Decomposing random mechanisms

Random mechanisms have been used in real-life situations for reasons such as fairness. Voting and matching are two examples of such situations. We investigate whether the desirable properties of a random mechanism survive decomposition of the mechanism as a lottery over deterministic mechanisms that also hold such properties. To this end, we represent properties of mechanisms–such as ordinal strategy-proofness or individual rationality–using linear constraints. Using the theory of totally unimodular matrices from combinatorial integer programming, we show that total unimodularity is a sufficient condition for the decomposability of linear constraints on random mechanisms. As two illustrative examples we show that individual rationality is totally unimodular in general, and that strategy-proofness is totally unimodular in some individual choice models. We also introduce a second, more constructive approach to decomposition problems, and prove that feasibility, strategy-proofness, and unanimity, with and without anonymity, are decomposable in non-dictatorial single-peaked voting domains. Just importantly, we establish that strategy-proofness is not decomposable in some natural problems.     

Nonlinear dynamical systems and inventory management

Surprisingly, deterministic time series can generate highly irregular, random-appearing trajectories. These deterministic time series result from nonlinear dynamical systems of differential or difference equations. The random appearance displayed by these systems is called nonlinear dynamical complexity. Properties of nonlinear complex systems include aperiodic random appearance, sensitive dependence on initial conditions and model parameters, and nonstationarity. Experiments involving the operation of simulated business environments and theoretical nonlinear dynamical models for inventory are reviewed to explore motivating factors that can give rise to demand with nonlinear complexities. The experimental and theoretical evidence reviewed indicates that nonlinear complexities in demand have significant implications for inventory management. Thus, researchers and practitioners in inventory management need to consider these properties when choosing inventory management methods. Characteristics of nonlinear dynamical systems and their implications for inventory management are presented in this paper. The use of the Brock, Dechert, and Scheinkman (1987) (BDS) test for nonlinear dependence is demonstrated on actual demand data.     

Much Ado About Nothing: the Mixed Models Controversy Revisited

We consider a well-known controversy that stems from the use of two mixed models for the analysis of balanced experimental data with a fixed and a random factor. It essentially originates in the different statistics developed from such models for testing that the variance parameter associated to the random factor is null. The corresponding hypotheses are interpreted as that of null random factor main effects in the presence of interaction. The controversy is further complicated by different opinions regarding the appropriateness of such hypothesis. Assuming that this is a sensible option, we show that the standard test statistics obtained under both models are really directed at different hypotheses and conclude that the problem lies in the definition of the main effects and interactions. We use expected values as in the fixed effects case to resolve the controversy showing that under the most commonly used model, the test usually associated to the inexistence of the random factor main effects addresses a different hypothesis. We discuss the choice of models, and some further problems that occur in the presence of unbalanced data.     

Asset price dynamics with heterogeneous beliefs and local network interactions

In this paper we investigate the effects of network topologies on asset price dynamics. We introduce network communications into a simple asset pricing model with heterogeneous beliefs. The agents may switch between several belief types according to their performance. The performance information is available to the agents only locally through their own experience and the experience of other agents directly connected to them. We model the communications with four commonly considered network topologies: a fully connected network, a regular lattice, a small world, and a random graph. The results show that the network topologies influence asset price dynamics in terms of the regions of stability, amplitudes of fluctuations and statistical properties.     

Investments in education and welfare in a two-sector,random matching economy

We consider a random matching model where heterogeneous agents choose optimally to invest time and real resources in education. Generically, there is a steady state equilibrium where some agents, but not all of them, invest. Regular steady state equilibria are constrained inefficient in a strong sense. The Hosios (1990) condition is neither necessary nor sufficient for constrained efficiency. We also provide restrictions on the fundamentals sufficient to guarantee that equilibria are characterized by overeducation (or undereducation), present some results on their comparative statics properties, and discuss the nature of welfare improving policies.     

Random assignments of bundles

We propose a model studying the random assignments of bundles with no free disposal. The key difference between our model and the one where objects are allocated (see Bogomolnaia and Moulin (2001)) is one of feasibility. The implications of this difference are significant. Firstly, the characterization of sd-efficient random assignments is more complex. Secondly, we are able to identify a preference restriction, called essential monotonicity, under which the random serial dictatorship rule (extended to the setting with bundles) is equivalent to the probabilistic serial rule (extended to the setting with bundles). This equivalence implies the existence of a rule on this restricted domain satisfying sd-efficiency, sd-strategy-proofness, and equal treatment of equals. Moreover, this rule only selects random assignments which can be decomposed as convex combinations of deterministic assignments.     

An analysis of the effect of noise in a heterogeneous agent financial market model

Heterogeneous agent models (HAMs) in finance and economics are often characterised by high dimensional nonlinear stochastic differential or difference systems. Because of the complexity of the interaction between the nonlinearities and noise, a commonly used, often called indirect, approach to the study of HAMs combines theoretical analysis of the underlying deterministic skeleton with numerical analysis of the stochastic model. However, it is well known that this indirect approach may not properly characterise the nature of the stochastic model. This paper aims to tackle this issue by developing a direct and analytical approach to the analysis of a stochastic model of speculative price dynamics involving two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the stationary measures of a stochastic dynamical system. Using the stochastic method of averaging and stochastic bifurcation theory, we show that the stochastic model displays behaviour consistent with that of the underlying deterministic model when the time lag in the formation of price trends used by the chartists is far away from zero. However, when this lag approaches zero, such consistency breaks down.     

Panel Data模型设定的新思路--固定效应与随机效应的统一

经典PanelData模型研究中一直存在着固定效应与随机效应的判断与争论问题，这种模型设定形式的不准确常常导致模型参数估计的无效性以及一维（one-way）与二维（two-way）误差成分模型的混淆。在此，本文提出建立一种新的同时囊括随机与固定两种效应的误差成分一般模型，其中一维（one-way）情况的模型仅为二维（two-way）模型的特例模型，单一的随机效应或固定效应模型亦为其特殊情况的一种。在这种一般误差成分模型的基础上，我们力图将有关PanelData模型的讨论纳入到一个更加一般和统一的分析构架中予以研究。     

Random scheduling with deadlines under dichotomous preferences

A group of individuals share a deterministic server which is capable of serving one job per unit of time. Every individual has a job and a cut off time slot (deadline) where service beyond this slot is as worthless as not getting any service at all. Individuals are indifferent between slots which are not beyond their deadlines (compatible slots). A schedule (possibly random) assigns the set of slots to individuals by respecting their deadlines. We only consider the class of problems where for every set of relevant slots (compatible with at least one individual) there are at least as many individuals who have a compatible slot in that set: we ignore the case of underdemand. For this class, we characterize the random scheduling rule which attaches uniform probability to every efficient deterministic schedule (efficient uniform rule) by Pareto efficiency, equal treatment of equals, and probabilistic consistency (Chambers, 2004). We also show that a weaker version of the probabilistic consistency axiom is enough to achieve our result. Finally we show that efficient uniform rule is strategyproof.     

评标专家均衡随机抽取模型

在分析原有评标专家抽取模型不足的基础上,本文提出了评标专家均衡随机抽取模型。这种新的抽取模型不仅可以保证抽取过程的随机性,还能改善一段时间内专家被抽取状况的均衡性。本文介绍了新模型的构建思路和算法步骤,并利用实际数据进行仿真实验,验证了新模型的优势。评标专家均衡随机抽取模型的提出对提高招投标工作的公平性和公正性具有重要的现实意义。     

农地股份合作组织盈余分配机制的利益衡量

当前我国农地股份合作组织的盈余分配机制主要有盈利分红、收益不保底,收益保底、盈利不分红和既收益保底、又盈利分红三种形式。各地股份合作组织对于盈余分配机制的选择,一般都会受到农民收入和农地股份合作组织盈余两个利益因素的影响。本文以庞德的利益衡量理论对这两种利益进行了分析,认为现阶段我国农地股份合作组织采用既收益保底、又盈利分红的盈余分配机制是适当的,并提出了完善的建议。     

Multiproduct price competition with heterogeneous consumers and nonconvex costs

This paper extends the oligopolistic model of price competition to environments with multiple goods, heterogeneous consumers, and arbitrary continuous cost functions. A Nash equilibrium in mixed strategies with an endogenous sharing rule is proven to exist. It is also shown that, in environments with fixed costs and constant marginal costs, all (symmetric and asymmetric) equilibria exhibit price dispersion across stores. Furthermore, the paper identifies scenarios in which prices will necessarily be random. In these markets, stores keep each other guessing because, given the fixed costs, they would incur a loss if their price strategies were anticipated and beaten by competitors. This is interpreted as an important economic feature that is possibly behind random price promotions such as weekly specials.     

On construction of admissible quadratic estimators

A random linear model for spatially located sensors measured intensity of a source of signals in discrete instants of time is considered. A basis of a quadratic subspace useful in quadratic estimation of a function of model parameters is given. Received: December 1999     

Statistical analysis of change in networks

A survey is given of random graphs and random graph processes which can be used to describe and analyze networks that are changing with time. Marko-vian change over time, log-linear models for change, and conditionally uniform models for change are described. It is noted that estimation is usually complex if the random graph involves dependent dyads. Models with deterministic change over time may be a way to avoid the difficulties implied by dependent dyads. Logit regression methods are described that can be used to estimate such models.     

基于双自适应Lasso惩罚的随机效应分位回归模型研究

研究目标：解决随机效应分位回归模型中固定效应和随机效应系数同时估计和选择问题。研究方法：对固定效应和随机效应系数同时实施自适应Lasso惩罚,并为参数估计设计交替迭代算法。研究发现：新方法不仅对随机误差分布具有较强的稳健性,而且在不同稀疏度模型下均有着良好的表现,尤其是在高维情形时。研究创新：本文提出的方法在对模型中重要自变量进行选择的同时能够充分考虑随机效应的影响;交替迭代算法不仅有效解决了需要选择两个惩罚参数的困境,而且收敛速度快。研究价值：为实际工作者对面板数据和纵向数据的分析提供了有效的建模方法。     

On the preservation of deterministic cycles when some agents perceive them to be random fluctuations

Some recent equilibrium models give rise to complex but deterministic fluctuations. We modify the hypothesis of universal perfect foresight by injecting into the economy a nonnegligible fraction of less informed agents who optimize their expected utility with respect to the statistical distribution of prices in the deterministic dynamics. For the standard overlapping generations model with money (the 'Samuelson' case) it is proved that if the fraction of consumers with limited knowledge is sufficiently high, then all equilibrium cycles of period k ≥ 2 disappear. The global properties of the case of 2-cycles are studied in detail. A brief analysis of the 'classical' case is also given.     

The structure of strategy-proof random social choice functions over product domains and lexicographically separable preferences

We characterize the class of dominant-strategy incentive-compatible (or strategy-proof) random social choice functions in the standard multi-dimensional voting model where voter preferences over the various dimensions (or components) are lexicographically separable. We show that these social choice functions (which we call generalized random dictatorships) are induced by probability distributions on voter sequences of length equal to the number of components. They induce a fixed probability distribution on the product set of voter peaks. The marginal probability distribution over every component is a random dictatorship. Our results generalize the classic random dictatorship result in Gibbard (1977) and the decomposability results for strategy-proof deterministic social choice functions for multi-dimensional models with separable preferences obtained in LeBreton and Sen (1999).     

石油产区社会经济系统的非平衡态研究

运用自组织理论,探讨石油产区社会经济系统相变扰动因素及扰动结果,分析石油产区社会经济系统非平衡态及其驱动方向,指出石油产区如何实现社会经济系统可持续发展与生态环境改善协同发展,最终形成高度自组织动态平衡。     

Testing joint hypotheses when one of the alternatives is one-sided

We propose a class of statistics where the direction of one of the alternatives is incorporated. It is obtained by modifying a class of multivariate tests with elliptical confidence regions, not necessarily arising from normal-based distribution theory. The resulting statistics are easy to compute, they do not require the re-estimation of models subject to one-sided inequality restrictions, and their distributions do not require bounds-based inference. We derive explicit distribution and power functions, using them to prove some desirable properties of our class of modified tests. We then illustrate the relevance of the method by applying it to devising an improved test of random walks in autoregressive models with deterministic components. In this example, the usual alternative to a unit root is one-sided in the direction of stable roots, while deterministic components are allowed to go either way, and we show that it is beneficial to take the partially one-sided nature of the alternative into account.     

NONPARAMETRIC AND SEMIPARAMETRIC PANEL DATA MODELS: RECENT DEVELOPMENTS

In this paper, we provide an intensive review of the recent developments for semiparametric and fully nonparametric panel data models that are linearly separable in the innovation and the individual-specific term. We analyze these developments under two alternative model specifications: fixed and random effects panel data models. More precisely, in the random effects setting, we focus our attention in the analysis of some efficiency issues that have to do with the so-called working independence condition. This assumption is introduced when estimating the asymptotic variance–covariance matrix of nonparametric estimators. In the fixed effects setting, to cope with the so-called incidental parameters problem, we consider two different estimation approaches: profiling techniques and differencing methods. Furthermore, we are also interested in the endogeneity problem and how instrumental variables are used in this context. In addition, for practitioners, we also show different ways of avoiding the so-called curse of dimensionality problem in pure nonparametric models. In this way, semiparametric and additive models appear as a solution when the number of explanatory variables is large.