International Symposium on Health Care
Systems in Asia
January 22, 2005
Hitotsubashi Memorial Hall, Hitotsubashi University
Tokyo, Japan
Measuring Hospital Efficiency:
DEA and Stochastic Frontier
Approaches
Pongsa Pornchaiwiseskul
Centre for Health Economics, Faculty of Economics
Chulalongkorn University
Content
• Paper’s research questions and
objectives
• Research Methodology
– Conceptual Framework
– Models
• Brief Results
• Conclusion of Research Study
Health Insurance Categories
All the existing forms of governmentadministered general health insurance can be
categorized as follows:
• Government Employee Benefit (CSMBS)
• National Social Security System by SSA
• Social Welfare
• Voluntary Health Card (non-existent after
2003)
• National Health Security
Government Employee Benefit
• full coverage to compensate low salary pay
• zero employee contribution
• also cover immediate family (parent, spouse
and children)
• full reimbursement
• benefit has been cut recently but it is still
considered a privilege
• alarmingly rising cost
Social Security System (SSS)
• employee/employer/government contribution
• limited coverage
• start in 1990 for employers with at least 20
employees. Now extended to self-employed
or small employers
• administered by government agency
• service provider payment by capitation basis
• cost containment pressure on provider
• possible reimbursement for catastrophic
illness
Social Welfare Card
• First covered only the poor.
• Benefit was not automatic. Poor must be
identified on case-by-case basis.
• Low-income Card system introduced. The
poor must apply for the benefit before they get
ill
• limited benefit
• Now cover the elderly and school children
Voluntary Health Card
• start in 1984 known as Family Health Card
• for those with no other forms of insurance
• Only 500 Baht will entitle the cardholder and
family for limited health care services at
government-owned health centers/hospitals
• providers will receive fixed capitation fee
supplement from government budget.
• cost containment and abuse problems
National Health Security (1)
• meant to replace Family Health Card but to
provide same coverage as SSS
• start in 2002 known as 30-baht scheme. Now
called “Gold” Card.
• No cost for the Card. But user cost is 30
Baht/episode which is below average cost.
• Providers are supplemented by fixed
capitation fee from government budget.
• Make the services affordable to many poor
National Health Security (2)
• cost containment pressure on providers
• financial risks on providers/staff. Unpaid or
uncertain capitation payment by government
• alarming high turnover of staff. Doctors
moved from public sector to private sector
• few privately-owned providers participated
due to low capitation payment.
• More complaints about quality of health care
services
Health Insurance Coverage
Year->
1999
2002
Gov Employee
8.90%
5.02%
SSS
7.10%
8.83%
Social wefare
32.10%
35.27%
VHI
18.60%
0.01%
Gold Card
0.00%
29.63%
Uninsured
33.30%
21.23%
Research Questions
• Did the recent health care reforms really
improve efficiency of health care system?
Many tertiary care hospitals have complained
about high cost of servicing SSS and Gold
card patients while patients also complained
about the declining service quality.
• Is inefficiency related to capitation payment?
Quality complaints seem to inversely vary
with the capitation payment.
Research Objectives
Main Objective
• To determine the effects of customer/patient
types on the efficiency or inefficiency of
provincial hospitals.
Specific Objectives
• To estimate the production function for fully
efficient provincial hospitals
• To estimate output indices for multiple service
outputs of hospitals
Scope of Study
• Aggregate Provincial hospital service
level
• 72 cross-sectional data by province in
2002. Bangkok Metropolitan Area
excluded.
Assumptions (1)
• Constant return-to-scale CobbDouglas production. Hospitals in the
province can be aggregated to a
representative hospital
• medical doctors and patient beds are
two inputs to be considered. Other
inputs are assumed to be complement
of these two inputs
Assumptions (2)
• The following are considered multiple
outputs:
– birth cases
– inpatient-days
– outpatient visits by 21 causes of illness
• Hospital inefficiency could be due to
patient types.
• Allocative efficiency is assumed.
Inefficiency is purely technical.
Conceptual Framework (1)
• Determination of Output Envelope
Multiple hospital outputs are to be
aggregated as a single output index.
Inpatient-days will be treated as output
numeraire. That is, all the other outputs
will be converted to numeraire
equivalence.
Conceptual Framework (2)
Y2
Production Possibility Frontier
(given input X)
C
B
Y1 Equivalence of
output bundle A
A
D
Y1 (Numeraire)
Conceptual Framework (3)
• Data Envelopment Analysis (DEA)
model is used to analyze the crosssectional data to estimate the aggregate
hospital production output for each of the
72 provinces.
• The difference between the ideal
production output and the aggregate
provincial output is due to pure
uncertainty and technical inefficiency of
the hospitals
Conceptual Framework (4)
B
A’
Y
Uncertainty
component
Inefficiency
component
B’
A
Mean Production
Function of Fully
Efficient Hospital
X
Conceptual Framework (5)
• Aggregate output of 72 provinces will be
used to estimate the frontier production
or the production of the fully efficient
hospitals.
• Stochastic Production Frontier Model
will be used to estimate the production
function of the CRS fully efficient
hospitals
• Technical inefficiency is due to patient
types.
Model (1)
DEA Model (Aigner, Lovell and
Schmidt, 1977) for CRS hospital i with
multiple outputs and inputs is the
following LP problem:
μYi
max
μ, 1 , 2
s.t.
 1MDi  2 BEDi  1
μY j  1MD j  2 BED j  0, j  1,2,...,72
μ, 1 , 2  0
Model (2)
μ  1
2
 Y1i 
Y 
 2i 
Yi   Y3,1i 


  
Y3, 21i 


3,1  3, 21 
Model (3)
where
MDi = log of number of medical
doctors employed by province i
BEDi = log of number of inpatient beds
employed by province i
Y1i = log of inpatient-days in
province i
Y2i = log of number of birth cases in
province i
Model (4)
Y3mi = log of number of OPD visits
by cause of illness m in
province i,m=1,..,21
Aggregate Output measured in terms of Y1
Yi  (μYi ) / 1
Model (5)
Stochastic Frontier Model (Coelli, 1996)
for CRS Cobb-Douglas production
function of hospital i
Yi   0  1MDi  (1  1 ) BEDi   i  ui
where
 i  iid N(0,   ) for all i  1,...,72
2
u i  iid tr N(Zi ,  ) for all i  1,...,72
2
u
Z i   0  1GCi   2WCi   3 SS i   4GVi
Model (5)
i = pure uncertainty component
ui = non-negative inefficiency
GCi = log of number of Gold Cardholders
in Province i
WCi = log of number of Welfare
Cardholders in Province i
SSi = log of number of SS insured
in Province i
GVi = log of number of privileged
government employees in Province i
Empirical Results (1)
Aggregate output for selected provinces
according DEA
Province
Y1
Y1
Chiangmai 14.218 17.217
Suratthani 13.729 16.820
Khonkaen 13.914 17.119
Saraburi
13.170 15.224
Empirical Results (2)
ML estimates for SF Model
coeff
 0  2.10
1 1.00
 0 .725
1 .086
 2 .210
 3 .006
 4  .401
SE
t - stat
.066
 31.7
.0012
829
.522
1.39
.098
.880
.076
2.75
.065
.092
.114
 3.52
Key Conclusions
1) Gold card policy and Social Security
schemes do not seem to significantly hurt
hospital efficiency
2) Welfare cardholders and privilege
government employees cause opposite
pressure on the hospital efficiency. Even
though hospital expenditure on welfare
cardholders will be reimbursed, it is not
very welcome.
Key References
Aigner, D.J., C.A.K. Lovell and P. Schmidt
(1977), “Formulation and Estimation
Stochastic Frontier Production Function
Models”, Journal of Econometrics, 6, 2137
Coelli, T.J. (1996), “A Guide to
FRONTIER Version 4.1: A Computer
Program for Frontier Production Function
Eestimation”, CEPA Working Paper
96/07, Department of Econometrics,
University of New England, Armidale