Changing migration rates in England and Wales over a 40-year period: Is mobility declining?

Research using data for the United States has pointed towards a long-term pattern of falling migration rates. Similar research in England and Wales has also found declining migration rates when observing all migrants. Using the Office for National Statistics Longitudinal Study (ONS LS), we study the patterns of migration observed over 10-year periods for persons in 10-year birth cohorts over each intercensal period from 1971 – 1981 through to 2001 – 2011. When the sample population is considered as a whole, the results from the LS are consistent with earlier findings: There has been a decade-on-decade decline in the migration rate as observed in longitudinal data. When disaggregated by cohort, it is apparent that this decline is not always observed for young adults, but it is consis-tently observed for those in their 30s and older, for whom each successive cohort has a lower migration rate than the previous one and also for whom there is a steady within-cohort decline in the migration rate over time. This is observed at both short and longer distances of move. Alternative results from successive censuses looking at migration observed for single years do not appear to confirm this decline in migration, although data collection and processing issues may be part of the explanation for this finding, and it is also the case that these data may be more subject to cyclical effects.

had 'generally declined since about 1950' (p. 5). Molloy et al. (2011) compared the decline in migration across different demographic and socio-economic groups and found that rates had fallen for nearly all subgroups. They also compared mobility in the United States to European countries, largely supporting the supposition that mobility was higher in the United States than in Europe and also pointing to decline in migration over the period 1999-2008 in Britain. International comparisons of migration remain difficult due to significant differences in data collected, and thus, comparisons often tend to be limited to specific countries and require extensive data husbandry prior to analysis (e.g. Stillwell et al., 2000Stillwell et al., , 2001; however, a review of internal migration in 66 countries was carried out by Bell et al. (2017), with temporal trends in migration intensity computed for interregional moves in over 40 of the countries. The term migration intensity follows the usage outlined by van Imhoff and Keilman (1991) in using intensity to refer either to transition probabilities (in data based on observation of migrants) or movement rates (in data based on observation of migrations-a distinction being that within an observation period, individual migrants may make more than one migration). Bell et al. (2017) declined over the period 2000-2010 in most countries, although the exception to this was in Europe, where more countries were observed to have rising migration intensities than were observed to have falling intensities.

Migration intensities reported by
As regards England and Wales, Champion and Shuttleworth (2017a) found from analysing time-series administrative data that there had not been a substantial fall in overall longer distance migration rates since the 1970s, but, in a companion paper (Champion & Shuttleworth, 2017b) using the ONS Longitudinal Study (ONS LS), compared 10-year migration transitions across four intercensal periods from 1971-1981 to 2001-2011 and found a marked decline in migration rates, with the differences between these two findings hypothesised as being related to the distance of move, and variations in the extent to which the two data sources could capture short-distance moves. The present paper expands upon their work and in particular aims to explore whether or not reductions in mobility are observed for all age and sex groups across the period 1971-2011 and also whether this is true for both short and longer distance moves.
The paper starts by exploring the challenges posed by the data available for analysis and goes on to discuss patterns observed in successive sets of cross-sectional migration data for England and Wales.
The bulk of the paper then discusses migration rates as observed in census longitudinal data for England and Wales using three overlapping samples: firstly, a set of sample members who were repeatedly mobile (i.e. they have moved in each intercensal decade, 1971-1981 through to 2001-2011); secondly, a set of sample members who were present at each census 1971-2011 (the repeatedly mobile being a subset of this group); and thirdly, a set of sample members who were present for at least two successive censuses 1971-2011 (the second group in turn being a subset of this group). The first of these groups are used to explore regional patterns of migration. The repeatedly mobile sample, whilst not directly informing the question of changes in migration rates over time, are useful in that they set the context of the spatial patterns of movement over a relatively long observation period. They demonstrate the utility of the data, showing that the sample size is sufficient to select a specific population and follow them across five censuses. The same population is observed throughout, and within that population, overall migration rates do not change: there is one net migration event in each decade. However, the data are disaggregated by region and therefore give some indication of variations in the length of migration over time for a broad cohort. The second and third groups are used to examine changes in migration rates over time for sets of period-cohort observations in order to determine whether Champion and Shuttleworth's findings hold true for cohorts. Period-cohort observations are those for a given birth cohort over a given time period, for example, the 1961-1971 birth cohort observed over the period 1981-1991. In the context of census longitudinal data, this is an observation of migration transition: we can observe the place of residence of each sample member at the start of the period and at the end of the period and can therefore determine whether there has been a change. The paper then goes on to subdivide the third group-those who had been present for at least two successive censuses-on the basis of distance moved in order to explore whether patterns observed for all migrants remain the same or differ when different migration lengths are taken into account.

| DATA AND METHODS
Two families of census data outputs are used in this paper-crosssectional observations and longitudinal observations. We describe here the data and the methods applied to them.

| Cross-sectional observations
The cross-sectional observations are drawn from successive sets of  (Champion et al., 1998). Further issues with consistency (from the perspective of comparison over time) were introduced in the 2001 Census with the One Number Census project (Brown et al., 1999).
Other changes in population coverage issues between the 2001 and 1991 (and earlier) censuses were identified by Rees et al. (2002), including the assumed usual residences of students and the definitional process used with infant migrants, whereas a separate class of problems was discussed by Stillwell and Duke-Williams (2007), namely, variant data biases introduced by different forms of statistical disclosure control used for successive censuses.
Some of these concerns can be partially addressed by adjustments to the reported data. For instance, Boyle and Feng (2002) developed a methodology that could be used to remodel migration flows reported with one geographic system and estimate equivalent flows for another and used this to transfer migration data from the 1981 and 1991 censuses to the 2001 reporting geographies, with results produced with and without pro rata allocation of migrants with unstated origins.
In order to compare overall levels of mobility over time, we calculated the proportion of the population that were migrants according to the census definition (a change in usual residence in the year prior to the census), by sex, using the versions of the SMS prepared by Boyle and Feng (2002). These versions allow for variations in the reporting geography and reallocate flows with no stated origin.
The mean distance moved was calculated for all migrants. Distances were determined as the Euclidean distance between local authority centroids; for moves within a local authority, the distance was assumed to be half of the radius of a circle of the same area as the local authority. Similar calculations were made for the 2011 census data, although substantial changes in the local authority geography mean that these are not directly comparable with the earlier results.
Comparisons of mobility between cross-sectional observations are also complicated here by variations in the universe over which moves are observed: Some data are available for the whole of the United Kingdom, whereas other data omit Northern Ireland. The cross-sectional measures were calculated for moves within England and Wales only in order not only to create a comparable time series but also to provide appropriate context for the analysis of data from the LS.

| Longitudinal observations
The distribution of move distances is not known, but it is assumed that some of these moves were of a very short distance, and therefore, that some short-distance moves excluded from the LS were not in fact false positives. However, it is assumed that the total number of these is small enough not to affect analysis elsewhere.
Thus, it is possible to look at the 10-year migration observations for each intercensal period in the LS, but it should be remembered that there is still some noise within the results, due to differential measurements of migration. Unlike the cross-sectional data, the LS does not have fully imputed records, nor does it have imputed usual residences, from which the migration event is inferred. The imputation of 'migrant origins' is only relevant to cross-sectional data, for it is an imputation of unknown data (a response that has been omitted or not fully completed on the census form), whereas in the case of the longitudinal data, the 'origin' is a known item: the place of residence at the time of the census, which by definition cannot be missing if the sample member has been included in the dataset for that census.
A further point to note is that the date of each census in the period 1971-2011 has not been the same, meaning that the observa- This final sample was further constrained by requiring that persons were aged less than 20 at the time of the 1971 Census, such that they would potentially follow a broadly similar narrative, starting out mostly co-resident with their parents in 1971 and then moving through early adulthood and progression through working life. Up to 1991, students will have been recorded at their parental address, and thus, this cohort is unlikely to have a migration narrative in the LS that includes a student term-time address. In each case, we aggregated the total number of persons in a sequence of 10-year age groups who had migrated in each 10-year period and constructed a migration intensity or rate for each group, using the population (of movers and non-movers) who were present at the beginning of the 10-year period and were still alive and present at the end of the period. We have assumed these to equate to corresponding 10-year birth cohorts, running on the census calendar: Thus, what we refer to as a 1961-1971 cohort contains persons born in the 10 years up to the date of the 1971 Census (based on age at the time of the census). Given that the census does not take place on the same date in each round (see above), the actual cohort inclusion will contain a small amount of error. Although the ONS LS contains the single-year ages of all sample members, it is clear that at upper ages, the numbers of sample members can be too small to permit further disaggregation: Exploratory analysis was done in order to determine an effective upper age group that could be reliably reported without the absolute numbers falling below the publication threshold.

| Cross-sectional context
We turn first to the cross-sectional observations of internal migration, which allow comparison of levels of migration propensity at intervals throughout the time period examined using the longitudinal data.
These provide some context for the longitudinal results, but do not necessarily have the same characteristics. They exhibit more volatility through cyclical effects. However, cross-sectional observations are easier to obtain than longitudinal ones, and thus, it is useful to explore whether or not the two approaches suggest similar results. These cross-sectional data do not therefore fit the pattern seen elsewhere of falling migration propensities. However, caution should be attached to these results, due to the cyclical factors noted elsewhere and the aforementioned variations in disclosure control, imputation approach and population coverage: the full effect of those is unknown but may be larger than the changes in migration propensity and distance seen in these results. In particular, different approaches to the processing of migrants with an unstated origin (the number of which can be large) make it difficult to approach these cross-sectional results with total confidence.
Cyclical economic effects that may affect labour demand are more likely to be 'evened out' in the decadal periods between the longitudinal observations than they are should they coincide with the 1-year period of the cross-sectional observations. Another important qualifier is that it is necessary to consider the growth in the numbers of students since 1971 and at the same time changes in the recording of students' usual residence from 2001 onwards.

| Regional patterns of repeatedly mobile persons
The selection criteria for the LS analysis of movements at regional level required that sample members had moved in each intercensal period observed and had been aged less than 20 in 1971. There were a total of 13,983 persons in the LS who satisfied these selection criteria. As the LS is a 1.1% sample, this suggests a total of around 1. For each intercensal period, a 10 × 10 area matrix using standard government office regions (GORs) of England, and Wales, was constructed, with an aggregate set of net moves for all persons. The GOR geography typically used for reporting from 1998 onwards was employed, and data from earlier censuses were aggregated on that basis in order to establish a common spatial framework. Each move was determined using a comparison of address at the start and end census points, although the precise algorithm has varied slightly from census to census, as described above in the data section. All comparisons share the characteristic that only a 10-year net move is considered: Someone who lived at a given address at the start point, moved away and then moved back to the same address at the end point would not be considered to have moved using this indicator, and someone making a sequence of moves within or between multiple regions would only be recorded as making a single move between the usual residence locations at the start and end of the intercensal period.
The ONS LS data usage agreements require that small numbers should not be published. The region-level matrices for the most part produce numbers above the publication thresholds, although this is not the case for every region-to-region flow-a small number of the lower volume flows were below the publication threshold. Given that some of the results cannot be disclosed, the complete set of matrices were transformed so as to split the flows into deciles (based on absolute value) and then to report which decile each matrix cell fell into. In each case, it is the same group of sample members that are observed in each matrix, and thus, changing migration behaviour associated with age might be seen. In the first matrix (1971)(1972)(1973)(1974)(1975)(1976)(1977)(1978)(1979)(1980)(1981) have stayed within the same region for the whole period. There was regional variation in the likelihood of repeatedly moving within the same region; Table 2 shows the regional breakdown. Yorkshire & Humberside was the region in which the repeatedly mobile were most likely to end up (in 2011) in the same region as they had been in 1971 and also the region with the highest percentage of those repeatedly moving within the same region. The most striking feature however is that the proportion of repeatedly mobile persons staying within London (24%) for the whole period (1971-2011) was much lower than in all other regions. This is consistent with the description by Fielding (1992) and Champion (2012) of the South East (in this case with London as a focus) as an escalator region that people move to and then away from at a later career stage.
Demographic variations were also observed in the population who had been repeatedly mobile but had always stayed within the same region. Repeated migration within the same region was slightly more common for women than men (50% of repeatedly mobile women had stayed in the same region, compared with 47% of repeatedly mobile men) and was more common for people with a dependent child (observed in either 1991 or 2001) than for those without a F I G U R E 1 Interregional migration 'staircase'-ONS LS sample members, England andWales, 1971-1981 Table 3 and show considerable differences. Of those repeatedly mobile persons who were classified (in 2011) as 'professional', 27% had stayed within the same region over the whole period, with the rest having changed region at least once. This was the lowest observed level: that is, of all repeatedly mobile persons, professionals were most likely to have changed region at least once. Those classified in 2011 as 'managerial/technical' also exhibited the characteristic that the majority of persons have moved region at least once. In contrast, the majority of the repeatedly mobile who were classified (in 2011) as anything other than professional or managerial/technical had stayed in the same region throughout (although this is only marginally true for the 'non-manual skilled' group). This would therefore support assumptions of a relationship between social class (and perhaps social mobility) and geographical mobility and may be associated with the South East as an escalator region. It should be noted that here we simply divide the repeatedly mobile into two groups: those who have stayed within their original region throughout and those who have made an interregional move at least once. The latter group is diverse and includes those with a single interregional move and those with repeated such moves.

| Period-cohort observations
In order to study period-cohort patterns, two (overlapping) samples were constructed: the firstas for regional patternsof sample members who had been present at every census, and for whom there was a valid value in all of the 10-year migration indicators (whether positive or not), and the second being a less restrictive sample comprising all persons who were present at any stage for two or more consecutive censuses, and for whom there was therefore at least one valid 10-year migration indicator.
In each case, we aggregated the total number of persons in a sequence of 10-year age groups who had migrated in each 10-year period and constructed a migration intensity or rate for each group. We have assumed these to equate to corresponding 10-year birth cohorts, running on the census calendar; as discussed above, the census does not take place on the same date in each round, so the actual cohort inclusion will contain a small amount of error.
In order to calculate migration intensities, it is necessary to determine the populations at risk of migration. Bell et al. (1999) describe a comparison framework for age-period-cohort migration data and discuss requirements for populations at risk in analysis of such data. We follow the terminology there and identify within the LS data a sequence of period-cohort migration transitions.
In order to be at risk of migration in any intercensal period (assessed through observation at the end of the period), it is necessary for the individual to be present at both the start and the end of the period. That population can therefore be calculated as all persons present at both time points (regardless of mover status). However, the subpopulation of interest in the first sample in this analysis is subject to more constraints: They must have been present in each period.
Thus, we define the population at risk for any period-cohort cell in the first sample as being the total cohort population. The 10-year migration indicator variables in the data require that the individual was alive in order to be classified as a mover or non-mover. We do not include observations for persons aged under 10 as they cannot have been enumerated at a previous census, even though it is clearly possible that they may have migrated during that part of the intercensal decade in which they were alive. Subject to possible error described above in cohort inclusion, we assume our observations to be of require the population at risk to be that population present at both the start and end of the 10-year period, in each relevant age group.
Separate calculations were done for male and female populations in both cases. Figure 2 shows results for the sample of LS members present at each census from 1971 to 2011, in the form of a Lexis diagram (Vandeschrick, 2001). The left-hand image shows results for males, and the right-hand image shows the results for females. Each quadrilateral shape shows the migration intensity for a given 10-year birth cohort in a given 10-year period, with the exception of the final group, which is an open-ended cohort.
The 'stripe' starting at the bottom left is the 1961-1971 cohort, the next stripe above the 1951-1961 cohort and so on. The uppermost stripe on the figure is for a pre-1921 group, with no lower birth-year bound; for this group, the age axis shows the lower age bound for the group at the start of each intercensal period. In each case, the period-cohort block is shaded using a contrast ramp across the range of values with darker cells showing higher intensities and the lighter cells showing lower intensities. The migration rate is also shown as a numeric value. The number of movers and the denominators (total of movers and non-movers for each cohort who survived the whole period) are shown in Table 4 Figure 3 shows the migration rates for the second of the two samples in this section: those who were present in at least two successive censuses and had at least one valid 10-year migration indicator. In this case, the total numbers were larger (as the selection criteria were more broad), permitting more recent cohorts to be followed and also permitting the earliest born cohorts to be observed at older ages. In each case in Figure 3, the oldest cohort in each intercensal period is open-ended: For the intercensal period 1971-1981, it is the pre-1911 cohort; for the period 1981-1991 it is the pre-1921 cohort; and so on. The labels for these cohorts are shown with parentheses around the starting year; in each case, the cohort is open only for the oldest age observation.
Taken as a whole, the results show a decline in mobility over time.
For the first group, who had been present at every census, mobility declined in each intercensal period, for both men and women. For men, it fell from a 63% intercensal rate (across all observed cohorts) in 1971-1981 to a 32% rate in 2001-2011; for women, the decline was very similar from 63% to 31%. These observations are for a fixed set of cohorts, whose members aged over the observation period. A decline was also observed for the second group-those who had been present for at least two successive censuses. For this group, total mobility (across all ages from 10 to 19 at the end of the period) within a 10-year period fell for both men and women from 56% in 1971-1981 to 45% in 2001-2011. These findings would therefore support arguments of an overall decline in mobility, both for fixed cohorts followed over time and for successive cohorts with equivalent age structures. However, closer inspection of the data shows that although this was true for aggregate populations, it was not universally true for at all ages. For those who were present at each census, a continuous decline (in which the migration rate fell in each successive intercensal period) was observed for men for the 1921-1931, 1931-1941 and 1941-1951 Figure 3. Again, it can be observed that there is a decline in migration rate for both men and for women within cohort and between successive cohorts for fixed age groups for older cohorts and for older age groups, but that this is not the case for the younger age groups. As before, the reduction in migration rates can be observed in women at a lower age level than is the case for men.

| DISCUSSION AND CONCLUSION
The two families of data used in the paper appear to show inconsis- Ireland and between them and the rest of the United Kingdom is different in structure to the extent that it would affect overall patterns, but given the large difference in population sizes, this seems unlikely.
A part of the explanation for the apparent increase in migration rates in successive cross-sectional data may lie in the changing manner in which missing migrant origins and missing records have been imputed.
The One Number Census process set out with the aim of restoring missing data, and some of the missing records were those of migrants; meanwhile, changes to item-level imputation could move reporting of migrants from having an 'unstated origin' to having a stated origin. It is easy to exclude the former from analysis, especially if one is simultaneously concerned with migration distances, and therefore need to place all migrants within a spatial framework. An obvious potential explanatory factor for changing migration rates of young adults is the growth in higher education (HE) participation rates over the period that the LS covers, although the changes in 10-year migration rates are much smaller in scale than the changes in HE participation. The fastest growth in HE participation occurred in the 1990s, and although the longitudinal data do show an increase in migration rates for young adults compared with the previous decade, it would seem fairer to observe that the outlier decade in this is the 1980s rather than the 1990s, with migration rates both men and women aged under 30 (at the start of the decade) having a pronounced decline in the 1980s compared with the rates observed in the 1970s, followed by a partial recovery in the 1990s. This pattern would not seem to be explained by HE participation alone. Again, it is instructive to consider changes in the way that data have been captured in the decennial censuses. In the 2001 Census, the assumed usual residence of students changed from being their 'vacation' or 'parental' address to being their term-time address. This change in definition would have led to a greater number of students being recorded as migrants if the observation period (the year prior to the census) coincided with a move from a parental address to a (different) term-time one. The apparent growth ( Looking at the effect of distance of migration supports earlier observations that the decline in migration rates is largely about a decline in short-distance migration and about the balance of different migration lengths. The overall decline in migration hides an increase in the 1990s and onwards of longer distance migration amongst young adults, and it is this element that is perhaps most likely to be associated with changes in HE participation rate. The rapid expansion in HE in the 1990s has plateaued, and it will be instructive to see the effect on migration rates over a longer time period. The new hypothesis that migration rates are falling would suggest that we should see declining rates over the period 2011-2021 following linkage of data from the 2021 Census. The study of repeatedly mobile persons (those who had moved at least once in each intercensal decade) does not directly add to the exploration of changes in migration propensity, as it is for a fixed group of persons over a long period. Variations in the actual number of migration events from decade to decade for this cohort would be expected as with any other cohort. The patterns illustrated in Figure 1 do demonstrate the importance of London as a destination in early adulthood, and the South East in mid-career ages, supporting the escalator region hypothesis. The analysis of longitudinal data in this paper offers partial support to the views expressed elsewhere that migration in England and Wales has declined over several decades.
Although it is true that this is the case for the four decades from 1971-1981 through to 2001-2011 when observed for all persons in the LS sample, it was not universally true when considered for separate age groups. A steady decline in migration rates was observed for the middle aged and older, but this was not the case at younger ages.
The study design allows both cohorts and age groups to be compared.
We can see, for example, that those aged 10-19 in 1971 had higher migration rates over the period 1971-1981 that did those aged 10-19 in 1981 over the period 1981-1991. However, following those two cohorts forward, we see that the latter group had higher migration rates in the following decade than had been the case for the former group and that this was true for both men and women. Though the longitudinal observations show overall declines in mobility, there remain variations that may be driven either by cohort effects or by age/life-stage specific effects of wider economic conditions.