Knowledge that Transforms

IN this essay I apply a method for inferring the age distribution of a stock, where the size of the stock and its turnover rate are known, to estimating the distribution of accrued but unrealized gain on corporate shares by the elapsed time over which the gain has accrued.' Without this distribution, we cannot predict accurately even the revenue effects of a change in the legal definitions of holding periods which qualify capital gains for privileged tax treatment. Going beyond such trivial uses, a knowledge of the distribution enables us to estimate the aggregate interest advantage which holders of appreciating assets enjoy from tax deferment and, therefore, to determine that rate of tax on realizations which reduces the advantage to zero. Incorporating the distribution's generating function into a simulation model along with data on prices, turnover rates, and additions to and subtractions from the stock of shares owned by domestic holders, we could generate annual accruals and realizations of capital gains under alternative interest and tax rates and at least make a start on the objective evaluation of the effects of taxing gains at death or of going over to a strict accrual concept of income for tax purposes.

T HIS PAPER PRESENTS a behavioral equation which was developed to explain the long-run (1910-1963) growth of credit. For recent years, the findings of the of Finances show the characteristics of individual borrowers.' What follows is an attempt to use what is known about individual motivation to formulate a long-run hypothesis about how much consumers in the aggregate wish to borrow, given the level of important related aggregate variables, such as income, the number of income-receivers, and individual holdings of liquid assets. In section III, multivariate analysis is used to estimate the relevant parameters. For early years, Goldsmith's and Nugent's data are used. More recent data are taken from the publications of the Federal Reserve Board (especially the Flow of Funds) and the Department of Commerce. The data used, and their sources, are given in table 1. Tobin,2 using cross-sectional data, argued in 1957 that, Other things equal, households with large debts tend to reduce, and households with small or zero debts to increase, their indebtedness. According to these results, there are certain average equilibrium debt levels to which households tend to adjust their debt if their circumstances remain unchanged. The relevant circumstances include a family's liquid asset holdings, income, change in income, and life cycle. It will be assumed here that an equilibrium level of aggregate has similarly been determined by related aggregate variables. The equilibrium level may be thought of as representing consumers' collective aspirations. At any particular moment, institutional factors, such as war-time restrictions or a lengthening of the terms of borrowing, might make it more or less difficult for them to achieve their aspirations, but the equilibrium pattern should show up statistically over the long run.3 The nature of the available data complicates the analysis because consumer credit is measured in a number of different ways. Data on extended during a year (published by the Federal Reserve Board) are available only as far back as 1929, and only for installment debt (which is by far the largest category). Goldsmith has made estimates of outstanding at the end of the year which go back to 19 10,4 and these form the basis for the conclusions drawn here about tendencies for years before 1929. Secondly, the aggregate data cover several categories of borrowing. The most comprehensive include charge accounts and service as well as installment debt and single* The author is a lecturer in Economics at Swarthmore College. She is greatly indebted to two sources of assistance which made possible the study and research underlying the present paper: a Ford Faculty Research Seminar conducted at the University of Pennsylvania by Professor Dorothy Brady in the summer of 1960, and a fellowship granted for 1962-1963 by the Radcliffe Institute for Independent Study. ' These have been very usefully interpreted by J. B. Lansing, E. S. Maynes, and M. Kreinin in Factors Associated with the Use of Credit in Board of Governors of the Federal Reserve System Instalment Credit, Vol. I, Part II (Washington: U.S. Government Printing Office, 1957) 487-520; and by Jerry Miner in Consumer Debt: An Inter-Temporal Cross-Section in I. Friend and R. Jones, eds., Consumption and Saving, Vol. II (University of Pennsylvania, 1960), 400461. 2James Tobin, Consumer Debt and Spending: Some Evidence from Analysis of a Survey in Instalment Credit, Vol. I, Part II, 521-545.

W l tE REPORT here on the construction and AV Vapplication of a method of estimating the parameters of an aggregative vintage model of potential output in the postwar United States nonfarm business sector. The model admits capital-embodied as well as unembodied technical progress. It posits that ex post and ex ante substitution possibilities between (of any vintage) and cooperating labor are alike. There are constant returns to scale. Ultimately, we resort for convenience to the Cobb-Douglas function, although certain estimates, such as that of the marginal productivity of investment, do not hinge upon this specification. Theoretical aspects of the model have been studied by Solow [11] and Phelps [7]. The model has been estimated by a conventional method most recently by Berglas [1] and Intriligator [5]. The principal novelty of our method of estimation is the use of Samuelson's factor price frontier construct [10]. This approach permits us to dispense with stock data. The virtue of this is that, frequently, stock estimates areunavailable because of the absence of early investment data. Moreover, as Fisher has recently proved [3], an aggregate production function relating aggregate output to aggregate effective capital exists, even in a one-product model, only if ex post and ex ante substitution possibilities are alike and any capital-embodied technical progress can be represented as solely capital-augmenting (i.e., as if all capital-embodied change could be expressed by a improvement factor). Since stock data for the United States business sector are available and since, in our model, there is ex post substitutability and embodied progress can be describ d as capital-augmenting, our method of estimation can be regarded as unnecessary. We present it, however, in the hope that other investigators will be stimulated to apply our method to more general models in which an aggregate production function does not exist and to countries for which no stock data exist. Further, we hope that our results will be welcomed for purposes of comparison with those from other techniques of estimating the same model. Turning to our results, we should like to emphasize that our statistical procedure is somewhat amateurish, that the data may be insufficiently accurate and that there is serious misspecification in the model (especially with respect to the ex post substitutability of and labor). Nevertheless, we cite the following findings for whatever they are worth: (1) the rate of technical progress increased significantly over the postwar period (accelerating technology); (2) the elasticity of output is much smaller than capital's relative share, which suggests that there is a large element of monopoly rent in capital's income; (3) embodied progress was negligible in the early postwar years but eventually exceeded unembodied progress by the end of the period; (4) the marginal productivity of investment began at about 30 per cent in the late forties, fell to 17 per cent in the middle fifties, and recovered to 25 per cent in the late fifties; (5) what we call the rate of obsolescence (the proportionate rate at which the price of new goods in efficiency units declines relative to the price of consumption goods) was about five per cent in the middle fifties and nine per cent in the late fifties; (6) so that, if the rate of physical depreciation was about four per cent, the one-period social rate of return was about eight per cent in the middle fifties and about 12 per cent in the late fifties. * This study was supported by the Cowles Foundation and the Economic Growth Center, both at Yale University. The work is also an exploratory effort in a joint project, Future United States Economic Growth, of M.I.T. and Yale. We are grateful to the members of this project for their suggestions and comments on this study.

Frederic L. Pryor, Trade Barriers of Capitalist and Communist Nations Against Foodstuffs Exported by Tropical Underdeveloped Nations, The Review of Economics and Statistics, Vol. 48, No. 4 (Nov., 1966), pp. 406-411

regardless of the initial conditions. [8 p. 261] This means that the difference between the equilibrium value and the actual value of x is bounded for a large enough t, and that this difference tends to zero as t becomes large. So, it has been attractive to assume a monotonic convergence and to approximate the process of adjustment (or convergence) by an adjustment equation such as that used implicitly by Koyck [3] and explicitly by Nerlove [6, 7]

Economists and other users of statistical methodology often posit a probabilistic model of some real world phenomenon which has more unknown parameters than there are sample observations. In such cases it is usually impossible to estimate jointly all parameters from the sample data. Even in those instances where there are well established estimation procedures when the number of sample observations, n, is than the number of parameters, r, these methods are generally inadequate when n < r, as the necessary calculations cannot be carried out. Furthermore, when n is only slightly larger than r, such estimates often prove to be unreliable in more than one sense. One particular example of such a problem that frequently occurs in analysis of psychological and economic data can be paraphrased as follows: the researcher posits a linear regression model as defined in equation (1) below with r 1 independent variables, but only n < r observations are available. Since the standard least squares procedure cannot be applied, he may ask the following seemingly reasonable question: What subset of the r 1 independent variables should I select for inclusion in a new model to which I can apply the standard least squares procedure? Our purpose here is to demonstrate that one frequently used ad hoc method for determining such a subset by ordering simple sample correlation coefficients can be highly misleading. Any procedure which uses a given set of sample data both to determine the structure of the model to be estimated and to estimate parameters of this model is intuitively unsettling. Here we present tables which quantitatively demonstrate how dangerous such ad hoc methods can be. II Ad Hoc Use of Simple Correlation Coefficients to Determine Model Structure

The time series of consumption is explained as a consequence of expenditure. The quantity theory hypothesis relates the level of consumption in money terms to the nominal quantity of money. This is, of course, a variant of the normal quantity theory where the level of money income is determined by the amount of money. By subtracting investment from the dependent variable, one makes the quantity theory formulation directly comparable to its Keynesian rival. Money exerts its influence on consumption directly or via elements of expenditure such as investment. With a different definition of autonomous expenditure, we get rather different results for United Kingdom data. Specifically, the monetary hypothesis is more successful for our early period up to the First World War, while the inter-war years are a strongly Keynesian period. After the Second World War, neither model has very high explanatory power, while for the overall period, there is a slightly better fit with expenditure. Exogeneity of Money

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.