The Aggregate Demand for Treasury Debt

Arvind Krishnamurthy, Northwestern University and NBER

Annette Vissing-Jorgensen, Northwestern University, NBER and CEPR

November 2011

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Yield spread between Moody’s Aaa bond yield and long term Treasury yield versus

Publicly held US Treasury Debt/US GDP. 1919-2009.

1919

1920

1921 1922

1923

1924

1925

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2004 2005

2006

2007

2008

2009

0 .5 1 1.5 2

Aaa−Treasury spread

0 .2 .4 .6 .8 1 1.2

Debt/gdp

Standard monetary theory: Money is (1) medium of exchange, (2) very liquid, (3)

very safe (in nominal terms).

Our paper: Treasury bonds offer (2) and (3). The figure is akin to a

money-demand function, but for government debt.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Time series version of the same relation:

0 .5 1 1.5 2

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Year

Aaa−Treasury spread Debt/gdp

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Findings

1

Investors value U.S. Treasury bonds (beyond CCAPM value)

I Changes in Treasury supply have large effects on a variety of yield spreads.

2 Low yield on Treasuries is due to their extreme safety and liquidity

I Safety: Find two assets with similar liquidity but different safety. Show that

Treasury supply moves spread.

I Liquidity: Find two assets with similar safety but different liquidity. Show that

Treasury supply moves spread.

3 Quantity evidence further shows that Treasuries have similarities to

money (safety, liquidity)

I When supply of Treasuries falls, reducing overall supply of liquid and safe

assets, supply of bank-issued money (M2-M1, time and savings deposits)

rises.

4 Average convenience yield on Treasuries is large: 72 bps.

Implications: (1) Treasury seignorage, (2) riskless rate, (3) foreign Treasury

holders, (4) QE1 and QE2, and (5) optimal Treasury structure

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Related prior literature

1 Money demand literature

2 Ricardian equivalence literature: Barro (1974)

I We show that government debt is non-Ricardian. Main novelty relative to

literature is looking at spreads rather than level of Treasury interest rates.

3 Non-default component of spreads (corporate-Treas, swap-Treas):

I Literature estimates default component of spread. Large residual is referred

to as non-default component.

Collin-Dufresne, Goldstein, and Martin (2001), Longstaff, Mithal, and Neis (2005), Duffie and Singleton(1997), Grinblatt (2001), Liu,

Longstaff, and Mandell (2004), Feldhutter and Lando (2005)

I We offer a direct test of Treasury convenience value: It should be affected by

the supply of the convenient asset (Treasuries).

I Prior evidence on correlation between Treasury supply and spreads:

Cortes (2003): Interest rate swap spreads, 1994-2003.

Longstaff (2004): Refcorp bond yield minus Treasury yield, 1991-2001.

Friedman and Kuttner (1998): CP-bill, 1975-1996.

I We use a much longer sample (1919-2008), control for default risk, isolate

liquidity and safety effects, provide quantity evidence on relation to money.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Related subsequent literature on supply effects in bond markets

Is there a demand for particular Treasury maturities?

Greenwood and Vayanos (2010): Yes, relative supply of long vs. short Treasuries

drives the slope of the yield curve.

Can corporations step in too fill in the maturity structure?

Greenwood, Hanson and Stein (2010): Partially, corporate maturity structure

responds negatively to Treasury maturity structure, but not one-for- one.

Very recent literature on the impact of quantitative easing (buying long bonds,

issuing short-term claims).

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
1. The convenience yield on Treasuries

Representative agent who maximizes,

E

X∞

t=1

β

t

u(Ct )

where Ct is the agent’s consumption plus “convenience" benefits:

Ct = ct + ν(θ

A

t

, GDPt; ξt ).

Convenience assets (A=total, T=treasuries, P=private sector substitutes):

θ

A

t = θ

T

t + k

P

θ

P

t

.

Assume homogeneity of degree 1 in income and holdings. Define:

v

„

θ

A

t

GDPt

; ξt

«

GDPt ≡ ν(θ

A

t

, GDPt; ξt ).

and assume and v

0

(·) > 0, v

00(·) < 0, and v0

(·) → 0 for large holdings.

Work out spreads between corporate bonds and Treasuries (short, long).

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Treasury (zero-coupon, any maturity):

−

P

T

t

Qt

u

0

(Ct ) + βEt

"

P

T

t+1

Qt+1

u

0

(Ct+1)

#

+

P

T

t

Qt

v

0

(θ

A

t /GDPt, ξt )u

0

(Ct ) = 0

Qt is price level at date t. Buy zero coupon Treasury bond for a nominal price P

T

t

. Real

holdings θ

A

t

rises by P

T

t

Qt

, which gives convenience P

T

t

Qt

v

0

(θ

A

t /GDPt, ξt )u

0

(Ct ).

P

T

t =

Et[Mt+1P

T

t+1

]

1 − v

0(θ

A

t

/GDPt; ξt )

≈ e

v

0

(θ

A

t

/GDPt;ξt)Et[Mt+1PT

t+1

]

where

Mt+1 = β

u

0

(Ct+1)

u0(Ct )

Qt

Qt+1

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Corporate bond (zero-coupon, one-period):

P

C

t = Et[Mt+1

“

1 −  ̃Lt+1

”

] ≈ e

−λt Lt+1−covt[Mt+1,

 ̃Lt+1

]/Et[Mt+1]Et[Mt+1]

where  ̃Lt+1 = 0 if no default, L ̃

t+1 = Lt+1 if default, and Lt+1 is loss given default and

default happens with probability λt .

Corporate bond (zero-coupon, any maturity):

P

C

t = λtEt[Mt+1(1 − Lt+1)|Default] + (1 − λt )Et[Mt+1P

C

t+1|No Default]

Simplify using Duffie-Singleton (1997) formulation:

Default over next period is uncorrelated with M (but changes in expectations

about future default, i.e. downgrades, can be correlated with M).

Payoff if default is fraction 1 − Dt of market value if no default:

Et[Mt+1(1 − Lt+1)] = Et[Mt+1P

C

t+1

](1 − Dt )

Then

P

C

t = λtEt[Mt+1(1 − Lt+1)] + (1 − λt )Et[Mt+1P

C

t+1

]

= (λt (1 − Dt ) + (1 − λt ))Et[Mt+1P

C

t+1

] ≈ e

−λtDt Et[Mt+1PC

t+1

].

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Prediction 1-3: Impact of Treasury supply on spreads, expected returns

1 One-period spread: St,1 = i

C

t,1 − i

T

t,1 = −ln PCt + ln PT

t

St,1 = v

0

„

θ

A

t

GDPt

; ξt

«

+ λtLt+1 + covt[Mt+1, L ̃

t+1]/Et[Mt+1].

St,1 = v

0

„

θ

A

t

GDPt

; ξt

«

+ λtDt

2 τ-period spread:

St,τ = i

C

t,τ − i

T

t,τ = −

1

τ

ln PC

t +

1

τ

ln PT

t

=

t+Xτ−1

j=t

1

τ

Et[v

0

(θ

A

j /GDPj; ξ

L

j )] +

t+Xτ−1

j=t

1

τ

Et[λjDj] −

t+Xτ−1

j=t

1

τ

covt (mj+1, R ̃

j+1)

3 Expected excess returns:

Et[Mt+1R ̃

t+1] = v

0

(θ

A

t /GDPt; ξt )

Et[R ̃

t+1] = 1

Et[Mt+1]

“

v

0

(θ

A

t /GDPt; ξt ) − covt (Mt+1, R ̃

t+1)

”

.

(Realized excess return involves updates to expectations about future v’s, future

default, and future covariances – lots of noise.)

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Testing predictions 1, 2, 3

Test whether increases in θ

T

t cause the spreads to fall and predicts lower excess

returns.

Regression coefficients are net of private-sector response – this is the most

interesting outcome

I But finding our hypothesized negative relation requires that θ

A

t = θ

T

t + k

P

θ

P

t

increases in θ

T

t

.

I Private sector reaction should not offset more than one-for-one. Extremely

unlikely, and we can also check for this using quantities.

Our regressions assume that θ

T

t does not respond to the spread

I If anything government probably expands Treasury supply if spreads rise,

making it harder to find our hypothesized negative relation.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Estimation of yield regressions

Spreadt = a + b1 ln Debtt/GDPt + b2 controlst + errort

Log functional form: Only one parameter to estimate, but does not asymptote to

zero. Different functional form later.

Both left and right-hand side persistent. We run OLS, modeling error as AR(1)

(based on Box-Jenkins analysis)

Why not GLS? Convenience yield term is Et[

Pv

0

(θ

A

t )], proxied by ln Debtt /GDPt .

Measurement error magnified by GLS

Controls for expected default: EDF, stock market volatility

Control for time-varying risk premium (covt): Slope of yield curve (state of

business cycle)

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Estimation of excess return regressions

Realized excess returnt = a + b1 ln Debtt/GDPt + b2 controlst + errort

Excess return is on long corporate Aaa/Aa index minus long Treasury index

(Ibbotson)

OLS with standard errors assuming ARMA(1,1) error terms

(AR(1)+noise=ARMA(1,1))

Controls for time-varying risk premium (covt): Slope of yield curve (state of

business cycle).

Good: No controls needed for expected default (doesn’t affect expected excess

return)

Bad: Lots of noise in realized excess returns: Std. dev. is 3.72 pct, compared to

0.45 pct for Aaa-Treasury yield spread. Controls to remove part of noise in

realized excess returns:

I Credit hedge: Excess return of junk bonds over Baa bonds

I Duration hedge: Excess return on long over short Treasuries (to capture any

duration mismatch).

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Table I. Impact of Treasury Supply on Bond Spreads: Log Specification

Panel A: Aaa-Treasury Panel B: Baa-Treasury

(1) (2) (3) (4) (5)

Period 1919-2008 1969-2007 1926-2008 1969-2007 1926-2008

log(Debt/GDP) -0.744 -0.910 -0.797 -1.752 -1.304

[-4.32] [-3.35] [-5.06] [-5.98] [-7.54]

EDF 0.953 1.206

[3.57] [3.71]

Volatility 1.294 6.364

[1.90] [6.88]

Slope 0.045 0.080 0.175 0.309

[1.05] [1.86] [2.04] [4.64]

Intercept 0.111 0.052 0.078 0.208 0.737

[0.62] [0.18] [0.49] [0.66] [4.34]

R

2

0.447 0.623 0.568 0.669 0.690

ρ 0.572 0.402 0.528 0.066 0.012

N 90 39 83 39 83

(1): One-σ decrease in Debt/GDP from mean value of 0.426 to 0.233 ⇒

Convenience yield component of the Aaa-Treasury spread up by 45 bps.

(2): One-σ increase in EDF (in volatility) ⇒ Aaa-Treasury +21 bps (+10 bps)

(5): One-σ decrease in Debt/GDP ⇒ Baa-Treasury +79 bps.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Table I. Impact of Treasury Supply on Bond Spreads: Log Specification

Panel C: CP-Bills Panel D: CPP2-Bills

(6) (7) (8) (9)

Period 1920-2008 1969-2007 1926-2008 1974-2007

log(Debt/GDP) -0.728 -1.006 -0.550 -1.919

[-4.37] [-2.21] [-3.52] [-3.86]

EDF 0.024 0.086

[0.05] [0.16]

Volatility 1.947

[2.33]

Slope -0.123 -0.085 -0.105

[-1.30] [-1.42] [-1.13]

Intercept 0.095 -0.269 0.229 -0.813

[0.56] [-0.55] [1.49] [-1.58]

R

2

0.224 0.211 0.259 0.282

ρ 0.183 -0.023 0.018 0.122

N 89 39 83 34

Short spread less likely to be affected by omitted controls for time-varying

expected default or default risk premium (all callability issues)

Literally zero defaults on A1/P1 over 1972-2000 for which Moodys provide data.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Table II. Impact of Treasury Supply on Bond Excess Returns

(1) (2) (3)

Period 1926-2003 1926-2003 1926-2003

log(Debt/GDP) -0.851 -1.696 -1.826

[-1.29] [-2.21] [-1.83]

CreditHedge 0.160 0.121

[2.89] [2.22]

Slope 0.678

[1.64]

DurationHedge -0.117

[-2.56]

Intercept -0.301 -1.245 -1.127

[-0.46] [-1.60] [-1.13]

R

2 0.009 0.100 0.162

N 78 78 78

Return results alleviate concerns about insufficent controls for expected default

(doesn’t affect expected returns).

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
2. What drives the convenience yield on Treasuries?

v

“

θ

A

t

GDPt

; ξt

”

is a reduced form convenience benefit function.

1 Liquidity demand:

I Aiyagari and Gertler (1991), Heaton and Lucas (1996), Vayanos and Vila

(1998),Rocheteau (2009)

I Comment: These are all two-agent models. So do not take our

representative agent formulation literally.

2 Short-term safety demand: Stems from absolute certainty of nominal

repayment

I Information costs: Low information costs/agency costs to buying

Treasuries. Related to theories of limited participation (Vissing-Jorgensen

2003).

I Collateral: Safe collateral pledged in derivatives and settlement (Gorton

2010).

I Check-backing: Households require that banks and money funds hold safe

collateral to back checking accounts (Bansal and Coleman 1996).

I Comment: Says that the relation b/w price and expected default is very

steep for low expected default, and the slope is steeper the lower the supply

of Treasuries.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Illustrating the impact of safety demand on price:

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
3 Long-term safety demand: Stems from absolute certainty of nominal repayment

I Some investors (e.g. pension funds, insurance companies) demand safe

long-term nominal payoffs.

I Preferred habitat: Modigliani-Sutch (1966), Greenwood and Vayanos (2010).

But with special demand for extremely safe long-term assets.

Convenience components on short-term Treasuries:

vT,short (·) = vliq 

θ

T

t + k

liqθ

P,liq

t

GDPt

; ξ

liq

t

!

+ vshortsafe 

θ

T,short

t + k

shortsafeθ

P,shortsafe

t

GDPt

; ξ

shortsafe

t

!

.

Convenience on long-term Treasuries:

vT,long(·) = vliq 

θ

T

t + k

liqθ

P,liq

t

GDPt

; ξ

liq

t

!

+ vlongsafe 

θ

T,long

t + k

longsafeθ

P,longsafe

t

GDPt

; ξ

longsafe

t

!

.

Corporate-Treasury spreads are functions of both liquidity and safety components =⇒

Consider other spreads to test for separate existence of each Treasury attribute.

If Treasuries have a given attribute, changing Treasury supply should affect the

equilibrium price of that attribute.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Prediction 4-6: Impact of Treasury supply on price of short-term safety,

long-term safety, liquidity

4. A pure short-term safety spread: P2 - P1 commercial paper

S

P2−P1

t,1 = (k

shortsafe

P1 − k

shortsafe

P2 )v

0

shortsafe 

θ

T,short

t + k

shortsafeθ

P,shortsafe

t

GDPt

; ξ

shortsafe

t

!

+λt,P2Dt,P2 − λt,P1Dt,P1.

Similarly illiquid:

I Little secondary market trading in any commercial paper (about 2% of total

volume).

I In cross-section of short commercial paper, spreads to Treasuries are mainly

determined by default risk, not liquidity (Covitz and Downing (2007)).

Different default risk:

I Moodys, 1972-2000, over 3-month period: 0.00% for A1/P1, 0.02% for

A2/P2.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Prediction 4-6: Impact of Treasury supply on price of short-term safety,

long-term safety, liquidity

5. A pure long-term safety spread: Baa-Aaa spread

S

Baa−Aaa

t,τ = (k

longsafe

Aaa − k

longsafe

Baa )

t+Xτ−1

j=t

1

τ

Et

"

v

0

longsafe 

θ

T,long

j + k

longsafeθ

P,longsafe

j

GDPj

; ξ

longs.

j

!

+

t+Xτ−1

j=t

Et[λ

Baa

j D

Baa

j − λ

Aaa

j D

Aaa

j

] −

t+Xτ−1

j=t

1

τ

covt (mj+1, R ̃ Baa−Aaa

j+1

).

Similarly illiquid:

I Similar high bid-ask spreads: 58 bps for Baa, 52 bps for Aaa (Chen,

Lesmond and Wei (2008)).

Different default risk:

I Moodys, 1920-2004, over 10-year period: 1% for Aaa, 8% Baa.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Prediction 4-6: Impact of Treasury supply on price of short-term safety,

long-term safety, liquidity

6. A pure liquidity spread: Insured bank deposits-Treasuries

S

FDIC

t,1 = i

FDIC

t − i

T

t = (1 − k

liq)v0

liq 

θ

T

t + k

liqθ

P,liq

t

GDPt

; ξ

liq

t

!

.

FDIC: Rate on 6-month CDs, post 1984 (i.e. after phasing out of Regulation Q)

FDIC: Rate on all time and savings deposits, 1935-1965 (i.e. before Regulation Q

was binding). 75% were insured. Assume 6-month average maturity.

Other possibility: On-the-run/off-the-run spread. Works, but short sample.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Table III. Impact of Treasury Supply on Price of Safety, Price of Liquidity

Panel A: Price of Safety

Assets with similar liquidity and different safety:

S

Baa−Aaa SP2−P1

Period 1926-2008 1926-2008 1974-2007 1974-2007

log(Debt/GDP) -0.506 -0.879

[-3.42] [-4.47]

log(Debt > 10 year mat/GDP), -0.310

instr. by powers of (Debt/GDP) [-2.40]

log(Debt ≤ 1 year mat/GDP) -1.453

instr. by powers of (Debt/GDP) [-2.94]

Volatility 5.070 6.311 0.321 0.029

[6.53] [6.66] [0.38] [0.03]

Slope 0.229 0.209 0.014 0.054

[4.15] [3.24] [0.40] [1.14]

Constant 0.660 0.241 -0.500 -2.662

[4.52] [0.648] [-2.45] [-2.56]

N 83 83 34 34

R

2

0.600 0.486

Estimation method OLS IV OLS IV

Error term AR(1) AR(1) AR(1) AR(1)

Impact of -1 σ supply +41 bps +26 bps

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Table III. Impact of Treasury Supply on Price of Safety, Price of Liquidity

Panel B: Price of Liquidity

Assets with similar safety and different liquidity:

S

FDIC insured CDs-Bills STime & Savings Accounts-Bills

Period 1984-2008 1935-1965

log(Debt/GDP) -1.904 -0.639

[-1.83] [-2.37]

Slope 0.137 1.013

[1.32] [8.48]

Constant -1.500 -0.070

[-1.63] [-0.41]

N 25 31

R

2

0.271 0.720

Estimation method OLS OLS

Error term i.i.d. i.i.d.

Impact of -1 σ supply +115 bps

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
3. Money and Treasuries

Convenience yield on money (money demand function) driven by:

1 Medium-of-exchange for goods transactions

2 Liquidity in financial transactions

3 Safety, as in secure store of value

We have argued that Treasuries share (2) and (3). If so, then money should be a

substitute asset for Treasuries.

Focus on parts of money that has (2) and (3) but not (as much) (1):

I M2-M1 (excl. MMMF holdings of Treasuries):

Small denomination savings and time deposits – FDIC insured

I Exclude M1 (currency, demand dep.). Has (1) and not controlled by private

sector.

I Also evidence for M3-M1 (excl. MMMF holdings of Treasuries):

Adds large savings and time deposits, repos and Euro dollars.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Prediction 9: Impact of Treasury supply on supply of substitute asset

If the supply of money (specifically bank deposits) is price elastic, then θ

Money

t

and θ

T

t

will be negatively related.

Prediction 8: Impact of Treasury supply on yield of substitute asset

i

corp

t − i

money

t = k

liqv0

liq 

θ

T

t + k

liqθ

P,liq

t

GDPt

; ξ

liq

t

!

+ v

0

shortsafe 

θ

T,short

t + k

shortsafeθ

P,shortsafe

t

GDPt

; ξ

shortsafe

t

!

+ λtDt.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Money (M2-M1) versus Debt/GDP, 1934-2008:

1934

1935

1936

1937

1938

1939

1940

1941

1942

1943

1944

1945

1946 1948 1947 1949

1950

1952 1951

1953

1954

1956 1955

1957

1958

1960 1959

1961

1962

1963

1964

1965

1966 1967 1968

1969

1970

1971

1972 1973

1974

1975

1976

1977

1978

1980 1979

1981

1982

1983

19841985 1986

1987

1988

1989

1990

1991

1992

1993

19941995

1996

1997

1998

1999

2000

2001

2002

2003

2004 2006 2005

2007 2008

.2 .3 .4 .5

non−M1M2/gdp

.2 .4 .6 .8 1 1.2

Debt/gdp

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
.2 .4 .6 .8 1 1.2

1930 1940 1950 1960 1970 1980 1990 2000 2010

Year

non−M1M2/gdp Debt/gdp

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Table V. Response of Money to Treasury Supply, 1934-2008

Panel A: Reduced Form

(1) (2) (3)

Dep. Var. non-M1M2/GDP non-M1M2/GDP non-M1M3/GDP

Period 1926-2008 1959-2005 1959-2005

Debt/GDP -0.305 -0.352 -0.553

[-5.52] [-4.16] [-3.34]

Year 0.001 0.007

[1.86] [5.99]

Intercept 0.502 -1.467 -12.161

[18.26] [-1.38] [-5.69]

R

2 0.601 0.534 0.802

N 75 47 47

Estimation method OLS OLS OLS

Standard errors AR(2) AR(2) AR(2)

When Treasury supply is reduced by $1, private sector supply of money

increases by $0.55.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Table V. Response of Money to Treasury Supply, 1934-2008

Panel B: Structural Form

1st Stage of IV 2nd Stage of IV

Dep. Var. S

Baa−nonM1M2

log(non − M1M2/GDP)

Period 1935-1965, 1935-1965,

1984-2008 1984-2008

Log(Debt/GDP) -1.587 S

Baa−nonM1M2 0.394

[-2.10] [2.29]

Volatility 7.942 Volatility -2.717

[2.81] [-1.47]

Slope 0.440 Slope -0.140

[2.27] [-1.37]

Intercept 2.279 Intercept -2.439

[3.94] [-4.13]

N 56 56

Estimation method OLS IV

Standard errors AR(1) AR(1)

Confirms Shows that money response

Prediction 8 works via spread channel

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
4. Quantifying average convenience yields

We have fit:

Spreadt = f (θ

T

t /GDPt ) + b0 + b1 controlst + errort

with a log-function for f.

More realistic to impose that f (∞) → 0.

Then the convenience yield is the distance between the predicted spread and the

estimated asymptote.

Specifically, assume kink function, with f = 0 for θ

T

t /GDPt > b2:

f (Debt/GDP) = b1 × max[b2 − Debt/GDP, 0].

Then asymptote is b0 and conv. yield is f (Debt/GDP) (de-mean the controls).

Estimate by non-linear least squares, again with AR(1) errors.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Table VI. Impact of Treasury Supply on Bond Spreads: Piecewise Linear

Specification

Panel A: Aaa-Treasury Panel B: Baa-Treasury

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

Period 1919-2008 1926-2008 1919-2008 1926-2008

b0 0.319 0.346 1.019 1.199

[ 1.80 ] [ 2.51 ] [ 1.94 ] [ 7.29 ]

b1 2.579 3.060 4.310 4.941

[ 4.02 ] [ 5.07 ] [ 2.64 ] [ 6.75 ]

b2 0.585 0.549 0.625 0.545

[ 6.96 ] [ 9.56 ] [ 4.22 ] [ 12.92 ]

Volatility 1.189 6.236

[ 1.90 ] [ 7.05 ]

Slope 0.095 0.330

[ 2.38 ] [ 5.03 ]

R

2

0.477 0.612 0.290 0.704

N 90 83 90 83

Avg. conv. yield 46 bps 72 bps

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Average convenience yield over 1926-2008 sample: 72 bps

Long-term safety: Lower bound from Baa-Aaa (Aaa not riskless): 26 bps

Liquidity: Upper bound from Aaa-Treas (Aaa not riskless): 46 bps

Our average convenience yields are probably downward biased (conservative):

Asymptote b0 identified off of 1940s and 1950s.

Fed set Treasury price floor for long Treasuries =⇒ Treasury yield artificially low

=⇒ Spread artificially high =⇒ b0 too high.

More intervention in T-bill market (large Fed purchases, T-bills as bank reserves)

=⇒ Short spreads not useful for calculating avg. conv. yield.

Similarly, our saturation point, b2: Debt/GDP=0.55, is probably too low.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Summary

1 Treasuries have a convenience yield:

I Treasury supply ↓ ⇒ Spread b/w non-conv. and conv. Treasury assets ↑.

I True for many spreads, and after default controls.

I Robust to tax issues (Treasuries exempt from state and local taxes), and

callability of corporates (not relevant for short spreads).

2 Source of Treasury convenience yield: Liquidity, long-term & short-term safety

attributes of Treasuries

I Treasury supply ↓ ⇒ Price of liquidity ↑, Price of safety ↑.

3 Money also offers liquidity and safety and is thus a Treasury substitute

I Treasury supply ↓ ⇒ Money supply ↑.

4 The average convenience yield is high: 72 bps (at the long end).

Next: Implications

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Implication 1. Government seignorage from Treasuries

Government (tax-payers) benefit from being able to fund Federal debt with asset that

has low yield.

Average seignorage on government debt

= Average of (convenience yield × Debt-to-GDP)

= 0.24% of GDP

For comparison: Seignorage on money, year 2007 (pre-QE1):

= M0 × 4%

= 0.24% of GDP.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Implication 2. Riskless rate

Do not teach students to use Treasury yield as the riskless rate in the CAPM!

A corporation with a beta of zero cannot borrow at the Treasury rate

Need to add Treasury convenience yield

Do not buy Treasuries unless you want extreme safety and liquidity

You can earn 72 bps more if you are ok with almost complete safety and less

liquidity.

And the equity premium is 72 bps smaller when using the convenience-adjusted

riskless rate.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Implication 3. Effect of foreign official holders on interest rates

Table VII. Debt Holdings, by Group

Group Debt-to-GDP Panel A: Who holds Treasury Debt?

Mean Std. Dev. 1945 1975 2008

Federal Reserve Banks 0.138 0.040 0.097 0.199 0.075

Foreign Official Holdings 0.113 0.088 0.010 0.141 0.367

State/Local Governments 0.088 0.042 0.022 0.064 0.076

Banks/Credit Institutions 0.201 0.116 0.416 0.222 0.017

Households and Mutual Funds 0.260 0.051 0.265 0.263 0.169

Foreign Private Sector 0.042 0.049 0.000 0.010 0.140

Fedrl/State/Local Govt. Ret. 0.035 0.022 0.006 0.006 0.045

Private Pensions 0.028 0.020 0.008 0.029 0.029

Insurance Companies 0.048 0.023 0.093 0.022 0.025

Concern about FOH holding 37% of Treasuries. What will happen if they sell?

More Treasury supply for others ⇒ Lower Treasury prices, higher Treasury yields,

lower spreads.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Table VII. Debt Holdings, by Group

Panel B: Bond Market Portfolio Composition

Treasury Agency Long-term Short-term

Corporate Corporate

Federal Reserve Banks 0.983 0.017 0.000 0.001

Foreign Official Holdings 0.948 0.052 0.000 0.000

State/Local Governments 0.720 0.217 0.029 0.034

Banks/Credit Institutions 0.526 0.312 0.141 0.020

Households and Mutual Funds 0.563 0.095 0.223 0.118

Foreign Private Sector 0.240 0.084 0.479 0.197

Fedrl/State/Local Govt. Ret. 0.387 0.108 0.487 0.018

Private Pensions 0.233 0.142 0.583 0.042

Insurance Companies 0.172 0.078 0.726 0.024

We estimate that FOH have vertical demands. Consistent with them holdings

almost exclusively Treasuries.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
D(θ

T ;  )

t t

Yield Spread, St

θ θ

T

t

t

T

Demand from 

all investors, 

excluding FOH

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
FOH sale is an increase in supply available to others

Demand curves shown have same slope – slope comes from non-FOH.

So we can evaluate drop in yield as impact of increased supply using current

overall demand curve.

Based on estimated demand functions, and at historical average Debt/GDP:

I Baa-Treasury, piecewise linear: Raise long Treasury yield by 59 bps

Baa-Treasury, log: Raise long Treasury yield by 41 bps

I CP (P2)-Bills: Raise short Treasury yield by 60 bps

Effects will differ if they sell now: Smaller because of high current Debt/GDP, but

larger if higher than average convenience demand. Hard to assess.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Implication 4. QE – Krishnamurthy and Vissing-Jorgensen (Brookings,

Fall 2011)

Objective: Evaluate effects of Fed purchase of long-term Treasuries and other

long-term bonds (QE1 in 2008-2009 and QE2 in 2010-2011) on interest rates.

What are the effects on a variety of interest rates?

What are the channels through which QE affects rates?

The channels matter for whether all long rates react the same regardless of what

you buy, or not.

Approach: Event study using a host of interest rates and derivatives data

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Our main findings on QE: It matters that Treasuries are “special”

1 Inappropriate to focus only on Treasury rates as a policy target: QE works

through several channels that affect particular assets differently.

Channels: Long-term safety channel, signaling channel, and inflation channel

for both QE1 and QE2, and MBS pre-payment channel and corporate bond

default risk channel for QE1.

I Changes in the safety convenience yield on long Treasuries (and agencies

and for QE1 Aaa corporate) for both QE1 and QE2. As large as 160 bps for

QE1, about 5-10 bps for QE2

I Liquidity effect for QE works to increase Treasury yields, so look at

(CDS-adjusted) Baa - Agencies to see full long-term safety effect.

2 Effects on particular assets depend critically on which assets are purchased.

I Treasuries-only purchases in QE2 had a disproportionate effect on

Treasuries and Agencies relative to MBS and corporates

I MBS purchases in QE1 were crucial for lowering MBS yields as well as

corporate credit risk and thus corporate yields for QE1

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Implication 5: Optimal Treasury structure.

What are current convenience yields?

We found that based on the average demand curve, the saturation point was

Debt/GDP=0.55. As of 2011:Q2 Debt/GDP is $9.7T/$15.0T=0.65.

But our estimate of the saturation point was likely too low due to intervention in

the Treasury market during the war and post-war years.

And, under QE, Fed has “taken out” a lot of the Treasury supply, $1.6T as of

2011:Q2. If you take out current Fed holdings, Debt/GDP is about

($9.7T-$1.6T)/$15.0T=0.54.

And, if anything, current demand is probably higher than usual.

So let us look at a bit more data to assess whether current Treasury convenience

yields are positive.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
At the long end: Current convenience yield is large

For recent years we have derivatives prices that help sort this out more precisely

We can risk adjust corporate-treasury spreads using CDS rates on corporate

bonds.

And inflation swaps to allow us to construct another comparison for Treasuries

that are not affected by default risk: TIPS+Inflation swap. Probably does not have

the same safety properties (e.g. appeal to central banks, use in collateral etc.)

and likely to be less liquid.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
0 1 2 3 4 5

2005 2006 2007 2008 2009 2010 2011 2012

(TIPS+Infl swap)−Treas (10 yr) Aa corp−Treas (10 yr)

Aa corp−Treas−Aa corp CDS (10 yr)

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
At the short end: Current conv. yield is very small, perhaps even zero

Using the latest Fed CP data and Treasury yield data, Nov. 10, 2011:

I A1/P1 non-financial CP, 1-month: 10 bps

I Treasury constant maturity, 1-month: 1 bps.

I So Treasury convenience yield relative to highly rated CP is at most 9 bps,

and likely less with the slight risk in the CP.

I Historical average A1/P1-Treasury yield, 1920-2008, is 78 bps.

Even stronger conclusion from approach of Greenwood, Hanson and Stein

(2010) of looking at whether yield-curve pricing errors are negative for the

shortest T-bills.

I Estimate regression of yields on cubic in maturity for each date, using only

securities with maturities beyond 3 months (and only non-callable). Look at

residuals for T-bills with maturities less than 3 months. Currently near zero.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
−.01 −.005 0 .005

Yield curve residual

1940 1950 1960 1970 1980 1990 2000 2010

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
What does this teach us about optimal Treasury maturity structure?

Suppose tax payers think Treasury’s objective should be to maximize dollar

convenience yield for given amount of debt (since conv. yield is how much

cheaper they borrow than what they think would be “fair” given the duration)

Then convenience yields should be equalized across maturities

Currently they are not. Need to have relative more long-term debt.

In particular: No need to issue more T-bills to satisfy “money-demand” since that

demand is saturated, though this is likely related to large reserve increase under

QE (+$740B since 2008) and could change once QE is unwound.

Actual policy:

Historically, the Treasury has picked higher maturity when Debt/GDP is higher.

This is optimal, with respect to maximizing convenience yields, if the convenience

demand a the long end is saturated at a slower rate than that at the short end.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
.2 .4 .6 .8

Debt/GDP

2 4 6 8 10

Avg. debt maturity (years)

1940 1950 1960 1970 1980 1990 2000 2010

Avg. debt maturity (years) Debt/GDP

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Our findings also suggest another key Treasury choice variable:

The number of bonds issued

Tradeoff:

More bonds =⇒ Can issue at many different maturities to match safety demand

for particular maturities precisely

But more bonds =⇒ Issue sizes get smaller and this reduces liquidity

Questions:

Are we at the right number of bonds?

How much should the number of bonds increase with funding needs?

Actual policy:

Since around 1975, the Treasury has increased the number of issues with

Debt/GDP and kept issue sizes/GDP fairly constant. We need more analysis of

whether that is optimal.

Important: This is a distinct question from how many auctions should be held per

year since one can issue into an already existing CUSIP at a given auction.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
.2 .4 .6 .8

Debt/GDP

0 50 100 150 200 250

Number of securities outstanding

1940 1950 1960 1970 1980 1990 2000 2010

Number of securities outstanding Debt/GDP

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
.2 .4 .6 .8

Debt/GDP

0 .005 .01 .015 .02

Average security size

1940 1950 1960 1970 1980 1990 2000 2010

Average security size Debt/GDP

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011
Conclusion

Liquidity and extreme safety are asset-attributes that are demanded by investors.

There is a broad aggregate of assets that satisfy the demand.

Treasuries are an important component of the aggregate. So are money,

high-grade corporate bonds (and probably agency bonds).

Historical average conv. yield on Treasuries is 72 bps (liquidity conv. yield≤ 46

bps; long safety conv. yield ≥ 26 bps).

Results have implications for many first-order issues in finance and macro.

Krishnamurthy, Vissing-Jorgensen (Northwestern) The Aggregate Demand for Treasury Debt November 2011