Hospital Cost Containment and Length of Stay: An Econometric Analysis.

Kathleen Carey [*]

In recent years, concern in the United States over rising health care costs has led to precipitous reductions in the lengths of hospitalizations. While perceptions of compromised medical care quality following this practice and others have prompted policy makers to consider stricter regulation of health insurance organizations, little attention has been given to the extent to which length of stay reductions are responsible for decreasing hospital costs. This paper provides empirical evidence on that point. The method utilizes a hospital total operating cost function estimated on 2792 U.S. hospitals for the period 1987-1992. Three different panel data estimating techniques are applied, including a random effects model that is distinctive in allowing for correlation between hospital effects and observable regressors, circumventing inconsistency problems following from standard generalized least-squares estimations. The cost elasticity of length of stay is calculated from the regression results. This measure is low, falling in the range 0.09-0.12. It suggests that common perceptions regarding the extent of cost savings resulting from length of stay reductions have been overestimated.

1. Introduction

Concern in the United States over the rising share of national resources consumed by health care costs has become widespread in recent years. Hospitals, accounting for approximately 40% of this expense, have been a primary focus of cost control strategy, as both government and private insurers have pressured them to absorb an increasing portion of the financial risks associated with their treatment decisions. A predominant response to these pressures has been reduction in the number of days that patients remain hospitalized. Perceptions of compromised medical care quality following this practice and others have prompted policy makers to consider stricter regulation of the conduct of health care providers and insurance organizations.

The length of hospitalization issue has become prominent with the general public and for some procedures has been widely criticized for being extreme. Maternity and newborn care, for example, became a heavy target for insurers who in many cases were limiting reimbursement for stays to only 24 hours. This case became very controversial, eventually rising to high political ground and resulting in recent Congressional action requiring insurers to cover 48 hours of hospitalization for these patients. The U.S. Congress as well as numerous state legislatures currently face a number of articles of proposed legislation that directly or indirectly regulate the length of hospitalizations. These include measures that give physicians more authority over treatment decisions, that make health plans legally liable for their actions, and that establish appeals procedures for treatment not deemed medically necessary or appropriate by health plans.

While controversy surrounding length of stay reductions have focused on the quality of service being delivered by the health care system, attention given to the economics of this strategy is limited. It is unclear to what extent length of stay reductions are responsible for decreasing hospital costs. Presumably, the inpatient days that are now being eliminated are the least costly ones. A provocative stance has been taken by Reinhardt (1996) who argues that the strategy of length of stay reduction in the United States is single minded and unproductive. He hypothesizes that the hospital is not the expensive setting that is commonly perceived.

Researchers have tracked carefully the trends in hospital lengths of stay and have explored the effects of various reimbursement strategies on hospital utilization. Previous studies have also addressed the potential tradeoff between length of stay and quality of care. If quality has not diminished, then longer hospitalizations may have been largely superfluous. This is a clinical issue. Little empirical effort, however, has been aimed at determining what costs are actually saved by these measures. This paper aims to provide evidence on this point. Rather than asking what health interests might be foregone as a result of shorter hospitalizations, the inquiry here is what economic benefits are being gained. This research takes a hospital cost function approach to measuring the cost savings achieved by U.S. hospitals through reduction in length of hospital stays. The remainder is organized as follows. Section 2 provides background to the problem and the next section describes an econometric model for addressing it. Section 4 presents the data and describes the functional form. Section 5 discusses empirical results and section 6 provides discussion. The final section concludes.

2. Background and Institutional Framework

Broad attempts at controlling hospital expenditures began in the 1980s. The most notable single event was the step taken in 1983 by Medicare, the government program of health care funding for the elderly, and hospitals' largest third-party payer. Medicare adopted the Prospective Payment System (PPS) that altered the basis of reimbursement from reasonable cost to prices based on historical costs for specific diagnoses across hospitals. This initiative by the Federal Government was followed by more gradual changes in the forms of private insurance payment. Over time, the nonfederal sector has become increasingly dominated by managed care organizations. These insurers attempt to control expenditure growth through negotiating discounted prices and establishing utilization management protocols with hospitals and by performing reviews of the appropriateness and necessity of hospital care.

Changing reimbursement systems have altered the financial incentives facing hospitals. Historically, on the private payer side, hospitals were reimbursed for reasonable cost on a per diem basis, receiving a flat payment for each hospital day provided. Under current managed care plans, negotiated prices largely retain this linear structure, thereby failing to account for falling daily treatment costs as stay lengthens. While this system of payment allows hospitals to recover greater fixed cost as marginal cost declines, payers are eager to obtain contractual arrangements that reduce the lengths of hospitalizations.

Under Medicare's PPS policy, hospitals are reimbursed for well-defined hospital cases based on diagnosis-related groups (DRGs). While not an unprecedented arrangement, PPS transformed hospital incentives on a wide scale, because at the time of its implementation in 1983, Medicare produced approximately 40% of hospital revenues. Some private insurers followed the government initiative and adopted similar payment systems. Case-based reimbursement mechanisms create strong incentives within hospitals to shorten lengths of stay and increase admissions.

Much research effort has gone into documenting the effects of PPS on hospital performance. This literature is well reviewed by Coulam and Gaumer (1991). In sum, the average length of stay initially declined relative to historic norms. Concern over increased admissions was mitigated; admission rates actually declined during the early PPS period for reasons that are not well understood. In general, research shows slower rates of growth in hospital expenditures under PPS (Guterman et al. 1988; Hadley, Zuckerman, and Feder 1989; Hadley and Swartz 1989; Russell and Manning 1989).

Studies of managed care effects attribute cost containment progress to a range of factors. Miller and Luft (1993) found fewer resources consumed by health maintenance organization (HMO) patients because of lower use of ancillary services during hospitalization as well as shorter lengths of stay. In a study that more broadly models hospital strategy for managing care, Conrad et al. (1996) find payment incentives, use of systematic clinical strategies, and sharing of resource use information with clinicians to be the prime movers in improving hospital efficiency. Stem et al. (1989) report lower lengths of stay but comparable costs for HMO versus fee-for-service patients at one major teaching hospital between 1983 and 1985.

While the reviews of PPS and of managed care effects were appearing and being interpreted, the shape of the U.S. hospital itself as an institution began changing. The first stage of managed care replaced the traditional fee-for-service system with new forms of insurance plans that attempted to reduce costs by restrictions on provider options, negotiation of lower prices with providers in return for volume of patients, and emphasis on preventive care. The second wave of managed care is now underway. This is characterized by large-scale rearrangement of formerly separate entities in the provision of health care. Distinctions between hospitals, physicians, and insurers are fading, and new models of health care delivery marked by vertical or horizontal integration are emerging. Hospitals occupy a centrality within these organizational hybrids or organized delivery systems that offer a continuum of care that may also include prevention and ambulatory services, home health, long-term care, and hospice care, among other features (Robinson 1994; Shortell, Gillies, and Devers 1995; Morrisey et al. 1996). Hospital economic incentives are changing yet again under this second generation of managed care. Patients increasingly are insured according to capitation contracts under which revenue is provided for each enrollee at a fixed rate per member per month. Under capitated budgets, hospitals are cost centers and volume of service is directly tied to profits. However, shortening length of stay may be less effective in maintaining viability of capitated systems than covering a greater number of lives and spreading fixed costs more broadly.

In his maverick view, Reinhardt (1996) goes so far as to suggest that length of stay reduction in the United States actually may be counterproductive. Theoretically speaking, he points to the failure of current HMO per diem policies to abide by the Ramsey Principle in which welfare-maximizing pricing would recover greater fixed cost from price-inelastic (non-discretionary early) days and relatively less from price-elastic (discretionary later) days of care. From a practical perspective, Reinhardt argues that while we are ostensibly cutting expensive care, we are busily transferring patients to alternative sites that may include the hospitals' own outpatient surgery units. Length of stay reductions have also spurred the growth of subacute care and home care industries, incurring significant fixed costs that add to health spending from a systemwide point of view. With greater penetration of vertically integrated delivery, Reinhardt predicts that managers will discover that the hospital is a relatively inexpens ive place for patients to convalesce.

3. Methods

Hospital Cost Functions

An extensive literature has formed concerning appropriate estimation of the hospital cost function. Early average cost functions were behavioral in nature. Considered to be lacking in theoretical foundation, they largely were replaced by total cost functions that use multiple outputs and input prices exclusively as regressors (Cowing and Holtmann 1983). Various functional forms have appeared. Much work has followed McFadden (1978) in using flexible (generally the translog) forms (Vitaliano 1987; Vita 1990; Gertler and Waldman 1992; Gaynor and Anderson 1995; Keeler and Ying 1996). The current trend in this literature is hybrid forms that include explanatory variables in addition to output quantities and input prices (Grannemann, Brown, and Pauly 1986; Carey 1997). A consensus has not been reached on the form of the hospital cost function.

Length of stay has been included as a regressor in the cost function by some researchers who consider it to be a measurable dimension of inpatient output. Its role as a determinant of cost, however, has not been scrutinized previously. One problem posed by the inclusion of this variable is its potential endogeneity. The record shows that hospitals have responded to cost containment pressure by shortening hospital stays, suggesting that hospitals have control over this variable. Moreover, the majority of hospital cost functions fail to control for quality, a potentially weighty determinant of cost that is very difficult to quantify. If quality of care is systematically related to hospital length of stay, has a significant effect on cost, and is omitted from the regression, then length of stay measures will be correlated with the error. The remainder of this section describes how panel data modeling can be used to address these econometric problems.

Panel Data Estimation

The majority of hospital cost function estimations have relied on single year cross-sectional data. Yet researchers are aware of likely individual hospital differences that are systematic although unobservable. By applying a structure to the unobservables, panel data models have some capability in capturing these individual differences and purging behavioral parameters of omitted variables bias. A variety of models have been developed to take advantage of individual heterogeneity that is embodied in combined time-series and cross-sectional data sets. The standard method is the fixed effects (alternatively referred to as the within or the least-squares dummy variable) estimator that treats the individual effect as a fixed parameter. However, efficient estimation is by random effects (or error components) models that treat the individual effect as a random component of the error term. The model assumes a structure on the error term, and a feasible generalized least-squares (GLS) technique determines the parame ters. However, this approach has a major drawback: the assumption (commonly made) that the unobserved individual effect is uncorrelated with the observed regressors. GLS estimation yields biased and inconsistent parameters in the presence of such correlation.

A model that circumvents the correlation problem has been proposed by Chamberlain (1982, 1984) and applied by Jakubson (1988) and Carey (1997). This is a correlated random effects model that takes into account the relationship between the unobservables and the observed regressors. Unlike the conventional random effects model that assumes no correlation, this model assumes correlation between the individual effect and the observed regressors and directly models that correlation. Unlike other models, each period in a multivariate framework is estimated as a separate equation. Rather than a single equation panel model in two dimensions, we have T equations in one cross-sectional dimension where T is the number of time periods. The workings of the conventional panel model are well known. The discussion now turns to the mechanics of the correlated model.

The Correlated Random Effects Model

Consider the following equation:

[y.sub.it] = [[beta].sub.t][x.sub.it] + [c.sub.i] + [[micro].sub.it] (1)

where [y.sub.it] are total costs of hospital i (i = 1, 2, ..., N) in time period t (t = 1, 2, ..., T), [x.sub.it] are observable characteristics of hospital i in period t, [c.sub.i] represents unobservable effects that vary by hospital, and [[micro].sub.it] is a random disturbance term. For clarity of presentation, Equation 1 has only one explanatory variable. However, the results generalize easily to accommodate multiple regressors. Assume further that [[micro].sub.i] = ([[micro].sub.i1], [[micro].sub.i2], ..., [[micro].sub.iT]) is independent of [x.sub.i] = ([x.sub.i1], [X.sub.i2], ..., [x.sub.iT]) and [C.sub.i], and has a normal distribution with zero mean and variance [sigma].

Correlation between the individual effect and the observable explanatory variables is formalized by the expression

[c.sub.i] = [[lambda].sub.1][x.sub.i1] + [[lambda].sub.2][x.sub.i2] + ... + [[lambda].sub.T][x.sub.iT] + [[omega].sub.i]. (2)

Error term [[omega].sub.i] is assumed to be normally distributed and independent of [x.sub.i] and [[micro].sub.i]. If [C.sub.i] is uncorrelated with [x.sub.it], then the parameters [[lambda].sub.1], ..., [[lambda].sub.T] will be equal to zero. Substituting Equation 2 into 1:

= [y.sub.it] = [[beta].sub.t][x.sub.it] + [[lambda].sub.1][x.sub.i1] + [[lambda].sub.2][x.sub.i2] + ... + [[lambda].sub.T][x.sub.iT] + [[omega].sub.i] + [[micro].sub.it]. (3)

The values of x in all periods enter the cost function in time t through their correlation with the individual effect. Let the following set of T equations represent the unrestricted (reduced) form of Equation 3:

[y.sub.it] = [[pi].sub.t1][x.sub.i1] + [[pi].sub.t2][x.sub.i2] + ... + [[pi].sub.tT][x.sub.iT] + [[omega].sub.i] + [[micro].sub.it]. (4)

If [pi] is the T X T matrix of coefficients in Equation 4, then the set of restrictions implied by Equation 3 requires that

[pi] = [beta][I.sub.T] + [j.sub.T][lambda]' (5)

where [beta] is the vector of elements [[beta].sub.t], [I.sub.T] is a T-dimensional identity matrix, [j.sub.T] is a T vector (column) of ones, and [lambda]' is the vector of elements [[lambda].sub.t].

Finally, the minimum distance method (Malinvaud 1970) imposes the restrictions in Equation 5 on the reduced form coefficient estimates. Intuitively, this estimator minimizes a function of the distance between the vectors containing the estimated unrestricted parameters and the structural parameters implied by the restrictions. More specifically, let [k.sub.t] represent the number of explanatory variables (including leads and lags) in each of the T unrestricted cross sections in Equation 4 and K = [[sigma].sup.T].sub.t=1] [k.sub.t]. Let [pi] be the K-vector containing the rows of the reduced form [pi] matrix and let [pi] be its estimator. Allow the K X K covariance matrix of [pi] to be represented by [omega] and let [omega] be its estimator. If [theta] is the q-vector of structural parameters (q [less than] K), and g([theta]) is the function that maps [theta] into [pi], then the desired estimator [theta] is chosen to minimize

D([theta]) = [[pi] - g([theta])]'[[omega].sup.-1][[pi] - g([theta])]. (6)

The value of [theta] that minimizes expression 6 is equal to

[theta] = [(g'[[omega].sup.-1]g).sup.-1]g'[[omega].sup.-1][pi] (7)

(Hsiao 1986). Under the null hypothesis that the restrictions are correct, D([theta]) is distributed [[chi].sup.2](k-q).

4. Data Description and Functional Form

Two independent sources provide the majority of data for this study: the American Hospital Association's Annual Survey of Hospitals and the Health Care Financing Administration's (HCFA) Hospital Cost Reporting Information System files (PPS data). The panel includes data for 2792 hospitals for the years 1987 through 1992. The sample contains all hospitals for which both AHA and PPS data were available, after eliminating specialty hospitals and all inclusive rate payers. [1]

Most researchers argue that a short run total cost (variable cost) rather than a long run total cost function is preferable. The argument is made on theoretical (Cowing and Holtmann 1983; Vita 1990) as well as empirical (Carey and Stefos 1992) grounds. Following this precedent, the dependent variable is the total of all direct costs, excluding capital-related expenditures (PPS source). The PPS measures of discharges and average length of stay (inpatient days/discharges) and the AHA measure of outpatient visits are the principal output variables. The only available measure of input prices is that of local area wage rates produced by HCFA for use in hospital reimbursement. Variation in the cost to the hospital of energy and food may be partially reflected in wage rates that compensate workers for higher costs of living. A fixed capital input is appropriate to the variable cost function; this is the PPS calculation of total fixed assets. Cost and capital values are converted to 1987 dollars using the Medicare P PS input price index.

Other factors are included in order more fully to explain hospital costs. HCFA's DRG case mix index is used to control for variation among patients not captured by the primary output variables. The AHA measure of staffed beds can be interpreted as a proxy for capacity. Finally, dummy variables for teaching status, population density, and ownership are included. Large teaching hospitals are those having a residency program and bearing membership in the Council of Teaching Hospitals as reported in the AHA data. Large urban hospitals are those located within a Metropolitan Statistical Area of greater than one million (AHA data source) and proprietary hospitals are defined according to the PPS ownership category. Summary statistics describing the data and how they are measured appear in Table 1.

The specification used for estimation most closely follows that of Grannemann, Brown, and Pauly (1986) that features a log transformation of the dependent variable and second and third order terms on the principle outputs. (While many researchers use translog flexible functional forms, such procedures require a large number of parameters to be estimated and have the drawback of collinearity among their many terms. The focus of the cost function estimated here is the marginal effects of average length of stay. Loss of precision on that variable's coefficients in order to gain additional flexibility did not seem warranted in this case.) In construction of Equation 2, admissions, length of stay (linear terms), and case mix index are the variables assumed correlated with the individual effect contained in the error term. This choice is based on theoretical consideration and exploratory analysis. (Preliminary regressions indicated that the leads and lags on the remaining explanatory variables were insignificant i n explaining cost variations.)

5. Estimation Results

The fixed and random effects estimates are reported in Table 2. From the above discussion, these estimates will differ if the unobservable individual effects are correlated with the observed explanatory variables. Evidence of such orthogonality can be statistically obtained through the Hausman (1978) specification test. Under the null hypothesis of no correlation, the two sets of estimates should not differ significantly because both OLS fixed and GLS random effects parameters are consistent. Alternatively, the former is consistent but the latter is not. [2] The Hausman test statistic is distributed [[chi].sup.2] (k) where k is the number of unknown parameters. Its calculated value is 559. Because the critical value at the 1% level is 28, the null hypothesis of no correlation is easily rejected.

The discussion now proceeds to the correlated random effects model. Two issues are helpful here in clarifying the operations of the model. First, the unrestricted estimates corresponding to the [pi]s of Equation 4 are estimated using the GLS technique of seemingly unrelated regression (SUR). This method is more efficient than OLS if the individual hospital disturbances are correlated across equations (over time). Second, in order to isolate the individual effect (i.e., to disjoin the [beta]s and the [lambda]s), the minimum distance estimation places a set of restrictions on the correlated variables in the [pi] matrix. Although the minimum distance method allows for all correlated variables to be treated in this manner, the estimation performed here only restricts average length of stay (the variable of interest). The reason for this is that while discharges and case mix are modeled as correlated, separation of their [beta]s from their [lambda]s is not useful in calculating length of stay elasticities (below) yet would reduce the precision on the average length of stay coefficients. The complete set of panel estimates are the SUR estimates for all variables except average length of stay (Table 3) and the minimum distance estimates for average length of stay (Table 4).

Comparing Tables 2 and 3 shows that the results of all three panel methods are similar in basic ways. The coefficients on the three output measures entering in cubic form exhibit the anticipated signs. The coefficients on the remaining variables also behave as expected. The case mix index, wage index, fixed assets, and teaching measures are positively related to costs and generally highly significant. The negative sign on the interaction between discharges and outpatient visits suggests economies of scope between these two outputs. The log of beds is a positive and a very significant determinant of costs except in the fixed effects case where its effect is void owing to very small variation over time. The proprietary hospital dummy variable has a positive and significant sign in both the random effects and SUR models. This result is at variance with the bulk of previous literature that fails to find a relationship between profit/nonprofit status and cost. The sign on the urban area dummy variable is signific antly positive in the random effects case and for the earlier years in the SUR models.

Table 4 lists the estimated values of the [beta] and [lambda] parameters on length of stay in the correlated random effects model. As expected, the values of [beta] are positive and significant. The estimates of [lambda] indicate positive correlation between average length of stay and the individual effect for 1987 and negative correlation for 1991 and 1992. As discussed above, D([theta]), described in Equations 6 and 7, is distributed [[[chi].sup.2].sub.(k-q)]. Its calculated value is 51.6. Because the critical value for 24 degrees of freedom (K - q = 36 - 12) at the 5% level is 36.4, we must reject the null hypothesis that the set of restrictions is a full characterization of the reduced form.

The practical advantages and disadvantages of the three panel data models estimated here were discussed in section 3. Evaluation of their relative merits also requires that the economic interpretation of each structure with regard to the unobservables be considered. Variation in unobservable quality, severity, managerial ability, and input prices not reflected in the wage index are all potential sources of variation in cost. The conventional random effects model assumes that these variables are uncorrelated with the observable regressors. This is a dubious assumption for hospitals, where it is preferable to allow for quality to be affected by length of stay, severity correlated with hospital size, and managerial ability related to output. Neither the fixed nor correlated random effects models requires this assumption. The latter has an advantage in that the hospital effect is solved directly from the explanatory variables, and results are generated for individual years. However, the model does not fully accou nt for the pattern of leads and lags found in the data.

6. Discussion

Length of Stay and Cost

The main purpose of this analysis is to obtain evidence regarding the extent of hospital cost savings attributable to length of stay reductions. In this section, we apply the cost function estimates reached above to this task. While implications are drawn from the results of the fixed and correlated random effects models, some general results are presented for all three models in Table 5. A useful starting point is calculation of cost effects expressed in elasticity terms. The first column of Table 5 lists the mean values of the length of stay (LOS) elasticities. [3] At first glance, the Reinhardt hypothesis appears to be borne out. The numbers are relatively low, ranging from 0.064 for the correlated random effects model in 1992 to 0.121 for fixed effects. The correlated random effects elasticities fall between the two conventional panel results, averaging 0.092 over the six-year period. Elasticities and marginal costs of discharges and outpatient visits are also listed in Table 5. [4] The elasticities for these two outputs and the marginal costs of outpatient visits are lower for the correlated random effects than for the conventional models. In each model, however, the length of stay elasticities are small in comparison with the discharge elasticities. This is an important result signifying that it is the number of patients and not the number of days of hospitalization that is driving costs.

The marginal cost of discharge estimates falls within a wide range of results found in previous literature. For example, Gaynor and Anderson (1995) report $854 using a national sample and Vita (1990) reports $2043 for a sample of California hospitals (both in 1983 dollars). However, the marginal costs of outpatient visits estimated here are much lower than found by these researchers (Gaynor and Anderson, $193; Vita, $74). The scale economy estimates from existing literature are also mixed. Vita finds scale diseconomies while Gaynor and Anderson find evidence of large scale economies. The models estimated here generate constant returns to scale for conventional random effects, and scale economies for fixed and correlated random effects. The latter model (summing discharges and outpatient visit elasticities to equal 0.464) yields results in the neighborhood of those of Gaynor and Anderson (0.581).

As the next step, we simulate the cost savings obtainable from a universal hypothetical stay reduction of one. Savings are the difference between the predicted values of total cost and the predictions calculated at LOS minus one day (ceteris paribus). Columns 2 and 3 of Table 6 report the means of these savings expressed both in dollars and as a percentage of total costs. The dollar range is 364 to 498 thousand or 1-2%. The overall averages are 409 and 436 thousand dollars for the fixed and correlated random effects models, respectively, or a mere 1.4-1.5% of total costs. These simulations are based on lengths of stay averaged at the hospital level. It is understood that savings may vary considerably across different diagnoses; however, such effects are beyond the scope of this analysis. [5]

While it can be argued that the above simulation results indicate that cost savings are low, they do represent real gains for providers. Assessing whether these savings warrant the LOS reductions is outside the scope of this analysis. However, these results can be used to place the findings in another perspective. Consider the following question: By how much would staffed bed capacity need to be reduced in order to achieve cost savings equivalent to the one-day LOS reductions? Previous work on estimating the cost of empty hospital beds suggests that debedding programs may be a promising area for hospital cost savings (Gaynor and Anderson 1995; Keeler and Ying 1996; Carey 1998). The fourth column of Table 6 reports the cost elasticities associated with staffed beds. [6] Columns 5 and 6 list the amount of debedding that would achieve the same cost savings as resulting from the simulated LOS reductions (reported in columns 2 and 3). Over the six-year period, hospitals could reach the cost savings equivalent of a one-day LOS reduction by lowering their levels of staffed beds by an average of 10 beds or 5.4% of capacity. Considering that the average occupancy rate over the period (for this sample) was 59%, it appears that this might be a preferable economic approach.

Table 7 reports the result of the one-day reduction in stay simulation for a two-level stratification of hospitals by LOS. The shorter LOS group is the lower half of the sample sorted by length of stay. (For ease of exposition, the six annual groups are averaged in the correlated random effects model.) The longer LOS group is the remaining half of the sample. The shorter group, which has an average of 5.1 days, is smaller hospitals with a relatively lower average case mix. These hospitals stand to gain more than the longer (12.0 days) group of hospitals, from further reducing LOS. However, the 0.085 and 0.086 elasticities still only translate to 1.5-1.7% of total costs. This compares to a 1.3% of total cost for the longer group, for which patient days at the margin are relatively less costly.

The preceding simulations provide evidence that common perceptions of the extent of cost savings resulting from length of stay reductions are exaggerated. It was alluded to above that too little regard may be given to the diminution of costs during periods of convalescence. Lowering lengths of stay is a form of reduction in quantity of service. The change in service, however, is not necessarily proportionate to the length of stay reduction, and it is possible that the average intensity per patient day could rise as stay falls. It also should be recognized that some portion of length of stay reduction during this period was independent of cost control pressures. Remarkable recent developments in technologies are responsible for an increase in the portion of procedures that are performed noninvasively. Such advances in many cases have eliminated the need for an overnight stay and in many others have reduced the necessary number of overnights.

Length of Stay and Quality

An issue offshooting from this analysis is the relationship between the length of hospitalization and the quality of care. If we accept the assumptions that quality varies by hospital, is constant over a short time horizon, and is the major component of the unobservable individual hospital effect, we can use the results of the correlated random effects model to speculate about whether discharging patients earlier compromises quality. The values of [lambda] in Table 4 denote the correlation between the individual effect and the length of stay. This term is significant in only three years with a positive value for 1987 and negative values for 1991 and 1992. The 1987 result is consistent with the common fear associated with shorter stays, that is, that acting under cost containment pressure, hospitals will discharge patients sooner than is clinically appropriate. However, the opposite effect is observed for 1991/1992. The negative [lambda]s conform with a different view in which poor hospital quality causes pro longed stays as patients get well more slowly. For example, adverse drug events (ADEs) have been found to be frequent and costly. One recent study estimates additional lengths of stay attributable to preventable ADEs to be 4.6 days with additional annual costs to a large tertiary care hospital of 2.8 million dollars (Bates et al. 1997).

The lack of consistency in the sign and significance of [lambda] restricts the drawing of any conclusions from the above speculation concerning the correlation between hospital quality and average length of stay. One possibility is that the true underlying relationship encompasses a variety of factors working in opposite directions and is too complex to characterize here. Alternatively, the assumptions about quality may be unwarranted. In particular, the individual hospital effect may be influenced by other important factors such as managerial efficiency. The correlated random effects model is not capable of disentangling such effects. It is acknowledged that our understanding of this issue is limited.

7. Conclusion

This paper raises the question of whether there has been an overresponse to cost containment pressures on the part of hospitals and insurers in their efforts at reducing the lengths of hospital stays. It provides a measure of the benefits (cost savings) associated with this practice. This follows from the results of a cost function estimation using panel data techniques for a sample of 2792 hospitals over the period 1987-1992. The elasticities of cost with respect to length of stay estimated using three different panel data methods suggest that only a small portion of overall cost containment during this period is attributable to shorter hospitalizations. The results indicate that the inpatient component of hospital output is better conceptualized as discharges rather than days. From a policy perspective, this suggests that strategies such as prospective payment and utilization review that serve to reduce the number of days of hospitalization may be less effective in substantially reducing costs than is comm only presumed. Evidence for a systematic relationship between the length of hospitalizations and the quality of care could not be established. Large clinical studies may be required to determine whether quality of care is eroding as managed care is permeating the health care system.

Since the time period reflected in this study sample, major changes have continued to occur in the market for health care. In particular, the nature of hospital services has become increasingly price competitive. Hospital days per capita have declined even further due to continuing reductions in both lengths of stay and numbers of admissions. One could speculate that current cost effects of reduced reliance on hospitalization are a continuation of those documented in this paper; however, the situation is not necessarily so straightforward. It is possible that the hospital days saved in the time period studied here were of lower acuity and therefore lower cost than reductions we are experiencing today. We may be looking at a moving target and it is possible that hospitals are now saving more money associated with higher acuity. It is important that this question be re-examined at a future date. In any case, economic benefits of reduced utilization must be considered in the context of total societal cost. Whil e the data requirements for quantitative analysis of such effects may be unavailable, it needs to be recognized that a portion of the cost of care may merely be shifted. The burden may be transferred to home health care or to skilled nursing settings, or even out of the health care sector altogether and onto patients themselves or their families.

As managed health care evolves into more integrated forms of delivery, so will hospital incentives for cost containment. Strategies will need to go beyond reduction in intensity of service and should focus on tactics such as improvements in hospital management and data systems, better information exchange among clinicians, and promotion of formal systems of clinical care. Such directions will be advantageous to delivery systems that are responsible for a more comprehensive continuum of care and in which the management incentives of both provider and payer are increasingly synthesized.

(*.) Management Science Group, U.S. Department of Veterans Affairs, 200 Springs Road, Bedford, MA 01730, USA; E-mail [e-mail].

The author thanks Jim Burgess and two anonymous reviewers for very useful comments. The views expressed here are those of the author alone and do not necessarily represent those of the Department of Veterans Affairs.

Received January 1999; accepted January 2000.

(1.) For more detail refer to Management Science Group (1993), chapter 3.

(2.) The specification is based on the statistic

m = ([[beta].sub.1] - [[beta].sub.2])'[([M.sub.1] - [M.sub.2]).sup.-1]( [[beta].sub.1] - [[beta].sub.2])

where [[beta].sub.1] are the parameter estimates and [M.sub.1] is the covariance matrix from the random effects estimation and [[beta].sub.2] and [M.sub.2] are the corresponding estimates from the fixed effects model.

(3.) Table 5 results follow from analytic calculations using the parameter estimates applied to each hospital's actual values and then averaging over hospitals.

(4.) The retransformation of predicted values to unlogged form are adjusted using the smearing estimate of Duan (1983).

(5.) Aggregation to the hospital level may augment the degree of bias due to hospital level omitted variables (Hanushek, Rivkin, and Taylor 1996).

(6.) This excercise was not performed for the fixed effects model that did not yield a significant elasticity value for beds.

References

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Appendix

American Hospital Association, Annual Survey of Hospitals

HCFA, Hospital Cost Report Information System File

HCFA, Medicare Case-Mix Index File

HCFA, Wage Index