Interaction Analysis

Figure 7.1 shows the effect of the ideological position of the leading government party on government size for several levels of the veto player variable. As the number of veto players increases, the slope of ideology flattens. The conditional coefficients and their t-statistics given in table 7.2 confirm this visual interpretation³¹. The ideology effect is almost nullified when the number of veto players exceeds three. The coefficient of ideology is quite large when a government party does not face any other veto players and decreases as the number of veto players increases. With four or more veto players, the ideology effect virtually vanishes.

31 Note that in contrast to the models in table 7.1, the coefficients in table 7.2 are based on centered but unstandardized variables. Unstandardized variables allow for the identification of empirically meaningful levels of the interacting variables. Conditional ideology effects at a certain number of veto players are more revealing than conditional effects at one or two standard deviations above or below the mean of the variable.

However, for comparative reasons, the unstandardized conditional coefficient at the mean of veto players is also given in table 7.2. It corresponds to the standardized coefficient of ideology given in model 2 of table 7.1. The unstandardized regression results for the full models are presented in table A9.

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Figure 7.1: Simple Regression Lines of Civilian Government Consumption on Ideology as a Function of Veto Players, 1965-1979

Change in Government Consumption

RIGHT-LEFT

-39.1342 37.1992

-2 -1 0 1 2

———– Simple slope on ideology at one veto player

— — — Simple slope on ideology at two veto players – – – – – Simple slope on ideology at three veto players

Notes: Conditional effects plot according to Kohler and Kreuter (2001: 224-226), all other independent variables are set to their means.

The counterfactual estimates given in table 7.2 indicate that government ideology had a substantial effect on changes in the dependent variable in the sixties and seventies. The figures represent the difference in the dependent variable that is due to different ideological positions of government at various levels of the veto player variable. In other words, they reflect the difference in the predicted value when ideology is set to its tenth and ninetieth percentile, respectively, and all other variables in the regression, except the veto player indicator, are set to its mean.

If the veto player variable is also set to its mean, the counterfactual estimate is based on the ideology coefficient given in model 2 in table 7.1. Here, a change in the ideology variable from its tenth to its ninetieth percentile is associated with a 1.26 percentage point increase in the change of government consumption. Taking into account that the average change in

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the dependent variable for the period is 2.81 %, a difference of 1.26 % between right and left parties is considerable.

Table 7.2: Ideology Effect on Civilian Government Consumption Conditional on Veto Players; and Counterfactual Estimates, 1965-1979

IDEOLOGY t-1 1 Veto

Player 2 Veto

Players Mean of

Veto Players 3 Veto

Players 4 Veto

Players 5 Veto Players

Coefficient 0.040** 0.029** 0.026** 0.018* 0.007 -0.004 (1.94) (1.94) (1.88) (1.45) (0.48) (0.18)

Counterfactuals 1.93 1.41 1.26 0.88

Notes: t statistics in parentheses based on panel-corrected standard errors; coefficients are based on unstandardized variables; estimates are based on model A2 in table A9; * significant at 10%; **

significant at 5%; *** significant at 1% (one-tailed tests); counterfactuals give the difference in the predicted values that results from a hypothetical change in the ideology variable from its 10th (far right) to its 90th (far left) percentile at different levels of veto players and when all other independent variables are set to their means..

Choosing the tenth and the ninetieth percentile for the calculation of the effect sizes is not too liberal. The tenth percentile of ideology corresponds closely to the ideology score of the German Christian Democratic Party in 1964 and the ninetieth percentile to the score of the British Labor Party in 1976. Neither of these parties exhibits extreme ideological positions. In addition, the raw scores of these percentiles are roughly -25 and +25, whereas the ideology variable can theoretically range from -50 to +50.

The 1.26 % increase in the dependent variable reflects the average effect of ideology over all possible numbers of veto players. Comparing the effect sizes for different numbers of veto players illustrates the constraining effects these have on the discretion of the leading government party. Where a party is governing alone and does not face any institutional veto players, the change in the predicted value amounts to 1.93 %. This effect is more than halved to 0.88 % if a government party faces two other veto players.

A note of caution is in order here. The differences in predicted values are given to aid in the interpretation of effect sizes. Of course, the regression coefficients also represent effect sizes, but they often do not convey their impact on the “real world”. However, a

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shortcoming of predicted values is that they do not give any information about the uncertainty involved in their estimation (King et. al., 2000: 356). Hence, the differences in predicted values should not be regarded in isolation, but only in combination with the t-statistics of the regression coefficients and their statistical significance. For this reason, only counterfactual estimates for statistically significant conditional effects are given and only their slopes are graphed in conditional effects plots like figure 7.1.

To sum up, this section showed that government ideology had a substantial effect on changes in government consumption during the sixties and seventies. The extent to which leading government parties could realize its favored policy outcome apparently depended on the number of veto players. The next section explores how robust these results are and describes the regression diagnostics performed.