The positive maximum entropy distribution

The maximum entropy (ME) principle is applied to samples from a positive population, yielding a positive ME distribution with one truncated exponential component distribution. This approach is easily extended to double-constrained variables such as proportions (e.g., market shares and budget shares).     

The symmetric maximum entropy distribution

The symmetric maximum entropy (ME) distribution is introduced based on symmetrized order statistics. Its properties (including higher-order moments) are compared with those of the non-symmetric ME distribution.     

The evolutionary approach to entropy: Reconciling Georgescu-Roegen's natural philosophy with the maximum entropy framework

The paper explores the relevance of recent developments in the Maximum Entropy hypothesis for reinstating Georgescu-Roegen's natural philosophy, with special emphasis on the concepts of evolution and time. The key point is the naturalization of the notion of ‘subjectivity’ in both the Georgescu-Roegen framework and Jaynes's subjectivistic interpretation of thermodynamics and statistical mechanics. I introduce the concept of ‘observer relativity’ with reference to the evolution of ‘physical inference devices’. Then, the MaxEnt formalism can be understood as a principle underlying natural selection. Further, given natural selection, maximum entropy production (MEP) results from the confluence of maximum power (Lotka) and the maximization of information capacity, driven by energy dispersal. In these processes, hierarchical structures of gradients of energy dissipation reflect alternative positions of system boundaries, and hence different perspectives of observer-relativity. Thus, I can distinguish between observer relative Entropy_OR and observer independent Entropy_OI. This allows to reconstruct conceptually the two notions of time proposed by Georgescu-Roegen, with subjectivistic time seen as time relative to the evolutionary process involving incommensurable qualitative change. I claim that this philosophical view offers a powerful conceptual framework for recent empirical research into the energetics of economic growth.     

A maximum entropy approach to the specification of distributed lags

The maximum entropy (ME) criterion is used to justify three different specifications of distributed lags. For lag distributions in several dimensions, the ME criterion yields a considerable simplification.     

Simulation evidence on the ridge and the shrinkage of the maximum entropy variance

Haque's and Meisner's (1980) analysis of the expectations of the ridge and shrinkage of the maximum entropy variance is extended to include their standard deviations and correlation coefficients.     

An application of maximum entropy estimation: the demand for meat in the United Kingdom

In many econometric studies of demand relationships the design matrix is frequently subject to severe collinearity. In this paper the Generalized Maximum Entropy methodology is introduced and used to estimate a set of demand relationships. The ability of Generalized Maximum Entropy to estimate economic relationships that are typically subject to a high degree of collinearity among the explanatory variables, thus potentially causing traditional methods of estimation to be unreliable, is explained. The results derived by this alternative method of estimation, for a UK meat demand data set, are analysed and examined. The potential for this emerging estimation methodology is discussed.     

Maximum entropy: a stochastic frontier approach for electricity distribution regulation

The literature on incentive-based regulation in the electricity sector indicates that the size of this sector in a country constrains the choice of frontier methods as well as the model specification itself to measure economic efficiency of regulated firms. The aim of this study is to propose a stochastic frontier approach with maximum entropy estimation, which is designed to extract information from limited and noisy data with minimal statements on the data generation process. Stochastic frontier analysis with generalized maximum entropy and data envelopment analysis—the latter one has been widely used by national regulators—are applied to a cross-section data on thirteen European electricity distribution companies. Technical efficiency scores and rankings of the distribution companies generated by both approaches are sensitive to model specification. Nevertheless, the stochastic frontier analysis with generalized maximum entropy results indicate that technical efficiency scores have similar distributional properties and these scores as well as the rankings of the companies are not very sensitive to the prior information. In general, the same electricity distribution companies are found to be in the highest and lowest efficient groups, reflecting weak sensitivity to the prior information considered in the estimation procedure.

     

A generalized theorem of the maximum

Summary This paper generalizes the Theorem of the Maximum (Berge [2]) to allow for discontinuous changes in the domain and the objective function. It also provides a geometrical version of the (generalized) theorem.This research was supported in part by National Science Foundation Grant SES-86-19012. Financial assistance was also provided, for Lawrence Ausubel, by the Lynde and Harry Bradley Foundation, and for Raymond Deneckere, by the Kellogg School of Management's Beatrice/Esmark Research Chair. We thank Alejandro Manelli and Israel Zang for many helpful conversations.     

Inverse of the Berge maximum theorem

Summary We consider an inverse of the Berge maximum theorem. We also give an application of our result to fixed point theory.     

The entropy weight fuzzy comprehension evaluation of enterprise knowledge competitiveness

With the constant development of knowledge-based economy, knowledge has become the core competitiveness of enterprise, which plays a vital role in the development of enterprise and market competition. It will be helpful for enterprise managers to improve their knowledge competitiveness, if they can judge the advantage and disadvantage of knowledge competitiveness reasonably. According to the nature and the characteristic of knowledge competitiveness of enterprise, a system of evaluation index has been designed about the knowledge competitiveness of enterprise. Taking the enterprise A as an example, it is appraised by using fuzzy comprehension evaluation based on entropy weight, and has provided a new idea for the knowledge competitiveness of enterprise.     

A new proof of the maximum principle

Summary. We offer a new proof of the maximum principle, by using the envelope theorem that is frequently used in the standard microeconomic theory. Received: April 11, 2002; revised version: June 26, 2002 Correspondence to: K. Shimomura     

Generalized entropy and the measurement of distributional change

The analogy between information theory and income distribution analysis is exploited to derive a number of measures of distributional change. These include not only counterparts of the regular entropy measures, but also of the entire, rich ‘generalised entropy’ family. The paper analyses the properties of these measures, and in particular their performance in response to ‘independent’ transfers and to cases where an income transfer in the old distribution automatically produces a corresponding transfer in the new distribution. The relationship of such ‘functionally dependent’ transfers to a measure of tax progression is examined.     

基于熵权的TOPSIS法在智能电表评标中的应用

在智能电网设备招投标的整个过程中,最能有效避免风险的两个重要环节就是对投标单位的资格审查和评标。对国家电网公司来讲,评标是招标中至关重要的环节,它将直接关系到对提供智能电表企业的选取结果,而评标方法又是评标工作能否客观、顺利开展的决定性因素。针对传统信息系统项目评标中单纯由主观判断确定指标权重方法的不足,提出了将主观判断与客观情况相结合、定性定量相结合的熵权法来确定指标的权重系数,进而将TOPSIS法与熵权系数综合集成进行合理方案的评价。将该方法应用于智能电表评标过程实践中,取得了较为满意的结果。     

The distribution of regional earnings in the UK

Utilizing a micro sample of 7317 individuals extracted from the General Household Survey 1973, we show that money earnings and real earnings vary considerably across British regions even when other factors such as education and industry mix are held constant. We also find that real earnings do not follow the pattern of money earnings; if anything, quite the reverse. Whereas monetary rewards are the greatest in the South East of England, real rewards are the greatest in the Midlands and the North East of England. Scottish regions, however, appear to fare the worst in both money and real terms.     

Invariance of conditional maximum utility

The consumer benefit in a discrete choice model is often measured by maximum utility. We characterize the conditional (on the chosen alternative) and the unconditional distribution of maximum utility. We show that among a wide class of distributions (independent with convex supports) of error terms, the Type I extreme-value distribution is the unique distribution which ensures that all the conditional distributions of maximum utility coincide. Moreover, we show that for i.i.d. (with convex support) error terms, the invariance of conditional expected maximum utility characterizes the multinomial logit model.     

The diffusion of computers and the distribution of wages

When the costs are decreasing workers adopt technology at the point where the costs equal the increased productivity. Output per worker increases immediately, while productivity benefits increase only gradually if costs continue to fall. As a result, workers in computer-adopting labor market groups experience an immediate fall in wages due to increased supply. On the other hand, adopting workers experience wage increases with some delay. This model explains why increased computer use does not immediately lead to higher wage inequality. More specifically, the results of the model are shown to be consistent with the question why within-group wage inequality among skilled workers as a result of computer technology adoption in the United States increased in the 1970s, while between-group wage inequality and within-group wage inequality among the unskilled did not start to increase until the 1980s. The model also predicts that the more compressed German wage structure leads to a lagged diffusion of computer technology along with smaller changes in wage inequality. Our empirical analysis suggests that this is consistent with the actual developments in Germany since the 1980s. Finally, the theoretical predictions seem to be of the right magnitude to explain the empirical quantities observed in the data.     

The industry life-cycle of the size distribution of firms

This paper analyzes the evolution of the distributions of output and employment across firms in U.S. manufacturing industries from 1963 until 1997. The firm size distribution changes significantly as an industry goes through stages of its life-cycle. The evolutions of the employment and output distributions also differ significantly, but display strong inter-industry regularities, including that the nature of the evolution depends on whether the industry is experiencing growth, shakeout, maturity, or decline. The observed patterns have implications for theories of industry dynamics and evolution.     

The brain drain and the world distribution of income

Skilled emigration (or brain drain) from developing to developed countries is becoming the dominant pattern of international migration today. Such migration is likely to affect the world distribution of income both directly, through the mobility of people, and indirectly, as the prospect of migration affects the rate of return to education in both the sending and receiving economies. This migration pattern will therefore affect human capital accumulation and fertility decisions in both the sending and receiving economies. This paper analyzes these effects in a dynamic two country model of the world economy where agents in both countries make optimal fertility and human capital decisions. The implications of the analysis for the world distribution of income are derived in the light of recent empirical findings of the brain drain literature. The analysis shows that the current trend towards predominantly skilled emigration from poor to rich countries may in the long run increase inequality in the world distribution of income as relatively poor countries grow large in terms of population. In the short run however, it is possible for world inequality to fall due to rises in GDP per capita in large developing economies with sufficiently low skilled emigration rates.