Chinese airline efficiency under CO2 emissions and flight delays: A stochastic network DEA model

    Chinese Airline Efficiency under CO2 Emissions and Flight Delays: A Stochastic Network DEA Model Zhongfei Chen, Peter Wanke, Jorge Junio Moreira Antunes, Ning Zhang PII: DOI: Reference:

S0140-9883(17)30318-3 doi:10.1016/j.eneco.2017.09.015 ENEECO 3763

To appear in:

Energy Economics

Received date: Revised date: Accepted date:

18 April 2017 14 August 2017 11 September 2017

Please cite this article as: Chen, Zhongfei, Wanke, Peter, Antunes, Jorge Junio Moreira, Zhang, Ning, Chinese Airline Efficiency under CO2 Emissions and Flight Delays: A Stochastic Network DEA Model, Energy Economics (2017), doi:10.1016/j.eneco.2017.09.015

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ACCEPTED MANUSCRIPT Chinese Airline Efficiency under CO2 Emissions and Flight Delays: A Stochastic Network DEA Model Zhongfei Chen1, Peter Wanke2, Jorge Junio Moreira Antunes2, Ning Zhang3

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1. Corresponding author. School of Economics, Jinan University, No.601 Huangpu West Road, Guangzhou, Guangdong 510632, China. Phone: + 86 15913197920; E-mail: [email protected]

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2. COPPEAD Graduate Business School, Federal University of Rio de Janeiro, Rua Paschoal Lemme, 355, 21949-900 Rio de Janeiro, Brazil.

3. School of Economics, Jinan University, No.601 Huangpu West Road, Guangzhou, Guangdong

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510632, China.

Abstract: This article is focused on the efficiency assessment of 13 major Chinese airlines from 2006-2014, applying a stochastic network DEA (SNDEA) to account for

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randomness in undesirable outputs such as flight delays and CO2 emissions. Two stages

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are considered: flight and network efficiency. Efficiency estimates are computed using multivariate copulas to control for time (trend) and individual (DMU) effects. A robust

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regression approach is subsequently developed to address the impact of contextual variables on efficiency levels. Results suggest that more progress has been made over the course of the years in terms of controlling flight delays that in terms of reducing

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CO2 emissions. These results call for specific policies that can target the latter issue more properly: authorities should pay a closer look on airlines listed in the stock market and that operate international flights to apprehend best practices and design regulatory marks to the sector. This paper also lends a distinctive contribution to the literature by modelling the first time the trade-off between flight delays and CO2 emissions in airline efficiency problems.

Keywords: Chinese airlines, stochastic network DEA, undesirable outputs, CO2 emissions, flight delays

1.

Introduction 1

ACCEPTED MANUSCRIPT Accelerated economic growth over the past decades due to a globalized flow of people and goods has substantially increased airlines´ energy costs and CO2 emissions. According to statistical data of the International Air Transport Association (IATA,

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2015), in 2012, the total energy cost for airlines was more than 160 billion dollars,

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measured on a worldwide base. Besides, the CO2 emission volume was more than 0.676 billion tons at that time. In fact, the aviation industry is one of the few sectors

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where energy consumption has increased at a rate of more than 6% over the past 10 years. This research focuses on the technical efficiency of Chinese airlines by using a novel SNDEA model for network and flight efficiency, built upon multivariate copulas

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and capable of handling undesirable outputs such as CO2 emissions and flight delays. It is important to mention now to readers the distinctive nature of the word “network” that appears in this research. It appears both as the descriptor of the modelling approach

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adopted – Network DEA, for a productive process that encompass several sequential stages – and as the name of one of the productive stages modelled within the ambit of

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the airlines´ operation – network efficiency, for an airline that efficiently converts

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physical and human resources into landings and take-offs with minimal delays. Previous research on airlines have adopted to use several methods such as (i)

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factor productivity approach (Bauer, 1990; Oum and Yu, 1995. Barbot et al., 2008); (ii) Stochastic Frontier Analysis or SFA models (Good et al, 1993, Baltagi et al., 1995; Tsionas et al., 2017); (iii) Turnquist total factor productivity index (Coelli et al., 2003;

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Barbot et al., 2008); (iv) Data Envelopment Analysis or DEA models (Merkert and Hensher, 2011; Barros et al., 2013; Barros and Peypoch, 2009; Barros and Couto, 2013; Cao et al., 2015; Li et al., 2015; Wanke and Barros, 2016; Cui and Li, 2017; Zhang et al., 2017); and (v) multi-criteria decision-making models such as TOPSIS (Barros and Wanke, 2015; Wanke et al., 2015). On the other hand, it is worth noting that, within the airline efficiency ambit, DEA-based studies are the most numerous when compared to the SFA-based methods and other minor approaches used (Wanke et al., 2015; Barros and Wanke, 2015; Wanke and Barros, 2016; Li and Cui, 2017; Cui and Li, 2017 a, b). This not only replicates a pattern that is found in papers focused on efficiency analysis in other industries such as ports and banking (e.g. Wanke et al., 2016 a,b), but may be also derived by the flexibility provided by DEA models in modelling productive processes composed of two or more stages.

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ACCEPTED MANUSCRIPT In fact, several different issues have been addressed by DEA-based airline research studies in different countries or regions. Besides efficiency rankings and slack comparisons, it is possible to point out, for instance, that the impacts of network size,

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ownership, and regulatory measures on the performance of the airline industry have

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been addressed by regressing efficiency scores onto contextual or environmental variables (Barros et al., 2013; Barros and Wanke, 2015; Cao et al., 2015; Li and Cui,

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2017; Cui and Li, 2017a, b; Zhang et al., 2017). Recent papers still maintain this focus (Wanke and Barros, 2016). Readers should refer to these authors for a comprehensive literature review on this subject, which is synthesized in the Appendix with respect to

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the variables and methods used.

It is important to note, however, that only very recently, it is verified an

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increased focus on the energy/fuel efficiency of airlines, although the treatment of CO2 emissions as an undesirable output is still scarce (Cui and Li, 2016; Cui et al., 2016; Cui and Li, 2017a, b; Ko et al., 2017). For example, Babikian et al. (2002) analyzed the fuel

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efficiency of different aircraft types and the results showed that fuel efficiency

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differences could be explained largely by differences in aircraft operations. Morrell (2009) analyzed the potential for greater fuel efficiency by using larger aircraft and

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different operational patterns. Miyoshi and Merkert (2010) evaluated the carbon and fuel efficiency of 14 European airlines during the period from 1986 to 2007 to understand the relationship between fuel efficiency and fuel price, distance flown, and

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load factors. Zou et al. (2014) employed ratio-based, deterministic, and stochastic frontier approaches to investigate fuel efficiency of 15 large jet operators in the U.S. The results showed that potential cost savings of mainline airlines could reach approximately 1 billion dollars in 2010. Cui and Li (2015) applied a VFB-DEA to measure the energy efficiencies of 11 airlines from 2008 to 2012, and further they employed a dynamic Epsilon-Based Measure model to evaluate the dynamic efficiencies of 19 major international airlines from 2009 to 2014 (Cui and Li, 2017a). They found out the global financial crisis that broke out in 2008 has significant negative effects on the airlines' energy efficiency. Following the principle of CNG2020 strategy, Cui and Li (2017b) calculated the emission limit for each airline. Two models, Network Range Adjusted Measure with natural disposability and Network Range Adjusted Measure with managerial disposability are proposed to discuss the efficiency change.

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ACCEPTED MANUSCRIPT Yet, as regards the emerging research topics in airline efficiency, it is also important to note that the cross-impact of the quality of the services provided on airline efficiency is still understudied (Fan et al., 2014). To the best of our knowledge, as

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regards airline efficiency, only Wanke et al. (2015) and Tsionas et al. (2017) addressed

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the issue between quality of the services provided and technical efficiency within the ambit of the airline industry in Asia. The authors found a positive, albeit weak,

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relationship between higher levels of service quality and efficiency. This result may suggest the existence of a trade-in between operational/financial efficiency and service quality, different from the classical trade-off between efficiency and service where

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higher levels of service are obtained to the detriment of lower levels of efficiency. An additional distinctive aspect of almost all these previously mentioned papers

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listed was their locus. They mostly focused on airlines from the US (Barros et al., 2013; Greer, 2008; Sjögren and Söderberg, 2011; Evans and Schäfer, 2013; Winchester et al., 2015), Canada (Bauer, 1990; Assaf, 2009), Europe (Distexhe and Perelman, 1994;

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Greer, 2008; Barros and Peypoch, 2009; Pablo-Romero et al., 2017), Asia (Baltagi et

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al., 1995; Wanke et al., 2015), Africa (Barros and Wanke, 2015), and Latin America (Wanke and Barros, 2016). Given the relative importance of China to the world

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economy, it is possible to affirm that Chinese airlines consist of a relatively understudied topic in the academic field. As a matter of fact, only a few studies were devoted to this particular industry (Chow, 2010 and Wu et al., 2013; Cao et al., 2015;

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Wanke et al., 2015; Cui et al., 2016; Cui and Li, 2017a, b; Zhang et al., 2017), without systematic analysis the energy efficiency as well as the service quality (Chai et al., 2014; Fan et al., 2014; Tsionas et al., 2017). Therefore, this paper builds upon the existing body of knowledge by presenting a novel SNDEA model for technical efficiency and undesirable outputs - like CO2 emissions and flight delays - within the ambit of the Chinese airline industry. Not only is China one of the fastest growing areas in the world, which justifies the relevance of this study, but this paper also fills a literature gap by presenting and developing a model where overall airline efficiency is decomposed into network and flight efficiency in light of multivariate random copulas to control for time (trend) and individual (DMU) effects.

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ACCEPTED MANUSCRIPT Differently from previous researches, this paper presents several methodological innovations. First of all, it is the first time copulas are used within the ambit of NDEA models to bring up the stochastic aspects of inputs, outputs and intermediate variables

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uncertainty over the course of time and at the DMU level. Second, this is the first time

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that not only undesirable (CO2 emissions) and exogenous (delays) outputs are treated simultaneously in an airline efficiency study, but also that a trade-off is stablished

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between in them in terms of a non-cooperative game approach within the ambit of the NDEA modelling. Third, to the best of our knowledge, this is the first time a robust regression approach involving three well-known techniques – Tobit, Beta, and Simplex

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– is developed and applied to solve such problem.

This paper is structured as follows: after this introduction, the contextual setting

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is presented including a description of the Chinese airlines. Then, the methodology section, where the SNDEA model for undesirable outputs is further discussed, is presented. Section 4 presents the discussion of the results. Conclusions are presented in

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2. Contextual Setting

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Section 5.

It has not witnessed the rapid development of Chinese airline industry until 1978, when the government embarked on the "reform and opening up" policy and

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switched to a market-oriented economy from a central-planned one. During the next three decades, China has experienced the growth miracle and blossoming of economy, rapidly increased trade with other countries around the world, as well as the fast expansion of civil aviation industry. After entering the World Trade Organization (WTO), the economic globalization and regionalization of production has driven the growth of Chinese air transport business to new wave of high-level development (See Fig. 1). Meanwhile, as the largest population and their increased income, the demand on air transport also push its mushroom development in China. Despite the Chinese airlines’ revenue and profits are mostly derived from domestic markets, the one with large scale continues to participate into the international market and flights (Wang et al., 2015). Up to date, China has been the second largest aviation market in the world in terms of the volumes of passengers and air cargo moved in its domestic market since

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ACCEPTED MANUSCRIPT 2005 (Chen et al., 2017). In the expected future, the air transportation as well as the airline companies still will be in fast growing mode in China. 500

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450

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400 350

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300 250 200 150 100

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1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

0

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passenger (mil)

6 5 4 3 2 1 0

cargo (mil tons)

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Fig. 1: the development of Chinese civil aviation (RHS: passenger, LHS: cargo)

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Before the year of 1978, the air transport was fully and tightly controlled by the central government under the CAAC (Civil Aviation Administration of China),

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collaborating with the Air Force of China. The CAAC was once a branch of the Ministry of Transport in 1958, and finally was affiliated to the State Council in 1962. After the year of 1978, the government successively established six state-owned airlines companies1, which were separated from the CAAC. To decrease the monopoly

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power of exisiting airline companies, some new airline companies funded by the local governments or government-owned enterprises also entered into the market during this period (Jiang and Zhang, 2016). The foreign investment has been allowed to flow into the civil aviation sector since 1997. Thereafter, the CAAC further deregulate the Chinese civil aviation sector and open it to private investors, and the number of private airlines has grown rapidly (Wang et al., 2016), including the low-cost carrier. To enhance the efficiency and competitiveness as well as avoid the vicious price war, the state-led and market-driven consolidation has also taken place during this period, especially after the Asian financial crisis as well as the global financial crisis that broke out since 2007. More details can be found in the work of Wang et al. (2016). Through the M & A (merging and acquisition), the "Big three", i.e. Air China, China Southern 1

It includes Air China, China Eastern Airlines, China Southern Airlines, China Southwest Airlines, China Northwest Airlines, and China Northern Airlines.

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ACCEPTED MANUSCRIPT and China Eastern, have seize most of the market share in the domestic civil aviation sector (Lei and O’Connell, 2011). Like most of state-owned companies in China, the "big three" or the local

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government owned airline companies successively implemented the joint-stock reform

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and has been listed on the stock market since 1990s. This can enhance the efficiency of

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their operation through introducing market supervision and reducing government intervention. During the late 2000s, some private airline companies also seek to be

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listed on the stock market, so that to attract more funds and increase their scale.

3. Methodology

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This section describes all the methodological steps adopted in this research. It is structured into five subsections that are interconnected to each other. Section 3.1 depicts the inputs, (un)desirable outputs, intermediate variables, and contextual variables used

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in this research, addressing the major underlying hypotheses on how contextual

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variables would impact efficiency levels in airline operations. Section 3.2 focusses on the major steps adopted for determining the best distributional fit for each airline-

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variable pair. These results serve as the marginal distributions for Section 3.3, where they are plugged into a single multivariate distribution by means of correlated copulas. Once the data generation structured is defined for the inputs, (un)desirable outputs, and

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intermediate variables, it is possible to design the SNDEA model for undesirable and exogenous outputs, as in Section 3.4. The concept of bi-level programming within the ambit of non-cooperative game approach is presented as a solving approach for the proposed SNDEA model. At last, in Section 3.5 a framework for robust regression – involving Tobit, Beta and Simples models - is given so that efficiency scores are properly regressed against the contextual variable set. 3.1.

The Data

The data on 13 selected Chinese airlines were obtained from the Wind database (www.wind.com.cn) and their annual financial reports on the website of Shanghai Stock Exchange (www.sse.com.cn) and Shenzhen Stock Exchange (www.szse.cn). The majority of airline companies as well as the big ones that located at the Mainland China are all included in the sample. Other small airlines are dropped as the data is not 7

ACCEPTED MANUSCRIPT available. Because the data accessibility, the sample period is from 2006 to 2014. The descriptive statistics for their productive resources (i.e., inputs, desirable and undesirable outputs, and intermediate variables) as well as their contextual variables are

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presented in Table 1. Inputs, (un)desirable outputs were not only chosen in accordance

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to data availability, but also observing the most common ones found in previous studies on airline efficiency. Readers should refer to Wanke et al. (2015 and 2016) and Wanke

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and Barros (2016) for a comprehensive listing of airline efficiency studies over the past 25 years as well as the Appendix part in this paper. Broadly speaking, it is possible to affirm that these variables are the most common used ones to describe airline operations

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at the macro-level, although there are some scant previous studies that try to capture the impact of fleet mix – aircraft type and size – on airline efficiency levels (cf. Wanke et

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al., 2015).

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Table 1: Descriptive statistics for the Chinese airlines productive resources and

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Mean

SD

CV

Inputs

Fuel (tons) Number of planes Number of employees

793.00 2.00

5729424.00 500.00

967390.38 96.37

1442100.27 136.18

1.49 1.41

131.00

97548.00

16875.44

26047.88

1.54

Intermediates

Number of landings and take-offs

304.00

611018.00

122612.24

158278.49

1.29

Delays (% of total)

14.91

64.72

28.38

9.79

0.35

2497.95 18047685.60 3047279.68

4542615.85

1.49

436.30

289183.46

1.34

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Min

Desirable Undesirable Outputs s Outputs

Variables

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contextual variables

CO2 (tons)

Cargo (tons)

1146728.90

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215710.92

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0.00

1.33

28

13

7.71

0.59

0

100

43.27

40.38

0.93

Listed 53.85% Private 38.46% M&A 46.15% Both 69.23%

Listed in stock market Stateowned/private M&A

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Both international and domestic flights

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Not listed 46.15% Public 61.54% Not M&A 53.85% Only domestic 30.77%

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Age Percentage of Boeing (%)

70611294.00 14287796.74 18966695.25

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Contextual variables

Number of passengers

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3.1.1. Underlying hypothesis regarding contextual variables The impact of contextual variables related to the airline´s age, fleet mix (percentage of Boeing´s aircrafts), stock market governance (whether or not listed in

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stock-markets), ownership type (whether public or private), network span (whether the

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airline flies both domestic and international routes or only domestic routes), and whether or not it has undergone a previous merger and acquisition process (M&A) in

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the past. Previous studies such as those conducted by Wanke et al. (2015), Barros and Wanke (2015), and Wanke and Barros (2016) suggest that fleet mix may affect airline efficiency levels by means of economies of scale (better match between aircraft number

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of seats and demands), while network span may affect them by means of economies of scope imposed by hub operations. Although these authors also point out that public ownership may favor higher airline efficiency levels in development countries due to heavily subsidized operations, the general rule is to expect higher efficiency levels in private operations. As for the M&A activities on airline efficiency, Merkert and Morrell (2012) find the M&A/consolidation is seen as a ‘‘game-changer’’ and mandatory to survive in aviation markets. However, there is an optimum size of airline companies to operate efficiency. Lenartowicz et al. (2013) further analyze the key success factor for M&A activities in the civil aviation industry of EU. It means more robust corporate governance when listed on the stock market for an airline company. Wang et al. (2011) investigate the mechanism how the status being a listed airline companies affect the efficiency.

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ACCEPTED MANUSCRIPT 3.2.

Distributional Fit

The subsequent step to the collection of the inputs, intermediate variables, and

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(un)desirable outputs was their adjustment to best continuous distribution for each

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DMU. The goodness of fit procedure used in this research followed two steps: first, an indicative approach to the best fit by the Cullen & Frey (1999) analysis. Second, a

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Maximum Likelihood Estimation (MLE) to derive the parameters of the chosen distributions in the first step (Delignette-Muller and Dutang, 2014). Delignette-Muller and Dutang, (2014) warn that skewness and kurtosis are not considered to be robust,

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due to their high variance, and suggest a nonparametric bootstrap procedure in order to take into account the uncertainty of the estimated values of the data’s degree of kurtosis

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and skewness (Efron and Tibshirani, 1994). A resample size of 100 was adopted in this research.

Once selected, one or more parametric distributions may be fitted to the data set.

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The distribution parameters were estimated by maximizing the likelihood function,

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considering the observations of each criterion and the density function of the parametric distribution. Numerical results returned the parameter estimates, the estimated standard

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errors (computed from the estimate of the Hessian matrix at the maximum likelihood solution), the log likelihood, the Akaike and Bayesian information criteria (the so-called AIC and BIC), and the correlation matrix between parameter estimates. Tables 2 and 3

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summarize the best fitting probability distributions and their estimated parameters for each input, intermediate variable, and output at each airport (Delignette-Muller and Dutang, 2014). Readers should note that distributional fits were conducted by year and DMU separately. This was done to control for, respectively, time (trend) and individual (DMU) effects. Results suggest that beta distribution (B) exhibited the best fit for almost all variables for different DMUs and years, with the exception of a few cases were gamma (G) and lognormal (logn) presented better fits. Besides, NAs for Donghai Airlines and China Post Air in Table 3 just indicate that these airlines do not operate passenger traffic. Therefore, it was not possible to perform a distributional fit for them with respect to this variable. These distributions and the respective parameters were used in the Multivariate Copula modelling presented next. It is worth mentioning that all productive resources (inputs, intermediate variables, and

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ACCEPTED MANUSCRIPT undesirable/desirable outputs) were rescaled in a unity-based normalization, bringing all

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values into the range (0, 1).

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Table 2. Outcomes for the best distributional fit (*) – time effect (grouping by year) Number of planes

Number of employees

Delay

Number of landings and Take Offs

2006 B ( 0.24 ; 1.827 )

B ( 0.237 ; 1.565 )

B ( 0.227 ; 1.632 )

B ( 0.356 ; 1.27 )

2007 B ( 0.235 ; 1.588 ) B ( 0.218 ; 1.311 )

B ( 0.21 ; 1.359 )

2008 B ( 0.251 ; 1.709 ) B ( 0.231 ; 1.282 )

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Year Fuel

Number of passengers

Cargo

B ( 0.314 ; 1.968 )

B ( 0.24 ; 1.827 )

B ( 0.271 ; 1.612 ) B ( 0.297 ; 2.044 )

B ( 0.528 ; 2.045 )

B ( 0.303 ; 1.63 )

B ( 0.235 ; 1.588 ) B ( 0.28 ; 1.534 )

B ( 0.221 ; 1.428 )

B ( 0.543 ; 1.844 )

B ( 0.289 ; 1.524 )

B ( 0.251 ; 1.709 ) B ( 0.324 ; 1.798 ) B ( 0.286 ; 1.628 )

2009 B ( 0.256 ; 1.532 ) B ( 0.223 ; 1.097 )

B ( 0.194 ; 1.01 )

B ( 0.79 ; 2.807 )

B ( 0.278 ; 1.212 )

B ( 0.256 ; 1.532 ) B ( 0.34 ; 1.688 )

2010 B ( 0.226 ; 1.136 ) B ( 0.203 ; 0.885 )

B ( 0.225 ; 1.24 )

B ( 1.307 ; 2.819 )

B ( 0.263 ; 1.047 )

B ( 0.226 ; 1.136 ) B ( 0.278 ; 1.114 ) B ( 0.244 ; 0.944 )

2011 B ( 0.23 ; 1.05 )

B ( 0.224 ; 1.081 )

B ( 1.581 ; 3.925 )

B ( 0.296 ; 1.093 )

B ( 0.23 ; 1.05 )

2012 B ( 0.212 ; 0.857 ) B ( 0.179 ; 0.611 )

B ( 0.169 ; 0.668 )

logn ( -1.335 ; 0.434 ) B ( 0.302 ; 1.011 )

2013 B ( 0.196 ; 0.698 ) B ( 0.213 ; 0.682 )

B ( 0.14 ; 0.492 )

B ( 3.136 ; 6.432 )

B ( 0.308 ; 0.928 )

B ( 0.196 ; 0.698 ) B ( 0.252 ; 0.902 ) B ( 0.276 ; 0.779 )

2014 B ( 0.176 ; 0.56 )

B ( 0.114 ; 0.346 )

B ( 7.069 ; 13.598 )

B ( 0.295 ; 0.802 )

B ( 0.176 ; 0.56 )

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B ( 0.219 ; 0.643 )

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B ( 0.2 ; 0.774 )

CR

CO2

B ( 0.284 ; 1.639 )

B ( 0.274 ; 1.245 )

B ( 0.289 ; 1.103 ) B ( 0.263 ; 0.914 )

B ( 0.212 ; 0.857 ) B ( 0.274 ; 1.01 )

B ( 0.269 ; 0.849 )

B ( 0.208 ; 0.687 ) B ( 0.261 ; 0.655 )

Table 3. Outcomes for the best distributional fit (*) – individual effect (grouping by DMU)

Fuel

Number of planes

Number of employees

Delay

Number of landings and Take Offs

CO2

Cargo

Number of passengers

Air China

B ( 23.119 ; 17.131 )

B ( 12.465 ; 9.652 )

B ( 7.942 ; 5.955 )

B ( 2.861 ; 15.531 )

B ( 28.088 ; 23.541 )

B ( 23.119 ; 17.131 )

B ( 22.694 ; 12.518 )

B ( 10.603 ; 6.616 )

Chengdu Airlines

B ( 3.827 ; 319.396 )

B ( 2.909 ; 225.804 )

B ( 3.661 ; 497.749 )

B ( 19.916 ; 32.463 )

B ( 4.027 ; 166.379 )

B ( 3.827 ; 319.396 )

B ( 43.457 ; 4067.173 ) B ( 2.994 ; 128.155 )

China Eastern Airlines

B ( 10.563 ; 9.011 )

B ( 6.04 ; 1.365 )

B ( 13.743 ; 8.275 )

B ( 0.968 ; 8.224 )

B ( 14.415 ; 9.962 )

B ( 10.563 ; 9.011 )

G ( 221.018 ; 485.084 ) B ( 9.23 ; 6.256 )

China Express

B ( 2.64 ; 805.91 )

B ( 0.797 ; 93.185 )

B ( 1.11 ; 329.841 )

B ( 29.67 ; 44.619 )

G ( 2.651 ; 123.487 )

B ( 2.64 ; 805.91 )

B ( 1.633 ; 5995.995 )

China Post Air

B ( 40.969 ; 4849.902 ) G ( 15.686 ; 585.882 )

B ( 36.134 ; 3038.446 )

B ( 2.419 ; 12.565 )

B ( 19.605 ; 1032.736 )

B ( 40.969 ; 4849.902 ) B ( 13.923 ; 127.007 )

NA ( NA ; NA )

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Name of Airline

B ( 1.677 ; 251.407 )

China Southern Airlines B ( 3.997 ; 1.775 )

B ( 10.471 ; 7.04 )

B ( 3.715 ; 1.566 )

B ( 2.035 ; 14.976 )

B ( 6.029 ; 1.659 )

B ( 3.997 ; 1.775 )

B ( 5.259 ; 1.789 )

B ( 4.795 ; 1.532 )

Donghai Airlines

B ( 1.607 ; 246.729 )

B ( 1.085 ; 492.397 )

B ( 7.383 ; 2.206 )

B ( 2.865 ; 413.238 )

B ( 3.544 ; 952.439 )

B ( 3.366 ; 73.39 )

NA ( NA ; NA )

B ( 3.544 ; 952.439 )

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Hainan Airlines

B ( 6.914 ; 47.682 )

B ( 11.808 ; 76.105 )

B ( 7.668 ; 41.358 )

B ( 1.454 ; 6.71 )

B ( 16.987 ; 86.338 )

B ( 12.838 ; 65.669 )

B ( 7.2 ; 31.896 )

Juneyao Air

B ( 1.573 ; 53.435 )

B ( 2.053 ; 56.934 )

B ( 1.853 ; 83.739 )

B ( 1206.731 ; 2394.09 ) B ( 1.934 ; 38.905 )

B ( 1.573 ; 53.435 )

B ( 2.773 ; 102.804 )

B ( 1.842 ; 33.183 )

Okay Airways

B ( 3.923 ; 335.067 )

B ( 2.335 ; 102.307 )

B ( 3.414 ; 332.419 )

B ( 378.524 ; 1107.05 )

B ( 2.128 ; 72.541 )

B ( 3.923 ; 335.067 )

B ( 6 ; 370.496 )

B ( 2.61 ; 109.872 )

Shandong Airlines

B ( 6.411 ; 96.976 )

B ( 6.971 ; 72.531 )

B ( 9.023 ; 169.591 )

B ( 1.033 ; 7.674 )

B ( 10.274 ; 57.663 )

B ( 6.411 ; 96.976 )

B ( 9.78 ; 122.059 )

B ( 6.239 ; 44.187 )

Sichuan Sirlines

B ( 4.382 ; 41.858 )

B ( 6.025 ; 47.768 )

B ( 6.238 ; 118.644 )

B ( 1.953 ; 8.435 )

B ( 8.497 ; 44.346 )

B ( 4.382 ; 41.858 )

B ( 31.381 ; 200.838 )

B ( 5.267 ; 27.398 )

Spring Airlines

B ( 2.338 ; 62.133 )

B ( 2.01 ; 47.499 )

B ( 2.588 ; 115.199 )

B ( 136.08 ; 252.52 )

B ( 2.579 ; 39.686 )

B ( 2.338 ; 62.133 )

B ( 4.078 ; 149.178 )

B ( 2.68 ; 28.366 )

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TE D

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US

CR

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B ( 6.914 ; 47.682 )

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ACCEPTED MANUSCRIPT

13

ACCEPTED MANUSCRIPT 3.3.

Multivariate Copula After adjusting the best distributional fit to capture time and individual effects

separately, it is necessary to incorporate the tail dependence structure within the ambit

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of the stochastics inputs, intermediate variables, and desirable/undesirable outputs,

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through the statistical measure of covariance. Results for the non-parametric Kendall

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Tau´s correlation are presented in Table 4.

Table 4. Non-parametric linear correlation matrix for the productive resources

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1.00

0.99 0.38

0.96 0.40

1.00

0.95 0.95 0.90

0.98 0.99 0.96

0.43 0.38 0.40

1.00 0.99 1.00 0.97 0.98

1.00

0.95

0.98

0.40

0.99 0.99

0.97

D

1.00 0.38

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0.99 0.99 0.98 0.99

Number of CO2 Cargo passengers

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0.95

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Fuel Number of planes Number of employees Delay Number of Landings and Take-Offs CO2 Cargo Number of passengers

Fuel 1.00

Number of Number Landings of Number of and Takeplanes employees Delay Offs

1.00

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Since all inputs are positively correlated with each other, as well as all other outputs and the intermediate variable – with the exception of flight delays - are also positively correlated with each other, this implies that one variable is above (below) its mean value when the other variable is above (below) its mean value. It is important to note that flight delays impact linearly on fuel consumption and, therefore, CO2 emissions in the following manner, as explained by Horiguchi et al. (2017). These authors measured that “scheduled departure time” and “scheduled arrival time” are important features for predicting fuel consumption. They affect the amount of fuel consumption because the congestion of runways and that of airways depend on time, and they cause extra time for take-off and landing, which consumes an amount of fuel. Up to a certain extent, it appears to be a trade-in between CO2 emission and flight delays, where reductions in the latter lead to reductions in the former. 14

ACCEPTED MANUSCRIPT 3.3.1. Background on multivariate copulas In fact, the concept of tail dependence can be embedded within the copula theory (Schmidt & Stadtmuller, 2006). An n-dimensional distribution function C: [0, 1]n ->[0,

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1] is called a copula if it has one-dimensional margins that are uniformly distributed on

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the interval [0, 1]. Copulas are functions that join or “couple” an n-dimensional distribution function F to its corresponding one-dimensional marginal distribution

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functions Fi, i = 1, . . . , n, in the following way: F(x1, . . . , xn) = C (F1(x1), . . . , Fn(xn)). Copulas have become a popular multivariate modeling tool in many fields where multivariate dependence is of interest (Yan, 2007). They differ not so much in the

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degree of association they provide, but rather in which part of the distributions the association is strongest (Nelsen, 1999). They are particularly useful, for instance, if one

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wants to model the impact of tail dependence on decision-making (Wang & Pham, 2012). Tail dependence describes the amount of dependence in the tail of a bivariate distribution. In other words, tail dependence refers to the degree of dependence in the

D

corner of the lower-left quadrant or upper-right quadrant of a bivariate distribution

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(Schmidt & Stadtmuller, 2006).

Precisely, a copula is a multivariate distribution whose marginals are all uniform

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over (0,1]. Combined with the fact that any continuous random variable can be transformed to be uniform over (0,1] by its probability integral transformation, copulas can be used to provide multivariate dependence structure apart from the marginal

AC

distributions (Yan, 2007). According to Table 5, different choices of generators yield several important families of copulas. Similarly, different dependence parameters are closely related to some level of bivariate dependence, measured by Kendall's τ coefficient of non-parametric correlation (Yan, 2007).

Table 5: Archimedean copulas, their generators, and measures of dependence Family

Clayton (1978) Frank (1979)

Generator ∅(𝑡)

Dependence parameter (α) space

𝑡 −𝛼 − 1

α≥0

𝑒 −𝛼𝑡 − 1 −𝑙𝑛 −𝑡 𝑒 −1

α≥0

Kendall's τ 𝛼 𝛼+2 1−

15

4 {𝐷 (−𝛼) − 1} 𝛼 1

ACCEPTED MANUSCRIPT Gumbel (1960)

(− ln 𝑡)𝛼

1 − 𝛼 −1

α≥1

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It is worth noting that, although Archimedean copulas with dimension three or

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higher only allow positive association, negative association is allowed for bivariate Archimedean copulas (Yan, 2007). Fig. 2 compares Clayton (1978), Frank (1979) and

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Gumbel (1960) copulas, with normal marginals, to the traditional bivariate normal distribution. One can easily discern that, for different families of copulas and dependence values, the resulting bivariate distribution may indicate a stronger

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relationship between higher (lower) values of the variables under analysis (Nelsen, 1999). Although copulas have been often used in actuarial and finance applications in banking, such as for risk assessment, measurement and pooling (Fantazzini, 2009,

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Dobrić and Schmid, 2005) thus far their use within the ambit of DEA models have not been noticed or restricted to very few papers (Wanke et al., forthcoming; Huang et al.,

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CE P

TE

D

2017).

Fig. 2. Examples of Archimedean copulas for different values of Kendall's τ

The Archimedean copulas are often chosen for modelling purposes due to their following characteristics: (1) compatibility with “fat tail” distributions sensitive to large losses, but less sensitive to small losses; (2) simple and robust parameter estimation 16

ACCEPTED MANUSCRIPT methods; (3) familiarity with practitioners and regulators; and (4) easy to implement. Specifically, the first criterion reflects a well-known phenomenon that large losses tend to come as surprises – the “fat tail”. In this sense, Archimedean copulas outperform the

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elliptical class, as these copulas do not have fat tails. These distinctive features can be

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noted in Figs. 3 and 4, where 2D and 3D scatter plots are presented for a 100 samples obtained for each generator – considering the data previously presented in Tables 2, 3,

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CE P

TE

D

MA

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and 4.

Fig. 3. Scatter plot for the Archimedean copulas adjustment – time effect (trend)

17

CE P

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D

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Fig. 4. Scatter plot for the Archimedean copulas adjustment – individual effect (DMU)

Next section discusses the SNDEA model developed in this research to handle both undesirable outputs – flight delay and CO2 emissions. At the end, a pseudo code for solving this model under multivariate copula generation is presented.

3.4.

The Proposed SNDEA model DEA was proposed by Charnes et al. (1978) as an approach for measuring the

efficiency of DMUs – DMUs - that use multiple inputs to produce multiple outputs. One of the pitfalls of classic DEA modelling is that the internal process of a DMU (Decision Making Unit) is a “black box”. Therefore, efficiency cannot be measured within the 18

ACCEPTED MANUSCRIPT ambit of any specific sub-structure of a DMU. In fact, a DMU may consist of several sub-substructures that may impact overall efficiency levels differently. Network DEA models were proposed to overcome this limitation. One of the earliest and simplest

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network structures is the two-stage DEA model, in which two serially connected

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productive processes or sub-structures are assumed to work together in the main DMU. In other words, DMUs are composed by two stages connected in series, in which all the

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outputs from the first stage become the inputs of the second one (Golany et al., 2006). This consists of a particular case of the multi-stage network structure firstly introduced in Fare (1991), and subsequently extended in Fare and Whittaker (1995), Fare and

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Grosskopf (1996a, 1996b, 2000) and Tone and Tsutsui (2009, 2010). Readers should note that, when modeling network DEA, both multiplicative and

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additive efficiency decomposition can be proposed depending on the variations of twostage structures and the CRS/VRS assumptions adopted. One of the major computational issues in additive efficiency decomposition, as demonstrated by Guo et

D

al. (2017) is that fact that one has to determine the weights combining the efficiencies of

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the two individual stages. Note that predetermined weights are cumbersome to use, since the best solution is not known unless all possible values of weights are tested. On

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the other hand, Kao and Hwang (2008) indicate that the overall efficiency can be decomposed into the product of efficiency of each stage under the standard network – where the first stage outputs become the only inputs to the second stage to generate

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second stage outputs and so on - and the assumption of CRS. It is important to mention that network DEA models built upon multiplicative efficiency decomposition are extremely nonlinear and cannot be converted into linear models using the CharnesCooper transformation (Charnes and Cooper, 1962) when VRS is assumed and/or the network model allows for exogenously defined inputs and outputs. In this research, flight delay is treated as an exogenous undesirable output, since it leaves the system between stages 1 and 2. The multiplicative efficiency decomposition, adopted in this research, can be solved, however, by setting efficiency lower and upper bounds for a given stage based on a non-cooperative game approach between both stages using a technique called Bi-Level programming. Cook et al. (2010) showed that all the DEA approaches for measuring the efficiency of DMUs with twostage network process can be categorized as being both non-cooperative (leaderfollower) within the ambit of a game approach. Actually, in evaluating the efficiency of 19

ACCEPTED MANUSCRIPT two-stage network structures a conflict may arise between two stages: the first stage may have to increase its outputs (intermediate measures) in order to be efficient while on the other hand, this action implies a reduction in the efficiency of the second stage.

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This being the case, “flight efficiency” levels could be maximized to the detriment

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of sub-optimal “network efficiency” levels. In terms of CO2 emissions and flight delays, which present a positive linear correlation sign (cf. Table 4), this non-

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cooperative game approach unveils a non-linear relationship between these undesirable outputs, where CO2 emissions could be reduced in a proportionally higher fashion when compared to flight delays, within the ambit of a two-stage

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productive process.

As regards game approaches in network DEA, Liang et al. (2008) introduced a

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two-stage network model from the perspective of non-cooperative theory. In the noncooperative game model, the two stages are characterized by the leader-follower relationship. Chen et al. (2009) and Wang et al. (2010) considered the case when the

D

two stages of each DMU are not independent and used a weighted harmonic mean

TE

approach to obtain the integrated efficiency of each DMU. Moreover, Zha and Liang (2010) extended the existing approaches by considering the case when two stages share

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some input. Later on, Wu (2010) developed a new bi-level programming DEA for decentralized companies with constraint resource. Recently, Du et al. (2011) and Zhou et al. (2012) proposed a Nash bargaining game for measuring efficiency in two-stage network structures. These previous models were based upon CRS assumption, but

DMU.

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Wang (2014) extended these to VRS models for exploring differences in scale of each

This research develops a non-cooperative game approach, solved by bi-level programming, to address the multiplicative efficiency decomposition problem of a twostage network DEA model, considering simultaneously undesirable and exogenous outputs as depicted in Fig. 5, within the ambit of Chinese airlines.

20

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Fig. 5. Network DEA for defined undesirable and exogenous outputs in Chinese

3.4.1. Bi-level programming

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airlines.

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Bi-level programming problem is referred to as nested optimization, a problem

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in which feasible space of the first problem is implicitly determined by another optimization problem. Bi-level programming problem has two hierarchical levels,

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namely the upper level and the lower level, which are associated with the leader and its follower, respectively. In such hierarchical decision structure, the decision maker at the top of the hierarchy (the leader) makes its decision based on its own objective and the

AC

rational reaction of the lower level decision maker (the follower) who makes the decision after it. After the first decision maker has made its decision, the second decision maker executes its policies based on its objective function and the decision made by the first decision maker. In this research, a heuristic technique is applied to handle the linear program transformation in presence of undesirable outputs (CO2 emissions and flight delays), one of which is exogenous (flight delays). Although both stages can be chosen as the leader within this non-cooperative leader-follower approach for the network DEA model, the one whose performance is more important - “flight efficiency” – is picked up as the leader to the detriment of the follower – “network efficiency”. In this case, CO2 emissions are the key variable to be optimized to the detriment of flight delays, kept sub-optimal. Once this choice is made at the heuristic ambit, the

21

ACCEPTED MANUSCRIPT efficiency of the follower is then computed subject to the requirement that the efficiency of the first stage remains fixed. Assume that there are n DMUs and each 𝐷𝑀𝑈𝑗 (𝑗 = 1,2, . . . , 𝑛) consists of two

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stages. Let first stage of 𝐷𝑀𝑈𝑗 utilize input vector 𝑥𝑗 ∈ ℝ𝑚 and produce intermediate

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product 𝑧𝑗 ∈ ℝ𝐷 , consumed by second stage to produce output vector 𝑦𝑗 ∈ ℝ𝑆 . As

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depicted in Fig. 5, subscripts U and D denote, respectively, “undesirable” and “desirable”. Being more precise, for each 𝐷𝑀𝑈𝑗 , stage 1 is composed by a set of inputs (𝑥𝑖𝑗 )𝐷 , 𝑖 = 1,2, … , 𝑚 and undesirables outputs (𝑦𝑐𝑗 )𝑈 , 𝑐 = 1,2, … , 𝐶′ and stage 2 is composed 𝑈

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2 by a set of undesirable outputs (𝑦𝑟2′ 𝑗 ) , 𝑟′ = 1,2, … , 𝑆′ and desirable outputs (𝑦𝑟𝑗 ) ,𝑟 = 𝐷

1,2, … , 𝑆. The intermediates measures (𝑧𝑑𝑗 )𝐷 , 𝑑 = 1,2, … , 𝐷 is the desirable output for

MA

stage 1 and input for stage 2.

The efficiency levels for the each one of the individual stages, and the overall

D

system, after the Charnes and Cooper (1962) transformation, are defined as follows:

TE

Stage 1

′

𝑆. 𝑇.

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𝐶 ′ 𝜃1𝑜 = 𝑚𝑎𝑥(∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑜 )𝐷 − (∑𝑐=1 𝑙 𝑐 𝑦𝑐𝑜 )𝑈 + 𝑈𝑜

AC

(∑𝑚 𝑖=1 𝑣𝑖 𝑥𝑖𝑜 )𝐷 = 1

′

𝑚 𝐶 ′ (∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑗 − ∑𝑖=1 𝑣𝑖 𝑥𝑖𝑗 )𝐷 − (∑𝑐=1 𝑙 𝑐 𝑦𝑐𝑗 )𝑈 + 𝑈𝑜 ≤ 0 ∀𝑗

(1)

𝑣𝑖 , 𝑤𝑑 , 𝑙′𝑐 , ≥ 𝜖 ∀ 𝑖, 𝑑, 𝑐 Stage 2 ′

𝑆 2 2 ) ′ 𝜃2𝑜 = 𝑚𝑎𝑥(∑𝑆𝑟=1 𝑢𝑟 𝑦𝑟𝑜 𝐷 − (∑𝑟 ′ =1 𝑢 𝑟 ′ 𝑦𝑟 ′ 𝑜 ) + 𝑈𝑜 𝑈

𝑆. 𝑇. (∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑜 )𝐷 = 1 ′

𝑆 2 2 ′ (∑𝑆𝑟=1 𝑢𝑟 𝑦𝑟𝑗 − ∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑗 ) − (∑𝑟 ′ =1 𝑢 𝑟 ′ 𝑦𝑟 ′ 𝑜 ) + 𝑈𝑜 ≤ 0 ∀𝑗 𝐷

𝑈

𝑢𝑟 , 𝑤𝑑 , 𝑢′𝑟 ′ ≥ 𝜖 ∀ 𝑟, 𝑟 ′ , 𝑑 22

(2)

ACCEPTED MANUSCRIPT Overall system ′

𝐶 𝑆 ′ 1 2 𝜃𝑜 = 𝜃1𝑜 ∗ 𝜃2𝑜 = 𝑚𝑎𝑥 ((∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑜 )𝐷 − (∑𝑐=1 𝑙 𝑐 𝑦𝑐𝑜 )𝑈 + 𝑈𝑜 ) ∗ ((∑𝑟=1 𝑢𝑟 𝑦𝑟𝑜 )𝐷 − ′

(∑𝑆𝑟 ′ =1 𝑢′ 𝑟 ′ 𝑦𝑟2′ 𝑜 ) + 𝑈𝑜2 )

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𝑈

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𝑆. 𝑇.

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𝐷 (∑𝑚 𝑖=1 𝑣𝑖 𝑥𝑖𝑜 )𝐷 = 1 (∑𝑑=1 𝑤𝑑 𝑧𝑑𝑜 )𝐷 = 1 ′

𝑚 𝐶 ′ 1 (∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑗 ) − (∑𝑐=1 𝑙 𝑐 𝑦𝑐𝑗 ) − (∑𝑖=1 𝑣𝑖 𝑥𝑖𝑗 ) + 𝑈𝑜 ≤ 0∀𝑗 𝐷

𝑈

𝐷

′

(3)

𝐷

𝑣𝑖 , 𝑢𝑟 , 𝑤𝑑 , 𝑙′𝑐 , 𝑢′𝑟 ′ ≥ 𝜖 ∀𝑖, 𝑟, 𝑟 ′ , 𝑑, 𝑐

MA

𝑈

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2 2 (∑𝑆𝑟=1 𝑢𝑟 𝑦𝑟𝑗 ) − (∑𝑆𝑟 ′ =1 𝑢′ 𝑟 ′ 𝑦𝑟2′ 𝑜 ) − (∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑗 )𝐷 + 𝑈𝑜 ≤ 0∀𝑗

Where 𝜃1 , 𝜃2 and 𝜃 represents the efficiency for 𝐷𝑀𝑈𝑜 of stage 1, stage 2 and Overall,

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respectively. The variables 𝑣𝑖 , 𝑙′𝑐 are the weights that multiplies the inputs and

TE

undesirable outputs for the stage 1, respectively. Also, the 𝑢𝑟 , 𝑢′𝑟 ′ are the weights that multiplies the desirable outputs and undesirable outputs for the stage 2 respectively and

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𝑤𝑑 is the weight for the intermediate vector. In addition, the 𝜖 is Archimedean value that, 𝑈𝑜 is the constant, free in sign, for the VRS frontier characterization and 𝑈𝑜1 , 𝑈𝑜2 are the constant for the VRS frontier characterization for stage 1 and stage 2 used in model

AC

(3), respectively.

3.4.2. The non-cooperative model An alternative to measuring the efficiency of DMU is the leader-follower approach. In this approach, the upper-bound efficiency of each stage is determined by computing the efficiency under a non-cooperative condition. For Stage 1 dominating the system the efficiency is: ′

𝑈 𝐶 ′ 𝜃1𝑜 = 𝑚𝑎𝑥(∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑜 )𝐷 − (∑𝑐=1 𝑙 𝑐 𝑦𝑐𝑜 )𝑈 + 𝑈𝑜

𝑆. 𝑇. (∑𝑚 𝑖=1 𝑣𝑖 𝑥𝑖𝑜 )𝐷 = 1

23

ACCEPTED MANUSCRIPT ′

𝑚 𝐶 ′ (∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑗 − ∑𝑖=1 𝑣𝑖 𝑥𝑖𝑗 )𝐷 − (∑𝑐=1 𝑙 𝑐 𝑦𝑐𝑗 )𝑈 + 𝑈𝑜 ≤ 0∀𝑗

(4)

𝑣𝑖 , 𝑤𝑑 , 𝑙′𝑐 , ≥ 𝜖 ∀𝑖, 𝑑, 𝑐

T

Alternatively, for Stage 02 dominating the system, the efficiency is:

𝑈

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𝑆. 𝑇.

IP

′

𝑆 2 𝑈 2 ) ′ 𝜃2𝑜 = 𝑚𝑎𝑥(∑𝑆𝑟=1 𝑢𝑟 𝑦𝑟𝑜 𝐷 − (∑𝑟 ′ =1 𝑢 𝑟 ′ 𝑦𝑟 ′ 𝑜 ) + 𝑈𝑜

(∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑜 )𝐷 = 1 ′

𝑆 2 2 ′ (∑𝑆𝑟=1 𝑢𝑟 𝑦𝑟𝑗 − ∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑗 ) − (∑𝑟 ′ =1 𝑢 𝑟 ′ 𝑦𝑟 ′ 𝑜 ) + 𝑈𝑜 ≤ 0 ∀𝑗

(5)

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𝐷

𝑈

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𝑢𝑟 , 𝑤𝑑 , 𝑢′𝑟 ′ ≥ 𝜖∀𝑟, 𝑟 ′ , 𝑑

𝑈 𝑈 In model (4) and (5), the superscript U in 𝜃1𝑜 and 𝜃2𝑜 indicates the upper-bound

D

efficiency of each stage 1 and stage 2 respectively.

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3.4.3. The cooperative model

The overall efficiency is the cooperative product of stage 1 and stage 2, as ′

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𝑆 2 2 ) ′ 2 described by model (3). Let, however, ((∑𝑆𝑟=1 𝑢𝑟 𝑦𝑟𝑜 𝐷 − (∑𝑟 ′ =1 𝑢 𝑟 ′ 𝑦𝑟 ′ 𝑜 ) + 𝑈𝑜 ) = 𝜆. 𝑈

This means that overall efficiency is parameterized as a function of Stage 2 (leader).

AC

Then model (3) is converted into: ′

𝐶 ′ 1 𝜃𝑜 = 𝑚𝑎𝑥 ((∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑜 )𝐷 − (∑𝑐=1 𝑙 𝑐 𝑦𝑐𝑜 )𝑈 + 𝑈𝑜 ) ∗ 𝜆

𝑆. 𝑇.

′

𝑆 2 2 ) ′ 2 (∑𝑆𝑟=1 𝑢𝑟 𝑦𝑟𝑜 𝐷 − (∑𝑟 ′ =1 𝑢 𝑟 ′ 𝑦𝑟 ′ 𝑜 ) + 𝑈𝑜 = 𝜆 𝑈

(∑𝑚 𝑖=1 𝑣𝑖 𝑥𝑖𝑜 )𝐷 = 1 (∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑜 )𝐷 = 1 ′

𝑚 𝐶 ′ 1 (∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑗 )𝐷 − (∑𝑐=1 𝑙 𝑐 𝑦𝑐𝑗 )𝑈 − (∑𝑖=1 𝑣𝑖 𝑥𝑖𝑗 )𝐷 + 𝑈𝑜 ≤ 0 ∀𝑗 ′

2 2 (∑𝑆𝑟=1 𝑢𝑟 𝑦𝑟𝑗 ) − (∑𝑆𝑟 ′ =1 𝑢′ 𝑟 ′ 𝑦𝑟2′ 𝑜 ) − (∑𝐷 𝑑=1 𝑤𝑑 𝑧𝑑𝑗 )𝐷 + 𝑈𝑜 ≤ 0 ∀𝑗 𝐷

𝑈

𝑣𝑖 , 𝑢𝑟 , 𝑤𝑑 , 𝑙′𝑐 , 𝑢′𝑟 ′ ≥ 𝜖 ∀ 𝑖, 𝑟, 𝑟 ′ , 𝑑, 𝑐 24

(6)

ACCEPTED MANUSCRIPT ′

𝑆 2 𝑈 2 ) ′ 2 Since it is known that 0 ≤ ((∑𝑆𝑟=1 𝑢𝑟 𝑦𝑟𝑜 𝐷 − (∑𝑟 ′ =1 𝑢 𝑟 ′ 𝑦𝑟 ′ 𝑜 ) + 𝑈𝑜 ) ≤ 𝜃2𝑜 , 𝑈

the overall efficiency can be obtained by searching the parameter 𝜆 in the bounds 𝑈 ] 𝑈 [0, 𝜃2𝑜 by using the following heuristic. Let 𝜆 = 𝜃2𝑜 − 𝑘𝛥𝜖, where 𝛥𝜖 is the step size 𝑈 𝜃2𝑜

T

and 𝑘 𝑚𝑎𝑥 is the maximal integer which is smaller than or equal to

. Model (6) can be

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𝛥𝜖

solved to obtain 𝜃𝑜 (𝑘) by increasing k each step. The efficiency of whole system can be

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estimated as 𝜃𝑜∗ = 𝑀𝑎𝑥𝜃𝑜 (𝑘) and k* is the k value for the maximum overall efficiency 𝑈 ∗ step. Stage 2 efficiency is 𝜃2𝑜 = 𝜃2𝑜 − 𝑘 ∗ 𝛥𝜖 and Stage 1 efficiency (follower) can be 𝜃∗

∗ computed indirectly by 𝜃1𝑜 = 𝜃∗𝑜 . An alternative transformation of model (3) can be 2𝑜

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carried out by using Stage 1 as the leader at the parameter 𝜆. All models discussed here

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rely on the VRS frontier assumption. To change to the CRS frontier assumption, all

variables 𝑈𝑜 , 𝑈𝑜1 and 𝑈𝑜2 must be set equal to 0.

Fig. 6. General framework for the NDEA model with undesirable and exogenous outputs

In order to solve the stochastic version of the NDEA model presented in Fig. 6, the principles of chance-constrained programming should be observed. Charnes and Cooper (1959) developed first the chance-constrained programming to assess efficiency levels in cases of uncertainty and to apprehend how this uncertainty would turn the 25

ACCEPTED MANUSCRIPT linear programming model into one infeasible to solve. Thore (1987), Banker (1993), and Land et al. (1993, 1994) addressed uncertainty in DEA inputs and outputs by means of its stochastic variations. In order to handle such random variations, the constraint

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equations of the model should be altered and the logic of the chance-constrained

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formulation introduced by Land et al. (1993) should be applied, so that only inputs and outputs generate beyond a percentile threshold could be used. Table 6 provides the

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pseudo-code for the random generation of the inputs, intermediate variables, and the outputs, with an external constraint check given by a threshold level of 0.95 for the multivariate copulas percentile and their different generators. The pseudo-code

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describes the flow of the Monte Carlo simulation, which is actually how the problem is solved. At each iteration, a set of inputs, intermediate variables, and outputs is drawn from data generated by the multivariate copula adjustment to the original dataset - to

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are later used to compute statistics.

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solve the problem. At the end of each iteration efficiency scores are computed2, which

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Table 6. Pseudo-code for solving the stochastic version of the NDEA model with

1.

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undesirable and exogenous outputs (SDEA) Adjust the corresponding probability distribution for the inputs, intermediate variables, and

desirable/undesirable outputs of the data set 2.

Run N – a sufficiently large number – times. In this research, N = 2,500 Generate artificial data using multivariate copulas – and its different generators - in

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a.

accordance to each corresponding probability distribution and to the correlation matrix 3.

Compute the efficiency scores for the overall system and for each stage by solving the bi-level

programming for the network DEA by using only the runs where multivariate percentiles were at least 0.95 a.

Record these chance-constrained efficiency scores

b.

Repeat this step until a minimal level of 200 samples were achieved for each

multivariate copula generator 4.

Compute relevant statistics for the stochastic version of the NDEA model

5.

Finish

3.5.

Stochastic Programming for Combining Bootstrapped Regressions

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Each iteration covers executions of the model for all the observations, so each iteration actually returns a set of efficiency scores, one for each observation.

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ACCEPTED MANUSCRIPT In this research, the impacts of the contextual variables related to the Chinese airlines are tested by a robust regression approach. In this approach, Tobit (Wanke et al. 2016b), Simplex (Wanke and Barros, 2016), and Beta regressions (Wanke et al., 2016),

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individually designed to handle dependent variables bounded in 0 and 1, are combined

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by means of stochastic non-linear programming and bootstrapping. This is justified because most regression approaches produce biased results in two-stage DEA analysis

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because they do no often take into account the underlying issues caused by the lack of discriminatory power of the scores computed in the first stage (Wanke et al., 2016). The discriminatory power is low because efficiency scores tend to be upwards-biased

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towards one. Therefore, a robust regression approach should reflect an adequate distributional assumption in order to handle this type of bias. This may be obtained via

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bootstrapping (Simar and Wilson 2007, Simar and Wilson 2011) and combining forecasts to yield smaller prediction errors (James et al. 2013, Ledolter 2013). The non-linear stochastic optimization problem for the combination of Beta and

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Tobit bootstrapped regressions is presented in model (7), where w1 represents the

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weight assigned to the residuals of the Tobit regression (Rt), w2 represents the weight assigned to the residuals of the Simplex regression (Rs), and Rb represents the residuals

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of the Beta regression. This model optimizes the values of w1 and w2 so that the variance (Var) of the combined residuals is minimal. Both regressions were bootstrapped and combined 1,000 times so that a distributional profile of w1 and w2

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could be collected for the stage 1, stage 2, and overall best efficiency predictions. min 𝑉𝑎𝑟(𝑤1𝑹𝒕 + 𝑤2𝑹𝒃 + (1 − 𝑤1 − 𝑤2)𝑹𝒔) 𝑆. 𝑇. 𝑤1 ≤ 1 𝑤1 ≥ 0

(7)

𝑤2 ≤ 1 𝑤2 ≥ 0 𝑤1 + 𝑤2 ≤ 1 𝑤1 + 𝑤2 ≥ 0

Model (7) was solved using differential evolution (DE) technique. DE is a member of the family of genetic algorithms, which mimic the process of natural selection in an evolutionary manner; see Holland (1975). A genetic algorithm solves 27

ACCEPTED MANUSCRIPT optimization problems with biology-inspired operators of crossover, mutation and selection, generating successive populations of individuals (solutions or generations). In addition, the DE algorithm finds the global optimum of the objective function,

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which does not require to be either continuous or differentiable; see Thangaraj et al.

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(2010) and Mullen et al. (2011). The R package named DEoptim, which implements the DE algorithm and was first published on CRAN in 2005. Interested readers should

package.

Analysis and Discussion of Results

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4.

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refer to Ardia et al. (2011) and Mullen et al. (2011) for a detailed description about the

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Results of the NDEA model for the original dataset are presented in Figs 7 (aggregate), 8 (depicted by year), and 9 (depicted by airline). They were obtained by solving a bi-level programming for a non-cooperative game approach, where CO2

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emissions verified in stage 2 (“flight efficiency”, the leader) can be traded-off, up to

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some extent, by flight delays verified in stage 1 (“network efficiency”, the follower). When taken in aggregate (Fig. 7), these results suggest that Chinese airlines are

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proportionally more “flight efficient” than “network efficient”, leading to a median overall efficiency level around 0.50, indicating there are great potentials to be improved. Readers should note that overall efficiency levels are smaller than those

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verified in stages 1 and 2 because of two major causes. First of all, overall results are suboptimal, that is, they are computed taken into consideration that flight efficiency is maximized to the detriment of network efficiency, which is, therefore, suboptimal. Second, overall results are computed in a multiplicative fashion, as depicted in Section 3.4, thus imposing an “additional penalty”, in comparison to the weighted additive fashion, when the efficiency scores for each individual stages are far below one. When these aggregate results are decomposed by year (cf. Fig. 8), it is worth noting a modest increasing trend over 2012-2014, although in previous years overall, stage 1, and stage 2 efficiency levels appeared to be stagnant. This is consistent with the empirical results of Wanke et al. (2015) and Cao et al. (2015). It also can be verified by the recovery of the volume of passengers and cargo just described by the Fig. 3. On the other hand, when depicted by DMU (cf. Fig. 9), results suggest that Chinese airlines are extremely heterogeneous, although they appear to be consistently 28

ACCEPTED MANUSCRIPT more “flight efficient” than “network efficient”, with the exception of China Express and Shandong Airlines. It is mainly because they both have much higher utilization rate of airplanes comparing to other peers. Meanwhile, these results suggest not only the

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impact of specific contextual variables - which are business-related - on efficiency

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levels, but also the impact of a modest trend component on recent years. That is why the subsequent analyses, which incorporate the stochastic component into the NDEA

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model, attempt to decompose these three different efficiency scores in terms of individual and time effects.

Figs. 10 and 11 depicts the results for the SNDEA scores obtained computed

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using the approach presented in Table 6. It is worth noting that the introduction of the stochastic element – distributional assumption, variances, and covariances - into the

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productive process not only yields to bias corrected efficiency estimates but also sheds some light into the case of extreme joint events, such as modelled by Gumbel and Clayton generators. As regards the first issue, stochastic efficiency scores tend to be

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higher due to the incorporation of a positive correlation matrix in random number

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generation, where outputs, intermediate variables, and inputs do not vary detached from each other. Not taking into account the impact of correlation in the input/output

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data matrix is one clear limitation of traditional DEA models. On the other hand, efficiency levels, especially when depicted by year, are extremely sensitive to positive spikes and negative valleys within the ambit of productive resources. As a general rule, efficiency appears to be higher under Gumbel generator and lower under Clayton

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generator, respectively, taking Frank copula as basis of comparison.

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Fig. 7. Results for the NDEA model for undesirable outputs under a non-cooperative game approach.

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Fig. 8. Results for the NDEA model depicted by year.

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Fig. 9. Results for the NDEA model depicted by DMU.

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Fig. 10. Results for the SNDEA model depicted by DMU considering different multivariate copula generators.

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Fig. 11. Results for the SNDEA model depicted by year considering different multivariate copula generators.

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ACCEPTED MANUSCRIPT As regards the distributional fits of each one of these three types of efficiency scores, considering different multivariate copula generators, Figs. 12 and 13 depict the Gaussian, Simplex, and the Beta adjustments for their inverse cumulative distributions.

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It is not possible to affirm, at the first sight, however, whether a specific distribution is

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preferable to the other, thus suggest that combining Tobit, Simplex, and Beta regressions results may be a sound approach. In fact, results for the Kullback-Leibler

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(KL) divergence presented in Table 6 indicate that differences between these three types of adjustments are eventually minimal, sometimes favoring one distributional assumption – that is, one specific regression type - to the detriment of the other. The

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closer to zero, the better is the KL divergence.

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ACCEPTED MANUSCRIPT Fig 12. Inverse cumulative distributions for the different efficiency scores under

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different copula generators (individual effect).

Fig 13. Inverse cumulative distributions for the different efficiency scores under different copula generators (time effect).

Table 6. KL divergence results for Beta, Simplex, and Gaussian assumptions. DMU Effect Stage Clayton Frank

Simplex Fit

Beta Fit

Year Effect Gaussian Fit

Stage

Simplex Fit

Beta Fit

Gaussian Fit

Stage 1

0.077882

0.010698

1.310159 Stage 1

0.091223

0.005395

0.750578

Stage 2

0.057362

0.023140

1.986892 Stage 2

0.113977

0.021156

0.519254

Overall

0.093699

0.011399

0.336545 Overall

0.183030

0.006360

0.063404

Stage 1

0.070529

0.035003

1.016543 Stage 1

0.077127

0.022398

1.370247

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0.018348

1.771077 Stage 2

0.068334

0.019149

1.434005

Overall

0.109302

0.008093

0.362651 Overall

0.128016

0.029213

0.148041

Stage 1

0.081797

0.058433

0.937688 Stage 1

0.034727

0.013602

1.719406

Stage 2

0.045791

0.037019

2.188000 Stage 2

0.039155

0.025365

2.264529

Overall

0.097390

0.012471

0.320754 Overall

0.072822

0.030491

0.240800

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Gumbel

Stage 2

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The results for the stochastic non-linear optimization on the 1,000 bootstrapped

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Tobit, Simplex, and Beta regression residuals are presented in Fig. 14. It suggests an unequal division of the weighs among these three types of assumptions, especially when

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individual effects are assessed, where Tobit regression was assigned with a median weight of at least 0.50. On the other hand, a more even weight split was found when

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analyzing time effects, thus suggesting that different causes may underlie efficiency scores when analyzing it in light of individual and trend effects, as depicted in Figs. 15

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and 16.

Fig 14. Distribution on the optimal values of w1 and w2 for each efficiency distribution (Left: individual effect. Right: time effect).

As regards individual effects, results presented in Fig. 15 suggest that “network efficiency” (stage 1) is significantly impacted by governance, age, and network span, while “flight efficiency” (stage 2) is impacted by governance and previous M&A. Besides, it was not possible to verify a significant impact of ownership, fleet mix and 37

ACCEPTED MANUSCRIPT copula generator within the ambit of the three types of efficiency analyzed. These results suggest the prominent role of governance, imposed by opening an airline´s

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capital in the stock market, in terms of achieving lower levels of CO2 emissions and

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flight delays. This not only denotes a better commitment to sustainable development but

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also to better customer service levels practices. It is noteworthy, however, the subsidiary aspect of a learning curve, proxied by age, in achieving higher network efficiency levels, while M&A may help in spreading best operational practices that eventually

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reflect in higher efficiency levels. It is also interesting to note the difficulties that may

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arise due to a larger network span, mainly in coordinating connecting flights in hub operations, definitely a strong underlying cause of delays and CO2 emissions. Although the non-significance of the copula generator type suggest that extreme random shocks

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equally impact all airlines and therefore do not discriminate them, the technology assumption, whether observing constant or varying returns to scale is significant in

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terms of “flight” and “overall” efficiency levels. This suggests that CO2 emissions, differently to flight delays, are subject to the size of the operation, opening a room for

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discussing Carbon footprint policies in terms of either increasing or diminishing returns to scale in civil aviation. On the other hand, in accordance to Fig. 16, when time effects are put into perspective, one can easily note a positive trend over time towards higher “network efficiency” levels, although “flight efficiency” levels remain stagnant. The type of copula generator is also significant to better apprehend how efficiency in the Chinese airline industry evolve over the course of time. Specifically with respect to Gumbel generator, readers should note that its positive impact on efficiency levels is derived due to its thinner upper edge in comparison to those verified under Frank and Clayton generators (cf. Fig. 2 also). Broadly speaking, Gumbel generator would be representing

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ACCEPTED MANUSCRIPT a strong positive random shock at the output level, with minimal dispersion between them. These results not only suggest that learning curve/age may help in fact in

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achieving higher levels of “network efficiency” over the course of time - thus defining

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flight delays as managerial problem to be solved - but also suggest that - apart from

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technological and regulatory changes - overall CO2 emissions in the Chinese industry tend to remain unchanged in a temporal perspective. That is CO2 emissions are rather subject

to

fluctuations

imposed

by

extreme

shocks

than

by

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overall

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decreasing/increasing trend. Policy implications should explicitly address CO2 emission

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goals in the long term for Chinese companies listed in stock markets in order to

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overcome this situation.

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Fig 15. Combined bootstrapped regression results for the intercepts (individual effect) within each efficiency type.

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Fig 16. Combined bootstrapped regression results for the intercepts (time effect) within each efficiency type.

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ACCEPTED MANUSCRIPT 5.

Conclusions This paper presents an analysis of the efficiency of Chinese airlines during

2006-2014, using a novel stochastic network DEA (SNDEA) to account for randomness

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in undesirable outputs such as flight delays and CO2 emissions. It gauges the “network

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efficiency” in the first stage, while estimates the “flight efficiency” in the second stage, following a bi-level programming for a non-cooperative game approach. Meanwhile, we apply multivariate copulas to control for time (trend) and individual (DMU) effects

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when calculate the airline efficiency of different stages. At last, different from the

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traditional method, we employ the stochastic non-linear model to examine the impact of contextual variables on the efficiency, solved by differential evolution, which combines bootstrapped Simplex, Tobit and Beta robust regression results.

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Through these innovative models and empirical analysis, it concludes that the

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majority of Chinese airlines are proportionally more “flight efficient” than “network

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efficient”, and the median of overall efficiency level is about 0.50. Moreover, during the period of 2006-2012, the efficiency level of different stages has always kept stagnant.

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After that, there was a slow growth started in the next several years. When introducing the stochastic factors that addressed uncertainty in DEA inputs and outputs, we found that efficiency scores tend to be higher. When analyzing the influence of contextual variables, we decompose these three different efficiency scores in terms of individual and time effects. For the former, it shows that the “network efficiency” is significantly impacted by governance, age, and network span, while “flight efficiency” is impacted by governance and previous M&A. Meanwhile, for the latter, it indicates that there is a positive trend over time towards higher “network efficiency” levels, despite “flight efficiency” levels remain stagnant.

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ACCEPTED MANUSCRIPT These results shed lights on improvement of management and future reform for the Chinese airline companies and industry. Firstly, there is great potential for these

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airline companies to improve their efficiency when taking account of the undesirable

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outputs, which include flight delays and carbon emissions together. As most Chinese

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airlines have higher “flight efficiency” score than “network efficiency” score, it is urgent to improve their management on the network efficiency and increase the airline's customer's service quality. Secondly, better corporate governance and much effective

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market supervision will not only help to a better commitment to sustainable

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development but also to better customer service levels practices for the Chinese airline companies. As the Chinese stock market (Shanghai Stock Exchange and Shenzhen Stock Exchange) is on the way of rapid development since 1992, more airline

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companies should be encouraged to enhance their management through financial market. Furthermore, when the airline companies participate into the international flights, they

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will tend to have lower punctuality rate due to a larger network span. Moreover, the airline companies will benefit from M&A activities to realize increase return to scale

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and reduce the carbon emissions. As there is learning curve existed in the airline industry of China, the punctuality rate has been slightly improved with more management practices are accumulated. However, the flight efficiency of Chinese airlines should be also paid attention as it is still stagnant as well as the airline companies play an important role increasing the emissions of greenhouse gas. To achieve sustainable development, China has planned to reduce carbon dioxide emissions per unit of GDP by 40% to 45% by 2020 comparing with the level of 2005, and by 60% to 65% by 2030 3 . Under the binding targets, eexcept for measures to improve the passengers load factor, using more renewable energy to reduce CO2 emissions should

3

Enhanced Actions on Climate Change: China’s Intended Nationally Determined Contributions.

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ACCEPTED MANUSCRIPT be also considered for the Chinese airline companies in the long run. Thirdly, when evaluating the airline efficiency for benchmarking, it should take account of the

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uncertainty or external shocks in the outputs and inputs, so that to reduce the bias of

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underestimation of efficiency and acquire more robust results. The new SNDEA model

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can significantly reduce the limitations of traditional DEA models and should be recommended to employ in the airline performance evaluation. Lastly, as the empirical results shows, there are heterogeneous behaviors among the Chinese airlines, different

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policies should be implemented for different groups during the civil aviation reform and

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regulations.

It is quite different from the work of Fan et al. (2014) and Cui and Li (2015, 2016, 2017a, 2017b), who just take account of one of them in the research. However,

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more research is still needed to further confirm the present conclusion in this paper. This paper just focus on the major Chinese airlines. When more airline companies

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implications.

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outside of China are put into analysis for comparison, it will provide more policy

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Estimate the efficiency of 13 major Chinese airlines from 2006-2014.

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A stochastic network DEA to account for flight delays and CO2 emissions.

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Chinese airlines are almost more “flight efficient” than “network efficient”.

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Network efficiency is impacted by governance, age and network span.

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Flight efficiency is impacted by governance and previous M&A.

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