Aviation infrastructure performance and airline cost: a
statistical cost estimation approach
Mark M. Hansen
*, David Gillen, Reza Djafarian-Tehrani
Institute of Transportation Studies, National Center of Excellence in Aviation Operations Research,University of California at Berkeley, Berkeley, USA
Abstract
The relationship between the performance of the US National Airspace System (NAS) and airline costs is examined by estimating airline cost functions that include NAS performance metrics as arguments, using quarterly data for 10 US domestic airlines. Performance metrics that vary by airline and quarter are de-veloped by applying principal component analysis to seven underlying variables, including average delay, delay variance, and the proportion of ¯ights that is cancelled. This analysis reveals that variation in the seven variables can be adequately captured by three or fewer factors, which we term NAS performance factors. If three factors are used, they can be interpretted as ``delay'', ``variability'', and ``disruption'', the latter two of which are merged into a single ``irregularity'' factor in the two-factor model. Cost function estimation results con®rm the anticipated link between NAS performance and airline cost. In the cost models with two and three performance factors, the irregularity and disruption factors are found to have the strongest cost impacts. These results challenge the prevailing assumption that delay reduction is the most important bene®t from NAS enhancements. Using the estimated cost models, we predict airline cost savings from substantially improved NAS performance in the range $1±4 billion annually. Ó 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction
The need to understand and quantify the bene®ts of public and private investments in the National Airspace System (NAS) has never been greater. On the public side, executive order 12893, published in 1994, requires the Federal Aviation Administration (FAA) along with other federal agencies to conduct systematic analysis of bene®ts and costs of all infrastructure
*
Corresponding author. 107B McLaughlin Hall, Berkeley, CA 94720, USA. Tel.: 2880; fax: +1-510-642-1246.
E-mail address:hansen@ce.berkeley.edu (M.M. Hansen).
1366-5545/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved.
investments involving annual expenditures in excess of $50 million. The analysis is to ``quantify and monetize bene®ts and costs to the maximum extent possible (FAA, 1998)''. Moreover, the FAA acquisition management system, published in 1997, mandates an ``investment analysis'' prior to the initiation of a new acquisition program, including, among other things, the identi-®cation of alternatives and assessments of their bene®ts and costs (FAA, 1998). Such analyses are required for a host of Air Trac Management (ATM) and Communications-Navigation-Surveillance (CNS) programs through which FAA intends to modernize the NAS over the next two decades (FAA, 1999).
Private investments, particularly those by airlines in advanced avionics for new aircraft, are also getting closer economic scrutiny. According to Allen et al. (1998), ``the industry is getting to the point where the achievement of business case maturity may be more important than technical maturity''. Business case maturity includes the ability to explicitly identify bene®t mechanisms triggered by CNS/ATM investments, credible estimates of the dollar values ¯owing from these mechanisms, and explicit analysis of investment risk (Allen et al., 1998). The CNS/ATM focused team (C/AFT), whose membership includes airframe manufacturers, airlines, and the FAA, has been working since 1997 to develop and apply a methodology for developing such business cases. While the need for bene®t quanti®cation is growing, industry stakeholders are also recognizing that the performance of the NAS is multi-dimensional, and therefore not adequately captured by traditional, delay-based, metrics. For example, the C/AFT has identi®ed six categories of per-formance, including, in addition to delay, predictability, ¯exibility, eciency, access, and cost of service (Alcabin, 1999). These concepts are considered to ``de®ne the elements of value to the scheduled airline business'' as well as ``the common criteria for developing economic models needed to predict bene®ts. . .(Alcabin, 1999)''.
Taken together, these trends imply a need for bene®t valuation methodologies that incorporate multiple dimensions of NAS performance. The purpose of this paper is to demonstrate one such methodology, based on statistical cost estimation. The work presented here builds on an earlier analysis by Hansen, Gillen, and Djafarian-Tehrani (forthcoming) that employs simple Cobb± Douglas (log-linear) models. Here, we employ translog models and more sophisticated estimation techniques. However, our key results are largely consistent with those in the earlier work.
In Section 2, we review and critique existing bene®t valuation methodologies, and suggest various ways of improving them. In Section 3, we overview the approach adopted in this paper, the essence of which is to incorporate NAS performance metrics into airline-level cost functions. Section 4 presents our methodology for developing the performance metrics, while Section 5 discusses the speci®cation and estimation of the cost function. Estimation results are considered in Section 6. In Section 7, the results are used to estimate industry cost savings from improved NAS performance. Section 8 concludes the paper.
2. Review and critique of current practice
link (ATS Data Link Focus Group, 1999), considered to be a path-breaking eort within the industry, identi®es four bene®t categories. Two involve communication cost savings, one is in-creased availability of communication between aircraft and airline operation centers (this was guessed to be worth anywhere between $16 and $48 per ¯ight), and the last category is delay cost savings (valued at $25 per min based on aircraft direct operating cost).
Thus, even as industry stakeholders recognize that NAS performance has many aspects, only delay is routinely monetized. Even here, however, there is ample room for skepticism about the procedures. Virtually all delay cost calculations involve nothing more than the application of a cost factor based on reported values for the average direct aircraft operating cost per block hour to quantities of delay measured in time units. For air transport aircraft, the cost factor is in the range $20±25 per min. A few studies re®ne this ®gure by dierentiating between delay taken at the gate, on the ground, and in the air (Geissinger, 1988; Odoni, 1995). Others extend the calculations by disaggregating expense by functional category, such as fuel, ¯ight personnel, maintenance, and capital, and estimating how delay, portrayed as changes in the quantity of block hours, aects each one (Kostiuk et al., 1998).
These approaches to delay cost estimation are based on strong assumptions that are rarely scrutinized or even acknowledged. These include that the cost of delay is an additive function of the cost of individual delay events, and that the cost of each event is a linear function of the duration of the delay (perhaps taking into account the phase of ¯ight in which it occurs). Such assumptions ignore the possibility that delay cost is non-linearly related to duration, subject to combinatorial eects, and includes sizable indirect components.
It is probable that the cost of a delay varies non-linearly with the duration of the delay. For example, one 40-min delay is likely to be more costly than 40 one-min delays. The 40-min delay is far more likely to disrupt ground operations, gate assignments, crew schedules, and passenger itineraries. Conversely, airlines sometimes add delays to ¯ights in order, for example, to avoid having a ¯ight arrive at a hub in the middle of a departure bank. If this is rational behavior, then the relationship between cost and delay must not only be non-linear, but also non-monotonic.
Delay costs are also subject to combinatorial eects. The severity of the impacts noted above is likely to depend not only on the duration of delay to a speci®c ¯ight but also on the interaction of delays for many ¯ights. This is particularly evident in a hub-and-spoke network in which ¯ights are scheduled in connecting banks. If all the ¯ights in an inbound bank are delayed by the same amount, then the eect may be far less severe than if half the ¯ights are delayed by a larger (or even the same) amount.
Finally, the prevalence of delays may generate sizable indirect costs through airline adaptation behaviors. Carriers may take a variety of measures to make their operations more robust to delay. These include building more padding into scheduled block times, providing ¯ights with additional fuel, and having extra aircraft, ¯ight crew, and ground personnel available. While these measures decrease the cost of delays when they occur, they also increase costs of day-to-day operation. In this way the cost of delay may permeate throughout the entire cost structure of the airline in ways that are not tied to individual delay events.
Simulation is one possibility. To address the questions under consideration here, a simulation would have to be highly detailed. It would need to capture how airlines respond on a real-time basis to operational irregularities and the cost implications of that response. The problem gets especially complicated when major adjustments such as rerouting of aircraft and reassigning crews are considered. While such a simulation may eventually be possible, it is beyond our present capabilities.
A second possibility is to systematically query airline personnel. For example, one might present dispatchers with dierent scenarios concerning the operation of their assigned ¯ights throughout the day or month, and ask them to choose which scenarios are more desirable. If the scenarios were carefully chosen, this procedure would reveal the preferences of the participants, and thereby allow the estimation of utility functions whose arguments would be various dimen-sions of NAS performance. Such a study might yield useful results, but is also subject to a number of objections. First, it is not clear how such a methodology could allow monetary valuation of NAS performance, since this would require participants to choose between scenarios that involve money as well as ¯ight operations. Second, it is not obvious that dispatchers, or any other airline personnel, have sucient knowledge of the airlineÕs interest to make choices that accurately re¯ect it. Finally, the results of such a study might be biased by principal/agent eects, with respondents making choices that are best for them rather than for the airline as a whole.
This paper focuses on a third approach, which is to estimate airline cost functions including NAS performance measures as arguments. Using published, quarterly, airline-level data, we es-timate relationships between airline operating expense, outputs, factor prices, and other variables. Included among the latter are a set of variables, which we term ``NAS performance factors'', that quantify the airlineÕs operational experience in the NAS during the quarter. By observing how these variables in¯uence airline expense, we establish a direct empirical basis for translating various dimensions of NAS performance into monetary terms. Any quanti®able aspect of NAS performance can, in principle, be accommodated in this framework. Moreover, because rela-tionships are derived from observed co-variation between performance variables and cost, the results entail a minimum of assumptions about the mechanisms involved.
This paper presents the ®rst step in using cost estimation to assess the economic value of NAS performance. It employs a relatively small data set and, accordingly, a limited set of NAS per-formance variables and a simpli®ed form for the cost function. Nonetheless, it yields plausible results, including industry-wide estimates of the costs from ``sub-optimal'' NAS performance that are comparable with results of more conventional studies based on delay cost factors. This sug-gests that statistical cost estimation is a promising avenue for assessing the economic bene®ts of NAS improvements.
3. Cost estimation approach
The cost function of a ®rm is de®ned as the lowest cost at which it can produce a given set of outputs,~Y, given the prices it pays for inputs,~P. Equivalently, it represents the cost of acquiring the optimal set of inputs, ~X, given the outputs and prices. Thus we have
where the subscripti denotes a particular ®rm (airline), andt identi®es the time period. The cost function, like the production function, is a way of depicting the technology available to the ®rm, i.e., its ability to transform inputs into outputs. Implicit in (1) is that all airlines have the same technology, an assumption that could be relaxed by adding airline subscripts to the cost and conditional demand (~X) functions.
Eq. (1) can be considered a long-run cost function because it assumes that all inputs have been adjusted to their optimal levels. Some inputs, particularly capital inputs, cannot be varied in-stantaneously. A short-run cost function relaxes the assumption of optimal capital stock by treating capital as a quasi-®xed factor and removing capital costs from the dependent variable. This results in capital being an argument in the short-run, or operating, cost function. Thus we have
OCOSTit~PitX~ ~Yit; ~Pit;Kit O ~Yit; ~Pit;Kit; 2
where capital is excluded from the price and conditional demand vectors.
It has long been recognized that costs depend on the nature and quality of airline outputs as well as the quantity. For example, airlines have been shown to have economies of density, whereby the cost for a given total output increases with the size of the airlineÕs network. Several additional variables are included to capture such eects. These are incorporated into the vector~Zit.
This yields a short-run cost function of the formO ~Yit; ~Pit; ~Zit;Kit. This form, as well as the
long-run version in which capital is not an argument, has been widely studied in the airline economics literature (Caves et al., 1984; Gillen et al., 1990; Hansen and Kanafani, 1990; Encaoua, 1991; Windle, 1991), and serves as the point of departure for the present study.
In this study, we add one additional vector argument, ~Nit, which characterizes airline iÕs
op-erational experience in the NAS during time periodt. In general,N~it is based on variables such as
average delay, delay variance, and the proportion of cancelled ¯ights. It can be viewed as the performance of the NAS from the standpoint of an individual airline. This is not to suggest that
~
Nit depends only on the performance of public aviation infrastructure; rather it derives from the
interaction between that infrastructure and operational decisions taken by the airline.N~itmay also
be aected by factors completely unrelated to the infrastructure, such as mechanical problem, labor actions, or severe weather. Nonetheless, both public and private investments in the NAS are primarily intended to change ~Nit for the better.
Thus, our analysis revolves around estimating the operating cost functionO ~Yit; ~Pit; ~Qit;Kit; ~Nit.
The ®rst four arguments are standard ones in the airline cost estimation literature. The last, which is the focus of our investigation, implies a relationship between NAS performance, measured at the airline-level, and airline operating cost. In order to quantify that relationship, one must ®nd and develop an N~it vector which captures airline-level NAS performance in a compact, yet
comprehensive way.
4. NAS performance measurement
provided by the public aviation infrastructure, but also the airlinesÕability to plan and manage their operations. Both of these factors depend on exogenous events, particularly weather, as well as the competence (and perhaps luck) of service providers and users. Thus, when we refer to high or low performance levels, we are not axing credit or blame to either the FAA or the airlines, but rather assessing operational outcomes in which both, along with a host of exogenous factors, play a role.
We must quantify NAS performance by airline and quarter, the smallest time unit for which ®nancial and trac data are available. To do so, results for thousands of ¯ights must be sum-marized by a much smaller set of metrics. There is no uniquely valid way of doing this. One might, for example, base metrics on the ¯ight, the ¯ight complex, the day, or the airport-day. (To illustrate the last possibility, one might categorize for a particular airline, airport, and day as ``smooth'', ``mildly irregular'', or ``highly irregular'', determine the proportions of airport-days in each category, and use these as the performance metrics.) Here, we opted for the more conven-tional ¯ight-based approach, reserving the others for subsequent work.
Even while con®ning ourselves to ¯ight-based metrics, there is a huge number that might be employed. To keep the analysis tractable, we employed a two-step approach. In the ®rst step, we evaluated seven metrics for each airline and quarter in our data set. Next, we employed principal component analysis to collapse these metrics into a smaller number of factors, and calculated the factor scores for each airline and quarter. These factor scores were used to compose the~Nitvector
used in the subsequent cost estimation.
The seven underlying metrics are de®ned in Table 1. The ®rst two metrics pertain to delay, and are thus the most closely related to the conventional approach for measuring NAS performance. The third metric focuses on more extended delays, which, as argued above, may have qualitatively and quantitatively dierent impacts on costs. The next two metrics re¯ect variability in ¯ight operations. The sixth metric is the standard metric for service reliability; it depends on both the mean and the variance of delay. The ®nal metric re¯ects the incidence of conditions when operations become suciently irregular to result in ¯ight cancellations. All of the metrics were evaluated by airline and quarter ± for the 11 quarters extending from the winter of 1995 through the summer of 1997 ± using the airline service quality program (ASQP) data base, which presents scheduled and actual departure times for every domestic ¯ight of the top 10 US carriers. Thus, our data set includes 110 observations. Since we employ a log-linear cost function speci®cation, and all metrics were consistently positive, logarithms of these metrics are used in the subsequent analysis.
Table 1
Performance metric de®nitions
Variable (in log form) De®nition
Average arrival delay Dierence between scheduled and actual arrival time, averaged over all ¯ights. Average departure delay Dierence between scheduled and actual departure time, averaged over all ¯ights. Average >15 min arrival delay Sum of all arrival delays in excess of 15 min, divided by total number of ¯ights. Arrival delay variance Variance of the dierence between scheduled and actual arrival time.
Departure delay variance Variance of the dierence between scheduled and actual departure time. Unreliability Proportion of ¯ights with an arrival delay over 15 min.
As shown in Table 2, the seven performance metrics are highly inter-correlated. All correlations are greater than 0.4, and the majority in excess of 0.6. This suggests the use of principal com-ponent analysis as a way of capturing most of the information contained in the seven performance metrics in a smaller number of variables. Principal component analysis identi®es a set of factors ± linear combinations of the original variables ± which together account for as much of the total variation in the original data as possible. The factors are obtained by ®nding eigenvectors of the correlation matrix. The higher the eigenvalue, the greater the explanatory power of the associated eigenvector. By convention, each factor has zero mean and unit variance. By virtue of being eigenvectors, the factors are also mutually orthogonal.
The results of the principal component analysis of the NAS performance data are summarized in Table 3. The ®rst component has high, positive, loadings on all seven factors and accounts for 72 percent of the total variation. The second factor, which accounts for about half of the residual variation, has positive loadings on the variance metrics and negative loadings on delay and un-reliability. Thus, airlines scoring high on this factor tend to have unusually high delay variances and/or unusually low delay averages. The third factor explains eight percent of the total variation, and has a high positive loading on ¯ight cancellations and a negative loading on departure delay variance. Altogether, these factors explain about 94 percent of the variation in the total data set. In principal component analysis, the standard procedure is to determine the number of factors to be extracted from the data, and then rotate these factors so that factor loadings are close to either 0 or 1, in order to simplify their interpretation. In choosing the number of factors, one
Table 2
Performance metric correlations
Variable (in log form) ADD AAD A15AD ADV DDV UNRE CANR Average depature delay (ADD) 1 0.82 0.83 0.54 0.53 0.53 0.81 Average arrival delay (AAD) 0.82 1 0.83 0.47 0.51 0.43 0.93 Average >15 min arrival delay (A15AD) 0.83 0.83 1 0.85 0.75 0.66 0.90 Arrival delay variance (ADV) 0.54 0.47 0.85 1 0.80 0.65 0.57 Departure delay variance (DDV) 0.53 0.51 0.75 0.80 1 0.44 0.60
Unreliability (UNRE) 0.81 0.93 0.66 0.65 0.44 1 0.53
Cancellation rate (CANR) 0.53 0.43 0.90 0.57 0.60 0.53 1
Table 3
Results of principal component analysis
Variable (in log form) Factor 1 Factor 2 Factor 3
Average arrival delay 0.85468 )0.46316 )0.05345
Average departure delay 0.86167 )0.31608 0.07645
Average >15 min arrival delay 0.98444 0.02062 )0.03112
Arrival delay variance 0.81784 0.51105 )0.08456
Departure delay variance 0.77662 0.38233 )0.42532
Unreliability 0.91327 )0.31949 )0.02627
Cancellation rate 0.70281 0.31987 0.61739
Proportion of variance explained 0.7203 0.1324 0.0828
must make a judgment about when the additional variation explained by a factor is sucient to justify retaining it. In the present case, we decided to con®ne our attention to no more than three factors, since none of the remaining ones accounted for more than 3 percent of the total variation. The choice between one, two, and three factors was more dicult. An oft-cited rule-of-thumb is to include only those factors which account for more than oneNth of the variation, whereNis the number of variables in the data set. Applying this to the present case, we ®nd that only one factor should be retained. On the other hand, this leaves out nearly 30 percent of the variation in the original data set, suggesting the possibility of adding a second or third factor. Rather than ®xing on a single alternative, we chose to estimate cost models including one, two, and three NAS performance factors.
Varimax factor rotation was then performed on the two-factor and three-factor representa-tions. The results appear in Table 4. In the two-factor case, the ®rst factor correlates more highly with the delay variables, including the average delays, average delays over 15 min, and unreli-ability. The second factor has the highest loadings on the departure and arrival delay variances, the cancellation rate, and, like the ®rst factor, average delays over 15 min. One might summarize this by terming the ®rst factor ``delay'', and the second factor ``irregularity''. When three factors are used, the ®rst one is virtually identical to that in the two-factor case. The second factor is also quite similar, except that the loading on cancellation rate is considerably lower. The third factor has a very high loading on cancellation rate, along with some correlation with arrival delay variance and average delay over 15 min. The three factors might be described as ``delay'', ``variability'', and ``disruption''. A carrier with a high score on the ®rst factor has ¯ights that depart and arrive later (relative to schedule) than those of the average carrier. If the second factor score is high, then delays ¯uctuate more widely than average, while a high score on the third factor means that conditions requiring ¯ight cancellation are more prevalent than average.
Figs. 1 and 2 present average factor scores for the one-factor analysis, by airline and quarter, respectively. Fig. 1 reveals that, using the one-factor analysis, the two carriers experiencing the best NAS performance (i.e., with the lowest factor score) are USAir and Southwest, while Delta, United, and TWA experience the worst performance. Fig. 2 shows that the quarters with the worst NAS performance include the winters of 1996 and 1997, along with the summer and fall of
Table 4
Rotated factor patterns for one, two, and three factors
Variable (in log form) One factor Two factors Three factors Factor 1 Factor 1
``Delay''
Factor 2 ``Irregularity''
Factor 1 ``Delay''
Factor 2 ``Variability''
1996. Good quarters include the springs and summers of 1995 and 1997. While there is some seasonal pattern in the data, it is not particularly strong, as evidenced by the fact that two of the three summer quarters are among the best while the third is among the worst.
Figs. 3 and 4 present airline and quarterly averages for the three-factor analysis. These provide a more complete picture of NAS performance trends. We see that Southwest is the only carrier to be better than average for all three factors, while United is the only one to be below average for all three. A number of carriers feature performance far better than average for some factors and worse than average for others. For example, Northwest has relatively low delay (Factor 1), but high variability and disruption (Factors 2 and 3). In contrast, Delta has low disruption but high
Fig. 1. Average factor score, one factor analysis, by airline.
variability and delay. Because the factors are, by construction, orthogonal the lack of a consistent pattern in the airline factor scores is to be expected.
These dierences among airlines may derive from either the conditions in which they operate or how they respond to such conditions. For example, Northwest may have more variability and disruption than Delta because it operates out of hubs in the northern US where severe storms occur. Alternatively, it may be that, as a matter of operational strategy, Delta is willing to accept greater delays in order to avoid cancelling ¯ights. These dierent possibilities highlight the point
Fig. 3. Average factor score, three factor analysis, by airline.
that the factors capture the interaction between aviation infrastructure and its users, not just the performance on one or the other.
From Fig. 4, we see that just two quarters ± the spring and summer of 1995 ± have better than average performance on all three dimensions, while two others ± fall, 1996 and winter, 1997 ± are consistently worse than average. We also see from Fig. 4 that the horri®c winter of 1996 was particularly bad from the standpoint of delay and disruption, but average from the standpoint of variability. A similar, but less pronounced pattern is seen in the winter of 1997, while in the winter 1995 only disruption was worse than average. Disruption is consistently less of a problem in the spring and summer quarters, as is delay except for 1996. Finally, there is some evidence of a secular trend to worse performance on the variability dimension: four of the ®rst ®ve months are better than average in this respect, while each of the last six months is worse than average.
5. Cost model speci®cation and estimation
We now consider the relationship between the airline-level NAS performance factors derived in Section 3 and airline operating cost, using the cost function framework explained in Section 2. To do this, we use the performance factors to compose the NAS performance vector,N~it, which in
turn is used as an argument for the cost function. We consider ®rst the variables to be included in the cost function, and then discuss issues of functional form and estimation method.
The speci®c variables included in the model are detailed in Table 5. Two outputs, revenue passenger miles, and ``other'', are considered. The latter combines freight miles, mail ton-miles and other miscellaneous outputs in a divisia index normalized so that this output is 1 for American Airlines in the ®rst quarter of 1995. Three production factors, fuel, labor, and `mate-rials', are included. Fuel and labor prices are calculated using fuel expense per gallon and labor expense per employee, respectively. The latter is somewhat imprecise because it does not take into
Table 5
Cost estimation variable descriptions Variable De®nition
QUARTER Quarter of year (1Winter, 2Spring, etc.)
TIND Time counter (1 for 1Q 95, 2 for 2Q 95,. . ., 11 for 3Q 97)
ALF Average load factor (revenue passenger miles/revenue seat miles)
IDO Index of output other than passenger miles (cargo, freight, etc.). Normalized to American Airlines in 1Q, 1995.
TOC Total operating cost for quarter ($) RPMS Revenue passenger miles (000) WAV Total labor expense per employee ($) WFUEL Fuel expense per gallon ($)
WMAT Producer price index (proxy for price for materials and services)
WK Working capital ($)
SDEP Number of scheduled ¯ights BASE Number of points served CARRIER Carrier code
account hours worked or employee classi®cation (pilots versus ¯ight attendants for example). As a proxy for materials price, we use the producer price index (PPI), which varies by quarter but not by airline. The three operational characteristics are average load factor, the number of points served, and scheduled departures. These variables capture qualitative features of an airlineÕs output that are likely to in¯uence cost. Our measure of airline capital stock is the sum of the airlineÕs net asset value, working capital, and accounts receivable, minus accounts payable. The capital stock variable is subject to some error because of the rather arbitrary depreciation rules used by airlines. With the exception of the PPI, all of these data are obtained from the airline balance sheet, trac, and expenditure data published in the Department of TransportationÕs Form 41 data base.
As noted previously, we employ NAS performance factor scores to de®ne the N~it vector. An
alternative would be to choose a representative variable for each factor (the one with the highest loading, for instance). We chose to use the factors themselves because they are mutually or-thogonal, while as shown in Table 2, there is signi®cant correlation between each pair of the original variables. We estimate models in which N~it contains one, two, and three-factor scores,
employing the rotated factors. As a result of the rotation, the factors employed in the three models are all dierent from one another, as shown in Table 4. By virtue of being factor scores, all have zero mean and unit variance. Also, because the factors are linear combinations of the logarithms of the seven original performance variables, they enter into the model in linear rather than log-linear form.
Since our data set is a panel, it is important to consider the use of ®xed eects. We chose to estimate models both with and without airline ®xed eects. The models with ®xed eects recognize that dierent carriers may have consistently higher or lower costs, ceteris paribus, due to dier-ences in productivity and other omitted variables. Use of ®xed eects also avoids the confounding eect that could occur if cost-ecient carriers were also adept at managing their operations to attain high NAS performance levels. On the other hand, models without ®xed airline eects are able to capture long-run impacts of persistent inter-airline dierences in NAS performance which, as argued earlier, could result in adaptations such as more schedule padding, reserve crew stang and so on. Fixed eects, when included, are likely to absorb such impacts.
We do not, on the other hand, include time period ®xed eects in our model. As shown in Fig. 4, there is substantial inter-period variation in the NAS performance factors. This implies that time period dummy variables are correlated with the performance variables. Including the former would therefore compromise our ability to discern the impact of the latter. Instead, we employ models with a time trend variable taking the value 1 in the ®rst quarter of our data set, 2 in the second quarter, etc. There is some potential for even the time trend variable to absorb NAS performance eects ± indeed changes in the NAS appear to be among the few factors that could create a meaningful trend in airline eciency over the 11 periods covered in our data. To test the sensitivity of our results to the inclusion of a time trend, we estimate models both with and without it.
eects and time trend). As an alternative, we reduce the set of second-order terms by including only those that involve factor prices, in order to preserve degrees of freedom.
In the ®rst approach, the model speci®cation (with ®xed eects and the time trend) is
ln OCOSTit aist
where OCOSTitis operating expense for airlineiin time periodt;ta time trend variable (1 for the
®rst time period, 2 for second time period, etc.);Yjitthe quantity of the outputjfor airlineiin time
periodt; Wkit the factor price for input kfor airline i in time periodt; Z`it the value of operating
characteristic`for airlineiin time periodt;Kitworking capital for airlineiin timet;Nmitthe value
for NAS performance factormfor airlineiin timetandeitis a stochastic error term. (The models without ®xed eects setai afor all i.)
To increase eciency, this model is estimated jointly with the input share equations
oln OCOSTit
whereSkit is the expenditure share for inputkof airlineiin time t; andukit is a stochastic error term.
The above method allows ecient estimation of coecients involving factor prices, since these appear in more than one equation and are subject to the homogeneity restrictions. It provides little advantage in estimating the numerous non-price coecients in the models, however. In the full translog model with three NAS performance factors and ®xed eects, for example, there are some 65 coecients that appear only in the cost equation and are not subject to homogeneity restrictions. Given the small data set (10 airlines over 11 quarters, or 110 observations) and the large number of non-price factors in our model, there is a shortage of degrees of freedom, par-ticularly since our estimation methods yield standard errors that are valid only asymptotically. To mitigate this problem, simpli®ed versions of the translog model were also estimated. In these simpli®ed versions, all second order terms that do not involve factor prices are eliminated. This yields
In this simpli®ed version of the three-factor model with ®xed eects, the number of non-price coecients is reduced from 65 to 20. We refer to the speci®cation in (6) as the ``quasi-translog'' form.
Following standard practice, the models were estimated in deviations form so that ®rst order coecients can be read as elasticities at mean values of the data. When estimated in this way the translog can be interpreted as a second order approximation to an arbitrary function about the mean values in the data set.
6. Estimation results
Tables 6±8 summarize our estimation results. Table 6 presents results for models with ®xed (airline) eects and the quasi-translog speci®cation (Eq. (6)). We consider this the preferred speci®cation both for the reasons cited in Section 5, and on the basis of the estimation results obtained. Table 7 contains results for the full translog models (Eq. (3)) with ®xed eects. Tables 6 and 7 each include results for model variants with one, two, and three NAS performance factors, and with and without a time trend variable ± six dierent models altogether. Finally, Table 8 contains estimates for three-factor models without ®xed eects, including both full and quasi-translog speci®cations, with and without time trends. In all of these tables, we present results for only the ®rst-order coecients in order to conserve space. As explained above, these coecients re¯ect sensitivity of cost to the various regressors at the sample mean.
Cost function estimation results, quasi-translog models with ®xed eects
One-factor models Two-factor models Three-factor models
With time trend W/O time trend With time trend W/O time trend With time trend W/O time trend
Estimate St. err. Estimate St. err. Estimate St. err. Estimate St. err. Estimate St. err. Estimate St. err.
RPMS (b1) 0.187 0.150 0.523 0.134 0.241 0.155 0.490 0.129 0.257 0.156 0.512 0.131
IDO (b2 0.098 0.018 0.103 0.020 0.100 0.018 0.107 0.019 0.098 0.018 0.105 0.019
WLABOR (x1) 0.375 0.002 0.375 0.002 0.375 0.002 0.375 0.002 0.375 0.002 0.375 0.002
WFUEL (x2) 0.136 0.001 0.136 0.001 0.136 0.001 0.136 0.001 0.136 0.001 0.136 0.001
WMAT (x3) 0.490 0.002 0.490 0.002 0.490 0.002 0.490 0.002 0.490 0.002 0.490 0.002
ALF (c1) )0.186 0.181 )0.419 0.185 )0.224 0.184 )0.398 0.177 )0.195 0.187 )0.379 0.181
DEPS (c3) 0.353 0.160 0.055 0.152 0.315 0.162 0.108 0.147 0.300 0.163 0.089 0.149
POINTS (c2) 0.203 0.082 0.146 0.088 0.208 0.082 0.179 0.085 0.215 0.083 0.183 0.086
WK (j) )0.056 0.028 )0.028 0.029 )0.050 0.028 )0.029 0.028 )0.048 0.028 )0.026 0.028
Time (s) 0.006 0.001 0.004 0.002 0.005 0.002
NAS performance ``Overall'' (k 11)
0.006 0.003 0.008 0.003
NAS performance ``Delay'' (k 12)
0.002 0.004 )0.002 0.003
NAS performance ``Irregularity'' (k 22)
0.010 0.006 0.019 0.005
NAS performance ``Delay'' (k 13)
0.002 0.004 )0.001 0.004
NAS performance ``Variability'' (k 23)
0.001 0.007 0.009 0.007
NAS performance ``Disruption'' (k 33)
0.010 0.004 0.014 0.004
AdjustedR2 0.9986 0.9983 0.9990 0.9989 0.9991 0.9989
Returns to scale 1.26 1.24 1.21 1.16 1.20 1.15
a
Values inbold italicsare signi®cant at 5% level.
Values inboldare signi®cant at 10% level.
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1±23
Table 7
Cost function estimation results, full translog models with ®xed eectsa
One-factor models Two-factor models Three-factor models
With time trend W/O time trend With time trend W/O time trend With time trend W/O time trend
Estimate St. err. Estimate St. err. Estimate St. err. Estimate St. err. Estimate St. err. Estimate St. err.
RPMS (b1) 0.242 0.211 0.684 0.250 0.258 0.240 0.609 0.261 0.239 0.242 0.569 0.262
IDO (b2) 0.072 0.039 0.077 0.050 0.074 0.043 0.097 0.050 0.130 0.048 0.155 0.056
WLABOR (x1) 0.375 0.002 0.375 0.002 0.375 0.002 0.375 0.002 0.375 0.002 0.375 0.002
WFUEL (x2 ) 0.136 0.001 0.136 0.001 0.136 0.001 0.136 0.001 0.136 0.001 0.136 0.001
WMAT (x3) 0.490 0.002 0.489 0.002 0.490 0.002 0.489 0.002 0.490 0.002 0.489 0.002
ALF (c1) )0.107 0.256 )0.487 0.315 )0.122 0.291 )0.387 0.331 0.021 0.291 )0.208 0.333
DEPS (c3) 0.062 0.221 )0.149 0.278 0.012 0.256 )0.217 0.292 0.021 0.257 )0.213 0.291
POINTS (c2) 0.210 0.124 0.161 0.158 0.295 0.157 0.288 0.184 0.429 0.166 0.399 0.196
WK (j) )0.133 0.062 )0.090 0.078 )0.146 0.073 )0.051 0.080 )0.179 0.072 )0.113 0.082
Time (s) 0.008 0.001 0.008 0.002 0.007 0.002
NAS performance ``Overall'' (k 11)
0.006 0.003 0.009 0.004
NAS performance ``Delay'' (k 12)
0.001 0.004 )0.003 0.005
NAS performance ``Irregularity'' (k 22)
0.007 0.009 0.023 0.009
NAS performance ``Delay'' (k 13)
0.003 0.004 0.001 0.005
NAS performance ``Variability'' (k 23)
)0.003 0.011 0.009 0.012
NAS performance ``Disruption'' (k 33)
0.013 0.006 0.025 0.007
AdjustedR2 0.9992 0.9986 0.9997 0.9995 0.9998 0.9997
Returns to scale 1.93 1.41 1.79 1.35 1.44 1.22
aValues inbold italicsare signi®cant at 5% level. Values inboldare signi®cant at 10% level.
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for several other coecients are strongly sensitive to whether the time trend is included. In par-ticular, removing the time trend increases the RPMS coecient estimate, while reducing those for DEPS, POINTS, and WK. These four variables are all related to an airlineÕs scale of operation, and are thus highly correlated. The impact of the time trend is to shift the scale eect from certain of these variables to others. This can be seen by comparing the returns to scale implied by the various models. Building on Caves et al. (1984), we de®ne this parameter as
RTSP 1ÿj
jbj
P
`6ALFc`
: 7
RTS is the percent increase in output, points served, and departures made possible by a one percent increase in operating expense and capital stock at the sample mean. As shown in Table 6, the RTS parameter is much less sensitive to the time trend than the individual coecients used in its calculation. In all six models, it is approximately 1.2. This relatively high value may derive from the use of ®xed eects, which absorb cost dierences from persistent inter-airline disparities in the scale of operation. A similar phenomenon was documented in Caves et al. (1987), who corrected it using a between-®rm estimator and then obtained constant returns to scale. We do not attempt this here, but note that, as shown in Table 8, models without ®xed eects have RTS parameters of less than one, implying diseconomies of scale.
Turning now to the results that are the focus of our study, Table 6 supports the hypothesis that poor NAS performance increases airline operating cost. Moreover, the results point clearly to Table 8
Cost function estimation results, three-factor models without ®xed eectsa
Full translog model Quasi-translog model
With time trend W/O time trend With time trend W/O time trend Estimate St. err. Estimate St. err. Estimate St. err. Estimate St. err. RPMS (b1) 0.567 0.121 0.603 0.118 0.670 0.050 0.663 0.049
IDO (b2 ) 0.075 0.035 0.095 0.032 0.176 0.019 0.178 0.019
WLABOR (x1) 0.375 0.002 0.375 0.002 0.375 0.002 0.375 0.002
WFUEL (x2 ) 0.136 0.001 0.136 0.001 0.136 0.001 0.136 0.001
WMAT (x3) 0.490 0.002 0.490 0.002 0.490 0.002 0.490 0.002
ALF (c1 ) )0.439 0.158 )0.380 0.157 )0.710 0.130 )0.662 0.118
DEPS (c3) 0.261 0.122 0.223 0.119 0.278 0.043 0.286 0.041
POINTS (c2) 0.349 0.115 0.311 0.112 0.174 0.043 0.167 0.042
WK (j) )0.114 0.080 )0.106 0.081 )0.158 0.022 )0.159 0.022
Time (s) 0.003 0.002 0.002 0.002
NAS performance ``Delay'' (k 31 )
)0.001 0.005 0.000 0.006 )0.004 0.006 )0.004 0.006
NAS performance ``Variability'' (k 32 )
0.002 0.013 0.008 0.012 0.015 0.011 0.018 0.011 NAS performance
``Disruption'' (k 33 )
0.022 0.008 0.026 0.007 0.014 0.007 0.015 0.007
AdjustedR2 0.9994 0.9994 0.9947 0.9948
Returns to scale 0.89 0.90 0.89 0.90
aValues inbold italicsare signi®cant at 5% level.
which performance dimensions are important. When two performance factors are used, ``irreg-ularity'' is statistically signi®cant, while ``delay'' is not. In the three-factor model, where irregu-larity is essentially decomposed into ``variability'' and ``disruption'', the latter is clearly more important, with the delay estimate small and insigni®cant as before. These results hold for models both with and without a time trend, although excluding the trend variable increases the apparent impact of NAS performance, particularly the irregularity and variability factors.
The quantitative interpretation of the results in Table 6 is based on the fact that the NAS performance factors are standardized variables. Thus, a one-unit change in a factor corresponds to a dierence of one standard deviation. So, for example, in the three-factor model with a time trend, an airline whose disruption score is one standard deviation above average would have costs about 2 percent higher than if its disruption score were a standard deviation below average. The dollar values associated with such changes are discussed in the next section.
Estimation results from the full translog model, presented in Table 7, are somewhat less sat-isfactory. Fewer of the ®rst order coecients are statistically signi®cant, although the majority still is. The RTS parameter estimates are at once more variable and considerably higher than those for the quasi-translog models. The NAS performance coecient estimates are more sensitive to the presence of a time trend, and of reduced signi®cance when the latter is included. All of these results re¯ect the drastically greater number of second order parameters in the full translog model and consequent shortage of degrees of freedom. Of equal concern is the limited validity of the asymptotic standard error estimates when degrees of freedom are so limited.
The above results suggest that the three-factor models best capture the relationship between NAS performance and airline cost. Table 8 reveals the impact of removing airline ®xed eects from these models. In addition to reducing the RTS parameter from above to below 1, eliminating ®xed eects reduces the time trend coecient estimate, while increasing the estimated coecients on disruption and variability. The latter dierences are consistent with the hypothesis that per-sistent airline dierences in NAS performance force airline adaptations whose costs are masked by the airline ®xed eects. Other interpretations are also possible, however. For example, NAS performance disparities may result from inter-airline dierences in managerial competence that also, independently, aect cost.
7. Potential bene®ts from improved NAS performance
In this section, we employ the results presented in Section 6 to estimate the potential gains, in terms of reduced airline operating cost, from improved NAS performance. The estimates we present are, in a very rough way, comparable to estimates of the cost of delay to US airlines, such as those reported by the FAA Airline Policy Oce (1995), Odoni (1995), Geissinger (1988), Citrenbaum (1999), and several others. Our estimates dier from the others in two important ways, however. First, they are not based on delay but on the broader concept of NAS perfor-mance. Second, they are based on cost comparisons involving a scenario in which performance is substantially improved, but not perfect. Thus, whereas the studies cited estimate the cost savings from the impossible feat of reducing delay to zero, here we estimate the savings from a con-ceivable, albeit dramatic, improvement in NAS performance.
We consider two hypothetical scenarios for improved NAS performance, both based on the three-factor cost models. In the ®rst scenario, we assume that each airline experiences the lowest level of disruption (as measured by its factor score) observed among the 110 observations in our data set. This value is )2.22, which occurred for Delta in the spring of 1996. The delay and variability factors retain their baseline values in this scenario. In the second scenario, we also modify the variability score in each observation to the lowest value found in the data set ()2.20 for USAir in the winter of 1995) while again retaining the baseline delay score. We consider this scenario because the variability coecient, while statistically insigni®cant in most of the models, has a fairly high estimated value in several.
To estimate the cost savings under the scenarios, we predicted the cost for each observation under the baseline and assuming improved performance. We used the quasi-translog models ± with and without time trend and ®xed eects ± to make the predictions. Use of the dierent models allows the sensitivity of the estimates to model speci®cation to be gauged.
Table 9 summarizes our results on an industry-wide, annual, basis. (To arrive at annual ®gures we simply summed cost savings over all 11 quarters and multiplied by 4/11.) The estimated savings range from $1 to $3.6 billion. The model with ®xed eects and a time trend yields the lowest estimates, which are similar for both improvement scenarios. The highest estimates are obtained from models without ®xed eects under the second improvement scenario. As explained previously, the higher estimates derived from models without ®xed eects may re¯ect long-term adjustment carriers must make to deal with consistently poor levels of NAS performance. Removing the time trend also has a sizable impact on the results, particularly in the models with ®xed eects.
Table 9
Estimated annual airline operating cost savings from improved NAS performance, in billions, by improvement scenario and model
Factor 3 scenarioa Factor 2 and 3 scenariosb
Fixed eects No ®xed eects Fixed eects No ®xed eects
Time trend $1.03 $1.49 $1.05 $3.22
No time trend 1.45 1.54 2.47 3.57
aAssumes that factor 3 takes lowest value observed in data set, with factors 1 and 2 at baseline values. b
For the reasons explained previously, these estimates are only roughly comparable to pre-viously published ones of the cost of delay. Nonetheless, the latter oer useful benchmarks. The most recently published estimate, due to Citrenbaum and Juliano (1998), places the total direct operating cost of delay to air carrier and air taxi operators at $1.2 billion in 1996. However, this estimate is derived solely from comparisons between actual and scheduled gate-to-gate time, and thus does not consider costs of departure delays or the phenomenon of schedule padding. Earlier FAA estimates (Aviation Policy Oce, 1995) are based on arrival delays instead of gate-to-gate delays, and yield annual ®gures of $2.5 billion, in current year dollars, throughout the early 1990s. Geisinger (1988) disaggregates delay by phase of ¯ight and applies dierent cost factors for each phase, and obtained a cost of $1.8 billion in 1986 (using the ATA composite cost index, this equates to $2.5 billion in 1997). Odoni (1995) places the cost of delay, non-optimal ¯ight trajectories, and ¯ight cancellations to airlines in the $2±4 billion range in 1993. Our estimate values of $1±4 billion are consistent with this range of estimates. It must be re-called, however, that our improvement scenarios are more conservative than those implicitly assumed in these earlier studies, which contemplate the elimination of all delay, cancellations, and so forth.
These estimates are also consistent with those from the earlier paper by Hansen, Gillen, and Djafarian-Tehrani (forthcoming) which place the cost savings from improved NAS performance between $1.7 and $2.3 billion. In addition to being based on dierent econometric models, the earlier estimates adopt a somewhat dierent set of NAS improvement scenarios.
Table 10 presents the percentage reductions in operating cost predicted for the dierent airlines under the two improved performance scenarios. Northwest, TWA, Continental, and USAir generally have cost reductions greater than the industry norm, while Southwest, Delta, and American have consistently smaller gains than average. These dierences primarily re¯ect the varying levels of variability and disruption experienced by the dierent airlines during the study period. It is interesting that the carriers with smaller predicted savings operate primarily in the southern, more temperate, part of the US, while the big gainers have a northern orientation. The
Table 10
Percentage reduction in operating cost, models with time trend, by airline, improvement scenario, and model Factor 3 scenarioa Factor 2 and 3 scenariob
Fixed eects (%) No ®xed eects (%) Fixed eects (%) No ®xed eects (%)
AA 2.1 3.0 1.9 7.4
AS 1.9 2.7 2.2 4.9
CO 2.4 3.4 3.0 7.6
DL 0.8 1.2 0.9 5.9
HP 1.9 2.6 2.7 6.1
NW 2.9 4.2 2.8 8.2
TW 2.9 4.1 3.3 7.4
UA 2.4 3.4 2.1 6.4
US 2.5 3.6 2.4 5.0
WN 1.5 2.2 1.7 3.3
Overall 2.1 3.0 2.1 6.4
a
Assumes that factor 3 takes lowest value observed in data set, with factors 1 and 2 at baseline values.
b
improved NAS performance contemplated in our scenarios would provide the latter with a cost advantage of 2±3 percent relative to the former.
8. Conclusions
Our results support the view, suggested by several earlier studies, that improvements in the performance of the NAS can generate billions of dollars in annual cost savings. Unlike previous work, however, the estimates presented here derive from observed co-variation between airline expenditures and NAS performance levels. As a result, they neither rest on the strong and im-plausible assumptions required to calculate costs from quantities of delay, nor even on the as-sumption that delay is the critical cost driver. It is reassuring that such a fundamentally dierent methodology yields potential savings of a comparable magnitude.
Despite this agreement as to the ``bottom line'' our study presents a qualitatively dierent view of the link between NAS performance and airline cost. Of the performance metrics considered, we ®nd quantities of delay to be among the least important. Instead, we ®nd the critical cost drivers to be the levels of irregularity and disruption in the system. If we had to choose a single metric to track this dimension, it would be the ¯ight cancellation rate rather than the average delay per ¯ight. This may have signi®cant implications for how NAS investments should be prioritized. In general, investments that increase the ``robustness'' of the system by preventing ``all hell from breaking loose'' appear to be more promising than those leading to incremental delay reductions in a broader range of conditions. This begs the question of how much disruption is avoidable through technological improvements and how much is directly tied to phenomena beyond human intervention, such as weather. Even in the latter case, however, improved prediction and response capabilities (such as collaborative decision making, a major FAA initiative at the present time) may substantially reduce operational and economic impacts.
Methodologically, this study illustrates the potential role of statistical cost modeling as a means of translating the emerging, multi-dimensional, view of NAS performance into improved capa-bility for investment analysis. Any dimension of NAS performance that can be measured at the airline-level can, in principal, be related to airline cost using the methods set forth here. The only practical limitation is that the impact be strong enough to be detectable through the statistical noise. As data accumulate, our detection capability will improve. In light of the sharp disparities between our empirical ®ndings and the conventional wisdom, it is clearly important to check them using a larger data set.
As previously noted, there are other approaches to representing NAS performance that may more aptly capture cost impacts. One approach would be to categorize days, or airport-days, in terms of their regularity and then base performance metrics on the number of days in each category. Another would be to categorize total delay minutes according to type of ¯ight, phase of ¯ight, duration, and other factors and then develop metrics that summarize how delay is dis-tributed across these categories. Other investigative approaches, including structured questioning of airline decision makers and detailed simulation of airline operations, may also yield important insights.
delay to passengers at roughly the same magnitude as its cost to airlines (Citrenbaum, 1999). But the passenger estimates are subject to many of the same objections as the airline ones. Moreover, while airline cost is directly observable, passenger utility is not. So signi®cant advances in valu-ation on the passenger side would require a substantially dierent, and probably more dicult and costly research approach.
While further study of the relationship between NAS performance and airline cost is important, it is equally necessary to improve our understanding of the link between various investments and NAS performance. The prominence of delay-based metrics in present-day investment analysis derives in part from the availability of tools that can predict delay and its response to a wide array of NAS changes. Unless similar capabilities can be developed for other dimensions of NAS performance, knowledge of their economic signi®cance is of little practical value.
This should not, however, be used as a rationale to continue using traditional approaches to NAS investment analysis. To do so is to risk the pursuit of programs that, even if technically successful, will yield bene®ts that are largely illusory, at the expense of other endeavors that could yield much higher gains. To avoid this outcome, a fundamental reassessment of the linkages between infrastructure investments, system performance, and economic bene®ts is required. Only this can enable analyses of public and private investments in aviation infrastructure that capture their true bene®ts, and investment decisions that will earn the maximum return.
Acknowledgements
This research was funded by the Federal Aviation Administration through a grant to the National Center of Excellence in Aviation Operations Research (NEXTOR) for ``Fundamental Research in Air Trac Management''. The enthusiastic support of George Donohue, Randy Stevens, Steve Bradford, and Norm Fujisaki for this program is gratefully acknowledged. An earlier version of this paper appeared in the Transportation Research Record. Helpful comments from the editor, Professor Bill Waters, and two anonymous referees are also appreciated.
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