Migration Models

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Decisions about migration are shaped by economic, social, and cultural factors. Migration models formalize these determinants. They also may describe the effects of migration at its origin and destination and the interactions between those effects.

Economic Determinants

Most formal migration models focus on economic determinants: opportunities and constraints on income at migrant origins (limited capital and technology, scarcity of employment, imperfect market environments), income opportunities at migrant destinations (demand for migrant labor in urban centers), and migration costs (travel costs, networks of contacts at prospective migrant destinations, border policies). Not all context variables are exogenous to migration; some may be influenced by migration decisions, as occurs when migrant remittances create labor scarcities or loosen financial constraints on production in migrant-sending areas, with ramifications for both migrant and nonmigrant households. A growing body of migration research attempts to elucidate these indirect or feedback effects of migration.

Although the results of sociological research usually agree that migration is the result of rational decisions by individual actors, such research often adds noneconomic variables to the list of determinants, viewing migration as a social process. Anthropological research generally deemphasizes formal or quantitative modeling in favor of ethnographic research, viewing migration within a cultural, historical, and political-economic context. This article focuses on formal approaches that employ quantitative and statistical methods to model migration phenomena.


The primary objective of migration models is to provide an analytic structure through which the direct and indirect influences on migration are identified, migration trends are charted, and the impact on migration of exogenous shocks, including policy changes, are predicted. Statistical models are used to test specific hypotheses derived from migration theories and estimate the magnitude of migration determinants and impacts. Estimated models, along with programming techniques, are used to explore or simulate the effects of policy and other influences on migration decisions. Simulations alter exogenous context variables, which are the only variables that researchers and policy makers are free to change directly.

The evolution of migration theory shapes both models and data collection. The earliest migration models are rooted in the theory of the geographer E.G. Ravenstein (1834–1913), who proposed 11 laws of migration based on the observation of migration patterns in Great Britain and, later, the United States. He proposed that although most migrants travel short distances, longer-distance migrants prefer to go to centers of commerce or industry; each stream of migration produces a counterstream; large towns owe more of their growth to migration than to natural increase; the volume of migration increases with the development of industry and commerce and as transportation improves; most migration is from agricultural areas to centers of commerce and industry; and the main causes of migration are economic. These observations motivated a plethora of quantitative models of migration flows and the aggregate variables that affect those flows.

Gravity Models

Ravenstein's (as well as Newton's) influence is clear in gravity models, which posit that migration between place i and place j, Mij, is a positive function of repulsive forces at i (Ri) and attractive forces at j (Aj) and is inversely related to the "friction" or distance between i and j (Dij):

Mij= f(Ri, Aj)/g(D)

In practice, most formulations of the gravity model simply assume that migration between i and j is directly proportional to the product of the two places' populations and inversely proportional to the intervening distance (Mij = Pij/D). Stouffer (1940) extended gravity models by introducing the notion of intervening opportunities: Migration over a given distance is held to be directly proportional to the number of opportunities at that distance and inversely proportional to the number of possible alternative migration destinations between i and j. In this approach the nature of particular places may be more important than distance in determining where migrants go.

These aggregate models, particularly gravity models, had the advantage of being simple to estimate, but they offered no insight into who migrated and who did not; how changes in policies, markets, and trade affected migration; or the social process of migration. Distance and population alone were not sufficient to explain migration behavior. Lee (1966) hypothesized that both the destination and the origin have characteristics that attract or repel migrants and that perceptions of these characteristics differ between migrants. The complexity of migration models has increased as research has evolved to address these and other questions.

Table 1 summarizes different migration models in terms of the variables included. The models range from early formulations, which included only a few variables, to new economics of labor migration (NELM) models, which contain many variables at the individual, household, and community levels, as well as policy instruments to influence migration.

The Models of Lewis and Schultz

In the 1950s and especially the 1960s economic models assumed a central role in migration research. W. Arthur Lewis's (1954) dual economy model of economic development with unlimited supplies of labor was not an explicit model of migration. Nevertheless, in this model migration is the means by which surplus labor in the traditional (agricultural) sector is redeployed to fill rising modern (urban) sector labor demands. Migration is demand-or employment-driven rather than being driven by wages, which are assumed to be fixed. The Lewis model assumes that a labor surplus exists. Thus, the loss of


labor to migration does not reduce agricultural production or affect wages. This assumption, which accords with a classical economic perspective, was called into question by some economists, most notably Theodore W. Schultz (1964).

Once migration eliminates rural labor surpluses, urban wages must rise to lure additional workers from the rural sector. Wages adjust to ensure that both rural and urban labor markets clear. This is the essence of neoclassical migration models, which are of the form:

Mij= f(Wi, Wj, C)

where Wi denotes wages at place i; j denotes wages at place j, and Cij denotes migration costs.

In neoclassical models, intersectoral wage differentials are the primary factors driving migration. Population and distance play a role only insofar as they influence or are "proxies" for wages or migration costs and condition the scale of the overall process. Empirical models document that migrant flows are usually from low-wage to high-wage places and respond negatively to migration costs. However, wage-driven migration models cannot explain migration in the context of high rates of urban unemployment and explain only a small share of the variation in migration flows.

Alternative Models

Michael P. Todaro (1969) proposed an alternative formulation of neoclassical migration models in which prospective migrants maximize their expected income; in the aggregate migration equation above, Wi and j are replaced by expected incomes at places i and j, respectively. Nearly all empirical tests of the Todaro expected-income hypothesis use aggregate data on migration flows and wages and assume a random job-allocation process so that expected income equals the wage times the employment rate (or 1 minus the unemployment rate). The wage-driven neoclassical model may be viewed as a special case of the Todaro model in which the probabilities of employment at migrant destination and origin equal 1.

The power of the Todaro model lies in its ability to explain the persistence of migration in the context of unemployment at migrant destinations. A higher wage in the urban sector than in the rural sector is not a sufficient or even necessary condition for migration because the probability of finding a job at the prevailing wage also matters. Like its neoclassical precursors, expected-income models imply that an equilibrium eventually is reached, after which migration pressures abate. The Todaro equilibrium is where expected incomes (not wages) are equalized across sectors, adjusting for migration costs.

In the 1970s most statistical tests of the Todaro hypothesis used data on aggregate place characteristics and migration flows. They generally supported the hypothesis that migration flows from places where expected incomes are low to places where they are high and that unemployment rates have an effect on migration that is independent of wages. These aggregate models, however, were an uneasy fit with the theoretical models of migration behavior on which they ostensibly were based. They left fundamental questions unanswered: Why do some individuals migrate while others do not? What distinguishes the labor "lost" to migration from that remaining in the rural sector?

Micro Behavioral Models

In the 1980s research emphasis shifted from aggregate to "micro" behavioral models that focus on individuals' migration decisions. Most migration behavior models are based on the assumption that an individual n at place i will migrate to place j if the net benefits from migration exceed the migration costs, that is, if

The diversity of migration models in the last two decades of the twentieth century reflects differing hypotheses about what constitutes migration benefits and costs, and those hypotheses in turn reflect evolving theories of migration behavior. For example, in a wage-driven neoclassical model, Bi and j are replaced by wages at places i and j, respectively. In a Todaro model, they are replaced by expected wages: pniWni and pnjWnj. (The model posited by Todaro actually was dynamic and hypothesized that individuals migrate if their discounted future stream of urban-rural expected income differentials exceeds migration costs.) Extensions of these models incorporate job search, migration networks, and risk as benefits or costs. In risk models migration benefits are hypothesized to be functions of both expected incomes and income risk.

Methodologically, micro models of migration behavior shift the researcher's focus from aggregate migration flows (estimated by using standard regression techniques) to individual migration decisions (modeled with probit or logit models or other related statistical methods). They require explicit consideration of differences among individuals in terms of migration benefits and costs. Human capital theory had a fundamental impact on migration research by positing that differences in individuals' earnings, and thus the economic returns from migration, can be explained by differences in skill-related attributes across workers, including experience and schooling.

Human capital migration models usually replace migration benefits and costs with human capital and other variables. In a few cases these benefits and costs are explicitly modeled as a function of human capital and other variables and their effects on migration decisions are estimated directly by using simultaneous-equation methods. In addition to human capital, social capital in the form of migration networks, or contacts with family and friends at prospective migrant destinations, plays a key role in some migration models. Migration networks may assist migrants in job searches and reduce migration costs and risks while creating a process of cumulative causation by which past migration makes future movements more likely. Empirically, networks are often the most significant variables explaining migration behavior.

The Impact of Remittances

Models of individual migration behavior do not provide a rationale for continuing interactions between migrants and source households, especially through income remitted, or sent home, by migrants. They also do not provide a useful basis for understanding the impacts of migration and remittances on migrant source areas. In the 1970s and early 1980s some researchers attempted to model the impacts of remittances separately from migration determinants, based on surveys of remittance use for productive investments by migrant source households. However, those studies did not investigate the indirect effects of remittances on migration decisions in the migrant source areas.

The New Economics of Labor Migration

The need to integrate the analysis of migration determinants and impacts stimulated a new genre of migration research in the 1980s and 1990s known as the new economics of labor migration (NELM). NELM models hypothesize that migration decisions are made not by isolated actors but by larger units of related people, typically households or families; that people act collectively not only to maximize income but also to minimize risks and loosen the constraints created by various inadequacies of markets in source areas, including missing or incomplete capital and insurance markets; and that migration decisions may be influenced by the behavior of other actors within the prospective migrant's social group.

In the imperfect-market environments that characterize most migration source regions, migrants create benefits and impose costs that are ignored by individual-decision migration models. In the absence of well-functioning credit and insurance markets, migrants serve as "financial intermediaries," providing source households with capital to invest in local production as well as income insurance (e.g., a promise to remit if a crop or family business fails). NELM theory implies new migration determinants (household capital constraints, risk, and community-level variables), as well as new potential impacts (positive effects of remittances on family production but also negative impacts of losing family labor to migration). It also draws attention to new forms of policy interventions to influence migration. Whereas a Todaro model would call for policy interventions in labor markets to influence migration, NELM modelers emphasize that interventions in capital and insurance markets can provide alternatives to migration as a means for households to obtain investment capital or income security.

A trademark of NELM models is their simultaneous consideration of migration determinants, remittance behavior, and impacts. This makes the application of NELM models relatively demanding in terms of both estimation methods and data needs. Empirical modeling provides evidence that production and incomes in migrant source areas are affected negatively by the loss of labor to migration but positively by migrant remittances and that household and community variables as well as individual variables affect migration and remittance behavior. It also offers support for the hypothesis that the characteristics of social groups, such as average incomes and inequality, both influence and are influenced by migration. Village-wide general-equilibrium models incorporating migration and remittances allow explanation of the effects of policy changes on overall village economic outcomes. These models reveal that many of the determinants and effects of migration are found outside the households that actually send migrants and receive remittances.

See also: Economic-Demographic Models; Multistate Demography.


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J. Edward Taylor

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Migration Models

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