Knowledge that Transforms

IN economic welfare terminology, the social benefits of education result in an outward extension of society's utility possibility function.' These can be divided into current and future benefits with some accruing directly to the family whose child is being educated, while other benefits are mainly indirect. It is likely that of all the benefits of education, one of the most important is the gain in productivity and earnings of students. Public education increases the knowledge and skills of students and, therefore, tends to increase their potential earnings. While there is general agreement that the level of education attainment has a positive effect on income, relatively little is known about the magnitude of this relationship when differences due to other factors are taken into account.2 It is to this problem that we will address ourselves in this paper. Our procedure will be to advance a hypothesis about those factors, including years of schooling, affecting a person's income. We will then test this hypothesis by submitting survey data to a multivariate analysis, thus obtaining, in a case study, estimates of the net relation between education and future income. These findings will be used to estimate incremental lifetime earnings resulting from education and their present values, so that comparisons can be made between these benefits and corresponding annual education costs. Finally, some estimates of the rates of return of education investments will be made.

THE use of distributed lag techniques in econometric research has greatly advanced the methods of analyzing short-run and long-run patterns of behavior. In this article, we shall be particularly interested in estimating quantitatively the differences between shortrun and long-run marginal propensities to consume (MPC) by means of a distributed lag consumption function, where current consumption is a function of a series of past incomes with geometrically decreasing weights. Estimates of this general kind have already been carried out in earlier work by Friedman, Klein, and Nerlove.' However, while these studies are based on time series data, the estimates in the present article are based on cross section data. The latter data have, as far as I know, never been used for this purpose. Clearly one cannot estimate a distributed lag consumption function from a single period cross section of families. One may however make use of reinterview surveys to provide the necessary time dimension. Since, in our study (as is usually the case), the reinterview surveys extend over two periods only, the distributed lag function to be used must be limited to the very simple type mentioned above. While the economic formulation of the consumption function to be used is based entirely on the three foregoing works, the statistical analysis is different and involves the application of new techniques in dealing with the least squares bias inherent in our particular problem. The outline of this article is as follows. In section II we review the formulations of the economic relationship. The statistical problems of the least squares bias and of consistent estimation are taken up in section III. In section IV, we discuss some points concerning the statistical data which are based on three reinterview surveys. The empirical results are presented and discussed in section V. Finally, section VI deals with some qualifications of our conclusions.

T HE econometric study described here is an attempt to discover and explain patterns in the rate of commercial construction. It focuses on the construction of office buildings and retail stores, which together account for some 85 per cent of the total. Models constructed on the basis of cross-section analysis are fitted with aggregate time-series data. In the cross section, office construction is studied for the central city and metropolitan ring of 13 of the country's largest standard metropolitan areas (SMSA's) and store construction for 18. The time-series analysis is based on national data for metropolitan areas and covers the 11year period 1949-1959. Two previous studies of the industry provided the theoretical foundation for the models developed.' A third reported the cross-section analysis separately.2 The results presented here are consistent with those ideas presented in the previous work. The analysis is divided into four phases. In the first, the basic hypothesis is stated and modified to exploit characteristics peculiar to the industry. In the second and third the empirical work is described and evaluated. In the fourth, conclusions are summarized.

Several years ago I inferred that the stock demand elasticity of non-farm housing with respect to income is about unity from a time-series regression analysis of the rate of new construction on income, other determinants of desired stock demand, and the actual housing stock.1 In a recent paper, Tong Hun Lee argues that I used an improper measure of the rate of interest and, because credit terms which I omitted were positively correlated with income, my estimate of the income elasticity of housing demand was upward biased.2 Lee concludes that this elasticity is substantially less than unity. In this comment I shall argue that Lee's results are inconsistent with other recent evidence on the income elasticity of housing demand and that his interpretation of the relation between interest rates and contract lengths is unsatisfactory on both a priori and empirical grounds. Even if Lee's criticism could be accepted at face value, his modification of my flow demand equation for non-farm housing yields an estimated income elasticity which is inconsistent with other recent evidence. In my study, I estimated the income elasticity of housing demand in several ways, one of which was a comparison of the rental value of housing with the housing stock and income. This comparison yielded an estimated income elasticity of 0.94,3 which is quite close to the value I inferred from my flow demand regression equation. Now, this latter estimate in no way depends upon the rate of interest or other aspects of the cost of capital to home buyers. While the profitability of adding to the housing stock, and hence the stock in existence at any time, is influenced by the cost of capital, the rental value of the existing housing stock depends only upon the size of this stock and the position of the demand curve for the services of housing. I am the first to admit that this estimate of mine could be in error for several reasons, but the omission of credit terms is not one of them. More recently, Margaret G. Reid's exhaustive analysis of the effect of income on housing demand suggested that the income elasticity is substantially larger than unity, perhaps as large as two.4 Lee mentions her results in a footnote but claims they are upward biased because she, too, omits credit terms.5 In my opinion, however, Lee brushes Reid's results aside much too lightly. Her comparisons of the expenditures of tenants with their incomes are completely free of any bias due to the omission of credit terms for the reasons already discussed in the paragraph above. These estimates are all substantially larger than those shown by Lee in his equations (6) and (11), the latter being about 0.34. In addition, while the value of housing an owner inhabits is influenced by the cost of borrowing for him, there is no reason to expect the cost of borrowing to differ among different borrowers in the same city at a given time apart from differences associated with different administrative costs and risk premiums for different kinds of mortgage loans. (Of course, owners may have originally acquired their homes at differing times, but there is likewise little reason to suppose that differences in the cost of borrowing associated with different time of acquisition is systematically associated with income differences among owners.) income elasticities Margaret Reid found for owners in different parts of the same metropolitan area at a given time exceed Lee's estimates even more than do her estimates for renters.6 I conclude, therefore, that Lee's findings are highly questionable because his income elasticity estimate is so much less than those referred to above. Many economists believe that, in addition to contract interest rates, measures of contract maturities and loan-to-value ratios are needed to describe the cost of borrowing on mortgages. When interest rates fall, so the argument goes, mortgage lenders reduce contract interest rates but also will make longrer maturity and higher loan-to-value ratio loans than previously. If some borrowers prefer longer maturities and lower down payments, the more generous terms which lenders allow reduce the cost of borrowing in addition to the cost reduction resulting from the fall in contract interest rates. 1 Richard F. Muth, The Demand for Non-Farm Housing, in Arnold C. Harberger, ed., Demand for Durable Goods (Chicago: University of Chicago Press, 1960), 29-96. 'Tong Hun Lee, The Stock Demand Elasticities of Non-Farm Housing, this REVIEW, XLVI (Feb., 1964), 82-89. 3 Richard F. Muth, op. cit., 64. 'Margaret G. Reid, Housing and Income (Chicago: University of Chicago Press, 1962). 'Tong Hun Lee, op. cit., footnote 31, p. 88. 'Margaret Reid, op. cit., especially Chaps. 7 and 8, pp. 162-207.

turities on borrowing costs has little empirical support either. In addition, these results provide little support for the more conventional assertion that a lengthening of either contract lengths or loan-tovalue ratios is indicative of a reduction of borrowing costs to home buyers. Admittedly, the strongly negative coefficient of G in equation (3) suggests that something is wrong with my original equation.10 I find little merit, however, in Lee's contention that I used an improper measure of borrowing costs and that my estimate of the income elasticity of housing demand is substantially upward biased as a result.

DURING the last decade there have been increasing numbers of empirical studies made on technological advance of an aggregate economy or a sector of an economy. The most commonly used procedure for empirical investigations of this kind nets out intermediate product inputs consumed in the production processes. Netting out the intermediate inputs from both sides of the production function implies that there is no substitution between primary inputs and intermediate inputs. It is common knowledge, however, that some intermediate product inputs, e.g., fertilizers and weedkillers, are substitutes for primary inputs, such as land and labor. In reference to the general experience of advanced countries, specifically in reference to Japanese experience of agricultural development, an important objection may be raised. In this paper, I shall focus my attention on the measurement of the elasticity of substitution between labor and non-labor inputs by the use of data both including and excluding intermediate product inputs. I shall estimate the elasticities of substitution by combining cross section and time series data in postwar Japanese agriculture. Indices reflecting changes in production efficiency will be obtained. Finally, I shall compare the results of the grossoutput approach and the value-added approach with respect to both substitution of inputs and improvements in production efficiency. II An Estimating Model of the Elasticity of Substitution Between Labor and Non-Labor Inputs

Other calculations show that this conclusion is not particularly sensitive to the choice of bo. However, if the growth of capital per laborer were double or triple what we actually experienced, then, of course, the sensitivity of growth of output to the elasticity of substitution is significant. For example, the U.S.S.R. experienced approximately a 200 per cent increase in capital per man hour over the 1947-1960 period.7 Column 2 of table 1 shows that the effect of this large an increase in capital per man hour is much more sensitive to the elasticity of substitution. But even in this case, compared with the 140 per cent increase in output per man hour actually achieved in the Soviet Union over this period of time, the differences in the predictions of the effects of the growth of capital appear relatively small. The above analysis suggests that while the CES model may have significant advantages over the Cobb-Douglas model for analysis of growth of output in economies where the capital-labor ratio is changing rapidly, for analysis of growth of output in the United States it does not do much that the old Cobb-Douglas model didn't do. The road to improvement in our presently very unsatisfactory growth theory must lie in other directions. ublished data from Richard Moorsteen.