Knowledge that Transforms

RECENT efforts by the Federal Reserve and Treasury to affect the shape of the yield curve have aroused considerable interest and controversy. These efforts, known as operation twist or nudge, were designed to keep short-term interest rates fairly high for balance-of-payments purposes, while keeping intermediate and long rates at moderate levels in order to stimulate domestic growth.' Two divergent positions are involved in the controversy. The first, held by many of the proponents of the only policy, is that expected interest rates for various future periods are perfectly elastic, causing different sectors of the yield curve to move together in a fixed proportional manner.2 In this regard, Riefler contends that while initial response to action by the monetary authorities is reflected in the price of the particular security that is bought or sold, the action is later felt throughout the entire yield curve, due to substitution and arbitrage.3 Given this interest-rate behavior, the sector of the yield curve in which the monetary authorities choose to operate makes little difference. The ultimate effect is essentially the same whether open market operations are conducted in bills or in long-term securities. Due to the greater depth, breadth, and resiliency of the bill market, a logical case can be made for confining operations to bills. The second position is that expected interest rates for various future periods are less than perfectly elastic, moving with some degree of independence. To the extent that operations by the monetary authorities in longor intermediate-term securities can affect interest-rate expectations for some future periods independently of expectations for others, the shape of the yield curve can be altered in a manner not possible by operations in short-term securities or only. In this paper, interest-rate expectations are examined empirically through the use of singleand multiple-year errorlearning models. These models are tested using monthly Treasury yield-curve data that appeared in the Treasury Bulletin for the 19541963 period, and the evidence obtained is seen to support the supposition that expected interest rates for various future periods change with some degree of independence.

N this study, intrafirm technical progress, or improvements in the state of the arts, are separated from scale economies and productivity changes due to interfirm shifts of resources, by fitting production functions and employing covariance analysis. With a view toward determining the sources of the resulting series of intrafirm technical change, several hypotheses are formulated and tested by using the distributed lag models and other relations. The Covariance Matrix method employed in this study (which method has not been used extensively, partly because the equations are non-linear in the coefficients) has a number of theoretical and statistical advantages over the traditional methods of measuring productivity, such as the single equation least squares method and the factor shares method. First, it permits the separation of technical advance from the contributions of physical factors without building into the empirical model the twin restrictive assumptions of constant returns to scale and competitive factor-pricing both being necessary conditions in the factor shares method ' as used by Solow,2 Kendrick,3 and others. Second, it enables us to dispense with the necessity of (artificially) imposing the condition of constancy (linear or log-linear) on the rate of technical change, as is commonly done in fitting production functions to timeseries data.4 Third, it is supposed to reduce the simultaneous equation bias of single equation least squares regressions 5 and weaken the tendency towards indeterminacy of the production function coefficients due to multicollinearity in aggregate time-series data.6 Last, being computed rather than obtained as a residual, the technical change series is net of random errors which, in the traditional residual methods, are collected in the productivity index.

T HIS PAPER considers a variety of theories of investment and attempts to find the importance of each of them. The theories considered fall into several groups. We shall consider these as parts of a single structure of investment which considers both supply and demand. The demand side of the model employs first, the acceleration principle using output, change in output, and expected output as explanatory variables. Next, this side of the model considers the cost of funds using the rate of interest, the flow of internal funds, and the debt-asset ratio. Finally, prices in the factor and product markets are considered. Supply restraints were taken into consideration by using the volume of unfilled orders and by restricting the analysis to the post Korean War period. This model is developed and discussed in the next section of this paper. It is well known that the investment process by an individual firm does not take place instantaneously but that there is a significant lag between the appearance of the need for additional capital goods and the actual investment. The lag structure employed is discussed in the third section of this paper. In the fourth section the data are discussed. This paper fails to find any significant effect on investment of prices or the volume of unfilled orders. All of the output variables and the cost of funds variables are of considerable importance. In particular, the rate of interest, flow of funds and debt asset ratio all play important roles. These empirical results are discussed in the fifth section below. II Theories of Investment Behavior

IN their audit of the sources of economic growth a number of writers have, in recent years, focussed on technical and improvements in the quality of capital and labor rather than increases in the quantity of factors of production. Implicitly, if not explicitly, this work has generated new theoretical propositions about aggregative production functions and has led to the revival of efforts to estimate them. This research has been pursued on a number of fronts, but much of it is centered in its applications on the United States economy. This paper reports the results of some experiments with a model that postulates technical progress together with possible nonconstant returns to scale using data relating to the United States economy. Though the assumption of embodiment of technical in factors of production is one of the latest fashions in growth models, the conventional trim is constant returns to scale. Models allowing for scale economies or diseconomies may even seem somewhat old-fashioned, although a number of studies have, in fact, emphasized the combination of improvements in factor qualities and increasing returns in explaining United States growth.' R. M. Solow, observed by A. Smithies 2 to be the Pied Piper of research on technical change, though consistently assuming constant returns for the United States economy whether he is leading us in the direction of disembodied or embodied change, has recently reported some statistical calculations for the German economy without the constant returns restriction.3 The relationship of economic to the size of the economy has been the subject of speculation for as long as there have been economists.4 Contemporary attempts at measurement, however, may not only have failed to give sufficient emphasis to the role of scale economies or diseconomies, but may have made, as a consequence, faulty assessments of the role played by other influences on the growyth process. A model that postulates constant returns to scale, one suspects, would overstate the growth resulting from technical when confronted with data generated by a generally growing economic system subject to increasing returns and, vice versa. The model would understate the growth due to technical change when the data are generated by a growing economy subject to decreasing returns. A. A. Walters [13], for example, obtains sharply increasing returns to scale for the Cobb-Douglas model of disembodied technical change applied to 1909-1949 data for the United States economy and finds a much lower rate of shift (i.e., technical progress) of the production function than Solow [9] with the same model applied to the same time period but with the restriction of constant returns.5 One should also recognize that for some models which assume constant returns, identification of both growth and scale parameters may not even be possible.

I N 1953 the Federal Open Market Committee concluded that it was desirable to confine its open market transactions to short-term securities, preferably Treasury bills. This policy was announced to the public in a speech by Chairman Martin, Transition to Free Markets, and has subsequently been called the bills-only policy.' Federal Reserve operations were to be limited to those necessary for supplying or withdrawing reserve funds and the authorities would not ordinarily intervene to prevent fluctuations in prices or yields of government securities. With very few exceptions, the Federal Reserve followed these principles, and open market transactions in Treasury certificates, notes and bonds were virtually eliminated. Except for 1955, and in 1958 when the market approached disorderly conditions, the Federal Reserve held its operations in certificates, notes, and bonds to something like one per cent of its total open market transactions. The policy was discarded in early 1961 when we were confronted with a balance-of-payments deficit at a time when the economy was operating at close to recession levels. In this paper, we present a statistical investigation of the movements in interest rates since 1953 to determine whether they conform to the suppositions of the bills-only theory. The substantive propositions of this theory concerning interest rate behavior are summarized in section I. In section II, we suggest several tests of this theory and summarize the statistical evidence. The conclusions are presented in section III.

W HILE students of the American economy IV, I are blessed with some excellent data for measuring the functional distribution of personal income for individual states, there are virtually no statistics on the size distribution of income for these areas. (Stigler's state-by-state estimates of the income shares of the upper one per cent of the population are the best effort yet made to get at the latter kind of information.)' Nor does the present paper give income size distributions for states. My purpose here is the much more modest one of reporting the results of a try at deriving indicators of income inequality that can be used as a basis for comparing each state with the others. The first part of this report describes how Gini indexes of income were constructed for states and the District of Columbia for the year 1959. The bulk of the remainder is occupied with assaying the credibility of these indexes. This evaluation may be thought of as a test of the hypothesis that the Gini indexes of income possess merit as a basis upon which to compare these 51 areas. The test consists of correlations of the indexes with corresponding Gini indexes for housing and education, created especially for this purpose, as well as a few other characteristics for these areas. Alternatively, were one disposed to simply accept the Gini indexes of income as being adequate for their professed role, it might be interesting to regard the following exercise as a test of the hypothesis that there is a demonstrable interrelationship among various sorts of measurable inequality.

G. S. Maddala, Joseph B. Kadane, Some Notes on the Estimation of the Constant Elasticity of Substitution Production Function, The Review of Economics and Statistics, Vol. 48, No. 3 (Aug., 1966), pp. 340-344