Distributive and Additive Costsharing of an Homogeneous Good

Individual users demand different quantities of a homogeneous good produced under variable returns. We describe the family of costsharing methods that allocate costs in proportion to demands when returns are constant, and commute with the additivity and composition of cost functions. Two simple such methods are average cost pricing and incremental costsharing. All other methods in the family combine elements of the average cost and incremental ones. Serial costsharing stands out prominently in the family, whereas the Shapley–Shubik method, and all values from the associated stand alone cooperative game, are excluded.Journal of Economic LiteratureClassification Numbers: D63, C71.     

Causality: a Statistical View

Statistical aspects of causality are reviewed in simple form and the impact of recent work discussed. Three distinct notions of causality are set out and implications for densities and for linear dependencies explained. The importance of appreciating the possibility of effect modifiers is stressed, be they intermediate variables, background variables or unobserved confounders. In many contexts the issue of unobserved confounders is salient. The difficulties of interpretation when there are joint effects are discussed and possible modifications of analysis explained. The dangers of uncritical conditioning and marginalization over intermediate response variables are set out and some of the problems of generalizing conclusions to populations and individuals explained. In general terms the importance of search for possibly causal variables is stressed but the need for caution is emphasized.     

Fe-O-S样品的Hugoniot线测量

对Fe-O-S混合物的Hugoniot线进行了试验测量，该混合物Hugoniot线的实测结果与用体积可加性原理计算得到的相同组分混合物的Hugoniot线的符合性很好；研究结果亦为今后对外地核各中浓度比Fe-O-S体系候选组分高温高压物态方程及物性的进一步研究奠定了基础。     

Additivity of Deflated Input–Output Tables in National Accounts

Input–output tables deflated by chained prices indices are not additive over product rows. This paper discusses the reasons and suggests a remedy. The new method proposed is based on a distinction, in concept, between ‘real value’, on the one hand, and variation in ‘volume’, on the other. The first corrects for the monetary variation of the unit of account resulting from inflation, while the latter isolates the variation of one product price relative to the other products, caused by the forces of supply and demand on each individual commodity market. An example of the resulting growth analysis is compiled for the Dutch economy between years 1990 and 2000.     

Fourier-analytic measures for heavy-tailed insurance losses

We propose a family of three ‘Fourier-analytic’ measures to extend the conventional concepts of standard deviation, variance, and coefficient of variation to insurance losses with arbitrarily heavy tails. After motivating and computing their mathematical forms, we apply the proposed measures to the case of Lévy-stable loss portfolios. Finally, the new measures are used to study the diversification properties of heavy-tailed losses.     

Monotone continuous multiple priors

Summary. In a multiple priors model á la Gilboa and Schmeidler (1989), we provide necessary and sufficient behavioral conditions ensuring the countable additivity and non-atomicity of all priors.Received: 25 November 2002, Revised: 24 June 2004, JEL Classification Numbers: D81.We thank Roko Aliprantis, Maristella Botticini, Erio Castagnoli, Larry Epstein, Paolo Ghirardato, Itzhak Gilboa, Luigi Montrucchio, David Schmeidler, Marciano Siniscalchi, an Associate Editor, and an anonymous referee for helpful discussions. Fabio Maccheroni and Massimo Marinacci gratefully acknowledge the financial support of MIUR and NOMOS Sistema (Milano).     

Consistent loss prediction for a portfolio and its subportfolios

In the present paper, we consider a portfolio of risks consisting of two subportfolios, and we study the problem of whether or not the predictors based on the subportfolios are consistent with those based on the full portfolio. We study this aggregation problem for both the chain-ladder method and the additive method (or incremental loss ratio method). In the case of the chain-ladder method we extend results of Ajne and Klemmt, using the duality of the chain-ladder method applied to incremental losses; we also give a short proof for this duality, which was first observed by Barnett, Zehnwirth & Dubossarky. In the case of the additive method the aggregation problem has not been studied before and its solution is surprisingly simple.     

Expected utility without continuity: A comment on Delbaen et al. (2011)

This paper presents preference axiomatizations of expected utility for nonsimple lotteries while avoiding continuity constraints. We use results by Fishburn (1975), Wakker (1993), and Kopylov (2010) to generalize results by Delbaen et al. (2011). We explain the logical relations between these contributions for risk versus uncertainty, and for finite versus countable additivity, indicating what are the most general axiomatizations of expected utility existing today.     

Simple axioms for countably additive subjective probability

This paper refines Savage’s theory of subjective probability for the case of countably additive beliefs. First, I replace his continuity axioms P6 and P7 with a simple modification of Arrow’s (1970) Monotone Continuity. Second, I relax Savage’s primitives: in my framework, the class of events need not be a σ-algebra, and acts need not have finite or bounded range. By varying the domains of acts and events, I obtain a unique extension of preference that parallels Caratheodory’s unique extension of probability measures. Aside from subjective expected utility, I characterize exponential time discounting in a setting with continuous time and an arbitrary consumption set.     

Interval Estimation of Treatment Effects In Randomized Trials: When do Confidence Intervals Have Nominal Coverage?

In the classical theory of randomized trials (RTs), the treatment effect is defined as a mean difference of potential outcomes. To achieve nominal coverage probability for confidence intervals (CIs) on treatment effects in RTs, certain assumptions are necessary. Specifically, one must either make assumptions about the joint distribution of potential outcomes or enroll subjects in the trial by random sampling of the target population on which the treatment effect is defined. In practice, no such sampling usually takes place and assumptions about the joint distribution of potential outcomes cannot be verified based on observed data. Furthermore, the most common of these assumptions, such as treatment‐unit additivity (TUA) or independence are biologically implausible in most RTs involving human subjects. Hence, it is not usually possible to construct CIs on treatment effects with nominal coverage probability. However, for any joint distribution of potential outcomes, the standard estimator of the variance of the difference of two independent sample means produces CIs with asymptotic coverage at least at the nominal level. This interpretation of CIs as conservative bounds may not always hold in conventional regression models applied to RT data.