Schmid Comparative Migration Studies (2020) 8:25 Page 16 of 20 Fig. 3 Aggregate trends in IRO and CRI 1980–2010. Lines represent the mean and standard deviation of IRO and CRI, aggregated across 23 democracies from 1980 to 2010; reference lines indicate 1992 and 2001 to distinguish historical periods; IRO is based on selected policy components measuring the openness of immigration regimes according to IMPIC (Helbling et al. 2017). CRI is composed of the policy components of CITRIX (original dataset based on temporal expansion of selected items from MIPEX and based on the data by Stadlmair (2017) and Fitzgerald et al. (2014) and DEMIG and GLOBALCIT) measuring the inclusiveness of citizenship regimes dimensions are uncorrelated. Solutions with non-orthogonal rotations show not only the same pattern of two-dimensionality, but also confirm that the correlation between IRO and CRI is low (PROMAX estimates a correlation of − 0.07; OBLIMIN estimates a correlation of − 0.03). Using the IRO and CRI scales with (for IRO, transformed) arithmetic means is more adequate, because they are completely free of any assumptions and, in addition, are not dependent on variable parameters that go into the estimation of correlations between the dimensions when using PROMAX (I used the default Kappa = 4) and OBLIMIN (I used the default Delta = 0). Table 3 shows that there is a conditional cross-case correlation between IRO and CRI: it increases over time. While there was virtually no correlation during the last decade of the Cold War, it increases to 0.18 during the 1990s, and to 0.36 after 9/11 (coefficients are Spearman’s rho because of the ordinal nature of the data). The overall correlation is substantially low (0.19) but has a very low p-value. Though there is only a Table 3 How IRO-CRI cross-sectional correlations increase over time Historical Period Pooled Cold War 1992–2001 Post 9/11 rho 0.19 0.08 0.18 0.38 p-value 0.000 0.164 0.007 0.000 N 713 276 230 207 Entries are Spearman correlation coefficients and number of observations