Computing Equilibria in Finance Economies

Computational methods, asset pricing, general equilibrium, incomplete markets.

Computing Equilibria in Finance Economies with Incomplete markets and Transactions Costs

Transaction costs on financial markets may have important consequences for volumes of trade, asset pricing, and welfare. This paper introduces an algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets and transaction costs. We show that economies with transaction costs can be analyzed with differentiable homotopy techniques and thus in the same framework as frictionless economies despite the existence of non-differentiabilities of agents’ asset demand functions and the existence of locally non-unique equilibria. We introduce an equilibrium selection concept into the computation of economic equilibria that picks out a specific equilibrium in the presence of a continuum of equilibria

Computing Equilibria in Finance Economies with Incomplete Markets and Transaction Costs

Transaction costs in financial markets may have important consequences for volumes of trade, asset pricing and welfare. In the economic literature they are often given as one reason for the incompleteness of asset markets, which is a striking example of their potential impact on volumes of trade. We argue that analytical results on the impact of transaction costs are hard to obtain and a computational approach is needed. This paper introduces the first algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets and linear transaction costs on the financial markets. The algorithm is based on the homotopy principle and is able to deal with the two major technical difficulties of the model, namely the existence of non-differentiabilities of agents'' asset demands as a function of the asset prices and the existence of locally non-unique equilibria. Several numerical examples give a first glimpse of the impact of transaction costs on the nature of the equilibria. We show that the consequences of transaction costs for volumes of trade and prices can be counterintuitive even for small economic models.microeconomics ;

An interior point algorithm for computing equilibria in economies with incomplete asset markets

Computing equilibria in general equilibria models with incomplete asset (GEI) markets is technically difficult. The standard numerical methods for computing these equilibria are based on homotopy methods. Despite recent advances in computational economics, much more can be done to enlarge the catalogue of techniques for computing GEI equilibria. This paper presents an interior-point algorithm that exploits the special structure of GEI markets. We prove that the algorithm converges globally at a quadratic rate, rendering it particularly effective in solving large-scale GEI economies. To illustrate its performance, we solve relevant examples of GEI market

A Dual Method of Empirically Evaluating Dynamic Competitive Equilibrium Models with Market Distortions, Applied to the Great Depression & World War II

I prove some theorems for competitive equilibria in the presence of market distortions, and use those theorems to motivate an algorithm for (simply and exactly) computing and empirically evaluating competitive equilibria for dynamic economies. Although a competitive equilibrium models interactions between all sectors, all consumer types, and all time periods, I show how my algorithm permits separate empirical evaluation of these pieces of the model and hence is practical even when very little data is available. I then compute a neoclassical growth model with distortionary taxes that fits aggregate U.S. time series for the period 1929-50 and conclude that, if it is to explain aggregate behavior during the period, government policy must have heavily taxed labor income during the Great Depression and lightly taxed it during the war. In other words, the challenge for the competitive equilibrium approach is not so much why output might change over time, but why the marginal product of labor and the marginal value of leisure diverged so much and why that wedge persisted so long. In this sense, explaining aggregate behavior during the period has been reduced to a public finance question -- were actual government policies distorting behavior in the same direction and magnitude as government policies in the model?

Computing Equilibria of Semi-algebraic Economies Using Triangular Decomposition and Real Solution Classification

In this paper, we are concerned with the problem of determining the existence of multiple equilibria in economic models. We propose a general and complete approach for identifying multiplicities of equilibria in semi-algebraic economies, which may be expressed as semi-algebraic systems. The approach is based on triangular decomposition and real solution classification, two powerful tools of algebraic computation. Its effectiveness is illustrated by two examples of application.Comment: 24 pages, 5 figure

AN INTERIOR POINT ALGORITHM FOR COMPUTING EQUILIBRIA IN ECONOMIES WITH INCOMPLETE ASSET MARKETS

Computing equilibria in general equilibria models with incomplete asset (GEI) markets is technically difficult. The standard numerical methods for computing these equilibria are based on homotopy methods. Despite recent advances in computational economics, much more can be done to enlarge the catalogue of techniques for computing GEI equilibria. This paper presents an interior-point algorithm that exploits the special structure of GEI markets. We prove that the algorithm converges globally at a quadratic rate, rendering it particularly effective in solving large-scale GEI economies. To illustrate its performance, we solve relevant examples of GEI markets.