Knowledge that Transforms

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.

1. THE theory of public goods 1 is sometimes confused with the theory of joint production. This is in the nature of a pun, or a play on words: for, as I have insisted elsewhere, as we increase the number of persons on both sides of the market in the case of mutton and wool, we converge in the usual fashion to the conditions of perfect competition. But when we increase the number of persons in the case of a typical public good, we make the problem more indeterminate rather than less. To elucidate the difference, I shall fill in what appears to be a minor gap in the literature, namely a needed statement in terms of modern welfare economics of the various optimality conditions as they appear in the case of joint products. The analysis is straightforward; and after it is before us, we can clearly see the difference between it and the well-known optimality conditions for the case of public goods. 2. I begin with an examination question given recently at the Massachusetts Institute of Technology: Corn is produced by land and labor; and so are wool-bearing mutton-bearing sheep. Assume the totals of available land and labor to be fixed. Write down the various welfare optimality conditions in the case where all people happen always to consume wool and mutton in the same proportions that sheep bear these products. And then, by contrast, write down the conditions that would have to prevail if individuals' indifference contours for wool, mutton, and corn involve the usual variability of proportions. This proved a difficult question for first-year graduate students in economic theory. Still many perceived that in the first case they could essentially work with two rather than three goods, substituting sheep as a kind of composite good for wool and mutton, and thereby ending up with the standard welfare conditions for two ordinary (private) goods, corn and sheep.

IN a previous article with Professor Harold Watts, the authors demonstrated empirically the loss of information in the parameter estimators when data are aggregated prior to computing least-squares regressions [3]. These results came from simulations with a simple economic model containing identical microcomponents. Specifically, in addition to the error term, each component spent 0.9 of its previous income and 0.2 of its cash balance. The main point of our previous paper was that estimation prior to yielded substantially greater precision in the estimates of the parameters and their standard errors than did estimation of the same parameters after aggregation. The implications of this for hypothesis testing and the development of satisfactory policy response models seemed obvious. On the basis of a variety of evidence, including the paper with Watts and a paper by Orcutt [4], the case for seeking and frequently using disaggregated data seemed strong but one nagging concern remained. Suppose, as seems likely, the microcomponents exhibit different behaviors. In this case it might not be sensible to pool the data and treat it as a single sample from a single universe. However, if estimators from each micro equation are computed separately, would it still be desirable to use disaggregated data instead of data aggregated over all components? This turned out to be the case with identical components but would it be with nonidentical components in which something more than constant terms were different? This paper copes directly with this issue, and we demonstrate the importance of using disaggregated data even when microcomponents exhibit different behaviors. We do not deal with cases where microcomponents have nonlinear relations, but the need for disaggregated data in such cases seems fairly obvious without Monte Carlo experiments. If we wish to compare the accuracy of estimation at different levels of aggregation, we need a measure of merit different from the extent of bias and variance of parameter estimators, which we used in our previous study, because in an aggregate model whose components have different behaviors, the expected values of the estimators may be meaningless or nonstationary [Zellner, pp. 3-5]. Therefore, we use the accuracy of the out-of-sample forecasts to measure the merit of the estimated equations. In particular, we forecast the aggregate expenditure for the eight time periods following the last sample period. The rootmean-square forecast errors from models based on data at different levels of provide the yardstick for comparisons. Our results suggest that models estimated from micro data will give generally superior out-of-sample forecasts. This finding is at variance with the belief that one reaps an aggregation by aggregating the micro data prior to estimation. The concept of a possible gain was formalized in a 1960 article in this Review by Grunfeld and Griliches: