Estimation methods for stochastic volatility models: a survey

Abstract.  Although stochastic volatility (SV) models have an intuitive appeal, their empirical application has been limited mainly due to difficulties involved in their estimation. The main problem is that the likelihood function is hard to evaluate. However, recently, several new estimation methods have been introduced and the literature on SV models has grown substantially. In this article, we review this literature. We describe the main estimators of the parameters and the underlying volatilities focusing on their advantages and limitations both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S&P 500 stock price index.     

Union games: technological unemployment

Summary. Given a production economy, we define union games by considering strategic behavior of the suppliers of factors. We refer to the Nash equilibria of this game as union equilibria. We analyze situations where the unemployment of factors is supported as a union equilibrium. The degree of unemployment depends on technological conditions. This allows us to model a source of unemployment which differs from the usual sources provided in the literature. We state a limit result that demonstrates that, as the market power of unions decreases, the corresponding sequence of union equilibria converges to the Walrasian equilibrium, that is, to full employment of factors. We also provide some examples that illustrate the main results.Received: 21 October 2004, Revised: 14 December 2004, JEL Classification Numbers: D51, C72. Correspondence to: Emma Moreno-GarcíaE. Moreno acknowledges financial support from the Research Grant BEC2000-1388-C04-01 (Ministerio de Ciencia y Tecnología and FEDER). G. Fernández de Córdoba and E. Moreno acknowledge financial support from the Research Grant SA091/02 from Junta de Castilla y León. We are indebted to C. Alós-Ferrer, C. Pita, D. Anisi, J. A. Ortega, F. Jimeno, J. P. Torres-Martínez, M. Steinert and C. Hervés for helpful comments and insights. We are particularly grateful to T. Kehoe and an anonymous referee for suggestions that improved this paper.     

Prescribed conditional interaction structure models with application to the analysis of mobility tables

The present paper considers some new models for the analysis of multidimensional contigency tables. Although the theoretical background used here appeared already in Haberman (1974), prescribed conditional interaction (PCIN) models were introduced by Rudas (1987) and their mathematical properties were worked out by Leimer and Rudas (1988). These models are defined by prescribing the values of certain conditional interactions in the contingency table. Conditional interaction is defined here as the logarithm of an appropriately defined conditional odds ratio. This conditional odds ratio is a conditional version of a generalization of the well known odds ratio of a 2×2 table and that of the three factor interaction term of a 2×2×2 table and applies to any number of dimensions and any number of categories of the variables. The well known log-linear (LL) models are special PCIN models. Estimated frequencies under PCIN models and tests of fit can be computed using existing statistical software (e.g. BMDP). The paper describes the class of PCIN models and compares it to the class of association models of Goodman (1981). As LL models are widely used in the analysis of social mobility tables, application of more general PCIN models is illustrated.     

On the generic impossibility of truthful behavior: A simple approach

Summary We provide an elementary proof showing how in economies with an arbitrary number of agents an arbitrary number of public goods and utility functions quasi-linear in money, any efficient and individually rational mechanism is not strategy-proof for any economy satisfying a mild regularity requirement.The authors wish to thank William Thomson, Salvadpr Barberá, José Angel Silva and an anonymous referee for helpful comments. The remaining errors are our exclusive responsibility. Financial support from DGICYT under project PB 91-0756 and the Instituto Valenciano de Investigaciones Económicas is gratefully acknowledged.     

Strategic Environmental Standards, Wage Incomes and the Location of Polluting Firms

The purpose of this paper is tostudy how the choice of environmental standardsby governments is affected by the existence ofwage incomes when firms locations areendogenous. In developed countries labor isunionized, which allows positive wage incomesto arise. Thus, each government has incentivesto persuade firms to locate in its countrysince social welfare depends on suchincomes. But, as pollution damages theenvironment, each government will only try toattract polluting firms to thecountry, to obtain the wage incomes, whenthe valuation of environmental damage showsthat it is low.     

Employment shifts, economic reform and the changes in public/private sector wages in Mexico: 1987–1997

Over the last decade, the public sector in Mexico experienced substantial fiscal reform, divestiture of public enterprises, and the elimination of many regulations affecting pay and employment. This study analyzes the changes in the public/private sector differences in wages during the 1987–1997 period. The results from analyzing microdata from the Encuesta Nacional de Empleo Urbano show that relative public sector wages increased from 1987 to 1997. Most of the relative wage increase in the public sector can be explained by increases in the price of skills and by changes in sorting across sectors. The results have important public policy implications since they suggest that public sector workers earn more and their wages have grown faster than those of their private sector counterparts. As such, policies contemplating public sector reform should take into account the effect of these measures on the inter-sectoral income distribution and the overall economic growth. First version received: April 2000/Final version received: December 2000     

On the fundamental thought behind voting rules

The theme is Arrow's requirement in his theorem of 1951 on methods for group choice, that the choice be independent of irrelevant alternatives. The attention is drawn to (1) his own explanation of this requirement in 1972, which is a quite different understanding than has been discussed in the voluminous literature on the theorem, (2) that Arrow, in fact, in 1985 showed an understanding for how irrelevant alternatives might in a meaningful way influence the group choice, (3) that admittedly the border-line between irrelevant and relevant alternatives in Arrow's original statement is arbitrary, and (4) that Arrow, if he had observed the final thought in the origin of the group theory by Borda, which he admittedly did not, might have realized that Borda's method stringently estimates the relevance of each alternative for the result.The author expresses his surprise that a theoretical conclusion based on an arbitrary fundament has been admired so long.