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INDUSTRIAL DIVERSIFICATION AND ECONOMIC STABILITY:
A CASE STUDY OF MICHIGAN

presented by

Martin Paul Grueber

has been accepted towards fulﬁllment
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M- A- degree in Geography

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INDUSTRIAL DIVERSIFICATION AND ECONOMIC STABILITY:
A CASE STUDY OF MICHIGAN

By
Martin Paul Grueber

A THESIS
Submimd to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

MASTER OF ARTS

Department of Geography

1988

5 44.3 475%

ABSTRACT

INDUSTRIAL DIVERSIFICATION AND ECONOMIC STABILITY:
A CASE STUDY OF MICHIGAN
By
Martin Paul Grueber

This research examines the change in Michigan's industrial structure from 1979 to
1985, and its effect on the industrial diversiﬁcation of 14 regions in the State. The
relationships between diversiﬁcation, employment stability, and income are also examined
at the regional level for 1985.

State-level annual employment estimates for 1960-85 were gathered for 21 sectors
of the Michigan economy. These data, in conjunction with, regional employment
proportions by sector, are used in a portfolio analytic model of industrial diversiﬁcation.
This model generates diversiﬁcation indices, where diversiﬁcation is a factor of both
regional employment proportions and State-level sectoral stability.

The State, as well as, the 14 employment regions, experienwd a decline in relative
diversiﬁcation from 1979 to 1985. This decline is due primarily to the effects of the 1982-
83 recession on sectoral stability. However, the severity of this decline is not regionally
uniform. It is also shown that signiﬁcant relationships exist between industrial

diversiﬁcation, and regional employment and income stability.

ACKNOWLEDGEMENTS

A project of this magnitude can never be accomplished without the aid and support
of many individuals. I ﬁrst and foremost wish to thank Dr. Bruce Pigozzi for his time and
patience, intellectual guidance, and friendship. The experience of working with Dr.
Pigozzi has yielded many beneﬁts far beyond the completion of this thesis. I also wish to
thank Dr. Assefa Mehretu for his many helpful comments on the content and form of this
research and Dr. Richard Groop for serving as rotator for the thesis defense, his time, on
very short notice is greatly appreciamd.

I gratefully acknowledge Dr. Gary Manson and the entire Department of Geography
for academic and ﬁnancial support throughout my graduate program.

I wish to speciﬁcally thank the department's secretaries, Amy, Carolyn, Marilyn,
and Harriet for assistance above and beyond the call of duty. The "morning crew" made all
those early mornings much easier to hear.

I also wish to express my deep gratitude to the Friday afternoon Regional Analysis
cluster, a.k.a. Bruce's Advisees: Engdawork, Ron, Joan, Joyce. Your camaraderie and
constructive criticisms were of unmeasurable value.

I also must thank my parents, in-laws, and family members. There is no way this
research or my graduate program could have been completed without the emotional,
ﬁnancial, and nutritional support of my families. For this support I dedicate this thesis to
them.

Finally I must specially thank the loving support of my wife Kim. She has put up
with long hours, sometimes very little attention, and an often tired and moody husband.

This research would never have been completed without her undying patience and love.

TABLE OF CONTENTS

List of Tables .................................. vi
List of Figures .................................. vii
Chapter Page
I. Introduction ................................ 1
Objectives of Study
Indusuial Diversiﬁcation, Economic Stability,
and the Michigan Economy
Concepts of Cyclical Stability, Diversiﬁcation,
and Industrial Structure

II.

III.

IV.

Research Hypotheses, Study Area, and Data

Conclusions

Survey of Industrial Diversiﬁcation Measures
Portfolio Analytic Model of Diversiﬁcation
Regional Economic Instability

Introduction

Research Hypotheses
Study Area

Data and Data Somces

Calculating the Portfolio Index of Indusuial Diversiﬁcation
Measurement of Regional Economic Instability

Computing Procedures

Normality Tests

Formal Hypotheses

Hypotheses Results

State-level Applications

Regional Applications

Case Study Applications: Battle Creek and Flint MSAs

Evaluation of the Small Region Use of the Portfolio Model
Summary of Results
Future Research

iv

..... 22

Methods of Data Analysis ........................ 33

Results and Applications ......................... 54

..... 81

Appendix A. Michigan Employment Region Area Definitions ......... 88

Appendix B. Regional Sectoral Employment Proportions: 1985 ....... 89
Appendix C. Regional Sectoral Employment Proportions: 197 9 ....... 90
Literature Cited ................................ 91

LIST OF TABLES

1. 21 Sectors of Michigan Economy and Corresponding SIC Codes ......... 31
2. Methods of Obtaining Relative Residuals .................... 38
3. Kolmogorov-Smirnov One Sample Test Using Standard Normal Distribution . . . 47
4. 1985 Industry Variance (Diagonal) and Instability (Column Sum) Values ..... 63
5. Regional Diversiﬁcation Indices: 1979 and 1985 ................ 67
6. Percentage Increase in Portfolio Diversiﬁcation Indices from 1979 to 1985 . . . . 68
7. Regional Instability Indices: Employment (1985) and Income (1984) ....... 70
8. l9 Sectors Used in Case Study Applications ................... 74
9. Increase in Regional Income and "New" Diversiﬁcation Indices

- Battle Creek MSA ............................. 77
10. Increase in Regional Income and "New" Diversiﬁcation Indices

- Flint MSA ................................. 79

$9999.“

LIST OF FIGURES

Michigan Employment Regions Used In This Study ............... 27
The Time Series of Michigan's Construction Employment for 1960-1985 ..... 36
The State-level Quadratic Trend of the Construction Time Series .......... 36
Vertical Lines Indicating the Size of Each Residual, Yi, - 9i, ............ 37
The "Vectorization" Procedure .......................... 50
Regional Income Change and Diversiﬁcation - Battle Creek MSA ......... 76

Regional Income Change and Diversiﬁcation - Flint MSA ............. 79

vii

Chapter I
Introduction

The economy of the the State of Michigan has long been used as me example of an
unstable economy. Regional economists have noted the "swings" of Michigan's economy
between prosperity and stagnation and believe this economic instability is due primarily to
the State's heavy dependence on durable manufacturing. It has been assumed and
hypothesized in the literature that a distinct relationship between industrial diversification
and regional economic stability exists. This relationship has been quantiﬁed, with some
recent success (Conroy,l972; Kort,198l; Brewer,l985), but much needs to be done to
determine its exact natme and strength. The past instability of Michigan's economy and the
State's extreme concentration of durable manufacturing (especially automobile production)
provides a unique study area to further examine the relationship between industrial

diversiﬁcation and regional economic stability.

Objectives of Study

This study examines the industrial structure of Michigan, through the use of a mm
mm of industrial diversiﬁcation. With this model, it is possible to identify the
effect industrial diversiﬁcation has on the stability of the Michigan economy. The study
also examines many of the State's regional economies to determine the relationship between

the State's overall economy and the economic stability of these individual regions.

This study has three primary goals.
1. Examine the industrial structure of Michigan.

The industrial structure of Michigan will be examined to determine if it has signiﬁcantly
changed between 1979 and 1985; 1979 being the year of the State's last employment peak
prior to the most recent recession. In analyzing this change, it will also be possible to
determine whether the State has become more or less diversiﬁed during this time period.
Part of this examination of Michigan's industrial structure will also focus on determining
which industries have become more (or less) stable over time. Of primary importance in
this total analysis is to compare and contrast the regional economies that have developed
arormd the State's industrial structure.

To further the study of the relationship between industrial diversification and economic
stability, the portfolio diversiﬁcation index will be compared to various measures of
W— Similar comparisons have been used by others
(Conroy,1972; Kort, 1981; Jackson, 1984; Brewer, 1985) to measure the strength of the

relationship between these two measures of a regional economy.
2. Examine possible uses of the portfolio analytic model for planning.

Industrial diversiﬁcation indices are most often used for regional comparisons. Though
useful in this regard, most diversiﬁcation indices are of somewhat limited practical use.
The results of the portfolio analytic model of industrial diversiﬁcation lend themselves well
to many uses in planning and economic development. Possible uses consist of weighing
additions to regional income (through increased regional sectoral employment) against their
impact on the regional industrial diversiﬁcation level and also identifying those industries

that have had an overall stabilizing impact on the State's economy.

3

3 . Carry out a critical evaluation of the use of the portfolio analytic model of

diversiﬁcation to measure "small region" industrial diversiﬁcation.

The use of a portfolio analytic model of industrial diversiﬁcation, along with the
resulting diversiﬁcation indices, has been shown to be the best available measure of
industrial diversiﬁcation (Conroy, 1,972; Brewer, 1985). As part of this study, I will
evaluate the application, of this fairly recent development in measuring industrial
diversiﬁcation, to State and regional level data. Though the portfolio analytic technique has
been applied to other ”small region" data, very little work has been undertaken which
identiﬁes speciﬁc problems related to the use of "small region" data with the portfolio
analytic model of industrial diversiﬁcation.

Industrial Diversiﬁcation, Economic Stability, and the Michigan Economy
George Borts, in one of the most detailed studies of regional manufacturing
employment cycles (1960, pp. 157-158), stated,
In terms of industrial composition the most variable states are characterized
by a high proportion of durable- goods manufacture, speciﬁcally
transportation equipment (e. g. automobiles), primary and fabricated metal

products, machinery and lumber. The least variable states are characterized
by nondurable manufacttnes: textiles, shoes, apparel, tobacco and food

products.
In his ranking of the states by average variability, Michigan was ranked number one.
Kozlowski (1979, p. 7) describes the variability of the State: "Michigan, with its heavy
dependence on the automobile industry, is the most cyclically sensitive state in the region
and . . . has a long standing reputation as such because of its past boom and bust
performance." Haber et a1. (1959, p. 62) state,

"When slumps develop in the nation, Michigan tends to be affected more

severely than the country as a whole, with a consequent higher

unemployment rate. In periods of general prosperity, on the other hand,

economic activity in Michigan tends to rise more rapidly than that in the
national economy."

4

This variability or economic instability, due to the high proportion of durable
manufacturing in the State, must be re-examined due to recent structural changes in the
Michigan economy.

The Michigan economy, as well as the economies of some of its neighbors, is going
through the process of deindusm'alization or a decline in industrial production. This
represents a signiﬁcant change in the industrial structure of these States. Schnorbus and
Giese (1987) examined the manufacturing output for the states of the Seventh Federal
Reserve District, of which Michigan is part. They conclude, "that since 1970 the Seventh
District's manufacturing sector has been producing fewer and fewer goods. This decline
represents deindusuialization in the sense of an absolute decline in output" (p. 8).
Corresponding to this decline in output is a reduction in the employment necessary to
produce it. Though the industrial output still ﬂuctuates up and down as demand ﬂuctuates,
the overall trend as shown by Schnorbus and Giese is toward reduced output. As the
Michigan economy continues through this process of deindustrialization, and the resulting
reductions in manufacttuing employment needs, how will these employment reductions
effect the total employment variability and the level of industrial diversiﬁcation in the State
and regional economies?

McLaughlin (1930, p.148), in his pioneering work on the effects of diversiﬁcation on
stability, suggests, "there may be some relation between degree of concentration and the
severity of cyclical, as well as seasonal, ﬂuctuations." Much recent regional economic
literature suggests that the relationship between stability and industrial diversiﬁcation
exists, but opinions differ as to the strength and nature of this relationship. If this
relationship exists, Michigan being the most variable state (according to Borts) could
beneﬁt greatly from a policy of diversiﬁcation. Indeed, the Michigan Beyond 2000 Report
(Hudson Institute, 1985) recognizes the need for Michigan to diversify its economy; but
will the present nature of the State's economy and workforce allow it to? This need was

also recognized in 1959, by Haber et a1. as a way to, "mitigate the swings in production

5

and employment in the auto industry and in certain other durable industries." They
comment further, "Now, diversiﬁcation becomes a 'must' for the State in order that we
may compensate for the loss of . . . auto jobs." (Haber et al. , 1959, p. 242). As is shown
by these historical statements, the possible beneﬁts of industrial diversiﬁcation have been
known for over 30 years yet the State continues to be dominawd by durable manufacturing.

Koval (1970) in his analysis of the industrial diversiﬁcation of Michigan gives
many insights into the possibilities of diversifying the Michigan economy. He points out
the necessity of diversiﬁcation, but also cautions against random diversiﬁcation efforts
(p. 138):

Although it is recognized that industrial diversiﬁcation of the Michigan

economy at a more rapid pace will bring mixed blessings to the state, it is

the recommendation of this report that a selective policy designed to

encourage increased industrial diversiﬁcation be adopted as the ofﬁcial

policy of the State of Michigan.

The emphasis on a carefully controlled policy of selective industrial

diversiﬁcation cannot be overstawd. If anything comes through loud and

clear in this report, it is that Michigan's approach to industrial diversiﬁcation

should be a highly selective one —- that is, the approach should employ the

"riﬂe" technique as opposed to the "shotgun" approach. The diffusion of

energies through the random pursuit of all types of indusn'y is not only

inefficient, but will also likely prove to be largely unproductive.

A major factor underlying State-level industrial diversiﬁcation is the recognition that the
State is not a unique economic entity per se. The State's economy is in fact the summation
of its many regional economies, with each regional economy reﬂecting, to some degree, an
overall State economic structure. Clark, Gertler, and Whiteman (1986) discuss these
relationships between national and state economic structures and local economic structure.
The larger regional economic structures of Michigan, especially Detroit, Grand Rapids,
Lansing, Flint, and Saginaw, are direct reﬂections (or causes) of the heavy dominance of
durable goods production, especially automobile production, in the State. Clark, Gertler,
and Whiteman, however, do not feel all specialization is necessarily detrimental: "It is

important to note that a process of sectoral specialization between places produces

6

geographical differentia which are not necessarily problems in themselves, and indeed may
be signs of vitality" (p. 25). This seems to concur with the ideas of Conroy (1972) and
Hoover and Giarratani (1984) that a region's economic stability is not negatively affected
by specialization in general, but by specialization in cyclically sensitive industries. This
study uses the portfolio analytic model to examine the relationship between industrial
diversiﬁcation (specialization) and the cyclical sensitivity of Michigan's industries.

Concepts of Cyclical Stability, Diversiﬁcation, and Industrial Structure

The use of cyclical stability in the literature focuses primarily on the relationships
between industries, regions and the business cycle. Brieﬂy, the W, is the
response of the economy to the changes in the supply and demand for money, and the
effect these changes have on the cost of money (interest rates). When interest rates are
low, people and ﬁrms spend money on goods and services. They keep spending, and
begin relying on credit. As more people depend on and demand credit, interest rates begin
to increase. As interest rates increase, people and ﬁrms cut back on expenditures and save
more. This reduction in expenditures, reduces the need for credit, so interest rates decline
again. This illustrates, in a simple way, the ups and downs associated with the business
cycle. W refers to the ability to remain "steady" as the business cycle goes
through these "ups and downs". Industrial cyclical stability (or industrial stability) is
directly relawd to the demand elasticity for the goods and services produwd by a ﬁrm or
industry. As prices increase (higher interest rates) the demand for new housing
(commotion sector) will decline greatly, but the demand for food (food and kindred
products sector) will not decline very much. Since there is a direct relationship between
demand and production, as demand decreases so will production (and hence employment).
Regional cyclical stability (or regional economic stability) refers to the composite group of

industries in the region and the joint effect their stability has on the ﬂuctuations in total

7

regional employment. Much recent economic research has been trying to quantify this
cause and effect relationship between industrial stability and regional stability.

A dimﬁedjndnmmm is generally considered a positive regional economic
goal, but how it should be obtained is the subject of much debate. Part of this problem lies
in the deﬁnition of a diversiﬁed industrial structure. This concept has taken on many
different meanings in the regional economic literature. An evaluation of this concept may
help to exemplify why a diversiﬁed industrial structure is difﬁcult to deﬁne and will set
forth the use of this terminology in this research.

The term Wig) has been deﬁned in many ways in the literature.
In general, it deals with, "the presence in an area of a great number of different types of
industries" (Rodgers, 1957, p. 16). This deﬁnition has been qualiﬁed many times in the
literature, which in turn adds to the confusion. Qualiﬁers such as, "balanced", "absolute",
"normal", and "average" lead one to believe that diversiﬁcation can be easily measured and
that a speciﬁc level is desired. There has also been an assumed relationships between
diversiﬁcation and population size, in that larger regions are by necessity more diversiﬁed
(Thompson, 1965; Clemente and Sturgis, 1971). The problem with such simple
descriptions of diversiﬁcation lies in that there is no standard for measuring the diﬂ’erences
between industries. This study measures these differences in industries not only in sectoral
size differentials, but also by the State-level cyclical stability of each sector.

What deﬁnes an industry, is subject to much historical bias. Past measures of
industrial diversiﬁcation used the terms "industrial" and "manufacturing" synonymously.
Most of these past measures used variables such as percent of employment in
manufacturing or value added in manufacturing as the indicator of industrial structure.
Only recently has the scope of industry been broadened to include service activities and
governmental employment, since these industries can have a profound impact on national,
state, and local economies. This study uses the term 10m to represent any non-

agricultural employment sector in the State.

8

The concept of mm is probably the most vague of the three terms. Structure is
often used to refer to the set of industries in an area. This deﬁnition is rather limiting,
when the vast nature of industries is examined. The structure of a 3mm industry is in
part due to its mode of operation; is an industry capital intensive or labor intensive, what is
the skill level required in the industry (and its resulting impact on wages), and is the
industry growing or in a state of decline. The structure of the set of industries in a region
relates to the linkages and the basic/non-basic relationships between these industries.
Regional industrial linkages, in terms of production and consumption, can be analyzed
through the use of Input-Output analysis. This measure of structure, however, does not
easily take into account (or measure) diversiﬁcation and economic stability. The term
mm in this study, will represent the set of industries in a region and the relationships
that exist between industries in terms of cyclical stability.

The speciﬁcs of industrial structure and how to determine if that structure is diversiﬁed
or not are still not totally agreed upon. It has been shown that a ﬁrm's inter-relationships
can most deﬁnitely vary from industry to industry, but can also vary greatly from region to
region. This regional variation, and its inﬂuence on a particular measrne of industrial
diversiﬁcation, can often bias results. The measruement of industrial diversiﬁcation is also
hampered by data availability. Though it inherently has its faults, employment levels are
most often used to measure and depict industrial structure due to the availability of these
data. It can be ascertained from these discussions that the measurement of industrial
diversiﬁcation is not an exact science, but one that needs to be examined to the greatest

extent possible.

Survey of Industrial Diversification Measures
The methods developed to measme industrial structure, and speciﬁcally industrial
diversiﬁcation, vary greatly in scope and complexity. The two most detailed surveys of

industrial diversiﬁcation measrnes are Bahl, Firestine, and Phares (1971) and Conroy

9

(1972). In both these studies the advantages and disadvantages of each index are analyzed,
as well as, compared to indices derived by the authors.

The following survey discusses various measrues developed and used in the past to
measure industrial diversiﬁcation. They are discussed roughly in order of complexity and
historical development.

5 C m . ES . 1° .

This method, as discussed by Isard (1960, p. 271), "measures the extent to which the
distribution of employment by industry classes in the given region deviate from such
distribution for the United States." Simply, it compares two percentage distributions, by
examining the deviations between the two. The coefﬁcient of specialization has the limits
of 0 (industrial diversiﬁcation) and approaching 1 (single industry concentration). The

coefﬁcient of specialization can also be used at sub-national scales, by using a state as the
all inclusive region and counties or MSA as the individual regions. This measme is useful
for comparing regions for similarity in indusuial mix, but by using the nation or state as a
standard of reference the measure is biased by the existing industrial mix of the larger
region. If the larger region itself is poorly diversiﬁed, measuring a region against this
industrial proﬁle is of limited use.

WW

Past attempts at explaining regional cyclical variations used industrial diversiﬁcation
measures based on the proportion of durable manufacturing in a region. Examples include
the works of Siegel (1966) and Cutler and Hansz (1971). Using the size of the durable
goods manufacturing sector as the sole indicator of industrial diversiﬁcation leaves much to
be desired. Though these industries are historically the most sensitive to movements in the
business cycle, limiting diversiﬁcation analysis to only these industries will tend to bias the
results against larger urban areas. Larger urban areas tend to have a larger proportion of
their labor force engaged in durable manufacturing due to the beneﬁts gained by these

industries locating in the urban environment and possible agglomeration economies.

10

A number of attempts at measuring indusuial diversiﬁcation fall into this category.
These methods measure regional industrial diversiﬁcation as some form of deviation from a
given "normal" mtoral employment distribution; "normal" in terms of an ideal or expected
level. Many types of "normal" proportion distributions are examined in the literature.

Bahl, Firestine, and Phares (1971), summarize these measures by categorizing them into
three groups: (1) equal percentage (or ogive); (2) national average; and (3) minimum
requirements. These measures have been used mostly with employment data, but have also
been used with income data.

Probably the oldest and most often used of the three types of "normal" proportion
measures are the W measures. The equal percentage or ogive measures of
industrial diversiﬁcation use as a premise that each industrial sector should have equal
percentages of employment to be totally (and optimally) diversiﬁed. An example of the
equal percentage concept would be that if 8 industrial sectors exist, each sector should have
12.5 percent of the region's total employment to be completely diversiﬁed. The ﬁrst uses
of this type index are found in McLaughlin (1930) and Tress (1938). One of the most cited
example of the use of this type of measure is Rodgers (1957). Rodgers' use is slightly
different than most in that he construcwd cumulative percentage (ogive) or Lorenz curves
and compared these to the optimum diagonal (equal percentage in each sector) hence the
term "ogive" is often used to refer to this type of industrial diversiﬁcation measure.

The equal percentage measures have gained a wide acceptance and are still used due to
their case of use and calculation. Keinath (1985) used a modiﬁed equal percentage measure
as his industrial diversiﬁcation index. Keinath's index is a summation of absolute
deviations from the equal percentage value, instead of using squared deviations. He felt
this modiﬁcation allowed for better interpretation of an individual sector's contribution to
the overall index.

11

The major criticism of the equal percentage measure is the arbitrarily implied equal
percentages for optimal (maximum) diversiﬁcation. The goal of an equal percentage of
employment in each sector is probably impossible to achieve in a planning context and has
no empirical justiﬁcation. To arbitrarily establish that all sectors in a given region should
possess the same percentages of some economic variable (employment, income, etc.)
allows for no differences in market structme between diﬁerent sectors. Economic realities
such as scale economies, regional differences in demand, and the differences in input
quantities used by the different sectors are totally ignored.

The second group of "normal" percentage measures are referred to as the national
mg: measures. These measures use as the "normal" percentage distribution the national
average percentage in each sector. The use of national average measures, is represented by
the works of Florence (1948), and Borts (1960). Though this type of measure repreSents
the sizeofeach sectorbetterthantheequalpercentage measures, itis still averyrough
approximation. Regional differentiation in production capabilities, demand, resources, and
other components of a regional economy causes these measures to over-estimate or under-
estimate the size of sectors in the regional economies. The national average measures can
also extremely bias the results if a region does not include a speciﬁc sector.

The third type of "normal" proportions measure is the WW technique
developed by Ullman and Dacey (1960). The authors characterize urban sectoral
employment structures into "minimum requirement" employment and excess employment.
The "minimum requirement" employment is that percentage needed to maintain the internal
viability of a region. They conclude this employment level is the "minimum requirement"
necessary since the percentages are empirically derived (through regression analysis). The
employment percentage that remains in excess of the minimum required, according to
Ullman and Dacey approximates the export or basic employment of the region. Ullman and
Dacey do however categorize cities by sizes, acknowledging that different sized cities may

need different percentages to maintain viability. Therefore they have derived a "norm " or

12

"necessary" percentage employment in each sector for a given city size classiﬁcation.
Although Ullman and Dacey primarily developed this technique as a quick method for
estimating the economic base of a city or region, they also developed an index of
diversiﬁcation from their method. The uncorrecwd diversiﬁcation index is a summation of
the squared deviations from each sector's "minimum requirements" percentage divided by
its "minimum requirements" percentage. The index is then corrected for city size by
dividing the unadjuswd index by the ratio of squared basic employment percentage and the
total minimum requirements employment percentage.

Bahl, Firestine, and Phares (1971) contend that this index is already corrected for city
size differentials in the regression process used to estimate the minimum requirements
percentages. They therefore use as their Adjuswd Minimum Requirements Index only the
numerator of the Ullman and Dacey equation.

Though both minimum requirements approaches use unique ways of determining the
"normal" proportions, they both fall short in several respects. The minimum requirements
percentages may differ not only by city size differentials but also by regional differentials.
The calculation of the "minimum requirements" percentage ﬁom a cross section of US.
cities implies a "natio " scale to these indices, causes this measure to be biased in a way
similar to the "national average" measure discussed previously.

12 E I 1 [12' 'ﬁ .

Recent attempts at measuring industrial diversiﬁcation have considered the concept of
entropy in deﬁning what is concentrated and what is diversiﬁed. Entropy, as a physics or
thermodynamics construct, measures the amount of disorder within a given system. This
measurement of disorder has been used to analyze the spatial distribution of various socio-
economic variables, including the geographic concentration of industry (Garrison and
Paulson, 1973). These uses assume a relationship between entropy and equity, in that the
more drspersed' a variable is (higher entropy), the more equitable the distribution. The

proponents of the regional economics application of entropy assume that a highly

13

specialized regional economy is highly ordered, and therefore has a low entropy value.
This assumption equates high entropy levels with well diversiﬁed economies. Hackbart
and Anderson (1975), were the ﬁrst to apply the concept of entropy speciﬁcally to the
measmement of industrial diversiﬁcation. In this study they calculated industrial
diversiﬁcation indices for several regions in Wyoming for the purpose of regional
comparison. Wasylenko and Erickson (1978), in the ﬁrst test of the statistical relevance of
the regional economic application of the entropy measure, found a high degree of
correlation between the entropy measure and the equal percentage or ogive measure
(Spearman's r = .98, statistically signiﬁcant at .001). They cited problems with both
meastues similar to those mentioned previously for the equal percentage measures.
Wasylenko and Erickson feel that if the measures are so similar, the use of the more widely
used and accepwd equal pr0portion measme is warranted based on ease of calculation
alone.

Kort (1981) applied an entropy measure of industrial diversiﬁcation to 106 SMSAs in
the United States. In this study he uses his diversiﬁcation index as an independent variable
to predict a measure of regional economic instability. This regression relationship is similar
to the one teswd by Conroy (1972) and suggested by Siegel (1966). Kort noted that the
residuals of this initial regression exhibiwd marked heteromdasticity (unequal variance) in
that the residual values from smaller regions tended to be larger. These unequal variances
violate one of the major assumptions of the regression model. Kort, based on a discussion
by Thompson (1965), assumed this heteroscedasticity to be related to city size differentials.
Thompson (1965, p. 118) states that,

large urban economies tend to have diversiﬁed industrial structures and,
therefore, tend to replicate the national degree of cyclical instability; the
smaller urban economies exhibit a much greater range of cyclical instability,
as some tend to specialize in the more unstable and some in the more stable

industries.

Kort corrected the heteroscedasticity by using a weighted least squares (WLS) regression

with the variables weighted by the square root of population. He found the resulting

 

14

equation signiﬁcant with an increase in adjusted R2 from .080 to .642. This result was
criticimd by Brewer and Moomaw (1986) as being incorrect. They stated that Kort had
fallen into a common pitfall of miscalculating the adjusted R2 of a WIS regression. When
Brewer and Moomaw, using the same data used by Kort, recalculated the regression and
the adjuswd R2 correctly, explanatory power was signiﬁcantly decreased from Kort's value
of 64. 2% to 7. 5%. However, the further explanation of the relationships between
industrial diversiﬁcation, regional economic instability, and city size is seen as a signiﬁcant

accomplishment (Brewer, 1985).

Portfolio Analytic Measure of Industrial Diversification

The use of the portfolio analytic measure of diversiﬁcation originated with the analysis
of securities in a ﬁnancial portfolio. Markowitz (1959) developed portfolio analysis as a
method of measuring the risks associated with the returns to various portfolios of ﬁnancial
securities (stocks), and the effect diversiﬁcation has on the level of this risk. Financial risk
is measured as the historical variability, of the returns to a dollar, inveswd in a speciﬁc
stock (the greater the historical variability, the greater the risk). A covariance matrix,
whose elements represent the similarities between different stocks in historical risk
ﬂuctuation, is calculated from the "time series" of the individual stocks past returns. The
portfolio index consists of the summation of values from the calculated covariance matrix,
each weighted by the proportion of the total portfolio in each stock.

Com'oy (1972) applied the Markowitz portfolio analysis model to the analysis of
regional industrial structures. Conroy measured returns in terms of employment level and
measured diversiﬁcation as an aggregate, expected measure of risk, where the variability
in employment level is considered the risk. This variability (or risk) is measured in terms
of the covariance of residuals from detrended sectoral employment "time series". To derive
the regional diversiﬁcation values this calculated covariance matrix, "provides the basis for

estimating the theoretical variability of the industrial structures in each region on the

 

 

 

 

 

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15

assumption that the covariability of individual industries is identical across the nation"
(Conroy,1972, p. 128). A lower measure of risk, and therefore a 19m: index
value, indicates a more cyclically stable, more diversiﬁed industrial structure.
This inverse relationship between actual diversiﬁcation kid and the Markowitz-Conroy
portfolio analytic diversiﬁcation mm is due to the fact that a stable industry (low
variance and covariances) has a positive effect on actual diversiﬁcation level, but reduces
the index value.

Conroy uses regression analysis to examine the relationship between diversiﬁcation
and regional economic instability for 52 SMSA in the United States. He calculates four
different indices of diversiﬁcation: an ogive or equal percentage measure, a national average
measure, a percent durable measme and the portfolio analytic meastne. Using these
various measures of diversiﬁcation as the independent variable in a number of simple
linear regression models, he tries to explain the dependent variable, regional economic
instability (which is a standardized amplitude measure based on the standard error of the
estimate of a time series each region's manufacturing employment). The results of
Conroy's tests indicate that of these four industrial diversiﬁcation indices, the portfolio
analytic technique signiﬁcantly outperforms the other three by more accurately predicting
regional economic instability. Conroy reports that the portfolio index explains 42.16% of
regional economic instability and is signiﬁcant at the .01 level, whereas the other indices
could explain no better than 8.45% with less statistical signiﬁcance. Conroy argues that
this approach re—establishes the validity of the link between diversiﬁcation and economic
stability. Conroy (1972, p. 143-44) states:

It would appear doubtful that any other single factor can be expected to
account for as much as 42% of the variation in a cross section as small as 52
cities. In the opinion of the author [Conroy] , such signiﬁcance for the data
series which were previously established as a mind the most important,

lends more-than—adequate credibility to a policy of careful diversiﬁcation in
order to stabilize regional economies.

16

A number of problems and concerns have been identiﬁed with Conroy's approach.
One major problem is that he used a national level covariance mauix to determine the
industrial su'ucture to be applied to the SMSA. This procedure precludes any regional
differentiation in the relationships between industries. As Conroy (1972, p. 162) noted,
"the assumption that the variance-covariance matrix of employment in alternative industries
was identical for all regions . . . is likely to have introduced further spurious variation."
Brown and Pheasant (1985), identify two other difﬁculties with Conroy's approach: 1) that
Conroy excludes non-manufacturing industries, and 2) Conroy examines only metropolitan
areas. These are seen to be major problems due to the role non-manufacturing industries
play in regional employment, and the vast differences in regional economic structlne
between industrial/urban regions versus more agricultural/rural regions.

The major concern with the use of the portfolio index of industrial diversiﬁcation is the
large amount of data needed to calculate the full Markowitz covariance mauix. To calculate
this matrix, temporal data is nee®d for each industry to be examined. This problem is
compounded by the desire to have as much sectoral or industry disaggregation as possible,
since as the number of industries increases the size of the covariance matrix becomes very
large.

Brown and Pheasant (1985) attempt to eliminate some of the problems with Conroy's
method by employing an alternative rrrethod of portfolio analysis developed by Sharpe
(1963). Sharpe's technique measures the risk of ﬁnancial return in terms of the correlation
with an economic index such as the Dow Jones Industrial Average. The percentage not
correlated with this index is considered to be the "risk" level for that security, since the
correlation value measrues the sensitivity to the national market. Those securities that have
low correlations with the economic index, though their returns may be higher, are more
risky in that it is more difﬁcult to predict the "ups and downs" of the particular stock. The
regional economic application of the Sharpe technique is based on the assumption that an

area's individual economic sector's rate of growth can be separated into that part which is

17

not responsive to an economic indicator index (such as unemployment rate) and that which
is; and apart from their correlation with the index the rates of growth are uncorrelated. The
Sharpe type index, as noted by Brown and Pheasant, omits any linkage or inter-industry
effects (similarities between two diﬂ'erent industrial sectors' variability). They feel this is
not a problem at the county level, but that it could be at the SMSA level. This distinction
seems very vague since many SMSAs are single county in size. This technique also has
problems identifying those industries that are doing well in times of economic slowdown or
recession. If employment in the economy as a whole is declining, a low correlation value
may indicate either an indusu'y experiencing an even more difﬁcult period or an industry
that is maintaining its growth in the recessionary period (some services, "high tech"
oriented industries). The primary reason Brown and Pheasant chose the Sharpe method
was to eliminate the need to calculate the large number of covariances. Calculating these
covariances with a microcomputer has reduwd the time and

difﬁculty of calculation, that the possible inaccuracies of the Sharpe technique far outweigh
its time saving merits.

A number of studies using modiﬁcations or elaborations of the Conroy-Markowitz
portfolio index exist in the literature. Barth, Kraft, and Wiest (1975) developed an index in
a similar context as the Conroy-Markowitz index with the exception that instead of
detrending each time series by removing a quadratic trend, they eliminate the "predictable
component in industry employment" using a ﬁrst-order autoregressive model (using the
previous year's employment to predict the present year's employment). This is seen by the
authors to be a simplistic technique but ﬁne for "illustrative" purposes. St. Louis (1980)
further develops the theoretical aspects of the Markowitz and Sharpe methods and modiﬁes
the Conroy technique by "using the notion of an efﬁciency frontier." St. Louis'
covariance matrix is calculated ﬁom time series consisting of deviations from the mean
growth rate. Using a quadratic programming technique (critical line method), he ﬁnds, "a
ﬁnite number of adjacent portfolios on the efﬁcient frontier that differ from one another

18

with respect to the status of at least one . . . industry." These adjacent portfolios are termed
"corner portfolios". St. Louis uses as his measure of diversiﬁcation, the minimum
"distance" between the region's portfolio index (which will be within the efficiency
frontier) and a "corner portfolio". None of these adaptations of the portfolio analytic model
of industrial diversiﬁcation examine the relationship between diversiﬁcation and regional
economic instability as did Conroy (1972) or Kort (1981) so that comments as to the
relative statistical merits of these various methodologies is impossible.

Brewer (1985), replicating Conroy's study, found heteroscedasticity in the residuals,
when the portfolio diversiﬁcation index is used in a regression equation to explain regional
economic instability. This pattern of heteroscedasticity is similar to the one found by Kort
(1981) in his comparable regression model. As mentioned previously this pattern has been
suggested by Kort (1981) to be related to city size. When Brewer corrects for this hetero-
scedasticity using a Weighted Least Squares (WLS) regression (weighted by the square
root of population size), the adjusted R2 value increased to .521 in comparison to Conroy's
value of .422. This lead Brewer (1985) to state, "The results further indicate that a
portfolio measure of diversiﬁcation deserves increased recognition in future research
compared to the more traditional measures of regional diversiﬁcation. "

Jackson (1984) performed a study similar to Conroy's in that he calculates various
types of diversiﬁcation indices and compares them to a measure of regional economic
insrability. He attempts to address some of the applicability questions of the portfolio
analytic technique of measuring industrial diversiﬁcation and the policy implications of
industrial diversiﬁcation in general. Jackson's results lead him to state that, "... policy
decisions should not be based on the relationship between currently available measmes of
industrial diversity and regional employment stability." This pessimism, however,
probably stems from the results of his analysis. Interpreting Jackson's results, however, is
a bit difﬁcult due to some problems with his data aggregation and collection methodologies.

He comments further on the complexity of regional economies and the large number of

19

variables a policy maker must consider in making development decisions. Jackson (1984,
p. 109) states,

rapid growth, cyclically sensitive industries are often preferable to more

stable, slow growth industries. This tradeoff is but one of many, and leads

one to question whether employment stability and growth are in fact the

appropriate measmes of risk and return.
He fails to realize, however, that the portfolio model of diversiﬁcation, provides a very
useful method for determining the Local stability of industries for planning and development
purposes (this method is further developed in the Chapter 4 of this study). Jackson also
comments that the relationship between economic stability and historical diversiﬁcation
levels is, "... crucial in a policy context" ( 1984, p.106). This relationship needs to be
established in order to use the actual diversiﬁcation index in a planning application.

In one of the most unique uses of the portfolio analytic model of diversiﬁcation, Bolton
(1986) examines State-level diversiﬁcation using income data for 48 "sectors" of the
economies of the New England states. Bolton's study is very unique in two respects.
First, Bolton's analysis differs from that of Conroy in that he removes both trend and
cyclical ﬂuctuations. He removes these two types of ﬂuctuations by eliminating a "constant
growth-rate trend plus ﬁrst- and second-order autocorrelated deviations from the trend,
measured relative to the trend." Bolton states, "This trend-cycle is variability in income that
is expected by the decision maker." This analysis assumes that cyclical variability is
expected and that people adjust the use of their income accordingly by saving or spending
differently. Second, Bolton's study is unique in that he includes the non-employment
incorrre categories of property income and transfer income as two of his "sectors". He
argues that in measuring diversiﬁcation in a region's total income, the effects on stability of
these two income generating sectors must be included. They are included since they may
account for a relatively large proportion of total personal income and the stabilization effects
of these two types of income are very important.

20

In this context, my study will use the portfolio analytic model of diversiﬁcation to
examine the industrial structme of Michigan, and the change in this industrial structure
from 1979-85. The study will also explore the possible uses of the portfolio analytic
model's results. for planning and policy purposes.

Regional Econonric Instability

As has been noted, much of the discussion of industrial diversiﬁcation relates to the
effect the level of diversiﬁcation has on the economic stability of a region. Conroy (1972,
1975b) outlines the historical development of regional economic thought concerning
cyclical stability and its regional effects. The concept of regional economic instability was
ﬁrst measured as such by Siegel (1966). Regional economic instability as a measure (tool)
is most often used as a mgionmiﬁc measure of employment variability. The calculation
of regional economic instability therefore yields an index which measures the instability of
a regional economic variable over time. Similar to the portfolio index, a 191:: value for
regional economic instability indicates a more stable regional economy, and
consequently a larger, value indicates a less stable economy.

The concept of regional economic instability may have been applied earlier than Siegel
(1966) since it is based simply on the standard error of the estimate of a trend line ﬁt
tluough a time series of a regional economic variable (in this case employment). Siegel and
Conroy (1972) use the residuals, from a detrended total manufacturing employment time
series, to calculate regional economic instability. Kort (1981), however, uses total non-
agricultural employment as his variable to measme instability due to the inclusion of many
non-manufacturing sectors in his analysis. Both Conroy and Kort use employment
variables in their diversiﬁcation indices and try to explain, through regression analysis,
their instability measures which are based on regional employment. However, regional

economic instability can be calculaed using a number of variables.

21

The measurement of regional economic instability has not been limited to techniques
based on the standard error. Brewer (1984), used as his measure of regional economic
instability a ratio of returns to risk. The ratio consists of the percent change in
manufacturing employment (returns) divided by the change in unemployment (risk)
experienwd in each of the SMSAs in his study. Brewer feels that, "together they [the two
variables in the ratio] provide a picture of the stability of each region by capturing the in and
out migration of the labor force as well as the changing experience of the more permanent
labor force. " Though the theoretical basis for the returns : risk ratio is logical, a
measurement of economic instability based solely on a one year change will be biased by
large ﬂuctuations that may occur in either variable during the particular year period. The
measure will also be biased by the sign (positive or negative) of the ratio. It is assumed in
Brewer‘s study that a positive ratio is more stable and desirable, yet a positive percent
increase in manufacturing employment divided by a negative percent change (decrease) in
unemployment would yield a negative ratio. Also a negative percent change in number
unemployed, for no other reason than those who were unemployed migrated out of the
region, would be seen as having an important stabilizing impact. These problems with this
ratio measme of stability makes the use of the measure questionable.

The present study will examine (as did Conroy, (1972); Kort, (1981); Jackson (1984);
and Brewer (1985)) the relationship between industrial diversiﬁcation and regional
economic stability. This relationship is seen to be crucial in establishing the validity of
diversiﬁcation measurement techniques, as well as to regional economic development
efforts. Unlike past attempts however, this study will examine the relationship between
industrial diversiﬁcation and regional economic instability measured not only with regienel
employment, but also with regienaljneeme. A temporal comparison between historical
diversiﬁcation (1979) and present (1985) regional economic stability will also be examined

due to the possible policy implications of this historical relationship.

 

Chapter II
Hypotheses, Study Area, and Data

Introduction

The economy of the State of Michigan is, and has been, extremely reliant on the
dtnable goods industries, especially the automobile industry. This State reliance is
transformd into regional economic dependence, within the State, on these same industries.
However, regional differentiation exists in the reliance on these durable goods industries,
with some regions becoming more diversiﬁed into the nondurable industries and into the
service sectors. This study aims to explore this regional differentiation by examining the
State's industrial structure in 1979 and 1985 and the various regional responses to this
structure.

This study will give further insight into the industrial structure of Michigan, in hopes of
gaining a perspective on the possibility of Michigan diversifying its economy. The study
will identify those sectors which are the most (and least) stable in the State, in order to
provide alternatives for futtne industrial development. It will also identify those regions in
the State that have had the greatest ability to maintain stability in an economy that can at best
be described as volatile.

The use of the portfolio analytic model of diversiﬁcation to provide measures of
variability (or risk) of possible industrial structures that may be evaluated in a policy and
planning context. These measures help identify possible alternatives for developing the
industrial structure of a regional economy, giving policy makers many options in deciding
which industrial structure to pursue.

The use and evaluation of the portfolio analytic model will further expand the literature

on this recent development in measming industrial diversiﬁcation.

22

 

23

Research Hypotheses

As part of this study seven research hypotheses are tesed to examine the industrial
structure of Michigan and the regional differentiation in response to this su'ucture. The
applicability of the portfolio model of diversiﬁcation for planning or development purposes

is also examined in a number of hypotheses.

l. A signiﬁcant change in the regional diversiﬁcation indices has occurred

between 1979 and 1985.

This hypothesis examines the change in regional diversiﬁcation levels from the pre-
recession employment peak (1979) to the present (1985). It is felt this time span of six
years, by encompassing the recessionary employment trough, will yield a signiﬁcant
change in the regional diversiﬁcation pattern.

2. A signiﬁcant change in the industrial structure of Michigan (as measured by

the inter-industry covariance matrix) has occurred between 1979 and 1985.

This hypothesis, actually a sub-hypothesis of the ﬁrst, is used to test if the economic
recovery from the most recent recession might be attributed in part to a change in the
industrial structme between 1979 and 1985. Though Thompson feels (1965, p. 21),

"... as much as two decades may elapse between shifts from one economic base to a
substantially new one" I believe the inclusion of 1982-83 recession warrants examination
of the six year span. Due to a national trend toward a service economy, the
deindustrialization of the Midwest region, and the State's recovery ﬁom the recent
recession it is hypothesiwd that a signiﬁcant change in the industrial structure in Michigan
has occurred. The results of this hypothesis will also detail the hypothesized change in

regional diversiﬁcation indices.

n.—

24

3. A signiﬁcant positive relationship exists between the regional diversiﬁcation

indices (1985) and regional employment instability (1985).

This relationship is similar to those tested by Conroy and others, and is used to
determine the strength of the relationship between diversiﬁcation levels and regional
economic stability. The relationship is important in a policy context, since a policy maker's
arsenal to effect regional economic stability is limied. The ability to effect industrial
diversiﬁcation through tax incentives, public ﬁnancial assistance, and other methods at a
more local level is possible , and therefore may be used to improve regional economic

stability.

4. A signiﬁcant negative relationship exists between the regional industrial

diversiﬁcation indices and population.

It is a common assumption that larger, more populated areas are by function and
necessity going to be more diversiﬁed (theory of urban hierarchies). A positive
relationship between industrial diversiﬁcation and population size has been hypothesized
(Thompson, 1965) and examined (Clemente and Sturgis, 1971) but was tested using other,
cruder measures of industrial diversiﬁcation. The hypothesis is cast as a negative

relationship due to a 19m index value indicating a mere diversiﬁed economy.

5. A signiﬁcant relationship exists between regional employment instability and

regional income instability.

This hypothesis is designed to test the relationship between employment stability and
income stability. The relationship between these two measures is difficult to foresee. The
difﬁculty lies in the numerical sensitivity of the two indices. Since regional employment
instability is measured using a time series of annual total non-agricultural employment

every employee in a region is treated as every other; a strict count. However, in the

25

measurement of regional income instability qualitative differences exist in terms of an
employee's income. The two employees which count the same in the employment measme
may have diﬂ‘erent incomes (doctor vs. student) and thus are qualitatively and quantitatively
different. The effect of the employment or unemployment of these two workers is very
different on each measure. The ambiguous nature of this relationship is heightened by the
knowledge that those industries in Michigan that historically have had the higher wages are
also those most sensitive to cyclical ﬂuctuations (transportation equipment, fabricated

metals).

6. A signiﬁcant positive relationship exists between the regional industrial

diversiﬁcation indices and regional income instability.

This hypothesis examines the relationship between industrial diversiﬁcation and
regional income stability. The hypothesis stems from the assumption that a well diversiﬁed

regional economy, may be better able to maintain regional income stability.

7. A signiﬁcant positive relationship exists between the historical regional
industrial diversiﬁcation index (1979) and present regional economic

instability (1985).

This hypothesis examines the role historical diversiﬁcation plays in determining present
day regional economic instability. This relationship is seen by Jackson (1984) to be very
important from a policy context. If a positive relationship does not exist, the practical use
of using present diversiﬁcation levels to guide policy and development decisions is very
limited. The strength of this relationship will also indicate to what degree future stability
can be "expected" to follow present diversiﬁcation.

26

Study Area

The primary focus of this research is to examine regional differentiation within the State
of Michigan. Though it would be desirable to examine this differentiation at the county
level, data requirements of the portfolio model and the desire for as much sectoral
disaggregation as possible precludes analysis at this level. The regional breakdown
chosen, as shown in Figure 1, includes the eleven Metropolitan Statistical Areas (MSA),
deﬁned by the 1980 census and used by the Bureau of Labor Statistics (BLS) and three
Labor Market Areas (LMA) as identiﬁed by BLS and the Michigan Employment Security
Commission (MESC). A W is deﬁned as,-"An economically integrated
geographical unit within which workers may readily change jobs without changing their
place of residence." (MESC, 1986).

Due to the "metropolitan" aspect, the MSAs are by mum in the more populaed areas
of central and southern Michigan. The three LMAs used, are those for which suitable
sectoral detail was available, due to their population size. The Upper Peninsula LMA is
also divided into a number of smaller LMAs but the use of these individual units is
hampered by non-disclosure regulations. The use of the entire Upper Peninsula of
Michigan as an LMA seems to violate the "commuting" deﬁnition of an LMA but for the
pm'poses of this study its use is better than having no representation of the Upper Peninsula
whatsoever.

The use of these 14 regions in the study, will only give a partial picture of the regional
differentiation in the State of Michigan. The 14 regions include 40 of the State's 83
counties. (See Appendix A. for county composition of each employment region). Though
this is less than half of the State's counties, these 14 regions account for 89.8% of the
State's 1985 total non-agricultural employment. The large percentage accounted for by the
14 regions, gives credibility to their use in examining the regional differentiation in

diversiﬁcation and economic stability in Michigan.

'hi E R'n

omseeswwr

Upper Peninsula LMA
Grand Traverse LMA
Alpena LMA
Saginaw MSA
Muskegon MSA
Grand Rapids MSA
Flint MSA

Lansing MSA

Detroit MSA
Kalamazoo MSA
Battle Creek MSA
Jackson MSA

Ann Arbor MSA
Benton Harbor MSA

27

 

 

 

 

 

l
A
Q
(3
0 3
r. ‘
5 7
81"“ 9

 

 

 

 

[to 11 12 13

 

 

 

14

 

 

Figure 1. Michigan Employment Regions Used In This Study

28

Data and Data Sources

State and most regional employment data for this study were obtained with the
assistance of the Michigan Employment Secmity Commission's Bureau of Research and
Statistics. Most of the data are available from the Michigan Employment Statistics Volume
I (Michigan), Volume II (Ann Arbor and Detroit MSA) and Volume III (Battle Creek,
Benton Harbor, Flint, Grand Rapids, Jackson, Kalamazoo, Lansing, Muskegon, Saginaw
MSA and the Upper Peninsula LMA ). Regional employment proportions for the LMA of
Grand Traverse/leclanau counties and Alpena county were gathered from separate, non-
published MESC materials to better represent the northern Lower Peninsula. These data,
used in this study, consist of annual employment averages by sector for the State from
1960-1985, and regional employment levels by sector for 1979 and 1985. State-level data
from 1956-1959 is available, but due to disclostn'e and aggregation problems, and the post
Korean War recession these data do not ﬁt the study well.

These MESC data are survey based and therefore are estimates of the true employment
values. MESC, which collects data for the Bureau of Labor Statistics (BLS), uses the
Current Employment Statistics (CBS) Survey methodology as established by BLS. The
CBS Survey is different ﬁ'om the Census "household" surveys.

The "household" survey includes unpaid family workers, domestic

workers, proprietors and other self-employed persons while all are excluded

by the CES survey. The "household" survey provides more detailed

data on the characteristics of the employed while the CBS provides more

detailed information on the industrial and geographical distribution of the

employed. (MESC, 1986, p. 164).
Due to the survey nature of these data, the values are often rounded to the nearest
hundreds. This "rounding" causes some problems when the value is near the cut-off in one
year and just over the cut-off in another year. This problem would give the indication of a
100 person shift from one year to the next, biasing the results. Though using employment

estimates is less than ideal for these reasons, it is the best available data which meet the

rigorous requirements of the Conroy-Markowitz technique while still providing suitable

29

regional detail to examine the regional economies of Michigan. It also the most readily
available data used by State and local economic development in Michigan.

Due to differences in SMSA and MSA boundaries, changes in Standard Industrial
Classiﬁcation (SIC) codes, and disclosme problems, a small amount of additional data was
needed for clarifying and replacing some missing portions in the above data set. These data
were gathered from the MESC's Wage and Earnings Employment Reports and the County
Business Patterns published by the Bureau of the Census of the U.S. Commerce
Department. The direct use of County Business Patterns (CBP) data is not appropriate,
since the two survey techniques are diﬁ‘erent. To reduce this possible bias, only
proportions were calculated from the CBP data and then applied to the corresponding
MESC data. This procedure was particularly useful when disaggregating the unfortunate
grouping of the mining and service sectors in some of the MESC reports. The ratio of
mining to the sum of mining and services from the CBP data was calculaed and then
applied to the MESC data to disaggregate the grouping.

The data requirements of the portfolio analytic model of industrial diversiﬁcation
include detrended State-level employment time series and regional sectoral employment for
a given year. However, these regional sectoral employment values must be converted into
proportions for use in the model. The regional sectoral employment levels are divided by
the region's total non-agricultural employment to obtain these employment proportions for
each of the 14 regions in the study. A similar procedure was also used to obtain State-level
sectoral employment proportions by dividing the total State employment in each sector by
the total State non-agricultural employment. In hopes of still further minimizing the bias
introduced by the rounding of employment values by the MESC, the regional, sectoral
employment proportions were calculated to only three decimal places. By examination,
additional Mimal places began adding unwarraned detail to the employment proportions.
These employment proportions are given in Appendix B (1985) and Appendix C (1979).

30

In order for the diversiﬁcation index to be of use, as much sectoral disaggregation as
possible is necessary. From the above data som'ces an all inclusive 21 "sector" breakdown
(disaggregation) of Michigan's total non-agricultural employment is possible. These
"sectors" were determined based on two criteria. The ﬁrst and foremost criteria is based on
State-level "time series" data availability. This was supplemented by a second, more
subjective, criteria based on State-level employment in the sector, along with regional data
availability. Some sectors such as Furniture Manufacturing (Grand Rapids) and Electrical
Machinery (Benton Harbor) though a large regional employment proportion exists in each,
are so regionally unique that regional employment levels for these two sectors could not be
obtained for all the regions. In these instances both Furniture Manufacturing and Electrical
Machinery are aggregated into Other Durable Manufacturing. The sectors and their
corresponding SIC codes are given in Table 1.

As stated in Chapter 1, the calculation of regional economic instability for this study
will use two different variables. First, to calculate a measure of employment instability, a
total non-agricultural employment time series was gathered for each region from available
MESC data. This presented a minor problem in that the regional subdivision into Labor
Market Areas (LMA) had not been deﬁned prior to 1970, and therefore data for years prior
to 1970 could not be colleced for the LMAs. Thus the employment time series for the
MSAs are from 1960-85 and for the LMAs the employment time series are from 1970-85.
This is not seen as a signiﬁcant problem due to the relationship between the formulation of
regional economic instability and the standard error of the estimate of a regression. Since
the standard error is the square root of the sum of the squared deviations divided by N-2,
the differences in the "length" of the series alone, should not cause the regional economic
instability results for the LMAs to differ by any order of magnitude from the MSAs results.
Though some loss of information will result from the use of these shorter time series for
the LMAs, I feel the information gained from inclusion of these northern Michigan regions
far outweighs any possible bias that may be introduced.

31

Table 1
21 Sectors of Michigan Economy and Corresponding SIC Codes.

Sam W
Mining 10, 13, 14
Construction 15, 16, 17
BMW

Lumber and Wood Products 24

Primary Metal Industries 33
Fabricated Metal Industries 34
Non-electrical Machinery 35
Transportation Equipment 37

Other Durable Good Manufacturing 25, 32, 36, 38, 39
Alamdumlzmmm

Food and Kindred Products 20

Paper and Allied Products 26

Printing and Publishing 27

Chemical and Petroleum Products 28, 29

Other Nondurable Good Manufacturing 21-23, 30, 31
S . Er l . L l .

Transportation and Public Utilities 40-42, 44-49
Wholesale Trade 50, 51

Retail Trade 52-59

F.I.R.E. 60-67

Services 074, 075, 078, 70-89
Federal Government --

State Government --

Local Government --

32

Second, I will use regional wage and employment income available from the Bureau of
Economic Analysis (BEA) to calculate a measure of regional economic stability to examine
the relationships between regional employment and income stability (RII, Regional Income
Instability). This index is a region speciﬁc summary value of instability of all income
earned in all sectors of employment. These BEA data were gathered by county and
aggregated to the 14 regions, for the years 1962, 1965-84, the only series available. It is
hypothes'md that the regional differentiation possible with regional income instability, will
diﬁ'er ﬁom regional employment stability, and will give a better insight into the total effect
industrial diversiﬁcation has on a regional economy.

The speciﬁcs of the calculation of both the portfolio model of industrial diversiﬁcation

and regional economic instability are given in the next chapter.

Chapter III
Methods of Data Analysis

This chapter details the procedtnes used to calculate the portfolio analytic model of
industrial diversiﬁcation, including speciﬁcs on model speciﬁcation. The chapter also
describes the calculation of the two measures of regional economic instability. The chapter
ends with formal hypotheses statements and a description of the statistical methods used to

test each.

Calculating the Portfolio Analytic Index of Industrial Diversiﬁcation

Since the portfolio analytic index of industrial diversiﬁcation measures diversiﬁcation
as a function of both the stability of the industry and the proportion of a region's
employment in the industry, there are two major steps involved in the calculation of the
model. The ﬁrst step used in calculating the Michigan regional portfolio indices is to obtain
detrended, employment time series for each sector at the State level. The original data used
to obtain these time series consists of annual employment averages, by sector, for the years
1960-1985 (See Figure 2). The process of detrending the raw annual data removes the
effect of growth from the time series. Without the removal of the growth trend, those
sectors that experienced growth would be treated as highly variable and in a Markowitz
sense, would be "risky". Through regression analysis it is possible to remove the growth
trend component from each sector's time series. The residuals from this detrending
regression model, are the measure of each year's "risk" or variability. If the annual
employment averages conform to the trend, the "predictive" power of the trend is strong,
and the risk is seen to be small. The more the actual values deviate from the trend the more

"risky" the sector is assumed to be Each time series is subjected to detrending using a trend

33

of 1

tht

cy

Jo

34

of the basic form:
Y=a+b1T+sz2+e
where: Y = the annual employment average
T = time, 1960=1, 1961=2, ..., 1985=26
e = residual

This type trend, which removes both a linear time component (T) and a squared time
component (T2), is termed a quadratic trend. Figure 3 depicts a quadratic trend line
through the time series of Michigan's annual employment in the construction sector.
Conroy (1972) found the quadratic trend to be statistically better ﬁtting than either a simple
linear trend or a log-linear mend. He also explains that a simple linear trend is a subset of
the quadratic form, when the b2 coefficient is 0.00, making the use of the quadratic even
more applicable. Upon examination of trends from higher order polynomial regressions
(including T3, T4, T5, T5, terms) the residuals obtained either did not differ greatly from
those obtained using the quadratic, or the trend equation began "ﬁtting" and eliminating the
cyclical ﬂuctuations I wish to examine.

Conroy, however, does not detail his procedure for handling residuals from an
equation with a 0.00 (statistically insigniﬁcant) coefﬁcient on either the T or T2 term.
Johnston (1984, p. 262) discusses the problem of insigniﬁcant variables in a regression
equation.

it is more serious to omit relevant variables than to include irrelevant
variables since in the former case the coefﬁcients will be biased, the
disturbance variance overestimated, and conventional inference procedures
rendered invalid, while in the latter case the coefﬁcients will be unbiased,
the disun'bance variance properly estimated, and and the inference
procedures will be valid. This constitutes a fairly strong case for including
rather than excluding variables from a regression equation. There is,
however, a qualiﬁcation to this view. Adding extra variables, be they

relevant or irrelevant, will lower the precision of estimation of the relevant
coefﬁcients.

Fr.

ICE

for

As

em

cm;
As

C011

35

From examination of residuals from sample regression equations, with and without
insigniﬁcant coefﬁcients, the residuals do not indicate any majer differences. Therefore,
since the sole purpose of the regression analysis is to remove the growth trend effects and
net for speciﬁc coefﬁcient estimation, and for the sake of simplicity, the quadratic trend is
removed from all sectoral annual time series.

The residuals (e) from a regression, may also be expressed in a different notational

form:

residual (e) for sector (i) and time (t): cit = Yit - ?i

where: Yit = the actual employment level
9n = the estimated employment level

As staed above, it is the size of these residuals that indicates the variability in the sectors
employment (small residuals = low variability; large residuals = high variability).
Figure 4 graphically depicts the "size" of the residuals for Michigan's consu'uction

employment sector (the construction sector was chosen due to its apparent high variability).
As can be seen, the large residuals of the construction employment, indicate that the

construction sector is extremely variable and "risky".

uCOFEAG—Lrﬂmu ﬁC_uU-asz..vnv _=:Cc< .....untknzlptmn 23.202.27.5er ~...:2:<

Annual Construction Employment
(in thousands)

36

 

140

130--

120--

110%-

1co-L

 

 

 

10

YEAR(T)

30

Figure 2. The time series of Michigan's Construction employment for 1960 - 1985.

Annual Construction Employment
(in thousands)

 

140

130--

120--

110'

100-

90-.

V

‘

 

 

 

80

Figme 3. The State-level quadratic trend of the Construction time series.

10

YEAR(T)

30

_- a»
nl—Vph-v.i-dFV- F.-
” e

Sen

sad

The

best

C017

Ihe.

37

 

140 ‘ljr

130"

 

120-:

 

110--

 

100'

Annual Construction Employment
(in thousands)

90"

 

 

 

 

80. i i
0 10 20 30

YEAR(T)
Figtne 4. Vertical lines indicating the size of each residual, Yit -?it.

In order to compare industries of different orders of magnitude in employment (e. g.
Services compared to Mining) Conroy divides the residuals by the mean of the original time

series, thus creating a series of mean-relative residuals:
A .—
Yit - Yit/ Yi

There are a number of methods available for making the residuals "relative" or scaled
among the different sectors. In order to better understand the process and to determine the
best method ﬁve alternative methods were examined for a sector and subjected to a
correlation analysis to determine what similarities exist. Table 2 lists the ﬁve methods and

the correlation matrix of these ﬁve methods.

38

Table 2.
Methods of Obtaining Relative Residuals (Results from Mining Sector)
1. Divide the residuals by the mean of the sectors time series as per Conroy (MEAN).
2. Standardize the residuals from the regression analysis (STDRES).

3 . Standardize the original employment time series and use residuals from the
regression analysis of these data (STDDATA).

4. Residuals measured as a percent of the trend estimate values (PCTEST).
5 . Residuals measured as a percent of the actual employment levels (PCI‘ACT).

Pearson's Correlation Matrix

MEAN ST'DRES STDDATA PCI'EST PCI‘ ACT
MEAN 1.000
STDRES 1.000 1.000
STDDATA 1.000 1.000 1.000
PCI'EST 0.998 0.998 0.998 1.000
PCT ACI' 0.992 0.992 0.992 0.995 1.000

All values statistically signiﬁcant at .05 two-tailed conﬁdence limit.

This table shows the extreme correlation between all ﬁve methods of scaling a sector's
residuals, indicating that there is a statistically signiﬁcant relationship between any of the
ﬁve alternatives. The values derived from each of the scaling methods will differ in actual
magnitude, but will not differ in relative magnitude. Using any of the scaling methods for
all 21 sectors will not yield a sector variability ranking different from that obtained using
any of the other methods. Since the mean-relative method, as used by Conroy (1972) is
the least Operationally complex, and can be represented very easily mathematically I have
used this method also.

ind

39

The set of 21 sectoral, mean-relative residual series are used to calculate the inter-

industry covariance matrix (Gij). This covariance matrix is calculated as:

N _ A __
2; [(Yit‘?it / Yi)(th-th/ Yj)]
p

Gij =

 

N-2
where i andj are two distinct sectors. In those cases where i =j (the diagonal of the

covariance matrix), i j yields the variance for that industry. When i ¢ j, the covariance

(measming the similarity in variability between the two sectors over time) is calculated.
Given this inter-industry covariance matrix, a measure of the instability (variability) of
each industry can be obtained by summing over j, a column sum (or by summing over i, a
row sum, since the covariance matrix is symmetrical). This summation will give a measure
of the stability of the industry considering mm the variability of the indusuy (the industry's
employment ﬂuctuations) and the effects due to the linkage or coincidental covariance
relationships with the remaining industries. This value can be compared to the industry
variance (from the covariance matrix diagonal) to determine the proportion of the industry's

instability that is due to its own variance.

A regional portfolio index (0p); ) is derived by weighting the State based inter-

industry covariance matrix by a particular region's sector employment proportions (Xik and

X33, proportion of region k 's employment in sectors i and j respectively).

pro:
ind;
div:

cov
Thl
incr
divt
con
cm]

“CC

40

The equation for the portfolio index of diversiﬁcation:

 

ka = E Ext]: Xjk Gij

3:1 r=l

N N
wherez Xi]; = 2 X3]; = 1.000
i=1 i=1

This weighting of the covariance matrix and subsequent summation of the elements
produces an index that measures diversiﬁcation as a function of the State-level inter-
industry relationships and the regional sectoral size differentials. This relationship between
diversiﬁcation and the size of the covariance matrix values causes the inverse relationship
between the portfolio model's diversiﬁcation index value and the actual diversiﬁcation level
(higher index value = lower actual diversiﬁcation level). A region with a large
proportion of its employment in those unstable industries with large variances and
covariances, will have a large index value, indicating that the region is many diversiﬁed.
Thus, diversiﬁcation can be achieved by reducing employment in an unstable sector or by
increasing the employment proportion in a stable sector. The ability to increase the
diversiﬁcation level (reduction in the index) through additional employment is gained by the
condition that the sum of the employment proportions must equal 1.000. If the
employment in a stable sector increases (larger proportion), all other proportions must
necessarily decrease slightly (in effect decreasing the proportion in any unstable industries

in the region).

4 1

This ability to diversify through either reducing employment or increasing employment,
is unique to the portfolio model of diversiﬁcation. This procedure for measuring
diversiﬁcation, allows a region to specialize, while remaining fairly diversiﬁed if the mix of
its other sectors is stable. The ability to do this however, depends on the size of the
industry variances when compared to the size of inter-industry covariances, and in which
sectors the employment changes occur (This relationship will become more apparent in the
Case Study Applications in Chapter 4). A region with a large proportion of its
employment in those unstable industries with large variances and covariances, will have a
large index value, indicating that the region is My diversiﬁed.

As part of this study, regional industrial diversiﬁcation indices are calculated for 1979
and for 1985 for all 14 regions in the study. Having diversiﬁcation indices for two time
periods will allow a temporal comparison to be made. However,'the examination of this
relationship poses a problem not confronted in any of the existing literature using the
portfolio index of industrial diversiﬁcation.

The covariance mauix is calculated ﬁom the mean-relative residuals from the
detrending regression analysis. The detrending process removes the effect of the quadratic
trend estimates from the actual employment values. The State-level sectoral employment
time series, used in this study, extend from 1960 to 1985. Since this study examines the
change in industrial structure from 1979 to 1985, two time periods are to be examined;
1960-79 and 1960-85. This will allow a diversiﬁcation index to be calculated for 1979 and
for 1985. Due to the overlap in the employment series, a question arises as to which time
period's trend to remove? The removal of trend, from each sector's employment series,
and its impact on the size of the residuals is very important for this model, in that the

removal of an incorrect trend could bias the results.
Two options for temporal trend removal exist:
1. Removal of each period's speciﬁc trend,
2. Removal of a base period's trend.

42

These options, in turn pose additional questions. The removal of each period's speciﬁc
trend is operationally the most simple, however, it inherently has some theoretical
questions, since the genial employment ﬂuctuations used to calculate the trend from T=1 to
T=20 are a "subset" of the employment ﬂuctuations used to calculate the mend from T=1 to
T=26. This " subset" notion leads one to consider the possibility of removing a base
period's trend from each period under examination. However, the decision as to what base
period to use is difﬁcult.

In order to better understand these relationships, both options are explored by

examining the residuals from the Consmuction sector detrended as follows:

Series 1) 1960-1979; mend calculated from this series and removed;
Series 2) 1960-1985; mend calculated from this series and removed;
Series 3) 1960-1979; mend calculated from 1% series and removed.

Ideally, it would be desirable to also remove from the 1960-85 Consmuction employment
series, the quadratic mend obtained from the 1960-79 employment series, however, it
would be Operationally complex and theoretically questionable. The use of the 1960—79
series to base the mend on, is suspect (since 1979 was chosen speciﬁcally due to the
occurrence of the last State total non-agricultural employment peak). Also of major concern
is that the predictive power of regression analysis should be limited to data within the range
of data for which the model is ﬁt. It is for these reasons that this fourth method is not
explored.

Examination of the residuals from the three different methods, yielded interesting
results. The Series 3 results are, by nature of the methodology, identical to the ﬁrst 20
residuals in Series 2. These results would seem to indicate that the removal of a "base"
periods mend would be the desired method. This would cause any changes in the
calculated covariance matrix to be a direct result of the additional six years (1980-1985).

However, it became apparent that this method would not allow for simple temporal

43

comparisons, especially in a planning context. With each additional year added to the
employment series, a new mend can be calculated and removed. Using the base year
methodology would require that every year, all previous years would need to be
recalculated to maintain this base year comparison. The comparison between Series 1
residuals and Series 2 residuals yielded a Pearson's Correlation coefﬁcient of .968 when
comparing the ﬁrst 20 residuals of each series. This indicates that even though the actual
mends used to get these residuals were different, the residuals for the years 1960-79 are
very similar. A Pairwise T-test also indicated that both series could have come from the
same population; T-statistic = -0.296, Two-tailed probability = .771. Calculating each
speciﬁc period's mend (Series 1 and Series 2) has the Operational advantage that once
calculated, the detrending for that period is complete. This would allow the portfolio model
to calculate a diversiﬁcatiOn index for 197 9, using Series 1 methodology, that would be a
set value for future comparisons. It is for these reasons that for the remainder of this
study, only employment residuals obtained with Series 1 and Series 2 methodology are
used to calculate the diversiﬁcation indices for 1979 and for 1985.

Measurement of Regional Economic Instability

As noted in Chapter 1, regional economic instability is a W measurement
of the instability (or variability) in the region's economy, as measured by a speciﬁc
variable. The measurement of regional economic instability is based on the standard error
of the estimate from a regression analysis. However, to enable inter-regional comparisons,
quadratic detrended, mean-relative residuals (similar to those used in the calculation of the
portfolio model) are used to calculate the instability value, due to regional size differences.
This formulation for the use of mean-relative residuals is the same formulation used by

Conroy (1972). The formulation of economic instability for region k :

44

 

IV

A .-
1((Ytlt - Ytlt )/ Yr )2
N-2

t:

 

Economic Instabilityk =

where: Ya; = the actual regional employment level
9n; = the quadratic estimated regional employment level
(Y a . 9a; ) = the residuals from quadratic regression analysis
.Y-k = the mean regional employment level
N = the number of years in the employment series

Though I use the same formulation as Conroy, I have calculated regional economic
instability using two different variables. I have calculated regional instability, for each
region, using a total non-agricultural employment time series, as did Kort (1981), since I
have included many non-manufacturing industries in my analysis. To use the abbreviation
REI can be very confusing since I have calculated regional economic instability using not
only employment but also income. The use of the abbreviation, REI, will be limited to the
instability of regional employment (REI: regional employment instability ). I have also
calculated regional economic instability measured with income data (hereto referred to as
RII, regional income instability ) using BEA Wage and Employment Income data.

Computing Procedures

As indicaed, the calculation of the portfolio analytic model of industrial diversiﬁcation
has two distinct computational steps: 1) the regression analysis needed to obtain the mean-
relative residuals used in the model; and 2) the actual calculation of the portfolio
diversiﬁcation indices.

The regression analysis used in this study, was performed using the SYSTAT Version
3.0© statistical package for IBM© compatible microcomputers.

The actual calculation of the portfolio model was achieved through the use of
PORTFOLIO, a program written in Microsoft FORTRAN© by the author. This program

45

uses as inputs the mean-relative residuals from the demended, State-level, employment time
series for the 21 sectors and the sectoral employment proportions for each of the 14
regions. The output ﬁom the PORTFOLIO program includes an echo printing of the
regional employment proportions mamix, various tabulation ﬁles, summary values, and the
portfolio index of diversiﬁcation for each of the 14 regions (as well as the State value and

and equal proportions portfolio index).

Normality Tests

The analysis of the hypothesimd relationships and the small number of observations
used in this study, warrant the use of correlation analysis to determine the suength of these
relationships. Regression analysis would allow the eansality of the relationships to be
tested, but the problems with degrees of freedom associated with a small number of
observations (14 regional observations) preclude its use (some regressions will be utilized,
however, for comparison to the results of Brewer (1985), Conroy (197 2), and Kort
(1981)). In correlation analysis, the decision has to be made as to which type of test to use
(Pearson's paramemic correlation or Spearman's non-paramemic, rank-order correlation).
The condition of bivariate normality, that is an assumption of the Pearson's correlation test,
is often not even addressed in the literature. For this study the normality of each variable
was tested using the Kolmogorov-Smrimov (KS) one-sample test of normality available
within SYSTAT. Due to the small sample size, the Lilliefors option was used, which
yields probabilities corrected for a small sample size. All variables used in the KS -
Lilliefors tests were first standardized (condition of Lilliefors option) and then subjected to
the KS test to determine normality. The hypotheses for a KS test are smuctured:

Ho: There is no statistical difference between the variable's distribution and
a normal distribution.

H1: There is a statistical difference between the variable's distribution and a
normal distribution; the distribution is not normal.

with Alpha = .05, two tailed rejection level.

46

The KS hypotheses structure is unique in that to obtain the most desirable result, the Ho
hypothesis will be acceped. The results of the KS tests are shown in Table 3. Due to an
initial probability plot, the variable POP84 was predetermined to be non-normal. In an
attempt to achieve normality the natural log of POP84 was computed and is represented by
LOGPOP84.

It can be seen in Table 3 that the Ho hypotheses can be rejected for only POP84, and
the two smucture variables, STRUCT85 and STRUCI'79. The natm'al log mansformation
of POP84 is shown to be successful, since the Ho hypothesis for LOGPOP84 was
accepted, indicating that the variable is normal. These results indicate that most
relationships examined in this study, can be tested using the more efﬁcient Pearson's
correlation test. The correlation tests were performed using the SYSTAT computer

package also.

47

Table 3.

Kolmogorov-Smirnov One Sample Test Using Standard Normal Dismibution

where:

 

 

 

Variable MaxDif Lilliefors Probability (2-tail)
PDIV85 .1 17 1.000

PDIV79 .169 .356

POP84 .401 .000

LOGPOP84 .173 .318

RBI (1985) .209 .099

RH (1984) .157 .493

STRUCT 85 .214 .000

STRUCI‘79 .201 .000

PDIV85 = portfolio diversiﬁcation, 1985

PDIV79 = portfolio diversiﬁcation, 1979

POP84 = regional population, 1984

LOGPOP84 = the log of POP84

REI = regional employment instability, 1985

R11 = regional income instability, 1984
STRUCT85 = Michigan industrial smucture, 1985
STRUCI'79 = Michigan industrial smucture, 1979

48

Formal Hypotheses

The research hypotheses as stated in the previous chapter are now restated in a formal
statistical smucture. The choice of statistical test used to test each hypothesis depends
foremost on the normality of the variables in question. A Dependent Student's T-test is
used for Hypothesis 1, since the indices are region dependent. The formal hypotheses

and the statistical test(s) used for each are as follows:

WLL

A signiﬁcant change“ in the regional diversiﬁcation indices (PDIV79 and
PDIV85) has occurred between 197 9 to 1985.

Ho: PDIV79 = PDIV85
H1: PDIV79 at PDIV85
Test used: Dependent (Pairwise) Student's T-Test, alpha=.05, two-tailed.
A non-directional hypothesis is appropriate, since no a priori assumptions can be made as
to whether the regions will become more diversiﬁed or less diversiﬁed. A Dependent
Student's T-test is used for Hypothesis 1, since the indices are regimidepegdem.

amnesia.

A signiﬁcant change in the industrial structure of Michigan (as measured by
the inter-industry covariance matrices; STRUCT79 and STRUCT85) has
occurred between 1979 and 1985.

Ho: STRUCT79 = STRUCT 85
H1: STRUCT79 it STRUCT 85

Test(s) used: Non-parametric Wilcoxon Signed Ranks Test,
alpha = .05, two-tailed.

Spearman's Rank Order Correlation, ('T-Test for signiﬁcance),
alpha = .05, two-tailed.

Once again two-tailed, non-directional hyp0theses are appropriate since a direction cannot

be attributed to the change in smucture, prier to the calculation of the model. To test

49

whether the State's industrial smucture, as measured by the inter-indusmy covariance
matrix, has signiﬁcantly changed between 1979 and 1985, and to examine the degree of
change, we tests will be used. A Wilcoxon test was chosen to examine the smﬁstieal
diffeienee between the two year's indusmial smucture. The Wilcoxon test is a non-
parametric, dependent comparison test, equivalent to a parametric Dependent T-test. A
non-parametric test is warranted since both STRUCT79 and STRUCT85 are non-normal
(see Table 3). Hammond and McCullagh (1978, p. 207) describe the Wilcoxon method.

The Wilcoxon test for paired samples (let us call them A and B), although

used to compare data on an interval scale, is a non-parametric test in that the

differences between pairs of data from the two samples are ranked - i.e. are

put on an ordinal scale - and signiﬁcance levels depend upon the allocation

of these ranks between those cases where A is greater than B, and those

where B is greater than A.
A Spearman's Correlation analysis will be used to examine the WM
between the State's indusmial smucttne in 1979 and 1985.

Testing the similarities between the two covariance matrices (and mamices in general) is
difﬁcult, so by using both types of measures I hope to use one as a partial check for the
other. In order to use these two tests the form of the inter-industry covariance mauix must
be changed, since both are tests on vectors of numbers. Since the inter—indusmy covariance
matrix is symmetrical those numbers above the diagonal will be deleted (a triangular
mamix) since including them would add unwarranted signiﬁcance to the statistical tests.
The remaining values from the inter-industry covariance matrix will be "vectorized" in the
sense that each column of the triangular matrix will be placed below the previous (see
Figure 5). The matrix values, once calculated, are independent of their position within the
matrix, but are dependent on the two industries used to obtain the value. Therefore, as
long as the "vectorizing" allows comparison of a industry speciﬁc 1979 value with the
same indusmy speciﬁc value for 1985, this procedure will not unduly change any possible

result. This "vectorizing" procedure is used only to allow the application of readily

available comparison, tests.

50

A A
BC B
DEF D
GHIJ G
C

I E
H

F

I

J
II.

Figure 5. The "Vectorization" Procedure

I. A miangular matrix after the elements above the diagonal have been removed.
II. The mauix when "vectorized".

51

The remaining ﬁve hypotheses are all tested using Pearson's Product Moment
Correlation. This test is chosen for these ﬁve hypotheses due to the normality of the
variables (see Table 3) and the desire to test a relaﬁeneiu'p. A Student's T-test is used in
each case to test the statistical signiﬁeanee of the Pearson's Correlation coefﬁcient.

Meatball.
A signiﬁcant positive relationship exists between the regional diversiﬁcation
index (PDIV85) and regional employment instability (REI).

Ho: r = 0.000
H1: r > 0.000

Test used: Pearson's Correlation Coefﬁcient (T -Test for signiﬁcance),
alpha = .05, one-tailed.

A positive directional hypothesis is used in this case, since a positive relationship was
shown to exist between these two variables by Conroy (1972), Kort (1981), and Brewer
(1985). It is also chosen due to the fact that both indices are based on employment. A
diversiﬁed regional employment smucture should be better situated to withstand cyclical

shocks to particular industries and thereby maintain stability.

W14.
A signiﬁcant negative relationship exists between the regional diversiﬁcation
index (PDIV85) and the log of population (LOGPOP84).

Ho: r = 0.000
H1: r < 0.000

Test used: Pearson's Correlation Coefﬁcient ('T-Test for signiﬁcance),
alpha = .05, one-tailed.
A directional hypothesis is used for Hypothesis 4, due to the assumed positive relationship
between city size and diversiﬁcation as discussed in Thompson (1965) and Clemente and

Sturgis (1971). A negan'xe relationship, however, is hypothesized in this study. This

52

negative hypothesis smucture is an artifact of the inverse name of the portfolio

diversiﬁcation indices, in that more diversiﬁed economies will have We: index values.

HxntlthssiLs.

A signiﬁcant relationship exists between regional employment instability
RED and regional income stability (RID.

Ho: r = 0.000
H1: r at 0.000
Test used: Pearson's Correlation Coefficient (T-Test for signiﬁcance),
alpha = .05, two-tailed.

The smucture of this hypothesis is very difﬁcult to establish. As noted in the discussion of
the research hypotheses in Chapter 2, the numerical sensitivity of the two indices precludes
any directional assumptions to be applied to the hypothesis smucture. It is even possible
that due to this sensitivity, no relationship exists. It is for these reasons that a non-

directional, two-tailed hypothesis smucture is warranted.

Wadi.

A signiﬁcant positive relationship exists between the regional diversiﬁcation
indices (PDIV85) and regional income instability (RII).

Ho: r=0.000
H1: r>0.000

Test used: Pearson's Correlation Coefficient (T-Test for signiﬁcance),
alpha = .05, one-tailed.

This hypothesis is smuctured as a positive directional due to the perceived positive
relationship between employment diversiﬁcation and regional income stability. Those
regions with a diverse employment proﬁle will also have a diverse income proﬁle between
industries and within indusmies. This diverse income proﬁle will allow a region to

maintain income stability.

53
Manual.

A signiﬁcant positive relationship exists between the historical (1979)
regional diversiﬁcation indices (PDIV79) and present (1985) regional
employment instability (RED.

Ho: r = 0.000
H1: r > 0.000
Test used: Pearson's Correlation Coefﬁcient ('T-Test for signiﬁcance),
alpha = .05, one-tailed.

The smucture of this hypothesis is designed to test the name of the relationship between
pment economic stability and histgnga‘diversiﬁcation as discussed by Jackson (1984). In
actuality, it is testing the possibility of using a m diversiﬁcation level, in an economic
development context, to "forecast" a possible mm stability of a region. The positive
direction follows from the same arguments used to justify the positive direction in
Hypothesis 3.

Chapter IV
Results and Applications

The following chapter presents the results of the statistical tests of the hypotheses, and
discusses and examines the use of the results of the portfolio analytic model of

diversiﬁcation for State or regional economic development purposes.

Hypotheses Results
The examination of the results from the statistical tests of the research hypotheses will
be in the order stated.

mm
A signiﬁcant change in the regional diversiﬁcation indices (PDIV79 and
PDIV85) has occurred between 1979 to 1985.
This hypothesis compares the regional diversiﬁcation indices of 1979 with those of 1985 to
determine if a signiﬁcant change has occurred
Remus; Paired Sample T-Test on PDIV79 vs. PDIV85 with 14 Cases
Mean Difference = 0006
SD Difference = 0.003
T = -8.136 Df = 13 Two-tailed probability = .000

The null hypothesis is rejected and the alternative accepted, indicating a signiﬁcant change
in the regional diversiﬁcation levels has occurred between 1979 and 1985. Directionality
(One-tail T-Test) is not warranted since the direction could not be determined a priori, since

some regions may have become more diversiﬁed and others less diversiﬁed.

54

5 5
W
A signiﬁcant change in the industrial structure of Michigan (as measured by
the inter-industry covariance matrices; STRUCT79 and STRUCT85) has
occurred between 1979 and 1985.
This second hypothesis (actually a sub-hypothesis of the ﬁrst), examining the change in
industrial smucture from 1979 to 1985, will give further insight into the changing regional
diversiﬁcation levels. It will also allow conclusions to be drawn as to what effects
deindustrialization, and the recent recession and recovery have had on the indusmial
smucture of Michigan.
Results; Wilcoxon Signed Ranks Test Results

Counts of Differences (Row Variable Greater Than Column)

STRUCT79 smucrss

 

STRUCT79 0 62 l
STRUCT85 169 0 l
I 231
Two-tailed Probability: .000
Spearman Rank Order Correlation (rs)
STRUCT79
STRUCT 85 0.785
T-statistic: 19.176 Number of Observations: 231

The null hypothesis is rejected for this relationship, indicating that the industrial smucture in
1979 (STRUCT79) W from the indusmial structure in 1985
(STRUCT85). Due to a large sample size for this test (N = 231), a corresponding
paramemic Dependent (Pairwise) Student's T-Test was also calculated. As expected, the
results correspond with the Wilcoxon test's results, with a T-statistic equal to 9.036,

indicating exmeme signiﬁcance. Even though STRUCI79 and STRUCT85 are statistically

5 6
different, the Spearman Correlation analysis indicates an extremely signiﬁcant historical
relationship between the smucture values of 1979 and those of 1985. This is to be expected
since a six year time span would be a very short amount of time for any major shifts in the
industrial proﬁle of a State to occur. This may possibly indicate that the recession and net
deindustrialization has caused the major change in the industrial smucture of Michigan. If
the results of these statistical tests are examined together, it would seem to indicate that the
absolute magnitudes of the covariance matrix values have signiﬁcantly changed from 1979
to 1985 (structme has become less diversiﬁed), but the relative magnitude of the inter-
indusmy relationships continue to be very similar (r3 = .785). This similarity in the inter-
indusmy relationships indicates that the State's recovery from the recent recession, is more
likely a function of a national economic recovery, rather than a change in the industrial
smucture. However, within the 231 values of the miangular covariance mauix it is possible
that some individual values (certain industries' relationships) have changed dramatically.
This possibility will be examined in greater detail in the next section.

W

A signiﬁcant positive relationship between the regional diversiﬁcation indices
(PDIV85) and regional employment instability (REI).

This hypothesis is used to determine the strength and signiﬁcance of the relationship

between industrial diversiﬁcation and regional economic instability for the regional

economies of Michigan.
Results; Pearson's Correlation (r)
PDIV85
REI .665
N: 14 T-statistic: 3.085 One-tailed Probability: .005

These results indicate a signiﬁcant positive correlation, thus the null hypothesis of no

relationship is rejected These results parallel those of Conroy (1972, 1975a, 1975b), and

57

Brewer (1985) indicating that there is a signiﬁcant relationship between industrial
diversiﬁcation (as measured by the portfolio analytic model) and regional employment
instability.

For direct comparison to the results of these two authors a regression analysis must be
used. As mentioned previous, the problems with very low degrees of freedom for this
small data set limits the usefulness of regression results. For comparisons sake only, an
ordinary least-squares regression was run ( REI: dependent variable; PDIV85: independent
variable).

The regression equation, with T-statistic in parentheses:

REI = -0.005 + 1.183 PDIV85
(—0.376) (3.085)

adjusted R2 = .396

These results show diversiﬁcation can explain almost 40% of the variation in regional
economic instability in Michigan. This adjusted R2 value is very close to that obtained by
Conroy of .423 (1972). An attempt was made to examine the residuals from this
regression for heteroscedasticity as per Kort (1981) and Brewer (1985). Determining the
presence of heteroscedasticity with such a small sample is extremely difﬁcult. Both the
Goldfeld-Quandt test and graphic portrayal proved unsatisfactory. The residuals when
plotted against population exhibit a pattern somewhat similar to, but not as pronounced as,
that found by Kort (1981), but due to the small sample size and the overwhelming size of
the Demoit MSA not much information could be gathered from the plot. However, since
this heteroscedasticity was found by both Kort (1981) and Brewer (1985) I, for the sake of
cruiosity, continued with the assumption that the residuals were indeed heteroscedastistic
and corrected for this problem using the same Square Root of Population correction as did
these authors. The resulting Weighted least Squares (WLS) regression equation ('1‘-

statistic in parentheses):

58

(RBI * SQRPOP84) = -0.013 (SQRPOP84) + 1.415 (PDIV85 * SQRPOP84)
(0.765) (3.167)

adjusted R2 = .410

Although these regression results do not duplicate the degree of causality exhibited in
Brewer (1985), the slight increase in the adjusted R2 value and in the signiﬁcance indicates
that by accounting for the effects of population size, the power of the portfolio index of
industrial diversiﬁcation to explain regional economic instability (RED does increase in
even a small study such as this one.

At least two possible explanations for the smaller than anticipated increase in adjusted
R2 exist. First, the overwhelming size of the Detroit MSA may be biasing the results.
When an WLS regression analysis is run on the sample with the Detroit MSA removed, the
adjusted R2 increased to .491 . This value is closer to the value that Brewer obtained. A
second reason for the less than anticipaed adjusted R2 when accounting for the effects of
population, may be due to the unique relationship between industrial diversiﬁcation and
regional population size in Michigan. This relationship is further examined in Hypothesis
4.

59

111991112514.

A signiﬁcant negative relationship exists between the regional diversiﬁcation
indices (PDIV85) and population (LOGPOP84).

This hypothesis examines the smuctural relationship between indusmial diversiﬁcation and
regional population size. As stated previous, a negati_ve relationship is hypothesized due to
the inverse nature of the portfolio diversiﬁcation index.
Results; Pearson's Correlation (r)
PDIV 85
LOGPOP84 .254
N: 14 T-statistic: 0.911 One-tailed Probability: .190

The null hypothesis for this relationship ems; be rejected. Not only is the relationship
between the two variables insigniﬁcant, the implied negative directionality is not shown.
The results indicate that no signiﬁcant correlation exists between indusmial diversiﬁcation
(as measured by the portfolio analytic model) and population size; the statement that more
populated regions are by necessity structurally more diversiﬁed cannot by accepted for this
sample. This result is directly opposite of the results obtained by Clemente and Sturgis
(1971). These results indicate that regional size alone will not impact the portfolio model of
diversiﬁcation. This factor may make the portfolio model of diversiﬁcation a very helpful
tool for Michigan economic development planners, who have to deal with the exmeme size

of the Detroit MSA.

WLS.

A signiﬁcant relationship exists between regional employment instability
(RBI) and regional income instability (RII).

One would assume that as regional employment stability increases so would regional
income stability. However, the numerical sensitivity of these indices does not allow

directionality of the regression to be hypothesized. The effect of the loss of 100 jobs on

60

employment stability would probably be minimal. If, however, they were all $25,000 per
year jobs then the effect on regional income stability may be significant.

Results; Pearson‘s Correlation (r)
RII
RBI .475
N: 14 T-statistic: 1.870 Two-tailed Probability: .086

The null hypothesis for this relationship cannot be rejected. However, a two-tailed
probability of .086 indicates that though the hypothesis is rejected at a two-tailed alpha of
.05, it could not be rejected if a positive directional hypothesis is used (One-tailed
Probability: .043). This one tailed probability may indicate that a tenuous positive
relationship between RBI and RH exists, and that for the most part employment ﬂuctuations

occm' throughout the salary range.

W31.

A signiﬁcant positive relationship exists between the regional portfolio
indices (PDIV85) and regional income instability (R11).

This hypothesis is used to further examine the relationships between employment
characteristics and regional income stability. Due to the wide variations in income potential
among employment sectors, a positive relationship between industrial diversiﬁcation and

regional income instability is hypothesized.

Results; Pearson's Correlation (r)
PDIV85
R11 .457
N: 14 T-statistic: 1.781 One-tailed Probability: .050

The null hypothesis for this relationship must be rejected, though the T—statistic is right at

the 95% rejection level. There is a statistically signiﬁcant relationship between industrial

61

diversiﬁcation and regional income stability. This result indicates that by diversifying a
region's employment proﬁle, the income proﬁle of the region is also diversiﬁed (a wide
range of incomes will exist) making that region's total income less susceptible to economic
shocks. A policy of industrial diversiﬁcation may have a positive impact not only on

employment stability (exhibited by Hypothesis 3) but also on income stability as well.

W

A signiﬁcant positive relationship between the historical (1979) regional
portfolio indices (PDIV79) and present (1985) regional employment instability
(REI).

This hypothesis is very important in terms 0f using the portfolio model of diversiﬁcation
for planning or economic development purposes. As explained in Chapter 3 this
hypothesis will test whether or not it is justiﬁed to assume present diversiﬁcation will have
any relationship to futtn'e employment stability. If the hypothesis is accepted, a present
plan of diversiﬁcation may be able to modify the future stability value to a more desirable
one. However, if the positive relationship is not accepted, the portfolio diversiﬁcation
index will be of limited use.

Remus; Pearson's Correlation (r)
REI
PDIV79 .633
N: 14 T—statistic: 2.836 One-tailed Probability: .008

The null hypothesis for this relationship must be rejected, indicating a signiﬁcant
relationship between historical diversiﬁcation (1979) and present regional employment
stability exists. These results give credibility to Jackson's (1984) statement linking
historical diversiﬁcation with present regional economic instability, and to the credibility of

using the portfolio index of diversiﬁcation as a regional economic development tool.

62

State-level Applications

A great amount of information about the industrial structure of Michigan can be gained
by examining individual values from the inter-industry covariance matrix calculated as part
of the portfolio model.

The values on the diagonal of the covariance matrix are measures of the variance of the
employment levels within each industry. From Table 4 it can be seen that typically, the
most variable industries in the State are the durable manufacturing sectors. The very high
employment variance of the Construction sector might be explained by the extremely
cyclical nature of this sector.

Two comments on these variance values are in order. First, the Other Non-Durable
manufacturing sector's extreme variance is most likely an artifact of the industry groupings
used for this study, where this category is the non-dmable employment remaining after
other individual industries (Food, Chemical Products, Printing, Paper) are removed.
Second, the possible effect of unionization may be seen in the relatively higher employment
stability value for the Transportation Equipment industry.

Table 4 also shows the small employment variance of the industries that can be termed
"service producing industries ", such as F.I.R.E., Services, Federal Government, and
Transportation and Public Utilities. The extremely small variance of the Food & Kindred
Products industry has many connotations. This industry group has been targeted by the
State of Michigan as a industrial sector to be promoted and developed due to its great
potential. The variance value would lead one to believe that the State made a wise decision
in selecting the Food & Kindred Products sector as a target industry. This optimism, for
this sector and for the portfolio model in general, must be calmed in light that this sector's
State employment has declined from 60,400 employees in 1960 to 43,200 employees in
1985, a decline of greater than 25%. Before this sector is to be promoted, research into
why its total employment is

63

Table 4.

1985 Industry Variance (Diagonal) and Instability (Column Sum) Values

Ranked Most Stable (l) to Least Stable (21)

ﬁesta:

Food and Kindred Products
IRIJRJE.

Services

Federal Government
Transportation and Public Utilities
ReudFTnuk:

Wholesale Trade
Sune<30venunent

Chemical and Petroleum Products
Local Government

Printing and Publishing

Other Durable Good Manufacturing
Paper and Allied Products
Primary Metal Industries
Transportation Equipment
Lumber and Wood Products
thung

bknbekxuhmdhdmﬂuneqr
Construction

Fabricated Metal Industries

Other Nondurable Good Manufacturing

.00051
.00075
.00085
.001 13
.00135
.00137
.00165
.00173
.00175
.00194
.00344
.00375
.00455
.00609
.00653
.00708
.007 37
.00837
.00864
.00897
.01238

(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)

.01420
.01251
.01663
.00497
.02173
.02657
.02847
.01252
.01509
.01520
.01280
.04520
.01161
.06042
.05702
.04683
.02560
.05100
.06937
.06493
.06925

(6)
(3)
(9)
( 1)
(10)
(12)
(13)
(4)
( 7)

. (3)

(5)

(14)
(2)

(18)
(17)
(15)
(11)
(16)
(21)
(19)
(20)

64

declining at such a rate must be completed. This employment decline in the Food and
Kindred Products industry is primarily due to the increasing use of automation in this
sector. This low variance value is also an example of why caution must be used in
interpreting the portfolio model's results, in that it measures stability around a given trend
(growth or decline). This problem will be discussed further in the evaluation section.

By summing the columns of the covariance matrix a measure of total sector instability
(versus sector variability or variance) can be calculated. These instability values are also
shown in Table 4. These values are an overall measure which incorporates the speciﬁc
industry variance with the covariance measures of the inter-industry cyclical relationships
(the lower the instability value, the more stable the sector). These instability values give a
better view as to the total effect a sector has on the regional economy.

From these values, the overall instability of the durable goods industries can again be
seen by their uniformly high instability values. The non-durable goods industries show
much more stability than the durable goods industries.

Of special note is the very low instability value for the Federal Government
employment sector. This low value shows that Federal Government employment is very
stable and counter-cyclical to almost all other sectors, making it a very desirable sector to
incorporate into a regional economy. However, it is usually beyond the control of the local
region to effect Federal Government employment numbers.

The examination of the "vectorized" matrices and the difference in the matrix values
from 1979 to 1985, reveals that of the improvements occurring, most of the increases in
sector stability (and likewise decrease in sector variability) can be attributed primarily to
three sectors: Non-electrical Machinery, Chemical and Petroleum Products, and Federal
Government Employment. These three sectors account for 35 of the 62 decreases
(STRUCT79 value > ST'RUCI‘85 value) in the State inter-industry covariance mauix. This

examination shows that even though the industrial structure of the overall Michigan

65

economy has become less diversiﬁed, as measured by the portfolio model of
diversiﬁcation, some sectors have improved measurably.

By incorporating the total State's employment proportions into the portfolio model it is
possible to derive a State diversiﬁcation index for 1979 and 1985. These values can be
considered a State diversiﬁcation average.

1979 State of Michigan Diversiﬁcation: .0307

1985 State of Michigan Diversiﬁcation: .0366
Percent Change in Diversiﬁcation Index: 19.22%

These increasing values show that the level of diversiﬁcation in the State has declined
19.22% during this six year time span (since the index increased). These values, when
compared to the regional diversiﬁcation values given in Table 5, reveal that in 197 9, seven
regions were more diversiﬁed than the State, while in 1985, eight regions were more
diversiﬁed. The Saginaw MSA became more diversiﬁed than the State during this time
period. This diversiﬁcation, however, was due primarily to reductions in the Saginaw
MSA's proportions in most of the Durable Manufacturing sectors and Construction. These
proportion reductions were caused mostly by unemployment in these sectors versus
increased employment in others. The Saginaw MSA's total non-agricultural employment
declined from 156,300 in 1979 to 145,100 in 1985.

Regional Applications

The major purpose of the portfolio analytic model of industrial diversiﬁcation is to
measure the level of diversiﬁcation for the speciﬁed regions. Though historically,
diversiﬁcation values were used to compare regions, the portfolio model of diversiﬁcation
allows for some additional uses of the regional values in conjunction with the State-level
covariance matrix. The regional diversiﬁcation values are calculated from the State-level

covariance mauix weighted by the proportion of each region's employment in each sector.

-—

66

In the temporal examination of the change in the diversiﬁcation indices from 1979 to 1985
one can make comments on the regional changes based on sector stability changes and on
regional proportion changes. These comments may give rise to areas, questions, and
policy issues for further study. The diversiﬁcation levels for the two time periods and their
makings are given in Table 5 (the lower the diversiﬁcation index, the more diversiﬁed).

As indicated in Table 5, all regions have experienced an increase in their respective
diversiﬁcation index values from 1979 to 1985. This overall effect can be attributed
primarily to the effects of the 1982-1983 recession, its effect on employment levels, and the
resulting impact on the calculation of the portfolio analytic model of diversiﬁcation. The
extreme employment decline from the sectoral employment peaks (primarily occurring in
1979) resulted in 18 of the 21 sectors becoming more variable or unstable. Since a
majority of the values of the State-level covariance matrix increased, the regional
diversiﬁcation indices for 1985 demonstrate this increase also. Most important, however,
in terms of this study, is the regional differentiation between the two time periods.
Although the pattern of regional diversiﬁcation makings are very similar, a number of
interesting changes did occur. It can be noted from Table 5 that the increases in the
diversiﬁcation indices were not regionally uniform. The largest percent increases occurred
in those regions that were relatively well diversiﬁed in 1979 (Table 6 gives the percentage
increase in the diversiﬁcation indices from 1979 to 1985).

6'7

TakaS.

Regional Diversiﬁcation Indices: 1979 and 1985

Ranked Most Diversiﬁed (1) to Least Diversiﬁed (14)

REGION
AUpemthLA
AnnrAuborthA.
lhnﬂeCkeekhdSAr
IBenuanhuborhdSAl
Detroit MSA

Flint MSA
(handlhuﬁdshdSAr
Chandiﬁnnmmy:lldﬁt
Jackmmrhm3A.
IGﬂmmmmoohdSAr
LamﬁnghdSAr
LduﬂnugnrhﬂSA.
SaghmwvhdSAr
IhnerenhmukLLbLA

W W
.0286 (6) .0359 (7)
.0306 (7) .0348 (6)
.0282 (4) .0297 (1)
.0309 (8) .0378 (11)
.0320 (11) .0371 (10)
.0399 (14) .0438 (14)
.0321 (12) .0382 (12)
.0231 (2) .0339 (4)
.0320 (10) .0368 (9)
.0258 (3) .0325 (2)
.0271 (5) .0346 (5)
.0346 (13) .0391 (13)
.0312 (9) .0365 (8)
.0205 (1) .0333 (3)

68

Table 6.

Region

Battle Creek MSA
Flint MSA

Muskegon MSA

Ann Arbor MSA
Jackson MSA

Detroit MSA
Saginaw MSA

Grand Rapids MSA
Benton Harbor MSA
Kalamazoo MSA
Alpena LMA

Lansing MSA

Grand Traverse LMA
Upper Peninsula LMA

Percentage Increase in Portfolio Diversiﬁcation Indices from 1979 to 1985.

W

5.17

9.70
13.20
13.55
15.14
16.10
17.09
18.83
22.06
25.73
25.76
27.76
46.83
62.62

69

Though the regional rankings have changed somewhat, the increase in the
diversiﬁcation values (decreasing diversiﬁcation) was dramatic. The most dramatic
increases in the diversiﬁcation values from 1979 to 1985 occurred primarily in the three
LMAs. These three regions in the northern parts of the State are, at present, extremely
tourism oriented, and their employment characteristics (high proportions in services and
retail, with very low proportions in the manufacturing sectors) reﬂect this fact. The
recessionary period of employment instability is reﬂected in the State 1985 inter-industry
covariance mauix, where the industry variance for both of these industries more than
doubled in the six years, causing the regional diversiﬁcation indices of the Alpena LMA,
Grand Traverse LMA, and the Upper Peninsula LMA to increase 25.76%, 46.83%, and
62.62% respectively. The Lansing MSA also had a substantial increase in its
diversiﬁcation index value. From examining the region's employment proportions it is
seen that during the six year span from 1979-85 the Lansing MSA's proportions in the
more stable sectors of Federal and State Government declined, while the proportions in the
retail and especially the service sectors increased. As mentioned above these two sectors'
instability (combined with large regional proportions) along with a decline in the regional
proportions of the "stabilizing" government employment caused the Lansing MSA's
diversiﬁcation value to increase by 27.76%.

The interesting anomaly to these scenarios, is the diversiﬁcation change of only 5.17%
for the Battle Creek MSA. One can conclude from this value that the economic
development in this region between 1979 and 1985 not only made the Battle Creek MSA
the most stable region in the State, but also cushioned the region against the severe
employment shocks stemming from the 1982-1983 recession. Another interesting result
obtained from the analysis of Table 6 is that except for the Battle Creek MSA, the Flint
MSA had the lowest percentage increase from 1979 to 1985 (9.8%). This may indicate that
the Flint region is slowly becoming more diversiﬁed. However, this change in the

diversiﬁcation index may be caused by automotive unemployment (thus reducing the

'—
rt .iﬁ

7 0

regional proportion in the Transportation Equipment sector, increasing the proportions in
the other 20 sectors and changing the portfolio index) than to a realignment of its regional
industrial structme. Both the Battle Creek and the Flint MSAs will be examined in greater
detail in the next section.

More can be learned of the regional economies by examining the regional economic
instability indices calculated for each region. These instability values, calculated with both
total non-agricultural employment and wage income, are given in Table 7.

Table 7.

Regional Instability Indices: Employment (1985) and Income (1984)
Ranked Most Stable (l) to Least Stable (14)

852193 mm mm
AlpenalMA .0386 (7) .0040 (13)
AnnArborMSA .0414 (11) .0031 (10)
Battle Creek MSA .0298 (3) .0029 (8)
BentonHarborMSA .0424 (13) .0021 (2)
Detroit MSA .0418 (12) .0029 (9)
FlintMSA .0472 (14) .0043 (14)
Grand Rapids MSA .0353 (6) .0026 (5)
Grand TraverseLMA .0412 (10) .0025 (4)
Jackson MSA .0407 (8) .0032 (11)
KalamazooMSA .0324 (4) .0021 (1)
Lansing MSA .0291 (2) .0022 (3)
Muskegon MSA .0351 (5) .0028 (6)
Saginaw MSA .0412 (9) .0035 (12)
Upper Peninsula LMA .0269 (1) .0028 (7)

71

It can be seen from these values that in every case employment instability is much
greater than income instability. One can conclude that regional income is much "stickier"
than regional employment. A possible cause of this difference could be that in prosperous
times new employees are hired (at starting salaries) and during a recession these same
employees are laid off. This could give large ﬂuctuations to the employment numbers, but
the loss to regional income of losing these starting salaries is not a large percentage of the
total regional income. (Example: the hiring of 20 students at minimum wage and laying
them oﬁ would not have the same effect on each instability~ index as hiring 20 machinests at
$20.00 per hour and then laying them off).

An examination of particular regional values shows that except for the Kalamazoo and
Lansing MSA none of the regions have relatively low values for allmmejngﬁm
(diversiﬁcation, employment instability, income instability). These two areas are similar in
that along with a fairly well diversiﬁed manufacturing economy both are inﬂuenced by the
stability of post-secondary education employment. The Battle Creek MSA matches its
industrial diversiﬁcation with employment stability (low instability value) but has a
relatively high income instability value. This condition may indicate that even though the
regional economy is well diversiﬁed, the employment stability may be more an artifact of
people remaining employed in lower paid jobs (under—employment) than becoming
unemployed. If my automation premise of the Food and Kindred Products industry in
Battle Creek is correct, these laid-off employees may be ﬁnding work in lower income
retail or perhaps food service occupations.

It is interesting to note that the Upper Peninsula LMA has the most stable employment
of all the regions in the sample. It has been shown that the Upper Peninsula is fairly well
diversiﬁed (though a little too dependent on the "service producing industries") and has a
very stable regional employment. Yet this region remains, for the most part, ignored by the

State government's employment expansion efforts, except for those related to the Upper

72

Peninsula's natural resource endowments (e. g. forestry, mining). Some of this optimism
for the Upper Peninsula must be tempered, however, due to the unfortunate size of this
region and possible effects region size has on the diversiﬁcation and instability values.
This problem will be better addressed in the evaluation section.

Case Study Applications: Battle Creek and Flint MSAs

The literature on the use of the portfolio model to answer questions of "What to do
next?" focuses primarily on determining m or best portfolios. This search for
eﬁicient portfolios is prevalent in the ﬁnancial literature (Markowitz, 1959; Sharpe, 1963)
as well as in the regional economics literattn'e (Conroy, 1972, 1975b; St. Louis, 1980,
Brewer, 1985). The search for an efﬁcient ﬁnancial portfolio can be justiﬁed, since the
owner of the portfolio has almost complete ﬂexibility in the choice of which stocks and
other assets to purchase or sell. This ﬂexibility in asset selection, however, is not feasible
in a regional economic sense; there are too many variables to consider. A region's
industrial proﬁle is inﬂuenced by a composite of variables including local supply and
demand, resource availability, population size, and historical location decisions. A
region's economic development agency does not have the option of "selling off" the
"unproﬁtable" industries (such as those with low incomes or unstable employment
demands) when the need arises. It is for these reasons that I feel the search for an efﬁcient
regional industrial portfolio, though a interesting theoretical abstract, is not a "real world"
practical application of the portfolio model.

The search for a better portfolio, however, does not necessarily have to center on pure
efﬁciency. By manipulating the regional proportions, one can calculate new diversiﬁcation
indices, which can give an idea as to the effect a change in regional, sectoral employment
will have on the level of diversiﬁcation. These values can then be used to aid in the

decision as to which industries a region may want to promote, pursue, or avoid. It is this

73

methodology, an extension of one developed by Conroy (197 4) that I employ in examining
the Battle Creek and Flint MSA.

For this exercise, I have chosen to increment an individual sector's proportion by .001,
with a corresponding decrease of .00005 in each of the remaining 20 proportions;
amounting to 21 vectors of sectoral proportions for each region. These corresponding
decreases are to meet the portfolio analytic model's requirement that a region's sectoral
proportions must sum to 1.000. The .001 increase is equal to approximately 54 persons in
the Battle Creek MSA and 171 persons in the Flint MSA. The .001 value was chosen for
operational simplicity and also because both values could easily represent the additional
employment from a single new ﬁrm. From these values, the portfolio model was used to
calculate a diversiﬁcation index for each different regional proportion vector (i.e. 21 vectors
for lmh MSA).

To use these values for economic development pin-poses, beyond identifying stable
sectors, they need to be evaluated in the context of other regional economic measures. I
have chosen to evaluate diversiﬁcation against its possible effect on Total Sectoral Wage
Income for 1985, made available from MESC ﬁles. Since the two sectors, Other Durable
Manufacturing and Other Non-durable Manufacttning, are collections of a number of
distinct industries, wage income data for these two "sectors" are not available. Therefore,
these two "sectors" are not used. Those sectors included in the case studies, as well as, a

numerical code for use in the MSA graphs are given in Table 8.

74

Table 8.

l9 Sectors Used in Case Study Applications

Cede Sector Code 85910:

1 Mining 11 Chemical and Petroleum Products
2 Construction 12 Transportation and Public Utilities
3 Lumber and Wood Products 13 Wholesale Trade

4 Primary Metal Industries 14 Retail Trade

5 Fabricated Metal Industries 15 F.I.R.E.

6 Non-electrical Machinery 16 Services

7 Transportation Equipment 17 Federal Government

8 Food and Kindred Products 18 State Government

9 Paper and Allied Products 19 Local Government

10 Printing and Publishing

To evaluate the change in diversiﬁcation and the corresponding change in regional
income only total employment increases were examined. This methodology could also be
used, however, to analyze the effects of decreasing sectoral employment.

A ratio formulation was used to determine the increase in regional incorm that would

occur with increased employment in a sector.
(Income '85 / Employment '85) al- .001(Employment '85) = Regional Income Increase

Though the proportional increase in regional employment will not necessarily equal the
proportional increase in regional income, this equality is suitable for the illustrative use of
the technique. With more detailed information, this proportional equality is not necessary.
Figure 6 and Figure 7 show these positive changes in regional income plotmd against the
diversiﬁcation level achieved by increasing the various sectoral employment proportions by
the .001. The vertical line indicates the present diversiﬁcation value for 1985. Table 9 and
Table 10 detail the data used to plot the MSA graphs.

As shown in Figure 6, by increasing the proportion in 12 of the 19 sectors, of the

Battle Creek regional economy it would become possible for the region to become even

75

more diversiﬁed than it was in 1985 (left side of vertical line). As a regional economic
development tool, this examination technique could give a policy maker many alternatives
to examine in terms of attracting industries. In a strict ﬁnancial gain sense, the
development professional would have to advise the region to further increase its dominance
in the Food and Kindred Products (8) industry. This industry while reducing the
diversiﬁcation value also will increase the regional income the most. If however, stability
is of prime importance the attraction of Federal Government (17) employment or the Paper
Products (9) industry will decrease the diversiﬁcation value by the greatest amount. Figure
6 also shows the possibility of increasing regional income by attracting Non-electrical
Machinery (6) ﬁrms, but also shows the negative impact on the diversiﬁcation level. This
examination technique allows the policy makers to weigh the beneﬁts of this increased
regional income against the negative effect on the diversiﬁcation of the region.

Figtue 7 presents a similar graph for the Flint MSA. Due to the larger size of the Flint
economy the dollar value of the positive change in regional income is larger. The Flint
regional economy can become more diversiﬁed by increasing the regional employment
proportion in 13 of the 19 sectors. Only the Durable Manufacturing (3, 4, 5, 6, 7) sectors,
Mining (1) or Construction (2) would cause Flint to become less diversiﬁed. An
interesting ﬁnding is shown in the Flint MSA graph. Increasing the employment in the
Chemical and Petroleum Products (11) sector not only will improve the region's
diversiﬁcation, but will also yield the largest increase in regional income ($7,473,472).
Once again the "stabilizing" effect of Federal Government (17) employment is prevalent in
the graph, as increasing the regional proportion in Federal Government employment would
decrease the diversiﬁcation index to .043712.

Increase in Regional Income
(in millions)

76

 

 

 

 

 

BATTLE CREEKMSA
3
24 '8
I6
9 I 4
I. 18. I12

1-»:7 '13 I 5 . 2

10 llS I19

'16
l '7
I“ I14 fl.
0 i i t u t E
29.65 29.67 29.69 29.71 29.73

DIVERSIFICATION x 10"-3

Figure 6. Regional Income Change and Diversiﬁcation - Battle Creek MSA.

Vertical line indicates present (1985) diversiﬁcation value.

77

Table 9.

Increase in Regional Income and 'New" Diversiﬁcation Indices - Battle Creek MSA

mm

1. Mining 3 453,287 .029682
2. Construction 5 973,245 .0297 23
3. Lumber and Wood Products $ 447,370 .029680
4. Primary Metal Industries 1: 1,309,061 .029707
5 . Fabricaed Metal Industries $ 1,048,328 .029670
6. Non-electrical Machinery $ 1,672,882 .029699
7 . Transportation Equipment S 575,015 .029694
8. Food and Kindred Products $ 2,015,577 ' .029655
9 . Paper and Allied Products 3 1,256,162 .029643
10. Printing and Publishing 3 920,875 .029642
1 1. Chemical/Petroleum Products $ 395,872 .029658
12. Transport. and Public Utilities $ 1,11 1,623 .029667
13. Wholesale Trade $ 1,044,420 .02967 2
14. Retail Trade S 493,205 .0296? 3
15. F.I.R.E. $ 844,456 .029657
16. Services $ 692,915 .029661
17. Federal Government $ 1,184,814 .029641
18. State Government 3 1,153,189 .029663
19. Local Government 5 841,044 .029667

 

Present (1985) Level

.029679

 

Increase in Regional Income
(in millions)

78

 

 

 

 

 

FLINTMSA
I 11 7. 5 I
6"
I5
I
.17 .13 Z
4” 1° 8 .12
9 I. ‘19
1? '16
2" I14 _4
.18 I l .3
0 i i i i i 3 IL 3
43.72 43.74 43.76 43.78 43.80

DIVERSIFICATION x 104-3

Figure 7. Regional Income Change and Diversiﬁcation - Flint MSA.
Vertical line indicates present (1985) diversiﬁcation value.

79

Table 10.

Increase in Regional Income and 'New" Diversiﬁcation Indices - Flint MSA

1. Mining 3 1,024,169 .043740
2. Construction 3 4,945,088 .043798
3. Lumber and Wood Products $ 845,316 .043766
4. Primary Metal Industries $ 1,457,487 .043790
5. Fabricated Metal Industries $ 7,254,843 .043798
6. Non-electrical Machinery $ 5,097,933 .043771
7. Transportation Equipment $ 7,301,264 .0437 89
8 . Food and Kindred Products 3 3,285,279 .043730
9. Paper and Allied Products $ 3,185,096 .043719
10. Printing and Publishing $ 3,358,797 .043722
1 1. Chemical/Petroleum Products 5 7,473,472 .0437 32
12. Transport. and Public Utilities 3 3,858,465 .043738
13 . Wholesale Trade 3 4,771,836 .043746
14. Retail Trade $ 1,732,794 .043745
15. F.I.R.E. $ 2,821,916 .043726
16. Services 3 2,791,102 .043732
17. Federal Government 5 4,606,945 .043715
18. State Government 3 1,170,673 .043726
19. Local Government 3 3,221,785 .043731

 

Present (1985) Level

.043753

80

by .001 will decrease the diversiﬁcation value by the greatest amount. It is interesting to
note that the graph also shows the economic rational behind Flint maintaining its
automotive employment base. The Transportation Equipment (7) sector, while a major
cause of the poor diversiﬁcation and stability of the Flint economy, is one of the highest
paying sectors of its economy. While decreasing the employment in this sector (as well as
in the Fabricated Metals (5) sector) may be better in the long run for the stability of the Flint
economy, the ﬁnancial burden (through loss of regional income) this would place on the
region would be very unpopular with the residents.

This very simple graphical technique allows many alternatives to be examined in a
relatively short amount of time, once the original data is obtained. It could also be used to
examine the relationship between diversiﬁcation and other quantiﬁable variables such as tax
base increase, infrastructure costs, etc- To accommodate the addition of more than one
industry or a larger employment proportion change than .001, would require simple
modiﬁcations of the region's sectoral proportions vector. Though a very simple technique,
this graphical method can be a very useful tool for regional economic development and

planning.

Chapter V
Evaluation and Conclusions

This ﬁnal chapter begins with an evaluation of the use of the portfolio analytic model of
industrial diversiﬁcation for "small region" economic analysis and the effect "small region"
data has on the model. A discussion of the research objectives, how the model helped
meet research objectives, and a summary of the hypotheses results is put forth in the

second section. The chapter will close with a discussion of future research possibilities.

Evaluation of the Small Region Use of the Portfolio Model

The use of small scale or small region (sub-State, MSA, county, city) data with the
portfolio analytic model of diversiﬁcation must be used with caution. These data are often
lacking in detail, that if not recognized, may lead to some spurious conclusions. This
section will discuss ﬁve concerns with this model involving small region data: 1) data
requirements; 2) sectoral aggregation; 3) regional aggregation; 4) regional sectoral
responses; and 5) growth instability.

The W for the portfolio analytic model of diversiﬁcation, while large,
are not beyond the scope of smaller region analysis. However, caution must be taken in
the collection of these data from different sources. Different sources with differing
collection techniques may produce slightly different results. In larger region analysis these
differences may be slight enough to ignore, but in smaller regions these differences are
often proportionally very large. This problem became very evident in this study when
comparing MESC data with County Business Patterns data. At the State scale employment
values from each source were fairly consistent. However, when analyzing certain single

county MSA's, the MESC data employment values would disagree with the County

81

82

Business Patterns data by as much as 20%. These discrepancies can be attributed to
differences in srmvey methodology and in the universe that is sampled

Of prime concern in using the portfolio model with smaller regions is the soctoml
W that is available. Many common sources of smaller region
data can be disaggregated to only 9 or 10 sectors for inter-regional comparisons. Though
it is possible to use the portfolio model with only 10 sectors, the analysis and interpretation
of the results would be crude, due to the differences among industries within these sectors.
The wide variety of cyclical variations found in the durable manufacturing sectors is a
prime example. Aggregating all durable manufacturing into a single sector, as is often
done, often misrepresents the industrial proﬁle of the region. In the use of the portfolio
model, as in most regional economic investigations, as much sectoral disaggregation as
possible is desired.

A problem inherent in smaller region data use is the problem of mgionaloggmgation.
To meet non—disclosure criteria, counties are often grouped together for data publication
(sectoral aggregation is also used to avoid disclosure problems). In multi-county regions,
such as some MSA, the use of employment proportions in the portfolio model, further
obscures the differences between counties in their industrial proﬁles. A region may contain
two counties, each concentrated in a speciﬁc sector. Stability differences between these
two sectors may cause the stability and diversiﬁcation levels of these two counties to be
quite different. However, these county differences would be dampened in the regional
aggregation since the regional proportions would be lower. Examples from this study
include the Upper Peninsula LMA, and the Saginaw MSA. The Upper Peninsula LMA is
an extreme example of regional aggregation for the sake of meeting non-disclosure criteria.
The need to aggregate 15 counties into a single region for disclosure purposes gives an
indication of the sparseness of industrial activity in the Upper Peninsula. The Saginaw
MSA, however, is an example of the effect regional aggregation for other reasons

(population census regionalization) can have on employment values. Saginaw County

83

employment is concentrated in the durable goods manufacturing sectors, whereas Midland
County manufacturing is almost completely dominated by the chemical industry. The
regional aggregation available, the MSA, aggregates these two counties with Bay County to
form the Saginaw MSA. This reduces the proportions since the employment is now a
proportion of the three county total non-agricultural employment. This regional
aggregation problem is very common, when using published data som'ces. It is often the
case that to obtain better regional disaggregation you must settle with poorer sectoral
disaggregation or vice versa.

The use of employment proportions in the portfolio model also causes problems
identifying Wm. Regional sectoral response refers to a region's
employment proportions effected primarily by very localized events. The portfolio index
can be seen to be a weighting of tie regional employment proportions of each sector by the
State structure (measured by the inter-industry covariance matrix) for the given sectors.
Using these sectoral employment proportions to represent the region's industrial proﬁle,
can cause an large proportion in an industry (good or bad), to cause the region to have a
larger index value, due to the formulation of the model. The Grand Rapids MSA and the
Consmuction sector provide a good example. The Grand Rapids region is growing very
rapidly. This regional growth leads to a great demand for new construction and therefore,
Construction employment. However, at the State level the Commotion sector is very
unstable. A large Construction employment proportion, combined with the high sectoral
instability, causes an undesirable increase in the Grand Rapids diversiﬁcation value. Yet
for this region, the large employment proportion in the Construction sector is a sign of its

growth.

84

One problem inherent in the portfolio analytic model of diversiﬁcation, due to its
formulation, is the problem of W or ﬂuctuations in the growth trend of an
industry. In calculating the inter-industry covariance matrix, the removal of the quadratic
trend transforms the time series for each indusmy into a series of deviations from this trend.
It is, however, possible that two industries with different trends (6. g. one growing, one
declining) may have nearly the same deviation pattern, and therefore, yield inter-industry
variance measures that are approximately the same. By not accounting for the differences
in trend, in the calculation of the portfolio model, a stable and growing industry is treated
exactly the same as a stable and declining industry.

Intuitively, this problem seems to be a major drawback of the portfolio model.
However, the portfolio model captrn'es the diversiﬁcation of the region at a ﬁnite point in
time; at a given instant the industry is not growing or declining. The use of the year
designation still implies a ﬁnite point, since employment levels are changing all the time and
the data values are measured for a speciﬁc instant. Given this realization, the growth
instability question is not difﬁcult to handle given sufﬁcient information. As long as the
planners and policy makers understand the nature of the employment trend, a negative
growth trend is not necessarily a problem. The Food and Kindred Products sector in
Michigan is a prime example of a negative growth trend. The stability of the sector has
been shown, and through the case study of Battle Creek, the desirability of this sector for
its impact on regional income is also shown. A negative growth mend indicates that
employment in that sector m declining. The trend does not show that the indusmy
will continue to decline. If development efforts are successful in bringing in new (or
expanding the existing) Food and Kindred Products ﬁrms, employment will increase and
the trend may be reversed.

l_.

85

Summary of Results

This study uses a portfolio model to examine the industrial structure of Michigan.
From the results of the model, the Michigan economy has been shown to have become
signiﬁcantly less diversiﬁed from 1979 to 1985. This result is due primarily to the effects
of the 1982-83 recession and its effects on sectoral employment stability. The recent
economic recovery the State is experiencing, is seen to be more a phenomenon of an overall
national recovery, than ﬁom a signiﬁcant change in Michigan's industrial structure from
1979 to 1985. Examination of the individual values from the inter-industry covariance
matrix calculated as part of the portfolio model yielded many interesting results. The
relative instability of the Durable Manufacturing sectors as well as the Construction sector
is easily demonstrated. The relative stability of the Non-dtnable Manufacturing industries,
as well as some of the service producing industries, is also shown. Though most of the
sectors of the State's economy have become less stable, three sectors Federal Government,
Chemical and Petroleum Products, and Non-electrical Machinery have become more stable.

The portfolio model also shows the effect the changes in the State-level inter-industry
covariance matrix has had on the regional diversiﬁcation pattern in Michigan. The regions
of Michigan are shown to have become signiﬁcantly less diversiﬁed during this six year
time span. However, the percent change in diversiﬁcation levels varied quite dramatically
across the State.

Many of the hypotheses examined the relationships between industrial diversiﬁcation
(as measured by the portfolio index) and other measures of the regional economies. A
signiﬁcant positive relationship is demonstrated between industrial diversiﬁcation and
regional economic (employment) instability. This result corresponds with the recent works
of Conroy (1972), Kort. (1981), and Brewer (1985) and gives credence to a policy of
promoting industrial diversiﬁcation to maintain regional cyclical stability. The relationship

between diversiﬁcation and regional income stability is also examined. Though the

86

relationship is weak (r = .457) it is shown to be statistically signiﬁcant. The examination
of the relationship between regional employment stability and regional income stability
indicates that these two measures have a slight positive relationship. These results would
seem to give additional rational for an emphasis on State and regional level industrial
diversiﬁcation. The relationship between diversiﬁcation and regional population size is
also tested. It is found that no signiﬁcant relationship exists; size alone does not inﬂuence
the diversity of a region's industrial structure. This result, which is contrary to Thompson
(1965) and Clemente and Sturgis (1971), may be an artifact of the portfolio model.
However, this is seen as a beneﬁt in the planning use of the model, since the size does not
inﬂuence the diversiﬁcation values.

The examination of possible planning oriented uses of the portfolio analytic model of
diversiﬁcation was centered mainly on the interpretation of the many results of the model.
As mentioned above, tle model discerns those industries that are stable at present, the
temporal comparison allowed comments on those industries that became increasingly stable
from 1979 to 1985, and allows policy makers the option of "choosing" which industries to
attract and mmintain. The graphical technique of examining the effect a change in a region's
sectoral employment will have on diversiﬁcation and how that change relates to changing
regional income is a useful and interesting tool. The ability to examine different regional
sectoral employment proportions allows the planner to see the effect a speciﬁc ﬁrm may
have on industrial diversiﬁcation. This ability to foresee a positive or negative effect on
regional diversiﬁcation levels may inﬂuence the decision as to whether or not to give
necessary zoning variances, tax incentives, or public ﬁnancing assistance. The comparison
to other economic indicators, such as the positive change in regional income used in the
case study applications, give the planners and policy makers an even better idea as to the
regional economic beneﬁts and costs of a given location decision.

Finally, the evaluation of the use of the portfolio model of diversiﬁcation for small
region data discussed many pitfalls these data have and their impact on the model's results.

87

The common problems of data requirements, sectoral aggregation, and regional aggregation
all effect the portfolio model in unique ways. The use of sectoral employment proportions
in the model causes it own unique problems, especially when the proportion is responding
to a very localized condition. The last concern of growth instability, although a problem,
can be sufﬁciently dealt with, as long as the model's results are thoroughly examined and
interpreted with the beneﬁt of some additional information.

Future Research

The portfolio analytic model of industrial diversiﬁcation lends itself well to many
applications. The ability to examine the variance and stability of a regional economic
variable is very interesting. Many research possibilities exist with the use of this model for
Michigan or other small region applications. It would be very interesting to calculate the
portfolio model using other regional economic variables. Two interesting examples, data
permitting, would be income diversity (as per Bolton (1986)) as well as diversity in terms
of capital investment or value added.

A Michigan analysis at the county level would be very desirable. Often economic
development policy issues are decided based on MSA or planning region designations. A
county level diversiﬁcation analysis would help determine where in the region the
development efforts should be concentrated, and what counties would be affected.

A possible extension of the portfolio model would be to combine it with Input-Output
analysis. From this combination it would be possible to examine industry stability and
how it relates to the industry technical coefﬁcients of the State. Are those industries, with
very localized markets, stable? Is the stability of an industry more closely related to those
industries it sells (forward linkages) to or to those industries it purchases ﬁom (backward
linkages)?

88

APPENDIX A.

WW3.

Alpena LMA

Ann Arbor MSA
Battle Creek MSA
Benton Harbor MSA .
Detroit MSA

Flint MSA

Grand Rapids MSA
Grand Traverse LMA
Jackson MSA
Kalamazoo MSA
Lansing MSA
Muskegon MSA
Saginaw MSA

Upper Peninsula MSA

Alpena County
Washtenaw County
Calhoun County
Berrien County

Lapeer, Livingston, Macomb, Monroe,
Oakland, St. Clair, and Wayne Counties

 

Genesee County

Kent and Ottawa Counties

Grand Traverse and Leelanau Counties
Jackson County

Kalamazoo County

Clinton, Eaton, and Ingham Counties
Muskegon County

Bay, Midland, and Saginaw Counties

Alger, Baraga, Chippewa, Delta, Dickenson,
Gogebic, Houghton, Keweenaw, Iron, Luce,

Mackinac, Marquette, Menominee,
Ontonagon, and Schoolcraft Counties

89

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