Country-level panel data on irregular (unauthorized) migration in Poland, combining administrative records from the Social Insurance Institution (ZUS), Border Guard, and Police. Covers non-Schengen countries of origin with at least one insured foreigner registered in ZUS during 2019–2024.
Format
A data frame with 1,382 rows and 8 variables:
- year
Year of observation (factor, 2019–2024).
- sex
Sex (factor:
"Female","Male").- country_code
ISO 3166-1 alpha-3 country code (e.g.
"UKR").- country
Country name in English.
- continent
Continent (
"Africa","Americas","Asia","Europe","Oceania").- m
Observed count: foreigners apprehended by the Border Guard for unauthorized stay (the variable whose hidden population we estimate).
- n
Auxiliary count: foreigners identified by the Police (a second, partially overlapping administrative source).
- N
Reference population: foreigners registered in ZUS (social insurance). Used as a proxy for the total known foreign population from a given country.
Source
Social Insurance Institution (ZUS) — register of insured foreigners
Border Guard — apprehensions for unauthorized stay
Police — identification of foreigners
Details
The dataset is used to estimate the size of the unauthorized foreign population using the power-law model of Zhang (2008).
The key assumption of the estimation framework is that \(m\) and \(n\) are partial observations from a larger unauthorized population of size \(\xi\). The reference population \(N\) (insured foreigners) serves as a scaling anchor: countries with more insured foreigners are assumed to also have more unauthorized residents, with the elasticity governed by the parameter \(\alpha\).
Observations with N = 0 have been excluded. About 49\
observations have m = 0 and 48\
large number of small countries with no recorded apprehensions.
References
Zhang, L.-C. (2008). Developing methods for determining the number of unauthorized foreigners in Norway. Documents 2008/11, Statistics Norway. https://www.ssb.no/a/english/publikasjoner/pdf/doc_200811_en/doc_200811_en.pdf
Beresewicz, M. and Pawlukiewicz, K. (2020). Estimation of the number of irregular foreigners in Poland using non-linear count regression models. arXiv preprint arXiv:2008.09407.
Examples
data(irregular_migration)
head(irregular_migration)
#> year sex country_code country continent m n N
#> 1 2019 Female AFG Afghanistan Asia 0 0 269
#> 2 2019 Female AGO Angola Africa 2 0 15
#> 3 2019 Female ALB Albania Europe 0 1 64
#> 4 2019 Female ARG Argentina Americas 0 1 52
#> 5 2019 Female ARM Armenia Asia 8 17 1089
#> 6 2019 Female AUS Australia Oceania 2 0 44
# Basic model
fit <- estimate_hidden_pop(
data = irregular_migration,
observed = ~ m, auxiliary = ~ n, reference_pop = ~ N,
method = "poisson"
)
summary(fit)
#> Unauthorized population estimation
#> Method: POISSON | vcov: HC3
#> N obs: 1382
#> Gamma: 0.001831 (estimated)
#> Log-likelihood: -11380.65
#> AIC: 22767.3 BIC: 22782.99
#> Deviance: 20158.5
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> alpha 0.736646 0.040258 18.298 < 2.2e-16 ***
#> beta 0.575046 0.091861 6.260 3.85e-10 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> -----------------------
#> Population size estimation results:
#> (BC = bias-corrected using model-based variance)
#> Observed Estimate Estimate (BC) CI lower CI upper
#> (all) 27,105 290,597 290,498 127,726 660,703