WORKING 

PAPERS 

The Accuracy of Hospital Merger Screening Methods

Christopher Garmon 

WORKING PAPER NO. 326 

August 2015 

FTC Bureau of Economics working papers are preliminary materials circulated to stimulate discussion 

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 

the Commission itself. Upon request, single copies of the paper will be provided. References in 

publications to FTC Bureau of Economics working papers by FTC economists (other than 

acknowledgment by a writer that he has access to such unpublished materials) should be cleared with the 

author to protect the tentative character of these papers. 

BUREAU OF ECONOMICS 

FEDERAL TRADE COMMISSION 

WASHINGTON, DC 20580
1

The Accuracy of Hospital Merger Screening Methods

Christopher Garmon1

Bureau of Economics

Federal Trade Commission

Draft: August 2015

Abstract: This paper analyzes the accuracy of various prospective hospital merger screening

methods used by antitrust agencies and the courts. The qualitative and quantitative predictions

of the screening methods calculated with pre‐merger data are compared with the actual post‐

merger price changes of 26 hospital mergers measured relative to controls. The evaluated

screening methods include traditional structural measures (e.g., Herfindahl‐Hirschman Index

associated with various market definitions), measures derived from hospital competition

models (e.g., diversion ratios, Willingness‐to‐Pay, and the Logit Competition Index), and

hospital merger simulation.  Diversion ratios, Willingness‐to‐Pay, and the Logit Competition

Index are found to be more accurate at predicting post‐merger price effects than traditional

methods.  

                                                      

1 The views expressed in this paper are mine and not necessarily those of the Commission or any individual

Commissioner.  I thank Keith Brand, David Schmidt, Dan Hosken, Sean May, Michael Vita and participants of the

International Industrial Organization Conference and FTC Microeconomics Conference for their suggestions and

Michael Bohne, Chris Carman, Laura Kmitch, and Jordan Rhodes for their research assistance.
2

1. Introduction

The hospital industry is one of the largest and most dynamic sectors in the United States

economy.  In 2012, hospital services accounted for 5.4 percent of U.S. GDP, more than any

other category of health expenditure.2

  A large fraction of U.S. hospital expenditures (40

percent) are financed with private health insurance or patient out‐of‐pocket payments.  In

recent years, the growth of privately‐financed hospital expenditures has been driven almost

entirely by hospital price increases.3

  In most states, hospital prices charged to private health

insurance companies are unregulated and determined by negotiations between hospitals and

health insurance companies.  The negotiated prices are determined in large part by local

competitive conditions and the ability of health insurance companies to substitute with

competing hospitals in their managed care networks.  Hospital antitrust enforcement plays a

significant role in U.S. health care cost containment by preserving hospital competition and

limiting hospital price growth, while also promoting quality and access to health care.  

Over the past twenty years, hospital antitrust enforcement has undergone a

transformation. Between 1993 and 2000, during the largest hospital merger wave in U.S.

history, federal and state antitrust authorities challenged eight proposed hospital mergers in

federal court and failed in each attempt.  This string of setbacks led to an explosion of research

on hospital competition and the effects of hospital mergers. One branch of the literature

retrospectively studied the effects of past hospital mergers and found that the tools and

assumptions upon which courts relied during the 1990s often led to incorrect conclusions about

the likely effects of hospital mergers.  Another branch of the literature attempted to model

price formation in hospital markets and developed a set of tools to directly predict the price

effects of hospital mergers. These tools (e.g., diversion ratios, Willingness‐to‐Pay, the Logit

Competition Index, and merger simulation) were used by the federal antitrust agencies in

recent hospital merger challenges and, unlike the 1990s, most of these challenges have been

successful.  

With the recent use of the new hospital merger screening tools in antitrust

enforcement, it is important to evaluate their accuracy in predicting post‐merger price changes.  

The original papers that developed the screening tools did not assess the accuracy of their

predictions against actual post‐merger outcomes.  This paper offers the first comprehensive

comparison of the predictions of a wide range of screening tools against the actual post‐merger

price changes of a relatively large sample of hospital mergers.  The actual post‐merger price

changes (measured relative to controls) of 26 hospital mergers are compared to the qualitative

(and, in some cases, quantitative) predictions of various screening methods.  The screening

methods include diversion ratios, Willingness‐to‐Pay (WTP), WTP‐based merger simulation, the

                                                      

2 Centers for Medicare & Medicaid Services, Historical National Health Expenditure Data,

http://www.cms.gov/Research‐Statistics‐Data‐and‐Systems/Statistics‐Trends‐and‐

Reports/NationalHealthExpendData/NationalHealthAccountsHistorical.html (accessed on 3/11/2014) 3 2012 Health Care Cost and Utilization Report, Health Care Cost Institute, http://www.healthcostinstitute.org

(accessed on 3/11/2014)
3

Logit Competition Index (LOCI) and the traditional Herfendahl‐Hirschman Index (HHI) calculated

with various market definitions and market share measures.

The focus of the analysis is on evaluating methods that can be implemented with data

that are likely available to regulators during the initial preliminary investigation of a merger.  It

is at this stage that delineating between possible anti‐competitive mergers and beneficial or

innocuous mergers is most useful and imposes the least regulatory cost.  While a full phase

investigation can provide the regulator with detailed data and other evidence to increase the

precision of its estimates, a full phase investigation imposes significant costs on the merging

parties and the regulator.  The ideal screen for an initial investigation avoids “casting a wide

net” and instead focuses the regulator on the mergers most likely to be anti‐competitive.  All of

the screening methods evaluated in this paper can be calculated with data that is often

available without a full phase investigation: patient discharge data and other public data sets

(e.g., HCRIS and AHA data). It is important to note that this excludes merger simulations

calibrated with health insurance claims data, as described in Brand and Balan (2013) and Brand

and Garmon (2014). This paper only evaluates merger simulations calibrated with less‐detailed

hospital and discharge data.

Any evaluation of merger screening methods is complicated by active antitrust

enforcement.  Post‐merger price effects are inherently noisy as hospital mergers are associated

with many changes (e.g., cost changes, management changes, etc.) apart from reductions in

competition.  In an era of active and effective hospital antitrust enforcement, most mergers

that are likely to be anti‐competitive on balance are blocked or never proposed.  Thus, a sample

of consummated mergers taken from a period of active antitrust enforcement may be

truncated and biased toward mergers with limited reductions in competition and significant

pro‐competitive effects (e.g., cost savings) (See Carlton (2009)).  To address this issue, our

sample of consummated hospital mergers includes 10 mergers in North Carolina that occurred

between 1997 and 2001.  This period was at the tail end of the federal and state hospital

antitrust losing streak and before the successful hospital merger challenges of recent years.  In

addition, North Carolina introduced a hospital Certificate of Public Advantage (COPA) regulatory

program in 1995 that gave merging hospitals participating in the program antitrust immunity.  

Only one pair of merging hospitals participated in North Carolina’s COPA program,4 but the

option to participate, coupled with recent court rulings favoring hospital mergers, likely

contributed to an environment in which competing hospitals felt safe to merge with less risk of

an antitrust challenge.

Analyzing hospital mergers from North Carolina in the late 1990’s and early 2000’s may

lessen the truncation problems caused by antitrust enforcement.  However, the hospital

industry has undergone many changes since the early 2000’s, potentially limiting the

                                                      

4 In December 1995, Memorial Mission Hospital and St. Joseph’s Hospital—the only two short‐term, general acute

care hospitals in Asheville, NC—entered into a joint management agreement to form Mission Health and

simultaneously entered into a COPA agreement with the state of North Carolina, granting the merger antitrust

immunity in exchange for regulation of Mission Health by the state. This merger is not included in the sample of

hospital mergers analyzed in this paper.  
4

applicability of findings from that period.  Some have argued that methods used in hospital

merger review and enforcement should evolve and account for the changes in health care

delivery and finance that have occurred since the passage of the Affordable Care Act. (Guerin‐

Calvert, Maki, and Vladeck (2015))  To address these concerns and test the accuracy of hospital

merger screens in this potentially new regime, our sample of hospital mergers also includes 16

recent transactions from 2007‐2012.

The comparison of the actual post‐merger price changes against the pre‐merger

predictions of the screening tools reveals that, apart from merger simulation, the new

screening tools (i.e., diversion ratios, WTP, and LOCI) are more accurate than traditional

concentration measures at flagging potentially anti‐competitive hospital mergers for further

review.  However, the relationship between the new screening tools and post‐merger price

changes is not precise or robust to alternate specifications, so care should be taken when using

the tools to screen mergers for further investigation.  Merger simulation performs poorly, but

this may be due to the limited data available to calibrate the simulation in the initial

investigation.  Finally, all of the traditional concentration measures tested are inaccurate at

predicting post‐merger price changes.

The paper is arranged as follows.  Section 2 reviews hospital antitrust enforcement over

the past 20 years and the hospital competition literature that developed alongside it.  Section 3

describes the evaluated new screening tools and traditional concentration measures in detail.  

Section 4 describes the data, the criteria for merger selection, price measurement and price

change estimation, and the construction/estimation of the screening tools.  Section 5 compares

the screening tools to the post‐merger price changes and Section 6 concludes.  

   

2. Literature and Case Review

Starting with the FTC’s failed attempt in 1994 to block the merger of the only two

hospitals in Ukiah, California, the federal and state antitrust authorities unsuccessfully

challenged eight hospital mergers between 1994 and 2001. (Ashenfelter et al. (2011)) In six of

the eight challenges, the courts found that the proposed merger was unlikely to reduce

competition significantly because of the presence of numerous remaining competitors. These

determinations were based on the courts’ acceptance of relatively large geographic antitrust

markets established using the Elzinga‐Hogarty (EH) test (Elzinga and Hogarty (1973)) and Critical

Loss Analysis.  

The EH test posits that the relevant geographic market for antitrust analysis is the area

for which inflows (i.e., sales by firms in the area to customers from outside the area) and

outflows (i.e., sales by firms outside the area to customers living in the area) are sufficiently

small.  The two most common EH inflow/outflow thresholds used for market definition are 25

percent (a “weak” EH market, i.e., if the inflows into and outflows from an area are both less

than 25 percent) and 10 percent (a “strong” EH market).  Operationally, to determine an EH

market for a particular merger, one would first find the smallest area from which the merging
5

firms, and other nearby firms, draw 75 percent (or 90 percent for the “strong” standard) of

their customers.  If more than 25 percent (or 10 percent) of the customers who live in this area

go outside to purchase the good, areas are added to the base draw area until the inflows and

outflows are both below 25 (or 10) percent.

Critical Loss Analysis (CLA) is another related method for defining geographic markets in

hospital merger challenges using patient flows.  CLA calculates the loss of patients above which

a small price increase (e.g., 5 percent) would be unprofitable for a hypothetical owner of all of

the hospitals in an area (i.e., the “critical loss”).  If estimates of the actual loss in response to

the price increase exceed the critical loss, adjacent areas and hospitals are added to the market

until the estimated actual loss no longer exceeds the critical loss.

Although the EH algorithm and CLA do not necessarily produce a unique area, the

ubiquity of patient discharge data and the relative ease with which EH/CLA markets can be

calculated with patient discharge data made the EH and CLA methods widespread in hospital

merger challenges in the 1990s.  However, as became apparent in the hospital merger

challenges of the 1990s, the EH test and CLA often produce extremely large geographic hospital

markets, particularly when the “strong” 10 percent criterion is applied in the EH test.  In urban

areas, the weak EH criterion will almost always result in a geographic market encompassing the

entire metropolitan area and the strong criterion will often produce a market larger than the

metropolitan area.  For example, in overturning a lower court’s ruling that the merger of the

only two hospitals in Poplar Bluff, Missouri would be anticompetitive, the 8th Circuit U.S. Court

of Appeals found that the relevant market included competing hospitals in Cape Girardeau (85

miles away from Poplar Bluff) and St. Louis (150 miles away) because significant numbers of

patients in the merging parties’ service area sought treatment in Cape Girardeau and St. Louis.  

Echoing the defendants’ CLA arguments, the 8th Circuit U.S. Court of Appeals concluded that

“the compelling and essentially unrefuted evidence that the switch to another provider by a

small percentage of patients would constrain a price increase, shows that the FTC's proposed

market is too narrow.”5

In two of the eight unsuccessful hospital merger challenges in the 1990s, the merging

parties argued—and the courts agreed—that the merging parties would not exercise any

additional market power obtained through the merger because they were non‐profit hospitals.

Together, the courts’ use of large EH/CLA‐inspired geographic markets and its limited

acceptance of the merging parties’ non‐profit defense prevented federal and state antitrust

authorities from enjoining proposed hospital mergers they felt were anti‐competitive.  This

spurred health economists to study the effects of hospital competition.  Starting in the mid‐

1990s, a large hospital competition literature developed along two tracks.  In the first track,

economists empirically measured the cross‐sectional relationship between hospital competition

and outcomes (both price and quality) and retrospectively analyzed past hospital mergers to

                                                      

5 United States Court of Appeals, Eighth Circuit. FEDERAL TRADE COMMISSION; State of Missouri,

by and through its Attorney General, Jeremiah W. (Jay) Nixon, v. TENET HEALTH CARE CORPORATION; Poplar Bluff

Physicians Group, Inc., doing business as Doctors Regional Medical Center; 186 F.3d 1045
6

study their effects.  Vogt and Town (2006) summarize this literature and conclude regarding

price that “the great weight of the literature shows that hospital consolidation leads to price

increases, although a few studies reach the opposite conclusion.  Studies that examine

consolidation among hospitals that are geographically close to one another consistently find

that consolidation leads to price increases of 40 percent or more.”  Summarizing the literature

on hospital competition and quality Vogt and Town conclude that “on balance, the evidence

suggests that increasing hospital concentration lowers quality.”  Further, most analyses of

hospital competition found a positive correlation between concentration and price even among

non‐profit hospitals.  In addition, numerous retrospective studies of mergers of competing non‐

profit hospitals found significant post‐merger price increases, casting doubt on the argument

that non‐profit hospitals do not exercise post‐merger market power. (Vita and Sacher (2001),

Haas‐Wilson and Garmon (2011), Tenn (2011))

While the cross‐sectional and retrospective hospital competition literature severely

undermined the logic behind the courts’ rulings in the 1990s, it did not provide tools to replace

the EH test and CLA.  In the second track of the new hospital competition literature, economists

modelled hospital markets and developed new screening methods for hospital mergers.  Town

and Vistnes (2001) and Capps, Dranove, and Satterthwaite (2003) developed a new market

power measure for hospitals—commonly referred to as Willingness‐to‐Pay (WTP)—from a

bargaining model of the negotiation between health insurance companies and hospitals.  

Gaynor and Vogt (2003) developed a Bertrand model of hospital price competition and, from

this model, Antwi, Gaynor, and Vogt (2013) derived a market power measure for hospitals,

which they denote as the Logit Competition Index (LOCI).  Both WTP and LOCI are based on the

first‐order pricing incentives of hospitals.  In that regard, they are similar to the Upward Pricing

Pressure Index (UPPI) (Farrell and Shapiro (2010)), which is often used to measure the potential

lost competition from a merger in a differentiated products industry.  Like UPPI, both WTP and

LOCI predict a significant price increase after a hospital merger when the merging hospitals are

close substitutes as measured by diversion ratios.  Both WTP and LOCI can also be used as the

basis for reduced‐form hospital merger simulations. Gowrisankaran, Nevo, & Town (2015)

recently developed a generalized model of hospital price formation in which the WTP and LOCI‐

based models are special cases.    

   

In recent years, WTP, LOCI, diversion ratios, and merger simulation have been used in

hospital antitrust litigation and regulation in both the U.S. and abroad.  In the recent joint

Federal Trade Commission (FTC)/State of Ohio challenge to Promedica’s acquisition of St. Luke’s

Hospital in Toledo, Ohio, the plaintiff’s economic expert used diversion ratios, WTP, and merger

simulation to argue that the merger would significantly reduce hospital competition and lead to

higher prices.  The federal district court agreed with the plaintiff’s analysis and issued a

preliminary injunction, while the plaintiffs also prevailed in administrative litigation and the

defendant’s appeal to the Sixth Circuit.6  In the FTC’s challenge of the proposed merger

between OSF Healthcare and Rockford Health, the FTC’s economic expert used diversion ratios

                                                      

6 http://www.ftc.gov/enforcement/cases‐proceedings/101‐0167/promedica‐health‐system‐inc‐corporation‐matter

(accessed on September 30, 2014)
7

and WTP to argue that the merger would be anticompetitive and, again, the federal district

court sided with the FTC and enjoined the merger.7  Finally, the U.K. Competition Commission

recently used LOCI to measure competition as part of its investigation into the private hospital

industry in Britain.8

   

To date, there has been limited research on the accuracy of the new screening tools

despite their widespread use in antitrust challenges and regulation.  Three recent working

papers have explored the accuracy of the most‐widely used of the new screening tools,

Willingness‐to‐Pay (WTP).  Fournier and Gai (2007) find that post‐merger WTP changes

estimated using pre‐merger data are accurate predictors of actual post‐merger WTP changes

that occurred after two hospital mergers. For one of these mergers, they also find that the price

change implied by a WTP‐based merger simulation using pre‐merger data produced a

conservative estimate of the actual post‐merger price change. (Data limitations prevented the

measurement of the post‐merger price change for the second merger in their study.) May

(2013) compares the qualitative predictions of WTP changes estimated using pre‐merger data

against the actual post‐merger price changes of two hospital mergers and finds that the merger

predicted to have the largest post‐merger price increase had the smallest actual price increase

of the two mergers.  Brand and Balan (2013) conduct a Monte Carlo‐like exercise in which they

compare the predictions of various merger screens (including WTP) against data produced by a

bargaining model of the negotiations between hospitals and health insurance companies and

find that diversion ratios, WTP changes, and merger simulation produce accurate predictions of

post‐merger price changes simulated by the bargaining model.  While this finding implies the

new hospital merger screening tools are theoretically sound, the evidence from Fournier and

Gai (2007) and May (2013) comparing the predictions of the WTP screen against actual post‐

merger price changes is mixed and limited to a meta‐sample of only three mergers.  Apart from

May (2013) and Fournier and Gai (2007), there has been little research on the accuracy and

reliability of WTP, LOCI, diversion ratios, and hospital merger simulation in predicting the price

effects of actual hospital mergers.9

This paper makes three primary contributions to the literature. First, this paper

significantly adds to the sample size of mergers considered by Fournier and Gai (2007) and May

(2013), increasing the likelihood of a meaningful evaluation of the accuracy of hospital merger

screening tools. Second, the analysis does not assess the accuracy of a particular screen in

isolation, but instead compares the predictions of various screening methods.  While it is useful

                                                      

7 http://www.ftc.gov/enforcement/cases‐proceedings/d‐9349‐111‐0102/osf‐healthcare‐system‐rockford‐health‐

system (accessed on September 30, 2014) 8 See http://www.competition‐commission.org.uk/assets/competitioncommission/docs/2012/private‐healthcare‐

market‐investigation/ais_app_b_toh_1_annex_2_loci_note_housestyled.pdf (accessed on 3/21/2014) 9 Ron Kemp, a senior economic officer for the Dutch Authority for Consumers and Markets, has recently compared

the post‐merger price changes of 12 hospital mergers in the Netherlands (described in Kemp, Kersten, and

Severijnen (2012)) with the pre‐merger price increase predictions of LOCI. This comparison is described in the April

22, 2015 presentation “Ex‐Post Analysis of Dutch Hospital Mergers,” available at

http://www.oecd.org/daf/competition/workshop‐expost‐evaluation‐competition‐enforcement‐decisions.htm

(accessed on June 2, 2015)
8

to assess the absolute accuracy of a screening tool, it is more important to evaluate its relative

accuracy compared with previous traditional screening methods.  Do any of the new screening

tools provide information beyond the traditional market‐based screening methods that can

help more accurately predict the effects of hospital mergers? If so, are some of the new

screening tools better than others at providing this additional information?

Finally, one advantage of the new hospital merger screening tools is that most (e.g.,

diversion ratios, WTP, and LOCI) can be implemented without the traditional exercise of

defining product and geographic markets and calculating market shares.  However, courts

continue to require the definition of a relevant antitrust product and geographic market as part

of any merger challenge.  In addition to evaluating the relative accuracy of the new screening

tools, this paper also evaluates the accuracy of the traditional market power measure, HHI,

under various market definitions and share metrics.

All of the screening tools are evaluated by comparing their predictions for each merger

to the merger’s actual price change.  Other potentially important effects of mergers, such as

changes in quality or access to care, are not evaluated.  

   

The following section describes the new hospital merger screening tools in more detail,

as well as traditional concentration measures used as a benchmark for comparison.  

3. Merger Screening Methods

Willingness‐to‐Pay (WTP)

Willingness‐to‐Pay (WTP) was developed by Town and Vistnes (2001) and Capps,

Dranove, and Satterthwaite (2003) from a bargaining model of the negotiation between a

managed care organization (MCO) and a hospital over the contractual price per admission paid

by the MCO for its members seeking care at the hospital.  Consider MCO k that negotiates with

each hospital in the set Φ of hospitals that would provide positive value to k’s network of

hospitals.  We assume there are no impediments to reaching an agreement (e.g., asymmetric

information, negotiation deadlines with random communication delays, etc.) if a positive

surplus is available, so that, in equilibrium, each hospital in Φ will reach an agreement with k.  

The focus of the model is on the negotiation between k and hospital jεΦ, assuming that the

outcomes of the negotiations between k and the remaining hospitals Φ‐j are taken as given

(e.g., because of simultaneous negotiations).  Given the vector of hospital prices p = {pi}iεΦ

negotiated by MCO k and the hospitals in its network, k sets a health insurance premium ρ to

maximize profits, taking the premiums and network configurations of its competitors as given

(e.g., as in Bertrand health insurance competition).  MCO k faces a total membership demand of

Xk(ρ,ρ‐k,Φ) where ρ‐k is the vector of competitor premiums.  k chooses ρ to maximize:

௞ߨ

௛௞ݕ௛݌෍െ ሻ௞ܺሺ௞ܥ െ௞ ܺߩ൝ ఘݔܽܯ ൌ∗ 

௛∈஍

ൡ (1)
9

where yki is the number of k’s patients treated at hospital i and Ck are k’s non‐hospital costs.  

Denote as Rkj k’s equilibrium profits apart from payments to hospital j (i.e., Rkj = πk

* + pjyj).  If we

assume that the negotiation between MCO k and hospital j satisfies the axioms of generalized

Nash bargaining and we assume, without loss of generality, that hospital j loses all of k’s

members if it is not part of k’s network, then the price that k and j negotiate will solve:

ܯܽݔ௣ೕ ቄൣܴ௞௝ሺΦሻ െ ߨ௞

∗ ൫Φି௝൯െ݌௝ݕ௝௞൧

ሺଵିఊሻ

൯൧ఊ௞௝ݕ൫௝ܿ െ௞௝ ݕ௝݌ൣቅ (2)

where cj(ykj) are hospital j’s costs of serving k’s patients and γ is a split parameter reflecting the

relative bargaining abilities of the hospital and MCO.  If we assume that hospital j’s price to k

does not affect a member’s demand for hospital j, as long as j is in k’s network (e.g., k’s health

plan design is a PPO that charges the same copay for in‐network hospitals), then the price that

solves (2) is:

݌ ௝ൌ ߛ ቀܴ௞௝ሺΦሻ െ ߨ௞

∗ ൫Φି௝൯ቁ ൅ ሺ1െߛሻ ቀܿ௝൫ݕ௝௞൯ቁ

௝௞ݕ

(3)

As seen in (3), hospital j’s market power is proportional to ቀܴ௞௝ሺΦሻ െ ߨ௞

∗ ൫Φି௝൯ቁ, the additional

profit k receives from having hospital j in its network.  Town and Vistnes (2001) and Capps,

Dranove, and Satterthwaite (2003) proxy for ቀܴ௞௝ሺΦሻ െ ߨ௞

∗ ൫Φି௝൯ቁ with the aggregate

consumer surplus hospital j adds to k’s network.  The change in consumer surplus associated

with j’s inclusion into k’s network is WTP.  Assume that, conditional on needing hospitalization,

each of k’s members have preferences over the hospitals in Φ of the form ܷ௛௜ ൌ ܸ௛௜ ൅ ߳௜ where

Vhi is a linear function of hospital characteristics and the stochastic term εi is independently and

identically distributed according to the extreme value distribution (i.e., the distributional

assumption consistent with logit estimation).  In this case, WTP for hospital j is defined as the

aggregate change in consumer surplus associated with adding hospital j to k’s network:

ܹܶܲ௞௝ ൌ ෍ 1

௜ߙ

൤ܧሾ݉ܽݔ௛ఢ஍ሺܸ௛௜ ൅ ߳௜ሻሿ െ ܧ ቂ݉ܽݔ௛ఢ஍షೕሺܸ௛௜ ൅ ߳௜ሻቃ൨

௜∈ூೖ

ൌ ෍ 1

௜ߙ

൥݈݊ ൭ 1

௜ݏെ1

௝൱൩

௜ఢூೖ

(4)

where αi is the marginal utility of income for patient i and si

j

is the estimated probability that

patient i chooses hospital j.  si

j

are the predicted probabilities associated with the conditional

logit estimation of ܸ௝௜.  We cannot directly observe αi, so WTP is operationalized by ignoring αi,

although it is subsumed within the estimated WTP coefficient of WTP‐based merger simulations

(described below).  Furthermore, individual MCOs usually cannot be observed in the discharge

data most commonly used to estimate WTP, so WTP is typically estimated across all commercial

MCOs:
10

ܹܶܲ௝ ൌ ෍ ൥݈݊ ൭ 1

௜ݏെ1

௝൱൩

௜ (5)

WTP can be used to analyze the market power created by the merger of two competing

hospitals (or hospital systems) by measuring the net change in WTP associated with the

combination of the two hospitals (or systems).  When used in this way, it is implicitly assumed

that the combined hospitals will negotiate in an all‐or‐nothing manner (i.e., in order to contract

with either hospital, the MCO must contract with both). This collective negotiation by multiple

competing hospitals worsens the MCO’s threat point in (2).  For example, consider the merger

of two competing hospitals L and M.  Before the merger, if the MCO fails to reach an agreement

with L, the loss in welfare for the MCO’s members may be relatively small with M available as

an alternative in the payer’s network.  Post‐merger, if L and M negotiate on an all‐or‐nothing

basis, the loss in welfare if the MCO fails to contract with both hospitals will be greater than the

sum of the losses associated with each hospital individually.  This is because L and M are

competing hospitals, in the sense that some of the MCO’s members who prefer L see M as an

alternative and vice versa.  If there were no members for which this were true, the WTP of L

and M would equal the sum of the WTP of L and the WTP of M and there would be no net

increase in WTP associated with the merger.  In this way, a merger of competing hospitals,

along with post‐merger all‐or‐nothing negotiation by the merged hospital system, may lead to a

disproportionate worsening of the MCO’s threat point, resulting in a price increase.  The net

change in WTP with the merger can be used as a measure of the worsening of the MCO’s threat

point.

Diversion Ratios

A merger of competing hospitals can also lead to a price increase even if the hospitals

do not negotiate in an all‐or‐nothing manner and continue to negotiate with the MCO

separately.  In this case, the merger improves the threat point of the hospital in (2).  For

example, before the merger, if L fails to reach an agreement with the MCO, some of the MCO’s

current patients who prefer L will instead seek care at M.  Post‐merger, when L is negotiating

with the MCO, both parties know that failure to reach an agreement will result in less real

diversion from L, as those patients who switch to M remain internal to the combined entity.  

This improved threat point will lead L to be more aggressive in the negotiation, resulting in a

higher price despite the lack of all‐or‐nothing bargaining from L and M.  A similar post‐merger

dynamic exists in M’s negotiation with the MCO.  This effect of the merger, due to the change

in each hospital’s threat point, occurs because of the collective ownership of both hospitals,

even if the negotiations remain separate after the merger.  

Whether the post‐merger negotiations are collective or separate, both of the merger

effects are driven by the potential diversion between the merging hospitals, which is a measure

of the substitutability of the hospitals in the eyes of the MCO’s members.  In other words, the

effect of the merger on the negotiated price should be proportional to the number of patients
11

who would switch from a hospital to its merger partner in the event the former is dropped from

the MCO’s network.  Therefore, another measure of the lost competition between two merging

hospitals is the diversion ratio: the percentage of the patients treated at a hospital who would

go to its merger partner if the former is dropped from the MCO’s network.  Using the predicted

probabilities associated with the conditional logit estimation of ܸ௝௜ and the logit property that

diversion is proportional to the probability of selection for each patient type, the diversion ratio

from hospital L to hospital M is:

݀௅ெ ൌ

௜ݏ ൬∑ ௜ݏ௅

ெ

௜ݏെ1

௅ ௜ ൰

௜ݏ ∑

௅

௜

(6)

This diversion ratio calculation implicitly assumes that no patients would continue to seek

treatment at L if it is dropped from the MCO’s network.  Otherwise, the diversion ratio could be

calculated by incorporating the probability that each patient type would stay with his or her

preferred hospital if it is dropped from the network.

WTP‐Based Merger Simulation

Equation (3) can also be used as the basis of a reduced‐form merger simulation.  WTP

per adjusted discharge WTP_PAD (where the adjustment accounts for variations in acuity

across patients) can be used as a proxy for (ቀܴ௞௝ሺΦሻ െ ߨ௞

∗ ൫Φି௝൯ቁ /ݕ (௝௞in equation (3) and

form the basis of a reduced‐form econometric model:

(7) ௛ߝ ൅ ௛ܺߚ ൅ ௛ܿଶߚ ൅ ௛ܦܣܲ_ܹܶܲଵߚ൅ߛൌ௛ ݌

Ph is the case‐mix adjusted price of hospital system h, ch is the average variable cost of hospital

system h, and Xh is a vector of other determinants of price.  The coefficient of WTP_PAD is

estimated (e.g., via OLS) and then used along with the predicted post‐merger change in

WTP_PAD to estimate the post‐merger price change.

As described in Brand and Garmon (2014), the usefulness of a reduced‐form merger

simulation may be limited by the data that is available to estimate (7).  In most cases, only

cross‐sectional data is available to estimate (7) and the estimated WTP_PAD coefficient may

suffer from omitted variable bias if there are factors related to the hospital/MCO negotiation

that cannot be observed or measured.  This bias may be compounded in the context of an

initial investigation when payer data is not available and only hospital‐level price estimates can

be calculated.  Furthermore, the use of accounting data to measure average variable cost may

introduce endogeniety bias as non‐profit hospitals with market power may classify some profits

as costs. (For instance, see Robinson (2011).)
12

Logit Competition Index

Gaynor and Vogt (2003) and Antwi, Gaynor, and Vogt (2013) do not use a bargaining

model as the basis for their measure of hospital market power, but instead develop a measure

from a Bertrand model of hospital price competition in which hospitals simultaneously set price

to maximize profit:

(8) ሻቁቃ݌ሺ௝ܦቀ௝ ܥ െ ሻ݌ሺ௝ܦ௝݌ቂ ೕ௣ݔܽܯ

The first‐order necessary condition for profit maximization is:

௝ܥ߲ ൌ௝ ݌

௝ܦ߲

௝ܦ െ

௝ܦ߲

(9) ൘ ௝݌߲

Gaynor and Vogt (2003) and Antwi, Gaynor, and Vogt (2013) also assume that patients have

preferences over hospitals of the form ܷ௛௜ ൌ ܸ௛௜ ൅ ߳௜ where Vhi is a linear function of hospital

characteristics (including price) and the stochastic term εi is independently and identically

distributed according to the extreme value distribution.  With this assumption, the second term

on the right‐hand side of (9) can be expressed as 1

ߙΛ௝ ൗ   where α is the marginal utility of

income (assumed constant across all patients) and Λj is the Logit Competition Index (LOCI):

Λ௝ ൌ ෍ ݏ௜

௝

௜ݏ ∑

௝

௜ ௜

൫1 െ ݏ௜

௝

൯ (10)

Using this model, Antwi, Gaynor, and Vogt (2013) develop a first‐order approximation of the

price increase associated with the merger of two hospitals.  Consider the merger of competing

hospitals L and M.  The post‐merger price increase for hospital L (as a proportion of its pre‐

merger markup over marginal cost) should be approximately equal to ൭Λ௅ெ

Λ௅Λெ ൗ ൱  where ΛLM

is a measure of the overlap of M relative to L or “LOCI‐Overlap.”

Λ௅ெ ൌ ∑ ݏ௜

௜ݏ௅

ெ

௜

௜ݏ ∑

௅ሺ1െݏ௜௅ሻ ௜

(11)

The commercial discharge weighted average of the merging hospitals’ LOCI‐Overlap price

increase estimate is used as the overall price increase estimate of the merger.  

Herfindahl‐Hirschman Index

For each hospital merger analyzed below, the new merger screening tools (WTP,

Diversion Ratios, Merger Simulation, and LOCI) are juxtaposed against the traditional measure
13

of market power used by the antitrust agencies and the courts: the Herfindahl‐Hirschman Index

(HHI) or the sum of the squared market shares (sh) for the hospitals in the market (M):

ܫܪܪெ ൌ ෍ሺݏ௛ሻଶ

௛ఢெ

(12)

The HHI depends on the definition of the product and geographic market M and the method

and metric used to calculate the market shares.  One significant conceptual benefit of the new

tools over the HHI is that none of the new tools require a product or geographic market for

calculation, except for restrictions on products and hospitals necessary to make the conditional

logit choice model estimation feasible.  To expedite comparison, the product market used for

all of the screening tools in this paper (including the new tools described above) are services to

commercially insured patients with general acute care (GAC) conditions who are treated at

short‐term, GAC hospitals.  This closely matches the “cluster” product market established by

the courts in most of the hospital merger challenges over the past 20 years.

Three geographic markets and share calculation methods are used to calculate HHIs.  

First, as a conservative approximation of the concentration measures used by the courts in the

hospital merger challenges of the 1990s, an HHI is calculated based on the Hospital Referral

Region (HRR) (defined by the Dartmouth Atlas of Health Care) of the merging hospitals with

shares based on the staffed beds of the hospitals located within this HRR.  The HRR is used

instead of an EH‐defined market because the EH procedure will not necessarily produce a

unique area for each merger.  However, each HRR is roughly similar to a hospital’s 90 percent

service area, as it is designed to capture the market for high‐acuity services.  The retrospective

hospital competition literature has found that geographic markets of this size are often too

large to correctly predict the effects of a hospital merger with an HHI.  In addition, this share

calculation method suffers from the “all‐in‐or‐all‐out” problem.  Hospitals within the market are

factored into the HHI calculation with their full capacity, even if they are not located near the

merging hospitals, and hospitals located outside of the market are not counted at all, even if

they serve many of the patients living near the merging hospitals.  To rectify these problems,

we calculate two alternative HHIs.  

The second HHI uses the Hospital Service Area (HSA) (defined by the Dartmouth Atlas)

of the acquired hospital and calculates the market shares based on the patients residing in the

area, not the hospitals located within the area.  The HSA is typically smaller than the HRR and is

meant to capture the market for low and medium‐acuity cases.  Shares are calculated based on

the admissions of patients residing in the area, even if they are treated at hospitals outside of

the area. Defining the geographic with the HSA is still arbitrary, so the final HHI calculation

employs a weighted service area.  For each zip code, the share of each hospital is calculated

based on the patients who reside in that zip code (regardless of the location of the hospital).  

Then these shares are weighted based on the importance of the zip code to the merging

hospitals (i.e., the weights are the percentage of the combined hospitals’ admissions that come

from the zip code).  The HHI is then calculated as the sum of the squares of the weighted

shares.  This HHI completely solves the “all‐in‐or‐all‐out” problem by including all patients and
14

all hospitals, regardless of location, but doing so in a way that focuses on the area most

important to the merging hospitals.  This measure is also similar to weighted concentration

measures commonly used in the hospital competition literature (e.g., Capps and Dranove

(2004)).  Appendix A provides an example of each HHI using a simple hypothetical hospital

market.  

   

4. Data and Estimation

All of the hospital merger screening methods described above can be implemented with

patient‐level inpatient discharge data and data on the characteristics of the merging hospitals

and potential competitors.  The discharge data used for the analysis was provided by the

Arkansas Department of Health (2007‐2011), the Connecticut Department of Public Health,

Office of Health Care Access (2007‐2013), the Georgia Hospital Association (2007‐2013), the

Oklahoma Department of Health (2007‐2011), the Pennsylvania Health Care Cost Containment

Council (PHC4) (2007‐2013), the New York Department of Health (2007‐2012), and the

company formerly known as Solucient for North Carolina (1997‐2002).  The data is restricted to

patients treated at non‐federal, short‐term, general acute care (GAC) hospitals.  In other words,

patients treated at federal hospitals (Veterans Affairs or military), long‐term acute care

hospitals, rehabilitation hospitals, and psychiatric and substance abuse facilities are excluded.

In addition, patients treated at non‐federal, short‐term GAC hospitals for non‐GAC conditions

(i.e., rehabilitation, psychiatry, and substance abuse) are excluded.  Finally, newborns, patients

transferred from other hospitals, and court‐ordered admissions are excluded to avoid double‐

counting patient choices or counting admissions that were mandatory.  

Hospital characteristics are taken from the American Hospital Association’s (AHA)

Annual Survey and the Centers for Medicare and Medicaid Services’ (CMS) Healthcare Cost

Report Information System (HCRIS).  Hospital ownership and changes in ownership are taken

from the AHA data and confirmed with background research. The HCRIS and discharge data are

used to construct the hospital price estimates as described below.  For each merger, the data

used to construct the screening tools was that of the calendar year before the year in which the

merger was consummated.  If the merging hospitals are located near a state border or are

located in different states, we use the discharge data of both states to construct the screening

tools.  Otherwise, only the discharge data from the merging hospitals’ state is used.  

To focus on mergers of competing hospitals, we include all of the mergers captured in

our discharge data between short‐term GAC hospitals in the same MSA or adjacent MSAs, as

long as we have at least one year of pre‐merger discharge and price data and at least one year

of post‐merger discharge and price data.10  We also exclude acquisitions of Critical Access

Hospitals (CAH) and acquisitions of failing or failed hospitals.  The former are excluded because

CAHs are small hospitals serving isolated rural areas and, thus, usually do not compete with

                                                      

10 For rural mergers, we include all mergers involving hospitals in the same county or adjacent counties. Mergers

involving hospitals close to a border of a state for which we do not have discharge data are excluded.  
15

other hospitals.11  The latter are excluded because merger screens are irrelevant if one of the

parties involved in the merger would exit the market absent the merger.12  Finally, we also

exclude cases in which a hospital system acquires multiple hospitals at the same time. The

selection criteria result in a sample of 26 mergers: 16 of which occurred between 2007 and

2012 between hospitals in Arkansas, Connecticut, Georgia, New York, Oklahoma, and

Pennsylvania and 10 of which occurred between hospitals in North Carolina between 1997 and

2001.  The mergers included in our sample are listed in Appendix B, in alphabetical order of the

acquired hospital.

The ideal sample to assess the accuracy of a merger screen would be a random selection

of mergers that are as likely to trigger the screen as not.  However, mergers occurring in a

period of active antitrust enforcement are more likely to be those that have or would have

passed through the screen.  In an era of antitrust enforcement in which the screen is actively

used, mergers that the screen would identify as anti‐competitive are less likely to occur

because they are blocked or deterred.  Thus, sampling mergers from such an era will hamper an

analyst’s ability to fairly assess the accuracy of a screen in predicting post‐merger effects,

particularly for mergers that the screen identifies as anti‐competitive (Carlton (2009)). The

North Carolina mergers were added to the sample to ameliorate the bias caused by merger

selection during a period of antitrust enforcement.  Hospitals merging in North Carolina in

1997‐2001 did not possess blanket antitrust immunity.  However, hospitals merging in this

period likely felt relatively safe from antitrust challenges for two reasons.  First, this period was

at the tail end of the federal and state hospital antitrust losing streak and before the successful

hospital merger challenges of recent years.  Second, North Carolina introduced a hospital

Certificate of Public Advantage (COPA) regulatory program in 1995 that gave merging hospitals

participating in the program antitrust immunity conditional on submitting to state regulation.  

None of the hospitals in our sample participated in North Carolina’s COPA program, but the

option to participate, if the merger were challenged by federal or state antitrust authorities,

may have reduced the likelihood of an antitrust challenge for these mergers.  The sample of

recent mergers also includes a merger that was challenged by the FTC, but allowed to proceed

by the courts.

Price Measurement

Hospital prices are difficult to measure due to the variety and complexity of services

offered.  A typical short‐term, acute care hospital offers services that support the treatment of

patients across a broad range of diagnoses, exhibiting a broad range of severity.  The price

charged to any particular patient and his or her insurance company can be a function of many

factors that affect the cost of treating the patient: the patient’s diagnosis, the severity of the

                                                      

11 By law, CAHs can have no more than 25 acute care beds and must be at least 35 miles from the next nearest

hospital (except in areas of mountainous terrain or other unique circumstances where the hospital is deemed a

“necessary provider” despite proximity to another hospital of less than 35 miles).   12 An earlier draft of this paper included two acquisitions of failing or closed hospitals. Their inclusion would not

materially affect the results.  
16

diagnosis, the procedures performed in treating the patient, the manner in which the patient

was admitted (e.g., through the emergency room), additional conditions present in the patient

when admitted to the hospital (i.e., comorbidities), complications that arise during treatment,

etc.  To accurately measure the overall hospital price paid by patients with private commercial

insurance, one not only needs to accurately measure the payments made by the insurer and

patient to the hospital.  It is also necessary to properly adjust these payments to account for

changes in the diagnoses treated and procedures performed, along with changes in severity,

complications, and comorbidities. These latter adjustments are often collectively referred to as

“case mix adjustment.”

The ideal type of data for hospital price measurement is comprehensive, all‐payer claims

data that provides detailed information on each patient and treatment episode and the

amounts actually paid by (not just the list price charged to) the patient and insurance company

for each treatment and procedure.  The discharge data described above provides detailed

information about each patient stay, but it only includes the total list price for all services, not

the amount actually paid.  Unfortunately, few states collect all‐payer claims data and only two

(New Hampshire and Maine) make this data available to researchers and have a panel of

hospital claims data stretching back far enough to capture pre and post‐merger periods.  

However, we are aware of no mergers of competing hospitals in New Hampshire or Maine

during the time period of their claims data collection.  Private collections of claims data

available for research either fail to provide a comprehensive collection of commercial insurers

or are restricted to make it difficult to identify hospitals and measure their commercial

revenues.

Alternatively, some states collect aggregate hospital financial data and make it available

to researchers.  A few states collect aggregate financial data in sufficient detail to allow

estimates of each hospital’s commercial price when the data are combined with discharge data.  

For instance, an estimate of each hospital’s average inpatient commercial discount can be

calculated from the financial data and applied to the hospital’s commercially‐insured inpatients

listed in the discharge data to estimate the hospital’s case‐mix adjusted commercial inpatient

price.  Numerous researchers studying hospital competition have used this approach and Levit,

Friedman, and Wong (2013) find that commercial prices calculated with state‐level financial

data are accurate estimates of commercial prices calculated from private claims data.  

Unfortunately, the states that collect and disseminate hospital financial data with detail

sufficient to accurately estimate commercial inpatient prices are too few to allow the study of

more than a handful of hospital mergers.  

To estimate hospital prices for a relatively large sample of hospital mergers spread

across multiple states and across time, we use financial information in the HCRIS data and the

commercial price estimation procedure described in Dafny (2009).  Dafny (2009) estimates the

case‐mix‐adjusted commercial price for each hospital using estimates of net inpatient

commercial revenue and commercial inpatient discharges derived from HCRIS data and each

hospital’s case‐mix index taken from CMS’s Impact Files. Each hospital’s estimated price is:
17

ܲ௛ ൌ

௛ܥܵܫܦܱܰܶܥ െ 1ቀ ሻ௛ܥܰܣܲܫ ൅ ௛ܥܫܲܫ ൅ ௛ܥܲܵܫሺ

௛ܸܧܴܱܴܵܵܩ

௛ܲܣܥܯ െ௛ ܯܫܴܲܥܯ െ ቁ

௛ܫܯܥሻ௛ܪܥܵܫܦܯ െ௛ ܪܥܵܫܦሺ

(13)

where IPSCh is the hospital’s inpatient routine service charges, IPICh is intensive care charges,

IPANCh is inpatient ancillary charges, CONTDISCh is contractual discounts, GROSSREVh is gross

revenues, MCPRIMh is the hospital’s Medicare primary payer amounts, MCAPh is the Medicare

total amount payable,13 DISCHh is the hospital’s total inpatient discharges, MDISCHh is Medicare

inpatient discharges, and CMIh is the hospital’s case‐mix index (i.e., the average Diagnosis

Related Group (DRG) weight for its inpatients).  The only change we make to the Dafny (2009)

formula in (13) is to substitute the hospital’s case‐mix index for commercial inpatients

calculated from the discharge data for the Impact File case‐mix index, which reflects the

hospital’s Medicare population.  

The price estimate in (13) is not an ideal proxy for each hospital’s commercial price, as it

does not deduct Medicaid revenue and the discount factor applied to inpatient charges reflects

inpatient and outpatient discounts.  However, our research suggests that, while it is a noisy

measure of price, it correlates to commercial price measures calculated with state‐level

financial data for hospitals with at least 200 commercial patients per year.  Using financial data

from PHC4 for Pennsylvania short‐term, acute care hospitals, we calculated case‐mix adjusted

commercial inpatient prices and regressed these estimates onto commercial inpatient prices

calculating using the Dafny (2009) method described above, while suppressing the constant and

restricting the sample to hospitals with at least 200 commercial discharges per year. The

resulting estimated coefficient was 0.99 with an R2 of 0.90.  Thus, the commercial price

estimate calculated using (13) is likely an unbiased, but somewhat noisy measure of the

hospital’s actual commercial price and is appropriate to use when studying a relatively large

sample of mergers, as in Dafny (2009) and the current analysis, even though it may not be

appropriate for the study of a particular merger.  However, some merger retrospective studies

find that post‐merger price changes estimated using HCRIS data are consistent with price

changes estimated using detailed claims data. (Haas‐Wilson and Garmon (2011))   

Post‐Merger Price Change Estimation

The merger screens described above are meant to capture the loss of competition

associated with a hospital merger.  To assess the accuracy of their price predictions, the screens

should be compared to the price change associated with the loss of competition from the

merger, apart from other changes that occur coincident with the merger.  In other words, the

screens should be compared to the difference between the post‐merger price change and what

it would have been absent the merger.  Apart from the price measurement issues described

above, the former price difference is straightforward to calculate.  The latter price difference is

impossible to calculate as the merger did, in fact, occur.  Thus, following the general difference‐

in‐differences (DID) literature, we select control groups of hospitals to serve as a proxy for the

                                                      

13 MCPRIM+MCAP is the total reimbursement to the hospital for Medicare inpatients.
18

merging hospitals in the counterfactual absent the merger.  These control groups should be

made up of non‐merging hospitals that are similar to the merging hospitals.

Unlike the typical DID comparison of a treatment group with a control group to estimate

the effect of treatment, in this case each treatment group—the merged hospitals—is a

singleton.  For this reason, the standard methods of selecting a control group (e.g., propensity

scoring) do not necessarily result in a control group that is similar to the merging hospitals apart

from the merger.  In addition, a merger may affect nearby non‐merging hospitals by lowering

the overall level of competition in the market (Dafny (2009)).  Thus, the use of nearby hospitals

in the control group, which otherwise may be optimal because they face cost and demand

conditions similar to the merging hospitals, may bias the estimated price change.

For each merger, the post‐merger price change is measured relative to a control group

of non‐merging hospitals similar in size and cost‐structure to the merging hospitals, but outside

of their immediate area.  Most of the mergers in the sample involve urban, short‐term GAC

hospitals with more than 100 staffed beds.  In these cases, the control group is the set of all

non‐merging urban short‐term GAC hospitals in the same state (but outside of the merging

hospitals’ MSA) with more than 100 staffed beds.  In other cases, the control group is adjusted

to match the size and cost structure of the merging hospitals.14  In all cases, the control groups

exclude hospitals specializing in the treatment of children and hospitals with fewer than 200

commercial admissions in the pre or post‐merger years.  In addition, hospitals outside of the

merged hospitals’ MSA that are owned by the acquiring hospital system are excluded from the

control group and the merging hospitals’ price change estimates.  We also report results that

use an alternate control group in which the size restrictions are relaxed.

The post‐merger price change for each merger is calculated using the hospital prices in

effect in the first full calendar year after the merger and is measured relative to the prices in

effect in the last full calendar year before the merger.  Where it is feasible to do so, we also

measure the price change using prices in effect two years after the merger to account for lags in

the post‐merger contracting process between the merged hospitals and insurers (Tenn (2011)).  

The price change is measured relative to the mean price change across the control group.  Thus,

the statistical significance of the relative price change can be interpreted as a comparison of the

merged hospitals’ price change and the distribution of price changes across the control group.15  

The relative price change for each merger is calculated by estimating the following equation

using weighted least squares estimation, where the weights are the number of commercial

discharges:

                                                      

14 For mergers that involve rural hospitals with more than 100 staffed beds, the control group includes all non‐

merging urban and rural short‐term GAC hospitals in the same state with more than 100 staffed beds.  In cases in

which the merger involves the acquisition of a hospital with fewer than 100 staffed beds, the control group is

selected with a smaller bed‐size threshold and these thresholds are listed in Appendix B.  In all cases, critical access

hospitals are excluded from the control group. 15 The null hypothesis is that the merging parties’ price change is equal to the mean price change across the control

group. Thus, instead of reporting the standard error of the estimated coefficient, the p‐value for the t test

comparing the merging parties’ price change and the distribution of control price changes is reported.  
19

(14) ݐ݄ߝ ൅ ݄ߜ ൅ ݐ݄ܯ2ܱܲܵܶߚ ൅ ݐ1ܱ݄ܲܵܶߚ൅ߙൌ ݐ݄ܲ

where Pht is the log of hospital’s commercial price as calculated in (13) above, POSTht is an

indicator for the post‐merger period (i.e., the year after the merger), POSTMht is an indicator for

the hospitals in the merged entity in the post‐merger period, and δh are hospital fixed effects.  

The relative post‐merger price change is calculated as:

∆ܲ ൌ ݁ఉ

෢మ െ 1 (15)

Choice Model Estimation

The new hospital merger screening tools (e.g., diversion ratios, WTP, and LOCI) are

constructed from the predicted probabilities of a conditional logit choice model.  We use the

estimates from a parametric choice model in which the patient’s choice is modeled as a

function of hospital characteristics and patient characteristics. The probability that patient i

selects hospital j is:

݅ݏ

ሻܼ݄ܺ݅݅ߴ൅ܻ݄ܺ݅ߚ൅ܼ݄݅ߛሺ݁ ൌ ݄

ܪ݆߳ ൯ܼ݆ܺ݅݅ߴ൅ܻ݆ܺ݅ߚ൅ܼ݆݅ߛ൫݁∑ 

(1)

where Zih are characteristics specific to patient i and hospital h, Xi is a vector of patient

characteristics, and Yh is a vector of hospital characteristics.  In other words, patient i’s hospital

choice is assumed to be a function of hospital characteristics unique to the patient and

characteristics common to all patients.  Further, patient preferences for these characteristics

are allowed to vary across patient types.  The patient‐specific hospital characteristics Zih consist

of the driving time (under normal traffic conditions) between the center of the patient’s zip

code and the hospital and the driving time squared.16  The patient characteristics consist of the

patient’s DRG weight, a gender indicator, an indicator for emergency room admissions, an

indicator for obstetrics, and an indicator for cardiac surgery.  The hospital characteristics consist

of the hospital’s residents and interns per bed (a measure of teaching intensity), a for‐profit

indicator, an indicator for hospitals that offer obstetrics services, and an indicator for hospitals

that offer cardiac surgery.  

To test the sensitivity of the merger screens to the choice model type and specification,

we also use the predicted probabilities from the semiparametric choice model described in

Tenn (2014) in which patient bins are defined iteratively and probabilities are estimated using

the observed shares within each bin. As in Tenn (2014), the bins are defined (with a minimum

                                                      

16 Driving times are taken from ArcGIS, version 10.
20

bin size of 25 patients) using the following patient characteristics, in declining order of

importance: patient’s county, patient’s zip code, major diagnostic category (MDC), whether the

patient was admitted through the emergency room, whether the service provided was medical

or surgical, the severity of the patient’s diagnosis (defined with Diagnosis Related Group (DRG)

weight quartiles), DRG, age category, and gender.  Recent research (Raval, Rosenbaum, and

Wilson (2014)) indicates that the Tenn model generally is the most accurate model, of those

commonly used, at predicting actual changes in patient choices in response to the removal of a

hospital from the patient’s options, and that more accurate models tend to predict greater

likelihoods of harm when hospitals are substitutes.  Thus, the Tenn semiparametric model

tends to produce diversion ratios, WTP changes, and LOCI price increase estimates that are

larger than those produced using parametric approaches.  Therefore, our primary results

employ the more conservative parametric merger screens.   

Both models are estimated over all of the commercial GAC inpatients in the acquired

hospital’s HRR in the year prior to the merger.  The choice set H is restricted to all hospitals that

served at least 0.5% of these patients.17  The choice of a hospital outside of this set is

aggregated into an outside option.18  

Merger Simulation

The basis for the merger simulation, condition (7), is estimated via a system‐level

regression of price on WTP_PAD, average variable cost, and other covariates.  The dependent

variable is the weighted average commercial price (as calculated in (13)) across all of the

hospitals in each system in each metropolitan statistical area (MSA) in the year prior to the

merger (where the weights are the number of commercial discharges).  WTP_PAD is

constructed by first estimating the choice model across all of the patients in each MSA in the

state in the year prior to the merger using the specifications and choice set selection criteria

described above.  Each system’s WTP is then calculated from the predicted probabilities and

divided by the system’s aggregate DRG weight to produce the system’s WTP_PAD.  The system‐

wide operating cost per adjusted admission (where the adjustment accounts for the hospital’s

outpatient scale) is used as the proxy for average variable cost.  Finally, the other covariates

consist of a for‐profit indicator (to capture differences in for‐profit and non‐profit pricing) and

MSA indicators (to capture differences in market conditions across MSAs).   

The estimated coefficient of WTP_PAD is then used to predict the post‐merger price

change by applying it to the predicted change in WTP_PAD associated with the merger.  The

bootstrapped 95 percent confidence intervals of the price change estimate for each merger are

listed along with each estimate.  Because the estimation of (7) is only carried out for urban

                                                      

17 For two mergers, the HRR is so large that one of the merging hospitals is not included in the choice set using this

inclusion criterion. In these cases, the choice model is estimated over all of the commercial GAC patients in the

merging hospitals’ combined primary service area instead of the HRR.   18 The coefficient estimates, standard errors, and fit statistics for the estimation of (16) for each merger are

available upon request.
21

hospital systems in each state, a merger simulation is not conducted for the rural hospital

mergers.

5. Results

Ex ante merger screens designed to identify mergers that are likely anti‐competitive can

be used in one of two ways.  First, they can be used to establish a threshold above which the

merger is presumed to be anti‐competitive, absent extenuating circumstances (e.g., mergers

with a change in the screen above X% are likely anti‐competitive).  We will refer to this as the

“threshold” approach.  Second, they can be used to make a prediction about the likely effects

of a merger (e.g., an X% increase in the screen is associated with a Y% increase in price on

average). We will refer to this as the “relationship” approach. The first approach largely differs

from the second by making no presumption about mergers below the threshold.  We will

evaluate the merger screens with both uses in mind.  First, are there thresholds of the merger

screen above which price increases are likely and price decreases are unlikely?  Second, is there

a relationship between the merger screen and the post‐merger price changes?

Table 1 lists the price change relative to controls for each merger along with each

merger screen calculated using pre‐merger data.  9 of the 26 mergers resulted in statistically

significant price increases larger than the mean increase across the controls, while 2 resulted in

statistically significant relative price decreases (i.e., an absolute price decrease or an increase

less than the mean increase across the controls).19  The latter mergers highlight the fact that

not all mergers of competing hospitals are anti‐competitive and some may lead to lower prices

(or smaller price increases than normal) due to, for instance, cost savings resulting from the

merger.  The mean price change relative to controls across all 26 mergers is 4.7 percent and the

median is 5.3 percent.   

The first three rows in Table 1 list the traditional post‐merger HHI and change in HHI

based on the three market definitions and share measures described previously.  Following the

Federal Trade Commission (FTC) and Department of Justice (DOJ) joint Horizontal Merger

Guidelines,20 mergers resulting in a post‐merger HHI of 2500 or more with an HHI increase of

200 or more “will be presumed to be likely to enhance market power.”  As described in the

Guidelines, this presumption is not sufficient to conclude that a merger is likely to substantially

lessen competition.  However, an antitrust regulator using the HHI as a screen is likely to focus

on mergers with a post‐merger HHI greater than 2500 and a change greater than 200 for

                                                      

19 Statistical significance is measured at the 95% level.  It is important to note that a lack of statistical significance

does not necessarily imply economic insignificance. For instance, one merger (24) in Table 1 was associated with a

13.2% relative price increase, potentially indicating an anti‐competitive merger, but the null hypothesis that this

merger’s price increase is the same as the mean control price increase cannot be rejected because of the high

variance of control price changes.  Likewise, two mergers (7 and 15) are associated with relative price decreases

exceeding 20%, potentially indicating pro‐competitive mergers, but neither is statistically significant because of the

high variance of control price changes.   20 http://www.ftc.gov/sites/default/files/attachments/merger‐review/100819hmg.pdf (accessed on 3/27/2014)
22

further investigation.  The mergers that would be flagged under this condition are highlighted in

bold in Table 1.

   Of the three HHI measures, the HHI calculated using bed shares in the merging parties’

HRR is the most likely to produce a false negative.  Of the 9 mergers with post‐merger price

increases, this screen flags only 3.  This largely confirms the criticisms of most health

economists that the EH‐based geographic markets used by the courts in the 1990s (which

closely resemble HRR markets) were, in many cases, too large to accurately predict the effect of

a hospital merger.

On the other hand, the HHI calculated using discharge shares in the acquired party’s

HSA is most likely to produce a false positive.  This screen flags all but 2 of the 26 mergers as

potentially problematic, including both of the mergers with post‐merger relative price

decreases.  The HHI calculated using discharge shares in the merging parties’ weighted service

area is only slightly better.  This screen flags 19 of the 26 mergers as potentially problematic,

including both mergers with price decreases.   

The new merger screening tools are listed in the bottom rows of Table 1.  Also listed in

Table 1 is the product of the diversion ratios for each merger.  The last row of Table 1 lists the

price increase estimates for each merger based on the reduced form WTP‐based merger

simulation.  The change in WTP closely tracks the two other choice‐model‐based merger

screens: the LOCI price change estimate and the diversion ratios.  This is not surprising as the

WTP change and the LOCI price increase approximation are both largely based on the overlap

between the merging hospitals in each patient type, which is also the basis for the diversion

ratios.  The correlation between the product of the diversion ratios and the WTP change is 0.98.  

The correlation between the product of the diversion ratios and the LOCI price change estimate

is 0.99.  Finally, the correlation between the WTP change and the LOCI price increase estimate

is also 0.99.  Because of the near perfect correlation between the WTP change, LOCI price

change estimate, and the product of the diversion ratios, we will focus on the most commonly

used of the three, the WTP change.  

For each new screen, there are no established thresholds—like the Guidelines’ HHI

thresholds—above which a merger is presumed problematic.  However, WTP was used by the

FTC in two recent hospital merger challenges.  In the FTC’s challenge of Promedica’s acquisition

of St. Luke’s, a projected 13.5% change in WTP was cited by the FTC in its public decision.21  In

the FTC’s challenge of the proposed merger between OSF Healthcare and Rockford Health, a

WTP change of 19% was cited by FTC staff in its pre‐trial brief to the court.22 In our sample,

three mergers have a WTP change exceeding 13.5% and two of these mergers resulted in

statistically significant price increases.

                                                      

21 http://www.ftc.gov/sites/default/files/documents/cases/2012/06/120625promedicaopinion.pdf , page 49

(Accessed on September 30, 2014) 22 www.ftc.gov/sites/default/files/documents/cases/2012/04/120404ccpretrialbrief.pdf , page 44 (Accessed on

June 9, 2015)
23

A lower threshold may be more appropriate when using WTP to screen for mergers that

warrant further investigation.  Graph 1 plots the mean price change for mergers with WTP

change values above a certain threshold.  At the threshold WTP change of roughly 5%, there is a

discrete jump in the mean price change for mergers above this threshold from roughly 5% to

more than 10%.  (A WTP change threshold of 5% roughly corresponds to a diversion ratio

product of 0.0129 and a LOCI price change estimate of 14.4%.)  

Table 2 compares the threshold performance of WTP (using the 5% change threshold) to

the three HHI screens using the Guidelines’ thresholds.  Of the four screens, WTP makes the

correct prediction (i.e., flags mergers associated with statistically significant price increases and

does not flag mergers not associated with statistically significant price increases) most often.  In

addition, WTP has the lowest incidence of false positives (i.e., flagging a merger as potentially

problematic when the merger is not associated with a statistically significant price increase).  

Furthermore, of the 9 mergers with statistically significant price increases, 5 had a WTP change

greater than 5% and both of the mergers with statistically significant price decreases had WTP

changes less than 5%.  The average price change across mergers with a WTP change greater

than 5% was 11.2%, whereas the average price change for mergers with a WTP change less

than 5% was 0.7%.  For the three HHI screens, the average price change for the flagged mergers

is much closer to the overall mean price change of 4.7% and all of the HHI screens flag at least

one of the mergers with a statistically significant price decrease as problematic. This suggests

that a WTP change threshold of 5% more accurately flags hospital mergers that warrant further

investigation than any of the evaluated HHI screens using the traditional Guidelines thresholds.   

A closer examination of mergers with relatively large screen values reveals some of the

relative advantages and disadvantages of the screening methods.  There are 6 mergers with

post‐merger HHIs of at least 3000 and HHI deltas of at least 500, across all of the geographic

markets and share metrics considered.  For three of these mergers, the WTP change is also

greater than 10% and the average price change across these three is 21%. For the remaining

three mergers, the WTP change is less than 5% and the average price change for these is ‐13%.  

This highlights that the new screening tools can capture situations in which short‐term GAC

hospitals are not as competitive as their geographic proximity would suggest because they

serve somewhat different populations.  In this way, the new screening tools can capture

subtleties in product and geographic differentiation that the antitrust market definition

exercise cannot capture.  This finding also suggests that the relative performance of the HHI

screens compared to the new screens would not improve with higher thresholds than in the

Guidelines.

Graphs 2 through 8 plot the post‐merger price changes against each merger screening

tool.  For the HHIs, the price change is plotted against the HHI change (i.e., “HHI Delta”) with

larger dots signifying larger post‐merger HHI levels. Hollow dots represent the mergers in North

Carolina between 1997 and 2001, while solid dots represent the recent mergers.  Table 3 lists

the coefficient estimates and fit of the OLS regression of the price change on each merger

screen.  In each case, there is a great deal of unexplained variation in the price changes.  This is
24

not surprising, as the screens are only meant to capture the loss of competition resulting from

the merger and not other changes coincident with the merger (e.g., cost savings, management

changes, etc.).  Still, the new merger screens (diversion ratios, WTP, and LOCI) do a better job of

predicting price changes than the HHIs.  For the product of the diversion ratios, the WTP

change, and the LOCI price change estimate, the relationship between the merger screen and

the post‐merger price change is positive and statistically significant.  By contrast, there is no

statistically significant relationship between the post‐merger price change and the HHI screens,

regardless of the geographic market or share metric employed.   

Merger simulation also performs poorly, likely due to the limited data available to

identify the relationship between WTP and price and the other limitations of merger simulation

described above.  With the data available in an initial investigation, one can only measure the

commercial price of each hospital and not the price charged to each MCO, which would more

closely fit the first order condition in (3).  With limited cross‐sectional observations, the

estimates of the relationship between price and WTP are imprecise, as exhibited by the wide

confidence intervals around each estimate in Table 1.  While merger simulation may be a useful

tool for analyzing a hospital merger with detailed payer data, this suggests that it is not a

worthwhile exercise in the initial stages of an investigation when data are limited.

The predictive power of the new merger screens is robust to price changes measured

relative to the alternate, less restrictive control group, but the results are not robust to other

specification changes and alterations.23  As seen in graphs 1 through 7, the relationship

between the merger screens and the price change is heavily influenced by an outlier, Merger

20.  If Merger 20 is excluded, there is no longer a statistically significant relationship between

the price change and any merger screen, although the relationships between the price change

and the new screens (diversion ratios, WTP change, and LOCI price change estimate) remain

positive (but statistically insignificant).   

The excessive influence of Merger 20 on the results presents a dilemma for their

interpretation.  Ideally, one would like to observe additional mergers, like Merger 20, with large

values of the merger screens to see if they also result in large price increases.  However, in an

era of active antitrust enforcement, it is unlikely that such mergers would be proposed, no less

consummated.  As such, Merger 20 should not be ignored as a simple outlier because it

represents what a merger with large merging screening values can produce.  On the other

hand, mergers such as Merger 20 are likely to trigger any and all merger screens (including the

HHI for almost all reasonable geographic markets and share metrics), so the inclusion of Merger

20 may reveal little about the relative advantages or disadvantages of the new screens over

traditional methods, particularly for less extreme mergers.  It is with the less extreme mergers

that screens are more useful to antitrust regulators, to distinguish mergers that are likely

innocuous from those that require further investigation.

                                                      

23 An expanded version of Table 1 with alternate price changes, control groups, and merger screens is available

upon request.
25

The estimated relationships between the price changes and the screens for the 1997‐

2001 North Carolina mergers are similar to the overall sample.  The relationships between the

new screens and the price changes are each larger than in the overall sample, but are not

statistically significant, likely due to the smaller sample size of mergers.   

For 17 mergers, data are available to calculate the relative post‐merger price change

using the second year after the merger.  As seen in Graph 9, these price changes are generally

of the same sign as the first year price changes, but are more pronounced.  For instance, of the

9 mergers with statistically significant price increases after one post‐merger year, data are

available to calculate relative price increases using a subsequent year for 6 mergers.  All 6 have

price increases after two years and, for 4 of these mergers, the relative price increase after two

years is larger than the relative price increase after one year. However, only 3 of the 6 price

increases are statistically significant due to the smaller size of the control group and larger

variance of price increases across the control group. (Data are not available to calculate price

changes after two years for the two mergers with statistically significant price decreases.)  Of

the remaining 15 mergers without a statistically significant price change after one year, data is

available to calculate a second‐year price change for 11.  Of these, 3 have statistically significant

price increases after two years and 3 have statistically significant price decreases after two

years.  Overall, the greater variance of second‐year price changes weakens the relationship

between the price changes and the merger screens, as seen in the third‐to‐last and second‐to‐

last columns of Table 3, which exclude mergers in which second‐year price changes are

unavailable.  

Finally, as seen in the last column of Table 3, the relationship between the new merger

screens and the price changes is not robust to the alternate, semiparametric choice model of

Tenn (2014).  This is because the screens using the semiparametric model are typically larger

than the screens using the parametric model, when there is a difference between the two.  For

example, Graph 10 plots the semiparametric WTP changes against the parametric WTP

changes.  For many mergers, the WTP changes produced by the two models are similar, but

there are six mergers for which the semiparametric WTP change is much larger (more than 10

percentage points larger) than the parametric WTP change.  There are fewer mergers for which

the opposite is true and none for which the parametric WTP change exceeds the

semiparametric by more than 10 percentage points.  Due to this, there is not a statistically

significant relationship between the price changes and the semiparametric WTP changes and

there are a number of mergers with large semiparametric WTP changes, but without a

statistically significant price increase.  For instance, of the nine mergers with a semiparametric

WTP change greater than 10%, six are not associated with statistically significant price increases

and one results in a statistically significant price decrease. This highlights that it is important to

avoid reliance on only one choice model specification when using the new tools to screen

hospital mergers.  

    

   
26

6. Conclusion

Recent research on hospital competition has produced new screening tools that attempt

to capture the post‐merger pricing incentives of hospitals better than the traditional techniques

of concentration measurement.  This paper is the first large‐scale evaluation of the new

screening tools, comparing their predictions to the actual price effects of a relatively large

sample of past consummated hospital mergers, using pre‐merger data like that readily available

in an initial investigation.  The results suggest that most of the new hospital merger screening

tools (in particular, diversion ratios, WTP, and LOCI) are more accurate at flagging mergers that

are potentially anti‐competitive than the traditional tools of market definition and

concentration measurement.  This is because the new tools capture information about the

differentiation in hospital markets that the traditional exercise of market definition cannot

capture.  However, the relationship between the new merger screens and post‐merger price

changes is not robust to all changes in model specification, highlighting the importance of

calculating the new merger screens using multiple choice models and specifications.  WTP‐

based merger simulation performs poorly at predicting post‐merger price changes, but this may

be due to the limited data available to calibrate the simulation in an initial investigation.  

Merger simulations may be more accurate when calibrated with detailed health insurance

claims data.  Finally, for the traditional exercise of market definition and concentration

measurement, none of the evaluated geographic market definitions and share metrics was

accurate in predicting post‐merger price changes.  Going forward, better data is needed to

more precisely estimate post‐merger hospital price changes and more detailed hospital

competition models are needed to more accurately predict post‐merger price changes.  

   
27

References

Antwi, Y. A., Gaynor, M., & Vogt, W. (2013). A Competition Index for Differentiated Products

Oligopoly with an Application to Hospital Markets. Working Paper.

Ashenfelter, O., Hosken, D., Vita, M., & Weinberg, M. (2011, February). Retrospective Analysis

of Hospital Mergers. International Journal of the Economics of Business, 18(1), 5‐16.

Brand, K., & Balan, D. (2013). Simulating Hospital Merger Simulations. Working Paper.

Brand, K., & Garmon, C. (2014). Hospital Merger Simulation. American Health Lawyers

Association.

Capps, C., & Dranove, D. (2004). Hospital Negotiation and Negotiated PPO Prices. Health Affairs,

23(2), 175‐181.

Capps, C., Dranove, D., & Satterthwaite, M. (2003). Competition and Market Power in Option

Demand Markets. RAND Journal of Economics, 34(4), 737‐763.

Carlton, D. (2009). Why We Need to Measure the Effect of Merger Policy and How to Do It.

Competition Policy International, 5(1), 77‐90.

Dafny, L. (2009). Estimation and Identification of Merger Effects: An Application to Hospital

Mergers. Journal of Law and Economics, 523‐550.

Elzinga, K., & Hogarty, T. (1973). The Problem of Geographic Market Delineation in Antimerger

Suits. Antitrust Bulletin, 18, 45‐81.

Farrell, J., & Shapiro, C. (2010). Antitrust Evaluation of Horizontal Mergers: An Economic

Alternative to Market Definition. The BE Journal of Theoretical Economics, 10(1), 9.

Fournier, G., & Gai, Y. (2007). What does Willingness‐to‐Pay Reveal About Hospital Market

Power in Merger Cases? Working Paper.

Gaynor, M., & Town, R. (2012). The Impact of Hospital Consolidation ‐ Update. Robert Wood

Johnson Foundation, The Synthesis Project.

Gaynor, M., & Vogt, W. (2003). Competition Among Hospitals. RAND Journal of Economics,

34(4), 764‐785.

Gowrisankaran, G., Nevo, A., & Town, R. (2015, January). Mergers When Prices are Negotiated:

Evidence from the Hospital Industry. American Economic Review, 105(1), 172‐203.

Guerin‐Calvert, M., Maki, J., & Vladeck, B. (2015). Re‐Aligning Prospective Hospital Merger

Guidance: Moving Beyond Concentration to More Meaningful Approaches.

Haas‐Wilson, D., & Garmon, C. (2011). Hospital Mergers and Competitive Effects: Two

Retrospective Analyses. International Journal of the Economics of Business, 18(1), 17‐32.

Kemp, R., Kersten, N., & Severijnen, A. (2012). Price Effects of Dutch Hospital Mergers: An Ex‐

Post Assessment of Hip Surgery. De Economist, 160, 237‐255.

Levit, K., Friedman, B., & Wong, H. (2013). Estimating Inpatient Hospital Prices from State

Administrative Data and Hospital Financial Reports. Health Services Research, 48(5),

1779‐1797.

May, S. (2013). How Well Does Willingness‐to‐Pay Predict the Price Effects of Hospital Mergers?

Working Paper.

Raval, D., Rosenbaum, T., & Wilson, N. (2014, December 5). Industrial Reorganization: Learning

about Substitution Patterns from Natural Experiments.

Robinson, J. (2011). Hospitals Respond to Medicare Payment Shortfalls by Both Shifting Costs

and Cutting Them, Based on Market Concentration. Health Affairs, 30(7), 1265‐1271.
28

Tenn, S. (2011). The Price Effects of Hospital Mergers: A Case Study of the Sutter‐Summit

Transaction. International Journal of the Economics of Business, 18(1), 65‐82.

Tenn, S. (2014, December 16). A Monte Carlo Analysis of a Semiparametric Hospital Choice

Model.

Town, R., & Vistnes, G. (2001). Hospital Competition in HMO Networks. Journal of Health

Economics, 20, 733‐753.

Vita, M., & Sacher, S. (2001). The Competitive Effects of Not‐For‐Profit Hospital Mergers: A Case

Study. Journal of Industrial Economics, 49, 63‐84.

Vogt, W. B., & Town, R. (2006). How has Hospital Consolidation Affected the Price and Quality of

Hospital Care? Robert Wood Johnson Foundation, The Synthesis Project.
Table 1: Post‐Merger Price Changes and Screening Tools (Mergers 1‐14)

(Standard errors are in parentheses, except as noted)

Merger: 1 2 3 4 5 6 7

Price Change Relative to Controls 6.4% 3.4% ‐3.2% 24.8% 16.9%  ‐4.6% ‐21.8%

P‐value of t Test: Price Change vs. Mean

Control Price Change 0.06 0.74 0.06 0.01 0.00 0.12 0.16

Bed Shares in HRR Post HHI 951 2285 2002 2648 570 1722 3115

HHI Delta 10 416 599 425 23 74 558

Discharge Shares in HSA Post HHI 4656 6445 6740 4662 3427 6673 5797

HHI Delta 812 2606 2969 1802 1165 3304 2490

Discharge Shares in

Weighted Service Area

Post HHI 4229 3674 2804 3373 1396 5415 3886

HHI Delta 1724 674 1293 928 401 1081 1551

Diversion Ratio A to B 16.4%

(0.2%)

5.3%

(0.1%)

8.7%

(0.1%)

8.0%

(0.1%)

3.5%

(0.0%)

10.2%

(0.1%)

5.3%

(0.1%)

B to A 15.5%

(0.2%)

21.4%

(0.1%)

14.8%

(0.1%)

17.0%

(0.2%)

9.0%

(0.0%)

13.0%

(0.1%)

10.2%

(0.2%)

Product of Diversion Ratios 0.0254 0.0113 0.0129 0.0136 0.0032 0.0133 0.0054

Change in Willingness‐to‐Pay 8.8%

(0.1%)

4.2%

(0.1%)

5.8%

(0.1%)

5.7%

(0.1%)

2.9%

(0.0%)

6.8%

(0.1%)

3.6%

(0.0%)

LOCI Price Change Estimate 21.2%

(0.4%)

12.6%

(0.1%)

14.5%

(0.1%)

14.4%

(0.3%)

6.5%

(0.0%)

14.8%

(0.1%)

8.4%

(0.1%)

WTP‐Based  

Merger Simulation

Estimate 1.1% 0.9% 0.1% 1.5% 12.5%

CI High 11.3% 8.3% 9.5% 5.5% 56.3%

CI Low  ‐9.1% ‐6.5% ‐9.4% ‐2.5%  ‐31.3%

Merger: 8 9 10 11 12 13 14

Price Change Relative to Controls  ‐5.4% 9.3% ‐0.6% 8.9% ‐2.6% 19.9% ‐15.2%

P‐value of t Test: Price Change vs. Mean

Control Price Change 0.47 0.02 0.26 0.08 0.40 0.00 0.00

Bed Shares in HRR Post HHI 1151 589 2084 734 4285 1944 5867

HHI Delta 13 42 67 114 1434 290 1329

Discharge Shares in HSA Post HHI 3095 1421 4572 3493 7523 5019 7164

HHI Delta 1390 119 155 404 2623 1446 3540

Discharge Shares in

Weighted Service Area

Post HHI 1999 876 3803 2180 4970 3165 5456

HHI Delta 316 80 138 653 1729 1138 618

Diversion Ratio A to B 1.9%

(0.0%)

6.3%

(0.0%)

1.0%

(0.0%)

20.4%

(0.1%)

6.4%

(0.1%)

12.1%

(0.1%)

5.0%

(0.1%)

B to A 4.4%

(0.0%)

11.3%

(0.0%)

18.0%

(0.1%)

5.2%

(0.1%)

27.8%

(0.2%)

13.2%

(0.1%)

32.6%

(0.2%)

Product of Diversion Ratios 0.0008 0.0071 0.0017 0.0106 0.0177 0.0160 0.0163

Change in Willingness‐to‐Pay 1.4%

(0.0%)

4.1%

(0.0%)

0.9%

(0.0%)

4.1%

(0.1%)

4.8%

(0.1%)

6.8%

(0.1%)

3.5%

(0.1%)

LOCI Price Change Estimate 2.9%

(0.0%)

9.0%

(0.1%)

2.7%

(0.0%)

11.5%

(0.1%)

15.3%

(0.2%)

15.7%

(0.2%)

16.9%

(0.2%)

WTP‐Based  

Merger Simulation

Estimate  ‐0.1% 1.5% 0.0% 0.2% 0.9% 0.5%

CI High 0.5% 6.3% 3.0% 2.4% 8.4% 5.4%

CI Low  ‐0.7% ‐3.3% ‐2.9% ‐1.9% ‐6.6%  ‐4.3%

  
Table 1: Post‐Merger Price Changes and Screening Tools (Mergers 15‐26)

(Standard errors are in parentheses, except as noted)

Merger: 15 16 17 18 19 20 21

Price Change Relative to Controls  ‐26.5% ‐6.7% ‐1.2% 15.6% 30.4% 34.1% 16.1%

P‐value of t Test: Price Change vs.

Mean Control Price Change 0.17 0.03 0.39 0.00 0.00 0.00 0.00

Bed Shares in HRR Post HHI 1391 1118 2825 845 1792 8461 3199

HHI Delta 294 68 1050 4 531 2453 987

Discharge Shares in

HSA

Post HHI 3075 7806 8464 4181 5571 6615 4301

HHI Delta 426 1661 3355 778 1912 2538 1818

Discharge Shares in

Weighted Service Area

Post HHI 1857 5483 4408 3172 2549 5600 3756

HHI Delta 401 1148 1535 594 939 2117 1592

Diversion Ratio A to B 5.9%

(0.1%)

4.7%

(0.1%)

17.5%

(0.2%)

1.3%

(0.0%)

4.4%

(0.0%)

34.2%

(0.9%)

20.6%

(0.3%)

B to A 13.3%

(0.2%)

16.1%

(0.1%)

43.0%

(0.2%)

4.3%

(0.0%)

21.1%

(0.1%)

62.7%

(0.7%)

24.9%

(0.5%)

Product of Diversion Ratios 0.0079 0.0075 0.0751 0.0006 0.0093 0.2140 0.0512

Change in Willingness‐to‐Pay 4.2%

(0.0%)

3.5%

(0.1%)

14.1%

(0.2%)

1.0%

(0.0%)

3.9%

(0.0%)

34.8%

(1.2%)

13.6%

(0.2%)

LOCI Price Change Estimate 10.4%

(0.1%)

9.0%

(0.1%)

43.6%

(0.4%)

2.2%

(0.0%)

10.0%

(0.0%)

133.6%

(3.9%)

53.2%

(0.9%)

WTP‐Based  

Merger Simulation

Estimate 1.0% ‐0.4% 0.6% ‐2.3% ‐0.1% 18.3% 9.9%

CI High 4.4% 6.8% 18.3% 34.6% 3.6% 66.4% 28.0%

CI Low  ‐2.5% ‐7.5% ‐17.1% ‐39.2% ‐3.7%  ‐29.7%  ‐8.3%

Merger: 22 23 24 25 26

Price Change Relative to Controls 8.2% ‐7.7% 13.2% 4.3% 6.3%

P‐value of t Test: Price Change vs.

Mean Control Price Change 0.10 0.73 0.11 0.06 0.00

Bed Shares in HRR Post HHI 2382 549 4024 2808 1977

HHI Delta 261 17 1142 209 288

Discharge Shares in

HSA

Post HHI 3624 3974 6923 4096 3785

HHI Delta 254 1841 2578 1723 655

Discharge Shares in

Weighted Service Area

Post HHI 3818 1159 5316 3678 2629

HHI Delta 423 220 1912 1535 378

Diversion Ratio A to B 4.3%

(0.0%)

1.0%

(0.0%)

16.5%

(0.4%)

7.5%

(0.2%)

11.6%

(0.1%)

B to A 21.3%

(0.1%)

7.1%

(0.0%)

36.1%

(0.4%)

10.3%

(0.2%)

32.4%

(0.1%)

Product of Diversion Ratios 0.0092 0.0007 0.0595 0.0077 0.0376

Change in Willingness‐to‐Pay 3.6%

(0.0%)

1.1%

(0.0%)

11.7%

(0.3%)

4.7%

(0.1%)

9.5%

(0.0%)

LOCI Price Change Estimate 10.2%

(0.0%)

2.4%

(0.0%)

37.4%

(0.8%)

10.1%

(0.2%)

26.9%

(0.1%)

WTP‐Based  

Merger Simulation

Estimate 0.4% 4.3% ‐2.6%

CI High 1.3% 39.7% 3.3%

CI Low  ‐0.5% ‐31.2% ‐8.5%
Table 2: Selection Based on Thresholds

Correct

Prediction

False

Positive

Strong

False

Positive

False

Negative

Mean Relative Price

Change for Flagged

Mergers

HHI  

(HRR Bed Shares)

Guidelines

14 6 1 6 5.8%

HHI

(HSA Disch Shares)

Guidelines

9 16 2 1 4.7%

HHI

(WSA Disch Shares)

Guidelines

12 12 2 2 6.7%

Change in WTP

> 5%

17 5 0 4 11.2%

Correct Prediction = (Flagged merger as problematic and merger associated with statistically

significant relative price increase) or (Did not flag merger as problematic and merger not

associated with statistically significant relative price increase)

False Positive = (Flagged merger as problematic and merger not associated with statistically

significant relative price increase)

Strong False Positive = (Flagged merger as problematic and merger associated with statistically

significant relative price decrease)

False Negative = (Did not flag merger as problematic and merger associated with statistically

significant relative price increase)

Guidelines = Horizontal Merger Guidelines thresholds = Post‐Merger HHI > 2500 and HHI Delta

> 200
Table 3: Regressions of Price Change on Screening Tools

Entire Sample

(N = 26) North Carolina (N = 10) Excluding Merger 20 (N = 25) Alternate Control Group (N=26) Alternate (2‐Year) Price Change (N=17) Price C

Alter

Coefficient

(SE) R2 Coefficient (SE) R2 Coefficient (SE) R2 Coefficient (SE) R2 Coefficient (SE) R2 Coe

Bed Sharesin HRR

PostHHI

‐2.1x10

‐5

(4.8x10‐5) 0.06

‐4.2x10

‐5

(5.4x10‐5) 0.17

‐4.4x10

‐5

(4.6x10‐5) 0.05

‐1.2x10

‐5

(4.9x10‐5) 0.03

‐2.2x10

‐5

(7.4x10‐5) 0.01

3

(4

HHIDelta

1.1x10

‐4

(1.5x10‐4)

5.2x10

‐5

(1.6x10‐4)

8.6x10

‐5

(1.4x10‐4)

7.7x10

‐5

(1.5x10‐4)

4.0x10

‐5

(2.2x10‐4)

‐1

(1

DischargeShares in

HSA

Post

HHI

2.0x10

‐6

(3.1x10‐5) 0.02

‐3.7x10

‐5

(3.7x10‐5) 0.30

‐2.7x10

‐6

(2.8x10‐5) 0.05

1.9x10

‐5

(3.0x10‐5) 0.05

‐1.6x10

‐7

(4.7x10‐5) 0.06

3

(3

HHIDelta

‐2.1x10

‐5

(5.1x10‐5)

3.3x10

‐6

(4.8x10‐5)

‐2.5x10

‐5

(4.7x10‐5)

‐5.2x10

‐6

(5.1x10‐5)

‐4.1x10

‐5

(7.7x10‐5)

‐5

(5

DischargeShares in

WeightedService Area

Post

HHI

‐2.9x10

‐5

(2.8x10‐5) 0.09

‐5.2x10

‐5

(2.9x10‐5) 0.34

‐3.3x10

‐5

(2.7x10‐5) 0.07

‐2.1x10

‐5

(2.9x10‐5) 0.06

1.9x10

‐5

(4.4x10‐5) 0.11

‐1

(3

HHIDelta

9.7x10

‐5

(6.6x10‐5)

6.8x10

‐5

(5.9x10‐5)

6.5x10

‐5

(6.4x10‐5)

8.2x10

‐5

(6.7x10‐5)

‐1.1x10

‐4

(9.6x10‐5)

4

(7

DiversionRatio

A to B 0.81*

(0.47) 0.19

0.93

(0.53) 0.35

0.62

(0.52) 0.06

0.92*

(0.47) 0.19

‐0.75

(0.96) 0.07

B to A 0.01

(0.27)

‐0.15

(0.34)

‐0.10

(0.30)

‐0.07

(0.27)

0.58

(0.56)

Product of Diversion

Ratios

1.46**

(0.58) 0.18 2.25 (2.15) 0.12 1.08 (1.48) 0.02 1.31* (0.65) 0.15 0.11 (0.86) 0.00 

Change in Willingness‐

to‐Pay

0.97**

(0.39) 0.20 1.87 (1.09) 0.27 0.79 (0.77) 0.05 0.89** (0.40) 0.17 0.11 (0.56) 0.00 

LOCI Price Change

Estimate

0.24**

(0.10) 0.19 0.35 (0.38) 0.10 0.19 (0.22) 0.03 0.22** (0.11) 0.16 0.02 (0.14) 0.00 

WTP‐Based Merger

Simulation1

0.50

(0.70) 0.03 2.73 (2.38) 0.18 ‐0.88 (0.93) 0.05 0.39 (0.70) 0.02 ‐0.27 (0.99) 0.01 

The coefficients are statistically significant at the 99% (***), 95% (**), and 90% (*) levels as indicated.1 For the WTP‐based merger simulation, the sample size is reduced by 5 to account for rural mergers.
1

Graph 1: Mean Price Change for Mergers above WTP Threshold

0 .1 .2 .3 .4

Mean Price Change

0 .05 .1 .15 .2

WTP Threshold

Mean Price Change Above Threshold
2

Graph 2: Post‐Merger Price Change and HHI Delta (Bed Shares in the HRR)

(Larger dots indicate larger post‐merger HHI levels. Hollow dots are North Carolina.)

    -.4 -.2

0 .2 .4

Post-Merger Price Change

0 500 1000 1500 2000 2500

HHI Delta HRR Beds

HHI HRR Bed Shares
3

Graph 3: Post‐Merger Price Change and HHI Delta (Discharge Shares in the HSA)

(Larger dots indicate larger post‐merger HHI levels. Hollow dots are North Carolina.)

    -.4 -.2

0 .2 .4

Post-Merger Price Change

0 1000 2000 3000 4000

HHI Delta HSA Discharges

HHI HSA Discharge Shares
4

Graph 4: Post‐Merger Price Change and HHI Delta (Discharge Shares in the Weighted SA)

(Larger dots indicate larger post‐merger HHI levels. Hollow dots are North Carolina.) -.4 -.2

0 .2 .4

Post-Merger Price Change

0 500 1000 1500 2000

HHI Delta WSA Discharges

HHI WSA Discharge Shares
5

Graph 5: Post‐Merger Price Change and the Product of the Diversion Ratios

(Hollow dots are North Carolina.) -.4 -.2

0 .2 .4

Post-Merger Price Change

0 .05 .1 .15 .2

Product of Diversion Ratios

Parametric Choice Model

Product of Diversion Ratios
6

Graph 6: Post‐Merger Price Change and WTP Change

(Hollow dots are North Carolina.) -.4 -.2

0 .2 .4

Post-Merger Price Change

0 .1 .2 .3 .4

WTP Change

Parametric Choice Model

WTP Change
7

Graph 7: Post‐Merger Price Change and LOCI Price Change Estimate

(Hollow dots are North Carolina.) -.4 -.2

0 .2 .4

Post-Merger Price Change

0 .5 1 1.5

LOCI Price Change Estimate

Parametric Choice Model

LOCI Price Change Estimate
8

Graph 8: Post‐Merger Price Change and WTP‐Based Merger Simulation

(Hollow dots are North Carolina.)

    -.4 -.2

0 .2 .4

Post-Merger Price Change

-.05 0 .05 .1 .15 .2

Merger Simulation Price Change Estimate

Parametric Choice Model

Merger Simulation Price Change
9

Graph 9: Post‐Merger Price Change vs. Alternate Second‐Year Post‐Merger Price Change

   

45° Line

-.2 -.1

0 .1 .2 .3

Alternate Post-Merger Price Change

-.4 -.2 0 .2 .4

Post-Merger Price Change

Alternate Price Change vs. Price Change
10

Graph 10: Semiparametric WTP Change vs. Parametric WTP Change

45° Line

0 .1 .2 .3 .4 Parametric WTP Change

0 .1 .2 .3 .4 .5

Semiparametric WTP Change

Semiparametric WTP Change vs. Parametric WTP Change
1

Appendix A: Example of HHI Calculations

Consider a hypothetical hospital market in which there are 5 hospitals, each located in

one of 5 contiguous areas (e.g., zip codes).  The hospitals, locations, and sizes are as follows:

Hospital Area Staffed Beds

A 1 100

B 2 150

C 3 50

D 4 200

E 5 250

In each area live 100 patients. The following table lists the patients by their hospital of

treatment and their resident location.

Hospital Area 1

Patients

Area 2

Patients

Area 3

Patients

Area 4

Patients

Area 5

Patients

Total Patients

Treated at Hospital

A 40 5 10 10 5 70

B 25 50 15 10 5 105

C 5 5 30 5 5 50

D 10 20 20 60 10 120

E 20 20 25 15 75 155

Consider a proposed merger between hospitals A and B.  Suppose A and B’s HRR is the

combination of areas 1 through 4.  Using the first HHI calculation method (bed shares in the

HRR), only hospitals A, B, C, and D are in the market with shares of 20% (100/500) for A, 30%

(150/500) for B, 10% (50/500) for C, and 40% (200/500) for D.  The pre‐merger HHI is (20)2 +

(30)2 + (10)2 + (40)2 = 3,000 with a delta of 2(ShareA)(ShareB) = 1,200 for a post‐merger HHI of

4,200.  

Suppose B’s HSA is the combination of areas 1 and 2. Using the second HHI calculation

method (discharge shares in the HSA), A has a pre‐merger share of 45/200 = 22.5%, B has a pre‐

merger share of 75/200 = 37.5%, C has a pre‐merger share of 10/200 = 5%, D has a pre‐merger

share of 30/200 = 15%, and E has a pre‐merger share of 40/200 =20%.  The pre‐merger HHI is

(22.5)2 + (37.5)2 + (5)2 + (15)2 + (20)2 = 2,562.5 with a delta of 2(ShareA)(ShareB) = 1,687.5 for a

post‐merger HHI of 4,250.

For the third HHI calculation method (discharge shares in the weighted service area), we

first have to determine the fraction of the merged entity’s business that originates from each

area. Of the 175 total patients treated by A and B, 65 (37.1%) come from Area 1, 55 (31.4%)

come from Area 2, 25 (14.3%) come from Area 3, 20 (11.4%) come from Area 4, and 10 (5.7%)

come from Area 5.  A’s weighted share is (0.371)(40) + (0.314)(5) + (0.143)(10) + (0.114)(10) +

(0.057)(5) = 19.3%.  B’s weighted share is (0.371)(25) + (0.314)(50) + (0.143)(15) + (0.114)(10) +

(0.057)(5) = 28.6%.  C’s weighted share is (0.371)(5) + (0.314)(5) + (0.143)(30) + (0.114)(5) +

(0.057)(5) = 8.6%.  D’s weighted share is (0.371)(10) + (0.314)(20) + (0.143)(20) + (0.114)(60) +

(0.057)(10) = 20.3%.  E’s weighted share is (0.371)(20) + (0.314)(20) + (0.143)(25) + (0.114)(15) +

(0.057)(75) = 23.3%.  The pre‐merger HHI is (19.3)2 + (28.6)2 + (8.6)2 + (20.3)2 + (23.3)2 = 2,215.5

with a delta of 2(ShareA)(ShareB) = 1102 for a post‐merger HHI of 3,317.5.
Appendix B: Sample of Mergers

State Data Used Control Bed Threshold MSA Choice Population Acquiring System Primary Hospital in Acquiring System 

NC 100 HRR Cone Health Moses Cone Memorial Hospital 

PA/NY 100 Combined PSA Upper Allegheny Health System Olean General Hospital Bradford Reg

NC 100 Wilmington HRR New Hanover Regional Medical Center New Hanover Regional Medical Center Cape Fe

NC 100 Greensboro‐Winston‐Salem‐High Point HRR Novant Health Forsyth Memorial Hospital Commu

NY 100 Syracuse HRR Upstate University Hospital Upstate University Hospital Community‐General Hospita

NC 100 Raleigh‐Durham‐Chapel Hill HRR Duke University Health System Duke University Medical Center Durh

NC 100 Hickory‐Morganton‐Lenoir Combined PSA Carolinas Healthcare Valdese General Hospital 

AR 0 Hot Springs HRR Mercy St. Joseph's Mercy Health Center 

GA 100 Atlanta‐Sandy Springs‐Marietta HRR Piedmont Healthcare Piedmont Hospital 

NC 100 Greenville & Rocky Mount HRR UHS East Pitt County Memorial Hospital 

NC 100 Fayetteville HRR Cape Fear Valley Health System Cape Fear Valley Health System Highsmith‐Rain

CT 100 New Haven‐Milford HRR Yale New Haven Health System Yale‐New Haven Hospital Hos

PA 100 Philadelphia‐Camden‐Wilmington HRR Abington Health Abington Memorial Hospital PA 100 Scranton‐‐Wilkes‐Barre HRR Community Health Systems Regional Hospital of Scranton M

CT 50 HRR Western Connecticut Health Network Danbury Hospital 

GA 100 Albany HRR Phoebe Putney Health System Phoebe Putney Memorial Hospital Pa

GA 100 Atlanta‐Sandy Springs‐Marietta HRR Piedmont Healthcare Piedmont Hospital Piedm

NC 50 Charlotte‐Gastonia‐Rock Hill HRR Novant Health Presbyterian Hospital Presbyterian 

NC 100 Raleigh‐Durham‐Chapel Hill HRR University of North Carolina Hospitals University of North Carolina Hospitals 

GA 100 Atlanta‐Sandy Springs‐Marietta HRR Emory Healthcare Emory University Hospital Saint Joseph

PA 100 HRR Schuylkill Health System Pottsville Hospital Goo

AR/OK 0 Fayetteville‐Springdale‐Rogers HRR Community Health Systems Northwest Medical Center Siloam Sprin

NY/PA 100 Elmira HRR Arnot Health Arnot Ogden Medical Center 

CT 100 Hartford‐West Hartford‐East Hartford HRR Hartford Healthcare Hartford Hospital The Hospital o

PA 100 Pittsburgh HRR UPMC UPMC Presbyterian Shadyside 

NC 100 Greensboro‐Winston‐Salem‐High Point HRR Cone Health Moses Cone Memorial Hospital Wesley Long