Knowledge that Transforms

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.

R EGIONAL input-output tables have long been acclaimed as useful tools in regional forecasting, especially long-run forecasts, yet surprisingly few regional projections have made a serious attempt to use them. This paper reports on one effort in this direction an inputoutput based projection for the State of Washington for the year 1980. Because of the time constraints no effort will be made to describe how the 1963 State of Washington table was developed. Rather, it is given as datum [3]. In addition, again because of time, not all of the details in the projection process are included. Finally, because few are interested in the results, no bulky tables have been included.

ONE of basic facts of life confronting econometric researchers is that in order to test any hypothesis it is necessary to assume validity of other assumptions which cannot be tested. An important part of art of practical econometrics is knowing how much to include in maintained hypothesis; if too much is assumed there may be little or nothing left to test, while if too little is assumed it may be impossible to reach any conclusions, or else analysis may become hopelessly complex. In a recent article in this Review 1 Robert Eisner and M. I. Nadiri have examined critically one of essential maintained hypotheses used by Dale W. Jorgenson, James A. Stephenson, Robert E. Hall, and Calvin D. Siebert in a substantial body of empirical research on demand for capital goods.2 This assumption maintains that long-run partial elasticity of flow of capital services, stock of capital, flow of gross investment demand, or flow of net investment, with respect to price of output (p) divided by price of capital services (c) should be unity. By respecifying Jorgenson's model in a logarithmic form, Eisner and Nadiri have produced tests of hypothesis that long-run price elasticity of demand for capital stock is unity. Not only do they find that estimated elasticity with respect to (p/c) is significantly less than one, but all of their preferred point estimates of this parameter are less than 0.16 and in some cases do not differ significantly from zero. The first of seven conclusions summarized by Eisner and Nadiri is that the role of relative prices, critical element in approach, is not confirmed. I In principle, Eisner-Nadiri goal of relaxing and testing crucial maintained hypotheses is a laudable one. Their conclusions, if they can be sustained, have far-reaching implications. If their estimated elasticities are correct, then fiscal and monetary policy-makers have little, if any, direct influence on investment expenditures. A cautious to importance of Eisner-Nadiri conclusions would seem justified, however, in view of fact that others have also undertaken task of critically examining maintained hypotheses in Jorgenson model. While none of other critics of Jorgenson has defended precise manner in which he has specified his model, without exception results have been favorable to essence of neoclassical approach to investment functions assumption that relative prices do matter.4 The next section of this paper is essentially an exercise in detective work aimed at finding out why Eisner and Nadiri obtained results contrary to body of other research. The analytical method used is to carry goal of Eisner and Nadiri relaxing and testing maintained hypothesisone step further. The maintained hypothesis I relax and test involves assumption of serially independent errors.5 * Support for this research was provided under contract DACA31-67-C-0141, U.S. Army Corps of Engineers, for Office of Emergency Planning, and by National Science Foundation and Ford Foundation through grants to Cowles Foundation for Research in Economics. I am very grateful to Professors Robert Eisner, Robert J. Gordon, David Grether, Dale Jorgenson, Franco Modigliani, and Marc Nerlove and to members of Workshop in Econometrics and Mathematical Economics of University of Chicago, for criticisms of earlier versions of this paper, and to Petter Frenger for extremely helpful research assistance. '[7]. Eisner's criticisms have been amplified in [5] and [6]. 2This body of research includes [12] [13] [16] [17] [19] [20] [21] [22]. 3[7], p. 380. 'See [2] [3] [4] [9]. Some of this evidence is discussed briefly in section III below. The evidence on demand for factors other than capital, and on direct estimation of CES production functions, is also relevant, at least indirectly. See [23] for discussion of this evidence. 'As I note below, stochastic assumption I make that errors are a first order autoregressive process -is only one step more general than that used by Eisner and Nadiri. I do not wish to imply that this stochastic assumption is anything more than a minimal improvement; only reasons for not using other types of assumption was my desire to minimize computational problems.

T HE object of this paper is to formulate a normative model for selecting a bank's Government security portfolio. Two major problems arise in constructing a model of bank portfolio selection. First, the model must handle uncertainty. This includes not only uncertain future events but also the decision maker's preferences for the outcomes associated with these events. Second, it must recognize the intertemporal or multi-period character of the decision making process. This means that a decision made in one period will influence subsequent decisions and hence, that subsequent decisions must be considered in arriving at the present one. The present paper applies Bayesian and sequential decision theory to handle both the expectationally stochastic and the dynamic aspects of this important decision problem simultaneously and consistently. No previous model of commercial bank portfolio selection handles either or both problems satisfactorily. Porter's model of bank asset selection recognizes uncertainty by treating future cash flows and security prices as random variables, but it is only one period in length. Moreover, it does not consider the decision maker's preferences.' Since the objective function is linear, the model produces a portfolio diversified between securities and loans only through the selection of distribution functions describing the random variables. These transform the function into a nonlinear one upon integration. Cheng's model of bank security portfolio selection is, in effect, a one period formulation also.2 It incorporates uncertainty and the decision maker's preferences through Markowitz's efficient portfolio concept.3 An efficient portfolio is one which maximizes expected return for a given variance of return (or minimizes the variance of return for a given expected return). As Tobin points out, however, this criterion assumes, quite restrictively, that either the variable return is normally distributed or that the decision maker has a quadratic utility function.4 Cheng also makes the highly unrealistic assumption that securities are held to maturity. Multi-period bank portfolio selection models are all based on the assumption that future events are known with certainty. One such model formulated by Chambers and Charnes attempts to reflect the risk inherent in different portfolio configurations by including the Federal Reserve's capital adequacy formula as a constraint.5 Used in the supervision of banks, the capital adequacy formula allocates a bank's capital to designated asset categories on a fractional basis. The values of the fractions are designed to measure the percent by which the different asset categories would decline in market value if they had to be liquidated quickly.6 The choice of these values is somewhat arbitrary. Moreover, the formula itself implicitly assumes a particular preference structure and a certain probabilistic occurrence of future events. Neither assumption is likely to represent accurately either the decision maker's preferences or expectations.7

The practice which we will refer to here as is a technique for arriving at a measure of value when one has available the value of gross output and materials inputs and also price indices for gross output and for materials inputs. The double deflation technique, despite its rather wide use, has been regarded as crudely empirical, with little, if any, justification from the point of view of theory.' The purpose of this note is to demonstrate that one can justify double-deflation as a fixed-weight linear approximation to an ideal variable-weight logarithmic index under assumptions no more restrictive than those required to justify the notion of real value added itself. Analysis of production relations is simpler if we can restrict ourselves to looking at two inputs at a time. Hence in studies using disaggregated data, it is convenient to consider the contribution of capital and labor to gross output separately from the contribution of materials inputs. In order for such separate treatment to be justified, the production function must be separable. Taking y to be gross output, K to be capital, L to be labor, and M to be materials, the separability condition required is

AS Professor Samuelson has recently redemonstrated, the following two problems cannot be logically separated: (1) how much of a public good it is efficient to produce, (2) how in justice the costs of the good are to be borne by the public.' Even under the stringent assumptions of constant marginal cost for the public good, and constant marginal utility of income for all consumers, allocative efficiency in no way logically determines how cost burdens should be shared even when the income distribution, before taxes and before public good production, is considered just. As a result, public authorities are generally denied the luxury of sequential, independent, or separable decision rules for allocative efficiency and distributional equity. An omniscient decision maker, interested in maximizing social welfare as defined by some social welfare function, must simultaneously determine the quantity of the public good to produce, the share of the cost burden so generated to be charged each person, and income transfers among individuals or groups. There is, however, one tax-allocation-and-public-good-supply decision rule, namely, the Lindahl voluntary exchange decision rule which leaves the initial (i.e., pre-tax, pre-benefit) income distribution unchanged, and hence can argue for separation between allocation and distribution decisions. These conclusions derive from the following propositions: 1) Where the costs of public good production must be shared by individuals in predetermined proportions (by customs or fixed tax laws, etc.) and no direct income transfers are allowed among individuals, the decision of how much public good to supply is ethical. At the supply feasible under these conditions, the MC of production need not equal the sum of individual MRS's. In this case the restrictions on transfers and on variable tax rates generally insure that the best feasible outcome is not Pareto-efficient. 2) If either direct lump-sum income transfers or variable cost sharing tax burdens are allowed, such that the authority deciding how much public good to produce can also vary one of these two factors, then the choice of a final utility distribution dictates a unique Pareto optimal public goods supply decision. This public goods supply will be efficient in the sense that MC = X MRS; it need not be true, however, that each individual's MRS equals that individual's marginal cost share. Relaxing either of the restrictions in 1, insures that Pareto efficiency in resource allocation can be achieved. There exists an infinite number of Pareto optimal public goods supplies each related to a particular utility distribution. 3) If both tax shares are variable and lumpsum income transfers are allowed, then the optimal utility distribution is Pareto-efficient (i.e., MC = I MRS) and can be achieved as a Lindahl solution to the public good supply problem (i.e., MRS of each individual equals that individual's marginal cost share). In this case also, as in 2, the utility distribution choice determines a particular level of public goods supply. One purpose of this paper is to demonstrate the foregoing propositions. This is done in part I with the aid of ordinary box diagrams. In part II the demonstration is repeated with simple mathematics. Part III summarizes the implications of the foregoing for the theory of taxation and expenditure and particularly for the viability of the theory of the public household as containing separable allocation and distribution branches.