Open AccessA new approach to identifying generalized competing risks models with application to second‐price auctions
Author(s) -
Komarova Tatiana
Publication year - 2013
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe111
Subject(s) - common value auction , uniqueness , constructive , nonparametric statistics , identification (biology) , constructive proof , mathematical optimization , computer science , mathematical economics , observable , mathematics , econometrics , discrete mathematics , statistics , mathematical analysis , botany , physics , process (computing) , quantum mechanics , biology , operating system
This paper proposes an approach to proving nonparametric identification 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 identification is constructive and is based on establishing the existence and uniqueness of a solution to the system of nonlinear differential 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 demonstrate how this approach can be applied to obtain identification in auctions with a stochastic number of bidders. Furthermore, I show that my results can be extended to generalized competing risks models.