This paper considers the effect of aggregation on the variance of parameter estimates for a linear regression model with random coefficients and an additive error term. Aggregate and microvariances are compared and measures of relative efficiency are introduced. Necessary conditions for efficient aggregation procedures are obtained from the Theil aggregation weights and from measures of synchronization related to the work of Grunfeld and Griliches.
and FORTRAN IV which is designed to accommodate most researchers' everyday econometric needs. However, this program is particularly useful when spectral methods are combined (in an ex post sense) with regression and simultaneous equations estimation., Residuals from regression or simultaneous equations estimation are easily saved by EAS and used in later spectral computations by using only two program statements.1 All spectral computations are highly efficient since the fast Fourier transform techniques developed by Cooley and Tukey [2] are used throughout. The program also allows algebraic expressions to be used directly in regression statements to define dependent or independent variables. Hence, special regression equations like the harmonic analysis model can be easily estimated with a single program statement. A partial enumeration of the program's capabilities is as follows: ordinary and weighted least squares regression; multivariate regression and estimation of Zellner's seemingly unrelated regression system; structural estimation of simultaneous equations by two-stage least squares, three-stage least squares, limited information maximum likelihood, k-class, double k-class, h-class, and Nagar's minimum bias k-class methods; power spectrum analysis, cross spectrum analysis, and simple frequency domain regression; random number generation and Monte Carlo methods; principal components analysis; estimation of partially nonlinear models by likelihood search techniques; and estimation of certain distributed lag models by Dhrymes' [3] methods. The program accommodates problems in which the sample size and number of yariables do not exceed 32,767 and 1,823, respectively, but the dynamic core allocation features of PL/1 are used to economize on all smaller problems. The design of the program is especially useful when a large data bank (subject to the abQve limitations) is to be maintained, updated, and periodically accessed for various types of econometric analyses. Most small- to medium-sized
An Arrow social welfare function was designed not to incorporate any interpersonal comparisons. But some notions of equity rest on interpersonal comparisons. It is shown that a generalized social welfare function, incorporating interpersonal comparisons, can satisfy modifications of the Arrow conditions, and also a strong version of an equity axiom due to Sen. One such generalized social welfare function is the lexicographic form of Rawls' ARRow (1) INVESTIGATED the problem of how to amalgamate the personal welfare orderings of the members of a society into a social welfare ordering. His approach was deliberately designed to avoid making any kind of interpersonal comparison. He was then able to show that such an approach must fail as long as one insists on certain other apparently appropriate conditions. It would therefore seem that an obvious way around Arrow's impossibility theorem is to make interpersonal comparisons and to use them in the construc- tion of a social ordering. Moreover, some considerations of equity which many people would think relevant for making social choices are specifically excluded by Arrow's approach. This paper shows how, if interpersonal comparisons are made in a certain way, one can construct a social welfare ordering by a method which satisfies suitably modified forms of Arrow's 1963 conditions. Moreover-as is just as well, given that the interpersonal comparisons are deliberately based on a notion of equity- it is also possible to satisfy an extra condition, which is a kind of equity axiom. The lexicographic extension of Rawls' difference principle, or maximin rule, satisfies all these conditions. In addition, it is the only rule or principle which satisfies a condition which underlies Suppes' grading principle, together with these condi- tions. Section 2 presents preliminary definitions and notation, and shows how some considerations of equity are excluded by Arrow's approach to social choice. Section 3 shows how these considerations of equity may be represented by ordinal interpersonal comparisons of the kind discussed in Sen (6), how they are related to an equity axiom due to Sen (7), and how Sen's equity axiom may be generalized. Section 4 defines generalized social welfare functions (GSWF's) and shows how Arrow's conditions can be modified to apply to GSWF's. Section 5 'This is an expanded and subsequently revised version of a paper presented to the European
[Keynes' general attitude toward mathematical economics and econometrics, respectively, is discussed in Sections 2-3. The remainder of the paper is devoted to a description and analysis of the interaction between the Keynesian revolution of the mid-1930's and the revolution that had actually started somewhat earlier with respect to the preparation of current official estimates of national income. In this connection an attempt is made to explain why Kuznets' work in the U.S. in the early 1930's was immediately integrated into official national income estimates in the U.S., where Colin Clark's work in Britain was not--with the result that official British national income estimates did not begin to appear until almost a decade later.]
[This paper develops a simulation model to study the income distribution effects--total and factorial-of optimum restrictions on the flows of factors and products across national boundaries. Imposing both optimum tariffs and optimum taxes on factor flows allows an increase in national income that is much larger than the sum of the two effects evaluated separately. Often there are large shifts in the incomes of factors even though total income changes only slightly.]
Economic researchers are rarely able to conduct surveys or design experiments to obtain evidence with which to assess theories or hypotheses but must rely on information, such as the national income accounting data, compiled by the government bureau of statistics. The bureau revises its national income estimates as more information becomes available or as a result of changes in methods of estimation or minor changes in definitions or classifications. The purpose of this paper is to show that the correlation structures and the autoregressive moving average representations of a number of Australian quarterly time series extracted from the income accounts are relatively insensitive to data revision. The same is true of the cross correlation functions between the pre-whitened series.
[A logically consistent specification of the adaptive expectations hypothesis in continuous time is derived from an underlying discrete time model. We distinguish between (i) the time interval between predictions and (ii) the time horizon over which predictions are made. Taking limits of the expectation equation as these time intervals approach zero, we derive a mixed difference-differential equation and a mixed total-partial differential equation, respectively, describing actual changes. When these are combined with other equations in an economic model, the expectation mechanism provides a simultaneous determination of both expected and actual dynamics. New results are obtained in three separate applications: (i) the short-run stability of multi-asset markets, (ii) a heterogeneous capital goods model, and (iii) a Phillips curve model of wage-price inflation.]
[The paper derives a function that describes the size distribution of incomes. The two functions most often used are the Pareto and the lognormal. The Pareto function fits the data fairly well towards the higher levels but the fit is poor towards the lower income levels. The lognormal fits the lower income levels better but its fit towards the upper end is far from satisfactory. There have been other distributions suggested by Champernowne, Rutherford, and others, but even these do not result in any considerable improvement. The present paper derives a distribution that is a generalization of the Pareto distribution and the Weibull distribution used in analyses of equipment failures. The distribution fits actual data remarkably well compared with the Pareto and the lognormal.]