The central idea of the business cycle is of a pervasive cyclical movement of economic indicators. This paper shows that the concept of such simultaneous movements can be given a precise meaning by performing a principal component analysis of spectral density matrices or, with a different shade of meaning, coherence matrices. It suggests also a new method of computing spectral approximations for models that are nonlinear in their variables. The methods are applied to the Klein-Goldberger model for the United States.

IN THEIR PAPER [1] with the above title, Blattberg and Sargent have suggested a method for estimating regression parameters when disturbances are generated by a symmetric stable law. This procedure was originally suggested by John Wise [4]. Wise arrived at this estimator by confining attention to the class of linear unbiased estimators and minimizing the scale parameter. He also suggested that his procedure might be considered as a generalization of the classical least squares procedure which fails when the second moments of the disturbances do not exist. Blattberg and Sargent have compared various estimators by using simulated data. The main purpose of this note is to show that the procedure suggested by Wise and Blattberg and Sargent has an optimal property, namely that it yields an estimator that has minimum mean absolute error among the class of all linear unbiased estimators. The model is the well-known linear regression model given by

[An exact discrete model is derived from a recursive model consisting of a set of rth order stochastic linear differential equations with constant coefficients such that observations generated at equidistant points of time by the differential system satisfy the discrete model irrespective of the length of sampling interval. The difficulty of estimating the exact model subject to a priori restrictions makes it necessary to approximate the differential system by a non-recursive discrete model that maintains the structural form. This discrete model has a moving average disturbance term of order r - 1, but the co-variance function of this process is approximated by a function that is independent of the parameters of the continuous model. The eigenvalues and eigenvectors of the approximations to the differential system as well as their asymptotic variance matrices are also derived but, like the approximate asymptotic variance matrices of the parameter estimates, these variances are about biased probability limit]

[An attempt is made to set out the implications of the log transformation on the stochastic properties of the model, which are postulated in the original multiplicative relationship. The estimation of the mean of the dependent variable, given some vector of explanatory variables, is accomplished by minimizing the mean square error within a certain class of estimators allowing for biased estimators, assuming known variance. The resulting estimator is modified in order to face the problem of unknown variance. This modified estimator turns out to dominate (in MSE) the least-squares, the ML, and the MVU Bradu and Mundlak estimator.]

This book is a report on a research project in which computer simulation techniques were used to test the rationality of alternative methods of priee calculation in industrial firms.Most of the work was done at the Norwegian School of Economies, with the aid of the Computation Centre of the University of Bergen.Drawing as it must from the various fields of economies, accounting, mathematics, statisties, and computer science, the book is partlya product of a rich interdisciplinary academic milieu, in which I am grateful for having had the opportunity to work.Its defects, however, may be attributed to me.The project was financed by grants from AfS Norsk Varekrigsforsikrings Fond and

[The nonlinear Kaldor theory of macroeconomic business cycles is combined with a classical growth mechanism to derive a deterministic model of business cycle phenomena. Sufficient conditions for the existence, uniqueness, and orbital asymptotic stability of a limit cycle are given. It is shown that the model also exhibits stochastic stability when the deterministic variables are randomly disturbed.]

The fact that long term interest rates have been higher on average than short rates in the twentieth century has often been interpreted in the term structure literature as evidence of the existence of positive or term premiums. The purpose of this paper is to point out that an average differential between long and short rates does not necessarily represent a differential between returns realized by holders of long versus short term bonds. In particular, it is shown that if short term rates are positively autocorrelated, interest rate differentials overstate differentials in realized rates of return. We conclude that liquidity or term premiums properly estimated from the Durand yield curve data are not consistent with the liquidity preference theory. LONG TERM INTEREST RATES have been higher on average than short term rates during the twentieth century. The average differential over the period 1900-1958 between long term interest rates and spot one year rates in the Durand yield curve data increases monotonically with term to about half a percentage point at forty years. The interpretation given to these differentials in the term structure literature is that they are the additional rate of return earned on average by capital invested in long term bonds. The purpose of this paper is to point out that an average differential between long and short term interest rates does not necessarily represent a differential between realized rates of return. This is because the realized increment to capital invested in a sequence of short term bonds depends on the ex post product of uncertain future spot rates. The expected value of this ex post product will in general differ from the product of expected future spot rates. We show that if short term rates are positively autocorrelated, the interest rate differentials overstate differentials in realized rates of return. We shall refer to differentials in realized rates of return as term premiums. The proper interpretation of interest rate differentials is important to the assessment of the evidence for various theories of the term structure. The liquidity preference theory of J. R. Hicks [4, pp. 144-147] predicts that a term premium will be earned by capital invested in long term bonds because their holders require compensation for risk of capital fluctuation. Forward interest rates will exceed one period spot rates on average by the amount of premium which rises monotonically with horizon. The positive and monotonic average differentials between forward and spot one year rates in the Durand data have been

[The estimation of a CES production function for real sectoral value added with factor augmenting technological change first is discussed, with emphasis on the possible effects of the deflation procedure utilized and on the attempt to estimate relatively long-run parameters. The estimates of that function for nine Chilean sectors then are examined with respect to the implied degree of sectoral flexibility, the absorption of surplus labor, the implications for linear assumptions about Chilean production functions, the distribution of income, and the degree of constraint on long-run growth due to a relative shortage of a primary factor.]