Migration Anticipation and Preparedness

9. What future developments can be expected in migration forecasting?

How to measure the potential effect of policies in countries of destination?

There has been a growing interest in approaches to causal interpretation of potential policy effect employing synthetic control methods, machine learning approaches and more general stochastic processes settings.

Since its introduction (Abadie, Diamond and Hainmueller, 2010[1]), the Synthetic Control Method (SCM) has become a powerful statistical technique used to evaluate the effects of interventions or treatments in comparative case studies, particularly when a single unit (e.g. a country, region, or city) undergoes an intervention, and suitable control units are available for comparison. SCM constructs a weighted combination of control units to create a “synthetic” version of the treated unit, which approximates what would have happened in the absence of the intervention. This method has been widely applied across various fields, including economics, political science, and public health. Klößner and Pfeifer (2017[2]), for instance, explored the use of SCM as a pure forecasting tool. By applying SCM to the United States GDP growth, the authors demonstrate that it performs competitively compared to alternative forecasting methods. This idea has now been embraced by several scholars to study the impact of external events (e.g. economic crisis, war, climate events) on migration flows.

SCM has increasingly attracted the attention of migration experts as well particularly for policy impact analysis and natural experiments, like macro shocks (e.g. climate change, conflict). Rodríguez Sánchez et al. (2023[3]), for instance, explored the ability of Bayesian Structural Time Series (BSTS) models (Scott and Varian (2014[4])) in the context of irregular border crossings forecast. BSTS is a robust statistical approach for time series analysis, particularly suited for causal inference in observational data with complex temporal patterns. In that particular application, the model constructs a synthetic counterfactual by forecasting what the number of arrivals would have been in the absence of policy, based on historical trends and covariates such as climate, political events, and economic factors. The BSTS framework uses a Bayesian approach to incorporate prior knowledge and quantify uncertainty around the estimates, making it highly reliable for causal inference in dynamic systems.

Many variant and innovative approaches of causal inference for time series have been developed in recent years (see Box 9.1). In all these variants, two considerations are very important. The first consideration is the accurate selection of control units. The choice of the donor pool is crucial to ensure that the synthetic control closely matches the treated unit’s pre‑intervention characteristics. The accurate selection is important because these methods always produce “technical” counterfactuals, as an output of a weighting method. If within the pool of control units there are members who are structurally different from the treated unit, the final estimated impact will include bias due to confounding factors. The second consideration concerns the underlying assumptions. Researchers must be mindful of the assumptions underlying SCM, such as the stability of relationships over time (meaning that all the predictors used and the outcome variable have a static relationship, an assumption that is rarely true in migration flows as shown by, e.g. (Carammia, Iacus and Wilkin, 2022[5])), and the absence of spillover effects between units which is quite likely in migration flows because of the complexity of the phenomena, the networking effects, etc.

Box 9.1. Other approaches to causal inference

Goldin et al. (2024[6]) introduced an innovative approach to causal inference in panel data settings by leveraging advanced time series forecasting techniques. The focus is on the ability of different deep-neural network algorithms to produce counterfactual evolutions for treated units by incorporating both historical data for the treated units, and contemporaneous data from control units. Using a holistic approach, the proposed model captures both temporal dynamics and cross-sectional relationships.

In a recent contribution, Cinquini et al. (2025[7]) address the challenge of estimating causal effects of interventions in dynamical systems over time. The authors introduce a formal framework to define and analyse causal interventions within the framework of Discrete‑Time Stochastic Processes (DSPs), which are models representing systems that evolve in discrete time steps with inherent randomness. In this context it is possible to show, under certain conditions, the equivalence between the equilibrium state of a DSP and a traditional structural causal model (SCM). This equivalence allows for the application of causal inference techniques traditionally used in SCMs to time‑series data. In particular, it is possible to explicitly map VAR models to linear SCMs. This mapping accommodates potential cyclic relationships and unmeasured confounders, enhancing the interpretability of VAR models in causal terms. Authors’ experiments demonstrate that the framework achieves strong performance in observational forecasting and accurately estimates the causal effects of interventions on dynamical systems.

For a general review of causal inference in time‑series forecasting see also Runge et al. (2023[8]).

Is conformal prediction the final frontier in time series forecasting?

Conformal prediction is a statistical framework that provides valid prediction intervals for machine learning or pure statistical models, ensuring that the true value of a prediction lies within a specified interval with a certain confidence level. This method has been applied across various domains typical of the i.i.d. (independent and identically distributed) setting and has been recently extended to time series analysis. The basic assumption of conformal prediction is exchangeability of the data. Exchangeability means that the order of the data points does not matter, and any permutation of the data points has the same joint probability distribution. This assumption is weaker than the often‑used i.i.d. assumption but still remains crucial for the validity of conformal prediction.

The basic idea behind conformal time‑series forecasting (Stankeviciute, Alaa and van der Schaar, 2021[9]) is to adapt the conformal prediction framework to time‑series data, allowing for the creation of prediction intervals that provide a predefined, valid coverage probability regardless of the underlying model or data distribution. The approach extends the conformal prediction methodology, traditionally used for i.i.d. data, to handle dependent time‑series data where observations are typically autocorrelated. The adaptation consists of addressing the temporal dependencies by calibrating residuals from a forecasting model in a way that accounts for the autocorrelations between observations. The advantage of conformal time‑series forecasting is that it is model agnostic, i.e. it can in principle be applied to any base forecasting model, including neural networks, ARIMA, or other machine learning-based models, as long as the model provides point predictions. The algorithm proposed by Stankeviciute, Alaa and van der Schaar (2021[9]) is designed to handle multi-step forecasts, constructing prediction intervals for multiple future time steps simultaneously. The intervals reflect uncertainty at each forecast horizon. Despite its advantages, conformal prediction is still not easy to apply and remains under explored in the context of migration forecasting.

How can forecasting results in one migration category affect forecasting in other categories?

Migration categories – such as international students, labour migrants, asylum seekers, and family reunification migrants – do not function in isolation. Changes in one category can trigger cascading effects on others. For policymakers and forecasters, understanding these interdependencies is crucial for producing accurate and actionable migration forecasts.

One illustrative example of cross-category influence is the transition of international students into the labour market. For example, former international students who have graduated in the host country are an important feeder for labour migration in many countries and the share of educational permits changed to a work permit accounted for a large share of total admissions for work (for OECD countries, OECD (2022[10]); for the United States, Beine, Peri and Raux (2023[11]), for the United Kingdom, Brindle and Sumption (2024[12]), for the Netherlands, Didier and Merve Nezihe (2014[13])). Therefore, in order to accurately forecast labour migration, it is essential to first estimate the number of incoming international students, and then to account for student retention rates following graduation in the workforce or even transition to family permits.

Another example of interconnection between migration categories is family migration. Family migration can be considered a typical example of chain migration. Chain migration is due to earlier arrivals, including settled migrants who bring family members (Böcker, 1994[14]). In all OECD countries, the family reunification process is legally bound by the presence of a sponsor (principal applicant) already in the country for a certain duration of time, usually labour migrants, beneficiaries of international protection, as well as host-country nationals (OECD, 2017[15]). Future family migration is therefore a function of past migration flows of the aforementioned categories. Forecasting family migration of foreign nationals requires four key pieces of information: i) the current and expected future flows of migrants, categorised by types of migration (e.g. labour migration, highly skilled labour, international protection); ii) the proportion of migrants in each category who return to their home country early, before any family reunification process begins (see for instance Viné (2021[16]); iii) the number or share of family members joining the principal applicants who remain in the host country (adjusted by the proportion returning early from point ii); iv) the average time lag between the arrival of the principal applicant in the host country and the arrival of their family members.

Using longitudinal data from the population register in the Netherlands, Wijkhuijs and Jennissen (2010[17]) estimated that the average number of family members who joined third-country national labour migrants was 0.75, while it was 0.66 for Polish labour migrants and 0.45 for EU15 nationals. Exploiting a regularisation act in the United States (IRCA 1986), Cascio et al. (2024[18]) estimated that each regularised Mexican migrant was responsible for the subsequent immigration and legal admission of one relative, in total, through 2019.

Given these interdependencies, migration forecasts must incorporate feedback loops between categories. Rigid, siloed models may overlook how trends in one group influence another. To improve forecasting accuracy and policy preparedness, dynamic, multi-category forecasting models should be employed to integrate multiple migration pathways and capture transition probabilities between categories (e.g. student-to-labour force retention rates).

Policymakers should be aware of these interconnections to avoid unintended consequences when designing migration policies. For instance, changes in student visa policies may have long-term labour market effects that should be factored into workforce planning. By acknowledging and incorporating cross-category influences, migration forecasting can provide a more comprehensive foundation for policymaking, reducing uncertainty and enhancing preparedness for future migration trends.

How can forecasts in one country affect forecasts in other countries (i.e. interaction across countries)?

Migration is a complex phenomenon that involves not only one mobility from a country A to a country B. Migration is not necessarily a finite process; it can also be circular (back and forth from a country A to a country B) or involve multiple transit countries. Therefore, migration flows in one country can affect flows in other countries, sometimes to a great extent. This is particularly true in the European context, where immigrants, after crossing the external borders of the EU, enjoy a degree of unconstrained mobility within the Schengen area. They can therefore move more easily from one Member State to another. This may lead to asylum claims being lodged not in countries other than the first country of arrival: in 2023 and 2024, EU countries received 185 258 and 167 561 “Dublin” requests, respectively, i.e. requests to reaccept third-country nationals who have applied for asylum or crossed into a country different from the responsible country (usually their country of first entry within the EU).

Against that background, OECD countries, whenever possible, increasingly use data from other countries to anticipate their own migration flows. The United States use Mexico’s encounters of irregular migrants to forecast their own irregular migration (Table 5.1). The DynENet model proposed by Carammia et al. (2022[5]) (see section on machine learning models) analyses interactions across countries for forecasting purposes as well. For instance, it showed that events in Türkiye may have a different effect on asylum applications by Syrians from one EU country to another, depending on migration drivers between Syria and each EU country. As a consequence, forecasts run in transit countries, and in particular in neighbouring countries to an OECD country, may significantly affect the forecast for this OECD country. That interaction is stronger for forced migration forecasting but should not be overlooked for other migration categories. Indeed, an economic crisis in a country A may encourage labour migration flows or international students to go further in a country B, especially among the most highly skilled. Similarly, a policy decision in one country can divert migration flows (forced or not) to another country B.

In order to produce the most reliable results, forecasts in one country must therefore take into account forecasts in other countries, where routes exist between them. While this seems obvious from a statistical point of view, its practical implementation is far from simple. As forecasts are usually sensitive, their dissemination may be limited outside national boundaries. Even national migration data are not necessarily disseminated abroad, especially the most sensitive ones, which are often used in forecasting. Irregular border crossing data at the EU external border are available through EU agencies such as Frontex (https://www.frontex.europa.eu/what-we-do/monitoring-and-risk-analysis/migratory-map/) or Eurostat (https://ec.europa.eu/eurostat/databrowser/view/migr_eipre/default/table?lang=fr&category=migr.migr_man.migr_eil), but border crossings within the EU, when available, are seldom disseminated even with the countries sharing a common border. Border crossing data within the EU are implicitly limited, and do not fully capture actual crossings, as the data lack coverage in the context of open borders, and depend on varying levels of border control effectiveness and the size of the border force mobilised over time.

All in all, OECD countries could develop more accurate forecasting models if they had access to other geographically connected countries’ forecasts and data. That requires more co‑ordination between them and regular contacts between forecasting data providers. This also implicitly requires a certain level of data comparability across OECD countries. In order to do so, a greater alignment of definitions and frequencies across OECD countries is needed. Data harmonisation also requires regular contacts between data providers and an international co‑ordination body to ensure a unique definition is clearly defined and applicable. Although full harmonisation may be challenging, this is indeed an important condition under which cross-country forecasting can realistically improve. In the end, all these exchanges would not only improve the quality of migration forecasts but also foster stronger collaboration between forecasting units across OECD countries.

References

[1] Abadie, A., A. Diamond and J. Hainmueller (2010), “Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program”, Journal of the American Statistical Association, Vol. 105/490, pp. 493-505, https://doi.org/10.1198/jasa.2009.ap08746.

[11] Beine, M., G. Peri and M. Raux (2023), “International college students’ impact on the US skilled labor supply”, Journal of Public Economics, Vol. 223, p. 104917, https://doi.org/10.1016/j.jpubeco.2023.104917.

[14] Böcker, A. (1994), “Chain migration over legally closed borders: Settled immigrants as bridgeheads and gatekeepers”, The Netherlands’ Journal of Social Sciences, Vol. 30/2, pp. 87-106.

[12] Brindle, B. and M. Sumption (2024), International students entering the UK labour market, https://migrationobservatory.ox.ac.uk/resources/commentaries/international-students-entering-the-uk-labour-market/.

[5] Carammia, M., S. Iacus and T. Wilkin (2022), “Forecasting asylum-related migration flows with machine learning and data at scale”, Scientific Reports, Vol. 12/1, https://doi.org/10.1038/s41598-022-05241-8.

[18] Cascio, E., E. Lewis and C. Zhang (2024), How Good are Proxies for Legal Status? Evidence from the Legalization of Two Million Mexicans, National Bureau of Economic Research, Cambridge, MA, https://doi.org/10.3386/w32632.

[7] Cinquini, M. et al. (2025), “A Practical Approach to Causal Inference over Time”, Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 39/14, pp. 14832-14839, https://doi.org/10.1609/aaai.v39i14.33626.

[13] D., F. and Ö. M.N. (2014), International mobility of students - Its impact on labour market forecasts and its contribution to the Dutch economy, University of Maastricht, https://doi.org/10.26481/umarot.2014006.

[6] Goldin, J., J. Nyarko and J. Young (2024), “Forecasting Algorithms for Causal Inference with Panel Data”, Proceedings of the 25th ACM Conference on Economics and Computation, pp. 1205-1205, https://doi.org/10.1145/3670865.3673641.

[2] Klößner, S. and G. Pfeifer (2017), “Outside the box: using synthetic control methods as a forecasting technique”, Applied Economics Letters, Vol. 25/9, pp. 615-618, https://doi.org/10.1080/13504851.2017.1352071.

[10] OECD (2022), International Migration Outlook 2022, OECD Publishing, Paris, https://doi.org/10.1787/30fe16d2-en.

[15] OECD (2017), “A portrait of family migration in OECD countries”, in International Migration Outlook 2017, OECD Publishing, Paris, https://doi.org/10.1787/migr_outlook-2017-6-en.

[9] Ranzato, M. et al. (eds.) (2021), Conformal time-series forecasting.

[3] Rodríguez Sánchez, A. et al. (2023), “Search-and-rescue in the Central Mediterranean Route does not induce migration: Predictive modeling to answer causal queries in migration research”, Scientific Reports, Vol. 13/1, https://doi.org/10.1038/s41598-023-38119-4.

[8] Runge, J. et al. (2023), “Causal inference for time series”, Nature Reviews Earth & Environment, Vol. 4/7, pp. 487-505, https://doi.org/10.1038/s43017-023-00431-y.

[4] Scott, S. and H. Varian (2014), “Predicting the present with Bayesian structural time series”, International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 5/1/2, p. 4, https://doi.org/10.1504/ijmmno.2014.059942.

[16] Viné, R. (2021), “Economic Drivers of Family Reunification in the Context of International Migration”, SSRN Electronic Journal, https://doi.org/10.2139/ssrn.3761361.

[17] Wijkhuijs, L. and R. Jennissen (2010), Arbeidsmigratie naar Nederland.