Knowledge that Transforms

war Economy (Washington: Brookings Institution, 1963). [4] Jaffee, D., Credit Rationing and the Commercial Loan Market, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1968. [5] Keynes, J. M., General Theory of Employment, Interest and Money (New York: Harcourt, Brace and World, Inc., 1936). [6] Lipsey, R. G., The Relation Between Unemployment and the Rate of Change of Money in the United Kingdom, 1862-1957: A Further Analysis, Economica, 27 (Feb. 1960), 1-31. [7] Perry, G. L., Unemployment, Money Wage Rates, and Inflation (Cambridge: Massachusetts Institute of Technology Press, 1966). [8] , Wages and the Guideposts, American Economic Review, 57 (Sept. 1967), 897-904.

D ISTRIBUTION of the population by urban, rural nonfarm and farm residence is one of the oldest and most established causes of differentials in fertility cited by demographers.' Geographical region is also frequently mentioned in demographic studies as a source of variation in fertility in the United States. Race and social class, the latter often measured by occupational status, are additional variables popular with both demographers, and less specialized sociologists, as sources of variation in fertility.2 In most of the studies by demographers, a major difficulty with the factors proposed as causes of variation in fertility is that there is no way of knowing whether the variables are separate and independent explanations of birth rate differentials. To some extent, this is due to the fact that the statistical methodology consists of simple correlations, or more frequently, tabular and graphical presentations, which limit the analysis to two or three dimensions. A more fundamental criticism is that the discussion of the causal relationship between the independent variables and the fertility differentials does not attempt to assay whether basic factors, such as income and economic conditions, and the costs and benefits of having children, are common explanations of the variations in fertility by community of residence, geographical region, class, race, etc. Analyses of birth rate differentials by economists usually are based on a stronger statistical methodology than the studies by demographers but suffer from a similar weakness in their analytical formulation. independent contribution of the variables to fertility differentials is determined by means of multiple regression or partial correlation analysis. Although meaningful statistically, the regression results usually afford little insight into the fundamental relationship between population growth and economic development and/or economic conditions. One source of confusion in economic crosssection studies of birth rates may be the unfortunate choice of data. Some economists apparently ignore the demographers' findings that a considerable portion of the variance in fertility within a country is due to geographical differentials, and attempt a cross-section analysis of fertility on a very heterogeneous sample composed of different countries.3 It would seem that a more homogeneous sample of observations within a country is a more propitious beginning for an interpretation of the relationship between birth rates and economic variables. Economists have benefited from one of the findings of demographers. A popular variable for inclusion is the fraction of the population classified as farm or the per cent of the labor force employed in nonagricultural industries. Weintraub suggests that the ratio of the popu* This paper is a revision of an earlier version presented at the annual meeting of the Western Economic Association at Corvallis, Oregon, August, 1968. It has benefited from a critical reading by our colleague Jerzy F. Karcz who made a number of helpful suggestions. Our appreciation goes to Dana Burtness who assisted us in all phases of this study but especially in making our interactions with the IBM 360 Computer pleasant. Additional credit goes to John Danforth and Ken Gralla who assisted us in the early stages of this study. 'Ben Franklin noted this causal relationship between birth rate differentials and population distribution as early as 1786. 2The following references are typical of the analysis of differential fertility by demographers. Donald J. Bogue, of the United States, Free Press of Glencoe, Illinois (1959), chapter 12 -The Fertility of the United States Population (contributed by Wilson H. Grabill). Warren S. Thompson, Problems, McGraw-Hill Book Co. (1965), chapter 11 -Some Factors Affecting Fertility. As an example in the same vein by a sociologist, refer to the book by T. Lynn Smith, Fundamentals of J. P. Lippincott Co. (1960), chapter 13Differential Fertility. 3 Typical of the multiple regression cross-section analysis of fertility differentials in different countries conducted by economists are Irma Adelman, Econometric Analysis of Growth, American Economic Review, 52, no. 3 (1963); Robert Weintraub, The Birth Rate and Economic Development, An Empirical Study, Econometrica, 40, no. 4 (Oct. 1962).

Robert Ferber, John Forsythe, Harold W. Guthrie, E. Scott Maynes, Validation of a National Survey of Consumer Financial Characteristics: Savings Accounts, The Review of Economics and Statistics, Vol. 51, No. 4 (Nov., 1969), pp. 436-444

W HEN the surface of the economist is 14/1 7 scratched we generally find a belief that vertical integration in the corporate sector has increased during the past few decades, if not longer. This proposition, however, has not been put to a rigorous empirical test for the entire corporate sector. According to Professor Bain, We must, in the present state of knowledge, confine ourselves to a few remarks based on miscellaneous scraps of evidence. I In this note a measure of vertical integration in the corporate sector is developed. The measure is calculated for the year 1929 and for the period 1948 through 1965. The conclusion reached on the basis of this empirical evidence is that there has not been any discernible increase in the degree of vertical integration in the corporate sector. If anything, there might have been a slight decline. The index we use is the ratio of corporate sales to gross corporate product standardized to abstract from the changes in output mix. A rise in this index implies a decline in corporate vertical integration and vice versa.2 Because industry sales data are on a consolidated basis by corporation and most of the gross corporate product is on an establishment basis, this series reflects a preponderance of any general movements on the part of corporations to merge with suppliers or customers. If, for example, firm A has a gross corporate product of 500 and sales to firm B of 1000 (firm A's purchased material inputs are 500) and firm B has a gross corporate product of 500 and sales of 1500, then total corporate sales for both firms equal 2500 and total gross corporate product equals 1000. In this instance the ratio of sales to gross corporate product equals 2.5. If these two firms merge, total corporate sales will then be 1500 and gross corporate product will still be 1000. The new ratio of corporate sales to gross corporate product will be 1.5. Vertical integration has caused a decline in our ratio. As is readily aDDarent. neither pure horizontal integration nor a pure conglomerate movement will affect our ratio.3 There are natural differences among industries which preclude the meaningfulness of comparing the degree of vertical integration in one industry with that of any other industry. Thus a corporation in the service or mining industry will naturally have a much lower sales to gross corporate product ratio than a corporation in the retail or wholesale trade industry. If the proportional mix of total gross product is changing, we could very easily find a change in the aggregate sales to gross product ratio without any changes in this ratio for any specific industry. Any conclusions about changes in the ratio which are due to such changes in the proportional mix implies interindustry comparisons. In order to avoid the mix problem we calculate the aggregate ratio using the proportional mix of one base period. More explicitly our methodology is as follows: For any year t, total corporate sales, St, is equal to the sum of total corporate sales for each industry i. Thus,

M ODERN investment functions, springing from the work of Jorgenson,' differ from earlier investment functions in that they start with an explicit assumption about the economy's aggregate production function. In particular, Jorgenson assumes a Cobb-Douglas production function. Starting with an explicit production function means that it is possible to calculate algebraically the impact of factors, such as interest rates, that could not be isolated in earlier investment functions. Choosing the correct production function is important in estimating partial effects, but the proper definition of the cost of capital variable is also central to their correct estimation. Formulations other than those of Jorgenson are possible. If one had priors about the differences in the opportunity cost of capital under the Duesenberry supply of funds hypothesis,2 the cost of capital could be defined to embody these priors. Doing so would lead to different estimates of the partial effects of tax rates, interest rates, and depreciation policies. Thus, the partial effects that emerge from a modern investment function are a product of the initial specifications of the production function and the cost of capital variable. In addition to choosing the correct production function and the correct definition of the cost of capital, there are other directions in which the modern investment function can be modified. In Jorgenson's neoclassical equilibrium world the cost of capital and the marginal product of capital are always identical. Thus, the desired capital stock at any moment of time is equal to output divided by the marginal product of capital (the cost of capital) multiplied by the elasticity of output with respect to capital. Thus, the only problems are ones of correct data measurement and estimation of the lag structure. This formulation has some theoretical problems. Introducing lags means that the economy is not in equilibrium. actual capital stock lags behind the desired capital stock. Therefore, the cost of capital and the marginal product of capital are not equal. Even if they were equal, the marginal product of capital will differ before and after expansion of the capital stock. Thus output should be divided by the expected cost of capital rather than the actual cost of capital to determine the desired capital stock.3 In a disequilibrium world, the cost of capital and the marginal product of capital can diverge. Profit maximizing firms invest to eliminate the gap between the marginal product of capital and the cost of capital. investment necessary to eliminate this gap depends upon the economy's production function. This paper investigates a disequilibrium investment function based on a Cobb-Douglas production function and Jorgenson's definition of the cost of capital. I was led to investigate such a model in the process of attempting to use the Jorgenson investment function.4 Several problems emerged in addition to those investigated elsewhere.5 (1) Although the Jorgenson investment function fit quarterly time series data for producers' * author would like to thank the referee for many useful comments. 'Dale W. Jorgenson, Anticipations and Behavior, in J. S. Duesenberry, E. Kuh, G. Fromm, and L. R. Klein (editors), Brookings Quarterly Econometric Model of the United States (Chicago: Rand McNally, 1965). Rational Distributed Lag Functions, Econometrica, XXXIV (Jan. 1966), 135-149. With Calvin D. Siebert, A Comparison of Alternative Theories of Corporate Behavior, American Economic Review, XVIII (Sept. 1968). Optimal Capital Accumulation and Corporate Behavior, Journal of Political Economy, LXXVI (Nov./Dec. 1968), 1123-1151. With J. A. Stephenson, The Time Structure of Behavior in United States Manufacturing, 1947-60, this REvIEw, XLIV (Feb. 1967), 16-27. Investment Behavior in U.S. Manufacturing, 1947-60, Econometrica, XXXV (April 1967), 169-220. 2J. Duesenberry, Business Cycles and Economic Growth (New York: McGraw-Hill, 1968), 87-112. 3This was pointed out to me by my colleague Duncan Foley. 'Anyone wishing the detailed econometric results of my attempts to fit the Jorgenson model to producer's durable equipment and nonresidential structures can have them by writing to me. 'Robert Eisner and M. I. Nadiri, Investment Behavior and Neoclassical Theory, this REvIEw, L (Aug. 1968).

Benton F. Massell, Consistent Estimation of Expenditure Elasticities from Cross-Section Data on Households Producing Partly for Subsistence, The Review of Economics and Statistics, Vol. 51, No. 2 (May, 1969), pp. 136-142

Charles W. Haley, The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets: A Comment, The Review of Economics and Statistics, Vol. 51, No. 2 (May, 1969), pp. 220-221

N this study we formulate and estimate a cost function for the United States local service airline industry. Section I discusses certain characteristics of the industry and its regulation by the Civil Aeronautics Board (CAB) which influence the form of the cost function and the method of estimation chosen. The model is outlined in section II. The data available and the method of estimation are discussed in section III. Some tentative conclusions are presented in section IV.