An algebraic theory of multi-product decisions

Summary. We exploit the existence of matrix group symmetries on a production possibility set to identify group symmetries on the profit function. The groups are isomorphic, and provide a pre-ordering on firm preferences over prices. Together with additional structure on the technology, symmetries generate comparative statics on price responses. Linear and other invariances place bounds on firm choice vectors. Reflection group asymmetries on the feasible choice set also support welfare rankings over prices. The methods are adapted to study consumer decisions.Received: 12 August 2002, Revised: 30 January 2004, JEL Classification Numbers: D11, D21, C60, L23. Correspondence to: David A. Hennessy     

Estimation of the change point of a distribution based on the number of failed test items

This paper discusses the family of life distributions with failure rate functions which decrease initially until a change point and remain constant thereafter. The paper focuses on the estimation for the change point of the failure rate function. While point estimation of the change point of the failure rate function has been discussed by some authors, one can hardly find any existing work on the interval estimation of the change point. In this paper, a method for constructing approximate confidence intervals for the change point is proposed. The proposed approximate confidence intervals are based on the number of failed test items at or before a fixed inspection time. Received: September 1999     

A non-parametric independence test using permutation entropy

In the present paper we construct a new, simple, consistent and powerful test for independence by using symbolic dynamics and permutation entropy as a measure of serial dependence. We also give a standard asymptotic distribution of an affine transformation of the permutation entropy under the null hypothesis of independence. The test statistic and its standard limit distribution are invariant to any monotonic transformation. The test applies to time series with discrete or continuous distributions. Eventhough the test is based on entropy measures, it avoids smoothed non-parametric estimation. An application to several daily financial time series illustrates our approach.     

The measurement of structural differences between economies: An axiomatic characterization

Summary. In empirical studies concerning comparison of economic structures and/or structural changes of economies, it is quite useful to employ an aggregate index to describe the structural difference (similarity). This paper offers an axiomatic characterization of the measurement of structural difference between economies that leads to some difference (similarity) index which is practically useful in empirical studies. Received: September 3, 1999; revised version: November 9, 1999     

Testing for coefficient constancy in random walk models with particular reference to the initial value problem

This article is concerned with Locally Best Invariant tests for coefficient stability in a univariate random walk coefficient regression model. In particular, we explore the effects that different assumptions about the initial value of the random walk process have on the form and asymptotic distribution of the resulting test statistics. When this initial value is allowed to be random, it is shown that the test statistics are either exactly the same, or possess the same asymptotic distributions, as when the initial value is fixed.     

Measurement and structural invariance of entrepreneurial investment climate: A cross-country scale development

Testing invariance is important in cross-cultural studies because a lack of invariance may bias empirical results and lead to improper theoretical inferences. This study introduces and validates a scale for measuring entrepreneurial investment climate, consisting of four factors: Societal stability, Labor and Regulations, Quality of Infrastructure, and Ease of Finance. The instrument was developed using World Bank Group data from 51,169 firms and 72 institutional profiles to determine investment climate. Confirmatory factor analyses reveal the validity of the scale and its robustness across country types and time. The study’s implications for practice and future research are discussed.     

Characterization of the Average Tree solution and its kernel

In this article, we study cooperative games with limited cooperation possibilities, represented by a tree on the set of agents. Agents in the game can cooperate if they are connected in the tree. We first derive direct-sum decompositions of the space of TU-games on a fixed tree, and two new basis for these spaces of TU-games. We then focus our attention on the Average (rooted)-Tree solution (see Herings et al. (2008)). We provide a basis for its kernel and a new axiomatic characterization by using the classical axiom for inessential games, and two new axioms of invariance called Invariance with respect to irrelevant coalitions and Weighted addition invariance on bi-partitions. We also solve the inverse problem for the Average (rooted)-Tree solution.     

Statistical Inference under Symmetry

We explore the consequences of adjoining a symmetry group to a statistical model. Group actions are first induced on the sample space, and then on the parameter space. It is argued that the right invariant measure induced by the group on the parameter space is a natural non-informative prior for the parameters of the model. The permissible sub-parameters are introduced, i.e., the subparameters upon which group actions can be defined. Equivariant estimators are similarly defined. Orbits of the group are defined on the sample space and on the parameter space; in particular the group action is called transitive when there is only one orbit. Credibility sets and confidence sets are shown (under right invariant prior and assuming transitivity on the parameter space) to be equal when defined by permissible sub-parameters and constructed from equivariant estimators. The effect of different choices of transformation group is illustrated by examples, and properties of the orbits on the sample space and on the parameter space are discussed. It is argued that model reduction should be constrained to one or several orbits of the group. Using this and other natural criteria and concepts, among them concepts related to design of experiments under symmetry, leads to links towards chemometrical prediction methods and towards the foundation of quantum theory.     

打开内部评级法的黑箱:假设、模拟与监管实践

内部评级法的风险权重模型实质上是建立在单一系统性风险因子假设基础上的条件违约概率。内部评级法有两个主要特点:一是单一风险因子假设,假设信用风险的系统风险由单个共同因子控制;二是组合不变性,组合具有良好的分散性以使所有特殊风险充分多样化。这些假设在促成内部评级法成为简单易行、具有一定的可比性资本监管工具的同时,也对监管当局自身形成了挑战:一是如何针对不同银行的组合粒度补提"剩余"的监管资本,二是如何选择与本经济体相称的资产相关系数。在中国,由于政府主导经济,体制相关性较高,后一个问题尤显重要。     

Labor tax reform, unemployment, and search

A key obstacle to reducing payroll taxes in many industrialized and transition countries is the direct revenue loss to the government that it implies. This paper studies a simple and practical labor tax reform of reducing a payroll tax and increasing a progressive wage tax that keeps the marginal tax wedge unchanged. Such a strategy increases employment, reduces the equilibrium unemployment rate, and increases public revenue as long as workers do not have all the bargaining power in wage negotiations. Moreover, welfare rises if workers’ bargaining power is sufficiently large to exceed a critical value determined by the second-best Hosios condition.