Contributions published at Quantitative Business Administration

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In this paper we consider a canonical stochastic overlapping generations economy with sequentially complete markets. We examine how aggregate and individual shocks translate to changes in the distribution of wealth and how these movements in the wealth distribution affect asset prices and the interest rate. We show that effects are generally small if agents have identical beliefs but that differences in opinion lead to large movements in the wealth distribution. The interplay of belief heterogeneity and life-cycle savings motives creates very large movements of asset prices and can potentially generate realistic moments of asset returns.

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We analyze complex bond portfolios within the framework of a dynamic general equilibrium asset-pricing model. Equilibrium bond portfolios are nonsensical and imply a trading volume that vastly exceeds observed trading volume on financial markets. Instead, portfolios that combine bond ladders with a market portfolio of equity assets are nearly optimal investment strategies. The welfare loss of these simple investment strategies, when compared to the equilibrium portfolio, converges to zero as the length of the bond ladder increases. This article, therefore, provides a rationale for naming bond ladders as a popular bond investment strategy.

Static and dynamic games are important tools for the analysis of strategic interactions among economic agents and have found many applications in economics. In many games equilibria can be described as solutions of polynomial equations. In this paper we describe state-of-the-art techniques for finding all solutions of polynomial systems of equations and illustrate these techniques by computing all equilibria of both static and dynamic games with continuous strategies. We compute the equilibrium manifold for a Bertrand pricing game in which the number of equilibria changes with the market size. Moreover, we apply these techniques to two stochastic dynamic games of industry competition and check for equilibrium uniqueness.

In this article, decomposition methods for two‐stage linear recourse problems with a finite discrete distribution are discussed. First, we cover the L‐shaped decomposition method which represents a breakthrough concerning numerically efficient methods for solving two‐stage recourse problems. This algorithm was the basis for the development of several other decomposition methods. After giving an overview of these algorithms, we present regularized decomposition and stochastic decomposition in a more detailed fashion. Variance for recourse‐constrained problems and special cases including simple recourse with a random technology matrix are also considered. With reference to stochastic decomposition, the scope of which is not restricted to finite discrete distributions, algorithms for the continuous‐distribution case are discussed briefly with references to the literature.

Risk aversion plays a central role in the decisions made in the face of uncertainties, and climate-change mitigation should be no exception. However, the interlinkage of risk aversion and climate-change uncertainties has hardly been investigated numerically, in part because of the computational difficulties of stochastic optimization. In this paper, we apply the numerical techniques of stochastic optimization to the economic modeling of climate change, with the aim of modeling the decision preferences of a risk-conscious agent in the face of unpredictable climate change. The model underlines the critical role played by the risk-aversion parameter in determining the effects of uncertainties on mitigation, not only in level but also in sign.

Dental schools use a variety of clinic management models with the goals of promoting patient care, student education, and fiscal responsibility. In 2004, the University of the Pacific Arthur A. Dugoni School of Dentistry transitioned to a more generalist model with these goals in mind. The purpose of this study was to evaluate the outcomes of this clinic model change relative to the quantity of specific procedures completed by students. The quantity of procedures completed by each student from the classes of 1995 through 2009 were compiled from our electronic clinic management system and analyzed. The post-transition group (2004–09) showed a greater number of completed oral diagnosis and treatment planning and root planing procedures per student compared to the pre-transition group (1995–2003), but fewer crowns, root canals, operative procedures, and dentures. Because the higher procedure numbers were for low-cost procedures, our transition to a generalist model did not necessarily enhance clinic income but may support student learning and enhanced patient care.

Multiplicity of equilibria is a prevalent problem in many economic models. Often equilibria are characterized as solutions to a system of polynomial equations. This paper gives an introduction to the application of GrÄobner basis methods for ¯nding all solutions of a polynomial system. The Shape Lemma, a key result from algebraic geometry, states under mild assumptions that a given equilibrium system has the same solution set as a much simpler triangular system. Essentially the computation of all solutions then reduces to ¯nding all roots of a single polynomial in a single unknown. The software package Singular computes the equivalent simple system. If all coeficients in the original equilibrium equations are rational numbers or parameters then the GrÄobner basis computations of Singular are exact. This fact implies that the GrÄobner basis methods cannot only be used for a numerical approximation of equilibria but in fact may allow the proof of theoretical results for the underlying economic model. Three economic applications illustrate that without much prior knowledge of algebraic geometry GrÄobner basis methods can be easily applied to gain interesting insights into many modern economic models.

In this paper we examine the likelihood of multiple real steady states in deterministic exchange economies with overlapping generations. There is a single good and a single agent per generation with constant relative risk aversion expected utility. In order to test for multiple equilibria we employ methods from computational algebraic geometry. In our examples, we find that multiplicity becomes less likely as the life span of agents increases but becomes more likely as the coefficient of risk aversion increases. For moderate values of risk aversion, multiplicity is very unlikely when agents live for five or more periods. (JEL: C61, C63, D50, D58)

In this paper, we examine non-parametric restrictions on counterfactual analysis in a dynamic stochastic general equilibrium model. Under the assumption of time-separable expected utility and complete markets all equilibria in this model are stationary. The Arrow-Debreu prices uniquely reveal the probabilities and discount factor. The equilibrium correspondence, defined as the map from endowments to stationary (probability-free) state prices, is identical to the equilibrium correspondence in a standard Arrow-Debreu exchange economy with additively separable utility. We examine possible restriction on this correspondence and give necessary as well as sufficient conditions on profiles of individual endowments that ensure that associated equilibrium prices cannot be arbitrary. Although restrictions on possible price changes often exist, we show that results from a representative-agent economy usually do not carry over to a setting with heterogeneous agents.

This paper develops a method to compute the equilibrium correspondence for exchange economies with semi-algebraic preferences. Given a class of semi-algebraic exchange economies parameterized by individual endowments and possibly other exogenous variables such as preference parameters or asset payoffs, there exists a semi-algebraic correspondence that maps parameters to positive numbers such that for generic parameters each competitive equilibrium can be associated with an element of the correspondence and each endogenous variable (i.e. prices and consumptions) is a rational function of that value of the correspondence and the parameters. This correspondence can be characterized as zeros of a univariate polynomial equation that satisfy additional polynomial inequalities. This polynomial as well as the rational functions that determine equilibrium can be computed using versions of Buchberger's algorithm which is part of most computer algebra systems. The computation is exact whenever the input data (i.e. preference parameters etc.) are rational. Therefore, the result provides theoretical foundations for a systematic analysis of multiplicity in applied general equilibrium.

Many bond portfolio managers argue that bond laddering tends to outperform other bond investment strategies because it reduces both market price risk and reinvestment risk for a bond portfolio in the presence of interest rate uncertainty. Despite the popularity of bond ladders as a strategy for managing investments in fixed-income securities, there is surprising little reference to this subject in the economics and finance literature. In this paper we analyze complex bond portfolios within the framework of a dynamic general equilibrium asset-pricing model. Equilibrium bond portfolios are nonsensical, implying a trading volume that vastly exceeds observed trading volume on ¯nancial markets. Such portfolios would also be very costly and thus suboptimal in the presence of even very small transaction costs. Instead portfolios combining bond ladders with a market portfolio of equity assets are nearly optimal investment strategies, which in addition would minimize transaction costs. This paper, therefore, provides a rationale for bond ladders as a popular bond investment strategy.

Optimization problems are ubiquitous in economics. Many of these problems are sufficiently complex that they cannot be solved analytically. Instead economists need to resort to numerical methods. This article presents the most commonly used methods for both unconstrained and constrained optimization problems in economics; it emphasizes the solid theoretical foundation of these methods, illustrating them with examples. The presentation includes a summary of the most popular software packages for numerical optimization used in economics, and closes with a description of the rapidly developing area of mathematical programs with equilibrium constraints, an area that shows great promise for numerous economic applications.