Using VEA to assess effectiveness in the development of human capabilities


In this paper, we use value efficiency analysis (VEA) to assess effectiveness by means of a model decision making unit which is used as an overall benchmark. The latter is unanimously agreed that is “doing the right things” and defines a range of operating input/output mixes that is preferred by experts. We then decompose the effectiveness estimates into an efficiency component capturing the extent of “doing things right” and a mix component capturing the relative distance of the assessed units’ operating mix from the preferred range of operating mixes. The latter is residually estimated as the ratio of data envelopment analysis and VEA efficiency scores. We use the proposed approach to examine the effectiveness of countries in utilizing their economic prosperity to further develop their citizens’ social prosperity or human capabilities using UN data for the year 2015. The empirical results provide useful insights that help detecting countries which may need a shift of focus to relatively neglected aspects, in order to further enhance the capabilities of their citizens.

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  1. 1.

    For example, in assessing effectiveness in transport industry, inputs usually refer to number of vehicles, fuels and labor, outputs refer to the produced transport capacity (e.g., seat miles), while outcomes refer to the extent that produced capacity is consumed by customers (e.g., passenger-kilometer and ton-kilometer) (Yu and Lin 2008). Another example provided by Hanson (2018) is the assessment of military forces effectiveness, where inputs refer to resources such as personnel and equipment, outputs to countable services or goods such as the number of military units and the quality of their training, and outcomes to country-wide valued states and public goods such as peace, sovereignty or freedom.

  2. 2.

    Different types of weight restrictions may be used, such as absolute or relative bounds on the multiplier weights, resulting in a set of equal, common across DMUs, or DMU-specific input and output multipliers.

  3. 3.

    A detailed presentation of VEA can be found in Joro and Korhonen (2015).

  4. 4.

    See Korhonen et al. (2002) for more details regarding the several alternatives underlying the choice of the model DMU.

  5. 5.

    The mix component is similar (but not the same) to Filippetti and Peyrache (2011) compositional index and to the Li and Zhao (2015) dimension mix index, with the main difference being that their non-DEA frontiers result from a set of common (across DMUs) weights which in terms of Fig. 1 implies a linear frontier; see Fig. 1c.

  6. 6.

    Effectiveness scores are never higher than efficiency scores, as the VEA frontier envelops the DEA frontier.

  7. 7.

    VEA can also lead to a common set of weights. If for example both DMUs A and B were selected as MPS units (Fig. 1a), the VEA frontier would extend only facet AB toward the axes, thus creating a common set of weights that nevertheless defines again a range of preferred mix ratios. The same would occur if the inefficient DMUs I or J were selected to be the MPS, as for both of them the efficient peers identified by DEA are DMUs A and B.

  8. 8.

    DMUs may be “favored” by specific weight restrictions more or less than others, as e.g., DMUs J and F: The former is more (less) favored by the green (red) line of common (equal) weights, while the opposite holds for the latter. However, the same holds for effectiveness by means of the VEA model, as some DMUs are favored by the chosen MPS more or less than others: with DMU B as the MPS in Fig. 1a, DMU E is ineffective while if DMU D is chosen as the MPS the DMU E would be effective instead.

  9. 9.

    The capability approach is the underpinning of the construction of the Human Development Index (HDI), which concentrates in a set of basic and universally valued capabilities—longevity and education as well as gross national income.

  10. 10.

    “The income of a person can tell us a good deal about her ability to do things that she has reason to value” (Anand and Sen, 2000, p. 100).

  11. 11.

    Anand and Sen (2000, p. 101) also referred to outlier countries that are “doing much more to enhance life expectancy than their GNP per capita would suggest.” These outlier countries need to be identified and used as benchmarks for other countries.

  12. 12.

    DEA is a nonparametric methodology for estimating production frontiers and measuring efficiency. Compared to its parametric counterpart, stochastic frontier analysis (SFA), there are advantages and disadvantages. The main advantage of using DEA is that it does not require any information more than input and output quantities, while SFA requires an explicit specification of a functional form for the production function and an explicit distributional assumption for the inefficiency terms. Also, in DEA all deviations from the frontier are readily attributed to inefficiencies, i.e., it does not incorporate stochastic noise in the data as is done by SFA. The latter is a particularly important advantage when additional restrictions are incorporated in the model (as is the case of present paper), as the extension of the DEA frontier by the extra restrictions (see e.g., Fig. 1(a)) is not guaranteed to take place in the presence of stochastic noise.

  13. 13.

    All previous studies using this model assumed variable returns to scale, in order to reflect the diminishing returns as income increases and used an output orientation to gauge efficiency. Output orientation displays a focus toward increasing the current provision of health and education given the resources currently available. It also reflects the views of Ranis et al. (2000) and Suri et al. (2011) that improving levels of education and health should have priority or at least move together with direct efforts to enhance growth.

  14. 14.

    Ranis et al. (2000, p. 200) offer an example of such a spillover effect, citing studies that provide evidence that “education, especially female, tends to improve infant survival and nutrition.”

  15. 15.

    In terms of Fig. 1, Norway corresponds to DMU J.

  16. 16.

    This normalization scheme also avoids the process of truncating normalized values to unity, which is criticized by Lind (2019, p. 410) since it “suggests that human development has an upper limit.”

  17. 17.

    According to Färe and Karagiannis (2017) denominator rule, the aggregate values are computed using potential output shares. However, as we have more than one outputs for which there are no market prices, we have to approximate their “market” shares. Here, we follow the approximation suggested by Färe and Zelenuyk (2003) that assumes that the value of the total amount of any output is the same as the value of the total amount of any other output. This implies that the aggregation weights are equal to the unweighted average of the shares of the individual countries corresponding to each output, i.e., \(\frac{1}{K}\sum\nolimits_{j = 1}^{J} {\left( {y_{j}^{k} /\sum\nolimits_{k = 1}^{K} {y_{j}^{k} } } \right)}\).

  18. 18.

    The efficient countries are (in alphabetical order) Australia, Burundi, Central African Republic, Cuba, Georgia, Hong Kong, Iceland, Italy, Israel, Japan, Kyrgyzstan, Liberia, Moldova, Nepal, Republic of Congo, Solomon Islands, Switzerland, Tajikistan, the UK and Uzbekistan.

  19. 19.

    The respective information for the 2015 country clustering by income class was retrieved from the World Bank.

  20. 20.

    A case of reward funds is considered  by Golany and Thore (1997): the evaluation by the World Bank or some UN agency of loan requests made by developing countries.

  21. 21.

    Ranis et al. (2000) refer to the proportion of government expenditures for sectors related to human development that is attributed to such priority areas as HD priority ratio and argue that the latter is affected positively by the extent of government decentralization.


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We would like to thank three anonymous referees for useful comments and suggestions. The first author acknowledges financial support by the Hellenic Foundation for Research and Innovation (HFRI) and the Greek General Secretariat for Research and Technology, under the HFRI PhD Fellowship grant (GA. no. 698).

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Correspondence to Panagiotis Ravanos.

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Ravanos, P., Karagiannis, G. Using VEA to assess effectiveness in the development of human capabilities. Econ Change Restruct 54, 75–99 (2021).

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  • DEA
  • VEA
  • Efficiency
  • Effectiveness
  • Human capabilities
  • Social efficiency
  • Social prosperity