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Migration and Local Labor Markets
Stephan J. Goetz, Penn State University

1. Characteristics of Migrants vs. Places

One way of classifying migration studies is to separate them into those focusing on individual's characteristics that influence migration behavior and those that look more at the characteristics of places as determinants of migration. A general conclusion from research conducted in the past is that the young are the most restless. So are the more-educated, although for this variable the relationship is sometimes ambiguous.

1.1. Characteristics of Migrants

Numerous studies have been carried out to identify the characteristics that make some individuals more likely to migrate than others. Life-cycle factors, such as marrying, divorcing, graduating from school, entering the workforce and starting a career or retiring from work, and having children or an "empty nest" are important reasons for migrating (Greenwood 1985, 527; Maynard et al. 1997; Long 1988 and Cadwallader 1992). In addition, variables such as physical well-being (health), age, gender, skills, education and income can affect the decision to migrate. Studies of the independent effects of various socioeconomic characteristics on mobility and migration propensities are reviewed in detail later on.

1.1.1. Age

One of the most consistent empirical findings in the literature is that age influences the propensity to migrate in a fairly predictable manner. For the most part, this can be explained by migration as an investment in human capital–an idea originally proposed by Sjaastad (1963) and later examined by Bowles (1970) and Greenwood (1975). The empirical regularity here is that, despite the relative importance of retirement migration, migration probabilities decline with age, holding other determinants of migration constant. According to Sandefur (1985) and others, the rationale for this relationship is usually that people move when they marry and when they have children (see Figure III.1: Migration Rates by Age Group; Source: Calculated by author from census data).

Important insights into the characteristics of migrants can be obtained from data collected in the Current Population Survey (CPS), administered and analyzed every March by the Census Bureau. A recent report finds, for example, that young adults are the most likely of all groups to move in general, including within counties (Hansen 1997, 2). Hansen reports data for any move, including moves from abroad. Figure 1 shows rates that were calculated separately using a transcounty move as the cutoff criterion for what constitutes migration. In general, the patterns that emerge in Figure III.1 above and those shown in Hansen (Figure 2, 2) are consistent with one another.

The median age of all movers (other than those coming from abroad) in the March 1996-97 CPS was 26.6 years. For those staying in the same county it was 26.3 years, while it was 27.3 for those moving into a different county, and 27.9 years for those moving into a different census region. In comparison, the median age for the entire U.S. population was 34.7 years, which highlights the greater mobility of the younger population.

1.1.2. Education

Another empirical regularity appears to be that those who have a higher level of educational attainment are more likely to migrate, because they receive greater returns for their skills when they migrate. This underlies the statement by Plane and Rogerson (1994) in Section I.12 that migration is associated with a certain degree of "elitism" in developed countries. Previous studies show that education does have an effect on the likelihood of migration (Bogue 1985, Greenwood 1975), although the effect is not necessarily robust in multiple regression models.

Migration can change the characteristics of the population in an area, and it is crucial to study the features of the migrants to fully understand what is happening in an area. For example, Greenwood 1985 (526) writes, "[a]lthough the South was exporting human beings [prior to 1970], it may have been importing human capital. ... The infusion of human capital due to net migration may have served as a catalyst that encouraged subsequent southern employment growth."

Only 2.7% of people with less than a ninth-grade education migrated across county borders between March 1996 and March 1997, compared with 4.3% of those who were high-school graduates. Both of these percentages are well below the rate of 6.4% for those who hold a bachelor's degree. Thus, individuals with the least amount of formal education tend to have the lowest migration propensity. This suggests that labor markets may adjust less well over space for this group than for those with a college degree.

1.1.3. Income

An individual’s current income can influence the likelihood of migration, but not necessarily in the direction one might expect given the discussion about costs of migration as a barrier in Section II. CPS data for the years 1996-97 show that the highest migration propensity is observed for those in the per capita income range of $22,500 to $24,999: 6.3% of the members of this group migrated across a county line. The lowest propensity is observed for those in the range of $85,000-$99,999 (3.2%), followed by the ranges of $100,000 and above, $75,000-$84,999, and $45,000-$49,999 (each with 4.4%). Even for those with a per capita income in the range $17,500-$19,999, the migration rate was 5.4%. All of this suggests that low income does not necessarily reduce the likelihood of migration. In fact, it may increase that likelihood, if individuals migrate in order to improve their economic well-being.

Additional insights into these issues, especially related to low-income households, are provided in studies by Fitchen (1994, 1995) and Schachter, Jensen and Cornwell (1998, 40, abstract), who detect "...a pattern of urban to rural migration among the poor." Schachter et al. conclude that the urban poor are being "pushed" into rural–and often declining–areas by the need to find affordable housing, and not to find employment.

1.1.4. Race

Racial minorities tend to have lower migration propensities than whites. Often the reason given for this is that minorities have lower access to information, have more limited resources to move, and may face discrimination at the migration target (see also Lee and Roseman 1997). Note that this generalization does not necessarily hold historically for all groups of migrants. During the early part of this century a large-scale migration of African Americans from the South to the industrial North took place, as was mentioned in Section I. Considerable evidence exists that African Americans are moving back into the South–Atlanta in particular–in large numbers. Some of this evidence is presented in Table I.7.

Hansen also writes that "Whites have lower overall rates of moving (15.7 percent) than either Blacks or Asian and Pacific Islanders–about 20 percent for both groups." She goes on to write that these differences, which are also observed among movers from abroad, are due in part to structural factors such as the average age of each group. She calculates that 3.2% of all moves involved a move from overseas, 15.2 involved a different state, 18.8% were to a different county within the same state, and fully 62.8%, or almost two-thirds of all moves, were within a county. Therefore, including this latter group among migrants will skew the overall results quite heavily towards representing the characteristics of those most likely to move only within a county.

This result reported by Hansen is seemingly at odds with results of the research discussed in the first paragraph of this subsection, and it underscores the importance of the definition of migration as opposed to a mere change of residence within a county. In particular, if we count only moves across a county boundary as migration, then 5.63% of all whites migrated between March 1995 and March 1996, compared with only 4.92% of all African Americans. In comparison, 15.25% of all whites moved overall, compared with 18.47% of all African Americans (not counting movers from abroad).

Thus, the hypothesis presented earlier that African Americans face more barriers to migration for various reasons appears to hold. As a result, although they may move from one dwelling to another within their community (county) more frequently than whites, African Americans are less likely to venture into a distant county than whites. A study by Lee and Roseman (1997) sheds important light on the role of kinship ties at the migration target for African American migrants.

1.1.5. Marital Status

The most recent results on Geographical Mobility from the CPS (the March 1996 to March 1997 survey) can be used to calculate migration rates across a county border or further, based on additional characteristics of individuals. For example, in terms of marital status, the following rates of migration across county borders are calculated:

Single (never married): 6.6%   

Married, spouse present 4.2%

Married, spouse absent 8.3%

Widowed 2.8%

Divorced 6.6%

Source: Author’s calculations using CPS data.

Clearly, marital status exerts a powerful influence on average migration propensity. Not surprisingly, one-person households were considerably more likely to move across county lines (6.4% of all households) than households with six people (3.5% of these households moved).

1.1.6. Regional Differences

Of all northeasterers 3.8 % moved, compared with 5.0% of midwesterners, 6.3% of southerners and 6.0% of westerners. Among other things, this means that moving companies had more business (per capita) in the South than in the Northeast. It is not clear to what extent this reflects intrinsic characteristics of individuals, as opposed to aggregate economic conditions prevailing in these regions, although the latter no doubt played a nonnegligible role.

1.1.7. Attachment to State of Birth

Another way of identifying both the characteristics of migrants and the relative attractiveness of a place as a migration target, is to look at the percentage of its residents born in their state of residence (Table 1). Results in this table have to be interpreted with caution, of course, because states that attract many migrants will have a high proportion of residents who were born out of state. Thus, the data in Table 1 also show the relative attractiveness of a state to out-of-state residents. This table serves as a transition to subsection 1.2, which presents data on total in-migrants and out-migrants for each state between 1985 and 1990. Together, these two pieces of information provide some clues about the desirability of a state for in-migrants as opposed to a low propensity of individuals to want to leave. (Note, however, that to draw a definitive conclusion, we would need to control for economic conditions in the state to identify the independent effect of residents’ preferences to remain in their states of birth.) For the United States as a whole, 61.8% of the population were born in the state of residence.

Pennsylvania ranks first in the nation in the percentage of state residents who were also born within the state (80.2%). The next-highest ranked states are Louisiana (79.0%), Iowa (77.6%) and Kentucky (77.4%). These statistics tell us two things: first, these states have received fewer in-migrants; second, residents of these states may feel a special attachment to their states, and migrate out reluctantly. Without additional data, such as the number of historical in- and out-migrants (covering the current generation of state residents), it is not possible to separate one effect from the other.

The lowest-ranked states in terms of population born in the state are Nevada (21.8% of residents were born in the state), followed by Florida (30.4%), Alaska (34.0%), Arizona (34.2%), Washington, D.C. (39.3%) and Wyoming (42.6%). The rankings of some of these states are more easily explained than others. For example, Florida and Arizona rank low because they have attracted large retirement populations, as has Nevada. The District of Columbia includes representatives from all 50 states who may reside in Washington only while they are legislators. Its situation illustrates the difficulty of defining and explaining migration behavior. Should legislators properly be counted as migrants? Wyoming and Alaska also raise questions. Both of these states have attracted proportionally large numbers of people from other states for reasons that are not altogether obvious. Those moving to Alaska from elsewhere may have been attracted by the energy industry, a sense of adventure or both.

1.2. Characteristics of Migration Origins and Targets

Migration researchers use the terms "push" and "pull" to describe the forces causing individuals to migrate. These can be viewed as characteristics of migrants or of places. Often these forces act independently, but they can also interact to accelerate the decision to migrate. A recent study looks at whether foreign immigrants into a state "push" out those living in poverty, and whether states with high welfare benefits per capita are magnets for poverty-stricken individuals (Frey et al. 1995). An underlying assumption is that foreign immigrants with few skills compete with low-skill existing residents in a state, and thus "push" them out to seek employment elsewhere, i.e., to states with fewer immigrants and thus less competition for low-skill jobs.

Frey et al. find that a "high volume of immigration to selected U.S. states does affect a selective out-migration of the poverty population, which is stronger for whites, blacks, and other non-Asian minorities, as well as the least educated." Using data from the 100 most-populated metro areas, Wright, Ellis and Reibel (1997) come to the opposite conclusion, indicating that (234, abstract):

...the net migration loss of unskilled native workers from metropolitan areas is probably a function of those cities’ population size rather than immigrant flow to them. We conclude that the net migration loss of [unskilled] native-born workers from large metropolitan areas is more likely the result of industrial restructuring than of competition with immigrants.

Frey et al. find no evidence that high welfare benefits attract poor families and individuals, or that low-benefit payments tend to serve as a push factor.

Table 2 presents data on the number of in-migrants, out-migrants and net migrants (in minus out) for each state. The migration period covers the five years before 1990, and the data are calculated using 1990 census records. Over this period, Iowa and Kentucky both lost about 300,000 residents. However, Kentucky gained almost as many people due to in-migration as it lost to out-migration, so the net loss was only 20,000. In contrast, Iowa gained only about 200,000 residents due to in-migration, so that its population loss was closer to 100,000, or five times that of Kentucky's. Comparing these numbers is of interest because both of these states have virtually identical shares of population that were born within the state.

Florida lost about 1,000,000 people over the 1985-90 period to out-migration, but gained over 2,000,000 in return. California gained just a few more people than it lost, while Texas gained 1.2 million people but lost 1.5 million to out-migration. Over this period, New York lost the most people of any state: 821,000. For every in-migrant into the state, two people migrated out. Of course, these numbers do not tell us anything about total population change, which depends also on net births and foreign migration.

The Federal Reserve Bank of Cleveland (Cleveland FRB 1997) reports and interprets more recent data on population migration between states in its newsletter, Economic Trends. In the April 1997 letter (available on-line at: www.clev.frb.org/research/Et97/0497/intpop.htm), for example, the bank reports that the states making up the Rust Belt experienced ongoing out-migration of population over the years 1990 to 1996. This conceivably reflects the sustained shift toward a service-oriented economy and away from a manufacturing basis, which is leading to a spatial redistribution of employment opportunities in the United States. Ohio and Pennsylvania each saw a decline in the share of the population employed in manufacturing, with 3.0 and 1.8 percentage point reductions.

Even so, the largest population losses over the period 1990 to 1996 on balance were from California (2 million more out-migrants than in-migrants), followed by New York, Illinois and New Jersey. States experiencing the fastest rate of in-migration were located in the Southeast and Southwest. To a large degree, this is driven by retirement migration. According to the bank newsletter, 800,000 more people migrated into than out of Florida, for example. Although that number is smaller than the 1 million migrants between 1985 and 1990 (Table 2), this works out to about 365 people per day!

For the present discussion, the following quote from the Cleveland Fed’s April newsletter is particularly interesting: "... the four states listed above as big net migration losers [California, New York, Illinois and New Jersey] had higher-than-average unemployment rates. The states with the lowest unemployment rates, however (which are mainly in the Midwest) were not the biggest gainers of net migration." This shows the profound importance of economic opportunity as a determinant of migration behavior; in this case, economic conditions in the place of migration origin–rather than the destination–exert the strong influence on migrants.

An insight into the effect of amenities on population migration is provided in a recent study by Cromartie (1998). He found that areas in the Great Plains with a high level of natural amenities experienced a net in-migration rate of population of 0.54 between 1994 and 1996, while areas with medium amenity levels had a rate of 0.33. However, areas with low amenities experienced out-migration rates of 0.11 over the same period.

1.3. Historical U.S. Migration Patterns

Historical migration patterns in the United States across county borders are plotted in Figure III.2: Mobility Rates Across U.S. County Borders,1947-97 (source: Prepared by author from census data). In each case, the ending year of the migration period is presented: 1997 refers to movement between 1996 and 1997, for example. Data are not available for 1972 to 1975 and 1977 to 1980, so simple averages calculated from the period endpoints were substituted.

Note the overall downward trend in this data series, which showed a decline of about 0.5 percentage points between 1947 and 1997. Also, a rather dramatic decline occurs after the most recent recession in the United States (1990-91). This declining trend is interesting in light of the argument that people are becoming more rather than less mobile in terms of their employment, the significant number of layoffs due to downsizing in the 1990s, and the argument in Plane and Bitter (1997, 148) that "... high mobility is one of the defining characteristics of modern economies."

1.4. Other Migrant and Migration Characteristics

1.4.1. Seasonality of Moves

Some intriguing details about the seasonality of moves and duration of residence–that is, the time between moves–are revealed in a recent Census Bureau report that uses data from the 1993 Survey of Income and Program Participation (Hansen 1998). Note that a move here is defined as a change in residence without reference to administrative borders such as county or state lines. The SIPP asked respondents 15 and older about the month and year they last changed residences, i.e., about the prior and current home (see data set description in Section IV, 5.1.2).

The summer months of June and August are the peak periods in which people move (Figure III.3: Distribution of Moves by Month of Move (Percentage of All Moves); Source: Hansen 1), while the fewest moves occur in February and March. This likely reflects a preference to move when temperatures are warmer and when children are out of school, and this possibly is also a function of graduation ceremonies at colleges and universities. According to the previous section, individuals in the age group of typical college graduates are traditionally the most likely to move. Close to one-half (48.4%) of all moves take place during the summer months (Hansen 1).

Perhaps not surprisingly, the pattern shown in Figure III.3 for moves across all population segments do not vary significantly across racial or ethnic lines, according to whether the mover was born in the United States or a foreign country, and whether the mover owned or rented the dwelling. A slight difference emerges in the seasonality of moving by age bracket. Those who are 65 years or older have the highest probability of moving in September (13.1% of all moves of 65+ year olds). Those who are 20 to 29 years old, or 30 to 44 years old, or 45 to 64 years old are most likely to move in June, with 13.0%, 13.0% and 13.3% of all moves, respectively, for each age group.

The data also suggest that families with children are less likely to move at the beginning of the school year–September or October–than all families combined. This illustrates some of the family-related constraints imposed on potential migrants. Another noteworthy result from the analysis of the SIPP data is that people moving over greater distances are more likely to make their move during the months of June, July and August. According to Hansen (3), "[r]ates of moving in the three summer months increase from 34.8 percent for those moving within the same county, to 35.0 percent for those moving between counties in the same state, and to 41.0 percent for those making interstate or international moves."

1.4.2. Duration of Residence

According to the SIPP data, respondents had lived in their current homes for a median duration of 5.2 years. Thus, 50% of all respondents had lived in their current residences longer than 5.2 years, and 50% had lived there fewer than 5.2 years. Nearly 15% of respondents (14.6%) had lived in the same house for one year; just about the same percentage (15.3%) had lived in the same house for 20 years or longer; and one in forty (2.5%) had lived in the same house for more than forty years.

Perhaps not surprisingly, renters had spent a shorter median number of years in their current residences (2.1 years) than owner-occupiers (8.2 years). However, there is a convergence of sorts in the median durations at current residences between owners and renters as age increases. For respondents 65 years and older, the median number of years at the current residence was 5.2, while it was 4.0 years for renters.

Differences in median duration of residence arise across racial groups and by Hispanic versus non-Hispanic origin. To some extent the longer duration of residence of whites (5.5 years) relative to that of African Americans (4.2 years), Asian or Pacific Islanders (3.3 years) and those of Hispanic origin (3.1 years) is a function of the fact that whites are more likely to live in their own home than a rental unit. For example, seven out of every ten whites live in an owner-occupied dwelling, compared with about only five in ten African Americans.

A final difference in the amount of time individuals stay in a place relates to gender. Overall, females have a median duration in their present residences of 5.6 years, compared with only 4.9 years for males. For females in owner-occupied homes, the difference in median duration is as high as 1.2 years (8.8 for females, 7.6 years for males). For rental properties, the median duration is 2.2 years for females, and 2.0 for males. In part this result may reflect differences in longevity for females and males. Also, these numbers do not reflect the marital status of the respondents. The medians would probably diverge even more if data were available for female-only and male-only households.

These differences in residential duration point to important variations in the propensities of various types of people to migrate over time. Furthermore, results of studies such as these provide suggestions about which explanatory variables to include in regression analyses of migration behavior.

2. Econometric Studies of Migration Using Ordinary Least Squares

2.1. Lowry’s Study

Because his work stimulated so much subsequent research on migration topics, Lowry’s (1966) ordinary least squares regression results are reported here (Table 3). Recall from the discussion in subsection 4.2 of Section II that Lowry used data at the SMSA-level and for the years 1955-60. In the table below results are presented for two different types of models. The first was referred to by Lowry as a "basic" model, and the second an "economic" model. Note that the effect of distance was not statistically significant in the basic model (and it had the wrong sign), but that it did become significant in the economic model, i.e., once the unemployment rate and wages were included. Neither unemployment nor wage rates in the place of origin were statistically different from zero, which led Lowry to the controversial conclusion that economic conditions at the migration origin did not affect migration decisions.

2.2. Time-Series Data

In a time-series study, Barkley (1990) examined independent factors that affected occupational mobility or labor migration out of farming over the period 1940-85. His dependent variable was formulated as a simple percent change over time:

M=[L_1(t-1) - L_1(t)]/L_1(t-1)

where L_1(t) is agricultural employment in year t. In Barkley's study, individual farmers compare returns from different occupations (farm and nonfarm) net of pecuniary and psychic costs of changing between occupations. The specific comparison in the empirical work is between returns to labor in farming relative to returns in the nonagricultural sector. All of the explanatory variables are lagged by one year so as to reduce any potential endogeneity bias.

As explanatory variables Barkley includes the ratio of value added per worker in the nonfarm to farm sectors to measure relative returns to labor; the ratio of nonfarm to farm employment to capture the likelihood that a job can be found in the nonfarm sector; the real price of land as a measure of farmers' wealth; the rate of unemployment in the nonagricultural sector; farm program payments from the government; as well as two dummy variables relating to definitional changes in the farm work force and an anomaly for female farm employment.

Barkley concludes that farm labor is highly mobile, as measured by the response of out-migration from farming to relative returns to labor in the two sectors modeled. Also, a larger share of employment in the nonfarm sector over time had the expected effect on out-migration (and was statistically significant), but the unemployment rate failed to yield the expected sign. The wealth effect measured in the form of land prices was, as expected, negative. Overall, Barkley's results provide important insights for policy-makers and planners concerned with maintaining the U.S. farm population to achieve a certain distribution of people in rural and urban areas.

2.3. Cross-Sectional Data

2.3.1. State-Level Data

A recent cross-sectional study at the state level examined the effect of state income tax policies on labor migration. Using 1985 to 1989 data, Saltz (1998) estimated this model:

where t-statistics are in parentheses, M_j is the rate of net in-migration into the jth state from all other states; INC_j measures expected real income in the jth state (a function of the cost of living, nominal median family income and the unemployment rate), TAX_j is a dummy variable indicating whether (=1) or not (0) the state has an income tax, WEST_j is a dummy variable for western states (to capture "amenities") and AGE_j is the percentage of the state’s 1985 population that is younger than 55. This last variable is supposed to capture a "friends and neighbors" effect in the sense that migrants are on balance younger and will prefer to locate in states with larger populations of young people.

Saltz concludes that his study has (600) "important policy implications for those states hunting for revenues and considering the income tax as a potential new revenue source. The introduction of such a tax is likely to reduce the long-term influx of population and hence to reduce the long-term economic growth and development of the state.

2.3.2. County-Level Data

The study by Goetz and Debertin (1996) had an objective similar to Barkley's but was based on cross-sectional data rather than time-series data, and considered overall rural population change rather than change in specific occupations. Their study used the 2,323 nonmetro counties of the United States as the unit of analysis, and regressed population change between 1980 and 1990 in each county on a number of explanatory variables. The measure of population change was the natural logarithm of the population in 1990 divided by the population in 1980 in each county i: pop_i=ln(pop90_i/pop80_i), and one of the regressors included in the equation was pop80_i. A basic accounting identity was used in the study to track population change between 1980 and 1990 (pop_i):

pop_i=m_i + b_i - d_i + r_i

where m_i is the net migration rate excluding retirement migration, b_i and d_i are birth and death rates and r_i is the rate of in-migration due to retirement. In Section IV we see that this equation relates to the residual or survival method of calculating net migration. In the study, only m_i was considered to have an economic content or to be subject to economic influences that needed to be modeled explicitly in the econometric equation.

Goetz and Debertin (1996, 522) examined only the features of places (i.e., counties) in their study, and not the characteristics of individuals. As Greenwood (1985) points out, traits of individuals (such as educational attainment or age) are virtually impossible to detect in such aggregated studies and often yield insignificant coefficient estimates. The reason is that only a limited correlation exists between these variables and the characteristics of the migrant population.

The cross-sectional, county-level study found that higher shares of federal farm program payments in total farm cash receipts encouraged population out-migration from rural communities. In addition, higher unemployment rates in a county pushed migrants out, as expected, and the status of being a retirement community had a positive effect on population growth. Estimates of both coefficients were statistically different from zero at well below the 1% level.

2.4. Studies Estimating Amenity Values

Numerous studies have been published on the implicit valuation of amenities, including a study by Blomquist, Berger and Hoehn (1988). Table 4 shows results obtained by Clark and Knapp (1995) in their study of the value that college and university professors attach to certain amenities (or dis-amenities). Only coefficients for amenity variables are reported here. In addition, Clark and Knapp used institutional measures (type of college), size and metropolitan measures. Fiscal measures and location dummy variables were included along with disequilibrium controls. Clearly, professors at all ranks attach a value to the amenity of sunshine and the dis-amenity of violent crime.

3. Migration Studies Using Limited Dependent Variables Method

Many statistical studies of migration fall into a class of econometric procedures involving so-called limited dependent variables. Unlike the distribution of the dependent variable assumed in the studies reviewed in the previous section, which is a normal distribution, many migration variables are truncated or censored in the following sense: A migrant has to decide whether or not to move. Here there are only two choices, and the variable has a nonstandard distribution. Or, an individual has to decide how far to move, i.e., within a county, across a county line, or across a state line. The statistical estimation methods required to deal with these problems, and produce unbiased and efficient coefficient estimates explaining migration behavior, are reviewed in this section.

3.1. Logit and Probit Probability Models

Two of the most basic limited dependent variable models are the logit and probit models, which are estimated using maximum likelihood methods. We start with a latent, unobserved variable y*, which depends on a vector of independent variables, x, as follows:

y*=ax +

where ± is a coefficient vector to be estimated and µ is a disturbance term. As indicated, we do not observe y*; however, we do observe the states of the world, y=1 or y=0. Suppose y* denotes the unobservable, latent propensity of an individual to migrate. In this case y=1 describes an individual's actual migration (which means y*>0, but we do not know by how much), and y=0 describes a situation in which no migration has taken place (y*=0).

The likelihood function for this problem is (Maddala 1988, 22):

where F denotes the cumulative distribution function associated with the error term . If that distribution turns out to be the logistic distribution, then the logit model is relevant. In that case:

and

A logistic regression is used, for example, by Polachek and Horvarth (1977, 139) to arrive at the following regression model (M=1 [=0] denotes that the individual has [not] moved):

Prob(M=1)=–1.4 + 1.7 Migration History – 1.5 Relatives* – 0.5 Wife in nonmenial work

– 0.03 Age – 0.13 Education of Wife* + 0.05 Predicted wage change*

Here the * denotes that the coefficient estimate is different from zero at the 5% level or below.

If, on the other hand the distribution of µ is the standard normal distribution, a probit model is relevant:

where is the standard deviation of the error term, . An example of a probit model of migration is given below.

3.2. Multiple Choice Models

White and Mueser (1994, 247) attempt to separate out "the effect of changing population composition from the effects of ‘structural’ changes in producing overall shifts in the mobility of the population." They are interested in identifying variation over time in the parameter estimates of migration models, rather then simply forecasting the impacts of nonstructural changes such as the aging of the population or increasing levels of skills among workers. The paper by White and Mueser was referenced above in the discussion of falling barriers to migration Section I.6, which can affect the structural relationship captured in migration equations and change the impact of a given sociodemographic trait on mobility or migration propensities.

White and Mueser use a multinomial logit model to estimate the probability that the ith individual makes the jth type of move. In this case, four different types of moves are permitted: (1) no move, (2) a move within a county, (3) a move within a county within a state and (4) a move across a state line. Note that this study very nicely uses the data as they are reported by the Census Bureau; this is discussed in greater detail in Section IV below.

The multinomial logit model is defined as follows, with P_ij denoting the probability that individual i chooses one of the four types of moves, j=1,2,3,4:

The vector x_i contains socioeconomic characteristics or traits of each person along with a constant, and ß_j is a parameter vector to be estimated using maximum likelihood methods. For example, ß₂ is the parameter vector for those who move within a county. Details about the estimation and the interpretation of results are described in greater detail, along with asymptotic properties, goodness of fit tests, and tests for violations of assumptions, in textbooks such as Greene 1993. In this kind of study it is necessary to select a reference type of move against which the other moves can be compared. White and Mueser set ß₁=0 for this purpose, which is convenient because these are the nonmovers in the population.