WORKING 

PAPERS 

Simulating a Homogeneous Product Merger:

A Case Study on Model Fit and Performance

Daniel Greenfield 

Nicholas Kreisle 

Mark Williams 

WORKING PAPER NO. 327 

October 2015 

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and critical comment. The analyses and conclusions set forth are those of the authors and do not 

necessarily reflect the views of other members of the Bureau of Economics, other Commission staff, or 

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author to protect the tentative character of these papers. 

BUREAU OF ECONOMICS 

FEDERAL TRADE COMMISSION 

WASHINGTON, DC 20580
1

Simulating a Homogeneous Product Merger: 

A Case Study on Model Fit and Performance

Daniel Greenfield

Nicholas Kreisle

Mark Williams1

October 28, 2015

Abstract

This paper studies Tesoro’s 2013 acquisition of British Petroleum’s Los Angeles refinery. We 

present a merger simulation model tailored to the gasoline market, which includes Cournot firms 

and a price-taking fringe. This hybrid model generates margins that are more plausible than 

those generated by the standard Cournot model. We also test the predictive accuracy of the 

models relative to empirical estimates of the acquisition’s price effect. We estimate the effect of 

the acquisition using both difference-in-differences estimation and the synthetic control 

method. Both methods suggest the acquisition had little if any effect on Los Angeles gasoline 

prices. We can reject the price effect predicted by the standard Cournot model, but not that of 

the hybrid model.

 1 The views expressed in this article are those of the authors and do not necessarily reflect those of the Federal Trade 

Commission.
2

1. Introduction

This paper studies Tesoro’s 2013 acquisition of British Petroleum’s (BP’s) Los Angeles

refinery, a transaction the United States Federal Trade Commission investigated for nine months

before concluding the acquisition was not likely to lessen competition substantially.

2

 The paper 

has two primary goals. First, we simulate the price effect of the acquisition using a variant of the 

Cournot model, which includes a competitive fringe of price-taking firms.

3 This hybrid model

generates margins that are more plausible than those generated by the standard Cournot model. 

Second, we empirically estimate the price effect of the acquisition. We can reject the price effect 

predicted by a standard Cournot model but not that of the hybrid model.

The Cournot model is a standard framework for analyzing issues of market power in 

homogeneous goods industries.4

 However, margins in the California gasoline market are likely 

smaller than market shares and demand elasticity estimates imply in Cournot equilibrium. 

Specifically, the Cournot model implies marginal costs below the cost of crude oil. We do not 

observe refinery marginal costs, yet the cost of crude oil is a plausible lower bound, given that it

is the primary input for gasoline production. That the standard Cournot model implies marginal 

cost below the cost of crude oil suggests the model does not fit the California gasoline market.

Introducing a competitive fringe of price-taking firms breaks the strict relationship 

between overall market shares and margins found in the standard Cournot model. We calibrate 

the hybrid model restricting equilibrium marginal costs to the range of plausible values, between 

 2 See FTC press release, FTC Closes Investigation into Tesoro's Acquisition of BP Refinery, May 17, 2013. 

Available at https://www.ftc.gov/news-events/press-releases/2013/05/ftc-closes-investigation-tesoros-acquisitionbp-refinery. 3 Borenstein and Bushnell (1999) use a similar model to study market power in a wholesale electricity market. Also 

see Borenstein, Bushnell, and Knittel (1999) and Borenstein, Bushnell, and Stoft (2000). 4 Surveys on economic theories relevant to antitrust emphasize the importance of Cournot models for homogeneous 

goods industries. See, for example, Werden and Froeb (2008) and Kaplow and Shapiro (2007). 
3

the cost of crude oil and the price of gasoline. After calibrating both versions of the model, we 

simulate the effect of the acquisition. The hybrid model predicts a price increase between zero 

and one percent, depending on assumed pre-merger margins, while the standard Cournot model 

predicts a price increase of six percent.

We use two methodologies to empirically estimate the causal effect of the transaction and 

test the models’ predictions. First, we estimate a difference-in-differences regression model

using data from Los Angeles and 18 control cities. Second, we apply the synthetic control 

methodology introduced by Abadie and Gardeazabal (2003) and Abadie, Diamond and 

Hainmueller (2010). Using two methodologies allows us to test the robustness of our 

conclusions to alternative identifying assumptions and alternative forms of statistical inference.

The difference-in-difference regressions apply equal weight to each city. They assume

Los Angeles would have experienced the same conditional mean price change as the 18 control 

cities but for the acquisition. Alternatively, the synthetic control method constructs a weighted 

average control city that best approximates pre-acquisition prices and predictors of price in Los 

Angeles. The synthetic control city’s prices then serve as the post-acquisition counterfactual 

prices for Los Angeles.

Following Abadie, Diamond and Hainmueller (2010), we perform a placebo exercise to 

evaluate the significance of our synthetic control estimates. We test for a placebo effect in each 

of the control cities, iteratively re-implementing the synthetic control method for each control 

city. This generates an empirical distribution of effects. If the effect estimated for Los Angeles

is an outlier among the placebo effects, we can be confident that there is evidence of an 

acquisition effect. The empirical distribution also reveals the probability of finding an effect 

comparable to that found in Los Angeles if we were to randomly select the treatment 
4

(acquisition) city from our data. This form of exact inference contrasts with traditional 

hypothesis testing, where standard errors reflect sampling uncertainty, under the assumption that 

the data are a sample from a larger population.

Neither empirical method provides robust evidence of a price change after the 

acquisition. All of our difference-in-differences estimates are statistically indistinguishable from 

zero. We can reject the 6% price increase predicted by the Cournot model, but not the 1% price 

increase predicted by the hybrid model. With the synthetic control method, the placebo exercise 

indicates that there is a better than 50% chance of finding as large an effect as that found in Los 

Angeles if we were to randomly select the treatment city from our sample. 

Our results contribute to the merger retrospective literature, a growing body of studies 

that estimate the price effects of mergers. Recent examples on mergers in the petroleum industry 

include Hosken, Silvia and Taylor (2011), Silvia and Taylor (2013), and Kreisle (2015).5

 

Hosken, Olson, and Smith (2012) study horizontal mergers in the U.S. grocery industry and 

appear to be the first authors to use synthetic control methods for a merger retrospective.6

Our study also contributes to the industrial organization literature by evaluating a 

simulation model tailored to a specific market. Carlton (2010) and Werden (2015) note the 

importance of evaluating specific analytic tools used during the merger review process. Other

papers that evaluate the accuracy of merger simulation models relative to empirical estimates of

merger price effects include Peters (2006), Weinberg (2011), and Weinberg and Hosken (2013).

7

 5 Earlier examples include Taylor and Hosken (2007) and Simpson and Taylor (2008).

6 Also, see Hosken, Olson, and Smith (2015), who use the synthetic control method to estimate price changes 

following entry and exit by grocery retailers. See Kwoka (2014) for a recent survey of the merger retrospective 

literature.

7 Budzinski and Ruhmer (2010) survey the broader merger simulation literature.
5

The next section of the paper outlines the standard Cournot model and introduces our 

hybrid variant. Section 3 describes the California gasoline market and refinery production 

technology. Section 4 applies both models to industry data and demonstrates the superior ex ante 

fit of the hybrid model. Section 5 simulates the Tesoro/BP transaction under our baseline 

assumptions and section 6 explores how the simulations change with alternative 

parameterizations. Section 7 presents the empirical analysis, which we use to assess the ex post

accuracy of the simulation models. Finally, Section 8 concludes.

2. The Models

Consider a homogeneous goods market with inverse demand PP(QQ) and NN Cournot firms

simultaneously choosing output. We can write firm ii’s first order condition, PP(QQ) + qqiiPP′(QQ) −

CCii′(qqii) = 0, in Lerner index form:

PP − CCii′

PP = ssiiεε

, (1)

where QQ = ∑ii qqii is total output, CCii

′ is the marginal cost of firm ii at equilibrium, ssii is firm ii’s 

share and εε is the absolute value of the elasticity of market demand. In equilibrium, margins are 

proportional to market shares and inversely proportional to εε. 

Less elastic market demand implies larger margins and larger differences in marginal 

costs between firms with different market shares. Firms with larger market shares operate at

lower equilibrium values of marginal costs because marginal revenue is decreasing in qqii. This 

equilibrium relationship is true regardless of the functional form of demand or costs. 

Now consider the same homogeneous goods market, yet with two sets of firms: FF pricetaking firms and SS strategic firms (FF + SS = NN). Price-taking firms choose output where price 
6

equals marginal cost. We assume strategic firms choose output in a Cournot fashion under the 

belief that price-takers expand production until their marginal costs equal the market price. 

The mechanics of the hybrid model are analogous to those of a dominant firm model. 

The residual demand facing the strategic firms is the difference between market demand and the 

supply from price-takers, QQrr(PP) = QQ(PP) − ∑ii∈FF qqii (PP). The following identity defines the price 

elasticity of residual demand:

εεSSssSS = εε + ssFFηηFF (2)

where ε is the absolute value of the market demand elasticity, εεSS is the absolute value of the 

residual demand elasticity facing the combined strategic firms, ssSS is the combined market share 

of the strategic firms, ssFF is the combined share of price-taking firms and ηηFF is the elasticity of 

price-taking firms’ supply.8

Just as in the standard Cournot model, each strategic firm’s first order condition implies 

an equilibrium relationship between market shares and margins: 

PP − CCii′

PP = ssii

SS

εεSS

(3)

where ssii

SS is the share of firm ii within the group of all strategic firms. This implies that each 

strategic firm’s price cost margin remains proportional to its share among the strategic firms. 

Because marginal cost curves are upward sloping, price takers can earn positive variable or total 

profits, but zero incremental profits. 

 8 This identity holds when the price-taking firms have increasing marginal cost curves. Constant marginal costs

would imply perfectly elastic supply and residual demand.
7

Assignment of firms to the strategic or price-taking groups is a challenge that dates at 

least as far back as Stigler’s (1947) investigation of oligopoly pricing.

9 However, this 

assignment is in principle no more challenging than deciding when the textbook dominant firm 

model may apply. We initially calibrate the hybrid model assuming all firms with a market share 

greater than 10% are strategic and explore how the simulation results change as we alter the 

strategic group.10

3. The California Gasoline Market

Gasoline sold in California must meet emissions standards set by the California Air 

Resources Board (CARB). Thus, refiners intending to produce gasoline for the California 

market produce California Reformulated Blendstock for Oxygenate Blending (CARBOB). The 

additional processing required to meet California specifications tends to make CARBOB more 

costly to produce than blendstocks used in other parts of the country. Distribution terminals 

typically combine nine parts CARBOB and one part ethanol to make finished California 

gasoline.

11

CARBOB is a Homogeneous product with a distinct wholesale market given that the 

specification is unique to California. According to the California Energy Commission (CEC), in 

2012 nine firms produced CARBOB in fourteen California refineries and sales of finished 

CARB gasoline totaled 14 billion gallons.12 We calculate market shares based on crude oil 

 9 While Stigler admits his criteria for inclusion in the oligopolistic group are “an unsatisfactory substitute” he notes 

that they “focus attention on the relevant variables,” namely, the combined share of the oligopolistic (here, 

“strategic”) group and the share of the largest excluded firm relative to the market leader.

10 Tesoro and BP are the second and third largest firms, and are always strategic firms in our analysis. A merger 

between two price-taking firms (not becoming strategic as a result of a merger) would have no impact on the market 

price.

11 The market for ethanol is unconcentrated as discussed in Federal Trade Commission (2014), which summarizes 

ethanol capacity and concentration since 1998. 12 See http://energyalmanac.ca.gov/petroleum/refineries.html
8

distillation capacities, which, according to the CEC, are roughly proportional to gasoline 

production shares. Table 1 lists the refineries and these crude distillation capacities.

TABLE 1—Crude Distillation Capacity of CARBOB-producing California Refineries, 2012

To calibrate the models to the pre-acquisition data, we use a market price of $127 per 

barrel, the average Los Angeles spot price of CARBOB in 2012.13 We assume a crude oil cost 

 13 Source: http://www.eia.gov/dnav/pet/pet_pri_spt_s1_d.htm.

Refinery Barrels per Day Market Share

Chevron, U.S.A., Inc. 27.3%

Richmond Refinery 276,000

El Segundo Refinery 245,271

Tesoro Refining & Marketing Company 14.2%

Golden Eagle Martinez/Avon Refinery 166,000

Wilmington Refinery 103,800

BP West Coast Producs LLC 12.6%

Carson Refinery 240,000

ConocoPhillips 11.4%

Wilmington Refinery 139,000

Rodeo San Francisco Refinery 78,400

Valero 11.0%

Benicia Refinery 132,000

Wilmington Refinery 78,000

Shell Oil Products US 8.2%

Martinez Refinery 156,400

ExxonMobil Refining & Supply Company 7.8%

Torrance Refinery 149,500

ALON USA 6.1%

Bakersfield Refinery 66,000

Paramount Refinery 50,000

Kern Oil & Refining Company 1.4%

Bakersfield Refinery 26,000

Source: CEC
9

of $105 per barrel, the average West Coast crude acquisition cost in 2012.14 Lastly, consistent 

with prior literature we assume a demand elasticity of -0.3.15

Refineries produce multiple products, including gasoline of different grades, diesel fuel, 

jet fuel, heating oil, and other heavier products.16 We focus on gasoline because it is generally 

the highest-valued product, and because it represents the plurality if not majority of production at 

California refineries.17

A typical refinery has thousands of production constraints, including the capacity of 

individual processing units, available tankage, and blending requirements of inputs and outputs. 

For a given stock of capital, the marginal cost of producing gasoline tends to increase as output 

expands and additional production constraints bind. Moreover, for a given amount of crude oil 

and other feedstocks running through the refinery, marginal cost increases as the refinery can 

only increase gasoline production at the expense of reducing the production of other products.

Oil refiners use linear programming (LP) models to choose a profit-maximizing vector of 

inputs and outputs, subject to the model’s constraints and expected market prices (e.g. the prices

of crude oils, intermediates, and finished products).

18 That refinery models maximize profits 

subject to fixed market prices suggests price-taking behavior, at least if refineries strictly follow 

the production plans generated by these LP models (using unbiased estimates of future expected 

pricing). What is more, investigations of refinery pricing have found evidence that refineries 

 14 Source: http://www.eia.gov/dnav/pet/pet_pri_rac2_dcu_nus_m.htm. 15 We believe -0.3 is a reasonable estimate of the price elasticity of demand over a yearly period, based on research 

including Lin and Prince (2013), Levin, Lewis, and Wolak (2015) and Coglianese, Davis, Kilian, and Stock (2015).

16 As this paper uses crude distillation capacity as its measure of market share of gasoline production, if we were 

instead to model the acquisition’s effect on diesel prices (also using distillation capacity as the relevant measure of 

diesel production), we would get the same theoretical results, subject to a different choice for the demand elasticity 

for diesel fuel.

17 See http://energyalmanac.ca.gov/petroleum/refineries.html. 18 See Federal Trade Commission (2006), Leffler (2008), and Gary, Handwerk and Kaiser (2010).
10

generally take prices as given. For example, a recent FTC investigation of gasoline pricing found 

that refiners typically “assume their short-run operational decisions do not affect market prices.”19

By contrast, Borenstein, Bushnell and Lewis (2004) argue that despite evidence consistent 

with price-taking behavior, it would be surprising if producers did not consider the effect of their 

own production levels on California gasoline market prices. Our hybrid model allows for both pricetaking and strategic behavior to exist simultaneously. This additional degree of freedom allows the 

hybrid model to better match plausible industry margins, given market shares and demand elasticity

estimates.

4. Fitting the Models to the California Gasoline Market

In the standard Cournot model, a firm’s margin is a function of its market share and the 

price elasticity of demand. Hence, we can calculate equilibrium marginal costs with information 

on market shares, price, and the price elasticity of demand. Again, we use crude distillation 

capacity shares as a proxy for gasoline output shares. Table 2 shows the quantity, implied 

margins, and implied marginal costs for each firm in California assuming Cournot equilibrium. 

The standard Cournot assumption implies equilibrium marginal costs that are lower than the cost 

of crude oil for all firms except Kern Oil.

 19 See Federal Trade Commission. (2006). The report does note that “although refiners state that they generally 

adhere to the LP model, some refiners occasionally deviate from the model if their internal analyses and judgment 

indicate that such a deviation is necessary to maximize refinery profitability.” A refinery planner may run the LP 

model with the quantity of gasoline constrained based on feedback from marketing and trading personnel on the 

price sensitivity of demand. If a refinery planner introduces such a “demand” or “marketing” constraint into the 

model, the LP model output will show a positive incremental margin on the constrained product. Positive 

incremental margins can also arise due to capacity constraints on refining units, pipelines, and storage facilities.
11

TABLE 2—Implied Margins in the Standard Cournot Model

Surely, models must abstract from some industry details, but such a glaring inconsistency 

with basic industry facts suggests that the Cournot model is not appropriate for the California 

gasoline market.20 It is important to emphasize the poor fit of the Cournot model does not 

depend on the functional form of demand or costs. The same relationship between equilibrium 

marginal costs and market shares exists whether marginal costs are constant or increase rapidly 

beyond some level of output. 

Fitting the standard Cournot model to pre-merger data required solving for the unknown 

values of equilibrium marginal costs. The hybrid model, however, has an additional unknown,

the elasticity of residual demand (defined by the elasticity of supply from the price-taking firms). 

The extra unknown necessitates additional information or assumptions. 

 20 Werden, Froeb, and Scheffman (2003) and Werden and Froeb (2008) discuss the importance of model fit in policy 

settings. In two non-merger antitrust cases where economic experts used a Cournot model, judges excluded expert 

testimony due to poor model fit with industry facts. In Heary Brothers, for example, the judge noted that profit 

margins were similar for firms with vastly different market shares, a fact inconsistent with Cournot equilibrium. 

See, Concord Boat Corp. v. Brunswick Corp., 207 F.3d 1039 (8th Cir. 2000) and Heary Bros. Lightning Prot. Co. v. 

LIGHTNING PROT. INSTITUTE, 287 F. Supp. 2d 1038 (D. Ariz. 2003). Also, see Coate and Fischer (2000).
12

For this case study, we take advantage of the fact that the price of crude oil is a 

reasonable lower bound for the marginal cost of producing gasoline. In our baseline calibration, 

we assume that the largest strategic firm (Chevron) has equilibrium marginal costs equal to the 

cost of crude oil, the lower bound of the plausible range for marginal costs. In section 6, we 

relax this assumption and show how the predicted merger effect varies with assumed marginal 

costs, a relationship illustrated in Figure 1. 

Table 3 shows the baseline calibration of the hybrid model, assuming all firms with a 

market share below 10% are price-takers and the largest firm’s marginal cost is equal to the cost 

of crude oil. Here, the strategic firms are BP, Chevron, ConocoPhillips, Tesoro, and Valero.21 

By design, every firm’s marginal cost falls between the cost of crude oil and the market price of 

gasoline. The implied residual demand elasticity is 2.0 and the implied supply elasticity from the 

price-taking firms is 5.2.22

TABLE 3—Implied Margins in the Hybrid Model

 21 Table 6 examines the effect of changing the composition of the strategic group. 22 Firms can change production levels of all products, substitute CARBOB production for other grades of gasoline, 

substitute gasoline production for other types of refined products (e.g. changing the gas/diesel split), or import 

CARBOB from non-California sources. 

Quantity* C' (P - C' )/P

Chevron 27.34 104.69 0.18

Tesoro 14.15 115.66 0.09

BP 12.59 116.96 0.08

ConocoPhillips 11.40 117.94 0.07

Valero 11.02 118.27 0.07

Shell 8.20 127.43 0.00

Exxon 7.84 127.43 0.00

ALON 6.08 127.43 0.00

Kern Oil & Refining 1.36 127.43 0.00

Total 100.00

*Total market output normalized to 100. We use crude distillation capacity shares as a 

proxy for gasoline output shares.
13

5. Simulating Tesoro’s Acquisition of BP Carson

Tesoro acquired BP’s Southern California refining, marketing and logistics business on 

June 1, 2013. The assets included BP’s Carson refinery, marine terminals, land terminals, and 

pipelines, all of which were adjacent to Tesoro’s Wilmington refinery. Tesoro announced plans

to gradually integrate the two refineries over a number of years and undertake significant

investments in pipeline interconnections and refinery capacity improvements in 2015.

23 Our 

simulations examine the potential for a price increase due to the Tesoro/BP combination but do 

not consider possible efficiencies related to refinery integration. 

To simulate the effects of the acquisition, we assume both market demand and firm 

marginal costs are linear. Inverse demand is PP = aa − bb , where total market output is QQ =

∑ qqii

NN

ii=1 . We consider a cost function that has been widely used for merger analysis.24 Firm ii’s 

total cost function is qqii

2/2kkii, with marginal costs, MM ii = qqii⁄kkii.

25 The reciprocal of the slope 

term, kkii, can be viewed as representative of each firm’s capital stock. A merger between firms 1 

and 2 creates a new firm with kk12 = kk1 + kk2. The resulting marginal cost function is thus the 

horizontal summation of the pre-merger firms’ marginal cost curves.

With these demand and cost functions, each Cournot firm maximizes profits with respect 

to their own quantity, yielding the following first order conditions: aa − bbqqii − bb =

qqii⁄kkii. Solving the nn first order conditions results in equilibrium quantities:

 23 See, Thomson StreetEvents (2012). 24 See, for example. Perry and Porter (1985), Farrell and Shapiro (1990), McAfee and Williams (1992), and Werden 

and Froeb (2008).

25 To be sure, the quadratic function is stylized approach to modeling costs. Assuming constant marginal costs, an 

even more stylized approach, would suggest the merged firm simply transfers all production to the lower marginal 

cost firm.
14

qqii = aa

bb �

bbkkii

bbkkii + 1

1 + ∑ bbkkii

bbkkii + 1 nn

ii=1

� . 26

(4)

It is straightforward to solve for the parameters of the demand function based on the 

market price, quantity, and assumed elasticity of demand. Simulating a merger occurs in two 

steps. First, we recover the kkii using the first order conditions. Second, we calculate the postmerger equilibrium qqii given the post-merger values of kkii.

TABLE 4—Simulation Results from the Standard Cournot Model

Table 4 shows the results of the Cournot simulation. Tesoro’s predicted post-merger 

output is 26% less than the combined output of BP and Tesoro before the acquisition. 

Equilibrium marginal costs are lower as the merged entity restricts output along its new marginal 

cost function. Conversely, all of the non-merging firms increase output in response, with their 

marginal costs increasing as they expand output. Overall, industry output decreases by 2%. 

Based on the demand parameters, the Cournot model predicts the merger will increase prices by

6%.

 26 McAfee and Williams (1992) use the same notation. They derive this equilibrium and study the welfare 

implications of horizontal mergers.

Quantity* C' (P - C' )/P

Chevron 29.19 12.04 0.91

Tesoro 19.78 51.99 0.62

ConocoPhillips 12.17 84.31 0.38

Valero 11.76 86.07 0.37

Shell 8.76 98.82 0.27

Exxon 8.37 100.46 0.26

ALON 6.50 108.43 0.20

Kern Oil & Refining 1.46 129.83 0.05

Total 97.98

*Pre-acquisition total market output normalized to 100.
15

To simulate the merger with the hybrid model, we assume a linear supply function from 

the price-taking firms, with parameters defined by the pre-merger equilibrium price, quantity,

and the same supply elasticity for each price-taking firm. From this, one can algebraically derive 

the residual demand function facing the strategic firms. The simulation proceeds as under the 

standard Cournot model above, with the exception that we replace the overall market demand 

function with the residual demand function, and replace the overall market shares with the share 

of each strategic firm within the strategic group. Table 5 presents the results.

TABLE 5—Simulation Results from the Hybrid Model

Tesoro reduces output less than predicted with the standard Cournot merger simulation: 

7% rather than 26%. This difference reflects the more aggressive output expansion of the pricetaking firms. In the hybrid simulation, strategic firms outside the merger increase output by 1%, 

while the non-strategic firms increase output by 2%. Overall, output falls by 0.3% and the 

hybrid model predicts that price increases by approximately 1%. 

6. Alternative Parameterizations

In Table 6, we derive simulated price effects as we change the composition of the 

strategic group. The first column assumes the strategic group includes only Chevron, BP, and 

Quantity* C' (P - C' )/P

Chevron 27.60 105.67 0.18

Tesoro 24.83 107.97 0.16

ConocoPhillips 11.51 119.05 0.07

Valero 11.12 119.38 0.07

Shell 8.59 128.63 0.00

Exxon 8.21 128.63 0.00

ALON 6.37 128.63 0.00

Kern Oil & Refining 1.43 128.63 0.00

Total 99.66

*Pre-acquisition total market output normalized to 100.
16

Tesoro. Moving to the right, the strategic group includes additional firms, added in descending 

market share order. The middle column, which includes five strategic firms, is the baseline case 

presented in section 5. Notably, the order-of-magnitude of the simulated price effect does not 

change with the composition of the strategic group.

TABLE 6—Price Effect with Different Strategic Groups

One might expect that the price effect would increase as additional firms join the strategic 

group and the hybrid model ostensibly looks more like a standard Cournot model. However, 

note that the margin of the largest strategic firm remains constant as we move to the right in the 

table.27 In order to maintain the level of margins, the elasticity of supply from the price-taking

firms must increase, as defined by equations (2) and (3). Intuitively, as the share of the 

competitive fringe shrinks, the remaining price-taking firms must possess greater supply 

elasticity to maintain the assumed margin of the largest strategic firm.

28

In our baseline results, we calibrate the residual demand elasticity by assuming the largest 

firm’s equilibrium marginal cost equals the cost of crude oil (the bottom of the plausible range of 

values for marginal costs), with smaller strategic firms’ having higher marginal costs, as implied 

by equation (3). Crude oil is the primary input for gasoline and a given volume of crude oil will 

produce an approximately equal volume of refined products. Thus, the cost of crude oil is a 

 27 Residual demand elasticity declines as you move right in the table, ranging from 2.8 to 1.7. The decline reflects 

the fact that the largest firm’s share of the strategic group decreases while holding its margin constant. 

28 A researcher with access to firm-level production data could validate the implied supply elasticity of the pricetaking fringe, and perhaps pin down the most realistic grouping. Qualitative evidence about firms’ business 

strategies could also guide assignment to the strategic and price-taking groups.

Strategic Firms Chevron, 

Tesoro, BP

+ Cononco +Valero +Shell +Exxon

Price Effect (% change) 1.04% 0.99% 0.94% 0.91% 0.88%

Supply Elasticity of Price-Takers 2.68 3.57 5.25 8.06 16.54
17

proxy for the minimum marginal cost of producing gasoline. Relevant marginal costs may also 

include additional purchases of materials, labor, and capital, or the opportunity cost of forgone 

output of other products. Hence, equilibrium marginal cost likely falls somewhere between the 

cost of crude oil and the price of gasoline.

 Figure 1 illustrates the relationship between the largest firm’s pre-acquisition 

equilibrium marginal cost and the predicted price effect from the Tesoro/BP acquisition. Smaller 

assumed margins translate to more elastic residual demand, greater supply elasticity from pricetaking firms, and smaller predicted price effects. The dashed vertical line, indicating where 

marginal cost equals the cost of crude oil, intersects the curve at our baseline predicted price 

effect, 0.94%. The price effect declines to zero as assumed marginal cost increases from a 

neighborhood of crude oil costs to that of the market price ($127). Smaller margins imply 

greater supply elasticity from the price-taking fringe, which limits the market power of strategic 

firms. To summarize, the predicted acquisition effect from the hybrid model depends critically 

on assumed margins. However, nowhere in this plausible range of marginal costs does the 

hybrid model’s predicted merger effect approach the 6% level implied by the standard Cournot 

model.
18

FIGURE 1—Relationship between Assumed Margins and the Predicted Acquisition Effect

The choice of market demand elasticity does not affect the size of the merger’s price 

effect in the hybrid model, given our strategy of identifying the model’s parameters by restricting 

the largest firm’s marginal cost to a plausible range. As long as the group of strategic firms is 

unchanged, equation (3) sets the relationship between the residual demand elasticity, market 

shares, and margins. In other words, assumed margins imply the residual demand elasticity 

facing the strategic firms. Changing the overall market demand elasticity will change the supply 

elasticity of the price-taking firms (and therefore their quantity response), but will not change the 

predicted price effect of the acquisition.

Changing the choice of demand elasticity will change the predicted price effect in the 

standard Cournot model. Implied margins would also change. Indeed, it is possible to obtain 
19

implied marginal costs for the largest firm close to the cost of crude oil if one is willing to 

assume a demand elasticity of -1.3. In that case, the predicted price effect would be 1.2%. 

Hence, in some sense, the practical difference between the hybrid and standard Cournot models

rests on the assumed elasticity of demand. However, we believe a market demand elasticity of -

1.3 is implausible, and other researchers share this view. Coglianese, Davis, Kilian, and Stock 

(2015) describe a price elasticity of -0.46 as “the upper end of the range of elasticity values that 

seem economically plausible and indeed is higher than many economists would be comfortable 

with.”

7. Estimating Merger Price Effects 

The standard Cournot and the hybrid model predict respective price effects of 6% and 1%

using our baseline calibrations. To assess the accuracy of these predictions we estimate the 

actual effect of the acquisition on Los Angeles wholesale gasoline prices. The standard approach 

in the merger retrospective literature is to use a difference-in-differences model, comparing the 

evolution of prices in markets affected by the transaction with the evolution of prices in markets 

not affected. Lacking an ideal control for Los Angeles prices, we supplement the difference-indifferences approach with the synthetic control method.

We start by comparing the average pre/post-acquisition price difference in Los Angeles 

with the same difference in all 18 cities for which we have data. This difference-in-differences 

regression analysis allows us to conduct traditional statistical inference and test the null 

hypotheses from the simulation models. In this approach, we assume the 18 controls cities are a 
20

sample drawn from a larger population, and that the conditional mean price change in that 

population is the same change that would have occurred in Los Angeles but for the acquisition.29

The primary drawback of this approach is that Los Angeles prices might have followed a 

different path than the average price in the control cities if the acquisition had not occurred. 

Unobserved variables that differentially affect Los Angeles and one or more control cities will 

lead to correlation between the error term and treatment dummy. We could select—based on our 

best judgment—a particular control city that we believe experienced the same time-varying 

shocks. Yet this approach may raise concerns about the objectivity of our choice of control city 

and the degree to which its prices are a credible proxy for Los Angeles’s counterfactual prices. 

The synthetic control methodology, which selects a control group using a data-driven 

procedure, reduces the ability of the researcher to influence results and makes the selection 

process more objective. After finding the optimal synthetic control city and estimating the effect 

of the transaction on Los Angeles prices, we conduct a placebo experiment that applies the 

synthetic control method to each of the control cities. We can then assess whether the estimated 

effect in Los Angeles is large relative to the distribution of placebo effects. 

Section 7.1 describes our data set. Section 7.2 presents the difference-in-differences 

regression analysis. Section 7.3 describes the synthetic control methodology. Section 7.4

presents the synthetic control results. 

 29 Assuming prices in Los Angeles are precisely measured and the price effect in Los Angeles is the relevant 

statistic, the standard errors reflect sampling uncertainty arising because we do not observe every control city in the 

population. Abadie, Athey, Imbens, and Wooldridge (2014) discuss how traditional standard errors can also reflect 

the fact that, even if the researcher observes outcomes for all subjects in the population, there are additional potential 

outcomes for each subject with different levels of treatment. 
21

7.1. Data and Sample

We construct a panel dataset with 19 cities and 48 monthly observations from January 

2011 to December of 2014. The variable of interest is the wholesale price of gasoline. We 

construct monthly averages using the daily average rack price of branded and unbranded 

gasoline published by Oil Price Information Service (OPIS). Gasoline retailers and distributors 

can purchase gasoline at distribution terminals referred to as racks.30

We include data on Metropolitan Statistical Area annual per capita personal income, from 

the U.S. Bureau of Economic Analysis, to capture demand. That these data are annual is not

problematic as both the synthetic control method and the regression analysis use pre-acquisition 

and post-acquisition averages.31 To control for costs, we use Refiner Acquisition Cost of Crude 

Oil compiled by the U.S. Energy Information Administration (EIA). EIA calculates these data 

for five Petroleum Administration for Defense Districts (PADDs) and these data are unavailable

on a finer geographic basis.

Table 7 shows the average crude oil acquisition cost, per-capita income, pre-acquisition 

price, and post-acquisition price for each city in our sample. The final column shows the percent 

change in average price between the pre- and post-acquisition periods. This percent change is 

approximately equal for Los Angeles and the average of all the control cities. By definition, the 

point estimates in the first specification of our regression analysis, which includes no controls for 

demand or cost, reproduce the 8.1% decrease in prices for the average control city and a

difference-in-differences estimate that rounds to 0.0%.

 30 Seven of the potential control cities have reformulated gasoline. In those cities, we use the average wholesale 

price of reformulated gasoline. We use the average wholesale price of conventional gasoline in the remaining cities 

where reformulated gasoline is not sold.

31 The 2014 personal income data are not yet available from the BEA. We set the 2014 annual per capita personal 

income equal to the 2013 value in each metro area. Note that the synthetic control results, and the regressions 

specifications presented in columns 1 and 3 of table 8, do not depend on 2014 income data.
22

Table 7—Control Variables and Pre- and Post-acquisition Prices, Averages by City

7.2. Difference-in-Differences Regressions

We estimate the regression models using time-differenced data that capture the change in 

each variable from the pre-merger period to the post-merger period. The regression equation 

takes the form:

ln �

PPii

pppppppp

PPii

pp pp � = αα + ββAA AAAA AAAAAAAA ii + γγ ln � IIii

pppppppp

IIii

pp pp � + δδ ln �

CC ii

pppppppp

CC ii

pp pp � + εεii,

where PPii

pppppppp and PPiipp pp respectively are the post- and pre-acquisition average prices for city ii. 

The variables ii and CC ii represent per-capita income and crude oil acquisition costs. 

Finally, AA AAAA AAAAAAAA ii is an indicator variable for Los Angeles. The parameter ββ is the 

coefficient of interest: the log-point change in prices attributed to the merger.

Crude Cost Per-Capita Pre-Acquisition Post-Acquisition

($/barrel) Income Price (cpg) Price (cpg)

Los Angeles 102.2 $47,373 302.4 278.8 -8.1%

Atlanta 106.7 $40,795 287.0 268.2 -6.8%

Boston 106.7 $60,824 296.9 275.1 -7.6%

Chicago 90.8 $48,217 297.1 273.0 -8.4%

Cleveland 90.8 $44,849 294.6 275.1 -6.8%

Dallas 101.4 $46,207 291.0 264.2 -9.7%

Denver 84.8 $51,055 287.6 270.2 -6.2%

Detroit 101.4 $42,272 293.2 269.4 -8.5%

Fairfax 106.7 $61,367 292.0 270.3 -7.7%

Houston 101.4 $50,893 288.8 261.1 -10.1%

Louisville 90.8 $40,863 299.8 279.6 -7.0%

Miami 106.7 $44,743 288.8 266.3 -8.1%

Minneapolis 90.8 $50,502 289.2 261.3 -10.2%

New Orleans 101.4 $44,174 283.2 257.3 -9.6%

Newark 106.7 $58,575 294.5 271.5 -8.1%

Phoenix 102.2 $38,292 303.0 278.4 -8.5%

Salt Lake City 84.8 $40,684 288.2 275.3 -4.6%

Seattle 102.2 $54,080 296.3 270.0 -9.3%

St. Louis 90.8 $45,056 295.1 270.0 -8.9%

Average Control City 98.2 $47,969 292.6 269.8 -8.1%

Percent Price 

Change
23

The goal is to capture the price effect from Tesoro’s acquisition. We need a window of 

time long enough for firms to adjust output in response to the post-merger allocation of capital, 

yet short enough to avoid contaminating effects from unrelated changes in the industry. The 

possibility that firms change their behavior before the actual transaction further complicates 

matters. For example, Kim and Singal (1993) find that merging airlines increase prices after the 

firms reach an agreement but before they actually consummate their deal.

The resulting challenge of determining the appropriate window of analysis has been 

widely acknowledged in the merger retrospective literature.32 We proceed by specifying three 

different pre/post periods. The first window of analysis utilizes our full dataset, spanning 

January 2011 through December 2014, with June 2013 as the first post-acquisition period. The 

second window uses a 12-month period immediately preceding the acquisition and a 12-month 

period immediately following the acquisition. The third window has a 12-month period that 

begins 18 months before the acquisition and a 12-month period that begins 6 months after the 

acquisition. Using a 6-month transition window on either side of the acquisition should 

minimize the influence of any anticipatory or delayed acquisition effects.

Averaging the data across the various pre- and post-acquisition periods obviates the need 

to account for serial correlation. Bertrand, Duflo and Mullainathan (2004) demonstrate that 

serial correlation can lead to significant biases in OLS standard errors and examine the efficacy 

of several solutions. They find that collapsing the time series is the most reliable solution when 

the number of cross sectional subjects is relatively small.

33 Other merger retrospectives that rely 

 32 See Ashenfelter, Hosken, and Weinberg (2009) and Greenfield (2014) for overviews. 33 Donald and Lang (2007) propose an analogous two-step regression procedure.
24

on time-aggregated data include Tenn (2011), Tenn and Yun (2011), Thompson (2011), and 

Haas Wilson and Garmon (2011).

34

TABLE 8—Difference-in-Differences Regression Models

 34 Our time-differenced model is equivalent to a two-period city fixed effects model.

Variables 1 2 3 4

ACQUISITION 0.000 -0.002 0.001 0.003

(0.015) (0.016) (0.015) (0.017)

Δ ln(INCOME ) 0.115 -0.2

(0.475) (0.539)

Δ ln(COST ) 0.106 0.125

(0.089) (0.106)

Constant -0.081*** -0.0841*** -0.0755*** -0.0693***

(0.003) (0.013) (0.006) (0.018)

R-squared 0.000 0.004 0.081 0.089

ACQUISITION -0.002 -0.003 -0.002 -0.004

(0.011) (0.012) (0.012) (0.012)

Δ ln(INCOME ) 0.455 0.479

(0.775) (0.845)

Δ ln(COST ) 0.007 -0.006

(0.064) (0.069)

Constant -0.037*** -0.039*** -0.037*** -0.039***

(0.003) (0.005) (0.003) (0.005)

R-squared 0.002 0.023 0.003 0.024

ACQUISITION -0.008 -0.01 -0.007 -0.008

(0.014) (0.015) (0.014) (0.015)

Δ ln(INCOME ) 0.397 0.167

(0.545) (0.590)

Δ ln(COST ) 0.099 0.089

(0.079) (0.088)

Constant -0.079*** -0.084*** -0.073*** -0.076***

(0.003) (0.008) (0.006) (0.012)

R-squared 0.018 0.049 0.106 0.111

N 19 19 19 19

*** p<0.01, ** p<0.05, * p<0.1

12-month pre and post periods, no transition window

12-month pre and post periods, 12-month transition window

Full Sample (Jan '11-May '13 pre period and Jun '13-Dec '14 post period)
25

Table 8 presents the regression results. There are four different specifications, with 

different combinations of the control variables. The same qualitative conclusion arises from 

every specification. The change in Los Angeles prices is statistically insignificant. We cannot 

reject the 1% increase predicted by the hybrid model, yet can reject the 6% increase predicted by 

Cournot model, in all specifications. 

7.3. Synthetic Control Method

The synthetic control method constructs a weighted average of the 18 available control 

cities. It selects weights so that the synthetic control city best approximates pre-acquisition 

characteristics of the Los Angeles market. The synthetic control city’s post-acquisition prices 

then form the estimate of Los Angeles’s post-acquisition prices but for the merger.

Let jj = 1, 2, ... ,JJ + 1 index cities and tt = 1,2, ... , index time. There are JJ potential 

control cities (Los Angeles is jj = 1) and pre–acquisition periods. A synthetic control city is 

defined by a (JJ × 1) vector of weights WW = �ww2, ... , wwJJ+1�

′

, which are non-negative and sum to 

one. Each element, wwjj, represents the weight assigned to potential control city jj. XX11 is a (kk × 1)

vector of pre-merger characteristics in Los Angeles. In our study, XX11 is a 3 x 1 vector including

the pre-acquisition average of per-capita income, the pre-acquisition average of refinery crude 

acquisition costs, and the pre-acquisition average of wholesale prices. The (kk × JJ) matrix XXoo

contains the same variables as XX11 for the potential control cities. 

The optimal set of weights, WW∗, is the vector that minimizes the distance

‖XX11 − XX00WW‖VV = �(XX11 − XX00WW)′

VV(XX11 − XX00WW),

subject to ww1 + ⋯ + wwJJ = 1 and wwJJ ≥ 0. Hence, WW∗ defines the synthetic control city that most 

closely resembles Los Angeles as measured by the VV-weighted distance between the vectors XX11
26

and XX00WW. VV is a diagonal matrix with elements that apply weights to the variables in XX11 and XX00, 

determining their importance as relevant characteristics.

We choose VV∗ by minimizing the mean square prediction error (MSPE) of the synthetic 

control city relative to Los Angeles during the pre-acquisition period. That is, we choose VV∗

such that it minimizes

�YY11 − YY00WW∗(VV)�

′

�YY11 − YY00WW∗(VV)�,

where YY11 is a 0 × 1 vector of pre-acquisition prices in Los Angeles and YY00 is a ( × JJ) matrix 

of the pre-acquisition prices in the control cities.35

The synthetic control estimator for the acquisition’s effect is the difference between the

Los Angeles price and the synthetic control city price in a given post-acquisition period: 

PP1 − ∑ wwjj

∗

PPjj

JJ+1

jj=2 . Abadie, Diamond and Hainmueller (2010) derive the synthetic control 

estimator and discuss its theoretical properties using a model that generalizes the standard

difference-in-differences model. They demonstrate how it accounts for time-varying 

confounders. The intuition is that the synthetic control group can fit XX11 only if it also fits the

unobserved predictors of price. They are able to put bounds on the associated bias and 

demonstrate that the synthetic control estimator does a better job of accounting for transitory 

shocks if the number of pre-acquisition periods is large relative to the scale of unobserved 

confounders.

 35 Finding WW∗ and VV∗ is a nested optimization problem. We use a software package developed in the R programing 

language to implement the synthetic control method and solve the nested optimization problem. The software runs 

the optimization twice. It uses two sets of starting values (equal V weights and a regression-based method of 

selecting initial V weights) and returns the solution with the lower loss. Abadie, Diamond and Hainmueller (2011) 

explain the functionality of the package in detail. Our results are qualitatively unchanged if we assign equal weight 

to each variable, solving for WW∗ with a predefined V.
27

7.4. Synthetic Control Results

The optimal synthetic control city for Los Angeles applies weights of 0.73 to Phoenix, 

0.27 to Boston, and less than 0.001 to all other potential control cities. The components of VV∗

assign weights of 0.84, 0.15, and 0.01 to the pre-acquisition price level, per-capita income, and 

crude costs, respectively. Boston and Phoenix have relatively high gasoline prices and crude

costs, similar to Los Angeles. While Boston’s income is higher than Los Angeles, Phoenix’s is 

lower, resulting in a weighted average that approximates Los Angeles. 

FIGURE 2—Price Levels in Los Angeles and the Control Cities

Figure 2 plots the level of prices in Los Angeles over time, as well as those of the 

synthetic control group and an equally weighted average across all 18 control cities. The 

synthetic control city’s prices clearly track Los Angeles better than the average control city does. 
28

In addition, there is no obvious change in the slope or level of Los Angeles prices relative to the

control groups. 

The average pre-acquisition price gap is 1.12 cents per gallon and the pre-acquisition 

MSPE (the mean of the squared price gap) is 57.68. Post-acquisition, the average price gap is 

1.32 cents per gallon and the MSPE is 54.40. The slight decline in prediction error suggests that 

the synthetic control group’s ability to replicate Los Angeles did not worsen. Hence, there is no 

evidence that the acquisition affected prices.

An increase in MSPE from the pre- to post-acquisition period is an important condition 

for reaching a conclusion that the acquisition had a causal effect on prices. The pre-acquisition 

MSPE quantifies the synthetic control city’s ability to replicate the Los Angeles gasoline prices. 

If the MSPE does not increase following the acquisition, any post-acquisition gap may well 

reflect the inherent inability of the synthetic control group to replicate Los Angeles prices 

precisely, rather than a causal effect form the acquisition.

We further assess the significance of our estimates by performing a series of placebo 

tests. We use the synthetic control method to test for a price change during the sample period in 

each of the potential control cities. We iteratively apply the synthetic control method to every 

city in the data. For each iteration, we reassign the acquisition city to one of the 18 control cities

and shift Los Angeles to the pool of potential cities for the synthetic control. Each iteration is a 

placebo test where we test for a merger effect in a city where no merger occurred. This 

generates an empirical distribution of estimated price effects. We can be confident there is 

evidence of an acquisition effect if the estimated effect in Los Angeles is an outlier among the 

distribution of placebo estimates.
29

Table 9 reports the mean gap between Los Angeles and the synthetic control city prices 

and the MSPE for the pre- and several post-acquisition periods. It also summarizes the 

distribution of these statistics from the placebo exercise. The post/pre MSPE ratio facilitates 

comparison between the Los Angeles estimate and the placebo estimates by creating a strictly 

positive measure that is normalized based on a particular synthetic control city’s ability to predict 

prices before the acquisition.

Table 9—Mean Price Gap and MSPE, Los Angeles and the Placebo Tests

Again, the average gap between the synthetic control city and Los Angeles during the 

post-acquisition period is 1.32 cents per gallon, approximately 0.4%. That falls within the 

interquartile range of the empirical distribution from the placebo exercise. Moreover, the 

post/pre MSPE ratio of 0.94 falls below the median of the distribution of the post/pre MSPE

ratio. Together these facts suggest there is a greater than 50% chance of finding an effect of 

equal or greater magnitude if we were to relabel the acquistion city in our dataset at random. 

Table 9 reports similar statistics for two alternative post-acquisition periods; the qualitative 

results are unchanged.

Mean Price 

Gap MSPE

Mean Price 

Gap

Post/Pre 

MSPE

Mean Price 

Gap

Post/Pre 

MSPE

Mean Price 

Gap

Post/Pre 

MSPE

Los Angeles 1.12 57.68 1.32 0.94 2.22 1.44 2.21 1.16

 Mean -0.01 46.82 -1.32 2.47 -1.10 2.12 -1.31 2.78

 5th Percentile -1.13 5.11 -9.30 0.52 -8.10 0.44 -11.10 0.56

 10th Percentile -0.75 8.48 -5.45 0.66 -6.76 0.57 -7.22 0.84

 25th Percentile -0.04 17.05 -3.60 0.93 -2.87 0.95 -3.81 1.08

 Median 0.00 31.58 -2.00 1.67 -0.96 1.55 -1.77 1.68

 75th Percentile 0.03 74.07 2.16 2.74 2.15 2.62 1.77 3.28

 90th Percentile 1.17 95.16 4.33 5.53 2.92 3.81 6.05 6.69

 95th Percentile 1.41 111.66 5.19 6.91 3.14 5.31 7.54 7.65

Distribution from Placebo Exercise (includes Los Angeles estimate)

Dec 2013 - Nov 2014

Pre-Acquisition Period Three Alternative Post-Acquisition Periods

Jan 2011 - May 2013 Jun 2013 - Dec 2014 June 2013 - May 2014

Full Sample First 12 Months 12 Months, 6-month transition
30

Similar to the regresion analysis, there is no evidence of a price change. That is not to 

say that the placebo exercise provides a weak test. If we had found a 3% change in Los Angeles

prices (9 cpg), the distribution from the placebo exercise would allow us to infer that there is a 

5.2% (1/19 cities) chance of finding a comparable effect if we were to randomly select the 

treatment city from our dataset.

8. Conclusions

We model the California gasoline market using a variant of the Cournot model, which

includes a competitive fringe of price-taking firms. This hybrid model performs better than the

standard Cournot model for two reasons. First, the hybrid model implies more plausible margins

than does the standard Cournot model, given widely accepted estimates of market demand 

elasticity. Second, the hybrid model more accurately predicts the price effect of the Tesoro/BP 

acquisition, relative to empirical estimates of the acquisition’s price effect.

We estimate the effect of the acquisition using two methodologies. Difference-indifferences yields an estimate that is not statistically different from zero, nor is it statistically 

different from the 1% price increase predicted by our hybrid model. We can, however, reject the 

6% price increase predicted by the standard Cournot model. Inference with the synthetic control 

method takes a different approach but yields a similar conclusion. Our placebo exercise 

indicates that if we relabel the acquisition city in our dataset at random, the probability of 

obtaining a result of the magnitude that we obtained for Los Angeles is greater than 0.5.

.
31

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