Assessing time series models for forecasting international migration: Lessons from the United Kingdom

• Author: Allan M. Findlay,George Disney,Jakub Bijak,Arkadiusz Wiśniowski,Jonathan J. Forster,Peter W.F. Smith
• Date: 01 August 2019
• Published date: 01 August 2019
• DOI: http://doi.org/10.1002/for.2576

RESEARCH ARTICLE

Assessing time series models for forecasting international

migration: Lessons from the United Kingdom

Jakub Bijak

1,2

| George Disney

1,3

| Allan M. Findlay

1,4

| Jonathan J. Forster

1,2

|

Peter W.F. Smith

1,2

| Arkadiusz Wiśniowski

1,5

1

ESRC Centre for Population Change, UK

2

University of Southampton, UK

3

University of Melbourne, Australia

4

University of St Andrews, UK

5

University of Manchester, UK

Correspondence

Jakub Bijak, Department of Social

Statistics and Demography, University of

Southampton, Southampton SO17 1BJ.

Email: j.bijak@soton.ac.uk

Funding information

Economic and Social Research Council,

Grant/Award Number: ES/K007394/1;

Home Office Science, Grant/Award

Number: HOS/14/040

Abstract

Migration is one of the most unpredictable demographic processes. The aim of

this article is to provide a blueprint for assessing various possible forecasting

approaches in order to help safeguard producers and users of official migration

statisticsagainst misguided forecasts.To achieve that, we first evaluatethe various

existing approaches to modellingand forecasting of internationalmigration flows.

Subsequently, we present an empirical comparison of ex post performance of var-

ious forecasting methods, applied to international migration to and from the

United Kingdom. The overarching goal is to assess the uncertainty of forecasts

produced by using different forecasting methods, both in terms of their errors

(biases) and calibration of uncertainty. The empirical assessment, comparing

the results of various forecasting models against past migration estimates, con-

firms the intuition about weak predictability of migration, but also highlights

varying levels offorecast errors for different migration streams. Thereis no single

forecasting approach that would be well suited for different flows. We therefore

recommend adopting a tailored approach to forecasts, and applying a risk man-

agement framework to theirresults, taking into account the levels of uncertainty

of the individualflows, as well as the differences in their potentialsocietal impact.

KEYWORDS

ARIMA models, Bayesian methods, decision making, forecasting, international migration,

uncertainty

1|INTRODUCTION

Forecasting migration flows is characterised by high

levels of error, higher than for the other components of

demographic change: fertility and mortality (Bongaarts

& Bulatao, 2000), yet these errors are of crucial impor-

tance for overall population forecasts (idem; Long,

1991). There are many social, economic, political and

environmental drivers which impact migration flows

(Massey et al., 1993), yet there is no single, robust migra-

tion theory that can be used for forecasting purposes

(Arango, 2000). Migration is also susceptible to events

that are difficult to predict in terms of timing and

impact, such as changes in the economic cycle, policies

or political circumstances. Besides, even if credible expla-

nations of past migration flows existed, their tenets

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This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the

original work is properly cited.

© 2019 The Authors Journal of Forecasting Published by John Wiley & Sons Ltd.

Received: 1 November 2017 Revised: 10 September 2018 Accepted: 31 January 2019

DOI: 10.1002/for.2576

470 Journal of Forecasting. 2019;38:470–487.wileyonlinelibrary.com/journal/for

would be difficult to extrapolate into the future –for that

reason, most of the formal forecasting models rely on

time series analysis, be it frequentist or Bayesian

(Azose & Raftery, 2015; Bijak, 2010; Bijak & Wiśniowski,

2010; Cappellen, Skjerpen, & Tønnessen, 2015; de Beer,

1993, 2008; Wiśniowski, Smith, Bijak, Raymer, &

Forster, 2015).

Given the inherently uncertain nature of future events,

and the history of shock changes to migration flows, the

main aim of this paper is to provide a blueprint for

assessing possible forecasting approaches to help safe-

guard producers and users of official migration statistics

against misguided forecasts. To do so, we evaluate the

various existing approaches to forecasting of migration

flows, and present an empirical comparison of ex post per-

formance of various forecasting methods, applied to inter-

national migration to and from the United Kingdom

(UK). Even though we focus on international mobility,

the findings and general recommendations also apply to

internal migration, which typically exhibits more stable

and regular features (an observation made since

Ravenstein, 1885), yet still can have considerable volatil-

ity (see e.g. Raymer, Abel, & Rogers, 2012). Throughout

this paper, ‘migration’is thus used as shorthand for

‘international migration’. Besides, the terms ‘forecast’

and ‘prediction’are used interchangeably; ‘projections’

being reserved mainly for the results of deterministic cal-

culations of future population size and structure under a

set of specific assumptions (Keilman, 1990).

This paper considers three sources of uncertainty in

migration forecasts: the inherent uncertainty of future

events, errors in the data (Section 2), and uncertainty

related to relying on a particular forecasting model

(Section 3). In the empirical analysis, various models are

compared based on their forecast errors and the accuracy

of calibration of the forecast uncertainty (Section 4). The

results obtained for forecasts using data leading up to

the two major ‘shocks’observed for UK international

migration patterns –the enlargement of the European

Union (EU) in 2004; and the economic crisis in 2009 –

are subsequently presented (Section 5) and assessed using

a forecast assessment algorithm we outline. Finally, we

make recommendations related to the usefulness of vari-

ous forecasting approaches for policy‐makers, with focus

on the role of uncertainty (Section 6).

2|UNCERTAIN MIGRATION,

UNCERTAIN DATA

A vital consideration in forecasting migration is how to

incorporate uncertainty into the estimates. There are

three broad sources of uncertainty we consider in this

paper. The first one is the inherent uncertainty about

future events. Some level of error in migration forecasting

is always inevitable, as any inference about the future is

made under uncertainty (Alho & Spencer, 1985).

The second source of uncertainty is associated with

migration data. Sources of migration data from different

countries are often based on differing definitions (Raymer,

Wiśniowski, Forster, Smith, & Bijak, 2013). The available

data are often inaccurate, inconsistent and incomplete.

Migration into and out of the UK is no exception. The pre-

cise volume of international migration flows are difficult to

measure; data collection systems used to record migrants

often produce biased and inaccurate estimates (Disney,

2015; Kupiszewska & Nowok, 2008; Willekens, 1994;

Wiśniowski, Forster, Smith, Bijak, & Raymer, 2016).

Related to that is the uncertainty in how migration is

operationalised –as net or gross figures, for each area

separately or jointly for a multiregional system, as crude

numbers or rates, the latter additionally involving uncer-

tainty in the population at risk (see e.g. Raymer et al.,

2012).

The third source of uncertainty comes from the fore-

casting models. Applications of different models to the

same data can produce different forecasts, including dif-

ferent assessments of the uncertainty of the predictions.

If the forecasts from various competing models are com-

bined using formal criteria, additional uncertainty about

the model is introduced (Bijak & Wiśniowski, 2010).

In the UK, the main source of data on long‐and short‐

term migration is the International Passenger Survey

(IPS). The IPS is supplemented by a range of administra-

tive data: Home Office statistics on refugees and asylum

seekers, new National Insurance Numbers (NINo) issued

to foreign nationals by the Department of Work and Pen-

sions, and data on foreign students from the Higher Edu-

cation Statistics Authority (HESA). At the moment, there

is not much quantitative data on emigration from the UK

except for the IPS, especially available in the public

domain, although the situation is changing, with the

increasing availability of data on exit checks. These data

are already collected by the Home Office and shared with

the Office for National Statistics for analytical purposes,

such as those related to the numbers of international stu-

dents in the UK (Home Office, 2017).

Each of the sources of data can be assessed in relation

to the concept of ‘true flow’(Raymer et al., 2013;

Wiśniowski et al., 2016), defined as the unknown number

of migrants that is being estimated under a given defini-

tion of a migrant. It represents the number that one

would obtain if one was able to monitor the given defini-

tion of immigration perfectly, without bias and under-

count, and with complete coverage of the population.

For the purpose of this paper, the concept of a true flow

BIJAK ET AL.471