Lattices of capacities,and related topologies1

Capacities are defined as set functions with regularity properties in terms of two general families K and G of ‘inner’ and ‘outer’ sets (K = compact sets, G= open sets in the standard case). The space C of all such capacities is a complete lattice with respect to its natural partial order. The lattice structure of C is studied in combination with the natural topology of C. Also some subspaces are investigated.     

The dominant firm with convex technology

The paper analyses a dominant firm model in which firms have convex production sets. The model is shown to be determinate, and to be expressible by a set of (n+1) equilibrium conditions. A previous attempt to obtain comparative statics results is criticized as being invalid, and a new framework for comparative statics is developed.     

Incomplete markets, ambiguity, and irreversible investment

The problem of irreversible investment with idiosyncratic risk is studied by interpreting market incompleteness as a source of ambiguity over the appropriate no-arbitrage discount factor. The maxmin utility over multiple priors framework is used to model and solve the irreversible investment problem. Multiple priors are modeled using the notion of κ‐ignorance. This set-up is used to analyze finitely lived options. For infinitely lived options the notion of constant κ‐ignorance is introduced. For these sets of density generators the corresponding optimal stopping problem is solved for general (in-)finite horizon optimal stopping problems driven by geometric Brownian motion. It is argued that an increase in the set of priors delays investment, whereas an increase in the degree of market completeness can have a non-monotonic effect on investment.     

Extracting cover sets from free fuzzy sorting data

Assignment of items to multiple categories requires suitable statistical methods. The present paper provides a new approach to solve this task. The concept of fuzzy sets is extended to cover sets (sets of overlapping clusters) in a simple manner introducing a vector of item membership sums. The application of the new concept is exemplified by modifying the fuzzy cluster analysis algorithm of Kaufman and Rousseeuw (Finding groups in data: an introduction to cluster analysis, 1990) to cover set cluster analysis appropriately. Wide equivalence of the numerical problems is demonstrated from Lagrange multipliers and Karush-Kuhn-Tucker conditions. Additionally, some extensions are introduced to the algorithm to improve its behavior for suboptimal large or small numbers of clusters. The adapted algorithm in most cases reproduces single sortings for correct numbers of clusters. Two applications to empirical free fuzzy sorting data sets are provided. Limitations of the algorithm are discussed.     

Insuring against the shortfall risk associated with real options

We would like to insure against the risk that a geometric Brownian motion, correlated with the price process of a certain traded asset, is in a set E at time T. In this paper it is shown that the best action one can take to insure against this risk is to buy a binary option on the traded asset. We give explicit formulas in the case that E is an infinite interval. The setting of all our investigations is the Black-Scholes model. Mathematics Subject Classification (2000): 91B28, 60J65, 62P05, 91B30, 62F03 Journal of Economic Literature Classification: G31     

Cointegration Vector Estimation by Panel DOLS and Long‐run Money Demand*

We study the panel dynamic ordinary least square (DOLS) estimator of a homogeneous cointegration vector for a balanced panel of N individuals observed over T time periods. Allowable heterogeneity across individuals include individual‐specific time trends, individual‐specific fixed effects and time‐specific effects. The estimator is fully parametric, computationally convenient, and more precise than the single equation estimator. For fixed N as T→∞, the estimator converges to a function of Brownian motions and the Wald statistic for testing a set of s linear constraints has a limiting χ²(s) distribution. The estimator also has a Gaussian sequential limit distribution that is obtained first by letting T→∞ and then letting N→∞. In a series of Monte‐Carlo experiments, we find that the asymptotic distribution theory provides a reasonably close approximation to the exact finite sample distribution. We use panel DOLS to estimate coefficients of the long‐run money demand function from a panel of 19 countries with annual observations that span from 1957 to 1996. The estimated income elasticity is 1.08 (asymptotic s.e. = 0.26) and the estimated interest rate semi‐elasticity is ?0.02 (asymptotic s.e. = 0.01).     

Efficient sets with and without the expected utility hypothesis

Consider a feasible set, X, of c.d.f.'s. Assume that the set of decision makers, who must choose from X, includes non-expected utility decision makers who are risk averse in some weaker notions. We show that in this case the efficient set of X expands relative to the expected utility case. We characterize the efficient sets for each notion of risk aversion including the expected utility case. It is also shown that the limited-coverage insurance policies, which are not efficient under the expected utility hypothesis, belong to the efficient set when weakly risk-averse non- expected utility functionals are assumed to exist.     

Review

In this study we extend prior research on the international analysis of accounting conservatism (Joos and Lang, 1994; Ball et al., 2000; Giner and Rees, 2001), by examining the level of accounting conservatism across eight European countries (United Kingdom, Germany, France, Switzerland, the Netherlands, Italy, Spain and Belgium), and assessing the statistical significance of the differences among them. The definitions of conservatism that we use are, on the one hand, the Feltham and Ohlson (1995) definition, which implies a persistent understatement of book value of shareholders' equity (balance sheet conservatism). On the other hand, we use the one proposed by Basu (1997), that is, a timelier recognition of bad news in earnings relative to good news (earnings conservatism). We also address the possible scale problems of the models used to measure balance sheet conservatism. Finally, we check whether our comparative results could be influenced by a different sample composition in each country. Our results show that there are both balance sheet and earnings conservatism practices in all countries under study. In addition, while continental countries show larger balance sheet conservatism, differences in earnings conservative practices between countries are not that pronounced, although they tend to be larger in the UK. We also find that the existence of balance sheet conservative practices is associated with reduced levels of earnings conservatism, which is consistent with the results in Pope and Walker (2003).     

“Trilemmas”: Characterising the Japanese Concept of “amae” with a Three-Way Forced-Ranking Technique

A ‘trilemma’ procedure is introduced for collecting ‘dominance data’ (i.e. rankings of a set of items along a scale of relevance, preference, etc.). Trilemmas are three-way forced choices where the three items comprising each trilemma are selected on the basis of a multidimensional scaling solution (MDS) for the item set, ensuring that each choice is as stark and informative as possible. A questionnaire designed on this principle is easily understood and rapidly administered. The data are convenient to record and show less fluctuation among informants than existing techniques. We demonstrate the procedure with a set of 45 short generalisations about behaviour, designed for assessing child attachment. A three-dimensional ‘map’ of these items was obtained by applying MDS to multiple sets of similarity data. The same structure emerged from English-language and Japanese translations of the items. Thirty trilemmas based on this map were used to rank the items by degree of association with the Japanese concept of amae, characterising the concept in terms of its behavioural correlates.     

Constitutional implementation

We consider the problem of implementing a social choice correspondence H in Nash equilibrium when the constitution of the society is given by an effectivity function E. It is assumed that the effectivity function of , is a sub-correspondence of E. We found necessary and efficient conditions for a game form to implement H (in Nash equilibria), and to satisfy, at the same time, that , the effectivity function of , is a sub-correspondence of (which guarantees that is compatible with E). We also find sufficient conditions for the coincidence of the set of winning coalitions of and , and for . All our results are sharp as is shown by suitable examples. Received: 15 December 2000 / Accepted: 3 September 2001     

Estimation and testing of crossing‐points in fixed design regression

Many phenomena in the life sciences can be analyzed by using a fixed design regression model with a regression function m that exhibits a crossing‐point in the following sense: the regression function runs below or above its mean level, respectively, according as the input variable lies to the left or to the right of that crossing‐point, or vice versa. We propose a non‐parametric estimator and show weak and strong consistency as long as the crossing‐point is unique. It is defined as maximizing point arg max of a certain marked empirical process. For testing the hypothesis H₀ that the regression function m actually is constant (no crossing‐point), a decision rule is designed for the specific alternative H₁ that m possesses a crossing‐point. The pertaining test‐statistic is the ratio max/argmax of the maximum value and the maximizing point of the marked empirical process. Under the hypothesis the ratio converges in distribution to the corresponding ratio of a reflected Brownian bridge, for which we derive the distribution function. The test is consistent on the whole alternative and superior to the corresponding Kolmogorov–Smirnov test, which is based only on the maximal value max. Some practical examples of possible applications are given where a certain study about dental phobia is discussed in more detail.     

Projection justification of generalized minimum aberration for asymmetrical fractional factorial designs

Recently, Xu and Wu (2001) presented generalized minimum aberration criterion for comparing and selecting general fractional factorial designs. This criterion is defined using a set of _u(D) values, called J-characteristics by us. In this paper, we find a set of linear equations that relate the set of design points to that of J-characteristics, which implies that a factorial design is uniquely determined by its J-characteristics once the orthonormal contrasts are designated. Thereto, a projection justification of generalized minimum aberration is established. All of these conclusions generalize the results for two-level symmetrical factorial designs in Tang (2001).Acknowledgements The authors are grateful to the editor, the associate editor and the referees for their valuable comments. This paper is supported by NNSF of P.R.China grant No. 10171051. and RFDP grant No. 1999005512.     

The optimal consumption function in a Brownian model of accumulation Part A: The consumption function as solution of a boundary value problem

We consider a neo-classical model of optimal economic growth with c.r.r.a. utility in which the traditional deterministic trends representing population growth, technological progress, depreciation and impatience are replaced by Brownian motions with drift. When transformed to ‘intensive’ units, this is equivalent to a stochastic model of optimal saving with diminishing returns to capital. For the intensive model, we give sufficient conditions for optimality of a consumption plan (open-loop control) comprising a finite welfare condition, a martingale condition for shadow prices and a transversality condition as t→∞. We then replace these by conditions for optimality of a plan generated by a consumption function (closed-loop control), i.e. a function expressing log-consumption as a time-invariant, deterministic function of log-capital . Making use of the exponential martingale formula we replace the martingale condition by a non-linear, non-autonomous second-order o.d.e. which an optimal consumption function must satisfy; this has the form , where . Economic considerations suggest certain limiting values which and should satisfy as , thus defining a two-point boundary value problem (b.v.p.) — or rather, a family of problems, depending on the values of parameters. We prove two theorems showing that a consumption function which solves the appropriate b.v.p. generates an optimal plan. Proofs that a unique solution of each b.v.p. exists are given in a separate paper (Part B).     

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.     

Beyond spatial representation

The correspondence between theory and observation is often evaluated by a comparison between a hypothesized constraint matrix and the spatial representation of a pxp similarity matrix. This comparison of constraint and proximity matrices assumes the accurate translation of similarities to proximities. If the translation is not exact (i.e., a stress or alienation coefficient greater than zero), the hypothesized structure is evaluated using a false representation of the observed data. The proposed model eliminates the need for spatial representation by making a direct comparison between the hypothesized constraint matrix and the multivariate structure of the bivariate similarities. Goodness of fit indices are used for three model comparisons; (1) single data set, one hypothesized structure; (2) single data set, two hypothesized structures; and (3) two data sets, one hypothesized structure.     

A profit-center game with incomplete information

Profit centers in a firm in multidivisional form agree in the ex ante stage upon a plan about their joint production and profit imputation. The plan is executed in the subsequent two periods of the interim stage: the setup period and the manufacturing period. In the setup period, each center has its private information, but a part of its information is revealed to the other centers through its action. Based on the information endogenously pooled this way, the centers take another round of actions in the manufacturing period. A core plan is defined as a Bayesian incentive-compatible plan of the grand coalition of profit centers, upon which no coalition can improve using its Bayesian incentive-compatible plan. A core plan is called full-information revealing if each center fully reveals its private information in the setup period. Three existence theorems for a full-information revealing core plan are established. The first two theorems impose alternative conditions on returns to scale: (1) the neoclassical convex technology, and (2) increasing returns to scale. In case (2), a stronger condition than Scarf's distributiveness is imposed on the total production set. The third theorem is based on a specific supplier-customer relationship among the divisions. Received: 13 October 1997 / Accepted: 26 July 1999     

Information structures and viable price systems

A dynamic model of capital/financial markets is developed. A surprise is a stopping time that is not foretellable. We show that if agents' preferences exhibit a kind of time complementarity, then between ex-dividend dates a viable price system can make discrete changes only at surprises. Under the same preference condition, when the information in the economy can be modeled by a Brownian motion, a viable price system is an Itô process between ex-dividend dates. The martingle characterization of a viable price system originated by Harrison and Kreps (1979) is extended to our economy. This martingale result is independent of the time complementarity of preferences alluded to above.     

Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model

A simultaneous confidence band provides a variety of inferences on the unknown components of a regression model. There are several recent papers using confidence bands for various inferential purposes; see for example, Sun et al. (1999) , Spurrier (1999) , Al‐Saidy et al. (2003) , Liu et al. (2004) , Bhargava & Spurrier (2004) , Piegorsch et al. (2005) and Liu et al. (2007) . Construction of simultaneous confidence bands for a simple linear regression model has a rich history, going back to the work of Working & Hotelling (1929) . The purpose of this article is to consolidate the disparate modern literature on simultaneous confidence bands in linear regression, and to provide expressions for the construction of exact 1 ?α level simultaneous confidence bands for a simple linear regression model of either one‐sided or two‐sided form. We center attention on the three most recognized shapes: hyperbolic, two‐segment, and three‐segment (which is also referred to as a trapezoidal shape and includes a constant‐width band as a special case). Some of these expressions have already appeared in the statistics literature, and some are newly derived in this article. The derivations typically involve a standard bivariate t random vector and its polar coordinate transformation.     

The Impact of Natural Disasters on Third World Agriculture: An Exploratory Survey of the Need for Some New Dimensions in Development Planning*

Abstract . This is essentially an exploration of the available information on the effects of natural disasters on Third World agriculture. These effects are a powerful partial explanation of the lack of agricultural self-sufficiency in a large number of low income countries; and consequently go some way in explaining the occurrence of hunger and poverty in such countries. The paper argues for the systematic collection of economic data on disasters and its analysis and for the establishment of agricultural planning mechanisms in natural disaster-prone developing countries, to mitigate the adverse effects of such disasters. The mechanisms should be linked to national development planning. The paper also sets out the need for international action on a continuing basis in this field.