382
0
008
009
0
0
0.0398903
0.0033664
0.0149694
0.0444169
0.0012244
0.0001731
0.0306286
0.1406081
0
0
7.965E-05
0.0133238
0.0084684
0.0014931
0.0024918
0.0010668
0.0288062
0.000831
0.0291489
0
010
0.0246647
3.82E-05
0.1457979
0
0.0286101
0.0109516
0.0100199
0.0209305
0.0085987
0.0844744
0
011
0.0071188
6.375E-06
0.060382
0.0245881
0.0122961
0.0159237
0.0045375
0.0276629
0.0085836
0.0520796
0
^
I-(I-M )A
001
002
003
004
005
006
007
008
009
010
011
001
0.930158
0.000000
-0.073093
-0.001415
-0.009436
-0.003127
-0.007754
-0.007606
-0.000450
-0.012866
0.000000
002
-0.001095
0.998242
-0.094629
-0.012578
-0.054563
-0.010327
-0.006962
-0.016063
-0.001469
-0.064439
0.000000
003
-0.105226
-0.008229
0.815102
-0.000322
-0.020755
-0.005646
-0.078528
-0.006334
-0.001166
-0.005866
0.000000
004
-0.000049
-0.004352
-0.159866
0.994102
-0.002403
-0.069446
-0.012103
-0.014770
-0.006807
-0.017589
0.000000
005
-0.000002
-0.011260
-0.061053
-0.001240
0.923767
-0.007839
-0.019568
-0.001694
-0.000025
-0.019132
0.000000
006
-0.000474
-0.000007
-0.188705
-0.001067
-0.004359
0.980788
-0.009944
-0.028775
-0.009095
-0.037336
0.000000
007
-0.016757
-0.001039
-0.079230
-0.000185
-0.004775
-0.085960
0.998709
-0.030919
-0.006068
-0.013338
0.000000
008
0.000000
0.000000
-0.039890
-0.003366
-0.014969
-0.044417
-0.001224
0.999827
-0.030629
-0.140608
0.000000
009
0.000000
-0.000080
-0.013324
-0.008468
-0.001493
-0.002492
-0.001067
-0.028806
0.999169
-0.029149
0.000000
010
-0.024665
-0.000038
-0.145798
0.000000
-0.028610
-0.010952
-0.010020
-0.020930
-0.008599
0.915526
0.000000
011
-0.007119
-0.000006
-0.060382
-0.024588
-0.012296
-0.015924
-0.004537
-0.027663
-0.008584
-0.052080
1.000000
[I - ( I – M^) A]-1
001
002
003
004
005
006
007
008
009
010
011
Total
001
002
003
004
005
006
007
008
009
010
011
1.087898
0.001064
0.106110
0.001670
0.014424
0.006516
0.017365
0.010162
0.001263
0.018496
0.000000
1.264967
0.020223
1.003794
0.146658
0.012978
0.065754
0.016570
0.021105
0.020365
0.003318
0.077715
0.000000
1.388482
0.144944
0.010865
1.261186
0.000900
0.031784
0.017830
0.101358
0.013398
0.002886
0.015917
0.000000
1.601067
0.027292
0.006422
0.228544
1.006375
0.010183
0.076872
0.031713
0.020698
0.008921
0.028906
0.000000
1.445925
0.011990
0.013079
0.094982
0.001610
1.086653
0.012597
0.029357
0.004609
0.000832
0.026112
0.000000
1.281822
0.031376
0.002309
0.255883
0.001491
0.013343
1.026277
0.031437
0.033832
0.011331
0.050418
0.000000
1.457698
0.033753
0.002254
0.130474
0.000613
0.010482
0.091755
1.013270
0.035911
0.008488
0.025989
0.000000
1.352989
0.015201
0.001091
0.094954
0.003842
0.023965
0.049546
0.011470
1.007070
0.032909
0.159376
0.000000
1.399425
0.004309
0.000405
0.028655
0.008673
0.004049
0.005517
0.004011
0.030297
1.002252
0.037370
0.000000
1.125538
0.053899
0.002291
0.213606
0.000433
0.040271
0.017874
0.029293
0.026658
0.010914
1.101003
0.000000
1.496242
0.021232
0.001189
0.102360
0.025061
0.018689
0.022275
0.014360
0.031656
0.010714
0.065115
1.000000
1.312652
Following the computation procedure presented above, the non-competitive I-O
multipliers were estimated for output, income and employment in the Philippine
economy. An I-O model has the ability to identify the important sectors of an
economy at a national (or even at a regional level). Key sectors are identified in
term of multipliers; the higher the multiplier, the stronger is the ability of the
corresponding sector to create multiple impacts in the economy.
Among the 11 major industries, the Manufacturing Industry yields the
largest final-demand to output multiplier of 1.60. This means that for every one (1)
unit increase in final demand in the manufacturing sector, there is a corresponding
increase of 1.60 times in the economy.
The Private Services and the Transportation, Communication and Storage
Industry constitute the second and third most important output generating
industries with both multipliers of 1.49 and 1.46, respectively.
Table 2. Final Demand to Output Multiplier
Major Industry Groups
Code
01
Agriculture, Fishery and Forestry
02
Mining and Quarrying
03
Manufacturing
04
Construction
05
Electricity, Gas and Water
06
Transportation, Storage and Communication
07
Wholesale and Retail Trade
08
Finance
09
Real Estate
10
Private Services
11
Government Services
Multipliers
1.264967
1.388482
1.601067
1.445925
1.281822
1.457698
1.352989
1.399425
1.125538
1.496242
1.312652
Table 2 shows that
6.2 Domestic multipliers for major industries; and
6.3 Result of the evaluation of multipliers using the 1994 IO Accounts of the
Philippines
6.4 Recommend an institutionalization plan.
7. Conclusion and Recommendation
This paper quantified the multipliers of the 11 major industries for the
Philippine economy using input-output technique.
As the economic importance of the 11 major industries is growing among the
policy makers and researchers, this study applied input-output technique to
determine multipliers that will measure the significance of these industries in
generating output, income and employment.
The obtained multipliers showed that among major industries, the
Manufacturing Industry showed the highest final demand to output multiplier.
The results of the study will still have to be evaluated when the NSCB will
release the latest I-O table.
8. Appendices (Taken from the Part I of the Study)
8.1 Input-Output Analysis
There are a number of methodologies developed to determine the multipliers.
The most widely used approach is the input-output technique. The major strength
of the input-output analysis is that it provides detailed information on the direct
and indirect effects of spending on all economic measures for different industries
in the local economy (Loomis and Walsh, 1997). Therefore, in order to satisfy the
aforementioned objectives, the methodology employed in this paper in based on
Leontief input-output techniques where structure of an economy is analyzed in
terms of inter-relationships between economic sectors (e.g. Miller and Blair, 1985).
The input-output technique of a particular economy represents the flow of goods
and services among its different industries for a particular time period. In the
framework of the input-output technique, the relationships between economic
sectors can be described in a system of linear equations where total output
produced by each sector is either consumed as an intermediate input by other
sector, or, sometimes internally by the producing sector itself, or, by the final
demand sector, or both. The presentation of the flow of goods and services could
be expressed either by physical units or in money terms. To define, let there be an
economy with n-producing sectors and a final demand sector. Total output of
sector i will be:
Supply = Demand
n
Qi   qij  Fi
(1)
j 1
where Qi = gross output of industry i; qij = the sales of industry i to industry
j; Fi = the final demand vector; i = 1, …, n.
a
Let ij be the technical (input) coefficient which represents the amount (value)
of sector i’s output needed to produce one unit (one peso) of sector j’s output; thus
using the assumption of constant production coefficient, we get:
aij 
qij
Qi
or
qij  aij Q j
This means that the total value of purchases of goods and services by sector j
from sector i is aij Q j .
Therefore, for a given target of final demand on goods and services, F, this
relation defines how much each producing industry must produce in order to satisfy
a particular bundle of final demand on goods and services, i.e., Equation (1) in
reduced matrix form can be written as:
Q  AQ  F
(2)
Solving the Equation (2) can be found as:
(3)

Q  I  A F
In equation (3), Q is the output vector; I is an identity matrix and I  A is
the total requirement matrix or mostly known as Leontief inverse matrix.

The general solution of Equation (3) determines how much each industry of
the economy must produce in order to satisfy a given level of final demand. It is
mandatory that I  A should be a non-singular matrix meaning that the
determinant
of I  A does not equal to zero to have a unique solution
in the form


of I  A . When the Leontief inverse matrix is assumed to be I  A = Z, then z ij ’s
stand for the elements of the Leontief inverse matrix. Each element of the Leontief
inverse matrix shows the direct and indirect requirements of output sector i per unit
of final demand.
8.2 Output Multiplier
The final demand-to-output multiplier is used to measure the impact of a change
in final demand on the output of individual industries and the whole economy. This
will tell us about the additional output generated in each industry given an impact
increase in the investment in each industry (impact variable).
An output multiplier for sector j is defined as the total value of production in all
sectors of the economy that is necessary in order to satisfy a peso’s worth of final
demand for sector j’s output. For the simple output multiplier, this total production
is the direct and indirect output effect, obtained from a model in which households
are exogenous. The initial output effect on the economy is defined to be simply the
initial peso’s worth of sector j output needed to satisfy the additional final demand.
Then formally, the output multiplier is the ratio of the direct and indirect effect to
the initial effect alone.
The output multiplier measures the sum of direct and indirect output
requirements from all sectors needed to deliver one additional peso of output of i
industry to final demand. It is derived by summing the z ij ’s or the entries in the
column under industry i in the Leontief inverse matrix tables. Although the output
multiplier represents total requirements per unit of final output, it is not particularly
useful concept except as indicator of the degree of structural interdependence
between each sector and the rest of the economy. In economic impact studies we
are more usually concerned with income or employment generating effects, and
these require income or employment multipliers.
8.3 Income Multiplier
Changes in an industry’s output can impact on household income. To
quantitatively determine the impact of changes in each industry’s output on
household income, a household income multiplier analysis is needed. This tells us
about the additional household income in the whole economy due to a one-peso or
one-unit change in final demand for each industry.
The income multiplier
is obtained by multiplying the row vector of income

coefficients, say e with the z ij ’s, which are entries in the column under industry
 i in
the Leontief inverse matrix tables. Row vector of income coefficients or e are
referred to as salaries and wages (compensation) for each industry divided by the
corresponding output. This gives us the following equation for income multiplier:

I  eI  A
1
(4)
8.4 Employment Multiplier
Impact analyses are frequently preoccupied with employment-creating effects of
industrial expansion, because policymakers may be primarily and legitimately
concerned in forecasting jobs in a particular area. For this reason, it is often useful to
be able to derive not only income multipliers from an I-O model, but as well as
employment multipliers.
The following method was used to estimate employment multipliers. The
employment coefficients, l , defined as employment per million pesos of outputs,
was multiplied by the z ij ’s, which are entries in the column under industry i in the
Leontief inverse matrix tables, in order to obtain the multiplier. Mathematically,
employment multiplier is expressed as follows:

L  l I  A
1
9. References
Miller, Ronald E. and Blair, Peter D. Input-Output Analysis: Foundations and
Extensions. Englewoods Cliffs, N.J. Prentice Hall 1985.
Thijs Ten Raa. The Economics of Input-Output Analysis. Cambridge University
Press 2005.
National Statistical Coordination Board. The 2000 Input-Output Accounts of the
Philippines. Economics Statistics Office 2000.
National Statistics Office. 2000 Census of Philippine Business and Industry.
Presentation Material of Dr. Cid L. Terosa, UA&P Professor.
Presentation Material of Mr. Francisco Secretario, Freelance Consultant.
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