80 Chapter 4 democratic and other left parties in government based on their seat share in parliament, measured in percentage of the total parliamentary seat share of all governing parties, weighted by the number of days in office in a given year (Armingeon et al., 2023a, 2023b). Also included is trade union density as a control for the bargaining power of domestic labour (Armingeon et al., 2023a; Visser, 2016). For deindustrialisation, we follow the method proposed by Iversen and Cusack (2000). The study accounts for differing GDP per capita and the fiscal pressure that can stem from unemployment. Finally, we account for the number of beneficiaries for each spending category using the unemployment rate, old and young dependency ratios, and the disability rate. As we only have data until 2013 for the disability rate, the time period for incapacity spending is limited to 2004 – 2014. 4.3.5 Method To examine the relationship between immigration and welfare, this study utilises pooled time-series cross-sectional data for the analysis. The model employs panel-corrected standard errors (PCSE) with a Prais-Winsten correction for serial correlation and country fixed effects. Previous studies typically rely on the de facto Beck-Katz standard, which combines fixed effects with a lagged dependant variable, to account for serial correlation (Gaston & Rajaguru, 2013; Lipsmeyer & Zhu, 2011; Soroka et al., 2006; 2016). However, the lagged dependent variable, which is used to correct for serial correlation, can be a source of considerable bias known as Nickell bias (Nickell, 1981). The lagged dependent variable is highly correlated with the dependent variable and consequently causes bias in the standard errors. This is especially prevalent when t is smaller than 20, which it is in our study. Thus, we use PCSE with the Prais-Winsten correction to correct for panel-heteroscedasticity and contemporaneous spatial correlation, which is argued as the more appropriate method by Plümper et al. (2005). However, in our robustness section, we present the results of an error correction model for comparison, which does include a lagged dependent variable as well as the lagged level and change of each variable included in the main model specifications. As is conventional, we lag the explanatory variables by one year as it is theoretically reasonable to expect that changes in certain independent variables can take time to affect the dependent variable. For example, the policy process is often slow, and policy decisions will not be immediately reflected in levels of welfare spending. Methodologically, lagging the explanatory and control variables can help to mitigate endogeneity issues arising from reverse causality. In addition to country fixed effects to address cross-sectional heterogeneity of the intercepts and omitted variable bias, we use three specific time dummies to control for when different EU countries lifted labour market restrictions on EU migrant citizens from the new member states. Consequently, we do not include additional time dummies, however we believe
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