Efficiency of Indian Thermal Power Plants and Suspended Particulate Matter: Findings Across Technological Assumptions and DEA Models

Abstract

Suspended particulate matter (SPM) emissions from coal-based thermal power plants (CTPPs) cause respiratory illness. However, this has not been given its due importance in the efficiency assessment of CTPPs. This study contributes to the literature by incorporating suspended particulate matter in the benchmarking exercise for Indian CTPPs. In such a study, the theoretical assumptions regarding pollution generating technology or the choice of evaluation tool may impact the ranking of CTPPs. To draw robust inferences, we present a comparative study of two alternative microeconomic approaches (joint and by-production technologies) and two types of data envelopment analysis tools (graph–hyperbolic and directional distance function) applied on two representative samples of Indian CTPPs. Results indicate that Indian CTPPs are moderately inefficient. Choice of technological assumption or data envelopment analysis model does not impact the ranking of CTPPs. Ownership and plant load factor play vital roles in determining inefficiency, and impacts of these factors remain stable across models.

JEL Classifications: C61, D22, Q40, Q50

Keywords

Bad output by-production joint production directional distance function graph hyperbolic power plants

Introduction

Coal-based thermal power plants (CTPPs) are the primary source of energy for India. However, the use of coal as the primary input for electricity generation produces various pollutants such as suspended particulate matters (SPM), CO, CO₂, nitrogen oxides (NO_x) and SO₂. In an emerging economy like India, electricity is an essential input for economic growth. Nevertheless, the problem of high local air pollution also needs to be addressed. To understand health costs associated with Indian CTPPs better, interested readers may refer to Mahapatra et al. (2012) and Cropper et al. (2013).¹ The coal used in the Indian power sector has a high ash content, making SPM the key local air pollutant released from CTPPs (Kumar & Rao, 2003; Sengupta, 2007). Sengupta (2007) suggests replacing age-old boilers and introducing ash tax as policy measures to curb SPM emissions from Indian CTPPs.

To address negative externalities related to CTPPs, the Government of India introduced the Environmental Management Award scheme² in 2008 and finally set up some new emission regulation standards for power plants in December 2015. An overview of the Indian thermal power sector and current policies to address energy efficiency and sustainability are found in Malik et al. (2015), Shukla and Zia (2016) and Kumar (2017). In this context, regular performance evaluation of Indian CTPPs may help us to identify the plants that require attention from the environmental sustainability perspective and explore the trade-off between increasing electricity generation and reducing local air pollutant emissions. Effective management may reduce emissions and overall energy consumption of CTPPs, which can help to achieve sustainable development of the whole industry. From managerial and policy perspectives, it is essential to determine whether the energy–environment balance is dealt with more efficiently by private or public enterprises. Auxiliary power consumption in Indian CTPPs is on a higher side than CTPPs in other developed countries due to poor plant load factor, the use of poor coal quality, obsolete equipment and aging of equipment (Mandi & Yaragatti, 2014). Thus, auxiliary power consumption and hence emissions can be reduced by improving the plant load factor (Mandi & Yaragatti, 2014).

In this study, we utilize data envelopment analysis (DEA) — a non-parametric method to evaluate the efficiency of Indian CTPPs (decision-making unit or DMU as per DEA terminology) generating both electricity (socially desirable or ‘good’ as per DEA vocabulary) and SPM emissions (socially undesirable or ‘bad’ as per DEA jargon). Under the DEA modelling approach, one compares the actual output levels produced by a DMU with the best achievable output levels of that particular DMU. Scholars have used DEA in assessing both productive and environmental performances of electric utilities or other entities to figure out laggard DMUs (Sueyoshi et al., 2017). In DEA literature, one can accommodate a bad output in one of the three different ways: (a) bad output as input; (b) bad output as an unintended output of production process or joint-production (JP) approach as proposed by Färe et al. (1989); and (c) bad output as a by-product of the production process or by-production (BP) approach as propositioned by Murty et al. (2012). Among these alternative methodologies, JP and BP approaches are most popular in empirical research to accommodate bad output in the production process.

Although the production process assumes a positive correlation between good and bad outputs in both methodologies, they are fundamentally different from each other. Under the JP approach, it is assumed that producing good output will generate bad output, which is unavoidable. So, given an input level, we cannot unilaterally dispose of bad output. The reduction in bad output is always linked with a reduction in good output. On the other hand, the BP approach assumes that bad output arises because of specific input’s use to generate good output. Thus, reduction in bad output is possible only by cutting down the use of that particular input. So, we can say that unlike the JP approach, the BP approach imposes an additional constraint on the use of input also. As DEA is deterministic, introducing such additional constraints may lead to a variation in the efficiency measures. From an empirical perspective, the difference in efficiency measures stemming from the alternative methodologies might create difficulty in practical benchmarking exercises, because the ranking of DMUs may alter across two sets of model assumptions.

Moreover, choosing a particular DEA model can also impact efficiency scores and the ranking of DMUs. Sometimes the ranking of DMUs may also vary across DEA models (for a given technology) due to models’ inherent nature. For instance, suppose a decision-maker tries to increase good output and reduce bad output generation simultaneously. In that case, he/she might choose either the Directional Distance Function (DDF) model or graph–hyperbolic (GH) model to compute the inefficiency and technical efficiency (TE) measures. However, the nature of those two models is significantly different from each other. The DDF is a straight forward linear optimization problem where the GH is a non-linear optimization problem.

This study considers both the economic (electricity generation) and environmental (SPM emissions) aspects of thermal power generation to balance economic and environmental forces while determining the efficiency of Indian CTPPs. We study the sensitivity of efficiency measures and ranking of Indian CTPPs in the presence of SPM as bad output, by using two alternative DEA models (DDF and GH) under two different technological assumptions (JP and BP). This modelling strategy will help us to draw robust inferences regarding the effect of ownership and plant load factor on efficiency. The rest of our paper is organized as follows. The second section provides a literature review followed by a detailed methodological discussion in the third section. The empirical model and data source of the study are mentioned in the fourth section. We present the results from our empirical models in the fifth section and concludes our study in the last section.

Literature Review

The literature on energy efficiency reveals that researchers follow different technological assumptions to incorporate bad output in the production process and adopt different models to evaluate power plants. Numerous studies have been conducted to evaluate the productive and environmental performance of CTPPs in both developed and developing nations (Mardani et al., 2017; Xu et al., 2020). Here, we consider recent empirical studies to provide the reader with a glimpse of various methodologies adopted for efficiency evaluation of Indian CTPPs and main results. Murty et al. (2007) use a parametric DDF model, which captures the effort to increase electricity generation and reduce emissions for five CTPPs under the Andhra Pradesh Power Generation Corporation. To estimate DDF, they use monthly observations on electricity generation and various air pollutants (SPM, SO₂, NO_X) as outputs, while coal consumption, wage bill and total capital stock of CTPPs as the inputs during the period from 1996-97 to 2003-04. Their DDF model’s result indicates a ‘win–win’ situation as the representative plant can increase its electricity by 6% while cutting down emissions by the same proportion.

Shrivastava et al. (2012) compute Technical Efficiency (TE) of 60 Indian CTPPs for the year 2008-09 applying input-oriented versions of traditional DEA models on a technology set defined over one output (electricity generation) and three inputs (coal consumption, oil use and auxiliary power consumption). The results suggest that TE of small-sized CTPPs are comparatively lower than medium and large-sized CTPPs, and state government-owned CTPPs are more inefficient than central government and privately owned CTPPs. Yadav et al. (2014) evaluate the performance of 65 Indian CTPPs for the year 2008-09. Their model specification includes two outputs (electricity and CO₂ emissions) and two inputs (installed capacity and coal consumption). They used an input-oriented DEA model to find out inefficient CTPPs. The study also uses the slack-based model to realize the improvement direction for an inefficient CTPPs. The result shows that state government-owned CTPPs are highly inefficient compared to their counterparts. The slack-based analysis suggests that inefficient CTPPs should reduce their coal consumption to improve operational performance.

Sahoo et al. (2017) examine the energy efficiency for 71 CTPPs in India for 2010. The technology set of their study incorporates two outputs (electricity generation and CO₂ emissions) and five inputs (plant capacity, load factor, plant availability, coal consumption and secondary fuel consumption). The study assumes a joint production relation between electricity generation and CO₂ emissions and follows Färe et al. (1989) DEA model to compute the energy efficiency scores for CTPPs. Apart from the energy efficiency scores, they have used the slack-based model to calculate the energy savings potential of Indian CTPPs. The results show that market-based targets are much lower than actual targets, and there exists substantial room for improvement in the energy-use system. Jain and Kumar (2018) estimate quadratic directional output distance function using linear programming (LP) approach by using a sample of 56 Indian CTPPs for 2000–2013 to compute TE and shadow prices of CO₂ emissions. They find that over time, the inefficiency of the thermal power sector has been increasing.

Murty and Nagpal (2019) measure TE of Indian CTPPs using output-based Färe, Grosskopf, and Lovell efficiency index. The study uses plant-level annual data of 48 CTPPs from 2003 to 2015. The model specification contains two outputs (electricity generation and CO₂ emissions) and three inputs (plant capacity, operating availability and fuel use). They follow the BP approach to model CO₂ emissions (bad output) in the technology set. They define overall technology as an intersection of two sub-technologies—intended or ‘good’ technology and emission causing or ‘bad’ technology and decompose the Färe, Grosskopf, and Lovell index into TE and environmental efficiency indices. The environmental efficiency index is calculated relative to ‘bad’ technology, while TE is measured relative to ‘good’ technology. The high environmental efficiency score over time indicates that significant improvement in CO₂ emission control performance cannot be achieved by reducing the use of emission causing input. The study finds that average TE scores remained more or less the same. However, an increase in the percentage of high-performing plants and a decrease in the percentage of low-performing plants in the inefficiency distribution suggest an improvement in electricity generation performance across the study period.

Jindal and Nilakantan (2021) enumerate TE of 129 Indian CTPPs over the period 2005–2014, applying input-oriented versions of radial DEA model and non-radial slacks-based measure DEA model. They define a technology set over one output (gross electricity produced) and six inputs (coal consumption, fuel oil use, auxiliary power consumption, installed capacity, plant load factor and plant availability factor). They find that average TE declined from 0.847 in 2005 to 0.742 in 2014. The bootstrapped truncated regression results suggest that efficiency increases with plant size, and privately owned CTPPs operate at higher efficiency levels than their public sector counterparts.

At the backdrop of the literature, our study aims to make some humble contributions to the existing body of knowledge. To the best of our knowledge, the impact of plant load factor on TE of Indian CTPPs has not been studied before. This is only the second study that focuses on SPM emissions as bad output, after Kumar and Rao (2003) who have analysed data from the 1990s. Our study tries to answer the following research questions:

Do ownership and plant load factor significantly affect inefficiency and TE of CTPPs across alternative DEA models under different technological assumptions?

Given technology assumption, is the ranking of CTPPs robust across alternative DEA models?

How does technology assumptions affect the ranking of CTPPs, given a DEA model?

Methodology

Staring from the microeconomic foundations, Ray (2020) provides an overview of the DEA methodology for radial and non-radial measurements of efficiency and alternate ways to combine undesirable ‘bad’ output with the ‘good’ output in DEA models. The interested reader may also refer to Dakpo et al. (2016), who summarize theoretical developments around the inclusion of bad outputs in production technology modelling and related DEA-based models. As mentioned earlier, variation in efficiency/inefficiency measures for a given CTPPs (across technological assumptions or DEA models) may lead to an inconsistency in benchmarking, and drawing robust inference on the role of non-discretionary factors on TE may be difficult. This study tries to overcome these problems by implementing the following strategy.

First, we adopt both JP and BP methodological approaches to accommodate bad outputs and aim to compute TE under both technological assumptions.

Second, we use two alternative DEA models (DDF and GH) under both technological assumptions to compute inefficiency and TE measures.

Third, we conduct a second-stage regression analysis to identify whether the ownership factor affects TE of Indian CTPPs across alternative technologies and DEA models.

Suppose we have N number of DMUs producing one ‘good’ or desirable output (Y) and one ‘bad’ or undesirable output (B) using a set of inputs (X). A DMU should be given credit for good output generation and penalized for its bad output generation. In this study, we discuss two different methodologies, where both these outputs (i.e., good and bad outputs both) are treated asymmetrically in the performance evaluation.

We start our discussion with the JP approach, introduced by Färe et al. (1989), where it is assumed that both the outputs are jointly produced from a given input set that is freely disposable. However, to model bad output in the production technology set, they have introduced two additional assumptions (i.e., null jointness and weak disposability of bad output with good output) in their production technology. The null jointness assumption says that bad output is produced jointly with good output; so, it is impossible to produce any good output without producing any bad output. The weak disposability assumption implies that any proportional contraction in bad output is possible only if the good output is reduced in the same proportion. In other words, for a given input set, a DMU can reduce its bad output only if the good output is also reduced. The idea of weak disposability assumption suggests that bad output disposal is costly, which restricts good output production. However, Färe et al. (1989) assume that good output is freely disposable, indicating that a DMU can produce less amount of good output with the same amount of bad output at a given input level.

Based on null jointness of outputs, weak disposability of bad output with good output, and free disposability of good output Färe et al. (1989) have constructed the following production possibility set (a.k.a. technology set):

T^{J P} (X) = \{(Y, B) : X c a n p r o d u c e (Y, B)\} = \{\begin{matrix} \begin{matrix} \sum_{j = 1}^{N} λ_{j} Y_{j} \geq Y_{j} \\ \sum_{j = 1}^{N} λ_{j} B_{j} = B_{j} \\ \sum_{j = 1}^{N} λ_{j} X_{j} \leq X_{j} \end{matrix} \\ \sum_{j = 1}^{N} λ_{j} = 1 \end{matrix}\} .

(1)

In Equation (1), T(X) defines the technology set followed by the DMU and λ_j is the intensity vector (or DMU specific non-negative weights). The convex combinations of outputs in the technology set, i.e. and $\sum_{j = 1}^{N} λ_{j} B_{j}$ specify the frontiers for good and bad outputs, respectively. Similarly, input frontier is represented by a convex combination of inputs (i.e., $\sum_{j = 1}^{N} λ_{j} X_{1 j}$ ). The convexity constraint (or $\sum_{j = 1}^{N} λ_{j} = 1$ ) confirms that T(X) follows variable returns to scale (VRS).³ The inequality constraints $\sum_{j = 1}^{N} λ_{j} Y_{j} \geq Y_{j}$ and $\sum_{j = 1}^{N} λ_{j} X_{j} \leq X_{j}$ imply that good output and input are strongly disposable, while the equality constrains $\sum_{j = 1}^{N} λ_{j} B_{j} = B_{j}$ represents weak disposability of bad output with good output.

The JP approach suggests that a DMU cannot reduce its bad output without cutting down its good output, which implies a positive correlation between outputs at a given input level. However, at a given input level, a reduction in both output levels may result from resource diversion from good output production to abatement of bad output. The primary criticism against the JP approach is that it fails to model the abatement activities explicitly in the technology set. To accommodate the abatement activity regarding bad output in the technology set, Murty et al. (2012) propose an alternative modelling framework known as BP approach under which, DMU has two conceptually different production technologies: good output generation and bad output generation. Førsund (2021) also champions the philosophy behind the BP approach as generation of good output is independent of generation of bad output and vice versa. However, these separate technologies for the good and bad outputs are linked through common input use in the production process. The input associated with the good technology is defined as neutral input (X₁), while input that causes bad output is called polluting input (X₂). To produce good output, DMU requires both types of inputs, while for the generation of bad output, DMU only needs polluting input. According to Murty et al. (2012), the generation of good and bad outputs is independent. They use two different sets of intensity vectors to model both sub-technologies for the DMU. In this case, a DMU is said to be efficient DMU if and only if it is efficient relative to both sub-technologies.

However, Ray et al. (2017) criticize the idea of independent sub-technologies proposed by Murty et al. (2012). They argue that in the presence of input (mainly for polluting input) sharing between two sub-technologies, use of two sets of intensity vectors leads to two different peer groups (for a single inefficient DMU), which is not desirable from an empirical point of view. So, they propose some modifications to the BP approach. They assume that bad output and polluting input are jointly disposable in the corresponding sub-technology, ensuring that reduction in bad output is always linked with a simultaneous reduction in polluting input. Second, they use a single intensity vector (in the production technology) to choose a single peer group for an inefficient DMU.

In this study, we follow a combined approach of Murty et al. (2012) and Ray et al. (2017) to model the bad output in the production possibility set. Like Murty et al. (2012), we assume that overall technology is an intersection of good and bad technology. However, we follow Ray et al. (2017) to use a single intensity vector for both technologies. However, we modify the assumption of joint disposability in Ray et al. (2017) as follows. A DMU cannot substitute its polluting with any other inputs due to its usages in both sub-technologies. So, reducing bad output by cutting down the polluting input use might affect its good output generation. An advantage of the modified joint disposability assumption is that it ensures a balance between both outputs when the DMU mitigates its bad output. We define our BP technology set as

\begin{matrix} T_{1} (X) = {Y : (X_{1}, X_{2}) c a n p r o d u c e Y} = {\begin{matrix} \sum_{j = 1}^{N} λ_{j} Y_{j} = Y_{j} \\ \sum_{i = 1}^{N} λ_{j} X_{1 j} \leq X_{1 j} \\ \sum_{j = 1}^{N} λ_{j} X_{2 j} = X_{2 j} \\ \sum_{j = 1}^{N} λ_{j} = 1 \end{matrix}} \\ T_{2} (X) = {B : X_{2} c a n p r o d u c e B} = {\begin{matrix} \sum_{j = 1}^{N} λ_{j} B_{j} = B_{j} \\ \sum_{j = 1}^{N} λ_{j} X_{2 j} = X_{2 j} \\ \sum_{j = 1}^{N} λ_{j} = 1 \end{matrix}} \\ T^{B P} (X) = {(Y, B; X_{1}, X_{2}) : (Y; X_{1}, X_{2}) \in T_{1} (X) a n d (B; X_{2}) \in T_{2} (X)}, \end{matrix}

(2)

where T₁(X) defines good technology while T₂(X) is the bad output technology, and the overall technology is defined by T^BP(X), which is the intersection of both sub-technologies. The intensity vector λ_j is same for both sub-technologies. Like Equation (1), we assume VRS in our BP approach as defined in Equation (2). Equality constraints $\sum_{j = 1}^{N} λ_{j} Y_{j} = Y_{j}$ and $\sum_{j = 1}^{N} λ_{j} X_{2 j} = X_{2 j}$ imply that joint disposability holds between good output and polluting input, while equality constraints $\sum_{j = 1}^{N} λ_{j} B_{j} = B_{j}$ and $\sum_{j = 1}^{N} λ_{j} X_{2 j} = X_{2 j}$ suggest joint disposability of bad output with polluting input. This study uses two orientation free DEA models—GH and DDF—to evaluate the performance of DMUs under both JP and BP approaches via LP technique. For j^th DMU, the DEA-LP models under two different approaches can be defined as follows.

Case I: DEA-LP for GH Model Under JP Approach

Here the objective is to find the optimal value, up to which we can simultaneously expand good output production and reduce (proportionately) the bad output generation. To obtain the value of θ*_JP for j^th DMU, we solve the following optimization problem:

θ_{J P, j}^{*} = \max θ_{j}

Subject to

\begin{array}{l} \sum_{j = 1}^{N} λ_{j} Y_{j} \geq θ_{j} * Y_{j} \\ \sum_{j = 1}^{N} λ_{j} B_{j} = \frac{1}{θ_{j}} * B_{j} \\ \sum_{j = 1}^{N} λ_{j} X_{j} \leq X_{j} \\ \sum_{j = 1}^{N} λ_{j} = 1 \\ θ_{j} u n r e s t r i c t e d . \end{array}

(3)

Note that in the this optimization problem (Equation (3)) the bad output restriction involves non-linear equality. To make it linear, we use first-order Taylor’s series approximation for the non-linear constraint. We define $(θ) = \frac{1}{θ}$ , then at θ = θ₀

f (θ) \approx f (θ_{0}) + f^{'} (θ_{0}) (θ - θ_{0}) = \frac{2 θ_{0} - θ}{θ_{0}}

Hence, at θ₀ = 1 we get

f (θ) \approx 2 - θ

(4)

So, using this approximation (Equation (4)), we can rewrite Equation (3) as

θ_{J P, j}^{*} = \max θ_{j}

Subject to

\begin{array}{l} \sum_{j = 1}^{N} λ_{j} Y_{j} \geq θ_{j} * Y_{j} \\ \sum_{j = 1}^{N} λ_{j} B_{j} + θ_{j} B_{j} = 2 B_{j} \\ \sum_{j = 1}^{N} λ_{j} X_{j} \leq X_{j} \\ \sum_{j = 1}^{N} λ_{j} = 1 \\ θ_{j} u n r e s t r i c t e d . \end{array}

(5)

Case II: DEA-LP for DDF Model Under JP Approach

Like the GH model, we try to find the optimal scaling factor to expand the production of good output while reducing bad output simultaneously. To obtain the value of δ*_JP> for j^th DMU, we solve the following optimization problem:

δ_{J P, j}^{*} = \vec{D} ({Y_{j}, B_{j}; X}_{j}) = \max δ_{j}

Subject to

\begin{array}{l} \sum_{j = 1}^{N} λ_{j} Y_{j} \geq (1 + δ_{j}) Y_{j} \\ \sum_{j = 1}^{N} λ_{j} B_{j} = (1 - δ_{j}) B_{j} \\ \sum_{j = 1}^{N} λ_{j} X_{j} \leq X_{j} \\ \sum_{j = 1}^{N} λ_{j} = 1 \\ θ_{j} u n r e s t r i c t e d \end{array}

(6)

Note that we set our direction vector to (1, −1), to keep our model simple.

Case III: DEA-LP for GH Model Under BP Approach

Our objective is to get the optimal value to expand good output while reducing the bad output by cutting down the polluting input use in the case of BP approach. To get the optimal value for j^th DMU, we solve the following problem:

θ_{BP, j}^{*} = \max θ_{j}

Subject to

\begin{array}{l} \sum_{j = 1}^{N} λ_{j} Y_{j} \geq θ_{j} * Y_{j} \\ \sum_{j = 1}^{N} λ_{j} B_{j} = \frac{1}{θ_{j}} * B_{j} \\ \sum_{j = 1}^{N} λ_{j} X_{1 j} \leq X_{1 j} \\ \sum_{j = 1}^{N} λ_{j} X_{2 j} = \frac{1}{θ_{j}} * X_{2 j} \\ \sum_{j = 1}^{N} λ_{j} = 1 \\ θ_{j} u n r e s t r i c t e d \end{array}

(7)

Here also we use the first-order Taylor’s series approximation to make the non-linear restriction linear one. So, based on our approximation result in Equation (4), we rewrite our Equation (7) as follow:

θ_{B P, j}^{*} = \max θ_{j}

(8)

Subject to

\begin{array}{l} \sum_{j = 1}^{N} λ_{j} Y_{j} = θ_{j} Y_{j} \\ \sum_{j = 1}^{N} λ_{j} B_{j} + θ_{j} B_{j} = 2 B_{j} \\ \sum_{j = 1}^{N} λ_{j} X_{1 j} \leq X_{1 j} \\ \sum_{j = 1}^{N} λ_{j} X_{2 j} + θ_{j} X_{2 j} = 2 X_{2 j} \\ \sum_{j = 1}^{N} λ_{j} = 1 \\ θ_{j} u n r e s t r i c t e d \end{array}

Case IV: DEA-LP for DDF Model Under BP Approach

The following DEA–LP objective is to find an optimal strategy to expand the production of good output while reducing bad output by cutting down polluting input use. Hence, our DEA–LP model can be written as:

δ_{B P, j}^{*} = \vec{D} ({Y_{j}, B_{j}; X}_{1 j}, X_{2 j}) = \max δ_{j}

Subject to

\begin{array}{l} \sum_{j = 1}^{N} λ_{j} Y_{j} = (1 + δ_{j}) Y_{j} \\ \sum_{j = 1}^{N} λ_{j} B_{j} + (1 - δ_{j}) B_{j} \\ \sum_{j = 1}^{N} λ_{j} X_{1 j} \leq X_{1 j} \\ \sum_{j = 1}^{N} λ_{j} X_{2 j} = (1 - δ_{j}) X_{2 j} \\ \sum_{j = 1}^{N} λ_{j} = 1 \\ θ_{j} u n r e s t r i c t e d . \end{array}

(9)

Following standard practice (Ray et al., 2017), we set the direction vector as (1, −1, −1) to make our model simple.

Once we solve all optimization problems, we use regression analysis as a second-stage study to identify factors that cause variation in the performance level. In this study, we have computed four different scaling factors θ*_JP, δ*_JP, θ*_BP and δ*_BP. So, we estimate four models, one for each scaling factor to recognize non-discretionary factors. We consider the following regression model for j^th DMU:

I_{j t} = Z_{j t}^{'} β + ε_{j t},

(10)

where I (N × 1) vector of calculated inefficiency or efficiency score, Z is (N × K) vector of exogenous variables, β is (K × 1) vector of parameters, ε is an (N × 1) vector of error term of the model and t indicates the time. Many scholars note that TE varies between zero to one and suggests a Tobit model to identify non-discretionary factors. However, McDonald (2009) argues that efficiency scores are fractional data, and the Tobit model may provide inappropriate findings. So, we decide to adopt the pooled regression model with robust standard errors to estimate Equation (10). Figure 1 illustrates the analytical steps used when we begin with the BP technology assumption.⁴

Figure 1.

Source: The authors.

Empirical Model and Data Source

This study adopts a technology set involving two inputs and two outputs. In our analysis, net electricity generation and SPM emissions are considered as good output (Y) and bad output (B), respectively. For the input set, we have two inputs: the plant’s net capacity (X₁) and total coal use (X₂). In the case of BP approach, the capacity variable is considered as neutral input for our study, while coal is used as polluting input. The data that goes into the construction of our empirical models are collected from the Central Electricity Authority’s annual publications (Central Electricity Authority, 2013, 2015). Each annual review offers detailed plant-level data regarding electricity generation, generation capacity, coal use per unit electricity generation, operation availability, electricity consumption for operation purpose, ownership status, capacity utilization and SPM emissions range. These data are voluntarily shared with the Central Electricity Authority, leading to missing information and an unbalanced panel.

We utilize annual data for two different years 2012-13 and 2014-15. We cannot use more recent data as annual reports stop providing data on SPM emissions after 2015. In 2014-15, the annual review covers 167 CTPPs, out of which we get full information on 70 CTPPs. Similarly, for 2012-13 we get information on 70 CTPPs. Out of these CTPPs (i.e., 70 CTPPs in 2012-13 and 70 CTPPs in 2014-15), we have 66 CTPPs contributing data for both years. As the data source does not reveal any information on labour use at CTPPs, we cannot include labour input in our models. However, as CTPPs are highly technology intensive, labour probably plays a minor role in productivity (Sahoo et al., 2017). This study constructs the following variables to measure the inefficiency scores.

Net electricity: We subtract the auxiliary consumption from gross electricity generation to get the net electricity generation (in GWh) of a plant.

SPM emissions: We take average of the maximum and the minimum SPM emissions and create SPM emissions (in mg/Nm³) level of each plant.

Net capacity: During a year, CTPPs do not operate at their full capacity. To get the actual capacity, we multiply the plant’s total capacity by its operational availability and get a plant’s net capacity (in MW), which is considered neutral input in our analysis.

Coal use: We multiply coal use per KW of a plant with its gross electricity generation to get total coal use (in thousand tonnes) by that particular plant.

After DEA calculations, we merge each year’s data set to a single data set and make a balanced panel of CTPPs to identify the possible non-discretionary factors. We utilize inefficiency and efficiency scores (calculated from Equations (5), (6), (8) and (9)) as dependent variables in the second stage regression model. Previous studies on efficiency analysis of CTPPs include type of fuel, plant’s age and size as explanatory variables in the second-stage regression model. However, in this study, we do not consider these variables as explanatory variables. Given the data limitation, plant age determination is complicated and hence ignored. Second, a high correlation between the number of units in a particular plant and net capacity of that plant restricts the use of the units variable in second stage regression.

We use ownership dummies, capacity utilization and year dummy as explanatory variables in the second stage regression model. Indian CTPPs can be classified into three categories based on the ownership: central government-owned, state government-owned, and privately owned CTPPs. The different ownership dummies help us to capture the impact of management on plant’s efficiency level. Similarly, better capacity utilization is expected to improve the performance level of the plant. Again, over time performance of CTPPs may improve due to technological progress. Note that we consider private company owned CTPPs as a base category and compare that with the other two ownership categories in our analysis. Similarly, we consider the year 2012-13 as the base year for our analysis. Definitions of all regressors are as follows.

Central: If the central government owns the plant, the dummy takes value 1, otherwise 0.

State: For state government-owned plant, the dummy takes value 1, otherwise 0.

Plant load factor: To capture the capacity utilization effect, we use the plant load factor, which is defined as the ratio of actual energy generated by the plant and maximum energy generated by it.

Y14: If the data belongs to 2014-15, the Y14 dummy takes value 1.

The descriptive statistics for each variable are summarized in Table 1 for each year. Table 1 shows a small increase in average net electricity generation from 2012-13 to 2014-15. However, the mean value of the average SPM emission decreases across the year. We also notice an increase in net capital and coal use during our study period. The positively skewed net electricity, average SPM emission, net capital and coal use distributions imply that most of CTPPs in our analysis are relatively small. On the other hand, we see that the plant load factor’s mean value has declined from 2012-13 to 2014-15. However, negatively skewed plant load distribution suggests better capacity utilization by Indian CTPPs. Out of 132 total observations, 80 observations are from 40 state government-owned CTPPs, followed by 36 observations from 18 central government-owned and 16 observations from 8 private CTPPs.

Table 1.

Descriptive Statistics of Sample.

Year: 2012-13 (N = 66)
Average SPM emissions (mg/Nm³)	746.6	465.8	73.50	11,932
Net electricity generation (GWh)	6,479	4,761	175.6	24,495
Net capital (MW)	935.7	712.1	53.21	3,508
Coal use ('000 Tonne)	5,065	3,517	231.1	18,816
Plant load factor (%)	71.30	74.54	14.21	100
Year: 2014-15 (N = 66)
Average SPM emissions (mg/Nm³)	630.9	469	91.50	8,503
Net electricity generation (GWh)	6,578	4,896	54.35	27,696
Net capital (MW)	944.1	718.7	25.95	3,781
Coal use ('000 Tonne)	5,160	3,719	104.1	20,702
Plant	load factor (%)	65.41	72.80	7.360	93.90

Source: The authors.

Note: SPM = suspended particulate matter.

Results and Discussion

In this section, we report and discuss our findings based on the DEA-LP models (Cases I–IV) followed by second-stage regression analysis. We first summarize our efficiency/inefficiency measures obtained from DEA models in Table 2. In Panel A of Table 2, we report the efficiency/inefficiency scores derived from DEA models under BP technology assumptions. In Panel B, similar measures obtained from the same DEA models under JP technology assumptions are shown.

Table 2.

Descriptive Statistics of GH Efficiency and DDF Inefficiency Scores.

	Mean	Median	CV	Skewness	CTPPs on Frontier
Panel A: By-production technology
Graph hyperbolic 2012-13 (GH-12)	0.912	0.927	9.058	–0.723	19 (28.8%)
Graph hyperbolic 2014-15 (GH-14)	0.914	0.927	8.136	–0.644	16 (28.2%)
Dir. distance function 2012-13 (DDF-12)	0.106	0.078	103.275	1.161	19 (28.8%)
Dir. distance function 2014-15 (DDF-14)	0.102	0.078	93.921	0.996	14 (21.2%)
Panel B: Joint production technology
Graph hyperbolic 2012-13 (GH-12)	0.881	0.901	12.524	–0.750	16 (24.2%)
Graph hyperbolic 2014-15 (GH-14)	0.885	0.905	11.111	–0.732	12 (18.1%)
Dir. distance function 2012-13 (DDF-12)	0.156	0.110	106.656	1.353	14 (21.2%)
Dir. distance function 2014-15 (DDF-14)	0.145	0.105	98.185	1.211	12 (18.1%)

Source: The authors.

Note: CTPPs = coal-based thermal power plants; CV = coefficient of variation; DDF = directional distance function; GH = graph hyperbolic.

Table 2 shows that both efficiency and inefficiency measures derived from both GH and DDF models have changed drastically between two alternative technologies. For example, under the BP technology assumption, the mean efficiency measure obtained from the GH model (for the period 2012-13) is 0.912, which is higher than the mean efficiency measure (0.881) derived under the JP technology. Similarly, during the same period (i.e., 2012-13), we observe that the mean inefficiency measure from the DDF model is much lower under the BP assumptions, than the JP technology case. These findings suggest that Indian CTPPs are less efficient under JP assumptions than BP technological assumptions. Under the BP technology assumption, the primary objective is to increase the good output and to reduce the bad output by cutting down the polluting input in the same proportion. However, under the JP technology case, a DMU can only reduce its bad output by cutting down its good output in the same proportion. Note that DEA results are sensitive to constraints imposed in the model. So, both efficiency and inefficiency measures may change due to the introduction of additional constraints (i.e., coal use constraint) in the BP technology. In this context, the difference in measures between those two technologies may lead to a change in the ranking of Indian CTPPs. To check whether the ranking of CTPPs is changed significantly or not (across two alternative technology), we use Spearman rank correlation and summarize the result in Table 3.

Table 3.

Spearman Rank Correlation (ρ) of Matrix Across Technology.

	GH-12	DDF-12	GH-14	DDF-14
Panel A: By-production technology
Graph hyperbolic 2012-13 (GH-12)	1.000	–	–	–
Dir. distance function 2012-13 (DDF-12)	–0.989	1.000	–	–
Graph hyperbolic 2014-15 (GH-14)	0.852	–0.863	1.000	–
Dir. distance function 2014-15 (DDF-14)	–0.849	0.863	–0.993	1.000
Panel B: Joint production technology
Graph hyperbolic 2012-13 (GH-12)	1.000	–	–	–
Dir. distance function 2012-13 (DDF-12)	–0.990	1.000	–	–
Graph hyperbolic 2014-15 (GH-14)	0.843	–0.850	1.000	–
Dir. distance function 2014-15 (DDF-14)	–0.841	0.851	–0.997	1.000

Source: The authors.

Note: All ρ values are significant at 1% statistical significance level. DDF = directional distance function; GH = graph hyperbolic.

The Spearman rank correlation test is a non-parametric test to check the association between rank of DMUs based on efficiency/inefficiency measures under different technological assumptions. The value of test statistic ρ lies between +1 to −1. A score of zero implies no association. If |ρ| increases in magnitude, that indicates two rank variables turn out to be closer to being perfectly monotone functions of each other. In Panels A and B of Table 3, we summarize the Spearman’s ρ between GH and DFF models under BP and JP technologies, respectively. Note that the DDF model shows the level of inefficiency while the GH model provides the efficiency of CTPPs, so we get a negative correlation coefficient between these two models. From Panel A, we see that the association between these alternative two models is almost perfect (correlation coefficients are −0.989 and −0.993 for the year 2012-13 and 2014-15, respectively), suggesting that ranking of Indian CTPPs remains almost the same between GH and DDF models under BP technological assumption. An analogous situation is found in Panel B. In Panels A and B of Table 4, we present the rank correlation coefficient between BP and JP technologies under alternative DEA models. There also, high |ρ| values indicate that across technology, both GH and DDF models provide a consistent ranking of CTPPs.

Table 4.

Spearman Rank Correlation (ρ) Matrix Across DEA Models.

	BP-12	JP-12	BP-14	JP-14
Panel A: Graph hyperbolic model
By-production 2012-13 (BP-12)	1.000	–	–	–
Joint production 2012-13 (JP-12)	0.957	1.000	–	–
By-production 2014-15 (BP-14)	0.852	0.837	1.000	–
Joint production 2014-15 (JP-14)	0.850	0.843	0.985	1.000
Panel B: Directional distance function
By-production 2012-13 (BP-12)	1.000	–	–	–
Joint production 2012-13 (JP-12)	0.968	1.000	–	–
By-production 2014-15 (BP-14)	0.863	0.835	1.000	–
Joint production 2014-15 (JP-14)	0.862	0.851	0.984	1.000

Source: The authors.

Note: All ρ values are significant at 1% statistical significance level. DEA = data envelopment analysis.

In this study, we use the contemporaneous frontier (i.e., frontier based on cross-sectional data) to evaluate the performance of the Indian CTPPs. So, both efficiency and inefficiency measures may vary over time because of change in the reference points to construct the frontier. To know whether there is any change in efficiency/inefficiency distribution (i.e., shape and location parameter of the distribution) over time, we perform three non-parametric tests: Wilcoxson rank-sum test (to know whether the shape of distribution has changed or not), median test (to check whether two distributions have the same median or not) and Kruskal–Wallis test (to see whether samples originate from the same distribution). However, these test statics indicate that neither the shape nor location parameter of the distribution has changed over time. So, we pool yearly efficiency/inefficiency measures into a single data set to increase observations under all ownership categories. Table 5 presents a comparative picture of summaries of GH efficiency and DDF inefficiency measures across different ownerships of CTPPs. As per expectation, the mean and median performance levels of Indian CTPPs significantly vary across alternative technological assumptions, which is expected. Under the BP approach, both mean GH efficiency and mean DDF inefficiency measures suggest that state government-owned CTPPs are most inefficient, while privately owned CTPPs are most efficient ones. For JP approach, we also observe a similar trend.

Table 5.

Mean and Median GH Efficiency and DDF Inefficiency Scores Across Ownership.

	Central (N = 36)		State (N = 80)		Private (N = 16)
	Mean	Median	Mean	Median	Mean	Median
Panel A: By-production technology
GH efficiency	0.929	0.946	0.892	0.899	0.982	1
DDF inefficiency	0.082	0.056	0.130	0.112	0.019	0
Panel B: Joint-production technology
GH efficiency	0.909	0.927	0.853	0.861	0.975	1
DDF inefficiency	0.111	0.078	0.192	0.161	0.027	0

Source: The authors.

Note: DDF = directional distance function; GH = graph hyperbolic.

Next, we are interested to identify the poorly performing CTPPs for the most recent year under consideration, that is, 2014-15. Table 6 shows ‘laggard’ CTPPs (with inefficiency scores falling in the upper or 4th quartile of the inefficiency distribution in the case of DDF–DEA or with efficiency scores falling in the lower or 1st quartile of the efficiency distribution in the case of GH–DEA) under both BP and JP approaches. Table 6 reveals that DDF inefficiency (GH efficiency) scores under the JP approach are relatively higher (lower) than those obtained under the BP approach. Irrespective of the difference between the efficiency/inefficiency measures, we observe that 14 CTPPs appear in all four listings. Eight CTPPs obtain same ranks across four models. For the remaining six CTPPs, the change in the ranking across models is not substantial. Table 6 also reveals that poorly performing CTPPs are mostly state government owned. No privately owned CTPP appears in that list of laggards. Plant level DDF inefficiency and GH efficiency scores (for a given technology) are useful for regulators and managers to set targets for both ‘good’ and ‘bad’ outputs such that an inefficient DMU knows how much adjustments are required to become fully efficient. For instance, under the BP approach, DDF inefficiency and GH efficiency of Ennore plant CTPP are 0.414 and 0.707, respectively. The DDF inefficiency score implies that the Ennore plant can simultaneously increase its net electricity generation by 41.4% and reduce its average SPM emissions by cutting down the coal use by the same percentage. However, the GH efficiency score suggests that Ennore can reduce both SPM emissions and coal use by 70.7% of its observed levels and simultaneously scale up electricity generation by 1.414 times (reciprocal of the GH efficiency score). Let us now focus on the worst 10 CTPPs for each year. Across all four models for both years, we observe that the performances of CTPPs in the ‘bottom 10’ list are consistently low. There are seven CTPPs (Ennore, Bhusawal, Koradi, Bandel, Parli, Bokaro B and Kolaghat), which are common in eight ‘bottom 10’ lists generated through our analysis.

Table 6.

List of Poor-Performing CTPPs Across Technologies and Data Envelopment Analysis Models for 2014–2015.

By-Production Technology				Joint-Production Technology
Dir. Distance Function		Graph Hyperbolic		Dir. Distance Function		Graph Hyperbolic
CTPP Name	Ineff.	CTPP Name	Eff.	CTPP Name	Ineff.	CTPP Name	Eff.
Ennore	0.414	Ennore	0.707	Ennore	0.569	Ennore	0.637
Bhusawal	0.334	Bhusawal	0.749	Bhusawal	0.543	Bhusawal	0.648
Koradi	0.307	Koradi	0.765	Bandel	0.508	Bandel	0.663
Bandel	0.289	Bandel	0.776	Koradi	0.474	Koradi	0.679
Bokaro B (DVC)	0.258	Bokaro B (DVC)	0.795	Bokaro B (DVC)	0.386	Bokaro B (DVC)	0.721
Paras	0.236	Paras	0.809	Chandrapur STPS	0.353	Chandrapur STPS	0.739
Amarkantak	0.231	Amarkantak	0.812	Amarkantak	0.336	Amarkantak	0.749
Parli	0.227	Parli	0.815	Parli	0.334	Parli	0.750
Kolaghat	0.216	Kolaghat	0.822	Kolaghat	0.320	Kolaghat	0.758
Chandrapur STPS	0.214	Chandrapur STPS	0.824	Paras	0.318	Paras	0.759
Tenughat	0.203	Tenughat	0.831	Tenughat	0.282	Tenughat	0.780
Durgapur (DVC)	0.201	Durgapur (DVC)	0.833	Khaparkheda	0.268	Khaparkheda	0.789
Badarpur	0.200	Badarpur	0.834	Durgapur (DVC)	0.260	Durgapur (DVC)	0.794
Khaparkheda	0.188	Khaparkheda	0.841	Badarpur	0.243	Badarpur	0.804
Rajghat	0.185	Rajghat	0.844	Rayalseema	0.239	Rayalseema	0.807
Nasik	0.178	Nasik	0.849	Nasik	0.218	Nasik	0.821

Source: The authors.

Note: Ranking of CTPPs is done in such a way that most inefficient CTPP under each case appears first followed by the second most inefficient CTPP and so on. Here, Ineff. means directional distance function inefficiency score and Eff. means graph hyperbolic efficiency score. CTPPs = coal-based thermal power plants.

Table 7 presents second-stage regression results to see the impact of ownership and other non-discretionary factors on efficiency/inefficiency measures derived from different DEA models under various technological assumptions. Under both technologies (i.e., BP and JP), we observe that both central and state government ownership dummies are statistically significant. For GH models the coefficients are negative, while for DDF models, the coefficients are positive. These imply that both central and state government-owned CTPPs are less efficient compared to privately owned CTPPs. One possible explanation of such a result may be that private CTPPs have better management, enhancing the performance level. Significant plant load factor coefficients indicate that better capacity utilization improves the performance of the CTPPs for both GH and DDF models, respectively under both technology approaches. The insignificant year dummy across our regression models suggests that the performance of CTPPs has not changed over the short time-span, which is in line with our non-parametric test results.

Table 7.

Second-Stage Pooled Regression.

	Joint-Production Technology		By-Production Technology
	Case I GH Efficiency	Case II DDF Inefficiency	Case III GH Efficiency	Case IV DDF Inefficiency
Central	–0.073*** (0.022)	0.094*** (0.030)	–0.059*** (0.017)	0.071*** (0.021)
State	–0.101*** (0.024)	0.133*** (0.034)	–0.075*** (0.018)	0.090*** (0.023)
PLF	0.002*** (0.001)	–0.003*** (0.001)	0.002*** (0.000)	–0.002*** (0.001)
Y14	0.017 (0.016)	–0.031 (0.024)	0.011 (0.012)	–0.017 (0.016)
Constant	0.807*** (0.054)	0.295*** (0.083)	0.857*** (0.041)	0.193*** (0.056)
Observations	132	132	132	132
R-squared	0.327	0.331	0.313	0.321

Source: The authors.

Note: Robust standard errors are shown in parentheses; * 10% significance level, ** 5% significance level, and *** 1% significance level. DDF = directional distance function; GH = graph hyperbolic.

Conclusion and Policy Discussion

This study aims to contribute to the growing body of literature on the efficiency of Indian CTPPs producing electricity and SPM, a harmful local air pollutant that has not been given due consideration. Previous efficiency studies on Indian CTPPs have derived interesting conclusions based on a specific assumption on pollution generating technology and a particular DEA model. We adopt and empirically compare four modelling options (combinations of two influential approaches to model pollution generating technologies: JP and BP, and two popular DEA tools: GH and DDF) to study their implications for benchmarking. The results from all four models suggest that on average Indian CTPPs are moderately inefficient in joint production of electricity and SPM emissions. Model outcomes suggest that efficiency/inefficiency scores vary somewhat across alternative models, but ranking of CTPPs remains almost the same across two DEA tools and technological assumptions.

In this study, we have covered 22 different electricity producing companies under three different ownership status. Out of these 22 companies, state governments own most of the utilities (15), followed by private sector (5) and the central government (2). The TATA Power Company Limited and Reliance Industries Limited own the most efficient CTPPs across DEA models and technological assumptions. On the other hand, Maharashtra State Power Generation Company Limited turns out to be the most inefficient utility company in our study. Under central government owned utilities, the Damodar Valley Corporation performs poorly across alternative models and technological assumptions. The positive (negative) significant correlation between efficiency (inefficiency) scores and plant load factor across technological assumptions suggests that better capacity utilization by a company is directly linked with its performance level.

The second-stage regression findings reveal that non-discretionary factors are similar across different technological assumptions and DEA models. Regression results confirm that CTPPs owned by private companies have performed better both in terms of efficiency compared to the central or the state government-owned power enterprises. The better utilization of the capacity helps the plant to improve productive performance. This modelling exercise will be of interest to various stakeholders to understand the ‘win–win’ moves, that is, the extent of potential to expand electricity generation and contract SPM emissions if CTPPs operate efficiently.

However, our findings are subject to two major limitations. First, due to the unavailability of labour data, we fail to accommodate the labour input in the technology set. Second, there may be a technological difference between public sector owned CTPPs and private company owned CTPPs. However, our study fails to address this issue due to the insufficient number of privately owned CTPPs. Despite such limitations, our study may provide a robust benchmarking of Indian CTPPs, which may help policymakers develop strategies to improve the overall performance level of the Indian thermal energy sector. The government should either go for public–private participation models for the better managerial experience or upgrade the infrastructure of public-owned CTPPs to generate more electricity with fewer emissions.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

Notes

ORCID iD

Deep Mukherjee

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