71 31,296
-

ROBB, Edward Howard, 1942A QUARTERLY ECONOMETRIC MODEL OF MICHIGAN.
Michigan State University, Ph.D., 1971
Economics, general

University Microfilms, A XEROX C o m p a n y , Ann Arbor, M ichigan

71 31,296
-

ROBB, Edward Howard, 1942A QUARTERLY ECONOMETRIC MODEL OF MICHIGAN.

Michigan. State University, Ph.D., 1971
Economics, general

University Microfilms, A XEROXCompany, Ann Arbor, Michigan

A QUARTERLY E C O N O M E T R I C M O D E L OF MICHIGAN

By
Edw a r d H Q Robb

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Economics

1971

PLEASE NOTE:
Some Pages h a v e i n d i s t i n c t
print.
Filmed as r e c e i v e d .

U N I V E R S I T Y M I C R O F I LMS

ABSTRACT

A QUARTERLY ECONOMETRIC MODEL OF MICHIGAN
By
Edward H . Robb

The quarterly econometric model of Michigan pr e ­
sented in this paper provides a mechanism for estimating
and forecasting personal income by major categories.

The

model gives special attention to the durable and nondurable
goods m a n u facturing industries, particularly motor vehicles
and equipment.

It also provides an analytical description

of the Michigan economy and,

in particular, the interplay

between broad aggregate sectors.
Al though the model contains 21 stochastic equations,
only the parameters of those of the personal income subset
were estimated.

The equations for consumption and invest­

ment were not estimated due to the lack of data.

The equ-

tions whi c h were estimated represent 11 wage and salary
components of personal

income and 6 nonwage and salary c a t ­

egories.

the model includes employment in

In addition,

motor vehicles and equipment among the endogenous variables.
The m o del contained in the paper was the first state
model to employ a systems method of estimation.

The esti­

Edward H. Robb

mation technique was three-stage least squares.

However,

due to the presence of autocorrelation in several equations,
the normal three-stage technique had to be modified to a c ­
count for the lack of independence.
of the model,

Given the assumptions

the technique utilized implies both consistant

and efficient parameter estimates.
Statistically,

the results were quite satisfactory.

With the exception of the equation for employment in motor
vehicles and equipment the sample data fit the theoretical
relationships very well.
As is typically the case,

the forecasting results

for some equations were better than others.
however,

Fortunately,

the results for those components included in tax­

able income were quite good wit h the exception of nonfarm
proprietors'

income.

The forecasts for the wage and salary

components were especially encouraging since this portion
of personal income comprises the withholding base for the
Mic h i g a n personal income tax.
The development and the presentation of the model
itself was carried out with the explicit aim of mak i n g the
study useful to policy makers.

Some of the results g e n e r ­

ated by the model indicate its utility for planning and
budgeting p u r p o s e s .
The most common form of forecasting methodology
employed in state government is trend analysis,
normal growth pattern.

i.e.,

the

The problem with this method is that

Edward H . Robb
it fails to account for m a j o r swings in the economy and the
pattern of change throughout the forecasting period.
test of this point,

As a

the forecasting results of the model were

compared with the forecast generated by assuming a normal five
percent growth.

In addition,

the forecasting results of a

previous econometric model of M i c h i g a n we r e also tested.

The

model presented in the paper yielded far mo r e accurate fore­
casts than either of the other models, w i t h only a 1.8
cent error for the six

per­

quarter forecasting period.

In terms of Michigan's major revenue sources,
individual income and sales taxes,

the

the 1969 forecast generated

by the model had a combined error of only 1.2 percent.

An­

other area where the model may prove useful in its ability to
help predict the impact of major strikes in the automobile
industry on personal income and the yie l d of the State's
personal income tax.
an example.

The experience of 1970 provided such

The 2 1/2 month strike caused an estimated p r o ­

duction loss of over 1.2 m i l l i o n units.

In terms of the

model this would imply

a $20 5 m i l l i o n reduc t i o n in personal

income and nearly a $6

mill i o n

revenues.

loss in personal income tax

ACKNOWLEDGMENTS
The construction of the econometric model presented
in this paper was made possible only wit h the assistance of
many people.

I am indebted to the entire staff of the

Research Section of the Bureau of Programs and Budget of
the State of Michigan, particularly A. Thomas Clay and
Doctor Gerald Miller who reviewed this proj e c t and offered
valuable suggestions.

I am also grateful for the help

rendered by Marylyn Donaldson of the Comp u t e r Laboratory
of Michigan State University wit h the seemingly endless
variety of computer problems I encountered.

I am especially

indebted for the time and efforts of Doctor Jan Kmenta who
served as my thesis director.

In addition,

the suggestions

and comments of Doctor James Ramsey and Doctor Mark
Ladenson contributed greatly to the development and p r e ­
sentation of the model.

As usual, however,

the author

claims sole responsibility for all.errors and omissions.

TABLE OF CONTENTS
Page

LIST OF............ T A B L E S ............................

V

F I G U R E S ...........................

vi

LIST OF
CHAPTER
I.
II.

III.

INTRODUCTION

...............................

1

ANALYSES OF PREVIOUS STATE ECONOMETRIC
M O D E L S ...................................

11

California Model
............ . . . . .
Michigan Model
..........................
Massachusetts Model .....................
Ohio Model
.....................

12
17
19
20

A QUARTERLY ECONOMETRIC MODEL
OF
M I C H I G A N ................................

27

Analytical Framework
..................
Theoretical Background
................
Discussion of the E q u a t i o n s ............
Estimation of the M o d e l ................
Empirical Results
Forecasting Results .....................
Concluding Summary
.....................

33
36
40
59
68
83
87

C O N C L U S I O N .................................

91

BIBLIOGRAPHY ..........................................

98

n

IV.

APPENDIX
A.

DESCRIPTION OF PREVIOUS STATE ECONOMETRIC
MODELS:
CHAPTER I I .....................

100

Page
B.

C.

D.

VARIABLE PARTICIPATION MATRIX OF THE
MICHIGAN MODEL: CHAPTER III
............

122

ORDINARY LEAST SQUARES RESULTS:
CHAPTER I I I ................................

124

SOURCES AND CONSTRUCTION OF SAMPLE DATA:
CHAPTER I I I ................................

128

iv

1

LIST OF TABLES

Table
1.

2.

Page
State of Michigan, General Fund, general
purpose revenue and expenditures,
1950-1968 ...................................

4

State of Michigan, record of revenue
estimates, General Fund Budget
.........

7

3.

Michigan personal income

...................

34

4.

Forecasting results of the m o d e l ..........

84

5.

U.S. passenger car production

88

6.

Comparison of annual personal income
forecast, 1969

v

............

95

LIST OF FIGURES AND ILLUSTRATIONS

Figure

1.

Variable participation mat r i x of the
Massachusetts Model ..........................

2»

The casual ordering of the Ohio Model

3o

Variable participation mat r i x of the
Ohio M o d e l .........
.....................

4.

Variable participation
general Michigan Mode.

. . . .

,x of the
...................

CHAPTER I
INTRODUCTION

Government has,

in the last two d e c a r d e ^ undergone

a tremendous expansion in both the size and scope of its
activities.

Accompanying this increased activity has come

a concomitant need for increased information, both q u a l i t a ­
tive and quantitative,

to enable the legislative and e x e c u ­

tive branches of government to fulfill their functions more
effectively.

While this need has not gone unnoticed at the

federal level which each year witnesses more sophisticated
methods of analysis being developed to close the "information
gap," the same cannot be said for most state and local g o v ­
ernmental organizations.'*'

This lag in the development and

adoption of the newer and more powerful socio-economic tools
on the state and local level is made more disturbing since
the growth of state and local government activity has been
even more pronounced than that at the federal level.

Over

the period from 1950 to 1968 total federal government receipts

While it is indeed true that the federal government
has been responsible for the development of the vast majority
of new techniques and data, it too has been slow in the im­
plementation of these improvements.
The result is that a
mass of sophisticated (and presumably helpful) analyses and
techniques has been filed away far from the individuals
actually making the decisions.

1

2
and expenditures grew 254 per cent and 345 per cent re­
spectively

(non-defense expenditures 279 per c e n t ) .

Total

state and local government receipts and expenditures, m e a n ­
while, grew at respective rates of 402 per cent and 382
per cent.
The lack of both reliable data and comprehensive
analysis in state and local government has been acutely
prevalent from the viewpoint of economic theory and e c o n o ­
metrics,

two tools which have received only the m o s t meager

attention from state and local governments.
under-utilizations

While their

(and in a few cases, misuse)

represents

a disquieting oversight from an efficiency oriented p o s i ­
tion,

in that the predictive powers of these tools have

gone needlessly untapped,

it is even more disturbing given

the institutional constraints faced by state and local
governments.
Unlike the federal government which controls the
money supply,

not to mention being able to incur both short

and long-run deficits,

state and local governments are not

only denied the use of the presses but are typically p r o ­
hibited by their constitutions and/or legislative bodies
from operating at a deficit.

Given their more restrictive

c o n s t r a i n t s , it would seem that state and local governments
would have even a greater incentive to avail themselves of
the growing body of econometric techniques.

iA

The adoption

3
of these tools would not only enable states to forecast
their revenues more a c c u r a t e l y , but could also make more
efficient the allocation of their revenues between competing
alternatives.
The State of Michigan has been no exception to the
general rule of inadequate fiscal planning.

As Table 1 so

palpably s h o w s , Michigan has displayed the common pattern
of boom or bust.

During the period 1950 through 1968,

General Fund-General Purpose expenditures have more than
quintupled,

rising from a level of $200 million in fiscal

1950 to $1,153 million in fiscal 1968 an increase of 476.5
per cent or at an average annual rate of 9.1 per cent
per cent from 1950 to 1964).

The increase, however, has

been characterized by a very erratic pattern.
years have resulted in several

(6.5

Deficit

"fiscal crises" and the

subsequent enactment of austerity budgets, while surpluses
have usually given rise to pronounced expenditure increases.
In contrast to the average annual increase in expenditures
of $35 million, the period 1952-1954 saw no increases in
expenditures while periods such as 1954 to 1958,
1962, and 1965,

1960 to

1966, and 1967 have seen expenditures in-

creasing at the rate of over ten per cent per year.

2

(See

Table 1)

2

The respective increases in fiscal years 1965,
1966, and 1967 were at the extremely rapid rates of 22,
24 and 32 per cent.

4

Table 1.--State of Michigan, General Fund, general purpose
revenue and expenditures, 1950 to 1968.
(Millions
of dollars)
Accumulated
Fiscal Year
Annual
Surplus (+) or
Ending
Expenditures Revenue
Surplus (+)
Deficit (-)
June 30
or Deficit (-)
(End of Year)
_

1950
1951
1952
1953
1954

200.4
206 .0
223.7
225. 3
223.1

156 .8
179.7
194.1
240 .8
261.1

43.6
26.3
29.6
+ 15.5
+ 38.0

21.4
40 .9
65.3
31.3
+
5.8

1955
1956
1957
1958
1959

252 .8
277.7
330 .9
367.0
376.3

264 .6
286 .3
312.1
328.7
298.8

+ 11.8
+
8.6
18.8
- 38.3
- 77.5

+ 17.0
+ 25.6
+
6.7
21.2
- 95.5

1960
1961
1962
1963
1964

386.2
429.9
476 .4
492.3
523.5

418.1
430.6
458.8
564.0
596 .0

+
+
+
+

31.9
0.7
17.6
71.7
72.5

64.0
- 71.7
- 85.6
22.8
+ 57.1

1965
1966
1967
1968

650.2
793.9
1,049.2
1,152.5

746.3
841.9
893.3
1,186.8

+ 96.1
+ 48.0
-155.9
+ 34.3

+153.2
+201.2
+ 45.3
+ 79.6

Source:

-

-

-

-

-

-

-

-

1950-1964 figures are taken from Harvey E. Brazer,
"Michigan's Fiscal Outlook," Wayne Law Review, Vol.
2, No. 2 (1967), pp. 430-50.
1965-1968 figures by
State of Michigan, Executive Office, Bureau of the
Budget, Budget Division.

5
This highly unstable pattern of expenditures not
only imposes intense pressures upon state personnel and
programs, but also makes efficient planning and programing
nearly impossible.

A further consequence is the difficulty

it causes in attempting to maintain a level and quality of
government services commensurate with the capacity of the
State's economy and the demands of its citizens.

With

Michigan's population growing at approximately 1.2 per cent
per year and with prices paid by the State
and salaries of State employees)

(including wages

rising at over three per

cent, the per capita supply of government services of co n ­
stant q u ality mu s t necessarily be curtailed or the quality
reduced anytime the year-to-year increase in appropriations
falls bel o w 4 to 4.5 per cent.
The reasons for this pattern of fiscal instability
have been varied.

As with any government institution, p o l i ­

tics is inextricably tied to both the level and allocation
of expenditures.

Nevertheless, the primary constraint in

determining the level of expenditures has to be the level
of its revenues.

Given certain institutional constraints

(including the state's tax structure),

the level of e x p e n d i ­

tures is b asically determined by the forecasted level of
its revenues.

Given the state's desired minimal level of

services, h o wever arrived at,

if the forecasted level of

revenues is at least sufficient to meet the expenditure level

6
implied by the desired level of services, no further action
is immediately required.

If the forecasted level of r e v e ­

nues falls short of the necessary level of expenditures,
further action,
cated.

e.g., a rise in tax rates, etc.,

is indi­

However, a p r ob l e m many states have experienced in

the past,

including Michigan,

3

is that of accurately fore-

casting the level of the state's revenues.

4

The techniques

employed for this purpose range from the crystal ball at one
extreme to econometric analysis on the other.

Unfortunately,

most state and local forecasting has not been at the

"other"

extreme or even close to it, with the "normal" pattern,

i.e.,

time trend a n a l y s e s , probably being the most prevalent fore­
casting method.

The prob l e m with using this type of analysis

is that in a very real sense it is merely a facade covering

3
Michigan has done extremely well m forecasting
total revenue in the last several years as Table 2 indicates.
4

The problem of forecasting tax revenues, muc h the
same as forecasting anything else in a wor l d of imperfect
knowledge, is a difficult one.
Forecasting tax revenues,
however, interjects an added phenomenon.
Due to the p e r ­
sistent tendency on the part of the individuals doing the
forecasting to be conservative, a tendency which seems to be
accentuated the less sophisticated the methodology and, hence,
the less confident they are with their forecast, mos t revenue
estimates understate the actual yields.
Building in a strong
downward bias to be on the "safe side" is bad enough, esp e ­
cially from an academic viewpoint, but such a phenomenon, if
at all recurrent, seldom goes unnoticed by state legislators
for very long, and as a result of compensating for the bias,
they in essence do the final forecasting.

Table

2 . — State of Michigan, record of revenue estimates,
General Fund budget (in t h o u s a n d s ) .

For
Fiscal
Year

1949-1950
150-1951
1951-1952
1952-1953
1953-1954

Long-Range Estimate
(18 Mos. or More Ahead)
Total
Fund
(2)

General
Purpose
(1)
$

228,949
229,895
265,766
301,888
306,557

Short-Range Estimate
(6 Mos. or Mo r e Ahead)

$

384,621
400 ,893
462,191
529,615
532,396

General
Purt jse
(3)
$

223,491
259,505
293,774
304,222
371,081

Total
Fund
(4)
$

400,388
449,366
505,991
525,240
586,167

1954-1955
1955-1956
1956-1957
1957-1958
1958-1959

365,541
246,171
315,003
335,782
333,542

574,826
415,995
505,046
541,286
545,769

373,206
287,955
316,364
316,015
290,466

588,500
474,662
518,441
524 ,086
514,551

1959-1960
1960-1961
1961-1962
1962-1963
1963-1964

307,858
409,328
477,921
468,350
560,591

539,134
644,852
734 ,929
733,256
839,164

415,882
443,117
452,384
546,353
593,957

650,231
686,830
711,082
819,979
887,024

1964-1965
1965-1966
1966-1967
1967-1968
1968-1969

674,570
756,145
878,036
932,909
1,337,065

910,401
1 ,034,210
1 ,268,155
1 ,358,833
1 ,864 ,288

727,459
816,436
896,355
1,159,644

991,570
1 ,174 ,562
1 ,299,429
1 ,619,068

8

Table 2.— Continued)
_ . , „
Actual Revenue
General
Purpose
(5)
$

Fund
(6)

Percentage Varia t i o n
_
,TT , * „ . . . x
(Actual Over or (Under) Estimate)
Col.

5

Col. 6
vs 2

Col. 5
vs 3

Col. 6
vg 4

402,492
460,140
493,617
577,669
581,411

1.5
13.3
7.3
15.8
20.5

4.6
14.8
6.8
9.1
9.2

-

.4
.4
- 2.9
14.9
.4

.5
2.4
- 2.4
10.0
.8

383,213
286,332
312,063
328,661
298,784

605,726
473,678
502,505
535,639
522,668

4.8
16.3
.9
- 2.1
-10.4

5.4
13.9
.3
- 1.0
- 4.2

2.7
.6
- 1.4
4.0
2.9

2.9
.2
- 3.1
2.2
1.6

418,103
430,573
458,750
563,993
614,008

654,746
676,019
720,469
842,806
909,137

35.8
5.2
- 4.0
20.4
9.5

21.4
4.8
- 2.0
14.9
8.3

.5
- 2.8
1.4
3.2
3.4

.7
- 1.6
1.3
2.8
2.5

746,337
841,873
893,228
1,171,811

1,004 ,283
1,171,375
1,281,249
1,644,964

10.6
11.3
1.7
a

10.3
13.3
1.0
a

2.6
3.1
.3
1.0

1.3
.3
- 1.4
1.6

232,475
260,550
285,172
349,684
369,445

$

New tax b a s e .
Source:

State of Michigan,
grams and Budget.

Executive Office,

Bureau of P r o ­

9
up one's ignorance of the true causes of a given phenomenon.
On a pragmatic level its use also has the disadvantage of
not enabling one to forecast severe deviations from the
trend, which is the major contributing factor to bad revenue
forecasts.
However,

from a broader perspective the seemingly

dominant role of accurate revenue estimation in overall
fiscal planning is often mitigated.

This is due to the

separate,

though related, prob l e m of the correct time

horizon.

Mo s t state legislators,

and more importantly

members of the executive branch, have exhibited a very
short time horizon wit h regard to both revenues and e x ­
penditures,

the most common horizon being one year.

The

p r o b l e m with a one year horizon is that it is not long
enough to insure that the level of governmental services
will be sufficient to m e e t the present and future demands
of the population.

Wha t is n e e d e d is not only more ac­

curate revenue forecasts,
expenditure)

but in addition revenue

(and

projections for more than the ensuing fiscal

year.
The under-utilization of economic tools on the part
of state and local governments may be waning,
far as M i chigan is concerned.

at least as

In the last few years M i c h i ­

gan has begun to exhibit some jigns of closing the informa­
tion gap.

Most notable was the state's purchase of an

10

E conometric Model of M i c h i g a n
Suit's Model)

in 1966

(more commonly known as the

and m o r e recently the implementation

of cost-benefit analysis to aid in a better allocation of
state

revenues.

ing, there

Although these actions have been enco u r a g ­

is still a need for better econometric models,

particularly in light of the fiscal reform package enacted
in 196 7 which added two new m a j o r revenue sources to the
state's tax system— a personal and corporate income tax.
In that good forecasts rest ultimately on a good
understanding of the process to be forecasted,
hoped

it is to be

that the quarter l y econometric model presented here

w i l l provide a m o r e accurate description of the economic
framework of Mic h i g a n and aid in improving forecasts of
the all important revenue base.
Chapter II of this dissertation reviews previous
state

econometric models.

Chapter III presents a quarterly

econom e t r i c model of Michigan.

The model provides a basis

for estimating current levels of personal income by major
components.
economy,

Due to the

special nature of the Michigan

special attention is given to the durable goods

m a n u facturing industries, particularly motor vehicles and
equipment.

C h a p t e r IV contains

an evaluation of the re ­

sults and some concluding remarks.

CHAPTER II
ANALYSIS OF PREVIOUS STATE ECONOMETRIC
MODELS

In contrast to the situation at the national level,
there has been little work done in the area of state and
regional econometric models.

Underscoring this is the fact

that to date only four state income models have been con­
structed.^

The first of these was A Quarterly Economic

Model for the State of California developed by Richard P.
Burton and John W. Dyckman in 1965.

The second effort, An

Econometric Model of M i c h i g a n , was prepared by the U n i v e r ­
sity of Michigan's Research Seminar in Quantitative Economics
under the direction of Daniel B. Suits in 1966.

The third

model, An Econometric Forecasting Model for a R e g i o n , was
constructed for the State of Massachusetts by Frederick W.
Bell in 1967.

The most recent endeavor is An Econometric

Model of Ohio developed by W. L. L'Esperence, G. Nestel,
and D. Fro m m in 196 8.

All four models have as the primary

This enumeration does not include a number of
state and regional growth models, e.g., the model of the
Upper M i d w e s t constructed by J. Henderson and A. Krueger
and the growth model of Georgia constructed by H. Thomassen.

11

12
goal the estimation and extrapolation of a major indicator
of economic activity— either gross state product and/or the
equivalent of state personal or d isposable income.

Appen­

dix A provides a general comparison of the overall charac­
teristics of the four state econometric models.
addition,

the models of Michigan, Ohio,

are reproduced in their entirety.
ever,

because of its size

In

and Massachusetts

(See Appendix A.)

(over 100 equations)

How­

the C a l i f o r ­

nia model is not presented except for a general analysis of
its methodological approach.

California Model
The first m a j o r effort at constructing a state
econometric m o d e l , A Quarterly Economic Model for the State
of C a l i f o r n i a , was surprisingly the mos t ambitious of all
the attempts.
terly basis,

First of all,
and secondly,

it was formulated on a q u a r ­

it attempted to do more in the

sense that it carried disaggregation further than either
the Michigan, Massachusetts,

or Ohio models.

While the

latter three models estimate only total personal or d i s ­
posable income,

the California model estimated personal

income by major sector,
Standard Industrial Code

including wages and salaries in 59
(SIC) groupings,

and five nonwage

2
With the exception that the employment subset of
the Michigan model is omitted.

13
and salary income sectors exclusive of personal contribu­
tions for social insurance
non-farm proprietors'
payments).

(other labor income,

farm and

income, property income and transfer

A unique feature of the wage and salary subset

is that w i thin each of the 59 SIC groupings payrolls are
further disaggregated into three exclusive and exhaustive
catego r i e s - “wage and salary disbursements originating from
inter-industry,

final local, and export d e m a n d — where such
3

disaggregation was meaningful.

The model also includes

an employment subset which covers m o s t of the wage and
salary subsectors.

In addition, self-assessed taxable
4
sales by nine categories
were estimated, as wer e total
corporate net income for financial and non-financial

insti­

tutions, assessed motor vehicle gasoline g a l l o n a g e , and
total unemployment.

In view of the scope of the model,

the

only analysis which will be set forth will be that which is
applicable to the entire m o d e l .
In many respects the model is perhaps a little too
ambitious given the data constraints which have and do

3

In some instances where inter-industry or localfinal demand was less than five pe r ce n t o r where inter­
industry demand is generated by many customer industries,
local-final and inter-industry demand were combined.
^Those categories are building supplies and furni­
ture, general merchandise and specialty items, food, auto­
mobiles, gasoline, apparel, business and personal services,
restaurants and bars, manufacturing, wholesaling, contract­
ing, and miscellaneous.

14
plague attempts at constructing regional and state models.
In their effort to circumvent the difficulty imposed by the
scarcity of data, Burton and Dykeman had to postulate two
more or less tenuous assumptions.
I.

That wage and salary disbursements in the ith

industry are reasonably good

"surrogate" for that industry's

physical output as m e a s u r e d in v a l u e - a d d e d terms.
II.

That the relative proportions of demand in an

industry between inter-industry,

local-final, and export

demand are constant over t i m e .
The first assumption was n e c e s s i t a t e d by the in­
tended scope of the model and the lack of corresponding
data.

The second assumption,

the limitations of the data

likewise, was the result of

(the e s t i m a t e d values of the

individual demand proportions re s t u p o n a single annual
observation).
The question as to the plausibility of the two as ­
sumptions aside,

the model does contain a blatant and p e r ­

haps damaging fault.

The e stimation method used was OLS,

w h i c h under the assumptions of the general "classical"
linear regression model exhibits all of the desirable
qualities of an estimation technique.

The p r o b l e m regard­

ing the California model is that not all of these a s s u m p ­
tions are m e t — namely,

that of the independence between

regressor and regressand.

For all b u t a very few exceptions:

the general form of the equations is as follows:

L

where
X

is the wage and salary disbursements in the
st
s subset

(1 = local final, 2 = interindustry,

3 = export)
X t _i

is the total wage and salary disbursements
the X

til

industry

in

(the sum of local final,

interindustry, export)
AZ.
3t-l

is the first difference of any other independent variable

e,
t

is the structural disturbance term,

The authors state that this general type of equa ­
tion was chosen in an attempt to eliminate serial correla­
tion,

"In this way the mutual dependence of successive

observations,

i.e., trend is explicitly taken into account."

The p r oblem with this methodological approach is
that the ratio of X

/X
(s = 1,2,3), for all industries
st
and time periods are constants since the estimates for the
shares in each of three demand subsectors were generated
from a single observation.

Hence, the equations could be

rewritten a s :

5
A Quarterly Economic Model for the State of C a l i ­
fornia , pi! 40.

where
a? = a,/k
1
1

However,

and

k = X

st

/X

t

since the estim a t i o n technique employed was OLS,

the necessary independence of regressor and regressand is
not maintained and the estimate of the parameters will be
biased, although still r etaining the desirable asymptotic
properties.
If indeed the inclusion of the dependent variable
lagged one period among the regressors was for the purpose
of eliminating serial correlation,
authors,

as stated by the

the correct procedure w o u l d entail altering the

estimation technique, replacing the OLS estimates w i t h ones
which were more efficient.

This approach wou l d also have

eliminated including independent variables for whi c h no
theoretical justification has bee n made.
While on the subject of estimation techniques,

it

would seem that the entire approach of the Calif o r n i a model
is questionable.

A l th o u g h not explicitly specified as such,

the model is a system of simultaneous structural equations.
Furthermore,

it reduces to a recursive system as the

variable participation m a t r i x

(VPM) of the equations readily

17

g
demonstrates.

Given the fact that all of the equations

are over-identified,

at least w i t h respect to the order

c ondition of identification,

it w o u l d seem that instead

of m a k i n g the possible heroic a ssumption that the con t e m ­
porary disturbances b e t w e e n individual equations are not
correlated,

i.e., E e ., e ., = 0 for all t and i ^ j
it
jt

(this

is in addition to the usual a s s u m p t i o n of a lack of any
serial correlation E e ^ t

(t-s) = ® ^°r a ^

^ anc^ ^ an ^

s ^ 0) it w o u l d be b e t t e r to make only the usual assumption
as to the lack of any serial correlation and then employ
either three-stage least squares
m a x i m u m likelihood

(FIMLE)

(3SLS) or full information
7
estim a t i o n methods.

M i c h i g a n Model
The model of M i c h i g a n p r e s e n t here

(or the Suit's

Model as it is commonly known)

was taken intact from An

Econometric Model of Michigan,

Technical Report No.

3 , pub­

lished by the State Resource Planning Division, Michigan
D epartment of Commerce.

In its final published form the

presentation of the model leaves muc h to be desired from
anything but a very elementary vantage point since the

This analysis does n ot apply to the employment
subset.
The dimension of the V P M of the rest of the system
is 123 x 123 and therefore is not presented.
7

If there is serial correlation, it can be taken
into account by m a king allowance for it in either of the
two estimation procedures.

18
statistics relating to the coefficients and the equations
we r e omitted and were not available from other sources.

In

an attempt to rectify this inadequacy it was necessary to
re-run the data published in the Report to generate the
mi s s i n g statistics.
OLS,

The parameters were estimated using

the estimation technique employed by Suits.
The most salient characteristic of the refitted

equations are the remarkably small values of some of the
coefficients of determination corrected for degrees of
freedom

_2
(R ).

While the major equations, especially those

for gross state product

(GSP) and gross state product

originating in manufacturing

(GSPMFG), exhibit very good

—2
fits, only five other equations have a R
statistic greater
than

_2
.800, and ten have a R
statistic less than one-half

(the equation for Mich i g a n retail sales by food stores has
a startlingly low value of only 0.094).

From these values

it wou l d seem that utilizing the complete model for fore­
casting purposes wou l d be at a m i n i m u m a risky undertaking.
Another characteristic, almost as disquieting,
the fact that many of the coefficients
the constants)

is

(13 not including

are not significant at over the 90 per cent

confidence level.

The mos t notable are the equations for

Mic h i g a n Retail Sales of Building,

Lumber and Hardware

Michigan Retail Sales of Food Stores where not only is the
constant insignificant at the 90 per cent level
quite common)

(which is

but neither is the only other independent

variable, United States Automotive Expenditures.

19
In addition,

there is at least one instance of

positive serial correlation, namely in the equation for
retail sales by furniture stores
by Furniture S t o r e ) .

(Michigan Retail Sales

The critical levels

(lower bounds)

of the Durbin-Watson statistic b e i n g respectively 0.59 and
0.82 at the 0.01 and 0.05 confidence levels.
twelve other equations have a

In addition,

Durbin - W a t s o n statistic

which falls between the upper and lower b o u n d a r i e s , and
hence inferences as to serial correlation are not possible.

8

Massachusetts Model
The econometric forecasting model of Massachusetts
written by Frederic Bell is the mos t mathem a t i c a l of the
four state models and exhibits the strongest ties with
m icro-economic theory.

It splits the total state received

income into two compon e n t s — export income and local service
income,

thus explicitly d e lineating the effect of non-

regional forces on the state's economy.
three income determination equations,
deals with the state's production,

Other than the

the rest of the model

investment, population,

The other widely used test for serial correlation,
the Von Neumann ratio test of Theil and Nagar is not app l i ­
cable in this instance since the equations were e stimated in
first difference and hence do not me e t the requirement that
the first and higher order differences of the explanatory
variable are small compared w i t h the range of the corres­
ponding variables themselves.
For a complete exposition on
this point see Theil and Nagar, "Testing the Independence
of Regression Disturbances," A m e r i c a n Statistical A s s o c i a ­
tion Journal, M a r - A p r . , 1961, pp. 793-806.

20
labor supply and labor demand functions.

Hence,

in a sense,

it represents a m i n i atu r i z a t i o n of the national GNP models.
As the variable partic i p a t i o n m a t r i x
readily demonstrates,

(Figure 1)

the syst e m is an integrated one.

All the equations are ov e r - i d e n t i f i e d using the order
criterion.
However,

The primary estim a t i o n technique was

2SLS.

since some of the equations are functions of only

predetermined variables,

the OLS estimates of their

parameters are also 2SLS estimates since no endogenous
variables appear on the right hand of these e q u a t i o n s .

The

capital stock equation was estimated using reduced-form
least squares

(RFLS).

The production function was also estimated using
OLS.

However,

the elasticities of factor inputs were esti­

m at e d by using the geometric means of factor shares whi c h
were taken as unbiased estimates of these parameters.
constant is the 1947 base value.

Hence,

The

the only OLS esti­

mate is that of the rate of technological c h a n g e — whi c h is
the output residual

(i.e., output unexplained by factor

increases).

Ohi o Model
The most recent state model, A n Econometric Model
of O h i o , represents a vas t improvement over the pioneering
efforts of the models for Mich i g a n and California.

The

model is truly an econometric one, qualifying to be called

21

1

1.

I
m

2.

Inm

3.

U

4.

s

5.
6.

8.

K

11.
12.
13.
14.

4

5

6

7

8

9 10 11 12 13 14 15 16 17
*

*
*

*
*

*
*

*

*

*

*

*
*

V2
L

10 .

3

V1

7.

9.

2

*

*

*

*
*

*
*

*

*

*

Km
K

nm

Ne
N

*

*
*

*
*

*

*

o
*

Po
*
Pe

15.

X

16.

M

17.

W

*
*
*

Figure 1.— Variable participation matrix of the Massachusetts
Model.

22
such by even the most ardent theoretic b e h a v i o r i s t s .

Its

micro and macro-economic underpinnings are solid, as w i t ­
nessed by the investment and personal income equations.
Fr o m the point of being a truly useful analytical
tool and aid for state policy decisions,
the four models.

In addition,

it is the best of

it has among its p r e d e t e r ­

mined variables several policy variables of the U.S. Federal
Government

(as does the California model) which allows some

analysis of the impact of changes in these instruments on
the Ohio economy.
F r o m a critical viewpoint,

little can be said to

detract from the model other than the qualifications im­
posed by the paucity of data and those enumerated by the
authors themselves.

However,

as with all the other models,

the estimation technique employed is open to a m o d i c u m of
. . .
9
criticism.

As indicated in Appe n d i x A, the Ohio Model contains
27 equations.

Eleven of these are identities.

The r e m a i n ­

ing 16 equations are identified, at least according to the
order condition
tion) .

(a necessary but not a sufficient c o n d i ­

The parameters in eight of the equations were

estimated using both 2SLS and OLS.

The parameters of the

g
The asymptotic properties of an estimator may be
of little comfort, however, in the case of the Ohio and
Massachusetts Model where the number of observations is
small and where the relative small sample properties of
the estimators may be more relevant.

23
other eight were estimated solely by OLS since their 2SLS
estimates are identical with those obta i n e d b y OLS.

The

causal ordering of the model is reproduced in Figure 2.
The arrows indicate the causal order i n g among the
endogenous variables.
The interdependence in the model
is due to the interaction among the consumer sector,
income flows and gross state products in services, fi­
nance, insurance, real estate and trade.
For example
in Figure 1, sales by ne w car dealers (A) affects the
annual change in automobile registration (AAR) and
gross state product in trade (GSPtd) w h i c h in turn a f ­
fects disposable personal income (DPI) w h i c h is an
explanatory variable of sales by n e w car dealers (A).
The interdependence is contained in Block II (Figure
1).
Blocks I and III are r e c u r s i v e . 1°
It would seem, given this approach, that the authors
are implying that the model is non-integrated,
three blocks are independent.

i.e., the

If this is the case, matrix

of coefficients of the predet e r m i n e d variables

(B) is block

diagonal and the variance-covariance matrix is also block
diagonal having the same size blocks as does B, then the
separate estimation techniques applied to the three d e l i n ­
eated blocks w o uld have yielded consi s t e n t estimates of the
respective parameters with i n the equations of those blocks.
However,

as the Ohio V P M demonstrates

not the case.

(Figure 3) such is

Instead of being block diagonal,

the B

matrix is integrated.
In summary,

the previous state models have suffered

from one of several shortcomings.

The

least damaging is

^^An Econometric Model of Ohio, p. 1 4 .

Causal Ordering of the Ohio Model
1, Frp
AR
2
O
3, AAR
o
4, T c
rH
CQ
5,
6. A
7. R
8. ADPI
9. DPI
1 0 . FIT
11 , PI
H
12 AGSP
H
13. GSP
14.
GSP (other)
O
O 15. AGSP(other)
rH
CQ 16. AGSP(known)
17, GSP (known)
18, GSPfi
19, GSP so
2 0 . GSPtd
rr . G S P CC
H 22 » Ima
f—I
H 23 . Isam
^4 24 . Imma
O 25 • I G F m 2
4r
O
rH 26 • GSPma
<r
CQ
27 . AGSP_
ma

Exogenous Variables

H

1

,

AR-i
AR_i

-*=j
<-

(AAC)/AC, a r _ x
DPI
■-i

.

Source:

GSP_i
GSP(other)_i
GSP (known)_i

*\

GSP. , GSP ,
fg'
slg

HP
RCE
IGF

2

An Econometric Model of O h i o / p.

,

,

ma-1'

Isma y4 RTS
-I
,

o

G S P m a -i
AGNF
; MPC
ma
15.

Figure 2.— The causal ordering of the Ohio Model.

n

l a

Block

III

Block

II

Block

I

Ohio
VPM
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
2 4.
25.
26.
27.

1 2
X

3

Ft
* *
AR
* *
AAR
*
Ts
C
A
R
ADPI
DPI
FIT
PI
GSP(other)
GSP
a GSP
AGSP(other)
a GSP (known)
GSP (^own)
GSPfi
G S P so
GSPtd
GSPcc
Ima
Isma
Imma
IGFma
GSPma
AGSPma

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

*

*
*
*
*

*
*

*
*

*
*

*
*

*
*
*

*
*

*
*
*

*
*

*
*
*
*

*
*
*

*
*

*
*

*
*

*

Figure 3.— Variable participation matrix of the Ohio Model.

*
*

*
*

*

*

*

*
*
*
*

*
*
*

*
*
*

*
*

*
*

*
*
*

26
the annual format employed in the Massachusetts, M i c h i g a n
and Ohio Model.

The p r o b l e m wit h the annual format is a

pragmatic one in that it does not allow one to readily up
date the model, nor observe shorter run economic f l u c t u a ­
tions which may have serious revenue implication.

The

remaining criticisms have to do wit h the e s timation t e c h ­
nique employed.

In the case of the C alifornia Mod e l the

method of estimation

(OLS) does not yield c onsistent esti

mates of the parameters.

A n d more generally,

all of the

models fail to utilize the more efficient estimation
techniques available.

In order to eliminate these faults

the model of Michigan set out in the following chapter
employs a quarterly format and utilizes 3SLS w h i c h given
the assumptions of the model implies both consistent and
efficient parameter estimates.

CHAPTER III
A QUARTERLY ECONOMETRIC M O D E L OF MICH I G A N

In contrast to mo s t national,
econometric models,

regional, or state

the model p r e s e n t e d in this paper deals

solely with personal income.

Its prim a r y purpose is to

provide a vehicle for forecasting M i c h i g a n personal income.
While the model prese n t e d here does not contain
either a disposable income or tax subset,

it does provide

a starting point for the devel o p m e n t of such sectors.
Since the intended goal of this model was to aid in im­
proving the accuracy and current estimates of Michigan's
tax r e v e n u e s , in particular the income and consumption
taxes, the construction of a q u a r t e r l y mod e l of personal
income appeared to be the most germane and fruitful first
step.
The general model e nvisioned for M i c h i g a n ma y be
set out as follows:

(3.1)

PI = WS + NWS

(3.2)

WS =

16
I WS1
i=l

27

T H IC K N E S S

FEET

„-2

r
H

. in

F IG U R E
C H E M IC A L

C O M POSITIO N
DIAMOND

OF

D R ILL

S
SCALES
H O LE

CR

D 64

-2 0 %

-10%

AVG.
F«0

10%

20%

30%

-3 0 %

-2 0 %

-10%

AVO.
T102

10%

20%

-2 0 %

AVG.
-1 0 % AUO,

I__________ ■

F IG U R E
C H E M IC A L

C O M POSITIO N
DIAMOND

OF

D RILL

5
SCALES
HOLE

CREEK

D 64

FLOW

1

10%
■

-5 0 %

-4 0 % -3 0 %

-2 0 %

-10%

AVG.
Nq*0

10%

2(

_l_____ I_____ i_____ l_____ I_____ iZ ---- 1----- 1

t h ic k n e s s

in

f e e t

Oo

FIG U R E
C H E M IC A L

COM POSITION
DIAM OND

OF

D R IL L

6
SCALES
HOLE

CREEK

SL 5

FLOW

20%

EK

-10% 4 I2 0 j

FLOW

10%

20%

-4 0 %

-3 0 %

-2 0 %

-10%

NOjO

10%

20%

30%

40%

30%

60%

-7 0 %

-6 0 %

-9 0 %

-4 0 %

-3 0 %

-2 0 %

-10%

K jO

10%

20%

30% j

AVG.
-7 0 %

-5 0 %

-6 0 %

-4 0 %

-3 0 %

-2 0 %

-1 0 %

K

10%

20%

30%

40%

50%

50%

70%

60%

90%

100%

T H IC K N E S S IN

FEET

AVG,
-2 0 %

-1 0%

MgO

10%

20%

30%

40%

-2 0 %

-1 0 %

F iO

10%

20%

30%

CHEM ICAL

-3 0 %

-2 0 %

-1 0 %

MVb,

T102

FIGURE
C O M P O S IT IO N
OF
D IA M O N D

D R IL L

AV
10%

20%

7
SCALES
H O LE

30%

CREEK

NK 3

40%

FLOW

30%

-3 0 %

-2 0 %

-1 0 %

A l2 !

26

-3 0 %

|

-2 0 %

-f0 %

AVG.
TiOg

iO %

20%

It

FIGURE 7
C O M P O S IT IO N
OF SCALES

I

DIA M O N D

D R IL L

H O LE

30%

CREEK

40%

30%

-3 0 %

-2 0 %

-1 0 %

FLOW

NK 3

x m

AVG.
A l2 03

10%

20%

-4 0 %

- 90%

-2 0 %

-1 0 %

AVG.
N o2 0

10%

20%

30%

40%

26

20 %

- 40%

-3 0 %

-2 0 %

-1 0 %

AVG.
N«2 0

10%

20%

30%

*0 %

-7 0 %

-6 0 %

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AVO.
K jO

10%

20%

30%

40%

50%

27

10%

NK 3
AVG
SiOp

10%

20%

-3 0 %

-2 0 %

-10%

THICKNESS

IN

FEET

10%

SL5
AVG.
SI02

FIGURE
SILICON

OXIDE

VARIAT ION

8
IN

SC AL ES

CRE EK

FLOW

D 64
AVG.
Si02

FIGURE
SILICON

OXIDE

VARIATION

8
IN

SCALES

CREEK

FLOW

CALCIUM

OXIDE

THICKNESS

IN

FEET

fe

30%

•4 0 %

-3 0 %

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-10%

NK 3
AVG.
CaO

10%

20%

30%

40%

D Q U E B m C „*-0WL

FIGURE
CALCIUM

OXIDE

VARIATION

9
IN

SCALES

CREEK

-6 0 %

-3 0 %

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J____ I____ L

J----------------1_________ I_________ L

FLOW

28

-10%

GURE
ION

NK 3
AVG.
CaO

10%

20%

30%

40%

9
IN

SCALES

CREEK

FLOW

-6 0 %

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D 64
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10%

20%

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-20

SL 5
AVG.
-10% NlgO

10%

20%

30%

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-20 %

-10%

Mgl

<

55aa_.

'

—

THICKNESS

IN

FEET

>

-—

■---------- ^

240

-1m

*

280

FI GURE
MAGNESIUM

OXI DE

VARIATION

I

29

fo -2 0 %

-10%

NK 3
AVG.
MgO

FI GURE
VARIATION

10%

20%

30%

4 0%

-3 0 %

10
IN

SCALES

CREEK

FLOW

-2 0 %

-10%

0 64
AVG.
MgO

10%

20%

30%

FIGURE
I RON

OXIDE

VARIATION IN

II
SCALES

CREEK

FLOW

-2 0 %

-10%

NK3
AVG.
FeO

10%

20%

30%

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ov

$>/

FI GURE II
DE

VARIATION IN

SCALES

CREEK

FLOW

-10%

D 64
AVG.
FeO

10%

20%

30%

40%

-3 0 %

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i

10%

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20%

i

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THICKNESS

IN

FEET

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FIGURE
TI TANI UM

OXIDE

VARIATION

I
IN

-2 0 %

-10%

NK 3
AVG.
TiOg

10%

20%

30%

— i---- 1-----t—-1-- 1____ i____ ■

FI GURE
VARIATION

40%

50%

■____ ■

12
IN

SCALES

CREEK

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D 64
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10%

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10%

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^

"

=

r

1

J

-

^ D O L E R I T I C ___ zol

40

►

1

80

u 120
lii

u.

1
W 160

to

HI
O
X

V200

/

_

240

/

^

\

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^

>

\

0 /v^

1

/

/

/

1
j

"V ,

/

!

280

FIGURE
ALUMINUM

x m

OXIDE

VARIATION

IN

13
SCALES

CREEKl

SL 5
AVG.
%

Al20 3

10%

20%

-3 0 % -2 0 %

-10%

NK 3
AVG.
AlpO,

0 64

AVG.
10%

20%

DOLERITIC

FIGURE
ALUMINUM

OXIDE

VARIATION

IN

-20%

Z O N E ___

13
SCALES

mm

CREEK

FLOW

-10%

AlgOg

10%

SODIUM

NK 3

AVG.
30%

40%

5 0%

60%

- 4 0 % -3 0 %

-2 0 %

-10%

N o2 0

10%

20%

30%

40%

-I_____________k

uPP6R _

SPJ^ERitic

ZQNf

FI G U R E
SODIUM

OXIDE

VARIATION

IN

14
SCALES

CREEK

FLOW

3%

40%

UPP6R

EK

FLOW

50%
*

-4 0 % - 3 0 % - 2 0 %
*

&Q.LER>TI£ - Z- N-T -

1

-10%
1

0 64
AVG.
NaoO

10%
«

20%
■

30%
«—

40%

50%

60%

THICKNESS

IN

FEET

'%

20%

«

30% • 40%

‘

50%

»

60%

1

70%

1

00%

■

90%

*

100%

*

-8 0 %

-7 0 %
»

-6 0 %
■

-5 0 %
»

-4 0 %
■

-3 0 %
■

-2 0 %
«

-1 0 %
■

------------- __ 00LEmric__ Z O N E

FIG URE
POTASSIUM

OXIDE

VARIATION

IN

34

NK 3
%

-6 0 %

-5 0 %

-4 0 %

-3 0 %

-2 0 %

-1 0 %

FIG URE
SSIUM

OXIDE

VARIATION

AVG.
K,

IN

1 0%

20%

30%

40%

15
SCALES

CREEK

FLOW

50%

-5 0 %

-4 0 %

-3 0 %

-2 0 %

-1 0 %

D 6
AVd
K2 a

34

10%

ES

20%

CREEK

30%

40%

50%

-5 0 %

-4 0 %

-3 0 %

FLOW

m m

-2 0 %

-1 0 %

D 64
AVG.
K2 0

10%

20%

30%

40%

50%

60%

Pyroxene Analyses

Originally several hundred pyroxene samples were density sepa­
rated and it was intended to concentrate on their chemistry in this
study.

Pyroxenes were chosen because the lack of diverse composition

and the existence of only one phase renders the plagioclase somewhat
less valuable than the pyroxenes in studying basaltic magma variation.
However, due to difficulty in obtaining pure samples and the impos­
sibility of ever separating the pigeonite and augite, the study was
limited to two sets of minerals.
Sixteen samples of pyroxenes were separated from the St. Louis 5
drill hole and partial chemical analyses were made on them (Table 5).
The peaks of the graph of the FeO/MgO ratio (Figure 16) representing
the highest FeO/MgO ratios correspond with thin sections that have
both pigeonite and augite present.

This agrees with the work of

Hess (1941).
An attempt was made by the author, assisted by Milo Nielsen of
the Buick Motor Division, to apply an electron microscope to the
study of the pyroxene grains.
on one grain (Photo 1).

Semi-quantitative results were obtained

However, great difficulty was encountered

due to the electrical charges on the grain surface (Photo 2).

Even­

tually, by coating the grain with gold the charge could be removed
and the grain analyzed.

This method would be suggested for further

study since the mixed pyroxene grains could then be individually
analyzed.

It must be cautioned that such a procedure is slow and

very expensive.
Eight pyroxene samples were separated from the Osceola 3 diamond

36

48ISEC176298INT
10K
HS: 2 0 E V / C H
5j.fi

I \ \ \
M gAi

Si

Co Co

Ti

\ \
Ti

Fe

Fe

Kioto 1.

Semi-Quantitative Analysis of an Augite
Grain.

Photo 2.

Electron Microscope Picture of Augite Grain
Showing Charge Effect on Surface, X1000.

37

Table 5.

Chemical Analyses of the Pyroxenes from the
Scales Creek Flow, Diamond Drill Hole SL5.

FeO

FeO/
MgO

0.76

16.45

21.68

13.72

9.93

22.25

2.24

36.70

9.28

8.05

23.09

2.87

14/64

38.63

14.95

7.94

20.48

2.58

17/80

49.47

19.72

11.22

13.60

1.21

25/120

71.67

18.12

14.01

14.83

1.06

29/140

52.45

15.18

12.51

17.16

1.37

33/160

46.91

17.18

10.61

13.75

1.30

36/175

42.73

16.75

15.40

14.16

0.92

40/195

47.34

16.32

14.70

16.32

1.11

46/225

10.13

18.48

15.00

11.28

0.75

47/230

47.71

17.31

13.55

13.85

1.02

48/235

47.59

17.70

13.39

14.38

1.07

49/240

48.23

17.98

13.07

14.31

1.09

50/245

48.70

17.53

13.32

13.29

0.99

51/249

46.36

17.78

11.80

15.56

1.32

Sample/
Depth

Si02

CaO

1/0

37.72

22.68

3/10

38.65

10/45

MgO

38

FeO/MgO

40

T H iC K N E S S

120

160

240

280
FIGURE

IG.

FoO/MgO
FROM

RATIO

SCALES

OF

PYROXENES

CREEK

FLOW

drill hole which penetrates the Greenstone lava flow where it is
only 108 feet thick.

These were analyzed (Table 6) and the FeO/MgO

ratio was graphed (Figure 17).

This ratio tended to increase

toward the center of the flow, a trend that was expected from the
work of Hess (1941).

40

Table 6 . Chemical Analyses of the Pyroxenes from the Greenstone
Flow, Diamond Drill Hole 03.

Sample/
Depth

Si02

CaO

MgO

FeO

A 12°3

FeO/
MgO

3/10

50.46

18.88

16.17

9.35

6.54

0.578

4/15

55.03

18.35

10.89

9.73

6.00

0.893

8/35

47.55

20.73

17.66

14.36

12.60

0.813

10/45

41.16

17.14

25.61

21.93

10.78

0.856

15/70

48.74

17.96

12.65

12.69

9.34

1.003

17/80

47.05

17.14

13.08

14.08

10.78

1.076

21/100

46.99

17.04

13.59

13.21

10.10

0.972

23/108

49.40

18.39

16.01

10.90

7.11

0.680

FeO/MgO

FIGURE

17.

F tO /M flO RATIO
FROM

OF PYROXENES

GREENSTONE

FLOW

42

Kearsarge Flow

The chemical analyses (Table 7 and Figure 18) of 13 samples
from the Kearsarge Flow add substantially to prior studies of the
Portage Lake Lava Series.

These samples were chosen to correlate

this study with previous chemical studies of the Keweenawan lava
flows.

Twelve samples were taken at three foot intervals from the

Star 10 diamond drill hole in Keweenaw County.

This hole penetrates

the total 32'9" thickness of the flow in this location.

One addi­

tional sample was taken at a depth of 12% feet for analysis since
megascopic study indicated the possibility of unique lithology.
Although the flow is only 33 feet thick in this location,
trends remarkably similar to those found by Broderick (1935) in the
Kearsarge Flow are revealed by these chemical analyses.

The upper

half of the flow has the highest percentages of Si02> Ti02> Na20,
K2O, and MnO and the lowest values of

CaO, and MgO.

Since

iron was analyzed as FeO, petrographic study was combined with the
analyses to indicate high

anc* l°w FeO in the top portion.

These tendencies are maximized in sample 6 taken 12% feet below the
top where several dark brown bands 1/2" to 3/4" thick occur.

Analyses

of this sample of rock taken from such a band indicate a very high
amount of Si02 and low percentages of CaO, MgO, FeO, and A^O^.

Thin

section study indicates that this rock is coarser than the surrounding
rock, and quartz and albite are present as expected. These bands
obviously represent doleritic tendencies despite the fact that the
flow is very thin at this point.
The araygdaloidal zone has the expected high percentage of Fe202

THICKNESS

IN

FEET

op

op

40%

-2 0 %

-1 0 %

AVO.
M flO

AV<3.
10 %

-20%

-10%

FtO

10%

20%

-4 0 %

-3 0 %

-2 0 %

-1 0 %

T iO j

10%

F IG U R E
C H E M IC A L

C O M PO S ITIO N

DIAM OND

D R IL L

20%

30%

*2 0 %

*1 0 % Al.

(8

OF
HOLE

KEARSARGE
STAR 10

FLOW

10%

20 %

OF
LE

KEARSARG E
STAR 10

FLOW

10%

20%

AVG.

-3 0 %

-2 0 %

-10%

,0

10%

20%

30%

40%

30%

-6 0 %

-5 0 %

-4 0 % -3 0 %

-2 0 %

-10%

K20

— l---------- 1-------------------------J------------ 1------------ 1------------| - n

XUM

10%

20%
1

30%

Table 7.

Chemical Composition of the Kearsarge Lava Flow, Diamond Drill Hole Star 10.

Sample

Depth

Si02

CaO

MgO

FeO

Ti02

A 12°3

Na2°

k 2o

MnO

1

0

34.43

27.90

2.66

5.17

1.14

14.96

0.44

0.86

0.107

2

3

37.81

9.61

9.23

15.22

2.61

14.92

0.38

4.05

0.196

3

6

46.99

7.95

9.40

11.50

2.56

15.59

3.26

0.42

0.223

4

9

48.00

6.72

8.52

10.94

2.73

16.89

3.49

0.37

0.195

5

12

47.36

5.65

9.03

10.43

2.70

16.26

4.51

0.42

0.214

6

12.5

59.82

2.22

7.81

8.93

1.58

11.74

2.36

0.97

0.175

7

44.38

8.43

7.90

14.44

6.91

8.28

12.84

14.44
15.09

2.68
4.02

0.192

45.73

3.01
2.46

0.61

8

15
18

0.87

0.203

9

21

45.89

6.33

9.48

14.41

2.30

14.94

4.44

0.57

0.211

10

24

45.87

8.46

8.53

12.63

2.53

15.43

2.68

0.47

0.205

11

27

48.09

6.95

8.80

10.58

2.34

16.02

3.11

0.81

0.161

12

30

46.38

8.50

9.63

10.71

2.04

16.68

3.11

0.51

0.172

13

32.7

47.59

5.00

9.20

12.39

2.34

15.16

5.35

0.29

0.145

45
and the basal chill zone has a higher amount of FeO, Sif^, K 2O, and
Ti02 than the rock immediately above.

A similar tendency was found

by Cornwall (1951a) in the Greenstone Flow.

Sample number one

produced somewhat anomalous results due to the large amount of calcite
deposited in vesicles in the flow top.

Sample thirteen, at the

bottom, had an excess of Na20 evidently due to alteration.

The

plagioclase in this sample was oligoclase (Anj^).
Calculation of the FeO/MgO ratio indicates an increase from the
bottom to the center of the flow.

Below the amygdaloidal zone,

which had a high FeO/MgO ratio due to iron concentration, the ratio
was relatively low and decreased downward until below the zone show­
ing doleritic tendencies.

Cornwall (1951a) found a similar trend

for the FeO/MgO ratio in the Greenstone Flow.
These analyses found the same distribution of oxides through the
flow as was found by Broderick (1935).

Table 8 serves to compare the

work of Broderick (1935) with the present study.
the two sets of samples are:

Differences between

(1) thickness of the flow where studied

by Broderick was 164 feet and (2) the pegmatitic layer in the part of
the flow in this study is very distinct as compared to the vague
pegmatitic tendency found elsewhere by Broderick (1935).

Table 8.

Comparison of Chemical Analysis of Two Drill Holes
in the Kearsarge Lava Flow.

Broderick (1935)

Present Study

Oxide
Ophite

Dolerite

Ophite

Dolerite

Si02

48.04

48.78

45.87

59.82

AI2O 3

16.88

14.51

15.43

11.74

MgO

7.12

8.53

7.81

CaO

9.83

6.11
6.35

8.46

2.22

Na20

2.39

4.37

2.68

4.51

K20

0.46

0.82

0.47

0.97

PETROLOGY

The present study was conducted only on the Scales Creek Flow.
Petrographic thin sections were prepared of samples chosen by mega­
scopic examination of the core.

The following composite description

is based on petrographic analysis of 188 samples and is considered
valid because of the lateral homogeneity of the flow.

Petrographic Description

The main minerals in the Scales Creek Flow are labradorite laths
and anhedral, ophitic augite grains with minor amounts of pigeonite
and subhedral, altered olivine.
hematite, and ilmenite.

Accessory minerals include magnetite,

Plagioclase changes from labradorite in the

main body of the flow to albite-oligoclase near the top and bottom.
The amygdaloidal flow tops have typical red coloration in the
hand specimen due to the presence of hematite.

Minerals forming the

groundmass of the amygdaloidal tops are randomly distributed, altered
plagioclase microlites, often in radiating groups, surrounded by chlo­
rite and hematite that obscures all other minerals (Photo 3).

Glomero-

porphyritic groups of plagioclase phenocrysts show alteration to
chlorite, calcite, paragonite, and epidote.
Amygdules of the flow top have been filled with epidote, quartz,
prehnite, calcite, chlorite, and various zeolite minerals.

Most

vesicles contain more than one mineral, often having rims of epidote
or hematite and central fillings of quartz or calcite (Photo 4).
47

48
Veins of quartz or calcite often cut the amygdaloidal zone.

Photo 3.

Flow Top Showing Plagioclase in Matrix of
Hematite. Ainygdule is Filled with Quartz
and Epidote. Crossed Nicols, X53, Sample
LS30-1.

Photo 4.

Portion of an Amygdule Showing Hematite
and Epidote Rims with Central Quartz
Filling. Crossed Nicols, X53, Sample
SL5-1.

The upper chill zone of the flow is a raicrocrystalline,
amygdaloidal rock with a diabasic texture.

This grades downward

through a zone of subophitic basalt with interstitial pyroxene into

49
an ophitic texture with the plagioclase laths poikilitically included
in the pyroxene (Photo 5).

Photo 5.

The ophitic texture becomes coarser with

Plagioclase Poikilitically Included in
Pyroxene. Crossed Nicols, X133, Sample
SL5-36.

depth in the flow until approximately the center, below which the
grain size tends to decrease.

Evidence of crystal settling is found

in large pyroxene and olivine grains that occur above the basal chill
zone (Photo 6).
In the central ophitic portion of the flow the plagioclase
microlites often show alignment around larger mineral grains.

These

larger minerals, such as altered olivine and plagioclase laths appear
to have been pushed aside to form channels through which microlite
swarms moved (Photo 7).

Other microlites appear in a swirled arrange­

ment in the matrix giving the impression that the magma crystallized
under mobile and somewhat turbulent conditions (Photo 8).

This is

also noted in the pyroxenes, may of which contain poikilitically
included, semi-aligned feldspar microlites.
Pyroxenes of the central flow portion are not single crystals but

Photo 6.

Large Plagioclase and Pyroxene Above
the Basal Chill Zone. Crossed Nicols,
X80, Sample SL5-46.

Photo 7.

Microlite Swarm Around Altered Pyroxene
and Plagioclase. Crossed Nicols, X133,
Sample G7S-16.

groups of randomly oriented small equant crystals set in a matrix
of chlorite, plagioclase microlites, and magnetite grains.

Two

pyroxenes, augite and pigeonite, occur mutually, although augite is
the most abundant as the pigeonite occurs only as trace amounts.
visible exsolution lamellae are present in the pyroxenes.

No

This,

along with the lack of hypersthene, is to be expected from the studies

Photo 8.

Microlites Showing Swirled Arrangement.
Crossed Nicols, X80, Sample NK3-18.

of Hess (1941) although Cornwall (1951a) did find a small amount of
hypersthene in some thick flows.

Distinction between augite and

pigeonite, which was difficult in cases because the pigeonite occurs
in such small grains, was made mainly on the basis of 2V angles
estimated from optic axis figures obtained with a petrographic micro­
scope. The 2V for pigeonite is 15° and for augite is 42°.

Index

tests were not made due to difficulty in working with the fragments
and so no estimates of molecular composition are available.
The magnetite occurs as blebs in the matrix between plagioclase
laths.

Altered olivine is also found in the matrix and sometimes is

included in the pyroxene granules.

Many large plagioclase laths

occur in glomeroporphyritic masses in the matrix.

These laths are

often fractured across their breadth and incipient alteration to
chlorite has taken place along these fractures.
Very coarse-grained doleritic or pegmatitic concentrations of
euhedral laths of oligoclase-andesine and augite (ferroaugite?)
occur near the top of the flow and possibly near the bottom (Photo 9).

Photo 9.

Doleritic Zone Showing Large Altered
Plagioclase Laths and Quartz. Crossed
Nicols, X80, Sample NK3-9.

These zones are indicated on Figures 7 through 14.

The upper doler­

itic zone is better developed than the lower zone although it can be
distinguished by both petrographic study and chemical analysis
(Photo 10).

Pegmatitic zones have been recognized for many years

in the upper portions of Keweenawan lava flows but have not been
reported before for the lower portions of such flows.
Observation indicates that the thickness and the coarseness of
the upper dolerite is proportional to the lava flow thickness.

Inter­

stitial to the large laths of plagioclase in these pegmatitic zones
are smaller grains of dendritic magnetite, hematite, ilmenite, and
quartz.
The upper doleritic zone is highly altered.

Plagioclase has

changed to epidote, paragonite, carbonate, pumpellyite, and chlorite.
Augite has altered to chlorite and secondary hornblende (Photo 11).
Augite and labradorite are slightly altered.
all cases, been destroyed by secondary alteration.

The olivine has, in
The alteration

Photo 10.

Large Altered Plagioclase Laths and
Quartz in the Bottcm Doleritic Zone.
Crossed Nicols, X80, Sample NK3-54.

Photo 11.

Pyroxene Altered to Secondary Hornblende.
Crossed Nicols, X200, Sample NK3-24.

products are chlorite, serpentine, magnetite, hematite, iddingsite,
and bowlingite.

In many instances, it is felt by the author that the

alteration products of the olivine occur as a fine-grained inter­
mixture lacking definite optical properties.

Bowlingite, a magnesium-

rich clay mineral, is characterized by green color, strong pleochroism,
third order interference colors, and lamellar structure with extinction

82

Statistically,

the results seem satisfactory. With

the exception of the m o t o r vehicles and equipment employment
equation,

the sample data fit the theoretical relationships

very well.
equation,

Besides the relatively low value of R

2

for this

the coefficients of both the capital stock and

the dummy variable for improved quality control were insig­
nificant.

Furthermore,

the standard error of the OLS fit

is quite high, over 10 percent of the 1968 values.

While

several factors could possibly explain these problems,
likely candidate is the dependent variable itself.

a

Employ­

ment was chosen as a proxy for the more meaningful man-hours
variable in keeping wi t h the theoretical structure of the
general model.

Given the empirical results,

a slight m o d i ­

fication of the original hypothesis may be well-advised.
Alternatively, the results w o u l d probably be improved by
redefining employment in the industry to include the nearly
250 thousand workers who are classified in Standard Indus­
trial Codes other than 371.
Two additional equations pos e d minor problems.
sign on U.S.

automobile production in the payroll equation

for transportation,
was wrong,

The

communications,

and public utilities

since intuitively one w o u l d expect this variable

to be positively related to payrolls.

The same was true

for the sign of the wa g e rate variable in the equation for
payrolls in mining.
was not significant.

However,

in this case the coefficient

83

Fo recasting Results
The primary purpose for constructing an econometric
model of Michigan was to provide a mecha n i s m for forecast­
ing personal income.

As a meas u r e of how we l l the model

performs in this aspect, the forecasting results are
presented in Table 4.

Although not entirely satisfactory,

the results w e r e encouraging and pro v i d e insights

for

future i m p r o v e m e n t s .
As is usually the case, the results for some
equations w e r e better than others.

Fortunately, however,

the results for those components included in taxable income
were quite good with the exception of n o n f a r m proprietor's
income.

The forecasts for the w a g e and salary components

were especially encouraging since this portion of personal
income comprises the w i t h h o l d i n g base for the Michigan
personal income tax.
In terms of the forecasting errors, the m o d e l did
very well.

The percentage errors for the six q u a r t e r f o r e ­

casting period were respectively 1.51,
2.08,

and 3.0 7 percent.

was 1.81 percent.

1.08,

0.76, 2.17,

The overall error for the period

The model p redicted not only all the

correct signs of the actual changes but, in addition,
accurately predicted the signs of the rates of year-ago
quarter changes.
9.9,

8.3,

8.5,

The actual y e a r - a g o quar t e r moves we r e

8.1,

5.2,

and 8.7 percent.

changes were respectively 8.2,
percent.

7.1, 7.6,

The

forecasted

5.7, 3.0, and 5.3

84

Table 4.

Forecasting results of the model.

MIN
WS
Forecasted Actual

1969
1969
1969
1969

CC
WS^
Forecasted Actual

371
WS
F orec a s t e d Actual

1
2
3
4

25.3
26.7
27.9
29.1

23.4
26.8
29.0
28. 8

233.1
319. 8
353.5
359.4

272. 3
332.0
398.4
378. 3

1 ,10 3 .8
1,043.9
1,041.0
1,0 80.2

1,173.2
1,064.7
1,040.4
1,108.2

19 70 1
1970 2

25. 8
26.1

23.8
27. 8

354.1
355.7

279.3
332.7

893.2
1,005.2

1,019.9
1,018.0

wsFflK

WS0D
Forecasted Actual

1969
1969
1969
1969

Forecasted Actual

wsTEX
Forecasted Actual

1
2
3
4

1,3 19.3
1,2 9 8 .8
1,291.9
1,338.0

1,2 6 6 .8
1,3 0 7 .5
1,271,4
1 ,38 8 .8

96.1
100. 3
107. 3
105.5

98.6
102.7
110.2
112. 8

47.8
47.9
45.5
50.1

50.2
47.2
53.9
50.1

19 70' 1
1970 2

1,3 1 5 .1
1 ,259.3

1,2 54.5
1,288.0

98.1
101.2

100.9
109.0

43.7
45.5

41.1
43.0

WSMFG

ws0ND
Forecasted Actual

Forecasted Actual

wsTCU
Forecasted Actual

1
2
3
4

301.6
306. 3
315.0
317.4

305.6
315.4
312.2
349.1

2,8 68.6
2,797.2
2,8 00.7
2,891.2

2,894.4
2,837.5
2,788.1
3,009.0

311. 7
318.2
329.1
347.9

317.2
328.2
349.0
360.6

1970 1
1970 2

327.7
326.6

315.9
313.9

2,687.8
2,725.1

2,732.3
2,785.4

314.4
329.4

330. 5
352.2

1969
1969
1969
1969

85

Table 4.

Continued.

„„WT
WS
Forecasted Actual
1969
1969
1969
1969

__ RT
WS
Forecasted Actual

SE R
WS
Forecasted Actual

1
2
3
4

311.6
314.1
328.4
345.8

313.0
310.5
324.0
352.0

527. 8
542.9
572.4
596.9

524.5
549.5
564.0
624. 5

565.1
583.3
612.4
655.6

562.7
609.1
647.5
698. 7

1970 1
1970 2

341.0
349.5

350.6
335.8

584. 3
583.9

561.0
586. 8

641.2
661.6

658. 3
691.9

MWS
Forecasted Actual

OLI
Forecasted Actual

PROPNF
Forecasted Actual

1
2
3
4

5,927.5
6,006.9
6,039.8
6,430.5

5,991.8
6,098.3
6,115.4
6,656.5

393.0
404.2
404.0
405.2

406.2
406.2
406. 3
406.3

547.5
582.2
582.1
653. 4

604.6
561.0
538.0
595.4

1970 1
1970 2

6,123.0
6,282.6

6,127.9
6,363.6

497.7
501.3

505.0
505.0

549.5
609.2

575.2
664.7

1969
1969
1969
1969

PROPY
Forecasted Actual
1969
1969
1969
1969

TRANS
Forecasted Actual

EECFSS
Forecasted Actual

1
2
3
4

1,112.2
1,133.0
1,142.6
1,187.9

1,087.1
1,138.5
1,153.0
1,217.4

605.5
609.9
618.7
619.0

619. 3
622.2
640.2
640. 3

250.2
265. 8
222.6
131.4

265.5
265.2
222. 7
158.0

1970 1
1970 2

1,141.1
1,193.7

1,221.3
1,228.7

651.3
697. 3

723. 3
815.4

255.7
268.1

258.4
260.0

86

Table 4.

Continued.

CFSI
Forecasted Actual

MNWS
Forecasted Actual

MPI
F o recasted Actual

1
2
3
4

337.6
337.1
287.4
209.6

333.3
334.5
287.1
226.1

2,392. 3
2,463.9
2,531.8
2,727.7

2,455.6
2,465.1
2,522.2
2,705.1

8.317.8
8,470.8
8,571.6
9,158.2

8,447.4
8,563.4
8,637.6
9,361.6

1970 1
1970 2

333.0
334.6

338.0
342.1

2,577.8
2,738.1

2,758.0
2,942.9

8,700.8
9 ,020.7

8,885.9
9,306.5

1969
1969
1969
1969

Forecasted Actual
1
2
3
4

397.9
387.0
369.7
406.7

401.6
393.9
394.4
403.2

1970 1
1970 2

396.4
382.0

369.6
366. 8

1969
1969
1969
1969

87

Concl u d i n g Summary
With regard to the pri m a r y purpose of the model,
the results seem very satisfactory as attested to by the
high degree of accuracy of the forecasts for personal
income and, in particular,

the wag e and salary component.

The average forecasting e r r o r for the payroll component
was only 1.5 percent, or $90.5 million.
income tax rate of 2.6 percent,

Given the personal

this w o u l d imply an average

error of $2.4 million for withholding.

For the 1969-70

fiscal year, this w o u l d indicate an error of $9.6 million,
or 2.0 percent of the actual w i t h h o l d i n g collections of
$4 86.2 million.

22

Fro m a b u d g e t i n g viewpoint an error of

this magnitude is well w i t h i n manageable bounds, especially
since short-run revisions are possible b a s e d upon the
current rate of collections.

Underscoring this point is

the fact that the error of the official forecasts for the
withholding component of the personal income tax for the
1969-70

fiscal year was $12.9 million, or 2.7 percent of

actual collections.

23

A secondary goal of the study was to cast some
light on the role that the automobile industry plays in
shaping the Michigan economy.

22

To this end, U.S.

automobile

Detail for this revenue source was provided by
A. Thomas Clay of the E x e c u t i v e Office, Bur e a u of Programs
and Budget.
23t u . ,
Ibid.

88

production was specifically included among the exogenous
variables of the model.
is, at best,

Although the following analysis

a cursory one, it does provide some indication

of the impact of the industry on economic activity in
Michigan.

Table 5.

U.S. p asseng e r car production.

1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970

5,806,756
6,120,029
4,247,371
5,599,468
6,703,108
5,522,019
6,943,334
7,644,337
7,745,492
9 ,335,227
8,604,712
7,412,659
8,848,620
8,224,392
6,549,058

Source:
19 71 Economic Report of the G o v e r n o r ,
Appendix, Table B-29,~p7 12 7.

To begin, one may w r i t e the reduced form ordinary
least squares equation for total wages and salary disbu r s e ­
ments as
MWS = 360.924 - 208. 5 8 3 q 1 - 161.655q2 - 4 5 . 2 5 1 q 3
+ 0.171 USAP + Z
where Z represents the remaining predetermined variables
in the reduced-form equation.

This equation w o u l d tend to

89
indicate that the marginal contribution of a single a u t o ­
mobile assembly to total Michigan payrolls is only $171.
Given the average factory price of around $2,000 over the
sample period, the coefficient w o u l d intuitively s e e m to
be much too small.

However,

several factors must be taken

into account before drawing such a conclusion.
First, Michigan only accounts for approximately
one-third of final assemblies.

Given this fact, the m a r ­

ginal contribution of a Mich i g a n assembly w o u l d be $516
per car.

Furthermore,

the U.S.

relates only to assemblies,

automobile production

and,

as a consequence, does not

reflect the manufacture of parts o r equipment.
form equation, therefore,
of an automobile.

The reduced-

reflects only the marginal cost

It implicitly assumes, therefore,

the cost of the parts, overhead, etc.,

that

are zero and that

the marginal unit requires no additional employment,

capital,

or other factors of production.
As shown in Table 5, U.S.

automobile produ c t io n has

fluctuated widely during the sample period,

from a low of

4,24 7 thousand units in 19 58 to 9,335 thou s a n d units in
19 65.

While data relating to industry cost curves is

unavailable,

it w o u l d seem likely that they w o u l d exhibit

relatively constant average and marginal cost over a b r o a d
range.
tion,

Hence, during periods of comparatively low p r o d u c ­
a figure of $516 w o u l d seem reasonable as a measure

of the marginal contribution to total state payrolls.

90

However, during periods of high production,

this figure

w o u l d indeed be too small since it w o u l d fail to capture
such factors as overtime

(at p r e m i u m pay r a t e s ) , the addi­

tional cost of prod u c i n g the parts,

and added employment.

CHAPTER IV
CONCLUSION

The purpose for constructing the model prese n t e d in
the previous chapter was twofold.

The bro a d objective was

to provide an analytical description of the Michigan
economy.

It was hoped that the model w o u l d contribute

towards a better underst a n d i n g of the workings of the econ­
omy and, in particular,
gate sectors.

the interplay between broad aggre­

On a more pragmatic level, the model was

intended to serve as a m e c h a n i s m for forecasting personal
income,

also by broad categories.

As previously indicated,

the model was relatively successful on both counts.
addition,

In

it was hop e d to improve both the methodology and

estimation techniques previously employed in the construc­
tion of state econometric models.

It is in this area that

the model presented in Chapter III perhaps makes its
greatest contribution.
To date, the previous state econometric models,
with the exception of the Ohio model, have been lacking
from one of several vantage points:
theoretical basis;
instances,

(1) no w e l l - d e f i n e d

(2) use of inefficient and,

inconsistent estimation techniques;

91

in some
and

92

(3) a general disregard for any practical application.
the process of solving these shortcomings,

In

it was necessary

to create a new data series— namely, quarterly personal
income by broad sectors

(unadjusted for seasonal v a r i a t i o n ) .

The quarterly personal income data series for Michigan con­
tained in Appendix D represents the first time such a series
has been constructed.

The choice of the quarterly format

for the model set out in Chapter

III, and hence

the n e e d to

build the data series, was bas e d

upon two consid e r a t i o n s —

the increased utility the quarterly approach offers for
analysis and forecasting purposes and, simultaneously,

the

larger number of observations it affords.
In an economy such as Michigan's,

whi c h

relies

heavily upon both c o n s u m e r s 1 and p r o d u c e r s ' durable goods
manufacturing industries,

it is essential to be able to

quickly detect maj o r economic fluctuations.

The limitations

imposed by an annual format severely limits this capability.
A quarterly format reduces these limitations since it has
the advantage of bein g able to utilize current data.
consequence,

As a

it allows for a more accurate description of

economic activity and,

ceteris paribus, more accurate

estimates and forecasts of tax revenues.

Theoretical Background
The formulation of the model was explicitly designed
so as to maintain a solid link with economic theory.

The

93
advantages this approach affords are obvious.

First, it

allows the user the ability to compare and criticize the
model from more than the "proof of the pudding"
i.e., how well it forecasts.

Secondly,

argument,

a well defined model

yields more information than a loosely designed one since
it allows a larger numb e r of inferences regarding parameter
values, possible constraints,

etc.

The choice of the p r e d e t e r m i n e d variables in the
model was influenced by two r e q u i r e m e n t s :

the ease with

which they themselves may be forecasted and, whe n possible,
their inclusion in one o f the larger national econometric
models.

This approach greatly simplifies the forecasting

process and,

at the same time,

allows one to determine the

sensitivity of the Michi g a n forecast for the range of
values generated by the national models.

Estimation Technique
The model prese n t e d in Chapter III is the first
state model to employ a systems m e t h o d of estimation.

The

most sophisticated technique utilized previously was twostage least squares in both the Massachusetts

and Ohio

m o d e l s , whereas the. model set out in this paper has been
estimated by the more efficient m e t h o d of three-stage
least squares.

94
Policy Implication
A n d finally,

the d e velopment and the presentation

of the model itself was carried out with the explicit aim
of making the study useful to policy makers.

Some of the

results generated by the model indicate its utility for
planning and budgeting p u r p o s e s .
As mentioned in Chapter I, the most common form
of forecasting methodology employed in state government
is trend analysis,

i.e.,

the normal growth pattern.

The

p r o b l e m wi t h this method is that it fails to account for
both major swings in the economy and the pattern of change
throughout the forecasting period.

Table 6 presents the

personal income forecasts generated by the model in C h a p ­
ter III, the

"naive"

normal growth,

forecast based upon a five percent

and in addition,

the forecasting results

of the Suits model.
As Table 6 indicates,

the quarterly model yielded

far more accurate forecasts than either the "naive" fo r e ­
cast or that generated by the Suits model.
Michigan's major revenue sources,
and sales taxes,

In terms of

the individual income

the 1969 forecast generated by the q u a r ­

terly model w o uld have implied a yield of $726 million for
the sales tax and $464 million for the personal income
tax withholding.

The actual revenue yields from these two

tax sources were $729 million and $475 million, or a co m ­
bined error o f Only 1.2 percent.

In comparison,

the Suits

Table 6.

Comparison of annual personal income forecasts,

, . ,
Actual

v, .
Naive

Percent
„
Error

Suits
Model

1969.

Percent Quarr. ,
Error
terly
Model

Percent
_
Error

Personal Income

35,010

33,833

3.36

33,700

3.74

34,520

1.40

Wage and Salary
Disbursements

24,862

23,810

4.23

23,660

4.83

24,410

1.82

Other Sources of
Personal Income

10,148

10,023

12.3

10,040

1.06

10,110

0.37

96
model indicated sales tax receipts of $741 million, or an
error of 1.65 percent compared to the quar t e r l y model's
0.42 percent.

24

Another area where the model may prove useful is
its ability to help predict the impact of m a j o r strikes
in the automobile industry on personal
yield of the personal income tax.

income and the

The experience of 1970

provides such an example.
The 2 1/2 m o n t h United Automobile Workers

strike

at the General Motors Corporation caused an estimated
production loss of 1.2 million units.
model,

In terms of the

this loss would imply a $205 million reduction in

personal income and a $5.3 million loss in withholding
under the Michigan personal income tax.

Actual losses

due to the strike are estimated at $8.9 million.

25

Areas for Future Improvements
While the results of the model presented in Ch a p ­
ter III are encouraging,
final product.

they by no means represent the

The m o s t obvious areas for expansion and

improvement would be the inclusion of the consumption and
tax subsets which are currently being developed by the

24

Revenue implication for the quarterly model fore­
cast were prepared by the Executive Office, Bureau of P r o ­
grams and Budget.
25T,
Ibid.

97
State of Michigan.

In terms of individual equations,

those

for payrolls and employment in mot o r vehicles and equipment,
pr operty income,

and contract construction present areas

where concrete improvements should be forthcoming.

As with

all such models the first results always seem to spawn co n ­
structive discussion and analysis.

It is hoped that this

paper will likewise provide an impetus for additional r e ­
search of the Michig a n economy.

BIBLIOGRAPHY

BIBLIOGRAPHY
Articles and Periodicals

Bell, Frederick W.
"An Econometric Forecasting Model for
a Region."
Journal of Regional Science, Vol. 7,
No. 2 (1967), pp. 109-27.
Brazer, Harvey E.
"Michigan's Fiscal Outlook."
Wayne
Law R e v i e w , Vol. II, No. 2 (1967), pp. 430-50.
Kmenta, Jan.
"On Estimation of Simultaneous Equation
Systems with Autocorrelated Disturbances,"
Michigan State University Econometrics Work s h o p
Paper No. 6910 (May, 1970).
L'Esperance; Nestel, Bilbert; and Fromm, Daniel.
"Pre­
diction and Policy Analysis with an Econometric
Model of a State," 1968 Proceedings of the A m e r i ­
can Statistical Association, Business and E c o n o ­
mics Statistics S e c t i o n , 19 68, pp. 317-328.
Page
references in text refer to original draft.
Theil, H . , and Nagar, A. L.
"Testing the Independence of
Regression Disturbances," Journal of the American
Statistical A s s o c i a t i o n , Vol. 5, No. 29 (1961) ,
pp. 793-806.

Books
Burton,' R . , and Dyckman, J.
A Quar t e r l y Economic F o r e ­
casting Model for the State of C a l i f o r n i a .
University of California, 1965.
Christ,

C. F.
Econometric Models and M e t h o d s .
J. Wiley, 1966.

Ne w York:

Duesenberry, J. S., et a l . The Brookings Quarterly
Econometric Model of the United S t a t e s . Chicago:
Rand McNally, 1965.

98

99
Evans, M. K . , and Klein, L. R.
The W h a r t o n Economic
Forecasting Model.
University of Pennsylvania,
1968.
Goldberger, A. S.
Econometric T h e o r y .
Wiley, 1964.
Johnston, J.
Econometric Methods.
Hill, 1963.

Ne w York:

Ne w York:

J.

McGraw

Klein, L. R. and Goldberger, A. S.
An Econometric Model
of the United States, 1 9 2 9 - 1 9 5 2 . Amsterdam:
North-Holland, 1955.
Klein, L. R.
Economic Fluctuations in the United States
1 9 2 1 - 1 9 4 1 . Cowles Commission Monog r a p h 11.
Ne w
York:
J. Wiley, 1950.
Research Seminar in Q u antitative Economics.
Econometric
Model of Michigan.
University of Michigan, 1965

Public Documents
Department of Commerce.
Office of Business Economics.
Survey of Current B u s i n e s s . Vol. 50, No. 8,
August, 1970.
_______

Office of Business Economics,
by S t a t e s . 1956.

Michigan.

Personal Income

1971 Economic Report of the G o v e r n o r .

APPENDIX A

APPE N D I X A

DESCRIPTION OF PREVIOUS STATE ECONOMETRIC
MODELS:

California,

CHAPTER II

(Burton and Dyckman)

- Phase II Model

1. Type of data

Quarterly data.
All personal income
(wage and non-wage) and miscellaneous
(corporate income, retail sales, etc.)
variables are in current dollars.

2. Period covered

For most of the variables:
First
quarter 1950 through the fourth q u a r ­
ter, 1962 .

3. M e thod of Estimation

OLS

4. Number of stochastic
equations

Personal I n c o m e :
a. Wage and salary:
a maximum possi­
bility of three wage and salary
disbursement equations per indus­
try (59 industries)--some indus­
tries are represented by only one
or two equations, however.
Total number = 108
b . Non-wage i n c o m e :
-Other Labor inc o m e — 1 equation
-Non-Farm Proprietor's income— 1
equation
-Farm Proprietor's income--l
equation
-Property income— 1 equation
-Transfer P a y m e n t s — 1 equation
-(minus) Personal Contributions
for Social Insurance— 1 equation
Total number = £ equations
Total number of Personal Income
Equations = 114

100

101

Miscellaneous:
a. Maj o r self-assessed taxable sales—
9 equations
b. Employment trans l a t o r s — 53 equations
c. Net Income of C o r p o r a t i o n — 1
equation
d. A s s e s s e d mot o r vehicle gasoline
g a l l o n a g e — 1 equation
Total number of miscellaneous
equations = 65
Total number of stochastic equ a ­
tions = 179
5. Definitional
equations

-Personal income iden t i t y — 1 equation
-Wage and Salary i dentities— 36
equations
-Those identities listed on the b o t ­
tom of p. 59 — 14 equations
-Employment equations (M. =W. /E. )—
5 3 equations
1t
1t
1t
Total number of definitional
equations = 104

6. Total number of
equations

179 stochastic + 104 definitional
equations = 283

7. Main institutional,
technical and b e h a v ­
ioral equations

Personal income
Employment
M i s cellaneous (they are listed under
(8 )).

8. Endogenous
variables

Wage and salary disbursements in 59
California industries (each indus­
try is broken down into final
inter-industry and export d e m a n d ) .
Non-wage component of personal income
(other labor income, farm p r o p r i e ­
tors' income, non-f a r m proprietor's
income, property income and tra n s ­
fer p a y m e n t s ) .
Personal Contributions for Social
Insurance.
Employment in 53 California industry
groups.
Miscellaneous (major self-assessed
taxable sales, corporation income,
gasoline gallonage, and
unemployment).

102

9. Main exogenous
variables

The 20 national variables listed in
Table 6 (8) on p. 20

10. Dynamic features

Use of autogressive terms and rate of
change v a r i a b l e s .
Lags up to three quarters in nonautogressive variables.

11. Other noteworthy
features

Extensive use of first differences to
guard against m u l t i - c o l l i n e a r i t y .
The model consists of three succes­
sive parts.
The temporal ordering
is as follows:
the first part is
personal income; the second, e m ­
ployment; and the third, miscellaneous,

Massachusetts

(Bell)

1. Type of data

Annual data.
All variables are in
constant 1947 dollars.

2. Period covered

1947-1962.

3. Method of estimation

OLS, R F L S , 2SLS (RFLS is reduced-form
least s q u a r e s ) .

Number of
stocastic equations

8

Definitional
equations
Total number of
equations

14

Main institutional,
technical and b e ­
havioral equations

Export
Local consumption
M a n ufacturing
investment
Non-manufacturing
investment

8. Endogenous variables

Export income
Local service
income
Total received
income
Total produced
income

Production
Expected labor
supply
Migration
Wage Bargain

Investment in nonM anufacturing
sector
Employment
Labor Supply

103

9. Exogenous variables

10. Dynamic features

Total capital
stock
Manufacturing
capital stock
Non-manufacturing
capital stock
Investment in
manufacturing
sector

Expected labor
supply
Population
Expected population
Annual wage per
employee
M igration
Unemployment

Gross national
product
Birth rate minus
the death rate
Prospective u n ­
employment

Capital stock in
m anufacturing
Capital stock in
non-manufacturing
Time

One year l a g s .
All equations are linear except the
production and wage bargain e q u a ­
tions . The manufacturing investment
equation has been linearized by tak­
ing a logarithmic transformation of
the original specification.

11. Other noteworthy
features

Michigan

Links national and regional
variables.

(Research Seminar in Quantitative Economics)

1. Type of data

Annual data in constant 1954 dollars.

2. Period covered

1949-1964.

3. Method of estimation

OLS

4. Number of
stochastic equations

Gross state product and components 8
Retail sales
9
Employment, unemployment, labor
force
2
Personal income
8
Eight industries (3 equations for
each
24
Services
4
Construction
3

Number of non­
stochastic equations

Employment, unemployment,
force
Total

labor
6
64

104

5. Number of defi n i ­
tional equations

Employment, unemployment,
force

labor
14

6. Total number of
equations
7. Main institutional
technical and b e ­
havioral equations

78
Gross state
product
Retail Sales
Employment
Labor force

8. Main endogenous
variables

Personal income
Increase in
added
Value added
man hour
Increase in
hours per

value
per
annual
wor k e r

Total GSP (broken down into GSP by
manufacturing, trade, mining, co n ­
struction, agriculture, government
and o t h e r ) .
Retail Sales (broken down into a u t o ­
motive dealers; general stores;
furniture stores; apparel stores;
food stores, eating and drinking
places; building, lumber, and h a r d ­
ware; and o t h e r s ) .
Employment (broken down into m a n u ­
facturing, non-manufacturing, self
employment, government, and
agriculture).
Michigan population,

age 14 and over.

Net migration into Michigan.
Increase in M i c h i g a n labor force.
Change in M i c h i g a n unemployment.
Personal Income (broken down into
seven major c l a s s i f i c a t i o n s ) .
Increase in value added, value added
per man hour, and increase in annual
hours per worker.
Various state taxes:
mot o r vehicle,
corporate vehicle, corporate fran­
chise, other state local property
and income t a x e s .

105

9. Main exogenous
variables

Total U.S. expenditure for new and
net used automobiles by all U.S.
consumers.
Total expenditure by all U.S. b u s i ­
nesses for producers' durable
equipment.
Total privately produced U.S. gross
national product other than automo­
biles and producers 1 durable
equipment.
U.S. increases in expenditures for
gas and oil, transportation services,
food and beverages, and construction
other than housing.
M ichigan financial variables:
demand
and time deposits, savings and loan
shares.
New automobile registrations in
Michigan.

10. Dynamic features

Use of autoregressive schemes.

11. Other noteworthy
features

Incorporates Michigan's GSP and com­
ponents in the specification of the
model.
A l s o the relationships among
output, productivity and employment
are stressed.

Ohio

(L'E s p e r a n c e , Nestel and Fromm)

1. Type of data

Period covered

Annual data in physical units (e.g.,
gallons) or in constant 1958 dollars.
1945-1965; all equations are fitted
to subsets of that period.

3. Method of estimation

OLS,

4. Number of stochastic
equations

16

Definitional
equations

11

2SLS.

106

6. Total number of
equations

27

7. Main institutional
technical and b e ­
havioral equations

Retail sales

(2 e q u a t i o n s ) .

Personal income and federal income
tax.
GSP of Ohio

(7 c o m p o n e n t s ) .

Sales tax receipts.
B as e s of motor vehicle fuel and
mot o r vehicle registration taxes.
8. Main endogenous
variable

Total GSP

(and 7 c o m p o n e n t s ) .

Personal income, income taxes, and
disposable personal income.
Retail sales

(2 c o m p o n e n t s ) .

M a n u f a c t u r e r s ' investment expe n d i ­
ture (2 c o m p o n e n t s ) .
Various state taxes and/or their
bases; sales tax, motor vehicle fuel
tax, mot o r vehicle registration tax.
9. Exogenous variables

First difference of GNP in m a n u f a c ­
turing; two interest rates, percentage
rate or change of level of U.S. auto­
mobile installment credit; Ohio housing
permits;
lagged values of various
endogenous variables^ including com­
ponents of GSP, GSP in state and local
government; GSP in federal government;
M i l i t a r y prime contract awards in
Ohio; a total of 15.

10. Dynamic features

Use of autoregressive terms in
identities; use of first differences
of endogenous variables; lags in in­
vestment equation.
All equations are
linear.

11. Other noteworthy
features

Some of the exogenous variables are
government policy v a r i a b l e s .

Source:

An Econometric Model of Ohio, pp.

28-33.

107

An Econometric Model of Michigan

Endogenous Variables
GSP

GSPMFG
GSPWR
GSPMIN
GSPCC
GSPAGR
GSPOTH

MRST
MRSAD
MRSGS
MRSFUS
MRSAS
MRSFOS
MRSEAD
MRSB L H
MRSOTH
MPI
MPIWS
MPIWSMFG
MP IWSWR
M P IWSMIN
MPIWSCC
MP I W S T R
MPIWSOI
MPIPROP
MPIOLI
MPINFPI
MPITR
MPIAGRI

Gross state p r o d u c t — estimated by the University
of Michigan Research seminar in Quantitative
Economics.
Gross state product originating in manufacturing,
Gross state product originating in w holesale and
retail trade.
Gross state
product originating in mining.
Gross state
product originating in contract
construction.
Gross state
product originating in agriculture.
Gross state
product originating in all other
sectors
Total retail sales.
Retail sales by automotive dealers.
Retail sales by general stores.
Retail sales by furniture stores.
Retail sales by apparel stores.
Retail sales by food stores.
Retail sales by eating and drinking establishments
Retail sales by building, lumber, and hardware
stores.
Retail sales by all other stores.
Personal income.
Total wages and salaries.
Wages and salaries paid
by manufacturing.
Wages and salaries paid
by wholesale and retail
trade.
Wages
and salaries paid by mining.
Wages
and salaries paid by contract construction.
Wages
and salaries paid by transportation.
Wages
and salaries paid by all other industries.
Property income.
Other labor income.
Non-farm proprietors income.
Transfer payments.
Agricultural income.

Predetermined Variables
USAE
USPDE
USGNPOT

U.S. automobile expenditures.
U.S. producers' durables expenditures.
Other private non-imputed GNP
(compiled by the
Research Seminar in Quantitative Economics)

108

USNRCC
GSP
GSP-2
GS P M F G - 1

U.S. non residential construction.
Past peak Michigan GSP.
Michigan GSP two years ago.
Last y e a r ’s Michigan GSPMFG.

In general
XYZ-1
USGAO
USTSE
USFAB
USGNPPVT
GSPGOV
MPIWSGOV
MUEMP

Last year's X Y Z .
U.S. gas and oil expenditures.
U.S. transportation service expenditures
U.S. food and beverage expenditures.
U.S. privately produced GNP.
GSP originating in government.
Wages and salaries paid by government.
Michigan unemployment (in t h o u s a n d s ) .

Equations

(as published)

AGSP
AGSPMFG
AGSPWR
AGSPMIN
AGSPCC
AGSPAGR
AGSPOTH
AMRST
AMRSAD
AMRSGS
AMRSFUS
AMRSAS
AMRSFOS
AMRSEAD
AMRSBLH
AMRSOTH
AMP I
AMPIWSMFG
AMPIWSWR
AMPIWSMIN
AMPIWSCC
AMPIWRSTR
AMPIWSOI
AMPIWS

-0.626 + 0.228 AUSAE + 0.136 AUSPDE
-0.734 + 0.220 AUSAE + 0.044 AUSPDE
-0.023 + 0.033 AUSAE + 0.022 AUSPDE
-0.002 + 0.018 AUSNRCC
0.002 + 0.0304 (GSPMFG - GSP)
+ 0.020 (GSP - GSP - 2)
Trend value
0.100 + 0.002 AUSAE + 0.037 AUSPDE
0.1960
0.0677
0.0195
0.0011
0.0056
0.0493
0.0033
0.0044
0.0209

0.187 AUSAE
0.111 AUSAE
0.014 AUSAE
0.010 AUSAE
0.007 AUSAE
0 .023 AUSAE
0.006 AUSAE
0.009 AUSAE
0 .012 AUSAE

+
+
+
+

0.020
0.004
0.012
0.010

+ 0.080 AUSGNPOT
+ 0.066 AUSGNPOT
+ 0.006 AUSGNPOT

+ 0.006 AUSGNPOT

AUSGNPOT
AUSGNPOT
AUSPDE
AUSPDE

0.001 AUSGNPOT
0.003 AUSGNPOT

0.4049 + 0.141 AUSAE + 0.159 AUSPDE
0.02722 + 0.160 AUSAE + 0.066 AUSPDE
0.03711 + 0.009 AUSAE + 0.027 AUSPDE
-0.00308 + 0.00096 AUSGAO + 0.0078 AUSNRCC
0.00427 + 0.0361 AUSNRCC
-0.00226 + 0.0044 AUSAE + 0.0058 AUSPDE
+ 0.0313 AUSTSE
0.03341 + 0.0059 AUSPDE + 0.0243 AUSFAB
7 ZAMPIWS.*
(x)
1

*The summation extends over the seven wage and salary
categories listed, i.e., manufacturing, wholesale and retail
trade, mining, contract construction, transportation, other
industries, and government.

109

AMPIPROP
AMPIOLI
AMPINFPI
AMPITR
AMPIAGRI

= 0.0728 + 0.0145 AUSAE
=
0.02409 + 0.052 AMPIWS
= -0.08103 + 0.0021 AUSGNPPVT + 1.14 AMPIWSOI
=
0.5758 + 0.869 AMUEMP**
= Trend value

Refitted Equations
AGSP = -0.500 + 0.222 AUSAE + 0.163 AUSPDE + 0.065 AUSGNPOT
(0.201) (0.052)
(0.065)
(0.016)
R2
=
.931
D.W. = 1.227
AGSPMFG = -0.596 + 0.219 AUSAE + 0.076 AUSPDE - 0.050 AUSGNPOT
(0.171) (0.045)
(0.055)
(0.014)
R2
=
.919
D.W. = 1.692
AGSPWR = -0.035 + 0.030 AUSAE + 0.020 AUSPDE + 0.006 AUSGNPOT
(0.037) (0.010)
(0.012)
(0.003)
R2
=
.839
D.W. = 1.277
AGSPMIN = -0.002 + 0.017 AUSNRCC
(0.004) (0.005)
R2
=
.461
D.W. + 2.098
AGSPOTH = 0.102 + 0.001 AUSAE + 0.037 AUSPDE - 0.005 AUSGNPOT
(0.037) (0.001)
(0.012)
(0.003)
R2
=
.750
D.W. = 1.413
AMRST = 0.273 + 0.224 AUSAE + 0.008 AUSGNPOT
(0.130) (0.035)
(0.008)
R2
=
.812
D.W. = 1.547
**The Michigan unemployment variable while listed as
exogenous here is an endogenous variable in the complete M i c h i ­
gan model.
It is treated as being exogenous since the employ­
ment subset is not included.

110

AMRSAD = 0.010 + 0.129 AUSAE - 0.00 3 AUSGNPOT
(0.044) (0.035)
(0.003)
R 2
=
.930
D.W. = 1.917

AMRSGS = 0.031 + 0.014 AUSAE + 0.007 AUSPDE
(0.013) (0.006)
(0.006)
R2
=
.492
D.W. = 1.829
AMRSFUS = 0.0004 + 0.010 AUSAE + 0.005 AUSPDE
(0.009)
(0.004)
(0.004)
R2
=
.503
D.W. = 0.786
AMRSAS = 0.009 + 0.006 AUSAE
(0.006) (0.002)
R2
=
.368
D.W. = 1.343
AMRSFOS = G.079 + 0.009 AUSAE
(0.016) (0.006)
R2
=
.094
D.W. = 1.060
AMRSEAD = 0.023 + 0.009 AUSAE + 0.001 AUSGNPOT
(0.011) (0.003)
(0.001)
R2
=
.402
D.W. = 2.168
AMRSBLH* = 0.002 + 0.009 AUSAE
(0.015) (0.006)
R2
=
.111
D.W. = 1.482
AMRSOTH = 0.024 + 0.014 AUSAE + 0.00002 AUSGNPOT
(0.024) (0.006)
(0.002)
R2
=
.300
D.W. = 1.250

Ill

AMPI = 0.399 + 0.142 AUSAE + 0.146 AUSPDE
(0.104) (0.050)
(0.059)
R2
=
.712
D.W. = 2.386
AMPINSMFG = 0.027 + 0.128 AUSAE + 0.104 AUSPDE
(0.078) (0.037)
(0.044)
R2
=
.749
D.W. = 1.764
AMPIWSWR = 0.036 + 0.009 AUSAE + 0.026 AUSPDE
(0.007) (0.003)
(0.004)
R2
= .884
D.W. = 1.368
AMPIWSMIN = -0.00 7 + 0.012 AUSGAO + 0.00 8 AUSNRCC
(0.006) (0.014)
(0.003)
R2
= .595
D.W. = 2.131
AMPIWSCC = 0.004 + 0.036 AUSNRCC
(0.012) (0.015)
R2
= .281
D.W. = 1.736
AMPIWSTR = -0.002 + 0.004 AUSAE + 0.006 AUSPDE + 0.030 AUSTSE
(0.004) (0.001)
(0.002)
(0.016)
R2
= .84 8
D.W. = 1.016
AMPIWSOI = 0.033 + 0.005 AUSPDE + 0.025 AUSFAB
(0.011) (0.004)
(0.008)
R2
= .780
D.W. = 2.207
AMPIPROP = 0.072 + 0.014 AUSAE
(0.017) (0.006)
R2
= .2 37
D.W. = 2.028

. -=

112

AMPIOLI = 0.024 + 0.052 AMPIWS
(0.013) (0.017)
R2
=
.402
D.W. = 1.252
AMPINFPI = -0.096 + 0.002 AUSGNPOT + 1.32 3 AMPIWSOI
(0.027) (0.001)
(0.369)
R2
=
D.W. =

.631

AMPITR = 0.056 + 0.001 AMUEMP

(0 .020) (0 .0002)
R2
=
.582
D.W. = 2.631

113

Econometric Mod e l of Massachusetts

Edogenous Variables
Export income.
Sj.
t
(V^)t

Local service income,

(v£)t

Total produced income.

Total received income.

Total capital stock.
(Km )t

Manufacturing capital stock.

(K

Nonmanufacturing capital stock.

)t

(I )t

Investment in manufa c t u r i n g sector.

(In m )t

Investment in nonmanufacturing sector.

Lt

Employment.

(No)t

Labor supply

(actual).

(Ne)t

Expected labor supply

(Po)t

Population

(Pe)t

Expected population

(natural increase).

(actual).
(natural increase).

Annual wage per employee.
Mt

Migration.

U^_

Unemployment

Predetermined Variables
GNPt
(B-D)t
(Ne-L)t-l

Gross national product.
Birth rate (per thousand)
(per thousand)

minus the death

rate

Prospective unemployment (difference between
natural increase in the labor force and labor
demand).

(Km )t-1

Capital stock in manufacturing.

(K m )t-l

Capital stock in nonmanufacturing,

t

Time.

114

Equations
1.

X

=

430.55 + 6.71 G NP
(103.86)
(.329)

(OLS)

R2
=
.967
D.W. = 1.114
2.

Sfc = -135.1 + .7297

( V ^

(RFLS)

3.

(log K, - log K
) = .5113 (2SLS)
t
t-i m (1>007)

+ .939 log X*
(.289)
v

- 1.023 log K
(.211)

*-

.0062
(.0032?

R2
=
.712
D.W. - 1.447

4.

(log K. )
= .8389 + .798 log
10 nm
(.2265) (.096)

S*(2SLS)
Z

R2
= .927
D.W. - 1.251
5.

(V„)
2

6.

(Ne)

= 6422 K * 29 L * 71

Z

= .4009 (Pe)
(.00027)
Z

(1.013)t
(.00128)

(Factor Shares OLS)

(OLS)

R2
=
.988
D.W. = 1.465
7.

M

=
Z

R2
D.W.
8.

W.

=

t

106.22 - 1.0385
(33.63)
(.279)

(Ne-L)

=
.500
= 1.504
2657

(1.017)t

(.0011)

R2
=
.944
D.W. = 1.533

(OLS)

,

(OLS)

115

Definitions and Identities
9.
10.
11.
12.
13.
14.

Pe =

(Po)t-1 +

(B - D ) ( P o ) t . x
(Pe). + .4009 M fc
t

(No). = .4009
t

(V2 )t/ ( V l )t = *9° 7
< V

= st + x t

Ut =

(No)t - Bfc

Kt =

(V m

+

(V n m

All variables are statistically significant at the
5 per cent level including the reduced-form least-squares
(not s h o w n ) . Hypotheses of positive autocorrelation re ­
jected at the 5 per cent level for all equations.
Asterisk
indicates computed v a l u e s .

116

A n Econometric Model of Ohio

Endogenous Variables
A
AR
AAR
C
DPI
ADPI
Ft
FIT
GSP
agsp

GSP
cc
GSP
fi
GSP

(known)

GSP

ma
AGSP
ma
GSP
(other)

Sales by all new car dealers in Ohio.
Automobile registrations in Ohio.
Annual change in AR.
Sales by all establishments selling at the
retail level in Ohio.
Ohio disposable personal income.
Annual change in DPI.
Gallons of taxable motor fuel sold in Ohio.
Federal income taxes of Ohio.
(PI-DPI)
Ohio's Gross State Product.
Annual change in Ohio's Gross State Product.
Gross State Product in contract construction.
Gross State Product in finance, insurance,
and real estate.
GSP
+ GSP
+ GSP. , + GSP
+ GSP^. + GSP^
ma
cc
td
so
fi
fg
+ GSP ,
slg
GSP originating in manufacturing in Ohio.
Annual change in GSP
r
ma
GSP - G S P (known). G S P (other)

is also the sum

of gross state products in agriculture
(GSPagr ^) , min i n g (Gspm;Ln ) / transportation

agsp

(other)
GSP.
so
GSP
td
IGF
ma

ma

mma
'sma

(GSP ) and communications and public utilities
(GSP
).
cpu
GSP. ..
, - GSP.
,
.
(other)
(other) - 1
Gross State Product in services and other.
Gross State Product in trade.
"Internally Generated Funds" in manuf a c t u r ­
ing (profit-type income originating in
manufacturing plus capital consumption
allowances originating in manufacturing) in
Ohio.
Total investment expenditures for plant
(structures) and machinery by all manufacuring establishments (existing, and those not
yet in operation) in Ohio.
Investment expenditures for machinery by all
manufacturing establishments in Ohio.
Investment expenditures for plant (structures)
by all m a n ufacturing establishments in Ohio.

117

Personal income in Ohio.
Retail sales in Ohio excluding ne w car dealer
sales.
(R = C - A ) .
Retail sales tax receipts.

PI
R
T

Predetermined Variables
AR ^

Last year's A R in Ohio.

AAC/AC =
(AC-AC ,)/AC

AC represents dollars of automobile inst a l l ­
ment credit outstanding in the U.S.
Last year's DPI in Ohio.

AGNP
GSP

Change in gross national product in
manufacturing.
Last year's Ohio GSP.

ma

-1

GSP

fg
GSP
(known)-1
GSP
ma-1
GSP
(other)-1
GSP

slg

HP
IGF

ma-1

IS

ma-1
MPC
RCB
RTBS

Equations
1.

Gross State Product in federal government.
Last year's GSP

(known)
Last year's GSP
in Ohio.
J
ma
Last year's G S P (0 ^ h e r ) ’
Gross State Product in state and local
government
New housing units authorized in per m i t issuing
places in Ohio.
Last year's IGF
in Ohio.
J
ma
Last year's IS
in Ohio.
J
ma
Military prime contracts awarded in Ohio.
Interest rate on corporate b o n d s .
Interest rate on 90-day U.S. Treasury bills.

(The OLS and TSLS estimates are shown)

R = 3.741 + 0.305 DPI
(0.376) (0.031)
9.96
14.30
R

= 0.94

(OLS)

1949-1963

R = 3.780 + 0.303 DPI
(0.427
(0.024)
8.84
12.48

1949-1963

(TSLS)

118

2.

A = -1.075 + 0.306 DPI + 0.613 AAC/AC - 0.888 A R ,
(0.450) (0.090)
(0.301)
(0.396)
"X
-2.39
3.42
2.04
-2.24
R

= 0.77

(OLS)

1949-1963

A = -1.0126 + 0 . 2 9 2 DPI + 0.624 (AAC)/AC - 0.825 A R 1
(0.520)
(0.108)
(0.337)
(0.475)
-1.91
2.71
1.85
-1.74
1949-1963
3.

C = A + T

4.

I
Sma

R
5.

0.288 + 0.263 I
- 0.058 RCB
(0.101
(0.093) 111,11113 (0.017)
2.85
2.82
-3.48

= 0.6 7

1951-1963

I
= -1.150 + 0.144 IGF
+ 0.384 IGF
,
Tama
(0.434) (0.101
10X1
(0.094)
ma“1
-2.65
1.42
4.06
+ 0.919 I
(0.440)
2.09
R

= 0.6 8

I
= I
+ I
ma
sma
mma

7.

IGF

R

(OLS)

= 0.501 + 0.156 AGSP
+ 0.193 GSP
ma
ma
(0.208) (0.036)
(0.019)
2.40
4.40
10.35

= 0.92

1948-1965

PI = -2.161 + 0.865 GSP - 0.259 AGSP
(0.801) (0.031)
(0.082)
-2.71
27.53
-3.14
R

8'.

ma

, + 0.064 RTRS
(0.037)
1.71

1952-1968

6.

8.

(OLS)

= 0.98

(OLS)

1948-1963

PI = -4.075 + 0.926 GSP + 0.065 AGSP
(1.587) (0.059)
(0.042)
-2.57
15.65
1.54

1949-1963

(TSLS)

(OLS)

(TSLS)

119

9.

DPI = PI - FIT

10.

ADPI = DPI - D P I _ 1

11.

FIT = -0.902 + 0.169 PI
(0.204) (0.011)
-4.42
15.95
R 2 = 0.94

1946-1963

11'. FIT = -0.995 + 0.173 PI
(0.303)
-3.29

(OLS)

(TSLS)

(0.015)
11.53
1946-1963

12 .

AGSP

= -0.515 + 0.115
GNP
+ 0.263 MP C
(0.099) (0.005)
ma
(0.077)
-5.18
21.90
3.39

ma

R 2 = 0.97
13.

GSP., =
ta

R2 =
13' .

GSP. , =
ta

1951-1965

-1.682 + 0.343 A
(0.413) (0.177)
-4.07
1.94

0.96

(OLS)

+ 0.552 R
(0.070)
7.84

(OLS)

+ 0.671 R
(0.0843)
7.95

(TSLS)

1947-1964

-2.234 + 0.039 A
(0.447) (0.248)
-5.00
0.16
1949-1963

14.

GSP

R2 =
15.

= -0.055 + 2.344 I
(0.216) (0.338)
-0.26
6.93
0.85

+ 0.013 HP
(0.003)
3.94

1954-1963

GSP.. = -0.919 + 0.197 DPI = 0.096 ADPI
11
(0.092) (0.005)
(0.029)
-10.03
36.84
-3.33
R 2 = 0.99

(OLS)

1947-1963

(OLS)

120

15' .

GSP.. = -1.045 + 0.203 DPI - 0.082 ADPI
3:1
(0.112) (0.006)
(0.031)
2.66
-9.29
32.17

(TSLS)

-

1949-1963
16.

GSP
so

R
16 1 .

= -1.094 + 0.141 DPI + 0.082 ADPI
(0.121) (0.007)
(0.036)
-0.91
19.94
2.30

= 0.97

GSP
SO

(OLS)

1950-1963

= -0.470 + 0.148 DPI = 0.024 ADPI
(0.154) (0.009)
(0.042)
-3.04
17.14
-0.56

(TSLS)

1949-1963
17.

AGSP,
. = 0.020 + 0.073 A G S P »
.
(other)
(0.02 7) (o.ois)
(known)
0.73
3.85
R

17' .

= 0.45

A G S P (other)

(OLS)

1948-1965
= 0.016 + 0.091 AGSP
(known)
(0.024) (0.018)
0.64
5.19

(TSLS)

1949-1963
+ AGSP

18.

AGSP = AGSP

19.

GSP = G S P _ 1 + AGSP

20.

GSP ,,
x = GSP
+ GSP
+ GSP. , + GSP
+ GSP .
(known)
ma
cc
td
so
fi

(other)

(known)

+ GSP.
+ GSP ,
fg
slg

21.

AGSP(known)

22.

G S P (other)

~ GSP (known)

GSP

ma

- I

= G S P agri + GSPmin + G S P t + G S P cpu
= GSP (other)

23.

G S P (known)

= GSP _ , + AGSP
ma-1
ma

- 1 + A G S P (other)

121

24.

F
Z

= -0.115 + 0.902 A R
(0.073) (0.024)
-1.59
37.76

R 2 = 0.99
25.

26.

1945-1964

AAR = 0.107 + 0.170 A - 0.087 A R
(0.039) (0.035)
(0.017)
2.77
4.90
-4.88
R2

- 0.95

T

= -0.085 + 0.028 C
(0.021) (0.002)
-4.07
14.00

S
R2
27.

(OLS)

= 0.93

1948-1963

1947-1964

A R = A R _ X + AAR

(OLS)

(OLS)

APPE N D I X B

APPENDIX B
VARIABLE PARTICIPATION MAT R I X OF TH E COMPLETE MODEL:
CHAP T E R III

Block I
1

2

*

*

1.

MPI

2.

MWS

3.

wsMFG

4.

ws371

5.

E M P 371

6.

ws0D

7.

wsFAK

8.

wsTEX

9.

ws0ND

10.

wsTCU

11.

wsMIN

12.

wscc

13.

wsWT

*

14.

wsRT

*

15.

wsSER

*

*

3

4

5

6

7

*
*

*
*

*
*

*

*

122

8

9

10 11 12 13 14 15

123

Block II

1
1.

MPI

2.

MNWS

3.

OLI

4.

PROPNF

5.

PROPY

6.

TRANS

7.

CFSJ

8.

TECFSS

9.

EECFSS

2

3

4

5

6

7

*

*

*

*

*

*

*

8

9

APPENDIX C

APPENDIX C
ORDINARY AND TWO-STAGE LEAST SQUARES RESULTS: CHAPTER III

Block I:

Wage and Salary Disbursements

•371

371

771

WS

= -786.6639 + 28.0010q.
(14.3645)
R 2 = .960

- 12.0039q
(14.4030)

+ 7.3496q + 1.8140EMP
(14.8868J
(0.1070)

d = 1.676

+ 318.7459w
(11.8801)

(2SLS)

371

37

> /J- = 429.4879 + 5.1030q, - 5.0678q, + 26.6458q., + 0.0742USAP - 0.0701JT
+ 117.6889d
(44.4014) (14.8005)1 (14.8163)
(20.3843)
(0.0183)
(0.0150)"
(23.6825)
.513

WS°D = 70.5578 - 55.1828q,
(28.7476) (16.8880)
R2 =

.954

WSFAK = 316.9208 - 6.9370q,
(57.7883) (1.2260)
R2 =

.942

d

= 0.616

(OLS)

- 43.8998q
- 84.4439q_ + 0.2146WS371 + 12.4379MFGDNO ,
(20.3853)2
(23.4568)
(0.1333)
(1.8734)
d

= 0.706

(2SLS)

- 2.9810q
+ 3.0999q^ + 0.9239TIME - 232.0048MUSAHE
(1.2252)^
(1.2231)J (0.0498)
(49.3541)
d

= 1.154

(OLS)

,TEX = _ 2 0 .5785 - 1.2234q1 - 0.1463q + 0.1443q^ + 0.3967AWE371 + 6.4143d.
(2.0090) (0.8457)
(0.8456)^
(C.8456)
(0.0183)
(0.9845)
R 2 = .969

d = 1.248

(OLS)

124

R2 =

WS0ND = 14.1509 - 13.3704q,
(8.4593)
(3.6213)

- 11.0155q9 - 9.2528q9 + 0.3915GNP
(3.6193T
(3.6192)J (0.0148)

R 2 = .938

d = 0.342

WSTCU = -83.9192 - 19.0042q,
(33.1669)
(2.0532)
R2

= .984

WSMIN = 14.5642 - 3.4399q.
(4.9655) (0.5713)
R2

= .693

(OLS)

- 7.4597q9 - 9.9544q. + 0.0845WSMFG - 0.0206USAP + 0.0247POP
(2.0964)-3
(2.9209)-3 (0.0056)
(0.0032)
(0.0052)
d = 1.181

(2SLS)

- 1.0555q
- 1.0800q- - 0.1531wMI N - 0.1951TIME + 0.1885MFGNO
(0.5807)^
(0.5784)‘;S (2.4358)
(0.0475)
(0.0293)
d = 0.811

(OLS)

WSCC = 34.0838 - 54.5818q1 - 24.3327q9 + 13.9353q9 + 31.1091wCC + 0 . 5 0 9 1 (KM F G -kM 5'G )
(20.4906)
(6.9694)
(6.9841)Z
(6.9936)-15
(8.6936)
(0.0502)
R2
WS^

= .927

= 10.7164 - 16.7807q.
(3.2419)
(3.0120)
R2

= .991

d = 0.770

(OLS)

- 13.7226q9 - 7.2221q9 + 0.0148MPI + 0.6060*73^
(2.0250)^
(l.SSOO)"3
(0.0032)
(0.0941)
d = 2.179

(2SLS)

WSRT = 2.8182 - 38.5943q-, - 9.4634q9 - 11.7995q, + 0 .0296MPI + 0.5673WSR^
(4.1878)
(4.3429)
(2.3184)Z
{2.S923)6
(0.0052)
(0.0840)
R2

= .996

d = 2.256

(2SLS)

W S SER = -50.0735 - 25. 0113q.
(13.9776)
(4.3426)
R 2 = .997

- 1.5664q9 - 0.6955q + 0.0372MPI + 0.4330WSSER + 0.4502CPI
(2.6034)^
(2.7745)J
(0.0065)
(0.1042)
(0.2343)
d = 2.237

(2SLS)

wsm G = ws371 + ws0D + wsFAK + wsTEX + ws0ND
mws

= wsFARM + wsMIN + wscc + wsMFG + w s ^ + wsRT + wsTCU + wsFIRE + wsSER + wsG0V
+ WS

01

MPI = MWS + MNWS

Block II;

Other Sources of Personal Income

OLI = 57.7031 - 0.7273q1 - 0.9042q? - 1.3734q- + 147.4682LICMFG + 0.2587MICMFG
(4.4235) (4.496 j )
(4.4963P
(4.4963)J
(6.4494)
(0.0297)
R 2 = .980

d = 0.460

(OLS)

PROPNF = -59.2905 - 43.6109q7 - 18.2558q9 - 13.3489q, + 0.0843MPI - 0.0713PROPNF
(146.2988) (10.5745)
(5.5713)^
(5.6088)J
(0.0121)
(0.1399)
- 2.7684CPI
+ 0.0501POP .
(0.6975)
M
(0.0262)
R 2 = .981

d = 1.748

(2SLS)

PROPY = 83.6703 - 62.0371q.
(9.8790)
(7.6308)
R2 =

.992

- 32.1868q9
(8.4028) ^
d

TRANS = -204.5558 - 3.0464q.
(153.0681) (5.9426)

- 46.5154q
+ 0.0130USCP ^
(7.8681)J(0.0048)
~-L

= 1.435

+ 0.0439ML .
(0.0019)

(OLS)

65+
- 1.8847q? - 9.0664q^ + 0.3233UEMP + 0.4727POP ^
(5.7164)z
(5.5772)J
(0.0265)
(0.2932)

+ 2.0322MED . + 0 . 5 2 0 3 0 A S . + 0 . 2 3 7 8 [ (MAXTY)(SSR)]
(0.4800)
"
(0.2878)
X
(0.0507)
R2 =

.986

d

= 1.402

(OLS)

EECFSS = 7.0571 + 0 . 4 2 1 9 [ (SSR)(MWS)(q.)] + 0.1267 { [ (SSR)(MAXTY)(EMPW S ) ] (1.9874) (0.0097)
(0.0028)
+ 0.1195{[ (SSR) (MAXTY) (EMPW S ) ]

- (EECFSS_1

+ EECFSS_2 )} (q3 )

+ 0 . 0 8 5 9 { [ (SSR) (MAXTY) (EMPW S )]

- (EECFSS_1

+ EECFSS_2 + EECFSS_2 )} (q4 )

.984

CFSI = 14.0286 - 8.9132q,
(1.1223) (1.4366)
R2 =

.997

d

= 2.062

(OLS)

- 7.2491q0 - 8.4795q^ + 1.1776TECFSS
(1.4386)z
(1.3805)-3
(0.0094)
d

= 1.120

(2SLS)

TECFSS = EECFSS + SECFSS
MNWS = OLI + PROPF + PROPNF + PROPY + TRANS - CFSI
MPI = MNWS + MWS

127

R2 =

(EECFSS 1 )]}(q2 )

A PPE N D I X D

APPENDIX D
SOURCES AND CONSTRUCTION OF SAMPLE DATA
CHAPTER III

The principle source of information was the 1971
Economic Report of the G o v e r n o r , hereafter referred to as
the Economic R e p o r t .

In addition, two other governmental

agencies, the U. S. Department of Commerce, Office of
Business Economics

(OBE) and the Michigan D epartment of

Labor, Michigan Employment Security Commi s s i o n

(MESC)

provided valuable information and insights into the data
problems encountered in preparing this document.

Computation
WS

FARM

Payrolls

in

farms

(millions of d o l l a r s ) .

wgFARM _ (la)

WSM IN

WS

cc

Payrolls

in

WSMIN =

(lb)

MFG

(millions of d o l l a r s ) .

Payrolls in contract construction
dollars).
CC
WSCU =

WS

mining

Payrolls
WSMFG =

(millions of

(lc)
in manufacturing
(If)

128

(millions of dollars)

129

WS

371

Payrolls in motor vehicles and equipment
(millions of dollars).
W S 371 =

WS0D

Payrolls in other durable goods manufacturing
(millions of d o l l a r s ) .
WS0D =

WS

FAK

(2a)

(2d) -

(2a)

Payrolls in food and kindred products
of d o l l a r s ) .
WSFAK =

(millions

(2b)

m p y

WS

Payrolls in textile mill products and apparel
(millions of d o l l a r s ) .
WSTEX =

W gOND

(20

Payrolls in other nondurable goods m a n u f a c t u r ­
ing (millions of d o l l a r s ) .
WS0ND =

(If) -

(2d) -

(2b) -

(2c)

Mrn
WS

Payrolls in w holesale trade
W S WT =

WS

RT

(2e)

Payrolls in retail trade
W S RT =

(millions of dollars)

(lg) -

(millions of d o l l a r s ) .

(2e)

p T D p

WS

Payrolls in finance, insurance,
estate (millions of d o l l a r s ) .
WSFIRE _

WS

TCU

SER

(lh)

Payrolls in transportation, communications, and
public utilities (millions of d o l l a r s ) .
WSTCU -

WS

and real

(li)

Payrolls in services
W S SER =

(lj)

(millions of dollars).

130

WS

GOV

Payrolls in government
WSG0V =

WS

01

(11)

(lb)

Other labor income
OLJ =

PROPF

Fa r m proprietors'

EECFSS

income

(millions of dollars)

(7)1/4
(millions of d o l l a r s ) .

(lp)
(millions of d o l l a r s ) .

(lq)

Employee contributions for social security
(millions of d o l l a r s ) .
EECFSS =

SECFSS

(lo) -

Transfer payments
TRANS =

(millions of dollars).

(7)1/4

Property income
PROPY =

TRANS

income

Nonfarm proprietors'
PROPNF =

PROPY

(millions of d o l l a r s ) .

(In)

PROPF =
PROPNF

(millions of

Total payrolls (wage and salary disbursements
(millions of d o l l a r s ) .
MWS =

OLI

(lk)

Payrolls in other industries
dollars).
WS01 =

MWS

(millions of d o l l a r s ) .

(5)

Self-employed contributions for social security
(millions of d o l l a r s ) ,
SECFSS =

(6)

131

TECFSS

Total contributions for social security
lions of d o l l a r s ) .
TECFSS =

CFSI

(Ir)

Total nonwage and salary components of personal
income (millions of d o l l a r s ) .
MNWS =

MPI

(lm)

Michigan pers o n a l income
MPI =

USAP

U.S. automobile p r o d u c t i o n

U.S. new orders in m a n u f a c t u r i n g
dollars).

(billions of

(10)

U.S. new order in durable goods manufacturing
(billions
of d o l l a r s ) .
MFGDNO =

j^MFG

(billions of

(9)

MFGNO =
MFGDNO

(millions of dollars).

(8)

U.S. gross national product
dollars).
GNP =

MFGNO

(millions o f d o l l a r s ) .

(la)

USAP =
GNP

(6)

Total contributions for social insurance
(millions of d o l l a r s ) .
CFSI =

MNWS

(5) +

(mil­

(11)

Capital stock in manufacturing,
lions of d o l l a r s ) .
KMFG =

deflated

(bil­

(12)

Capital stock in transportation equipment,
flated (billions of d o l l a r s ) .

K 37 = (13)

de­

132

TIME

Time.

TIME = (14)
Population, end of quarter

POP

POP =
POP

65 +

371

(15)

Population 65 and older, end of quarter
(thousands).
POP

AWH

65+

=

371

WS

Employer contributions for employee group life,
accident, and sickness insurance (dollars).

MED

(20)

Employer contributions
expenses (dollars).
MICMFG =

CPI

(18)/(19)

(4)

LICMFG =
MICMFG

(32)

Average quarterly total wage and salary e m ­
ployment (thousands).
EMPWS =

LICMFG

(17) x

Ratio of M i c h i g a n to U.S. average hourly
earning in manufacturing.
MUSAHE =

EMP

(17)

Average quarterly weekly earnings in SIC 371
(dollars).
A W E 371 =

MUSAHE

(16)

Average quart e r l y weekly hours in SIC 371.
r371
AWH'
=

AWE

(thousands)

for employee medical

(21)

Detroit average quarterly consumer price index,
medical care c o m p o n e n t .
CPjMED

_

(2 2 )

133

SSR

Social security tax rate
SSR =

M A XTY

(23)

M a x i m u m taxable earnings subject to the social
security tax (dollars).
MAXTY =

MFG
USCPJ

(24)

U.S. corporate profits in manufacturing,
after taxes (billions of d o l l a r s ) .
USCPMFG =

USDIV

371

MIN

(28)

(29)

Total public medical assistance payments
lions of d o l l a r s ) .

(mil­

(30)

Hourly wage rate for assemblers in SIC 371
(dollars).
w

w

(thousands).

Social security payment to Michigan residents
(millions of d o l l a r s ) .

MED =
W

(billions of dollars)

Average quarterly number of unemployed

OAS =
MED

(26)

(27)

UEMP =
OAS

(25)

Michigan liquid assets
ML =

UEMP

net

U.S. dividends paid, cash, all industries
(billions of d o l l a r s ) .
USDIV =

ML

(per c e n t ) .

371

=

(32)

Hourly wage rate for iron and copper ore miners
(dollars).
w

MIN

=

(33)

134
w

CC

Hourly wage rate for common laborers
w

USMINW

=

(34)

U.S. m i n i m u m wage rate
USMINW =

(32)

(dollars).

(dollars)

135

Sources

1.

Michigan quarterly personal income by major sources:
a.
b.
c.
d.
e.
f.
gh.
i.
j•
k.
1.
m.
n.
o.
Pqr.

2.

Total personal income
Total wage and salary disbursements
Farms
Mini n g
Contract construction
Manufacturing
Wholesale and retail trade
Finance, insurance, and real estate
Transportation, communications, and public utilities
Services
Government
Other industries
Total other sources of personal income
Other labor income
Proprietors 1 income
Property income
Transfer payments
Contributions for social insurance

1955-1959

U n published data from the State of
Michigan, Executive Office, Bureau
of Programs and Budget.

1960-1968

Economic R e p o r t , Appendix Table
B=TI

Michigan quarterly payrolls for the following categories
a.
b.
c.
d.
e.

Motor vehicles and equipment (SIC 371)
Fo o d and kindred products
Textile mill products and apparel
Durable goods manufacturing
Wholesale trade

Annual Report of the Mich i g a n Employment Security
C o m m i s s i o n , each year.
3.

Employment in motor vehicles and equipment, quarterly
average:
constructed by averaging monthly data in the
Annual Report of the Michi g a n Employment Security Co m ­
mission^ each year.

136

4.

Total wage and salary employment, quarterly average:
constructed by averaging monthly data in the Annual
Report of the Mich i g a n Employment Security C o m m i s ­
sion , each year.

5.

Employee contributions for social security, quarterly:
Information by letter from the U.S. Department of
Health, Education, and Welfare, Social Security A d ­
ministration, dated April 26, 1970.

6.

Self-employed contributions for
annual:
Information by letter
ment of Health, Education, and
Security Administration, dated

7.

Farm p r o p r i e t o r s '

i n c o m e ,a n n u a l :

1956-1965

Latest revisions were provided
from unpublished data from O.B.E.
by letter, dated January 12, 1971.

1966-1968

Survey of Current Business
Aug u s t 1970, p. 36.

social security,
from the U.S. D e p a r t ­
Welfare, Social
April 26, 1970.

(O.B.E.),

8.

U.S. automobile production, quarterly:
Automobile
Facts and Figures, Automobile M a n ufacturxng A s s o c i a ­
tion, assorted issues.

9.

U.S. gross national product:
tics (O.B.E.), pp. 4 and 193.

1969 Business Stat i s ­

10.

U.S. new orders in manufacturing:
1969 Business
Statistics (O.B.E.), pp. 33 and 213.

11.

U.S. new orders in durable goods manufacturing:
1969 Business Statistics (O.B.E.), pp. 33 and 213.

12.

Capital stock in manufacturing, end of quarter, in
constant dollars (1958 = 100):
U n published data
from the State of Michigan, Executive Office, Bureau
of Programs and Budget.

13.

Capital stock in transportation equipment (SIC 37),
end of quarter, in constant dollars (1950 = 100):
Unpublished data from the State of Michigan, E x e c u ­
tive Office, Bureau of Programs and Budget.

14.

Time:

1950 1 = 1 .

137

15.

P o p u l a t i o n , as of July 1 of each year:
R e p o r t , A p p e n d i x Table B-l.

Economic

Intervening end of quarter data by interpolation.
16.

Population 65 and older:
Unpublished data from the
State of Michigan, Executive Office, Bureau of
Programs and Budget.

17.

Average quarterly weekly hours in SIC 371:
con­
structed from unpublished monthly data provided by
M.E.S.C. by letters, dated April 11, 1968 and
November 20, 1969.

18.

Michigan average hourly earnings in manufacturing,
annual:
Economic R e p o r t , Appendix Table B-25.

19.

U.S. average hourly earnings, in manufacturing,
annual:
Economic R e p o r t , Appen d i x Table B-25.

20.

Employer contribution for employee group life,
accident and sickness insurance, annual:
Unpub­
lished data from the State of Michigan, Executive
Office, Bureau of Programs and Budget.

21.

Employer contributions for employee medical ex ­
penses, annual:
U n published data from the State of
Michigan, Executive Office, Bureau of Programs and
Budget.

22.

Detroit average quarterly consumer price index,
medical care component:
constructed from monthly
data contained in the Consumer Price Index (U.S.
Department of Labor, Bureau of Labor S t a t i s t i c s ) ,
each month.

23.

Social security tax rate:
Complete historical
series provided by letter from the U.S. Department
of Health, Education and Welfare, Social Security
Administration, dated April 3, 1969.

24.

M a x i m u m taxable earnings subject to the socialsecurity tax:
Complete historical series provided
by letter from the U.S. Department of Health, Edu­
cation and Welfare, Social Security Administration,
dated April 3, 1969.

138

25.

U.JS. corporate profits in manufacturing, net after
taxes:
1955-58
1959-60
1961-62
1963-64
1965-68

26.

U.S.

1959
1961
1963
1967
1969

Business
Business
Business
Business
Business

Statistics
Statistics
Statistics
Statistics
Statistics

(OBE)
(OBE)
(OBE)
(OBE)
(OBE)

p.
p.
p.
p.
p.

97.
96.
101.
101.
101.

p.
po
p.
p.
p.

97.
96 .
101.
101.
101.

dividends paid, cash, all industries:

1955-58
1959-60
1961-62
1963-64
1965-68

1959
1961
1965
I9T67
1969

Business
Business
Business
Business
Business

Statistics
Statistics
Statistics
Statistics
Statistics

(OBE),
(OBE) ,
(OBE) ,
(OBE) ,
(OBE) ,

27.

Liquid assets, end of year:
Economic R e p o r t , A p p e n ­
dix Table B-35.
Intervening end of quarter i n f o r m a ­
tion by interpolation.

28.

Average quarterly number of unemployed:
constructed
from monthly information contained in the Annual RePort of the Michigan Employment Security C o m m i s s i o n ,
each year.

29.

Social security payments to Michigan residents:
Information provided by letter from the U.S. D e p a r t ­
ment of Health, Education, and Welfare, Social
Security Administration, January 26, 1970.

30.

Total public medical assistance p a y m e n t s : Informa­
tion provided by letter from the State of Michigan,
Department of Social Services, Research Section,
dated April 21, 1969.

31.

U.S. m i nimum wage rate:
Information provided by
letter from the U.S. Department of Labor, Wage and
Labor Standards Administration, dated June 18, 196 8.

32.

Hourly wage rate for assemblers in SIC 371:
1955-1966

Wage Chronology, General Motors C o r ­
poration, 1 9 3 9 - 1 9 6 6 , U.S. Department
of L a b o r , Bureau o T Labor Statistics,
October, 1966.

1967-1968

By telephone from the United Automobile
Workers of America, July 9, 1969.

139

33.

Hourly wage rate for iron and copper ore miners:
Information provided by letter from Uni t e d Steel
Workers of America, dated September 17, 1969.

34.

Hourly wage rate for common laborers:
Information
provided by letter from Laborer's International
Union of North America, dated September 2, 1969.

S3

wsFARM

ih A

19 56

-vrsrr
19 5 c
1959

~VT6TT
1961
19 6 2

1-61
19o 6
1965

1 1 F
1967

19 6c

1
/.50
1 . 717

i i.2 n
6,50
T 7 W
c ,6 0
8,40
i ,° n
d, i n
7.60

C » Vr
b .5 n
1 2 ,6 0

2
11.90
T5TTTT

3

4

13 «1 u
14.'30

15.60

14 i-4C

16.10

17 ,1 0
TF777'

11. 5 Q
T T T7T
12 60
15 3 0
T3~ W
14 Cu
13 90
~T4“ W
15 2 0
13 9 0
T 3 ~ "3TT
12 3 0
14 2 0

T5TTTT
15 .v U
16.20
“16 17 U~
15,50

16,30

16*40
T5T5T
I6,6g

14.00

15. 5Q

T473F
14.7 0
12.9 0

T5T4T
15,40

13 ,1 0

ws

MIN

?YEAR
1956

1
21,70

2
23.6U

3
22,53

4
26,10

l W ----------- 22,1 0------------- 25T70
Z^TZl
1 95b
19,7(1
18.80
19,60
1959
19,60
23,20
19,30
----------- 2— r?fl------------ 24T.-6U------------2^TT0----------

ZA~Ttt
21^90
19.80
Z^TW

1961
1962

19, 60
18, g-D

22,20
21, 60

22.30
2lj30

t^trt

t/-,-9o

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1956

1
2921,30

T75~7-----------------

2

3

4

2914*CC
3213.60
2 9 8-4-. 4-Q--------- 2968, 60----------30 81. 4 iT
2728.40
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3014.7 0
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3085.90
3231.90
2906.21

1961
1762
71,"95-7
1964
19 65
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176 7
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2963.40
3219,80
Ov ^'^IV-TO
3 -0 ..9 0
4 -77,40
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4 9 61,90
54 8 5 , 5 0

3 0 7 5 . 30
3325,10
3577 , U
3 8 8 7.50
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4 7 74 , . u
5 0 4 C .2 u
5566.30

3075,10
3331*20
3 5 9 6 , 7y

3960.20
4385*20
5 £i3 4 *4 ij
5091*40
5543*80

33Q 4. ‘2U
3562.70
36 8 5 * 6 0
4 238,6 0

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6 1 8 3 * y i!

5328.60
6 0 8 7.40

156

195 8
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PROPNF
2 3®

VEAK
1956
lT?tr7

1
302♦ 6(1
iStJTlO

2
3
'♦
366,90
356, DO
396,50
363.50-----------3'54T91----------398', 8D

19 5 6
317,00
344.50
1959
34l,3n
3 77. . 0
1 4-frv— --------- 33 5; 4 n------------- 3"5&,"1 ii-----------1961
323.40
3 6 1 . QC
1962
545,20
372.30

351,30
396^20
38 7* 30
39 8. 4 r;
3o'8,l0----------3 70 , 7o
4 0 1 . UO
3 7 8 , 9Q
413.10

--------------------3 5 4 ,' 471----------------------3 H 2 7 vu----------------------3 W
1964
1965
T9Tj6----------1967

393,70
424,70
424,5(1
478.9 0
T o -rt~ T n ------------- 5 1 0 .‘3 0-----------472.30
529.70

t 97]--------------------4r2^T&TT

441*20 .
495,’40
4 9 8 ,4 0
555,20
528191]----------- 5 F 5 T T U
524,60
608.40

IE

PROPY

Yfc'Ar1

1

2

3
470*20

4

1956
42;]. 30
4 3 8, 0
504,50
T ^ 5 7 ‘------------ ^6v,-3n------------ 4 7 8 , 7 U----------- 4 8 3 *"Jg----------- 4 9"9'rSTT
1958
461,30
476,60
481,30
500.30

1959

451,50

507.50

535,3 0

562790

----------- 535-.10---------- 5-3 6 . 4 0------------P 5 3 r fS----------573 .~4tr
1°61
1 Q 62

526.80
575.un

539.30
592.70

5 8 2 , 0Q
592,30

1"9^3..........-6-3^1-7-fi-

fr6"4-r2ti

3. 964
3 ,c 6 5

722, 60
a 14, 5 0

650 *10
7Q8*80

69 5 . 50
7 94 , on

807*80

624.90
6 6 2, 00

721? rotr
792*10
9 2 1 , 70

T^6t---------- 5 5 - .170---------- STTVTZ----------- 899 .-60---------- 96'9,-STT
19 6 7

1966

92 6, 10
1007,40

954 ,60
10 6 3 . 5 0

9 4 1 , lg
1072*50

1005.20
1129.60

TRANS

- • r* - ,
C. ^

4
7
2
3
193c
i 9 i ,?n
2 0 9, 4 u
20 8 , 1 0
222,80
<£x 7 , ~a n
' ...............
9 95.2 2 6, 4 u
234,-10 ' ' ' ....'2'4 8, 30....... ..... "
1959
3 0 7, a n
3 4 9 . 7U
324,10
292.60
1959
2 9 j ,s n
2 7 6 , 6U
279*83
30 Q ,20
' '
" 1"? ot.... . .._ "I'D5,"5*5 .... ' ' " " 2 ^ G ~ . ? rU ..... . ' •" '3f5"r4H ' ■
3 1 Q .6 U
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J_ > *
3J.
3 1 3 ,9 n
360 , 7u
3
39.2 0
344*40
3 5 1 , in
1951
3 3 6 , i>0
335.20
343,4 0
..... ......... * 9 6 :
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^3481 n j -- - 3 3 6 , 5 rr
345,80
353,50
1?64
3 6 2 , ?n
3 5 7 ,6 u
355,6u
360,10
1"65
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369,70
394,00
412*80
3 90
42 9 , 6 n
4 3 0 •4 0
4 2 2 . BD
'■ T 4 5 T 2 1 .. ~ '
5 02 , 3 n
1?0 7
520.10
521.90
521*70
19 6'.
553,30
576,50
584.00
594*00

b-»
o\

EECFSS
30-

YEAR
1
2
3
4
1956
52,30
47.20
46,30
32,00
1
-------------- fr-jr?n------------58-. 9 d--------------- 46 , 5 g------------- 3trr5T)-------------------------1958
54,30
50,60
43.7 j
29,70
£
1959
65,00
68,50
57,10
36.90
M
.196 0
66,50
8 4 ,6 0
o7 ♦ 7 g
41*6 0
1961
78,50
81,20
65*60
44,90
1962
9i,gO
91,6 0
69,51
41*50

t963---------- llir.-9-fl---------- 113-, 2 0----1964
1965

W
1967
1968

121,70
132,90

120,20
134.20

---------- 172; r0
191, 60
216,20

1 8 2 . 1C
2 2 9 , lu

SlT^U----------- 4T t 67]----------------------84,10
88.90

46,70
54720

---------- tS5-7-7t----------- ttftrT0----------------------174,30.
110.90
1 8 6 , 80

1 4 1 . 70

SECFSS
34-

5.3 0

5.4Q

4
5,4 0

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5.70
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17,40

17.40

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O'
W

TECFSS
33—
YEAP
1956
i'yj 7
1956
1 9b V
I '7 6 0
196-'.
1962
..... ' " ".......... 19 6 6 ■■■
19 6 9
1966
1965
1967
196s

1
5 7, f n
~ 6 6, 7 0
59.90
7 2 , u0
94,30
6 6,30
99. *n
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i3 1 ,u n
i 4 3.10
i 6 5 • 71)
2 0 6,60
237!, 30

2
52.5u
6 4,90
56,30
75.5 0
92.70
8 9.20
I00.lt)
12 c . 9 0
129.6 0
? 44.40
j 9 3,90
1-7.40
246.50

3
51. 7 C
52*50
49,4n
64.1Q
7 5 T 9 O'
73,60
78,00
91*00
93,50
99,20
169*40
189,60
204,20

4
3 7.40
3 6.60
35.40
43*90
.......T 9 T E C
52.90
50,00
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64 ,5 3
121,40
126.20
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1
73,10
..........15 4 ,7lT 32,00
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19^2
196 3
1954
1965
■"1 ^ 6 ..... 196/

19I>

109,30
122,30
145,70
1.53,60
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2/6,;0

2
6 8 , 7d
3 T ,- 6 T
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3
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67*90
91,30

4
53,10
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114,10
124.12
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174, 7 J

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246,70

296,/g

93,12
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246,50

75,50
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27 =

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1 956

.... ...

i 95 5
1959
19 1 1961
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2039, ?n
214 7. 70
2211.60
2 3 3 8 . BO

3
1168,80
1 c 0 5 *0 0
1300,60
1334,70
1358,70
1442*30
1467*10
15577015 “
17 0 b . 1 c
1937,40
2068*40
2143*30
2420*40

"

'

4
1243.91)
1283,21)
13 4 6 • 3 U
1411^7?)
14 3 9 , 2 0
1528.80
1588*20
169 4 . 1 U
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2122.40
219 7.60
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h-4
On
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YE A 6
1956
T9^7
1956
1959

1
3 9 5 1 , 3(1
4 x 7 3 ,u n
4 04 3 , 7 1
4 0 7 3,4n

2

3
4 0 3 9 , 10
4T5 9,10
4032,20
4340,20

4082*80
4 1 7 3 * 6'Q
4 G 4 1 + 20
4 4 2 0 »6Q

19tn?----------4^''3'3_,"6-n--------- 41S9713--------- 4^9
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4317,90

4
4457,50
4 3 6 4 , 60
4 3 6 1 . 00
4643.60

9 j-------- 4oYT0"r2Ti'

4 4 6 1 . 73
4517*40
4 8 3 3 . 00
1962
4618,20
4752,50
4798,30
5150.90
--------- 49-36 ,-9n----------- -4494--FC---------- ------------------- 5 5 7 9 ."70
1965899.10
5538.5i
5660*30
6102.90
1966
5 639,40
6178.30
6 3 2 2 + 60
7056.80
T9"6t"--------- 65 9 6 1 4 0 ----------- 6 75 5 .9 0------------ 7 1 U 2 . 8 C ---------- 7381T5T]
19 6 7
7001,20
7187, 9 u
7234,7?
7682.30
1967697,10
790 7 .1 0
7964,2?
8662.60

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1

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1^56
1742,90
1449,70
1042*2Q
1567.10
1 9 a /---------- 17 9^; ,6 0----------- t^SOTolJ------------------041271
17 56
1 2 3 3 , 70
10G3.7C
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1369,80
1959
1 o 0 0,40
1633,70
1052,70
1257'.00
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1961
1 1 6 8 , 2 0
1548,6J
949,30
1830,20
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1765,80
1354.20
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2059.30
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196a
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2290.40
1 3 5 0 *90
1959,00
1966
2 5 6 i,9 0
2599.80
1547,50
2626,00

t W --------- g-4"
95 .-lfl---------- 24-26x60-------- 125~6~,8!--------- ?4gtSImr
1967
1966

1673,30
282],60

2171.70
2522,80

1249*30
1480,60

2118,30
2524,60

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61-

1
2
3
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86.70
84.70
85,10
83.20
------------ 8 7 . 3 0------------- S ?-, ? -Q-------------- 83 , 70------------ 797
3.958
79,4.1
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1937
87,20
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95,70
88^40
------------ 9- ,tr-n--------------9 1 . -t?-------------- 9 i~, 5 3 ------------ ay; m
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89,20
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93,90
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98,00
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1964
1 05 . 80
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111.9b
1965
114.70
120,20
124,40
120.90
------------ 1-2-6 ,77)----------- 1 35 . 2D------------- 1 3 8 , 8 0 ------------1 3 4 . 2 0
1967
134,00
131,60
138*30
134710
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?.on
2 , 30

i ,:

1.959

2

3
0*90

4
1.00

i t t o

mrs

r i w

1.90
2, 40

2*10
2,6q

2,20
2,3Q

0,80

n

19 61

ZT^ri------------------------ 2 T 4 D ---------------------- 7 7 4 7 -------------------- 3 T 7 T T
4,10
6.2 0
7,50
8,2 0

1967

y,m

r

w

--------------------

--**$■3

1°64
1969
tvt5

“ •.... « l 6'fr

9 , on
ly .60

19 67

rrrrn
12 , ? n

196 9

36 , an

a.oc
& 7 B w

10,20
11.20

9*00
-9TTU
10,60
13.7Q

9,10
BTT5H

10.20
12,90
tttttu------------ 757 tc---------- p n v n
22.50
36*20
36,80
4 1 • 9L
i
43*40
4 6 * 3 0

47-

YEAN
1956
------------^
--------

1
2 , OH
_---------

2

3
4
2,0b
2*05
2.05
2-.— 5--------------- 2— til-------------- trttr

195«
2, in
2,10
2.*2Q
2.30
1959
2,30
2.3J
2*40
2,40
----------------2v4-fl--------------- 2 V 4 3-------------- 2 * 4 0 --------------2 . 4 5
1961
2,45
2.45
2.50
2,50
1962
2,60
2,6b
2,6Q
2,'70
x 9 6 <-------------- ?r71)-------------- 2 , 7 7 -------------- 2,75'-------------- 2 T 7 3

1964

2 , 7 5

1965

?,R5

2.75
2.65

2,85
2,85

r w ------------ tttti----------------------19 6 7
1968

3.15
5.43

3,23
3,43

2^85
2790

zyvn------ srinr
3,23
3,43

37 4 3
3.62

MIN
w

YEAH

1

1956

2. •> 7

2

3

4

2, 4 7

2,58

2.58

--------------. ('1----------- 2V&1------------ 2j71------------- 2t7T
1958
>', 76
2,76
1959
7,61
2 . cl
t w --------------- r r * t ------------- 2TBit-------------1961
2,86
2,86
1962
2,06
2.96

2«83
2*81
2j m --------------2,86
2,96

2.80
2^81
2rtrr
2*66
2.96

l96i<----- -----------------------2-.?o------------- >796------------ 2T915
1964
1966
t t t t --------------1967
1968

2,96
2,96
2,06
2,96
Brrts------------- 3”,T6-------------6,26
3,26
3,35
3.35

2*96
2,96
3 v2'6--------------3,35
3,61

2.96
3.26
3 '".'26"
3.35
3.61

4

nn

w.CC
49-

YEA-;
1956

1
2,sn

•—
1956
1959
■' .1 9 6 9 ......
19 6 'J
19 6 2
- .... 1 9 6 5 ......—
1964
19 65
1066

2
2,33

3
2,33

4
2*33

------------ rrrb------------ ----------------- ZTirf
2,45
2,53

2,63
2,73
2 •H 3
1,93
5,15
< f 55
i>, 4.n

196/

3,35

196b

5,51

2,53
2 ,fti
” -

"2-,6'B..... .
2.33
2.93
2 , 5 5~
3,15
3.2 u
3 ,4 0
3,55
4. 1

2*53
2,63
2,63
2.83
2,93
3 , 1]3
3,15
3,2 f
3*41

3,55
4 • Q1

2.53
2.63
---- 2.73- — ...... . ... . ” ....
2.83
2.93
3.08
3*15
3,20
3 ,4 J

3,55
4.01

"

...