Intro Theory Empirics Empirics Primary Dealership References

Academic Perspectives on The Design of Treasury

Auctions

Ali Horta ̧csu, University of Chicago

Workshop on Auction Dynamics, November 16, 2012
Intro Theory Empirics Empirics Primary Dealership References

Multiple (Discriminatory) vs. Uniform price auctions





 









 

























(a) Discriminatory auction

Market clearing

price

Aggregate Bid Function

Supply

Quantity

Price

(b) Uniform price auction

Aggregate Bid Function

Supply

Quantity

Price

Market clearing

price
Intro Theory Empirics Empirics Primary Dealership References

Different contexts....

Most countries use multiple price (39 of 43)

U.S. (as of Dec. 1998), Switzerland, Denmark, Nigeria use

uniform

6 countries experimented with uniform but reverted to

discriminatory (Mexico, France, Italy, Belgium, Gambia,

Tanzania)

Source: Survey by Bartolini and Cottarelli (1997)
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Different perspectives....

“Uniform price auctions can allow the Treasury to make

improvements in the efficiency of market operations and

reduce the costs of financing the federal debt.” Lawrence

Summers, October 27, 1998.

“California’s deregulation scheme is a colossal and dangerous

failure. (...) overhaul the crazy bidding process for electricity,

which currently guarantees that every generator is paid

according to the highest bid, rather than their own bid.” Gov.

Gray Davis, January 8, 2001.
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Bidders don’t know the price where market will clear

0 0.05 0.1 0.15

83.5

84

84.5

85

Quantity as % of total supply / Frequency of market clearing price

Price
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Equivalently, bidders don’t know the residual supply curve

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

83.5

84

84.5

85

85.5

Quantity −− % of total supply

Price

Residual supply faced by bidder 2

Residual supply

Bidder 2 
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Wilson (1979) model of bidding

In multiple price auction:

p(q)

|{z}

bid for q units

= v (q)

|{z}

marginal val for q units

−

H(p, q)

∂H(p,q)

∂p

| {z }

“shading” factor

In uniform price auction:

p(q)

|{z}

bid for q units

= v (q)

|{z}

marginal val for q units

−q













∂H(p,q)

∂y

∂H(p,q)

∂p













| {z }

“shading” factor
Intro Theory Empirics Empirics Primary Dealership References

Insights from Wilson (1979)

In both auctions, bidders have incentive to “shade” their bids

Shading depends on how “pivotal” a bidder thinks her bids

are in terms of affecting market clearing price

Both auction formats lead to inefficiencies in allocation (i.e.

some winners will have lower value than some losers)

If ability to shade optimally is costly, then larger, more

sophisticated bidders are favored

It is not possible to say which auction format is going to yield

higher revenue based on theory alone

Multiple Price <> Uniform Price
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Winner’s curse

Fear of winning the auction because you made the most

optimistic forecast

Rational bidders shade against this possibility

Probably a very important issue for IPO bidders (e.g.

Groupon, Facebook)

Are Treasury securities subject to a winner’s curse?

Theory gives some intuition that uniform price auctions may

lower winner’s curse

Less fear about bidding too high, because you do not pay your

bid

Multiple Price < Uniform Price
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Theory bottomline

Relative revenue/efficiency performance of multiple vs.

uniform price is largely an empirical question

Even if theory were to make clean predictions, results assume

that bidders behave optimally

“Behaving optimally” in both auction formats is a

mathematically and computationally daunting task: thus both

formats have a skew towards large/experienced bidders with

the resources to optimize behavior
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Empirical Studies I

Ideal approach would be to randomly pick auction mechanism

every time, and compare outcomes, especially revenues –

controlling for external factors affecting demand.

Feasible approach has been to analyze changes in auction

mechanism

Umlauf (1993): Mexico, uniform ¿ multiple

Simon (1994): US Treasury, 1970s switch, uniform ¡ multiple

Nyborg and Sundaresan (1996), Malvey and Archibald (1998):

US Treasury, 1990s switch, uniform ¿ multiple, but not

statistically significant

Due to idiosyncracies of each market, it is not easy to

generalize the result of one empirical study to another setting
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Empirical Studies II

Unfortunately, in many other settings, we do not have a policy

change to analyze

However, we do have access to detailed data from current

mechanism

In the structural approach (Horta ̧csu and McAdams (2010),

Kastl (2010)), use bid data from current mechanism to fit

model, then predict what bidders would do under the

alternative mechanism

Main assumption: bidders follow optimal strategies

Main result: revenue differences across multiple price and

uniform price auctions not large (data from Turkey, Czech

Republic, South Korea)

Again, however, the result is context-dependent
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Step 1: use Wilson equations to estimate marginal values

from bids

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

83.5

84

84.5

85

85.5

86

Quantity as % of total supply

Price − TL

Bid of bidder #2 

Point estimate of marginal valuation 

Upper/lower envelope of marginal valuation
Intro Theory Empirics Empirics Primary Dealership References

Step 2: predict revenue under alternative mechanism

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

83.5

84

84.5

85

85.5

86

Price

Quantity as % of total supply

Aggregated upper envelope of estimated marginal valuations

Aggregated bids 
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Best Practice?

If data from policy experiment available, analyze that

Otherwise, use data on bids to conduct structural analysis

Do bidders follow economic theory: large bidders get very

close; but smaller bidders depart from theory (Horta ̧csu and

Puller (2008))
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Primary Dealership Model

Not much systematic analysis in the Treasury auction context

We know from other industrial settings that

retailers/distributors can add considerable value esp. through

knowledge of local demand, but downstream margins restrict

the market

To the extent that large customers (e.g. institutional

investors, sovereigns) have to bid through PDs, PDs also have

informational advantage

Hortacsu and Kastl (2012) find that in Canada about a third

of PD profits attributable to information flow from large

customers

For further analysis of PD mechanisms we need data on both

PD bids/allocations, and what they do in the aftermarket
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Papers cited:

Wilson, R., “Auctions of shares,” Quarterly Journal of

Economics, 1979, 675-689.

Umlauf, S., “An empirical study of the Mexican treasury bill

auctions”, Journal of Financial Economics, 1993, v.33,

313-340.

Simon, D., “The Treasury’s experiment with single-price

auctions in the mid 1970’s: winner’s or taxpayer’s curse?”,

Review of Economics and Statistics, 1994, v. 76, 754-760.

Nyborg, K. and S. Sundaresan, “Discriminatory versus uniform

treasury auctions: evidence from when-issued transactions”,

Journal of Financial Economics, 1996, v. 42, 63-104.

Malvey, P. and C. Archibald, “Uniform price Auctions: update

of the Treasury experience”, Technical Report, Department of

The Treasury, October 1998.
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Papers cited (cont.):

Hortacsu, A., and D. McAdams, “Mechanism choice and

strategic bidding in divisible good auctions: An empirical

analysis of the Turkish treasury auction market”, Journal of

Political Economy, 2010, v. 118, 833-865.

Kastl, J. “Discrete bids and empirical inference in divisible

good auctions”, Review of Economic Studies, 2010, v. 78,

978-1014.

Hortacsu, A. and S. Puller, “Understanding strategic bidding

in multi-unit auctions: a case study of the Texas electricity

spot market”, RAND Journal of Economics, 2008, v. 39,

86-114 .

Hortacsu, A. and J. Kastl, “Valuing dealers’ informational

advantage: a study of Canadian treasury auctions”,

forthcoming, Econometrica.