Robustness of the Results
Appendix I presents a series of alternative model specifications to test the robustness of the results (see Tables A6.1-A6.3). Let me briefly highlight a number of relevant insights. First, individual-level intergovernmental preferences exert a significant negative effect on parliamentarians' support for interparliamentary cooperation (see Model 1) if the models include country dummy variables instead of country-level explanatory factors. Within countries, it appears, intergovernmentalists tend to be more opposed to interparliamentary cooperation than federally oriented deputies.
Second, the two institutional factors are consistently significant and have strong substantial effects regardless of model specification. Adding these two factors, which are both located at the country-level, moreover reduces the country-level residual variance in the data by a factor of 6 (Model 1), more than 10 (Model 2), and 2 (Model 3). In Model 3, the institutional factors are mostly insignificant, although in some model specifications (that is, excluding Germany or entering only one of the two factors into the model) they have a significant and negative effect. Institutional constraints clearly undermine support for a direct parliamentary role in the case of reform proposals that are not compatible with a focus on domestic oversight. It appears that domestically compatible reform proposals do not run into institutional constraints. However, against the background of the not entirely consistent results of the robustness tests, it cannot be ruled out that institutions might have a constraining effect even then.
Third, regarding the party-level variables, governing status is not significant in several specifications of Models 1 and 2, while being consistently significant and positive in variations of Model 3. The party leadership's support for the EU consistently has a negative and significant effect in Model 2 but loses significance after the exclusion of some countries. Most importantly, the effect disappears entirely if the analysis is restricted to parties with levels of EU support of five, or even three, or higher, the clear majority of parties in the data. In other words, the effect is driven by around ten very EU-sceptical parties that account for only 50 individual-level observations.