The main results of the regression analyses are presented in Table 2.4. For each out- come variable, estimates are provided for two models: one excluding a time trend (i.e. variable year) and the other including it. In situations where there are few notable differ- ences in the results generated by these two approaches, the discussion below focuses on the estimates produced by the models including a time trend (Models II, IV, and VI). To provide meaningful and accurate representations of the interaction terms in these models, three plots of marginal effects are included (see Figures 2.2, 2.3, and 2.4).
Beginning with the results for firm-based vocational training, the estimates confirm that the dispersion of authority and coordination legacies are interactively related to the development of this system type. As Figure 2.2 shows, the marginal effect of federalism on 5As Beck and Katz (2011) have highlighted, many data series used to compare political economies can appear to be non-stationary in the short run even though they are actually stationary in the long run. With the exception of GDP per capita, all of the measures included in this study have upper bounds – mathematical or conceptual. This means that they have to be stationary in the long run.
firm-based training increases strongly as the intensity of coordination legacies moves from weak to strong. With regard to substantive effects, a change in the coordination measure from 0 (e.g., the United States) to 3 (e.g., Germany) for a country with strong federalism is associated with a 1.482 point increase in the scale of firm-based training (ranges from 0 to 6), holding all else equal.6 Though not presented graphically here, the marginal effect of coordination legacies follows a similar pattern, as it increases as federalism shifts from non-existent to strong. For a country with robust coordination legacies, a shift from a unitary structure (e.g., Sweden) to a federal structure (e.g., Germany) is also associated with a 1.482 point increase in the scale of firm-based training. The confidence bounds for both sets of marginal effects never include zero, which indicates that they consistently meet the conventional threshold (p-value<0.05) for statistical significance.
Looking at the political variables, three of the four estimated effects are statistically sig- nificant. Two of these three variables, democracy and social cleavages, are negatively asso- ciated with firm-based training, which is consistent with what was expected. In substantive terms, a two standard deviation increase in the level of democracy (11.50 points) would, all else being equal, result in a 0.587 point decrease in the scale of firm-based training. A comparable shift in the cleavage variable (1.18 point increase) would produce a -0.695 point change in the same scale. The other significant variable, union density, exhibits a pos- itive relationship with firm-based training; a two standard deviation jump in union density (26.74 points) would increase the index of firm-based training by 1.043 points. While the estimated coefficient for liberal-socialist government has a positive sign, it does not meet the standard cut-off for statistical significance.
None of the economic factors included in this set of analyses have effects that are the- oretically consistent and statistically significant. Contrary to what was predicted, GDP per 6For the purposes of interpreting substantive effects, the 10th-and 90th-percentile values are used for the federalism and coordination variables because of their ordinal nature.
capita is positively related to firm-based training, with a 1 percent increase in affluence be- ing associated with a 0.012 increase in the scale of firm-based training.7 Therefore, a two standard deviation increase from the mean GDP per capita (a 73.7 percent increase) would add 0.884 points to the firm-based training score. The estimate for trade openness also contradicts existing theory, as it is negatively signed and relatively weak – a two standard deviation jump in this predictor would only result in a 0.258 point increase in the index of firm-based training. The proxies for the remaining two variables, industrial activity and economic diversity, have substantively and statistically insignificant effects.
In the models for school-based vocational training, the federalism and coordination regressors have meaningful and significant effects. Figure 2.3 presents a graphic represen- tation of the marginal effect of federalism on school-based training, which confirms that the negative effect of authority dispersion (i.e. positive effect of authority centralization) increases as coordination legacies shift from weak to strong. The substantive impact of a change in the coordination measure from 0 to 3 for a country with strong federalism is a -0.900 point change in the scale of school-based training. To make this finding more intu- itive for this study, the federalism measure has been inverted (thus creating a measure of centralization) and the marginal-effect plot reconstructed. The end result, which is found in Figure 2.4, is a new plot that simply mirrors the federalism plot, with the x-axis being the line of reflection. Therefore, in this inverted specification, a 0-to-3 jump in the coordi- nation index in a country with centralized authority (e.g., a shift from the UK to Sweden) generates a 0.900 increase in the scale of school-based training.
Among the estimates for the political variables in the models for school-based training, only the two representing democracy and cleavages exhibit consistent statistical signifi- cance. In this case, the level of democracy is positivity associated with the development of 7In a level-log relationship, the effect of the logged explanatory variable (log(x)) on the level outcome variable (y) can be interpreted in the following manner: a 1 percent change inxis expected to produce a Beta/100unit increase iny.
training, with a two standard deviation rise in the polity score producing a modest 0.219 gain in the index of school-based training. Similarly, the number of non-class cleavages is positively related to the expansion of school-based training; a two standard deviation increase in this variable results in a 0.485 increase in the training scale. Both of these rela- tionships contradict what had been hypothesized. Although liberal-socialist government is positively signed in both models, its coefficient is only significant in one model and not the other. The union density variable also fails to reach statistical significance in both models for school-based training.
Similar to the prior set of results, none of the of the economic regressors have con- sistently significant and meaningful effects on the index of school-based training. The estimates for GDP per capita and industry’s share of GDP flip in sign when a time trend is introduced into the model, and the latter estimate loses its statistical significance. In both models, the coefficient for trade openness hovers around zero and thus has no statistically distinguishable relationship with school-based training. Of these factors, territorial area comes the closest to having a strong and consistent association with the outcome variable. Drawing on the results from Model IV, a two standard deviation increase in this measure (around 377 percent of the mean value) would lead to a 0.604 decline the score of school- based training. The direction of this effect matches that which was hypothesized, but it is not statistically significant in both sets of results for school-based training.
Turning to the final set of regression estimates, the effects of federalism and coordina- tion and their interaction match the anticipated pattern, with an increase in one negatively affecting the effect of the other on the development of general education. Figure 2.5 shows the impact of this relationship on the marginal effect of federalism: the positive effect of federalism on the scope of general education wanes markedly as coordination legacies be- come more salient. In substantive terms, a change in the coordination measure from 0 to
3 for a country with strong federalism is associated with a 51.2 point decline in the enroll- ment rate for general-education schools at the secondary level. This interactive effect is statistically distinguishable from zero except when the value for the coordination variable is equal to 3 (i.e. strong legacies). Likewise, the marginal effect of coordination legacies on the outcome variable is not statistically significant when the authority structure is highly centralized.
The political and economic variables have surprisingly little statistical relevance in ex- plaining the variation in general education enrollment rates. GDP per capita and union density are estimated to have positive and significant effects on the expansion of general education in Model V, but these effects do not hold after a time trend is introduced. This lost of significance is not entirely unexpected for GDP per capita given that it is a measures with a strong upward trends, but controlling for this trend has no meaningful impact on the statistical significance of other variables.