Knowledge that Transforms

analysis; analysis 2 is the first additional analysis referred to above; analysis 3 is the second. It should be noted that use of the BLS series rather than Suits's series raises the square of the multiple correlation coefficient from o.85 (implying an adjusted coefficient of multiple correlation of 0.93) to 0.95, significantly higher. However, when contract duration is still used to divide real retail price (analysis 2), the coefficient of the ratio, and hence the elasticities with respect to price and contract duration, are not significantly altered. However, treatment of average contract duration as a separate variable (analysis 3) significantly changes the price elasticity but leaves the elasticity with respect to contract duration unchanged. Analysis 3 yields a price elasticity which is not markedly different from those obtained by previous investigators. The conclusion must be, I think, that by dividing real retail price by average contract duration, Suits imposed an unwarranted restriction on his statistical analysis and reduced his price elasticity to an unreasonably low level, while increasing his income elasticity to a level somewhat beyond that found in earlier investigations. Thus the influence of the automobile manufacturers on the sales of their product may well be greater than we might be led to believe on the basis of Suits's analysis. One further shortcoming in the way in which Suits introduces credit terms stems from the fact that credit terms are likely to affect new car sales differently in a decline than in an upswing. Availability of credit is a limiting factor primarily in those periods when, for other reasons, there are pressures for rapid expansion in sales. Thus, the marked easing of automobile credit terms in I955 may be regarded as permissive rather than causal. The fact that automobile credit remained relatively easy in I958 did little to stem the decline. One way ;to take account of this asymmetry in the effect of credit terms would be to allow for different elasticities with respect to average contract duration in periods in which sales were declining and in periods in which sales of new cars were increasing. However, Suits did not do this.9

SIX years ago, the author proposed that technological change be taken into account in a dynamic input-output model by making the input coefficients themselves vary with capital expenditures for growth and change-over. The proposal was rooted in the notion that the input structure of an industry at any given time was an output-weighted average of input structures characterizing technologies of different vintages. Investment in new equipment would increase the relative weight of the latest techniques in the industrial average while scrappage would decrease the relative weight of older techniques. If the technologies representing new capacity installed at various times were known, it would be possible to predict changes in the average technique from these and the time pattern of expenditures on equipment. Considerable effort during the past several years has been directed toward evaluating this approach to the explanation of technological change, that is, to seeing to what extent changes in input structure over time could be predicted from technical parameters for best practice technologies and expenditures on equipment over the period.' Direct verification of a dynamic input-output system with changing coefficients was undertaken,2 but was plagued with three major difficulties: (i) we have not had comparable coefficient matrices at two points of time; (2) available estimates of plant and equipment expenditure for individual industries have been crude, at best; and (3) the system as originally stated incorporated the hypothesis about technological change into the Leontief dynamic system, making the interpretation of its outcome await the solution of the same theoretical problems.3 In view of the obstacles to a satisfactory test in the general equilibrium context, it seemed expedient to investigate the specific question of the relation of technical change to investment more directly, and in particular, separately from the question of what determines the rate of investment itself.4 Last year certain cross-sectional material was made available by the Bureau of the Census for a pilot study in the analysis of technological change.5 On the basis of this information, we began to investigate in some detail to what extent it is possible to account for changes in the distribution of input coefficients of individual plants in a given industry in terms of the distribution of their equipment expenditure patterns. Specifically, the present study treats the question: to what extent is it possible to explain changes in the distribution of individual plants' input coefficients in terms of their respective equipment expenditure patterns and a common incremental or best practice production function. The approach will be successful to the extent that the specific characteristics of installed equipment govern quantitative inputoutput relationships and that plants in a given industry tend to purchase the same kinds of equipment at the same time. General experience tells us that neither of these conditions prevails entirely, in any industry. During the same period, some plants will be buying new process equipment and other plants new materials-handling equipment. Older plants will be limited in their alterations, while newer plants will be able to take advantage of a wider range of alternatives. Initial differences in technology, related to product quality or location, may be expected to govern additions to, or replacements of, capacity as well.

D. S. Bridgman, Problems in Estimating the Monetary Value of College Education, The Review of Economics and Statistics, Vol. 42, No. 3, Part 2. Higher Education in the United States: The Economic Problems (Aug., 1960), pp. 180-184

M ETHODS used to fit cost functions either to time series or cross-section data have been extensively criticized.' In a recent article Johnston2 has reexamined some of these criticisms and has to some extent succeeded in reestablishing the validity of the two major findings, i.e., (i) constant marginal cost, (2) decreasing long-run average cost. There are, however, criticisms made by Friedman (and Stigler) which Johnston is less successful in countering. The first which we shall consider here is a version of the classical regression fallacy. Friedman expresses this as follows: a firm produces a product the demand for which has a known two year cycle, so that it plans to produce ioo units in year one, 200 in year two, ioo in year three, etc. Suppose also that the best way to do this is by an arrangement that involves identical outlays for hired factors in each year (no 'variable' costs). If outlays are regarded as total costs, average cost per unit will obviously be twice as large when is ioo as when it is 200. If, instead of years one and two, we substitute firms one and two, a cross section study would show sharply declining average costs. When firms are classified by actual output, essentially this kind of bias arises. The firms with the largest outputs are unlikely to be producing at an unusually low level; on the average they are clearly likely to be producing at an unusually high level, and conversely for those that have the lowest output (page 236). And Stigler says: that three firms on average (over say a decade) produce ioo units each per year at an average cost of $io. In any one year because of weather, catastrophe, illness or death of a salesman, regional differences in business, etc. ('chance fluctuations') the firms will have sales (outputs) above or below the decade average of i0o. Suppose firm A sells only 8o units in a given year, firm B, Ioo units and firm C, I20 units. Suppose further that for each firm costs include (I) $500 of fixed costs plus (2) $5 of variable costs per unit of output. Tabulating the results: