Economies of scale in Norwegian electricity distribution: a quantile regression approach

ABSTRACT

In this article, we investigate scale economies in Norwegian electricity distribution companies using a quantile regression approach. To the best of our knowledge, this is the first attempt to apply this estimation technique when analysing scale economies. We estimate the cost elasticities of the two output components: network length and number of customers, to calculate returns to scale. Our results show large potential of scale economies, particularly for the smallest companies. We also find that returns to scale is increasing over time. These findings have important implications for policymakers when they are deciding the structure of the industry in the future.

KEYWORDS:

• Norwegian electricity distribution companies
• policymakers
• economies of scale
• returns to scale
• quantile regression

JEL CLASSIFICATION:

• C23
• D00
• D39
• D42
• D29

Acknowledgements

The work in this study is a part of the project Benchmarking for Regulation of Norwegian Electricity Networks (ElBench). The project is funded by Norwegian Water Resources and Energy Directorate, Energy Norway and six electricity companies in Norway (Agder Energi Nett, Skagerak Nett, Eidsiva Nett, Hafslund Nett, BKK Nett and Istad Nett). Support from the Research Council of Norway through project 228811 is gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ For example, the effects from the various outputs (such as length of network or number of customers) could be different in the lower and upper tail of the TOTEX distribution.

² The Skewness and kurtosis indicate that our dependent variable, total costs (TOTEX) and ln(TOTEX) are not normally distributed. This is supported by the Shapiro–Wilk test which rejects the null-hypothesis of normal distribution in both TOTEX and ln(TOTEX). See Table A1 in the appendix for test statistics.

³ In the regulatory model of NVE, the number of network stations (NT) is also included. However, as one referee pointed out, there is a strong multicollinearity between the output variables. The variance inflation factors (VIF) between the output variables reduce from (NT = 42.76), (Q = 18.04), (N = 16.92) to (Q = 6.60), (N = 6.61) when we drop number of network stations from the model to avoid strong multicollinearity.

⁴ CAPEX includes annual depreciations and return on book values including 1% working capital. OPEX includes operational and maintenance costs. External costs of interruptions for customers consist of a cost of interrupted effect in the powerlines and losses per MWh (300 NOK). All distribution companies in Norway are by law obligated to report numbers on production and costs; see the website of the Norwegian Ministry of Petroleum and Energy: https://www.regjeringen.no/no/dokumenter/forskrift-om-okonomisk-og-teknisk-rappor/id507169/.

⁵ 1 USD = 7.72 NOK, 1 EUR = 9.56 NOK per 1 February 2018.

⁶ All costs are in 2010 NOK. The evolution of total costs from 2000 to 2013 is presented in Table A2 in the appendix.

⁷ Not to be confused with the standard error term from OLS, as the distributional properties are not intended to meet the same criteria as standard regression models.

⁸ Data and model specifications are available from the authors upon request. Test statistics are available in Table A3 in the Appendix.

⁹ RTS > 1 is to be interpreted as follows: if you double your inputs, you will more than double your output. At optimal scale RTS = 1, meaning that if you double your inputs, your outputs will also double.

¹⁰ For the interested reader, tables with mean, median, standard errors, p-values and confidence intervals for each quantile for each cost elasticity and RTS are to be found in the Appendix, see Tables A4–A6.

¹¹ Note that since we apply panel data from 133 firms, ranging from year 2000 to year 2013, some of the firms that have changes in input and output values can appear in different quantiles. However, since our goal is to estimate cost elasticities and RTS on the industry, this will not violate the results obtained in our estimation. If someone would like to use this method to derive firm-specific measures, this issue should be handled with caution. By reducing the number of quantiles, the number of ‘shifts’ will be reduced.

¹² The 95% confidence intervals are computed by the Delta-method. The Delta-method is a method for deriving the variance of a function of asymptotically normal random variable with known variance using a Taylor series expansion; see https://cran.r-project.org/web/packages/modmarg/vignettes/delta-method.html#fn7 for more details.

¹³ All Data and R-code used in this analysis are available on request.

¹⁴ The results are presented in Table A7 in the Appendix.

¹⁵ We would like to thank the referee who correctly pointed out that the increase in RTS over time could be affected by firms merging over time. Since we use unbalanced panel data in our analysis, this could be the case. However, to check this we have also run the model with a balanced panel data, and the effect on RTS increasing over time is higher; see Figure A1 in the appendix.

¹⁶ There are several reasons that firms experience different RTS (see, e.g. Coelli et al. 2005).

Additional information

Funding

The project is funded by Norwegian Water Resources and Energy Directorate, Energy Norway and six electricity companies in Norway (BKK Nett, Eidsiva Nett, Hafslund Nett, Helgeland Kraft, Lyse Elnett and Skagerak Nett).