Competing Networks, Spatial and Industrial Concentration in the US Airline Industry

Abstract

The paper uses Gini decomposition analysis to evaluate changes in the spatial distribution and industry shares of total US air traffic, as well as analysing the decomposition components for individual airlines and airports for the period 1990–2002. The paper develops explicit relationships between two of the main decomposition schemes used in the income inequality literature and shows the insights that such analysis may provide for evaluation and examination of air transport networks and traffic distributions. A multi-dimensional Gini and its decomposition are derived using an adjustment method derived from the relationship between the two Gini decomposition schemes.

Réseaux concurrents, concentration spatiale et industrielle dans l'industrie aérienne américaine

Résumé Cet article utilise l'analyse de la décomposition de l'indice de Gini afin d’évaluer les changements dans la distribution spatiale et les parts industrielles du trafic aérien total de l'Amérique, ainsi que l'analyse des composants de la décomposition pour les compagnies aériennes et les aéroports individuels pendant la période allant de 1990 à 2002. L’étude développe les relations explicites existantes entre deux des procédés principaux de décomposition dans la documentation sur l'inégalité des revenus, et donne la nouvelle perspective qu'une telle analyse peut fournir une évaluation et un examen des réseaux de transport aérien et de distributions du trafic. Un indice multidimensionnel de Gini et sa décomposition dérivent de l'utilisation d'une méthode d'ajustement provenant de la relation entre les deux procédés de décomposition de Gini. Mots clés: Compagnies aériennes; décomposition de Gini; concentration spatiale; réseaux en étoile.

Redes en competencia, concentración espacial e industrial en la industria aeronáutica de los EE.UU.

Resumen El estudio usa el análisis de descomposición de Gini para evaluar los cambios en la distribución espacial y cuotas por industria de todo el tráfico aéreo americano, además de analizar los componentes de descomposición de aeropuertos y aerolíneas individuales en el período 1990–2002. Este estudio desarrolla relaciones explícitas entre dos de los principales esquemas de descomposición usados en la literatura sobre desigualdades en los ingresos. Asimismo, señala los conocimientos que este análisis puede brindar a la evaluación y el análisis de las redes de transporte aéreo y la distribución del trafico. Utilizando un método de ajuste derivado de la relación entre los dos esquemas de descomposición de Gini, se deriva un coeficiente de Gini multi-dimensional y su descomposición. Palabras claves: aerolíneas, descomposición de Gini, concentración espacial, redes radiales.

Keywords:

• Airlines
• Gini decomposition
• spatial concentration
• hub-and-spoke networks

JEL classification :

• I32
• L11
• l93

Introduction

Since airline deregulation in the US in 1977 and 1978, the volume of air traffic has grown enormously and has become more concentrated around a smaller system of airports. Some of the airports have experienced rapid and sustained growth in their traffic shares, while others have gone through periods of expansion and decline, closely linked to the fortunes of the airlines servicing them. The airline industry has gone through several economic cycles in the last 30 years and changed significantly in terms of the firms, networks/products, technology, strategy and geographical market scope.

The academic literature has been concerned with measuring and modelling the effects of carrier network structures on several aspects of firm behaviour and decision making. The airline's network represents its production plan and also its range of products. The network structure gives rise to cost interdependencies among the routes in the carrier's system. Economies of scope and density associated with hubs yield efficiencies to larger ‘hubbing’ carriers under a variety of circumstances (see, for example, Brueckner & Spiller, 1994). The carrier's dominance at its hub airports gives rise to fare mark-ups and increased yields compared to carriers with smaller traffic volumes at these airports and has been considered a barrier to entry by new carriers (Borenstein, 1989). The network structure influences demand patterns, as passengers evaluate the generalized travel costs arising from indirect vs direct routing options. In the recent period, the new entrant low-cost/low-fare carriers have had a growing impact on fares and market shares at the larger airports and have generally tended to offer point-to-point direct service in contrast to the legacy ‘hubbing’ carriers (US Department of Transportation, 1996; US General Accounting Office, 1999).

There is considerable concern in the EU at present regarding the regional and national implications of changes in ownership and regulatory policies that will facilitate consolidation in the airline industry. Despite liberalization of the European internal market and recent moves to privatize or part-privatize several of the state-owned ‘national carriers’, external ownership requirements have resulted in a relatively small degree of consolidation in the European industry so far compared with the USA following deregulation. With consolidation in the European industry expected in the medium to longer term, issues relating to network structures, the spatial distribution of air traffic, the location of key air transport hubs and the bases used by surviving or merged carriers are of tremendous strategic importance for all European regions. Whether these changes will collectively give rise to greater concentration in the spatial distribution of European air traffic is of great importance given the link between accessibility and economic growth, particularly growth derived from knowledge economy activities.

The results of the US analysis presented in this paper suggest that after the initial restructuring of carrier networks in the early 1980s there has been very little change in the overall spatial distribution of traffic across the airports system despite the economic and industry events of the past 20 years. Furthermore, even with the growing impact of low-cost carriers in the domestic market, the aggregate spatial distribution of air traffic has shown very little change in the most recent period. That these trends may be mirrored in Europe is a topic for study in future research.

While the economic significance of increasing or decreasing spatial concentration may be unclear, it is important to monitor the impacts of policy changes that significantly impact on long-term trends. The same argument can be made for aggregate industrial concentration or concentration levels in specific industries (White, 2002). Recently Borenstein & Rose (2003) examined the effects of bankruptcies on domestic air service levels. They demonstrate that the medium-sized hubs have the greatest estimated effect in terms of reduced air services. However, when the distribution of all flight service changes nationally is examined, no discernable bankruptcy effect is evident. A suitable framework for analysing and tracking micro-level to macro-level changes and impacts is necessary in these circumstances. This paper develops such a framework for analysing individual airline and airport activities and relating them to aggregate national or continental trends.

The application of Gini analysis in economics has tended to be focused on issues related to income inequality and financial portfolio evaluation, with its application more recently to the evaluation of spatial concentration of employment (Krugman, 1991; Kim, 1995; Ellison & Glaeser, 1997). Typically in these analyses, per capita household income brackets are defined and the frequency distribution is analysed and decomposed by factor components. The factor components will be distributed across all of the income categories, but usually with a different frequency. Individual component Ginis, income shares and ‘Gini correlation ratios’ are isolated and related to the overall Gini index.

Yitzhaki & Lerman (1991); Yitzhaki (1994) and Milanovic & Yitzhaki (2002) have developed an alternative decomposition, taking account of the fact that some income categories will have no factor components present. This decomposition focuses on the notion of stratification existing within the factor components, and the decomposition scheme proposed captures component Gini coefficients, shares and the degree of overlapping between component distributions. In the income inequality literature, typically, the number and range of income categories do not change over time. The two decomposition schemes will be set out and the relationship between them for individual data will be derived.

With a transportation system, the number of nodes receiving service can change from period to period and/or the number of firms in the industry can change. A method is presented for isolating the effects of changes in the system size between evaluation periods. Using this method, a new decomposition scheme is derived. This scheme is further extended to take account of multi-dimensional variation in the traffic distribution. A combined spatial and industry concentration measure is put forward for the air transport sector with individual airline network structures and airport traffic distributions related to the overall trends. This allows for integrated analysis and monitoring of trends in the distribution of air traffic over time, across the airports hierarchy and across the airlines in the industry. An overview of the application of this framework to US air traffic distributions for the period 1973–2002 is then presented.

2 Gini Coefficient and Decomposition Schemes

The Gini coefficient is used in a variety of circumstances but most frequently in economics to measure inequality in the distribution of income. The Gini coefficient may be computed in a variety of different ways.1 The Gini coefficient has been used in a wide variety of applications in the physical and human sciences. The Gini coefficient is typically applied to a univariate distribution and different formulae have been developed depending on whether the data are of a continuous or discrete nature. In this paper, the Gini coefficient will be used to measure the extent of concentration in the distribution of air traffic across the set of US airports, and the extent of concentration in the distribution of airline traffic shares across the airline industry. The formula presented by Pyatt et al. (1980) and elaborated upon by Lerman & Yitzhaki (1984) will be used in this paper. These formulations may be presented as

1

where F(x) is the cumulative distribution function of air traffic and µ is its mean (Lerman & Yitzhaki, 1984; Dorfman, 1979). This is the empirical formulation of the population Gini, as the number of individuals in the sample goes to infinity. The second formulation is the sample Gini, given as

2

where n is the number of individual airports sampled, is the mean of x, cov(x,r _x ) is the covariance between the air traffic distribution, x, and the ranks of airports according to their traffic shares (r _x ) from the smallest (r _x =1) to the largest (r _x =n).

In decomposing the overall Gini into subgroups, two decomposition schemes have been proposed in the literature (the first in Lerman & Yitzhaki, 1984, 1985 and the second in Yitzhaki & Lerman, 1991 and Yitzhaki, 1994). These have been used extensively to examine inequality in the distribution of income sources (Garner, 1985) and to examine regional and intercontinental differences in the income inequality (Milanovic & Yitzhaki, 2002). Lerman & Yitzhaki (1985) show that the overall Gini coefficient based upon i subgroup components is

3

The first decomposition is thus

4

where R _i is the rank correlation ratio, G _i is the relative Gini of component i, and S _i is component i's share of total traffic (Lerman & Yitzhaki, 1984). This decomposition requires that each subgroup has a distribution over the same range as x. Thus the number of observations will be the same for each subgroup as it is for x, since it is only in these circumstances that the covariance may be decomposed as shown in equation (3) and that . In applying this decomposition to air traffic distributions, we can decompose the overall air traffic across the system of airports by individual carriers or by groupings of carriers. Alternatively, we can decompose industry concentration by individual airport, or groups of airports. We note also that the Gini coefficient is directly related to the concentration ratio, an alternative and commonly used measure of the relative size of firms in relation to the industry as a whole (Fei et al., 1978; Kakwani, 1980; Rao, 1969). Denoting C _i as the concentration ratio for firm i,

5

The second decomposition scheme put forward by Yitzhaki & Lerman (1991) and refined in Yitzhaki (1994) allows subgroups to cover a subset of the range of x. This decomposition is given as

6

where is the relative Gini coefficient for carrier i over airports in its network, S _i is the traffic share for carrier i as before, O _i is an ‘overlapping index’ and G _b is ‘between group’ concentration. The overlapping index, O _i , is discussed at length in Milanovic & Yitzhaki (2002) and defined as:

7

the ratio of the covariance between carrier i's traffic distribution ranked by the overall air traffic distribution for airports served by carrier i, to the covariance of carrier i's traffic distribution ranked by its own air traffic distribution across airports in its network. The O _i component for carrier i is the sum of overlaps with all other carriers. This component may be interpreted as a measure of multi-market contact for individual carriers with all other carriers. It is noted that the components R _i (in equation (4)) and O _i both involve ratios of the covariance between x _i and the overall ranking of airports to the covariance between x _i and the ranking of airports within the airline's network. The difference is that where R _i makes this assessment over all the entire airports system, O _i makes the comparison only for airports served by the airline. Clearly the ratio of O _i to R _i approaches 1 as the number of airports in the airline's network approaches N, the total number of airports in the national airways system.

Yitzhaki & Lerman (1991) argue that the O _i component could be further decomposed to yield measures of overlap between pairs of subgroups, yielding measures of multi-market contact between pairs of individual carriers when applied to air traffic distributions. This further decomposition is not presented in this paper, but could be used to make pairwise comparisons of network overlaps among any two carriers.

The ‘between group’ concentration is twice the covariance between the average traffic for each carrier and its mean rank in the overall traffic distribution, divided by the overall average air traffic, i.e.

8

The number of carriers or carrier subgroups and the distributional range of the subgroups will influence the size and sign of G _b . This component captures the extent to which differences among the set of airports served by carriers contribute to overall concentration of air traffic. As the number of subgroups increases, the G _b effect may be expected to increase. The greater the degree of ‘stratification’2 in the range of airports occupied by each carrier, the larger the G _b component will become, and the smaller will be the ‘within group’ concentration (i.e. concentration arising from how an individual carrier concentrates its traffic within its own network of airports). The limiting case would be where the carrier subgroups each occupy one single airport, in which case all of the variability will be between groups, with no within group variation. However, G _b may be positive or negative depending on the skewness in individual subgroup distributions. Indeed, Yitzhaki & Lerman cite an example of how this can arise with a skewed distribution in their 1991 paper, but do not offer an interpretation of its meaning in these circumstances.

The Gini coefficient has also been used to measure industrial concentration and we wish to consider airline industry concentration as well as air traffic spatial concentration. Deltas (2003) has demonstrated a bias in the Gini coefficient for small samples and argues that the size of the bias is large compared to the standard error. He also shows that this bias varies substantially across different distributions. He proposes an adjustment to the Gini coefficient of (n/n − 1) in order to reduce this bias and demonstrates its application among shipping cartels. The Gini coefficient has been applied recently to the measurement of spatial concentration in patterns of employment (Krugman, 1991; Kim, 1995; Ellison & Glaeser, 1997). The application presented for the air transport system in this section examines both spatial and industrial concentration patterns in the distribution of air traffic across US airports and among airlines. The units of observation will be individual airports and airlines, thus avoiding the ‘modifiable areal unit problem’ (MAUP). In examining changes in concentration over time, explicit account needs to be taken of changes in the number of firms operating in the market and in the number of airports receiving air services in a given year. An adjustment factor is derived to account for that component of concentration change due to variations in the number of firms and airports and that component due to changes in the distributions of traffic among firms and within individual firm networks.

So, the overall Gini measuring aggregate spatial concentration (or industrial concentration) in the distribution of all air traffic may be broken down in a consistent manner to give airline-specific (or airport-specific) measures of market share (S _i ), carrier (airport) rank correlation with the overall traffic distribution (R _i ), carrier (airport) overlap or multi-market contact (O _i ), carrier network (or airport) concentration, indicating for example, hub-and-spoke vs point-to-point network strategies (G _i or ), and, overall ‘between carrier’ (or ‘between airport’) differences (G _b ).

3 Relationship between Decomposition Schemes and Derivation of an Alternative Decomposition Scheme

In this section, by relating the two decomposition schemes it is possible to derive a new scheme that gives an alternative measure of the G _b component that will depend on carrier market shares and cannot take on a negative value.

The decomposition scheme presented earlier in equation (4) above assumes that each subgroup will have observations over the full range of airports, hence , the overall mean. The subgroup Gini computed in equation (6), however, is the carrier Gini for the range of airports present in the carrier's network. Typically, the number of airports in carrier i’s network (n _i ) will be less than the total number of airports in the national airways system, N. The two Gini coefficients are then related in the following way. The covariance of x _i with its cumulative distribution evaluated across the full range of x is

9

while the covariance of x _i with its cumulative distribution evaluated across the range of x _i only is

10

This gives the relationship between the two subgroup Gini coefficients as

11

Substituting for G _i in equation (4) yields a new decomposition:

12

This breaks down the overall Gini into (i) that part due to the effect of distributions within each individual subgroup and (ii) that part due to differences between subgroups, allowing that subgroups may have a different number of observations. Clearly, when n _i = N, equation (12) reduces to equation (4). The ‘between group’ factor presented by Yitzhaki & Lerman (1991), in contrast, does not explicitly take account of the impact of the number of subgroups or the range of the overall distribution occupied by the subgroups, but is clearly influenced by these factors. If all subgroups vary over the full range of x, then R _i and O _i components in equations (4) and (6) coincide and G _b =0.

The individual carrier Gini index scores have been used in previous studies to measure the extent to which carriers operate hub-and spoke network strategies compared to point-to-point strategies (Reynolds-Feighan, 1999; Burghouwt et al., 2003). The decomposition frameworks facilitate relating individual carriers’ behaviour or variations in network organization strategies to overall trends in spatial concentration.

The relationship in equation (12) can also be used to adjust the Gini index in order to estimate the effect of the changes in the number of observations between different periods. In this case, N represents the number of observations in period t and n _i can represent the number of observation in period t + 1. The adjustment to the Gini index then reflects the extent of changes in the number of observations. This ‘adjusted Gini index’ will be used in the US air transport application in the next section to isolate the changes in the Gini index between time periods due to changes in the number of observations (a shift factor) and changes in the distribution of shares.

So far, the decompositions have been proposed to measure spatial concentration and industry concentration separately. In analysing transport flow patterns it would be very useful and insightful to measure both industry and spatial concentration jointly, thus measuring the extent to which traffic is distributed across a set of airports and a set of carriers.

A two-dimensional Gini index can be developed where x is a variate subdivided among M subgroups and these subgroups themselves form a distribution which can be ranked from the smallest share to the largest. The two-dimensional Gini index further decomposes the variate x as follows:

13

where F ^ij is the cumulative distribution of x over both i and j entities. Each x _ij represents the level of x in category i for subgroup j. The Gini index involves a pairwise comparison of each cell in this (M×N) matrix. The two-dimensional Gini is then a weighted average of the Gini for the i and j entities. The Gini index applied to the distribution of air traffic across the airports measures spatial concentration. The Gini index across the airline traffic shares measures industry concentration. The two-dimensional Gini index is a weighted average of industrial concentration and spatial concentration, with the weights being determined by the relative number of airports (N) and airlines (M). This multivariate Gini index turns out to be equivalent to the ‘distance Gini’ formulation presented in Koshevoy & Mosler (1997).

The two-dimensional Gini index further decomposes the variate x as follows:

14

where r* is the ranking of x over both i and j entities. This distribution of r is derived by adding the column rank and the row rank and this is equivalent to taking the cumulative distribution of x summed over both the rows and columns. Decomposing this two-dimensional Gini into subcomponents as in equation (9) above gives the following relationship:

15

where the four components measure spatial concentration due to variations within airports, concentration due to variations between airports, industry concentration due to within airline concentration, and industry concentration due to between airline concentration.

The two-dimensional aggregate Gini, G ^2D , may be adjusted to take account of changes in the number of observations for i and j in the same way that the univariate Gini index was adjusted in equation (8) above. The general equations presented in this section allow for variations in the number of observations within subgroups and can measure concentration for a given distribution across two sets of subgroups. These formulations may be applied in a variety of applications to link spatial or regional aspects of a distribution with variations across groupings of economic agents or sectors.

4 Empirical Application: the US Air Transport System

The methodology outlined in the previous section was applied to the US air transport system, using the T100 and T3 databases maintained by the Department of Transportation.3 These databases record different measures of air traffic activity. The main tables reported below use the total onboard passenger volume (outbound4) from all US airports receiving ‘certificated’ traffic in this period. One disadvantage of using this database for the more recent period is the fact that regional jet traffic is not included and these aircraft have become increasingly important in short-haul markets. The T100 database covers domestic and international traffic of US and non-US carriers since 1990. For comparison purposes, the T3 database going back to 1973 is also used and the passenger traffic measure in this case is the total number of enplanements.5 This will allow for a long-run analysis of the overall traffic distribution pattern prior to and after deregulation. In the T3 database, US carriers’ domestic and international passengers are included, although non-US passenger statistics are not. For each year of analysis, a traffic matrix giving air passenger volumes by airport and by airline was generated. The traffic is given by airport and carrier. An alternative accounting framework could be generated using the FAA hub classification scheme rather than airports. The FAA hub classification scheme monitors air traffic by air transport community rather than by airport. In communities with multiple airports, the traffic distribution will be aggregated over all of the airports serving the community. The problem with this approach is that the traffic shares and the distance between the airports may vary significantly so that the air services offered from airports within a community may not be close substitutes. In regions with large conurbations, the allocation of airports to communities becomes an administrative or political decision, rather than a decision based on the functional airport hinterland or region. For these reasons, it was decided to use data for individual airports rather than for communities.

4.1 Overall Trends in Spatial and Industry Concentration

The US airline industry experienced rapid growth during the 1990s and recovered quickly from the adverse impacts of the first Gulf War in 1990/1991. During the mid-1990s, several new carriers entered the market and domestic growth was driven by these predominantly low-cost/low-fare carriers. The legacy carriers focused their expansion on international markets and took advantage of new freedoms offered through the large number of ‘open-skies’ agreements signed from 1992 onwards. Most of the larger carriers entered international airline alliances facilitating more streamlined flows among networks of alliance members’ traffic systems. The market experienced an expansion in the number of non-national carriers operating into US airports. A significant number of airports began handling international services during this period.

The impacts of these changes on the spatial distribution of traffic are examined for the period 1990–2002 using the T100 database and for the longer 1973–2002 period using the T3 database. Figure 1 shows the Gini index for the US airports system for the period 1990–2002 (the ‘T100 spatial Gini’) and for the period 1973–2002 for US carriers only (the ‘T3 spatial Gini’). The spatial Gini increases between 1991 and 1997 and falls gradually until 2001, rising slighty to 0.837 in 2002. The standard error of the annual spatial Gini estimates range from 0.01 in 1997 to 0.014 in 2000. The T3 spatial Gini shows a similar trend in the 1990s, but has Gini values 3% lower on average than the T100 estimates. This difference is due to the large number of international carriers.

Figure 1.  Trends in the spatial concentration of US air traffic, 1973–2002.

The unadjusted spatial Gini trend over time is very similar to the trend in the number of airports, as Figure 2 illustrates. This figure shows the number of airports included in the analysis using the T100 and T3 databases. Many of the airports at the lower end of the airports hierarchy experienced cycles of jet service withdrawal and short-term provision as the industry went through cycles of growth and downturns and carriers experimented with fine-tuning their network structures and extent. The inclusion of these ‘marginal’ airports in the analysis has a statistically significant impact on the spatial Gini coefficient.

Figure 2.  Number of airports in the T100 and T3 air traffic databases, 1973–2002.

The adjusted spatial Gini coefficients derived using equation (11) are also depicted in Figure 1 and show very different trends. The ‘T3 adjusted Gini’ shows a significant increase in spatial concentration after deregulation in 1978 and, following a 10-year adjustment period, very little change thereafter. By accounting for changes in the number of airports from period to period, the adjusted Gini coefficient isolates changes in the distribution of traffic across the rest of the hierarchy. Kuby & Reid (1992) note the impact of changing the number of nodes in the analysis of spatial concentration and suggest keeping the number of nodes fixed. In the analysis of air traffic distributions, equation (11) allows explicit measurement of the impact of changes in the number of nodes on the Gini measure.

The Gini index for the airline market shares is illustrated (‘industry Gini’) in Figure 3. Once again the T100 and T3 are depicted for the ‘raw’ Gini scores (varying the number of carriers) and for the adjusted Gini scores. The T3 adjusted Gini index shows a significant reduction in the years immediately after deregulation. The industry becomes more concentrated in the 1980s with the larger number of consolidations and financial failures peaking in 1991. In the last 10 years concentration has decreased once again with the entry of new low-cost carriers and many international carriers.

Figure 3.  Concentration in the US airline industry, 1973–2002.

Figure 4 shows the two-dimensional Gini coefficient defined in equation (14) and this is adjusted to take account of the number of carriers and airports over time. The combined T3 ‘spatial and industry’ Gini shows an increase in the 10 years following deregulation, and a further increase in the period 1986–1988 (reflecting the increased industry concentration in this period), with very little change in the most recent decade. So, in the decade following deregulation there was a significant and permanent adjustment in the air traffic distribution, with traffic becoming more concentrated at the busier airports and among the largest carriers. Since then there have been relatively small variations in combined spatial and industry concentration.

Figure 4.  Combined spatial and industry concentration, 1973–2002.

4.1.1 Decomposition of spatial gini coefficients

The decomposition of spatial concentration into ‘within’ and between’ components is illustrated in Figure 5, using the decomposition scheme introduced in equation (12). This separates overall spatial air traffic concentration into that part due to differences within carrier network structures and that part due to differences between carriers or carrier groupings. Nine groupings of carriers were used initially and compared with a more detailed decomposition by each individual carrier. The ‘between carrier’ concentration component increased between 1994 and 1998 from 0.65 to 0.70, indicating an increased difference between carrier network traffic distributions. In comparing the nine carrier categories to the decomposition using all individual carrier distributions separately, the ‘between group’ concentration increases as more groupings are used. But because this measure of between group concentration weights each category by its traffic share (S _i ), and both classifications use data for the top five carriers individually, the extent of the increase in the between group component averages 0.05. Figure 6 compares this performance to the within and between decomposition for the Yitzhaki–Lerman scheme of 1992 (hereafter YL92), and two significant differences are apparent. Firstly, the ‘between group’ component is negative because of the skewed nature of the traffic distribution. Secondly, this effect becomes far more pronounced when the individual carrier distributions are utilized. The YL92 scheme is far more sensitive to changes in the number of subgroup categories used, as groups are not weighted by their market shares. It is difficult to interpret the meaning of the YL92 decomposition results in these circumstances.

Figure 5.  Within and between concentration for the spatial Gini.

Figure 6.  Comparison of Gini decompositions into within and between components, using different carrier categories.

Table 1 records the decomposition components for the T100 nine carrier grouping for 2002 for illustration purposes. The nine groups are made up of (1) the top six carriers individually, carrying between 7.5% and 14.5% of total traffic (S _i ); (2) Continental, America West and Alaskan, together accounting for 11% of total traffic; (3) all other US carriers (4) other North American carriers and (5) non-North American carriers.

Table 1 . Decomposition components for nine carrier groupings using the T100 database for 2002

Carrier category	Total number of airports served (1)	Correlation with rank of total traffic (2)	Gini of carrier category (3)	Gini for carrier network (4)	Overlap index (5)	Traffic share (6)	YL ‘within group’ concentration (7)	Contribution to total concentration (8)	New ‘within group’ concentration (9)	New ‘between group’ concentration (10)	Share of traffic concentration (11)
	N	R i	G i		O i	S i		R i G i S i		S i R i (N − n i /N)	Ii=(R i G i S i )/G
DL	124	0.9543	0.9113	0.7531	1.1748	0.1435	0.1272	0.1247	0.0371	0.0877	0.1486
AA	108	0.9602	0.9243	0.7582	1.1774	0.1404	0.1256	0.1246	0.0320	0.0926	0.1484
WN	59	0.8727	0.9110	0.4797	1.1031	0.1302	0.0694	0.1036	0.0093	0.0942	0.1233
UA	87	0.9651	0.9350	0.7423	1.3031	0.1033	0.1002	0.0932	0.0187	0.0745	0.1110
NW	122	0.9324	0.9129	0.7536	1.1518	0.0773	0.0672	0.0658	0.0192	0.0466	0.0784
US	68	0.8919	0.9357	0.6737	1.1463	0.0748	0.0580	0.0624	0.0089	0.0536	0.0744
(CO:HP; AS)	113	0.9410	0.9264	0.7753	1.6320	0.1131	0.1434	0.0986	0.0270	0.0716	0.1174
Other US	320	0.9292	0.7850	0.7683	0.9717	0.1563	0.1168	0.1140	0.1035	0.0105	0.1358
Other North American	53	0.9649	0.9490	0.6680	1.5100	0.0087	0.0737	0.0080	0.0009	0.0071	0.0095
International	142	0.9257	0.9242	0.8158	0.0000	0.0523	0.0000	0.0448	0.0163	0.0285	0.0533
System	345	1.0000	0.8396	0.8396	0.0000	1.0000		0.8396	0.2727	0.5669	1.0000
Total within concentration					0.8815		0.2727
Between group concentration					−0.0419		0.5669

The decomposition components given in equations (4) and (6) were then computed for each individual carrier for each of the years 1990–2002. Figures 7–10 illustrate some of the interesting trends emerging from analysis of these subcomponents.

Figure 7.  Trends in carrier Gini index scores () for the top 10 carriers, 1990–2002.

Figure 8.  Full service and low-cost carriers Gini index and concentration ratio scores, 2002.

Figure 9.  Trends in carrier overlap (O _i ), scaled to [0,1] for the top eight carriers, 1990–2002.

Figure 10.  Airport Gini index and concentration ratios for top 20 airports, 2002.

4.1.2 Carrier-specific decomposition components

The Gini index () captures the concentration of traffic in individual carrier networks and clearly distinguishes ‘point-to-point’ from ‘hub-and-spoke’ strategies. This measure was applied extensively by Reynolds-Feighan (2001) to assess long-run US carrier network strategy patterns. Figure 7 illustrates the trends in the carrier Gini measures for the period 1990–2002 for the top 10 carriers. This figure clearly illustrates the different network strategy operated by Southwest Airlines (WN) compared to all of the other large full-service carriers (FSCs). The significant reduction in USAir's Gini index between 1991 and 2002 is noted, reflecting the restructuring and contraction in the carrier's network in the last 3 years and the more dispersed nature of traffic distribution among remaining airports in its network.

Figure 8 shows the Gini index and concentration ratio scores for full-service networking carriers and low-cost carriers in 2002. Where the Gini index measures concentration for a carrier's traffic distribution within its own network, the concentration ratio measures the extent to which the carrier's traffic distribution is focused on the busiest airports in the US air transport system. So the higher the concentration ratio for a carrier, the greater the extent to which the carrier operates from airports at the top of the airports hierarchy. The ‘legacy carriers’ are very similar in terms of Gini scores and concentration ratios. Thus the legacy carriers’ networks are highly concentrated and focused at the top of the airports hierarchy. The low-cost carriers, by contrast, have generally less concentrated traffic distribution patterns within their networks and tend to be focused lower down the airports hierarchy. This is not the case for America West (HP), National (N7), and Frontier (F9). In general, this figure illustrates the fact that all of the carrier networks are focused on busier airports rather than small community airports.

The ‘market overlap’ measure O _i captures the extent of market overlap between a carrier's traffic distribution in the subset of airports in its network, ranked by the carrier's ranking compared with the aggregate traffic ranking. Figure 9 illustrates trends in O _i for the top eight carriers between 1990 and 2002. This can be further decomposed to give a pairwise measure of multi-market contact or overlap for any carriers operating to airports in a given carrier's system, though it is not reported here. The ‘O _i ’ measure varies from 0 to 2, indicating increasing overlap with the ranking of total traffic at the airports. A significant change in the pattern of the ‘O _i ’ variable is observed in the period 1991–94 in particular. Southwest's overlapping index is at 1.58 (or 0.79 on a [0,1] scale) in 1991 and declines significantly in subsequent periods as its network expands to airports that did not have a strong FSC presence. The airports around which traffic growth has been focused have much lower rankings in the national distribution than in Southwest's system and the carrier faces a lower level of competition in its larger network. This measure of multi-market contact is based on the set of airports served rather than based on routes that carriers may have in common. The airport-based measure will implicitly take account of common routes among carriers. However, it also captures the notion of competing networks, where the legacy carriers, for example, offer alternative routings between origin–destination pairs and may not necessarily have common routes with other carriers. The measures of airline multi-market contact presented in the literature to date have focused on route overlaps rather than common nodes (Evans & Kessides, 1994; Gimeno, 1999; Lijesen et al., 2002).

The international carriers consistently have the highest market overlap, since their operations focus on the main international gateways and these will tend to be at the top of the US airports hierarchy. The decline in the overlap measure for these carriers in the period 2000–2002 is noted and related to more liberal ‘open-skies’ agreements that have facilitated direct international access to a greater number of US airports.

4.1.3 Industry concentration and airport measures

The industry concentration measure may be decomposed in the same manner as spatial concentration, yielding a variety of summary statistics for individual airports based on the traffic distributions of carriers serving the airports. Figure 10 illustrates the airport-specific Gini index () and concentration ratio scores for the top 27 airports in 2002 (corresponding to FAA large hubs, but counting airports rather than communities). The key airport hubs for the FSC_s have very high Gini index scores (), reflecting the dominance of the hubbing carriers at those airports. Hartsfield Airport in Atlanta (ATL), O'Hare Airport in Chicago (ORD), Charlotte Airport in North Carolina (CLT) and William Hobby Airport in Houston (IAH) have the four highest Gini index scores among the top 20 airports. The high value of the concentration ratio indicates the ranking of airlines at the individual airports.

The second grouping that is clearly discernible in Figure 10 is the international gateway airports at Los Angeles (LAX), New York (JFK), Miami (MIA) and Honolulu (HNL). These airports have lower Gini index scores and lower concentration ratios, reflecting the much greater influence of the large number of international carriers at the airports. The low-cost carrier bases have high concentration ratio values but generally lower Gini index scores, indicating the less concentrated traffic distributions among carriers serving the airports. The airport Gini index scores can be traced over time to track the impact of carrier network changes and carrier entry and exit effects on traffic distributions at particular airports. There are several examples of dramatic changes in these component scores for particular airports (e.g. significant traffic declines at St Louis, Missouri; Raleigh Durham, North Carolina; Dayton, Ohio and dramatic traffic growth at Las Vegas and Reno, Nevada and Midway Airport in Chicago, Illinois). There is much scope for further regional-and carrier-specific analysis of these trends. This analysis quantifies the effects that Borenstein & Rose (2003) identify and provides a framework for tracing individual carrier or airports impacts on overall trends in industry or spatial concentration. While the overall trend shows little change in spatial and industry concentration in the US passenger air traffic patterns in the past decade, there can be dramatic and significant changes at individual airports or for individual airlines. It is possible to examine how particular airports have performed over time by using ‘Gini mobility’ statistics.

5 Conclusions

This paper has examined the two main Gini decomposition schemes used in the poverty and income inequality literature. The relationship between the two schemes was set out and used to develop a general mechanism to take account of changes in the number of observations between periods and to put forward an alternative decomposition of the overall Gini index. The development of a framework for evaluating changes in two sets of subgroups and relating them to overall trends in concentration was put forward. The adjustment mechanism was extended to take account of variations in the number of units of analysis in both sets of subgroups in different time periods.

This framework has many possible applications. The framework was applied to the US air transport industry and used to relate individual carrier and airport activity to overall national trends in industry and spatial concentration. It was shown that in the decade following deregulation in 1978 there was a significant and sustained increase in the spatial concentration of air traffic. In the more recent period, spatial concentration has remained stable at similar levels for the past 20 years. This would indicate that a new equilibrium was reached in the USA in the late 1980s in terms of the size of the airport hierarchy handling ‘certificated’ air traffic. Industry concentration has also remained stable since the 1990s.

The carrier decomposition of spatial concentration produced measures of (i) carrier market share, (ii) market overlap or multi-market contact for individual carriers, and (iii) carrier network organization strategy. The individual carrier Gini index measures clearly demonstrated the different network organization strategy employed by Southwest Airlines vis-à-vis the other large network carriers. Further research will examine at a micro level the impact of individual carriers’ behaviour in terms of market overlap and pricing strategy. A European application could contribute to the debate and analysis of the future direction of the industry under scenarios of consolidation, changes in ownership requirements for international (extra-EU) services and enlargement of the internal market. The statistics relating to carrier behaviour can be related to financial and cost aspects of carrier operations. This paper has presented a framework for relating the performance and strategy of individual carriers or airports to overall continental trends in spatial and industry concentration. These micro-and macro-level linkages allow the overall significance and impacts of firm and airport behaviour to be properly measured and contextualized. The two-dimensional analysis gives a broad overview of all of the components of the continental air transport system and again provides consistent linkages for relating firm-and airport-level changes to overall system performance.

The two-dimensional Gini approach presented in the paper may also be applied to decomposition of other economic trends by region or by industrial sector. Using continuous data, explicit account of structural changes in regions or sectors may be accounted for and their impacts isolated from distributional changes.

6 Carrier and Airport Codes

6.1 Carrier Codes Used in the Figures and Table1

Table

AA	American
AS	Alaskan
B6	JetBlue
CO	Continental
CS	CO—Micronesia
EV	Atlantic Southeast
F9	Frontier
FL	AirTran
HP	America West
9N	Trans States
N7	National
NJ	Vanguard
NK	Spirit Air
NW	Nortwest
SY	Sun Country (New)
TZ	American Trans
UA	United
US	USAIR
WN	Southwest

6.2 Airport Codes Used in the Figures:

Table

ATL	Atlanta, GA
BOS	Boston, MA
BWI	Baltimore, MD
CLT	Charlotte, NC
CVG	Cincinnati, OH
DEN	Denver, CO
DFW	Dallas/Fort Worth, TX
DTW	Detroit, MI
EWR	Newark, NJ
FLL	Fort Lauderdale, FL
HNL	Honolulu, HI
IAH	Houston, TX
JFK	New York (Kennedy), NY
LAS	Las Vegas, NV
LAX	Los Angeles, CA
LGA	New York (Laguardia), NY
MCO	Orlando, FL
MDW	Chicago (Midway), IL
MIA	Miami, FL
MSP	Minneapolis/Saint Paul, MN
ORD	Chicago, IL
PHL	Philadelphia, PA
PHX	Phoenix, AZ
PIT	Pittsburgh, PA
SAN	San Diego, CA
SEA	Seattle, WA
SFO	San Francisco, CA
SLC	Salt Lake City, UT
STL	Saint Louis, MO
TPA	Tampa, FL

Notes

1. See Kendall and Stuart (1977), Dorfman (1979) or Xu (2003) for a detailed explanation of the derivation of the basic formulae and the links between continuous and discrete distributional formulations.

2. ‘Stratification’ in the current context refers to the extent to which a single carrier specialises in exclusively serving a subset of airports within the overall system.

3. Under the US Code Title 14, Vol 4, Parts 200–1199, the reporting requirements for US and non-US air carriers serving US markets are set out under the ‘Uniform system of Accounts and Reports for Large Certificated Air Carriers’ (Title 14, Chapter II, Part 241). Carriers are required to file on a monthly basis, Form 41 Schedules T-100 and T3, US air traffic and capacity data by non-stop segment and on-flight.

4. The total number of revenue passengers transported outbound over a single flight stage, including those already on board the aircraft from a previous flight stage.

5. A count of the number of passengers boarding and tons of cargo loaded on an aircraft. For this purpose, passengers and cargo on aircraft entering a carrier's system on interchange flights are considered as enplaning at the interchange point; and passengers and cargo moving from one operation to another operation of the same carrier, for which separate reports are required by the Department of Transportation, are considered as enplaning at the junction point.