No Rockets, No Feathers, No Cycles:
A Study of the Groningen Retail Gasoline Market
Tadas Bruˇ
zikas
∗August 27, 2012
Master’s Thesis
Thesis supervisor:
Dr. Pim Heijnen
∗Affiliation: University of Groningen, Faculty of Economics and Business. Study programme:
Abstract
In this thesis, I analyze the pricing behavior of gasoline stations in Groningen, the Netherlands. Unlike previous studies, I do not find any signs of Edgeworth cycles in the Groningen market. I also consider the response asymmetry of retail prices to costs shocks and I find that gasoline stations respond to changes in their costs symmetrically. Finally, since the data contain a lot of missing values I suggest the expected maximum likelihood estimator to estimate a simple spatial panel data model. I use the latter to test for the presence of cartel-like behavior. I reject my hypotheses due to a lack of economic significance.
JEL Classification: C13, D40, L10, L41
Contents
1 Introduction 4
2 Theoretical background and previous findings 6 2.1 Edgeworth cycles . . . 7 2.2 “Rockets and feathers” . . . 8
3 Data 9
4 Testing for Edgeworth cycles 11 5 Asymmetric response to spot price changes (at the market level) 13 5.1 Analysis using weekly-averaged data . . . 15 5.2 Analysis using original data . . . 16 6 Relationship between spatial dependence and spot prices 18 6.1 Some heuristics . . . 18 6.2 Expected Maximum Likelihood estimator . . . 20 6.3 Results . . . 21
7 Summary and conclusions 23
References 24
A Appendix 26
1
Introduction
Since gasoline is a prime example of a homogeneous good, one might expect that firms, who are selling it in the retail market, act accordingly to competitive theories. Nonetheless, the literature on gasoline retailing counts many examples where various asymmetries and cycles are observed (Eckert, forthcoming). Sometimes it appears that the findings may be so extraordinary due to very selective samples. Hastings (2004) and Taylor et al. (2010) study vertical relationships and competition in the same market and find very different results. The difference in their findings appears to be due to Hasting’s select sample. Another example is Noel (2007b) who analyzes Edgeworth cycles in Toronto and only selects stations on the main roads in the city, however the Western part of Toronto is uncovered so his sample does not seem to be random. In order to show what one may naturally expect from analyzing retail gasoline markets, I choose the city of Groningen, a small but distinct market in the North of the Netherlands. I exclude only 3 out of 25 stations due to extremely poor availability of data which represents a small market share of these stations.1
The aim of this thesis is to learn as much as possible from the data about the pricing behavior in the Groningen retail gasoline market. In a survey by Eckert (forthcoming), research on the Edgeworth price cycles, a rather rare but very interesting pattern, receives a lot of attention. I use a fleet card data set to analyze whether Edgeworth cycles can potentially be present in Groningen. Asymmetric pricing phenomenon (also known as “rockets and feathers”) is also one of the most popular topics in gasoline retailing literature. Personal experience shows that consumers are aware of this pattern, i.e. drivers often think that gasoline stations absorb positive cost shocks more quickly than the negative ones. People also have a notion that those markets are less competitive than others due to collusive behavior. The data that I use include several independent unbranded gasoline stations who usually drive competition in a market (Noel, 2007a), however the majority of the market is shared among well known brands like Shell, BP, Esso, and Total. Therefore, one might expect to observe “rockets and feathers” in the Groningen market. To conclude, I believe it is interesting to study a particular retail gasoline market and consider both pricing patterns, i.e. Edgeworth cycles and “rockets and feathers”, because in this way we can get insight to the extent to which the market is competitive or collusive.
My findings confirm that Edgeworth cycles are a very rare phenomenon. Using some
1I use a fleet-card data set, so if prices are rarely observed at particular station it shows that consumers
comparative statistics suggested by Atkinson (2009), I conclude that it is very unlikely that Edgeworth cycles exist in Groningen. With respect to asymmetric pricing, I replicate Borenstein et al. (1997) to find that gasoline stations in Groningen respond to cost shocks symmetrically. These results corroborate the findings of Faber (2009).2
It is often overlooked by researchers that retail gasoline markets have a clear locational structure where distances between stations are important. The spatial dimension is very important in this context because any two stations are always competing for a consumer who appears to be or live in between them. In the Salop (1979) circle model, an indifferent consumer is located exactly halfway between two stations in the equilibrium with equal prices. However, if one station lowers the price it attracts more consumers living closer to its competitor because, on the one hand, the transportation or search costs become smaller, and on the other hand, cheaper station is more attractive. In this thesis, I apply spatial econometrics techniques to account for these spatial relationships between gasoline stations. Existing methods from spatial econometrics are not capable of dealing with missing data. Therefore, we develop an expected maximum likelihood (EML) approach to deal with this problem.
In their model with fluctuating marginal costs, Athey et al. (2004) suggest that colluding firms may have an incentive to undercut cartel price since other cartel members cannot identify if this is a result of intentional deviation or lower marginal costs. This in turn implies that in the event of a negative one-cent cost shock a firm will decrease its price by more than one cent. Likewise, a station has an incentive to increase price by less than one cent after a positive one-cent cost shock. I consider a spatial model which helps to identify these effects. However, the results show that the asymmetry from spatial perspective is not economically significant.
The thesis is structured as follows. In Section 2, I review the relevant literature. Sec-tion 3 introduces the data. SecSec-tion 4 considers the presence of Edgeworth cycles in the Groningen market. In Section 5, I analyze the response asymmetry whereas in Section 6 I look at the asymmetry of pricing among the stations from a spatial perspective. Finally, Section 7 summarizes the findings and concludes.
2Faber (2009) studies the whole country. However, conversations with the researcher reveal that most
2
Theoretical background and previous findings
The last three decades has seen intensive research on gasoline retailing. This is very likely a consequence of antitrust concerns and increased availability of data (Eckert, forthcom-ing). Retail prices are easily observed from large billboards. However, only recently has technology allowed car rental companies to collect the data using fleet cards. In his sur-vey, Eckert (forthcoming) collected 102 studies which have been done in this field, most of them (79 out of 102 papers) being published in the 2000s. These papers can be roughly classified into four strands of literature: 1) station-level price dispersion due to individual characteristics or level of competition, 2) mergers and regulatory impact on retail gasoline prices, 3) existence of the Edgeworth cycles, and 4) asymmetric pricing in response to positive and negative cost shocks. In this thesis, I mostly focus on the last two strands of literature so theory and previous literature of Edgeworth cycles and asymmetric pricing will be reviewed in detail in the next two subsections. Below, I briefly discuss the main contributions to the first two categories of gasoline retailing literature.
The work of Clemenz and Gugler (2006), whose main finding confirms a theoretical proposition that higher density of firms lead to lower market prices, represents the first strand of the literature. Using an Austrian data set, they find that if the distance between competitors is smaller this drives the equilibrium price down. Finally, Clemenz and Gugler are able to show that station density causally affects prices.
2.1
Edgeworth cycles
Edgeworth cycle is an asymmetric price cycle, theoretically formalized by Maskin and Tirole (1988). Their model is rather simple. Consider two identical independent firms competing in a single homogeneous product market and facing no capacity constraints. The latter assumption allows one firm to serve the whole market. Firms maximize their long-term profits. Consumers buy from the firm which sets the lowest price. If prices are equal, they share the demand equally. Firms compete in prices which are chosen from a discrete grid and are set for two periods because firms are only allowed to make their moves sequentially in different periods. Maskin and Tirole (1988) show that there is a stable Markov perfect equilibrium. This outcome is an asymmetric price cycle that starts with a large one-period jump from marginal costs to the price above monopoly level which then is followed by many gradual decreases back to marginal cost level.
Noel (2007a,b) analyses retail gasoline markets in Canada. In his first article he analyses nineteen major Canadian cities on weekly basis. Noel (2007a) applies Markov-Switching Regression to differentiate cycle phases from non-cycle phases. The former is further di-vided into relenting (price increase from marginal cost to (above-) monopolistic level) and undercutting phases. A similar approach is used to analyze Toronto retail gasoline market where Noel (2007b) uses privately-gathered twelve-hourly data. This article shows that Edgeworth cycles in Toronto are actually predictable, i.e. they usually start at the begin-ning of the week on Mondays. Noel (2007b) is able to measure the average price increase during the relenting phase and price decrease during the undercutting phase, the duration of both phases, and the length and the asymmetry level of the representative cycle. He also shows that major firms tend to initiate recoveries (increases) of the price while smaller (independent) firms take the lead in the undercutting phase. Atkinson (2009) who uses bi-hourly price data of 27 gasoline stations in Guelf, Ontario (Canada), finds similar re-sults as Noel (2007b). As de Roos and Katayama (2010) show, Edgeworth cycles may be observed even in the environment where many of the assumptions underlying Maskin and Tirole (1988) model are violated. On the other hand, Foros and Steen (2009) emphasize that the price cycles that are present in Norway look similar to the Edgeworth ones, but they are the outcome of coordinated behavior.
in several countries (Canada, the USA, Australia; see e.g. Noel, 2007a,b; Atkinson, 2009; Doyle et al., 2010; de Roos and Katayama, 2010), and they are more prevalent in markets where there is greater penetration of small stations (Noel, 2007a). For this reason one of my aims is to analyze whether the Groningen retail gasoline market features the exis-tence of Edgeworth cycles. There are 15 papers published from 2000 in this field (Eckert, forthcoming), so it might also seem that these cycles are very common. Therefore, I will use the data of Groningen retail prices to shed some light on the price movements in the Netherlands.
2.2
“Rockets and feathers”
The fourth strand of the literature focuses on the response asymmetry of retail prices to positive and negative shocks in marginal costs. This phenomenon is also referred to as “rockets and feathers” because most often the data suggest that retail prices react much faster to the increases in marginal costs rather than the decreases (see e.g. Borenstein et al., 1997; Faber, 2009; Lewis, 2011). Peltzman (2000) finds this pattern in a significant share of industries including gasoline retailing from more than 200 that he is studying. According to Eckert (forthcoming), this is the most popular topic in gasoline retailing literature - he counts 26 such studies.
Earlier this pattern used to be interpreted as an outcome of collusive behavior, however the literature is lacking solid theoretical explanation for this (Eckert, forthcoming).3 As
Borenstein et al. (1997) put it, in case of the decrease in marginal costs the previous retail price might be a focal point to tacitly collude on. On the contrary, if costs are increasing firms will adjust their retail prices more carefully in order not to lose their profit margins. In light of this reasoning I interpret the asymmetric pricing as a possible sign of collusive pricing. Since the asymmetric pricing is even more often observed than Edgeworth cycles, I am going to test whether gasoline stations in Groningen respond asymmetrically to the changes in marginal costs. I will apply the error correction model used by Borenstein et al. (1997) which will be formally described in Section 5.
3
Data
In this section, I describe the data that I am going to use. My data set contains daily retail gasoline4 prices in 22 stations in Groningen over 1283 days (from 3 October 2005 until 7
April 2009).5 These data are being published by Athlon Car Lease, the largest car-leasing
company in the Netherlands. The gasoline stations in the sample are all stations within the non-industrial areas of Groningen, except two stations which were excluded from the sample due to very few observations (62 and 88 out of 1283) and, more importantly, being small and specific industrial stations.6 All stations are mapped in Figure 1. Note that the station in the North-West (No. 23) appears on the map but it is actually outside the city area. Finally, Elan Nadorstplein (No. 26) is not observed during the whole sample period, however Athlon Car Lease have recently started to quote prices of this station too. The average price during the whole period is 1.381 euros per liter and it ranges from 1.10 to 1.64 euros per liter. In his paper on Edgeworth cycles, Noel (2007b) analyses a set of 22 selected gasoline stations in Toronto. His sample does not look random if one takes a look at Figure 4 in Noel (2007b, p. 79). However, I believe that considering all stations which are active in the market leads to more reliable and robust results. The only drawback of the data set I use is that retail prices are not observed perfectly, i.e. some daily quotes are missing. Since there are N = 22 stations followed for T = 1283 days, there should be 22 × 1283 = 28226 quotes in total, however we have only 17942 observations. I address the missing data problem by developing the EML estimator in Section 6.
Additionally, this data set includes the coordinates of each gasoline station, therefore I can actually measure the distance between any pair of stations. This is useful for the spatial analysis in Section 6. In the following sections I consider retail prices excluding the taxes which are the excise duty per each liter of fuel and the 19 percent VAT paid over raw price and excise duty.7 Moreover I append the data set with a proxy for the marginal
costs of gasoline stations. The true marginal costs of each gasoline station are their private information due to arrangements with the refineries or major companies (Borenstein et al.,
4To be precise, I am considering regular unleaded gasoline of octane number 95 or simply Euro-95. 5I am very thankful to Pim Heijnen, Marco Haan and Adriaan Soetevent who collected and kindly
shared the data.
6These two stations are Allesco Esso Center Gotenburgweg and Firezone Groningen (No. 24 and 25 in
Figure 1 to the East and North-East from the city center respectively). These stations are in the industrial areas of Groningen and they usually serve trucks. I exclude these two stations from the sample because they do not compete with other stations.
7The excise duty during the sample period was (in euros per 1000 liter): 676.28 in 2005-2006; 687.02 in
Figure 1: Gasoline stations in Groningen.
1997), therefore I use the Amsterdam-Rotterdam-Antwerp (ARA) Conventional Gasoline Regular Spot prices instead.8 This is the main wholesale price of gasoline in the Netherlands
and is commonly used to approximate for marginal costs (see e.g. Faber, 2009). Since the prices are expressed in dollars (USD) per gallon, I use daily EUR/USD exchange rates (obtained from the European Central Bank, ECB) and liters per gallon ratio to convert the spot prices into euros per liter. The problem with the spot prices is that the wholesale market is closed during weekends and national holidays or religious days, therefore it has an impact on the sample size. This becomes critical in the analysis of asymmetric pricing where I have to use price changes and 3rd-order lags which essentially means that at the best we have only two observations per week.
4
Testing for Edgeworth cycles
In this section, I will attempt to answer the question whether the fluctuations of gasoline prices in Groningen resemble Edgeworth cycles. Previous research (Noel, 2007b; Atkin-son, 2009) shows that due to the sharp asymmetry of Edgeworth cycles, they are easily observable even without a very thorough analysis.
The Edgeworth cycle theory (Maskin and Tirole, 1988) suggests that competing firms undercut each other until they come to the phase where they set price equal to marginal cost. From this one could expect that firms competing in Edgeworth cycles charge at the minimal (market) price for similar amount of time. However, the data prove different, i.e. the cheapest (on average) stations tend to charge the minimum price most often. Table 1 shows that three cheapest stations charge prices equal to the lowest one 81.50, 10.78, and 51.99 percent of the time that they are active on the market. This does not necessarily mean that stations do not compete in Edgeworth cycles. As Eckert (2003) shows larger (and probably more expensive) firms might match the price rather than undercut the opponent. Nevertheless, two most expensive (on average) stations charge the lowest price only 0.20 and 0.11 percent of the time. Moreover, these stations charge the highest price in the market most of the time (64.76 and 52.83 percent respectively).
Another important statistic is the daily price differences. Theoretically, in Edgeworth cycle equilibrium prices should be falling for most of the time or at least they should be falling more frequently than increasing. Since there are too many missing values to concentrate on the station specific price differences, I consider city-wide price averages and modes over time. These statistics are given in Table 2. The average retail price rises and falls 509 and 546 times respectively, so it decreases 1.07 times more often than it increases. Since even the smallest changes in the average price are treated as such I correct it somehow by assuming that the differences between −0.001 and 0.001 euros per liter are insignificant. This does not change the latter result too much (1.04 times). Similar holds for the mode retail price, i.e. the mode price jumps up and falls down 237 and 229 times respectively, so here prices rise even more often than they fall but the difference is very small. Atkinson (2009) reports rather different statistics in his study on bi-hourly retail gasoline prices in Guelph, Ontario, Canada, where he observes Edgeworth cycles. According to Atkinson (2009, p. 93) “city-wide mean (mode) price falls 3.1 (4.3) times more often than it rises”.
Table 1: Minimum and maximum price distribution by station.
Station Station % of days when % of days when No. Brand and Street p¯s pst = mins(pst) pst = maxs(pst)
17 Tango Odenseweg 1.3519 81.50 0.13 7 Tinq Helper Weststraat 1.3563 10.78 7.80 3 Tinq Groningerweg 1.3573 51.99 1.44 16 Elan Akeleiweg 1.3627 16.57 1.52 18 Q8 Rijksweg 1.3668 10.39 1.71 9 Tinq Helperzoom 1.3717 8.08 0.73 13 Gulf Turfsingel 1.3798 4.64 4.26 4 Bim Kerklaan 1.3799 5.85 6.40 20 Shell Zonnelaan 1.3807 1.76 3.21 5 Shell Rijkstraatweg 1.3810 2.86 5.7 10 Shell Europaweg 1.3818 7.08 9.93 14 Total Oliemuldersweg 1.3820 3.07 17.69 6 Shell Vershuurlaan 1.3825 2.34 6.31 8 Gulf Paterswoldseweg 1.3828 2.69 3.39 19 BP Pleiadenlaan 1.3831 0.63 3.34 11 Bim Hoendiep 1.3835 3.39 4.70 22 Total Amkemaheerd 1.3859 3.28 25.44 2 Total Rijkstraatweg 1.3862 0.78 13.19 21 Esso Friesestraatweg 1.3896 0.75 30.95 15 Esso Pop Dijkemaweg 1.3906 2.47 9.28 12 Q8 Laan 1940-1945 1.3949 0.11 52.83
1 BP Emmalaan 1.3968 0.20 64.76
Notes. ¯ps is a station-specific price average over the whole sample period which is
equal to
P
tpst
Ts where Ts is a number of price quotes at station s; measured in euros
per liter. Gasoline stations are ordered in the ascending order based on this statistic.
and −0.0135) respectively. Atkinson (2009) on the other hand reports that the means of the average (mode) price increases are 2.9 (4.1) times larger than decreases in Guelph market. Consequently, prices in Guelph seem to be following asymmetric cycles similar to Edgeworth cycles. On the contrary, statistics reported in Table 2 suggest that either the price cycles in Groningen retail gasoline market are symmetric, or there are no cycles at all.
Table 2: Summary statistics of the first differences of daily price average and mode. ∆¯pt ∆¯pt ∆ modt(pst) Interval > 0 0 < 0 ≥ 0.001 (-0.001, 0.001) ≤ −0.001 > 0 0 < 0 No. Obs. 509 15 546 424 205 441 237 604 229 Mean 0.0053 0 −0.0050 0.0062 −0.0001 −0.0060 0.0144 0 −0.0135
Notes. ¯pt is a daily average price in Groningen equal to P
spst
Nt where Nt is a number of price
quotes on day t; measured in euros per liter.
that of cost-based pricing, i.e. the retail price (excluding taxes) follows the spot price level very accurately, there are no apparent asymmetric price cycles, and the (profit) margin between retail and spot prices seems to be relatively constant.9 Since I cannot find any signs
that the price cycles might be present in Groningen, I do not employ more sophisticated techniques (e.g. Markov-Switching Regression) to test the presence of Edgeworth cycles formally in this thesis.
5
Asymmetric response to spot price changes (at the
market level)
Noel (2007a) shows that Edgeworth cycles are the outcome of fierce competition rather than the evidence of collusive behavior. Since in the previous section I have shown that it is very unlikely for the Groningen retail gasoline market to exhibit Edgeworth cycles, in this section I am considering a phenomenon of asymmetric pricing. This pattern used to be interpreted as a possible result of the cartel (Eckert, forthcoming). Many authors find that gasoline stations, indeed, respond asymmetrically to the changes in spot prices (Eckert, forthcoming). The aim of this section is to answer the question whether gasoline stations in Groningen price asymmetrically. These findings could suggest that Groningen market has some signs of collusive behavior. Hence, I am not going to analyze the underlying reasons of asymmetric pricing, but rather I consider the methods developed for time series data and apply them on panel data in order to test the hypothesis of asymmetric pricing in Groningen.
Consider the error correction model suggested by Borenstein et al. (1997) extended to
9I have looked at the graph with lower time frequency so that fluctuations are more clearly visible. I
0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40 1,60
Sep-2005 Apr-2006 Nov-2006 May-2007 Dec-2007 Jun-2008 Jan-2009
Mode retail Mode retail excl. taxes ARA spot
Figure 2: Dynamics of mode retail (incl. and excl. taxes) and ARA spot prices.
panel data: ∆pst = a X l=0 βl+∆spot+t−l+ b X l=0 βl−∆spot−t−l+ c X l=1 γl+∆p+s,t−l+ d X l=1 γl−∆p−s,t−l +α(ps,t−1− δ0 − δ1spott−1− δ2t) + µs+ νst (1)
where a, b, c, and d are the numbers of lags to be included, [ps,t−1− δ0− δ1spott−1− δ2t] is
the error term from long run relationship (p = δ0+ δ1spot + δ2t) lagged by 1 period where
t is a time trend to account for possible effects of inflation, for example, µs is a
station-specific fixed effect, and νst is a white noise error term with zero-mean. The estimation of
model (1) gives the parameter estimates necessary to calculate the cumulative adjustment functions (see Appendix A for the expressions of cumulative adjustment functions).10 The comparison of cumulative adjustment functions (as responses to positive and negative one-cent changes in spot price) reveals whether the retail prices respond asymmetrically to spot price changes.
Table 3: AIC and BIC statistics. a b c d AIC BIC 1 1 1 1 -28439.78 -28376.99 2 2 2 2 -28545.66 -28457.76 3 3 2 2 -28608.83 -28508.38 2 2 3 3 -28561.88 -28461.42 3 3 3 3 -28653.03 -28540.02
Notes. Number of observations is fixed to 3938 in all estimations.
5.1
Analysis using weekly-averaged data
Unfortunately, the estimation of model (1) is somewhat cumbersome. First, I attempt to estimate model (1) by fixed effects using (averaged) weekly data.11 I choose a = b =
c = d = 3 as suggested by both Akaike and Schwartz-Bayes information criteria (AIC and (S)BIC), see Table 3 for details.12 The cumulative responses to positive and negative
shocks of 1 euro-cent in spot prices and corresponding asymmetry are presented in Figure 3. The results are quite surprising in the sense that we find that retailers react more quickly to the negative than to the positive shocks in spot prices. What is even more unexpected, the asymmetry in the third and fourth weeks after the shock is significantly different from zero at the one-percent level.13 This is a rather rare finding - only Wlazlowski et al. (2012) find similar, consumer welfare-improving pattern. One-cent shock in spot prices is almost fully accumulated in two weeks (including week 0 when the shock occurs). Using the delta method we cannot reject the null that cumulative responses in week 1 are significantly different from 1.0 at the five-percent level. Faber (2009) notes that the use of weekly data may lead to biased results since the pricing decisions are actually made more frequently than once a week. This suggestion is rather plausible since averaging data from daily to weekly causes a loss of important variance. For this matter I also estimate model (1) using the daily data to see whether doing so will yield different results.
11Hausman test rejects random effects at the one-percent significance level: Chi2(16) = 110.39, p −
value = 0.0000.
12For simplicity, I use AIC and BIC based on the GLS log-likelihood value. As we will see later, this
causes some problems when using daily data which contains considerable fraction (approx. 36 percent) of missing values.
13I use the delta method (Hayashi, 2000) to calculate standard errors of positive and negative cumulative
-0,2 0 0,2 0,4 0,6 0,8 1 1,2 0 5 10 15 20 25 R+ R-Asymm. CI [99%]
Figure 3: Cumulative response functions and asymmetry using averaged weekly data.
5.2
Analysis using original data
The original data set contains missing values. Nevertheless, it is possible to estimate the model by simply ignoring the missing points. Moreover, I make one additional but reasonable assumption that spot price changes do not have any instantaneous effect. I defend this assumption on two grounds. Firstly, pricing decisions at station level are usually made in the morning (hence the spot price of the current day is not available, see Faber (2009), for instance). Secondly, gasoline spot prices in the data set are the closing market prices. Therefore, they are not available even in the afternoon when some price adjustments may take place. I estimate model (1) (excluding the current-day spot price changes) again by means of fixed effects (as indicated by Hausman test). Here I also choose a = b = c = d = 3 in equation (1).14 The cumulative responses to one-cent positive and negative shocks in spot prices and the level of asymmetry are given in Figure 4. I find that response asymmetry is not significant at the one-percent level. Nevertheless, it is significant at the five-percent level in the third day after the shock. These findings reveal
14However, the AIC and BIC suggest to use a = b = c = d = 1. This is because the likelihood of
-0,4 -0,2 0 0,2 0,4 0,6 0,8 1 1,2 0 5 10 15 20 25 R+ R-Asymm. CI [99%] CI [95%]
Figure 4: Cumulative response functions and asymmetry using original data set.
that the situation is not as the weekly data suggest, i.e. the level of asymmetry on the 21st day after the shock is only −0.005 cents per liter whereas Figure 3 shows the asymmetry on week 3 around −0.088. Consequently, we should not trust the weekly averaged data.
Unfortunately, the daily data are not of satisfactory quality either. Missing values amount to 36.4 percent of the whole data set. However, due to the specification of model (1) (first-differences and three lags of retail and spot prices) in the estimation we are able to use only 6.5 percent of the full data set (if we had one) or 10.3 percent of all available data points. Moreover, six gasoline stations have less than 50 observations for the estimation and 11 stations have data in less than 100 days from 1283 which is the length of the sample period.15 For these reasons, I re-estimate model (1) with a reduced sample to 16 stations
which have at least 50 observations.16 From Figure 5 we see that the response asymmetry
is insignificant at five-percent level. The level of asymmetry on the third day after the shock also diminished from −0.148 to −0.128 cents per liter.
Although it is rather complicated to draw clear conclusions due to the imperfections of data, the research reveals that the retail gasoline stations do not react to positive
15On top of this, two thirds of the observed price changes are zero.
16I exclude stations No. 3, 4, 7, 14, 15, and 16. In this way the number of observations reduces only
-0,4 -0,2 0 0,2 0,4 0,6 0,8 1 1,2 0 5 10 15 20 25 R+ R-Asymm. CI [95%]
Figure 5: Cumulative response functions and asymmetry using reduced sample.
shocks in spot prices quicker (or slower) than to the negative ones. The retailers are pretty quick to react to the shocks, although on average prices change only every third day. Generally, in three weeks from the initial shock around 96 percent of the shock is absorbed with 80 percent of the shock accumulated within the first week. The results also show how important the frequency and especially the quality of the price data are for empirical research in industrial organization. Finally, I have to conclude that Groningen retail gasoline market is very standard in terms of pricing behavior.
6
Relationship between spatial dependence and spot
prices
6.1
Some heuristics
different marginal costs due to the contracts with refineries and/or major oil companies.17 Unfortunately this is their private information. In case of a cartel it would be hard to determine and coordinate on the collusive price level due to this asymmetric information. However, if we assume that on average marginal costs fluctuate in parallel with the ARA spot prices, the latter may be used to coordinate collusive prices. Hence, the cartel price could be determined by adding a monopoly profit margin on the spot price. On the other hand, each cartel member would have an incentive to profitably deviate from this cartel price as Athey et al. (2004) suggest. Therefore, this might give incentives for firms to always reduce retail prices by a little more than the spot price decrease, and to raise retail prices by less than the spot price increase, in order to undercut the competitors.
Previous studies show that the time dimension is exploited quite heavily, however eco-nomics lacks attention towards the spatial dimension in retail gasoline pricing. Therefore, I contribute to the gasoline retailing literature by taking the spatial relationships into account. One attempt to do so is a working paper by Hogg et al. (2011). The spatial models clearly make sense for gasoline retailing because effectively stations are competing only with their closest rivals since consumers are not willing to travel too far for cheaper gasoline due to the search costs they face. Prices of competitors are perfectly observable (but not marginal costs) so when making the pricing decisions gasoline stations take rival prices into account. Recall that I have already argued that positive and negative shocks in spot prices may be treated differently. Consequently, taking both the rival price and the spot price changes into account, stations should respond somewhat more to the price changes of neighbors when the spot price decreased in order to undercut competitors. I expect this result because if a station wants to undercut its competitors after a negative change in spot price, it should lower the price by more than its neighbors.18 Therefore, I
hypothesize that spatial dependence between gasoline stations is stronger when the spot prices decrease rather than when they increase (H1).
It is also possible that spatial relationships might be affected by the magnitude of spot price changes. The main underlying reason is that if the spot price change is very small, e.g. less than 1 euro-cent per liter, stations do not adjust their retail prices because gasoline prices in the Netherlands are usually set on the price grid with minimum steps of 1 euro-cent per liter. Consequently, another hypothesis (H2) is that after relatively small spot price change, i.e. ≤ 0.01 euros per liter, gasoline stations react to their neighbors’ prices
17See Borenstein et al. (1997) for a market structure description of the USA.
18Here I implicitly assume that in general gasoline stations lower/raise their prices after negative/positive
less than after a larger change in spot prices (> 0.01 euros per liter).
6.2
Expected Maximum Likelihood estimator
To test my hypotheses, I consider a general model where firms (stations) are distributed on the road network (e.g. as in Figure 1) and thus each station has N − 1 = 21 neighbors rather than two as in Salop (1979) circle. However, the idea is similar. Since each neighbor station has an effect some particular station, the magnitude of that effect is determined by the distance between two stations and measured by the so-called spatial weight wsr =
d−1sr · (P
r6=s
dsr)−1. The model can be given in a form of reaction function as follows:
∆pst = α + β
X
r6=s
wsr∆prt+ εst (2)
where ∆pst is retail gasoline price change at station s on day t, wsr is an element of the
spatial weight matrix measuring the strength of the spatial effects between stations s and r, s 6= r, β is a spatial parameter, and εst is normally distributed error term with zero-mean
and variance σ2. The β parameter can be roughly interpreted as a degree (from 0 to 1)
to which gasoline stations respond to the price changes of their neighbors. We can also rewrite (2) in a matrix form:
∆pt= αι + βW ∆pt+ εt (3)
where ∆pt is an N × 1 vector of price changes in all stations on day t, WN ×N is a spatial
weight matrix, and εt is an N × 1 vector of the errors.
constant term) and I split the sample to control for lagged positive and negative changes in spot prices.
I consider four sub-samples since this is necessary to test my hypotheses. First of all, I differentiate between positive and negative spot price changes to test my first hypothesis.19
Then to test the second hypothesis, I further split these two sub-samples based on the magnitude: < −0.01 or > 0.01 euros per liter. In this way we can learn whether negative and positive spot price changes indeed have different effects on the degree to which gasoline stations react to rival prices. Moreover, we can see if the magnitude of spot price changes matter. Finally, splitting the sample allows us to partly control for spot price changes because this variable is excluded from the model. I split the sample based on one-period lagged spot price changes since gasoline stations are not able to observe spot prices of the current day, as I have explained earlier.
The estimator is called EML because not 100 percent of the prices are observed. There-fore, based on the conditional distribution of the missing values (given observed price changes), the missing price changes are replaced by their conditional expectations. The expected log-likelihood function is given as follows:
E L = −1 2
T
X
t=1
[N log 2π + log det Σt
+(q1t− µ1t)0(S11t+ Σ−111tΣ12tS21t+ S12tΣ21tΣ−111t)(q1t− µ1t) + (N − Kt)] (4)
where q1t(q2t) is a sub-vector of ∆ptincluding only observed (unobserved or missing) price
changes, Σt is variance-covariance matrix of vector qt = (q1t0 q 0 2t)
0, µ
it denotes the mean of
qit, Σijt and Sijt are the appropriate partitions of Σt and Σ−1t respectively (see Sydsæter
et al. (2005, 19.48) for the full expressions), and Kt ≤ N is a number of observed price
changes on day t.20 Maximizing this function numerically with respect to α, β, and σ
yields EML estimates which are presented in the following subsection.
6.3
Results
In Table 4, I present the estimation results of model (2) based on four different sub-samples. I calculate the Variance-Covariance matrix as an inverse of the Hessian. The t -values are
19Note that spot price changes equal to zero are not observed. 20Note that Σ
tand Σ−1t are time-dependent because every day prices are unobserved in different stations
Table 4: The EML parameter estimates of model (2).
Sub-sample Parm. Estimate t-value lower 95 upper 95 Obs. α−2 -0.0016 -25.1353 -0.0017 -0.0014 ∆pst|∆spott−1 < −0.01 β−2 0.6939 63.8117 0.6726 0.7152 2508 σ−2 0.0048 69.7561 0.0047 0.0050 α−1 -0.0004 -16.2475 -0.0005 -0.0004 ∆pst| − 0.01 ≤ ∆spott−1 < 0 β−1 0.6628 100.7293 0.6499 0.6757 6974 σ−1 0.0041 53.4372 0.0039 0.0042 α1 0.0003 7.0549 0.0002 0.0003 ∆pst|0 < ∆spott−1 ≤ 0.01 β1 0.6838 202.2442 0.6772 0.6904 8008 σ1 0.0041 125.8754 0.0040 0.0041 α2 0.0015 11.0077 0.0012 0.0017 ∆pst|∆spott−1 > 0.01 β2 0.7153 34.3569 0.6745 0.7561 2002 σ2 0.0050 61.3834 0.0049 0.0052
Table 5: The t -statistics of the differences between the spatial parameter estimates.
Hypothesis t -stat |β−2− β2| = 0 28.5741
|β−1− β1| = 0 164.0752
|β−2− β−1| = 0 91.0270
|β2− β1| = 0 46.4211
calculated to test the null hypothesis H0 : βi = 0. The 95-percent confidence interval
bounds are found as ˆβi± t∗· si where t∗ is a critical value of the Student t -statistic (approx.
1.96) and si is the standard error of the parameter estimate. To judge if the parameter
estimates from each sample are significantly different from each other is very hard only by looking at the confidence intervals. To circumvent this problem I use the t -test to test whether the differences in parameter estimates are significant. The Welch (1947) t -statistic is given as follows: tij = ( ˆβi − ˆβj) − (βi− βj) r s2 i ni + s2 j nj (5)
where ni is the number of observations used to estimate the parameters. In Table 5 I
Results show that the differences between parameter estimates are statistically signifi-cant, however it is clear that those differences are economically insignificant because all β parameters are approximately equal to 0.7 so the differences are negligible. My hypothesis with respect to negative and positive shocks in spot prices is not supported because the data suggest that gasoline stations react to the prices of their neighbors more actively when the positive cost shock is observed, i.e. opposite to what was predicted.21 My second
hypothesis with respect to the magnitude of spot price changes is also not supported by the data because the differences between β−2 and β−1, and β2 and β1 are economically
in-significant. I conclude that although spatial autocorrelation proves to be significant itself, retailers do not price asymmetrically in any respect.
7
Summary and conclusions
The literature of gasoline retailing has seen many examples of very interesting pricing phenomena such as Edgeworth cycles, or “rockets and feathers”. In this thesis, I analyzed a panel data set representing the Groningen retail gasoline market to answer the question whether any of these seemingly common patterns are actually observed so often.
Using some simple summary statistics of the data, I showed that retail prices do not cycle but rather accurately follow the spot prices in Groningen. I also used an error correction model to differentiate between the effects of positive and negative spot price differences on the changes of retail prices. However, I found no evidence that gasoline stations respond to positive and negative cost shocks asymmetrically even though this pattern is often observed in retail gasoline markets. A somewhat more “positive” result is that distances between gasoline stations matter, however they are taken into account too rarely by the researchers in this field. I hypothesized that in a collusive market, firms lower their prices after a negative shock in marginal costs by more than they would increase prices after a positive shock. For this purpose, the expected maximum likelihood estimator is developed to deal with the missing data problem and the sample is split based on lagged spot price changes in order to test two specific hypotheses. The results show that there are no signs of cartel-like behavior in the Groningen market. I stress that further research in spatial econometrics is needed to improve expected maximum likelihood estimators to avoid data imputation.
21I have also split the sample in two based on the lags of positive and negative spot price differences
Even though the literature counts numerous studies which examine interesting or un-usual pricing behavior, I find no such phenomena in the Groningen retail gasoline market. My research shows that neither Edgeworth cycles nor “rockets and feathers” are observed in a distinct retail gasoline market of Groningen. However, evidence shows that far more relevant is the spatial dependence among the gasoline stations. The competitive forces of local competition seem to be more common to every market rather than what many economists are currently focused on.
References
Athey, S. C., K. Bagwell, and C. W. Sanchirico (2004): “Collusion and Price Rigidity,” Review of Economic Studies, 71, 317–349.
Atkinson, B. (2009): “Retail Gasoline Price Cycles: Evidence from Guelph, Ontario Using Bi-Hourly, Station-Specific Retail Price Data,” The Energy Journal, 30, 85–109. Borenstein, S., A. C. Cameron, and R. Gilbert (1997): “Do Gasoline Prices
Respond Asymmetrically to Crude Oil Price Changes?” The Quarterly Journal of Eco-nomics, 112, 305–339.
Clemenz, G. and K. Gugler (2006): “Locational Choice and Price Competition: Some Empirical Results for the Austrian Retail Gasoline Market,” Empirical Economics, 31, 291–312.
de Roos, N. and H. Katayama (2010): “Retail Petrol Price Cycles in Western Aus-tralia,” 39th Australian Conference of Economists ACE10, Sydney.
Doyle, J., E. Muehlegger, and K. Samphantharak (2010): “Edgeworth Cycles Revisited,” Energy Economics, 32, 651–660.
Eckert, A. (2003): “Retail Price Cycles and the Presence of Small Firms,” International Journal of Industrial Organization, 21, 151–170.
——— (forthcoming): “Empirical Studies of Gasoline Retailing: A Guide to the Litera-ture,” Journal of Economic Surveys, doi: 10.1111/j.1467-6419.2011.00698.x.
Faber, R. P. (2009): “Asymmetric Price Responses of Gasoline Stations: Evidence for Heterogeneity of Retailers,” Tinbergen Institute Discussion Paper 2009-106/1.
Foros, O. and F. Steen (2009): “Gasoline Prices Jump Up on Mondays: An Out-come of Aggressive Competition?” NHH (Norwegian School of Economics and Business Administration) Discussion Paper.
Hastings, J. S. (2004): “Vertical Relationships and Competition in Retail Gasoline Markets: Empirical Evidence from Contract Changes in Southern California,” American Economic Review, 94, 317–328.
Hayashi, F. (2000): Econometrics, Princeton, New Jersey: Princeton University Press. Hogg, S., S. Hurn, S. McDonald, and A. Rambaldi (2011): “A Spatial
Economet-ric Analysis of the Effect of Vertical Integration on Retail Gasoline PEconomet-ricing,” Australasian Meeting of the Econometric Society, July 5-8, Adelaide, Australia.
Lewis, M. S. (2011): “Asymmetric Price Adjustment and Consumer Search: An Exami-nation of the Retail Gasoline Market,” Journal of Economics and Management Strategy, 20, 409–449.
Maskin, E. and J. Tirole (1988): “A Theory of Dynamic Oligopoly II: Price Compe-tition, Kinked Demand Curves and Edgeworth Cycles,” Econometrica, 56, 571–599. Noel, M. D. (2007a): “Edgeworth Price Cycles, Cost Based Pricing and Sticky Pricing
in Retail Gasoline Markets,” Review of Economics and Statistics, 89, 324–334.
——— (2007b): “Edgeworth Price Cycles: Evidence from the Toronto Retail Gasoline Market,” Journal of Industrial Economics, 55, 69–92.
Peltzman, S. (2000): “Prices Rise Faster Than They Fall,” Journal of Political Economy, 108, 466–502.
Rao, C. R. (1973): Linear Statistical Inference and Its Applications, New York: John Wiley & Sons, Inc.
Soetevent, A. R., M. A. Haan, and P. Heijnen (2008): “Do Auctions and Forced Divestitures Increase Competition? Evidence for Retail Gasoline Markets,” Tinbergen Institute Discussion Paper 2008-117/1.
Sydsæter, K., A. Strøm, and P. Berck (2005): Economists’ Mathematical Manual, Berlin: Springer.
Taylor, C. T., N. M. Kreisle, and P. R. Zimmerman (2010): “Vertical Relation-ships and Competition in Retail Gasoline Markets: Empirical Evidence from Contract Changes in Southern California: Comment,” American Economic Review, 100, 1269– 1276.
Welch, B. L. (1947): “The Generalization of ‘Student’s’ Problem when Several Different Population Variances are Involved,” Biometrika, 34, 28–35.
Wlazlowski, S., B. Nilsson, J. Binner, M. Giulietti, and N. Joseph (2012): “New York Mark-Ups on Petroleum Products,” The Manchester School, 80, 145–171.
A
Appendix
Here I present the expressions of cumulative adjustment functions based on Borenstein et al. (1997). R+
q is the q-th cumulative response to a one-cent positive shock in spot price
and it is given by: R+1 = β1+ R+2 = R1++ β2++ α(R+1 − δ1) + γ1+max(0, R + 1) + γ − 1 min(0, R + 1) .. . (A.1) R+q = Rq−1+ + βq++ α(R+q−1− δ1) + q X l=1 γl+max(0, R+q−l− R+q−l−1) + γl−min(0, R+q−l− R+q−l−1)
The q-th cumulative response to a one-cent negative shock in spot price, Rq−, is found by replacing the plus superscripts with the minus ones in (A.1). The response asymmetry is simply the difference between R+
q and R −
q. Note that in our case for q > 3 the parameter
endogenous (changes of retail gasoline prices) nor the exogenous (changes of spot prices) variables.
B
Appendix
Here I derive the expected log-likelihood function given in (4). For convenience, I drop the time index t in the remainder of this appendix. Using the same notations as in the main text, ∆p is multivariate normally distributed with mean (IN − βW )
−1 αι and covariance matrix σ2(I N − βW ) −1 (IN − βW ) −10
. Moreover, the distribution of the missing price changes q2 is multivariate normal with mean µ2+ Σ21Σ−111(q1− µ1) and variance-covariance
matrix Σ22− Σ21Σ−111Σ12 (Rao, 1973, pp. 522-523).
Knowing the conditional distribution of the missing values, we can maximize expected log-likelihood by taking expectations over the missing price changes conditional on the observed ones. The log-likelihood contribution of q (on day t) is given by:22
`t = − N 2 log 2π − 1 2log det Σ − 1 2(q − µ) 0 Σ−1(q − µ). (B.1) One can easily check that (q − µ)0Σ−1(q − µ) can be rewritten as:
(q1− µ1)0S11(q1− µ1) + (q1− µ1)0S12(q2− µ2)
+(q2− µ2)0S21(q1− µ1) + (q2− µ2)0S22(q2− µ2)
Note that the conditional expectation of q2− µ2 is Σ21Σ−111(q1− µ1). Using this result, the
conditional expectation of (q − µ)0Σ−1(q − µ) can be written as:23
(q1− µ1)0(S11+ Σ11−1Σ12S21+ S12Σ21Σ−111)(q1− µ1) + E(q2− µ2)0S22(q2− µ2) (B.2)
To evaluate the last expression, I will use the following lemma:24
Lemma B.1 Let X ∼ Np(0, Σ) and A be a positive definite matrix. Then E[X0AX] =
tr AΣ.
Proof. Since A is positive definite, there exists a matrix Q such that A = Q0Q. Define a new variable Y = QX which is normally distributed with variance covariance matrix
22See Sydsæter et al. (2005, 34.15) for the multivariate normal distribution function. 23Since Σ is symmetric, Σ0
12= Σ21.
QΣQ0. Then we have:
E[X0AX] = E[Y0Y ] = E[Y12+ Y 2 2 + · · · + Y 2 p] = tr QΣQ 0 = tr AΣ. Applying this lemma to E(q2 − µ2)0S22(q2− µ2) yields tr S22(Σ22− Σ21Σ−111Σ12).25 We
know that S22 is the inverse of Σ22− Σ21Σ−111Σ12 (Sydsæter et al., 2005, 19.48). Hence
E(q2− µ2)0S22(q2− µ2) = N − K. Using this result and (B.2), (B.1) becomes:
E `t = − N 2 log 2π − 1 2log det Σ −(q1− µ1)0(S11+ Σ−111Σ12S21+ S12Σ21Σ−111)(q1− µ1) − N − K 2 (B.3)
Finally, one can easily see that summing (B.3) over time yields (4), i.e.
T
P
t=1E `
t= E L.
25Note that S
