The effect of activity-based financing on hospital efficiency: a panel data analysis of DEA efficiency scores 1992-2000.

Abstract

Activity-based financing (ABF) was implemented in the Norwegian hospital sector from 1 July 1997. A fraction of the block grant from the state to the county councils has been replaced by a matching grant depending upon the number and composition of hospital treatments. As a result of the reform, the majority of county councils have introduced activity-based contracts with their hospitals. This paper studies the effect of activity-based funding on hospital efficiency. We predict that hospital efficiency will increase because the benefit from cost-reducing efforts in terms of number of treated patients is increased under ABF as compared with global budgets. The prediction is tested using a panel data set from the period 1992-2000. Efficiency indicators are estimated by means of data envelopment analysis (DEA) with multiple inputs and outputs. Using a variety of econometric methods, we find that the introduction of ABF has improved efficiency when measured as technical efficiency according to DEA analysis. The result is less uniform with respect to the effect on cost-efficiency.

Full text

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UNIVERSITY
OF OSLO
HEALTH ECONOMICS
RESEARCH PROGRAMME
The effect of activity-
based financing on
hospital efficiency:
A panel data analysis of
DEA efficiency scores
1992-2000
Erik Biørn
Department of Economics
Terje P. Hagen & Tor Iversen
Center for Health Administration
University of Oslo
Jon Magnussen
SINTEF Unimed Health Services Research
Working Paper 2002: 8

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The effect of activity-based financing
on hospital efficiency:
A panel data analysis of DEA efficiency scores 1992-20001
Erik Biørna,e, Terje P. Hagenb,e,*, Tor Iversenc,e and Jon Magnussend,e
30 April 2002
Health Economics Research programme at the University of Oslo
HERO 2002
a
Department of Economics, University of Oslo, PO Box 1095 Blindern, NO-0317 Oslo, Norway.
E-mail: erik.biorn@econ.uio.no
Center for Health Administration, University of Oslo, Rikshospitalet, NO-0027 Oslo, Norway.
E-mail: t.p.hagen@samfunnsmed.uio.no
Center for Health Administration, University of Oslo, Rikshospitalet, NO-0027 Oslo, Norway.
E-mail: tor.iversen@samfunnsmed.uio.no
SINTEF Unimed Health Services Research, NO-7465 Trondheim, Norway.
E-mail: jon.magnussen@unimed.sintef.no
Health Economics Research Programme at the University of Oslo (HERO)
Corresponding author
b
c
d
e
*
1 The paper presents results from an evaluation project initiated by the Norwegian Ministry of Health and Social
Affairs. Financial support from the Ministry and from the Norwegian Research Council to the Health Economics
Research Programme at the University of Oslo is acknowledged. We wish to thank participants at the Nordic
Health Economists’ Study Group Meeting in Lund 2000, discussant Peter Smith and other participants at the
Health Economics Workshop at Universitat Autonoma de Barcelona 26-27 January 2001, and participants at
various seminars at the University of Oslo for constructive comments on previous versions of the paper. The
usual disclaimer applies.
© 2002 HERO and the author – Reproduction is permitted when the source is referred to.
Health Economics Research programme at the University of Oslo
Financial support from The Research Council of Norway is acknowledged.
ISSN 1501-9071, ISBN 82-7756-088-5

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Abstract:
Activity-based financing (ABF) was implemented in the Norwegian hospital sector from 1
July 1997. A fraction (30 to 50 per cent) of the block grant from the state to the county
councils has been replaced by a matching grant depending upon the number and composition
of hospital treatments. As a result of the reform, the majority of county councils have
introduced activity-based contracts with their hospitals. This paper studies the effect of
activity-based funding on hospital efficiency. We predict that hospital efficiency will increase
because the benefit from cost-reducing efforts in terms of number of treated patients is
increased under ABF compared with global budgets. The prediction is tested using a panel
data set from the period 1992-2000. Efficiency indicators are estimated by means of data
envelopment analysis (DEA) with multiple inputs and outputs. Using a variety of econometric
methods, we find that the introduction of ABF has improved efficiency when measured as
technical efficiency according to DEA analysis. Contrary to our prediction, the result is less
uniform with respect to the effect on cost-efficiency. We suggest several reasons why this
prediction fails. Keywords are poor information of costs, production-oriented drive, tight
factor markets and soft budget constraints.
JEL Classification: I11, I18, C23, L32
Keywords: Public hospitals, financing, efficiency, DEA-scores, panel data, Norway

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1. Introduction
The question of optimal hospital reimbursement schemes has been widely discussed in the
literature (see e.g. Newhouse, 1996, for an overview). The main trade-off is generally
believed to be between providing incentives for efficiency in the production of hospital
services and avoiding adverse patient selection. Put simply: high powered prospective
payment systems are generally believed to increase efficiency, but may generate problems due
to creaming, skimping or dumping (Ellis, 1998). Fee-for-service systems, on the other hand,
may give rise to serious inefficiencies in the hospital system.
When hospital reimbursement schemes have received attention in the literature, the main
distinction has often been made between retrospective (e.g. fee-for-service) and prospective
(e.g. fixed price per DRG) systems. Hence, much of the empirical literature deals with the US
transition from a fee-for-service system to a prospective DRG-based system for its Medicare
population in 1983 (Hadley et al., 1989; Hodgkin et al., 1994; Newhouse, 1989). Recently,
Yip and Eggleston (2001) have also published a similar study of the change from
retrospective to prospective reimbursement with Chinese data. In many European countries,
however, the policy question has been (and is) whether to finance hospitals by global budgets
or introduce activity-based financing systems. Hence, the choice is between two different
forms of prospective payment. In this respect the insight gained from the US studies is of
limited interest.
The empirical evidence of the effects of reforming systems based on global budgets is scarce.
The Thatcher reforms in Great Britain in the early 1990s aimed at improving efficiency both
by introducing competition between hospitals and by changing contracts based on costs to
contracts based on costs and volume. Unfortunately, there is little published evidence on the
results of this reform. Le Grand (1999) reports an annual increase in efficiency post-reform of
2 per cent compared with 1.5 per cent prior to the reform. Koen (2000) is, however, skeptical
about these results. In a summary of the evidence of the effects of increased competition,
Propper (1997) is unable to find any effects. In a study of a reform with certain similarities in
Sweden, Gerdtham, Rehnberg and Tambour (1999) find that a switch from budget-based
allocations to output-based allocations leads to a 13 per cent decrease in costs among Swedish
hospitals. The study utilizes data from two years, 1993 and 1994. Later analyses, in particular

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Charpentier and Samuelsson (1999) have studied productivity changes in the county of
Stockholm in the period from 1992 to 1997. They find productivity gains in 1993 and 1994
and productivity reductions in the following years.
In Norway, there are three levels of government: the state or central government, the counties
and the municipalities.1 In the period we analyze, hospitals are owned and financed by the
county councils.2 Before 1980 hospital costs were reimbursed on a per diem basis. This
system was costly, and from 1980 hospitals were given annual global budgets. This led to a
period of cost containment; annual expenditures increased by an average of around 1.1 per
cent per year, but questions were raised about the efficiency of the hospital sector. Activity-
based financing (ABF)3 was implemented in the Norwegian hospital sector from 1 July 1997.
A fraction of the block grant from the state to the county councils has been replaced by a
matching grant depending on the number and composition of hospital treatments. At first, 30
per cent of the DRG-based cost of a treatment was refunded from the state. From 1 January
1998, the percentage was increased to 40 and from 1 January 1999, to 50.
The government’s arguments for introducing ABF were put forward in a white paper from the
Ministry of Health and Social Affairs (1995). An increase in the number of elective
treatments was considered to be needed in order to fulfil the waiting list guarantee adopted by
the parliament. Furthermore, an increase in the block grant to the county councils was
assumed to be insufficient because of the leakage to other sectors for which the county
councils are responsible, in particular secondary schools and transportation. A reform of the
financing mechanism was therefore sought. By introducing a matching grant to the county
councils the government intended to influence the county councils’ cost of hospital treatment
relative to other services, and hence, shift the county councils’ priorities in the direction of
hospitals. The government’s and the parliament’s intention was that the activity-based
financing should also be implemented as activity-based contracts between a county council
and its hospitals. The county councils were, however, free to decide the kind of funding
mechanism they would use. It turned out that 15 of Norway's 19 county governments

1 For a general description of the Norwegian health care system, see van den Noord et al. (1998) and European
Observatory on Health Care Systems (2000).
2 The central government has taken over both ownership and financing from January 2002. See
http://www.dep.no/shd/sykehusreformen/aktuelt/rapport/030071-990126/index-dok000-b-n-a.html for a brief
description.
3 The term used in Norwegian is ´Innsatsstyrt finansiering´ or the abbreviation ´ISF´.

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introduced activity-based financing (ABF) of their hospitals when the matching grant was
implemented. Another two county governments introduced activity-based financing of their
hospitals from 1 January 1998, another one from 1 January 1999 and the last one from 1
January 2000.
In this paper we study the effect of this reform of the Norwegian financing system on hospital
efficiency. The study may provide a valuable supplement to the literature on financing
reforms. The present study comprises data for 48 somatic hospitals over a period of nine
years, five prior to the reform and four after the reform. Thus, compared with other European
studies (cf. Gerdtham, Rehnberg and Tambour, 1999; Le Grand, 1999; Sommersguter-
Reichmann, 2000), we are able to analyze effects of the reform over a longer period of time.
Our paper is organized as follows: Section 2 presents our main hypothesis that activity-based
funding of hospitals will improve efficiency relative to a situation where hospitals are funded
by global budgets. This hypothesis is derived from a stylized model of hospital decisions. In
Section 3, our data on hospital inputs and outputs are described. The estimation of efficiency
is made using Data Envelopment Analysis (DEA) with data from the period 1992 - 2000. On
average, technical efficiency is higher at the end of the period than at the beginning, while the
average level of cost-efficiency is lower. Section 4 contains the empirical analysis of the
hypothesis. We find that the introduction of ABF has improved efficiency when measured as
technical efficiency according to the DEA analysis. The results are less uniform with respect
to the effect on cost-efficiency. In some cases the estimated ABF effect is insignificant, in
other cases it is significantly negative. According to our model predictions, we would have
expected an increase in cost-efficiency as a result of the introduction of ABF. In the
concluding remarks we suggest several reasons why this prediction fails. Keywords are poor
information of costs, production-oriented drive, tight factor markets and soft budget
constraints.

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2. An economic model of the effect of activity-based financing on hospital
efficiency
Inspired by the development of hospital financing in the US, the replacement of cost-based
(retrospective) reimbursement by output-based (prospective) financing is studied in several
works (see Dranove and Satterthwaite (2000) for a review). Under retrospective
reimbursement the insurer covers hospital costs irrespective of their magnitude. Hence, there
are no incentives to make efforts that aim at reducing production costs. With output-based
financing a hospital’s revenue is independent of previous costs (prospective financing). The
hospital now reaps the gains from cost-reducing efforts, and an incentive for undertaking
these efforts is created.
The effect of replacing a fixed, global budget with output-based financing is less obvious.
Since both systems are prospective, the agent keeps the results of cost-reducing efforts in both
systems4. In this section we study the economic mechanisms behind the hypothesis that:
Hospital efficiency is expected to be greater with activity-based financing (ABF) of hospitals
than with fixed budgets.
The model we present summarizes the economic logic behind activity-based financing.
Hospitals are complex organizations performing such multiple tasks as treatment of patients,
education and research. A tractable formal model of hospital behavior may easily miss points
of importance for actual decision-making and results. On the other hand, less formal
reasoning may lead to logical inconsistencies between assumptions and conclusions. We shall
comment on this further in the concluding remarks.
As already noted, in the Norwegian hospital sector there are three levels of decision-makers:
the state, the county council and the hospital management. The county council, as hospital
owner, receives revenue from the state as insurer. The county council is free to decide the
type of financing system for its own hospitals. When ABF is introduced, a fraction of the
block grant from the state to the county councils is replaced by a matching grant depending on
the number and type of hospital treatments. Accordingly, for a county council the cost of

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hospital treatment is reduced relative to other activities under the county council’s
responsibility. Due to the familiar substitution effect, this change in relative cost encourages
the county council to increase hospital budgets relative to other budgets under its control. The
effect of this budget increase on hospital efficiency is likely to depend on whether a fixed
budget or ABF is in operation. On the other hand, hospital efficiency is likely to influence the
county council’s willingness to pay for hospital treatment. Hence, there is an interaction
between the county council’s and the hospital’s decisions. In Appendix 1 this interaction is
modeled as Nash equilibrium with decisions at the state level regarded as exogenous. In this
section we concentrate on the economic mechanism that determines a hospital’s composition
of cost-reducing efforts and number of treatments, leaving the county council’s decisions as
exogenous. This analysis creates the necessary link between the theory and the empirical
analysis that follows in Sections 3 and 4.
We assume that the hospital management has an additively separable utility function5:
U = u(n) - g(e)(1)
where
'''' ''
u (n)>0, u (n)<0, (e)>0, (e)>0,
γγ
' ''
(e)>0, (e)>0
γγ
, and the superscript ' ('')
denotes first (second) order derivative, n is the number of treated patients, and e is the level of
cost-reducing efforts6. Cost reductions often require change in tasks and organization that
involves discomfort and hence, have a negative impact on the utility of managers and
employees. The marginal disutility of cost-reducing efforts is assumed to increase with the
level of effort.
Since hospitals in this paper are non-profit institutions, profit is not an argument in (1). A hard
budget constraint is assumed:
B + wn ≥ c(n,e) + g(2)

4 However, even in a formal system of global budgeting, cost-compensation may occur in practice.
5 Teaching and research are omitted from the model. Costs that are driven by these activities are also excluded
from the empirical model.
6 Since cost-reducing efforts often involve resources (for instance time for meeting and discussion) with an
alternative use in treating patients, the effect of cost-reducing efforts on costs should be interpreted as a net
effect.

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where the left-hand side of the inequality sign is the hospital’s revenue and the right-hand side
is the cost. B is fixed revenue, w is revenue per treated patient, g is a cost component
exogenous to the hospital. This cost component depends upon the age and composition of
hospital buildings, the geographical location of the hospital, etc. The effect of number of
treatments and level of effort on cost is described by the cost function c(n,e). We assume
positive and non-decreasing marginal costs of treating patients; i.e.
'( , ) 0
nc n e >
and
''( , )
nn
cn e ≥ . An increasing marginal cost is likely to exist when some resources are fixed in0
the short run and capacity utilization is high. For instance, when waiting times occur at the x-
ray department and the laboratories, an increase in a patient’s length of stay is likely to occur.
The level of cost-reducing effort may have an impact on costs through many sources. For
instance, a reorganization of personnel on call may release resources now available for
elective treatments. Improved planning and utilization of operating theatres and other
measures may increase the flow of patients. The cost function is assumed to be decreasing in
effort at an increasing rate; i.e.
'( , )0
ec n e < and
''( , )
ee
c n e > .0
If the level of effort only influences fixed costs (for instance costs related to personnel on call,
and regular staffing of operating theatres), the effect of an increase in effort on marginal cost
is obviously zero. If the level of effort also influences variable costs, we assume the marginal
effect of effort on marginal cost to be greater (in absolute value) the higher the level of
capacity utilization is. Hence, we assume the interaction term between number of treatments
and effort to be
''( , )
ne
c n e ≤
0.
Since profit is not an argument in Eq (1), Eq (2) is obviously fulfilled with equality.
Maximizing the objective function Eq (1) constrained by the budget Eq (2) gives from the
first-order conditions of an interior solution of the Lagrangian7:
''
n
'( ) ( , )
( , )
c n e
'( )[ ( , )
e c n e
wn
=
]0
0
e
u n c n ew
gB
γ
−
+−=
+−
(3)

7 That n is considered as decision variable implies that emergency cases that the hospital cannot control, are
ignored. These emergency cases account for a considerable proportion of a general hospital’s patients. Our
argument is still valid, because the main purpose of the reform of the financing system was to encourage an
increase in the number of elective admissions.

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and the second-order condition for a constrained maximum of the objective function is :
'
n
2 '''
n
' ''
ee
'
e
''
ne
''
e
2 ''
'' ''
nn
[ ( , )
c n e
] ( ) [ ( , )
ec n e
+
−
>
] ( )
w u n c
( , )
n e
2 ( , )
c n e c
γ
( , ) ( ) [ ( , )]
n e u n
( )
( ) ( , )
e
e c n e c
( , )
n e
0
D
−
w
c n e u n
γ≡−−
−
(4)
Sufficient conditions for D>0 are:
(i)
'
[ ( , )]0
nc n ew
−≥ ; i.e. the revenue per treated patient is less than the marginal cost.
(ii)
''( , )
ne
c n e = 0; i.e. the effect of e on the marginal cost of treating patients is zero.
(i) is fulfilled since we have assumed
''( , )
nn
cn e ≥ , i.e. 0
'
n
( , )
c n e
n
( , )
c n e
≥
, and we consider a
system with per case payment covering only a proportion of the average cost. According to
our assumptions regarding the cost function, (ii) may not be fulfilled, and then pulls in the
direction of a convex Lagrangian. The second-order condition states that this effect is small
enough to ensure a concave Lagrangian.
Eq (3) determines n and e as functions of w and B:
?
?
( , )
n w Bn
=

?
?
( , )
e w Be
=
where the sign under a functional argument shows the sign of the impact of an increase in the
variable. Due to the interaction effect,
''( , )
ne
cn e , the sign of all effects are in general
indeterminate. With a small absolute value of interaction effect, an increase in B has an
income effect that leads to an increase in the number of treatments (n) and a decline in cost-
reducing efforts (e). Similarly, an increase in the revenue per treatment (w) has an income
effect that pulls in the direction of increased n and reduced e, while the substitution effect
pulls in the direction of an increase in both n and e. Hence, the total effect on n is positive,
while the total effect on e is indeterminate, even if the interaction effect is small.
We model the change from a global budget to a mixed system as an increase in w and a
reduction in B of a magnitude allowing the hospital to choose the same n and e after the
change as chosen before the change. The reduction in the fixed budget is then assumed to be -
no∆w, where no is the optimal number of patients treated under a global budget and ∆w is the
increase in revenue per treatment. By means of differentiating (3) we find:

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'
1[ '( ) ( , )]
e c n e
Dγ
0
o
e
n
w
n
B
n
∂
∂
∂
∂
−= −>
(5)
and
'
n
1[ ( , )
c n e
D
]0
o
e
w
e
B
nw
∂
∂
∂
∂
−=−>
(6)
Hence, the hospital’s optimal n is expected to increase when revenue per treatment replaces a
part of the fixed budget in the financing system. Accordingly, e is also expected to increase.
Hence, we have:
0
|
?
(
h w
, )
B
dB n dw
=
+
e
=
(7)
We are now able to sum up the predictions:
− an increase in the budget is in general predicted to have an indeterminate effect on effort
and hence, on hospital efficiency
− a change from a fixed budget to a combination of fixed budget and revenue per treatment
is predicted to result in an increase in the level of effort and hence, an increase in hospital
efficiency.
These predictions are tested in the Section 4.
3. Measures of efficiency
In order to analyse the effects of ABF on hospital efficiency, we need to establish measures of
efficiency. This again raises two questions: the measurement of hospital production, and the
choice of method when establishing efficiency measures.
Input and output of hospital production
Hospitals are multi-product firms, treating a variety of patients with a variety of inputs. There
is no established consensus as to how one should most accurately measure the outputs of
hospital production. Since the conceptual output, relative change in health, is unobservable,

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we go on by measuring health services, rather than health. We have chosen the following
outputs:8
Inpatient care: Inpatient care is measured as number of discharges adjusted for case-mix by
weighting discharges by diagnosis related groups (DRGs). Day care is included in the
measure of inpatient care.
Outpatient care: Outpatient care is measured as number of outpatient visits weighed by the
fee paid by the state for each visit. Thus a hospital´s revenue from outpatient care is an
approximation of the volume of outpatient care adjusted for case-mix. Outpatient revenue
measured in NOK 1000 (Norwegian Kroner)is deflated to 2000 prices.
Hospital inputs are measured as:
Physician FTEs (full-time equivalents): The physician input is measured as number of FTEs
per year. This is only an approximation of the number of hours actually worked, and may
distort the efficiency measures if use of overtime varies substantially between hospitals and
over time. Evidence suggests that the number of hours worked per FTE is fairly constant over
the period studied here.9
Other labour FTEs: All other types of labour than physician labour are merged in one
category. A more detailed specification of labour input did not alter the results.
Medical expenses: Medical expenses are measured in NOK 1000, and deflated to 2000 prices.
Total running expenses: Total running expenses are used as alternative input in one model,
where the purpose is to provide a measure of cost-efficiency. Running expenses measured in
NOK 1000 are deflated to 2000 prices.

8 A variety of other specifications have been chosen as well. None present a picture that substantially differs
from the one chosen here.
9 A survey among 2100 hospital physicians (Hagen and Nerland 2001) indicates that approximately 78 per cent
of the respondents spend an equal number of working hours on patient related work in 2001 as they did before
the introduction of ABF, 10 percent reported an increase and 12 percent reported a reduction in the number of
patient related work hours. Approximately 35 percent indicated that the number of work hours spent on
administrative work has increased a bit.

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Norwegian hospital cost data are imperfect in the sense that capital costs are not included. If
the use of high-cost medical equipment has increased over this time period, the results given
here are likely to overstate the growth in hospital efficiency. Summary statistics are given in
Table 1.
(Table 1)
Efficiency concepts
The basic efficiency concept used in this paper is that of technical efficiency. A hospital is
said to be technically efficient if an increase in an output requires a decrease in at least one
other output, or an increase in at least one input. Alternatively, a reduction in any input must
require an increase in at least one other input or a decrease in at least one output. This is the
usual Pareto-Koopmans notion of efficiency. The measures used in this paper originated with
Farrell (1957) and were further developed for piecewise linear technologies in Fare and
Lovell (1978), Charnes, Cooper and Rhodes (1978) and Banker, Charnes and Cooper (1984).
The non-parametric mathematical programming approach used in this paper has come to be
known as Data Envelopment Analysis (DEA).
One advantage of DEA is that it accommodates a setting with multiple inputs and multiple
outputs more easily than parametric models. Moreover, this approach does not require a
specific functional form for the technology or specific distributional assumptions about the
efficiency measure. A deterministic approach is susceptible to measurement errors. In this
case we have used data that were collected and checked for errors by the Statistics Norway
and the Norwegian Patient Register. Thus, we believe that we have taken sufficient steps in
securing the quality of the data.
Formally, the efficiency measures are derived by first defining the reference technology
relative to which efficiency is measured. Let y=(y1,.....,ym) ∈ℜ+m denote a vector of outputs
and x=(x1,.....,xn) ∈ℜ+n denote a vector of inputs. Assuming constant returns to scale we can
obtain a measure of input-saving technical efficiency (for unit 0), TECRS, by solving the
following LP problem:

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Here k is the number of hospitals, Y is the k*m matrix of observed outputs, X is the k*n matrix
of observed inputs, and λ is the intensity vector.
The efficiency frontier is based on a pooled set of observations, i.e. we calculate an
intertemporal efficiency frontier (Harris et al., 2000, Tulkens & Vanden Eeckauout, 1993).
This is done in order to be able to compare efficiency between years.
We also provide a measure of “cost-efficiency” by measuring inputs in costs. The measure of
cost-efficiency will be equal to Farrell’s (1957) measure of total efficiency, i.e. the product of
technical and allocative efficiency. When we measure the development in cost efficiency we
note, however, that this may change due to a wage and price increase that deviates from the
price deflator, and not necessarily due to suboptimal combinations of inputs.
Results
Average levels of efficiency are presented in Table 2. Best practice implies a level of 100;
thus an average technical efficiency of around 82 in 2000 implies that hospitals on average are
18% below best practice.
(Table 2)
Technical efficiency increases over this period. Thus hospitals seem to improve their
utilization of resources, and in particular to increase patient throughput. There is a large
positive shift in efficiency the first year after the reform of the funding system. We return in
Section 4 to the question of whether this can be attributed to the reform.
,
0
0
:
0,1,....,
TECRS
crs
MIN
subject to
Y
X
λ
λ≥
TE
y
TE x
i
=
k
λ
ι
λ≥
≤

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The trend in cost-efficiency is roughly equal to the trend in technical efficiency until 1996
when we observe a substantial decline in cost-efficiency. This is believed to be due to a
particularly large increase in physician wages at that time. We also note that there is a decline
in cost-efficiency between 1998 and 1999, while technical efficiency is constant. This is
believed to be related to an expensive increase in activity between these two years.
4. Empirical specifications and results
As pointed out in the introduction, 15 of the country's 19 county governments introduced
activity-based financing (ABF) of their hospitals at the same time as the central government
introduced the matching grant (1 July 1997). Another two county governments introduced
activity-based financing from 1 January 1998, another one from 1 January 1999 and the last
from 1 January 2000. The main question to be answered is whether the introduction of ABF
of hospitals has affected hospital efficiency as stated in Eq. (7).
Operationalization of the models
Based on the theoretical arguments in Section 3, we assume that hospital efficiency (E),
measured as technical efficiency (TE) and cost-efficiency (CE), is affected by the six
variables defined in Table 3.
(Table 3)
BUD is standardized per hospital bed to correct for differences in hospital size. As discussed
in Section 3, outpatient revenues are included in the output vector in the efficiency analysis
(DEA) to account for numbers of outpatients. We are forced to do this since data on the
number of outpatients are lackin for many of the large hospitals in the period we are
analyzing. However, outpatient revenues have both a price and a volume component. Since
fees for outpatient services have increased in the period, we may overestimate the change in
efficiency. To take account of this, we include a variable measuring outpatient revenues as a
share of total hospital revenues (OUT). Furthermore, we include a variable representing the
share of patient-days with irregularly long lengths of stay (LONG) to capture possible effects