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Introduction to migration analysis


Migration is the third process (with fertility and mortality) that governs population change. For most national populations, its contribution to population change is small relative to those of births and deaths, but as the civil division of interest becomes smaller, the salience of migration typically becomes larger. Migration differs from fertility and mortality not only in magnitude, but more fundamentally in the nature of the process. Migration involves moving across some geographically-defined boundary, with the intent or result of changing place of normal residence. Thus whereas a birth and a death are largely unambiguous, a migration depends upon geographically-defined spatial units (civil divisions) and on intent or subsequent behaviour. A person can be a migrant to the analyst looking at change in provincial population but not a migrant to another analyst focusing on national population change. The first task, therefore, in any analysis of migration is to establish the geographic focus of the study. A second task is to define what counts as a migration, as opposed to broader mobility. The issue is further confused by the existence of several different types of migration. In addition to “ordinary” change of usual residence, there are circular migration flows, daily or weekly commuter flows, seasonal flows and refugee flows, all with specific characteristics. Given these definitional issues, and the fact that migrations can effectively be reversed in terms of population stocks (unlike births and deaths), it is no surprise that measurement is also complicated.

Apart from this, capturing data on migration is also more problematic. Although developing countries often lack complete systems of birth and death registration, completeness is improving and some methods have been devised to make use of the less than complete data. However, registration data on migrants/migrations in most countries cannot be relied on to produce reliable estimates of immigrants, let alone of internal migrants/migrations. In addition, for various reasons (illegal status, temporary residence of recent migrants, fear of xenophobia, etc.) migrants (especially immigrants) are usually underrepresented in censuses and surveys.

Methods for measuring migration are broadly similar for both internal migration (in- or out-migration) and international migration (immigration or emigration), except in one very important respect. A census or survey can measure international immigration by identifying persons born abroad, but it is much harder to identify emigrants because it is not possible to carry out a census/survey in all recipient countries. Approaches to estimating emigration include: (i) systematic identification of nationals in censuses of other countries (UN Population Division 2011); (ii) including census/survey questions about usual household members living abroad (e.g. in the Swaziland Censuses of 1986 and 1996); (iii) asking about the residence abroad of close relatives, especially a woman’s children or a respondent’s siblings (Zaba 1985); and (iv) using intercensal residual methods to estimate numbers of missing residents at the time of a second census. The first approach is dependent on receiving countries having, and being willing to share, relevant data and only captures migration of the native-born population; the second approach depends on the, perhaps vague, concept of household membership, and will also fail to cover entire households that have moved away; the third also fails to capture entire missing families, does not provide estimates of recent emigration, and in small experimental surveys has not proven convincing. Only the fourth can be expected to give plausible estimates of recent outflows, provided both censuses count the population reasonably accurately, but gives no potentially useful information about destination.

With these limitations and problems of accurate data collection, the field of migration analysis has developed largely independently from mainstream demography, leading to it concentrating primarily on developed countries where the quality of data available to measure migration is typically much better than it is in developing countries, and possibly because migration in these countries is often a matter of greater political and public policy concern. A further consequence of these factors is that the field has developed its own terminology and techniques, which are often quite far removed from the demography discussed elsewhere in this manual.


As noted above, a migration is defined as a move across a geographically-defined (usually administrative) boundary of interest to the analyst with the effect of changing a person’s place of usual residence. Assuming that the boundary can be clearly defined, this immediately raises two questions: how does one define usual place of residence, and how does one determine whether it has changed? Unfortunately, no very precise answers can be given to these two questions, giving rise to inevitable uncertainty in measurement. The preferred definition of usual residence is in terms of length of residence: that if one intends to live, or after one has lived, in a place for a period of time (e.g. one year) one becomes a usual resident. Note that usual residence is not the same thing as legal residence. The Principles and Recommendations for Population and Housing Censuses (UN Statistics Division 2008: 102, para. 1.463) defines usual residence as follows:

“It is recommended that countries apply a threshold of 12 months when considering place of usual residence according to one of the following two criteria:

(a) The place at which the person has lived continuously for most of the last 12 months (that is, for at least six months and one day), not including temporary absences for holidays or work assignments, or intends to live for at least six months;

 (b) The place at which the person has lived continuously for at least the last 12 months, not including temporary absences for holidays or work assignments, or intends to live for at least 12 months.”

However, this definition does not deal with the situation of a person with two homes who regularly spends about six months in each. In general, we have to rely on people to self-define as residents or not, although some tests could be implemented (such as asking where their car is registered, where taxes are paid, where they voted, where the person sleeps at night on a regular basis, etc.). For most purposes, a person can distinguish between whether he or she is a usual resident and visitor, and this simple distinction suffices.

Data sources

Migration has been the Cinderella of demography, kept in the background as far as possible, and dedicated migration surveys are few, far between, and specialized (an excellent example is the description of the Mexican Migration Project by Massey, Alarcon, Durand et al. (1987)). Dedicated migration surveys typically include full migration histories, which, though raising complex analytical issues, tend not to be focussed on the estimation of numbers of migrants/migrations. In this section we do not cover the analysis of such full histories (there are very few general principles that would apply to a useful number), but rather deal with the sorts of data collected by population censuses and general household surveys and sometimes, developed countries, by some form of registration.


The most widely collected data relevant to migration is place of birth. In comparison with place of residence at the time of a survey, this information describes lifetime migration. The information provides limited information about timing of migration, and is ‘net’ migration in the sense that it misses, entirely, migrations that have been reversed (back to the place of birth) and all intermediate migrations. At the time of data collection, decisions have to be taken about the granularity of the data: i.e., for those born abroad, how many countries should be explicitly recorded and for those born in the country, what level of geography should be recorded. For the analyst, of course, these decisions were made at the questionnaire design stage, but some degree of greater aggregation may be required. The analysis of data on birthplace is described below, but it is useful to make two points here. First, if data on birthplace by age and sex are available for two points in time, it is possible to estimate net migration (by age and sex) during the interval. Second, although birthplace reflects lifetime migration, the length of “lifetime” varies by age, and (provided the census data on children is reasonably accurate, which it often isn’t in many developing countries) the migration of 0-4 year olds may be used as an indicator for recent migration of their parents (Raymer and Rogers 2007).

Residence at some specified time in the past

This information is very often collected in addition to that on birthplace, with the express objective of providing data on recent migration. The time point specified is generally five years earlier, but sometimes a one year period is used. However, it tends to work better if the time point is associated with a memorable event, such as the previous census, on the assumption that the coverage of that previous census was largely complete (so that people remember being counted). The longer time period identifies more migrants, but misses intermediate moves, whereas the shorter time period is more susceptible to reference period error (I moved “about a year ago”).

Place of previous residence

This information is almost always collected as an alternative to residence at some specified time in the past, and is generally combined with an additional question about duration of current residence (or date of last move). The objective again is to provide data on recent migration.

Duration of current residence

The question refers to duration of residence in the civil division (such as a town or province), not in an individual dwelling unit. This question is of limited use on its own and tends to be paired with the one above to provide a time frame for estimates.

Intercensal population change

Though not involving a direct question about migration, intercensal population change by age and sex can, provided both censuses are reasonably accurate counts of the population, provide residual estimates of net migration between the two censuses (Hill 1987; Hill and Wong 2005; UN Population Division 1967). Intercensal population change (for cohorts or age groups) by age and sex is adjusted for the effects of intercensal fertility and mortality to provide a residual estimate of intercensal net migration (i.e., treating migration as the balancing item in the fundamental demographic balance equation). Migration is generally concentrated in the age range 20 to 40, ages at which mortality rates are, at least in the absence of HIV/AIDS, relatively low and fertility irrelevant, so residual migration estimates are insensitive to assumptions about fertility and mortality (except in populations severely affected by HIV/AIDS where using these data to estimate migration is not recommended). Such estimates are extremely sensitive, however, to even small changes in census coverage; such errors may be manifest in high age-specific migration rates over age 50, where migration is usually low.

Migration measures

It is not the purpose of this introduction to provide a comprehensive summary of all the measures and definitions – the interested reader is referred to the UN manual on internal migration (UN Population Division 1970) – but two are of particular importance for the chapters that follow.

Migration stocks        

Stocks of migrants are typically thought of as numbers of persons (by age group and sex) not born in the civil division of enumeration. The proportions born elsewhere (in the country or in other countries) give a good general sense of the magnitude of in-migration and immigration, but no sense of any dynamic changes that may have occurred recently. However, changes in stocks can be used to estimate immigration (net of any onward or return migration of the foreign-born).

Migration rates

Assuming that migration events can be fully and accurately identified, occurrence/exposure rates can be calculated for out-migration or emigration in exactly the same way as for mortality, dividing events in a period by exposure time; such rates can be crude (both sexes, all ages) or age-sex specific. The same is not the case (or at least not usefully) for in-migration or immigration, since the population exposed to the risk of migrating into a civil division is the entire population of the world living elsewhere. In-migration and immigration rates are always calculated by dividing events by the exposure time of the one population group not exposed to risk, the current residents; such rates can be crude (both sexes, all ages) or age-sex specific. Defining rates in this way has the advantage of satisfying the needs of the demographic balancing equation, since rates of gain and loss are measured relative to the same population. This confers a further advantage in that net migration rates can be estimated from the demographic balancing equation as population change between two time points (e.g. censuses) minus gains due to births in the interval plus losses due to deaths in the interval. However, this approach does have the disadvantage of removing the scale limits on “normal” occurrence/exposure rates; for example, at the extreme, a person moving into a previously unoccupied civil division creates an in-migration rate of infinity.

Description of methods covered

The chapters in this section focus on the estimation and quantitative description of immigration and internal in- and out-migration. They are not meant to provide comprehensive coverage of all measures of migration, and specifically they do not cover the important, but problematic, issue of measuring emigration (other than by mentioning that the method of estimating immigration (net of return/onward migration) of foreigners, can be applied to the data of the main countries of destination of emigrants to get some sense of the age profile and magnitude of emigration.

Chapter 35 concentrates on the basic methods of using data from censuses to estimate the numbers (net of return/onward migration) of immigrants from the change in stock of foreigners, and of internal in- and out-migration from the change in stock by place of birth and from the place of residence at some date prior to the census.

Chapter 36 describes the selection and fitting of one of the Rogers-Castro multi-exponential models to estimates of migration probabilities (or rates) derived from estimates of the number of migrants/migrations using non-linear optimisation procedures.

Chapter 37 describes the multiplicative and log-linear models for capturing, comparing and analysing the mass of inter-regional migration flows from places of origin to places of destination. The chapter also provides an introduction to the method of offsets for extending the use of these models to estimate inter-regional flows from marginal flows (i.e. total flows out of, or into, regions). The intention is to expand the material on the method of offsets into an additional chapter at a later date, which will be placed on the Tools for Demographic Estimation website. 

Further reading and references

As mentioned above, UN Manual VI (UN Population Division 1970) provides a comprehensive, if dated, introduction to the description and measurement of internal migration. Those looking for an overview of indirect methods of estimating migration are referred to the useful, if also somewhat dated, review by Zaba (1987). More specifically, Hill (1987) attempted to apply the logic underlying the Generalized Growth Balance method of adult mortality estimation (described in Chapter 24) to estimate undocumented migration, while Hill and Queiroz (2010) sought to estimate net migration in parallel with the estimation of mortality. Unfortunately neither method has proved to be particularly successful.

Those interested in reading more about the models of migration (multi-exponential, multiplicative and log-linear) or the method of offsets are referred to work by Rogers, Willekens and colleagues (e.g. Little and Rogers (2007), Raymer and Rogers (2007), Rogers (1980, 1986) and Willekens (1999)).


Hill K. 1987. "New approaches to the estimation of migration flows from census and administrative data sources", International Migration Review 21(4):1279-1303.

Hill K and B Queiroz. 2010. "Adjusting the general growth balance method for migration", Revista Brasileira de Estudos de População 27(1):7-20. doi:

Hill K and R Wong. 2005. "Mexico–US migration: Views from both sides of the border", Population and Development Review 31(1):1-18. doi:

Little JS and A Rogers. 2007. "What can the age composition of a population tell us about the age composition of its out-migrants?", Population, Space and Place 13(1):23-19. doi:

Massey DS, R Alarcon, J Durand and H Gonzalez. 1987. Return to Aztlan: The Social Process of International Migration from Western Mexico. Berkeley and Los Angeles: University of California Press.

Raymer J and A Rogers. 2007. "Using age and spacial flow structures in the indirect estimation of migration streams", Demography 44(2):199–223. doi:

Rogers A. 1980. "Introduction to multistate mathematical demography", Environment and Planning A 12:489-498. doi:

Rogers A. 1986. "Parameterized multistate population dynamics and projections", Journal of the American Statistical Association 81(393):48-61. doi:

UN Population Division. 1967. Manual IV: Methods for Estimating Basic Demographic Measures from Incomplete Data. New York: United Nations, Department of Economic and Social Affairs, ST/SOA/Series A/42.

UN Population Division. 1970. Manual VI: Methods of Measuring Internal Migration. New York: United Nations, Department of Economic and Social Affairs, ST/SOA/Series A/47.

UN Population Division. 2011. International Migration Report 2009: A Global Assessment. New York: United Nations, Department of Economic and Social Affairs, ST/ESA/Series A/316.

UN Statistics Division. 2008. Principles and Recommendations for Population and Housing Censuses v.2. New York: United Nations, Department of Economic and Social Affairs, ST/ESA/STAT/SER.M/67/Rev2.

Willekens FJ. 1999. "Modeling approaches to the indirect estimation of migration flows: From entropy to EM", Mathematical Population Studies 7:239-278. doi:

Zaba B. 1985. Measurement of Emigration Using Indirect Techniques: Manual for the Collection and Analysis of Data on Residence of Relatives. Liège: Belgium: Ordina Editions.

Zaba B. 1987. "The indirect estimation of migration: A critical review", International Migration Review 21(4):1395–1445. doi: