Pay-as-bid auctions in theory and practice

Abstract

The pay-as-bid auction, also called the discriminatory price auction, is among the most common auction formats to price and allocate assets and commodities. Trillions of dollars each year are traded in pay-as-bid auctions. The format is the natural multiunit extension of the first-price auction of a single item. Bidders specify a price for each unit they want to buy. The market clears at the price where supply intersects aggregate demand and winning bidders pay their bids for each unit won. In the first chapter of my thesis, I explain strategic differences and similarities between the single-item and multi-unit case. In practice, it is rare that multi-unit auctions take place in isolation. The second chapter introduces a model of interconnected pay-as-bid auctions. The auctions run in parallel and offer perfectly divisible substitute goods to the same set of symmetrically informed bidders with multi-unit demand. This connects the demand side of both auctions. The supply side is linked because the total amounts for sale may be correlated. I show that there exists a unique symmetric Bayesian Nash equilibrium when the marginal distributions of supply have weakly decreasing hazard rates. I then develop practical policy recommendations on how to exploit the interconnection across auctions to increase revenues. These theoretic insights are the basis for the final chapter of my thesis. In collaboration with Jason Allen (Bank of Canada) and Jakub Kastl (Princeton University) I use data from auctions of Canadian debt to quantify the extent to which demands for securities with different maturities are interdependent. Generalizing methods for estimating demand schedules from bidding data to allow for interdependencies, our results suggest that 3, 6 and 12-month bills are often complementary in the primary market for Treasury bills. We present a model that captures the interplay between the primary and secondary markets to provide a rationale for our findings.