[This paper provides an explanation for the observed widespread use of a money good with little intrinsic value. The explanation derives from the result that if agents expect some particular good to play the role of money, then sequential, pairwise trading leads to an economy-wide Pareto optimal allocation.]
For a general vector linear time series model we prove the strong consistency and asymptotic normality of parameter estimates obtained by maximizing a particular time domain approximation to a Gaussian likelihood, although we do not assume that the observations are necessarily normally distributed. To solve the normal equations we set up a constrained Gauss-Newton iteration and obtain the properties of the iterates when the sample size is large. In particular we show that the iterates are efficient when the iteration begins with a VN- consistent estimator. We obtain similar results to the above for a frequency domain approximation to a Gaussian likelihood. We use the asymptotic estimation theory to obtain the asymptotic distribution of several familiar test statistics for testing nonlinear equality constraints.
[This paper is concerned with the sources of variation in the earnings of American scientists over the decade 1960-70. It focuses on sources of variation over time as well as at a point in time. Earnings variation over time is decomposed into sources due to measurable variables representing an earnings function, a random effect individual variance component in the level of earnings, a random effect individual component in earnings growth, and a serially correlated transitory component. Maximum likelihood estimates of the implied parameters are presented and a method for obtaining GLS estimates of the earnings regression function, when the residual variance components are given, is explored.]
THE PRESENT PAPER adds some new results to the rapidly growing literature on social welfare judgements based on interpersonal utility comparisons.2 A. K. Sen [9] and J. Rawls [7] must be credited for stimulating interest in this essentially normative perspective on collective choice. Attention is centered on orderings which a planner wishes to define on the n-dimensional Euclidean space, interpreted as the utility space. These orderings are required to satisfy the strong Pareto principle and a symmetry or anonymity axiom. Two cases are studied. In the first case, the planner is allowed to compare utility levels interpersonally and prevented from comparing utility gains. Under this asumption, there must be what we call rank dictatorship. This term refers to a two-step comparison between utility vectors: first, the planner must rank utility levels from the lowest to the largest within each utility vector and secondly, in order to compare vectors, he must always endorse the strict preference of one particular rank. This rank which wins in every comparison is chosen exogeneously. Turning to the second case, we allow the planner to attach significance to statements of the form: for a given utility vector, individual i is better off than individual j; while no meaning can be given to statements of the form: for a given utility vector, i's utility gain over j is larger than h's utility gain over k, assuming the gains have the same sign and the two pairs of individuals do not overlap. So far there is no difference at all with case one. In the second case, however, we endow the planner with a finer discriminating power. He is now allowed to consider as meaningful interpersonal comparisons of utility gains of the following form: going from one particular utility vector to another, individual i gains more (or less) than individual j. In this case, there exists a set of nonnegative numbers, each of which is associated with a particular rank and which is such that any given utility vector is strictly preferred to any other by the planner whenever its weighted sum is strictly larger than the corresponding sum associated with the other vector. It should be clear that rank dictatorial orderings make up a subset of the set I just described. They can be obtained by assigning zero weight to all ranks but one.
The notion of stability in the sense of Lyapunov is applied to economic dynamic processes of the Champsaur-Dreze-Henry type. Our purpose in this note is to fill a small gap in the literature concerning dynamic processes in economic theory, of the type presented by Champsaur, Dreze, and Henry [3]. Indeed, these authors do not discuss stability in the sense of Lyapunov [7]. However, a recent result of Maschler and Peleg [9] on this kind of stability (presented in a discrete model) can easily be applied to both continuous and discrete processes used in economics. We shall present this result for a very general class of such processes and conclude with references to a few economic applications. For our purpose a (set valued) dynamic system is simply a pair 〈X,φ〉, where X is a compact subset of R and φ a correspondence from X to its nonempty subsets. Let T be a subset of [0,∞) containing 0 and x0 an element of X. Then a φ-process starting at x0 is a pair of functions: x(·) : T → X, ẋ(·) : T → R, such that: x(0) = x0 and, ∀ t ∈ T , ẋ(t) ∈ φ(x(t)). If T = {0, 1, 2, · · · , } and ẋ(t) = x(t + 1) then the process 〈x(·), ẋ)(·)〉 is called discrete. If T = [0,∞), if x(·) is absolutely continuous on any interval [0, τ ] in T , and ẋ(t) = dx(t)/dt for almost every t in T , then the process 〈x(·), ẋ(·)〉 is called continuous. In the first case the Econometrica, 47(3), 733-737, 1979. As pointed out by Negishi [10], this is the same as Samuelson’s stability of the second kind [11]. The term “stability in the sense of Lyapunov” is used by Arrow and Hahn [1]. Heal [5] and Hori [6] also use this concept of stability. See Champsaur, Dreze, and Henry [3, Section 5].
[In an economy with incomplete markets, firms' profits at different dates and contingencies cannot be aggregated into a single index and so profit maximization is not well-defined. In this paper we propose an objective for firms to pursue which is a generalization of the idea of profit maximization. We show that, if firms' managers can transfer current income between shareholders at the first date, and if shareholders have what we call competitive perceptions concerning the effect of a change in production plan on share prices, then each firm will maximize a weighted sum of shareholders' private valuations of the firm's production plan, where the weights are the initial shareholdings. We then define, and prove the existence of, a competitive equilibrium in which firms pursue this proposed objective. Finally, we analyze the optimality properties of the competitive equilibrium.]
It is proved that Groves’ scheme is unique on restricted domains which are smoothly connected, in particular convex domains. This generalizes earlier uniqueness results by Green and Laffont and Walker. An example shows that uniqueness may be lost if the domain is not smoothly connected.