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An Appraisal of Nonsurvey and Minimum Survey Techniques
For Estimating the Lansing Tri-County
Region Input-Output Tabies

presented by

Lutfi Ibrahim Nasoetion

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AN APPRAISAL OF NONSURVEY AND MINIMUM SURVEY TECHNIQUES
FOR ESTIMATING THE LANSING TRI-COUNTY

REGION INPUT-OUTPUT TABLES

BY

Lutfi Ibrahim Nasoetion

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Resource Development

1979

ABSTRACT
AN APPRAISAL OF NONSURVEY AND MINIMUM SURVEY TECHNIQUES

FOR ESTIMATING THE LANSING TRI-COUNTY
REGION INPUT-OUTPUT TABLES

BY

Lutfi Ibrahim Nasoetion

The application of a regional input-output model is
invariably a compromise between the desire for theoretical
satisfaction and comprehensive data coverage, on the one
hand, and the need to economise on time and resources on
the other. Nonsurvey and minimum survey techniques for
constructing regional input-output tables are attractive
to regional analysis because of the relatively smaller
cost involved as compared with direct survey techniques.
Yet, attempts at such nonsurvey and minimum survey tech-
niques have not been successful. The distance between the
survey and the nonsurvey direct cofficients matrices is
quite large in absolute terms. In fact, until recently
there were no accurate comparisons between tables con—
structed by survey and nonsurvey methods. Thus, a study
on nonsurvey and minimum survey techniques of construct-
ing regional input-output tables would likely contribute
greatly to progress in regional economics.

In order to make this contribution, the relative
efficiency of six reducing techniques--(l) Simple Loca-
tion Quotient, (2) Purchase Only Location Quotient,

(3) Cross Industry Quotient, (4) Modified Supply-Demand

Lutfi Ibrahim Nasoetion

Pool, (5) RAS, and (6) Schaffer—Chu Iterative Procedure--
in estimating the Tri-County Region's (Eaton, Clinton and
Ingham Counties of Michigan) direct coefficients, the Type
I and Type II income multipliers were compared and eval-
uated.

The relative efficiency of each reducing technique
was measured as distance or relative distance between the
estimated direct coefficients, the Type I and the Type
II income multipliers, and the "True" direct coefficients,
the Type I and the Type II income multipliers computed
from the survey table. In judging which of the estimated
coefficients and multipliers are closest to the equival-
ent survey based table, three comparative tests were used:
(1) The mean absolute percentage deviation, (2) The mean
of relative change, and (3) The mean of similarity index.

In estimating the regional direct coefficients, none
of the reducing techniques appraised in this study were
entirely satisfactory. The distance between the survey
and nonsurvey matrices was too large, to be accptable to
the author. It was apparent that the RAS technique pro-
duced superior estimates when judged by the three compar-
ative techniques. This is not entirely surprising, given
the technique employs a certain amount of survey data.
Among the purely nonsurvey techniques, the Schaffer-Chu
Iterative procedure and the Cross Industry Quotient tech-

nique emerged as being superior to the other nonsurvey

Lutfi Ibrahim Nasoetion

techniques, when judged by the mean of similarity index,
which is the most ideal comparison test employed in this
study.

This study revealed that the relative efficiency
of the six reducing techniques was better when they were
used to estimate the Type I and the Type II multipliers,
than when they were used to estimate the regional direct
coefficient. It was observed, that the RAS technique pro-
duced the best estimates of the Type I and the Type II
multipliers when judged by any comparison tests employed
in this study. Among the purely nonsurvey techniques, the
Schaffer-Chu iterative procedure and the Cross Industry
Quotient produced the best simulation of the Type I and
Type II income multipliers.

In estimating regional direct coefficients, Type I,
and Type II income multipliers, it was found that the
greatest deviations occurred in three groups of sectors:
(1) Sectors in which the regional economy is highly
specialized, (2) Sectors of primary activities, and
(3) Sectors which have been obtained through a high de-
gree of aggregation. In order to obtain more acceptable
results, it was recommended to use field surveys to ob—
tain the regional direct coefficients of these three

groups of sectors.

Dedicated to

Ros and Rina Nasoetion

ii

ACKNOWLEDGMENTS

The writer wishes to express his sincere apprecia-
tion to Dr. Milton H. Steinmueller who, as chairman of
the Guidance Committee, gave his help, encouragement,
support and friendship throughout my entire doctoral pro-
gram. Gratitude is also expressed to Dr. Daniel E. Chap-
pelle for guiding the thesis work, and to Dr. Raleigh
Barlowe and Dr. Garland P. Wood for serving on the Guid-
ance Committee and reading the thesis.

In addition, the writer is indebted to first, Bogar
Agricultural University which sent him to Michigan State
University to pursue the program-~special thanks here to
Dr. Oetik Koswara, and Dr. Andi Glakim Nasoetion, Presi-
dent of Bogar Agricultural University, who continuously
encouraged the completion of the study; and second to
MUCIA_AID mission to Indonesia which provided the funds
that enabled the writer to stay in the United States dur-
ing his masters and doctoral program.

The writer wishes to acknowledge his friends in his
home country and the United States--special thanks to
Dedi Fardiaz, Uben Parhusip, Hadi K. Purwadaria, and Lukito
Sukahar, who have made innumerable contributions to the
enjoyment and accomplishment of this endeavor.

Finally, to my wife Ros Nasoetion and my child
Karina Nasoetion, who gave and still will give unenduring
love, encouragement, and understanding, the writer offers

his warmest gratitude.
iii

LIST OF

CHAPTER

I.

II.

III.

TABLE OF CONTENTS

TABLES O O O O O O O O O O O O O O O O O O 0

INTRODUCTION . . . . . . . . . . . . . . . .

Problem Setting . . . . . . . . . . .
Objectives of the Study . . . . . . . .
Limitations of the Study . . . . . . . .
Outline . . . . . . . . . . . . . . . .

LITERATURE REVIEW . . . . . . . . . . . . .

The Theoretical Foundations of Input-Output
AnaIYSiS O O O O O I I O O O I O O O O I O

Transactions Matrix . . . . . . . . . .
Input Coefficients . . . . . . . . . . .
Gross Output Needed to Produce Given
Final Demand . . . . . . . . . . . . .
Prices in Input-Output System . . . . .

Some Problems of Input-Output Analysis . . .
Theoretical Problems . . . . . . . . . .
Operational Problems . . . . . . . . . .

RESEARCH METHODS . . . . . . . . . . . . . .

Review of Some Previous Reducing Techniques

Which Are Not Appraised in this Study . .

Modification of National Technical
Coefficients . . . . . . . . . . . . .
The Supply-Demand Pool Technique . . . .
McMenamin—Haring Technique . . . . . . .
Test of Accuracy of Regional Nonsurvey
Techniques . . . . . . . . . . . . . .

Reducing Techniques Appraised in this
Study I O O O O O O O O O I I O C O O O O

The Simple Location Quotient Technique .

iv

Page

vii

\l\lUlD-‘ |-‘

\O

10
10

ll
13

15
15

19

l9

19

21

24

24
26

IV.

The Purchase Only Location Quotient
Technique . . . . . . . . . . . . .
The Cross Industry Quotient Technique
The Modified Supply-Demand Pool
Technique . . . . . . . . . . . . .
The RAS Method . . . . . . . . . . .
The Schaffer-Chu Iterative Procedure

Income Multiplier Analysis . . . . . . .

The Aggregate Income Multiplier
Sectoral Income Multiplier . .
The Type I Income Multiplier .
The Type II Income Multiplier .

Comparative Techniques . . . . . . . . .

The Mean Absolute Percentage
Deviation . . . . . . . . . . . . .

The Mean of Relative Change . . . . .

The Mean of Similarity Index . . . .

The Structure of the Lansing Tri—County
Region Input-Output Tables . . . . . .
Sector Aggregations . . . . . . . . . . .

RESULTS AND DISCUSSION . . . . . . . . .

The Assumptions of the Six Reducing
Techniques Compared . . . . . . . . .

The Simple Location Quotient' . . . .
The Purchase Only Location Quotient .
The Cross Industry Quotient . . . . .
The Modified Supply-Demand Pool . . .
The RAS Method . . . . . . . . . . .
The Schaffer-Chu Iterative Procedure

Comparisons of Relative Efficiency of the
Six Reducing Techniques in Estimating
Direct Coefficients . . . . . . . . . .

Income Multiplier Analysis . . . . . . .

The Type I Income Multiplier . . . .
The Type II Income Multiplier . . . .

SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS

Introduction . . . . . . . . . . . . . .
Summary of this Study . . . . . . . . . .

Relative Efficiency of the Six Reducing

Techniques in Estimating the Direct
Coefficients . . . . . . . . . . .

Page

28
28

29
31
35

38

39
40
42
43

43

44
46

46
50

55

110

Page

Relative Efficiency of the Six Reduc-

ing Techniques in Estimating the

Type I Income Multiplier . . . . . . lll
Relative Efficiency of the Six Reduc-

ing Techniques in Estimating the

Type II Income Multiplier . . . . . . 112

Possible Sources of Errors . . . . . . 113
Conclusions and Recommendations . . . . . . 114
APPENDIX 0 O O O O O O O I O I O O O O O O 0 O O O 118

A, ESTIMATED DIRECT COEFFICIENTS
GENERATED BY THE SIX REDUCING TECHNIQUES
COMPARED TO THE TRUE DIRECT COEFFICIENTS
COMPUTED FROM SURVEY DATA . . . . . . . . 118

B. THE RESULTS OF SECTORAL INCOME MULTIPLIER
ANALYSES o o o o o o o o o o o o o o o o 144

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . 153

vi

Table

1.

10.

LIST OF TABLES

Page

Evaluation of Simulated Tables: Methods
Ranked for Each Test . . . . . . . . . . . . . 25

The Study Area Aggregation Scheme . . . . . . 48

The Estimated Location Quotient (LQi) and
Purchase Only Location Quotient (POLQi) . . . 60

The Statistical Characteristics of the "True"
Direct Coefficients (Survey Method) Compared

to the Statistical Characteristics of the

Estimated Direct Coefficients (SLQ) . . . . . 61

The Statistical Characteristics of the ”True"
Direct Coefficients (Survey Method) Compared

to the Statistical Characteristics of the

Estimated Direct Coefficients (POLQ) . . . . . 65

The Statistical Characteristics of the "True"
Direct Coefficients (Survey Method) Compared

to the Statistical Characteristics of the
Estimated Direct Coefficients (CIQ) . . . . . 67

The Statistical Characteristics of the "True"
Direct Coefficients (Survey Method) Compared

to the Statistical Characteristics of the

Estimated Direct Coefficients (MSDP) . . . . . 71

The Statistical Characteristics of the "True"
Direct Coefficients (Survey Method) Compared

to the Statistical Characteristics of the

Estimated Direct Coefficients (RAS) . . . . . 74

The Statistical Characteristics of the ”True"
Direct Coefficients (Survey Method) Compared

to the Statistical Characteristics of the

Estimated Direct Coefficients (SCM) . . . . . 76

Comparison of the Relative Efficiency of the
Six Reducing Techniques . . . . . . . . . . . 81

vii

Table

11.

12.

13.

14.

15.

16.

17.

Evaluation of Estimated Tables:

Reducing

Techniques Ranked for Each Comparison Test .

The Type I Income Multiplier of the Tri-
County Region (Survey Method) Compared to the
Type II Income Multiplier Produced by the

Six Reducing Techniques, Appraised in this

Study . . . .

Comparison of the Relative Efficiency of the
Six Reducing Techniques in Estimating the

Type I Income Multiplier .

Evaluation of Estimated Type I Income Mul-
Reducing Techniques Ranked for

tiplier:
Each Test . .

Type II Income Multipliers of the Tri-County
Region (Survey Method) Compared to the Type
II Income Multipliers Produced by Bach Reduc-

0

ing Technique Tested in this Study .

Comparison of the Relative Efficiency of the
Six Reducing Techniques in Estimating the

Type II Income Multipliers .

Evaluation of Estimated Type II Income Mul-
Reducing Techniques Ranked for Each

tiplier:
Comparison Test

viii

Page

82

88

93

94

97

101

102

CHAPTER I

INTRODUCTION

Problem Setting

 

In general, most state, regional and county planners
are interested in local socio-economic evaluation and po-
tential impacts of resource programs and plans. Informa-
tion on costs, benefits, and other regional and environ-
mental trade-offs are needed by decision makers, planners,
and local participants, before recommending and implement-
ing a plan. Indeed, this information cannot be just a
localized national economic development display, but has
to reflect the regional economy, including the interindus-
try and intraindustry flow of goods and services. Reli-\_
able information has to be developed so that alternative _
regional develOpment plans and strategies can be prepared.
and analyzed. In general, two major kinds of information/
are necessary: reliable estimates of structural relation;
ships in a regional economy and direct and indirect impacts
of planned economic activities. New economic activities
must be translated into shifts in final demand on an indus-
try by industry basis. For this purpose, input—output

models are very useful, because they can be used to

estimate structural relationships in a regional economy
and impacts of planned new economic activities.

Wassily Leontief spent a number of years in construct-
ing input-output tables for the U. 8. economy for 1919 and
1929. His results, which he used to analyze the working
of American economy were published in 1941 and 1951.1 An
87 sector input-output model of the U.IS. economy for the
year 1958, was published by the Office of Business Econom-
ics (now Bureau of Economic Analysis) in 1964. The larg-
est U. S. economy input-output model is the 370 sector
table published by Bureau of Economic Analysis in 1969 for
the year 1963. The newest national model was published in
1974 for 1967. "With the publication of these results, the
number of comparable benchmark input-output tables is in-
creased to four and the time span covered by these studies
is extended to 20 years covering the period of 1947 to
1967."2

Leontief in his analyses focused his attention on
intersectoral relations, and based his analysis upon gen-
eral equilibrium theory. While the general equilibrium

theory of Walras did not go beyond writing down a set of

equations with symbolic coefficients, Leontief estimated

 

lLeontief, Wassily. 1941, 1951. The Structure of
American Economy. New York: Oxford University Press.

2U. S. Department of Commerce, Bureau of Economic
Analysis, "The Input-Output Structure of the U. S. Economy:
1967," Survey of Current Business, LIV (February, 1974),
24-560

 

 

 

such a system with empirically obtained numerical coef-
ficients. In his conception, the statistical data collec-
ted fill in the "empty box" of the theory. Hypothetical
production and consumption equations gain explicit meaning
as soon as the algebraic symbols are replaced by observed
numerical values. Once empirical foundations are thus es-
tablished, the vague generalities of abstract theoretical
statements acquire empirical significance.

The endeavors to make general equilibrium theory
correspond to economic reality led to linearization of
economics. This, together with the development of aggrega-
tion schemes wherein millions of households could be repre-
sented by a single sector and hundreds of firms of an indus-
try by another, and so on, made the system amenable to an-
alysis by use of matrix algebra. And Leontief used it with
a telling effect.

Essentially, input-output is a method of analysis
that takes advantage of the relatively stable pattern of
the goods and services in the short run, among elements of
the economy to bring a more detailed statistical picture
of the system into the range of manipulation by economic
theory.

Input-output analysis is applied intensively in the
study of regional economy. An important reason for this
is that input-output techniques can be implemented empir-
ically in a field where data shortages and underdeveloped

theoretical constructs restrict the scope for hard empirical

research. Moreover, it provides virtually the sole avenue
of escape from partial equilibrium analysis.1 The other
general equilibrium theories available, Walrasian general
equilibrium, Neo-Keynesian interregional macroeconomics,
may be a little more satisfying theoretically but they are
much more difficult to apply empirically. In particular,
interregional trade flows are much easier to measure and
make consistent with theory within an input-output frame-
work. Moreover, some versions of interregional input-
output models of which the gravity technique is typical,
have the added advantage for analysis of the space economy
that they take distance in the form of transportation cost
explicitly into account as a relevant variable.

There are at least four basic purposes of an input-

output model:

1) It can provide a detailed description of a na-
tional or regional economy by quantifying link-
ages among sectors of the economy and the
sources and origin of exports and imports,

2) Given a set of final demands (exogenous), total
output in each industry and requirements for
primary factors and resources can be determined,

3) The effects of change in final demands, arising
in either the private or public sector, can be
traced and predicted in detail,

4) Changes in production technology or relative

prices can be incorporated by changing the
technical coefficients of production.

 

1Richardson, Harry W. 1972. Input-Output and Re-
gional Economics. Trowbridge, Wiltshire, England: Redwood
Press Limited, 294 p.

2Lewis, W., Cris. 1971. Regional Economic Develop-
ment: The Role of Water (Logan: Utah State University
Foundation) p. 5).

 

 

These advantages go a long way to offset the well
known drawbacks--the restrictive assumptions, the high cost
involved in obtaining data required, and practical obstacles
in the way of operationalizing the dynamic models needed for
long run regional planning. However, because of its useful-
ness, regional economists in most cases must depend heavily
upon input-output analysis. Their involvement can usually
be traced to pragmatic grounds--that given the objective of
their research, available data and research resources, in-
put-output modeling is the most useful technique currently

available.

Objective of the Study

 

The implementation of regional input-output models
is invariably a compromise between the desire for theor-
etical satisfaction and comprehensive data coverage, on the
one hand, and the need to economise on time and resources
on the other. Nonsurvey and minimum survey methods for
constructing regional input-output tables are attractive
to model builders because of the relatively smaller cost
involved as compared with full survey methods. Yet, at-
tempts at such nonsurvey and minimum survey techniques have
not been successful. The distance between the survey and
the nonsurvey direct coefficients matrices is quite large
in absolute terms. In fact, until recently there were no
accurate comparisons between tables constructed by survey

and nonsurvey methods. Thus, a study of nonsurvey and

minimum survey methods of constructing regional input-out-
put tables would likely to contribute greatly to progress
in regional economics.

Input-output tables of the Lansing Tri-County Region
(Eaton, Ingham and Clinton Counties) have been constructed
by O'Donnell, 32 al., of Michigan State University in 1960,1
for the year of 1958 based upon primary data collected by a
survey method. The purpose of this study is to construct
nonsurvey and minimum survey input-output tables for the
same region, for the year 1958, based upon the United States
national input-output tables for 1958, by using six reducing
techniques, i.e.: (1) The Simple Location Quotient,

(2) The Purchase Only Location Quotient, (3) The Cross In-
dustry Quotient, (4) The Modified Supply-Demand Pool,

(5) The RAS Method, and (6) The Schaffer-Chu Iterative
Procedure.

The Type I and Type II sectoral income multipliers
will be computed based upon the direct coefficients matrices
produced by each reducing technique.

The direct coefficients estimated by the nonsurvey
and minimum survey techniques, as well as the Type I and
Type II income multipliers generated by each technique will
be compared to the "True" direct coefficients, the Type I

and Type II multipliers computed by O'Donnell, 33 El:

 

1O'Donnell, John L., et al., 1960. Economic and Pop-
ulagion Base Study of the Lansifig Tri-County Area: An In-
ter-Industry Rélatién Analysis. Michigan State University,
31§"p. ‘

 

 

Comparisons will be performed by using three tests:
(1) The Mean Absolute Percentage Deviation, (2) The Mean

of Relative Change, and (3) The Mean of Similarity Index.

Limitations of the Study

 

The results of this study are applicable only to the
Lansing Tri-County Region. Although the techniques ap-
praised here may be applied elsewhere, extension of speci—
fic quantitative results is not warranted.

The empirically derived input-output model of the Tri-
County Region is a regional version of the traditional
Leontief open, static input-output model, and thus the non-
survey and minimum survey techniques tested in this study
produced input-output model which suffers from all problems
and limitations of the Leontief open, static input-output
model.

The basic assumption of all techniques is that the
national direct coefficients assumed appropriate at the
regional level and that the regional direct coefficients
differ from the national direct coefficients to the extent
that goods and services are imported from, or exported to
other regions. This assumption clearly implies the con-
straints that the regional direct coefficients must always.

be less than or equal to the national coefficients.

9112.12.22
Background information on previous related studies

is presented in Chapter II. Research methodology is

described in Chapter III. Results of this study are dis-
cussed in Chapter IV. Finally, Chapter V provides a sum-
mary, conclusions, and recommendations for further re-
search on the nonsurvey and minimum survey input-output

techniques.

CHAPTER II

LITERATURE REVIEW

The Theoretical Foundations of
Input-Output Analysis_

 

The theoretical foundations and problems of input-
output analysis are discussed briefly in this chapter, to
facilitate presentation and discussion of nonsurvey and
minimum survey techniques in Chapter IV. The more elabor-
ate discussions on this topic can be found in Richardson
(1972),1 and Miernyk (1965)2.

The input-output method is an adaptation of general
equilibrium theory to the empirical study of the quantita-
tive interdependence between interrelatedieconomic activi-
ties. Leontief’s idea was as follows: An economy consists
of a large number of consumers and producers who conduct
among themselves transactions--sales and purchases of goods.
The interdependence between the individual industries of
the given system may be described by a set of linear equa-

tions. Coefficients of these equations must be determined

 

lRichardson, Harry W. 1972. Inputsgutput and Re-
gional Economics. Trowbridge, Wiltshire, England: Redwood
Press Limited[—294 p.

 

 

2Miernyk, W. H. 1965. The Elements of Input-Out—
put Analysis. New York: Random House.

 

 

10

empirically. In the analysis of structural characteris-
tics of an economy they usually are derived from a so-

called statistical input-output table.

Transactions Matrix

 

Assume that one industry produces one commodity,
there is no joint production. Hence, the number of indus-
tries is the same as the number of commodities. Assume
further that no changes occur in inventories of the commod-

ities. By definition:

jglxij + xj = x1 , i = 1,2,...n... (1)
where:
xij = intermediate demand for the ith industry's
output by the jth industry's output;
i = 1,2,...n.
xj = final demand by consumers for the ith indus-
try's output; j = 1,2,...n.
xi = Gross output of industry i; i = 1,2,...n.
The [xij] form a transaction matrix of processing sectors.

Input Coefficients

 

The static input output model assumes constant pro-
portions among inputs and outputs for each industry. This
production relationship rules out factor substitutability.
Ratios between input from each industry and the total outlay,

aij = xij/Xj ; 1,3 = 1,2,...n. (2)

11

are called input or direct coefficients and can be arranged

as follows:

 

 

l 2 ............ ...... n

1 all a12 . ......... ........ a1n
2 a21 a22 ............... ... a2n
n an1 an2 ann
a01 a02 aOn

It should be noted that all of these coefficients are non-

negative.

Gross Output Needed to Produce Given Final Demands_

A model to compute gross output needed to produce

given final demands is needed in constructing an input-

output table as well as in forecasting. ‘The model can be

formulated as follows:
From (2),

xij = aij - Xj; i,j = 1,2,...n
Substituting (3) into (1),

Z a..°X. + x. = X.; i,j = 1,2,

n
=1 13 3 J 1

j

(3)

...n (4)

12

Let:
a = input coefficient matrix = [aij]
E = column vector of xi; i = 1,2,...n
R = column vector of x.; i = 1,2,...n

1

Then in matrix notation, (4) can be written as follows:

AX + i = Y; (5)
Therefore:

TIT—37;? = i
If TI_:_AT is nonsinglular, then,

if = Wk; (6)

In formula (6), the (i,j) element of the Leontief inverse

(I - A5 1 indicates by how much the gross output of the ith

industry has to be changed corresponding to a_unit increase

th

or decrease in the j industry‘s final demand. In this

sense, each element of the Leontief inverse can be called
multisector multiplier. In input-output analysis the mul-
tiplier represents the propagation effects through inter-
mediate demand.

For Example,

_ 1
x1 ’ v (311x1 + lexz

where v is the determinant of (I - A) and Bij are cofactors

of the (i,l) elements of (I - A). The rate of change of
th

+ ... + Bnlxn) (7)

the first industry's gross output with respect to the i

industry's final demand is:

3X1 Bil

___ = ___ (8)

13

Feasible Outputs

 

In input-output analysis, output of the economy is
limited by available primary factors. For an output vector

X, the total labor needs are:

n n ' _1
x0 = jilxoj = ji1a0jxj = a0 (I - A) x (9)
where:
aoj = the employment coefficients that is the ratio
between the labor input and output
a0 = column vector of aoj; j = 1,2,...n
Xj = total outlay

Prime indicates transpose of the matrix or vector.

The Prices in Input-Output Systems

 

Let the prices of n commodities be pi; the price of
labor be w, and the total labor needs for sector j (j =

1,2,...n) are xO then for each commodity,

jr
+ wx . = p.X. (10)

13' 03 J 3

substituting (3) and (4) in (10),

n
2 .a..X. + wa .X. = .X. (11
i=1p1 1] 3 OJ 3 p3 3 )
Therefore:
n

iilpiaij + waoj = pj (l2)

14

Let:
p = column vector of pi; i = 1,2,...n. Then in matrix

notation (12) is equivalent to

p'A + waO = E (13)
That is,

p' (I-A)=vT6 (14)

5' = wag, (I - A) l (15)

Thus, ceteris paribus, given the wage rate, the prices of

 

the commodities are determined by the input coefficients.

Post multiply (14) through by X, obtaining,

5' ___—(I - 33.)")? = w—aoi (16)

and premultiply (7) through p', obtaining

5' 73—7753? = 5'? (17)
Expressions (l6) and (17) imply that,

(7:363? = 5'; (18)

Expression (18) states that income of the factor, labor,
equals expenditure on final goods.

Assuming constant returns to scale, the relative
prices of the commodities are determined by the tech-
nological condition represented by A, independently of

output levels of these commodities.

15
Some Problems of Input-Output Analysis

Theoretical Problems

 

Input-output models incorporate the basic assumptions
of the general Leontief model. Theoretically, each commod-
ity is supplied by a single industry or sector of produc-
tion, only one process is used for producing each commodity
and each sector has only one primary output. There are,
therefore, no joint products. Inputs purchased by each
sector are a function only of the output of that sector.
However, the translation into empirical tool involved lump-
ing together only those plants with similar output and in-
put structures. The practical solution is to group pro-
cesses and products which differ in some respect but which
behave sufficiently uniformly to be used as a basis for
aggregation.

The emphasis on linear production relationships also
creates some problems. The essence of the Leontief model
is the technological relationship that purchases of any
sector (except final demand) from any other sector depend,
via a linear production function, upon the level of output
of the purchasing sector. The constant and linear produc—
tion function assumption solves some kinds of difficulties,
for instance it eliminates factor substitution and econom-
ies of scale, but creates others. Time is missing, yet the
purchase of inputs by one industry to make goods to sell to
other industries implies a period analysis. Moreover, the

notion of a linear production function is not very

16

meaningful in many nonindustrial sectors such as agricul-
ture, services sectors and the government sectors, where
production functions are usually not linear. In 1951,
Samuelsonl showed how the assumption of linear relation-
ship and no factor substitution are not as rigid as first
appears. The Samuelson theorem as it is called, assumes
that each industry produces only one commodity and that
each industry uses only one scarce primary factor which is
homogeneous for all firms in the industries. If it is
further assumed that there are constant returns to scale,
Samuelson found that even if each firm had a wide choice
of alternative production processes, it is compatible with
overall efficiency for each firm to use only one of the
processes available.

Extending input-output analysis to an interregional
setting creates more problems, because it is necessary to
make additional assumptions. A regional interindustry
analysis must not only assume stable direct coefficients
but also stable trading coefficients, so that repercussions
of autonomous changes are not distorted by geographical
differences in the location of final demand or in sources
of supply. This means that all consuming industries ab-
sorb the domestic output of any given type of good and

service combined in a fixed pr0portion with a certain

 

1Samuelson, P. A. 1951. Abstract of a Theorem Con-
cerning Substitutability in Open Leontief Model. In: T. C.
Koopmans (ed.) Activity Analysis in Production and Allo-
cation. John Wiley, pp. BIZ—146T

17

type of its competitive imports, the proportion itself
being determined by the ratio of the total imports of the
particular type of goods to their total supply. This as-
sumption freezes the spatial structure of each region, and
implies fixed regional supply areas for each and every
consuming industry using a particular input. This assump-
tion is restrictive since in reality the supply patterns
of individual sectors for a given input may vary widely
because of vertical integration, competition, different
locations within a given region, entry of new firms, exit
of firms or institutional ties.

The interregional input-output analysis also implies
comparative stability in relative prices between regions
and no changes in interregional competitiveness in the
supply of particular commodities. This implication is
restrictive since in reality, there is probably even less
justification for expecting stability in imports coeffic-
ients than in direct coefficients.

Finally, interregional input-output analysis as-
sumes that imports enter a region only through the matrix
of interdependence. Imports of a commodity are therefore
considered as inputs and are fed directly into producing
sectors, they enter final demand only indirectly as part
of a regional industry domestic output. In some cases, it
may be unrealistic to assume that imports enter only the
producing sectors as inputs and never go directly to final

consumption; for example, if a large consuming center is

18

located near the supplying region's boundary while the
production plants of a sector are located at the maximum
distance from that boundary, we would expect to find sup-
plies of finished goods being sent directly to the point
of consumption rather than the commodity being exported
as an input to the distant plants, converted into final

output and returned to the consumption center.

Operational Problems

 

A major drawback to the widespread application of
input-output models at the urban and regional levels is a
shortage of the requisite data. The successful implementa-
tion of an input—output model demands an extensive data
set which few other models need. Data are rarely published
in a form directly useful for regional input-output stud-
.ies, so the local analyst must collect all or some of the
data through empirical survey, or can attempt to produce
an inputdoutput table from the available published statis-
tics. The former option will clearly be-the most expensive,
the latter the least accurate, but often the most attrac-
tive from the cost point of view. It should be noted that
although survey based input-output tables are probably
more accurate than the nonsurvey or minimum survey table,
the former are frequently out of date when published,
since research workers rarely pay for the cost of continu-
ous updating. Thus, in most cases, nonsurvey tables may

have to be based upon out-of—date input-output tables.

CHAPTER III

RESEARCH METHODS

This chapter consists of six parts. The first is a
brief review of some previous reducing techniques which are
not appraised in this study. In the second part, the pro-
cedure and assumptions of the six reducing techniques
appraised in this study will be discussed. In the third
part, the procedure and assumptions of income multiplier
analysis are outlined. In the fourth part comparative
techniques employed in this study are presented. Part
five contains a description of the structure of the Lansing
Tri-County Region input-output tables. Finally, in the
sixth part, the procedure and assumptions of sector aggre-
gations adepted in this study are discussed.

Review of Some Previous Reducing Techniques
Which Are Not AppréiSed in this Study

 

Modification of National Technical Coefficients

 

These techniques involve the modification of national
coefficients as a result of detailed knowledge of certain
local characteristics obtained either from an empirical
survey or from published data. Into this cateogry can be

placed the work of Isard and Kuenne on Greater New York-

19

20

Philadelphia,1 and the work of Moore and Petersen on Utah.2

They obtained a crude transaction table by using national
direct coefficients to obtain sector columns from control
totals. They then adjusted the row and column distribution
for each industry in the light of regional production pro-
cesses, marketing practices and product mix.

Although in some respect this method could result in
a more realistic regional input—output matrix, the subjec-
tivity involved when changes are made in individual cells
makes it difficult to test the reliability of the table in
the absence of a survey based input-output table. The
only other possible evaluative test for this technique is

to assess the forecasting power of the table.

The Supply-Demand Pool Technique

 

Actually, this approach involves extending balance
of trade computations to construct a regional input-output
table. Commodity balances for each industry i is the dif-
ference between input requirements and locally produced
supply. If the commodity balance is positive, the national
production coefficient can be substituted for the regional
coefficient, sets imports to zero, and the surplus is

assumed equal to export. If the commodity balance is

 

1Isard, W., and R. E. Kuenne. 1953. The Impact of
Steel upon the Greater New York-Philadelphia Urban Indus-
trial Region. Review of Economics and Statistics 35:289—301.

 

2Moore, F. T., and J. W., Petersen. 1955. Regional
Analysis: An Interindustry Model of Utah. Review of Econ-
omics and Statistics 37:363-383.

 

 

21
negative, exports are set at zero, imports are calculated
as the difference between regional input requirements and
locally available requirement plus imports for final de-
mand and regional coefficients are estimated as:
a.. = A..(x./r.)

13 13 1 1
where aij is regional direct coefficient, A.. is the na-

1]
tional direct coefficient, xi is the regional output of in-
dustry i, and ri represents total regional requirements
(for inputs and final demand) of product 1. Thus, the re-
gional direct coefficient is obtained by multiplying the
national direct coefficient by the ratio of regional sup-
ply to regional demand of producing sector i.- This pro-
cedure allocates local production, where adequate, to meet
local needs. Where the local output is inadequate, to meet
local needs, however, the procedure allocates to each pur-
chasing industry j its share of regional output 1, based on

the needs of the purchasing industry itself to total needs

for output 1.

McMeanamin-Haring»Technique

 

In 1974, McMenamin and Haring proposed a new method
for estimating regional input-output tables.1 This method
is simple in application and cost effective in that it re-
quires little input data. It is only applicable to the

problems of estimating a regional table at one date (year 1)

 

lMcMenamin, D. G., and J. E. Haring. 1974. An
Appraisal of Nonsurvey Techniques for Estimating Regional
Input-output Models. Journal of Regional Science 14(2):
191-206.

22

based on similar table from an earlier point in time
(year 0). The technique adjusts the regional table at
year 0 for changes in price, the effect of substitution
and the effect of fabrication which have taken place be-
tween year 0 and year 1. First of all it is appropriate
to introduce some notations which are used in the discus-

sion of this technique,

X = xij = regional input-output table for year 0

Y = yi = vector of total gross output for year 1
Z = zj = vector of total gross outlay for year 1
X3 = xt, ij = the regional input-output table after

t/2 iterations

i = 1,2,...m = the number of rows, including the

payments sectors, and

j = 1,2,...n = the number of columns, including the

final demand sector.

First of all this technique adjusts the regional input-
output (year 0) for changes in relative prices, giving an
estimated table X*. The iterative procedure begins by
constraining the row sums of the gross flows (sales) in

X* to the associated total gross output:

The column sums of these row constrained gross flows
(purchases) are further constrained to the total gross

outlay:

23
n

These column-constrained gross flows can be constrained to
the total gross output. The technique alternates in this

fashion until in iteration number t/2,

n
xt-1,ij - (Yi/ kilxt'z’ik) (xt-Z'ij)
m
xt' ij = (zj/ kilxt~l'kj) (xt-l'ij)

The process is continued until the vectors of row and col-
umn totals for the estimated matrix have converged to within

e of the total gross output and total gross outlay,

The matrix thus obtained, X is the estimated regional

t'
input-output table for year 1.
The assumption behind the method are exactly par-

allel to those RAS processes, and thus it is subject to

the aggregation problem and uniform substitution effect. How-
ever, it avoids the problem of having to estimate the total
intermediate output and total intermediate input vectors.

The only data needed for the procedure are an inputéout-

put table for year 0 and total gross outlay vectors for

year 1.

24

Test of Accurapy of Regional
Nonsurvey Techniques

 

 

Morrison and Smith1 compare the results of the appli-
cation of several regional nonsurvey input-output tables
in a consistent way with a survey based input-output model
for the city of Peterborough, England. Their results are
tabulated in Table 1.

It is apparent from the table that the RAS method
produces a superior simulation when judged by some of the
measure distances. Of course, this is not entirely sur-
prising given that the technique employs certain amounts
of survey material. Some interesting features do emerge,
for example, the Simple Location Quotient technique emerges
as being superior to the Purchase Only Location Quotient
on all five tests. The Cross Industry Quotient approach
produced the poorest simulations on three most reliable
tests and ranked seventh out of eight on the other two.

It is perhaps a little surprising that the simplest of the
tested methods (SLQ) emerges, on the whole, as the best

of the purely nonsurvey approaches.

Reducinngechniques Appraised in this Study
In this part the procedure and assumptions of the six

reducing techniques tested in this study are discussed.

 

lMorrison, W. I., and P. Smith. 1974. Nonsurvey
Input-Output Techniques at the Small Area Level: An Eval-
uation. Journal of Regional Science l4(l):l-l4).

 

25

 

 

 

 

 

Table 1. Evaluation of Simulated Tables: Methods Ranked
for Each Test*
Test
Mean . Mean Infor-- .
Rank Absolute nggiiizion Similarity mation chire
Difference . Index Content q
1ent
1. RAS RAS RAS RAS RAS
2. SLQ SDP SLQ SLQ CMOD
3. POLQ SLQ POLQ POLQ SLQ
4. CMOD POLQ SDP CMOD POLQ
5. SDP CMOD CMOD CILQ CILQ
6. CILQ CILQ CILQ SDP SDP
*Source: Morrison, W. I., and P. Smith. 1974.
Nonsurvey Input-Output Techniques at Small
Area Level: An Evaluation. Journal of
Regional Science.l4(l):1-14)
Key initials of nonsurvey methods are as follow:

SLQ:
POLQ:
CILQ:
CMOD:
SDP:

RAS:

Simple Location Quotient

Purchase Only Location Quotient

Cross Industry Location Quotient

Modified Cross Industry Quotient

Supply—Demand Pool

RAS

26

The Simple Location Quotient Technique

 

The Location Quotient is a measure comparing rela-
tive importance of an industry in a region and its rela-

tive importance in the nation. Thus, for industry i,

where xi represents the regional output of industry 1, x

is the total regional output, X.

1 is the national output

of industry i and x is the total national output.

If LQi :11, we assume that local production is ade-

quate to supply local needs, then we may set aij Aij'
where aij is regional direct coefficient defined as
Xij/Xj' and Aij is the national direct coefficient defined
as xij/Xj' Knowing regional industry outputs xj and hav-

ing established aij’ we may compute regional interindustry

flow as:

Since, Aij = aij'

d A.. = X.. X.
an 13 13/ 3
then, xij = xij(xj/Xj)

If the remainder of local final demand is known, as the
region's share of national consumption, investment and gov-
ernment expenditure vector (yif = Yif - x/X), where f in-
dicates one of t final demand columns. Then, the exports

27
of industry 1 may be computed as a residual:

t

n
I x.. - Z yif
3

e. = x. - 13 f

l 1

If LQi < l, we assume that regional production is

inadequate to satisfy local needs, then we may set a.. =

1]
LQi-Aij, and regional gross flow as:
xi: = 313 *3
Since aij = LQi Aij’
and Aij = Xij/xj'
then x.. = x.. L . x. X.
13 13 Ql( 3/ 3)

Imports of product i (mij) are computed as the amount

necessary to satisfy production requirements,

mij : Aij xj - xij

The procedure just outlined empirically is grossly
deficient. There is no guarantee, for example, that local
production is adequate to satisfy local needs when LQi Z 1,
nor that local production is inadequate to supply local
needs when LQi < 1. Thus, because of the problems of these
assumptions, to insure success in using the Simple Loca-
tion Quotient technique, the local industry structure must
resemble the national structure, this requirement is

seldom met.

28

The Purchase Onlprocation
gpotient Technique

 

 

Due to problems encountered in using the Simple Loca-
tion Quotient technique, Charles Tiebout suggested a modif-
ication of that technique for the CONSAD Corporation to use

1

in constructing state input-output models. The Purchase

Only Location Quotient may be defined as:

!
xi/x

LQi = x.7x'

1

where the prime indicates that summation includes only the
outputs of those industries which purchase from industry i.
Formulations for computing regional direct coefficients

are not affected by the modification. The difference in
these approaches lies in the values of the location quo-
tients and thus in the determination of which industries
are export producing andwhich are not. We cannot predict
whether the Simple Location Quotient approach or the Pur-
chase Only Location Quotient approach will yield the larger

regional coefficients.

The Cross Industpy Quotient Technique

 

This quotient compares the proportion of national
output of selling industry 1 in the region to that for

purchasing industry j,

 

1CONSAD Corporation. 1967. Regional Federal Pro-
curement Study. United States Department of Commerce
Contract.

 

29

x./X.
CIQ..= 1 1
ij xj7Xj
If CIQ.. > 1, a.. = A.. for cell ij. Since the output of
13 —- ij 1]

industry i is larger than that of industry j in the region
relative to the nation, we assume that local industry 1

can provide all of the output required by local industry

j. The reason is, if industry 1 in the region is producing
a larger percentage of the national economy's product 1
than regional industry j is producing its product, it is
likely that industry j can obtain all the product i it
needs within the region. If CIQij < l, aij = CIQij’Aij.
The regional direct coefficients becomes the national dis-
tribution coefficient for industry i weighted by the ratio

of the regional size of the selling industry to that of

the purchasing industry.

The Modified SupplyrDemand Pool Technique

 

The pool technique has been modified in several ways.
Kokat suggested an alternative which adjusts the Supply-
Demand Pool technique for the case in which regional final

demands are predetermined.l

The Supply-Demand Pool is

not affected if commodity balances are positive. The dif-
ference arises when commodity balances are negative. Im-

ports are assumed to enter the region as inputs but never

for final demand, and exports are set at zero.

 

lKokat, R. G. 1966. The Ecopomic Compgpent of a
Regional Socioeconomic Model. IBM Technical Report 17-210,
IBM, Inc. Advanced System Development Division.

 

 

30

The procedure in this approach is as follows: Com-
pute input requirements based on national technology and

estimates of local output,

Given the final demand matrix for the region (Yif) compute

total regional demand for goods excluding exports (ei),

s t
r. = X r.. + 2 y-
i j 13 f if

Compute commodity balances (bi)'

where xi is total gross output of industry 1.
Where bi is positive, substitute the national direct coef-
ficient for regional coefficients, set imports at zero and

compute exports,

aij Aij

x.. r..
13 .1]

mij = 0

ei = (xij/xi) bi

Where bi is negative, compute imports (mij)’ set exports

at zero and compute regional flows and-coefficients,

31

S
mij = (rij/g rij) ’ b1
mij = (rij/(ri ’ Y1) (r1 ’ xi)

where yi is total final demand sector which can be treated
as a priori assumption. Regional flows are computed as

residuals,

.. .. m..
13 13 13
or

Xij rij (Xi - Yi)/(ri - Yi)

This expression indicates that to each purchasing industry
j we allocate its share of regional output i available to
producers, based upon the needs of purchasing industry it-

self relative to the needs of all purchasing industries.

gag
Stone and Brown,1 developed a method of estimating an
input-output table for a certain date (year 1) , from a table
constructed for an earlier date (year 0). This technique,
called the RAS method, obtains the estimated table through
adjustment of the direct coefficient, aij' of the base
year table to account for changes which have been taken

place between these two periods. These changes are of the

following three types: (1) changes in the relative level

 

lStone, R., and A. Brown. 1962. A computgble Model
of Economic Growth (A Progpamme for Growth 1). London:
Chapman and HdlIL

 

 

32

of prices, (2) changes in the degree to which commodity

i has uniformly been substituted for or replaced by other
intermediate inputs (called the substitution effect), and
(3) changes in the degree to which intermediate inputs

have uniformly increased or decreased in weight in the fab-
rication of commodity j.

In this study the RAS method has been adopted to the
problem of estimating regional input-output tables from
the national table. The adjustment process forms an iter-
ative procedure which has been shown to converge under cer-
tain conditions. The method requires the following data
as input: (1) the national direct coefficient matrix,

(2) the regional total gross output vector, (3) the regional
total intermediate input and intermediate output vectors.
Stone and Brown obtained the total intermediate input vec-
tor by subtracting the value added vector and import vec-
tor from the total gross output vector. They obtained
the-total intermediate output vector as the difference be-
tween the total gross output vector and the total final
demand vector.

Assumptions of the technique can be summarized as
follows:

(1) Price differences operate uniformly along rows,
whenever there is difference in the average
price of the products of a sector, it is charged
in the same proportion to all users.

(2) Whenever there is a substitution of one product

33

for another due to difference in demand or in-
dustry mix, it affects all users to the same
extent.

(3) Wherever there is a change in the degree of
fabrication, it unifromly affects all produc-
tive processes.

In the skeletal procedure below, the notational con-
ventions are that the lower case letters refer to vectors,
upper case letters refer to matrices, hatted letters de-
note diagonalized vectors, subscripts refer to successive
estimates, a prime indicates a transposed matrix, and i is
the identity vector. A is the matrix of national input-
output coefficients, and u, v, and x are vectors of re-
gional intermediate output, intermediate input and gross
output respectively.

In the first stage of the procedure, the national
input-output matrix is treated as a first estimate of the
regional table and is combined with the vector of regional
gross output to yield an estimated vector of intermediate

outputs. Thus,

u1 = Alx

The matrix is then adjusted to conform with row constraint

(u) .

A2 = uul Al

The matrix A2 is then used to estimate a vector of

34

intermediate inputs,

= ' I
v1 ixA2
The matrix is then adjusted to conform with the column

constraint (v),

A3 = szv

The matrix A3 is then substituted into 111 = Alx, and this
process is repeated until the matrix converges to a state
in which both row and column constraints are fulfilled.

The RAS method was tested in national level (Belgian
input-output table) by Paelinck and Waelbroeck.1 It seems
that the RAS method tends not to work very well, probably
because the method spreads any changes evenly along rows
and down columns and such spreading may be inappropriate.
Czamanski and Malizia, adopted the RAS method to the problem
of estimating regional input-output tables from national
tables.2 This study also measured the accuracy of the
estimated tables through the use of a summary of the "de-
viations between estimated and true regional input-output
coefficients.“ The authors concluded

It appears that although national input-output tables

cannot be used for the purposes of regional studies.

without considerable adjustments, acceptable results

can be achieved by the methods tried on the Washing-
ton State table.

 

lRichardson, Harry W. 1972. Op Cit., p. 175.

2Czamanski, S., and E. E. Malizia. 1969. Applicabil-
ity and Limitations in the use of National Input-Output
Tables for Regional Studies. Papers and Proceedings, Re-
gional Science Association 23:65-77, p. 77.

 

3S

Czamanski and Malizia are concentrating on obtaining the
interindustry direct coefficient. However, this is only
part of the bigger problem of estimating an entire regional
input-output table, which includes estimating final demand
by sector, value added and imports. Particularly trouble-
some in regional tables is the generation of imports and
exports by industry. Yet Czamanski and Malizia have ig-
nored these problems and have in fact assumed these sector
levels to be known. Thus, the accuracy tests performed by
them give results under the best possible conditions and
thus place a lower limit on the possible errors generated

by the method.

Schaffer-Chu Iterative Procedure
Schaffer and Chul have constructed input-output tables
from national tables using a technique that they called the

iterative simulation technique. The Regional Input-Output

Table (RIOT) simulator not only assumes that the national
direct coefficient applies, but also attempts to distribute
local production according to both the national sales
pattern and local needs.

Simply stated, they compute the required inputs
(rij) for producing estimated regional output (xj) for

each industry and estimate local final demand rij as a

 

lSchaffer, W. A., and Kong Chu. 1969. Nonsurvey
Techniques for Constructing Regional Interindustry Models.
Papers and Proceedings, Regional Science Associations
23:83-101.

36

proportion of national final demand. They then allocate
local sales for each industry, basing the initial step on
the national sales distribution pattern. Next, they use
an iterative process to reallocate local sales, row by
row until local production and consumption needs are
satisfied to the extent possible. If local output is in
excess of locally required sales for an industry, the ex-
ports are computed as a remainder. They record imports in
a matrix as the positive difference, for each cell in the
regional transactions matrix between local production re-
quirements and the local output available to meet these
requirements. This completes the computations for a re-
gional gross flow table.

In a more formal expression the procedure may be de-
scribed as follows:

(1) Compute purchases required to produce regional

output (rij), based upon national direct coef-

ficients matrix (Aij),

r.. = x.-A..
1] J 13
(2) Distribute regional sales (dij) initially by

national distribution,

dij = xi (Xij/xi)

(3) Compare requirements and allocations to deter-

mine surplus allocation to cells (zij) and con-

struct for each row i a pool of surplus

37

available for allocation (POOLi) and pool of
needed reallocations (NEEDSi). The final de-
mand matrix (zyif) is treated the same way;

therefore,

POOLi = sum of all pOSitive zij and zyif

NEEDSi = sum of all negative zij and zyif
(4) Allocate sales for industries with exportable

surpluses POOLi > —NEEDSi,

x.. = r..
13 1]

yif Cir

ei = POOLi + NEEDSi

Each buying industry receives all its needs of
product i and the remainder is exported.

(5) Reallocate local sales of industries with out-
puts insufficient to meet local needs (0 < POOLi

< -NEEDS.)
-' 1

zij is positive or zero,

xij = rij

When zij is smaller than zero, compute

38

xij = dij + POOLi (dij/Xi)

This procedure is iterated until POOLi goes to zero. When
POOLi is equal to zero there is nothing to add to dij;
thus, the iterations cease. This spreads the surplus of
local output among industries on the basis of relative
need.

In general, the Schaffer-Chu Iterative procedure
differs from the Supply-Demand Pool technique in attempting
to follow the national sales pattern to distribute local
output and in reallocating local sales from one cell to
another as necessary to best satisfy local needs. It
thus appears to represent the feasible maximum of local

trade.

Income Multiplier Analysis

 

The propagation effects of change in the level of
expenditure upon income in a region can be estimated by a
multiplier. The concept of the multiplier was first in-
troduced into economic theory by R. Kahn in his article
"The Relation of Home Investment to Unemployment" pub-

lished in the Economic Journal in June 1931. The multi-

 

plier concept was elaborated, adapted and made an import-
ant part of his theory of income and employment by J. M.

Keynes.l Both Keynes and Kahn dealt primarily with

 

lKeynes, J. M. 1935. The General Theory of Emplpy-
ment, Interest and Money. Harcourt, Brace ahd Co., New
York, pp. 112-131.

 

 

39

aggregate multipliers. In general, they were interested
in measuring the total income and employment changes in a
national economy resulting from exogenous changes in in-
vestment. Of course, such aggregate economic analyses
have become important guides to national economic policy
decisions.

Aggregate economic analysis is sufficient for many
purposes. But if we are interested in the impact of
changes in a single sector upon all other sectors, it is
necessary to go beyond the aggregative analysis. The
advantage of the input-output model is that it permits
the analyst to focus attention on individual sectors of
the economy. Given the available data--in the form of
production and consumption functions--it is possible to
compute income multipliers for the sectors defined by an

input-output table.

The Aggregate Income Multiplier

 

The general expression for the Keynesian income

multiplier is:

K=1-199-
AY
where:
K = the multiplier
AC = changes in consumption
AY = changes in income

The above equation indicates that aggregate income

4O

multiplier is a function of the marginal prOpensity to
consume. It is assumed that with each increment of income
there would be an increase in consumer spending, but that
some fraction of the increment to income would also be
saved. Thus, the marginal propensity to consume would al-
ways be less than one. Keynes made the further assumption
that as income continued to rise the propensity to consume
would become smaller. In this formulation of the multiplier
the only leakage is that to savings. It also indicates

that each injection of new income will produce successive

rounds of consumer spending.

Sectoral Income Multiplier

 

The technique for estimating a sectoral income multi-
plier is more complex than procedure described above. This
is true at the level of national economy, moreover the
difficulties are increased when sectoral income multipliers
are estimated for region, as have been done in this study.
The reasons are: (a) the requirement that a consumption
function for each regional sector must be computed,

(b) the problem of additional leakages which make estima-
tion of sectoral consumption rather difficult.

Sectoral income multipliers have been calculated
in some earlier input-output studies. However, the Moore

and Petersen,1 and Hirsch2 studies were pioneering studies

 

lMoore, F. T., and J. W. Petersen. 1955. Regional
Analysis: An Iterindustry Model of Utah. The Review of
Economics and Statistics. Vol. XXXVII, No. 4, pp. 368-383.

 

 

41

in regional input-output analysis, and they represent an
improvement over earlier input-output studies. In these
studies, however, only a limited number of sectoral con—
sumption functions were used, and these are based upon
national data. Thus, in neither case were the writers

able to show the leakages in consumer spending with given
increases in income and this imparted an upward bias to
their regional income multipliers. Although this is re-'
cognized by the author of this study, it was not possible

to make the necessary improvements, because of lack of data.

Two types of sectoral income multipliers have been
computed for this study: i.e., (1) Type I Multiplier,
and (2) Type II Multiplier. The Type I income multiplier
is the ratio of direct and indirect to direct income
change resulting from the delivery of one dollar to final
demand by a given sector. Type II multipliers are the
ratio of direct, indirect and induced to the direct in-
come change, resulting from the delivery of one dollar
to final demand by a given sector.

Thus the Type I multipliers should be considered as
first approximation, particularly for an "open" economy.
The Type II multipliers, which are larger in every sector
are more accurate estimates of the income changes pro-

duced in the region by changes in final demand. In other

 

2Hirsch, W. Z. 1959. Interindustry Relation of
A Metropolitan Area. The Review of Economics and Statis-
tics. Vol. XLI, No. 4, pp. 360-369.

42

words, the Type II multipliers show the effects of suc-

cessive rounds of consumer spending (including the induced

effects) in addition to the direct and indirect effects of

increases in sales to final demand.

The procedures for computing these multipliers can

be described as follows:

The Type I Income Multipliers

 

(l)

(2)

(3)

(4)

(5)

Define,

A

a 20 by 20 matrix of direct coefficients,

aij’ where the household sector is not in-

cluded in the processing sector.

»
ll

h a 21 by 21 matrix of direct coefficients,
h
13'
in the processing sector.

a , where household industry is included

Compute the Leontief inverse,

(I - A)’1

where I is an identity matrix.

Define Hr as the vector of direct income change,
where Hr is the household row of matrix Ah.
Calculate the direct and indirect income change

as:

(I - A)-l . Hr

Calculate indirect income change as: Direct
and indirect income change - Direct income

change (see Appendix B, Table 1-7, column 4).

43

(6) Compute the Type I income multiplier as:

Direct and indirect income change
Direct income change

 

The Type II Income Multiplier

 

(1) Define:

Ah = a 21 by 21 matrix of direct coefficients,
agj, where household industry is included
in processing sectors.

(2) Compute Leontief inverse using the augmented

matrix Ah,

-1

where I is an identity matrix.

(3) Define the direct, indirect and induced income
change as the household column of (I - Ah)-l.

(4) Compute Indirect and induced income change as:
Indirect income change + Induced income change
(see Appendix 7, Tables 1-7, column 7.

(5) Compute the Type II income multiplier as:

Direct, indirect, and induced income change
Direct income dhange

 

Comparative Techniques

 

An important part of this study is to establish and
select some objective means of evaluating the distance--
or relative distance--between matrices. In other words,

it is desirable to have some consistent test of judging

44

which of the estimated coefficients matrices is closest

to the equivalent survey based table. Indeed, this implies

that the coefficient of the survey based table are assumed

to be "true" (assume that no error exiSts).

In this study three comparative techniques are used
in evaluating the efficiency of each reducing technique.
Those are:’

(1) The mean absolute percentage deviation,

(2) The mean of relative change, and

(3) The mean of the similarity index.

First of all it is appropriate to introduce some

notations which will be used in the discussion of this

part,
aij = direct coefficient for the survey table
bij = direct coefficient for the estimated table
n = number of industries in producing sector
m = total number of direct coefficients.

The Mean Absolute Percentage Deviation

Define the absolute percentage deviation as:

Iaij ' bijl
dij — aij , for aij # O

 

The mean of these absolute is thus,

 

ij m

45

The standard deviation of these absolute percentage is:

 

m n 2 m n 2
s = Z 2 di' - ( Z 2 di')
i=1 j=l 3 i=1 j=l 3
This technique is not ideal, the diSadvantage is
that it cannot handle a situation where aij is zero and
bij is not zero--a situation which is not uncommon in
this type of study. In this case, such elements are
omitted in the calculation, and no credence is given to

actual estimated values. Instead, the technique is used

only as a tentative measure.

The Mean of Relative Change

Define the index of relative change as:

aij - bi.|
Rcij = 172(aij+hij)

 

The mean of these indexes of relative change is thus,

P45
Mb

Rij
= j=l i=1
RC m

 

A rather unconventional feature of this mean is that it
ranges from zero to two. The closer the value to zero,

the better the estimates.

46

Mean of the Similaritnyndex

 

The similarity index is defined as:

The value of this index ranges from zero to one. Of
course, the closer the value is to one the better the es-
timates.

The Structure of the Lansinngri-County
Region Input-Output Tables

 

 

In this part the structure of the Lansing Tri-County
Region input-output tables is discussed briefly. The more
elaborate discussion of this topic can be found in O'Donnel,
a 21.1

The Lansing Tri-County region input-output tables
consist of 24 intermediate demand or processing sectors
and six final demand or autonomous sectors. The process-
ing sectors are: (1) Livestock, Dairy and Poultry,

(2) Crops, Vegetables, Fruits, and Nuts, (3) Food and

Kindred Products, (4) Lumber and Furniture, (5) Printing

 

lO'Donnell, John L. 1960. Economic and Population
Base Study of the Lansing Tri-County Area: An Inter-
Industry Relation Analysis. Michigan State University,
319 p.

 

 

 

47

and Publishing, (6) Chemicals and Allied Products,

(7) Miscellaneous Nondurable Products, (8) Primary Metal,
(9) Fabricated Metal Products, (10) Machinery including
Electrical, (11) Motor Vehicles, (12) Miscellaneous Dur-
able Products, (13) Electric Power and Gas, (14) Transpor-
tation and Communication, (15) Wholesale Trade, (16) Retail
Trade, (17) Finance and Insurance, (18) Real Estate and
Rental, (19) PerSonal Services and Amusements, (20) Bus-
iness Services, (21) Repair Services, (22) Medical and
Other Professional Services, (23) Education and Non-Profit
Organizations, and (24) Mining and Others.

The final demand sectors are: (1) New and Mainten-
ance Construction, (2) Non-Competitive Imports, (3) Federal
Government, (4) State and Local Governments, (5) Gross
Private Capital Formation, and (6) Households.

The aggregation scheme adopted in this study, as
well as the definition for each category will be presented
in Table 2.

It is not possible to make definite appraisal in
general about the accuracy of the entries in the table.

On the average 60 percent of the inputs of the processing
sectors were obtained by direct survey method. Wherever

possible the data in the table cover the calendar year of
1958, but in some cases some small and medium sized firms
reported fiscal year of 1958 data.

The numbers in the transaction table are in thou—

sand dollars, each set of numbers in particular column

48

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50

represents the purchases or receipts of the sector name in
the caption (at the tOp) from the sectors listed at the
left side (in the stubs). Conversely, the set of numbers
in a particular row represents the sales of the sector
named in the stub to the sectors listed in the column cap-

tions.

Sector Aggregations

 

Most of the practitioners of input-output analysis
are aware of the importance of the aggregation problem and
the fact that results of the analysis depend upon the aggre-
gation procedures employed. The purpose of introducing the
aggregation process into input-output analysis is to reduce
the number of equations and unknowns. A user of input-
output analysis often needs to reduce a given table to
smaller size. A large tabel--say 100 by 100--is cumber-
some for many purposes. It should be recognized, however,
that if the results are to be useful, the system must be
reduced to manageable size and yet still must describe
significant relationships between many components of the
aggregates. It is even possible that the particular infor-
mation lost may be of greater importance than the more gen-
eral information available in the solution made possible
by aggregation. Thus, the aggregation decision involves
a trade off between information lost due to aggregation and
cost of data analysis.

The sector aggregation decisions in this study are

51

based upon several considerations, i.e.:

(l)

(2)

(3)

The purpose of the study. The purpose of this
study is to evaluate six nonsurvey and minimum
survey reducing techniques for estimating the
Lansing Tri-county region input-output table.
In general, a very detailed input-output table
is not necessary for testing reducing techniques,
because results of this study cannot be used
directly to guide policy making.

The nature or sector detail of the base model
input-output analysis in this study is based on
a 87 sector model of national input-output for
1958. Working with a 87 by 87 matrix is not
only cumbersome but also expensive.

Cost of data analysis. Budget available for
this study is very limited, and the cost of
inverting a matrix rises exponentially with

the size of the matrix.

In this study, two base model matrices were used,

(1)

(2)

A 87 by 87 matrix of 1958 National input—output
table.
A 24 by 24 matrix of 1958 Tri-county Region

input-output table.

The purpose of the aggregation procedure in this

study is to reduce the size of both matrices to a 20 by 20

standard matrix (that is the size of matrix we used in

52

this study). The reason for adopting this aggregation
scheme is that even if in general the national table is
less aggregated than the regional table, for some specific
sectors the regional table is more detailed (e.g., sectors
number 22 and 23 of 1958 Tri-county region matrix). Thus,
these sectors must be aggregated to match the corresponding
national sectors. The entire sector aggregation scheme

is shown in Table 2.

As illustrated in Table 2, four aggregations have
been performed in reducing the 24 by 24, 1958 Tri-county
region matrix to a 20 by 20 standard matrix. The four
aggregations are:

(1) Sector number 2 and number 3 of the Tri-county
matrix (the Crops, Vegetables, Fruits, and Nuts;
and Food and Kindred Products respectively) have
been aggregated into one sector and termed Other
Agricultural, Fishery Products and Services.

(2) The Wholesale and Retail Trade sectors (sector
number 15 and 16 respectively) of 1958 Tri-
county matrix have been aggregated into one
sector, that is the Wholesale and Retail Trade
sector (sector number 14 in the standard matrix).

(3) The Finance and Insurance; and Real Estate and
Rental sectors (sector numbers 17 and 18 re-
spectively) of 1958 Tri-county matrix have been
aggregated into one sector, that is the Finance,

Insurance, Real Estate and Rental sector

53

(sector number 15 of the standard matrix).

(4) Sector numbers 22 and 23 (Medical and Other Pro-
fessional Services; and Education and Nonprofit
Organizations sectors respectively) of 1958
Tri-county matrix have been aggregated into one
sector--Medical, Educational and Nonprofit
Organizations--that is sector number 19 in the
standard matrix.

In order to be compatible with these aggregations, the

87 by 87 endogenous sectors of 1958 national matrix have
been aggregated, following guide lines as suggested by Cen-
sus of Employment data.

Before discussing results of this study, it is appro-
priate to point out some assumptions made in preparing the
study area input-output model from the national model.

Assumption 1. Sector composition of the study area
is similar to the national sector composition.

Sectors are composed as a rule, of firms having sim-
ilar input requirements. To the extent that a sector at
the regional level contains firms with different input re-
quirements from those in the nation, some aggregation er-
rors may be introduced to the results of the study. The
greater the aggregation, the less troublesome will be a
violation of this assumption; but also the less detailed
will be the conclusions, which can be drawn about a spec-
ific industry.

Assumption 2. The production function of any sector

54

i is similar in the study area as for in the nation.

This implies that all inputs produce with the same
degree of efficiency in the region as in the nation. It
leaves cpen the possibility that some industries will have
to import from outside the region. The reducing techniques
tested in this study contain mechanisms to adjust the co-
efficients for imports (if the region industry 1 is able
to supply only half of the total requirements of other en-
dogenous industries for product i, the remainder will be

imported).

CHAPTER IV

RESULTS AND DISCUSSION

This chapter consists of three parts. In the first
part the assumptions of the six data reducing techniques
appraised in this study will be discussed and compared.
The second part will concern the relative efficience of
each reducing technique in estimating the regional direct
coefficients derived from the national tables. Finally,
in the third part, the relative efficiency of each reduc-
ing technique in estimating the value of the Type I and
the Type II multipliers is evaluated.

The six reducing techniques tested in this study em-
ploy mechanical routines to adjust the direct coefficients
of the United States model to reflect the economic struc-
ture of the Tri-county region.

The six methods differ in their data requirements.
The first three methods, i.e.: the Simple Location Quo-
tient, the Purchase Only Location Quotient, and the Cross
Industry Quotient, require only the total gross output fig-
ures for each industry in the study area. The Supply-
Demand Pool and the Schaffer-Chu Iterative techniques re-

quire the total gross output and the final demand data of

55

56

the study area which are estimated from the final demands
of the United States model. The last technique, the RAS,
requires not only the total gross output, but also the total
intermediate input and total intermediate output of every
industry in the study area.

Each technique involves different costs, however,
the RAS technique is the most costly because it employs a
certain amount of survey data.

The Assumptions of the Six Reducing
Techniques Compared

 

 

As may be expected, the relative efficiencies of
reducing techniques is adjusting the national input-output
model to reflect the economic structure of the Tri-county
region differ from one another. These differences are due
to differences in assumptions. Thus, it is important to
discuss and compare the assumptions of each technique.
This may facilitate the interpretation of the results of

this study.

The Simple Location Quotient Technique

As has been pointed out earlier, the Location Quo-
tient is the ratio between the percentage of total output
supplied by industry i in the region, and the percentage
of total output supplied by industry i in the nation. Thus,
a location quotient of unity for industry 1 means that the
region has its proportionate share of the entire production

of industry in the nation economy judged in terms of total

57

regional production, relative to total national production.
Then, if LQi Z 1, it is assumed that the region is
producing more than its local consumption and has product
available for exports. If LQi i 1, regional production is
assumed to be inadequate to supply local requirements; so
that imports are necessary. The reader must be aware of the
limitations of these assumptions. These assumptions must
be seriously qualified. Indeed, there is no guarantee that
a surplus for exports will exist when LQi i 1, nor that
local production is inadequate to supply local needs, in
case LQi < l. The reasons are: (1) tastes and propensity
to consume among households of the same type and income
differ between region. In Southern Florida, little fuel
is needed by households; in Michigan greater amounts. This
means that for the fuel manufacturing sector, a location
quotient of one for Southern Florida may involve exports of
fuel, and for Michigan it will most likely involve major
import of fuel oil; (2) income levels of households differ
among regions. Families in Michigan consumed, per house-
hold, more shoes than is the case in Georgia. Given this,
a location quotient more than one in Michign for the shoe
manufacturing industry could be consistent with imports of
shoes, meanwhile, a location quotient below unity in Georgia
may result in net exports; (3) production efficiency dif-
fer among regions, and (4) industrial mixes vary consider-
ably among regions.

The shortcomings of these assumptions have far

58

reaching implications for the direct coefficients genera-
ted by the Simple Location Quotient technique. It has been
described earlier that if LQi 1 1, that the regional dir-
ect coefficient is identical to the national direct co-
efficient; and if LQi < l, the regional direct coefficient
is equal to LQi times the national direct coefficient.
Thus, the national direct coefficient can only be adjusted
downward but not upward. As a consequence, this method
cannot handle adequately a situation where a "true" re-
gional direct coefficient is far larger than the correspond-
ing national direct coefficient. The downward adjustment
process in this procedure also has some drawbacks. To i11-
ustrate this, we may define aij as the regional direct
coefficient, and Aij as the national direct coefficients of
row i. Even if aij is larger than Aij' in a case of
LQi < 1, it follows that Aij must be adjusted further down-
ward. Thus, the adjustment process is based upon "average
variation" among rows and cannot handle variations within
a row. This discussion suggests that the Simple Location
Quotient technique is likely to give satisfactory results,
that is, it generates regional direct coefficients that
adequately represent the region's economic structure or
sectoral linkages when the local industry structure closely
resembles the national model structure.

The preceeding discussions regarding the problems
of the Simple Location Quotient technique does not mean to

suggest that the Simple Location Quotient technique is

59

useless, but rather to point out some of its limitations,
so that the reader is aware of the problems of this tech-
nique.

The location quotient for each industry in the Tri-
county region has been calculated in this study and the
results are presented in Table 3.

As can be observed from Table 3, on the surface it
would appear that only two industries--(l) Motor Vehicles,
and (2) Medical, Educational Services and Nonprofit Or-
ganizations--whose location quotients are more than unity,
are exportrindustries, and the rest (18 industries) whose
location quotients are less than unity are import indus-
tires. This statement must be partially rejected. Indeed,
the "Motor Vehicles" and the "Medical, Educational Ser-
vices, and Nonprofit Organizations" are export industries.
However as the survey based table revealed,l there are
three more export industries-~(l) Other Agricultural, Fish-
ery Products, and Services, (2) Chemical and Allied Pro-
ducts, (3) Finances, Insurance, Real Estate and Rental—-out
of the 18 industries, whose location quotients is less than
unity. Thus, it may be concluded that, even if an indus-
try's location quotient is smaller than unity, it is not
necessarily an import industry.

Based upon the location quotient in Table 3, the es-

timated direct requirement per dollar of output were

 

1O'Donnel, John L., pp al., 1960, gp_cit., p. 256.

6O

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61

developed for the Tri-county region and the results are
presented in Appendix A-l.

Estimated regional direct coefficients are compared
with "true" regional direct coefficients later in this
chapter. However, at this stage, it is appropriate to com-;
pare statistical characteristics of the estimated coeffici-
ents to the true direct coefficients. The comparison is
presented in Table 4.

Table 4. The Statistical Characteristics of the "True"
Direct Coefficients (Survey Method) Compared to

the Statistical Characteristics of the Estimated
Direct Coefficients (SLQ)

 

 

 

Techniques
Characteristics 1 2
DSM SLQ
Mean .019 .009
Variance .002 .001
Standard deviation .050 .024
Kurtosis 31.249 62.153
Skewness 5.191 6.830
lDSM = Direct Survey Method
2SLQ = Simple Location Quotient

As shown in Table 4, the Simple Location Quotient
technique on the average, underestimates the regional dir-
ect coefficients by around 50 percent. And, it follows

that both variances and the standard deviation are

62

underestimated by 50 percent also. Indeed, this is not
really surprising, because only two sectors--(l) Motor
Vehicles, and (2) Medical, Educational Services, and Non-
profit Organizations--out of 20 sectors, have location quo-
tients greater than unity. Thus, the estimated direct co-
efficients of these two sectors remained identical to the
United States coefficients, since in these two sectors ade-
quate local production is available to meet both proces-
sing and final demands requirements. The estimated direct
coefficients of the other 18 sectors were computed by ad-
justing downward the corresponding national direct coef-
ficient by the average of their location quotients.

Kurtosis is that property of a distribution which ex-
presses its relative peakedness. The greater the value of
kurtosis, the more peaked will be its distribution. A
normal distribution has a kurtosis value of 3, and is called
mesokurtic. If the kurtosis is greater than 3, as in this
case, the distribution is called leptokurtic. As seen in
Table 4, the kurtosis of the estimated direct coefficients
produced by the Simple Location Quotient is almost two
times as large as the kurtosis of the "true" regional dir-
ect coefficients.

Skewness means lack of symetrical distribution. A
negative sign indicates that the tail of the distribution
is skewed to the smaller values. If the sign is positive,
as in this case, the distribution will be skewed to the

right. Thus, the mean is located to the right of the mode

63

and the median.

To help understand the implications of differentials
in value of kurtosis, we may perceive the distribution of
estimated direct coefficients consists of three areas:

(1) area around its mean, (2) area between area 1 and its
minimum, and (3) area between area 1 and its maximum. In
this case, the shape of the distribution of the estimated
direct coeffiCients is more peaked than the distribution of
the "true" direct coefficients. This means that while the
Simple Location Quotient technique overestimates the value
of the direct coefficients around its mean, this technique
underestimates the direct coefficients in area 2 and area 3.

The Purghase Only Location Quotient
(POLQYiTechnique

 

 

In essence, the Purchase Only Location Quotient is
not so different from the Simple Location Quotient, thus
it also inherits most of the drawbacks of the Simple Loca-
tion Quotient technique. The difference is in summation of
total gross output of both the region and the nation. In-
stead of using total gross output of the region and the
nation in computing the location quotient, this technique
uses only the total output of the industries which purchase
from industry 1. The formulas are not presented here, be-
cause they have been presented in Chapter III.

This technique generates either a larger or smaller
estimated direct coefficient than the Simple Location Quo-

tient depending upon the size of the output of the

64

industries which are exluded, both at regional and national
levels.

Theoretically there are at least two advantages of
this method over the Simple Location Quotient approach.
They are:

(1) By this procedure, the adjusted coefficient is
not affected by large outputs of industries
which are not directly related to the selling
industries.

(2) This technique can handle a situation where the
needs of regional industries for output i, rel-
ative to the needs of the national industries
for output 1, are not the same as the ratio of
total regional to total national output, a
situation which the Simple Location Quotient
technique can not handle adequately.

The Purchase Only Location Quotient for each industry
in the Tri-county region has been computed, and presented
in Table 3. The regional direct coefficients generated by
this method are presented in Appendix A-l.

The statistical characteristics of the direct coef-
ficients produced by the Purchase Only Location Quotient
have been computed. In Table 5, these characteristics are
compared to the statistical characteristics of the direct
coefficients obtained from the direct survey table.

Compared to the Simple Location Quotient, estimates

generated by the Purchase Only Location Quotient differ

65

Table 5. The Statistical Characteristics of the "True"
Direct Coefficients (Survey Method) Compared to
the Statistical Characteristics of the Estimated
Direct Coefficients (POLQ)

 

 

 

Techniques

Characteristics 1 2

DSM POLQ
Mean .019 .010
Variance .002 .001
Standard deviation .050 .027
Kurtosis 31.249 52.828
Skewness 5.191 6.443

1

DSM = Direct Survey Method

2POLQ = Purchase Only Location Quotient

slightly in two major characteristics: the mean and the
kurtosis. The mean of estimates generated by the Purchase
Only Location Quotient is slightly larger, but its kurtosis
is smaller.

This situation can be explained by the value of the
Purchase Only Location Quotient, relative to the Location
Quotient (see Table 3). In comparison to the values of
the Location Quotient, the values of the Purchase Only
Location Quotient are similar in 9 sectors, slightly larger
in 9 sectors, and more than unity in two sectors. Thus,
direct coefficients for both methods are similar in 11 sec-
tors, because when the quOtient is larger than unity, value

of the estimated direct coefficients are identical to the

66

national coefficients. Thus, difference occurs only in
9 sectors. That is probably the reason the mean of the
estimated direct coefficients generated by the Purchase
Only Location Quotient are just slightly larger than the
mean of those coefficients generated by the Simple Location
Quotient. In contrast the kurtosis and skewness of direct
coefficients generated by the Purchase Only Location Quo-
tient are slightly smaller than those generated by the
Simple Location Quotient.

The foregoing discussion indicates that this tech-
nique makes only marginal impacts upon the results, as

compared to the Simple Location Quotient technique.

The Cross Industpy Quotient (CIQ) Technique

One of the potential drawbacks of the Location Quo-
tient technique is that only the size of the selling in-
dustry is taken into account, although theoretically the
relative size of the purchasing industry may also be of
crucial importance. An advantage of the Cross Industry
Quotient technique is that it enables import proportions
to vary within the rows, whereas the Simple Location Quo-
tient technique establishes import needs in constant pro-
portion to the appropriate rows. The Cross Industry Quo;
tient compares the proportion of national output of selling
industry 1 in the region to that of the purchasing indus-

h

try j. The ijt cell of the national direct coefficient

matrix is then adjusted according to the corresponding

67

cross industry quotient, as has been discussed in Chapter
III.

The cross industry quotient for each cell of the
transaction matrix has been computed in this study and then
used to estimate the direct coefficient matrix for the Tri-
county region. The direct coefficient for the Tri-county
region generated by this method is presented in Appendix
A-l. The summary of the statistical characteristics of
these estimates is presented in Table 6.

Table 6. The Statistical Characteristics of the "True"
Direct Coefficients (Survey Method) Compared to

the Statistical Characteristics of the Estima-
ted Direct Coefficients (CIQ)

 

 

 

Techniques
Characteristics 1 2
DSM CIQ
Mean .019 .022
Variance .002 .003
Standard deviation .050 .054
Kurtosis 31.249 20.142
Skewness 5.191 4.309
1DSM = Direct Survey Method
2CIQ = Cross Industry Quotient

As can be seen from Table 6, in contrast to the
Simple Location Quotient and the Purchase Only Location

Quotient, the Cross Industry Quotient overestimates the

68

direct coefficients in an average of about 25 percent.

While the two location quotient techniques adjust the na-

tional direct coefficients downward drastically, the Cross

Industry Quotient tends to overestimate the regional direct

coefficients.

There are some reasons why the Cross Industry Quo-

tient technique overestimates the regional direct coef-

ficients:

(1)

In contrast to the location quotient techniques,
the adjustment process in the Cross Industry
procedure takes place within the rows. Hence,
there is a tendency that the Cross Industry
Quotient will take more national direct coef-
ficients than the location quotient techniques.
For example in this study the estimated direct
coefficients generated by this technique are
similar to the national direct coefficients in
222 cells. In contrast, the estimated direct
coefficients produced by the Simple Location
Quotient and the Purchase Only Location Quotient
are similar to the national direct coefficient
in only 40 cells each. If the average of the
national direct coefficients is significantly
larger than the average of the regional direct
coefficients, like in this study, then there is
a tendency of the Cross Industry Quotient to

overestimate the regional direct coefficient.

69

(2) The Cross Industry Quotient has a very dis—

tinct property, that is:

CIQij = LQi/LQj

Clearly, if i = j, it follows that LQi = LQj. Thus,
for every cell where i = j (those diagonal cells) the value
of CIQij is unity and the estimated direct coefficient for
the cells is identical to the corresponding national dir-
ect coefficients. In other words, the implicit assumption
is made that every sector can obtain all its requirements
of output from its own sector locally, regardless of the
size of the sector. It is felt by the author that this is
a somewhat misleading assumption to make, particularly for
a relatively small sector.

From the discussion it may be concluded that:

(1) there is a tendency that the Cross Industry Quotient
overestimates the regional direct coefficients; (2) the
average of the estimated regional direct coefficients gen-
erated by this technique is the closest to the average of
the national direct coefficients as compared to those dir-

ect coefficients generated by the other methods tested in

this study.

The Modified Supply-Demand Pool Technique

 

The Modified Supply-Demand Pool technique relies on
computing the commodity balance between regional output of

good i and the local requirements of good i. The local

7O

requirement of good i is estimated by using national direct
coefficients. If the commodity balance is positive, it is
assumed that regional supply is sufficient to satisfy re-
gional demand and that the national direct coefficients may
be used in row i of the regional trade coefficients matrix.
When the commodity balance for row i is negative it is
assumed that the regional demand is larger than regional
supply and importation of good i is necessary. In this
case, the national direct coefficients of row i are re-
duced by the ratio of regional output to the regional re-
quirement.

The Tri—county regional direct coefficients ahve been
estimated by using this technique and the results are pre-
sented in Appendix Table A-1.

Before comparing the relative performance of the
Modified Supply-Demand Pool technique to performance of the
other reducing techniques in estimating regional direct
coefficients, it is appropriate to discuss briefly the
statistical characteristics of estimates produced by this
technique (Table 7).

As can be seen from Table 7, the Modified Supply-
Demand Pool technique is similar to the Location Quotient
technique in underestimating the regional direct coeffici-
ents. As in the Location Quotient technique, in this pro-
cedure downward adjustments of national direct coefficients
are carried out if the balance of commodities for that row

is negative. The estimated value of direct coefficients

71

Table 7. The Statistical Characteristics of the "True"
Direct Coefficients (Survey Method) Compared to
the Statistical Characteristics of the Estimated
Direct Coefficients (MSDP)

 

Techniques

 

Characteristics 1 2

DSM MSDP
Mean .019 .022
Variance .002 .001
Standard deviation .050 .033
Kurtosis 31.249 29.545
Skewness 5.191 4.834

 

lDSM = Direct Survey Method

2MSDP = Modified Supply-Demand Pool

is identical with the value of national coefficients if
the balance of commodities is positive. Thus, the national
direct coefficients would never be adjusted upward. The
difference between the Modified Supply-Demand Pool tech-
nique and the Location Quotient technique lies in the dif-
ference of factors used to adjust the national direct co-
efficients downward. In Location Quotient techniques the
value of the location quotient is used, while in the Mod-
ified Supply-Demand Pool technique, the ratio of regional
output and regional requirement is used. Since the ratio
of regional output and the regional requirement average
larger than the average of the location quotients, the

mean of the estimated direct coefficient produced by the

72

Modified Supply-Demand Pool technique is larger than the
mean of the same coefficient generated by the Location

Quotient technique.

RAS Me thod

 

As has been pointed out in Chapter II, the RAS
method was developed for the purpose of projecting input-
output tables, using a base period matrix and projection
period row and column totals introduced as constraints.

In this study the RAS method has been used to project the
1958 national input-output table to regional dimensions by
being made to conform with regional constraints. This
study involved the use of the following sources of data:

(1) 1958 Tri-county region total gross output (x)

(2) 1958 Tri-county region total intermediate

output (u)
(3) 1958 Tri-county region total intermediate input
(V)
(4) 1958 The United States input-output coeffici-
ents (Aij)
The regional data were obtained through direct survey.

The logic of this technique is simple. The adjust-
ment process forms an iterative procedure. Each stage of
iteration generates a new estimated total intermediate out-
put and total intermediate input. The ratio of regional
total intermediate output to estimated total intermediate
output is used as an adjustment factor for corresponding

rows. Likewise, the ratio of regional total intermediate

73

input to estimated total intermediate input is used as an
adjustment factor for associated columns. Thus, adjust-
ment processes take place in two directions, row and column.
At some stages of iterations, in this study after 12 iter-
ations, the value of estimated total intermediate output
equals the value of regional total intermediate output, and
in parallel the value of estimated total intermediate input
equals the value of regional total intermediate input.

Thus, the adjustment factor for both rows and columns
reaches unity and the iterative process ceases.

This method has been used to estimate the Tri-county
regional direct coefficients, and the results are presented
in Appendix Table A-1.

The direct coefficients estimated by the RAS method
will be compared to the "true" direct coefficients computed
from survey table in the second part of this chapter. At
this stage it is appropriate to compare their statistical
characteristics. This comparison is presented in Table 8.

As can be seen from Table 8, the RAS method in aver-
age underestimates the value of direct coefficients. How-
ever its kurtosis, was almost two times the kurtosis for
the "true" direct coefficients. This means the distribu-
tion shape of direct coefficients produced by the RAS method
is more peaked than the distribution of "true" direct co-
efficients. To explain this situation, the frequency dis-
tribution of "true" direct coefficients can be divided into

three areas: (1) area around its mean, (2) area between

74

Table 8. The Statistical Characteristics of the "True"
Direct Coefficients (Survey Method) Compared to
the Statistical Characteristics of the Estimated
Direct Coefficients (RAS)

 

 

 

Techniques
Characteristics 1 2
DSM RAS

Mean .019 .015
Variance .002 .003
Standard deviation .050 .053
Kurtosis 31.249 51.936
Skewness 5.191 6.969

lDSM = Direct Survey Method

2RAS = RAS

area 1 and its maximum, (3) area between area 1 and its
minimum. Information from Table 8 suggests that while the
RAS method underestimates the value of direct coefficients
in area 2 and area 3, this method underestimates the value
of direct coefficients in the area around its mean.

Because the total frequency of distribution in area
2 and area 3 is larger than the total frequency in area
1, the RAS method on the average tends to underestimate the

"true" regional direct coefficient.

Schaffer-Chu Iterative Method (SCM)

 

The first step in the Schaffer-Chu technique is to

calculate inputs requirements for producing regional output

75

j by using national direct coefficients. Then, regional
sales are distributed in accordance with the national

sales distribution patterns. Next, requirements and sales
are compared, and a pool of surplus available for reallo-
cations are constructed for each row i. If Pooli is larger
than Needsi, each buying industry receives all its require-
ments of product i, and the excess is exported. On the
other hand, in sectors where pooli is smaller than needsi,
the pool is spread by an iterative process among indus—
tries in accordance with their relative need, until pooli
diminishes to zero. In this study, pooli diminishes to
zero after two iterations and then the iteration process
ceases.

The estimated direct coefficients obtained by using
this method are presented in Appendix Table A-1.

The value of estimated direct coefficients will be
compared to the "true" direct coefficients (obtained from
the survey table) later in the second part of this chapter.
At this point, however, it is appropriate to compare the
statistical characteristics of the estimated direct coef-
ficients to the statistical characteristics of the "true"
direct coefficients. This comparison is presented in
Table 9.

As illustrated in Table 9, the Schaffer-Chu tech-
nique on the average overestimates the value of direct
coefficient by around 40 percent. This situation can be

analyzed in relation to the kurtosis of both distributions.

76

Table 9. The Statistical Characteristics of the "True"
Direct Coefficients (Sruvey Method) Compared to
the Statistical Characteristics of the Estimated
Direct Coefficients (SCM)

 

 

 

Techniques
Characteristics 1 2
DSM SCM
Mean .019 .026
Variance .002 .003
Standard deviation .050 .056
Kurtosis 31.249 15.799
Skewness 5.191 6.513
lDSM = Direct Survey Method
2SCM = Schaffer—Chu Iterative Procedure

The distribution of "true" direct coefficients is more
peaked than the distribution of the estimated direct coef-
ficients. Assuming that the distribution of the regional
direct coefficients consists of three parts: (1) area
around its mean, (2) area between area 1 and its maximum,
and (3) area between area 1 and its minimum. The informa-
tion from Table 9 suggests that while underestimating the
direct coefficients around its mean, the Schaffer-Chu
technique overestimates the regional direct coefficients
in area 2 and area 3. Because the total frequency of dis-
tribution in area 2 and area 3 is larger than the total
frequency distribution in area 1, therefore the Schaffer-

Chu technique on the average overestimates the value of

77

direct coefficients. The difference in skewness is not
singificant. Thus, the differences in the mean of direct
coefficients generated by these methods may be attributed
to the differences in kurtosis.

Comparisons of Relative Efficiency of the Six

Reducing Techniques in Estimating
Direct Coefficients

 

In this section, relative efficiencies of the six
techniques tested in this study are compared. Relative
efficiency means the degree of closeness in value of direct
coefficients generated by each technique to the "true"
direct coefficients obtained from the direct survey (assum-
ing zero error).

The relative efficiency of each reducing technique
has been judged by using three comparison tests. These
are: (l) the mean absolute percentage deviation, (2) the
mean of relative change, and (3) the mean of similarity
index. The prOperties of the comparison tests have been
discussed in Chapter III. However, to facilitate interpre-
tations of the results of this study, it is appropriate to
discuss elaborately the properties of the comparison tests
used in this study.

Throughout the discussion of this chapter aij is
defined as the direct coefficient of the direct survey
table, and bij as the direct coefficient of the estimated
table.

The first comparison technique employed in this study

78

is the mean absolute percentage deviation (dij). The dij

can be defined as follows:

[a.. = b..|
d.. = 11 ll_
13 a..
13
Two advantages of this statistic are that it is
easy to calculate and to understand. For example, a dij
equal to .50 means that the deviation is equal to 50 per-
cent of the "true" direct coefficient. However, this tech-
nique is deficient in other properties. The most serious
deficiencies of this technique are:
(1) It can not handle a situation in which aij is
equal to zero and bij is positive. In this
., d.. is
J 1]
infinite if aij is zero. Thus, in the situation,

case, regardless of the value of bi

where aij is zero and bij is also zero no credit
is given to the relative efficiency of the re-
ducing technique. Because a zero aij is not
uncommon in this type of study, this technique
is likely not ideal.

(2) Deviations between small coefficients affect
the results far more than deviations between
large coefficients. In other words, this
technique may give different weights to the
same absolute percentage deviation. To make
clear this deficiency, one might consider two

cases:

79

Case No. l

 

 

 

 

Let a.. = .100
l]
b.. = .001
13
Thus,
_ L.100 - .001] _
Case No. 2
Let a.. = .001
13
b.. = .100
13
Thus,
_ .001 - .100 _
dij - .OOId’ — 99.000

If we compare case No. 1 and No. 2, it is clear that even
if the absolute deviations are the same in both cases,
that is .099, the dij of case No. 2 is one hundred times
larger than dij of case No. 1. In interpreting the re—
sults, the reader must be aware of this problem.

The second comparison technique used in this study
is the mean of relative change. This technique lacks some
of the deficiencies inherent in the mean absolute percent—
age deviation technique. The mean relative change (Ri.)

3
can be defined as follows:

Advantages of this technique are:

(1) It could handle a situation where aij is equal

80

to zero.

(2) Deviations between small coefficients affect
the results in the same degree as with between
large coefficients.

However, this technique is deficient in another re-
spect, that is, it ranges in value from zero to two. This
value is not only awkward but also confusing.

The third technique, the mean of similarity index,
is the most satisfactory comparison technique used in
this study. The similarity index can be defined as fol-
lows:

Iaij_- b
Sij=l'(a..+b
13

J__
)

i.)
ij

It should be recognized that the closer the value of Sij
to unity, the better the relative efficiency of the par-
ticular reducing technique.

In general, this technique lacks the deficiencies
inherent in the first two comparison tests (this technique
can handle a situation where aij is equal to zero, and its
value is not confusing because it ranges from zero to one,
however it is somewhat difficult to compute.

The direct coefficients produced by the six reducing
techniques tested in this study have been judged by using
the three comparison tests outlined earlier, and the re-
sults are presented in Table 10.

Based upon data in Table 10, the six reducing tech-

niques have been ranked in accordance with their relative

81

Table 10. Comparisons of the Relative Efficiency of the
Six Reducing Techniques Used in This Study

 

Comparison Techniques

 

Reducing

Techniques The mean abso- The mean of The Mean of

 

 

lute percentage relative similarity
deviations change index
SLQ 1.099 .987 .507
POLQ 1.126 .980 .510
CIQ 2.230 .940 .530
MSDP 2.798 .942 .529
RAS .9399 .694 .653
SCM 1.759 .857 .572
l

SLQ = Simple Location Quotient; POLQ = Purchase
Only Location Quotient; CIQ = Cross Industry Quotient;
MSDP = Modified Supply-Demand Pool; RAS = RAS; SCM =
Schaffer-Chu Iterative Procedure.

efficiency, and the results are presented in Table 11.

As can be seen from Table 10 and Table 11, it is
apparent that the RAS method produces the best estimates
when judged by any of the three comparison techniques.
Indeed, this seems logical, given that the technique re-
quires a certain amount of survey data. However, the de-
gree of its superiority is not significant. For example,
the mean absolute percentage deviation for the best non-
survey method, that is the SimpleLocation technique, is

only around 10 percent higher than that produced by the

RAS method. Consistently, the RAS method produces a

82

Table 11. Evaluation of Estimated Tables: Reducing
Techniques Ranked for Each Comparison Test

 

Comparison Tests

 

 

Rank
The mean abso— The mean of The mean of
lute percentage relative similarity
deviations change index

1 RAS RAS RAS

2 SLQ SCM SCM

3 POLQ CIQ CIQ

4 SCM MSDP MSDP

5 CIQ POLQ POLQ

6 MSDP SLQ SLQ

 

Note: SLQ = Simple Location Quotient; POLQ = Pur-
chase Only Location Quotient; CIQ = Cross Industry Quo-
tient; MSDP = Modified Supply-Demand Pool; RAS = RAS;

SCM = Schaffer-Chu Iterative Procedure
superior result when judged by the mean of relative change
and the mean of similarity index.

Among the purely nonsurvey reducing techniques, there
are more variations in the results. The Simple Location
Quotient and the Purchase Only Location quotient emerge
as being superior to the other reducing techniques when
judged by the mean absolute percentage deviation test,
however, both of the techniques perform poorly when judged
by the mean relative change and the mean of similarity

index. In contrast, the Schaffer-Chu and the Cross Indus-

try Quotient techniques emerge as being inferior to the

83

other techniques when judged by the mean absolute percent-
age deviation test, but they perform better when judged

by the mean similarity index and the mean of relative
change tests.

These inconsistencies are probably due to the tend-
ency of the Schaffer-Chu and Cross Industry Quotient to
overestimate the smaller value of regional coefficients.
This in turn will cause a significant increase in the value
of the mean absolute percentage deviation for each over-
estimated cell. On the other hand, when we overcome this
problem, that is when we judged the Schaffer-Chu and the
Cross Industry Quotient technique with the mean of rela-
tive change and the similarity index, it seems that these
two techniques perform better than the Simple Location
Quotient and the Purchase Only Location Quotient techniques.

The Modified Supply-Demand Pool technique, is the
poorest reducing technique when judged by the mean abso-
lute percentage deviation test. However, it is interest-
ing that it emerges as being superior to the Simple Loca-
tion Quotient and the Purchase Only Location Quotient
techniques when judged by the last two comparison tests.

As is apparent from Table 10, the relative effici-
encies of the six reducing techniques appraised in this
study are not really satisfactory to the author. Conse-
quently it is appropriate at this stage to discuss briefly
possible source of errors in estimating direct coeffici-

ents, when using the six reducing techniques.

84

As has been pointed out earlier, the models in this
study are based on the 1958, 78 by 78 input-output table
of the United States and the 1958, 24 by 24 input-output
table of the Tri-county region. Both matrices have been
aggregated into a 20 by 20 standard matrix, which was
used in this study. Probably by increasing the degrees
of aggregation, the likelihood of including more firms
with different production functions into one sector in-
creased. Indeed this situation may introduce more aggre-
gation error into the results of this study. For further
study in this field, this writer recommends using a less
aggregated matrix.

Next, a more detailed examination of errors by sec-
tor will be made. A close observation of the estimated
direct coefficients generated by each technique reveals
that the greatest deviations occur in sectors in which the
regional economy is specialized. All reduction techniques
appraised in this study performed poorly in estimating
the direct coefficients for this type of sector. In-
cluded in this type of sector are: (1) Motor Vehicles,
(2) Medical, Educational Services and Nonprofit Organiza-
tions, and (3) Chemical and Allied Products. Probably
the sectors in which the regional economy is highly
specialized have a different technology from the national
average, and their input-output coefficients cannot be
estimated by the shortcut techniques used in this study.

The second group of sectors in which large deviations

85

are to occur are those in primary activities. In this
group are included: (1) Other Agricultural, Fishery Pro-
ducts and Services, and (2) Mining and Others. Agricul-
tural crops in the Tri-county region, for example would
include different activities from the United States av-
erage. This may be even more true of mining. Many types
of mining activities included in the United States sector
do not exist in the Tri-county region.

The last factor which may be responsible in intro-
ducing errors into the results of this study is the size
of the Tri-county region relative to the size of the
United States. The Tri-county region constitutes only a
small part of the United States. It seems that the smaller
the region the less the probability that the economic
structure of the region will resemble the economic struc-

ture of the nation. And ceteris paribus the less similar

 

the economic structure of a region compared to the na-
tional economy, the more errors will be introduced in es-
timating the input-output coefficients of the region from

the national input-output table.

Income Multiplier Analysis
In this part the relative efficiency of the six re-
ducing techniques in estimating the Type I and the Type II
income multipliers will be compared. In comparing the
results, it is assumed that the Type I and Type II multi-

pliers produced by the direct survey method are "true"

86

(assuming zero error). Thus, the relative efficiency of

a reducing technique is a measure of closeness of the mul-
tipliers estimated by the technique to the "true" multi-
pliers computed from the survey table.

As has been pointed out earlier, the Type I income
multiplier is the ratio of direct and indirect income
change to the direct income change resulting from the
delivery of one dollar to final demand by a given sector.
The Type II income multiplier is the ratio of direct, in-
direct and induced to the direct income change, resulting
from the delivery of one dollar to final demand by a given
sector.

In computing the Type I income multiplier, it is
assumed that the local household consumption expenditures
(direct sales to local household) as being exogenous to
the model.

The Type II income multiplier assumes local house-
holds consumption expenditures as being endogenous to the
model. This means that local households are treated as
another industry in the system. Households rent property,
sell labor, provide financing, etc., and their purchases
of locally produced goods and services are considered to
be parallel with those emanating from other local indus-
tiral sectors. It should be recognized, however, that
when households are treated asaaprocessing sector, house-
hold inputs are assumed to vary preportionally with house-

hold output. As is true of other processing sectors, a

87

"production function" is assumed for households. Because
households are in fact final consumers, this amounts to

the assumption of a linear homogenous consumption function.
Indeed, this is a somewhat rigid assumption. However,

due to very limited resources, there is no attempt here

to relax the homogeneity assumption by developing, for
example, linear nonhomogenous consumption functions using
national consumption data. However, there are strong econ-
omic arguments for treating local households as an indus-
try. When output changes in response to a change in final
demand (assuming constant population), by definition house-
hold income increases. The increment of income in turn
theoretically results in new household consumption expend-
itures and new savings. New expenditures generate reper—
cussions of their own on the local economy. The Type II
income multiplier is used to estimate the magnitude of

these repercussions on an industry to industry basis.

The Type I Income Multiplier

 

The Type I Income Multipliers, based upon the direct
coefficients estimated by the six reducing techniques
have been computed in this study. The results, along with
the Type I multipliers computed from the direct survey
input-output table are presented in Table 12. The more
complete results of multiplier analysis (including the
direct, indirect and induced income changes) for each re-

ducing technique are presented in Appendix B (Tables 1—7).

 

88

 

 

 

 

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89

In the following tables an abbreviated sector name

is used, in addition to the sector number, for conven-

ience in reading the table. The full sector names and

abbreviations are as follow:

Sector Abbreviated
Number Sector Name

 

l. LVSTOCKPRD
2. OTAGFISHPRDTS
3. WOODPRDTS
4. PRINTPRDTS
5. CHMCLPRDTS
6. MISNONPRDTS
7. PRIMA
8. FABMEPRDTS
9. MACHINELECT
10. MOVEHIC
11. MISDURPRDTS
12. ELPOGASA
13. TRANSCOMM
l4. WHORTRAD
15. FBRSERVICE
16. PERSERAM
l7. BUSSERVICE
18. REPSERVICE
l9. MDEDNONPRT

Full Sector Name

 

Livestock and Livestock Products

Other Agricultural, Fishery Pro-
ducts and Services

Furniture, Lumber and Wood Products

Printing, Publishing and Allied
Products

Chemical and Allied Products
Miscellaneous Non-durable Products
Primary Metals

Fabricated Metal Products
Machinery including Electrical
Motor Vehicles

Miscellaneous Durable Products
Electric Power, Gas and Santiary
Transportation and Communication
Wholesale and Retail Trade

Finance, Insurance, Real Estate and
Retail

Personal Service and Amusements
Business Services
Repair Services

Medical, Educational Services and
Non-Profit Organizations

9O

20. MINOTHER Mining and Others
In the same manner, in the following tables, the

reducing techniques, are known by their initials as set

below:
DSM = Direct Survey Method
SLQ = Simple Location Quotient
POLQ = Purchase Only Location Quotient

CIQ = Cross Industry Quotient

MSDP = Modified Supply-Demand Pool
RAS = RAS
SCM = Schaffer-Chu Iterative Procedure

The Type I multipliers discussed here should be
considered first approximations, particularly for an econ-
omy as "open" as that of Tri-county region. The Type II
multipliers which will be discussed later, are larger in
every case, and are more accurate estimates of the income
changes produced in the area by changes in final demand.
The latter shows the effects of successive rounds of con-
sumer spending (including induced effects), in addition
to the direct and indirect effects of increases in sales
to final demand by each of the processing sectors.

As is apparent from Table 12, we could classify the
six reducing techniques into three groups: (1) techniques
which in every sector underestimate the Type 1 income
multipliers for every sector, (2) techniques which in
every sector overestimate the Type I multipliers for every

sector, and (3) techniques which overestimate the Type I

91

multipliers in some sectors, while underestimating them

in the other sectors.

In a more detailed fashion the interpretation of

Table 12,

(l)

(2)

(3)

This

can be summarized as follows:

The Simple Location Quotient and the Purchase
Only Location Quotient techniques underesti—
mate the Type I income multipliers in all sec-
tors.

The Cross Industry Quotient technique overes-
timate the Type I income multipliers in 14
sectors and understimate them in 6 sectors.
The Modified Supply-Demand Pool technique over-
estimates the value of the Type I multipliers
in 7 sectors, while underestimating them in 13
sectors.

The RAS method overestimates the Type I multi—
plier in 5 sectors, while underestimating them
in 15 sectors.

The Schaffer-Chu technuque overestimates the
Type I multipliers in all 20 sectors.

fact is not entirely surprising. The value of

estimated Type I multipliers to some extent depends upon

the estimated direct coefficients. As has been discussed

earlier, both the Simple Location Quotient and the Pur-

chase Only Location Quotient techniques tend to underes-

timate the direct coefficients. From 20 sectors of the

Tri-county region, only in two sectors are the location

92

quotients greater than unity. In these two sectors (40
cells), the estimated direct coefficients are identical
to the national coefficients, while in the remaining 18
sectors, the national direct coefficients have been ad-
justed downward. In contrast, the Cross Industry Quo-
tient and the Schaffer-Chu procedures take the value of
the national coefficients in 222 cells and 206 cells re-
spectively. Because the national direct coefficient in
general is larger than the regional direct coefficients,
the estimated Type I multipliers generated by the Cross
Industry Quotient and the Schaffer-Chu techniques in most
cases are larger than those produced by the Simple Loca-
tion Quotient and the Purchase Only Location Quotient
techniques. This finding is consistent with the fact that
the value of the Type I multiplier of a large region is
usually larger than that of smaller regions for a partic-
ular sector. From the discussion we may conclude that
the more likely a reducing technique takes the value of
the national direct coefficients, the greater the possi-
bility that the technique overestimates the Type I mul-
tipliers.

The relative efficiency of each reducing technique
in estimating the Type I income multipliers has been com-
puted in this study. Three comparison tests: (1) the
mean absolute percentage deviation, (2) the mean of rela-
tive change, and (3) the mean of similarity index, have

been used to judge the reliability of estimates generated

93

by each reducing technique. The results are presented
in Table 13.
Table 13. Comparison of the Relative Efficiency of the

Six Reducing Techniques in Estimating the Type
I Income Multiplier

 

Comparison Tests

 

 

Reducing
Techniques The mean abso- The mean of The mean of
lute percentage relative similarity
deviation change index
SLQ .207 .242 .879
POLQ .196 .227 .887
CIQ .152 .138 .931
MISP .215 .215 .893
RAS .150 .130 .935
SCM .154 .135 .932

 

Based on data in Table 13, the six reducing techniques
have been ranked in accordance with their relative effici-
ency, and the results are presented in Table 14.

As may be expected, it is apparent that the RAS
matbod generates the best estimates when evaluated by the
‘Unree comparison tests used in this study. Probably this
is due to the fact that the RAS method used a certain
Mount of direct survey data. However, the degree of its
Superiority is not significant. For example, the mean ab-

SOlute percentage deviation of the second best technique,

94

Table 14. Evaluation of Estimated Type I Income Multi-
plier: Reducing Techniques Ranked for Each
Comparison Test

 

Comparison Tests

 

 

Rank
The Mean abso- The mean of The mean of
lute percentage relative similarity
deviation change index
1 RAS RAS RAS
2 CIQ SCM SCM
3 SCM CIQ CIQ
4 POLQ MSDP MSDP
5 SLQ POLQ POLQ
6 MSDP SLQ SLQ

 

that is the Cross Industry Quotient, is .152, while the
RAS method's mean absolute percentage deviation is .150.
Among the nonsurvey techniques, the Cross Industry
Quotient emerges as being superior to the Simple Location
Quotient and the Purchase Only Location Quotient techniques
when judged by the three comparison tests. The Schaffer-
Chu Iterative procedure emerges as being the second best
when judged by the last two comparison tests. The Modi-
fied Supply-Deman Pool technique is the poorest technique
when judged by the mean absolute percentage deviation
test, however, this technique produces a better result

when judged by the last two comparison tests.

95

One general conclusion can be suggested from this
discussion: all of the techniques tested in this study
perform better in estimating the Type I income multipliers
than in estimating the direct coefficients. For example,
the range of the mean absolute percentage deviations in
estimating the Type I multipliers is between .150 and .215,
the range of this index is between .9399 and 2.798 when-
ever the six techniques are used to estimate the direct
coefficients. Thus, it seems that the use of these tech-
niques to estimate the Type I multipliers is really prom-
ising.

We next proceed to a detailed examination of errors
by sector. Below is the list of sectors, in which the
greatest deviations do occur when we use these techniques
to estimate the Type I income multipliers.

Simple Location Quotient and Purchase
Only Location Quotiént

 

 

l. Livestock and Livestock Products
2. Other Agricultural, Fishery Products and Services
3. Primary Metal

4. Finances, Insurance, Real Estate and Rental

Cross Industry Quotient

 

1. Chemical and Allied Products

2. Primary Metals

Modified Supplnyemand Pool

 

l. Livestock and Livestock Products

96

2. Other Agricultural, Fishery Products and
Services

3. Chemical and Allied Products

4. Miscellaneous Nondurable Products

5. Primary Metals

6. Transportation and Communication

7. Business Services

1. Livestock and Livestock Products
2. Other Agricultural, Fishery Products and

Services

Schaffer-Chu Iterative Procedure

 

1. Other Agricultural, Fishery Products and
Services
2. Chemical and Allied Products
In concluding, it is fair to say that most of the
reducing techniques appraised in this study perform poorly
when used to estimate the Type 1 income multipliers in
Livestock and Livestock Products, and Other Agricultural,

Fishery Products and Services.

The Type II Income Multipliers

 

The results of the Type II income multiplier anal-
ysis of the Tri-county regional economy are summarized
in Table 15. The more complete results of multiplier an-
alysis which include the direct, indirect and induced in-

come change are presented in Appendix B.

97

 

 

 

 

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98

Theoretically, the values of the Type II income mul-
tiplier are a constant multiple of the values of the Type
I income multiplier. The ratio of the two multipliers

1
can be expressed as:

1
l - {h+Hr(I-A)

 

1
Hc}

R = the ratio of the Type II and the Type I
multipliers

= direct coefficients matrix

intrahousehold consumption coefficient

= row vector of household coefficients

31:25:15
II

= column vector of household consumption expendi-
ture coefficients

Aside from the apparent novelty of this formula, there is

a practical gain in that once the Type I multipliers are

known, it is no longer necessary to construct an aug-

mented matrix which includes the household sector and ob-

tain its inverse in order to derive the Type II income mul-

tipliers.

However, the reader must be aware that the ratio of
the Type II and the Type I income multipliers is constant
only if the total final demands is equal to total payments
when the model is closed, that is when the household sec-

tor is moved into the processing sector. In a situation

 

lRichardson, Harry W., 1972, 9p Cit., p. 43.

99

where the total final demand is not equal total payments,
when the model is closed, as in the Tri—county input-out-
put model,1 the ratio of the two multipliers may not be
constant. That is the reason that the ratio of the Type
II and the Type I multipliers computed from the survey
table (see Appendix B, Table l) are not equal to a con-
stant.

As can be seen from Table 15, the Simple Location
Quotient and the Purchase Only Location Quotient underes-
timate the Type II multipliers in all sectors. In con-
.trast, the Cross Industry quotient and the Schaffer-Chu
techniques overestimate the Type II multipliers in all
but one sector. The Supply-Demand Pool underestimates
the multipliers in 17 sectors, while overestimating them
in 3 sectors. The most balanced technique is the RAS.
While it overestimates the multipliers in 8 sectors, it
underestimates them in 12 sectors.

As shown in Table 15, the values of the Type II
income multiplier in 5 sectors: (1) Livestock and Live-
stock Products, (2) Other Agricultural, Fishery Products
and Services, (3) Motor Vehicles, (4) Wholesale and Re-
tail Trade, and (5) Finances, Insurance, Real Estate and
Rental, are relatively larger than in other sectors.
Based on their properties we may classify these 5 sectors

into two groups: (1) Sectors in which the Tri-county

 

lO'Donnell, John L., 33 al., 1960, Op Cit., p. 256.

100

region is highly specialized, and (2) Sectors which have
been obtained through high degree of aggregation. In the
first group, it seems logical that in sectors where the
region is specialized the indirect and induced income
change are relatively larger than the direct income change.
Because in computing the value of the Type II income mul-
tiplier we divide the direct, indirect and induced income
change by the direct income change, we may expect that the
Type II multipliers in these sectors are relatively higher
than in the other sectors. In the second group, we arti-
ficially enlarge the sectors by aggregation. It is poss-
ible that the larger the sector, the larger the indirect
and induced income change relative to the direct income
change. So that it is not surprising that the Type II
multipliers of these sectors are relatively higher than

of those smaller sectors.

From our discussions we may conclude that the value
of Type II income multipliers may be very high in two
groups of sectors: (1) sectors in which the Tri-county
region is specialized, and (2) large sectors, which have
been obtained through a high degree of aggregation.

The relative efficiency of the six reducing tech-
niques in estimating the Type II multipliers have been
computed in this study. Three comparison tests: (1) the
mean absolute percentage deviation, (2) the mean of rela-
tive change and (3) the mean of similarity index, have

been used to evaluate the relative efficiency of each

101

technique, and the results are presented in Table 16.

Table 16. Comparison of the Relative Efficiency of the
Six Reducing Techniques in Estimating the
Type II Income Multipliers

 

Comparison Tests

 

 

Reducing

Techniques The mean abso- The mean of The mean of
lute percentage relative similarity

deviation change index

SLQ .318 .438 .781

POLQ .308 .391 .804

CIQ .191 .177 .911

MIDP .284 .293 .854

RAS .159 .123 .938

SCM .199 .173 .914

 

Based upon data in Table 16, the six reducing
techniques have been ranked according to their relative
efficiency in estimating the Type II multipliers. The
results are presented in Table 17.

If we compare the efficiency of the six techniques
in estimating the Tyep II income multipliers to their
efficiency in estimating the Type II income multipliers,
we may conclude that the relative efficiency of each tech-
nique in estimating the latter is lower. Indeed, this
situation is not surprising because when a technique is

used to estimate the Type II income multipliers induced

102

Table 17. Evaluation of Estimated Type II Income Mul-
tiplier: Reducing Techniques Ranked for Each
Comparison Test

 

Comparison Tests

 

 

Rank The mean abso- The mean of The mean of
lute percentage relative similarity
deviation change index
1 RAS RAS RAS
2 CIQ SCM SCM
3 SCM CIQ CIQ
4 MSDP MSDP MSDP
5 POLQ POLQ POLQ
6 SLQ SLQ SLQ

 

income change is estimated in addition to direct and in-
direct income change. Thus, it is only natural that some
errors are introduced when the technique to estimate the
induced income change is used.

The results in general are promising. The superi-
ority of the RAS method is apparent. Its mean absolute
percentage deviation is only 15.88 percent. However, this
situation is not unexpected, because this method employs
a certain amount of survey data. Moreover, even the purely
nonsurvey technique produced satisfactory results. For
example, the Cross Industry Quotient, the second best

technique when judged by the mean absolute percentage

103

deviation test, produced estimates which on the average
deviate from the "true" value by only 19 percent. The
Simple Location Quotient and the Purchase Only Location
Quotient techniques are among the poorest when judged by
all comparison tests. The Schaffer-Chu Iterative pro-
cedure gives superior results among the purely nonsurvey
techniques, when judged by the mean of relative change and
the mean of similarity index.

Thus, by observing the results, we may come to the
conclusion that the use of RAS,tflueCross Industry Quo-
tient and the Schaffer-Chu Iterative techniques to esti-
mate the Type II multipliers is promising.

Next, we could proceed to a more detailed examina-
tion of errors by sector. A close observation of the
estimated Type II income multipliers produced by each
technique would reveal that the greatest deviations oc-

cur in the following sectors.

Simple Location Quotient

 

1. Livestock and Livestock Products
2. Other Agricultural, Fishery Products and Ser-
vices

3. Miscellaneous Nondurable Products

4. Primary Metals

5. Mining and Others

The mean absolute percentage deviations of these
five sectors is 49.76 percent, while the mean of total

deviation is 31.79 percent.

104

Purchase Only_Location Quotient

1. Livestock and Livestock Products

2. Other Agricultural, Fishery Products and Ser-

vices

3. Miscellaneous Nondurable Products

4. Mining and Others

The mean absolute percentage deviation of these four
sectors is 51.51 percent, while the mean of total devia-

tion is 30.81 percent.

Cross Industry Quotient

1. Chemical and Allied Products

2. Business Services

The mean absolute percentage deviation of these
two sectors is 53.54 percent, while the mean of total

deviation is 19.09 percent.

Modified Supply-Demand Pool
1. Livestock and Livestock Products
2. Chemical and Allied Products
3. Primary Metals
4. Mining and Others
The mean absolute percentage deviation of these

four sectors is 60.06 percent, while the mean of total

deviation is 28.37 percent.

105

l. Livestock and Livestock Products
2. Other Agricultural, Fishery Products and
Services
The mean absolute percentage deviation of these
two sectors is 62.25 percent, while the mean of total de-

viation is 15.88 percent.

Schaffer-Chu Iterative Procedure

1. Chemical and Allied Products

2. Miscellaneous Nondurable Products

The mean absolute percentage deviation of these
two sectors is 54.47 percent, while the mean of total de-
viation is 19.90 percent.

This analysis concludes the discussion of the re-
sults of this study. The summary and conclusions from the

results are presented in the next chapter.

CHAPTER V

SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS

Introduction

 

In the last two decades, the demand for input—output
models at the small region level has been increasing, and
is reflected to some extent by the number of studies
which have been completed and are currently in progress.
In general this trend has been allied with an increasing
awareness of planning as a continuous and cyclical pro-
cess. In a planning process input-output models could be
used to elaborate the implications of alternative strat-
egies, they can help in the evaluation of these alterna-
tives and consequently also could be useful in formulat-
ing and reformulating the planning objectives.

A major obstacle to the widespread application of
input-output analyses at the regional level is a short-
age of requisite data. An implementation of an input-
output model requires extensive data which few other mod-
els require. However, few other models possess the com-
prehensiveness of the input-output analysis. Unfortunately
data are rarely collected and published in a form directly

appropriate for regional input-output analyses, so the

106

107

regional analysts must collect all or a part of the data
through direct survey or can attempt to produce an input—
output table from the available published data.

As discussed in Chapter II, many attempts have
been made to produce a matrix of regional direct coeffic-
ient from a matrix of national direct coefficients. Yet
efforts at such nonsurvey and minimum survey techniques
have not been highly successful in the past. Thus a
study on nonsurvey or minimum survey techniques could con-
tribute greately to progress in empirical regional econ-

omic analysis.

Summary of this Study

 

As has been pointed out earlier, an empirical input-
output table constructed for the Lansing Tri-county region
for the year 1958 by O'Donnell, epqgl., has provided this
study a basis for testing of the relative efficiency of
nonsurvey and minimum survey techniques, based upon the
United States input-output tables for the year 1958. The
purpose of this study is to integrate previous work on
nonsurvey and minimum survey input-output techniques at
the regional level by comparing results of the applica—
tion of the most promising of the earlier nonsurvey and
minimum survey tehcniques in a consistent way with an
empirically derived survey-based input output model for
the Lansing Tri-county region. The empirically derived

input-output model of the Tri-county region is a regional

108

version of the traditional Leontief Open, static input-,
output model, and thus the nonsurvey and minimum survey
techniques tested in this study produced tables of this
nature.
The sectoring arrangement adopted in this study is
presented in Table 2. The purpose of the aggregation pro-
cedure was to reduce the size of a 87 by 87 national in-
put-output table, and a 24 by 24 input-output table of the
Tri-county region to a 20 by 20 standard matrix.
The six reducing techniques appraised in this study
divide naturally into three major categories. These are:
a. Quotient Approaches
Included in this category are: (l) The Simple
Location Quotient, (2) The Purchase Only Loca-
tion Quotient, and (3) The Cross Industry Quo-
tient.
b. Commodity Balance Approach
Included in this category is the Modified Supply-
Demand Pool technique.

c. Iterative Approaches
Included in this category are: (l) The RAS
technique, and (2) The Schaffer-Chu Iterative
Procedure.

All the techniques operated on the national input-
output matrix and attempt to adjust the coefficient to
produce regional coefficients that adequately represents

the Tri-county region's economic structure or interindustry

109

linkages. The basic assumption of all techniques is that
the national technology is assumed the same with technol-
ogy at the regional level and that the regional direct co-
efficients differ from the national direct coefficients
to the extent that goods and services are imported from
or exported to other regions. This assumption clearly
implies the constraint that the regional direct coeffici-
ents must alwasy be less than or equal to the national
coefficients. If the goods and services are exported

to other regions, the direct coefficients of the export-
ing industry are identical to national coefficients for
the particular row, and if goods and services are im-
ported from other regions, the national direct coeffici-
ents are adjusted downward.

Based upon the direct coefficients produce by each
technique, the Type I and the Type II income multipliers
were computed.

An essential part of this study was to establish
some objective means of evaluating the relative efficiency
of each technique. The relative efficiency is a measure
of distance or relative distance between the value of
estimated direct coefficients, the Type I and the Type II
income multipliers, and the "true" direct coefficients,
the Type I and the Type II income multipliers computed
from the survey-based input-output table. For this pur-
pose three comparative tests have been employed. These

are: (l) The mean absolute percentage deviation, (2) The

110

mean of relative change, and (3) The mean of similarity
index.

The mean absolute percentage deviation test has
two major deficiencies. These are: (1) It can not han-
dle a situation where the "true" direct coefficient is
zero, and (2) In this test, deviations between small co-
efficients affect the results far more than those between
large coefficients.

The mean of relative change and the mean of simil-
arity index lack of these deficiencies. However, the
mean of relative change has another problem, that is its
value ranges from zero to two. This feature is not only
confusing but also awkward. Thus, it may be suggested
that the mean of similarity index is the most ideal of the
three comparison tests employed in this study.

Relative Efficiengy of the Six Reducing Techniques
in Estimating Ehe Direct Coefficients

 

When judged by the three comparison tests, it ap-
pears that the RAS technique produces the best estimates.
However, the degree of its superiority is not really sig-
nificant. For example, the mean absolute percentage de-
viation of estimates generated by the RAS method is only
10 percent lower than the mean absolute percentage devia-
tion of estimates produced by the second best technique
(the Simple Location Quotient). Among the purely non-
survey reducing techniques, there is more variation in the

results. The Simple Location Quotient and the Purchase

111

Only Location Quotient emerge as being superior to the
other reducing techniques when judged by the mean abso-
lute percentage deviation test. However, both techniques
perform poorly when judged by the mean of relative change
and the mean similarity index. In contrast, when judged
by the mean of similarity index and the mean of relative
change, the Cross Industry Quotient and the Schaffer-Chu
Iterative techniques produced better estimates than those
produced by the other techniques. These inconsistencies
are probably due to the fact that the Cross Industry Quo-
tient and the Schaffer-Chu techniques tend to overestimate
the small regional direct coefficients.

The Modified Supply-Demand Pool technique produced
the poorest estimates when judged by the mean absolute
percentage deviation test. However, it is interesting
that it emerges as being superior to the Simple Location
Quotient and the Purchase Only Location Quotient when
judged by the other two comparison tests.

Relative Efficiency of the Six Reducing Techniques
in Estimating the Type I Multipiier

It was observed that all of the techniques tested in
this study perform better in estimating the Type I multi—
pliers than in estimating the regional direct coefficients.
For example, the range of the mean of absolute percentage
deviation in estimating the Type I multipliers is between
.150 and .215, while this range is between .939 and 2.798

whenever the six techniques are used to estimate the direct

112

coefficients.

As may be expected, it was apparent that RAS method
generated the best estimates of the Type I income multi-
pliers when judged by any of the comparison tests.

Among the purely nonsurvey techniques, the Cross
Industry Quotient emerges as being superior to the Simple
Location Quotient and the Purchase Only Location Quotient
when evaluated by the three comparison tests. The Schaf-
fer-Chu technique produced the second best estimates
when judged by the mean of relative change and the mean
of similarity index. The Modified Supply-Demand Pool
technique produced the poorest estimates when judged by
the mean absolute percentage deviation. However this
technique emerges as being superior to the Simple Location
Quotient when evaluated by the other two comparison tests.

Relative Efficiencyyof the Sic Reducipg Techniques
in Estimating the Type II Income Mdltiplier

 

 

If the efficiency of the six methods in estimating
the Type II income multipliers to their efficiency in
estimating the Type II income multipliers is compared, it
can be concluded that, in general, their efficiency in
estimating the latter is decreased. However, this situa-
tion is not really unexpected, because when a technique
is used to estimate the Type II multipliers, in addition
to estimating the direct and indirect income change, it
also estimates the induced income change. Thus, probably

additional error was introduced when the technique is

113

used to estimate the Type II income multipliers.

The results of the Type II multiplier analysis were
promising in general. The superiority of the RAS method
was apparent. Its mean absolute percentage deviation was
only 15.88 percent. Moreover, even the purely nonsurvey
technique produced satisfactory results. For example,
the Cross Industry Quotient technique, the second best
technique when evaluated by the mean absolute percentage
deviation test, produced estimates which on average de-
viate from the "true" value by only 19 percent. The
Simple Location Quotient and the Purchase Only Location
Quotient techniques are among the poorest when judged by
all comparison tests. The Schaffer-Chu Iterative pro-
cedure gave a superior result when evaluated by the mean

of relative change and the mean of similarity index.

The Possible Sources of Estimation Errors

 

In estimating regional direct coefficients, Type I
and Type II income multipliers, the greatest deviations
have occurred in three groups of sectors.

The first group of sectors in which large deviations
were expected to occur were those in which the Tri-county
regional economy is highly specialized. In this study,
this group was represented by the Motor Vehicles sector.
It seems that sectors in which the Tri-county regional
economy is highly specialized have different production

functions than the United States average. Consequently,

114

their direct coefficients cannot be estimated from na-
tional coefficients by using mechanical techniques.

The second group of sectors, which we may call pri-
mary activities, were represented in this study by three
sectors: (1) Livestock and Livestock Products, (2) Other
Agricultural, Fishery Products and Services and (3) Min-
ing and Others. Probably it may be safe to assume that
these high levels of errors can be largely explained by
the difference of mix of economic activities within a
given sector. For example, agricultural crops or fish
products in the Tri-county region may include different
activities from the national average.

The last group of sectors in which large deviations
were expected to occur were those sectors which have been
obtained through a high degree of aggregations. By in-
creasing the degree of aggregation, it is likely this will
simultaneously increase the possibility of including more
and more firms with different production functions into
one sector. This situation may introduce more aggrega-

tion errors into the results of the study.

Conclusions and Recommendations
In estimating the regional direct coefficients,
none of the reducing techniques appraised in this study
were entirely satisfactory to the author. The distance
between the survey and nonsurvey direct coefficients

matrices is still too large in absolute terms to be

115

acceptable. The Simple Location Quotient and the Pur-
chase Only Location Quotient appeared to adjust some co-
efficients downward drastically. In contrast, the
Schaffer-Chu iterative procedure and the Cross Industry
Quotient technique appeared to overestimate some coeffic-
ients.

This study revealed that the more frequently a re-
ducing technique equates the regional direct coefficints
to the national direct coefficients, the more likely that
the technique overestimates the regional direct coef-
ficients.

While the RAS method performs slightly better than
nonsurvey techniques, it must be remembered that the method
employed a certain amount of survey data. Of course, data
collection requires costs. It should be noted that (l) the
RAS method produced estimates which only slightly better
than the other techniques,(2) the RAS method likely is
less cost effective than the other techniques. Therefore,
from a cost point of view, the RAS method is not neces-
sarily more effecient than the other techniques.

Among the purely nonseuvey techniques, it was ob-
served that the Simple Location Quotient and the Purchase
Only Location Quotient produced superior estimates of dir-
ect coefficients when evaluated by the mean absolute per-
centage deviation test. However, when judged by the mean
of relative change and the mean of similarity index, it

appeared that the Cross Industry Quotient and the

116

Schaffer-Chu iterative procedure emerged as being super—
ior to the other nonsurvey techniques. These inconsisten-
cies were probably due to the tendency of the Cross In-
dustry Quotient and the Schaffer-Chu techniques to over-
estimate the small regional direct coefficients.

This study revealed that the relative efficiencies
of the reducing techniques were better when used to esti-
mate the Type I and Type II income multipliers, than when
used to estimate regional direct coefficients.

It was observed that the RAS method (the best tech-
nique when judged by all comparison tests) produced the
estimates of the Type I and Type II multipliers with mean
absolute percentage deviation of 15.0 percent and 15.9
percent respectively. Among the purely secondary data
reducing techniques, the Schaffer-Chu procedure and the
Cross Industry Quotient, consistently produced the best
estimates of the Type I and the Type II income multipliers
when judged by any of the comparison tests. Therefore,
the most promising techniques for estimating the Type I
and the Type II multipliers are: (l) the RAS technique,
(2) the Schaffer-Chu iterative procedure, and (3) the
Cross Industry Quotient technique.

In estimating the regional direct coefficients, and
Type I and Type II income multipliers it was found that
greatest deviations occurred in three groups of sectors:
(1) Sectors in which the regional economy is highly

specialized, (2) The Primary Activity sectors, and

117

(3) Sectors which have been obtained through a high de-
gree of aggregation. In order to obtain more acceptable
results, it is recommended that a field survey be used to
obtain regional direct coefficients for these three groups
of sectors.

It is also recommended that national and regional
input-output statistics be published in greater detail
(less aggregation), especially with regard to service in-
dustries. This would be of considerable benefit to plan-
ners and other regional analysts desiring to apply some
kind of nonsurvey and minimum survey techniques.

Further research and experimentation with the six
reducing techniques appraised in this study is needed
in order to improve their relative efficiency in estimat-
ing direct coefficients, and the Type I and Type II in-
come multipliers. If relative efficiencies of the reduc-
ing techniques can be improved significantly, it will
help planners and other regional analysts in making appro-
priate response to policy questions by using input-output

models.

APPENDICES

APPENDIX A

ESTIMATED DIRECT COEFFICIENTS GENERATED BY
THE SIX REDUCING TECHNIQUES, COMPARED TO THE "TRUE"

DIRECT COEFFICIENTS COMPUTED FROM SURVEY DATA

APPENDIX A

ESTIMATED DIRECT COEFFICIENTS GENERATED BY
THE SIX REDUCING TECHNIQUES, COMPARED TO THE "TRUE"

DIRECT COEFFICIENTS COMPUTED FROM SURVEY DATA

The Results of Direct Coefficients Estimation
Direct requirements per dollar of gross output

for each sector estimated by each reducing technique
are presented in Table A-1. To facilitate comparison,
these coefficients have been placed side by side with the
"true" direct coefficients computed from survey data.

In an ateempt to save the space, a sector appears in
Table A-1 as its number, instead of its full name. Row
numbers refer to producing industries, while the column
numbers refer to purchasing industries. The sector num-

bers and the full sector names are as follow:

 

Sector
Number Full Sector Name
1. Livestock and Livestock Products
2. Other Agricultural, Fishery Products and Services
3. Furniture, Lumber, and Woods Products
4. Printing, Publishing and Allied Industries
5. Chemical and Allied Products

118

Sector
Number

6.

13.
14.
15.
16.
17.
18.

19.

20.

119

Full Sector Name

 

Miscellaneous Non-durable Products

Primary Metals

Fabricated Metal Products

Machinery including Electrical

Motor Vehicles

Miscellaneous Durable Products

Electrical Power, gas and Sanitary Services
Transportation and Communication

Wholesale and Retail Trade

Finances, Insurances, Real Estate and Rental
Personal Services and Amusements

Business Services

Repair Services

Medical, Educational Services and Non—Profit
Organizations

Mining and Others

In addition each reducing technique appears in Table

A-1 in its initials as shown below:

SLQ :
POLQ:
CIQ :

MSDP:

Simple Location Quotient
Purchase Only Location Quotient
Cross Industry Quotient
Modified Supply-Demand Pool

RAS

Schaffer-Chu Iterative Procedure

Direct Survey Method

 

120

 

 

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HQON. ONHH. HOOH. OOOO. OHVN. OOON. OOON. O O
OOOO. ONOH. vOOO. OOOO. HOvH. OONH. vONN. O O
OOOO. .O HOOO. OOOO. HOOO. HOOO. .O O O
OOOO. ONOO. OOOO. NONO. OOOO. NOOO. OOOO. O O
HOOO. HOOO. OOOO. NHOO. OOOO. OOOO. .O o O
ovOO. OHOO. OOOO. OOOO. OOHO. OOHO. OOHO. O O
OOOO. HOOO. HOOO. OOOO. NOOO. NOOO. .O N O
.O .O .O .O . . HOOO. H O
OOOO. HOOO. OHOO. OOOO. OOOO. OOOO. OHHO. ON O
OOOO. OOOO. HHOO. OOOO. OOOO. OOOO. OOOO. OH O
Sum m<m mom: OHU OHOm OHm 2mm
GEDHOU 30m

 

iiiirintlfliilll 1.0.. III...‘I(III-

moqusnowB

lilliillliillil‘itullpl illtlllltiv) ‘1 3-1) 0|. lililiil .1 . .1'i . 1‘ 1i |..(3.1iiiv

 

HOODGHHCOUV .Hla OHDMB

128

 

 

 

 

NOOO. OHOO. ONOO. NOOO. OvOO. OvOO. OHOO. NH O
OONO. OOOO. NOOO. OONO. HOHO. OOHO. OHHO. HH O
HOOO. OOOH. OOHO. ONOO. HOOO. OOOO. OOOO. OH O
OOVO. OONO. OHHO. OOvO. HONO. OONO. NOOO. O O
OOOO. NONO. OONO. OOOH. OOOO. OOOO. OOHH. O O
OONO. OOHO. HOOO. OONO. HOHO. HOHO. ONOO. O O
OOOO. HHOO. OHOO. OOOO. NOOO. NOOO. .O O O
OOHO. ONOO. OOOO. OOHO. HOOO. HOOO. OOOO. O O
ONOO. HOOO. OOOO. OHOO. HHOO. HHOO. NOOO. o O
OOVO. OHOO. OHHO. OOOO. HONO. OONO. OONO. O O
OHNO. OOOO. HOOO. OHNO. OHHO. OHHO. NHOO. N O
HNOO. NOOO. OOOO. HNOO. NHOO» NHOO. OOOO. H O
ONOO. .O OOOO. ONOO. vHOO. NHOO. OHOO. ON O

.O .O .O .O .O .O OH O

.O .O .O .O .O HOOOO. OH O
OOOO. HOOO. NOOO. OOOO. vOOO. OOOO. .O OH O
oOOO. .O HOOO. OOOO. NOOO. HOOO. .O OH O
20m m<m mom: OHU OHOO OHm Ema

GEDHOU 30m
mosvHsnuoe
HomssHuoouv .Hld oHnoe

129

 

 

 

 

 

 

 

HNOO. ONOO. OOOO. NHOO. OOHO. OOHO. OvOO. OH O
OONN. OOOO. OOOH. OONN. OOOO. OOOO. OOOH. O O
Ova. ONHO. OvOO. OOvO. OONO. OONO. OOOO. O O
OOOO. OOHO. OONO. OHNO. OOOO. OOOO. OOOO. O O
OHOO. NOOO. NHOO. OHOO. OOOO. OOOO. OHOO. O O
OOOO. OOOO. OOOO. OOOO. ONOO. ONOO. HNOO. O O
OOOO. NOOO. ONOO. OOOO. NHOO. NHOO. OOOO. o O
OHHO. NOOO. NOOO. OHHO. HOOO. HOOO. OOOO. O O
OOOO. OOOO. HNOO. OOOO. OOOO. OOOO. ONOO. N O
OOOO. .O vOOO. vOOO. NOOO. NOOO. OOOO. H O
OOOO. HOOO. OHOO. vOOO. OOOO. OOOO. ONHO. ON O
OOOO. VOOO. NOOO. OOOO. OOOO. OOOO. NOOO. OH O
OOHO. OOOO. OOOO. HOHO. OOOO. NOOO. OOOO. OH O

.O .O .O .O . . OHOO. OH O
OOOO. OOOO. vOOO. OHOO. OOOO. OOOO. OHOO. OH O
OOOO. NOOO. HOOO. OOOO. NOOO. NOOO. HOOO. OH O
ONOO. OOOO. OOOO. ONOO. OHOO. OHOO. NOOO. OH O
OHOO. OOOO. OOOO. OHOO. OOOO. OOOO. OHOO. OH O

20m mg mam: OHU OHOm OHm 2mm—
:ESHOU 30m
moqucnome
HomssHucovv .HI< OHnt

130

 

 

 

HNOO. OOOO. HNOO. HNOO. HNOO. HNOO. OOOO. O OH
.O .O .O .O .O .O O OH
.O .O .O .O .O OOOO. O OH
NOOO. NOOO. NOOO. NOOO. NOOO. .O O OH
OOOO. OOOO. OOOO. OOOO. OOOO. OHOO. O OH
OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. N OH
OOOO. HOOO. OOOO. OOOO. OOOO. OOOO. OHOO. H OH
OONO. OOOO. OOHO. OONO. OOOO. OOOO. OOHO. ON O
OOOO. OOOO. OOOO. NOOO. OOOO. OOOO. OHOO. OH O
OOHO. OOOO. OHNO. OOHO. OOOO. OOOO. NNOO. OH O
OOOO. OOOO. OONO. OOOO. OOHO. OOHO. OOOO. OH O
OHOO. OOOO. OOHO. HOHO. OOOO. OOOO. OOOO. OH O
OOOO. OOOO. NHOO. OHOO. OOOO. OOOO. .O OH O
OOOO. OOOO. OOOO. ONOO. OHOO. OHOO. NOOO. OH O
OHHO. OHOO. OOOO. OHHO. HOOO. HOOO. OHOO. OH O
OHOO. NOOO. OOOO. OOOO. OOOO. OOOO. HOOO. NH O
OOOO. OOOO. OONO. HOOO. OOHO. OOHO. OOOO. HH O
20m mdm momz 0H0 OHOO OHm Ema
:EDHOU 30m
mostcsomB

..\II

II.

:11 .Ill'li‘t'll."ll

HGODCHHCOUV

.Hlfl OHQOB

131

 

 

 

 

OOOO. OOOO. OOOO. HOOO. ONOO. ONOO. OOOO. O HH
OONO. OOOO. OOHO. OONO. OOOO. OOOO. HOOO. O HH
OOOO. OHOO. OOOO. OOOO. NNOO. NNOO. OHOO. N HH
NOOO. .O HOOO. NOOO. HOOO. HOOO. HOOO. H HH
OHOO. .O OHOO. OHOO. OHOO. OHOO. OOHO. ON OH
HOOO. .O HOOO. HOOO. HOOO. HOOO. .O OH OH
OOOH. OOOO. OOOH. OOOH. OOOH. OOOH. OOOH. OH OH
NOOO. .O NOOO. NOOO. NOOO. NOOO. OOOO. OH OH
.O .O .O .O . .O HOOO. OH OH
NOOO. HOOO. NOOO. NOOO. NOOO. NOOO. .O OH OH
ONOO. NOOO. ONOO. ONOO. ONOO. ONOO. OOOO. OH OH
ONOO. OOOO. ONOO. ONOO. ONOO. ONOO. ONHO. OH OH
HOOO. .O HOOO. HOOO. HOOO. HOOO. OOOO. NH OH
OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. HH OH
OOON. OOOO. OOON. OOON. OOON. OOON. OOON. OH OH
OHHO. OOOO. OHHO. OHHO. OHHO. OHHO. ONOO. O OH
OOHO. ONOO. OOHO. OOHO. OOHO. OOHO. OOOO. O OH

20w mdm mom: 0H0 OHOm OHm Ema
CEDHOU 30m

mmooHccuoe

HooocHucooO .H(< oHnee

132

 

 

 

 

OOOO. OOOO. ONOO. OOOO. OHOO. OHOO. NOOO. H NH
OOOO. OHOO. OOOO. OOOO. ONOO. ONOO. OOOO. ON HH
OOOO. OOOO. OHHO. OOOO. OOOO. OOOO. NOHO. OH HH
HHHO. OOOO. OHHO. OOHO. OOOO. OOOO. OOOO. OH HH
ONOO. OOOO. OOHO. ONOO. HOOO. HOOO. OOOO. OH HH
HONO. OOOO. OOHO. ONNO. NOOO. NOOO. ONOO. OH HH
OHOO. NHOO. OHOO. OHOO. OOOO. OOOO. OOOO. OH HH
ONOO. OOOO. HOOO. OOOO. ONOO. ONOO. HNOO. OH HH
ONOO. OOOO. ONOO. OOOO. OHOO. OHOO. OOOO. OH HH
OHOO. OOOO. OHOO. OHOO. OOOO. OOOO. OHOO. NH HH
ONON. OOOO. OHOH. ONON. HOOO. HOOO. OOOO. HH HH
OOOO. OOOO. OOHO. OOOO. NOOO. NOOO. OHHO. OH HH
OONO. OOOO. OOHO. OONO. OOOO. OOOO. OOHO. O HH
OOHO. HOOO. OOHO. OOHO. OOOO. OOOO. OOOO. O HH
OHHO. OOOO. OOOO. NHHO. OOOO. OOOO. OOHO. O HH
OOOO. HHOO. OOOO. OOOO. ONOO. ONOO. OOOO. O HH
HOHO. OOOO. OOOO. HOHO. NOOO. NOOO. OOOO. O HH

20m m<m mom: OHU OHOO OHm 2mm
:EoHou 30m

moqusnomB

HomosHusovv .HI< OHQOB

133

 

 

 

OOHO. OHOO. OOHO. OOHO. OOOO. ,OOOO. OHNO. OH NH
OHHO. OOOO. OOOO. OHHO. HOOO. HOOO. NOOO. OH NH
OOHO. OOOO. ONHO. OOHO. OOOO. OOOO. OONO. OH NH
OOOO. OOOO. NOOO. OOOO. OHOO. OHOO. OOOO. OH NH
OHNO. HOOO. OOHO. OHNO. OOOO. OOOO. OOOO. OH NH
NOOO. HNOO. OOOO. OOOO. ONOO. ONOO. OOOO. OH NH
OOOH. OOOO. HONH. OOOH. OOOO. OOOO. OOHO. NH NH
ONOO. OOOO. OOHO. NOHO. OOOO. OOOO. OHNO. HH NH
OOOO. OONO. OOOO. NOOO. ONOO. ONOO. HOOO. OH NH
OOHO. OOOO. OOOO. OOOO. ONOO. ONOO. ONHO. O NH
OOHO. OOOO. OOOO. OOOO. OOOO. OOOO. HONO. O NH
NONO. OONO. OONO. NONO. NNHO. NNHO. OOHO. O NH
OOOO. ONOO. HOOO. OOOO. NOOO. NOOO. OOOO. O NH
OOHO. OOOO. OHHO. OOHO. OOOO. OOOO. OOOO. O NH
OOOO. OOOO. NOOO. OOOO. OHOO. OHOO. HOOO. O NH
OOOO. OOOO. NOOO. OOOO. OOOO. OOOO. OOOO. O NH
HOOO. OOOO. OOOO. HOOO. ONOO. ONOO. OOOO. N NH
sum m<m mom: OHU OHOO OHO Ema

GEDHOU 30m

moqucnumB

Ill-1.3!, IZI ii-v.‘x‘ilnliilll'l .1111) I. I.

AcwocHucouv .HI¢ OHQMB

134

 

 

 

OOOO. NOOO. OOOO. OOOO. HOOO. HOOO. NOHO. OH OH
OOOO. OOHO. OOOO. OOOO. OOOO. OOOO. HNHO. OH OH
OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. HOOO. OH OH
NOOO. OONO. OOHO. NOOO. OOHO. OOHO. HOOO. OH OH
HOHO. OOOO. OOOO. ONHO. OOOO. OOOO. OOOO. NH OH
OOOO. OOHO. ONHO. OOOO. NHHO. NHHO. OOOO. HH OH
OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. OH OH
OOHO. OOHO. OOOO. OOHO. HOOO. HOOO. OOHO. O OH
OOHO. NOHO. OOOO. OOHO. OOOO. OOOO. OOHO. O OH
HOOO. NHOO. OOHO. OOOO. OOHO. OOHO. OOHO. O OH
ONOO. OHHO. OHHO. ONOO. OOHO. .OOHO. OHHO. O OH
OOOO. OOOO. OOOO. NOOO. OOOO. OOOO. OOOO. O OH
OHNO. OOOO. OOOO. HONO. OOOO. OOOO. ONNO. O OH
OOOO. OOOO. OOHO. OOOO. OOHO. OOHO. OOOO. O OH
OHOO. OONO. OOHO. OONO. OOOO. OOOO. ONNO. N OH
NOHO. OOOO. OOOO. OOHO. OOOO. OOOO. OHOO. H OH
OOHO. OOOO. OOOO. OOHO. OOOO. OOOO. OOHO. ON NH
NOOO. OOHO. OOHO. OOOO. NOOO. NOOO. OONO. OH NH
20m m¢m mom: OHD OHOm OHm 2mm

:EoHou 30m

mesoHsaumB

.1 'III ..." '11..) ‘.ll-

HUODGHHCOUV .HI< OHQOB

135

 

 

 

 

 

 

 

OONO. ONOO. OOHO. OONO. OOHO. OOHO. NONO. OH OH
ONHO. NHOO. OOOO. ONHO. OOOO. OOOO. HOOO. NH OH
NHOO. OOOO. OONO. NHOO. OONO. OONO. OHHO. HH OH
OOOO. OOOO. OOHO. OHHO. OOHO. OOHO. OOOO. OH OH
OOOO. OOHO. OONO. OOOO. OHNO. OHNO. OOHO. O OH
OOOO. OOOO. OONO. OOOO. NONO. NONO. OOHO. O OH
ONOO. OOOO. OHNO. ONOO. OOHO. OOHO. NOHO. O OH
OONO. OHOO. OOHO. OONO. OOHO. OOHO. OOOO. O OH
ONOO. OHOO. OOHO. ONOO. OOHO. OOHO. OOOO. O OH
OONO. OHOO. ONHO. OONO. HHHO. HHHO. NOOO. O OH
NOOO. HHHO. HOOO. NOOO. OOOO. OOOO. HOHO. O OH
OOOO. OOOO. OOHO. OOOO. HOHO. HOHO. OHNO. N OH
OOOO. OHHO. OOHO. OOOO. NOHO. NOHO. OOOO. H OH
OONO. OOOO. OOOO. OONO. OOOO. OOOO. OOOO. ON OH
OOHO. ONHO. OOOO. ONOO. OOOO. OOOO. OOHO. OH OH
HOOO. OHOO. OOOO. OOOO. NOOO. NOOO. NOHO. OH OH
OOOO. NOOO. OOOO. OOOO. OOOO. OOOO. OOHO. OH OH

Sum mg mamz OHU OHOQ OHm 2mm
:ESHOO 30m

mmsoHsnome

HomscHusoov .Hlm OHQOB

136

 

 

 

 

 

OOHO. OOHO. NOHO. OOHO. OOOO. OOOO. OOHO. HH OH
ONOO. HOOO. NOOO. OOOO. OOOO. OOOO. ONOO. OH OH
HOHO. HONO. HOHO. HOHO. OOOO. OOOO. NOOO. O OH
ONHO. OOHO. OOHO. OHNO. OHHO. OHHO. OOHO. O OH
OOHO. OOHO. OOHO. OOHO. OOOO. OOOO. OOOO. O OH
NOHO. OOOO. OHHO. HOHO. OOOO. OOOO. HOOO. O OH
HOHO. OOOO. OOHO. HOHO. OOOO. OOOO. OOHO. O OH
OOOO. OOOO. NHOO. OOOO. OONO. OONO. OOHO. O OH
HONO. OHOO. OOHO. OONO. OHHO. OHHO. OOHO. O OH
OHHO. OOOO. OOOO. OHHO. OOOO. OOOO. HOOO. N OH
OOHO. NOOO. OOHO. OOHO. OOOO. OOOO. OHNO. H OH
NOHO. OHOO. OOOO. NOHO. OOOO. OOOO. OOOO. ON OH
OOOO. NOOO. OOOO. HOOO. OOOO. OOOO. HONO. OH OH
OOOO. OHOO. OOOO. OOOO. OOOO. OOOO. NOOO. OH OH
ONOO. OOHO. HOHO. NONO. NOOO. NOOO. OOOO. OH OH
HOOO. OOOO. OOHO. HOOO. OOHO. OOHO. OOHO. OH OH
HOHO. OOOO. OOOO. NOHO. HOOO. HOOO. OOHO. OH OH
NOHO. HHOO. HOOO. NOHO. OOOO. OOOO. OHOO. OH OH

Sum mdm mom: 0H0 OHOO OHm 2mm
:EdHOU 30%

mwschnoms

.oooeeoeooc .H-e oHoee

137

 

 

 

OHOO. OOOO. OHOO. OHOO. OHOO. OOOO. .O O OH
NHOO. OOOO. OOOO. NHOO. OOOO. OOOO. .O O OH
OHOO. OOOO. OOOO. OHOO. OOOO. OOOO. .O O OH
OOOO. NOOO. OOOO. OOOO. OOOO. OOOO. .O O OH
OHOO. HOOO. OHOO. OHOO. OOOO. OOOO. NNOO. O OH
ONOO. HOOO. ONOO. ONOO. OHOO. NHOO. .O O OH
OOOO. NOOO. OOOO. OOOO. NOOO. NOOO. NOOO. N OH
.O .O .O . . .O .O H OH
NOOH. HOOO. ONOH. NOOH. OOOO. OOOO. ONHO. ON OH
HONO. OOOH. NOOO. NONO. NHOO. NHOO. OOOO. OH OH
NOOO. OOOO. NNOO. ONOO. HOOO. HOOO. NHOO. OH OH
OOOO. NHNO. OOOO. OOOO. OONO. OONO. NONO. OH OH
ONOO. OOOO. OOOO. ONOO. OOOO. OOOO. OOOO. OH OH
HONH. OONN. HOOO. HONH. OOOO. OOOO. OOON. OH OH
OOOO. OONO. OOOO. OOOO. OOOO. OOOO. NOOO. OH OH
ONOO. OONO. OOOO. ONOO. HONO. HONO. OOOO. OH OH
OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. OOHO. NH OH

Sum m<m mam: OHU OHOm OHm Ema
CEOHOO 30m

mosvHsnome

 

' Iiilllvi! O. .. l!.l|ul| ‘Il‘ ‘1'.|

HOODCHHCOUO .HI< OHQMB

138

 

 

 

 

OHOO. ONOO. OHOO. OHOO. OOHO. OOHO. OOOO. O OH
OONO. OOOO. OOOO. OONO. OOOO. NOOO. OOOO. O OH
NOHO. HOOO. OOHO. HOHO. ONOO. ONOO. OOHO. O OH
HNOO. ONOO. OONO. OOHO. OOOO. OOOO. OOOO. N OH
OHOO. .O OHOO. OHOO. OOOO. OOOO. .O H OH
NOOO. .O HOOO. NOOO. HOOO. HOOO. .O ON OH
HNOO. OOOO. OOOO. HNOO. OOOO. OOOO. NNOO. OH OH
.O .O .O .O .O . NOHO. OH OH
OOOO. OHOO. OOOO. OOOO. OOOO. OOOO. NNHO. OH OH
OOOO. OONO. OOOO. ONOH. OOOO. NHOO. ONOO. OH OH
OOOO. OOOO. ONOO. OOOO. ONOO. OHOO. NHOO. OH OH
OOOO. OOOO. ONOO. OOOO. ONOO. OHOO. .O OH OH
OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. NOOO. OH OH
.O .O .O .O .O . .O NH OH
OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. .O HH OH
.O ONOO. OOOO. .O OOOO. OOOO. .O OH OH
OOOO. NHOO. OHOO. OHOO. OHOO. OOOO. .O O OH

Sum mg mom: OHU OHOm OHm Ema
:EOHOO 30m

mODUHsnoma

HooscHusouv .H|< mHomB

 

139

 

 

 

 

OOOO. OOOO. OOOO. OOOO. HNOO. HNOO. OOOO. N OH
ONOO. NHOO. OHOO. ONOO. NHOO. NHOO. NOOO. H OH
OOOO. HOOO. OOOO. OOOO. OOOO. NOOO. OOOO. ON OH
OOOO. OOOO. OONO. HOOO. OOOO. OOOO. HOOO. OH OH
OONO. OOOO. OONO. OOOO. NOOO. HOOO. OOOO. OH OH
NONO. NHOO. NONO. NONO. OOOO. OOOO. OOOO. OH OH
OOHO. OHOO. ONOO. OOHO. OOOO. OOOO. OONO. OH OH
OHHO. OOOO. HONO. OHHO. OOOO. OOOO. OOOO. OH OH
OOOO. NNOO. OOOO. OONO. HHHO. HHHO. OOOO. OH OH
OOHO. NHOO. OOHO. OOHO. OOOO. OOOO. OOOO. OH OH
OOOO. OOOO. OHHO. OOOO. ONOO. ONOO. ONOO. NH OH
NOHO. OHOO. HONO. OOHO. OOOO. OOOO. OOOO. HH OH
OONO. OOHO. OONO. OOOO. HOOO. HOOO. OOOO. OH OH
OOOO. OOOO. HONO. OOHO. OOOO. OOOO. OOOO. O OH
NOHO. OHOO. OOHO. OOOO. HOOO. OOOO. OOOO. O OH
ONOO. OHOO. NOHO. HOOO. HNOO. HNOO. OHOO. O OH
OOHO. OOOO. OOHO. OOHO. ONOO. ONOO. OOOO. O OH

Sum m<m mam: OHU OHOO OHm 2mm
GESHOU 30m

moquG:OOE

HumscHusoov .Hld OHQMB

140

 

 

 

 

NNOO. OOOO. OHOO. OOOO. NHOO. NHOO. ONOO. OH OH
OOHO. OOOO. OOHO. OOHO. OOOO. OOOO. OONO. OH OH
OOOO. OOOO. OOOO. OOOO. OOOO. HOOO. OOOO. OH OH
OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. OOHO. OH OH
ONOO. OOOO. OHOO. ONOO. OHOO. OHOO. OHOO. OH OH
OOOO. OOOO. OOOO. OOOO. HOOO. NOOO. OOOO. OH OH
ONNO. OOOO. OOHO. ONNO. NNHO. ONHO. OHNO. OH OH
OHOO. OHOO. OHOO. OHOO. OOOO. OOOO. ONOO. NH OH
OOOO. ONOO. OHOO. HNOO. HHOO. HHOO. OOOO. HH OH
OOOO. OOOO. OOOO. . NOOO. NOOO. OHOO. OH OH
OHOO. OOOO. OOOO. OOOO. OOOO. OOOO. ONOO. O OH
ONOO. OOOO. OHOO. ONOO. NHOO. NHOO. NNOO. O OH
OOOO. OHOO. OOOO. OOOO. OOOO. OOOO. OHOO. O OH
OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. NNOO. O OH
OOOO. OOOO. OOOO. OOOO. OOOO. OOOO. ONOO. O OH
HHOO. OOOO. OOOO. HHOO. OOOO. OOOO. HHOO. O OH
HOOO. OHOO. HOOO. HOOO. OOOO. OOOO. OOOO. O OH

20m mdm mom: OHU OHOm OHm Ema
cEDHou 30m

mosvHsnooe

HowssHucouv .Hid poeB

141

 

 

 

fl III II I'll-l»!

eeoo. eooo. oHoo. oHoo. OHoo. oHoo. emoo. OH oH
NOoo. omoo. Hmoo. Hmoo. Hmoo. Hmoo. Heoo. OH OH
HHoo. mooo. HHoo. HHoo. HHoo. HHoo. Once. OH oH
meoo. mooo. HHoo. HHoo. HHoo. HHoo. eeoo. mH mH
Hooo. Oooo. oooo. eooo. mooo. oooo. .o NH mH
mHoo. mooo. «Hoe. mHoo. NHoo. NHoo. omoo. HH oH
oHoo. Hmoo. OHoo. Hooo. oHoo. oHoo. HHoo. OH OH
eHoo. NHoo. HHoo. HHoo. HHoo. HHoo. Hmoo. o OH
eHoo. oooo. HHoo. eHoo. sHoo. OHoo. omoo. O OH
«Hoe. mHoo. NHoo. NHoo. NHoo. NHoo. «Hoe. A mH
oHoo. mooo. oHoo. oHoo. oHoo. OHoo. oooo. O mH
HHoo. mHoo. NHoo. mHoo. NHoo. NHoo. NHoo. m oH
HHoo. Nooo. HHoo. HHoo. HHoo. HHoo. mace. O OH
OHoo. Hooo. eHoo. eHoo. mHoo. eHoo. Hmoo. m oH
mooo. eooo. oooo. oooo. mooo. oooo. Oooo. H OH
Omoo. OHoo. emoo. emoo. emoo. emoo. mmoo. H OH
.o .o .o .o .o .o OmHo. om eH

sum wee mom: oHo cHoa OHm zmo
:EsHOU 30m

mmochsowe

It. "|‘. .1. It 1'.“ I'll!

HooocHucooO .Hu< oHnee

 

142

 

 

 

HOOO. .O .O HOOO. OH ON
OOOH. OOOO. ONHO. OOHO. NH ON
HOOO. OOHO. OOOO. HOOO. HH ON
.O .O .O . OH ON
OHOO. HOOO. HOOO. OOOO. O ON
OOOO. HOOO. .O OHOO. O ON
OOOO. NHOO. OOOO. OOOO. O ON
NOOO. ONOH. HOON. OOOO. O ON
NOOO. OHOO. OHOO. OOOO. O ON
.O .O .O .O O ON
.O .O .O .O O ON
NOOO. OOOO. NOOO. OOOO. N ON
.O .O .O OOHO. H ON
.O OOOO. OOOO. .O ON OH
OOHO. OOHO. OOHO. NOOO. OH OH
HOOO. HHOO. HHOO. OHOO. OH OH
HOOO. NOOO. NOOO. OOOO. OH OH

mg mom: OHU Ema
chHou 30m

mmqusnowB

HooscHucouv .H|¢ wHome

143

 

 

 

 

OHNO. OOOO. OHHO. OHNO. HOOO. OHOO. OOHO. ON ON
.O .O .O .O .O .O .O OH ON
.O .O .O .O .O .O .O OH ON
.O .O .O .O .O .O .O OH ON
.O .O .O .O .O .O .O OH ON
OHOO. ONHO. OOOO. OOOO. NOOO. HOOO. .O OH ON
HOOO. HOOO. .O .O .O .O .O OH ON

20w med mom: OHO OHOO OHm 2mm
:EsHOO 30m

moochnooe

AposcHucoov .HI< oHome

APPENDIX B

THE RESULTS OF SECTORAL INCOME MULTIPLIERS

ANALYSIS

APPENDIX B

THE RESULTS OF SECTORAL INCOME MULTIPLIERS

ANALYSIS

The Results of Sectoral Income Multipliers Analyses

In this section, the results of sectoral income multi-
pliers analyses are presented. Each table contains the in—
formation as to: (1) direct, (2) direct and indirect,
(3) indirect, (4) direct, indirect and induced, and (5) in-
direct and induced income change, as a result of delivery
of one dollar to final demand sectors, by a particular sec-
tor. In addition the Type I and Type II income multipliers
are also presented. The estimates produced by a reducing
technique are presented separately one from the other.

In these tables (Table B-1, Table B-2, Table B-3,
Table B-4, Table B-5, Table B-6, and Table B-7) an abbrevi-
ated sector name is used, in addition to the sector number,
as a convenience in reading the table. The full sector

names and abbreviations are as follows:

 

 

Sector Abbreviated

Number Sector Name FUIl Sector Name
1. LVSTOCKPRD Livestock and Livestock Products
2. OTAGFISPRDSERV Other Agricultural, Fishery,

Products and Services

144

Sector
Number

12.

13.
14.

15.

16.
17.
18.

19.

20.

Abbreviated
Sector Name

 

WOODPRDTS

PRINTPRDTS

CHMCLPRDTS
MISNONPRDTS
PRIMA
FABMEPRDTS
MACHINELECT
MOVEHIC
MISDURPRDTS

ELPOGASA

TRANSCOMM
WHORETRAD

FBRSERVICE

PERSERAM
BUSSERVICE
REPSERVICE

MDEDNONPFT

MINOTHER

145

Full Sector Name _

 

Furniture, Lumber, Wood Products

Printing, Publishing and Allied
Products

Chemical and Allied Products
Miscellaneous Non-durable Products
Primary Metals

Fabricated Metal Products
Machinery including Electrical
Motor Vehicles

Miscellaneous Durable Products

Electric Power, Gas and Santiary
Services

Transportation and Communication
Wholesale and Retail Trade

Finances, Insurance, Real Estate"
and Rental

Personal Services and Amusements
Business Services
Repair Services

Medical, Educational Services and
Non-profit Organizations

Mining and Others

146

 

 

 

NOOO.N NNOO. OOOO. OOHO.H HOON. ONOO. OOOO. mmmeosz .ON
ONON.N OOOO. ONOO.H OOOO.H ONOO. NONO. OOOO. amazozomoz .OH
OOOO.H NOOO. OHOO. OOOH.H OOOO. ONOO. OOOO. muH>mmmmmm .OH
OOOO.H NOON. OOOO. OOON.H OOOH. OOOO. OOOO. muH>mmmmDm .OH
NOOO.H HOOO. OOOH.H OOOH.H ONOO. OOOO. OHOO. Edmmmmmm .OH
OOO0.0 NOOO.N OOOH.O OHNO.H OOHO. OOOO.H OHOO. moH>mmwmmm .OH
HOO0.0 OOOO.N OOO0.0 ONHO.H ONON. ONOO. OOOO. Odmamomz .OH
OOOO.N OOOH.H OONO.H OOOO.H ONOO. OOOO. OOOO. zzoomz<ma .OH
OHOO.N OOOO. OOOH.H OHON.H HNOH. ONHO. NOOO. ¢m<womqm .NH
OOOO.H HOOO. OOOO. OOOO.H HOOH. OOOO. OOHO. whommmoomHz .HH
OOO0.0 OOOO. OOOO. ONOO.N OOON. HOOO. OOOH. UHmm>OS .OH
HOOO.H OOOO. OOOO. OOOO.H OOON. OOOO. OOOO. BUMHmszOOZ .O
OOOO.H OOON. OOOO. OOOO.H NHOH. HONO. OHOO. meommmzm<m .O
OOHO.N OONO. NHOH.H OOOO.N HNOO. OOOO. OHOO. «SHOO .O
NOO0.0 OOOO. OOOO.H OOOO.H OOOH. OOOO. OOON. meommzozmHz .O
OOOO.N OOHN. OOH.O ,ONOO.H OOOO. HOON. OOON. OBQMOHOSOU .O
OOHO.H HOOO. OOOH.H HOOO.H OONO. HONO. OOOO. mammmBszm .O
OOOO.H NOHO. NONO. OOOO.H OOOH. OOOO. OOOO. maommoooz .O
OOO0.0 HOOO.N OOOO.N OOOO.N OHOO. OHOO. OOOO. >mmmnmmmHmw<Bo .N
HOO0.0 OOOO.H OOOO.H OHOO.N OONO. NONO. OHOO. ommxooem>q .H

HOHHQ oeoosH OMWMWMW HOHHQ OHGO mEoosH OHGO Houomm

(HuHoz omosocH . OOHH :H IHHHDS mEoosH uuouHcsH oeoucH OcHos OH
HH OQOB .uomHHosH w .o H come uomuHocH .uoouHo MUOHHO . O m

uoouHo . .
mHnmu

Oo>Hsm ECHO pwsHmubo .HOOOHV :oHOom OussouIHHB one Hem mHmHHmHuHDE OEOOGH .Hum meoe

147

 

 

 

 

NOOO.H OHNO. OONO. OONO.H OOHO. OOHO. OOOO. mmmeosz .ON
OOHO.H NHOO. OONO.H OOOO.H OONO. OOOO. OOOO. BOOZOZOMOE .OH
OOOO.H OOOH. ONNO. HOOO.H OONO. OOOO. OOOO. MUH>mmmmmm .OH
OOON.H OHHH. OHOO. OOOH.H OOOO. OONO. OOOO. moH>mmmmDm .OH
OOOO.H OOOO. OOOO. OOOO.H OOOO. NOOO. OHOO. Edmmmmmm .OH
NHO0.0 HOOO.H OONO.H OOOO.H OOON. OONO. OHOO. MOH>mmmmmm .OH
HON0.0 OOOO.H HOOO.N ONON.H OOOH. OOHO. OOOO. ommemomz .OH
OOOO.H OOOO. OOOO.H OOOH.H OOOO. OOOO. OOOO. SEOOOZOOB .OH
NOOO.H HOOO. .OOOO. OOOH.H OOOH. NOOO. NOOO. mmcwomHm .NH
OOOO.H OOOH. HOOO. NNOH.H ONOO. OHOO. OOHO. OBQOOODQOHE .HH
HOO0.0 OONO. OOHO. HHOH.N OOON. OOOO. OOOH. OHmm>oz .OH
OOHO.H OOOH. OHOO. OOON.H OOOO. ONOO. OOOO. BOMHmszOOZ .O
ONOO.H OOOH. NONO. OOON.H HOOH. OOOO. OHOO. mecmmmzmam .O
OOOO.H OOON. HOOO. OOOO.H ONON. NOOO. OHOO. OZHOO .O
NONN.N OOON. NONO. OHOO.H OOHO. HHON. OOON» weommzozmHz .O
OONO.H OOOO. OHON. OOOH.H ONOO. NOON. OOON. OBOOOHOZOO .O
OOON.H OOOH. OHOO. OOOH.H HOOO. OOOO. OOOO. OBQmOBszO .O
NOON.H HOOH. HNHO. OHOH.H OHOO. OOOO. OOOO. meomdoooz .O
ONON.O ONON.H OHON.H OHON.H OOOH. NOOO. OOOO. >mmmommmHmO<BO .N
OOOO.N OOHO. OONO. NNOH.H OOOO. OOOO. OHOO. OOOMUOBO>H .H
oEoonH

uoHHo oEoucH cousccH HoHHm OHno oEounH OHnO Honoow
IHuHsz cousan . ooHHOcH IHuHsz oEoonH uuoHHonH oeoonH Ooaooooum
HH oQOB .uooHHocH w . H omwa uuoHHocH .uooHHc HooHHo .

pooHHc
ucoHuoso noHuoUOH onEHm

onu On OoumEHumo .HOOOHO noHOom OD:SOOIHHB on» How mHoHHmHuHsE oeounH .Nim oHnoe

 

148

ONOO.H OOOO. OOOO. ONOO.H NOHO. OHNO. OOOO. mmmeozoz .ON

 

OOOO.H OOOO. OHOO.H OOOO.H HONO. OOOO. OOOO. amazozomcz .OH
OOOO.H OOOH. HONO. OOOO.H OONO. NOOO. OOOO. muH>mmmmmm .OH
OOOO.H OOHH. OOOO. HOOH.H HOOO. OONO. OOOO. muH>mmmmDm .OH
OOHO.H OHHO. HOOO. HOOH.H NOOO. OONO. OHOO. scammmmm .OH
OOO0.0 OOOO.H OOOO.H ONOO.H OOON. OONO. OHOO. moH>mmmmmm .OH
OOO0.0 OOOO.H OOOO.N OOON.H OOOH. OOHO. OOOO. o<m9momz .OH
HONO.H OOOO. OOOO.H OOOH.H OOOO. NHOO. OOOO. zzoumzama .OH
NOOO.H OOOO. OOOO. OOOH.H OOOH. NOOO. NOOO. «OOOOOHM .NH
OOOO.H OOOH. OOOO. OOOH.H ONOO. ONOO. OOHO. maammmoomHz .HH
OOO0.0 OOOO. OONO. ONOH.H OOON. OOOO. OOOH. UHmm>oz .OH
OONO.H OOOH. OOOO. NOON.H OOOO. OOOO. OOOO. BUMHMZHOO<Z .O
OOOO.H OOOH. OONO. NOON.H OOOH. OOOO. OHOO. OBOOOMZOOO .O
OONO.H HNOO. OOOO. OOOO.H OOON. OHOO. OHOO. OSHOO .O
OOON.N OOON. HOOO. ONOO.H OOHO. OHON. OOON. meommzozmHz .O
HHOO.H OOOO. OOON. HOOH.H OOOO. OOON. OOON. OBQOOHUEOU .O
HOON.H OHOH. NOOO. OOOH.H OOOO. OHOO. OOOO. msammeszm .O
OOON.H OOOH. ONHO. OOOO.H HOOO. HOOO. OOOO. maommoooz .O
OON0.0 OOOO.H OOHO.H OOOO.H OOOH. OOHO. OOOO. >mmmommmHmO¢eo .N
OOOO.N OOOO. NOOO. OHON.H ONOO. OOOO. OHOO. OOOMUOBO>H .H
oEoonH

HoHHo oeoocH cousan HoHHm OHnO oeoonH OHnO Houoom
IHHHoz cocoonH .uuoHHonH IHuHsz oeoonH uoouHonH oEoonH OdHusooum
HH omOe .uooHHccH . H omwe uooHHonH .uooHHo uoouHQ .

.uuoHHQ

unoHuooO GOHHMOOH OHCO
omonousm on» On oouoeHumo .HOOOHV :oHOom OHGSOOIHHB one Hem mHoHHmHuHSE oeounH .Olm oHnoB

149

 

 

 

OOOO.H OOON. OOOO. OOON.H OOHH. OONO. OOOO. mmmeozoz .ON
OOOO.N HHOO.H OOOO.H OOOO.H OONO. MOOHO. OOOO. Emmzozomaz .OH
OONO.H OOOO. NOHO. OOOH.H OOOO. OOHO. OOOO. moH>mmmmmm .OH
OOOO.N OOOO. OOOO. ONOO.H NONN. OOOO. OOOO. muH>mmmmDm .OH
OOON.N OOOO. OOON.H OOOH.H OHOO. OOOO. OHOO. 24mmmmmm .OH
NOON.O OOOO.N OOO0.0 NOOH.N ONOO. OOON.H OHOO. moH>mmmmmm .OH
OOO0.0 OOO0.0 OOO0.0 OHNO.H HOOO. OOHH.H OOOO. Odmsmomz .OH
OOOH.O OOON.H OOOO.H OONO.H ONOO. OOOO. OOOO. SEOUOZOmB .OH
ONOO.N OOOO. HOHO.H OOOO.H HOOO. OOOO. NOOO. <O<OOOHM .NH
OOOO.N OOOO. OOOO. NOOO.H OOHO. OOOO. OOHO. meommmsomHz .HH
OOOH.O OOOO. NOOO. NOHN.N OONN. HOHO. OOOH. UHnm>oz .OH
HOOO.N OOOO. OOOO. OOOO.H OONO. OOOO. OOOO. BUHHMZHOUOS .O
OOON.N OOOO. OOOO. OOOO.H OOON. ONOO. OHOO. meommmzm<m .O
OOO0.0 OOOO. OOOO.H OOOO.N HOOO. OOOH.H OHOO. <2Hmm .O
OOO0.0 OOOO. ONNH.H OOOO.H OOOH. OOHO. OOON. meommzozmHz .O
ONON.O HHOO. OOOO. OOOH.N OHON. OOOO. OOON. meammHUZOU .O
ONOO.H HOOO. OOOH.H ONOO.H OOOO. OONO. OOOO. meomOBszm .O
OOOH.N OHOO. OOOO. OOOO.H OOON. OOOO. OOOO. whammoooz .O
OOO0.0 OOON.O HOO0.0 OHOO.N OOOO. HOOO. OOOO. >mmmommmHmw¢eo .N
NOO0.0 OOOO.H OHOO.H OOOO.H OOON. OOOO. OHOO. ommxuoem>H .H
oEoosH
eoHHm oEoonH cousan eoHHm OHCO oEounH OHnO Hoeoom
(HeHoz coooccH . IHeHsz oEoonH eooeHonH oEounH
euoeeocH mnHosooem
HH omwe .eooeHosH . . H omOB eooeHonH .eooeHQ euoHHo
eooeHo
enoHeoso meemsonH

mmoeu one On ooeoEHemo HOOOHO nOHOom OeCSOOIHee one HOH meoHHmHeHSE OEOOCH .Olm oHnoB

150

 

 

 

OOHO.H HONH. .ONOO. OOOH.H OOOO. ONOO. OOOO. mmmeosz .ON
OOOO.H OOOO. NOOO.H ONOO.H OONO. OOHO. OOOO. emmzoznmoz .OH
ONOO.H OHON. OOOO. OOOH.H OOOO. OOOO. OOOO. muH>mmmmmm .OH
OOOO.N ONOO. ONNO.H HOOO.H OONO. OOOO. OOOO. muH>mmmmDm .OH
OOOO.H OHOO. OOOO.H OOHH.H HOOO. OOOO. OHOO. Edmmmmmm .OH
OOO0.0 OOOO.H HOOO.N OOHO.H OOOO. OHNO.H OHOO. muH>mmmmmm .OH
OOO0.0 OHOO.N OHH0.0 OOOO.H OHON. OOOO. OOOO. Dememomz .OH
ONHO.N NOOO. HOOH.H OOOH.H NOOO. HOOO. OOOO. Ezovmzema .OH
OOOO.N OOOO. HOOH.H ONOO.H OOOH. OOOO. NOOO. émdwooqm .NH
OOOO.H ONNO. OHOO. ONHO.H HOOH. ONOO. OOHO. meommmsomHz .HH
OOON.O OHHO. OOOO. OONH.N OOHN. OOOO. OOOH. OHmm>oz .OH
OOOO.H OOOO. OOOO. OOOO.H OOON. OOOO. OOOO. BomqmszU¢z .O
OOOO.H NOOH. HOOO. OOOH.H HOOO. OOOO. OHOO. meommmzmflm .O
OOOO.H OOOH. OOOO. OOOO.H OOOH. OOOO. OHOO. «szO .O
OOOO.N ONOO. OOOO. OOOH.H OOOO. OOON. OOON. OBOOOZOZOHS .O
OOOH.O ONOO. OOOO. OOOO.N NNOO. OOOO. OOON. mammmHUSnU .O
OOOO.H OOOO. OOOO.H OOOO.H OOON. ONOO. OOOO. mBQmOeszd .O
OOON.H HOHH. HONO. OOOO.H OOOO. OOOO. OOOO. meommoooz .O
OOO0.0 OOOO.H HOOO.N OOOO.H OOOH. OOOO. OOOO. >mmmommmHmo¢eo .N
OOO0.0 OOOO. OOOO.H OOHO.H OONH. OONO. OHOO. OOOMUOBO>H .H
eoHHQ oEoonH OMWMMHW HoHHm OHCO oEoonH OHGO Hoeoom
(HeHsz cousan .eooeHonH IHeHoS oEoocH eooHHonH oEoocH onHospoem
HH omOB .eooeHonH . . H omaa eooeHonH .eooeHQ eooHHQ .
eooeHo
Hoom comeoolmHmmom coHHHooz
one On ooeoEHemo .HOOOHO coHOom OeCDOOIHeB one HOH meoHHmHeHsE oEoonH .Oim oHnoB

151

 

 

 

OHOO.N NONO. OONO.H OOOO.H OOON. NNOO. OOOO. mmmeosz .ON
OOHN.N OOOO. HHOO.H OONO.H OHNO. OOOO. OOOO. amazozomaz .OH
OOOO.H ONOO. OOHO. NOOH.H HOOO. OOHO. OOOO. MUH>mmmmmm .OH
OOON.H NNOO. ONOO. ONOO.H OOOO. OHOO. OOOO. moH>mmmmDm .OH
OOOO.H OOOO. NOOH.H OOOO.H OHOO. OOOO. OHOO. aflmmmmmm .OH
OOO0.0 NOOO.N OOOH.O OOOO.H OOOO. ONOO.H OHOO. moH>mmmmmm .OH
OON0.0 OOHO.N OOON.O HOOO.H OOOO. OOOO. OOOO. o¢memom3 .OH
HOOO.N OOOO. OOOO.H NOOO.H OOON. OOOO. OOOO. zzoomz<me .OH
OOOO.N OOOO. OONH.H OOHN.H OOHH. OOOO. NOOO. «mflwomHm .NH
OOOO.H OOON. OOHO. OOOH.H OOOO. OOOO. OOHO. mammmmoomHz .HH
OHO0.0 OOOO. NOOO.H OOON.H OOON. OOOO. OOOH. OHmm>Oz .OH
OOOO.H OOON. OONO. OOON.H OOOO. OOOO. OOOO. HOHHmszU<Z .O
OOOO.H OOON. OOOO. OONO.H OOHH. OOOO. OHOO. meommm2m<m .O
HOON.N OOOO. OOOO. OHOO.H OOON. OOOO. OHOO. dszm .O
OOH0.0 OOOO. OOOO. OOON.H OOOO. OOOO. OOON. meammzozmHz .O
OOOO.H OOOO. OOON. OOOO.H OOOO. HOHN. OOON. meommeuzmu .O
OOOO.H OOOO. OOOH.H HOHO.H OOOO. OOOO. OOOO. meommeszm .O
NOOO.H OONN. OOOO. ONHN.H OOOO. OOOO. OOOO. mammmoooz .O
NOON.O OHOO.N OHO0.0 OOOO.N OOHO. OOOO. OOOO. >mmmommmHm0¢eo .N
OOO0.0 OOOO.N NHOO.N NOOO.N OOOO. OOOO. OHOO. OOOMOOBO>H .H
oEoonH
moHHm oEoonH oooomcH eoHHm OHGO oEoonH OHno Hoeoom
i eHsz cocoonH _ (HeHsz oEoocH eooHHo:H oEoonH

. .eooeHonH . . OnHooooem

HH omOB .eooeHonH . . H omOB eooechH .eooeHo eooeHa
eooeHa
coneoz

Odm one On ooeoEHemo .HOOOHO noHOom OensoonHeB one eoH mHoHHmHeHSE oEounH .Oim oHnoe

152

 

 

 

OHON.N HOOO. ONOO. OOOO.H NOON. OOOO. OOOO. mmmaosz .ON
ONOO.N OHOH.H OOHO.H OOOO.H HOOO. OONO. OOOO. amazozommz .OH
NOOO.H OOOO. OONO. OOOH.H OOOO. OOHO. OOOO. moH>mmmmmm .OH
OOOO.N ONOO. ONOO. OONO.H OOOH. OOOO. OOOO. moH>mmmmDm .OH
OOOH.N OOOO. OOON.H OOOH.H OOOO. OOOO. OHOO. Sfimmmmmm .OH
ONO0.0 ONO0.0 OOO0.0 OOOH.N OOOO. HONN.H OHOO. mUH>mmmmmm .OH
OON0.0 HNO0.0 OHO0.0 OONO.H OOOO. OONH.H OOOO. aemamomz .OH
OONN.O OHON.H ONOO.H OONO.H OOOO. NOOO. OOOO. zzoumz¢ma .OH
HOOO.N OOOO.H OOOO.H OOOO.H OONO. OOOO. NOOO. OmfiuomHm .NH
OOON.N OHOO. OOOO. OOOO.H NOOO. OONO. OOHO. whommmoomHz .HH
NOON.O OOOO. OOOO. OOHN.N OONN. OOHO. OOOH. UHmm>oz .OH
HOOO.N OHOO. OONO. OOOO.H NONO. NHOO. OOOO. BUMHMZHOUOZ .O
OOHO.N OOOO. OOHO. OOOO.H HOON. OOOO. OHOO. meammmzmmm .O
OOOO.N OOOO. OHOH.H OOOO.N OOOO. HOOO. OHOO. dszm .O
OON0.0 OHOO.H OOOO.H OOOO.N OONO. OHOO. OOON. meommzozmHz .O
OOO0.0 OONO. OONO. OHOO.H OOON. OOOO. OOON. OBDOOHUSOU .O
OOOO.H HHOO. OOOH.H OOOO.H HHOO. OOOO. OOOO. meommeszm .O
NOOH.N HOOO. HOOO. HOOO.H OOON. OOOO. OOOO. menmmcooz .O
NHON.OH ONO0.0 ONO0.0 NOOO.N OOOO. NOHO. OOOO. >mmmommmHmw<Bo .N
OONN.O OOOO.H HOOO.H OOOO.N OOOO. NOOO. OHOO. ommMUOBO>H .H
oEOonH

HoHHm oeousH couponH HoHHQ OHno oEoosH OHnO Hoeoom
IHeHoz ooODOGH uHeHsZ oeoocH eooeaonH oEoonH

. .euoeHonH . . mnHosooem
HH omOB .eooeHocH . . H oQOB eooernH .eooHHo eooeHQ .

eooeHo
oeooouoem o>HeoeoeH snuneomeonum
one On ooeoEHemo .HOOOHV :OHOom headcouHeB one HOH mHoHHmHeHsfi oEoonH .Oim oHnma

BIBLIOGRAPHY

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, and M. Cox. 1970. An Inventory of Regional
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Bureau of Business Research. 1965. A Preview of the Input-
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Czamanski, S., and E. E. Malizia. 1969. Applicability and
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