TOTEX Malmquist index for CPI-X regulation: Does it correctly estimate the true frontier shift?


The X in CPI-X regulation aims to adjust price or revenue allowances to changes in total factor productivity and input prices. If calculated correctly, both terms together correspond to the change in efficient costs which can be determined by applying a cost Malmquist index. However, regulators typically lack the required data on input quantities and prices. As an alternative, regulation authorities may apply a TOTEX Malmquist index to measure the total cost change. We study under which conditions this total cost change correctly estimates the true efficient cost change. Overall, we conclude that the TOTEX Malmquist approach can be used for CPI-X regulation. However, regulators should be aware of the limitations and make adjustments in the implementation where necessary.

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Fig. 1

Source: own illustration

Fig. 2

Source: own illustration

Fig. 3

Source: own illustration based on data by Destatis (2019b, c, d)

Fig. 4

Source: own illustration based on data by Destatis (2019a)


  1. 1.

    To be more precise, in CPI-X-regulation, regulators use the general rate of inflation (CPI), instead of the sector specific difference between input price change and change in total factor productivity. Accordingly, X is a correction term for CPI that captures the deviations between the sectoral and overall developments. As we will explain further below, X consists of four terms.

  2. 2.

    The energy regulator in Germany, Bundesnetzagentur (BNetzA), has started to apply the Malmquist Index for the regulation of the energy networks in 2018 and 2019 for gas and electricity distribution and transmission network operators, respectively.

  3. 3.

    See also Polynomics and Jacobs University Bremen (2016).

  4. 4.

    See e.g. see Coelli et al. (2005).

  5. 5.

    Regulatory practice distinguishes between “individual X-factors” reflecting the relative inefficiencies and catch-up factors on the one hand, and the “general X-factor”, reflecting the overall productivity change as in the frontier shift on the other hand. For an overview of international practices to treat inefficiencies in regulation see e.g. Jamasb and Pollitt (2000, 2004).

  6. 6.

    While TFP is defined as a positive productivity change, TC is defined negatively as the reduction of input uses in period 1 compared to period 0.

  7. 7.

    For instance, the efficiency value CE (w0,x1, w0x*0 ) results as a firm’s benchmark using its actual inputs from period 1 but prices from period 0 against all remaining firms with inputs and prices from period 0. Hence, calculating CTC requires separate information on price and quantity data for each observation period.

  8. 8.

    Alternatively, the condition also holds if changes in technical and allocative inefficiency exactly compensate each other, which would be a rather unlikely coincidence, however.


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This paper is based on a study for Netze BW. The authors would like to thank Netze BW and especially Eva Deuchert for valuable contributions and comments. Furthermore, we are grateful for useful comments at the international IAEE conference 2018 in Groningen and those by an anonymous referee of this journal.

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Correspondence to Roland Meyer.

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Meyer, R., Brunekreeft, G. & Elias, G. TOTEX Malmquist index for CPI-X regulation: Does it correctly estimate the true frontier shift?. J Regul Econ 58, 78–97 (2020).

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  • Price regulation
  • Malmquist index
  • Total factor productivity
  • Data envelopment analysis

JEL Classification

  • L51
  • D24