Showing papers in "Econometrica in 1966"

Equilibrium in a capital asset market

Abstract: This paper investigates the properties of a market for risky assets on the basis of a simple model of general equilibrium of exchange, where individual investors seek to maximize preference functions over expected yield and variance of yield on their port- folios. A theory of market risk premiums is outlined, and it is shown that general equilibrium implies the existence of a so-called "market line," relating per dollar expected yield and standard deviation of yield. The concept of price of risk is discussed in terms of the slope of this line.

Specification and estimation of Cobb-Douglas production function models

Abstract: In this paper we consider the specification and estimation of the Cobb-Douglas production function model. After reviewing the "traditional" specifying assumptions for the model which are based on deterministic profit maximization, we develop a model in which profits are stochastic and in which maximization of the mathematical expectation of profits is posited. "Sampling theory" and Bayesian estimation techniques for this model are presented. IN THIS PAPER we take up the problem of specifying and estimating a model of a profit maximizing firm operating with a Cobb-Douglas production function. Our model differs from the traditional production model considered in the literature, in that we assume that: (a) the production process is neither instantaneous nor deterministic; and (b) entrepreneurs are aware of the stochastic nature of production in their profit maximizing endeavors. This fundamental conceptual difference in our approach leads us to a new model with properties different from that of the traditional model.2 Also we develop both sampling theory and Bayesian estimation procedures for the new model. The order of presentation is as follows. In Section 2 we review the traditional model, and then go on in Section 3 to formulate the new model. In Section 4, sampling theory estimation procedures are developed for the new model. In contrast with the traditional model, it is found that classical least squares provides consistent estimators of the parameters of the Cobb-Douglas production function. With a normality assumption, these are also unbiased and maximum likelihood estimators. Finally, in Section 5, a Bayesian analysis of the new model is presented.

The Typical Spectral Shape of an Economic Variable

Abstract: In recent years, a number of power spectra have been estimated from economic data and the majority have been found to be of a similar shape. A number of implications of this shape are discussed, particular attention being paid to the reality of business cycles, stability and control problems, and model building.

Existence of competitive equilibria in markets with a continuum of traders.

Abstract: : It is well known, and easy to establish, that there exist markets that do not have competitive equilibria, provided the traders do not have convex preferences--that is, that the set of commodity bundles preferred or indifferent to a given bundle is not always convex. It is proved, nevertheless, that in a market consisting of a continuum of traders, each one individually insignificant, there is always a competitive equilibrium, even when the preferences are not convex. (Author)

Quasi-cores in a monetary economy with nonconvex preferences

Abstract: : A model of a pure exchange economy is investigated without the usual assumption of convex preference sets for the participating traders. The concept of core, taken from the theory of games, is applied to show that if there are sufficiently many participants, the economy as a whole will possess a solution that is sociologically stable--i.e., that cannot profitably be upset by any coalition of traders.

Stock market prices and volumes of sales

Abstract: or vice versa will inevitably yield incomplete if not erroneous results. SUMMARY THE PRESENT investigation is a part of a study of the stock market which is motivated by three basic considerations: (1) Existing demand theory is inadequate for analyzing the problem of speculative prices and thus incapable of providing a valid prediction theory for this type of price mechanism. (2) The volume of sales in a commodity market has an economic significance in its own right and thus deserves much more attention by economists than it has received so far. (3) Prices and volumes of sales in the stock market arejoint products of a single market mechanism, and any model that attempts to isolate prices from volumes or vice versa will inevitably yield incomplete if not erroneous results. While the theoretical model and its implications will be presented elsewhere, the empirical results reported here serve as a basis for the proposed theory. Among the significant results so far found are: (1) A small volume is usually accompanied by a fall in price. (2) A large volume is usually accompanied by a rise in price. (3) A large increase in volume is usually accompanied by either a large rise in price or a large fall in price. (4) A large volume is usually followed by a rise in price. (5) If the volume has been decreasing consecutively for a period of five trading days, then there will be a tendency for the price to fall over the next four trading days.

Use of the durbin-watson statistic in inappropriate situations

Abstract: IN RECENT years the Durbin-Watson statistic has been used uncritically to test for serial correlation in the residuals of relationships containing lagged endogenous variables which are estimated by single or simultaneous equations methods. When lagged endogenous variables are included in an equation estimated by ordinary least squares, however, the Durbin-Watson statistic is asymptotically biased towards 2 (the value which it should have if no serial correlation is in fact present). It is doubtful, therefore, that the statistic should be used either to test for serial correlation in the residuals or to provide any indication of the extent of such correlation when the estimated equation contains lagged values of any endogenous variable. The widespread use of the Durbin-Watson statistic in inappropriate situations may stem from misinterpretation of a remark in one of Durbin's later papers. In the original papers setting forth their test, Durbin and Watson stated: "It should be emphasized that the tests described in this paper apply only to regression models in which the independent variables can be regarded as 'fixed variables'. They do not, therefore, apply to autoregressive schemes and similar models in which the lagged values of the dependent variable occur as independent variables" [2, p. 159]. In a subsequent paper, however, showing that the statistic could be used with some slight modification in systems of simultaneous equations, Durbin wrote: "In some formulations certain of the x's coincide with lagged values of the y's. The theory becomes much more complicated in such cases, and we shall not consider them except to point out that the results obtained later in the paper, which are exact for the model specified above, may be expected to hold approximately for models containing lagged dependent variables" [1, p. 370]. This later paper discussed the distribution of the Durbin-Watson statistic under the null hypothesis of no serial correlation and did not cover the test's power against alternatives. While the original Durbin and Watson papers showed that the test has high power against Markov alternatives, the asymptotic result, derived from a result obtained by Malinvaud and presented below, indicates that this conclusion does not hold when lagged endogenous variables are included. In a paper in which expressions for the asymptotic bias of least squares estimates of regression coefficients in various models containing lagged dependent variables and serially correlated residuals were derived, Griliches commented that "in most cases the addition of the lagged dependent variable to the regression will reduce the serial correlation of the residuals" and hence increase the Durbin-Watson statistic [3, p. 70]. The asymptotic results were extended to cover the bias in the estimated 235

A survey of the theory of international trade: part 3, the modern theory

Abstract: THE CELEBRATED factor price equalization theorem has a curious history. Ohlin (1933) introduced to English-speaking readers an important modification to international trade theory, replacing the classical simplification, of constant costs but differing production functions among countries, with the alternative simplification of identical production functions but differing factor endowments. While many economists have remarked on the unrealism of Ohlin's simplification, an important aspect of it has not, it would seem, always been sufficiently appreciated. This is the fact that the classical model assumed that production relations in different countries differed in a quite arbitrary fashion; no satisfactory way had been provided for explaining how such production relations differed. In the Ohlin model, on the other hand, an element of continuity was introduced, since continuous variation of factor endowments would yield continuous (rather than arbitrary) variation in production relations. Even if differences in production relations (specifically, in transformation functions) cannot be completely explained in terms of differences in factor endowments, the Ohlin model is nevertheless susceptible to amendments that preserve meaningful relationships between different countries' production functions. Ohlin's writings were greatly influenced by Heckscher (1919), whose work was not made available in English until 1949. Heckscher, in turn, acknowledged the influence on his thought of Wicksell (1919).' Ohlin asserted that there was a tendency towards factor price equalization as a result of free trade, but he tempered his argument with many qualifications, even to the point of asserting that equalization would never be complete. The partial equalization argument was taken up and made rigorous by Stolper and Samuelson (1941), and later Samuelson (1948,

A general theory of rational behavior in game situations

Abstract: The von Neumann-Morgenstern theory of games does not yield determinate solutions (corresponding to unique payoff vectors) for two-person variable-sum games and for n-person games. The present paper outlines a general theory of rational behavior in game situations which does yield determinate solutions for all classes of games. The theory is based on two classes of rationality postulates: those defining rational behavior as'such, and those defining rational expectations concerning the other players' behavior. It is argued that this new approach greatly increases the possibilities for the application of game theory in economics and the other social sciences.

Invariance axioms and economic indexes

Abstract: exhibited. We present axiom systems for indexes of several economic variables: inputs, outputs, prices, wages, inflation, and technological change. In addition to conventional smoothness and proportionality conditions, in each case an Invariance Axiom is proposed. For technological change this says, in a sense, that when there is no technological change there is no change in the index. One can prove that in each case there is a unique index satisfying the axioms, and this is a Divisia index.2 Since these continuous indexes are not generally independent of the path, the problem of how often to change index weights may be viewed in the light of a choice between invariance and independence. We show that the unique invariant measure of technological change is a natural generalization of Solow's measure to the case of many commodity types.

Errors of measurement and least squares estimation in a simple recursive model of dynamic equilibrium

Abstract: where Yt and Xt are subject to random errors of measurement ut and vt, respectively, with E(u) = E(vt) = 0, E(u2) = u, E(v2) = 2, E(utvt) = , and E(utu')E(vtsv) = 0 for t # t', is applied to a simple system of difference equations. The paper treats two such models, which differ in that one system is specified as deterministic except for measurement error, while the second model includes random "shocks" in the equations as well. The investigation focuses on the possible consistency of least squares estimates of structural parameters in both cases. Mann and Wald [3] have demonstrated the consistency property of least squares estimates in stochastic difference equations which contain a shock term, and T. W. Anderson [1] has more recently shown such estimates to possess asymptotic normal distributions. One way argue, and perhaps quite legitimately, against the inclusion of measurement errors and shocks as separate entities in systems such as those under consideration. This separation, however, does provide a useful contrast with regard to the consistency property of LS estimates as compared to the case when only shocks (which subsume measurement error) are present in the specification of the system. When measurement errors are separated from shocks, LS yields consistent estimates for the explosive case of cobweb equilibrium and inconsistent estimates under convergence. The above phenomenon rests on the perhaps more interesting results for a recursive model where only measurement errors are present. This change in how the random terms enter the system, as contrasted to the Mann and Wald or Anderson formulations, causes zero correlation between observed variables and inconsistent LS estimates in the equations under convergence. Again, under explosion, LS provides consistent estimators of structural parameters.

Decision and horizon rules for stochastic planning problems : a linear example

Abstract: Analytic decision rules and horizon rules are developed for the warehousing problem. A stochastic warehousing problem is defined and solved, first by backwards induction, then by means of a forward working algorithm. The influence of holding costs and discount rates on forecasting horizons is illustrated.

The price elasticity of liquor in the u.s. and a simple method of determination

Abstract: Arc elasticity is estimated for liquor by simply comparing state sales before and after price increases, standardized by states in which price did not change. The technique can be used wherever there are several economic units independent with respect to price changes; it allows causal interpretation and it permits comparison of various length-of-run elasticities.

Specification Analysis in the Estimation of Parameters of a Simultaneous Equation Model with Autoregressive Residuals

Abstract: Several related estimators of the parameters of a single equation of a simultaneous equation model are proposed. They are shown to be consistent and asymptotically efficient when the residual of the equation follows the first-order autoregressive process. One of these estimators, called MS2SLS, is designed to be consistent under a more general assumption about the stochastic process of the residual. A numerical analysis shows that the efficiency of MS2SLS is much higher than that of 2SLS under a general assumption about the stochastic process of the residual.