Incentivizing centrally regulated units to improve performance: Pitfalls and requirements

Abstract

This paper explores the foundations for developing incentives for influencing units operating within centrally managed organizations. We begin by laying out the theory of managerial control in principal-agent contexts and draw from the incentive mechanisms developed in the related field of economic regulation. In particular, we highlight issues, differences and similarities in three recently proposed approaches under these circumstances, not only to compare them, but more importantly to motivate and arrive at requirements that should be met by incentivization systems in centrally managed multi-unit organizations. The stipulated requirements are not intended to be exhaustive but rather aim at defining conceptual foundations for further discussions and encouraging avenues for future research in this field. Our investigations are supported by graphical examples and an analysis of empirical data from banking.

Keywords:

• Data envelopment analysis
• central management
• incentive regulation
• incentivization mechanism

Acknowledgements

This work was supported by the Deutsche Forschungs-gemeinschaft (DFG) in the context of the research fund AH 90/5-3.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 In a broader context, an appropriate modification of the approaches being discussed in this paper may be used in cases in which there exist natural monopolies instead of usual competitive markets. Examples are those of large infrastructure industries like water, electricity and gas networks. For a comprehensive overview see, e.g., Bogetoft (2013); Agrell and Bogetoft (2017); Agrell and Bogetoft (2018); Afsharian et al. (2022).

2 Note that these approaches have also been further developed for other purposes of incentivization in centrally managed multi-unit organizations. For example, Afsharian et al.’s approach is used as a basis to design a system of incentives for units that are organized into a few distinct management groups (see Afsharian, 2020). More recently, it was also suggested that radial DEA models in Fang’s approach should be replaced with slack-based models to capture more appropriately the efficiency scores (Davtalab-Olyaie et al. 2021). There are also other methods for the sake of incentivization (see, e.g., Afsharian et al., 2019; Dai, 2021). A comprehensive consideration of such methods is not pursued here as they are not built upon the three approaches discussed in this paper.

3 As argued in Ylvinger (2000), the grand unit (or the average unit in this case) can be used to evaluate the efficiency for a system of units when a reallocation of inputs across the units is allowed. Otherwise, the use of the average unit may bias the measure of the overall efficiency. Hence, the application of the program in (6)(6) $$\begin{array}{c}\mathit{\text{Eff}}=\underset{}{\mathrm{\text{max}}}\sum _{j=1}^n\sum _{r=1}^s{u}_r^{}{y}_{\mathit{\text{rj}}}^{}+n\mu \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\\ \mathrm{s}.\mathrm{t}.\sum _{j=1}^n\sum _{i=1}^m{v}_i^{}{x}_{\mathit{\text{ij}}}^{}\hspace{0.17em}=\mathrm{ }\hspace{0.17em}1,\\ \sum _{r=1}^s{u}_r^{}{y}_{\mathit{\text{rj}}}^{}\hspace{0.17em}-\sum _{i=1}^m{v}_i^{}{x}_{\mathit{\text{ij}}}^{}+\mu \hspace{0.17em}\le \mathrm{ }\hspace{0.17em}0,j=1,\hspace{0.17em}\dots \hspace{0.17em},n\\ v_i^{}\ge \mathrm{ }\hspace{0.17em}0,i=1,\hspace{0.17em}\dots \hspace{0.17em},m\mathrm{ }\hspace{0.17em}\\ u_r^{}\ge \mathrm{ }0,r=1,\hspace{0.17em}\dots \hspace{0.17em},s\\ \mu \hspace{0.17em}\mathit{\text{free}}\hspace{0.17em}\hspace{0.17em}\mathit{\text{in}}\hspace{0.17em}\hspace{0.17em}\mathit{\text{sign}}.\end{array}$$(6) is only advised where this requirement is met (see also the discussions in Afsharian, 2021).

4 An extended program was also proposed in Afsharian et al. (2017) to result in a unique optimal solution with unique efficiency scores, if multiple solutions (though rarely) exist for the grand unit.

5 Determined by the decentralized approach.

6 Our program in (6)(6) $$\begin{array}{c}\mathit{\text{Eff}}=\underset{}{\mathrm{\text{max}}}\sum _{j=1}^n\sum _{r=1}^s{u}_r^{}{y}_{\mathit{\text{rj}}}^{}+n\mu \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\\ \mathrm{s}.\mathrm{t}.\sum _{j=1}^n\sum _{i=1}^m{v}_i^{}{x}_{\mathit{\text{ij}}}^{}\hspace{0.17em}=\mathrm{ }\hspace{0.17em}1,\\ \sum _{r=1}^s{u}_r^{}{y}_{\mathit{\text{rj}}}^{}\hspace{0.17em}-\sum _{i=1}^m{v}_i^{}{x}_{\mathit{\text{ij}}}^{}+\mu \hspace{0.17em}\le \mathrm{ }\hspace{0.17em}0,j=1,\hspace{0.17em}\dots \hspace{0.17em},n\\ v_i^{}\ge \mathrm{ }\hspace{0.17em}0,i=1,\hspace{0.17em}\dots \hspace{0.17em},m\mathrm{ }\hspace{0.17em}\\ u_r^{}\ge \mathrm{ }0,r=1,\hspace{0.17em}\dots \hspace{0.17em},s\\ \mu \hspace{0.17em}\mathit{\text{free}}\hspace{0.17em}\hspace{0.17em}\mathit{\text{in}}\hspace{0.17em}\hspace{0.17em}\mathit{\text{sign}}.\end{array}$$(6) .

7 With our notations, its intermediate efficiency score, i.e., ${\theta }_2^{\mathit{\text{int}}}=$ 0.978.

8 As the authors illustrate their approach with the same banking data set given in Table 3, an example could be useful: Let us assume that we seek to find the subset of k outstanding branches that have the greatest impact on the overall efficiency of the whole system of 16 branches. Applying their mixed-integer program, in case k = 1, branch 12 is recognized as outstanding. This result is not surprising as this branch shows the highest super-efficiency score of 1.027 within Afsharian et al.’s approach. However, in case of, e.g., k = 3, the identified branches are 1, 2 and 7. This means that this subset of three branches has an impact, which is the largest compared to any other subset of three branches that could have been selected. Interesting to note that—in Afsharian et al.’s approach—while branches 1 and 7 are already recognized as super-efficient, branch 7 has an efficiency score of 0.978. Nevertheless, the mixed-integer program also suggests branch 7 as outstanding. For more details, see Section 4 in Afsharian and Bogetoft (2020).