0N LOWERING TI-IE LEVEL OF
SPECIFICITY IN MIGRATION VARIABLES

Dissertation for the Degree of Ph. D.
MICHIGAN STATE UNIVERSITY
FRED McLEOD GROSE
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0N LOWERING THE LEVEL OF SPECIFICITY IN

MIGRATION VARIABLES
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ABSTRACT

ON LOWERING THE LEVEL OF SPECIFICITY
IN MIGRATION VARIABLES

By
Fred McLeod Grose

Migration research that has been performed from the
perspective of place and stream analysis has employed data
of a relatively high degree of aggregation. Net migration
for the total population was frequently regressed on inde-
pendent variables at a comparable aggregate level. Some
slight improvement took place when net migration was dis-
aggregated into in- and out-migration, and when demographic
characteristics were disaggregated by race, sex and broad
age categories. The purpose of this dissertation is to
examine the value of further disaggregation of migration
variables into more specific groups in order to better
understand migration processes, and thus predict migration
of metropolitan areas.

The relationships between net, in- and out-migration as
the dependent variables and unemployment, income and size of
place as independent variables are examined by simple correla-
tion and multiple regression analysis. Data from the 1970

U.S. census are specified by sex for the population age five

.9 Fred McLeod Grose

and over and for five year age groups ranging from age twenty
to forty—four. Standard metropolitan statistical areas over
250,000 population are the units of analysis. In addition,
the relationship between in- and out-migration by age and

sex is analyzed.

Results of the study show that there is a marked
difference in regression coefficients across age-sex specific
levels of analysis. Coefficients for the population age
five and over vary from the specific age groups, and specific
ages vary from each other. There are variations when
coefficients for males alone and females alone are compared
with each other or with the coefficients based on aggregations
of male plus female. In- and out-migration flows are highly
correlated whether measured by rates or absolute values.
However, the degree of correlation varies by age and sex
categories.

The general conclusion is that aggregated data for the
total p0pulation are inadequate for explaining the relation-
ships between migration and independent variables that are
utilized most frequently; and disaggregation provides consid-
erable insight into the complexity of the relationships
between migration and economic opportunity structures of

metropolitan areas.

ON LOWERING THE LEVEL OF SPECIFICITY
IN MIGRATION VARIABLES

By
Fred McLeod Grose

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Sociology

1974

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Chapter

II

III

IV

V

TABLE OF CONTENTS

INTRODUCTION.
LITERATURE AND THEORY .

Migration Models.

Methodological Issues of. Disaggregation
Current Population Surveys. . .
Summary

METHODOLOGY
Dependent and Independent Variables
Hypotheses to be Tested .
Data Sources.
FINDINGS.
Hypothesis 1.
Net Migration .
In-Migration. .
Out-Migration .
Hypothesis 2.
Net Migration
In-Migration. .
Out-Migration .

Hypothesis 3.

SUMMARY AND CONCLUSIONS

Appendix

Bibliography.

ii

103

 

 

Tabl

IC

11

 

Table

10

ll

LIST OF TABLES

Simple Correlation Coefficients (r) of
Net Migration and Unemployment.

Unstandardized Regression Coefficients of
Net Migration on Unemployment Controlling
for INC and SOP

Coefficients of Multiple Determination (R2)

of Net Migration on Unemployment, INC and
SOP . . . . . . . . . . . . . . . . .

Simple Correlation Coefficients (r) of
In-Migration on Unemployment.

Unstandardized Regression Coefficients of
In-Migration on Unemployment Controlling
for INC and SOP .

Coefficients of Multiple Determination (R2)

of In-Migration on Unemployment, INC and
SOP . . . . .

Simple Correlation Coefficients (r) of
Out-Migration and Unemployment.

Unstandardized Regression Coefficients of
Out-Migration on Unemployment Controlling
for INC and SOP . . . . . .

Coefficients of Multiple Determination (R2)

of Out-Migration on Unemployment, INC and
SOP . . . . . . . . . . . . . .

Simple Correlation Coefficients (r) of
Net Migration and INC .

Unstandardized Regression Coefficients of
Net Migration on INC Controlling for

‘Unemployment and SOP.

iii

Page

45

45

53

54

56

58

60

61

63

66

66

 

 

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Table Page

12 Simple Correlation Coefficients (r)
of In-Migration and INC. . . . - . . . . . . 71

13 Unstandardized Regression Coefficients of
In-Migration on INC Controlling for
Unemployment and SOP . . . . . . . . . . . . 71

14 Simple Correlation Coefficients (r) of
Out-Migration and INC . . . . . . . . . . . 74

15 Unstandardized Regression Coefficients
of Out-Migration on INC Controlling
for Unemployment and SOP . . . . . . . . . . 75

16 Simple Correlation Coefficients (r) of
In-Migration and Out-Migration . . . . . . . 83

iv

 

 

10

 

Table

10

LIST OF APPENDIX TABLES

Correlation (r) and Unstandardized
Regression Coefficients for Net
Migration (Male Plus Female).

Correlation (r) and Unstandardized
Regression Coefficients for In-Migration
(Male Plus Female).

Correlation (r) and Unstandardized
Regression Coefficients for Out-Migration
(Male Plus Female).

Rank of Standard MetrOpolitan Statistical
Areas Utilized in Regression Analysis

Means and Standard Deviations by Age
for Males Plus Females.

Means and Standard Deviations by Age
for Males

Means and Standard Deviations by Age
for Females

Unstandardized Regression Coefficients
for Males Plus Females.

Unstandardized Regression Coefficients
for Males

Unstandardized Regression Coefficients
for Females

Page

93

93

94

95

97

98

99

100

101

102

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CHAPTER I
INTRODUCTION

The intent of this research is to determine if the
general practice of using aggregated data for the population
accurately represents the components of the total in migration
analysis. That is to say, will the statistics used to examine
relationships among variables in migration models be different
for the aggregated level (total population 5 years and over)
as compared with specific levels of 5 year age-sex groupings?
To address this question, the study will calculate simple
and multiple correlations at the aggregate level and at
age-sex specific levels for several variables that are
frequently used in migration studies. Methodological studies
on problems of aggregation indicate we will find variances
of correlation coefficients for the total population as
compared with specific groups. This study will address
substantive issues of aggregation within the context of
place analysis.

In the United States, efforts to explain why people
migrate usually employ data for standard metropolitan
statistical areas (SMSAs). The data for this study represent
64 SMSAs that were over 250,000 population according to the

1970 census. Although there are practical problems involved

with studying migration below the SMSA level, we would
expect any theoretical findings on population characteristics
to be relevant to all geographical levels.

Today the requisite data exist so we can conduct
migration research at more specific levels than is found
presently in the demographic literature. The term ”levels"
will refer to degree of aggregation of population character-
istics in contrast to geographic levels such as city, county,
state, etc. Migration will be associated with two variables
that indicate economic opportunity, and with the size of
each SMSA.

Total population figures of places represent the broadest
level of analysis in regards to population characteristics
because they are aggregations of all characteristics; male
and female, all ages, all occupations, the full range of
income and education groups, etc. Early demographic researchers
such as Ravenstein and Zipf had to be content with studying
data for total populations. Even if they could have obtained
data at levels comparable to the United States 1970 census
they could not have made adequate use of it because of the
absence of computer technology to manipulate data.

The research that has become known as "stream analysis"
utilizes data on migrants five years of age and older. In
order to do stream analysis the researcher needs to know
the number of in- and out-migrants and their places of origin

and destination. A study of streams involving ninety SMSAs

would require data from a 90 x 90 matrix showing migration

to and from each place. It would be possible to construct

matrixes containing the number of migrants to and from each
county in the U.S. by sex and five year age groups or other
characteristics. The creation of such data files from the

1970 census is presently under consideration by the Bureau

of Census and interested agencies.

The type of work that has been dubbed "place analysis"
often incorporates more detailed data about the migrants
and their place of destination than does stream analysis.
Given today's capabilities of reporting and publishing, it
is not difficult for the Census Bureau to report detailed
age, sex, education, occupation, etc. data for a number of
places. But it is costly to create matrixes such as the
one mentioned above for migration by county of origin and
destination. The data for a number of places can be arrayed
in a series of unrelated vectors without much trouble. It
is much more difficult to construct the desired migration
matrixes because, unlike the series of unrelated vectors for
places, each vector in the matrix depicts a relationship
that exists between it and all other vectors.

This study falls into the category of "place analysis."
However, if the results indicate disaggregation of variables
is useful in a place analysis framework, there would be
reason to suspect that disaggregation would be appropriate

in stream analysis also. The dependent variable (migration)

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will be expressed as rates and absolute numbers for net
migration, in-migration and out-migration. Employment by
age-sex categories as an independent variable will be stated
in terms of rates and numbers. The other independent vari-
ables will be income by age and sex, and size of place.
Analyses will be calculated for six age levels: (1) popula-
tion age 5 and over, (2) ages 20-24, (3) ages 25-29, (4) ages
30-34, (5) ages 35-39, and (6) ages 40-44. Altogether thirty-
six equations will be calculated. The intent is to see how
the variables behave at various levels of specificity as
compared with the broadest level which represents the popu-
lation age 5 years and over. This research is not intended

to create another migration model or to discover new variables
that explain migration.

Demographers would like to have the capability of
explaining migration precisely enough to permit the construc-
tion of prediction models for small geographic areas such as
cities. The best that the field can do at this point is to
make rough predictions for large market areas such as SMSAs
over 250,000 population. The Current Population Survey (CPS)
report on detailed characteristics of migrants. However the
geographic level of reporting for CPS data is on broad levels
for the nation and regions. Therefore we cannot use CPS
data to derive probabilities of migrating that would be
appropriate for predicting migration to SMSAs. Findings from

CPS are important to researchers interested in place and

 

 

 

 

 

 

stream analysis at the SMSA level. Hypotheses based on CPS
data that are confirmed over and over certainly should be
consistent with hypotheses drawn from SMSA data. This thesis
does not incorporate CPS as a source of data; however, CPS
findings will be compared with our findings.

Current Population Surveys also attest to the importance
of disaggregating below the category of population five years
of age and over. The Surveys detail the age-sex differentials
that exist among migrants. Knowing that differentials exist,
we should not expect the hypotheses pertaining to total
population that are found in place and stream analysis to
adequately explain specific groups of the population.

This thesis on lowering the level of specificity in
migration analysis contributes to our understanding of migra-
tion processes in three ways. The major contribution is to
help determine if it is worth the cost of gathering the
data required to perform future studies at age-sex specific
levels. Our intuitive sense and some explicit statements
from previous researchers lead us to expect the expenditure
required to lower the level of specificity is warranted.
However, this is the first time, to my knowledge, that a
place analysis framework has employed such a specific level
of detail. It is possible that only slight differences
exist among the various levels of analysis. If this is the
case, migration models employing only the total pOpulation
age five and over may be as accurate in predicting migration

as models that employ several times as much detail.

'7

The second contribution of the thesis pertains to the
economic opportunity variables that are included in the study.
Unemployment and income have been included as variables in
previous migration studies that used data for 1960 or before.
Even though the main purpose of inputing 1970 data is to
fulfill the major contribution as discussed above, the
analysis will also serve as a type of replication of economic
opportunity variables using the most current data. The third
contribution is like the second in that, in addition to its
role in the major contribution, the analysis of in- and out-
migration also serves as a type of replication of the
relationship between in- and out-migration.

The organization of the dissertation will be as follows.
Chapter II will review the literature and theory pertaining
to this analysis. Specific variables, hypotheses and data
sources will be set forth in Chapter III, and the findings
will be discussed in the Fourth Chapter. In the final
chapter, the summary and conclusions will be presented.

Supporting evidence will be found in the appendix tables.

 

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CHAPTER II

LITERATURE AND THEORY

There are many paths of thinking that may lead the
researcher to select a particular topic for investigation.
The topic of this thesis can be viewed as the logical result
of three heuristic paths. The first is what appears to

be prima facie truth that detailed knowledge of the parts

 

aids in understanding the whole. It seems reasonable to
expect demographic research conducted on age-sex specific
levels to be more informative than that done on broader levels.
The second path that leads to the t0pic of this thesis
is called scientific borrowing. An idea that has proven its
value in one area of research might be borrowed to aid research
in another area. There are many examples in demography
where narrowing the levels of analysis have contributed to
better understanding. Crude birth and death rates are of
little use to a demographer, unless more specific data are
not available, because crude rates fail to consider the age
structure of the population. Some research problems require
very narrow levels of analysis. The study of infant mortality
is a case in point. Most infant deaths occur in the first
month of life, yet the term "infant" refers to the first year

of age. Therefore, any precise study of infant mortality

must disaggregate the data by intervals of occurrences less
than one year. It may never be possible or desirable to
define the limits of migration analysis as narrowly as infant
mortality is defined presently. This thesis contributes to
the determination of the most appropriate levels of analysis
given the cost of generating the input data and the value

of the findings.

The third path that leads to the proposed research topic
is through the demographic literature on migration. The
literature brings us to ask about the value of lowering the
level of specificity in place analysis (in contrast to CPS)
by explicit and implicit suggestion. Several direct state-
ments in the literature call for utilizing more detailed data
on population characteristics in future investigations.

Galle and Taeuber [1966, p. 13] note that various metropolitan
areas of the country perform different tasks within the
economy and display different rates of economic growth.
Predicting volume of in- and out-migration during a specified
time, they say, would be aided if the trends and differentials.
in growth could be predicted or explained. If places have
different roles in the national economy and experience varying
rates of growth, as Galle and Taeuber suggest, then it is
reasonable to expect places to experience different patterns
of migration. Galle and Taeuber go on to discuss the related
problem of disaggregating migrants by specific characteristics

as seen in the following excerpt:

"Another problem in migration theory is that of

disaggregation. In Stouffer's model, as in

currently available census data on specific

migration streams, a migrant is a migrant. But

the paths of redistribution of blue-collar workers

within the nation obviously differ from the

paths of retired persons, students, military

personnel, executives, and so forth. And once

migrants were disaggregated into appropriate

categories, it would be profitable to experi-

ment with categorizing metropolitan areas

according to their functions and site features,

rather than solely by their locations relative

to one another in social or physical space."

Lowry, [1966, p. 26] suggests that ". . .the fit (of the
migration model) could be further improved by disaggregation
of the population-at-risk so as to differentiate groups with
varying propensities to migrate. There are several dimensions
along which such disaggregation might reasonably proceed:
age, sex, color, education, occupation, family status, etc.
Insofar as SMSA populations differ from each other in these
terms, their aggregate propensities to migrate would also
differ." Further in his report [p. 33], Lowry says, "I hope
this report will stimulate the generation of additional data
and the exercise of statistical ingenuity,. . ." "For the
present, the possibilities of experiment are sadly limited
by dependence on the 1955-60 matrix of place-to—place migration
flows."

Stone [1971] views the relevant causal processes of
migration as operating at the individual level [p. l6ff and

p. 22ff]. However, probabilities at the individual level

would have a low level of accuracy due to lack of sufficient

10

data. Therefore, he concerns himself with constructing "group
probability" of migrating while cautioning that this average
probability has no meaning until the relevant group is identi-
fied. Stone deals with specific socio-economic groups and the
factors that explain their share of certain migration streams.
Earlier the demographic literature was described as the
third path that could lead to the decision that lowering the
level of analysis regarding population characteristics in
place analysis (and stream analysis inferentially) might
make a useful contribution to migration research. Several
examples from the literature were cited because they gave
explicit support to disaggregating migration variables. The
literature also makes implicit suggestions regarding disaggre-
gation. Particular forms of future research are not justified
solely on the grounds that previous writers have explicitly
suggested those forms. Perhaps the most valuable contribu-
tions are developed because many researchers read the basic
premises of earlier writers and draw similar conclusions
regarding follow-up studies. A reading of the major models
in place and stream analysis leads this writer to the con-
clusion that disaggregation of migration variables might be
an informative endeavor even if the previous researchers had

not made the same suggestion explicitly.

Migration Models

 

The following paragraphs will briefly review the major

migration models from Ravenstein to Karp and Kelly with the

ll

purpose of implicitly surfacing the justification for dis-
aggregation of variables in place and stream analysis.

Ravenstein.--In 1885 E. G. Ravenstein presented a paper

 

to the Royal Statistical Society entitled "The Laws of Migra—
tion." Four years later he presented an expanded version to
the Society under the same title. A summary of his conclusion
includes the following points.
(1) Distance: Most migrants move short distances. The
number of migrants going to a particular place decreases
as the distance to that place increases. Centers of
commerce and industry attract persons from greater
distances.
(2) Stages: Migrants locate in new environments in
stages instead of extremes such as moving from moderate
to tropical climates. The inhabitants of the rural
areas immediately surrounding a fast growing city flock
to it. The gaps they leave are filled by migrants from
more remote districts until the city attracts them also.
(3) Streams: Each main stream of migrants (Ravenstein
used the word "current") produces a compensating
counterstream.
(4) Urban-rural differences: The natives of towns are
less migratory than residents of the rural areas.
(5) Predominance of females: There appears to be a
predominance of females among short distance migrants.
(6) Technology: Increases in the means of transportation

and the development of manufacturing and commerce leads

 

 

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12

to an increase in migration.

(7) Dominance of economic motive: The most compelling

motive for migrating is the desire to better oneself in

material terms.

§12£,—-While Ravenstein is generally acknowledged as
having made the first substantial contribution toward a
theoretical statement of the relationships between the vari-
ables in the migration process, George K. Zipf pioneered the
attempt to operationalize migration theory in an appropirate
manner for testing hypotheses and predicting volume of migra—
tion for specific places. Zipf's [1946, p. 677-86] formulation
posited the size of population of City 1 and City 2 as the
attractive forces to migration and the distance between the
two cities as the resistance to migration; or /P1P2/D. The
similarity between formulating migration processes in this
manner and the laws of gravitation in physical science is
obvious. It has led to the Ple/D type of models being
dubbed as "gravitational" or "Newtonian" models.

Ravenstein's theoretical statement points to the
important difference in the migration experience of males
and females. However, Zipf's model does not incorporate
variables to explore the sex specific migration differentials.
This observation is not necessarily a criticism of Zipf's
contribution. He advanced our analytical capabilities and,
obviously, each advance cannot be the final step. Therefore,

the observation that Zipf did not continue the process of

13

specification that Ravenstein suggested can be interpreted
as a direction for future research.

Even though the Zipf model left many questions unanswered,
it has had an important impact on migration theory. Writers
following Zipf have found it necessary to take a position in
regards to P1P2/D type models.

Stouffer.--Samuel A. Stouffer added the important concept

 

of intervening opportunities to the basic relationship of
distance and migration that Ravenstein and Zipf had described
earlier. Stouffer's first paper on the subject was published
in 1940 under the title "Intervening Opportunities: A Theory
Relating Mobility and Distance." He suggested that a general
theory of intervening opportunities could be useful in study-
ing the selections of marriage mates, crime and residence of
criminals, choice of colleges and the use of leisure time.
However, his application of the theory was to residential
mobility. The basic premise of Stouffer's theory is that,
while distance is indirectly associated with mobility,
migration is a function of the spatial distribution of
opportunities. The volume of migrants to City 1 from City
2, for example, is directly prOportional to the number of
opportunities in City 1 and inversely proportional to the
number of opportunities that are closer to City 2 than City 1.
In 1960 Stouffer reformulated the 1940 version of the
intervening opportunities theory in a paper entitled

"Intervening Opportunities and Competing Migrants." This

14

second formulation states that the number of migrants from
City 1 to City 2 (Y) is a direct function of the number of
opportunities in City 2 (X1), and an inverse function of the
number of opportunities intervening between City 1 and City
2 (X3) along with the number of other migrants competing for
the opportunities in City 2 (XC). Therefore, Y is propor-
tional to X1/XBXC.
Stouffer's first intervening opportunities model was
formulated as an alternative to Zipf's distance model where
P1 and P2 represent the population of Cities 1 and 2, and
where D is the distance between the cities. In Stouffer's
conception of migration the total number of out-migrants from
City 1 can be substituted for P1, total in-migrants to
City 2 can replace P2, and "size-effect" variable can replace
D. The size-effect (XM) is defined as the total number of
in-migrants from all other cities to City 2 (X1) times the
total number of out-migrants from City 1 to other cities

(X or XM = XlXO’

O);
Intervening opportunities between City 1 and City 2
(X3) is defined as the total number of potential in-migrants
to City 2 (excluding actual migrants to City 2). A person
moves to a place because there is an opportunity for him there.
The total number of in-migrants therefore represents the total

number of opportunities. In-migrants to City 2 are omitted

because we are looking for an estimate of the number of

opportunities that intervene between City 1 and City 2.

15

Competing migrants (XC) is the total number of migrants who
had moved out of a city and were presumedly looking for a place
or an opportunity to occupy. Therefore, migration (Y) is
a function of size-effect (XM) divided by the product of
intervening opportunities (XC) and competing migrants (XC).

The data Stouffer used to test his second model represented
migrants during 1935-40 for 116 migration streams between 16
large cities and Los Angeles, Denver, Chicago and New York.

Galle and Taeuber.-—In 1966 Galle and Taeuber replicated

 

Stouffer's model of intervening opportunities and competing
migrants. They used 1960 census data on migration from
1955-60 for the same 116 streams that Stouffer studied. Their
results led them to state that Stouffer's model was superior to
models relying on distance alone. The variables in the
Stouffer model were relatively stable over the time between
the 1935-40 migration period to the 1955-60 period. However,
variables involving distance decreased in explanatory power
during the interval.

Stouffer's migration models, and therefore the models of
Galle and Taeuber, were reactions to P1P2/D type of formula-
tions. His reaction challenged a basic conceptual component
of the PIPZ/D models, i.e., distance. Stouffer asserted
that the conceptualization of distance as formulated by Zipf
was of secondary importance. The primary affect of distance
on migration should be conceptualized as spatial distribution

of opportunity. Criticisms of Stouffer, and Galle and Taeuber

16

(e.g., Karp and Kelly, 1971) did not attack the concept of
distance as the spatial distribution of opportunity. The
criticism focused on the operationalization of variables
that measure economic opportunity. In like manner, the
reaction implied in this thesis is not one that rejects
Stouffer's conceptual formulation of distance and migration.
We can agree with the criticisms of Karp and Kelly (to be
discussed) and still posit that the Stouffer models would
benefit from disaggregating the appropriate variables by
age and sex--assuming the availability of data.

The place and stream analysis type of research since
1966 has a direct relationship to the Galle and Taeuber
replication of Stouffer's model. This is the case for
several reasons. First, Stouffer's theory has stood over
time as one of the best attempts to model the migration
process. It is therefore a good starting point for a researcher
trying to improve migration theory. Galle and Taeuber were
replicating the "recognized leader" in migration modeling.
Since they confirmed the leader, they are often mentioned in
subsequent literature pertaining to place and stream analysis.
Second, until recently the only data available to do similar
studies were the 1955-60, or earlier data.

ngry.--In 1966 Lowry published the results of two
migration models he had tested. The first model correlated
the number of migrants going to and from two specific places

with other characteristics of the places. The data were for

17

a sample of 800 migration streams that were drawn from a
total of 8,010 streams of 1955-60 data on SMSAs. The follow—
ing variables were examined:

(1) Number of migrants from place i to place j.

(2) Number of persons in the nonagricultural labor force

at i and j, respectively.

(3) Unemployment as a percentage of the civilian non-

agricultural labor force at i and j, respectively.

(4) Hourly manufacturing wage, in dollars, at i and j,

respectively.

(5) Airline distance from i to j, in miles.

In contrast to the above model, Lowry's second model
took the form of place analysis. In-migrants to a specific
place were viewed as having originated in all other places
in the U.S. Likewise, out-migrants from the place were
depicted as moving to all other places. Estimates of migra-
tion from 1950-60 by age, sex and color were calculated by
Lowry using the Census Survival Method. Data for the fifty-
two largest SMSAs were studied by means of regression analysis.
The variables were as follows:

Net change in population attributable to migration,

referred to as "net migration."

Net change in the number of residents 15-64 years of

age in the absence of migration, referred to as "natural

increase."

Net change in civilian nonagricultural employment.

Net change in the number of Armed Forces personnel.

18

Net change in the number of school enrollees 14-29 years

of age.

Change in median income for "families and unrelated

individuals.”

The basic assumptions of this model were that total volume of
out-migration from place i is a function of the size and
structure of place i's population, and if place i's share of
in-migrants is a function of the size and condition of i's
labor market, then the explanation of net migration to i can
be explained without direct comparison to characteristics of
place i to each other place. We need to know the overall
mobility of the population of the United States (a function
of its size and structure) and the condition of the national
labor market.

Lowry had two purposes in mind when he tested the models
outlined above. First, like other demographers, he attempted
to identify some of the determinants of migration. Second,
he tried to forecast migration in a manner that would be
useful for local planning functions. Lowry's first model
takes the form of stream analysis. It would have been
unwieldly, if not infeasible, for him to gather data on all
his variables for all places in the United States. Lowry
found that place analysis, in his second model, generated
high coefficients of correlation, and it was relatively simple
to implement from a data gathering standpoint. In short,

place analysis appeared to be an effective and practical

l9

forecasting device. Its major shortcoming, according to Lowry,
was that it did not make separate estimates of in— and out-
migration. The dependent variable was the net change in
population attributable to migration.

The relationship of this thesis to the work of Lowry
is clearer than is its relationship to earlier models. It
is not possible to disaggregate all the variables used by
Ravenstein, Zipf and Stouffer into age-sex specific categories.
However, it would be possible, though costly, to obtain 1970
age-sex data on all the variables employed by Lowry, except
airline distance.

Karp and Kelly.--The work of Karp and Kelly [1971]

 

represents a major shift in attempting to construct migration
theory in that (1) they discount much of the findings by
Stouffer, and Galle and Taeuber as being based on specious
correlations and (2) they focus more on the economic structure
of places than the distance between places. The 1971 study
of Karp and Kelly is divided into two parts. Part I is a
test of the general approach found in the P1P2/D and Stouffer
models. Karp and Kelly do not replicate the studies by
Stouffer, and Galle and Taeuber because, in their opinion,
the operational definitions of variables such as size-effect
and economic opportunity lead to specious conclusions in

that the dependent variable (migration) is part of some
independent variables. Economic opportunity and size are

independent variables in the Karp and Kelly test of Stouffer‘s

20

approach, but the definitions of the variables are different.
The variables used in the test were as follows:

(1) Index of climate for destination and origin.

(2) Population size for destination.

(3) Percent unemployed for destination and origin.

(4) Percent families with income under $3,000 for

destination.

(5) Percent engaged in manufacturing for destination

and origin.

(6) Distance.

The test study examined the same migration streams that the
1960 Stouffer study and the 1966 Galle and Taeuber study
examined.

In Part II, Karp and Kelly present another study. The
second study is cast in an ecological framework where the
community is defined as a concentration of differentiated
(basic VS service oriented activities) but functionally
interdependent or complementary activities. The general
hypothesis is that migration represents a response to func-
tional expansion. The hypothesis assumes that migrations
function to balance any disequilibrium in the number of
persons needed to provide a particular function at a demanded
level and the number of persons available locally for that
function. In other words, if more workers are needed in the
service sector of the local economy to meet the demands of
that sector, the needed persons will migrate from a less

dynamic economy.

21

The data for the Part II study represents migration from
1955-60 for 89 SMSAs which had a population of 250,000 or
over in 1960. The independent variables were as follows:

(1) Population size

(2) Population potential

(3) Distance to nearest neighboring SMSA

(4) Distance to nearest largest SMSA

(5) Percent employed in service activity

(6) Basic-nonbasic activity ratio
Karp and Kelly used the data in two ways. The first is place
analysis in that the values for all 89 places are plotted
and regression lines fitted. In this analysis the findings
for an "average" place confirms the hypothesis that net
population growth attributable to migration varies in direct
proportion to the prevalence of conditions requisite for
expansion. The second method was stream analysis. The
results did not confirm the hypothesis, i.e., population
growth attributable to migration is not generally a function
of in-migration from places with a relatively low prevalence
of conditions requisite for expansion.

Like the work of Lowry summarized earlier, the population
variables in the models of Karp and Kelly could be disaggre-

gated by age-sex specific categories.

Methodological Issues of Disaggregation

 

This dissertation on disaggregating migration variables

is a substantive piece of research that pertains to methodological

22

inquiries by Hannan [1970] and Robinson [1950]. A discussion
of the relevant issues on aggregation will be presented here
to demonstrate the methodological context in which this
present work is being conducted. Much of the work on mathe-
matical considerations in aggregation has been done in
econometrics and biostatistics. Hannan applies these consid-
erations to problems of aggregation and disaggregation in
sociological research. He does not discuss the implications
for migration analysis per se, but the relevance of the
issues is not hard to perceive.

The level of analysis of a particular study is labeled
as either micro or macro. A researcher may decide to change
from one level to another. Perhaps only macro data are
available, but the researcher makes inferences about individ-
uals. He has employed the homology thesis which assumes there
is a basic consistency between micro and macro levels. The
structuralist would see consistency from the top down, while
the interactionalist would perceive the opposite.

Before valid inferences can be drawn about one level of
analysis based on results of another level, the consistency
criterion must be satisfied. In short, this criterion is
that there is consistency only when the micro relations,
macro relations and aggregation relations are the same models.
Valid aggregation relations occur only when macro variables
are simple mathematical transformations of corresponding

micro-variables. The consistency criterion is therefore a

23

formalization of the homology thesis. Of course, sociological
models seldom, if ever, fulfill the requirements of consistency.

The essence of the above discussion is that, from a
methodological standpoint, it is not sound to employ avail-
able aggregated data to make inferences to micro relationships.
However, place analysis in migration literature has not
committed this fallacy. The substantive problems of aggrega-
tion addressed in this dissertation are related but different
from the general problem of translating from macro to micro,
or vice versa. All the data employed here are macro. Some
represent the total population while others represent age-sex
specific groups. But none refers to individuals. Nevertheless,
some of the mathematical problems of moving from micro to
macro levels also apply when moving between macro data on
total population and specific groups. Some of these problems
that are addressed in the substantive issues of this research
will be discussed next.

One problem that is addressed in the thesis is that the
range of variation within the variables affects the magnitude
of the correlation coefficients. Of course, the variations
within data for large metropolitan areas is quite wide. To
narrow the range it is necessary to select subgroups that are
relatively homogeneous in regards to migration, i.e., groups
with similar migration propensities.

The second problem that is central to discussions on

aggregation and disaggregation is the apparent necessity to

 

 

 

 

S

 

24

shift levels because apprOpriate data are missing. Early
demographic researchers possessed neither detailed data nor
computer facilities to manipulate data. However, it is
feasible now, though costly, to employ data for subunits

of the population which are relatively homogeneous and thus
have more narrow ranges of variation.

A third problem has to do with the criterion that was
used to select the places for analysis. Place analysis has
utilized data for SMSAs over 250,000 population because data
were available without great costs and inconvenience. There-
fore the aggregation criterion was that only large places
would be chosen. The fact that all the places were large
became a "hidden” Operative variable. This variable should
be defined explicitly. It refers not only to size but also
implies degrees of industrialization, education and cultural

opportunity, etc.

Current Population Surveys

 

While the Current Population Surveys are not a theoreti-
cal source per se, the data that have come from the Surveys
have described the characteristics of migrants in the U.S.
for over two decades. These annual estimates of migration
that began in 1948 have produced consistent findings on
characteristics such as age, sex and employment status. Any
theoretical research; whether it is based on survey methods,
regression analysis, etc.; should consider how its findings

relate to CPS. This dissertation makes frequent reference to

 

25

the Surveys. Therefore, a brief statement about this data
is in order.

The twenty-three annual surveys that have been conducted
since 1948 have asked a sample of the U.S. population where
they lived one year earlier. The sample comprises about 860
counties and independent cities, with coverage in each state
and the District of Columbia. Approximately 50,000 occupied
households are eligible for interview each month. Because
of the relatively small sample, findings are published for
only four broad regions: Northeast, North Central, South
and West. The Surveys report local moves as intracounty
and migration as intercounty. The latter are further
reported as intrastate and interstate.

According to the Surveys, peak mobility rates occur
among persons in their early twenties--the age when children
are going to college, serving in the military, seeking
employment and setting up households of their own. Mobility
rates generally decrease with increasing age. Employment
status, i.e., employed, unemployed, or not in the labor force,
is associated with mobility in that the unemployed are more

prone to move.

Summary

The overall purpose of this dissertation is to determine
if it would be informative to do migration analysis on more
detailed, or specific, levels than are generally found in

demographic literature. The intent of this section on

26

literature and theory is to review the relevant studies and
determine if the thesis topic might make a contribution to
our understanding of migration. It is the writer's opinion
that the thesis tOpic is justified in the literature in that:
(1) Several studies recommend explicitly that migration
data should be disaggregated, e.g., Galle and Taeuber,
Lowry, and Stone.
(2) A review of the major place and stream analyses
leads to the conclusion that, intuitively, it would be
reasonable to expect that more detailed data inputs
would enhance our understanding, and that more detailed
data than what has ever been used before can be provided
from the 1970 census in the near future.
(3) The substantive problems addressed by this disser-
tation must be seen in the mathematical context of issues
on disaggregation as discussed by Hannan [1970]. Just‘
as the consistency criterion must be satisfied before
translating from macro to micro levels of analysis,
consistency must be present before shifting from broad,

macro aggregations to more specific macro levels.

CHAPTER III

METHODOLOGY

Dependent and Independent Variables

 

There is a wide disparity between the type of data that
a researcher would like to have to fulfill his conceptual
criteria and the data that are usually available. The lack of
available data affects research designs of migration studies
just as it does most scientific efforts. All of the models
discussed in the previous section probably would have looked
quite different if the researchers had had all the data at
their use that they wanted. In fact, much of the similarity
among research designs for migration studies is due to the
very limited variety in data that one can employ. The in-
and out-migration tabulations for SMSAs that were reported
in the 1960 census were the most current and most complete
data available at the time of the studies cited above.

The research design of this thesis does not escape the
delemma posed by the absence of preferred data. The data that
were chosen for this study are comparable to some of the
variables used in earlier place analysis type of studies,
e.g.,[Lowry 1966]. It is not considered feasible or

necessary to collect data that would be comparable to all the

27

28

variables used previously in place analysis in order to
address the overall question of this research, i.e., would
lowering the level of specificity in variables aid in under-
standing the migration process? The data for this study
represent variables on migration, economic opportunity and
size of places. These variables do not exhaust the list of
variables that have been used previously, but they are the
central variables in previous studies. If disaggregation
of these variables appears to be a useful exercise, then
disaggregation of other variables could follow.

Migration as the dependent variable(s) is expressed as
rates and absolute values for net migration, in-migration
and out-migration by age and sex. The independent variables
that indicate economic opportunity are expressed by age-sex
specific levels. Those variables are percent unemployed in
the experienced civilian labor force for 1970, number of
unemployed, and median income of persons for 1969. The size
of each place, as measured by the population age five years
of age and over, is an independent variable in correlations
at the level of total population for each age specific level.
A list of the variables with their symbols follows:

(1) NMR

net migration rate
(2) IMR - in-migration rate
(3) OMR - out-migration rate
(4) NMN - net migration number
(5) IMN - in-migration number

(6) OMN - out-migration number

29

(7) INC - median income

(8) UER - unemployment rate of the experienced civilian
labor force, 1970

(9) UEN - number unemployed in the experienced civilian
labor force, 1970

(10) SOP - size of place (Population 5 years of age and

over)
With the exception of the size of place variable, all variables
are broken down by age. All variables are specified by sex
as follows: male plus female, male alone and female alone.
The age categories are ages 5 and over, ages 20-24, 25-29,
30-34, 35-39, and 40-44. It would be feasible to perform
calculations for each five year age group between age 20
and age 75 plus. Data for the variables relating to age
45 and over are not reported exactly the same as data for
ages 20-44. Additional data manipulation and estimation
could generate correlations for ages 45-54, 55-64 and 65 plus.
However, the younger array of age groups provide sufficient
data on which to test the proposed hypotheses. Analysis
of the older ages could be performed if findings from the
thesis suggest such effort would be warranted.

When the first nine variables are specified by six age
groups and three sex specific levels, and when the size of
place variable by sex is considered, a total of 165 variables
are generated. However, we are not as interested in the

number of variables, large or small, as we are in the levels

30

of analysis. There are nine levels of analysis: six age
groups and three sex categories.

An abbreviated depiction of the variables that will make
up the thirty-six equations can be presented by employing

the symbols of variables listed previously. Such a depiction

 

 

 

 

follows:

Equations Levels of Analysis

Sex Age

NMR = UER + INC + SOP M+F 5 +
IMR = " " ” M 20-24
OMR = " " " F 25-29
NMN = UEN + INC + SOP 30-34
1}”; = II II II 35-39
OMN = ” " ” 40-44

 

 

 

For example, the second equation for the male population is
NMR (males age 20-24) = UER (males 20-24) + INC (males 20-24)

+ SOP (Pop. 5+)

Multiple and simple correlation analysis are the methods
used to examine the relationships among the dependent and
independent variables. When dependent variables are matched
with their appropriate independent variables (i.e., specific
levels of age-sex, whether measurement is by rates or numbers)
a total of 108 multiple regressions can be derived. Since

the coefficient of multiple determination (R2) indicates the

31

amount of variance that is "explained" by the combination
of independent variables it is often cited in demographic
literature to evaluate the accuracy of prediction models.
An equation for total population that has a high R2 may not
maintain the high level of explanation when age-sex specific
data are substituted in the equation. We are not attempting

to construct prediction equations with high R23, but we

2 behaves at various levels.

do want to observe how the R

The most informative analysis should take place with
the simple order correlations and the unstandardized regres-
sion coefficients that are generated at each age-sex level.
There will be eighteen matrixes of simple correlations and
an equal number of sets of regression coefficients.

Obviously there are many population characteristics
that could be selected for disaggregation. Age, sex, race,
employment, income, occupation and education are character-
istics most often employed in demographic analysis. The
variables that are disaggregated in this thesis were chosen
for two related reasons. First, the variables have been
found to be associated with migration in previous studies.
Second, data on the variables are available.

The theoretical rationale for selecting the proposed
variables, and for disaggregating by age and sex is supported
by the citations in the literature and theory section of

this proposal and by repetitive findings from the Current

Population Surveys. Ravenstein noted the predominance of

32

females among short distance migrants. While Lowry did not
disaggregate all variables by age and sex, his analysis led
him to the conclusion that such disaggregation would be
beneficial. Current Population Surveys [1972] report that
peak mobility rates occur among persons in their early
twenties when children normally leave parental homes, and
that mobility rates generally decrease with increasing age.
CPS reports little variation in mobility between males and
females. There is a small predominance of females in short
distance movers while males demonstrate a similar margin

of dominance in long distance migration.

Economic opportunity is a broad variable that has been
central to most attempts to explain migration. This broad
variable has been operationalized by different variables.
Unemployment, or its counterpart, has had more success than
income as a correlate of migration. Ravenstein noted the
importance of economic motive in migration; Stouffer Opera-
tionalized economic Opportunity in terms of the number of
competing migrants; Lowry correlated the size of the non-
agricultural labor force; while Karp and Kelly studied the
economic structure of the places of origin and destination.
Income was a variable in the formulations of Lowry, and Karp
and Kelly. The findings of CPS show that higher earners
(over $7,000 per year) tend to migrate farther than low
earners. The value of this finding is not clear because
the collapsing of income categories into over $7,000 and

under $7,000 may conceal complex relationships between income

33

and mobility. Income has had a low explanatory value in

the past. However, it is useful for our purposes because

we want to see if its value changes at different levels.
Suppose we find coefficients for income that range between
.35 and zero for the various age-sex levels. None of the
coefficients is high. But the fact that the coefficients
vary over age-sex categories is important because it suggests
that aggregated data for total population do not represent
all the components.

The Zipf formulation used size of place and distance
as the only independent variables. Other analysts mentioned
above retained size of place in their calculations but gave
it a less prominent role. Persons probably are not attracted
to a place by size per se, but places take on certain
attributes at various states of growth that are attractive
to migrants. Unfortunately the research design of the CPS
is not appropriate for drawing conclusions about the relation-
ship between size of place and migration.

Migration is stated in terms of net, in- and out-migration
because all three forms are used in migration models. In- and
out-migration are, of course, essential elements to stream
analysis and they are desirable in place analysis. Net
migration can be used in place analysis, but it is a poor
variable since a small net value can result from either

small or large volumes of offsetting migration.

 

u—r‘;

 

34

Unemployment and migration are measured by rates and
absolute values because there is a lively discussion in
demographic literature over the best procedure for calcu-
lating rates, and whether rates or numbers are more appropriate.
It is not the intention of this paper to address that dis-
cussion. However, the rates used here are in conformity
with the most widespread practice of calculating rates (see
section on data sources). The question of using rates or

numbers is addressed by presenting both.

Hypotheses to be Tested

 

The general expectation is that correlations of the
dependent variable, migration with the independent variables
vary at age-sex specific levels as compared with the total
population age five years old and over. If these expecta-
tions are confirmed in the study we would have additional
evidence to corroborate (1) our intuitive sense, and (2) the
related findings from demogrpahic literature cited earlier
that lowering the level of specificity in migration analysis
would be informative. No attempt will be made at this time
to state how the correlations for one age group might vary
from the correlations for the total population. The principal
interest is whether there is variance because its presence
would suggest that the aggregated level for the total popula-

tion does not accurately represent its component parts.

35

Three hypotheses that incorporate the general model
of expectations with operational variables have been con-
structed. The first two hypotheses pertain to the variables
that are indicative of economic opportunity. Unemployment
(Hypothesis 1) is often used as an indicator of the economic
opportunity of a place. There is general agreement that
migrants are attracted by favorable employment conditions
[Lowry, 1966] but unfavorable conditions are not sufficient
to drive migrants from a place, except extreme unemployment.
Therefore, we would expect that:

Hypothesis 1: Unemployment, as measured by numbers

and rates, is correlated with migration, but

the correlations vary between age-sex levels

of analysis. The degree and direction of
correlations of unemployment and net, in- and
out-migration are as follows: net and in-migra-
tion have relatively high negative correlations,
and out-migration is a relatively low positive
correlation.

Median income typically accounts for only a small
portion of the unexplained variance in migration. Therefore,
it can be expected that:

Hypothesis 2: Median income is correlated with
migration, but the correlations vary between
age-sex levels of analysis. The degree and
direction of correlations of income and net,
in- and out-migration are as follows: net and
in-migration have relatively low positive
correlations, and out-miration has a relatively
low negative correlation.

Hypotheses l and 2 deal with the relationship between

migration and the economic variables. The last hypothesis
pertains to the relationship between the various forms of the

dependent variable. There has been substantial interest

36

expressed in the demographic literature about the relation-
ship between in-migration and out-migration [Miller, 1967]
which would lead us to expect that:
Hypothesis 3: In- and out-migration, as measured
by rates or numbers, are highly correlated

with each other, but the correlations will vary
between age-sex levels of analysis.

Data Sources

 

The migration data came from Migration for State

 

Economic Areas, PC(2)-2E, Table 2; Bureau of the Census, 1970.

 

The data elements from this source that were utilized are
the number of in-migrants and out-migrants by age and sex
as specified earlier, and the size of the corresponding
cohort in 1970. This latter item is adjusted as described
below and becomes the base for calculating three rates: net,
in-migration and out-migration. The net migration is the
sum of in- and out-migration. The population age 5 and over
by sex was used as the size of place variable for each
age level.

The base of net, in- and out-migration rates is calcu-
lated by subtracting the amount of in-migration from the 1970
census for a particular age group and adding the out-migration
fOr that age group. The volume of migration by age and sex
is divided by the appropriate base and multiplied by a
thousand to derive a rate per thousand population. The
rationale for calculating the base as described above for

out-migration is that the base estimates the population that

37

was exposed to the risk of migration for the duration of
the period 1965-70. Deaths that occurred during the period
are excluded by starting with the size of the cohort in
1970. Births during the period are excluded because only
the population at least 5 years of age in 1970 are included
in the calculations.

Rates typically follow the practice of taking the
population exposed to risk of particular occurrences, e.g.,
migration, as the base. This practice cannot be followed
very well in the case of in-migration since theoretically
the whole world is at risk of in-migrating to a place. The
population of the place of destination usually becomes the
base for in-migration. The rationale for using this figure
is, first, a matter of practicality since it would be
exceedingly difficult to use the population of the places
of origin for in-migrants to a particular place. Second,
apparently, the population at the place of destination is
"indicative" of the attraction a place exerts upon the
migration process. For these reasons, then, I have chosen
to use the same base for in-migration that was used for
out-migration. The rationale for using the same base figure
for net migration that was used for in- and out-migration is
simply that it has become the standard method. It has
become standard because it provides a consistent base that
is practical to use, and because a better base has not been

devised. The fact that net migration is the balance of in-

38

and out-migration means that net data has little value in
research and a theoretically pure base is not available.
The economic data for the independent variables are

published by the Bureau of the Census in Detailed Character-

 

istics, PC(1)-D, 1970, Tables 164 and 193. These data are
available for SMSAs that had a population of 250,000 and
over in 1970. The migration data are for all state economic
areas. The boundaries of metropolitan state economic areas
correspond to SMSA boundaries except where SMSAs have added
or deleted counties since 1967. In some cases it is possible
to sum migration data for two or more state economic areas to
equal one SMSA. SMSAs in New England are drawn around city
boundaries instead of counties. Therefore, New England
states were excluded from the analysis to prevent having
a sprinkling of city units in with the county-based data.

In 1970 there were 125 SMSAs with population of 250,000
or over. Regression analysis for fifty-two of these places
was precluded because (1) data on the independent variables

from Detailed Characteristics were not organized by the same

 

boundaries as were migration data, or (2) SMSAs were drawn
around city boundaries. The following five places were
excluded from analysis due to their high levels of military
activity: San Diego, Norfolk, Honolulu, San Antonio, and
El Paso. Finally, New York was deleted because its extreme
values would distort the regressions. New York had a 1970 '

population that was four and one-half million larger than

39

the second ranked place of about seven million residents.
Appendix Table 4 identifies the sixty-four places that were

analyzed.

CHAPTER IV
FINDINGS

It is expected that the simple and multiple regression
coefficients generated in this research will show a marked
difference across age-sex specific levels of analysis. The
correlations for the population age five and over will vary
from the specific age groups, and specific age groups will
vary from each other. There will be variation when correla-
tions for males alone and females alone are compared with
each other or with the correlation based on aggregations of
male plus female. This model of expectations does not
suggest that particular correlations will be positive or
negative, nor does it mention particular forms of the
dependent or independent variables. It is intended as a
summary model. Therefore, the results pertaining to these
general expectations will be presented in the "Summary and
Conclusion" section after the more specific hypotheses have
been discussed.

Hypotheses one and two are stated in two parts. The
direction and degree of correlation between a form of the
dependent variable (net, in- and out-migration) and the
independent variable are predicted. This prediction is

enlarged by stipulating that there will be differences in

40

41

correlation between age-sex levels of analysis. The form of
the third hypothesis is the same except the hypothesized
relationship is between two forms of the dependent variable:
in- and out-migration.

Findings in terms of simple correlation coefficients
(r) and unstandardized regression coefficients will be
presented to evaluate each hypothesis in regard to (l) the
direction and degree of correlation and (2) the variation at
specific levels. The r statistic measures the degree of
relationship between two variables. In contrast, the
regression coefficient can be interpreted as the amount of
change in the dependent variable that is associated with
change in the independent variable while controlling for the
other independent variables. Together these two statistics
will provide evidence for accepting or rejecting the hypotheses.

The correlation coefficient of multiple determination
(R2) measures the amount of variation that is explained by
all the independent variables acting together. Its value
ranges between zero and 100. The R2 cannot be used to
evaluate the directional part of hypotheses one through three
since it does not indicate the direction of correlation.
However, by comparing the R2 values that are generated from
numbers and rates for the various age-sex groups, we can
evaluate the prediction that there will be variance in the
reported statistics across age-sex levels.

A general comment about how the coefficients in the

42

analysis will be interpreted is appropriate at this point.
There is no doubt that correlation and regression analysis
are powerful tools that can be employed in social science;
though not with the same level of precision found in physical
science. However, the proper interpretation of coefficients
is not always clear. A cautious approach to interpreting
the coefficients generated in this research will be employed.
Very little importance will be attached to the reported
coefficients for a particular age-sex group. Instead, the
focus will be to identify patterns that emerge in the
coefficients.

A standard format of reporting the findings for the
three hypotheses will be employed so the citing of many
coefficients will be an organized flow of statistics.

First, the results that pertain to the direction of correla-
tion will be cited. This will include the simple and regres-
sion coefficients of correlation for the male plus female
population age five and over. The coefficients based on
absolute numbers will precede those calculated from rates.
Next, the hypotheses will be evaluated by comparing age
specific coefficients, including R2, with coefficients for
the aggregated population. Finally, sex specific coefficients
will be examined to determine if there is a variance in
results for males plus females in contrast to males alone
and females alone. Reporting for the third hypothesis will
follow a similar format except only simple correlation

coefficients will be cited.

43

The data for this study refer to places that have total
populations of 250,000 and over. However the figure that is
used as the size of place variable for the smallest place
is less than the 250,000 because only the population age 5
and over is included. Births occurring since 1965 are not
included in the migration data. The smallest place in the
regression analysis had 225,026 persons age 5 and over; the
largest place had 6,374,184. The mean size of place was
382,127. There is strong evidence in the demographic litera-
ture [Miller, 1967] that SMSAs which have high in-migration
also have high out-migration. The findings presented in this
thesis support this view. The male plus female population age
5 and over had a meah in-migration of 53,580; a mean out-
migration of 50,090; and mean net migration of 3,490.

Standard deviations were as follows: 47,241 for in-migration,
52,248 for out-migration, and 22,712 for net migration.

The above descriptive statistics demonstrate that, due
to the off-setting nature of in- and out-migration, the
average place in this study has a very small absolute number
of net migrants in comparison to the population over 5 years

of age; or as compared to the number of in- and out-migrants.

Hypothesis 1

 

Unemployment, as measured by numbers and rates, is
correlated with migration, but the correlations vary between
age-sex levels of analysis. The degree and direction of

correlations of unemployment and net, in- and out-migration

44

are as follows: net and in-migration have relatively high
negative correlations, and out-migration has a relatively

low positive correlation.

Net Migration

Summary Findings

 

The correlation coefficients provide a rather weak
confirmation of the prediction that net migration has a
relatively high negative correlation with unemployment. The
prediction that correlations vary between age-sex levels is
confirmed.

First, the simple and regression coefficients in Tables
1 and 2 that pertain to the male plus female population will
be reviewed to support the above finding on the negative
correlation between net migration and unemployment. Next,
the r values and regression coefficients will be examined
along with the R2 values in Table 3 to support the statement
about variations across age-sex groups.

The simple correlations (Table l) for the male plus
female population indicate the negative relationship between
net migration and unemployment. The coefficients based on
rates are preferable to those based on absolute values
because the former provide a control for the effect of the
size of place.

The 25-29 age group is generally an anomaly throughout
this thesis. The reason is that this age cohort is different

occupationally from the others. They are more prone to

45

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 1. Simple Correlation Coefficients (r) of Net Migration and
Unemployment.
Sex Ages
5+ 20-24 25-29 30-34 35-39 40—44
Male plus
a: Female —.44 -.16 .52 —.18 -.40 -.40
“82
:3
3‘” Male -.46 -.47 .69 -.06 -.44 -.42
m8
Qz Female -.43 .00 .24 -.32 -.35 -.38
Male plus
Female —.03 .00 -.09 -.10 -.09 -.03
U)
LL]
3 Male .03 .ll -.06 -.12 -.09 .00
Female -.11 -.20 -.O7 -.15 -.O9 -.06
Table 2. Unstandardized Regression Coefficients of Net Migration on
Unemployment Controlling for INC and SOP
Sex F Ages
5+ 20—24 25-29 30-34 35-39 40—44
Male plus
E; Female - .02 .10 2.58 2.05 .79 .49
2
23%? Male .87 .41 1.72 1.53 .44 .36
a:
a Female 1.83 .00 3.53 2.59 1.41 .34
Male plus
Female -2.43 -5.10 -l.04 -4.52 -2.41 - .61
no
u:
3 Male 1.37 -1.98 -5.44 —7.85 -5.42 --1.40
Female «4.44 -20.97 -2.00 -5.67 -2.18 -1.56

 

 

 

 

 

 

 

 

46

migrate because (1) some are unskilled members of the labor
force who are laid off first, (2) some are rising professionals
who have a history of migration to better opportunities and

(3) they have fewer financial and emotional ties to particular
places. The 20-24 group share many of the above migratory
influences. In addition they are also affected by military
and college participation. These trends have been documented
repeatedly by the Current Population Surveys.

Table 1 reports an r value of .52 for age 25-29 while
all other age groups have negative values. This anomaly is
created because very large places are able to retain a large
number of net migrants in this age due to the diverse oppor-
tunities and attractions of these major economic and cultural
centers. A high number of unemployed will not affect all
new comers alike because, for many, their particular financial
well being is not influenced by conditions in the dominate
labor market of the place. We see that the anomalous condition
ceases when size of place is controlled by inputing rates
into the regression.

Now we will consider the hypothesized relationship
between net migration and unemployment as measured by the
unstandardized regression coefficients for male plus female
age 5 and over in Table 2. The regression coefficients based
on numbers are positive except for the population 5 and over
WhiCh has an BXtremely small coefficient. In contrast, the

coefficients of rates are all negative. Note also that the

47

regression coefficients of numbers are in the opposite
direction from their counterparts of simple coefficients,
except for the 25-29 group. The reason for the inconsistency
is obviously rooted in using absolute values in the regression
since the simple and regression coefficients of rates are
consistent. The problem is caused by multicollinearity
between the independent variables of unemployment number (UEM)
and size of place (SOP). The correlation coefficient (r)
between these variables is very high for all ages; an average
0f .90 for male plus female (see Appendix).

Even though the intercorrelation of the independent
variables affects the regression coefficients, there is not
a necessary, predictable relationship between the simple
correlations and the regression coefficients. These two
measures will usually agree in regard to the direction of
correlation, but they may take different signs. The following
example demonstrates how the r statistic may have the opposite
sign of its counterpart of regression coefficient. This
example was developed by Tom Obrimsky, statistical consultant
for the Computer Institute for Social Science Research,

Michigan State University.

 

Given:

1 3 2 X = 2 S - /273
2 2 1 2 x2

3 1 0 1X2 = 10/3

 

 

 

, _ 1 2
C°mP“te- rxlx2 " s T

=-1

Solve for b2 and b3 to substitute in the equation:

X1 = b2X2 + b X ( + error term)

3 3
b (i i ) (i i ) 14 8
2 2 2 2 3
L t b =[ ; M = 0:
8 1b3 [(x3x2) (x3x3)] [8 5:]

The constant column matrix would be:
I
c = (xlxz) = (IOJ
x1 (X1x3) 4
14 8‘ b2 = 10
We have: Mbb = CX1 = 8 SI b3 4

So: 14b2 + 8b3 = 10 Solution: (b2 = 3; b3 = -4)

8b2 + 5b3 = 4

 

Note that b2 = 3, and yet rx1x2 = -l

The above example uses two independent variables whereas
there are three independent variables in each of our equations.
Income has low explanatory power in this research so it can
be ignored for the sake of illustrating why the simple corre-
lation and regression coefficients took opposite signs in
Tables 1 and 2. Of course, income has varying levels of
influence in the equations that are generated, and there are

varying levels of multicollinearity present. Therefore, a

49

simple statement that neatly describes the relations between
all instances of the r values and the regression coefficients
is not feasible.

A pattern of shifting signs does not exist for coeffi-
cients calculated for rates because multicollinearity is
eliminated or reduced in the process of calculating rates.

It will be preferable to give more authority to the coefficients
based on rates.

There are three problems with the data of this research
that should be kept in mind when evaluating the coefficients.
The first two are the off-setting nature of net migration data,
and the problem of multicollinearity. Both have been discussed
already. The third was mentioned in the "Literature and
Theory" section as an aggregation criterion. It will be
discussed further now. The method of calculating regression
coefficients controls for the influence of other independent
variables. Size of place is therefore "controlled" in all
regression coefficients that are cited in this study. However,
the control ranges from about 250,000 to about six million
which are the parameters of the size of place variable. An
uncontrolled influence of size remains in that all the places
are relatively large. Any demographic characteristic that is
associated with large places is going to influence our
regression coefficients. In other words, the control that

is built into these regression coefficients refers to relative

50

size of the places under analysis as compared with each other.
Largeness per se is not controlled.

The findings presented in Tables 1 and 2 strongly con-
firm the prediction that the correlations will vary between
age-sex levels of analysis. Notwithstanding the danger of
misinterpreting the correlations based on numbers, the
correlations of absolute values can be employed to depict
variations at specific levels compared with the total popula-
tion. Simple correlations of the male plus female population
over age 5 that were calculated from number range from -.44
to .52 for the various age groups. Male and female coeffici-
ents vary from each other and from coefficients for aggregated
data on both sexes. Males and females age 20-24 display more
variation than any other age group. Males report an r of
-.47 as compared with a zero value for females. Coefficients
(r) of net migration rates and unemployment rates display a
similar range of variation between age-sex levels. Again the
20-24 year old males and females deviate furthest from their
aggregate.

A thorough explanation of each reported variation is not
the goal of this dissertation. However, a plausible explana-
tion of the male-female deviation at age 20-24 can be derived
from the pattern of coefficients and from what we know about
employment opportunities of the young working ages. Females
age 20-24 display a higher negative association between net

migration and unemployment than do either other female ages

51

or any male groups, especially males 20-24. While this
observation is equally true for in-migration, it does not

hold for out-migration where males and females are about equal.
Apparently the occupational structure, and therefore the
mobility patterns, for young females is different from that

of older females and all ages of males. Young females are
more likely to be found in relatively unskilled service jobs.
In contrast, the influence of unemployment constrains young
male migrants less.

The regression coefficients (Table 2) also vary by
age-sex levels. Correlations for male plus female (numbers)
range from -.02 to 2.58. While the values based on rates are
different from those based on numbers, the range of variation
is about the same; -2.43 to -5.10. It was mentioned previously
that females age 20-24 deviated from their male counterparts
and from all other categories.

Regression coefficients equal the covariance of the
dependent variable (Y) and the independent variable (X)
divided by the variance in X. The coefficients indicate a
complex set of relationships among the variables that include:
(1) amount Y changes in relation to X, (2) direction of change,
(3) variation within X and Y, and (4) other Y variables that
are controlled. Since the age groups employed in this study
may be quite different from each other in terms of the above
mentioned influences on the regression coefficients, a

comparison of coefficients across age-sex categories is

52

limted. It is appropriate to compare direction of correlation,
but little can be said about the numerical values attached to
the sign of correlation. A regression coefficient of 4 in
one age group is not necessarily better than a coefficient of
2 for the same variable in another age. In contrast, an R2
of .90 is better than an R2 of .70.

When findings based on regression coefficients are
discussed in this dissertation the direction of correlation
and the range of values will be cited. The rationale for
citing the range, even though coefficients for different
age-sex groups cannot be compared directly, is that the range
indicates the groups vary in regard to the set of relation-
ships among variables that create the coefficients. If the
amount and direction of changes in Y for each unit of X, the
variation within X and Y, and controlling for other X variables
vary across specific groups then there is evidence that we
must disaggregate in order to measure the relationships
among variables for each group.

The coefficients of multiple determination (R2)
presented in Table 3 show that the independent variables have
little value for explaining migration. However the values are
useful for the purpose of this research because they show
that the independent variables have varying levels of explan-
atory power at different age-sex levels of analysis. The R2
statistic for male plus female ranges from .15 to .34 for the

net number of migrants. The range for the net migration rate

53

is zero to .10. Coefficients for males and females, respec-
tively differ from each other and from the aggregated male
plus female coefficients.

Table 3. Coefficients of Multiple Determination (R2) of net migration
on Unemployment, INC and SOP.

 

 

 

 

 

Sex Ages
5+ 20-24 25-29 30-34 35-39 40-44
Male plus
9, Female .25 .15 .34 .26 .23 .22
9‘2
:3
3% Male .30 .42 .53 .30 .34 .29
U)
a Female .32 .00 .25 .31 .25 .22
Male plus
Female .02 .10 .03 .01 .01 .00
m
2‘ Male .04 .26 .19 .08 .05 .02
Female .04 .14 .01 .03 .04 .05

 

 

 

 

 

 

 

 

In Migration

Summary Findings

 

The correlation coefficients provide a rather weak
confirmation of the prediction that in-migration has a relatively
high correlation with unemployment. The prediction that
correlations vary between age-sex levels is confirmed.

The r coefficients based on absolute values in Table 4
are high positive correlations because of the largeness of the
analyzed places as discussed earlier under the section on

net migration. It will be recalled that the comparable

54

coefficients for net migration were moderately high and
negative. This condition resulted from the combined influences
of largeness per se of the places and the offsetting effect
of in- and out-migration. The coefficients for in-migration,
and later out-migration, are high and positive because the
offsetting effect has been eliminated, but the largeness
remains. Large places have high numbers of in-migrants and
unemployment because by definition they have many incidents
of almost all social phenomena. Therefore large positive
correlations result when the absolute number of in-mdgrants
is regressed on the number of unemployed. These r values are
not useful for determining the direction of association
between in-migration and unemployment, but they can be used

later to demonstrate variation of correlation at age-sex

 

 

 

 

 

levels.
Table 4. Simple Correlation Coefficients (r) of In-Migration on
Unemployment.
Sex A es
5+ 20-24 25-29 30—34 35-39 40-44
Male plus
E Female . 76 . 59 . 87 . 82 . 80 . 78
3 ‘3 Male . 81 . 75 . 86 . 79 . 78 . 78
U)
5 a Female . 73 .55 .88 .85 .84 . 79
Male plus
Female .08 .11 -.07 -.16 -.13 -.01
U)
E; Male .15 .18 -.03 -.10 -.04 .15
Female .09 .00 .302 -.10 -.O3 .02

 

 

 

 

 

 

 

 

55

Most of the simple coefficients based on rates (male
plus female) in Table 4 have low negative values. Only the
total population and ages 20-24 have low positive values.
These coefficients are certainly very low and support only
a weak confirmation of the hypothesized relation between
in-migration and unemployment. In fact, more credence should
be given to the observation that four out of the six categor-
ies have negative signs instead of the degree of correlation.
Regression analysis, in general, is such that many factors
that are external to the question under study can affect a
particular coefficient. Therefore, we should refrain from
getting excited when one coefficient confirms our prejudice.
Instead we should look for patterns in the results.

The low values in Table 4 do not refute the established
finding that in-migration is negatively associated with
employment opportunity. As mentioned earlier, metropolitan
areas have relatively diverse economic bases. Unemployment
in even the dominate labor market will not preclude migration
to other sectors of the market, or to sectors such as military
and college participation which are mostly independent of
employment cycles. This dissertation looks at disaggretation
by age and sex. Disaggregation should also be pursued by
occupational categories and by stratifying places in homo-
geneous groups--not necessarily by size.

Regression coefficients in Table 5 are consistent, in

general, with their counterparts of simple coefficients in

56

the preceding table. Most of the categories that are
negative in one form of correlation also indicate a negative
relation in the other form. Obviously, the numeric value
attached to the sign of correlation varies between simple

and regression coefficients. The variance results because

the range of values that each statistic may take is different,
and because the two statistics measure different relation-
ships. Simple correlations may range from -1 to +1. Regres-
sion coefficients are not limited to such a definitional
parameter. In addition, the regression coefficients here have
controls for income and size of place variables which the r
values lack. Multicollinearity does not manifest itself in
opposite signs between r and regression coefficients as it

did in net migration. However, it is preferable to give
limited authority to regression coefficients based on absolute
numbers.

Table 5. Unstandardized Regression Coefficients of In-Migration on
Unemployment Controlling for INC and 80?.

 

 

 

 

 

Sex Ages
5+ 20-24 25-29 30-34 35-39 40-44
Male plus
EH Female .79 - .12 1.99 1.59 1.12 .85
§§ Male .77 .30 1.23 .34 - .40 .04
£2 Female 3.64 - .16 3.08 2.57 1.82 .60
Male plus
Female 3.81 1.46 - .13 -4.84 - .28 4.29
g Male 8.38 1.80 -2.24 -8.76 -3.75 9.23
5 Female 3.02 -17.15 2.80 -5.26 .44 1.08

 

 

 

 

 

 

 

 

57

The results in Tables 4 and 5 vary across age and sex
groups. Simple correlations of absolute values for male
plus female range from .59 to .87 with all the five year
specific age cohorts varying from the aggregated population
5 and over. Correlations (r) of in-migration rates and
unemployment rates for males plus females range from -.16 to
.11. The total population and one age specific group (20-24)
have positive signs in contrast to the negative values for
other ages. Male and female values, respectively in Table 4,
vary from each other and from values for the aggregated male
plus female populations.

Regression coefficients determined from absolute numbers
also vary by age-sex categories. The 20-24 age has a
coefficient of -.12 while other ages range as high as 1.99.
None of the separate male and female values approximate each
other or their aggregate. Similar patterns of age-sex
variance are found among the regression coefficients of rates
in the lower panel of Table 5.

It was noted earlier that the coefficients of rates
in Tables 4 and 5 for ages 25-44 are consistent with our
general understanding that in-migration is negatively
associated with unemployment while the total population and
age 20-24 represent slight anomalies. This pattern can be
explained in that the older ages are comprised of more
stable and homogenous labor participants. Whereas age 20-24

is less homogeneous and consists of young working ages,

58

military and college population. In addition to the
disparate population in the 20-24 ages, the total population
has children, older working ages, retired persons, housewives,
etc. Therefore these two relatively nonhomogeneous groups do
not respond to labor market influences as do groups that

are predominately stable and employment oriented.

The R2 statistics (Table 6) calculated from numbers and
rates contain the degree of variation found in the simple
correlation and regression coefficients. The rate of
in-migration, which is more relevant than the number,

2

produces R values that range from .04 (males 25-29) to .37

(males 20-24).

Table 6. Coefficients of Multiple Determination (R2) of In—Migration
on Unemployment, INC and SOP.

 

 

 

 

 

Sex Ages
5+ 20-24 25-29 30-34 35-39 40-44
Male plus
Female .69 .71 .81 .72 .68 .65
m (D
53‘: Male .71 .75 .84 .76 .71 .69
U)
a; Female .71 .71 .83 .75 .72 .67
Male plus
Female .07 .15 .06 .10 .11 .09
U)
I!)
5 Male .13 .37 .04 .11 .10 .09
Female .08 .17 .06 .11 .13 .13

 

 

 

 

 

 

 

 

59
Out-Migration

Summary Findings

The data provide a weak confirmation of the prediction
that out-migration has a relatively low positive correla-
tion with unemployment. The prediction that correlations
vary between age-sex levels is confirmed.

Simple correlations of the number of out-migrants and
the number of unemployed (Table 7) are comparable in direction
and degree to correlations of the number of in-migrants and
unemployment in Table 4. The reason for this similarity of
correlation was stated earlier. Large metropolitan places
experience high volumes of both in- and out-migration. And,
of course, these places have many persons unemployed simply
because the places are large. When large positive numbers
of out-migrants are regressed on large positive numbers of
unemployed the result is high positive coefficients. These
coefficients are not appropriate for addressing the hypothe-
sized relationship of the degree and direction of correlation

between out-migration and unemployment.

The correlation coefficients based on rates are in
line with the hypothesis. However, two categories of male
plus female pOpulation (30-34 and 35-39) have negative
coefficients. Two other groups (25-29 and 40-44) have
extremely small positive coefficients. These negative and

small positive correlations are not sufficient to reject the

60

hypothesis since almost all the other correlation coefficients
of rates support it. The negative correlations and the very
low positive correlations for ages 25-44 can be accounted for
by the fact that persons are more prone to migrate to
economic opportunity than they are to leave a place when
opportunity sours. This observation is particularly relevant
for the older working ages which have developed ties to a
place. However, this explanation should be considered
tentative and of tertiary importance to the goal of the
dissertation which is to demonstrate whether or not lower
levels of specificity in place analysis should be pursued.
Even though we know that older ages have stronger ties,

we would want to analyze data on variables other than just

income and size before a regression model is attempted.

 

 

 

 

 

Table 7. Simple Correlation Coefficients (r) of Out-Migration and
Unemployment.
Sex Ages
5+ 20-24 25-29 30-34 35-39 40-44
Male plus
Female .88 .67 .85 .86 .91 .91
583
Fan: Male .91 .89 .82 .82 .89 .90
‘38
U)
E 2 Female .86 .64 .90 .92 .94 .93
Male plus
Female .19 .34 .01 -.14 -.11 .01
U)
2’ Male .23 .26 .04 -.02 .04 .24
Female .30 .41 .11 .00 .05 .10

 

 

 

 

 

 

 

 

61

The regression coefficients of rates in the lower panel
of Table 8 support the conclusion that out-migration is
positively associated with unemployment. The small negative
r value for age 35-39 in Table 7 changes to a positive value
when income and size of place are controlled for in the
regression coefficient of rates. The preceding age (30-34)
keeps the negative sign for the regression coefficient as it
had in the simple correlations. Much more detailed analysis
on each age group would have to be done before one would

want to defend a particular coefficient as the most accurate

measurement of change in Y for a particular X.

 

 

 

 

 

Table 8. Unstandardized Regression Coefficients of Out-Migration on
Unemployment Controlling for INC and SOP.
Sex Ages
5+ 20-24 25-29 30-34 35-39 40-44
Male plus
Id Female .82 - .22 - .58 - .45 .33 .36
SE
.3
8% Male - .lo — .10 - .48 -1.18 - .85 - .31
a Female 1.81 - .16 - .45 - .02 .41 .26
Male plus
Female 6.25 6.56 .95 - .33 2.11 4.85
U)
E Male 7.02 3.75 3.24 - .98 1.67 10.52
Female 7.46 3.81 4.84 .40 2.61 2.62

 

 

 

 

 

 

 

 

The above discussion pertains to the direction of

correlation between out-migration and unemployment.

Results

in Tables 7 and 8 provide stronger confirmation that these

62

correlations vary at age-sex levels. Simple coefficients of
absolute numbers for the male plus female population range from
.67 for the 20-24 category to .91 for both 35-39 and 40-44
years old. When male plus female are disaggregated they vary
from each other and from the aggregated results. The same
pattern of variance is found in the simple correlations based
on rates. The r value for age 30-34 is -.14 as compared to

.34 for the 20-24 group. Males and females differ from each
other and from their aggregate.

The problem of multicollinearity is evident more in
regression coefficients on out-migration than it was for
in-migration. Half of the age groups shift signs when r
coefficients are compared to regression coefficients. It is
clear from the correlation of the independent variables SOP
and UEN that multicollinearity has to be considered when
coefficients are interpreted. It is not clear exactly how
much influence multicollinearity exerts. Regression coeffi-
cients are a measure of complex relationships. Care must be
exercised when it comes to interpreting any value that
purports to summarize such complexity into a single figure.
In short, limited credence should be given to the regression
coefficients of absolute numbers.

Regression coefficients of rates for the male plus
female population range in value from -.33 to 6.56. These
numerical values cannot be compared to each other as simple

correlations can, but they do indicate that the covariations

63

of X and Y, and the variations within X are different at the
age-sex level.

R2 values (Table 9) for out-migration are comparable
to those reported for in—migration (Table 6). When high
volumes of out-migration are regressed on large absolute
numbers of unemployment, high positive coefficients result.
These coefficients decrease substantially when rates of
out-migration and unemployment are used. Even though there
are age-sex differences in the R2 values these differences
are not great.

Table 9. Coefficients of Multiple Determination (R2) of Out-Migration
on Unemployment, INC and SOP.

 

 

 

 

 

Sex Ages
5+ 20-24 25-29 30-34 35-39 40-44

Male plus

Female .94 .95 .89 .89 .89 .91
Male .94 .98 .89 .91 .91 .93
Female .95 .96 .92 .91 .92 .93
Male plus

Female .15 .23 .15 .14 .15 .15
Male .17 .23 .29 .10 .09 .12
Female .18 .37 .18 .15 .15 .14

 

 

 

 

 

 

 

 

The next hypothesis pertains to the relationship between
migration and economic opportunity as measured by median
income. Previous studies indicate that income accounts for

only a small proportion of the unexplained variance in migration.

64

This certainly does not mean that income is a secondary
motivation for migrating, especially for the age groups con-
sidered in this study. Median income of large SMSAs,
however, is too crude of a variable to permit accurate pre-
diction whether or not large numbers of persons will decide
that they can improve their individual financial status by
migrating. A place that had a strong economy and thus a

high median income could experience a downturn in a major
segment of its productivity that would generate a relatively
high unemployment without a proportionate change in its
median income. An increase in unemployment from 4 percent to
8 percent would be too small to affect the income for the total
population or specific age group. Such a change would be
registered only in the occupation groups directly effected

by unemployment.

There are other situations where data on median income
may fail to reflect the ability of a place to attract flows
of migrants. A place could have a moderate median income and
still attract migrants due to employment opportunities in
specific occupations and other specialized interests. The
student population is a good example of persons migrating
with little regard to the median income of the total popula-
tion, or their own age group, at the place of destination.
The income variable in this study failed to explain migra-
tion largely because the places are large, economically
complex places that attract and repel migrants who have a

wide range of motivations. It is not surprising to find

that the direction and degree of correlation for in- and out-
migration were almost identical. Economic opportunity is
clearly a determinant in migration. But median income is not

a sensitive manner of operationalizing economic opportunity.

Hypothesis 2

 

Median income is correlated with migration, but the
correlations vary between age-sex levels of analysis. The
degree and direction of correlations of median income and
net, in- and out-migration are as follows: net and in-migra-
tion have low positive correlations, and out-migration has

a relatively low negative correlation.

Net Migration

Summary Findings

 

The results of this research do not warrant accepting or
rejecting the hypothesis that net migration has a low posi-
tive relation with median income. That correlations vary
by age and sex is confirmed.

The simple correlations in Table 10 which are based on
absolute numbers and rates of migration in the male plus
female population fail to show any correlation between
migration and income. Likewise, the regression coefficients
in Table 11 do not indicate there is a predictable relation-
ship between migration and income. Since there are correlations
at some age-sex specific levels, the prediction of a low

positive correlation should not be rejected outright. The

66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 10. Simple Correlation Coefficients (r) of Net Migration and INC.
Sex Ages
5+ 20-24 25-29 30-34 35-39 40-44
Male plus
E Female -.09 -.32 .23 .07 .01 -.01
9&3
ens:
8 Male -.23 -.46 .53 .24 .06 .03
2
Female -.08 -.Ol .27 -.07 .02 .01
lMale plus
Female -.05 —.31 .15 .03 .06 .02
(I)
u:
5 Male -.19 —.51 .43 .24 .13 .09
Female -.02 -.ll .09 -.06 .14 .15
Table 11. Unstandardized Regression Coefficients of Net Migration on
INC Controlling for Unemployment and SOP.
Sex Ages
5+ 20-24 25-29 30-34 35-39 40-44
Male plus
g3 Female - .05 -l.42 .09 .01 .OO .00
38
agilale -l.56 -2.33 1.08 .54 .32 .23
a Female 13.81 - .18 1.45 .25 .55 .54
Male plus
Female .00 - .06 .00 .00 .00 .00
en
E3 Male - .01 -.13 .06 .02 .01 .00
Female .00 - .10 .01 .00 .02 .02

 

 

 

 

 

 

 

 

 

67

offsetting effect that is inherent in net migration data
affects the total population more than some age groups.
Therefore the lack of correlation at the aggregated level can
be interpreted as a result of (l) the confounding of in-

and out-migration, and (2) the relative insensitive nature

of the income variable as mentioned earlier.

The age-sex groups vary widely in the recorded simple
correlations (Table 10). While the correlation of the net
number and income for the group age 5 and over (males plus
females) is -.09, the range of values for the five specific
ages is -.32 as compared with values for male specific ages
that range from -.46 to .53. The values for females are
quite dissimilar from the male coefficients. Also, the
correlations among the female age groups differ from each
other. The coefficient of the number of female migrants and
income for age 25-29 is .27 whereas the other specific age
groups and the total population have coefficients close
to zero.

The findings based on the net migration rate and income
are replications of simple correlations based on absolute
numbers mentioned in the preceding paragraph. The variation
between the total population and its component parts, as
well as among the parts, is comparable to the values stated
above. The population five plus and the 20-24 age have
negative signs to contrast to the positive association for

other ages. The degree of relationship is much smaller in

68

the total population than in the 20-24 group. Total popula-
tion is probably affected more by the offset of in- and out-
migration. Evidently military and college participation
attracts persons in the 20-24 bracket to SMSAs with little
regard to the income level Of the places.

The direction of correlation, as well as the variation
among age-sex groups, that was found for simple correlation
is replicated in the regression coefficients of Table 11.
For the most part, the coefficients of absolute numbers and
rates for the first two age categories (5 plus and 20-24)
of male plus female have negative signs as they do for
simple correlations. The other coefficients are either
positive or zero. The value for the absolute number of
females age 5 plus (13.81) is an obvious anomaly in the
table. This single coefficient could be explained by tracing
the exact numerical values representing each of the 64 cases
that were regressed. There would be little to gain by the
exercise since a pattern of such anomalies is not present.
The comparable coefficients based on rates are consistent
in indicating there is no correlation between net migration
of these places and this particular measurement of economic
Opportunity; median income.

A striking pattern in Tables 10 and 11, as mentioned
above, is the consistent negative association for ages 5
plus and 20-24 in contrast to the consistently positive

values for other ages. Ages 20-24 are Of particular interest

69

because: (1) the results are more consistent than other

ages, (2) it is a more homogeneous group than age 5 plus,

and (3) the coefficients support CPS findings that this cohort
is attracted to places for reasons other than the income

level of places. On the first point (consistency), we note
that the 5 plus cohort had small negative signs for r values
of rates, and changed to zero correlation for regression
coefficients of rates. In contrast, the 20-24 year olds
maintained consistent low negative coefficients for simple
correlations and regression coefficients.

The regression coefficients of rates for age 20-24 are
higher than others in that panel of Table 11. But this
observation doesn't tell us much. The other coefficients that
would go into a regression equation with -.06 for the male
plus female population age 20-24 are; intercept - 287.11,
unemployment rate = -5.10, and size of place = zero.

Another pattern in Tables 10 and 11 is that age 25-29 is
not only consistently positive but is also higher than the
other ages. High employment participation in that age group
would account for its having a higher positive correlation
than most other groups. The results are consistent with data
from the Current Population Surveys.

If we looked only at the results for ages 25-29 we
would accept the hypothesized relation between net migration
and income. However, our reaction would be the opposite if

we relied solely on any of the other age categories. It is

7O

obvious that the aggregated data are inappropriate for making

predictions about how median income will affect net migration.
Coefficients of multiple determination that were

presented in Table 3 are applicable to the analysis of age-sex

variation in correlations of net migration and income just

as they were in the section on net migration and unemploy-

ment earlier. It will be recalled that these results displayed

wide variance in R2 values that were based on absolute terms

and on rates.

In-Migration

SummarygFindings

 

The findings are too inconclusive to reject or confirm
the hypothesis that in-migration has a low positive correla-
tion with median income. It is clear, however, that the
association of in-migration and income do vary between age-sex
levels.

The results on in-migration and income in Tables 12 and
13 are very similar to those on net migration discussed
previously. The r statistics on the number of male plus
female population are all low positive values (Table 12).
Previous results on net migration were positive for the four
oldest specific age cohorts but negative for the 20-24 and
total populations. As mentioned in the section on net
migration, the negative results are probably created by the
offsetting effect of net migration, and by military-college

effects. This difference in the direction of correlation

71

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 12. Simple Correlation Coefficients (r) of In-Migration and INC
Sex Ages
5+ 20-24 25-29 30-34 35-39 40-44
___.___,__
Male plus
m Female .17 .05 .17 .18 .19 .18
“8
D |
5“,: Male .34 -.O6 .44 .50 .49 .47
35 I
z I Female .50 .37 .59 .59 .49 .46
Male plus
Female —.01 -.36 .14 .15 .20 .17
(I)
:2 Male -.29 -.60 .02 .08 .10 .06
B
Female -.09 -.33 .00 -.03 .15 .18
Table 13. Unstandardized Regression Coefficients of In-Migration on INC
Controlling for Unemployment and SOP.
Sex Ages
5+ 20-24 25-29 30-34 35-39 40-44
_._____I,._..__
Male plus
a: Female .46 -l.27 .19 .14 .12 .09
ga
oé‘a' Male - .31 -2.79 .69 .97 .68 .51
35
Female 18.56 - .71 3.49 1.70 1.44 1.15
Male plus
Female .00 - .06 .00 .00 .00 .00
en
g Male - .02 —.16 .01 .02 .01 .00
Female .00 - .15 .03 .04 .06 .05

 

 

 

72

for net migration and in-migration ceases when r is computed
from rates. The 5 plus and 20-24 population have negative
coefficients of rates and the remaining ages remain positive.

Regression coefficients on rates should provide the best
test of the direction of correlation between in-migration
and median income. Male plus female data generated zero
correlation in Table 13, as was the case for net migration
in Table 11.

That differences in degree of correlation exist at
age-sex levels is clear from Table 12. The range of correla-
tion for male plus female rates has a high of .20 for 35-39
and a low of -.36 for 20-24. This latter group (20-24)
continues to indicate that forces other than median income
attract them to metropolitan places. Disaggregated data
for males alone and females alone vary from each other and
from their aggregates.

In the bottom panel Of Table 13, all age groups except
20-24 report zero correlation between rates of in-migration
and income for males plus females. There are differences
in coefficients based upon sex, but the range of differences
is relatively small since all the coefficients, except 20-24,
are extremely low. Median income performs so poorly as an
explanatory variable that it would have to be altered
before using it in a prediction equation. Perhaps better
results would be obtained if income by occupation, age and

sex were available. The more homogeneous the units of

73

analysis can be, the more we would expect the variables
to explain.

Earlier the coefficients of multiple determination
found in Table 6 were cited to demonstrate age-sex variation
for in-migration and unemployment. Of course, these same
results support hypothesis 2 since the coefficients are ‘
derived from the same independent variables: unemployment, r]

2

income and size. It will be recalled that R s for male

 

plus female in Table 6 ranged from .15 for the 20-24 age to .r
.06 for 25-29 year olds. Also coefficients on disaggregated
sex data varied from their aggregates.

Out-Migration

Summary Findings

 

The results do not warrant accepting or rejecting the
hypothesis that out-migration has a low negative correlation
with median income. There is ample support, however, to
confirm the prediction that correlations vary by age and sex.

The results pertaining to out-migration and income are
so similar to those in the previous section on in-migration
that the discussions of the findings for in- and out-migration
could have been interwoven into one discussion, except such
a presentation would tend to be confusing due to the multi-
plicity of age-sex coefficients that need to be cited. The
reasons for the similarity between the results on in- and

out-migration will be discussed in regard to the third

74

hypothesis. The following paragraphs will cite the correla-
tion coefficients that pertain to out-migration to give
support to the above statement Of summary findings, and to
demonstrate the similarity of these findings with those

for in-migration.

All of the simple correlations of absolute numbers for
male plus female (Table 14) have low positive values.
Coefficients of in-migration for the categories that are
counterparts to those under discussion here had very similar
values. Results based on rates of out-migration (male plus
female) also have low positive values except for age 20-24
which is -.22. The findings in Table 14 appear to reject
the hypothesized direction of correlation between out-migration
and income. These results should not be interpreted to mean
out-migration and income are positively correlated, but that
median income as used here has failed to operationalize

economic opportunity adequately.

Table 14. Simple Correlation Coefficients (r) of Out-Migration and INC.

 

 

 

 

 

 

 

Sex Ages
5+ 20-24 25-29 30-34 35-39 40—44
Male plus
I3 Female .20 .23 .11 .15 .17 .17
s E
3% Male .40 .21 .32 .42 .43 .42
9 Female .50 .44 .56 .58 .46 .43
Male plus
E Female .05 -.22 .01 .19 .24 .24
a Male -029 -041 _050 -013 .01 000
Female -.14 -.55 -.11 .02 .09 .13

 

 

 

 

 

 

75

The apparent weakness of median income as an explanatory
variable that was noted above is supported by the regression
coefficients of rates in Table 15. All age categories for
male plus female have zero correlation. The low positive
simple correlations reported in Table 14 may be due to the
influences of the unemployment variable which is not controlled
in r statistics as it is in the regression coefficients.

Table 15. Unstandardized Regression Coefficients of Out-Migration on
INC Controlling for Unemployment and SOP.

 

 

 

 

 

Sex Ages
5+ 20—24 25-29 30-34 35-39 40-44
Male plus
Female .51 .14 .10 .13 .12 .09
:33,
and Male 1.25 -.46 - .38 .43 .36 .27
8%
Qz Female 4.74 -.53 2.04 1.44 .89 .61
Male plus
Female .00 .00 .00 .00 .00 .00
U)
‘2' Male - .01 -.02 - .05 .00 .00 .00
Female .00 -.04 .02 .04 .04 .02

 

 

 

 

 

 

 

 

Even though median income has shortcomings as an
operationalization Of economic opportunity, it can be used
to demonstrate the variations of correlation that occur at
different age-sex levels. The range of variation in simple
correlations of rates in -.22 to .24. The widest range in
male and female coefficients (disaggregated) is found in the

25-29 group where forty points separate males from females

76

and fifty-one points separate males from the male plus
female aggregated value.

Regression coefficients of numbers also show variation
between specific categories. The population age 5 plus
recorded a value of .51 as compared to the lowest coefficient
of .09 for age 40-44. While all of the male plus female
results are positive, three of the sex specific coefficients
have negative signs. Of course, there is little variation
among coefficients of rates since all of them are at or
near zero.

The R2 values relevant to this discussion of variation
in out-migration correlations were presented in Table 9.

It will be recalled that coefficients based on rates displayed
a wider range of variation than those derived from numbers.
The range for male plus female groups in nine percentage
points as compared with a range of twenty points for males
alone and twenty-three points for females.

Throughout the above findings for hypothesis 1 and 2
patterns of correlation have emerged for certain age categor-
ies. The older working ages (30-44) have resembled each
other. Evidently their relative homogeniety and stability
in the labor market have created the pattern of the results.
The ages dominated by military, college and novice employment
(20-24) have been an anomaly as compared to other categories.
These results are consistent with the demographic literature

in general and the Current Population Surveys in particular

 

77

in that young adults migrate to large urban centers in
search of educational and employment Opportunities. The
volume of in-migrants age 20-24 far exceed the level of
economic Opportunity, as measured by employment and income,
at the point of destination, and a negative correlation
results.

Correlations on the population age 5 and over have
consistently varied from all other age groups. Frequently
the direction of correlation for the total population has
agreed with the 20-24 group. No intuitive explanation for
this Observation comes to mind. One would expect the total
population to resemble the working ages that possess the
majority of population. In this study the majority would
be ages 30-44. Instead coefficients for ages 5 and over
have a closer resemblance to the most anomalous cohort; 20-24.
The nearest thing to an explanation is that the relative
similarity of the total population to the 20-24 group and
its dissimilarity to other ages depicts the inappropriateness
of using aggregated data to analyze migration. The processes
of migration are different for specific groups. In order to
reveal and understand these processes we must specify
migration variables further than what is current practice
in place analysis.

Whereas hypotheses l and 2 dealt with the relationship
of migration as a dependent variable and some independent

variable, the third hypothesis deals with the relationship

 

78

between two forms of the dependent variable; in- and
out-migratiOn. However, the intent here is the same as it
is in the previous hypotheses, i.e., to determine if aggre-
gated data can be relied upon to reveal the important
processes that take place in population migration, or is it
necessary to do analysis on more specific levels? This
question is addressed in two ways by the data pertaining to
hypothesis 3. The first has to do with using net migration
data in migration studies in contrast to using data that is

disaggregated into in- and out-migration. If the number

 

of out-migrants is nearly equal to the number of in-migrants,
then data on net migration is inadequate for understanding
the migration processes that are present. While it is true
that the volume of net migration measures how much a place
gained or lost due to migration, such measurement does

not explain migration.

The second way that data pertaining to the third
hypothesis evaluates the usefulness of aggregated data is
to examine correlations of in- and out-migration at age-sex
specific levels. It is possible that in- and out-migration
are not highly correlated at certain ages, and therefore
net migration data for those ages would reveal the major
processes that explain the migration.

The question of the relationship between in- and out-
migration has been researched previously. The work of

Miller [1967] presents a concise statement of the importance

79

and major conclusions on the topic. Therefore a review of
her 1967 article will be presented next as a preface to the
findings on hypothesis 3.

Miller examined data on the movement of employed persons
into and out of the forty-three largest U.S. metropolitan
statistical areas, excluding five places where military
activity distorted migration statistics. The data measured
net migration, in-migration and out-migration by sex, color
and occupation between 1955 and 1960. Correlations were
calculated from the absolute number of migrants as well as
rates of migration. The rates for each place were created
by dividing the number of in-migrants and out-migrants,
respectively by the number of non-migrants and multiplying
by 1,000. Therefore this research by Miller falls into the
cateogry of place analysis in contrast to stream analysis.

In respect to total population, Miller found there was
a clear tendency for the rates of in-migration and the rates
of out-migration to rise together. She reports a coefficient
of correlation of .67 for total in-migration and total
out-migration. However, in Miller's own words, "The behavior
of totals for employed persons in a specific area can, of
course, mask very considerable differences in the behavior
of the various components of that total. . ." (pp. 1422).

She then procedes to examine the correlations of four sex-color
components of the total population. The findings, by order

of highest correlation, were: white females; r = .72, white

 

80

males; r = .65, nonwhite males; r - .57 and nonwhite
females; r = .45.

The sex-color data mentioned above was not adequate to
address an important question that Miller wanted to examine.
She was concerned to know if in-migrants and out-migrants
were interchangeable units, i.e., are they the same kind
of people? If they are the same kind of people and filling
the same function in the economic system, then each incre-
ment of growth through net migration is costly. On the
other hand, if doctors are the in-migrants and lawyrers are
the out-migrants, then the migration flow may be a necessary
and (costwise) efficient process to the economic balance of
the place. Sex-color categories such as white males and
females, and nonwhite males and females are not homogeneous
enough for Miller to assume the in- and out-migrants are the
same kind of people. Therefore she disaggregated the data
by occupational groups. Miller found (PP. 1423) that within
each classification of operatives, service workers, clerical
workers and laborers there were high correlations between
in-migrant ratios and out-migrant ratios. This finding seems
to support the idea that in- and out-migrants are relatively
similar units in the labor market. Professionals, which
are not a very homogeneous group, had lower correlations
of in- and out-migration rates.

Miller's general finding is that .for the major

metropolitan areas of the United States, the association

81

between in-migration and out-migration for relatively homo-
geneous segments of the labor supply was very close in the
1955-1960 periods, regardless of whether this association is
measured on a relative or an absolute basis" (pp. 1428).

This statement can be paraphrased to parallel the intent

of our third hypothesis without doing an injustice to Miller's
findings. The paraphrase should make explicit the relevance
of the above discussion of Miller's research to this thesis.
The paraphrase is: the association between in-migration and
out-migration for the total population is high, but the
correlation varies for homogeneous segments of the labor
supply depending on the degree of homogeniety. Miller
disaggregated data along lines of sex, color and occupation
group, whereas our disaggregation is to specific levels of
sex and age. But our inquiry is the same. That is, in order
to explain migration, we must examine specific, homogeneous
subgroups of the population. Now that the context of the
third hypothesis is set, we are ready to present the results

pertaining to the hypothesis.

Hypothesis 3

 

In- and out-migration, as measured by rates or numbers,
are highly correlated with each other, but the correlations
will vary between age-sex levels of analysis, Summary
findings: Results of this study confirm that in- and out-

migration are highly correlated. Even though all the age-sex

82

specific correlations are in the same direction, positive,
the coefficients vary by age and sex.

The simple correlation coefficients based on the number
of in- and out-migrants (Table 16) are very high. The lowest
coefficient is .83. The meaning of these values is that
there is a clear tendency for the volumes of in-migration
and out-migration to rise together. In other words, places
experiencing in-migration also experience a similar volume
of out-migration. This is true whether the place is a SMSA
of 250,000 pOpulation or several million inhabitants.

Unlike the coefficients on the number of out-migrants and
the number of unemployed (Table 7), the r values in Table

16 are not merely corollaries of the size of place variable.
It was noted earlier in regards to the values in Table 7
that the high coefficients could be misleading. The degree
of correlation of absolute values reported in that table
can be explained by the fact that large places, experience
large volumes of migration and unemployment by virtue of
their size alone. But this type of misleading correlation
does not apply to the coefficients pertaining to hypothesis
3. The earlier coefficients on unemployment could not be
taken at face value because they could be interpreted to
mean change in the number of unemployed caused changes in
migration. This was not necessarily the case. It is true
that the dependent and independent variables changed together

but not necessarily because of a causal relation. Changes

83

in the two variables were concomitant with each other but
were caused by changes in the size of place variable. In
the third hypothesis we are not asserting a causal relation
between in- and out-migration. But correlation analysis is
being used to study the structure of migration to and from
places.

Table 16. Simple Correlation Coefficients (r) of In-Migration and
Out-Migration.

 

 

 

 

 

Sex Ages
5+ 20-24 25-29 30-34 35-39 40-44

Male plus
a: Female .90 .84 .94 .93 .92 .89
gs
a; Male .90 .83 .94 .93 .92 .89
Q Female .89 .89 .94 .93 .91 .89

Male plus

Female .74 .41 .48 .69 .75 .73
g Male .73 .34 .40 .67 .76 .72
g Female .75 .53 .57 . 71 .73 .74

 

 

 

 

 

 

 

 

The r statistics in Table 16 that are based on rates of in-
and out-migration are also high, and therefore support the
conclusions drawn from the coefficients based on the number
of migrants. However, the correlation of rates diSplays a
much wider range of variation at different levels of analysis.
Age groups 20-24 and 25-29 have values of .41 and .48,

respectively, and compare with a r coefficient of .74 for the

population age 5 and over. The three remaining age groups

84

(30-34, 35-39 and 40-44) report correlations that are very
close to the total population. Therefore, we would not

expect to find a flow of in-migrants to a place to be accom-
panied by a similar proportion of out-migrants for the college
and young working ages. This observation, of course, is
consistent with the findings on the 20-24 and 25-29 age groups
that were discussed under previous hypotheses.

Sex differentials in the correlation of in- and out-
migration rates are prevalent only in the college and young
working ages mentioned in the preceding paragraph. The rate
of male migrants age 20-24 differ from the aggregated rate
for males plus females age 20-24 in that they are seven
points under the aggregate. Whereas the female migrants of
the same age are twelve points over the aggregate. Therefore
the variance between rates for males and females age 20-24
is nineteen points. A similar range of variation is recorded
for ages 25-29. The males of this cohort are eight points
under the total migrants, while female migrants are nine
points over the aggregate. None of the other age groups
reported sex differentials in correlation coefficients.

It will be recalled that Miller concluded that while in-
and out-migration were highly correlated, whether measured
by rates or numbers of migrants, more homogeneous groups
could be expected to show a higher correlation in the two-way
flows of migrants. Our findings in the above paragraph

corroborate her conclusion. However, the two cohorts that

85

span the decade of age 20 through age 29 possess low degrees
of homogeneity. A large proportion of the cohorts migrates
into and out of large urban centers to pursue educational
opportunities. Most of the balance of the cohorts migrate

in response to employment openings. Of course most of the
student pOpulation later become job seekers. Since young
persons entering the labor force while they are still in their
early twenties, especially laborers, are relatively unskilled
they experience the highest rate of unemployment. In contrast
to this young college and working age population, the older
cohorts are more established in their fields. They are there-
fore more stable and experience fewer status changes. In
short, the older groups are more homogeneous in regards to

employment status than the younger cohorts.

CHAPTER V
SUMMARY AND CONCLUSIONS

The goal of this research is to determine if it is
necessary to lower the level of migration analysis from the
aggregate level that has been employed in previous models of
place and stream analysis. At the beginning of the chapter
on findings a general model of expectations was presented
in which it was predicted that marked differences in corre-
lation of migration variables would be found by age and sex
levels. This general statement is intended as a summary of
the three hypotheses, each of which deals with a limited
part of the research. The hypotheses are stated in such a
manner as to interweave this research on age-sex variation
of correlations with migration analysis that has been presented
in the main stream of demographic literature. For example,
hypothesis 1 deals with the degree and direction of corre-
lation between net migration and unemployment. This topic
has been addressed by many researchers, though with less
current data than is employed here. Hypothesis 1 also
incorporates the analysis of association between net migration
and unemployment with a prediction that the association
varies by age and sex. A similar format is used for the

other hypotheses.

86

87

The format of this "Summary and Conclusion" section will
be to: (1) address the general model of expectation by
summarizing the hypothesized findings that pertain to variation
by age and sex, (2) summarize results on the association of
migration and independent variables in hypotheses l and 2,
and the association of in- and out-migration in hypothesis 3,
(3) draw conclusions based on the general model of expecta-
tions and the specific hypotheses, and (4) recommend a focus
for future research.

The general model of expectations for this research is
that the simple and multiple regression coefficients generated
here will show a marked difference across age-sex specific
levels of analysis. The correlations for the population
age five and over will vary from the specific age groups,
and specific age groups will vary from each other. There
will be variations when correlations for males alone and
females alone are compared with each other or with the
correlations based on aggregations of male plus female.

The results pertaining to hypotheses one through
three demonstrate that correlations between the dependent
and independent variables most frequently used in migration
analysis vary when simple and multiple coefficients for the
total population are compared with coefficients for specific
age-sex groups and when specific age-sex groups are compared
with each other. Generally, the statistics for each of the

five specific age groups vary from the statistics for the

88

total population age five and over. While the population Of
college and young working ages, especially 20-24, deviate
consistently and markedly from the aggregate and from other
specific ages, older ages also display different coefficients
from the total population and from other specific groups.

The most conformity with the aggregate and with other groups
is displayed by older, more occupationally stable cohorts age
35 and over. These results are consistent with findings

that have been reported by CPS for many years.

The differences in correlation coefficients of age
groups noted above persist when the male plus female popula-
tion is disaggregated into males alone and females alone.
Also, the correlation for specific age-sex groups vary from
their counterpart. For example, in most cases, females age
5 plus vary from males age 5 plus and from the total of males
plus females age 5 and over. Likewise, correlations for
five year specific age groups of females vary from their
respective male and male plus female counterparts.

Results pertaining to hypothesis 1 provide a weak
confirmation of the hypothesized association of migration
and unemployment. The predicted association of migration
and median income (hypothesis 2) could not be accepted or
rejected because the results were too inconclusive. The
reason for the weak confirmation in hypothesis 1 and the
inconclusiveness in the second hypothesis is that unemployment

and median income of the places analyzed are not sensitive

89

indicators of economic opportunities available to particular
occupational groups in large metropolitan areas. A place
can have a relatively high unemployment rate and still be
able to attract in-migrants to occupations that are not
experiencing high unemployment. On the obverse side, a
place can have low unemployment and still experience out-
migration. Like unemployment, median income fails to indicate
economic opportunities that are available to particular
groups of potential in- or out-migrants. An SMSA with high
median income may not be able to offer new jobs to a large
number of hourly workers and thus record a substantial

flow of in-migration.

Three conclusions should be drawn from the summaries
stated above. The first comes from the general model of
expectations. It therefore represents the capsulization
of this research. Ideally, all research should allow us to
draw some definite conclusion. The primary conclusion to be
drawn from this research is that in order to get a better
understanding of the migration processes, we need to utilize
data that are disaggregated to at least age-sex specific levels.
Aggregated data for the total population is inadequate for
explaining the relationship between dependent and independent
variables for any of the component pOpulation groups. The
variation in explanations that is derived for the college
and young working ages (20-29) as compared with the total
population would be particularly detrimental to any effort

to develop a predictive model of migration to and from places.

90

It may be feasible to aggregate data on some ages without
adversely affecting any forecasting efforts. The older, more
occupationally stable ages, (in this study ages 30-44)
demonstrate relatively homogeneous relationships between
measurements of migration and independent variables.

The findings on the association of migration as the
dependent variable with unemployment, median income and size
as independent variables lead to the second conclusion.

In addition to disaggregating by age and sex, it will be
necessary to disaggregate data on migration variables by
occupational groups if we are to get a better understanding
of migration processes in general, and of particular anomalies
such as the lack of correlation between broad indicators of
economic opportunity and migration.

Another conclusion is derived from results on the
association of in- and out-migration. It is obvious that
measurements of net migration cannot be relied upon to
estimate in- and out-migration. Detailed breakdowns of in-
and out-migration to large and small places are prerequisites
if substantial improvements to migration modeling are to
be made.

The findings of this research regarding age-sex patterns
of mobility are consistent with results of the Current
Population Surveys. We have seen that the college and young
working ages do not respond to indicators of economic

opportunity (unemployment and income) as either older, more

91

economically stable ages do, or as the total population age
5 and over does. The younger ages migrate to and from large
metropolitan places for reasons other than employment.
Educational opportunity and military duty account for much
of the migration flow of the younger cohorts. Apparently,
there is a large segment of this young population that is on
the move for the sake of going to new places. Females also
display different mobility patterns from their male cohorts.
In general, males are less responsive to economic variables,
especially in the younger ages.

In the past, migration analysis has focussed on the
total population age five and over. This dissertation
lowered the level of specificity to selected five year age-sex
categories, in addition to the total population. Future
research on migration to and from places should focus on
the most specific, homogeneous populations as possible.

Data on in- and out-migration by age, sex, race, occupation
and income should be correlated with independent variables
at comparable levels of specificity, e.g., unemployment by
age, sex, race occupation, and income prior to unemployment.

Presently SMSAs over 250,000 provide the data for
migration analysis. Data on smaller places, perhaps 10,000
and above, should be included. Effort needs to be expended
in grouping places into homogeneous categories for analysis.
Size of place is an Obvious criterion for grouping places,

and it is utilized presently. Other criteria such as

92

economic functions and economic growth characteristics of
places should be considered also.

The above conclusions assume it is feasible to obtain
more specific data on migration and explanatory variables.
But would it be feasible to obtain the level of specificity
that is recommended? The answer is yes. Age-sex specific
data on in- and out-migration by employment, income and
other socio-economic variables for large and small places
could be generated from the 1970 census. The pertinent data
were collected with the fifteen percent sample questionnaire.
It would be possible, though costly, for the Bureau of the
Census to generate the desired matrixes from the work file
that contains the responses for the fifteen percent

questionnaire.

APPENDIX

Appendix Table 1.

93

Correlation (r) and Unstandardized Regression

Coefficients for Net Migration (Male plus Female).

 

 

 

 

 

 

 

 

 

Correlation Coefficients (r) Regression
Coefficients
Age Net Migration
Between and Between and Between and Between and
SOP UEN NMN SOP NMN UEN mm m1
5+ .87 -.51 -.44 -.02
20-24 .73 —.28 -.16 .10
25-29 .91 .36 .52 2.58
30-34 .92 -.34 -.18 2.05
35-39 .95 -.46 -.40 .79
40-44 .95 -.45 -.40 .49

 

 

 

 

 

1Controlling for INC and SOP.

Appendix Table 2.

Correlation (r) and Unstandardized Regression

Coefficients for In-Migration (Male plus Female).

 

 

 

 

 

 

 

 

 

Correlation Coefficients (r) Regression
Coefficients
Age Net Migration
Between and Between and Between and Between and
sop UEN IMN SOP IMN UEN INM UFNl
5+ .87 .82 .76 .79
20-24 .73 .83 .59 - .12
25-29 .91 .88 .87 1.99
30-34 .92 .83 .82 1.59
35-39 .95 .81 .80 1.12
40-44 .95 .79 .78 .85

 

 

 

 

 

Appendix Table 3.

94

Correlation (r) and Unstandardized Regression
Coefficients for Out-Migration (Male plus Female).

 

 

 

 

 

 

 

 

 

 

Correlation Coefficients (r) Regression
Coefficients
Age Net Migration
Between and Between and Between and Between and
SOP UEN OMN SOP OMN UEN OMN UENl
5+ .87 .96 .88 .82
20—24 .73 .97 .67 -.22
25-29 .91 .94 .85 -.58
30-34 .92 .94 .86 -.45
35-39 .95 .93 .91 .33
40-44 .95 .94 .91 .36

 

 

 

 

 

1Controlling for INC and SOP.

95

Appendix Table 4. Rank of Standard Metropolitan Statistical Areas
Utilized in Regression Analysis.

 

 

 

Bank Standard Metropolitan Statistical Areas 1970
Population
1 Chicago, 111. 6,978,947
2 Philadelphia, Pa.-N.J. 4,817,914
3 Detroit, Mi. 4,199,931
4 Pittsburgh, Pa. 2,401,245
5 Newark, N.J. l.856,556
6 Minneapolis-St. Paul, Minn. 1,813,647
7 Seattle-Everett, Wash. 1,421,869
8 Atlanta, Ga. 1,390,164
9 Paterson-Clifton-Passaic, N.J. 1,358,794
10 Buffalo, N.Y. 1,349,211
11 Miami, Fla. 1,267,792
12 Denver, Colo. 1,227,529
13 San Bernardino-Riverside-Ontario, Calif. 1,143,146
14 San Jose, Calif. 1,064,714
15 Tampa-St. Petersburg, Fla. 1,012,594
16 Portland, Oreg.-Wash. 1,009,129
17 Phoenix, Ariz. 967,522
18 For Worth, Tex. 762,086
19 Albany-Schenectady-Troy, N.Y. 721,910
20 Oklahoma City, Okla. 640,889
21 Syracuse, N.Y. 636,507
22 Gary-Hammond-East Chicago, Ind. 633,367
23 Fort Lauderdale-Hollywood, Fla. 620,100
24 Jersey City, N.J. 609,266
25 Omaha, Nebr.-Iowa 540,142
26 Youngstown-Warren, Ohio 536,003
27 Jacksonville, Fla. 528,865
28 Tulsa, Okla. 476,945
29 Orlando, Fla. 428,003
30 Fresno, Calif. 413,053
31 Tacoma, Wash. 411,027
32 Knoxville, Tenn. 400,337
33 Lansing, Mi 378,423
34 Oxnard-Ventura, Calif. 376,430
35 Canton, Ohio 372,210
36 Tucson, Ariz. 351,667
37 West Palm Beach, Fla. 348,753
38 Wilkes-Barre-Hazleton, Pa. 342,301
39 Utica-Rome, N.Y. 340,670
40 Bakersfield, Calif. 329,162
41 Columbia, 8.0. 322,880
42 Lancaster, Pa. 319,693
43 Beaumont-Port Arthur, Tex. 315,943
44 Albuquerque, N. Mex. 315,774

96

Appendix Table 4. Con't.

 

 

 

Rank Standard Metropolitan Statistical Areas 1970
Population
45 Chattanooga, Ten.-Ga. 304,927
46 Trenton, N.J. 303,968
47 Reading, Pa. 296,382
48 Austin, Tex. 295,516
49 Shreveport, La. 294,703
50 Madison, Wis. 290,272
51 Stockton, Calif. 290,208
52 Spokane, Wash. 287,487
53 Des Moines, Iowa 286,101
54 Baton Rouge, La. 285,167
55 Fort Wayne, Ind. 280,455
56 Las Vegas, Nev. 273,288
57 Rockford, Ill. 272,063
58 Duluth-Superior, Minn.-Wis. 265,350
59 Santa Barbara, Calif. 264,324
60 Erie, Pa. 263,654
61 Johnstown, Pa. 262,822
62 Lorain-Elyria, Ohio 256,843
63 Huntington-Ashland, W. Va.-Ky.-Ohio 253,743
64 Augusta, Ca.-S.C. 253,460

 

 

Appendix Table 5.

Means and Standard Deviations by Age for Males

97

Plus Females.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable Age Groups
5+ 20-24 25-29 30-34 35-39 40-44

NMR mean 22 45 27 21 14 15
standard

deviation 60 176 102 68 55 51

IMR mean 174 342 307 231 177 135
standard

deviation 86 194 111 95 84 74

OMR mean 152 296 279 209 162 119
standard

deviation 47 69 85 67 57 47

NMN mean 3,489 725 1,078 342 161 178
standard

deviation 22,712 4,794 2,802 1,600 1,307 1,209

IMN Imean 53,580 9,133 7,545 4,624 3,434 2,775
standard

deviation 47,241 8,535 7,636 4,290 3,146 2,530

OMN [mean 50,090 8,408 6,467 4,282 3,272 2,596
standard

deviation 52,248 8,687 6,100 4,388 3,364 2,702

INC [mean 4,655 3,276 5,471 5,946 6,301 6,546
standard

deviation 2,372 912 2,195 2,930 3,147 3,139

UER ean 4.6 7.0 4.4 3.7 3.4 3.2
tandard

eviation 1.7 2.9 2.0 1.8 1.7 1.6

UEN Fean 7,031 1,593 779 535 504 547
tandard

eviation 9,501 3,242 1,143 742 704 733

SOP ean 382,127 382,127 382,127 382,127 382,127 382,127
tandard

eviation 518,890 518,889 518,889 518,889 518,889 518,889

 

 

Appendix Table 6.

Means and Standard

98

Deviations by Age for Males.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable Age Groups
5+ 20-24 25-29 30-34 35-39 40-44

NMR mean 22 40 33 21 16 15

standard

deviation 64 209 112 72 57 54
IMR mean 181 347 323 245 192 146

standard

deviation 90 222 110 97 88 79
OMR mean 159 306 289 224 176 130

standard

deviation 48 68 93 70 6O 51
NMN mean 2,850 48 1,392 400 156 156

standard

deviation 22,809 5,313 3,118 1,668 1,390 1,279
IMN mean 53,799 8,721 7,833 4,871 3,669 2,941

standard

deviation 47,804 8,012 8,103 4,623 3,356 2,680
OMN mean 50,948 8,672 6,440 4,471 3,513 2,785

standard

deviation 53,706 9,579 5,914 4,589 3,642 2,897
INC mean 6,813 3,902 7,570 8,775 9,324 9,561

standard

deviation 981 799 746 961 1,138 1,128
UER mean 4.0 7.2 3.5 2.6 2.4 2.4

standard

deviation 1.5 3.1 1.7 1.0 1.0 1.0
UEN mean 8,085 1,577 864 557 517 556

standard

deviation 10,971 2,103 1,271 782 754 769
SOP Imean 368,039 368,039 368,039 368,039 368,039 368,039

standard

deviation 500,865 500,865 500,865 500,865 500,865 500,865

 

99

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix Table 7. Meand and Standard Deviations by Age for Females.
Variable Age Grogps
5+ 20-24 25-29 30-34 35-39 40-44
NMR mean 22 50 21 22 13 15
standard -
deviation 57 138 91 64 53 47
IMR mean 168 336 291 218 161 124
standard
deviation 82 162 110 92 77 69
OMR mean 145 286 269 195 148 108
standard
deviation 44 69 75 61 51 40
NMN mean 4,128 1,402 763 283 166 199
standard .
deviation 22,777 4,144 2,429 1,540 1,229 1,145
IMN mean 53,359 9,546 7,257 4,376 3,198 2,608
standard .
deviation 47,048 9,073 7,191 3,951 2,929 2,380
OMN mean 49,230 8,144 6,493 4,092 3,031 2,408
standard -
deviation 51,158 7,760 6,327 4,204 3,072 2,501
INC mean 2,497 2,650 3,372 3,117 3,277 3,531
standard —-
deviation 960 492 455 357 325 363
UER mean 5.2 6.8 5.4 4.8 4.4 4.1
standard '
deviation 1.7 2.7 1.9 1.7 1.7 1.6
UEN mean 5,977 1,608 694 514 491 538
standard —_
deviation 7,703 4,095 1,002 704 657 700
SOP mean 396,215 396,215 396,215 396,215 396,215 396,215
standard .
deviation 539,905 539,905 539,905 539,905 539,905 539,905

 

 

 

 

 

 

100

 

 

 

 

 

 

 

 

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BI BLIOGRAPHY

 

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