Online Appendix Pricing Dynamics, Leadership, and Misreporting: Evidence from a Mandatory Price-Disclosure Intervention Jorge Lemus and Fernando Luco Contents A Additional Descriptive Evidence of the Website and the Industry
iii
A.1 Features of the Website . . . . . . . . . . . . . . . . . . . . . . . . . .
iii
A.2 The Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
B Theoretical Distribution of a Random First Mover B.1 Derivation of the Probability Distribution . . . . . . . . . . . . . . .
C Leadership by Definition and Product
D Additional Results
viii ix
x
xi
D.1 Maximum Margin by Leadership Definition . . . . . . . . . . . . . . .
xi
D.2 Margin Dispersion by Leadership Definition . . . . . . . . . . . . . .
xi
D.3 Speed of Price Adjustments . . . . . . . . . . . . . . . . . . . . . . .
xiii
D.4 Impact of Leaders on Asymmetric Wholesale Price Changes . . . . .
E Alternative Market Definitions
xiv
xviii
E.1 Market Definitions in the Literature . . . . . . . . . . . . . . . . . . . xviii E.2 Leadership Over Time . . . . . . . . . . . . . . . . . . . . . . . . . . xxii E.3 Impact of Leadership on Margins . . . . . . . . . . . . . . . . . . . . xxii
ii
A
Additional Descriptive Evidence of the Website and the Industry
A.1
Features of the Website
iii
Figure A.1: Different features of the website
(a) List
(b) Map
(c) Characteristics
iv
A.2
The Industry
Table A.1: Summary Statistics: Price Changes and Station Characteristics Gasoline 93 octanes
95 octanes
97 octanes
Mean
Std. Dev.
Mean
Std. Dev.
Mean
Std. Dev.
# of price changes per week
1.14
0.40
1.12
0.37
1.15
0.41
Margin ($CLP per liter)
74.88
19.04
72.36
17.32
75.03
19.15
Has convenience store (%)
36
48
35
48
39
49
Has pharmacy (%)
2
15
2
15
3
16
Has repair service (%)
26
44
26
44
28
45
Has self-service pumps (%)
9
29
9
29
10
31
Open 24 hours (%)
61
49
60
49
64
48
Figure A.2: Number of gas stations per Region
Fraction of all stations
.3
.2
.1
0 0
5
10 15 Administrative region The figure considers all stations that sell gasoline of 93 octanes. Figures are similar for other fuel products
v
Table A.2: Number of gas stations by region controlling for population size. Region
(#) of Stations
Region
per 100,000 ppl.
Antofagasta
6.26
Araucan´ıa
12.33
Arica y Parinacota
8.78
Atacama
10.56
Ays´en
18.46
B´ıo B´ıo
9.79
Coquimbo
8.30
Gral. Bernardo O’Higgins
11.97
Los Lagos
10.34
Los R´ıos
10.88
Magallanes
12.75
Maule
12.18
Metropolitana
6.78
Tarapac´a
7.42
Valpara´ıso
9.59
vi
Figure A.3: Number of gas stations by brand .4
Fraction of all stations
.3
.2
.1
0
Copec
Petrobras
Shell Terpel Other Brand The figure considers all stations that sell gasoline of 93 octanes. Figures are similar for other fuel products
Figure A.4: Wholesale Price Changes over Time 40
Pesos per liter
20
0
−20
Gasoline 93 Gasoline 97
−40 01jan2012
01jul2012
01jan2013
01jul2013 Week
01jan2014
01jul2014
The figure reports week-to-week changes in wholesale prices for gasoline of 93 and 97 octanes, as reported by ENAP.
vii
B
Theoretical Distribution of a Random First Mover
In this section, we derive the distribution of duration of a first mover, when the first mover is chosen at random. To illustrate the ideas we start with an example Example Suppose there are n firms in a market and we observe them for three weeks. We represent a possible outcome for the duration of first movers by the vector (x1 , x2 , x3 ) 3 P where xi ∈ {0, ..., 3} and xi = 3. These outcomes and their interpretation are i=1
described below.
• (0, 0, 3): The same firm that was the first mover every week. • (0, 2, 1): One firm was the first mover consecutively for the first two weeks and a different firm was the first mover in the third week. • (1, 0, 2): One firm was the first mover consecutively for the last two weeks and a different firm was the first mover in the first week. • (1, 1, 1): One firm was the first mover in the first week, a different firm in the second week, and a firm different to the first mover in the second week was the first mover in the third week. These are all the possible combinations of first mover outcomes that we can observe in three weeks. In a market with n firms, the probability distribution of the outcomes described above is:
(0, 0, 3), (0, 2, 1), (1, 0, 2), (1, 1, 1),
with probability
1 n2
with probability
n−1 n2
with probability
n−1 n2
with probability
(n−1)2 n2
viii
In general, if we consider w instead of three weeks, the number of first mover outcomes is 2w−1. In the next section, we deive the distribution of outcomes in a market with n firms that is observed for w weeks.
B.1
Derivation of the Probability Distribution
Let Xw = (x1 , ...xw−1 , xw ), where xi ∈ {0, ..., w} and
w P
xi = w, be an outcome of
i=1
first movers when we observe a market for w weeks. Denote by Υw the set of possible outcomes for a given window of observation w. Let C(Xw , n) be the number of ways to obtain Xw ∈ Υw when there are n firms in the market. Notice that when w = 1 we have Υ1 = {(1)} and C(X1 , 1) = n. If we add an extra week of observation, Υ2 = {(1, 1), (0, 2)}. The only way to go from (1) to (1, 1) is when the first mover in the second week is different to the first mover in the first week. Therefore, (1, 1) can only be obtain of C(X1 , 1) · (n − 1) ways. The only way to go from (1) to (0, 2) is when the first mover in the second week is the same first mover in the first week. Therefore, (0, 2) can only be obtain of C(X1 , 1) · 1 ways. We derive C(Xw , n) recursively noticing that if we add an extra week, for each outcome Xw ∈ Υw there are two possible outcomes in Υw+1 given by a b Xw+1 = (x1 , ...xw−1 , xw , 1) and Xw+1 = (x1 , ...xw−1 , 0, xw + 1).
a The number of ways to obtain Xw+1 is C(Xw , n) · (n − 1) and the number of ways to a obtain Xw+1 is C(Xw , n) · 1. Finally, the distribution of first mover outcome is:
Xw with probability
ix
C(Xw , n) . nw
C
Leadership by Definition and Product Figure C.1: Leadership by definition and product over time .8 .8
.7
Markets and leadership
Markets and leadership
.7
.6
.5
Leadership based on Brand
.4
.6
.5
Leadership based on Brand
.4
Station January12
July12
February13
August13
March14
Station
October14
January12
July12
(a) Gasoline 93
August13
March14
October14
(b) Gasoline 95 .8
.8
.7
Markets and leadership
.7
Markets and leadership
February13
.6
.5
.6
.5
.4
.4 Leadership based on Brand Station
.3 January12
July12
February13
August13
March14
Leadership based on Brand Station
.3
October14
January12
(c) Gasoline 97
July12
February13
August13
March14
October14
(d) Diesel
Local polynomial smoothings with a 95% confidence interval. The vertical red lines mark the day when the system was implemented and enforced in the whole country.
x
D
Additional Results
D.1
Maximum Margin by Leadership Definition
Figure D.1: Cumulative effect of leadership on the maximum margin at the market level 2
1.5
Percentage change
Percentage change
1
.5
0
1.5
1
.5
−.5
0
−1 1
2
3
4
5
6
7
8
9
10
Weeks with same leader Regressions exclude monopoly markets
1
2
3
4
5
6
7
8
9
10
Weeks with same leader Regressions exclude monopoly markets
(a) Leadership at Station level
(b) Leadership at Brand level
Note: In Figure D.1a, price leaders are based on station identifiers. In Figure D.1b, price leaders are based on brand identifiers. The plots correspond to the sum of the estimated coefficients (confidence intervals adjusted accordingly).
D.2
Margin Dispersion by Leadership Definition
xi
Figure D.2: Cumulative effect of leadership on maximum margins by markets Range 4
4
Percentage change
Percentage change
2
0
−2
2
0
−4
−6
−2 1
2
3
4
5
6
7
8
9
10
1
Weeks with same leader Regressions exclude monopoly markets
2
3
4
5
6
7
8
9
10
Weeks with same leader Regressions exclude monopoly markets
(a) Leadership at Station level
(b) Leadership at Brand level
Interquartile Range 2
Percentage change
Percentage change
5
0
0
−2
−4
−5
−6 1
2
3
4
5
6
7
8
9
10
1
Weeks with same leader Regressions exclude monopoly markets
2
3
4
5
6
7
8
9
10
Weeks with same leader Regressions exclude monopoly markets
(c) Leadership at Station level
(d) Leadership at Brand level
Standard Deviation 4
3
2
Percentage change
Percentage change
2
0
−2
1
0
−1
−4 −2 1
2
3
4
5
6
7
8
9
10
1
Weeks with same leader Regressions exclude monopoly markets
2
3
4
5
6
7
8
9
10
Weeks with same leader Regressions exclude monopoly markets
(e) Leadership at Station level
(f) Leadership at Brand level
Difference in Two Lowest Margins 5
15
Percentage change
Percentage change
10
5
0
−5
0
−5
−10 −10 1
2
3
4
5
6
7
8
9
10
Weeks with same leader Regressions exclude monopoly markets
(g) Leadership at Station level
1
xii
2
3
4
5
6
7
8
9
10
Weeks with same leader Regressions exclude monopoly markets
(h) Leadership at Brand level
D.3
Speed of Price Adjustments Figure D.3: Leadership by definition and product over time 60
50
40
30 Monopolists First movers 20
Hours after ENAP’s announcement
Hours after ENAP’s announcement
60
Followers Jan12
Jul12
Feb13
Aug13
Mar14
50
40
30
Monopolists First movers
20
Oct14
Followers Jan12
Jul12
Feb13
Date
Mar14
Oct14
Date
Linear fit including station fixed effects.
Linear fit including station fixed effects.
(a) Gasoline 93
(b) Gasoline 95 60
50
40
30
Monopolists First movers
20
Followers Jan12
Jul12
Feb13
Aug13
Mar14
Oct14
Hours after ENAP’s announcement
60
Hours after ENAP’s announcement
Aug13
50
40
30
Monopolists First movers
20
Followers Jan12
Date
Jul12
Feb13
Aug13
Mar14
Oct14
Date
Linear fit including station fixed effects.
Linear fit including station fixed effects.
(c) Gasoline 97
(d) Diesel
Note: The figures report the number of hours elapsed between ENAP’s announcement of a new wholesale price (Wednesday at 7pm) and when stations change their retail prices, as a function of station type (first mover or follower) in oligopolies, and also for monopolies, over time. The figures are binned scatterplots with the associated linear fit that follows from a regression that includes station fixed effects to control for station-specific time-invariant characteristics. In the figure, the vertical red line marks the day when the system was implemented and enforced across the whole country.
xiii
D.4
Impact of Leaders on Asymmetric Wholesale Price Changes
We finish this section by studying whether the impact of leadership is dependent on the direction of wholesale price changes.1 To do this, we estimate Equation 1 in the text, separately for weeks in which wholesale prices increase and decrease, and for leadership based on brand, owner, and station identifier.2 Our results are reported in Table D.1 and Table D.2. Table D.1 shows a positive and significant impact of one-week price leadership on margins, when leaders are defined at the brand level. When leadership is defined at the owner or station level, however, we find significant effects only when when wholesale prices increase, but we find no effect of leadership on margins when wholesale prices decrease. Finally, Table D.2 reports the estimated impact of leadership on the speed of price adjustment. The results show that, though in all cases stations react faster to changes in wholesale prices when leaders are present, they react almost twice as fast when wholesale prices increase than when they decrease. Indeed, our estimate show that while stations react between 80 and 90 minutes earlier in the presence of a leader when wholesale prices increase, they react between 40 and 50 minutes earlier when wholesale prices decrease. Overall, our results suggest that the impact of leadership on margins is asymmetric. Indeed, our findings show that leaders play a major role in periods in which wholesale prices increase, inducing stations to react faster and allowing them to sustain higher margins than in markets with no leaders. At the same time, we find that when wholesale prices decrease, if leaders are defined at the station level, there is no difference 1 2
Deltas (2008) shows that market power may drive asymmetric responses. We are restricted to evaluate the impact of one-week leadership on market outcomes because the
sign of the change in wholesale prices shows little persistency. Hence, conditioning on consecutive weeks with changes in wholesale prices that go in the same direction reduces the available data significantly.
xiv
between the margins of stations that participate in markets with leaders and stations that participate in markets without leaders. We still find, however, that stations in markets with leaders react faster than stations in markets with no leaders, though the difference is smaller when wholesale prices decrease.
xv
Table D.1: Impact of Leadership on Margins by Sign of Change in Wholesale Prices Cost Increased Leadership
Leader
Cost Decreased
Brand
Owner
Station
Brand
Owner
Station
(1)
(2)
(3)
(4)
(5)
(6)
0.589∗∗∗
0.679∗∗∗
0.677∗∗∗
0.535∗∗∗
0.106
0.0679
(0.0988) (0.0783) (0.0790)
(0.104)
(0.0919) (0.0930)
Cost controls
Yes
Yes
Yes
Yes
Yes
Yes
Product FE
Yes
Yes
Yes
Yes
Yes
Yes
Market FE
Yes
Yes
Yes
Yes
Yes
Yes
Week FE
Yes
Yes
Yes
Yes
Yes
Yes
64.54
64.54
64.54
66.47
66.47
66.47
N
260146
260146
260146
113873
113873
113873
R2
0.769
0.769
0.769
0.725
0.725
0.725
Mean Margins
Note: Standard errors, in parentheses, are clustered at the market level. p < 0.10,
∗∗
p < 0.05,
∗∗∗
∗
p < 0.01. In all columns, the dependent variable is the
average margin at the market level. Columns 1 to 3 consider only observations that correspond to increases in wholesale prices, while columns 4 to 6 consider only observations that correspond to decreases in wholesale prices. Each column uses a different definition of leadership. Columns 1 and 4 define leadership at the brand level. Columns 2 and 5 define leadership at the owner or operator level. Columns 3 and 6 define leadership at the station level.
xvi
Table D.2: Impact of Leadership on the Speed of Price Adjustments by Sign of Change in Wholesale Prices Cost Increased Leadership
Cost Decreased
Brand
Owner
Station
Brand
Owner
Station
(1)
(2)
(3)
(4)
(5)
(6)
-89.64∗∗∗
-81.91∗∗∗
-81.60∗∗∗
-40.50∗∗∗
-48.82∗∗∗
-50.31∗∗∗
(8.581)
(7.139)
(7.163)
(9.340)
(8.677)
(8.669)
Cost controls
Yes
Yes
Yes
Yes
Yes
Yes
Product FE
Yes
Yes
Yes
Yes
Yes
Yes
Market FE
Yes
Yes
Yes
Yes
Yes
Yes
Week FE
Yes
Yes
Yes
Yes
Yes
Yes
Mean Speed
1363.3
1363.3
1363.3
1355.9
1355.9
1355.9
N
369229
369229
369229
108746
108746
108746
R2
0.344
0.344
0.344
0.404
0.404
0.404
Leader
Note: Standard errors, in parentheses, are clustered at the market level. p < 0.10,
∗∗
p < 0.05,
∗∗∗
∗
p < 0.01. In all columns, the dependent variable is the
average time elapsed, in minutes, between the change in price by the fist mover and the rest of the stations in the market. Columns 1 to 3 consider only observations that correspond to increases in wholesale prices, while columns 4 to 6 consider only observations that correspond to decreases in wholesale prices. Each column uses a different definition of leadership. Columns 1 and 4 define leadership at the brand level. Columns 2 and 5 define leadership at the owner or operator level. Columns 3 and 6 define leadership at the station level.
xvii
E E.1
Alternative Market Definitions Market Definitions in the Literature
Defining markets in the absence of quantity or volume data requires the researcher to decide which stations compete with each other. Part of the literature on retail gasoline has defined markets using circles of fixed radius around gas stations and has assumed that each gas station competes with those stations that are located within the circle that is centered at that station (e.g., Chandra and Tappata 2011; Lewis 2011). This approach is attractive because of its simplicity and because it recognizes that competition in the retail gasoline industry is mostly local. However, because this approach results in one market per station in the data, it considers stations more than one time as these repeat in different circles centered at stations that are near each other. Furthermore, by using a predefined radius, this approach does not recognize that though stations may be located within a fixed radius from each other in a map, driving distances do not necessarily coincide with the distance predefined by the researcher. Finally, a variation of this approach defines a market as all stations within a prespecified driving distance of the station of reference, rather than using linear distances (i.e., Hastings 2004). An alternative to circles of fixed radius is to use administrative boundaries. For example, depending on the question being studied, a researcher may define a city or a state as the relevant market (e.g., Deltas 2008; Lewis 2011; Clark and Houde 2014). This approach may be attractive in many settings but it is not in ours as it results in very large markets that make difficult to identify a leader. In other words, this approach does not consider the role of local competition in a way that is useful for the purpose of our research. A third alternative is to define markets using grids. In this case, the researcher specxviii
ifies the dimensions of the grid and considers all stations located within a cell to be part of the same market. This approach, that is similar to the one that uses administrative boundaries, has the benefit (relative to circles of fixed radius) of considering each station once. This advantage is shared by the market definition based on administrative boundaries. On the other hand, the main disadvantage of both this approach and the one that uses administrative boundaries is that stations that may be located very close to each other (for example, in different corners of an intersection) may be considered in different markets if the boundary of a cell is defined at the intersection. Finally, an additional disadvantage of all the methods described so far is that they do not recognize that driving distances may differ from distances in a map, and that even stations within a narrowly defined cell may be, in practice, far from each other if a consumer cannot easily go from one to the other (consider, for example, stations on opposite sides of a highway). A fourth alternative, if data on commuting paths are available, is to define markets along the path (i.e., Houde 2012). We do not consider this approach because this type of data does not exist in our setting. Because of the drawbacks of each of the approaches described above, in this paper we follow a different one. As explained in the main text, we use cliques to define markets and use driving time, considering the actual direction of streets, to define markets. That is, we specify a driving time (five minutes), and consider all stations that are within five minutes of each other to be a market. This approach has a number of advantages over the approaches described above. First, because we consider driving time, stations that may be close to each other on a map but that are separated in practice because of the direction of streets, may be in different markets. Second, similar to what happens with circles of fixed radius, this approach does not define boundaries as grids do. Hence, stations that would be in different cells or administrative units will be in the same market if the driving time required to go from one to the
xix
other is less than the pre-specified one. Finally, this approach results in (weakly) less “double” counting of stations relative to what circles of fixed radius does. However, some stations are still considered more than once so this is a disadvantage relative to grids, but a smaller one than in the case of circles. Because there is not a unique way to define markets in the absence of quantity or volume data, we focus most of our analysis on cliques defined with a five-minute driving distance. In addition, in this Appendix we replicate part of the analysis presented in the main text using three alternative market definitions. First, we recompute the cliques using a ten-minute driving time instead of a five-minute one. Second, we define markets using a 2km-by-2km grid partition. Finally, we use administrative boundaries defined at the municipality level. Below we present two sets of results for each alternative definition. First, we show that regardless of how markets are defined, leadership increased over our sample period. Second, we report our estimates of the impact of leadership on the average and minimum margin for each market definition. We show that our results are qualitatively similar to those we present in the main text. However, as the area covered in each market increases significantly, the standard errors increase as well and the impact of a single station on mean margins is less significant than before. Nonetheless, the results show that there is a clear change in the level of margins in the presence of leaders. Interestingly, all market definitions show that the minimum margin increases significantly in the presence of leaders. Finally, we find that as the area covered by each market increases, brand leadership has a bigger effect on margins than station leadership.
xx
Figure E.1: Leadership over time for alternative market definitions (gasoline of 93 octanes) 1
Markets and leadership
.8
.6
.4
.2 Leadership based on Brand Station
0 July12
February13
August13
March14
October14
(a) Cliques: d = 10 minutes
Markets and leadership
.8
.7
.6
Leadership based on Brand
.5
Station July12
February13
August13
March14
October14
(b) 2km-by-2km Grid .8
Markets and leadership
.7
.6
.5
Leadership based on Brand Station
.4 July12
February13
August13
March14
October14
(c) Municipality boundaries
Local polynomial smoothing with a 95% confidence interval. We focus on gasoline of 93 octanes because for all other fuel products the figures look qualitatively identical. Each figure considers a different approach to define markets. Figure E.1a defines markets using cliques with a ten-minute driving time. Figure E.1b uses a 2km-by-2km grid. Figure E.1c defines markets using municipality boundaries. The figures show that regardless of xxi how markets are defined, leadership increased over time.
E.2
Leadership Over Time
E.3
Impact of Leadership on Margins
Figure E.2: Cumulative effect of leadership on margins at the market level, for different definitions of leadership Leadership at the brand level 1.5
2
1
0
Percentage change
1.5
Percentage change
Percentage change
3
1
.5
0
1
.5
0
−.5 −1
−.5 1
2
3
4
5
6
7
8
9
10
1
Weeks with same leader Regressions exclude monopoly markets
2
3
4
5
6
7
8
9
10
1
Weeks with same leader Regressions exclude monopoly markets
(a) Cliques: d = 10 minutes
2
3
4
5
6
7
8
9
10
Weeks with same leader Regressions exclude monopoly markets
(b) 2km-by-2km Grid
(c) Municipality boundaries
Leadership at the station level 1.5
2
1.5
1
0
−1
1
Percentage change
Percentage change
Percentage change
1
.5
0
.5
0
−.5
−2
−.5
−3 1
2
3
4
5
6
7
8
9
Weeks with same leader Regressions exclude monopoly markets
(d) Cliques: d = 10 minutes
10
−1 1
2
3
4
5
6
7
8
Weeks with same leader Regressions exclude monopoly markets
(e) 2km-by-2km Grid
9
10
1
2
3
4
5
6
7
8
9
10
Weeks with same leader Regressions exclude monopoly markets
(f) Municipality boundaries
Note: In the first panel, leaders are based on brands. In the second panel, leaders are based on station identifiers. The plots correspond to the sum of the estimated coefficients (confidence intervals adjusted accordingly). The figure shows that, though the standard errors increase significantly when using grids (as these cover a larger geographical area), the level of margins (point estimates) increases the longer a leader is in place. In addition, the figure shows that when a market covers a larger geographical area, brand leadership is more important than station leadership.
Minimum Margins
xxii
Figure E.3: Cumulative effect of leadership on the minimum margin at the market level Leadership at the brand level 3
3
0
−1
Percentage change
Percentage change
Percentage change
1
2
1
−2
2
1
0
0 −3
−1 1
2
3
4
5
6
7
8
9
10
1
Weeks with same leader Regressions exclude monopoly markets
2
3
4
5
6
7
8
9
10
1
Weeks with same leader Regressions exclude monopoly markets
(a) Cliques: d = 10 minutes
2
3
4
5
6
7
8
9
10
Weeks with same leader Regressions exclude monopoly markets
(b) 2km-by-2km Grid
(c) Municipality boundaries
Leadership at the station level 3
Percentage change
Percentage change
4
2
0
2
1.5
2
Percentage change
6
1
0
1
.5
0 −2 −1 1
2
3
4
5
6
7
8
9
Weeks with same leader Regressions exclude monopoly markets
(d) Cliques: d = 10 minutes
10
−.5 1
2
3
4
5
6
7
8
Weeks with same leader Regressions exclude monopoly markets
(e) 2km-by-2km Grid
9
10
1
2
3
4
5
6
7
8
9
10
Weeks with same leader Regressions exclude monopoly markets
(f) Municipality boundaries
Note: In the first panel, leaders are based on brands. In the second panel, leaders are based on station identifiers. The plots correspond to the sum of the estimated coefficients (confidence intervals adjusted accordingly). The figure shows that, with the exception of one case, the minimum margin increases the longer a leader is in place.
References Chandra, Ambarish, and Mariano Tappata. 2011. “Consumer search and dynamic price dispersion: an application to gasoline markets.” The RAND Journal of Economics, 42(4): pp. 681–704. Clark, Robert, and Jean-Fran¸cois Houde. 2014. “The Effect of Explicit Communication on pricing: Evidence from the Collapse of a Gasoline Cartel.” The Journal xxiii
of Industrial Economics, 62(2): 191–228. Deltas, George. 2008. “Retail gasoline price dynamics and local market power.” The Journal of Industrial Economics, 56(3): 613–628. Hastings, Justine S. 2004. “Vertical relationships and competition in retail gasoline markets: Empirical evidence from contract changes in Southern California.” The American Economic Review, 94(1): 317–328. Houde, Jean-Fran¸cois. 2012. “Spatial Differentiation and Vertical Mergers in Retail Markets for Gasoline.” American Economic Review, 102(5): 2147–82. Lewis, Matthew S. 2011. “Asymmetric price adjustment and consumer search: An examination of the retail gasoline market.” Journal of Economics & Management Strategy, 20(2): 409–449.
xxiv
