Seller Density, Average Price and Price Dispersion Evidence From the General Aviation Fuel Market

Marcus Laszlo Stromeyer April 27th, 2015

IECO 401 Advisor: Professor Vroman International Economics Senior Thesis

Words: 8502 (11.5 TNR)

What is the relationship between seller density and price? Furthermore, how does an increase in the number of sellers in a given geographic region affect price dispersion? This empirical study utilizes data from the general aviation fuel market to address these two questions. It finds, with high levels of confidence, that an increase in seller density results in a decrease in average avgas prices. Moreover, the data suggests that increased seller density causes higher price dispersion. By combining both theoretical work and empirical evidence from a yet-unexplored market, this work contributes to a long line of economic work on seller density and prices.

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Acknowledgements

There are a lot of people who made this work possible. First and foremost, Id like to thank Professor Vroman, Professor Albrecht and Professor Cumby for all their support, mentorship and feedback throughout this process. It was a challenging, thrilling and highly satisfying experience to conduct original research under their guidance. Id also like to recognize the professors in the economics department, such as Professor Schwartz and Professor Evans, who met with me to discuss my research. Id like to thank my brother, Christopher Stromeyer, for always hearing out my ideas and pushing me to continue digging deeper. In addition, this experience was made that much more special by all the countless hours spent in Lauinger library with Lucia Wei, Lexi, Claire and Manu - its been a great ride, team. Finally, Id like to thank my father for introducing me to the joy of aviation and flight.

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Table of Contents I. Introduction ................................................................................................................................................... 3 II. Roadmap and Methodology .................................................................................................................... 4 III. Literature Review ........................................................................................................................................ 4 IV. General Aviation Fuel Market and Avgas Sellers ........................................................................ 12 V. Data and Data Concerns ......................................................................................................................... 14 VI. Empirical Strategy .................................................................................................................................... 15 VII. Results: The Impact of Seller Density on Average Price .......................................................... 19 VIII. Results: Seller Density and Price Dispersion ................................................................................ 23 IX. Theory and Empirical Results: Bringing it Together ................................................................ 26 X. Conclusion and Opportunities for Further Research ................................................................ 27 I. Appendix 1: Kernel Density Estimate of Density Calculation .................................................. 29 II. Appendix 2: Histogram of Fuel Prices ............................................................................................... 30 III. Appendix 3: Kernel Density Estimate of Prices ............................................................................. 31 IV. Appendix 4: Map of Airports/Sellers ................................................................................................. 32 V. Appendix 5: Comparison of Airports in my Dataset and All Airports That Sell Fuel ...... 33 I. Table 1: Overview of Variables ............................................................................................................ 35 II. Table 2: Seller Density and Average Price ....................................................................................... 36 III. Table 3: Seller density and Price Dispersion (Without Gini) .................................................... 37 IV. Table 4: Seller density and Price Dispersion (With Gini) ........................................................... 38

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I. Introduction These fuel prices are a rip-off. General aviation pilots utter these words of frustration at airports all

across America. In a market selling an identical good, the variance in aviation gas prices from airport

to airport is certainly conspicuous1. Therein lies our puzzle. Namely, what are the determinants of

aviation fuel prices? Or rather, how can we account for price variance when sellers in a given market

are selling perfect substitutes? Students in their first college economics course will learn that prices

of such a good should theoretically converge. Why is this not the case for aviation fuel? That is the

task at hand.

With this puzzle in mind I bring forth three questions for this study. In doing so, I center my

analysis around the underlying assumption of this work: that seller density is a key determinant of

prices. The questions, which will be examined with a theoretical and empirical lens, are as follows:

Answers to these questions are important, not just because they will bring clarity for an angry mob of

pilots; instead, the goal of this work is to contribute to the study of economics by furthering work on

price determination. General aviation fuel prices are simply the case study.

This study offers two primary findings in response to these questions. First, I find robust

empirical evidence that an increase in seller density results in a decrease in prices. This finding

should not come as a surprise. Second, the data suggests that an increase in seller density leads to an

increase in price dispersion. This result, on the other hand, may seem counter-intuitive at first but can

nevertheless be theoretically explained. 1 In fact, in my dataset of prices the range of prices is from $3.30 at Umatilla Municipal Airport to $6.74 at Merced County Airport. If one includes large commercial airports, the price ceiling rises to $8.73 at SFO.

Q1: What is the impact of seller density in a given geographical region on the average price?

Q2: Moreover, how can seller density help explain price dispersion in a given geographical region?

Q3: Finally, what characteristics can we infer about the general aviation fuel market from these results?

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There exists a plethora of theoretical work on seller density, spatial analysis and prices,

which by no means presents unanimous conclusions. In addition to the theoretical work, much

attention has been placed on the retail gasoline market. However, this paper is the first examination

of general aviation fuel prices. Therefore, as I proceed, there are a variety of interesting questions:

Which theoretical model will best fit this scenario? Will this study uphold the findings made in the

retail gasoline market? What can the niche aviation fuel market teach us about market theory?

II. Roadmap and Methodology This study follows a six-stepped approach. (1) First, I examine the existing literature, both theoretical

and empirical, to set the stage. This includes an overview of three distinct theories on seller density,

average price and price dispersion. (2) A brief analysis of the data, and most importantly its

limitations, is then necessary to set the stage. (3) I then proceed to explain the empirical methodology

and strategy of this study, much of which is inspired by prior work. (4) I move on to present the

results of my regressions and analyze their implications, while also remaining mindful of the works

limitations. (5) In the penultimate section, I bring everything together, linking the theory derived in

part one with the empirical results of part four. (6) I finish by suggesting opportunities for further

study and offer some concluding thoughts. The goal of this methodology is clear: I rely both on

theory and empirical analysis, often intertwining the two, to present my analysis.

III. Literature Review There is no consensus in the literature on market concentration, average price and price dispersion.

Much of the disparity is found in the analysis of the latter, price dispersion. For example, Baye et al.

(2004) examine consumer electronics sold by online retailers and find that an increase in the number

of sellers decreases price dispersion. In a similar fashion, both Lewis (2008) and Barron et al. (2004)

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find this outcome in the retail gasoline market, when controlling for heterogeneous station-level

characteristics2.

On the other hand, a portion of the literature presents what one may consider a counter-

intuitive conclusion. Best known is the work of Joseph Stiglitz (1987), which asks, Are Duopolies

More Competitive than Atomistic Markets? He grounds his hypothesis on the assumption that an

increase in the number of firms also increases search costs. A similar argument is also presented by

Carlson and McAfee (1983), who find that the variance in prices increases with the number of firms.

Walsh and Whelan (1999) find empirical evidence of such a phenomenon in the Irish grocery market.

This begs the vital question: how can one account for such different conclusions across the

literature? The key lies in the different consumer search models applied by the authors.

Three Models of Seller Density, Average Price and Equilibrium Price Dispersion3

As I provide an overview of these three models, the reader should keep a close eye on the

different underlying assumptions of these models. Namely, specific focus must be placed on whether

products, search costs and seller costs are homogenous or heterogeneous. These key factors help

differentiate the three models4.

(1) Monopolistic Model with Heterogeneous Visiting Costs - Barron et al. (2004) note that

monopolistic competition arises when consumers perceive differentiated products across sellers

(1044). In addition, such a model assumes that all sellers experience the same marginal costs of

production and that there is a common distribution of visiting costs for each consumer. This model

becomes relevant, however, if one pays attention to the work of Perloff and Salop (1985). In

proposition 2, they hypothesize that the assumptions mentioned above can lead to a single

2 There is a little bit more nuance to Lewis conclusions, which are examined later on. 3 Note: Barron et al. (2004) do a phenomenal job at taking the reader through these three key models. I therefore derived much of the structure of this section from their work. I also often refer to their conclusions. 4 There is a table summarizing all these models on page 10.

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equilibrium price. In other words, the price in such a market is determined by the typical average cost

limitations. This therefore begs the question: how can this model account for price dispersion?

The literature suggests a variety of solutions. However, for the sake of this study, I focus on

heterogeneity in the distribution of visiting costs across sellers (Barron et al. 2004, 1044). The

model assumes several seller groups that have distinct visiting costs. This is an assumption that

corresponds nicely with the characteristics of general aviation. In other words, it is safe to assume

that some airports are easier or less costly for pilots to reach than others. Most important to derive

from this is that differences in visiting costs result in different price elasticities of demand for sellers,

if one holds prices constant for each seller (Barron et al. 2004, 1044). Consequently, differences in

price elasticity across sellers means that identical prices for all sellers will not satisfy the standard

profit-maximizing conditions (Barron et al. 2004, 1045).

Let us examine the profit maximizing price function:

pi =mii, where i =1,...,N where i is the marginal cost, which is constant across firms, and mi can be broken up as follows:

mi =eiei 1

>1, where ei = (qi /pi )(pi / qi )

In this case, as ei (price elasticity for seller i) changes, so will the profit-maximizing price, pi5. Due

to heterogeneous visiting costs across seller groups, this elasticity of demand is unique to each seller

group; thus explaining price dispersion in the monopolistic model. Consider three airports/sellers:

5 In this equation, qi signifies quantity for firm i and pi is the price for firm i.

Seller Type #1 Not Isolated Low Visiting Costs Low Elasticity of Demand

Seller Type #2 Somewhat Isolated Medium Visiting Costs Medium Elasticity of Demand

Seller Type #3 Very Isolated High Visiting Costs High Elasticity of Demand

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The primary distinguishing factor across airports, and therefore sellers, is the level of isolation. As

the level of isolation increases, so do the visiting costs and the elasticity of demand. Elasticity of

demand and degree of isolation are positively correlated because consumers face a tradeoff between

expected gain from visiting an airport and cost of visiting that given airport. Buyers will therefore be

more sensitive to changes in expected gain for more remote airports. If a Seller Type 3 raises their

price, many consumers may decide that the high visiting costs are no longer worth the price gains

from visiting this given seller.

However, the level of isolation is not the only determinant of elasticity. One must also

account for the number of sellers in each group. It then becomes a reasonable extension of this model

that an increase in sellers will increase the price elasticity across the various seller groups (Barron et

al. 2004, 1045).6 These more elastic demand functions will reduce the average price or markup

across the entire market. In addition, as prices converge towards a zero-profit equilibrium, the price

dispersion will be reduced.

(2) Search Theoretic Model with Informed and Uninformed Consumers Varian (1980) remains

the seminal work for search theoretic models of price dispersion. He begins by borrowing elements

from the Salop-Stiglitz model explained in Bargains and Ripoffs (Salop and Stiglitz 1977). Salop

and Stiglitz divide consumers into two groups: the informed, who understand the complete

landscape of prices and the uninformed, who know nothing about the distribution of prices. Upon

making this assumption, Varian goes on to explain that firms engage in sales behavior in an attempt

to price discriminate between the informed and uninformed customers (Varian 1980, 652). Varian

maps out each stores density function f(p), which indicates the probably of a store charging a

specific price (See Figure 1 below). In this figure, p* represents the sellers reservation price and r

indicates the buyers reservation price. Most important to recognize is that firms have a higher 6 Note that this model assumes that the number of seller group types remains constant as the number of sellers increases.

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probability of charging extreme prices over prices in the middle of the spectrum. In other words,

the value of f(p) is higher as you approach the seller and buyer reservation prices. In other words,

firms aim to either lure the informed buyers with low prices or sell to the uninformed buyers at high

prices.

In addition, Varian assumes that the ratio of uninformed to informed buyers remains

constant. Therefore, as the number of firms increases, the volume that one firm can sell to informed

customers decreases. In other words, as the number of firms increases, the profits from selling to

informed buyers decrease; with this, we see an increase in average price. This is demonstrated in

Figure 2, in which Dale Stahl maps out the different equilibrium density functions as the number of

firms (N) increases. The probability of a firm catering to informed buyers decreases dramatically as

N increases. Finally, in terms of price dispersion, Varians model assumes that an increase in the

number of firms will increase the variance in prices (Barron et al. 2004, 1049). This is because an

increase in firms will result in a more distinct spectrum of from the equilibrium density function f(p).

Figure 1 (Varian 1980, 656) Figure 2 (Stahl 1989, 708)

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(3) Search Theoretic Model with Heterogeneous Seller and Search Costs The final model that

merits our attention was primarily developed by Carlson and McAfee (1983) and it addresses the

prices for a homogenous commodity. Their work develops a search-theoretic approach, which

assumes heterogeneous seller costs and heterogeneous visiting or search costs. They refer to Stigler

who observed that price dispersion is ubiquitous even for homogenous goods and try to find an

explanation (Stigler 1961, 213). Ratchford best explains their model, [Consumers] search

sequentially for the lowest price using a stopping rule in which search is terminated when the

expected gain from additional search is less than the constant cost of the additional search

(Ratchford 2010, 95). From this, they derive the following demand curve:

qj / q =1 (1 /T )(pj p), where j indicates the firm and the bar indicates the average. The term T is the ceiling value of the

uniform distribution of search costs7. In sum, this demand equation indicates that an increase in T,

and therefore an increase in search costs, leads to a decrease in demand elasticity.

With this, Carlson and McAfee conclude that an increase in the number of sellers decreases

markups (Barron et al. 2004, 1048). This is because an increase in the number of sellers comes from

either an increase in market size or a decrease in the fixed cost. Either way, more sellers mean that

there is a downward shift in the distribution of search costs. This leads to lower average prices.

In terms of price dispersion, Carlson and McAfee eventually conclude that, ceteris paribus,

the variance of prices is increased by an increase in the number of firms. (492). This theory is the

result of supply side dynamics. They hypothesize that if all firms have the same average costs, then

there will be no price dispersion; or rather, price dispersion is driven entirely by differences in unit

costs in this model (Ratchford 2010, 95). Therefore an increase in the number of firms will increase

price dispersion because each firm faces a slightly different cost function. 7 In addition, qj represents quantity and pj represents price for firm j.

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Summary - These results (summarized in Table 1 above) are somewhat of a surprise. Only the

monopolistic model infers a negative correlation between the number of sellers and price dispersion.

Even more surprising, the second model infers a positive correlation between seller density and

average price. Therefore, this literature review, and the conclusions it brings forward, constitutes a

prima facie challenge to the preliminary hypothesis I made when embarking on this study. .

These counter-intuitive theories are certainly not ignored by the literature. Hopkins (2006)

notes the positive correlation observed by Varian and points to the work of Baye et al. (2004) to

counter Varians argument. Lewis (2008) notes, somewhat ambiguously, that the results of Varian

(1980) and Carlson & McAfee (1983) are almost unique within the consumer search literature

(665). He goes on to argue that many search models, including Reinganum (1979) and MacMinn

(1980), assume a continuum of firms and are unable to make predictions about the relationship

between the number of firms and the equilibrium price distribution. (665) Finally, as an aside,

Sorensen (2000) examines the prescription drug market and finds that drugs with higher frequency of

use have lower price dispersion; thus suggesting another factor at play. Therefore, as this empirical

Model Product Differentiation Search Costs Seller Costs

Correlation between

seller density and average

price

Correlation between

number of sellers and price

dispersion

Monopolistic Model with Heterogeneous Visiting Costs

Yes Heterogeneous Heterogeneous Negative Negative

Search Theoretic Model with Informed and Uninformed Consumers

No Heterogeneous Homogenous Positive Positive

Search Theoretic Model with Heterogeneous Seller and Search Costs

No Heterogeneous Heterogeneous Negative Positive

Table 1

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study proceeds, it will remain cognizant of this literature, while also appreciating the existing

ambiguity. In many ways, it allows us to keep an open mind.

Evidence From The Retail Gasoline Market

While the theoretical work is rather mixed in its conclusions, the empirical work from the

retail gasoline market offers a somewhat more consistent voice: seller density lowers both average

prices and price dispersion. Barron et al. (2004) convincingly state that an increase in station density

consistently decreases both price levels and price dispersion across four geographical areas (0).

Barron et al. also mention that their results are most consistent with the theoretical framework of

monopolistic competition (Barron et al. 2004, 24)8.

Matthew Lewis, who builds on the work of Barron et al. by dividing the sellers into high and

low brand groups, splits his analysis on price dispersion into two parts: city-wide dispersion and local

dispersion. In regards to the former, he finds that price dispersion is lower for both high brand and

low-brand stations when there are more competitors of their own type in the local market (Lewis

2008, 677). This result refers to unexplained deviations from the city average price (Lewis 2008,

673). When Lewis examines local dispersion (unexplained deviations from the local average price

(673)), his result is the opposite9. Namely, Lewis concludes that an increase in sellers in a small

region leads to an increase in price (673). Therein lies a particular strength of Lewis work: he takes a

nuanced view at competition and seller heterogeneities.

To explain an increase in price dispersion at the local level, Lewis argues that an increase in

high-brand stations will lower dispersion across high-brand stations but will simultaneously increases

dispersion across low brand groups (675). To account for this result, Lewis suggests that market

8 They also note that, in terms of average price, the theory presented by Carlson and McAfee (1983) also fits with the results. However, this is not the case for price dispersion. They completely dismiss the theoretical predictions made by Varian (1980). 9 He uses a 1.5-mile radius to determine which stations are local competitors.

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composition effects may lead to greater dispersion among stations of the opposite type (676) at the

local level.

The literature on the retail gasoline market is indicative of the various factors at play. There

are station-level characteristics that one must account for; results are impacted when one changes the

geographic area under review; and finally dispersion is impacted by an interaction between different

station-types. I keep these factors in mind as I proceed with my own analysis of the general aviation

fuel market.

IV. General Aviation Fuel Market and Avgas Sellers Before proceeding, it is worth quickly examining the characteristics of general aviation and 100LL

avgas. General aviation is all civilian flying except scheduled passenger airlines (AOPA). In other

words, it ranges from operations such as weekend hobby flying to traffic helicopters for the local

news. In fact, only about 20% of all pilots in the United States are hired full-time as pilots (AOPA).

Most of these general aviation pilots fly small single engine planes that can carry between one and

five passengers.

The fuel used by these airplanes, and the subject of this study, is 100LL avgas. This is not the

same fuel used by large airplanes or even executive jets. It is very specific to general aviation. Most

general aviation planes can carry approximately 40-60 gallons of fuel, but this number is often less

due to weight limitations. A normal plane may burn around 10 gallons per hour; nonetheless, this

figure can vary drastically from plane to plane.

Finally, there are different types of airspace. For the sake of this study one should know that

the largest airports, such as SFO and JFK, are surrounded by what is known as Class Bravo

airspace. These observations were dropped from the dataset. Slightly smaller airports, such as San

Jose International, are surrounded by Class Charlie airspace. These airports were kept in the

sample but were controlled for using a dummy. It is very common for such airports to have a lot of

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general aviation activity in addition to their commercial traffic. Airports in all other types of airspace

were included without a dummy control.

Survey of 100LL Avgas Sellers I reached out to a variety of sellers all across the country and asked them how and when they determine their prices10. The survey, which is certainly qualitative and not quantitative, provided one

overarching insight: sellers set prices in a variety of ways. First, I learned that some sellers update

their prices every day based on supply and demand.11 Others only update prices when they receive

a load of fuel. Furthermore, some sellers reported that they always just make a cost plus margin

calculation. For example, one such respondent stated that their margin is always 75 cents, while

another seller reported that their markup is 50 cents for self-service and $1 for full-service. In

contrast to this constant margin method, a different seller explained that they always attempt to be

lowest in the area. There is certainly a visible contrast between the sellers that look at the landscape

to determine their price and sellers that impose a constant margin without adjusting to the

competition.

Finally, this survey indicated just how competitive this market can be. One respondent

explained:

Understanding that if you don't meet the number of gallons goal, it

can't be made up the next month in volume as you will have to raise

your price to make up what you lost the previous time period and now

you are no longer competitive as your competition is not the other guy

on the field, but the previous and the next stop for the customer.

This insight clearly shows that sellers are aware that they are often not the only option for buyers. In

addition, not all sellers get the same wholesale price; Some Airports only receive 1/2 loads of fuel, 10 It was difficult to convince the sellers that I was a student and not a competitor. Therefore, I only received 6 responses after reaching out to over 50 sellers. 11 In order to convince respondents that I was not a competitor, I had to make the survey anonymous. I therefore cannot attribute a quote to a given respondent.

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because they do not have large holding tanks, so the fuel will cost more, wrote one respondent.

Overall, this survey shined light on a variety of market characteristics: intense competition, different

pricing strategies and heterogeneous seller costs. These qualitative results will be helpful as we

attempt to explain the forthcoming empirical results.

V. Data and Data Concerns The dependent variables, average price and price dispersion, are measured using cross-sectional price

data purchased from FlightAware, a global software company specializing in aviation data. The

dataset includes the airports IATA code12, the facility name, the price of 100LL avgas13 and the

timestamp of the last price update. There are 1,497 observations for airports across the United States.

Appendix 2 and 3 show the distribution of these prices, while Appendix 4 demonstrates a map of

every airport for which I have data and every airport in the continental United States that sells 100LL

avgas. Finally, it is worth emphasizing that this price data represents a current snapshot of prices;

it does not track how prices have changed over time.

The second dataset is the FAAs Airport Facilities Data. It includes a plethora of variables,

including geographic location, closest city to the airport and the number of flight operations per year.

The 19,304 public and private facilities in the United States are all included in this dataset14.

The final source of data is the 2013 American Community Survey. It allows me to access

county specific population and economic data, thus allowing me to control for a variety of factors

that might play a role in impacting fuel prices. I use this data to get population data, household

income data, gini coefficients and population density numbers.

Data Concerns

12 For example, for San Francisco international airport the code is SFO. 13 The data includes price data both for self-service and for full service. For some observations, there is no self-service price available. Therefore, the regression analysis will include a dummy variable to control for this. When both prices are available, I simply use the self-service price and ignore the full service price. 14 There are 13,090 airports after one drops heliports and other facilities.

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Finally, it is worth briefly highlighting some specific data concerns. First, this study

examines a snapshot of prices. One would therefore hope that all the price data is from a single

point in time. However, some of the price data for more remote airports is delayed by a couple of

days, and sometimes even weeks15. Second, the data collection method used by FlightAware is not

ideal. While some of the data is self-reported by FBOs, much of the data is crowd-sourced by pilots.

It is therefore worth highlighting that there is the possibility that some data points are incorrect.

Fortunately, such error is randomly distributed and therefore should not compromise the model.

Finally, the data acquired from FlightAware is not fully indicative of all the airports in the

United States that sell fuel. In Appendix 5, I compare four key variables between all airports that sell

100LL avgas (3243) and all airports in my dataset (1497). There emerges one overarching pattern:

airports in my dataset are generally busier. In other words, they experience more daily traffic and

have more planes parked there. This should not come as a surprise, given that the price data is crowd-

sourced and will therefore be biased towards airports more frequently visited by pilots. Nevertheless,

it is worth remaining mindful of these limitations as I proceed with this analysis.

VI. Empirical Strategy This empirical strategy is inspired by the work of Lewis (2008) and Barron et al. (2004), while

simultaneously keeping in mind the characteristics that differentiate this niche market. With this in

mind, I will first explain my custom approach to calculating seller density and will then move to

outline the regression specifications.

Calculating Seller Density

The work in the retail gasoline market (Lewis 2008, Barron et al. 2004) used a rather simple

method to calculate density: counting the number of sellers within in a 1.5-mile radius. I would like

to improve on that methodology. I therefore develop a density variable using the following formula: 15 No data point is older than four weeks.

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= 5 105 = 50!!

The equation weighs the airports, and therefore also the sellers, based on distance between the origin

airport and the nearby competition. For example, an airport that is 30 nautical miles from origin

airport, such as KLVK in Figure 3 below, will only add 2/5 to the weighted density variable. An

airport that is 19 nautical miles away, on the other hand, adds 4/5 to the density variable; thus being

weighted considerably more16 17.

16 The use of 50NM as the radius, while not completely scientific, does have some underlying logic. The difference between the 25% and 75% percentile prices in my data is exactly $1 ($4.4 to $5.4). In addition, a plane going 110 knots will take just under 30 minutes to fly 50NM. Assuming that a plane consumes 10 gallons per hour, the trip to and back from an airport exactly 50NM will burn 10 gallons. Taking the average price from the data sample ($4.9), this trip would cost $49. Most single engine planes hold approximately 50 gallons of fuel. Therefore, the cost of going to the cheaper seller ($49) is almost equal to the benefits ($50), assuming you get a full tank of fuel (note that planes do have to hold reserves and therefore will not burn their entire fuel load). While imperfect and filled with assumptions, this process is meant to demonstrate that the 50NM radius does have some underlying logic. 17 I use the terms seller and airport interchangeably across this paper.

Figure 3 (Authors Sketch)

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Appendix 2 demonstrates the Kernel density estimation for this measure of density. It represents a

nice distribution for airports across the United States. The values range from 0 for Truth or

Consequences Municipal Airport in New Mexico to 23.8 for Sky Manor Airport in New Jersey,

which has an astonishing 46 different competitors within a 50NM radius. Finally, to ensure that all

bases are covered, the regression analysis will also include specifications in which density is simply

the number of sellers within 25NM.

Regression Model

My regression specifications are primarily inspired by the work of Lewis (2008) and Barron

et al. (2004). They posed the same question in the retail gasoline market and employ a two-step

methodology. First, they regress fuel price on a variety of variables, including seller density and

weekly hours of operation. They capture the error terms of this regression and use its square as the

dependent variable in the subsequent regression. In other words, after controlling for a variety of

station-specific factors in the first regression, they assume that the squared residuals indicate the

level of price dispersion. The second regression then regresses the squared residuals on seller density;

thus examining the relationship between seller density and price dispersion.

Step 1: Testing Q1 and Collecting Residuals The goal of the first step is two-fold: to analyze the relationship between seller density and average

price and also to collect the unexplained residuals for step two. With this in mind, I employ the

following regression specification:

ln(Fuel Price) = + 1SellerDensity + 2DistanceFromCBD +

3NumberOfSingleEnginePLanesPlanes + 4OperationsGALocal +

5OperationsGAItinIn + 4MedianHouseholdIncome +

6PopulationPerSquareMile + 7NumberOfPilotsInState +

8NoSelfServiceDummy + 9ClassCharlieDummy + u1

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First, note that this regression is set up as a log-linear model. Therefore, a one-unit change for a

specific regressor is associated with a (100 Coefficient) % change in price. In addition, Table 2

below provides an explanation and overview of each variable in this regression. Finally, I have 868

data points that have the self-service price. For the other 629 observations, I use the full service price

and control for the effect using a dummy (NoSelfServiceDummy).

This regression was run with four different specifications. First, seller density was measured both by

the previously mentioned weighted density variable and by counting the number of sellers within

25NM. Second, this model was run both as a simple OLS regression and by using fixed effects.

Fixed effects are used to control for state-specific characteristics18. In this case, 46 separate

regressions were run, one for each state in the dataset19.

18 Every State has different taxes placed on aviation fuel. This is something that is not accounted for in the standard OLS regression but is controlled for by using fixed effects. 19 Did not have fuel data for all 50 states.

VARIABLES LABELS/ DESCRIPTION DATASET N mean min max

DistanceFromCBD Dist. from Central Business District (In Miles) FAA AFD 1,496 3.699 0 68

NumberOfSellersWithin25NM Number of Sellers Within 25 Nautical Miles FAA + Author 1,497 4.274 0 17

WeightedDensity Weighted Density Calculation FAA + Author 1,497 7.357 0 23.80

llfullservicePriceInteger 100 LL Full Service Price FlightAware 1,102 5.309 3.450 7.990

llselfservicePriceInteger 100 LL Self Service Price FlightAware 868 4.890 3.300 6.740

NoSelfServiceDummy Dummy if No Self Service FAA AFD 1,497 0.420 0 1

NumberOfSingleEnginePlanes # of Single Engine Plane at Airport (In Tens) FAA AFD 1,490 5.882 0 81.20

OperationsGALocal # of Local GA Operations (In Hundreds) FAA AFD 1,497 161.9 0.300 2,128

OperationsGAItinInHundreds # of Itinerant GA Operations (In Hundreds) FAA AFD 1,497 149.0 0.480 3,321

ClassCAirspaceDummy Dummy if Airport is in Class Charlie Airspace FAA AFD 1,497 0.045 0 1

PopulationPerSquareMile Pop Per Square Mile for County (In Tens) ACS 1,497 32.15 0.050 549.5

NumberOfPilotsInState Number of Pilots in the State (In Thousands) ACS 1,497 21.21 1.037 64.53

MedianHouseholdIncome County Median HH Income (In Thousands) ACS 1,497 49.37 21.86 106.7

StateGiniCoefficient State Gini Coefficient ACS 1,497 0.469 0.418 0.510

Table 2

19

Step 2: Testing Q2 Assuming step one correctly defines the determinants of aviation gas price, I can now safely join

Lewis (2008) and Barron et al. (2004) in assuming that the squared residuals measure the

unexplained variance in prices across markets. (Barron et al., 1060). With this in mind, I use the

following regression equation:

An explanation of each variable can be found in Table 2 above. Why are the controls from the first

equation not present in this equation? In contrast to Step 1, airport-specific characteristics did not

seem to have any significant effect on price dispersion in any of my tests20. These variables were

therefore dropped.

In addition, because Step 1 constituted four different regression specifications, the same holds

true here. In short, by regressing seller density on the squared unexplained residuals from Step 1, I

can now examine the relationship between seller density and price dispersion. If I find a negative and

statistically significant coefficient 1, I will have shown that price dispersion decreases with

increased competition.

VII. Results: The Impact of Seller Density on Average Price The results, which are shown in Table 2 of the appendix, provide a robust answer to Q1 outlined in

the introduction. Namely, an increase in seller density in a given geographic area leads to a

decrease in average price. In addition, these regression results not only shine light on this specific

question but also provide insight on a variety of price determinants for avgas. I will therefore analyze

the results line by line in the forthcoming paragraphs. 20 Including these controls, however, did not alter the sign nor significance on the coefficient of seller density. The results are the same whether the controls are included or not.

ui2= + 1SellerDensity + + 2NumberOfPilotsInState +

3StateGiniCoefficient + vi

20

However, before proceeding, I wish to argue that Specification (3) should be the focus on our

analysis. As a reminder, these are the four specifications:

Specification (1) Specification (2) Specification (3) Specification (4)

Measure of Density

Weighted Density Calculation

Number of Sellers Within 25NM

Weighted Density Calculation

Number of Sellers Within 25NM

Fixed Effects NO NO YES YES

There are two reasons for this choice. First, by using fixed effects, I am able to control for a variety

of state-specific factors that could have distorted a standard OLS regression. For example, each state

has slightly different taxes levied on avgas. Second, the weighted density calculation previously

presented respects the particular characteristics of general aviation. Namely, that flying 5NM to a

different seller is a much smaller burden, both financially and time-wise, than flying 25NM.

Therefore, while I list the results from each specification, my analysis will focus primarily on

specification three21.

Seller Density and Average Fuel Price

The coefficient on seller density is negative and significant at the 1% level. This is expected.

As the amount of competition in a given area increases, prices should fall22. The causal mechanism

between a decrease in competition and increase in prices is quite clear: the pilot does not have any

other options. Typical single engine general aviation planes hold enough fuel for about three hours of

operation. Pilots flying long distances, such as San Francisco to Los Angeles, are often not simply

able to wait until the next airport to fuel up. In other words, the nature of general aviation means that

isolated airports face quite inelastic demand curves. 21 The different specifications are also listed to show that the results are generally consistent from specification to specification. 22 Similar results are found when substituting the weighted density value with a count of sellers within a 25 nm radius. The coefficients from (2) and (4) indicate that one more seller in this given radius is expected to decrease the price by approximately 0.4%.

21

Airport Specific Characteristics

The study implemented a variety of controls, many of which are airport-specific. The

coefficients from these controls both validate the robustness of our answer to Q1 and shine light on

the determinants of general aviation fuel prices.

One concern when undertaking this study was that the regression analysis would be unable to

isolate the increased transportation costs for isolated airports from the impact of seller density. One

way this was addressed was by including a variable, DistanceFromCBD, which indicates the distance

in miles of the airport to the nearest business district. The results show that, as expected, an increase

in this distance leads to an increase in prices23; thus indicating that airports farther removed from

population centers ask higher prices.

The volume of customers also affects a sellers pricing strategy. Hence, with this in mind, I

control for the number of single engine general aviation planes at the given airport. The data

demonstrates that for every 10 more customers, the price of 100LL avgas decreases 0.15% - a

coefficient that is significant at the 5% level.

Finally, the number of flight operations at the given airport presents one of the most

interesting findings of this study. The count of flights is divided into two categories: local flights

(OperationsGALocal) and itinerant operations (OperationsGAItin). Local traffic is defined as flight

operations within 20NM of the airport while all other traffic is defined as itinerant operations. In this

case an increase in local operations is found to lower prices, while an increase in itinerant operations

raises prices. While this may seem contradictory at first, I suspect that these results are in fact

ordinary. Airports with a lot of local operations will have highly informed buyers who are very

familiar with the different sellers in the area. On the other hand, itinerant operations represent out of

town pilots who will fly into the airport without knowing the market characteristics of the region.

An increase in such pilots or fuel buyers could therefore easily lead to an increase in prices. 23 For every 1 mile distance between the nearest business district and the airport, the price goes up 0.1%.

22

Therefore, for every 100 such flights, it is certainly probable that the fuel price rises 0.01% - a

coefficient that is significant at the 1% level.

County-Level Controls

By pulling county-level data from the American Community Survey, I control for local

factors that may play a role in setting the fuel prices. One such variable was the median household

income of the airports county. The coefficient for median household income is negative and

significant at the 10% level a rather unexpected result. General intuition would expect that with an

increase in income, prices should rise as well because wealthier customers have more inelastic

demand. One possible explanation for this phenomenon is that general aviation pilots are not a

normal cross-section of the population. In other words, general aviation pilots tend to be wealthier

than the population and a statistic that examines the entire spectrum is not indicative. It is possible

for the median income to be low but for the top 10% of earners to be very wealthy24.

The population density variable offers another unexpected result. This control was added to

account for isolated airports that incur higher transportation costs. However, the regression

coefficient indicates that as the population density increases, so does the price. Once again, this

coefficient is significant at the 1%. It is very likely that a premium is being charged at airports in

metropolitan airports; thus leading to this result.

Finally, for the two specifications that did not include fixed effects, the number of pilots in

the state was used as a control variable. As expected, an increase in buyers led to a decrease in price.

Sellers in states with higher aviation activity experience more volume and can therefore offer lower

prices.

24 This is indicative of a broader issue when controlling for county-level factors. It is hard to determine just how the local community is related to the airport itself.

23

Dummy Variables

The dummy controls, their coefficients and levels of significance, give credence to the results

from this regression. First, a dummy was included to control for instances in which a self-service

price is not available. Its coefficient is both positive and highly significant, thus indicating that the

price is higher for services such as a fuel truck coming to the plane an expected result. This is also

shown in Appendix 3, where the kernel density estimate distribution is shown for both self-service

and full-service prices. The second dummy, which indicates whether the seller is at a Class

Charlie airport25, is also positive and highly significant. Fuel at these larger airports, which often but

not always have commercial traffic, is more expensive. This is another anticipated result. In sum,

these dummy variables have the correct sign and help nail down the determinants of fuel prices.

Concluding Thoughts Overall, these results are very positive. Theory and general intuition predicts that increased

seller density lowers average prices. This prediction is validated with robust conclusions and

coefficients. While some unexpected results arise in the county-level controls, they represent that

airports are often not completely indicative of their surroundings. Having established these

determinants, we can now move on to the analysis on price dispersion.

VIII. Results: Seller Density and Price Dispersion Addressing Q2, the impact of seller density on price dispersion, is not as straightforward as the

preceding section. All things considered, these results are simply not as robust; even though the

coefficients have a high level of significance. The regression was run with two different

specifications, one that included a control for the state gini coefficient and one that did not. The

results are listed in Tables 3 and 4 of the Appendix.

25 See section 4 for explanation of class charlie.

24

Seller Density and Price Dispersion Specification (3) demonstrates, with a high level of significance, that an increase in seller

density also increases price dispersion. This holds true both when I control for the states gini

coefficient and when I do not. This result contradicts both my original expectation and some of the

evidence in the retail gasoline market (Lewis 2008, Barron et al. 2004)26. However, the literature

review did present two theories, presented primarily by Varian (1980) and Carlson and McAfee

(1983), which predicted such an outcome.

So how can we explain these results? It is most likely driven by a combination of the causal

mechanisms presented by Varian (1980) and Carlson and McAfee (1983). Varian suggests that an

increase in sellers decreases the returns from competing at low margins. A higher level of

competition decreases the volume you can sell at such a low price point. Hence, rather than

converging towards a low price, the sellers will most likely try to target different consumers, some

which will be highly informed and some which will be uninformed. Carlson and McAfee (1983)

would add that every seller that joins the market faces a different cost curve27. They will therefore

offer different prices and, as a result, will increase price dispersion. Finally, it is important to note

that Lewis (2008) did obtain the same result when he examined local price dispersion (1.5 mile

radius). I would argue that this result by Lewis is more important than his results for citywide

dispersion. This is because examining dispersion at the local level addresses the same spatial

competition questions tackled by this work.

Number of Pilots in State

All specifications from Table 3 demonstrate a positive correlation between the number of

pilots in the state and the price dispersion. This is an expected result. An increase in the number of

pilots leads to a higher number of different consumer groups that sellers can target with different 26 Lewis did have the same result as I did when he focused on a 1.5 mile radius and not on city-wide dispersion. 27 My qualitative survey of sellers did confirm that not all sellers receive the same price for the fuel from the suppliers. They therefore have different cost curves.

25

pricing strategies. Unfortunately, this finding does not hold true in the Table 4, when one controls for

the state Gini coefficient.

County Gini Coefficient and Price Dispersion

Specification (3), which has been the focus of this analysis, demonstrates that an increase in

inequality in a given state leads to an increase in price dispersion. This is certainly an anticipated

phenomenon28. Increased inequality means that sellers face drastically different elasticities of

demand across the consumer base; they will therefore undertake a variety of different pricing

strategies to maximize profit. Not only is this result highly significant but it also accounts for a large

part of the observed price dispersion29.

How robust are these results?

These results are certainly not far-fetched. While they do not align with my preliminary

hypothesis when starting this work, they do support various theoretical assumptions. Nevertheless, I

suspect that these results are better taken as a hint or indication than as a final conclusion. In this, I

disagree with the approach taken by both Lewis (2008) and Barron et al. (2004) in their respective

studies. The significance levels of our respective empirical works are very similar. However, they are

much quicker to make conclusions on seller density and price dispersions based on these results than

I am. There are three reasons for my cautious interpretation.

First, the expectation is that the first regression should encompass all determinants of fuel

prices. Only then can we assume that the squared residuals are in fact the price dispersion. Having no

way of determining whether all the effects are captured in the first step, the second steps credibility

28 This regression was also run using the airports county gini coefficient. In this case, the coefficient on the gini value was not significant. This once again demonstrates the disconnect between airports and their surrounding communities. Or rather, what determines the characteristics of an airport is not the nearby town but the larger market as a whole. It is therefore no surprise that the state gini had an effect while the county did not. 29 The adjusted R squared for the specification (3) with Gini coefficients is three times as high as when the gini coefficient is not included.

26

is somewhat compromised. Omitted variable bias in the first regression could easily be distorting

these results.

Second, it is worth highlighting that these results are only achieved when the residuals from

the fixed effects regressions in the first step are used in a standard OLS regression in the second step.

In other words, the effect seems to be so small that it does not achieve levels of significance if one

uses fixed effects in the second step. This is certainly a cause of concern.

Finally, while the first regression was able to derive credibility from a variety of controls,

that is not the case here. In other words, the expected coefficients for the control values in the first

regression matched, for the most part, the actual results. This type of test is not available because this

regression did not include regressors with straightforward expected values. Hence, these results,

while certainly significant, are not as robust as the findings on seller density and average price.

Nevertheless, on the whole, the indication is that there is a positive relationship between seller

density and price dispersion in the aviation fuel market.

IX. Theory and Empirical Results: Bringing it Together The empirical results indicate a negative correlation between seller density and average price and

suggest a positive relationship between seller density and price dispersion. These results beg the

question: how do we reconcile these results with the theories presented in the literature review?

In terms of average price, the predictions prescribed by both the monopolistic model and the

search model with heterogeneous sellers hold true. On the other hand, Varians conclusion that an

increase in sellers will cause more sellers to target uninformed buyers was not endorsed by the data.

In terms of price dispersion, the data corresponds with both the predictions of Varian (198)

and Carlson and McAfee (1983). It is very likely that both effects are at play. Varian suggested that

as more sellers enter a market, firms will be less likely to target informed buyers; thus leading to an

increase of different pricing strategies targeting a mix of uninformed buyers and informed buyers

27

with high search costs. Carlson and McAfee (1983), which approached this question from a supply

side perspective, argue that an increase in sellers leads to an increase in different cost functions.

Because these cost functions are directly responsible for price variance, this means that price

dispersion will rise.

In sum, the model that best predicted these results was Carlson and McAfees. Their model

assumes a homogenous product, heterogeneous seller costs and a distribution of different search

costs. All the assumptions apply to the aviation fuel market, in which a commodity is sold by

different sellers with distinct cost functions to consumers with individual search costs. In hindsight,

given this theoretical literature, these results should have been expected prior to embarking on this

work.

X. Conclusion and Opportunities for Further Research The goal of this research was three-fold. First, it was to examine the relationship between seller

density and average price in the aviation fuel market. The data robustly demonstrated a negative

correlation. Second, I addressed the interaction between seller density and price dispersion and

revealed that the data weakly suggests a positive correlation. By tying these results back to the

theory, I was able to demonstrate that these outcomes should have been expected, given the

characteristics of the general aviation fuel market.

Third, the goal of this study was to learn more about the general aviation market as a whole.

The president of AOPA (Aircraft Owners and Pilots Association) recently wrote that the GA

industry has had an especially tough time in the recent recession. And the pilot community has been

shrinking for years (Mark Baker, 2014). The main cause for this phenomenon has been the rising

costs associated with aviation, with fuel prices being one of the primary factors. This study has

addressed these fuel costs and placed specific focus on the conspicuous variation in prices across the

28

United States. The results clearly indicate that a driving cause for such high costs is the lack of

competition in certain geographic areas.

This study has contributed to a long line of work around seller density and prices. Sorensen

(2000) examined the prescription drug market. For Walsh and Whelan (1999) it was the Irish grocery

market. Rose and Borensteins (1994) case study was the car insurance market. In this case, it was

the general aviation fuel market that served as a vehicle for a broader study around prices. Therefore,

while this work represents the first look at the general aviation fuel market, the questions it poses and

answers are certainly not new.

On the whole, this analysis is incomplete. There are a lot of questions that remain

unanswered. What precisely is the causal mechanism between an increase in sellers and an increase

in price dispersion? We have weak evidence for the phenomenon taking place. However, further

empirical work should try to find an explanation. In addition, this study had difficulty establishing

the relationship between county-level characteristics and fuel prices. It is possible that the two are

isolated. Or rather, how intertwined are airports with their surrounding environments? Do they cater

to a subset of the population and therefore have little interaction with local factors? This is certainly

another interesting question worth examining.

Finally, future study should also expand the scope of this study. The data studied here

represented a snapshot of prices. Forthcoming work should not only look at the impact of seller

density on current prices but should also examine how prices change over time to determine the

relationship between seller density and price rigidity. The general aviation fuel market is an

interesting market that should help address broader theoretical questions in economics.

To the pilots who constantly find themselves saying, These fuel prices are a rip-off, this

study has helped explain this frustration. The large variation in aviation gas prices across the United

States is largely determined by the amount competition in the surrounding area.

29

I. Appendix 1: Kernel Density Estimate of Density Calculation

0.0

5.1

Dens

ity

0 5 10 15 20 25WeightedDensity

kernel = epanechnikov, bandwidth = 0.8338

Density Calculation - Kernel Density Estimate

30

II. Appendix 2: Histogram of Fuel Prices

0.2

.4.6

.8De

nsity

3 4 5 6 7llselfservicePriceInteger

0.2

.4.6

Density

3 4 5 6 7 8llfullservicePriceInteger

31

III. Appendix 3: Kernel Density Estimate of Prices

0.2

.4.6

3 4 5 6 7 8Price

Full Service Price Self Service Price

32

IV. Appendix 4: Map of Airports/Sellers (ArcGIS)

33

V. Appendix 5: Comparison of Airports in my Dataset and All Airports That Sell Fuel

0 10 20 30 40 50 60 70

All Airports That Sell Fuel My Dataset

Number of Pla

nes

Average Number Of Single Engine Planes

0 0.5 1 1.5 2 2.5 3 3.5 4

All Airports That Sell Fuel My Dataset

Miles Average Distance From Central Business District

34

0 2000 4000 6000 8000 10000

12000 14000 16000 18000

All Airports That Sell Fuel My Dataset

Number of Loc

al Operations

Average Number Of Local Operations

0 2000 4000 6000 8000

10000 12000 14000 16000

All Airports That Sell Fuel My Dataset

Number of Ite

rant Operation

s

Average Number Of Iterant Operations

35

I. Table 1: Overview of Variables

VARIABLES LABELS/ DESCRIPTION DATASET N mean min max

DistanceFromCBD Dist. from Central Business District (In Miles) FAA AFD 1,496 3.699 0 68 NumberOfSellersWithin25NM Number of Sellers Within 25 Nautical Miles FAA + Author 1,497 4.274 0 17 WeightedDensity Weighted Density Calculation FAA + Author 1,497 7.357 0 23.80

llfullservicePriceInteger 100 LL Full Service Price FlightAware 1,102 5.309 3.450 7.990

llselfservicePriceInteger 100 LL Self Service Price FlightAware 868 4.890 3.300 6.740

NoSelfServiceDummy Dummy if No Self Service FAA AFD 1,497 0.420 0 1

NumberOfSingleEnginePlanes # of Single Engine Plane at Airport (In Tens) FAA AFD 1,490 5.882 0 81.20

OperationsGALocal # of Local GA Operations (In Hundreds) FAA AFD 1,497 161.9 0.300 2,128

OperationsGAItinInHundreds # of Itinerant GA Operations (In Hundreds) FAA AFD 1,497 149.0 0.480 3,321

ClassCAirspaceDummy Dummy if Airport is in Class Charlie Airspace FAA AFD 1,497 0.045 0 1

PopulationPerSquareMile Pop Per Square Mile for County (In Tens) ACS 1,497 32.15 0.050 549.5

NumberOfPilotsInState Number of Pilots in the State (In Thousands) ACS 1,497 21.21 1.037 64.53

MedianHouseholdIncome County Median HH Income (In Thousands) ACS 1,497 49.37 21.86 106.7

StateGiniCoefficient State Gini Coefficient ACS 1,497 0.469 0.418 0.510

Table 2

36

II. Table 2: Seller Density and Average Price

(1) (2) (3) (4) VARIABLES ln(Fuel Price) ln(Fuel Price) ln(Fuel Price) ln(Fuel Price) WeightedDensity -0.0043*** -0.0058*** (0.001) (0.002) NumberOfSellersWithin25NM -0.0038*** -0.0041** (0.001) (0.002) DistanceFromCBD (In Miles) -0.0003 -0.0003 0.0010* 0.0010* (0.001) (0.001) (0.001) (0.001) NumberOfSingleEnginePlanes (In Tens) -0.0020*** -0.0018*** -0.0015** -0.0016** (0.001) (0.001) (0.001) (0.001) OperationsGALocal (In Hundreds) -0.0001** -0.0001** -0.0001*** -0.0001*** (0.000) (0.000) (0.000) (0.000) OperationsGAItin (In Hundreds) 0.0001*** 0.0001*** 0.0001*** 0.0001*** (0.000) (0.000) (0.000) (0.000) MedianHouseholdIncome (In Thousands) 0.0011*** 0.0009*** -0.0007* -0.0010** (0.000) (0.000) (0.000) (0.000) PopulationPerSquareMile (In Tens) 0.0006*** 0.0005*** 0.0006*** 0.0005*** (0.000) (0.000) (0.000) (0.000) NumberOfPilotsInState (In Thousands) -0.0010*** -0.0010*** (0.000) (0.000) NoSelfServiceDummy 0.0888*** 0.0888*** 0.0855*** 0.0866*** (0.007) (0.007) (0.011) (0.011) ClassCAirspaceDummy 0.1020*** 0.1042*** 0.1031*** 0.1045*** (0.017) (0.017) (0.024) (0.024) Constant 1.5711*** 1.5649*** 1.6444*** 1.6366*** (0.016) (0.016) (0.018) (0.018) Observations 1,489 1,489 1,489 1,489 Adjusted R-squared 0.214 0.208 0.235 0.226 State FE NO NO YES YES Number of StateNumCode 46 46 Robust standard errors in parentheses *** p

37

III. Table 3: Seller density and Price Dispersion (Without Gini)

(1) (2) (3) (4) VARIABLES Price Dispersion

(Squared Residuals) Price Dispersion

(Squared Residuals) Price Dispersion

(Squared Residuals) Price Dispersion

(Squared Residuals) WeightedDensity 0.0003* 0.0005*** (0.000) (0.000) NumberOfSellersWithin25NM 0.0001 0.0002 (0.000) (0.000) NumberOfPilotsInState (In Thousands) 0.0001*** 0.0001*** 0.0001*** 0.0001*** (0.000) (0.000) (0.000) (0.000) Constant 0.0132*** 0.0145*** 0.0127*** 0.0151*** (0.001) (0.001) (0.001) (0.001) Observations 1,489 1,489 1,489 1,489 Adjusted R-squared 0.012 0.012 0.015 0.012 State FE NO NO NO NO

Robust standard errors in parentheses

*** p

38

IV. Table 4: Seller density and Price Dispersion (With Gini)

(1) (2) (3) (4) VARIABLES Price Dispersion

(Squared Residuals) Price Dispersion

(Squared Residuals) Price Dispersion

(Squared Residuals) Price Dispersion

(Squared Residuals) WeightedDensity 0.0003* 0.0004*** (0.000) (0.000) NumberOfAirportsWithin25NM 0.0001 0.0002 (0.000) (0.000) StateGini 0.0900** 0.0980** 0.1308*** 0.1433*** (0.045) (0.045) (0.047) (0.048) NumberOfPilotsInState (In Thousands) 0.0001* 0.0001** 0.0000 0.0001 (0.000) (0.000) (0.000) (0.000) Constant -0.0276 -0.0302 -0.0464** -0.0502** (0.020) (0.021) (0.022) (0.022) Observations 1,437 1,437 1,437 1,437 Adjusted R-squared 0.015 0.015 0.020 0.017 State FE NO NO NO NO

39

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