Another job market season is in the books, as Brad Larsen was the last job talk I made it to this year. Here’s something you may not have known: there is an industry which sells lots of used cars at auctions. Each year, they sell eighty billion dollars worth of cars at these auctions! I’ve written auction theory papers before, and yet have never even heard of this industry. The complexity of economics never fails to impress, but this is good; it means there is always something interesting for us economists to study.
Now when you hear “inefficient bargaining” and “autos”, you probably immediately think of Stiglitz’ lemons model. But selection really isn’t a big issue in these used-auto auctions. Car rental agencies that participate, for instance, sell off an entire season of cars all at once. The real inefficiency is of the Myerson-Satterthwaite type. In that classic result, your private value for a good and my private value for a good are drawn from overlapping distributions – and “draw” and “distribution” may be over the set of all possible buyers or sellers as in Harsanyi purification – then there is no price at which we would agree to a transaction. (You must know Myerson-Satterthwaite! Among other things, it absolutely destroys the insight behind the Coase theorem…) Myerson and Satterthwaite, as well as a handful of other others, later fully described the second-best mechanism when first-best trade is impossible. This second-best mechanism turns out to be quite complicated. Almost all of the auto auction houses use a seemingly strange mechanism instead. First, sellers set a secret reserve which is told to the auctioneer. Then the car is sold in an English auction. If the auction ends below the reserve price, then sellers and potential buyers can opt to bargain individually over the phone, perhaps asynchronously. At the end of these bargains, there are still many cars that go unsold.
This brings up the obvious question: how close to the second-best optimum is this strange selling mechanism? Larsen got access to some amazing data, which included outcomes of the auction, all of the sequential offers made over the phone, seller secret reserve prices, and tons of data at the level of the car and the buyer. The problem, of course, is that we don’t have access to the seller and buyer types (i.e., their private valuations of the car). Indeed, we don’t even have knowledge of the distribution of their types. If you are a regular reader of this blog, you know what is coming next – we can perhaps back out those distributions, but only if theory is applied in a clever way. (And, wow, how are job market speakers not permanently nervous? It’s one thing to stretch the Myerson-Satterthwaite framework to its limits, but it’s another thing to do so when Mark is sitting in the front row of the seminar room, as was the case here at Kellogg. Luckily, he’s a nice guy!)
The high bid in the auction helps us get buyer valuations. This high bid is, if bidders bid truthfully, equivalent to the second-order statistic of bidder values. Order theory turns out to give us a precise relationship between the underlying distribution and distribution of draws of its second-order statistic (when the second order is from a set of N draws from the distribution). Larsen knows exactly how many people were at each auction house, and can use this to roughly estimate how many bidders could potentially have bid on each car. Homogenizing each car using observable characteristics, therefore, the order statistic method can be used to gather the underlying distribution of buyer values for each car.
On the seller side, it is the secret reserve price that really helps us estimate the bargaining game. If the post-auction bargaining never results in a price lower than the last bid, then bidders have a dominant strategy to bid truthfully. Costly bargaining in addition to truthful bidding by buyers means that the optimal seller reserve price must be strictly increasing in the seller’s type. And what does strict monotonicity give us? Invertibility. We now know there is a link between the seller reserve price and the seller type. The structure of post-auction bargaining helps us to bound the relationship between seller type and the reserve. Finally, multiple rounds of bargaining let us bound the disutility costs of bargaining, which turn out to be quite small.
So how does the auto auction bargaining mechanism do? In this market, given the estimated type distributions, the Myerson-Satterthwaite second-best gives you 98% of the surplus of a first-best (informationally impossible) mechanism. Real-world dynamic bargaining captures 88-96% of that second-best surplus, with the most inefficiency coming from small sellers where, perhaps, screening problems result. That’s still leaving money on the table, though. Larsen, among others, suggests that these types of strange dynamic mechanisms may persist because in two-sided markets, they roughly are equivalent to committing to giving buyers a large chunk of the gains from trade, and we know that attracting additional potential buyers is the most important part of successful auctions.
January 2013 working paper (No IDEAS version).