Passenger Facility Charge vs. Airport Improvement Program...

To appear in Transportation Research Part E: Logistics and Transportation Review

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Passenger Facility Charge vs. Airport Improvement

Program Funds: A Dynamic Network DEA Analysis for

U.S. Airport Financing

Young-Tae Chang1, Hyosoo (Kevin) Park1, Bo Zou2, Nabin Kafle2,

1 Graduate School of Logistics, Inha University, Incheon, Korea

2 Department of Civil and Materials Engineering, University of Illinois at Chicago, Chicago, USA

Abstract: Passenger Facility Charge (PFC) and the Airport Improvement Program (AIP) are two major

sources to finance U.S. airports. This paper develops a novel dynamic network DEA framework to

investigate the substitutability between PFC and AIP funds. We find that the studied U.S. airports can

substitute PFC for 8-35% of the current AIP funds and contribute significantly to the proposed plan of

the US congress to cut AIP funding. In addition, the amount of PFC-for-AIP funds substitution

negatively correlates with the productive efficiency of airports. The findings send an important message

for future policy reforms on U.S. airport financing.

Keyword: Passenger Facility Charge (PFC), Airport Improvement Program (AIP), Substitution,

Dynamic network DEA, Airport efficiency

1 Introduction Passenger Facility Charge (PFC) and the Airport Improvement Program (AIP) are two major

sources for airport financing in the U.S. PFC is a service fee charged to departing and connecting

passengers at an airport, collected by airlines and then forwarded to the airport. AIP is a U.S. federal

grant program administered by the Federal Aviation Administration (FAA) to provide funds to airports.

PFC funds a broad range of capacity enhancing projects, for both airside and landside at airports. PFC

can also be used for making payment for airport debt services. The use of AIP funds is similar to PFC,

but usually limited to the planning and construction of projects related to aircraft operations

improvement, covering runways, taxiways, aprons, noise abatement, land purchase, etc. Commercial

revenue producing facilities (such as those related to shop concessions) are not eligible for AIP funding

(Kirk, 2010). Together, the two financing sources account for about 46% in total airport funds in the

U.S. (Dillingham, 2007).

PFC and AIP funds have a complementary relationship. This is because PFC and the formula part

of AIP funds, which accounts for 70-76% in total AIP funds (Kirk, 2009), are levied and allocated based

on passenger enplanement. Moreover, according to the FAA rule, AIP funds allocated to large and

medium airports will be foregone by 50% or 75% if those airports charge PFC at $3.00 or $4.50 per

enplanement (Kirk, 2009). The complementary relationship has brought to the arena of policy debate

the issue of potential substitution between the two types of airport financing sources, especially given


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the pressure for the federal government to reduce outlay on AIP and the fact that the current PFC scheme

remains unchanged for many years. Indeed, AIP funds have experienced a decline in recent years (GAO,

2014; AMAC, 2014) and the $4.50 cap on the amount of PFC that airports can levy per enplanement

has not been increased since 2000, when the Congress passed the Wendell H. Ford Investment and

Reform Act for 21 Century (AIR-21).

There have been many advocates for lifting PFC by itself or in place of AIP funds. They come

down to mainly two arguments. The first argument relates to inflation: the Airport Council International

– North America (ACI-NA) believes that the $4.50 ceiling set back in 2000 should be raised to $7.00

(ACI-NA, 2015); Airports United, a national airport group, argues that PFC should be “modernized”

by raising it from $4.50 to $8.50 (Laing, 2015). The second argument for increasing PFC is that PFC

can reduce federal expenditures on AIP and thus help alleviate the possible funding shortage. In line

with this argument, the Congressional Research Services has considered partial defederalization as an

option for future airport financing, by allowing large and medium hub airports to opt out of the AIP

program in favor of unrestricted higher PFC (Kirk, 2009). Two additional evidences in support of the

second argument: the H.R. 608 FAA Reauthorization and Reform Act in 2011 proposed annual AIP

funding cut by $500 million from 2012 through 2014; in 2015 the White House’s budget proposal called

for elimination of AIP support for large hub airports in return for an $8.00 PFC (GAO, 2014).

Despite the advocates and arguments on potential reforms of airport financing policy – in particular

the substitution between PFC and AIP funds – there is almost no academic literature that investigates

the implications of PFC-for-AIP funds substitution for airport production efficiency. The only study we

are aware of is Zou et al. (2015), who use second-stage regression in a two-stage Data Envelopment

Analysis (DEA) approach and find positive and negative impacts of PFC and AIP funds on airport

production efficiency. The authors argue that the finding is consistent with the greater flexibility airports

have in utilizing PFC than AIP funds. However, the study does not provide answers to the question of

substitutability between PFC and AIP funds. In addition, the dynamic relationship between PFC and

AIP funds is not recognized: determination of AIP funds for an airport in the current year depends on

passenger enplanement in the previous year, which directly relate to the previous year’s PFC revenues.

The present paper intends to fill these gaps and contributes to the literature on airport efficiency

modeling and financing in six ways. First and foremost, we look into the substitutability of PFC for AIP

funds, by taking into explicit consideration the existing complementary relationship between these two

airport financing sources. Second, we specifically account for the inter-temporal dynamics of airport

passenger enplanement, PFC, and AIP funds allocation, i.e., the fact that passenger enplanement

determine both PFC revenue in the current year and AIP funds in the following year. Third, we specify

sub-structures while modeling the airport production process, which allows for more detailed

characterization of how airports use inputs to generate intermediate and final outputs. The three

contributions are integrated into a dynamic network Data Envelopment Analysis framework, which is

the first time in the airport efficiency literature. Fourth, the results from our modeling provide important

policy insights that support the growing arguments for PFC-for-AIP funds substitution in the US airport

sector. Fifth, using random effect Tobit regression, the relationship between the amount of substitutable

AIP funds and airport efficiency scores is estimated. Finally, while focusing on PFC-for-AIP funds

substitution, the methodological framework proposed in this study can be generalized to investigate

substitutability between any two complementary resources in transportation and non-transportation

production systems.


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The paper continues with a review of existing literature on airport efficiency modeling in Section

2. The dynamic network structure, and subsequently three models on PFC-for-AIP funds substitution,

airport efficiency measurement, and the substitution-efficiency relation are presented in Section 3.

Section 4 presents the data, followed by modeling results and discussions in Section 5. Conclusions and

directions for future research are given in Section 6.

2 Literature review The field of airport efficiency modeling has an established body of literature. Two most popular

methods are DEA and stochastic frontier analysis (SFA). Gillen and Lall (1997) are among the earliest

researchers introducing DEA to measure airport efficiency and derive relevant performance indices.

Both airport terminal efficiency and movement efficiency are quantified. Sarkis (2000) uses a variety

of DEA models to find the effect of airport hub status, being in a snowbelt, and being part of a multi-

airport system on the operational efficiency of U.S. airports. Later Sarkis and Talluri (2004) apply

clustering analysis to DEA results to identify the benchmarking airports with similar resource utilization

structure. Different from DEA which draws frontiers using deterministic mathematical programming,

SFA incorporates random errors in deriving the airport production frontier line. Pels et al. (2003) use

SFA to estimate the efficiency and investigate the returns-to-scale properties for air transport

movements and passenger movements at 34 European airports. SFA is also employed by Oum et al.

(2008) to explore the relationship between airport ownership structure and airport efficiency, and by

Scotti et al. (2012) to assess the impact of airport competition on the technical efficiency of Italian

airports. All these studies consider airport production as an “all-in-one” process, i.e., inputs are

converted to outputs without dealing with what occurs inside the production process. On the other hand,

airport production can be described in more detail, for example, one can consider that airports first use

labor and capital to attract flight traffic, which then produces passenger enplanement and cargo

throughput.

The theoretical DEA literature has evolved recently into incorporating internal structures and inter-

temporal dynamics of production processes. DEA models with internal structures is frequently termed

“network DEA” and models with inter-temporal dynamics named “dynamic DEA”. Network DEA

models are first introduced by Färe and Grosskopf (2000), who enrich traditional all-in-one DEA

models by enabling the characterization of sequential or parallel processes in production. Liang et al.

(2006) develops a network DEA model to measure efficiency of firms in a supply chain. The model

considers the case that a supplier and a retailer are under coordination or in a leader-follower

relationship. The supplier’s improvement influences that of the retailer’s, and the way the influence

works depends on the relationship specified. Yu and Lin (2008) evaluate the performance of European

railways using a network DEA model. The model divides the railway operation into passenger, freight,

and consumption processes, and allocates common inputs (e.g., the number of employees and length of

line) to different operations. Tone and Tsutsui (2009) develop a network model using slacks-based

measures (SBM), which has the advantage of not requiring all inputs or outputs to be improved equi-

proportionally.

Dynamic DEA models consider how production of a firm in one period affects its production in

the next period while measuring efficiency. Nemoto and Goto (1999) first extend traditional DEA to a

dynamic framework by incorporating the adjustment cost of investment and inter-temporal substitution.

Färe et al. (2007) and Tone and Tsutsui (2010) propose dynamic SBM models to capture inter-period

“carryovers”. Applications of dynamic DEA abound, in fields such as electric utilities (Nemoto and


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Goto, 2003), agriculture production (Jaenicke, 2000), and retail department stores (de Mateo et al.,

2006). Recently Lu et al. (2014) use dynamic SBM to evaluate life-insurance firms and recognize the

fact that firm debt and equity in one year will be transcended to the next year.

The DEA literature has further seen combining the network and dynamic aspects of firm

production into a single DEA framework. Färe and Grosskopf (2000) and Färe et al. (2007) lay the

stepping stones of the dynamic network DEA, with adapted definitions of production possibility sets

and efficiency measures. Bogetoft et al. (2009) develop a dynamic network DEA model to examine the

optimal investment path for U.S. manufacturers. The authors decompose total outputs of the chosen

U.S. manufacturers into final outputs (consumption), private investment, and public investment.

Production in one period generates final outputs and investment, which are used as inputs along with

capital stock for the next period. The model then finds the amount of investment that maximizes the

final outputs throughout the investigation periods. Dynamic network DEA has also been considered

lately in the context of SBM (Tone and Tsutsui, 2014). Interested readers may refer to Cook et al. (2010)

and Kao (2014) for detailed review on network and dynamic DEA models.

The literature reports several applications of network DEA to measuring airline performance. Zhu

(2011) uses a virtual price network DEA model to analyze the efficiency of 21 airlines in the world.

The production network comprises two sub-processes: first operational costs producing load factor and

fleet size, which then generate revenue and revenue passenger miles. Tavassoli et al. (2014) develops a

two-stage network SBM model with shared inputs to assess performance of 11 domestic airlines in Iran.

The first stage evaluates airline technical efficiency in relation to capacity building. The second stage

measures the service effectiveness, i.e., how efficiently a given capacity generates passenger and cargo

flows. Mallikarjun (2015) uses an unoriented network DEA model to measure the efficiency of U.S.

domestic airlines, with a three-stage production process: operation, service, and sales. The consideration

of the sales stage is particularly interesting because the ultimate goal of an airline is maximizing revenue

and all other airline network DEA papers confine their analysis up to the service stage. Li et al. (2015)

follow the network structure in Mallikarjun (2015) and develop a virtual frontier SBM model to assess

the performance of 22 international airlines. A hypothetical frontier is constructed to discriminate

efficiency scores among efficient airlines, by using maximum output and minimum input sets. We note

that none of the above studies consider inter-temporal features of the airline production, although this

naturally exists in airline businesses. For instance, airline debt can be carried over from one period to

another.

Network DEA has also been applied to the airport sector. Yu (2010) uses network SBM model to

assess the efficiency of domestic airports in Taiwan. In the paper airport operations are divided into

“production” and “service” stages. The service stage is further disaggregated into airside and landside

services. The author finds that service efficiency is far lower than production efficiency for Taiwanese

airports. Lozano et al. (2013) develops a directional distance function DEA model with a network

structure. Airport operations are divided into “aircraft movements” and “aircraft loading” stages. The

model incorporates the possibility that decreasing airport flight delay restricts the number of aircraft

movements, and shows that network DEA model has more discriminatory power than traditional, all-

in-one DEA model. A virtual price network DEA model is applied to Brazilian airports by Wanke

(2013). It delineates airport operations into two stages pertaining to “physical infrastructure” and “flight

consolidation”. Flight regularity, location, and international status are found to have positive impacts

on the efficiency of flight consolidation. Some of the major features of the above three airport DEA

studies are summarized in Table 1. We note that the network structures in Lozano et al. (2013) and


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Wanke (2013) are largely consistent, with the first stage producing aircraft movements and the second

stage generating passenger enplanement and cargo throughput. Yu (2010) put aircraft movements as an

output in the second stage. The choice of inputs differs in the three studies, which may be because of

data availability. Again, it should be noted that none of these studies consider inter-temporal dynamics

in the airport production process.

Table 1. Application of network DEA in airport analysis

Yu (2010) Lozano et al. (2013) Wanke (2013)

Data Taiwanese airports Spanish airports Brazilian airports

First stage Production Aircraft movement Physical infrastructure

Second stage Service Aircraft loading Flight consolidation

Input Number of employees, runway

area, apron area, terminal area

Runway area, apron

capacity, number of

boarding gates,

number of baggage

belts, number of

check-in counters

Terminal area, aircraft

parking spaces, number of

runways

Intermediate

output between

stages

Runway capacity, terminal

capacity Aircraft movements

Number of aircraft landings

and take-offs

Output Aircraft movements, passenger

movements, cargo volume

Passenger movements,

cargo handled,

number of delayed

flights, accumulated

flight delay minutes

Number of passengers, cargo

throughput

For airport finance in the U.S., as mentioned before academic research to support and inform the

heated policy debate on whether and ways to reduce federal government aids is almost non-existent.

Specifically for the potential substitution of PFC for AIP funds and its implication for airport production

efficiency, we are only aware of Zou et al. (2015) as a relevant study. By developing a two-stage DEA

model, the authors find a positive linkage between airport production efficiency and PFC use, but a

negative linkage between airport production efficiency and the use of AIP funds. Although the study

investigates indirectly the potential change in airport efficiency under hypothetical PFC-for-AIP funds

substitution scenarios, it does not examine the substitutability between the two airport financing sources

conditional on production feasibilities. In addition, the study does not capture any inter-temporal

interactions nor considers the sub-structures of the airport production process.

3 Model This section presents the model formulation. We first specify in subsection 3.1 the dynamic

network structure of the airport production and the choice for production inputs/outputs. Then


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subsections 3.2 and 3.3 present the mathematical models for PFC-for-AIP funds substitution and airport

efficiency measurement. The PFC-for-AIP funds substitution is from the FAA perspective, whereas

airport efficiency measurement is from the standpoint of individual airports. Building on these models,

subsection 3.4 further specifies a random effect Tobit regression model to estimate the relationship

between the amount of substitutable AIP funds and airport efficiency.

3.1 Dynamic network structure

The dynamic network structure of the DEA model considered in our study is shown in Figure 1.

In terms of the network feature, we divide airport production into two stages, termed “aircraft movement”

and “aircraft loading”, based on the previous airport efficiency studies using network DEA (Lozano et

al. (2013) and Wanke (2013), as in Table 1). For the dynamic feature, we explicitly consider the fact

that airport production in year t affects airport production in t+1, through passenger enplanement.

Figure 1. The dynamic network structure of the DEA model

The first stage in the dynamic network structure, “aircraft movement”, uses labor, materials and

capital (net assets) inputs to produce aircraft operations. In addition, the first-stage production generates

flight delay as an undesirable output. The second stage, “aircraft loading”, describes the process of how

aircraft movement produces passenger and cargo flows. At the second stage, promotion is further

considered as an external input, which is defined as the amount of money spent on marketing and

advertising to attract passenger and cargo demand. The two-stage network structure implies that airports

do not generate passengers and cargoes directly from using labor, materials, and capital inputs; rather,

aircraft movements mediate between use of these inputs and passenger/cargo flows.

In terms of inter-temporal dynamics, passenger enplanement in year t determines PFC in year t

and AIP funds in year t+1. Since PFC is levied on a per passenger basis, the number of passengers

enplaned in year t times the amount of PFC levied per passenger gives total PFC in year t. By contrast,


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AIP funds are allocated by the FAA to airports in year t+1 based on the passenger enplanement in year

t. This is why we position “PFC determined” at the end of year t, and “AIP determined” at the beginning

of year t+1 in Figure 1. It should be noted that both AIP funds and PFC are included in capital (net

assets) in the FAA data reporting (see Section 4). Thus there is no need to consider AIP funds and PFC

separately as two additional inputs.

3.2 PFC-for-AIP funds substitution model

3.2.1 Defining production possibility set

The first step to specify the PFC-for-AIP funds substitution model is to define the production

possibility set (PPS), in which airports are assumed to be operable. Defining PPS is important because

airports should be ensured that the optimal PFC-for-AIP funds substitution path is attainable.

As mentioned above, the airport production process is decomposed into two stages. At stage k

(k=1,2) and in year t, an airport o uses a combination of inputs ( )t t t

k1o k2o kIox ,x ,...,xt

kox to produce

outputs ( ).t t t

k1o k2o kRoy , y ,..., yt

koy In particular, an intermediate output 1

t

oz , i.e., aircraft operations, is

produced from stage 1, which is used as an input for stage 2. Then PPS for the airport is the set of

vectors 1( , , )t

ozt t

ko kox y satisfying the following constraints:

1

1

1 2

1 1

(i) , , , ,

(ii) , , , ,

(iii) ,

nt t t

kj kij kio k

j

nt t t

kj krj kro k

j

n nt t t t

j j j j

j j

x x i I k t

y y r R k t

z = z t

(1)

where t

kj is a weight imposed on airport j = 1,…,n to construct the frontier space. n is the number of

airports in the dataset. kI and

kR represent the sets of inputs and outputs in stage k. For inequalities

(1)-i and (1)-ii, the left-hand side (LHS) corresponds to the sets of airports that lie on the production

frontier. The crucial difference between traditional all-in-one DEA models and the network DEA model

presented here is the role of intermediate outputs described in equality (1)-iii. The equation indicates

that the amount of intermediate outputs produced in stage 1 on the frontier should be equal to the amount

used as inputs in stage 2 on the frontier, although in general the intermediate output could be lost or

added from external sources (Tone and Tsutsui, 2009; 2014). In our study, the intermediate output from

stage 1 is aircraft operations, which are not possible to change once produced. Thus the equality

relationship (1)-iii is used. Note that (1)-iii does not require the intermediate outputs to be lower or

higher than the observed level. Tone and Tsutsui (2009; 2014) name this “free link.” If the intermediate

output is restricted to be equal to the observed amount, it will be “fixed link.” To specify the fixed link,

(1)-iii will be substituted by the following constraint:

1 2

1 1

, .n n

t t t t t

j j j j o

j j

z = z z t

(2)

where toz is the observed amount of the intermediate output at time t. As we do not want aircraft

operations to change by PFC-for-AIP funds substitution, the fixed link assumption is more appropriate


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than the free link assumption. In other words, we replace constraint (1)-iii by constraint (2) in

characterizing the PPS for each airport.

3.2.2 Model formulation

The objective of the PFC-for-AIP funds substitution model is to find the maximum amount of AIP

funds that can be replaced by PFC at each airport, while guaranteeing that the airport production is

feasible. In this study, we view that the substitution is from the FAA perspective, and this substitution

departs from the existing complementary relationship between PFC and AIP funds stipulated by the

FAA formulas and rules. The mathematical expressions for the existing complementary relationship

between PFC and AIP funds are rather complex. Details about the relationship is provided in Appendix

A.

To be more specific about the departure from the existing complementary relationship between

PFC and AIP fund through substitution, we define receivable and desirable PFC (AIP funds).

Receivable PFC and AIP funds are PFC and AIP funds that an airport can collect under the current FAA

formulas and rules. In other words, they denote the amounts that we currently observe. Desirable PFC

and AIP funds are PFC and AIP funds when PFC-for-AIP funds substitution were in place. We use the

term “desirable” since we consider it to be the policy direction that the FAA wants to pursue. In sum,

we have:

(i) Desirable PFC = Receivable PFC + Substitutable amount

(ii) Desirable AIP funds = Receivable AIP funds − Substitutable amount (3)

Following the above discussions, we formulate the dynamic network model for PFC-for-AIP funds

substitution as the following linear program:


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1 11 1

,

1 1

1

1

1 2

1 1

1

1

maximize

s.t.

(i) , 1, 2, , ,

(ii) , 1, 2, , ,

(iii) , ,

(iv) ,

T Tt t

pa o ao

t t

nt t t

kj kij kio k

j

nt t t

kj krj kro k

j

n nt t t t

j j j j

j j

nt t t

j j o

j

s s

x x k i I t

y y k r R t

z = z t

z z

1

2

1

1 1 1 1 1 1

2 2 ,

1 1

1 1

1 2

1

,

(v) 1, 1, 2, ,

(vi) , ,

(vii) , 1,..., 1,

(viii) (

nt

kj

j

nt t t

j j o

j

n nt t t t t t

j j o j j pa o

j j

nt t t

j j j j

j

t

k t

e e t

f e s t T

e

1

1 1

2 ,

0 1

1 1 1 1

1 2 ,

1

1

,

, ) ( ) ,

1, 2,...5, 1,..., 1,

(ix) 26 ( , ) , 1,..., 1,

0, 1,2, , ,

,

u un nt t t t t t

o d d n n j j pa o ao

d j

nt t t t t t t

j j j j o pa o ao

j

t

kj

t

pa o a

f c a a a e s s

n t T

e f s s t T

k j t

s s

1

2

0, 1,... 1,

where

0.5 Large, Medium hub airports and 3,

( , ) 0.25 Large, Medium hub airports and 3,

1 Non, Small hub airports.

t

o

t

o

t t t t

j j o o

t T

o f

e f o f

o

(4)

The objective of the linear program is to maximize a weighted sum of two terms: 1) the amount of

PFC-for-AIP funds substitution, 1

,

t

pa os , and 2) the amount of possible redundant AIP funds after the

substitution, 1t

aos . An arbitrary small number 1 distinguishes the priorities between the two

objectives. Note that 1

,

t

pa os and 1t

aos can only be calculated starting from the second year based on

passenger enplanement of the first year, as reflected in the summations.

Two additional points are worth noting for the objective function. First, the research question of

our interest is to measure the substitutability between PFC and AIP funds. Hence the first term of PFC-

for-AIP funds substitution is given a higher weight (i.e., one as opposed to a small number ). Second,

we include 1t

aos to ensure that the relationship between the amounts of receivable and desirable AIP

funds (i.e., Eq. (3)-ii) holds in linear program (4), in addition to finding redundant AIP funds, if there


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is any. More details for keeping the second term in the objective function of (4) and how it leads to the

relationship (3)-ii are presented in Appendix A.

The linear program is subject to several constraints. Constraints (4)-i to (4)-vi regulate the

improvement path of inputs and outputs, as well as the intermediate output from stage 1. That is, these

constraints define the PPS of airport o, as in (1) and (2). More specifically, constraint (4)-i denotes that

the use of each input should be no less than the level on the frontier. Likewise, (4)-ii means that the

outputs should not be higher than the level on the frontier. Constraints (4)-iii and (4)-iv characterize the

“fixed link” relationship for the intermediate output which is already explained in subsection 3.1.

Constraint (4)-v permits variable returns-to-scale operation of airports. In constraint (4)-vi, we consider

that passenger enplanement with and without PFC-for-AIP funds substitution should be the same

(denoted by t

oe ). By holding passenger enplanement constant, we can more conveniently compare the

amount of AIP funds before and after PFC-for-AIP funds substitution. Constraint (4)-vii and (4)-viii

describe the use of PFC and AIP funds, which involve the amount of PFC-for-AIP funds substitution

and the possible amount of redundant AIP funds. In these two constraints, 1t

j is the observed PFC

at airport j in year t+1; 1t

j

the observed AIP funds at airport j in year t+1; 1t

of

the PFC per

passenger at airport o in year t+1. Further details about the two constraints can be found in Appendix

A. Simply speaking, constraint (4)-vii and (4)-viii can be viewed as the more elaborate expressions of

(3)-i and (3)-ii. Constraint (4)-ix reflects the cap set by the FAA on the amount of AIP funds an airport

can receive, equal to $26 million. Finally, all ’s are non-negative. So are the amount of PFC-for-AIP

funds substitution and possible redundant AIP funds.

3.3 Efficiency measurement model

While the FAA is keen to understand the maximum possible amount of PFC-for-AIP funds

substitution, individual airports are interested in their own productive efficiency. In addition, it is of

policy relevance to understand the relationship between the substitutable amount of PFC for AIP funds

and the productive efficiency of airports. To this end, measuring airport productive efficiency, which is

the focus of this subsection, is necessary.

We consider an input-oriented network SBM model, whose specification is first proposed by Tone

and Tsutsui (2010; 2014), for measuring airport efficiency. Compared to other DEA models, SBM

models have the advantage of not requiring all inputs or outputs to be improved equi-proportionally.

Moreover, SBM models have relatively high discriminatory power. Under an SBM model specification,

the efficiency of an airport is obtained from solving the following linear program:


11

2

1 1 1

1

1

1 2

1 1

Minimize 1

s.t.

(i) , 1, 2, , ,

(ii) , 1, 2, , ,

(iii) , ,

(iv)

km t k tTkio

tt k i k kio

nt t t- t

kj kij kio kio k

j

nt t t

kj krj kro k

j

n nt t t t

j j j j

j j

w w s

m x

x + s x k i I t

y y k r R t

z = z t

1

1

1

2

1

1 1 1 1 1 1

2 2 ,

1 1

, ,

(v) 1, 1, 2, ,

(vi) , ,

(vii) , 1,..., 1,

(viii)

nt t t

j j o

j

nt

kj

j

nt t t

j j o

j

n nt t t t t t

j j o j j pa o

j j

z z t

k t

e e t

f e s t T

11 1 1 1

1 2 2 ,

1 0 1

1 1 1 1

1 2 ,

1

( , ) ( ) ,

1, 2,...5, 1,..., 1,

(ix) 26 ( , ) , 1,..., 1,

0, 1

u un nnt t t t t t t t t

j j j j o d d n n j j pa o ao

j d j

nt t t t t t t

j j j j o pa o ao

j

t

kj

e f c a a a e s s

n t T

e f s s t T

k

2

, 2, , ,

0, 1, 2, , ,

where

0.5 Large, Medium hub airports and 3,

( , ) 0.25 Large, Medium hub airports and 3,

1 Non, Small hub air

t -

kio k

t

o

t t t t

j j o o

j t

s k i I t

o f

e f o f

o

ports.

(5)

where km is a parameter denoting the number of inputs in stage k,

t

kios slack of input type i in stage

k, i.e., the amount of redundant input. The input slacks in the objective are weighted by and k tw w ,

which are the weights imposed on stage k and time t. We assign equal weights to each stage and time

period: wk = 0.5 (k = 1, 2) and wt = 0.2 (t = 1,…,5). All other notations follow the ones in (4). Only

inputs are considered in the objective because increasing passenger or cargo flows is assumed beyond

the managerial discretion of airports (Zou et al., 2015). The model has a similar structure to (4) except

that constraint (4)-i is replaced with (5)-i. Indeed, linear program (5) maintains the same dynamic

network structure as linear program (4), though the objective is different.


12

After running linear program (5) for an airport, airport efficiency scores that are stage-time-specific,

stage-specific, time-specific, and the overall average can be calculated as follows:1

*

1

*

1 1

*

1 1

1 : efficiency of stage at time ,

1 : average efficiency of stage over periods,

1 : average efficiency at time

k

k

k

m tt kiok t

i k kio

m t tTkio

k tt i k kio

m k tKt kio

tk i k kio

sk t

m x

w sk

m x

w st

m x

*2

1 1 1

.

1 : overall efficiency.km t k tT

kio

tt k i k kio

w w s

m x

(6)

where the asterisks denote the optimal solution from solving linear program (5).

3.4 Substitution-efficiency relation model

After the amount of PFC-for-AIP funds substitution and airport efficiency are obtained, a random

effect Tobit regression model is used to examine the statistical relationship between the substitutable

amount and airport efficiency. The choice of a random effect Tobit model is based on the following

features of the data. First, we consider the substitutable amount as the dependent variable, for which

negative values are not possible and many zero values may exist from solving linear program (4). In

this case, Tobit regression is more appropriate than conventional regression models, the latter of which

do not account for data censoring. Second, the data consist of information for 41 airports over 5 years.

There may be characteristics inherent to an airport but not reflected in the explanatory variables included

in the model. By incorporating random effect, we can account for such airport-specific effect and avoid

underspecifying the model. Third, airports considered in our study are only a small portion of the entire

U.S. airports (due to data availability), and considerable variations in airport size exist in the dataset.

This is a typical condition that a random effect model specification is more effective than other

specifications (Greene, 2012).

Following the above discussion, the random effect Tobit regression model is specified as follows:

0 1 , + ,it it n n it i it

n

Substitution Efficiency X u (7)

where subscripts i and t are airport and year indicators. 0 1, , n are the parameters to be estimated;

,n itX the independent variables other than the efficiency score; iu the airport-specific effect; and it

the error term. Similar to Zou et al. (2015), ,n itX includes runway utilization factors, airport hub type,

and year dummies. Runway utilization factors include passengers per runway, cargo tonnage per

runway, and flight delay per runway. For the Efficiencyit variable, we experiment with both average and

stage-specific efficiencies for an airport in a year, i.e., t and

t

k (k = 1, 2) in (6).

1 For brevity, the airport index o is omitted on the LHS.


13

We conjecture that the amount of PFC-for-AIP funds substitution is negatively correlated with

airport efficiency. This is because more efficient airports may already use their resources – including

PFC and AIP funds – efficiently, thus leaving less room for substitution than less efficient airports. It

should be noted that we treat airport efficiency as an explanatory variable, which is different from

existing studies in which airport efficiency scores are considered as the dependent variable in post-DEA

second-stage regression analysis, e.g., Gillen and Lall (1997), Adler and Liebert (2014). Those studies

intend to identify the determinants for airport efficiency, whereas this study seeks the impact on the

amount of PFC-for-AIP funds substitution of airport efficiency.

4 Data Yearly data of 41 U.S. airports during 2009-2013 are collected for this study. They represent the

full list of airports for which complete information on inputs and outputs is available. The airports are

listed in Table 4. For inputs, information on the physical use of labor and materials is not available. We

instead use the costs associated with input consumptions. Labor cost includes personnel compensation

and benefits provided to airport employees. Materials cost refers to costs to communication, supply and

material, contractual service, insurance and other operating expenses. We characterize capital input (net

assets) as the property values of the airports net of debts. Inputs data are collected from the FAA Form

5100-127 (FAA, 2012). As already mentioned in subsection 3.1, capital input in Form 5100-127

includes AIP funds and PFC revenue received by an airport. For outputs, passenger enplanement and

cargo tonnage are also directly obtainable from FAA Form 5100-127.

In addition to labor, materials, and capital, we consider flight delay as an undesirable output in the

aircraft movement stage, and promotion as an external input in the aircraft loading stage. For flight

delay, we used the inverse of total flight delay at the airport under study in a year. The flight delay

information is compiled using the Airline On-Time Performance Database in the U.S. Bureau of

Transportation Statistics (BTS, 2013). We convert all monetary values to constant dollars in 2009 using

Consumer Price Index (United States Department of Labor, 2014). While promotion information is

available in FAA Form 5100-127, as shown in Table 2 some airports did not have promotion

expenditure. When this occurs, we adopt the approach in Tone (2001) by removing the promotion term

in linear programs (5) and (6). This way, the airport will have no input slacks for promotion and thus

no associated input inefficiency.

Note that FAA Form 5100-127 provides precise records of PFC but not of AIP funds. The best

proxy we can use for AIP funds is the “grant” item in Form 5100-127, which includes AIP funds and

state/local aids. According to Kirk (2009, 2010), state/local aid accounts for 14% in the reported grants.

As a further check, we manually review the Comprehensive Annual Financial Report (CAFR) of some

airports included in our study, and find that state/local aids hold an even smaller percentage in the

“grants” item. For example, the share of state/local aids in grants is about 2% for Columbus Regional

Airport and Chicago O’Hare International Airport. In view of this, we consider the reported grants as a

reasonably good approximation for AIP funds.

Table 2. Summary statistics of variables

Variable Min. Med. Mean. Max.

Delay (mins) 7,571 260,700 554,700 4,907,000

Cargo (tons) 43,170,000 369,100,000 812,000,000 6,995,000,000

Enplanement 96,491 3,266,309 6,859,602 33,297,578


14

Labor cost ($) 1,479,607 24,117,710 39,709,059 339,551,360

Material cost ($) 742,146 25,144,824 57,898,615 341,442,496

Net asset ($) 4,753,000 337,500,000 555,600,000 3,755,000,000

Promotion ($) 0 482,744 856,309 10,140,734

Aircraft operation

(flights) 17,801 159,697 241,826 3,614,710

PFC ($) 62,145 10,862,739 25,672,257 124,762,198

AIP fund ($) 27,362 8,430,216 14,305,416 201,038,977

Charnes et al. (1985) state that inputs and outputs should meet isotonicity, i.e., increasing inputs

should lead to higher outputs. To test whether this is the case in our data, we conduct correlation analysis

between inputs and outputs. The correlation coefficients are reported in Table 3. Overall, it is observed

that the data meet the isotonicity condition.

Table 3. Correlation between inputs and outputs

Delay Cargo handled Enplanement Aircraft operations

Labor cost 0.712*** 0.597*** 0.856*** 0.447***

Material cost 0.921*** 0.578*** 0.957*** 0.529***

Net asset 0.595*** 0.674*** 0.770*** 0.413***

Promotions 0.314*** 0.364*** 0.451*** 0.221***

The results for correlation test with H0: rho=0 and N=205 (41*5) are reported, where ***p < 0.01.

5 Results

Table 4 presents the values for t

pas , the amount of receivable AIP funds, and their ratio. t

pas

comes from solving the PFC-for-AIP funds substitution model; whereas the amount of receivable AIP

funds is the observed (actual) amount of AIP funds allocated to airports. As shown, the ratio varies

widely over airports. For example, in 2010 airports range from having no substitution to having up to

86% of AIP funds substitutable. The no-substitution case occurs to 21 out of the 41 airports. Meanwhile,

at airports such as Cleveland-Hopkins, Cincinnati/Northern Kentucky, and Washington Dulles, the

substitution ratio exceeds 80%. Similar conclusions can also be drawn for the other three years.

Table 4. The amount of substitution (in $ million) and percentage proportion by airport

Airport

Year 2010 Year 2011

t

pas

①

Receivable AIP

funds

②

①/②

t

pas

①

Receivable AIP

funds

②

①/②

Albany International 0.35 4.35 8% 0.31 4.29 7%

Boise Air Terminal/Gowen Field 0.00 4.43 0% 0.00 4.43 0%

Baltimore/Washington

International Thurgood Marshall 0.00 3.27 0% 0.00 3.43 0%

Columbia Metropolitan 0.27 3.41 8% 0.11 3.34 3%

The Eastern Iowa 0.00 3.33 0% 0.00 3.18 0%

Cleveland-Hopkins International 1.80 2.14 84% 1.33 1.94 69%


15

City of Colorado Springs

Municipal 1.30 3.94 33% 0.97 3.87 25%

Cincinnati/Northern Kentucky

International 1.66 2.08 80% 1.48 1.75 84%

James M Cox Dayton

International 0.00 4.28 0% 0.00 4.29 0%

Denver International 0.00 6.50 0% 0.00 6.50 0%

Des Moines International 0.98 3.89 25% 0.03 3.89 1%

Detroit Metropolitan Wayne

County 3.44 4.74 72% 3.08 4.73 65%

Fresno Yosemite International 0.88 3.50 25% 0.27 3.51 8%

Bishop International 0.32 3.33 10% 0.00 3.37 0%

Fort Wayne International 0.00 2.16 0% 0.00 2.22 0%

Spokane International 0.03 4.56 1% 0.29 4.62 6%

Grand Forks International 0.00 1.26 0% 0.00 1.39 0%

Honolulu International 0.00 2.98 0% 0.00 3.04 0%

Washington Dulles International 3.14 3.64 86% 3.20 3.68 87%

Wichita Mid-Continent 2.73 3.70 74% 0.25 3.73 7%

Indianapolis International 0.00 1.69 0% 0.00 1.70 0%

Jackson-Medgar Wiley Evers

International 0.00 3.56 0% 0.00 3.53 0%

Jacksonville International 0.00 1.47 0% 0.00 1.45 0%

McCarran International 0.00 5.94 0% 0.00 5.76 0%

Los Angeles International 0.00 6.50 0% 0.00 6.50 0%

Long Beach /Daugherty Field/ 0.03 4.50 1% 0.00 4.49 0%

Orlando International 0.00 4.96 0% 0.00 5.04 0%

Harrisburg International 0.58 3.54 16% 0.16 3.60 5%

General Mitchell International 0.00 7.02 0% 0.00 7.96 0%

Will Rogers World 2.32 4.76 49% 0.27 4.72 6%

Chicago O'Hare International 0.00 6.50 0% 0.00 6.50 0%

Philadelphia International 0.00 4.60 0% 0.00 4.56 0%

Phoenix Sky Harbor

International 0.00 5.48 0% 0.00 5.53 0%

Pittsburgh International 1.23 7.05 18% 0.46 7.13 6%

Southwest Florida International 0.69 6.77 10% 0.25 6.75 4%

Shreveport Regional 0.00 2.12 0% 0.00 2.11 0%

Norman Y. Mineta San Jose

International 1.26 7.43 17% 0.00 7.14 0%

Salt Lake City International 0.00 3.26 0% 0.00 3.33 0%

Sacramento International 0.00 1.91 0% 0.01 1.87 1%

Tampa International 1.39 2.90 48% 1.18 2.84 41%

Tucson International 0.13 4.87 3% 0.00 4.89 0%


16

Table 4. Continued

Airport

Year 2012 Year 2013

t

pas

①

Receivable AIP

funds

②

①/②

t

pas

①

Receivable AIP

funds

②

①/②

Albany International 0.50 4.27 12% 3.84 4.27 90%

Boise Air Terminal/Gowen

Field 0.00 4.42 0% 0.00 4.36 0%

Baltimore/Washington

International Thurgood

Marshall

0.00 3.57 0% 0.00 3.59 0%

Columbia Metropolitan 0.40 3.34 12% 0.69 3.38 20%

The Eastern Iowa 0.00 3.09 0% 0.00 3.21 0%

Cleveland-Hopkins

International 1.64 1.91 86% 1.56 1.88 83%

City of Colorado Springs

Municipal 0.00 3.79 0% 2.86 3.80 75%

Cincinnati/Northern Kentucky

International 1.42 1.64 86% 1.28 1.52 85%

James M Cox Dayton

International 1.00 4.30 23% 4.09 4.33 94%

Denver International 0.00 6.50 0% 0.00 6.50 0%

Des Moines International 0.00 3.94 0% 0.00 4.03 0%

Detroit Metropolitan Wayne

County 2.27 4.81 47% 3.96 4.80 83%

Fresno Yosemite International 0.76 3.52 22% 2.18 3.57 61%

Bishop International 0.07 3.24 2% 0.33 2.92 11%

Fort Wayne International 0.00 2.23 0% 0.00 2.26 0%

Spokane International 2.19 4.56 48% 4.09 4.53 90%

Grand Forks International 0.00 1.40 0% 0.00 1.50 0%

Honolulu International 0.00 3.05 0% 0.00 3.07 0%

Washington Dulles

International 3.09 3.64 85% 3.02 3.55 85%

Wichita Mid-Continent 3.11 3.72 84% 2.52 3.73 67%

Indianapolis International 0.00 1.70 0% 0.00 1.68 0%

Jackson-Medgar Wiley Evers

International 0.23 3.53 7% 1.68 3.53 48%

Jacksonville International 0.00 1.45 0% 0.00 1.42 0%

McCarran International 0.00 5.82 0% 0.00 6.00 0%

Los Angeles International 0.00 6.50 0% 0.00 6.50 0%

Long Beach /Daugherty Field/ 0.92 4.56 20% 3.01 4.67 64%

Orlando International 0.00 5.21 0% 0.00 5.19 0%

Harrisburg International 0.56 3.58 16% 1.57 3.59 44%

General Mitchell International 0.00 7.79 0% 0.00 6.81 0%

Will Rogers World 2.84 4.78 59% 3.82 4.85 79%

Chicago O'Hare International 0.00 6.50 0% 0.00 6.50 0%

Philadelphia International 0.00 4.66 0% 0.93 4.59 20%

Phoenix Sky Harbor

International 0.00 5.68 0% 0.00 5.83 0%


17

Pittsburgh International 5.79 7.19 81% 6.41 7.05 91%

Southwest Florida International 1.36 6.91 20% 3.93 6.71 59%

Shreveport Regional 0.00 2.24 0% 0.00 2.29 0%

Norman Y. Mineta San Jose

International 0.00 7.22 0% 6.46 7.15 90%

Salt Lake City International 0.00 3.36 0% 0.00 3.29 0%

Sacramento International 1.03 1.85 56% 1.08 1.85 59%

Tampa International 2.56 2.86 90% 2.59 2.87 90%

Tucson International 0.00 4.87 0% 0.00 4.86 0%

The aggregate results for t

pas , the amount of receivable AIP funds, and their ratio across all 41

airports and by year are presented in Table 5. The amount of receivable AIP funds highly depends on

total passenger enplanement in a year, as is clearly shown in the second column of Table 5 and from

the FAA AIP funds allocation formulas and rules (see Appendix A). Overall, the amount of receivable

AIP funds steadily increases with passenger enplanement over time, except for 2013. In contrast, greater

fluctuations are observed in t

pas , which sharply increases in 2012 after dipping to the lowest in 2011.

t

pas reaches its maximum of $58 million in 2013, more than double that in 2010. The ratio between t

pas

and the amount of receivable AIP funds also varies significantly, with the highest at 35% in 2013 and

the lowest at 8% in 2011.

Given these results on PFC-for-AIP funds substitution, we are interested in how these substitution

numbers are compared to the $500 million AIP funding cut plan between 2012 and 2014, as proposed

by the H.R. 608 FAA Reauthorization and Reform Act (see Section 1). The results here suggest that the

PFC-for-AIP funds substitution in 2012 and 2013 would save AIP funds by $93 million ($35 million +

$58 million), and this is based on 41 airports. If the analysis were extended to cover all U.S. airports,

the PFC-for-AIP funds substitution would contribute more significantly to the $500 million AIP funding

cut plan.

Table 5. Total amounts of substitution (in million units)

Year Enplanement

t

pas

①

Receivable AIP funds

②

①/②

2010 277.46 24.54 168.32 15%

2011 279.44 13.85 168.61 8%

2012 283.32 35.08 169.21 21%

2013 282.61 58.06 168.03 35%

Table 6 lists the total amounts of PFC-for-AIP funds substitution by airport type, for each year and

over four years. Four airport types are considered: non-hubs, small hubs, medium hubs, and large hubs.

We observe zero substitution possibility for non-hub airports, which may be ascribed to the fact that


18

non-hub airports have small passenger bases and most of them do not collect PFC as much as the other

airport types. Thus these airports have limited PFC revenue, and AIP funds plays a very important

financing role. Small hub airports present the largest potential for PFC-for-AIP funds substitution in

terms of the overall absolute amounts. However, this may be attributed to a larger portion of small hubs

in the data set (16 out of the 41 airports are small hubs). Medium hubs have the largest

t

pas Receivable AIP funds ratio. More than half of the receivable AIP funds (over $20 million) for

medium hubs could be substituted in 2013, and the four-year average is nearly one third (28%). For

large hubs, the substitution potential is less significant, on average presenting 14% of their total amount

of receivable AIP funds.

One reason for the different potentials of PFC-for-AIP funds substitution among airport types is

their relative distance from the production frontier (i.e., efficiency). As already mentioned, our

conjecture is that inefficient airports can substitute more PFC for AIP funds than more efficient airports.

Because more efficient airports use resources (including PFC and AIP funds) closer to the production

frontier, the substitution possibility is more limited and cost of doing so would be higher than less

efficient airports. This conjecture indeed can find its argument in other efficiency modeling studies. For

example, Lee et al. (2002) measure the shadow price of noxious gas emissions in terms of the amount

of foregone output, i.e., how much output should be foregone to reduce the emission. The authors

conclude that shadow price for less efficient firms is lower than for more efficient firms as efficient

firms have little flexibility in reallocating resources. On the contrary, inefficient airports can reallocate

resources to a greater extent to further improve production efficiency.

Table 6. Total amounts of substitution by hub type (in million dollars)

Hub type

t

pas

①

Receivable AIP

funds

②

①/② Average efficiency

Year 2010

N 0 5.55 0% 1.000

S 9.93 63.94 16% 0.362

M 6.65 37.56 18% 0.160

L 7.96 61.28 13% 0.385

Year 2011

N 0 5.72 0% 1.000

S 2.67 63.77 4% 0.445

M 3.54 37.69 9% 0.281

L 7.45 61.43 12% 0.325

Year 2012

N 0 5.87 0% 1.000

S 12.58 63.52 20% 0.487

M 11.24 37.66 30% 0.254

L 7.92 62.17 13% 0.457

Year 2013

N 0 6.05 0% 1.000

S 30.68 63.64 48% 0.417

M 20.72 36.06 57% 0.158

L 10.51 62.28 17% 0.463


19

Total

N 0 23.19 0% 1.000

S 55.86 254.87 22% 0.881

M 42.15 148.97 28% 0.850

L 33.84 247.16 14% 0.931

Note: N (n=3): non hub, board more than 10,000 but less than 0.05% of total system-wide enplanement; S

(n=16) = small hub, board 0.05% but less than 0.25%; M (n=9) = medium hub, board 0.25% but less than 1%; L

(n=13) = large hub, board 1% or more. Sample sizes are in parentheses.

One way to confirm our conjecture is to check the airport efficiency scores and the amounts of

PFC-for-AIP funds substitution by airport type. We find that, in general, the more inefficient an airport

is, the more it can substitute PFC for AIP funds, as shown in Table 6. The most inefficient hub airport

type is medium hubs, of which an airport on average can substitute PFC of $4.7 million for AIP funds

over the four-year period. In the case of small and large hubs, their amounts of PFC-for-AIP funds

substitution over the four-year period are $3.5 and $2.6 million per airport respectively. Non hub

airports have zero PFC-for-AIP funds substitutability because they are efficient. Detailed airport

efficiency scores by stage and year are presented in Appendix B.

To further investigate the effects of airport efficiency on the PFC-for-AIP funds substitutability,

we estimate three random effect Tobit regression models. The three models differ in the efficiency

variable included. Model 1 uses the average airport efficiency of the two production stages (aircraft

movement and aircraft loading), while Models 2 and 3 uses the stage-specific airport efficiency. The

estimation results are reported in Table 7.

Table 7. Tobit regression results

Variables Model 1 Model 2 Model 3

Time-specific efficiency -6.588***

(1.139)

Time-stage-1 specific

efficiency

-3.446***

(1.222)

Time-stage-2 specific

efficiency

-3.492***

(0.68)

Runway utilization factors:

a. Passengers per runway -4.30e-07

(5.01e-07)

-5.87e-07

(5.47e-07)

-3.31e-07

(5.50e-07)

b. Cargo tonnage per runway -2.21e-09

(1.71e-09)

-3.62e-09**

(1.60e-09)

-3.00e-09

(2.13e-09)

c. Flight delay per runway 7.30e-07

(5.56e-06)

-9.48e-07

(5.88e-06)

-1.99e-06

(5.54e-06)

Large hub 5.6

(300.997)

10.289

(407.949)

9.366

(390.59)

Midium hub 5.701

(300.995)

10.276

(407.947)

9.837

(390.588)

Small hub 6.268

(300.993)

10.076

(407.945)

9.082

(390.587)


20

Year 2011 -0.125

(0.325)

-0.704**

(0.346)

-0.068

(0.329)

Year 2012 1.002***

(0.349)

0.302

(0.351)

0.922***

(0.348)

Year 2013 1.895***

(0.307)

1.584***

(0.328)

1.900***

(0.304)

Constant -3.576

(300.993)

-7.535

(407.946)

-7.841

(390.587)

Sigma u 1.394 1.591 1.677

Sigma e 0.997 1.12 0.989

Pseudo-R2 0.267 0.221 0.238

Rho 0.662 0.668 0.742

Observations 164 164 164

Cluster robust standard errors in parentheses.

***p < 0.01, **p < 0.05, *p < 0.10.

The results suggest that all efficiency types have significant impacts on the PFC-for-AIP funds

substitutability. The sign of all efficiency variables is negative in all three models, which supports our

conjecture that less efficient airports have greater potential for PFC-for-AIP funds substitution. In

contrast, more efficient airports already use the resources efficiently, leaving less room for the

substitution. This finding implies that the potential substitution of PFC for AIP funds would mostly

occur to the less efficient airports. For the more efficient airports, the substitution would be smaller and

consequently their productive efficiency would be less affected. Overall, Model 1 has a higher pseudo-

R2 than the other two models; thus considering efficiency from both production stages is preferred to

accounting for efficiency from only one stage.

Besides the efficiency variables, the estimation results suggest that the runway utilization factors

and hub sizes have almost no effects on the PFC-for-AIP funds substitution, except for cargo tonnage

per runway in Model 2. A possible explanation for this is that the efficiency scores already entail

information on runway utilization and hub size. For example, Zou et al. (2015) find that efficiency

scores will be greater at airports with higher runway utilization rate and larger size. Lastly, it is

interesting to note that more recent years have greater potential for PFC-for-AIP funds substitution than

earlier years.

6 Conclusion This paper investigates the possibility of substituting PFC for AIP funds as a viable option to

reform airport financing in the U.S. By extending Zou et al. (2015), which provides empirical evidence

on why AIP funds should be replaced by PFC, this study investigates whether and how much

substitution would be feasible for an airport and assesses the relationship of the substitution with airport

production efficiency. A model framework based on a dynamic network DEA structure with policy-

consistent financing constraints is developed. The model reflects more realistically airport production

in two aspects: 1) decomposing airport production into the aircraft movement and aircraft loading stages;

2) incorporating inter-temporal dynamics for airport financing. Using the model, the amount of

desirable PFC-for-AIP funds substitution are computed for 41 airports in the U.S. In addition, the


21

productive efficiencies of these airports are estimated by employing a network SBM model. The results

of the PFC-for-AIP funds substitution model and the efficiency measurement model are further used in

a random effect Tobit model, to test the relationship between the amount of PFC-for-AIP funds

substitution and airport productive efficiency.

Three major findings can be summarized as follows: first, the PFC-for-AIP funds substitution is

viable. The studied U.S. airports can substitute PFC for 8-35% of the current AIP funds, which amounts

to about $14-58 million annually. If extending to the entire U.S. airport system, this could contribute

significantly to the three-year $500 million AIP funding cut plan proposed by the U.S. Congress. Second,

it is not possible for non-hub airports to substitute PFC for AIP funds, probably because these airports

have smaller passenger bases and collect less PFC than other airports, thus relying heavily on AIP funds

for airport financing. By contrast, small and medium hubs are major targets for the PFC-for-AIP funds

substitution. Third, inefficient airports can substitute more PFC for AIP funds than efficient airports, as

the inefficient airports have more room to readjust their resource utilization.

We suggest a few directions for extending the present investigation. First, AIP funds in our study

are approximated by total grants reported in the FAA database. If data become available, more accurate

information on AIP funds can be used to reduce potential bias arising from the approximation. Second,

one could explore alternative network structures and input/output variable choice. Third, the potential

increase in PFC may discourage air passenger travel demand. It would be interesting to examine the

associated welfare loss and compare it with the AIP funds savings as a result of the substitution.

Acknowledgement We would like to thank Danielle Rinsler from the U.S. Federal Aviation Administration for

insightful initial discussions which motivated the conduct of this research.

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78.

Appendix A: The complementary relationship between PFC and AIP funds

and the mathematical expression for (3) In this appendix, we derive the mathematical expressions for (3) that entail the complementary

relationship between PFC and AIP funds. The amount of desirable PFC for an airport would equal the

amount of receivable PFC given passenger enplanement plus the substitutable amount. Likewise, the

amount of receivable AIP funds under the current appropriation formulas and rules minus the

substitutable amount would be the amount of desirable AIP funds. Feasible substitution also requires

the amounts of desirable PFC and AIP funds in the PPS. Note that although constraints (1)-i, (1)-ii, and

(2) define the PPS for inputs, outputs, and intermediate outputs, they do not explicitly specify the

amounts of desirable and receivable PFC and AIP funds. To specify them, here we consider the

following equations:

1 1 1 1 1 1

,

1 1

1 1 1 1 1

,

1

(i) , 1,..., 1,

(ii) ( , ) , 1,..., 1,

n nt t t t t t

j j o j j pa o

j j

nt t t t t t t

j j j j pa o ao

j

f e s t T

AIP e s s t T

(A1)

where t

j , t

j , and t

je denote the actual level of PFC, AIP funds, and passenger enplanement at

airport j in year t. t

j is a weight imposed on airport j at time t.2

Eq. (A1)-i describes the possibility of PFC-for-AIP funds substitution based on the amounts of

desirable and receivable PFC. On the LHS, 1 1

1

nt t

j j

j

denotes the amount of desirable PFC that

airport o would collect given the maximum substitution between PFC and AIP funds. On the right-hand

side (RHS), parameter 1t

of indicates the actual PFC level that airport o collects from each passenger

enplanement in year t+1. 1 1

1

nt t

j j

j

e

is the passenger enplanement that airport o would achieve if the

airport were run as a most efficient one (i.e., on the production frontier). Thus 1 1 1

1

nt t t

o j j

j

f e

gives

the amount of receivable PFC that airport o would collect given the actual PFC level and passenger

2 As the discussions in the Appendix do not involve stages, t

j does not have a stage subscript. However, the

stage subscript is added in the full model (4).


25

enplanement on the frontier. The difference between 1 1

1

nt t

j j

j

and 1 1 1

1

nt t t

o j j

j

f e

, ,

t

pa os , is

then the amount of PFC that airport o would use to substitute for AIP funds in year t+1.

Eq. (A1)-ii describes the possibility of PFC-for-AIP funds substitution based on the amounts of

desirable and receivable AIP funds. The FAA AIP funds allocated to an airport typically comprise a

part that is based on formulas and rules (termed “formula funds”) and a discretionary part (termed

“discretionary funds”) (Kirk, 2009). In the present study, we only consider formula AIP funds, for the

following reasons. First, discretionary AIP funds account for a relatively small portion (24-30%) in total

AIP funds (Kirk, 2009). More importantly, by its name discretionary AIP funds cannot be determined

using formulas. In contrast, formula AIP funds can be exactly quantified based on passenger

enplanement. Focusing on formula AIP funds will allow us to accurately capture the relationship

between passenger enplanement from the previous time period and consequent formula AIP funds

received in the current time period. In the remainder of the paper, the term “AIP funds” denotes formula

AIP funds.

On the RHS of Eq. (A1)-ii, 1( , )t t t

j jAIP e is the amount of receivable AIP funds for airport o

at time t+1 given passenger enplanement level 1

nt t

j j

j

e

. The exact functional forms for

1( , )t t t

j jAIP e depend on the FAA formulas and rules, which are specified below. On the LHS,

similar to Eq. (A1)-i, 1 1

1

nt t

j j

j

represents the amount of desirable formula AIP funds given the

maximum substitution between PFC and AIP funds. The difference between 1( , )t t t

j jAIP e and

1 1

1

nt t

j j

j

consists of two parts: 1) the amount that is substitutable by PFC, 1

,

t

pa os ; and 2) the

amount of possible redundant AIP funds after the PFC-for-AIP funds substitution, 1t

aos .

We now specify the exact functional forms for 1( , )t t t

j jAIP e based on the FAA formulas and

rules, which consist of three parts. First, the FAA stipulates that the amount of formula AIP funds for

an airport relates to passenger enplanement as follows (Kirk, 2009):

$ 7.80 per passenger for the first 50,000 passengers

$ 5.20 per passenger for the next 50,000 passengers



$ 0.50 per passenger for the excess of 1 million passengers

Second, the FAA sets the rule that large- and medium-sized airports forego a portion of their

formula AIP funds calculated by the above formulas. Specifically, if an airport charges non-zero PFC

equal to or less than $3/enplanement, then the airport foregoes its formula AIP funds by an amount

equal to 50% of its projected PFC revenue up to foregoing 50% of its formula AIP funds. The percentage

foregone increases to 75% if PFC is at the level of $4.5/enplanement. Empirical evidence suggests that


26

the caps of 50% and 75% of an airport’s formula AIP funds foregone are always active for large and

medium hub airports which charge PFC (Zou et al., 2015).

Third, the formula AIP funds for an airport cannot exceed $26 million.

As a consequence of the FAA formulas and rules, the amount of receivable formula AIP funds of

an airport can be expressed as a piecewise linear function of the airport’s enplanement. To this end, we

form a vector c = (c1, c2, c3, c4), where c1=50,000; c2=50,000, c3=400,000, and c4=500,000. We further

let vector a = (a1, a2, a3, a4, a5) = (7.80, 5.20, 2.60, 0.65, 0.50) denote the average AIP funds per

enplanement in the respective enplanement intervals 1[0, ]c ,

2

1

1

( , ]i

i

c c

, 2 3

1 1

( , ]i i

i i

c c

,

3 4

1 1

( , ]i i

i i

c c

, and 4

1

( , ).i

i

c

The amount of receivable AIP funds for airport o, given passenger

enplanement at the production frontier at time t+1, i.e., 1( , )t t t

j jAIP e, must satisfy the following

constraints:

1

1

1 1

1

1 1 2 1

1 1

2

3

1 1 1

(i) ( , ) ( , ),

(ii) ( , ) + ( ) ( , ),

(iii) ( , ) (

n nt t t t t t t t

j j o j j j j

j j

n nt t t t t t t t

j j o j j j j

j j

n nt t t t t

j j o i i j j

j i j

e f a e AIP e

e f a c a e c AIP e

e f a c a e

2

1

1

3 31

4

1 1 1 1

4 4

5

1 1 1 1

) ( , ),

(iv) ( , ) ( ) ( , ),

(v) ( , ) ( )

t t t

i j j

i

n nt t t t t t t t

j j o i i j j i j j

j i j i

n nt t t t t t

j j o i i j j i

j i j i

c AIP e

e f a c a e c AIP e

e f a c a e c AIP

1

1

1

( , ),

(vi) ( , ) 26 ( , ),

t t

j j

nt t t t t t

j j o j j

j

e

e f AIP e

(A2)

where parameter 1

( , )n

t t t

j j o

j

e f

denotes the portion of formula AIP funds airport o would actually

receive in year t+1, which as mentioned before is based on passenger enplanement and the PFC level

in year t. For the four airport types considered in our dataset (i.e., large hubs, medium hubs, small hubs,

and non-hubs. See Section 5), only large and medium hub airports charge PFC. As a result,

1

( , )n

t t t

j j o

j

e f

can be expressed as follows:

1

0.5 for Large, Medium hub airports and 3,

( , ) 0.25 for Large, Medium hub airports and 3,

1 for Non, Small hub airports.

t

on

t t t t

j j o o

j

f

e f f


27

The LHS in inequalities (A2)-i to (A2)-v denote the amount of receivable formula AIP funds as

passenger enplanement 1

( )n

t t

j j

j

e

fall into the following intervals respectively: 1[0, ]c ,

2

1

1

( , ]i

i

c c

,

2 3

1 1

( , ]i i

i i

c c

, 3 4

1 1

( , ]i i

i i

c c

, and 4

1

( , ).i

i

c

The smallest LHS value among inequalities (A2)-i to

(A2)-v occurs to the constraint whose passenger enplanement interval contains 1

nt t

j j

j

e

. To illustrate

this, let us consider the case that passenger enplanement 1

nt t

j j

j

e

fall in the interval 2

1

1

( , ]i

i

c c

.

Then, we can verify that:

2 1 1

1 1

2

3 2

1 1 1

(the LHS of Eq. (A2)-ii) (the LHS of Eq. (A2)-i) = ( , )( )( ) 0 ,

(the LHS of Eq. (A2)-ii) (the LHS of Eq. (A2)-iii) = ( , )( )( )

n nt t t t t

j j o j j

j j

n nt t t t t

j j o i j j

j i j

e f a a e c

e f a a c e

2

4 2 3 4 3

1 1 1

5 2

1

0,

(the LHS of Eq. (A2)-ii) (the LHS of Eq. (A2)-iv) = ( , ){( )( ) ( )} 0,

(the LHS of Eq. (A2)-ii) (the LHS of Eq. (A2)-v) = ( , ){( )

n nt t t t t

j j o i j j

j i j

nt t t

j j o

j

e f a a c e c a a

e f a a

2

3 5 3 4 5 4

1 1

( ) ( ) ( )} 0.n

t t

i j j

i j

c e c a a c a a

.

Thus the LHS of inequality (A2)-ii, which corresponds to the amount of receivable AIP funds

given the passenger enplanement, is the lowest among all LHS in inequalities (A2)-i to (A2)-v.

We further introduce0 0 0c a . Then the expressions of constraints (A2) can be generalized as:

11

1 0 1

1

1

( , ) ( ) ( , ) 1,2,...5, 1,..., 1,

( , ) 26 ( , ) 1,..., 1.

n n nt t t t t t t t t

j j o d d n n j j j j o

j d j

nt t t t t t t

j j o j j o

j

e f c a a a e AIP e f n t T

e f AIP e f t T

(A3)

Substituting 1( , )t t t

j jAIP ein (A3) by the LHS of Eq. (A1)-ii, we obtain,

11 1 1 1

,

1 1 0 1

1 1 1 1

,

1 1

( , ) ( ) 1,2,...5, 1,..., 1,

26 ( , ) 1,..., 1.

n n n nt t t t t t t t t

j j j j o d d n n j j pa o ao

j j d j

n nt t t t t t t

j j j j o pa o ao

j j

e f c a a a e s s n t T

e f s s t T

(A4)

which are also constraints (4)-viii and (4)-ix in the PFC-for-AIP funds substitution model. Note that

constraint (A4) alone does not ensure that at least one of the inequalities in (A4) is binding. In other

words, the amount of receivable AIP funds computed by (A4), which equals

n

j

t

oa

t

opa

t

j

t

j ss1

,, , can

be always less than the actual amount of receivable AIP funds (which equals the smallest of the LHS


28

over all inequalities in (A2)), given 1

nt t

j j

j

e

and t

of . The strict equality of at least one of the

inequalities in (A4) is achieved once we maximize ,

t

pa os and t

aos in the DEA objective. In this way,

the amount of receivable AIP funds computed by (A4) will equal the actual AIP funds from using the

FAA formulas and rules.

Appendix B: Airport efficiency scores by stage and year

Table B1. Stage efficiency

Airport Stage 1:

aircraft movement

Stage 2:

aircraft loading

Albany International 0.344 0.268

Boise Air Terminal/Gowen Field 1.000 1.000

Baltimore/Washington International Thurgood Marshall 0.866 0.030

Columbia Metropolitan 0.768 0.278

The Eastern Iowa 1.000 0.135

Cleveland-Hopkins International 0.115 0.003

City of Colorado Springs Municipal 0.528 0.685

Cincinnati/Northern Kentucky International 0.087 0.370

James M Cox Dayton International 0.330 0.063

Denver International 0.692 0.150

Des Moines International 0.381 0.556

Detroit Metropolitan Wayne County 0.344 0.026

Fresno Yosemite International 0.511 0.123

Bishop International 0.936 0.130

Fort Wayne International 0.964 0.803

Spokane International 0.359 0.132

Grand Forks International 1.000 1.000

Honolulu International 0.036 1.000

Washington Dulles International 0.036 0.001

Wichita Mid-Continent 0.453 0.069

Indianapolis International 0.089 1.000

Jackson-Medgar Wiley Evers International 0.786 0.509

Jacksonville International 0.348 0.031

McCarran International 0.454 0.353

Los Angeles International 0.205 1.000

Long Beach /Daugherty Field/ 0.220 0.237

Orlando International 0.027 1.000

Harrisburg International 0.605 0.081

General Mitchell International 0.418 0.017


29

Will Rogers World 0.228 0.155

Chicago O'Hare International 0.815 1.000

Philadelphia International 0.716 0.399

Phoenix Sky Harbor International 0.283 0.476

Pittsburgh International 0.125 0.004

Southwest Florida International 0.142 0.142

Shreveport Regional 1.000 1.000

Norman Y. Mineta San Jose International 0.124 0.608

Salt Lake City International 0.305 0.204

Sacramento International 0.060 0.019

Tampa International 0.072 0.155

Tucson International 0.237 0.692

Average 0.439 0.388

Table B2. Time efficiency

Airport Year 2009 Year 2010 Year 2011 Year 2012 Year 2013

Albany International 0.223 0.228 0.386 0.490 0.202

Boise Air Terminal/Gowen Field 1.000 1.000 1.000 1.000 1.000

Baltimore/Washington International Thurgood Marshall 0.500 0.516 0.520 0.183 0.520

Columbia Metropolitan 0.601 0.466 0.530 0.513 0.505

The Eastern Iowa 0.508 0.521 0.583 0.614 0.612

Cleveland-Hopkins International 0.051 0.058 0.060 0.063 0.064

City of Colorado Springs Municipal 1.000 0.268 0.669 0.710 0.388

Cincinnati/Northern Kentucky International 0.039 0.343 0.317 0.213 0.231

James M Cox Dayton International 0.166 0.190 0.244 0.209 0.174

Denver International 0.346 0.348 0.060 0.603 0.747

Des Moines International 0.354 0.213 0.374 0.697 0.705

Detroit Metropolitan Wayne County 0.205 0.226 0.033 0.193 0.267

Fresno Yosemite International 0.275 0.287 0.368 0.339 0.314

Bishop International 0.437 0.419 0.548 0.697 0.565

Fort Wayne International 0.418 1.000 1.000 1.000 1.000

Spokane International 0.236 0.263 0.344 0.220 0.165

Grand Forks International 1.000 1.000 1.000 1.000 1.000

Honolulu International 0.516 0.518 0.519 0.520 0.517

Washington Dulles International 0.014 0.014 0.018 0.022 0.024

Wichita Mid-Continent 0.239 0.226 0.284 0.288 0.267

Indianapolis International 0.539 0.545 0.545 0.547 0.548

Jackson-Medgar Wiley Evers International 1.000 1.000 0.430 0.431 0.378

Jacksonville International 0.093 0.115 0.528 0.112 0.101

McCarran International 0.280 0.341 0.160 0.472 0.766

Los Angeles International 0.628 0.618 0.509 0.637 0.621

Long Beach /Daugherty Field/ 0.252 0.097 0.215 0.385 0.193


30

Orlando International 0.512 0.513 0.513 0.515 0.514

Harrisburg International 0.288 0.300 0.356 0.372 0.400

General Mitchell International 0.121 0.107 0.244 0.505 0.112

Will Rogers World 0.272 0.137 0.167 0.200 0.180

Chicago O'Hare International 1.000 1.000 0.536 1.000 1.000

Philadelphia International 1.000 0.500 0.071 0.951 0.266

Phoenix Sky Harbor International 0.228 0.202 0.154 0.674 0.637

Pittsburgh International 0.061 0.066 0.069 0.065 0.062

Southwest Florida International 0.101 0.123 0.159 0.159 0.167

Shreveport Regional 1.000 1.000 1.000 1.000 1.000

Norman Y. Mineta San Jose International 0.547 0.059 0.564 0.570 0.087

Salt Lake City International 0.119 0.108 1.000 0.025 0.021

Sacramento International 0.032 0.028 0.040 0.052 0.046

Tampa International 0.081 0.095 0.133 0.142 0.118

Tucson International 0.265 0.180 0.624 0.629 0.626

Average 0.404 0.372 0.412 0.464 0.417

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