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Identification and Inference in Ascending Auctions with Correlated Private Values
, 2012
"... We introduce and apply a new nonparametric approach to identification and inference on data from ascending auctions. We exploit variation in the number of bidders across auctions to nonparametrically identify useful bounds on seller profit and bidder surplus using a general model of correlated priva ..."
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Cited by 11 (3 self)
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We introduce and apply a new nonparametric approach to identification and inference on data from ascending auctions. We exploit variation in the number of bidders across auctions to nonparametrically identify useful bounds on seller profit and bidder surplus using a general model of correlated private values that nests the standard IPV model. We also translate our identified bounds into closed form and asymptotically valid confidence intervals for several economic measures of interest. Applying our methods to muchstudied U.S. Forest Service timber auctions, we find evidence of correlation among values after controlling for a rich vector of relevant auction covariates; this correlation causes expected profit, the profitmaximizing reserve price, and bidder surplus to be substantially lower than conventional (IPV) analysis of the data would suggest. ∗ We are very thankful to the editor JeanMarc Robin and three anonymous referees for their insightful feedback;
Information Structure and Statistical Information in Discrete Response Models
, 2011
"... Discrete response models are of high interest in economics and econometrics as they encompass treatment effects, social interaction and peer effect models, and discrete games. We study the impact of the structure of information sets of economic agents on the Fisher information of (strategic) intera ..."
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Cited by 7 (1 self)
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Discrete response models are of high interest in economics and econometrics as they encompass treatment effects, social interaction and peer effect models, and discrete games. We study the impact of the structure of information sets of economic agents on the Fisher information of (strategic) interaction parameters in such models. While in complete information models the information sets of participating economic agents coincide, in incomplete information models each agent has a type, which we model as a payoff shock, that is not observed by other agents. We allow for the presence of a payoff component that is common knowledge to economic agents but is not observed by the econometrician (representing unobserved heterogeneity) and have the agents’ payoffs in the incomplete information model approach their payoff in the complete information model as the heterogeneity term approaches 0. We find that in the complete information models, there is zero Fisher information for interaction parameters, implying that estimation and inference become nonstandard. In contrast, positive Fisher information can be attained in the incomplete information models with any nonzero variance of player types, and for those we can also find the semiparametric efficiency bound with unknown distribution of unobserved heterogeneity. The contrast in Fisher information is illustrated in two important cases: treatment effect models, which we model as a triangular system of equations, and static game models. In static game models we show this result is not due to equilibrium refinement with an increase in incomplete information, as our model has a fixed equilibrium selection mechanism. We find that the key factor in these models is the relative tail behavior of the unobserved component in the economic agents’ payoffs and that of the observable covariates.
Web Supplement to Inference of BiddersRisk Attitudes in Ascending Auctions with Endogenous Entry
, 2014
"... when the value distribution is continuous over [v; v) with a probability mass at v. The model assumptions considered in this section are almost identical to that in Section 3 in Fang and Tang (2014), except for the probability mass at v. Assumption M1. Conditional on K, private values Vi are indepen ..."
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when the value distribution is continuous over [v; v) with a probability mass at v. The model assumptions considered in this section are almost identical to that in Section 3 in Fang and Tang (2014), except for the probability mass at v. Assumption M1. Conditional on K, private values Vi are independent draws from the same continuous marginal distribution FV jK which has positive density almost everywhere with respect to the Lebesgue measure over [v; v) with a probability mass at v. Entry costs across auctions are independent draws from a continuous distribution FK with a support [k; k]. Let the notations be de
ned as in the text. To begin with, recall the auction theory suggests that a bidders dominant strategy in a English auction is still to exit at the true value Vi even in the presence of probability mass at v and regardless of the assignment rules when more than one biddersprivate values tie at v. 1.1 Identi
cation For any generic integrable function g, we use R v g(s)ds and R r g(s)ds as shorthands for the improper integrals limv"v R v g(s)ds and limv#r R v g(s)ds respectively. Let!(k;i) denote expected utility for bidder i conditional on paying entry cost k and potential competitors entering with probabilities i = (j)j2Nnfig (1;:; i1; i+1;:; N). Under Assumption M1,!(k;i) u(k)FV jk(r) +