Table 4.4: Empirical models
Model 1 Model 2 Model 3 Model 4
Outputs
Capacity Capacity Capacity Capacity
Speed Speed Speed Speed
Inputs
ME Carbon Emissions ME Power ME Power ME Power
AE Carbon Emissions ME SFOC ME SFOC ME SFOC
ME Carbon Factor ME Carbon Factor ME Carbon Factor AE Carbon Emissions AE Power
AE SFOC
AE Carbon Factor
To ensure the obtained results are not driven by the model formulation and are robust to alterna-tive specifications, a sensitivity analysis is conducted in section (4.5.3).
Table 4.5: Technical efficiency score results with respect to sector-specific frontiers
Sector Original eff.
score
Bias-corrected eff. score
Lower bound Upper bound Mean bias
Bulk carrier 0.838 0.826 0.813 0.836 0.012
Chemical Tanker 0.866 0.852 0.839 0.863 0.014
Container ship 0.941 0.936 0.931 0.940 0.005
Gas carrier 0.848 0.829 0.805 0.846 0.019
Oil tanker 0.852 0.841 0.830 0.851 0.011
with the largest sample size, but its average bias of 1.2% is higher than the container shipping sector’s average bias of 0.5%. This is most likely due to the observations in the container ship-ping sector being more homogeneous than those in the bulk carrier sector. Hence, there appears more variability in the input-output structure of bulk carriers and, thus, more diversity in ship designs from an energy efficiency perspective. Further, for all considered sectors, the uncorrected average efficiency scores are located outside the constructed confidence intervals. This emphasizes the utility of bias-correction in this application and the risk of using uncorrected efficiency scores, especially if one would be interested in the relative performance of the individual observations (De Borger et al., 2008; Fallah-Fini et al., 2012).
I will now turn to the interpretation of the derived results. In general, efficiency scores smaller than one represent the magnitude of improvements that could be achieved in the outputs without requiring additional inputs. The scope for efficiency improvements ranges, on average, from 6.4%
to 17.4%, depending on the sector. To illustrate, on average, bulk carriers could increase their output capacity and speed by 17.4% without requiring additional machinery or energy inputs. In contrast, container ships, on average, can only improve their outputs by 6.4% given the inputs.
The scope for average efficiency improvements in the other three sectors appears rather similar, ranging from 14.8% to 17.1%, but focusing on a single point-wise measure only yields an incomplete picture of the analysis. To provide a more detailed description, the distribution of bias-corrected
efficiency scores per sector is presented in Figure (4.2) in the appendix. To illustrate, the efficiency score distributions for the oil and chemical tanker sectors appear concentrated around the average efficiency score, and few observations are located close to the frontier. On the other hand, in the gas carrier sector, the global maximum is around a value of 0.77, and there is a larger dispersion of efficiency score values, with many observations located close to the sector frontier.
Based on the preceding interpretation, one might conclude that if one sector has a higher average efficiency than another, it implies that the sector is more efficient. However, the results of Table (4.5) only present the relative performance of vessels compared to their sector-specific frontiers, which might differ in location. Hence, the efficiency scores derived from benchmarks against differ-ent sector frontiers cannot be directly compared with each other. The results for the metafrontier analysis, allowing for industry-wide comparisons across sectors, are reported in the following sec-tion.
4.5.2 Results for metafrontier
In this section, the industry metafrontier enveloping the group frontiers is constructed to en-able comparisons of relative performance across sectors according to the methodology in section (4.4.2.3). For this purpose, all observations were pooled to compute a common industry metafron-tier representing the current state of ship design technologies across all considered sectors. Table (4.6) shows the average bias-corrected efficiency scores with respect to the group frontiers and the metafrontier, as well as the metatechnology ratios, for each sector.
Overall, the average metatechnology ratios range from 82.8% to 95.0% across sectors. To give the reader a specific example, the average technical efficiency in the chemical tanker sector with respect to the group frontier is 0.852. This means that, on average, chemical tankers could improve their outputs by 14.8% without requiring additional machinery or energy inputs. When compared to the industry metafrontier, the average technical efficiency of chemical tankers drops to 0.705. Thus, the potential for output improvements (given the inputs) is twice as high for chemical tankers when considering the unrestricted industry metafrontier instead of the restricted sector frontier. Another
Table 4.6: Summary of the technical efficiency corresponding to each sector in the pooled dataset
Technical efficiency group frontier
Technical efficiency meta-frontier
Metatechnology ratio
Sector Mean Std. Dev. Mean Std. Dev. Mean Std. Dev.
Bulk carrier 0.826 0.045 0.725 0.054 0.878 0.045
Chemical Tanker 0.852 0.045 0.705 0.048 0.828 0.035
Container ship 0.936 0.046 0.890 0.076 0.950 0.062
Gas carrier 0.829 0.081 0.740 0.054 0.898 0.073
Oil tanker 0.841 0.053 0.752 0.069 0.895 0.069
Note: Table (4.6) reports the bias-corrected efficiency scores. Differences in the estimated bias for each vessels with respect to the group frontier and metafrontier leads in rare instances (0.7% of total observations) to metatechnology ratios marginally greater than one.
way of stating this observation is by looking at the average metatechnology ratio, which is 0.828 for the chemical tanker sector. On average, given the machinery and energy inputs, the maximum output that can be achieved by a chemical tanker is 82.8% of the output that is feasible given the current state of ship design technologies in the maritime industry. In contrast, the average metatechnology ratio for the container shipping sector is 0.95. This large value also implies that the container shipping sector’s frontier is more tangent to the industry metafrontier than the chem-ical tanker sector’s frontier. Hence, the container shipping sector plays a bigger role in spanning the unrestricted industry metafrontier than the chemical tanker sector. A similar observation can be made for gas carriers, where the average metatechnology ratio is 0.898. Although the average potential for improving outputs with respect to the sector frontier is 17.1%, their maximum output that can be achieved is already 89.8% of the feasible output; thus, the sector frontier is adjacent to the industry metafrontier.
Lastly, the results from the pooled metafrontier model allow for a test of whether there are any statistically significant differences in the efficiency scores of the considered sectors. For this, the Kruskal–Wallis test is utilized to test whether efficiency scores of the sector samples originate from
the same distribution (Kruskal & Wallis, 1952). The test rejects the null hypothesis that the mean ranks of the sectors are the same at the 1% level. Thus, it can be concluded that there are statis-tically significant differences between the efficiency scores of vessels in the different sectors. This further validates the usefulness of the metafrontier framework in this application to compare the relative performance across considered sectors.
4.5.3 Sensitivity analysis and robustness
In this section, the robustness of the derived relative performance measures is assessed. This is an important task, as it is known that estimated relative efficiency scores are sensitive to a variety of factors, which might jeopardize the generalizability of the derived results (Cooper et al., 2004). In this study, two of the main concerns are the sensitivity of the computed results with respect to the empirical model formulation and potential idiosyncratic data mistakes.
Because the theoretical framework outlined in Figure (4.1) allows for multiple input and output set formulations, one can ex ante only hypothesize about the appropriate model specifications based on contextual reasoning. However, this choice has direct implications for the estimated ef-ficiency scores and the precision of the DEA estimator. In general, increasing the dimensionality of the technology set by increasing the number of input/output variables leads to, ceteris paribus, (weakly) increasing efficiency scores. In addition, the sample bias is increasing in the number of output/input variables, requiring much larger sample sizes to derive precise estimates (Simar &
Wilson, 2008). Therefore, the efficiency scores for the alternative model formulations summarized in Table (4.4) were computed as a robustness check.
Outliers due to idiosyncratic data mistakes are another prime concern when using the DEA ap-proach. Especially, if such an outlier is located at the frontier, its existence might impact the relative performance of several other observations through, e.g., facilitating unrealistic convex combinations to span the frontier (Bogetoft, 2013). Thus, the sensitivity of efficiency scores was evaluated for all models in Table (4.4) by excluding all potential data mistakes identified in section (4.4.1.1) as an additional robustness check. Table (4.7) summarizes the average standard efficiency
scores for these robustness checks alongside the results for Model 3 for comparison.
Table 4.7: Sensitivity analysis with respect to model specification and data validation outliers
Model 1 eff.
scores
Model 2 eff.
scores
Model 3 eff.
scores
Model 4 eff.
scores
Sector All
obs.
Outliers excluded
All obs.
Outliers excluded
All obs.
Outliers excluded
All obs.
Outliers excluded
Bulk carrier 0.819 0.821 0.838 0.839 0.838 0.840 0.840 0.841
Chemical Tanker 0.861 0.877 0.866 0.884 0.866 0.884 0.874 0.893 Container ship 0.940 0.948 0.940 0.949 0.941 0.950 0.947 0.952
Gas carrier 0.833 0.842 0.848 0.851 0.848 0.852 0.850 0.866
Oil tanker 0.849 0.883 0.852 0.887 0.852 0.888 0.853 0.888
Note: Table (4.7) reports uncorrected efficiency scores for the considered models with all observations and with outliers excluded. The conclusion does not change when considering bias-corrected efficiency scores.
In general, the average efficiency scores across sectors are, as expected, increasing in the number of input and output variables and are only minorly different from the results of Model 3. This observation confirms that the derived results are not driven by the empirical model choice based on contextual reasoning. The biggest deviation from the presented results can be observed in Model 1 for the bulk carrier sector, with an absolute difference in average efficiency scores of 1.9%. Simi-larly, when excluding outliers, the average efficiency scores are increasing across sectors compared to the models with all observations. This can be explained by the reduced number of observations when constructing the sector-specific frontiers, which (weakly) increases the efficiency scores, as well as the potential bias due to the reduced sample size. However, the changes in average effi-ciency scores are overall only moderate across sectors. The largest absolute difference in average efficiency scores ranges from 3.4% to 3.6% for the oil tanker sector. This can be explained by the fact that in this sector, more outliers are located at the frontier. However, this does not imply that all excluded outliers are idiosyncratic data mistakes, as the presented data validation approach does not capture the correction and adjustment factors incorporated in the EEDI formula. Hence,
it is a rather cautious evaluation by removing all potential idiosyncratic data mistakes to ensure the robustness of the analysis. To conclude, the results from the sensitivity analysis show only slight deviations from the presented results, which is reassuring.