Migration Anticipation and Preparedness

6. How should the forecasting model be developed?

Is it still accurate to use traditional statistical and econometric time series analysis?

The use of econometric models to forecast international migration took off in the 1990s, when discussions about the enlargement of the European Union to include Central European countries began. Forecasting potential labour mobility from new Member States (NMS) was high on the policy agenda. Forecasts had to take into account the transitional arrangements (i.e. restrictions on mobility), some of which remained in place after accession in 2004. Many academic researchers ran econometric models before the anticipated enlargement (Boeri and Brucker, 2001[1]; Dustmann et al., 2003[2]) or after the enlargement (Brücker, Damelang and Wolf, 2009[3]). These regression-based models (see Bijak (2011[4]) for details on various approaches) estimated different dependent variables (e.g. migration flows, migrant stocks, immigration rates) between destination and selected EU candidate countries, conditional on a set of traditional predictors such as labour market outcomes or income differences, GDP per capita and dummy variables denoting geographic or cultural distance. These forecasts failed to correctly anticipate what was going to happen, giving results far lower than actual flows. However, unemployment rates have been confirmed since then as a powerful explanatory factor (Bijak et al., 2019[5]) for all categories of migration, and not only to forecast labour migration. The models employed at the time have nevertheless been criticised for shortcomings of model specification, especially with respect to demographic variables and country-specific effects, which were missing in many studies (Bijak, 2011[4]). In particular, most assumed that past times series were stationary, an assumption that cannot hold in uncertain time (such as the global economic crisis which occurred in the late 2000s) and with such a volatile phenomenon as migration.

An additional problem with using covariates of migration in forecasting models, or in scenarios, is that they also need forecasting, either separate from or with migration. This means that the predictive uncertainty of migration is compounded by the predictive uncertainty of the covariates, and by the uncertain nature of the relationships between migration and its drivers (Bijak, 2011[4]; Barker and Bijak, 2025[6]). Still, this approach continues to be used in forecasts, as well as in migration scenarios, which chart several possible rather than likely future trajectories of migration (e.g. Acostamadiedo et al. (2020[7]) or Wiśniowski et al. (2023[8])). Such scenarios can be based on pre‑selected trajectories of drivers, perhaps described qualitatively rather than necessarily being quantified. An alternative approach could involve a driver-less statistical approach to scenario-setting, based on the frequency and magnitudes of rare migration events (Bijak, 2024[9]).

In addition to the aforementioned econometric models involving explanatory variables, another important group of migration forecasting approaches can be based on the traditional analysis and extrapolation of time series. It includes standard approaches to time series extrapolation such as Auto-Regressive Integrated Moving Average (ARIMA) models, including Generalised Autoregressive Conditional Heteroskedasticity (GARCH) and Stochastic Volatility (SV) extensions, as well as Vector Auto-Regressive (VAR) models (Barker and Bijak, 2025[6]). Bijak, et al. (2019[10]) assessed migration forecasting approaches using the United Kingdom data with various extrapolation methods and econometric models. Econometric models evaluated yield poor or only reasonable calibration with middle‑sized or even high measurement errors. Traditional extrapolation of time series are also miscalibrated or biased in most cases. This is true when forecasts are based on shorter series of data, or/and when series are non-stationary.

Some migration phenomena are nevertheless sufficiently stationary to be forecasted through traditional time series analysis based on past data only (e.g. family migration, see Box 6.1 and Table 4.1). Therefore, except for these few migration categories that are likely stationary, forecasts of other migration flows increasingly rely on Bayesian or Machine learning models.

Box 6.1. The use of traditional statistical analysis as a relevant forecasting tool: The example of time series analysis for family migration and survival analysis for naturalisations in the United States

The United States receives more family migration than any other OECD country. To predict the number of family visas issued, USCIS forecasts starting from the number of application forms completed by principal sponsors. Historical data shows the average time between the submission of the application and the actual issue of the visa, depending on the migratory category and the profile of the sponsor.

As time series data for family migration is very stable, forecasts require much less complex models than for “forced” migration. Forecasts are run for each of the specific family migration categories, which are governed by different rules according to sponsor citizenship. In almost all family migration categories, the United States uses standard forecasting models with no predictive variables included, except the numerical limits applying to each category. Possible models, such as exponential smoothing or ARIMA, are generated through R packages. The plausibility of candidate models is then assessed by MAPE (Mean Absolute Percent Error). The model chosen is usually the one with the lowest MAPE level, unless another model is deemed more reasonable by the forecasting unit’s experts. The forecasting unit does not use other predictive variables.

When forecasting family migration in the United States, it is particularly relevant to estimate the number of family members of US citizens. The latter can apply for family reunification for a large set of family members, often without a cap. As a result, naturalisations leading to family immigration have to be forecasted as well.

By using survival analysis, USCIS can follow cohorts of foreign nationals until they are naturalised and thus establish profiles of future Americans and the time they take to obtain nationality. These profiles by country of origin, age, migratory category and length of permanent residence are then assigned a rate of chance of being naturalised, with the rate varying according to procedural “shocks” (more applications before the elections or before the implementation of a higher procedure fee, for instance). Based on historical data for each profile of new American citizens, it is eventually possible to predict the number of family members joining them, as well as the time between naturalisation and application (the vast majority being made within the first six months).

If the use of survival analysis is relevant to better predict family migration from newly naturalised US citizens, it is worth noting that, for family members of US-born citizens, the traditional times series analysis described above are still used, given the stability of that inflow.

Checklist:

• Is the phenomenon being forecasted stationary?

  • Yes: Consider using basic time series models such as ARIMA or VAR, which can perform well for stationary processes (e.g. family migration).

  • No: Traditional statistical and econometric models may have limited predictive power. Alternative methods (e.g. machine learning or mixed approach with expert opinions) should be considered.

What are Bayesian Models, their principles, and key features?

The contemporary methodological mainstream of statistical migration forecasting largely relies on Bayesian statistical methods as a natural way of describing the predictive uncertainty (e.g. Bijak (2011[4]); (Bijak and Wiśniowski (2010[11]); Azose and Raftery (2015[12]); Welch and Raftery (2022[13])). Two approaches dominate: time series models – univariate or multivariate – and hierarchical models, which also usually include time series components. In either case, past data are used as the primary source of information about the likely future developments of migration processes, augmented by expert opinion. The models can include additional, theory-based covariates (e.g. BSTS) or be atheoretical and entirely data-driven, as in the case of autoregressive models. The main arguments for the latter are that migration theories are not very predictive anyway and any covariates would need to be forecast themselves (Bijak, 2011[4]). Typical practical applications usually involve forecasting total migration inflows and outflows, with increasing literature looking into origin-destination flows (Welch and Raftery, 2022[13])) or flows additionally disaggregated by age (Raymer and Wiśniowski, 2018[14]) or type (Bijak et al., 2019[10]). The use of Bayesian statistical and econometric time series models augmented by expert-based knowledge is indeed particularly useful for non-stationary migration categories with medium volatility, such as labour migration and international student mobility (Table 4.1). This is also a relatively good alternative for highly volatile categories such as asylum and border crossings when machine learning models cannot be implemented easily (Figure 4.1).The key principles and features of Bayesian statistics are discussed elsewhere – an excellent resource for applied work is for example Bayesian Data Analysis (Gelman et al., 2013[15]) – but in summary, the main elements of Bayesian inference are as follows. As in other statistical approaches, the point of departure is a set of data, x, which are assumed to be generated by a statistical model with parameters θ. The likelihood of the particular data being generated by a model with given parameters is described by a probability distribution p(x|θ), where the symbol ‘|’ denotes that the distribution is conditional on θ. In the Bayesian analysis, the aim is to estimate the posterior distribution of the parameters given the observed data, p(θ|x). Based on the Bayes Theorem, a mathematical relationship dating back to the 18th century, the posterior distribution can be obtained by multiplying the likelihood by the prior distribution of the parameters, p(θ). The posterior distribution is then proportional to the prior distribution multiplied by the likelihood. The prior reflects additional knowledge about the parameters beyond what is contained in the data, and can be subjective. More generally, Bayesian statistical inference is based on a subjective notion of probability as a measure of subjective belief, the initial assessment of which (prior) gets continually updated as new data become available, producing new (posterior) knowledge.

The main advantage of using Bayesian methods in the context of migration forecasting are sixfold (see Bijak (2011[4])).

• First, for such uncertain processes as migration, Bayesian methods by design integrate different sources of uncertainty and error.

• Second, the approach allows for incorporating extraneous information, for example, information elicited from subject-matter experts, in a formal and coherent way.

• Third, the use of prior information, for example expert-based, allows to correct for some of the common drawbacks of migration data, such as short series, possibly resulting in better-calibrated forecasts.

• Fourth, the underlying subjective definition of probability as a continuously updated measure of belief is more accurate for unique and non-repeatable phenomena than approaches based on probability seen purely as a frequency of events.

• Fifth, Bayesian methods, by producing full probability distributions of the estimates and forecasts, offer a natural departure point for formal statistical decision analysis.

• Sixth, the Bayesian approach offers a natural mechanism for continually updating the forecasts in the light of new data, in line with the best forecasting practice (e.g. Tetlock and Gardner (2015[16])).

Checklist:

• Do I need to incorporate expert knowledge into the model?

  • Bayesian methods allow integration of expert-elicited information, especially when data is scarce or incomplete.

• Do I need full probability distributions rather than single‑point estimates?

  • Bayesian approaches provide a full predictive distribution, offering a richer understanding of uncertainty.

• What is the best model for regular forecasting updates?

  • Bayesian forecasting is well-suited for iterative updates, making it ideal for dynamic policy environments.

• Am I forecasting labour migration, student migration, asylum flows, or border crossings?

  • Bayesian methods have shown particular effectiveness in forecasting these types of flows due to their flexibility and ability to handle uncertainty.

How to include contextual knowledge in forecasting: Expert opinion and Delphi surveys

Country experts may be able to offer valuable opinions, which incorporate implicit knowledge about the functioning of migration processes from their field of expertise.

Given that the role of expert judgement in informing prior assumptions can be important for forecasting models, especially for short or non-stationary series of data (such as most regulated migration categories, see Table 4.1 for more details), an important question arises about robust ways of eliciting such information from experts, who are not trained statisticians in general. The contemporary literature on expert elicitation is very broad. Specifically in regards to eliciting uncertain information in a probabilistic manner from subject-matter experts, an important reference work is Uncertain Judgements (O’Hagan et al., 2006[17]).

Some important guidelines for the forecasting expert running the elicitation as well as critical discussion on the choice of experts for this exercise are available in the literature (e.g. Rowe and Wright (1999[18])), but the general considerations are as follows. First, experts should be knowledgeable in the subject matter (migration processes), but do not need to be statisticians or forecasters – it is for the elicitation team to explain exactly what is sought from the experts and prepare the right tools (see O’Hagan et al. (2006[17]) and the following section for details). Secondly, the group of experts should be neither too small, nor too large: the recommended group size typically involves between five and 20 experts (Rowe and Wright, 1999[18]). Thirdly, the group of experts should ideally be heterogeneous, so that a variety of views is represented in the study. Depending on the task, this can involve, for example, civil servants from migration administrations or international organisations, academics from various migration-related disciplines, NGOs representatives or experts from neighbouring countries.

It is worth bearing in mind that in many practical applications, the expert views will not be directly used to forecast migration, but rather will inform the forecasting models through prior distributions, which will be modified and updated by the data. In other words, the expert input can be an important ingredient of forecasts – but is far from being the only one.

Checklist:

• Do I need to mobilise a network of experts?

  • Where data in some areas are limited or uncertain, expert elicitation can significantly enhance the model’s outputs by incorporating informed judgment.

• Does the expert group include a diverse range of profiles?

  • Ensure representation from national administrations, international organisations, academia, NGOs, and, where relevant, experts from neighbouring countries.

• Have I included participants who are not data experts?

  • A mix of technical and non-technical perspectives strengthens the breadth of insights and avoids over-reliance on quantitative expertise alone.

• Is the group size manageable?

  • Keeping the group within a range between 5‑20 experts helps balance diversity of input with the practicalities of co‑ordination and decision making.

• Can the expert network be maintained overtime with limited turn over?

How to run a Delphi survey and how to include expert replies in the model?

The outcome of elicitation should ideally be expressed in probabilistic terms, to feed in the forecasting models for example through prior assumptions about their parameters. Generally, information elicited from experts can be used to inform migration forecasts. For example, following the 2014 Scottish independence referendum, experts were asked about possible ranges of future migration conditional on different referendum results (Wiśniowski, Bijak and Shang, 2014[19]). In such cases, the experts are typically asked about the ranges of their beliefs about future value of migration flows in a certain year, and their responses are subsequently converted into probability distributions describing the parameters in question. Combinations of these distributions for all experts, for example obtained by calculating weighted “averages” (formally called statistical mixture distributions) provide prior distributions for these mode parameters (Wiśniowski, Bijak and Shang, 2014[19]). Information collected from expert opinions can be used for scenarios, with experts providing probabilities of different scenarios or driver trajectories and the expected numbers of total migrants or flow levels on selected migration categories (Acostamadiedo et al., 2020[7]) or information about possible drivers and the composition of migration flows (Wiśniowski, Kim and Campbell, 2023[8]) (see also Box 6.2 for examples of questions asked to experts). Alternatively, the experts can be asked to comment on the statistical features of the models, such as stationarity, and the possible values of model parameters, ideally using visualisations to aid understanding. In such cases, the experts can be asked about the ranges of their beliefs about certain parameters of a model (for example, an autoregression coefficient) or a variance of the error term. They can also be asked about the probability that any particular model from a given set of models is likely to be true (Bijak and Wiśniowski, 2010[11]). The responses can then be averaged following a similar approach as discussed above. The elicitation can be set as a multi-stage process, with interim feedback, for example following the template of Delphi studies, which have been used for over 50 years for decision support (Dalkey, 1969[20]). In forward-looking migration studies, Delphi methods were pioneered by Drbohlav (1997[21]).

Box 6.2. Examples of Delphi questionnaires towards migration experts

Questioning expected numbers of migrants under different scenarios

IOM (Acostamadiedo et al., 2020[7]) questioned 110 experts on the migration inflows of some categories (Total inflows, labour migration, highly skilled inflows, first asylum applications and irregular border crossings) in the EU‑28 (excluding free mobility) until 2030, according to four broad migration scenarios validated by a previous two‑round Delphi Survey of 178 experts. After an introduction sentence giving the current number of non-EU inflows, questions were asked as follows:

• “What would be the approximate number in the year 2030 in the EU-28 for each of the scenarios described above?”: The answers were completely opened

• “How confident are you about your estimation? Please provide a percentage based on the scale below”: The answers were built from 5 modalities, from 80‑100% confidence i.e. very confident, to 1‑19% confidence, i.e. very unsure.

• “What is the probability of each of the scenarios becoming a reality in 2030 measured by a percentage between 0 (very improbable) and 100 (very probable)? The percentages must add up to 100 across all scenarios. If all scenarios are equally probable, each should have 25”

Questions were asked again on wave 2, after having shown median and mean estimates from wave 1 aggregated responses.

A relatively similar exercise was conducted to assess expected changes in the number of various migration flows from Middle East and North Africa (MENA) to Europe, including family, labour, refugee and return migration through a factorial survey (Boissonneault and Costa, 2023[22]). The expert panel’s estimates were made using a selection of vignettes that provided assumptions about the evolution of the general context in origin and destination countries. Each expert was randomly presented with four vignettes out of the 128 vignettes created and asked the following:

• “Compared to 2019, the total number of migrants from the Middle East & North Africa to Europe will be in 2030…” The answers were chosen from 11 modalities, from ÷5 to ×5, through e.g. no change or ×1.5.

The survey also asked the level of confidence about the chosen value and include questions about the expert’s profile (thought about the future of migration in the job, familiarity with migration drivers, highest level of education, sector of activity, and years of experience on migration issues). Information on expert profiles may help weight each expert’s answers differently according to their expertise on the specific question.

Questioning possible drivers and composition of migration flows

The FUME project (Future migration scenarios for Europe) conveyed a Delphi survey among experts on migration policies, where they were asked to predict for 2030 key migration drivers, future migration policies and the composition of migration by gender, level of skills and regions of origins and destination (Wiśniowski, Kim and Campbell, 2023[8]). The questions were the following:

• “In the next 10 years, what drivers/motivations of migration from various regions to the EU will be most important?” The answers were selected from a list of 15 drivers/motivations grouped in 5 categories (demography and education, economy, environment, governance, society, other to be specified by the expert) and the relevant drivers had to be put in a table crossing region of origins (rows) and EU destinations (columns).

• “Which regions will dominate in sending immigrants to the different parts of the EU? Please check up to three routes in the table.” The same question was asked for skilled and low-skilled migration, as well as for intra-EU migration and migration from non-EU countries (four questions in total). The reply tables crossed the regional disaggregation applied previously.

• During 2009-2018, the proportion of flows of male immigrants to the EU‑27 member states was higher than female migrants (Males=54% vs. Females=46%. Source: Eurostat database). Compared with the above statistics, what gender balance do you expect in the number of immigrants in next 10 years?” Answer modalities included decreased, maintained or increased gender gap.

• “How will the COVID-19 pandemic affect the economic growth in the EU in the next 10 years? Please specify a probability for each of the scenarios making sure that they sum up to 100%.” Answer modalities included slow recovery, fast recovery, stagnation and persistent negative growth, in an addition to an open answer to be specified by the expert.

Other questions discussed issues that will be considered by policymakers in the future, migration policy priorities and impact of COVID‑19 on migration policies and the society at large. Information built from these answers can help understand the drivers and hypothetical scenarios, which influence experts in their previous answers.

In short, Delphi surveys are voluntary and completely anonymous, with no individual opinions cited at any point. Researchers running the survey always insist there are no “right” or “wrong” answers, as they are interested in opinions in the experts’ personal capacity, not in opinions from their affiliated institution (Wiśniowski, Kim and Campbell, 2023[8]). A Delphi survey involves at least two rounds among experts, who are asked to independently answer a series of questions intended to inform the forecasting model. In the second (and any subsequent) round, the study additionally includes anonymised information from the first round, allowing the experts to reconsider their views and thus enabling convergence of opinion. Still, in the context of such an uncertain phenomenon as migration, too much convergence and alignment of views could be potentially seen as problematic; it is natural that the uncertainty of the phenomenon should be reflected in the uncertainty of the expert views. At the same time, the second round of a Delphi survey can clarify the method and ensure shared understanding of what is expected from the elicitation exercise (e.g. Wiśniowski, Bijak and Shang (2014[19])). For that reason, and to allow exchange of views between the experts, it is recommended that the Delphi surveys contain two rounds, with the second one aimed at informed fine‑tuning of expert answers following a deliberative process, in which new information may be anonymously shared within the expert group.

Reviewing expert input, including probabilities of different scenarios, requires the same general principles applied as in the case of forecasts, discussed at the end of Chapter 4. Indeed, there is a need for a structured updating process, for example every year or two, augmented by ad hoc re‑elicitation of the required quantities every time the circumstances radically change (Bijak, 2024[9]). In the context of expert-based input into forecast and scenarios, providing a formal institutional framework for the elicitation process could be valuable. For institutions mandated with making forecasts, establishing formal advisory bodies, and re‑evaluating expert judgement both periodically and on an ad hoc basis whenever required, can greatly improve the supply of necessary expert-based information for amending the forecasts and scenarios.

Alternatively to traditional Delphi surveys, recent advances in expert elicitation also include online software (MATCH, Morris, Oakley and Crowe (2014[23])), which allows for intuitive probabilistic elicitation from multiple participants in real time by allowing them to “bet” imaginary stakes (with no financial element) on certain future outcomes. In the context of migration, the software was applied by Wiśniowski, Bijak and Shang (2014[19]) to predict migration between Scotland and the rest of the United Kingdom.

Checklist:

• How many rounds of Delphi survey are efficient?

  • Conducting at least two rounds of surveys is the best practice. It ensures experts independently provide input across multiple rounds to refine estimates and encourage convergence of opinions.

• Have I clearly defined the type of input required from experts?

  • Experts may be asked about: Expected numbers or evolution of specific migration flows, probabilities of different migration scenarios, forecast estimates or assessments of key migration drivers.

• Do I have a plan to update expert input periodically?

  • Consider refreshing expert opinions annually or biannually, or more frequently if there are major shifts in context or drivers.

How to develop machine learning models?

Machine learning models are best-fit to use both administrative traditional historical data and innovative data such as digital traces (see Chapter 5 and Box 5.1 for further details on those data). Carammia et al. (2022[24]) extended the use of the Elastic Net algorithm to the context of time series forecasting and applied it to asylum-seekers applications. The idea behind the Elastic Net model (Zou and Hastie, 2005[25]) is to constrain a high-dimensional linear model by adding both a LASSO and a Ridge penalty to take into account predictor selection while maintaining robustness against multicollinearity. The DynENet model proposed by Carammia et al. (2022[24]) introduced a dynamic approach that allows for non-stationary time series (such as those described in Table 4.1) and multiple data frequencies (collected in particular for asylum and border crossings). By employing a rolling time window to train the model, DynENet remains adaptive to shifting patterns in the data, ensuring robust and accurate forecasts. Its parameters are fully explainable as in a standard linear model. Additionally, the moving window approach facilitates the use of the Importance‑Frequency (IF) space (Carpi et al., (2022[26]); Qi et al., (2024[27])), which offers insights into the temporal and spatial persistence of selected predictors. The IF space is particularly valuable for identifying variables that consistently influence migration flows, enabling a deeper understanding of the underlying mechanisms driving these flows and that can be used to inform causal models.

Golenvaux et al. (2020[28]) applied Long Short-Term Memory (LSTM) neural network models to forecast legal migration inflows to OECD countries. LSTM models are deep-learning models based on recurrent neural networks (RNNs). They are powerful but typically black-box models by nature. While LSTMs excel at capturing complex temporal dependencies, their interpretability is inherently limited. Typical measures of explainability like the SHapley Additive exPlanations (SHAP (Lundberg and Lee, 2017[29]), Saliency Maps (Simonyan, Vedaldi and Zisserman, 2014[30]), Partial Dependence Plots (Friedman, (2001[31])) can be used in the attempt to understand the relative importance of the predictors. Like most deep-learning models, LSTMs are prone to overfitting. It has been particularly more investigated to forecast highly volatile phenomena, such as forced migration categories. A growing demand to use this approach for regulated migration categories might merge going forward, as little academic work has been done so far for these more stable categories, with few exceptions (Box 6.3).

Box 6.3. Machine learning approach to forecast outflows of international students from OECD countries

Given that international student mobility is not as volatile as forced migration, little academic work has been done to forecast such flows. Using a dataset of outbound student mobility between 1998 and 2018 from Chinese Taipei to ten OECD countries (the United States, the United Kingdom, Australia, Japan, Canada, France, Germany, New Zealand, Spain and Korea), a recent study (Yang et al., 2020[32]) employed a machine learning approach. The aim of the study was to propose a hybrid model, “FSDESVR,” which combines feature selection (FS, using a random forest method to select the most important features) with support vector regression (SVR, as developed by Drucker et al. (1997[33])) and differential evolution (DE as developed by Storn and Price (1997[34])). The experimental results indicate that FSDESVR achieved higher forecasting accuracy than other models tested (ETS, ARIMA, VAR, SVR, and DESVR).

Checklist:

• Am I forecasting asylum flows or border crossings?

  • Machine learning models are well-suited for non-stationary phenomena that evolve over time, such as forced migration due to their complexity and unpredictability.

• Are multiple data frequencies involved in the forecast?

  • Machine learning can efficiently handle datasets with varying temporal resolutions (e.g. daily, weekly, monthly inputs).

• Have I considered using the Dynamic Elastic Net model?

  • The Dynamic Elastic Net provides a balance between accuracy and robustness, making it a reliable choice for forecasting complex migration patterns.

How to incorporate migration drivers into the machine learning models?

Several machine learning and statistical models (for example, BSTS, prophet (Chapter 5), DynENet (see section above), etc.) and some multidimensional time series models (e.g. VAR) explicitly include migration drivers (or push/pull factors) among their predictors. Adaptive models like BSTS and DynENet, tend to select those that are particularly relevant for the given migration flow. Other models, like prophet, keep all of them with estimated weights, and VAR keep them all. Models such as Garch or ARIMA are based solely on historical values of the target migration flow. While BSTS and DynENet are very light in terms of assumptions, VAR models require each predictor to be stationary. For time series analysis at high frequency (daily to monthly), which is usually the case for asylum applications or border crossings, it is important to correctly handle event data (like wars, policy enforcements, etc). Those data are usually sparse variables, or static data (like GDP, diaspora size, etc.), which may induce effects of spurious correlation. Not correctly processing such migration drivers may induce effects of spurious correlation. These exogenous variables do not cause much trouble in static models (like regression models, gravity models, etc.) but can be distortive in VAR models.

Checklist:

• Have I identified relevant migration drivers to include in the model?

  • Migration drivers may include economic indicators, conflict data, visa policy changes, demographic trends, or climate‑related variables.

• Am I using an adaptive model capable of selecting key drivers?

  • Models such as BSTS (Bayesian Structural Time Series) and Elastic Net can automatically identify and weight the most relevant migration drivers.

• Is the model designed to update as new information becomes available?

  • Adaptive models are particularly suited for dynamic environments, where the influence of different drivers may shift over time.

How to model causal influence in migration forecasting?

Causal influence in migration forecasting involves identifying and analysing the factors that drive migration to improve predictive models, or it implies examining how policies may impact future migration flows learning from previous facts.

In his manifesto arguing for causal migration forecasting, Willekens (2019[35]) postulated 12 ideal characteristics that such causal forecasts should exhibit. Importantly, the underlying forecasting models should be designed at the individual level (examples include agent-based models (ABM) or microsimulations), with modelled individuals described by a range of attributes and their own life histories, of which migration is one important part (see Courgeau (1985[36])). Crucially, the modelled processes need to be stochastic, which constitutes one of several important sources of uncertainty that need to be acknowledged in the forecasts. As with other uncertain migration forecasts (see Bijak (2011[4]) for an overview), Willekens (2019[35]) also argues that in causal models, the Bayesian statistical approach provides a natural language for describing the uncertainty of the underlying micro- and macro-level processes.

There are several examples of successful models of causal mechanisms driving various migration processes, chiefly implemented through agent-based simulations based on individual-level decision rules (e.g. Kniveton, Smith and Wood (2011[37]) for climate‑induced migration; Naivinit et al. (2010[38]) for labour migration; Suleimenova and Groen (2020[39]) for asylum migration). While there is agreement that such models can help shed light on the explanations behind the observed trends and patterns of migration, their predictive capabilities are much more contentious. Once the many unknown elements and parameters in such models are identified and quantified, especially in relation to the rules driving human behaviour (see Klabunde and Willekens (2016[40])), the resulting predictive uncertainty can quickly become too large to be useful for meaningful forecasting applications (Bijak, 2022[41]). Therefore, ABMs are generally not used as predictive models, as they are deemed computationally expensive, not easy to accurately implement, difficult to parameterise and dependent on arbitrary assumptions (Hinsch and Bijak, 2023[42]).

On the other side of causal interpretation of effects, there is a growing interest in synthetic control methods, machine learning approaches and more general stochastic processes settings (beyond the traditional time‑series approach) (See Chapter 9). A parallel and less explored set of models is the pure Directed Acyclic Graph (DAG) approach (Pearl, 2009[43]) (See Box 6.4).

Checklist:

• Am I aiming to identify causal mechanisms behind migration drivers?

  • Agent-based models are effective for exploring causality but are generally not suited for predictive forecasting.

• Are there alternative methods for analysing causal influence?

  • Synthetic control methods and machine learning approaches are increasingly used to assess causal effects in migration research.

• Is it important to balance explanatory power with predictive performance?

  • Consider combining causal modelling approaches with forecasting techniques where appropriate, depending on the policy need.

Box 6.4. Directed Acyclic Graph

The DAG approach relies on the identification of graph to express causal relationships. In a DAG the causal structure is represented through nodes and edges. The nodes represent variables relevant to, for example, migration, such as economic conditions, political instability, social networks, migration policies, and environmental changes, while the edges represent causal relationships that are determined based on theoretical knowledge, domain expertise, or statistical discovery algorithms.

The theoretical advantages of DAGs are that:

1. they clarify causal mechanisms, improving the interpretability of forecasts;

2. they ensure that only the relevant predictors are included in the forecasting model, avoiding spurious correlations and.

3. confounding is explicitly addressed, enhancing the robustness of predictions.

Still, DAGs require integration with time series models (e.g. ARIMA, BSTS) or other machine learning techniques for prediction as mentioned above, because DAGs do not possess an explicit prediction capability. Best practices involve integrating the discovered DAG with forecasting models like Bayesian networks, dynamic causal models, or machine learning frameworks to propagate causal effects into the future. As far as DAG discovery is concerned, a few wide‑spread algorithms exist: those based on testing conditional independence (see, e.g. Spirtes and Glymour, (1991[44]); Spirtes et al., (2001[45]), or Dynamic Bayesian Networks (Murphy, 2002[46]) to name a few.

Figure 6.1. A hypothetical DAG illustrating a sequence of causal relationships

Figure 6.1 shows a made‑up example of a DAG describing a sequence of causal relationships among predictor variables (X’s: climate/war events, economic situation, displacement, diaspora, migration policies) and the target variable “Asylum Seekers Applications” (Y). These causal relationships are being tested through causal inference techniques. The DAG is the hypothesised state of the system, then causal inference methods will validate the existence of the edges.

References

[7] Acostamadiedo, E. et al. (2020), Assessing Immigration Scenarios for the European Union in 2030 – Relevant, Realistic and Reliable?, International Organization for Migration and the Netherlands Interdisciplinary Demographic Institute.

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