Environmental Efficiency and Urban Ecology

Evaluating organizational efficiency involves measuring outcomes, such as revenues, value of goods and services produced, productivity, etc. However, a sustainable environment requires not only economic outcomes but also good quality of life in an area. Therefore, this research proposes a balanced assessment to evaluate environmental efficiency from the perspectives of urban ecology. We first adopted the bad output data envelopment analysis to evaluate the efficiency of a metropolitan area followed by a biotope area factor to assess the ecological effectiveness of an area. Next, a censored regression model evaluates the relationship between environmental efficiency and biotope area factor. The empirical studies were conducted in Taichung, Taiwan. Empirical results suggest that typical efficiency evaluation of a metropolitan area is significantly overrated because it excludes external diseconomies such as CO2 emissions which have a profound impact on the environment. The regression results indicate that environmental efficiency and Taiwan biotope area factor are complementary and can be improved simultaneously while CO2 emission reduction is at present. We also show that current utilization of area for non-agriculture and human activities poses a negative impact on Taiwan biotope area factor.


Background
The pursuit of economic development, over-consumption, and global climate change has caused disruptive damages to the earth we live on and many others inhabit the same space with us. Especially environmental issues like dengue fever, avian influenza, heat island effect, endocrine disrupting chemicals, etc. have become normality in urban areas (NOAA, 2018). Many environmentally friendly Theoretical Economics Letters policies are being adopted and executed, for examples, green roof (Mills & Rott, 2020;Thuring & Grant, 2016), green building (Wang et al., 2014), ecologic passageway (Peng et al., 2017), etc. However, the effectiveness of these policies in improving urban ecology remains to be investigated. Therefore, this study aims to investigate environmental efficiency and urban ecology from regional (metropolitan) level. We first evaluated efficiency by the bad output data envelopment analysis (please refer to Tone, 2001Tone, , 2002Tone, , 2003Zhou et al., 2013) in which we incorporated CO 2 emissions in the empirical studies. Second, in evaluating the ecological effectiveness of a metropolitan area in Taiwan, we consulted el-Baghdadi and Desha (2017) and the Berlin Biotope Area Factor (BAF) and established Taiwan biotope area factor (TBAF) as a proxy variable. Finally, we developed a statistical regression model to test the relevance between environmental efficiency and Taiwan biotope area factor. The main contribution of this research lies in the inclusive of external diseconomies and urban ecology in the evaluation of efficiency. In the next section, we will review literature related to efficiency evaluation and urban ecology.

Literature Review
Typically, in evaluating the efficiency or productivity of a decision-making unit (DMU), data envelopment analysis (DEA) or stochastic frontier analysis are adopted by many researchers and therefore, many applications and modifica- sults were able to distinguish benchmark airports and identified slacks in outputs for inefficient airports to improve. Chang et al. (2013) discussed efficiency for the transportation industry in China with concerns of energy consumption and environmental pollution. The input was fuel uses from different transportation systems and the output included CO 2 emissions and energy consumptions.
The empirical results suggested that the transportation industry in China lacks eco-efficient transportation systems and the industry was inefficient environmentally. Bai et al. (2018) utilized the super-efficiency data envelopment analysis model to assess urban eco-efficiency. They utilized principal component analysis to quantify level of urbanization of 281 cities during 2006-2013 in China. Results of a spatial econometric analysis indicated that there existed an N-shaped relationship between urbanization and urban eco-efficiency. Our research logic follows that of Bai et al. (2018) but we focus on urban ecology and biotope area factor instead of urbanization. Liu et al. (2018) Dramstad et al. (1996) andForman (2014). Starting from the 1990s Berlin started to use biotope area factor (BAF), an index to measure the ecological score of a surface based on the land use plan, Senate Department for Urban Development, 1990. The higher BAF score, the better protection of biotopes, species, and the land. The application of BAF in academia and practices started to spread to the rest of Germany (Sukopp & Weiler, 1988;Yilmaz et al., 2010) and around the world.
Main contributions of our research to the literature includes: 1) we estimated and compared the technical and environmental efficiencies of a metropolitan area by data envelopment analysis with bad output, carbon dioxide emissions; 2) we established a biotope area factor specifically to evaluate the ecological effectiveness of metropolitan areas in Taiwan from the perspective of urban ecology; and; 3) utilizing scatter charts and censored regression model to investigate the relationship between environmental efficiency which incorporates economic, environmental and social factors and Taiwan biotope area factor. The remainder of this paper is organized as follows: Section 3 presents the construction of mathematical models to evaluate efficiency and Taiwan biotope area factor; Section 4 provides the empirical results and discussions; finally, conclusions and constraints of the study are presented in Section 5.  Charnes et al. (1978) developed one of the well-known models for evaluating technical efficiency known as the Charnes, Cooper and Rhodes (1978)  [ ]

Measuring Technical Efficiency
represent the input and output matrices of all DMUs respectively. Let θ be the technical efficiency of a DMU and λ is the weights vector.
Thus, the linear programming model to evaluate the technical efficiency of a DMU can be given as: where θ lies between (0,1). If θ = 1, the technical efficiency of the DMU under evaluation is on the efficiency frontier. As θ approaches 0, we consider the DMU operating inefficiently.

Measuring Environmental Efficiency
To evaluate the environmental efficiency that incorporates undesirable outcomes requires adjustments to the previous CCR model. Tone (2001Tone ( , 2002Tone ( , 2003 introduced slacks-based measure (SBM) DEA model. Related literature includes Chuang and Wu (2006), Taskin and Zaim (2001), Seiford and Zhu (2002), Portela et al. (2004), and Wang et al. (2013). The advantage of SBM models is that it enables the consideration of both desirable and undesirable outputs and com- . Therefore, the production possibility set is given by Let s − , s g , and s b represents the slack vector of input excess, good output shortfall, and bad output excess respectively. Then, the efficiency of a certain DMU 0 in the SBM model incorporating bad outputs can be written as, , , , 0. , it means that * 1 ρ = and the DMU 0 is fully efficient. If * 1 ρ < , the DMU 0 is not utilizing its resources efficiently. For DMU 0 to become more efficient, it must reduce its inputs, bad output or increase good outputs.
x y y be the project point onto the efficiency frontier and we then calculate the room for improvement in efficiency for DMU 0 using the following equation:

Measuring Ecological Effectiveness in Taiwan: Taiwan Biotope Area Factor
To construct Taiwan biotope area factor, we consulted with Berlin Biotope Area Factor (BAF) which is based on concept of landscape ecology. BAF is a system developed by the Berlin administration to evaluate the impact of urban developments with an aim of preserving and creating living places among living things (Senate Department for Urban Development, 1990). BAF reflects the ratio of the ecologically effective surface area to the total land area. Different types of surfaces are weighted according to their ecologically effective value (weighting factor). The more permeable to water and air or the more plant growth of a surface, the higher the weighting factor is. Let i A denote the land area and i w be the weighting factor for surface type i. Thus, the ecologically effective area (EEA) of surface type i is calculated in Equation (12) and the biotope area factor (BAF) for an area of n different types of surfaces is given by Equation (13).
Based upon the above Berlin BAF calculation, we obtained a complete spatial database of photogrammetry, a land use investigation report of Taiwan and utilized a Geography Information System to determine types of land uses, vegetation areas, water body, geographic information, etc. in Taichung city in 2017.
Detailed sources of data are specified in Section 4. Furthermore, a Delphi questionnaire of 20 experts in the field of urban ecology was conducted and a con- In Equation (14),  Table 1 and i W represents the weighting assigned to surface type i. N W is the weighting assigned to the interaction variable N A , N = (D, I, J) and adj is the adjustment made to ensure that the TBAF score lies between 0 and 1.
The higher the TBAF value of an area, the better quality of the plant and animal habitats as well as the better the residential environment in that area.

Data
Our proposed model to evaluate environmental efficiency and TBAF was applied to Taichung city, located in Central Taiwan, comprising 29 administrative districts. It is the second largest metropolitan in Taiwan with an area of 2215 km 2 . Figure 1 illustrates current space allocation of Taichung city. It is observed that  To reflect the environmental efficiency, we obtained data from different aspects of the city: environmental, economic, and social factors. Economic factors include 1) labor, 2) area for agriculture and forest uses, 3) area for other use which includes commercial, residential, industrial areas, and public facilities, and 4) value-added (production value). CO 2 emissions and Taiwan biotope area factor values are the two environmental factors in the study. Electricity and water consumptions are used to compute the level of carbon dioxide emissions. As this research was conducted, the average CO 2 emissions were 0.53 kgCO 2 e per kWh of electricity consumption and 0.152 kgCO 2 e per M 3 of water consumption in 2016 based on data provided by the Bureau of Energy, Ministry of Economic Affairs, Taiwan. Therefore, Equations (15) & (16) shows the computation of CO 2 emissions from the electricity and water consumption of Taichung respectively and Equation (17)  CO CO E CO W = + However, 8 out of 29 districts in Taichung did not have independent data regarding water consumption. Thus, the total water consumption was distributed to districts according to their percentages of population. Social factors include: 1) living assistance for disadvantaged children and youth, 2) living assistance for

Comparison of Technical and Environmental Efficiencies
This section presents our results from the SBM data envelopment analysis of Equation (6) by DEA-Solver 8.0. Specifically, we compare the efficiency of SBM without CO 2 emissions (technical efficiency) and with CO 2 emissions (environmental efficiency). Input variables are labor (L) and area for other use (AO) which includes areas for industrial, commercial, and residential areas, and public facilities. Output variables include value-added (VA), CO 2 emissions (CO 2 ) calculated from electricity (QE) and water (QW) consumption, total number of people received social assistance per dollar (SW), and city government budget (BUG). SW is a collective index to represent social welfare output per dollar. SW = (S1 + S2 + S3 + S4)/BUG. Before executed the SBM data envelopment analysis, a statistical test was conducted to examine whether our variables satisfy monotonically increasing property which is a necessary condition to perform DEA models. Table 3 shows the correlation coefficients between input and output variables. It is observed that variables were all positively related except for the relation between AO and SW which was not significant statistically. All variables in our modeling displayed a monotonically increasing property which justified the use of DEA models in the empirical study. Table 4 compares SBM results of technical efficiency (without CO 2 emissions) and that of environmental efficiency (with CO 2 emissions) in Taichung. It is observed that the median of technical efficiency of the sample is 0.6221 which is higher than the median of environmental efficiency 0.4664. It reveals that without considering the external diseconomies (CO 2 emissions) derived from economic activities, productivity is likely to be overestimated. Meanwhile, the average environmental efficiency of the sample is 0.5813 indicating a 42% room of improvement is required to reach full efficiency. Appendix Table A1 shows slacks in each of the variables and room of improvement for all 29 districts in the sample, among them 21 were environmentally inefficient districts. Furthermore, a benchmark district means that a district has an efficiency value of one and the district is fully efficient in utilizing input resources. In the sample, Cental, Dengshi, Houli, Tanzi, Xinshe, Shigang, Daan, and Longjing districts are environmentally efficient benchmark districts. These districts are mostly covered by residential  and agriculture areas that are of low inputs, low value-added, and relatively low CO 2 emissions. The poorest performance in environmental efficiency appears in Nantun district. In terms of input variables, it is noted that 11 out of 21 inefficient districts are efficient in labor productivity. It is suggested that AO needs to be reduced to a greater extent than labor and that the way Taichung utilizes area for industrial, commercial, and residential uses is critical in enhancing the environmental efficiency. Social welfare is another area that requires a considerable improvement. On the other hand, the output level of value-added is satisfying.
Only the east district requires a 25.23% increase in efficiency. Furthermore, all districts require a considerable reduction in the level of CO 2 emissions. Dajia district needs the least of 3.22% and Qingshui district needs the most reduction of 50.18% in CO 2 emissions. To conclude results of the SBM analysis, inefficient utilization of non-agriculture or non-forest areas, excessive CO 2 emissions, and insufficient social welfare are accounted for the low environmental efficiency in Taichung. The average TBAF value is 0.414, the median value is 0.365 and most districts has a TBAF value ranging between 0.2 and 0.6, indicating that Taichung's ecological value is considerably low. In other words, the existing landscape of the city is unfavorable to the animal and plant habitat and the residential environment and, of course, the ecosystem does not support sustainability. Heping district, however, outperformed the rest of the districts with TBAF = 0.9. It is in the west part of Taichung where it is mostly forest and agriculture areas. The lowest TBAF value is in Nantun district which also has the lowest value in environmental efficiency as shown in Appendix Table A1. The environmental quality of the district is compromised by the flourishing economic activity since value added in Nantun district is fully efficient.

Results of Taiwan Biotope Area Factor and Its Relationship with Environmental Efficiency
Scatter plots in Figures 3-5 show the relations between pairs of TBAF, EE, CO 2 , and agriculture and forest area (AAF). We observe from Figure 3 that EE and TBAF are positively related and those districts with low values in both EE and TBAF are highly urbanized districts. Figure 4 displays the negative relation between CO 2 and EE as well as between CO 2 and TBAF suggesting that CO 2  emissions threat not only the ecosystem but efficiency. Figure 5 shows that agriculture and forest area is positively related to TBAF; however, it is negatively related to EE. It can be inferred that agriculture and forest area provides green areas and promotes the ecological value of an area, but the current economic or social output of the area is insufficient from the perspective of sustainability that simultaneously considers economic, social, and environmental factors.   In addition, we investigated the correlation coefficients between pairs of TBAF, EE, and logarithms of variables, AAF, AO, L, VA, SW, and CO 2 . Results in Table 5 reconfirm the positive relationship between EE and TBAF. However, except for L and CO 2 , both has a negative impact on TBAF and EE, the rest of variables in the study have inconsistent effects on EE and TBAF. For examples, agriculture and forest area has a positive impact on TBAF but not on EE, or area for other use has a negative impact on EE but its impact on TBAF is not clear. Therefore, to further identify the relationships among variables, we constructed a regression model shown in Equations (18) Equation (18) examines the impact of EE on TBAF. Agriculture and forest area was not included in the estimation of EE, therefore, we added LAF in Equation (18) to test its impact on TBAF. , 1~3 i i ε = is error terms. Equation (19) also investigates the impact of EE on TBAF, but EE is replaced with input and output variables in the estimation of EE, i.e. CO 2 , AO, L, VA, and SW. Note that in Table 5 we observed there existed an issue of collinearity among CO 2 , L, and VA and that the relation between SW and EE was not significant. Therefore, we kept CO 2 that concerns the ecosystem the most and removed L, VA, and SW from Equation (19) and became Equation (20). Results from Equations (18) & (20) will be our focus of discussion. The Censored Tobit Regression Model and Newton-Raphson optimization are utilized to estimate the coefficient of the regression model. Regression results are shown in Table 6. Results in Equation (18) indicated that every 1% improvement in environment efficiency enhances TBAF values by 0.238%. Agriculture and forest areas promote TBAF values. The same observation can be seen from results of Equation (20). Every 1% increase in the input of agriculture and forest areas increases TBAF values by 0.070%.   Note: 1. Numbers in parentheses are Z values. ***, ** and * denotes significance at the 1%, 5% and 10% levels respectively. 2. Numbers in brackets are variance inflation faction (VIF). VIF>10, i.e. R 2 > 0.9, suggesting there exists collinearity between variances. Data is prepared by this study.
When we replaced EE with CO 2 and AO, it is observed that both have a negative impact on TBAF. In fact, AO influences TBAF to a greater extent than CO 2 emissions. It is suggested that current urban landscape of Taichung does not consider the ecosystem attentively enough that the ecological effectiveness is compromised by human activities. We show values of EE, TBAF, and percentages of agriculture and forest area (PAF) of individual districts in the geographic maps of Taichung in Figures 6-9. To summarize results from Table 5 & Table 6 and Fig-ures 6-9, we observed that EE and TBAF can be improved simultaneously but this conclusion is grounded only when CO 2 emissions and AO input are reduced under the same level of economic activities, i.e. value-added. Agriculture and forest areas improve TBAF, but do not have a significant impact on environmental efficiency. Thus, this city requires attention on resource depletion from the water and electricity consumptions and the wellbeing of the ecosystem, such as a better vegetation structure and water permeability so that the efficiency and ecological value of the area can be both improved.

Empirical Results and Discussions
This research aims at investigating efficiency from the perspective of urban ecology. To this end, we establish an ecological   analysis which considers economic, social, and environmental factors is constructed to evaluate environmental efficiency. A censored regression model is then conducted to examine the relationship between environmental efficiency and Taiwan Biotope Area Factor. Key empirical results are summarized as below: 1) Typical efficiency evaluation without considering the external diseconomies, CO 2 emissions in our research, overestimates resource utilization in the context of urban ecology. The average environmental efficiency in the city where we conducted the empirical studies was 0.58 suggesting a 42% of room of improvement is required to achieve full efficiency in the utilization of resources; 2) Although increasing agricultural and forest area enhances the ecological effectiveness of a region, it does not improve environmental efficiency because the area does not improve labor employment nor social welfare. That is, the productivity of agricultural and forest area is inefficient. Therefore, a trade-off exists between human developments and the quality of the ecosystem upon which human developments are simultaneously dependent; 3) Environmental efficiency and ecological value of a region can be improved simultaneously, however, it can be achieved only under the circumstances of reduced CO 2 emissions and a more environment centric consideration in urban landscape planning for commercial, industrial, and residential areas. Main contributions of this research lie in: 1) providing a comprehensive and structured framework to evaluate environmental efficiency which considers external diseconomies and establishing an ecological effectiveness evaluation system for the metropolitan areas in Taiwan; and 2) providing policymakers with empirical results to examine each individual district in Taichung enabling them to adjust resource allocation and plan for urban landscape accordingly.
There are several research constraints in this research. First, we were unable to obtain data of capital stock which could be used to examine the impact of machinery or technology on environmental efficiency. Second, there were eight districts out of 29 districts in Taichung lacked individual data for water consumption. Therefore, in the empirical studies, the water consumption for these eight districts was calculated by distributing the total water consumption of the eight districts according to the percentage of population in each district. Third, being confined by the size of our sample, we adopted only four social welfare variables out of many social factors and combined them into one collective index in the empirical studies. Our proposed methodology is established with the aim of continuously monitoring in compliance with national policies regarding sustainable development. For future research, we propose to expand research region and employ the meta-frontier data envelopment analysis which allows us to group cities or districts according to different attributes, for instance, levels of urbanization of an area and then compare environmental efficiency and biotope area factor across groups.