Knowledge that Transforms

G. S. Maddala, Joseph B. Kadane, Some Notes on the Estimation of the Constant Elasticity of Substitution Production Function, The Review of Economics and Statistics, Vol. 48, No. 3 (Aug., 1966), pp. 340-344

PpTHE GROWING dependence of the local public sector on intergovernmental aid and the current interest in new forms of aid to be directed to the development of slower growing regions, such as Appalachia, make an increased knowledge of the relationship between these intergovernmental grants and the actions of the local public sector of particular importance. Have these intergovernmental grants increased or decreased the activity of the local public sector? Is there a discernable difference in the impact of federal as opposed to state aid and in the impact of the programs among individual states? One method of measuring the effect of aid programs would be to consider the relationship between these transfers and expenditure levels.' In this paper, however, the focus is on the impact upon the proportion of locally received income disbursed to the public sector or local fiscal effort. Consideration of this particular relationship is useful because of the interest centered on local fiscal effort in the literature on intergovernmental relations. As intergovernmental aid is only one of the several factors which should bring about changes in the level of local fiscal effort, multivariate regression analysis is used to estimate the impact of all these factors. Before considering the details of the multivariate analysis, a review of the nature of the expected relationship between the local fiscal effort and intergovernmental transfers is useful. For lack of a better model let us assume that local governments complement the operation of the private market in providing goods which the private market cannot effectively handle. Attacking the problem in this framework means that the effect of an increase in intergovernmental transfers on fiscal effort can be thought of as the result of a combination of three factors: (1) the marginal evaluation by the community of the benefits of public consumption versus private actions concerning present or future private consumption and work effort or leisure, (2) the degree of legislated controls and restrictions over the use of transfers imposed by the donor jurisdiction, and (3) the institutional structure. Any community has available to it a package of state and federal aid programs. Some of these programs are tied to expenditure levels or require local matching as a prerequisite for participation. community is able to purchase an additional amount of a specific public good at a discount. actions of the community will reflect both an income and substitution effect. If the community chooses to increase its consumption of the cheaper public good, it will have to raise its fiscal effort. Other aid programs fall into a category of income grants that are not encumbered by matching provisions. It would seem reasonable to assume that a community would spend part of this additional income on public goods. In the process of making the remaining income available for private uses local fiscal effort as defined in this paper must be reduced. This means that aid has some positive effect on public expenditures, but some of the aid is used as a substitute for local charges. If more than one type of public service is being provided, adjustments may take * author is Assistant Professor of Economics and Research Associate in the Bureau of Business and Economic Research at the University of Maryland. This research, undertaken while the author was at the University of Pittsburgh, was supported by Area Redevelopment Administration Technical Assistance Grant No. Co-6042. Computations performed at the University of Pittsburgh Computation Center were partially supported by National Science Foundation Grant No. G-11309. author is indebted to Professors Harvey Brazer, George Break, Jerome WVells, George Green, and Alarina v. N. Whitman for their helpful criticism, and to William Duffy for his assistance in collecting data. 1 For some recent direct estimates of the effect of intergovernmental grants on the expenditures of specific types of jurisdictions see Edward F. Renshaw, Note on the Expenditure Effect of State Aid to Education, Journal of Political Economy (Apr. 1960), 170-174; S. Sacks and R. Harris, The Determinants of State and Local Government Expenditures and Intergovernmental Flows s of Funds, Nratio,tal Tax Jouirnal, (MIarch 1964), 75-85; and George A. Bishop, Stimulative versus Substitutive Effects of State School Aid in New England, National Tax Journal (June 1964), 133-143.

BY exploitation, we mean that a factor of production is receiving less than its marginal revenue product. Relative exploitation connotes that the marginal rate of technical substitution of two factors is not equal to the ratio of their scarcity prices. Hence, either both factors may be exploited, but in different degrees, or one factor may be exploited while the other is not. In the present paper, a measure of the change in relative exploitation of capital and labor is presented together with empirical results for three two-digit industries (machinery except electric, primary metal industries, and electric and gas utilities), where the observations are drawn from the period, 1948-1960. Knowledge of variations in relative exploitation is useful in quantifying and explaining the sources of change in the distribution of income between the factors of production. This, in itself, is sufficient justification for focusing on the change in relative exploitation rather than the level. Although there may be more intrinsic interest in a measure of the level of exploitation as defined above, the framework used below does not lend itself to such a measure. The paper is laid out in the following manner. An elementary model of exploitation within a constant elasticity of substitution (CES) framework is presented first. This is followed by an econometric specification of one of the equations which must be tested in order to derive the required measure, while the succeeding section is devoted to the direct estimation method of the second required equation, the CES production function. Next, the empirical results for three selected industries are presented and discussed. The subsequent section contains the quantification of the changes in relative exploitation. In a later section, some problems with the framework and measuring procedures are discussed.

PpTHE conventional wisdom on the subject of marketing boards in primaryexporting economies has long been that their principal function is that of domestic stabilization.' It has been argued elsewhere that the performance of Nigerian marketing boards should be evaluated instead on the basis of their roles as revenue earners (through the earning of trading surpluses) for the development effort.2 It is worth considering, nevertheless, what exactly has taken place with respect to domestic stabilization through marketing board action in Nigeria. It is difficult to discuss the stabilization issue in isolation from other related policy issues. There may, after all, be several policy targets, (including for example, the maximization of export receipts or of trading surpluses), of which stabilization is only one. Stated still more broadly, there may be legitimate doubt as to the possibility of separating stabilization from development issues. Overall development will, after all, ultimately bring the flexibility of factor use and the diversification of the output-mix which are the best guarantees against extreme economic instability. It has also been argued, though never proven, that the degree of instability found in an economy, of itself, has effects upon the pace of development. Thus 4. ..a full case [for stabilization] only exists when it can be shown that a scheme can be devised which will remove some or all of the harmful effects of instability without itself having even more harmful effects on the longrun economic welfare of the community.7 3 Still, interrelationships between growth and instability are, at least in the short run, not sufficiently important that they make a pure discussion of stabilization 'illogical or uninteresting. It will be helpful, for the purpose of evaluating the success of interseason stabilization efforts, to have summary measures of the degree of instability of producer prices, producer incomes, world prices, and export receipts potentially distributable to the producer (potential producer income). With these, one can begin to compare actual experience with that which would have been obtained in the absence of the marketing boards. The simplest such measure is average percentage annual change, always expressed, for the sake of yearto-year comparability, as a percentage of the higher of the two observations. That is,

T HE theoretical role of technology in economic growth is no mystery. It provides new machines and processes (improved capital quality) that raise output relative to input, or productivity. Yet for several reasons, once it comes to pursuing this truth by observation, hypothesis, and testing, every manner of obstacle seems to appear. One may be told that technology per se is rarely susceptible of measurement, that productivity increases can be attributed to many causes, impossible to untangle, or that the precise link between embodied technological change and productivity is too hazy. Such doubts are often justified. At times, however, they may unduly discourage those whose curiosity is not satisfied by aggregate production functions, and who would prefer to investigate more closely some particular reasons for productivity increases. To be clear on this point, technological innovation frequently is difficult to represent quantitatively. Output per unit of input often does rise for non-technological reasons (economies of scale, changes in rates of utilization of capacity, or optimal factor combinations), but there must be important cases where the reverse is true. One such case seems to be electrification of manufacturing industries. Here the rate of technical change can be reasonably well measured in terms of horsepower capacity of power equipment and consumption of power (work output). Furthermore, this revolution in the application of power can be viewed against the background of clear, known changes in manufacturing productivity changes which remain mostly unexplained. Specifically, it might be expected that there would be a relationship between electrification and reduced costs of production.' More broadly, the case of electrification might illustrate how the quantitative link between technological change and productivity can be developed. To this end, what follows (section I) traces some suggestive findings regarding the rise of electric power and changes in productivity in American manufacturing, and (section II) attempts to construct a theoretical framework for measuring the impact of electrical technology on factor costs. It is hoped that section II will help shed more light upon the broader question mentioned above, by providing procedures that could be adapted to a wide range of technologyproductivity cases.

T HIS paper represents recent estimates of the rate of growth of output and labor productivity in wholesaling and retailing foods of farm origin destined for United States civilian consumption.' Technically, primary interest in the paper is in the results of using different measures of output for a trade group. These measures include an index of gross output and two indexes of net output, a double-deflated value added series and a margin-weighted series. The double-deflated value added series is nearest to an ideal measure of unduplicated output, whereas the margin-weighted index is a compromise usually dictated by available data.2 Margin-weighted net output indexes were used by Barger [2], Kendrick [5], and Alterman and Jacobs [1] in order to measure net output in total trade. As far as I know, there have been no previous attempts to estimate double-deflated value added net output for trade. I know of no previous studies of labor productivity in food trade. The major findings presented in this paper are: (a) net output per man-hour in wholesaling and retailing farm-originated foods grew at an average yearly rate of 2.8 per cent from 1929 to 1958, substantially faster than in the private nonfarm sector but less than in agriculture; (b) the double-deflated value added measure of net output rose significantly more than the margin-weighted measure during the period; and (c) gross output grew at about the same average yearly rate for the three decades as a whole as net output measured by doubledeflated value added.

HE absence of any observable flow of net in the world argues for exclusive adherence to an income-originating interpretation of the value added by particular industries or sectors. Yet, the merit of the quest for a net production measure cannot be gainsaid. The notion of splitting up gross national product into the constituent contributions made by individual sectors of the economy carries persistent appeal despite the fact that the finalgoods and services produced by many industries never actually enter the physical flow of GNP. It has motivated recent efforts by the Office of Business Economics at the Department of Commerce to construct a set of accounts showing measures of the physical volume of the gross national product originating in the various industries of the Nation, which in principle aggregate to the physical volume of obtained by deflating final expenditures.' This appeal is, of course, buttressed by the same conventions against double-counting that underlie the current dollar GNP concept. Paralleling the concern with the total economy's capacity to produce 'goods and services to satisfy final demand, there is an abiding reluctance to attribute the results of the application of factor services at all the preceding production stages to that activity which happens to come last in the sequence of fabrication. Hesitancy on thispoint is reinforced by the 'knowledge that the degree of integration varies among industries at any moment in time, as well as over the course of time within individual industries. Given variations of the latter kind, a disinclination to accept the movements of an actual physical series as an indication of the contribution made to GNP by the industry in auestion is thoroughlv reasonable. What is wanted is a measure which excludes the contribution made to the given industry's physical by inputs purchased from other industries. A measure of real net output in that sense would be entirely meaningful. Having reaffirmed the usefulness of the theoretical notion of net commodity output, it is all the more necessary to acknowledge that during an earlier exercise in conceptual tub cleaning undertaken by the writer,2 the proverbial baby seemed to slip out along with the bath water. On that occasion it was shown that the residual, or double-deflation approach to the ideal index of net output suggested by Fabricant and Geary leads to an unfamiliar and rather harrowing index number problemone which manifests itself in the appearance of negative value added estimates.3 The index number problem in question will arise even in the absence of aggregation, because the relative product and materials prices pertaining to a given industry at a specified date reflect a particular technological nexus (between the quantity of input and output) which need not be appropriate to the production conditions prevailing at some other date. Eschewing resort to the Fabricant-Geary formula, and all the difficulties of interpretation associated with the index numbers it