## Abstract

Recent studies investigating convergence in energy consumption at the sectoral level within a country suggest that aggregate energy consumption could mask considerable differential impacts that might be observed at the sectoral level. This study aims to contribute and complement the existing convergence literature with an attempt to analyze sectoral convergence in energy consumption from the developing country perspective. To this end, we choose Turkey as a developing country and employ both the conventional unit root tests and the residual augmented least squares-Lagrange multiplier (RALS-LM) methodology to investigate stochastic conditional convergence in per capita energy consumption at the sectoral level. Our findings suggest some interesting outcomes that could be relevant from the sectoral energy consumption perspectives for developing countries. While energy consumption in Turkey shows a trending upward, the leading sectors of industry and transport energy consumption per capita diverge from the mean consumption and, therefore, lead to further increases in energy consumption and energy-related emissions. Moreover, agriculture and the other sector, whose consumption per capita values are below the mean, converge towards the mean. Overall, Turkish sectoral energy consumption trends follow developing countries’ patterns, and the empirical findings suggest that this trend is worrying from the sustainability perspective.

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## Notes

- 1.
We should approach this claim cautiously, especially when we analyze stochastic conditional convergence in energy consumption from a developing country perspective. As discussed in the following pages of this paper in detail, stochastic conditional convergence is mainly defined as the deviations from the sample average, which generally has upward trend for developing countries. Therefore, even if we find sectoral convergence in per capita energy consumption for a developing country, sectors might converge to a higher level of energy consumption, but not to a lower level.

- 2.
According to S-shaped relationship between energy consumption and economic development, at the early stages of economic development, which refers to labor-intensive agriculture-oriented economies, the energy consumption is relatively slow compared with economic growth. When economies transit to become more industrial, the energy consumption increases with this type of transformation as more capital and energy-intensive sectors require more demand for energy use. At final stage, transforming to a service sector, energy demand again stabilizes as these sectors are less energy-intensive and able to employ more energy-efficient technologies (Deichmann et al. 2018).

- 3.
Please note that the shares of fossil fuel and renewables cannot be quantified for final energy consumption for each sector since electricity consumption for these sectors does not provide a detailed information with regard to energy types.

- 4.
It should be noted that the figures do not add up to 100%. This is because we do not include heat generation or renewables as their shares have not changed significantly or become very small.

- 5.
Abramovitz (1986), Baumol (1986), and De Long (1988) can be regarded as the earlier empirical works in this direction. However, it is equally important to note that the number of studies on income convergence dramatically increased after Mankiw et al. (1992), which emerge as the fundamental empirical framework in the existing literature to test for

*β*convergence using cross-section data based on the Solow (1956) cross-country growth regressions. These regressions are then estimated using panel data estimators, i.e., fixed effect, random effect, difference GMM, or system GMM (Islam 1995; Caselli et al. 1996; Bond et al. 2001). It is worth noting that while several empirical studies including Carlino and Mills (1993), Evans (1996), and Li and Papell (1999) have investigated stochastic convergence, Durlauf and Johnson (1995), Papageorgiou (2002), Masanjala and Papageorgiou (2004), and others have examined the club convergence. - 6.
Gujarati (2004: 818) states that “An important assumption of the DF test is that the error terms are independently and identically distributed. The ADF test adjusts the DF test to take care of possible serial correlation in the error terms by adding the lagged difference terms of the regressand. Phillips and Perron use nonparametric statistical methods to take care of the serial correlation in the error terms without adding lagged difference terms. Since the asymptotic distribution of the PP test is the same as the ADF test statistic (...)”. Baltagi (2011: 383) simply explains that “All tests for unit root have the hypothesis of non-stationarity as the null with the alternative being that the series is stationary. Two unit roots tests with stationarity as the null and non-stationarity as the alternative are given by Kwaitowski et al. (1992) (...) Test known as KPSS is an analog of the Phillips-Perron test (...)”. Gujarati (2004:819) also highlights that “Most tests of the DF type have low power; that is, they tend to accept the null of unit root more frequently than is warranted. That is, these tests may find a unit root even when none exists. (...) In applying the unit root tests one should therefore keep in mind the limitations of the tests.” Enders (2014:35) confirms this with “A test with good power would correctly reject the null hypothesis of a unit root when the series in question is actually stationary. Monte Carlo simulations have shown that the power of the various Dickey Fuller tests can be very low.” For a detailed comparison between these unit root tests, see Arltová and Fedorová (2016).

- 7.
Note that LM test employed here is sometimes called as transformed LM and differs from LM test developed in LS (2003).

- 8.
- 9.
While the two-step LM unit root test depends only on the number of structural breaks, it is invariant to the size and location of the breaks (Lee et al. 2012: 102). On the other hand, RALS-LM tests have good size and power properties even when the sample size is relatively small (Meng et al. 2014: 353). As in our study, Meng et al. (2013) and Akram et al. (2020) using LM and RALS-LM methods also carried out their analysis using 51 and 47 years, respectively.

- 10.
For further information on data transformation process, see data Appendix in the supplementary file or visit https://data.mendeley.com/datasets/tgmk8dgz4v/2.

- 11.
Some researchers, however, define stochastic convergence as a deviation from a reference economy, and in this case, averagePCEC

_{t}is replaced by PCEC_{1t}, where 1 is the index for the reference country (Islam 2003). - 12.
For empirical results of ADF, PP, and KPSS unit root tests, see data Appendix in the supplementary file.

- 13.

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We would like to thank anonymous reviewers for their valuable and constructive comments and suggestions.

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Karakaya, E., Alataş, S. & Yılmaz, B. Sectoral convergence in energy consumption from developing country perspective: The case of Turkey.
*Energy Efficiency* **13, **1457–1472 (2020). https://doi.org/10.1007/s12053-020-09891-3

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### Keywords

- Sectoral convergence
- Energy consumption
- Unit root tests
- Turkey