This chapter turns to quantitative methods, conventionally seen as opposed to the qualitative ones, even if this dichotomous distinction is seen as ambiguous. In this chapter, quantitative research will be seen as an ‘umbrella’ term (Bryman, 2012), a departing point to present and discuss a range of methodological issues relevant for migration studies.

Methodology and methods differ between and within disciplines and this is also the case for migration research. On the one extreme, economics relies largely on quantitative approaches. On the other, anthropology relies largely on qualitative fieldwork, with other disciplines placing themselves in between (e.g. for a variety of methods used in population geography, see Findlay and Li (1999)). Additionally, disciplines in various regions often follow different traditions regarding the methods they use. For example, quantitative methods are prevalent in sociology and political sciences in the USA (Castles, 2012), and less popular in the UK (Payne, 2014). Recently researchers have more often resorted to mixed-method approaches (defined as combining qualitative and quantitative research, see Tashakkori & Teddlie, 2003) or proposed interdisciplinary research in areas such as migration and development. This adds a new level of complexity and allows uncovering the multiple facets of migration (Castles, 2012). In the last years, big data and computational social science have opened up a new and promising avenue for studying migration and mobility, raising new issues and ethical challenges (Spyratos et al., 2018; Zagheni & Weber, 2015).

This chapter engages with social surveys and experimental research as examples of quantitative approaches to studying migration. Surveys have been a much more popular choice among migration researchers than experiments, but it is the juxtaposition of the two types of research that highlights their specificities, advantages, and limitations. Further, the chapter discusses in more detail two topics: cross-national designs and longitudinal data. Cross-national and longitudinal studies are not the most prevalent, but they are perhaps the most challenging in quantitative research on migration and important because of the particular insights they can offer. Necessarily, quantitative methods in migration research cover a broader range of issues than this chapter will address. However—with non-specialist language for non-quantitative researchers—this chapter will aim to gently introduce the described topics whilst pointing to literature for further exploration.

1 What Is So Specific About the Survey and Experimental Research on Migration?

1.1 Survey Research on Migration

More generally, in social research surveys are designed to produce systematic and structured data, to describe, in a quantitative way, selected aspects of the population under study (e.g. De Vaus, 2002; Fowler, 2014; Gideon, 2012). Over the years, surveys have also extensively been used to address the demand for data (or more data) on migration (Font & Méndez, 2013a), to provide statistics and quantitative descriptions on a wide range of topics, including, among others, the first and second generation, and the process of economic, social, and political integration. In general, the focus of existing studies has been more on substantive issues and less so on specific methodological challenges related to this kind of research, even if a general survey methodology applied to migration research usually requires adaptations and new strategies, in particular related to sampling and data-collection (Font & Méndez, 2013a).

Surveys, as opposed to censuses, collect information from a sample to make inferences to the whole population, when studying the whole population would be more time-, energy-, and cost-intensive. However, one of the first issues in migration research may be an operational definition of the population under study. For instance, in the context of surveying ethnic minorities in the UK, Erens (2013) highlights the very different ways in which ‘race’ and ‘ethnicity’ have been defined, with reference to country of birth, nationality, language, religion, skin colour, culture, and ancestry. Even if the target population is well defined, the sampling frame (a list of individuals in the population from which a sample is drawn) may be missing or it is inadequate to study selected groups of migrants, as it is a case of migrants without a legal residence status or highly mobile expats. In the face of a lack of good sampling frames, some non-random sampling strategies have been used, which do not use probability methods but other criteria for sample selection. These include, among others, Respondent-Driven Sampling (RDS, originally proposed by Heckathorn (1997) to study hidden and stigmatised populations), a version of snowball sampling, which starts with an initial set of respondents, called ‘seeds’, who initiate chain recruitment within their networks. In the RDS, unlike in snowball sampling, the recruitment process is tracked by researchers via the transfer of individualised coupons (for examples of RDS in migration research, see Johnston & Malekinejad, 2014; Tyldum & Johnston, 2014). In turn, Adaptive Cluster Sampling (ACS) can be used in case of rare populations with tendencies to cluster, like migrants of a particular ethnic origin in a city. The ACS relies on a two-step strategy, combining probability sampling and, after identifying households from the ethnic group of interest, including neighbouring addresses in the sample (Lavallée, 2014). This said, to be successful, both the RDS and ACS strategies usually require some exploratory research to gain knowledge about the population under study before the survey is carried out.

Apart from sampling, migration surveys also face specific data collection issues. In survey research where interviewers administer questionnaires, interviewers are typically trained to collect information, to persuade reluctant respondents to take part and to probe (if the respondents did not give complete answers) to ensure high data quality (de Leeuw, 2008). Nevertheless, interviewers can also become a source of bias (Groves et al., 2009), when the characteristics of the interviewer are related to the contents of the question. In migration surveys, the ethnic background of an interviewer can be, more generally, one among a set of similar characteristics shared by interviewer and respondent, and as such, it may be related to higher cooperation rates (Durrant et al., 2010). Studies that addressed the question if the interviewers from different ethnic backgrounds receive systematically different answers to the same survey questions, brought mixed results (for an overview, see Van Heelsum (2013) about different populations’ surveys, research topics, and possible explanations of interviewer effect in case of interviewers from different ethnic backgrounds than respondents).

Apart from standardised interviews (administered by the interviewer), recent years also saw the development of online surveys (self-administered by respondents when it is convenient to them). While there is a general concern about bias in online research (Askitas & Zimmermann, 2015; Bethlehem, 2010), online surveys can provide new sampling strategies for migrant populations (e.g. Pötzschke & Braun, 2017). Online surveys also solve some data collection issues, in that they allow the researcher to reach a geographically dispersed population and to do so relatively fast and relatively cheap, especially compared to face-to-face interviews (for one example, see Kaša and Mieriņa’s (2019) large-scale Emigrant Communities of Latvia survey describing in detail transnational and national belonging).

These difficulties related to sampling and data collection can be summed up by describing migrants as a “difficult to survey population” (Tourangeau et al., 2014). Depending on the studied group, these challenges may be multiple: migrants can be highly mobile, they can be difficult to access because of their unauthorised residence status, they can lack trust towards the destination society, they can be stigmatised, or not speak the survey language (for a more comprehensive overview of issues see Massey (2014)).

Survey research can be used on its own or in combination with other methods. Ethnosurvey is one example of a mixed-methods approach in the migration field. Ethnosurvey is a combination of a survey using probability sampling, which is informed by and informs ethnographic fieldwork. The Mexican Migration Project utilised ethnosurvey in studying communities on both sides of the Mexico-US border. This allowed recording the richness of migration patterns (temporary and circular, return), changes in settlement status, shifts in forms of economic and social activity and recording migration without authorised status (see original articles by Massey (1987, 1999), which inspired research in other parts of the world using similar methodology).

1.2 Experimental Research on Migration

Social surveys are used to provide quantitative descriptions and explain patterns of association in the data, but they are limited regarding cause-effect associations, which are studied using experiments. Conventional definitions describe how the experiments usually consist of two measurements made at the beginning and the end of the experiment (that is, after the experimental treatment is administered) for the treatment group (which undergoes intervention) and the control group (which does not receive any treatment). A statistically significant difference in the amount of change between the two measurements for treatment and control groups is interpreted as the causal impact of the treatment (see handbooks by Davis (2003); Friedman & Sunder, 1994).

Unlike survey research, experimental methods have been used to a much lesser degree in migration studies and are also missing in major broad overviews of migration (as noted by Baláž and Williams (2017)). Among experimental research, quasi-experiments or natural experiments are most common. Natural experiments focus on real-life behaviour and its changes with external events, such as exchange rate shocks or natural disasters. In natural experiments, as opposed to field and laboratory ones, the researchers cannot control the sample or the change that occurs, but on the advantages side, the sample sizes are large and external validity high (Baláž & Williams, 2017). Examples of natural experiments cover research on how origin households responded to changes in exchange rates (related to the 1997 Asian financial crisis), such as Philippine overseas migrants in several destinations (Yang, 2008; Yang & Martinez, 2006); on famine and seasonal migration in Bangladesh (Bryan et al., 2013); on political shocks and skilled migration (Chand & Clemens, 2008).

Natural experiments evaluating policy interventions are sometimes referred to as “policy experiments” (McKenzie, 2012), examining the impact of migration, for instance, on income (McKenzie et al., 2010) and health (Stillman et al., 2009). This strand of research examines data coming from visa lotteries employed in some destination countries. McKenzie (2012) enlists sampling strategies, which include use of administrative data (on applicants to the lottery, both winners and losers), combined with migrant tracking (McKenzie et al., 2010); personnel records from a technology company, since many of its employees applied to the lottery (Clemens’ (2010) research on H1-B visa channel for highly skilled migrants to the US) or surveying households in the migrant-sending country for lottery winner and loser household members (Gibson et al., 2013).

In turn, field experiments or “researcher-designed experiments” are more focused on studying migration processes rather than policy interventions (McKenzie & Yang, 2010). Sampling is more often reliant on convenience sampling strategies, which bears implications for the external validity of this type of research. Some topics covered in this strand of experimental methods are savings and remittances (Ashraf et al., 2011; Chin et al., 2011); studies of discrimination faced on the labour market by job applicants with foreign experience or foreign-sounding names (Oreopoulos, 2011); or discrimination on the housing market (Bosch et al., 2010).

Laboratory experiments in migration research are rare, and they are usually conducted on small and selective samples, making external validity problematic. The focus of enquiry in laboratory experiments in experimental economics, behavioural economics, and experimental psychology differs, ranging from examining the impact of economic institutions on individual behaviour (experimental economics) to impact of individual characteristics (experimental psychology) (see Baláž and Williams (2017) also for an overview of the studies and topics).

A study by Bah and Batista (2020) exemplifies an application of an incentivised lab-in-the field game (moving the experiment from a laboratory to a more natural setting, making it closer to real-life behaviour), studying irregular migration from West Africa to Europe using hypothetical scenarios referring to the probability of death on the way to Europe and possibility of securing legal residency status in the destination.

One particular advantage of experimental research in the migration field is that it holds the potential to overcome selection challenges in studying migration. McKenzie (2012) explains that experiments allow comparisons where the reason why household members who engage in migration and those who do not engage in it, are just pure chance. Other advantages are more related to characteristics of experimental research in general, including more control to identify relationships by design; more variation, with the treatments designed by the researcher, regardless of the fact if they occur in the real world; and selectivity, with cases allocated randomly into the experimental and control groups (Baláž & Williams, 2017).

2 Selected Issues: Cross-National Designs and Longitudinal Studies

2.1 Cross-National Designs

While surveys in the migration context face specific challenges, comparative cross-country designs add a new layer of complexity to a single-country study (Lynn et al., 2006). In this section, the focus will mostly be on cross-national survey research in the context of multilingual and multicultural studies (Harkness et al., 2010a). International survey programmes and smaller-scale comparative surveys on migration draw comparable samples and prepare comparable sets of questions. Once the data is collected, the datasets from the countries involved are pooled together, and researchers seek to identify patterns and assess how these patterns differ by country. The purpose of such cross-country research, as with surveys, can be descriptive in aim or explanatory, with comparative logic used to explain similarity and variation across countries. Importantly, the challenge of comparative research is to uncover the ‘real’ differences between studied contexts rather than differences that can be attributed back to the methodological differences (referring to sampling, data collection process, coding frames, see De Vaus, 2008). Cross-national surveys require special methodological considerations which allow studying and comparing results on two or more populations of interest, including issues at the different stages of the survey process, design of questions and pretests, pretests, translation and adaptation, data collection, documentation, harmonisation, quality frameworks, and analysis (Harkness et al., 2010b).

Crucially, cross-national surveys can vary in a way in which they are deliberately designed comparatively, with regards to sampling strategies, data collection, documentation of the process and data harmonisation (Harkness et al., 2010b). The two main approaches to harmonisation of the survey data (to ensure comparability across countries) are ex-ante and ex-post harmonisation. Ex-ante harmonisation is a part of survey design (“surveys comparative by design”, see Lynn et al. (2006)) and occurs before data collection. The European Social Survey (ESS) is an example of a large-scale survey programme, academically driven and cross-national, paying particular attention to develop standards of rigour in cross-national research. It is a general population survey that enquires, among others, about attitudes towards migration. In turn, ex-post harmonisation only harmonises output, so it makes comparable already existing datasets (for migration example, see the International File of Immigrant Surveys by van Tubergen, quoted in Wolf et al. (2016)).

In cross-national research, indicators provide the basis for comparisons, and functional equivalence of the indicators can be assessed using several analytic techniques (Braun & Johnson, 2010). Scheuch (1968) describes difficulties in achieving functional equivalence, using as an example a question from the Bogardus social distance scale, asking about the extent to which one would accept certain ethnic and religious groups as a neighbour living in the same street. The question asked in the German context altered the wording, asking about having a ‘greeting acquaintance’ instead, as this category worked well in the German context to describe the social distance scale of respondents. This example shows that knowledge about cultural contexts is valuable when developing such indicators. Ideally, the indicators are developed before reaching the final version of the questionnaire in the process of pretesting and instrument refinement, but due to time and financial constraints, this is not always practice followed in the multiple survey locations (Mohler & Johnson, 2010).

Cross-national research often requires specific translation strategies and assessment procedures. Harkness et al. (2010c) highlight the rule of thumb according to which the translated text of the target questionnaire is supposed to ‘stay close’ to the source/master text, and questions should have semantically similar contents and format. Word-for-word translations are often neither possible nor acceptable. The need for translation may reflect that the population for which the translation is carried out operates in the context of different social and cultural norms; hence close relation between design translation and adaptation is necessary. However, current theoretical debates are missing context when developing questionnaires and translating them in comparative research (Harkness et al., 2010c).

With regards to sampling, often uniform sampling designs across all countries are not possible in cross-country research (Heeringa & O’Muircheartaigh, 2010). For instance, when researching newly arrived migrants in Germany and the Netherlands, researchers can use local population registers as a sampling frame, but countries like Ireland and the UK lack comparable sources of information, which is a great challenge for comparative research (Diehl et al., 2016).

Finally, cross-national research experience also includes challenges related to organisational demands and survey traditions across countries, communication channels in multinational settings and documentation (Harkness et al., 2010b).

2.2 Longitudinal Studies

Longitudinal designs, as opposed to cross-sectional ones, involve data collection across time, usually from individuals. We can distinguish between prospective longitudinal research designs (panels) and retrospective data. In the latter case, biographic data is collected just once, reconstructing individual biography in time, but not entailing a longitudinal research design (Beauchemin & Schoumaker, 2016; Elliott et al., 2008).

Quantitative retrospective research on migration has mainly referred to internal migrations and focused on themes of residential mobility, family formation (including marriages and births) and socio-economic trajectories (including education and employment spells). It allowed reconstructing migration trajectories from the life course perspective, analysing links between spatial mobility and other life spheres, such as family, education, employment (Beauchemin & Schoumaker, 2016). In research on international migration, retrospective data allowed uncovering processual character of migrations, including documenting phenomena such as seasonal and circular migrations (such as an ethnosurvey, mentioned earlier). What is more, retrospective research can involve sampling in destination and origin (both-ways or bi-national research, see Rallu (2008); Guendelman (2014) to understand better the consequences of migration (sampling in the destination only captures migrant stayers, excluding the out-migrants who re-migrated, and how their integration trajectories may differ). To facilitate respondents’ recollection of the past, researchers have developed various instruments and techniques to aid respondents with the recollection of events, among these life history calendars, sequential questionnaires and matrices (Beauchemin & Schoumaker, 2016). One example of retrospective research is the MAFE survey, examining migration between Sub-Saharan Africa and Europe and collecting data about individual life histories of migrants, non-migrants and returnees (Beauchemin & González-Ferrier, 2011).

Prospective surveys (panels) follow the same individuals over time, with several measurements made in time (Jasso, 2014). We can distinguish between panels focused on migrants like in case of studies as Longitudinal Survey of Immigrants to Australia or Canadian Longitudinal Survey of Immigrants (for a more comprehensive list, see Font and Méndez (2013a)) and general population panels oversampling migrants (like the German Socio-Economic Panel). The focus of panel studies has been on the socio-economic outcomes in the destinations, and particularly important have been studies of recent migrants to track the inclusion and exclusion in different social spheres in the destination (Jacobs, 2010). Panel studies tend not to focus on migration because of challenges to repeated measurement in the case of mobile respondents. Not finding the respondent at the following measurement may mean that the person has moved (internally or internationally), but other reasons for attrition are possible. Comparisons between the absentees to the panel (among whom some will be migrants) and the rest of the sample seek to answer sets of questions about the scale of out-migration in the area covered by the survey; about determinants of this out-migration and, finally, about the consequences of out-migration on the origin (however keeping in mind possible other sources of attrition, see Beauchemin & Schoumaker, 2016). Analytically, using longitudinal data of several cohorts of migrants allows distinguishing between cohort and duration effects, that is, conditions at the time of migration in origin and destination versus conditions related to experiences in the destination (Jasso, 2014).

Still, longitudinal research is rare; in particular, panel studies take time to carry out and entail higher financial costs and face panel attrition risk. In turn, retrospective studies deal with data quality issues, including memory biases, as normally recollecting the events from the past entails mistakes, memory lapses and distortions. Also, the duration of an interview recording life histories can become lengthy. Regarding ethics, the particular challenges raised in longitudinal research are confidentiality, where more information is amassed about each individual, raising concerns about the risk of identification. Researchers need to obtain repeatedly informed consent from participants (Elliott et al., 2008).

3 Conclusion

This chapter offers an overview of selected topics within a broad literature on quantitative methods in the migration field, describing survey and experimental research along with cross-national and longitudinal approaches. This overview guides the reader through some of the key advantages and challenges of doing quantitative research on migration.

While surveys and experiments bring us a better understanding of migration, they do so from different angles. Surveys provide quantitative descriptions and patterns of relationships between the variables. Perhaps the notion of ‘hard-to-survey’ populations best highlights the challenges that are involved at various stages of research on migrants (with questions of access, trust and linguistic issues, among others). The experiments, ideally, aim for studying cause-effect associations. Adding a cross-national perspective in migration research usually provides a valuable comparative angle, where various contexts matter for understanding studied phenomena. However, research in various countries multiplies methodological choices and issues faced by research in a single country study. Finally, longitudinal approaches allow us to see migration as a process over time, but migrants who remain on the move are particularly hard to research as time passes by.

While full of challenges, quantitative methods are also fascinating, with the space for open, flexible and creative approaches for studying migrations. More traditional survey and experimental approaches will continue to provide knowledge on migration processes, but we also observe the emergence of big data analyses in the migration field, which is likely to continue in the years to come and provide new insights into the migration phenomena.

Suggested Readings

To position quantitative research on migration against other methodological choices, readers should refer to the qualitative research chapter by Zapata-Barrero and Yalaz. Kraler and Reich in their chapter write about migration statistics. The Migration Research Hub contains resources on descriptive research and classification, correlation and causal analysis, longitudinal, network analysis, quantitative text analysis, big data analysis, and other methods.