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ECONOMETRICS: MEASUREMENT I N ECONOMICS1 I As the first incumbent of a new Chair in this University, I thought that in this lecture I should set out the econometric approach in economics and explain how I see this branch of study, 'applied econometrics', fitting into the work of a Division of Economic Studies. Although econometrics, as we understand it, is a relativeIy young discipline, measurement in economics is not new. Indeed, as long as people have been interested in social phenomena, there has been the urge and need to measure. An early Census is recorded in z Samuel, when King David numbered the fighting men of Israel, and called down a plague in doing so - though, as the great Udny Yule has remarked,2 it seems that divine disapproval was directed against the militaristic purpose of the Census, rather than the Census itself. One can only hope that not all economic and social measurement is so judged. But applied econometrics means more than just counting, sorting and comparing. I t implies a particular approach to the problem of measurement which I will try to illustrate by developing two examples. I1 First, I will discuss a relationship with which we are all familiar - so familiar in fact that perhaps we are a little tired of hearing about it: one which, nevertheless, has an important bearing on immediate and future economic development. We may add up in money terms all the final expenditures on the market which are recorded in a year in Britain. These comprise expenditure by consumers, public authorities, by industry for investment goods, and by other countries for our exports. Suppose we ask the question: what is the ratio of imports into Britain to total final expenditure ? Since both aggregates are measured in money terms, this is a perfectly straightforward question to answer, The ratio is called the average propensity to import with respect to final expenditure, and over the post-war years has been of the order of about 1 7 to 18 per cent. This is an empirical fact, but by itself does not tell us very much and, perhaps, is not of much interest, and does not contribute much to our understanding of economic processes. But suppose we consider the question in the following context. Total final expenditure is a measure of that final demand which results in economic activity in a country. The level of demand, that is to say, is a measure of the driving force which generates economic activity. As the level of final expenditure rises, there is an increasing demand for goods and services. Some part of this increasing demand will be met directly by bringing in more imports, the An Inaugural Lecture delivered on 16 February 1972, by R. J. Nicholson, M.A., Professor of Econometrics in the University of Sheffield. G. Udnv Yule and M. G. Kendall, An Zntrodvction to the Theory (14th _ ofStutistics . _ ed., Griffin, London, 1950), p. xiv. 4 ECONOMETRICS: MEASUREMENT IN ECONOMICS remainder from home production which itself may require more imports in the way of semi-finished goods or raw materials. A fall in the level of final demand has the opposite effect. What we have done is to trace out a causal relationship from changes in final expenditure to changes in the flow of imports. Can we estimate the strength of this relationship quantitatively ? Our first step must be to formulate the relationship explicitly. Let us put it this way: the quantum level of imports is a function of the level of final expenditure; changes in the level of imports, a function of changes in the level of final expenditure. This, of course, involves a very great simplification. Imports consist of many types of goods; goods far consumers' final expenditure, investment goods, and raw materials. We might prefer a formulation of the relationship which explicitly relates imports to these different categories of final expenditure,l to different states of technology, to businessmen's dccisions regarding the levels of stocks they wish to hold, and to consumers' tastes; we might wish to have separate relationships for different types of imports. But we will limit ourselves to this one aggregative proposition : changes in the quantum level of imports are a function of changes in the level of final expenditure.2 We are not now concerned with matters of description, but with causal processes and with structural relationships. To handle this relationship quantitatively, we must next express it in an explicit mathematical form. We ask, for example, is this relationship a proportionate one or one which changes with different levels of final expenditure? We will put forward the hypothesis (which in fact does well in practice) that it can be treated as a proportionate relationship; that is to say a relation which, on a graph, can be represented by a straight line (cf. Fig. I ) . Mathematically a Changes i n total filial expenditure FIG.I . Changes in total final expenditure and imports ( Amillion) straight line is defined by two constants, one of which measures the slope of the line, the other its spatial position. The two constants are the parameters in our function, and if we can estimate them we shall have estimated the structural relationship we derived from our simple analysis. 1 Such an approach is developed in 'Forecasting Imports', National Institute Economic Review, no. 33 (August.I965)>PP- 35-43. a See R. J. Nicholson, Economlc Statistics and Economic Problems (McCraw-Hill, London, 1g6g), PP. 42-5. ECONOMETRICS: MEASUREMENT IN ECONOMICS 5 We now require a technique which enables us to make these estimates from observed empirical data, and, of course, a n adequate amount of suitable data. The technique is a statistical one the properties of which are investigated and developed in the theory of statistics, namely elementary linear regressi0n.l Relevant data are available from the estimates of imports and final expenditure which are made regularly for British National Income Accounts, adjusted to constant prices to avoid the effects of price changesa Everything is to hand, and we can estimate this particular relationship. You may be interested to know that the slope of the line I described, measured from British post-war data, is 0.31, which indicates that on the average an increase of L;I,OOO in final expenditure leads to an increase of some L300 in imports. This relationship is called the marginal propensity to import with respect to final expenditure, and the ratio of 30 per cent, is substantially higher than the average propensity I mentioned earlier of 18per cent. I t follows that as the economy expands there are pressures which cause the average propensity to import to rise continuously. This in turn has implications for economic growth, and quantifies the effect which expansion may have on our import bill and hence on our Balance of Payments. The exercise is useful in three ways. First, if the relationship can be convincingly established, it is a confirmation of our economic thinking and economic theory. Secondly, by quantifying the relationship it adds to our knowledge of economic magnitudes which are used in economic theorizing, and thirdly, by implication, it provides results which may be used in the formulation of economic policy. I take my second illustration from the field of consumer demand analysis. Economic theory leads us to consider demand for a particular commodity as determined by the price of that commodity relative to general prices, consumers' real income, prices of competitive goods and substitutes, a number of special factors which may be specific to particular goods such as credit or hire purchase facilities, consumer's age, and the possibly changing pattern of consumers' tastes. Demand related to these influences is expressed as a demand function, the parameters, or the structural constants, of which measure how demand for the good will be affected by changes in the explanatory factors. The function thus represents a causal relation deduced from economic analysis, from the determining influences to consumers' demand. Estimating the demand function means estimating the structural constants from observed data. The function is obviously a very complex one and we will simplify by considering just a part of it; the relation between changes in demand and changes in real income. This restricted relationship is usually estimated from data collected from a sampIe of households. These household expenditure surveys record household 1 Regression analysis is explained in all general statistical texts and, with particular reference to economics,in the now rapidly increasing number of books devoted to econometrics. Four in the latter category to which students may be referred are, in order of difficulty: A. A. Walters, An Introduction to Econometrics (MacMillan, London, 1968); E. J. Kane, Economic Statistics and Econometrics (Harper International Edition, New York, 1969); R. J. Wonnacott and T. H. Wonnacott, Econometrics (Wiley, New York, 1970); and J. Johnston, Econometric Methods (McGraw-Hill, New York, 1963). 2 See National Income and Expenditure, 1971 (C.S.O.), Tables I and 14. 6 ECONOMETRICS: MEASUREMENT I N ECONOMICS income, or some indicator of it, and expenditure on particular g0ods.l Before we can estimate the relationship, however, we must formulate it mathematically. Consider a diagram which plots on one axis the household incomes recorded in our sample, and on the other, the household's expenditure on the good we are considering. The scatter of points can generally be represented by a smooth curve which swings up as income increases, expenditure on a good usually increasing with income (cf. Fig. 2). This curve is called an Engel curve, and Household expenditure on a specified good */* Household iiicotne FIG. z. An Engel curve specifying the form of our functional relationship in the present context means specifying the mathematical shape of the Engel curve. Complications arise here because we would expect the Engel curves for different goods to he of different forms, that is to say, to have different properties. For example, for necessities behaviour in the region of low incomes is relevant and important. For more luxury type goods we may have to reach a certain income level before any expenditure on the good is recorded. Again, some goods may reach a saturation level as income increases, others may be more responsive to high incomes. These different properties may be illustrated geometrically by Engel curves of different shapes; analytically they are represented by different mathematical formulations of the relationship. I t follows that different explicit mathematical formulations of the relationship have diffcrent economic implications. Or, in other words, the economic interpretation of estimated relationships is restricted, or constrained, by the analytical form used. An investigator must therefore be aware of the consequences of his specification when formulating any particular relation. Once the formulation of the relationship has been decided upon, it is the econometrician's job to estimate it, that is, to estimate the descriptive parameters from actual data. Thus, again we require an estimating technique and a n adequate amount of basic data. The present problem I have described is a very familiar one in applied econometrics, and estimates of many different Engel curves exist in the literature. Their quantitative specifications enable us to answer such questions as : given a I per cent increase in real income, by what percentage would we 1 The locus classicus of this sort of analysis is S. J. Prais and H. S. Houthakker, The AnaCysis of Family Budgets (C.U.P., Cambridge, 1955). An elementary treatment is given in R. J. Nicholson (op. cit.), Chapter 9. ECONOMETRICS: MEASUREMENT IN ECONOMICS 7 expect demand for a particular good to change? For food the answer is something less than a quarter of a per cent, for certain consumer durables the answer is more than one per cent. These results reflect differences in the demand for goods which are basic necessities and those which are in the nature of luxuries, the demand for which responds more to high incomes. They are results which may be important for market research, results which enable us to understand and anticipate the way the pattern of consumer demand, and hence the pattern of production to meet the demand, is likely to change as the national level of real income rises, and they are results which may be relevant to government policy - for example in the imposition of indirect taxes. I11 The two examples I have given illustrate four fundamental elements in applied econometric work. First, one is concerned with an economic problem, and one's approach to it is governed by economic analysis and by what one learns from economic theory. One must get one's thinking right at this stage before proceeding. Secondly, one is concerned with formulating explicitly the relationships developed from the economic analysis. This aspect of the work we may describe as model building, the various relations which we develop being, as it were, economic mode1s.l This model building may well involve a considerable simplification and formalizing of the problems and, since these models are expressed in mathematical form, will certainly require mathematical technique of greater or less sophistication. I n its explicit, estimatable form, the model is defined by certain relationships or parameters. Thirdly, the applied econometrician must have an adequate technique in statistics to be able to carry out what is perhaps his own distinctive work, the estimation of his model. He must know what techniques are appropriate to particular problems and which are not. He must know how far the material he is handling demands particular estimating procedures, and he must know the possibilities and limitations of the tools he is using. Fourthly, all that he can do is governed by, and limited by, a supply of adequate data. The two examples I have discussed illustrate the two main types of data used in economic statistics: time series data, where observations are recorded sequentially over time, as they would be if one were using annual figures of imports and final demand; and cross-section data, where a set of many observations is recorded, usually as a result of a sample - in our illustration a household expenditure survey -for the same period of time. But it has to be faced that in many situations the quality and appropriateness of data are not all that can be desired, even if they are available a t all. I n these circumstances, to make any progress it may be necessary to invent proxy or surrogate variables which represent in some perhaps indirect way the influence we are trying to examine. For example in estimating production functions, which relate output to capital and labour, it may be desirable to incorporate a variable which measures the changing quality of labour over time. To represent this Model building is specifically discussed in Carl F. Christ, Econometric Models and Methods (Wiley, New York, 1966),pp. 49-241. 8 ECONOMETRICS: MEASUREMENT IN ECONOMICS we may have to use a variable which measures over time the proportion of school children staying on to receive higher education - variations on this idea have indeed been used for this purp0se.l The point is that the precision and reliability of our estimates may be blunted not because of inadequate economic thinking, or over-restrictive model building, or inadequate statistical techniques, but because of the limitations of the data with which we work. Indeed, as I shall show later, data considerations may actually dictate one's approach to an econometric problem. There is a difference between what we would like to do - indeed what we know we ought to do - and what in fact we can do. One may remark in passing that one has, too frequently, seen applied economic work undertaken by post-graduate students abandoned because data were not available. I n this respect, quantitative workers in the social science fields are at a disadvantage compared with their counterparts in the natural or physical sciences where often the appropriate data can be generated by controlled experiment. I t will be obvious from what I have said that much of the econometrician's work, model building and statistical estimation, depends on special techniques, in particular statistical techniques. Basically, an economic model represents or embodies an economic hypothesis, and when one is estimating a model, one is in a sense testing this hypothesis. The techniques brought together under the general heading of econometric methods are, in fact, part of the wider field of statistical estimation theory and are not, in themselves, anything to do with economics. But the subject matter of economics, and the nature of economic processes, give rise to special problems which require special techniques or emphasize particular developments of traditional techniques. The nature of economic data and relationships give rise to estimating problems which, though not exclusive to economics, are characteristic of it and occur more regularly in economic work perhaps than in other work. I would like to mention two problems characteristic of economic work.2 The most widely used estimating technique in econometric work is what is called regression analysis. In the simplest situations this may involve estimating the constants in a straight line relationship between two variables. The example I used for imports and final expenditure was of this form. I n general, many more variables will be included, since economic processes are functions of many influencing factors. We must ask, at this stage, what, in a more fundamental sense, are we estimating; what interpretation can be put on the numerical constants we have computed? The data with which we work represent as a rule a sample set of observations, a limited time period, or a limited coverage of a population. We are in effect using our data to estimate underlying structural relations from which our limited, observed, data are generated, but which are affected by possibly wide random fluctuations in the system. It is, however, these underlying structural relations which concern us. * See 0. Niitamo, 'The Development of Productivity in Finnish Industry, 1g25-52', Productivity Measurement Review, no. 1.5, 1958, pp. 1-12, and E. Denison, The Sources of Economic Growth in the United States and the Alternatives before us (Supplementary Paper, no. 13, Committee for Economic Development, U.S.A., 1962). I am not, here, attempting to list all the main problems in statistical estimation characteristic of econometric work - e.g. autocorrelation, so often arising from the use of time-series, and heteroscedasticity. These are treated in the standard econometrics texts. ECONOMETRICS: MEASUREMENT IN ECONOMICS 9 We are therefore concerned with the statistical properties of our estimates; whether they are biased or unbiased, with their reliability or precision. Consider, then, the following problem: economic processes, as I have stated, are affected by very many different influences. I n model building this is reflected in models which contain large numbers of explanatory variables. Think for a moment of a production function which relates output to capital employed and to labour. We may distinguish various categories of capital long term fixed capital and short term capital in the form of stocks; various categories of labour - men, women, labour of particular skills and related to different management levels, and we may introduce separate variables to account for all of them. We may also introduce variables to account for changing techno1ogy.l The difficulty arises from the fact that economic variables are themselves interrelated; in some cases to a very considerable degree. For instance the variables in the categories I have just listed, if measured over time as they usually are, will show a high degree of intercorrelation, particularly since most of them increase steadily over time. Indeed, this intercorrelation is frequently a problem when time-series are used as explanatory variables, though, as I shall show later, it is by no means confined to time-series data. The point is, however, that when two or more variables are closely interrelated it is impossible by statistical analysis to separate out their individual contributory influences. In certain circumstances there are certain ad hoc remedies. For example, it may be possible to estimate the effect of one explanatory factor from a different sort of data from that used to estimate the other. Alternatively, estimates may be made by imposing certain acceptable restraints on the relationships. But there is no general solution to this problem. Certainly techniques are being sought which are hoped to handle in some ways this problem of multi-collinearity, or at least reduce its consequences,2 but if multi-collinearity is serious, there is very little that can be done about it. What does this mean in terms of economic analysis? If intercorrelation between explanatory variables is strongly marked, it has the consequence that coefficients estimated by statistical analysis are, in technical terms, nonsignificant. You will recall that I have said that estimating a model involves, essentially, testing an economic hypothesis. We are concerned with whether certain economic influences, as measured by the explanatory power of a particular variable are relevant ones. If a particular element in an economic hypothesis is not relevant, we will expect statistical analysis to show the variable which carries that part of the hypothesis to be non-significant. The variable 1 Estimation of Production Functions is a classical problem in econometrics. For a n introduction to the literature see: A. A. Walters (op. cit.), pp. 269-341 ; L. R. Klein, An Zntrodwtion to Econometric.r (Prentice-Hall International, London, ~ g f i z )pp. , 84--II I ; C. E. V. Lcscr, Econometric Techniques and Problems (Griffin, London), pp. 61-74. A more advanced discussion is given by Marc Nerlove, Estimation and Identification of CobbDouglus P r o d d o n Functions (North Holland Publishing Co., Amsterdam, I 965). For example, component analysis, generalized inverse estimation, and ridge regression. These are techniques not normally treated in elementary texts. A classical use of component analysis in economic work isJ. K. N. Stone, 'On the Inter-dependence of Blocks ofTransactions', yournal of the Royal Statistical Society, Sufiplement Vol. 9, 1947, pp. 1-32. Ridge regression is set out 'in A. E. Hoerl and R. W. Keiinard, 'Ridge Regression: Applications to Non-Orthogonal Problems', Technornetrics, 12, 1970, pp: 69-82, and generalized inverse estimation in 1). W. Marquandt, 'Generalized Inverses, Ridge Regression, Biased Linear Estimation and NonLinear Estimation', Technometrics, 12, 1970, pp. 591-61 I . I 0 ECONOMETRICS: MEASUKEMENT IN ECONOMICS and the associated part of the economic hypothesis can then be dropped from the analysis. But when we are dealing with extreme multi-collinearity, we find that the statistical consequence is that coefficients inevitably have low significance. To drop variables, which remember, reflect economic influences, from the analysis in these circumstances may be a dangerous practice. T h e analysis would not necessarily have shown that a particular economic line of thought is irrelevant, but only that its influence is so inextricably linked with that of other factors that, from the data at hand, it cannot be separately distinguished -which is quite another matter. I t is here that we find a fundamental conflict between the economic specification of a model and what can be established by statistical analysis from available data. If one is interested only in prediction from a statistical function, that is to say estimating how one variable, say output, changes as certain explanatory variables, say capital and labour, change, the elimination of one variable highly correlated with another does not much matter; its contribution in statistical terms, is taken care of by the remaining variables. But if one's task is explanation or assessment of a particular economic hypothesis, then what goes into the model must be determined by economic analysis and not by what can be included to give satisfactory results with significance tests. This seems to me a particular problem in econometrics, and I do not think there is any entirely satisfactory solution to it. I now turn to the second example I wish to give to illustrate the demands economic data and analysis may make on statistical methods. The one I have discussed gives rise to problems which are riot peculiar to economics, though it illustrates difficulties almost always encountered in applied econometric work. This second one, however, arises directly from the nature of economic processes. I t is a consequence of the fact that economic relationships cannot always be treated in isolation, but may be part of a much more comprehensive set of relations. For example, the first illustration was concerned with the relation between imports and final demand. We may well consider this as one of several interrelated relationships in a wider model of economic growth. Others may involve home investment, employment, consumers' disposable income, the supply of money . . . and so on. The question is: what problems arise when we concern ourselves with only one relation which is really part of a more gcneral system of relations. T o illustrate the difficulties I will take a simple example developed from the theory of consumers' demand. We have seen that consumcrs' demand for a good is related to many variables, prices, prices of competing goods and substitutes, income, tastes, a g e . . . etc., and in our second illustration we isolated on particular aspect, the relation between demand and incomc. I will discuss now another facet of the demand function; the relation between demand for a good and its own price. When presenting elementary economic theory, we argue that 'other things being equal', that is, abstracting from the influence of other determining forccs, more will be dcmanded of a good at a low price than at a high price. That is to say that as price rises, 'other things being equal', demand tends to fall. If one considers a graph with price on the horizontal axis and quantities demanded on the vertical (which is the most natural way of assigning the axes, though many economists persist obdurately in doing the opposite) this relationship would be represented by a downward sloping schedule. Economic analysis also requires us to consider the supply of goods to the market, and the argument ECONOMETRICS: MEASUREMENT IN ECONOMICS I1 goes that 'other things being equal' the higher the price he can get, the more will a supplier be willing to supply to the market. So that on the same axes as before we can consider a rudimentary supply schedule which slopes upwards (cf. Fig. 3). We argue that there is an equilibrium position at which quantities I I I P Price FIG. 3. Demand and supply schedules demanded and quantities supplied a t the ruling price are equal; this equilibrium position determining simultaneously market price and quantities exchanged. This is, of course, a highly simplified model, hedged round with the 'other things being equal' qualification, but it does yeoman service in setting out an approach to market relationships. With its aid we analyse what happens when, say, a tax is imposed on suppliers, how market price and quantities exchanged react given different types of demand schedules, and so on. For our present purpose, this model is a model of three fundamental relationships which can be expressed as a set of three equations? (I) (2) (3) The demand function, which expresses quantities demanded as a function of price The supply function, which expresses quantities supplied as a function of price A market equilibrating relationship qd =fi(P) qE = f d P ) qd = 4 s = q I t will be appreciated that we have gone through the preliminary steps I have already indicated, first of economic analysis, then of setting up a model which reflects this analysis. By recording at different times the prices ruling on the market and the quantities bought at those prices, we can provide a supply of data. Given this, can the econometrician estimate the demand function, the first of the above relations, which says 'quantity demanded is a function of' price' ? The answer is unequivocally, that he cannot. I t is not, in this situation, that his data are not good enough, nor is it the fact that he has only a limited amount of data -with an unlimited amount of this sort of information he could not proceed. Nor, yet, is it a limitation of available statistical methods. I t is simply that what is being asked of the econometrician at this stage is impossible. Moreover, it can be proved to be impossible with the same sort of rigour that 1 This model is used as an introduction to simultaneous equations problems in most econometrics texts. The presentation used here follows that of L. R. Klein, op. cit. I2 ECONOMETRICS: MEASUREMENT IN ECONOMICS the mathematician is able to prove that 'squaring the circle' is impossible. The reason is that in terms of this model the data with which the econometrician is provided reflect the consequence of the market equilibrating process, the demand schedule interacting with the supply schedule, and nothing else. The price and quantity actually observed in any period involves both the demand schedule and the supply schedule. The demand function says 'quantities demanded are a function of price'. The supply function says 'quantities supplied are a function of price'. Simply relating equilibrium quantities exchanged to equilibrium prices, which is what market data provide, gives a relation which cannot be interpreted as either of the schedules: it is some sort of mongrel. Both schedules relate quantities to price, and statistically one cannot tell one from the other. We say that in this case neither the demand function nor the supply function is identijed. Therefore before one attempts the process of measurement, in this case of estimating the demand schedule, it is necessary to consider first whether it can be done at all. I n the situation which I have outlined, it cannot. How then can we proceed? We must re-examine our specification of the model, and we are here back in the field of economic analysis again. What we have to do is to take explicitly into account some of the influences on demand and supply which we have suppressed in our simplifying caveat 'other things being equal'. Although we may make this assumption for the purpose of elementary exposition, and for isolating certain important relations, the cconometrician cannot makc it in the same way in his statistical analysis. Since he is dealing with real world data, generated by real world economic processes, it is essential that his models reflect the important real world aspects of the processes which enable him to distinguish one relation from another. I t may well be, in fact, an impossibility to move from a simple, though adequate expository model to real world measurement. Developing the model so that it is suitable for statistical estimation involves including further explanatory variables or modifying the structure of the system. Let us assume that this has been done. We are now at the stage where we require a n appropriate statistical estimating technique to proceed. Can we estimate our now adequately specified demand schedule in the same way that we estimated the import/final expenditure relation, or the Engel curve expenditure/income relation which we previously discussed ? Can we take the particular relationship we are interested in, out of the system of relations to which it belongs and estimate it on its own? The answer to this is that we cannot; the techniques suitable in the previous examples are inadequate. I n order to estimate functions which are integral parts of fuller economic models, different, more sophisticated estimating techniques are required. The need being appreciated, these techniques have been developed, and it is in this particular field, that of estimating in the context of sets of functional relationships that greatest steps forward in the development of econometric methods have been and are being made.l 1 Most elementary econometrics texts discuss 'indirect least squares' and 'two-stage least squares' estimation. Other procedures such as 'three-stage least squares' and likelihood methods are only treated in more advanced texts, e.g. J. Johnston, op. cit.; H. Theil, Principles of Econometrics (North Holland Publishing Go., Amsterdam, 1971) and E. Malinvaud, Statistical Methods OJ bconometrm (North Holland Publishing Go., Amsterdam, I g66), and in specialized articles. ECONOMETRICS: MEASUREMENT I N ECONOMICS '3 IV I have so far been describing the econometric approach to measurement in economics, and the various sorts of problems to which it gives rise. I would like to develop these ideas a little more fully by reference to some work with which I a m currently concerned. I t is concerned with an aspect of investment analysis; not however, in the private business sector, wherein such work has long proved fruitful and has established an important body of results,l but in the public sector of capital expenditure by local authorities. This field of activity deserves special study because the amount of resources involved is considerable, and it is a sobering fact that not much is known about their detailed allocation. The sorts of questions my colleague Topham and I are asking are these : How do local authorities allocate resources between alternative fields - housing, education, etc., and how can we explain the variation in capital expenditure by diffcrent authorities in the same field, for example, housing? We are therefore concerned with an allocation problem, the sort of problem which is of the essence of economics. What we are attempting to do is to see how far we can explain and understand local authority investment decisions in economic terms. To this end we have been looking at local authorities as if they were firms. As decisions are taken by firms which involve the allocation of resources, so they are taken by local authorities, and just as it is assumed that there is some coherent way of analysing and explaining actions by firms, so do we feel that we may look for some coherent way of analysing and explaining capital expenditure decisions by local authorities. Most of our work to date has been concerned with housing, and what I say now is to be related to the housing investment decision.2 Our first need is to develop an acceptable theoretical framework. The starting point is the assumption that local authorities are concerned to improve the conditions of the community which they serve. Thus, just as firms make profits (the excess of revenue over costs) so local authorities provide welfare (the excess of social and private benefits over social and private costs). Rational behaviour in this sector is consistent with - indeed, some would say implies some attempt to maximize these benefits. This being the case, the projects which first enter into the capital programmes of local authorities are those which give the greatest net benefit to the community. Local authorities may be thought of as including in their capital programmes the projects with the highest rate of return first, then the next highest . . . and so on. By analogy with private investment, the return of a particular project is called the Social Marginal Efficiency of Investment (SMEI), the word Social being included to underline the fact that in this case social costs and benefits are included in the investment arithmetic. We conceive, then, of a schedule, the SMEI schedule (shown in Fig. 4) which indicates the relationship between, on the one hand, the rate of return from investment, and on the other, the level of investment. An introduction to the extensive econometric literature relating to investment analysis is given in M. K. Evans, Macroeconomic ActiviQ (Harper and Row, New York, 1969), Chapters 4 and 5. An interesting general study is D. W. ,Torgemon and C. D. Siebert, 'Theories of Corporate Investment Behaviour', American Economic Review, 4, 1968, p. 681. * R. J. Nicholson and N. Topham, 'The Determinants of Investment in Housing by Local Authorities: An Econometric Approach', Journal of the Royal Statistical Society, A, Vol. 134, 1971, PP. 273-320- 14 ECONOMETRICS : MEASUREMENT IN ECONOMICS I t may be assumed that authorities will continue to undertake projects until such time as projected return is equated with costs of funds at the margin. This leads us to look at the other side of the picture, the cost of funds. This cost will increase with the size of the programme during dear money periods because authorities use the average rate of interest on all projects as the relevant rate. But the real marginal cost of funds will also increasc with increasing investment programmes, because as debt-asset ratios rise, so will certain risks to which local authorities are exposed increase, for example the risk of increasing rates (if you like, the risk of distributing a negative dividend). For local authorities, pplitical risk is also a factor which must be taken into account. We therefore conceive of a schedule which measures, if you like, the risk-rate in obtaining funds as investment increases. This schedule which we assume rises as investment increases (as shown in Fig. 4), we call the Social Marginal Cost of Funds (SMCF) schedule. We conceive, then of investment in housing in a local Real rate , of interest I I 1- 1 Investment FIG. 4. SMEI and SMCF schedules authority proceeding to the position a t which these two schedules are in equilibrium, geornctrically where they intersect, this position determining the level of investment undertaken (I),and the equilibrating rate between the rate of return from the investment and the risk rate of incurring the necessary debt ( r ) . It is obvious that this model has very considerable similarities to the simple supply and demand model which we previously examined. Indeed, the model can be formulated as three structural equations : SMEI schedule SMCF schedule Equilibrating Condition ym =f@) re =fz(I) rm = re = r This however, is merely a skeleton framework, and it has to be filled in. For just as the simple supply and demand model made heroic assumptions about 'other things being equal', so does this Social investment model. And since econometricians work with data derived from the real world, so must we take explicit account of those other influences which affect, or in some instances govern, the local authority decisions. We have grouped what we believe to be the most important influences into three classes. First, those which specifically affect the SMEI schedule. These are factors such as size and condition of housing ECONOMETRICS : MEASUREMENT IN ECONOMICS 15 stock, overcrowding, population growth, the socio-economic condition of the area, and so o n . . . which govern the net benefits of capital expenditure on housing. They may be denoted X I , Xz . . . Secondly, we consider factors which affect the risk associated with the financial implications of the investment programme. For example, ratio of interest payments or total loan charges, to the local authority's total rateable value, rate poundage, etc.; that is to say variables which reflect increasing financial pressures. These may be denoted Yl,Yz . . . Finally we consider a third group of variables which are designed to reflect the attitudes, or local drive, of individual local authorities. Such factors are certainly relevant in conventional investment analysis ; there are go-ahead firms, laggards and unenterprising firms, but to my knowledge these differences have never been taken explicitly into account. We have tried to represent them by such measures as dominance of a particular political party, the local authority's proportion of total housing stock, and the importance of current investment in housing to that in the past -which indicates local impetus. They may be denoted 51, 5 2 . . . and our assumption is that these attitude variables can affect either schedule. The first two equations of the model are then formally expressed as : SMEI schedule rm SMCF schedule rc =fi =f2 (I,XI, Xz, . . . ,