Bid Shading and Bidder Surplus in U.S. Treasury

Auctions

Ali Horta ̧csu, Jakub Kastl, Allen Zhang

University of Chicago, Princeton University, U.S. Treasury

December 1, 2014

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U.S. Treasury Auction System

In 2013, U.S. Treasury auctioned 7.9 trillion dollars of debt

ODM charter: “Lowest cost of financing over time”

Auctions as sale mechanism

Discriminatory/pay-as-bid until 1998, since then: uniform price

How do (different classes of) bidders behave?

Do (some) bidders possess significant market power?

Could changes in mechanism lead to significant

revenue/efficiency gains?

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Bidder’s problem

3 / 20
Auction Data

Detailed bidding data from auctions between July 2009-Oct

2013

Data on 3 categories of bidders:

Primary Dealers

Direct Bidders

Indirect Bidders (they route bids through PDs)

4 / 20
Quantity Patterns

22 PDs purchase 63% of auction volume

Concentration measures:

HHI: 561 (bills), 450 (bonds) , C4: 21%, C10: 44%

Direct bidder share rising over time (especially for notes):

from almost less than 10% to 19%.

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Market shares over time

Bills 2009 2010 2011 2012 2013

PD 59% 65% 65% 69% 69%

Direct 7% 6% 9% 9% 8%

Indirect 34% 29% 26% 22% 23%

Notes 2009 2010 2011 2012 2013

PD 50% 49% 51% 50% 47%

Direct 9% 14% 13% 18% 19%

Indirect 41% 37% 36% 32% 34%

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What about bids?

PDs bid lower prices (higher yields) than Direct Bidders, who

bid lower than Indirect Bidders

The patterns clearer for note/bond auctions vs. bill auctions

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Bid Regressions

Bills Notes

(1) (2) (3) (4)

Dep. Var. QwBid(bp) QwBid(bp) QwBid(bp) QwBid(bp)

Direct -2.457*** -0.929*** -5.974*** -0.965***

(0.0580) (0.0600) (0.270) (0.314)

Indirect -4.204*** -2.529*** -10.89*** -4.437***

(0.0604) (0.0613) (0.356) (0.399)

%Q Total 10.04*** 61.75***

(0.219) (5.452)

Constant 13.87*** 11.99*** 172.0*** 165.0***

(0.0316) (0.0426) (0.261) (0.460)

Observations 41,359 41,359 13,692 13,692

R-squared (within) 0.254 0.289 0.086 0.099

No. of auctions 822 822 153 153

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How to interpret bid regressions

Quantity-weighted average bids lower for bidders who demand

higher quantity: this suggests that market power may play an

important role!

In any model we can think of writing:

BID = WTP − SHADING

How to decompose bids into strategic (shading) vs.

non-strategic (WTP/demand) components?

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With discrete bids - Kastl (REStud 2011)

E (P

c

|bk > P

c > bk+1)

| {z }

BID BY A PRICETAKER

= v (qk )

| {z }

WTP

−

qk

Pr(bk > Pc > bk+1)

∂E (P

c

; bk ≥ P

c ≥ bk+1)

∂qk

| {z }

MARKET POWER (SHADING)

This is very similar to the familiar monopoly pricing formula

P = MC − Q ∗ P

0

(Q)

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Intuition

Alternative expression: the inverse elasticity pricing formula

P = MC + 1

|ε|

∗ P

Typically, one recovers MC by estimating elasticity of demand,

utilizing variation in Q due to variation in P

In an auction, the relevant demand (supply) curve is made up

of bid schedules of other bidders, i.e. the “residual supply.”

Moreover, residual supply is random from perspective of each

bidder

Hence, bidder optimizes expected profit against the

distribution of the market clearing price (which is a function

of the residual supply curves)

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Estimation in the symmetric iid case (Horta ̧csu and

McAdams, JPE 2010)

We need the distribution of the market clearing price

Obtain this distribution by simulating residual supply

Draw with replacement (N − 1) bids from the observed bids,

add them up

Subtract from the supply and intersect thus obtained residual

supply with a bidder’s bid to obtain one possible market

clearing price.

Many such simulation draws will result in a distribution of the

market clearing price

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Resampling method

0 0.2 0.4 0.6 0.8 1

985.8

986

986.2

986.4

986.6

986.8

987

987.2

987.4

987.6

Resampling procedure for bidder 1

Quantity (fraction of total supply)

Price in 1000s

Actual bid function

Residual supply functions

985.8 986 986.2 986.4 986.6 986.8 987 987.2

0

200

400

600

800

1000

1200

1400

1600

1800

Histogram of p for bidder 1

Market clearing price (in 1000s)

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Modelling Challenges Posed by U.S. Treasury Auction

Context

Bidders are not symmetric. Clear differences in bid patterns

across groups.

Bidders have differential information

PDs observe the bids of their customer IBs.

Given customer/IB bids, PDs can make better forecasts of the

market clearing price distribution

Fortunately, we can incorporate this informational asymmetry

in our estimation method (treat IB bids as “known” and not

random from the perspective of PDs)

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Bid Updating by PDs (from Canadian Treasury Auctions,

Horta ̧csu and Kastl (ECMA 2013))

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

987.15

987.2

987.25

987.3

987.35

987.4

Quantity Share demanded

Price (Bid) (in 1000s)

Updating of Bids

Original dealer bid

Updated dealer bid

Customer bid

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Using the estimates to analyze strategic bid shading

Strategic Shading (in bp)

Bills Notes

(1) (2) (3) (4)

Direct -0.862*** -0.771*** -0.0954*** -0.0480***

(0.0727) (0.0884) (0.0103) (0.0105)

Indirect -1.125*** -1.025*** -0.122*** -0.0608***

(0.0813) (0.0978) (0.0116) (0.0129)

%Q Total 0.600* 0.584***

(0.330) (0.108)

Constant 1.174*** 1.062*** 0.125*** 0.0579***

(0.0441) (0.0756) (0.00883) (0.0122)

Observations 41,264 41,264 13,692 13,692

R-squared 0.015 0.015 0.062 0.069

No. of auctions 822 822 153 153

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How does the uniform price auction do?

With our estimates of bidders’ values, we can answer the

following questions:

1 How much money did the mechanism fail to extract (ie bidder

surplus)?

2 Did the mechanism implement an efficient allocation? If not,

how much surplus was lost?

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Estimates of Bidder Surplus

PD Surplus DB Surplus IB Surplus

Maturity (bp) (bp) (bp)

CMBs 0.17 0.02 0.04

4-Week 0.04 0.00 0.002

13-Week 0.13 0.02 0.008

26-Week 0.33 0.03 0.026

52-Week 0.68 0.08 0.14

2-Year 7.40 1.15 0.91

5-Year 13.07 1.87 1.39

10-Year 22.22 3.58 1.73

Overall 2.3 0.35 0.23

If the mechanism were able to extract all consumer (i.e.

bidder) surplus, the auctioneer would have gained an extra

2.3 bp in terms of revenue.

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Estimates of (In)efficiency of Allocation

Maturity Efficiency Loss (in basis points)

1-month 0.67

3-months 0.68

6-months 0.76

12-months 0.65

2-year 2.08

5-year 4.50

10-year 6.41

Overall 2.05

Had the bills/notes been allocated to the bidders with highest

values, the total surplus would have been about 2 bp higher.

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Preliminary Conclusions

There is considerable heterogeneity in bidding patterns across

PD, DB, IB

PDs bid the lowest (highest yield), followed by DB and then IB

We find similar differences in bid shading

However, the surplus that PDs derive from the auctions,

although higher than the surplus of DB and IB, is quite

modest

Modest surplus and inefficiency together suggest that the

market is quite competitive, and changing the mechanism

design is likely not going to have that much impact on

revenues (or efficiency)

Interesting avenue for future research: did the participation of

direct bidders affect the surplus of primary dealers?

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