View original document

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

July 1997

Volume 3 Number 9

Designing Effective Auctions for Treasury Securities
Leonardo Bartolini and Carlo Cottarelli

Most discussions of treasury auction design focus on the choice between two methods for
issuing securities—uniform-price or discriminatory auctions. Although auction theory and
much recent research appear to favor the uniform-price method, most countries conduct their
treasury auctions using the discriminatory format. What are the main issues underlying the
debate over effective auction design?

The widespread growth of public debt in industrial
countries in the 1980s has intensified policymakers’
concern with implementing effective methods to sell
government securities. Treasury auctions—in which a
government sells securities to finance its debt—are a
natural, but often overlooked, candidate for institutional
reform. By broadening participation in treasury auctions
and increasing auction revenues, governments could
potentially save millions of dollars.
Consider, for example, the savings that might be
realized by a country auctioning $1 trillion of securities
annually. (In recent years, the U.S. Treasury has auctioned
more than $2 trillion of marketable securities annually.) If a
more cost-effective design could be identified and adopted,
each 0.01 percent reduction in auction yields achieved
through the design change would lower that country’s
annual federal deficit by more than $100 million.
In this edition of Current Issues, we examine the two
main auction methods in use today to issue treasury
securities—discriminatory and uniform-price auctions.
Drawing on the theory of auction design and the empirical
findings of earlier researchers, we discuss the revenue
potential of these two auction methods and their vulnerability to noncompetitive behavior by bidders. We then
compare researchers’ views of the two methods with the
actual practices of forty-two countries holding auctions of

treasury securities. Surprisingly, while much of the literature suggests that uniform-price auctions may outperform discriminatory auctions in producing revenues
for treasuries and limiting the scope for noncompetitive
behavior, most countries conduct their treasury auctions
using the more traditional discriminatory format. This
split between theory and practice is likely to lead to
increased experimentation with new auction formats in
the next several years.
Discriminatory and Uniform-Price Auctions
Most treasury auctions fall into one of two categories: discriminatory auctions or uniform-price auctions.1 In both
types of auction, the winning bids are the highest bids that
exhaust the whole issue on sale. In a discriminatory auction,
however, all winners pay their own bids, while in a uniformprice auction all winners pay a uniform price. This uniform
price, the lowest price that exhausts the auction supply, is
set at one price unit above the highest losing bid. For
instance, suppose that at an auction for two one-dollar
treasury bills, participants A, B, C, and D bid $0.99,
$0.97, $0.96, and $0.92, respectively, for a single bill. A
discriminatory auction would award one bill to A for a
charge of $0.99 and one bill to B for a charge of $0.97. By
contrast, a uniform-price auction would award the bills to
A and B for a common charge of $0.97.


counter the risk of incurring a loss in the secondary market
for the security.

Recently, the relative merits of these two types of
auction have been under review. Since introducing its
auctions for bills in 1929, the U.S. Treasury has used a
discriminatory method to auction most of its securities
(except for a short period—in 1973-74—when uniformprice auctions were held for long-term securities). In
September 1992, however, the Treasury began to auction
two- and five-year notes using a uniform-price method.
Similar initiatives were undertaken in Mexico, Italy, and
other countries in recent years.

The Winner’s Curse and the Choice of Auction Method.
Much of the theoretical research on auctions has focused
on determining the auction method that better mitigates the
downward bias caused by the winner’s curse. A useful
introduction to this literature is provided by the early work
of Vickrey (1961), which examines private-value auctions
of a single object with risk-neutral bidders. Vickrey shows
that discriminatory and uniform-price auctions under these
conditions would yield the same revenue.

Revenue Implications of Treasury Auction Design
An important criterion in evaluating auction methods is
their effectiveness in maximizing revenues. To assess how
well the discriminatory and uniform-price methods meet
this criterion, we first need to consider the incentives facing
auction participants.

At first glance, this conclusion may seem surprising—
in a uniform-price auction, all winners pay the same low
bid, whereas in a discriminatory auction, winners appear
to pay a higher amount, namely their own bid. In a discriminatory auction, however, the bidder that values the
object on sale most would not bid its own valuation: a bid
just slightly above the second-highest valuation would
win the auction. By bidding just enough to overwhelm the
second-highest valuation, the bidder can win the auction
by paying the same price it would have paid in a uniformprice auction. As a result, the auctioneer’s effort to extract
the surplus below the demand curve by charging all parties
their own bids is frustrated by a downward shift in the
demand curve itself.3 Hence, in this type of private-value
auction, auctioneers can expect to earn the same revenue
from discriminatory and uniform-price auctions.

Downward Bias in Bids. Most discussions of incentives in
the auction literature underscore an important difference
between treasury auctions and other varieties of auctions.
Treasury auctions, a type of common-value auction,
involve the sale of items whose post-auction value is
essentially the same for all participants; the value is equal
to the secondary-market price of the security. This type of
auction contrasts with private-value auctions, in which
each participant’s valuation of the object on sale is relatively independent of other participants’ valuations (as in,
for example, the auctions of goods purchased for private
consumption, such as artwork or antiques).2

The same is not true, however, for common-value
auctions such as those of treasury securities. In this type of
auction, bidders attempt to forecast the same post-auction
price, causing the revenue equivalence of the discriminatory and uniform-price methods to break down. Aware of
the winner’s curse, bidders will tend to lower their bids to
avoid losses, and an auctioneer can expect some downward pressure on revenues, whether the auction is discriminatory or uniform-price. The question then arises:
Which of the two methods is likely to cause participants
to shade bids downward to a greater extent?

Unlike participants in a private-value auction, participants in treasury auctions are likely to agree on the
security’s value after the auction is completed, when the
resale value is determined in the secondary market for the
security. Nevertheless, they are likely to have different
information—or hold different beliefs—about the security’s
value before the auction takes place. This difference
influences the outcome of the auction in a crucial way. A
bidder that wins the auction by placing the highest bid is
effectively making an above-average assessment of the
resale price (or “true” value) of the security—a fact that
raises the likelihood of a loss in the post-auction market.

The answer is discriminatory auctions. Because in this
format winners pay their own bid, they are charged fully
for their errors in overassessing the object’s resale value.
In contrast, in uniform-price auctions winners pay a
price—close to the highest losing bid—that reflects, to
some extent, other bidders’ view of the object’s value.
This feature lowers the winners’ risk of paying a price that
far exceeds consensus and hence encourages more aggressive bidding. Thus, as a means of maximizing revenues, the
uniform-price method is likely to outperform the discriminatory method in treasury auctions because it is less vulnerable to the winner’s curse.

Suppose, for example, that the resale price of the security in our earlier example settles at the average valuation
attached to it by the four bidders, or $0.96. In a discriminatory auction, bidder A, which placed the highest bid at
$0.99, would incur a loss of $0.03 for each security. In
contrast, in a uniform-price auction, bidder A would pay
$0.97 and thus incur a loss of $0.02 for each security. Thus,
with either method, winning involves a loss if auction
participants ignore the risk involved in placing bids that
exceed consensus. This “winner’s curse” will cause auction
participants to shade their bids downward relative to their
subjective assessment of the security’s resale value to


As we have noted, the strength of the winner’s curse
rests largely on bidders’ uncertainty about a security’s


resale price. One way a treasury can reduce uncertainty is
by fostering the development of secondary markets and
forward (or “when-issued”) markets for treasury securities,

ior? Unfortunately, there is no clear answer. The argument
put forward by Milton Friedman in his 1959 testimony
before the Joint Economic Committee and reiterated by
him in subsequent years is that the simplicity of uniformprice auctions could reduce participants’ costs of preparing
bids, broaden their participation in auctions, and reduce
incentives to funnel bids through brokers, thus narrowing
the scope for brokers to collude and corner markets
(Friedman 1959, 1991).

As a means of maximizing revenues, the
uniform-price method is likely to outperform
the discriminatory method in treasury auctions
because it is less vulnerable to the winner’s curse.

Other researchers, however, have claimed that uniform-price auctions may be more vulnerable to such
behavior because they provide fewer incentives for ring
members to deviate from the agreed-upon strategy.4 To
understand this viewpoint, consider again the simple case of
a uniform-price auction for a single object. A ring formed
among bidders could designate a ringleader whose task
was to post an overly high bid so as to win the auction on
behalf of the ring. In turn, all other ring members would
be required to post very low bids so as to keep low the
price charged the ringleader. With this agreement in place,
ring members would have no incentive to break the ring to
win the auction on their own account; to do so they would
have to top the ringleader’s bid, then pay slightly more
than the ringleader’s bid to purchase the object, thus
incurring a loss. For the same reason, bidders outside the
ring could not win the auction except at a loss.5

where investors share views about a security’s present and
future value. The publication of auction results can also
lessen bidders’ uncertainty about the behavior of their competitors and of the treasury, especially when the treasury
takes an active role in the auction (for instance, by setting
undisclosed cutoff prices below which it will not award the
securities). We return to this theme later in our analysis.
Noncompetitive Behavior in Treasury Auctions
A second consideration in evaluating auction methods
is their vulnerability to noncompetitive bidding behavior. Lack of competition is likely to reduce investors’
participation in a treasury auction and restrict a security’s
supply in the secondary market, preventing that security’s
efficient allocation among investors. In the United States,
concern over this issue rose sharply in the spring of 1991
when Salomon Brothers effectively violated the 35 percent limit set by the Treasury for each bidder. By controlling the awards for itself and its customers, Salomon gained
control of 94 percent of a U.S. Treasury Department twoyear note auction (see U.S. Treasury Department et al.

In contrast, these researchers argue, collusion is more
difficult to sustain in discriminatory auctions. In these
auctions, the only way for a ring to make substantial profits would be to instruct all its members to tender bids

Noncompetitive behavior in auctions
for government securities arises when a single
broker, or a ring of brokers, attempts to gain an
unfair—and illegal—competitive advantage in
either the primary auction market or in the
subsequent secondary market for the security.

Noncompetitive behavior in auctions for government
securities arises when a single broker, or a ring of brokers,
attempts to gain an unfair—and illegal—competitive
advantage in either the primary auction market or in the
subsequent secondary market for the security. For
instance, a few brokers may collude to gain sufficient
market power to win the auction with a lower than competitive bid. Alternatively, a single broker or a ring of brokers
may try to overwhelm the competition by tendering a
higher than competitive bid in the primary market. In this
case, the broker’s ultimate goal would be to gain control of
the secondary market, where huge profits can be realized by
“cornering” those investors that sold the security forward
before the auction and are thus committed to purchasing it
back in the secondary market.

below the security’s true value (higher bids would
increase the price charged to winners and erode the
ring’s profits). This behavior would expose the ring to
profitable, collusion-breaking bids that exceed the ring’s
agreed-upon bid.
As we see, the guidance provided by the theoretical literature on the best auction method is not unambiguous.
Disagreement exists over which auction method is the
more resistant to noncompetitive behavior. Furthermore,

Of discriminatory and uniform-price auctions, which
is likely to be more susceptible to noncompetitive behav-



certain general features of auctions, such as bidders’ aversion to risk, and some specific features of treasury auctions—most notably, the fact that they involve the sale of
multiple units of homogeneous securities—make the
application of theoretical models to actual treasury auctions
difficult. Nonetheless, the view that uniform-price auctions
should outperform discriminatory auctions in boosting
revenues clearly predominates in the theoretical research.6

The empirical evidence relating to other types of auctions also favors the uniform-price method over the discriminatory method. Feldman and Reinhart (1995) study
the International Monetary Fund’s auctions of gold from
1976 to 1980—a sample consisting of thirty-five discriminatory auctions and ten uniform-price auctions. The
authors find that revenues from the uniform-price auctions
are significantly higher than revenues from the discriminatory auctions. By studying Zambia’s weekly auctions of
foreign exchange from 1985 to 1987—conducted first with
a uniform-price method and then with a discriminatory
method—Tenorio (1993) also concludes that uniform-price
auctions yield greater revenues and achieve broader
investor participation than discriminatory auctions.

Empirical Evidence on Auction Methods
According to some researchers, the empirical analyses of
auctions cast an even stronger vote in favor of uniformprice auctions as the more effective method. Evidence
from the U.S. Treasury’s experiment with uniform-price
auctions in the 1973-74 period, for example, suggests that
the U.S. Treasury may have increased revenues from auctions of long-term securities by up to 0.75 percent.7 This
evidence remains controversial, however, because it relies
largely on data from the August 1973 auction, which was
undersubscribed and which awarded a large portion of
the security to U.S. government accounts.8 Nevertheless,
other evidence supports the finding that uniform-price
auctions lead to a rise in revenues. Umlauf (1993), for
instance, studies the Mexican Treasury’s experience with
uniform-price auctions from 1990 to 1993. Comparing
returns from these auctions with returns from discriminatory auctions held from 1986 to 1991, he finds evidence
of higher revenues from the uniform-price method.

Overall, empirical research on auctions appears to narrow the gap left by more theoretical research on auctions:
uniform-price auctions may indeed allow a treasury to
finance its debt at a lower cost. If this conclusion about
the relative performance of uniform-price and discriminatory auctions is accurate, however, we would expect most
treasuries to favor the use of uniform-price auctions over
discriminatory auctions. Do the auction practices of treasuries around the world conform to this expectation?
Cross-Country Evidence on the Design of Treasury
To find the answer, we surveyed the auction practices of
seventy-seven countries in early 1994 (the latest date
for which we had access to comparable cross-country
information). We restricted our analysis to auctions of
treasury bills, the most common security issued worldwide. We collected detailed country-specific information
from government publications, local treasury officials, and
the International Monetary Fund.9 Industrial countries
(including all Group of Seven countries) made up onequarter of our sample; developing and transition countries
made up the remaining three quarters (see Table 1).
Treasury auctions were used in forty-two (slightly more
than half) of our sample countries. Other, more informal
methods of selling treasury securities—such as over-thecounter, or “on tap,” sales—were used mostly by the
developing and transition countries.

Other studies reach a similar conclusion in a more
indirect way—by measuring the spread between auction
prices and secondary market or forward prices of a security.
A negative spread suggests that bidders are responding to
the winner’s curse. Following this methodology,
Cammack (1991) finds that from 1973 to 1984, auction
prices of U.S. Treasury bills were four basis points
smaller than their contemporaneous secondary-market
prices. She also finds that, consistent with the predictions
of auction theory, the gap between auction and secondary
market prices increases as investors become more uncertain about the future price of the security. Researchers on
the U.S. Treasury staff turn up similar results for discriminatory auctions held in 1991-92 (Malvey, Archibald, and
Flynn 1995). They find that yields from these auctions
significantly exceeded their contemporaneous forward
yields but do not uncover similar evidence for the uniformprice auctions held in 1992-95. To be sure, this evidence
is difficult to interpret because of the greater volatility
exhibited by revenues in the uniform-price auctions. The
Treasury also found, however, that the uniform-price
method broadened the public’s participation in treasury
auctions. In light of its findings, the Treasury decided to
extend the uniform-price experiment for two- and fiveyear note auctions indefinitely.

Table 1

Composition of Sample

Total number
of countries
Number of countries
with auctions



Developing Transition
Countries Countries









Sources: International Monetary Fund; information gathered from country
sources; authors’ calculations.



Table 2

secretive about auction results: 30 percent did not publish
the lowest winning bids, 46 percent did not publish the minimum bid accepted at the auction, and 83 percent did not
publish the number of bids or bidders in the auction. At the
time of the survey, the United States published more
information than any other country in the sample.

Prevalence of Auction Techniques
Number of Countries
Bidding Method









Interest in the design of treasury auctions has intensified
in recent years, reflecting both the need to devise more
effective strategies to finance large public debts and the
desire to minimize noncompetitive behavior in auctions. To
assess the relative merits of the uniform-price and discriminatory auction methods, the U.S. Treasury began
using uniform-price auctions for the sale of two- and fiveyear notes in 1992. Although early evidence from the
Treasury’s experience with uniform-price auctions is far
from clear-cut, it has encouraged the Treasury to continue
its initiative with this group of securities.

Sources: International Monetary Fund; information gathered from country
sources; authors’ calculations.

Our survey of auction techniques in the forty-two
countries using auctions indicated that discriminatory
auctions were by far the most common—90 percent of the
sample relied on this method (Table 2). Denmark and
Nigeria were the only two countries using uniform-price
auctions. Spain used a mixed uniform-discriminatory format in which bidders posting less than average bids were
charged their bid, while remaining bidders were charged a
uniform average bid. Interestingly, six countries—
Belgium, France, Italy, Gambia, Mexico, and Tanzania—
had used uniform-price auctions in the past but returned
to discriminatory auctions before the survey was taken.
We found no occurrence of a permanent shift from discriminatory to uniform-price auctions.

Further experimentation with treasury auction design,
particularly in countries where the need for a cost-effective
allocation of public debt is even more acute than in the
United States, is warranted. While much of the research on
auctions appears to favor the uniform-price method, discriminatory auctions are overwhelmingly prevalent worldwide. This contrast between theory and practice raises
challenges for both scholars and policymakers: On the
one hand, researchers of auctions may need to consider the
disparity between their findings and the actual conduct of
treasury auctions worldwide. More accurate and comprehensive models of treasury auctions may emerge from this
appraisal. Policymakers, on the other hand, may need to
reevaluate the effectiveness of the auction formats in use
in their countries. Only further direct evidence on the performance of auction methods is likely to reveal the best
course for government treasuries to take.

The data also point to a contrast between theory and
practice regarding the publication of auction outcomes. As
noted earlier, research suggests that auctioneers in common-

Our survey of auction techniques in the
forty-two countries using auctions
indicated that discriminatory auctions were
by far the most common—90 percent
of the sample relied on this method.

1. The term “discriminatory” reflects the choice involved in charging different prices to different bidders. When a single object is on
sale, discriminatory auctions are also known as first-price auctions;
under the same conditions, uniform-price auctions are sometimes
called second-price auctions.

value auctions would benefit by publishing auction results.
Such efforts could help reduce investors’ uncertainty about
the behavior of their competitors and of the treasury itself in
future auctions and thus reduce uncertainty about future
auction outcomes. Of course, publishing too-detailed information on individual bids may make a ringleader’s task of
monitoring ring members’ behavior easier, broadening the
scope for collusion. Still, this consideration would not rule
out the publication of information on winning bids or on the
number of bids and bidders recorded in the auction. We
found most countries in our sample, however, to be rather

2. Treasury auctions often require bidders to tender yields or discounts rather than prices, so that the winning participants are those
tendering the lowest yields or the lowest discounts. This article does
not focus on this minor distinction and discusses auctions as if bids
were always tendered in terms of prices.
3. If a bidder does not know the other bidders’ valuations, it will try
to guess other bidders’ valuations and, if behaving rationally, will
make a correct guess on average.
4. See Milgrom (1987) and Back and Zender (1993) for a review of
these issues.




5. A limitation of many collusion models of auctions is that they focus
on collusive outcomes and overlook other possible outcomes. In the
example, for instance, a bidder outside the ring could try to disrupt the
ring’s quest by posting a bid between the ring’s high and low bids.
While this sort of collusion-disrupting behavior entails no immediate
gain for the ring breaker and thus cannot be relied upon, auctioneers
often adopt a similar strategy to mitigate collusion by posting cutoff
prices below which the objects are not sold.
6. See, for instance, the survey by McAfee and McMillan (1987).
7. For a discussion, see Friedman (1991).
8. See Malvey, Archibald, and Flynn (1995).
9. The full results of the survey are published in Bartolini and
Cottarelli (1997).

Back, Kerry, and Jaime Zender. 1993. “Auctions of Divisible
Goods.” Review of Financial Studies 6: 733-64.
Bartolini, Leonardo, and Carlo Cottarelli. 1997. “Treasury Bill
Auctions: Issues and Uses.” In M. Blejer and T. Ter-Minassian,
eds., Macroeconomic Dimensions of Public Finance, 267-336.
London: Routledge.
Cammack, Elizabeth. 1991. “Evidence on Bidding Strategies and
the Information Contained in Treasury Bill Auctions.” Journal of
Political Economy 99: 100-30.
Feldman, Robert, and Vincent Reinhart. 1995. “Flexible Estimation of
Demand Schedules and Revenue under Different Auction
Formats.” International Monetary Fund Working Paper no. 95/116.

Friedman, Milton. 1959. Testimony in Employment, Growth, and
Price Levels: Hearings before the Joint Economic Committee.
86th Cong., 1st sess. October 30.
Friedman, Milton. 1991. “How to Sell Government Securities.” Wall
Street Journal, August 28, p. A8.
Malvey, Paul, Christine Archibald, and Sean Flynn. 1995 “UniformPrice Auctions: Evaluation of the Treasury Experience.”
Washington, D.C.: U.S. Treasury Department.
McAfee, Preston, and John McMillan. 1987. “Auctions and
Bidding.” Journal of Economic Literature 25: 699-738.
Milgrom, Paul. 1987. “Auction Theory.” In T. Bewley, ed., Advances in
Economic Theory. 1-32. London: Cambridge University Press.
Milgrom, Paul, and Robert Weber. 1982. “A Theory of Auctions and
Competitive Bidding.” Econometrica 50: 1089-122.
Tenorio, Rafael. 1993. “Revenue Equivalence and Bidding Behavior
in a Multi-Unit Auction Market: An Empirical Analysis.” Review
of Economics and Statistics 75: 302-14.
Umlauf, Stephen. 1993. “An Empirical Study of the Mexican Treasury
Bill Auction.” Journal of Financial Economics 33: 313- 4 0.
U.S. Treasury Department, Securities and Exchange Commission,
and Board of Governors of the Federal Reserve System. 1992.
“Joint Report on the Government Securities Market.”
Washington, D.C.: U.S. Government Printing Office.
Vickrey, William. 1961. “Counterspeculation, Auctions, and
Competitive Sealed Tenders.” Journal of Finance 16: 8-37.

About the Authors
Leonardo Bartolini is a senior economist in the Bank’s International Research Function and
Carlo Cottarelli is a division chief in the European I Department of the International Monetary Fund.
The views expressed in this article are those of the authors and do not necessarily reflect the position of
the Federal Reserve Bank of New York or the Federal Reserve System.

Readers interested in obtaining copies of Current Issues in Economics and Finance through the Internet
can visit our site on the World Wide Web ( From the Bank’s research publications
page, you can view, download, and print any edition in the Current Issues series, articles from
the Economic Policy Review, and certain issues of Staff Reports. You can also view abstracts for Staff Reports
and Research Papers and order the full-length, hard-copy version of any paper in these series electronically.
Current Issues in Economics and Finance is published by the Research and Market Analysis Group of the Federal
Reserve Bank of New York. Dorothy Meadow Sobol is the editor.
Editorial Staff: Valerie LaPorte, Mike De Mott, Elizabeth Miranda
Production: Graphics and Publications Staff
Subscriptions to Current Issues are free. Write to the Public Information Department, Federal Reserve Bank of
New York, 33 Liberty Street, New York, N.Y. 10045-0001, or call 212-720-6134. Back issues are also available.