A test for long-run memory that is robust to short-range dependence is developed. It is a simple extension of Mandelbrot's "range over standard deviation" or R/S statistic, for which the relevant asymptotic sampling theory is derived via functional central limit theory. This test is applied to daily, weekly, monthly, and annual stock returns indexes over several different time periods. Contrary to previous findings, there is no evidence of long-range dependence in any of the indexes over any sample period or sub-period once short-term autocorrelations are taken into account. Illustrative Monte Carlo experiments indicate that the modified R/S test has power against at least two specific models of long-run memory, suggesting that stochastic models of short-range dependence may adequately capture the time series behavior of stock returns.
A set of n objects and an amount M of money is to be distributed among m people. Example: the objects are tasks and the money is compensation from a fixed budget. An elementary argument via constrained optimization shows that for M sufficiently large the set of efficient, envy free allocations is nonempty and has a nice structure. In particular, various criteria of justice lead to unique best fair allocations that are well behaved with respect to changes of M. This is in sharp contrast to the usual fair division theory with divisible goods. Copyright 1991 by The Econometric Society.
This paper deals with error correction models (ECM's) and cointegrated systems that are formulated in continuous time. Long-run equilibrium coefficients in the continuous system are always identified in the discrete time reduced form, so that there is no aliasing problem for these parameters. The long-run relationships are also preserved under quite general data filtering. Frequency domain procedures are outlined for estimation and inference. These methods are asymptotically optimal under Gaussian assumptions and they have the advantages of simplicity of computation and generality of specification, thereby avoiding some methodological problems of dynamic specification. In addition, they facilitate the treatment of data irregularities such as mixed stock and flow data and temporally aggregated partial equilibrium formulations. Models with restricted cointegrating matrices are also considered.
This paper introduces an ARCH model (exponential ARCH) that (1) allows correlation between returns and volatility innovations (an important feature of stock market volatility changes), (2) eliminates the need for inequality constraints on parameters, and (3) allows for a straightforward interpretation of the "persistence" of shocks to volatility. In the above respects, it is an improvement over the widely-used GARCH model. The model is applied to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987. Copyright 1991 by The Econometric Society.
It seems inconsistent to model boundedly rational action choice by assuming that the agent chooses the optimal decision procedure. This criticism is not avoided by assuming that he chooses the optimal procedure to choose a procedure to . . . to choose an action. The author shows that, properly interpreted, this regress, continued transfinitely, generates a model representing the agent's perception of all his options, including every way to refine his perceptions. In this model, the agent surely must choose the perceived best option. Hence, it is not inconsistent to model limited rationality by assuming that the agent uses the "optimal" decision procedure. Copyright 1991 by The Econometric Society.
The authors demonstrate existence of a perfect foresight equilibrium under borrowing constraints in a one-sector model with infinitely-lived heterogeneous agents. The class of admissible preferences includes, but is not limited to, recursive preferences. Existence is proven using a t$2Ctonnement argument under appropriate conditions on preferences and technology. A new measure of discounting, the norm of marginal impatience, is used to determine which technologies are admissible. Depending on the norm of marginal impatience, the admissible technology may either allow for permanent growth or have a maximum sustainable stock. Copyright 1991 by The Econometric Society.
AN AUCTION IS A MECHANISM for allocating a single indivisible object to one of several competing bidders. The winner is the bidder who is awarded the object. The rules of the auction specify two functions. The first is the probability with which a bidder wins, as a function of everyone's bids. The second is the payment each bidder makes to the seller, as a function of all the bids and whether or not he wins. For instance, a first-price auction awards the object to the highest bidder with probability one (providing there are no tie bids), the winner pays his bid, and the losers pay nothing. The bidders in an auction differ significantly. These differences are captured by the bidder's type. A type may be the bidder's personal valuation of the object for sale, his degree of risk aversion, or perhaps his information about the object. (Maskin and Riley (1984) discuss a number of different economically meaningful examples of bidder types.) From the viewpoint of the seller and the other bidders, each bidder's type is a random variable. In this analysis we confine attention to auctions in which the types are independently and identically distributed according to a known probability distribution. The Revelation Principle asserts that every auction is strategically equivalent to an auction in which bidders bid by announcing their type and no bidder has any incentive to lie. Such an auction is called an incentive compatible direct auction. We will confine our attention to the probability functions for direct auctions, and let the incentive compatibility conditions restrict the payment functions. Each bidder can compute the probability that he wins, conditional on his own type, by averaging over the types of the other bidders. The function relating a bidder's type to his probability of winning is the reduced form of the auction. The literature on optimal auctions usually addresses the problem of maximizing expected revenue for the seller. For this purpose, all the relevant information about the probability function of an auction is contained in its reduced form. It is the reduced form that determines each bidder's behavior and hence the seller's expected revenue. In a symmetric auction each bidder's reduced form is identical, so that expected revenue is a functional defined on reduced forms, which are functions of one variable, namely, types. This makes the seller's problem somewhat tractable. To design an auction, a seller must be able to recognize a reduced form and recover the underlying auction. Reduced forms satisfy an intuitive feasibility condition. Given a set of types, the
We study the problem of implementing social choice correspondences using the concept of undominated Nash equilibrium, i.e. Nash equilibrium in which no one uses a weakly dominated strategy. We show that this mild refinement of Nash equilibrium has a dramatic impact on the set of implementable correspondences. Our main result is that if there are at least three agents in the society, then any correspondence which satisfies the usual no veto power condition is implementable unless some agents are completely indifferent over all possible outcomes. Many common welfare criteria, such as the Pareto correspondence, and several familiar voting rules, such as majority and plurality rules, satisfy our conditions. This possibility result stands in sharp contrast to the more restrictive findings with implementation in either Nash equilibrium or subgame perfect equilibrium. We present several examples to illustrate the difference between undominated Nash implementation and implementation with alternative solution concepts.