Bayesian econometrics:conjugate analysis and rejection sampling using mathematica

Mathematica is a powerful "system for doing mathematics by computer" which runs on personal computers (Macs and MS-DOS machines), workstations and mainframes. Here we show how Bayesian methods can be implemented in Mathematica. One of the drawbacks of Bayesian techniques is that they are computation-intensive, and every computation is a little different. Since Mathematica is so flexible, it can easily be adapted to solving a number of different Bayesian estimation problems. We illustrate the use of Mathematica functions (i) in a traditional conjugate analysis of the linear regression model and (ii) in a completely nonstandard model -where rejection sampling is used to sample from the posterior

Optimal football strategies: AC Milan versus FC Barcelona

In a recent UEFA Champions League game between AC Milan and FC Barcelona, played in Italy (final score 2-3), the collected match statistics, classified into four offensive and two defensive strategies, were in favour of FC Barcelona (by 13 versus 8 points). The aim of this paper is to examine to what extent the optimal game strategies derived from some deterministic, possibilistic, stochastic and fuzzy LP models would improve the payoff of AC Milan at the cost of FC Barcelona.football game; offensive & defensive strategies; Deterministic LP; fuzzy LP; stochastic LP; Nash equilibria;

Application of Quantitative Software in Economics and Decision Science

Mathematics is often used to facilitate a clear and organized presentation of economic theories and problems. It provides a simplified approach for setting up models, making explicit assumptions about the models, finding optimal solutions, and extending the results by varying the parameters and assumptions of the models. Many economists would agree that a large gain in clarity and economy of effort can be achieved by incorporating mathematics into economic teaching. What limits the use of mathematics in teaching economics is inadequate preparation of students in quantitative methods. In addition, some mathematical manipulations and calculations turn out to be time consuming and tedious for class presentations. This paper argues that both of these problems can be overcome by using modern mathematical software in teaching economics

Small Noise Asymptotics for a Stochastic Growth Model

We develop analytic asymptotic methods to characterize time series properties of nonlinear dynamic stochastic models. We focus on a stochastic growth model which is representative of the models underlying much of modern macroeconomics. Taking limits as the stochastic shocks become small, we derive a functional central limit theorem, a large deviation principle, and a moderate deviation principle. These allow us to calculate analytically the asymptotic distribution of the capital stock, and to obtain bounds on the probability that the log of the capital stock will differ from its deterministic steady state level by a given amount. This latter result can be applied to characterize the probability and frequency of large business cycles. We then illustrate our theoretical results through some simulations. We find that our results do a good job of characterizing the model economy, both in terms of its average behavior and its occasional large cyclical fluctuations.

Solving General Equilibrium Models with Incomplete Markets and Many Assets

This paper presents a new numerical method for solving general equilibrium models with many assets. The method can be applied to models where there are heterogeneous agents, time-varying investment opportunity sets, and incomplete markets. It also can be used to study models where the equilibrium dynamics are non-stationary. We illustrate how the method is used by solving a one-- and two-sector versions of a two--country general equilibrium model with production. We check the accuracy of our method by comparing the numerical solution to the one-sector model against its known analytic properties. We then apply the method to the two-sector model where no analytic solution is available.

Higher-order perturbation solutions to dynamic, discrete-time rational expectations models

We present an algorithm and software routines for computing nth order Taylor series approximate solutions to dynamic, discrete-time rational expectations models around a nonstochastic steady state. The primary advantage of higher-order (as opposed to first- or second-order) approximations is that they are valid not just locally, but often globally (i.e., over nonlocal, possibly very large compact sets) in a rigorous sense that we specify. We apply our routines to compute first- through seventh-order approximate solutions to two standard macroeconomic models, a stochastic growth model and a life-cycle consumption model, and discuss the quality and global properties of these solutions.Macroeconomics - Econometric models ; Business cycles ; Monetary policy

Coalition formation in transmission expansion planning

The study of a decentralized coalition formation scheme in a specific power systems transmission expansion scenario is the purpose of this paper. We define first who are the agents in the expansion game and provide a decentralized coalition scheme based on Bilateral Shapley values. Finally, we allocate the total costs of expansion amongst the agents, based on the coalition history, and we compare our method with a centralized scheme.published_or_final_versio

Bargaining Power and Value Sharing in Distribution Networks: A Cooperative Game Theory Approach

This paper illustrates a methodology for analyzing bargaining games on network markets, by means of numerical models that can be calibrated with real data. Economic incentives to join or to expand a network depend on how the network surplus is being distributed, which in turn depends on a variety of factors: position of each agent (e.g., a country) in a specific network, its reliability in the cooperation scheme (e.g., geo-political stability), existence of market distortions and availability of outside options (e.g., alternative energy sources). This study is aimed at presenting a game theory methodology that can be applied to real world cases, having the potential to shed light on several political economy issues. The methodology is presented and illustrated with application to a fictitious network structure. The method is based on a two-stage pro- cess: first, a network optimization model is used to generate payoff values under different coalitions and network structures; a second model is subsequently employed to identify cooperative game solutions. Any change in the network structure entails both a variation in the overall welfare level and in the distribution of surplus among agents, as it affects their relative bargaining power. Therefore, expected costs and benefits, at the aggregate as well as at the individual level, can be compared to assess the economic viability of any investment in network infrastructure. A number of model variants and extensions are also considered: changing demand, exogenous instability factors, market distortions, externalities and outside options

[[alternative]]A Study of the Competition Strategies Among Intercity Modes in the Case of Introducing High Speed Rail

計畫編號：NSC94-2416-H032-003研究期間：200508~200607研究經費：492,000[[abstract]]傳統的存貨模式大都是基於買方或賣方單方面的考量，來探討生產及訂購策略等問 題，如此往往使雙方資訊無法整合而造成損失。近年來，及時化的製造策略受到廣泛 利用，由於其專注於買方與賣方的整合，因此需要買方與賣方能夠充分合作，方可利 用雙方資訊的整合，訂定合理的長期採購合約，做到真正的及時化採購，從而降低相 關存貨系統的總成本。 近年來，有關整合性的存貨模式愈來愈受到重視。過去的相關研究大多著重於買賣 雙方最適訂購、生產與運送批量的決定，並未考慮到當批量中含有不良品時對整合買 賣雙方總成本的影響。在實務上，因為生產製造過程的瑕疵，管理維護不當，或是運 送過程的不小心，買方經常會在訂購批量中發現不良品。 本計劃主要是考慮當需求不確定，且前置時間的長度可控制及買方收到的批量中含 有不良品的情況下，如何整合買方和賣方的製造與訂購策略，並提出兩個整合存貨模 型。在本研究中，我們採部份檢查(sub-lot inspection)的策略來檢查批量中的不良品項。 針對此檢查策略，我們假設前置時間內的需求量服從常態分配，其次探討前置時間內需 求量的機率分配為未知的情形，並且利用大中取小分配不拘程序求解。我們亦分別針對 此兩種情形(前置時間內需求量的機率分配為常態分配或分配不拘)建立求得最適生 產、訂購策略之演算法，並利用數值範例說明買賣雙方整合後的利益，確實是高於整合 前的個別利益。同時，本研究也將分析各參數變動對於決策所造成的影響，作為提供給 管理者之重要參考依據。[[sponsorship]]行政院國家科學委員