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# Evaluation

The evaluation phase starts with the evaluation of the results. Especially in large datasets, it is often difficult to interpret the results and to present them in a meaningful way. Summary statistics and visual tools can help to get additional insights. Even more important is the presentation for policy makers (or for those interested in the research). Interpreting radial efficiency scores is rather straightforward, whereas non-radial scores are more difficult to interpret and present. By presenting the initial results to the decision makers, a first sounding board is possible.

Closely related to this initial evaluation of the results is the review of the process. Having obtained the results, it is important to consider why particular observations are obtaining ‘odd’ results. These ‘odd’ results could arise from outliers remaining in the sample, from particular input-output combinations, or due to assumptions in the model (e.g., weight restrictions or CRS). Obviously, the results are what they are and a particular observation could not perform as efficient as expected (even after checking the assumptions).

Still, particular observations could be influenced by the exogenous environment. Thanks to environmental characteristics, the observations could obtain a higher efficiency score when the characteristics are favourable and, as such, behave as an additional (but unmeasured) input. Contrarily, when the environmental characteristics are unfavourable, they behave as an additional (but unmeasured) output. Therefore, the environment where the entity is operating in should be included in the analysis. Several procedures exist (see below for the selection of the variables), such as the frontier separation approach, the all-in-one model, multi-stage models, bootstrapping techniques and conditional efficiency estimates (see Fried et al., 2008; Daraio and Simar, 2007). Each of these techniques has its peculiarities and drawbacks (see De Witte and Marques (2008) for a review). If the researcher opted not to include the operational environment in a first stage, it is definitely worth examining the influence of the environment in a second stage. Simar and Wilson (2007) developed a double-bootstrap procedure which estimates the impact of exogenous characteristics on the production process (see also Fried et al. (2008) for a complementary intuitive explanation of the procedure).

Different model specifications (both in terms of model assumptions as VRS, input-orientation or environmental variable inclusion) could yield different outcomes, it could also be interesting to see whether these outcomes significantly differ. Indeed, so if there is no significant difference between the several models, it matters less which model assumptions are specified. A Monte Carlo comparison of two production frontier estimation methods and a set of statistical tests were developed by Banker and Natarajan (2004). Post-hoc statistical tests (Schaffnit et al., 1998), regression analysis (Camanho et al., 2009) and classification and regression tree (Emrouznejad and Anouz, 2010) can be performed to investigate the impact of external factors on efficiency scores obtained in DEA.