Capacity Utilization and Unit Variable Cost: Evidence from California Hospitals

Transcription

1 Capacity Utilization and Unit Variable Cost: Evidence from California Hospitals Ramji Balakrishnan Naomi Soderstrom Ernst & Young Professor Associate Professor W346 Tippie College of Business 419 UCB Leeds School of Business The University of Iowa University of Colorado Iowa City IA Boulder CO July 2006 Comments welcome We thank the State of California Office of Statewide Planning and Development for providing data. The second author gratefully acknowledges financial support of the German-American Fulbright Commission. We thank Mahendra Gupta, W. Bruce Johnson, Ranjani Krishnan, Mina Pizzini, Taylor Randall, and workshop participants at Arizona State University, University of Colorado, Michigan State University, Manukau Institute of Technology, National University of Singapore, University of Texas at Dallas, and Washington University for comments.

2 Capacity Utilization and Unit Variable Cost: Evidence from California Hospitals Abstract This paper uses data from California hospitals to test the validity of estimating variable costs as the product of unit variable cost and activity volume, when the firm is operating in its normal range of operations. Focusing on nursing costs, we find that unit variable costs increase reliably in capacity utilization, with the increase becoming significant even when the firm operates marginally above expected utilization. A variance-analysis like decomposition shows that managers appear to stretch resource usage (reduce hours and dilute mix) to combat higher wage rates. We also find differences in responses by hospital ownership, suggesting a strong role for incentives in determining the organizational response to increased utilization.

3 2 Capacity Utilization and Unit Variable Cost: Evidence from California Hospitals I. INTRODUCTION Management accountants often employ a linear model to predict expected costs. While accounting literature has extended the model in several directions, some fundamental characteristics remain. For example, we could view activity-based costing (e.g., Cooper and Kaplan 1992) as adding more terms to the fixed component of the basic cost model. Studies on the cost of congestion (e.g., Banker, Datar, and Kekre 1988, Balakrishnan and Soderstrom 2000, Gupta, Randall and Wu 2005) examine the validity of the linearity assumption beyond a threshold level. 1 However, all of these models estimate variable costs as the product of unit variable cost and activity volume, when the firm is operating in its normal range of operations. This paper examines the validity of this central feature of cost models. A linear model is acceptable as an approximation of the underlying cost function if the resulting error is small. The actual magnitude of this error is an empirical question. Organizations plan resource purchases for some expected activity level. Moreover, they usually purchase and consume resources in imperfect markets. Thus, increasing the availability of labor involves transactions costs. Acquiring additional raw material in spot markets or storing unneeded materials similarly triggers unanticipated costs, which increase the variable cost of operations. However, volume discounts and efficiency gains reduce unit variable cost as the scale of operations increases. Managerial incentives also might lead to actions that limit the error. Firms usually employ a linear model when calculating variances used in performance evaluation. A manager 1 We view studies such as Anderson (1995), which examine the cost of complexity, as examining interactive effects. Investigations of sticky costs (e.g., Anderson, Banker and Janakiraman 2001, Balakrishnan, Petersen, and Soderstrom 2004) posit an asymmetric curve for increases and decreases in activity levels. Noreen and Soderstrom (1994) examine the validity of the ABC model.

4 3 might therefore strategically alter the quantity and mix of inputs to counter higher spot prices, thus maintaining the constancy of unit variable cost. Our investigation complements arguments that underlie the concept of a relevant range. Garrison and Noreen (2000, 194) define the relevant range as that range of activity within which the assumptions about cost behavior made by the manager are valid. Horngren, Foster and Datar (2001, 35) define it as the normal activity level or volume in which there is a specific relationship between the level of activity or volume and the cost in question. These definitions set the boundaries of the relevant range in terms of cost behavior. Thus, we also could view this paper as examining the width of the relevant range. Is the assumption of a constant unit variable cost, which defines the relevant range, valid only for a short range of utilization or does it span the normal range of operations? Our tests employ data from 311 hospitals in the State of California over five years. We measure installed capacity as the number of available beds. Demand is the number of patient days, measured using industry-standard methodology to convert outpatient treatments to equivalent inpatient days. We reduce measurement biases by scaling the resulting capacity utilization for a hospital-year by the hospital s average utilization during the sample period. 2 Our tests focus on the cost of nursing, a direct cost that, in our sample, averages 15% of hospital operating costs. We focus on nursing costs because hospitals schedule nurses in 4-hour blocks and pay them only for hours worked. 3 These characteristics suggest that nursing costs are variable in patient volume. Thus, following the standard accounting model, nursing cost per patient day should be constant. 2 Inferences are unaltered when we scaled by maximum rather than average utilization. We view maximum utilization over five years is a reasonable estimate of practical capacity. 3 Hospitals usually exceed the guaranteed minimum number of hours per month. This floor serves to make nursing costs behave more like a fixed cost. If this feature of nursing cost dominates, unit cost should decrease in capacity utilization, which is opposite from our hypothesis.

5 4 After adjusting for factors such as ownership and teaching status, we find a reliably positive relation between capacity utilization and unit variable cost. This finding is robust to alternate measures of capacity utilization, restricted samples, and sensitivity tests. When we restrict the sample to lie within 20% of average utilization, a 10% change in capacity utilization triggers a 3.7% change in unit variable cost. Our finding underscores that the assumption of constant unit variable cost in the traditional cost models may not hold even when the firm operates within the normal volume of operations. We then partition observations into four groups. Observations designated as Slack and Congested years correspond to activity levels below 80% and above 120% of a hospital s average utilization during the sample period, respectively. The designation Low Normal (High Normal) marks observations that lie between % ( %) of average utilization. We find that relative to values obtained during Low Normal utilization, unit variable costs are reliably higher during High Normal and Congested years. We conclude that unit variable cost begins to increase reliably once operations exceed average values. This finding adds to the literature on the cost of congestion by showing that the threshold for the costs of congestion to manifest might be quite low. Stated differently, the relevant range, as defined by textbooks, does not likely span a firm s normal range of operations. In the spirit of variance analysis, we next explore the nature of the organizational response to higher capacity utilization. Suppose that an organization faces higher than expected resource prices (e.g., overtime premiums) because of higher demand. It could respond by decreasing the quantity of resources supplied and/or by altering the mix of inputs employed. When analyzing total cost, these features could offset each other, leading to no overall observed effect. Such a tactical response to manage current costs, however, could lower the quality of service,

6 5 thereby adding to future costs. This tradeoff is similar to that examined in the literature on the cost of quality (e.g., Atkinson, Hamburg, and Ittner 1994), where a firm trades off current investments to increase quality with future costs arising from product failure. We investigate three factors comprising the cost of providing nursing: personnel mix, resource intensity, and price. We document that while there is no change in the mix of nursing personnel, higher capacity utilization reduces the total number of nursing hours per patient day. We also find evidence of significantly higher wage rates for all levels of nursing personnel, as increased capacity utilization drives up demand. The increase likely arises from overtime premiums and hiring of temporary staff (see Banker and Hughes 1994). These findings hold whether we employ the full sample or restrict the analysis to years that lie within 20% of average utilization (reported). We conclude that, on average, hospitals try to manage the increased cost per unit resource by decreasing the intensity of resource usage. Our final research question investigates cross-sectional differences in organizational response. We examine two factors: variance in capacity utilization and the effect of ownership. A rich literature (e.g., Argyris 1994) examines the effects of experience on individual and organizational ability to cope with change. We investigate whether experience with varying levels of capacity utilization results in organizations making operational choices that differ from those made by others with operations that are more stable. Our investigation complements Anderson (1995), who shows that experience in managing a wide range of products reduces the adverse cost impact of product mix heterogeneity. Our data do not reveal any systematic differences in the response between the hospitals with stable operations and those with greater variance in capacity utilization.

7 6 Our investigation of ownership is motivated because of its influence on managerial incentives. For-profit hospitals most closely conform to the traditional economic view of an entity and managers in these hospitals often have profit-based incentive contracts (Brickley and Van Horn 2002, Roomkin and Weisbrod 1999). Broader social concerns drive managers in governmentowned hospitals, weakening the power of financial incentives (Tirole 1994). In addition, structural factors such as location (e.g., government hospitals tend to be located in poorer areas) and governance (e.g., government hospitals may have elected supervisors) constrain their acceptable set of responses for managing operating pressures. Not-for-profit hospitals lie between these two extremes. Like government hospitals, not-for-profit hospitals have social goals. However, unlike government hospitals that can rely on state funds, non-profit hospitals must generate a surplus to keep up-to-date on medical technology, improve services, and expand charitable care. Data from government hospitals do not exhibit the positive relation between utilization and unit variable cost. We infer that managers in these hospitals focus on maintaining unit variable cost within tight limits, perhaps because of bureaucratic controls and reporting systems. 4 Investigation of underlying factors reveals that wage rates per hour supplied increase for forprofit and non-profit hospitals but not for government hospitals. However, the number of nursing hours supplied per patient day reliably decreases only in for-profit hospitals. These results suggest that while managers in government hospitals use (perhaps exogenous) wage limits to control costs when utilization increases, managers in for-profit hospitals rely more on managing resource usage. We organize the remainder of this paper as follows. In section II, we develop our theory and hypotheses. We describe our data, empirical measures, and design in section III. We discuss results in section IV and offer concluding comments in section V. 4 We note that the difference between the kinds of hospitals is not significant at conventional levels.

8 7 II. THEORY AND HYPOTHESES A linear relation between activity volume and cost is the foundation for most cost models. Examples include the partitioning of costs into fixed and variable costs in the traditional Cost-Volume-Profit equation (cf., Garrison and Noreen 2002). Allocations of common costs to cost objects also maintain linearity; by construction, allocated costs are proportional to the number of driver units consumed by the cost objects. Activity-based costing models improve cost estimation by increasing the number and variety of cost pools for partitioning fixed costs, the cost drivers considered, and by paying attention to the distinction between the supply and demand for capacity resources (Copper and Kaplan 1992). However, all of these models compute total variable cost as the product of unit variable cost and activity volume. We posit that, within a firm s normal range of operations, unit variable cost might change because of changes in the prices or quantities of resources. Price premiums incurred for augmenting resource capacity at short notice increase direct costs (Banker and Hughes 1994). 5 Turning to resource demand, research in operations management (e.g., Delp et al. 2005; Fowler et al. 1997; Schoemig 1999) demonstrates a curvilinear relation between the throughput rate and cycle time. Even with ample capacity, increasing the throughput rate increases the cycle time for the average product. The intuitive argument is that higher capacity utilization reduces the firm s ability to absorb process variations, lowering efficiency and increasing cost. 6 In contrast, volume discounts might reduce unit variable cost as utilization (and therefore resource demand) increases. In addition, efficiency gains from learning also might reduce resource consumption as volume increases. Finally, managerial incentives might lead to actions 5 Extant accounting literature focuses on the costs of complexity or congestion. In particular, as Zimmerman (2003) argues, the unit cost curve becomes convex after capacity utilization crosses a threshold level. Balakrishnan and Soderstrom (2000) and Gupta et al. (2005) provide confirmatory evidence. 6 See Fry and Blackstone (1988) for a comprehensive review of the relation between capacity utilization and operating performance.

9 8 that reduce the variance between actual and the cost expected per the linear model. Seeking to reduce reported variances in the current period, managers could control actual costs by reducing resource usage and by shifting resource mix toward low cost inputs. In sum, the net effect on the magnitude of the deviation between actual and predicted costs is an empirical question, even if we restrict attention to operations within the firm s normal range of operations. In our health-care setting, nursing costs are a direct cost of operations. Hospitals aggressively seek to manage this cost component because nursing accounts for about 15% of operating costs. Thus, while many hospitals maintain a registry of nurses to call on, they usually schedule nurses in 4-hour blocks, meaning that these costs exhibit little fixity. Indeed, virtually all research on hospital cost structure (e.g., Balakrishnan et al. 1996) models a linear relation between nursing costs and the number of patient days. We conjecture that capacity utilization might affect nursing costs per patient day. Increased work hours triggered by additional demand might trigger overtime premiums, which increase cost. A national shortage of nursing staff means that it is not possible to expand the registry of nurses on call to meet peak demand. Some hospitals also employ temporary staff from nursing agencies to meet peak demand. However, studies show that agency (also known as temp or traveling ) nurses, who command premium salaries, are less efficient than staff nurses (PWC study 2003; First Consulting Group 2001). Use of agency nurses would inflate the nursing cost per patient day by increasing both the number of hours needed to supply the same quality of care and the cost per hour supplied. Volume discounts are unlikely in our healthcare setting. Efficiency gains too are unlikely; fatigue decreases efficiency and new personnel are usually less efficient than seasoned nurses. Even so, hospital managers could countervail increases in nursing costs by reducing, within lim-

10 9 its, the number of hours supplied per patient day. They also could substitute lower skilled (and lower compensated) Licensed Vocational Nurses (LVNs) and nurse aides for highly skilled (and highly compensated) Registered Nurses (RNs). 7 However, while such strategies might stem the increase, it is unlikely that they would result in overall lower nursing costs per patient day. We therefore hypothesize (in alternate form): H1: Nursing costs per adjusted patient day do not decrease with higher rates of capacity utilization. Congestion versus Capacity Utilization In analyses that augment H1, we explore the threshold at which the costs of congestion begin to appear. Congestion costs arise because organizations make investments in long-lived capacity resources, which define the organizations installed capacity. As Zimmerman (2003) observes, after capacity utilization crosses a threshold level, costs increase because high utilization lowers efficiency by reducing the ability to absorb process variations. Price premiums incurred for augmenting resource capacity at short notice add to this effect. Finally, the need for greater coordination in a constrained environment may also increase administrative costs. Banker, Datar and Kekre (1988) provide the formal background for Zimmerman s intuitive arguments. Using data from maternity wards, Balakrishnan and Soderstrom (2000) empirically show that congestion affects operating decisions; the rate of caesarian sections among select patient groups is higher in congested wards. In the context of a printing firm, Gupta, Randall and Wu (2004) show that congestion increases processing time and cost, while decreasing quality. Both of these papers set high thresholds for defining congestion (typically 90% of capacity) in their investigations. 7 Resource availability might constrain ability to substitute. A survey from the State of California (California Employment Development Department 2004) reports that 47% percent of employers say they have a somewhat or very difficult time finding experienced candidates for LVN positions; sixty-two percent of responses indicate the same for RN positions.

11 10 Our investigation complements the literature on the cost of congestion by examining cost behavior even when the firm operates within normal parameters. Specifically, we distinguish between facilities with high but normal utilization and congested facilities with unusually high utilization. Clearly, there is much in common in the factors driving change in the two subsets. However, the effects are likely convex in capacity utilization, leading to systematic differences in cost behavior in the two ranges for capacity utilization. We therefore explore (without positing formal hypotheses) the change in unit variable cost for different ranges of capacity utilization. This investigation sheds light on the threshold at which congestion costs begin to manifest. Sources of Variation Our second set of hypotheses investigates mangers cost management strategies. As noted earlier, managers could control costs by changing the quantity and mix of nursing hours supplied. It is unclear that managers could influence directly the wage rates or the overtime premiums paid to the different classes of nursing personnel. Consider the number of hours supplied. Increasing the number of patient-days proportionately increases demand for nursing staff. Indeed, demand may increase more than proportionately. Newer staff or agency nurses may exhibit lower efficiency, since they must learn hospital-specific policies and procedures. Finally, with more overtime, fatigue may affect efficiency. On the other hand, the ability to adjust service quality makes it possible to increase resources less than proportionately to the increase in demand. Such an action may be optimal if the hospital perceives the increased demand as temporary; bringing additional staff into the system results in transaction costs and there are regulatory limits on the amount of overtime worked. Nevertheless, hospital administrators also know that attempts to reduce nursing hours might actually increase total cost if the reduction compromises quality, thereby increasing the probability of large costs stemming from subsequent product failure (cf. Morse et al. 2003).

12 11 H2A: Increased capacity utilization affects the number of nursing hours per adjusted patient day. In settings with substitutable resources, a second avenue for cost control is altering the mix of inputs. The manager could alter the mix of resources toward those that are cheaper or are more readily available, even if the move is away from the optimal mix of inputs (given their long-term prices). Of course, such a move is costly. Needleman et al. (2006) show that diluting the nursing mix is not cost-efficient in the long term, as the change adversely affects a hospital s service quality. In our setting, a hospital may employ a greater number of Licensed Vocational Nurses (LVNs) rather than Registered Nurses (RNs) because there is a smaller pool of RNs and because LVNs command a lower wage, leading to a smaller premium (see California Employment Development Department 2004). H2B: Higher capacity utilization decreases the percentage of RNs relative to other types of nurses. Any increase in the quantity of resources used relative to planned quantities (whether the increase is proportionate or not) triggers the need for temporary augmentation of resource levels. As Banker and Hughes (1994) observe, such purchases are usually at premium prices, increasing cost. Thus, ceteris paribus, increased utilization should increase the average cost per nursing hour. In contrast, we expect any changes in the mix of nurses to reduce the wage rate as hospitals substitute away from higher wage RNs. We expect the primary wage effect to dominate for three reasons. First, because hospitals staff for an expected level of operations, higher utilization triggers overtime, increasing average wage rates. Second, the use of agency nurses increases cost, as these personnel command a significant wage premium. 8 Finally, medical guidelines restrict the extent to which LVNs could substitute for RNs. 8 While we include the theoretical argument, our dataset mingles the cost of agency nurses with professional fees paid to image technicians, labs, etc. We therefore exclude the costs but not hours from our analysis. Such exclusion

13 12 H2C: Higher capacity utilization is associated with a greater average wage rate for nursing. Experience Effects Attempts to manage current period costs by altering the quantity and mix of resources used have both direct and indirect costs. While the hospital realizes direct costs immediately, potential reduction in service quality can result in indirect costs. This tradeoff is similar in principle to the tradeoff in managing the cost of quality. The cost of quality literature classifies quality efforts into prevention and appraisal aimed at increasing outgoing quality, and the outcomes as internal and external failure. Data indicate that investments in prevention and appraisal have huge returns from reducing costs stemming from internal and external failure (e.g., Morse et al. 2003, ). In our context, reducing current period costs by reducing the number of nursing hours or diluting the mix of nursing quality potentially impairs service quality, which could trigger future costs. Because of this tradeoff, hospitals that experience high variance in capacity utilization may find it cost-effective to install mechanisms (e.g., develop an auxiliary or reserve list of registered nurses) that reduce the increase in wage rates. This mechanism may also allow them to avoid labor market-induced changes in the mix of nursing staff. High variance in utilization might also provide more experience in stretching existing resources to meet demand spikes. Such expertise could mitigate the need for additional labor hours, further reducing any inflation in average wage rates. Experienced hospitals may also have learned the threshold levels to which they could stretch resources without adversely affect quality. If these levels are low, these hospitals might optimally prefer not to stretch resources. We summarize this discussion with the following hypothesis. We do not predict a sign as we view this analysis as exploratory. decreases the power of our tests because these nurses earn premium wages (a majority of responding hospitals report 20% or higher premium), although they provide lower efficiency (First Consulting Group report to the AHA, 2001).

14 13 H3: Experience with varying levels of capacity utilization changes the relation between high utilization and organizational response. Ownership and Cost Management We next examine the relation between incentives (measured by organizational ownership) and the avenues chosen to manage costs. We categorize hospitals into three groups: forprofit, not-for-profit, and government owned. For-profit hospitals fit into the traditional economic view of an entity; their objective functions emphasize increasing owners value (Gray 1986). In order to align managers interests with those of the firm, many for-profits use incentive contracts with managers and link top management pay to financial performance (Brickley and Van Horn 2002, Roomkin and Weisbrod 1999). In addition, they have fewer institutional pressures from communities and government organizations. Thus, managers in these organizations are more likely to experiment with alternate profit-creating strategies, making these firms more nimble in their response to changing environmental conditions. Government hospitals are at the opposite end of the spectrum. These organizations have a more complex set of objectives, such as serving the indigent population, proving communitybased health education programs, and outreach, which weaken the power of financial incentives (Tirole 1994). Relative to the types of concerns faced by managers in for-profit hospitals, broader social concerns likely drive managers in these organizations. In addition, structural factors such as location (e.g., location in rural or poor areas) and governance (e.g., elected supervisors) place constraints on acceptable responses for managing operating pressures. Because of the complexity of their objective functions, institutional constraints, and differences in governance, these hospitals rarely use incentive contracting with top managers (Eldenburg and Krishnan 2003, 2005; Eldenburg et al. 2003). Finally, government owned hospitals are arguably less responsive

15 14 to financial pressures. These hospitals are often subject to soft budget constraints while the government will likely subsidize the hospitals following poor performance, the hospital also must remit any surpluses to the governing agency (Duggan, 2000). Thus, unlike for-profit hospitals, government hospitals could show a deficit for several years in a row without fear of a change in management. Not-for-profit hospitals are in the middle of the spectrum; they exhibit characteristics of both for-profit and government owned hospitals. Mission statements for not-for-profit hospitals often articulate social objectives, so profit is not the sole (or perhaps even primary) driver of managerial actions. However, not-for-profit hospitals (or their sponsoring charities) are selfsustaining organizations that cannot rely on subsidies for operations. Over the last few years, to encourage managers to exert effort on cost reduction and revenue enhancement, not-for-profit hospitals have begun to use compensation contracts that link pay to performance (Lambert and Larcker 1995; Eldenburg and Krishnan 2005). Empirical research shows that increases in incentive contracting cause managers in not-for-profit entities to act more like managers of for-profit entities (Leone and Van Horn 2005). Further, for the most part, not-for-profit hospitals cannot rely on donor support to fund on-going operations. Thus, revenue from operations must fund these costs. If not-for-profit hospitals incur losses, managers have similar pressures as for-profit managers, i.e., a need to return to profitability. In our context, the effect of the different incentives is unclear. Whereas low-powered financial incentives might lead managers in government hospitals into letting unit variable cost increase with utilization, mangers in for-profit hospitals might aggressively curtail any increase. However, a bureaucratic focus on current period costs might spur government hospitals to keep unit variable cost with pre-set limits, while a long-term view of costs by mangers in for-profit

16 15 hospitals might induce them to bear a current increase to lower future costs. We therefore do not make a directional prediction for the following hypothesis. H4: Hospital ownership moderates the relation between capacity utilization and unit variable cost. III. MODEL DEVELOPMENT & DATA In this section, we first describe measurements of our theoretical constructs and the models we employ to test the predicted relations. We then describe the data. Hypothesis 1: Unit Variable Cost and Capacity Utilization The dependent variable for this test is nursing cost per adjusted patient day. The numerator for this metric is total nursing compensation. Our measure includes the cost of float nurses (not assigned to any particular unit), but excludes amounts paid to nursing administrators and agency nurses. We do not distinguish among the types of nurses (e.g., RN, LVN, nurse aides) for this test of aggregate cost impact. We scale all dollar-denominated cost variables by the annual Metropolitan Statistical Area-level wage index to control for cost differences across regions and time. The denominator is the number of adjusted patient days, where the adjustment accounts for the proportion of outpatients. While they consume nursing and other medical services, these patients do not occupy in-patient beds. Ignoring outpatients would therefore severely understate the demand for nursing staff and inflate cost per patient day. The industry-standard methodology is to measure demand as adjusted patient days, grossing up inpatient days by the ratio of outpatient to inpatient gross revenue. Our independent variable of interest is capacity utilization. However, the wide range of resources used to treat different kinds of patients makes capacity difficult to measure. The traditional measure for capacity is the number of hospital beds (cf. Staten et al. 1988, Fenn et al. 1994, and Gaynor and Anderson 1995). This metric is also highly correlated with other measures, such as the number of physicians and hospital size. (An exploratory factor analysis identi-

17 16 fies a single factor explaining over 86% of the variance.) Finally, as we expect, the number of beds in a hospital changes little over the sample period, meaning that changes in demand are the primary cause for changes in utilization. 9 We measure utilization as the number of adjusted patient days per available bed. For convenience in presentation, we divide this measure by 365 to obtain the percent of occupied days (CapUtil). This raw metric has two deficiencies. First, the process of adjusting demand for outpatients means that ceteris paribus, hospitals with a greater proportion of outpatients would score higher on our raw measure of utilization. (We later report extensive sensitivity tests related to this deficiency.) Second, the normal range of operations, our construct of interest, might also systematically differ across hospitals. For example, one hospital might expect to experience average utilization of 85% while another might plan for average utilization of 65%. We address both issues by using each hospital as its own control. In particular, we obtain a measure of scaled capacity utilization (Scaled CapUtil) by dividing raw capacity utilization by the hospital s average utilization over the sample period. (Note that this scaling makes division by 365 days superfluous.) Scaling by the mean allows us to define capacity utilization relative to a point in the center of the normal volume of operations. We conduct sensitivity tests that scale the raw value by the median or maximum value. Scaling by the maximum might be justified by arguing that the maximum utilization proxies for the hospital s practical capacity (Cooper and Kaplan 1992). 10 We include several control variables to correct further for systematic differences across hospitals. First, we control for patient mix by including the percent of inpatients (Pctinp), the 9 Considering the range of the change in installed beds during the sample period, the median change in available beds is seven and the inter-quartile range is 25. However, three hospitals had changes of over 100 beds. Omitting these observations does not change results. 10 Scaling also reduces any effect due to having adjusted patient days in the both the denominator of the dependent variable and in the numerator of the raw measure. We also note that any residual effect biases against results.

18 17 complexity of services provided (Casemix), and the percent of days in Intensive Care Units (ICU days). All of these factors increase the average nursing cost per patient day. These metrics also increase the demand for skilled nursing staff such as RNs. Second, we control for factors representing the mix of payors: Medicare (%Medicare) and MediCal 11 (%MediCal) percentages. We do so because the amount and intensity of delivered care might vary across patient groups. We also adjust for average length of stay (alos) because the intensity of nursing required usually declines after the initial contact. Finally, prior literature (cf. Eldenburg and Soderstrom 1996; Leone and Van Horn 2005; Krishnan and Eldenburg 2003) shows that organizational characteristics affect operating choices and cost structure. Accordingly, we control for ownership (Not-forprofit, For-profit and Government), teaching status (Teaching versus non-teaching), whether the hospital is a member of a hospital system (System versus non-system), and size (Licensed beds). The model we estimate is: Nursing cost per adjusted patient day = β 0 + β 1 Scaled CapUtil + Controls + ε (1) where the dependent variable is nursing cost per adjusted patient day and other variables are as defined above. The traditional model asserts that β 1 = 0. Our alternate hypothesis is β 1 > We augment H1 with analyses that explore the threshold at which cost effects manifest. We use the labels Slack and Congest to denote observations that lie below 80% and above 120% of average utilization, respectively. In addition, we denote observations between 80 to 100% (100 to 120%) of average utilization as falling in the Low Normal and High Normal range. With these definitions, and using Low Normal as the baseline case, we estimate: Nursing cost per adjusted patient day = β 0 + β 1 Slack +β 2 High Normal 11 MediCal is Medicaid for the State of California. 12 Notice that the presence of any fixed cost in the dependent variable would bias against results. We also estimated the model in levels with total nursing cost as the independent variable and demand as an independent variable. The coefficient on the interaction between demand and capacity utilization is then the construct of interest. Results are qualitatively similar.

19 18 + β 3 Congest + Controls + ε (1A) Based on the literature on the cost of congestion, we expect β 3 > 0. A reliably positive value for β 2 indicates that costs begin to increase even if capacity constraints are not binding. That is, merely increasing capacity utilization is enough for unit variable costs to increase. With respect to β 1, to the extent that nursing contains some fixed costs, increasing capacity utilization from very low levels could lead to a decline in the cost per activity unit. However, the other arguments for increasing costs, advanced earlier, also apply. In sum, we do not make a directional prediction for β 1 and β 2. Hypothesis 2: Sources of Variation While the model in equation (1) helps detect if capacity utilization affects unit variable cost, it is not useful in detecting the mechanism by which these incremental costs manifest. The model resembles an aggregate variance, which might mask the effects of individual variances. We decompose nursing costs by examining the effect of capacity utilization on the total supply of resources (nursing hours), on the price per unit resource (higher wage rates), and the mix of resources employed (percent of nursing hours by RNs). 13 hours: We investigate changes in levels of resource utilization through examination of nursing NHoursPD = β + β ScaledCapUtil + Controls +ε (2A) 0 1 where NHoursPD is the total number of nursing hours per adjusted patient day. From H2A, we expect β 1 0 because utilization rates likely affect the efficiency of operations. We examine the changes in resource mix by estimating the following: 13 Managers likely make quantity and mix choices simultaneously taking wage contracts and labor market conditions as exogenous. While this argument calls for a system of equations, the decision process is likely complex, meaning that any system would be necessarily incomplete and ad hoc. As a preliminary analysis, we therefore estimate independent effects. Our approach is similar to variance analysis, which turns one dial at a time.

20 19 Mix = β + β ScaledCapUtil + Controls +ε (2B) 0 1 where Mix is the percentage of nursing hours from Registered Nurses. From H2B, we expect the main effect to be negative; i.e., β 1 < 0. Finally, we estimate price changes by regressing the average wage rate, overall and by type of nursing resource, on capacity utilization. Wagerate = β + β ScaledCapUtil + Controls +ε (2C) 0 1 where Wagerate is average wage per hour for the nursing staff. We expect β 1 > 0. Hypothesis 3: Experience Effects Our next analysis examines cross-sectional differences stemming from experience with differing levels of utilization. Based upon the sample median, we partition hospitals into two groups: High and Low variance in operations. We measure variance in utilization as the variance in the Scaled Capacity Utilization (which by construction has a mean of 1). Using a 0-1 dummy variable to denote the two groups, with High variance observations having value 1. We estimate: Nursing cost per patient day = β 0 + β 1 Scaled CapUtil + β 2 Dummy +β 3 Dummy Scaled CapUtil + Controls + ε (3) We do not make a directional prediction for β 2 or β 3 because we view this analysis as exploratory. Hypothesis 4: Effects of ownership Our final model tests for cross-sectional differences arising from differing incentives. Ownership is our proxy for the strength of monetary incentives. We group hospitals into forprofit, not-for-profit and government hospitals. We then estimate: Nursing cost per patient day = β 0 + β 1 Scaled CapUtil +β 2 For-profit + β 3 For-profit Scaled CapUtil + β 4 Government + β 5 Government Scaled CapUtil + Controls+ ε (4) where For-profit = 1 if the hospital is for-profit, and zero otherwise; Government = 1 if the hospital is government-owned, and zero otherwise.

21 20 In equation (4), not-for-profit hospitals are the baseline because we expect their behavior to lie between the two extremes occupied by for-profit and government hospitals. As with model (3), we do not make directional predictions, viewing this analysis as exploratory. Tests Our panel dataset raises concerns regarding heteroskadasticity and sample dependence. We reduce the effect of heteroskadasticity by scaling the dependent variable by adjusted patient days (see Barth and Kallapur 1996). To mitigate the sample dependence problem, we report Huber-White robust standard errors (Rogers 1993, generalizing White 1980). This maximumlikelihood estimation procedure assumes and estimates a common component of the variance and co-variance matrix for all observations from the same hospital and the standard errors are robust to heteroskedasticity and serial correlation (StataCorp 1999, 257). We also perform diagnostic tests for influential observations and multi-collinearity. We estimate all regressions after deleting observations whose values fall below (above) the 1 st (99 th ) percentile of the distribution for the relevant dependent variable. Inferences are unchanged if we omit identified influential observations. Multicollinearity does not appear to be a problem in our analyses as all condition indices are below 10. Data Our dataset consists of annual account-level data for 311 short-term general hospitals in California for fiscal We obtain the data from the California Office of Statewide Health Planning and Development, which requires hospitals to submit extensive financial data on an annual basis. We omit hospitals with fewer than 50 beds and district hospitals from the sample, as the capabilities, cost, and staffing patterns in these hospitals may differ significantly from other hospitals. (See also Eldenburg and Krishnan 2003.)

22 21 Descriptive Statistics As reported in panel A of table 1, the average hospital has 246 beds, provides approximately 66,000 adjusted patient days over the year, and incurs annual operating expenses of over $81 million. Average capacity utilization (CapUtil) is 74 percent, indicating that on average, a bed is occupied for 270 days out of the year ( days). The maximum value for this measure of capacity utilization (not tabled) exceeds 100%. This counter-intuitive feature obtains because we use adjusted patient days in the numerator and beds in the denominator. As discussed earlier, the presence of outpatients increases the numerator but not the denominator of the capacity utilization metric, enabling the raw utilization metric to exceed 100%. We accordingly scale the metric with the hospital s average value during the sample period. The scaled metric ranges from 0.33 to 1.6, indicating wide variation in capacity utilization. In the sample, 93.3 percent of hospitalyear observations fall within 20% of the average value for the hospital. We define the normal range of operations as years where 0.8 < Scaled CapUtil < 1.2. (Defining the range as 0.9 < Scaled CapUtil < 1.1, which includes 73% of observations, weakens the results but does not change inferences.) Average nursing cost (adjusted by the local index) is $11.97 million, with a median of $8.31 million. Nursing cost constitutes on average 15% of total operating expense. The average hospital receives approximately 71% of its revenue from inpatients. Medicare and MediCal make up a significant portion of hospital activity. On average, 39.8% of hospital patient days are for Medicare patients and 22.7% of patient days are for MediCal patients. Average length of stay is just under six days. While a majority of the hospitals report zero days in the ICU, the average proportion of ICU days is 3%.

23 22 As reported in panel B of table 1, most hospitals are not-for-profit organizations (166 of 311). The sample also includes 123 for-profit and 22 government-owned hospitals. Teaching hospitals, defined as any hospital that offers a residency program, comprise about 30% of the sample (95 hospitals). (Defining teaching hospitals as organizations affiliated with a University does not alter results.) Finally, a vast majority (70%) belong to a system of hospitals. IV. RESULTS Table 2 reports results from estimating equation (1). Referring to the first column, our primary finding is that unit variable cost increases with capacity utilization (Scaled Capacity Utilization) for nursing cost per patient day. This finding is qualitatively unaltered when we use maximum utilization as the scaling variable. 14 Other estimates in tables 2 are consistent with intuition and prior research. Relative to not-for-profit hospitals (the base case), for-profit hospitals, on average, have lower nursing expenses per day. An obvious explanation is that there are differences in incentive compensation across hospital types. Greater complexity in operations (as measured by Casemix) and the proportion of days in the ICU increase the cost per adjusted patient day. The average length of stay correlates negatively with cost. The first part of a patient s hospital stay tends to be the most resource-intensive, as the latter portion consists primarily of room, board, and monitoring the patient s progress. The percent of patients from government programs such as Medicare and Medi- Cal correlates negatively with costs, perhaps because these programs are prospective payment systems, which impose more intense cost pressure. The lower cost could also stem from a difference in the nature of services required or provided for patients from these programs, who are either the elderly (Medicare), or poor (MediCal). Finally, these patients tend to experience longer 14 We also examined the behavior of nursing administration costs, which are likely fixed. We obtain significant decline in costs only when we scale by maximum utilization.

24 23 lengths of stay, which correlates negatively with nursing costs, as service intensity is very high during the early part of a patient s stay. We report sub-sample analyses in panel A of table 3. We first restrict operations to lie within the relevant range (0.8 < Scaled CapUtil < 1.2). In this range, a 10% change in utilization leads to a 3.7% change in unit variable cost. (The numerator is $ , and the denominator of $ is the prediction at the average of all other independent variables.) Next, we mitigate concerns about the adjustment for outpatients. We estimate equation (1) considering observations that are in the bottom quartile of outpatient revenue. (No hospital in our sample has zero revenue from outpatients.) Finally, in untabled results, we explore alternate measures for capacity utilization. This measure constructs equivalent inpatient days by setting five outpatient visits equal to one inpatient day. (We also tried four and six visits as the conversion rate.) Inferences are unaltered in all instances. Panel B of table 3 reports additional sensitivity tests. Data reported in the first column indicate that differences in the absolute level of (raw) capacity utilization do not drive the result. There is no detectable difference between hospitals with high and low scores (relative to the median value) on the raw utilization measure (CapUtil). Second, the result is robust to patient mix. Partitioning the observations by whether the percent revenue from outpatients is high or low reveals no differences. Finally, we consider alternate measures of demand, and separately estimate the effect from inpatient days and outpatient visits. We find that demands from inpatient care drive the result. Threshold for Cost Effect Table 4 presents analyses that seek to determine thresholds where capacity utilization begins to affect nursing costs. Column 1 reports the analysis with an indicator variable only for Congest observations. Consistent with literature (Balakrishnan and Soderstrom 2000, Gupta et al.

25 ) we find that costs (variable in our case but total in earlier studies) increase reliably with very high utilization. Data in the next column break out observations from the slack years but shed little additional light. The final column has the observations in the Low Normal years as the base. Relative to this baseline, both High Normal and Congest observations exhibit reliably higher costs. This finding suggests that the costs of congestion might begin to manifest even when utilization is somewhat above average and where capacity constraints are unlikely to be binding. There is weak evidence (the difference between High Normal and Congest is weakly significant, p=0.07, one-sided test) that the rate of increase accelerates as we experience greater utilization. Sources of Variation Table 5 presents analyses that disentangle the cost effect of capacity utilization for nursing costs. We confine analyses to observations that fall within our definition of the normal range of operations (0.8 < Scaled CapUtil < 1.2). Inferences are similar when we use the full sample. Results pertaining to the use of nursing hours provide evidence of lower intensity of resource utilization due to extent of capacity utilization: the coefficient on Scaled CapUtil is significantly negative (p < 0.01). As detailed earlier, while our dataset records the hours provided by agency nurses separately, it mingles costs for agency nurses with other professional fees. Including the hours supplied by agency nurses does not change the results, although the statistical significance is lower (p = 0.06). Because agency nurses are perceived to be less efficient than staff nurses (First Consulting Group, 2003), we interpret these results as the hospital cutting back on the quantity of nursing hours supplied. Results reported in the second column of table 4 indicate that increased capacity utilization does not change the mix of resources used We do find a reduction in the use of RNs when we use the raw utilization measure, however.

26 25 Results in the third column indicate that hospitals with higher utilization report a reliably higher wage per nursing hour (p < 0.001). Wage rates for all categories of nurses show similar behavior; this finding holds when we estimate wage rates individually for RNs, LVNs, and Nurse Aides (results not tabled). In all three models, coefficients for control variables are broadly consistent with literature. Greater complexity (Casemix, ICU days) increases nursing hours and the mix of nurses, while payor mix (Medicare, MediCal) and average length of stay (alos) exert a downward pressure. For-profit hospitals seem more aggressive in controlling the quantity of supply, although they supply a mix that is more highly skilled. Collectively, these results suggest that hospitals experiencing increased capacity utilization alter their resource utilization to control current costs, but cannot eliminate cost increases. Moreover, because reducing hours supplied likely reduces service quality, the results suggest that the entire cost impact of these decisions may not be felt immediately. Experience Effects We next examine whether experience with varying capacity utilization influences a hospital s choices for managing resource scarcity, thereby affecting the relation between capacity utilization and unit variable cost. Recall that each hospital in the sample has a mean value of 1 for scaled utilization (Scaled CapUtil). We partition hospitals into High and Low variance groups, based on their actual variance relative to the median value for the variance across hospitals. To increase confidence in our variance estimates, we restrict this analysis to hospitals with data for the entire sample period. Results reported in table 6 do not indicate a difference in behavior across these two groups of hospitals.