Lifetime Migration in the United States as of 2006–2010: Measures, Patterns, and Applications

Abstract

Though most US migration analyses in recent years have relied upon 1-year and 5-year residence information, analyses of lifetime migration may be more revealing of state-level trends in the relative ability to retain the native born and to attract in-migrants from other states and abroad, and of the effect of such exchanges on the composition of its population in terms of education and other characteristics. This chapter reviews a number of measures of native retention and migrant attraction, and examines the formal relationships among these measures; presents some state-specific lifetime migration measures as of 2006–2010, with special attention to education and the impact of immigration; analyzes the degree of change in these lifetime measures centering on 1990; and uses these measures to decompose a state’s proportion of college graduates into elements that highlight the relative importance of retention and attraction and illustrates how these can contribute to appropriate policy formulation.

Appendices

Appendices

1.1 Appendix A13: Basic Algebra of Lifetime Migration Measures

As noted in the text, the two questions on place of birth and current residence yield three independent measures for each state: B is the total number born in a state, E is the number of native born leaving the state, and D is the number of in-migrants to a state. These building blocks can be combined in various ways to yield a number of measures, which capture several facets of the lifetime migration process. These measures are interrelated since they utilize one or more of the same elements. This appendix reviews a number of these measures and their interrelationships.

1.1.1 A13.1 Basic Notation

The three independent quantities observed are B, E, and D. B _i is the total number born in state i, who are alive and living somewhere in the enumerated area, not necessarily the state of birth. E _i is the number of native born who have left state i at some point prior to enumeration. D _i is the number of in-migrants to state i – those enumerated in state i but born elsewhere, including another country. To simplify the notation, i will be dropped from the equations.

As lifetime migration analysis often focuses on inter-state exchanges, it is often restricted to the native born, since immigrants from abroad cannot have a domestic place of birth. In this analysis, however, we often include both native-born migrants and immigrants from abroad to show the total impact of migration; and this also serves to show the importance of immigration from abroad. Immigrants from abroad are in effect treated as coming from a (mythical) place with no in-migrants and only out-migrants.

When necessary we use the notation D _N for native in-migrants and D _I for immigrants from abroad to distinguish these two sources.

A major focus of the analysis is on the effect of education on migration and to distinguish the three educational levels employed we use the letters P, S, G to distinguish those among three different educational categories.

P indicates those who had a primary school education, but less than a high school diploma. S represent those who have graduated secondary school or have some college. G represents those who have graduated college with a BA degree or higher. Thus, B_G would indicate the count of those who were born in state i and attained a college degree. Likewise, D_I.G represents in-migrants from abroad with a college degree.

Simple addition and subtraction produce two additional quantities of importance:

$$ \mathrm{C}=\mathrm{B}\hbox{--} \mathrm{E} $$

(A13.1)

$$ \mathrm{T}=\mathrm{B}\hbox{--} \mathrm{E}+\mathrm{D} $$

(A13.2)

Equation A13.1 represents the number of those born in a state who are still residing in the state at the time of enumeration. Equation (A13.2) is the total population of the state at the time of enumeration as a sum of the exits, E and the entrants D. Note that Eq. (A13.2) can be simplified by using C instead of the sum of B and E.

1.1.2 A13.2 Basic Measures

A prime use of lifetime migration data in past studies has been to study exchanges between states or the degree of gain or loss due to migration (Shyrock 1964; Eldridge and Kim 1968; Lee et al. 1957; and Siegel and Swanson 2004).

The key measure employed is the Net Migration Rate for a State, which is equivalent to the Percent Gain or Loss due to migration:

$$ \mathrm{G}=\left[{\mathrm{D}}_{\mathrm{N}}-\mathrm{E}\right]\times 100/\mathrm{T} $$

(A13.3)

where the numerator measures the net gain or loss in native migrants and the denominator the total native population residing in state i, regardless of state of birth. The numerator, which is the numerical amount of gain or loss due to migration is sometimes referred to as the Birth Residence Index (Siegel and Swanson 2004, pp 511–512; Shyrock 1964, pp 19–20).

For the country as a whole, the net gains and losses of the native population across the states balance out to zero. The Interstate Migration Rate for the country is defined as the number of native born not living in their state of birth, divided by the total native population. As shown in Table 13.1, for the US as a whole in 2006–2010, 38% of the native population 25 years of age and over was not living in their state of birth.

In addition to the gain and loss measures, other key measures include those reflecting retention and attraction measures of a state.

$$ {\mathrm{R}}_{\mathrm{N}}={\mathrm{C}}_{\mathrm{N}}/{\mathrm{B}}_{\mathrm{N}}=\left({\mathrm{B}}_{\mathrm{N}}\hbox{--} {\mathrm{E}}_{\mathrm{N}}\right)/{\mathrm{B}}_{\mathrm{N}}=1\hbox{--} \left({\mathrm{E}}_{\mathrm{N}}\hbox{--} {\mathrm{B}}_{\mathrm{N}}\right) $$

(A13.4)

The Retention proportion is the probability that a native person born in a state resides in the state at the time of enumeration. This is of course equal to 1 minus its complement – the proportion of native born in a state who emigrate from the state. For the country as a whole, the complement of the retention proportion is the Interstate Migration Rate, as it represents the proportion of the native population not living in their state of birth.

These measures may be made specific for race, gender, age, or education as well as other measured characteristics.

The Attraction proportion is defined as the proportion of the current population who are native or foreign in-migrants.

$$ \mathrm{A}=\mathrm{D}/\mathrm{T}=\mathrm{D}/\left(\mathrm{B}\hbox{--} \mathrm{E}+\mathrm{D}\right) $$

(A13.5)

Note that while R is a true probability in that all members of the denominator are at risk of emigrating that is not true for the attraction measure. A portion of the denominator – those born in the state and still residing there – are not at risk of migrating there.

To construct a true probability of attraction, we first define for each state the pool of possible in-migrants (H), which is the sum of in-migrants from all states minus the out-migrants from that state, since they are not at risk of being in-migrants to their state of birth.

The pool is defined as:

$$ \mathrm{H}=\varSigma \left(\mathrm{D}\hbox{--} \mathrm{E}\right) $$

(A13.6)

so that

$$ \mathrm{P}=\mathrm{D}/\mathrm{H} $$

(A13.7)

P is the probability of a state receiving a migrant from among all those migrating.

For the reasons touched on in the text, larger states will most often attract a larger absolute number of migrants than smaller ones. As discussed there, this observation has been incorporated into a number of models of migration. As a result, the probability measure is highly correlated with population size.

In the current analysis, the correlation between the probability of a state receiving a lifetime migrant aged 25–59 as of 2006–2010 and the size of the state is 0.95. In a statistical analysis, it would be possible to control for size, but it is also desirable to develop a measure of expected probability for each state so that its actual probability can be contrasted with its expectation. To analyze the success of areas in attracting migrants over a period, independent of size, we have developed a measure of expected probability of in-migration and contrasted that with the actual.

This follows the precedent of Bachi (1957), who developed a Migration Preference Index based on the ratio of actual to expected number. As Bachi’s interest was in analyzing specific migration streams his measure of expected is based on the population of both the place of origin and of destination. A detailed explanation of Bachi’s index and a sample calculation is presented in U.S. Census Bureau 1973, v.2, pp 656–657 and Shryock 1964, pp 267–275.

As our goal is for a more general measure of expected to compare with actual, we use the simpler method of employing a state’s proportion of the total population as of 1990 – part way through the relevant time period – as an estimate of the expected probability to compare with the actual probability.

Thus, our measure may be defined as:

$$ \mathrm{X}={\mathrm{T}}_{1990}/\varSigma {\mathrm{T}}_{1990} $$

(A13.8)

Where T ₁₉₉₀ is the total population in 1990 for a state divided by the sum of the population across all states in 1990. Thus, X is nothing more than the relative size of a state in 1990 compared to all other states.

$$ {\mathrm{M}}_{\mathrm{G}}=\mathrm{X}\times {\mathrm{H}}_{\mathrm{G}} $$

(A13.9)

The expected number of lifetime college graduate migrants, M _G , is the product of X by the pool of migrants with college degrees, H _G .

To illustrate for Florida, its expected probability is .0520 based on its population size in 1990 relative to the US total. The expected number of lifetime college grads is thus.052 multiplied by the pool of eligible domestic and foreign college grads, (24,621,086) to yield the expected number of in-migrant lifetime college graduates of 1,280,296 as shown in Table 13.7.

1.1.3 A13.3 Interrelationships Among Measures

As noted in the text, since the basic measures utilize one or more of the independent factors, they are interrelated in various ways. This section illustrates a number of these interrelationships that are relevant to the analyses presented.

$$ \mathrm{Since}\ \mathrm{A}=\mathrm{D}/\mathrm{T}\ \mathrm{and}\ \mathrm{P} = \mathrm{D}/\mathrm{H}\ \mathrm{then}\ \mathrm{P}=\mathrm{A}\times \left(\mathrm{T}/\mathrm{H}\right)=\mathrm{A}/\left(\mathrm{H}/\mathrm{T}\right) $$

so that a state’s probability of receiving an in-migrant, P is a function of its attraction ratio (A), its current size (T), and the total pool of in-migrants for that state (H). Since the total pool will vary less from state to state than state size, the formula shows that for a given attraction ratio, larger states will generally have a higher probability than smaller ones, as the denominator in the formula will be smaller.

This relationship is illustrated in Table A13.1 for ages 25–59 with four states selected from Table 13.5 (for measures) and Table 13.3 for population size.

Table A13.1 The relationship between attraction probability and the attraction ratio^a

Although the four states have almost identical attraction ratios, as shown in column 1, they vary a great deal in population size (column 2), and consequently they vary widely in the probability of gaining in-migrants, with those states with greater populations showing higher probabilities.

By the same token, for a given probability, a larger state will have a smaller attraction ratio than a smaller one, as illustrated in Table A13.2.

As shown in Table A13.2, although Colorado, Maryland, and Pennsylvania have almost identical attraction probabilities of attraction, the attraction ratio decreases as the population size increases across the three states.

Table A13.2 The relationship between the attraction ratio and population size^a

The attraction ratio gives a current snapshot for a state of the relative prominence of in-migrants in their total population as a function of the gains and losses that have occurred over the years. This can be seen more clearly if the attraction ratio is rewritten as:

$$ \mathrm{A}=\mathrm{D}/\mathrm{T}=\mathrm{D}/\left(\mathrm{C}+\mathrm{D}\right)=1/\left[\mathrm{C}/\mathrm{D}\right)+1\Big] $$

(A13.10)

As a reminder, D indicates the number of in-migrants to a state and C is the number of those born in a state who are still living in the state of birth. As the equation makes clear, the larger the ratio of native born to in-migrants, the larger the denominator and therefore the lower the attraction ratio, and vice versa.

Table A13.3 shows the attraction ratio and its two elements, C and D, for Nevada and Florida – two states with high attraction ratios and for Pennsylvania, a state with a low attraction ratio.

Table A13.3 The relationship between the attraction ratio and the relative share of the migrant population^a

The high ratio of native born still residing state of birth (C) in Pennsylvania relative to the number of in-migrants (D), leads to the low attraction ratio, in comparison to Florida and Nevada, where the heavy influx of in-migrants leads to a low ratio of C/D and hence to a high attraction ratio.

On the other hand, the probability measure reflects a state’s success, relative to other states, in attracting in-migrants from the pool of those moving over the years. It is not dependent on the size of the resident native population. It should be noted from Table A13.3 that Pennsylvania, despite its low attraction ratio has experienced many more in-migrants in absolute terms than Nevada and as a result also has a higher probability of in-migration (.025), as defined above, than Nevada (.016). This illustrates further the point that the probability measure is highly correlated with population size.

There is also a close relationship between the retention proportion and the attraction ratio.

Since: (C + D)/T = 1, then C/T + D/T = 1, which may be written as

$$ \begin{array}{l}\left(\mathrm{B}/\mathrm{T}\right)\times \left(\mathrm{C}/\mathrm{B}\right)+\mathrm{D}/\mathrm{T}=1,\ \mathrm{so}\ \mathrm{that}\ \mathrm{R}\times \mathrm{B}/\mathrm{T}+\mathrm{A}=1\ \mathrm{and}\\ {}\mathrm{A}=1\hbox{--} \left(\mathrm{R}\times \mathrm{B}/\mathrm{T}\right),\ \mathrm{and}\\ {}\mathrm{R}=\left(1\hbox{--} \mathrm{A}\right)\times \mathrm{T}/\mathrm{B}\end{array} $$

The retention probability is a function of the attraction ratio and the ratio of those born in the state to the total population, and conversely.

1.2 Appendix B13: Decomposition of the Number of College Graduates in a State and the Percentage of Residents Who Are College Graduates

A useful analytic device is to decompose a measure of interest into components that can point to key factors that affect that measure. Given the strong interest that most states have in increasing their college-educated population to enhance economic growth and development, the following section presents a decomposition of this number and its share of the total population into elements. The elements are the state’s production of college graduates from their native born, the ability to retain these graduates, and the level of success in attracting college-educated in-migrants from within the country and from abroad.

Equation (B13.1) simply presents the number of college grads from each key source: college graduates born in the state and living there; native college graduates from other states who migrate in; and college-educated immigrants who move to the state.

$$ {\mathrm{T}}_{\mathrm{G}}={\mathrm{C}}_{\mathrm{G}}+{\mathrm{D}}_{\mathrm{N}.\mathrm{G}}+{\mathrm{D}}_{\mathrm{I}.\mathrm{G}} $$

(B13.1)

Equation (B13.2) decomposes each element into factors of interest, so that:

$$ {\mathrm{T}}_{\mathrm{G}}=\mathrm{B}\times \left[\left({\mathrm{B}}_{\mathrm{G}}/\mathrm{B}\right)\times \left({\mathrm{C}}_{\mathrm{G}}/{\mathrm{B}}_{\mathrm{G}}\right)\right]+\left[{\mathrm{H}}_{\mathrm{N}.\mathrm{G}}\times {\mathrm{P}}_{\mathrm{N}.\mathrm{G}}\right]+\left[{\mathrm{H}}_{\mathrm{I}.\mathrm{G}}\times {\mathrm{P}}_{\mathrm{I}.\mathrm{G}}\right] $$

(B13.2)

The first term on the right represents the number of native born with a college degree residing in the state, arising from the total number born there, the proportion obtaining a college degree (which can occur out of state) and the retention rate of these college graduates. The second term on the right represents the number of college graduates residing in the state who were born in another state expressed in terms of the probability of attracting such a person and the total pool of these college graduates. The third term is similar but refers to the probability of attracting a college graduate from abroad and the total pool of college graduated immigrants.

The proportion of a state’s population who are college graduates is simply the number in Eq. (B13.2), divided by the state’s total population, as shown in Eq. (B13.3):

$$ {\mathrm{T}}_{\mathrm{G}}/\mathrm{T}=\mathrm{B}/\mathrm{T}\times {\mathrm{B}}_{\mathrm{G}}/\mathrm{B}\times {\mathrm{C}}_{\mathrm{G}}/{\mathrm{B}}_{\mathrm{G}}+{\mathrm{P}}_{\mathrm{N}.\mathrm{G}}/\mathrm{T}\times {\mathrm{H}}_{\mathrm{N}.\mathrm{G}}+{\mathrm{P}}_{\mathrm{I}.\mathrm{G}}/\mathrm{T}\times {\mathrm{H}}_{\mathrm{I}.\mathrm{G}} $$

(B13.3)

Table 13.8 in the text uses Eq. (B13.1) to show the proportion of college graduates coming from each major component and Table 13.9 uses Eq. (B13.3) to further subdivide the college graduates of each state into the production and retention elements.

The elements of Eq. (B13.3) are given below for three very different states – California, Michigan, and West Virginia – to show how the decomposition can reveal important dynamics that can prove useful in policy and program decisions.

Table B13.1 Decomposition of the sources of the college population for selected states, population 25–59: 2006–2010^a

The percentage distribution of the components of the total proportion of college graduates in a state, as shown in Table 13.9, is obtained simply by dividing the total percentage by the percentage from each source. For example, the percentage of California graduates due to production and the retention of native born is 11.4/30.9 or 37.1 as shown in Table 13.9.