Probability theory in fuzzy sample spaces

This paper tries to develop a neat and comprehensive probability theory for sample spaces where the events are fuzzy subsets of The investigations are focussed on the discussion how to equip those sample spaces with suitable -algebras and metrics. In the end we can point out a unified concept of random elements in the sample spaces under consideration which is linked with compatible metrics to express random errors. The result is supported by presenting a strong law of large numbers, a central limit theorem and a Glivenko-Cantelli theorem for these kinds of random elements, formulated simultaneously w.r.t. the selected metrics. As a by-product the line of reasoning, which is followed within the paper, enables us to generalize as well as to bring together already known results and concepts from literature.Acknowledgement. The author would like to thank the participants of the 23rd Linz Seminar on Fuzzy Set Theory for the intensive discussion of the paper. Especially he is indebted to Professors Diamond and Höhle whose remarks have helped to get deeper insights into the subject. Additionally, the author is grateful to one anonymous referee for careful reading and valuable proposals which have led to an improvement of the first draft.This paper was presented at the 23rd Linz Seminar on Fuzzy Set Theory, Linz, Austria, February 5–9, 2002.     

On estimating the mean of the selected normal population under the LINEX loss function

Following Parsian and Farsipour (1999), we consider the problem of estimating the mean of the selected normal population, from two normal populations with unknown means and common known variance, under the LINEX loss function. Some admissibility results for a subclass of equivariant estimators are derived and a sufficient condition for the inadmissibility of an arbitrary equivariant estimator is provided. As a consequence, several of the estimators proposed by Parsian and Farsipour (1999) are shown to be inadmissible and better estimators are obtained. Received January 2001/Revised May 2002     

Environmental uncertainty, supply chain relationship quality and performance

Environmental uncertainty is a fact of life in today's supply chains. In this paper we develop a model of environmental uncertainty, supply chain (SC) relationship quality and SC performance. We use data from the electronics sector in Ireland to test our model. Our results provide mixed support for the model, with the moderating role of both demand and supply uncertainty being supported, but technological uncertainty not supported. We reflect on these findings and suggest a research agenda based on our results.     

Nash-equilibria in a heterogeneous oligopoly with fuzzy information

We consider a model of an oligopolistic market with heterogeneous firms and products where neither the cost nor the demand functions are common knowledge. Instead, each firm only has some vague ideas about the price strategies adopted by its competitors which is modelled by a fuzzy set. In analogy to the notion of an "equilibrium of actions and beliefs" we define and characterize a generalized Nash-equilibrium and show its existence under general conditions. Furthermore, the impact of the fuzzy information on the equilibrium outcome is analyzed by means of a comparative static analysis within a particular model framework.Received: 28 May 2002, Accepted: 25 December 2002, JEL Classification: D43, D80, L13We wish to thank Bernhard F. Arnold, the editor Murat Sertel , and two anonymous referees for helpful comments. Of course, we are responsible for all remaining errors.     

Measuring volatility with the realized range

Realized variance, being the summation of squared intra-day returns, has quickly gained popularity as a measure of daily volatility. Following Parkinson [1980. The extreme value method for estimating the variance of the rate of return. Journal of Business 53, 61–65] we replace each squared intra-day return by the high–low range for that period to create a novel and more efficient estimator called the realized range. In addition, we suggest a bias-correction procedure to account for the effects of microstructure frictions based upon scaling the realized range with the average level of the daily range. Simulation experiments demonstrate that for plausible levels of non-trading and bid–ask bounce the realized range has a lower mean-squared error than the realized variance, including variants thereof that are robust to microstructure noise. Empirical analysis of the S&P500 index-futures and the S&P100 constituents confirms the potential of the realized range.     

Rationing in open economy and dynamic macroeconomics: A survey

Summary A survey of rationing in micro theories of macroeconomics is presented. The survey starts with a closed economy with money and inventories, which consists of a representative household, a firm and government. After a discussion of the notional demands and supplies and the properties of the Walrasian equilibrium, a discussion of the effective demands and supplies leads to an analysis of the four regimes (Keynesian unemployment, classical unemployment, repressed inflation and underconsumption). A fiscal and monetary contraction decreases sales and employment when there is Keynesian unemployment, but is expansionary (neutral) when there is repressed inflation (classical unemployment). The survey continues with an analysis of the effects of rationing in a small open economy. It considers the one-sector model and a model with a traded and a nontraded sector. The latter model is used to discuss the effects of an oil discovery on the Gulf countries and on Latin American countries. The survey ends with a discussion of rationing in dynamic economies, which leads to an analysis of the effects of expectations about future constraints on current regimes and to a discussion of boot-strap equilibria.The author is Director of the Network for Quantitative Economics. This paper is a brief and eclectic survey of rationing models of closed one-period and two-period economies and of small open economies. It contains no significant new material. The author is grateful to Professor Theo van de Klundert for his constructive comments on an earlier version of this survey.     

Income distribution,economic structure and employment in South Africa

This paper discusses the impact of a redistribution of current income from the White to the Black population on the distribution of sectoral output, and total employment by means of a semi‐closed input‐output model.

The results show that a redistribution of current income towards Black households — which no doubt will have positive social and political repercussions — has a non‐negative effect on GDP and a definite positive effect on the performance of sectors with a high private consumption expenditure component, as well as on total employment.     

De produktiestructuur van Nederland in de periode 1950-1966

Summary In 1961 Arrow, Chenery, Minhas and Solow presented their C.E.S. production function, which was based on the relation between the real wage rate and the average labour productivity. They argued that, if the aggregate production function is continuous, lineair and homogeneous, then, with perfect competition and profit maximalization prevailing, the relation between the real wage rate and the average labour productivity is reflection of the production structure. This relation can, therefore, be used for specifying the production structure.In the present paper, the same line of thought is applied to the Dutch economy. Several hypotheses on the relation between wage rate and average labour productivity are tested. Statistically, it turns out that in the Dutch economy the elasticity of substitution between capital and labour is not a constant: it declines with increasing capital-labour ratio. Two statistically acceptable production equations that have this feature are presented.The efficiency parameter appearing as an integration constant in both production equations shows a decline: with labour productivity constant, the capital-labour ratio is falling over time. This means that the relation between labour productivity and capital-labour ratio shifts over time. Another outcome of this study is that technical progress is capitalaugmenting and that it brings about 50 percent of the growth in the labour productivity.De schrijvers zijn dank verschuldigd aan Prof. Dr. F. J. de Jong voor zijn stimulerende kritiek en aan de heren J. G. Althuis, F. J. van Bolhuis, J. D. Flikweert, H. Jager en B. S. Wilpstra, assistenten bij de afdeling Algemene Economie van de Economische Faculteit der Rijksuniversiteit te Groningen, voor hun bereidwillige medewerking aan dit onderzoek.