Does privatization make Brazilian airports more efficient?

Does priva za on make Brazilian airports more efficient? A priva zação torna os aeroportos brasileiros mais eficientes? Fernanda Silva Toledo1, Viviane Adriano Falcão2, Flávia de Castro Camioto3, Paulo Afonso Lopes da Silva4 1Federal University of Rio de Janeiro, Rio de Janeiro – Brazil, fernanda.toledo@coc.ufrj.br University of Pernambuco, Pernambuco – Brazil, viviane.afalcao@ufpe.br 3Federal University of Triângulo Mineiro, Minas Gerais– Brazil, flaviacamioto@yahoo.com.br 4Military Ins3tute of Engineering, Rio de Janeiro – Brazil, pauloafonsolopes@uol.com.br 2Federal Recebido: 14 de fevereiro de 2020 Aceito para publicação: 5 de fevereiro de 2021 Publicado: 25 de agosto de 2021 Editor de área: Alexandre Gomes de Barros Keywords: Airports Priva3za3on. Data Analysis Envelopment. Tobit Regression. Airport efficiency. SBM. Airport Infrastructure. Palavras-chave: Concessões. Aeroportos. DEA. SBM. Regressão Tobit. DOI:10.14295/transportes.v29i2.2304 TRANSPORTES | ISSN: 2237-1346 ABSTRACT Airport concessions to private management began in Brazil in 2011 to address infrastructure bo9lenecks and the need for investments. Produc3vity improvements a;er priva3za3on need to be measured and efficiency gains can help to iden3fy strategic points where to intervene both in current and upcoming concessions. However, previous studies have applied neither the Slacks-Based Measure Data Analysis Envelopment models nor the second stage Tobit regression to evaluate airport efficiency, especially in the context of Brazilian airport priva3za3on. The objec3ve of this study is to verify if priva3za3on contributes to improving Brazilian airports' produc3ve efficiency compared with public airports, using variable slacks and iden3fying new socio-economic variables that may influence the produc3ve efficiency index. A two-stage SBM-DEA approach found that only 40% of the sample among 28 airports are efficient, evidencing poor management overall, and the slacks show the sectors that need most a9en3on and investments. Based on the produc3ve process and the sample evaluated, the study concludes that priva3za3on of Brazilian airports did not improve their produc3on efficiency. A revision of the contracts in the first round of concessions is suggested, as contractual obliga3on may result in lower produc3on efficiency. RESUMO As concessões dos aeroportos à gestão privada começaram no Brasil em 2011 para resolver gargalos de infraestrutura e a necessidade de inves3mentos. Melhorias de produ3vidade após a priva3zação precisam ser medidas e os ganhos de eficiência podem ajudar a iden3ficar pontos estratégicos em que intervir tanto nas concessões atuais quanto nas futuras. É notório na literatura estudos que aplicaram DEA para medir a eficiência aeroportuária. No entanto, estudos anteriores não aplicaram os modelos SlacksBased Measure Data Analysis Envelopment nem a regressão Tobit de segundo estágio para avaliar a eficiência aeroportuária, especialmente no contexto da priva3zação de aeroportos brasileiros. O obje3vo deste estudo é verificar se a priva3zação contribui para melhorar a eficiência produ3va dos aeroportos brasileiros em relação aos aeroportos públicos, u3lizando folgas nas variáveis e iden3ficando novas variáveis socioeconômicas que podem influenciar o índice de eficiência produ3va. Uma abordagem SBMDEA em dois estágios constatou que apenas 40% da amostra, dentre 28 aeroportos, são eficientes, evidenciando uma má gestão no geral, e as folgas mostram os setores que precisam de mais atenção e inves3mentos. Com base no processo produ3vo e na amostra avaliada, o estudo conclui que a priva3zação dos aeroportos brasileiros não melhorou sua eficiência produ3va. Sugere-se a revisão dos contratos da primeira rodada de concessões, pois a obrigatoriedade contratual pode resultar em menor eficiência produ3va. Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 1. INTRODUCTION Brazilian air transportation has experienced a fast growth in demand in the last few decades, which led to higher demand for infrastructure. In this scenario, the Brazilian government transferred in concession some of the main Brazilian airports to the private sector to accelerate and allow for modernization of facilities, investments in infrastructure, and technological innovations. The investments required would improve productivity and service quality (INFRAERO, 2016), but the main problem is airport operational inef,iciency and how the effect of privatization is evaluated in these terms. Airport concessions started in Brazil in 2011. To date, 22 airports have been privatized and 22 public airports are in the National Program for Concessions to be transferred in 2021. The performance assessment is crucial to evaluate the demand adequacy and to evaluate the results of the current concessions and the upcoming ones in airport productivity considering that privatization of airports in Brazil was carried out following the concession model. Although the main purpose to privatize an airport is to improve its ef,iciency, there is no evidence of performance bene,its (Graham, 2011). In the case of Brazil, the concessions are the result of restrictions on public investments considering a greater ,lexibility of private investments. The objective of this paper is to verify if Brazilian airport concessions lead to the improvement of the production ef,iciency of the privatized airports, evaluating their ef,iciency index and variable slacks and considering their operational aspects. The Slack-Based Measurement (SBM) model is used to measure ef,iciency scores and identify ways for the inef,icient units to reach the ef,iciency frontier based on the slacks in each variable, to obtain the ranking position of the airports granted in concession, the country overall scenario and the in,luence of macro and socioeconomic variables in the ef,iciency in a second stage Tobit regression. Ownership of airports is one of the most studied factors to explain ef,iciency, but a consensus has not been found yet (Iyer and Jain, 2019). Thus, research is still required to clarify this effect (Carlucci et al., 2018; Lo Storto, 2018). On the other hand, considering the economic crisis in Brazil since 2014, despite optimistic demand projections for large investments – mandated by a concession contract –losses are to be expected in the upcoming years. Therefore, the investments should be directed to areas that need them the most, so the existing resources can be used optimally. Data Envelopment Analysis (DEA) is a technique to measure ef,iciency through a production frontier based on linear programming. It has the advantage of computing multiple inputs and outputs at the same time, measuring a relative ef,iciency among samples. Several studies have applied DEA to evaluate the operational ef,iciency of airports in Argentina (Barros, 2008), Asia and Paci,ic (Tsui et al., 2014), China (Jiang et al., 2015), Italy (Carlucci et al., 2018), United States (Bazargan and Vasigh, 2003), and Turkey (O@ rkcü et al., 2016). Generally, studies are limited to mathematical models with either constant or variable returns to scale using only input or output orientation. Some studies include airports’ details and characteristics to develop a new model (Bazargan and Vasigh, 2003; Chang et al., 2016; Olfat et al., 2016), which is the main dif,iculty in DEA application, or use distance minimization methods (Suzuki et al., 2012). The Slack-Based Measure (SBM-DEA) was used in a weighted form in European and Australian airports, and in a fuzzy extension of SBM dynamic network approach (Olfat et al., 2016) to study the variation of ef,iciency determined by variables related to internal airport functions which affect community and are related to passengers. TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 This paper focusses on the slacks of each variable, besides the ef,iciency index, to identify points to improve management. This proposition aims to ful,ill the research gap (Iyer and Jain, 2019) on the application of ef,iciency scores to improve airport performance because the use of performance assessment by airport authorities to monitor individual airports was not fully explored (Iyer and Jain, 2019). Brazilian airports have been studied using bootstrap DEA (developed by Simar and Wilson, 1998) to measure their operational ef,iciency (Pé rico et al., 2017), or network DEA (Wanke, 2013), but no studies have used slack-based measure, especially in the context of privatization. Fernandes and Pacheco (2018) applied the Malmquist Index and variable returns to scale (BCC) output-oriented model to evaluate the performance of public airports under INFRAERO management. In this paper, we used SBM-DEA with simultaneous orientation (both to input and output), which allowed the model to consider both the product increase and the reduction of the resources to form the ef,icient frontier, an advantageous analysis within the current context of economic and political crisis in Brazil. As far as the authors know, the SBM model (developed by Tone, 2001) has not yet been applied to the airport infrastructure in the non-oriented form. Furthermore, this model, as non-radial (Constant and Mello, 2017), permits to identify the optimal increase or decrease in each variable separately, to achieve the ef,iciency frontier and not a simple change of equal proportion of all the inputs or outputs, as proposed by classic models, like CCR (Charnes, Cooper and Rhodes, 1978) and BCC (Banker, Charnes and Cooper, 1984). Therefore, this paper applies an existing technique in a new way and aims to throw some new light on their applicability in the airport infrastructure domain. So, it is possible to identify which aspects make an airport inef,icient, not only looking at the input or output, but also to both. Measuring airport ef,iciency is important for both the companies and the Brazilian State to understand the requirements and saturation of each airport. Furthermore, it is substantial to evaluate the airports granted in concessions in their role of ful,illing required investments and maintaining the airport operational ef,iciency. A second stage analysis is an option to explain DEA results, as the environmental aspects do not take part in the score and the results are deterministic among the variables used. The second stage approach usually applies a simple regression, truncated regression, or bootstrapping. In this study, we used an Inverted Frontier (Soares de Mello et al., 2008) to increase discrimination in the ef,iciency frontier and a Tobit regression to investigate the effects of macroeconomic and socioeconomic variables. The use of a model that proposes a reduction of resources to reach ef,iciency, does not mean to encourage the reduction of investments in airports. Therefore, this article aims to identify the underused sectors that could have their capacity used in an optimum way and adapt resources from different activities to a new section or saturated sector. This paper focus on productive ef,iciency especially throughout an economic crisis, when the resources are scarce, an approach applicable to a broad range of settings and organizations. Also, the study aims to spread the knowledge of using this method in a non-obvious way. TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 2. DATA ENVELOPMENT ANALYSIS Data Envelopment Analysis (DEA) is a technique used to measure the productivity of business units, proposed by Charnes et al. (1978) and Banker et al. (1984), both based on Farrel (1957). DEA is based on non-parametric linear programming, therefore there is no prede,ined function of the input-output-ef,iciency relationship. This technique comprises data of each variable to establish an ef,iciency frontier composed by units in which it is not possible to bene,it one more characteristic without demeaning the others, called the Pareto-Ef,icient (Wanke et al., 2009, Camioto et al., 2016). This technique identi,ies the most ef,icient units in a sample and computes a measure of inef,iciency for the other Decision-Making Units (DMUs). Therefore, it does not ,ind an absolute ef,iciency but compares the productive units to each other considering the inputs used and the products generated (Wanke et al., 2009; Falcã o and Correia, 2012). The constant returns to scale (CCR) model, based on the contributions of Charles, Cooper, and Rhodes (1978), generates a frontier of constant return to scale. Therefore, any input variation produces a proportional variation of outputs. If there are n DMUs under analysis, each consumes a variable quantity of each input to generate different outputs. The result is ℎ , a number between 0 and 1 that represents the relative ef,iciency of each DMU. The model can be output-oriented when the objective is to maximize outputs for each DMU without changing the current inputs, or input-oriented to minimize the resources until the current outputs are not reduced (Mariano et al., 2015). In that case, for the CCR model, the orientation does not in,luence the measure of ef,iciency since the return of scale is constant. The Banker, Charles, and Cooper (1984) model (BCC) uses a more realistic premise based on a convexity constant ∑ = 1, which modi,ies the straight line of the frontier to a convex cone (WANKE et al., 2009). For that reason, the BCC model replaces the proportionality of the CCR inducing a convex frontier, which allows variable returns to scale (Mariano et al., 2015). 2.1. DEA Model – SBM With a close connection between CCR and BCC models, the SBM (Slack-Based Measure) model deals directly with an excess of input and output de,icits of the decision-making units. First proposed by Tone (2001), SBM-DEA allows simultaneous orientation to input and output, minimizing the distances to reach the ef,iciency frontier. Tone (2001) also revealed that, unlike the CCR model, the DEA-SBM model seeks the maximum virtual pro,it, with results based on radial measures. The comparison between the two models reveals that the SBM generally computes lower ef,iciency values, due to the existence of slacks and the fact that all variables contribute to the ef,iciency evaluation, even at lower levels. Other models allow null weights to exclude the contribution of variables that would lead to a decrease in the scalar ef,iciency (Tone, 2001). The following expressions identify the SBM model with variable returns according to Tone (2001): = − (1/ ) / (1) Subject to: / TRANSPORTES | ISSN: 2237-1346 + =1 (2) Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 . . ! ! + − − . , in which − . + = 0, $%& ' = 1,2 … = 0, $%& ' = 1,2 … * ! = ≥0+ >0 : : DMU k participation in the target DMU under analysis; Quantity of input j of the DMU k; : : Quantity of output i of the DMU k; Quantity of input j of the DMU under analysis; : Quantity of output i of the DMU under analysis; Number of units under evaluation; Number of outputs; Number of inputs; Slacks variable of output i; Slacks variable of input j; /: *: : : : (3) (4) (5) : Linear adjustment variable. In addition to measuring the relative ef,iciency of DMUs, this method also allows us to compute the slacks, which express by how much each DMU should increase the value of each variable to achieve ef,iciency. Thus, slacks indicate how far the current performance of a DMU is from its ideal performance for each variable, where the ideal performance is a target symbolized by a virtual DMU (benchmark), located at the ef,iciency frontier and calculated according to the expressions: 01&2+ 3 45 = '0 − , $%& = 1, 2, 3 … (6) 01&2+ 75 45 = 0 + $%& = 1, 2, 3 … * (7) Given that the relative slack is based both on the current and the ideal performances, it is expressed by the percentage of improvement required of each variable. 2.2. Tobit Regression Econometric models with censored error or truncated terms are normally used for dependent variables that have speci,ic limits, as is the case of the ef,iciency index whose value is comprised between 0 and 1. The Tobit model devised by Tobin (1958) is normally used in these situations, where the dependent variable has a limiting value such as zero. In this case, the Tobit stochastic model may be expressed by the equations (McDonald & Mof,itt, 1980): (8) 8 = 8 9 + 58 if :8 9 + 58 > 0 = 0 if : 9 + 5 ≤ 0 , (9) 8 8 8 t = 1, 2, ..., N, where N represents the number of observations, 8 the dependent variable, :8 is a vector of independent variables, 9 is a coef,icient vector and 58 is an independently distributed error term, which is assumed to be normally distributed with zero mean and variance < = . The model assumes a stochastic index equal 8 9 + 58 only when the result is positive, which certi,ies it as an unobserved latent variable. The use of this model may indicate the relationship between macroeconomic and socioeconomic variables that in,luence airport ef,iciency. 2.3. DEA APPLIED TO AIRPORTS The Data Envelopment Analysis (DEA) technique has been applied to airports by several studies TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 such as Barros (2008) to estimate the technical ef,iciency of airports impacted by a reduction of 50% of air traf,ic in Argentina from 2003 to 2007, a period of an intense economic crisis. Despite the economic crisis and visible changes in output variables in the years under review, some airports remained ef,icient. Relatively ef,icient airports started the period as inef,icient but recovered in the end to achieve their best practices, showing that the larger airports remained immune to the crisis, while smaller and regional ones were more sensitive to it. Tsui et al. (2014) investigated the operational ef,iciency of 21 airports in Asia and in the Paci,ic, with data covering the years from 2002 to 2011, in a window analysis. They suggested that the variation in airport ef,iciency could be explained by the percentage of international passengers’ traf,ic, the number of airport employees, dominant airlines, and per capita GDP growth. Jiang et al. (2015) conducted a study covering 9 Chinese airports. On the coastal region of the country, the density of civil airports reached one per city, but large-scale airports were supersaturated while medium and minor ones operated in de,icit, suggesting an airport alliance as a solution to the survival of the medium and small ones. The operational and ,inancial performance of Italian airports were studied by Barros and Dieke (2011) using data from 2001 to 2003 and a BCC model to identify management skills. As a result, the performance of airports under private initiative had higher rates. Merkert and Mangia (2014) focused on the cost ef,iciency of Italian and Norwegian airports. For regional and small airports, the level of competitiveness impacts airport ef,iciency, while airports in full concession are more ef,icient than airports with partial concessions. For the US airports grouped by size, Bazargan and Vasigh (2003) used ,inancial and operational data to identify inef,icient airports that are dominated by the most ef,icient ones. O@ rkcü et al. (2016) assessed the operational ef,iciency of Turkish airports, they identi,ied a decline in ef,iciency due to the increase in the physical capacity of airports and the non-re,lection of this increase on passenger and cargo traf,ic. However, there is progress in terms of technology. Moreover, factors such as hours of operation and percentage of international traf,ic explain the variations in inef,iciency. Carlucci et al. (2018) analyzed total ef,iciency, technical and scale ef,iciency using CCR and BCC models with data of 34 Italian regional airports from 2006 to 2016. The research also investigated the impact of other factors on ef,iciency and economic sustainability. Their ,indings reveal that airport size, cargo traf,ic, and low-cost carriers are signi,icant variables, together with privatization and deregulation which can bene,it airport ef,iciency. All those studies were based on the CCR and BCC models; therefore, with a single orientation to input or output. In this work, however, we used a slacks-based model with simultaneous orientation. Suzuki et al. (2012) developed a Distance Friction Minimization (DFM) model as a generalization and extension of the BCC model to obtain a more appropriate con,iguration of ef,iciency improvement projection for airports in Europe. DFM does not consider ,ixing irregular or immutable factors, such as airport runways, as these variables will not change in the short term. Generally, the new methodology indicates a way to reach the ef,iciency frontier that less affects the airport, with minor reductions of inputs. Lo Storto (2018) developed a DEA model using meta-frontier concept. Most of public-private partnership (PPP) airports showed higher technical ef,iciency using data of 45 Italian airports in 2012. The inputs were terminal size, apron size, total runway length, number of employees, TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 labor cost and soft opening costs, while the outputs were aviation and non-aviation revenues. Data of passengers, cargo, and movements were used either as input or as output in different model speci,ications. Three models encompass technical ef,iciency and revenue ef,iciency, both output-oriented and cost ef,iciency as input-oriented. Adler and Liebert (2014) used a weighted additive slack-based model, input-oriented, considering that managers only have control over operational costs and not on capacities, with minor control over traf,ic volume in general. The DEA variables included staff costs, operating costs, runway capacity, number of passengers, cargo handled, aircraft movements, and non-aeronautical revenue. For second-stage analysis, they applied a linear regression model, in a robust among – cluster approach, with data combination that concerns ownership structure, economic regulation, level of the potential hub, and local competition. They analyzed the variation of ef,iciency scores from 1998 to 2007. The policy implications suggested it is better to privatize the airport completely to avoid con,licting objectives in case of partial privatization. Olfat et al. (2016) used an extension of fuzzy dynamic network SBM DEA with a threepronged approach to add internal functions to the model, factors related to either to passengers, or the community itself. The analysis was made for each node of the airport, community, and passengers in the network of 28 airports. Although using an extension of the slack-based model, this study does not focus on the slacks but only the measured score to compare ef,iciencies. Chang et al. (2016) developed a dynamic network DEA framework in the context of US airport ,inancing. The model investigates the substitutability between the two major sources of ,inancing: Passenger Facility Charge (PFC) and Airport Improvement Program (AIP), considering an input-oriented network SBM model, proposed by Tone and Tsutsui (2010, 2014) using data of 41 airports from 2009 until 2013. The authors used ,light delays as undesirable output, and the following variables: delay (in minutes), cargo handled, enplanement, aircraft operations as outputs and labor cost, material cost, net asset, promotion, PFC, while AIP funds were used as inputs. This study proves that U.S. airports can substitute PFC for AIP funds in the proportion of 8-35% of the current AIP, but this substitution negatively correlates to productive ef,iciency. The network DEA has recent applications in airport analysis (Yu, 2010; Lozano et al., 2013; Wanke, 2013). Yu (2010) applied this method in Taiwanese airports using production and service in the ,irst and second stages respectively, considering number of employees, runway area, apron area and terminal area as inputs. Intermediate variables were runway capacity and terminal capacity, while the outputs were aircraft movements, passenger movement, and cargo volume. Operational ef,iciency is divided into production and service ef,iciency, and the latter is divided into landside and airside, considering multi-stages in series and in parallel with environmental factors in the analysis. Lozano et al. (2013) focused on Spanish airports, with aircraft movement for the ,irst stage and aircraft loading for the second stage. Similarly, Wanke (2013) used the two-stage production process of the Brazilian airports, where the ,irst stage represents their physical infrastructure, and the second stage concerns ,light consolidation. Airport privatization and concession to private management were addressed in Brazil by Fernandes and Pacheco (2018). DEA BCC output-oriented was applied to 60 main airports under INFRAERO administration between 2009 and 2015 – three years before and after concessions began in 2012. The objective was to evaluate the situation of INFRAERO before and after TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 concessions and not the performance of airports transferred. Airports under INFRAERO administration showed a loss of market share and declining performance, therefore the company was unable to improve performance in this scenario. Other methods can be used to assess ef,iciency. Oum et al.(2006) used a variable factor productivity measure to compute productivity for the major airports in Asia-Paci,ic, Europe, and North America in 2001-2003. Contrary to expectations, they found strong evidence that airports owned and managed by a mixed enterprise with a government-owned majority is less ef,icient than 100% of airports publicly owned and operated. Oum et al. (2008) applied Stochastic Frontier to explore the relationship between the airport ownership form and its cost ef,iciency using panel data of the world’s major airports. According to results, a 100% governmental ownership is better than mixed ownership with government majority. These results suggest that countries that consider privatization should keep the majority share of the airport’s ownership. 3. METHODOLOGY The DEA technique is used to measure productive ef,iciency in this study. The Decision-Making Units (DMU) in this research are Brazilian international airports located in state capitals, in addition to other airports with a high movement of passengers and airports that are being considered for concessioning, resulting in a sample of 28 Brazilian airports. The application of a DEA variant with simultaneous orientation allows the most ef,icient DMU, which is the one that produces more with fewer resources, an advantageous concept for ef,iciency measures. However, the use of this model in,luences the choice of variables in the study and how the proposed variations will be interpreted. An input-oriented model is the best ,it to data related to debts and expenses, but this data lacks availability for this sample in a standardized way. Variables related to physical space and infrastructure can identify underused capacities that demand attention, saturated sectors, or even a capacity surplus that can serve a future growth in demand. According to Gillen (2011), the usual metrics of ef,iciency do not contribute to information on the optimal size of the airport or a range of optimal sizes, as airports may achieve cost ef,iciency but may be operating on the wrong scale. In general, the most recurrent variables used as inputs in DEA applications are, in order of frequency: passenger terminal area, number of apron positions, runway length, number of employees, apron area, runway area, parking lots, number of the baggage carousel. The most common outputs are: the number of passengers, the amount of cargo handled, aircraft movement, mail, aeronautical revenue, and non-aeronautical revenue. Based on the availability of data for the selected airports, the literature review, and the correlation between inputs and outputs, the following input variables were assigned: • Passenger terminal area (m²) (Tsui, 2014): total passenger terminal area, including the area for commercial activities. The total value is the sum of passenger terminal areas when an airport has multiple passenger terminals. • Total runway length (m) (Jiang et al., 2015): represents the sum of the runway length when an airport has more than one runway. • Apron area (m²) (Lo Storto, 2018): the total apron area includes the passenger apron area, the cargo apron, general aviation apron area, and other aircraft parking areas. TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 Inputs related to airport infrastructure are important because airport infrastructure expansion is often impossible in the short-term (Innes and Doucet, 1990), therefore their usage should be optimal and meet future demand. The apron area variable is a general indication to apron capacity, as the number of positions depends on the aircraft size, moreover the total runway length variable can incorporate the number of runways. Outputs considered in this study were: • Passenger movement: total passengers carried (embarked and disembarked) in national and international, regular and non-regular ,lights; • Cargo handling (t): total air cargo and mail loaded, unloaded and in transit for national and international, regular and non-regular ,lights; • Aircraft movements: the total number of aircraft arrivals and departures, national and international, regular and non-regular ,lights. Passenger movement is an important factor for airport managers (Suzuki et al., 2003). The outputs selected are the three most recurrent outputs in DEA studies and they are proxies for revenues from aeronautical activities. The number of variables for a DEA approach is limited depending on the number of DMUs, following the equation (Cooper et al., 2001): > ≥ *1 {* >, 3 (* + >)} (20) Data from 28 airports in 2015 were collected from INFRAERO reports and reports of airports granted to concession, available on their of,icial websites. With the collected data, it was possible to evaluate the correlation among the variables. Using the stepwise method (Wagner and Shimshak, 2007), it was determined that the variable ‘aircraft movement’ did not interfere in the airport ef,iciency ranking and the score was considered constant without this variable. This variable is also strongly correlated to the other output variables. For these reasons, the variable ‘aircraft movement’ was removed from the model. After that, the SBM-DEA model with the formulation of Tone (2001) (equations 1 to 7) was applied to the remaining variables, to obtain the productive ef,iciency measures of each airport in the sample. Besides evaluating the ef,iciency score, this paper evaluated the slacks in each variable to enable the airport to reach its ef,iciency frontier. The Inverted Frontier was used as a discriminatory tool for the 100% ef,icient airports. It consists of a Frontier of Inef,iciency calculated by swapping inputs and outputs. A Composite Index is evaluated as the arithmetic mean between the ef,iciency of the standard frontier and (1 - ef,iciency on the Inverted frontier) (Soares de Mello et al., 2008). Thereafter, this Composite Index is normalized. This approach distinguishes the most ef,icient DMU among the ones that form the frontier. Afterwards, a second stage Tobit regression model was built to identify explanatory variables to the measured ef,iciency. The use of this method is more suitable than a simple OLS regression because DEA results are truncated from below at once. An innovative idea of this paper is to search for a socio-economic impact on the airport ef,iciency. This study evaluates the in,luence of the variables: population in the airport city, GDP per capita, airport site, HDI, Gini Index, and privatization on the ef,iciency index. The privatization variable was used as a dummy variable. Tobit estimation in the second stage outperforms parametric methods, estimating the impact of contextual variables on a production correspondence (Banker and Natarajan, 2008). For the Tobit econometric model, variables selected have the latest data available up to 2015: TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 • Population at the airport’s city (hab): 2013 estimated data by the Brazilian Institute of Geography and Statistics (IBGE); • Gross Domestic Product (GDP) per capita (millions R$): IBGE data from 2012; • Airport Site (million m²): represents the airport size, data from 2015; • Human Development Index (HDI) of the airport’s city: IBGE data from 2010; • Gini Index of the income per capita: measure of statistical dispersion that represents the income inequality, latest data available from 2010 at Datasus, processed by the Institute of Applied Economic Research (IPEA); • Privatization as a dummy variable: value 1 if done until 2015. The effects of socioeconomic variables and privatization on the airport's productive ef,iciency measure are investigated using the Tobit econometric model. The expected effects of these variables are to investigate the contribution of better socioeconomic indices in the city in the airport’s movement (output variables in the DEA model) and indirectly better use of idle facilities. Table 1 shows descriptive statistics for variables. Table 1 – Descriptive statistics of the variables Minimum Maximum Arithmetic mean First Quartile Median Third Quartile Standard Deviation Airport Site (m²) HDI Gini Index 63,760 805,400,000 75,343,483 435,913 1,415,000 6,157,500 GDP per capita (millions R$) 8.81 270.51 33.93 14.79 22.72 34.05 6,319 14,050,000,000 3,473,784,516 8,623,876 719,600,000 6,347,750,000 0.65 0.85 0.76 0.74 0.75 0.79 0.42 0.69 0.58 0.55 0.60 0.63 183,165,402 48.30 4,535,756,235 0.04 0.07 Terminal (m²) Runway (m) Apron Area (m²) Passengers Cargo (t) Population (hab) 1,982.00 280,000.00 48,299.02 7,710.00 23,094.01 65,871.75 1,701.00 7,180.00 3,368.80 2,375.00 2,842.50 3,890.75 17,550.00 712,895.00 132,970.60 41,457.00 66,979.00 148,755.75 347,592 38,985,000 6,619,573 1,478,310 3,283,223 8,528,072 577.00 76,084.00 45,083.96 3,036.50 11,040.50 39,142.00 63,920.44 1,471.15 157,921.26 8,487,727 93,769.58 4. RESULTS AND DISCUSSION Table 2 shows the airports included in the study. The application of the SBM variant model resulted in 11 ef,icient airports (39% of the sample): BSB, CNF, CGH, FLN, GRU, MAO, NVT, PVH, STM, THE, and VCP, considering all ,ive variables. Only four of the ef,icient airports were privatized until 2015 (BSB, GRU, CNF, VCP). FLN was privatized only in 2017, along with the inef,icient ones: POA, SSA, and FOR. Table 2 shows the ef,iciency measured by the SBM model for each airport, the relative slacks of each variable, their ranking, and the BCC output-oriented scores for comparison. Among the inef,icient units, only CGB, FOR and POA have a score higher than 50%. Based on the relative slacks, the model suggests a reduction in input variables and an output increase for each DMU to reach the ef,icient frontier. CGB has the highest ef,iciency score among the inef,icient ones and the model speci,ies that to achieve ef,iciency there should be an increase in cargo handling, although it is considered a benchmark for inef,icient DMUs relating to other variables. Regarding the entire sample, the mean relative slacks in inputs are almost insigni,icant compared to the mean relative slacks in outputs. Therefore, passenger and cargo movements are the variables with the highest slacks, indicating that these are the variables which need more attention. TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 The slack cannot be a ,ixed goal but an indication of the most detrimental performance variable, from a productive point of view. This consideration is important because the sample is not homogenous and the production processes may differ from each other, e.g. depending on the rate of commercial and aeronautical purposes. Thereby, there are probably no possibilities to decrease or increase variables indicated by slacks, limited to the current structure and economic scenario (Camioto et al., 2017). Table 2 – Airport efficiency and relative slacks for each variable Manaus (MAO) Navegantes (NVT) Teresina (THE) Viracopos (VCP) Confins (CNF) Florianópolis (FLN) Brasília (BSB) Guarulhos (GRU) Porto Velho (PVH) Congonhas (CGH) Santarém (STM) Várzea Grande (CGB) Fortaleza (FOR) Porto Alegre (POA) Recife (REC) Belém (BEL) São Luiz (SLZ) Macapá (MCP) Curitiba (CWB) João Pessoa (JPA) Salvador (SSA) Rio Branco (RBR) Campo Grande (CGR) Galeão (GIG) Natal (NAT) Maceió (MCZ) Boa Vista (BVB) Foz do Iguaçu (IGU) Arithmetic mean SBM Efficiency BCC Ranking 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 68.4% 58.8% 54.1% 49.5% 33.4% 31.8% 28.4% 25.1% 22.1% 21.8% 20.5% 19.7% 16.6% 14.9% 11.8% 5.6% 2.8% 56.6% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 92.2% 64.3% 72.4% 50.1% 37.9% 40.3% 37.2% 31.3% 42.6% 37.7% 28.1% 52.4% 43.5% 33.2% 28.8% 17.7% 26.4% 65.6% 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 - Inputs reduction Terminal Runway Apron 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 43.6% 60.8% 0.0% 0.0% 0.0% 0.0% 23.1% 0.0% 6.3% 0.0% 0.0% 31.4% 0.0% 42.2% 0.0% 26.7% 8.4% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 3.7% 44.9% 38.1% 0.0% 9.9% 7.6% 26.8% 0.0% 54.4% 6.7% 6.7% 7.9% 10.3% 0.0% 7.8% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 2.2% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 21.6% 34.3% 14.2% 0.0% 0.0% 0.0% 2.6% Outputs increase Passengers Cargo 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 9.5% 0.0% 136.7% 178.9% 63.5% 149.0% 212.9% 54.8% 49.9% 233.1% 47.3% 130.1% 150.0% 45.4% 365.3% 92.7% 68.% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 92.3% 81.2% 92.1% 62.5% 129.6% 285.8% 354.7% 296.1% 628.5% 567.2% 541.7% 509.5% 583.3% 895.4% 1172.3% 2911.5% 6197.6% 550.0% Identifying inef,icient airports can help decision-making to enhance airport management and also identify airports with underused capacity that can have a higher importance in the air network when hubs are too saturated, as well as an option when an airport is shut down, to enhance the network resilience. Nonetheless, productive ef,iciency depends not only on the infrastructure variables analyzed but also on the number of service counters, the number of x-rays, infrastructure for baggage claim, number of employees, loading and unloading equipment for luggage and cargo, platforms, and vehicles for transporting people over apron area. Among the airports under concession (BSB, CNF, GRU, NAT, GIG, VCP), four of them were ef,icient, except GIG and NAT that achieved considerably lower ef,iciencies (16.6% and 14.9% respectively). The results obtained do not directly imply poor management in airports when the ,irst privatizations had a contractual obligation to develop infrastructure above the demand observed, TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 which leads to a capacity surplus and consequently lower productive ef,iciency (the case of GIG and NAT) and inef,iciency in dealing with economic crises. This may indicate problems in the ,irst government concessions and the need for orientation to review current contracts and the next concessions contracts. VCP also had a problem with infrastructure capacity surplus due to contractual obligations that did not meet the real demand. Although VCP is considered ef,icient in this study, the expansion work continued in the following years. It can also be observed that small and large airports performed better than medium-sized airports, indicating inadequate management in medium-sized airports, probably due to the lack of benchmarking in this group or their minor role in the air network as saturated airports are prioritized as hubs. This solution would also supplement the idea of operational optimization in airports, since the input reduction proposed by the model could be overcome by an increase in the products, probably because of a rearrangement of routes or other measures. The aim to identify sectors of poor performance is to help allocate governmental and private resources, e.g. direct to sectors that have no input slacks, indicating a possible limit capacity achieved. Higher input slacks may indicate airports that still have the infrastructure to generate more outputs, based on benchmarks, and new investments can produce outputs at a higher rate than invested, whether the airport operates in crescent returns to scale. We compared the ef,iciencies measured with SBM to the output-oriented BCC model (Table 2), frequent in literature. As expected from the literature, ef,icient DMU in the SBM model was also ef,icient in the BCC model, however, SBM application reduced inef,icient airport scores due to the slacks. For SBM, the ef,icient unit should have no slack, therefore the optimal quantity of resources and products. The mean ef,iciency is lower in the SBM application, a more discriminatory variant, and a different ef,iciency ranking. Besides, the SBM model indicates changes for each variable to make the DMU reach the frontier, when the BCC model suggests the same increase in all outputs (when output-oriented) or the same reduction to all inputs (when input-oriented). The non-oriented model leads to a new kind of possible users, which considers the possible outputs increase along with the best infrastructure management. This study opens a possibility to use this model in the airport infrastructure, and following studies could introduce variables such as check-in positions, x-ray, baggage belts, exploring an allocative idea. Due to the number of ef,icient units, we applied an Inverted Frontier to discriminate these airports. The Composite Index considered that CGH, a public airport, was the most ef,icient airport considering these variables and SBM model, hence the one able to produce more with its resources, without slacks. The most ef,icient privatized airport is VCP (4th), followed by GRU (8th) and CNF (9th). CGH is strategically located in Sã o Paulo, the largest business center in Latin America, where many companies and ,inancial institutions are located. CGH is the airport with higher business traf,ic in Brazil, is located near the city center and serves domestic ,lights. In 2003, INFRAERO started a renovation plan for the airport complex to meet demand. Nevertheless, the airport operates with its capacity limited, especially related to the runway, besides being the most competitive and saturated airport in Brazil (INFRAERO, 2016). This paper relates to productive ef,iciency and not to service level (the perception of quality by the customer), thereby an ef,icient unit may offer a low level of service to its customers. In 2015, CWB was considered the airport with the highest quality service perception but achieved an ef,iciency of 25.1%. TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 Furthermore, airport managers should plan at extending the airport’s catchment area or focus on new strategies to attract carriers and other business activities to enhance ef,iciency, particularly cargo activity that represents an important effect in its ef,iciency (Carlucci et al., 2018). In order to verify contextual variables that could in,luence the ef,iciency measured with the SBM model, we applied a Tobit regression. This application aims to add socioeconomic variables, not used in previous studies. The ef,iciency value is used as a dependent variable and the independent variables of the best statistical model obtained are population at airports cities, GDP per capita, airport site size, HDI of the city, Gini Index and a dummy variable for airports granted to concession until 2015. Table 3 shows the results of the Tobit model. Other variables were tested (number of air companies operating in the airport, mean distance between the three closest airports, GDP, vehicle parking slots, passenger capacity per year, mean yield between airports of the sample), but their inclusion resulted in worse statistical goodness-of-,it measures. Table 3 – Tobit model results Constant Population 2012 GDP per capita Airport site HDI Gini Index Privatized until 2015 Chi-square Log of likelihood Schwartz Criterion Coefficient Standard error z p-value -2,1044 1,2563 -1,675 0,0939 -1,5e-9 0,0015 -3,375 0,0007 -0,0019 0,0015 -1,288 0,1978 4,4e-11 1,6e-11 2,752 0,0059 5,2093 1,8241 2,856 0,0043 -2,1969 1,1149 -1,970 0,0488 0,0369 0,1824 0,2021 0,8399 15,0726 p-value -6,6543 Akaike Criterion 39,9663 Hannan-Quinn Criterion * *** *** *** ** 0,0197 29,3087 32,5669 * significance level of 10% ** significance level of 5% *** significance level of 1% It was veri,ied that the error follows a normal distribution, with a signi,icant p-value. Note that the variables that present a signi,icant p-value at 5% are Gini Index, HDI, the size of the airport site, and the population in the airport city. However, the coef,icient has a negative value for both the population and Gini Index variables. There is a statistically signi,icant in,luence of the socioeconomic level of the city, de,ined by the HDI and income inequality measured by the Gini Index. Analyzing the coef,icients signs, greater ef,iciency is obtained for cities with higher HDI and lower Gini index, indicating lower income inequality. The size of the airport site is positively related to the greater ef,iciency measured as they probably have better infrastructure to handle more traf,ic movement ef,iciently. To validate the results, we used the Variance In,lation Factor (VIF) to identify the collinearity problem among variables. The VIF measures how much of the variance in each regression coef,icient is in,lated when the independent variables are not correlated, identifying multicollinear independent variables (Biagge et al., 2017). Multicollinearity indicates the exact linear relationship between explanatory variables in a regression model, which may occur due to the data nature or inadequate sampling (Elian, 1998; Gujarati and Porter, 2011). The result was also con,irmed by the Belsey-Kuh-Welsch collinearity diagnosis. Despite having a positive coef,icient, the dummy variable for airports granted to concession is not statistically signi,icant, which excludes concession impact in the measured ef,iciency. TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 Some studies suggest that publicly owned airports perform better than privately owned ones (D'Afonso et al., 2015; Merkert and Mangia, 2014; Curi et al., 2010 and Kan Tsui et al., 2014). In other countries, a reason could be the easier availability of public funds, which is not the case in Brazil. Also, joint ownership may be slower in responding to market changes because there is a need to satisfy multiple councils, with different objectives, which leads to lower ef,iciency (Iyer and Jain, 2019). Moreover, studies show that total concessions may perform better than partial concessions to private management (Iyer and Jain, 2019). Oum et al. (2006 found no statistical difference in ef,iciency performance between airports managed by government departments and airports managed by airport authorities. Therefore, contrary to common belief, there is no evidence that airports operated by private sector are more ef,icient than public corporations or operated by US government branches. The results of this study are consistent with those ,indings. As 100% of public airports are more ef,icient than PPP airports (Oum et al., 2006), when the objective is private ,inancing, it is relevant for the government to sell a majority stake, although 100% of private ownership is not more ef,icient than 100% of government-owned airports. Oum et al. (2008) found that privatization of at least one airport in cities with multiple airports would improve their ef,iciency. Airports owned or controlled mainly by private ,irms, autonomous public corporations or independent authorities are more ef,icient than the ones controlled by governmental branch (city/state) or multiple government. Therefore, most of the private and fully publicly owned airports are the most cost-ef,icient ones, while mixed publicprivate owned airports (especially the ones whose ownership is mainly public) are the least cost-ef,icient airports (Oum et al., 2008). This may be due to fewer con,licting objectives, as privatized airports seek pro,it while public airports aim output maximizers (Gillen, 2011). Meanwhile, being the public-private ventures the most inef,icient ones, they need further investigation. Therefore, there is no evidence that privatizations make Brazilian airports more ef,icient, as there is no statistically signi,icant effect. The results and literature lead to the question from Oum et al. (2006): why have concessions failed to improve ef,iciency in airports? This question needs further investigation in future studies. We hereby emphasize that the results obtained are limited to the selected variables, the sample, and the year of the study. It may also be that the gains from privatization take longer to materialize or that they do not even materialize during a crisis, as the contracts were developed for a period of economic growth. 5. CONCLUSIONS DEA is a recognized evaluation method to investigate airport ef,iciency which does not require productive functions among variables and computes multiple variables of different nature. This paper uses a non-oriented SBM model to improve the discrimination of airports' productive ef,iciency, not used before in this research ,ield in a non-oriented form, especially in the context of airport privatization. The decision-making units were main Brazilian airports, with variables related to infrastructure, passenger, and cargo movement. The objective of this article was to evaluate the productive ef,iciency in the operational aspect and verify if Brazilian airport concessions contribute to higher ef,iciency, with focus on the variable slacks. Also, the paper aimed to search whether socio-economic variables could in,luence airport ef,iciency. TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 Only 39% of the airports sample were considered 100% ef,icient in a productive view. Inef,icient airports had scores below 50%, except for CGB, FOR, and POA. Among the privatized airports in the analysis (BSB, GIG, NAT, CNF, GRU, and VCP), four of them were considered ef,icient, however, GIG and NAT presented low ef,iciencies (16.6% and 14.9%, respectively). In general, the relative slacks indicated the need for improvement in cargo and passenger traf,ic to enhance ef,iciency, with a capacity surplus in infrastructure in terms of productive process. The purpose to use a non-oriented model, which suggests input reduction as a way to reach the ef,iciency frontier, does not imply in reducing investments in airports, but to identify sectors that need more attention, which may be poorly managed and resources that could generate more products than they currently do. The results do not directly suggest poor management in airports, as the ,irst privatizations had a contractual obligation to develop infrastructure above the observed demand, leading to lower productive ef,iciency (the case of GIG and NAT) along with inef,iciency to deal with economic crisis. This probably indicates a problem in the ,irst government concessions, therefore the need for orientation to review current contracts and include more realistic terms for the next concessions contracts. DEA is shown as an effective method that could be used in different ways from the ones in literature. The potential impact of the results is a wider technical and scienti,ic use of the method that could spread its use and interpretation, as well as the capacity to reduce costs and loss of revenue possibly inherited from productive inef,iciency, advantage for the companies and the State that receive part of the revenue. The slacks cannot be interpreted as a ,ixed goal since the sample is not entirely homogeneous and units can have different production processes. Contrarily, it is possible, within limits, to incentive technology transfer (Camioto et al., 2017) among airports. As CGH can be a reference of practices, airports with the lowest ef,iciency score and highest slacks demand more attention. Airport benchmarking identify operational aspects that need more attention, becoming bottlenecks in the process. The presented results to identify strategic points to intervene, sectors that should be an investment priority and surplus in resources for an increase in demand. This paper also aimed to identify the possible in,luence of macroeconomic and socioeconomic variables in the measured ef,iciency. The introduction of socioeconomic variables in this scenario is novel to literature and the results indicate a positive relationship between the ef,iciency of an airport and its city HDI, and an inverse relation with the Gini Index, representing a low income inequality. The airport site size and the city population are also signi,icant variables. The slacks analysis, Composite Index and Tobit regression can help to allocate government and private resources to sectors and airports with higher needs in an optimum way. The identi,ied literary gap enables the use of a wide range of variables for future studies, sustainability, ,inancial ef,iciency, and Brazilian performance worldwide. As a limitation of this study, DEA application does not enable inference to another sample, results depend on variables and sample used. Adjusting the results interpretation, the novel use of non-oriented DEA can be replicated in other study ,ields. The results show that the ,irst privatizations of Brazilian Airports are not considered statistically signi,icant to improve their ef,iciency and some privatized airports are still inef,icient in TRANSPORTES | ISSN: 2237-1346 Toledo, F. S.; et at. Volume 29 | Número 2 | 2021 this productive process. Although, other unobserved variables also affect airport ef,iciency (Oum et al., 2008). In the same way as Oum et al. (2006) we claim the importance of testing different measurement methodologies before a conclusion to the ef,iciency effects of privatization and corporatization of airports. ACKNOWLEDGEMENTS This study was ,inanced in part by the Coordination for the Improvement of Higher Education Personnel (CAPES) – Finance Code 001, as well as the National Council for Scienti,ic and Technological Development (CNPq), through MCTIC/CNPq Nº 28/2018 – Universal: 436236/2018-4. REFERENCES Adler, N.; Liebert, V. 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