Learning in owner-managed small firms: Mediating artefacts and strategic space

The authors focus on the way in which owner-managers in smaller firms improve their businesses through the creation of ‘strategic space’. The term ‘strategic space’ refers to the process by which owner-managers are able to access resources, motivation and capability to review existing practices. The starting point is the owner-manager's human capital and their capacity to engage in critical reflection about their business. We highlight three concepts central to the creation of strategic space, first, social capital, which refers to the network relationships that provide access to a wide range of resources and information. Second, absorptive capacity, which describes the way in which organizational members identify, acquire and utilize knowledge from external sources. Third, mediating artefacts, which represent existing knowledge but also facilitate the translation and transformation of understanding within and between communities of practice. This process is essential to the renewal of knowledge and knowing within firms. The contribution this paper makes is to bring together these elements – human and social capital, absorptive capacity and mediating artefacts – to offer a conceptual model that illustrates the mechanism by which owner-managers create strategic space. This model provides a deeper understanding of the evolution of knowledge in smaller organizations.     

Existence of equilibria in economies with externalities and non-convexities in an infinite-dimensional commodity space

We prove an equilibrium existence theorem for economies with externalities, general types of non-convexities in the production sector, and infinitely many commodities. The consumption sets, the preferences of the consumers, and the production possibilities are represented by set-valued mappings to take into account the external effects. The firms set their prices according to general pricing rules which are supposed to have bounded losses and may depend upon the actions of the other economic agents. The commodity space is L_∞(M,M,μ), the space of all μ-essentially bounded M-measurable functions on M.As for our existence result, we consider the framework of Bewley (1972). However, there are four major problems in using this technique. To overcome two of these difficulties, we impose strong lower hemi-continuity assumptions upon the economies. The remaining problems are removed when the finite economies are large enough.Our model encompasses previous works on the existence of general equilibria when there are externalities and non-convexities but the commodity space is finite dimensional and those on general equilibria in non-convex economies with infinitely many commodities when no external effect is taken into account.     

A new approach to inter-rater agreement through stochastic orderings: the discrete case

We wish to study inter-rater agreement comparing groups of observers who express their ratings on a discrete or ordinal scale. The starting point is that of defining what we mean by “agreement”. Given d observers, let the scores they assign to a given statistical unit be expressed as a d-vector in the real space. We define a deterministic ordering among these vectors, which expresses the degree of the raters’ agreement. The overall scoring of the raters on the sample space will be a d-dimensional random vector. We then define an associated partial ordering among the random vectors of the ratings, illustrate a number of its properties, and look at order-preserving functions (agreement measures). In this paper we also show how to test the hypothesis of greater agreement against the unrestricted hypothesis, and the hypothesis of equal agreement against the hypothesis that an agreement ordering holds. The test is applied to real data on two medical observers rating clinical guidelines.     

The Aubin private core of differential information economies

Abstract We establish characterizations of Radner equilibrium allocations via private core notions in the framework of differential information economies with a finite number of states of nature and a measure space of agents that may have atoms. The commodity space is an ordered separable Banach space whose positive cone admits an interior point. We introduce the notion of Aubin private core and prove that it provides a characterization of Radner equilibrium allocations. We show that the Aubin private core is equivalent to Edgeworth private equilibria and to privately non-dominated allocations of suitable associated economies. Mathematics Subject Classification (2000): 91B50, 91B44 Journal of Economic Literature Classification: D51, D82, D11     

Urban Distinctions: Class,Culture and Sociability in the City of Porto

This essay employs Pierre Bourdieu's theory of practice and the methodology of Multiple Correspondence Analysis (MCA) to extend the mapping of the dynamic relations between class and culture presented in Bourdieu's Distinction to encompass urban space, drawing on data from a multi‐method research project on the city of Porto, Portugal. We present a detailed analysis of the formation and structure of local social space and show its relevance for the study of the (re)production of urban lifestyles. Differences in the volume and composition of the capital of city residents are identified and shown to underpin the relations between social positions, dispositions and position takings in various realms of cultural consumption. Meaningful configurations of ‘lifestyle modalities’ have clear roots in the city's social space, which in Portugal, as in France, can be interpreted in terms of distinction, pretension and necessity.     

Asymptotic expansion of the minimax value in survey sampling

Summary Suppose that a real numbery _u is associated with each unitu of a populationU and that the functiony:u →y _u onU is known to be an element of the parameter space Θ. The statistician has to select a samples ⊂U ofn units and to employy _u;u ∈s to estimate the arithmetic mean of ally _u,u ∈U. The performance of such a strategy is assessed by its mean square error or, more simply, by the supremum of the mean square error. This supremum cannot be determined exactly for the parameter space of Scott/Smith (1975). We propose, therefore, an asymptotic approximation; this approximation is based on the assumption, that the sample sizen is fixed and that linear estimators have to be used.     

An Introduction to Best Empirical Models when the Parameter Space is Infinite Dimensional*

Ploberger and Phillips (Econometrica, Vol. 71, pp. 627–673, 2003) proved a result that provides a bound on how close a fitted empirical model can get to the true model when the model is represented by a parameterized probability measure on a finite dimensional parameter space. The present note extends that result to cases where the parameter space is infinite dimensional. The results have implications for model choice in infinite dimensional problems and highlight some of the difficulties, including technical difficulties, presented by models of infinite dimension. Some implications for forecasting are considered and some applications are given, including the empirically relevant case of vector autoregression (VAR) models of infinite order.     

Estimating consumer preferences using market data—an application to us automobile demand

This paper explores the possibility of using market data to identify consumer preferences. A utility function composed of ‘homogeneous’ characteristics and goods-specific effects is used as a basic link between the goods space and the characteristics space. The functional form for the hedonic price equation, the data requirements and issues of measurement errors for estimating demand and supply of characteristics are discussed. We illustrate the methodology by considering the US automobile demand using 1969–86 data compiled from Consumer Reports and Ward's Automotive Yearbook.     

Slotting Allowances and Scarce Shelf Space

Slotting allowances are payments made by manufacturers to obtain retail shelf space. They are widespread in the grocery industry and a concern to antitrust authorities. A popular view is that slotting allowances arise because there are more products than retailers can profitably carry given their shelf space. We show that the causality can also go the other way: the scarcity of shelf space may in part be due to the feasibility of slotting allowances. It follows that slotting allowances can be anticompetitive even if they have no effect on retail prices.     

Over Factoranalyse

Summary This paper is an exposition about the model and techniques in factor analysis, a method of studying the covariance matrix of several properties on the basis of a sample co-variance matrix of independent observations on n individuals. The indeterminacy of the basis of the so called factor space and several possibilities of interpretation are discussed. The scale invariant maximum likelihood estimation of the parameters of the assumed normal distribution which also provides a test on the dimension of the factor space is compared with the customary but unjustified attack of the estimation problem by means of component analysis or modifications of it. The prohibitive slowness of convergence of iterative procedures recommended till now can be removed by steepest ascent methods together with Aitken's acceleration method. An estimate of the original observations according to the model assumed, as to be compared with the data, is given.     

The non-existence of smooth demand in general banach spaces

We study the questions of existence and smoothness of demand functions with an infinite number of commodities. The main result obtained, under some hypothesis, is: if a C¹ demand exists in a commodity space B, then B can be given an inner product structure. For example, if B is L_p, 1p∞, and if there exists a C¹ demand function defined on B then p must be 2. Another result is: if a demand function exists, defined for all prices p and income, then the commodity space must be reflexive. For example, if B is L_p and a demand function exists on B, defined for all prices and incomes then 1<p<∞. We also study the cases L_∞ and L₁ with weaker assumptions. We finish the paper proving that the demand function is always defined for a dense set of prices and convenient incomes.     

On a bayesian criterion for choosing predictive sub-models in linear regression

Summary We treat the model selection problem in regression as a decision problem in which the decisions are the alternative predictive distributions based on the different sub-models and the parameter space is the set of possible future values of the regressand. The loss function balances out the conflicting needs for a predictive distribution with mean close to the true value ofy but without too great a variation. The treatment is Bayesian and the criterion derived is a Bayesian generalization of Mallows (1973)C _p , the Bivar criterion (Young 1982) and AIC (Akaike 1974). An application using a graphical sensitivity analysis is presented.     

Equilibria in large economies with a separable Banach commodity space and non-ordered preferences

The purpose of this paper is to provide an existence result of equilibria for economies with a measure space of agents, a non-trivial production sector and an infinite dimensional commodity space. The commodity space is modeled by an ordered separable Banach space whose positive cone has a non-empty interior. The discretization approach proposed in this paper, allows us to extend the existence results in Khan and Yannelis [Equilibrium in markets with a continuum of agents and commodities. In: Khan, M.A., Yannelis, N.C. (Eds.), Equilibrium Theory in Infinite Dimensional Spaces. Springer, Berlin, 1991] and Podczeck [Economic Theory 9 (1997) 585] to economies with a non-trivial production sector and with possibly non-ordered but convex preferences as well as partially ordered (possibly incomplete) but non-convex preferences.     

A characterization of the normal distribution by sufficiency of the least squares estimation

Summary For a linear modelY =ϑ + Z,ϑ ∈V,V ⊂ ℝ ⁿ a linear space, the following theorem is proved under simple conditions on the subspaceV: The projection onV (i.e. the least squares estimate forϑ) is a sufficient statistic iffZ is normally distributed. Further, this result is extended to the case of a multivariate linear model.     

Non‐Economic Factors in Economic Geography and in ‘New Regionalism’: A Sympathetic Critique

In the current debate on local and regional development and after several ‘turns’, dominant critical models have found some security in institutional, cultural and evolutionary approaches. Interest today centres on success and competitiveness and how they are reproduced in a few paradigmatic regions. A distinctive feature of these regions and places is the embeddedness of certain non‐economic factors such as social capital, trust and reciprocity based on familiarity, face‐to‐face exchange, cooperation, embedded routines, habits and norms, local conventions of communication and interaction, all of which contribute to a region’s particular success. Although these approaches may not deny the forces of the capitalist space economy, they do not explicitly acknowledge them or take them on board and so they tend to discuss non‐economic factors and institutions as autonomous forces shaping development. This essay provides a critique of these concepts based on their (1) inadequate theorization, (2) depoliticized view of politics and de‐economized use of economics and (3) reduction of space to territory. The essay concludes that we need a far more penetrating renewal of radical critique of the current space economy of capitalism. Old concepts such as uneven development, the social and spatial division of labour, the geographical transfer of value, accumulation and imperialism must be combined with cultural and institutional issues, with those non‐economic factors mentioned above.     

The multiresolution histogram

We introduce a new method for locally adaptive histogram construction that doesn’t resort to a standard distribution and is easy to implement: the multiresolution histogram. It is based on aL ₂ analysis of the mean integrated squared error with Haar wavelets and hence can be associated with a multiresolution analysis of the sample space.     

Externalities do not necessarily require larger message spaces for realizing pareto-efficient allocations

Classes of economies with consumption externalities and decisive, nonwasteful, and informationally decentralized allocation mechanisms on classes including these classes of economies are constructed. The informational size of the message spaces is shown to be minimal among the message spaces used by any allocation mechanisms with the same properties on the same class of economies. The message spaces are shown to be as large as n(l- 1)n(\ell - 1) -dimensional Euclidean space, where n is the number of economic agents and l\ell is the number of commodities. The presence of consumption externalities does not necessarily require larger message spaces for realizing Pareto-efficiency.     

On Social Statement Spaces

In this fundamental draft we shall introduce the concept of social propositional spaces as a general notion of social science and in particular language, logic and methodology. This should help us bridge an old gap between extension and cognition, or said in more specific words, between space as conceived in mathematics or physics and space as is brought in by social location, by the meaning of predicates, their explanation and logic. ¹ We shall not rely on the idea of factor analysis where some “main components” are fit into the data. Because the notion of euclidean normalization and orthogonality, in this context, is a bit artificial. We first show how combinatorial manifolds of statements can be represented in finite vector spaces over the Galois field F₂. This space which we denote as logic statement space can be spanned by generators of alternating codes. In this way the old concepts of truth tables and interaction attributes can be linked to informatics and in particular code theory and geometry. Extending the logic statement space onto a real vector space by mapping units of the finite rings onto units of the real rings we obtain logistic statement spaces. It turns out that vectors in logistic statement spaces represent cross-tables of logits connected with logistic regression analysis. As a completion of the theory we show that the logit is the first derivative of entropy with respect to probability.