WORKING 

PAPERS 

For-Profit Status & Industry Evolution in Health Care Market: 

Evidence from the Dialysis Industry

Nathan E. Wilson 

WORKING PAPER NO. 314 

February 2013 

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For-Profit Status & Industry Evolution in Health Care Markets:

Evidence from the Dialysis Industry

Nathan E. Wilson ∗†

February 15, 2013

Abstract

Over the last 25 years, for-profit facilities have supplanted non-profits as the modal providers

of hemodialysis treatment to American sufferers of end-stage renal disease. To understand what

may underpin this dramatic change in industry structure, this paper uses a dynamic equilibrium

model to develop intuition about how variation in different economic primitives might affect the

evolution of industry structure. Subsequently, the paper exploits a comprehensive 20+ year

panel dataset to examine entry, exit, and output patterns in relation to changes in demand

and local market structure. Examining the empirical results in light of the model’s comparative

statics suggests that for-profit firms enjoy a significant advantage in static competition, perhaps

as a result of lower marginal costs. By comparison, I find negligible evidence that for-profit

facilities have lower entry costs. Interestingly, the data also suggest that competition among

dialysis clinics may be differentiated.

JEL Codes: D4, I11, L10

Keywords: dialysis, entry, market dynamics, organizational structure, for-profit status

∗The views expressed in this article are those of the author. They do not necessarily represent those of the Federal

Trade Commission or any of its Commissioners. Contact: 600 Pennsylvania Avenue NW, M-8059, Washington DC,

20580. Phone: 202-326-3485. E-mail: nwilson@ftc.gov.

†

I am grateful for help and comments from my colleagues Dan Hosken, Chris Taylor, Brett Wendling, Chris

Adams, John Yun, Pauline Ippolito, and Joe Breedlove as well as Matt Grennan, Tom Buchmueller, Andrea Chung,

Anne Bowers, and audiences at both the Department of Justice and the Federal Trade Commission. The usual caveat

applies.

1
1 Introduction

Having undergone dramatic structural changes over the last 40 years, the U.S. renal dialysis industry makes for an interesting setting in which to consider industry evolution due to variation

in managerial “technologies” (Bloom and Van Reenen, 2010, Bloom et al., 2012). In particular, it

offers an opportunity to consider the role of perhaps the most fundamental managerial technology:

the profit motive. This is because, like other areas in health care, the dialysis industry is “mixed” in

terms of ownership: some participants operate on a for-profit basis, while others do not. Moreover,

the industry has seen enormous changes in structure over time: whereas the majority of treatment

facilities initially were atomistic non-profit organizations, for-profit chains now predominate.1

Though long aware of the rising importance of for-profit dialysis providers (Farley, 1993), scholars and practitioners have not reached a consensus as to what might underpin it. This is concerning

for both theoretical and substantive reasons. Theoretically, it limits understanding of the behavioral

implications of the profit motive. Practically, it keeps policymakers from developing an accurate

sense of whether or not there are benefits to non-profit ownership large enough to justify their

tax subsidies (Schlesinger and Gray, 2006). These benefits are of very substantial magnitude due

to the size of the dialysis industry: As a result of the rising prevalence of end-stage renal dialysis

(ESRD), around half a million Americans now regularly need dialyzation, and the bulk of this

expense is borne by the taxpayer. Indeed, Medicare’s expenditures on ESRD alone now account for

approximately one percent of the entire Federal budget (Ramanarayanan and Snyder, 2012).

To partially disentangle these issues, I first develop a dynamic equilibrium model tailored to

the institutional details of the dialysis industry. The model illustrates how differences in various

underlying economic primitives across ownership types should differentially affect the evolution of

market structure. I then exploit a comprehensive dataset of over 20 years of linked annual censuses

of all facilities providing treatment to ESRD sufferers in the country to see how actual industry

evolutionary patterns compare to the model’s predictions.

The paper’s chief empirical findings are as follows. First, I consistently find evidence of significant

1

Indeed, between 1988 and 2008, the share of facilities operated by for-profit companies increased from 52 percent

to 79 percent. In addition, the industry has become quite concentrated with around 60 percent of all facilities

associated with the two leading for-profit chains – DaVita and Fresenius (USRDS, 2011). Antitrust authorities have

taken considerable interest whenever recent mergers or acquisitions have been proposed. For example, the Federal

Trade Commission (FTC) recently required that DaVita sell off 29 dialysis centers in order to preserve competition

in 22 different local markets. See http://www.ftc.gov/opa/2011/09/davita.shtm.

2
behavioral differences across ownership types after controlling for differences in facility and market

characteristics. Examinations of the likelihood of exit show that non-profits are more likely to exit

on average, and that they are more responsive to changes in the level of demand. By contrast,

comparing entry rates across facility types reveals that for-profit facilities are both more likely to

enter and more broadly responsive to changes in demand. Meanwhile, I find that the presence of

for-profit facilities has a consistently larger impact on exit and output. All of these results are

consistent with the patterns that would be expected if for-profit facilities have an advantage in

static competition. Moreover, the results – especially those having to do with asymmetric market

structure effects and variation in exit behavior – do not support the idea of large differences in

entry costs.

These findings contrast with those of Chakravarty et al. (2006), who concluded that the rise

of for-profit hospitals during roughly the same period stemmed from their lower costs of entry,

and occurred despite having higher marginal costs. My results also run contrary to the findings of

Harrison and Laincz (2008) who found low exit rates for non-profits generally, though they did not

have data to examine the exit behavior of otherwise similar for-profit organizations.

In addition, I find surprisingly tenuous evidence of the influence of concentration measured at

the county level on economic behavior. I show that the average Hirschmann-Herfindahl Index (HHI)

for a county has increased by over one percent a year after controlling for market size, but analyses

of entry, exit, and treatment production do not suggest that this rapid rise in concentration has

produced dramatic changes in behavior. While I find weak evidence suggestive of increased output

per facility in more concentrated markets, the analyses of entry rates imply that this facility-level

increase in production has not occured as a result of restricted supply of facilities.

Though the evidence that for-profit facilities possess a static advantage is strong, the question of

whether the advantage derives from a superior ability to attract patients or lower marginal costs (or

both) cannot be conclusively answered. Some of the prior literature (e.g., Held and Pauly (1983))

provides evidence consistent with the idea that for-profit facilities are more efficient at performing

hemodialysis treatments. However, looking at the number of hemodialysis treatments performed, I

find evidence that for-profits perform more treatments, holding demand and competition constant.

While possibly consistent with differences in upward-sloping marginal cost functions, this result

could also suggest the presence of demand advantages given that there is very little price competition

3
since Medicare pays for 82 percent of patients. The latter seems especially plausible given that the

analyses do not suggest evidence of capacity constraints at non-profit facilities. Moreover, analyses

of output and entry suggest asymmetric diversion ratios across ownership types.

On its face, evidence of differentiated demand is surprising. After all, why should patients consistently prefer one type of facility providing ostensibly homogeneous treatments at the same price?

Arguably, the evidence can be rationalized by focusing less on patients’ tastes than on their referring

physicians’ preferences. For example, the results for output are consistent with the idea that those

physicians that prefer for-profit do so more fervently than those physicians preferring non-profit

facilities. Such strong preferences could stem from the growing commonality of formal affiliations

between the largest dialysis providers and local physician practices.2 After all, research has shown

that physicians do respond sharply to financial incentives (Helmchen and Lo Sasso, 2010, HennigSchmidt et al., 2011, Van Dijk et al., 2012, Swanson, 2012), and one would presume that referrals

to facilities within an organization are rewarded relative to those outside the firm. Moreover, this

belief is consistent with recent litigation designed to inhibit “self-referrals” by nephrologists vertically affiliated with related services providers.3 Alternatively, the data might reflect physicians’

belief that for-profit facilities consistently provide higher quality. However, this runs contrary to

conventional wisdom and much of the existing literature.4

Overall, this paper contributes to a number of literatures. First, it extends our understanding

of the role managerial differences may play in driving industry evolution by providing a detailed

analysis of a specific industry that has undergone sizable changes. This is particularly useful in the

health care context given the longstanding argument about the desirability of extending support to

non-profits through the tax system (Schlesinger and Gray, 2006). Second, the paper contributes to

a burgeoning economic literature that uses the dialysis industry as a laboratory in which to consider

issues ranging from quality-differentiated competition (Cutler et al., 2012, Grieco and McDevitt,

2012) to the role of information disclosures in quality determination (Ramanarayanan and Snyder,

2See, for example Fresenius’ page on their relationships with nephrologists: http://www.fmcna.

com/fmcna/PhysicianStrategies/PhysicianServices/medicalstaffdevelopment/index.htm. In addition,

DaVita has announced their intention to form an Accountable Care Organization following their acquisition of the physician group HealthCare Partners (see, e.g., http://www.fiercehealthcare.com/story/

healthcare-partners-davita-merger-turns-aco/2012-05-22).

3For more details, see, http://www.floridatoday.com/viewart/20130110/HEALTH/130110020/

Court-upholds-controversial-dialysis-law.

4See, inter alia, Grieco and McDevitt (2012), Zhang et al. (2011); however, Brooks et al. (2006) find no statistical

effect of ownership status on mortality.

4
2012).5 While the previous contributions have noted important factors about the dialysis industry,

they have relied upon cross-sectional data or panel datasets with a small time series dimension.

Thus, they have been informative about relatively contemporaneous states of the industry but

unable to explore the longer-run questions considered in this paper.

2 Industry Setting & Data

2.1 End-Stage Renal Disease

A diagnosis of ESRD means that an individual has permanently lost kidney function. It typically

arises as a by-product of serious health conditions such as chronic kidney disease, coronary disease,

hypertension, diabetes, and other progressive, chronic conditions. ESRD is fatal without treatment,

which may take two forms: kidney transplant or chronic dialysis. As noted in Ramanarayanan

and Snyder (2012, p. 8), physicians view transplantation as the preferred option insofar as it is

associated with lower mortality and healthier lives relative to those on dialysis. Unfortunately, the

number of ESRD patients vastly outnumbers the number of kidneys available for transplantation.

Consequently, 70 percent of ESRD patients are regularly dialyzed.6

Effective in 1973, the Social Security Act extended Medicare benefits to all patients diagnosed

as having permanently lost kidney function. ESRD is the only catastrophic illness whose care is

financially covered by a national public program regardless of patient age or financial status. For

individuals with ESRD who still have insurance through their employer (or union), the group health

plan is the primary payer for the first 30 months, while Medicare is the secondary payer. Once the 30

months have elapsed, Medicare is the principal payer.7In 2010 (the most recent year for which data

are available), Medicare covered 489 thousand ESRD sufferers, while other payers accounted for an

additional 105 thousand patients. Similarly, Medicare’s expenditures accounted for $33 billion out

of a total of $47.5 billion.8

Given its dominant role, Medicare has been able to exert a considerable influence on mini5The economics papers themselves complement a large literature in medicine and public health regarding the

industry (see, e.g., Lee et al. (2010) and citations therein).

6See http://kidney.niddk.nih.gov/kudiseases/pubs/kustats/ for ESRD treatment statistics. See Farley

(1993) for more details on the origins and early evolution of the retail dialysis industry.

7See, e.g., CMS’ brochure on Medicare coverage at http://www.medicare.gov/publications/pubs/pdf/10128.

pdf.

8Approximately 10 percent of Medicare expenditures actually reflect spending by Medicare Advantage programs.

The data can be found in the U.S. Renal Data System “Annual Data Report” at http://www.usrds.org/atlas.aspx.

5
mum standards of facility staffing and other characteristics relating to quality. It has also dictated

terms on pricing. Since 1983, Medicare has reimbursed dialysis centers on a fixed fee basis for each

hemodialysis treatment. The payment contains an invariant component known as the “base rate,”

which covers the bundle of services, tests, and particularly routine drugs for up to three treatments

in a week.9In addition to the base rate, dialysis centers receive variable compensation for other

items and services, particularly injectable drugs (for example, erythropoietin (EPO), iron sucrose,

vitamin D), and non-routine laboratory tests that are not included in the base rate. These variable

components represent about 40 percent of total Medicare payments per dialysis treatment.10 Overall, Medicare covers approximately 80 percent of treatment costs; patients cover the remainder out

of pocket, or through supplemental insurance policies.11 Other payers are free to negotiate their

own reimbursement rates as for other clinical procedures.

Owing to ESRD’s increasing commonality, the number patients receiving treatment has risen

substantially over time. For the whole population, the incidence of ESRD – meaning the number

of patients newly diagnosed – increased from less than 0.1 percent to 0.35 percent (USRDS, 2011)

between 1980 and 2008. For some demographic groups, however, the increase was much steeper. For

example, in 1980, around 0.25 percent of Americans over the age of 75 contracted ESRD. By 2008,

this figure had increased to around 1.75 percent. As a consequence of both the growing commonality

of the condition and its increasing severity (Farley, 1993), Medicare’s ESRD expenditures have

increased to the point where they acounted for close to one percent of the entire federal budget in

2010 (Ramanarayanan and Snyder, 2012).

2.2 The Retail Dialysis Industry

The decision to have Medicare cover ESRD treatment created an industry of facilities dedicated

to providing care to qualifying patients. These facilities are differentiated in multiple respects.

The most obvious distinction is between those affiliated with hospitals, which often also provide

transplantation services, and freestanding centers that primarily exist to provide dialysis services

9The level of the base payment has changed several times partly as a result of changes in the cost of inputs but

partly also in connection to beliefs about improvements in treatment technology. The base rate is adjusted by a

drug add-on payment to account for changes in the drug pricing methodology that occurred in 2005 and by age and

body size. One of the changes had to do with the extent to which variation in labor costs were incorporated into the

payment. Originally set at 40 percent, it increased to 53.7 percent in 2006 (DeOreo, 2006).

10See https://www.cms.gov/Medicare/Medicare-Fee-for-Service-Payment/ESRDpayment/.

11For in-clinic dialysis, Medicare covers exactly 80 percent. For additional copay information, see, e.g., http:

//www.carepathways.com/MedicareCoverage.cfm.

6
(perhaps accompanied by related testing and/or drug infusion services). After taking account of

whether or not a center is affiliated with a hospital or not, the chief way in which clinics differ is

whether they are operated by for-profit or not-for-profit entities.12 Be they non-profit or for-profit,

clinics are also differentiated by whether or not they are independently owned or part of chains.

Past research has not reached much of a consensus about behavioral differences attributable to

ownership form. For example, the literature has not consistently indicated that for-profit facilities

provide better levels of quality. On the contrary, the working hypothesis in the literature has tended

to be that the opposite is true, and Garg et al. (1999), Lee et al. (2010), Zhang et al. (2011), and

Grieco and McDevitt (2012) have found evidence that for-profit facilities do perform worse on some

quality metrics than non-profit facilities. However, other authors have found no statistical difference

in quality across facility types (Ford and Kaserman, 2000, Brooks et al., 2006).13 In contrast to

the mixed results for quality, the existing literature is in broader agreement that for-profit dialysis

facilities are more cost-efficient (Griffiths et al., 1994, Hirth et al., 1999, Ozgen and Ozcan, 2002).

This might help to explain the rise of for-profit facilities, but the extent and implications of any

cost differences remain uncertain. Moreover, many of the studies only had access to cross-sectional

data, and therefore were unabled to fully account for the possibility of significant unobserved but

persistent variation.

2.3 Data

This paper exploits data from two sources. The first is the United States Renal Dialysis System

(USRDS), which collects, analyzes, and distributes information about the prevalence and treatment of ESRD in the United States. The USRDS receives its funding from the National Institute

of Diabetes and Digestive and Kidney Diseases (NIDDK), a part of the National Institutes of

Health (NIH). The data that I use come from the Facility file, which is constructed from the Center

of Medicare and Medicaid Services’ (CMS) Annual Facility Survey, the Center for Disease Control’s (CDC) National Surveillance of Dialysis-Associated Diseases, and the CMS Dialysis Facility

Compare database.

12It should be noted that hospital affiliation encompasses a number of different relationships. The most obvious

example is that the hospital contains a nephrology center that regularly performs treatments. It is common, however,

for hospitals to affilate with separate physical entities in their service area that focus explicitly on providing chronic

dialyzations. The data used in this paper do not permit one to identify the specific relationship with the hospital.

13Ford and Kaserman (2000) find that some types of for-profit facilities have identical outcomes to non-profits, but

show evidence that other types of for-profit facilities perform worse.

7
From 1980 through 2008, the USRDS facility data include information on the number of patients

treated, facility age (by reference to its certification date), whether affiliated with a hospital, forprofit status (after 1988), and chain affiliation (after 1988).14 Location is provided at the zipcode

level. All other information is at the facility level. Facilities are linked across years by unique

identification numbers.

The USRDS data define chains as being affiliations of at least 20 different facilities. Hence, the

data provide conservative estimates of the overall presence of multi-unit organizations.15 Table B-1

in the Appendix indicates for the different chains identified in the data the years in which they

were present, their profit status, and the total number of facility-year observations they are linked

with. The Table shows that the overwhelming majority of chains identified in the USRDS data are

for-profit. Only Dialysis Clinic, Inc. (DCI) – the fifth largest chain by total number of observations

– is non-profit.16

Beginning in 2002, the USRDS recorded some facilities’ ownership status as “Unknown.” In

order to conserve observations, I assumed that if no change in chain affiliation was recorded, a facility

with an “Unknown” for-profit status continued to have its previously recorded status. Similarly,

where no change in affiliation was recognized, I assumed that previous years with “Unknown” status

have the same value as later years. When these rules did not apply, I left the facility categorized

as having “Unknown” profit-status, which causes it to be dropped from the analyses. Finally, I

cleaned the data based on the assumption that one-time deviations in status represent error on

the part of the survey responder rather than evidence that a facility changed owners twice in three

years time. Further details are available upon request.

14Individual facilities are not named. Instead, their affiliation with a particular brand is recorded if that brand is

associated with 20 or more distinct facilities.

15In some cases, when a facility changes hands, which has regularly occurred in recent years (Pozniak et al., 2010),

the identification number may also change. This may be true even if most staff and location remain unchanged;

however, casual observation of the data indicates that there are numerous occurrences when chain affiliation changes

and the identification number does not. Nevertheless, this is a concern. However, if there are such errors in variables,

it should lead to attenuation, making it more difficult to identify differences. Hence it is a conservative approach.

16Examining the connection between profit-status and chain affiliation, it became evident that the raw USRDS

data contain errors. In reality, all of the chains are universally either for- or non-profit. However, a non-trivial number

of observations assign the “wrong” profit status to a facility affiliated with a given chain. Upon investigation, I came

to the conclusion that the problems stemmed from lags in updating a given facility’s status following a change in

ownership. As a result, I have cleaned the data by imposing that a facility’s for-profit status should match its chain

affiliation. To the extent that acquisitions presumably took place below the threshold for appearing as a chain in the

data or simply among independents, however, the status identifier will contain measurement error. In the econometric

analyses, this should make it more difficult to cleanly identify differences across for- and non-profit facilities, and

hence is a conservative approach.

8
The second source of data is the Surveillance, Epidemiology and End Results (SEER) Program,

which is also affiliated with the NIH. From SEER, I obtained data on county-level demographic

information over the sample period. Since zipcodes do not map perfectly to counties, I assigned

each zipcode to the county it was most closely associated with (in terms of population).17 Since

ESRD is more common among older Americans, I proxy for local demand for dialysis services using

the county population that is over 60.18

2.4 Market Definition

I follow Chakravarty et al. (2006) in considering market dynamics at the county level.19 This differs

slightly from the approach taken by Grieco and McDevitt (2012), and others, of using hospital

service areas (HSAs) to define geographic markets. HSA’s are slightly larger – on average – than

counties, but the main reason that counties are attractive relative to HSAs is that HSAs may

span state borders. This is problematic as there is regulatory variation across state lines due to

differences in certificate-of-need regulations, which Ford and Kaserman (1993) found to have a

substantial influence on dialysis facility entry patterns.20 Overall, there are 1766 different counties

in the data and 32785 different county-year observations. There are 84616 distinct facility-year

observations, and 73667 that identify ownership status.

Table 1 provides summary statistics for all facility-level observations. In addition to providing

information on facility-level characteristics and the average market composition, the Table provides

some sense of the degree of concentration of local markets using county-level HHIs. The HHIs shown

in the Table are based on the shares of the number of facilities in a given county associated with

each of the major chains identified in the data. Independents are assumed to be atomistic. Insofar

as the data only identify chain affiliations if there are at least 20 member facilities, this means that

17In some cases, the USRDS data did not match prefectly cleanly. Details on how such problems were addressed

are available upon request.

18For summary statistics on the prevalence of ESRD, the interested reader is referred to the USRDS’ “Atlas

of Chronic Kidney Disease and End-Stage Renal Disease in the United States,” which can be found at: http:

//www.usrds.org/2011/slides/indiv/v1index.html.

19To be clear, I am not attempting to construct antitrust markets, e.g., using the Hypothetical Monopolist Test

as described in the Horizontal Merger Guidelines. Instead, the goal is to employ a simple methodology that allows

me to examine similar sets of dialysis service providers providing similar services within broadly similar geographic

regions. In most cases, one would expect antitrust markets to be smaller than the markets analyzed here.

20As is well-known (Gaynor et al., 2011), an arbitrary use of geographic boundaries can give misleading inferences

when assessing the impact of market structure on competitive tactics. Therefore, all econometric analyses control

for market-level heterogeneity that may be correlated with the other explanatory variables. This may not perfectly

address problems associated with geographic limitations, but it should substantially attenuate them.

9
the HHI values are conservative estimates of the degree of concentration. The results are all but

identical when the shares are done based on the number of hemodialysis treatments performed in

a given year by the different chains in a given county.

Table 2 shows summary statistics after distinguishing by profit status (results for facilities with

“unknown” profit status are not shown). Simple comparison of means tests suggest that for- and

non-profit facilities operate differently, but also exist in distinctly different market environments.

For example, on average, for-profit facilities are located in larger markets and face more competitors.

The data also show that the average for-profit facility performs more treatments, while being more

likely to enter and less likely to exit than the average non-profit during the sample period. Nonprofit facilities tend to be older, much more likely to be affiliated with hospitals, and much less

likely to be affiliated with a chain.

Table 1: Descriptive Statistics for All Observations

Obs Mean SD Min Max

Pop Over 60 (’000s) 74105 145.9 247.3 0.292 1429

Hospital Affiliated 74109 0.231 0.422 0 1

Chain Affiliation 74109 0.522 0.500 0 1

Time since Certification 69513 9.853 7.786 -1 42

Number of Competitors 74109 12.72 22.80 0 144

Number of For-profit 74109 9.984 20.13 0 133

Number of Non-profit 74109 2.601 3.795 0 20

Number of Unknown 74109 0.138 0.470 0 6

Market HHI 74109 4778 3482 170.4 10000

Treatments 73720 8514 7082 0 245340

Entry 74109 0.0694 0.254 0 1

Exit 74109 0.0177 0.132 0 1

3 Descriptive Analysis

3.1 Changes in industry size and composition over time

Figure 1(a) depicts how the industry has grown and changed in structure over time. Its results are

consistent with the massive increase in ESRD incidence described above. In 1980, there were only

1017 facilities. In 2008, there were 5446. Insofar as the Figure indicates that the number of nonprofit facilities remained virtually constant over time, this means that the vast majority of growth

10
Table 2: Descriptive Statistics by Profit Status

For-profit Non-profit

Obs Mean SD Obs Mean SD T-Stat

Pop Over 60 (’000s) 52628 157.1 269.0 21035 116.6 178.5 23.82

Hospital Affiliated 52628 0.0320 0.176 21039 0.717 0.450 -214.34

Chain Affiliation 52628 0.681 0.466 21039 0.135 0.342 175.44

Time since Certification 49228 8.768 7.316 19935 12.38 8.109 -54.54

Number of Competitors 52628 14.06 24.93 21039 9.162 15.58 32.06

Number of For-profit 52628 11.51 22.07 21039 5.976 13.24 41.73

Number of Non-profit 52628 2.389 3.671 21039 3.103 4.037 -22.24

Number of Unknown 52628 0.158 0.510 21039 0.0830 0.330 23.58

Market HHI 52628 4859 3419 21039 4621 3642 8.15

Treatments 52424 8936 6886 20928 7534 7480 23.44

Entry 52628 0.0790 0.270 21039 0.0397 0.195 21.99

Exit 52628 0.0144 0.119 21039 0.0253 0.157 -9.08

occurred via entry by new for-profit facilities. The increase in the share of facilities operated for

profit does not simply reflect differences in the average capacity of for- and non-profit facilities

across time. Figure 1(b) shows essentially the same trends for the actual number of hemodialysis

treatments performed as for the number of treatment facilities.

Although the number and utilization of facilities grew dramatically, other aspects of the industry

stayed fairly constant. In particular, the number of hospital-affiliated facilities varied little during

the time that the variable was tracked. This can be seen clearly in Figure 2(a), which also shows that

the number of hospital-affiliated facilities operated for-profit remained comparatively small despite

the increasing commonality of that type of organizational structure. Overall, Figure 2(b) shows the

relative commonality of hospital-affiliated facilities has been declining since the late 1980s. Most of

this decline comes from the increasing prevalence of non-profit dialysis facilities that do not have an

explicit connection to a hospital. The declining relative importance of hospitals holds if one focuses

on the number of treatments rather than the number of clinics, as the resulting graph would look

as close to Figure 2(a) as Figure 1(b) does to Figure 1(a).

Figure 3 shows that chain affiliation has become dramatically more common over time. Unsurprisingly, the increase is particularly dramatic for for-profit facilities, though the share of non-profit

facilities affiliated with a chain (i.e., DCI) also grew significantly. Much of the increase in the share

of for-profit facilities comes as a result of the rapid expansion of DaVita and Fresenius. Between

11
0 2000 4000 6000 Number of Facilities

1980 1990 2000 2010

Year

Total For-profit

Non-profit Unknown

By Type

Stock Dialysis Facilities

(a) Number of dialysis facilities in the United States

0 10 20 30 40 50 Number of Hemodialysis Treatments (in millions) 1980 1990 2000 2010

Year

Total For-profit

Non-profit Unknown

By Type

Number of Dialysis Treatments

(b) Number of Treatments Performed

Figure 1: Market Structure Statistics

12
0

2

4

6 Number of Hemodialysis Treatments (in millions) Performed in Hospital-Affiliated 1990 1995 2000 2005 2010

Year

Total For-profit

Non-profit Unknown

By Type

Number of Dialysis Treatments

(a) Number of Facilities Affiliated with a Hospital

0 .2 .4 .6 .8 Share of Facilities Affiliated with Hospitals 1990 1995 2000 2005 2010

Year

Total For-profit

Non-profit

By Type

Share of Dialysis Facilities Affiliated with Hospitals

(b) Share of Facilities Affiliated with Hospitals

Figure 2: Market Structure Statistics

13
0 .2 .4 .6 .8 Share of Facilities in Chains

1990 1995 2000 2005 2010

Year

For-profit Non-profit

By Type

Share of Dialysis Facilities in Chains

Figure 3: Share of Facilities Affiliated with Multi-Unit Chain

1995 (the first year for which both firms were recognized as major chains in the USRDS data)

and 2008, their share of all non-profit facilities rose from 32 to 73 percent while their share of all

facilities from 20 to 58 percent.

3.2 Concentration

Figure 3 indicated that an increasingly large share of the overall industry is associated with just

a few large chains. However, it did not speak to how concentrated local markets have become.

As a first pass at answering these question, I consider the annual average of county-level HHIs

over time. Figure 4 shows that by this metric the industry has actually grown less concentrated

over time. However, this approach suffers from significant methodological problems. In particular,

it does not account for the fact that the number of possible counties is largely fixed while the

industry has grown extensively. This could lead to downwardly biased estimates if much of the

growth occurred in areas with one pre-existing facility, and the entrant did not share exactly the

same chain affiliation. Therefore, I now turn to analytical methods that hold more things constant.

The importance of controlling for growth can be seen in Table 3, which shows the result of

simple regressions of the log of county HHIs controlling for the relative size of markets in different

ways. In Column 1, this is done especially crudely, restricting the sample to just those markets with

more than one dialysis facility. I do this because there can be no possibility of variation in HHI

14
2500 3000 3500 4000 Average County HHI

1980 1990 2000 2010

Year

Raw Concentration over Time (Facilities)

Figure 4: Average Concentration

within markets whose number of participants remains constant at one. The results indicate that,

on average, HHIs increased by almost one percent per year during the sample period. This result

remains robust when the number of different facilities capable of providing hemodialysis treatment

is held constant as shown in Column 2. In this model, identification occurs cross-sectionally and over

time across counties that have the same total number of facilities. Thus, the result is saying that as

time passes, the likelihood that a county with two treatment facilities would see them both affiliated

with the same corporate parent increased. Interestingly, the rate of increase in concentration across

different markets systematically varied as indicated in Column 3 which adds a measure of demand

(the log of population over 60 in thousands). The results shows that those markets experiencing

the largest increases in demand also grew more concentrated more rapidly.

3.3 Discussion

While broadly informative about the changing competitive structure of the dialysis industry, Table

3 – along with the foregoing Figures – leaves unaddressed the key question: What is driving the

massive change in industry composition? In order to examine this question while taking account of

the possible strategic choice of markets entered by the different types, I now turn to more formal

methods of examining industry evolution.

15
Table 3: Market Concentration (Log(HHI)) as a Function of Time and Market Size

(1) (2) (3)

b/se b/se b/se

Year 0.025*** 0.025*** 0.026***

0 0 0

Log(Pop over 60) 0.031***

0.01

Number of Competitors FE No Yes Yes

At Least 2 Facilities Yes Yes Yes

County FE No No No

N 27653 27649 27649

* p<0.10, ** p<0.05, *** p<0.01.

4 A Model of Industry Evolution via Entry and Exit

4.1 Model Description

In order to develop intuition about the different factors that might cause industry structure to

evolve, I exploit a model of dynamic competition adapted from that of Pakes et al. (2007) (which

is itself a special case of the general Ericson and Pakes (1995) family of dynamic, discrete-time

games).21

Consistent with the fact that price is largely exogenous for dialysis facilities, the model assumes

that competition is between individual facilities of two different types, j, and occurs through entry

and exit in discrete time over an infinite time horizon. The two facility types are n and f, which

represent non-profit and for-profit facilities, respectively. For the sake of simplicity, I assume that all

facilites of the same type are identical. Thus, the model abstracts from variation between facilities

aside from their types.22 All facilities wish to maximize the net present value of their expected

stream of profits. Obviously, this runs contrary to the expressed goal of many non-profits. However,

as shown in Lakdawalla and Philipson (1998, 2006), the marginal decision-making of non-profits

interested in providing output will resemble those of for-profit entities but with lower marginal costs.

Therefore, I believe my approach captures the marginal incentives for the industry reasonably well.

The game proceeds as follows. At the start of every period t, each existing facility i receives a

stochastic draw ξi for the scrap value that the owner would receive if it exited that period. Insofar

21The specific parameterization of the model used to produce the motivational Figures, as well as details on how

it was computationally solved, are presented below in Appendix B.

22As discussed in Grieco and McDevitt (2012), this ignores a certain amount of variation in the industry. However,

I think that extending the model to allow for capacity issues would not lead to meaningful additional insights, while

requiring large amounts of additional complexity.

16
as there is comparatively little variation in the physical capital at a dialysis clinic (the equipment

is largely standard), I assume that all ξ are drawn from the same distribution regardless of type.

While incumbent facilities evaluate whether or not to remain in the market, potential entrants

consider the desirability of entering. The entrants do not observe the choices of the incumbents

before making their own decisions, which are based on whether the expected stream of profits from

entering exceeds their stochastic sunk cost draw κ

j

i

. Unlike the scrap values ξ, I allow the entry

cost draws to be from different firm-type distributions. For the sake of simplicity, I assume that

only the first moment varies between the distributions of κ

f and κn

.

Once the stochastic draws have been received, but before the entry and exit decisions are realized, incumbent facilities engage in static competition in each market m. Demand within a market

is given by Qmt. Overall, markets are assumed to be in equilibrium, however, demand is allowed to

experience intermittent shocks, which occur prior to the dynamic decisions described above. Consistent with the institutional details of the dialysis industry, I assume that static competition does not

involve price-setting. Instead, profits are a deterministic function represented as πit(Qt, ωt, γ, c

j

i

).

In the profit function, ωt = (Nj , N−j ) indicates the local market structure (i.e., the number of both

types of dialysis facilities currently in the market); γ captures the extent of horizontal differentiation across types, which which would cause the diversion ratio from facilities of the same type to be

higher than across types; and c

j

represents the marginal cost – assumed to be constant – of type j.

Assuming that the entry and exit draws are independent, and that static competition is done

without regard to its impact on future events, these modeling assumptions imply that incumbents

evaluate the following Bellman equation:

V Ci(Qt, ωt, ξij ) = max{πit(Qt, ωt, γ, cj ) + ξi, πit(Qt, ωt, γ, cj ) + δV C(Qt, ωt)} (1)

to determine their optimal continuation/exit strategies, where V C(·) indicates the continuation

value and δ is the discount rate. Similarly, after normalizing the value of their outside option to 0,

potential entrants’ decisions solve the following Bellman equation:

V Ei(Qt, ωt, κij ) = max{0, −κ

j

i + δV C(Qt

, ωt)}, (2)

where V E(·) is the value of entry. The solution of these equations constitutes a Markov Perfect

17
Equilibrium whose existence is guaranteed (though it need not be unique as discussed in Doraszelski

and Satterthwaite (2007)).

4.2 Implications for Industry Evolution

Over the long run, differences across facility types in one or more model primitives will lead to

different equilibrium market structures. I now turn to the task of assessing just what the comparative

statics, as well as the “comparative dynamics,” are for various differences in facility-type primitives.

These are summarized in Table 4. To support the discussion, I graphical the results for given

parameterizations of the model. Details on the model’s particulars and computation can be found

in the Appendix.

Table 4: Comparative Statics of Theoretical Model

Variable

Outcome Marginal Cost

Advantage

Entry Cost

Advantage

Horizontal DifferentiationVertical Differentiation

Entry + + None +

Entry Sensitivity + + None +

Competition Effects Everyone more

sensitive to

low-cost type,

especially

high-cost type

None Everyone more

sensitive to

presence of

own type

Everyone more

sensitive to

low-cost type,

especially

high-cost type

Exit - None None -

Exit Sensitivity - None None -

Production - None None +

Differences in Marginal Costs

Economists and public health researchers have long explored the hypothesis that variation in profit

status might lead to variation in marginal costs. The general perspective has been that the higher

powered incentives provided by the profit motive lead to higher profits (Alchian and Demsetz, 1972,

Borjas et al., 1983, Philipson et al., 2010). However, there is also a theoretical literature in health

economics suggesting that a focus on output should lead non-profits to behave as though they had

lower marginal costs (Lakdawalla and Philipson, 1998, 2006), which has found empirical support

18
in studies focusing on hospitals (Sloan et al., 2001, Chakravarty et al., 2006).

Regardless of which firm-type has a marginal cost advantage, the question of how it would

change equilibrium market structure remains. First, it is clear that lower marginal costs should

produce higher static profits absent any other differences between the two types. These higher

static profits increase V C, which will reduce the likelihood of exit and increase the desirability of

entry. Thus, the type of firm with lower marginal costs should be both more likely to enter and less

likely to exit, holding all else constant.

Second, variation in marginal costs should impact firms’ sensitivities to changes in demand.

To understand why this might occur, consider a market in equilibrium where one high-cost and

one low-cost firm compete. In this market, the firm with higher marginal costs is the marginal

competitor. Since the market is equally split and prices are fixed, its profits are lower, meaning

that it would take a smaller exit shock to induce exit. Thus, in the event of a negative demand

shock, the marginal firm’s probability of exit should be expected to increase more dramatically

than that of the lower cost firm.

To demonstrate that this intuitive story holds in the formal model, I compare the computed

equilibrium exit behavior for high- and low-cost facilities in the wake of a significant negative

demand shock. Figure 5 shows the difference in the change in likelihood of exit following a negative

demand shock between high- and low-cost firms. Only those states where it is possible for exit by

both types of firms to take place are considered. The differences are weighted by the likelihood that

the industry was in a given state, where the weights come from the computed limiting distribution

for the Markov process for the earlier demand environment.23

Roughly the same logic applies to how variation in marginal costs should influence entry rates

following a change in demand. Consider a given market that just supported the existing number of

facilities but did not justify new entry. If demand rises, it is much more likely that a low-cost facility

will enter than a high-cost facility since they can earn a profit with lower levels of demand than the

high-cost facility. Again, this simple story is supported by contrasting the computed equilibrium

behavior of high- and low-cost firms following a demand change. Figure 6 shows the difference

between the changes in the likelihood of entry between low- and high-cost firms. Once more, I focus

only on those states where entry by both types is possible, and weight by the limiting distribution.

23Out of long-run equilibrium, it is possible for the double difference to have the opposite sign. However, such states

would not be expected to occur empirically.

19
Figure 5: Expected difference in change of likelihood of exit following negative shock.

Figure 6: Expected difference in change of likelihood of entry following positive shock.

20
Third, variation in marginal costs also will lead to asymmetric effects from the presence of

different types of competitors. For example, consider an incumbent non-profit facility in a market

with one competitor. If for-profit facilities have lower costs, then in the absence of significant

horizontal differentiation a non-profit incumbent will be more likely to exit if its competitor is

for-profit. This is because the continuing value is affected by the possibility of future periods where

the firm has more market power due to the exit of competitors. Thus, if one type of firm has lower

marginal costs, then all firm types’ expected longevity in the market should be more negatively

influenced by the presence of that type since it is less likely to exit. Moreover, unless demand

is highly horizontally differentiated, high-cost firms will be more impacted. (The story is exactly

analogous with respect to entry.) An example of such differences can be seen by comparing the

probability of exit for low- and high-cost firms conditional on market structure as depicted in

Figure 7. The graphs indicate, intuitively, that the probability of exit is increasing in the number

of either type of competitor, but that the slope for the number of low cost competitors is higher.

Figure 7: Probability of exit for low- and high-cost facilities conditional on market structure.

Differences in Entry Costs

Over time, differences in the costs of entry for different firm-types could also lead to dramatic

shifts in industry market structure. It may be most straightforward to think of entry cost varation

as stemming from differential access to capital. For example, Sloan et al. (1990) indicate that

21
the amount of capital hospitals were able to raise from philanthropic organizations plummeted

between the 1960s and the 1980s. Chakravarty et al. (2006) note that this was consistent with

tax-policy changes during that period that may have negatively impacted the ability of non-profit

organizations’ ability to raise funds. Although the prior literature focused on hospitals’ access

to capital, there is no reason that similar arguments could not apply equally to dialysis-centric

organizations.

Variation in κ

j would have straightforward effects on equilibrium market structure. First and

most obviously, the facility type with the higher κ

j would have a lower entry rate, because they

would be less likely to receive draws low enough to justify entering before competitors of the

opposite type did so. Thus, we would expect facilities with lower average κ

j

to disproportionately

account for new entry. Similarly, the model implies that the facility type with lower entry costs

should respond more quickly to changes in demand.

Secibd, in contrast to the discussion of differences in factors affecting static competition, it is

important to emphasize that differences in entry cost distributions should not lead to differences in

exit rate behavior. In other words, holding constant the number of facilities competing in a market,

we would not expect differences in average entry costs to cause market structures to vary in their

influence on entry or exit behavior. In other words, if the only thing that distinguishes for-profit

and non-profit dialysis providers is their costs of capital, then holding constant the level of demand

and the number of competitors, local market structure should not have any impact on model fit

when looking at the likelihood of exit directly or in response to changes in demand. To illustrate the

difference, Figure 8 shows the calculated likelihood of exit when there is no difference in marginal

costs, and only their entry cost distribution differs. Consistent with the discussion above, it shows

none of the market structure dependence evident in Figure 7.

Third, as for exit, variation in entry costs will not lead to asymmetric competitive effects. This

is because conditional on entry having already occurred, the facilities have identical V C.

Horizontal Differentiation

Although the past literature on the dialysis industry has not devoted itself to the possibility, the

possibility that facility types might engage in horizontally differentiated competition is interesting to

22
Figure 8: Probability of exit for low- and high-cost facilities conditional on market structure when

only entry costs vary.

explore.24 Such differentiation might occur if referring doctors consistently differed in their attitudes

towards for-profit status organizations. The existence of such preferences should be detectable by

considering variation in entry and exit behavior of different firm types. First, holding the total

number of clinics in the market constant, one would expect higher exit rates for firm i of type j

when more of the competing clinics were also of type j. There should be similar results for models

looking at the number of treatments performed within a given period. Analogously, one would

expect to see higher entry rates for clinics of type j when the number of incumbent clinics of type

j was low. These uncontroversial predictions are borne out in the formal model’s result (Figures

available upon request). Second, while the presence of a low-cost competitor would exert a more

negative influence on all types, horizontal differentiation only implies that one is more negatively

impacted by the presence of more similar competitors. Moreover, there should not be differential

responses to changes in demand, for example.

24Insofar as price is not endogenously set by competitors, one would not expect to see cases like that considered

in Mazzeo (2002) where competitors are vertically differentiated but consumers’ willingness to trade off quality for

lower prices differs.

23
Demand Advantage

The formal model abstracts from the possibility of consistent vertical differentiation; however, it is

worth considering how it would affect dynamic competition. To the extent that patients or their

referring physicians observed any quality difference, it would have the equivalent implications for

entry and exit to variation in marginal costs. The high quality type’s behavior relative to the low

quality type would look identical to a low-cost type relative to a high-cost type. Stronger preferences

could, however, be identified in other ways. In particular, so long as the facilities’ marginal costs

were not upward sloping – a possibility the model ignores – which could cause the higher cost type’s

marginal cost curve to intersect the fixed price line before the low cost type’s, then one could infer

from observing higher output that the type of facility was inherently more desirable.

Summary

The foregoing discussion of the comparative statics of a dynamic entry and exit model show how

differences across types in the various parameters would influence industry evolution. While there

are overlapping implications, there are also many areas of departure. To try to identify which factors

appear to be most responsible, I now employ a series of straightforward econometric frameworks

to consider differences in exit, static competitive, and entry behavior across different facility types.

Their results will be used, in conjunction with Table 4, to try to infer what factors are most

responsible for the rise of for-profit dialysis providers.

5 Econometric Methodology & Results

5.1 Hazard of Exit

5.1.1 Empirical Approach

My approach to using exit data to test assumptions about the behavior of for- and non-profit facilities resembles that of Chakravarty et al. (2006). Their realization was that estimating a discrete

choice model of exit for different firm types j allows one to contrast the estimated coefficients across

types. This, in turn, provides insight into factors such as sensitivity to variation in demand, or market structure, that should be informative as to the relative magnitudes of the underlying paramaters

affecting dynamic competition. In other words, Chakravarty et al. (2006) suggest estimating general

24
models of the form:

Prob(Dijmt) = Dj (Ximt, fm + eijmt), (3)

for all facility types j where Dijmt is an indicator that firm i of type j exited market m between

time t and time t + 1. Xijmt is a vector of controls for firm, type, and market variation, and fm is

a market fixed effect.

My estimation approach departs from that of Chakravarty et al. (2006) in several ways. First,

rather than estimate separate models for non- and for-profit firms, as Chakravarty et al. (2006) do,

I estimate a nested model of the form:

Prob(Dijmt) = D(F Pitα + Ximtβ + (F Pit ∗ Ximt)δ + fi + eimt), (4)

where F Pit is an indicator variable that takes a value of 1 if i is a for-profit facility. This nested

approach allows more direct testing of the hypothesis that different explanatory variables have

an equivalent impact on both types of facility. In essence, one simply examines the δ coefficients,

which will indicate the degree to which for-profit facilities differ in their behavior from otherwise

identical non-profit ones. Since both F P and the X are separately controlled for, this represents a

differences-in-differences approach to identification.

In X, I proxy for the level of demand using the log of the population over 60 (in 1000s)

in the county. Following Berry (1992), I approximate the market structure ωmt as ln(Nmt + 1),

i.e., the log of the number of competing facilities in the market. In some models, I disaggregate

this variable to allow for different effects from different types of facilities. In such cases, I allow

ωmt = [ln(N1t + 1), ..., ln(Njt + 1), ..., ln(NJt+1)]. To address the possibility that there are important

time-varying, facility-level factors that might be associated with both exit and organizational status,

I include indicator variables for whether or not the facility is connected to a hospital. I also include

information on the time since its certification date. Otherwise one might worry about confounding

the effect of age with that of non-profit status given that type of facility’s early prevalence. To

explore the possibility that chain affiliation makes a difference, I examine whether including controls

for membership in large chains makes a difference. Finally, in some models, I also include information

25
on the degree of concentration in the market.25

All models also include year-effects interacted with facility type. These controls should address

the possibility that different types of firms react differently to regulatory changes affecting all firms

simultaneously.26

My second major difference from the approach taken in Chakravarty et al. (2006) is that my

preferred models include firm-specific effects, fi. The inclusion of these controls help to address the

possibility of substantial omitted variable bias due to time-invariant characteristics of individual

facilities. In other words, they account for the possibility that facilities may possess unobservables

that lead to an increased likelihood of exit (or lack of exit). In the current context, the most obvious

candidates for such unobserved factors are location characteristics or managerial differences. Because these factors seem plausibly correlated with the included controls, my preferred, conservative

approach is to estimate the model with fixed effects (FE). In their absence, one might reasonably

fear that the estimated effects only reflected the correlation between the dependent and independent

variables as a result of their mutual correlation with the omitted factors.27

The advantages of the fixed effect models come at the cost of identifying effects off of the subset

of facilities that ultimately exit but which do not exit in their first (only) period in the sample.

For this reason, the length of my sample is especially beneficial as it includes 1198 different exiting

facilities out of a total of 6654 facilities included in the FE models. Thus, one does not need to

worry greatly that results are being driven by an unusual subset. It should be noted, however, that

the amount of within-facility variation in factors like hospital and chain affiliation tends to be quite

small. Thus, care must be taken in assessing the results for those variables given the inclusion of

facility-level fixed effects.

My preferred approach to estimation is to use linear probability models (LPMs), accounting for

concerns about heteroskedasticity by clustering at the facility-level. Though there are legitimate

theoretical concerns about LPMs, Wooldridge (2002, p. 454-5) notes that in practice their estimates

25It should be recognized that this follows most of the literature in taking what Gaynor and Town (2011) describe

as the “Structure-Conduct-Performance” approach to modeling the influence of concentration and competition. It

is admittedly atheoretical insofar as there is no theoretical model that directly links HHIs to industry behavior.

However, I believe – in line with the large literature following the approach – that this approach should be broadly

informative about the impact of concentration if concentration has a major impact.

26Robustness checks that included state-level time-trends for both for-profit and non-profits did not lead to qualitatively different results and are not included in the paper. Details are available upon request.

27See, for example, Allison and Christakis (2006) for a lucid discussion of the importance of accounting for unit

level heterogeneity in another hazard model setting.

26
tend to do a good job of approximating the marginal effects of common covariates. Consistent with

this, models estimated using Chamberlain’s fixed effect logit model in Table B-2 in the Appendix

lead to qualitatively similar results.28 Moreover, if one calculates the approximate marginal effects

for the logit models using the standard approach of multiplying the estimated coefficient by the

average probability of exit times one minus the average probability of exit, the results are larger

but of similar magnitudes to those from the linear models. Hence, I believe that estimation via OLS

leads to reasonable estimates of the relationships of interest.

5.1.2 Results

Table 5 contains the results of six different approaches to estimating Equation (5). They differ in

how they model the competitive environment and account for facility-level heterogeneity. Columns

1 and 2 omit facility FE. They differ in that only Column 2 includes controls for chain affiliation.

Columns 3 and 4 are exactly analogous, but now include the controls for time-invariant stationlevel heterogeneity. Column 5 retains the chain controls and allows for the possibility of different

competitive impacts from the different types of facilities, while Column 6 adds the log of HHI to

control for local market concentration.

The dramatic differences in the estimated coefficients between the models with and without

facility-level FE suggests the importance of accounting for systematic unobserved differences across

them. The differences strongly suggest that the potentially more efficient OLS models are biased.

In line with this, several of the results in the non-FE models do not seem reasonable. In particular,

they suggest that the survival of non-profit facilities is unaffected by the level of local demand, a

result that seems implausible on its face. For these reasons, I much prefer the facility FE models

and only discuss them going forward.

Between the facility fixed effects and year-facility-type indicator variables, a for-profit indicator

variable cannot be identified in the FE models. Therefore, at the base of each column, I report

the average predicted unobserved but time-invariant impact on the likelihood of exit for for-profit

and non-profit facilities (i.e.,  ̄ˆfi). I do this only for those facilities in markets where both types

of facilities are present to preclude the possibility of large market selection effects. The  ̄ˆfi values

should be reflective of consistent unobserved, type-specific variation in behavior and should be

28The only significant exception is for concentration, which may have to do with the inability to control for time

effects in the discrete choice models; including even a year trend causes the models not to converge.

27
Table 5: Likelihood of Exit as a Function of Demand & Competition

(1) (2) (3) (4) (5) (6)

b/se b/se b/se b/se b/se b/se

Log(Pop over 60) 0.013 0.014 -0.066*** -0.067*** -0.045*** -0.051***

0.02 0.02 0.01 0.01 0.01 0.01

Log(Pop over 60) * For-Profit -0.074*** -0.073*** 0.026*** 0.026*** 0.011* 0.016***

0.02 0.02 0.01 0.01 0.01 0.01

Hospital Affiliated 0.015*** 0.010** -0.105*** -0.105*** -0.108*** -0.110***

0 0.01 0.02 0.02 0.02 0.02

Hospital Affiliated * For-profit 0.018** 0.020** 0.039*** 0.041*** 0.042*** 0.042***

0.01 0.01 0.01 0.01 0.01 0.01

Time since certification 0.001*** 0.001*** 0 0 0 0

0 0 0 0 0 0

Time since certification * For-profit 0 0 0.001** 0.001** 0.001** 0.001**

0 0 0 0 0 0

Log(Number of Competitors) 0.093*** 0.093*** 0.077*** 0.077***

0.01 0.01 0.01 0.01

Log(Number of Competitors) * For-profit -0.035*** -0.035*** -0.042*** -0.042***

0.01 0.01 0.01 0.01

Log(Number of For-profit) 0.037*** 0.030***

0 0

Log(Number of For-profit) * For-profit -0.013** -0.008

0.01 0

Log(Number of Non-profit) 0.023*** 0.002

0.01 0.01

Log(Number of Non-profit * For-profit) -0.022*** -0.005

0.01 0.01

Log(Number of Unknown) -0.014* -0.005

0.01 0.01

Log(Number of Unknown) * For-profit 0.009 0.001

0.01 0.01

Log(HHI) -0.034***

0.01

Log(HHI) * For-profit 0.028***

0.01

P(Exit) for Non-profit 0.05 0.06 0.06 0.06

P(Exit) for For-profit -0.01 -0.02 -0.01 -0.01

P-value of H0: diff == 0 0.00 0.00 0.00 0.00

Status * Year FE Yes Yes Yes Yes Yes Yes

Facility FE No No Yes Yes Yes Yes

Chain FE No Yes No Yes Yes Yes

Status * County FE Yes Yes No No No No

Observations 69159 69159 69159 69159 69159 69159

* p<0.10, ** p<0.05, *** p<0.01 in 2-sided tests. + p< 0.1 in 1-sided test. All standard

errors clustered at the facility level.

28
informative as to the underlying likelihood of exit for the different types. To help assess whether

any differences are of statistical significance, I report the p-value for the t-statistic assessing whether

the two averages are statistically different from each other.29

Overall, the results provide strong evidence that for- and non-profit dialysis clinics operate in

quite dissimilar fashions. This is in line with the simple graphs presented above, which showed

very divergent trends for the two types of dialysis providers. In particular, the average unobserved

factors of for-profit facilities make them much less likely to exit in all models. As noted above,

this may suggest that for-profits have have an advantage in static competition. Moreover, it runs

contrary to what would be expected if there were only differences in entry costs. Although the

magnitude of the difference between  ̄ˆfi may appear small, it should be viewed in the context of the

unconditional likelihood of exit, which is under 2 percent. Thus, the 6 percentage point difference

between for-profit and non-profit facilities is of very large economic significance.

In addition, each model suggests that for-profit facilities’ likelihood of exit is statistically significantly less sensitive to changes in the level of demand. As discussed above, greater sensitivity

is consistent with being the marginal competitor. Thus, the models’ results again suggest a static

disadvantage for non-profit dialysis facilities. Once more, as the difference is of economic as well as

statistical significance. Using the estimated coefficients in Column 4, a one standard deviation decrease in population over 60 (i.e., 247,300) increases the likelihood of non-profit exit by 28 percent;

by contrast, it would only increase the likelihood of for-profit exit by 19 percent.

In addition, the results in Table 5 indicate asymmetric effects from the presence of different types

of competitors. Although both facility types’ likelihood of exit is increasing especially rapidly in the

number of for-profit competitors, non-profit competitors are much more impacted by the presence

of other non-profit facilites than are their for-profit competitors. Indeed, Columns 3 and 4 suggest

that the number of non-profits has no competitive impact at all upon for-profit clinics. As indicated

in Table 4, such asymmetric effects could, but need not, indicate horizontally differentiated demand

as well as the fact that for-profit facilities possess advantages in static competition.

Asymmetric competition effects from the presence of different types of facilities is difficult

to reconcile with many alternative stories about industry behavior. In particular, it is hard to

29In other words, I am comparing the averages of the estimated ˆfi. One might also focus on the predicted likelihoods

of exit after netting out the facility-specific factors like affiliation with a hospital or age. Preliminary work along these

lines does not point to large qualitative differences.

29
understand why – all else constant – a non-profit should care about the character of its competition if

its mission is simply to provide services to populations that would otherwise go untreated. Therefore,

I do not think that differences in behavior can be attributed to the ostensible differences in objective

function between for-profit and non-profit facilities.

Across the different models, I find broadly intuitive estimated impacts for the facility-level

control factors. Facilities connected to hospitals are less likely to exit, which is consistent with the

idea that they are larger investments, capable of performing more services. Thus, on average, it

would take a much larger draw from the scrap value distribution in order to induce them to exit.

By contrast, time since certification is weakly associated with exit. Interestingly, both factors are

more associated with the exit of for-profit facilities. The results of the sixth model imply that more

concentrated markets experience less exit, though the effects are larger for non-profit than for-profit

facilities.

Ultimately, the results are consistent with all elements of the hypothesis that for-profit facilities

have lower marginal costs. Similarly, they could be in line with the the presence of some degree

of differentiated demand. However, their implications run strongly against the possibility that the

driver of for-profit facilities’ rise in prominence can be attributed to lower entry costs or other

factors.

5.2 Utilization

5.2.1 Empirical Approach

In order to further assess the competitive relationship between for- and non-profit dialysis treatment

centers, I exploit the USRDS data’s inclusion of utilization statistics. The overall goal, much as for

the exit analyses, is to see how the number of hemodialysis treatments that a facility performs in a

year changes depending on its profit status as well as market characteristics. Thus, I again estimate

models of the form:

Hijmt = H(F Pitα + Ximtβ + (F Pit ∗ Xijmt)δ + fi + eijmt), (5)

where Hijmt is the log of the number of hemodialysis treatments performed by the facility in a

given period. Although I continue to allow for the possibility of different demand effects across

30
facility-types, theory offers little guidance as to its impact on output. Once more, I estimate the

model with facility fixed effects using OLS while allowing for the possibility that the standard errors

are clustered at the facility level.

5.2.2 Results

Table 6 reports the results of four models of hemodialysis treatments. The specifications are exactly

analogous to the last four shown in Table 5. The first model omits chain fixed effects and does not

distinguish between the competitive influence of different types of facilities. The second model

adds chain fixed effects, while the third allows for differences in the impacts of for- and non-profit

facilities. The fourth model adds controls for the levels of concentration in the market. As before,

at the base of each column, I report the average predicted unobserved but time-invariant effects on

output for for-profit and non-profit facilities, limiting attention to those facilities in markets where

both types of facilities are present.

Examining the average unobserved production effect suggests that for-profit facilities are innately more productive at any level of demand. Indeed, in the considered markets, the results

suggest an average 15 percentage point difference in output between for- and non-profit facilities.

This could be consistent with the hypothesis that for-profit facilities have a static advantage in

either providing care or attracting patients. For example, if – contrary to the theoretic model’s

assumption of constant marginal costs – facilities’ marginal cost functions slope upward, then the

facility type with higher marginal costs might perform fewer treatments if their marginal cost curve

intersected the fixed price line before the point implied by their share of residual demand under

the assumption of constant marginal costs. An extreme example of this would be if non-profits are

more capacity constrained. Alternatively, they could be providing more care because ceteris paribus

their residual demand curves are higher as a result of some degree of vertical differentiation.

The results suggest that firm-type has no consistent impact on how the number of treatments

performed by a given facility change in response to a percentage change in demand. This is somewhat

misleading insofar as the log-log specification implies that as demand grows the proportion of

treatments performed by facilities would stay the same. Thus, the difference in the proportion of

patients treated by competing for- and non-profit would not converge. The estimated coefficient

of 0.67 from Column 3 implies that in response to a 10 percent increase in the demand proxy,

31
the number of treatments performed by each facility would rise, on average, by 6.7 percent. This

is quite a strong supply response, suggesting that facilities are not very capacity-constrained or

can comparatively easily increase capacity in response to demand changes. The latter story seems

particularly likely insofar as facilities are usually small enough to fit in strip-malls and require

little in the way of heavy capital equipment. While the skilled labor that is required may not be

universally abundant, the ratio of necessary personnel to patients is not likely to be high.

Given that non-profits appear to be able to ramp up production in the wake of demand increases,

this suggests that a key part of the reason that for-profits perform more dialysis treatments is that

they possess an advantage in attracting patients. Such a finding is consistent with the vertical

move of several of the major dialysis chains into affiliations and partnerships with local providers.30

Insofar as their compensation would be expected to correlate strongly with patients referred intraorganization, one would expect such doctors to have strong attachments to facilities related to their

employer (Helmchen and Lo Sasso, 2010, Hennig-Schmidt et al., 2011, Van Dijk et al., 2012), which

might produce the observed correlations in the data. Anecdotally, the existence of a Florida law that

explicitly constrains Florida’s nephrologists from referring their patients to affiliated institutions

suggests that it occurs in practice as well.31

The results for utilization also lend some support to the idea that demand is horizontally differentiated. For example, in Columns 3 and 4 show that production at both types is disproportionately

negatively impacted by the presence of similar competitors. Whereas non-profits are roughly equivalently impacted by the presence of either type of competitor, for-profits are much more affected by

the presence of for-profit competitors. This may suggest that some doctors weakly prefer to direct

patients to non-profit facilites, while others are much more likely to refer patients to for-profit

facilities.

The remaining results are broadly consistent with intuition. Hospital affiliation is associated with

a 15-20 percent decrease in hemodialysis treatments for non-profit facilities, and a 40-50 percent

decrease for for-profits. The direction of these effects accords with the idea that hospital-affiliated

dialysis facilities may have the capability to provide more specialized care, the returns (financial

and otherwise) of which may be much higher to operator and patients alike. Thus, one would expect

30See, e.g., http://www.ama-assn.org/amednews/2012/06/04/bisf0607.htm.

31As previously noted, see http://www.floridatoday.com/viewart/20130110/HEALTH/130110020/

Court-upholds-controversial-dialysis-law for more details.

32
Table 6: (Log) Number of Hemodialysis Treatments as a Function of Demand & Competition

(1) (2) (3) (4)

b/se b/se b/se b/se

Log(Pop over 60) 0.780*** 0.767*** 0.667*** 0.674***

0.07 0.07 0.07 0.07

Log(Pop over 60) * For-Profit -0.023 -0.02 -0.012 -0.014

0.04 0.04 0.04 0.04

Hospital Affiliated -0.184** -0.191** -0.160* -0.156*

0.09 0.09 0.09 0.09

Hospital Affiliated * For-profit -0.301*** -0.254*** -0.270*** -0.270***

0.07 0.07 0.07 0.07

Time since certification 0.014** 0.015** 0.013** 0.013**

0.01 0.01 0.01 0.01

Time since certification * For-profit -0.009** -0.012*** -0.011** -0.011**

0 0 0 0

Log(Number of Competitors) -0.588*** -0.583***

0.04 0.04

Log(Number of Competitors) * For-profit 0.079* 0.080*

0.04 0.04

Log(Number of For-profit) -0.349*** -0.343***

0.03 0.03

Log(Number of For-profit) * For-profit 0.004 0.002

0.03 0.04

Log(Number of Non-profit) -0.299*** -0.283***

0.05 0.05

Log(Number of Non-profit) * For-profit 0.109** 0.101**

0.05 0.05

Log(Number of Unknown) -0.063 -0.07

0.06 0.06

Log(Number of Unknown) * For-profit 0.024 0.028

0.07 0.06

Log(HHI) 0.026

0.04

Log(HHI) * For-profit -0.01

0.04

Prediction for Non-profit -0.21 -0.21 -0.21 -0.21

Prediction for For-profit -0.09 -0.08 -0.06 -0.06

P-value of H0: diff == 0 0.00 0.00 0.00 0.00

Status * Year FE Yes Yes Yes Yes

Facility FE Yes Yes Yes Yes

Chain FE No Yes Yes Yes

N 65373 65373 65373 65373

* p<0.10, ** p<0.05, *** p<0.01 in 2-sided tests. + p< 0.1 in 1-sided test. All standard errors

clustered at the facility level.

33
them to perform fewer dialyzations all else equal if there are resource constraints. Finally, older

facilities actually have higher output for non-profits, while the effect for for-profits is essentially

zero. Interestingly, Column 4 shows that concentration is weakly associated with higher-output per

facility.

To check the robustness of the conclusion that for-profits have a static advantage in production,

I considered the impact of a change in profit status on output for the subset of facilities whose

status changed during the sample period. The evidence supports the idea that ownership structure

is correlated with output. First, I considered the difference between the estimated  ̄ˆf for those facilities that switched to for-profit ownership and those that did not. This difference was statistically

significant only when all values for the switchers were used but statistically insignificant when only

the years prior to the change were used to identify the time invariant effects. Insofar as the effects

identified with the entire sample period represent an average of the unobserved effects from before

and after the profit-status transition, these results support the idea that for-profit status increases

output. Furthermore, using models that control for time-invariant facility characteristics, time period, and county location, I find that those facilities that switched to for-profit status increased

their output approximately 43 percent more than those that switched to non-profit status over a

two year period.32

Overall, the results of analyses of hemodialysis production lend additional support to the hypothesis that for-profit facilities possess a static competitive advantage. I now turn to exploring

whether entry patterns also support this perspective.

5.3 Rate of Entry

5.3.1 Empirical Approach

In order to understand the drivers of industry expansion across geographic markets, I estimate

models of the general form:

Ejmt = Ej (Xmt, fjm + ejmt), (6)

where Ejmt is the total number of entrants of type j in market m at time t. In contrast to the

32Somewhat interestingly, there is evidence that becoming for-profit leads to lower output in the first year, perhaps

indicating disruptive reorganization investments.

34
previous section, I allow each type of facility to have its own “birth” function of a set of market

characteristics Xmt, a market fixed effect fjm, and an i.i.d. error term ejmt.

To estimate the different Ej , I exploit the conditional poisson model developed by Hausman et

al. (1984). The traditional poisson model has a single parameter, λ, and would suggest that the

probability of observing Ejmt entries of type j in market m at time t as:

Prob(Ejmt) =

e

−λjλ

Ejmt

j

Ejmt!

. (7)

The conditional poisson model allows λj to vary both as a function of observable market characteristics X and unobserved, time-invariant fixed effect f:

λjmt = e

Xmtβj+fjm, (8)

where β is the parameter vector of interest.

In order to understand how the conditional poisson approach addresses the possibility of consistent unobserved heterogeneity across markets, it is useful to review the likelihood function. Each

element fed into the likelihood is the probability of observing the series of Ejt for each m:

Prob(Ejm1, ..., EjmT ) =

e

PT

t=1 λjmt QT

t=1 λ

Ejmt

jmt

(

QT

t=1 Ejmt)!

, (9)

after conditioning out the total number of entrances of type j in market m over time:

Prob(X

T

t=1

Ejmt) = e

−

PT

t=1 λjmt (

PT

t=1 λjmt)

PT

t=1 Ejmt

(

PT

t=1 Ejmt)!

. (10)

By rearranging terms, the element in the likelihood function simplifies to:

Prob(Ejm1, ..., EjmT |

X

T

t=1

Ejmt) = Y

T

t=1 

e

Xmtβj

PT

s=1 e

Xmsβj

!Ejmt

·

(

PT

t=1 Ejmt)!

QT

t=1(Ejmt!)

. (11)

Thus, the market-specific fixed effect cancels out of the likelihood function, facilitating computation

and precluding the possibility of incidental parameters bias from estimating the market parameters directly in an unconditional model. Moreover, the estimates remain robust to time invariant

35
differences across markets, perhaps the most important expected source of omitted variable bias.

The model does have the implication, however, of not being able to identify parameters in markets

that never experienced any entrances. Therefore, out of a total sample of 27653 county-year observations relating to 1763 counties, I am only able to use 15315 observations from 858 counties for

the for-profit models and 6130 observations from 324 counties for the non-profit models.

For the entry models, I include a smaller set of covariates than in the models of exit and

utilization. To proxy for demand, I use the lagged value of the log of the population over 60 (in

1000s). Similarly, I use lagged values of the various approaches to modeling the market structure.

Since the models are more aggregated, I do not include facility-level detail on things like hospital

affiliation or age. In essense, I am modeling the changes in market structure ∆ωjt as a function of

the state of the world at t − 1.

In all models, I allow for the possibility of heteroskedastic standard errors. Calculating standard

errors robust to violations of the assumption (implied by the poisson specification) that the conditional mean equals the conditional variance does not lead to dramatic changes in the statistical

precision of the estimates (Wooldridge, 1999).

Table 7: Descriptive Statistics for Entry Samples

For-profit Non-profit

N mean sd N mean sd T-Stat

Entry 15315 0.21 0.61 6130 0.09 0.31 19.32

Log(Pop over 60) 15315 3.17 1.07 6130 3.61 1.16 -25.71

Log(Number of Competitors) 15315 1.23 0.67 6130 1.49 0.83 -22.33

Log(Number of For-profit) 15315 0.95 0.72 6130 0.99 0.93 -3.24

Log(Number of Non-profit) 15315 0.48 0.61 6130 0.89 0.66 -42.26

Log(Number of Unknown) 15315 0.01 0.11 6130 0.03 0.15 -6.75

5.3.2 Results

Table 7 shows summary statistics for the markets used in the analysis of for-profit and non-profit

entry. Consistent with the descriptive evidence considered above, the Table shows much lower mean

rates of entry for non-profit facilities. Interestingly, however, the Table indicates that despite on

average being in smaller markets, new non-profit facilities have opened in larger markets than

new for-profit facilities. This does not support the idea that non-profits systemattically target

36
underserved, low demand areas.

Table 8 shows the results of three different pairs of models. Columns 1 and 2 show the coefficient results for models considering the impact of demand and market structure on the number

of for-profit and non-profit facilities entering a given market without distinguishing between the

competitive effects of for-profit and non-profit facilities. Columns 3 and 4 allow for different impacts

depending on facility type. Columns 5 and 6 consider the possibility that the level of concentration

could influence entry rates.

Because fixed effects cannot be identified in non-linear models such as the conditional poisson

due to the incidental parameters problem (Wooldridge, 2002), I no longer provide mean estimated

predicted effects. To gain insight, however, I re-estimated the models via linear panel methods –

which lead to qualitatively similar results for the coefficients of interest finding that the average

number of for-profit entrants is much larger when time-invariant heterogeneity is accounted for.

These results can be found in Table B-4 in the Appendix.

Across all pairs of the conditional poisson models, I find that for-profit entry is more impacted

by demand changes. Indeed, I find that for-profit entry is remarkably sensitive when the competitive

environment is not disaggregated. The estimated coefficient in Column 1 implies an elasticity greater

than 1. In other words, a 10 percent increase in the demand proxy would produce an almost 14

percent increase in entry. By contrast, the same increase in demand would only be expected to

produce a 4 percent increase in the number of non-profits. Overall, these results support the idea

that for-profit facilities have an advantage in static competition; however, they would also be

consistent with the presence of lower entry costs.

The Table also provides additional evidence consistent with asymmetric competitive effects.

Entry rates by for-profit and non-profit firms are both substantially more influenced by the presence

of like facilities than they are unlike facilities. However, the data again show that the entry rate

of non-profit facilities is quite impacted by the presence of for-profit competitors, while for-profits

are not impacted at all by the presence of non-profit facilities. These results are consistent with

the idea that for-profit dialysis facilities have a static advantage in attracting patients, treating

patients at lower cost, or both.

Perhaps the most important takeaway from the entry results concerning market structure is that

they are inconsistent with the idea that the rise of for-profit facilities stems entirely from having

37
Table 8: Entry as a Function of Demand & Competition

(1) (2) (3) (4) (5) (6)

FP Entry NP Entry FP Entry NP Entry FP Entry NP Entry

b/se b/se b/se b/se b/se b/se

Log(Pop over 60) 1.367*** 0.433 0.425+ 0.127 0.41 0.166

0.35 0.74 0.32 0.74 0.32 0.73

Log(Number of Competitors) -2.243*** -2.023***

0.16 0.29

Log(Number of For-profit) -1.336*** -0.789*** -1.352*** -0.757***

0.17 0.16 0.18 0.17

Log(Number of Non-profit) 0.059 -1.151*** 0.041 -1.071***

0.12 0.21 0.13 0.24

Log(Number of Unknown) 0.004 -0.438 0.016 -0.482

0.14 0.4 0.14 0.4

Log(HHI) -0.037 0.127

0.1 0.15

Year FE Yes Yes Yes Yes Yes Yes

County FE Yes Yes Yes Yes Yes Yes

N 15315 6130 15315 6130 15315 6130

* p<0.10, ** p<0.05, *** p<0.01 in 2-sided tests. + p< 0.1 in 1-sided tests. Standard errors are robust to

heteroskedasticity.

lower average entry costs. If this were the case, then entry might be higher on average for them, but

entry rates would not differ as a function of the local market structure. Thus, these results strongly

suggest that variation in costs of capital do not explain much of the change in market structure

over time in the dialysis industry relative to factors having to do with static competition.

While consistent with the patterns seen elsewhere, the overall precision of the estimates is

markedly less than in models controling for greater facility level heterogeneity. Therefore, for robustness purposes, I ran several models examining the determinants of ownership status conditional

on entry taking place. Consistent with the lack of precision in the market level results, I found considerable heterogeneity. Interestingly, I found that the two dominant chains were more responsive

to changes in demand than non-profits, but that other for-profits were actually less so. These results suggest that, consistent with the rise of concentration, the large chains have some advantages

not possessed by other competitors. Details on the simple conditional analyses described above are

available upon request.

38
6 Conclusion

This paper has investigated the evolution of the dialysis industry over the last three decades, examining whether or not the evidence supports or contradicts different explanations for the rise of

for-profit facilities. Consistent with much of the non-health care literature, I find evidence consistent with the longstanding hypothesis that for-profit organizations are more efficient (Alchian and

Demsetz, 1972, Borjas et al., 1983, Philipson et al., 2010). This is also in line with the findings

of several past papers on the dialysis industry in public health (Griffiths et al., 1994, Hirth et

al., 1999, Ozgen and Ozcan, 2002). However, it runs contrary to a theoretical literature in health

economics suggesting that a focus on output should lead non-profits to behave as though they had

lower marginal costs (Lakdawalla and Philipson, 1998, 2006), which has found empirical support

in studies focusing on hospitals (Sloan et al., 2001, Chakravarty et al., 2006).

In addition, I also find significant evidence consistent with the idea that diversion between facility types is quite asymmetric. In particular, diversion from for-profit to non-profit facilities appears

less than from non-profit to for-profit. This could reflect higher perceived quality. Alternatively,

it may stem from efforts to vertically integrate upstream with referring physicians by the major

dialysis chains, which the largest chains are now emphasizing. In future work, I hope to focus more

attention on this issue.

Overall, the policy implications of the analysis are ambiguous. For example, based on the revealed preference evidence documented in this paper, the replacement of all non-profit facilities by

for-profit ones would occasion some utility loss (though whether of the referring doctors or the ultimate recipients of the treatments is not clear). That said, it would be unlikely to lead to substantial

reduction in access to treatment. However, the overall implications for welfare analysis depend on

factors not directly examined in this paper. In particular, they are highly dependent upon the

existence and magnitude of the effects of competition and for-profit status on quality. I hope to

investigate these issues in subsequent research. In addition, I hope to focus more attention on issues

that arose in this paper; in particular, the likelihood of behavioral differences within the broader

categories of for-profit and non-profit facilities, as well as the possible implications of DaVita and

Fresenius’ vertical expansions.

39
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A Theoretical Model Details

Below, I quickly describe the details of the theoretical model used to generate the Figures from Section

4 of the text. As noted above, the model is in the Ericson and Pakes (1995) class of models, bearing the

closest resemblance to that used in Pakes et al. (2007). I assume that demand is in long-run equilibrium and

then experiences unexpected shocks that market participants do not anticipate. Incorporating rational (or

otherwise) expectations about the possibility of the shocks as is done in Pakes et al. (2007) or Wilson (2012)

would be a simple, yet tedious, process, requiring that the different possibilities include an additional loop

characterizing the different demand states. I do not believe there is sufficient probative value in the current

setting from formally accounting for this factor to justify the additional computational complexity.

A.1 Static Competition

As noted above, I model demand in a simple way designed to capture the most salient characteristics of the

retail dialsysis industry. In particular, I fix the price p that all market participants receive per dialyzation

performed. The share of total demand, Qmt, served by a particular facility i of type f is determined according

to a modification of the familiar Hotelling model of differentiated demand.

If demand is not horizontally differentiated, then I impose that it is equally shared amongst all market

participants. If, however, demand is purely horizontally differentiated by factor γ, where γ ∈ [0, 0.5], then I

assign facilities’ locations on the Hotelling line in the following way. Assume that there are nllow-cost and

nh high-cost facilities, and that nl + nh = N total facilities. Then, when nl ≥ nh, define the “boundary”

42
point h on the Hotelling line as h =

nl

N − (nl − nh) ∗ γ. I assume then that all nl are distributed such that

they each serve h

nl

of the total market, while each high-cost facility serves exactly 1−h

nh

. (Should nh > nl, an

analogous approach determines the boundary point and individual facilities’ shares.)

Although somewhat idiosyncratic, this approach straightforwardly accommodates horizontal demand

differentiation, assuming that roughly equal shares of the population prefer each type of facility. As γ

approaches 0.5, consumers so strongly prefer one type of facility that entrants only cannibalize the treatments

performed by others of the same type. Alternatively, as γ converges on 0, consumers do not prefer one type

of facility to another, and all facilities in the market will perform an equal number of treatments.

A.2 Dynamic Factors

I largely follow the approach taken in Pakes et al. (2007) with respect to the stochastic entry and exit

distributions. Thus, I assume that all ξ and κ represent draws from exponential distributions. The choice

of the exponential distribution is unapologetically made to simplify computation. As noted in Pakes et

al. (2007), it implies that the expected payoff of choosing to exit conditional on a given market structure

configuration can be written as:

E(ξ|ξ > V C(Q, ω)) = V C(Q, ω) + σ, (12)

assuming that ξ is distributed exponentially with cdf F(ξ) = 1 − exp(−

1

σ

ξ). Similarly, the probability of

entering can be computed in the following manner. First, establish whether the value of entry exceeds the

minimum entry cost, κ:

M = max(0, β ∗ V E(Q, ω) − κ0). (13)

Then, the probability that entry occurs is simply:

Pr(entry) = 1 − exp(−α ∗ M) ∗ (1 + α ∗ M), (14)

where κ is exponentially distributed with parameter α.

A.3 Parameterization

In developing the Figures used in the paper to illustrate the implications of variation in economic primitives

for market structure evolution, I explored a variety of parameterizations to ensure the robustness of the

results. For the specific results presented in the text, however, I parameterized the model as follows.

In all models I assume that the fixed price p = 1.5, the discount factor β is 0.9, the exit draw parameter

σ is 0.5, and that the maximum number of each type of facility is 8. I also assume that static competition

entails paying a fixed cost of 1 per period.

For the level of demand when marginal costs differ, I assume that Q = 10 or Q = 12. My assumption

is that high-cost facilities’ marginal costs are 10 percent higher than those for low-cost facilities, which is

set to 1. Thus, for Figure 5 (Figure 6), I contrast the calculated exit (entry) policy functions when Q = 10

relative to when Q = 12 holding all else constant. Figure 7 is produced using Q = 12.

When examining the implications of entry cost variation, I increase low-cost facilities’ marginal costs to

the same level as high-cost facilities. When focusing on the impact of variation in marginal costs, I assume

that both types of facilities have entry cost parameters α of 0.5 and that their minimum cost of entry is

1

α = 2. When focusing on the impact of variation in entry cost, I keep both α’s the same, but set the

minimum cost of entry for the low-cost type at 1.6 instead of 2. Demand is set at Q = 12 for Figure 8 in

order to ensure comparability with Figure 7.

I present no results for the impact of allowing for horizontal differentiation, keeping γ fixed at 0 in all

models. However, in unincluded results, I experimented with a number of alternative parameterizations. The

results were intuitive.

43
A.4 Computation

All programs were written and run in Matlab 7.4. I solve for facilities’ equilibrium strategies using a variant

of the Gaussian procedure described in Pakes and McGuire (1994). The limiting distribution was found by

first calculating a large matrix indicating the likelihood of transitioning from one state to another from one

time period to the next. This matrix was raised to higher and higher power until it converged on the limiting

distribution.

Code for all aspects of the modeling is available upon request.

44
B Additional Tables

Table B-1: Chain Identities and For-Profit Status

Chain Name First Year Last Year Total Obs For-Profit Obs Non-Profit Obs

ARA 2005 2008 237 237 0

DAVITA 1995 2008 8886 8886 0

DCI 1988 2008 2846 0 2846

EVEREST 1996 2008 171 171 0

FRESENIUS 1988 2008 15651 15651 0

GAMBRO 1996 2008 4902 4902 0

INDT 1988 2008 35441 16806 18193

LIBERTY 2008 2008 41 41 0

NATIONAL 1999 2008 388 388 0

NRA 2006 2008 101 101 0

NRI 2006 2008 243 243 0

RCG 1996 2008 2876 2876 0

REGDCA 2005 2008 123 123 0

REGRRI 2005 2008 144 144 0

REGSATHC 2006 2008 108 108 0

RENALADVAN 2005 2008 296 296 0

RTC 1993 1997 357 357 0

VIVRA 1988 2008 1298 1298 0

45
Table B-2: Conditional Logit Estimates of the Likelihood of Exit

(1) (2) (3)

b/se b/se b/se

1(For-profit) 2.93 -3.57 3.221

3.68 4.71 11.92

Log(Pop over 60) -2.970** -4.541*** -5.550***

1.33 1.66 1.69

Log(Pop over 60) * For-Profit 1.850+ 3.658** 4.275***

1.16 1.5 1.57

Hospital Affiliated 1.943 2.01 1.9

2.03 1.96 1.96

Hospital Affiliated * For-profit -2.351 -1.513 -1.221

1.89 1.76 1.77

Time since certification 1.393*** 1.367*** 1.352***

0.09 0.08 0.08

Time since certification * For-profit 0.507*** 0.576*** 0.573***

0.11 0.09 0.1

Log(Number of Competitors) 10.197***

0.96

Log(Number of Competitors) * For-profit -5.057***

1.19

Log(Number of For-profit) 12.101*** 13.765***

1.09 1.27

Log(Number of For-profit) * For-profit -5.410*** -5.846***

1.33 1.44

Log(Number of Non-profit) 2.679*** 4.709***

0.74 1.12

Log(Number of Non-profit) * For-profit -2.824*** -3.972***

0.96 1.35

Log(Number of Unknown) 5.047*** 5.870***

1.76 1.77

Log(Number of Unknown) * For-profit -4.856** -5.255***

1.91 1.94

Log(HHI) 3.012**

1.24

Log(HHI) * For-profit -0.979

1.32

Status * Year FE No No No

Facility FE Yes Yes Yes

Chain FE No No No

N 8641 8641 8641

* p<0.10, ** p<0.05, *** p<0.01 in 2-sided tests. + p< 0.1 in 1-sided test.

46
Table B-3: Additional Models of Hemodialysis Treatment Production

(1) (2) (3) (4)

b/se b/se b/se b/se

1(For-profit) -0.036 0.178* -0.138*** -0.081

0.03 0.1 0.03 0.21

Log(Pop over 60) 0.895*** 0.863*** 0.813*** 0.775***

0.07 0.07 0.07 0.06

Hospital Affiliated 0.042*** 0.042*** 0.010** 0.009*

0 0 0 0

Time since certification -0.820*** -0.793*** -0.442*** -0.388***

0.05 0.05 0.07 0.07

Log(Number of Competitors) -0.737*** -0.732*** -0.540*** -0.531***

0.02 0.02 0.02 0.02

County FE Yes Yes No No

Year Yes Yes Yes Yes

Facility FE No No Yes Yes

Chain FE No Yes No Yes

N 65373 65373 65373 65373

* p<0.10, ** p<0.05, *** p<0.01 in 2-sided tests. + p< 0.1 in 1-sided test. Standard errors

clustered at facility level.

47
Table B-4: Linear Entry Models

(1) (2) (3) (4) (5) (6)

FP Entry NP Entry FP Entry NP Entry FP Entry NP Entry

b/se b/se b/se b/se b/se b/se

Log(Pop over 60) 0.192*** 0.122* 0.120* 0.091+ 0.135** 0.091+

0.07 0.07 0.07 0.07 0.07 0.07

Log(Number of Competitors) -0.273*** -0.187***

0.02 0.02

Log(Number of For-profit) -0.195*** -0.096*** -0.145*** -0.099***

0.02 0.02 0.03 0.02

Log(Number of Non-profit) 0.021 -0.117*** 0.083** -0.124***

0.03 0.02 0.04 0.02

Log(Number of Unknown) 0.104 -0.055+ 0.068 -0.052+

0.1 0.04 0.1 0.04

Log(HHI) 0.098*** -0.01

0.04 0.02

Predicted Non-Profit 0.10 0.10 0.10

Predicted For-Profit 0.37 0.37 0.37

P-value of H0: diff == 0 0.00 0.00 0.00

Year FE Yes Yes Yes Yes Yes Yes

County FE Yes Yes Yes Yes Yes Yes

N 15315 6130 15315 6130 15315 6130

* p<0.10, ** p<0.05, *** p<0.01 in 2-sided tests. + p< 0.1 in 1-sided tests. Standard errors clustered at the

county level.

48