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Modelling Carbon Emissions Efficiency from UK Higher Education Institutions Using Data Envelopment Analysis

Aims: To correlate the energy and carbon emission efficiency relative to research income, gross internal area, and population for all the Higher Education Institutions (HEIs) in the UK and to assess the comparative carbon emission efficiency of HEIs relative to economic metrics. Study Design: Analytical panel data study. Place and Duration of Study: This paper evaluates the energy efficiency of 131 HEIs in the UK subdivided into Russell and non-Russell groups from 2008 to 2015. Methodology: Data Envelopment Analysis (DEA) and Malmquist productivity indexes (MPI) are used for the efficiency calculations. Results: The empirical results indicate that UK HEIs have relatively high energy efficiency scores of 96.9% and 77.6% (CRS) and 98.5%, 86.3% (VRS) for Russell and non-Russell groups respectively. Original Research Article Oloruntoba and Oladipo; JENRR, 3(3): 1-18, 2019; Article no.JENRR.51133 2 Conclusion: The evidence from this study reveals that HEIs are not significantly suffering from scale effects, hence, an increase in energy efficiency of these institutions is feasible with the present operating scale but would need to work on their technical improvements in energy use. Malmquist index analysis confirms the lack of substantial technological innovation, which impedes their energy efficiency and productivity gain. Findings show that pure technical efficiency accounts for the annual efficiency obtained in the DEA model, the technological progress in contrast is the source of their energy inefficiency.


INTRODUCTION
It is predicted that the nearest decades would experience enormous socioeconomic challenges, chiefly because of the current trends in energy consumption and its impact on the built environment.
Today's centralized and fossil dominant energy in the face of escalating global population is confronted with resource depletion and high carbon emission rates. This necessitates the ongoing call and debate on energy transition especially in Europe. The extensive objectives of this transition are centred on energy efficiency and decarbonization at the level of economic activities.
The United Kingdom in its capacity is building a sustainable framework to achieve net zero carbon future and have singled out Higher Education sector as a pivotal sector to drive energy efficiency and carbon reduction across Britain [1,2,3].

Energy Consumption and Carbon Emission Trends in the UK Higher Education Institutions (HEIs)
The traditional myths that universities are solely academic habitat is fast eroding, chains of diverse activities are going on at these institutions on the daily basis. This is giving the institutions a good replica and nomenclature of a city model. The education sector is consistently witnessing substantial growth in terms of population, income and the area of their buildings in terms of gross internal area (GIA). Notably, the population of full-time equivalent students in the UK is estimated as 2,280,830 in 2016/17 from 166 providers which is 3.4% of the total UK population. This makes the sector bigger than many UK cities [4], this growth is also accompanying with high energy demand and high carbon emissions. In England, the yearly cost of energy is £200 million with a consequential release of over 3million tonnes of CO 2 e into the atmosphere [2]. However, the commitment of higher education (HE) sector to reduce the sector emission by 43% by 2020 from a 2005 baseline, has witnessed relative reductions in emission levels over the year. It is without doubt that the reduction in carbon emission, also known greenhouse gases (which are made up of carbon dioxide, methane, nitrogen oxide, aerosols among others) will reduce environmental pollution [5].
Recent findings show that, consequent to high energy consumption and with only 3 years to 2020 target, only 32% of England HEIs are on track to meet the emission target, while about 60% are most likely to default [6]. In addition to this, only 17% emissions reduction is recorded so far against 2005 baseline and should the trend prolongs, the HE sector would only achieve the maximum of 23% reduction of carbon emissions by 2020. This is a reflection of a slow decrease in emission, until now, the best carbon offset was in 2015/16 where about 2million tCO2e was offset representing 7% drop in emission levels [6].
According to Roy et al. (2005) [7], most education institutions increase in their emission levels as a result of a rise in population and energy demand. This study therefore seeks to evaluate the energy efficiency of UK HEIs from the angle of emission levels, population, building area and financial metrics.
There is no unequivocal definition and quantification of energy efficiency, however, in a simple term, it involves cutting down the amount of energy needed to execute an action. In other words, it is the ratio of useful output of a process to the Energy input into a process. Energy efficiency plays a major role not only in reducing the level of energy consumption but enhances the possibility of reducing greenhouse gas (GHG) emissions especially in the short-to midterm. The strength and the future of energy efficiency is entrenched in right policymaking, in the UK, certain policies have been promulgated to support the national high energy efficiency goal; Carbon Emission Reduction Target (CERT), Community Energy Saving Programme (CESP), under the National Energy Efficiency Data-Framework (NEED) [8], among others.
Several approaches are considered for assessing the energy efficiency of any sector or organization. However, one similarity among them is the estimation of the principal factors that influence energy consumption relative to the accompanying economic activities and structural switches in the economy. Technical and non-technical improvements are the metrics.
Some studies measure consumption-based energy balances which involve the quantification of direct and indirect energy use, identification of potential thresholds in energy utilization per economic activity and conducting material and energy flow analysis. Another approach is the analytical predictive method which involves numerical modelling and simulation. This includes the design of fuel economy low-emission, and waste energy recovery systems and scenarios with the aim of translating it into industrial applications [9].
In recent times, several econometric methods have gained acceptance in measuring energy efficiency performance, this includes; regression analysis [10], simple ratio analysis and Data envelopment analysis [11,12,13]. The flexibility and ability to handle multiple input and output without being bias towards unit make data envelopment analysis (DEA) better suitable for performance measurement.

Data Envelopment and Malmquist Index in Energy Efficiency Modeling
Although energy efficiency levels across economic sectors in the world has attracted exceptional academic interest over the decades, very few studies had focused on the higher education sector. The reason for this is not farfetched, levels of emissions from HE sector relative to energy consumption was previously regarded as insignificant [7].
Few scholars in the past have attempted to investigate or review the energy efficiency of English HEIs using econometric tools [14,15,16,17]. Common in their findings is that English HEIs relatively have higher mean technical efficiency scores than their counterparts in other countries, however, a low average level of efficiency is found when only financial metrics are computed. The drawbacks to these studies include; evaluating efficiency based on research output performance, within a cross-sectional data framework and not over time, short or old timeframe covered and the failure to consider the undesirable environmental variables especially the carbon emission data. Only Johnes and Tone (2017) [15], attempted to investigate energy efficiency by incorporating environmental metrics but again the study is deficit as it fails to comprehensively account for sources of inefficiency nor the change in efficiency across the time period, instead it focuses on the consistency of evaluation methods. These gaps are properly covered in this study by using DEA and Malmquist productivity index (MPI) models.
DEA also known as Frontier Analysis is a more flexible technique for performance measurement [18]. DEA is a non-parametric linear programming technique used for estimating the relative efficiencies of a similar set of organizations (widely called decision-making units (DMUs)). Efficiency refers to potential to reduce input units or to maximize the output units without wastage of the inputs. The key strengths of DEA over methods include the ability to handle multiple outputs and multiple input and removal of restrictions functional specifications [19]. to which their input is increased while the latter was constructed on the assumption that organizations might not reproduce their output in the same proportion with the increase in their input unit [19]. Any inefficiency from the latter depicts scale effect. MPI on the other hand, evaluates the relative CO 2 emissions performance from the perspective of production efficiency, with a strong advantage of identifying the sources of efficiency or inefficiency. MPI was utilized to measure the total factor carbon emission performance of world's 18 top CO 2 emitters from 1997 to 2004 and it was concluded that technological progress accounted for the 24% improvement in emission reduction performance [21]. DEA and MPI have been extensively used in eco-efficiency, banking, and manufacturing literature. Therefore, to further understand how efficiency changes across the year, Malmquist productivity index (MPI) has been used by several authors on the principle of DEA [22]. To the best of the authors' knowledge, no emission efficiency study for British HEIs has been undertaken that used DEA and Malmquist productivity index to calculate the energy and carbon emission efficiency relative to research income, gross internal area, and population for all the HEIs in the UK. This study will fill this gap and in addition to this, it will also estimate the change in their efficiencies and from this generate an efficiency ranking for each model. This is a profound approach to investigating universities energy and emission efficiencies.

Data
A dataset for 131 institutions in the UK from England, Northern Ireland, Scotland and Wales for the period between 2008-2014 are used in this study. The HEIs are divided into Russell and Non Russell groups out which 20 and 111 HEIs respectively are selected, some institutions are excluded due to missing information. The data are collected from Higher Education Statistics Agency (HESA), an accredited organization with 24 years of operation designated by Higher Education & Research Act 2017 to provide up-todate UK higher education data [23]. These institutions were chosen in no particular order.

Variable Selection
With the objective to evaluate the energy and carbon emissions efficiency of UK HEIs, the method of Chang et al. (2013) [24] which allow for the integration of undesirable output (carbon emission) in the production function while assuming free disposability. In total, five metrics are extracted from the dataset. These include data on; research income (£), gross internal area (m 2 ), population (fulltime equivalent of teaching students, research students and staff), energy (kwh) and carbon emission equivalent (tCO 2 e).
Energy consumption, staff full-time equivalent (FTE), GIA are selected as input while research income, teaching student FTE and research student FTE are selected as the output. Carbon emission is chosen as the undesirable output. The choice of these input and output variables is supported by the literature. Table 1 indicates the summary of the relationship between input and output variables while Tables 2 and 3 shows the summary of descriptive statistics of the variables for Russell and non-Russell. Significantly, total staff FTE have strong correlation with research income, research student FTE, GIA and carbon emission representing (0.91, 0.92, 0.87 and 0.85 respectively), energy consumption and GIA are strongly correlated (0.85) whereas Teaching student FTE and CO 2 emissions have a relatively weak correlation (0.45) which depicts CO 2 emissions can be reduced without reducing the population of the students which has its best relationship with the staff population. This is in agreement with Fetcher (2009) [25] and Klein-Banai and Theis (2013) [26] argument that floor area has a positive correlation with carbon emissions and that of Disli et al., (2016) [27] that there is an inverted U-shaped relationship between carbon emissions income. However, the findings of Martinez and Maruotti, (2012) [28] reveal that the efficiency of carbon emission is strongly dependent on the energy consumption. Therefore, carbon emission must be integrated into estimating energy efficiency.

Methodology
DEA method is chosen for this study because it can accommodate multiple variables regardless of the measurement units and can provide the efficiency of the individual participating institution (usually called DMUs). It requires no complex transformation of data and does not require specification of function. The efficiency score of DEA is often expressed between 0 -1 or 0-100%.  This study utilizes CRS and VRS DEA models under the input orientation approach. The CRS model (also known as CCR model) is built on the assumption that a small firm should be able to operate efficiently as a large one while (VRS also known as BCC model) recognizes positive or negative economies of scale. Based on these differences, many authors prefer to evaluate efficiency using both models. The linear programming formulation of these models are given belowː CRS Model [29] [19] Where y 0 and x o vector are output and input quantities respectively, l indicates the weights, X and ʏ represents the input and output matrix. The key discrepancy between these two models is the introduction of convexity constraint ( ℮l = 1 ), this produces the pievewise linear and concave identities.
This study also uses DEA Malmquist productivity Index (MPI) to measure change in efficiency under input orientation. MPI decomposes change in efficiency into five componentsː efficiency change, pure technical change, technological change, scale efficiency change and total factor productivity change. MPI estimates utilized in this is calculated using Fare et al., (1994) [30] mathematical formulation as given in equation 3.
Where t represents the base year (2008), t+1 represents the reference technology, x and y represent the input and output quantities, I indicates input orientation, D indicates the distance function. The scores are categorized into three: when it is equal to 1, it means there is no change (no improvement), greater than 1 (>1) means a positive change and values lesser than one (<1) depicts a negative change, regression especially for technological change.

Efficiency Estimates Under CRS, VRS and Scale Assumptions
The results of the top energy efficiency performers for Russell and non-Russell HEIs are presented in Tables 4 and 5 respectively. As shown in the   Similarly, as revealed in Table 6 and Fig. 1 Table 3 and Fig. 2.

Efficiency change Technological change
More so a relatively high scale efficiency performance is found for all the HEIs (Figs. 2 and  3), this suggests that all HEIs are operating in the right scale, most especially the Russell group, their efficiency range between 97.4%to 99%. Notwithstanding, a lower mean annual scale efficiency score is found across all the 111 Non Russell institutions of 90.3%, implying that the mean size of these institutions is less than 10% from the optimal size. Some of the HEIs in this group are most likely affected by their scale of operation.
Consistent with CRS and VRS results, in the year 2011 the SE plummets to the least for all the HEIs.
In general, considering the results obtained from three DEA models, HEIs do not show a distinct efficiency pattern. The average annual efficiency undulates across the 8 year period, this suggests that energy consumption has not been overtaken by the right technology that will perpetually upwardly push the efficiency. This therefore implies that the success of HEIs in increasing their energy efficiency will therefore not bother on operating at the right scale or cutting down activities. Interestingly, the results obtained from the scale efficiency dissociates HEIs from being affected by operational size.
Although, the CRS and VRS models show that Russell group HEIs are more energy efficient than the non-Russell group HEIs. In practice, this may not be holistically due to the difference in their sample size. According to Nguyen et al. (2016) [32], DEA could result in biased efficiency scores when comparing samples of varying sizes. Malmquist index analysis is therefore another important tool used in this study to further probe the efficiency change across the HEIs and years. Additionally, it will offer in-depth evidence about the productivity of these HEIs and alleviate the DEA sensitivity to sample size.

Malmquist Productivity Index Estimates
The mean annual Malmquist indexes for both HEIs groups are reported in Tables 7 and 8. The results shows that the values for the mean efficiency changes (effch), technological progress changes (techch), pure technical efficiency change index (pech), scale efficiency change index (sech), total factor productivity indexes (tfpch) are (1.0141, 0.849, 1.002, 1.012, 0.861-non Russell group) and (1.001, 0.7233, 1.00095, 1.0001, 0.7286-Russell group) respectively. Notably, among the 131 institutions, none experiences productivity improvement and technological progress. Across the five Malmquist index spectrums, Russell group do not hold substantial performance, as none records improvement in TECHCH and TFPCH. However, 80% of these HEIs maintain a constant pure technical efficiency change while only 15% records growth. With respect to non-Russell HEIs, a significant number of HEIs (82 out of 111), record improvement in their scale efficiency change and about 60% HEIs improve in their pure technical efficiency. The technological efficiency change (techch) and total factor productivity (tfpch), indicate a negative trend of efficiency drop by 27.7% and 27.1% respectively Russell HEIs and 15.1% and 14%. However, the pure efficiency change, scale efficiency change(pech) [0.1%-Russell, 1.36% -non-russell], and efficiency change (effch), [0.01%, and and 1.16%] depict improvement. With a mean annual total factor productivity change score of 0.860 and 0.729 for Russell and non-Russell HEIs respectively, it shows that the level of efficiency has declined over the whole period. The source of this regression is primarily due to technological change (0.723 and 0.860 for Russell and non-Russell HEIs respectively) and the source of inefficiency is principally a scale issue. By implications, most of the HEIs who are not efficient in their energy utilization are probably not exploring latest technology for their energy consumption. Conversely, this finding indicates that UK HEIs are yet to make significant achievements in technological innovation that could influence their energy efficiency positively and that HEIs operational efficiency level does not notably depend on its size or its function.
According to Li and Lin (2015) [33], the totalfactor energy productivity analysis framework, delivers a viable orientation database for assessing the potential for energy efficiency improvement. As shown in Fig. 4, there is no significant difference in the productivities of

Efficiency Performance without Emission Metrics
Another approach to evaluating HEIs energy efficiency performance is to shift attention from the reduction of CO 2 emission. In this regard, emission metric is excluded from the performance indicators, this essentially would help provide further evidence on the HEIs energy efficiency status and sources since it is shown that technological innovation is the backstop of HEIs efficiency relative to carbon emission.
As revealed in Fig. 5, neglecting CO 2 emission gives rise to higher mean annual energy efficiency levels for both HEIs groups (representing 98.5% and 86.3%) with Russell group maintaining the efficiency lead. More so, consistent efficiency pattern is also observed across the years. The implication of this is that emission reduction has a significant influence on the overall energy efficiency. Hence, policy makers will default in attaining an adequate reduction of energy efficiency if they fail to take carbon emission levels into account.
Notably, the total factor productivity reflects the overall efficiency of all inputs to a production process and its connection to technological improvements and other non-technical factors. As shown in Figs. 6 and 7, a further regression is recorded in the mean annual total factor productivity (-13.2%russell and -9.81%non-Russell) across the two HEIs groups which is a direct product of decline in the technological innovation (-13.8%russell and -10.2%non-Russell). However, it is evident that with further regression in technological change, both Russell and non Russell HEIs needs to invest more in available best effective technologies.
According to Yang, (2010) [34], there is a significantly relationship between energy or carbon performance and better resource grants. Hence, TPFCH and TECHCH results raise questions for policymakers on the effect of the deployment of the latest efficient technologies on energy and carbon efficiency; and to what extent can increase in research grant promote overall energy efficiency and carbon reduction.  Since DEA does not adequately address issues related to measurement error, one future opportunity is to apply the mixed DEA and stochastic frontier analysis (DEA-SFA) approach. With this method, the impact of statistical noise would be addressed and the estimation of an individual institution's efficiency that SFA cannot account for is also made possible.

CONCLUSION
This study utilizes DEA model to evaluate the energy efficiency of 131 higher education institutions in the UK. The HEIs are divided into Russell and non-Russell groups from which 20 and 111 HEIs respectively are analyzed.
Malmquist index analysis is also conducted to assess changes in the overall integrated efficiency change, productivity improvement and to rank the energy efficiency performance of the HEIs from 2008 to 2015.
The key findings from this study are outlined below: 1. Constant return to scale (CRS) and the variable to scale (VRS) assumptions show that there is no discrete efficiency pattern, instead, it undulates across the 8 years period of investigation. Based on the mean annual, HEIs have relatively high energy efficiency scores of 96.9% and 77.6% (CRS) and 98.5%, 86.3% (VRS) for Russell and non-Russell groups respectively. The results of these estimates suggest that Russell HEIs are operating on variable return to scale rather than constant return to scale, since more of HEIs efficient on the latter and are less affected by scale. Additionally, the results suggest that Russell HEIs are more efficient than the non-Russell HEIs. However, since DEA results are sensitive to sample size, caution is essential in applying the results implicitly in any policy framework. 2. Notably, the results obtained show that 2011 is the worst performing year due to a dip in research income by 2.08% and research student by 1.74% for the nonresearch based group while efficiency decline is principally a product of reduction in the staff population by 4.8%. 2010 is also a bad performing year for the non-Russell group as a result of the extreme cold weather conditions that account for high energy demand. No Russell group HEI is below 70% efficiency regardless of the assumption model while no greater than 30% of the HEIs have their energy efficient gradient below 70% except for 2008 (45 out 111 HEIs) and 2011(65 out of 111 HEIs) are grossly inefficient. The evidence from this study reveals that an increase in the energy efficiency of these institutions is feasible with the present operating scale. This requires that institutions work on their technical progress in order to become energy efficient. 3. There is a general carbon emission efficiency improvement over the years as the relative carbon emission performance of HEIs across the period of observation increased slightly. 4. Based on the Malmquist index analysis for the research and non-research groups, the improvement of efficiency change for both HEI groups fluctuate with values of 1.001 and 1.014 respectively, technological innovation (0.7233 and 0.849, which both depicts regression), pure technical efficiency (1 and 1.002, Russell group remain unchanged , non-Russell improves), scale efficiency change(1.0001 and 1.012, depicts both improves), and total factor productivity change (0.7286 and 0.861, means both deteriorates). 5. Malmquist index analysis confirms the lack of technological innovation, which impedes HEIs energy efficiency and productivity gain. While pure technical efficiency accounts for the annual efficiency obtained in the DEA model, the technological progress in contrast is the source of their energy inefficiency. 6. Furthermore, energy efficiency evaluation without considering undesirable emission data results into higher performance and also reveals further dip in technological change and total factor productivity. Therefore, a reasonable strategy to address this issue would require that HEIs investigate their activities and facilities, and figure out where and how to switch to the latest technologies that would boost their energy and emission efficiency. Better still, HEIs should invest more in technical innovations. Another effective method to address this subject is to review and improve the efficiency of resource allocation, and specific actions include increasing the enrolment of research students and research grants. 7. UK HEIs have high energy consumption and total carbon emission rates, the longterm approach for reducing energy consumption would principally require diversification from fossil-based energy sources.

ETHICAL APPROVAL
All authors hereby declare that all analysis have been examined and approved by the appropriate ethics committee and have therefore been performed in accordance with the ethical standards laid down in the 1964 declaration of Helsinki.