Scale and zonation effects on internal migration indicators in the United Kingdom

Consistent data from the last two population censuses in the United Kingdom are utilised in this paper to compare migration intensity and impact between two 1-year periods and to identify the scale and zonation effects on the selected migration indicators. The picture of change that emerges is one of declining migration intensities and a diminution in the distribution of migrants from urban to rural areas, with the exception of students and young workers whose net migration losses from rural areas are increasing and whose migration effectiveness is increasing. Scale effects are more apparent for migration intensity than effectiveness, the two components of the aggregate net migration rate, whereas zonation effects are relatively unimportant across scale for intensity but become more significant as zones become larger for effectiveness.


| INTRODUCTION
Quantitative studies of internal migration tend to rely on the use of indicators to measure, in summary form, the propensities, patterns and trends in population mobility in one or more time periods. The identification of indicators that represent the various domains of internal migration and that can be used to compare migration behaviour in different countries around the world has been pioneered by Bell et al. (2002). In most previous national studies, migration data availability or access restrictions dictate that analysis is undertaken at a limited range of spatial scales (often only one) and little attention is paid to the possibility that scale and zonation effects, collectively known as the modifiable areal unit problem (Openshaw, 1983), may exist, let alone how they may vary over time.
One of the twin aims of this paper is to investigate the MAUP effects on internal migration in the United Kingdom (UK), using age-specific flow data published at the local authority district (LAD) scale from the last two population censuses and a methodology that involves the progressive aggregation of the initial data into increasingly larger spatial units. In particular, we examine how one migration impact indicator, the aggregate net migration rate, together with its components, the crude migration intensity and the migration effectiveness index, vary according to spatial scale and the different zonal Censuses to inform our understanding of changes in internal migration between the two time periods, 2000-01 and 2010-11. This paper therefore aims also to fill this gap and contribute to the discussion on how migration propensities are changing in different parts of the world (Champion et al., 2017) and what trends are emerging in the UK in particular, complementing analysis by Lomax et al. (2014) and Champion andShuttleworth, 2016a, 2016b). The paper continues in the next section with a short contextual review of recent work on internal migration in the UK and an introduction to the methodology and software used to perform the scale and zonation analysis. This is followed by a discussion of the data and of the means employed to adjust the data to achieve a more consistent set of flow estimates for the two periods in question. Thereafter, crude migration rates are used to demonstrate how migration intensities have fallen over the intervening period, net migration rates are mapped to show the inter-LAD changing spatial patterns of redistribution of people in broad age groups, and intra-LAD migration rates reveal their own unique patterns of change. Variation in scale and zonation effects on the aggregate net migration rate and its components are then explored and the relationship between the crude migration intensity and the migration effectiveness index is revealed for different age groups. Some conclusions are presented in the final section of the paper.

| REVIEW
There is a long history of studies of migration in the UK at different spatial scales which starts with Ravenstein (1885) and is exemplified by early post-war contributions from Newton and Jeffery (1951) and Rowntree (1957) through to more recent studies by Champion (2005), Fielding (2012) and Lomax and Stillwell (2017). Recent interest in changing levels of national mobility in the UK was stimulated by Cooke's (2011) time-series analysis in the USA based on data from the US Census Bureau's Current Population Survey (CPS), showing a declining rate of internal migration caused initially by the great recession but also due to increasing secular rootedness. Champion and Shuttleworth (2016a) have subsequently used longitudinal data from the last five censuses in England and Wales to suggest that whilst short-distance (intra-district) moves are in long-term decline, this trend is less evident in longer-distance (inter-LAD or inter-region) migration propensities, once fluctuations due to economic cycles are accounted for. Evidence from annual time-series data for England and Wales since the 1970s reported by Champion and Shuttleworth (2016b) also suggests no long-term decline in the overall intensity, a conclusion supported by Lomax and Stillwell (2017) using an estimated time series of patient reregistration data for moves between LADs in the UK in the 2000s. Champion et al. (2017) contains a number of case studies of migration trends in different countries, showing a diversity of experience across the more developed world.
When analysing migration propensities and patterns and investigating migration trends over time, many researchers (e.g., Bates & Bracken, 1982;Dennett & Stillwell, 2010;Raymer et al., 2007) have used migration data for different age groups since age is proxy for life-course stages and although age itself is not a determinant of migratory decisions, individuals or households in particular age groups are influenced by certain social, cultural and economic drivers associated with being at specific stage within the life course which determine whether a person will migrate or not (Stillwell, 2008). Rogers and Castro (1981) produced the seminal work on age variations, providing models of migration age schedules with indicators and parameters enabling comparisons to be made between countries and regions. Age data were used in the policy sensitive MIGMOD model of internal migration created for the Office of the Deputy Prime Minister (ODPM) in the UK (Champion et al., 2002;Fotheringham et al., 2004). De Jong and Graefe (2008) and Geist and McManus (2008) have also emphasised the relationship between age and migration intensity and demonstrated the links between life course and migration behaviour including employment status, family status, housing preference and retirement, all of which are related to age since there are patterns where specific age groups are more likely to be influenced by the same factors. A classic example is those in the student age groups who choose to leave home to extend their education, a key life-course event encouraging long-distance migration (Duke-Williams, 2009;Faggian et al., 2006). Scale is of major importance when it comes to identifying spatial patterns of internal migration and changes taking place therein. Whilst standard regions may be appropriate for monitoring long-distance moves such as those between the north and the south (Lomax & Stillwell, 2017), smaller spatial units such as LADs are more suitable for capturing patterns of counterurbanisation (Champion, 1989(Champion, , 2005, the predominant feature of sub-national migration in the UK over the last 50 years, although Stillwell et al. (2000) aggregated LADs into more meaningful functional regions to examine this phenomenon. Lomax and Stillwell (2017) suggest that this movement down the urban hierarchy from large cities to smaller cities, towns and rural areas has waned in the 2000s with a decrease in moves from metropolitan to non-metropolitan areas. Since the majority of migration takes place within LADs and typically occurs over shorter distances as residential mobility, a system of spatial units based on wards or output areas is more appropriate for understanding processes such as suburbanisation or reurbanisation. Whilst there are examples in the literature of analysis at ward level focused on ethnic migration at a national level (Simon, 2010) and for particular regions (Stillwell, 2010), the census data for migration at this scale remain underexploited and patient reregistration data are partial and inaccessible. It has become common practice to use individual or micro data to model residential mobility using spatial microsimulation or agent-based modelling techniques (e.g., Jordan et al., 2012) at small area scales in contrast to the gravity or spatial interaction models traditionally used to model internal migration over longer distances (e.g., Flowerdew & Lovett, 1989).
Explanations of the different macro and micro approaches to migration modelling can be found in Stillwell and Congdon (1991) and Champion et al. (1998).
Previous studies of internal migration in the UK, whether descriptive or model-based, have utilised a particular spatial scale and methodology that best fits their purpose, thereby ignoring how scale might affect the measurement of area-based indicators and the relationships between variables. The MAUP was first identified by Gehlke and Biehl (1934), almost 50 years before Openshaw (1983) distinguished two components of the MAUP as the scale effect, the difference in results due to what size of units are being used, and the zonation effect measuring the difference that occurs depending on how the area is divided, even when the same scale (number of zones) is being used. In attempting to make comparisons of internal migration indicators in different countries, the IMAGE (Internal Migration Around the GlobE) project (https://imageproject.com.au/) was challenged with the need to address the MAUP because of the differing spatial systems used for the collection of migration data in different countries.  report the results gained from constructing an inventory and show national differences in the type of data collected on internal migration, the sources used to derive migration data, the ways they measure migration, the time intervals adopted, the periodicity of the collection processes, the scope of the questions, and the spatial frameworks employed.
The IMAGE project built on earlier work (Bell et al., 2002) identifying the lack of research comparing various dimensions of migration in different countries using a basket of indicators. Consequently, an IMAGE data repository was constructed containing origin-destination internal migration flows from different countries around the world, together with associated data on populations at risk and zone boundaries. A methodology was required to facilitate comparison and the IMAGE Studio was therefore developed to aggregate data on all-age migration flows, populations and boundaries for basic spatial units (BSUs) to different scales and zonations as specified by the user, and to compute migration indicators for systems of aggregated spatial regions (ASRs). Details of the structure and operation of the IMAGE Studio software are available in Stillwell et al. (2014). Essentially, there is an Aggregation subsystem within the Studio that requires the user to specify (i) a scale increment with which to aggregate BSUs on an iterative basis and (ii) the number of zone configurations required at each scale. Implementing the aggregation process involves choosing a spatial algorithm that is fed automatically with normalised data from the Data Preparation subsystem of the IMAGE Studio to produce zone centroid coordinates, inter-zonal distances, zone contiguities, interzonal flow matrices and zone populations for each set of zones referred to as aggregated spatial regions (ASRs) which can then be used to compute global migration indicators and their summary statistics at each spatial scale. Two algorithms are available for aggregating initial BSUs to larger ASRs based on the automated Initial Random Aggregation (IRA) procedure first introduced by Openshaw (1977).
The initial IRA algorithm provides a high degree of randomisation to ensure that the resulting aggregations are different during the iterations (Stillwell et al., 2018). The IRA-wave aggregation algorithm is a hybrid version of the former algorithm with strong influences from the mechanics of the Breadth First Search (BFS) algorithm. If N ASRs are required, the first step of the IRA-wave algorithm is to select N BSUs randomly from the initial set of BSUs and assign each one to an empty region (ASR). Using an iterative process until all the BSUs have been allocated to the N ASRs, the algorithm identifies the BSUs contiguous with each ASR, targeting only the BSUs without an assigned ASR and adds them to each ASR respectively.
The relationship between aggregate crude migration intensities (ACMIs) and zone scale was used to estimate ACMIs for total mobility in countries where these data were unavailable (following the equation for Courgeau's k) and to produce league tables (Bell, Charles-Edwards, Ueffing, et al., 2015), demonstrating significant variations between countries with high rates of migration such as New Zealand, USA, Australia and Canada, and countries with low rates such as India, North Korea, Egypt and Venezuela. Whilst Rees et al. (2017) have used the IMAGE Studio to configure geographic zones and implement new measures to compare migration data across large samples of different countries, by examining the relative contributions of migration intensity and effectiveness to crossnational variations, the software was used by Stillwell et al. (2016) to compare distances of internal migration and distance decay parameters across different countries at a national scale. In terms of age group variations at national level, Bernard et al. (2014) have used techniques in association with the IMAGE Studio to investigate internal migration intensity, age profile and spatial impact and how they vary between countries around the world.
In summary, the IMAGE project was the first attempt at a global comparison of indicators of intensity, impact and distance for all-age migration flows, and the IMAGE Studio was the software created to provide data at a series of spatial scales with which to enable comparison in a consistent way. In this paper, the IMAGE Studio has been used with age group data for the whole of the UK to examine variations in aggregate net migration rates, crude migration intensities and migration effectiveness indices using data sets for two consecutive census periods as explained in the following section.

| DATA
The most comprehensive understanding of the migration behaviour of the UK population is attained once every 10 years through the census of population, which asks respondents where they lived 1 year prior to the census date. By comparing respondent locations, the migration flow information can be extracted and used to build a picture of change over time, both in terms of migration intensities (e.g., Champion & Shuttleworth, 2016a) and spatial patterns of residential relocation (e.g., Lomax et al., 2014). Whilst NHS patient reregistration data provides a more frequent time series than the decadal census, the latter provides data on flows within the UK as a whole and reliable estimates of movements within LADs as well as between these spatial units. After merging the 2011 data for the City of London and Westminster, North Cornwall and the Isles of Scilly, Mid Bedfordshire and South Bedfordshire, and North Shropshire and South Shropshire, a set of 404 LADs with consistent boundaries provided the BSUs for subsequent aggregation and analysis.
Since age is a critical internal migration selectivity factor, the data used in this paper has been sourced via the UK Data Service Census Support platform (https://census.ukdataservice.ac.uk/) and includes age-specific migration flows from 2001 Census Special Migration Statistics (SMS) Level 1 Table 1: Age by sex (24 age groups including single year groups for ages 0 and 15, 2-year groups for ages 1 to 19, 5-year groups between 20 and 89 followed by 90+) and 2011 Census SMS Merged LA/LA [Origin and destination of migrants by age (grouped-mid) by sex (including those aged under 1)]-MM01BUK_all-Safeguarded (23 age groups, 5-year groups between 20 and 89 followed by 90+ group). To achieve consistency, the data for these ages have been aggregated to 11 groups (0-4, 5-9, 10-14, 15-19, 20-24, 25-34, 35-44, 45-59, 60-64, 65-74 and 75+) and Census dates (ONS, 2012b), partly due to the changing level of fertility but largely due to the increase in the number of immigrants from abroad that reached unprecedented levels during the 2000s (Bijak et al., 2016). Total internal migration in the UK, that is all changes of usual place of residence within the year prior to the census, also increased from 6.64 to 6.9 million between the two census 1-year periods but the migration rate decreased by nearly 0.35%, from 11.3% in 2000-01 to 10.9% in 2010-11. The all-age statistics shown in Table 1 suggest that around 6 out of 10 internal migrants relocated to usual residences within LADs in both periods whilst the other four moved between LADs and therefore tended to migrate over longer distances. It is apparent that the intra-LAD migration rate declined between the two 1-year periods, a finding in line with the longer-term fall in shorter-distance migration identified by Champion and Shuttleworth (2016b) using data from the ONS Longitudinal Study for England and Wales. The rate of inter-LAD migration, involving movement over longer distances, also experienced a marginal fall. This migration rate has tended to fluctuate over the last 50 years, influenced rather more than intra-LAD migration by changes in national economic conditions (Champion & Shuttleworth, 2016a).
The spatial patterns of inter-LAD migration can be effectively summarised using the net migration (in-migration minus out-migration) for each LAD expressed as a percentage of its population. The to lose migrants at a decreasing rate in both cases and corresponding reductions in rates of net gain in many rural LADs. Table 2 contains a summary of inter-district and intra-district migration flows and rates within the UK for both periods for the four broad age groups, illustrating that the increases in all-age migration occurring at both scales (Table 1) were largely as a result of substantial increases in the number of students and younger workers moving home over longer and shorter distances respectively, although their corresponding migration rates declined at both scales. Lower migration rates were also apparent for the family and retired groups with the latter experiencing the largest percentage variation in intra-district mobility between the periods of all the age groups at both scales. The rates for mature workers, on the other hand, changed the least and actually increased at the within-district scale.
The highest intra-LAD migration rates can be found in southern LADs such as Oxford, Brighton and Hove and Southampton with rates of over 11% respectively in 2010-11 (Figure 3a). Some of the lowest

| VARIATIONS IN AGGREGATE NET MIGRATION AND ITS COMPONENTS
Whilst the explanation of patterns such as these has been the focus of many deterministic studies, including the MIGMOD model mentioned earlier, our focus in this paper is to ascertain how stable are indicators of internal migration at different spatial scales. Across any system of sub-national regions, the overall impact of net migration on the pattern of settlement is most effectively captured by the aggregate net migration rate (ANMR), defined ashalf the sum of the  (Stillwell et al., 2000). Migration intensity is determined by various explanatory factors including household financial decisions and individual life course plans as well as macro-economic or housing market conditions whilst migration effectiveness provides the degree of (a)symmetry or (dis)equilibrium in the network of inter-regional migration flows (Bell & Muhidin, 2009). The scale and zonation effects of both these components on all-age migration in the UK are shown in The anomaly amongst the age groups appears to be those aged 15-19 whose mean MEI is much higher at BSU level but whose value reduces significantly as the number of ASRs gets smaller and the size of the zones gets larger. Moreover, the scale effect for this age group increases from 2000 to 01 to 2010-11. This age group contains the students who migrate to their places of higher or further education and those spatial pattern of net migration is almost the reverse of that of other age groups as suggested in Figure 2. Both graphs in Figure 7 indicate that scale is therefore only an important consideration for 15-19 year olds; the impact of migration measured by the MEI for this highly mobile group reduces by more than half when the number of ASRs falls from 400 to 50 and the scale effect is greater in 2010-11.
The graphs in Figures 6 and 7 have illustrated the scale effect but have excluded any visualisation of the zonation effect. These graphs become too muddled when the range values are included so, in order to compare between age groups effectively, a measure of total zonation effect has been computed for each age group as the summation of the maximum value minus the minimum value (the range) for each indicator at each scale divided by the mean standardises for variation in the indicator between age groups. The results of the total zonation effects are shown in Table 3 (Champion et al., 2017).
It is evident that patterns of all-age net migration continue to reflect the relatively longstanding process of counterurbanisation but the intensity of urban losses and rural gains has diminished between the two census periods, predominantly due to changes in family mobility. A significant proportion of rural LADs experienced a switch from net gain to net loss in the broad family age group, whereas the changes for mature workers and the more elderly involved reducing net gains in rural areas and lower rates of net loss in urban areas.
However, in the case of students and younger workers, net migration losses intensified across many LADs in England and Northern Ireland and gains increased in towns and cities with large higher education institutions, reflecting the expansion of this sector of education during the early 2000s in particular.
It is the student and young worker age group ( increases. The IMAGE studio might prove useful in providing an optimum set of zones for analysis of certain indices.
One of our priorities was to undertake a 'national' analysis of internal migration within the whole of the UK and consequently the census provided the most appropriate source of data although we are aware that using two single-year time periods 10 years apart has its limitations, particularly since the second period came fairly soon after the global recession when mobility levels might have been lower than average. Further work based on annual data on patient registrations might usefully be undertaken to provide corroborating evidence of our results though this would require substantial effort to acquire and estimate flows for Scotland and Northern Ireland and integrate them with data for England and Wales. As well as the limitation set by the time periods, it is also necessary to acknowledge that the age groups for which data are available and the broad age groups used for summarising patterns are not altogether appropriate for representing the migration behaviour of individuals or families influenced by the same explanatory factors.
The IMAGE Studio has been used previously to assist in the comparison of internal migration in different countries around the world. This is the first paper that reports results of analysing migration within one country disaggregated by age. Our experience of using the software has generally been positive though, for those seeking to undertake similar work, perhaps for a different country, it is worth giving prior consideration to the system of BSUs and to the variables used for disaggregation, not least because of the amount of time taken to prepare and process the data. Age is a good variable to use Finally, our analysis in this paper has been confined to an examination of the scale and zonation effects on just the ANMR, CMI and the AEI using inter-LAD age group data but further research using other indicators (such as distance or zone connectivity) and migration flows disaggregated by other variables (such as occupation, gender or ethnicity) might prove useful. The use of data between wards rather than LADs is another possible avenue of investigation but transition to this scale of BSUs for the UK as a whole would involve using huge and very sparsely populated matrices because of the distance decay effect associated with migration; it might be more appropriate to conduct analysis of one particular region, such as Greater London (Chatagnier, 2020). Moreover, the availability of migration flow matrices from the 2021 Census will provide the opportunity in due course to extend the comparison reported in the paper across another decade although caution will be required because the corona virus pandemic is likely to have had a significant influence of internal migration behaviour in the UK in 2020-21.