UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION

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2 Distribution: Limited. COM/WS/156 Paris, 4 November 1970 Original: English UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION TOWARD A SYSTEM OF QUANTITATIVE INDICATORS OF COMPONENTS OF HUMAN RESOURCES DEVELOPMENT Study XI The Assessment of the Validity of Human Resources Indicators by means of a Cobb-Douglas Type Production Function by H.V. Mühsam Hebrew University Jerusalem, Israel Human Resources Analysis Division Office of Statistics Not to be quoted without permission from Unesco

3 COM/toS/156 Human resources have been operationally defined by the Panela) to comprise all attributes of a population, which contribute to the economic productivity of its labour force. Mary but not all social and cultural characteristics of a population are therefore included in the concept of human resources, the criterion for inclusion being their contribution to the productive capacity of the economy. On the ether hand the quality, efficiency, technology etc. of capital equipment are not "human resources" as understood by the Panel, although they affect the productivity of labour; but these are not attributes of the population. The Panel has also come to the conclusion that, at the present level of knowledge, human resources cannot be measured directly, but only through appropriate indicators. Each such indicator is a measurable attribute of the population, which either contributes directly or indirectly to the productive capacity of the labour force, or is assumed to reflect somehow an attribute which - again at the present level of our knowledge - cannot be measured. The percentage of the labour force which has graduated from technical college is an example of a factor which, it is assumed, contributes directly to productivity, while the percentage which has graduated in arts or the number of teachers per 1,000 schoolage population, would only contribute indirectly. Finally we may cite the crude birth rate as an indicator of "modernization" which certainly contributes to productivity but is not directly measurable. In view of the diversity of attributes, a multitude of indicators has been proposed to measure components of human resources. The multitude of proposed Indicators creates the problem of selection of - the most significant ones and that of testing the appropriateness of the choice. The problem of selection can be divided into several successive interrelated steps. The first question which arises is: What is the most appropriate number of indicators to be included in a composite index? The next one is: What is the best set of the desired size and further how should the different indicators be combined into a single, composite index? Conclusions with respect to all three aspects can only be drawn after testing the success with which this composite indicator measures human resources. It is with the problem of this test that the present study is concerned. It has been proposed by the Panel to test the success of any indicator measuring human resources by computing the cross-country correlation between the indicator and a measure of productivity such as the per capita gross domestic product (GDP). It has also been argued that the G3P, or per capita GDP, is net the best measure of the aspect of economic activity which reflects the impact of human resources, and that the GDP should be modified by taking, somehow, the mode of production into account, say, by combining GNP with energy consumption, thereby obtaining a composite index involving these two variables. It has also been suggested that the absolute or relative annual increment in GDP or GNP per capita may supply a better criterion for the same purpose than the level of GDP or GNP. The choice between the level and the increment has both practical and conceptual implications. But the conceptual level which has, logically speaking, priority over the practical level, is again well beyond the preoccupations of this Panel, it is a philosophical rather than a methodological question, whether we are dynamically or statically minded or, in practice, attach more importance to the level reached or to the progress made. (1) The Panel of Experts on Methodology of Human Resources Indicators set up in 1969, and which met for the first time at Unesco Headquarters from 15 to 20 December 1969.

4 CCÍ0/S/15S - page 2 There are, at any rate, certain dangers involved in using increments as a criterion. It is indeed often claimed that those who start at a low level may find it easy to make rapid progress (this is for instance true in fighting disease, illiteracy, etc.) particularly if progress is measured in relative terms (an increment in literacy from 1# to 2$ is a relative increment of 100$) and it is even more often claimed that the "take off" is the most difficult step in develcpnent. As long as this difference of opinion subsists, it seems, to say the least, dangerous tc take Increments as a criterion for whatever other variable one wishes to measure. Independently of whether we prefer to deal with levels or with increments it should be stressed that the Panel is not concerned with the problem of the appropz'iate measure of economic activity, productivity or the product. Ihis problem has been studied intensively by experts in social accounting and, as far as I know, they have expressed general agreement in recommending the GDP or GNP as the best overall measure of the economic output of a society. It is obviously possible that for the Panel another measure of the product would be - more appropriate; but this problem is certainly beyond the scope of this paper. It i3 on the other hand within the scope of the assignment of this Panel to discuss Yíhüther an index of human resources should be capable to -predict levels of, or increments in,gdp. This claim is challenged by the following. It has in fact been proposed to the Panel to use the strength of the correlation between an index of human resources and levels of, or increments in,gdp as a measure of the success of the index in measuring human resources. In the following it will be questioned whether it is an acceptable rationale to consider the individual indicator, or the composite index based on several indicators, which shows the highest correlation with levels of, or increments in,gdp as the best measure of hur.an resources. It will be asserted that this is not a reasonable approach. Not only because of the difficulties connected with increments which have already been mentioned, but because of the fact that the use of levels would lead to the trivial - or rather absurd - conclusion that per cepita GDP itself is the best possible measure of human resources. Indeed, from the conceptual point of view both levels and increments of per capita GDP comprise all the aspects of knowhow, efficiency, modernization, organization, etc. which make up "human resources'* and from the formal point of view each correlates perfectly with levels or increments of GDP respectively. But these are not the real reasons for rejecting the correlation between the human resources index and per capita GDP as the criterion for the adequacy of the index. In order to select a criterion for judging the success in measuring human resources we should indeed return to our original definition of human ren sources: they are assumed to contribute to production or, in other words to be a factor of production. This implies that there are other factors, capital being obviously the foremost among them. In order to gauge the contribution of human resources, we should therefore consider how human resources are assumed to contribute to GDP and what are the other contributing factors, as well as how they contribute. This leads to the consideration of a production function involving human resources. A suitable function which will rally a wide degree of acceptance will be a Cobb-Douglas type of function. In its original form the Cobb-Douglas production function considers only two factors: labour and capital, and expresses their respective contributions and interaction by a function of the type P = K*L (1-0C)

5 COlVtoS/156 - page 3 where P is the GDP, L is the amount of labour and K is the amount of capital used in production, while OC and (l-oc) are elasticities. That the elasticities add up to unity is a, consequence of economic theory, with which we are not concerned here. When we discuss the productivity of labour, and this is our main concern in the present paper, we may restrict the discussion to the GDP per unit of labour (p). _ = p = _ E* - ( E 7 - k where the lower-case letters (p and k) are "per unit of labour". This production function has been generalized by different recent authors so as to account for additional factors assumed to affect GDP. In the Economic Survey of Europe (1) the productivity of the labour force and in a ÜNRISD (2) publication by Drewnowski and Subramaniantwo factors, the "technological level of capital" and "human welfare" are introduced. In the present study we shall follow the approach suggested by Drewnowski-Subramanlan because they supply, together with their method, empirical data which permit some experimentation in view of testing various modifications and specifications of their approach. The Drewnowski-Subramanlan production function reads as follows p s 1? T* tf where p, k and a have the same meaning as before, T is the technological factor and H the human welfare factor, and 2 and Y are the respective elasticities«before the problem of the measurement of human resources is tackled it should be shown that Drewnowski-Subramanian*s technological factor is meaning-* less. Scrutinizing Drewnowskx-Subramanian's data it is easily seen that, whereas for the countries included in their study, per capita capital varies within the range 1 to 64 and the level of welfare varies between 1 and U, the technological factor varies only within the range 1 to 1.5. This is why the "elasticity" of-the last-mentioned factor appears, In their computations, to be relatively high. But this relatively high level is in fact spurious. It reflects nothing but the lack of variability of the variable. Drewnowski- Subramanlan were misled through forgetting that, In the original Cobb-Douglas production function both independent variables, capital and labour, are measured in, what can be called, natural units: capital in dollars and labour in manyears. The elasticities have therefore "absolute" meanings, namely the additional product obtained per additional dollar of capital or man-year of labour. And it is obvious to any student that if capital is measured In, say, millions of dollars (instead of in single dollars) the elasticity of capital Increases a million fold, etc. It is also obvious that the assessment of the relative importance of the contribution of capital and labour to the value of the product is a meaningless question within the frame of Cobb-Douglas functions because capital and labour are not measurable and nor are the respective elasticities. All this seems to have escaped the attention of Drewnowski-Subramanlan and they do not pay any attention to the units In which the technological level and human welfare are measured. To the contrary, they take care of "standardizing" some of their variables but not others and in fact only their human welfare variables are "standardized" (inverted commas are used because Drewnowski-Subramanian' s method of standardization is a little unconventional.

6 COrVttS/156 - Pas 0 * If a Cobb-Douglas type production function is fitted to standardized variables, elasticities gain a new meaning. Indeed, like correlations, they measure the strength of the relationship between the Independent and the dependent variable; they can therefore be interpreted to indicate the importance of each independent variable in determining the dependent variable (or the criterion) and it is in this sense that these elasticities are comparable. Thus, in the case of a production function in which all variables are standardized, each elasticity can be interpreted as the weight of the corresponding variable in determining per capita GDP. It should however be remembered that these elasticities cannot be identified with shares in the product like the elasticities of the original Cobb-Douglas production function. The elasticities of Drewnowski-Subramanian* s standardized variables are oc. = ß z Y * Q.3Q8Ò Thus, the elasticity of the technological factor ( ß ) is so small that there is no doubt that this factor has no effect on per capita product. This is what we refer to as meaningless. We are consequently dropping this factor from the production function. We shall thus be concerned with a production function of the following type, which omits the technological factor, but introduces a new factor, h: p - k h. where h is an indicator or index of human resources and a the corresponding elasticity. Now, the basic hypothesis of the present study can be tested: is the goodness of fit of this production function a sensitive measure of the appropriateness of human resources indicators? Obviously, we are not able, a priori, to rank indicators and indices. Thus, all we can expect from this approach is to enable us to differentiate, in a sensible way, between different possible indicators and indices. Until now the following three indicators and indices have been tried as measures of human resources and introduced as variable h in a production function: (Further experimentation is in progress) 1. Per cent of labour force not engaged in agriculture - this is a rough and ready measure of modernisation of the economy or of its labour force, encompassing simultaneously the extent of industrialization, marketing and servicing. 2. The number of radio and television receivers per capita. This is also a measure of modernization, but restricted to mass communication media. 3. A combined index of 1 and 2, unweighted.

7 COM/WS/156 - page 5- (Rev. 1) k. Combined primary and secondary education enrolment as percent of the age group 5-I9. This is a measure of the flow of human resources rather than of existing supplies. 5. Number of telephones per 100,000 population. This is an indicator of the degree of modernisation of the_ economy rather than of human resources. The following are the elasticities of per capita capital and each of the five human resources indicators, as well as correlation coefficients measuring the goodness of fit per capita product as predicted by the five production functions and the observed values. Human ~ Resources 2 Indicator a g R 1 O.65U O.3U T T *92 3U77 939U k 7^27 22U ^7 1*357 90U7 It is easily seen that for the different production functions the elasticities of either factor do not vary extremely. This can perhaps be interpreted as meaning that each factor measures, in each instance, the same component of production. The relatively high value of the elasticity of human resources indicator No. 5 is, however, disturbing. It should be noted that this indicator measures less an attribute of the population than the structure of the economy and its technical equipment; it is therefore not surprising that it affects production more strongly than purely human factors. It is obvious that random errors of measurement affecting the observed values of the different human resources indicators do not affect the elasticities, at least so long as such random errors are small compared with the variability of the indicator. Thus, if the differences between our five human resources indicators were nothing but random errors in measuring human resources we would expect them to be equal, within the limits of random fluctuations of the elasticities as computed here. The significant differences found between the elasticities can only be ascribed to differences in the meaning of the indicators. Our five indicators obviously do not measure the same thing and each of them expresses a certain aspect, or component, of human resources which may have its own elasticity with respect to GDP per labour unit. The correlation coefficients reflect, together with the success in explaining differences in product per unit labour of the human resources indicator under consideration together with capital per labour unit, the following effects: a. random and systematic errors in each of the indicators in measuring human resources, b. errors in the measurement of GDP per unit labour and capital per labour unit.

8 COM/WS/156 - page 6. (Rev. 1). c. the impact of factors other than capital and human resources on GD?, d. the success of the proposed production function in representing genuine relationships. If nil measures were perfect and the production function a complete and true representation of the existing relationships, the correlation would be unity. It is obviously impossible to break into its various components, the distance of the observed correlation coefficients from unity. But as all components, except errors of the indicators in measuring human resources, remain constant, the comparison between correlation coefficients throws light on the appropriateness of the different indicators or indices for measuring human resources. In view of this, it is not surprising that the component index (No. 3) appears to be, of the selected five, the best measure of human resources, and the primary and secondary enrolment rate (No. k) the worst. It shouldbe emphasized that we have no proof that any one of our five indicators actually measures human resources, at all, or with the different degrees of success mentioned before. All we can say with certainty is that each indicator (with the exception of No.5) represents a characteristic of the population and has been shown to be a factor in production. But it seems to us that this is a better proof of their being aspects of human resources, as we want to define them, than the fact that they correlate with GDP. And the strength of the correlation between GDP per unit labour, as expected in view of the amount of capital used in production, and what we assume to be a human resources indicator, seems to be a better measure of the appropriâtenes of the human resources indicator than the strength of the correlation between the indicator and per capita GDP. References 1. united Nations Economic Survey of Europe in I96I. Sales N0.6U.II.E.I., Geneva 196^. 2. Drewnowski, Jan and Subramanian, Muthu. A Suggestion for an Empirical Production Function Representing the Productivity Effect of Social Factors. (UNRISD/68/C.12 GE.68-6lU6(Rev.l)).