Was George a Dreamer or a Realist?

Abstract . The republication of Steven Cord's Henry George: Dreamer or Realist? makes available once more a work which dealt with insight and depth of analysis with the misconceptions, factual inaccuracies and offhand dismissals of the American economist and social philosopher's theories. Although he alienated many in the academic community, George attracted many leading scholars in it to significant research on basic problems of our times.     

Developing a Continuous Space Representation of a Simulated Population

Abstract

Spatial microsimulation models typically match census of population data with survey data in order to simulate synthetic populations of individuals and households within small-scale geographic areas. For most spatial microsimulation applications this level of spatial precision is satisfactory. For others, more precise information on the location of simulated units may be required. To this end this paper develops a continuous space representation of a simulated population. It presents a statistical matching approach for assigning simulated households from a spatial microsimulation model to unique spatially-referenced residential locations. The allocation is based on a random assignment after splitting the simulated households into two groups: those predicted to reside in apartments and those predicted to reside in houses. The resulting ‘geohouseholds’ have a range of potential applications in economic and spatial analysis.

Création d'une représentation spatiale continue d'une population stimulée

Résumé Les modèles de microsimulation spatiale assortissent généralement les données de recensement de la population à des données de sondages, afin de simuler des populations synthétiques de particuliers et de foyers au sein de régions géographiques à échelle restreinte. Dans la plupart des applications de microsimulation spatiale, ce niveau de précision spatiale est satisfaisant. Dans d'autres, des informations plus précises sur l'emplacement d'unités simulées pourront s'avérer nécessaires. A cette fin, la présente communication crée une représentation spatiale continue d'une population simulée. Elle présente une méthode de correspondance statistique permettant d'affecter des foyers simulés, issus d'un modèle de microsimulation spatiale à des lieux résidentiels unique à référence spatiale. Cette allocation est basée sur une affectation aléatoire après la subdivision des foyers simulés en deux groupes : ceux dont on prévoit qu'ils résideront en appartement, et ceux dont on prévoit qu'ils résideront dans un maison. Les « géofoyers » résultants présentent toute une série d'applications potentielles pour les analyses économiques et spatiales.

Desarrollo de una representación espacial continua de una población simulada

Extracto Típicamente, los modelos de microsimulación espacial emparejan el censo de datos de la población con datos de encuestas, con objeto de simular poblaciones sintéticas de individuos y hogares dentro de áreas geográficas a pequeña escala. Para la mayoría de las aplicaciones de microsimulación espacial este nivel de precisión espacial es satisfactorio. Para otras, podría requerirse información más precisa sobre la ubicación de unidades simuladas. Con este objetivo, este trabajo desarrolla la representación espacial continua de una población simulada. Presenta un planteamiento de emparejamiento estadístico para asignar hogares simulados procedentes de un modelo de microsimulación espacial a ubicaciones residenciales únicas referenciadas espacialmente. La colocación se basa en una asignación al azar después de dividir los hogares simulados en dos grupos: los que se predice que residirán en apartamentos y los que se predice que residirán en casas. Los ‘geohogares’ resultantes ofrecen una gama de aplicaciones en potencia en el análisis económico y espacial.

     

On the existence of a probability measure compatible with a total preorder on a Boolean algebra

If an economic agent's beliefs about the relative likelihood of events are characterized by a total preorder ? on the algebra $\text{A}$ of events, the problem arises to know under which conditions, ? is representable by a probability measure. Here we show that there exists a probability measure compatible with a total preorder on a Boolean algebra, if and only if, the Boolean algebra is well bounded, weakly Archimedean, and perfectly separable, this last condition substituting for Villegas' monotone condition used in Chateauneuf and Jaffray (1984); if σ-additivity is required. Villegas' monotone condition, must merely be added.     

Consistency of a nonparametric estimation of a density functional

LetX be a random variable with distribution functionF and density functionf. Let ? and ψ be known measurable functions defined on the real lineR and the closed interval [0, 1], respectively. This paper proposes a smooth nonparametric estimate of the density functional \(\theta = \int\limits_R \phi (x) \psi \left[ {F (x)} \right]f^2 (x) dx\) based on a random sampleX ₁, ...,X _n fromF using a kernel functionk. The proposed estimate is given by \(\hat \theta = (n^2 a_n )^{ - 1} \mathop \sum \limits_{i = 1}^n \mathop \sum \limits_{j = 1}^n \phi (X_i ) \psi \left[ {\hat F (X_i )} \right]k\left[ {(X_i - X_j )/a_n } \right]\) , where \(\hat F(x) = n^{ - 1} \mathop \sum \limits_{i = 1}^n K\left[ {(x - X_i )/a_n } \right]\) with \(K (w) = \int\limits_{ - \infty }^w {k (u) } du\) . The estimate \(\hat \theta \) is shown to be consistent both in the weak and strong sense and is used to estimate the asymptotic relative efficiency of various nonparametric tests, with particular reference to those using the Chernoff-Savage statistic.     

Existence of a convex extension of a preference relation

In this paper we say that a preference (i.e. irreflexive) relationP isregular (or aweak order) if both it and its non-comparability relation are transitive; we also say that a preference relationP ^* is aconvex extension of another preference relationP ifP?P ^* holds andP ^* is regular and convex-valued. We prove that a convex extension ofP exists if and only if every non-empty and finite set of alternativesA is not included in the convex hull of ∪ _x∈A P(x).     

When is a Compositional Effect not a Compositional Effect?

The question of compositional effects (that is, the effect of collective properties of a pupil body on the individual members), or Aggregated Group-Level Effects (AGLEs) as the author prefers to call them, has been the subject of considerable controversy. Some authors, e.g. Rutter et al. [Fifteen thousand hours: Secondary Schools and Their Effects on Children. London: Open Books.], Willms [Oxford Review of Education 11(1): 33–41; (1986). American Sociological Review, 51, 224–241.], Bondi [British Educational Research Journal, 17(3), 203-218.], have claimed to find such effects, while on the other hand Mortimore et al. [School Matters: the Junior Years. Wells: Open Books.] and Thomas and Mortimore [Oxford Review of Education 16(2): 137–158.] did not. Others, for example Hauser [1970], have implied that many apparent AGLEs may be spurious, while Gray et al. [Review of Research in Education, 8, 158–193.] have suggested that at least in certain circumstances such apparent effects may arise as a result of inadequate allowance for pre-existing differences. A possible statistical mechanism for this is outlined in the work of Burstein [In R. Dreeben, & J. A. Thomas (Eds.), The Analysis of Educational Productivity. Volume 1: Issues in Microanalysis, Cambridge, MASS: Ballinger, pp. 119–190] on the effect of aggregating the data when a variable is omitted from the model used. This paper suggests another way in which spurious AGLEs can arise. It shows mathematically that even if there are no omitted variables, measurement error in an explanatory variable could give rise to apparent, but spurious, AGLEs, when analysed using a multilevel modelling procedure. Using simulation methods, it investigates what the practical effects of this are likely to be, and shows that statistically significant spurious effects occur systematically under fairly standard conditions.     

Defining and measuring the development of a country over time: a proposal of a new index

This paper introduces the concept of harmonic growth as an extended acceptation of the notion of development, and discusses its measurement via the Harmonic Growth Index (HGI). The growth is seen as harmonic when the behaviour of a benchmark time series, which here is a measure of wealth, such as per capita GDP, is followed by a similar pattern in socio-economic series. Unlike most widely used indicators in the literature, which take into account the measurement of development over a single time, HGI measures the degree to which a social indicator’s time series pattern matches with the GDP’s. The index is a function, ranging in [0, 1], of the coefficients of the uniform B-splines fitted to each time series, according to the functional data framework. A case study on Mediterranean welfare countries (Greece, Italy, Portugal, and Spain), in the period 1996–2007, shows critical differences in the selected indicators which can be ascribed to their dissimilar specific development models. HGI can be also considered as a general index to measure the similarity between time patterns, or as an alternative to correlation for (non-necessarily linear) time series.     

Graphical Analysis of Capability of a Process Producing a Product Family

Statistical techniques are effective and powerful means of quantifying the variability of processes, analyzing this variability with reference to product requirements, and eliminating this variability in product manufacturing. Many process capability indices have been effectively and widely used to determine whether the quality of a process meets preset targets. However, conventional process capability indices cannot be applied to assess the entire process capability of a product family with nominal-the-best specifications. This work presents a novel process capability index (C_pp^T), which takes into account all family members. The index C_pp is a simple transformation from index C_pm, and C_pp^T provides additional, individual information concerning the accuracy and precision of a process. Vännman’s (δ, γ)-plot [Vännman and Deleryd, Quality and Reliability Engineering International 15(3): 213–217 (1999)] is revised to compare the process capabilities of family members under both 100% inspection and sampling plans. Examples are provided to demonstrate the method’s practical application.     

Technological inefficiency indexes: a binary taxonomy and a generic theorem

Over the years following Debreu’s (1951) seminal formulation of a “coefficient of resource utilization”, a large number of indexes of technological inefficiency have been specified and a spate of papers has examined the properties satisfied by these indexes. This paper approaches the subject more synthetically, presenting generic results on classes of indexes and their properties. In particular, we consider a broad class of indexes containing almost all known indexes and a partition of this class into two subsets, slacks-based indexes and path-based indexes. Slacks-based indexes are expressed in terms of additive or multiplicative slacks for all inputs and outputs, and particular indexes are generated by specifying the form of aggregation over the coordinate-wise slacks. Path-based indexes are expressed in terms of a common contraction/expansion factor, and particular indexes are generated by specifying the form of the path to the frontier of the technology. Owing to an impossibility result in one of our earlier papers, we know that the set of all inefficiency indexes can be partitioned into three subsets: those that satisfy continuity (in quantities and technologies) and violate indication (equal to some specified value if and only if the quantity vector is efficient), those that satisfy indication and violate continuity, and those that satisfy neither. We prove two generic theorems establishing the equivalence of these two partitions: all slacks-based indexes satisfy indication and hence violate continuity, and all path-based indexes satisfy continuity and hence violate indication. We also discuss the few indexes that do not belong to either of these two sets. Our hope is that these results will help guide decisions about specification of the form of efficiency indexes used in empirical analysis.     

Options as a Marketing Tool: Pricing a Promotional Scheme for a Product with a Secondary Market

Adding options to durable products allows new opportunities for manufacturers and retailers in markets with a secondary market to create better segmentation schemes, provide creative means to differentiate their products and services, and increase the value they offer consumers. This raises the need for sellers to properly price such options. This work presents a few examples of incentive programs for the car industry, develops models and calculates their cost to the seller, demonstrating the applicability of the proposed methodology. Our numerical results indicate that such options are surprisingly inexpensive for car manufacturers and dealers. Copyright © 2015 John Wiley & Sons, Ltd.     

Calculating Cumulants of a Taylor Expansion of a Multivariate Function

A method, which we believe is simpler and more transparent than the one due to McCullagh (1984) , is described for obtaining the cumulants of a scalar multivariate stochastic Taylor expansion. Its generalisation is also suggested. An important feature, previously not reported, is that the expansion of every cumulant of order ≥ 2 is made up of separate subseries.
In order to handle certain frequently occurring sums over permutations of members of compound index sets, we introduce a new notation  [ m ]_*,  where   m   is a positive integer.     

Unbiased estimates for a lognormal regression problem and a nonparametric alternative

Given a normal sample with means \({{\bf x}_{1}^{\prime} {\bf \varphi}, \ldots, {\bf x}_{n}^{\prime} {\bf \varphi}}\) and variance v, minimum variance unbiased estimates are given for the moments of L, where log L is normal with mean \({{\bf x}^{\prime} {\bf \varphi}}\) and variance v. These estimates converge to wrong values if the normality assumption is false. In the latter case estimates based on any M-estimate of \({{\bf \varphi}}\) are available of bias \({O\left(n^{-1}\right)}\) and \({O\left(n^{-2}\right)}\). More generally, these are given for any smooth function of \({\left({\bf \varphi}, F\right)}\), where F is the unknown distribution of the residuals. The regression functions need not be linear.     

Revelations of a gambler

Knowing that a decision maker maximizes expected utility with respect to some (unknown) utility U and some (unknown) probability P, what can one tell about P by observing his decisions? We discuss this revealed preference question primarily in the simple case of a two-element (H and T) state space, and show that the possible revelations of P_T/P_H are precisely those of the form P_T/P_Hε∪^K_k=1 (γ_k,δ_k), for some algebraic numbers γ_k,δ_k.     

On a two-step estimation of a multivariate logit model

In this article the author studies the properties of the two-step estimation method proposed by Domencich and McFadden (Urban Travel Demand, North-Holland, 1975) for a multivariate logit model and shows that it is consistent but asymptotically less efficient than the maximum likelihood estimator. Its computation, however, can be considerably simpler than that of the maximum likelihood estimator, especially in models involving several dependent variables.     

Systemic analysis of a manufacturing process based on a small scale bakery

The main aim of the article is to present two new innovative concepts of reliability of a functioning manufacturing system in the process of making bread in small-scale bakeries. Reliability is understood as one of the representations of an operator acting on specific streams in time t_o to t. One of these represents the global reliability of a system as a function of parallel action of all the streams of the system in time t_o to t and is denoted as P_g^(t). The second representation of reliability is a scalar value, P_ss It shows a new function of global reliability of a manufacturing process as a product of system stream reliability. In order to plot the flow of the manufacturing process’s global reliability function, we need to perform detailed calculations, computations, and analysis of the differences of individual values in real time, as well as plan an algorithm of the flow of system streams. This needs a lot of effort, translating however, to a detailed picture of the process. In the analysed example, measurements and research revealed an important increase of the value of reliability in a transition from a traditional to a robotised bakery. The article also presents a new concept of the reliability of a technological process, based on the analysis of relations of elements of the following streams: energy, matter, information, time, and finances. It shows the method of specifying streams and the method for defining the reliability of important and supportive relations. Important relations between stream elements are defined as having the reliability value of one in time. Supportive relations bear the reliability within a continuum between zero and one. Important relations are designated based on research, experience, and knowledge. Stream systemic reliability P_ss is a scalar value, i.e. a number from the continuum between zero and one. The P_ss value characterises failure-free operation of the whole system. Its average value in the normative time t_n expresses the efficiency of the manufacturing system. The value P_ss is a quotient of the number of important relation and the sum of important and supportive relations. The formula for P_ss shows the method of optimising the process through the increasing of the number of important relations between the input stream components. The concept has been applied to study the efficiency of operation of a small-scale bakery. Systemic analysis of a bakery allows for important increase in the reliability of baking bread if robotisation has been implemented. The concept of systemic-stream reliability P_ss may be applied to analyse the efficiency of any technological process and optimisation of any manufacturing process.

     

R&D in a strategic delegation game revisited: a note

In this note we reconsider the paper of Zhang and Zhang (1997), published in Managerial and Decision Economics, who analyze a strategic delegation model with R&D spillovers in an imperfectly competitive market. We were motivated to study their setup by a puzzling result given in their paper: delegating the production and R&D decisions to managers is never beneficial for the owners of the firm. When we tried to understand the driving forces of this result, we found however that the findings of Zhang and Zhang (1997) are incorrect. We explain why their derivations are wrong and demonstrate via counterexamples that the main propositions in their paper do not hold. In addition, we show how the correct solution of this R&D model with spillovers can be obtained. Copyright © 2006 John Wiley & Sons, Ltd.     

Derivation of a joint occupancy distribution via a bivariate inclusion and exclusion formula

Consider a supply of balls randomly distributed into n distinguishable urns and assume that the number of balls distributed into any specific urn is a random variable with probability function . The joint probability function and binomial moments of the number K_i of urns occupied by i balls each and the number K_j of urns occupied by j balls each, i≠j, given that a total of S_n=m balls are distributed into the n urns, are derived in terms of convolutions of q_x, x=0,1, . . . and their finite differences. Also, some illustrating examples are discussed.     

Internal competition in a nonprofit museum context: development of a scale

• External competition and marketing have been extensively researched in the for-profit environment and to a lesser extent in the nonprofit environment. However, the concept of competition within a nonprofit organization is indicative of another type of competition, that of ‘internal competition’. Internal competition, operating in the nonprofit's endemic environment of scarce resources, takes place between departments, between individuals, and even within individuals in terms of time and energy spent on differing objectives. Internal competition manifests itself as internal conflicts over not only objectives but also the means for achieving the objectives. This research examines the construct of ‘internal competition’ in the museum portion of the nonprofit sector where marketing is often seen as a ‘necessary but evil’ tool essential for survival. Museum retailing, which has taken on an increasingly vital role in the financial support of museums, offers an opportunity to analyze the nature of internal competition and for developing a scale for measuring internal competition.

Copyright © 2007 John Wiley & Sons, Ltd.     

Estimating a restricted normal mean

Let X ₁, X ₂, ..., X _n be a random sample from a normal distribution with unknown mean μ and known variance σ ². In many practical situations, μ is known a priori to be restricted to a bounded interval, say [−m, m] for some m > 0. The sample mean , then, becomes an inadmissible estimator for μ. It is also not minimax with respect to the squared error loss function. Minimax and other estimators for this problem have been studied by Casella and Strawderman (Ann Stat 9:870–878, 1981), Bickel (Ann Stat 9:1301–1309, 1981) and Gatsonis et al. (Stat Prob Lett 6:21–30, 1987) etc. In this paper, we obtain some new estimators for μ. The case when the variance σ ² is unknown is also studied and various estimators for μ are proposed. Risk performance of all estimators is numerically compared for both the cases when σ ² may be known and unknown.