Hospital reserve margins: structural determinants and policy implications using cross-section data.

As is well known, hospitals - like electric utilities, urban freeways and telecommunication systems - do not generally operate at full capacity. The reasons are essentially twofold - uncertain demand for hospital services and the high cost of changing capacity quickly. In the case of hospitals, the resulting excess bed capacity is known as reserve margin and plays a key role in determining costs, efficiency and the potential benefits of both increased competition and hospital consolidation. The purpose of this study is to analyze the determinants of hospital reserve margins using a recent cross section of U.S. short-term care hospitals.

A number of empirical hospital studies have looked at the relationship between hospital costs and excess capacity - or excess capacity and its relationship to specific variables, e.g., hospital ownership, regulation or competition - but none have attempted a comprehensive analysis of the factors determining a hospital's reserve margin using recent data. For example, in a pioneering study Joskow [7] looked at the relationship between reservation quality - a concept closely related to reserve margin - and both certificate-of-need (CON) regulation and hospital competition. His model, however, assumed a Poisson hospital-admissions distribution, did not include a broad range of variables (other than CON and market structure variables) and used 1976 data on 346 private nonprofit U.S. hospitals. A more recent study by Mayo and McFarland [10] also looked at the impacts of regulation and market structure on hospital costs and hospital bed growth using data for 120 short-stay Tennessee hospitals over the period 1980-1984, but did not focus specifically on factors determining hospital reserve margins. Finally, a recent and innovative study of excess capacity by Gaynor and Anderson [4] used a cost function model derived for stochastic demand and data on over 5000 U.S. hospitals for the period 1983-87. Their analysis, however, focused on the cost of excess capacity rather than on the specific causes. Thus, a number of interesting and useful empirical studies of hospital costs and excess capacity have been carried out recently, but none of them have focused directly on the issue of reserve margin determination using a broad set of potential explanatory factors.

The paper is organized as follows. The first section presents the reserve margin model used in this study, followed by a discussion of data issues. Our empirical results are included in the third section, and the paper concludes with a brief discussion of research implications.

I. Reserve Margin Model

A hospital's reserve margin, typically measured in terms of excess beds, is the result presumably of a decision which takes a number of both demand and supply factors into account, including the demographic, market, regulatory and medical environments within which the hospital operates. In addition, the type, size, complexity and teaching status of the hospital should also be regarded as determining factors. Thus, the reserve margin model can be written in general terms as:

RESMARGN = f(HC, HSC, OWN, HIO, MS, REG, DEC) (1)

where RESMARGN is the hospital's reserve margin; HC and HSC represent hospital and hospital service characteristics, respectively; OWN indicates ownership variables; HIO includes hospital internal organization features; MS represents market structure variables; REG includes hospital regulation variables; and DEC represents local demographic and economic characteristics.

In this study, the hospital reserve margin is measured as

RESMARGN = (statistical beds - average daily inpatient census)/statistical beds. (2)

A statistical bed is defined by the American Hospital Association as a hospital bed which is set up and staffed, so that this type of excess capacity is available for use on fairly short notice. Hospital beds which are available but not staffed would take considerably longer to become operational, and thus were not included in our definition of reserve margin.

Hospital Characteristics

Perhaps the two most important hospital characteristics affecting the reserve margin are the price of hospital services (PRICE) and the total number of available hospital beds (BEDS). We use average inpatient revenue (inpatient revenue/inpatient days) as our measure of hospital service price since our reserve margin model focuses on the determinants of inpatient excess capacity. The total number of available beds represents a hospital size or capacity measure.(1) The price of inpatient services should have a positive impact upon reserve margin (holding size constant) since an increase in price should reduce the demand for hospital services. Hospital size as measured by beds should be negatively related to reserve margin, since although larger hospitals will require a larger absolute number of excess beds the relative amount of the excess capacity needed will be less.(2) Of course, the amount of excess hospital capacity needed (both absolute and relative) will also depend upon the degree to which hospital beds of different kinds (e.g., surgical, obstetrics, medical) are substitutable, but this relationship should be picked up by one of several casemix variables.

In our analysis we include two separate casemix variables - CASEMIX and NUMWARDS - to account for differences in both the range and complexity of hospital casemix. Our CASEMIX variable is defined in terms of the number of casemix procedures performed by the hospital, while NUMWARDS reflects the number of hospital wards. While alternative measures of casemix could have been used, we think that these two measures are adequate for capturing casemix impacts on hospital reserve margin. If a hospital offers a wider range of services, as reflected by one or both of the casemix variables, it should be able to attract more admitting physicians and patients, thus enabling it to make more efficient utilization of its capacity. In either case, this should reduce the reserve margin.

Two additional hospital characteristics were included, PROPMCARE measuring the proportion of Medicare to total inpatient days, and OPVIS/BD measuring the number of non-emergency outpatient visits per bed. As the proportion of Medicare patients in a hospital's caseload increases, the hospital's reserve margin should increase since Medicare patients have a greater likelihood of suffering additional complications after being admitted to the hospital. Such complications will increase the unexpected number of bed days that such patients may require. On the other hand, an increase in the number of nonemergency outpatient visits per bed should reduce the reserve margin (holding hospital size constant) if outpatient services are at least a partial substitute for inpatient services.

Hospital Service Characteristics

Our hospital service characteristics are meant to capture the quality dimension of hospital services, and include continuous measures of quality as well as several dummy variables. The hospital reserve margin should be negatively related to service quality in general since an increase in quality holding hospital size constant will increase the demand for services. This in turn will reduce excess capacity and hence the reserve margin. In addition, prospective non-emergency patients should be willing to wait longer for admission to higher quality hospitals, further reducing the need for excess capacity. Continuous measures of hospital service quality include ADDDAYS and MALPRAC/BD, while the quality-related dummy variables include MEDSCHOOL, JCAHACCRD and PPOAFFIL.

ADDDAYS, an index of the number of days added to the expected lifetimes of Medicare patients by services provided by the hospital, is one of the measures of hospital service quality used in this study. This index was constructed with a zero mean, so that hospitals adding more days of life on average have positive index values (indicating higher relative quality) while hospitals adding fewer days of life on average have negative index values (indicating lower relative quality). MALPRAC/BD, a hospital's total expenditures on malpractice insurance per bed, is an inverse measure of quality since larger expenditures should reflect lower quality. Thus, the sign on the MALPRAC/BD coefficient should be positive.

MEDSCHOOL and JCAHACCRD are dummy variables reflecting additional dimensions of hospital service quality. MEDSCHOOL reflects whether or not the hospital is affiliated with a medical school. The training and research focus associated with medical schools should enhance the quality (or at least the perceived quality) of affiliated hospitals. JCAHACCRD indicates accreditation by the Joint Commission on Accreditation of Healthcare Organizations (JCAH), and is therefore an index of hospital quality. Thus, both variables are expected to be negatively related to hospital reserve margin. Finally, PPOAFFIL is a dummy variable indicating affiliation with a preferred provider organization (PPO). PPO affiliation is expected to increase the reserve margin since hospitals must hold higher levels of reserve margins to meet the quality requirements of PPOs.

Hospital Ownership

Two hospital ownership dummy variables were included in this study, GOVOWN indicating public non-profit hospitals and FORPROF indicating private for-profit hospitals.(3) It is tempting to assume that for-profit hospitals, because of the profit motive, will place greater emphasis upon efficiency and cost control, resulting in smaller reserve margins. Government hospitals, on the other hand, might be expected to have higher reserve margins given their more open admissions policies and their mandate to provide backup capacity as a public institution. However, a more thorough theoretical analysis of the relationship between reserve margin and hospital ownership does not support these contentions.(4) Thus, we have no clear a priori expectations concerning the impacts of these two variables upon hospital reserve margins.

Internal Organization

Harris [6] has argued that the internal organization of a hospital, especially that related to physician/administrator relationships, is an important component of hospital decision-making. Thus, we have included several such variables as possible explanatory factors in our hospital reserve margin model. These variables include the number of staff physicians per bed (MDS/BED) and a dummy variable for whether or not there is a physician in the hospital who acts as a paid liaison between the hospital administration and the medical staff (LIAISON).

An increase in the number of staff physicians per bed (MDS/BED) will in part reflect a higher quality of hospital services, and should therefore result in lower reserve margins. In addition, Harris has noted that when the staff physicians of a hospital perceive a shortage of beds, they attempt to hold on to their share of beds by ordering extra services for their patients. By keeping these beds tied up with their patients, physicians preempt the use of these beds by other physicians, thus increasing the time available to find a new patient ready to fill the bed. If all staff physicians engage in this behavior, the reserve margin of the hospital will decline. Furthermore, competition among staff physicians for beds reduces the power of the physicians coalition vis-a-vis that of the hospital administration. This relative shift of power within the hospital gives the administrators more power to contain costs by rationing services to physicians, including reserve margin beds.

Since hospitals hold reserve margins in part to appease the demands of admitting physicians, the presence of a paid liasison physician should result in more effective scheduling of hospital beds and thereby reduce the need for reserve beds. Thus, we expect the estimated coefficient for this variable to be negative.

Market Structure

The market structure variables used in this study include several characteristics of the medical market - including physicians, other hospitals and HMOs - within which each hospital operates.(5) The expected signs associated with the various market structure variables depend critically upon whether one assumes that non-price or price competition generally prevails in hospital markets. Non-price competition assumes that hospitals compete for admitting physicians - and thus indirectly with other hospitals in the area since the total local supply of physicians can be assumed to be fixed, at least in the short run - and patients using such non-price variables as the quality of hospital services offered and the availability of hospital beds, i.e., the reserve margin. The price competition model assumes that hospitals compete primarily in terms of price, and hence cost and efficiency, to gain economic benefits from serving the clients of health insurance organizations and other large groups of insured patients. Thus, the effects of market structure variables, such as the Herfindahl index, on the reserve margin provides an indirect test of these alternative hypotheses.(6)

The Herfindahl index (HERF), based on the hospital's share of total hospital beds within the county, was used as one measure of market concentration, with both HERF and HERF-squared (HERFSQ) included in the reserve margin regressions. Since a larger value of the Herfindahl index indicates greater monopoly power, we would expect a negative effect of this variable on the reserve margin under the non-price competition hypothesis and a positive effect under the alternative price competition hypothesis.(7) The squared Herfindahl index variable was included to capture any non-linearities in the reserve margin/competition relationship, with a negative effect supporting the price-competition hypothesis.

Several other market structure variables were also included: the number of JCAH accredited hospitals in the county (NUMJCAH), the ratio of a hospital's (average inpatient service) price to that of the county average (PRATIO), the number of county physicians per 1000 population (MDS/1000), and the number of county HMOs per 1000 population (HMO/1000). We would expect a larger number of JCAH accredited hospitals, as well as a larger number of county HMOs per 1000 population, to result in a higher reserve margin if the hospital uses its reserve margin as a strategic competitive variable. The NUMJCAH variable indicates the degree of competition in the county from other high-quality hospitals, while the HMO/1000 variable indicates the presence of other competing health organizations with which the hospital must compete for admitting physicians. The PRATIO variable reflects the possibilities of price competition among competing hospitals, although the sign effect is ambiguous. This is because a higher value of PRATIO is likely to lead to both a reduction in the demand for the hospital's services and a reduction in the number of beds if the hospital responds with attempts to increase efficiency and reduce costs. The net effect on the reserve margin will depend upon which of the two individual effects is stronger, so that the direction of the overall impact is indeterminate. Finally, the greater the number of physicians in the hospital's market per 1000 population, the less the effort hospitals will need to make to attract admitting physicians. Accordingly, we would expect a negative impact upon the reserve margin.(8)

The last market structure variable is a dummy variable (URBAN) which captures the urban/rural nature of the county within which the hospital is located. Being located in an urban area will have two effects on a hospital's reserve margin. First, it allows the hospital to enter into patient-sharing agreements with other hospitals, equivalent to sharing excess capacity. Thus, the reserve margin for any single hospital can be reduced. Second, higher levels of price competition in urban areas will force hospitals to reduce reserve margins to order in reduce costs and hence prices. Overall, the effect of the URBAN dummy variable on reserve margins should be negative.

Hospital Regulation

Four regulatory variables were used in this study, three dummy variables (CON1, RATEREG and BLUECROSS) and one discrete variable (CON2) measuring the number of years that each state has had certificate-of-need or CON regulation. CON1 indicated whether or not the state in which the hospital was located had a CON law, RATEREG indicated whether or not any kind of state hospital rate regulation existed, and BLUECROSS indicated whether or not the hospital had a Blue Cross/Blue Shield contract. Since effective regulation should reduce the incentive for the hospital to increase beds, we expect CON1, CON2 and RATEREG to have negative effects on the reserve margin. We also expect a negative impact from the BLUECROSS dummy variable since the market power of Blue Cross allows it to dictate lower reimbursement rates to hospitals in exchange for hospital access to the large pool of Blue Cross patients. The restricted reimbursement rate should reduce the willingness of hospitals to hold reserve margin beds.

Demographic/Economic Characteristics

The demographic and economic variables used in this study were all defined at the county level, and included county population (POP), the percent change in county population from 1983 to 1986 (POP%CHNG), the percent of the population less than 5 years of age (POPLT5), the percent of the population between 55 and 74 years of age (POP5574), the per capita income per place of residence in the county (PCINC/RES) and the average reimbursement level for hospital and medical insurance in the county (INSURANCE). Since each of these variables reflects various aspects of the demand for hospital services, one might expect positive impacts as hospitals increase reserve margins to accommodate the greater expected demand. However, since the demands for both hospital services and capacity (i.e., total number of beds) are affected, the net effect on the reserve margin is actually ambiguous. The essential point here is recognition of the difference between the demand for hospital services and the demand for reserve margins. Furthermore, the supply of hospital services given the total number of beds can be adjusted fairly quickly in response to demand shifts, whereas adjusting hospital capacity is a long run decision.

II. Data

The data for 1987 used in this study came from several available data sets: the 1987 Annual Survey of Hospitals of the American Hospital Association (AHA), and the PPS Minimum Cost Reports, the Medicare Casemix Index, and the Medicare Added Days of Life Index, all produced by the Health Care Financing Administration (HCFA). In addition to this hospital specific data, economic and demographic data at the county level were obtained from the Area Resource File of the Bureau of Health Professions, U.S. Department of Health and Human Services. Data on state-level hospital regulation were taken from Sherman [13] and Kimmith [9] for CON regulation and Smith et al. [14] for rate regulation.

Because there was no common hospital identification system or merge key for the AHA and HCFA data sets, it was necessary to first construct a "crosswalk" procedure between the two data sets in order to merge them. This procedure consisted of using successively the FIPS state code, the FIPS county code and the ownership type of the hospital. An additional merge criterion used was the hospital name.(9) In addition to the observations lost in this primary merge, additional observations were discarded because of inconsistencies in the ownership type reported in the two data sets for matched hospitals. The final merged data set consisted of 4311 hospitals. However, missing values for some of the variables further reduced the number of hospitals used in the final regressions.

Tables I and II contain information on the variables used to estimate the reserve margin model, equation (1). Table I includes the names and definitions of all variables used in the study, while Table II contains summary statistics from the final data set of 3461 observations.

III. Results

The empirical results of this study are summarized in Tables III and IV. Tests for heteroscedasticity and endogeneity were carried out, and the test results are reported in Table III. In particular, the endogeneity tests indicated that simultaneity problems were likely to be present for BEDS and PRICE but not for CASEMIX or OPVIS/BDS. Thus, instrumental variables were constructed for the first two variables.(10) The final regression results are reported in Table IV, which shows four columns of results - Models A-D. Models A and B include alternative sets of explanatary variables but without the endogeneity corrections for BEDS and PRICE. Results using instrumental variables for BEDS, PRICE and PRATIO are shown under Models C and D, with Model D including only statistically significant variables. The following discussion focuses on Model D since, in our judgement, it represents the best set of results.(11)

In general, the estimation results shown in Table IV for each of the four alternative models display a remarkable robustness both in terms of statistical significance and estimated magnitudes. For example, PRICE, BEDS, CASEMIX, OPVIS/BDS, ADDDAYS, MEDSCHOOL, JCAHACCRD, GOVOWN, MDS/BED, LIAISON, PRATIO, HMO/1000, CON2, POP%CHNG and PCINC/RES indicate highly significant effects across all four models. The only notable exceptions to this general result of robustness are MDS/1000, URBAN and FORPROF.

Turning to the results for Model D, PRICE and BEDS are both significant at the 1% confidence [TABULAR DATA FOR TABLE II OMITTED] level and have the expected signs, positive for PRICE and negative for BEDS. Thus, the results indicate that increasing the average price of inpatient services results in a larger reserve margin, presumably the result of a price-induced reduction in the quantity of hospital services demanded, while larger hospitals are able to utilize smaller (relative) reserve margins to meet unexpected demands for hospital beds.(12) The two casemix variables, CASEMIX and NUMWARDS, clearly indicate that casemix effects are important even though the NUMWARDS coefficient was not significant. The CASEMIX effect indicates that hospitals offering a wider variety of inpatient procedures require smaller reserve margins, suggesting that reserve beds may be substitutable [TABULAR DATA FOR TABLE III OMITTED] across specializations. The results for the last two hospital characteristic variables, PROPMCARE and OPVIS/BDS, indicate significant impacts with expected signs. It appears that increasing the proportion of Medicare to total inpatient days and reducing the number of non-emergency outpatient visits per bed both increase the need for holding larger reserve margins. In particular, our results strongly suggest that the current trend towards the increasing use of outpatient facilities for procedures that used to use inpatient beds has had a significant impact in terms of reducing hospital reserve margins.

The results from our hospital service characteristic variables are also interesting, with ADDDAYS, MEDSCHOOL and JCAHACCRD indicating significant and negative effects, while the impacts of MALPRAC/BD and PPOAFFIL are not statistically significant. The results for ADDDAYS indicate that higher levels of hospital service quality in terms of improving the expected lifetimes of Medicare patients results in lower reserve margins. The MEDSCHOOL and JCAHACCRD affiliation dummy variables also show strong negative effects indicating that medical school affiliation and JCAH accreditation result in smaller hospital reserve margins.

The ownership type impacts on reserve margins shown under Model D in Table IV indicate that for-profit hospitals do not have higher reserve margins compared to private non-profits whereas public hospitals do.(13) The GOVOWN effect is statistically significant at the 1% confidence level and highly robust across the four models shown, suggesting that government-owned hospitals do hold higher reserve margins as part of their public mandate. However, our results also suggest that private for-profits do not have smaller reserve margins due to an efficiency motive as has been frequently suggested in the literature.(14)

[TABULAR DATA FOR TABLE IV OMITTED]

With respect to the two internal organization variables, MDS/BED and LIAISON, both have statistically significant and negative coefficients. These results confirm Harris's thesis that the internal organization of hospitals is an important determinant of hospital behavior. In particular, our results indicate that having more staff physicians per bed results in smaller reserve margins. This may be the result of the higher quality levels of service thereby provided or because having more staff physicians per bed means that hospitals can be more flexible in utilizing existing capacity. Our results also strongly indicate that the presence of a paid staff liaison physician results in smaller reserve margins, presumably the result of more efficient scheduling and utilization of hospital beds.

The market structure variables, however, yield more mixed results. The market concentration variables, HERF and HERFSQ, are positive and negatively, respectively. The positive sign on the HERF coefficient offers support for the price competition hypothesis, since under the non-price competition hypothesis one would expect a negative sign. The positive sign for this coefficient presumably reflects the increased cost pressure resulting from a more competitive hospital market. The negative sign on the HERFSQ coefficient is also inconsistent with the non-price competition hypothesis. The PRATIO coefficient is consistently and strongly negative across all four models shown, suggesting that the impact on hospital beds or hospital size dominates the demand effect. However, the positive sign on the HMO/1000 coefficient can be interpreted as supporting the non-price competition hypothesis. This is because higher numbers of HMOs per thousand population may induce a hospital to increase its reserve margin in order to compete more effectively for admitting physicians. Finally, our results indicate that hospital reserve margins are not significantly related to the number of county physicians per thousand population or an urban location.

Among the more interesting results contained in Table IV are those related to the hospital regulation variables - CON1, CON2, RATEREG and BLUECROSS. The only regulatory variable that is consistently and strongly significant across all four models is CON2, the number of years that the state has had CON regulation. Thus, it appears that state hospital rate regulation and Blue Cross/Blue Shield affiliation have little or no impact on hospital reserve margins. Certificate-of-need regulation, however, does appear to be effective in terms of reducing the proportion of reserve beds, a result which Joskow's study also found. In measuring the potential impact of CON regulation, it is important to incorporate some measure of the seriousness with which such regulation is administered such as the number of years that CON regulation has been in effect. Previous studies by both Joskow [7] and Mayo and McFarland [10] have used such measures and their results, like ours, have indicated significant CON regulatory impacts.

Finally, our results with respect to the demographic and economic variables describing the location of the hospital are interesting. First, several of these variables - POPLT5 and POP5574 are not statistically significant. Second, several variables are significant at the 5% confidence level but have negative signs. For example, the POP, POP%CHNG and INSURANCE coefficients are all negative, with the first two being robust across the four alternative models shown, indicating that increases in each of these variables result in lower (rather than higher) reserve margins. As discussed earlier, these results indicate that there is a crucial difference between the demand for hospital services and the demand for reserve margins, with the latter related to both hospital service and capacity demands. Given an increase in demand, our results strongly suggest a larger, and perhaps more immediate, effect on the demand for hospital services so that reserve margins actually decline. It may be that this reflects a more short-run response to demand shifts, but even in the long run after changes in capacity have taken place it is not clear that relative reserve margins will necessarily increase. Indeed, our results suggest the opposite. However, the per capita income variable PCINC/RES does have a positive effect on hospital reserve margin, a result which is also robust across models.

IV. Conclusions

To our knowledge, this is the first comprehensive empirical examination of the factors determining hospital reserve margins. Because of the relatively large number of various types of explanatory factors considered - e.g., structural, ownership, regulatory, internal organization and market structure - there are relevant policy implications in several different areas. We focus in particular on the implications with respect to hospital consolidation, competition, regulation and structural differences. We also offer several ideas for further research in this area suggested by our results.

Much of the recent hospital policy debate has been concerned with whether or not hospitals should be encouraged to consolidate even further. Our results strongly suggest that the answer is yes. Larger hospitals hold smaller relative amounts of excess beds - i.e., smaller reserve margins - even after adjusting for differences in case mix. Our results also indicate that hospitals providing a more diverse array of inpatient procedures have smaller reserve margins, suggesting that beds in different wards can be substituted for each other, a kind of economies-of-scope characteristic with respect to reserve margin costs. Since the cost of holding an excess bed can be substantial, there may be significant cost savings from pursuing hospital consolidation policies which encourage a smaller number of larger and more diverse hospitals, at least in urban areas where patient travel costs are not likely to be significant.(15)

With respect to the policy debate on hospital competition, our results are somewhat mixed. Two distinct types of hospital competition have been discussed in this literature - non-price and price. Our results indicate that hospitals may compete for patients both indirectly through competing for admitting physicians and more directly through price competition. For example, our Herfindal index and PRATIO results (positive and negative coefficients, respectively) suggest that the reserve margin is not used as a strategic competitive variable since hospitals with less market power as well as those with relatively higher inpatient service prices both hold smaller reserve margins. Since these results are inconsistent with the use of reserve margins to attract both physicians and patients, it offers at least indirect support for the price-competition hypothesis. On the other hand, the positive coefficient for HMO/1000 clearly suggests that hospitals do compete, at least with respect to HMO health-care providers, by increasing reserve margins. Thus, both hospital competition hypotheses may be correct.

Regulatory policy with respect to hospitals has concentrated on the regulation of both beds and rates. Our results indicate that states having CON regulation which has been in effect for some time are likely to be effective in reducing excess capacity and to be more effective the longer the rules have been in use. On the other hand, there is no evidence that either rate regulation or Blue Cross/Blue Shield affiliation has reduced hospital reserve margins. Of course, they may have been successful in reducing hospital rates but our model is not designed to test such hypotheses, at least not directly. There is some indirect evidence, however. For example, our results suggest a negative relationship between the relative price of inpatient services and reserve margin, indicating perhaps that policies that reduce hospital rates relative to those of nearby hospitals may also induce hospitals to hold smaller reserve margins. Finally, there is strong evidence from our results that the increased use of outpatient facilities does lower hospital reserve margins, so that regulatory policies which promote the substitution of outpatient for inpatient facilities do appear to have a significant impact on reserve margins and hence hospital costs.

There are also some interesting results with respect to structural differences across hospitals. For example, government-owned or public hospitals hold significantly higher reserve margins on average, whereas there appears to be no statistically significant difference with respect to reserve margins between private for-profit and non-profit hospitals. Thus, the efficiency hypothesis in favor of for-profits is not sustained by our results in terms of reserve margin differences. Several internal organization variables - MDS/BED and LIAISON - indicate consistent and significant impacts on hospital reserve margins, suggesting that such variables do need to be taken account of both in the analysis of hospital behavior and in designing more effective public policy towards hospitals.

Finally, some suggestions for further research. We think that our results strongly support the feasibility and need for further examination of the role of and factors determining hospital reserve margins. One area for further examination is the role of uncertainty and the stochastic demand for hospital services. Observed reserve margins presumably contain two components, one related to expected variations in the long-run demand for hospital services and a second residual component related to short-run, inefficiency and other behavioral characteristics. Since public policy should be focused primarily on the second, reserve margin models need to be able to separate these two components by taking explicit account of the impact of uncertainty on hospital reserve margins.(16) A second area for suggested research is further examination of the role of structural differences in ownership type, regulatory policy and market structure on hospital reserve margins. Such research is an obvious prerequisite for greater understanding of the relationships involved and the design of more effective public policy.

Table AI. First-Stage Instrumental Variable Regressions

Dependent variable: BEDS

Variable                  Parameter Estimate          t-value

INTERCEPT                      76.544564              5.078(***)
GOVOWN                        -11.738014             -2.610(***)
FORPROF                       -50.936709             -8.734(***)
COTHMEMB                      271.654677             33.831(***)
ALLIANCE                       53.463635             12.508(***)
MULTIHOSP                      34.418696              8.584(***)
SUBSID                         33.730370              6.551(***)
HMOAFFIL                        1.113718              0.258
PPOAFFIL                       10.286328              2.475(**)
URBAN                          76.840600             15.459(***)
MDS/1000                      212.900242             12.629(***)
CON1                           31.101851              3.537(***)
CON2                           -1.359844             -2.426(**)
RATEREG                        14.969538              2.875(***)
TRKCST/B                        0.000404              2.236(**)
PROPMCARE                     -74.897267             -5.421(***)
PROPMCAID                     -45.169209             -2.018(**)
SOUTH                          34.817675              5.384(***)
MIDWEST                         3.068302              0.488
WEST                          -25.193979             -3.509(***)
POP%CHNG                      -80.916324             -2.606(***)
PCINC/RES                      -0.006931             -1.064
%UNPOV                         -0.083292             -2.275(**)
POP5574                         0.000303              2.116(**)
POPGT74                        -0.000645             -1.528
INSURANCE                      -0.000803             -0.794

N = 3924
F Value = 228.154
Prob [greater than] F = 0.0001
R-square = 0.5940
Adj. R-sq = 0.5914
Table AII. First-Stage Instrumental Variable Regressions

Dependent variable: PRICE
Variable                  Parameter Estimate          t-value

INTERCEPT                     181.333649               1.941(*)
GOVOWN                        -45.618202             - 3.206(***)
FORPROF                       176.977609               9.487(***)
COTHMEMB                      101.206771               4.104(***)
MULTIHOSP                      -2.821382              -0.188
JCAHACCRD                     130.101654               9.062(***)
MCARECERT                     -95.812143              -1.367
CATHOLIC                       36.416200               1.987(**)
A230                           -0.284386              -0.022
A260                           24.597011               1.876(*)
HMOAFFIL                       73.300504               6.095(***)
BLUE CROSS                     14.246145               0.549
BENIF_ID                        1.155456               5.477(***)
DEPEX_ID                       -0.364561              -1.089
INTEX_ID                        0.757037               4.200(***)
OTHEX_ID                        1.512623              26.710(***)
URBAN                          13.170158               0.829
MDS/1000                      125.120519               2.263(**)
CON1                          105.013368               3.836(***)
CON2                           -3.436561              -1.951(*)
RATEREG                      -111.124254              -6.953(***)
HERF                         -232.624890              -2.274(**)
HERFSQ                        110.974330               1.445
SOUTH                          85.689588               4.336(***)
MIDWEST                         9.917601               0.508
WEST                          178.786423               8.031(***)
PCINC/RES                      -0.032060              -0.994
%UNPOV                         -0.450024              -3.872(***)
PROPMCARE                     142.611669               3.312(***)
PROPMCAID                     210.035213               3.019(***)
POPLT5                          0.000046866            0.092
POP5574                        -0.000295              -0.651
POPGT74                         0.002238               1.688(*)
INSURANCE                       0.017068               5.272(***)

N = 3761
F Value = 182.374
Prob [greater than] F = 0.0001
R-square = 0.6176
Adj. R-sq = 0.6142

Table I. Variable Definitions

1) Hospital Characteristics:

RESMARGN - Reserve margin [(stat. beds - ADC)/(stat. beds)]

PRICE - inpatient revenue/inpatient days

BEDS - total number of available hospital beds, including both staffed and unstaffed beds

CASEMIX - number of casemix procedures performed

NUMWARDS - number of hospital wards

PROPMCARE - ratio of Medicare inpatient days to total inpatient days

OPVIS/BD - number of non-emergency outpatient visits per bed

2) Hospital Service Characteristics:

ADDDAYS - index of number of days added to expected Medicare patient lifetime by hospital services

MALPRAC/BD - malpractice insurance expenditures per bed

MEDSCHOOL - medical school dummy (1 if have, 0 otherwise)

JCAHACCRD - JCAH accreditation dummy (1 yes, 0 no)

PPOAFFIL - PPO affiliation dummy (1 yes, 0 no)

3) Hospital Ownership:

GOVOWN - government-owned (public non-profit) dummy (1 yes, 0 no)

FORPROF - private for-profit dummy (1 yes, 0 no)

4) Hospital Internal Organization:

MDS/BED - number of staff physicians per bed

LIAISON - paid liaison physician dummy (1 yes, 0 no)

5) Market Structure:

HERF - Herfindahl index based on hospital's share of total beds in hospital's county

HERFSQ - hospital Herfindahl index squared

NUMJCAH - number of JCAH accredited hospitals in the county

PRATIO - ratio of hospital's average inpatient service price to county average

MDS/1000 - number of county physicians per 1000 population

HMO/1000 - number of county HMOs per 1000 population

URBAN - urban/rural location dummy (1 if urban, 0 if rural)

6) Hospital Regulation:

CON1 - state certificate-of-need regulation dummy (1 yes, 0 no)

CON2 - number of years state has had CON regulation

RATEREG - state hospital rate regulation dummy (1 yes, 0 no)

BLUECROSS - hospital Blue Cross/Blue Shield contract dummy (1 yes, 0 no)

7) Demographic/Economic Characteristics:

POP - county population (thousands)

POP%CHNG - percent change in county population, 1983-1986

POPLT5 - percent of county population under 5 years of age

POP5574 - percent of county population between 55 and 74 years of age

PCINC/RES - average income per county resident

INSURANCE - average county hospital/medical reimbursement

Table AIII. Variable Definitions - I.V. Regressions

PRICE - inpatient revenue/inpatient days

BEDS - total number of available hospital beds

PROPMCARE - ratio of Medicare inpatient days to total inpatient days

PROPMCAID - ratio of Medicaid inpatient days to total inpatient days

OPVIS/BED - number of non-emergency outpatient visits per bed

TRKCST/BD - Total HCFA reimbursable capital costs per bed

BENIF_ID - Benefits expenses per inpatient day

DEPEX_ID - Depreciation expenses per inpatient day

INTEX_ID - Interest expenses per inpatient day

OTHEX_ID - Other expenses per inpatient day

MEDSCHOOL - medical school dummy (1 if have, 0 otherwise)

COTHMEMB - Council of teaching hospitals dummy (1 yes, 0 no)

ALLIANCE - Alliance member dummy (1 yes, 0 no)

MULTIHOSP - Owned by chain (1 yes, 0 no)

SUBSID - Hospital operates subsidiary (1 yes, 0 no)

MCARECERT - Medicare certification dummy (1 yes, 0 no)

JCAHACCRD - JCAH accreditation dummy (1 yes, 0 no)

PPOAFFIL - PPO affiliation dummy (1 yes, 0 no)

HMOAFFIL - HMO affiliation dummy (1 yes, 0 no)

CATHOLIC - Catholic hospital dummy (1 yes, 0 no)

GOVOWN - government-owned (public non-profit) dummy (1 yes, 0 no)

FORPROF - private for-profit dummy (1 yes, 0 no)

MDS/BED - number of staff physicians per bed

LIAISON - paid liaison physician dummy (1 yes, 0 no)

HERF - Herfindahl index based on hospital's share of total beds in hospital's county

HERFSQ - hospital Herfindahl index squared

MDS/1000 - number of county physicians per 1000 population

HMO/1000 - number of county HMOs per 1000 population

URBAN - urban/rural location dummy (1 if urban, 0 if rural)

CON1 - state certificate-of-need regulation dummy (1 yes, 0 no)

CON2 - number of years state has had CON regulation

RATEREG - state hospital rate regulation dummy (1 yes, 0 no)

BLUECROSS - hospital Blue Cross/Blue Shield contract dummy (1 yes, 0 no)

POP - county population (thousands)

POP%CHNG - percent change in county population, 1983-1986

POPLT5 - percent of county population under 5 years of age

POP5574 - percent of county population between 55 and 74 years of age

POPGT74 - percent of county population greater than 74 years of age

PCINC/RES - average income per county resident

%UNPOV - percent of county population under the poverty line

INSURANCE - average county hospital/medical reimbursement

SOUTH - regional location dummy (1 if south, 0 if otherwise)

MIDWEST - regional location dummy (1 if midwest, 0 if otherwise)

WEST - regional location dummy (1 if west, 0 if otherwise)

This project was supported by grant number HS 06905-01 from the Agency for Health Care Policy and Research. The authors would also like to thank participants at the Second Annual Conference of the Health Care Policy and Regulation Workshop, Lake George NY, May 1996, for useful comments, as well as an anonymous referee. Remaining errors are, of course, our responsibility.

1. Thus, we measure hospital size in terms of total available beds whether staffed or unstaffed, whereas reserve margin is measured in terms of statistical or staffed beds. This is because we define reserve margin, and hence implicitly excess capacity, in terms of beds which are available upon fairly short notice.

2. It has been suggested that BEDS per capita, rather than BEDS and POP, should be used as an explanatory variable. Since our dependent variable, RESMARGN, is measured in relative terms, we prefer the less restrictive specification which includes BEDS and POP separately and thus allows us to look for size effects due to both hospital and market size.

3. Thus the implicit control group is private non-profit hospitals.

4. See Graham [5] for further discussion of this point.

5. For data availability and merging reasons, a hospital market was defined as the county in which the hospital was located.

6. Of course, it is possible that both kinds of competitive behavior exist either in the same market or across different hospital markets.

7. Under the price competition hypothesis, hospitals faced with increased competition will respond with lower prices as the result of reduced costs, increased efficiency and smaller reserve margins.

8. As noted above, however, the expected signs for these variables will depend critically upon which model of hospital competition is assumed, so that our results should permit at least an indirect test of these two hypotheses. Of course, it is possible that hospitals use both forms of competition, either simultaneously or at different times depending upon the circumstances.

9. As with the identification numbers used in the two data sets, the reported hospital names were also not necessarily the same. Most of these differences emanated from the extensive use of abbreviations in the AHA data, while other differences resulted apparently from the use of different names for the same hospital. Substrings from a hospital name were used in an attempt to overcome this "abbreviations" problem.

10. Instrumental variable regression results and variable definitions are shown in Appendix Tables AI-AIII.

11. Given the lack of research on hospital reserve margins and the specific set of explanatory variables to include, and our desire to keep our estimated model relatively simple, additional specifications and specification tests were not considered. However, given that heteroscedastic errors are a common problem in hospital cost data, we decided to test and correct for this problem. For a similar approach in a recent study, see [4, 304].

12. An alternative cost-side explanation has been suggested in terms of the SMC curve and the fact that increases in output for a fixed number of beds (capacity) may become rather expensive as hospital size is increased. Thus, the high marginal cost of further increases in output may also induce larger hospitals to maintain smaller reserve margins. One problem with this explanation is that it assumes that beds are the only, or at least the primary, fixed input in hospital technology.

13. Our results are consistent with other studies also showing no behavioral differences between for-profit and non-profit hospitals. See Becker and Sloan [1], for example.

14. Our results also suggest that the efficiency differences across different types of hospitals, at least with respect to the impact of reserve margins, is between public and private rather than between non-profit and for-profit hospitals. That is, the ownership type rather than the profit motive may be more important in determining hospital behavior.

15. For recent estimates of the cost of an empty hospital bed, see Gaynor and Anderson [4], Keeler and Ying [8], Pauly and Wilson [11], Friedman and Pauly [2; 3] and Schwartz and Joskow [12].

16. The recent study by Gaynor and Anderson [4] is clearly an important step in the right direction, but more remains to be done in dealing with this issue.

References

1. Becker, Edmund R. and Frank A. Sloan, "Hospital Ownership and Performance." Economic Inquiry, January 1985, 21-36.

2. Friedman, Bernard and Mark Pauly, "Cost Functions for a Service Firm with Variable Quality and Stochastic Demand: The Case of Hospitals." Review of Economics and Statistics, November 1981, 620-24.

3. -----, "A New Approach to Hospital Cost Functions and Some Issues in Revenue Regulation." Health Care Financing Review, March 1983, 105-14.

4. Gaynor, Martin and Gerald F. Anderson, "Uncertain Demand, the Structure of Hospital Costs, and the Cost of Empty Hospital Beds." Journal of Health Economics, 1995, 291-317.

5. Graham, Glenn G. "Uncertain Demand, Reserve Margins and Hospital Costs." PhD. dissertation, SUNY Binghamton, 1995.

6. Harris, Jeffrey E., "The Internal Organization of Hospitals: Some Economic Implications." Bell Journal of Economics, Autumn 1977, 467-82.

7. Joskow, Paul L., "The Effects of Competition and Regulation on Hospital Bed Supply and the Reservation Quality of the Hospital." Bell Journal of Economics, Autumn 1980, 421-47.

8. Keeler, Theodore E. and John S. Ying. "Hospital Costs and Excess Bed Capacity: A Statistical Analysis." Working Paper #93-029, April 1993, Department of Economics, University of California at Berkeley.

9. Kimmith, Dean V., "A National Look at CON Laws." Michigan Hospitals, February 1989, 29-32.

10. Mayo, John W. and Deborah A. McFarland, "Regulation, Market Structure and Hospital Costs." Southern Economic Journal, January 1989, 559-69.

11. Pauly, Mark V. and Peter Wilson, "Hospital Output Forecasts and the Cost of Empty Hospital Beds." Health Services Research, August 1986, 403-28.

12. Schwartz, William B. and Paul L. Joskow, "Duplicated Hospital Facilities: How Much Can We Save By Consolidating Them?" New England Journal of Medicine, December 18, 1980, 1449-57.

13. Sherman, Daniel. "The Effect of Statute Certificate-of-Need Laws on Hospital Costs: An Economic Policy Analysis." Research report, January 1988, Bureau of Economics, U.S. Federal Trade Commission.

14. Smith, David W., Stephanie L. McFall, and Michael B. Pine, "State Rate Regulation and Inpatient Mortality Rates." Inquiry, Spring 1993, 23-33.