This paper deals with the theoretical development of some aspects of the trend removal problem. The objective is to show the difference between the two most popular trend removal methods: first differences and linear least squares regression. On the one hand, we show that if first differences are used to eliminate a linear trend, the series of residuals would be stationary but would not be white noises as they contain a first lag autocorrelation of -0.50. Furthermore, the spectral density function (SDF) of these residuals relative to that of a white noise series would be exaggerated at the high frequency portion and attenuated at the low frequency portion. On the other hand, we show that the regression residuals from the linear detrending of a random walk series would contain large positive autocorrelations in the first few lags. Relative to that of white noises, the SDF of the regression residuals would be exaggerated at the low frequency portion and attenuated at the high frequency portion.
[A recent paper by D. J. Roberts and A. Postlewaite [1] shows a possible justification for the assumption that participants in a market behave as price-takers when the number of participants becomes large. The present note compares this justification with other approaches to the same question and argues that the various approaches are complementary rather than alternative since, in order to demonstrate the viability of a system with price-taking behavior, all types of feasible deviations from such behavior must be explored. The note introduces a taxonomy for such deviations which may be useful in comparing various approaches and contributions found in the literature.]
[This paper describes a market in which firms vary their quantities of production according to a new adjustment process. Each firm bases its new production entirely upon a knowledge of its own previous productions and profits. It has no knowledge of the payoff functions of the market. Numerical analysis of the process indicates an approach to equilibrium for all initial states. The set of allowed limit points is rigorously characterized, and determined explicitly in the case of two firms. Some exact solutions are found. The process can be regarded as a way of playing a continuous game with a minimum of information.]
This paper examines the durability of capital goods produced under different market structures when tax considerations are included. Since investment tax credit and depreciation allowances are realized by the owner of the durable good, the durability of products produced by an industry which sells its output differs from that of an industry which rents. For each of these two commercial forms we consider both monopolistic and competitive market structure. Potential gains from different forms of regulation are discussed.
THE SMALL SAMPLE PROPERTIES of the estimators of parameters in a single equation of a system of equations have been investigated in several ways. Some of the many Monte Carlo studies that have been conducted are reviewed in Johnston [8]. Nagar [14] used expansions in powers of terms whose order in probability was T1, where T is the sample size, to obtain approximations of the small-sample behavior of the members of Theil's k-class estimators [18]. Basmann [4, 5], Kabe [9], Richardson [15], Sawa [17], and others, present exact distributions for the two-stage least squares estimators for certain models. Mariano and Sawa [13] give the exact distribution of the limited information estimator for the coefficient in a single equation containing two endogenous variables. The studies of the exact distributions show that the limited information estimator does not possess moments and that the first two moments of the two-stage least squares estimator exist only for certain levels of overidentification. Kadane [11] presents an approximation to the bias and mean square error of the k-class estimator and the limited information estimator in terms of an expansion in o-, where o_2 iS (a multiple of) the variance of the residuals in the equation. Kadane's results for the k-class agree with those of Nagar [14]. Recently asymptotic expansions of tie distribution function of the estimators of a single equation have appeared (e.g., see Anderson [1], and Sargan and Mikhail [16]). We present a modification of the limited information estimator and demonstrate that the modified estimator possesses finite moments and that one member of the class has bias of order T2. The estimator is a member of the k-class estimators originally introduced by Theil [18]. We also introduce a modification of the Nagar [14] fixed k-class estimators to ensure finite moments. The modified estimators have the same limiting distribution as the unmodified estimators, and the approximations presented by Nagar hold for the first two moments of the modified k-class estimator. Restricting the modified k-class estimator and the modified limited information estimator to have the same, but arbitrary, bias we show that to order T2 the modified limited information estimator dominates the k-class 1 Journal Paper number J-8374 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa; Project 2039. This research was partly supported by the United States Bureau of the Census through Joint Statistical Agreements 74-1 and 75-1.
By looking at approximate multivariate risk premiums a matrix measure of multivariate local risk aversion is introduced for a multi-attributed utility function u. This matrix function R(x) = [-uij(x)/ui(x)] generalizes the univariate measure of Pratt [11] and the conditional measure of Keeney [7]. It has particular advantages in assessing the attitude of a decision-maker toward correlated risks, a concern of Richard [13], and is more informative than the scalar measure proposed by Kihlstrom and Mirman [8]. Simple characteristics of the absolute risk aversion matrix R determine whether a utility function is additive or concave. Assumptions of either constancy or proportionality of R are shown to lead to specific restrictions on the form of u which are more stringent than those of Rothblum [15].
There has recently been a resurgence of interest in specifying more completely the relationship between Walrasian microeconomic models of economic behavior and Keynesian macroeconomic models.On the face of it, these two approaches to economic reality seem very different.The Walrasian model assumes agents engage in maximizing behavior taking as given a common perception of relative prices.The relative prices then adjust to equilibrate the system.The Keynesian model specifies that agents' be- havior obeys certain ad hoc rules relating quantity variables of the sys- tem.These quantities then adjust to equilibrate the system.Keynesian analysis is often thought to concern itself primarily with a case where price signals are fixed or adjust very slowly; Walrasian
This paper reports the testing of hypotheses concerning: (i) whether the household is better viewed as planning over a single-period versus a multiperiod horizon; (ii) whether the household is better viewed as planning in a single-asset or a multiasset framework; (iii) the relative importance of substitution and wealth effects as sources of change in the stock demand for automobiles. The findings are that a multiperiod, multiasset model best describes stock demand, that the separation theorem which implies a zero wealth effect is rejected, and that substitution effects are seven times more important than wealth effects. THE ECONOMIC LITERATURE CONTAINS several empirical studies of household automobile demand [3, 7, 8, and 10] and theoretical models of the household [1, 4, 5, 6, and 14] which are or could be applied to automobile demand. Two aspects of theory which are not fully reflected in the empirical studies are the implications of a multiperiod horizon and the possibility of substitution among assets. Theoretical models [5 and 15] which assume a multiperiod horizon imply that relevant asset prices are user costs and the appropriate constraint is wealth. In contrast, most empirical studies use purchase prices rather than user costs, and income rather than wealth. In addition, theoretical models [4 and 5] permit substitution over a variety of goods, whereas most empirical studies restrict substitutions to automobiles and consumption goods. To the extent that estimated equations are misspecified, the prevailing conclusion that income effects are more important than substitution effects may be due to left-out-variable bias. This paper investigates each of these three issues-the length of the horizon, the range of substitutions, and the relative importance of substitution and wealth effects-by estimating over the same set of data a variety of alternative equations which reflect different assumptions about the horizon and range of substitutions. Initially, a multiperiod, multiasset model of the household consumption-saving decision is stated and used to derive the appropriate arguments for the broadest estimating equation. A linear approximation of this equation is estimated using quarterly United States data covering the years 1952-1972. Then this estimate is compared to competing equations derived under restrictions on the multiperiod, multiasset model. Specifically, demand equations derived under multiperiod, single-asset, single-period, single-asset, and single-period, multiasset assumptions are estimated and compared to the broadest multiperiod, multiasset equation. In addition, versions of the restricted equations which have appeared in the literature are estimated and compared. The findings are: (i) a multiperiod, multiasset equation best describes automobile stock demand, (ii) estimates of substitution and wealth effects are quite sensitive to specification bias, and (iii) substitution effects are seven times more important than wealth effects in the dominant equation.