Are Global Companies Better in Environmental E ﬃ ciency in India? Based on Metafrontier Malmquist CO 2 Performance

: There is a rapid increase in inﬂows of foreign direct investment (FDI) into developing countries such as India. Some researchers argue that FDI has a positive impact on sustainable development in terms of environmental e ﬃ ciency and brings innovative green technology to the host country. In contrast, others claim that FDI brings considerable pollution to the host country, and their motive is only to yield proﬁt. To address this issue, this paper analyzes environmental e ﬃ ciency between FDI and domestic ﬁrms in India for seven years between 2012 and 2018. The research aims to evaluate the performance of FDI ﬁrms in terms of environmental e ﬃ ciency in India after implementing certain policy regulations, nationally and globally. In this analysis, we use the non-radial metafrontier Malmquist CO 2 performance index (NMMCPI) with three decomposition indices: e ﬃ ciency change index, best practice gap index, and technological gap change index. Our empirical results indicate that domestic ﬁrms have performed well in terms of better catch-up and innovation performance. On the other hand, FDI ﬁrms only demonstrated higher technology leadership performance, indicating weaker catch-up performance and weaker innovation performance. From the results, we proposed that policymakers should harmonize between the FDI promotion and regulation in its sustainable performance because global companies are not sensitive to the local regulations, and not very proactive in implementing the global standard of eco-friendliness.


Introduction
At present, carbon dioxide (CO 2 ) emissions from human activities have increased rapidly due to the rapid industrialization, urbanization, population explosion, and exploitation of natural resources, etc. According to the Mauna Loa Atmospheric Reference Observatory in Hawaii in 2018, CO 2 levels reached 411 parts per million, the highest monthly average ever recorded in history [1]. A recent report indicates that countries like China, United States, and India are the major emitters of CO 2 in the world. In terms of CO 2 output, India has recorded more than half of the increase in global CO 2 since 2013 [2].

Socio-Managerial Contexts
Foreign direct investment (FDI): In recent decades, we have also witnessed a sharp increase in inflows of foreign direct investment (FDI) to developing countries. FDI in India began in 1991 under the Foreign Exchange Management Act (FEMA) with a baseline of USD 1 billion in 1990. Since then, India has been one of the most popular destinations preferred for FDI. India ranks the 9th to receive Gross Domestic Products (GDP): FDI is one of the important factors that promote economic growth in India. Thus, the Indian government has gradually relaxed restrictions on FDI to achieve rapid growth. For example, on 25 September 2014, the Prime Minister of India published an international marketing strategy called "Make in India" to encourage foreign firms to invest in India to strengthen the country's manufacturing sector [5]. Figure 2 provides some details on FDI equity inflows by sector in India as of 2018 [4]. As shown in Figure 2, the main sectors of FDI inflows to India are services sectors, computer software and hardware, telecommunications, construction development, trading, automobile industry, chemicals, infrastructure, drugs and pharmaceuticals, etc.  Gross Domestic Products (GDP): FDI is one of the important factors that promote economic growth in India. Thus, the Indian government has gradually relaxed restrictions on FDI to achieve rapid growth. For example, on 25 September 2014, the Prime Minister of India published an international marketing strategy called "Make in India" to encourage foreign firms to invest in India to strengthen the country's manufacturing sector [5]. Figure 2 provides some details on FDI equity inflows by sector in India as of 2018 [4]. As shown in Figure 2, the main sectors of FDI inflows to India are services sectors, computer software and hardware, telecommunications, construction development, trading, automobile industry, chemicals, infrastructure, drugs and pharmaceuticals, etc. the Foreign Exchange Management Act (FEMA) with a baseline of USD 1 billion in 1990. Since then, India has been one of the most popular destinations preferred for FDI. India ranks the 9th to receive FDI inflows as in 2019, against 12th in the previous year, among the largest recipients of FDI in the world reported by UNCTAD, 2020. Indian government proactively induced FDI due to its quantitative contribution in the local economy as well as the qualitative contribution for innovative technology transfer and advanced know-how for the sustainable development of India. Unfortunately, it does not always seem true in the performance of FDI firms. As shown in Figure 1, the trend in FDI inflows from 2001 to March 2016 corresponds to CO2 emissions in India [3,4]. This means that there is a direct relationship between CO2 emissions and FDI inflows into India. The Indian government may be concerned about this phenomenon as it expects qualitative contributions from FDI companies, including sustainable and environmentally friendly management of these global firms. Gross Domestic Products (GDP): FDI is one of the important factors that promote economic growth in India. Thus, the Indian government has gradually relaxed restrictions on FDI to achieve rapid growth. For example, on 25 September 2014, the Prime Minister of India published an international marketing strategy called "Make in India" to encourage foreign firms to invest in India to strengthen the country's manufacturing sector [5]. Figure 2 provides some details on FDI equity inflows by sector in India as of 2018 [4]. As shown in Figure 2, the main sectors of FDI inflows to India are services sectors, computer software and hardware, telecommunications, construction development, trading, automobile industry, chemicals, infrastructure, drugs and pharmaceuticals, etc.   Corporate Social Responsibility (CSR): Due to strict environmental regulations in developed countries, investors have been discouraged from investing in pathways that produce much natural pollution and thus create a heavier response on its corporate social responsibility (CSR) for the community, resulting in overseas investments toward developing countries, where the environmental regulations are not very severe, and the global company has the invisible privileges on the local regulations. For these reasons, FDI investors still prefer countries where legal, environmental regulations have not yet been determined, ignoring the negative consequences of the investment they make, which in turn leads to environmental degradation. Due to the need for all kinds of industrial activities such as low-income level, insufficient property rights, and lack of development of environmental awareness, developing countries do not give much importance to environmental regulations [6]. As a result, the increased transfer from developed to developing countries by high CO 2 -emitting industries such as energy-intensive industries has started to create an environmental hazard. Consequently, to avoid this type of negative impact situation and to increase its rigor, developing countries have also begun to improvise their environmental regulations. For example, the Reserve Bank of India has said that political action is needed to put in place an enabling environment for fostering green investment as well as advancing the net-zero carbon delivery program in India [7].
Energy-related policies in India: Some of the highlighted energy-related policy Acts and plans proposed and adopted by the Indian government are Energy and carbon taxes supported by the United Nations Framework Convention on Climate Change. A carbon tax is a step to help India reduce the amount of CO 2 released per unit of gross domestic product (GDP) and reach its voluntary target of 25% over 2005 levels by 2020. India has already introduced a national carbon tax, generally in the transport and energy sector of 50 rupees (Rs) per ton of coal consumed by any economic sector on July 1, 2010. The carbon tax has been further increased, and currently, the carbon tax amounts to Rs 400 per ton in India in all sectors emitting CO 2 . Nationally Determined Contributions (NDCs) under the Paris Agreement, 2016. India is one of the few developing countries on the way to achieving the goals of the Paris Agreement by the "nationally determined contributions" or NDCs. On 2 October 2016, India ratified the Paris Agreement with a 4.1% reduction goal by 2030 in global CO 2 emissions. Based on NDCs, the three main objectives have been set by the Indian government. The first objective is to increase the share of non-fossil fuels to 40% of total electricity production capacity. The second objective is to reduce emission intensity in the economy from 33% to 35% by 2030 compared to the 2005 level. The third objective is to create an additional carbon sink of 2.5-3 billion tons of CO 2 equivalent for the period 2020-2030. Now, the question is whether this rosy pathway does affect the sustainable management of FDI companies in India. The Indian government gave easier access on the market to the FDI firms with the expectation of these FDI firms' leadership coming from the global standard on the qualitative contribution to the local economy, including the environmentally friendly economic activities in India.

Research Motivation and Objective
In the literature, however, many studies have argued on the potential impacts of FDI inflows and environmental sustainability, such as pollution from CO 2 emissions, energy consumption, etc. The influence of environmental regulations on FDI firm performance for decades has been an increasingly important subject for researchers around the world [8]. In one view, FDI can bring advanced technologies to the host country and improve the country's sustainable growth because FDI raises its level of technical progress through "learning by doing" in sustainable ways [9,10]. Another extreme point of view is that developed countries are shifting polluting industries to developing countries. It has brought much pollution to developing countries by transferring energy-intensive and much pollution-oriented plants. Therefore, the increase in the inflow of FDI could have adverse effects on the host countries, causing severe environmental pollution and degradation of the environment [11][12][13][14][15]. It is a widely debated subject whether India benefits from FDI or not in environmental perspectives. Based on the above argument, this research aims to evaluate the environmental efficiency between FDI and domestic firms in India and determine the performance of FDI in the period between 2012 and 2018. Since the evaluation should be based on the dynamic effect over time with multi-inputs/outputs model, we will use the non-radial metafrontier Malmquist index to analyze our data.

Research Contribution
There are two types of firms in India; FDI and domestic firms. The FDI firm implies that a company takes controlling ownership in a business entity in another country. To take advantage of cheaper wages, FDI firms invest directly in the fast-growing Indian market and change the business environment in India. A domestic firm is defined as a local investor who can conduct business in his home country. Since this research aims to compare all FDI firms with domestic ones, it will be essential to also focus on the average variation in the productivity of each firm over time.
This study contributes to understanding how vital FDI is to build a sustainable ecosystem in India, taking into account the environmental impact. How will regulatory policies affect these firms to reduce CO 2 emissions and to improve environmental performance in India? To the best of our knowledge, no one has explored this research area in India so far. Since there is no comprehensive comparison between FDI firms and domestic firms to determine the environmental efficiency of FDI in India, this paper attempts to compare FDI and domestic firms by measuring their environmental efficiency. Therefore, the purpose of this research is empirically to analyze whether FDI inflows to India increase its CO 2 emissions or vice-versa.
The structure of the paper is as follows; in Section 2, we present a literature review in the related areas to find out our strategic variables and methodologies; in Section 3, we develop our empirical models to evaluate the environmental efficiency of FDI and domestic firms in India; we discuss our empirical result and its implications in Section 4; in Section 5, we conclude our study by providing some policy implications.

Literature Review
Many policymakers and academics professionals have paid considerable attention to the relationship between FDI inflows and the effectiveness of environmental sustainability in the host country. However, the impact of FDI on the environment is still unclear. Some studies argue that FDI can improve the environmental efficiency of the host country [16][17][18], while others find that it can damage the environment of the host country [19].
Most of the literature in energy and environment (E&E) analysis uses the multi-inputs and outputs to handle the coupling and decoupling between the potentially conflicting variables of desirable outputs such as profits or GDP, and undesirable outputs such as CO 2 emission, as shown in Table 1.
Since the data envelope analysis (DEA) is very popular for handling multi-inputs/outputs models, it is also possible to utilize this approach for our research in the comparison between FDI and domestic firms as well [20,21]. The DEA approach does not need any specific form of the production function for this multi-inputs/outputs model. Thus, it is very popular to evaluate the relative efficiency for all decision-making units (DMUs), FDI, and domestic firms in our model. Thus, we first examine research papers that are related to the environmental efficiency of FDI using DEA. As shown in Table 1, we classify the previous research into three categories. First, FDI has a positive effect on the environmental efficiency of the host country [16]. Second, FDI harms (negative) the environmental efficiency of the host country [19]. Third, FDI may have a mixed effect with positive and negative impacts on the environmental efficiency of the host country [22][23][24]. Pan et al. [25] used the slacks-based measure (SBM)-Data Envelopment Analysis (DEA) model to measure more accurately the energy efficiency of the quality of FDI in China. They found that the quality of FDI had a significant positive effect on energy efficiency in China. Wang [26] measured the energy efficiency of FDI on energy efficiency in China and concluded that FDI significantly improves energy efficiency. Mastromarco et al. [27] analyzed FDI and time on catching up and found that FDI influences productivity by increasing efficiency and improving technological change. Yue et al. [28] measured the effectiveness of FDI from China using the SBM-DEA. They found that FDI significantly improved energy efficiency. Song et al. [29] examined FDI in China using the DEA model to measure efficiency. They found that FDI inflows can play a positive role in local economic and technological development in China, especially in some rapidly economically developing areas.
However, Yang et al. [30] compared the environmental efficiency of FDI and exports from China. They concluded that FDI reduces industrial environmental efficiency in China. Likewise, export from China also has a significant negative impact on industrial environmental efficiency. Lei et al. [31] have researched the attractiveness of FDI in Chinese provinces and found that only eastern provinces have great development potential. Zang et al. [32] have used a super-efficiency DEA model to evaluate energy efficiency from FDI in developing countries and found that FDI has a negative impact in developing countries.
Monaheng et al. [33] examined FDI and economic performance in BRICS countries. They found that FDI had a positive impact on the economic performance of the BRICS countries except for China. Guo et al. [11] analyzed the regional influence of FDI in China by measuring energy efficiency using the DEA model. They recognized that FDI inflows improve local energy efficiency in the central and eastern regions but reduce energy efficiency in the western region. Finally, Luo et al. [34] have studied FDI from China to measure environmental performance. They have argued that FDI has a positive Sustainability 2020, 12, 8359 6 of 19 impact on the environment as well as a negative impact on the country's environmental efficiency. For example, FDI has improved local energy efficiency in the eastern and central regions due to the aggregate result of the technological effect, the scale effect, and the structure effect of FDI. However, FDI has reduced energy efficiency in the western zone due to the lower level of economic development.
As shown in Table 1, the authors used diverse DEA models to measure economic performance, environmental efficiency, energy efficiency, CO 2 emission performance, and efficiency of FDI in the host country. Existing literature has extensively studied the effects of FDI on a country's economic development and environmental pollution simultaneously. However, there is no comprehensive comparison between FDI firms and domestic firms to evaluate the environmental performance of FDI. Therefore, this paper attempts to measure the environmental efficiency of FDI in India by comparing the environmental efficiency of FDI and domestic firms in India.

Production Technology Set
In E&E studies, the term "environmental production technology" is defined as the basic directional distance function of all the interrelated variables without any specific production frontier constraints a priori, because environmental production technology unambiguously encompasses multiple outputs, differently from other parts of traditional production theory in economics. This environmental production technology encompasses two classical inputs of the capital (x 1 ) employees (x 2 ) and the specialized input of energy (x 3 ), with the sales turnover variables (B) as desirable output and CO 2 (C) as an undesirable output. Therefore, we selected the three inputs and two outputs in this study, based on the traditional approach to the production function. We collected data from the annual reports of each FDI and domestic firms from different sectors that emit CO 2 . Environmental production technology is defined as the causal relationship between the firm's capital (x 1 ), employee (x 2 ), and energy (x 3 ) as an input, and the desirable as well as undesirable outputs of firms' sales turnover (B) and CO 2 (C), respectively. According to Lee and Choi (2018), this can be expressed in the mathematical form [35]: where the set of production possibilities T is assumed to satisfy the standard axioms of the production theory [36]. For example, finite amounts of input can only produce limited amounts of output because inactivity is always possible [37]. Additionally, inputs and desirable outputs are often assumed with undesirable output freely disposable (weak disposability), implying that a reduction of the undesirable output such as CO 2, should match with less desirable outputs in the production process. The elimination of CO 2 can be possible if and only if by stopping production, on T concerning regulated environmental technologies (null-jointness) [38]. These two hypotheses can be expressed in the mathematical expression as follows: Once the environmental production technology (T) is defined, we can specify the frontier. Consequently, we can formulate T for N FDI and domestic firms under constant returns to scale as follows [39]: where Zn is an intensity variable. By using a convex combination, it can build environmental production technology. Although the assumptions of variable returns to scale are widely adopted in the various literature, we selected the constant returns to scale (CRS) for T in this study because the CRS method is easily generalized to multiple types of firms.

CRS Non-Radial Directional Distance Function
There are two types of distance functions for E&E studies, which are widely adopted Shephard distance function and the directional distance function (DDF) [40,41]. Shephard distance function is known for minimizing the inputs and undesirable output, at the same rate, maximizes the desirable output simultaneously. However, this function has several limitations. The most outstanding difficulty in Shephard distance function may come from the radial approach for its coupling issues between the desirable and undesirable outputs. To solve this coupling issue of the radial approach, the generalized directional distance function is introduced. The common limitation is that the Shephard distance function may overestimate the effectiveness when some slacks exist [42]. Using the directional weight vector (g), conventional DDF can overcome this overestimation. It can be expressed in mathematical form as follows: On the other hand, the non-radial efficiency measure is more generalized and personalized for E&E studies due to its advantage to overcome the many limitations of the radial efficiency functions, with a more generalized form that takes into account undesirable outputs [37,43,44]. Thus, our study also adopts the non-radial DDF (NDDF), which is expressed mathematically as follows: The symbol 'diag' in the Equation (4) denotes diagonal matrices, which are related to the numbers of all variables and can be expressed as follows: W T = (W x 1 , W x 2, W x 3, W B, W C ) T denotes a normalized weight vector; g denotes an explicit directional vector which can be expressed as g = −g x 1 , −g x 2 , −g x 3 , g B , −g C ; β = (β x 1 , β x 2 , β x 3 , β B , β C )T ≥ 0 represents individual inefficiency measures by denoting the scaling vector for all variables. In order to avoid the diluting effect of non-energy variables, we set the directional vector of capital and labor to be zero, because capital and labor do not directly affect CO 2 emissions [45]. Therefore, the directional vector of this study is g = 0, 0, −g x 3 , g B , −g C and the weight vector is (0, 0, 1/3, 1/3, 1/3). We can, therefore, define NDDF value in the mathematical form [46]: In Equation (5), we can modify the directional vector g, according to our different political objectives of reducing CO 2 emissions. If → D (x 1 , x 2 , x 3 , B, C; g) = 0, this would indicate that a specific FDI or domestic firm under the evaluation is located in the best-practice production frontier in the g direction [37]. We also formulated the static total-factor CO 2 emissions performance index (TCPI) as the ratio of the actual carbon intensity to the potential target carbon intensity [43]. If β * C and β * B are the optimal solutions that correspond to undesirable output CO 2 emissions and desirable output sales turnover in Equation (5), then, the TCPI can be described as follows, In this study, Equation (6) can be used to measure the performance of CO 2 emissions from FDI and domestic firms and measure the maximum possible reductions in CO 2 intensity over the 2012-2018 period. If the TCPI is higher, then the CO 2 emission performance will be better. Besides, the TCPI lies between zero and unity; therefore, the best CO 2 emission performance of FDIs and domestic firms will be located along the frontier when the TCPI is equal to unity.

Non-Radial Metafrontier Malmquist CO 2 Performance Index (NMMCPI)
Based on the metafrontier Malmquist index, some authors have proposed a Non-radial Metafrontier Malmquist CO 2 Performance Index (NMMCPI) to measure the dynamic total-factor CO 2 emission performance [47,48]. Here, the MMCPI is defined as the difference between the weighted average rates of change of (negative) inputs, (positive) outputs, and (negative) outputs. The NMMCPI measures the change in TCPI during period t and t + 1. It is useful to evaluate environmental performance change over time. Thus, we adopted the non-radial metafrontier Malmquist CO 2 Performance Index (NMMCPI) to examine the environmental efficiency of FDI and domestic firms in India.
To define and decompose the NMMCPI in this study, we need to define the three sets of environmental technologies, i.e., contemporaneous environmental technology, intertemporal environmental technology, and global environmental technology. We determine these sets as follows [49]. The first sets of environmental technologies called the contemporaneous environmental technology of R h can be expressed as T C R h = x 1t , x 2t , x 3t , B t , C t : x 1t , x 2t , x 3t can produce B t , C t where t = 1 . . . T For a particular period t and group R h , it constructs production technology set in Equation (2). The second set of environmental technologies is an intertemporal environmental technology and its R h an be expressed as T I . This is constructed from observations for group R h which consists of a single technology over the whole period. This implies that the observations for an intertemporal environmental technology are assumed to be unable to access different intertemporal environmental technologies easily. For the distinct intertemporal technologies, we assumed that there are h groups subsequently. Finally, global environmental technology is considered in the third set of environmental technologies that can be expressed in the form: which is constructed from all observations for FDI and domestic firms groups over the 2012-2018 period. This implies that global environmental technology encompasses all intertemporal environmental technologies. For the sake of analysis, we assume that every observation (theoretically and potentially) can access global technology through its innovations.
Based on these three decomposed technologies, our environmental technologies under the non-radial directional distance functions in Equation (4)  and → D G = (x 1 S , x 2 S , x 3 S , B S , C S ), where S = t, t + 1. With these three technologies, NDDF can be solved using Equation (5) as follows: where the superscript d on → D d (.) can be a contemporaneous, intertemporal, and global environmental technology, which represents the type of NDDF. Besides, the symbol "con" under designates the construction conditions of three environmental technologies. If we want to construct the contemporaneous NDDF, we required the conditions d≡C and con ≡ {n R h to build the intertemporal NDDF, we need the conditions set d≡I and con ≡ {n R h s 1, 2, T]}; and the requirements should be d≡G con ≡ {n [R 1 ∪ [R 2 ∪ . . . ∪ R H ], s 1,2, . . . , T]}, for the global NDDF. Using Equation (7), we can solve the six different NDDF models in Equation (6).
where S = t, t + 1 and d = (C, I, G). We define the NMMCPI, based on the formulation of the metafrontier Malmquist index within the framework of the global environmental technology set [46]. It can be expressed as the ratio.
NMMCPI measures the variations of the TCPI from Equation (9), on the T G for the period between t and t + 1. Now, NMMCPI can be decomposed into a technical efficiency change (EC) index of CO 2 emissions, a best-practice gap change (BPC) index of CO 2 emission reduction technologies, and a technology gap change (TGC) as follows [47,48]: In the Equation (10) the term efficiency change or EC index measures the "catching-up" effect, which measures the technical efficiency changes of CO 2 emissions for a specific FDI or a domestic firm for two time periods (t, t + 1) within a specific group. The EC Index captures how close an FDI or a domestic firm is toward contemporaneous environmental technology. If EC > 1, there is an efficiency gain, and if the EC < 1, there is a loss of efficiency [39]. The best practice gap change or BPC index is the change in the best practice gap in two adjacent periods between contemporaneous environmental technology and intertemporal environmental technology. Here, if BPC > 1, the contemporaneous environmental technological frontier in period t + 1 is closer to intertemporal environmental technology than in period t, and if BPC < 1, the contemporaneous technological frontier is further from the intertemporal environmental technological frontier [45]. BPC is also seen as the innovation effect since innovation allows a shift of the frontier. The Technology Gap Change or TGC Index is the change in technological leadership during the two periods between the intertemporal environmental technology frontier and the global environmental technology frontier for reducing CO 2 emissions. For example, TGC> (or <) 1 indicates that a technical gap between a specific group of intertemporal technology and global technology is reduced (increased). Therefore, TGC measures the effect of technological leadership for a given group. Figure 3 shows NMMCPI and its decomposed components. Here, contemporaneous environmental technology is presented as T C R 1 and T C+1 R 1 in the group R 1 or the periods t and t + 1.
Intertemporal environmental technology is presented as T I R 1 for group R 1 and global environmental technology for two groups is presented as T G R 1 [50]. Here, the intertemporal technological set is the envelope of all contemporaneous technological set in the current period of a particular group, and the global technological set is the envelope of all intertemporal technologies set. Here, the observed FDI and domestic firms for the two periods t and t + 1 are a 1 and a 2 because it is a case of two groups (R 1 , R 2 ) and two periods (t, t + 1), respectively.

Data Collection and Preprocessing
Since this study aims to compare the environmental efficiency of FDI firms with domestic firms, we collected data on 50 firms belonging to both groups from 2012 to 2018. Concerning the industrial sector, the following sectors were chosen: chemicals, constructions, pharmaceuticals, power, automobile, infrastructure, and others. We selected these sectors because they have the largest inflow of FDI to India, subject to the percentage of total inflows in 2018 (see Figure 2). Additionally, we selected 25 FDI companies and 25 domestic companies in India, based on the availability of firm data and FDI equity inflows by sector in India as of 2018. These firms could be considered the representative companies of these sectors, which have high CO2 emissions [51]. The service sector and telecommunications sectors were excluded because of their low emission volume and the scarcity of data. Based on the argument on Table 1, we collected three input variables, capital (x ), labor (x ), and energy (x ), and two output variables, sales turnover (B) and CO2 emissions (C). All the data concerning capital, labor, energy, sales turnover, and CO2 were collected in the annual report of each

Data Collection and Preprocessing
Since this study aims to compare the environmental efficiency of FDI firms with domestic firms, we collected data on 50 firms belonging to both groups from 2012 to 2018. Concerning the industrial sector, the following sectors were chosen: chemicals, constructions, pharmaceuticals, power, automobile, infrastructure, and others. We selected these sectors because they have the largest inflow of FDI to India, subject to the percentage of total inflows in 2018 (see Figure 2). Additionally, we selected 25 FDI companies and 25 domestic companies in India, based on the availability of firm data and FDI equity inflows by sector in India as of 2018. These firms could be considered the representative companies of these sectors, which have high CO 2 emissions [51]. The service sector and telecommunications sectors were excluded because of their low emission volume and the scarcity of data. Based on the argument on Table 1, we collected three input variables, capital (x 1 ) labor (x 2 ) and energy (x 3 ) and two output variables, sales turnover (B) and CO 2 emissions (C). All the data concerning capital, labor, energy, sales turnover, and CO 2 were collected in the annual report of each FDI and domestic firm between 2012 and 2018. We selected seven-year data from 2012 to 2018 because the classification in this study was based on two types of the policy paradigm shift in India to reduce CO 2 emissions. These two policies are energy and carbon taxes under the United Nations Framework Convention on Climate Change, 2010, and Nationally Determined Contributions (NDCs) under the Paris Agreement, 2016. According to THE HINDU in 2018, environmental regulations in India have very few impacts on FDI firms [13]. The World Resources Institute India declared in June 2019 that after biomass combustion, companies are the second largest contributor to PM2.5 in India [52]. Concerning this, we wanted to analyze the environmental efficiency of FDI and domestic firms in India based on the policy paradigm shift in India.
For the capital input, we extracted the data on fixed assets from the published annual reports of each FDI and domestic firms from 2012 to 2018. We collected the employees per head of each company, as shown in the annual report of each DMU. For energy input data, since there is no right amount of energy consumption provided by each firm in their report, we had to convert the power and fuel consumption into total energy consumption equivalent value from the annual report published by the firms. For sales turnover output, we collected the revenues of the firms generated by the operations. For the CO 2 emissions data, we extracted the CO 2 values using the macro level of the FDI and domestic firm's data of power and fuel consumption rate [37,53]. These descriptive statistics (all the variables) are shown in Table 2.  Table 3 illustrate the correlation matrix of input and output variables of FDI and domestic firms from 2012-2018. The result shows that the correlation between all types of input and output variables is positive. Capital and labor are positively linked to sales turnover because they are representative variables to explain production; in particular, capital and turnover show a highly significant relationship. On the other hand, energy shows a positive relationship for both sales turnover and CO 2 emissions; in particular, energy and CO 2 emissions show a highly significant relationship [54,55]. In this study, the result verifies the suitability of analyzing the data from an environmental point of view.  Table 4 shows the average value of the NMMCPI index and its decomposition for FDI and the domestic firm in India. Due to the firm's confidentiality, we used the firm's id in our results in Table A1. First, we can see that the overall NMMCPI of the FDI firms remains stable with a slightly lower growth rate of 0.15%, while domestic firms show 1.48%. This result implies that domestic firms improve their performance in implementing the environmental regulatory regime during the study period, compared to FDI firms in India. In terms of the average EC index of FDI firms, the growth rate is 0.53%, indicating a lower growth rate in efficiency during the study period. At the same time, domestic firms show an annual increase of 1.15%, implying that domestic firms do better for the best catch-up effect, suggesting the more proactive movement towards the contemporary environmental technological frontier. In terms of the average BPC index, FDI firms show the value lower than unity (0.9990), while domestic firms show a 0.23% increase. Since the BPC index captures the "innovation effect," this result implies that domestic firms expanded their production level under the environmental regulatory regime. The average annual TGC index of FDI and domestic firms is 0.9982 and 1.0019, respectively. This implies a lack of technological leadership among FDI firms in India during the study period. The gap between the intertemporal frontier and the global frontier has narrowed for FDI firms, as the TGC index is a measure of changes in technological leadership for a given group. Figure 4 shows the trends in the NMMCPI for FDI and domestic firms during 2012-2018. Regarding the dynamic perspective over time, we can see that the performance of FDI firms in annual total factor CO 2 emissions shows a lower growth rate during the study period, which is close to unity. This could be due to the lack of policy effect on FDI firms in India because policy in India has a soft signal for the foreign market [13]. Therefore, there is a missing link in the role of the Indian government for FDI firms. We suggest that the Indian government should be aware of this phenomenon and take certain measures to reduce the differences between local firms and FDI firms. Like FDI firms, domestic firms also show a low growth rate in the performance of total factor CO 2 emissions from 2012 to 2017, which is 1.0120. However, after 2016-2017, the graph shows an upward trend, which is above the unity of 5.85% in 2018. This J-curve effect means that there is an effect of government regulation on domestic firms in India. This may be due to the implementation of the policy that the Indian government has adopted. Indian government set a very clear and strong CO 2 reduction target in 2016, called Nationally Determined Contributions (NDC), under the Paris Climate Agreement. Consequently, all of the firms that emit the most CO 2 are under pressure to reduce their CO 2 emissions. Due to the higher regulatory costs, this type of strict regulation could affect a firm's performance at the initial level. That is why the performance of domestic firms was observed highly enhanced after 2016-2017. Even if there are no strong regulations yet for the FDI firms in India, they should show their efforts to reduce CO 2 emissions under the mixed economy such as India. It also supports Porter's hypothesis that if a country has tighter environmental regulations, it will increase the efficiency of that particular country and encourage innovation for a more environmentally friendly production process [53].

Result and Its Implications
performance at the initial level. That is why the performance of domestic firms was observed highly enhanced after 2016-2017. Even if there are no strong regulations yet for the FDI firms in India, they should show their efforts to reduce CO2 emissions under the mixed economy such as India. It also supports Porter's hypothesis that if a country has tighter environmental regulations, it will increase the efficiency of that particular country and encourage innovation for a more environmentally friendly production process [53].  Figure 5 shows the trends in the EC index of FDI and domestic firms from 2012-2018. In this figure, the FDI shows an M-shaped trend. The EC index of FDI firms for 2012-2014 shows a value less than or equal to unity, indicating the loss of catch-up performance. However, the EC index alternately goes above or below, for the 2014-2018 period, but remains close to unity. This means that the catch-up performance of FDI firms remains unchanged during the study period. This needs to be investigated by Indian policymakers to determine why there is a lower growth rate efficiency of FDI firms in India. Policymakers should, therefore, come up with appropriate policy solutions that will be easily adopted by FDI firms in India, as some foreign firms are not very sensitive to local regulations. The EC index of domestic firms for the period 2012-2014 shows a value of less than unity. This indicates that during these years, the catch-up performance decreased. However, after 2013-2014, the EC index was higher than unity, which suggests that their catch-up performance in reducing CO 2 emissions has improved. Given that, in a specific group, the EC index measures to what extent an FDI and domestic firm increase its efficiency. There is a gain in efficiency if EC > 1, and there is a loss in efficiency if EC < 1 [39]. Therefore, in terms of the catch-up effect, domestic firms perform better than FDI firms. This means that domestic firms in India have improved efficiency by the catch-up effect of the best practice frontier during the period 2012-2018. This may be because most of the FDI companies come from market-oriented economies and are therefore not very serious about emission reduction policies. Therefore, Indian policymakers should adopt more robust, transparent, and predictable policies for FDI companies in India.
Sustainability 2020, 12, x FOR PEER REVIEW 14 of 19 Figure 5 shows the trends in the EC index of FDI and domestic firms from 2012-2018. In this figure, the FDI shows an M-shaped trend. The EC index of FDI firms for 2012-2014 shows a value less than or equal to unity, indicating the loss of catch-up performance. However, the EC index alternately goes above or below, for the 2014-2018 period, but remains close to unity. This means that the catch-up performance of FDI firms remains unchanged during the study period. This needs to be investigated by Indian policymakers to determine why there is a lower growth rate efficiency of FDI firms in India. Policymakers should, therefore, come up with appropriate policy solutions that will be easily adopted by FDI firms in India, as some foreign firms are not very sensitive to local regulations. The EC index of domestic firms for the period 2012-2014 shows a value of less than unity. This indicates that during these years, the catch-up performance decreased. However, after 2013-2014, the EC index was higher than unity, which suggests that their catch-up performance in reducing CO2 emissions has improved. Given that, in a specific group, the EC index measures to what extent an FDI and domestic firm increase its efficiency. There is a gain in efficiency if EC > 1, and there is a loss in efficiency if EC < 1 [39]. Therefore, in terms of the catch-up effect, domestic firms perform better than FDI firms. This means that domestic firms in India have improved efficiency by the catchup effect of the best practice frontier during the period 2012-2018. This may be because most of the FDI companies come from market-oriented economies and are therefore not very serious about emission reduction policies. Therefore, Indian policymakers should adopt more robust, transparent, and predictable policies for FDI companies in India.   . Overall, domestic firms perform better than FDI firms in terms of the innovation effect in the Indian firm scenario. We suggest that policymakers should support innovative companies and offer them a reward for sustainable development. Additionally, other companies should consider particular innovative companies as their benchmark for creating sustainability. As shown in Figure 7, the TGC index of FDI and domestic firms shows the contradictory trend between them. For example, in 2012-2014 and 2017-2018, the performance of FDI was less than unity, indicating a decrease in the performance of technology leadership. At the same time, the performance of domestic firms in terms of technology leadership is greater than unity in the same year. However, in 2014-2017, the results show that the performance of FDI was greater than unity, indicating an improvement in the performance of technology leadership and vice-versa for the domestic firms. This suggests that there has been conflicting technological leadership performance by FDI and domestic firms during the study period. Compared to unity, if TGC> (or <) 1, there is a decrease (increase) in the technology gap between the intertemporal technology and the global technology for a specific group. Although the average annual value of domestic firms in the TGC index is a little higher than that of FDI firms, dynamic trends show that there is an increase in the performance of FDI firms during the study period from 2012-2018. Policymakers should understand technological revolutions and encourage companies to initiate and lead the commercialization of technological advancements and coordinate their use of technology to achieve sustainable goals.

Conclusions
In this study, we analyzed the environmental efficiency of both FDI firms and domestic firms in India for the seven years (2012-2018), based on NMMCPI. This methodology could incorporate group heterogeneity; it could provide each firm with more optimized implications and solutions.
Our main findings and suggestions are summarized as follows: first, according to the NMMCPI index, the result implies that domestic firms have improved their performance in the implementation of the environmental regulatory regime, compared to FDI firms in India. This could be due to the As shown in Figure 7, the TGC index of FDI and domestic firms shows the contradictory trend between them. For example, in 2012-2014 and 2017-2018, the performance of FDI was less than unity, indicating a decrease in the performance of technology leadership. At the same time, the performance of domestic firms in terms of technology leadership is greater than unity in the same year. However, in 2014-2017, the results show that the performance of FDI was greater than unity, indicating an improvement in the performance of technology leadership and vice-versa for the domestic firms. This suggests that there has been conflicting technological leadership performance by FDI and domestic firms during the study period. Compared to unity, if TGC> (or <) 1, there is a decrease (increase) in the technology gap between the intertemporal technology and the global technology for a specific group. Although the average annual value of domestic firms in the TGC index is a little higher than that of FDI firms, dynamic trends show that there is an increase in the performance of FDI firms during the study period from 2012-2018. Policymakers should understand technological revolutions and encourage companies to initiate and lead the commercialization of technological advancements and coordinate their use of technology to achieve sustainable goals. As shown in Figure 7, the TGC index of FDI and domestic firms shows the contradictory trend between them. For example, in 2012-2014 and 2017-2018, the performance of FDI was less than unity, indicating a decrease in the performance of technology leadership. At the same time, the performance of domestic firms in terms of technology leadership is greater than unity in the same year. However, in 2014-2017, the results show that the performance of FDI was greater than unity, indicating an improvement in the performance of technology leadership and vice-versa for the domestic firms. This suggests that there has been conflicting technological leadership performance by FDI and domestic firms during the study period. Compared to unity, if TGC> (or <) 1, there is a decrease (increase) in the technology gap between the intertemporal technology and the global technology for a specific group. Although the average annual value of domestic firms in the TGC index is a little higher than that of FDI firms, dynamic trends show that there is an increase in the performance of FDI firms during the study period from 2012-2018. Policymakers should understand technological revolutions and encourage companies to initiate and lead the commercialization of technological advancements and coordinate their use of technology to achieve sustainable goals.

Conclusions
In this study, we analyzed the environmental efficiency of both FDI firms and domestic firms in India for the seven years (2012-2018), based on NMMCPI. This methodology could incorporate group heterogeneity; it could provide each firm with more optimized implications and solutions.
Our main findings and suggestions are summarized as follows: first, according to the NMMCPI

Conclusions
In this study, we analyzed the environmental efficiency of both FDI firms and domestic firms in India for the seven years (2012-2018), based on NMMCPI. This methodology could incorporate group heterogeneity; it could provide each firm with more optimized implications and solutions.
Our main findings and suggestions are summarized as follows: first, according to the NMMCPI index, the result implies that domestic firms have improved their performance in the implementation of the environmental regulatory regime, compared to FDI firms in India. This could be due to the lack of policy effects on FDI firms in India. Therefore, there is a missing link in the role of the Indian government for FDI firms. We suggest that the Indian government should be aware of this phenomenon and take certain measures to reduce the differences between local firms and FDI firms. Second, based on our study, we found that domestic firms showed better catch-up performance (EC) and better innovation performance (BPC) than FDI firms in India. This may be since most of the FDI firms come from market-oriented economies, and thus they are not very serious for the emission abatement policies. Therefore, Indian policy-makers should adopt stronger transparent and predictable policies for the FDI firms in India. Otherwise, it is just a tiger drawn in the paper for the FDI firms with negotiable powers with the local government. Third, although the average annual value of domestic firms in the TGC index is higher than that of FDI firms, the overall dynamics of the TGC index of FDI firms show an increasing trend. In contrast, domestic firms decline from the period 2012-2018. Many global companies are not sustainable in their host country due to their weak accountability of global standards in the host economy and lack of surveillance of local government. Finally, many local governments expect too much of FDI firms with the same level of regulations as domestic firms. Still, this is not strong enough for global companies. Therefore, they must understand that their bad behavior can have a significant negative effect not only on the host country but also on all other local markets in the world, especially developing countries. It is time for FDI firms to shift their paradigm of local management in the host country into sustainable and inclusive economic perspectives.
Due to the scarcity of data and the low volume of emission, we excluded the service sector and telecommunications sectors, which represented the highest FDI inflows to India in 2018. Our future research will include both the service sector and the telecommunications sectors to analyze the efficiency of FDI and domestic firms in India. In addition to our model, we could use regression analysis for local and global companies to thoroughly test Porter's hypothesis through statistical analysis on the determinants of CO 2 emission performance. On the other hand, this paper could be further extended with the MNMCPI bootstrap for total factor CO 2 emission performance and its decompositions to perform statistical inference.

Conflicts of Interest:
The authors declare no conflict of interest.