Indicador De Desarrollo.pdf

MARIO BUNGE

DEVELOPMENT

INDICATORS*

(Received 6 May, 1980) ABSTRACT. This paper discusses some of the methodological problems involved in the design of indicators of development. To begin with, two kinds of social indicator are distinguished and defined: descriptive and normative. Unlike the former, the latter involve value judgments. Secondly, the very notion of development is briefly discussed. The idea favored by economists, that development is identical with industrialization, is criticized. It is proposed that genuine development is not only economic but also biological, cultural, and political, for each of these factors conditions the other three. The matter of independent vs. dependent development is discussed, to dispel the illusion that increase in GNP is a faithful development indicator. An indicator of dependence is introduced. Then a whole battery of development indicators is proposed, some of them dominant, others weak, some relative, others absolute, some stray, and others systemic. A case for systemic or theoretical, as opposed to stray or empirical, indicators is made. Finally some ideas on development dynamics are proposed, as a possible basis for a set of deeper and more faithful indicators of development.

INTRODUCTION The construction and use o f social indicators pose a number o f intriguing methodological problems that the sociologist usually solves along the way in a more or less tacit and intuitive fashion. Some such problems are: What is an indicator", What exactly is it we want it to indicate?, Must every indicator be descriptive or should some indicator be normative?, How are indicators related to nonobservable variables?, Are indicators definitional or hypothetical?, and How are indicators validated? The applied social scientist, faced as he is with urgent tasks o f social significance, has rarely time to deal with methodological issues and cannot wait for the theoretical sociologist to solve them. This pragmatic attitude is not only nearly unavoidable but it often works and it may prod the theoretician. But it is not without dangers. This paper will attempt to show some o f the dangers lurking behind the use o f insufficiently analyzed development indicators. It will also make certain constructive proposals. These proposals concern mainly the introduction o f normative indicators, t h e incorporation o f indicators o f independence and o f fairness into the set o f development Sociallndicators Research 9 (1981) 369-385. 0303-8300/81/0093-0369501.70 Copyright 9 1981 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston, U.S.A.

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indicators, and the construction of an absolute indicator of overall development, i.e. one not dependent upon any particular country taken as a base line. We shall also emphasize the need for u~ng systemic rather than stray indicators - which amounts to stressing the need for building deffmite dynamical models of development involving, among other variables, the development indicators.

1. D E S C R I P T I V E

AND NORMATIVE

INDICATORS

Until a few years ago social science proper, in contrast to social philosophy, tried to keep clear from value judgments and normative or prescriptive statements. The increasing application of the social sciences to the solution of social problems, as well as the birth of decision theory, have changed that attitude. Today there is a tendency to face up to values and norms, rendering them explicit and keeping them under control instead of just ignoring them and thereby being at the mercy of tacit valuations and norms. However, this change does not seem to have penetrated the important field of social indicators: practically all of the work in this field is limited to descriptive indicators. We shall argue for the need to use both descriptive and normative indicators. But first a quick characterization of each. The parameters of an income distribution are descriptive. On the other hand the parameters of an optimal income distribution are normative. Likewise the actual degree of participation in social or political matters, as indicated e.g. by the percentage of the population taking part in political decision making, is a descriptive indicator. A corresponding normative indicator would be the optimal degree of participation ensuring both a fair distribution of power and an efficient running of the social machine. There is nothing wrong with a normative indicator, just as there is nothing wrong with a prescription, whether technological, medical, social or of any other kind, intending to correct an imbalance of some sort, as long as there are reasons to believe that the corresponding balance is better than the imbalance. For one thing a normative indicator can be just as objective as a descriptive one. Indeed in principle it is possible to determine which value or values of a variable correspond to the goal or goals agreed on beforehand. (Think of nutrition indicators.) For another, some of the normative indicators are just maximal (or minimal) values of the corresponding descriptive indicators. For example, the optimal life expectancy may be taken to be the one actually attained in Scandinavia.

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Of course the construction of normative indicators may present problems but so does the construction of descriptive indicators. Let us look into this matter. 2. T H E C O N S T R U C T I O N O F N O R M A T I V E I N D I C A T O R S . T H E C A S E OF EQUITY

A first problem posed by the construction of normative indicators is of course how to decide what the optimal value or values of a variable are. In principle this problem could be solved rigorously if it were possible to set up an accurate model of the community in question and moreover a dynamical model, and preferably a whole family of models enabling one to compare the effects of choosing different goal values of the variable(s) concerned. But in practice such models are scanty, so we must resort to less rigorous methods. Take for instance the determination of the optimal fraction of free leisure time (as opposed to forced leisure or unemployment). In highly industrialized countries the working week could be as low as 24 hrs provided waste were controlled and a slightly lower standard of living were accepted. On the other hand in some developing countries twice as long a working week might not be enough to attain the preset goals. In any case if the goals are formulated explicitly and the productivity is known, it is possible to compute the optimal number of working hours per week. This value will depend on the region concerned and will serve as a development indicator: the more leisure time the greater the degree of development. It may of course be rejoined that this method presupposes that the choice of normative indicators is wholly in the hands of the technocrat, while in practice it is the people, or else the politicians, or perhaps the big corporations, that will choose whatever optimizes their own utilities. But this, even if true, is no argument against the possibility of setting up technically correct normative indices, i.e. indicator values that are optimal from a technical point of view even though, for some reason or other, they may not be accepted by the powers that be. Once the optimal value, or the optimal distribution, of a variable has been established the actual construction of the corresponding normative indicator is straightforward. Thus a possible formula for a normative indicator N consisting in a single number is this: N= 1

Optimal value - Actual value max (Optimal, Actual)

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If the indicator is a whole distribution of something (e.g. wealth, political power, or number of schooling years), then the first step is, as indicated, to establish the optimal distribution of the same variable - call it X. And the second step is to measure the deviation from the actual distribution of X. There are two possibilities: either the optimal distribution is symmetrical or it is not. In the former case the greater the asymmetry the greater the imbalance or inequity. That is, the inequity in the distribution of X equals the skewness Sk(X) or, if preferred, its absolute value. (This can in turn be taken to be Pearson's skewness measure or, what is perhaps more practical, Yule and Kendall's, which is assigned a value between - 1 and 1 .) If the skewness measure is normalized to unity, then the equity (or equilibrium) in X can be defined as

Eq(X)= 1 -Sk(X). Maximal equity corresponds thus to minimal asymmetry in the distribution and conversely. If on the other hand the optimal distribution is asymmetrical (as is the case with longevity and the number of schooling years) then the skewness value itself, or some linear function of it, may be taken as a measure of equity. Finally, in the case of a cumulative distribution (such as a Lorenz curve of land distribution) one would presumably adopt the Gini index as a measure of inequality. I submit, in sum, that it is possible to construct normative indicators. Moreover I suggest that normative indicators of economic equity, social balance and cultural opportunity are among the most important development indicators. 3. D E V E L O P M E N T :

INDUSTRIAL

INDEPENDENT,

OR INTEGRAL, UNFAIR

DEPENDENT

OR

OR FAIR

Many a study of development rests on at least one of the following assumptions: (i) Development is the same as industrial growth (or in general modernization), or at least the overriding variable is the rate of industrialization. (ii) Whether or not development is attained at the cost of gross inequities is irrelevant.

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(iii) Whether or not development is essentially self reliant (independent) is immaterial. So much are these assumptions taken for granted in many studies, that whereas the fraction of manufactured goods in the GNP is regarded as a dominant indicator of development, the degree of equity and the degree of independence are simply ignored. And when the importance of these variables is pointed out no effort is made to quantify them, so that their discussion remains at the intuitive or even the ideological level. I submit that all three presuppositions should be subjected to critical scrutiny and moreover that the choice of an alternative set of assumptions need not throw us into the arms of any unscientific ideology, for it is possible to fred objective measures of both equity and independence. (For the former see Section 2, for the latter see the second half of the present section.) Ad industrialization. After praising industrialization for its own sake, for over two centuries, we are beginning to realize that industrialization is far from being good in itself: it is a means and as such it should be controlled. Suffice it to mention that unbridled industrialization has certain evil side effects such as pollution, the decay of agriculture, an excessive urban concentration, the disappearance of crafts, and a feeling of anomie and alienation. To be sure these effects can be brought under control at least to some extent. But the point is that industrialization, if reckless, can bring about a disastrous and in some cases irreversible degradation of certain values, whence a distinctive backward motion of society in a number of important respects. If these other respects are not taken into account when computing the overall degree of development of a society, then an unrealistic result is bound to be obtained. We need then not only descriptive indicators of industrialization but also normative indicators telling us what the imbalance (in excess or in defect) with respect to an optimal value is. Or, if this proves technically difficult to achieve, then we should include among the development indicators those concerning the effects of industrialization. It may well turn out that these effects are largely negative in certain cases, so that their contribution offsets that of industrialization. Ad equity. If we agree that fairness or equity is a desideratum then we cannot fail to include it amongst the development indicators. Take again industrialization. Whereas in some countries it has contributed to equity in others it has exaggerated the existing inequities to the point of threatening the stability of the social fabric. Just think of the destruction of the village

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society and the corresponding emergence of the shanty town society composed of former peasants hoping to be employed in the industries or in the services, and leading an almost marginal existence. To discard these and other effects of industrial growth is to entertain a queer notion of development. Ad independence. If a country, region, company or any other group pushes the development of another area for its own benefit, then such a development is bound to be lopsided or even harmful to the developing region. Thus, much of what goes under the name of development, when controlled by foreign interests, consists in the sheer plunder of the natural resources of the developing nation or region. Just as with the case of equity, we have got to include independence among the development indicators, for an industrialized colony is not more highly developed than a moderately industrialized but independent country. But before we can include independence indicators among the development indicators we must build them. Let us then proceed to this task.

4. I N D E P E N D E N C E I N D I C A T O R S

The qualitative concept of independence is insufficient, for a country or region may be independent in some respects and dependent, though perhaps not entirely, in others. We need a concept of dependence relative to a definite respect (e.g. f'mances) and one allowing us to compare degrees of dependence, in a given respect, of various countries or regions. We should, in other words, be able to say that country A depends upon country B in respect C to degree D. Thus in the case of financial dependence we may take the ratio: Foreign investments/Total investments, or D f = FIT for short. Hence the degree of financial independent would be defined by If--- 1 - F I T . Let us generalize this notion. Let P be the set of countries or regions under consideration and R the set of respects in question (e.g. industrial and cultural). Then for each k in R there will be a function from the country-country pairs to the real numbers in the unit interval, i.e.

/k : exe-

[o,1]

such that, for any p and q in P, Ig (p, q) = 1 - Volume of item k in country p controlled by country q Total volume of item k in country p

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is the degree of independence, in respect k, of country p with respect to country q. In some cases the independence indicators are already there and so are the data necessary to evaluate them. The total fraction of imported manufactured goods is a case in point. In other cases, such as those of political and cultural independence, it is not obvious what can be taken to be the volume occurring in the above formula. However there is no reason to suppose that it is impossible to fred an adequate measure in the cases concerned. Once the various independence indicators have been adopted and evaluated we can compute the total degree of independence of each country in any given respect k:

Finally we may wish to assign each such value a certain weight wk in the range 0 to 1. This would allow us to compute the overall independence indicator for each country:

I p ~X~_R wklk(P, q). An interesting result would probably be that no industrial giant is wholly independent and that no small country is totally dependent. In other words, dependence comes in degrees.

5. D O M I N A N T A N D W E A K D E V E L O P M E N T I N D I C A T O R S

It is well known that one of the curses of social science is not the dearth of empirical data but rather the overload of unimportant and highly correlated empirical information. (Other curses are the scarcity of good mathematical models and of good social indicators - both of which go hand in hand.) Consequently one of the problems in every field of social science is to find dominant, independent and reliable indicators that will enable one to dispense with the weaker, dependent and ambiguous ones. Let us take for example the health indicators. Both the number of physicians and the number of beds per 1 000 inhabitants can be misleading indicators of public health even though they are valuable in themselves. Indeed if the doctors and hospitals are concentrated in few and distant towns then they may not give good service. And even if they are in plenty and well distributed this may indicate either poor health or

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BUNGE

affluence or a lack of public sanitary education or poor organization of the health services or even professional incompetence. So those are poor health indicators. We should look for better ones. It so happens that, after all, doctors, hospitals and other health services are means to keep the population in good health or improve it. And the only way to gauge the efficiency of such means is to look at the results. In this case the singly most important result is longevity, for normally only healthy people live long. Why then not take life expectancy as the main health indicator? This does not entail discarding the others: they should be kept in order to know what should be done to improve the life expectancy. To be sure, life expectancy is not an unambiguous indicator of industrial growth, as some social scientists have been quick to point out. But if we are concerned with integral development rather than with just one facet of it (namely industrialization) then the objection holds no water. No matter how industrialized a country may be it cannot be regarded as advanced if it has an abnormally low life expectancy. The general problem is that of discerning and constructing a subset of social indicators with the properties of dominance, independence and reliability. To discover how to go about this task it may help to list some typical indicators, whether available or desirable, and class them.

6. C A T E G O R I E S

OF SOCIAL INDICATORS

A useful partition of the set of social indicators (not just development indicators) is into the following categories: biological, economic, sociopolitical, and cultural. We list only a few indicators per category just for purposes ot illustration. And we mark with a + sign those which prima facie look lik~ good candidates for dominant indicators. 1. Biological indicators

1.1 Family + Averagefamily size (counting all relatives living under one roof) Average number of children per family Concentration of births in relation to mother's age 1.2 Health Per capita consumption of proteins No. of physicians per 1 000 inhabitants + Life expectancy 2. Economic indicators 2.1 Production

Per capita GNP Percentage of manufactured goods in GNP

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+

Agricultural and industrial surplusses 2.2 Organization Percentages of skilled labor force (blue and white collar) Efficiency of the commercialization net + Economic (agricultural, industrial and financial) independence

3. Sociopolitical indicators 3.1 Social Spontaneous social cohesion + Equity of wealth distribution Fraction of national budget devoted to social services 3.2 Political + Popular participation in political and social decision making Political independence vis ~ vis other countries Political stability

4. Cultural indicators 4.1 Educational + Number of schooling years Literacy rate + Percentage of scientific and technological graduates 4.2 Cultural proper + Humanistic output + Scientific output + Technological output

Most of the indicators in the above list are available. The rest can in principle be built and evaluated with the help of existing data. It is of course debatable whether the ones singled out as being possibly dominant and consequently marked with a + sign are in fact dominant. For example it might be thought that both political independence and political stability under heading 3.2 are key indicators. However it may be rejoined that popular participation subsumes them both, in the sense that the stronger it is the greater both independence and stability are. But a detailed discussion of these matters goes beyond the limits of the present study. (See Bunge and Garcla-Sucre, 1976). If all the indicators are quantitative and are uniformly normalized, so that their values lie within the unit interval, their ordering becomes a trivial task. What is not trivial is, of course, the assignment of relative weights with a view to constructing an overall indicator of some sort, be it of economic soundness or of cultural level or of degree of development. We turn next to this problem.

7. O V E R A L L D E V E L O P M E N T I N D I C A T O R S : R E L A T I V E AND A B S O L U T E

There exists an indicator of overall development, namely Ivanovid's. (See Unctad 1970, and Unesco 1973.) lvanovid's is a relative overall indicator in

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the sense that it takes an arbitrary country as a base line and computes the degree of development of any given country relative to that country. It might be of some interest to attempt to construct, in addition, an absolute overall development indicator, i.e. one not depending upon any particular country taken as a base line and moreover one assigning different weights to different indicators, according as they are dominant or not. In the following we sketch a method for constructing a whole class of overall indicators of this kind. Let X = {X1, X2 ..... Xn ) be n development indicators defined as so many functions

Xk : P x T ~

[0, 1]

such that Xk (p, t), for p in P and t in T, is the degree to which the kth respect has been developed in country p at time t. Furthermore pick the subset X i of the total set X such that no two members of X i are strongly correlated. (That is, X i is a set of practically mutually independent indicators. To build it we must begin by finding the value rpq of the linear correlation coefficient of every pair (Xp, Xq) of indicators in the original set X. We assume this statistical job to have been performed.) Suppose the set X i of independent indicators has m ~
D(p, t) = kZl wk(p, t)Xk(p, t),with ~ w k = 1, where w k (p, t) is the weight or importance of the kth aspect for country p at time t. Note that the weights wg have been assumed to be country and time dependent, for (a) what is important to one country may not be so to another, and Co) the same factor may acquire or lose importance as the goals are attained or recede further away. Note also that those weights are not related to the degree of statistical independence of the corresponding variables. The problem of the statistical independence is supposed to have been solved prior to the selection of the subset X i of independent indicators. The weights wg are assigned by those who design development plans, not by the statistician. Finally suppose we reduce further the set of development indicators by picking only the dominant ones, i.e. those which, being statistically independent, have also maximal weight for the country and time in question.

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INDICATORS

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That is, form the subset X a of X i and assume that there are q indicators in this set. Suppose further that these indicators are all equally important, i.e. set w s = 1[q for every X, in X a. Then the formula for the overall degree o f development simplifies to q

O(p, t) = (l/q) s~=l Xs(p, t), with X s in X a. It goes without saying that the rate o f overall development is defined by the time derivative of D:

R(p, t) = dD(p, t)/dt. These are absolute indicators. But of course they allow one to compare levels (or rates) of development of different countries. That is, an absolute indicator gives all the information a relative indicator conveys without introducing any irrelevant information, namely the one referring to the base line country.

8. I N D I C A T O R S :

STRAY AND SYSTEMIC

Lest it be thought that the study of development is restricted to the construction and evaluation of development indicators, let us hasten to recall that (a) indicators are validated not in isolation from but in conjunction with definite mathematical models, and (b) mathematical models, if deep, will contain unobservable variables, such as social differentiation, social cohesion, economic equilibrium, political power, and cultural level. Such unobservables cannot be read off directly from statistical yearbooks. But of course they will not become scientific concepts unless they are somehow linked to observables or indicators that can be read off or at least computed out of statistical yearbooks. Let us emphasize that the unobservable-observable relations (in particular functions) are hypothetical. They do not consist of arbitrary definitions although they are sometimes mistakenly dubbed 'operational definitions'. That is, the deep variable-indicator relations are assumptions that may be true or false and must therefore be subjected to rational criticism and empirical test. For example, if it be claimed that the number of newspapers printed per 1 000 inhabitants is a reliable indicator of cultural level, then it must be shown that the population in question takes newspapers for the information they convey rather than, say, not to miss the sales in the department stores.

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In sum an indicator is valuable insofar as it indicates a feature that is not directly observable and insofar as it is part and parcel of a body of theory. This holds for indicators of molecular weight as well as for development indicators. Hence in order to make the most out of development indicators and validate them we should try and set up full fledged mathematical models of development rather than resting satisfied with a bunch of correlations and trend lines. It is common knowledge that correlations are often spurious and trend lines temporary. On the other hand a scientific theory proper, one including laws and in particular dynamical laws, can tell us something about development dynamics. It can therefore offer a firm ground for forecast, where trend lines are insecure extrapolation tools. Let us therefore wind up our study by sketching how models of development can be built.

9. D E V E L O P M E N T

KINEMATICS

A kinematical model consists of a set of assumptions, definitions, and deductive consequences of either, concerning evolving systems of some kind. Each assumption, definition, or theorem, will in turn be a formula (e.g. an equation) involving certain variables, each of which will represent some property of the system concerned. Since we are interested in developing countries, the referents of our models will be developing countries. And since we are interested in development we must choose only variables that are favorably relevant to development. These variables must be 'positive', such as literacy rather than illiteracy rates, and degree of freedom from parasitosis rather than parasitosis rates. Whether or not our variables are observable is immaterial as long as all of the unobservables in the model are functionally related to either direct observables or to indicators, so that the values of the former can be inferred from the values of the latter with the help of definite unobservable-observable hypotheses. Assume that we pick n 'positive' aspects of development and represent each of them by a quantitative concept. More precisely, suppose we have n functions A k, with 1 ~< k ~< n, of the kind

Ak : P x T ~ R , where P is the set of countries (or zones of some kind), T the time interval,

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DEVELOPMENT INDICATORS

and R the set of real numbers. Then the value Ak (P, 0 , for p in P and t in T, will represent the level of development of country p, at time t, in respect k. For example, if A s represents the degree of industrial independence, then 'A s (P, t) = 0.5' means that the degree of industrial independence of country p at time t is one half. Likewise if we represent by

Rk(P, t)

=

d/dAk/dt

the rate of change of the kth aspect, then a formula such as 'Rs(p, t) = 0.1' means that country p, at time t, is obtaining its industrial independence at the rate of 10% per unit time (e.g. per annum). Since development is a many sided process we need all the variables and their rates of change. Moreover we had better lump each set into a column matrix, so as to be able to deal with all aspects at the same time. In other words, we display the level of development of country p at time t by writing

A I (p, t) A2(p, 0

a(p, O= an(p, 0 and the rate of development as the time derivative of the former:

Rl (p, t) R2(p, t) R(p, t)=

"

,with Rk(p, t)= dA(p, t)/dt

Rn (p, t) The state of development of country p at time t may be construed as the ordered pair = .

This may be regarded

as a vector whose fh'~t coordinate or component summarizes the level, and the second the rate of development. As time goes on this vector (or rather its tip) describes a trajectory in the state space of the developing country, which space is a 2n dimensional cartesian space. So much for the kinematics of development.

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10.

BUNGE

DEVELOPMENT

DYNAMICS

Charting or describing the development of a country consists in tracing the motion of the tip of its state in the state space of the country. It requires no theory proper: the conceptual framework we have just sketched suffices for that task. Planning the development of a country is another matter, as it consists in controlling, so to speak, the rate matrix R, i.e. in having its entries acquire certain values, so that the development level matrix A itself (or rather its elements) will attain the desired value at the end of a certain period. Scientific planning, then, requires a knowledge of the law of motion of A, hence of the 'forces' regulating its evolution. In other words planning, at least if thoroughly rational, is based on some dynamical model. In particular, the rational planning of development rests on some dynamical model or other. The gist of a dynamical model for a system (e.g. a country) p is an equation of the form

dA (p, t) _ dt F(p, t) where the RHS is the prescribed 'force' matrix, each element Fk of which is supposed to 'drive' the corresponding state variable Ak. In general each Fk is a function of time and of Ag itself as well as of some other variables in the set A = {,41, A2 ..... An) of state variables. In other words, the development equation is in general of the form d__AA= G(A, t) dt for each country p. Knowing the initial values of the various state variables and prescribing the F~s we shall be able to forecast the future values of all the components of Ak. If these values do not agree with the desired or goal values then we shall have to change the 'force' assumptions. It goes without saying that such readjustments cannot be made arbitrarily but are constrained by the natural and human resources of the country concerned as well as by the psychological, economic and social laws, not to speak of considerations of political opportunity. The simplest (and therefore perhaps also the worst) G function is of course the linear function. In any case we may start by hypothesizing that the rate

DEVELOPMENT'INDICATORS

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of development in any given respect depends linearly upon the development level in every respect. For a two property system this assumption boils down to the equations dA1 dt - a l l A t +a12A2 dA2 dt - a21A1 + a ~ A 2

where the aq, for i, ] = 1,2, are real numbers. For certain combinations of these coefficients there will be progressive development on both fronts, for others decay, for still others stagnation, and again for others a combination of the various elementary modes of development. Thus for a n = azz = 0 and al2 = a21

= c 4:

O, the solutions are

At(t) = aie cr + bte-Ct, at, bi E R .

In this case there will be growth in the two aspects just in case at I> bt; otherwise there will be decay. We emphasize that the above is only a general framework for development models. The actual construction of specific models, be they descriptive or prescriptive (normative), is a tough task that goes far beyond methodology. Yet it may well be the case that a closer look at methodological matters could speed up the process of modelling development.

CONCLUDING REMARKS

We have glanced at the complex methodology of development indicators. We have seen that the design of suitable indicators is a tricky affair involving a considerable amount of analysis and theorizing - not to speak of the experience and flair needed in every field of research. And we have suggested that the study of development indicators can do with some improvements. For one thing the very notion of development does not seem to have been sufficiently analyzed. We should be able to answer in a precise manner questions like these: Development in which respects?, Development for whom?, and Development at what price? For another thing the notion of development should be made into the central concept of a number of alternative development models, or explicit mathematical theories concerning developing

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nations. This warning may sound pedantic but it does look necessary in view o f the fact that development is often equated with industrial growth - which should be just one aspect of a many sided process. If development is conceived as an integral affair, one involving the biological, economic, social and cultural aspects of a community, then the very choice of development indicators is bound to differ from the usual set of indicators. For one thing indicators of self reliance (or independence) and of fairness (or equity) should be included among the dominant indicators of development. Now, an indicator of equity or balance in the level or the distribution of something, be it consumer goods or educational opportunities, is not a descriptive indicator like, say, the GNP: it is a normative or prescriptive indicator. As such it is unacceptable to anyone committed to the ideal of a value free social science. We have suggested that this ideal is wrong and dead anyway: that the proper scientific attitude is not to ignore values but to reckon with them and, whenever possible, to regard them as optima (not necessarily maxima). By so doing we do not escape objectivity but rather on the contrary, and we come to share the attitude of the biologist and the engineer, both of whom are centrally interested in Finding or even prescribing the optimal values of certain parameters, i.e. those corresponding to the most efficient functioning of the system, be it organism or machine. Accordingly we have proposed methods to construct quantitative normative indicators, in particular development indicators, that should be included in any formula for the overall development indicator. We have also proposed an absolute indicator of the latter kind, i.e. one that does not depend on any particular country chosen as a base line. This absolute indicator, giving the overall development level D(p, t) of country p at time t, allows one to compute the distance, in development level, between any two countriesp and q at a given time t, namely thus: d(p, q, t) = ID(p, t) - D ( q , t) I. The converse inference is of course impossible.) Finally we have sketched a nonspeeifie model of the dynamics of development and stressed that all the development indicators should participate in some such models, for otherwise they bring little insight and they cannot be validated in a reliable matter.

McGill University, Montreal

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NOTE * An earlier version of this paper was presented to the UNESCO meeting on Indicators of Social and Economic Change, Paris, 2 0 - 2 2 May 1974.

BIBLIOGRAPHY Bunge, Mario, and MLximo Garcia-Sucre: 1976, 'Differentiation, participation, and cohesion', Quality and Quantity 10, pp. 171-178. Unctad: 1970, Research Memo No. 41, Geneva, 5 November 1970. Unesco: 1973, Study XXIV, Division of Methods and Analysis, 10 June 1973.