26 Chapter 2 ever, the difference is more likely to be the result of a substantive reason, such as the two indicators measure slightly different aspects of welfare state effort. Arguably, the generosity index is a better indicator for policy changes and how politicians aim to redistribute social risk, but it excludes a large number of social programmes such as family benefits, certain types of unemployment insurance, and healthcare. As aggregate indicators have been used, there could be specific programmes driving the changes in spending that are not included within the generosity index. Moreover, the generosity index combines the three welfare programmes it covers equally. For social spending, however, the budget is not equally split between its component programmes and that different weighting could lead to slightly differing effects. Another possibility is that because the generosity index is created through combining replacement rates and benefit rule changes, there could be opposing effects happening on these constituent parts of the indicator leading to a neutral result. Finally, it may be that different mechanisms apply to the different programmes included in the generosity index; hence the net effect is neutral. An area for future research could be to untangle these different associations for specific programmes outside of spending, which would complement this article and the research conducted by Soroka et. al. (2016). Largely, however, neither measure indicates that any retrenchment of the welfare state is taking place as a result of immigration. 2.4.2 Sensitivity Analysis In order to check the robustness of the results, three main tests were undertaken. First, because of the mixed results regarding panel stationarity, a first-differences model has been estimated in Table 2.5. Second, Table 2.6 shows the results of the two-way fixed effects model and third, Table 2.7 presents the results of an instrumental variable (IV) regression. Overall, the effect of foreign-born on spending and generosity remains stable across the various models employed. Table 2.5 shows the results for spending and generosity as a lagged firstdifferences model. In this model the number of observations drops, and the explanatory power of the model reduces, but the foreign-born population remains statistically significant and positively associated with social spending, while there is still no relationship with the generosity index. Moreover, the magnitude of the coefficient for foreign-born is similar to the original model of lagged levels. Table 2.6 then shows the original specification but with the inclusion of two-way fixed effects. Again, the results for foreignborn hold for both dependent variables, although the magnitude of the effect for social spending reduces.
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