Nonparametric Identification of k-Double Auctions using Price Data∗

This paper 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 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, I show that because 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 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, I show 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.