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Using measures of competitive harm for optimal screening of horizontal mergers

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Antitrust practitioners often use measures like the Herfindahl-Hirschman Index and Upward Pricing Pressure in order to predict whether a horizontal merger is likely to be anti-competitive. However, such measures suffer from two drawbacks. First, there is little empirical work analyzing the accuracy of these measures in predicting competitive effects. Second, these measures either do not have associated decision rules for determining whether a horizontal merger is likely to be anti-competitive, or the relationship between the decision rules and results from theoretical or empirical economic models is unclear. To address these issues, this paper investigates the relationship between standard merger enforcement screening measures and predicted competitive effects in depth and uses decision-theoretic models to develop optimal decision rules for merger enforcement based on these measures. We find that across a range of common strategic interactions all measures correctly predict when a merger is likely to have little anti-competitive effect. In contrast, we find that these measures do a poor job of predicting the magnitude of these effects when they are likely to be large. Finally, the optimal decision rules we derive depend critically on the mix of competitive models that are believed to exist in the population of potential mergers.
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Using measures of competitive harm for optimal screening of
horizontal mergers?,??
Charles Taragina, Margaret Loudermilkb,
aFederal Trade Commission, Bureau of Economics, 600 Pennsylvania Ave NW, Washington DC 20580
bUS Department of Justice, Antitrust Division, Economic Analysis Group, 450 5th St. NW, Washington DC
20530
Abstract
Antitrust practitioners often use measures like the Herfindahl-Hirschman Index and Up-
ward Pricing Pressure in order to predict whether a horizontal merger is likely to be
anti-competitive. However, such measures suer from two drawbacks. First, there is
little empirical work analyzing the accuracy of these measures in predicting competitive
eects. Second, these measures either do not have associated decision rules for deter-
mining whether a horizontal merger is likely to be anti-competitive, or the relationship
between the decision rules and results from theoretical or empirical economic models is
unclear. To address these issues, this paper investigates the relationship between standard
merger enforcement screening measures and predicted competitive eects in depth and
uses decision-theoretic models to develop optimal decision rules for merger enforcement
based on these measures. We find that across a range of common strategic interactions all
measures correctly predict when a merger is likely to have little anti-competitive eect. In
contrast, we find that these measures do a poor job of predicting the magnitude of these ef-
fects when they are likely to be large. Finally, the optimal decision rules we derive depend
critically on the mix of competitive models that are believed to exist in the population of
potential mergers.
Keywords: Herfindahl-Hirschman Index, upward pricing pressure, merger simulation,
?The views expressed herein are entirely those of the authors and should not be purported to reflect those
of either the Federal Trade Commission or the US Department of Justice.
??We would like to thank Chris Adams, Yong Chao, Eric Lewis, Nathan Miller, Gloria Sheu, Phillippe
Sulger, Nathan Wilson, and participants at the 2019 International Industrial Organization Conference, DC
IO Conference, and US Department of Justice Antitrust Division seminar.
Corresponding author
Email addresses: ctaragin@ftc.gov (Charles Taragin), margaret.loudermilk@usdoj.gov
(Margaret Loudermilk)
Preprint submitted to Elsevier October 2, 2019
merger enforcement, unilateral eects
1. Introduction
Antitrust practitioners employ a variety of measures to predict whether a horizontal
merger is likely to be anti-competitive. Some measures, like the number of significant
competitors in the market and the combined market share of the merging firms, are based
on the documented positive correlation between these concentration measures and industry
prices across markets and over time. Other measures, like Upward Pricing Pressure (UPP)
and Compensating Marginal Cost Reduction (CMCR), are derived from non-cooperative
game theoretic models whose aim is to capture how a horizontal merger can change the in-
centives of the merging parties. One commonly used measure, the Herfindahl-Hirschman
Index (HHI), has not only been derived from theoretical models but has also been shown
to be positively correlated with industry prices. However, the accuracy of these measures
in predicting the the potential anti-competitive, unilateral eects of horizontal mergers is
not well understood.
Accurately predicting whether a horizontal merger is likely to substantially lessen com-
petition is important. The harm to competition and consumers from not identifying poten-
tially anti-competitive mergers can be large. In addition, it is costly to investigate poten-
tially anti-competitive mergers and even more costly to stop mergers that are thought to
be anti-competitive. Nonetheless, there is little empirical work analyzing how accurately
these measures predict either the likelihood of significant competitive eects or the mag-
nitude of harm or benefit from horizontal mergers. This paucity stems from two related
problems. First, for many markets, it is dicult to collect the requisite information before
and after the merger in order to conduct an evaluation. Second, it is often intractable to
suciently control for the myriad of factors that change in a market concurrent with the
merger.1
As a result, the majority of research on the performance of screening measures arises
from the academic literature on the structure-conduct-performance paradigm, which il-
lustrates a positive relationship between concentration measures and industry prices. In
particular, the positive correlation between HHI and and merging firm prices is well docu-
mented.2However, it is unclear to what extent an increase in the HHI causes market out-
1As an alternative, the FTC uses the case study method in its evaluation of merger remedies. For exam-
ple, “The FTC’s Merger Remedies 2006-2012: A Report of the Bureaus of Competition and Economics”
includes case studies of 50 merger settlements.
2Examples include Borenstein (1989), Manuszak and Moul (2009), Manuszak and Moul (2008), Pinkse
et al. (2002), and Schmalensee (1989).
2
comes like industry prices or welfare to change post-merger. In fact, Farrell and Shapiro
(1990) show that reliance solely on HHI can be misleading in merger analysis. Similarly,
Hosken et al. (2011) find no consistent relationship between HHI and industry wholesale
or retail prices after two changes in ownership among San Francisco Bay Area gasoline
refineries.
A separate strand of the literature addressing the ecacy of screening measures fo-
cuses on merger simulation methods, arguably the primary modern tool for assessing the
predicted unilateral competitive eects of horizontal mergers.3Werden and Froeb (1996)
investigates in a simulation study whether the combined share of the merging firms or post-
merger HHI are useful predictors of price and welfare eects. In a dierentiated product,
Nash-Bertrand setting with Logit demand, Werden and Froeb find that both measures are at
best mediocre predictors of price and welfare eects, and both measures exhibit variation
that increases with the change in market concentration. In a retrospective analysis, Haus-
man and Sidak (2007) find no relationship between HHI and consumer prices for wireless
telephone service in the EU. Miller et al. (2017) demonstrate that UPP acts as an accurate
screen with log-concave demand specifications in Monte Carlo experiments but finds that
UPP understates price eects under more convex demand assumptions. Similarly, Che-
ung (2016) used a cross-section of data on airline market routes to compare hypothetical
horizontal merger predictions between UPP and merger simulation. Cheung found that
the correlation between the UPP and merger simulation results increased as the size of
the merging firms or cost savings from the merger decreased. Dutra and Sabarwal (2019)
investigate the accuracy of UPP as a screening measure in the presence of merger-specific
cost eciencies by Monte Carlo simulation, concluding that the standard UPP formulation
substantially over predicts price eects.
This paper extends the eorts of this research stream, further investigating the perfor-
mance of common measures employed by antitrust practitioners using simulation meth-
ods. We simulate markets from a set of commonly used demand and supply models and
use these markets to compute the price eects from a merger.4It is then simple to compare
the simulated merger eects to those predicted by the screening measures.5We find that
3Surveys of simulation methods for merger analysis can be found in Werden and Froeb (2006) and
Budzinski and Ruhmer (2009). See also Nevo and Whinston (2010) for a discussion of the use of merger
simulation in antitrust analysis as well as Peters (2006), Weinberg (2011), and Bjornerstedt and Verboven
(2016) for comparison of results from merger simulation and retrospective estimates.
4The sensitivity of merger simulation estimates to assumptions about demand and supply specifications
is well-known. See Weinberg and Hosken (2013), Crooke et al. (2003), Bass et al. (2008), Bokhari and
Mariuzzo (2018) and Knittel and Metaxoglou (2011).
5It is important to note that in our simulation study because all the models assume that market participants
are playing a non-cooperative game our analysis can only be used to assess how well these measures predict
3
across a range of common demand and supply specifications all the measures correctly
predict when a merger is likely to have little anti-competitive eect. In contrast, we find
that these measures do a poor job of predicting the magnitude of these eects when they
are likely to be large.
A second serious drawback with the aforementioned measures is that many lack a de-
cision rule for determining whether a horizontal merger is likely to be anti-competitive
ex-ante. For those that do have an associated rule, the underlying theoretical or empiri-
cal economic justification is often unclear. To remedy this, we use two decision-theoretic
models to develop optimal decision rules for merger enforcement based on these mea-
sures. We find that the optimal decision rules depend critically on the mix of competitive
models that are believed to exist in the population of potential mergers. In general, higher
thresholds would be warranted under the belief that the population of potential mergers is
largely comprised of firms competing according to a dierentiated products auction model.
We also find that the current thresholds would be most relevant in a population with the
majority of industries engaged in Cournot competition.
Two papers are most similar in spirit to ours, each with a somewhat dierent focus.
Garmon (2017) also assesses the accuracy of merger screening methods. However, Gar-
mon’s study is specific to methods used in hospital mergers and employs a retrospective
analysis. Coate (2011) compares concentration measures to the outcomes of FTC merger
challenge decisions and uses these to infer a benchmark merger screen level for UPP of
less than 15%.
The paper proceeds as follows: Section 2 summarizes the set of models, concentra-
tion measures, and data generating processes employed in the simulation study. Section 3
reports the results of these numerical simulations. Section 4 considers two optimal screen-
ing rules for initiating horizontal merger investigations, using concentration as a proxy for
anti-competitive harm, and section 5 concludes.
2. Monte Carlo Experiments
2.1. Demand and Supply Specifications
Here, we describe the game-theoretic models that underpin our numerical experiments.
These include: Cournot with quadratic costs and log-linear as well as linear demand;
Bertrand with Almost Ideal Demand (AIDS), Constant Elasticity of Substitution (CES)
demand, and Logit demand; and a second score auction with Logit demand.6We selected
the Cournot, Bertrand and 2nd score auction models for two reasons. First, versions of
unilateral merger eects. Potential coordinated merger eects are not addressed.
6See Appendix A for details of the demand and supply model specifications.
4
these models have been employed by both the FTC and the DOJ in publicly litigated mat-
ters. For example, in 2011 the Division used a Bertrand pricing game with linear demand
to simulate the eects of a merger between HR Block and TaxAct, two firms that spe-
cialize in tax preparation. In 2017, The Division also employed a Bertrand model, this
time to simulate the eects of a horizontal merger between two health insurers, Aetna
and Humana. In the same year, the Division used a 2nd score auction model to simulate
the eects of a merger between Anthem and Cigna, two other large heath insurers. Fi-
nally, in 2018, the FTC used a Cournot model to simulate the eects of a merger between
Tronox and Cristal, two of the largest producers of titanium dioxide. Second, while other
papers have established that for the Bertrand model, the curvature of the demand curve
can significantly aect the magnitude of the post-merger price changes, to our knowledge,
little research has been done analyzing the eect that the assumed form of the suppliers’
strategic game has on post-merger price changes.
We selected the linear and log-linear demand systems for study under Cournot com-
petition because in our experience, the Cournot model is often used to simulate merger
eects in homogeneous good industries and the linear and log-linear demand systems cap-
ture this feature nicely, while also allowing us to explore two extreme cases with regard
to curvature. Linear demand has no curvature (second derivatives equal 0), whereas log-
linear demand exhibits substantial curvature, particularly at high prices. Logit demand is
used in the 2nd score auction model largely for convenience and tractability but is also one
of the few functional forms previously used in published work.
For the Nash-Bertrand game, we selected the AIDS, Logit and CES demand systems.
First, like log-linear demand in Cournot, AIDS can have large second derivatives, partic-
ularly at high prices. In contrast, the Logit model and to a lesser extent the CES model
generally have smaller second derivatives. Including these three specifications allows us
to assess the eect of demand curvature for a given model of supply. Second, while the
choice of demand specification is heavily influenced by the particulars of an industry, data
limitations often influence the set of models that can be implemented in practice since the
data requirements of these models dier.7
Also of interest are the demand models that we did not include, most notably log-linear
and linear demand for Bertrand. Without additional restrictions these demand systems
require estimation of a large number of parameters, and it is often the case in practice that
there is insucient data to obtain reliable estimates. Further, unlike AIDS, Logit, and CES,
without further restrictions log-linear and linear demand are not necessarily consistent with
7Typically, both AIDS and CES demand are estimated using expenditure shares while Logit demand is
estimated using quantity shares, for example.
5
the axioms of consumer choice theory8. As a result, it is dicult to calculate the welfare
measures that are important in assessing the competitive eects of a merger.
2.2. Measures of Competitive Harm
A number of indicia are commonly used as proxies for the anticipated competitive
eects of a horizontal merger, including industry firm counts, merging party size rank,
combined party market share, HHI, UPP, and CMCR. Many of these indicia consist of two
parts: an algorithm for calculating the index and a threshold decision rule for determining
whether a horizontal merger is likely to raise competitive concerns. Here we describe the
“thought experiment” underlying each of these indicia, as well as some of their properties,
advantages and drawbacks.
Before doing so, it is important to reiterate that we are only examining the ability of
these indicia to predict relatively short run unilateral eects from horizontal mergers. It is
possible that some of these measures may also be useful predictors of other adverse eects
from horizontal mergers, like coordinated eects. However, testing these properties would
require implementation of more sophisticated models. Such extensions are beyond the
scope of this paper.
2.2.1. Firm Count
The intuition underlying the “firm count” indicia is that a merger reduces the number
of firms in a market from Nto N1, which would tend to raise prices and harm consumers,
ceteris paribus. The magnitude of the price eect is expected be small when Nis large
and large when when Nis small. Calculating this indicia is easy: 1) Identify firms in the
market; 2) Count the firms (N); and 3) Reduce the number of firms by 1 (N1).
Interpreting the Firm Count measure is more dicult. On one hand, it seems plausible
that a merger reducing the number of firms from 100 to 99 is unlikely to yield substantial
harm. On the other hand, it is plausible to believe that a merger reducing the number
of firms from 2 to 1 yields substantial harm. But what about a 10 to 9 merger or a 5
to 4 merger? In addition, this measure assumes each firm included in the market is as
competitively significant as every other firm (i.e., Firms are in some sense “symmetric”.),
but what if some firms have more sales than others? What if manufacturing costs vary
across firms, consumers value the attributes of each product dierently, or some firms
oer a portfolio of products while others only sell a single product? It seems plausible that
most if not all of these factors distinguish one firm from another in ways that render this
measure noisy.
8von Haefen (2002) describes how Slutsky Symmetry is typically violated by these demand models and
derives the parameter restrictions needed to satisfy this assumption.
6
The firm count measure also provides no guidance as to which firms should be included
in the antitrust market of interest. Rather, it assumes that the contours of the market are
clearly identified, which is rarely true in dierentiated product markets. This criticism of
Firm Count is true of nearly all the measures we consider and thus is not repeated in each
of the subsequent sections.
2.2.2. Merging Party Size Rank
The “Party Rank” measure, which identifies the size rank of the merging parties (e.g.
the merging parties are the 1st and 3rd largest firms in the market), addresses one criticism
of the firm count metric by partially internalizing the potentially asymmetric nature of the
merging parties. A merger reducing the number of asymmetric firms in a market from N
to N1 may raise prices by a substantial amount, depending upon the sizes of the merging
firms. The magnitude of the price eect will be small, all other things equal, when either
both merging parties are small and therefore have low rank OR one party has a high rank
and the other a low rank. Thus, Party Rank attempts to capture the dierence between the
the 1st and 2nd largest firms merging out of ten from the 9th and 10th largest merging. In
this example, the Firm Count for both mergers is 10 to 9 although we would expect larger
competitive eects from a merger of the market’s largest firms.
2.2.3. Merging Party Combined Share
One important drawback of both the Firm Count and Party Rank measures is that they
do not capture information about the magnitude of the size dierences between firms. The
“Party Share” measure, which equals the combined market share of the merging parties,
remedies this by explicitly using information on the size of the merging parties. The
intuition behind this measure is straightforward: all else equal, mergers where the parties
have a higher combined share control more of the market post-merger and therefore have
a greater incentive to raise prices.
Aside from its intuitive appeal, the importance of this indicia has been recognized
at times by both the U.S. Courts and antitrust enforcement agencies. In United states v.
Philadelphia National Bank, the U.S. Supreme Court ruled that mergers where the com-
bined party share is greater than 30% are presumptively anti-competitive.9Moreover, the
now superseded 1992 Horizontal Merger Guidelines (HMG) published by the U.S. FTC
and DOJ indicate that if the combined party share is greater than 35%, then the agencies
will view the merger as presumptively anti-competitive. While the most recently revised
2010 HMG no longer enumerates a combined share threshold, the HMG still recognizes
the import of merging party market shares, stating “The Agencies also may consider the
9United States v. Philadelphia Nat’l Bank, 374 U.S. 321 (1963)
7
combined market share of the merging firms as an indicator of the extent to which others
in the market may not be able readily to replace competition between the merging firms
that is lost through the merger.10
Although intuitive, the Party Share measure has two drawbacks. First, it does not dis-
tinguish between dierent market compositions that could aect competitive interactions
such as between markets with a few large non-merging parties versus a market with only
many small non-merging firms. Second, this measure does not provide a way to quantify
the magnitude of harm associated with a particular concentration level. This criticism is
also shared by nearly all of the measures studied.
2.2.4. Herfindahl-Hirschman Index
The Herfindahl-Hirschman Index explicitly uses information on firm size and quanti-
fies the dierences in market composition, remedying some weaknesses of the previous
measures. Specifically, the HHI is calculated as the sum of the squared shares of firms in
the relevant market, yielding an indicia that is between 0 (perfect competition) and 10,000
(monopoly). It can be shown algebraically that the post-merger change in the HHI, HHI,
is given by 2 times the product of the merging firms’ market shares.
The HHI has a number of useful properties. First, it may be derived from a standard
Cournot quantity-setting game, one of work-horse game-theoretic models in the IO litera-
ture. Second, the HMG articulate criteria describing under what conditions a merger may
or may not be cause for concern in terms of the HHI. As shown in Figure 1 if the post-
merger HHI >2,500 and HHI >200 then, according to the HMG, the merger should
be considered presumptively anti-competitive. If the post-merger HHI is >2,500 and 100
<HHI 200 OR post-merger 2,500 HHI 1,500 and HHI >100 the merger may
potentially raise significant competitive concerns. If the post-merger HHI <1,500 or
HHI 100 then it is considered unlikely to have adverse competitive eects. A HHI =
200 could result, for example, from the merger of two firms each with a 10% market share.
Another feature of the HHI is that it can be readily converted into a measure of the
eective number of symmetric firms in a given market, Ne f f =10,000/HHI. Among
other things, this useful result aids in interpreting the HMG HHI thresholds since a post-
merger HHI of 2,500 implies 4 equal-sized firms, while a 1,500 HHI implies roughly 7
equal-sized firms. Therefore, loosely speaking, the HMG states that mergers resulting in 4
or fewer equal-sized firms in a market are presumptively anti-competitive, while mergers
where 7 or more firms remain in the market are unlikely to be anti-competitive. Despite
these useful properties, the HHI does not quantify how much harm is likely to be generated
at the Guidelines’ thresholds.
10U.S. Department of Justice and Federal Trade Commission (2010), p.18
8
2.2.5. Upward Pricing Pressure
Upward Pricing Pressure (UPP) attempts to directly quantify the competitive eects
of a horizontal merger and is derived as a first order approximation of the merging parties
equilibrium pricing strategy under the Nash-Bertrand pricing game. Intuitively, the UPP
measure asks ‘When a firm raises its price on a product, how much of the sales it loses
will shift to its merging partner (diversion), and how much are those sales by the merging
partner worth (margin)?’ Recapturing sales diverted from the merging partner lessens the
cost of raising price, creating additional incentive to increase price, referred to as “upward
pricing pressure”.
UPP is often quantified by the Generalized Upward Pricing Pressure Index (GUPPI).
The GUPPI is obtained by expressing the value of a firm’s sales diverted to the merging
partner as a fraction of the firm’s price. Calculating the GUPPI requires the prices of
both firms, one of the firm’s price-cost margins, and a measure of diversion between the
merging firms under the assumption that firms are competing through price setting. For
example, if Firm 1 with pre-merger price p1is acquiring Firm 2 with pre-merger price p2,
price-cost margins, m2, and diversion from firm 1 to 2, d12, then the GUPPI for Firm 1 can
be calculated as
GUPPI1=(d12)(m2) p2
p1!
While there is no direct link between a particular value of the GUPPI and the magni-
tude of price eects or other quantifications of harm resulting from a horizontal merger, a
larger number indicates a larger incentive to raise price post-merger and has been shown to
be positively correlated with post-merger party prices11. UPP has the benefit of potentially
allowing comparisons to a common benchmark, and some practitioners have suggested
a “safe-harbor” level of 5-10%.12 However, each merger can result in a multiplicity of
GUPPI figures. For example, two merging firms each selling 3 products in a single market
results in 6 UPP numbers. There is no theoretical or empirical guidance regarding which
of the resulting numbers to use in evaluating the competitive eects or on how to weigh
dierent results across products or markets.
11See Miller et al. (2017) for further details.
12One example is found in former FTC Commissioner Joshua Wright’s dissenting statement in the Fam-
ily Dollar/Dollar Tree merger. See “Statement of Commissioner Joshua D. Wright Dissenting in Part and
Concurring in Part In the Matter of Dollar Tree, Inc. and Family Dollar Stores, Inc.”, FTC File No.
141-0207, July 13, 2015, https://www.ftc.gov/system/files/documents/public_statements/
681781/150713dollartree-jdwstmt.pdf
9
The main diculty in calculating the GUPPI is obtaining reasonably accurate estimates
of the merging party’s margins, prices and diversions. While margin and price estimates
can often be obtained from accounting data, care must be taken to ensure that the margins
and prices match as closely as possible to the products that are explicitly included in the
merger simulation and the theoretical margins in the model approximated by the GUPPI.
Accurate diversion estimates can also be dicult to obtain. Common sources for diversion
include: party win-loss data, bidding opportunity data, or own- and cross-price elasticities
from published industry or academic studies. Care must be taken to ensure as much as
possible that the diversion estimates reflect losses to a particular product due to that prod-
uct experiencing a relative price increase. Observing that customers switched between the
parties’ products, without knowing the reason for switching is only a proxy for diversion,
and the dierence can have substantial eects on estimates of anticompetitive harm.
2.2.6. Compensating Marginal Cost Reduction
The compensating marginal cost reduction (CMCR) considers the dual problem to
those discussed previously. Instead of asking by how much prices will rise after a merger,
CMCR can be thought of as the proportional reduction in the merging firms’ marginal costs
needed to oset a price increase. CMCR indicates that the merging parties’ will lower
their product prices post-merger if anticipated marginal cost reductions are greater than
what CMCR predicts and raise their product prices post-merger if anticipated marginal
cost reductions are less than what CMCR predicts for all the parties’ products. CMCR
makes no prediction regarding post-merger price eects if some of the parties’ anticipated
cost reductions are above CMCR predictions while others are below CMCR predictions.
CMCR uses the same inputs as the GUPPI and as a result, all the issues with obtaining
accurate estimates for margins, prices, and diversions apply to CMCR as well. However,
CMCR is an exact prediction of the unilateral eects of a horizontal merger - not a first
approximation like UPP. A further benefit of CMCR is that the formula can be derived un-
der various forms of strategic interaction among firms, including Bertrand (Werden (1996)
) and Cournot (Froeb and Werden (1998) ) competition. For a merger between two single-
product firms under Bertrand competition with price-cost margins (mi), prices (pi), and
diversion from firm i to j (dij ), CMCR for Firm 1 is given by
CMCR1=m1d12d21 +m2d12 (p2/p1)
(1 m1)(1 d12d21 ).
2.3. Data Generation
In order to assess the ecacy of the measures in Section 2.2, we use the models de-
scribed in Section 2.1 to simulate the eects of a large number of horizontal mergers
across dierent market conditions. For all simulations, we assume that in the pre-merger
10
state there are N∈ {3,4,5,6,7}single-product firms “inside” the market of interest and
an outside good. We restrict our attention to markets with fewer than 7 firms post-merger
because, given the other assumptions underlying our simulations, mergers in markets with
more firms rarely yield more than a 5% industry-wide price increase and frequently yield
price increases of less than a 1%. We restrict our attention to markets with at lease 3 firms
pre-merger to exclude the case of merger to monopoly.
The firms and the outside good are assumed to interact strategically in the pre-merger
state, but only the inside goods change their prices in the post-merger state. The single-
product firm shares are drawn from a Dirichlet distribution with all Nconcentration pa-
rameters equal to 2.5. Setting the concentration parameters in this fashion yields firm
shares with mean 1/Nand variance equal to N1
2.5N+1. In addition, we assume that in ev-
ery simulated market, the outside firm’s product costs $6 and that the outside firm earns
a margin of $2. Finally, the outside firm’s share is drawn from a Uniform Distribution
restricted to be between 0.1 and 0.7.13 We then use the pre-merger first-order condition
for the outside good as well as the the specified demand system to calibrate the model’s
demand parameters.
For Cournot, these assumptions are also sucient to identify plant-specific cost pa-
rameters. For, Bertrand and the second score auction, however, these assumptions are not
sucient to separately identify firm marginal costs and prices. To remedy this, we assume
for the Bertrand and Auction models that marginal costs are equal to $2 for all firms14.
We simulate 50,000 markets for each demand-supply model specification described in
Section 2.1. For each market, a horizontal merger is created by randomly assigning two
firms as the merging parties. Among these two firms, the one with the largest market share
is designated as the acquirer and the other as the target firm. In all our models, a horizontal
merger is represented as an ownership change, with the merging parties’ products (or
plants) placed under common control.
Next we test that each simulated market meets the criteria to be both a valid antitrust
market, using the Hypothetical Monopolist Test (HMT) at the 5% level, and to require
pre-merger notification under the Hart-Scott-Rodino Antitrust Improvements Act of 1976,
referred to subsequently as an HSR filing. In the context of our numerical simulations, the
13We chose this range in order to to determine how sensitive merger eects are to the attractiveness of the
outside good. We limit the range of outside shares to [0.1, 0.7] because our parameter calibration strategies
rely heavily on the value of the outside share, and outside shares beyond this range tended to yield more
markets with implausible model parameters (i.e. negative marginal costs for Cournot) or implausibly large
price eects.
14Doing so guarantees that all firm prices and marginal costs are positive and that firms’ pre-merger prices
are not too close to zero, thereby preventing price changes expressed as a percentage of pre-merger prices
from becoming explosively large.
11
HMT identifies markets that do not contain all the alternatives consumers would plausibly
view as substitutes to products included in the market. Both the FTC and DOJ use this
test to evaluate whether a set of products constitutes a relevant antitrust market.15 This
test is important because all of the indicia discussed here are calculated using data from
firms included in the market, and if the market does not contain all plausible alternatives,
the indicia are more likely to incorrectly identify a merger as anti-competitive when it is
not. More than 6% of the simulated markets failed the HMT at the 5% level and were
excluded.16
As of 2018, an HSR filing is required if one party has annual revenues of at least 168.8
million USD and the other has revenues of at least 16.9 million USD.17 To implement this
restriction we assign the acquiring firm the HSR threshold of 168.8 million USD. Doing
so implies both a total market size and the revenues of the target firm. If the revenues of
the target firm are greater than or equal to 16.9 million USD, we assume that the merger
meets the HSR filing requirements. About one-quarter of the simulated markets failed
the notification thresholds and were excluded. Eliminating markets that do not meet both
the HMT and HSR criteria results in approximately 222,000 simulated HSR reportable,
antitrust markets. Henceforth, this set is referred to as the ‘sample markets’. Restricting
our sample in this way allows us to focus on the performance of indicia in the set of
markets that would be relevant to antitrust enforcement authorities.
Table 1 summarizes market revenue, elasticity, and share of the outside goods for the
sample markets at the 5th, 25th, 50th, 75th, and 95th percentiles. Market revenues are re-
ported in millions of US dollars. The share of the outside good is reported as a percentage.
This table reveals that our numerical simulations represent a diverse set of markets with
annual market revenues typically between $300 million and $2.8 billion, the distribution
of outside shares appearing roughly uniformly distributed between 0.1 and 0.7, and market
elasticities ranging from very elastic to very inelastic.
Table 2 summarizes the competitive eects implied from the simulated mergers defined
above for the sample markets at the 5th, 25th, 50th, 75th, and 95th percentiles by demand-
supply model. Consumer harm and producer benefit are reported in millions of US dollars.
The sensitivity of the merger simulation results to the assumed demand-supply model
is clearly illustrated with Cournot competition with log demand consistently producing
15U.S. Department of Justice and Federal Trade Commission (2010), p.8-13
16Over 90% of markets that failed the HMT were Cournot with linear demand.
17There are addition requirements for “size of transaction” that consider the value of voting se-
curities and assets of the merging parties. These considerations are outside the scope of the pa-
per. See the FTC’s Pre-merger Notification Program website at https://www.ftc.gov/enforcement/
premerger-notification-program.
12
Table 1: Sample market features
Feature 5% 25% 50% 75% 95%
Market revenues 318 500 741 1,171 2,762
Outside share 13 24 38 52 66
Market elasticity -5.4 -2.1 -1.3 -0.76 -0.33
the largest competitive eects estimates. Once again, this table shows that the simulated
markets exhibit a wide range of competitive eects with predicted industry and merging
party price changes ranging from approximately zero to 40%.
3. Results
Given the set of sample markets derived from our numerical simulations, we construct
the measures of competitive harm described in Section 2.2. Note that all the measures are
constructed using data from products included in the market. For example the diversion
ratios used for both UPP and CMCR are based on shares from products included in the
market, excluding the share of the outside good. We make this assumption for two rea-
sons. First, it allows for the various measures considered here to be readily compared. For
example, shares used to construct HHI ( both in levels and in changes) are same as the
shares used to construct diversion ratios. This essentially allows us to examine the benefit
that adding an incremental piece of information, such as margins, has in terms of predict-
ing post-merger prices. Second, proponents of UPP have advocated its use as a merger
screening tool in the early stages of an investigation. As investigators are unlikely to have
access to either reasonable estimates of diversion or the share of the outside good early on
in an investigation, using diversion according to inside share is likely to be the best proxy
available for actual diversion when a screening tool is the most useful.
Table 3 presents summary statistics for the indicia. The range of values for Firm Count,
Party Rank, Party Share, and HHI arise largely by construction from the data generating
process described above. The distribution of these values for the 5th, 25th, 50th, 75th, and
95th percentiles are reported along with those for HHI, UPP, and CMCR.
There is significant positive correlation between all pairs of measures, as shown by the
correlation matrix in Table 4, which is unsurprising due to the fact that all the measures
to some degree rely on market shares. The correlations provide some quantification of
the potential for combinations of indicia to provide additional information in the merger
screening process. For example, if the merging parties’ combined share is known then
little additional information is gained by calculating the change in HHI resulting from the
merger (correlation is 0.96 between the measures), but also knowing the upward pricing
pressure could add valuable information if UPP does a good job of screening for unilateral
13
Table 2: Sample market outcomes, by model
Outcome Supply Demand 5% 25% 50% 75% 95%
Log 8.1 23 53 142 601Cournot
Linear 4.3 13 31 72 235
Aids 1.4 4.4 10 23 88
Logit 2.3 5.6 10 18 37
Bertrand
Ces 1.1 2.8 5.9 11 27
Consumer Harm ($)
Auction Logit 1.6 3.8 6.9 12 28
Log 0.6 1.8 4.3 10 41Cournot
Linear 0.29 0.98 2.3 5 13
Aids 0.13 0.56 1.6 4.4 22
Logit 0.2 0.69 1.6 3.4 9.2
Bertrand
Ces 0.19 0.6 1.2 2.8 7.7
Industry Price Change (%)
Auction Logit 0.13 0.47 1.1 2.4 7.5
Log 0.6 1.8 4.3 10 41Cournot
Linear 0.29 0.98 2.3 5 13
Aids 0.42 1.3 3 6.9 29
Logit 0.96 2.1 3.8 6.5 13
Bertrand
Ces 0.9 1.9 3.1 5.2 11
Merging Party Price Change (%)
Auction Logit 0.71 1.5 2.6 4.6 10
Log 5.9 15 33 86 353Cournot
Linear 3.3 8.8 21 47 148
Aids 0.48 1.7 5 14 50
Logit 0.74 2 4.8 10 23
Bertrand
Ces 1.2 2.7 5.6 13 39
Producer Benefit ($)
Auction Logit 1.6 3.8 6.9 12 28
Table 3: Indicia summary
Index 5% 25% 50% 75% 95%
Firm Count 3 4 5 6 7
Party Share 18 30 41 56 79
Post-Merger HHI 2,002 2,523 3,306 4,693 6,711
HHI Change 120 355 703 1,339 2,762
UPP 1.2 3.4 6.3 11 24
CMCR 1.7 5.7 13 30 119
14
Table 4: Correlations among indicia (Spearman)
Party Share Post-merger HHI HHI Change UPP CMCR
Firm Count 0.69 0.90 0.65 0.56 0.57
Party Share 0.85 0.96 0.78 0.80
Post-merger HHI 0.81 0.67 0.69
HHI Change 0.82 0.81
UPP 0.99
competitive eects (correlation is 0.78). Similarly, if the only measure known is Firm
Count then any indicia other than HHI could provide significant additional information.
However, the question of interest is whether such concentration measures contain su-
cient information to accurately predict harm from unilateral merger eects. This question
is addressed in Figures 2 - 9. Except for Figures 3 and 7, all figures are violin plots that
depict the distribution of simulated industry price changes as a function of the discretized
values of a particular indicia for the 6 dierent model specifications. We chose violin plots
because they do an excellent job at displaying asymmetric distributions. For a particular
discretized value, the horizontal lines in each violin plot depict the 25th, 50th, and 75th
percentile industry price changes. To make these plots more readable, we also chose to
censor the industry price changes at the 5th and 95th percentile across all model specifica-
tions. 18
3.1. Firm Count
Figure 2 depicts the distribution of industry price changes by Firm Count. First and
foremost, the plot reveals that across all models, markets with fewer firms have signifi-
cantly larger average eects on industry-wide prices than markets with more firms. Mar-
kets with fewer firms also have a larger range of plausible price eects than markets with
a larger number of firms. Thus, while the distribution of price eects is positively skewed
for all values (i.e., skewed toward larger industry price eects), the distributions are most
skewed in markets with fewer firms. This result is intuitive since firms have the greatest
potential to exercise market power in concentrated markets.
Relatedly, holding the number of firms constant, skewness appears to decrease as one
moves from the left-most model (Cournot, log-linear demand) to the right-most model
(Auction, Logit demand). This is partially due to the fact that Firm Count contains no
information about substitution to the outside good (i.e. market elasticity). Apparently,
merger eects under Cournot, where the product is homogeneous, are particularly sen-
18Interactive box and whisker plots using the same data may be found at https://daag.shinyapps.
io/ct_shiny/, under Mergers numerical simulations.
15
sitive to the magnitude of market elasticity, even after we exclude markets that do not
pass the Hypothetical Monopolist test at the 5% level. By contrast, merger eects under
dierentiated product regimes are less sensitive to the magnitude of the market elasticity.19
Notice that at the 5 to 4 level (highlighted in orange), representing the implied current
threshold, all model specifications produce mean industry price changes of less than 5%,
and more than 95% of all the simulations have industry-wide price eects less than 10%.
By contrast, the likelihood of a negligible industry price eect (less than 1%) is very small
for a 3 to 2 merger. Additionally, the probability of a negligible eect increases with the
number of pre-merger firms in the market as illustrated by the increasing mass below 1%
in each plot as Firm Count increases in each panel.
Taken together these observations suggest that a significant amount of information
about potential price eects is conveyed by the Firm Count measure. Both the likelihood of
a significant price eect and the predicted size of the eect increase as the number of pre-
merger firms in the market decreases. However, the measure also becomes increasingly
noisy as the number of firms decreases. This is consistent with the observations in Section
2.2.1 of factors that could substantially vary competitive conditions between markets with
the same number of firms.
3.2. Party Rank
Figure 3 displays a heat map summarizing the relationship between each of the merg-
ing parties’ size rank, as measured by market share, and median industry price changes,
with darker blue shading corresponding to larger price eects. These plots reveal that
that under the models considered the largest price eects typically occur when firms are
closely ranked. For example, in the Cournot model with log-linear demand, the largest
median price eects occur when the merging parties are ranked 2nd and 3rd, while some
of the smallest price eects occur when one party is ranked 1st and the other is ranked 7th
in terms of size. Notice, however, that while markets where the merging parties are ranked
sequentially typically have the largest price eects, the magnitude of the price eects tend
to decrease as the rankings of both parties increase. For example, the median price eects
are typically larger when the parties are ranked 2nd and 3rd than when they are ranked
4th and 5th. These results are intuitive for largely algebraic reasons since the greatest
gain in combined market share, and thus concentration, occurs when firms are similar in
size. Finally, notice that the rate at which these merger eects decay appears to vary across
19To see this more formally, note the Cournot first order condition in A.1 shows that the Cournot equi-
librium price is determined by weighted average equilibrium margins, the Herfindahl-Hirschman Index and
the equilibrium market elasticity. Hence, knowing the Herfindahl-Hirschman Index, which we have shown
is related to Firm Count, is insucient to identify equilibrium price levels.
16
models, with the left-most model (Cournot,log-linear) exhibiting the slowest rate of decay,
and the right-most model (Auction, Logit) suggesting the fastest rate of decay.
3.3. Party Share
Figure 4 displays the relationship between the pre-merger combined share of the merg-
ing parties and industry price changes. Highlighted in orange is the 30% threshold, which
has been historically identified as the threshold for establishing that a merger is presump-
tively anti-competitive. Similar to the “Firm Count” measure, we see that while median
price eects from the simulated mergers increase as party combined shares increase, so
does the plausible range of price eects. Critically, at the 30% threshold, notice that across
all the models, approximately 95% or more of the simulated markets experience less than
a 5% price eect, and half of all markets experience less than a 2% price eect. This
suggests that, if used alone, this threshold would lead to investigating a large number of
mergers with very small predicted price eects as compared to merger simulation results.
3.4. HHI
Figure 5 presents the distribution of estimated industry price changes by the level of
the post-merger HHI for each model. Across all models, both the level and the variance of
the quantiles of the estimated industry price changes increase with the change post-merger
HHI. However, it is apparent that the choice of model matters with the greatest variance in
the eects exhibited by the model with Cournot supply and log demand. In contrast, the
Logit demand model - the workhorse model for merger simulation - exhibits significantly
less variation in price eects in both the Bertrand and auction supply settings. Figure 5 also
illustrates that all models produce significantly larger price eects in a small fraction of
the simulated markets with price eects at the 95th percentile generally more than double
the median value.
The results are nearly identical in Figure 6, which presents the distribution of estimated
industry price changes by the change in HHI (HHI). However, the change in HHI has an
additional benefit, as the change in the HHI has a stronger negative correlation with a neg-
ligible price eect. This makes the change in HHI more useful as a screening metric since
it is likely to lead to fewer investigations of mergers that would not prompt an enforcement
action.
However, the HMG categorizes mergers by the combination of the level and change in
industry concentration. Figure 7 investigates whether there is an informative relationship
between pre-merger HHI and post-merger change in HHI across models as illustrated by
a heatmap. While Figure 7 shows price eects are more likely as both measures increase,
significant eects are only predicted on average at very high values. Thus, there is no
relationship between the two measures to clearly inform merger enforcement decisions.
17
3.5. UPP
Figure 8 displays the relationship between UPP and industry-wide price changes across
models. Before discussing these results, it is important to reiterate that UPP is at best
able to predict the amount by which the merging parties’ prices would increase, and is
therefore not explicitly designed to predict industry-wide price eects. With this caveat
in mind, Figure 8 confirms previous findings that UPP’s predictive power substantially
degrades as demand curvature increases. The predictions exhibiting the greatest varia-
tion in price eects are given by the Cournot-log and Bertrand-Aids specification, which
have substantial curvature. With the exception of Cournot-log and Bertrand-AIDS speci-
fications, UPP tends to over-predict merging party price eects and industry price eects
from a merger. For example, even in the Cournot model with linear demand, where UPP
performs generally well, industry price changes in the [8,10) interval are below 7% for
more than three-quarters of simulated markets, and for the Bertrand-Logit and Auction
models are almost never above 5%.
In general, we find that UPP typically over-states industry-wide price eects by any-
where from about 65% (25th percentile) to 537% (75th percentile), with UPP overstating
the industry-wide price eects for the median market by by 255%. We also find that UPP
typically over-states the merging party price eects by anywhere from about 36% (25th
percentile) to 185% (75th percentile), with UPP overstating the party eects for the median
market by 91%. These results were calculated using a diversion measure that excluded the
outside good, thereby overstating the degree to which the merging parties’ products are
substitutes. When we examine the relationship between UPP calculated with actual diver-
sion, we find that that gap between industry price change and UPP is typically between
-220% (UPP overstates the eect) and 3% (UPP understates the eect), with UPP overstat-
ing the industry-wide price eects for the median market by 145%. We also find that that
gap between merging party price changes and UPP is typically between -24% and 22%,
with UPP overstating the party price eects for the median market by about 8%.
3.6. Bertrand CMCR
Figure 9 displays the relationship between the CMCR, derived under Bertrand com-
petition, and industry-wide price changes across demand-supply models. As with the
other indicia, CMCR does have some predictive power. Like UPP, CMCR tends to over-
predict industry-wide price eects and models with substantial demand curvature exhibit
the largest increases in price dispersion. For the Bertrand model with Logit demand, where
one might expect CMCR to perform well, industry price changes in the highest reported
bin, 50-60%, are never above 10%.
In general, we find that CMCR is typically anywhere from 3.8 times (25th percentile)
to 15.4 times (75th percentile) larger than the industry-wide price eects, with CMCR
18
about 9.1 times larger than the industry-wide price eect for the median market. We also
find that CMCR is typically anywhere from about 2.5 times (25th percentile) to 6.5 (75th
percentile) larger than the merging party price eects, with CMCR about 4 times larger
than the party eects for the median market. As with UPP, these results were calculated
using a diversion measure that excluded the outside good, thereby overstating the degree
to which the merging parties’ products are substitutes. When we examine the relationship
between CMCR calculated with actual diversion, we find that CMCR is typically anywhere
from 1.5 times (25th percentile) to 6.7 times (75th percentile) larger than the industry-wide
price eects, with CMCR about 3.9 times larger than the industry-wide price eect for the
median market. We also find that CMCR is typically anywhere from about 1.25 times
(25th percentile) to 2.9 (75th percentile) larger than the merging party price eects, with
CMCR about 1.7 times larger than the party eects for the median market.
4. Optimal screening rules for investigating horizontal mergers
In this section, we develop two “optimal” decision rules for determining whether to
investigate a horizontal merger based on the measures of competitive harm previously
analyzed. It is important to emphasize that all of the rules discussed hinge on two impor-
tant assumptions: 1) the data generating process underlying the population of horizontal
mergers considered, and 2) the behavioral model for weighing the costs and benefits of a
particular decision rule. Initially, we will assume that the population of potential mergers
consists of the markets in our numerical experiments. In other words, we will assume that
all horizontal mergers can be described by the data generating process described in Section
2.3. Later, we will relax this assumption and consider how changing the composition of
models aects the decision rules.
It is important to stress that the behavioral models we consider here are relatively sim-
ple heuristics designed to weigh the harm from not pursuing a potentially anti-competitive
merger against the benefit from not investigating relatively benign mergers with both mea-
sures construed very narrowly. Neither behavioral model analyzed takes into account the
wealth of other considerations that antitrust enforcement agencies might also incorporate.
4.1. Type I/Type II error analysis
Suppose that the agencies are interested in investigating horizontal mergers that yield
substantial harm to consumers but are also interested in not investigating horizontal merg-
ers that are unlikely to yield substantial harm. Further, suppose that thresholds for deter-
mining what constitutes substantial harm are well defined.
Formally, Let VHdenote the average benefit an agency receives from investigating a
harmful merger and VSdenote the average cost an agency incurs from investigating an
19
innocuous merger. Further, suppose that a merger is considered harmful if it is expected to
increase average industry prices, p, by at least pHpercent, while a merger is considered
innocuous if it expected to increase pby no more than pS. Then, for a given index I
agencies choose threshold DIto maximize the ex ante net benefit from investigating future
mergers:
max
DI
VHPr(ppH|DI)VSPr(p<pS|DI).
For continuous decision rules, taking the derivative of the above w.r.t to DIand re-
arranging yields:
VH
VS
=
dPr(p<pS|DI)
dDI
dPr(ppH|DI)
dDI
,(1)
VH
VSrepresents how enforcement agencies value preventing anti-competitive mergers
relative to not investigating benign mergers, which we will refer to as the “enforcement
ratio”. Here we explore two cases. First, we consider the case when VH
VS=1. In this
case, agencies place equal weight on these two outcomes and consequently the thresholds
are only a function of the relative incidence of harmful and benign mergers. Second, we
consider the case when VH
VS=11, which is the value at which the Party Share and Post-
merger HHI decision thresholds predicted by this model closely match the 30% combined
share threshold articulated by the U.S. Supreme Court in United states v. Philadelphia
National Bank and the 2,500 post-merger HHI threshold articulated in the 2010 HMG.
This value of the enforcement ratio would suggest that agencies put much greater weight
on preventing potentially harmful mergers than on investigating benign ones.
In determining the optimal screening thresholds, we assume that any horizontal merger
that yields at least a 5% industry-wide price increase is anti-competitive, while any hori-
zontal merger yielding no more than a 1% industry-wide price increase is benign.20 Figure
10 displays the cumulative proportion of simulated markets for a given value of an index
that have 1) more than a 5% price eect (solid dark blue) and 2) less than a 1% price eect
(solid light blue). The green (dot-dashed) vertical line displays the most current threshold
for each index (if available). For example, the 30% “Party Share” rule occurs about where
the 5% and 1% thresholds cross near the maximum of the 5% rule, indicating that under
20We also experimented with a 10%/5% threshold and found that at those values no threshold existed for
most of the measures.
20
Table 5: Optimal thresholds,by model
Model Indicia Current Optimum Value Variance
Firm Count 5 6 1.9 17
Party Share 30 32 2.1 9.5
HHI 2,500 2,508 2 8.4
HHI Change 200 456 2.1 7.2
UPP 4.5 2.1 3.8
Type I/Type II
CMCR 8.4 2.1 1.7
Firm Count 5 5 92,043,644 42
Party Share 30 39 92,047,832 9.5
HHI 2,500 2,998 92,045,696 23
HHI Change 200 649 92,048,516 19
UPP 6.9 92,049,158 8.3
Agency
CMCR 14 92,049,315 6.8
our modelling assumptions, the 30% rule ensures that all harmful mergers are investigated
while about half of all benign mergers are also investigated. By contrast, the 200 point
“HHI Rule” also investigates all the harmful mergers, but also investigates almost 70% of
all benign mergers.
The pink (dashed) vertical line displays the optimal decision rule for each index under
the assumption that VH
VS=11 , so the agencies value preventing merger harm 11 times more
than not investigating benign matters. As this relative valuation was obtained by matching
the predicted thresholds to the observed thresholds for Party Share and Post-merger HHI,
it is unsurprising that those thresholds match so closely. Interestingly, however, the Firm
Count threshold is predicted to be 6, which is greater than the threshold of 5 that is inferred
from the HHI level with symmetric firms. Likewise, the HHI Change threshold is greater
than 400, more than twice the magnitude of the current 200 threshold. Also of interest are
the UPP and CMCR thresholds, which are about 5% and 9%, respectively, and in line with
proposed “safe-harbor” values in the literature. The red (dotted) vertical line displays the
optimal decision rule for each index under the assumption thatVH
VS=1 , indicating agen-
cies value preventing merger harm the same as investigating benign matters. Under this
assumption, the optimal thresholds are uniformly and substantially larger in magnitude.
The top half of Table 5 depicts the current rule (if available), the optimal rule, the
value of the objective function at the optimum, and the variance of industry-wide prices
in a neighborhood around the optimal decision rules when VH
VS=11. All the thresholds
that maximize the Type I/Type II decision rule are greater than the existing thresholds,
although the optimal values for Firm Count, Party Share and post-merger HHI are quite
similar under these assumptions. Further, note that the variance of industry-wide prices
changes around the optimum varies across the indices, with Firm Count having the largest
21
variance and CMCR the lowest.
4.2. Antitrust Agency Cost-Benefit Analysis
While a useful starting point for exploring optimal decision rules, the Type I/Type II
error framework suers from a two main drawbacks. First, this framework does not reflect
any of the resource constraints that agencies typically operate under. While agencies do
have substantial budgets, they are also tasked with evaluating a large and growing number
of mergers each year. For example, the DOJ Antitrust Division’s budget increased by
about 12% from $148 million in 2008 to $165 million in 2017, while the number of HSR
filings the Division received during that period increased by about 19% from 1,726 filings
in 2008 to 2,057 in 2017. These numbers suggest that the Division has fewer resources to
spend per HSR filing.
Second, by focusing only on the percentage change in industry prices, the above frame-
work ignores the fact that some mergers can have larger adverse eects because they oc-
cur in larger markets. For example, the above framework treats a 1% industry-wide price
increase in a $1 billion dollar market as being benign while a 5% industry-wide price in-
crease in a $100 million dollar market as being anti-competitive, even though the first mar-
ket yields roughly $10 million of harm per year while the second market yields roughly $5
million. Here we develop screening thresholds that are more closely based on the amount
of harm from a merger as well as the costs associated with investigating a merger.
Suppose in each year t, firms file NtHart-Scott-Rodino notices to merge with an en-
forcement agency. Further, suppose that when the agency is determining whether to open
investigations, they weigh the expected benefit from opening an investigation into a merger
against the costs associated with investigating the merger. We begin by identifying an op-
timal decision rule for determining whether to investigate a merger based on the change in
the HHI.
Formally, suppose that candidate decision rule DIbased on index I, the expected net
benefit to the agency is
E[NBt|DI]=
X
n=1
E[NBt|DI,N(t)=n]eλt(λt)n
n!(2)
E[NBt|DI,N(t)=n]=E[
d(n)
X
j=1Hjj
κeρSj|DI] (3)
where Hjis the harm from the jth merger, ρis the discount rate, Sjis is the arrival
time of notice n,j
κis the incremental cost associated with investigating a merger, and the
agency chooses to further investigate any merger with a change in index Igreater than
22
DI. Since the number of Hart-Scott-Rodino filings varies from year to year, we suppose
that N(t) follows a Poisson distribution with rate λ. Assuming that the size of the merging
parties is independent from when Hart-Scott-Rodino is filed, it can be shown that equation
(2) reduces to
E[NBt|DI]=2κE[DIHn]λPr(I>DI)(λtPr(I>DI)+2)
2κρ λ(1 eρt) (4)
where E[DIHn] is the expected amount of harm from a merger when the agency
chooses to investigate it further under rule DI. Hence, an optimal decision threshold D
Iis
one which maximizes equation (4) for a given indicia I.
To calculate these thresholds, we first assume that the actual distribution of horizontal
mergers corresponds to the data generating process underlying our Monte Carlo simula-
tions. Next, we calibrate κby assuming that the 2017 average variable costs for the DOJ
Antitrust Division are equal to the total number of HSRs received by the Division in 2017,
divided by the Division’s expenditures on HSRs. This is calculated by multiplying the per-
centage of total matters initiated in 2017 that were HSRs by the Division’s 2017 budget.
The value of κis then backed out from the definition of average variable costs.
Figure 11 summarizes the results. The black curve depicts agency expected net benefit
for a given threshold using (2). The green vertical line displays the current threshold, if
available. The pink vertical line displays the threshold that maximizes (2). This figure
depicts some interesting features of the optimization problem. First, the objective func-
tion achieves its highest values under UPP and CMCR, and its lowest value under Firm
Count, suggesting that at least on average, UPP and CMCR outperform the other indicia.
Second, CMCR has the “flattest” objective function, suggesting that it is the most robust
to relatively small deviations away from the optimum.21
The bottom half of Table 5 depicts the current rule (if available), the optimal rule, the
value of the objective function at the optimum, and the variance of industry-wide prices in
a neighborhood around the optimal decision rules when VH
VS=11. Note that CMCR is the
decision rule that maximizes the Agency decision rule. In addition, note that the variance
of industry-wide price changes varies across the indices, with Firm Count again having
the largest variance and CMCR the lowest.
4.3. Model composition and thresholds
One drawback of the decision rules depicted in Figures 10 and 11 is that they assume
that the underlying population of mergers follows a particular model distribution: 30%
21This is likely due to it’s explicit accounting for higher order eects on prices.
23
Table 6: Thresholds with dierent model weights, VH
VS=11
Cournot Bertrand Auction Firm Count Party Share HHI HHI Change UPP CMCR
0.9 0.05 0.05 7 23 1,856 215 2.1 3.4
0.7 0.1 0.2 7 24 1,986 272 2.4 3.8
0.5 0.3 0.2 7 27 2,144 328 3.2 5.4
0.5 0.1 0.4 7 27 2,154 328 2.6 4.2
0.3 0.5 0.2 7 31 2,403 413 4.2 7.6
0.3 0.3 0.4 6 32 2,446 453 4.2 7.5
0.3 0.1 0.6 6 32 2,499 452 4.2 6.7
0.27 0.55 0.18 6 32 2,508 456 4.5 8.4
0.1 0.7 0.2 5 39 2,914 633 5.7 12
0.1 0.5 0.4 5 39 2,996 648 6.5 15
0.1 0.3 0.6 5 40 3,053 667 8 18
0.1 0.1 0.8 5 42 3,505 676 8.4 21
Cournot, 50% Bertrand, and 20% Auction. Here, we explore how changing the model
composition can aect these thresholds.
Table 6 reports that under the simple model with VH
VS=11, the decision rules for
each indicia vary substantially as the model mix changes. For example, the Firm Count
threshold varies from 5 to 7 pre-merger firms, depending on the mix of competitive models.
The Party Share threshold varies from 23% when Cournot competition characterizes 90%
of markets to 42% when 80% of markets follow the Auction model. Interestingly, the
HHI Change threshold only approaches the current level of 200 when Cournot comprises
90% of markets. Table 6 also illustrates the range of potential UPP and CMCR thresholds
derived under this decision rule, approximately 2-8% and 3-21%, respectively.
Similar patterns occur in Table 7, which reports comparable results for the Agency
model. For example, the Firm Count threshold varies from 4 to 7 firms. The Party Share
threshold varies from 27% to 50%. Interestingly, the post-merger HHI threshold only
approaches the current threshold of 2,500 when Cournot competition characterizes about
50-70% of markets, and the HHI Change threshold never comes close to the current level
of 200. The UPP and CMCR thresholds exhibit a wider range as well at 2-13% and 4-36%,
respectively.
Taken together, these tables yield two observations of interest. First, they suggest that
the current HHI thresholds are best suited to a population of mergers in which industries
engaged in Cournot competition dominate. To the extent that the composition of the pop-
ulation of interest shifts toward firms playing either a Bertrand or Auction game, then
this analysis suggests that the HHI thresholds discussed in the HMG should be revides
accordingly.
Finally, these tables indicate that the Agency model, which includes more informa-
24
Table 7: Thresholds with dierent model weights
Cournot Bertrand Auction Firm Count Party Share HHI HHI Change UPP CMCR
0.9 0.05 0.05 7 27 2,101 315 2.5 4
0.7 0.1 0.2 7 30 2,334 385 3.1 5.1
0.5 0.3 0.2 6 33 2,634 467 4.4 8.3
0.5 0.1 0.4 6 33 2,646 465 4.4 9.3
0.3 0.5 0.2 5 38 3,094 606 6.7 14
0.3 0.3 0.4 5 37 2,932 605 7.4 18
0.3 0.1 0.6 5 39 2,973 630 8.5 22
0.27 0.55 0.18 5 39 2,998 649 6.9 14
0.1 0.7 0.2 4 46 3,776 920 9.3 22
0.1 0.5 0.4 4 47 3,834 969 10 27
0.1 0.3 0.6 4 47 3,854 986 11 31
0.1 0.1 0.8 4 50 3,854 975 13 36
tion regarding Agency caseload and investigative costs than the Simple model, also yields
thresholds that are typically 17% (25th percentile) to 36% higher (75th percentile) than
the simple model, with the median dierence between the models equal to about 29%.22
5. Conclusion
This paper contributes to understanding the relationship between horizontal merger in-
vestigation screening measures and predicted industry price eects from standard merger
simulation models. We find that across a range of common demand and supply speci-
fications all the concentration measures and other indicia of competitive harm correctly
predict when a merger is likely to have little anti-competitive eect (i.e small values of the
indicia are associated with small price eects). However, while large indicia values are as-
sociated with anti-competitive eects, in general these indicia do a poor job of accurately
predicting price eects when they are likely to be large. It is not surprising that simple
screens do a poor job of predicting continuous outcomes since much of the variation is
driven by factors not captured by the measures. Further, when merger eects are large the
outcome is farther away from the pre-merger equilibrium, making out of sample prediction
accuracy poor.
We also consider two optimal decision rules for merger enforcement based on com-
monly used measures of concentration and compare them to current screening thresholds
employed by US antitrust enforcement agencies. We find that in our first framework the
current thresholds suggest a significantly higher value is placed on investigating potentially
22These statistics exclude the “Firm Count” measure.
25
anti-competitive mergers than on avoiding investigating mergers that are unlikely to raise
competitive concerns. In addition, we find that across both frameworks optimal decision
rules depend critically on the mix of competitive models that are believed to exist in the
population of potential mergers. In general, higher thresholds would be warranted under
the belief that the population of potential mergers is largely comprised of firms competing
according to a dierentiated products auction model. In addition, the current thresholds
would be most relevant in a population with the majority of industries engaged in Cournot
competition.
An important implication of our Monte Carlo experiments and the results of the decision-
theoretic models is that measures that include information on substitution to the out-
side good (UPP, CMCR) appear to perform better than those that do not. This reflects
the importance of appropriately defined alternatives to the products at issue in a merger,
which is an under-appreciated driver of merger simulation results. While optimal decision
thresholds can be developed for any competitive screening measure, the resulting decision
thresholds perform better (both on average and in terms of dispersion) using indicia that
incorporate substitution to the outside good.
26
Figure 1: HMG HHI-based decision rule
27
Figure 2: summarizes the relationship between number of pre-merger firms and industry price changes. Highlighted in orange is the 5-4
decision rule implied by the HHI thresholds in the 2010 HMG. Industry price changes are censored at the 5th and 95th percentile. Horizontal
lines within each plot represent the 25th, 50th and 75th percentiles. Interactive box and whisker plots using the same data may be found at
https://daag.shinyapps.io/ct_shiny/, under Mergers numerical simulations.
28
Figure 3: displays a heatmap summarizing the relationship between the share ranks of the merging parties and median industry price
changes.
29
Figure 4: summarizes the relationship between the cod share of the merging parties and simulated industry price changes. Industry
price changes have been censored at the 5th and 95th percentile. Horizontal lines in each plot depict the 25th, 50th and 75th percentiles.
The bin containing combined shares of 30% and 35%, historically identified as thresholds for a presumptively anti-competitive merger,
is colored orange.Interactive box and whisker plots using the same data may be found at https://daag.shinyapps.io/ct_shiny/,
under Mergers numerical simulations.
30
Figure 5: displays violin plots summarizing the relationship between the HHI and simulated industry price changes. Industry price changes
have been censored at the 5th and 95th percentile, and the horizontal lines depicted in each plot represent the 25th, 50th and 75th percentiles.
The bin containing the post-merger HHI of 2500, a component of establishing that a merger is presumptively anti-competitive under the
HMG, is colored orange. Interactive box and whisker plots using the same data may be found at https://daag.shinyapps.io/ct_
shiny/, under Mergers numerical simulations.
31
Figure 6: displays violin plots summarizing the relationship between changes in HHI and simulated industry price changes. Industry
price changes have been censored at the 5th and 95th percentile, and the horizontal lines depicted in each plot represent the 25th, 50th
and 75th percentiles. HHI change of 200, a component of establishing that a merger is presumptively anti-competitive under the HMG,
is colored orange. Interactive box and whisker plots using the same data may be found at https://daag.shinyapps.io/ct_shiny/,
under Mergers numerical simulations.
32
Figure 7: displays a heatmap summarizing the relationship between pre-merger HHI, changes in HHI and median industry price changes.
33
Figure 8: displays violin plots summarizing the relationship between the Upward Pricing Pressure index (UPP) and simulated industry
price changes. Each panel summarizes the results from 50,000 Monte Carlo Simulations. Industry price changes have been censored at the
5th and 95th percentile, and the horizontal lines depicted in each plot represent the 25th, 50th and 75th percentiles. All simulations are run
assuming that the outside good has a price of $6 and $2 marginal costs. Interactive box and whisker plots using the same data may be
found at https://daag.shinyapps.io/ct_shiny/, under Mergers numerical simulations.
34
Figure 9: displays violin plots summarizing the relationship between the compensating marginal cost reduction (CMCR) and simulated
industry price changes. Each panel summarizes the results from 50,000 Monte Carlo Simulations. Industry price changes have been censored
at the 5th and 95th percentile, and the horizontal lines depicted in each plot represent the 25th, 50th and 75th percentiles. All simulations
are run assuming that the outside good has a price of $6 and $2 marginal costs. Interactive box and whisker plots using the same data may
be found at https://daag.shinyapps.io/ct_shiny/, under Mergers numerical simulations.
35
Figure 10: displays the cumulative percentage of markets exhibiting less than a 1% price increase (light blue) or greater than a 5% price
increase (dark blue) for a given level of each indicia. Green (dot-dashed) vertical lines depict the currently used threshold where available.
Pink (dashed) vertical lines depict the threshold that maximizes the gap between the light and dark blue lines, when the enforcement ratio
equals 11. The red (dotted) vertical lines depict the threshold that maximizes the gap between the light and dark blue lines, when the
enforcement ratio equals 1.
36
Figure 11: displays net benefit (harm averted less enforcement costs) to a hypothetical antitrust agency facing linear enforcement costs as
function of each indicia. Green vertical lines depict the current threshold for each (where available). Pink vertical lines depict the threshold
that maximize the agency’s net benefit.
37
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Appendix A Demand and Supply Specifications
A.1 Cournot
Suppose there are N∈ {3,4,5,6,7}firms playing a Cournot quantity setting game,
where single-plant firms with quadratic cost technology Cn(qn)=q2
n
2knsimultaneously pro-
duce qnunits of a homogeneous product once to maximize their profits.
Mathematically, each firm nsolves
max
qn
PqnCn(qn)
with demand equal to
P=
ab1Q,if linear
exp (a)Q1
,if log-linear,
where Q=P
jN
qjdenotes equilibrium output and =dQ
dP
P
Qdenotes the aggregate
elasticity.
Define mn=PdC
dqn
Pas plant n’s proportional margin and sn=qn
Qas plant n’s quantity
share. Pre-merger, the first order condition (FOC) of each firm can be arranged to yield
the Lerner condition mn=sn
, which is an implicit function of all firms quantities. Un-
der quadratic costs, it can be shown that this system of Nequations has a unique Nash
Equilibrium in quantities and that this equilibrium has a closed-form solution.
Moreover, the Lerner condition may be rearranged to yield an equilibrium relationship
between industry average margins, HHI, and market elasticities. Specifically, taking the
share-weighted average of all Nfirms’ Lerner conditions yields
X
nN
snmn=P
nN
s2
n
=HHI
To calibrate the model parameters, we first assume that market size Mis known and
draw Nshares from a Dirichlet distribution. Second, we assume that in the pre-merger
state, the equilibrium price is $6 and there is an outside Firm 0 playing the Cournot game
earning an equilibrium margin of $2 with quantity share s0drawn from a uniform distri-
bution between 0.1 and 0.7. We use Firm 0’s Lerner condition to solve for the aggregate
41
elasticity, and then the assumed price and aggregate output to solve for the remaining de-
mand parameters. Finally, we again use the Lerner condition, quantities and price to solve
for the cost parameters kn23.
Next, suppose that Firm 1 acquires Firm 2. We simulate the eect of the merger by
assuming that Firm 1 sets output on plants 1 and 2 jointly. Mathematically, Firm 1 solves
max
q1,q2
P(q1+q2)C1(q1)C2(q2)
Taking the FOC and rearranging yields
m1=m2=s1+s2
The functional form of the non-merging parties’ Lerner condition does not change as
a result of the merger. The outside product’s output is assumed not to adjust post-merger.
A.2 Bertrand
Suppose there are N∈ {3,4,5,6,7}firms playing a Bertrand price setting game, where
single-product firms with constant marginal cost technology Cn(qn)=cnqnsimultaneously
set their prices pnonce to maximize their profits.
Mathematically, each firm nNsolves
max
pn
(pncn)qn
Like Cournot, the pre-merger first order condition (FOC) of each firm can be arranged
to yield the Lerner condition mn=1
nn , which is an implicit function of all firms prices. In
general, this system of equations has no closed form solution, but a Nash equilibrium in
prices may be solved for numerically.
Moreover, it has been shown that the magnitude of the price eects in the Bertrand
model depends critically on the second order properties of the demand curve. These prop-
erties are captured by the own-price elasticities nn =qn
pn
pn
qn. Specifically, we will consider
the properties of three popular demand systems: Logit, CES, and AIDS
A.2.1 Logit Demand
Logit demand is based on a discrete choice model that assumes that each consumer is
willing to purchase at most a single unit of one product from the Nproducts available in
23From time to time, this procedure yielded plant margins that were greater than 1. When this occurred,
we simply discarded the market and sampled another one.
42
the market. The assumptions underlying Logit demand imply that the probability that a
consumer purchases product nNis given by
sn=exp(Vi)
1+P
kN
exp(Vk)
where snis product n’s quantity share and Vnis the (average) indirect utility that a
consumer receives from purchasing product n. We assume that Vntakes on the following
form
Vn=δn+αpn, α < 0
The Logit demand system yields the following own- and cross-price elasticities:
nn =α(1 si)pi
n j =αsjpj
It is helpful to note that because snis a probability, sn=sn|N(1 s0). sn|Ndenotes the
probability that product nis selected, conditional on one of the Nproducts in the market
being selected. s0denotes the probability that the outside good is selected.
A.2.2 CES Demand
Like the Logit, CES demand is based on a discrete choice model. However, CES
diers from the Logit model in that under CES consumers do not purchase a single unit
of a product but instead spend a fixed proportion of their budget on one of the nproducts
available in the market.24
The assumptions underlying CES demand imply that the probability that a consumer
purchases product nNis given by
24Formally, each consumer chooses the product nNthat yields the maximum utility Un=ln(δnqn)+
αln(q0)+i, subject to the budget constraint y=pnqn+q0. Here, qnis the amount of product nconsumed by
a consumer, δnis a measure of product ns quality, q0is the amount of the numeraire, yis consumer income,
and nare random variables independently and identically distributed according to the Type I Extreme Value
distribution.
43
where rnis product n’s expenditure share and Vnis the (average) indirect utility that a
consumer receives from purchasing product n. We assume that Vntakes on the following
form
Vn=δnp1γ
n, γ > 1
The CES demand system yields the following own- and cross-price elasticities:
nn =γ+(γ1)rn
n j =(γ1)rj
Functional form dierences aside, one important dierence between the CES and Logit
demand systems is that the Logit model’s choice probabilities are expressed in terms of
quantity shares, while the CES model’s choice probabilities are expressed in terms of
expenditure shares.
A.2.3 AIDS
AIDS without income eects assumes that the expenditure share rnfor each product
n∈ {N,0}in the market is given by
rn=αn+X
n∈{N,0}
βn j log( pj) for all n∈ {N,0}, βnn <0,
where rn=pnqn
x. Total expenditure xis given by
log (x)=η+X
jN
αjlog (pj)+X
kNX
jN
βk j log ( pk) log (pj)
The AIDS model yields the following own- and cross-price elasticities:
nn =1+βnn
rn
+rn, nn <0
n j =βn j
rn
+rj, n j 0
This version of the AIDS model assumes that βn j =βj j , satisfies homogeneity of degree
zero in prices, and that diversion occurs according to revenue share djn =rn
1rj=βn j
βj j .
44
... 5 The second approach, which we call the 4 The Gross Upward Pricing Pressure Index or "GUPPI' ' approximates the price effects from a horizontal merger between firms playing a Bertrand Pricing Game (Farrell and Shapiro (2010)). Taragin and Loudermilk (2019) show how the GUPPI-based on the Bertrand model can substantially over or under-predict merger effects, depending upon the true model. 5 This approach, for instance, is the primary implementation in the mergersim Stata package (Björnerstedt and Verboven (2014)). ...
Preprint
Full-text available
How practitioners model competition influences the predicted effects of a merger. We consider three models that are commonly used to evaluate horizontal mergers: Bertrand price setting, second score auction, and Nash bargaining. We first show how these models relate to one another, and specifically that the Bertrand and second score auction models can both be nested within a bargaining framework. Second, we show through numerical simulations how the predicted merger effects vary with model choice. Third, we show that two commonly used strategies for obtaining demand parameters can yield markedly different outcomes across the three models. Finally, we show how model and calibration strategy choices affect the magnitude of predicted harm in the 2012 Bazaarvoice/Power Reviews merger.
Article
We use ADHD drugs sales data from 2000-2003 and compare estimates of elasticities and merger simulations from three different demand models. Models include logit, random coefficients logit, and conditional AIDS demand model with multistage budgeting. The magnitude of cross-price elasticities is larger in the third model in comparison to the first two, and some of the cross-price elasticities are estimated to be negative. Hypothetical merger simulations show larger price effects for the multistage AIDS model in comparison to the discrete choice models.
Article
This article analyzes the accuracy of various prospective hospital merger screening methods used by antitrust agencies and the courts. The predictions of the screening methods calculated with pre-merger data are compared with the actual post-merger price changes of 28 hospital mergers measured relative to controls. The evaluated screening methods include traditional structural measures (e.g., Herfindahl-Hirschman Index), measures derived from hospital competition models (e.g., diversion ratios, willingness-to-pay, and upward pricing pressure), and hospital merger simulation. Willingness-to-pay and upward pricing pressure are found to be more accurate at flagging potentially anticompetitive mergers for further investigation than traditional methods.
Article
We use Monte Carlo experiments to evaluate whether “upward pricing pressure” (UPP) accurately predicts the price effects of mergers, motivated by the observation that UPP is a restricted form of the first order approximation derived in Jaffe and Weyl (2013). Results indicate that UPP is quite accurate with standard log-concave demand systems, but understates price effects if demand exhibits greater convexity. Prediction error does not systematically exceed that of misspecified simulation models, nor is it much greater than that of correctly-specified models simulated with imprecise demand elasticities. The results also support that UPP provides accurate screens for anticompetitive mergers.
Article
The Upward Pricing Pressure (UPP) test is a new merger screen that focuses on price effects instead of concentration changes. This article is one of the first to compare its empirical predictions against that of merger simulations. This is valuable for practitioners and economists alike, because it shows the extent to which a quick screening tool will lead to the same decision as a structural framework for market analysis. I use hypothetical mergers in a big cross-section of airline route markets to assess UPP's sign, rank, and magnitude predictions. In its “best case scenario,” it gives correct sign predictions in 90-percent observations; correct decile predictions in 75-percent observations; and a mean magnitude difference of $17, when compared against merger simulations. I investigate the performance of both the first and second terms of the UPP using different hypothetical mergers. Lastly, I explore whether certain market or product characteristics lead to large discrepancies in the UPP using model selection techniques.
Article
We analyze a large merger in the Swedish market for analgesics (painkillers). The merging firms raised prices by 40 percent, and some outsiders raised prices by more than 10 percent. We confront these changes with predictions from a merger simulation model. With basic supply side assumptions, the models correctly or moderately underpredict the merging firms' price increase. However, they predict a larger price increase for the smaller firm, which was not the case in practice, and they underpredict the outsiders' responses. We consider several supply side explanations: a plausible cost increase after the merger and the possibility of partial collusion.
Article
The upward pricing pressure (UPP) model was introduced in the 2010 revision of the Merger Guidelines, although little insight was offered for how to operationalize an UPP screen. Abstracting from the potential for efficiencies, this article defines an UPP-related benchmark of 15 percent using data from a review of Federal Trade Commission merger challenge decisions. While the historical record highlights the importance of diversion ratios, the other key input into the UPP index, the margin, appears to play little role in the review process. A supplemental analysis of the case-specific evidence associated with unilateral merger review serves to confirm the benchmark results. Moreover, a detailed case study of unilateral-effects analyses identifies a number of application issues that may negate the finding of an UPP-based competitive concern. Thus, careful study should be undertaken before (1) using an UPP index as a merger screen with a benchmark well below 15 percent (diversions well below 30 percent), (2) customizing the UPP calculation for either high or low values of the margin, or (3) using an UPP index to impose a strong presumption of a competitive concern.
Article
Antitrust enforcement agencies and courts use net effect on price as a touchstone for the legality of mergers. This paper derives a simple condition for implementing that standard when industry equilibrium is static Nash in quantities (Cournot), and that condition is robust to different specifications of demand and cost.
Article
This paper evaluates the efficacy of a structural model of oligopoly used for merger review. Using premerger data, we estimate several demand systems and use a static Bertrand model to simulate the price effects of two mergers. Using pre-and postmerger data, we directly estimate the price effects. The direct estimates imply that one merger resulted in moderate price increases, while the second left prices essentially unchanged. While some simulations are similar to the directly estimated price effects, overall simulations overstate the price effects in one case and understate them in the other. Explanations for the discrepancies are explored. © 2013 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.