Statistical Model

Because the dependent variable is a continuous measure bounded to the interval[0, 1] (the proportion of vague sentences in a decision document)¹⁷, I employ a fractional logit regression (Papke and Wooldridge, 1996). Fractional logit is a Quasi-MLE (QMLE) method with the conditional expectation of a fractional response variable:

E(y_i|x_i) =Λ(x_iβ) = ^exp(x_iβ)

1+exp(x_iβ) ^(4.1)

where y_i with 0 ≤ y_i ≤ 1 is the fraction of vague sentences in document i, Λ(.) is the logistic function and x_i refers to the explanatory variables of document i, a 1×K+1 vector for K independent variables. β is a K+1×1 vector of coefficients. The quasi-likelihood is the same as the Bernoulli log-likelihood used in the ordinary logistic regression case, with the individual contribution given by:

l_i(β) =y_ilog

Λ(x_iβ)^+ (1−y_i)log1−_Λ(x_iβ)^ (4.2)

Papke and Wooldridge (1996) show that variance misspecification can be an issue when estimating a fractional logit regression. In my application, such a misspecification could arise if the number of sentences in a decision document and some of the covariates are not independent. The usual standard errors from ordinary logistic regression are then misleading. As a fix for this, Papke and Wooldridge (1996) propose to use robust standard errors based on the well-known sandwich estimator (Papke and Wooldridge, 1996, 622). I follow this estimation strategy in the main analyses, but provide additional analyses based on bootstrapping as an alternative way to obtain estimates and standard errors in the robustness section.

In order to test H1 and H2 in the German application, the following model specifica-tion is estimated (Λ(.)is always the logistic function):

E(ProportionVagueSentences_i|x_i) =Λ(β₁+β₂IdeologicalDistance_i +β₃CaseComplexity_i

+β₄SecondSenate_i +β₅OralHearing_i

+β₆RiskNoncompliance_i)

17For the French application, it is the proportion of vague words in a decision document.

103

4.4. A COMPARATIVE APPLICATION

Testing H3a requires an interaction because the behavior of the GFCC in cases of high risk of noncompliance is argued to be conditional on the ideological distance to legislator. To test H3 in the German application, the following model is estimated:

E(ProportionVagueSentences_i|x_i) =Λ(β₁+β₂IdeologicalDistance_i +β3CaseComplexity_i

+β₄SecondSenate_i +β₅OralHearing_i

+β₆RiskNoncompliance_i

+β₇IdeologicalDistance_i×RiskNoncompliance_i) For the French application, the following models are estimated for H1 and H2:

E(ProportionVagueWords_i|x_i) =Λ(β₁+β₂IdeologicalDistance_i +β₃CaseComplexity_i

+β₄RiskNoncompliance_i)

The model for H3b in the French applications again contains an interaction term, because the behavior of the court in cases of a high perceived risk of noncompliance is conditional on the ideological distance between court and legislator. The following model is estimated:

E(ProportionVagueWords_i|x_i) =Λ(β₁+β₂IdeologicalDistance_i +β3CaseComplexity_i

+β₄RiskNoncompliance_i

+β₅IdeologicalDistance_i×RiskNoncompliance_i) Generally, positive coefficients suggest that a court writes more vague decisions and negative coefficients suggest that a court writes less vague (ergo, specific) deci-sions. Because the coefficients of fractional logit models are difficult to interpret, I use simulations to produce quantities of interest for sensible scenarios (King, Tomz and Wittenberg, 2000).

In the simulations, I use the so-called “observed value” approach (Hanmer and Ozan Kalkan, 2013). In this approach, only the variable(s) of interest are varied and each of the other independent variables are hold at their observed values for each observation in

104

CHAPTER 4. THE VALUE OF VAGUENESS

the data. Then, the relevant quantity of interest is calculated for each observation, and finally averaged over all observations (Hanmer and Ozan Kalkan, 2013, 264). Hanmer and Ozan Kalkan (2013) argue that the observed value approach has multiple advan-tages compared with the usually-used “average-case” approach¹⁸, most importantly that the obtained results better represent the collected data and that the findings are more robust to model misspecification. It needs to be emphasized that the expected values of these simulations are not the predicted probabilities of writing a vague decision, but the expected proportion of vague sentences in a decision vagueness. I also want to stress that the dependent variable in the German and French analysis is not the same:

in Germany, it is the proportion of vague sentences, in France it is the proportion of vague words in a decision. Thus, the expected values are not directly comparable.

4.5 Results

This section shows the results of the fractional logit models for the Judicial Uncertainty Hypothesis (H1), the Preference Divergence Hypothesis (H2) and the two hypotheses related to the perceived risk of legislative non-compliance for both analysis in Germany (Pressure Hypothesis (H3a)) and France (Defensive Mechanism Hypothesis (H3b)). I only show simulation results in this section, but provide the corresponding regression tables in the Appendix in Table C.2.

Results of the Judicial Policy Uncertainty Hypothesis

The formal model predicts that decision vagueness will increase as judicial policy uncertainty increases, because courts want to give discretion to the legislator if they face decisions which required specialized knowledge they do not possess. Figure 4.1 plots the effect of judicial policy uncertainty on decision vagueness for Germany (left side) and France (right side). For all graphs, I scaled the Yaxis such that it ranges from 0 -100, so that the numbers can be directly interpreted as percentages.¹⁹ For continuous variables, I visualize the inferential uncertainty in a “spaghetti”-style plot instead of directly summarizing it in confidence intervals. Each line in this plot represents the expected values based on one draw of the simulation. Confidence intervals are displayed using dashed white lines. The distribution of the independent variable of interest is shown by a density plot on the x-axis. This is because the usually used rugs do not reveal the number of observations in the data represented by each rug.

For both countries, we observe a positive and statistically significant effect of judicial policy uncertainty on decision vagueness. Just as the formal model predicts, this means

18In the average-case approach, the variable(s) of interest are varied and the values of the other independent variables are usually set at their mean or median.

19This simply means that the fractions are multiplied by 100.

105

4.5. RESULTS

Figure 4.1 – Effect of Judicial Uncertainty on Decision Vagueness, GFCC and CC

●

Note: Left Side: Expected percentage of decision vagueness for simple and complex cases, with the correspond-ing first difference uscorrespond-ing simulations. Simulations are carried out uscorrespond-ing N=1, 000 draws using Model 1 of Table C.3. For the simple and complex case scenario, the complex case dummy was set to zero and one, respectively.

The points represent the point estimates and the bars represent 90% confidence intervals.

Right side: Expected percentage of decision vagueness over a range of judicial uncertainty, including 90% con-fidence intervals using Model 1 of Table C.4. Judicial uncertainty is measured by the number of legal doctrines considered in a decision.

that the higher the judicial policy uncertainty of the judges, the higher the decision vagueness. In the German analysis, decision vagueness (percentage of vague sentences) increases by 0.1 percentage points when judges face a complex case compared with a simple case. This is a small but significant effect (the corresponding first difference is statistically significant at the 90% level).

In the French analysis, decision vagueness increases by about 0.36 percentage points from 0.39 percent (minimum judicial uncertainty) to 0.75 percent (maximum judicial uncertainty) decision vagueness (vague words per decision) over the range of judicial uncertainty (measured by the number of legal doctrines examined in a decision). This is, on average, around a 1.5 standard deviation increase in the predicted percentage of decision vagueness. Both analyses thus support the predictions of the formal model of Staton and Vanberg (2008) with respect to the Judicial Policy Uncertainty Hypothesis.

Results of the Preference Divergence Hypothesis

With respect to preference divergence, the formal model predicts that higher preference divergence, namely less ideological agreement between court and legislator, will lead to writing less vague decisions. This is because the courts are aware that if they give the legislator discretion by writing vague decisions, the final policy outcome will less strongly represent the preferences of the court and more the preferences of the legislator.

106

CHAPTER 4. THE VALUE OF VAGUENESS

While this is not a problem when the court and legislator share the same preferences, it is undesirable from the court’s perspective to write vague decisions in cases of a large preference divergence with the legislator.

Figure 4.2 plots the effect of preference divergence on decision vagueness. We observe different effects when looking at the GFCC (left side) and the CC (right side). In the analysis of the GFCC, there is, as expected, a negative effect of preference divergence on decision vagueness. This means that the higher the ideological distance between court and legislator, the less vague the decisions become. This is to ensure that the final policy outcome is not too distant to the GFCC’s ideal point. Therefore, the German analysis supports the formal model’s predictions. Please note that although the confidence intervals at the upper and lower end of the curve (minimum and maximum preference divergence) overlap, the corresponding first difference is statistically significant at the 90% level (see Appendix C.3).

However, when looking at the French court, we observe the opposite effect than in Germany: an increase in preference divergence leads the French judges to write increasingly vague decisions. This effect is statistically significant at the 95% level. This is against the formal model’s prediction. One reason for this finding might be that the French judges are willing to make more concessions to the legislator because of the highly political appointment procedure in France (Hönnige, 2009). Another explanation might be measurement error: the CMP scores used to measure the ideological distance between court and legislator are criticized with regard to their spatial and temporal comparability (Lowe et al., 2011; König, Marbach and Osnabrügge, 2013). I will have a closer look at this possibility in the robustness section. In summary, my analyses of the Preference Divergence Hypothesis shows that the formal model’s prediction is only confirmed when looking at the GFCC, but not for the CC.