On aggregate composite indicators

Abstract

In this paper it is shown that the unweighted arithmetic average is the theoretically consistent scheme to aggregate composite indicators, derived from the benefit-of-the-doubt model, across decision-making units.

Keywords:

• Composite indicators
• Benefit-of-the-doubt model
• Aggregation across decision-making units

Journal of the Operational Research Society advance online publication, 29 June 2016; doi:10.1057/jors.2015.81

Journal of the Operational Research Society advance online publication, 29 June 2016; doi:10.1057/jors.2015.81

Acknowledgements

This research has been co-financed by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program ‘Education and Lifelong Learning’ of the National Strategic Reference Framework (NSRF)—Research Funding Program: THALES-Investing in Knowledge Society through the European Social Fund.

Notes

1 The OECD (2008) handbook also mentioned another set of methods that can be used to estimate composite indicators. These are referred to as participatory methods and are the budget allocation process, the analytic hierarchy process and the conjoint analysis.

2 This has been interpreted as a 'helmsman', namely a collective decisionmaking apparatus underlying every unit being assessed, that attempts to steer all of the sub-indicators towards their maximum levels (Lovell and Pastor, 1999).

3 More on the radial DEA models with a single constant input can be found in Lovell and Pastor (1999), Caporaletti et al (1999), and Liu et al (2011). Notice also that the unitary input DEA models are equivalent to DEA models without explicit inputs.

4 Since the radial, single constant input DEA model exhibits constant returns-to-scale (Lovell and Pastor, 1999), the composite indicator can also be estimated by using the output-oriented formulation of the model.

5 If the kth DMU is efficient then with all other for .In turn (4) implies that I^k = 1.

6 Koopmans' (1957) theorem states that industry maximum profitisequal to the sum of firms' maximal profits as long as all firms face the same input and output prices.

7 In general, however, industry cost efficiency is equal to the share-weighting sum of DMU' scost efficiencies, with the aggregation weights being their share to industry total (observed) cost (see eg, Färe and Grosskopf, 2004, pp 118–119).

8 Alternatively, one can use the general cost efficiency aggregation rule as stated in footnote 7 and then notice that the input shares (ie, ) in this case simplify to 1/K as all DMUs have the same amount (namely, one unit) of the single input and face the same input price.

9 We disregard books (textbooks or others) because in their majority have not gone through a formal referee process.

10 This increase is related to three new faculty members that jointed the department in 2003 and their journal article publication record was above the departmental average.