Economics Research at the FTC: Information,Retrospectives, and Retailing

Individual Federal Trade Commission (FTC) cases invariably raise broad questions about consumers, markets, and effective enforcement policy. Recent consumer protection cases raise questions about information regulation. Horizontal merger enforcement has recently focused on retrospective analysis of mergers and the role of the retail sector in predicting the effects of manufacturer mergers. In this paper, we describe research by the FTCs Bureau of Economics that addresses these three areas. We argue that such research is well worth the agencys relatively small resource investment because it demonstrably contributes to more thoughtful policy analysis and better policy outcomes.     

Pricing European Options by Numerical Replication: Quadratic Programming with Constraints

The paper considers a regression approach to pricing European options in an incomplete market. The algorithm replicates an option by a portfolio consisting of the underlying security and a risk-free bond. We apply linear regression framework and quadratic programming with linear constraints (input = sample paths of underlying security; output = table of option prices as a function of time and price of the underlying security). We populate the model with historical prices of the underlying security (possibly massaged to the present volatility) or with Monte Carlo simulated prices. Risk neutral processes or probabilities are not needed in this framework.     

Exact Solutions of a Model for Asset Prices by K. Takaoka

We are concerned with a model for asset prices introduced by Koichiro Takaoka, which extends the well known Black-Scholes model. For the pricing of contingent claims, partial differential equation (PDE) is derived in a special case under the typical delta hedging strategy. We present an exact pricing formula by way of solving the equation. Mathematics Subject Classification(2000):91B28,35K15     

A Benchmark Approach to Filtering in Finance

The paper proposes the use of the growth optimal portfolio for pricing and hedging in incomplete markets when there are unobserved factors that have to be filtered. The proposed filtering framework is applicable also in cases when there does not exist an equivalent risk neutral martingale measure. The reduction of the variance of derivative prices for increasing degrees of available information is measured. 1991 Mathematics Subject Classification: primary 90A09; secondary 60G99; 62P20 JEL Classification: G10, G13     

Understanding the Implied Volatility Surface for Options on a Diversified Index

This paper describes a two-factor model for a diversified index that attempts to explain both the leverage effect and the implied volatility skews that are characteristic of index options. Our formulation is based on an analysis of the growth optimal portfolio and a corresponding random market activity time where the discounted growth optimal portfolio is expressed as a time transformed squared Bessel process of dimension four. It turns out that for this index model an equivalent risk neutral martingale measure does not exist because the corresponding Radon-Nikodym derivative process is a strict local martingale. However, a consistent pricing and hedging framework is established by using the benchmark approach. The proposed model, which includes a random initial condition for market activity, generates implied volatility surfaces for European call and put options that are typically observed in real markets. The paper also examines the price differences of binary options for the proposed model and their Black-Scholes counterparts. Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

Efficient rank tests for semiparametric competing risk models

We consider a semiparametric competing risk model given by k independent survival times. The paper offers an asymptotic treatment of tests for the semiparametric null hypothesis of equality of the underlying risks. It turns out that modified rank tests are asymptotically efficient for certain semiparametric submodels, where the baseline hazard is a nuisance parameter. In addition, the asymptotic relative efficiency of the present tests is derived. A comparison of asymptotic power functions can then be used to classify various tests proposed earlier in the literature. For instance a chi-square type test is efficient for proportional hazards. Data driven tests of likelihood ratio type are proposed for cones of alternatives. We will consider certain stochastically increasing alternatives as a special example. The paper shows how the concept of local asymptotic normality of Le Cam works for hazard oriented models.     

The association between two random elements: A complete characterization and odds ratio models

For random elements X and Y (e.g. vectors) a complete characterization of their association is given in terms of an odds ratio function. The main result establishes for any odds ratio function and any pre-specified marginals the unique existence of a corresponding joint distribution (the joint density is obtained as a limit of an iterative procedure of marginal fittings). Restricting only the odds ratio function but not the marginals leads to semi-parmetric association models for which statistical inference is available for samples drawn conditionally on either X or Y. Log-bilinear association models for random vectors X and Y are introduced which generalize standard (regression) models by removing restrictions on the marginals. In particular, the logistic regression model is recognized as a log-bilinear association model. And the joint distribution of X and Y is shown to be multivariate normal if and only if both marginals are normal and the association is log-bilinear.Acknowledgements The author thanks both referees for their helpful comments which improved the first draft of the paper.     

Employment Decisions in Self-Directed Work Teams: A Regulatory Compliance Perspective

Organizations are increasingly relying on self-directed work teams (SDWTs) to accomplish organizational tasks. The introduction of SDWTs into the workplace poses a number of managerial challenges. This paper will focus on one such challenge, the continuing need to comply with labor and equal employment regulations. We discuss several factors that potentially affect the legal compliance process. These include: (1) the impact of an increasingly diverse workforce on individual behavior and team processes, and (2) the role of procedural justice perceptions in effective HR compliance management. We conclude with some practical solutions to the challenge of managing compliance in SDWT settings.     

Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model <Emphasis Type="Bold">AX=B</Emphasis>

A multivariate measurement error model AXB is considered. The errors in [A,B] are rowwise independent, but within each row the errors may be correlated. Some of the columns are observed without errors, and in addition the error covariance matrices may differ from row to row. The total covariance structure of the errors is supposed to be known up to a scalar factor. The fully weighted total least squares estimator of X is studied, which in the case of normal errors coincides with the maximum likelihood estimator. We give mild conditions for weak and strong consistency of the estimator, when the number of rows in A increases. The results generalize the conditions of Gallo given for a univariate homoscedastic model (where B is a vector), and extend the conditions of Gleser given for the multivariate homoscedastic model. We derive the objective function for the estimator and propose an iteratively reweighted numerical procedure.Acknowledgements.A. Kukush is supported by a postdoctoral research fellowship of the Belgian office for Scientific, Technical and Cultural Affairs, promoting Scientific and Technical Collaboration with Central and Eastern Europe. S. Van Huffel is a full professor with the Katholieke Universiteit Leuven. This paper presents research results of the Belgian Programme on Interuniversity Poles of Attraction (IUAP Phase V-22), initiated by the Belgian State, Prime Ministers Office-Federal Office for Scientific, Technical and Cultural Affairs, of the Concerted Research Action (GOA) projects of the Flemish Government MEFISTO-666 (Mathematical Engineering for Information and Communication Systems Technology), of the IDO/99/03 project (K.U. Leuven) Predictive computer models for medical classification problems using patient data and expert knowledge, of the FWO projects G.0200.00, G.0078.01 and G.0270.02. The scientific responsibility is assumed by its authors. The authors would like to thank Maria Luisa Rastello and Amedeo Premoli for bringing the EW-TLS problem to their attention. The authors are grateful to two anonymous referees for the valuable comments.     

The Dynamics of Self-Esteem and Physical Self: Between Preservation and Adaptation

The aim of this study was to model and characterize the psychologicalprocesses that underlie the dynamics of global self-esteem and physicalself over time. Twice a day for 228 consecutive days, seven participantscompleted a short inventory (PSI-6, Ninot et al., 2001) measuring sixsubjective dimensions: global self-esteem, physical self-worth, physicalcondition, sport competence, physical strength, and attractive body.Each series was modeled by means of ARIMA procedures. The resultsshowed that a simple moving average model provided a satisfactoryaccount for the dynamics of all series. This model suggests that acombination of two opposite processes underlies the dynamics ofself-concept: preservation, which tends to restore the previousvalue after a disturbance, and adaptation, which tends to inflectthe series in the direction of the perturbation.