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Transportation Research Part E 80 (2015) 20–38 Contents lists available at ScienceDirect Transportation Research Part E journal homepage: www.elsevier .com/locate / t re Competition and efficiency in the Italian airport system: new insights from a conditional nonparametric frontier analysis http://dx.doi.org/10.1016/j.tre.2015.05.003 1366-5545/� 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +39 0677274105. E-mail addresses: dalfonso@dis.uniroma1.it (T. D’Alfonso), daraio@dis.uniroma1.it (C. Daraio), nastasi@dis.uniroma1.it (A. Nastasi). 1 Tel.: +39 0677274068. 2 Tel.: +39 0677274093. 3 According to Poole (2013), which reports data on Global Airport Privatizations happened in 2011–2012, airport privatization has taken place in Asia, Australia and New Zealand, Latin America and the Caribbean where major airports have been privatized. Several planned airport privatizations in Spain and Greece were put on hold due to the depressed state of these European economies, still recovering from the financial crises. See Albalate et a for further details on partial privatization in the European airport industry. 4 The global airport benchmarking study by the Air Transport Research Society (ATRS, 2013) reports that non-aviation revenues account for 40–80 revenues for 50 major airports around the world in 2012. Tiziana D’Alfonso ⇑, Cinzia Daraio 1, Alberto Nastasi 2 Department of Computer, Control and Management Engineering ‘‘Antonio Ruberti’’, Sapienza Università di Roma, Via Ariosto 25, 00185 Rome, Italy a r t i c l e i n f o a b s t r a c t Article history: Received 2 February 2015 Received in revised form 30 April 2015 Accepted 1 May 2015 Available online 2 June 2015 Keywords: Italian airports Competition DEA Conditional efficiency Two-stage analysis We analyse the effect of competition on technical efficiency of Italian airports by applying a novel conditional nonparametric frontier analysis for the first time to the airport industry. We find that competition affects mostly the frontier of best performers, whilst airports that are lagging behind are less influenced. A novel two stage approach shows that, on average, competition has a negative impact on technical efficiency. We estimate a measure of pure efficiency, whitened from the main effect of the competition, whose distribution has a bi-modal shape, indicating the existence of two differently managed groups of airports. � 2015 Elsevier Ltd. All rights reserved. 1. Introduction The nature of the airport industry has changed over the last few decades. The deregulation process has led to increased competition among carriers, decreased average fares, increased frequency, and new route services (D’Alfonso and Nastasi, 2014; Fu and Oum, 2014; InterVISTAS, 2006). Some new entrant airlines have been exploiting the opportunities offered by secondary airports (Thompson, 2002). Moreover, the low-cost business model, which has a relevant driver in airport costs, has enabled low-cost carriers (LCCs) to shop around airports (Dresner et al., 1996; Pels et al., 2009). In parallel, a major strategic action taken by full service carriers has involved the proliferation of alliances, both international and domestic, which is resulting in a more concentrated airline industry and new routes services (Czerny and Zhang, 2012; Jiang et al., 2015). The development of high-speed rail (HSR), interregional bus transportation and transport networks is an additional factor influencing competition among airports (OECD, 2009). Finally, many airports have been involved in a privatization3 and a commercialization process: non-aeronautical revenues have been growing to the point that they have become the main income source for many airports (Bracaglia et al., 2014; Graham, 2009).4 In this context, airports, many of which were treated as public service organizations directly controlled by government administrations, have increasingly been restructured to attract Europe, Portugal, l. (2014) % of total http://crossmark.crossref.org/dialog/?doi=10.1016/j.tre.2015.05.003&domain=pdf http://dx.doi.org/10.1016/j.tre.2015.05.003 mailto:dalfonso@dis.uniroma1.it mailto:daraio@dis.uniroma1.it mailto:nastasi@dis.uniroma1.it http://dx.doi.org/10.1016/j.tre.2015.05.003 http://www.sciencedirect.com/science/journal/13665545 http://www.elsevier.com/locate/tre T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 21 private investments, search for new sources of revenues and attract (competing) full service or low-cost carriers (Starkie, 2002). As a result, competition among airports has been growing and this has questioned the natural monopoly approach to regulation and has led to a much more competitive outlook on the part of airport managers. In this scenario, airport benchmarking is of increasing concern and source of debate for both academics and practi- tioners (Liebert and Niemeier, 2013). The comparison of decision-making units (DMUs), such as airports, has become a popular tool to enhance their efficiency and make airports survive in a competitive environment. Most of the efficiency analysis literature has focused on the estimation of the production frontier that provides the benchmark against which airports are evaluated. There has been a growing number of studies using Data Envelopment Analysis (DEA) to bench- mark airport efficiency (Adler et al., 2013; Arocena and Oliveros, 2012; Barros and Dieke, 2007, 2008; Curi et al., 2010, 2011; Fung et al., 2008; Gillen and Lall, 1997, 2001; Fernandes and Pacheco, 2002, 2003; Gitto and Mancuso, 2012; Wanke, 2012a, 2012b; Wanke, 2013). Some others analyse airport efficiency using stochastic frontier models (SFA) (Abrate and Erbetta, 2010; Assaf et al., 2012; Barros, 2008a, 2008b; Martin-Cejas, 2002; Oum et al., 2008; Scotti et al., 2012; Yoshida and Fujimoto, 2004; Yu et al., 2008). Other papers compare the DEA model with the SFA model (Pels et al., 2001, 2003). Some studies use total factor productivity measures (Hooper and Hensher, 1997). Recent studies are concerned with the explanation of efficiency differentials by including in the analysis environmental factors that, unlike the inputs and the outputs, cannot be controlled by the airport but may influence the production process. This is particularly relevant for the airport industry, characterized by regulatory constraints (Rate of Return, Price Cap, Single Till or Dual till), downstream market structure (high or low airline concentration), type of competitive envi- ronment (competitive versus monopolistic airports, HSR pressure), type of ownership (private, public, mixed) and so on. Generally speaking, these factors can be included in the analysis as exogenous variables that can help to detect and analyse influential factors which may affect airports’ productivity patterns, to explain the (in-)efficiency differentials, as well as to improve policy decisions. However, whilst lot of studies have analysed the impact of ownership form on efficiency (e.g., Barros and Dieke, 2007; Cruz and Marques, 2011; Lin and Hong, 2006; Oum et al., 2006, 2008), as well the effect of the regulation regime (e.g., Bel and Fageda, 2010; Marques and Brochado, 2008; Oum et al., 2004), few works have examined the relationship between efficiency and the level of competition from nearby airports. In fact, whether competition positively affects airport efficiency is still an open question. Dmitry (2009) builds an index of competition based on overlapping catchment areas into a SFA model and finds a positive effect of competition pressure on efficiency for a sample of European airports. Dmitry (2010) extends the results with a multi-tier model of competition and finds that the effect of competition on airport efficiency can be either positive or negative depending on a distance tier. Adler and Liebert (2014) investigate the combined impact of ownership form, economic regulation and competition on airport cost efficiency. They find that, under relatively non-competitiveairports’ productivity improvements. Assaf (2009) shows that large airports are generally more technically efficient and have less operational wastage than small air- ports, and that location could contribute to the efficiency differences. In this direction, Ha et al. (2013) show that the T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 37 hinterland per capita gross domestic product and the hinterland population are positively correlated with the efficiency scores, indicating that the hinterland with strong air travel demand may help bring up the corresponding airport efficiency, which is also consistent with the result of Chang et al. (2013). In this paper, we have provided an illustrative analysis on the impact of competition, analysing the ratios of conditional and unconditional efficiency scores and reporting illustrative examples based on the three dimensional plots which provide useful insights. This is a descriptive empirical evidence, following other contributions which have applied the conditional efficiency analysis in this field (e.g., Marques et al., 2014). The obtained results are preliminary and have an illustrative pur- pose, that is to show how the recently developed conditional nonparametric approach proposed by Badin et al. (2012) may apply to the airport sector. However, a bigger dataset would be useful in order to provide more formal statistical based anal- ysis, which could be implemented along the lines of Daraio and Simar (2014), and stronger results for median airports. Finally, extending the analysis to the evaluation of airports’ performances in a period of several years would also be inter- esting, in order to measure the efficiency change that the industry experimented through years. Acknowledgments We thank the editor, Jiuh-Biing Sheu, and three anonymous referees for insightful comments. We are grateful to partic- ipants to the 2012 Italian Management Engineering Association (AIIG) Annual Conference held in Matera (Italy) and the 2013 Air Transport Research Society (ATRS) Annual Conference held in Bergamo (Italy) for valuable suggestions. 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Furthermore, under potential regional or hub airport competition, economic regulation inhibits airports of any ownership form from operating and pricing efficiently. Ha et al. (2013) measure Chinese airport efficiency and investigate the impact of competition among airports (from other modes of transportation, such as HSR), measured by means of a dummy variable that indicates whether there is another airport competing significantly with the airport in concern (whether there is HSR operation near a sample airport). They find that competition among airports and competition from substitutable transportation modes always have a positive impact on efficiency scores of airports.5 Scotti et al. (2012) suggest an index of competition between two airports on the basis of the share of population living in the overlapped region of the airports’ catchment areas. Using a multi-output SFA model in a parametric framework, the authors find that the intensity of competition has a negative impact on Italian airports’ efficiency in the period 2005–2008. The aim of this paper is to fill this gap by assessing the impact of competition on airport efficiency, that is, we evaluate whether airports are more efficient when the intensity of competition is higher. We take into account the fact that airports differently located may be subject to heterogeneous environmental conditions. We ground on the recently introduced con- ditional efficiency measures (Daraio and Simar, 2005, 2007a, 2007b), which have rapidly developed into a useful tool to explore the impact of exogenous factors on the performance of DMUs in a nonparametric framework. In particular, this methodology does not rely on the separability condition between the input–output space and the space of the external fac- tors, and hence it does not assume that these factors have no influence on the frontier of the best practice. Moreover, it is based on partial frontier non-parametric methods which are more robust than traditional full frontier non-parametric meth- ods because they are less sensitive to extreme data and outliers. Finally, they do not suffer from the problem of the curse of dimensionality, which requires big datasets to provide estimates of a reasonable precision (for more details see Daraio and Simar, 2007a). To the best of our knowledge, Marques et al. (2014) is the only paper which has applied conditional efficiency mea- sures for the assessment of the efficiency of the airport sector by using the probabilistic approach proposed by Daraio and Simar (2005).6 In our paper, we make a methodological step further – with respect to Marques et al. (2014) – in the application of conditional efficiency measures to the airport sector. Indeed, we implement for the first time the new 5 See also Chi-Lok and Zhang (2009) for similar conclusions. 6 In that paper, the influence of the operational environment on airport efficiency is examined in a sample of 141 international airports. The conclusions show that the operational environment indeed matters and that privatization, regulation, traffic transfer and the existence of a dominant carrier have a positive effect on efficiency, whereas aeronautical revenues influence it negatively. However, the impact of competition on airport efficiency is not investigated. 22 T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 methodology proposed by Badin et al. (2012) which extends the Daraio and Simar (2005) approach. On the one hand, by applying this new method, we are able to disentangle the impact of competition on the production process in its two com- ponents: impact on the efficient frontier (that is the airports which are most efficient and hence are located on the efficient boundary of the production set) and the impact on the distribution of the efficiency scores. Indeed, external factors (i.e., conditional variables that cannot be controlled by the airport but may influence the production process) may affect either the efficient frontier or the distribution of the inefficiencies (that is the probability of being more or less far from the efficient frontier), or they can affect both. We investigate these interrelationships from an individual and a global perspective. On the other hand, for the first time, this paper examines the impact of competition on the airport production process by applying a new two-stage type approach – introduced by Badin et al. (2012) and detailed in Badin et al. (2014) – which avoids the flaws of the traditional two-stage analysis. This novel approach allows us to have a measure of inefficiency whitened from the main effect of the external factor, and permits to rank airports according to their managerial efficiency, even if they face hetero- geneous environmental conditions. Indeed, ranking airports according to the conditional measures can always be done but it is unfair, because airports face different external conditions, e.g., the different degree of competition, that it may make it easier (or harder) to reach the frontier. We focus on the Italian airport system. The Italian case has been investigated in the empirical literature. In particular, Barros and Dieke (2007, 2008) apply a Simar and Wilson (2007) two-stage procedure and find that hub, private and north parameters increase efficiency. Abrate and Erbetta (2010) extend the findings by Barros and Dieke and point out the exis- tence of low levels of efficiency among Italian airports. Curi et al. (2010), by using a Simar and Wilson (2007) two-stage approach, show that airports with a majority public holding are on average more efficient and the presence of two hubs is source of inefficiency. A bootstrapped DEA procedure is used by Curi et al. (2011) to estimate technical efficiency of Italian airports. They find that the airport dimension does not allow for operational efficiency advantages; on the other hand, it allows for financial efficiency advantages for the case of hubs and disadvantages for the case of the smallest airports. Moreover, the type(s) of concession agreement(s) might be considered as an important source of technical efficiency differ- entials. Gitto and Mancuso (2012) find that a significant technological regress has been experienced and highlight the exis- tence of a productivity gap between airports located in the North-central part of the country and those located in the South.7 However, to the best of our knowledge, Scotti et al. (2012) is the only study which investigates, by using a parametric stochastic approach, how the intensity of competition among Italian airports affects their technical efficiency. Thus, research on this issue still lacks maturity. The paper is organized as follows. In Section 2 we present the data, the input and output variables used in the analysis. Section 3 describes the methodology, while Section 4 discusses the results. Section 5 concludes the paper. 2. Data The Italian system consists of 45 airports open to commercial aviation8 (ENAC, 2011). Rome Fiumicino (FCO) and Milan Malpensa (MPX) are the most important intercontinental hubs, where traffic exceeds, on average, 10 millions passengers per year. The remaining airports can be classified as medium sized airports, providing further long haul and domestic routes, and regional airports providing a limited number of international and domestic connections. In many cases, management companies of airports open to commercial aviation hold a total concession agreement: the company gets all of the airport revenues for 40 years and is responsible for the infrastructure maintenance and develop- ment.9 This is the case of the hub airports, Rome Fiumicino or Milano Malpensa, and some other medium sized airports like Catania Fontanarossa or Napoli Capodichino. In some other cases, mainly for medium sized airports, management companies of airports hold a partial concession agreement, where the State collects revenues from runways andparking – and is respon- sible for their maintenance and development – while the airport management company gets revenues from infrastructures involving passenger and freight terminals. This is the case of airports such as Brescia Montichiari, Trapani or Treviso. Finally, in some cases, mainly for regional airports like Cuneo Levaldigi or Lamezia T. Sant’Eufemia, a precaria concession agreement is hold by the airport companies, who manage only the passenger and freight terminals, receiving only the revenue that is related to commercial activities inside the terminals. Data related to passenger traffic show a robust growth for Italian airports in 2010 – comparing to 2009 – driven by good results at Rome Fiumicino and Milan Malpensa, in addition to the excellent results of several medium sized airports such as Bari (+20.3%), Bologna (+15.3%), Brindisi (+47.2%), Genoa (+13.3%), Lamezia Terme (+16.4%), Trapani (+57.4%) and Treviso (+21%) (ICCSAI FactBook, 2011). In many cases, the growth has been driven by low-cost airlines: with respect to previous years, the growth has been achieved in airports other than those which have historically supported the development of 7 More recently, some other studies have included quality indicators in Italian airport efficiency benchmarking: overall perception of comfort level, percentage of delayed flights, waiting time in queues at check-in, baggage reclaim time, and mishandled bags (De Nicola et al., 2013) or environmental externalities such as noise and local air pollution (Martini et al., 2013a, 2013b). However, the impact of quality indicators on airport efficiency is out of our scope. 8 The whole Italian system consists of 113 airports – 11 exclusively open to military services and 102 to civil services. 9 This is a form of Public–Private Partnership (PPP) where two different models can be found: institutionalized PPP or a typical contractual regime, such as the concession arrangements. See Cruz and Marques (2011) for further details on recent developments in privatizations. Through a case study approach, the authors establish a comparative analysis of different PPP arrangements models used for airport management. 0 5 10 15 20 25 30 35 Passengers traffic Population GDP Source: Our elaborations on data provided by ENAC – Ente Nazionale Aviazione Civile (National Civil Aviation Authority). a Percentage per geographic area b Index number Italy=100 North-Ovest North-East North-Centre Centre South Islands Passengers Traffica 29.8 9.6 8.9 30.2 8.3 13.2 Populationa 25.8 12.5 14.8 14.8 20.9 11.2 GDPa 30.9 14.5 16.8 15.9 13.5 7.7 Pax/Firmb 26.9 18.2 13.7 59.6 10.9 35.1 Fig. 1. Disaggregation by geographical area of passenger traffic, population, GDP and passengers per firm in 2010. T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 23 low-cost carriers in Italy, such as Bergamo Orio al Serio, Pisa and Rome Ciampino. The analysis of traffic statistics with respect to some socio-economic indicators (Fig. 1) shows that there is a great heterogeneity among Italian airports: passen- ger traffic is concentrated in the North-Ovest part and in the Centre, where the most important intercontinental hubs are located. However, some differentiations arise when looking at the number of passengers per inhabitant, per GDP or per firm located in the area. Preliminary considerations about the level of competition among Italian airports arise analysing the percentage of com- peting Available Seats Kilometers (ASKs) and the share of competing routes (ICCSAI Factbook, 2011). The former represents the number of ASKs – related to the airport total offer – for which there is an alternative route serving any airport in the destination catchment area, either in terms of same destination airport or in terms of same destination area. The latter con- siders airport routes for which at least one alternative route exists in the airport catchment areas – within 100 km of the departure or arrival airport. Fig. 2 shows data relating to the biggest 34 Italian airports in 2010: the share of competing routes exceeds 60% in the case of Roma Fiumicino, Venezia Marco Polo, Bologna G. Marconi, among others, and 90% in the case of Catania Fontanarossa or Cagliari Elmas. The model for Italian airports is estimated using annual data on 34 airports for 2010, consisting of 16 airports located in the northern part of Italy, 7 in the centre and 12 in the southern part including islands. Small airports have been excluded due to the lack of economic data. Table 1 shows the characteristics of the airports included in the sample, with respect to the type of concession agreement and the total offer in terms of passengers, amount of cargo and movements. Traffic and technical airside information have been collected from ENAC (National Civil Aviation Association) and balance sheets of airport management companies. The data have been integrated with data on direct and indirect competition pro- vided by ICCSAI – International Center for Competitive Studies in the Aviation Industry. Table 2 presents inputs and outputs analysed in selected previous studies on the Italian airport system. According to this analysis, input variables used in this paper include: airport area (m2), number of runways, number of passenger terminals, number of gates, number of check-in counters and number of employees.10 With respect to the outputs, three variables have been collected: number of passengers, amount of cargo (tons) and the number of aircraft movements. This choice is consistent with other previous studies, e.g., Curi et al. (2011), Scotti et al. (2012) on the Italian airport system, Wanke (2012a) on Brazilian airports, Martin and Roman (2001) on Spanish airports and Sarkis (2000) on US airports. 10 In some cases, the cost of labour is preferred to the number of employees given the large and diversified use of part-time contracts in this sector (see Barros and Dieke, 2007, 2008). However, usually the problem concerning the existence of different employment formula can be overcome by referring to the full-time equivalent number of employees (Abrate and Erbetta, 2010), which is the case in this paper. See also Curi et al. (2011) and Scotti et al. (2012). Fig. 2. Percentage of competing ASKs and routes. Source: our elaboration on data from ICCSAI – International Center for Competitive Studies in the Aviation Industry. Table 1 Characteristics of Italian airports included in the sample, with respect to traffic, amount of cargo and number of movements. Source: Our elaborations on data provided by ICCSAI – International Center for Competitive Studies in the Aviation Industry. Total passengers Amount of cargo (tons) Number of movements Total concession 4259197.56 34066.61 50775.22 Partial concession 1665773.25 2918.38 19515.38 Precaria concession 370958.44 702.67 7256.44 24 T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 2.1. Competition factor We include in the analysis a competition factor calculated as the share of routes in competition provided by ICCSAI (ICCSAI Factbook, 2011). The share of routes in competition considers airport routes for which at least one alternative route exists in related catchment areas (within 100 km of the departure or arrival airport). This number is expressed as a fraction of the total number of routes offered between the departure catchment area and the destination catchment area, including any offers of alternative airports that lie entirely within these areas. This index is a measure of indirect competition among air- ports, which is defined for a specific route offered from a specific airport, as the existence of alternative routes offered by nearby airports to nearby or identical destinations. An alternative departure airport is considered ‘‘close enough’’, on the basis of our indices, if it is located within 100 km of the original airport. The assumption is that distance is a good proxy for the extra travel time incurred bypassengers (which would be the optimal driving variable, but is itself not easily mea- surable) and therefore of accessibility. The same criterion applies to alternative destinations.11 We note that the problem of how to separate Origin–Destination passengers from transiting passengers might arise, since it is not a choice to fly to an airport – because it is a substitute – but rather because it links to a third airport. However, these considerations are out of concern in this paper, since Italian airports are not considered central to the international air transport network. Table 3 shows the top 20 European and Italian airports in terms of Betweenness. The Betweenness of an airport is defined as the number of minimal paths (any path between a pair of airports containing the minimum number of steps for that pair) passing through it. From this point of view, an airport is considered central to a network if it commonly serves as an intermediate node for routes to other airports. The second indicator, Essential 11 For instance, consider a generic air connection between Rome Fiumicino and London Heathrow airports. The relevant market is the Rome–London route. Rome Ciampino airport lies less than 100 km away from Rome Fiumicino, and London Stansted is less than 100 km from London Heathrow. Hence, the Rome Fiumicino–London Heathrow connection is subject to indirect competition from the Rome Ciampino–London Stansted. The assumption related to the choice of the relevant threshold, has been used in literature by: Adler and Liebert (2014) in the definition of airport regional competition (the number of commercial airports with at least 150,000 passengers per annum within a catchment area of 100 km around the airport); Malighetti et al. (2007) and Scotti et al. (2012), in the definition of the airport competition index; Malighetti et al. (2008) in the definition of the Betweenness and centrality of an airport within a network. Finally, the radius of the catchment area has been also defined in line with Bel and Fageda (2010). Nevertheless, this assumption may have some limits, since fixed-radius techniques do not take into account neither the distribution of people living in the areas around the airport nor the real access time to reach it nor determinants of the demand for airport services in the area (Gosling, 2003). Table 2 Inputs and outputs used in previous studies on the efficiency of the Italian airport system. Selected studies Methods Units Input Output Abrate and Erbetta (2010) Input distance function 26 Italian airport 2000– 2005 Labour costs Number of passengers Soft cost Handling revenues Runway length Commercial revenues Apron size Total airport area Barros and Dieke (2007) DEA 31 Italian airports, 2001–2003 Labour costs Number of planes Operational costs excluding labour costs Number of passengers Capital invested Commercial sales Amount of cargo Aeronautical sales Handling receipts Barros and Dieke (2008) DEA and two-stage bootstrapping 31 Italian airports, 2001–2003 Labour costs Number of planes Operational costs excluding labour costs Number of passengers Capital invested Commercial sales Amount of cargo Aeronautical sales Handling receipts Curi et al. (2010) DEA and truncated regression model 36 Italian airports, 2001–2003 Labour costs Number of planes Operational costs excluding labour costs Number of passengers Capital invested Commercial sales Amount of cargo Aeronautical sales Handling receipts Curi et al. (2011) DEA and two-stage bootstrapping 18 Italian airport 2000– 2004 Employees Number of movements Apron size Number of passengers Number of runway Amount of cargo Gitto and Mancuso (2012) DEA-Malmquist with bootstrap 28 Italian airport 2000– 2006 Number of movements Labour costs Number of passengers Soft costs Amount of cargo Capital invested Aeronautical revenues Non-aeronautical revenues Scotti et al. (2012) SFA – two-stage analysis 38 Italian airport 2005– 2008 Runway capacity Yearly numbers of aircraft movementsNumber of aircraft parking positions Passengers movements Terminal area Amount of cargo Number of check-in desks Number of baggage claims Number of employees T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 25 Betweenness, counts the number of node pairs for which all (possibly the only) minimum paths pass through the airport in question. Without this airport, either the destination cannot be reached anymore, or it can be reached only through a longer path via other intermediary airports. Table 3 also shows the ratio between Essential Betweenness and Betweenness, an indi- cator of how ‘‘indispensable’’ an airport is for transiting paths. Rome Fiumicino is only ranked 19th, while all other Italian airport present a very low potential to serve as an intermediate stop. Table 4 summarizes and defines all the variables used in this paper, while Table 5 provides some descriptive statistics. 3. Methodology Within the nonparametric literature, DEA has been widely applied for efficiency estimation and benchmarking. In this framework, explaining inefficiency by looking for external or environmental factors has gained an increasing attention in recent frontier analysis studies. The performance of economic producers is often affected by external or environmental factors that may influence the pro- duction process – being responsible for differences in the performances of the DMUs – but, unlike the inputs and the outputs, are not under the control of production units: quality indicators, regulatory constraints, type of environment (competitive versus monopolistic), type of ownership (private–public or domestic–foreign), environmental factors (conditions of the envi- ronment) and so on. Generally speaking, these factors can be included in the model as exogenous variables and can help explaining the efficiency differentials, as well as improving policy. At this aim, the nonparametric literature on this topic has focused on three main approaches: the one-stage approach, the two-stage approach (including the semi-parametric bootstrap-based approach) and the conditional nonparametric approach. Table 3 The potential of European and Italian airport to serve as an intermediate stop. Source: ICCSAI – International Center for Competitive Studies in the Aviation Industry. Rank Airport Betweenness (A) % Connections Essential betweenness (B) Impact (B/A) (%) Rank ITA Rank EU Airport Betweenness (A) % Connections Essential betweenness (B) Impact (B/A) (%) 1 London Gatwick 62,364 25.50 2480 3.98 1 19 Roma Fiumicino 34,600 14.15 1084 3.13 2 Amsterdam- Schipol 57,646 23.57 1518 2.63 2 32 Milano Malpensa 22,930 9.38 196 0.85 3 Dublin 55,482 22.69 2234 4.03 3 57 Pisa Galilei 12,276 5.02 10 0.08 4 Stockolm- Arlanda 50,876 20.81 18,754 38.86 4 59 Olbia Costa Smeralda 11,682 4.78 88 0.75 5 Palma De Mallorca 49,948 20.43 1088 2.18 5 65 Bergamo Orio Al Serio 10,004 4.09 64 0.64 6 London Stansted 49,112 20.08 4194 8.54 6 66 Venezia Marco Polo 9762 4.00 8 0.08 7 Paris Charles De Gaulle 47,318 19.35 768 1.62 7 76 Bologna G. Marconi 8544 3.49 48 0.56 8 Munich F.J. Strauss 44,518 18.21 486 1.09 8 89 Palermo Punta Raisi 6568 2.69 6 0.09 9 Oslo 43,954 17.97 10,218 23.25 9 91 Milano Linate 6510 2.66 24 0.37 10 Dusseldorf 42,930 17.56 824 1.92 10 103 Verona 4998 2.04 44 0.88 11 Malaga 42,878 17.53 1598 3.73 11 107 Roma Ciampino 4794 1.96 – 0.00 12 Barcelona 42,784 17.50 352 0.82 12 109 Catania Fontanarossa 4554 1.86 12 0.26 13 Copenhagen 42,714 17.47 2934 6.87 13 111 Napoli Capodichino 4330 1.77 – 0.00 14 Edinburgh 38,564 15.77 1842 4.78 14 116 Cagliari Elmas 3602 1.47 54 1.50 15 Alicante 38,458 15.73 816 2.12 15 121 Torino 3290 1.35 22 0.67 16 Frankfurt 38,298 15.66 1196 3.12 16 126 Trapani Birgi 2762 1.09 32 1.20 17 Manchester 36,490 14.92 872 2.39 17 134 Treviso 2400 0.98 – 0.00 18 Madrid Barajas 35,908 14.68 712 1.98 18 143 Alghero Fertilia 1954 0.80 10 0.51 19 Rome Fiumicino 34,600 14.15 1084 3.13 19 146 Bari Palese 18220.75 2 0.11 20 Geneva-Cointrin 33,892 13.68 2968 8.82 20 170 Rimini Miramare 1224 0.50 4 0.33 26 T.D ’A lfonso et al./Transportation R esearch Part E 80 (2015) 20– 38 Table 4 List of inputs, outputs and competition variables. Variables Code Definition Inputs Airport area (m2) SED Total airport surface Number of runways NPI Number of runways dedicated to the landing and taking-off of planes Number of passenger terminals NTP Number of terminals excluding those dedicated to cargo handling Number of gates NGA Number of gates in all passengers terminals Number of check – in NCI Number of check-in counter desks in all passengers terminals Number of employees LAB Number of full-time equivalent employees directly employed Outputs Number of passengers APM Number of passengers arriving or departing and passengers stopping temporarily Amount of cargo (tons) CAR Amount of cargo in tons Number of movements ATM Number of plans that lands and takes-off from the airport Conditional variable Share of routes in competition SRC This indicator considers airport routes for which at least one alternative route exists in related catchment areas (within 100 km of the departure or arrival airport). This number is expressed as a fraction of the total number of routes offered between the departure catchment area and the destination catchment area, including any offers of alternative airports that lie entirely within these areas T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 27 The one-stage approach includes in the model the external factors either as freely disposable inputs or as undesired freely available outputs. The external variables are involved in the definition of the attainable set, but without being active in the optimization for the estimation of efficiency scores. In the two-stage approach, the nonparametric efficiency estimates obtained in a first stage are regressed in a second stage on covariates interpreted as environmental variables. Most studies using this approach employ in the second stage estimation either tobit regression or ordinary least squares. This approach has some serious inconveniences. In addition to problems related to the separability condition between the input–output space and the space of the external factors, the DEA estimates are by construction biased estimators of the true efficiency scores and they are serially correlated. Moreover, the error term in the second stage is correlated with the regressors, making standard approaches to inference invalid.12 In the nonparametric conditional approach, that is explained in details in the next section, conditional efficiency mea- sures are defined and estimated nonparametrically. Badin et al. (2012), in particular, show that the external factors can affect the attainable set of the production process and/or may impact on the distribution of the inefficiency scores. They propose a flexible regression of the conditional efficiencies on the explaining factors, which allows to estimate the residuals that may be interpreted as pure efficiency. This represents a technical efficiency level purified from the impact of the external or envi- ronmental factors and, therefore, it allows a fare ranking of units even when facing heterogeneous conditions. In this paper, we apply a nonparametric conditional approach (Badin et al., 2012) in an output oriented framework, con- sistently with previous works (Barros and Dieke, 2007, 2008; Curi et al., 2010, 2011; Gitto and Mancuso, 2012; Marques et al., 2014; Scotti et al., 2012). We are concerned with technical efficiency that might be attained by exploiting physical assets that do not easily change over a span of few years – like the number of runways, passenger terminals, gates, check-in counters, number of employees – in order to maximize outputs – like movements, passengers and cargo; therefore, we decided to adopt an output-oriented approach.13 Moreover, we assume variable returns to scale (VRS) because the sample dataset consists of airports of substantially different sizes ranging between 63.000 passengers at Bolzano airport, 1.4 million passengers at Alghero Airport, and more than 18 and 30 million passengers at Milano Malpensa and Rome Fiumicino airports. In doing so, we follow Adler and Liebert (2014).14 3.1. Marginal and conditional efficiency measures: local and global analysis DMUs transform resources (inputs) into products or services (outputs), but external or environmental conditions may affect this process. Let X 2 Rp þ denote the vector of inputs, Y 2 Rq þ the vector of outputs and Z 2 Rr the vector of environmen- tal factors that may influence by the process and the productivity patterns. 12 Simar and Wilson (2007) developed a semi-parametric bootstrap-based approach to overcome these problems and proposed two bootstrap-based algorithms to obtain valid, accurate inference in this framework. 13 An input orientation is consistent with the assumption that airport traffic volume is basically determined by airlines and thus it may be regarded as outside the control of managers. Nevertheless, airports now use different vertical agreements to internalize airlines’ choices (Fu et al., 2011). One example is the commercial revenue sharing contract: in this case, airports usually share their revenue from commercial activities with airlines, inducing them to bring in more passengers. This mechanism is based on the existence of a positive demand externality between aviation and non aviation services: since the demand for commercial services depend greatly on the passenger throughput of an airport, the airport charge may be reduced so as to induce a higher volume of passengers and increase the demand for concessions (Fu and Zhang, 2010; Zhang et al., 2010). If airlines were unable to benefit from concession sale activities at airports, they would ignore such a demand externality in making their decisions. 14 Similar considerations apply to the number of movement and tons of cargo. See also Table 4. Table 5 Descriptive statistics on inputs, outputs and competition variables. Variables Minimum Maximum Mean Std. deviation Inputs SED 164,000 15,900,000 3,101,828.57 3,012,989.42 NPI 1 4 1.37 0.65 NTP 1 4 1.11 0.53 NGA 2 91 14.77 19.17 NCI 2 430 44.29 82.58 LAB 28 3832 508 843 Outputs APM 62,259 36,337,523 3,899,824.14 6,725,579.64 CAR 0 432,674 26,238.69 77,968.00 ATM 2907 329,269 44,670.43 62,283.49 Conditional variable SRC 0.00 99.60 34.37 30.55 28 T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 The external factors Z may either affect the boundaries of the attainable set, or it may only affect the distribution of the inefficiencies inside the production set (that is the probability of being close or far from the efficient frontier may depend on Z), or it can affect both. Let consider a probabilistic model that generates the variables ðX;Y ; ZÞ, where P is the support of the joint distribution of ðX;Y; ZÞ. The conditional distribution of ðX;YÞ, given a particular value of Z, is described by 15 Rem holds, t Hðx; yjzÞ ¼ ProbðX 6 x; Y P yjZ ¼ zÞ; ð1Þ or any equivalent variation of it (e.g., the joint conditional density function or the joint conditional cumulative distribution function). The function Hðx; yjzÞ is simply the probability for a DMU operating at level ðx; yÞ to be dominated by DMUs facing the same environmental conditions Z, i.e., there exist DMUs that produce more outputs using less inputs with comparable levels of environmental variables. Given that ðZ ¼ zÞ, the range of possible combinations of inputs � outputs, W z, is the sup- port of Hðx; yjzÞ: W z ¼ fðx; yÞjx can produce yjZ ¼ zg: ð2Þ H(x, y) denotes the unconditional probability of being dominated, defined as: Hðx; yÞ ¼ Z Z Hðx; yjzÞf ZðzÞdz; ð3Þ having support W, that is the marginal (or unconditional) attainable set, i.e., which does not depend on Z, defined as15: W ¼ fðx; yÞjx can produce yg ¼ [z2ZW z: ð4Þ As described in Daraio and Simar (2007a), the two measuresHðx; yjzÞ and Hðx; yÞ allow us to define conditional and mar- ginal efficiency scores that can be estimated by nonparametric methods. Accordingly, the comparison of the conditional and unconditional efficiency scores can be used to investigate the impact of Z on the production process. The literature on efficiency analysis proposes several ways for measuring the distance of a DMU operating at the level ðx0;y0Þ to the efficient boundary of the attainable set. Radial distances (Farrell, 1957) are the most popular ones and they can be input or output oriented. In particular, in this paper, we use the output orientation, that is we consider the maximal radial expansion of the outputs to reach the efficient boundary, given the level of the inputs. From Daraio and Simar (2005), we know that under the assumption of free disposability of the inputs and of the outputs, these measures can be characterized by an appropriate probability function Hðx; yÞ, as defined above. We have, for the Farrell output measure of efficiency, kðx0;y0Þ ¼ supfk > 0jSYjXðky0jX 6 x0Þ > 0g; ð5Þ where SYjXðy0jX 6 x0Þ ¼ ProbðY P y0jX 6 x0Þ ¼ Hðx0;y0Þ=Hðx0;0Þ is the (nonstandard) conditional survival function of Y , non- standard because the condition is X 6 x0 and not X ¼ x0. If the DMU is facing environmental factors Z ¼ z0, then Daraio and Simar (2005) define the conditional Farrell output measure of efficiency as: kðx0;y0jz0Þ ¼ supfk > 0jðx0;ky0Þ 2 Wz0g; ð6Þ ¼ supfk > 0jSY jX;Zðky0jX 6 x0; Z ¼ z0Þ > 0g; ð7Þ where SY jX;Zðy0jX 6 x0; Z ¼ z0Þ ¼ ProbðY P y0jX 6 x0; Z ¼ z0Þ ¼ Hðx0;y0jz0Þ=Hðx0;0jz0Þ is the conditional survival function of Y , here we condition on X 6 x0 and Z ¼ z0. The individual efficiency scores kðx0;y0Þ and kðx0;y0jz0Þ have their usual ember that the joint support of the variables (X, Y, Z) is denoted by P. It is clear that, by construction, for all z 2 Z, Wz # W. If the separability condition he support of (X, Y) is not dependent of Z, equivalently Wz = W for all z 2 Z. T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 29 interpretation: they measure the radial feasible proportionate increase of output a DMU operating at the level ðx; yÞ should perform to reach the efficient boundary of W and W z respectively. In case the environmental factor Z has an effect on this boundary, the unconditional measure kðx0;y0Þ suffers from a lack of economic sounding, because, facing the external condi- tions z, this unit may not be able to reach the frontier of W, that may be quite different from the relevant one that is of W z. So, the conditional measure is more appropriate to evaluate the effort a DMU must exert to be considered efficient. In order to provide robust measures of efficiencies – robust to extreme data points or outliers – we also apply partial fron- tiers and the resulting partial efficiency scores16: while full frontiers are useful to investigate the local effect of Z on the shift of the efficient frontier, the partial frontiers are useful to analyse the impact of Z on the distribution of inefficiencies. In this case, we adopt order-a quantile frontiers, as defined in Daouia and Simar (2007). For any a 2 ð0;1� the order-a output efficiency score is defined as: 16 As e with re probabi a more require of the c 17 Not h, we a calculat kaðx0;y0Þ ¼ supfk > 0jSY jXðky0jX 6 x0Þ > 1� ag: ð8Þ Similarly, by conditioning on Z ¼ z0, the conditional order-a output efficiency score of ðx0; y0Þ is defined as: kaðx0;y0jz0Þ ¼ supfk > 0jSY jX;Zðky0jX 6 x0; Z ¼ z0Þ > 1� ag: ð9Þ In this framework, a value of a ¼ 0:5, which corresponds to the median frontier, provides complementary information on the effect of Z on the distribution of the inefficiencies. Nonparametric estimators of the conditional and unconditional efficiency scores are easy to obtain. For a DMU operating at level ðx0; y0Þ the estimation of the output efficiency score, i.e., k̂ðx0;y0Þ, is obtained, in the VRS case, by solving the following linear program: max c;k k s:t: ky0 6 Xn i¼1 ciyi x0 P Xn i¼1 cixi Xn i¼1 ci ¼ 1 k > 0; ci P 0 8i ¼ 1 . . . n ð10Þ Similarly we obtain the estimation of the output conditional efficiency score, i.e., k̂ðx0;y0jz0Þ, which can be computed solv- ing the linear program17: max c;k k s:t: ky0 6 X ijz�h6zo6zþh ciyi x0 P X ijz�h6zo6zþh cixi X ijz�h6zo6zþh ci ¼ 1 k > 0; h > 0; ci P 0 8i ¼ 1 . . . n ð11Þ The nonparametric partial frontier efficiency estimates are obtained by plugging the estimators bSYjX and bSY jX;Z , i.e.,bSYjXðy0jX 6 x0Þ and bSYjX;Zðy0jX 6 x0; Z ¼ z0Þ, in the expressions (8) and (9) defining the partial efficiency measures. For further details, the reader is referred to Badin et al. (2012). The local analysis of the individual ratios may also be of interest: the local effect of Z on the reachable frontier for a unit ðx; yÞ can be measured independently of the inherent inefficiency of the unit ðx; yÞ. Let consider ROðx; yjzÞ ¼ kðx; yjzÞ=kðx; yÞ 6 1, that is the ratio of the radial distances of ðx; yÞ to the two frontiers. The inherent level of inefficiency of the unit ðx; yÞ is cleaned off, in the following sense: xtensively illustrated in Daraio and Simar (2007a), partial nonparametric frontiers have advantages and drawbacks. On the one hand, they are robust spect to extreme values and outliers; they do not share the curse of dimensionality which is common to most nonparametric estimators; they rely on a listic formulation that allows us to introduce external factors in an effective way. Moreover, the value of a can be used as a trimming parameter to make realistic comparison taking out the a% desired level of robustness. On the other hand, the implementation of the partial nonparametric approach s the selection of a level of robustness (the value of a) and of a ‘‘smoothing parameter’’, i.e., h, which is the bandwidth, that is needed for the computation onditional efficiency scores. e that this provides a local convex attainable set, local in the sense of conditional on the external factors. Concerning the computation of the bandwidth pplied the Badin et al. (2010) approach. In particular, in the Appendix of that paper the Matlab program for the implementation of the bandwidth ion is reported. 18 The 19 Bad comple 20 Mo 30 T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 ROðx; yjzÞ ¼ kðx; yjzÞ kðx; yÞ ¼ kykkðx; yjzÞ kykkðx; yÞ ¼ ky@;zx k ky@xk ; ð12Þ where kyk is the modulus (Euclidean norm) of y and ky@xk and ky@;zx k are the projections of ðx; yÞ on the efficient frontiers (unconditional and conditional, respectively), along the ray y and orthogonally to x. Clearly ky@xk and ky@;zx k are both indepen- dent from the inherent inefficiency of the unit ðx; yÞ. Hence, the ratio measures the shift of the frontier in the output direc- tion, due to the particular value of z, along the ray y and for an input level x, whatever being the modulus of y. In the same fashion we calculate the ratios corresponding to partial score, e.g., RO;aðx; yjzÞ ¼ kaðx; yjzÞ=kaðx; yÞ 6 1. Consistent estimators of the ratios are directly obtained by plugging the nonparametric estimators of the efficiency derived as described earlier, i.e., k̂ðx0;y0Þ and k̂ðx0;y0jz0Þ. So we have bROðx; yjzÞ ¼ k̂ðx; yjzÞ=k̂ðx; yÞ.18 3.2. Second-stage regression and pure efficiency The aim of this section is to estimate the pure efficiency of DMUs through a novel two-stage approach, which allows us to purify kðx; yjZ ¼ zÞ from the impact of Z. Indeed, ranking firms according to the conditional measures kðx; yjZ ¼ zÞ can always be done but it is unfair, because firms face different external conditions that it may make it easier (or harder) to reach the frontier. To avoid this problem, we analyse the average behaviour of kðx; yjzÞ as a function of z, that is we analyse the expected value EðkðX;YjZÞjZ ¼ zÞ as a function of z. We use a location scale non-parametric regression, defining lðzÞ ¼ EðkðX;Y jZÞjZ ¼ zÞ and the variance r2ðzÞ ¼ VðkðX;Y jZÞjZ ¼ zÞ such that: kðX;Y jZ ¼ zÞ ¼ lðzÞ þ rðzÞe;ð13Þ where EðejZ ¼ zÞ ¼ 0 and VðejZ ¼ zÞ ¼ 1. Whereas lðzÞmeasures the average effect of z on the efficiency, rðzÞ provides addi- tional information on the dispersion of the efficiency distribution as a function of z. Several flexible nonparametric estima- tors of lðzÞ and rðzÞ could be applied; the reader is referred to Badin et al. (2012) for more details. Analysing the residuals, for a particular given unit ðx; y; zÞ, we can define the error term e as: e ¼ kðx; yjzÞ � lðzÞ rðzÞ : ð14Þ The error term e can be viewed as the part of the conditional efficiency score not explained by Z. If e and Z do not show a strong correlation, this quantity can be interpreted as a pure efficiency measure of the unit ðx; yÞ. If e and Z show some cor- relation, still the quantity defined in (14) can be used as a proxy for measuring the pure efficiency, since it is the remaining part of the conditional efficiency after removing the location and scale effect due to Z. Then, e can be used as a measure of pure efficiency because it depends only upon the managers’ ability and not upon the external factors (ZÞ. This approach allows us to purify the conditional efficiency scores from the effects of Z. In this way, we are able to compare and rank heterogeneous firms among them because the main effects of the external conditions have been eliminated. In particular, a large value of e indicates a unit which has poor performance, even after eliminating the main effect of the environmental factors. A small value, on the contrary, indicates very good managerial performance of the firm ðx; y; zÞ. Extreme (unexpected) values of e would also warn for potential outliers. 4. Results DEA and conditional DEA with VRS are applied in an output oriented framework. The model for Italian airports is esti- mated using annual data on 34 airports for 2010. As described in Section 4, the advantage of the partial frontier estimates and the related efficiency scores, i.e., kaðx; yjzÞ, is that they are less influenced by extreme values and hence more robust to outliers. Moreover, they are not affected by the well known ‘‘curse of dimensionality’’ shared by most nonparametric esti- mators (Daraio and Simar, 2007a). Under those circumstances, a dataset of 34 observations, although small, can be used to draw conclusions. We perform a local analysis on the effect of competition on technical efficiency of Italian airports and a second stage regression of the conditional efficiency scores on the competition factor which allows us to estimate the managerial efficiency scores.19 In particular, we provide an illustrative analysis on the impact of competition, analysing the ratios of conditional and unconditional efficiency scores and reporting illustrative examples based on the three dimensional plots which provide useful insights. This is a descriptive empirical evidence, following other contributions which have applied the conditional efficiency analysis in this field (e.g., Marques et al., 2014),20 as well as in other sectors (e.g., Mastromarco and Simar, 2014). reader is referred to Badin et al. (2012) for further details. in et al. (2010) report – in the Appendix – the Matlab code to perform the analysis presented in the paper. Some works are in progress for the tion of a user friendly toolbox, CONDEFF, that will be available free of charge (see Badin et al., 2014). re formal statistical based analysis could be implemented along the lines of Daraio and Simar (2014) but would require more data. 20 40 60 80 2.5 3 3.5 4 4.5 0.2 0.4 0.6 0.8 1 xz R O (x ,y |z ) Fig. 3. Full frontier ratios against Input Factor (X) and Competition (Z). T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 31 4.1. Factors on inputs, outputs and competition variables Due to the high dimensionality of the problem (6 inputs, 3 outputs, and 1 environmental factor) with the limited sample used here (34 units), we first reduce the dimension in the input � output � external factor space by using the methodology suggested in Daraio and Simar (2007a). Indeed the curse of dimensionality implies that working in smaller dimensions tends to provide better estimates of the frontier. Moreover, if we are able to reduce the frontier estimation at the simplest situation (one input one output) it is also possible to provide graphical bi-dimensional illustrations of the estimated efficient frontier. In particular, we divide each input by its mean (to be ‘‘unit’’ free) and replace the 6 scaled inputs by their best (non-centred) linear combination, defined as IF, i.e., Inputs Factor. By doing so, we check that: (i) we do not lose much information; and (ii) the resulting univariate input factor is highly correlated with the 6 original inputs. From a mathematical point of view, we are looking for a vector a 2 R6+ such that the projection of the (scaled) input data matrix X on the vector a represents the data matrix X (in terms of minimizing the sum of squares of the residuals). The vector of the 6 projections is determined by the resulting input factor IF ¼ Xa ¼ a1x1 þ a2x2 þ a3x3 þ a4x4 þ a5x5 þ a6x6, where X: (n � 6) is the (scaled) inputs data matrix. It can be shown that the optimal direction vector a is the first eigenvector of the matrix XTX corresponding to its largest eigenvalue e1. Note that, we are in a different situation than in the case of Principal Component Analysis (PCA): in this case, the data have not been centred, so that the eigenvalues do not represent the factors’ variances. Eigenvalues are rather the ‘‘inertia’’ (or moment of the second order) of the factor. Therefore, the ratio e1=ðe1 þ e2 þ e3 þ e4 þ e5 þ e6Þ indicates the percentage of inertia which is explained by this first factor. When this ratio is high (close to 1), it indicates that most of the information contained in the original six-dimensional input data matrix X is well summarized by the first factor IF. Correlation between IF and x1; . . . ; x6 indicates also how well this new one-dimensional variable represents the original ones. We obtain: 21 Con paper w extreme that bas IF ¼ 0:34x1 þ 0:58x2 þ 0:58x3 þ 0:29x4 þ 0:24x5 þ 0:25x6: ð15Þ We follow the same procedure with the 3 outputs. The results are: OF ¼ 0:61y1 þ 0:47y2 þ 0:64y3; ð16Þ where OF stands for Outputs Factor. IF explains 87.6% of total inertia of original data, while OF explains 89.2% of total inertia of original data. To be consistent with previous notation we use, in what follows, X;Y instead of IF;OF. 4.2. Local analysis of the effect of competition on technical efficiency of Italian airports We are in an output oriented framework. As stated in Section 3.1, the full frontier ratios bROðxi; yijziÞ are useful to inves- tigate the local effect of competition on the shift of the efficient frontier, whilst the partial frontier ratios, bRO;aðxi; yijziÞ, with a ¼ 0:5 (corresponding to the median),21 are useful to analyse the impact of competition on the distribution of inefficiencies. Fig. 3 illustrates a three dimensional plot of the full frontier ratios against inputs and competition, i.e., X and Z, whilst Fig. 4 shows a three dimensional plot of the partial frontier ratios against X and Z. cerning the selection of the a value for the robust estimation of the full efficient frontier (that is the frontier which envelops all the data point), in this e computed the partial frontier ratios with a ¼ 0:95 to check if some outliers might mask the impact of Z (we leave out of the comparison the 5% of most points). We find that, even if there are some extreme points, they do not affect the detection of the impact of Z. This analysis is different with respect to ed on a ¼ 0:5 that is reported for providing an illustrative view on the impact on the median of the distribution. 20 40 60 80 2.5 3 3.5 4 4.5 0.5 1 1.5 2 3 3.5 x z 2.5 R O , α (x ,y |z ) Fig. 4. Partial frontier ratios against Input Factor (X) and Competition (Z). (a ¼ 0:5, i.e., median of the distribution of efficiencies). 10 20 30 40 5060 70 80 90 0.2 0.4 0.6 0.8 1 Marginal Effect of X on the Efficient (full) frontier values of x R O (x ,y |z ) 2.5 3 3.5 4 4.5 0.2 0.4 0.6 0.8 1 Marginal Effect of Z on the Efficient (full) frontier values of z R O (x ,y |z ) Fig. 5. Marginal effect of X and Competition (Z) on the full efficient frontier. 32 T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 Without being able to rotate the three-dimensional figures, we have an idea of what happens complementing Figs. 3 and 4 with their two marginal views. Fig. 5 shows the ratios bROðxi; yijziÞ as a function of the input (top panel) and the competition factor (bottom panel) respectively, i.e., the marginal effect of inputs and of competition on the efficient full frontier. Similarly, Fig. 6 shows the ratios bRO;aðxi; yijziÞ as a function of X and Z respectively, i.e., the marginal effect of the input (top panel) and competition factor (bottom panel) on the distribution of inefficiency with respect to the median frontier. By inspecting the three dimensional plots (see Figs. 3 and 4), it can be easily seen that the input factor does not play any role on the full frontier levels nor on the partial frontier levels. This is also confirmed looking at the marginal effects (see top panels of Figs. 5 and 6). On the contrary, the competition factor Z has a positive impact on the full frontier ratios, i.e., there is an increasing (logarithmic) pattern of the full frontier ratios when the competition factor Z increases (see Fig. 5, bottom panel). The impact is heterogeneous and much less severe – showing a decreasing pattern – on the partial frontier ratios and so on the distribution of inefficiency scores (see Fig. 6, bottom panel). In other words, competition can be seen as a free disposable input for best performers: when competition is taken into account in assessing technical efficiency of airports, the output that can be produced given a fixed amount of inputs increases. On the contrary, the efficiency of airports that are on the median distribution (lagging behind the efficient frontier) is not affected by competition. Analysing the Italian airport system in 2010, we conclude that competition has an impact on the efficient frontier of air- ports, while it has an heterogeneous and lower impact on the distribution of the inefficiencies. 4.3. Second stage analysis on the conditional efficiency scores According to the procedure described in Section 3.2, we regress the estimated conditional efficiency scores against the competition factor, Z. We only remind here that the nonparametric model is: 10 20 30 40 50 60 70 80 90 1 2 3 Marginal Effect of X on the distribution of inefficiency values of x R O , α (x ,y |z ) 2.5 3 3.5 4 4.5 1 2 3 Marginal Effect of Z on the distribution of inefficiency values of z R O , α (x ,y |z ) Fig. 6. Marginal effect of X and Competition (Z) on the distribution of inefficiency (a ¼ 0:5, i.e. median of the distribution of efficiencies). 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2nd-stage regression Z values Lo g C on di tio na l E ff ic ie nc ie s μ(z) σ(z) data points Fig. 7. Effect of Competition (Z) on conditional efficiencies. 22 The T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 33 k̂ðX;YjZ ¼ zÞ ¼ l̂ðzÞ þ r̂ðzÞe where l̂ðzÞ characterizes the average behaviour of the conditional efficiency scores as a function of z, and r̂ðzÞ allows some heteroskedasticity. The residual e can be interpreted as a whitened version of the conditional efficiency where the influence of Z has been eliminated from kðX;Y jZ ¼ zÞ. Fig. 7 illustrates the results for the full-conditional efficiency estimates as a function of Z.22 We find that there is a local variable effect of competition (Z) on the average conditional scores. In particular, it appears that Z has a negative effect on k̂ðX;Y jZ ¼ zÞ, showing an adverse effect of competition on the technical efficiency of Italian airports. This seems to imply that airports which face higher competitive pressure are less efficient. In contrast, in the Italian sys- tem, an airport that is closer to the local monopoly model (i.e., those airports facing a lower degree of competition) has an efficient utilization of its inputs. The results are consistent with those of Scotti et al. (2012), who find that Italian airports confronted with higher levels of competition have lower technical efficiency, and Dmitry (2010), who provides evidence on negative effects of competition on the efficiency of a sample of European airports. In fact, the debate focusing on the rela- tionship between airport efficiency and competition is still open. Chi-Lok and Zhang (2009), Dmitry (2009) and Ha et al. analysis has been done in logs but we obtained a similar shape for the picture in original units. -2 -1 0 1 2 3 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Kernel Density of estimated PureEff Values of PureEff Fig. 8. Nonparametric density of estimated pure efficiencies of Italian airports (year 2010). 0 10 20 30 40 50 60 70 80 90 100 -1 -0.5 0 0.5 1 1.5 2 2.5 Values of Zi V al ue s of P ur eE ff Fig. 9. Correlation between Competition (Z) and PureEff. 34 T. D’Alfonso et al. / Transportation Research Part E 80 (2015) 20–38 (2013) show, for instance, a positive effect of competition on airport infrastructure efficiency. Adler and Liebert (2014) sug- gest that private, regulated airports are more efficient under monopolistic conditions whereas pure public and private air- ports operate equally efficiently given potential local, regional and gateway competition. Furthermore, ex-ante regulation at all airports located in a competitive environment is unnecessary and generates inefficiency of the order of 15%, which rises substantially at purely public airports. In this direction, future research would require substantially more data to permit an improved analysis of the combined effect of competition and regulation form (Bel and Fageda, 2010; Marques and Barros, 2010; Marques and Brochado, 2008; Oum et al., 2004) as well as the type of ownership and concession agreement, e.g., fully-private, public or public–private partnership (Barros and Dieke, 2007; Lin and Hong, 2006; Oum et al., 2006, 2008). This is extremely important if we are to be able to analyse the airport industry and provide sensible recommendations for future development. Fig. 8 shows a kernel nonparametric density distribution of estimated pure efficiencies of Italian airports, êi. These êi rep- resent pure efficiencies and have been computed eliminating the impact of the competing factor Z from the conditional effi- ciency score. Thus, we can compare the performance of airports, facing different competing environments, on the basis of their pure attitude, without taking into account the influence of the competitive environment faced. Interestingly, we observe a bi-modal distribution of the pure efficiency of Italian airports and a special attention should be devoted to inves- tigate on its generating process.23 23 This is beyond the scope of this work. Table 6 Conditional efficiency scores (1/CondEff) and pure efficiency (PureEff) of Italian airports (year 2010). DMU PureEff 1/CondEff Genova G. Colombo �0.855 1.000 Roma Fiumicino �0.851 1.000 Venezia Marco Polo �0.838 1.000 Bologna G. Marconi �0.836 1.000 Cagliari Elmas �0.831 1.000 Napoli Capodichino �0.788 1.000 Milano Malpensa �0.786 1.000 Ancona Falconara �0.782 1.000 Parma �0.779 1.000 Crotone �0.776 1.000 Perugia Sant’Egidio �0.771 1.000 Firenze Peretola �0.769 1.000 Trieste Ronchi dei Leg. �0.768 1.000 Bergamo Orio al Serio �0.768 1.000 Olbia Costa Smeralda �0.768 1.000 Treviso �0.767 1.000 Catania Fontanarossa �0.735 0.953 Roma Ciampino �0.642 0.899 Milano Linate �0.543 0.839 Bari Palese �0.293 0.626 Torino �0.279 0.670 Verona 0.049 0.510 Pescara Liberi 0.057 0.450 Alghero Fertilia 0.374 0.333 Pisa Galilei 0.738 0.419 Forlì Luigi Ridolfi0.764 0.253 Palermo Punta Raisi 0.771 0.438 Lamezia T. Sant’Eufemia 0.825 0.491 Trapani Birgi 1.003 0.237 Brindisi Casale 1.103 0.167 Rimini Miramare 1.438 0.174 Bolzano 1.755 0.090 Reggio Cal. Tito Menniti 1.840 0.092 Cuneo Levaldigi 2.332 0.057 Table 7 Comparison with respect to localization, type of concession agreement and size of conditional efficiency scores (1/CondEff) and pure efficiency (PureEff) of Italian airports (year 2010, average value). Effect PureEff 1/CondEff Effect of localization Centre �0.458 0.746 North �0.074 0.656 South 0.457 0.457 Effect of concession agreement Total �0.302 0.711 Partial �0.118 0.629 Partial precaria 0.393 0.448 Effect of size >5 millions �0.768 0.974 1 5 millions of passengers), such as Catania Fontanarossa, Bergamo Orio al Serio, Roma Fiumicino or Milano Linate, result more efficient given their level of competition. On the contrary, small airports (5 millions of passengers), such as Catania Fontanarossa, Bergamo Orio al Serio, Roma Fiumicino or Milano Linate, result more efficient given their level of competition. On the contrary, small airports (
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