1. Notice

Figures 10-12 have been updated with new legend.

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2. Disclaimer

This research does not provide official statistics on international migration. Rather, it is published to share experimental innovative methodological research on estimating international migration and, going forward, to be used in the development of Admin-Based Migration Estimates (ABMEs). The modelled estimates for March to June 2020 reported in this article have been incorporated into the early indications of UK population size and age structure, 2020.

It is important that the information and research presented are read alongside the model outputs to aid interpretation and avoid misunderstanding. These analyses and outputs must not be reproduced without this disclaimer.

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3. Main points

  • Travel and migration behaviours have changed in response to travel, economic and other social policies introduced by governments to address the coronavirus (COVID-19) pandemic.

  • Our definitions of "usual resident" and "international migrant" suggest a level of individual control over the decision to migrate and predictability in those decisions that may not be realistic during the pandemic.

  • We use State Space Models to estimate international migration flows for March 2020 and Quarter 2 (April to June) 2020 in the absence of the International Passenger Survey.

  • We emphasise uncertainty since it is not possible to accurately quantify international migration in this unprecedented period.

  • Our provisional modelled estimates suggest total immigration was negligible over this period, with more British nationals returning in March 2020.

  • Our provisional modelled estimates for emigration suggest more EU nationals left than Non-EU and British nationals.

  • Provisional modelled estimates suggest total net migration was negative over this period, with more people leaving than arriving.

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4. Introduction

The coronavirus (COVID-19) pandemic has led us on an innovative journey to model international migration in the absence of the International Passenger Survey (IPS)¹. ONS Methodology is developing methods for estimating international migration for March 2020, Quarter 2 (April to June) 2020 and beyond to support our ambition for improved migration and population estimates. We are making optimal use of available data sources and methods to estimate how international migration was affected by the coronavirus pandemic. The pandemic underlines that new and ambitious methods and alternative data sources are needed when our business-as-usual data collection and methods are disrupted.

Traditionally, data from the IPS are the main source for estimating international migration to and from the UK. The data primarily give estimates of immigration, emigration and net migration by citizenship and reason for migration. These estimates feed into the annual Mid-Year Population estimates for England and Wales that are published in June each year for the previous mid-year point.

In 2019, ONS Methodology began exploring time series modelling as an approach to estimate international migration using administrative outcomes-based data. Time series modelling was selected because of the strong seasonal trends that are evident in international migration over time. This research was accelerated during 2020 with the suspension of the IPS on 16 March 2020.

In this paper we describe our use of multivariate State Space Models² to estimate international migration. We are developing these with ONS Methodology time series experts and with modelling and migration experts at the Universities of Southampton and Warwick. We are indebted to colleagues at the Home Office (HO) for making data available to us and for their expertise and input. We use expert judgement on model assumptions to produce a range of provisional estimates for the coronavirus period. Uncertainty intervals around these estimates emphasise that it is not possible to accurately quantify international migration in this unprecedented period with a single point estimate. The estimates for this period are provisional as our models develop and will be subject to retrospective confirmation and adjustment as data become available or mature.

The research detailed in this paper is carried out in conjunction with an ongoing programme of work to transform population and migration statistics. This work, and the transformation of population and migration statistics, has been accelerated in response to the impact of the coronavirus. We have created an overview of our transformation work.

While the ONS has accelerated the move to Admin-Based Migration Estimates (ABMEs), the data used in this work only cover the period up until the end of March 2020 and do not cover the period which saw the main impact of the pandemic. A report on the first iteration of ABMEs has been published, using data from Department for Work and Pensions (DWP) Registration and Population Interaction Database (RAPID) and Home Office border crossing data. The international migration modelling work covered in this article will, as the ABME work progresses, form an important part of our transformed population and migration statistics system.

The figures reported in this article have been incorporated into the early indications of UK population size and age structure, 2020.

Estimates of visits to the UK by overseas residents are usually based on the IPS. Administrative data sources and modelling are used to provide estimates of numbers of international visitors and their characteristics for Quarter 2 (April to June 2020) while the IPS was stood down during the pandemic. International migration is a subset of travel to the UK. We compare our provisional estimates of international migration with estimates for travel and tourism for Quarter 2 2020 in Section 9 to understand coherence across the two sources of estimates.

Notes for: Introduction

  1. The International Passenger Survey (IPS), which underpins our existing UK international migration statistics, was suspended because of the impact of the coronavirus pandemic on 16 March 2020. While the IPS resumed operations in January 2021, the decision was taken and announced in the August 2020 Migration Statistics Quarterly Report (MSQR) that IPS data would no longer be used to calculate international migration.
  2. State Space Models are used to model change over time, including population dynamics.
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5. Challenge caused by the coronavirus (COVID-19) pandemic

The coronavirus pandemic presents a significant challenge to the UK and to the statistics we rely on. Vital information is needed more than ever to respond to the impact of this pandemic on the economy and society. Robust and timely population and migration statistics are core to this response as they underpin a wide variety of other statistics that support decisions and inform public debate. The pandemic has made it imperative for us to innovate with data and modelling methods to produce timely measures of how international migration has been affected.

It is not possible to reliably estimate international migration for Quarter 2 (April to June) 2020 from past trends alone, using existing survey or administrative data, or a combination of both. This is because travel and migration behaviours changed in response to travel, economic and other social policies introduced by governments to address the coronavirus pandemic. The current period is unstable and unpredictable, with the boundary between travel and migration uncertain. This sentiment was echoed by other National Statistical Institutes (NSIs) at the 27 to 29 October 2020 United Nations Economic Commission for Europe workshop on international migration. Moreover, our definitions of "usual resident" and "international migrant" imply a level of individual control over the decision to migrate and predictability in those decisions that may not be realistic during the pandemic.

Estimating international migration using non-survey data sources is complex and challenging, even before the coronavirus pandemic. Definitionally, 12 months or more need to pass before we can assume if someone who has travelled to or from the UK at the start of that period is a migrant according to the long-established UN international definition¹.

Although the International Passenger Survey (IPS) was intentions-based and produced timely estimates, adjustments were needed to reflect uncertain or changed intentions. We have long acknowledged that the IPS has been stretched beyond its original purpose and that we need to consider all available sources to understand international migration.

We are therefore accelerating use of administrative data sources to fill the evidence gap. However, these data sources are not designed to measure international migration flows; often there are coverage issues, they are less timely and have inherent time lags due to (a) when an individual interacts with a service for example and, (b) the definitional constraints for international migration. We are repurposing and using these data as a proxy for international migration.

Our exploratory analysis of available data sources (Section 6) highlights how traveller and migrant behaviours changed in the context of the coronavirus pandemic. Added to this is the impact of the EU exit and the new immigration system introduced in January 2021. It is hard to disentangle the impacts of the coronavirus and the EU exit on migration and it may take a few years for migration to return to "normal" levels or to new, presumably seasonal, patterns.

Notes for: Challenge caused by the coronavirus (COVID-19) pandemic

  1. The UN recommended definition of a long-term international migrant: "A person who moves to a country other than that of his or her usual residence for a period of at least a year (12 months), so that the country of destination effectively becomes his or her new country of usual residence".
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6. Data sources

We use International Passenger Survey (IPS) data from 2010 to February 2020 as a measure of seasonality and trends over the time period. Migration trends are often irregular, and impacted by a range of other one-off events, such as the 2008 economic recession, the UK's exit from the EU, among others. IPS data for March 2020 were modelled as only partial data were available for that month¹. These data were used to produce the published estimates of international migration for the year ending March 2020². In our modelling we have estimated international migration for March 2020, rather than using International Passenger Survey (IPS) estimates.

We explore the best available data sources such as:

  • Home Office (HO) border crossing data, Visa and Advanced Passenger Information data

  • Department for Work and Pensions (DWP) National Insurance Number allocations data

  • Civil Aviation Authority (CAA), Eurotunnel and Ferries data

  • Personal Demographic Service (PDS) data from the NHS

Further information on these sources are listed in Appendix 3.

Other sources were explored but were not considered as they were less timely. These included Higher Education Statistics Agency (HESA) data, and English and Welsh School Census data. Annual Population Survey (APS) data were also considered but not used as there would be circularity introduced into the model since APS data are weighted to population estimates that include an international migration component.

We investigated Her Majesty's Revenue and Customs (HMRC) Real Time Information (RTI) data but concluded that while these data have potential, they are only representative of movements into and out of the labour market, not migration. Additionally, we believe that the link between where people live and work during the pandemic has changed and this may not be reflected in RTI data. For example, some overseas nationals who are furloughed may choose to return to their home country to be with family.

We continue to explore other data sources as they become available and existing sources as they are updated. In the coming year, we anticipate data supplies that will shed light on migration behaviours during 2020, for example, DWP RAPID data³. The 2021 Census will provide the most robust and comprehensive picture of the England and Wales population possible and an opportunity to validate our estimates.

Notes for: Data sources

  1. The International Passenger Survey (IPS), which underpins our existing UK international migration statistics, was suspended because of the impact of the coronavirus pandemic on 16 March 2020. While the IPS resumed operations in January 2021, the decision was taken and announced in the August 2020 Migration Statistics Quarterly Report (MSQR) that IPS data would no longer be used to calculate international migration

  2. The latest available IPS data cover the vast majority of the year ending March 2020, which have been published in the August 2020 Migration Statistics Quarterly Report (MSQR).

  3. DWP Registration and Population Interaction Database (RAPID). RAPID provides a single coherent view of citizens' interactions across the breadth of systems in both DWP and HM Revenue and Customs (HMRC) including benefits, employment, self-employment, pensions and in-work benefit.

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7. Exploratory data analysis

We present our exploratory analysis of available data sources to shed light on the impact of the coronavirus (COVID-19) pandemic on travel and migration patterns and how behaviours may have changed. This analysis informs the assumptions underpinning our models (Section 7).

Our analysis focused on Quarter 2 (Apr to June) 2020 and was based on data available to us at that time. Our experimental analysis of Home Office border crossing data are based on visas granted and associated travel events as at October 2020. This analysis does not, therefore, give a complete picture of the trend in visas granted and associated arrivals and departures for the whole of 2020. We plan to model Quarter 3 (July to Sept) 2020 and Quarter 4 (Oct to Dec) 2020 as a next iteration of our model. The Quarter 3 2020 and Quarter 4 2020 iteration will include assumptions for Quarter 3 2020 and Quarter 4 2020 based on visas granted and visas expiring with associated travel events post October 2020.

Relationship between travel and migration

We compare International Passenger Survey (IPS) migration estimates with passenger flows from air, train and ferry data combined. International migration is a subset of all passenger flows. We found a relationship between the two for arrivals and departures.

For both in-flows and out-flows we observe seasonal outliers, primarily for the months of September for in-flows and July, August and September for out-flows. Students typically depart long-term after completing their studies and graduation over the summer and early autumn months.

We also observe an outlier for January 2020 in-flows, where a higher number of contacts were made with non-EU students in the IPS. Published IPS immigration estimates were adjusted downwards as this was believed to be an anomaly at the time. However, there is further evidence of an increase in study visas granted at the end of 2019, which may have led to higher arrivals in January (Section 6: visas granted).

We hypothesise that some study migrations may have been brought forward as the pandemic took hold in China. We have, for the purposes of modelling immigration, taken the decision to use the unadjusted IPS. This decision was endorsed by migration experts (Section 7).

Travel patterns during 2020

We compare air passenger arrival and departures data for January to December 2020 to the previous year. The focus for our exploratory analysis and modelling is Quarter 2 2020. Although these data are for all travel, not just migration, they provide additional insight into changing travel behaviours in response to UK government travel restrictions as well as other economic and other social interventions such as the UK lockdown on 23 March 2020.

Air passenger arrivals and departures

Figures 1 and 2 present Home Office Advanced Passenger (API) data for air arrivals and departures respectively, broken down by British, and non-British nationality groups. While our analysis and modelling focus on what may have happened in Quarter 2 2020, we have provided data up to December 2020. The data presented are a count of all arrivals or departures recorded in the API data rather than a true count of the number of passengers.

We saw a clear decrease in air passenger arrivals and departures across all nationalities from late March 2020 as strict lockdown measures and travel restrictions are introduced. Air passenger arrivals showed an increase during January 2020 for non-British nationals compared to 2019. Air passenger departures for non-British nationals increased during March and declined steadily during late March and April. The decline was steeper for UK nationals.

During Quarter 2 2020, there was minimal travel as this was restricted to essential travel only. We hypothesise that a higher proportion of travel during this quarter can be accounted for by motivated immigrants who travelled to the UK to take up essential jobs or join family in the UK. For emigrants, this will have been those who travelled from the UK to return home as their visas expired, or were no longer working, or returned to their countries of origin where they had more social and family connections. The largest number of arrivals may be accounted for by British nationals returning home.

As travel corridors opened and health measures were introduced at UK borders during June 2020, we saw travel picking up, but not at the levels seen in 2019. It is likely that most of this travel was a combination of holiday and essential travel. We cannot assume that migration accounted for a large proportion of travel during this time.

We can also see the effect of further England lockdown measures from 5 November 2020 with further falls in air passenger arrivals. Further analysis is provided by the Home Office in their publication Statistics relating to passenger arrivals since the COVID-19 outbreak, February 2021.

Civil Aviation Authority, Eurotunnel and ferry passenger flows

Travel by all routes declined steeply from March 2020. Air travel, as a proportion of all travel, declined sharply in Quarter 2 2020. There was a corresponding proportional increase in travel via ferries and Eurotunnel. During this period essential travel only was permitted.

We therefore hypothesise that motivated EU migrants would have used these transport routes to travel to and from the UK. Non-EU migrants’ travel by air would have been more restricted and they may have deferred travel until travel corridors opened. We acknowledge that the flows observed between April and June could be travel for work. Figures 5 and 6 show passenger in- and out-flows by mode as a proportion of all passenger flows.

Visas granted to non-EU visa nationals and associated arrivals

Figure 5 shows the marked decrease in work, study and family visas applied for and granted during Quarter 2 2020. Aside from the coronavirus pandemic impacting on migration plans, visa processing centres also had to be closed in March 2020. Prior to the official lockdown in the UK, the number of sponsored study (Tier 4) visas applied for and granted increased during Quarter 4 (Oct to Dec) 2019 and Quarter 1 (Jan to Mar) 2020 by 43.5% and 84.2% respectively (increases of 13,538 and 8,370 visas granted respectively) compared to the previous year.

We hypothesise that this change may be the result of migration plans being brought forward as the pandemic took hold around the world. Similarly, the International Passenger Survey (IPS) recorded an increase in immigration for study during Quarter 4 2019 and Quarter 1 2020 compared with previous years. Immigration for study was 175,0000 in year-ending (YE) December 2019 compared with 156,000 in YE December 2018, and 196,000 in YE March 2020 compared with 159,000 in YE March 2019. The change between YE March 2020 and YE March 2019 was statistically significant¹².

The number of visas granted for sponsored study began to recover in Quarter 3 (Jul to Sept) 2020. This recovery continued into Quarter 4 (Oct to Dec) 2020, with every month in this period having more grants than in 2019. October had the largest increase, with the number of visas granted being 420% or 31,274 higher than in 2019, reaching a total of 38,722 visas granted. The largest monthly difference in sponsored study grants coincides with the new student routes introduced on 5 October 2020.

In Quarter 4 2020, the overall number of work visa applications was 21% higher than the same period in 2019, largely due to the increase in applications for European Communities Association Agreement (ECAA) Businessperson visas. At the same time, the number of work visas granted was 17% lower. Numbers of visas granted began to recover at the end of Quarter 2 2020 and continued to do so until the end of Quarter 3 2020.

An increase in the number of family visas granted was also recorded in Quarter 4 2019 compared with Quarter 4 (Oct to Dec) 2018 (15,796 compared with 12,196 - an increase of 29.5%). This was less marked in Quarter 1 2020. The IPS recorded a statistically significant change in immigration for family reasons (accompany or join) in year ending (YE) March 2020 compared with the same period in 2019 (59,000 compared with 32,000) for non-EU nationals. There was a similar increase in YE December 2019 compared with the same period in 2018 (54,000 compared with 29,000), although this was not a statistically significant change. The number of family visas and permits granted fell by 13% in Quarter 3 2020, but in Quarter 4 2020 had increased by 15%, or 7,210 grants. Further data on visas granted is published by the Home Office.

Visa start date and associated arrivals

We use Home Office border crossing data to explore whether planned migrations for non-EU nationals may have been brought forward or postponed because of the pandemic. We look at the length of time between visa grant and the first (and last arrival) for work, study, and family routes.

Our analysis includes data up to October 2020, and we are in the process of updating these analyses to reflect visas granted and associated arrivals after this time point. Our analysis does not consider the recovery (Figure 5) in the number of visas granted, particularly for sponsored study during Quarter 3 2020 and Quarter 4 2020.

Our initial analysis, based on Home Office border crossing data up to October 2020 suggests:

  • before the coronavirus pandemic, visa holders typically travel within two months of their visa start date

  • from March 2020 onwards this pattern is disrupted as fewer arrivals are recorded across all major visa types because of travel restrictions

  • at the time of our analysis, these levels are not back to pre-coronavirus levels, suggesting that visa holders are delaying their arrival or deciding not to come

Figures 6 to 8 show plots of arrivals associated with visas granted for work, study and family respectively. The horizontal axis is date of arrival associated with a visa. The vertical axis is visa start date from Quarter 1 (Jan to Mar) 2018 to Quarter 4 2020. Each square represents a month in that quarter. The dark blue indicates that over 90% of granted visas have an associated arrival. The lightest shading indicates that less than 10% of granted visas have an associated arrival.

The lighter-shaded cells in the diagrams in Figures 6 to 8 indicate that visa holders began to defer their arrivals during the coronavirus pandemic, in a clear shift of migration behaviour when compared to previous years. These deferrals (or possibly cancellations) began to be seen in November 2019 for students and family visa-holders, and in January 2020 for holders of employment visas.

These charts are based on experimental analysis of Home Office border crossing data. We plan to update this analysis for visa arrivals after October 2020; therefore, percentages may change in further iterations of this chart. The charts cover work, study and family visas or extensions of leave granted to non-EU visa nationals, excluding categories granting permission to stay permanently (settlement) or those with right of abode who are family members of EEA nationals exercising Treaty rights.

We provide data from January 2018 in the data download. It should be noted that travel history data from Home Office border crossing data are incomplete prior to the introduction of the Exit Checks programme in April 2015. Further information on Home Office border crossing data is published annually by the Home Office.

Departures of non-EU visa nationals

Departures associated with visas due to expire before June 2021

Our analysis of Home Office border crossing data suggests that there was an increase in departures for all visa routes during March 2020 for visas due to expire before June 2021. This is primarily driven by departures for non-EU nationals on work, study and family routes. The number of departures fell during April and increased from July onwards. Some of these departures may be temporary and those departing may seek to return to the UK. Figure 9 shows a clear spike in non-EU departures in March 2020, followed by a sharp fall in April, reflecting the late March lockdown and travel restrictions. These departures were not captured by the IPS, which was stood down on March 16 2020.

Departure behaviours of non-EU nationals by visa route

We use Home Office border crossing data to understand whether planned departures for non-EU nationals are brought forward or postponed because of the coronavirus pandemic. We look at the length of time between visa expiry date and the last known departure (with no subsequent arrival) associated with work, study, and family visas. This analysis includes data up to October 2020, and we are in the process of updating these analyses to reflect visas expiring and associated departures after this time point.

Our initial analysis, based on Home Office border crossing data up to October 2020 suggests:

  • before the coronavirus pandemic, most visa holders leave the country for the last time at least one month before their visa expires

  • from March 2020 onwards this pattern is disrupted as departures are brought forward for all major visa types during this period due to travel restrictions

  • this may be a mixture of temporary behaviour (for example, because of family reformation in country of origin) with a desire to subsequently return for the remainder of the visa period, or where departures are brought forward with no intention to return

  • time and further data updates will reveal whether these were permanent departures

Figures 10 to 12 show plots of departures associated with visas granted for work, study and family respectively. The horizontal axis is date of last departure (with no subsequent arrival) associated with that visa. The vertical axis is date of visa expiry from Quarter 1 2018 to Quarter 4 2020. Each square represents a month in that quarter. The dark blue indicates that over 90% non-EU visa nationals remain in the UK on a valid visa. The lightest shading indicates that less than 10% remain on a valid visa.

From late 2019, in a break with the historic pattern, we begin to see early departures (indicated by the lightest shading), appearing to the left of the diagonal. These are departures being brought forward ahead of visa expiry.

Figures 10 to 12 are based on experimental analysis of Home Office border crossing data. We plan to update this analysis for visa departures after October 2020; therefore, percentages may change in further iterations of this chart. We look at departures occurring within a given month (horizontal axis) for visas due to expire within the following nine months, for example, for March 2020 we look at visas due to expire in March to November 2020.

We chose nine months because we assume a departure within nine months of an expiry date is more likely to be a final departure. If there is more unexpired time on a visa, it is more likely there will be a subsequent return.

The charts cover work, study and family visas granted to non-EU visa nationals, excluding categories granting permission to stay permanently (settlement), extensions of leave granted or those switching to different visa route, or those with right of abode who are family members of EEA nationals exercising Treaty rights. Last known departure (with no subsequent arrival) before October 2020 is shown on the horizontal axis.

We provide data from January 2018 in the data download. Travel history data from Home Office border crossing data are incomplete prior to the introduction of the Exit Checks programme in April 2015. Further information on Home Office border crossing data is published annually by the Home Office.

GP Patient registrations and Patient Demographic Service embarkations

We examine Patient Demographic Service data to shed light on whether there have been fewer new registrations from overseas (Flag 4) and more embarkations (de-registrations) during the coronavirus pandemic³.

Flag 4s and embarkations are a useful proxy indicator of whether someone has recently arrived from abroad and embarkations are a useful proxy indicator that someone has left the country. We recognise that they are incomplete as there is no obligation to register or deregister with a GP. However, deviation from historic trends can be used as a signal of changed migrant behaviour. They do not tell us whether someone is a long-term immigrant or emigrant. Our analysis shows:

  • an increase in new registrations (Flag 4) from overseas during January and February 2020 compared with 2019

  • a sharp decrease in new registrations between April and May 2020, which may be because of delays in registration systems or an indicator of fewer overseas nationals travelling because of the coronavirus travel restrictions

  • an increase in embarkations from January to June compared with 2019, that is more pronounced in Quarter 1 (Jan to Mar) 2020 and Quarter 2 (Apr to June) 2020

National insurance allocations to adult overseas nationals

We examine national insurance (NINo) allocations to adult overseas nationals for Quarter 1 (Jan to Mar) 2019 to Quarter 4 (Oct to Dec) 2020 to shed light on whether there was a reduction in the number of registrations since March 2020.

NINo registrations are a useful proxy indicator of whether someone has arrived from abroad but there are known lags in registration following arrival. Alone, they cannot tell us whether someone is a long-term immigrant or not. Aside from inherent lags in registration and the coronavirus pandemic impacting on migration plans, the pandemic also disrupted NINo services over this period. Our analysis suggests:

  • the number of new NINo registrations decreased rapidly during Quarter 2 (April to June) 2020 for both EU and non-EU nationals

  • the decline in NINo allocations for EU nationals began in Quarter 2 (April to June) 2019; the recovery in NINo allocations seen for non-EU in Quarter 4 (Oct to Dec) 2020 is not mirrored for EU nationals

Notes for: Exploratory data analysis

  1. The 95% confidence interval for the difference between the two estimates is used to ascertain the statistical significance of the change. Here, a change is considered statistically significant if the 95% confidence interval for the difference doesn't include zero.
  2. Processing and quality assurance of the International Passenger Survey (IPS) data for the first quarter (January to March) of 2020 identified a possible issue in the data, namely an unexpected large rise in the number of non-EU student contacts. Further detail is available in the August 2020 Migration Statistics Quarterly Report
  3. Flag 4 registrations are new registrations at GP practices where someone has lived overseas for 3 months or more. De-registrations are based on 'Embarkation' reason for removal.
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8. Multivariate State Space modelling

We use multivariate State Space Models (SSMs) to estimate international migration flows. Time series approaches are a good tool for modelling time-varying processes and their different features, such as trends, seasonality, and random components. SSMs offer the added flexibility of the time series approach by explicitly modelling the latent (unobserved) process and its (observed) measurements. These models are fitted to the historical International Passenger Survey (IPS), Home Office border crossing data, and air, train and ferry data.

Estimates are based on an extrapolation of the trend and seasonal components from the IPS, together with the Home Office border crossing and travel data for the period March to June 2020. Estimates are generated from the models for British, EU and non-EU nationals' immigration and emigration and are summed to estimate the corresponding totals. Net migration is calculated by taking the difference between immigration and emigration.

We are developing these models with time series experts in ONS Methodology and with modelling and migration experts at the Universities of Southampton and Warwick. We use a Delphi approach to gather expert judgement on model assumptions and early modelled estimates based on different scenarios. From this process we produce a range of provisional immigration, emigration and net migration estimates with uncertainty measures for Quarter 2 (Apr to June) 2020. This process was guided by expert input. Modelled estimates are presented in Section 8.

In Section 8 we provide uncertainty intervals around the migration estimates. These aim to reflect uncertainty in the predicted values from March onwards, where we do not have observations from the IPS. Please refer to Appendix 1 for further information on estimating uncertainty.

The uncertainty intervals for net migration are calculated using the sum of the prediction error variances derived from the immigration and emigration uncertainty intervals. They should be treated as indicative; in future iterations we will develop a more precise measure which will not necessarily be symmetrical around the estimated net migration values.

Appendix 1 gives further detail on the mathematical specification of the multivariate SSMs and model diagnostics.

The Delphi-approach

The modelling uses several assumptions, regarding:

1) the interpretation of International Passenger Survey (IPS) estimates for early 2020

2) whether the changes in migration behaviours observed for non-EU migrants in Home Office border crossing data also apply to EU and British nationals who are migrating

3) whether EU migrants had more opportunity to come to the UK or return home than non-EU migrants, given the continued operation of cross-channel travel services when air travel was virtually halted from April 2020

We invited migration experts and stakeholders to give us their view of the assumptions and invited them to provide further evidence that we should consider.

A meeting of experts on 23 March 2021 considered the assumptions listed in this section. The discussion was guided by a questionnaire and empirical evidence on each assumption.

Assumptions for International Passenger Survey (IPS) data for Quarter 4 (Oct to Dec) 2019

We are content that the IPS migration estimates for Quarter 4 2019 are broadly in line with other reporting on international migration for that period.

Assumptions for IPS immigration estimates for January 2020

The increased immigration of students from Southern Asia and China in January 2020 reported by the International Passenger Survey was real.

Assumptions for IPS estimates for March 2020

We should use modelled estimates for March 2020, not IPS. IPS results from 1-15 March did not capture changed migration patterns after March 16 2020.

Assumptions for Non-EU migration change in Quarter 2 (Apr to June) 2020

Flows for non-EU visa nationals in Home Office border crossing data are a true representation of changed patterns of arrivals and departures for this group in Quarter 2 2020. Time will reveal if these departures are long-term migrations. For now, we can use deferred arrivals, and departures up to nine months ahead of a visa end date, as an indicator of behavioural change.

Assumptions for EU migration change in Quarter 2 2020

We can use non-EU border crossing evidence of changed migration behaviour to model EU migration in Quarter 2 2020. We can modify this to reflect increased travel options for EU migrants.

Assumptions for GB migration change in Quarter 2 2020

We can use non-EU border crossing evidence of changed emigration behaviour to model British immigration in Quarter 2 2020.

We can use non-EU border crossing evidence of changed immigration behaviour to model British emigration in Quarter 2 2020.

Responses and models

Responses to the questionnaire and advice on further sources or avenues for research were received by ONS on 24 March 2021. The responses are summarised in Appendix 2. There was consensus that IPS estimates for Quarter 4 (Oct to Dec) 2019 were of consistent quality with previously released IPS estimates. There was some disagreement about whether the January spike in student arrivals was real. Since it does not affect the modelling (we set it as missing for modelling the time series) there is no further action. The advice from experts for assumptions 3 to 6 guided us towards two potential models for immigration and four potential models for emigration.

For both immigration and emigration for non-EU migrants the experts endorsed our modelled approach, from March onwards. For EU migrants the experts agreed that we should model both immigration and emigration from March 2020 but were divided on whether we should apply the increased travel options adjustment from April. For UK migrants there was support for modelling immigration and emigration using non-EU migration trends (in reverse, so non-EU emigrant patterns apply to UK arrivals and vice-versa) from March 2019, but there was also a suggestion that the IPS could be used for March 2020 instead of the model estimates.

We returned to the experts a report that included their collated comments and advice, together with outputs from the following six models:

Immigration models

  1. Model from March 2020 without travel adjustment (EU)

  2. Model from March with travel adjustment from April (EU)

Emigration models

  1. Model from March without travel adjustment (EU) and border crossing data on arrivals (Great Britain) from March

  2. Model from March without travel adjustment (EU) and IPS for March and border crossing data on arrivals in Quarter 2 (Great Britain)

  3. Model from March with travel adjustment from April (EU) and border crossing data on arrivals (Great Britain) from March

  4. Model from March with travel adjustment from April (EU) and IPS for March and border crossing data on arrivals in Quarter 2 (Great Britain)

The experts were invited to amend or confirm their prior advice. Their final feedback, received on 2 April 2020, is summarised in Appendix 2. In the second round we found a decisive majority of experts favoured the increased travel options adjustment for EU emigration (81%). While the experts were split on whether to apply the increased travel options adjustment for EU immigration, the numerical difference involved was marginal (net difference of 200 immigrants across March to June 2020) and, given the degree of uncertainty in the models, for consistency and coherence we opted to apply the same model to immigration and emigration.

Likewise, while opinion remained divided on whether to model March emigration for British nationals or use the IPS, for consistency and coherence with immigration of British nationals we chose to use the model. The difference between IPS and modelled British emigrants in March was 1,300 (IPS 5,000-Model 3,700).

Assumptions underpinning our models

Our assumptions are based on the evidence presented in Section 6 and expert input outlined in the section on our Delphi approach. A summary of the implemented assumptions for the immigration and emigration models following expert advice is provided.

Immigration

  • Non-EU: Model from March 2020

  • EU: Model from March 2020 but apply travel options adjustment from April 2020

  • Great Britain: Model from March 2020 using non-EU Home Office border crossing data on departures

Emigration

  • Non-EU: Model from March 2020

  • EU: Model from March 2020 but apply travel options adjustment from April 2020

  • Great Britain: Model from March 2020 using non-EU Home Office border crossing data on arrivals

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9. Modelled estimates for UK immigration, emigration and net migration

We present our modelled estimates, by month, based on the assumptions outlined in the section on assumptions underpinning our models for Quarter 2 (Apr to June) 2020 with a monthly International Passenger Survey (IPS) time series from January 2018 to February 2020. We estimate March 2020 following feedback from experts rather than use the March IPS estimates in the monthly IPS time series.

We also include the January IPS immigration estimate as an outlier in our models. The monthly estimates of international migration flows have been derived solely for the purpose of this research and should not be treated as official statistics or used in any other context.

We present modelled totals for immigration, emigration and net migration estimates. Further modelled estimates by nationality grouping (non-EU, EU and British) are provided in the data download. We also provide 95% uncertainty intervals to reflect that it is not possible to accurately quantify international migration in this period with a single point estimate. These uncertainty intervals are interpreted in the following way. If the assumptions we have made are correct, we would expect these intervals on average to capture true migration flows 95% of the time.

UK immigration

We estimate that total immigration was 21,200 in March 2020 (with an uncertainty range from 17,800 to 25,400). For the months between April and June 2020 we suggest total immigration ranged from 3,000 in May (with uncertainty from 2,400 to 3,700) to 4,700 in June (with uncertainty from 3,700 to 6,000).

Further modelled estimates for immigration, emigration and net for non-EU, EU and British nationals are available as a data download.

Our modelled estimates suggest:

  • non-EU immigration ranged from 450 in May 2020 (with uncertainty from 400 to 600) to 800 in June 2020 (with uncertainty from 600 to 1,000)

  • EU immigration ranged from 1,400 in May 2020 (with uncertainty from 900 to 2,000) to 2,100 in June 2020 (with uncertainty from 1,400 to 3,100)

  • immigration for British nationals was 10,600 in March 2020 (with uncertainty from 8,000 to 14,000) but fell to 1,100 in May 2020 (with uncertainty from 800 to 1,600)

Figure 16: Total UK immigration decreased from March 2020

Total immigration, by month, UK, January 2018 to June 2020

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Notes:

  1. Modelled estimates are based on the UN definition of an international migrant. That is a person who moves to a country other than that of his or her usual residence for a period of at least a year (12 months), so that the country of destination effectively becomes his or her new country of usual residence.

  2. Refugees and asylum seekers are excluded from modelling.

  3. The monthly estimates of international migration flows have been derived solely for the purpose of this research and should not be treated as official statistics or used in any other context.

UK emigration

We estimate that total emigration was 37,900 in March 2020 (with uncertainty from 30,400 to 47,600). For the months between April and June 2020 we suggest total emigration ranged from 15,700 in April (with uncertainty from 11,800 to 20,900) to 26,400 in June (with uncertainty from 19,600 to 35,800).

Our modelled estimates suggest:

  • non-EU emigration was 10,500 in March 2020 (with uncertainty from 8,500 to 12,900) and decreased to 1,700 in May 2020 (with uncertainty from 1,400 to 2,200)

  • EU emigration was 23,700 in March 2020 (with uncertainty from 16,400 to 34,200) but decreased to 13,400 in April 2020 (with uncertainty from 9,000 to 19,900)

  • emigration for British nationals was 3,700 in March 2020 (with uncertainty from 3,100 to 4,500) but fell to less than 500 in each month from April to June 2020

Figure 17: Total emigration increased in March 2020, driven by EU departures

Total emigration, by month, UK, January 2018 to June 2020

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Notes:

  1. Modelled estimates are based on the UN definition of an international migrant. That is a person who moves to a country other than that of his or her usual residence for a period of at least a year (12 months), so that the country of destination effectively becomes his or her new country of usual residence.
  2. Refugees and asylum seekers are excluded from modelling.
  3. The monthly estimates of international migration flows have been derived solely for the purpose of this research and should not be treated as official statistics or used in any other context.

UK net migration

We estimate that total net migration for March 2020 was negative 16,700 (with uncertainty from negative 26,600 to negative 6,700). For the months between April and June 2020, the modelled estimates suggest net migration ranged from negative 21,700 in June (with uncertainty from negative 31,900 to negative 11,500) to negative 12,000 in April (with uncertainty from negative 17,500 to negative 6,400). This reflects more people leaving the UK than arriving during the onset of the pandemic.

Our modelled estimates suggest:

  • non-EU net migration was negative 3,800 (with uncertainty from negative 6,500 to negative 1,100) and remained negative each month over the April to June 2020 period

  • EU net migration was negative 19,600 in March 2020 (with uncertainty from negative 28,700 to negative 10,600) and remained negative each month over the April to June 2020 period

  • net migration for British nationals was 6,800 in March 2020 (with uncertainty from 3,700 to 9,900) and remained positive each month between April and June as more British nationals were arriving than leaving during the onset of the pandemic

Figure 18: Total net migration was negative from March 2020, as more people left than arrived

Total net migration, by month, UK, January 2018 to June 2020

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Notes:

  1. Modelled estimates are based on the UN definition of an international migrant. That is a person who moves to a country other than that of his or her usual residence for a period of at least a year (12 months), so that the country of destination effectively becomes his or her new country of usual residence.
  2. Refugees and asylum seekers are excluded from modelling.
  3. The monthly estimates of international migration flows have been derived solely for the purpose of this research and should not be treated as official statistics or used in any other context.

We present cumulative net migration modelled estimates for total net migration, with further breakdowns for British, EU and non-EU for the year ending June 2020 in Appendix 4.

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10. Coherence with modelled travel and tourism estimates for Quarter 2 (Apr to June) 2020

Migration is a subset of all passenger flows across the UK borders. However, this relationship may have changed during the coronavirus (COVD-19) pandemic. Travel and tourism statistics are usually based on the results of the International Passenger Survey (IPS), but the survey was suspended on 16 March 2020¹ because of the coronavirus pandemic. Estimates were produced for April to June 2020 based on administrative data sources and modelling.

We compare the proportion of modelled migration and travel and tourism estimates of all in- and out-flows (Table 1). Table 1 suggests that during March 2020, migrants accounted for just 0.4% of in-flows to the UK and 0.8% of out-flows from the UK. During Quarter 2 2020 this proportion rose, particularly for out-flows, reaching 1.2% and 4.4% of in-flows and out-flows, respectively, in April. It seems appropriate that migrants would be more highly motivated than other travellers during the pandemic.

Notes for: Coherence with modelled travel and tourism estimates for Quarter 2 (Apr to June) 2020

  1. The International Passenger Survey (IPS), which underpins our existing UK international migration statistics, was suspended because of the impact of the coronavirus pandemic on 16 March 2020. While the IPS resumed operations in January 2021, the decision was taken and announced in the August 2020 Migration Statistics Quarterly Report (MSQR) that IPS data would no longer be used to calculate international migration
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11. Discussion

The coronavirus (COVID-19) pandemic presents a significant challenge to the UK and to the statistics we rely on. We used innovative modelling methods and the best available data to estimate international migration for the period March 2020, and Quarter 2 (Apr to June) 2020. We recognise that it is not possible to reliably estimate international migration for this period from past trends alone, using existing survey or administrative data, or a combination of both. Estimation is made even more challenging as people may be more uncertain of their migration intentions. Added to this is the impact of the EU exit and the new immigration system introduced in January 2021. It will be challenging to disentangle the effects of the EU exit and the coronavirus pandemic on international migration.

We have a rich data source on non-EU nationals' travel patterns in 2020 from Home Office border crossing data. There remains a lack of data available for immigrating EU and British nationals, and more so for emigration. We have used evidence for non-EU nationals to form assumptions about the migration behaviour of EU and British nationals in 2020. These assumptions, which underpin our models, were tested and endorsed in a Delphi approach with a panel of migration experts from across migration organisations, government and academia. Our modelled estimates are provisional, and as our models develop and more data become available or mature, they will be subject to retrospective confirmation and/or revision.

Going forward we plan to model international migration for Quarter 3 (July to Sept) and Quarter 4 (Oct to Dec) 2020. This will require new assumptions on migrant behaviour over this period and engagement with our panel of migration experts to validate our assumptions. Quarter 3 is typically dominated by international students beginning their studies at UK universities.

Whilst initial indications suggest visas granted for Tier 4 (sponsored) study have recovered in the last quarter of 2020, the question is, of course, whether students will travel to the UK, remain in their home countries and learn remotely, choose distance learning courses or reschedule or cancel their international study plans. We will consider the impacts of policy changes including the lifting of travel restrictions, introduction of travel corridors, the third lockdown in Quarter 4 2020 and the requirement for EU nationals to apply for visas from December.

We are in the process of analysing later extracts of Home Office border crossing data and are planning engagement with the Higher Education Statistics Agency and the university sector to understand international student behaviour in Quarter 3 2020. As the pandemic progresses it becomes less tenable that the migration patterns observed by the IPS will endure and we will reflect this in measures of statistical uncertainty for the modelled estimates.

Through its transformation programme, the ONS is developing Admin-Based Migration Estimates (ABMEs). Research statistics have been published for the period up until the end of March 2020 but do not cover Quarter 2 2020 onwards. We envisage further methodological development to bring together our tactical modelled approach with the ABMEs. We will consider using DWP RAPID data to inform migration for work. Important to this will be understanding data quality, in particular for emigration. Development of models for international migration will form an important part of our ambition to move towards a transformed population and migration system.

We need timely estimates that cover immigration and emigration; by nationality, reason and for population estimates by age and sex. Even before the coronavirus pandemic this was challenging as, definitionally, 12 months or more need to pass before we know if someone recorded in administrative data who has travelled to or from the UK is a migrant according to the UN definition. In the absence of intentions-based data, if our migration statistics are to be timely they will have to be predictions, produced as provisional figures that will be subject to later confirmation or revision as migration outcomes are revealed after 12 months. This research has demonstrated that migrant behaviour changed radically in response to the pandemic and its associated policy shifts and as expected this results in increased uncertainty in any estimates of migration. When we reach a new stability after the coronavirus pandemic and after the EU exit, we can begin to measure the new trends that will form the basis for admin-based migration predictions.

Most administrative data sources are not designed to directly measure international migration flows, and as set out in this article, there are often issues around coverage, timeliness and potential measurement error. At their best, we are repurposing and using these administrative data as a proxy for migration. More so than ever at this time, our definitions of "usual resident" and "international migrant" suggest a level of individual control over the decision to migrate and predictability in those decisions that may not be realistic during the pandemic. It is possible that people travelling to be with family or friends during the pandemic have become unintended "migrants" as they pass the 12-month UN definitional threshold. It may take a few years for migration to return to recognisable and predictable patterns.

We are very keen to receive feedback and observations on our statistical modelling work, including those who find it useful, and in particular those who think it needs further thought and refinement. Please contact us at demographic.methods@ons.gov.uk with any comments.

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12. Acknowledgement

Professor Peter Smith, Professor Jakub Bijak and Dr Jason Hilton from the University of Southampton Statistical Sciences Research Institute, Professor Jon Forster from Warwick University and Duncan Elliott, Principal Statistical Methodologist at ONS have helped us to develop the State Space Models described in this paper. We are also indebted to them for their comments and suggestions in the research and writing of this article.

We are also indebted to colleagues at the Home Office for making data available to us and for their expertise. Our thanks also go the experts who contributed to our assumption-setting Delphi process. We greatly value their time and expertise during the process of developing these models, as well as their inspiring and creative suggestions for further development of our models.

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13. References

Bijak, J. (2016) Migration forecasting: Beyond the limits of uncertainty. IOM Global Migration Data Analysis Centre, Data Briefing 6, 29 November 2016.

Bijak, J., Disney, G., Findlay, A.M., Forster, J.J., Smith, P.W.F., and Wiśniowski, A. (2019) Assessing time series models for forecasting international migration: Lessons from the United Kingdom. Journal of Forecasting*,* 38(5), pages 470 to 487.

Disney, G. (2015) Model-based estimates of UK immigration. PhD Thesis, University of Southampton.

Durbin, J. and Koopman, S. (2001). Time series analysis by state space methods. Oxford: Clarendon Press.

Eurostat (2020) Guidance on time series treatment

Helske, J. (2017) KFAS: Exponential Family State Space Models in R. Journal of Statistical Software, 78(10), pages 1 to 39.

R Core Team (2020) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.

Raymer, J. Wiśniowski, A. Forster, J. J., Smith, P.W.F. and Bijak, J. (2013) Integrated Modeling of European Migration. Journal of the American Statistical Association, 108(503), pages 801 to 819.

Wiśniowski, A., Bijak, J., Christiansen, S., Forster, J.J., Keilman, N., Raymer, J. and Smith, P.W.F. (2013) Utilising expert opinion to improve the measurement of international migration in Europe. Journal of Official Statistics, 29(4), pages 583 to 607.

Wiśniowski, A., Forster, J.J., Smith, P.W.F., Bijak, J. and Raymer, J. (2016) Integrated modelling of age and sex patterns of European migration. Journal of the Royal Statistical Society, Series A, 179(4), pages 1,007 to 1,024.

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14. Authors

Nicky Rogers, Louisa Blackwell, Duncan Elliott, Amy Large, Sonya Ridden, Mingqing Wu

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15. Appendix 1: Mathematical specification of the multivariate State Space Models and model diagnostics

This appendix contains the details of the mathematical specification of the multivariate State Space Model (SSM).

Purpose of the model

The multivariate SSM is fitted to the historical International Passenger Survey (IPS), and Home Office border crossing and travel data. Predictions are based on an extrapolation of the trend and seasonal components, together with the Home Office border crossing and travel data for the period March to June 2020. Predictions are generated from the model for British (GB), EU and non-EU immigration and emigration, and are summed to estimate the corresponding totals.

Data

IPS estimates for GB, EU and non-EU immigration and emigration, for the period January 2010 to February 2020. Note that we set January 2020 as an outlier by treating it as missing in the implementation.

Home Office border crossing (Exit Checks) data provide the number of incoming and outgoing non-EU migrants with a visa (of all types, be it for work, study, or family and other purposes). They are used in the models from March 2020 until June 2020.

The proportion of incoming and outgoing travellers using ferries or trains, from February 2020 until September 2020. This is calculated as the number of travellers using the ferry and train divided by the number of travellers using ferries, trains and flights (as identified in Civil Aviation Authority (CAA) data).

SSM equations

The multivariate SSM is a combination of a trend, seasonal, and an error component, for each IPS time series and for the administrative time series. SSMs consist of two equations:

  • The observation equation tells you the relationship between the observed vector of time series (IPS estimates and administrative time series) and the unobserved components of these series (trend, seasonal, and other components) contained within the state vector.
  • The transition equation tells you how the values of the components in the state vector change from one time-period to the next; in this case, the periodicity of the data is monthly.

Observation equations

Each observed time series y_t^i is the observed value of the outcome variable i, for i∈{GB,EU,nonEU,EXa,EXp,EX}, at time t, where EX refers to Exit Checks data , EXp to Exit Checks data adjusted by the proportion of travel by train and sea, and EXa refers to Exit Checks data for the opposite direction of movement for the IPS data. For example, if the IPS outcome variables are immigration (emigration) then EXa refers to Exit Checks data for departures (arrivals), EXp refers to Exit Check data for arrivals (departures) adjusted by the proportion of arrivals (departures) by air and sea, and EX refers to Exit Checks for arrivals (departures). The trend component is denoted μ_t^i, and γ_t^i is the seasonal component. The observation equation for the log of the IPS estimate for immigration (emigration), for stream s∈{GB,EU,nonEU}, in month t, denoted y_t^s, is

(1)

where ε_t^s~N(0, k_(s,t)^2 σ_(ε_s)^2) is an error component that accounts for the IPS sampling error (k_(s,t)^2 is the estimated variance of the IPS estimate in month t for stream s), and σ_(ε_s)^2 is to be estimated (but expected to be 1). It is also assumed that the sampling errors of the three IPS series are contemporaneously correlated. There are three of these equations for each direction of migration.

The remaining administrative based time series in the observation equation, a∈{EXa,EXp,EX} are also log transformed and modelled as:

(2)

where ϵ_t^a~N(0, σ_(ϵa)2) is an error component. These error terms are assumed to be independent of one another.

Transition equations

The unobserved components in the state vector evolve over time, with the following equations that are then incorporated into the transition equation. The trend components are as follows:

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

Where η_t^(μ_a )~N(0,σ_(μ_a)^2 ), for a∈{EXa,EXp,EX}, and η_t^(v_i )~N(0,σ_(ν_i)^2 ) for i∈{GB,EU,nonEU,EXa,EXp,EX}. For immigration

while for emigration

These equations say that the trend component in month t+1 is equal to that in month t plus a variable ν_t with error, plus the addition of an error term during the coronavirus (COVID-19) period, (determined by r_t and r_t^'), η_t^(μ_a ) for a∈{EXa,EXp,EX}. The latter term allows us to capture potentially large step changes in migration because of the coronavirus. On the original scale of the data, they are proportional modifications to what might have been expected had COVID-19 (and other effects during this period such as effects from the EU exit - it is not possible to distinguish between them) not happened. The proportional modifications are estimated from the large movements in the Exit Checks data time series.

The proportional modifications estimated by the unadjusted Exit Checks time series (EX) are used to modify the non-EU predictions from March (February) onwards for immigration (emigration) and also to modify the EU prediction for March (February and March) only for immigration (emigration). The proportional modifications estimated by the adjusted Exit Checks time series (EXp) are used to modify the EU predictions from April onwards. Proportional modifications estimated by Exit Checks data for departures (EXa) are used to model immigration by British nationals (GB) while those estimated by unadjusted Exit Checks arrivals are used to modify GB emigration. This is because we believe that the behaviour of GB nationals migrating back to the UK may be similar to visa holders’ early departures from the UK for home. Conversely, emigration by GB nationals is likely to be constrained, as evidenced in the deferred or cancelled arrivals seen for visa holders in the Exit Checks data.

A summary of proportional modifications and their corresponding equations.

Proportional modifications that multiply the predictions for IPS migration in the coronavirus period, and reference to the corresponding equations:

Immigration

  • British (GB): unadjusted Exit Checks departures; see equations (3) and (9)
  • EU: Unadjusted Exit Checks arrivals for March 2020 and adjusted Exit Checks arrivals from April onwards; see equations (5), (11), (13)
  • Non-EU: Unadjusted Exit Checks arrivals; see equations (7), (13)

Emigration

  • British (GB): unadjusted Exit Checks arrivals; see equations (3) and (9)
  • EU: Unadjusted Exit Checks departures for March 2020 and adjusted Exit Checks arrivals from April onwards; see equations (5), (11), (13)
  • Non-EU: Unadjusted Exit Checks departures; see equations (7), (13)

The seasonal components are modelled as:

(15)

(16)

(17)

for i∈{GB,EU,nonEU,EXa,EXp,EX}, where γ_(j,t)^i is the effect of season j at time t for series i, ω^i_(j,t), ω_(j,t)(i*)~N(0,σ_(ω_i)2 ). Note that both equations (16) and (17) are sets of 6 equations.

Matrix formulation

Model equations (1) to (17) can be written in matrix format – the required formulation for implementation in R. In the following notation, bold uppercase letters denote a matrix, bold lowercase letters denote a vector, and regular fonts denote a scalar (single value). Equation (18) is the matrix formulation of the observation equations, (1) and (2), and equation (19) is that of the transition equations (3) to (17). Note that the transition matrix T does not have a subscript t like the other terms because it is not time-varying.

(18)

(19)

where

where z^γ=(1,0,1,0,1,0,1,0,1,0,1), each 0 (bold, green font) represents a row vectors of length 11, each 0 represents a row vector of length 6, and

where 〖" η" 〗_"t" "~N" ("0," "Q" _"t" ) and the 81 x 81 covariance matrix

where

Note that the matrix σ_ε^2 has off-diagonal terms because it is assumed that the sampling errors of the three IPS series are contemporaneously correlated.

Model implementation

The model is implemented and fitted in R (R Core Team, 2020). First, the variances and covariances of the error terms in the observation and transition equation are estimated using maximum likelihood estimation with the Broyden–Fletcher–Goldfarb–Shanno algorithm (an iterative method for solving unconstrained nonlinear optimization problems) and the R optim function (does general-purpose optimization), through the Kalman Filter and Smoother (KFAS) package for state space modelling (Helske, 2017). Then the state vector, α_t, and the residuals, 〖 η〗_t and ϵ_t are estimated using the KFAS. Kalman filtering is an algorithm that estimates state variables that cannot be measured or observed with accuracy, and their uncertainties using a weighted average, with more weight being given to estimates with higher certainty. The initial values are set to zero with an infinite variance, which in terms of the Kalman Filter algorithm is referred to as exact diffusion initialisation. The exception is for components ε_tGB,ε_t^EU,ε_tnonEU which have initial mean states of zero and variance 1, since these are stationary and we expect the variance to be 1.

Uncertainty intervals

We account for uncertainty in our models and present uncertainty intervals in Section 6. Prediction intervals on the original scale of the data are based on the back transformation of prediction intervals from the model, where those predictions have been made on the logarithmic-scale (for log-transformed variables). The uncertainty of the predictions on the logarithmic scale accounts for the uncertainty in the estimation of the unobserved components in the state vector, given the prior distribution of the initial estimates. Uncertainty associated with the estimation of the covariances of the observation and transition error terms are not accounted for, which means that these intervals are likely to be underestimated.

Model diagnostics

The following set of diagnostic statistics and their corresponding p-values is provided for the standardised residuals for the fitted models: skewness (S), kurtosis (K), test for normality (N), test for Heteroscedasticity (H), and lags k for which Ljung-Box Q(k) is significant at the 5% level. See Durbin and Koopman (2001, Section 2.12.1) for details.

Table 1 gives the diagnostic statistics for immigration. There is some evidence of skewness in the distribution of the standardised residuals for IPS GB and EU, and some kurtosis in IPS all. The normality tests also suggest a lack of normality in IPS all, GB and EU. There is some evidence of residual autocorrelation for lags 2-24 for Exit Checks departures and lags 2-3 for Exit Checks arrivals. Some heteroscedasticity is indicated in IPS All. The Doornik-Hansen test for multivariate normality (test statistic 22.2, p = 0.07), provides no evidence to reject the null hypothesis that the data are multivariate normal.

Table 2 gives the diagnostic statistics for emigration. There is some skewness in the distribution of the standardised residuals for IPS all and GB, but no evidence of kurtosis, non-normality or heteroscedasticity. There is some evidence of residual autocorrelation for lag 22 for IPS non-EU. The Doornik-Hansen test for multivariate normality (test statistic 19.0, p = 0.17), provides no evidence to reject the null hypothesis that the data are multivariate normal.

Out of sample forecasting results for the benchmark model

The Mean Absolute Percentage Error (MAPE), in Tables 3 and 4, provides an indication of the performance of the benchmark model, which consists solely of seasonal and trend components. For each year, 2017 to 2019, we forecast four months ahead from January, from May and then from September, and then we calculate the MAPEs for the whole year (last three columns) based on these forecasts. The second column (2017 to 2019) is the MAPEs for all three years.

Table 3 shows that the forecast for total immigration is better than for any of the sub-series alone, which suggests that some of the errors in the latter are cancelled out in the sum. The forecasts for non-EU were more accurate than for GB and EU, with GB being the worst overall. The model is the most accurate for 2017, and the least accurate for 2018. Table 4 shows that for emigration the errors appear to cancel out again in the sum. The forecasts for GB were more accurate than for EU, but like those for non-EU.

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16. Appendix 2: The Delphi process

This section describes the Delphi process. Experts consulted for Delphi process, invitation, assumptions presented and expert feedback are included.

Introduction

The modelling makes assumptions regarding:

  • the interpretation of International Passenger Survey (IPS) estimates for early 2020

  • whether the changes in migration behaviours observed for non-EU migrants in Home Office border crossing data also apply to EU and GB migrants

  • whether EU migrants had more travel options than non-EU from April

We invited recognised migration experts and stakeholders to give us their view of the assumptions and to provide further evidence and insights.

Meeting on 23 March 2021

An invitation to attend the Delphi session was sent to 51 key stakeholders and migration experts. The meeting on 23 March 2021 included 20 external experts. Guided by a questionnaire and empirical evidence, the meeting considered the model assumptions. We invited feedback via questionnaires which we asked the experts to complete during the meeting. We received 11 completed questionnaires, with two additional responses, on March 24 2021. The questionnaires were from:

One academic expert and two experts from the Northern Ireland Statistics and Research Agency, from whom we did not receive permission to name in this report.

Helen Pennington, Home Office

Esther Roughsedge, National Records Scotland

Phil Rees, University of Leeds

Jon Forster, University of Warwick

Madeleine Sumption, University of Oxford/ Migration Observatory

Doug Rendle, Bank of England

Alan Manning, London School of Economics

Jonathan Portes, Kings College London

The model assumptions and initial expert feedback

Assumptions considered by experts, and their initial feedback includes:

International Passenger Survey (IPS) data for Quarter 4 (October to December) 2019:

  • Assumption: We are content that the IPS migration estimates for Quarter 4 2019 are broadly in line with other reporting on international migration for that period

  • Initial expert feedback: All experts agreed that the quality of 2019 IPS estimates were consistent with previously published estimates

IPS immigration estimates for January 2020:

  • Assumption: The increased immigration of students from Southern Asia and China in January 2020 reported by the International Passenger Survey was real

  • Initial expert feedback: There was some uncertainty and disagreement. The Home Office provided further evidence which we circulated to the experts

IPS immigration estimates for March 2020:

  • Assumption: We should use modelled estimates for March 2020, not IPS. IPS results from 1to 15 March did not capture changed migration patterns after March 16 2020.

  • Initial expert feedback:

    • Non-EU: All experts agreed with modelling from March
    • EU: There was agreement to model for March, but opinion was divided on using the extra travel options adjustment
    • GB: There was some support for using non-EU departures to model GB arrivals and vice-versa for Quarter 2 (Apr to June) 2020: two experts suggested modelling Quarter 2 2020 but using the IPS for March

Non-EU migration change in Quarter 2 2020:

  • Assumption: Flows for non-EU visa nationals in Home Office border crossing data are a true representation of changed patterns of arrivals and departures for this group in Q2. Time will reveal if these departures are long-term migrations. For now, we can use deferred arrivals, and departures up to 9 months ahead of a visa end date, as an indicator of behavioural change.

  • Initial expert feedback: All except one expert (who "couldn't say") endorsed modelling from March

EU migration change in Quarter 2:

  • Assumption: We can use non-EU border crossing evidence of changed migration behaviour to model EU migration in Quarter 2; we can modify this to reflect increased travel options for EU migrants

  • Initial expert feedback: Not everyone believed the scale of EU emigration implied by the increased travel options assumption for March; we opted to model from March and from April (the latter using IPS for March), with and without the increased travel option; we also decided to consider the effect of using the travel adjustment for Quarter 2 only, not for March, and invite further comment

GB migration change in Quarter 2:

  • Assumption: We can use non-EU border crossing evidence of changed emigration behaviour to model British immigration in Q2. We can use non-EU border crossing evidence of changed immigration behaviour to model British emigration in Quarter 2

  • Initial expert feedback: Experts felt that in the absence of any better data or intelligence we could continue with this assumption, at the same time giving careful thought to how to communicate it to users; two experts declined to comment or replied "can't say"

Candidate models from Round 1 of the Delphi process

Initial feedback from experts narrowed down the options for model assumptions, as summarised below:

Immigration

  • Non-EU: Model from March

  • EU:

    • Model from March without the travel options adjustment
    • Model from March but apply travel options adjustment from April
  • GB: Model from March using non-EU Home Office border crossing data on departures

Emigration

  • Non-EU: Model from March

  • EU:

    • Model from March without the travel options adjustment
    • Model from March but apply travel options adjustment from April
  • GB:

    • Model from March using non-EU Home Office border data on arrivals
  • Model from April using non-EU Home Office border data on arrivals and using IPS estimate for March

The initial feedbacks imply the following six models, two for immigration and four for emigration.

Immigration models:

  • Model from March 2020 without travel adjustment (EU)

  • Model from March with travel adjustment from April (EU)

Emigration models:

  • Model from March without travel adjustment (EU) and Home Office border crossing data on arrivals (GB) from March

  • Model from March without travel adjustment (EU) and IPS for March and Home Office border crossing data on arrivals in Quarter 2 (GB)

  • Model from March with travel adjustment from April (EU) and Home Office border crossing data on arrivals (GB) from March

  • Model from March with travel adjustment from April (EU) and IPS for March and Home Office border crossing data on arrivals in Quarter 2 (GB)

We collated user feedback into a single report and sent these back to experts, together with the outputs from the six models, inviting further comments and adjustment to feedback previously given.

Round 2 responses from experts

We received very few changes to the original responses. We considered the possibility that we may need to produce hybrid results. This might involve producing migration estimates that were a weighted average of different models, with weights derived by the weight of expert opinion favouring each model. We developed a method for deriving uncertainty intervals for a hybrid solution. We scored an opinion 0.5 if the expert chose two options, reflecting their uncertainty about which decision to make. This produced the balance of opinions summarised below.

We conclude: Consensus on assumption 1

We conclude on assumption 2 there is some disagreement and uncertainty. We welcome the additional evidence from Home Office in favour of this assumption. We will reflect these responses in our methodology report. This doesn’t affect the modelling so no further action is required.

We conclude on assumption 3 that for non-EU, there is consensus on using the model for non-EU migration for March 2020

Numerically the difference between the EU estimates for March is small and, considering the experts’ opinion on Quarter 2, for consistency we will use model 3 for March, that is, modelled using non-EU, including the travel adjustment from April onwards.

We will use the model estimates for British nationals in March, given the clear balance of experts in favour of this option.

We conclude that there is largely agreement that non-EU migration should be modelled from March and through Quarter 2 2020.

Experts chose the model for March immigration and emigration. Opinion is more divided on the travel adjustment for immigration than emigration. A clear majority favours the travel adjustment for emigration (favoured by 6.5 out of 8 or 81% of those giving a view). Given the small difference between model outputs for immigration (the differences cancel over time), we chose model 3 for immigration and emigration as a coherent approach that best meets expert advice.

Our conclusion: the evidence base on GB migration is very thin and in the absence of any better data or intelligence we will continue with using non-EU migrant behaviours to model GB migration. We will think carefully about how we communicate this in our reporting.

We are happy to provide fuller details from the Delphi process, please contact demographic.methods@ons.gov.uk.

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17. Appendix 3: Data Sources used in exploratory data analysis and modelling

Office for National Statistics (ONS) long-term international migration estimates

The main data source for estimates of long-term international migration was the International Passenger Survey (IPS), which captured migrant intentions. The ONS published two types of estimates for long-term international migration: the IPS and Long-Term International Migration (LTIM) estimates.

LTIM estimates are based on IPS data but with the following adjustments:

  • migrants not included in the IPS survey, such as asylum seekers and refugees, and migrants entering or leaving the UK across the un-surveyed land border with the Republic of Ireland

  • migrants changing their intentions with regards to length of stay

  • migrants with uncertain intentions

The IPS was suspended on 16 March 2020 because of the coronavirus (COVID-19) pandemic. While the IPS resumed operations in January 2021, the decision was taken and announced in the August 2020 Migration Statistics Quarterly Report (MSQR) that IPS data would no longer be used to calculate international migration.

Civil Aviation Authority (CAA) data

The CAA collects data on passengers carried on international scheduled and charter services between the majority of UK airports and foreign airports. The CAA figures may not reflect a passenger's entire air journey: the point at which a passenger disembarks from a particular service may not represent their ultimate destination.

It excludes passengers on airlines that the CAA do not have consent to publish, working crew members, aircraft chartered by government departments, and passengers at Carlisle, Edmiston London Heliport, Lydd and Shoreham. At the time of this analysis, Barra, Belfast City (George Best) and Three airports were not yet available for reporting in September 2020 and therefore excluded from the corresponding months in 2019 and 2020 comparisons. For more information, please see the notes and FAQ section of the CAA website.

Department for Transport (DfT) sea passenger statistics

Monthly sea passenger statistics produced by the Department for Transport (DfT) show the number of passengers travelling via short international ferry routes to Ireland and other European countries (Belgium, Denmark, Faroe Isles, Finland, France, Germany, Netherlands, Norway, Spain, Sweden). It includes passengers travelling for tourism, leisure and business travel, as well as freight drivers accompanying cargo. More information including data on other routes and guidance can be found on the Maritime and Shipping Statistics page by DfT.

Home Office data

Home Office immigration statistics provide the numbers of people who are covered by the UK's immigration control and related processes, based on a range of administrative and other data sources. The Home Office immigration statistics: user guide provides more detail and the Migration research and analysis page brings together a range of statistical and research reports on migration published by the Home Office.

Home Office border crossing data collect data on travellers arriving and departing the UK. These data are based on administrative data derived from the data matching system and analytical capability built by the Exit Checks Programme, the Initial Status Analysis (ISA). While the Exit Checks Programme closed in May 2016 having delivered its objectives, the ISA remains in place and is delivering results. The Home Office publishes a user guide on Home Office border crossing data and an annual report on statistics relating to Exit Checks.

Home Office data on air passenger arrivals and departures are derived from live operational systems - Advance Passenger Information (API). These data are not designed for statistical purposes, there are known issues in producing estimates of arrivals and departures from these sources.

API data primarily relate to passengers arriving and leaving the UK via commercial aviation routes. Counts of arrivals or departures are based on the amount of API data received rather than a true count of the number of passengers The data do not include those arriving or leaving by sea or train routes, by private aircraft or via the Common Travel Area (CTA). Nationality is derived from that recorded in the API. For dual nationals this may not be the same as the nationality presented at the border. Non-British nationals will include foreign nationals who are UK residents leaving the UK, dependants of UK residents, and other non-British nationals.

Department for Work and Pensions (DWP) data

The DWP National Insurance number (NINo) statistics count the volume of NINos registered to adult non-UK nationals. Further information, including detail on data sources, uses and limitations of the series, is provided in the background information and quality report.

Eurotunnel data

Eurotunnel trains transport freight and passengers in their motor vehicles between the UK and France. Our analysis of the data includes car and coach passengers travelling on the Eurotunnel between the UK and France. It excludes passengers travelling via trucks as these are categorised as freight related.

Patient Demographic Service (PDS) data

The PDS system is the master demographics database for the NHS in England, Wales and the Isle of Man. It is the primary source of information on a patient's NHS number, name, address and date of birth. It does not hold any clinical information. The master database contains approximately 74 million patient records. Records are created for newborns or when a patient makes contact with an NHS service, primarily by registering with a General Practitioner (GP) practice, but also through accessing Accident and Emergency (A&E) or attending hospital. The PDS is used by NHS organisations and enables a patient to be readily identified by a healthcare professional to quickly and accurately obtain their correct medical details.

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18. Appendix 4: Summary cumulative UK net migration charts

We present cumulative net migration modelled estimates for total net migration (Figure 1), with further breakdowns for British (Figure 2), EU (Figure 3) and non-EU (Figure 4), for the year-ending June 2020.

The cumulative net migration figures reflect that the year-ending June 2020 period mostly covers the months prior to the outbreak of the pandemic in the UK. Net migration for the year ending June 2020 was 282,300, largely driven by increased immigration and fewer departures by non-EU nationals. The notable change to net migration occurred in Quarter 2 (April to June) 2020 when the modelled estimates suggest -50,100 net migration.

Net migration for British nationals was positive from March 2020, likely to be explained by the combined effects of the EU exit and the pandemic. EU net migration was negative for the year ending June 2020. For non-EU migration, net migration was higher than in previous years. This is likely to be the result of relatively higher arrivals and fewer departures, in the context of fewer travel options and extensions of visas over the pandemic period. The second steep rise in the cumulative net migration curve for non-EU nationals could suggest that some planned immigration was brought forward from December onwards, while immigration stalled from March 2020.

In the following figures, modelled estimates use the UN definition of an international migrant, as someone who moves to a country other than that of their usual residence for at least 12 months. Refugees and asylum seekers are excluded from the modelling. The cumulative monthly estimates of international migration were derived for this research and should not be treated as official statistics.

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