Schmid Comparative Migration Studies (2020) 8:25 the volume of immigrant intake to a receiving country (Goodman 2014a, p. 814; Helbling et al. 2017, p. 82). These policies distinguish different types of immigrants, namely labour immigrants, immigrants that reunite with their families, and asylum seekers and refugees (Helbling et al. 2017). Examples are conditions such as job offer requirements for labour migrants or eligibility criteria such as age limits for family migrants. On the other hand, immigration regimes confer residence rights. These rights define how long an immigrant can stay in the receiving country under the relevant permit. This is not to be confused with the regulation of permanent residence proper, which may or may not depend on additional conditions. For instance, Green Card holders in the US receive permanent residence rights upon admission, whereas in other countries residence rights may not allow any category of migrants to renew their temporary visas or transition toward a permanent stay. Conceptualizing residence rights as a part of immigration regimes does not conflate immigration policy with immigrant policy. Non-transient residence rights short of the regulation of access to permanent residence proper are immigration rights, not immigrant rights. Indeed, regulating the duration of stay is a necessary component of any immigration policy; it is associated directly with entry permits. Depending on the number of possible permits and their variation in legal content, such permit rights do not only exhibit cross-national but also intra-national variation across entry tracks (cf. Ruhs 2013). By contrast, more general rights mainly show cross-national rather than intra-national variation (cf. Koopmans et al. 2012). General rights may still discriminate between various categories of migrants, but not based on permits. It is hard to give examples for rights in the two categories because the distinction is somewhat artificial, and the rights architecture can vary across countries – a fact that is usually not acknowledged and is hard to capture empirically. A safe bet for a general right is the right of non-citizens to vote in local elections. Here, states discriminate on grounds of nationality and duration of residence rather than residence permits (Schmid et al. 2019). Permit rights, and especially residence rights, constitute the inner belt of the territorial boundary instead of an intermediate stage between entry and naturalisation (Helbling et al. 2017; see also de Haas et al. 2015). Hence, immigration regimes, as conceptualised here, feature entry and stay as their constituent components. The less restrictive the regulations of entry and stay, the higher the level of Immigration Regime Openness (IRO). Regarding immigration, citizenship regimes comprise the regulations that define the conditions for immigrants to acquire the legal status of full membership in the sense of nationality (Goodman 2014a, 814). Based on a review of extant indices and other conceptualisations in the literature (e.g. Howard 2009; Fitzgerald et al. 2014; Blatter et al. 2017), this analysis focuses on four core policy components of citizenship regimes: (1) the strength of jus soli; (2) residence duration requirements; (3) the toleration of multiple citizenship; and (4) further naturalisation requirements (language and citizenship tests as well as economic and criminal record requirements). The less restrictive the requirements for citizenship acquisition for immigrants, the higher the level of Citizenship Regime Inclusiveness (CRI). The overarching concept of national boundary regimes regarding immigration therefore focuses the two fundamental ‘social closures of nation-states’ (Brubaker 1992, ch. 1; Weber 1946, p. 78). The inner boundary of citizenship is fundamental because it endows immigrants with the ‘highest standard of equal treatment’ (Bauböck et al. 2013, p. Page 4 of 20