Knowledge that Transforms

A Bayesian analysis of the linear regression model with only parts of the prior distribution specified or a robust Bayesian analysis lead to sets of posterior distributions. E. E. Leamer (1978) describes the region of posterior means for conjugate priors and varying prior covariance matrices. As an extension to Bayesian confidence sets (HPD regions) the authors introduce the concept of HiFi (high fiduciary) regions. The Hifi region is a union of HPD regions and is a tool for describing the dependence of the posterior distribution on the prior covariance. The authors assume that the prior covariance matrix varies in an interval of matrices. Copyright 1991 by The Econometric Society.

A celebrated result of Black (1948a) demonstrates the existence of a simple-majority winner when preferences are single-peaked. The social choice follows the preferences of the median voter: the median voter's most-preferred outcome beats any alternative. However, this conclusion does not extend to elections in which candidates differ in more than one dimension. This paper provides a multi-dimensional analog of the median voter result. We provide conditions under which the mean voter's most preferred outcome is unbeatable according to a 64%-majority rule. The conditions supporting this result represent a significant generalization of Caplin and Nalebuff (1988). The proof of our mean voter result uses a mathematical aggregation theorem due to Prekopa (1971, 1973) and Borell (1975). This theorem has broad applications in economics. An application to the distribution of income is described at the end of this paper; results on imperfect competition are presented in the companion paper, Caplin and Nalebuff (1991).

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Evolutionary games are introduced as models for repeated anonymous strategic interaction.The basic idea is that actions (or behaviors) which are more "fit," given the current distribution of behaviors, tend over time to displace less fit behaviors.Simple numerical examples motivate the key concepts of fitness function and compatible dynamics, and illustrate the relation to previous biological models.Cone fields are introduced to characterize the continuous-time dynamical processes compatible with a given fitness function.The analysis focuses on dynamic steady state equilibria and their relation to the static equilibria known as NE (Nash equilibrium) and ESS (evolutionary stable state).For large classes of dynamics it is shown that all stable dynamic steady states are NE and that all NE are dynamic steady states.The biologists' ESS condition is less closely related to the dynamic equilibria.The paper concludes with a brief survey of economic applications.

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.