Empirical Results

4.5.4.1 Data Robustness

Using the outlier detecting procedure, as proposed by Andrews and Pregibon (1978) and Wilson (1993), we find atypical observations in the data sample. Figure 4.3 presents the plot of the log-ratio of the geometric volume for the East/West model of HCK. We can observe a major peak with a value of about three that indicates a small value of the geometric volume; i.e. reducing the data sample by certain companies will result in a sounder dataset. This examines a value that is about 20 times higher

than the minimum value (=exp(3)=20). Thus, in the sample there are twelve companies found to be outliers and hence, they are removed from the sample of 335 distributors. Those skipped distributors contain the largest DSOs in the data amongst others when size is defined as the annual amount of electricity delivered. However, the representativeness remains almost untouched. The sample data covers 55% of the total number of distributors and 43% of the total electricity delivered.47

Figure 4.3: Outlier in DEA Model 2 of Hirschhausen, Cullmann, and Kappeler (335 obs.)

Source: Own calculation.

After controlling for outliers we re-examine the technical efficiency scores of the DSOs for the first three HCK models using DEA with bootstrapping with the reduced data set.48 In addition, we figured out the mean efficiency scores for both regions. The DEA results are outlined in Table 4.4.

Table 4.4: DEA Results under CRS of the Models of Hirschhausen, Cullmann, and Kappeler

Model Note Average

sample Average East Average West DEA 1 323 0.41 0.49 0.38

DEA 2 323, Inverse Density Index East/West Model

0.42 0.51 0.44

DEA 2, VRS 323, Inverse Density Index 0.45 0.49 0.40

Source: Own calculations.

We observe two major results: First, the average efficiency scores of approximately 42% are far less than the scores ranging from 60% to 70% found by HCK that appear to result from the different

47

Assuming that the results of the graphical analysis are representative for the entire data set, we do not undertake further outlier detecting for the models developed in this paper, because these models mainly use the data specified in HCK.

datasets; the bootstrapping bias accounted only for a reduction of about 5 percentage points in our calculation. Second, we find that the good performance of the East German DSOs is consistent across all model specifications. Thus, we can state that the atypical observations deleted from the sample only have a small impact on the sample results and hence, data robustness can be confirmed.

4.5.4.2 Specification Robustness

The TE scores of the models defined in section 4.5.3 are calculated using DEA CRS and VRS technology structures.49 Table 4.5 shows the average efficiency scores for the DSOs of the total sample as well as for the average East and West German DSO in contrast to the base HCK model (Base).

Table 4.5: DEA and SFA Results

Models Average sample Average East Average West

DEA SFA DEA SFA DEA SFA

CRS VRS CRS VRS CRS VRS

Base 0.42 0.45 0.80 0.49 0.51 0.82 0.40 0.44 0.79

H1 0.42 0.47 0.82 0.49 0.52 0.83 0.40 0.46 0.82

H2 0.43 0.45 0.81 0.50 0.52 0.84 0.40 0.43 0.81

H3 0.42 0.47 0.83 0.50 0.53 0.84 0.40 0.45 0.82

Source: Own calculations.

First, considering model H1 that also accounts for services for other DSOs as an output, we found that the efficiency scores are slightly increasing under VRS, but for the West German DSOs even to a greater extent. This supports our expectation that accounting for the utilization of the grid more explicitly affects efficiency positively but it also indicates that services subject to third party access not necessarily increase efficiency because there is no change under CRS technology. The results of the second models H2 considering the grid composition indicates slightly higher efficiency scores for the mean East German DSO but slightly decreasing scores for the mean West German DSO, indicating that the efficiency gap has even increased slightly. Turning to the third model that incorporates both issues of customer services and the grid composition, the results show slight efficiency increases under VRS for both average DSOs. However, we cannot observe remarkable changes neither in the efficiency scores nor in the efficiency gap.

Summing up, there are two main findings: First, our model specifications do not alter the efficiency scores remarkably. Second, the efficiency gap cannot be closed by accounting neither for different customer services nor for the grid composition under our base technology CRS as well as under VRS.

48

The other models of HCK are not recalculated because our dataset does not contain all relevant variables. 49

The composition of the peers shows that the initial DEA frontiers are generated jointly by East and West German distributors. Hence, we can conclude that our assumption of one technology for all DSOs is justified.

Referring to the robustness analysis, the alternative hypothesis of no efficiency differences under CRS has to be rejected and the null hypothesis of specification robustness can be confirmed.

4.5.4.3 Methodical Robustness

In order to evaluate the methodical robustness we apply the alternative benchmarking technique SFA in a first step for calculating efficiency scores for verification purpose and in a second step we assess the correlation among the models.

The SFA results are presented in Table 4.5 and show efficiency scores that are notably higher than the corresponding DEA scores among almost all models.50 Importantly, on the one hand, we also find a low variance of the TE scores but on the other hand, the results show the efficiency gap to be nearly vanished compared to the DEA results.

Table 4.6: Pearson Correlation Coefficients

Sample size: 304 DEA, CRS SFA

H1 H2 H3 H1 H2 H3 DEA H1 1.00 0.97 0.98 0.35 0.42 0.35 DEA H2 1.00 0.98 0.34 0.42 0.35 DEA H3 1.00 0.35 0.42 0.36 SFA H1 1.00 0.94 0.99 SFA H2 1.00 0.95 SFA H3 1.00

Source: Own calculations.

Table 4.6 shows the statistical significant Pearson correlation coefficients of the TE scores of the model specifications. Among the group of DEA and SFA models, the correlation of over 90% support the low variation of the different model specifications. Comparing the DEA models with the corresponding SFA models indicate low correlation ranging from 34% to 42%. Although Model H2 shows the highest correlation between the estimates of both techniques, such small values provoke us not to confirm coherence of the efficiency results based on the Pearson correlation coefficients. In addition, the higher efficiency scores for the East German DSOs almost disappear when applying SFA induces that the structural efficiency differences between the regions appear to result from data noise DEA does not control for.