Ravenstein Revisited: The Analysis of Migration, Then and Now


Ravenstein Revisited: The Analysis of Migration, Then and Now*

Philip Rees, Nik Lomax

Abstract: In 1876, 1885 and 1889, Ernst Ravenstein, an Anglo-German geographer, 
published papers on internal and international migration in Britain, Europe and 
North America. He generalized his fi ndings as “laws of migration”, which have in-
formed subsequent migration research. This paper aims to compare Ravenstein’s 
approach to investigating migration with how researchers have studied the phe-
nomenon more recently. Ravenstein used lifetime migrant tables for counties from 
the 1871 and 1881 censuses of the British Isles. Data on lifetime migrants are still 
routinely collected but, because of the indeterminate time interval, they are rarely 
used to study internal migration. Today, internal migration measures from alterna-
tive sources are used to measure internal migration: fi xed interval migrant data 
from censuses and surveys, continuous records of migrations from registers, and 
“big data” from telecommunications and internet companies.

Ravenstein described and mapped county-level lifetime migration patterns, us-
ing the concepts of “absorption” and “dispersion”, using migration rates and net 
balances. Recently, researchers have used lifetime migrant stocks from consecutive 
censuses to estimate country to country fl ows for the world. In the last decade, an 
Australian-led team has built an international database of internal migration fl ow 
data and summary measures. Methods were developed to investigate the modi-
fi able areal unit problem (MAUP), in order to design summary internal migration 
measures comparable across countries. Indicators of internal migration were pro-
duced for countries covering 80 percent of the world’s population. 

Ravenstein observed that most migrants moved only short distances, anticipat-
ing the development of “gravity” models of migration. Recent studies calibrated the 
relationship between migration and distance, using gravity models. For mid-19th 
century Britain, Ravenstein found the dominant direction of internal migration to 
be towards the “centres of commerce and industry”. Urbanization is still the domi-
nant fl ow direction in most countries, though, late in the process, suburbanization, 
counter-urbanization and re-urbanization can occur. Ravenstein focussed on place-
specifi c migration, whereas today researchers describe migration fl ows using area 

Comparative Population Studies
Vol. 44 (2019): 351-412 (Date of release: 07.05.2020)

Federal Institute for Population Research 2020  URL: www.comparativepopulationstudies.de
       DOI: 10.12765/CPoS-2020-10en
       URN: urn:nbn:de:bib-cpos-2020-10en2
    

* This article belongs to a special issue on “Internal Migration as a Driver of Regional Population 
Change in Europe: Updating Ravenstein”.



•    Philip Rees, Nik Lomax352

typologies, seeking spatial generality. Ravenstein said little about migrant attributes 
except that women migrated more than men. In recent decades, the behaviour of 
migrants by age, sex, education, ethnicity, social class and partnership status have 
been studied intensively, using microdata from censuses and surveys.

Knowledge about processes infl uencing internal and international migration has 
rarely been built into demographic projections. Scenarios that link migration with 
sub-national or national inequalities and with climate or environmental change are 
infl uencing the design of policies to reduce inequalities or slow global warming.

Keywords: Ravenstein’s laws of migration · Defi nitions and measures of migration · 
Migration Flows and counter-fl ows · Migration and distance · Migration 
and urbanization · Migration differentials by sex, age, education, socio-
economic status and ethnicity · Models of migration fl ows · Projection 
models

1 Introduction

In the eighth and ninth decades of the 19th Century, Ernst Georg Ravenstein, an 
Anglo-German cartographer, published three papers that used data from the 1871 
and 1881 Censuses to describe the patterns of internal migration across the British 
Isles (Ravenstein 1876, 1885). In a third paper, he extended his analysis to Europe, 
the United States and Canada, examining “the foreign element” in their popula-
tions (Ravenstein 1889). These papers continue to infl uence research into internal 
and international migration. The aim of this paper is to compare the data, methods 
and results of Ravenstein’s work with research on migration in recent decades, to 
show both the connections and differences between his ideas and contemporary 
approaches. This paper is therefore a review of the fi eld of internal migration with 
excursions into international migration. The raw material used are Ravenstein’s pa-
pers and a selection of papers and books published in recent decades on internal 
migration, which connect to themes introduced in the 19th century work. 

Ravenstein’s most cited paper published in 1885 has the title “Laws of Migra-
tion”.1 He presented the paper at the Statistical Society of London (later Royal Sta-
tistical Society), followed by a lengthy question and answer session (Ravenstein 
1885: 228-235). A key outcome of the “Discussion of Mr. Ravenstein’s Paper” was 
that both author and discussants agreed that the “laws” were not immutable rules 
but rather “empirical generalizations” specifi c to the time and place of the evidence. 
Table 1 presents these “Laws of Migration” from the 1885 paper. Tables A1 to A3 in 
the Appendix report interpretations of the “laws” by later scholars.

1 Google Scholar (9 March 2020) counts 4749 citations for Ravenstein (1885), 2159 citations for 
Ravenstein (1889) and 119 citations for Ravenstein (1876).



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 353

Ravenstein’s work on migration has been expertly reviewed and interpreted 
by subsequent scholars (Grigg 1977; Dorigo/Tobler 1983 and Greenwood 2019) so 
remarks here will be brief. In his 1876 paper, Ravenstein covers much the same 
ground as his 1885 paper on the British Isles, without the key ingredient that has 
grabbed the attention of later scholars, his list of seven Laws of Migration (Table 1). 
Greenwood (2019: 271) extracts fi ve key points from Ravenstein (1876), which an-

Tab. 1: Ravenstein’s “Laws of Migration” in his 1885 paper

Year-Law# Text Pages
The Laws of Migration, Ravenstein (1885)

1885-1 We have already proved that the great body of our migrants only proceed 
a short distance, and that there takes place consequently a universal 
shifting of displacement of the population, which produces “currents 
of migration” setting in the direction of the great centres of commerce 
and industry which absorb the migrants. In forming an estimate of this 
displacement we must take into account the number of natives of each 
county which furnishes the migrants, as also the population of the towns 
or districts which absorb them.

p.198

1885-2 It is the natural outcome of this movement of migration, limited in range, 
but universal throughout the country, that the process of absorption 
would go on in the following manner:  The inhabitants of the country 
immediately surrounding a town of rapid growth, fl ock into it; the gaps 
thus left in the rural population are fi lled up by migrants from more 
remote districts, until the attractive force of one of our rapidly growing 
cities makes its infl uence felt, step by step, to the most remote corner 
of the kingdom. Migrants enumerated in a certain centre of absorption 
will consequently grow less with the distance proportionately to the 
native population which furnishes them, and a map exhibiting by tints 
the recruiting process of any town ought clearly to demonstrate this fact. 
That this is actually the case will be found by referring to maps 3, 4, 8 and 
9. These maps show at the same time that facilities of communication 
may frequently countervail the disadvantages of distance.

p.198-9

1885-3 The process of dispersion is the inverse of that of absorption and exhibits p.199
similar features.

1885-4 Each main current of migration produces a compensating counter- p.199
current.

1885-5 Migrants proceeding long distances generally go by preference to one of p.199
the centres of commerce or industry.

1885-6 The natives of towns are less migratory than those of the rural parts of p.199
the country.

1885-7 Females are more migratory than males. p.199

Source: Ravenstein (1885: 198-199)



•    Philip Rees, Nik Lomax354

ticipate his 1885 Laws of Migration (Table A1). Ravenstein’s 1885 list (Table 1) mixes 
elaborate statements of the regularity in which more than one proposition is made 
(Laws 1885-1 and 1885-2)2 with pithy summary phrases (Laws 1885-3 to 1885-7). 
Grigg (1977) extends the list of Ravenstein laws to eleven (Table A2) using short 
sentences or phrases. Dorigo and Tobler (1983) interpret Ravenstein’s statements 
as constituting precursors for later generalizations about push and pull factors in-
fl uencing migration fl ows (Table A3). Dorigo and Tobler (1983) suggest that one of 
Ravenstein’s Laws (1983-1 in Table A3) anticipates the scale and zonation dimen-
sions of the Modifi able Areal Unit Problem or MAUP (Openshaw 1983). Another 
of Ravenstein’s Laws (1983-2 in Table A3), Dorigo and Tobler propose, anticipates 
the hypothesis in which previous migrations by “friends and families” channel later 
migration. This hypothesis was investigated by Swedish geographer Hägerstrand 
(1957), using detailed longitudinal migration records. A third suggestion is that the 
confi guration of the transportation system is likely to play a signifi cant role in chan-
nelling migration fl ows (Ravenstein’s Law 1983-3, Table A3). So, we have the seven 
original Laws proposed by Ravenstein plus four added by Grigg and three by Dorigo 
and Tobler, fourteen in total. Ideally, this impressive number of empirical gener-
alizations should be tested in any study of new internal migration data. Like most 
researchers, we select a sub-set to compare the approaches of Ravenstein then and 
migration scholars now.

We structure the rest of the paper as follows. Section 2 considers the wide set 
of defi nitions of migration used in data collection, presenting them in a common 
graphical framework. Section 3 discusses how “raw” data may be used to estimate 
“refi ned” indicators of migration behaviour and how gaps in empirical information 
can be fi lled. Section 4 reports on recent research on internal migration patterns, 
tracking recent work linked to Ravenstein’s generalizations. The fi nal section sets 
out an agenda for future research aimed at improving our knowledge of both inter-
nal and international migration.

2 Data: Defi nitions and sources then and now

To describe and understand migration requires robust defi nitions of the phenom-
enon and reliable quantitative and qualitative data based on one or more of the 
defi nitions. In this section of the paper, we review defi nitions of migration and offer 
a framework that links them.

2.1 What is migration? 

For Ravenstein, migration was displacement of population between their place of 
birth and their place of enumeration at the census because those were the only 

2 This numbering system links to the listing of the laws of migration in papers by date and order 
in Tables 1, A1, A2 and A3.



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 355

comprehensive records available from 19th century censuses. In the contemporary 
world we need to introduce distinctions between different types of migration based 
on national or local boundaries. If migration takes place between countries, prop-
erly it should be labelled “international migration”. If migration takes place within a 
country it is usually labelled as “internal” or “domestic” migration. Some scholars 
and some offi cial statistics agencies distinguish between local mobility (migrations 
within local areas) and inter-area migration. Ravenstein wondered about how urban 
and rural migration differed but the 1871 and 1881 censuses provided no direct 
information about migration within cities. We consider this distinction arbitrary be-
cause of its dependence on local government boundaries which in many countries 
are subject to periodic reorganization, destroying temporal comparability. So, the 
ideal data set should record the geo-coded address of origin and the geo-coded 
address of destination so that tables of fl ows for any spatial system or scale can be 
created.

Several diffi culties arise which mean this ideal is rarely achieved. Not everyone 
agrees with these distinctions. Ravenstein did not distinguish between internal and 
international migration, treating, for example, the Irish element in the population 
of England and Wales in a similar way to the foreign element. Papers that discuss 
international migration will use “migration” without any prior specifi cation that this 
is only convenient shorthand. The same occurs in papers about internal migration. 
The second diffi culty is that offi cial statistical agencies are reluctant to publish mi-
gration information for fl ows between small areas due to uncertainty or because of 
the risk of disclosure.  Offi cial Statistical offi ces (such as Australian Bureau of Statis-
tics) often perturb the counts in published census tables and create inconsistency 
across tables at the same spatial scale and across spatial scales for the same tables. 
A third diffi culty arises because it is diffi cult to capture geography in a census or 
survey question. Most statistical agencies rely on a write-in answer, but people’s 
knowledge of places may be defi cient. The cost involved in converting a write-in 
place name answer to a geocoded reference is considerable. So, in 1961, when the 
General Register Offi ce of England and Wales decided to introduce a question on 
migration in the year before the census, the tabulation of lifetime migration was 
restricted to “home” countries with the United Kingdom (UK) and foreign countries, 
dropping birthplace by county used in censuses from the 1871 to 1951 (Friedlander/
Roshier 1966).

2.2 Households or individuals?

Human migration is defi ned as the relocation between dwellings of groups of indi-
viduals known as households over time and space. People migrate in small groups 
(households), which are either a nuclear family unit or a couple or a single person 
or several unrelated individuals, who share some common aspect of life together 
such as meals or housework or a set of relationships (husband-wife, child parent, 
student-fellow student). Household numbers and compositions alter as individu-
als join to form households or leave households to create or join new ones. Mi-
gration is associated with both household formation and dissolution. As activities 



•    Philip Rees, Nik Lomax356

shared among members change, so do the precise defi nitions adopted in census 
or survey questionnaires. An alternative defi nition, which is necessary when using 
administrative records, defi nes a household as the group of people who live at the 
same address. However, migration of households is rarely studied, except in the 
Netherlands (Van Imhoff/Keilman 1992), because complex changes take place at the 
same time in household membership (e.g. separation of partners, death of spouse, 
birth of a new child). Most research using aggregate data on migration focusses on 
individuals, whose characteristics are either fi xed (e.g. place of birth), stable (e.g. 
gender) or change systematically (e.g. age).  However, there is large and expanding 
literature that analyses family and household mobility using household survey data. 
Mulder (2018) provides a comprehensive review of the fi eld to which she has con-
tributed many rigorous and insightful studies.

2.3 Migrant attributes

The literature which investigates aggregate migration fl ows focuses most attention 
on the age and sex differentials. However, many more attributes are important in 
migration processes. These include health status (Wallace/Kulu 2014), labour force 
status (Marois et al. 2019a), family status (Mulder 2018), educational attainment 
(Bernard/Bell 2018), motivations (Coulter et al. 2011) and ethnic status (Darlington-
Pollock et al. 2019). Such attributes have been investigated using census microdata 
or survey data. Note that migrant attributes tend to be measured at the end of the 
migration interval and so their impacts are not precisely measured unless longitudi-
nal microdata are available (e.g. from the population registers of Nordic countries or 
the census-based longitudinal studies of UK devolved administrations).

2.4 Usual residence

The term “usual residence” is the dwelling unit in which people normally reside 
(sleep, eat and do household work in). Sometimes a detailed defi nition is provided 
in the offi cial questionnaire, such as the place where people spend most of their 
nights. However, working members of a household may spend more time at a dis-
tant work location than at the residence they regard as “usual”. People who use 
more than one residence need to choose which to report as their usual residence. 
Administrative registers ranging from comprehensive population lists through reg-
istrations for local or national tax purposes require reporting of a de jure (legal) 
residence though many allow registration of temporary residences. 

2.5 A duration criterion for migration or an instantaneity?

To distinguish between usual and temporary residence, statistical offi ces employ 
length of residence as a criterion. For example, people who cross international 
boundaries are asked about how long they will be staying at their destinations. The 
United Nations specifi es that countries use a 12-month duration criterion to distin-
guish between long-term and short-term migrants, with the exact method of gath-



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 357

ering this information left to national statistical offi ces. This may involve gathering 
electronic information on all entries and exits, administering a sample survey at en-
try or exit or deriving the information from registers. The duration criterion is linked 
to visa regulations governing visits, temporary and permanent migration. When the 
duration of stay is short, usually up to 3 months but up to 6 months in many coun-
tries, the entrant is classifi ed as a visitor. For durations of 3 months/6 months to 12, 
the entrant is classifi ed as a temporary or short-term immigrant. 

2.6 Migration and space

Internal migration measurement is particularly sensitive to the number, size and 
shapes of regions as migration is recorded as people cross those region bounda-
ries. If a national territory is divided into a few regions, a lower count of migrants or 
migrations will be recorded than if a larger number of regions, necessarily smaller, 
is used. The exact shape and borders of regions will also affect the counts of mi-
grants or migrations. This dependence of a migration measures on the spatial sys-
tems used in measurement hampers comparison of internal migration across both 
countries and time periods. Bell and colleagues (Bell et al. 2002, 2015a/b, 2018;  Bell/
Muhidin 2011; Stillwell et al. 2014, 2016; Rees et al. 2017a; IMAGE Project 2020a)3 
have pioneered the development of system wide measures of internal migration, in 
which the effect of size and zonation of areal units is established and stable sum-
mary measures derived for international comparisons of internal migration. 

Stillwell et al. (2018) use zone design software that assembles basic areal units 
into larger zones (IMAGE Project 2020b) to investigate the effects of scale and zone 
confi guration on migration indicators and distance decay parameters. The results 
of this research are that, above a threshold number of regions, many system-wide 
measures remain reasonably constant. The test data set employed by Stillwell et 
al. (2018) consists of migrant fl ows between 404 Local Authority Districts in the 
UK derived from the Special Migration Statistics from the UK’s 2011 Census (Duke-
Williams et al. 2018). Note that the IMAGE software does not “solve” the MAUP. 
Rather, it allows the user to explore the effect of spatial framework design on their 
own migration system and select scales and zone systems which can be compared 
between countries or time periods. 

2.7 Full migration histories

It is vital, when using existing migration data or in designing new methods of meas-
urement, to understand the key concepts involved. Here we use a set of graphs 
(Fig. 1) to identify the most important types of measure.

Ideally, we would like to track the full migration career of individuals. Figure 1A 
shows an example history for one individual in a time-space diagram. The horizontal 
axis proceeds from left to right, from time t

b
 when the individual is born through to 

3 The IMAGE project compares Internal Migration Around the GlobE.



•    Philip Rees, Nik Lomax358

Fig. 1: Types of migration measure

Key to graphs 1A: Full migration histories, from full population 
registers

1B: Lifetime migrant, from a census or survey

1C: Last residence migrant, unknown interval 1D: Last residence migrant: fi xed interval



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 359

Fig. 1: Continuation

1E: Fixed Interval migrants by transition type, from transition demographic accounts

1G: Migrations of different types (from registers)

1F: Migrants, conditional on duration of residence

Source: Authors’ design



•    Philip Rees, Nik Lomax360

time t
d
 when they die. Vertical timelines, t

1
 and t

2,
 bracket a period of interest. The 

vertical axis divides space into two regions, i and j, between which the person can 
migrate. The open arrows, which straddle the border between regions i and j, repre-
sent a migration. The person experiences one migration from region i to region j in 
the t

b
 to t

1
 interval, a return migration from region j to region i in time interval t

1
 to t

2
 

and a further migration to region j in time interval t
2
 to t

d
. The individual makes three 

migrations over their lifetime, the second of which is return migration to region of 
birth and the third a return migration to a region with a previous spell of residence. 
A full set of migration histories from which migration could be measured would 
consist of all lifelines that entered, stayed in or left the system of interest. To meas-
ure the intensity of migration we would divide the number of events of migration 
by the person time of exposure in the regions of interest. Only the highest quality 
population registers, in the Nordic countries, provide the real-world equivalent of 
Figure 1A. In longitudinal studies based on censuses or surveys such as the Lon-
gitudinal Study of England and Wales (CeLSIUS 2019) there are missing elements. 
Reconstruction of migration histories through retrospective questions in surveys 
suffer from survivor bias as respondents who have died or emigrated cannot be 
interviewed. 

2.8 Lifetime migration

Lifetime migration data analysed by Ravenstein (1876, 1885), compare only place 
of birth with place of current residence (Fig. 1B). In the 1871 and 1881 Censuses, a 
question was asked about a person’s birthplace, using county as the geographical 
unit. Tables were constructed for the populations of England and Wales, Scotland 
and Northern Ireland by county of residence and county of birth. There is no in-
formation about the exact timing of the migration or about how many migrations 
occurred between birth and date of enumeration. In the decade 1871-1880, male 
life expectancy was estimated as 41.4 years and female as 44.6 years (ONS 2015). 
So, it is likely that most migration took place between 1831 and 1871. Similar tables 
of lifetime migration at county scale were produced in censuses from 1891 to 1951, 
except for 1931 (Friedlander/Roshier 1966).

In 1961, lifetime migration tables were restricted to UK home countries and a 
fi xed one-year interval question substituted (“where were you living one year 
ago?”). In the sample Census of 1966 and the full Census of 1971, two migration 
questions were asked using one-year and fi ve-year intervals. From 1981 to 2011, 
only the one-year question was asked.

2.9 Migrants by last residence

Common questions included in censuses are: “where was your last residence” (open 
interval) or “where was your last residence in the previous X years” (fi xed interval), 
because this is the easiest question for respondents to answer. Figure 1C shows the 
time-space graph for the open interval case where the timing is uncertain. Figure 1D 
presents the fi xed interval case where the location at the start of the fi xed interval 



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 361

is uncertain. Uncertainty is indicated by using a pecked timeline or lifeline for the 
migrant. Most countries that collect last migration data (with timing undefi ned) do 
also collect duration of residence. These data can be used to approximate fi xed 
interval measures, but only if the duration is reported in fi nely graded intervals, and 
if the space to which the duration refers is clearly specifi ed. These conditions are 
rarely satisfi ed. This type of question provides important descriptive information 
but like the lifetime migration question picks out only one migration without precise 
information about when the migration occurred. Rees (1985) showed that it was 
diffi cult to use the results as an input for estimating or forecasting the population. 
 However, Schmertmann (1999) proposes three methods for estimating multistate 
transition hazard rates from last migration data. The methods are compared using a 
micro-simulation model with invented test data. The author then applies the meth-
ods to estimate fi xed period transition fl ows from last migrant data for a Brazilian 
three state system (Parana, Sao Paolo, Rest of Brazil). He demonstrates that the 
back-projection method produces plausible estimates.

2.10 Fixed interval migrants

The left-hand graph in Figure 1D shows the lifeline of a typical fi xed interval migrant, 
based on a retrospective census or survey question. Data on fi xed interval migrants 
are generated by asking the question “where were you living X years ago?” (where 
X is typically, 1, 5 or 10 years) or “where were you living at the time of the last cen-
sus?” (as in the French census, where censuses have been held at irregular rather 
than regular intervals). It is diffi cult to compare migration volumes and intensities of 
questions with different time intervals because of return and repeat migration (Rees 
1977). Papers from the IMAGE project (Bell et al. 2015b; Stillwell et al. 2016 and Rees 
et al. 2017a) report on both 1-year and 5-year migration results but do not compare 
them directly. Rogers et al. (2003) and Dyrting (2018) have developed models for 
translating between 1-year and 5-year probabilities, so in future harmonization may 
be possible if the assumptions of the models hold for a country. However, Figure 
1D shows three graphs which have fi xed start and end states in the period which 
may not be captured by a census or survey question: the exist-die, born-survive and 
born-die transitions, all of which might involve an inter-regional migration. These 
additional life-state to life-state transitions were recognized by Rees and Wilson 
(1977) in their book on Spatial Demographic Analysis as building blocks of transition 
demographic accounts. In principle, the born-survive transition should be captured 
by a census question, either through cross-tabulating the residence region at the 
census of 0-year olds or 5-year olds against their place of birth, derived from the 
Births Register but this is rarely done. 

2.11 Fixed interval migrants, conditional on duration of stay

Many surveys of international migration (ONS 2019) incorporate a condition that to 
be counted as a long-term migrant that person must reside for 12 months or more, 
following a recommendation by the United Nations. Durations of stay of 3 months 



•    Philip Rees, Nik Lomax362

up to 12 months classify migrants as Short-Term while durations of less than 3 
months lead to classifi cation as Visitors (Fig. 1E). Nowok and Willekens (2011) devel-
op a framework that identifi es types of migrants, conditional on how long they stay 
at their destination after migration. The authors specify a general process of migra-
tion drawing statistical theory and, using a microsimulation model of an invented 
sample of migrants, show how different intensities result in different expected tran-
sitions over intervals of different lengths (Fig. 5 and 6 in Nowok and Willekens 2011). 
This work should be an important building brick in the development of a tool to 
handle the Modifi able Temporal Unit Problem (MTUP) discussed later in section 3.5. 

2.12 Migrations as boundary crossing events

Figure 1’s fi nal panel (1F), focuses on representations of migrations as boundary 
crossing events. The right most graph illustrates the situation when border cross-
ings are counted. A migrant may make more than one border crossing in a time 
interval of interest as in the middle graph. This person would have been recognised 
once as a fi xed interval migrant between region i and region j. Such migrants are 
recognised as “performing” repeat migrations (left hand graph in Fig. 1F). When 
those migrations are a sequence of region i to j and then region j to i, they are return 
migrants (right hand graph in Fig. 1F). Later in the paper we show that it is neces-
sary to estimate these two types of migrant and the number of moves they make to 
convert a migrant count into a migration count.

2.13 Sources of migration data

Bell et al. (2015a) reported on the types of internal migration data gathered by coun-
tries across the world. Table 2 identifi es the types of retrospective questions used 
in the 2000 round of censuses. The commonest question is asked about place of 
birth (lifetime migration), followed by duration of residence, last migration and then 
the fi ve-year, one-year and other interval questions, upon which most comparative 
analysis is based. In addition, Bell et al. (2015a) record the number of countries re-
porting migrations (events) from registers, though such data are gathered mainly in 
European countries.

The categories of Census, Register and Survey cover a range of strategies and 
coverages of the population. Censuses are normally designed to be complete enu-
merations of the population and surveys are normally samples, designed to be rep-
resentative of the national population. Often, diffi cult-to-handle questions, such as 
those about migration, are assigned to long-form representative samples to reduce 
the burden of coding geographic responses. In some cases, the migration ques-
tions are left out of the census and included in a separate national survey, as in 
the US Census of 2010 where no migration question was asked in the main census 
but included instead in the annual American Community Survey. This strategy is 
adequate for many kinds of migration measure (total infl ows, total outfl ows, age 
and gender profi les) for larger administrative units but provides little information on 
origin-destination fl ows, because the N categories of interest (e.g. ~3,000 US coun-



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 363

ties) turn into N2 fl ow dyads (3,000 by 3,000 or 9 million data points). The modern 
US migration researcher would have a hard time replicating Ravenstein’s analysis of 
counties of absorption and dispersion. 

Administrative Registers avoid the small sample problem by aiming to cover 
the whole of a target population such as all usual residents or all taxpayers or all 
patients in the health care system. So, coverage issues replace the sampling issues 
of survey or within census samples, substituting the advantages of continuous re-
cording and capacity to generate good time series of migration information. How-
ever, registers are often restricted in the range of co-variates available. For example, 
the National Health Patient Register used to measure UK migration provides just 
basic demographic information (location, gender, age) for statistical release and im-
poses very strict safeguards and terms and conditions of use for associated health 
data. Fully developed registration systems such as that of Finland (Statistics Finland 
2019) overcome this diffi cult by linking demographic information from the popula-
tion register with socio-economic information from the tax and benefi t records and 
employment data from the business register. 

For many questions about migration, researchers use national or international 
household surveys or microdata samples from censuses (Bell et al. 2015a). Such 
sample data are very useful where available, yielding new insights into migration 
behaviour by migration cohort (Bernard 2017) or by migration motivation (Coulter et 
al. 2011) by type of area, but they are too small for the analysis of the place to place 
migration that Ravenstein studied. 

Alternative detailed survey data are collected by commercial polling or market-
ing fi rms who also need detailed place-specifi c data. Thomas et al. (2014) explore 
the potential of a large commercial survey data, produced by marketing company 
(Axciom 2019). Under licence the authors had access to unit postcode data for re-
spondent households and their residents. They demonstrate that results for the de-

Tab. 2: Number of countries collecting internal migration data in the 2000 UN 
census round by world region

World Region Observation period
1 year 5 year Other Lifetime Last Duration Total

fi xed migration of countries
interval residence collecting

data

Africa 9 8 8 29 13 17 32
Asia 2 13 8 27 18 24 35
Europe 13 4 12 25 10 12 31
Latin America & 
the Caribbean 2 17 2 29 12 13 29
Northern America 1 2 0 2 0 0 2
Oceania 2 8 2 10 2 5 13

Total 29 52 32 122 55 71 142

Source: Bell et al. (2015a), Table 2, p5.



•    Philip Rees, Nik Lomax364

terminants of migration are close to those from offi cial surveys, and that unweight-
ed and reweighted data produce similar results. Stillwell and Thomas (2016) use 
postcode-to-postcode migration data to estimate intra-zonal migration distances. 
They show that traditional methods of estimating this variable are fl awed. Distance 
decay parameters calibrated for spatial interaction models of migration differ sig-
nifi cantly using individual rather than zone data.

There has been huge interest in using electronic data generated by users of in-
ternet platforms and of smartphone devices to provide statistical information on a 
comparable basis for member states (UN 2019a). To date, there has been relatively 
little progress. The data belong to private corporations, which make limited data 
available but retain the right to change the algorithms that generate the information. 
Migration is not a variable that is directly generated from available internet queries 
and phone location traces. Corporations are reluctant to release the most detailed 
data for testing or calibration purposes. Nevertheless, for many countries that lack 
good offi cial statistics systems, “big data” are a useful source, particularly for es-
tablishing the location of most used residence and for monitoring daily journeys 
(Manley/Dennett 2018). 

A second example of use of telecommunications data is provided by Lai et al. 
(2019). In a Namibia case study where both census and mobile phone call data re-
cords (CDRs) are available, the authors construct a model that predicted migration 
fl ows between 13 regions from CDR data and some fi xed co-variates. The aim was 
to develop migration fl ow data for years after the latest census up to the next. A lin-
ear model with co-variates had high goodness of fi t (R2 = 0.94). There is no way of 
fully testing the model until the next census, but it clearly has considerable potential 
for countries without continuous records of migration. Mobile phone penetration in 
less developed countries is already high and getting higher. 

An important study was carried out by a team of experts for the European Union 
to investigate the potential of using social media data to fi ll the gap between the 
latest offi cial Labour Force Survey data and “now” (European Commission 2019). 
The authors commented as follows: “the fi rst results of the application of the stocks 
model are experimental, but they are promising” but that “the approach taken to 
estimate EU Mobility Flows has not yet offered any plausible results” (European 
Commission 2019: 15). The problem, recognised by the authors, was that offi cial 
statisticians have virtually no control over social media data from Facebook or Twit-
ter. Use of call data records seems more promising.

3 Filling the gaps: Harmonizing and estimating migration

Ravenstein (1876) used lifetime migration from the 1871 Census of Great Britain and 
Ireland, while his 1885 paper employed similar tables from the 1881 Census. There 
were two gaps in the data: one spatial and one temporal. The spatial gap was the 
absence of fl ow data from between counties in one “home” nation (England and 
Wales together, Ireland and Scotland) and counties in another (Ravenstein 1885: 
Map 6). Outside the home nation only birthplace by home nation was made avail-



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 365

able. The temporal gap was the absence of migration fl ows from one census to the 
next. The timing of the transition between birth county and residence county was 
unknown. Ravenstein did not have the statistical tools to fi ll these spatial and tem-
poral gaps. Contemporary researchers take the view that once the phenomenon to 
be studied has been identifi ed, efforts should be made to use the partial data avail-
able along with auxiliary data and statistical models to make an estimate of the true 
fl ows. We now discuss a sequence of critiques, improvements and new estimates 
that have generated new estimates of migration, which can inform and improve of-
fi cial statistical practice.

3.1 Harmonizing spatial units used to measure internal migration

Ravenstein was fortunate in being able to study historic counties, whose bounda-
ries did not change between 1871 and 1881. American, Australian and Canadian 
researchers can use state or province boundaries which are fi xed from the date of 
admission to their respective Union, Commonwealth or Confederation, and French 
researchers can rely on boundaries for departéments, fi rst created in 1790 by the 
National Constituent Assembly of Revolutionary France. Other European countries 
have experienced greater volatility in both regional and municipal boundaries. The 
UK, for example, has experienced frequent changes in the boundaries of its local au-
thorities, which have shrunk in number and grown in population through mergers, 
in order to achieve economies of scale in administration. Look up tables based on 
the populations of the smallest geographical units are used to apportion population 
statistics from the “old” geographic units to “new” geographic units (Simpson 2002). 
This works reasonably well for statistics that apply to one spatial entity. However, 
for migration fl ows which refer to two spatial units, the origin and the destination, 
this method is problematic. To aggregate migration fl ows from one geography to 
another, it is essential to aggregate fl ows between small basic spatial units (BSUs), 
which ideally nest within the larger units of interest. If there are still overlaps, then 
the centroids of zones can be used to match BSUs via a point in polygon function 
(Bell et al. 2015a).

3.2 Estimating missing internal migration data

Since the 1966 UK Census (a 10 percent sample), migration origin-to-destination 
fl ow data sets have been produced, at fi rst on user demand at cost (1971, 1981) and 
then as publicly accessible data sets in 1991, 2001 and 2011, free at the point of use, 
though with restriction to safe settings for the most detailed tables (Duke-Williams 
et al. 2018). These fl ow data sets provide tables for regions, local authorities, and 
small areas (e.g. output areas and super-output areas), though the detail of the ta-
bles shrinks with spatial scale to avoid disclosure issues. However, the diffi culty that 
Ravenstein experienced of fl ow tables only being available within UK “home” coun-
tries and the lack of harmonised fl ow data for the years between censuses persists 
for fl ow tables derived from the main UK administrative register, the Patient Register 
of the National Health Service (NHS) (Lomax 2013a: Chapters 3 and 4). Flow tables 



•    Philip Rees, Nik Lomax366

are available for each mid-year to mid-year interval for each home country but fl ows 
between local authority districts (LADs) in one home country and LADs in another 
are not generated. Figure 2 (based on a similar diagram in Lomax et al. 2013b) sets 
out the status of information in each cell of the matrix of fl ows. The table has origin 
and destination LADs sorted by home country. LAD to LAD fl ows (represented by 
the green cells) are available within England, Wales and Scotland and between Eng-
land and Wales. Flows between LADs in Scotland and Northern Ireland and LADs in 
other home countries are not available (cells shaded in beige). For Northern Ireland 
LAD to LAD fl ows are also not available. The grey cells represent marginal totals (to-
tal infl ows and outfl ows of various kinds). The question is: “how can the full matrix 
be estimated?”

The solution is to borrow information from a closely aligned source, in this case 
the full 2001 or 2011 Census fl ows matrices and adjust these borrowed fl ows to 
agree with the known marginals derived from the home country NHS registers for 
years 2001-02 to 2010-11. The generic algorithm used is called “iterative propor-
tional fi tting” (IPF), applied to each sub-matrix in Figure 2 (Lomax 2013a/b; Lomax/
Norman 2016). The algorithm has been re-invented and renamed in many social 
disciplines. Yule (1912) used it to standardize cross-tabulations; Kruithof (1937) de-
veloped a double factor method for use with telephone call data; Deming and Ste-
phan (1940) employed the method to adjust census tables; Bishop et al. (1975) wrote 
a defi nitive guide to the method. IPF is known as bi-proportional fi tting in spatial 
interaction modelling (Wilson 1971) and employed in migration modelling (Stillwell 
1978, 1979). When employed in economics, IPF is referred to as the RAS method 
and used to estimate input-output accounts; when employed to re-weight sample 
survey results the term is referred to as statistical raking (Mercer et al. 2018). The 
Lomax work achieved consistent year by year estimates of migration fl ows between 
389 local authority districts in the UK using IPF techniques.

American demographer Andrei Rogers and colleagues have worked intensively 
on methods for estimating internal migration when direct data are not available. In 
the monograph The Indirect Estimation of Migration (Rogers et al. 2010), the authors 
summarise achievements of three decades of research on migration estimation, ac-
knowledging the key contribution of Willekens (1983) on the use of log-linear mod-
els to understand the contributions of origin, destination and interaction factors to 
migration fl ow matrices. One of the motivations for writing the book was concern 
that in 2010 the US Census Bureau would no longer ask a fi xed interval question on 
residence 5 years ago but instead rely on the annual (but sample) American Com-
munity Survey to provide information on internal migration with the United States 
(US Census Bureau 2019). Log-linear modelling helps to estimate missing fl ow data 
from marginals and proxy interaction data. The Rogers team also worked on model-
ling the age variation of migration intensity, using the migration by age data assem-
bled in the Migration and Settlement study at the International Institute for Applied 
Systems Analysis (Rogers/Castro 1981a; Rogers/Willekens 1986), developing a mul-
ti-exponential model of the age profi le of migrants. The average exponents of the 
profi le across the 17 country inter-regional matrices by age in the study have been 
widely used to disaggregate or improve migration by age information (e.g. Sander 



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 367

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•    Philip Rees, Nik Lomax368

et al. 2014a). Subsequently, the age profi le model has been refi ned by Wilson (2010) 
and linked to life course event profi les (Bernard/Bell 2015). The decomposition of 
migration by age is hinted at by Ravenstein (1876) but no data were available for 
investigation (Greenwood 2019: 271). 

3.3 Filling the gaps in international migration data

Despite the prominence of international migration in political discourses in most 
countries and the existence of national statistics (at least on immigration), there is 
no system for producing harmonised measures of international migration fl ows. The 
best data currently available are the national census tables of migrants by country of 
residence and country of birth, collected by the Statistics Division of the United Na-
tions and published by the UN’s International Organization for Migration (IOM 2019). 
These data are analogous to the 1871 and 1881 census data analysed by Ravenstein, 
referring to country to country fl ows rather than county to county fl ows. The United 
Nations Population Division assembles data from national statistical offi ces on net 
international migration where available and produces estimates as the residual bal-
ance after natural change is subtracted from total population change. The IOM data 
portal (IOM 2019) points to the category migrant fl ows, but these are only available 
in Europe from EUROSTAT (the Statistical Offi ce of the European Union). Flow es-
timates were compiled partially from data supplied by national statistical offi ces of 
EU member states and partially from estimates compiled by academic researchers 
working with EUROSTAT (Raymer et al. 2011, 2013). 

Poulain, Perrin and Singleton (2006) carried out a comprehensive survey of 
sources, defi nitions and measures of migration available from EU member states. 
The THESIM Report (Towards Harmonised European Statistics on International Mi-
gration) covers EU migration policy and data regulation, administrative systems of 
data collection, statistics on international migration fl ows (where available), resi-
dence and work permits, asylum applications, removals of persons refused leave to 
remain together with twenty-fi ve country reports written by national experts using 
a uniform template. The edited collection by Raymer and Willekens (2008) builds 
on the THESIM work by reviewing models available for generating better migration 
estimates. Raymer (2008) proposes a schema for carrying out the estimation by 
reconciling confl icting origin country and destination country estimates or by bor-
rowing information from other countries where it was not available for a country. In 
the case of the UK reliable data on fl ows to/from other EU countries were missing 
and had to be borrowed from origins or destinations with better statistics.

Raymer and colleagues working together in the MIMOSA (Migration Modelling 
for Statistical Analysis) project developed a model for estimating international mi-
gration fl ows between member states in the EU and EFTA and fl ows to and from the 
Rest of the World. The model combines the procedure for harmonization proposed 
by Van der Erf and Van der Gaag (2007), which works from most to least reliable es-
timates with the log-linear modelling framework set out in Raymer (2008), a gravity 
model for intra-EU and extra-EU fl ows in the European Union, where fl ow estimates 
are missing (Raymer/Abel 2009; Abel 2010; Raymer et al. 2011). The estimates were 



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 369

further refi ned in the IMEM (Integrated Modelling of European Migration) project 
which incorporates expert views about the reliability of fl ows by country and pro-
vides measures of uncertainty/confi dence (prediction intervals) around those esti-
mates within a Bayesian framework (Raymer et al. 2013).

These estimates of migration fl ows between EU and EFTA states have been used 
as inputs in a subsequent demographic forecasting project DEMIFER (Demographic 
and Migratory Flows Affecting European Regions and Cities) (Rees et al. 2010; Rees 
et al. 2012). Scenarios of future migration are developed that are linked to migration 
and regional development in national and EU policies. The projection model used 
a multi-level approach (Kupiszewski/Kupiszewska 2011), in which migration fl ows 
between EU states were explicitly forecast and then allocated to regions within EU 
states using information on immigration and emigration or population totals by re-
gion for EU states. Dennett and Wilson (2013, 2016) took the MIMOSA/DEMIFER 
estimates and used them to generate a full matrix of interregional migration across 
the EU that combines international fl ows between EU member states and internal 
interregional migration estimates. 

3.4 Estimating period migration data from lifetime migration data

Section 3.2 showed how migration fl ows can be estimated from partial data, where 
reliable sub-totals were available together with a full matrix of reliable proxy migra-
tion fl ows to adjust. Section 3.3 discussed ways in which a full fl ows matrix could be 
constructed from partial information by using information from destination coun-
tries with high quality statistics where origin countries had very poor information. 
In this section (3.4), we report on methods of estimating period-specifi c migration 
fl ows between counties (internal migration) or countries (international migration) 
from tables of population classifi ed by current residence and place of birth, the 
same as the lifetime migrant tables used by Ravenstein (1876, 1885). Table 3 sets out 
the contributions to these estimations.

The fi rst entry identifi es Ravenstein’s use of lifetime migrant data using informa-
tion from two censuses. He did not attempt to estimate period migration data but 
has stimulated subsequent researchers to investigate possible methods of doing 
so. Important work on the estimation of migrant fl ows from migrant stocks was 
carried out by Friedlander and Roshier (1966). The aim of the analysis was to use 
lifetime censuses from 1851 to 1951 to create period estimates for inter-census mi-
gration between counties in England and Wales. The authors built a model that 
uses two successive lifetime migrant tables, information on births and deaths in the 
inter-census intervals and three important assumptions. The fi rst is that persons 
who die do not make any migrations and die at their place of enumeration at the 
fi rst census. The second is that only one migration is recognised between censuses 
and additional (repeat) migrations are ignored. The third assumption is that fl ows 
from origin 1 to destination 2 are cancelled out by fl ows in the opposite direction. 
Age structures of lifetime migrants available from the 1911 census table are used 
to estimate age structures at other censuses. Death rates based on decennial life 
tables for England and Wales are used to compute survivors and non-survivors. All 



•    Philip Rees, Nik Lomax370

Tab. 3: Contributions to the estimation of period migrant fl ows from lifetime 
migrant stocks

Author(s) (Method) Source Data: Lifetime Number of Estimated Period
Migrant Stocks Territorial Units Migrant Flows

Ravenstein 1885 UK Census Tables 118 counties Not attempted
(Uses Lifetime Data Only) 1881

Friedlander/Roshier 1966 EW Census Tables 53 counties Net intercensal
(Survival Analysis & 1851,1861, 1871, 1881, migrant bi-lateral
Assumptions to generate 1891, 1901, 1911, 1931, fl ows, 6 ten-year
Net Migrant Flows) 1951 intervals and

2 twenty-year
intervals

Abel 2013 WB Stock Tables 191 countries Gross intercensal
(Formulation of problem 1960, 1970, 1980, migrant bi-lateral
as IPF estimation of 1990, 2000 fl ows, 4 ten-year
3 D migrant array, intervals
with maximum stayer
assumption)

Abel/Sander 2014 UN Stock Tables, 196 countries Gross migrant bi-
(Uses Abel 2013a methods 1960, 1970, 1980, lateral fl ows, 8 fi ve-
with UN Migrant Stock 1990, 2000 year intervals
Table, and Circular Migrant
Flows)

Dennett 2016 WB Stock Tables 191 countries Gross migrant bi-
(Uses apportionment 1960, 1970, 1980, lateral fl ows, 4 ten-
probabilities from Global 1990, 2000 year intervals
totals; compares estimates
against IMEM fl ow
estimates and UN fl ow
estimates used by Kim and
Cohen 2010)

Abel 2018 WB Stock Tables, WB 196 countries Gross bi-lateral
(Uses Abel 2013a method 1960, 1970, 1980, UN 232 countries migrant fl ows, for 
with both WB and UN Stock 1990, 2000, UN Stock 10-year intervals
Tables by Gender with Tables, 1980, 1990, (1960-1990) and
successive UN population 2000, 2010, 2015 fi ve-year intervals
and vital statistics (from 1990)
estimates in
comprehensive sensitivity
analysis that yields 90
global migration tables)

Azoze/Raftery 2018a, 2018b UN Stock Tables: UN 232 countries Gross migration
(Adapts Abel 2013a method 1990, 1995, 2000, bi-lateral fl ows for
using Bayesian methods that 2005, 2010, 2015 5-year intervals, 
relax the maximum stayer 1990-95 to 2010-15.
assumption. Factor up fl ows The method
by using ratios from internal converts estimates
migration studies relating of migrants into
1-year and 5-year migration) estimates of

migrations



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 371

this means that the Friedlander and Roshier model can only estimate minimum net 
migrant fl ows. It is not possible to deduce gross fl ows from net as there are many 
pairs of gross fl ow values that would report the same net fl ow. However, their maps 
of net migration fl ows show the dominance of coalfi eld counties (Glamorgan, Mon-
mouth) and of London as main benefi ciaries of net migration in the decades 1861-71, 
1871-1881 of Ravenstein’s analysis, and 1881-91 to 1901-11. The periods 1911-31 and 
1931-51 show a reversal of migration fl ows from South Wales and the North East 
as coal mining declined with a persistence of infl ows to London and surrounding 
counties.

Table 3 shows that we had to wait until the 2010s for a methodological break-
through to be made by Abel (2013). He has subsequently refi ned the estimates in 
four further papers. Figure 3 sets out the 3-dimensional cube of migration fl ows 
invented by Abel (2013) that enabled the estimation of period migration from life-
time migrant stocks. Abel skilfully uses simple numerical illustrations to explain the 
procedures for estimating period migration fl ows from two consecutive migrant 
stock tables. Two faces of the cube represent lifetime migrant data at two succes-
sive censuses (Matrix A and Matrix B). We wish to estimate the contents of the third 
face, migrant transitions for a fi xed time interval (Matrix C). Abel’s insight was to 
realise that if provisional estimates or assumptions of the elements in the three di-
mensional array were proposed, they could be adjusted to agree with the marginal 
totals in Matrices A and B. Matrix C elements were simply a sum of array elements 
over country of birth.

However, it is also useful to set out the general algebraic framework for the esti-
mation, as in Table 4. The notation derives from work on demographic accounting 
(Rees/Wilson 1977; Rees 1985 and Rees/Willekens 1986). The notation used is set 
out in Table 5. The variables to be estimated are migrant fl ows by country of birth 

Tab. 3: Continuation

Author(s) (Method) Source Data: Lifetime Number of Estimated Period
Migrant Stocks Territorial Units Migrant Flows

Abel/Cohen 2019 UN Stock Tables: UN 200 countries Gross bi-lateral
(Test out 6 alternative 1990, 1995, 2000, migrant fl ows,
methods for generating 2005, 2010, 2015 for 5-year intervals
bi-lateral international Validation data: (1990-2015).
migrant fl ows: 2 use stock 45 countries: Correlations of
differencing; 1 uses Immigration fl ows fl ows against
migration rates, 1 uses open Emigration fl ows validation data
demographic accounting + WPP2017:
IPF: 2 use closed Population counts
demographic accounting + Net migration fl ows
IPF or a pseudo-Bayesian
model)

Notes: Abel/Cohen (2019) also discuss two contributions (Beine et al. 2011 and Bertoli 
et al. 2015) which use the net differencing of country i to country j migrant stocks in two 
successive censuses. These methods resemble those used by Friedlander/Roshier (1966).



•    Philip Rees, Nik Lomax372

(i), country of origin at the fi rst census ( j) and country of destination (k), represented 
b y  t h e  v a r i a b l e       in Table 4D. How do we arrive at these period estimates of 
migrant fl ows by place of birth? We start with information on lifetime population 
stocks at the fi rst census,  (Matrix A in Fig. 3, Table 4A) and the second census,  

(Matrix B in Fig. 3, Table 4B). These marginal tables can be used to adjust an 
initial distribution (seed values) of migration fl ows in the full array . The problem 
translates into one familiar to users of contingency tables. Iterative proportional fi t-
ting methods can be used to estimate adjusted array elements, associated with an 
underpinning log-linear statistical model (Deming/Stephen 1940; Bishop et al. 1975; 
Willekens 1983; Rogers et al. 2010). Once an array of variables had been gen-
erated (Fig. 3), then the required migrant fl ows matrix (Matrix C in Fig. 3, Table 4E) is 
obtained as a sum over place of birth of the array variables, that is,  .

A condition for a successful solution to iterative proportional fi tting (IPF) is that 
the totals of elements in the constraint matrices (Matrix A and Matrix B in Fig. 3) 
are the same. Otherwise the IPF procedure will never converge. It is necessary to 
reduce the migrant total for Matrix A by the deaths that occur in the inter-census 
interval and to reduce the migrant total for Matrix B by the births that occur between 
censuses, as Friedlander and Roshier (1966) had earlier incorporated in their meth-
ods. In Table 4A the total deaths in a country, , are shaded in pink, indicating 
the counts are available from vital statistics records or UN estimations using, for 
example, the Demographic and Health Survey. The country of birth of persons dy-

Fig. 3: A framework for estimating period migration from lifetime migration

Source: Drawn by the authors, based on a model by Abel (2013). 

 

 

 

 

 

 

 



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 373

ing is not known, but can be estimated by applying the proportion  from the 
population stocks table to the total deaths over all birthplaces to produce a table 
of estimated deaths. Births are handled differently, simply by assigning total births 
to the country of residence at the second census, that is, .  S u b t r a c t i o n  o f 
deaths from population by country of residence at time t and subtraction of births 
from population by country of residence at time u produces two tables of estimated 
survivors in the third panels of Table 4A and 4B. The totals of these two sub-tables 
must be made equal, , for example, by constructing an average (Abel 2013, 
2018; Abel/Sander 2014). The two sub-table population elements are adjusted to 
agree with this common total.

The IPF estimation model requires specifi cation of initial or seed values of all 
array elements (Table 4C), designated . This process of estimating the origin-
destination-birthplace tables involves two steps: (1) making an assumption about 
the diagonal cells in the array (people who reside in the same country at both start 
and end of the time interval), and (2) estimating initial values of the off-diagonal 
elements (people who reside in a country at the end of the period from that at the 
start). The options for the diagonal include maximization of stayers (as in Abel 2013), 
minimization of stayers or an average of the two. Abel (2018) suggests options for 
the off-diagonal elements include adopting an independence model or introducing 
an interaction matrix which refl ects the diffi culty of moving between countries (e.g. 
spherical distance, airline connections). Azose and Raftery (2018a/b) use a weighted 
average of the assumption of maximum stayers and the independence model as-
sumption, developing a method for optimizing the weights. The IPF procedure is 
carried out conditional on the margin totals and diagonal elements.

A spatial interaction model could be developed for a sub-set of country-to-coun-
try migrant fl ows for which reasonable estimates have been made. Such a model 
was developed by Kim and Cohen (2010), fi tting their model to a UN data set of 
international migration fl ows between industrialized countries. However, the draw-
back would be that if researchers wanted to fi t a global spatial interaction model to 
estimated fl ows, there would be an element of “double-counting”. Given a choice 
of the seed values for the migrant fl ow array, estimates of the full array of migrant 
fl ows can be generated and then summed to produce the country to country matrix 
of fl ows (Matrix C in Fig. 3, Table 4E).

The Abel estimates generate migrant fl ows only for persons existing at time t 
and surviving at time u. Demographic accounting theory (Rees/Wilson 1977) dem-
onstrates that for a complete picture of population change and migration it is neces-
sary to consider migrants hidden in the deaths and births statistics. Table 6 expands 
the matrix in Table 4E by adding transitions for infants born in the period t to u, who 
survive in the destination country at time u (shaded green), the persons alive in the 
country of origin at time t who die in the t to u interval (shaded blue) and the infants 
born in the period who also die before the end of the time interval (shaded brown). 
The off-diagonal elements in each of these additional sub-matrices in Table 5 repre-
sent persons with (at least) one migration in the time interval. The number of such 
“hidden” migrants is likely to be small (perhaps 1 percent of exist-survive migrants) 

 

 

 

 



•    Philip Rees, Nik Lomax374

Tab. 4: Country to country migrant fl ows estimated using the Abel (2013, 2018) 
methods

Source: Based on an interpretation of Abel 2013, Abel/Sander 2014 and Abel 2018.



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 375

but it is better to estimate them than include in the closure error. Methods for esti-
mating these migrant fl ows are described in Rees and Wilson (1977).

Both Dennett (2016) and Azose and Raftery (2018a) regard the Abel estimates 
of bi-lateral migrant fl ows as under-estimates of the “true” fl ows. Of concern are 
migrants who return to their origin country during a time interval and migrants who 
make more than one migration. We have discussed these migration histories ear-
lier (see Fig. 1A). Both authors compared the Abel estimates with the estimates of 
international migration between EU member states (see earlier for a discussion). 
The claim of under-estimation derives from a comparison of Abel estimates with 
migration fl ow estimates between EU member states (Raymer et al. 2011; Raymer 
et al. 2013). However, these international migration estimates are based, largely, on 
adjusted counts of entries to and exits from national population registers, where 
commonly no duration of residence criterion is applied. So, these register-based 
estimates count migration events (Fig. 1F, rightmost graph) rather than (transition) 

Tab. 5: Variable and subscript notation for lifetime and period migrants

Variables Defi nition

P Population (stock)
D Deaths
B Births
X Seed (assumed) values of migrant fl ows before adjustment to migrant

stocks
T Transitions (between state at time t and state at time u)
LM Long-term migrants (UN defi nition)
M Migrations (events of migrating across borders between one area and

another
R Residual balance term in population accounts for migrations
G Grand total of inputs and outputs in population accounts for migrations

Subscripts Defi nitions
t Time at start of period/interval
u Time at end of period/interval
t,u Combination of start and end times, signifying a time period/interval
b Being born during a time period/interval
e Existing at the start of a time period/interval
s Surviving at the end of a time period/interval
d Dying during a time period/interval
i Place/zone of birth (e.g. county within country or country within world)
j Place/zone of residence at time t
k Place of residence at time u
n Number of zones in system studies
+ Sum over the subscript replaced

Note: Subscripts can be placed below the variable they are attached to or above.



•    Philip Rees, Nik Lomax376

migrants (Fig. 1D, leftmost graph). In other words, the comparison is between mi-
grants and migrations. Both are “true” fl ows, conditional on their defi nitions. The 
choice of which estimates to use depends on the application they are used in. Rees 
(1985) showed that either type of fl ow data could be used in a population projection 
based on a components-of-change model, but that a matching projection model 
needed to be used. If, for example, you wished to compute the carbon footprint of 
migrant travel, you would need to use the migration fl ows rather than the migrant 
fl ows. 

Azose and Raftery (2018a/b) make estimates of the migration events additional 
to the number of migrants by borrowing results from three pieces of work on inter-
nal migration that compared one-year migrant rates with fi ve-year migrant rates in 
censuses where the migration question had asked respondents where they were liv-
ing one-year and fi ve-years ago (Long/Boertlein 1990; Rogers et al. 2003 and New-
bold 2005). Azose and Raftery (2018a/b) use an average of 1.5 for the Long-Boertlein 
Index, the ratio of the measured fi ve-year interval migrants to fi ve times the one-
year interval migrants as generated from retrospective questions on previous resi-
dence. The method assumes that migration intensity is constant over the fi ve-year 
interval and that populations are approximately constant. Azoze and Raftery adopt a 
one-year retrospective interval equivalent to the 12-month duration (either prospec-

Tab. 6: Expanded country to country migrant fl ows adding transitions

Notes: Variables: T = transitions. Superscripts: e = exist at time t, s = survive at time 
t+1, d = die in interval t, t+1, b = born in interval t, t+1. Subscripts: 1 … n = individual 
countries in world
Source: Based on Rees/Wilson 1977.



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 377

tive or retrospective) recommended for the measurement of long-term international 
migration by the United Nations. The effect of this procedure is to lift the bilateral 
fl ows of Abel by around 200 percent over 5 years (Abel/Cohen 2019, Table 7). Note 
that despite the paper’s title, Azose and Raftery (2018a/b) do not identify the sepa-
rate contributions of return and transit migrations. Table 7 shows how the Azose 
and Raftery migration estimates fi t into an event-based population accounts table. 

The analyses in Table 3 are not the end of the story. It is necessary to extend 
the estimation to decompose migration fl ows by age, as in Friedlander and Roshier 
(1966). This would provide a better basis for using international migration fl ows in 
a global population projection than assumed the age profi le matched the average 
age profi le parameters of the 17 country case studies in Rogers and Castro (1981a). 
However, this assumes that country of birth and country of residence tables are 
available for age. The censuses and surveys containing lifetime migrant data should 
hold birth date or age at last birthday information, but special tabulations would 
need to be requested from censuses or might be generated from sample census 
microdata.

3.5 The “one-year/fi ve-year” problem

The problem of estimating consistent migration probabilities from data with dif-
ferent retrospective intervals had been observed for France by Courgeau (1973a), 
though his solution was to say that good longitudinal migration histories were 
needed to solve the problem. Courgeau’s paper fi rst identifi ed the clear distinction 

Tab. 7: Estimates of country to country migration fl ows

Notes: M = long-term migration using the UN 12-month duration definition. Migrant flow 
estimates derived from an average of minimum stayer and independence model by multiplication 
of five-year migrant estimates by the Long-Boertlein ratio (5-year migrant count/5× one-year 
migrant count) set to 1.5 based on empirical estimates in Rogers et al. (2003) and Newbold (2005). 

Source: Based on Azose/Raftery (2018a/b), Rees (1985) and Rees/Willekens (1986).



•    Philip Rees, Nik Lomax378

between migrants (persons making a spatial transition between two points in time) 
and migrations (the events of changing locations).

In the 1970s and early 1980s, an ambitious study of future population change 
at regional scale using multi-state methods for 17 countries was carried out at the 
International Institute for Applied Systems Analysis (IIASA) located in Laxenburg, 
Austria by Andrei Rogers and Frans Willekens (Rogers/Willekens 1986). As is usual 
in studies across countries, there were diffi culties in harmonizing the data need for 
input to the software for implementing the projections (Willekens/Rogers 1978). The 
key harmonization problem was to align national migration data with model require-
ments for migration over fi ve-year intervals, matched with fi ve-year ages. Coun-
tries with migration events derived from population registers simply added up fi ve 
years of migrations. Countries which relied on censuses for migration information 
could either supply data based on a one-year retrospective migration question or a 
fi ve-year question. Occasionally, two questions were asked in the national census, 
as in the UK in 1971 (Rees 1979). The existence of two sets of data for the UK ena-
bled Kitsul and Philipov (1981) to experiment with a high- and low-intensity movers 
model which gave reasonably good results, bearing in mind that the one-year data 
(1970-71) were available for just one-year of the fi ve in the fi ve-year data (1966-71).

Having surveyed contemporary research on estimating migrant and migration 
fl ows, we turn attention in the next section to contemporary research into a selec-
tion of Ravenstein’s empirical fi ndings. 

4 Recent research on internal migration patterns

This section is not designed to be a comprehensive review of what we know about 
contemporary internal migration but rather provides illustrations of how contem-
porary migration scholarship carries out analyses of the internal migration patterns 
that Ravenstein studied.

4.1 Comparisons of internal migration across countries: case study 
collections

Using lifetime migration data from censuses in the 1880s and earlier, Ravenstein 
(1889: Maps 1 and 2) describes the regional distribution of foreigners for the coun-
tries of Europe by region and the net gains (absorption) and losses (dispersion) 
in international migration at country scale. Drawing on the 1880 censuses in the 
United States of America (USA), he maps the distribution of the foreign-born pop-
ulation in 1880 across the states of the USA and the provinces of Canada (Map 
3), the gains and losses of state-born, national-born and foreign-born migrants by 
state and province (Map 4), and examples of migration fi elds of dispersion (Map 
5) and absorption (Map 6). Since the 1880s, the systematic comparison of internal 
or international migration patterns across countries has not fi gured prominently, 
with most work focussing on national case studies, brought together in edited and 
informative collections (Nam et al. 1990; White 2016; Champion et al. 2018). Com-



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 379

parison between countries was diffi cult because data types, variable defi nitions 
and theoretical frameworks differ from chapter to chapter, with the editors making 
heroic attempts in discussion chapters to overcome the differences in chapter de-
sign and achieve a true synthesis of knowledge. Rogers and Willekens (1986) sum-
marize the results of an international project covering 17 countries in which authors 
carried out and interpreted the same analysis, a multi-regional population projec-
tion incorporating inter-regional migration by age and sex using common software 
(Willekens/Rogers 1978). One common output across the case studies was a table 
of life expectancy by regions of birth and regions of subsequent residence (e.g. 
Rees 1979: Table 28). The span of life spent outside the region of birth was an index 
of internal migration intensity. In the late 1990s, a study for the Council of Europe 
(Rees/Kupiszewski 1999) focussed on internal migration within ten member states. 
Data on internal migration fl ows supplied by national collaborators at the smallest 
available scale made possible the elucidation of spatial patterns. These were urban 
concentration or de-concentration; the relationship of internal migration (or overall 
population change where internal migration statistics were not available) with popu-
lation density, the links between internal migration and economic conditions, sig-
nalled by unemployment rates, and the relationship of internal migration to gender 
and the life course. The study identifi ed that many countries were still urbanizing; a 
few had adopted a counter-urbanization; and other exhibited an intermediate pat-
tern of net fl ows both down the density gradient from the top and up the density 
gradient from the bottom.

4.2 Development of a robust methodology for comparing internal 
migration across countries

A step change in the ability to compare internal migration came with the publica-
tion of a paper proposing fi fteen measures organized by four measurement dimen-
sions for internal migration: intensity, distance decay, connectivity and effect on 
population redistribution (Bell et al. 2002). The main aim of the paper was to design 
summary indices of internal migration for a country which could be submitted to 
international statistical databases (UN 2019b/c) and constitute the internal migra-
tion component of a Human Migration Database equivalent to the Human Mortality 
and Human Fertility databases (HMD 2019; HFD 2019). In the 2010s, a team at the 
University of Queensland led by Martin Bell have, with funding from the Austral-
ian Research Council, been able to implement this agenda across countries of the 
world (IMAGE 2020a) in collaboration with the Asian Demographic Research In-
stitute, Shanghai. Bell et al. (2015a) provide an inventory of the data sets used, a 
mixture of census and register aggregate tables of migration fl ows, and of census 
and survey individual microdata sets from which fl ow data can be computed, held 
in the an international repository developed by the University of Minnesota (IPUMS 
2019). Table 8 summarises the signifi cant contribution of Bell and colleagues to our 
understanding of internal migration across countries that cover 80  of the world’s 
population.



•    Philip Rees, Nik Lomax380

Tab. 8: Contributions of IMAGE Project Participants to the Analysis of Internal 
Migration

Topic Description Reference

Theory Defi nes four structural dimensions and Bell et al. 2002
16 associated indices for describing
migration fl ows

Data Reviews sources of internal migration Bell et al. 2015a
data in countries of the work and 
describes IMAGE database

Software Describes IMAGE Studio, software for Stillwell et al. 2014
computing indices of migration fl ows at
multiple scales and zoning, to overcome
the MAUP problem in migration
measurement

Intensity Develops a method for standardising Bell/Muhidin 2009, 2011;
the measurement of migration that Bell et al. 2015b;
controls for number and size of zones Courgeau et al. 2012

Distance Investigates the effect of distance Stillwell et al. 2016
on migration fl ows using a spatial 
interaction model for a set of countries 
where detailed fl ow data are available

Impact Uses net migration and migration Stillwell et al. 2000, 2001
effectiveness indices to compare the 
impact of internal migration on 
population in two countries
Uses IMAGE indicators to compare Rees et al. 2017a
the impact of internal migration on 
population redistribution for sets of 
countries and develops a theory linking 
migration directions to urbanization-
counter-urbanization processes

Country Uses selected indicators from the Latin America: Bernard et al. 2017
comparisons IMAGE Studio to compare the structure Asia: Charles-Edwards et al. 
within of migration with continental groups of 2017a/b, 2019;
continents countries Bell et al. 2020

Europe: Rowe et al. 2019

Age Develops methods of harmonizing the Bell/Rees 2006;
age-period-cohort classifi cations of
migration 
Develops simpler models for describing Bernard/Bell 2012; Bernard et al.
the migration-age relationship 2014a,2016; Bernard/Bell 2015
Reconceptualises the migration-age Bernard et al. 2014b
relationship as a product of life
course transitions

Cohort Investigates the role of birth Bernard 2017;
cohort in infl uencing internal Bernard/Pelikh 2019; 
migration patterns in European Bernard et al. 2019
countries and China



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 381

At the core of the IMAGE research was a recognition that the MAUP (Openshaw 
1983) could potentially invalidate any comparison across countries and that meth-
ods were needed to compensate or control for the problem. The MAUP problem 
has two aspects. The fi rst, the scale problem, is that internal migration measures 
tend to increase with increasing numbers and decreasing sizes of the zones used. 
The second, the zoning problem, is that, for any given number of zones, there are 
multiple ways of creating those zones from smaller basic spatial units. Summary 
measures may differ drastically across different groupings of the same number 
of zones (Openshaw 1983: 24, Fig. 2). Stillwell et al. (2014) developed a software 
package that, given the input of a matrix of fl ows between basic spatial units for a 
country and associated populations, computes aggregations of the fl ow data for 
specifi ed numbers of zones and recomputes 15 national summary indices of migra-
tion (Table 2 in Stillwell et al. 2014). For any aggregation (number of zones), values 
of the summary indicators are computed for a user-defi ned number, up to 1,000, of 
different zoning systems with reports of the median, upper and lower quartile val-
ues. It is then possible to evaluate the effect of scale (number of zones) and zonation 
(number of different constructions of the same number of zones) on the outcome 
summary indicator. 

The scale effect is used to construct summary measures of migration intensity, 
drawing on an original proposal by Courgeau (1973b), further developed by Bell and 
Muhidin (2009, 2011) and Courgeau et al. (2012). Bell et al. (2015b) use the Courgeau-
derived methodology to compare migration intensities across the world, linking in-
tensities with development status, with confi dence that the intensities were compa-
rable. The authors used the Aggregate Crude Migration Intensity (ACMI), designed 
to be comparable across countries, to reveal the extraordinary variation in migra-
tion intensity around the world, from a high of 52 percent per annum in South Korea 
to a low of only 5 percent in India. Ravenstein did not discuss migration intensity 
directly in his papers because the period of exposure to the risk of migration in life-
time migrant data was uncertain.

Stillwell et al. (2016) compare the effect of distance on migration volumes using 
the IMAGE software suite to reveal the scale and distance effects and make pos-
sible robust comparisons (see sub-section 4.3). Rees et al. (2017) used measures 

Topic Description Reference

Education Educational differentials in internal Bernard/Bell 2018
migration across the countries of the
world

Temporal Extracts information on temporal Bell et al. 2018
Change change for selected countries and

assesses the intensity decline
hypothesis

Tab. 8: Continuation

Source: https://imageproject.com.au/framework/



•    Philip Rees, Nik Lomax382

of the impacts of internal migration to compare the effects of migration on popu-
lation redistribution, combining the crude migration intensity (CMI) and migration 
effectiveness index (MEI) measures to create a synthetic index of migration impact 
(INMI). A key fi nding was that the MEI was stationary over space down to 20 ASRs 
(Aggregated Spatial Regions, combinations of BSUs, Basic Spatial Units). This was 
an unexpected outcome and important because it was key to development of the 
cross-nationally comparable Index of migration Impact – the INMI. This might be 
regarded as one of the most important fi ndings of the IMAGE project.

Net migration measures were used to examine re-distribution patterns and a 
general theory linked to urbanization was proposed. Papers on Latin America, Asia 
and Europe (Bernard et al. 2017; Charles-Edwards et al. 2017a/b; Bell et al. 2020; 
Rowe et al. 2019) compare on countries within world regions across three of the four 
dimensions of internal migration identifi ed in Bell et al. (2002).

4.3 Distance and migration

The evidence that Ravenstein presented for his short distance generalization (1885-
1 in Table 1) and remarks on long-distance migration (1885-5 in Table 1) came from 
maps of migration rates to or from single counties or through tables of lifetime 
migrants and so were essentially qualitative observations. In the 20th century, re-
searchers measured distances from migrant origins to destinations and related the 
size of fl ows to the distances and other variables. A gravity model of inter-city move-
ment was proposed by Zipf (1946), based on Newton’s formulation of the attractions 
of planetary bodies. Since 1946, a very large number of gravity models of migration 
have been proposed and implemented and the model continues to be used. Poot et 
al. (2016) characterise some recent applications of the gravity model of migration 
as “the successful comeback of an ageing superstar”. The authors make interesting 
proposals for how the model might be used in other applications, such as popula-
tion forecasting.

However, the variety of model forms and explanatory variables in the corpus 
of gravity model case studies make it diffi cult to compare the impact of distance 
on migration across countries. The IMAGE project team therefore approached the 
task of comparing the effect of distance on migration by using a standard model 
for all countries: the doubly constrained spatial interaction model of Wilson (1971) 
with observed out-migration totals as the origin terms and in-migration totals as the 
destination terms, a negative power function and distance measured using national 
grid Cartesian co-ordinates (Stillwell et al. 2016). The IMAGE software was used to 
compute distance decay parameters at different population scales and employing 
different zoning solutions for a fi xed number of zones. Figure 4 presents results for a 
set of countries reporting fi xed interval migration for one-year data. Mean distance 
decay parameters (beta) are averaged over 1,000 different zoning confi gurations at 
each selected zone population size. 

The ranges of betas at different zonal population sizes (Stillwell et al. 2016, Fig-
ure 8) are moderate to small. The graphs of Figure 4 show a feature characteristic 
of most IMAGE analyses: over ranges where the population sizes are small and 



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 383

numbers of zones are large, the distance decay parameter varies substantially by 
size and moves in different directions in different countries. However, for systems 
with fewer, larger zones the parameters for each country are relatively stable and 
can be compared. For example, the mean betas in the population size range 200,000 
to 600,000 show few cross overs. We can be sure, for example, that Swiss migrants 
are more constrained by distance than Australian migrants. For one-year migrants, 
betas are stable from zone sizes of 100,000 population and larger. Countries ex-
hibit greater variation in betas when migrants are measured over fi ve years than 
one year. Stillwell et al. (2016: 1672) summarise that, of those countries which col-
lect one-year migration data, the frictional effect of distance is lowest in the USA, 
Canada, Australia and higher in much of Western Europe. For those countries that 
collect fi ve-year data, those with higher levels of development display lower levels 
of distance friction. 

Most demographic phenomena vary systematically by sex and age. The friction 
of distance is no exception. Figure 5 plots origin-specifi c distance decay parameters 
generated in a study for the UK government by a team led by Stewart Fotheringham 
and Tony Champion (ODPM 2002; Fotheringham et al. 2004). Gravity models were 
fi tted to a time series of migration fl ows (events) between 96 geographic zones in 
England and Wales over 14 years for 14 sex-age groups. The shaded box shows the 
upper quartile, median and lower quartile of the distribution of beta values across 
origin zones. The upper and lower whiskers are located 1.5 times the quartile-me-
dian difference, above and below the box. The numbered circles represent outlier 
zones beyond the whiskers. There is relatively little difference between male and 
female results by age, because men and women mostly migrate as couples or as 

Fig. 4: Mean distance decay parameter by population size, countries with (a) 
5-year and (b) 1-year migration data

0.5

1

1.5

2

2.5

3

0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000

M
e
ta

 b
e
ta

 (
D

is
ta

n
ce

 D
e
ca

y
 P

ar
am

e
te

r)

Mean Population (1,000s)

Norway

Sweden

Australia

Austria

Canada

Denmark

Finland

UK

Germany

Italy

Netherlands

USA

Source: Graph re-drawn based on Stillwell et al. (2016): 1667, Figure 6, with permission 
of the authors. 



•    Philip Rees, Nik Lomax384

families. There are two exceptions. At ages 16-19 many young people enter higher 
education, which in England and Wales often involves a migration. The lower me-
dian and downshifted box plot for young women probably refl ect a preference of 
either the daughters or their parents that they attend university closer to home. At 
ages 60 and over, the median for women and the boxplot extent are higher for wom-
en. At these ages men and women may no longer be together because of death or 
divorce. Men die earlier and so are less exposed to the necessity of migration after 
death of a spouse or partner. At other ages the male and female plots are very simi-
lar but vary systematically by age. Younger adult ages experience lower frictions of 
distance (that is, smaller negative numbers) in a pattern that resembles the plot of 
migration intensity by age.

4.4 Gravity models of migration

The gravity model has been used in hundreds of applications to understand fl ows 
of people, goods, services and investments. Economists have shown a revived in-
terest, as Poot et al. (2016) suggest. However, because disciplines still work in silos, 
Ramos (2016), in his review of gravity models, still claims that the recently assem-
bled UN and World Bank databases of lifetime migrants constitute “bilateral data 
on migratory fl ows”, whereas in section 3.4 we have reviewed the recent attempts 
to convert what is migrant stock data into estimates of migrant and migration fl ows 
over fi xed time intervals. There is not space here to treat gravity models (also called 
spatial interaction models) fully but we briefl y describe some important papers. Sen 
and Smith (1995) and Crymble (2019) provide valuable overviews of gravity models. 
Wilson (1971) developed a family of models based on entropy maximizing meth-
ods and Willekens (1983) showed how similar log-linear models could be derived 
from statistical theory. Flowerdew and Murray (1982), Flowerdew and Lovett (1988), 
Flowerdew (2010) and Congdon (1993) describe Poisson regression models which 
deal with small numbers or zeroes in origin-destination cells. 

Abel (2010) provides an example of a gravity model used to fi ll in missing cells in 
a fl ow table. He fi ts a binomial regression model using an expectation-maximization 
algorithm and co-variates suggested by theory to fl ows between European coun-
tries that are reliably estimated. The model is then used with known co-variates 
to estimate cells where there are no reliable fl ow estimates. Raymer et al. (2019b) 
extend this approach to estimating migration fl ows between ASEAN countries in 
which there are no reliable estimates at all and gravity model parameters are bor-
rowed from fi tting a model to migration fl ows between European countries instead. 
The model parameters are used with ASEAN country co-variates. Here we describe 
some recent work which has advanced our understanding or exposed problems 
that still need to be solved.

A key assumption made in gravity models of internal migration is that there are 
no restrictions on free movements within national spaces whereas between nations 
restrictions based on immigration policy are ubiquitous. History provides examples 
of violations of this assumption, ranging from the eviction of crofters in Highland 
Scotland by landowners leading to mass migration to Scotland’s cities and other 



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 385

countries in the Highland Clearances (1750 to 1860) to the example of China’s Hukou 
system (1950 to the present), which makes diffi cult the relocation of rural migrant 
families to the cities for which they provide vital labour because of restricted ac-
cess to benefi ts (Pradier 2018). On the other hand, Fotheringham et al. (2004) found 
policy variables at local scale (employment or investment programmes) to have lit-
tle infl uence on migration within England and Wales.

Some important decisions need to be made when constructing a gravity mod-
el of internal migration fl ows. First, it is necessary to choose the variable(s) that 
will represent the impedance between origin and destination. Normally, a simple 
distance measure is used. However, Shen (2016) has shown, in modelling inter-
provincial migration in China, that the mis-specifi cation of the spatial interaction 
effect (predictions of the “friction of distance”) leads to absolute mean errors of 
32 percent in migration fl ows compared with 15 percent for each of origin “emis-

Fig. 5: Box plots of origin-specifi c distance decay parameters by sex and age 
group generated from a model used to predict internal migration fl ows 
between 96 zones (Former Health Service Areas) in England and Wales, 
1983-84 to 1997-98

Distance Decay Parameter

Source: ODPM (2002), The Development of a Migration Model, Figure A21.7, p. 301. 
Crown Copyright.



•    Philip Rees, Nik Lomax386

siveness” and destination “attractiveness”. More attention is needed to investigate 
alternatives to the minimum distance between origin and destination. Linked ques-
tions arise about whether the model should be constructed using intra-zone mi-
gration (if available) and how the intra-zone distance might be estimated. Stillwell 
and Thomas (2016) show, employing a person level data set recording postcode of 
origin and destination available from Acxiom Ltd, a marketing technology and ser-
vices company (Acxiom 2019), that conventional geometric methods are inaccurate 
and that including intra-zonal fl ows and a more precise intra-zonal distance based 
on postcode locations improves the goodness of fi t of a spatial interaction model 
substantially. Second, it is necessary to experiment with the mathematical func-
tion of impedance which will be used, because predictions of fl ows are dependent 
on the decision. Openshaw and Connolly (1977) provide a methodology for spatial 
interaction modellers to use. Third, a decision is needed on whether to use a global 
distance prediction parameter (Stillwell et al. 2016) or a set of local parameters 
either attached to the origin or the destination. A related choice is whether to use 
a one-step model or a hierarchical model with several steps (Fotheringham et al. 
2004). Fourth, it is necessary to select or write software that will calibrate the cho-
sen model successfully (Dennett/Wilson 2016). Can the model be transformed into 
a linear equation for which standard regression software will fi t the coeffi cients, or 
should an iterative routine that searches for optimum parameters be used? Fifth, 
consideration is needed about which variables to include in predicting out-migra-
tion from origins and in-migration to destinations. We think Ravenstein would be 
proud of the sophisticated analyses that his simple “law” about migrants moving 
short distances has generated.

4.5 Directions of migration fl ows

Ravenstein’s empirical generalisations arose out of his detailed attention to places. 
His papers are fi lled with list of places (zones) from which lifetime migrants come or 
to which they go. Today such lists are regarded as the raw material from which we 
can discover spatial generalisations. Places have meaning if you are familiar with 
the geography of the country being studied, but we try today to attach numerical 
information to that general knowledge. Ravenstein, being a cartographer by train-
ing, drew many maps to illustrate the patterns or directions of fl ows.

But there is an issue. His maps and ours today are highly selective and convey 
only a fraction of the information embedded in the data. This can be termed a 3N 
problem, where N is the number of regions with a country for which you have mi-
gration information. To represent the matrix of fl ows, you need to draw N maps of 
outfl ows, N maps of infl ows and N maps of the balances. But there are many index-
es you can use: the raw numbers, the raw data converted into percentage shares 
by division by the total infl ow or outfl ow or presented as rates by division of the 
population of the sending region (outfl ows) or receiving region (infl ows). If V is the 
number of useful variables for characterising the fl ows (age, sex, education, ethnic-
ity) then 3N×V maps are needed. In effect, you have created an atlas of evidence for 
the directions of migration. Could not the maps be reduced by plotting simultane-



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 387

ously all the origin to destination fl ows as lines? Such a plot would be unreadable. 
Ravenstein (1885) does draw some line maps for selected sets of fl ows but is careful 
to avoid clashes. Friedlander and Roshier (1966) plot the largest fl ows, which reveal 
the importance of Glamorgan (where most of the South Wales coalfi eld is located) 
in the 1890/99 and 1900/09 decades. The French Demographer, Daniel Courgeau, 
who gave the term "migration fi eld" to the pattern of outfl ows or infl ows around a 
geographical zone, fails to produce any maps of migration in his monograph on 
Les Champs Migratoires en France (Courgeau 1970). For visualization, he relies on 
graphs of migration against generalised distance bands.

Several techniques can be used to overcome some of these problems. Figure 
6 shows how you can plot legible maps for net migration volumes using a propor-
tional circle to represent the absolute number, while using colour to represent direc-
tion (gain or loss), for three separate annual intervals during a decade. The maps 
show continuity of the patterns but with changes in intensity in the third interval 
when the world was still experiencing the consequences of the global fi nancial crisis 
of 2008/09. Another technique, promoted by British Geographer Daniel Dorling, is 
the population cartogram, in which zones are drawn with an area proportional to 
their population, using hexagonal grids. Dorling and Thomas (2004) plot an atlas of 
cartograms based mainly on information from the 2001 Census. Each page offers 
both the variable on a standard geographic base (a transverse Mercator projection 
of Great Britain, produced by Ordnance Survey GB) and the hexagonal population 
cartogram. On pages 61 to 75 of Dorling and Thomas (2004), lifetime migration from 
4 home countries and 11 countries outside the United Kingdom are plotted using 
the 2001 Census data together with change from the previous census in 1991. These 
maps are proud successors to those that Ravenstein drew in 1885 and Friedlander 
and Roshier produced in 1966. Local knowledge is brought to bear to explain unu-
sual changes. For example, “The English born share of the local population has risen 
by two percentage points or more in Corby (as Scottish born immigrants to the steel 
works there have left or died)” (Dorling/Thomas 2004: 61). 

One very successful graphic for depicting migration fl ows that is becoming 
widely used is the circular plot of migration, developed by Nikola Sander, using CIR-
COS open source software (Abel/Sander 2014; Sander et al. 2014a). Figure 7 adapts 
an example from Sander et al. (2018). The plot is for fl ows between regions in the 
UK. Design decisions include selecting the number of regions that can be read in 
the static plot (12) and arranging them in a logical order around the circle. Northern 
regions are placed at the top, Southern regions at the bottom; regions have neigh-
bours with which they exchange signifi cant fl ows; only the larger fl ows are depicted 
so that number of crossings is minimized. There is potential to design interactive 
versions of the circular plots, which can be referenced as part of the supplementary 
material associated with a publication. Failure to take good design decisions can 
result in what Sander et al. (2018) refer to as a “hairball”. Azose and Raftery (2018b) 
use CIRCOS based plots to demonstrate the differences between their estimates of 
country to country migration fl ows and those of Abel and Sander (2014). Circular 
plots are used for each of the 15 Asian country cases of internal migration in Bell et 
al. (2020).



•    Philip Rees, Nik Lomax388

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Ravenstein Revisited: The Analysis of Migration, Then and Now    • 389

4.6 Drivers of migration

It is helpful to consider two kinds of drivers (factors) which infl uence migration: the 
context of the places where migrants live and migrate between and the individual 
characteristics of the migrants which infl uence their propensity to migrate.

The most important contextual drivers are the level and changes in economic 
development, associated with industrialization and urbanization, as Ravenstein rec-
ognised. For most of history cities have been the organisers of the space-economy 
(Jacobs 1970). Starting from a low base in the late 18th Century, the share of the 
world’s population which lives in urban places has grown to 58 percent in 2018 (UN 
2018). In developed countries the urban population makes up between 68 percent 
and 82 percent of the total, with levels of 50 percent in Asia and 43 percent in Africa. 
The populations in some cities in eastern Europe, eastern Asia (Japan) and the rust 
belt of the USA have shrunk in recent decades. The main demographic component 
contributing to urban population growth has been internal migration supplemented 

Fig. 7: Circular plots of migration fl ows between UK regions, 2010-11

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Source: Redrawn by the authors based on Sander et al. (2018: 205, Fig. 16.1) published by 
Routledge.



•    Philip Rees, Nik Lomax390

by international immigration in some developed countries and by natural increase 
in developing country cities. In selected European countries and in the USA in some 
recent decades, there have been net fl ows out of cities (Rees/Kupiszewski 1999), 
which have been termed counter-urbanization. However, often, this counter trend 
has not persisted. A new wave of urban-ward migration has resumed. The popula-
tions in some cities in eastern Europe, eastern Asia (Japan, Korea) and North Amer-
ica have shrunk in recent decades, either as a result of manufacturing decline (e.g. 
Detroit, St Louis) or because of population ageing (e.g. Nagasaki, Busan). However, 
cities have also been spreading as new suburbs are added or new towns develop 
within the commuting fi eld of metropolitan centres. Suburbs and commuting towns 
are growing through internal migration from centre cities and sometimes through 
direct immigration from outside the country.

To monitor the migration processes producing urbanization, suburbanization, 
counter-urbanization and re-urbanization requires careful delineation of function-
al urban regions (FURs) split into cores, suburbs and peripheries. Many countries 
have developed geographical defi nitions of FURs and the European Commission 
has funded several projects to produce harmonised FUR defi nitions across EU 
member states. But FUR defi nitions differ across countries and most developing 
countries lack them. FURs also expand their boundaries over time, necessitating 
decisions about temporal harmonization of boundaries. Different zones within FURs 
(e.g. core, suburbs, periphery) contain rural settlements; zones outside FURs also 
contain urban settlements. Rees et al. (1996) analyses net internal migration trends 
using FUR and density frameworks, illustrating the complexities.

To surmount this defi nitional problem, Rees and Kupiszewski (1999) used pop-
ulation density by small areas within a country as a means of tracking changing 
internal migration patterns in ten EU member states, comparing results from the 
mid-1980s with those from the mid-1990s, straddling the revolution in political sys-
tems between 1989 and 1991. Figure 8, re-drawn from the Great Britain case study 
(Rees et al. 1996) illustrates the utility of the density classifi cation. The data used are 
internal migration fl ows, classifi ed by broad age for males (the female graphs are 
very similar), into and out of GB small areas (wards in England and Wales and postal 
sectors in Scotland) from which net migration rates were computed. Each graph 
plots the overall GB value for the net internal migration rate in each age band against 
density classes arranged from least dense (leftmost) to most dense (rightmost). 

All age bands except for young adult slope from left to right, with positive net 
migration into low density areas which falls away to zero at middling densities and 
becomes negative at the higher densities (the city cores). The declines are steepest 
for the middle working ages (30-44) of high labour force participation and family for-
mation. The graphs for the childhood ages (1-15) parallel those of 30-44 ages but are 
lower at the lowest density end, suggesting some differences between family and 
non-family migration. The downward slopes indicate strong suburbanization and 
counter-urbanization in the 1990-91 observation period, though this is likely to have 
been a high water for this process. The slope was less steep for the late working 
ages, 45 to pensionable age (65 for men and 60 for women in 1991). In the fi nal age 
band, pensionable age and above, there is net migration towards more dense areas 



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 391

Note: Counts of net internal migrants and population by electoral ward are aggregated to 
population density classes and rates computed. 
Source: Data from the 1991 Census, Special Migration Statistics, Crown Copyright. Indica-

tors computed by the authors. Re-drawn from Rees et al. (1996: 72, Fig. 16).

Fig. 8: Net internal migration gains and losses by density classes for age 
groups, males, Great Britain, 1990-91

-40.0

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Net Internal Migration Rate (per 1000 population)

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Net Internal Migration Rate (per 1000 population)

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A g e 6 5 +

Net Internal Migration Rate (per 1000 population)



•    Philip Rees, Nik Lomax392

on the left side of the graphs followed by migration away from dense areas. This 
was interpreted by the authors as a desire among retired migrants not to locate in 
the most remote areas but in small towns in metropolitan peripheries where health 
care and other services were more accessible.

Figure 8 represents the relationship between net internal migration and density 
for one country and time interval. Other researchers had studied this relationship 
across time in one country (Courgeau 1992) and across several countries (Fielding 
1989). The technique was not to group observation areas into density bands but to 
plot net migration rates against density for all areas and then fi t a linear regression 
against the logarithm of population density. Courgeau (1992) splits the 95 départe-
ments into rural and urban parts, showing clearly the transition from a strong ur-
banizing trend in 1954-62 and 1962-68, a fl at trend in 1968-75 and a strong counter-
urbanizing trend in 1975-82.

In the discussion above, we have seen how two individual drivers of migration, 
age and sex, interact with the context, represented by the population densities of 
different settlements. The age profi les of internal migration were studied in the Mi-
gration and Settlement project at IIASA led by Andrei Rogers. Rogers et al. (1978) 
fi rst proposed a model for describing the variation of migration rate with age as a 
set of multi-exponential functions linked to the labour force ages, childhood ages, 
and retirement ages. Rogers and Castro (1981a) used the model to characterise the 
internal migration profi les of the inter-regional migration fl ows in the 17 countries 
of the project.

Subsequently, additional functions were added for: post-retirement migration 
by the elderly (Rogers 1992) and the double peaks at entry to and exit from higher 
education (Wilson 2010). In a Migration and Settlement case study for the UK, Rees 
(1979) observed that that the retirement peak was confi ned to fl ows from big cities 
to retirement regions and that international migration infl ows had a subdued child-
hood slope and a later peak in the labour force function. Wilson (2020) has replaced 
the rising slope of migration intensity in the age band of retirement with a function 
that sees an increase followed by a decrease from age onwards. Rogers and Castro 
(1981b) analyse migration by age schedules by reason for migration, but data sets 
providing this additional information are rare in censuses though more common in 
surveys. The model of the variation of migration by age has been extensively used 
in other analyses and the schedule parameters have been borrowed to decompose 
all age migration fl ows (e.g. in Sander et al. 2014b as input to the Wittgenstein world 
projections of population and human capital).

Bernard, Bell and Charles-Edwards have presented an alternative scheme for 
working with age schedules of migration (Bernard/Bell 2012, 2015; Bernard et al. 
2014a, 2016), which is simpler to implement and more informative. Country profi les 
are classifi ed by age at peak (years), normalized migration intensity at peak and 
overall migration intensity. They defi ne three clusters of countries. The fi rst cluster 
comprises countries with young age peaks (ages 21 or 22), high concentrations at 
peak ages but low overall intensity. The second cluster has peak ages from 21 to 24 
with low concentrations at peak ages and moderate intensities. Countries in a third 
cluster have later peak ages (26 to 29), moderate to low concentrations at peak ages 



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 393

and relatively high overall migration intensities (Fig. 5 in Bernard et al. 2014a). In an 
important contribution to migration theory, Bernard et al. (2014b: 212) proposed:

“a framework that links contextual factors to the age structure of migra-
tion through proximate determinants that directly affect migration ages: 
the prevalence, timing, and spread of life-course transitions. We focused on 
four key transitions that are concentrated at young adult ages and mark the 
passage to adulthood – exit from education, entry to the labor force, union 
formation, and childbirth – and sought to link these to the early-to-mid-20s 
peak commonly found in the age profi le of migration. The proposed frame-
work enabled us to identify the determinants of cross-national differences 
in the age structure of migration and to quantify their relative importance 
across a global sample of 27 countries”.

Other migrant attributes also have important effects. In World Population and 
Human Capital in the Twentieth Century (Lutz et al. 2014; for a précis and review see 
Rees 2018), the authors incorporate fertility and mortality rates decomposed by ed-
ucational attainment categories into a model for projecting the population of world 
countries. Driven by an independent projection of how educational attainment will 
change over the current century, improving education raises survival rates but de-
creases fertility rates in the developing world. The outcome is a set of projected 
populations signifi cantly lower than those of the United Nations Population Division 
(UN 2015). Education provides skills and knowledge to improve both economic and 
social well-being. To a certain extent, education also acts as a surrogate for socio-
economic status, the occupational and income components of which can change 
through upward or downward social mobility, whereas the stock of an individual’s 
human capital is more stable, although subject to gradual obsolescence as knowl-
edge grows or to decreases in mental capacity at older ages. 

Bernard and Bell (2018) showed that, using IPUMS microdata from censuses and 
surveys, it was possible to measure the differences in propensity to migrate across 
educational attainment levels in a large set of countries. The authors showed that 
there was a near universal positive relationship between level of education and the 
propensity to migrate. Education was one of the few socio-economic variables for 
which this was the case. 

Therefore, it should be possible to introduce education as a driver of internal 
migration within sub-national population projections. The links between education 
and migration were largely ignored in Lutz et al. (2014). In recent work for the Euro-
pean Commission, Marois et al. (2019a/b, 2020) use a large microsimulation model 
of the European population to connect international migration to the attributes of in-
dividuals in the sample microdata in order to assess whether the negative economic 
consequences of population ageing can be mitigated through higher immigration, 
higher labour force participation and better integration of new arrivals into the la-
bour force. They fi nd that policies that raise labour force participation rates at older 
ages, that encourage women to enter the labour market and that promote integra-
tion of foreign workers will reduce the increase in the economic dependency rate 
and mean that immigration levels need not be higher than today.



•    Philip Rees, Nik Lomax394

Internal migration also varies by ethnicity and birthplace. International migrants 
by race or ethnicity or birthplace have initial distributions that differ from the native 
population. Subsequently, later generations migrate out of their initial settlement 
locations to other parts of the country. The consequences for the population com-
position by race have been monitored in US state projections by Frey (2015), for the 
population composition of local authorities in the UK by Rees et al. (2011, 2017b) and 
for the birthplace composition of Australian state and local populations by Raymer 
et al. (2019a). The USA has experienced a shift in the destinations of Hispanic im-
migrants from traditional ports of entry to interior cities. In the UK the concentra-
tion of ethnic minorities in large cities has been lessened through out-migration. In 
Australia immigration has been concentrated in the major state capitals but with 
destinations widening over time. The roles of internal and international migration as 
contributors to national and local ethnic population change have been assessed for 
2001-based projected populations (Rees et al. 2013). This analysis extended a de-
composition analysis developed for world population regions by Bongaarts and Bu-
latao (1999), who claim that, when the world is divided into two regions, developed 
and developing, migration does not matter. This is a view that does not apply when 
you drill down to individual countries, sub-national regions and ethnic populations.

4.7 Temporal trends in internal migration

In this review of contemporary analysis of internal and international migration, we 
have not referred to changes over time. Abel and Sander (2014) and Abel (2018) 
showed that the view of international migration as an expanding phenomenon was 
incorrect for the period 1960 to 2015. Yes, the volume of fl ows showed growth over 
time in line with world population change, but, when expressed as a rate in rela-
tion to population, exhibited fl uctuating trends rather than the explosive growth of 
popular commentators. Zelinsky (1971) sets out a profoundly infl uential set of hy-
potheses about the “mobility transition”. Note that his defi nition of mobility encom-
passed human movements including temporary migration, circular migration, daily 
commuting and visiting, a wider concept than the residential migration reviewed in 
this paper. He saw “circulation” as replacing the need for migration in later phases of 
the economic and social development of nation-states (Zelinsky 1971, Fig. 2). With 
hindsight we might extend Zelinsky’s defi nition of circulation to include greater lev-
els/distances of daily commuting, more working from home and telecommunica-
tions, including the internet and broad band replacing the need for migration. Other 
infl uential theories include the model of urbanization, counter-urbanization and re-
urbanization proposed by Geyer and Kontuly (1993). A theoretical framework linking 
development to population redistribution through net internal migration was pro-
posed by Rees et al. (2017a, Fig. 8) and used in the country studies of Latin America 
(Bernard et al. 2017), Asia (Charles-Edwards et al. 2017a/b, 2019; Bell et al. 2020) and 
Europe (Rowe et al. 2019). The relationship of internal migration with development 
was considered in most of the analyses in Table 8, though most are cross-sectional 
except for Bell et al. (2018).



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 395

To test these theories and to clarify the directions of recent change requires 
analysis of long national time series in a robust comparative framework as set out in 
Bell et al. (2002). Champion and Shuttleworth (2017a) assemble from offi cial statis-
tics on migration based on changes in patient address generated from the National 
Health Service Register to examine trends in longer and shorter distance migration. 
Champion and Shuttleworth (2017b) use the England and Wales Longitudinal Study, 
which links individuals across census from 1971 to 2011 to look at trends in the dis-
tances of migration, by type of person covering age, marital status, country of birth, 
occupation, and education. They tested the hypothesis, put forward by Cooke (2011, 
2013), that migration rates were now declining, after demographic composition 
changes (ageing) had been accounted for. In collaboration, Champion et al. (2018) 
recruited authors from the US, UK, Australia, Japan, Sweden, Germany and Italy to 
explore trends in internal migration in a set of highly developed countries. Bell et 
al. (2018) contributed a chapter which examined trends in intensity in 66 countries 
in the IMAGE database for which observations were available for more than one 
period, focusing on changes in the 2000-2010 decade. Was Cooke’s decline trend 
confi rmed? Well, yes and no and maybe (see Champion et al. 2018 for the range of 
case studies with differing outcomes). 

5 Summary and discussion

5.1 Since Ravenstein, how far have we come? 

In the introduction, we briefl y summarised Ravenstein’s key insights into internal 
migration in Britain and in other countries in Europe. His articles also reveal an 
interest in international migration through his maps of foreign-born immigrants in 
the British Isles, selected European countries, the USA and Canada. In section 2, we 
placed the data set used, tables of lifetime migrants by country of residence at the 
census by country of birth, in a more general conceptual framework of defi nitions of 
migrants and migration. In section 3, we tracked further use of this type of migration 
data to the present decade when solutions have been put forward for estimating 
fi xed period migration from lifetime migration data. We made suggestions for the 
further refi nement of these estimates. In section 4, we showed how some of Raven-
stein’s empirical and verbal generalizations had been theorized and quantifi ed in 
20th and 21st century research, covering the topics of migration and distance, gravity 
models of migration, migration fl ow patterns and visualizations, drivers of internal 
migration and the need for extending comparative internal migration analysis over 
time. We now set out an agenda for future work on both internal and international 
migration.



•    Philip Rees, Nik Lomax396

5.2 Agenda for making further progress

The goal in comparing internal migration across countries is to bring the “Cinder-
ella”4 of population change components (migration) to the demographic ball. Ide-
ally, tables of comparable measures of internal and international migration should 
appear alongside the tables of indicators for mortality, fertility and net international 
migration published by the United Nations, the International Organization for Migra-
tion and the World Bank. We ask a series of questions, the answers to which may 
contribute to further progress in estimating, for as many countries as possible, both 
international and internal migration fl ows where data are missing or inadequate.

How can we maximise the number of countries and time period for which 
we have comparable internal migration measures?

The fi rst suggestion focuses on using the rich resources assembled in the IMAGE 
database so that the measures of migration can be assembled for as many countries 
as possible and for as many time periods as possible. For example, the models used 
to produce international migration fl ow estimates from lifetime migrant data could 
be applied to improving estimates of internal migration. Bell et al. (2015a) fi nd that 
109 countries report collection of lifetime migrant data, but little use has yet been 
made of this resource in IMAGE project analyses. Many countries use census or sur-
vey questions on last migration/migrant data which often has an indeterminate time 
reference. Estimating fi xed interval migration from these sources would build up 
the space-time coverage of comparable internal migration measures. The IMAGE 
analyses report on 5-year and 1-year fi xed interval measures separately. The prob-
lem has been investigated many times, but no general solution has been adopted. 
Further research is needed, building on the literature and the recent model pro-
posed by Dyrting (2018). A method for investigating the spatial MAUP has been ena-
bled by the IMAGE studio. An equivalent tool for investigating the temporal MTUP 
(Modifi able Temporal Unit Problem) needs to synthesize the conditional framework 
of Nowok and Willekens (2011) and the migrant heterogeneity models (mover-stayer 
or high mobility-low mobility) of Dytring (2018) and Schmertmann (1999). A goal 
would be to specify a general method for conversion of migration data of different 
intervals to a common interval for international comparison, that derived the under-
pinning intensity of migration from the different data sets and then generated the 
estimation of migration transition rates based on a standard interval.

4 The Cinderella narrative is a global story with Greek and Chinese origins and versions in many 
different cultures (Wikipedia 2019).



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 397

How should we improve the estimates of internal and international 
migration fl ows?

In section 3, methods for fi lling gaps in internal and international migration fl ow data 
sets were discussed. Innovative measures that make best use of available data col-
lections have been proposed. However, offi cial statistical agencies are slow to take 
up these methods and use them to provide continuous time series, despite, in some 
cases, having funded the projects. There are no magic solutions to this problem. It 
is necessary to engage in an open dialogue with offi cial statisticians and other gov-
ernment departments (including local government) which use migration statistics. 
Useful venues are conferences attended by offi cial statisticians, other government 
departments meetings and academics. These conversations are best held outside 
of formal sessions over coffee or meals. Making solving the problem a shared task 
is better than an excuse for scoring points.

How can we use knowledge of internal and international migration in policy 
making?

Most countries and international organizations make use of population projections 
in formulating medium and long-term plans. Assumptions about internal and inter-
national migration are essential ingredients but these are rarely linked to policies. 
Internal migration assumptions usually involve continuation of inter-regional migra-
tion rates for a representative recent period. Poot et al. (2016) suggests there is 
scope to embody gravity models of migration into forecasts, although there would 
be a challenge in forecasting push factors at the origin and pull factors at the des-
tination, as well as a need for better measures of impedance as Shen (2016) has 
pointed out. The uncertainty around future population numbers can be handled 
through specifying variant projections based on judgement or through generating 
probabilistic projections which provide confi dence intervals. Scenarios that specifi -
cally link international migration to policies (Rees et al. 2012; Abel et al. 2016; Cafaro/
Dérer 2019; Marois et al. 2020) provide forecasts of future populations conditional 
on the acceptance of specifi c policies. Such scenarios need a body of evidence to 
show that policies will result in a set direction of change in migration. Time series 
extrapolation, no matter how sophisticated, has a poor track record in forecasting 
international migration (Bijak et al. 2019).

What is the case for a world migration survey?

Willekens et al. (2016: 898-899) have proposed a World Migration Survey (WMS), 
echoing a proposal by the International Union for the Scientifi c Study of Population:

“The WMS should include respondents and partnering institutes in coun-
tries and of origin, transit, and destination and, ideally, should be longitudi-
nal.”



•    Philip Rees, Nik Lomax398

Such a global migration survey might by implemented through the Internation-
al Organization for Migration, the UN Population Division and the Organization for 
Economic Co-operation and Development. The expertise should be harnessed of 
international population research centres such as the Max Planck Institute for De-
mographic Research (Rostock), the Wittgenstein Centre for Demography and Global 
Human Capital (Vienna) and the Economic and Social Research Council Centre for 
Population Change (Southampton) and global polling organizations such as the Pew 
Centre or Gallup organization. The WMS will no doubt be besieged by researchers 
wanting to load their questions into the survey. Procedures should be implemented 
to require question or design proposals to draw up realistic cost/benefi t analyses. 
Key questions that we suggest should be included are those that would unlock the 
value of current information so that existing but unsatisfactory data could be con-
verted to fi xed interval migration data. Willekens et al. (2016: 897) suggest estima-
tion of “fl ow data” as a target concept without elucidating how this is defi ned and 
measured. We hope that the measurement framework set out in section 2 of the 
paper will help clarify what measures should be included. Willekens et al. (2016) rec-
ommend “longitudinal data”, without specifying exactly what that means: alterna-
tives include regular cross-section surveys, surveys in which individuals are linked 
over time or full population registers.

What about climate change and migration?

Future research on migration cannot ignore the climate crisis, which threatens the 
existence of whole island nations and of a share of the world’s population that lives 
in low-lying land vulnerable to sea-level rise. A one degree rise in global mean tem-
perature has already increased storm frequency and the magnitude of droughts and 
increased fl ows of persons displaced by climate change. A requirement of future 
funding of migration research should be to take the climate emergency into as full 
an account as possible (Muttarak/Jiang 2015).

5.3 Concluding remarks

This paper began with a brief survey of the achievements of Anglo-German geog-
rapher, Ernst Ravenstein. His papers have infl uenced much research into migration 
in the century and a quarter since publication. We have reviewed how scholars now 
investigate the phenomena he wrote about. He was an international scholar and 
investigated migration both nationally and internationally. We hope he would be 
pleased with what the fi eld of migration research has achieved and would not be too 
daunted by the challenges of understanding migration in the modern world.

Acknowledgements
The authors are very grateful to the two referees of the paper for their insightful and 
helpful comments.



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 399

References

Abel, Guy J. 2010: Estimation of International Migration Flow Tables in Europe. In: Journal 
of the Royal Statistical Society A 173: 797-825 [doi: 10.1111/j.1467-985X.2009.00636.x].

Abel, Guy J. 2013: Estimating Global Migration Flow Tables using Place of Birth Data. In: 
Demographic Research 28,18: 505-546 [doi: 10.4054/DemRes.2013.28.18].

Abel, Guy J.; Sander, Nikola 2014: Quantifying Global International Migration Flows. In: 
Science 343: 1520-1522 [doi: 10.1126/science.1248676].

Abel, Guy J. et al. 2016. Meeting the Sustainable Development Goals leads to lower world 
population growth. In: PNAS 113,50: 14294-14299 [doi: 10.1073/pnas.1611386113].

Abel, Guy J. 2018: Estimates of Global Migration Flows by Gender between 1960 and 
2015. In: International Migration Review 52,3: 809-852 [doi: 10.1111/imre.12327].

Abel, Guy J.; Cohen, Joel 2019: Bilateral international migration fl ow estimates for 200 
countries. In: Scientifi c Data 6,82 [doi: 10.1038/s41597-019-0089-3].

Acxiom 2019: Power Exceptional Marketing Experiences with a Unifi ed Data & Technol-
ogy Foundation [https://www.acxiom.co.uk/, 06.05.2020].

Azose, Jonathan J.; Raftery, Adrian E. 2018a: Estimation of Emigration, Return Migra-
tion, and Transit Migration between All Pairs of Countries. In: Proceedings of the Na-
tional Academy of Sciences 116,1: 116-122 [doi: 10.1073/pnas.1722334116].

Azose, Jonathan J.; Raftery, Adrian E. 2018b: Estimation of Emigration, Return Migra-
tion, and Transit Migration between All Pairs of Countries: Supporting Information. 
In: Proceedings of the National Academy of Sciences [www.pnas.org/cgi/doi/10.1073/
pnas.1722334115, 06.05.2020].

Beine, Michel; Docquier, Frédéric; Özden, Çağlar 2011: Diasporas. In: Journal of Devel-
opment Economics 95,1: 30-41 [doi: 10.1016/j.jdeveco.2009.11.004].

Bell, Martin et al. 2002: Cross-National Comparison of Internal Migration: Issues and 
Measures. In: Journal of the Royal Statistical Society. Series A: Statistics in Society 
165,3: 435-464.

Bell, Martin; Rees, Philip 2006. Comparing migration in Britain and Australia: harmoni-
sation through use of age-time plans. In: Environment and Planning A 38,5: 959-988 
[doi: 10.1068/a35245].

Bell, Martin; Muhidin, Salut 2009: Cross-National Comparisons of Internal Migration. In: 
Human Development Research Paper 2009/30: 1-62 [hdr.undp.org/en/content/cross-
national-comparisons-internal-migration, 29.04.2020].

Bell, Martin; Muhidin, Salut 2011: Comparing Internal Migration Between Countries Us-
ing Courgeau’s k. In: Stillwell, John; Clarke, Martin (Eds.): Population Dynamics and 
Projection Methods. London: Springer: 141-164 [doi: 10.1007/978-90-481-8930-4_7]. 

Bell, Martin et al. 2015a: Internal Migration Data Around the World: Assessing Contem-
porary Practice. In: Population, Space and Place 21,1: 1-17 [doi: 10.1002/psp.1848].

Bell, Martin et al. 2015b: Internal Migration and Development: Comparing Migration In-
tensities Around the World. In: Population and Development Review 41,1: 33-58 [doi: 
10.1111/j.1728-4457.2015.00025.x].

Bell, Martin et al. 2018: Global Trends in Internal Migration. In: Champion, Anthony; Cooke, 
Thomas; Shuttleworth, Ian (Eds.): Internal Migration in the Developed World. Are We 
Becoming Less Mobile? Oxford: Routledge: 76-98 [doi: 10.4324/9781315589282].

Bell, Martin et al. (Eds.) 2020: Internal Migration in the Countries of Asia: A Cross-Na-
tional Comparison. Springer, in Press.



•    Philip Rees, Nik Lomax400

Bernard, Aude; Bell, Martin 2012: A Comparison of Internal Migration Age Profi le 
Smoothing Methods. In: Working Paper 2012/01. Queensland Centre for Popula-
tion Research, University of Queensland [https://www.yumpu.com/en/document/
view/37450540/a-comparison-of-internal-migration-age-profi le-smoothing-methods, 
29.04.2020].

Bernard, Aude; Bell, Martin; Charles-Edwards, Elin 2014a: Improved Measures for the 
Cross-National Comparison of Age Profi les of Internal Migration. In: Population Stud-
ies 68,2: 179-195 [doi: 10.1080/00324728.2014.890243].

Bernard, Aude; Bell, Martin; Charles-Edwards, Elin 2014b: Life-Course Transitions and 
the Age Profi le of Internal Migration. In: Population and Development Review 40,2: 
213-239 [doi: 10.1111/j.1728-4457.2014.00671.x].

Bernard, Aude; Bell, Martin 2015: Smoothing Internal Migration Age Profi les for Com-
parative Research. In: Demographic Research 32,33: 915-948 [doi: 10.4054/Dem-
Res.2015.32.33]

Bernard, Aude; Martin Bell; Elin Charles-Edwards 2016: Internal migration age patterns 
and the transition to adulthood: Australia and Great Britain compared. In: Journal of 
Population Research 33: 123-146 [doi: 10.1007/s12546-016-9157-0].

Bernard, Aude 2017: Levels and Patterns of Internal Migration in Europe: A Cohort Per-
spective. In: Population Studies 71,3: 293-311 [doi. 10.1080/00324728.2017.1360932].

Bernard, Aude et al. 2017: Comparing Internal Migration across the Countries of Lat-
in America: A Multidimensional Approach. In: PLoS ONE 12,3 [doi. 10.1371/journal.
pone.0173895].

Bernard, Aude; Bell, Martin 2018: Educational Selectivity of Internal Migrants: A 
Global Assessment. In: Demographic Research 39,29: 835-854 [doi: 10.4054/Dem-
Res.2018.39.29].

Bernard, Aude; Pelikh, Alina 2019: Distinguishing Tempo and Ageing Effects in Migra-
tion. In: Demographic Research 40,44: 1291-1322 [doi: 10.4054/demres.2019.40.44].

Bernard, Aude; Bell, Martin; Zhu, Yu 2019: Migration in China: A Cohort Approach to 
Understanding Past and Future Trends. In: Population, Space and Place 25,6: e2234 
[doi: 10.1002/psp.2234].

Bertoli, Simone; Fernández-Huertas Moraga, Jesus 2015: The Size of the Cliff at the 
Border. In: Regional Science and Urban Economics 51: 1-6 [doi: 10.1016/j.regsciur-
beco.2014.12.002].

Bijak, Jakub et al. 2019: Assessing time series models for forecasting international mi-
gration: Lessons from the United Kingdom. In: Journal of Forecasting 38,5: 470-487 
[DOI: 10.1002/for.2576].

Bishop, Yvonne; Fienberg, Stephen; Holland, Paul 1975: Discrete Multivariate Analysis: 
Theory and Practice. Cambridge: MIT Press.

Bongaarts, John; Bulatao, Rodolfo 1999: Completing the Demographic Transition. Popu-
lation and Development Review 25,3: 515-529 [https://www.jstor.org/stable/172345].

Cafaro, Philip; Dérer, Patricia 2019. Policy-based Population Projections for the Euro-
pean Union: A Complementary Approach. In: Comparative Population Studies 44: 
171-200 [doi: 10.12765/CPoS-2019-14en]. 

CeLSIUS 2019: The Offi ce for National Statistics Longitudinal Study (England and 
Wales). Centre for Longitudinal Study Information and User Support, Institute of Epi-
demiology and Health Research, University College London, UK [https://www.ucl.
ac.uk/epidemiology-health-care/research/epidemiology-and-public-health/research/
health-and-social-surveys-research-group/studies-10, 06.05.2020].



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 401

Champion, Tony; Shuttleworth, Ian 2017a: Is Longer-Distance Migration Slowing? An 
Analysis of the Annual Record for England and Wales since the 1970s. In: Population, 
Space and Place 23,3: 1-14 [doi: 10.1002/psp.2024].

Champion, Tony; Shuttleworth, Ian 2017b: Are People Changing Address Less? An Anal-
ysis of Migration within England and Wales, 1971-2011, by Distance of Move. In: Popu-
lation, Space and Place 23;3: 1-13 [doi: 10.1002/psp.2026].

Champion, Tony; Cooke, Thomas; Shuttleworth, Ian (Eds.) 2018: Internal Migration 
in the Developed World: Are We Becoming Less Mobile? London: Routledge [doi: 
10.4324/9781315589282]. 

Charles-Edwards et al. 2017a: Internal Migration in the Countries of Asia, and Spatial 
Impacts. In: ADRI Working Paper Series, ADRI-WP-2017/001. Shanghai: Asian Demo-
graphic Research Institute.[http://www.asianmc.org/wp-content/uploads/2017/10/
ADRI_Working_Paper_Internal_Migration_in_Asia_Final.pdf].

Charles-Edwards, Elin; Muhidin, Salut; Bell, Martin; Zhu, Yu 2017b: Migration in Asia. 
In: White, Michael J. (Ed.): International Handbook of Migration and Population Dis-
tribution. Dordrecht: Springer: 268-284 [doi: 10.1007/978-94-017-7282-2_13].

Charles-Edwards, Elin; Bell, Martin; Bernard, Aude; Zhu, Yu 2019: Internal migra-
tion in the countries of Asia: levels, ages and spatial impacts. In: Asian Population 
Studies 15,2: 150-171 [doi: 10.1080/17441730.2019.1619256].

Congdon, Peter 1993: Approaches to Modelling Overdispersion in the Analysis of Migra-
tion. In: Environment and Planning A 25: 1481-510.

Cooke, Thomas J. 2011: It is not just the economy: declining migration and the rise 
of secular rootedness. In: Population, Space and Place 17,3: 193-203 [doi: 10.1002/
psp.670].

Cooke, Thomas J. 2013: Internal migration in decline. In: The Professional Geographer 
65,4: 664-675 [doi: 10.1080/00330124.2012.724343].

Coulter, Rory; van Ham, Marten; Feijten, Peteke 2011: A longitudinal analysis of mov-
ing desires, expectations and actual moving behaviour. In: Environment and Plan-
ning A 43,11: 2742-2760 [doi: 10.1068/a44105].

Courgeau, Daniel 1970: Les Champs Migratoires en France. Travaux et Documents, Ca-
hier no58, Institut National d’Etudes Demographiques. Paris: Presses Universitaires 
de France.

Courgeau, Daniel 1973a: Migrants et migrations. In: Population (French Edition) 28,1: 
95-129 [doi: 10.2307/1530972].

Courgeau, Daniel 1973b: Migrations et Découpages du Territoire. In: Population 28,3: 
511-537 [doi: 10.2307/1530704].

Courgeau, Daniel 1992: Migration Nette et Densité: la France de 1954 à 1990. In: Popula-
tion 47,2: 462-467 [doi: 10.2307/1533918].

Courgeau, Daniel; Muhidin, Salut; Bell, Martin 2012: Estimating Changes of Residence 
for Cross-National Comparison. In: Population (English Edition) 67,4: 631-652 [doi: 
10.3917/pope.1204.0631].

Crymble, Adam 2019: Introduction to Gravity Models of Migration and Trade. The Pro-
gramming Historian [https://programminghistorian.org/en/lessons/gravity-model, 
29.04.2020].

Darlington-Pollock, Frances; Lomax, Nik; Norman, Paul 2019: Ethnic Internal Migration: 
The Importance of Age and Migrant Status. In: The Geographical Journal 185,1: 68-81 
[doi: 10.1111/geoj.12286].



•    Philip Rees, Nik Lomax402

Deming, William Edwards; Stephan, Frederick 1940: On a Least Squares Adjustment of a 
Sampled Frequency Table When the Expected Marginal Totals are Known. In: The An-
nals of Mathematical Statistics 11,4: 427-444 [http://www.jstor.org/stable/2235722].

Dennett, Adam; Wilson, Alan 2013: A Multilevel Spatial Interaction Modelling Frame-
work for Estimating Interregional Migration in Europe. In: Environment and Planning A 
45,6: 1491-1507 [doi: 10.1068/a45398].

Dennett, Adam 2016: Estimating an Annual Time Series of Global Migration: An Alter-
native Methodology for Using Migrant Stock Data. In: Wilson, Alan (Ed.): Global Dy-
namics: Approaches from Complexity Science. Chichester: John Wiley: 125-141 [doi: 
10.1002/9781118937464.ch7].

Dennett, Adam; Wilson, Alan 2016: Estimating inter-regional migration in Europe. In: 
Wilson, Alan (Ed.): Global Dynamics: Approaches from Complexity Science. Chiches-
ter: John Wiley: 97-124 [doi: 10.1002/9781118937464.ch6].

Dorigo, Guido; Tobler, Waldo 1983: Push and Pull Migration Laws. In: Annals of the Asso-
ciation of American Geographers 73,1: 1-17 [doi: 10.1111/j.1467-8306.1983.tb01392.x].

Dorling, Daniel; Thomas, Bethan 2004: People and Places: A 2001 Census Atlas of the 
UK. Bristol: The Policy Press. 

Duke-Williams, Oliver; Vassilis Routsis; John Stillwell 2018: Census interaction data and 
their means of access. In: Stillwell, John (Ed.): The Routledge Handbook of Census 
Resources, Methods and Applications. Routledge: London: 110-125.

Dyrting, Sigurd 2018: A Framework for Translating Between One-Year and Five-Year Mi-
gration Probabilities [doi: 10.13140/RG.2.2.24261.91362].

European Commission 2019: Measuring Labour Mobility and Migration from Big Data: 
Exploring the Potential of Social-Media Data for Measuring EU Mobility Flows and 
Stocks of EU Movers. Luxembourg: Publications Offi ce of the European Union [doi: 
10.2767/474282].

Fielding, Antony 1989: Migration and Urbanisation in Western Europe since 1950. In: 
The Geographical Journal 155,1: 60-69 [doi: 10.2307/635381].

Flowerdew, Robin; Aitkin, Murray 1982: A Method of Fitting the Gravity Model Based on 
the Poisson Distribution. In: Journal of Regional Science 22,2: 191-202 [doi: 10.1111/
j.1467-9787.1982.tb00744.x].

Flowerdew, Robin; Lovett, Andrew 1988: Fitting Constrained Poisson Regression 
Models to Interurban Migration Flows. In: Geographical Analysis 20,4: 297-307 [doi: 
10.1111/j.1538-4632.1988.tb00184.x].

Flowerdew, Robin 2010: Modelling Migration with Poisson Regression. In: Stillwell, 
John; Duke-Williams, Oliver; Dennett, Adam (Eds.): Technologies for Migration and 
Commuting Analysis: Spatial Interaction Data Applications. IGI, Global: Hershey: 261-
279 [doi: 10.4018/978-1-61520-755-8.ch014].

Fotheringham, Stewart et al. 2004: The development of a migration model for England 
and Wales: overview and modelling out-migration. In: Environment and Planning A 
36,9: 1633-1672 [doi: 10.1068/a36136].

Frey, William 2015: Diversity Explosion: How New Racial Demographics Are Remaking 
America. Washington, DC: Brookings Institution Press. 

Friedlander, Dov; Roshier, R. 1966: A Study of Internal Migration in England and Wales: 
Part I. In: Population Studies 19,3: 239-279 [doi: 10.1080/00324728.1966.10406016].

Geyer, Hermanus S.; Thomas, Kontuly 1993: A Theoretical Foundation for the Concept 
of Differential Urbanization. In: International Regional Science Review 15,2: 157-177 
[doi: 10.1177/016001769301500202].



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 403

Greenwood, Michael 2019: The migration legacy of E. G. Ravenstein. In: Migration Stud-
ies 7,2: 269-278 [doi: 10.1093/migration/mny043].

Grigg, David B. 1977: Ravenstein and the “Laws of Migration”. In: Journal of Historical 
Geography 3,1: 41-54 [doi: 10.1016/0305-7488(77)90143-8].

Hägerstrand, Torsten 1957: Migration and Area. In: Hannerberg, David; Hägerstrand, 
Torsten; Odeving, Bruno (Eds.): Migration in Sweden: A Symposium. Lund Studies in 
Geography. Series B, Human Geography N. 13. Lund, Sweden, C.W.K. Gleerup. 

HFD 2019: The Human Fertility Database. Max Planck Institute for Demographic Re-
search, Rostock, Germany and Vienna Institute of Demography, Vienna, Austria 
[https://www.humanfertility.org/cgi-bin/main.php, 29.04.2020].

HMD 2019: The Human Mortality Database. Department of Demography, University of 
California, Berkeley, USA and Max Planck Institute for Demographic Research, Ros-
tock, Germany [https://mortality.org/, 29.04.2020].

IMAGE Project 2020a: The Image Project: Comparing Internal Migration Around the 
Globe [https://imageproject.com.au/framework/, 06.05.2020].

IMAGE Project 2020b: IMAGE_Studio_rc. [https://github.com/IMAGE-Project, 
06.05.2020].

IOM 2019: Migration Data: The Bigger Picture. International Organization for Migration 
[https://migrationdataportal.org/?i=stock_abs_&t=2019, 29.04.2020].

IPUMS 2019: Harmonized International Census Data for Social Science and Health Re-
search: Integrated Public Use Microdata Series. Minneapolis, MN, USA: Minnesota 
Population Center. [https://international.ipums.org/international/, 06.05.2020].

Jacobs, Jane 1970: The Economy of Cities. London: Cape. 

Kim, Keuntae; Cohen, Joel E. 2010: Determinants of International Migration Flows to 
and from Industrialized Countries: A Panel Data Approach Beyond Gravity. In: Interna-
tional Migration Review 44,4: 899-932 [doi: 10.1111/j.1747-7379.2010.00830.x].

Kitsul, Pavel; Philipov, Dimiter 1981: The One-Year-Five-Year Migration Problem. In: Rog-
ers, Andrei (Ed.): Advances in Multiregional Demography. Research Report RR-81-
006: 1-33. Laxenburg, Austria: International Institute for Applied Systems Analysis. 

Kruithof, J. 1937: Telefoonverkeersrekening (Calculation of Telephone Traffi c). In: De 
Ingenieur 52,8: E15-E25 [https://wwwhome.ewi.utwente.nl/~ptdeboer/misc/kruit-
hof-1937-translation.html, 30.04.2020].

Kupiszewski, Marek; Kupiszewska, Dorota 2011: MULTIPOLES: A Revised Multiregion-
al Model for Improved Capture of International Migration. In: Stillwell, John; Clarke, 
Martin (Eds.): Population Dynamics and Projection Methods. Dordrecht: Springer: 41-
60 [doi: 10.1007/978-90-481-8930-4_3].

Lai, Shengjie et al. 2019: Exploring the Use of Mobile Phone Data for National Migration 
Statistics. In: Palgrave Communications 5,34: 1-10 [doi: 10.1057/s41599-019-0242-9].

Lomax, Nikolas 2013a: Internal and cross-border migration in the United Kingdom: har-
monising, estimating and analysing a decade of fl ow data. PhD Thesis. The University 
of Leeds, School of Geography. 

Lomax, Nik et al. 2013b: Subnational migration in the United Kingdom: producing a con-
sistent time series using a combination of available data and estimates. In: Journal of 
Population Research 30: 265-288 [doi: 10.1007/s12546-013-9115-z].

Lomax, Nik; Norman, Paul 2016: Estimating Population Attribute Values in a Table: “Get 
Me Started in” Iterative Proportional Fitting. In: The Professional Geographer 68,3: 
451-461 [doi: 10.1080/00330124.2015.1099449].



•    Philip Rees, Nik Lomax404

Long John; Boertlein, Celia 1990: Comparing Migration Measures Having Different In-
tervals. In: Perspectives in Migration Analysis. Current Population Reports, Special 
Studies Series P-23,166: 1-12. Washington, DC: US Department of Commerce, Bureau 
of the Census.

Lutz, Wolfgang; Butz, William; KC, Samir (Ed.) 2014a: World Population and Human Capi-
tal in the Twenty-First Century. Oxford: Oxford University Press. 

Manley, Ed; Dennett, Adam 2018: New Forms of Data for Understanding Urban Activ-
ity in Developing Countries. In: Applied Spatial Analysis and Policy 12: 45-70 [doi: 
10.1007/s12061-018-9264-8].

Marois, Guillaume; Sabourin, Patrick; Bélanger, Alain 2019a: How reducing differen-
tials in education and labour force participation could lessen workforce decline in the 
EU28. In: Demographic Research 41,6: 125-160 [doi: 10.4054/DemRes.2019.41.6].

Marois, Guillaume; Sabourin, Patrick; Bélanger, Alain 2019b: Forecasting human capital 
of EU member countries accounting for sociocultural determinants. In: Journal of De-
mographic Economics 85,3: 231-269 [doi: 10.1017/dem.2019.4].

Marois, Guillaume; Bélanger, Alain; Lutz, Wolfgang 2020: Does Europe need immigration 
for demographic reasons? In: PNAS 117,14: 7690-7695 [doi: 10.1073/pnas.1918988117].

Mercer, Arnold; Lau, Arnold; Kennedy, Courtney 2018: For Weighting Online Opt-In 
Samples, What Matters Most? Washington DC: Pew Research Center.

Mulder, Clara H. 2018: Putting family centre stage: Ties to Non-resident Family, Internal 
migration, and Immobility. In: Demographic Research 39,43: 1151-1180 [doi: 10.4054/
DemRes.2018.39.43].

Muttarak, Raya; Jiang, Leiwen (Eds.) 2015: Special Issue on Demographic Differential 
Vulnerability to Climate-Related Disasters. In: Vienna Yearbook of Population Re-
search 2015. Vienna: Austrian Academy of Sciences [doi: 10.1553/populationyear-
book2015s1].

Nam, Charles; Serow, William; Sly, David (Eds.) 1990: International Handbook on Inter-
nal Migration. New York: Greenwood. 

Newbold, K. Bruce 2005: Spatial Scale, Return and Onward Migration, and the Long-
Boertlein Index of Repeat Migration. In: Papers in Regional Science 84,2: 281-290 [doi: 
10.1111/j.1435-5957.2005.00018.x].

Nowok, Beata; Willekens, Frans 2011: A Probabilistic Framework for Harmonisation 
of Migration Statistics. In: Population, Space and Place 17,5: 521-533 [doi: 10.1002/
psp.624]. 

ODPM 2002: Development of a Migration Model. London: Offi ce of the Deputy Prime 
Minister [https://www.researchgate.net/publication/259308761_Development_of_a_
Migration_Model_Analytical_and_Practical_Enhancements, 06.05.2020].

ONS 2015: How has Life Expectancy Changed over Time? Offi ce for National Statis-
tics [https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmar-
riages/lifeexpectancies/articles/howhaslifeexpectancychangedovertime/2015-09-09, 
30.04.2020].

ONS 2019: International Migration − Terms, Defi nitions and Frequently Asked Ques-
tions [https://www.ons.gov.uk/peoplepopulationandcommunity/populationand-
migration/internationalmigration/methodologies/longterminternationalmigration-
frequentlyaskedquestionsandbackgroundnotes#migration-terms-and-definitions, 
30.04.2020].



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 405

Openshaw, Stan; Connolly, C. 1977: Empirically Derived Deterrence Functions for Maxi-
mum Performance Spatial Interaction Models. In: Environment and Planning A 9,9: 
1067-1079 [doi: 10.1068/a091067].

Openshaw, Stan 1983: The Modifi able Areal Unit Problem. Concepts and Techniques in 
Modern Geography (CATMOG) No.38. Norwich: Geo Books.

Pradier, Pierre 2018: The Chinese Hukou System Explained – What is “Hukou” and How 
it Works. Shanghai: New Horizons Global Partners Ltd. [https://nhglobalpartners.com/
author/pierre/, 06.05.2020].

Poot, Jacques et al. 2016: The gravity model of migration: the successful comeback 
of an ageing superstar in regional science. In: Investigaciones Regionales/Jour-
nal of Regional Research 36: 63-86 [https://core.ac.uk/download/pdf/74338682.pdf, 
30.04.2020].

Poulain, Michel; Perrin, Nicolas; Singleton, Ann (Eds.) 2006: THESIM: Towards Harmo-
nised European Statistics on International Migration. Louvain-La-Neuve: Presses Uni-
versitaires de Louvain.

Ramos, Raul 2016: Gravity Models: A Tool for Migration Analysis. In: IZA World of Labor 
239: 1-10 [doi: 10.15185/izawol.239]. 

Ravenstein, Ernst 1876: Census of the British Isles, 1871. Birthplaces and Migration. In: 
The Geographical Magazine July a: 173-177; August b: 202-206; September c: 229-
233.

Ravenstein, Ernst 1885: The Laws of Migration. In: Journal of the Statistical Society of 
London 48,2: 167-235 [doi: 10.2307/2979181].

Ravenstein, Ernst 1889: The Laws of Migration. In: Journal of the Royal Statistical Soci-
ety 52,2: 241-305 [doi: 10.2307/2979333].

Raymer, James 2008: Obtaining an Overall Picture of Population Movement in the 
European Union. In: Raymer, James; Willekens, Frans (Eds.): International Mi-
gration in Europe: Data, Models and Estimates. Chichester: Wiley: 209-234 [doi: 
10.1002/9780470985557.ch10].

Raymer, James; Willekens, Frans (Ed.) 2008: International Migration in Europe: Data, 
Models and Estimates. Chichester: Wiley. [doi: 10.1002/9780470985557].

Raymer, James; Guy, Abel 2009: The MIMOSA Model for Estimating International Mi-
gration Flows in the European Union [https://iussp2009.princeton.edu/papers/92501, 
30.04.2020].

Raymer, James; De Beer, Joop; Van der Erf, Rob 2011: Putting the Pieces of the Puz-
zle Together: Age and Sex-Specifi c Estimates of Migration Amongst Countries in the 
EU/EFTA, 2002-2007. In: European Journal of Population 27,2: 185-215 [doi: 10.1007/
s10680-011-9230-5].

Raymer, James et al. 2013: Integrated Modeling of European Migration. In: Journal of the 
American Statistical Association 108,503: 801-819 [doi: 10.1080/01621459.2013.789435].

Raymer, James et al. 2019a: Estimating a Consistent and Detailed Time Series of Immi-
gration and Emigration for Sub-State Regions of Australia. In: Applied Spatial Analy-
sis and Policy [doi: 10.1007/s12061-019-09310-w].

Raymer, James; Guan, Qing; Ha, Jasmine Trang 2019b: Overcoming Data Limitations to 
Obtain Migration Flows for ASEAN Countries. In: Asian and Pacifi c Migration Journal 
28,4: 385-414 [doi: 10.1177/0117196819892344].

Rees, Philip 1977: The Measurement of Migration from Census and Other Sources. In: 
Environment and Planning A 9,3: 247-272 [doi: 10.1068/a090247].



•    Philip Rees, Nik Lomax406

Rees, Philip; Wilson, Alan 1977: Spatial Population Analysis. London: Edward Arnold. 

Rees, Philip 1979: Migration and Settlement: 1. United Kingdom. In: Research Report 
RR-79-3. Laxenburg, Austria: International Institute for Applied Systems Analysis. 
[http://pure.iiasa.ac.at/id/eprint/1034/1/RR-79-003.pdf, 30.04.2020].

Rees, Philip 1985: Does It Really Matter Which Migration Data You Use in a Population 
Model? In: White, Paul; Van der Knaap, Gert (Eds.): Contemporary Studies of Migra-
tion. Norwich: Geobooks: 55-77. 

Rees, Philip; Willekens, Frans 1986: Data and accounts. In: Rogers, Andrei, Willek-
ens, Frans (Eds.): Migration and Settlement: A Multiregional Comparative Study. 
Dordrecht: Reidel: 19-38.

Rees, Philip; Durham, Helen; Kupiszewski, Marek 1996: Internal Migration and Region-
al Population Dynamics in Europe: United Kingdom Case Study. In: Working Paper 
96/20. United Kingdom: School of Geography, University of Leeds [http://www.geog.
leeds.ac.uk/fi leadmin/documents/research/csap/working_papers_new/1996-20.pdf, 
30.04.2020].

Rees, Philip; Kupiszewski, Marek 1999: Internal Migration and Regional Population Dy-
namics in Europe: A Synthesis. In: Population Studies No.32. Strasbourg: Council of 
Europe Publishing. 

Rees, Philip et al. 2010: DEMIFER: Demographic and Migratory Flows Affecting Euro-
pean Regions and Cities. Applied Research Project 2013/1/3. Annex D6 Report on Sce-
narios and a Database of Scenario Drivers, Annex D7 Regional Population Dynamics: 
A Report Assessing the Effects of Demographic Developments on Regional Competi-
tiveness and Cohesion. Luxembourg: The ESPON 2013 Programme. [https://www.es-
pon.eu/demifer, 06.05.2020].

Rees, Philip et al. 2011: A local analysis of ethnic group population trends and projec-
tions for the UK. In: Journal of Population Research 28,2-3: 149-184 [doi: 10.1007/
s12546-011-9047-4]

Rees, Philip et al. 2012: European Regional Populations: Current Trends, Future Path-
ways, and Policy Options. In: European Journal of Population 28,4: 385-416 [doi: 
10.1007/s10680-012-9268-z].

Rees, Philip; Wohland, Pia; Norman, Paul 2013: The Demographic Drivers of Future Eth-
nic Group Populations for UK Local Areas 2001-2051. In: The Geographical Journal 
179,1: 44-60 [doi: 10.1111/j.1475-4959.2012.00471.x].

Rees Philip et al. 2017a: The Impact of Internal Migration on Population Redistribution: 
An International Comparison. In: Population, Space and Place 23,6 [doi: 10.1002/
psp.2036].

Rees, Philip et al. 2017b. Population Projections by Ethnicity: Challenges and a Solution 
for the United Kingdom. In: Swanson, David A. (Ed.): The Frontiers of Applied Demog-
raphy. Switzerland: Springer: 383-408 [doi: 10.1007/978-3-319-43329-5_18].

Rees, Philip 2018: Education and Demography: A Review of World Population and Hu-
man Capital in the 21st Century (A Demographic Debate Contribution). In: Vienna Year-
book of Population Research 16: 1-17 [doi: 10.1553/populationyearbook2018s037].

Rogers, Andrei; Raquillet, Richard; Castro, Luis 1978: Model migration schedules 
and their applications. In: Environment and Planning A 10,5: 475-502 [doi: 10.1068/
a100475].

Rogers, Andrei; Castro, Luis 1981a: Model Migration Schedules. In: Research Re-
port 81-30. Laxenburg, Austria: International Institute for Applied Systems Analysis 
[https://www.researchgate.net/publication/301286423_Model_MIgration_Schedules, 
30.04.2020].



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 407

Rogers, Andrei; Castro, Luis 1981b: Age Patterns of Migration: Cause-Specifi c Profi les. 
In: Rogers, Andrei (Ed.): Advances in Multiregional Demography. In: Research Re-
port RR-81-6: 125-159. Laxenburg, Austria: International Institute for Applied Systems 
Analysis. [http://pure.iiasa.ac.at/id/eprint/1556/, 30.04.2020].

Rogers, Andrei; Willekens, Frans (Ed.) 1986: Migration and Settlement: A Multiregional 
Comparative Study. Dordrecht: Reidel.

Rogers, Andrei 1990: Requiem for the Net Migrant. In: Geographical Analysis 22,4: 283-
300 [doi: 10.1111/j.1538-4632.1990.tb00212.x].

Rogers, Andrei; James Raymer; Newbold, K. Bruce 2003: Reconciling and Translating 
Migration Data Collected over time Intervals of Differing Widths. In: The Annals of 
Regional Science 37,4: 581-601 [doi: 10.1007/s00168-003-0128-y].

Rogers, Andrei (Ed.) 1992: Elderly Migration and Population Redistribution. London: Bel-
haven. 

Rogers, Andrei; Little, Jani; Raymer, James 2010: The Indirect Estimation of Migration: 
Methods for Dealing with Irregular, Inadequate, and Missing Data. Dordrecht: Spring-
er [doi: 10.1007/978-90-481-8915-1]. 

Rogerson, Peter A. 1990: Migration Analysis Using Data with Time Intervals of Differ-
ing Widths. In: Papers of the Regional Science Association 68,1: 97-106 [doi: 10.1007/
BF01933910].

Rowe, Francisco et al. 2019: Impact of Internal Migration on Population Redistribution 
in Europe: Urbanisation, Counterurbanisation or Spatial Equilibrium? In: Comparative 
Population Studies 44: 201-234 [doi: 10.12765/CPoS-2019-18en].

Sander, Nikola; Abel, Guy; Riosmena, Fernando 2014a: The Future of International Mi-
gration. In: Lutz, Wolfgang, Butz, William; KC, Samir (Eds): World Population and Hu-
man Capital in the Twenty-First Century. Oxford: Oxford University Press: 333-396. 

Sander, Nikola; Abel, Guy; Bauer, Ramon; Schmidt, Johannes 2014b: Visualising mi-
gration fl ow data with circular plots. Working Paper No.2. Vienna: Vienna Institute of 
Demography [http://download.gsb.bund.de/BIB/global_fl ow/VID%20WP%20Visualis-
ing%20Migration%20Flow%20Data%20with%20Circular%20Plots.pdf, 04.05.2020].

Sander, Nikola; Stillwell, John: Lomax, Nikolas 2018: Circular Migration Plots. In: Still-
well, John (Ed.): The Routledge Handbook of Census Resources, Methods and Appli-
cations: Unlocking the 2011 Census. London: Routledge: 203-209. 

Schmertmann, Carl 1999: Estimating Multistate Transition Hazards from Last-Move 
Data. In: Journal American Statistical Association 94,445: 53-63.

Sen, Ashish; Smith, Tony 1995: Gravity Models of Spatial Interaction Behavior. Springer. 
[doi: 10.1007/978-3-642-79880-1].

Shen, Jianfa 2016: Error analysis of Regional Migration Modeling. In: Annals of the Associa-
tion of American Geographers 106,6: 1253-1267 [doi: 10.1080/24694452.2016.1197767].

Simpson, Ludi 2002: Geography Conversion Tables: A Framework for Conversion of 
Data between Geographical Units. In: International Journal of Population Geography 
8,1: 69-82 [doi: 10.1002/ijpg.235].

Solzhenitsyn, Aleksandr; 1991: The Gulag Archipelago, 1918-1956: An Experiment in 
Literary Investigation. English Translation by Ericson, Edward. London: Harvill.

Statistics Finland 2019: Tilastokeskus. Statistics Finland PxWeb Databases [http://
pxnet2.stat.fi /PXWeb/pxweb/en/StatFin/, 06.05.2020].

Stillwell, John 1978: Interzonal Migration: Some Historical Tests of Spatial-Interaction 
Models. In: Environment and Planning A 10,10: 1187-1200 [doi: 10.1068/a101187].



•    Philip Rees, Nik Lomax408

Stillwell, John 1979: Migration in England and Wales: A Study of Inter-Area Patterns, Ac-
counts, Models and Projections. PhD Thesis. Leeds, UK: University of Leeds.

Stillwell, Johnet al. 2000: Net migration and migration effectiveness: a comparison be-
tween Australia and the United Kingdom, 1976-96. Part 1: total migration patterns. In: 
Journal of Population Research 17,1: 17-38 [doi: 10.1007/BF03029446]. 

Stillwell, John et al. 2001: Net migration and migration effectiveness: a comparison 
between Australia and the United Kingdom, 1976-96. Part 2: Age-related migration 
patterns. In: Journal of Population Research 18,1: 19-38 [doi: 10.1007/BF03031953].

Stillwell, John et al. 2014: The IMAGE Studio: A tool for internal migration analysis and 
modelling. In: Applied Spatial Analysis and Policy 7,1: 5-23 [doi: 10.1007/s12061-014-
9104-4].

Stillwell, John; Thomas, Michael 2016: How far do internal migrants really move? Dem-
onstrating a new method for the estimation of intra-zonal distance. In: Regional Stud-
ies, Regional Science 3,1: 28-47 [doi: 10.1080/21681376.2015.1109473]. 

Stillwell John et al. 2016: Internal Migration Around the World: Comparing Distance 
Travelled and its Frictional Effect. In: Environment and Planning A 48,8: 1657-1675 
[doi: 10.1177/0308518X16643963].

Stillwell, John; Daras, Kostantinos; Bell, Martin 2018: Spatial Aggregation Methods for 
Investigating the MAUP Effects in Migration Analysis. In: Applied Spatial Analysis and 
Policy 11: 693-711 [doi: 10.1007/s12061-018-9274-6].

Thomas, Michael; Stillwell, John; Gould, Myles 2014: Exploring and Validating a Com-
mercial Lifestyle Survey for its use in the Analysis of Population Migration. In: Applied 
Spatial Analysis and Policy 7: 71-95 [doi: 10.1007/s12061-013-9096-5].

UN 2015: World Population Prospects: The 2015 Revision. Key Findings and Advance 
Tables. New York: United Nations, Department of Economic and Social Affairs, Pop-
ulation Division [https://population.un.org/wpp/Publications/Files/Key_Findings_
WPP_2015.pdf, 04.05.2020].

UN 2018: 2018 Revision of World Urbanization Prospects. New York: United Nations, De-
partment of Economic and Social Affairs [https://esa.un.org/unpd/wup/, 06.05.2020].

UN 2019a: Big Data: UN Global Working Group. United Nations, Department of Economic 
and Social Statistics, Statistics Division [https://unstats.un.org/bigdata/, 06.05.2020].

UN 2019b: Demographic and Social Statistics: International Migration. United Nations, 
Department of Economic and Social Statistics, Statistics Division [https://unstats.
un.org/unsd/demographic-social/sconcerns/migration/index.cshtml, 06.05.2020].

UN 2019c: Demographic and Social Statistics: Demographic Yearbook System. New 
York: United Nations, Department of Economic and Social Affairs, Statistics Divi-
sion [https://unstats.un.org/unsd/demographic-social/products/dyb/index.cshtml, 
06.05.2020].

US Census Bureau 2019: Census Flows Mapper. [https://fl owsmapper.geo.census.gov/
map.html, 06.05.2020].

Van der Erf, Rob: van der Gaag, Nicole 2007: An iterative procedure to revise available 
data in the double entry migration matrix for 2002, 2003 and 2004. Discussion Paper. 
The Hague: Netherlands Interdisciplinary Demographic Institute [http://mimosa.ge-
dap.be/Documents/Erf_2007.pdf, 06.05.2020].

Van Imhoff, Evert; Keilman, Nico 1992: LIPRO 2.0: An Application of a Dynamic De-
mographic Projection Model to Household Structure in the Netherlands. NIDI-CBGS 
Publication 23. Amsterdam: Swets and Zeitlinger. 



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 409

Wallace, Matthew; Kulu, Hill 2014: Migration and Health in England and Scotland: A 
Study of Migrant Selectivity and Salmon Bias. In: Population, Space and Place 20,8: 
694-708 [doi: 10.1002/psp.1804].

White, Michael (Ed.) 2016: International Handbook of Migration and Population Distribu-
tion. Dordrecht: Springer [doi: 10.1007/978-94-017-7282-2].

Wikipedia 2019: Cinderella [https://en.wikipedia.org/wiki/Cinderella].

Willekens, Frans; Rogers, Andrei 1978: Spatial Population Analysis: Methods and Com-
puter Programs. In: Research Report RR-78-18. Laxenburg, Austria: International In-
stitute for Applied Systems Analysis [pure.iiasa.ac.at/id/eprint/825/1/RR-78-018.pdf, 
04.05.2020].

Willekens, Frans 1983: Log-linear Modelling of Spatial Interaction. In: Papers of the Re-
gional Science Association 52: 187-205 [doi: 10.1007/BF01944102].

Willekens, Frans et al. 2016: International migration under the Microscope. In: Science 
352,6288: 897-899 [doi: 10.1126/science.aaf6545].

Wilson, Alan G. 1971: A family of spatial interaction models, and associated develop-
ments. In: Environment and Planning A 3,1: 1-32 [doi: 10.1068/a030001].

Wilson, Tom 2010: Model Migration Schedules Incorporating Student Migration Peaks. 
In: Demographic Research 23,8: 191-222 [doi: 10.4054/demres.2010.23.8].

Wilson, Tom 2020: Modelling Age Patterns of Internal Migration at the Highest Ages. 
Draft paper. Melbourne School of Population and Global Health, University of Mel-
bourne [https://www.researchgate.net/requests/r69779130, 06.05.2020].

Yule, G Udny 1912: On the Methods of Measuring Association Between Two Attributes. 
In: Journal of the Royal Statistical Society 75,6: 579-652 [doi: 10.2307/2340126].

Zelinsky, Wilbur 1971: The Hypothesis of the Mobility Transition. In: Geographical Re-
view 61,2: 219-249.

Zipf, George Kingsley 1946: The P1 P2/D Hypothesis: On the Intercity Movement of Per-
sons. In: American Sociological Review 11,6: 677-686 [doi: 10.2307/2087063].

Date of submission: 23.12.2019  Date of acceptance: 25.03.2020

Prof. Dr. Philip Rees (), Dr. Nik Lomax. School of Geography, University of Leeds. 
Leeds, United Kingdom. E-mail: p.h.rees@leeds.ac.uk, N.M.Lomax@leeds.ac.uk
URL: https://environment.leeds.ac.uk/geography/staff/1094/professor-philip-rees

https://environment.leeds.ac.uk/geography/staff/1064/dr-nik-lomax



•    Philip Rees, Nik Lomax410

Appendix: Summaries of Ravenstein’s Findings by Later Authors

Tab. A1: Key points from Ravenstein’s 1876 papers as interpreted by Greenwood

Year-# Text Pages

1876-1 Centres of industry and commerce tend to grow more rapidly p.271
than agricultural areas, with large towns growing more rapidly
than surrounding rural areas. The observed differences in
population growth patterns are due to migration.

1876-2 People migrate to towns from nearby rural areas, and migrants p.271
from more distant places fi ll the gaps left in the rural areas. Thus, 
Ravenstein sees migration occurring in stages, and he believes
that with respect to growing towns the nearby potential labour
supply is quickly depleted.

1876-3 Migration decreases with distance, an observation based on p.271
London and to a lesser extent on Glasgow, but other places as
well.

1876-4 Migration is not determined by distance alone, but rather also is p.271
shaped by ‘facility of access’ and ‘local circumstances’, which at
least in part apparently means the quality of roads and the
transportation system. Thus, at least in some limited sense, the
public sector may facilitate migration.

1876-5 Intervening opportunities tend to absorb migrants to any given p.271
urban destination.

Source: Ravenstein (1876), Greenwood (2019).



Ravenstein Revisited: The Analysis of Migration, Then and Now    • 411

Tab. A2: The summary of Ravenstein’s Laws by Grigg (1977)

Source: Grigg (1977).

Year-# Text Pages

1977-1 The majority of migrants go only a short distance. p.44

1977-2 Migration proceeds step by step. p.47

1977-3 Migrants proceeding long distances generally go by preference p.48
to one of the great centres of commerce and industry.

1977-4 Every migratory current has a counter-current. p.48

1977-5 The natives of towns are less migratory than those of rural districts. p.48

1977-6 Females are more migratory than males within the kingdom of p.49
their birth, but males move more frequently abroad.

1977-7 Most migrants are adults; families rarely migrated. p.49

1977-8 Towns grow more by migration than natural increase. p.50

1977-9 Migration increases as industries develop and the means of p.52
transport improves.

1977-10 The major direction of migration is from the rural areas to p.52
the towns.

1977-11 The main causes of migration are economic. p.53



•    Philip Rees, Nik Lomax412

Tab. A3: Key points made about Ravenstein’s work by Dorigo and Tobler (1983)

Source: Dorigo and Tobler (1983).

Year-Law# Text Pages
Push and Pull Migration Laws, Dorigo/Tobler (1983), quoted in
Greenwood (2019)

1983-1 ‘Counties having an extended boundary in proportion to their p.5
area, naturally offer greater facilities for an infl ow ... than others 
with a restricted boundary’ (Ravenstein 1885: 175). 
Boundaries, or the geographic size of the spatial unit over 
which migration is measured, are clearly of great importance, 
but this observation was not noted by others.

1983-2 (Migration streams) ‘sweep along with them many of the p.10
natives of the counties through which they pass (and) deposit, 
in their progress, many of the migrants, which have joined them 
at their origin’ (Ravenstein 1885: 191). With some imagination, we 
might view this statement of Ravenstein as an early indication of 
the family and friends hypothesis regarding migration. However, 
Ravenstein does not indicate any thoughts about what forces 
underlie the infl uence of family and friends-forces such as 
information provided by earlier migrants, their social ties, or the 
miniature private social benefi ts due to the presence of prior 
migrants from their origin who may provide food, shelter, and 
information to the newly arrived migrants.

1983-3 ‘Migratory currents fl ow along certain well defi ned geographical p.12
channels’ (Ravenstein 1889: 284). This point is related to that
immediately above, but is broader (Dorigo/Tobler, p. 12).
Features of the transportation system are likely to play a critical
role in this regard. A good example is found in US historical
migration from the South to the North. Railroad and highway
systems, as well as the Mississippi river, generally ran more or
less directly south to north with a chain of mountains 
(the Appalachians) separating the two south-to-north paths. 
Consequently, northern seaboard cities received migrants 
disproportionately from Florida, Georgia, the Carolinas, and 
Virginia, whereas Midwestern cities like Chicago, Detroit, 
Cleveland and St. Louis received migrants from Alabama, 
Mississippi, Louisiana, Texas, and Tennessee.



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