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

II. THEORY OF POPULATION MIGRATION
Question:  How does labor differ from other factors of production, such as capital, and why does this create the need for a separate theory of (population) migration?

Whereas owners of production inputs or commodities, such as bricks or bottles of wine, can ordinarily ship them away (so as to maximize profits or utility) while themselves staying put, owners of labor must usually move along with their labor. Furthermore, owners of labor have both feelings and independent will. Indeed, most aspects of human behavior, including migratory behavior, are both a response to feelings and an exercise of independent will. These simple observations divorce migration research from traditional trade theory as the former cannot be construed from the latter merely by effecting a change of labels. Stark 1991, p. 24.

1. Introduction and Overview

Theoretically, a number of variables influence an individual's migration decision. For analytical purposes, these variables can be classified into two categories of determinants:

First, differences in economic and other conditions, such as natural amenities in the target and origin areas (along with intervening opportunities or obstacles).

Both employment opportunities and local amenities available in different places have been used to explain migration behavior. In this section migration behavior motivated by employment considerations is initially discussed separately from migration motivated solely by "amenity-seeking." To some extent this distinction is artificial, because those seeking new jobs may also attempt to locate in areas offering better amenities. The two approaches are therefore merged subsequently.

Second, differences in the characteristics of individuals or their families may influence their responses to the differences in regional economic incentives they face.

For example, while individual A may migrate in response to a 10% regional difference in expected wages, individual B may find such a difference to not be worth the cost or effort of moving. Among other factors, the willingness and ability to respond to migration incentives (employment opportunities and amenities) depends on where an individual is on his or her life cycle, as measured by age (see Section III). This is also discussed under the rubric of mobility models below.

The next subsection presents a general theory of migration and outlines briefly how we can aggregate migration patterns from individuals to groups of migrants. The reader interested mainly in current theories of migration should skip subsections 3 and 4 after reading section 2, and proceed directly to subsection 5 on early behavioral models of migration. Readers interested in a historical review of the literature on migration theories will find more general descriptions in subsections 3 and 4, and detailed discussions of each subject in a hyperlinked appendix.

2. A General Theory of Migration

The postulates of a general theory of migration, for rational decision makers, must include the following as a minimum (see also Graves and Clawson 1981, 372):

  1. Individuals maximize utility (Ui), which is defined over attributes of places, i=0,1,2,...,p, which can include employment opportunities (or expected income, yi) and amenities (ai).

  2. Based on all the information available to them, individuals are able to rank any two locations, using the locations’ attributes.
  3. Preference orderings over locations are transitive: If place P1 is preferred to place P2 and P2 to P3, then place P1 is also preferred to P3.

Prospective migrants evaluate the expected utility of residing in different places over a given planning horizon. More specifically, they compare the utility derived at their current location (U0) with the utility that can be derived from other locations, net of costs of migrating, ci, between 0 and i:

=U(y0, h0, a0) – U(yici, hi, ai)

where refers to the net gain in utility that can be obtained through migration, h is hours worked, and all other variables are as described previously. According to this theory, utility-maximizing individuals will migrate whenever > 0. Otherwise they stay where they are.

Abstracting from amenities to simplify the notation, we can write the individual expressions for utility as follows:

and, likewise,

The additional notation introduced includes T, which is the planning horizon; Øi, which is the probability of earning income (i.e., of finding employment in the first place); ei, which denotes earnings; and the term exp–rt, which is a discount factor at rate of interest r. We have said nothing so far about costs of living in the different places. This would include differences in state and local taxes, and regional prices of goods and services. The above formulation is used in the study by Goetz and Debertin.

This microeconomic model of migration is, of course, set up for a single decision maker. When we aggregate over the decisions of each of these individuals, we arrive at accounting identities that capture the sum of these individual decisions. From gross in- (GIM) and out-migration (GOM) numbers we can calculate net migration, NIM=GIM–GOM, and each of these three quantities is still a function of the variables also influencing the behavior of individuals (Section V.3.2 discusses how this is done in practice). For example, Saltz (1998) specified the following model of net migration (rates) across the states:

NIM=f(y, t, W, a)

where y is expected income adjusted for each state’s relative cost of living, t is an indicator variable capturing whether or not a state has a system of income taxes, and W and a are amenity-type variables for the West and the share of population less than 55 years of age. These variables are nontraded and as such do not have explicit prices. Empirical results for this model and the rationalization of each variable is presented in Section III 2.3.1. This example illustrates how we can aggregate up from the level of individuals to the level of all migrants, and that migrants’ behavior in the aggregate still depends on the same factors as do the individual-level decisions.

3. Amenity or Non-Employment-Based Migration

For the first time in the world’s history pleasant living conditions–amenities–instead of more narrowly defined economic advantages are becoming the sparks that generate significant population increase, particularly in the United States. Ullman 1954, 119.

3.1. Climate and Natural Features

The role of amenities in migration has long been recognized, starting with studies such as those by Bright and Thomas (1941), Ullman (1954), Borts and Stein (1964), Fein (1965) and Muth (1972). Bright and Thomas used the term hedonistic to describe the character of migration to California prior to 1930. They argued that California "climate and legend," and not employment opportunities, accounted for the great influx of residents at that time. Similarly, Fein argued that people were moving to the South because of that region’s climate. Muth used a separate dummy variable for the West in his study of migration to capture the natural amenities offered in that part of the country.

Warm, dry climates and pleasant natural environments are perhaps the most obvious amenities attracting migrants, particularly retirees. The United States Department of Agriculture has compiled an amenity index for each county, consisting of latitude, mean annual temperature and presence of lakes. A recent study using this index found that counties with a high level of amenities experienced an income gain due to migration that was 11 times greater than the increase in income due to migration in counties with medium levels of amenities (Cromartie and Nord 45). Counties with low levels of amenities actually lost income due to migration; in other words, the people leaving those areas on balance had higher incomes than those moving in.

Other amenities sought by individuals may be good schools, hospitals or golf courses, with the relative importance of each depending on where the individual is on his or her life cycle. Certain types of amenities may become less desirable as more and more people attempt to consume them. These amenities are called incompatible-use goods. Lakefront properties on overcrowded lakes, or condos with scenic vistas of mountains or the ocean that are blocked by new construction demanded by newcomers, are obvious examples.

3.2. The Tiebout Hypothesis

Another important and enduring theoretical explanation of why people move, for reasons not related to employment, was formulated by Charles Tiebout (1956). Tiebout argued that people "vote with their feet" when it comes to choosing an optimal supply of public services (roads, schools, police and fire protection, welfare payments). Note that public goods and services either are or are not available in a community; they generally are not tradable (i.e., you cannot normally buy police protection services from a neighboring county). By definition, individuals cannot directly pick or change the supply of public goods except by moving, lobbying public officials or by waiting for the next election (although that will have an uncertain outcome), and this makes public goods very different from private goods (such as clothing, cars, confectionery).

More specifically, Tiebout argued that individuals select the communities in which they live by carefully balancing the taxes they must pay against the level of public services they receive in return. Rather than waiting for annual elections or voting referenda to express their preferences (which are satisfied only if they are in a majority), people find more immediate solutions to restoring imbalances that may suddenly arise between taxes and services: they move. One result of the threat to move is that it imposes competition on governmental units and, theoretically, forces them to be more efficient in supplying goods and services out of taxes.

The Tiebout model also has important implications for modeling how attractive a community is for firms and households. In particular, it is not sufficient to consider only the taxes levied within a community, as was done in some of the early industrial location studies. In addition to the tax level, it is necessary to consider what a community offers in return for taxes in the form of public services. High-tax communities may in fact be very desirable places in which to live, if the services provided are also of high quality.

The balance of taxes and services affect property values in a community, as illustrated by the following example adopted from Blair (1995, 253). Suppose a community decides to build a new public park, which results in a $100 per home annual increase in property taxes. Suppose further that there are two types of people in the world: those who do not care for or oppose public parks, and those who do care for them (perhaps couples with children, and senior citizens). Based on Tiebout's hypothesis, we would expect two things to occur as a result of the property tax hike.

First, the demand for housing in this community among those who like parks would increase. Second, there would be a decrease in demand for housing among those who do not care for, or oppose, the park. The latter group might articulate its preferences by simply moving away. These shifts in housing demand for the two groups are illustrated in the first two panels of Figure II.1. Actions by these two groups will lead to an increase in demand for housing in the community, resulting in higher house prices, but also a decrease in demand leading to lower prices. The overall effect on home prices in the community depends on which group is larger and feels more strongly about moving into or out of the community. The third panel of the figure assumes that those favoring the park outnumber those opposed to it, and consequently home values in the community are shown to increase. Clearly, in the long term, community officials and planners must implement public projects that are on balance favored by the majority of communitymembers, or they will see their population base erode.

[Figure II.1: Illustration of the Tiebout Model]

Thus, whenever individuals encounter a disequilibrium in terms of the local taxes they pay and the public services received in return, they will vote with their feet by moving or migrating between communities. This has important implications for such factors as the quality of schools. People with school-age children may move when they find that their local schools are not performing well. As Blair points out (276), this model is more applicable for explaining the choice of residence in a larger city than for explaining migration across states where costs of relocation are considerably higher.

Tiebout's ideas were also important in the formulation of environmental laws in the early 1970s. In particular, a concern existed at the time that states not imposing strict regulations would attract the most heavily-polluting industries, with adverse health consequences for the local population.

4. Employment-Based and Related Migration Models

Differences in net economic advantages, chiefly differences in wages, are the main causes of migration. (Hicks 1932, 76, quoted in Mueller 1982, 8).

4.1. General Early Models

One of the first researchers who attempted to develop laws of (or regularities associated with) migration was the geographer E.G. Ravenstein (1889 [1885]). Over one hundred years ago, he classified migrants according to their motivation for migrating, and his "laws of migration" based on so-called gravity principles have proven to be remarkably durable over time.

In early models migration was treated quite mechanically. It was often seen as based on the amount of "gravitational pull" between two places. The gravity model draws on physical laws related to mass and force to explain the movement of people between places. Just as planets that have greater mass and that are closer together exert a greater gravitational pull on one another, so do two places have greater flows of population between them if they contain more people to begin with and if they are closer to one another. These principles are shown in Figure II.2, and they can be captured algebraically as follows:

Here mij denotes the number of people migrating between places i and j (e.g., New York and Chicago); a and ß are parameters, with the latter reflecting the friction associated with distance; pi is population in place i and similarly for pj; and dij measures the distance between the two places in miles. Depending on the numerical value of ß, the term in the denominator represents a distance decay function .

[Figure II.2: Illustration of the Gravity Model]

Numerical Example

Consider the number of migrants expected to move between Chicago, Illinois (population in 1996 of 7,246,000) and Little Rock, Arkansas (population 474,000). According to the Rand McNally Ô Atlas, these cities are 657 miles apart. Suppose we set the scaling parameter a=1´10–9 (basically, this is done to reduce the dimension of the product of the two populations). Now, alternative values of ß lead to vastly different values for the degree of spatial interaction, m, as the following table shows.

ß m
0.10 343.4
0.5 25.6
1.0 5.228
1.5 0.204
2.0 0.0080

The very rapid decline in m as ß increases shows the enormous power of the exponential function, and the potential deterrent to migration that can arise from the "pain" of having to overcome distance. For example, a doubling of ß from 0.5 to 1.0 cuts m by a factor of about 5. The doubling from 1.0 to 2.0 cuts the amount of attraction by a factor of 654!

An increase in population in either or both places, and a reduction in physical distance, increases migration flows between places. Also note the interesting role played by parameter ß – the friction of distance, particularly in the case of commuting as opposed to migrating. If a high-speed rail line were to be built between two places, such as the TGV in France or the Bullet Train (shinkan) in Japan – the friction associated with distance would decline. Alternatively, if all residents were given a luxury automobile, the psychological costs of traveling might also decline because individuals would enjoy their trip more. These types of gravity models, which are based on Newtonian laws of physics, are quite commonly used in economic analysis. For example, they have been employed to explain shopping behavior of individuals over space, and trade between regions or nations.

Zipf (1946) successfully tested the predictions of the gravity model. He showed that a plot of the log of actual migration between major cities against the log of migration calculated using the above formula based on gravity very closely follows a 45o degree line. This relationship has become known as Zipf’s Law.

[Figure II.3: Graph of Zipf’s Law]

The following sections contain a brief overview of the early migration literature that focused primarily on reasons for moving other than amenities. This review draws in part on Mueller (1982). By clicking on the links you can obtain additional details on each topic. Readers less interested in the earlier literature should skip directly to subsection 5.

The "beaten path effect" has been used to explain migration behavior between two or more places. This can be compared to the paths wild animals follow, for example in Africa, when they migrate between water holes and various destinations over the course of a year. The idea is that the "beaten path" shows a clear way for others to follow, and the followers do not stray from that path, that is, they are not distracted by other opportunities they may encounter during their migration.

Later models became more sophisticated in how they introduced economic principles as determinants of migration. For example, income differential models start with wage differences over space. These differences are signals to potential migrants to engage in spatial arbitrage by withdrawing their labor from the lower-wage area and making it available to the high-wage area.

4.2. The Lowry Synthesis

The gravity- and wage-based approaches to migration can be merged, and the unemployment rate can be used as a determinant of the probability of obtaining employment (Lowry 1966):

Here ui (uj) is the unemployment rate in place i (j), and g denotes a functional form. If the unemployment rate in place i exceeds the rate in place j, i.e., ui>uj and everything else is held constant, then people will move from place i to place j. Economic conditions in both the place of origin and in the migration destination influence migration behavior. Furthermore, the relative effects are completely symmetrical, which need not always be true in reality.

When Lowry tested his theory empirically, using migration data from 90 Standard Metropolitan Statistical Areas (SMSAs) over the period 1955 to 1960, he came to a stunning conclusion. In particular, he found that economic conditions in the place of migration origin had no bearing on the propensity of individuals to migrate. He found that only the unemployment rate in the destination SMSA had the theoretically expected negative effect on migration: the higher this rate, the fewer the number of migrants who moved into that SMSA (Section III.2.1 has more on migration and unemployment rates). This was a profound result, because it suggested that declining communities could or would not solve their economic problems through out-migration. Lowry's findings also suggested that the behavior of in-migrants into an area could be studied separately from the behavior of out-migrants from an area. This led to a number of subsequent studies that examined in-migration and out-migration separately.

4.3. Models of In-Migration

Models of in-migration focus specifically on flows of migrants into cities or regions, and attempt to identify the factors that systematically explain these flows. They are not concerned with conditions prevailing in the places from which the migrants came. Mueller (1982) cites models developed in this category of migration studies: Job-vacancies models, structural models, and simultaneous equations models, which include alternative opportunities models.

As the name implies, in Job-vacancies models migrants respond to the opportunities that arise in places with excess demand for labor. Job-vacancies models are grounded in export base theory, which is reviewed elsewhere in the Web Book of Regional Science. This approach assumes that migration provides a perfectly elastic supply of workers to a region, and regions grow at different rates only because they are exposed to spatially varying forces of demand, which in turn are determined exogenously (i.e., outside the system). This assumption is at odds with the assumption of a perfectly elastic labor demand beyond an initial equilibrium, which is employed in simultaneous equations models (see below).

Structural models of in-migration incorporate additional local factors along with job vacancies as determinants of migration. In addition to employment opportunities, structural factors may include the condition of houses, fiscal policies, and industrial structure along with assorted amenities including city size and accessibility from other places as determinants. Structural models were among the first studies to explicitly treat amenities as factors in migration.

Simultaneous equations models of in-migration relate migration and regional economic growth. They were developed primarily to study economic growth, rather than to understand migration behavior. Assuming that the demand for workers is perfectly elastic beyond the current equilibrium wage, which is determined exogenously, regional differences in job growth are strictly the result of regional differences in migration.

Other simultaneous equations models consider the "alternative opportunities" available to migrants between their origins and destinations. Recall that the earlier gravity models considered economic conditions only in the migrant's original place and a single destination place as factors influencing migration behavior. The alternative opportunities model acknowledges that there are in fact a number of competing destination regions to which the migrant may move, and not just a single destination (Alperovich, Bergsman and Ehemann 1977). This model is a precursor to "place-to-place" models, which are presented below.

The equations involved when we consider multiple destinations necessarily become more complicated. In this case, "a move was considered to depend on the 'gravity structure' between the origin and destination relative to the gravity structure existing between the origin and all other places" (Mueller 1982, 19). To formalize this idea, consider the following equation:

Here mij is the number of people moving from place i to place j. This quantity is divided by the population (pi) in place i, which yields a migration probability or rate (relative to the total population of place i). The appendix for Section II has more details on this model.

4.4. Models of Out-Migration

Out-migration models fall into two categories: so-called propensity (to migrate) models and simultaneous equations models. The key emphasis is on economic conditions in the place of origin as a determinant of out-migration. Rates of out-migration from any given community depend on the characteristics of the population in that community, that is, the relative importance of people with high or low probabilities of migrating, or of being "at risk" of migrating. For example, one might argue that the people who still live in an economically depressed area at any moment in time have a very low inherent propensity to migrate, perhaps because they have close ties to the local community, including relatives and friends. The opposite would be true, in terms of probabilities, in booming cities that have recently received a large stream of in-migrants, such as Atlanta, Georgia. In fact, this variable plays an important role in some of the models reviewed in this section.

Propensity models focus on the independent effects of economic conditions in the places from where the migrants originate. If regional growth is interdependent with rates of in-migration, then growth must also depend on rates of out-migration. Presumably, communities facing prospects of reduced economic growth or economic decline will lose population, and vice versa. During the energy crisis of the 1970s, many mining-dependent rural counties experienced rapid rates of population growth, along with employment and income growth, only to see dramatic reversals once the energy crisis came to an end. This is the subject of simultaneous equations models of out-migration.

4.5. Models of Place-to-Place Migration

A new generation of studies, building on Lowry's work, attempted to synthesize insights obtained from both the in-migration and out-migration studies. This was accomplished by an explicit focus on place-to-place migration. Again following Mueller, this section presents two types of place-to-place models: allocation models and origin-destination models.

Allocation models get their name from the fact that they describe or explain the allocation of people among alternative regions or areas. Migration is modeled as a function of conditions both in the place of migration origin and the destination, which distinguishes them from the earlier-generation models described above. Also, in these models distance between places continues to play a central role in affecting migration behavior.

In this type of model, a ratio is formed using data on each migration origin-target combination relative to all migrants leaving a given origin. Thus, first calculate the number of migrants moving from place of origin i to target j. Second, divide this number by the total number of migrants leaving origin i for all other possible destinations in the country, producing an allocation rate.

Example: Calculation of Allocation Rates for U.S. Census Regions
Using the data in Table 3 in Section 1, we obtain the following migration allocation rates in 1996
for the four census regions.
  Northeast Midwest West South
NE   0.1881 0.2696 0.5422
MW 0.1523   0.2684 0.5794
W 0.0916 0.3032   0.6052
S 0.2224 0.4237 0.3539  

This table shows quite vividly (last column) that the South is receiving the proportionally largest shares of migrants of all regions. In this regard it is noteworthy that, according to Pisarski (1996, 22), "[t]here is evidence of a lessening of the shift to the sunbelt that has dominated national migration patterns since the 1950s."

A competing explanation of the role of distance between places in reducing migration is provided by so-called alternative opportunities models, which were already briefly described above. Here, migrants are basically tempted or attracted by opportunities that they encounter while migrating between two places. The greater the distance, the greater the "distractions" in the form of opportunity costs of alternatives that have to be foregone. Ignoring such opportunity costs may lead to an overstatement of the importance of distance as a deterrent to migrating (Levy and Wadycki 1974).

To capture the effects of intervening opportunities, one can use the population size, unemployment rate and wages of the most attractive alternative cities within the same distance of the migration origin as the eventual target (Figure 3). This distance criterion captures the fact that migrants might at best have knowledge about conditions in surrounding cities that are no further away than the selected target. Clearly, these models represent considerable refinements of the original gravity models, which considered only a single migration origin and target in isolation.

This model can be refined by using successively greater restrictions on the type of information available to the potential migrant (Wadycki 1974a). In the least restrictive specification, for example, the opportunity cost wage is represented by the highest wage prevailing anywhere in the country. The most restrictive specification considers (Mueller 1982, 43) "...only the best opportunities within a circle centered at the midpoint of the distance between the origin and destination. Thus, before their move migrants presumably only considered opportunities in a particular direction, which is revealed by the actual move."

[Figure II.4: Illustration of Intervening Opportunities]

What sets origin-destination models apart from the allocation models discussed previously is that the migration origin becomes an element of the feasible set of destination choices. One subset of these studies focuses on human capital factors as determinants of migration. Here, variables such as educational attainment, occupation or race take on the role of the variables measuring gravity.

5. Behavioral Models of Migration

Behavioral models of migration tend to be based on utility maximization under uncertainty and a total time constraint (e.g., Arora and Brown 1971). This type of model was already presented earlier in general terms in Section II.2. Migrants choose optimal allocations of time in the origin and the target place. Amenities in the migration targets and origin are used to weight expected real income streams. Thus, the discounted present value of real income, yi, that could be expected in migration target i is written as:

In this equation, d is the total duration of the planning horizon (perhaps measured in weeks or in months), do is the amount of time spent at the migration origin–where income is known with certainty, prob denotes the probability of earning income yit at migration target i in period t, which depends on a factor ³ that in turn varies positively with the amount of time devoted to residing in the migration target, and c denotes fixed costs of migrating between the origin and target places.

The theme of an "expected income" in the destination appears frequently in these types of migration studies. Researchers often use the unemployment rate as a proxy for this fact. For example, if average earnings per job in a community are $20,000 per year, but the unemployment rate in that community is 10%, then the expected earnings are only $18,000 per year (i.e., $20,000-(1-0.1)). In these models uncertainty simply serves to discount or reduce expected earnings.

Assuming a constant elasticity of substitution for the utility function, constant real income growth rates and using linear approximations for the income streams, ordinary demand functions can be derived for the amount of time spent by the migrants in either the origin or the target county (Arora and Brown). An intriguing aspect of this model is that when the individual migrant's time allocations and the explanatory variables are aggregated to the level of all potential migrants, an aggregate model is obtained that is not unlike those discussed earlier. This provides a microeconomic, or individual decision maker-based, foundation for the more macro-oriented or aggregated studies.

The migration problem facing individuals can also be specified using dual utility functions, u1 and u2(Grant and Vanderkamp 1976). The first function captures features of the migration origin (o), while the second pertains to characteristics of the migration target (i). There are a total of I feasible targets. Let vector zcontain characteristics of the origin and targets, and u1(zi) [u2(zo)] the fixed or nonstochastic component of the target's [origin's] utility functions. In that case, the odds that migration target i will be chosen by the migrant is:

This is a fairly common structure of choice models (including migration choices), as discussed in Section III on applications. With some further manipulation we can show that:

measures the probability that target i is preferred (and selected) over the migration origin o.

To illustrate, Grant and Vanderkamp included economic opportunities measured by using income levels and rates of unemployment, distance between migration origin and target, and amenities of population size and the share of the francophone population in the migration target. For characteristics of the migration origin, they used francophone population shares, unemployment and income levels. In the next section we examine so-called mobility models, which are also behavioral.

6. Mobility Models

Although the two terms are used interchangeably, mobility and migration can actually refer to two different events. Mobility is sometimes treated as a change in residence (home address) without necessarily involving a change in location (city or county). According to our definition, migration involves a move at least across a county border, that is, to a different locality. Thus, migration implies mobility, but mobility does not have to imply migration. Also, according to some researchers, migration involves a change in (local) labor markets (e.g. Rossi 1980, 19).

In mobility models designed to explain migration, the emphasis is on the individual's decision whether or not to move, and not the origin or destination of the individual. Usually, this decision is modeled as a function of the individual’s characteristics. In one of the first mobility studies, explanatory variables included the size of the mover’s family, whether the home was owned or rented, how long ago the family had been formed, how long it had resided in the current place, its migration history and income as well as the age, gender and educational attainment of the head of the family. In addition, the expected net gain in income from migrating was included as a regressor (Kaluzny 1975).

6.1. Mobility and Nontraded Goods

A common feature of mobility models is that individuals are assumed to maximize utility subject to some constraint. Graves and Linneman (1979) "...considered the migration decision to be a derived demand for nontraded or location-specific goods, which include amenities and employment opportunities. Migration was characterized as a response to changes in the demand for, or supply of, nontraded goods and in the cost of migration" (Mueller 1982, 60-61).

As the name suggests, nontraded goods are those that cannot be bought and sold over space. For example, an avid boater with a strong preference for a particular lake has to move into the vicinity of that lake to use it. Other examples of location-specific goods include national parks, professional sports teams and theaters (Broadway).

6.2. A Dynamic Model of Mobility

In the Graves and Linneman model, migration is the response to any disequilibrium in the supply of or demand for certain goods and services. For example, a boost in income or a change of status from working to retirement can trigger such a disequilibrium. In their study, changes in family sociodemographic characteristics such as education, family size and structure, health, earnings and employment were all related to changes in the derived demand for migration. On the cost side, factors used include social and religious ties to the community, the number of children in school, and tenure in the present job as explanatory factors.

A fundamental relationship between investment in education (human capital) and migration is at the center of the study by Polachek and Horvarth (1977), which is reviewed in Polachek and Siebert (1993, 242-43):

Not all (job) search takes place at a moment in time. In most instances search continues throughout one's life. Both job mobility and geographic mobility are examples, as people often view their job or location as a stepping stone for further advancement. Searchers can thus be viewed as 'perspicacious peregrinators' because they seek and weigh information on locational and occupational choices in each time period. Here mobility becomes an on-going rational process in which individuals continually gather information. However, individuals act on this information with a move or job change only when a move is economically efficient.

In a static model, people would find an ideal location, build their dream homes and remain in the same place forever after. In reality, and in a dynamic model, people are constantly seeking out new opportunities and ways of improving their situations. The average male in the United States changes jobs about ten times during his life, compared with an average of seven times for males in the United Kingdom (Polachek and Siebert, 1993). In a mobile society, these job changes are often also associated with changes in the place of residence. And younger individuals tend to move more often than older persons. Why?

Suppose that at any moment in time an individual owns a stock of information about the labor market. This stock consists of information about wages paid by other employers or other jobs in which the individual could work. In addition, of course, the individual knows the current wage, which can be compared with the other potential wages. When the worker decides to move to a new job, and only at that time, the information gets translated into an actual pecuniary benefit or gain. So over time, as the worker searches for and gains information about other, higher-paying jobs, the marginal gain that can be realized by switching jobs increases. The longer the search, the larger the highest wage about which the worker obtains information. This is shown in the attached figure as an upward-sloping marginal benefit line starting at a point in time marked 0.

In addition, the individual of course faces monetary costs associated with moving. These are not only the costs of paying the moving company and the real-estate agent when a new home is purchased, but also any foregone earnings during the period of the move. A rational decision maker will not make the move unless the marginal gain from moving exceeds the marginal benefit, everything else equal. Thus, workers wait until the marginal gain from moving reaches (or just exceeds) the marginal cost incurred. In the attached figure, the marginal cost is drawn as a constant line, and it so happens that the marginal cost equals the marginal benefit of moving at point A in this hypothetical case, or at point in time t1.

[Figure II.5: The Polachek and Siebert Model]

Polachek and Siebert’s model further implies that the stock of knowledge held by an individual becomes worthless (has a value of zero) as soon as the move takes place. In essence, once the worker has taken the new, highest-paying job, he or she has to start from zero in identifying new, higher-paying employment opportunities. Thus, using an optimal control model over a life cycle, an individual worker faces recurring moments in time when a move becomes economically rational. This can be described as a "periodicity" of moving (Mueller 1982, 61), which need not be regular. The lines for the marginal benefits in the figure are deliberately drawn in such a way that the slope becomes less steep over time. This is supposed to reflect the fact that it becomes increasingly more difficult for workers to improve their wages by finding better-paying jobs as they become older. This model is consistent with the actual migration behavior of individuals over their working life cycle.

From the above analysis, Polachek and Siebert specify a simple model of migration, which is familiar from previous discussions:

prob(migration)=f(Y, C)

where the probability that an individual migrates is a function of the expected change in income (Y) resulting from the migration and the associated costs of migration (C). This estimation structure is a simple probit model, involving both movers and stayers, which is discussed in more detail in Section III.5, in the context of the model presented in Nakosteen and Zimmer (1980).

6.3. Other Determinants of Mobility

Another set of models distinguishes between factors affecting an individual's job status and the individual's mobility. For example, tenure in a job and length of residence in a community may jointly affect mobility and employment status, but they might also exhibit independent effects. Finding such effects requires a linear regression analysis. Bartel (1979) studied this problem by modeling migration as consisting of three interrelated occurrences: resigning from a job and migrating (event 1); losing one's job and migrating (event 2); and transferring one's job with the same company and migrating (event 3). Thus, any one of these three events can trigger a migration response, but each event can also occur without the individual necessarily migrating. With appropriate data, the independent effects of variables affecting migration as opposed to those affecting resignation from a job, or a termination from a job, can be identified.

In an extension of previous work, DaVanzo (1977) was concerned with whether a spouse's work status affected an individual's mobility. One way of introducing this twist into the model of migration is to use family income rather than the income of only one individual in the Polachek and Horvath (1977) analysis. Out of this one would expect married individuals to be less mobile than single workers, since the search for higher-paying jobs in that case involves two individuals rather than only one.

These migration studies can be summarily labeled as primarily concerned with family-specific, life-cycle determinants of migration. A relatively recent emphasis in the literature has been on equilibrium as opposed to disequilibrium causes of migration behavior. In large part these new areas of study have been made possible by the development of individual-level, micro data sets (Greenwood 1985, 527), as described in more detail in sections III and IV below.

7. Equilibrium vs. Disequilibrium Models of Migration

The models of migration discussed so far generally assume that individuals respond to differences in economic conditions over space when making their migration decisions. In other words, they react to initial disequilibria in factors such as wages, home prices and unemployment rates. In the process of migrating, according to these models, they restore an equilibrium over space. In other words, migrants engage in spatial arbitrage, which creates a new set of equilibrium conditions.

7.1. The Importance of Amenities

A relatively new, key insight into modeling migration behavior was the recognition that individuals are willing to forego some income, or pay higher house prices, in exchange for the benefit of living near an amenity. In particular, if individuals want to change their consumption patterns of these nontraded amenities, they have to relocate. Thus, to the extent that migration of individuals and of firms over space causes economic development, regional differences in the availability of fixed amenities are a key factor leading to the development and growth of an area, according to this model.

Knapp and Graves (1989, 71) "...develop a framework which motivates a new assessment of existing alternative models of regional development, indicating the need for additional modeling efforts which focus upon amenities as critical elements in such analyses. The process of amenity capitalization via location and relocation enables researchers to explore the implicit value that society places upon amenities. This then permits the assessment of future regional development trends in a more comprehensive manner." In this context, amenity capitalization refers to the fact that the value of a site-specific, nontradable amenity is bid into local wages (negatively, i.e., by reducing wage rates) and rents (positively, i.e., by increasing rents).

To understand how these models are developed, it is useful to see how they relate to the earlier work on migration along the lines of Lowry (1966). Start with a low-income region, which contains jobs paying relatively low wages. As in international trade models, the low wages are caused by the fact that labor (l) is in relatively greater supply than another resource, such as capital (k), used to produce the single composite output, y:

y=f (l, k)

In this model, a corollary of low wages and low marginal physical products (or productivity) of labor is that returns to capital are high; that is, the marginal physical product of capital is large. If there is another region with opposite relative resource endowments–large amounts of capital and relatively few workers–then labor will migrate out of the low-wage area to the high-wage area. Capital will flow in the opposite direction assuming it is also mobile. In the process, wages and returns to capital will become equal over space, i.e., there will be a movement toward an equilibrium starting from a disequilibrium. This is in essence a demand side approach to modeling regional differences in productivity (as in the earlier work of Blanco 1963, Lowry 1966 and Mazek 1969).

In this approach the following relationship is posited (Knapp and Graves 1989, 73):

in-migration=f(wages[+], unemployment[-])

where the signs show the effect of each variable on in-migration (higher wages lead to more in-migration, everything else equal). The problem with this equation is that empirical research found an "embarrassing number of unhypothesized signs (with people migrating in large numbers to areas of low income or to high-unemployment destinations) and, at the same time, the explanatory power of the relation was low" (Knapp and Graves 1989, 76). In other words, variation in the explanatory variables failed to "explain" a large share of the variation in the dependent variable (in-migration) in these studied. The poor performance of these equations in empirical applications triggered a search for better theoretical explanations of in-migration behavior. Some important clues were provided by the work going on at the time among urban economists and labor economists.

In 1974, Rosen published a widely-cited paper in which he used hedonic prices to estimate the economic value of site-specific attributes. Derived from the Greek work for pleasure, "hedonic pricing" refers to valuing an asset or resource as a function of its characteristics. For example, a property on the oceanfront will in all likelihood have a higher value than the same property located in a nondescript area in the center of the country.

A home closer to the center of a monocentric city located on a featureless and flat plain, where people have their jobs, will have a higher value than the same home built in the hinterlands (or periphery) of the city. Why? The simple answer is that the reduced commuting costs will be bid or capitalized into the value of the properties and homes located closer to downtown. This hedonic pricing method is now commonly used in labor and natural resource economics to value location-specific amenities (e.g., Blomquist, Berger and Hoehn 1988). In the typical model, the independent effect of an amenity on both housing rents and wages is estimated or valued.

Differences in the demand for these properties, or location-specific amenities, lead to migration of population without necessarily causing a new equilibrium, and this is a key contribution of the disequilibrium literature. For example, "...unlike income, migration to a nice climate does not, in the process, reduce the quality of the climate–one expects that people move to desirable locations until wage (or rent, although this was not immediately perceived) compensation makes them indifferent among locations. Then, no further migration occurs due to amenity variation since compensation is present" (Knapp and Graves 1989, 76). Note that California represents a counterexample to this general rule. In that state rapid in-migration has led to problems with the consumption of environmental goods, such as clear air versus smog in the Los Angeles basin area (see also Graves and Clawson 1981).

7.2. Accounting for Differences in Amenities and Costs of Living

One of the key problems in the early migration studies was that they failed to control for costs of living. In other words, they merely examined income or wage differentials, without regard for differences in what it costs to live in an area on a daily basis. This, of course, is an important shortcoming because a correct and accurate accounting for costs of living may not only completely offset but perhaps even reverse any income or wage differentials that exist between two areas.

As an illustration, consider the cost of buying a home overlooking the San Francisco Bay with a home located in a sparsely populated rural areas with few amenities such as a Major League baseball team or improvements such as highways or Internet connections, and with a very poor climate. Clearly, the home in San Francisco commands a much higher price precisely because a majority of people would prefer to live in that location. And, a majority of people may be willing to forego some wages in exchange for living in a place with a good climate, many attractions and a beautiful view of the ocean. Yet, if these differences are not taken into consideration, then it is not surprising that the equations for in-migration discussed above yield unexpected signs for the coefficient estimates and have limited explanatory power.

Thus, Knapp and Graves (1989, 77) maintain that the assumption of a "featureless" plain (or city) was a key, longstanding problem:

The original urban literature, with its drab monocentric featureless-plain city, certainly gives one the impression that rents are costs, costs are associated with city size and the resulting value of nearness to the center. But, the seemingly small step of putting "access" as an amenity into the utility function makes it quite clear that rents represent a host of capitalized amenities-not just access but also presence of an ocean, views, school quality, crime, environmental quality, and so on. Rents are high at desirable locations; they are both a cost and a benefit in exactly the same way that a lobster dinner costs more, but also provides greater benefits, than does a bean dinner. Thus the often-cited truism that high wages in a location merely compensate for high rents is called into question.

In their analysis, Knapp and Graves consider site-specific goods, including a good climate and high environmental quality, which cannot be traded. Thus, individuals who want to change their level of consumption of these goods have to migrate to change that level. They will move toward areas with (positive) amenities, and away from areas with location-specific disamenities. In contrast, consumption levels of tradable goods (such as books or movie tickets), which are not location-specific, can easily be changed without migrating.

7.3. Changes in the Demand for Amenities

Changes in demand for location-specific goods can arise for a number of reasons. For example, better education about environmental problems may cause individuals to seek out less-polluted states, such as Utah or Colorado. Or, increases in income can raise the premium individuals are willing and able to pay to live in a resort town, such as near Lake Tahoe. Knapp and Graves (1989) go on to argue that it is inappropriate to distinguish migration related to employment from migration related to an individual's residence. Specifically (78), "Long distance moves between labor markets are shown to be, in many cases, related to demands for broadly defined residence traits, while many moves within a local labor market are related to one's job." Thus, they argue that an integrated treatment of the markets for labor and land (housing values) is necessary.

Environmental quality as an attractive feature for firms and workers figures prominently in the study by Goetz, Ready and Stone (1996). They argue that states with better environmental conditions were in a better position to attract firms and skilled workers, as well as wealthy retirees. In addition, worker productivity in these states was higher because workers were generally healthier. According to their model, these factors together contributed to faster per capita income growth over the business cycle.

7.4. Compensating Wage and Rent Differentials

An important concept that grows out of this analysis is that of a compensating differential in wages or rents. In particular, individuals may be willing to pay higher housing costs (rents) and accept lower wages in order to live in a nice place. Conversely, individuals demand compensation in the form of higher wages to put up with pollution and congestion. (See whether college professors’ salaries vary with amenities!) In other words, if workers move out of an area considered to be less-than-desirable relative to other areas, local wages will rise to reflect the greater scarcity of labor. In addition, it is possible that home prices and rents fall, reflecting reduced demand for housing. Eventually, however, firms may be forced to relocate as they are forced to pay higher and higher wages and increasing worker shortages. And, these firms may follow their former workers to the more desirable locations, which is an argument for "jobs following workers" (as opposed to "workers following jobs)."

These ideas can be expressed more formally, and graphically, as follows (based on Clark and Knapp 1995). Suppose individuals (workers) have an indirect utility function, U, defined over wages w, rents r (home prices) and natural or other amenities a: U=U(w, r, a). We abstract from prices of all other goods, which are assumed not to vary over space. Let the notation U* indicate that the same indirect utility level is reached across all regions. In other words, utility is at an equilibrium level. By appealing to the implicit function theorem, we can express wages as a function of the other variables, and U*:

w=w(U*, r, a)

When drawn in w–a space, this "wage acceptance" function traces out a line representing individuals’ indifference between wages and amenities. In other words, the line shows alternative combinations of w and a that leave individuals indifferent or equally happy.

[Figure II.6: Clark and Cosgrove’s (1991) Wage Offer/Acceptance Function]

Likewise, firms offer workers a wage schedule that incorporates the effect of amenities on worker productivity (Henderson 1982):

f=f(U*, r, a)

The higher the value of the amenities, the lower the wage that has to be offered by the firm. Through the bargaining process, individual workers and firms come to an agreement over wages that are mutually acceptable. In the process of this bargaining, a schedule Wo is traced out showing equilibrium combinations of wages and amenities that are acceptable both to workers and firms (Figure II.6). In this manner, we have derived an inverse relationship between wages and levels of amenities in a community.

Now the question arises, what will stop all workers and firms from moving into the most highly-desired locations of the country? The simple answer is that real wages–adjusted for costs of living–will become so low, and local rents so high, that even the most desirable places will become undesirable at a certain point. Along with pollution and agglomeration diseconomies including congestion, this automatic, negative feedback ensures that not all economic activity will end up in a single place.

Knapp and Graves maintain (1989, 83) that in the early years of U.S. economic development, people followed employment opportunities as they arose in different parts of the country. Differences in resource endowments and specific local conditions (such as the availablity of range land or coal mines) allowed some areas to enjoy more favorable production conditions than other areas, and this was the main cause for differences in economic growth rates over space. These differences in growth rates in turn provided an incentive to workers to migrate in pursuit of better economic opportunities. Over time, the effect of spatial differences has become less pronounced, due to innovations in communications technology, improved transportation infrastructure and the general shift toward the service economy.

7.5. Summary

The early theoretical research viewed migration as a necessary by-product of or response to employment search. A parallel literature examined the role of amenities in migration but did not explicitly consider compensating wage or rent differentials. While employment opportunities remain an important criterion in migration models today, family and life-cycle factors have taken on more prominent roles.

The two key theoretical approaches to migration–equilibrium vs. disequilibrium–are summarized in Figure II.7. What distinguishes these two approaches is the assumption made about the availability of information and the degree to which mobility is perfect or imperfect. An exchange in the Journal of Regional Science clearly demonstrates that the question of whether migration should be modeled as is a disequilibrium or an equilibrium phenomenon is far from settled (Harrigan and McGregor 1993; Graves and Mueser 1993; Schachter and Althaus 1993). Graves and Mueser attempt to reconcile the two approaches within a single model, which is presented in subsection 8.

[Figure II.7: Graves and Clawson’s (1981) Equilibrium vs. Disequilibrium Views of Migration]

8. Migration Dynamics

As a flow variable, migration naturally lends itself to dynamic modeling, as we already saw in the dynamic optimization model developed by Polachek and Siebert (1993). Diamantides (nd) develops a dynamic model of international migration that is based on the same principles as the diffusion patterns of molecules. Krugman (1993) presents a somewhat simpler model of population migration between two regions. A number of simplifying assumptions make the presentation more manageable.

Krugman’s (1993, 116-18) model of migration dynamics resulting from worker adjustments to wage differentials over space provides a simple but fairly useful insight into the roles of initial conditions (or history) and economic agents' expectations as determinants of population movement. Suppose we have a two-region economy (region u and s), workers are the only input and they are completely mobile, although they face costs of moving between the regions. Another assumption in Krugman’s model is that the wage differential between the two regions, wu-ws, depends solely and in a positive manner on the proportion of all workers (N=Nu+Ns) who reside in region u:

wu-ws=ß(Nu-,

where = (Nu + Ns)/2

So a larger share of workers translates into a larger market share, leading to higher wages. Note that when Nu=, wu=ws. In principle, the region with higher wages will attract workers. However, workers also face moving expenses, which have to be subtracted from total worker income to arrive at net income:

where the dot over the letter N denotes a rate of change over time and is a parameter representing the cost of moving (see also below). With perfect foresight about the evolution of future wages, workers can attach an asset value, v(t), at any point in time t, to locating in a given region:

where w(ML: CHARACTER) is the time path of wages (forecast over period and starting at time t), and r is the interest rate (rate of discount). Differentiation of this equation yields:

In other words, the rate of change in the asset value over time associated with living in a certain region equals the asset value discounted by the interest rate minus (or plus) a quantity that depends on the wage differential between the regions, which is in turn a function of the distribution of workers.

Krugman goes on to argue that workers will continue to move at a rate such that the marginal expenses associated with moving to region u are exactly equal to the net gain in income that results from the move (recall from above that parameter denotes the cost of moving):

With this, we have a dynamic system of variables defined for v and Nu, which is plotted in Figure II.8 in the form of a phase diagram. Anywhere along the line =0, the asset value associated with moving to the other region remains unchanged. This line also intersects the horizontal axis at the point at which Nu= .

The graph is divided into four quadrants by the horizontal axis and the line along which the asset value is constant. The arrows show the laws of motion that are exerted on a point in each of the four quadrants. For example, below the horizontal axis, v<0. According to the equation just discussed, this also means that u<0 at points below the horizontal axis, which is why the arrows point towards the west below the horizontal line, and to the east above the horizontal line. To understand the vertical forces (north-south), we need to look at the first dynamic equation of this system. This equation shows that, when Nu > (and the difference is larger than rv), the quantity becomes negative and v consequently falls. This is shown as the arrows that are pointing to the south.

The laws of motion in this phase diagram are such that if a disturbance takes the system away from the point at which Nu= , the system will not return to that (unstable) equilibrium point. Instead, the system reaches a new (stable) equilibrium only after all of the workers have migrated into one of the two regions. This simple illustration indicates that all of the workers in the economy will eventually end up either in region u or in region s. In fact, assuming positive roots for the two preceding differential equations, the workers end up in the region that had the larger share of workers in the first place.

[Figure II.8: Krugman’s Dynamic Migration Model]

In their intriguing contribution to the question of whether migration should be treated as an equilibrium or disequilibrium model, Graves and Mueser (1993) present the following dynamic model. This is an attempt to see, within a single model, under which conditions one modeling approach may be superior to the other, and when both might be appropriate.

We start with the premise that wages (w) and rents (r) change over space so as to equalize individuals’ utility (U*) and firms’ productions costs (C*). The first part of this idea is already familiar from the discussion in the previous subsection on compensating differentials. From this we get:

U*=U(w, r, a)

C*=C(w, r, b)

where, as before, a denotes natural amenities or amenities created by humans, and b denotes location-specific factors affecting costs of production other than wages and rents. In equilibrium, firms’ iso-cost line (C*) is downward-sloping when drawn in r–w space (not w–a space as above), as land is substituted for labor as the latter becomes increasingly costly to the firm. This is shown in Figure II.9.

[Figure II. 9: Dynamics of the Graves and Mueser (1993) Model]

Conversely, U* is upward-sloping in the same space, showing that individuals do not mind paying higher rents as long as their wages keep rising, everything else equal. A long-run equilibrium occurs at the point of intersection of these two curves, yielding equilibrium values r* and w*.

In Graves and Mueser’s model, dynamic equilibrium is brought about by migration of individuals (households), in response to any divergence between U* and U. Similarly, firms can change their demand for workers if actual costs C diverge from equilibrium costs C*:

a [U (w, r, a) – U* ]= ß [C* – C(w, r, b)]

where aand ß are the (speed of) adjustment parameters. In addition, households’ and firms’ total demand for land (D) must equal the supply (S):

D(w, r, N)=S

In this model, the market for land implicitly determines the number of households present in equilibrium in a given location.

Next, suppose that any point along line AA in Figure II.9 represents an equilibrium in the land market. Since this line is below the long-run equilibrium values of r* and w*, pressure exists for households to migrate into the area. The necessary adjustment takes place via the net migration mechanism in the equation shown above involving parameters a and ß, and it leads to a movement up along BB until the long-run equilibrium point is reached. As Graves and Mueser point out (1993, 81): "For population at any given level, the intersection of AA and BB indicates the ‘dynamic equilibrium,’ indicating the level of net migration."

They summarize the treatment of equilibrium and disequilibrium as follows:

...the question is whether the system remains "close enough" to the long-run equilibrium to make a useful approximation, or, more generally, whether movements in the equilibrium point approximate those observed in the system. Hence, if Equation (1) [involving U* and C* above] is close to being satisfied at all times, the population equilibrium model is valid. ... if a and ß are sufficiently large relative to shifts in exogenous factors, a and b, migration will maintain the system near equilibrium. In this case, levels of migration merely reflect changes in the equilibrium population level. On the other hand, sudden shifts in a or b will cause displacement from the equilibrium. (81)

9. Summary of Section II

This section has presented a general theoretical model of migration behavior, and reviewed the early and current literatures on theories of population migration, covering amenity- and employment-based migration as well as a synthesis of the two, in the form of compensating wage and rent differentials. The question of whether equilibrium or disequilibrium views of migration are more appropriate continues to generate discussions in the literature. Applications of the various theories reviewed are presented in Section III.


Exercises and Discussion Questions for Section II

  1. Postulate number 2 at the beginning of this section states that individuals have sufficient information available to them to be able to rank different locations. How realistic do you think this assumption is?

  2. The theoretical model of migration says nothing about differences in personal income taxes, inflation or costs of living over space. How would you introduce these factors into the migration model presented in subsection 2?

  3. Calculate the amount of interaction according to the gravity model between the following cities. Assume ß=1.0 and a=1x10–9. Populations are for 1996, and are in thousands. Distances are based on the Rand McNally Road Atlas.

  4. Cities and populations in square brackets
    (in thousands)
    Distance (miles)
    Atlanta [3,514 people] and New York [8,643] 854
    Atlanta and Boston [3,263] 1,108
    Atlanta and Chicago [7,734] 708
    Atlanta and San Francisco [1,655] 2,483
    New York and San Francisco 2.930
    New York and Salt Lake City [1,218] 2,189
    Los Angeles [9,128] and San Francisco 387

    What happens to the interaction between Atlanta and New York when ß drops to 0.5? Or, when it increases to 1.5?

  5. California is well-known for its favorable year-round climate. How do you explain the fact that about 2 million more domestic migrants moved out of than into that state between 1990 and 1997? In contrast, over the same period 66,000 people moved into Minnesota, a state known for its harsh winters. Do these facts suggest that the amenity-based theory of migration is flawed?

  6. "According to Tiebout, people will always prefer to live in low-tax communities over high-tax communities." Critically evaluate this statement.

  7. Compare and contrast the economic rationale underlying models of in-migration and out-migration. What are propensity models? What do these models assume about individuals’ indifference (i.e., utility) curves?

  8. What do Polachek and Siebert mean with the term "perspicacious peregrinators?" Do you think this is a good way of describing a migrant? What do they mean by the "periodicity of moving?"

  9. Discuss the meaning of the statement "amenity values are capitalized into local rents and wages." Do you believe that "high wages in a location merely compensate for high rents?" What is the meaning of "hedonic pricing," and "compensating wage differentials?"

  10. After reading through subsection 7 on equilibrium and disequilibrium models of migration, how do you explain the phenomenal increase in house prices in San Jose given in Section I? Keep in mind that factors other than natural amenities may explain the rapid rate of population growth in that area.

  11. As spatial information becomes more readily available, which of the two triads in Figure 5 do you expect to become more relevant for explaining observed migration?

  12. How might one introduce amenities into Krugman’s dynamic model of migration? How would you model the fact that average amenity benefits may decrease for certain types of amenities (such as seclusion from neighbors on a beach), as more and more people move into an area?

Section II Appendix: Clickable [Links] From Above

[E.G. Ravenstein]: One of the first students of migration

Among the first published works on the theory of migration was that by Ravenstein (1885 and 1889), more than 100 years ago. Ravenstein distinguished among four different types of migrants: local migrants; short-journey migrants; long-journey migrants; and migrants-by-stages. In addition, he separated permanent from temporary migrants and absorption from dispersion areas. At the core of his contribution was the idea that individuals migrate in response to differences in economic opportunity over space. Implicitly, large cities offered the most opportunities. Ravenstein devised the following seven laws of migration (as quoted in Isard 1960, 67-68):

(1) ...the great body of ... migrants only proceed a short distance, and ... there takes place ... shifting or displacement of the population ... in the direction of the great centres of commerce and industry ...
(2) ... the process of absorption ... [goes] on in the following manner: -The inhabitants ... immediately surrounding a town of rapid growth flock into it; the gaps thus left ... are filled up by migrants from more remote districts, until the attractive force ... makes its influence felt, step by step, to the most remote corner of the kingdom. Migrants enumerated in a certain centre of absorption will consequently grow less with the distance [from, and proportionately to,] the native population which furnishes them...
(3) The process of dispersion in the inverse of that of absorption...
(4) Each main current of migration produces a compensating counter-current.
(5) Migrants proceeding long distances generally go ... to one of the great centres of commerce or industry.
(6) The natives of towns are less migratory than those of the rural parts of the country.
(7) Females are more migratory than males.

Laws 1 to 5 are captured in the modern-day gravity model. Even in this early work, "economic opportunity" was believed to serve as an absorption factor, while physical distance was a deterrent to migration. These two phenomena have proven highly important in much of the theoretical research on migration that followed. Only recently Tobler (1995, 341) admonished fellow researchers to answer these questions:

What has been done with Ravenstein’s laws in the last 100+ years? Have any been refuted? If so, which ones? If not, why not? Are they irrefutable tautologies? Do they still hold today? Have any been extended? If so, which ones? Have any new laws been added? If so, what are they? If not, why not? What can we do today that Ravenstein did not? Is our theory, our methodology, or our technique better?

[The "Beaten Path" Effect]

Another early model of migration behavior appealed to social interactions among or connections among individuals as the major factor explaining why people moved. In these models, friends who had moved to other places shared information about those places with people who had stayed behind. This was labelled the "beaten path" effect, which can be viewed as similar to what happened when the West was explored in the United States or what happened when many African Americans moved from the South to the northern industrial regions in or near Detroit, Michigan, as well as elsewhere in the Midwest.

In these cases the flow of information, for example about job opportunities and wages, from the new areas to the old was an important cause of the migration. Studies of this important phenomenon have been carried out by Nelson (1959), Greenwood (1970), MacKinnon and Rogerson (1980) and Rogerson and MacKinnon (1982). Although information and transactions costs are difficult to measure in these studies, as discussed earlier, this literature points to the importance of considering these factors in studies of migration.


[Income Differential Models]

The idea of income differentials was expanded and applied empirically in the famous Todaro (1969) and Harris and Todaro (1970) migration models for developing countries. In these models, migration serves as a source of arbitrage for labor supply and demand, and thus wages, over space. Regions with relatively high wages (relative to other regions) attract workers, thereby increasing the supply of workers and depressing wages. In regions with relatively low wages, the reduced supply of workers, in principle, causes wages to rise. Thus, with everything else being equal, wages are expected to equilibrate over space over time, as a reflection of relative labor scarcities.

This model assumes that all economic agents have complete information about their income earning opportunities, zero transactions costs associated with moving, and that only income enters the utility function of individuals. Therefore, in this Hicksian model migration between places i and j is a direct function of differences in wages or income-earning opportunities in the two places:

Mij=f(wj/wi)

If wj>wi, people will move away from place i and to place j. The greater the wage difference in any given period, the greater the flow of population taking advantage of that differential. Arbitrage in the form of people migrating eventually drives the differential between wages to zero (or the ratio to one), everything else equal.


[Job-Vacancies Models]

Two of the first studies seizing on the Lowry's results used a job-vacancies model as determinants of migration behavior (Mazek 1966 and Glantz 1973). A challenge in these studies is the conceptualization of job vacancies, or excess demand for workers. Mazek explained changes in the labor force as a function of differences in potential unemployment levels across regions. These levels were estimated by calculating how much unemployment would have existed in a region if there had been no in-migration. He estimated separate models for different age and occupational groups of migrants, and studied the effect of migration on economically depressed areas. Mazek was one of the first researchers to introduce simultaneous equations models into the study of migration behavior, recognizing that in-migration and unemployment rates were in fact determined simultaneously.

In Glantz's model, job vacancies were measured as excess demand for labor. Glantz also constructed a potential employment variable, which measured how much employment would have grown if the region followed national trends–a calculation familiar from shift-share analysis. A second concept Glantz borrowed from shift-share analysis was that of a competitive share component. This measured how rapidly the jobs in industries in a region were growing relative to the national job-growth rate of each industry. He found that low-income migrants are especially attracted to an area by employment opportunities. The theory of job vacancies as a determinant of migration remains valid today, as job seekers scour newspaper advertisements in distant cities for job openings, and as analysts track help-wanted indices over the business cycle.


[Structural Models of In-migration]

Von Böventer (1969) explicitly modeled the effect of a city's size and its relationship to the surrounding countryside in migration decisions. In effect, his work was based on central place theory in which a hierarchy exists between the so-called core (the central city) and the periphery or surrounding regions (often referred to as the "hinterlands"). He posited "[a] non-linear relation between in-migration and city size ... since neither the costs of providing public services and infrastructure nor the benefits that firms and households derive from agglomeration economies are linearly related to population" (Mueller 1982, 13).

A noteworthy feature of von Böventer's analysis was that he explicitly modeled how accessible a city was to migrants coming from other cities or hinterlands. The relationship expected here was positive. In his study, highway and rail access were critical variables of accessibility.

In Pack's (1973) study, various structural variables played central roles in attracting migrants. More specifically Mueller (1982, 15) states:

Present economic opportunities were measured by median income and the unemployment rate, while potential economic opportunities were reflected by growth in median income and median years of education, an indicator of the city's innovativeness. Fiscal variables included per capita measures of residential taxes and public expenditures and a per recipient measure of welfare payments. The amenity variables related to the housing conditions in the central city. Presumably, migrants would prefer cities with high-quality stock of rental housing, as measured by the proportion of rental and of sound housing units. Population also was included to assess any locational preference for small or large cities.

One problem with Pack's conceptualization was that changes in income over time were not independent of migration rates. Cebula and Curran (1974) argued that a simultaneous equations model, containing migration and income change as endogenous variables, would have been a more appropriate way of modeling this problem. This criticism in turn led to another set of studies, which focused on endogeneity or simultaneity between migration and regional economic growth processes. These are reviewed in Section III.


[Simultaneous Equations Models of In-migration]

Olvey (1970) focused on the simultaneous relationship between in-migration into an area as a measure of growth in the number of workers, and growth in employment at the level of metropolitan areas within the United States. He distinguished between migrants moving across borders of adjacent states ("short-distance inmigrants") and those coming from states that were not adjacent ("long-distance immigrants"). The explanatory variables in his model included wage levels, wage levels prevailing elsewhere, climate, population in the destination area, and employment growth (endogenous). The other endogenous equation in the model (employment growth) was modelled as a function of various factors affecting labor force and employment growth within the metropolitan area.

In a similar set of studies, Greenwood (1973, 1975b, 1976) studied the effect on in-migration of endogenously determined factors such as change in income, employment and unemployment in an area, and rate of population turnover, measured using out-migration data. Median income levels, unemployment rates and regional indicator variables proxying for other exogenous factors affecting migration were included as explanatory variables in the study.


Model from Alperovich, Bergsman and Ehemann (1977)

The first term on the right-hand side of the equation consists of the population in place j multiplied by an exponential distance decay function divided by the sum of the population of all places, including i and j, similarly weighted by a distance decay function. The greater the distance, the less the attraction of the population size, and vice versa. Or, a larger population can offset the effect of a greater distance between migration targets, and vice versa. The second term in the equation consists of a set of constants, a or b, with subscripts c=0,...,C, that can be estimated econometrically, and variables Z which capture the features of the various places that influence migration (including employment opportunities, natural amenities, etc).

Note in this model that characteristics and distances related to all competing destinations are included (i.e., i and j). In the original models only the origin and destination attributes were included as determinants of migration. This model thus represents a substantial refinement in migration modeling. Specifically, the influences of space (distance) and population mass are reduced considerably by introducing the amount and proximity of competing economic opportunities and amenities.

The above model can be converted into an in-migration model by summing up all of the migration origins for any migration destination (Mueller 1982, 21). With some additional manipulations, the rate of inmigration to an area can be shown to depend on three factors: One is similar to the periphery effect proposed by von Böventer (1969) above; the second is attributes of each place weighted by population and distance between places in a gravity-type effect; and the third captures the influence of the competing migration destinations. In Section III, we will revisit this equation and discuss how it can be estimated using conditional logit models.


[Propensity Models]

Out-migration models of the propensity variety have been developed by Miller (1973), Trott (1971), Renshaw (1970) and Morrision and Relles (1975). Miller included median income and increases in the rate of unemployment as determinants of propensity to leave an area, in addition to size of the state's population and the average temperature in January, a commonly used measure of climate in these types of studies. In addition, he included in-migration rates as an indication that residents had already demonstrated that they were willing to migrate, as well as a measure of educational attainment. The latter variable, measured as the percentage of the population having attended at least one year of college, is hypothesized to raise the mobility of individuals. As discussed in Section I above, migrants are on average more highly educated than nonmigrants.

Trott focused specifically on individuals who were in the labor force since, he argued, that would result in a more representative sample of potential migrants. To a large extent, this also captures the labor force participation rate within a community. Trott was concerned that mixing together workers and nonworkers in the sample would attenuate or wash out any statistically significant effects. In his empirical analysis, Trott used only individuals who were actually working, i.e., were in jobs covered by Social Security contributions. Trott was able to include cohort-specific variables for each migrant with the data set he was using, as well as certain more aggregate variables. In addition, his work was innovative because he looked separately at short- and long-term expectations as influencing migration behavior.

Like Trott, Renshaw was concerned that inclusion of nonworkers in any data sample would lead to contamination of the results. In particular, he analyzed worker migration as a part of the natural process of job turnover. Today, American workers are expected to change jobs between 4 and 5 times within the first 10 years of entering the workforce, which facilitates or even encourages migration. Renshaw focused on the structural and institutional (legal) conditions that prevailed in individual local labor markets as affecting migration propensities. For example, areas of the country in which innovations in production processes were common and widespread would encourage flexibility, adaptability and mobility of workers between jobs. In stagnant areas, the opposite would be true. In this model, mobility also depends on whether workers need general skills, allowing them to easily move between jobs, or job-specific, narrow skills that are not "portable."

Renshaw also argued that it was critical to control for intrinsic migration propensities within the population, because otherwise there would be no statistical relationship between local economic conditions and migration rates. The reason for this is that the population in depressed areas consists disproportionately of people with low propensities to migrate, while the opposite would be true of booming areas.

The last early study of this genre was conducted by Morrision and Relles. After reviewing the previous studies, they argued that in the short run economic conditions in the place of origin did affect migration behavior, all else equal (including the migration propensity). In the long run, however, they concluded that these conditions played no significant role. These authors used a lagged out-migration rate, measures of propensity to migrate–including population shares between 18 and 32 years of age, in professional occupations, and having recently in-migrated–and rates of job growth as determinants of out-migration. It is noteworthy that "...Morrision and Relles drew conclusions similar to those of Lowry. They maintained that there is an asymmetry in the response of migration to economic opportunities. Migrants are pulled to destinations where employment growth is high but are not pushed from origins where employment growth is low" (Mueller 1982, 33).


[Simultaneous Equations Models of Out-migration]

Instead of focusing on potential employment that would have resulted in the absence of in-migration, Olvey (1970) focused on what the unemployment in a region would have been in the absence of out-migration. Olvey also included a climate measure and wages in the equation explaining out-migration behavior. Greenwood expanded on previous studies by controlling for migration propensities of the population. In addition to the propensity measures, which included in-migration rates, educational attainment, and age, he incorporated labor force size, income, unemployment rates and changes in unemployment, employment, and income in his simultaneous equations models.


[Allocation Models]

In the friends-and-relatives model, information exchange between friends and relatives is important in reducing the uncertainty associated with moving to a new place. In effect, having people who are trusted in the distant location can counteract the effect of distance on migration between places. Greenwood (1969) used place-to-place flows of migrants in one of the first attempts to model migration as a function of migration that had taken place in an earlier period using an allocation model.

Greenwood included the conventional factors of economic opportunities, amenities and propensity to migrate to explain the allocation rates.  In addition, however, he incorporated the urbanization ratio in the target and origin regions to control for rural-to-urban migration, along with the distance between places and the number of individuals who had previously migrated.

Allocation models were further disaggregated in a number of subsequent studies. The disaggregation concerned both race-related factors and regional differences, and it focused on whether the impact of distance varied according to these factors. As Mueller points out, these types of studies have two weaknesses. First, the migration origin is not considered as an alternative in the migration decision. This weakness was addressed in the models discussed in the following section. Second, allocation models assume an ideal state in that the competing opportunity has not only the highest wage but also the lowest unemployment rate and the largest population. In reality, there is no reason to expect this to be the case, since a city may rank the highest on one measure, but not on all three. And, if one wanted to somehow collapse each of these measures into a single optimal variable, the important question arises of how to weight each criterion. Giving each the same weight (one-third) is simplistic and may not be a good approximation of how real-world migrants choose among competing measures.


Origin-Destination Models (Human Capital Factors)

Sjaastad (1962) was the first to view the migration of individuals as increasing education or human capital. Rogers (1967) used per person salary and wage data as measures of income in place of average wages paid to manufacturing workers, which had been used in previous studies. Focusing only on migration within the state of California, he essentially confirmed Lowry's earlier findings that economic conditions in the migration origin had little bearing on the decision to migrate. Rogers examined migration between and among metro and nonmetro areas, and also separately examined migration stratified by socioeconomic characteristics such as age, gender and race.

Rabianski (1971) studied income-related incentives to migrate between a place of origin and a migration destination. He examined relative differences in unemployment, the share of workers in low-skill occupations, and earnings, which were adjusted for differences in local cost of living. These differences were expressed as ratios of the variables for the place of origin and destination. Holding constant each of these three factors, he was able to study the independent effects of the different earnings-related variables.

Rabianski's rationale for including the share of workers in low-skill occupations was that he believed they would be less mobile because they were more likely to be collecting welfare payments or unemployment compensation. This study is, therefore, an interesting precursor to studies predicting the effect of welfare reform on different regions of the country, particularly those with high shares of poverty, unemployment and welfare dependence.

Gallaway, Gilbert and Smith (1968) also studied the role of differential economic conditions in influencing migration behavior. They examined relative wages, unemployment and welfare payments received per person. In their analysis, they accounted for pecuniary and nonpecuniary costs of moving, which effectively reduced the gross benefit of changing locations. These costs include actual moving expenses and wages lost during the move, as well as psychic discomfort associated with such things as leaving behind friends and relatives. Because these costs are very difficult–if not impossible–to measure in practice, however, Galaway et al. simply used distance as a proxy for the costs.

Focusing on a specific racial group–African Americans–Cebula, Kohn and Vedder (1973) examined the role of discrimination or racial economic disadvantages on migration. To measure this phenomenon, they used the ratio of per person income of African Americans in the migration target to the per person income of African Americans prevailing in the migration origin: yblack,t/yblack,o, equivalent ratios for welfare payments per person, the share of African American population at the target, along with the physical distance between the destination and the origin. Their rationale for including the minority share variable was that it (Mueller 1982, 49) "...would reflect the psychic benefits of the presence of friends and relatives and would measure the cost of labor market information more accurately for blacks than would the unemployment rate, since blacks are relatively restricted in their job searches" because of racial discrimination. One criticism leveled at this study was the fact that welfare payments and migration levels may be simultaneously determined (Ziegler 1976).

A study by Greenwood and Sweetland (1972) examined the effect of the population in the migration target in greater detail. These authors argued that it was wrong to include this population, because its size depended through migration on income levels. In other words, a large population in a community was the result of high rates of in-migration because of high incomes, and vice versa. They dealt with this problem by dividing migrant numbers by the population in the target community, rather than the origin community, as virtually all of the previous studies had done.


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