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 the smoothness of optimal paths II: some local turnpike results

We study the local turnpike property for two classes of infinite-horizon discrete-time deterministic maximization problems which have common applications, e.g., optimal growth theory. We follow a functional-analytic approach and rely on an implicit function theorem for the space of the sequences which converge to zero. We shall assume the existence of an optimal path which is not necessarily a steady-state. Relying on material developped in Blot and Crettez (Decis Econo Finance 27:1–34, 2004), “On the smoothness of optimal paths” Decis Econ Finance, 21:1–34, 2004), we provide conditions under which a variation in the initial conditions (i.e., capital stock and discount rate) yields an optimal solution which converges toward a reference solution when time becomes infinite. We also provide new results on bounded solutions of difference equations. We gratefully thank the editor, Silvano Holzer, and two anonymous referees for remarks and advices on a previous version of this paper.     

Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies

This paper draws attention for the fact that traditional Data Envelopment Analysis (DEA) models do not provide the closest possible targets (or peers) to inefficient units, and presents a procedure to obtain such targets.It focuses on non-oriented efficiency measures (which assume that production units are able to control, and thus change, inputs and outputs simultaneously) both measured in relation to a Free Disposal Hull (FDH) technology and in relation to a convex technology. The approaches developed for finding close targets are applied to a sample of Portuguese bank branches.     

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.     

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.     

Pricing, learning, and strategic behavior in a single-sale model

Summary. We analyze an infinite horizon model where a seller who owns an indivisible unit of a good for sale has incomplete information about the state of the world that determines not only the demand she faces but also her own valuation for the good. Over time, she randomly meets potential buyers who may have incentives to manipulate her learning process strategically. We show that i) the seller's incentives to post a high price and to experiment are not necessarily monotonic in the information conveyed by a buyer's rejection; and ii) as the discount factors tend to one, there are equilibria where the seller always ends up selling the good at an ex-post individually rational price. Received: January 6, 1999; revised version: July 15, 2000     

The effect of fertility on labour force participation: The Spanish evidence

Abstract. The aim of this paper is to estimate the effect of fertility on the decision of labour force participation of married females in Spain, allowing for the existence of unobserved characteristics that affect both fertility and participation. We use a pooling of five waves of the European Household Panel for Spain (1994–1998). Results indicate that not taking into account the unobserved characteristics that affect both variables imposes on average a strong downward bias on the true effect of fertility on participation. This bias is especially strong for highly educated females. We are grateful to Raquel Carrasco and an anonymous referee for helpful comments. Financial support from Gobierno Vasco (PI-1999-160)), Ministry of Education and Science (BE2000-1394), Instituto de la Mujer and Universidad del País Vasco (UPV 00035.321-13511/2001) is gratefully acknowledged.     

Long memory in volatilities of German stock returns

We show that there is strong evidence of long-range dependence in the volatilities of several German stock returns. This will be done by applying a method using the difference of the classical log-periodogram regression estimator for the memory parameter and of the tapered periodogram based estimator. Both estimators give similar values for the memory parameter for each series and this indicates long memory. To support our findings we apply also a methodology using the sample variance and a wavelet based estimator to the data. Also these two methods show clear evidence of long-range dependence in the volatilities of German stock returns.First version received: December 2001/Final version received: March 2003The computational assistance of Eleni Mitropoulou and Björn Stollenwerck as well as the helpful comments of two unknown referees are gratefully acknowledged. Research supported by Deutsche Forschungsgemeinschaft under SFB 475. Stock returns were obtained from Deutsche Finanzdatenbank (DFDB), Karlsruhe.     

Fit performance of several programs used for non-linear least squares problems

Seven computerprograms for non-linear regression or curve fitting problems are compared. The comparison of the programs, running in different computing centra, is restricted to the fit performance. Six model functions are fitted according to the least squares criterion to data series, arising from practical work. The special least squares minimization programs turned out to be better suited for these problems than general optimizing programs.