Asymptotic and small sample analysis of the stochastic properties and certainty equivalents of winning bids in independent private values auctions$\!$

Summary. This paper investigates the stochastic properties of the first price and second price winning bids in auctions with risk neutral bidders with independent and identically distributed valuations. In such an environment, the winning first price bids second order stochastically dominate the second price winning bids. A key result of this paper is that the ratio of the variance of the winning first price bid to that of the winning second price bid is strictly less than one even as the number of bidders goes to infinity. This suggests that the stochastic dominance of the winning first price bids does not vanish even in the limit. Both the asymptotic and small sample properties of winning bids are investigated. In particular, the small sample results suggest that the identification power of econometric procedures that rely on winning bids can decline rapidly as the number of bidders increases. This paper also includes a systematic evaluation of the difference in certainty equivalents between the two auction formats for several common distributions and number of bidders for the case of auctioneers with constant coefficient of absolute risk aversion. These results are presented in a form that makes it easy to apply them to a specific auction of interest.Received: 15 July 2002, Revised: 7 April 2003, JEL Classification Numbers: D44.I would like to thank David Pearce for helpful comments and discussion and a referee for suggestions that have greatly improved this paper.     

Nonlinear perturbations of difference equations in population dynamics

A new method is proposed for the study of population dynamics in which the growth rate is impacted by population history, i.e., levels of one or more previous generations. In particular, nonlinear perturbations are incorporated into second-order difference equations, two fundamental time scales are assumed for the solution, and a differential system is generated to approximate the “slow” variation. Solutions of the approximating differential system are developed by computer simulation and the theory of nonlinear oscillations. The geometry of the phase planes describing the approximate “slow” variation is represented graphically and the interaction of fast and slow time scales analyzed. Relationships of the model to experimental data on small mammal populations are discussed. The experimental data was collected at the National Institute of Health under the direction of Dr. John B. Calhoun.     

POVERTY AND INCOME INEQUALITY IN LATIN AMERICA DURING THE 1980s

On average, poverty and income inequality increased in Latin America during the 1980s. Forty-six percent of the increase in poverty took place in the cities of Brazil alone, though part of this reflects the migration of poor rural inhabitants to urban areas. There is strong evidence that both income inequality and poverty mirrored the economic cycle, rising during recession and falling during recovery. Economies that grew (e.g. Colombia, Costa Rica) performed better with respect to poverty and income inequality than those that stagnated. In particular, countries that failed to stabilize effectively (e.g. Brazil, Peru) experienced substantial increases in poverty. Educational attainment has the greatest correlation with both income inequality and the probability of being poor. From a policy standpoint, there is a clear association between the provision of education, lessening of income inequality, and poverty reduction.     

Introduction to the Symposium

This file surveys recent contributions to auction theory and explores the implications they contain for future research in the field. I would like to express my deep appreciation to Roko Aliprantis for offering me the opportunity to edit this special collection of papers on auction theory, and for offering me support and guidance on numerous occasions along the way.     

Valuing Changes in the Quality of Coral Reef Ecosystems: A Stated Preference Study of SCUBA Diving in the Bonaire National Marine Park

We estimated the economic value of changes in the quality of a coral reef ecosystem to SCUBA divers in the Caribbean using a stated preference mail survey. Our sampling frame was all divers with U.S. home addresses who purchased a tag required for diving in the Bonaire National Marine Park in 2001. Divers were asked how they might have altered their trip choice had the quality of the coral reef system been different from what they experienced. From these responses we inferred the value of three different levels of quality defined by visibility, species diversity, and percent coral cover. We used random utility theory and mixed logit to analyze the choice questions. Our sample size was 211, and our survey response rate was 75%. For modest changes in quality we estimated per person annual losses at $45. For larger losses the value was $192. Presented at the 3rd World Congress of Environmental and Resource Economists in Kyoto, Japan, July 2006.