Knowledge that Transforms

F. Gerard Adams, Grace Milgram, Edward W. Green, Christine Mansfield, Undeveloped Land Prices During Urbanization: A Micro-Empirical Study Over Time, The Review of Economics and Statistics, Vol. 50, No. 2 (May, 1968), pp. 248-258

OR many years there has been deep concern as to whether a shortage of doctors exists either nationally or in particular localities. This study investigates how well the distribution of the national stocks of medics (the generic term used here to refer to physicians and dentists) among areas corresponds to the distribution of population, and what influence is exerted by other variables such as effective demand for medical service, barriers to migration, and the locational preferences of medics. The unit of area in this study is the state; this is mainly because of availability of data. However, differences of size among the states, as well as in the relative populations of rural and urban areas and in the distribution of the urban population among large and small cities, seriously affect the observations. To remedy the resulting distortions as fully as possible, one of the authors is now analyzing the determinants of physician location among counties with results to be presented in a subsequent paper. However, many more variables for longer periods of time can be analyzed for states as a whole than for smaller sub-divisions.' The substance of our findings is contained in the regressions presented in the various tables. In considering them, the reader should bear in mind the following points: (1) We have analyzed a number of distinct types of medics: All Physicians, Self-employed Physicians and Dentists. Where our findings apply to all types we make generic statements. (2) To avoid discursiveness we discuss only those coefficients believed indicative of pervasive long-run forces affecting the allocation of medics. (3) In section I, the discussion is purely descriptive, i.e., the regression coefficients reflect observed associations but are not estimates of the structural parameters of a particular model. They do, however, have theoretical relevance. Some estimates of demand and supply functions are discussed in section II. (4) The years studied are 1930, 1940, 1950 and 1960 or, for some variables, years close to them. Lack of data for a sufficient number of years makes satisfactory time series analysis impossible. Section III summarizes our findings, and comments briefly upon their empirical implications. Our dictionary of variables is as follows: X (i)-Number of medics in the ith state. X2 -) Population of the ith state. X3()(Total) personal income of the ith state. X4-Volume of training facilities (number of places in medical classes) in ith state. X5-i Barriers to entry (percentage of applicants for licensure who fail examinations) in ith state. X6Population in ith state living in urban areas of more than 2,500 persons. X7-) Average income of medics in ith state.

D IFFERENTIATING a production function with respect to capital and labor yields equations for the marginal productivity of capital and the marginal productivity of labor. The variables that determine the marginal products in these equations are the same as those in the production function. If the data used to estimate the parameters of the production function are inserted into the equations for the marginal products, the marginal productivities of both capital and labor can be estimated empirically. The same data and equations also make it possible to determine the causes of any changes in the marginal products. How much of the rising marginal productivity of labor is caused by technical progress; how much is caused by a rising capital-labor ratio? If the economy is in equilibrium and there are no economies or diseconomies of scale, actual and marginal returns should be identical. Any differences between the estimated marginal products and the actual returns to capital and labor means that the economy is in disequilibrium; the size of the differences measures the extent of disequilibrium. If disequilibrium does exist, what causes the observed pattern? What are its implications for investment decisions in both human and physical capital? This paper applies the above approach to the American economy from 1929 to 1965.

U NTIL the mid-1950's, the traditional view on the consumption of housing had been that the elasticity of housing consumption with respect to current income was less than unity.' However, recent literature on the theory of consumption function [15] [4] has pointed out that, in relating income to consumption, the concept of income should be that of permanent income rather than current or measured income, and that the use of measured income imparts a downward bias in estimating the effect of permanent income on consumption. Since housing consumption in particular may also be affected by the long-run prospect of income rather than by a single-year measured income, the permanent income elasticity may be higher than the previous estimates of the measured income elasticity of housing. The change in the concept of income encouraged a number of economists to test the effect of permanent income on housing consumption. Maisel and Winnick [14] tested the permanent income hypothesis of housing consumption by utilizing the I950 Survey of Consumer Expenditures. Contrary to the permanent income hypothesis, however, they reported that housing consumption was no more responsive to changes in permanent income than to changes in measured current income. Subsequently Margaret Reid [19] conducted an extensive cross-sectional study by using housing and income data obtained primarily from the 1950 Housing Census. Differing from Maisel and Winnick, Reid found that the demand for housing was indeed more responsive to changes in permanent income. Moreover, Reid's estimates of the permanent income elasticity of housing were substantially greater than one, and in fact ranged from 1.5 to 2. On the other hand, the author's recent time-series analyses [10] [11] indicated that while housing demand was more responsive to changes in permanent income, the permanent income elasticity of housing was still less than unity. The purpose of this paper is to obtain the cross-sectional estimates of permanent income elasticity on the basis of the 1960-1961-1962 reinterview Surveys of Consumer Finances. This study has three distinct features. First, this study differs from other housing studies in that it uses the instrumental variable method along the lines suggested by Livitan [12]. Livitan has recently shown that, for any year of analysis, the use of a lagged or future measured income as an instrumental variable yields a powerful test of the permanent income hypothesis. Second, since this study utilizes threeyear reinterview data, as a result both one-year and two-year lagged or future incomes can be used as instrumental variables. Due to the lack of data, Livitan [12] could not experiment with a two-year lagged or future income as an instrumental variable in his analysis of total consumption. Both Livitan [13] and Friedman [5], however, agreed that it is highly desirable to use a two-year lagged or future income as an instrumental variable. Finally, this paper develops and uses an extended version of Livitan's instrumental variable method in order to take account of the case in which a lagged or future income may not be a perfect instrumental variable for permanent income. The cross-sectional estimates of permanent income elasticity so estimated are substantially * The author is Professor of Economics at the University of Wisconsin-Milwaukee and a member of the Social Systems Research Institute at the University of Wisconsin, Madison. He is grateful to Melvin Lurie and Keith Phillips for their helpful comments on the initial draft of this paper. The author, however, remains responsible for the views expressed in this paper. This study was originally supported by the National Science Foundation under grant GS-631 and later by the Graduate School of the University of Wisconsin-Milwaukee. The data used in the study originally came from the Surveys of Consumer Finances conducted by the Survey Research Center, University of Michigan, in cooperation with the Board of the Governors of the Federal Reserve System. The author is indebted to the Social Systems Research Institute for making available the data coded on magnetic tapes. 1 For a brief account of the early history of housing studies, see the author's paper [10, pp. 82-83].

where W is the annual rate of change of money wages in manufacturing, P is the annual rate of change of consumer prices, U is the average annual civilian unemployment rate, and R is the average annual profit rate of manufacturing corporations.' On the assumption that P -(W), specifically, P = W r, where r is the trend rate of increase of output per man-hour in the private non-farm economy the steady-state solution for W is a a-blr + b3R + b2 t. (1.2) 1-b, 1-b,

SUBSTANTIAL interest in recent years has centered on the relationship between personal earnings and a myriad of education related variables.' In this paper we present estimates of the impact on earnings of schooling, an index of ability, and a set of other relevant variables for a cohort of recent entrants to the labor market who have had some graduate education in the arts and sciences. Aside from a purely intellectual curiosity, there are several other reasons for investigating the annual earnings for a group of this sort. First, estimates of an earnings function are necessary for calculation of rates of return to various quantities of educational investment. To date, very little work of an economic nature has been done in the growing field of graduate education.2 It is hoped that the estimates presented in this paper may be viewed as an exploratory attempt to come to grips with problems in this important and neglected area. Secondly, we have explicitly attempted the specification of an earnings relationship which allows the differential impact of schooling related variables to depend on the values of other relevant explanatory variables.3 The existence of such interactive effects is interesting in itself and has important implications both for the rate of return analyses already available in the literature and for any further work on graduate education which may be attempted. Finally, there is substantial interest in the specification of an earnings relationship which explicitly attempts to deal with the slippery concept of ability to earn income. We would like to know: (a) What sort of ability index is relevant in the context of highly educated persons, (b) the quantitative importance of an ability index, and (c) how parameter estimates of schooling related variables are changed by the inclusion of an ability variable. We do not hope to provide definitive statements on these issues, but our results should be of some interest to those working on related problems in the economics of education. The plan of the paper is as follows: Section I outlines the nature of the data, variables, and methods used in estimation. Sections II and III present the results of the additive and interactive models. Section IV contains a few concluding remarks.

T HE CES (constant elasticity of substitution) production function derived by Arrow, Chenery, Minhas, and Solow [2] has become widely known and widely used. Possibly the weakest point of the SMAC (Arrow, Chenery, Minhas and Solow) formulation is the assumption of. . . the existence of a relationship between V/L (value added per unit of labor) and W (the wage rates), independent of the stock of capital [2, p. 231]. If this assumption does not hold, the value of the elasticity of substitution derived from the estimated CES function may be biased. The CES function is also subject to the limitation that the value of the elasticity of substitution is constant, although not necessarily unity. However, when the capital/ labor ratio varies, due to changes in the factor price ratio, it is possible that the elasticity of substitution will vary as the capital/labor ratio varies. The purposes of this paper are (1) to derive a more general form of the CES production function that does not depend on the SMAC assumption of independence and with a property of variable elasticity of substitution, (2) to examine the elasticity of substitution of the new function, and (3) to present some evidence of the desirability of using the new function.

Trygve Haavelmo [1], in a question to Professor Leontief (2, p. 1062) has suggested the following interesting hypothesis about a developing country's savings function: I(t) = a[Y(t) + H(t)], where stands for gross investment, Y for GNP and H for capital inflows. That is to say, in Haavelmo's words, investment . . . is a function of . . . income including what they get from abroad. I think, Haavelmo adds, see the implications. It means, for example, that domestic savings could be negative if H is very large. The core of Haavelmo's suggestion is, believe, that domestic savings is not a function of national income alone but is also related, inversely, with the inflow of foreign capital. To impart more generality shall alter the Haavelmo equation slightly without distorting its central message. Let us postulate l(t) = aY(t) + bH(t). From this we have domestic savings, denoted by S(t), as given by S(t) = aY(t) + b'H(t), where b' = b 1.

Ryuzo Sato, Ronald F. Hoffman, Production Functions with Variable Elasticity of Factor Substitution: Some Analysis and Testing, The Review of Economics and Statistics, Vol. 50, No. 4 (Nov., 1968), pp. 453-460