'Have Europeans Grown Tired of Democracy? New Evidence from 18 Consolidated Democracies, 1981-2018.', British Journal of Political Science. Link
Most of the supplementary empirical evidence can be accessed through the 'Plots' subpage.
The GAM model is specified with a standard smoothing spline, which enables us to estimate the smoothed nonlinear cohort effects. By applying this specification, we assume that the cohort effect is smoothly changing. We follow Grasso by including age as a categorical variable with three levels (15-29, 30-59, 60+) and control for period specific differences as fixed effects (Grasso, 2014):
We included birth cohorts as random and fixed effects, which constrains period trends to 0 (Bell and Jones, 2015: 203). Still, period effects can to arise from the respondents’ social context, since they are included as random effects. We thus model respondents as nested in cohorts and periods as their distinct social contexts. In order to “assess the relative importance of the two contexts, cohort and period, in understanding individual differences” (Yang and Land, 2006: 87), we treat periods and cohorts as independent random variables (thus assuming a person born in 1965 might have been surveyed in any survey wave, see Rabash and Goldstein, 1994; Rabe-Hesketh and Skrondal, 2008: 473). Finally, due to the simultaneous occurrence of age, cohort and period effects, every APC statistical model requires the assumption that there are no countervailing temporal influences, which offset the impact of the other temporal effects.
This specification is embedded in country fixed-effects multi-level regressions to account for different attitude levels across countries. As HAPC models may provide misleading results for linear cohort and period effects (Bell and Jones, 2017), we avoided the assumption of linear effects by including age and cohort terms with polynomials on the second and third order. Further, we divided cohorts into independent groups, separated into 17 categories by the five-year span when the individuals turned 18. For each dependent variable and each country, we ran robust cross-classified hierarchical age-period-cohort mixed regression with the following specification (Bell and Jones, 2015):
We use the observed values approach (OVA, Hanmer/Kalkan 2013) to calculate predictions for the cohort, period and lifecycle effects. Since the estimation of standard errors differs between GAM and rHAPC models, we employ two slightly different approaches to obtain measures of uncertainty for our predictions. We first describe the OVA for the GAM models: In a first step, we retrieve the predicted values and the standard errors from the model. Since GAM models differ from linear models, the 95 % confidence interval (t = 1.96) does not reflect the actual uncertainty in the fitted function. In order to obtain a valid confidence interval for GAM results we employ simultaneous intervals (Simpson 2018). Using Rubin's Imputation Rules (King et al. 2001), we calculate average predicted values (and their uncertainty) for each cohort and period. For rHAPC models, the overall idea of the OVA holds. However, when estimating standard errors for the predictions, we need to employ bootstrapping methods, since uncertainty cannot be analytically derived from mixed models. Using a parametric bootstrapping methods, we obtain standard errors for the single predictions of the fixed effects, e.g. cohort and lifecycle effects. We do not report uncertainty measures for period effects, which enter the equation only as random effects.
In several instances, the final analyses as reported in the manuscript deviates from the pre-analysis plan. In the following, we document and justify the deviations.
We preregistered attitudes towards expert governments as a primary variable of interest, ascribing it the same status as attitudes towards authoritarian governments. However, in the main text we only plot attitudes towards authoritarian governments and we mention only briefly results on attitudes towards expert governments. Due to limitations in space, we decided that two analyses on abstract regime preferences (democracy, authoritarianism) would be sufficiently informative. Evidence on attitudes towards expert governments are reported in the Shiny Web Application.
Note that the development of attitudes towards expert governments followed a similar trajectory as the indicators that are reported in the main text: there are no consistent period or cohort effect. We do observe notable cohort disparities in the Netherlands, Switzerland and UK which ponit towards stronger acceptance among the young generations and which may deserve further country-specific attention. At the same time, however, we observe generational decline in the acceptance of expert governments in Poland and considerable downward period effects in Germany.
In the pre-registration plan (and in the accompanying analysis syntax), we did not specify how the plotted predictions would be calculated. In response to a reviewer suggestion, we decided to report predictions based on the observed-value-approach. We consider this approach preferrable to other alternatives (such as predictions at representative values) because the reported estimates include information on all observations in the sample.
We fixed several minor or major mistakes that were part of the pre-registered analysis syntax. For example, we used the wrong variable to conduct the analysis on political interest. Hence, running the pre-registered analysis syntax may not replicate the results reported in the final study.