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International Monetary Fund and Board of Governors of the Federal Reserve System, respectively. The views expressed are our own and do not necessarily reflect the views of our institutions. We wish to thank Leonardo Bartolini and Paul Masson for helpful comments and Greg Belzer for excellent research assistance.
Discriminatory- and uniform-price formats refer to auctions of multiple units. When a single item is being auctioned, the corresponding terminology is to first- and second-price formats, respectively. Reinhart (1992) and Feldman and Mehra (1993) discuss the confusing terminology applied to different auction formats in the academic literature and in the popular financial press.
Umlauf (1994) provides an interesting evaluation of that first shift. His results suggest a higher average selling price (lower borrowing cost) for these securities by switching to the uniform-price setup.
A study by Bartolini and Cottarelli (1994), which details the techniques used by various governments to auction government liabilities, finds that in auctioning such securities the discriminatory-price format is in much greater use than the uniform-price format. Kovanen (1994), in summarizing the various auction arrangements that have been employed by developing countries to allocate foreign exchange, finds that both uniform-price and discriminatory-price formats have been prevalent. Tenorio (1993) provides useful analysis of the switch between these two formats in the foreign exchange auctions in Zambia. His conclusions suggest that uniform-price auctions yielded significantly greater revenue.
Participants were allowed to submit multiple bids.
Other forums for selling gold, such as the London gold fixing (described in O’Callaghan (1993)), employ multiple rounds of bidding, with participants in a single room bidding in public, or connected by phone. Awards can be made at prices that are progressively lowered until the fixed amount of gold to be auctioned is sold--a descending-price (Dutch) auction; alternatively, prices can be progressively increased until arriving at a single price that just exhausts the fixed amount to be auctioned--an ascending-price (English) auction. This terminology follows the pioneering work of Vickrey (1961), and along with the sealed-bid, uniform-price (also termed second-price when a single item is being auctioned) and discriminatory-price (first-price for a single item) auction formats completes the four primary types of auctions distinguished in Vickrey’s work.
Some of the complications introduced by the more accurate assumption that there are multiple units for sale are discussed in Weber (1983).
And because bidders are symmetric, the same function applies across all n participants so that we do not have to index by individual.
In all the empirical work that follows, U.S. dollar bids at the auction will be converted into relative prices by dividing by the secondary market price of gold from the previous day. This helps to control the substantial variation on gold prices over the period. Given the substantial upward trend to gold prices over the period, we compare the uniform price auctions, which were concentrated early in the sample, with both the first 10 and remaining 25 discriminatory-price auctions.
An example when F(«) follows a uniform distribution is provided in V. Smith (1989).
As has already been noted, dollar prices have been converted into relative prices by dividing by the secondary market price of gold from the previous day. When pooling across auctions (where the amount sold varied from 444,000 ounces to 780,000 ounces), we divided the quantity bid by the auction stock.
It might help the geometric intuition to think of the distribution functions in the upper and lower panels as demand curves plotted with the axes reversed and the quantity scale inverted. In other words, the corresponding demand curves plotted in the (q,p) quadrant would look like those panels if the origin were given at the upper left of each panel--turn Figure 3 counter clockwise for one quarter rotation. Viewed that way, we see that the actual demand curve lies inside of the optimally chosen one.