Bounds for a joint distribution function with fixed sub-distribution functions: Application to competing risks

Peterson, Arthur V.

doi:10.1073/pnas.73.1.11

Cited by 217 publications

(124 citation statements)

References 1 publication

Supporting

Mentioning

120

Contrasting

Unclassified

Order By: Relevance

“…The study of partial identication in classical competing risks models was initiated by Peterson (1976), who obtained tight point-wise bounds on the joint and marginal survival functions. Crowder (1991) and Bedford and Meilijson (1997) obtained new results on bounds for those functions.…”

Section: Values Are Not Independentmentioning

confidence: 99%

Nonparametric identification in asymmetric second-price auctions: a new approach

Komarova¹

2009

View full text Add to dashboard Cite

)>IJH=?J This paper proposes an approach to proving nonparametric identication for distributions of bidders' values in asymmetric second-price auctions. I consider the case when bidders have independent private values and the only available data pertain to the winner's identity and the transaction price. My proof of identication is constructive and is based on establishing the existence and uniqueness of a solution to the system of non-linear dierential equations that describes relationships between unknown distribution functions and observable functions. The proof is conducted in two logical steps. First, I prove the existence and uniqueness of a local solution. Then I describe a method that extends this local solution to the whole support. This paper delivers other interesting results. I show how this approach can be applied to obtain identication in more general auction settings, for instance, in auctions with stochastic number of bidders or weaker support conditions. Furthermore, I demonstrate that my results can be extended to generalized competing risks models. Moreover, contrary to results in classical competing risks (Roy model), I show that in this generalized class of models it is possible to obtain implications that can be used to check whether the risks in a model are dependent. Finally, I provide a sieve minimum distance estimator and show that it consistently estimates the underlying valuation distribution of interest.

show abstract

Section: Values Are Not Independentmentioning

confidence: 99%

Nonparametric identification in asymmetric second-price auctions: a new approach

Komarova¹

2009

View full text Add to dashboard Cite

show abstract

“…Vijverberg (1993) is a good reference for sensitivity analysis in a Roy model. Peterson (1976) is an early example of bounds for the competing risks model which is a version of the Roy model. My argument uses structural models directly because they are interpretable in terms of theory and they explicitly recognize missing variables (''unobservables'').…”

Section: Sensitivity Analysismentioning

confidence: 99%

Rejoinder: Response to Sobel

Heckman

2005

Sociological Methodology

View full text Add to dashboard Cite

“…In the industrial organization literature, Haile and Tamer (2003) used partial identification methods to construct bounds on valuation distributions in second price auctions. In the statistics literature, the Frechet bounds on joint distributions given knowledge of marginals are well known (see also Heckman, Lalonde, and Smith (1999)), and these were used starting with the important result of Peterson (1976) in competing risks. In the labor literature, the bounds approach to inference has been prominent in the treatment-response and selection literature where several papers discuss and use exclusion restrictions to tighten the bounds and gain more information.…”

Section: Introductionmentioning

confidence: 99%

Market Structure and Multiple Equilibria in Airline Markets

2009

View full text Add to dashboard Cite

We provide a practical method to estimate the payoff functions of players in complete information, static, discrete games. With respect to the empirical literature on entry games originated by Bresnahan and Reiss (1990) and Berry (1992), the main novelty of our framework is to allow for general forms of heterogeneity across players without making equilibrium selection assumptions. We allow the effects that the entry of each individual airline has on the profits of its competitors, its "competitive effects," to differ across airlines. The identified features of the model are sets of parameters (partial identification) such that the choice probabilities predicted by the econometric model are consistent with the empirical choice probabilities estimated from the data.We apply this methodology to investigate the empirical importance of firm heterogeneity as a determinant of market structure in the U.S. airline industry. We find evidence of heterogeneity across airlines in their profit functions. The competitive effects of large airlines (American, Delta, United) are different from those of low cost carriers and Southwest. Also, the competitive effect of an airline is increasing in its airport presence, which is an important measure of observable heterogeneity in the airline industry. Then we develop a policy experiment to estimate the effect of repealing the Wright Amendment on competition in markets out of the Dallas airports. We find that repealing the Wright Amendment would increase the number of markets served out of Dallas Love.

show abstract

Bounds for a joint distribution function with fixed sub-distribution functions: Application to competing risks

Cited by 217 publications

References 1 publication

Nonparametric identification in asymmetric second-price auctions: a new approach

Nonparametric identification in asymmetric second-price auctions: a new approach

Rejoinder: Response to Sobel

Market Structure and Multiple Equilibria in Airline Markets

Contact Info

Product

Resources

About