NON‐LINEAR DYNAMICS,COMPLEXITY AND RANDOMNESS: ALGORITHMIC FOUNDATIONS

Abstract In this paper I make an attempt to describe, discuss and extend a few aspects of the rich mathematical tapestry that can be woven with rigorous notions of non‐linear dynamics, complexity and randomness, in terms of algorithmic mathematics. It is a tapestry that I try to weave with economic analysis, economic theory and economic modelling in mind. All three notions – that is, non‐linear dynamics, complexity and randomness – have a rich conceptual, modelling or analytic tradition in core areas of economic theory, both at the micro and macro levels. It is the algorithmic foundation I try to provide for them that could be considered the novel contribution in this paper. Once the algorithmic foundations are in place, it is, for example, almost natural to consider the famed difficulties of obtaining closed form solutions for non‐linear, complex or random dynamic models in economics almost a trivial vestige of a pre‐simulation era in mathematical modelling.     

Bridging the Gap between Different Statistical Approaches: An Integrated Framework for Modelling

This paper proposes a template for modelling complex datasets that integrates traditional statistical modelling approaches with more recent advances in statistics and modelling through an exploratory framework. Our approach builds on the well-known and long standing traditional idea of 'good practice in statistics' by establishing a comprehensive framework for modelling that focuses on exploration, prediction, interpretation and reliability assessment, a relatively new idea that allows individual assessment of predictions.
The integrated framework we present comprises two stages. The first involves the use of exploratory methods to help visually understand the data and identify a parsimonious set of explanatory variables. The second encompasses a two step modelling process, where the use of non-parametric methods such as decision trees and generalized additive models are promoted to identify important variables and their modelling relationship with the response before a final predictive model is considered. We focus on fitting the predictive model using parametric, non-parametric and Bayesian approaches.
This paper is motivated by a medical problem where interest focuses on developing a risk stratification system for morbidity of 1,710 cardiac patients given a suite of demographic, clinical and preoperative variables. Although the methods we use are applied specifically to this case study, these methods can be applied across any field, irrespective of the type of response.     

LINKING COGNITIVE, ORGANIZATIONAL AND POLITICAL FACTORS IN EXPLAINING STRATEGIC CHANGE

Much recent research on strategic decision-making and strategic change from many different perspectives challenges the view that decision outcomes are the product of rational choice. Allison's (1971) classification scheme is used to categorize recent strategic decision research within three different perspectives. Discussions of research on cognitive, organizational and political perspectives are followed by an integrative discussion showing how these three perspectives can be combined to deal with the full complexity of strategic decisions and the strategic change process.     

Rational and intuitive decision-making in sourcing teams: Effects on decision outcomes

According to dual process theory, individual decision-making can be based on rational procedures and experience-based intuition, and the decision-making approach can influence decision outcomes. We investigate how the application of rational procedures and experience-based intuition affects the outcomes of supplier selection decisions taken by cross-functional sourcing teams. Specifically, we examine whether the selected supplier׳s cost and quality/delivery/innovativeness performance is higher when more team members use a highly rational and/or a highly experience-based decision-making approach. From data on 54 teams, we find that the use of rational procedures enhances cost performance. Conversely, when sourcing team members use their experience-based intuition, the decision is more likely to result in satisfactory supplier performance along all tested performance dimensions.     

浅谈高等数学知识在现代经济管理中的应用

随着社会的发展,数学在经济管理中的应用日益广泛。本文结合数学与经济管理学之间的联系,从高等数学知识对经济管理的指导作用入手,将经济管理问题转化为数学问题,用数学方法对经济学问题进行分析,从而得到最优决策方案,更好地为经济建设服务。     

Classic rational bubbles and representativeness

The aim of this work is to describe a model of representative bubbles with infinitely lived agents that is accessible to a general audience. In particular, we shall compare this formalization of behavioral bubble dynamics with the classic rational one. The key role of the transversality condition for rational models will be clear, and we will discuss the necessity of its fulfillment when agents are not rational and arbitrageurs are faced with limited arbitrage possibilities. We shall analyze in detail what kind of nonrationality is taken into account and how it triggers bubbly dynamics. It will be plain that representative bubbles can explain the presence of bubbles even when rational models are not able to detect them.     

群体决策复合准则在供应商选择中的应用

供应商多属性的本质是供应商选择问题复杂性的主要原因之一,特别是属性为描述性质的模糊数时,有限理性的个体在决策制定过程中受到很大的局限。实际操作过程中,专家评分法运用广泛,在此基础上,文中将其与群决策理论相结合,首先指出了对供应商进行评价时常出现的平局问题,将群体决策复合准则引入到供应商选择过程中,然后建立模型,对其求解,最后结合算例,说明该方法的有效性。     

基于集对分析的第三方物流企业客户满意度评价研究

在集对分析原理的基础上,结合第三方物流企业客户服务的特点,构建第三方物流企业客户满意度评价体系和评价数学模型,并以实例进行满意度评价。实例研究表明,集对分析评价模型涵义明确,计算过程较为简单,具有一定的推广和应用价值,是分析不确定性多目标决策问题的有效方法。     

电力投资决策的期权博弈模型及其发展评述

电力投资决策对于电力企业甚至电力行业的发展有着举足轻重的作用,电力企业的投资选择是在外部环境竞争复杂性和不确定性的约束下进行的,需要研究复杂竞争环境和不确定因素条件下的投资决策方法。本文以电力投资决策模型分析入手,总结了电力投资决策模型的发展过程,探讨了电力投资的期权博弈模型发展过程、研究重点、缺陷、及发展方向,展示了电力投资决策期权博弈理论的发展脉络和思考重点。实践证明,该方法不仅能够对电力投资项目进行更加科学的而评估,还能够为电力行业的发展做出更加科学合理的决策。     

Advances in Joint Modelling: A Review of Recent Developments with Application to the Survival of End Stage Renal Disease Patients

The use of joint modelling approaches is becoming increasingly popular when an association exists between survival and longitudinal processes. Widely recognized for their gain in efficiency, joint models also offer a reduction in bias compared with naïve methods. With the increasing popularity comes a constantly expanding literature on joint modelling approaches. The aim of this paper is to give an overview of recent literature relating to joint models, in particular those that focus on the time‐to‐event survival process. A discussion is provided on the range of survival submodels that have been implemented in a joint modelling framework. A particular focus is given to the recent advancements in software used to build these models. Illustrated through the use of two different real‐life data examples that focus on the survival of end‐stage renal disease patients, the use of the JM and joineR packages within R are demonstrated. The possible future direction for this field of research is also discussed.     

The use of RAS and related models in manpower forecasting

With the increasing availability of statistics describing the occupational structures of different industries manpower forecasters are beginning to develop more sophisticated models. The economic rationale of such models has tended to be obscured by the mathematics involved and an understandable eagerness to put the data to use in forecasting. In addition, the systematic testing of the explanatory power of these models has been neglected where it has not been hampered by the shortage of data series. The RAS model has featured prominently in manpower discussions and this paper attempts an evaluation of its predictive ability and economic interpretation subject to the limits imposed by the data available for the British engineering industry. It is argued that such a model plays a useful initial role in the development of models for sectoral manpower forecasting but must lead on to a more sensitive treatment of the labour market and the decision problem of investing in human capital.     

Complexity in local government change

Abstract

This article discusses empirical research findings indicating that complexity is a dominant characteristic in local government change and addresses that the current complexity sets limits to rational reform processes and gives way to political leadership.

During the recent decade, intermunicipal co-operation has emerged as a major issue in local governance in Finland. Despite the fact that the need for intense co-operation is acknowledged in most surveys, practical steps are often difficult to take due to complexity of the interorganizational action. Actors come upon complex situations involving many issues; situations where the issues are continuously changing and complicatedly interdependent. Circumstances are further blurred by the fact that actors often hide their preferences.

In the changing local governance, complexity, paradoxes and uncertainty decrease the prospective of managerial and expert knowledge, because rational calculations do not give definitive support for decision making. From this perspective, we have reached the limits of rational, clear-cut reforming. More than before, the implementation of change depends on the emergence of political leaders willing and able to take responsibility for reforms.     

A nonlinear simultaneous probit-model for the investigation of decision-making processes: modelling the process of setting up a family in partnerships

This article proposes an approach for modelling the interactive influences of two (or more) actors in decision-making processes. We use a nonlinear simultaneous probit-model and show how the problem of identification for estimating the relative effects of the actors can be solved. The formal model will be applied to examine the decision-making process for setting up a family in partnerships. We model a trivariate distribution consisting of the wifes’ desire to have a child or disposition toward the generative decision, the husbands’ disposition and the joint generative decision. We show how the parameter can be used to assess the relative importance of both partners’ dispositions for the decision, the reciprocal influence of both partners’ dispositions within the interaction process, and the relevance of both partners’ biographical contexts in relation to their own disposition as well as to that of the partner. The analysis is based on a three-stage estimation strategy which is implemented in MECOSA 3 and we use data from the Bamberger married couple panel.     

Action variety of planners: Cognitive load and requisite variety

The complexity of planning tasks have increased over the past decade. There is relatively poor understanding what the implications are of increased task complexity in planning and scheduling operations. Previous work in the behavioral sciences have investigated the concept of cognitive load, addressing both task complexity and task workload or stress, and have concluded that decision makers tend to resort to routine action and reduce the variety in their actions with increasing complexity and workload. Alternatively, control theory suggests that a higher variety of actions is needed to deal with more complex problems. In this paper, we investigate the effects of task complexity in a chemical plant on the variety of actions deployed by the planners. The single work center resource structure and the availability of actual planning data from an MRP-application database allows us to both use field data and study a situation which is simple enough to measure the main effect. Our results suggest that increased task complexity without time pressure does indeed lead to increased action variety deployed by the planners.     

VARIATIONS ON THE THEME OF CONNINGa IN MATHEMATICAL ECONOMICS

Abstract The mathematization of economics is almost exclusively in terms of the mathematics of real analysis which, in turn, is founded on set theory (and the axiom of choice) and orthodox mathematical logic. In this paper I try to point out that this kind of mathematization is replete with economic infelicities. The attempt to extract these infelicities is in terms of three main examples and one general discussion: dynamics, policy and rational expectations and learning are the examples; a game theory without ‘subjectivism’, based on the axiom of determinateness, is discussed in general terms. The focus is on the role and reliance of standard fixed‐point theorems in orthodox mathematical economics.     

An Econometric Analysis of Polish Inflation Dynamics with Learning about Rational Expectations

Rational expectations modelling has been criticized for assuming that economic agents can learn quickly about and compute rational price expectations. In response, various authors have studied theoretical models in which economic agents use adaptive statistical rules to develop price expectations. A goal of this literature has been to compare resulting learning equilibria with rational expectations equilibria. The lack of empirical analysis in this literature suggests that adaptive learning makes otherwise linear dynamic models nonlinearly intractable for current econometric technology. In response to the lack of empirical work in this literature, this paper applies to post-1989 monthly data for Poland a new method for modelling learning about price expectations. The key idea of the method is to modify Cagan’s backward-looking adaptive-expectations hypothesis about the way expectations are actually updated to a forward-looking characterization which instead specifies the result of learning. It says that, whatever the details of how learning actually takes places, price expectations are expected to converge geometrically to rationality. The method is tractable because it involves linear dynamics. The paper contributes substantively by analyzing the recent Polish inflation, theoretically by characterizing learning, and econometrically by using learning as a restriction for identifying (i.e., estimating wth finite variance) unobserved price expectations with the Kalman filter. This revised version was published online in July 2006 with corrections to the Cover Date.     

Audit Fees in a Joint Audit Setting

Abstract

This paper uses the uniqueness of the French audit environment to conduct an in-depth study of audit pricing issues associated with the requirement to hire two independent auditors (joint audit). I use a model derived from Simunic's [(1980). The pricing of audit services: Theory and evidence. Journal of Accounting Research, 18(1), 161–190] seminal work to examine to what extent audit fees are influenced by the number of Big 4 joint auditors (zero, one, or two). After controlling for well-known drivers of audit fees that are specific to audit client firms (size, complexity, and risk), for governance characteristics and for auditor selection, the paper shows that the decision to hire two Big 4 auditors as joint auditors does not require the payment of a higher Big 4 premium compared to the choice of one Big 4 auditor paired with a smaller auditor, other things being equal. The choice of two Big 4 auditors thus appears to be a rational economic choice for large and international firms.     

Some applications of the fast Fourier transform algorithm in insurance mathematics This paper is dedicated to Professor W. S. Jewell on the occasion of his 60th birthday

Transform methods, together with the fast Fourier transform algorithm, can be used to compute various quantities of interest in risk theory and insurance mathematics. These include the total claim size distribution at a fixed time, the mean and variance of the claim size process as a function of time in the Sparre-Andersen model, and the probability of ruin. The associated discretization error can be reduced by applying Richardson's deferred approach to the limit. A theorem is given that puts the use of this technique on a mathematical basis in the context of compound distributions.     

Statistical Decision Problems and Bayesian Nonparametric Methods

This paper considers parametric statistical decision problems conducted within a Bayesian nonparametric context. Our work was motivated by the realisation that typical parametric model selection procedures are essentially incoherent. We argue that one solution to this problem is to use a flexible enough model in the first place, a model that will not be checked no matter what data arrive. Ideally, one would use a nonparametric model to describe all the uncertainty about the density function generating the data. However, parametric models are the preferred choice for many statisticians, despite the incoherence involved in model checking, incoherence that is quite often ignored for pragmatic reasons. In this paper we show how coherent parametric inference can be carried out via decision theory and Bayesian nonparametrics. None of the ingredients discussed here are new, but our main point only becomes evident when one sees all priors—even parametric ones—as measures on sets of densities as opposed to measures on finite-dimensional parameter spaces.