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Which cost drivers drive cost in the hospital sector?

INTRODUCTION

This paper aims to explain some reasons for the low adoption rate of the Activity Based Costing method (ABC). In the first part, we will compare ABC and a method known as Homogeneous Sections. In the second part, we will examine the problem surrounding the choice of the cost drivers considered as the basis for cost allocation. In the ABC method, the resource consumption may be expressed by volume, complexity and efficiency-based variables, whereas in the Homogeneous Sections Method, only volume-based variables are used. Analysis of literature on the subject indicates that different results can be obtained when looking for the best cost drivers. In the third part of the article we will carry out an empirical study in the health sector. We analyse the cost function of Swiss and French hospitals. The objective is to find out how many and what types of cost drivers are necessary to explain the level of hospital indirect costs. We will see that the volume-based cost drivers alone explain the major part of the indirect cost variation. These results lead us to believe that the allocation of the indirect cost, based on volume criteria, is sufficient to produce realistic product costs.

COMPARISON BETWEEN ABC AND THE HOMOGENEOUS SECTIONS METHOD

The Homogeneous Sections Method is a full cost method that appeared in France in the 1930's. In this method, cost centres, called sections, correspond simultaneously to responsibility centres and to the economic functions of the company. The indirect costs are allocated to the cost centres according to allocation criteria such as the number of machine- hours, or the number of labour hours. The cost of every cost centre is allocated to products according to allocation criteria, called "unites d'oeuvre". These allocation criteria are supposed to represent services supplied by each cost centre.

The ABC procedure is similar to that of the Homogeneous Sections Method. The indirect costs are allocated to the cost centres, represented here by activities, according to allocation criteria, called resource drivers. The cost of activities is then allocated on cost objects according to other allocation criteria, called activity drivers.

To undertake this comparison between the ABC and the Homogeneous Section method, we will resort to the most frequently accepted definitions. Both methods can be brought down to the following formulation:

TC = Sum i (CC i)

Sum i (CC i) = Sum j (PCj),

where TC: total cost, PC: product cost and CC: cost centre

In both methods we proceed with a two-step allocation: in the first place the indirect cost is allocated to the cost centres. Secondly, the cost of cost centres is allocated to the cost objects with the help of the pre-defined allocation criteria. The mechanism of the two methods being the same, only the terms "cost centre" and "allocation criteria" change. In this paper we are going to concentrate on the analysis of the allocation criteria, and in particular on the reason for the introduction of multiple cost drivers in the cost function.

The notion of "activity driver" in the ABC method is similar to the notion of "unite d'oeuvre" in the Homogeneous Sections Method. However, both of them express the link between the cost centres and the cost objects, some differences subsist, especially in theory. In the Homogeneous Sections Method every cost object is supposed to consume resources in proportion to the volume or on the basis of the variable cost. "Unites d'oeuvre" that allow for the allocation of indirect costs are: the direct labour, machine-hours or the price of the material. This method can be criticised considering the increasing importance of indirect cost and more and more negligible weight of the variable cost. The allocation approach based on volume does not allow to distinguish between the products made in big quantities from those produced in small quantities, which makes them insensitive to economies of scale. The volume-based approach reflects neither the complexity of tasks achieved nor the efficiency of the organization producing a given product.

Proponents of the ABC method claim to be able to overcome these shortcomings by using three types of cost drivers expressing volume, complexity and efficiency and letting the actors themselves define those drivers. This freedom to choose and a larger definition of cost drivers are supposed to translate better how costs accumulate in a company. However, the fact of working with multiple cost drivers represents a source of measurement errors (Datar, S. & Gupta, M., 1994). To justify the introduction of the complexity- and efficiency-based variables, it is necessary that they improve appreciably the algebraic representation of the cost function. Therefore, it is about defining a certain number of possible cost drivers and observing what combination makes up the best approximation of the observed cost. To illustrate our problem, we analysed several articles dealing with the topic of the cost drivers.

ANALYSIS OF THE LITERATURE

We observe three tendencies in the literature concerning cost drivers:
1 Volume-based cost drivers alone are significant (Foster, G. & Gupta,
M., 1990).

2 Volume-based cost drivers determine the indirect costs, however the
complexity and efficiency cost drivers are significant and help to
refine the cost function (Banker, R.D. & Johnston, H.H., 1993),
(Ittner, Ch.D., Larcker, D.F. & Randall, T., 1997) and (MacArthur,
J.B & Stranahan, H.A., 1998),

3 Complexity and efficiency cost drivers are more determining in the
cost formation of costs that the volume-based cost drivers (Banker,
R.D., Potter, G., Schroeder, R.G., 1995) and (Datar, S., Kekre, S.,
Mukhopadhyay, T. & Srinivasan, K., 1993).


We compared these articles according to different conditions under which these studies were conducted. These differences appeared especially at the level of: the number and type of the chosen variables, the methods of analysis, the sample and the hypothesis on the shape of the cost function.

We noted that variables used to illustrate the volume-, complexity- and efficiency-based cost drivers seemed to be chosen according to the author's initial hypothesis. Two articles that came to conclusion that volume-based cost drivers do not explain the level and variation of the indirect cost (Datar, S., Kekre, S., Mukhopadhyay, T. & Srinivasan, K.,1993) and (Banker, R.D., Potter & G., Schroeder, R.G., 1995) have in common the use of only one volume-based variable, represented by the "Cost of the direct labour". This definition of volume seems far too narrow with regard to the number of variables used to describe the complexity and the efficiency. By choosing only one variable to represent the volume, the above-mentioned authors skew excessively the results of the studies.

After having analysed the problematic of choosing appropriate cost drivers, we wanted to compare different methods of analysis adopted in the six surveys. We noticed that only one article (Foster, G. & Gupta, M., 1990) use simple and partial cross-sectional correlations between indirect costs and volume, complexity and efficiency variables. In their survey only volume-based cost drivers prove to be significant, while complexity and efficiency cost drivers were not sufficiently correlated with the indirect costs. This procedure of selection has been extensively criticized (Banker, R.D., Potter & G., Schroeder, R.G., 1995), (MacArthur, J.B & Stranahan, H.A., 1998) and (Noreen, E. & Soderstrom, N., 1994) as it makes an implicit hypothesis of the cost function linearity. A widespread method to determine statistically significant cost drivers is the multiple regression method (OLS or 2SLS).

As for the type of the sample, authors agree to prefer working with time series rather than with cross-sectional studies (Banker, R.D. & Johnston, H.H., 1993) and (Ittner, Ch.D., Larcker, D.F. & Randall, T., 1997). Banker, R.D., Potter & G., Schroeder, R.G. (1995) claim that: In a cross-sectional research design, there is a potential for spurious correlations to generate associations that are not based on causal relations. Working with a cross-sectional sample results in supporting a hypothesis of a homogeneous production process throughout the sample (Foster, G. & Gupta, M., 1990). This implicit hypothesis can constitute another source of erroneous conclusions. To avoid this risk, when a time-series database is not available, it is preferable to work with a sample of companies in the same sector of activity and comparable in size, functioning and technologies used.

As for the hypothesis on the shape of the cost function, the most widely used functions to graph costs are either the logarithmic functions (Banker, R.D., Potter, G. & Schroeder, R.G., 1995) and (MacArthur, J.B & Stranahan, H.A., 1998), or the linear functions (Datar, S., Kekre, S., Mukhopadhyay, T. & Srinivasan, K., 1993). The Leontief technology gives rise to a linear cost curve, while the Cobb-Douglas technology gives rise to a log linear cost function (Christensen, J. & Demski, J.S. (1995). However, the linear cost function precludes the notion of economies of scale. Noreen, E. & Soderstrom, N. (1994) tested the reliability of the hypothesis of the linearity of the cost function in the hospital sector. Formally, the tested relation can be written as following: c = pqb, where p represents the average cost and q the volume of activity. This equation becomes: ln (c) = ln (p) + b*ln (q), where b represents the relation between the marginal cost and the average cost and corresponds to the slope coefficient. The coefficient b < 1 translates existence of the economies of scale. In their survey, the authors point to an existence of economies of scale. Therefore, the hypothesis of the linearity of cost functions should be rejected. It is necessary to notice however that Noreen, E. & Soderstrom, N. (1994) retained the activity measures selected by the Washington State Department of Health. The way these measures were chosen (for example for the cost centre "Public Relations", "Total revenue" has been chosen as the activity measure) and the way institutions of different size were grouped should allow to nuance greatly their conclusions, according to Nerlove's analysis on cost and production functions (Nerlove M., 1963).

After this brief synthesis of the research work conducted in the field of cost drivers, we are able to confirm that the choice of variables and methods of analysis can affect significantly the outcome of a study. Consequently, we can set aside the first tendency in the literature (Foster, G. & Gupta, M., 1990), which suggests choosing only one cost driver. We can also set aside the third literature trend (Datar, S., Kekre, S., Mukhopadhyay, T. & Srinivasan, K., 1993) and (Banker, R.D., Potter, G., Schroeder, R.G., 1995) for their very subjective choice of volume-based variables. Therefore, we retain, as basis for the empirical part of this article, the second current of literature (Banker, R.D. & Johnston, H.H., 1993), (Ittner, Ch.D., Larcker, D.F. & Randall, T., 1997) and (MacArthur, J.B & Stranahan, H.A., 1998), supporting the idea that volume-based cost drivers determine the indirect costs, and that the complexity and efficiency cost drivers are significant and help to refine the cost function. However, if the complexity complements an explanation of the cost function, its insignificant weight would ruin one of the theoretical foundations of ABC.

APPLICATION OF THE ABC TO THE HOSPITAL SECTOR

Model

Although the variable "number of patient-days" is still widely used to reimburse hospitals, it may be not appropriate as a unique indicator driving hospital costs. Indeed, a hypothesis can be tested that the cost of hospitalisation is driven by the complexity of the medical task as well as by the gravity of the illness. Therefore, if this hypothesis were satisfied, the ABC approach should be chosen as the cost accounting method best adapted for the hospital sector. On the contrary, if the hypothesis were not satisfied, the traditional methods, based on the volume cost drivers, such as number of admissions, number of patient-days or number of hospital employees could be used.

Using the database provided, for Switzerland, by the Office Federal de la Statistique (OFS) and for France by the Programme de Medicalisation des Systemes d'Information (PMSI), we are going to verify if the application of the ABC is justified in the hospital sector. Therefore, we are going to study what is the impact of different measurable variables on the evolution of the total costs.

For the two samples, we adopted a similar reasoning. Supposing the existence of the linearity of the hospital cost function, we constructed a model of the hospital total costs observed C while bringing in all observable variables Vi:

C = [alpha] + [Zigma] [beta]i * Vi

At the following stage we eliminated all correlated variables using the Variance Inflationary Factor (VIF) method (Levine, D., Berenson, M. & Stephan, D., 1999). Then we analysed among the retained independent variables those that were statistically significant. Afterwards, we defined the model providing the best approximation of the total costs observed while using stepwise regression approach. The Mallows Cp statistics confirmed our results. Finally, a complete analysis of the retained model, including the analysis of residues, was completed. We also verified the hypothesis of the cost function linearity.

Cost driver analysis in the Swiss hospital sector

We tested our model on short stay Swiss hospitals. Our sample is composed of 33 hospitals offering a capacity going from 39 to 240 beds and having produced between 11'400 and 75'000 patient days in 1998. To put together the sample we chose hospitals satisfying three criteria: a) hospitals that make their figures public, b) general medical and surgical short-term facilities, c) hospitals with total costs below 55 millions of Swiss francs. We worked with OFS figures from 1998, analysing in detail several possible costs drivers. After having eliminated all highly correlated variables, the explanatory, independent variables that have been kept in the model are the following: X1 Beds available (capacity cost driver), X2 Number of services (complexity cost driver), X3 Number of Doctors, X4 Number of Administration staff and X5 Number of Supporting staff (volume cost drivers).

We wished to develop a regression model that includes the fewest number of explanatory variables allowing an adequate interpretation of the dependent variable "Total costs". Regression models with fewer explanatory variables are inherently easier to interpret, particularly because they are less likely to be affected by the collinearity problem (Levine, D., Berenson, M. & Stephan, D., 1999). We chose to use the Stepwise Regression Approach to determine the subset of all explanatory variables that yield an adequate and appropriate model. We confirmed our results choosing among alternative regression models (Best-Subsets Approach) with the help of the statistic Cp developed by Mallows (Levine, D., Berenson, M. & Stephan, D., 1999). The most significant variable representing the hospital cost function is the variable X1 Beds available. Then, in decreasing order come the variables X4 Administration staff, X5 Supporting staff, X3 Doctors and X2 Number of services.

After having analysed the results we notice that the model, that constitutes the best approximation of the observed total costs, is the four variables model. In this model, all coefficients except the intercept are statistically significant and represent volume cost drivers. The result is that in the Swiss case it is sufficient to take into account only volume-based cost drivers to describe the hospital cost function.

To be sure that the linear shape of the function corresponds to reality, we tested the equation: ln (c) = ln (p) + [beta]*ln (q) (Noreen, E. & Soderstrom, N., 1994). The relation between the marginal cost and the average cost is very close to one (beta] = 0.965), what means that there is no observable economy of scale in the sample representing Swiss hospitals. It justifies the linear shape adopted for the cost function.

Cost driver analysis in the French hospital sector

After having analysed cost drivers in short-stay Swiss hospitals, we wanted to compare the results achieved with cost drivers resulting from a similar procedure applied on sample of French short-stay hospitals. We chose to work with data released by the French Programme de Medicalisation des Systemes d'Information (PMSI). The sample consists of complete records of 107 hospitals with less than 5500 discharges per year. We can classify the data in four categories: 1) the volume-based cost drivers, 2) the capacity-based cost drivers, 3) the complexity-based cost drivers and 4) the efficiency-based cost drivers. We eliminated all the correlated variables by calculating the coefficient VIF. Six independent explanatory variables have been kept: X1 Number of medical employees, X2 Number of non-medical employees (volume-based cost drivers), X3 Minimum number of cases accounting for 80% of patient days, X4 Percentage of cases where patients older than 80 years old, X5 Number of Dialyse sessions and X6 Number of other sessions (complexity-based cost driver). In order to define what is the best model explaining the cost level we used the stepwise regression method. The following table represents the best out of six possible cost functions (using the criterion of R square and the partial F-test criterion):

Therefore, we keep as being the best approximation of the full model, the five-variables model. The Cp statistic, measuring the differences of a fitted regression model from a true model, confirms the result obtained with the stepwise regression. In this cost function we notice that the volume-based cost drivers alone explain 89.34% of the budget variation. With the help of the coefficient of partial determination r2 we can measure the proportion of the variation in the dependent variable that is explained by each explanatory variable while controlling for the other explanatory variables. Keeping the complexity cost driver constant 85.12% of the budget variation can be explained by the variation in the number of medical and non-medical staff. If we keep the volume cost driver constant, 23.35% of the budget variation can be explained by the variation of complexity cost driver. This shows the predominant importance of volume-based cost drivers.

Finally, we tested if the linearity hypothesis is satisfied. The coefficient [beta], expressing the relationship between the marginal cost and the average cost is very close to one ([beta] =1,0397) and slightly superior from the coefficient found in the Swiss hospitals. This result justifies the linear shape that we chose to express the cost function in the French short-stay hospitals.

Comparison between Swiss and French hospitals

The two models representing the cost function in the Swiss and French hospitals are very similar. In both cases the volume variables are the most significant to describe the hospital total costs. Moreover, there are the variables related to the hospital staff (medical and nonmedical staff) that play the most important role. It is not astonishing considering the fact that personnel expenses weigh heavily (an average of 75%) in the total amount of hospital expenses.

The result of our study of Swiss and French hospitals confirms our conclusions of the literature analysis. Indeed, it is possible to explain the level and variations of hospital indirect cost with a model made of volume variables only. The R square is very high, which is a good indicator of the cost function adjustment. In the French example, adding complexity-based variables moves the R square upwards from 89.34% to 92%. In the Swiss example, volume variables alone have been retained in the model. This difference can be explained by the fact that the French database is detailed and contains much more complexity and efficiency variables that does the Swiss database. In Switzerland, the obligation to disclose the information relative to the hospital activity is still very recent (since 1997) and hospital administrators remain reluctant to reveal any more information that necessary.

CONCLUSION

The dominant trend of the literature on the cost drivers shows that the volume-based cost drivers have a determining weight in the process of cost formation, whereas the complexity and efficiency cost drivers exercise only a restricted influence.

Our analysis of the Swiss and French hospital sector allows us to point out that only four or five hospital characteristics explain major part of total costs supported by the hospital. The cost drivers having the most impact on the level of total costs are the volume-based cost drivers. The complexity variables play only a minor part. This formal conclusion goes against the ABC assumption, and makes one of its justifications disappear. Our conclusions are confirmed by an article by Datar, S. & Gupta, M. (1994):
 There has been little systematic analysis of why an ABC system with
 multiple cost pools, activity drivers and allocation bases
 generates more accurate product costs. (...) More complex
 allocation bases make measurement errors in the total units of cost
 allocation bases and in the units of cost allocation base assigned
 to each product more likely.


Christensen, J. & Demski, J.S. (1995) consider that complexity-based variables proxy for inappropriate grouping of some products and suppression of others in the cost function identification:
 [The Activity Based Costing], by not time indexing products, groups
 them into classes and also focuses on some of these product
 classes, while suppressing others. This suppression and grouping
 lead to the notion of non-volume cost drivers. [...] Viewed in this
 fashion, non-volume cost drivers are a natural result of extensive
 output aggregation and the resulting potential misspecification of
 the cost function.


Therefore, we conclude that ABC, as cost calculation method, is not appropriate for the hospital sector. Our conclusion is supported with arguments resulting from an analysis of literature on the subject and an empirical study. Indeed, introducing numerous cost drivers in a cost accounting system in order to explain the level of the total cost doesn't make the product cost more accurate. On the contrary, measure errors accumulate and the resulting product cost is marred by mistakes. Besides, the ABC method is based on the naive idea that all costs are direct, which leads to a certain level of incoherence. Indeed, either we have direct costs and the ABC method remains without purpose, or indirect costs exist and ABC resembles all other classical methods and their arbitrary allocation rules.

REFERENCES

Banker, R.D. & Johnston, H.H. (1993). An Empirical Study of Cost Drivers in the U.S. Airline Industry, The Accounting Review, 68 (3), 576-601

Banker, R.D., Potter, G., Schroeder, R.G. (1995). An empirical analysis of manufacturing overhead cost drivers, Journal of Accounting and Economics, 19, 115-137

Christensen, J. & Demski, J.S. (1995). The classical foundations of " modern " costing, Management Accounting Research, 6, 13-32

Datar, S. & Gupta, M. (1994). Aggregation, Specification and Measurement Errors in Product Costing, The Accounting Review, 69 (4), 567-591

Datar, S., Kekre, S., Mukhopadhyay, T. & Srinivasan, K. (1993). Simultaneous estimation of Cost Drivers, The Accounting Review, 68 (3), 602-614

Foster, G. & Gupta, M. (1990). Manufacturing overhead cost driver analysis, Journal of Accounting and Economics, 12, 309-337

Ittner, Ch.D., Larcker, D.F. & Randall, T. (1997). The Activity-Based Cost Hierarchy, production Policies and Firm Profitability, Journal of Management Accounting Research, 9, 143-162

Levine, D., Berenson, M. & Stephan, D. (1999). Statistics for Managers, Prentice Hall

MacArthur, J.B & Stranahan, H.A. (1998). Cost Driver Analysis in Hospitals: a simultaneous equations approach, Journal of Management Accounting Research, 10, 279-312

Nerlove M.(1963). Returns to scale in electricity supply, in C. Christ, ed., Measurement in

Economics: Studies in mathematical Economics and Econometrics in memory of Yehuda Grunfeld, Stanford University Press

Noreen, E. & Soderstrom, N. (1994). Are overhead costs strictly proportional to activity?, Evidence from hospital service departments, Journal of Accounting and Economics, 17, 255-278

Zofia Swinarski Huber, University of Geneva, Switzerland

Bernard Morard, University of Geneva, Switzerland
Table 1: Result of the stepwise regression in the Swiss sample

Variable Regression Standard t Test
 Coefficients Deviation > 2.0395

Intercept -387'819 1'153'780 0.3361
X1 71'763 24'741 2.9006
X3 109'710 37'106 2.9567
X4 373'966 101'080 3.6997
X5 153'361 37'993 4.0366

Variable p Value Global F
 < 0.05

Intercept 0.7393 111.40
X1 0.0072
X3 0.0063
X4 0.0009
X5 0.0004

Variable Multiple Standard
 [R.sup.2] Error

Intercept 0.9409 3'043'064
X1
X3
X4
X5

Table 2: Result of the stepwise regression in the French sample

Variable Regression Standard t Test
 Coefficients Deviation > 1.983

Intercept 3'853'424 3410'345 1.1299
X1 675'756 145'354 4.6490
X3 359'209 24'199 14.8443
X4 86'008 34'034 2.5271
X5 -241'111 68'643 3.5125
X6 19'8681 9'840 2.0192

Variable p Value Global F
 < 0.05

Intercept 0.2612 227
X1 0.0000
X3 0.0000
X4 0.0131
X5 0.0007
X6 0.0461

Variable Multiple Standard
 [R.sup.2] Error

Intercept 0.9183 6'150'338
X1
X3
X4
X5
X6
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Title Annotation:MANUSCRIPTS; Homogeneous Sections Method
Author:Huber, Zofia Swinarski; Morard, Bernard
Publication:Academy of Accounting and Financial Studies Journal
Geographic Code:4EUFR
Date:Jan 1, 2001
Words:4028
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