Nonparametric Identification and Estimation of k-Double Auctions

Open Access
Author:
Li, Huihui
Graduate Program:
Economics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
May 03, 2016
Committee Members:
  • Joris Pinkse, Dissertation Advisor
  • Joris Pinkse, Committee Chair
  • Sung Jae Jun, Committee Member
  • Peter Newberry, Committee Member
  • Runze Li, Outside Member
  • Sung Jae Jun, Dissertation Advisor
Keywords:
  • Double Auctions
  • Bargaining
  • Nonparametric Identification
  • Kernel Estimation
  • Boundary Correction
Abstract:
This dissertation consists of two chapters on nonparametrically identifying and estimating the sealed-bid k-double auction models between single buyer and single seller. Chapter 1: Nonparametric Identification and Estimation of k-Double Auctions Using Bid Data This chapter studies the nonparametric identification and estimation of double auctions with one buyer and one seller. This model assumes that both bidders submit their own sealed bids, and the transaction price is determined by a weighted average between the submitted bids when the buyer’s offer is higher than the seller’s ask. It captures the bargaining process between two parties. Working within this double auction model, we first establish the nonparametric identification of both the buyer’s and the seller’s private value distributions in two bid data scenarios; from the ideal situation in which all bids are available, to a more realistic setting in which only the transacted bids are available. Specifically, we can identify both private value distributions when all of the bids are observed. However, we can only partially identify the private value distributions on the support with positive (conditional) probability of trade when only the transacted bids are available in the data. Second, we estimate double auctions with bargaining using a two-step procedure that incorporates bias correction. We then show that our value density estimator achieves the same uniform convergence rate as Guerre, Perrigne, and Vuong (2000) for one-sided auctions. Monte Carlo experiments show that, in finite samples, our estimation procedure works well on the whole support and significantly reduces the large bias of the standard estimator without bias correction in both interior and boundary regions. Chapter 2: Nonparametric Identification of k-Double Auctions Using Price Data This chapter studies the model identification problem of k-double auctions between one buyer and one seller when the transaction price, rather than the traders’ bids, can be observed. Given that only the price data is available, I explore an identification strategy that utilizes the double auctions with extreme pricing weight (k=1 or 0) and exclusive covariates that shift only one trader’s value distribution to identify both the buyer’s and the seller’s value distributions nonparametrically. First, as each exclusive covariate can take at least two values, the buyer’s and the seller’s value distributions are partially identified from the price distribution for k=1 or k=0. The identified set is sharp and can be easily computed. I provide a set of sufficient conditions under which the traders’ value distributions are point identified. Second, when the exclusive covariates are continuous, it is shown that the buyer’s and the seller’s value distributions will be uniquely determined by a partial differential equation that only depends on the price distribution, provided that the value distributions are known for at least one value of the exclusive covariates.