The impact of the economic crisis on the efficiency of Spanish airports: A DEA visualisation analysis

Abstract

We study DEA efficiencies of 47 Spanish airports over the period 2009–2013. Because the selection of inputs and outputs in the DEA model is problematic, we consider 186 input/output specifications obtained by combining four inputs and five outputs. Given the large differences in size between the airports, we use Variable Returns to Scale. Since it is a characteristic of economic crisis that some capacity remains idle, we use the output-oriented version of DEA. The results are visualised using the tools of multivariate statistical analysis. The analysis reveals six independent aspects of efficiency that can be assessed for an airport, and how their relative importance evolved during the economic crisis. Important changes in efficiency between 2009 and 2010 are revealed. They were followed by a period of slow return to the pre-crisis situation. The methodology presented here makes it possible to assess the strengths and weaknesses of each airport in terms of efficiency.

Introduction

Airports are public resources that require large investments, and there has been substantial interest in exploring whether such resources have been effectively and efficiently used. Some of the funds that were spent in Spanish airport infrastructure were provided by the European Union. European Commission European Court of Auditors (2014) investigated if investment expenditure in Spanish airports had been justified.

The study of the efficiency of airports has long been a matter of interest. Bezerra and Gomes (2016) give a literature review of performance measurement in airports. Some relevant studies are Gillen and Lall (1997), Parker (1999), Sarkis (2000), Bazargan and Vasigh (2003), Sarkis and Talluri (2004), Wang, Ho, Feng, and Yang (2004), Yu, 2004, Yu, 2010, Barros and Dieke (2007), Barros, 2008a, Barros, 2008b, Barros, 2009, Pathomsiri, Haghani, Dresner, and Windle (2008), Yu, Hsu, Chang, and Lee (2008), Assaf, Gillen, and Barros (2012), and Pacagnella Junior, Hollaender, Mazzanati, and Bortoletto (2021). This literature has been reviewed by Lieber and Niemeir (Lieber, 2013; Liebert & Niemeier, 2010). In Spain we can mention Murillo-Melchor (1999), Salazar de la Cruz (1999), Martin and Roman, 2001, Martin and Roman, 2006, Martin-Cejas (2002), Coto-Millan et al., 2007, Coto-Millan et al., 2014; Coto-Millan, Inglada, Fernandez, Inglada-Perez, and Pesquera (2016), Tapiador, Mateos, and Marti-Henneberg (2008), Martin et al., 2009, Martin et al., 2011, Tovar and Martin-Cejas, 2009, Tovar and Martin-Cejas, 2010, Lozano and Gutiérrez (2011), and Lozano, Gutierrez, and Moreno (2013).

A popular technique for efficiency assessment is Data Envelopment Analysis (DEA). DEA takes a particular airport whose efficiency is to be assessed as the focus of analysis and asks if the inputs used by such airport would have been better employed elsewhere. The question is basically: imagine that we close the airport under observation and distribute its inputs amongst other airports. Having expanded, the airports that have received extra inputs are expected to generate extra outputs. The question is if these extra outputs be at least as large as the outputs that were generated by the airport we consider closing. If the answer to this question is “yes”, then the airport under observation is deemed to be inefficient.

This paper reports the result of a study of Spanish airport efficiency over a five-year period that includes an economic crisis. Several issues are addressed using DEA and multivariate statistical methods. Since DEA efficiency scores depend on the outputs and inputs included in the model, we estimate efficiencies under a variety of combinations of inputs and outputs (specifications). This approach has the further advantage of avoiding the zero-weight problem that is common in DEA. It also serves to highlight the strengths and weaknesses of each airport in terms of efficiency. We do this for a five-year period. This results in 43,710 efficiency scores, a large amount of information that can only be fully understood using statistical methods. For this reason, we visualise the efficiency models and results using scaling methods. We think this is the first time that this methodology has been applied in this context.

DEA efficiency is measured in the form of a score between one (if the airport is fully efficient) and zero (if the airport is fully inefficient). These scores are often multiplied by one hundred and reported in the form of percentages. This way of proceeding is appropriate, but we would like to go beyond a mere score. We would like to know what is special about the airport being assessed, what are its strengths and what are its weaknesses. The methodology presented in this paper addresses this issue from a different perspective from previous studies such as Pacagnella Junior et al. (2021).

A major issue in DEA is the choice of inputs and outputs to be included in the model. DEA is not a statistical technique and there are no tools —such as t-tests in regression— to assess if an input or an output are important or could be deemed to be redundant and removed from the data. It is known that efficiencies depend on the number of inputs and outputs included in the specification. The more inputs or outputs included in the model, the higher the calculated efficiencies will be. For a discussion of the issues related to specification in DEA see, for example, Grosskopft, 1986, Grosskopft, 1996, Thrall (1989), Hughes and Yaisawarng (2004), and Pastor, Ruiz, and Sirvent (2002).

There are many possible input/output combinations (specifications) that can enter into a DEA study, and calculated efficiencies depend on the specification chosen. In fact, two different analysts working on the same data can come up with different results just because they have chosen different specifications. It is difficult to justify how two different results can arise from the same data when the analysis is performed by two perfectly competent people using the same technique. A solution proposed by Serrano-Cinca, Mar-Molinero, and Fuertes (2016) is to estimate a variety of specifications for each unit under observation and to analyse the results using Factor Analysis. This approach has been revealed to be very effective in various studies: Gutiérrez-Nieto, Serrano-Cinca, and Mar-Molinero (2007); Serrano-Cinca et al. (2016); and Sagarra, Mar-Molinero, and Agasisti (2017). Ripoll-Zarraga and Mar-Molinero (2020) applied this approach to study the efficiency of Spanish airports.

Extreme values are a problem in DEA since they may have considerable influence on the results. But an extreme efficiency value may just be consequence of the choice of inputs and outputs. Serrano-Cinca et al. (2016) demonstrated that whether a particular unit of assessment appears to be discordant depends on the particular choice of inputs and outputs incorporated in the specification. Airports that are associated with extreme efficiency values under a particular specification may not appear to present discordant behaviour under other specifications. For this reason, we have decided not to start the modelling by looking for extreme values, as it is common practice. By estimating a variety of specifications, we will be able to reveal the reasons why some airports present extreme behaviour, if any such units exist. This will disclose the strengths and weaknesses in the efficiencies of the various airports.

A standard problem in DEA studies is the treatment of zero weights. The methodology proposed here avoids it. Attaching a zero weight to an input (or to an output) is equivalent to removing this input (or output) from the analysis. Our methodology removes or includes an input (output) in an explicit way. If an input (output) has no impact on the assessment of efficiency, this will be revealed by the data reduction techniques of multivariate analysis that we adopt.

Airport efficiency studies tend to be static, in the sense that data on inputs and outputs are collected for a particular year, and the model is estimated. Here we take the analysis a step further by adding the time dimension to the analysis. Hence, our approach reveals the dynamics of airport efficiency over time.

The standard approaches used to incorporate time changes in DEA are the Malmquist index approach (Thanassoulis, 2001), or the multiperiod network model of Kao and Hwang (2014), Liu (2017), Fragoudaki, Giokas, and Glyptou (2016), and Ahn and Min (2014). However, these approaches suffer from the same limitations as the standard DEA approach in that a particular specification has to be selected, and no alternatives are normally considered.

Our data consists in four inputs and five outputs for 47 Spanish airports over a five-year period. DEA efficiency was calculated for each airport under an output-oriented variable returns to scale model (VRS). VRS is justified given the large difference in size between the various airports. Output orientation was selected as an approach because we considered that the 2008 economic crisis had left capacity under-utilised, and we wanted to see how this had impacted on efficiency. As for the specifications, many can be contemplated, but we were selective in the sense that some of them did not make much managerial sense and these were excluded from the analysis. For example, having Commercial Revenues but not Passengers in a specification seems not to make sense unless the commercial income is generated mostly by employees, which is unlikely to happen. But it is possible to have Cargo without Passengers. At the same time, any specification with Passengers, Cargo, or Percentage of Flights on Time will require having aircraft movements. Although some unrealistic specifications may be missed, the DEA-Visualisation approach proposed here will disregard any ‘uninteresting’ combination of inputs and outputs.

The final data set was a three-way table of airports by specifications by years. The cells in the table contained efficiencies. There is an efficiency score for each airport under each specification for each year. This generates a very large amount of information that may obscure any relevant findings.

To reveal the findings and make them accessible to anybody without a strong technical background we resorted to visualisation techniques. The approach followed to analyse the results was based on the Individual Differences Scaling (INDSCAL) model of Carroll and Chang (1970). This model returns a “common map” that reveals what has remained constant over the time period, and a set of weights that informs about any time effects that may exist.

The common map revealed that there are at least nine ways in which airport efficiency can be described, although only six such approaches to efficiency were explored. These are: a) efficient use of investment in order to generate Air Traffic Movements (ATM); b) cost efficiency with respect to aeronautical activity; c) efficiency in obtaining revenues in relation to Air Traffic Movements (ATM); d) cost efficiency in dealing with passengers; e) efficiency in dealing with cargo; and f) efficiency effects associated with runway length.

The relative importance of these approaches to efficiency changed as result of the 2009 economic crisis. We found that, after 2009, the emphasis appears to have shifted from generating ATM to generating passenger activity given the investment available in each airport. During the worst years of the economic crisis (2010 and 2011) cost efficiency in dealing with passengers appears to have taken great importance. Before the crisis, efficiency effects in dealing with cargo appear to have been prominent over efficiency effects in dealing with passengers. The situation was reversed during the crisis period, something that may just reflect the fall in cargo activity during the crisis.

The approach described in this paper, besides identifying the various efficiency aspects that can be associated with an airport, and the way in which their importance has evolved over time, permits to visualise the strengths and weaknesses of each airport. In the concluding section we show how to do this by concentrating in Vitoria airport.

This introductory section is followed by a discussion of data, particularly in what concerns airport inputs and outputs. The third section of the paper is technical. It describes how the efficiencies were calculated, the statistical model used, and visualises the findings. The paper ends with a discussion and conclusions section.