1It has long been known that taking a cohort perspective is useful for studying migration (Taeuber, 1966) as well as for demography in general (Ryder, 1965; Hobcraft et al., 1982), while some migration theories stress the importance of viewing migration as a life course process (e.g. Rossi, 1980; Bailey, 2009; Kley, 2011). Yet migration is analysed almost exclusively with period data and period measures, which contrasts with the widespread use of cohort measures in fertility and mortality research. Unlike a cohort perspective, period perspectives do not directly correspond to the actual life courses of individuals. Event history analyses of migration microdata use longitudinal data applied to actual birth cohorts and life histories. This line of research typically uses micro-level regressions and descriptive data to show life course patterns in migration, and it focuses less not only on cohort patterns at population levels but also on changes over time (e.g. Kulu, 2005; Kolk, 2017; Kulu et al., 2018).
2Researchers have less commonly used a population-level approach based on longitudinal micro-level data when examining migration in contrast to other demographic phenomena. One exception to this is research that applies register data (Westerlund, 1998; Lundholm, 2007; Malmberg and Pettersson, 2007; Bell et al., 2015a), an approach also taken in this study. Longitudinal data make it possible to study migration propensities based on previous experiences (cf. parity in fertility research).
3In this study, the total migration rate is calculated for both period and cohort data on internal migration. We show, first, how applying standard demographic fertility measures can provide important insights into the dynamics of migration and, second, why these measures should be more commonly incorporated into the toolkit of migration researchers. Total migration rates for internal migration as well as age-specific rates are presented using Swedish administrative register data from 1970–2012 for the entire Swedish-born population. Possible extensions of cohort measures, by migration order and for international migration, are discussed and examples are given on how a cohort perspective can be useful in the absence of micro-level longitudinal data.
I – Internal migration in Sweden
4Compared to that of other European countries, Sweden’s internal migration intensity is high. Approximately 14% of the population change residence in a year, which is comparable to US migration levels (Bell et al., 2015b). For most of the 20th century, Sweden has been characterized by rural-to-urban internal migration, a trend that has been increasing its pace since the 1990s (Kupiszewski et al., 2001). Earlier research on Swedish interregional migration from 1975–2001 shows that it has declined since the 1970s, although it has recovered slightly from even lower levels in the 1980s (Lundholm, 2007). One likely factor for the decrease in migration among settled individuals is the increase in female labour force participation, as relocation is more difficult for dual-earner couples in which both partners must find new jobs (Gärtner, 2016). Overall migration appears to be more concentrated among younger individuals who become less attached to their home municipality (Fischer and Malmberg, 2001; Lundholm, 2007; Brandén, 2013; Bernard and Kolk, 2019). Figure 1 shows migration intensities since 2000, based on the administrative divisions of Sweden. Parish migration is typically within the same city or town of residence, while intercounty migration typically represents moves of over 100 km. Municipalities constitute an intermediate level of aggregation, and intermunicipality migration within a county would represent reallocations within a greater urban area or region.
II – Previous perspectives on migration over the life course
5Migration researchers and demographers have long been interested in obtaining measures of migration propensity over the life course. The age patterns of internal migration have been studied extensively (Rogers et al., 1978; Rogers, 1988; Mulder, 1993; Mulder, 2007) because they are important for understanding internal migration flows between different regions within countries. These migration patterns change over the life course, and much theorizing on migration concentrates on the association of migration with family formation, housing careers, and other sociodemographic events (Rossi, 1980; Mulder and Hooimeijer, 1999; Kulu and Milewski, 2007).
6Beginning in the 1960s, migration researchers began to use life table techniques to study migration propensities over the life course (Wilber, 1963; Long, 1973; Bernard, 2017a) as well as differences in the intensities of internal migration across countries (Bell et al., 2015b). Much like demographers have used period data to estimate mortality and fertility indicators from a fictitious cohort, researchers have calculated the expected number of migration events over the life course. This approach can employ the cross-sectional data on individuals at different ages from a single region as well as from cross-sectional survey data. If some information on previous migration events is available, it is also possible to calculate migration histories (Bernard, 2017a; Bernard, 2017b; Kulu et al., 2018). Researchers have also developed various methods to infer age-specific migration rates (and thus the total number of migration events over an age range) from sources with incomplete data (e.g. Mulder, 1993; Rogers and Rajbhandary, 1997). It is also possible to calculate expected durations of residence through life table methods (DeWaard and Raymer, 2012).
Internal migration rates for moves within and across different administrative units of Sweden
Internal migration rates for moves within and across different administrative units of SwedenCoverage: Men and women of all ages born and residing in Sweden, 2000–2015.
III – Measures of migration
7The number of migration events over the life course can be seen as a direct analogue to both the total fertility rate (TFR) and the cohort total fertility rate (CTFR). It is calculated by summing the age-specific rates for a given age range. This measure has been given several different names, including ‘migration expectancy’ (e.g. Wilber, 1963; Long, 1973), ‘general migration rate’ (e.g. Rogers and Rajbhandary, 1997), and ‘total migration rate’ (e.g. Gödri and Spéder, 2010). The period measure will be referred to as the period total migration rate (PTMigR) and the cohort measure as the cohort total migration rate (CTMigR), which is analogous to fertility measures. The following notation refers to the rate for one year or, alternatively, cohort:
9where x = age, M = number of migration events in the population at risk, m = migration rate, P = population at risk, n = age interval for the occurrences and exposure (in this study, n = 1). PTMigR and CTMigR are calculated in a similar way, but the sum of age-specific rates for a cohort is used instead of rates for different ages at a single time point. The exposure for in-migration rates is typically difficult to define because the population at risk of migration into a country or region can be more or less large. The alternative of relating in-migration rates to the population of the destination is counter-intuitive because the at-risk population should be related to the origin population. This is less of a problem with national numbers of internal migration events—the exposure is related to a clearly bounded population—and where migration takes place within this bounded region. In this study, the end-of-year population  at a given age is used for the calculation of the exposure population. This allows us to calculate yearly rates by using administrative data for only the year being calculated, thus enabling use of a larger set of data. Furthermore, it is assumed that all migration events are evenly distributed over the year. Using data for which both occurrences and exposure are based on the same year is convenient for comparing cohort and period measures. However, this will slightly overestimate rates at higher ages because, as the exposure population is underestimated due to mortality over the year, the size of the underestimation is approximately half of mx, which is the probability of dying in the year for the age group in a life table. The exception is the first age group (1P0), to which is applied the mid-year population of that age group (assumed, for simplicity, to be half of the end-of-year population). Studies of migration age patterns do not always correct for exposure in the first year of life, which leads to underestimated age-specific migration rates by around 50%. This is because, otherwise, exposure is calculated from all children born over an entire year, while the children born in the latter half contribute to migration events for only a few months. Similar to the way in which TFRs are calculated, age-specific rates and total migration rates are based on the currently living population. As such, they reflect the number of migration events for a person who has lived an unusually long time, and most individuals will therefore make fewer moves than their population’s PTMigR. This paper will show how these measures vary when taking mortality into account.
10The notation above highlights the similarity to fertility measures, which will be even more apparent if one introduces order-specific migration rates (much like using parity in fertility analysis). The notation also allows for easily distinguishing among different age intervals, a crucial operation in migration analysis because migration in childhood is not ‘self-generated’ but rather related to parental migration decisions. The measure is sensitive to how a ‘migration event’ is defined (Bell et al., 2002). In this study, a migration event is defined as the crossing of a parish border. In Sweden, the national tax office tracks population residency in a central registry. Most mail is sent to the de jure address of an individual, and access to government services is complicated if the de jure and de facto residences differ. Therefore, compliance with keeping the government up to date with current residency is high. All migration events registered with the government are included, and the data are specified at monthly granularity, with some rare cases of multiple migration events occurring in the same month. An individual can therefore migrate more than once over a year. Migration is based on de jure changes in residence and, as such, includes moves related to the institutionalization of older individuals if they permanently change their address, although this is not typically the case for weekly or monthly stays at a hospital or in other institutions.
11The advantage of parish borders is that they are the administrative division with the stablest geographical borders over the study period and are the smallest administrative unit. However, the number of parishes began to decrease at an increasing rate from 1997 to 2012, through consolidation of adjacent parishes (Sweden had 2,655 parishes in 1972, 2,512 in 2000, and 1,432 parishes in 2012). One consequence is that the migration rates in the final period are to some degree reduced relative to the calculations for earlier periods.
12In this paper, the cohort includes the complete register-based population of all Swedish-born individuals and all migration events within the borders of Sweden. Individuals are permanently right censored after their first international migration. Cohort analyses using life course data, such as surveys with migration histories, would be interpreted in a similarly straightforward fashion. Cohort measures are also informative and can be used when it cannot be assumed that individuals in the study data are observed throughout their lives. This is the case when cohort total migration rates are calculated for a subregion. In such cases, the population under analysis is a pseudo-cohort consisting of a population that shares the same birth year but might not be identical in composition over time. For example, if for an area we know the population that will be age 10 in a year, age 11 the subsequent year, and so on, then we can calculate the CTMigR. However, the population at different ages may be compositionally different due to internal migration.
13The migration data come from Swedish administrative registers for the years 1970–2012 and for all Swedish-born men and women registered in Sweden. The data cover the complete population but are limited to individuals below age 75 for the period before 1990 and to migration events occurring below age 75 until 2004. Most results are presented for the 0–75 age range. In cases of first international out-migration, the person is right censored starting from the year the out-migration takes place. This paper’s online supplementary material provides several tables with all input data structured by cohort, period, and age.  These files include additional data for ages up to 109 after 2004.
IV – Results
1 – Age patterns in internal migration
14Figures 2A and 2B show age-specific period and cohort total migration rates for Sweden from 1970 onwards. No cohort has complete migration histories from age 0 to 75 because the data are limited to between 1970 and 2012; thus, the age-specific rates in Figure 2B are truncated. The figures illustrate familiar internal migration age patterns in which migration is high before children start school, rises rapidly around the end of high school, and peaks during the mid-20s, after which it begins to decline sharply. Migration propensities in the mid-20s are more than 6 times as high as those of adolescence and even higher compared to late adulthood. Overall, age patterns in migration are smooth over the life course; and other than the important transitions towards the end of high school, most trends are smooth in all periods. Unlike the internal migration age profiles from the United States and many other European countries (Rogers and Castro, 1981), Sweden shows no substantial increase in migration rates at a fixed age around retirement. This is likely due in part to the variable retirement age as a result of different collective agreements, disability pensions, and (after 2000) a retirement system that is flexible and actuarially fair to those retiring at different ages (Palme, 2005). For those oldest cohorts in the period when retirement was more uniform, a slight bump at age 65 can be observed. At advanced ages over 85, there is, however, some evidence of increasing rates (see online supplementary tables), while the rates for those over age 90 are comparable to the migration rates of those at age 50. Such migration is likely related to institutional care and hospitalization. Overall, the age pattern is very similar for cohort rates and period rates, which suggests that migration changes took place evenly across periods and cohorts. In other words, the results indicate that there were neither any period shocks (such as in economic cycles) nor any specific cohorts with unique behaviour, which deviates from a gradual shift towards a migration pattern that concentrates more in early adulthood over time.
Interparish migration rates by age and period
Interparish migration rates by age and periodCoverage: Men and women aged 0 to 75 born and residing in Sweden, from 1970 to 2010.
Interparish migration rates by age and birth cohort
Interparish migration rates by age and birth cohortCoverage: Men and women aged 0 to 75 born and residing in Sweden, all migration events from 1970 to 2012.
15Migration has become increasingly concentrated in early adulthood, which is visible in both period and cohort trends. In contrast, migration events involving children have decreased, while migration propensities have increased for those in their 20s and 30s. The decrease in migration at childhood ages occurred simultaneously with increases in migration rates for those in their 30s, and this suggests migration increases for less settled and childless individuals, while it decreases for settled individuals and families that move with their children. These patterns are highlighted in Figure 3, which uses period rates to compare cumulative migration in the years 1970 and 2000. Figure 3 clearly shows that in 1970 more migration took place during childhood, while rates after age 25 were higher in 2000, with a slight increase in cumulative migration at ages above 40 in 2010. These findings support previous research indicating not only that family formation is a strong inhibitor of migration (Fischer and Malmberg, 2001) but also that increases in the share of dual-earner couples among partnered individuals might be associated with decreasing migration rates for men and women in their 30s with coresident children (Mincer, 1978). The increasing migration rates for those in their early 20s are consistent with the extensive expansion of tertiary education in Sweden in the 1970s and 1990s (Chudnovskaya and Kolk, 2017).
Period total migration rate up to a given age, for all interparish migration events in 1970 and 2000
Period total migration rate up to a given age, for all interparish migration events in 1970 and 2000Coverage: Men and women aged 0 to 75 born and residing in Sweden.
2 – Cohort and period comparison of internal migration
16Figure 4 presents comparisons between period and cohort total migration rates from ages 20 to 40 for interparish migration events. The period measure PTMigR4020 begins from 1971, and the cohort measure CTMigR4020 begins with individuals born in the year 1949. Most migration occurs in these age ranges, and the age intervals allow comparisons between cohort and period rates. CTMigR4020 increases for cohorts in the 1950s to 1960s, from a little over 2.5 to 3.5 moves per person over the age span considered. PTMigR4020 for a comparable period in the 1970s and 1980s followed a largely similar pattern, hovering between 2.5 to 3.5 migration events per person. For later periods, when only cross-sectional period measures can be calculated, PTMigR4020 increases to a little less than 4. When complete cohort data can be analysed alongside period data for a time span, cohort rates show less variation over time than do period rates, an empirical pattern that can also be seen in cohort measures of mortality and fertility. A clear increase in the period measures for the early 1990s, a time of economic crisis in Sweden, is instead reflected in a more gradual and smooth monotonic increase for birth cohorts that were in their 20s and 30s during this period. Overall, the lower temporal variance in cohort total migration rates implies that even though period shocks might cause migration, it is likely that, to some extent, these were accelerated or postponed events that might otherwise have occurred at a different time for other life course–related reasons.
Period total migration rate (PTMigR4020) and cohort total migration rate (CTMigR4020) for interparish migration
Period total migration rate (PTMigR4020) and cohort total migration rate (CTMigR4020) for interparish migrationCoverage: Men and women aged 20 to 40 born and residing in Sweden.
17Figure 5 shows the separate results for men and women on the cumulative number of moves by age and cohort, starting from age 18. The heat map indicates the accumulated number of moves by an individual in a given cohort until a specific age. The accumulated numbers of moves over the life course of a birth cohort up to a given age are represented by a vertical line. Age 20 to 30 is the only age interval for which interparish migration events shows a clearly distinct pattern between men and women. Women have an accelerated pattern of migration related to their having a higher propensity for moving to pursue a university education, and they also leave the parental home at slightly earlier ages (Statistics Sweden, 2008). For the 1975 cohort, women have higher accumulated migration at all ages; but by age 43, the differences between men and women in accumulated moves have almost disappeared.
Accumulated interparish migration events from age 18 by birth year, age, and sex
Accumulated interparish migration events from age 18 by birth year, age, and sexCoverage: Men and women aged 18–43 born and residing in Sweden.
3 – Migration measures across the life course
18Figure 6 illustrates the PTMigR for different age ranges. Overall, similar period trends affected migration in all age ranges. The total number of moves across parish borders (the sum of the age-specific rates shown in Figure 2A) decreased from a PTMigR750 of about 6 migration events in the early 1970s to about 5 in the 1980s, after which it increases to 7. Around half of all migration from ages 0–75 took place between ages 20 and 40. After 2004, when data are available likewise for ages 76 and over, PTMigR1000 can also be calculated, indicating about 0.8 moves more than PTMigR750. The measures for the different age ranges show strong regularities. Without age-specific data for some ages, it nevertheless seems possible to use this regularity to extrapolate PTMigR estimates.
19Over the study period, migration increased primarily in early adulthood, while decreasing migration seems to concentrate in childhood. There is a stronger increase over time in the PTMigR4020 measure than in wider age spans. This is another reflection of the concentration of migration at earlier ages that took place in Sweden from the 1970s to the 2000s. Following the Swedish economic downturn in the early 1990s, migration increased. In contrast, a decline in migration rates occurs after 2007, but it takes place at the same time that parishes were being consolidated. Therefore, because country migration rates appear to be stable (not shown), this decline might reflect changing administrative boundaries.
Period total migration rate (PTMigR) for interparish migration events at different age intervals by year
Period total migration rate (PTMigR) for interparish migration events at different age intervals by yearCoverage: Men and women aged 0 to 100 born and residing in Sweden.
20PTMigR is based on age-specific rates of surviving individuals (like TFR). Migration rates are still quite high at very advanced ages, when only a small share of the population is alive (see age-specific rates in online supplementary material for 2004 onwards). Nevertheless, such measures increase PTMigR substantially when it is used over a wide age span in which individuals are assumed to be alive at all observed ages. Therefore, rather than following a cohort of only survivors, researchers interested in measuring migration over the entire lifespan might want to consider comparing their measures with a cohort’s true life course counts of migration events (comparable to the net reproductive rate used in fertility research). As an example, the cumulative migration of individuals aged 95 to 105 (PTMigR10595) in 2012 was 0.57 (see online supplementary tables). An example of such calculations is provided in Figure 6, which shows the period total migration rate weighted by survival of each age group. This is the sum of migration events after adjusting them according to the survival probability of reaching that age. The survival proportion (lx) applied in Figure 6 is based on period life tables from the Human Mortality Database (2017). For PTMigR1000, the difference is about 0.7 moves over the life course when adjusting / not adjusting for mortality. This difference would be larger with even older ages included. Similar calculations can be made using cohort measures if longitudinal data on migration and mortality are available for an entire life course.
V – Possible extensions of population-based migration measures
21All data presented in this study are based on internal migration (interparish moves). The methods are applicable to international migration, though finding a data source that allows observations across borders remains a challenge. Aggregated rates, for both cohort and period trends, can be calculated using data on out-migration from a country. For example, administrative registers make it possible to calculate not only the rate for first out-migration for native-born men and women (or its reverse, the never-migrated) but also the rate for second outmigration using the population of (first-time) returning immigrants. The measure of first, second, and higher-order total emigration rates for the entire life course could be added together. This sum would then equal the total international outmigration rate for a native-born cohort when it is used for all observed international immigration and emigration. However, such measures do not have an obvious life course interpretation, as the exposure time after the first return-migration is based only on the part of the life course spent in the country under study (excluding time spent abroad). Still, it would give a measure of the average number of out-migration events from the country of origin for any member of a given cohort for that country. For international migration events, such estimates are less meaningful because the exposure population prior to migration is not well defined and could be arbitrarily large (e.g. the world population).
22Similar to fertility measures for which analyses by parity are common, it is possible to calculate order-specific migration rates with longitudinal data. This allows us to decompose PTMigR into order-specific components to better understand order-specific aspects of migration behaviour (cf. Bernard and Kolk, 2019; Bernard, 2017a). This also makes it possible to calculate conditional age-specific rates (using only the order-specific population at risk as the denominator)—those that correspond to the (parity-specific) rates that are the dependent variable in an event history regression model—but only if the population composition by migration order is known (cf. Kolk, 2014; Kulu et al., 2018). Another extension to the calculations of life course migration is to decompose migration data into different kinds of migration events using different distance thresholds (based either on coordinate data or on different levels of administrative hierarchy in the geographical organization). It is also a straightforward matter to desegregate data by sociodemographic characteristics, such as educational level, sex, or country of origin.
23Contrary to what has been shown for earlier patterns of interregional migration (Lundholm, 2007), the results of this study reveal that interparish migration has increased since the 1970s and are instead consistent with a recent study on moves across labour market areas (Kulu et al., 2018). The increase is visible in both period and cohort trends, and it is concentrated in early adulthood. The results show that life course migration patterns, as revealed through cohort measures, are stabler than period measures, which are more subject to period shocks such as economic cycles. However, for a wider perspective, cohort measures can be used to track period measures closely. There are many advantages to taking a population-level view of migration events using micro-level data. For example, beyond giving an adequate and representative view of a population’s actual migration histories, they also constitute an appropriate level of analysis for studying interactions between migration, housing markets, and the general economy. Longitudinal population-level data are also required to translate the results from micro-level event history studies by using equivalent and standard population-level measures. Similarly, examining cohort and period trends simultaneously is essential for separating the effect of period shocks from longterm secular changes in migration. While it may be comparatively rare to find administrative data that include migration histories, representative longitudinal survey data that include migration histories are also adequate for such calculations (cf. Bernard, 2017a). If a sufficiently long time series can be obtained, it is also possible to calculate cohort rates based on a succession of similar period data estimates, as long as the period data include age. As such, cohort measures of migration have many applications, even when longitudinal micro-level data are absent. Using fertility and mortality measures in demography demonstrates how a cohort perspective can often be applied when facing a lack of complete life course longitudinal data.
24These methods can also be applied to international migration, though it would be a challenge to find data that follow individuals across countries (Swedish and Finnish register data are rare examples of this having been done). One solution to this problem is to study only the out-migration from a country for which the at-risk population is better known. By taking both a period and cohort perspective, the total migration rate makes a useful contribution to the toolbox of demographers involved in migration research.
It is possible to use the average of the population size at the end of 2 successive years, although this makes calculating the rate more data-demanding. It can be done if a full matrix of cohorts and periods are available (as in this study), which is not always the case. In many administrative data sources, only the end-of-year population constitutes the underlying data structure.