120 Chapter 6 is found. Moreover, after a number of robustness tests, including the use of an instrumental variable to account for reverse causality, the findings remain consistent. Accordingly, I find no evidence to suggest that increasing immigration leads to the retrenchment of the welfare state, despite earlier claims that increasing heterogeneity in Europe would lead to cut-backs in generosity (Alesina et al., 2001; Alesina & Glaeser, 2004; Alesina et al., 2019; Borjas, 1999; Collier, 2013; Freeman, 1986). The results support the ideas of the embedded liberalism thesis (Ruggie, 1982) and the compensation hypothesis (Rodrik, 1998; Walter, 2010), which in the case of the former posits that immigration can create a need to deliver compensatory welfare policies in order to garner support for more open economic policies or, in the case of the latter, increase the demand for them rather than diminish welfare state support or generosity to mitigate the risks of more open policies. This provides comparable results to more recent research that finds evidence of a neutral or compensatory effect of immigration on welfare state effort and contributes to a growing body of literature that challenges the notion that immigration necessarily leads to welfare state retrenchment (e.g., Gaston and Rajaguru, 2013; Lipsmeyer and Zhu, 2011; Römer, 2023; Taschwer, 2021), thus providing an important contribution to existing knowledge on the political economy of immigration and welfare, as well as the wider political debate. Chapter 3 aims to explore in greater depth the currently available data on immigration and identifies some key gaps in its coverage. First, the chapter draws attention to the lack of harmonised definitions across countries, even within the EU. Different countries define migrant stocks (total immigrant population at a given time) and flows (new entries and exits) differently. For example, most countries use country of birth to identify migrants but some, such as Germany, use nationality instead meaning that the stock of migrants identified is slightly lower as immigrants that have nationalised will not be counted in the statistics. Second, irregular migration remains difficult to track and measure because of clandestine crossings, visa overstays, and lack of registration. Moreover, asylum seekers whose claims have been rejected may become irregular migrants as removing these individuals once they have already arrived can be expensive or their country of origin may refuse to receive them. Data on the number of irregular migrants in the EU can range widely as the statistics are often based on extrapolations from enforcement data or surveys rather than systematic counts. Third, while inflows of immigration are reasonably well recorded, outflows of emigration are typically not well recorded. EU free movement makes tracking emigration outflows especially difficult, as many migrants leave without de-registering from population registries. Fourth, there is very little data on circular or seasonal migration as these short-term forms of mobility are difficult to track, especially across the Schengen zone as there is little incentive to register and deregister from population registries. Fifth, most migration
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