Health Care Regulation and the Operation Efficiency of Hospitals: Evidence fromTaiwan

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Health care regulation and the

operating eﬃciency of hospitals:

Evidence from Taiwan

Hsihui Chang

a,*

, Wen-Jing Chang

b

,

Somnath Das

c

, Shu-Hsing Li

d

a

Anderson Graduate School of Management, University of California at Riverside, Riverside, CA 92521, USA

b_{School of Management, National Changhua University of Education, Changhua 500, Taiwan} c_{College of Business Administration (MC: 006), University of Illinois at Chicago, Chicago,}

IL 60607, USA

d_{College of Management, National Taiwan University, Taipei 106, Taiwan}

Abstract

Using data from the Annual Survey of Hospitals compiled by the Department of Health in Taiwan for years 1994 through 1997, we employed Data Envelopment Anal-ysis (DEA) to evaluate the impact of a National Health Insurance (NHI) Program on the operating efficiency of district hospitals in Taiwan. We find that, on average, effi-ciency of district hospitals in Taiwan decreased following the implementation of the NHI Program. Our results are robust to the inclusion of control variables that have been shown to affect hospital operating performance in prior research, and alternative efficiency measurements.

*

Corresponding author. Tel.: +1 951 827 4284; fax: +1 951 827 3970. E-mail address:hsihui.chang@ucr.edu(H. Chang).

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Keywords: Hospital; Eﬃciency; DEA; NHI

1. Introduction

The increasing cost of health care delivery has become a worldwide phenom-enon. It has begun to raise concerns in parts of both the developed and the developing world. The rise in public and political debate over increasing costs and the demand for universal access has led policy makers and providers to encourage hospital cost control. Current debates, such as the one in the United States over ‘‘universal health coverage’’, also raise questions about their impact on hospital operating efficiency and the costs of health care delivery (Scott, 1999; Weil, 1992). In March 1995, Taiwan implemented a policy of ‘‘universal health coverage’’, commonly known as National Health Insurance (henceforth NHI). The introduction of universal coverage in Taiwan and the availability of data provide a unique opportunity to investigate changes in hospital operating efficiencies consequent to such a regulatory intervention using recent data. This issue is particularly important given that there is a need for ‘‘. . .additional re-search on methods for assessing the efficiency and effectiveness of hospitals.’’ (Mensah, 2000).

While there are many settings in which the cost impact of a regulatory inter-vention has been examined such as inSoderstrom (1993), few have considered the importance of using relative performance evaluation approach to assessing regulatory impacts. Specifically, it is necessary to measure and evaluate the rel-ative efficiency (or inefficiency) of hospitals, and to assess changes in the per-formance of hospitals following the implementation of universal health coverage. Traditionally, the parametric frontier cost model has been used to estimate relative efficiencies in the hospital sector (Zuckerman et al., 1994). However, input cost and output price data are often times susceptible to wide variations and managerial manipulations across comparable units. Hence, effi-ciency measures based on physical inputs and outputs often provide a better assessment of relative efficiency by abstracting away from costs and prices. Also, in many instances, as in the case of Taiwan hospitals, cost and price data are not easily available to researchers. Thus, to overcome some of the limita-tions of parametric model specificalimita-tions1 and the lack of cost data, we use the non-parametric Data Envelopment Analysis (DEA) that uses the input-output correspondence to estimate hospital efficiencies. These efficiencies are

1_See_{Banker et al. (1986)}_{for a discussion of the limitations implicit in such methods, including} the translog method which is perhaps the most versatile and ﬂexible.

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estimated for the sample of Taiwan hospitals both before and after the imple-mentation of the NHI program.Banker et al. (1986, 1989)show that the DEA method is particularly well suited for measuring relative performance evalua-tion across a cross-secevalua-tion of health care organizaevalua-tions.

In assessing the impact of universal coverage on hospital operating effi-ciency, we also control for cross-sectional differences in operational efficiencies between pre- and post-implementation of NHI that may be attributable to some key underlying efficiency drivers. For example, organizational factors such as hospital ownership may affect the level of production efficiency since different ownership patterns create different incentives for managers. In a sim-ilar fashion, the more severely ill patients are more costly to treat and therefore one would expect that the average resource usage per discharge would be high-er in hospitals that treat proportionately more sevhigh-ere patients. Our cross-sectional model examining variations in operating efficiency thus controls for such variables, to eliminate their possible confounding effect on changes in effi-ciency before and after the NHI program. This latter aspect is important since a common criticism of efficiency comparisons across hospitals has been that they do not adequately control for efficiency drivers such as differences in oper-ational and case-mix factors.

Another interesting feature of this paper is our focus on a specific type of hospitals. Hospitals in Taiwan have been grouped into three main categories i.e., medical centers, regional hospitals, and district hospitals. The payment sys-tems for similar types of services between health care providers at different hos-pital levels are different(Department of Health, Taiwan 1997, p. 97). Under the uniform payment system introduced as part of NHI, payments are homogene-ous within hospital categories but differ across categories. District hospitals, for example, received a relatively low payment compared to regional hospitals and medical centers for a similar type of service. It is also possible that the nat-ure of cases and patient types vary by hospital categories, with more severe pa-tients from district hospitals being referred to regional hospitals or medical centers. Thus pooling hospitals across different categories may sacrifice homo-geneity assumptions, since each category may have a different production function. To ensure homogeneity, we use the hospital classification scheme under the NHI. Of the three types of hospitals, the district hospitals comprise the largest number of health care service providers in Taiwan. The number of hospitals classified as regional hospitals and medical centers are relatively small. To avoid concerns regarding asymptotic properties of DEA estima-tors for small samples, this paper focuses only on district hospitals in Taiwan.

While this study also builds on earlier studies that assess the relative eﬃ-ciency of health care providers, our primary contribution is assessing the im-pact of a public policy i.e., universal health insurance on hospital operating eﬃciency. Prior research in the health care sector has not yet examined this

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issue, particularly in an international context.2 Using data over three years surrounding but excluding the year of NHI implementation (year 1995), the re-sults in this paper show that efficiency of district hospitals in Taiwan deterio-rated after the implementation of the NHI program. This result, which is contrary to commonly held beliefs, is obtained even after controlling for hos-pital specific characteristics that impact operational efficiency.

The remainder of this paper is organized as follows. In the next section, we discuss the health insurance systems in Taiwan, including the context of the National Health Insurance program and the economic consequences for hospi-tal eﬃciency. Section 3 describes the data, and discusses measurement of eﬃ-ciency and the control variables used in the study. Section 4 presents and discusses empirical results. In Section 5 we conclude the paper.

2. Health care insurance in Taiwan 2.1. Institutional background

Prior to the adoption of the National Health Insurance Program in 1995, about 60% of the population in Taiwan was covered by 13 health insurance schemes(Department of Health, Taiwan, 1994). The remainder of the popula-tion paid for treatments obtained. To care for the health of people, Taiwan government set up a planning committee under the Council for Economic Planning and Development in 1988 to draft mandatory and universal health insurance coverage called National Health Insurance Program which consoli-dated all 13 health care insurance systems into a single system. This program was implemented in March 1995 after the Legislative Yuan of Taiwan passed the National Health Insurance (NHI) Act in September 1994.

There are three primary reasons for establishing the national health insur-ance (NHI) program. The ﬁrst was to expand the insurinsur-ance coverage to the en-tire population of Taiwan. By December 1997, around 96% of the total population in Taiwan was covered under the NHI program (Department of Health, Taiwan, 1998). The second reason was to improve the quality of med-ical care by increasing competition among providers. Prior to the NHI pro-gram, patients were restricted to receive services from their choice of contracted providers. Under the NHI program, patients can select their provid-ers any time when they need medical care. The third was to control health care

2_{While Canada, United Kingdom and several other countries have provisions similar to} universal coverage, we are not aware of any recent studies that investigate the impact of introducing universal coverage on hospital eﬃciency. Propper et al. (1998)examine the impact of the 1989 regulatory reforms of the UK National Health Service. See alsoFetter (1985)for some evidence on international cost comparisons.

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costs and promote the search for better resource utilization among hospitals by gradually implementing the global budget payment systems and paying on a per case base instead of a per-visit base. This would ensure provision of health care services at least cost without conﬂicting with the quality of service. The introduction of the NHI Program in Taiwan, thus increased the size of the medical care industry, increased the extent of market competition, and induced incentives for the improvement of operating eﬃciency (better resource utilization).

2.2. Consequences of regulatory intervention

In order to examine the impact of NHI, a regulatory intervention by the Government, we consider the following three main consequences. First, impli-cations of the reimbursement scheme proposed under the NHI. Second, the im-pact of a potential increase in demand for services consequent to the NHI. Third, the impact of market competition on quality of services, if any, that was associated with the implementation of the NHI. We examine each of these issues in the following paragraphs.

To ensure ﬁnancial stability, the NHI Act provides for the contracted health care providers (hospitals) to be reimbursed initially on a per visit basis and then gradually transition to a fee-per-case basis using the global budget reimburse-ment system to discourage hospitals from promoting more services for more in-come (Department of Health, Taiwan, 1994). Essentially, the global budget system puts a cap on annual total medical expenditures. The increase in service quantities (i.e., number of visits or cases) would lead to a decrease in average pay-ment per treatpay-ment. As a result, health care providers have less incentive to pro-mote more treatments.3 While the global budget payment system has been gradually implemented since 1997, only certain clinic services including outpa-tient services, dental services are being reimbursed through this type of payment systems(Department of Health, Taiwan, 2002). Further, even now the payment system is still in essence a fee-per-visit basis with the exception of a few types of treatments such as normal delivery and caesarean section which are being reim-bursed on a fee-per-case basis(Department of Health, Taiwan, 1998). However, since our sample period represents the very early years of the implementation of NHI, our data principally comprises of reimbursements based on a fee-per-visit basis (Chang, 1998). To this extent, we believe that during our sample period, hospital response to health care delivery has not been aﬀected by changes in the reimbursement methods consequent to the adoption of NHI.

As described in Section 2.1 above, a signiﬁcant expansion of coverage (more than 95%) was observed in Taiwan after the adoption of the NHI program.

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This increased coverage however needs to be viewed in its proper context. The population prior to NHI consisted of (a) those who were insured through insurance i.e. the 60% and who continued their coverage under the new scheme, (b) those who were not insured and availed of health care services on a need-based by making spot payments per visit, (c) the population belonging to spe-cial categories such as the army or students who were independently covered under separate arrangements and who now will be covered under the NHI, and (d) the group of really poor people, though very few, who could not afford even need based service—this group is so poor that in the post-NHI period also they cannot afford the premiums required for coverage under NHI. Hence, on the face of it there was a significant increase in the number of people covered by health insurance after implementation of NHI. In practice, however, given the different categories of the population receiving care, it is not quite apparent that there was or would be a significant increase in the demand for healthcare services consequent to the NHI. To this extent, we believe that there was no significant change in the demand for health care services in the years immedi-ately following the implementation of NHI (i.e. during our sample period) as a consequence of the adoption of NHI. Finally, it should be noted that even if demand were to have increased, it would not be easy for hospitals to increase their resource (input) commitments in the short run to meet such increased de-mand. In other words, output cannot be increased in the short run unless there is a significant resource slack. Hence, our examination implicitly assumes that changes in demand consequent to the introduction of NHI did not materially influence any changes in hospital efficiency.

Prior to the NHI program, competition among hospitals was rather limited. Insurers were restricted to visit the contracted health care providers. The ad-vent of the NHI program opened up the market for competition. Patients can select any hospital of their choice for treatment. Under the NHI Act, co-payments by patients are similar across hospitals in the same level. Hence, hospitals compete for patients mainly on the quality dimension. In order to at-tract new patients and retain existing patients, hospitals have to improve their quality of services. While quality improvement helps spur output levels that may create economies of scale, input levels would increase as well since quality is not free. Thus, there are two consequences of competition among hospitals. One, in the absence of price competition, hospitals would perhaps compete on the quality dimension. This may lead to more resource consumption and hence lower efficiency. Two, increased competition should result in changes in de-mand, which would result in lower efficiency for those who are not able to at-tract patients, and higher efficiency for those who do. It should also be noted that even in health care markets such as the U.S. which are largely unregulated, there is very little price competition among providers since they are largely insulated by existing health insurance arrangements. However, as Farley (1985)notes the dominant influence of non-price competition among providers

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does influence hospital costs. On the other hand,Noether (1988)finds evidence that there is more quality competition in more competitive markets, but does not find evidence that costs or prices are higher in such markets. Hence, the adoption of the NHI program may not have a specific directional prediction on hospital efficiency.

In summary, there are two possible arguments underlying how a regulatory intervention might affect hospital efficiency. The first argument is that the inter-vention might increase the volume of demand for health care services at the individual hospital level, and thus lead to higher efficiency through more effec-tive use of available hospital inputs with other factors like the inceneffec-tive effects created by type of ownership, etc. controlled for. The second argument (a countervailing effect) is that the regulatory intervention might increase compe-tition among hospitals. To meet this compecompe-tition, hospitals would have to dif-ferentiate themselves, principally through increases in the quality of services offered. Increased service quality is costly, and thus its effect might lead to lower efficiency.

Based on the discussion in the preceding paragraphs, and the countervailing effects, we argue that the direction of change in hospital efficiency following the implementation of the NHI program is an empirical issue. Therefore, the pri-mary purpose of this paper is to document empirical evidence from Taiwan on the impact of the NHI program on hospital efficiency. More specifically, our goal is to empirically test whether, as expected by the general public and policy makers, the operating efficiency of hospitals actually improves with the imple-mentation of the NHI program, or does it decline.

3. Sample data and variable deﬁnitions 3.1. Description of data

In order to guide its policy for the development of medical manpower and facilities, the Department of Health in Taiwan conducts an annual survey of all hospitals. At the end of 1996, there were 773 hospitals in the Taiwan Area of which 578 hospitals were accredited.4Included in the survey are physical items such as number of physicians, number of nurses, number of patient beds, num-ber of ambulatory visit, and numnum-ber of patient days. This survey is the primary source of our data.5

4_{The purpose of hospital accreditation is to upgrade the quality of medical care so as to lay a} foundation for medical care at diﬀerent levels.

5_{The data on inputs and outputs were scrutinized, or revised as necessary, for consistency using} government budget related information.

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In this study, we use data collected from the 1994, 1996, and 1997 surveys of hospitals compiled by the Department of Health in Taiwan. The same survey questionnaire was used during all of the sample years.6We exclude the calen-dar year 1995 from our study, as it is the year of implementation of the NHI program. As described earlier, hospitals in Taiwan are classified into three ba-sic levels depending upon their primary functions i.e.: medical centers, regional hospitals and district hospitals. The reimbursement schedule under the NHI Act, while uniform within a given level of hospital, varies by the level of the hospital provider. The types of patients serviced (hospitals output) also vary by these different levels of hospitals. To ensure greater homogeneity in relative performance evaluation across comparable units, and taking account of sample size considerations, we focus on examining differences in efficiency for only one type of hospitals i.e.; district hospitals. There are 276 district hospitals that pro-vided complete information for all three sample years. Since the primary focus of this study is the change in operating efficiency consequent to the implemen-tation of the NHI program, we compare efficiency differences between 1994, the year prior to the introduction of the NHI program, with the years 1996 and 1997, the years after the implementation of NHI.

3.2. Measurement of hospital eﬃciency

Eﬃciency can be measured as minimal consumption of inputs for a given level of outputs or the augmentation of outputs at a given level of input usage. In this study we adopt the output-based eﬃciency measure. In general, hospital management and health care providers anticipate demand and invest in inputs necessary to support the expected level of demand. Therefore, in the short run, it is hard for them to adjust input levels. Furthermore, in our context, the implementation of NHI made it possible for hospitals within a given level to compete with each other for prospective patients. Hence, from a practical standpoint, it is more realistic to assume that hospitals would maximize output subject to the available inputs (capacity). This output-based approach meas-ures how much outputs can be expanded for a given level of inputs.

Typically, ex post-input–output data of individual organizations is used to map the production frontier using cross-sectional data. By definition, the pro-duction frontier is the efficient boundary of the propro-duction possibility set rep-resenting how much outputs are produced for a given level of inputs. Each firm or observation that is rated as efficient is used to define an efficient frontier, and firms less efficient are evaluated by comparison with a hypothetical firm or observation that is on the frontier, and which has the same input or output

6_{The raw questionnaire containing speciﬁc questions asked is available from the authors upon} request.

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mix as the firm being compared. Then, the efficiency of the firm being com-pared is the ratio of the actual output level to that of the hypothetical firm. 7 In this paper, we use the DEA approach developed byCharnes et al. (1978, hereafter CCR) and extended by Banker et al. (1984, hereafter BCC)to esti-mate the production frontier of Taiwan hospitals. While the CCR model main-tains the assumption of constant returns to scale, the BCC model allows for variable returns to scale to prevail. Appendix A briefly describes the DEA methodology.

Several studies have documented the flexibility of the DEA method over tra-ditional regression analysis for production function and efficiency estimation (Banker et al., 1986, 1987; Mensah and Li, 1993). Unlike traditional parametric estimation methods, DEA does not assume a particular functional form (e.g. translog) for the underlying production function. Instead, DEA approximates piecewise linear (or log-linear) functions, where the approximations are deter-mined endogenously to envelop the data tightly. A key advantage of the pro-duction correspondence implicit in the DEA specification used here is substitution within both inputs and outputs. This is important in the hospital sector as many hospitals often substitute within both inputs and outputs. For example, in the United States, registered nurses often substitute for many of the physician functions such as inoculations. Among others, Banker et al. (1986,

1989), Grosskopf and Valdmanis (1987), Burgess and Wilson (1996) and

Chang (1998)have employed DEA to evaluate hospital eﬃciency.

3.3. Hospital inputs and outputs

Prior research on hospital eﬃciency has used several measures of hospital inputs and outputs. A detailed review and discussion of the measurement of hospital outputs and inputs is provided in Tatchell (1983)and Banker et al. (1989). To date, there is no statistical technique to unambiguously determine inputs and outputs for measuring eﬃciency using DEA. Given the constraints of the available data, we consider four inputs and three outputs for the estima-tion of the DEA model.

In particular, we use the following four inputs: (i) Number of patient beds (X1) which includes general beds, special treatment beds, psychiatric beds, chronic beds, tuberculosis beds and leprosy beds; (ii) Number of doctors (X2) which includes physician and Chinese medicine doctors; (iii) Number of nurses

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The overall output measure of efficiency consists of two components—a technical and an allocative part. An organization is technically inefficient if it is not producing on the production frontier irrespective of relative prices. Even if the organization is operating on its production frontier, it may not be using the appropriate input mix, given relative input prices. This latter phenomenon is called allocative inefficiency. Since cost and price data are not available to us, we focus on the evaluation of technical efficiency.

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(X3) which includes registered professional nurses and registered nurses; and (iv) Number of medical supporting personnel including ancillary service (X4) which includes pharmacists, assistant pharmacists, medical technologist, med-ical technicians, medmed-ical radiologmed-ical technologist, midwives and dietitians.

The three outputs we consider are: (i) Number of patient days (Y1) which in-cludes general care, acute and intensive care, and chronic care patient days; (ii) Number of clinic visits (Y2) which includes ambulatory and emergency visits; and (iii) Number of patients receiving surgery (Y3).

An alternative output measure that is perhaps more relevant is the number of cases. This alternative output measure is particularly important since hospi-tals can improve eﬃciency if they maintained the number of patient days, but increased the number of patients treated through either better capacity utiliza-tion or through decreasing the length of stay, without sacriﬁcing quality. How-ever, it should be noted that in our context, there are two factors that lead us to use patient days and not number of cases as the output metric. First, is the non-availability of data on a case basis for the sample hospitals. Second, and some-what related is the fact that the reimbursements during our sample period were still on a fee-per-visit and not on a fee-per-case basis. To this extent, at least during our sample period, hospital managers are unlikely to have incentives that have the potential to distort hospital outputs as measured by patient-days. 3.4. Control variables

An additional feature of our paper is an assessment of whether the observed differential impact of NHI program, if any, on hospital efficiency persists even after controlling for certain hospital-specific variables. To this end, we identify, based on prior research, hospital specific factors that may contribute to the cross-sectional differences in efficiencies. In the following paragraphs we dis-cuss the variables that (a) represent hospital operating characteristics and (b) influence or are likely to be associated with case-mix differences.

3.4.1. Hospital operating characteristics

3.4.1.1. Hospital ownership. Prior work relating hospital ownership and per-formance has been inconclusive. Becker and Sloan (1985), for example, do not find any differences in hospital costs between for-profit and government run hospitals. In contrast, Cowing and Holtmann (1983) in a study of New York hospitals found that private proprietary hospitals had lower costs than non-profit hospitals. Similarly, Sharp and Register (1984) examining a set of Oklahoma hospitals, found significant differences in output levels, cost per unit, and revenue per unit across ownership categories. Grannemann et al. (1986)also found that public hospitals had lower costs than not-for-profit pri-vate hospitals. In a similar vein, Carter et al. (1997) using 1989 data from a sample of Texas hospitals found that administrative salaries, number of

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employees, and operational expenses are less for proprietary hospitals than other ownership structures.Burgess and Wilson (1996) also found differences in technical efficiency across hospitals classified by ownership structures. In contrast, some such as Sloan et al. (2001) and Duggan (2000) argue that non-profit hospitals have costs and/or quality similar to that of for-profits. Fi-nally,Eldenburg and Krishnan (2003)document that public not-for-profit hos-pitals exhibit lower operating margins than private not-for-profit hoshos-pitals, after controlling for differential reimbursement, quality of care, and charity care levels.

Hospitals in Taiwan can be broadly classified into two groups—government or publicly owned and privately owned. Since most public hospitals are an operational unit of government funds, they typically do not have to assume the risk of earnings or deficits. Thus, relative to private hospitals, they may not be as concerned about operating efficiencies either before or after the implementation of the NHI program.Chang et al. (2004)provide evidence that for the years 1996 and 1997 i.e., after the implementation of the National Health Insurance Program, private hospitals without intensive-care units out-performed their public counterparts in Taiwan. Hence, public hospitals are likely to have lower operating efficiency relative to private hospitals.

3.4.1.2. Market competition. The classical argument is that increased compe-tition in the market place will enhance efficiency. However,Nyman and Bricker (1989)argue that in the health care industry, increase in competitive pressures results in hospitals competing on the quality dimension, thus reducing their efficiency. Since our interest is on a measure of concentration within a local market, we invoke the Herfindahl index commonly used in the industrial organization literature to measure the extent of competition and concentration in an industry.8The Herfindahl index has also been used in the health care lit-erature byEastaugh (1984)to examine financial management, byMelnick and Zwanziger (1988) to study competition in California hospitals, and by Fizel

and Nunnikhoven (1993)to explain eﬃciency diﬀerence across nursing home

chains.

To balance the development of medical care resources in various areas, the Department of Health in Taiwan divides the Taiwan Area into 17 medical care regions. Field interviews with officials at the Department of Health in Taiwan indicate that differences exist primarily across regions since in Taiwan, the dif-ferences between urban and rural sectors, particularly by population density is not as stark as in many developed countries like the US. The officials also point out that regional medical care coordination committees are set up in each med-ical care region by local health authorities and other related organizations to

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coordinate matters concerning health and medical care services within a region, thus mitigating much of within region variations in service level. Evaluation shows that the standards for medical care manpower and facilities in each re-gion have been greatly improved(Department of Health, Taiwan, 1997, p. 17).

Each region thus represents a local market. The sample hospitals located in the same region will be considered as belonging to the same local market. With-in each local market, we measure this control variable by the With-inverse of the Herﬁndahl index (H), which is deﬁned as under:

H¼X i2K Bi P i2KBi 2 ð1Þ

where K is the number of hospitals in the same local market and Biis the

num-ber of patient beds for the ith hospital in that local market. Any hospital lo-cated in the same local market will have the same H value. Therefore, the inverse of H, denoted by IH, can be viewed as a variable that controls for the intensity of market competition in each region which affects hospital oper-ating efficiency. Higher IH implies higher competition intensity in the particu-lar region. When there is only one hospital in that region, IH has a value of 1 because the Herfindahl index is equal to 1, which is the least competitive status. Extant literature provides two alternative arguments for the relationship be-tween operating efficiency and the intensity of market competition. One argu-ment is that competition tends to force the hospitals to search for ways of improving efficiency. If this is the case, a positive association between this con-trol variable and hospital efficiency can be expected. The other argument takes a more pessimistic view and states that competition will minimize economies of scale, and hence the average operational efficiency will decline. Under this alternative, the association between this variable and efficiency will be negative. More specifically, extant literature suggests that under a cost-based reimburse-ment system competition increases quality and costs, while under price compe-tition, it leads to a reduction in costs. Based on the above analyses, we do not have any unequivocal directional prediction for this control variable.

3.4.1.3. Teaching mission. In addition to providing patient treatments, some district hospitals associated with medical schools also oﬀer training opportuni-ties for medical students and resident physicians. As a consequence, these hos-pitals having the teaching mission are more likely to consume more resources than those without the teaching mission (Grosskopf et al., 1997). Cameron (1985), for example, found that university teaching hospitals were 33% more costly than non-teaching hospitals. Major teaching hospitals and minor teach-ing hospitals were 18% and 9% more costly relative to non-teachteach-ing hospitals, respectively. Rich et al. (1990)also found that teaching hospitals cost 9–30% more than non-teaching hospitals while Feinglass et al. (1991)observed that

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operating costs in teaching hospitals are higher in part due to inefficient use of hospital resources by inexperienced residents. Results obtained byGrosskopf et al. (1997) are also consistent with higher cost of health care delivery being associated with hospitals with a teaching mission and correspondingly lower operating efficiency. Therefore, we expect the operating efficiency of hospitals with teaching mission to be lower than those without teaching mission. To con-trol for the impact of teaching mission, we use a dummy variable (TEACH) that takes on a value of one if the district hospital is associated with a medical school and zero otherwise.

3.4.2. Factors aﬀecting case-mix diﬀerences

3.4.2.1. Illness severity. Horn et al. (1985)was one of the earliest to document that severity of illness was directly related to hospital resource use and operat-ing costs. The severity of illness index used by them was constructed usoperat-ing pa-tient specific information that focused on the signs and symptoms of the patient. Although the index did not use resource use or length of stay in its con-struction, it was found to be highly correlated. In this paper, we measure sever-ity of illness by the number of occupied intensive-care patient bed days divided by the total number of occupied patient bed days.9Higher illness severity im-plies the hospital is devoting more resources to the intensive-care patients. Therefore, an increase in intensive-care patients will affect hospital efficiency adversely and we expect to see a negative association between this control var-iable and hospital efficiency.

3.4.2.2. Degree of specialization. Prior researchers such as Dranove (1987),

Farley and Hogan (1990),Chang (1998), and others have examined the impact of specialization on hospital operations.Eastaugh (1992), for example, shows that unit costs are higher in the less specialized hospitals. However, Chang (1998) in his study of Taiwan hospitals prior to the implementation of the NHI found more specialized medical centers to be less eﬃcient. In this paper, we measure specialization by the number of departments. The greater the num-ber of departments within a hospital, the greater is the extent of specialization, and hence the more diverse are the outputs generated by the hospital. In addi-tion to representing diﬀerences in patient case-mix, the underlying assumpaddi-tion here is that the greater the number of departments, the more specialized will be the groups that exist within the hospital. As a result, patients may perceive a more specialized hospital as one of better quality. Since they can chose the

9_{There are other types of complex cases outside of the Intensive Care Unit (ICU) that would} lead to a higher severity of illness, such as CCU (Cardiac Care Unit) admissions, some types of surgery, and some psychological cases. However, detailed data by such individual types of cases by hospital were not available to us and hence limited our ability to use alternative measures of illness severity.

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hospital they want to visit after the implementation of the NHI, more special-ized hospitals will be able to attract more patients. Therefore, we may observe a positive association between this control variable and hospital eﬃciency in Taiwan.

4. Empirical results 4.1. Summary statistics

Table 1provides the descriptive statistics on the inputs and outputs of sam-ple district hospitals. Both the average number of patient beds and the average number of nurses had increased in the post-NHI period. This indicates that health care providers increased input levels anticipating an increase in health care service demand. Similarly, with the exception of patient days, all other outputs have also increased in the post-NHI period. One possible explanation for this is that strict inspections of health care providers on hospital care and days of hospital stay and the auditing of the speciﬁcs of treatment as per pay-ment regulations of the NHI program perhaps reduced unnecessary treatments.

Using the input and output data, relative efficiencies of hospitals were esti-mated using both the BCC and CCR models of DEA. The mean estiesti-mated DEA efficiency scores are summarized in Table 2. There is a clear decline in efficiency scores in the post-NHI period for district hospitals.

4.2. Returns to scale characteristics

As described earlier in Section 3.2, the CCR model maintains the assump-tion of constant returns to scale, but the BCC model allows for variable returns

Table 1

Descriptive statistics on inputs and outputs of district hospitals

Variables Pre-NHI period

(1994, N = 276)

Post-NHI period (1996 and 1997, N = 552) Mean Std. dev. Mean Std. dev.

Inputs Patient beds 84 96 89 102

Doctors 10 12 9 11

Nurses 30 35 34 38

Medical support and ancillary personnel 8 8 9 9

Outputs Patient days 19,402 27,289 16,064 23,930

Clinic visits 80,644 72,135 82,449 73,007

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to scale to prevail. However, changes in the overall eﬃciency of hospitals may be due to the change in returns to scale characteristics i.e., hospitals moving predominantly from the constant returns to scale region to decreasing returns to scale region in the post-regulation period. To investigate this possibility, we examine possible diﬀerences in returns to scale by using the DEA-based statis-tical tests of returns to scale (Banker, 1996) for both the pre- and post-regula-tion periods.10The test results are reported in Table 3. As can be seen from

Table 3, the null hypothesis of constant returns to scale is rejected at conven-tional level for both the pre-NHI and post-NHI periods. In addition, the null hypothesis of non-increasing returns to scale hypothesis is rejected in 1994, indicating increasing returns to scale prevailed in the pre-NHI period. In con-trast, both the non-decreasing and non-increasing returns to scale hypotheses were rejected in the post-NHI period (1996 and 1997). This evidence suggests that returns to scale characteristics differ in different periods. To mitigate this concern, subsequent analysis is performed using the efficiency scores estimated from the BCC model which allows for variable returns to scale.

4.3. Equality in eﬃciency between the pre- and post-NHI periods

Our primary interest is in examining whether there are systematic differ-ences in hospital efficiencies before (pre) and after (post) the implementation of the NHI program. Hence, we test the null hypothesis that there are no dif-ferences in efficiencies between the pre- and post-implementation periods of the NHI program. We use two types of test procedures to test for this null hypothesis.

First, we use the two conventional tests (WelchÕs and WilcoxonÕs two-sam-ple tests) of differences in efficiencies.Table 4presents these statistical test re-sults for the DEA efficiencies. The mean DEA efficiency in the period after the

Table 2

Means and standard deviations of estimated DEA eﬃciency scores

Sample period DEA eﬃciency scorea

BCC CCR

Mean Std. dev. Mean Std. dev.

Pre-NHI period (1994) 0.629 0.223 0.555 0.207

Post-NHI period (1996 and 1997) 0.567 0.220 0.488 0.200

a _{DEA eﬃciency score is the reciprocal of the ineﬃciency h estimated from DEA models in Eq.}

(A.1)ofAppendix A.

10_See_{Banker (1996)}_{for details on the construction of DEA-based statistical tests of returns to} scale.

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NHI program is signiﬁcantly diﬀerent from that in the period prior to the introduction of the NHI program. This suggests that, for district hospitals,

Table 3

Statistical test results of returns to scale (F-statistics with p-values in parentheses) Null Hypothesis Alternate hypothesis Distribution of ineﬃciency Test statisticsa Period Pre-NHI (1994) Post-NHI (1996 and 1997) CRS VRS Exponential PNj¼1ð^h C j 1Þ .PN j¼1ð^h B 1Þ 1.388 1.379 (0.001) (0.001) Half-normal PN_j¼1ð^hC_j 1Þ2.PNj¼1ð^h B 1Þ2 1.660 1.545 (0.001) (0.001) NDRS DRS Exponential PN_j¼1ð^hC_j 1Þ.PNj¼1ð^h D j 1Þ 1.098 1.208 (0.134) (0.002) Half-normal PN_j¼1ð^hC_j 1Þ2.PN j¼1ð^h D j 1Þ 2 _1.106 _1.272 (0.200) (0.005) NIRS IRS Exponential PN_j¼1ð^hC_j 1Þ.PNj¼1ð^h

E j 1Þ 1.248 1.151 (0.004) (0.020) Half-normal PNj¼1ð^h C j 1Þ 2.PN j¼1ð^h E j 1Þ 2 1.437 1.187 (0.001) (0.044) Notes: CRS: constant returns to scale, VRS: variable returns to scale, NDRS: non-decreasing returns to scale, DRS: decreasing returns to scale, NIRS: non-increasing returns to scale, and IRS: increasing returns to scale.

^

hB_j is estimated from the BCC model of DEA as in Eq.(A.1), ^hC_j is estimated from the CCR model of DEA as in Eq.(A.1)after dropping the constraint(A.4), ^hE_j is estimated from the linear program in(A.1)by modifying the constraint(A.4)to read asP_kkk61, and ^h

D

j is estimated from the linear

program in(A.1)by modifying the constraint(A.4)to read asP_kkkP1.

a _See_{Banker (1996)}_{for the construction of these test statistics.}

Table 4

Statistical test results of equality of eﬃciency

Pre-NHI (1994) period vs. post-NHI period (1996 and 1997)

Test-statistics P-value

Welch two-sample test 3.79 0.01

Wilcoxon two-sample test 3.85 0.01

DEA-based test TEXP 1.29 0.01

DEA-based test THN 1.66 0.01

DEA eﬃciency score is the reciprocal of the ineﬃciency h estimated from the BCC model of DEA in Eq.(A.1)ofAppendix A.

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there is a signiﬁcant decrease in relative operating eﬃciencies in the post-NHI period.

Second, we use the two DEA-based statistical tests of efficiency differences proposed byBanker (1993). One test assumes DEA indices to be exponentially distributed, while the other assumes DEA indices to be half-normally distrib-uted. These DEA-based tests of efficiency differences between two groups have been found to outperform conventional parametric tests in Monte Carlo sim-ulation studies (Banker, 1996).Appendix Bprovides a more detailed descrip-tion on the exact statistics used. The results of these two DEA-based statistical tests are also reported inTable 4. The mean difference in efficiency between the pre- and the post-NHI periods is statistically significant at 1% le-vel, indicating that the operating efficiency of district hospitals reduced after the implementation of the NHI program.

4.4. Production function and relative eﬃciency change

The preceding results are based on the use of relative efficiencies of hospitals estimated using the same DEA model that pools all observations from both the pre- and post-NHI periods. Such a specification is based on the assumption that there is no shift in the production function (e.g., no technical progress) as a result of the regulatory intervention i.e.; the implementation of NHI. It is, however, possible that the implementation of NHI affected hospital produc-tion funcproduc-tions. To examine the sensitivity of our results to this assumpproduc-tion we allow for the possibility that hospital production functions changed from the pre- to the post-NHI period. Accordingly, we employ the modified multi-stage DEA approach formulated inBanker et al. (2003)to re-estimate the efficiency scores and evaluate the robustness of our earlier results. This modified DEA approach ofBanker et al. (2003)is appropriate when there is a technical pro-gress from the pre-NHI period to the post-NHI period for district hospitals.11 The results of relative efficiency change based on the framework ofBanker et al. (2003)between the pre- and post-NHI periods are reported in Table 5. We observe fromTable 5that the mean (median) relative efficiency decreased about 8.5% (6.3%). Consistent with the results reported inTable 4, hospital rel-ative efficiency decreased after the implementation of the NHI program since the mean as well as median relative efficiency changes are significantly different from zero at the 1% level. Thus, the results using the modified DEA approach ofBanker et al. (2003)are consistent with those reported in the earlier section

11_{The suggestion by a referee to use the modiﬁed DEA approach to}_{Banker et al. (2003)}_is gratefully acknowledged. Please seeBanker et al. (2003)for details on the estimation of technical progress and relative eﬃciency change.

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using the conventional DEA methodology which pools observations across sample years.

4.5. Understanding cross-sectional diﬀerences in eﬃciency

Prior research by Register and Bruning (1987), Fizel and Nunnikhoven

(1993)andChang (1998) have linked operational eﬃciency with a number of

hospital-specific attributes. It is therefore possible that the observed differences in efficiency inTable 4may be because these hospital specific attributes chan-ged from the pre- to the post-NHI period. To control for such a possibility, we identify a set of control variables, as discussed in Section 3.4.Table 6provides descriptive statistics on the hospital attributes stratified by pre- and post-NHI periods. As can be seen from Table 6, while the severity of illness remained qualitatively unchanged between the pre- and post-NHI period, market

compe-Table 6

Descriptive statistics of hospital attributes

Variables Pre-NHI period (1994) Post-NHI period (1996 and

1997)

Mean Std. dev. Mean Std. dev.

OWN 0.138 0.345 0.138 0.345

IS 0.018 0.050 0.019 0.040

IH 14.646 6.585 14.821 6.976

DEPT 5.6 4.4 6.1 5.3

TEACH 0.011 0.104 0.011 0.104

OWN: dummy variable for hospital ownership and takes a value of one if the hospital is a publicly-owned and 0 otherwise. IS: degree of illness severity. IH: local market competition intensity measured as the inverse of Herﬁndahl index. DEPT: degree of service specialization, measured in terms of number of departments. TEACH: dummy variable for hospitals with teaching mission and takes a value of one if the hospital is associated with a medical schools and 0 otherwise. Table 5

Statistical test results of relative eﬃciency change between pre-NHI period (1994) and post-NHI period (1996 and 1997)a

Relative eﬃciency change

Mean 0.085

P-value of T-test for mean = 0 0.001

Median 0.063

P-value of sign test for median = 0 (P-value) 0.001 P-value of signed rank test for median = 0 0.001

a

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tition intensity and degree of specialization increased slightly in the post-NHI period. However, there appears to be no change in the ownership structure and teaching status between the pre- and post-NHI periods.

Given these differences, our primary interest here is in testing whether after controlling for these contextual variables, there still remains a portion of the efficiency that is different between the year prior to and the years after imple-mentation of the NHI. We thus use a dummy variable to proxy for the period after the implementation of the National Health Insurance program. Specifically, we define NHI = 1 if year is 1996 or 1997 and NHI = 0 if year is 1994. The sign on this dummy variable will be positive if there is an improvement in efficiency subsequent to the implementation of the NHI program. To explore the relationship between hospital efficiency and the imple-mentation of the NHI program after controlling for the potential effects of the contextual variables, we estimate the following regression model using the OLS:

EFF¼ b0þ b1NHIþ b2OWNþ b3ISþ b4IHþ b5DEPT

þ b6TEACHþ e ð2Þ

where the dependent variable, EFF, is the DEA eﬃciency score, NHI is a dummy variable that takes on a value of one in the post-NHI period and zero prior to that, OWN is a dummy variable that takes on a value of one if it is a public hospital and zero otherwise, IS denotes illness severity, IH represents the logarithm of the intensity of market competition which is measured by the inverse Herﬁndahl index, DEPT is the number of departments, and TEACH is a dummy to denote the teaching mission of hospitals.

Our use of the two-stage approach of first estimating efficiency scores and then seeking to correlate these scores with various explanatory variables is motivated by prior research. For instance, Ray (1991) regresses DEA scores on a variety of socio-economic factors to identify key performance drivers in school districts. Banker et al. (2002) employ the two-stage DEA method to evaluate the impact of IT investment on public accounting firm productivity. In addition, Forsund (1999) observes that the two-stage DEA approach has been in use for over twenty years. More recently, Banker and Natarajan (2001) have provided theoretical justification for the use of the two-stage models in the DEA to evaluate contextual variables affecting DEA efficiency ratios.

The results of estimating Eq. (2)are presented in Table 7. Consistent with prior literature and our prediction, the coefficient of OWN is negative and sta-tistically significant for district hospitals in Taiwan. This suggests that public hospitals, relative to private hospitals, have lower operational efficiency. Con-trary to expectation, the coefficient on ÔISÕ is positive. However, it is statistically

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insignificant. The sign of IH, the variable capturing intensity of market compe-tition, is insignificantly negative. This is consistent with competition reducing the benefits of economies of scale and thus leading to a decline in average efficiency. DEPT, the variable capturing degree of specialization, is positive and statistically significant. This suggests that greater specialization helps

Table 7

Impact of NHI on hospital eﬃciency after controlling for hospital attributes (t-statistics in parentheses)

EFF = b0+ b1NHI + b2OWN + b3IS + b4IH + b5DEP + b6TEACH + b7NURPAT + e

Variables Parameter estimates Parameter estimates

Intercept 0.625*** 0.628*** (27.26) (27.83) NHI 0.064*** 0.056*** (3.97) (3.50) OWN 0.070*** 0.071*** (3.00) (3.06) IS 0.270 0.227 (1.50) (1.28) IH 0.001 0.001 (0.99) (0.60) DEPT 0.004*** 0.005*** (2.76) (2.90) TEACH 0.005 0.008 (0.07) (0.11) NURPAT – 0.002*** (5.45) F-statistics 5.43 9.05 Adjusted R2 _0.031 _0.064 ***

Indicates signiﬁcance at 1% level.

The dependent variable (EFF) is the efficiency score, the reciprocal of the inefficiency h estimated from the DEA model in Eq.(1)using pooled data for the years 1994, 1996 and 1997. All of the independent variables are control variables except NHI which is a dummy variable taking a value of one for years 1996 and 1997, the period after the implementation of NHI, and zero otherwise. All other variable definitions reproduced below are similar to those reported in

Table 4.

OWN: a dummy variable for hospital ownership and takes a value of one if the hospital is a publicly-owned and 0 otherwise. IS: degree of illness severity. IH: local market competition intensity measured as the inverse of Herﬁndahl index. DEPT: degree of service specialization, measured in terms of number of departments. TEACH: dummy variable for hospitals with teaching mission and takes a value of one if the hospital is associated with a medical school and 0 otherwise. NURPAT: ratio of nursing hours to patient days.

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improve the operating efficiency of hospitals.12 The coefficient estimate for TEACH is insignificantly negative, indicating that teaching mission does not have much impact on the efficiency of district hospitals.

With respect to the key variable of interest, NHI, we expect to see a signif-icant and positive regression coefficient for the intervention variable, NHI, if consistent with common wisdom, introduction of market mechanisms lead to improved operational efficiencies. On the other hand, if the introduction of NHI were to lead to decreases in efficiency consequent to the provision of man-datory services, 13then holding everything else constant, the coefficient would be expected to be negative.

As reported inTable 7, the coefficient estimate on NHI is negative and sta-tistically significant. While this may suggest that mandating the provision of health care resulted in a decrease in efficiency, there are also other potential explanations that our specification does not eliminate. In particular, the decline in efficiency in the post-NHI period may be attributed to the following factors. First, the increase in output levels due to greater demand was offset by the in-crease in input levels as shown in the descriptive statistics reported inTable 1. Second, a stricter and more thorough review and audit of health care providersÕ practices is carried out in the post-NHI period. This has resulted in the elimi-nation of unnecessary treatments given the ex-post-audit of service providers by the government, the primary insurer responsible for payment against claims. Consequently, one would expect to see a decline in the level of output or serv-ices rendered after the implementation of NHI, ceteris paribus. Third, several new standards and restrictions have been introduced by the NHI program such as restrictions on the length of stay which have the effect of reducing the total patient days. A fourth factor that may have contributed to the decline in effi-ciency is the improvement in the quality of services, which is also among the key objectives of the NHI program. Indeed, an associated problem of any form of universal coverage is the issue of ‘‘quality of service’’. Dranove (1987), for example hypothesizes that hospitals may engage in quality competition for pa-tients who are likely to be profitable to the hospitals. To the extent hospitals choose to compete on the quality dimension, there will be implications for effi-ciency. At the same time, it is well acknowledged that ‘‘Quality in health care is difficult to define and measure.’’ (Trinh and OÕConnor, 2000).

12

This result is consistent with the notion that greater specialization may serve as a signal of better quality, which helps attract and retain patients. Indeed, interviews with a few hospital managers from our sample hospitals suggest that greater specialization is perceived by patients as being synonymous with higher quality.

13_{TaiwanÕs Bureau of the National Health Insurance compares pattern of insurance claims} submitted across hospitals within the same level (category) of hospitals to detect usual claims. Upon request, hospitals have to provide detail description for justiﬁcation of their treatments.

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To control for the impact of service quality on hospital operating eﬃciency, we re-estimate Eq. (2) using OLS by including an additional quality proxy, NURPAT, to denote ‘‘nursing hours per patient day’’.14The regression results also reported inTable 7are in general similar to those without controlling for NURPAT.

Finally, to assess the robustness of our multivariate regression results, we used variance inﬂationary factors (VIF) to test the degree of multicollinearity among the independent variables in our regression model (Belsey et al., 1980). The re-sults show that the VIF values for all independent variables are less than 5, sug-gesting the absence of any multicollinearity. We also replicated our analysis after removing inﬂuential observations using the criteria proposed by theBelsey et al. (1980)and found the results to be invariant to the deletion of outliers.

4.6. Caveats and limitations

Like other empirical studies of hospital eﬃciency, our results are subject to the following caveats. First, patient/output mix may have changed after imple-mentation. This would arise as a consequence of the hierarchical health care delivery system established through the three types of hospitals, where the most severe patients are transferred to the medical centers and the least severe pa-tients are treated and discharged at the district hospitals. This transfer system did not formally exist prior to the implementation of the NHI. Examination of this issue would require individual patient history to trace their path across dif-ferent groups of hospitals.

Second, while we have included the ratio of nursing hours per patient day as a proxy measure of the quality of services, we are not sure whether it ade-quately captures the quality impact on operating efficiency. To the extent this proxy fails to capture the differences in the quality of services within the district hospitals, our results may be driven by such differences in quality, which re-main uncontrolled for in this study. However, we note that our study is not un-ique among studies of hospital efficiency in its conspicuous absence of a quality measure.Burgess and Wilson (1996)provide an extensive discussion of the lim-itations associated with measures of health care quality.

Third, hospital administrators typically do not decide on the usage of inputs in terms of sheer quantities. They make the decisions on the basis of relative cost, such as substituting costly physician labor with less costly nursing labor (where technically feasible). A strict focus on technical eﬃciency, as in this

pa-14_{The suggestion by a referee to use ‘‘nursing hours per patient day’’ as a quality proxy is} greatly acknowledged. The median NURPAT was increased from 3.1 nursing hours per patient day in the pre-NHI period (1994) to 5 nursing hours per patient day in the post-NHI period (1996 and 1997), indicating that the service quality was improved in the post-NHI period.

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per, might interpret such a substitution as technically inefficient, since total la-bor hours would increase, although there has been a shift from higher-priced to lower priced labor. This suggests the need for computing both technical and allocative inefficiency. Estimating allocative efficiency, however, requires data on input prices, something that is not available to us. The absence of allocative efficiency estimates thus is a limitation of our study. Our results based on tech-nical efficiency do not eliminate the possibility that some of the techtech-nical inef-ficiencies might be due to a substitution effect that is not captured by the current focus.

5. Concluding remarks and public policy implications

In this paper, we use the non-parametric DEA approach to assess the impact of a public policy/regulatory intervention (i.e., the National Health Insurance Program of Taiwan) on the operating efficiency of district hospital units. Since the NHI program increased the coverage rate substantially, a commonly held belief is that operational efficiency in the post-NHI period will increase. This belief is also consistent with the pattern of increasing efficiency during the pre-NHI period documented inChang (1998)for public medical centers in Tai-wan. The results in this paper indicate a statistically significant decline in the efficiency of district hospitals. These results obtain even after controlling for several hospital specific variables that prior literature has documented as hav-ing an influence on hospital operathav-ing performance.

Notwithstanding the caveats discussed in Section 4.6, our results have some limited public policy implications. Compared to the pre-NHI period, the post-NHI period is characterized by zero price competition since per-visit reim-bursement rates are capped. This forces hospitals then to compete on the basis of ‘‘quality of service’’ in order to attract patients. Hospitals unable to compete in the new environment are thus forced to go out of business. Hence, if health care providers do not improve their operating eﬃciency over the long-term, their survival would be at stake, since higher quality cannot be delivered free of additional costs. In fact, according to a recent report from the Central Daily News in Taiwan, more than 200 hospitals went out of business over the past 6 years after the NHI implementation (March 14, 2002), suggesting that compe-tition among hospitals continues to be an issue.

In essence, one possible effect of NHI is a consolidation in the health care field with fewer hospitals operating than before the adoption of NHI. Obvi-ously, if such a trend continues, either availability of health care could be af-fected negatively (an inevitable outcome unless there were too many hospitals in the pre-NHI environment), or the surviving ones (who have dem-onstrated relative efficiency and/or higher quality service delivery) have to ex-pand. The first possible outcome will be costly to society, since ultimately more

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hospitals have to be built to remedy the situation. But the second outcome could be deemed to be beneficial to society. If higher quality health care serv-ices can be delivered to society without costing more (in terms of health care spending in aggregate dollar terms), then there is a net benefit to society, even at the cost of higher inefficiency (measured in terms of total quantities of inputs used). If however, surviving hospitals are able to deliver the necessary health care services using more inputs but without requiring higher reimbursement rates, then the cost of the documented inefficiency in the post-NHI environ-ment will perhaps be absorbed by hospital employees and administrators through lower pay rates, etc. Alternatively, the documented inefficiency may exert pressure on the government to raise the reimbursement rates, or lead to deterioration in health care services because of fewer hospitals. These alter-native policy implications suggest that further research will be required in the Taiwan context to make a more comprehensive and unambiguous evaluation of the public policy implications pertaining to the impact of NHI.

Acknowledgments

We are grateful to Mark Anderson, Rajiv Banker, Peter Chalos, Leslie Eldenburg, Dana Fargione, Marty Loeb (Editor), Sumit Majumdar, Raj Mashruwala, Jimmy Tsay, two anonymous reviewers and participants at the Annual Meetings of the American Accounting Association for their comments and suggestions. We are also thankful to Jia-Chi Shiau and Sheng-Cheng Yang from the Directorate-General of Budgets, Accounting and Statistics, the Exec-utive Yuan-Taiwan, and Chin-Ho Lin from the Legislative Yuan-Taiwan for assistance in obtaining the data; and to Amy Cheng for her able research assistance.

Appendix A. DEA methodology

Let Yj= (y1j, . . . yrj, . . . yRj) P 0 and Xj= (x1j, . . . xij, . . . xIj) P 0, j =

1, . . ., N be the observed output and input vectors generated from an underly-ing production possibility set T = {(X, Y)j outputs Y can be produced from in-puts X} for a sample of N district hospitals in Taiwan. The technical ineﬃciency hjP1 of an observation (Xj, Yj)2 T, measured radially by the

reciprocal ofShephardÕs (1970)distance function, is given by hj h(Xj, Yj) =

s-up {hj(Xj, hYj)2 T}. Assume that the production set T is monotonically

increasing [i.e. (Xj, Yj)2 T, XkP Xj, Yk6Yj) (Xk, Yk)2 T], that the

produc-tion set T is convex [i.e. (Xj, Yj), (Xk, Yk)2 T ) k(Xj, Yj) + (1 k)(Xk, Yk)2 T

for all 0 6 k 6 1], and that the probability density function f(h) is such that f(h) = 0 if h < 1 andR₁1þdfðhÞ dh > 0 for d > 0, then following Banker (1993), a consistent estimator of the eﬃciency is represented by the reciprocal of ^hj

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which is obtained by solving the following BCC model (Banker et al., 1984) of DEA: ^ hj¼ Max h ðA:1Þ s:t: X k kkyrkP hyrj 8r ¼ 1; . . . ; R ðA:2Þ X k kkxik6xij 8i ¼ 1; . . . ; I ðA:3Þ X k kk¼ 1 ðA:4Þ h; kk P0 ðA:5Þ

The above ^hj is estimated under the assumption that the production set

exhibits variable returns to scale. However, if the production set exhibits con-stant returns to scale, then ^hjcan be obtained from the linear program in(A.1)

after dropping the constraint(A.4)as in the CCR model (Charnes et al., 1978) of DEA. In a similar way, if the production set exhibits non-decreasing (non-increasing) returns to scale, then ^hjcan be obtained from the linear program in

(A.1)by modifying the constraint(A.4)to read asP_kkk 61ð

P

kkk P1Þ.

Appendix B. DEA-based tests of eﬃciency diﬀerences

The following DEA-based hypothesis tests are based on test statistics de-scribed in Banker (1993).

Let N1 and N2 be the number of sample district hospitals in periods before and after 1995 (the year in which the National Health Insurance Program was implemented), respectively. If the ineﬃciencies hjare assumed to be

exponen-tially distributed for hospitals in periods, before and after year 1995, with means 1 + r1 and 1 + r2, respectively, then to test the null hypothesis H0:

r1= r2(indicating that hospitals in both periods have the same ineﬃciency

dis-tributions) against the alternative hypothesis H1: r1< r2(indicating that

hos-pitals in the period after 1995 are on average less eﬃcient than hoshos-pitals in the period before 1995), we employ the test statistic given by

Texp¼ X j2N 2 ð^hj 1Þ , X j2N 1 ð^hj 1Þ ðB:1Þ

which asymptotically follows the F-distribution with (2N2, 2N1) degrees of freedom. If the ineﬃciencies hj are assumed to be half-normally distributed

for district hospitals in both periods, before and after 1995, with means 1 + r1and 1 + r2, respectively, then to test the null hypothesis against the

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Thn¼ X j2N 2 ð^hj 1Þ 2 , X j2N 1 ð^hj 1Þ 2 ðB:2Þ

which asymptotically follows the F-distribution with (N2, N1) degrees of freedom.

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