Economies of scale and scope in Vietnamese hospitals

Social Science & Medicine 59 (2004) 199–208

ARTICLE IN PRESS

*Correspond

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doi:10.1016/j.so

Economies of scale and scope in Vietnamese hospitals

Marcia Weavera,*, Anil Deolalikarb

aDepartment of Health Services, University of Washington, 901 Boren Avenue, Suite 1100, Seattle, WA 98104, USAbDepartment of Economics, Sproul Hall, University of California, Riverside, CA 92521, USA

Abstract

Hospitals consume a large share of health resources in developing countries, but little is known about the efficiency of

their scale and scope. The Ministry of Health of Vietnam and World Bank collected data in 1996 from the largest

sample ever surveyed in a developing country. The sample included 654 out of 815 public hospitals, six categories of

hospitals and a broad range of sizes.

These data were used to estimate total variable cost as a function of multiple products, such as admissions and

outpatient visits. We report results for two specifications: (1) estimates with a single variable for beds and (2) estimates

with interaction terms for beds and the category of hospital. The coefficient estimates were used to calculate marginal

costs, short-run returns to the variable factor, economies of scale, and economies of scope for each category of hospital.

There were important differences across categories of hospitals. The measure of economies of scale was 1.09 for

central general and 1.05 for central specialty hospitals with a mean of 516 and 226 beds, respectively, indicating roughly

constant returns to scale. The measure was well below one for both provincial general and specialty hospitals with a

mean of 357 and 192 beds, respectively, indicating large diseconomies of scale. The measure was 1.16 for district

hospitals and 0.89 other ministry hospitals indicating modest economies and diseconomies of scale, respectively. There

were large economies of scope for central and provincial general hospitals.

We conclude that in a system of public hospitals in a developing country that followed an administrative structure,

the variable cost function differed significantly across categories of hospitals. Economies of scale and scope depended

on the category of the hospital in addition to the number of beds and volume of output.

r 2003 Elsevier Ltd. All rights reserved.

Keywords: Economies of scale; Economies of scope; Hospital cost functions; Vietnam

Introduction

Hospitals consume the largest share of health

resources in most countries. Barnum and Kutzin

(1993) reported that hospitals received 50 percent or

more of government health resources in 19 out of 29

developing countries for which data were available, and

hospitals received on average 54 percent of government

health resources in OECD countries. Hospitals received

54.3 percent of government health funds in Vietnam in

1996 (Le Duc Chinh, undated).

ing author. Tel.: +1-206-616-9173; fax: +1-

ess: [email protected] (M. Weaver).

e front matter r 2003 Elsevier Ltd. All rights reserve

cscimed.2003.10.014

Many public health experts believe that some of those

resources would be better spent on preventive and

primary care (World Bank, 1993). Even within the

hospitals’ share, questions are raised about the efficiency

of their scale and scope. The question about scale is

whether larger hospitals are more or less efficient than

smaller ones. On the one hand, hospitals require large

investments in capital such as buildings, equipment and

specialized staff, which may make it more efficient to

have one large hospital rather than two small ones. On

the other hand, hospitals are complex organizations to

manage, and at some point a smaller hospital may run

more smoothly than a larger one.

The question about scope is whether or not it is

efficient to combine outpatient and inpatient care at the

d.

ARTICLE IN PRESSM. Weaver, A. Deolalikar / Social Science & Medicine 59 (2004) 199–208200

same facility. Physicians often need to see patients on

both an inpatient and an outpatient basis; an outpatient

who receives diagnostic exams may later be admitted or

an inpatient that is discharged may need follow-up

visits. In some cases, it may be more efficient for

physicians to provide both types of care from a single

office at the hospital. In other cases, it may be more

efficient to reduce the daily flow of a large volume of

outpatients at the hospital by having separate facilities.

These questions may be answered with estimates of a

hospital cost function that shows the relationship

between cost and output. Although researchers have

estimated cost functions for hospitals in developing

countries (Anderson, 1980; Barnum & Kutzin, 1993;

Bitran-Dicowsky & Dunlop, 1993) and for non-hospital

health facilities in Nigeria (Wouters, 1993), their

research was limited by samples of a relatively small

number of facilities. The sample sizes ranged from eight

to 51 facilities. Even in pooled cross-section and time-

series samples, the largest sample size was 72 observa-

tions (Barnum & Kutzin, 1993). Barnum and Kutzin

(1993) recommended further research to examine

differences in hospital cost functions by hospital level

with a large sample of hospitals.

The Ministry of Health of Vietnam and the World

Bank conducted a survey of hospitals to collect

information on hospital activity, revenue and costs.

The survey provided 1996 data on one of the largest

samples of hospitals ever collected in a developing

country, with information on 654 out of 815 public

hospitals in Vietnam. The sample included six categories

of hospitals: four levels of hospitals (central, provincial,

district and other ministry) and two classes of hospitals

(general and specialty) at the central and provincial

level, as well as a broad range of sizes of hospitals as

measured by number of beds, admissions and out-

patients.

After a brief background section on hospital reforms

in Vietnam, we report estimates of the hospital variable

cost function using the data from the survey of hospitals

in Vietnam. These estimates were used to calculate

marginal costs, short-run returns to the variable factor

(SRVF), economies of scale, and economies of scope for

the six categories of hospitals.

Hospital reforms in Vietnam

The survey of hospitals occurred during a period of

rapid transformation of the health sector in Vietnam.

Historically, health care in Vietnam was provided

exclusively by public facilities funded by the government

or commune health centers funded by work brigades.

Hospitals were allocated by administrative units, with

central level hospitals in major cities, provincial

hospitals in provincial capitals, and district hospitals in

district capitals. The government specified the services

that would typically be offered at each level.

Three health sector reforms in Vietnam in the late

1980s and early 1990s affected hospitals: (1) the

introduction of user fees in hospitals, (2) the introduc-

tion of social insurance in 1993, and (3) a 1993

ordinance that legalized private medical practice and

pharmacies (World Bank, 2001). By 1996, revenue from

user fees and social insurance accounted for 35 percent

of hospital income, with the shares ranging from 39

percent of income at central general hospitals to 25 and

27 percent at central specialty and district hospitals,

respectively (World Bank, 2001; Weaver & Rubanowice,

1999). At the same time, real growth rates in government

spending on hospitals were low or negative. By 1996,

patient revenue was almost as large as a percentage of

income as government spending for central and provin-

cial general hospitals.

The growth in patient revenue affected hospital

expenditures on staff and drugs (World Bank, 2001;

Weaver & Rubanowice, 1999). Hospitals were allowed

to spend up to 35 percent of patient revenue on staff

bonuses and had discretion over how to allocate them.

By 1996, staff bonuses accounted for 30 percent of

personnel expenditures at hospitals, with shares ranging

from 47 percent at central general and provincial

specialty hospitals to 12 percent at district hospitals.

At the same time, the real growth rates of salaries were

negative. By 1996, bonuses were a larger percentage of

personnel expenditures than salaries at provincial

specialty hospitals. Expenditures on drugs also increased

and in 1996 accounted for 34 percent of expenditures at

hospitals. By 1996, expenditures on drugs exceeded

expenditures on personnel at central and provincial

hospitals.

The legalization of private medical practice did not

increase the number of private hospitals. In 1996, there

were only four private hospitals in Vietnam and this was

still true as recently as 2001 (World Bank, 2001). It did

increase the number of health personnel with licenses to

work in private practice. In 1996, 26,000 health workers

or about one-tenth of the health work force had licenses

for private practice. Almost half of them were public

employees who worked in the private sector during

evenings and weekends (World Bank, 2001).

Methods

Model

The hospital cost function estimates were based on a

multiple-product model, in which total costs were a

function of input prices and the level of output of

multiple products, such as inpatient days and outpatient

visits (Grannemann, Brown, & Pauly, 1986). Two

ARTICLE IN PRESSM. Weaver, A. Deolalikar / Social Science & Medicine 59 (2004) 199–208 201

features of the multiple-product model were: (1)

coefficients were estimated for each product, as opposed

to having to create a single index of products (e.g.

converting four outpatient visits into one inpatient day),

and (2) the model included interaction terms for

products to measure the economies of scope.

We used an extension of that model in which total

variable costs were a function of the number of hospital

beds as a proxy measure of the capital stock, as well as

input prices and multiple outputs (Vita, 1990). The

model was based on the assumption that hospitals could

use variable inputs like personnel and medical supplies

at cost-minimizing levels, but could not adjust the

number of beds in the short-run. Aletras (1999)

explained that the coefficient for the beds variable offers

a test of that assumption; a coefficient that was positive

and significant implied that the hospitals were not at

their long run equilibrium. Aletras (1999) tested the

assumption using data on public hospitals in Greece,

and concluded that the total variable cost model was

preferable to the total cost model.

The equation for the total variable cost function was

C ¼ ea0þa1bedsef ðY ;X Þ; ð1Þ

where Y is a vector of hospital products, such as

admissions, outpatient visits, and diagnostic exams. X is

a vector of independent variables that shift the cost

function, such as the region in which the hospital was

located and the category of the hospital. Input prices

were not included for reasons that are explained in the

variables subsection below.

The equation was estimated by taking the natural log

of both sides. It had a flexible functional form with

linear, squared and cubed values for admissions and

outpatients and an interaction term between admissions

and outpatient visits:

ln C ¼ a0 þ a1bedsþ b11Y1 þ b21Y 21 þ b31Y 3

1 þ b12Y2

þ b22Y 22 þ b32Y 3

2 þ b1�2Y1Y2

þXn

k¼3

bkYk þXm

l¼1

clXl ; ð2Þ

where Y1 is the number of admissions and Y2 is the

number of outpatient visits.

The coefficient estimates of Eq. (2) were used to

calculate marginal costs and measures of economies of

scale and scope. The marginal cost of admissions or

outpatient visits (or any product with linear, squared,

cubed and interaction variables) was

MCi ¼ Cðb1i þ 2b2iYi þ 3b3iY2i þ b1�2YjÞ; ð3Þ

where j is the outpatient visits if i is the admissions and

vice versa. The marginal cost of operations and

diagnostic exams (or any product with a linear variable

and no interaction) was

MCk ¼ Cbk: ð4Þ

Following Vita (1990) and Barnum and Kutzin

(1993), we derived measures of economies of scale and

scope. Eqs. (5a)-(7a) below are from Barnum and

Kutzin (1993). We substituted the term for total variable

cost from Eq. (2) and for marginal costs from Eqs. (3)

and (4) above into those equations. Then, we used

algebra to simplify the equations and obtain the

measures presented in Eqs. (5b)-(7b).

There were short-run and long-run measures of the

relationship between cost and scale. In the short run, the

number of beds was unchanged, and any gains in

efficiency from increasing output accrued to the variable

factors. These gains were called SRVF and measure how

cost changes as output increases when output mix and

the number of hospital beds were unchanged. The

equation for SRVF in Barnum and Kutzin (1993) was

SRVF ¼CPm

i¼1 MCi Yi

� �: ð5aÞ

With our functional form, the measure of SRVF was

SRVF

¼1

P2i¼1 Yiðb1i þ 2b2iYi þ 3b3iY

2i þ b1�2YjÞ þ

PmK¼3 Ykbk

h i:

ð5bÞ

If SRVF was greater than one, the level of output was

less than the most efficient level. If it was less than one,

the level of output was greater than the most efficient

level.

In the long run, the number of beds can change as well

as other factors to improve efficiency. Gains in efficiency

were called economies of scale (EOS) and the equation

for it in Barnum and Kutzin (1993) was

EOS ¼ð1� sC;bedsÞPm

i¼1 sC;Yi

� �;

ð6aÞ

where sa;b is the elasticity of a with respect to b: For thetotal variable cost function, sC;Yi

is the product of the

marginal cost of Yi and the ratio Yi=C: With our

functional form the measure of EOS was

EOS

¼ð1� a1bedsÞP2

i¼1 Yiðb1i þ 2b2iYi þ 3b3iY2i þ b1�2YjÞ þ

PmK¼3 Ykbk

h i;

ð6bÞ

and interpreted the same way as SRVF.

Economies of scope measured the relationship be-

tween cost and product mix. In the hospital cost

function, it measured whether it was less expensive to

provide both inpatient and outpatient care at the


hospital than to have a separate facility for outpatients.

The equation for economies of scope in Barnum and

Kutzin (1993) was

Scopes ¼½CðYsÞ þ CðYn�sÞ � CðY Þ�

CðY Þ: ð7aÞ

With our functional form, the measure of economies

of scope was

Scope2 ¼�2b1�2Y1Y2P2

i¼1 Yiðb1i þ 2b2iYi þ 3b3iY2i þ b1�2YjÞ

: ð7bÞ

If scope was greater than zero, it was more efficient to

jointly provide inpatient and outpatient care. If it was

less than zero, it was more efficient to provide them

separately. As shown, the sign of this measure was

determined by the coefficient b1�2; a negative coefficient

indicated economies of scope and a positive coefficient

indicated diseconomies.

Variables

The dependent variable, total variable cost, was total

expenditures on staff, drugs and medical supplies,

maintenance and repairs, and other expenses. The three

types of staff expenditures were salaries, allowances, and

bonuses. All of the numbers included both permanent

and contracted staff. Other expenses included sanitation,

utilities, gasoline, medical records, continuing education

and business travel. Other expenses may have included

some investment to the extent that continuing education

was an investment in human capital. Equipment

purchases were not included.

Table 1

Descriptive statistics by category of hospital

Total Central

general

Cent

spec

Sample means

Cost in VND (millions) 2540 19,900 5560

Cost in $USa 230,657 1,807,120 504,

Beds (hundreds) 1.39 5.61 2.26

Average length of stay 11.86 15.00 50.5

Occupancy rate% 94% 102% 100%

Admissions (thousands) 6.48 16.04 4.34

Outpatients (thousands) 44.00 119.34 29.2

Admissions�outpatients 556.07 2403.87 196.

Operations (thousands) 1.27 3.98 2.78

X-rays (thousands) 8.63 103.02 11.6

Lab tests (thousands) 64.38 566.13 81.6

Sample total

Admissions (thousands) 3868 160 78

Admissions as percentage of total

sample

4% 2%

Sample size 597 10 18

aThe exchange rate on July 1, 1996 was 11,012 Vietnamese Dong

As mentioned in the Model subsection, a variable for

beds was included as a measure of the capital stock.

Beds were measured in units of 100. We report results

for two specifications: (1) estimates with a single variable

for beds and (2) estimates with interaction terms for

beds and the category of hospital that allowed the

coefficient for the beds variable to vary across categories

of hospitals.

We explored two measures of inpatient care: admis-

sions and inpatient days. We selected the admissions

variable, because it was more appropriate for hospitals

with high occupancy rates. As shown in the sample

statistics in Table 1, the average occupancy rate was 94

percent and ranged from 106 percent at other ministry

hospitals to 90 percent at district hospitals. Under these

conditions, more admissions may reflect greater effi-

ciency, whereas inpatient days may be more or less

determined by the number of beds. In fact, the Pearson

correlation between beds and inpatient days was 0.98

compared to a correlation between beds and admissions

of 0.82.

Both measures of inpatient care were potentially

collinear with the beds variable, but the estimates with

the admissions variable performed better. The condition

index was 53.94 for estimates with admissions in Table 4

and 73.07 for estimates with inpatient days. The pattern

of results across categories of hospitals however, did not

differ substantially between the estimates with admis-

sions and those with inpatient days.

To account for differences in case mix across

hospitals, we included the index of case complexity

developed by Roemer, Moustafa, and Hopkins (1968).

ral

ialty

Provincial

general

Provincial

specialty

District Other

ministry

6820 4040 916 1410

904 619,324 366,873 83,182 128,042

3.57 1.92 0.76 0.84

9.06 35.9 6.17 8.96

102% 96% 90% 106%

17.52 6.71 4.36 3.58

3 96.15 49.22 34.71 7.05

79 2053.12 1066.28 178.24 24.63

4.47 2.16 0.38 0.62

3 27.58 13.24 1.90 3.04

8 198.98 99.00 20.83 24.43

1331 496 1678 121

34% 13% 43% 3%

76 74 385 34

(VND) per US dollar ($US) (Jei Corporation, 2002).


The index was

indexi ¼ ALOSiðOCCi=OCCsÞ; ð8Þ

where ALOSi was the average length of stay in hospital

i; OCCi was the occupancy rate of hospital i and OCCs

was the mean occupancy rate for the sample hospitals.

The index used ALOS as a measure of case complexity

and adjusted for exogenous supply and demand

influences that also affected length of stay with the

ratio of OCCi=OCCs:We explored estimates that distinguished admissions

to general beds from admissions to intensive and critical

care unit beds. None of the coefficients for intensive and

critical care unit admissions were significant, so the

results for total admissions were reported below.

Other output variables were outpatient visits, opera-

tions, lab tests, and X-rays. In estimates with higher

level terms for outpatient visits, the coefficients of the

outpatient-squared and outpatients-cubed variables

were not significant and a likelihood ratio test

(LR ¼ 1:32; p-value ¼ 0:52) rejected the specification

with those variables. Estimates with only the outpatient

visits variable were reported below. All of the output

variables were measured in units of 1000.

Finally, the vector of independent variables that

shifted the cost function included variables for each

category of hospital with the exception of provincial

general hospitals and for each region of the country with

the exception of the northern mountains.

The model did not include the prices of inputs, as

originally suggested by Grannemann et al. (1986). Input

price data were rarely available for estimates of hospital

cost functions. For public hospitals in Vietnam, salaries

were established by the government. To the extent that

government salaries were the same across hospitals, the

omission of input prices from the estimates did not bias

the other results. Staff bonuses however, varied across

hospitals. As explained in the section on Hospital

Reforms in Vietnam, hospitals were allowed to spend

up to 35 percent of patient revenue on staff bonuses and

had discretion over how to allocate them. We explored

whether or not staff bonuses could serve as a measure of

input prices in estimates that included the natural log of

the percentage of staff expenditures from bonuses. The

coefficient for that variable was not significant. The

results are not reported below, because the variable

for staff bonuses had a large number of missing values

that reduced the sample size or would have required

recoding.

Similarly, Grannemann et al. (1986) included sources

of revenue as independent variables that shifted the cost

function. It was possible that Vietnam’s new social

insurance program affected hospital costs. We explored

that possibility in estimates that included the percentage

of revenue from social insurance. The coefficient for that

variable was not significant. Those results were not

reported below, because this variable also had a large

number of missing values.

Sample

The analysis was conducted with 597 hospitals. The

original data set included 664 observations in at least

one of 14 files. After deleting four observations because

of duplicate identification numbers and six observations

that only appeared in one out of 14 files, there were 654

observations. Nineteen observations were excluded from

the analysis after examining inconsistencies across

variables. For example, eight hospitals had occupancy

rates greater than 200 percent. We did not have access to

the raw data, so in many cases it was not possible to

correct the data when an inconsistency was identified.

Thirty-eight observations were excluded, because data

were missing for one or more of the following variables:

cost (23 cases), admissions (16 cases), beds (12 cases),

inpatient days (10 cases) and region (two cases).

Recoding

Data were missing on outpatient visits for 78

hospitals, X-rays for 94 hospitals, operations for 88

hospitals, and lab tests for eight hospitals. These missing

values were recoded to zero based on two consistency

checks. First, the missing values were more likely to

occur at district hospitals where the services were less

likely to be available. Fifty-four out of 78 hospitals that

were missing data on outpatient visits were district

hospitals. Seventy out of 94 hospitals that were missing

data on X-rays were district hospitals. Second, the

frequency of a zero response for these variables was low,

suggesting that a zero was not entered as part of the skip

pattern of the data entry program. For example, there

were only four hospitals that reported zero outpatient

visits and three hospitals that reported zero X-ray

exams.

Estimation

The total variable cost Eq. (2) was estimated with

ordinary least squares using Stata, version 7. We

examined the estimates for multicollinearity and found

that it was not a problem.

The estimates were tested for heteroscedasticity using

the Cook and Weisberg test, also known as the Breusch–

Pagan test (Judge, Griffiths, Hill, & Lee, 1980), because

the residuals in cost function estimates may be

correlated with the independent variables. Heterosce-

dasticity does not affect the coefficient estimates, but can

cause incorrect inferences about their significance. All of

the tests showed heteroscedasticity. Consequently, ro-

bust standard errors were calculated using the Huber–


White method, and all inferences were based on these

standard errors.

The marginal costs in Eqs. (3) and (4) were calcu-

lated with the predicted value of cost. The predictions

were based on the smearing factor for a heterosce-

dastic normal distribution of the residuals (Manning,

1998). Statistics on kurtosis and skewness of the

residuals indicated that the normal distribution was

appropriate. Estimates with a logged dependent variable

require a special procedure for retransforming the

predicted value of the logged dependent variable back

into the original form; for example, transforming log

dollars into dollars. The predicted value must include a

smearing factor that transforms the geometric mean of

the logged dependent variable to the arithmetic mean of

the original variable. When the estimates are hetero-

scedastic, the smearing factor is different for each

observation and the predicted values of cost is calculated

with the mean of the predicted value rather than a

prediction based on sample means. The predicted value

of cost is

EðCÞ ¼ ea0þa1bedsef ðY ;X Þesmear=2; ð9Þ

where smear is the predicted value of the residuals-

squared when regressed on the independent variables in

the cost function.

Table 2

Variable cost function estimates with the coefficient for bed constrain

Variable Coefficient

Constant 19.76395

Central general 0.5584834

Central specialty 0.8276736

Provincial specialty 0.1850416

District �0.4532605

Other ministry �0.0034338

Beds (hundreds) 0.2161765

Admissions (thousands) 0.2022869

Admissions-squared �0.0074842

Admissions-cubed 0.0000814

Outpatients (thousands) 0.0022916

Admissions�outpatients �0.000095

Operations (thousands) 0.0151028

X-rays (thousands) 0.0006581

Lab tests (thousands) 0.0003646

Index of case complexity 0.0018437

Red river delta 0.2380451

North coast 0.3949181

Central coast 0.0422343

Central highland 0.1763819

South east 0.3149447

Mekong river delta 0.1001492

Sample size=597, adjusted R2=0.82, MSE=0.467, condition index=

Results

Descriptive statistics

The descriptive statistics in Table 1 show large

differences in the mean cost and number of beds across

categories. The mean cost ranged from $US 1.8 million

for central general hospitals to $US 0.5 million for

provincial general hospitals and $US 83,182 for district

hospitals. The mean number of beds ranged from 561 in

central general hospitals to 357 in provincial general

hospitals and 76 in district hospitals.

Despite the large size of the central general hospitals,

the majority of patients were treated at provincial

general and district hospitals. There were only 10 central

general and 18 central specialty hospitals compared to

76 provincial general, 74 provincial specialty and 385

district hospitals. Consequently, only 4 percent of

admissions were at central general and two percent at

central specialty hospitals, compared to 34 percent at

provincial general, 13 percent at provincial specialty and

43 percent at district hospitals.

The descriptive statistics also show clear differences in

the number of admissions and ALOS between specialty

and general hospitals. ALOS was 50 days at central

specialty and 36 days at provincial specialty hospitals

compared to 15 and 9 days at the central and provincial

general hospitals, respectively.

ed to be the same across categories of hospitals

Huber–White

standard error

T-statistic P-value

0.1165549 169.57 0.000

0.2465504 2.27 0.024

0.1474411 5.61 0.000

0.096631 1.91 0.056

0.0922304 �4.91 0.000

0.1264252 �0.03 0.978

0.0436749 4.95 0.000

0.0155873 12.98 0.000

0.0007868 �9.51 0.000

0.0000121 6.73 0.000

0.0004742 4.83 0.000

0.0000309 �3.07 0.002

0.0079839 1.89 0.059

0.0016786 0.39 0.659

0.004577 0.80 0.426

0.0018851 0.98 0.328

0.0732274 3.25 0.001

0.0636638 6.20 0.000

0.0629158 0.67 0.502

0.0744149 2.37 0.018

0.0882341 3.57 0.000

0.06135 1.63 0.103

38.84.


Cost function estimates

Results for the first specification are reported in Table

2. The estimate has a single variable for beds and

dummy variables for each category of hospitals.

Provincial general hospitals were the omitted category

and serve as the reference group. As shown, the

coefficient for beds was large and significant indicating

that the hospitals were not at their long-run equilibrium.

The coefficients for the linear, squared and cubed terms

for admissions were of the expected sign and significant.

The coefficient for outpatient visits was positive and

significant. The coefficient for the interaction of admis-

sions and outpatient visits was negative and significant,

indicating of economies of scope. The coefficients for the

category of hospital showed significantly higher cost at

the central hospitals and significantly lower cost at the

district hospitals. There were significant differences

across regions, indicating higher cost in some of the

more populated regions like the Red River where Ha

Noi is located and the South East where Ho Chi Minh

City is located. Finally, the index of case complexity was

positive, but not significant in the estimates with robust

standard errors.

Marginal costs, SRVF, economies of scale and

economies of scope are reported in Table 3. As shown,

results for the total sample of hospitals obscure

important differences across categories of hospitals.

For the total sample the marginal cost per admission

was $US 34, but it ranged from $US 170 for central

general hospitals to $US 12 for district hospitals. For the

total sample the SRVF was 1.07 indicating roughly

constant returns, but the SRVF ranged from 0.87 for

central general hospitals to 1.44 for district hospitals and

1.73 for other ministry hospitals. For the total sample

there were modest economies of scope, but the measure

ranged from 0.77 for provincial general and 0.56 for

central general hospitals to almost zero for other

ministry hospitals.

The measure of economies of scale was problematic,

because it was negative for central general hospitals. The

problem could have been due to misspecification of the

Table 3

Marginal cost, SRVF and economies of scale and scope based on co

Total Central

general

Centr

specia

Marginal cost per admission

($US)

34.04 169.64 82.83

Marginal cost per outpatient visit

($US)

0.46 2.92 1.08

SRVF 1.07 0.87 1.31

Economies of scale 0.65 �0.30 0.60

Economies of scope 0.12 0.56 0.05

variable cost function or to the small number of central

general hospitals. A second specification was estimated

that added interaction terms for beds and the category

of hospital. A likelihood ratio test confirmed that these

unrestricted estimates were a better specification than

those with only a single variable for beds (w2 50.29,

p-value 0.000). A third estimate was performed with

additional interaction terms for admissions and the

category of hospitals to test whether or not the cost

function should be estimated in subsamples for each

category of hospital. A likelihood ratio test rejected the

specification with interaction terms for admissions and

the category of hospital (w2=1.53, p-value=0.91).

Results for the second specification are reported in

Table 4. As shown, the coefficient of the interaction term

for beds and the category of hospital was negative and

significant for central general hospitals. The sum of the

coefficients for beds and the interaction term for

beds� central general hospitals was �0.084, which

may indicate that these hospitals were operating at

close to a long-run equilibrium. The coefficient of the

interaction term was positive and significant for district

hospitals and other ministry hospitals. Other results

were similar to those reported in Table 2.

Marginal cost, SRVF, economies of scale, and

economies of scope for the second specification are

reported in Table 5. As shown, the measure of

economies of scale for central general hospitals was no

longer problematic. The measure was 1.09 for central

general and 1.05 for central specialty hospitals indicat-

ing roughly constant returns to scale. The measure was

well below one for both provincial general and specialty

hospitals indicating large diseconomies of scale. The

measure was 1.16 for district hospitals and 0.89 other

ministry hospitals indicating modest economies and

diseconomies of scale, respectively.

Overall, the pattern of results across categories of

hospitals was the same in both specifications. In both

Tables 3 and 5, the measure of SRVF was less than one

for central general hospitals, but greater than one and

relatively large for central specialty, provincial general,

district and other ministry hospitals. In both Tables 3

st function estimates with a single variable for beds

al

lty

Provincial

general

Provincial

specialty

District Other

ministry

15.74 59.91 11.59 17.81

0.39 0.69 0.15 0.23

1.51 0.89 1.44 1.73

0.21 0.48 1.18 1.38

0.77 0.19 0.05 0.01

ARTICLE IN PRESS

Table 4

Variable cost function estimates with different coefficients for beds and intercepts for each categories of hospital

Variable Coefficient Huber–White

standard error

T-statistic P-value

Constant 19.86426 0.1555143 127.73 0.000

Central general 2.080689 0.2701646 7.70 0.000

Central specialty 1.064031 0.2790802 3.81 0.000

Provincial specialty 0.1679008 0.1699075 0.99 0.323

District �0.5722532 0.1507081 �3.80 0.000

Other ministry �0.3635885 0.1958996 �1.86 0.064

Beds (hundreds) 0.2403785 0.0444017 5.41 0.000

Beds� central general �0.3245729 0.0469689 �6.91 0.000

Beds� central specialty �0.1046962 0.0966887 �1.08 0.270

Beds�provincial specialty �0.0050618 0.0500218 �0.10 0.919

Beds�district 0.214922 0.0887296 2.42 0.016

Beds�other ministry 0.4493576 0.1557589 2.88 0.004

Admissions (thousands) 0.1563481 0.0163716 9.55 0.000

Admissions-squared �0.0054898 0.0008111 �6.77 0.000

Admissions-cubed 0.0000556 0.0000119 4.68 0.000

Outpatients (thousands) 0.0020004 0.0004577 4.37 0.000

Admissions�outpatients �0.0000689 0.0000254 �2.71 0.007

Operations (thousands) 0.0115129 0.0084942 1.36 0.176

X-rays (thousands) 0.0020988 0.0014386 1.46 0.145

Lab tests (thousands) 0.0007165 0.0004229 1.69 0.091

Index of case complexity 0.0014695 0.0018985 0.77 0.439

Red river delta 0.1995971 0.717298 2.78 0.006

North coast 0.364869 0.0601444 6.07 0.000

Central coast 0.0207992 0.0596734 0.35 0.728

Central highland 0.1767505 0.0747761 2.36 0.018

South east 0.2657614 0.0920049 2.89 0.004

Mekong river delta 0.1117064 0.0605943 1.84 0.066

Sample size=597, adjusted R2=0.84, MSE=0.4498, condition index=53.94.

Table 5

Marginal cost, SRVF and economies of scale and scope based on cost function estimates with a coefficient for beds for each category of

hospitals

Central

general

Central

specialty

Provincial

general

Provincial

specialty

District Other

ministry

Marginal cost per admission ($US) 85.32 57.97 14.06 42.18 9.39 16.93

Marginal cost per outpatient visit

($US)

2.10 0.87 0.51 0.59 0.14 0.25

SRVF 0.74 1.52 1.40 1.06 1.77 2.12

Economies of scale 1.09 1.05 0.20 0.58 1.16 0.89

Economies of scope 0.48 0.05 0.61 0.18 0.05 0.01

M. Weaver, A. Deolalikar / Social Science & Medicine 59 (2004) 199–208206

and 5, there were large economies of scope for central

and provincial general hospitals compared to the small

economies of scope for central specialty, district and

other ministry hospitals. One notable difference between

the specifications was that the marginal cost per

admission was lower in Table 5 than in Table 3 for all

categories of hospitals and about half as much ($US 85

vs. $US 170) for central general hospitals.

Discussion

The large sample of public hospitals in Vietnam

allowed us to test for differences across categories of

hospitals in marginal costs, SRVF, economies of scale

and economies of scope. The results demonstrated that

inferences based on the total sample obscured funda-

mental differences across categories. Results differed


across levels of hospitals and between general and

specialty hospitals. The pattern of results across

categories of hospitals persisted in two specifications of

the total variable cost function and with two different

measure of inpatient care.

Historically, public hospitals in Vietnam were allo-

cated primarily by administrative units rather than by a

market. In a system of public hospitals that follows an

administrative structure, returns to scale may depend on

the category of hospital in addition to the number of

beds and volume of output. Most previous research on

returns to scale has focused on the number of beds and

volume of output. For example, a recent review reported

consistent evidence of economies of scale for hospitals

with 100–200 beds, and diseconomies of scale for

hospitals with 300–600 beds (Sowden et al., 1996). In

contrast, in Vietnam the central general hospitals with a

mean of 561 beds exhibited constant returns to scale, as

did the central specialty hospitals with a mean of 226

beds. Provincial general hospitals with a mean of 357

beds and provincial specialty hospitals with a mean of

192 beds exhibited decreasing returns to scale. Among

the smaller hospitals, district hospitals with a mean of 76

beds exhibited increasing returns to scale, whereas other

ministry hospitals with a mean of 84 beds exhibited

decreasing returns to scale.

These results suggest that there were important

differences in managerial resources across categories of

hospitals. At the time of the hospital survey, there was

no justification for increasing the number of beds at

provincial hospitals with the managerial resources that

were available. It may be worthwhile to study hospital

management in different categories of hospitals to

identify problems at the provincial level and potential

solutions based on the experience of well-run hospitals.

It may also be worthwhile to explore ways to divide the

provincial hospitals into smaller units that would be

more appropriate for the managerial resources at that

level.

The results on SRVF also have policy implications.

SRVF were increasing for every category of hospital

with the exception of central general hospitals and

provincial specialty hospitals. These results imply that

there were gains to increasing admissions and outpatient

visits with the existing stock of beds. The increase in

admissions would require reducing the ALOS, because

the mean occupancy rates were high for all categories of

hospitals.

A rough comparison of marginal costs in Table 5 and

1995 hospital prices suggests that the price system

subsidized care at most categories of hospitals. Possible

exceptions were outpatient care at district hospitals and

inpatient care at specialty hospitals. The comparisons

were complicated by the fact that the price system was

by hospital type rather than hospital category (Govern-

ment of Vietnam, 1995). Central hospitals were gen-

erally in types one and two, district hospitals were

generally in types three and four, and provincial

hospitals were distributed throughout all four types.

The price of a general outpatient exam in types one and

two ranged from $US 0.14 to $US 0.27; the marginal

cost ranged from $US 2.10 for central general hospitals

to $US 0.51 for provincial general hospitals. The price in

types three and four ranged from $US 0.05 to $US 0.18;

the marginal cost of $US 0.14 for district hospitals fell

within that range.

For inpatient care, the rough comparison is based on

the marginal cost per admission in Table 5 divided by

the ALOS in Table 1. The price of an inpatient day at an

internal medicine department for types one and two

ranged from $US 0.54 to $US 0.91; the marginal

cost per admission/ALOS ranged from $US 5.86 for

central and $US 2.19 for provincial general hospitals to

$US 0.75 for central and $US 0.69 for provincial

specialty hospitals. The price for types three and four

ranged from $US 0.18 to $US 0.45, which was also less

than the marginal cost/ALOS of $US 1.03 for district

hospitals.

As mentioned in the Methods section, there was no

evidence that hospital reforms like bonuses for staff or

social insurance affected total variable cost. These data

were from an early stage of reforms in a health sector

that was undergoing rapid transformation. It may be

worthwhile to repeat the analysis with more recent data

by conducting a similar survey in this decade or

exploring data available through the Vietnamese health

information system.

As one of the first studies of hospitals in a developing

country with a large sample and a broad range of

hospital sizes, there were few studies in the literature

with which to compare our results. Barnum and Kutzin

(1993) was the only other study to calculate measures

for different levels of hospitals. They reported diseco-

nomies of scale and significant economies of scope for

their total sample of hospitals in China. When they

compared economies of scale and scope across levels

of hospitals, the diseconomies of scale were larger in

upper level hospitals than in middle and lower level

hospitals, and the economies of scope were smaller in

upper level hospitals than in middle and lower level

hospitals.

Despite the unprecedented quality of the Vietnamese

hospital data, the main limitation of this research was

that the estimates were performed with cross-section

rather than panel data. Carey (1997) and Arnould (2001)

estimated hospital cost functions with longitudinal data

from the United States and Wagstaff and Lopez (1996)

estimated them with longitudinal data from the Catalan

region of Spain. The longitudinal analysis adjusts for

unobserved individual effects of each hospital, such as

quality of services, unmeasured dimensions of case

complexity, and managerial ability. Carey (1997) com-


pared cross-section and longitudinal analyses and

rejected the null hypothesis of no correlation between

the coefficients estimated with cross-section data and

individual effects. The resulting bias in the cross-section

estimates affected the coefficients of the inpatient

variables and measures of economies of scale. Data on

the Vietnamese hospitals were available for 3 years, and

we will pursue longitudinal estimates of the hospital cost

function in future research.

Conclusion

In a system of public hospitals that followed an

administrative structure, the total variable cost function

differed significantly across categories of hospitals.

Economies of scale did not depend simply on the

number of beds and volume of output; large hospitals

in one category of hospital had constant returns to

scale, whereas smaller hospitals in another category had

large diseconomies of scale. Among the smaller hospi-

tals, district hospitals had modest economies of scale

and other ministry hospitals had modest diseconomies

of scale.

Acknowledgements

The authors would like to thank Drs. Vung, Vuu and

Trinh, and Lan Phuong Nguyen for providing informa-

tion about the health care system in Vietnam, Susan

Ettner for guidance on econometrics, and David

Rubanowice for work on the statistical analyses. They

are also grateful to two anonymous reviewers for

insightful comments. Partial funding for the analysis of

the Vietnamese hospital data was provided by the

Swedish International Development Agency (SIDA)

and the World Bank.

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Economies of scale and scope in Vietnamese hospitals

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