Indicating Potential Market Power based on Quality
Competition in the Dutch Hospital Market
Peter T. Dijkstra
*August 27, 2008
Abstract
In this paper we present a new competition index. Common indices use price. We use distance instead, because costs are covered by health insurers in the Netherlands. Based on a patient choice model we predict market shares that would arise if patients’ travel costs are halved. Then, patients will be more inclined to choose a hospital located farther away if it has a higher (perceived) quality. We use the percentage of switchers as a competition index. We find few treatments with low switching percentages: patients might be locked-in which is an indication of potential market power. For a few other treatments we find high switching percentages indicating a competitive market and potential profitable entry. JEL Classification Codes: C25, D12, I11, I19
Keywords: Competitiveness, Dutch Hospital Market, Market Power, Patient Choice Behavior, Patient Travel, Switching Behavior, Willingness to Travel
*
University of Groningen, The Netherlands. This research was conducted while being an intern at the Dutch Healthcare Authority (Nederlandse Zorgautoriteit, NZa). Email: peter.t.dijkstra@gmail.com. I would like to thank Marco Haan, Rein Halbersma, Ilaria Mosca and Ben Scharp for tips and research assistance provided. Any remaining errors are mine. The views are the author’s and need not reflect those of the NZa. I. Introduction
Since the (partial) deregulation of the Dutch health care market in 2005 competition has slowly started to emerge. Common tests applied to indicate market power, such as the Lerner index or the SSNIP test (a Small but Significant and Non-transitory Increase in Price), use price as an instrument. In the Netherlands insurers cover the costs, meaning that patients do not consider price in their decision for a health care provider. Instead, we use distance between the patient and the hospital as an instrument to explain the decision for a hospital. After estimating a discrete choice model we halve patients’ travel costs, and predict the market shares which would arise in the new (fictional) situation. By comparing the predicted and actual market shares we obtain the percentage of patients switching to a different hospital. We argue that the switching percentage is a measure of competitiveness. Treatments with low switching percentages potentially have hospitals with market power.
marginal cost of firm i. The index increases with the mark-up, a desirable feature. However, because marginal costs is a rather theoretical concept it is not useful for practical purposes. Especially in the Dutch hospital market where people do not respond much to price, because health insurers cover the costs (NZa, 2007b). Almost no price mechanisms are present: consumers pay insurance fees and obtain the actual care consumed for free or at a price below actual costs. Nevertheless, increasing the personal contribution for each treatment will lower the demand for health care (Keeler and Rolph, 1988).
Also the SSNIP test uses price (Motta, 2004). The SSNIP criterion tests whether a hypothetical monopolist could profitably increase its price by 5 till 10%. The criterion can be used as a measure of market power: a higher increase in profits in percentage terms if price rose by 5% till 10%, indicates more market power.
Because costs are covered by insurers, we have to look for a different instrument in order to indicate market power. Patients decide which hospital to visit based on waiting times, distance to, (perceived) expertise of, and own previous experience with the hospital (ECORYS-NEI, 2003). Only distance is quantifiable. We cannot use waiting times because the definition is ambiguous and publications are infrequently (RIVM, 2007). Quality cannot be used due to the recent development of more objective measures (NZa, 2007a), and previous experience is not recorded. We have patient discharge data which enables us to estimate a discrete choice model. It yields information about the importance of distance and of (perceived) quality, by different demography groups.
this (fictional) set-up, patients will be more inclined to visit a hospital with a higher (perceived) quality. We predict, based on the regression results, the new market shares. We argue that the percentage of switching patients indicates the competitiveness of the sector. A high switching percentage of patients means a more competitive sector. If the percentage of switchers is low, the hospitals are perceived heterogeneous and there might be a dominant market position. We show that patients are willing to switch hospitals when the distance to each hospital is proportionally reduced. This conclusion does not hold for all treatments we consider. The largest switching demography group is elderly.
In summary, we will present a new competition index, as an alternative to the SSNIP criterion. We use distance instead of prices as is common in the SSNIP test, because prices cannot be used in the Dutch hospital market. We will illustrate this with a patient choice model in the Dutch hospital market.
First, we will estimate what different demographic groups of patients find important when deciding which hospital they want to be treated at. This yields information about the relative importance of distance in comparison to quality. We will do this by means of a discrete choice model, based on patient choice data for several treatments in the Netherlands. These treatments have been performed between January 2006 and November 2007. This short period of time is chosen because the health care market changed drastically before 2006 and a new health insurance system came into effect on January 1st 2006. We estimate, based on this patient choice data, a conditional logit model. Its coefficient estimates show which hospitals are considered by patients for each treatment type, and the effect of distance on the final decision for a hospital.
Second, we will investigate the impact of halving the patients’ travel costs. This increases the chance of a hospital farther away to be chosen, and (perceived) quality of a hospital will become (relatively) more important than distance between patient and hospital. The percentage of switching patients is a proxy for competitiveness, and quality because better hospitals will be visited more often.
important in the decision for a hospital. Thereby, decreasing patients’ travel costs might help patients to find better care. However, potential entry is limited. For a few treatments with high switching percentages – indicating a more competitive market – and for treatments with many switching elderly, it might be worthwhile to enter. For treatments with low percentages of switching it is doubtful whether entry will be profitable, because patients are locked-in and are not inclined to switch.
The rest of the paper is organized as follows. In Section II we give a short overview of the Dutch health care market, and Section III describes our data set. Section IV explains the discrete choice model. Results are described in Section V, and we address the competition index in Section VI. Section VII concludes. Full regression results can be found in Appendix A, and predicted market shares and switching percentages when the patients’ travel costs halve in Appendix B.
II. The Dutch Health Care Market
The Dutch health care market has been deregulated since February 2005 when price competition for some treatments was introduced. From 2006 onward, patients choose their own health care insurance in a competitive insurance market. We discuss this in further detail below.
II.A. The Decision Process
Patients have the right to choose the hospital they want to be treated. However, general practitioners (GPs) are able to channel their patients towards a certain hospital, by suggesting a hospital or even by referring the patient immediately to a hospital.
Health insurers have the possibility to channel their clients as well, because insurers write contracts with hospitals about, e.g., the minimum number of treatments to be performed by the hospital and prices to be paid by the insurer. However, at the moment some hospitals only negotiate about volumes, i.e. the minimum number of patients the hospital should treat (NZa, 2007a).
Thus, if a client needs to be treated, the insurer will pay all costs if the client visits contracted hospital X. However, if the client prefers to visit hospital Y, the client will be compensated for the costs at hospital Y. The compensation is not necessarily a full refund. There are three types of refund: (i) a full refund, (ii) some percentage of the costs, or (iii) the costs the client would have incurred if he went to contracted hospital X1. Which of the three options above is executed depends on the insurer and the type of insurance. Nevertheless, in the Netherlands, almost each insurer contracted each hospital in order to provide care for each client everywhere (NZa, 2007b). Thereby, taking prices into account in our regressions would not be helpful in the explanation of the patient’s decision process, because in most cases the patient would face the same price at each hospital he could go to.
Hospitals are allowed to compete in prices (and quality) for several treatments. This list of treatments is defined by law, and is expanded every year. In 2007, price competition is allowed for 10% of all possible hospital treatments. Moreover, competition has been introduced in the health insurance market, effective January 2006. There is a basic health insurance, mandatory for every Dutch citizen, and each insurer must accept everybody who wants to buy insurance from the firm.
The introduced competition arises the important question about hospital market size. The (relative) distance between hospitals determines which hospitals are in the same geographic market. In this paper we address the question what effect distance has on hospitals considered, the final decision for a hospital and switching. We will look for differences between treatments and between demographic groups. By halving the patients’ travel costs we predict the percentage of switching patients, a measure we use to indicate (potential) market power.
II.B. Treatments with Price Competition
1
In the Netherlands all treatments and operations are categorized as Diagnosis Treatment Combinations (DBCs),2 a categorization system of hospital treatments. DBCs determine the exact treatment needed. The DBC-segment is divided into two groups: the A-segment has all DBCs where no price competition is allowed3 and the B-segment involves all DBCs where price competition is allowed. Which DBCs are part of the B-segment is defined by law, which might expand every year.4
DBCs are provided by hospitals and Independent Treatment Centers (ZBCs).5 ZBCs are small (private) clinics, and are restricted to patient day care for all A-DBCs – overnight stay at a ZBC is not allowed – but are allowed to perform any operation or provide care for each B-DBC. ZBCs can be a special unit of a hospital (or several hospitals) – they can even hire the same doctors – or ZBCs can be erected by medical specialists or just some entrepreneur(s) (NZa, 2007a). Hospitals are willing to erect a ZBC because different rules apply to ZBCs than to hospitals, such that ZBCs are able to charge lower prices for the same treatments than hospitals. However, from 2008 onward, the rules will be the same for hospitals and ZBCs (NZa, 2007a). Competition between ZBCs and hospitals is limited, because ZBCs provide only a small percentage of total health care (NZa, 2007c).6
Thus, hospitals and ZBCs are active on the same market. Nevertheless, the major players are the hospitals: hospitals consider other hospitals as their largest competitors, and ZBCs consider hospitals as their competitors, much more than other ZBCs (NZa, 2007a). A strong advantage of ZBCs is that they can compete fiercer in prices than hospitals. However, almost no ZBC or hospital wants to distinguish itself by means of price. They prefer to distinguish on quality, service towards patients and innovation (NZa, 2007a).
III. Data
We give an overview of the full data set in Section III.A, and explain how we defined a subdataset in Section III.B.
2
The Dutch term is Diagnose Behandelcombinatie. 3
Prices are determined by the Dutch Healthcare Authority (Nederlandse Zorgautoriteit, NZa). 4
An overview of the B-DBCs in 2006 and 2007 (up to November) we consider is given in Table 1. 5
The Dutch term is Zelfstandig Behandelcentrum. 6
III.A. Full Data Set
Our data is from the Minimal Data Set (MDS)7 which hospitals deliver to the DBC-Information System (DIS),8 available at the Dutch Healthcare Authority (NZa). By law, hospitals are required to report patient treatment information to the MDS. Data includes: the DBC, the hospital where the patient was treated, patient’s sex, patient’s year of birth, where the patient lives (zip code), patient’s insurer, and begin and end date of the DBC. We selected those treatments that started from January 1st 2006 onward, because the new health insurance system started on that date. There are over 1200 different procedures defined in the B-segment, where we classified them into 18 different groups (see Table 1; Kenniscentrum DBC’s van Zorgverzekeraars Nederland, 2007; DBC Onderhoud, 2006). Although data delivery is required by law, we experienced serious flaws in the data set. From the 96 hospitals in the Netherlands we have 10 hospitals with less than 30% valid data,9 one hospital only has 50% correct data, and the rest is almost perfect since more than 96% has been filled out correctly.10 The bad-reporting hospitals are not situated in one part of the Netherlands, but are spread out over the country. This complicated the process of finding a submarket, because each region has at least one bad-reporting hospital. Eventually, we defined a geographic submarket with five hospitals – all reporting well – and low import and export of patients, i.e. most patients from our geographic submarket decided to be treated at a hospital in our submarket.
Travel distance between the zip code of patient residence and the hospital’s zip code is calculated using zip code centroid data.11 The travel distance is derived from the
DriveTimeMatrix. This data is part of the 4-digit postcode data set The Netherlands
of 2005, available from Geodan IT BV. Patients visiting a hospital in their own zip code are assumed to have a travel time of zero minutes and zero kilometers.
We will estimate models using absolute distance in kilometers. Using travel time would be more complicated because we do not know at what time of day the patient (or its relatives) would travel. Because travel times fluctuate during the day we used distance to reflect the decision concerning travel best. We do not incorporate relative distance in our
7
The Dutch term is Minimale Data Set. 8
The Dutch term is DBC-Informatie Systeem. 9
This is due to non-existing zip codes, missing or unidentified sex, future dates of birth, and errors in health insurance like a missing value, special asylum insurances and treatments just being paid for because of serious illness (even without a health insurance, hospitals are obliged to deliver emergent care).
10
models, because driving 5 or 10 kilometers cannot be compared to driving 60 or 120 kilometers, although the relative distance in both cases equals one half.
DIS also reports waiting times. Unfortunately, the data is not completely accurate: until now, not all hospitals report these statistics, although they are required by law to provide waiting times data at least once every three months. Several months have not been reported, meaning that patients did not always have information on waiting times when making the decision which hospital they want to go to. If waiting times are known they are published on the internet by order of the Ministry of Health, Welfare and Sport (RIVM, 2007). If no data has been provided for three months or longer, no waiting times are published online. Moreover, there is no clear definition or procedure about how waiting times should be calculated. Thereby, the data on waiting times is in no way comparable. We dropped waiting times from our models due to the very low accuracy. The website kiesbeter.nl, from the Ministry of Health, Welfare and Sport, publishes information on hospital size as well: the number of beds, number of rooms with one bed, two or three beds, four beds or more than four beds. However, the question arises whether patients go to larger hospitals because there are more beds available, or are the hospitals large because many people would like to go to that hospital? This unclear causality made us decide not to include hospital size in our regressions.
Quality measures (and other product dimensions) might be important, because it provides information on hospital efficiency (Frech and Mobley, 2000). Unfortunately, quality measures are not well defined for the Dutch hospital market. At the moment, the Ministry of Health, Welfare and Sport is developing new quality measures which are more objective than the current ones (NZa, 2007a). However, the quality measures now available from the Netherlands Health Care Inspectorate (IGZ) are the ones published on the internet (IGZ, 2008), the only information source available to patients besides their own GP. Thus, even though these measures are subjective – they are based on questionnaires filled out by the hospital themselves – the information is the best a patient can obtain. These indicators are updated once every year: thus, in 2006 the patients get information about the hospital quality of 2005. However, some quality measures were missing for several hospitals, and because of the subjectivity of the quality measures we decided not to include them in our regressions.
11
We estimate a patient choice model for all B-DBCs together and for each B-DBC separately. A problem with the classification of DBCs is that if a patient needs multiple DBCs at the same time – so-called parallel DBCs – at the same specialism, the hospital cannot always make a declaration of expenses for the additional DBC(s). A new DBC for a different specialism will always be initiated. If the specialism is the same, the new DBC must have substantial additional costs: the additional costs must be around 40% or more of the average costs of the original DBC (see, amongst others, DBC Onderhoud, 2005, 2007a and 2007b). Because of these rules concerning DBC registration, our data set does not necessarily fully reflect all treatments performed and hospital choices made. If a patient was treated for two or more DBCs at the same time, there might be information missing. Nevertheless, the patient chose the treating hospital based on his first care request, which is fully reflected in our data. However, if the DBCs were performed contiguously, the patient probably did not choose a second time where to receive care, but stayed at the initial hospital. Thereby, we would have multiple records for one hospital choice. This will, however, not bias our results substantially if each hospital performed the same percentage of parallel DBCs.
Concerning compensation for the hospital: only registered treatment, i.e. a DBC, is paid for by the health insurer. The level of payment depends on the contract between the hospital and the insurer.
III.B. Defining a Geographic Submarket
We defined a submarket by starting with a hospital in a large city in the Netherlands. We intended to define a geographic submarket by means of the Elzinga-Hogarty test (Elzinga and Hogarty, 1973). The procedure resulted in a submarket covering more than half of the Netherlands. Unfortunately our statistical software package cannot estimate a discrete choice model with so many hospitals. Instead, we selected a region with a small number of ZBCs, such that most DBC-treatments are performed by hospitals. Although it does not matter to the patient whether the DBC is performed by a hospital or a ZBC, it would reduce our model’s validity. Hospitals can own a ZBC (NZa, 2007a) and can redirect the patient to their ZBC, if e.g. the waiting times are shorter there. Thereby, our data would reflect a too small market share for this hospital. We cannot control for ZBC patients in our model because we do not have data about them.
Moreover, almost all data from the hospitals in our defined region are correctly filled out, and has low numbers of import and export of patients, i.e. most patients visiting the hospitals in our region live in the region itself. Our geographic submarket includes 316 zip codes (out of a possible 4015), 29,985 DBCs and 5 hospitals.
The market shares and composition of patients of each B-DBC can be found in Table 1, and the market shares and composition of patients of each hospital in Table 2. The distance between each patient and each hospital is depicted in Figure 1.
Composition (%) Age (average)
B-DBC Market
share (%) F M F M
Ankylosing spondylitis (Bechterew) 0.81 27.57 72.43 48.4 49.2
Arthrosis (knees) 4.03 63.13 36.87 67.1 59.5
Arthrosis (pelvis, hips, thigh) 3.82 70.77 29.23 71.1 69.0
Calculus of kidney and ureter 3.25 39.90 60.10 56.2 56.2
Cataract 21.35 62.26 37.74 74.9 73.0
Cervix disorder 1.62 100.00 40.9
Diabetes mellitus 22.55 51.62 48.38 60.7 57.3
Diseases of tonsils & adenoids 10.93 50.27 49.73 11.1 8.6
Gastroenterology 0.88 66.67 33.33 52.3 50.2
Gastro esophageal reflux disease (GERD) 1.41 55.42 44.58 58.6 54.3
Gout 1.35 19.06 80.94 70.6 58.5
Incontinence 2.66 100.00 60.7
Inguinal hernia 4.96 10.29 89.71 37.1 51.0
Interstitial pulmonary disease 0.92 46.93 53.07 66.1 67.3
Lumbosacral (hernia) 10.01 47.07 52.93 50.3 48.6
Mamma reduction 0.47 99.30 0.70 37.4 37.0
Urinary bladder tumor 2.79 21.65 78.35 69.4 70.9
Varicose veins of lower extremities 6.19 77.37 22.63 48.4 51.0
Total 100.00 54.62 45.38 56.9 53.3
Table 1: Market share, composition and average age per sex for each B-DBC in our specified area (only valid patient entries, from January 2006 up to and including November 2007).
Source: Dutch Healthcare Authority (NZa), as of January 25th 2008.
Composition (%) Age (average)
Hospital ID Market share (%) F M F M 1 13.91 56.15 43.85 61.1 55.5 2 12.25 52.67 47.33 57.1 54.2 3 17.82 53.41 46.59 51.4 49.4 4 41.78 55.06 44.94 56.4 53.0 5 14.25 55.02 44.98 60.7 56.5 Total 100.00 54.62 45.38 56.9 53.3
Table 2: Market share, composition and average age per sex for each hospital in our specified area (only valid patient entries, from January 2006 up to and including November 2007).
We expect that patients prefer to go to a hospital nearby. The preference for a nearby hospital is because people do not like to travel a lot. People also like to have their family and friends close by while getting treated. Moreover, it is likely that friends and family live nearby the patients themselves; if not, it would not matter whether the first- or second-nearest hospital is chosen because family will (not) visit anyway.
There are several studies about patients’ willingness to travel in the United States. Cowing, Holtmann and Powers (1983) find that people might be willing to travel farther to visit a larger hospital because of suggested economies of scale for provision of routine services for hospitals up to 350 beds. Dranove, Shanley and Simon (1992) suggest economies of scale for complex technical services, which are mostly offered by large hospitals. And Luft, Hunt and Maerki (1987) find that higher volumes, i.e. more procedures, are associated with higher quality outcomes.
In the US, however, travel distances might be larger: in some rural areas the nearest hospital is a 100 kilometer drive. In the Netherlands travel distance is never that large, because of the large number of hospitals spread out over the country. Nevertheless, we still expect distance to be of significance to the patients. Urban hospitals are often larger
and more technically advanced than hospitals in rural areas, forcing patients to travel farther to an urban hospital if the operation needed cannot be performed in a rural area hospital. There are three DBCs which are not offered by some hospitals in our subdataset. Hospitals 1, 2 and 5 did not treat patients for Gastroenterology, Gastro esophageal reflux
disease (GERD) and Mamma reduction. Hospital 5 does not offer these DBCs, while
hospitals 1 and 2 only do not offer Mamma reduction procedures.
One possible caveat of our subset is that patients could go across the border to get treated, where, obviously, different laws and prices apply. Nevertheless, our conditional logit model does not incur any difficulties with this alleged problem, because of the Independence of Irrelevant Alternatives (IIA) and the principle of revealed preference. The IIA is a well-known assumption which means that if one alternative is omitted from the choice set, all consumers who chose this alternative will be proportionally distributed over all remaining alternatives.
However, the patients who went to a hospital in our area, showed preference for a hospital in this area over any other hospital. It is unimportant how many outside options there are as well as where they are. Moreover, the IIA assumption implies that if a patient did not visit a hospital in our area, he would assign the same relative probabilities to the 5 hospitals in our area if he had to choose between them. However, we do not know the characteristics of the patients that did not go to a Dutch hospital. Perhaps they do not value travel distance as much as the patients in our subdataset, but we cannot measure or control for these patients.
IV. The Model
In this section we present the model we estimate to find what patients find important when deciding which hospital to visit, where we focus on the importance of distance. First, we discuss the conditional logit model. Second, we give a résumé of our estimation procedure. Section IV.A draws heavily on Train (2003).
IV.A. The Conditional Logit Model
choice possibilities, naming it the conditional logit model. We use a combination of both models by including patient characteristics and choice characteristics, which will be estimated by means of a conditional logit model.
Coefficients of distance from patient to hospital do not necessarily vary over hospitals or over different patient groups. The conditional logit model allows these coefficients to be constant over groups, which cannot be done in the multinomial logit model. Nevertheless, by interacting terms, e.g. distance with each demographic group, we incorporate varying coefficients. Then, we can easily test whether some demographic group value distance or a hospital differently than other demographic groups.
A strong assumption of each logit model is the Independence of Irrelevant Alternatives (IIA). As mentioned above, the IIA means that if one alternative is omitted from the choice set, all consumers who chose this alternative will be proportionally distributed over all remaining alternatives. The assumption facilitates the estimation procedure, but does not hold in general yielding incorrect results. We test the IIA-assumption for all our regressions in Section V.C.
The patient’s process of choosing a hospital can be represented in a reduced form choice function. We present a random coefficients specification for utility. Let there be T different demography groups of patients which we label t=1,2,…,T.12 For each type t there are Nt number of patients, such that N N
T
t t =
∑
=1 with N the total number ofpatients. The utility of patient i depends on observed patient characteristics, hospital characteristics and its interactions. This includes a hospital specific intercept, a hospital intercept interacted with patient type t, the distance between patient and hospital, and distance interacted with patient type t and with hospital j. Thus, the utility of patient i (of type t) at hospital j (i∈{1,2,KNt}, j∈{1,2,KJ}, t∈{1,2,KT}) is
(
j tj) (
t j)
itj itj itj itjitj distkm v
U = ψ +θ + ϕ+η +ζ +ε ≡ β+ε ,
where Uitj is the indirect utility, distkmitj is the distance in kilometers between patient i of
type t and hospital j, vitj are characteristics of hospital j which can vary for each individual i of type t, β is a vector of parameters (the combination of the line above: a hospital intercept, a patient type specific hospital intercept; and several distance coefficients: a general one, a patient type specific, and a hospital specific), and εitj is a
12
random error which is independently identically distributed extreme value (Gumbel distribution). Note that vitj mostly consists of (multiplied) indicators.
The hospital intercepts might be thought of as the mean of patients’ valuations of an unobserved characteristic such as quality or waiting times, while the error represents the distribution of consumer preferences around this mean.
We included the square root of distance in 2 regressions because the Linktest did not indicate the linear model to be a correct specification. We selected the square root to give distance a diminishing impact on hospital choice, instead of an increasing effect if we had used squared distance. Thereby, we estimated
(
j tj) (
t j)
itj(
t j)
itj itj itj itjitj distkm distkm v
U = ψ +θ + ϕ+η +ζ + λ+τ +ξ +ε ≡ β +ε ,
adding coefficients for the square root of distance between patient and hospital: a general one, a patient type specific, and a hospital specific.
To find potential market power for the total B-DBC segment, we also estimated one regression for all DBCs together, i.e.
(
j tj d) (
t j d)
itj itj ditj itjditj distkm v
U = ψ +θ +ω + ϕ+η +ζ +ς +ε ≡ β +ε ,
where we used a subscript d to indicate the patient’s DBC. We added a DBC-specific intercept and a DBC-specific coefficient for distance. In the rest of this section we refer to the matrix of characteristics as vitj, but it also applies to the matrices vitj and vditj above.
Consumer i of type t selects hospital j if and only if the utility of choosing that hospital is higher than the utility levels corresponding to every other hospital, i.e.
{
U U k j}
{
v v k j}
Pitj =Pr itj > itk ∀ ≠ =Prεitj > itjβ − itkβ +εitk ∀ ≠ .
Note that consumer i selects exactly 1 hospital to receive care at. From the Gumbel distribution of the error F(
τ
)=exp[
−exp( )
−τ
]
, and the independently distributed errors follows that(
)
[
]
∏
≠ − − + −= i j itk itj itk
itj
itj v v
P |ε exp exp (ε β β) .
After integration and some algebraic manipulations we obtain the probability of individual i of type t selecting hospital j:
These probabilities are undefined: summation over all hospital choices results in a value of one, because adding an arbitrary constant to all Uitjs does not change the choice
probabilities. Thereby, in order to estimate the vector of parameters
β
we define a reference hospital and reference type such that the corresponding utility is zero, Uirr=0where r stands for reference type or reference hospital choice. This yields the relative odds of choosing hospital j over r, the so-called odds ratios.
(
)
(
)
[
]
[
(
)
]
= − = − = =β
β
β
β
β
β
itj irr itj irr itj irr itj irr itj v v v v v v v P P ~ exp exp exp exp exp ,where vitj ≡vitj −virr
~
meaning that we use characteristics as difference from the reference choice, and all other variables are defined as above. The reference hospital is the hospital where most patients were treated, for the DBC considered. In our tables we report which hospital is the reference hospital. The same holds for the demography group, and for DBC in the regression of all DBCs together.
From the odds ratio follows that we report exponentiated coefficients: exp
[ ]
β
. The odds ratios facilitate the interpretation of the coefficients. For a one unit increase of a variable for a hospital, we can expect a probability increase of selecting that hospital by 100*(
exp(β
)−1)
%, holding other variables constant.When more than one variable increases by one unit, both exponentiated coefficients can be multiplied. Denote the new values with an asterisk and let vitj =vitj+wcd
~ * ~
where wcd is a vector of zeros with ones at the c-th and d-th index. Then, the unit increase for the c-th and d-th variable yields an odds ratio increase of
[
β
]
β
β
β
cd itj itj itj itj itr itj itr itj w v v v v P P P P exp exp exp exp / / ~* ~ ~ * ~ * * = − = =[
β
cβ
d]
exp[ ]
β
c exp[ ]
β
d exp + = × =IV.B. The Estimation Procedure
We will estimate conditional logit models, using the statistical software package Stata 8.2SE. We will estimate a model for each B-DBC and for all B-DBCs together. These results will indicate what patients value highly in their decision for the hospital they want to be treated at. We maximize the Maximum Likelihood using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method (Train, 2003). The BFGS method uses the concept of the arc Hessian to approximate the Hessian: the slope of the gradient of the original function indicates the direction of the optimization. This method is faster than using the normal Hessian, because the Hessian is defined for infinitesimally small movements, while we start optimizing making large steps (Train, 2003).
For a few regressions the BFGS optimization method did not converge – yielding no insightful results – and we report the results using the Newton-Raphson (NR) optimization method. NR is based on a second-order Taylor’s approximation of the Log-likelihood function: the inverse Hessian matrix is used to calculate the step size and direction during the optimization (Train, 2003).
Both methods, BFGS and NR, are iterative procedures to determine the maximum likelihood estimates of the regression coefficients conditionally on the sets of values of the explanatory variables within each stratum. The conditional likelihood that is maximized is the product of the conditional likelihoods for each stratum.
V. Results
This section discusses our estimation results, which can be found in Appendix A. We show how our regression results are presented and the interpretation of the coefficients in Section V.A. In Section V.B we discuss the regression results, and Section V.C discusses the Independence of Irrelevant Alternatives assumption.
V.A. Reporting Regression Results
As mentioned in Section IV.A we report exponentiated coefficients: exp
[ ]
β
. This results from the definition of the relative odds of choosing hospital j over r, the so-called odds ratios (Train, 2003). Thereby, we tested whether the exponentiated coefficients are statistically significantly different from one.For each model we report the Goodness of Fit indicator, which is a likelihood ratio
) 0 ( ) ˆ ( 1 LL LL β ρ = − ,
where LL(βˆ ) is the log-likelihood function at the estimated parameters and LL(0) is the log-likelihood function when all parameters are set equal to zero (Train, 2003). The
Goodness of Fit indicator is the percentage increase in the log-likelihood function above
the value taken at zero parameters. The interpretation of this index is not straightforward, but a higher value indicates a better fit (Train, 2003). Because the log-likelihood values of different sets of data cannot be compared, the Goodness of Fit indicator cannot be compared either.
We also report the Linktest value, a specification test. None of the estimations indicate a misspecification, although this conclusion is not straightforward for
Lumbosacral (hernia) because of a 5.2% chance of a correct specification. We included
the square root of distance in 2 regressions because the Linktest did not indicate a correct specification. We selected the square root to give distance a diminishing impact on hospital choice, instead of an increasing effect if we had used squared distance.
V.B. Regression Results
We discuss all coefficients given all other explanatory variables, i.e. holding all other variables constant. The demography groups are coded numerically and can be found in Table 3. Obviously, (most) children did not decide which hospital to visit, but their parents did.
Description Age Female code Male code
Children 0-17 years 0 10
Young adults 18-44 years 1 11
Middle aged 45-64 years 2 12
Elderly 65+ years 3 13
Table 3: Codes for all demographic groups, as coded in the Appendixes.
quality indicators: the preference for a hospital – not considering distance – is being picked up by the intercept, thereby representing, amongst others, quality and waiting times. Hospital 5 is perceived better than hospital 4, which is perceived better than the other three hospitals.
Consider the interaction between distance and each demographic group: all coefficients are larger than one, and significant except for male elderly. Thereby, each demographic group has a higher willingness to travel when compared to female elderly. Moreover, the coefficients of the demographic groups decrease by age: the younger people are, the higher the willingness to travel. There is no significant difference between women and men concerning the willingness to travel.
The willingness to travel differs among DBCs as well, the significant coefficients are all larger than one, meaning that for these DBCs the willingness to travel is higher than for the reference DBC Diabetes mellitus. Note that it never occurs that an increase in distance means an increase in the willingness to travel, because even the highest coefficients (DBC Lumbosacral (hernia), male children and distance for reference hospital 4) being multiplied results in 1.0463*1.0490*0.8639= 0.9482 which is smaller than one.
To sum up, the willingness to travel differs among DBCs and demographic groups and even hospitals. Most important result is the decreasing willingness to travel in age: younger people are less sensitive to distance than elderly are.
Investigating our estimation results for each separate DBC, we find that each and every distance coefficient is smaller than one, meaning that patients are not willing to go the extra mile for a hospital farther away if it is the same as the hospital around the corner. Thus, if the reference hospital is further away, its chance of being chosen decreases. This result is in line with Abraham, Gaynor and Vogt (2007).
In several regressions the distance coefficient is significant, and the interaction term with one of the demography group is significant as well. This indicates that different demography groups value distance in a different way. The willingness to travel even differs over the DBCs. For regressions Ankylosing spondylitis (Bechterew),
Arthrosis (pelvis, hips, thigh), Cervix disorders, and Lumbosacral (hernia), there is one
willingness to travel should decrease in distance, our results need to be interpreted with care.
The willingness to travel differs among hospitals as well. All coefficients of the interaction terms of distance and a hospital are smaller than one. Thus, when distance increases for a hospital other than the reference hospital, the patients go to the reference hospital relatively more often (i.e. the willingness to travel is largest for the reference hospital).
For most regressions the reference hospital – the hospital with the largest number of patients – is number 4. For Ankylosing spondylitis (Bechterew) and Gout the reference hospital is different, but for hospital 4 the interaction term with distance is not significant.13 Thereby, the willingness to travel does not significantly differ among hospitals in these regressions, and overall the highest willingness to travel is to hospital 4, which has, obviously, the largest market share.
Note that several coefficients are either very small (<0.01) or very large (>100), which corresponds to chance differences of over 100.14 This might be due to the underrepresentation of the demography group associated with that coefficient. E.g., a demographic group consists of only 3 patients, and none of the 3 patients go to reference hospital 4. Instead, they only visit hospitals 1 and 2. Then, the estimated probability that some patient of this demographic group goes to hospital 1 can be over 1000 because the probability that this demographic group would visit the reference hospital is zero (in this subdataset). Note that this is not necessarily the other way around: some model specifications do not produce very large coefficients, while there are still only a few patients in some demographic groups.
V.C. Independence of Irrelevant Alternatives
A strong assumption of the conditional logit model, like any logistic model, is the Independence of Irrelevant Alternatives (IIA). We check whether this assumption holds by performing regressions for each DBC (and all DBCs together) on a subset of hospital choices (Hausman and McFadden, 1984). By means of a Hausman test we test for structural differences in the coefficients between the original model estimated and the model estimated on the subset of choices where we deleted hospital 2.
13
For Gout neither of the interaction terms between hospital and distance and for Ankylosing
spondylitis (Bechterew) the interaction terms of hospitals 2 and 4 and distance are insignificant. 14
We cannot reject the null hypothesis that the IIA assumption holds for the regression of all DBCs together because the Hausman test results in a negative chi2-value. Thereby, we cannot draw conclusions about the model’s specification. It is not clear why the test fails to yield results.
For the separate DBCs it is not always possible to draw conclusions as well. However, in these cases it is because of the small sample size. By deleting one hospital choice, we might delete a whole demographic group. This yields inaccurate results: a few variables and a few interaction terms will be deleted from the restricted regression, which will adjust the estimates of all other coefficients. Thereby, the Hausman test probabilities might be lower bounds. The Hausman test statistic returns a negative number in 5 of our regressions. Moreover, for Mamma reduction we cannot perform an IIA-test because omitting one of the two hospitals results in an undefined model.
We accept the IIA assumption for 3 DBCs: Diseases of tonsils & adenoids,
Gastroenterology and Incontinence. However, we reject the null that the IIA holds for the
following 10 regressions: Arthrosis (knees), Cataract, Cervix disorder, Diabetes mellitus,
GERD, Gout, Interstitial pulmonary disease, Lumbosacral (hernia), Urinary bladder
tumor, and Varicose veins of lower extremities. We cannot draw conclusions about the
IIA concerning the other 4 DBCs.
Thus, the Hausman test indicates that for most DBCs our discrete choice model is not suitable. Therefore, our results must be interpreted with care. Nevertheless, the discrete choice model is an illustration and, thereby, does not influence the results of our competition index.
VI. Switching as Indication of Market Power
The conclusion that patients are prepared to bypass the nearest hospital is apparent from the market shares per DBC. If all patients would go to the nearest hospital, the market shares would be different for each DBC. In our data the actual market shares equal the market shares when all patients visit the nearest hospital when we look at demography group level for each DBC: we have eight cases15 where six consist of only 1 or 2 patients, the others are 10 and 14 patients (but are less than 1.2% of the total number of patients of the corresponding DBC). This means that the decision is (at least partly) based on (perceived) quality of the hospitals.
We argue that differences between actual market shares and predicted market shares are due to quality differences. If each hospital would have the same level of quality, patients would solely base their decision which hospital to visit on distance. Then, each patient would visit the nearest hospital. Therefore, we argue that we obtain a proxy for quality investigating the market share of each hospital for each DBC. By halving the patients’ travel costs, patients will be more inclined to choose a hospital located farther away if it has a higher (perceived) quality. The willingness to travel has increased, thus patients necessarily visit the same hospital as before or a hospital which is located farther away: the utility difference between each pair of hospitals has decreased which increases the probability that a hospital farther away will be chosen.
We predicted the market shares per DBC and for all DBCs together. Although the effect of a higher willingness to travel are reflected in the market shares, we do not observe which patients switch hospitals. This means that, e.g., patients can go from hospital 1 to hospital 2, but the patients from hospital 2 can switch to hospital 1 as well. Thus, we only observe the net effects of all patients deciding which hospital to visit and is the lower bound of the real percentage of switching patients. By considering the new market shares at DBC level, demography level or both, we obtain additional information about the switching behavior of the patients, but we repeat that the percentages remain net switching effects.
Although there is a different composition of patients for each DBC, i.e. it might be that for some DBC the patients live (on average) further away from the hospitals than for other DBCs, our experiment does give a proxy for quality because patients still need to decide whether they want to surpass the nearest hospital or not.
15
The actual market shares and market shares when patients visit the nearest hospital coincide for
Results can be found in Appendix B, which are based on the regressions as presented in Appendix A.
We conclude that switching increases in age: parents prefer to stay at the hospital they initially visited with their children (5.00% switches) while elderly switch most (9.70%). This is in line with our conclusion that willingness to travel decreases in age: younger people were already prepared to surpass the nearest hospital, but elderly were more in favor of the nearest hospital. Decreasing the travel costs let some elderly decide to go to a better hospital as well. Thus, elderly do not only visit the nearest hospital or the hospital they know: they are prepared to switch.
Moreover, 7.61% of women switch while only 6.99% of men switch. We obtain additional switching information when we look into the DBC-specific regressions. Here as well, women switch more often than men (only considering DBCs available for both women and men): 10.11% vs. 9.52%.16 At 8 DBCs more switchers are women, while at the other 8 DBCs men switch more. Moreover, switching increases in age (4.36%, 6.64%, 9.07% and 13.05%, respectively).
The total percentage of switching patients differs among DBCs, from 0.18% (Mamma
reduction) till 18.29% (Cataract), with an average of 7.19% for all DBCs together. The
four DBCs with a switching percentage over ten percent are Calculus of kidney and
ureter, Cataract, Incontinence and Interstitial pulmonary disease. Additional to these 4
DBCs, for Arthrosis (knees) and Urinary bladder tumor there are more than 10% of elderly switching, the most switching demography group. Both DBCs have high shares of elderly.
Consider the regression of all DBCs together. The largest hospitals lose some market share but the smallest hospitals lose more. Hospital 5 is the only hospital to gain from the smaller travel costs, and attracts 50% more patients than before. When breaking down to demography we see that hospital 5 gains in every age group, and the first three hospitals lose patients in each group. Noteworthy is that hospital 4 attracts patients in the categories children, middle-aged and female young adults: these demography groups consider hospital 4 as better, whilst the other groups prefer to go to another hospital. However, the
Gastroenterology (male infants), GERD (female infants), Mamma reduction (female elderly and male young adults), and Urinary bladder tumor (male young adults).
16
demography groups switching to other hospitals are larger, such that hospital 4 loses a few percentage points: especially elderly switch to different hospitals.
Consider the DBC level, where a different conclusion results. In 13 cases hospital 5 increases its market share but has a smaller market share in the remaining 5 cases. The other hospitals have increasing market shares as well, although not as often as hospital 5. In only 5 instances there is one hospital gaining patients (4 times hospital 5, once hospital 4), and in all other cases there are two or even three hospitals attracting more patients (indicating that several hospitals are (perceived) good hospitals). Nevertheless, because of the high awareness that hospital 5 is a good hospital, a directed marketing campaign will not be helpful for hospital 5 to attract more patients.
Breaking down each DBC regression to demography group shows that in 12 cases a hospital is able to more than double its market share (8 times hospital 5, thrice hospital 1 and once hospital 3). There are three DBCs which have three hospitals doubling market shares: Ankylosing spondylitis (Bechterew), Cataract and Interstitial pulmonary
disease (including 6 times hospital 5 and all three occurrences of hospital 1). There are 5
cases where a hospital loses its complete market share, i.e. for female infants (hospitals 2 and 5 for Lumbosacral (hernia) and hospital 3 for Mamma reduction) and female young adults (hospital 4 for Arthrosis (pelvis, hips, thigh) and hospital 2 for Gout).
We argue that the changing market shares are an indication of quality. A hospital might be (perceived) better, e.g., because of shorter waiting times, better doctors or more one-person rooms. Thus, it might be worthwhile to shorten waiting times at good hospitals in order to give patients the best possible treatment possible.
If a hospital gains market share, it means that it becomes more attractive when travel costs decline. I.e. the hospital is perceived better, but because of patients’ travel costs they do not select it. When traveling is less of a problem, people do want to go to the hospital because it is (perceived) better than the hospital they went to at first.
The preference for a nearby hospital is also apparent from the market shares when the patients’ travel costs halve. Nevertheless, patients do take quality more into consideration, which is obvious from the model’s specification that only the distance coefficients have changed. Especially elderly switch more when the travel costs halve, because the preference for a close hospital is high for this age group. Nevertheless, we expect an increase in the willingness to travel in upcoming years, because people are getting more mobile recently, which means that people will be more inclined to go to a hospital farther away when it is perceived better.
The percentage of switchers does give an indication of entry possibilities by a hospital or ZBC. A high switching percentage indicates that there are better hospitals, but they were too far for the patients in the initial situation. However, when a low percentage of patients switch it is either because the patients are already at the best hospitals, or that travel costs remain very important and the better hospital is still considered too far away.
Thus, a high percentage of switchers means that patients are prepared to go to a better hospital. There are also good entry possibilities when the switching percentage is high. Also DBCs with large shares of switching elderly, are potentially profitable to enter. However, if there are not many switchers, it is less clear whether entry will be profitable. Patients could not switch because other hospitals are still considered too far away. In that case a potential entrant can attract these patients, if it enters at a desirable location. Thus, it could only be worthwhile to enter the market in a densely populated area. On the other hand, if patients are already visiting the best hospital, it will be really hard to enter the market. These patients are not inclined to go to another hospital because the hospital they visit is already of high quality. Thus, the new hospital needs to establish a good reputation before patients will visit. We argue that this second case is not very plausible. If only quality would be important in the decision for a hospital, there would be one hospital attracting (almost) all patients and the other hospitals would have very small market shares. Because this does not occur in our data, we argue that the first case of relatively important patients’ travel costs is more plausible.
VII. Discussion and Conclusion
In this paper we presented a new competition index. Common indices as the Lerner index and the SSNIP criterion use price. Because costs are covered by health insurers in the Netherlands, patients do not take price into consideration in their decision for a hospital. We tried to overcome this problem by using distance instead of prices. After running regressions we halved the patients’ travel costs. Then, patients will be more inclined to choose a hospital located farther away if it has a higher (perceived) quality. For this new (fictional) set-up we predicted the market shares that would arise, and compared them with the actual market shares. The percentage of switchers can be used as a competition index. If the switching percentage is too low, patients might be locked-in which is an indication of potential market power. High switching percentages indicate a more competitive market.
As an illustration, we investigated the willingness to travel for 18 different groups of B-DBCs in the Netherlands. All B-DBCs where price competition was allowed during the years 2006 and 2007 are included in the B-segment. However, because insurers covered the costs, patients did not include price in their decision for a hospital.
We estimated conditional logit models for all DBCs together and for each DBC separately. The conditional logit model assumes Independence of Irrelevant Alternatives. Our data does not suggest that this assumption holds. Moreover, in only three cases we accept the IIA assumption. Thereby, these results have to be interpreted with care.
The model of all DBCs together is most straightforward to interpret. There is a strong relation between demography group and the willingness to travel: younger people take distance less into account when deciding which hospital to visit, while elderly find distance the most important of all age groups. There is no significant difference between men and women concerning the willingness to travel.
Our competition index results are in line with the willingness to travel. We conclude that switching increases in age, and women switch slightly more than men. Higher percentages of switchers indicate a more competitive market, and potential more profitable entry. For a few DBCs, namely Calculus of kidney and ureter, Cataract,
Incontinence and Interstitial pulmonary disease, there are high switching percentages,
potentially competitive. However, also small percentages of switching can indicate profitable entry possibilities, as long as densely populated areas are entered when patients find distance very important in their decision. Small switching percentages can also be an indication of potential market power. The DBCs with the lowest switching percentages are Gastroenterology, Gastro esophageal reflux disease (GERD) and Mamma reduction. Moreover, the percentage of switchers is an indication of quality.
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A. Regression Results
In this appendix all regression results are presented. First, we show the estimation of all DBCs together. Second, all linear regressions are presented. Finally, we show the regressions results of 4 DBCs which might have estimation difficulties because of the small sample sizes in a few demographic groups.
Note that 15 regressions have been performed using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization method, while the other 4 regressions used the Newton-Raphson (NR) optimization. Note also that the levels of significance indicate whether the exponentiated coefficients are different from one.
All DBCs togethera All DBCsa hospital=1 0.2995*** hospital=2 0.3170*** hospital=3 0.3039*** hospital=5 2.7162***
hospital=3 & dbc=Ankylosing spondylitis (Bechterew) 5.1275*** hospital=3 & dbc=Arthrosis (knees) 0.4696*** hospital=3 & dbc=Arthrosis (pelvis, hips, thigh) 0.4932*** hospital=3 & dbc=Calculus of kidney and ureter 0.5017*** hospital=3 & dbc=Cataract 1.2770*** hospital=3 & dbc=Cervix disorder 0.6103*** hospital=3 & dbc=Diseases of tonsils & adenoids 0.2072*** hospital=3 & dbc=Gastro esophageal reflux disease (GERD) 0.2569*** hospital=3 & dbc=Gastroenterology 0.5087*** hospital=3 & dbc=Gout 1.8204*** hospital=3 & dbc=Incontinence 0.6300*** hospital=3 & dbc=Inguinal hernia 0.4363*** hospital=3 & dbc=Interstitial pulmonary disease 1.1917 hospital=3 & dbc=Lumbosacral (hernia) 0.2472*** hospital=3 & dbc=Mamma reduction 0.4150*** hospital=3 & dbc=Urinary bladder tumor 0.7010** hospital=3 & dbc=Varicose veins of lower extremities 0.7512*** hospital=5 & dbc=Ankylosing spondylitis (Bechterew) 0.8975 hospital=5 & dbc=Arthrosis (knees) 1.6416** hospital=5 & dbc=Arthrosis (pelvis, hips, thigh) 2.1800*** hospital=5 & dbc=Calculus of kidney and ureter 0.0429*** hospital=5 & dbc=Cataract 2.3592*** hospital=5 & dbc=Cervix disorder 0.3072* hospital=5 & dbc=Diseases of tonsils & adenoids 0.8498 hospital=5 & dbc=Gout 0.7728 hospital=5 & dbc=Incontinence 1.3617 hospital=5 & dbc=Inguinal hernia 1.1053 hospital=5 & dbc=Interstitial pulmonary disease 1.5659 hospital=5 & dbc=Lumbosacral (hernia) 0.3154*** hospital=5 & dbc=Urinary bladder tumor 0.9703 hospital=5 & dbc=Varicose veins of lower extremities 0.5294***
Distance (km) 0.8639*** distkm * hospital=1 0.9844*** distkm * hospital=2 0.9518*** distkm * hospital=3 1.0007 distkm * hospital=5 0.9111*** distkm * dem=0 1.0436*** distkm * dem=1 1.0292*** distkm * dem=2 1.0254*** distkm * dem=10 1.0490*** distkm * dem=11 1.0333*** distkm * dem=12 1.0265*** distkm * dem=13 1.0049
distkm * dbc=Ankylosing spondylitis (Bechterew) 1.0310+ distkm * dbc=Arthrosis (knees) 1.0245*** distkm * dbc=Arthrosis (pelvis, hips, thigh) 1.0106 distkm * dbc=Calculus of kidney and ureter 1.0419*** distkm * dbc=Cataract 1.0353*** distkm * dbc=Cervix disorder 0.9811 distkm * dbc=Diseases of tonsils & adenoids 0.996 distkm * dbc=Gastro esophageal reflux disease (GERD) 0.9832 distkm * dbc=Gastroenterology 0.9951
distkm * dbc=Gout 0.9957
distkm * dbc=Incontinence 1.0026 distkm * dbc=Inguinal hernia 1.0017 distkm * dbc=Interstitial pulmonary disease 1.0436*** distkm * dbc=Lumbosacral (hernia) 1.0463*** distkm * dbc=Mamma reduction 1.0005 distkm * dbc=Urinary bladder tumor 1.0058 distkm * dbc=Varicose veins of lower extremities 1.0158**
Goodness of Fit 0.5733
Linktest 0.610
IIA test b
Reference hospital 4
Reference demography 3
Reference DBC Diabetes mellitus
N 29,985
Exponentiated coefficients
+ p<0.1, * p<0.05, ** p<0.01, *** p<0.001
a This regression used the Newton-Raphson optimization method instead of the Broyden-Fletcher-Goldfarb-Shanno method. b
