Skip to main content
SpringerLink
Log in

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

  • Original Article
  • Published:
Journal of Regulatory Economics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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)

Similar content being viewed by others

Notes

  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. 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. See also Polynomics and Jacobs University Bremen (2016).

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

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

References

  • Albouyi, D., Chernoff, A., Lutz, C., & Warman, C. (2019). Local labor markets in Canada and the United States, Staff Working Paper 2019–12. Bank of Canada.

  • Baumol, W. J., & Sidak, J. G. (1994). Stranded costs. Harvard Journal of Law and Public Policy,18(3), 835–849.

    Google Scholar 

  • Bernstein, J. I., & Sappington, D. E. (1999). Setting the X factor in price-cap regulation plans. Journal of Regulatory Economics,16(1), 5–25.

    Article  Google Scholar 

  • BNetzA. (2018a). Beschluss im Verwaltungsverfahren nach §29 Abs. 1 EnWG i.V.m. §32 Abs. 1 Nr. 2a i.V.m. §9 Abs. 3 ARegV, February 21, 2018.

  • Card, D., Heining, W., & Kline, P. (2013). Workspace heterogeneity and the rise of West German wage inequality. The Quarterly Journal of Economics,128(3), 967–1015.

    Article  Google Scholar 

  • Caves, D. W., Christensen, L. R., & Diewert, W. E. (1982). The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica: Journal of the Econometric Society, 50(6), 1393–1414.

    Article  Google Scholar 

  • Coelli, T. J., Rao, D. S. P., O’Donnell, C. J., & Battese, G. E. (2005). An introduction to efficiency and productivity analysis. Berlin: Springer.

    Google Scholar 

  • Destatis. (2019a). Arbeitskosten je Vollzeiteinheit, Produzierendes Gewerbe und Dienstleistungen. Retrieved from: https://www.destatis.de/DE/Themen/Arbeit/Arbeitskosten-Lohnnebenkosten/Tabellen/nettoarbeitskosten-stunden-laender.html. Accessed November 2019.

  • Destatis. (2019b). Index der Arbeitskosten je geleistete Stunde, Energieversorgung. Retrieved from: https://www-genesis.destatis.de/genesis//online/data?operation=table&code=62421-0001&levelindex=1&levelid=1573908161502. Accessed November 2019.

  • Destatis. (2019c). Index der Erzeugerpreise gewerblicher Produkte, Statistisches Bundesamt, Datenbank GENESIS. Retrieved from: https://www-genesis.destatis.de/genesis/online?sequenz=statistikTabellen&selectionname=61241. Accessed November 2019.

  • Destatis. (2019d). Preisindizes für die Bauwirtschaft, Fachserie 17, Statistisches Bundesamt. Retrieved from: https://www.destatis.de/DE/Themen/Wirtschaft/Preise/Baupreise-Immobilienpreisindex/Publikationen/bauwirtschaft-preise-artikel.html. Accessed November 2019.

  • Deuchert, E. (2015). Berücksichtigung von Faktorpreisen bei der Berechnung von Effizienzwerten. Energiewirtschaftliche Tagesfragen. 9, September 2015.

  • EC. (2018). Labour market and wage developments in Europe; Annual Review 2018. Luxembourg: European Commission. Publications Office of the European Union.

  • EC. (2019). Labour market and wage developments in Europe; Annual Review 2019, European Commission. Luxembourg: Publications Office of the European Union.

  • EU Parliament. (2015). Wage developments in the euro area: Increasingly unequal? Briefing, July 2015, EU Parliament, Brussels.

  • Färe, R., Grosskopf, S., Lindgren, B., & Roos, P. (1994). Productivity developments in Swedish hospitals: A malmquist output index approach. In Data envelopment analysis: Theory, methodology, and applications (pp. 253–272). Dordrecht: Springer.

  • Färe, R., Grosskopf, S., Logan, J., & Lovell, C. K. (1985). Measuring efficiency in production: With an application to electric utilities. In Managerial issues in productivity analysis (pp. 185–214). Dordrecht: Springer.

  • Fisher, I. (1922). The making of index numbers: A study of their varieties, tests, and reliability (Vol. 1). Boston: Houghton Mifflin.

    Google Scholar 

  • Fuchs, M., Rauscher, C., & Weyh, A. (2014). Die regionalen Unterschiede in Deutschland sind groß. IAB Kurzbericht,2014, 17.

    Google Scholar 

  • Geis, A., Kapp, D. & Kristiansen, K. (2018). Measuring and interpreting the cost of equity in the euro area. Economic Bulletin Issues 4, June 2018, European Central Bank.

  • Jamasb, T., & Pollitt, M. (2000). Benchmarking and regulation: International electricity experience. Utilities Policy,9(3), 107–130.

    Article  Google Scholar 

  • Jamasb, T., & Pollitt, M. (2004). Benchmarking and regulation of electricity transmission and distribution utilities: Lessons from international experience, Cambridge working papers in economics (CWPE). University of Cambridge. https://doi.org/10.17863/CAM.5398.

  • KPMG. (2018). Cost of capital study 2018. KPMG.

  • Littlechild, S. C. (1983). Regulation of British Telecommunications’ profitability: Report to the Secretary of State, February 1983. Department of Industry.

  • Malmquist, S. (1953). Index numbers and indifference surfaces. Trabajos de Estatistica,4, 209–242.

    Article  Google Scholar 

  • Maniadakis, N., & Thanassoulis, E. (2004). A cost Malmquist productivity index. European Journal of Operational Research,154(2), 396–409.

    Article  Google Scholar 

  • Polynomics and Jacobs University Bremen. (2016). Die Ermittlung des technologischen Fortschritts anhand von Unternehmensdaten—Der Einsatz der Malmquist-Methode im deutschen Regulierungsrahmen. Final report. Study conducted for Netze BW GmbH, August 24, 2016.

  • Törnqvist, L. (1936). The Bank of Finland’s consumption price index. Bank of Finland Monthly Bulletin,10(1936), 1–8.

    Google Scholar 

  • Uri, N. D. (2001). Productivity change, technical progress, and efficiency improvement in telecommunications. Review of Industrial Organization,18(3), 283–300.

    Article  Google Scholar 

  • WIK. (2017). Gutachten zur Bestimmung des generellen sektoralen Produktivitätsfaktors. Überarbeitete Version nach Eingang der Stellungnahmen [in German]. Study Bundesnetzagentur, July 10, 2017.

Download references

Acknowledgement

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.

Author information

Authors and Affiliations

  1. Jacobs University Bremen, Bremen, Germany

    Roland Meyer & Gert Brunekreeft

  2. Polynomics, Olten, Switzerland

    George Elias

Authors
  1. Roland Meyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gert Brunekreeft
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. George Elias
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roland Meyer.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1007/s11149-020-09411-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11149-020-09411-2

Keywords

JEL Classification

Search

Navigation