Showing papers in "Econometrica in 1973"

An intertemporal capital asset pricing model

Abstract: An intertemporal model for the capital market is deduced from the portfolio selection behavior by an arbitrary number of investors who aot so as to maximize the expected utility of lifetime consumption and who can trade continuously in time. Explicit demand functions for assets are derived, and it is shown that, unlike the one-period model, current demands are affected by the possibility of uncertain changes in future investment opportunities. After aggregating demands and requiring market clearing, the equilibrium relationships among expected returns are derived, and contrary to the classical capital asset pricing model, expected returns on risky assets may differ from the riskless rate even when they have no systematic or market risk. ONE OF THE MORE important developments in modern capital market theory is the Sharpe-Lintner-Mossin mean-variance equilibrium model of exchange, commonly called the capital asset pricing model.2 Although the model has been the basis for more than one hundred academic papers and has had significant impact on the non-academic financial community,' it is still subject to theoretical and empirical criticism. Because the model assumes that investors choose their portfolios according to the Markowitz [21] mean-variance criterion, it is subject to all the theoretical objections to this criterion, of which there are many.4 It has also been criticized for the additional assumptions required,5 especially homogeneous expectations and the single-period nature of the model. The proponents of the model who agree with the theoretical objections, but who argue that the capital market operates "as if" these assumptions were satisfied, are themselves not beyond criticism. While the model predicts that the expected excess return from holding an asset is proportional to the covariance of its return with the market

Incentives in Teams

Abstract: This paper analyzes the problem of inducing the members of an organization to behave as if they formed a team. Considered is a conglomerate-type organization consisting of a set of semi-autonomous subunits that are coordinated by the organization's head. The head's incentive problem is to choose a set of employee compensation rules that will induce his subunit managers to communicate accurate information and take optimal decisions. The main result exhibits a particular set of compensation rules, an optimal incentive structure, that leads to team behavior. Particular attention is directed to the informational aspects of the problem. An extended example of a resource allocation model is discussed and the optimal incentive structure is interpreted in terms of prices charged by the head for resources allocated to the subunits.

Manipulation of voting schemes: a general result

Abstract: It has been conjectured that no system of voting can preclude strategic voting-the securing by a voter of an outcome he prefers through misrepresentation of his preferences. In this paper, for all significant systems of voting in which chance plays no role, the conjecture is verified. To prove the conjecture, a more general theorem in game theory is proved: a gameform is a game without utilities attached to outcomes; only a trivial game form, it is shown, can guarantee that whatever the utilities of the players may be, each player will have a dominant pure strategy. I SHALL PROVE in this paper that any non-dictatorial voting scheme with at least three possible outcomes is subject to individual manipulation. By a "voting scheme," I mean any scheme which makes a community's choice depend entirely on individuals' professed preferences among the alternatives. An individual "manipulates" the voting scheme if, by misrepresenting his preferences, he secures an outcome he prefers to the "honest" outcome-the choice the community would make if he expressed his true preferences. The result on voting schemes follows from a theorem I shall prove which covers schemes of a more general kind. Let a gameform be any scheme which makes an outcome depend on individual actions of some specified sort, which I shall call strategies. A voting scheme, then, is a game form in which a strategy is a profession of preferences, but many game forms are not voting schemes. Call a strategy dominant for someone if, whatever anyone else does, it achieves his goals at least as well as would any alternative strategy. Only trivial game forms, I shall show, ensure that each individual, no matter what his preferences are, will have available a dominant strategy. Hence in particular, no non-trivial voting scheme guarantees that honest expression of preferences is a dominant strategy. These results are spelled out and proved in Section 3. The theorems in this paper should come as no surprise. It is well-known that many voting schemes in common use are subject to individual manipulation. Consider a "rank-order" voting scheme: each voter reports his preferences among the alternatives by ranking them on a ballot; first place on a ballot gives an alternative four votes, second place three, third place two, and fourth place one. The alternative with the greatest total number of votes wins. Here is a case in which an individual can manipulate the scheme. There are three voters and four alternatives; voter a ranks the alternatives in order xyzw on his ballot; voter b in order wxyz; and voter c's true preference ordering is wxyz. If c votes honestly, then, the winner is his second choice, x, with ten points. If c pretends that x is his last choice by giving his preference ordering as wyzx, then x gets only eight points, and c's first choice, w, wins with nine points. Thus c does best to misrepresent his

A subordinated stochastic process model with finite variance for speculative prices

Abstract: S. Bochner's concept of a subordinate stochastic process is proposed as a model for speculative price series. A general class of finite-variance distributions for price changes is described, and a member of this class, the lognormal-normal, is tested against previously proposed distributions for speculative price differences. It is shown with both discrete Bayes' tests and Kolmogorov-Smirnov tests that finite-variance distributions subordinate to the normal fit cotton futures price data better than members of the stable family.

Alternative Tests of Independence between Stochastic Regressors and Disturbances

Abstract: IN TESTING HYPOTHESES on the coefficients of a linear regression model with stochastic regressors it is well known that the usual t test and F test are applicable if the stochastic regressors are statistically independent of the disturbances [3, p. 268; 5, pp. 27-28]. Also, there are cases in which economic hypotheses can be stated in terms of the independence of stochastic regressors and disturbances, the best known examples being the current versus the permanent income hypotheses and the recursiveness hypothesis in a simultaneous equations model. Therefore, it is desirable to develop a procedure that can be used to test the hypothesis that the stochastic regressors and disturbances are independent. In this paper, we examine four alternative tests of independence between the stochastic regressors and disturbances. In the rest of this section we specify the stochastic model and state the hypotheses to be tested. In Section 2 we present two finite sample tests. In Section 3 two alternative asymptotic tests are given and asymptotic power functions of all four tests are examined. In Section 4 we give examples of applications of the test in econometrics. We consider the following linear model:

Aggregation of preferences with variable electorate

Abstract: IN THIS PAPER we consider procedures for going from several individual preferences among several alternatives, called candidates, to something which may be called a collective preference. The individual preferences take the form of (total) orderings of the alternatives, and the collective preference is to take the form of a (total) weak ordering (i.e., ties allowed). We consider certain properties which seem desirable in such systems and investigate which systems have these properties. The point of view taken here differs from that of other work in this area (e.g., [1, 2, 3, 4]) chiefly in asking that the procedure work for all possible sizes of the voting population, rather than for a fixed population, given in advance. This permits us to require, for example, that if each of two bodies of voters prefers candidate A to candidate B under a given procedure, then the combination of these bodies should prefer A to B under the same procedure. In Section 1 we give the formal definitions of an aggregation procedure and discuss certain desirable features, namely "neutrality" (treats candidates symmetrically), "separability" (the condition mentioned above), "monotonicity," and an "Archimedean" property which says, roughly, that a sufficiently large body with a given distribution of preferences can impose its will on any body of fixed size. In Section 2 we introduce certain procedures: "point systems" and "generalized point systems" (roughly, point systems allowing "infinitesimal points"), which are neutral and separable. They are monotonic if and only if the points are arranged in the "natural" order, and the point systems are, in addition, Archimedean. In Section 3 we prove a converse, namely that any neutral and separable procedure can be realized by a generalized point system and, if it is Archimedean, by a point system. This part requires some familiarity with the notions of least upper bound of a set of real numbers and bases of vector spaces. In Section 4 (which is largely independent of Section 3), we consider "point runoff" systems which use point systems in a succession of eliminations. Such systems are neither separable nor monotonic but do satisfy some very weak separability and monotonicity conditions. While these probably do not characterize point runoff systems, we know of no other systems satisfying them.

Path independence, rationality, and social choice

Abstract: The paper provides several axiomatizations of the concept of "path independence" as applied to choice functions defined over finite sets. The axioms are discussed in terms of their relationship to "rationality" postulates and their meaning with respect to social choice models. IN ANSWER to critics of the first edition of Social Choice and Individual Values, Arrow advanced in the second edition ajustification for imposing his "consistency" or "rationality" conditions which had not previously appeared, explicitly, in the social choice literature [2, p. 120]. He argued that the rationality conditions were necessary in order for social choices to be independent of the path of choice. He provided no real elaboration on the point. Perhaps he felt no explanation was necessary, since much of the social choice literature, especially those papers which deal with cycles, implicitly place a premium on some type of path-independence property. The purpose of this paper is to report some results which bear on the meaning and usefulness of this type of property. Specifically, it is shown that path independence is implied by, but does not imply rational choice. The importance of the observation is threefold. First, if path independence, rather than rationality, is desired as a property of social choice, the stronger rationality conditions need not be imposed. One result of this relaxation is that the immediate impossibility result discovered by Arrow is avoided. Welfare economists then are free to explore the possible applications of the tools he provided. Secondly, the observations made raise issues pertaining to the reasons for investigating mathematical properties like path independence in the first place. Thirdly, it is shown that the lines which separate rationality properties, which induce immediate impossibility results, from path-independence properties are very thinly drawn. We will proceed as follows. Immediately below, in Section 2, a survey of the interpretations of the symbols is given. A glossary is also added at the end. Section 3 provides a brief summary of the arguments which have been advanced in support of "rationality conditions" in the case of social choice. These are presented in order that they can be separated from those arguments which are

On a class of equilibrium conditions for majority rule

Abstract: The various conditions for non-intransitivity of majority rule formulated over the past decade have been concerned with choices over arbitrary, usually finite, sets of discrete alternatives. In many economic and other social choice problems, however, the possible choices constitute a point set in some appropriately defined multi-dimensional commodity or policy space. It is shown that in problems of this kind, when voter preferences can be represented by quasi-concave, differentiable utility functions, the various equilibrium conditions for majority rule are incompatible with even a very modest degree of heterogeneity of tastes, and for most purposes are probably not significantly less restrictive than the extreme condition of complete unanimity of individual preferences.

The stability of models of money and growth with perfect foresight

Abstract: SEVERAL ECONOMISTS2 have argued that if individuals correctly perceive the rate of inflation so that their expectations are "rational," then deterministic models of money and economic growth are unstable. In this view, points on the steady state equilibrium paths examined by Tobin [9] and others are "saddlepoints," there being a tendency to diverge more and more from such a path as time elapses if the system is not initially on the path. The source of instability is understood most easily in the context of a model in which money is "neutral," with real growth and capital accumulation both being exogenous with respect to the money supply and price level and, moreover, with both equaling zero. Time is continuous. The price level P and money supply M are assumed at each moment to satisfy the demand function for real balances

The theory of parametric identification

Abstract: This paper sets out a general criterion for the identifiability of a statistical system, based on Kullback's information integral. It is shown that the general identification problem is equivalent to a maximisation problem, or where parameter restrictions are present, a problem in nonlinear programming. The relationship of this criterion to that based on the information matrix of the underlying distribution is also exhibited. THE COLLECTION OF results on the identification problem in econometrics is by now assuming the proportions of an imposing edifice. It is, however, a little surprising to note that this structure has been growing upwards and, more recently, outwards, without a corresponding strengthening in the foundations. It is true that in the case of work on linear simultaneous equation systems (and this, with the work of Koopmans and Reiersol [3] and Chapters 1-4 of Fisher [1] in particular, has almost assumed the status of a "classical" line of development), these results are founded on a pretty secure rock; to wit, the identifiability of the reduced form in the absence of any singularities in the data matrices. Nevertheless, with the development of other wings on our edifice, it seems desirable to look to more basic things. The recent paper by Thomas Rothenberg [5] provided a welcome attack on this subject. The identifiability of a parametric system is approached via the nonsingularity of R. A. Fisher's "information matrix" evaluated at the true value of the parameter. The present note generalizes this approach by providing a simple criterion for identifiability, which not only affords an approach to global identification, but also makes no assumptions about the regularity of the underlying distribution. Rothenberg's basic theorem emerges as a simple corollary to this result. The approach has a natural relationship with estimation theory and also provides a straightforward method for delineating the subspace of observationally equivalent parameters in the case of underidentification.

Public goods and income distribution: some further results'

Abstract: Aaron and McGuire recently put forward a new method for imputing benefits of government expenditures on public goods for various income classes. They fail to present conclusive empirical results, however, lacking a parameter whose value is heretofore unmeasured. This note uses three independent empirical estimates of this crucial parameter to compute estimates of the net incidence of the fiscal system. For the U.S., 1961, it is found that benefits from public goods are regressively distributed. It is further suggested that the desire to equalize incomes requires provisions of less, not more, public goods.

Tests for serial correlation in regression models with lagged dependent variables and serially correlated errors

Abstract: The paper compares the power of two tests for serial correlation in regression models with lagged dependent variables, recently suggested by Durbin, with that of the likelihood ratio test by means of two sets of Monte-Carlo experiments-one in which the exogenous series is taken to be the quarterly GNP series for the USA and the other in which the exogenous series is generated by a known autoregression.

A mixture-set axiomatization of conditional subjective expected utility'

Abstract: An axiomatization is presented for a Savage-type conditional subjective expected utility model. The axioms consist of extensions of the Herstein-Milnor [11] axioms for "measurable" utility, a generalization of an averaging condition in Bolker [4], and several structural conditions. The structural conditions are examined in some detail, and examples are given to show what happens to the numerical model when they do not hold. The numerical model expresses the utility of an act (or mixed act), given an event, as a weighted sum of the utilities of the act given events that partition the initial event, the weights being personal probabilities for the partition events conditioned on the initial event. The theory is compared to Savage's theory [18] and to a version of the theory of Luce and Krantz [14] for conditional expected utility. 1. DECISION UNDER UNCERTAINTY THE PREDICAMENT BETWEEN mathematical tractability and situational reality that is characteristic of mathematical models in the behavioral sciences is epitomized in the axiomatizations of subjective expected utility models. These axiomatizations include structural conditions that facilitate the derivation of the desired numerical representations for preference. Unfortunately, actual situations of decision making under uncertainty often fail to exhibit the structural properties that occur in the axiomatizations. Thus there is real concern about the applicability of such models to realistic decision situations. As might be expected, decision theorists have attempted to alleviate this predicament by weakening the structural conditions while maintaining the ability to derive the desired model from the axioms. An early move in this direction was made by Suppes [21] in his alternative to Savage's axiomatization [18]. The more recent axiomatizations of Bolker [3 and 4], based on Jeffrey's decision model [12], and of Pfanzagl [15 and 16] and Luce and Krantz [14], continue this line of research. The present paper is a further effort in this direction. To understand its approach we shall first review briefly some other theories. The formulation of the paper is set in the context of Savage's states-of-the-world approach to decision under uncertainty, and I shall therefore focus the discussion within this context. We suppose that the decision maker is to select an alternative, or act, from a set of acts. The consequence of his decision will depend not only on the selected act but also on which state in a set of exclusive and exhaustive states of the world obtains. The state that obtains is not known beforehand by the decision maker and does not depend on the selected act.3

Risk Independence and Multiattributed Utility Functions

Abstract: The concepts of conditional risk aversion, the conditional risk premium, and risk independence pertaining to multiattributed utility functions are defined. The latter notion is then generalized to what is called utility independence. A number of theorems useful for simplifying the assessment of multiattributed utility functions given certain risk independence and utility independence assumptions are stated. *Adapted from a thesis, supervised by Professor Howard Raiffa (Harvard), presented to the M.I. T. Operations Research Center in partial fulfillment of the requirements for the degree of Doctor of Philosophy, June, 1969. Additional supervision and other expenditures associated with the work reported herein were supported (in part) by the U.S. Army Research Office (Durham), under Contract Number DA-31-124-ARO-D-209 and (in part) by the Office of Naval Research under Contract Nonr-3963 (06), NR 276-004, at the M.I. T. Operations Research Center. During his doctoral program the author was supported by the Bell Telephone Laboratories' Doctoral Study Program. **Currently Assistant Professor of Civil Engineering and Staff Member of the Operations Research Center.