22 Chapter 2 effects with a lagged dependant variable (Gaston & Rajaguru, 2013; Lipsmeyer & Zhu, 2011; Soroka et al., 2006, 2016). However, the lagged dependent variable can be a considerable source of bias, known as Nickell bias (Nickell, 1981), as it is highly correlated with the dependent variable and thus causes an upward bias in the standard errors. Subsequently, the estimation model does not provide an accurate coefficient for the key explanatory variable. Accordingly, panel-corrected standard errors with the Prais-Winsten correction for serial correlation – argued for as more appropriate by Plümper et al (2005) – are used for the analysis. The main model specification is presented in levels, as a change from year to year is not as drastic as a five-year change, such as Soroka et. al. (2016) use in their analysis. Hence the overall volume (level) of migration from year-to-year may be more noticeable to natives. Notably, when testing the dependent variables for stationarity, a number of panels have a unit root but not all9. As a result, a model using changes is included as a robustness check. The explanatory variable and all controls are lagged by one year – Gaston and Rajaguru (2013) do the same, while Lipsmeyer and Zhu (2011) and Soroka et al. (2006; 2016) lag a selection. The reasoning is that in the case of certain variables, it makes theoretical sense – policy decisions can take time to be reflected in spending levels. Plus, lagging can help mitigate endogeneity issues arising from reverse causality. However, as reverse causality is an important methodological consideration10, an instrumental variable regression using lags of foreign-born as instruments is provided as an additional robustness check. Finally, country fixed effects are used in order to account for cross-sectional heterogeneity of the intercepts and omitted variable bias. By using country fixed effects, the aim is to ensure that time-invariant, country-specific aspects such as cultural influences that influence welfare state effort are accounted for. By doing so, all between-unit variation is eliminated, which narrows the analysis (Mummolo & Peterson, 2018). In addition, external, temporal shocks such as the expansion of the EU and the 2008 financial crisis may affect the results and so a two-way fixed effects model is provided as a robustness check. It is not provided as the main model specification as a two-way fixed effects model makes strong assumptions about pooled time-series cross-sectional datasets and requires a separate interpretation that can be difficult to conceptualise (Kropko & Kubinec, 2018). 9 Appendix B provides the p-values for each panel and both dependent variables. 10 To test for possible reverse causality, the lagged level of spending was regressed on the level of foreign-born and a positive statistically significant relationship was found. No such relationship was found for changes.
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