Dual-Systems Estimation of Irregular Migration
Also known as: Dual-System Estimation, Multiple-Systems Estimation of Irregular Migration, Capture-Recapture for Irregular Migrants, Truncated-Poisson Population Estimation
Dual-systems estimation, the two-list special case of capture-recapture, estimates how many irregular migrants exist by exploiting the overlap between administrative records that each capture only part of the population. The logic is borrowed from wildlife ecology: tag animals on one trapping occasion, see how many tagged animals reappear on a second, and the rate of overlap reveals how many were never caught at all. Applied to migration, the 'traps' become administrative lists — police apprehension records, hospital registers, deportation files — and the people who appear on no list are the quantity to be estimated. Van der Heijden, Cruyff, and colleagues showed in their 2003 Statistica Neerlandica paper that even a single police register can support estimation through the truncated-Poisson model, by using how often individuals are recorded to infer how many were never recorded. Böhning, van der Heijden, and Bunge's 2018 monograph consolidated the modern toolkit for the social and medical sciences, with explicit treatment of the two assumptions that make or break the method: that lists are not too strongly dependent and that the population is not too heterogeneous in its chance of being captured. The output is a defensible estimate of an irregular-migrant total that, by definition, no register sees in full.
Key highlights
- Estimates the unobserved share of an irregular-migrant population directly from existing administrative records, without surveying anyone.
- Works even from a single register through the truncated-Poisson and Chao frequency models, exploiting repeated appearances of the same individuals.
- Truncated-Poisson regression incorporates covariates to reduce heterogeneity bias and produce subgroup-specific size estimates.
- Rests on a transparent, well-understood statistical framework with mature tools for modeling list dependence and reporting sensitivity ranges.
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use dual-systems or capture-recapture estimation when you have two or more overlapping administrative lists that record identifiable irregular migrants — police, hospital, shelter, or deportation registers — or a single list that records individuals repeatedly, and you need an estimate of the total including those on no list. It is well suited to settings with reliable record linkage and a clearly bounded target population and time frame, and it is the natural complement to demographic residual methods because it draws on operational rather than census data. It is also valuable when the hidden population cannot be surveyed directly. The method is less appropriate when lists are strongly dependent in ways you cannot model, when capture heterogeneity is extreme and no covariates explain it, or when linkage quality is poor enough that overlap counts are unreliable, since all of these directly bias the estimate. It also requires that 'capture' be well defined and that the same individuals could in principle appear across sources.
Strengths & limitations
- Estimates the unobserved share of an irregular-migrant population directly from existing administrative records, without surveying anyone.
- Works even from a single register through the truncated-Poisson and Chao frequency models, exploiting repeated appearances of the same individuals.
- Truncated-Poisson regression incorporates covariates to reduce heterogeneity bias and produce subgroup-specific size estimates.
- Rests on a transparent, well-understood statistical framework with mature tools for modeling list dependence and reporting sensitivity ranges.
- Assumes lists are independent (or that their dependence can be modeled), but administrative registers are often linked by the very processes that create them.
- Sensitive to capture heterogeneity: if some migrants are far more catchable than others and this is unexplained, the total is typically underestimated.
- Critically dependent on record-linkage quality, since false or missed matches in the overlap count directly bias the size estimate.
- Requires a clearly defined, closed target population and time window; migration in and out of the frame violates the closure assumption.
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
How can overlap between two lists reveal people on neither list?
The key assumption is that, if the two lists capture people independently, the fraction of one list's members who also appear on the second list equals the overall capture rate of the second system. Once you know that capture rate, you can scale the first list up to the full population, including those captured by neither. Concretely, the dual-system estimator multiplies the two list totals and divides by their overlap; a small overlap relative to the list sizes implies the systems are catching different people and the hidden remainder is large, while a large overlap implies they are catching the same visible slice and the hidden remainder is small. The overlap is, in effect, a measurement of how incomplete the lists are.
What can go wrong if the administrative lists are not independent?
List dependence is the most serious threat to validity. If being recorded in one register makes a person more likely to appear in another — for example, an apprehension that automatically triggers a deportation file — the overlap is inflated and the simple estimator understates the hidden population; negative dependence does the reverse. Because administrative registers are often generated by linked bureaucratic processes, this is common in irregular-migration data. The remedy, detailed by Böhning and colleagues, is to use three or more lists so that interaction (dependence) terms can be estimated in a log-linear model, and to report a sensitivity range rather than assuming independence.
Can capture-recapture work with only one administrative source?
Yes, provided that single source records individuals more than once. The truncated-Poisson approach treats each person's number of appearances as a count that is observed only when it is at least one, fits a model to the frequencies of being seen once, twice, three times, and so on, and extrapolates to the people seen zero times. Van der Heijden and colleagues used exactly this to estimate illegal immigrants from a Dutch police register, and the related Chao estimator gives a robust lower bound from just the once- and twice-seen counts. Single-list estimation is a major practical advantage because irregular-migration data often come from one enforcement system rather than several linkable ones.
Sources
- 1.van der Heijden, P. G. M., Cruyff, M., & van Houwelingen, H. C. (2003). Estimating the Size of a Criminal Population from Police Records Using the Truncated Poisson Regression Model. Statistica Neerlandica, 57(3), 289-304.
- 2.Böhning, D., van der Heijden, P. G. M., & Bunge, J. (2018). Capture-Recapture Methods for the Social and Medical Sciences. Chapman and Hall/CRC.ISBN 9781498745314
You have read it. What now?
Cite this page
ScholarGate. (2026, June 23). Dual-Systems Estimation of Irregular Migration. ScholarGate. https://scholargate.app/migration-studies/dual-systems-estimation-irregular-migration