Violating the Law of One Price in the Dutch Retail Gasoline Market

Violating the Law of One Price in the

Dutch Retail Gasoline Market

Vincent J.C. Gaemers

Master Thesis

Rijksuniversiteit Groningen

Supervisor: Dr. M.A Haan

July 15, 2013

Abstract

1

Introduction

In the last few years many people have complained about gas-prices when buying gas. Gasoline prices in the Netherlands are at this moment (May 2013) the highest of the European Union with an average price of e1,78 per liter1. In 2008 people mostly argued high gasoline prices were caused by high oil prices (Brent oil was valued at almost 140$ per barrel). That argument however, has become invalid since gas prices declined heavily since then. By the end of 2009 Brent was trading at roughly 40$ per barrel. However, the retail gas price has not declined in equal measure. Multiple models have been used in the literature on these price movements. Yet a perfect fit has not been found. Where earlier papers try to describe the gas market from a demand point of view, recent studies give more attention to the seller side (Eckert, 2013). In this thesis I will also focus on the sellers side. Using a model of rank reversals I will explain the asymmetric price movements and relate this to the theory of consumer search.

The gasoline market is an interesting market because it has always violated the law of one price, one of the foundations of economic theory. The law of one price states that in any efficient market, all identical goods will have the same price. Assuming that gasoline is a homogeneous good, it is easy to acknowledge that the retail gasoline market does violate this law. Prices of gasoline vary between stations and over time. Since gas stations advertise their prices along the road, it is easy to observe prices. A possible explanation for this violation of the law of one price is consumer search.

In his 1961 paper Stigler challenges the law of one price by introducing his story with ”Knowledge is power”. He poses the question why products which are homogeneous tend to have different prices. He concludes that this is a natural outcome, consumers do not have all information available and therefore some of them will search for a lower price. The consumers who do not search will stay uninformed about prices. Anticipating on this behavior, a firm will be able to achieve higher profits by setting a higher price, increasing the markup and therefore achieve higher profits. However, a firm is also able to set a lower price, increasing the market share it has and capturing a larger turnover. In short, prices are not fixed and multiple good choices for pricing exist.

The idea of Stigler was challenged by Diamond (1971). In the Diamond model, consumers

1

are allowed to either buy a product at a firm, or incur search costs s in order to visit the next firm. Consumers are not able to obtain price information of any kind before visiting the first firm. The equilibrium outcome of this model is a monopoly price. Firms initially set prices at cost level c, if a consumer decides to visit another firm, he will need to incur costs s. Therefore, if the firm increases its prices to c+ s/2, consumers will still buy at the firm, because buying at another firm will have a total costs of c+ s. This holds for all levels of pricing for p < pm. In the case of p≥ pm firms will have less profit, therefore firms will never charge this price.

In the well cited paper of Varian (1980) titled ’A model of sales’, Varian shows a different take on the previous models. He proposes a concept in which neither none nor all consumers search. The result is that some of consumers are informed and the others are not. If a consumer is informed, he will buy at the firm offering the lowest price. If the consumer is not informed, he will buy at any firm in the market. By setting a low price, the firm will capture the informed consumers and half of the non-informed consumers (assuming two firms). However, this may not be a optimal result. Firms are able to maximize profits by setting a price higher, only selling to non-informed consumers and obtaining possible higher profits compared to the firm who set lower prices. In this model the symmetric equilibrium is that of mixed strategies. Since the consumer who does or does not search is unobservable, firms tend to pick prices from a set of prices, instead of having a monopoly or a perfect competition outcome. In order to maximize profits, firms will thus need to play a mixed strategy.

Search models can be applied to many markets: telecom, financial services, airline tickets, and natural resources. In this thesis I will restrict my self to the search on gasoline markets. For a deeper analysis of the other markets I refer to Baye et al (2006) which gives an excellent summary of these works.

The gasoline market is a market to which a search model is easily applied. Gas prices tend to change more frequently than most of the other goods. This makes it difficult for buyers to have information of prices at hand. Since not all consumers pay attention to prices until they buy, most of them are not informed. Moreover, consumers may not know wholesale prices and thus the overall level of prices of gas. Consumers will thus be split in informed and non-informed customers.

keeping in mind the fact that consumers might or might not be informed about pricing of competitors. This leads to firms setting monopoly level prices at some moments, or tending more towards Bertrand pricing competition outcomes in other cases.

In this paper I will focus on the Dutch gasoline market. The detail and richness of the data available on this market makes it a good candidate for this kind of research. On a large panel data set of the Dutch gasoline market I will look for evidence of price dispersion by searching for evidence of the presence of mixed strategies. This will be done using a model introduced by Chandra and Tappata (2011).

The structure of this thesis is as follows: first I shall introduce some basic concepts of microeconomics. Second I shall review the literature on asymmetric pricing and consumer search. Next I will explain the basics of a model of consumer search. Fourth I shall apply the model to the dataset, finally I shall conclude on my findings.

2

Price setting in Microeconomics

In this thesis I focus on an consumer search model. I will explain some basic microeconomics in order for the reader understands the model. I focus solely on a partial equilibrium outcome and I only look for the solution with one product and not at the effects on other markets. The concepts I will be covering are the following:

1. Monopoly pricing. 2. The Cournot game. 3. Basic game theory. 4. Mixed strategy in games.

I believe that the outcomes of these analysis make the profit concepts of a model of search more understandable. After introduction of these concepts I will further elaborate on the model which I will use in this thesis.

2.1 Monopoly

have a market of goods. There are seller(s) and buyers, a model of supply and demand. In the case of a monopoly the most important characteristic is that the monopolist is the only seller in the market or there is a lack of a viable substitute for the good. This induces the monopolist to behave in a different manner than in the case where we would have multiple firms. The main difference is that the monopolist has more market power. The equilibrium price that will prevail on the goods market is different since the monopolist is the only one selling. The fact that he is the only one selling the product, makes the monopolist able to set his own prices bearing only his own profit function in mind. The monopolist acts in a profit maximizing way without disturbance from other players on the market.

The model is created using the following assumptions. For consumers we assume a downward sloping demand curve; as prices increase one will demand less of the items and vice-versa. A basic model price function is then given by the following form:

p= 1 − q (1)

This is a linear downward sloping function where p is price charged and q quantity sold. Profits of the monopolist are given by Π which is the amount of goods sold times the price, minus the costs the monopolist had. A basic function is therefore:

Π= (p − c)q (2)

Here again we have p and q and now we add c which is the cost. Since the monopolist is a profit maximizer, he’s is now facing the following maximization problem:

∂Π

∂q = 0 (3)

Which yields solutions for q and p of respectively:

q∗=1

2 p

∗= 1

2 Profits of the monopolist therefore are:

In order to further understand this result, consider figure 1

Figure 1: Monopoly pricing.

2.2 Cournot

Already established as early as 1838 Cournot published his work on the behavior of firms which compete in a quantity setting. The basics are like the monopoly model, however we now have two firms. The model that results is a bit different from the previous one since we now have to deal with so-called ’reaction curves’. These are the lines that predict the outcome of the supply with respect to the behavior of your competitor. Formally we write:

p= 1 − q (4)

However, we now have to deal with two firms, so here q = q1+ q2 with q1 being output from

firm 1 and q2 output of firm 2. The profit maximization problem of firm 1 then becomes

π1 = (1 − q1− q2− c)q1. Following the same steps as for the monopolist we now have a profit

maximizing function of firm 1 including the output of firm 2:

R1(q2) =

1

Figure 2: Cournot Competition.

In a similar fashion, firm 2 obtains a maximizing function.

R2(q1) =

1

2(1 − q1− c)

Assuming c is the same for both first and both are aiming strictly at profit maximization, we can now solve this as a system of equations with 2 unknowns.

We now obtain the ’Cournot equilibrium’ by setting q∗ 1 = q

∗

2 = 1−c3 and we obtain profits of

π∗ 1 = π ∗ 2 = (1−c)2 9 . 2

The problem can be explained more easily using figure 2. [h] In this figure we see both reaction curves of the firm, changes in q1 or q2instantly change the amount of quantity supplied

by the other firm. From here we can also see that if we would allow for changes in c, the curves of the firms would shift. Assuming that costs are the same for both firms yields the most straightforward result.

Figure 3 shows the comparison of the results between the monopoly and Cournot outcome. Prices in the monopolist game are higher, whereas output is lower. Prices in the Cournot game are lower, and overall output is high (note that this is total output, not output per firm). Profits

2

In a game with n firms we would obtain q= q1+q2+...qnand the problem would then yield π1= (1−(n−1)q)q1,

Figure 3: Monopoly versus Cournot outcome.

of both firms are given by the square that is created when drawing a line from the origin to the tangent point of either pm and qm or pcand qc. Note the triangle which remains uncovered by both the squares. This is called the deadweight loss. This is the loss which results from inefficient allocation of prices by the monopolist against the competitive outcome of the Cournot equilibrium.

2.3 Nash Equilibrium

The result in the previous section is a so-called ‘Nash equilibrium’, which is in short explained by: ’given by what the other person is doing and taking into account that it is his response, this is my best response’.

years in prison. Formally we write:

C D

C -1,-1 -9,0 D 0,-9 -6,-6

Here C stands for cooperate, and D stands for defect. If both players cooperate they will both receive the pay-off of -1 and if they both defect they will receive -6. However, since 0> −1, defecting seems more profitable then cooperating. Moreover−6 > −9, which means that in both cases, defecting has higher payoffs then cooperating. Therefore both players will play the defect option and yield pay-off of -6,-6.

Formally we write the following: A strategy pair (q∗

1, q ∗

2) is a Nash equilibrium if for each player i ∈ N,

πi(qi∗, q ∗

j) ≥ πi(qi, qj∗), i ≠ j, i, j ∈ N

This formulation is best interpreted with the Cournot theory at hand. Recall π are profits and q are quantity’s. q∗ _{is equilibrium quantity. In this formulation we see that given the fact that}

player 2(q∗

2) plays their equilibrium quantity, in all cases q1∗exceeds combined profits of all other

options for q1. The profits for π(q1∗, q2∗) is the best response of firm 1 given the best response of

firm 2, which also creates the largest profits. This is a Nash equilibrium.

2.4 Mixed Strategies

An extension of the Nash Equilibrium when there are no pure strategies is called a mixed strategy. This occurs when there is no direct pure best strategy to follow. The best strategy in this game is given by a set of probabilities over all the options. Consider the game of two tennis players. They both may have vital information on how to beat their opponent; they start a set either with a service on the backhand, or on the forehand. However, using only one of the two cannot be feasible. The opponent will anticipate and you will probably be punished. In a game with a mixed strategy as best solution, we assign probabilities to both of the options. So we assign a probability of playing on the forehand of the other play of x and a probability of 1− x to playing on the backhand.

players, players A and B. Each player has a coin and need to put it down either heads or tails. Now the players reveals their pennies simultaneously. If the pennies match Player A keeps both pennies, so wins one from Player B. If the pennies do not match Player B keeps both pennies, so receives one from Player A. In a formal form:

Heads Tails Heads 1,-1 -1,1

Tails -1,1 1,-1

It is clear to see that there is no pure Nash equilibrium. In this case choosing either heads or tails does not yield a best response. In order that both players to maximize their expected outcome they need to randomize (mix) over the strategies. Since the game is symmetric both players will randomize with the same percentages, 50%. So in the mixed strategy Nash equilibrium both players will choose Heads and Tails with both 50% chance. In this case the expected payoff for both players yields 0.5× 1 + 0.5 × (−1) = 0. Both of them can’t do better by deviating to another strategy. In the next section I will elaborate more on use of the mixed strategy equilibrium in consumer search theory.

3

Literature

In the model I use, asymmetric pricing has a big impact on the behavior of both the firm and the consumer. According to Lewis and Marvel (2011), a rise in the wholesale prices of gasoline is almost immediately transferred to the pump. A drop in wholesale prices however, translates in a slower rate to retail prices. When these rising prices are associated with more search, the distribution of prices will contract as prices and expand when they decline. This behavior also works vice-versa. The asymmetric search behavior induces asymmetric price movements by firms.

3.1 Asymmetric Pricing

The academic debate and literature on gasoline markets is quite recent. Price changes in the gasoline market have been of interest to many economists for multiple reasons. One is the abundance of data and the observability of prices along the entire production process. Gasoline data therefore is flexible in its use, therefore there are many econometrics models built around this data. Second is the importance of oil to the global economy. Oil is one of the major benefactors of GDP for countries which are able to export the product. Importing countries on the other hand are also influenced by changes in crude oil prices. Moreover many energy authorities and antitrust policy makers attempt to monitor the market in search for flaws of the market mechanism, collusive behavior or non-competitive pricing.

An extensive part of this research is done on asymmetric pricing using retail oil prices. Prices tend to rise fast and only slowly decline. Early work on examinations of this phenomenon originates from 1988 when Maskin and Tirole formalized Edgeworth Cycles. An Edgeworth Cycle begins when one firm undercuts its competitors to gain a portion of the market. The other firms will respond by undercutting each other until the retail gasoline price is at the wholesale price. Once the price is at this level one of the firms will raise the price back to the Cournot competition value, assuming that consumers have some loyalty to a seller, he thus maximizes profits. All the other firms respond by also setting this price. Hereafter the process starts again. Edgeworth Cycles have been found in later papers by Eckert (2002) and Noel (2003, 2007). Noted by Noel (2007) is that Edgeworth Cycles are more likely to be found in countries where more private owned retail shops are located.

four different levels and obtaining data for all these levels, they are able to perform regressions on all four stages of the process. BCG’s reasoning behind this is that they now are able to uncover at which stage of the process the asymmetric pricing originates. They conclude that asymmetric pricing is present mainly in two stages: between terminal prices and crude oil prices and the stage between spot prices and the crude oil price. Reasons for this conclusion included are production and inventory lags but also the reaction of retailers to wholesale pricing. According to BCG this could be because of short-run market power of retail gas stations.

The data of this study were adopted by Bachmeir and Griffin in 2002 using a error correction model with two-step Engle-Granger estimation procedure reject the conclusions made by BCG and state that they could only find minor evidence of asymmetric pricing. Moreover, using a different dataset they find no evidence of asymmetric pricing in the U.S. While the methodology in all three papers is rather different, one of the most important differences could just be the country on which the data is based, Bacon uses U.K. data whereas BCG and Bachmeier and Griffin use data on the U.S.

Recently Fotis and Polemis (2013) find asymmetric pricing using a weekly data set on 11 Eurozone countries. They estimate an ECM on weekly price changes and using generalized method of moments on panel data. They are able to incorporate the effect of exchange rates and input prices to the model. They conclude that oligopolistic behavior of firms is one of the reasons for thriving asymmetry. However, they also state that asymmetry is likely to originate from other market parameters like regulatory barriers, legal framework and others.

3.2 Consumer Search

As the debate on how asymmetric pricing of gasoline is established is clearly unfinished, authors are now recently more interested in a different approach. If input prices are not the cause maybe is consumer search behavior the cause of retail gas station owners changing their prices.

hence a explanation of ’Rockets and Feathers’.

The model that will be used in this thesis is based on Tappata (2009) and Chandra and Tappata (2011). Lewis (2011) concludes the same as Tappata (2009). They both find evidence of consumer search in the gasoline market and it is the main explanation for asymmetric pricing. Differences between the models are mainly by how consumers differ in behaving after observing the cost function of the supplier. In Tappata costs can either be high or low. In Lewis costs are distributed in two ways. In the dynamic model costs are continuously distributed and are assumed to be based on the reference price. Whereas in the static model, he makes no assumptions about the determination of the distribution. Consumers are able to buy at a firm or pay the search cost to move on to the next. They are allowed to freely return to a previous firm in order to buy the good. Moreover, consumers are assumed to have no information on firms’ marginal costs.

A rather different approach which contributes to the discussion can be found in Castilla and Haab (2013). The question Castilla and Haab pose: ’Do consumers care about search costs?’. They propose a choice experiment in which consumers are asked whether search costs would influence buying behavior when buying gasoline. They conclude that consumers are not actively observing gasoline prices. Consumers do maker rational decisions but only based on costs of gasoline, however the costs of time spent searching often is higher than anticipated, leading to a loss of consumers surplus by searching for cheap gasoline. Consumers thus are able to make correct decisions based on prices of the good, but neglect the fact that search is costly.

In recent years most of the literature is about regulation and collusive behavior of firms in the market. Mergers at retail, wholesale and refiner level have been frequent (Eckert, 2013)

3.3 The Model

In this section I describe a simple straightforward model of consumer search. The model is taken from Chandra and Tappata (2011) and Tappata (2009) . As is noted in the introduction, the aim of this paper is to use data on gasoline markets in order to find evidence of consumer search. Reasons for the usage of the gasoline market in consumer search are straightforward:

1. Firms sell a homogeneous good.

3. Stockpiling is not a real option 4. Firms have the same marginal costs 5. Firms do not face capacity constraints.

Consider a homogeneous market for goods with n firms, where all firms have equal marginal and equal average cost functions. Costs, c are given at the beginning of the period and drawn by nature. Firms observe these costs and compete in prices.

The demand side is characterized by a mass unit of consumers who have inelastic demand and valuations v. Moreover they have information on the probability distribution of the firms marginal costs, c. Consumers are able to obtain market prices through non-sequential search. Non-sequential search implies that a consumer captures information on all prices of gasoline stations. After observation the consumer decides where to buy. Sequential search would mean that the consumer observes a price and then decides whether to buy or not to buy. If the consumer does not buy he continues his search until he finds a matching buy.

Following Varian’s model of sales we have a fraction λ∈ (0, 1) of the population who have zero search costs and are named ’shoppers’. Shoppers can be thought of a fraction of population who enjoy shopping and observe prices unintentionally while shopping or through advertisements. The fraction 1-λ has positive search costs which are different from each other and are called non-shoppers. Non-shoppers decide before observing the goods market whether they will pay the search costs s and obtain information about the cheapest store. If they do not pay s they buy from a random store. Search costs are drawn from a continuous cumulative distribution function with si ∈ S = [0, s] and [s, v]. Firms and consumers then take actions simultaneously.

Whether non-shoppers will search is affected by the expected price dispersion in the market and their search costs s. This means that consumers form rational expectations on pricing strategies of the firm, while the firm anticipates search costs of the consumers.

Search intensity is defined in the market by µ, which is the proportion of shoppers who decide to become informed. To solve the model it is necessary that for any search intensity µ∈ [λ, 1] the pricing strategy must be a Nash Equilibrium (NE). It is also necessary that the given search intensity µ∗ _{it is consistent with firms’ pricing strategies. Thus, when consumers}

In the case of µ= 0 we obtain a monopoly pricing situation. Demand is completely inelastic and the firm will set p= v in order to extract all of consumer surplus. In the case where µ = 1, firms have perfectly elastic demands with ”all knowing” consumers. Firms will thus set prices at p= c. In the other cases (0 < µ < 1), firms face downward sloping demand and there will be no equilibrium price. Stores will immediately undercut competition by an infinitesimally small amount ε, and capture all of the informed consumers in the market.

The results from the previous section eliminate both monopoly and Cournot outcomes. µ= 0 is not able to occur since we have a number of shoppers in our model, which increases the lower bound of informed consumers to µ ∈ [λ, 1]. On the other hand, since we implied that high search costs are allowed in the model (s > v), not all consumers will search. There will thus also always be uninformed consumers. Profit functions of the firms can be established in the following manner:

πf(p, c) = (1− µ) 2 (p − c) πs(p, c) = (1+ µ)

2 (p − c)

Given µ, a firm can f ail(πf) or succeed πs in capturing the informed consumers and therefore will have a different profit. If firms charge the highest allowed price (p= v), only uninformed consumers will buy from the firm:

π(v, c) = (1− µ) 2 (v − c)

So even if the firm behaves as a monopolist it will generate moderate but positive profits. Given the pricing behavior of the f ailing firm, the succeeding firm will now have a lower bound on its prices in order to have a profit which is≥ πf(v, c).

p∗= πs−1(π(v, c)) = c + (1− µ)

(1 + µ)(v − c)

Therefore, price will be on the domain [p∗_{, v}].

strategy of a firm by F(˙,c, µ).

πs(p, c)(1 − F(⋅ )) + πf(p, c)F(⋅ ) = π(v, c)

Notice that the firm’s profit function exhibits indifference between succeeding or f ailing as long as the amount of consumers captured is large enough. Profit captured of a firm by succeeding A higher price increases the markup of a firm but decreases quantity sold because of the informed consumers. Profit maximization is therefore neither reached by setting the highest or the lowest prices. Obtaining surplus (by obtaining πs(p, c)(1−F(⋅ )) or stealing business(πf(p, c)F(⋅ )) are the main trade-offs faced by the firms, these induce price dispersion or the existence of Varian’s Sales model.

From what precedes one is able to state that prices are drawn from a cumulative distribution:

F(p, c, µ) = ∫ p p∗ f(x, c, µ)dx. = 1 − ( 1− µ)(v − p) 2µ(p − c) for all p∈ [p∗= c +(1−µ) 1+µ , v]. 3

Comparative statics on informed consumers reveal that as µ increases, the captive market for each firm becomes smaller and profits made by charging p= v decrease. This results in a larger domain of prices from which firms are willing to randomize over in order to attract the informed consumer. However, the larger proportion of informed consumers also increases the stealing effect and the lower prices will let firms achieve higher amount of sales.

On the demand side consumers decide whether to become informed about prices at a cost s, or spend nothing and buy from a random store accepting a possibly higher price. Overall demand is composed of consumers who individually will not influence the intensity of the market search. Given the behavior of the firm, the gain of searching is given by the expected price and the expected minimum price:

E[p − pmin∣u] = Ee[∫ v p∗

p[1 − 2[1 − F(p, c, µ)]]dF(⋅ , c, µ)]

3

From Varian, in the n case this becomes: F(p; u, c, v, n) = 1 − [(1−µ)_µ (v−p)_(p−c)]

1 n−1

where p∈ [p∗=cnµ+(1−µ)v

This equation shows what the consumer is willing to search for and that large price dispersion across firms means that there are large surpluses to be gained. This however, depends on the size of the mass of informed consumers. If we assume a monopoly situation, in which µ = 0 and p= v, increases in µ increase the domain where prices are taken from. The decrease in the expected value of p induces more consumers to search.

Consumers take mainly into account their own gain of search. Shoppers will search for low prices in all cases whereas consumers with s≥ v will never search. In equilibrium we thus have λ informed consumers and a fraction (1 − g(v))(1 − λ) uninformed consumers. Optimal search strategies are given by qi(si < ˜s) = 1 and qi(si> ˜s) = 0, where ˜s is the lower bound search cost

of the indifferent consumer,

E[p − pmin∣µ = λ + (1 − λ)g(˜s)] − ˜s = 0

As long as there is a large number of shoppers (λ> µ) there is a unique equilibrium. When this is not the case there could be more than one solution to the last equation. The requirements for a unique market equilibrium are:

• λ> ˆµ, or • 0< λ < ˆµ and∂g−1 ∂µ > [p−pmin] ∂µ ∣ over µ ∈ [λ, ˆµ] 4

Here ˆµ denotes the number of informed consumers at which the gains from search are maxi-mized. From this we acknowledge that the equilibrium of the model is established through price dispersion and search behavior of consumers. The intensity of search is established through the expected production costs of the firm. These influence the price setting behavior of the firms and thus the intensity of search.

Although costs do not affect the trade-off between surplus gaining or business stealing, it does influence the size of the domain from which prices are taken. As a result the costs of attracting informed consumers are the same for a high cost or low cost firm. However, the increase in production cost increases the gap between the monopoly price and the lower bound of p∗_{. This leads non informed consumers to search less when they expect high costs. The gains}

from searching decrease as the gap between E[p−pmin∣µ] increases through a higher probability 4

of high production cost α.

In summary: The equilibrium search intensity and search cost decrease with α for the indifferent consumer.

4

Data

In this thesis I will use a dataset which has been used in various articles on microeconomic the-ory. In their paper on collusion, Heijnen, Haan and Soetevent (2012) apply a spatial statistics approach to the data in order to find evidence for regional collusion of stations. They find evi-dence for suspicious behavior of stations in multiple regions of the Netherlands. The conclusion however includes the fact that the results are heavily dependent on quality of the data. One cannot draw conclusion based on most of the data used. Therefore the method should only be used as a starting point for a deeper investigation.

In their 2012 paper, Lach and Moraga-Gonzalez use the dataset in order to apply a model of consumer information and heterogeneous pricing. Using a slightly larger dataset but from the same source, Haan, Soetevent and Heijnen (forthcoming) analyze the effect of auctioning gas stations located at regional highways on gasoline retail prices. As four competitors have a big amount of market power the Dutch government wanted to foster competition by letting the companies divest. After auctioning the prices of the auctioned gas station drop, as well as at stations which are located nearby. The drop in price of the nearby gas stations means that competition actually increased.

I use prices of Euro 95 gasoline from a sample of gas stations in the Netherlands. The price data are obtained from the website of Athlon Car Lease B.V. Car lessees have Athlon pay for their fuel using a personal credit card. Using these credit card data, Athlon is able to observe daily prices from a large part of the gas stations in the Netherlands. Athlon does not have contracts with gas station brands and the observed prices are therefore actual. The data consist of 944670 price observations and the number of gasoline stations observed is 3259.

For comparison, the Dutch competition authority NMa (2006a, p. 8) cites a total number of 3,625 outlets in the Netherlands in 20045. On each day there is an observation in 37.5% of all stations. The minimum price observed is 1.02 and the maximum is 1.67 euro’s. On average

5

Station level Euro 95 (in e) Minimum 3 1.02 Maximum 429 1.67 Mean 289 1.37 Std. Dev 119 0.07 N 3259 944670 Table 1: Descriptives

I observe a price of 1.37 euro’s with a standard deviation of 7 cents. The main strength of this dataset is that I am able to focus on daily data on gasoline stations. In most other articles they use weekly or even bi-weekly data. Table 1 summarizes descriptives of the data used.

In figure 4 below I have plotted minimum, maximum and means of observed prices of the entire set. Interesting to see is that deviations downwards tend to be larger in comparison to

0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 min max mean

Figure 4: Prices over time.

Date on the horizontal axis, prices ine on vertical axis.

5

Empirical approach and results

To use the data correctly in order to find evidence for consumer search I use a model look-ing for evidence of mixed strategy priclook-ing. Price dispersion can arise because the product is heterogeneous or because search is involved. Assuming gasoline is a homogenous good, I focus on modeling the data using consumer search. I did analysis by checking the variation over time in the price spread of markets of different size. I have defined markets for three different cutoff points. These are 1,2 and 5 kilometers respectively. Using the model on different sizes of markets allows me to compare results between stations which are based on small to larger distances. This is of particular importance in our model of search, since gas stations should have a higher degree of competition with nearby stations in comparison to gas stations which are further away. Furthermore search costs between stations which are closer to each other exhibit less search costs, therefore there should be more search and less differences in prices. I follow Chandra and Tappata (2011) (CT) in their model. I look for temporal price dispersion between gas stations.

This is done using the following model: Let Sij be a vector of price spread between two

gas stations (i, j) over Tij days, such that pit ≥ pjt is observed most of the time. Define rank

reversals between stations i and j as the proportion of observations in which pjt> pit

rij = 1 Tij Tij ∑ t=1 Ipjt>pit (5)

This shows us the average number of times in which the cheapest station (pjt) exceeds the price

of the more expensive station(pit). This statistic thus shows us how often the rank is reversed

between two stations. It denotes the percentages of time in which the firm with the lowest price has a higher price with respect to the station which has the highest price on average. Note however that when pit= pjt there is no leader in pricing. I deviate here from CT by setting no

exceed 0.5. Using this rank reversal I am able to model how often the less expensive firm (on overall) is more expensive compared to the on average most expensive firm. Assuming costs are all equal for all stations, the outcome of this test will shows strong evidence for mixed pricing strategies of the stations.

For a histogram of this result observe figures 5, 6 and 7. In table 2 I give descriptive statistics on the data. In figure 7 one can see that on 35% of the rank reversals are below .05. This means that in 35% of the cases, the gas station with on average the highest prices is in more than 90% of the observations the most expensive. On average a larger part of the figure is explained by stations which are constantly price leaders. However, peaks at the .45-.5 level are noticeable for all cutoff points. At this point there is heavy competition in the given market. Prices are changing on a high frequency or the same prices are observed.

Comparing the three figures visually shows that there is increased competition in market A compared to market C. Rank reversals tend to be higher in a smaller market. This is according to theory. Markets closer to each other leads to consumers having a lower search costs. Therefore a higher level of competition could lead to higher profit. Later in this section I will perform a formal test in order to provide addition proof for this result.

The American data used by CT were spread more evenly, however the average rank reversal did tend to be lower in all cases. Since my altered definition this makes sense. In CT when firms have equal prices, the overall rank leader ’stays’ rank leader. This will thus lead to a more leftward skewed histogram. Therefor in the American dataset competition could be underestimated. The Dutch data has more high rank reversals. Price leaders thus more often change. A higher rank reversal means that there is a higher level of competition in the market. From table 2 I am able to conclude that if we increase the size of the market the rank reversals tend to be lower. As markets’ geographical size is increased stations tend to have less competition from stations further away. The distance between the stations may become a more important factor making direct competition less intense. The smallest market has an average rank reversal of 0.1982, which means that in 19.82% of the observations the highest price is observed at the station which has on average the lowest price. Moreover, increasing the market size increases the average spread of rank reversals.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 50 100 150 200 250 300 350 400

Figure 5: Rank reversals Market A

Amount of observations on vertical axis, rank reversal on horizontal

to specify 2 markets to compare. One in which we know that search is absent and one where search is possible. I do this by creating a new market which has a cutoff point at 100 meters. If stations are located in less than 100 meters of distance, prices are freely observable by consumers. Therefore search is absent in this market. Because of this absence, only heterogeneity of the product is the factor of influence to the price. Therefore there should be a difference in price spreads between gas stations which are localized near each other and gas stations which are not directly visible by customers. In the small cutoff point case the gas stations do not compete on prices but on other factors. However, these stations do compete with stations which are just located outside of the visible range since prices are not known for all consumers. In the model we should thus expect lower rank reversals for stations that are in the ’visible’ area than stations which are farther apart but still are located in the same market. In order to observe this I follow the same steps again as Chandra and Tappata (2011). Assume that reversals between stations which are within the 100 meter cutoff margin are drawn from a distribution F1(r) and

that rank reversals which belong to both 100 meter cutoff and the larger distance matrices are drawn from F2(r). If search is important in the gasoline market, we expect F1(r)>F2(r). This

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 200 400 600 800 1000 1200 1400

Figure 6: Rank reversals Market B

Amount of observations on vertical axis, rank reversal on horizontal

away. The K-S test evaluates whether F1 O F2 against HKS ∶ F1 = F2. Alternative hypothesis

are given by H1 ∶ F1(r)>F2(r) and H2∶ F1(r) < F2(r).

The results of these tests can be found in Table 3. In all cases I am able to reject HKS,

therefore I can conclude that stations nearby have different pricing strategies in comparison with stations which are further apart from each other. If a station is thus ’around the corner’ it will behave differently and will therefore probably focus more on other services such as food and beverages.

Furthermore, H2cannot be rejected, rank reversals are larger in the larger sample compared

to the smaller sample. When stations are thus at viewing distance from each other (the 100 meter cutoff point) they tend to focus more on selling by offering other means. Price competition is less intense compared to the larger markets. Since I am not able to reject H1, competition

in larger area’s shows to be more focused on price differences, and stationary specifics may be of less interest to the seller. From these tests I can thus state that pricing behavior of stations around the corner is signifcantly different from pricing behavior from stations further apart.

The results of the K-S test show the same results as CT. The American data also rejects HKS and H1. Meaning that the used data shows evidence of search in the gasoline market.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 500 1000 1500 2000 2500 3000

Figure 7: Rank reversals Market C

Amount of observations on vertical axis, rank reversal on horizontal

then counts. I use an OLS regression in order to observe the impact of being around a corner on both the rank reversal and the standard deviation of the ranks. In this way we are able to observe impact of cornered stations. The OLS is estimated using the following equation:

rij = β0+ β1I[corner]ij+ β2Xij+ ij (6)

Here I[corner] is an indicator whether the stations are located within the 100 meter cutoff point, and rij represents the rank reversals. X contains the number of (private or company

owned) cars available in the area. The number of cars per market is constructed using the number of cars which is registered in the same 3-digit postal code as the station. If the number of cars is higher in a certain area we could expect more reversals since competition could be increased by a larger demand.

Euro95 dij < 1

Number of observations 1001 Avg. rank reversal 0.1982 Avg. spread 0.0236 dij < 2

Number of observations 3322 Avg. rank reversal 0.1727 Avg. spread 0.0265 dij < 5

Number of observations 6218 Avg. rank reversal 0.1603 Avg. spread 0.0281

Table 2: Descriptives per market

Where sijt∈ sij represents the price spread between(i, j) at day t, ¯sij is the average of days Tij

observed. The model is similar to the rank reversal model, only now I observe price differences between stations. The reason to use standard deviations over rank reversals is that the standard deviation captures more price information. Whereas the rank reversals only show changes in ranks, the standard deviation takes into account the size of the volatility in stations prices.

The results of these tests can be found in table 4. The quantile regression results are presented for the 25th, 50th, 75th, and 95th quantiles. Quantile regressions on a market with a cutoff point at 1 km yielded no convergence in results. The coefficients for the I[corner]ij

variable are in all cases negative for the standard deviation and positive for the rank reversals. The standard deviation also incorporates the size of price changes whereas the rank reversals only observe whether the rank is reversed or not. This could indicate that price changes are smaller when a station is near another station, however, the rank reversal increases. Competition is thus more intense but with smaller differences in prices. Increasing the size of the market increases the effect of the corner variable. In the situation where the market has only a cutoff point of 1000 meters, the effect of the corner variable is only .04. When looking at a market with a larger cutoff point this number increases.

Euro95 p D dij < 1 H1 0.0000 0.5170 H2 0.8472 0.0439 HKS 0.0000 0.5170 dij < 2 H1 0.0000 0.5478 H2 0.7876 0.0519 HKS 0.0000 0.5478 dij < 5 H1 0.0000 0.5623 H2 0.7631 0.0551 HKS 0.0000 0.5623

Table 3: Equality of distributions test for rank reversals. Corners vs. Market

H1∶ F1(r)>F2(r).

H2∶ F1(r) < F2(r).

HKS∶ F1= F2

small distances, firms compete less in prices. If we increase the size of the market however, we see increases in the rank reversals, prices are changing more and firms are competing more intensely. The quantile regressions show that area’s which include the 2nd and 3rdquantile are being influenced the mostly by the corner variable. Both rank reversal and standard deviation are only minimally influenced. In the 95% case, with cutoff point at 5000 meters the outcomes are insignificant.

Comparing this data to CT yields some different results. Whereas all of the coefficients of the rank reversal are positive on the Dutch data. The coefficients for the US data regressed on the rank reversals are all negative. A negative rank reversal would mean that there is less competition switching in price leadership. This argument can be used in two different ways.

informed about prices, heterogeneity of other factors may be the reason. Firms will therefore compete using complementary goods or extra services.

On the other hand, one could argue that a positive rank reversal increases competition on the price level when the corner variable is relevant. Prices of stations which are located near one another vary more. This also means increased competition. However, since data on the first of the two reasons are lacking and since the model does not includes differences along stations the Dutch market seems to fit the model better using the data provided.

Market Dep. Var. OLS Quantile Regression

25% 50% 75% 95% dij < 1 rij .0404316 [.0139817]∗∗ σij -.0035337 -.0031809 -.0054133 -.0039178 -.0047612 [.0017932]∗ _[.0007737]∗∗ _[.0013859]∗∗ _{[.0023652] [.0117755]} dij < 2 rij .1829831 .0992144 .3657953 .1541511 .023829 [.0264444]∗∗ _[.0083267]∗∗ _[.0447808]∗∗ _[.0488648]∗∗ _[.0100636]∗ σij -.0034053 -.0040323 -.0059439 -.0044246 -.0027574 [.001146]∗∗ [.0006767]∗∗ [.00081]∗∗ [.0016397]∗∗ [.0058444]∗ dij < 5 rij .188 .0834313 .3957537 0.182 .0237492 [7.3]∗∗∗ _[19.34]∗∗∗ _[7.25]∗∗∗ _[3.57]∗∗∗ _[1.35] σij -.0039978 -.0043334 -.0061837 -.0045417 -.0020345 [-7.16] [.0007196] [-3.54] [.0017716] [.0062488] Table 4: OLS Estimates

Rank Reversal and Standard deviation on I[corner]

6

Summary and Recommendations

6.1 Summary

After examination of the Dutch retail gas market using the rank reversal model I am able to establish a clear link between gas prices and consumer search. Using a rank reversal approach to the data I am able to conclude there is evidence that the consumer search theory is valid in the gasoline market. Using a rank reversal model I have shown that there is competition in the Dutch market for gasoline. Price differences tend to be small, but price leaders (the highest ranking firm regarding prices) change over time.

Testing for differences between groups using Kolmogorov-Smirnov tests has shown that stations ’around the corner’ have different pricing strategies than stations that are more distant from one another. Price dispersion in larger markets is consistently higher compared to price dispersion in stations which are located only at a minimum distance from each other. This is consistent with the theory of consumer search, as price differences of stations within visibility range are only driven by product differentiation or station specifics.

Using OLS regression on both rank reversal statistics and standard deviations I have shown that rank reversals are influenced by the distances between gasoline stations. Standard devia-tions have shown that price differences are smaller when stadevia-tions are nearer each other.

In overall I can conclude that stations do mix their prices over certain ranges in order to capture either market share or maximize profits. As is shown by the differences in rank reversals between stations. Stations which are located further away from another have increased price competition in comparison to stations close to each other. Therefore I have shown that search is a part of the Dutch retail gas market.

6.2 Recommendations

Furthermore, since the beginning of 20126, a new ’low cost’ brand has operated 46 gas sta-tions in the Netherlands. This brand sells gasoline at a discount of 16 cent on the recommended gas prices. Since this would induce a large price dispersion across stations, it therefore would be very interesting to use data from 2013.

6

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