Ex ante efficiency implies incentive compatibility

We show that when agents become informationally negligible in a large economy with asymmetric information, every ex ante efficient allocation must be incentive compatible. This means that any ex ante core or Walrasian allocation is incentive compatible. The corresponding result is false for fixed finite-agent economies with asymmetric information. An example is also constructed to show that the ex post version of the result does not hold. Furthermore, we show that the result is sharp in the sense that it will fail to hold if one relaxes any of the main assumptions, namely, strong conditional independence on the information structure, strict concavity on the utility functions, type independence on the utility functions and endowments.      

Is there a “true” diversity?

Jost [Jost, L., 2006. Entropy and diversity. Oikos, 113: 363-374.] recently discussed Hill's [Hill, M., 1973. Diversity and evenness: a unifying notation and its consequences. Ecology, 54: 427-431.] effective number of species and concluded by naming it the “true” diversity. In this note we comment on parts of Jost's work and argue that the true diversity is not what the name suggests.     

Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case

Summary. Suppose a large economy with individual risk is modeled by a continuum of pairwise exchangeable random variables (i.i.d., in particular). Then the relevant stochastic process is jointly measurable only in degenerate cases. Yet in Monte Carlo simulation, the average of a large finite draw of the random variables converges almost surely. Several necessary and sufficient conditions for such “Monte Carlo convergence” are given. Also, conditioned on the associated Monte Carlo -algebra, which represents macroeconomic risk, individual agents' random shocks are independent. Furthermore, a converse to one version of the classical law of large numbers is proved. Received: October 29, 2001; revised version: April 24, 2002 RID="*" ID="*" Part of this work was done when Yeneng Sun was visiting SITE at Stanford University in July 2001. An early version of some results was included in a presentation to Tom Sargent's macro workshop at Stanford. We are grateful to him and Felix Kübler in particular for their comments. And also to Marcos Lisboa for several discussions with Peter Hammond, during which the basic idea of the paper began to take shape. Correspondence to: P.J. Hammond     

Functional laws of the iterated logarithm for small increments of empirical processes

Let F , denote the uniform empirical distribution based on the first n ≥ 1 observations from an i.i.d. sequence of uniform (0, 1) random variables. We describe the almost sure limiting behavior of the sets of increment functions {F_n(t + h_n.) - F_n(t): 0 ≤ t ≤ 1 - h_n}, when {h_n: n ≥ 1) is a nonincreasing sequence of constants such that nh_n /log n ← 0.     

A primal-dual approach to nonparametric productivity analysis: The case of U.S. agriculture

Nonparametric methods for measuring productivity indexes based on bounds for the underlying production technology are presented. Following Banker and Maindiratta, the lower bound is obtained from a primal approach while the upper bound corresponds to a dual approach to nonparametric production analysis. These nonparametric bounds are then used to estimate input-based and output-based distance functions. These radial measures provide the basis for measuring productivity indexes. Application to times series data on U.S. agriculture indicates a large gap between the primal lower bound and the dual upper bound. This generates striking differences between the primal and dual nonparametric productivity indexes.Respectively, professor and associate professor of Agricultural Economics, University of Wisconsin-Madison. Seniority of authorship is equally shared. We would like to thank Rolf Färe and an anonymous reviewer for useful comments on an earlier draft of the paper. This research was supported in part by a Hatch grant from the College of Agriculture and Life Sciences, University of Wisconsin-Madison.     

Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable

In this paper we will consider hypothesis-tests for the (fuzzy-valued) mean value of a fuzzy random variable in a population. For this purpose, we will make use of a generalized metric for fuzzy numbers, and we will develop an approach for normal fuzzy random variables, and two different approaches for the case of fuzzy random variables taking on a finite number of different values. A real-life example illustrates the use of the last two approaches. Finally, a comparison between the introduced techniques is developed by means of simulation studies leading to close inferential conclusions.Acknowledgements.The research in this paper has been partially supported by MCYT Grants BFM2002-01057 and BFM2001-3494. Their financial support is gratefully acknowledged. The authors are sincerely grateful to their colleague Gil González-Rodríguez for all his comments and suggestions in connection with this paper; his scientific support has been very valuable. The authors want also thank the referees of the first version of the paper because of their useful hints to improve it.     

How numbers of the future are shaping today: The role of forecasts and calculations in public sector strategic thinking

This article examines the role of numbers in forming a city strategy in the case of Gothenburg, Sweden. The article illustrates how numbers make people act and react and shape the strategy process. The study is situated between the theoretical fields of accounting and strategy processes in cities. By relating them to the concept of ‘governmentality’, numbers are seen as helping render the city governable. Because strategizing is seen as concerning the future, the actors involved in drafting the strategy feel free to challenge historically institutionalized practices. The effect is paradoxical: the future‐looking strategy process becomes a forum for solving current problems.     

＂Differences＂are the Biggest Obstacle

China has the greatest numbers of both teachers and students worldwide ,who teach and learn English. Therefore ,to analyze the obstacles of learning English for Chinese is necessary. This article gives the idea of differences between Chinese and English mainly in languages and cultures fields. Through these we can see clearly that ＂differences＂ are the biggest obstacle in language learning.     

Stochastic Index Numbers: A Review

The stochastic approach is a new way of viewing index numbers in which uncertainty and statistical ideas play a central role. Rather than just providing a single number for the rate of inflation, the stochastic approach provides the whole probability distribution of inflation. This paper reviews the key elements of the approach and then discusses its early history, including some previously overlooked links with Fisher's work contained in his book The Making of Index Numbers. We then consider some more recent developments, including Diewert's well-known critique of the stochastic approach, and provide responses to his criticisms. We also provide a review of Theil's work on the stochastic approach, and present and extend Diewert's work on this topic within the context of the Country Product Dummy method which measures price levels internationally. The paper also contains some recent material on the value of information from the perspective of the stochastic approach, as well as illustrative applications.     

中西方文化中数字意义的简要对比

本文旨在探讨引起中西方文化中数字意义差异的原因,并通过各种生动的实例给予详细的解释。综合历史、文化和宗教对数字的影响,作者总结出了一些共同的规则,希冀使跨文化交际得以顺利进行,并最大程度的减少跨文化交际所带来的文化冲突。