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Modeling Migration.

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Models are an attempt to answer the question: WHY? Why did a certain phenomenon occur? Why did we observe some regularity in the real world? In the case of migration studies, we are asking why a certain migration phenomenon occurred? Why did an individual with certain characteristics or why some group migrate from one place to another? What were the consequences of the move for the migrants themselves or for others in the sending and/or in the receiving localities or regions or countries?

All migration models begin with the implicit assumption that the moves are voluntary. We know that many moves are not voluntary. Moves within the military, for example, are not voluntary. The movement of prisoners is not voluntary. The movements of many refugees are not voluntary if the individuals or groups are faced with death or persecution. Yet in our migration models we assume that potential migrants are free to move or not move, and if they move, they are free to select their most preferred destination. Thus, the migration is voluntary and utility maximizing.

A final very important thought: Good models are grounded in good theory. Our theory should allow us to make predictions regarding the direction of the influence of various independent variable on the migration outcome.

We now turn to the study of some different types of migration models.

1. The Gravity Model

J.Q. Stewart (1941)‏

F =GPiPj / D²ij


F = gravitational or demographic force

G = constant

Pi = population of origin

Pj= population of destination

Dij= distance from i to j

Mij= GPiPj Dαij

Mij= GPiβ1Pjβ2 Dαij

“Modified” Gravity Models

lnMij= lnβo +β1lnPi+β2lnPj+ β3lnDij

+ β4lnYi+β5lnYj


+ ∑ βinXin



+ ∑ βjnXjn


H. Makower, J. Marschak, and H.W. Robinson

(series of, in Oxford Economic Papers during the late 1930s).

They focus on two “incentives” to migrate

a. relative unemployment discrepancy

(Ui – Un) / Un

b. distance

Also considered the lag between incentive to move and migration.

MMR anticipated the “gravity model” of migration

“Quite a close relationship was found between discrepancies in the unemployment rates and migration of labour where allowance was made for the size of the insured population and the distance over which migrants had to travel.”

“An increase of distance by 1 percent reduces migration by from 1.6 percent to 2.1 percent.”

2. The Human Capital Model

The basic idea here is that rational individuals invest in human capital, which is some combination of education, training, and health that has a future payoff, presumably in the form of higher earnings, but perhaps in other respects as well (e.g., more enjoyment from reading, going to the theater, etc.). This investment usually occurs early in an individuals life cycle, so the rewards (or returns) to the investment may accrue over many years.

Because the returns accrue over many years, not only must the returns be discounted, but also they involve risks. For example, the individual may enter the labor force under better or worse economic conditions, which clearly could affect his personal economic outcome, not only for the immediate future, but also over the long run.

Another form of human capital investment is migration, which also has a future payoff, but involves many different costs.

Some implications of the human capital model:

a. The job search will require more time and the individuals will be better informed. Thus, they will respond more and more rapidly to various regional wage and employment signals.

b. The job search will extend over a wider area.

c. Individuals with more human capital will be more likely to migrate than those with less human capital.

d. When those with more human capital migrate, they will, on average, do so over greater distances than those with less human capital.

e. Those with more human capital will earn more in their new area of residence than those migrants with less human capital.

f. Those with more human capital are more likely to consider factors other than earnings when they migrate—factors like location-specific amenities. This is in part due to their higher earnings.

g. Those with more human capital will have greater impacts on their new area of residence as well as on the area from which they departed.

spatial job search models
Spatial Job Search Models

These models are an outgrowth of the human capital approach. They attempt to place the potential migrant in a situation in which he considers the benefits and costs of a move to various specific locations, but he must search to find exactly what his options are.

The key here is to place the PVij in a search context. The individual presumably searches over the many alternatives. For each alternative he receives a distribution of wage (or PV) offers. Some of these offers may yield PV>0 and some may yield PV<0. Even among the positive PVs, however, the individual may not select any if his reservation wage (or PV) is higher than any PV he observes.

The longer he seeks an acceptable alternative and fails to find one, the more likely his reservation wage is to fall. Not only may his reservation wage be dependent upon search time, it may also be dependent upon all sorts of personal characteristics, like age, marital status, and presence of children.

The cost of the individual’s search also comes into play because longer searches entail higher costs.

modeling migration with microdata
Modeling Migration with Microdata

Although the job-search models often present an exception to this statement, the types of models discussed above all tend to use aggregate migration data. A major revolution that has occurred in economics over the last 30 to 35 years is the development of various microdata sets. Such data sets are now used extensively to study migration, and this statement is especially true with respect to economists who study migration.

What are the limitations of using aggregate data to study migration?

1. Aggregate data of necessity use a fixed migration interval. Only the first and last location are available for study. This means that all sorts of moves are missed in the data. Intermediate and return moves are examples of two types of moves that are missed in aggregate data.

2. Aggregate data conceal the differences in the underlying determinants of migration for various population subgroups that are lumped together. Motives for migration differ for different groups, such as the young and the old, the more educated and the less educated, African Americans and white Americans. Although some stratification is found in aggregate data, it is very limited. Differences between groups could be studied with aggregate data, but differences within groups cannot be studied with such data.

3. Studies based on aggregate data fail to account for different types of moves such as new, repeat, and return migration, and long-distance migration compared to short-distance migration. The determinants of migration have been shown to differ significantly for these various types of moves.

4. Aggregate data frequently fail to account for the movements of institutional populations, of which the military and college students are important examples. The movements of such groups may have little or nothing to do with the typical determinants of migration studied (e.g., income differences).

5. Aggregate data, given the heterogeneity that exists within large regions (such as states) between which migration is measured, may not represent the average characteristics of many of the moves that occur. (Average area characteristics are used to represent the characteristics of potential movers.)

6. Aggregate data allow the study of the region-wide consequences of migration, but in no way do they allow the study of personal consequences of migration. Microdata are required to assess the personal consequences of moving, and these consequences were impossible to study in the absence of microdata.

Some potential advantages of microdata:

a. Various personal or household characteristics can be included in the model. These characteristics include such factors as sex, age, education, marital status, number and ages of children, income by source, and much, much more.

b. With such characteristics in hand, the researcher often can track multiple moves.

c. With knowledge of personal characteristics, researchers can place individuals and families in a distribution and thus may be able to estimate such factors as income taxes paid or educational benefits for one’s children.

d. With microdata, the researcher can organize and aggregate the data in any desired fashion. For example, if the goal is to study the sex, age, or skill composition of migration, which are aggregate phenomena, he can do so with microdata.