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Hotel and Dependency Costs of Residents in Old People's Homes

  • Bleddyn Davies and Martin R. J. Knapp

Abstract

A comparison of costs to the organization of alternative forms of care requires estimates for similar types of client. The degree of dependency is the main characteristic in which comparability is necessary with regard to services for the aged. This paper presents estimates of the costs incurred in providing residential care for clients of four degrees of incapacity for self-care – the capacity implicit in Bevan's residential hotel model of the old people's home, and three progressively more severe states of dependency. The estimates are for two cost concepts – average (unit) costs and marginal costs (the cost of caring for an additional person). The paper also estimates both long-run costs (costs that it is appropriate to take into account in decisions in which capital investment in new plant is being considered), and short-run costs (costs that it is appropriate to consider when the issue is the allocation of existing capacity between client groups). It also examines the consequences of the size of the home with regard to costs. Inter alia the paper shows:

(a) that the size of home beyond which costs do not fall with scale provides for as many as fifty places (equivalent to an average daily census of forty-six residents); and

(b) that, although the dependency components of costs are much smaller than the hotel components, dependency costs are large enough for it to be important to base comparisons of alternative forms of care on estimates of costs for clients which are comparable with respect to dependency.

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1 Davies, B. P., Planning Resources for Personal Social Services, James Seth Memorial Lecture for 1971, Bookstall for University of Edinburgh, London, 1972.

2 House of Commons Debates, Session 1947–1948, Vol. 444, col. 1,609.

3 Ministry of Health Circular 87:48, para. 35.

4 Ministry of Health Circular 3:55, para. 8.

5 Ministry of Health, Annual Report 1948–9, p. 311; and Circular 150:48, para. 4.

6 Deeble, J., ‘An Economic Analysis of Hospital Costs’, Medical Care, 3 (1965), 138–46; and Hurst, J. W., ‘Variations in Recurrent Costs for In-Patients by Length of Stay and Speciality’, mimeograph, Economic Advisor's Office, DHSS, London, 1975.

7 Wager, R., Care of the Elderly, Institute of Municipal Treasurers and Accountants, London, 1972.

8 See Kimbell, A., Townsend, J. and Bye, P., ‘A Report of a Census of Residents in Homes for the Elderly in the East Division of the County’, mimeograph, Social Services Department, Cheshire County Council, 1974; and Kimbell, A., Townsend, J. and Bird, M., ‘Elderly Persons' Homes: A Study of Various Aspects of Regime and Activities in Elderly Persons’ Homes and their Effect upon the Residents’, mimeograph, Social Services Department, Cheshire County Council, 1974.

9 DHSS, The Census of Residential Accommodation, Part I: Residential Accommodation for the Elderly and for the Younger Physically Handicapped, HMSO, London, 1970; see also Hutton, D. S. S., Imber, V. and Mitchell, H. D., ‘Personal Social Service Statistics’, Journal of the Royal Statistical Society, Series A, 137 (1974), 483531.

10 See Williams, R. G. A., Johnston, M., Willis, L. A. and Bennett, A. E., ‘Disability: A Model and Measurement Technique’, British Journal of Preventive and Social Medicine, 30 (1976), 71–8; and Bebbington, A. C., ‘Scaling Indices of Disablement’, British Journal of Preventive and Social Medicine, 31 (1977), 122–6.

11 See for example Ward, P. R. and Morgan, D. C., ‘Proposals for a Questionnaire for Use in the 1976 Census of Residential Accommodation’, Dependency Project Paper no. 1, University of Exeter, 1976; and Neugarten, B. L., Havighurst, R. J. and Tobin, S. S., ‘The Measurement of Life Satisfaction’, Journal of Gerontology, 16 (1961), 134–43.

12 Wager, op. cit.

13 See Hirsch, W. Z., ‘The Supply of Urban Public Services’, in Perloff, H. S. and Wingo, L. (eds), Issues in Urban Economics, Johns Hopkins University Press, Baltimore, 1968.

14 Total operating cost consists of expenditure on staff; maintenance and repair; fuel, light and cleaning; furniture and fittings; rates; equipment and tools; materials; personal needs; provisions; and laundry, clothing and uniforms.

15 See Griliches, Z., ‘Cost Allocation in Railroad Regulation’, Bell Journal of Economics and Management Science, 3 (1972), 2641; and Casson, M. C., ‘Linear Regression with Error in the Deflating VariableEconometrica, 41 (1973), 751–9. Contrariwise one must be careful to avoid the multicollinearity and heteroscedasticity problems when taking total cost as the regressand. Multicollinearity refers to the situation in which some or all of the explanatory variables in a linear regression are highly collinear. The effect on parameter estimation is not to introduce biases but to reduce the precision of estimation, making it difficult to disentangle the relative influences of the various regressors. In our estimated equation multicollinearity did not appear to be much of a problem. A simple ‘test’ for multicollinearity – regressing each explanatory variable on all others – revealed only weak interrelationships (see Farrar, D. E. and Glauber, R. R., ‘Multicollinearity in Regression Analysis: The Problem Revisited’, Review of Economics and Statistics, 49 [1967], 92107).

16 Casmas, S. T., ‘Inter-Hospital and Inter-Local Authority Variation in Patterns of Provision for the Mentally Disordered’, unpublished doctoral thesis, Institute of Science and Technology, University of Manchester, 1976; and Wager, op. cit.

17 Unfortunately, in his analysis of thirty-six homes in Essex, Wager dropped from his sample six homes either because at least half of their residents were classified as ‘elderly mentally infirm’ or because they were particularly large, with high running costs. We did in fact re-estimate his cost function, including in the sample the three homes previously judged to be ‘too large’, and found that an average cost curve consistent with our own cubic total cost function fitted the data far better than a simple linear form. Wager's working hypothesis of monotonically decreasing average costs must thus be rejected. We have also found that a cubic total cost function applies to a sample of old people's homes in Kent (see Knapp, M. R. J., ‘Economies of Scale in Residential Care’, PSSRU Discussion Paper no. 63, University of Kent at Canterbury, 1977) and to community and other homes for children in a single authority (see Knapp, M. R. J., ‘Instrumental Variable Estimation of a Dynamic Cost Function for Children's Homes’, PSSRU Discussion Paper no. 68, University of Kent at Canterbury, 1977).

18 See for example Friedman, M., ‘Comment on C. A. Smith “Survey of the Empirical Evidence on Economies of Scale”’, in Stigler, G. J. (ed.), Business Concentration and Price Policy, Princeton University Press, Princeton, 1955; Hall, M. and Winsten, C. B., ‘The Ambiguous Notion of Efficiency’, Economic Journal, 69 (1959), 7186; Johnston, J., ‘Statistical Cost Functions: A Reappraisal’, Review of Economics and Statistics, 40 (1958), 339–50; Johnston, J., Statistical Cost Analysts, McGraw Hill, New York, 1960; and Walters, A. A., ‘Production and Cost Functions’, Econometrica, 31 (1963), 166.

19 Davies, B. P., Barton, A. and McMillan, I., ‘The Silting-Up of Unadjustable Resources and the Planning of Personal Social Services’, Policy and Politics, 1 (1973), 341–55.

20 Missing from the model are data pertaining to factor price levels and the physical structure of homes. Variations in factor prices are unlikely to be great between homes in a single county. The omission of data about physical characteristics of homes is more serious, as we have already argued. The effect of these omissions is to bias downwards the estimated coefficients in the model.

21 For evidence on the relationship between size of home and physical design see Knapp, M. R. J., ‘The Design of Residential Homes for the Elderly: An Examination of Variations with Census Data’, Socio-Economic Planning Sciences, 11 (1977), 205–12.

22 Feldstein, M. S., Economic Analysis for Health Service Efficiency, North Holland Publishing Company, Amsterdam, 1967, p. 95. A further reason for preferring dependency proportions to numbers was that, while the number of residents at the time of the survey may have been considerably larger or smaller than the average number of residents during the year, the dependency proportions will probably have been fairly steady throughout the period. Instrumental variable estimates were also computed and were found to differ only slightly from the ordinary least squares values. Details of this and other technical aspects of the analysis are available upon request from the authors.

23 Conventionally, the correlation coefficient about the mean is reported. Strictly, however, it is the coefficient about zero which should be used as an indicator of goodness-of-fit. See Stewart, J., Understanding Econometrics, Hutchinson, London, 1976.

24 We assume below that existing homes may be closed down in the short run. This asymmetry characterizes the normal working of local authorities and is in no way inconsistent with economic theory.

25 Wager, op. cit.

26 The dependency cost function is differentiated with respect to H, A, L and M in turn, and the denominator of each is changed from N to RW through the use of a suitable factor of conversion. (A regression of RW on N yielded the conversion equation: RW=52.14N with R2=0.98.)

27 This dramatic discontinuity in the marginal cost function raises a number of theoretical and practical problems, many of which are being considered in the context of the Kent Community Care Project (see Davies, B. P., ‘The Kent Community Care Project: The Principle of the Scheme and its Evaluation’, KCCP Project Paper no. 1, PSSRU, University of Kent at Canterbury, 1976).

28 See Davies, , ‘The Kent Community Care Project’.

29 See Feldstein, op. cit.; and Verry, D. M. and Davies, B. P., University Costs and Outputs, Elsevier, Amsterdam, 1975.

30 We should be pleased to re-analyse better secondary data, if such are available, and even more pleased to participate in a special collection of such data.

31 Meacher, M., Taken for a Ride, Longman, London, 1972; and Townsend, P., The Last Refuge, Routledge and Kegan Paul, London, 1962.

32 See Billis, D., ‘Managing to Care’, Social Work Today, 6:2 (1975), 3843.

33 The theoretical issues here are not simple, and this is not the place to raise them. Interested readers are referred to any of the numerous texts on cost-benefit analysis for further discussion. In particular, see Layard, R. (ed.), Cost-Benefit Analysts, Penguin Books, Harmondsworth, 1972, pp. 4451; and S. A. Marglin, ‘The Opportunity Costs of Public Investment’, Quarterly Journal of Economics, 77 (1963), 274–89, reprinted in Layard, op. cit.

* Director of the Personal Social Services Research Unit (PSSRU), and Professor of Social Policy, University of Kent at Canterbury

Research Fellow in the Economics of the Personal Social Services, University of Kent at Canterbury.

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