^{page 141 note 1} Olson, M., ‘Social Indicators and Social Accounts’, in Socio-Economic Planning Sciences (Oxford), II, 1969, pp. 335–46.Google Scholar

^{page 141 note 2} See, for example, Blaug, M., ‘Approaches to Education Planning’, in The Economic Journal (London), 77, 1967, pp. 262–87.Google Scholar

^{page 141 note 3} To illustrate this it is only necessary to point to two major works that use mathematical programming in resource allocation within the education sector, namely I. Adelman, ‘A Linear Programming Model of Educational Planning: a case study in Argentina’, reprinted in Adelman, I. and Thorbecke, E. (eds.), Theory and Design of Eonomic Development (Baltimore, 1966), pp. 385–418Google Scholar, and Bowles, S., ‘The Efficient Allocation of Resources in Education’, in Quarterly Journal of Economics (Cambridge, Mass.), LXXXI, 2, 1967, pp. 189–219.Google Scholar Both use, either directly or indirectly, the contribution of education activity to G.N.P. (or a suitable proxy) as the decision criterion for the allocation of resources.

^{page 142 note 1} In a different but still relevant context is the current discussion in the United Kingdom on output measures of education. See, in particular, Chartered Institute of Public Finance and Accountancy, Output Measurement and Education Conference Papers, 1974.

^{page 142 note 2} For an attempt in this direction, see Shiefelbein, E., ‘An Approach to Introducing Quality in Educational Models’, reprinted in Correa, H. (ed.), Analytical Models in Educational Planning and Administration (New York, 1975), pp. 148–68.Google Scholar

^{page 142 note 3} Unesco, , Social Indicators: a problem of definition and selection (Paris, 1974),Google Scholar Reports and Papers in the Social Sciences, No. 30.

^{page 143 note 1} For a tangential discussion of this issue with regard to the National Health Service in Britain, see Geary, K., ‘Technical Deficiencies of R.A.W.P.’, in The British Medical Journal (London), 05 1977.Google Scholar

^{page 143 note 2} This is not to say that there are no other objectives - simply that manpower criteria dominate the discussion.

^{page 143 note 3} Throughout this article, in order to avoid any confusion, the presence of ‘sixth form’ courses in one private school has been ignored. With the increased pressure for this type of education, however, it should be pointed out that an expansion here can be accommodated within the proposed framework, as developed below.

^{page 144 note 1} See Geary, K., ‘Secondary School Leaver Tracer Survey - pre-trace study’, Ministry of Finance and Economic Planning, Mbabane, 1976.Google Scholar

^{page 144 note 2} For a discussion of individual pupil records in Britain, see Local Authorities Management Services and Computer Committee, Towards a Computer Based Education Management Information System (London, 1974).Google Scholar

^{page 144 note 3} If we let R be the published repetition rate and r the probability of a child repeating the grade one year, then if infinite repetition is allowed, R = r+r ³+r ³+ … = r/I-r and, therefore, r = R/i + R. By restricting repetition to two years, we have R = r+ r ², and solving we get r = (- 1+ (I + 4R)(½). This adjustment is only significant if R is large. A more appropriate adjustment would have been to include a separate ‘repeater’ row for each row already in the matrix.

^{page 144 note 4} For a discussion of this problem in the U.K., see Stone, R., ‘The Fundamental Matrix of the Active Sequence’, Fifth International Conference on Input-Output Techniques, Geneva, 1971.Google Scholar

^{page 145 note 1} This crucial issue is discussed briefly in ‘A Financial and Statistical Analysis of Swaziland's Educational System with Projections to 1985’, Ministry of Education, Mbabane, 1977, and was examined previously in more detail by Geary, K., ‘Analysis of Primary School Teacher Wastage Rates’, Ministry of Finance and Economic Planning, Mbabane, 1975.Google Scholar

^{page 145 note 2} The first data on teachers by age appeared in the Education Statistics Report (Mbabane, 1975). As one would expect, apart from the private schools - 104 per cent of the teaching force in 1975 - the Ministry of Education does have teacher records for e.g. salaries and retirement, but shortage of staff has prevented the extraction of such information.

^{page 145 note 3} Cf. ‘A Financial and Statistical Analysis of Swaziland's Educational System’.

^{page 146 note 1} See ibid.

^{page 146 note 2} For such matrices it is possible to derive single indicators of social inequality. Because of the constraint that the sum of each row be less than one, we must beware of double counting, but it will be feasible to recognise those elements which it is desired to increase. These are likely to be just above the main diagonal, and if M+_ij denotes the favoured Manzini district, and L+_ij the Lubombo district, with W_j as a political judgement of the ‘importance’ of reaching state j, then , would be an indicator of social inequality.

^{page 146 note 3} Cf. Armitage, P., Smith, C., and Alper, P., Decision Modelsfor Educational Planning (London, 1969).Google Scholar

^{page 149 note 1} In economic applications M can be interpreted as M = 1+ P² + P³+…, although the calculation of such a series embodies the assumption that transition probabilities are unchanging through time, and that the elements of M indicate characteristics of the present (or rather immediate historic) system which cannot be changed. For a discussion of the economic significance of M, see United Nations, Input-Output Tables and Analysis (New York, 1973), Studies in Methods, Series F, No. 14.

^{page 149 note 2} Source: the 1974 stock figures are given in Table H of the position paper for Swaziland, printed in the Report of the Third Regional Planning Conference - Central and Southern Africa (London, Commonwealth Secretariat, 1976).

^{page 150 note 1} Care should be exercised in a small country because the low numbers involved may preclude the use of ‘rates’.

^{page 150 note 2} For a definition of these types, see ‘A Financial and Statistical Analysis of Swaziland's Educational System’.

^{page 150 note 3} See B. Ivanovic, ‘A Method of Establishing a List of Development Indicators’, in Social Indicators: a problem of definition and selection.

^{page 150 note 4} Naturally this will require improved data collection - e.g. school-leaver surveys. What is being stressed here is the value of the Markov approach as a framework for such improvement. For a discussion of the manpower aspects, see O.E.C.D., Education and Development - Mathematical Models in Educational Planning (Paris, 1967).Google Scholar

^{page 151 note 1} See Unesco, , A Statistical Study of Wastage at School (Paris, 1972).Google Scholar

^{page 151 note 2} This latter point is discussed in a micro-analytic context in Culyer, A., Layers, R., and Williams, A., Health Indicators, reprinted in Shonfield, A. and Shaw, S. (eds.), Social Indicators and Social Policy (London, 1972).Google Scholar