Economic Research and Perspectives

Economic Research and Perspectives

Identifying the Determinants of Persistent and Transient Inefficiency in Iranian Thermal Power Plants: Evidence from a Four-Component Stochastic Frontier Analysis

Document Type : Original Research

Authors
Mostafa Farrokhfal 1
Alireza Shakibaei 2
Zeinolabedin Sadeghi 3
1 PhD Student in Economics
2 Professor of Economics
3 Associate Professor of Economics
10.48311/ecor.2025.115452.0
Abstract
Abstract
This paper identifies and disentangles the determinants of persistent and transient inefficiency in Iranian thermal power plants. To obtain reliable efficiency estimates, a four-component Stochastic Frontier Analysis (SFA) model with unbalanced panel data is employed, enabling the separation of persistent (time-invariant or long-term) inefficiency from transient (time-varying or short-term) inefficiency. This distinction facilitates more targeted policy recommendations aimed at reducing inefficiency, enhancing productivity, and lowering electricity generation costs. Steam, gas, and combined-cycle power plants operating between 2012 and 2022 are examined. The results indicate that, except for publicly owned steam power plants, most thermal power plants exhibit persistent efficiency levels exceeding 80%. The most influential determinant of transient inefficiency is the plant’s operation during peak load periods. Efficiency improved steadily until 2020; however, inefficiency increased in 2021 and 2022.
Purpose/Aims:
Since its introduction by Aigner et al. (1977), SFA has become one of the principal methods for measuring efficiency. In stochastic frontier models, the efficiency of production (or cost or profit performance) is assessed relative to an estimated production frontier. However, approaches to frontier estimation and inefficiency specification differ across model formulations. A defining feature of SFA models is the decomposition of the error term into two components: a symmetric statistical noise component and a non-negative inefficiency component. The statistical noise term captures random shocks and measurement error, whereas the non-negative component reflects technical inefficiency, defined as the shortfall of observed output from potential (frontier) output.
Methodology & Framework:
This study distinguishes between persistent and transient inefficiency determinants in Iranian thermal power plants by employing a four-component SFA model with unbalanced panel data. Specifically, we apply a third-generation SFA framework introduced by Colombi et al. (2014) and estimate a translog production function using R software.
In this specification, the composite error term is divided into four components: plant-specific heterogeneity, random noise, persistent inefficiency, and transient inefficiency . Estimation is conducted using a single-stage maximum likelihood approach, which simultaneously estimates the production function parameters and the variance components associated with inefficiency determinants. This framework enables a clear separation between persistent (time-invariant or long-term) and transient (time-varying or short-term) inefficiency effects. Such differentiation allows for more precise policy recommendations aimed at improving productivity and reducing electricity generation costs.
The empirical analysis covers steam, gas, and combined-cycle power plants over the period 2012–2022.
Findings:
The results indicate that fuel is the most influential input in electricity production, with an estimated elasticity of 0.925; thus, a 1% increase in fuel input increases output by approximately 0.925%. Capital is identified as the second most important production factor, with an elasticity of 0.164, whereas labor is statistically insignificant. The insignificance of labor likely reflects the high degree of mechanization in thermal power generation and the relatively limited role of labor in the production process.
The estimated scale elasticity suggests slightly decreasing returns to scale (DRS) (–0.058). Output increases modestly over time (0.004), and although this growth accelerates slightly (0.002), the overall magnitude remains limited.
Regarding transient inefficiency, the most important determinant is plant operation during peak load periods. A 1% increase in the peak load ratio (PLR) reduces the variance of transient inefficiency by 4.38%. Pollution intensity has a positive and statistically significant coefficient, while plant age has a negative and marginally significant coefficient, suggesting that older plants may exhibit lower transient inefficiency variance. In contrast, the producer price index and ambient temperature are statistically insignificant.
In the persistent inefficiency component, transitioning toward gas (–1.611) and combined-cycle (–9.449) technologies, as well as private ownership (–1.306), significantly reduces inefficiency variance.
Discussion:
With the exception of publicly owned steam power plants, most thermal power plants demonstrate persistent efficiency levels exceeding 80%. Given this relatively high persistent efficiency, variations in total inefficiency are largely driven by differences in transient inefficiency. Plants exhibiting higher transient inefficiency consequently experience greater overall inefficiency.
Among technologies, gas power plants display the lowest transient efficiency. Because transient efficiency is primarily influenced by the ratio of peak load to nominal capacity, the relatively higher transient efficiency of steam power plants can be attributed to operational constraints. Steam units require longer ramp-up times to return to maximum capacity; therefore, system operators tend to keep them online. In contrast, gas plants are more frequently taken offline during periods of lower demand, contributing to lower transient efficiency.
Efficiency trends indicate marked improvement during most of the study period. Between 2012 and 2020, total efficiency increased from 50% to 66%, while transient efficiency rose from 67% to 77%, corresponding to growth rates of 32% and 14.9%, respectively. However, both indicators declined in 2021 and 2022. Although the overall trajectory remains positive, the average total efficiency remains relatively low.
With respect to scale properties, steam power plants operate under nearly constant returns to scale (CRS), suggesting proximity to their optimal production scale given current technology. By contrast, gas power plants predominantly exhibit increasing returns to scale (IRS), indicating unrealized economies of scale. This pattern is particularly pronounced among privately owned gas plants, where scale efficiency improves over time.
Conclusion & Implications:
Despite substantial efficiency gains during most of the study period, the Iranian thermal power sector continues to operate below its potential. With an average total efficiency of approximately 60%, electricity generation could theoretically increase by around 66% using the same level of inputs if all plants operated on the production frontier.
The analysis of scale properties using the Delta method highlights important structural differences across technologies. Overall, 13% of plants operate under DRS, with no gas plants in this category. Approximately 25% of steam and combined-cycle plants exhibit DRS. Combined-cycle plants show the highest prevalence of CRS, while gas plants display the strongest IRS. These findings underscore the importance of technology-specific policy design. In particular, expanding the operational scale of gas power plants may play a pivotal role in enhancing overall efficiency in the electricity sector.
Keywords
Persistent Inefficiency
Returns to Scale
Stochastic Frontier Analysis
Thermal Power Plants
Transient Inefficiency
Subjects
References
Addo, F., & Salhofer, K. (2022). Transient and persistent technical efficiency and its determinants: The case of crop farms in Austria. Applied Economics, 54(25), 2916-2932. https://doi.org/10.1080/00036846.2021.2000580
Aigner, D., Lovell, C. A. K., & Schmidt, P. (1977). Formulation and estimation of stochastic frontier production function models. Journal of Econometrics, 6(1), 21-37. https://doi.org/10.1016/0304-4076(77)90052-5
Ajayi, V., Weyman-Jones, T., & Glass, A. (2017). Cost efficiency and electricity market structure: A case study of OECD countries. Energy Economics, 65, 283-291. https://doi.org/10.1016/j.eneco.2017.05.005
Asgari, M. & Institute for Trade Studies and Research (ITSR), Tehran, Iran. (2019). Technical efficiency in Iran’s industry sector: A Stochastic Frontier Analysis (SFA) Approach. Qua
rterly Journal of Economic and Planning Research, 24(3), 61-85. https://doi.org/10.29252/jpbud.24.3.61 [In Persian]
Azarbayejani, M. Emadzadeh, M & Sameti, M. (2022). Measuring the level of competitiveness in the Iranian electricity industry, structural and non-structural approach aimed at achieving sustainable economic growth. Quarterly Journal of The Economic Research (Sustainable Growth and Development). 22(4). 261-281. [In Persian]
Badunenko, O., & Kumbhakar, S. C. (2017). Economies of scale, technical change and persistent and time-varying cost efficiency in Indian banking: Do ownership, regulation and heterogeneity matter?. European Journal of Operational Research, 260(2), 789-803.
https://doi.org/10.1016/j.ejor.2017.01.025
Battese, G. E., & Coelli, T. J. (1992). Frontier production functions, technical efficiency and panel data: With application to paddy farmers in India. Journal of Productivity Analysis, 3(1-2), 153-169
https://doi.org/10.1007/BF00158774
Bernstein, D. H. (2020). An updated assessment of technical efficiency and returns to scale for U.S. electric power plants. Energy Policy, 147, 111896. https://doi.org/10.1016/j.enpol.2020.111896
Colombi, R., Kumbhakar, S. C., Martini, G., & Vittadini, G. (2014). Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency. Journal of Productivity Analysis, 42(2), 123-136.
https://doi.org/10.1007/s11123-014-0386-y
Cornwell, C., Schmidt, P., & Sickles, R. C. (1990). Production frontiers with cross-sectional and time-series variation in efficiency levels. Journal of Econometrics, 46(1-2), 185-200.
https://doi.org/10.1016/0304-4076(90)90054-W
Danish, M. S., & Roy, P. K. (2024). Examining the persistent and transient technical efficiency of the Indian fertilizer industry. Applied Economics, 57(36), 5552-5566. https://doi.org/10.1080/00036846.2024.2364939
Dehghan, H., Amin-Naseri, M. R., & Nahavandi, N. (2021). A system dynamics model to analyze future electricity supply and demand in Iran under alternative pricing policies. Utilities Policy, 69, 101165
https://doi.org/10.1016/j.jup.2020.101165
Emami, A, M. Amadeh, H & Amini, F. (2017) Comparison of technical efficiency and bio efficiency in selected thermal power plants of Iran. Quarterly Journal of Energy Policy and Planning Research, 8(3), 33-67 [In Persian]
Filippini, M., Geissmann, T., & Greene, W. H. (2018). Persistent and transient cost efficiency-An application to the Swiss hydropower sector. Journal of Productivity Analysis, 49(1), 65-77.
https://doi.org/10.1007/s11123-017-0522-6
Filippini, M., Greene, W., & Masiero, G. (2018). Persistent and transient productive inefficiency in a regulated industry: Electricity distribution. Energy Economics, 69, 325-334. https://doi.org/10.1016/j.eneco.2017.11.016
Greene, W. (2004). Distinguishing between heterogeneity and inefficiency: Stochastic frontier analysis of the World Health Organization’s panel data on national health care systems. Health Economics, 13(10), 959-980.
https://doi.org/10.1002/hec.938
Greene, W. (2005). Fixed and random effects in Stochastic Frontier Models. Journal of Productivity Analysis, 23(1), 7-32.
https://doi.org/10.1007/s11123-004-8545-1
Growitsch, C., Jamasb, T., & Wetzel, H. (2012). Efficiency effects of observed and unobserved heterogeneity: Evidence from Norwegian electricity distribution networks. Energy Economics, 34(2), 542-548
https://doi.org/10.1016/j.eneco.2011.10.013
Hailu, K. B., & Tanaka, M. (2015). A “true” random effects stochastic frontier analysis for technical efficiency and heterogeneity: Evidence from manufacturing firms in Ethiopia. Economic Modelling, 50, 179-192. https://doi.org/10.1016/j.econmod.2015.06.015
Javaheri, A., S. & Ostadzad, A. H. (2014). Estimating efficiency of thermal and hydroelectric power plants in Iranian provinces. Iranian Journal of Economic Studies, 3(2), 19-42 [In Persian]
Jondrow, J., Knox Lovell, C. A., Materov, I. S., & Schmidt, P. (1982). On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of Econometrics, 19(2-3), 233-238.
https://doi.org/10.1016/0304-4076(82)90004-5
Kaveh, Kh., Emami, A, M. Asgari, F & Kiani, K, H. (2022) Comparison of technical and environmental efficiency of selected power plants and determination of the Ramsey price. Quarterly Journal of Quantitative Economics (Former Economic Surveys), 21(4), 1633-2219.
https://doi.org/10.22055/jqe.2022.39360.2445 [In Persian]
Kumbhakar, S. C. (1990). Production frontiers, panel data, and time-varying technical inefficiency. Journal of Econometrics, 46(1-2), 201-211
https://doi.org/10.1016/0304-4076(90)90055-X
Kumbhakar, S. C., & Heshmati, A. (1995). Efficiency measurement in Swedish dairy farms: An application of Rotating Panel Data, 1976-88. American Journal of Agricultural Economics, 77(3), 660-674
https://doi.org/10.2307/1243233
Kumbhakar, S. C., Lien, G., & Hardaker, J. B. (2014). Technical efficiency in competing panel data models: A study of Norwegian grain farming. Journal of Productivity Analysis, 41(2), 321-337. https://doi.org/10.1007/s11123-012-0303-1
Kumbhakar, S. C., Parmeter, C. F., & Zelenyuk, V. (n.d.). Stochastic Frontier Analysis: Foundations and Advances, 2017.
Lai, H., & Kumbhakar, S. C. (2018). Panel data stochastic frontier model with determinants of persistent and transient inefficiency. European Journal of Operational Research, 271(2), 746-755
https://doi.org/10.1016/j.ejor.2018.04.043
Mamipoor, S. Mansuri, F. & Nazemi, A. (2018). Forecasting electricity price fluctuations in the Iranian electricity market using the Markov Switching GARCH model. Quarterly Journal of Econometric Modeling (Quarterly Journal of Applied Economic Theories), 9(1). 93-122. [In Persian]
Martini, G., Porta, F., & Scotti, D. (2024). Persistent and transient productive efficiency in the African airline industry. Journal of Productivity Analysis, 61(3), 259-278. https://doi.org/10.1007/s11123-023-00674-3
Meeusen, W., & Van Den Broeck, J. (1977). Efficiency estimation from Cobb-Douglas Production Functions with composed error. International Economic Review, 18(2), 435. https://doi.org/10.2307/2525757
Mehrabi, M. Sharifi, A & Saffari, B. (2024) Economic modeling of power pool of Iran and western neighbors using optimization approach. Quarterly Journal of The Economic Research (Sustainable Growth and Development), 24(1), 163-192. [In Persian]
Moeeni, Sh. Saffari, B. Sharifi, A & Hayati,S. (2019). Analysis of supply bidding in the pay-as-bid electricity market structure in Iran based on Holmberry approach. 24(4), 1-26 [In Persian]
Musau, A., Kumbhakar, S. C., Mydland, Ø., & Lien, G. (2021). Determinants of allocative and technical inefficiency in stochastic frontier models: An analysis of Norwegian electricity distribution firms. European Journal of Operational Research, 288(3), 983-991. https://doi.org/10.1016/j.ejor.2020.06.023
Nakaishi, T., Takayabu, H., & Eguchi, S. (2021). Environmental efficiency analysis of China’s coal-fired power plants considering heterogeneity in power generation company groups. Energy Economics, 102, 105511
https://doi.org/10.1016/j.eneco.2021.105511
Nguyen, B. H., Sickles, R. C., & Zelenyuk, V. (2022). Efficiency Analysis with Stochastic Frontier Models Using Popular Statistical Softwares. In D. Chotikapanich, A. N. Rambaldi, & N. Rohde (Eds.), Advances in Economic Measurement (pp. 129-171). Springer Nature Singapore
https://doi.org/10.1007/978-981-19-2023-3_3
O’Donnell, C. J. (2018). Productivity and Efficiency Analysis: An Economic Approach to Measuring and Explaining Managerial Performance. Springer Singapore. https://doi.org/10.1007/978-981-13-2984-5
Ohadi, N. Shahraki, J. Pahlavani, M & Mardani, M. (2019) Carbon environmental efficiency assessment with imprecise data using Fuzzy Data envelopment analysis (Case study: Iran and oil-producing countries). Quarterly Journal of The Economic Research (Sustainable Growth and Development), 19(4), 111-129. [In Persian]
Pajouyan, J.Mohammadi, T. Bahrami, J. & Etbaei, F. (2014). A comparative study of the auction mechanism of the Iranian electricity market with the market settlement price auction mechanism. Quarterly Journal of Economic Research, 53(2), 1-35 [In Persian]
Pérez-Arriaga, I. J. (Ed.). (2013). Regulation of the Power Sector. Springer, London. https://doi.org/10.1007/978-1-4471-5034-3
Pitt, M. M., & Lee, L.F. (1981). The measurement and sources of technical inefficiency in the Indonesian weaving industry. Journal of Development Economics, 9(1), 43-64. https://doi.org/10.1016/0304-3878(81)90004-3
Schmidt, P., & Sickles, R. C. (1984). Production frontiers and Panel Data. Journal of Business & Economic Statistics, 2(4), 367-374
https://doi.org/10.1080/07350015.1984.10509410
Shiva, R & Shahbazi, M. (2020). Assessing the competitiveness status and the impact of market power on electricity prices: A case study of the Iranian wholesale electricity market. Quarterly Journal of Energy Policy and Planning Research. 18(1), 67-108 [In Persian]
Sickles, R. C., Wang, Z., & Zelenyuk, V. (2024). Stochastic Frontier Analysis for Healthcare, with Illustrations in R. In S. Grosskopf, V. Valdmanis, & V. Zelenyuk (Eds.), The Cambridge Handbook of Healthcare (1st ed., pp. 404–444). Cambridge University Press.
 https://doi.org/10.1017/9781009483766.014
Sickles, R. C., & Zelenyuk, V. (2019). Measurement of Productivity and Efficiency: Theory and Practice (1st ed.). Cambridge University Press. https://doi.org/10.1017/9781139565981
Tovar, B., & Wall, A. (2024). Persistent and transient inefficiency in ports: An application to Spanish port authorities. Research in Transportation Business & Management, 54, 101124. https://doi.org/10.1016/j.rtbm.2024.101124
Tsionas, E. G., & Kumbhakar, S. C. (2014). Firm heterogeneity, persistent Ana Transient Technical Inefficiency: A generalized true random-effects model. Journal of Applied Econometrics, 29(1), 110-132
https://doi.org/10.1002/jae.2300
Tsolas, I. E. (2021). Efficiency analysis of lignite mining operations using production Stochastic Frontier modeling. Mining, 1(1), 100-111
https://doi.org/10.3390/mining1010007
Wang, H. J., & Ho, C. W. (2010). Estimating fixed-effect Panel Stochastic Frontier models by model transformation. Journal of Econometrics, 157(2), 286-296. https://doi.org/10.1016/j.jeconom.2009.12.006
Wang, J. & Wang, S. (2023). The effect of electricity market reform on energy efficiency in China, Energy Policy, 181(3), 122-137
https://doi.org/10.1016/j.enpol.2023.113722.