The Aggregate Demand for Treasury Debt

Arvind Krishnamurthy Annette Vissing-Jorgensen∗

May 12, 2010

Abstract

Investors value the liquidity and safety of U.S. Treasury bonds. We document this by showing that

changes in Treasury supply have large effects on a variety of yield spreads. As a result, Treasury yields

are reduced by 72 basis points, on average over the period from 1926-2008. The low yield on Treasuries

due to their extreme safety and liquidity suggests that Treasuries in important respects are similar to

money. Evidence from quantities supports this idea. When the supply of Treasuries falls, reducing the

overall supply of liquid and safe assets, the supply of bank-issued money rises.

∗Respectively: Northwestern University and NBER; Northwestern University, NBER and CEPR. We thank Ricardo Caballero, Mike Chernov, Chris Downing, Ken Garbade, Lorenzo Garlappi, Robin Greenwood, Dimitri Vayanos, Sam Hanson,

Mike Johannes, Bob McDonald, Monika Piazzesi, Sergio Rebelo, Suresh Sundaresan, Pierre-Olivier Weill, Tan Wang, Francisco

Palomino, Clemens Sialm, Gerard Hoberg, Henning Bohn, and participants at talks at UCLA, University of Chicago, Columbia

University, Michigan State University, Duke-UNC Asset Pricing conference, Fed Board of Governors, University of Michigan

Mitsui Life Symposium on Financial Markets, LSE-PWC conference, MIT, Moody’s-KMV, NBER AP meeting, NBER ME

meeting, NBER EFG meeting, UBC Winter Finance Conference, Northwestern University, NY Fed, University of Texas-Austin,

University of South Carolina, Queen’s University and the WFA for comments. Josh Davis, Chang Joo Lee, and Byron Scott

provided research assistance. We thank Moody’s KMV for providing their Expected Default Frequency data, Michael Fleming

for data on P2 rated commercial paper, and Henning Bohn for Debt/GDP data.
1 Introduction

Money, such as currency or checking accounts, offers a low rate of return relative to other assets. The reasons

behind this phenomenon are well understood. Money is (1) a medium of exchange for buying goods and

services, (2) of high liquidity, and (3) of extremely high safety in the sense of offering absolute security of

nominal repayment. Investors value these attributes of money and drive down the yield on money relative

to other assets.

We argue that Treasury bonds have some of the same features as money, namely (2) and (3), and

that this drives down the yield on Treasuries relative to assets that do not to the same extent share these

features. Figure 1A provides vivid evidence for this assertion. The figure graphs the yield spread between

Aaa rated corporate bonds and Treasury securities against the US government Debt-to-GDP ratio (i.e. the

ratio of the market value of publicly held US government debt to US GDP). The figure reflects a Treasury

demand function, akin to a money demand function. When the supply of Treasuries is low, the value that

investors assign to the liquidity and safety attributes offered by Treasuries (referred to below as the Treasury

convenience yield) is high. As a result the yield on Treasuries is low relative to the yield on the Aaa corporate

bonds which offer less liquidity and safety. The opposite applies when the supply of Treasuries is high. We

present detailed econometric evidence of the relation reflected in Figure 1 using several alternative yield

spread measures and controlling for corporate bond default risk.

The evidence in Figure 1 shows that Treasuries offer unique attributes that are valued by investors, but

does not identify the attributes. We further show that Treasuries share features (2) and (3) with money

in two ways. First, we examine the yield spread between a pair of assets which are different only in terms

of their liquidity, as well as the yield spread between a pair of assets which are different only in terms of

their safety. Under the hypothesis that liquidity/safety are priced attributes, the yield spread between these

pairs of assets should reflect the equilibrium price of liquidity/safety. We show that changes in Treasury

supply affect each of these yield spreads. The results indicate that Treasuries offer liquidity and safety so

that changes in the supply of Treasuries separately change the equilibrium price of liquidity and safety.

The second type of evidence that Treasuries share (2) and (3) with money relates the quantity of money

to the quantity of Treasuries. We show that when the supply of Treasuries falls, the supply of bank-issued

money (specifically, M2 minus M1) which offers (2) and (3), rises. We show that the channel underlying this

response is that a reduction in the supply of Treasuries increases the prices of liquidity and safety, lowering

the yield on bank deposits, and inducing the banking sector to issue more deposits.

These findings suggest that investors value liquidity and safety when pricing assets. We compute that

the value investors have paid on average over our main sample from 1926 to 2008 for the liquidity and safety

attributes of Treasuries is 72 basis points per year of which 46 basis points is for liquidity and 26 basis points

for safety. The government collects seignorage from the liquidity and safety attributes of Treasuries and we

1
compute that the government saves interest costs of 0.25% of GDP per year because of investors’ demand

for Treasuries. This figure is comparable in magnitude to the traditional notion of seignorage, which stems

from the public’s willingness to hold fiat money at zero interest. We compute that the latter seignorage is

around 0.24% of GDP per year.

In addition to their implications for asset pricing and seignorage, our findings have implications for the

demand for money. First, since Treasuries share some of the attributes of money, appropriately constructed

“money” aggregates should include the supply of Treasuries. Second, the demand for money stems from

demand for liquidity, safety, and a medium-of-exchange. It is likely that there is independent variation in

the demand and supply of each of these attributes. For example, during a financial crisis, the demand for

liquidity and safety in particular may rise. On the other hand, the extant literature on money demand

assumes that money reflects the price of a single attribute. We discuss how to use the yields on Treasuries

as well as other safe/liquid assets to recover the underlying demands for the different attributes of money.

These findings help shed light on sources of instability in estimates of the money demand function (see

Goldfeld and Sichel, 1990).

Finally, our findings imply that Treasury interest rates are not an appropriate benchmark for “riskless”

rates. Cost of capital computations using the CAPM should use a higher riskless rate than the Treasury rate

– a company with a beta of zero cannot raise funds at the Treasury rate. In addition, our results suggest

that the equity premium measured relative to Treasury rates will partly be driven by the liquidity and safety

of Treasuries and thus that these Treasury properties are partially responsible for the high equity premium.

Relation to Literature

Our finding of a significant non-default component in the corporate bond spread is consistent with some

recent papers in the corporate bond pricing literature (see Collin-Dufresne, Goldstein, and Martin (2001)

and Longstaff, Mithal, and Neis (2005)). Duffie and Singleton (1997), Grinblatt (2001), Liu, Longstaff,

and Mandell (2004), and Feldhutter and Lando (2005) argue for a significant non-default component in the

interest rate swap spread (the spread between the fixed rate in a fixed-for-floating interest rate swap contract

and the Treasury rate). Papers in the prior literature use information from the corporate bond market and

credit default swaps to estimate the default component of interest rate spreads, and label the residual as a

non-default component. Compared to the prior literature, the novelty of our work is to offer direct evidence

of the existence of a non-default component by documenting that the amount of Treasuries outstanding is

a key driver of the non-default component of the corporate bond spread (a similar relation holds for the

interest rate swap spread but we do not emphasize that here since swap rates are only available for a fairly

short period, starting in 1987).1

1Some of the papers in the prior literature show that the non-default component is related to the specialness of particular

Treasury securities. A particular Treasury bond is “special” if the cost of borrowing the bond in the repurchase market exceeds

2
We are aware of only a few papers in the literature that have noted a correlation between the supply of

government debt and interest rate spreads. Cortes (2003) documents a correlation between the US Debt/GDP

ratio and swap spreads over a period from 1994 to 2003. Longstaff (2004) documents a correlation between

the supply of Treasury debt and the spread between Refcorp bonds and Treasury bonds over a period from

1991 to 2001. Friedman and Kuttner (1998) show a correlation between the commercial paper to Treasury

Bill spread and the relative supply of these assets over the period 1975 to 1996.2 Relative to these papers we

study a much longer sample, provide a theoretical basis to study the relation, use several approaches to rule

out that the relation could be driven by time-varying default risk, decompose the Treasury convenience yield

into a liquidity and safety component, and show the similarity between money and Treasuries by showing

that private sector money supply reacts to Treasury supply.

There is a closely related literature that seeks to examine whether the relative supplies of long and shortterm Treasury debt has an effect on the term structure of Treasury yields. Early work in this literature was

motivated by the 1962-64 “operation twist,” where the government tried to flatten the term structure by

shortening the average maturity of government debt (see for example Modigliani and Sutch, 1966). More

recently, Reinhart and Sack (2000) show that the projected government deficit is positively related to the

slope of the Treasury yield curve, suggesting that this is evidence of a supply effect. More systematic evidence

of a relative supply effect is provided in Greenwood and Vayanos (2010), who examine data from 1952 to

2005 and show that relative supply of long and short Treasuries is related to the slope of the yield curve as

well as the excess return on long-term Treasuries over short-term Treasuries. These papers suggest that the

demand for Treasury attributes varies by maturity, and are complementary to our study.

In macroeconomics, there is a large literature exploring the Ricardian equivalence proposition (Barro,

1974), that the financing choices of the government used to fund a given stream of government expenditures

is irrelevant for equilibrium quantities and prices. One implication of the Ricardian equivalence proposition

is that the size of government debt has no causal effect on interest rates. Despite a large amount of research

devoted to studying this topic, there is yet no clear consensus on the effects of debt on interest rates (see, for

example, the survey by Elmendorf and Mankiw (1999)). Barro (1987), Evans (1986) and Plosser (1986) find

little or no effect of government debt on interest rates. Focusing on forward Treasury rates and projected

future Debt/GDP levels, Laubach (2007) reports a 3 − 4 bps effect per one percentage point increase in

projected Debt/GDP. We provide evidence that the stock of government debt affects the interest rates

that of other Treasury bonds with similar maturity and cash-flow characteristics. Specialness leads to the yield on the special

Treasury bond to fall below comparable Treasury bonds. See Krishnamurthy (2002) for further discussion of specialness. We

show that the entire Treasury market is “special” relative to other asset markets, and not just that one Treasury is special

relative to another Treasury.

2There is a related fixed income literature documenting that the auctioned amount of a specific Treasury security affects

the value of this security relative to other Treasury securities (Krishnamurthy (2002) and Sundaresan and Wang (2006) are

examples). We show an effect relative to non-Treasury securities.

3
on government bonds. But it is important to note that the effect we identify is on the spread between

government interest rates and corporate interest rates. It is possible that Ricardian equivalence fails in a

way that government debt has an effect on the general level of interest rates, both corporate and government.

Since we focus on spreads, we are unable to isolate such an effect. On the other hand, because we focus

on spreads we can be certain that the effect we identify on government interest rates is over and above any

possible effects of government debt on the general level of interest rates. From an empirical standpoint,

the advantage of focusing on spreads rather than the level of interest rates is that the spread measure is

unaffected by other shocks (such as changes in expected inflation) that affect the level of interest rates and

complicate inference. We also bypass endogeneity issues stemming from government behavior, since it is

unlikely that the government chooses debt levels based on the corporate bond spread.

This paper is laid out as follows. The next section lays out a theoretical framework to relate the demand

for the attributes offered by Treasuries to the price of Treasuries relative to other assets. The section develops

a series of predictions of the theory. We test each of the theoretical predictions in Section 3. In Section 4

we discuss the implications of our findings for a number of important issues in macroeconomics and finance.

The paper also includes an appendix providing details on the data construction as well as mathematical

derivations.

2 Theoretical Framework

We articulate our theory by modifying a standard representative agent asset-pricing model to include a term

whereby agents derive utility directly from holdings of a “convenience” asset. The modification is along

the lines of Sidrauski (1967) and Lucas (2000) who consider models where agents derive utility from their

holdings of money. We consider a representative agent who maximizes,

E

X∞

t=1

β

tu(Ct) (1)

where Ct is the agent’s consumption at date t. We introduce utility from holdings of a convenient asset as

follows. Suppose that the consumption of Ct is the sum of an endowment of ct plus “convenience” benefits:

Ct = ct + ν(θ

A

t

, GDPt; ξt). (2)

The benefits are a function of the holdings of convenience assets, θ

A

t

. One example which we elaborate on

below is that the function ν(·) captures the notion that holding more Treasury securities reduce costs that

would otherwise be incurred by transacting in a less liquid security such as corporate bonds.3 The argument

3To be more precise, we can define Ct = ct −cost(θA

t

, GDPt ; ξt), where the function cost(·) reflects costs that will be incurred

by holding less liquid securities. By holding more Treasuries, these costs are reduced. This is just a renormalization relative to

our defining a benefit function ν(·) that is increasing in θ

A

t

. The important aspect of the modeling is that dCt/dθA

t > 0.

4
θ

A

t

is the market value of the agent’s real holdings of convenience assets and include both Treasuries, θ

T

t

,

and any other private sector assets, θ

P

t

, that provide services similar to Treasuries:

θ

A

t = θ

T

t + k

P

θ

P

t

. (3)

The constant k

P measures the convenience services provided by the private sector assets relative to Treasuries.

The term ξt in the convenience function is a preference shock that affects how much utility is derived from

convenience assets. An example of such a shock is a “flight-to-quality” as during a financial crisis, where

investors may temporarily increase their valuation of convenient assets such as Treasuries.

We assume that the convenience function is homogeneous of degree one in GDPt and θ

A

t

. This captures

the idea that liquidity benefits double if both income and convenience assets double. Thus define,

v



θ

A

t

GDPt

; ξt



GDPt ≡ ν(θ

A

t

, GDPt; ξt). (4)

We assume that the convenience function is increasing in θ

A

t

GDPt

, but the marginal convenience benefit is

decreasing in θ

A

t

GDPt

and has the property lim θAt

GDPt →∞

v

0

(

θ

A

t

GDPt

; ξt) = 0. That is, holding more convenience

assets reduces the marginal value of an extra unit of convenient assets. Furthermore, this marginal value

approaches zero if the agent is holding a large amount of convenient assets.

Let us next consider what underlies our reduced form convenience function v(·). In the monetary economics literature, the convenience of money stems from three attributes: its role as a medium of exchange,

its superior liquidity, and its safety in the sense of retaining a certain nominal value. The demand for these

attributes drives the low yield on money relative to other assets. While Treasuries do not have the medium

of exchange attribute, we argue that they share the liquidity and safety attributes. Papers such as Aiyagari

and Gertler (1991), Heaton and Lucas (1996), Vayanos and Vila (1998), and Rocheteau (2009) show how the

superior liquidity of an asset will lead investors to pay a higher price for that asset. Under these theories,

an increase in the holding of liquid assets will lower the marginal liquidity service provided by any liquid

asset. That is, our earlier assumption that the marginal convenience, v

0

(·), is decreasing in θ

A

t

GDPt

is a natural

outcome of these models. We refer to these theories as describing a liquidity attribute.

The liquidity models we have cited are all heterogeneous agent models rather than homogeneous representative agent models. These models all have two classes of agents where one class trades with the other,

incurring transaction costs when such trade involves illiquid assets. In equilibrium, the prices of liquid assets

carry a premium over less liquid assets, producing a liquidity function resembling v(·). It is important to

keep in mind that while we introduce v(·) in a representative agent model, this reduced form function is

motivated by an underlying theoretical model with heterogeneous agents.

A second benefit of Treasuries is that they are widely believed to provide absolute certainty of nominal

repayment. Under some theories, this safety attribute can drive a convenience yield that is declining in the

5
supply of safe assets. Suppose that some investors face costs of understanding investment in risky assets,

as in the literature on the limited participation of investors in the stock market (Vissing-Jorgensen, 2003).

These investors will have a unique demand for riskless assets, driving up the price of riskless assets. The

existing literature has shown that participation costs can explain why risk premia on stocks may be high and

why interest rates on riskless assets may be low. In addition, in many limited participation models expanding

the stock of riskless assets reduces risk premia and raises riskless rates (see Gomes and Michaelides, 2008).

Another explanation for safety demand stems from the use of Treasuries as collateral in many financial

transactions. Gorton (2010) notes that there is a substantial demand for collateral for purposes of mitigating

counterparty risk in derivatives and settlement systems. The collateral in these transactions is required to

be extremely safe, thus also driving the demand for a safety attribute. Bansal and Coleman (1996) argue

that commercial banks and money market funds use Treasuries to back checkable deposits. Treasuries thus

inherit some of the medium-of-exchange convenience of money, lowering the yield on Treasuries. In this

explanation, it is again the safety of Treasuries that makes them good backing for checking accounts. We

will offer empirical evidence that the safety attribute of Treasuries is one of the drivers of the convenience

yield. However, we will not distinguish further on whether the underlying driver of safety demand is due to

limited participation, collateral, or the check-backing explanations.

Two points are worth noting. First, since long-term Treasury bonds carry interest rate risk it is unlikely

that the explanations offered in the previous paragraph also apply to long-term bonds. For this reason, we

refer to this Treasury property as “short-term” safety. In addition, this safety explanation is distinct from

that suggested by any of the standard representative agent model explanations of high risk premia in asset

markets. This literature has demonstrated how altering the preferences of a representative agent to feature

extreme forms of risk aversion can produce low riskless interest rates and high risk premia. However, the

quantity of convenient assets is unrelated to asset prices in the representative agent model. One needs a

richer model with heterogeneity and/or frictions, along the lines of the literature cited above, to rationalize

the quantity effect. The quantity-price relationship is at the heart of our study. Another way to think about

how safety demand works is that the relation between price and default risk is very steep near zero-defaultrisk. Furthermore, the slope of this curve near zero-default-risk decreases in Treasury supply. This latter

prediction generates a negative relation between the corporate-Treasury bond spread and Treasury supply.

There are also theories for why safe nominal long-term payoffs may be uniquely valued. Greenwood

and Vayanos (2010) suggest that investors such as defined benefit pension funds have a special demand for

certain long-term payoffs to back long-term nominal obligations. The same motive may apply to insurance

companies that write long-term policies. Chalmers (1998) describes how long-term Treasury bonds are

posted as collateral by municipalities to secure their own borrowings. Broadly, this explanation is similar

to the preferred habitat hypothesis of the term structure of interest rates (Modigliani and Sutch, 1966),

6
under which investors are hypothesized to prefer certain maturities of bonds. We refer to these theories as

a describing a long-term safety attribute.

We can represent these different theoretical rationales for convenience in our specification of v(·). Denote

θ

T ,long

t as the stock of long-term Treasury bonds, and θ

T ,short

t as the stock of short-term Treasuries (θ

T

t =

θ

T ,long

t + θ

T ,short

t

). Also define θ

P,liq

t as the stock of non-Treasury liquid assets, θ

P,short−safe

t as the stock

of non-Treasury short-term safe assets, and θ

P,long−safe

t as the stock of non-Treasury long-term safe assets.

Suppose that total convenience on short-term Treasuries can be written as the sum of two convenience

components:

vT ,short(·) = vliq 

θ

T

t + k

liqθ

P,liq

t

GDPt

; ξ

liq

t

!

+ vshort−safe 

θ

T ,short

t + k

short−safeθ

P,short−safe

t

GDPt

; ξ

short−safe

t

!

.

(5)

Similarly, we can specify the convenience on long-term Treasuries as

vT ,long(·) = vliq 

θ

T

t + k

liqθ

P,liq

t

GDPt

; ξ

liq

t

!

+ vlong−safe θ

T ,long

t + k

long−safeθ

P,long−safe

t GDPt; ξ

long−safe

t



.

(6)

The constants, k

liq, kshort−safe and klong−safe, measure the convenience that the private sector assets offer

relative to Treasuries.

Our specification emphasizes that the safety attributes may differ across short and long-term assets

and thus lead to a difference in convenience value in long-term assets relative to short-term assets. In

contrast, our specification assumes that both long and short-term Treasuries offer equal liquidity services.

The empirical literature has documented the existence of significant liquidity premia on both long-term

Treasuries (Krishnamurthy, 2002) and short-term Treasuries (Amihud and Mendelsen, 1991). We are making

the somewhat stronger assumption that long and short-term Treasuries are equally liquid (see Fleming, 2003,

for more on this point).

2.1 Spreads and Supply

We derive pricing expressions for short and long-term bonds based on these different specifications of convenience. As we describe below, decomposing the convenience in the manner above also yields empirical tests

of the existence of priced safety and liquidity attributes. Before describing these tests, let us turn to asset

pricing. We initially derive predictions of the convenience yield theory which do not distinguish between the

liquidity and safety motives. We then turn to predictions implied by each of these separate motives. In terms

of the framework above, our initial set of predictions implicitly assume that both vT ,long and vT ,short are

only functions of θ

T

t

(as opposed to functions of both total Treasury supply and short or long-term Treasury

supply). This will be the case if long and short Treasury supply moves in parallel (and if the demand shocks

are perfectly correlated), or if only a liquidity motive is present. We relax this assumption later.

7
Denote the price level at date t as Qt. If the agent buys a zero coupon Treasury bond for a nominal price

P

T

t

, his real holdings θ

A

t

rises by P

T

t

Qt

.

4 The first order condition for Treasury bond holdings is then,

−

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 (7)

Define the pricing kernel for nominal payoffs as,

Mt+1 = β

u

0

(Ct+1)

u

0(Ct)

Qt

Qt+1

, (8)

so that,

P

T

t = Et[Mt+1P

T

t+1] + P

T

t v

0

(θ

A

t /GDPt; ξt) ⇒ P

T

t =

Et[Mt+1P

T

t+1]

1 − v

0(θ

A

t

/GDPt; ξt)

. (9)

This expression indicates that a positive marginal value of convenience, v

0

(·), raises the price of Treasuries,

P

T

t

.

Let us next derive pricing expressions for a zero-coupon corporate bond that offers no convenience services.

Suppose that the corporate bond may default next period with probability λt and in default pays 1 − Lt+1,

where Lt+1 measures the amount of losses suffered in default. If the bond does not default, it is worth P

C

t+1.

Then, since the bond offers no convenience, its price satisfies

P

C

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

C

t+1|No Default] (10)

In our empirical work we estimate the convenience demand v

0

(·) by relating θ

T

t

to different measures of

the price difference between P

C

t and P

T

t

. There are three price measures we focus on: short-maturity yield

spreads between corporate and Treasury bonds, long-maturity yield spreads, and excess returns of corporate

bonds over Treasury bonds. We now derive expressions for each of these price measures and compare them.

For simplicity, we focus our derivations on zero-coupon bonds and continously compounded yields.

Consider first the case of one period bonds. For such bonds, P

C

t+1 = P

T

t+1 = 1. Then,

e

−i

T

t = 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+1] (11)

For the corporate bond, define L ̃

t+1 as a random variable that is equal to zero if there is no default, and

equal to Lt+1 if there is default. Then,

e

−i

C

t = P

C

t = Et[Mt+1]−Et[Mt+1]Et[L ̃

t+1]−covt[Mt+1, L ̃t+1] ≈ e

−λtEt[Lt+1]−covt[Mt+1,L ̃t+1]/Et [Mt+1]Et[Mt+1]

We thus have the following prediction:

4We deriving pricing expressions for zero-coupon Treasury and corporate bonds. In our empirical work, we examine coupon

bonds and assume that the impact of Treasury supply on coupon bond spreads are qualitatively similar.

8
Prediction 1 (Impact of Treasury supply on short-term spreads)

The one-period yield spread between corporate and Treasury bonds is related to the stock of Treasuries as

follows:

St,1 ≡ i

C

t − i

T

t = v

0



θ

T

t + k

P θP

t

GDPt

; ξt



+ λtEt[Lt+1] + covt[Mt+1, L ̃

t+1]/Et[Mt+1]. (12)

The yield spread reflects the sum of three terms: the convenience yield on Treasuries, the expected default

rate on the corporate bond, and a risk premium associated with the covariance between default and the pricing

kernel. Assuming that v

00(·) < 0, St,1 is declining in θT

t + k

P θP

t

. Consider next the relationship between St,1

and θ

T

t

. Project θ

P

t

linearly on θ

T

t

, so that θ

P

t = a0 + a1θ

T

t + error, where the error is uncorrelated with θ

T

t

.

Then θ

T

t + k

P θP

t = k

P a0 + (1 + kP a1)θT

t + k

P error. If 1 + kP a1 > 0, then St,1 is declining in θT

t

. The latter

condition will be satisfied if a1 > −1/kP , i.e. unless the private sector reduces its supply of substitutes by

more (in effective terms, k

P θP

t

) than the increase in the Treasury supply.

We verify the prediction of the convenience model that an increase in θ

T

t

causes the yield spread to fall. Our

regressions of the yield spread on θ

T

t

recover v

0

(·)



1 + k

P ∂θP

t

∂θT

t



rather than v

0

(·) because of private sector

reaction. In order to recover v

0

(·), we further need knowledge of k

P and ∂θP

t

∂θT

t

. We do not explore that in this

paper because for most questions of interest, it is more important to know v

0

(·)



1 + k

P ∂θP

t

∂θT

t



rather than

v

0

(·).

Note that it is possible that Treasury supply or private sector supply reacts accommodating to demand

shocks (ξt) or to increases in corporate default risk. This will bias the relation between spreads and Treasury

supply towards finding a positive relation, the opposite of the causal negative relation from Treasury supply

to spreads. However, we view it as unlikely that overall Treasury supply reacts substantially to demand

shocks or changes in the risk of corporate bonds. The more plausible reaction involves the private sector

supply or the government’s supply of particular maturities.

Let us next consider multi-period bonds. Define the τ period yields on corporate and Treasury bonds as,

i

T

t,τ = −

1

τ

ln P T

t

and, i

C

t,τ = −

1

τ

ln P C

t

. (13)

The spread between these bonds is St,τ = i

C

t,τ − i

T

t,τ .

Consider again the derivation for corporate bonds. Our derivation for multi-period bonds closely follows

Duffie and Singleton (1999), reflecting the standard practice in the corporate bond pricing literature. Suppose

that the event of default or no-default is non-systematic (i.e. uncorrelated with Mt+1). Then, we can drop

the conditioning on default/no-default and rewrite (10) as,

P

C

t = Et[Mt+1 

λt(1 − Lt+1) + (1 − λt)P

C

t+1

] (14)

Assume that we can write the expected present value of the payment in default as,

Et[Mt+1(1 − Lt+1)] = Et[Mt+1P

C

t+1](1 − Dt) (15)

9
for a suitable process Dt.

5 This is Duffie and Singleton’s “recovery of market value” assumption (RMV).

Then,

P

C

t = (λt(1 − Dt) + (1 − λt))Et[Mt+1P

C

t+1] ≈ e

−λtDtEt[Mt+1PC

t+1]. (16)

Note that the term P

C

t+1 is a function of Dt+1 and λt+1, which embody changes in future default expectations

such as downgrades. For high-grade corporate bonds, which are the focus our study, almost all of the defaultrelated risk is of this form rather than in terms of the bonds defaulting between t and t + 1. In our setup,

the latter default-related risk may be correlated with Mt+1 and carry a risk premium. Thus, our restriction

that the default event in the next period is non-sytematic is not a substantively important restriction, but

does help to simplify our pricing expressions.

Prediction 2 (Impact of Treasury supply on long-term spreads)

The yield spread between τ -period corporate and Treasury bonds is related to the stock of Treasuries as follows,

St,τ =

t+

Xτ−1

j=t

1

τ

Et[v

0

(θ

A

j /GDPj; ξj)] +

t+

Xτ−1

j=t

1

τ

Et[λjDj ] −

t+

Xτ−1

j=t

1

τ

covt(mj+1, R ̃

j+1) (17)

where, mj+1 = logMj+1 (= log β u

0

(Cj+1)

u0(Cj)

Qj

Qj+1

), is the log pricing kernel, and R ̃

j+1 is the one-period excess

return of corporate bonds over Treasury bonds. As long as θ

A

j

increases with θ

T

j

, increases in Treasury supply

lower the spread, St,τ .

The derivation of this spread expression is in the Appendix. The derivation assumes that all relevant

variables, including mt and changes in the corporate and Treasury bond yields, are normally distributed.

The spread reflects three terms: (1) the expected average convenience benefit over the next τ periods;

(2) the expected average amount of default; and (3) a risk premium that depends on the covariance between

the pricing kernel and the excess return on corporate over Treasury bonds.

Let us pause and compare the short-term and long-term spread expressions. Note that shocks to both

θ

A

t /GDPt and ξt have an impact on the short-term spread. The impact of these shocks on the long-term

spread depends on the persistence of the shocks. In the data, a flight to quality (liquidity and safety) shock

(ξt) is short-lived, and should primarily affect short-term spreads. The debt-to-GDP ratio is quite persistent

so that shocks to θ

A

t /GDPt will have a significant impact on both short and long-term spreads. This logic

tells us that the convenience yield as embodied in the long-term spread is primarily driven by θ

A

t /GDPt,

while variability in the short-term spread will partly be driven by ξt.

6 This is an advantage of using the

5Note that in expression (15), the left-hand side expectation is conditioning on default, while the right-hand side expectation

is conditioning on no-default. However, given the assumption that the default-event is non-systematic, we can drop the

conditioning.

6Here is a simple case to formalize these points. Suppose that the convenience yield function is

v

0

(θ

A

t

/GDPt; ξt) = b0 + b1 log(θ

A

t

/GDPt) + logξt.

10
long-term spread and data on θ

A

t /GDPt to estimate convenience yields. On the other hand, the corporate

bonds we use to construct the short-term spread are close to default free. The corporate bonds used in

the long-term spread carry greater default risk. Thus, the results based on the long-term spread are more

sensitive to precise controls for default risk.

The last price variable we examine is the excess return of (zero coupon) corporate bonds over Treasury

bonds. For Treasury bonds,

1 − v

0

(θ

A

t

/GDPt; ξt) = Et



Mt+1

P

T

t+1

P

T

t



(18)

We consider the return on a Aaa/Aa index of corporate bonds on which default over the holding period are

exceptionally rare. Downgrades are the relevant default-related event. Thus,

1 = Et



Mt+1

P

C

t+1

P

C

t



(19)

Prediction 3 (Impact of Treasury supply on excess returns)

The expected excess return of corporate bonds over Treasuries is related to the stock of Treasuries as follows,

Et[Mt+1R ̃

t+1] = v

0

(θ

A

t /GDPt; ξt). (20)

We can rewrite this expression as,

Et[R ̃

t+1] = 1

Et[Mt+1]



v

0

(θ

A

t /GDPt; ξt) − covt(Mt+1, R ̃

t+1)



. (21)

As long as θ

A

j

increases with θ

T

j

, an increase in θ

T

t

implies a decrease in the expected return on corporate

bonds over Treasury bonds.

Let us compare how the excess return regression compares to the yield spread regressions. The advantage

of studying returns over yields is that while time-variation in expected default affect yields such variation

does not affect expected returns. However, studying returns also has distinct disadvantages. If we take a

log-linear approximation, the excess return, R ̃

t+1 is approximately the change in the long-term yield spread,

−(τ −1)St+1,τ−1 +τSt,τ . We can substitute from the expression for St,τ (and St+1,τ−1) from above, and set

Here, we have written the demand shock, ξt, to enter additively in the convenience yield, and assumed a log convenience yield

function, as we do in most of our empirical tests. The short-term spread equally reflects a supply term b1 log(θ

A

t

/GDPt) and

a demand term b1 logξt. Suppose that log(θ

A

t

/GDPt) is AR(1) with coefficient ρ and that logξt is i.i.d. with mean zero. Then

it is easy to verify that the convenience yield component of the long-term spread is,

t+

Xτ−1

j=t

1

τ

Et[v

0

(θ

A

j /GDPj ; ξj)] = b0 + b1 log(θ

A

t /GDPt)

`

1 + ρ + ρ

2 + ... + ρτ−1

 ́ 1

τ

+

logξt

τ

.

If we take τ = 20 years (the maturity for the long spread in our study), and ρ = 0.95 (consistent with data on the Debt-to-GDP

ratio), then the supply coefficient `1 + ρ + ρ

2 + ... + ρτ−1

 ́

1

τ

is 0.64, while the demand coefficient 1/τ is 0.05.

11
λt = 0 (i.e. no defaults on the corporate bonds in the return index, over the next one period) to find R ̃

t+1:

R ̃

t+1 ≈ v

0

(θ

A

t /GDPt; ξt) − covt(mt+1, R ̃

t+1) (22)

−

t+

Xτ−1

j=t+1



Et+1[v

0

(θ

A

j /GDPj; ξj)] − Et[v

0

(θ

A

j /GDPj; ξj)]

−

t+

Xτ−1

j=t+1

(Et+1[λjDj ] − Et[λjDj ])

+

t+

Xτ−1

j=t+1



covt+1(mj+1, R ̃

j+1) − covt(mj+1, R ̃j+1)



The first line of this expression is the expected excess return. This expected return reflects the convenience

yield as well as the risk premium associated with the variability of corporate-Treasury returns. Changes in

θ

T

t will alter the convenience yield, and hence the expected return, in a similar manner as they affect the

short-term yield spread. To estimate the convenience yield using excess return regressions, we need to control

for any time variation in the risk premium. The long-term spread regressions also require us to control for

variation in risk premia, so that in this regard these two price measures have a similar disadvantage. However,

the second, third, and fourth lines indicate the disadvantage of studying returns, namely that realized excess

returns are affected by news about the convenience benefits on Treasuries, about default and about future

risk premia. Realized returns thus could differ dramatically from expected returns, making it statistically

difficulty to detect our predicted relation between expected returns and Treasury supply. Given the pros

and cons of studying returns versus yields, we present results from both approaches in our empirical work.

2.2 Liquidity and Safety Attributes

We now reintroduce the different liquidity and safety attributes of Treasuries and consider how one can

test if these attributes are priced. Following equations (5) and (6), long and short-term assets should be

expected to have different convenience yields. To be precise, let us reconsider the short and long-term spread

expression. The short-term spread reflects liquidity and short-term safety:

St,1 = v

0

liq 

θ

T

t + k

liqθ

P,liq

t

GDPt

; ξ

liq

t

!

+ v

0

short−safe 

θ

T ,short

t + k

short−safeθ

P,short−safe

t

GDPt

; ξ

short−safe

t

!

+λtEt[Lt+1] + covt[Mt+1, L ̃

t+1]/Et[Mt+1]. (23)

The long-term spread, for large τ , reflects the expected liquidity and long-term safety attributes over the

term of the bond:

St,τ =

t+

Xτ−1

j=t

1

τ

Et

"

v

0

liq 

θ

T

j + k

liqθ

P,liq

j

GDPj

; ξ

P,liq

j

!

+ v

0

long−safe 

θ

T ,long

j + k

long−safeθ

P,long−safe

j

GDPj

; ξ

long−safe

j

!#

+

t+

Xτ−1

j=t

1

τ

Et[λjDj] −

t+

Xτ−1

j=t

1

τ

covt(mj+1, R ̃

j+1) (24)

12
There are a few approaches to test for the existence of separate priced attributes. If we can treat variation

in the supply of long and short-term Treasuries as exogenous to other shocks, then a way of identifying the

short and long-term safety attributes is to ask whether an increase in θ

T ,short

t has a larger effect on the

short-term spread than an increase in θ

T ,long

t does, and whether an increase in θ

T ,long

t has a larger effect

on the long-term spread than an increase in θ

T ,short

t does. This approach, although not stated in terms

of safety attributes, is taken by Greenwood and Vayanos (2010) in their study of government maturity

structure and the slope of the yield curve. The difficulty with this approach for our purposes is that it is

quite clear that government maturity choices are not exogenous. As described by Greenwood and Vayanos,

the Treasury considers the slope of the yield curve and the size of the debt and deficit, among other factors,

in determining maturity structure. Greenwood and Vayanos use the Debt-to-GDP ratio as a instrument

for maturity structure. We need to find evidence for the existence of two attributes, and with only one

instrument, it is not possible to do so.

We instead take the following approach. We consider pairs of assets which have either equal liquidity and

different safety or equal safety and different liquidity. The yield spread between these assets only reflects the

price of liquidity or the price of safety. We can then test whether the price of the attribute captured by the

yield spread changes with the relevant supply of Treasuries.

Consider first the spread between P2 and P1 rated commercial paper. The former has a higher default

risk than the latter. The assets are short-term but similarly illiquid as we document in the next section.

Thus the P2 − P1 spread purely reflects the value of short-term safety convenience.

Prediction 4 (Impact of Treasury supply on price of short-term safety)

Consider that P2 and P1 rated commercial paper are equally liquid (i.e. k

liq

P2 = k

liq

P1

), but that k

short−safe

P1 =

1 > kshort−safe

P2

. Then, the spread between these bond yields is related to the stock of short-term Treasuries

as follows:

S

P2−P1

t,1 = (k

short−safe

P1 − k

short−safe

P2

)v

0

short−safe 

θ

T ,short

t + k

short−safeθ

P,short−safe

t

GDPt

; ξ

short−safe

t

!

+λt,P2Et[Lt+1,P2] − λt,P1Et[Lt+1,P1] + covt[Mt+1, L ̃

t+1,P2 − L ̃t+1,P1]/Et[Mt+1] (25)

If short-term safety is a priced attribute, then increases in the supply of short-term Treasuries will lower

S

P2−P1

t,1

(as long as θ

T ,short

t + k

short−safeθ

P,short−safe

t

increases in θ

T ,short

t

).

In terms of the estimation, the P2-P1 spread is directly a function of the supply of short-term convenient

assets. We have noted before that there is extensive evidence that both the private sector and the Treasury

actively manages the maturity structure of debt. To get around any endogenity issues stemming from this

behavior, we use instrumental-variables regressions, using θ

T

t

as an instrument for θ

T ,short

t

(a similar comment

applies for testing Prediction 5 and Prediction 8 below).

13
Next consider a similar prediction but based on the spread between two long-term corporate bonds:

Prediction 5 (Impact of Treasury supply on price of long-term safety)

Take two long-term corporate bonds, an Aaa-rated bond and a Baa-rated bond. Consider that these bonds

are equally liquid (i.e. k

liq

Aaa = k

liq

Baa), but that the k

long−safe

Aaa > klong−safeBaa . Then, the spread between these

bond yields is related to the stock of long-term Treasuries as follows:

S

Baa−Aaa

t,τ = (k

long−safe

Aaa − k

long−safe

Baa )

t+

Xτ−1

j=t

1

τ

Et

"

v

0

long−safe 

θ

T ,long

j + k

long−safeθ

P,long−safe

j

GDPj

; ξ

long−safe

j

!#

+

t+

Xτ−1

j=t

Et[λ

Baa

j DBaaj − λ

Aaa

j DAaaj

] −

t+

Xτ−1

j=t

1

τ

covt(mj+1, R ̃Baa−Aaa

j+1 ). (26)

If long-term safety is a priced attribute, then increases in the supply of long-term Treasuries will lower

S

Baa−Aaa

t,τ (as long as θ

T ,long

t + k

long−safeθ

P,long−safe

t

increases in θ

T ,long

t

).

A similar comparison, but now getting at the liquidity attribute is through the following.

Prediction 6 (Impact of Treasury supply on price of liquidity)

Consider a one-period Treasury bond which offers one unit of liquidity and is default free. Consider also

an FDIC insured bank deposit which is default free but only offers k

liq < 1 units of liquidity. Then, the

one-period spread between these bonds is related to the stock of Treasuries as follows:

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

!

. (27)

If liquidity is a priced attribute, then increases in the supply of Treasuries will lower S

FDIC

t,1

(as long as

θ

T

t + k

liqθ

P,liq

t

increases in θ

T

t

).

Our last test is for the existence of a long-term safety attribute and focuses on the holdings of agents who

for a priori reasons should only be expected to hold Treasuries for the long-term safety attribute. Consider

in particular pension funds and insurance companies that have long maturity liabilities and almost no need

to hold liquid assets. These investors, as we document, do hold Treasuries. A test for the existence of the

long-term safety attribute is therefore as follows:

Prediction 7 (Holders of long-term safety)

If changes in θ

T

t

change the price of the long-term safety attribute, then it should change the equilibrium

holdings of pension funds and insurance companies whose motive to hold Treasuries is driven by the longterm safety attribute.

14
2.3 Private Sector Substitutes

Private sector substitute assets are assets that carry one or more of the liquidity attribute, the short-term

safety attribute, or the long-term safety attribute. We next derive predictions for the behavior of subsitute

assets.

A leading substitute asset for Treasuries is money. Insured bank deposits carry the same safety as

Treasuries, but some have different liquidity. For example, time-deposits are less liquid than Treasuries,

while it is likely that checking accounts and savings accounts are as liquid as Treasuries. However, checking

accounts in particular also have a medium-of-exchange attribute, unlike Treasuries, which can drive the yield

spread between the interest rates on checking accounts and other assets.

The consideration of money as a convenience substitute asset gives us further predictions of the convenience theory.

Prediction 8 (Impact of Treasury supply on yield of substitute assets)

Consider insured bank deposits, which carry an equal amount of the short-term safety attribute as Treasuries

and k

liq units of liquidity. The one-period spread between a corporate bond with no convenience (liquidity or

safety) and the yield on insured bank deposits is related to the stock of Treasuries as follows:

i

C

t − i

FDIC

t = k

liqv0

liq 

θ

T

t + k

liqθ

P,liq

t

GDPt

; ξ

liq

t

!

+ v

0

short−safe 

θ

T ,short

t + k

short−safeθ

P,short−safe

t

GDPt

; ξ

short−safe

t

!

+λtEt[Lt+1] + covt[Mt+1, L ̃

t+1]/Et[Mt+1] (28)

If bank deposits are a liquidity and safety substitute for Treasuries, and if liquidity or safety are priced

attributes, then increases in the supply of Treasuries will lower i

C

t − i

FDIC

t

(unless the private sector reduces

its supply of substitutes by more in effective terms than the increase in the Treasury supply).7

Theory also suggests a relation between the quantities of private-sector substitute assets and Treasuries.

Prediction 9 (Impact of Treasury supply on supply of substitute assets)

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

M oney

t and θ

T

t will be negatively

related.

If as in equation (28), a reduction in Treasury supply lowers i

FDIC

t

, then banks will have an incentive to supply

more bank deposits (for example, to make profitable loans at i

C

t

). It is worth emphasizing that Prediction

9 is of a completely different nature from our other tests. The other predictions relate bond market spreads

to Treasury supply. On the contrary, Prediction 9 relates the quantity of substitute convenience assets to

Treasury supply.

7While we focus on one private-sector substitute, money, the general principal behind this prediction is that the spread

between a non-convenient asset and a private sector substitute asset should vary systematically with the supply of Treasuries

under the convenience yield theory.

15
3 Evidence

Details on the data construction for each table as well as the sources for all variables used in our regressions

are in the data appendix. The regressions all use data at an annual frequency and for as long a period as is

feasible given the variables included in the regression.

3.1 Impact of Treasury Supply on Price Measures

Predictions (1)-(3) state that under the convenience yield hypothesis increases in Treasury supply should

reduce short-spreads, long-spreads, and corporate-Treasury excess returns. Tables I and II present regressions

confirming these predictions.

The key explanatory variable in the regressions reported in the tables is the log of Debt/GDP, where

Debt/GDP is the market value of the outstanding stock of US Treasuries divided by US GDP. The measure

of government debt corresponds to what is referred to as publicly held debt. It includes debt held by the

Federal Reserve, but excludes debt held by other parts of the government such as the Social Security Trust

Fund. Our results do not change appreciably if we exclude the holdings of the Federal Reserve. The debt

measure is as of the end of the government’s fiscal year, i.e. end of June up to and including 1975 and end

of September from 1976 on.

The theoretical measure of convenience yield (convenience benefit) is v

0

(θ

A

t

/GDPt), where θ

A

t

includes

both Treasury debt and private sector convenient assets. Predictions (1)-(3) are that the convenience yield

is declining in θ

A

t

. As we have noted, as long as private sector assets substitute less than one-for-one for

changes in Treasury debt, we can verify predictions (1)-(3) by examining the impact of changes in Treasury

debt on price measures. The regression coefficient on Treasury debt should be interpreted as reflecting the

effect, net of private sector supply response, of a change in Treasury debt on the Treasury convenience yield.

3.1.1 Long-term spreads

In Table I the Treasury debt variable is the logarithm of the Debt-to-GDP ratio, while the dependent variable

in each regression is a bond yield spread measured in percentage terms. Panel A and B present results for

long-term spreads, namely the spread between long-term Aaa-rated corporate bonds and long-term Treasuries

(Panel A) and the spread between long-term Baa-rated corporate bonds and long-term Treasuries (Panel B).

We use the log functional form because it provides a good fit and requires estimation of only one parameter.

A drawback with the log function is that it does not asymptote to zero as Debt-to-GDP rises. We estimate

an alternative functional form with the asymptote property in Section 3.4.

The regressions in Table I are estimated using ordinary least squares (OLS). We report t-statistics adjusting the standard errors assuming an AR(1) error structure. The AR(1) structure is motivated by a

16
standard Box-Jenkins analysis of the autocorrelation function and partial autocorrelation function of the

error terms. The first-order autocorrelations are included in the table. Serial correlation is pronounced

only in the long-term spread regressions of Panel A. For consistency across columns, we use the AR(1)

adjustment in all columns though it makes little difference except in Panel A where t-statistics based on

“standard” OLS standard errors (assuming an i.i.d. error term) would be substantially larger than those

presented. An alternative to OLS estimation with an AR(1) standard error adjustment would be to use GLS

estimation. However, we suspect that log(Debt/GDP) is not a perfect measure of the convenience state variable in the long-term spread regressions, Pt+τ−1

j=t

1

τ Et[v

0

(θ

A

j

/GDPj; ξj)]. It is likely that the private sector

expectations of this sum involve variables other than the current Debt-to-GDP ratio (notably information

about the likely development of the government budget). If so, then Debt-to-GDP is measured with error

implying downward bias in the impact of Treasury supply on spreads (under standard assumptions about

the measurement error). GLS estimation would be more affected by the measurement error issue. To see

this, suppose the error autocorrelation was close to one. Then GLS would effectively transform the data to

run a first difference regression. While in levels the variance of log(Debt/GDP) is likely to be large relative

to that of the measurement error, in first differences this will not be the case since the high persistence of

log(Debt/GDP) means that the volatility of its first difference is low (a formal Monte-Carlo study of this

issue is available upon request). These considerations lead us to present OLS regressions with standard

errors adjusted for the serial correlation. We emphasize that our OLS regression coefficients are likely to be

conservative, understating the impact of Treasury supply on convenience yields.8

The coefficient of −0.744 in column (1) of Table I implies that a decrease of one standard deviation

in Debt-to-GDP from its mean value of 0.426 to 0.233 increases the convenience yield component of the

Aaa-Treasury spread by as much as 0.45% (45 basis points).

Default risk is an important component of the bond spreads. In column (2) and (3) we show that the

impact of Treasury supply on the Aaa-Treasury spread is robust to including default controls. Moody’s

Investors Service (2005) estimates, based on data from 1920 to 2004, that the default rate on Aaa rated

bonds over a 10 year period is around 1%, while for Baa bonds this default rate is 8%. In column (2), we

control for default risk using a default measure computed by Moody’s-KMV, who are the current industry

standard in calculating default probabilities for corporate bond pricing. Their computation is based on

Merton (1974) which treats the debt of a firm as a riskless asset minus a put option on the firm’s assets.

8A standard solution to the bias problem would be an IV approach. If the error term was serially uncorrelated one could use

lagged values of log(Debt/GDP) as instrument for log(Debt/GDP). With serially correlated errors one should lag the instrument

far enough to avoid correlation between the instrument and the error term. We find that the coefficient on log(Debt/GDP) is

larger in IV estimations and keeps increasing as the instrument is lagged further. This suggesting that the measurement error

concern is relevant, but that it is unclear how far to lag the instrument and therefore more conservative to report only OLS

results.

17
Using capital structure information and Merton’s option decomposition of capital structure, they infer the

firm’s asset value and asset value volatility. This information allows them to compute the distance to default

on debt (i.e. moneyness of the put option). Using historical default information in a non-linear regression,

they estimate how distance-to-default translates into default probabilities. We use the median EDF reported

by Moody’s-KMV for large firms (defined as firms with book value of assets > $300 million in current dollars).

The EDF measure is available from 1969-2007. The results in column (2) shows that the EDF default measure

is informative. Crucially, the coefficient on log(Debt/GDP) remains highly significant and of roughly the

same magnitude as in other specifications.9,10 The EDF measure is only available back to 1969, while we

would like a default measure that goes back to 1926. Because the EDF measure is option-pricing based,

the key input into the measure is stock return volatility. Thus for the longer sample we use stock return

volatility. We measure the weekly returns on the value-weighted S&P index based on daily returns. As the

volatility measure for a given year, we compute the standard deviation of the weekly log returns over the

year leading up to the end of the government fiscal year (the date of the Debt-to-GDP observation). We

annualize this standard deviation by multiplying by the square root of 52. Over the 39 years for which we

have both EDF data and stock market volatility estimates, the correlation of these two default measures

is 0.75. This provides strong support for the use of stock market volatility as a default control over the

full sample. Column (3) presents results using the stock return volatility measure. Volatility is significantly

related to the spread, but the coefficient on log(Debt/GDP) is roughly the same as in previous specifications.

Furthermore, the economic effects of changes in the default risk measures on the Aaa-Treasury spread are

modest compared to the effect of Treasury supply. A one standard deviation increase in the EDF increases

the Aaa-Treasury spread by 21 basis points while a one standard deviation increase in stock return volatility

increases it by 10 basis points.

The regressions in column (2) and (3) include the slope of the yield curve as a further control. We

measure the slope as the spread between the 10 year Treasury yield and the 3 month Treasury yield (slope).

The slope of the yield curve is a measure of the state of the business cycle. It is known to predict the

excess returns on stocks and may also pick up time-varying risk premia on corporate bonds. For example, if

9Another issue that arises in interpreting the long-term spread regressions is callability. Duffee (1988) points out that the

Moody’s Aaa index includes callable corporate bonds. Thus, the Aaa-Treasury spread may also reflect an interest rate option.

Duffee proxies for the moneyness of the call option using the level of interest rates and shows that yield spreads vary significantly

with the level of interest rates. Following this approach, we have investigated adding levels of short and long-term interest rates

as explanatory variables and have found that it has no appreciable effects on the coefficient on log(Debt/GDP). We also note

that callability does not affect the results on excess bond returns and short-term corporate bond spreads.

10A further issue that affects spreads between corporate bonds and Treasuries is that Treasuries are exempt from state taxes,

while corporate bonds typically are not. We have run regressions that include a control for the state tax effect on the spread

(the product of the average state tax rate and the Aaa yield) and find that our results are largely unchanged. The results are

available upon request.

18
investors are more risk averse in a recession, when the slope is high, they will demand a higher risk premium

to hold corporate bonds. Thus, the slope of the yield curve serves as a measure of variation in the risk

premium component of the bond spread, i.e. the term involving covt(·) in Prediction 2. We also note that

to the extent that corporate default risk is likely to vary with the business cycle, the slope variable can

furthermore help control for the default risk in the yield spread.

Turning to the results for the Baa-Treasury spread in Panel B, the coefficient on log(Debt/GDP) in

column (5) is considerably higher than the coefficient in column (3) for the Aaa-Treasury spread, and imply

that a decrease of one standard deviation in Debt-to-GDP from its mean value of 0.426 to 0.233 increases

the convenience yield component of the Baa-Treasury spread by 0.79% (79 basis points). The difference in

results between Panel A and B suggests that Aaa bonds offer some convenience services of Treasuries and

thus that the Baa-Treasury spread is more appropriate for capturing the full effect of Treasury supply on

the Treasury convenience yield. We present further evidence for this interpretation in Table III in section

3.4 below.

3.1.2 Short-term spreads

Panel C and D of Table I are based on short-term bond spreads, with Panel C showing results for the spread

between the highest rated commercial paper and Treasury bills, both of 3-month maturity, and Panel D

focusing on the spread between lower-grade commercial paper (A2/P2 rated paper) and Treasury bills. The

shorter time-period in column (9) is due to yields for lower-grade commercial paper being available only

starting in 1974.

Short and long-term spreads may contain different convenience attributes, so we should not expect the

coefficients on log(Debt/GDP) to be the same across the different maturities. Nonetheless, the regressions

for short-term spreads show that the effect of changes in Treasury supply on short-term spreads are of fairly

similar magnitudes as the effect on long-term spreads. Consistent with the results for long-term spreads,

the higher coefficients in Panel D than in Panel C is also indicative that the high grade commercial paper

in Panel C (like the Aaa-rated long-term bonds in Panel A) has some convenience attributes.

It is important to note that our evidence on the spread between commercial paper and T-Bills is less likely

to be affected by issues of omitted expected default or default risk premium controls than the evidence on the

Aaa-Treasury spread. This is the case because historical default rates on the highest rated commercial paper

(A1/P1) are very low, with literally zero defaults during the period 1972-2000 for which Moodys provide

data on commercial paper defaults. This latter observation can also explain why the default controls are

statistically not different from zero in the commercial paper regressions in columns (7) and (9). Over a three

month period, a highly rated firm may run into financial difficulties and be downgraded, but is unlikely to

enter bankruptcy.

19
3.1.3 Excess returns

Table II presents regressions where the dependent variable is the annual excess return on long-term corporate

bonds over long-term Treasury bonds. We use the Ibbotson corporate bond return index. This index gives the

total return from holding high grade (Aaa and Aa) corporate bonds with approximately a 20-year maturity

over the next month (we use 12 months of returns to compute an annual return). It is important to recognize

that Aaa bonds and Aa bonds almost never default over the next month. Moody’s Investors Service (2005),

using data from 1920 to 2004, reports that the default rate on Aaa bonds over the next year are 0.00% while

it is 0.06% on Aa bonds. The default rate over a one month horizon must therefore be close to zero for both

Aaa and Aa bonds. The default-events in holding these bonds is that the probability of default rises and

the bonds deliver a low return. The latter is the relevant default risk in holding high grade corporate bonds

over a short period. If a bond is downgraded during a particular month, Ibbotson includes its return for

that month in the computation of the index return before removing the bond from future portfolios.

We estimate the return regressions using ordinary least squares. We report t-statistics based on modeling

the error as an ARMA(1,1) process. Granger and Morris (1976) show that the sum of an AR(1) process and

a white noise process is an ARMA(1,1) process. In our setting, the realized excess return is the sum of the

expected excess return and an expectation error. We find that the Aaa-Treasury yield spread has an AR(1)

error term and would expect the expected excess return of Aaa-bonds over Treasury bonds to share this

component. The expectation error is white noise, assuming expectations are rational. In economic terms,

the expectation error captures news about expected convenience yields, default, and default risk premia as

shown in equation (22). Cochrane (2008) provides further discussion of the need for ARMA(1,1) processes

for return forecasting models. In practice, it turns out that standard errors in the return regressions are

similar whether we use OLS with standard errors adjusted assuming ARMA(1,1) error terms or OLS with

standard errors that assume i.i.d. error terms. Furthermore, coefficients and standard errors are similar to

the OLS results if we estimate the ARMA(1,1) model using maximum-likelihood.

The regression in column (1) includes log(Debt/GDP) as the only explanatory variable. The coefficient

estimate of -0.851 is similar to the coefficient estimate in the Aaa-Treasury yield spread regression in column

(1) of Table 1. This is not surprising since the bonds underlying the returns in Table II are long-term

bonds. Thus the coefficient on log(Debt/GDP) in Table II reflects the one period convenience on holding

long-term bonds. The fact that our Aaa-Treasury yield spread result is robust to analyzing returns alleviates

concerns that the effect of Treasury supply on the Aaa-Treasury yield spread could be reflecting a correlation

between Treasury supply and expected default on the Aaa bonds. This is the case since expected excess

returns, unlike yield spreads, should not vary systematically with changes in expected default as these affect

both expected cash flows and today’s price. The effect of Treasury supply on excess returns is, however,

not statistically significant. This is likely due to the fact that most of the variation in excess returns is

20
due to news (expectational errors); the standard deviation of annual excess returns is 3.72 percent while

the standard deviation of the Aaa-Treasury yield spread is 45 basis points. To help isolate the effect of

Treasury supply on expected excess returns, the results in columns (2) includes a “credit hedge” for changes

in default risk (a major component of the expectational error). The credit hedge is the contemporaneous

return on junk bonds relative to Baa bonds (obtained from Ibbotson). Including this hedge helps to reduce

the noise in realized returns that is unrelated to the convenience yield and thereby improves the power in

the regressions. For example, if credit risk rises between t and t + 1, then corporate bonds will deliver a low

return over this period. The return on junk bonds relative to Baa bonds will also be low during this period

and can serve to hedge out this change in credit risk. The R2in the regression column (2) is much higher

than that of column (1). When including the credit hedge, the effect of Treasury supply on excess returns is

statistically significant (and larger in magnitude). Column (3) adds an additional hedge, the excess return of

long-term Treasuries over Treasury bills, in order to capture news about shifts in the yield curve which could

affect excess returns of corporate bonds over Treasuries in case of any duration mismatch. We furthermore

include the yield curve slope to capture time-varying default risk premia. Adding these two controls do not

appreciably change the effect of Treasury supply.

3.2 Evidence for the Existence of Priced Liquidity and Safety Attributes

We next move to testing Predictions (4)-(7) that the convenience yield on Treasuries is a reflection of two

priced attributes: liquidity and safety. We consider pairs of assets with different liquidity but similar safety

or with different safety but similar liquidity. Table III and IV present the results.

The first two columns of Table III present evidence for the existence of a unique demand for long-term

safe assets leading to a positive convenience price of the long-term safety attribute. The dependent variable

is the spread between Baa and Aaa corporate bonds. Baa bonds carry more default risk than Aaa bonds

but are similarly illiquid. Chen, Lesmond and Wei (2008) study corporate bond liquidity in a large sample

of corporate bonds over the period 1995 to 2003 and report that the spread between bid and ask prices on

Aaa corporate bonds averaged 52 bps while they averaged 58 bps on the Baa corporate bonds. These spreads

compare to near 10 bp for Treasury bonds (Longstaff, 2004). Thus any convenience yield as measured in the

Baa-Aaa spread can only reflect the price of the long-term safety attribute, as opposed to a liquidity effect.

Column (1) shows that an increase in Treasury supply leads to a decrease in the Baa-Aaa spread, confirming

the existence of a priced long-term safety attribute driven by Treasury supply. Theory suggests that the

supply of long-term safe assets rather than the total supply of Treasuries should drive the price of long-term

safety. In column (2), we presents results using the supply of long-term Treasury debt, measured as the

supply of Treasuries with greater than 10 years maturity divided by GDP. Since the maturity structure of

government debt is likely to be endogenous, we instrument the long-term supply by powers of (Debt/GDP).

21
The first-stage of the instrumental variables regression is not reported for brevity, but shows a significant

relation between the total debt and the measure of long-term debt. The coefficient of −0.310 means that

a one standard deviation decrease in the supply of long term Treasuries (as a ratio to GDP) from its mean

value of 0.078 to 0.021 raises the price of long-term safety by 41 basis points.

Column (3) and (4) present evidence for the existence of a priced short-term safety attribute driven by

Treasury supply. The dependent variable is the spread between three month A2/P2 rated and A1/P1 rated

commercial paper. As noted earlier, over a three month period, based on data from 1972 to 2000, Moody’s

Investors Service (2000) estimates that the default probability on A2/P2 paper is 0.02%, while it is 0% for

A1/P1 paper. Thus there is a (small) difference in the safety of these short-term assets. As for liquidity,

there is little secondary market trading activity in commercial paper of any rating. Covitz and Downing

(2007) based on data from 1998 to 2003 report that most of the commercial paper activity is in terms of

new issuance. Secondary market transactions account for less than 2% of the new issuance activity on any

day. Using trading volume as a proxy for liquidity and EDF as a proxy for credit risk, Covitz and Downing

find that, in the cross-section of commercial paper, liquidity differences explain very little of the variation

in rates. Thus, any convenience yield as measured in the P2-P1 spread reflects the price of the short-term

safety attribute. In column (3) we use total Treasury supply while column (4) presents an IV regression,

where the supply measure is of Treasuries with maturity less than 1 year divided by GDP. The results in

both column (3) and (4) confirm the existence of a significant price of short-term safety. The coefficient of

−1.453 in column (4) means that a one standard deviation decrease in the supply of short-term Treasuries

(as a ratio to GDP) from its mean value of 0.124 to 0.104 raises the price of short-term safety by 26 basis

points.

The last two columns present evidence for the existence of a priced liquidity attribute of Treasuries,

comparing assets with similar safety but different liquidity. The dependent variable in column (5) is the

spread between the interest rate customers receive on 6 month FDIC-insured CDs and 6 month Treasury

bills. We start the CD series in 1984, corresponding to the phasing out of Regulation Q (see Gilbert, 1986).

Given FDIC insurance, any convenience yield documented via Treasury supply affecting this spread can only

reflect a liquidity attribute. The supply variable in the regression is the total supply of Treasuries, since all

Treasuries carry the liquidity attribute. The impact of Treasury supply on the CD-Treasury spread confirms

the existence of a significant price of liquidity over the 1984-2008 period. To obtain evidence going back

further, column (6) uses data on the spread between the average interest rate paid on time and savings

deposits and Treasury bill rates. Since interest rate ceilings set by Regulation Q were binding at various

points during the period from 1966 until their phase-out in the mid 1980s (see again Gilbert, 1986), we focus

on data from 1934 – the first year of FDIC insurance – to 1965 (we do not have CD rate data from this earlier

period). The interest rate on time and savings deposits is less ideal than the CD rate because FDIC insurance

22
does not apply to large deposits, so the interest rate on time and savings deposits reflect a mix of insured

accounts and non-insured accounts. The FDIC reports that insurance applied to approximately 75% of all

deposits at commercial banks over the period from 1934 to 1965 (Federal Deposit Insurance Corporation:

The First Fifty Years, a History of the FDIC, 1933-1983 (Washington: FDIC, 1984)). As a result, there is

a slight difference in the safety of the average time and savings deposit and of Treasuries. In addition, the

time and savings deposits are an amalgam of deposits with different maturities, making it more difficult to

maturity match the series to Treasuries. We match it to 6-month Treasuries. Subject to these qualifiers,

the evidence in column (6) of an impact of Treasury supply on the interest rate spread between time and

savings deposits and Treasuries provides further support that investors value liquidity with Treasury supply

driving the price of liquidity.11

We can gauge the magnitude of the liquidity effect in two different ways. First, note that the deposits in

column (6) include very short-term savings accounts which are quite liquid. That is the spread in column (6)

reflects the difference between a very liquid Treasury and a liquid bank account, so that the spread reflects an

underestimate of how much Treasury yields are reduced by the liquidity attribute of Treasuries. The spread

in column (5) is a more pure read on the liquidity impact on Treasury yields, although the sample is quite

short. The coefficient of −1.904 means that a one standard deviation decrease in the supply of Treasuries

(as a ratio to GDP) from its mean value of 0.426 to 0.233 raises the price of liquidity by 115 basis points. A

second estimate of the impact of Treasury supply on the price of liquidity comes from the regression in Table

I, column (7), which is the high-grade CP spread regression from 1969 to 2007. We have noted that data

from 1972 on indicates that there has never been a default on high grade CP. The coefficient on the default

controls in that regression are also small and statistically not different from zero. Using this spread as a

measure of liquidity, we find that a one standard deviation decrease in the supply of Treasuries (as ratios to

GDP) from its mean value of 0.426 to 0.233 raises the price of liquidity by 61 basis points.

Prediction 7 offers another way to demonstrate the existence of a priced long-term safety attribute. As

reported in Table VII, private and government pension funds and insurance companies together hold 11%

of the total stock of Treasuries, on average from 1945-2008. These Treasury holdings are on average 26%

of these groups’ portfolio allocation to long-term bond investments. It is likely that these groups holdings’

of Treasuries is only driven by their demand for the long-term safety attribute. Since they are long-term

investors, these groups are unlikely to have any liquidity demand. If changes in the price of Treasury

convenience cause these groups to change their holdings of Treasuries, this is indirect evidence that part

of the changing price of convenience is a change in the price of long-term safety. The regression should be

11Note that it is possible that bank deposit accounts have a medium-of-exchange attribute that is not shared by Treasury

bills. Even in this case, the coefficient on the Treasury supply variable in the regressions is only evidence of a priced liquidity

attribute, since variation in Treasury supply should not be expected to affect the price of the medium-of-exchange attribute.

23
read as the estimate of an inverse demand-curve. We regress the Baa-Aaa spread, as a measure of the price

of long-term safety, on the ratio of the groups’ Treasury holdings to GDP. Since the demand shocks to the

groups’ Treasury holdings affect both the spread and its Treasury holdings a standard endogeneity issue

is present, and the regression is therefore estimated by instrumental variables, using powers of Debt/GDP

as instruments. The results are in Table IV. The coefficient on log holdings is statistically significant at

the 10% level. The regression coefficient is −0.372 implies that a 50 basis point decrease in the spread is

associated with a 20 percent increase in the groups’ Treasury holdings relative to GDP. This shows that

these agents substantially increase their holdings of Treasuries when the (long-term safety) convenience yield

on Treasuries decreases, consistent with Prediction 7.

3.3 Evidence on Money

The results in Table III suggest that Aaa rated bonds and A1/P1 rated commercial paper share some of the

safety attributes of Treasuries. In this section we also show that time and savings deposits share some of

the safety and/or liquidity convenience of Treasuries. Specifically, we test Prediction 8 (that the supply of

Treasuries negatively affects the yield spread between non-convenient assets and time and savings deposits)

and Prediction 9 (that the supply of Treasuries negatively affects the supply of time and savings deposits).

The evidence validating Prediction 9 is particularly compelling for our convenience yield theory. All of

the other tests of the theory involve relations between Treasury supply and bond market spreads. There

may be lingering doubts that there is some common part of these spreads that for reasons other than our

theory (e.g. insufficient default controls) is correlated with Treasury supply. The evidence for Prediction 9 is

of a completely different nature and relates the quantity of substitute convenience assets to Treasury supply.

As one can see in Figure 2, the evidence in favor of Prediction 9 is striking. The vertical axis in Figure

2A is the quantity of small-denomination (and thus FDIC insured) time and savings deposits, measured as

M2 minus M1, all divided by GDP.12 This money aggregate is graphed versus the Debt/GDP ratio based

on annual observations from 1934 to 2008. The figure reveals a clear substitution pattern, consistent with

Prediction 9. When there are less Treasuries outstanding, the banking sector increases the supply of bank

deposits.13 The non-M1M2 money aggregate shares the safety and liquidity attributes of Treasuries. The

fact that a decrease in Treasury supply generates an increase in non-M1M2 therefore provides evidence that

12We exclude Treasury holdings of retail money market funds from M2 since we want to focus on substitutes for Treasuries

in this part of the analysis.

13There are a few other papers which have documented related substitution patterns. McDonald (1983) and Greenwood,

Hanson, and Stein (2008) document that the supply of corporate bonds is negatively related to the supply of Treasury securities.

McDonald shows a negative relation between the aggregate amount of corporate debt outstanding and the aggregate amount

of government debt over a sample from 1945 to 1978. Greenwood, Hanson, and Stein show a negative relation between the

maturity structure (long versus short) of corporate bonds and government bonds over a sample from 1963 to 2005.

24
Treasury supply drives the equilibrium price of safety and liquidity.

We exclude M1 (currency and checking accounts) in this analysis because it has the medium-of-exchange

attribute, unlike Treasuries. Currency outstanding is also directly controlled by the government, and therefore we may not expect the supply of such currency to be price elastic. The same applies to checking

accounts since banks must hold reserves against checking accounts and the supply of bank reserves is largely

determined by the Federal Reserve. Thus, it is cleanest to exclude M1 and focus on assets under the private

sector’s control that only offer safety and liquidity convenience.

Table V presents these results in regression form. In Panel A we regress measures of money on Debt/GDP.

In addition to the non-M1M2 measure, we also consider non-M1M3. The latter measure includes small and

large time and savings deposits, repos and Eurodollars.14 The M3 measure is available beginning in 1959. All

of the measures reveal a significant negative correlation between money and Treasury supply. The coefficient

in column (3) of −0.621 indicates that when Treasury supply falls by $1, the banking sector responds by

supplying $0.62 of deposits. In Panel B, we elaborate on the mechanism underlying the banking sector

response, showing that the change in the private sector supply is induced by price changes. In column (4),

we regress the spread between Baa rated bonds and the interest rate paid on the non-M1M2 bank deposits

on log(Debt/GDP), with controls. This regression indicates that a decrease in Treasury supply reduces the

interest rate on bank deposits relative to the Baa bond rate, consistent with Prediction 8. The channel here

is that the price of short-term safety/liquidity rises when Treasury supply declines, causing the interest rate

on bank deposits, which carry safety/liquidity attributes, to fall. In column (5), we then regress the supply

of bank deposits, measured as log(non-M1M2/GDP), on the fitted spread response. Column (5) is thus the

second stage of an IV regression where we regress the supply of bank deposits on the spread between Baa

rated bonds and non-M1M2, instrumented by total Treasury supply. The decrease in the bank deposit rate

induces the banking sector to supply more deposits. The regressions in Panel B exclude the Regulation Q

period of 1966 to 1983.

We have noted that the money evidence is particularly compelling for our convenience yield theory

because Prediction 9 is of a different nature than our other tests, and the relation as depicted in Figure 2 is

so striking. The money evidence is also interesting because it highlights that the effects suggested in Figure

1 are not merely about the pricing of Treasury bonds, but are more broadly about assets that offer liquidity

and safety services. Liquidity and safety are attributes that are priced in the asset market. Moreover, as

we discuss further in Section 4.2, this evidence is relevant for the larger literature in monetary economics on

the liquidity effects of money.

14We exclude both retail and institutional money funds’ holdings of Treasuries.

25
3.4 Quantifying the convenience yield

We next turn to quantifying the level of the convenience yield. Results from the log-specification pin down

the derivative of the convenience yield with respect to Treasury supply, but do not pin down the level of the

convenience yield as a function of Treasury supply. Theory suggests that the value of convenience should go

to zero given sufficient convenience assets. Imposing this asymptote property allows us quantify the level of

the convenience yield, since the convenience yield at some θ

T

t given an estimated relation between spreads

and Treasury supply of f(θ

T /GDP) is simply f(θT

t /GDPt) − f(∞) (i.e. the distance between the predicted

spread and the estimated asymptote).

The log function does not have the asymptote property.15 Table VI reports results in which we model

the convenience yield with a function that is piecewise linear in Treasury supply, b1 max[b2 − Debt/GDP, 0].

Visually, the piecewise linear function appears to be a good fit of the relation as depicted in Figure 1. Indeed,

the R2s for the piecewise linear function rise somewhat relative to the log function. Regressions are estimated

by non-linear least squares. As in Table I, the standard errors are adjusted assuming the error term is AR(1).

The term b1 max[b2 − Debt/GDP, 0] is the convenience yield on long-term Treasury debt as a function

of the Debt-to-GDP ratio. Consider the estimates from column (4) for the Baa-Treasury spread. We can

evaluate the convenience yield function at historical values of the Debt-to-GDP ratio from 1926 to 2008, and

average these numbers to come up with the average value of the convenience yield over our sample. This

computation gives 72 basis points. The Baa-Treasury spread reflects both long-term safety and liquidity.

We have argued that the Baa-Aaa spread is only driven by long-term safety, while the Aaa-Treasury spreads

are primarily driven by liquidity given the low default rate on Aaa bonds. To provide a sense of the relative

magnitudes of the safety and liquidity convenience components, we make the simplifying assumption that the

Aaa-Treasury spread only reflects liquidity, while the Baa-Aaa spread only reflects safety. Based on the AaaTreasury estimates of column (2), the average liquidity convenience is 46 basis points. This number should

be interpreted as an upper bound for liquidity convenience, since the Aaa-Treasury spread does contain some

safety convenience as well (since Aaa bonds are not quite as safe as Treasuries). Further, subtracting 46

from 72, gives us that safety convenience is worth 26 basis points on average (a lower bound since Aaas do

carry some default risk).

In the piecewise linear regressions, the constant term b0 is the average default component of the spread,

since the EDF, volatility and slope controls in the regressions are demeaned. Consider column (4) for the

Baa-Treasury spread. This regression indicates that b0 is 1.199, which is within the range of estimates from

15We can imagine estimating a function max(−log Debt/GDP, 0), which does have the asymptote property. Since the Debtto-GDP ratio exceeds one in only two data points during the 1940s, the coefficient estimate in this case will be virtually the

same as the one we report. However, this function implicitly assumes that the asymptote is reached when the Debt-to-GDP

ratio is one, when there no a priori reason to make such an assumption.

26
the corporate bond price literature of the default component of Baa bonds (see Elton et al (2001) and

Longstaff, Mithal and Neis (2006)).

Finally, the estimates of b2 of the piecewise linear specification provides an estimate of how large Debtto-GDP needs to be before the demand for convenience is fully saturated. The regressions for both the

Aaa-Treasury spread and the Baa-Treasury spread indicate that this limit is around 0.55. It is interesting

to note that the latest CBO projection of the Debt/GDP ratio for 2010 puts the ratio at 0.603, indicating

that if historical relationships prevail, the convenience yield is likely to fall to zero in the near future.

There is an important caveat in interpreting the piecewise linear estimates. The estimates of b0 and b2 are

heavily affected by observations in the right tail of Figure 1 (i.e. high Debt-to-GDP ratios). These high ratios

only occur during the 1940s and 1950s, so the parameter estimates are influenced by the idiosyncrasies of the

war period. In an effort to help finance the war debt at low interest rates, the Federal Reserve committed

to purchase long-term Treasury bonds at a floor below prevailing market prices, thereby inducing long-term

Treasury rates to be lower than market forces would have otherwise dictated. As events played out, the

Federal Reserve did not in fact accumulate much long-term Treasuries, but even so, the commitment to a

floor should be expected to affect prices. As a result, our estimates of b0 are biased upwards – implying

that our above estimate of an average Treasury convenience yield of 72 basis points is conservative – and

estimates of b2 biased downwards. The Federal Reserve intervened much more strongly in the Treasury bill

market. Policy at the time effectively allowed commercial banks to carry Treasury bills as interest bearing

reserves. In addition, beginning in 1943, the Federal Reserve directly purchased a large share of newly issued

Treasury bills, while long-term bonds were held by a variety of investors. The Federal Reserve directly held

72% of total Treasury bills outstanding in 1944. See Wicker (1969) for further details on all of these points.

We present piecewise linear regressions for the long-term spreads, subject to the caveat noted above, but

we do not present results for the short-term spreads on grounds that they are likely largely uninformative

about convenience yields. We also note, as can be seen from columns (2), (4), (7), and (9) in Table I, that

our main results about the impact of Treasury supply on yields hold for subsamples that do not include the

war period.

4 Implications

We have shown that: (1) Changes in Treasury supply drives the convenience yield on Treasuries; (2) Both

safety and liquidity drive the convenience yield; (3) Money offers safety and liquidity convenience and is thus

a Treasury substitute; and (4) The average Treasury convenience yield is large. In this section, we discuss

implications of our findings for a number of important issues in finance and macroeconomics.

27
4.1 Seignorage from Treasury Bonds

Investors purchase Treasury securities despite the fact that these securities offer a low return because they

convey convenience benefits. In this section, we evaluate how much seignorage the government collects from

being able to finance the US federal debt with securities that offer convenience benefits.

The historical average Debt-to-GDP ratio is 0.426. At this Debt-to-GDP, the convenience yield from the

Baa-Treasury piecewise linear specification in column (4) of Table VI evaluates to 59 basis points. Multiplying

these numbers together gives seignorage of 0.251% of GDP. Here is another seignorage computation. If we

evaluate the convenience yield at each of the Debt-to-GDP ratios in our sample, multiplying by that Debt-toGDP ratio, and then averaging, we find that average seignorage is 0.238% of GDP. These computations are

only for long-term convenience and therefore ignore the dependence of convenience on maturity and hence

how seignorage depends on the maturity structure of debt.

To put these numbers in perspective, consider the seignorage that the government derives from households’ willingness to hold fiat money at no interest. The monetary base at the end of 2007, prior to the Federal

Reserve’s quantitative easing experiment, was $848 Billion, corresponding to 6% of GDP. Suppose the federal

government had to repurchase the monetary base by issuing Treasury bills and that these Treasury bills had

a 4% nominal yield. Then the annual interest expense of this additional debt would be 4 × 0.06 = 0.24% of

GDP per year.

Together, these calculations suggest that the total benefit from the convenience yield on Treasuries is

large and that the seignorage to the government from being able to finance the current level of debt with

securities that have a convenience yield is of the same order of magnitude as the seignorage resulting from

the public’s willingness to hold fiat money at no interest.

4.2 Implications for Money Demand Relations

The factors that drive the demand for Treasuries also drive the demand for money. Figure 2 is fairly

compelling evidence for this point. The exercise in this paper has been to examine liquidity and safety

demands as they are reflected in the prices of Treasury securities relative to other securities. It is useful to

revisit the literature on money demand relations from the vantage of our study as it may shed light on some

of the sources of the instability in money demand on which many authors have commented (see Goldfeld

and Sichel, 1990).

The convenience yield on money, say as reflected by the spread between the interest rate on checking

accounts and corporate bond interest rates, is the sum of the convenience yields due to three underlying

attributes. The demand for money stems from demand for liquidity, short-term safety, and a medium-of28
exchange. Denote the money spread as SM

t

. Then analogous to Treasuries, we can express SM

t as

S

M

t = k

M,liq v0

liq(θ

A,liq

t

/GDPt; ξ

liq

t

) + k

M,short−safev0

short−safe(θ

A,short−safe

t

/GDPt; ξ

short−safe

t

)

+k

M,X v0

X (θ

X

t /GDPt, ξXt

) (29)

where “X” stands for medium of exchange.

The literature estimating money demand most commonly estimates a relation between the spread, SM

t

,

and measures of monetary aggregates such as M1, M2, or broader aggregates of short-term bank liabilities.

From equation (29), it is clear that the supply of Treasuries, both long and short, should be integrated

into monetary aggregates. The supply of Treasuries drives the prices of liquidity and short-term safety and

therefore drives part of the overall convenience yield on money. Ignoring variation in the supply of Treasuries

can lead to instability in the estimated money demand relations.

Many authors report increased stability when estimating a money demand function that weighs the subcomponents of money (currency, deposits, money-market accounts, etc.) by the convenience provided by the

sub-component (see for example Rotemberg, Driscoll, and Poterba, 1995). This approach follows the work

of Barnett (1980). Our suggestion to include Treasuries, with some weight, in money aggregates is similar to

these approaches and may likewise improve the stability of money demand estimates. However, it is worth

emphasizing that Barnett’s approach assumes that money contains the price of a single attribute, when it

seems likely from our study that money contains the prices of multiple attributes. Thus, different aggregates

of Treasuries (short-term and total), with varying weights, should be used to construct separate liquidity

and short-term safety aggregates. It seems possible that there is a stable demand for each of the underlying

attributes, but this is missed given the aggregation that is done in the literature.

The prices of liquidity and short-term safety are reflected in both SM

t and in the spreads of “non-money”

instruments such as the CP-Bills spread or the P2-P1 spread. That is, there is information in these other

spreads that is relevant for estimating the demand for the underlying attributes of money and hence for

estimating money demand. As far as we are aware, there are no papers in the money demand literature that

utilize the information contained in these other spreads. In Section 3.4 we estimate the convenience yield on

long-term Treasuries due separately to their liquidity and long-term safety by examining both the Baa-Aaa

spread as well as the Aaa-Treasury spread. A similar approach, using the short term CP-Bills and P2-P1

spreads, could be applied to estimating money demand.

To examine the demand for money in a similar manner as we have examined the demand for Treasuries,

the roadmap would be as follows. First, construct aggregates for the different attributes of money. To do so,

the key information that is needed is the weights (ks) on different supply aggregates. There are two possible

ways to recover the ks. One can use a-priori information to come up with ks. For example, we have argued

that insured bank deposits and Treasury bills should have the same weight in the short-safety aggregate

29
because both are default free. Alternatively, it is possible to recover some ks from regressions. For example,

from equation (27) we can see that k

liq of bank deposits can be recovered from the regression coefficient

on Treasury supply, when regressing S

FDIC

t,1 on Treasury supply. This approach needs to be broadened and

also applied to evaluate the ks for the medium-of-exchange attribute. The second step is to estimate the

demand for the different attributes (i.e. the functions v

0

liq(·), v0short−safe(·) and v

0

X(·)). This can be done

using a demand system. For example, the P2-P1 spread largely contains the price of the short-term safety

attribute, and hence the demand for short-term safety can be estimated using the P2-P1 spread. Likewise,

the A1/P1 CP-Bill spread largely contains the price of the liquidity attribute. The spread between T-bill

rates and checking deposit rates contains some mix of the price of liquidity and the medium of exchange

attribute. These three prices can be used in a demand system, also using the information of the relevant

supply aggregate, to separately recover the demand for each attribute of money (v

0

liq(·), v0

short−safe(·) and

v

0

X (·)). Aggregating the three estimated convenience demand relations gives us a money demand function.

4.3 Implications for the “Riskless” Interest Rate

Our finding of a convenience demand for Treasury debt suggests caution against the common practice of

identifying the Treasury interest rate with models’ riskless interest rate. We have argued that the observed

price of a one-period Treasury is P

T

t =

Et[Mt+1]

1−v

0(θA

t /GDPt;ξt)

(or interest rate of i

T

t ≈ −ln Et[Mt+1] − v

0

(·)). The

Treasury interest rate is lower than the “true” riskless interest rate. In order to recover the true riskless rate

from the data (the rate that can meaningfully be compared to the riskless rate from a model that ignores

the convenience benefits of Treasuries), one has to estimate the convenience yield and adjust Treasury rates

by this convenience yield. Our estimated demand curves may be used to measure the convenience yield and

make the adjustment.16

Our riskless rate finding has many implications for applications in finance. It implies that cost of capital

computations using the CAPM should use a higher riskless rate than the Treasury rate – a company with

a beta of zero cannot raise funds at the Treasury rate. The finding also has bearing for puzzles regarding

high measured return spreads and excess comovement of spreads. Since many asset market return spreads

are measured relative to Treasury interest rates, the demand for Treasury convenience and variation in this

demand will generate high average asset yield spreads over Treasuries as well as comovement in spreads

and excess returns across different asset classes. There is empirical support for both of these observations.

The literature has found that the high spread between corporate bond rates and Treasury rates, and the

16Duffie and Singleton (1997) make a similar point about riskless rates in the context of the term structure literature, and

advocate using interest rate swap rates instead of Treasury rates. Hull, Predescu, and White (2004) use data on credit default

swaps in conjunction with corporate bond data to conclude that the true riskless rate is approximately 10 bps below the rate

on interest rate swaps.

30
high equity premium, measured as the average excess stock market return over Treasury bill rates, are

hard to reconcile based on standard factors. Accounting for a true riskless rate that is higher than the

Treasury rate can go some way towards reconciling these findings. We find that true riskless rates should

be about 72 basis points higher than Treasury rates. In addition, the literature has documented patterns

of unexplained comovement in spreads across debt instruments. Collin-Dufresne, Goldstein, and Martin

(2001) show that credit spread changes within the corporate bond market are highly correlated. Boudoukh,

Richardson, Stanton, and Whitelaw (1997) document similar evidence from the mortgage backed securities

market. Gabaix, Krishnamurthy, and Vigneron (2007) show that corporate bond spreads and mortgage

backed spreads comove. The spreads examined in these studies are measured relative to Treasuries. Variation

in the Treasury convenience yield is one possible explanation for the comovement phenomena.

4.4 Effect of Foreign Official Demand on Treasury Yields

Table VII reports on who are the main holders of Treasuries and what fraction of overall bond holdings

Treasuries constitute for each group. We have commented earlier on the holdings of banks as well as

the holdings of the long-term investors (pension funds and insurance companies). In 2008, foreign official

holders own the largest share of Treasury debt at 37% of total Treasury supply. These holdings have

steadily risen over the post-war period from almost zero in 1945. The recent large holdings have been a data

point in a debate on the effects of global imbalances on interest rates (see, for example, Bernanke (2005),

Caballero, Farhi, and Gourinchas (2006), Caballero and Krishnamurthy (2009), and Jagannathan, Kapoor

and Schaumburg (2009).)

We evaluate the quantitative effect of foreign official demand on Treasury interest rates by asking how

much the convenience yield will fall if the foreign official holders were to sell their holdings, thus effectively

increasing the supply of Treasuries available to other Treasury holders. For this computation, we need to

know the elasticity of the holdings of foreign official holders to the convenience yield. We estimate the inverse

demand curve in a similar manner as for the long-term investors of Table IV. The results are quite different,

however. The coefficient on the log holdings of this group, when regressing the Baa-Treasury spread on the

log of the group’s holdings to GDP and instrumenting using the log of total Treasury debt to GDP as in

Table IV, is 15.2 with a t-statistic of 0.39. The result indicates that there is no relationship between the

foreign official investors’ holdings of Treasuries and the convenience yield (i.e. foreign official demand is

completely inelastic). We can also get a sense of this by looking at Panel B of Table VII. Foreign official

holders hold the bulk of their bond market portfolio in Treasury securities. It appears that when a foreign

central bank receives a dollar capital inflow and accumulates more dollar reserves, it buys Treasuries with

these reserves regardless of the relative price of Treasuries to other U.S. fixed income assets.

Suppose therefore that the holdings of foreign official holders at time t, θ

FOH

t

/GDPt, does not depend

31
on the convenience yield St. Here St denotes the convenience yield on long-term Treasuries. Denote the

demand function from all groups excluding foreign official holders by Dnot−FOH (St). Then the market

clearing condition is,

Dnot−FOH (St) + θ

FOH

t

/GDPt = θ

T

t

/GDPt,

giving a convenience yield of,

St = D

−1

not−FOH 

θ

T

t − θ

FOH

t

GDPt



.

To compute the effect of the sale of all foreign official holdings of Treasuries on Treasury yields (relative

to yields on non-convenient assets), we need to compute the difference between D

−1

not−FOH 

θ

T

t

GDPt



and

D

−1

not−FOH 

θ

T

t −θ

F OH

t

GDPt



. In empirical work, we regress spreads on θ

T

t /GDPt to recover a convenience yield

function f(θ

T

t

/GDPt). Because foreign official demand is inelastic, D−1

not−FOH (·) is simply f(θ

T

t

/GDPt)

shifted left by θ

FOH

t /GDPt. Therefore, D

−1

not−FOH 

θ

T

t

GDPt



minus D

−1

not−FOH 

θ

T

t −θ

F OH

t

GDPt



equals f



θ

T

t +θ

F OH

t

GDPt



minus f



θ

T

t /GDPt



.

At the historical average Debt-to-GDP ratio of 0.426, a sale of this magnitude (37% of Treasury supply)

will have a large effect on Treasury yields. We evaluate the estimated convenience yield function at holdings

of 0.426 and 0.584 = 0.426 × 1.37, both as a ratio to GDP. Based on the piecewise linear specification for

the Baa-Treasury spread (Table VI, column 4), the effect will be to raise long-term Treasury yields by 59

basis points relative to the Baa corporate bond yield. Based on the log specification for the Baa-Treasury

spread (Table I, column 5), the effect is to raise long-term Treasury yields by 41 basis points. The effect

on short-term yields, based on the CPP2-Bill specification (Table I, column 9) is to raise Treasury yields by

60 basis points. All of these computations are relative to corporate bond rates. Our computations do not

include any possible effect of foreign sales on the level of all interest rates.17

5 Conclusion

Investors value the liquidity and safety attributes of Treasuries. We document this by showing that changes

in Treasury supply have large effects on a variety of yield spreads. Evaluated based on the Baa-Treasury

17We report the impact of a sale at the historical average Debt-to-GDP ratio and using our estimated average convenience

demand function. The numbers should thus be interpreted not as the short-run impact of a sale but as an average impact

evaluated at “normal” supply and demand conditions. Current Treasury supply is higher than average, with the current CBO

projection of the Debt-to-GDP ratio for 2010 at 0.603. Our estimates, based on historical experience, implies that at this

high supply of Treasuries the convenience yield is zero, which suggests that sales of Treasury bonds will have no short-run

impact on yield spreads. However, there are two reasons this computation is inaccurate. First, the recent crisis has reflected

a flight-to-quality (demand) shock that has driven up the convenience yield and effectively increased b2 in the piecewise linear

specification. Second, the deterioration in the credit quality and liquidity of private sector assets implies that the supply of

non-Treasury convenient assets has declined. This makes it difficult to assess the short-run impact of a large Treasury sale. We

instead report the “long-run” impact at average supply and demand conditions.

32
spread (for long-term bonds), a one standard deviation reduction in Treasury supply (starting from mean

supply) lowers Treasury yields by 79 basis points relative to corporate bond yields. The effects based on the

CPP2-Bills spread (for short-term bonds) is of a roughly similar magnitude.

By studying pairs of assets with similar liquidity but different safety (higher and lower grade corporate

bonds and commercial paper) or with similar safety but different liquidity (FDIC insured CDs and Treasury

bills) we document that changes in Treasury supply drive both the equilibrium price of safety and the

equilibrium price of liquidity. This implies that Treasuries carry both a safety and liquidity attribute. Using

a piecewise linear specification, we estimate that the average convenience yield on long-term Treasuries over

the period 1926-2008 is 72 basis points, of which 46 basis points is driven by the liquidity of Treasuries and

26 basis points by the safety of Treasuries.

The low yields on Treasuries due to their extreme safety and liquidity imply that Treasuries in important

respects are similar to money. Evidence from quantities provide further support for this idea – the private

sector expands money supply (bank deposits) when the government reduces Treasury supply. While we

focus on money as a key substitute for Treasuries, our evidence suggests that other assets such as Aaa

rated corporate bonds and A1/P1 rated commercial paper carry some (but not all) of the convenience of

Treasuries.

Our results have immediate implications for asset pricing by showing that theoretical models need to

incorporate priced liquidity and safety attributes in order to be empirically succeesful in understanding

asset prices. We emphasize further implications of our findings for tax payers (Treasury seignorage), money

demand, the riskless rate, and the potential impact of a sale of Treasuries by foreign central banks.

33
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38
A Derivation for Prediction 2

We rewrite (9), using the approximation that 1−v

0

(·) ≈ e

−v

0

(·)

, so that the return from t to t+ 1 on holding

Treasury bonds satisfies,

1 = e

v

0

(θ

A

t /GDPt;ξt)Et[Mt+1P

T

t+1/P Tt

] = Et[Mt+1e

−(τ−1)i

T

t+1,τ−1+τiTt,τ +v

0

(θ

A

t /GDPt;ξt)

]. (30)

Likewise, for corporate bonds, rewriting (16), we find,

1 = e

−λtDtEt[Mt+1PC

t+1/P Ct

] = Et[Mt+1e

−(τ−1)i

C

t+1,τ−1+τiCt,τ−λtDt

]. (31)

The excess return on corporate bonds over Treasury bonds is,

R ̃

t+1 =

P

C

t+1

P

C

t

−

P

T

t+1

P

T

t

≈ −(τ − 1)St+1,τ−1 + τSt,τ .

We log-linearize to make the approximation. We make the following computations to arrive at an expression

for the spread St,τ . We assume that Mt+1 is lognormally distributed (where m ≡ ln M) and that all interest

rates are normally distributed. Then, it is straightforward to rewrite (30) as,

1 = e

v

0

(θ

A

t /GDPt;ξt )+Et[mt+1]+1/2vart[mt+1]−(τ−1)Et [i

T

t+1,τ−1

]+τiT

t,τ + 1

2

(τ−1)2vart(i

T

t+1,τ−1

)−covt(mt+1,(τ−1)i

T

t+1,τ−1−τiTt,τ )

,

and rewrite (31) as,

1 = e

−λtDt+E[mt+1]+1/2var[mt+1]−(τ−1)Et [i

C

t+1,τ−1

]+τiC

t,τ + 1

2

(τ−1)2vart(i

C

t+1,τ−1

)−cov(mt+1,(τ−1)i

C

t+1,τ−1−τiCt,τ )

.

We take logs and subtract these last two equations. We assume that the terms involving vart(i

T

t+1,τ−1

) and

vart(i

C

t+1,τ−1

) are approximately the same. That is, innovations in both corporate and Treasury rates have

the same variance. Then,

0 =

1

τ

(v

0

(θ

A

t /GDPt; ξt) + λtDt) + τ − 1

τ

Et[St+1,τ−1] − St,τ +

1

τ

covt(mt+1,(τ − 1)St+1,τ−1 − τSt,τ ),

or,

St,τ =

1

τ

(v

0

(θ

A

t /GDPt; ξt) + λtDt) + τ − 1

τ

Et[St+1,τ−1] −

1

τ

covt(mt+1, R ̃

t+1).

Solving this equation recursively for St,τ we find the expression in the text.

39
B Data

Table I:

Aaa-Treasury yield spread: The percentage spread between Moody’s Aaa-rated long maturity corporate bond yield and the yield on long maturity Treasury bonds. The Moody’s Aaa index is constructed

from a sample of long maturity (≥ 20 years) industrial and utility bonds (industrial only from 2002 onward),

available from 1919-2008. The yield on long maturity Treasury bonds is the average yield on long-term government bonds, available from 1919 - 1999. The Treasury bonds included are due or callable after 8 years for

1919-1925, 12 years for 1926-1941, 15 years for 1941-1951, 12 years for 1952, and 10 years for 1953-1999. We

use the yield on 20-year maturity Treasury bonds for 2000 - 2008. All three data series are from the Federal

Reserve’s FRED database (series AAA, LTGOVTBD, and GS20), with the exception that the long-term

Treasury yield data for 1919-1924 are from Banking and Monetary Statistics, 1914-1941, Table 128. We use

annual observations, sampled in July of the year up to (and including) 1975 and in October of each year

after that.

Baa-Treasury yield spread: The percentage spread between Moody’s Baa-rated long maturity corporate bond yield and the yield on long maturity Treasury bonds. The Moody’s Baa index is constructed

from a sample of long maturity (≥ 20 years) industrial and utility bonds (industrial only from 2002 onward),

available from 1919-2008. The Baa data series is also from the FRED database (series BAA). We use annual

observations, sampled in July of the year up to (and including) 1975 and in October of the year after that.

CP-Bills yield spread: The percentage yield spread between commercial paper and Treasury bills. For

1971-2008 the commercial paper yield is from the FRED database. For 1971-1996 it is the series CP3M (the

average of offering rates on 3-month commercial paper placed by several leading dealers for firms whose bond

rating is AA or equivalent) and for 1997-2008 the series CPN3M (the 3-Month AA nonfinancial commercial

paper rate). Prior to 1971 we use the commercial paper series for prime commercial paper, 4-6 month

maturity, from Banking and Monetary Statistics (Table 12.5 for 1941-1970 and Table 120 for 1920-1940).

The Treasury bill yield is for 3-month Treasury bills from 1971-2008 (from FRED, series TB3MS), 6-month

Treasury bills for 1959-1970 (from FRED, series TB6MS), and 3-6 month Treasury bills for 1920-1958 from

the NBER Macro History database (series M13029b for 1931-1958 and series m13029a for 1920-1930). We

use annual observations, sampled in July of the year up to (and including) 1975 and in October of each year

after that.

CPP2-Bills yield spread: The percentage yield spread between lower-grade commercial paper and

Treasury bills. Calculated as the sum of the CP-bills yield spread described above (i.e. high-grade commercial

paper minus Treasury bills) and the yield spread between 30-day A2/P2 nonfinancial commercial paper and

30-day AA nonfinancial commercial paper, with data for 1974-1997 obtained from Bloomberg and data from

40
1998-2007 obtained from the Federal Reserve. 18

Debt/GDP: The supply of Treasuries scaled by GDP, at market value. Calculated as (Debt/GDP with

Debt at face value)*(Total market value of Treasuries/Total face value of Treasuries).

The Debt/GDP series (with debt at face value) is from Henning Bohn’s web page for years 1919-2003.

The debt measure includes debt held by the Federal Reserve, but excludes debt held by other parts of the

government such as the Social Security Trust Fund. Debt is for the end of the government’s fiscal year, i.e.

end of June up to and including 1975 and end of September from 1976 on. GDP is for the calendar year in

which the government fiscal year started (fiscal year t starts in calendar year t-1), with GDP data used from

1929 on and GNP data used prior to that. We extend Bohn’s series up to 2008 using Treasury data from

Flow of Funds Table L.209 and GDP data from NIPA Table 1.1.5. For 2004-2008 we use GDP for the four

quarters leading up to the date of the fiscal year end.

The CRSP Monthly US Treasury Database is used to calculate the factor for translating face values to

market values (Total market value of Treasuries/Total face value of Treasuries). This data base starts in

1926. Prior to 1949 the amounts outstanding are missing for a lot of the Treasuries. From 1949 onward, at

least 97% of Treasuries in the database have values for both amounts outstanding and price, thus allowing

us to calculate the ratio of market value to face value for the U.S. Treasury market as a whole. We multiply

Bohn’s Debt/GDP series by the CRSP ratio of Treasury market to face value to get a series for the market

value of Treasury Debt/GDP. Over the period 1949-2008 the correlation between Debt/GDP at face value

and Debt/GDP at market value is 0.992 and the means and standard deviations of the two series are very

similar. Prior to 1949, one can still calculate the ratio of Treasury market to face value for the set bonds in

the CRSP data base for which the data are available. This set is somewhat skewed towards better coverage

of long maturities. We get similar results whether we use Debt/GDP at face value and Debt/GDP at market

value in the pre-1949 period. We report the results which use the market Debt/GDP series.

Prior to 1919 the CRSP data base is not available and we therefore do not make the market value

adjustment. In general, over the 1926-2008 period our results throughout the paper are very similar whether

the market value adjustment is made or not.

Volatility: Annualized standard deviation of weekly log stock returns on the S&P500 index. We calculate

weekly returns on the value-weighted S&P index based on daily returns obtain from CRSP. As the volatility

measure for a given year, we compute the standard deviation of the weekly log returns over the year leading

up to the end of the government’s fiscal year. We annualize the standard deviation of weekly log returns by

multiplying by the square root of 52.

EDF: Expected default frequency for corporate bonds. The data are obtained from Moody’s-KMV.

We use the median EDF reported by Moody’s-KMV for large firms (defined as firms with book value of

18We thank Michael Fleming at the Federal Reserve for help obtaining this data.

41
assets > $300 million in current dollars). The EDF measure is available from 1969 to 2007. We use annual

observations, sampled in July of the year up to (and including) 1975 and in October of each year after that.

Slope: Slope of the Treasury yield curve measured as the spread between the 10-year Treasury yield

and the 3-month Treasury yield. The interest rate on Treasuries with 10 year maturity is from FRED from

1953 to 2005 (series GS10). Prior to 1953 we use series m13033a (1926-1941) and m13033b (1942-1952) from

the NBER Macro History Database, with both these series referring to the yield on long-term Treasuries.

The interest rate on Treasuries with 3 month maturity is from FRED from 1934 to 2008 (series TB3MS)

and from the NBER Macro History database prior to that (series m13029a for 1926-1933, referring to 3-6

month Treasuries). We use annual observations, sampled in July of the year up to (and including) 1975 and

in October of each year after that.

In all tables, volatility, EDF and slope variables are demeaned.

Table II:

Excess return of corporate bonds over Treasuries: The one-year percentage excess return on

long term corporate bonds over long term government bonds. Both return series are from Ibbotson’s Stocks,

Bonds, Bills & Inflation Yearbook and begin in 1926 and end in 2003. The Ibbotson corporate bond index is

based on the total return from holding high grade (Aaa and Aa) corporate bonds with approximately 20-year

maturity. If a bond is downgraded during a particular month, Ibbotson includes its return for that month

in the computation of the index return before removing the bond from future portfolios. The Ibbotson long

term government bond index covers a one-bond (one Treasury issue) portfolio with a term of approximately

20 years and a coupon rate close to the current level of the yield curve. Returns are annual from July to the

next June for 1926 to 1975 and annual from October to the next September from 1976 on.

Excess return of corporate junk bonds over corporate Baa-rated bonds: The one-year percentage excess return on corporate bonds rated below Baa over corporate bonds rated Baa. Both series are

obtained directly from Ibbotson Associates (now part of Morningstar) and are available from 1926-1989.

From 1990 to 2003 we use data obtained from Lehman Brothers, specifically their Intermediate U.S. High

Yield minus their Baa Corporate. Returns are annual from July to the next June for 1926 to 1975 and

annual from October to the next September from 1976 on.

Duration hedge: The one-year percentage excess return on long-term government bonds over shortterm government bonds. The long-term government bond series is from Ibbotson (described above). The

short-term government bond series is the return on 90-day Treasury bills from the CRSP US Treasury and

Inflation database. Returns are annual from July to the next June for 1926 to 1975 and annual from October

to the next September from 1976 on.

Debt/GDP, slope: As for Table I.

42
Table III, Panel A:

Baa-Aaa yield spread: The percentage yield spread between the Moody’s Baa-rated long maturity

bond yield and Moody’s Aaa-rated long maturity bond yield. Both series are described under Table 1 above.

We use annual observations, sampled in July of the year up to (and including) 1975 and in October of each

year after that.

A2/P2-A1/P1 yield spread: The yield spread between 30-day A2/P2 nonfinancial commercial paper

and 30-day AA nonfinancial commercial paper, with data for 1974-1997 obtained from Bloomberg and data

from 1998-2007 obtained from the Federal Reserve. We use annual observations, sampled in July of the year

up to (and including) 1975 and in October of each year after that.

(Debt>10 year maturity)/GDP: The ratio of Treasury debt with more than 10 year remaining

maturity to GDP. From 1949-2008 the amount of Treasury debt is at market value and calculated using the

CRSP Monthly US Treasury Database. From 1926-1948 the amount of Treasury debt is at face value and

obtained from Banking and Monetary Statistics 1914-1941 Table 147 and Banking and Monetary Statistics

1941-1970 Table 13.5 D.

(Debt≤ 1 year maturity)/GDP: The ratio of Treasury debt with a year or less of remaining maturity

to GDP. From 1949-2008 the amount of Treasury debt is at market value and calculated using the CRSP

Monthly US Treasury Database (we only use this series in column (2) which is based on data from 1974

onward).

Debt/GDP, volatility, slope: As for Table I.

Table III, Panel B:

(FDIC insured CDs)-Bills yield spread: The percentage yield spread between the yield on 6-

month certificates of deposit and Treasury bills. The CD yields are the national average rates obtainable

by depositors on small-denomination (and thus FDIC insured) CDs of 6 month maturity, where smalldenomination means the account-opening minimum. The rates are from Bank Rate Monitor and are obtained

from the New York Times for 1984-1997 and from Bloomberg for 1998-2008. The Treasury bill yield used

is the yield on 6-month bills obtained from FRED (series TB6MS). Yields are annual, as of the end of

September.

(Time & Savings Accounts)-Bills yield spread: The percentage yield spread between time and

savings accounts and Treasury bills. We estimate the yield on time and savings accounts using data from

FDIC Historical Statistics on Banking, Table CB06 and CB15. Specifically, we divide the total annual

interest on deposits in domestic offices by the sum of savings and time deposits in domestic offices (using

averages of beginning and end of year values for the deposits). The FDIC series is available from 1935

43
onward. We compare this yield series to the yield on 6-month Treasuries, with data obtained from FRED

(series TB6MS) from 1959 on and from the NBER Macro History database prior to that (series m13029b

for 1931-1958 and series m13029a for 1926-1930, both referring to 3-6 month Treasuries). Since the yield on

time and savings accounts is an annual average, we use the annual calendar year average of 6-month monthly

Treasury bill rates for comparison.

Slope: Slope of the Treasury yield curve measured as the spread between the 10-year Treasury yield and

the 6-month Treasury yield. The interest rate on Treasuries with 10 year maturity is from FRED from 1953

to 2005 (series GS10). Prior to 1953 we use series m13033a (1926-1941) and m13033b (1942-1952) from the

NBER Macro History Database, with both these series referring to the yield on long-term Treasuries. The

interest rate on Treasuries with 6 month maturity is from FRED from 1959 to 2008 (series TB6MS) and from

the NBER Macro History database prior to that (series m13029b, referring to 3-6 month Treasuries). The

slope variable in column (5) is based on October values to match the timing of the left-hand side variable.

The slope variable in column (6) is (annual calendar year average of 10-year monthly yields)-(annual calendar

year average of 6-month monthly yields), in order to match the timing of the dependent variable which is a

calendar year average.

Debt/GDP: As for Table I.

Table IV:

Debt held by pension funds and insurance companies: Treasury holdings of pension funds and

insurance companies, from Flow of Funds Accounts of the United States, Table L. 209, groups Propertycasualty insurance companies, Life insurance companies, Private pension funds, State and local government

retirement funds, and Federal government retirement funds. To match the timing of Debt/GDP, the Treasury

holdings of pension funds and insurance companies are as of end of June up to 1975 and as of end of September

from 1976 on, with the exception that for 1945-1951 only end of year holdings are available.

Baa-Aaa yield spread: As for Table III, Panel A.

Debt/GDP, volatility, slope: As for Table 1.

Table V, Panel A:

(non-M1 M2)/GDP, (non-M2 M3)/GDP, (non-M1 M3)/GDP: We start our money supply

series in 1934 since this is the first year of FDIC insurance. Money supply data from 1934-1958 are from

Friedman and Schwartz (1970), Table 1. Subsequent money supply data are from Federal Reserve Statistical

Release H.6. M1 refers to currency, traveler’s checks, demand deposits, and other checkable deposits. M2

refers to M1 plus savings deposits (including MMDAs), small-denomination time deposits and retail money

market funds. M3 refers to M2 plus large time deposits, repos, Eurodollars, and institutional money market

44
funds. M3 data are available only for 1959-2005. We refer to M2 minus M1 as non-M1 M2, to M3 minus

M2 as non-M2 M3 and to M3 minus M1 as non-M1 M3.

In our measure of non-M1 M2 we exclude Treasury holdings of retail money market funds (thus focusing

on savings deposits, including MMDAs, small-denomination time deposits and non-Treasury retail money

market fund holdings). This is done because we are interested in studying the part of money which is

not Treasuries. Similarly, we exclude Treasury holdings of institutional money market funds from non-M2

M3 which thus consists of large time deposits, repos, Eurodollars, and non-Treasury institutional money

market fund holdings. Our series for non-M1 M3 then consists of savings deposits, including MMDAs, smalldenomination time deposits, non-Treasury retail money market fund holdings, large time deposits, repos,

Eurodollars, and non-Treasury institutional money market fund holdings. To estimate Treasury holdings of

retail money market funds and of institutional money market funds, we obtain holdings of money market

funds from Flow of Funds Table L. 121. We assume that retail and institutional money market funds have

the same ratio of Treasury holdings to total fund holdings.

Money data are as of end of June up to and including 1975 and end of September from 1976 on. From

1948 on GDP data used to define ratios of money to GDP are sums of quarterly GDP for the four quarters

leading up to the date of the money data used, with quarterly GDP data from NIPA Table 1.1.5. For

1929-1947 we use annual GDP data from NIPA Table 1.1.5 and prior to 1929 we use GDP data from Louis

D. Johnston and Samuel H. Williamson, What Was the U.S. GDP Then? MeasuringWorth, 2008. URL:

http://www.measuringworth.org/usgdp/.

Debt/GDP: As for Table I.

Year: A time trend.

Table V, Panel B:

Baa-(non-M1M2) yield spread: Percentage yield spread between the Moody’s Baa-rated long maturity bond yield and the yield on non-M1 M2. For the Baa yield, we use annual observations, sampled in

July of the year up to (and including) 1975 and in October of each year after that. We estimate the yield

on non-M1 M2 as the yield on time $ savings accounts from Table III, Panel B.

Debt/GDP: As for Table I.

Volatility: As for Table I, with the exception that we here use the standard deviation of the weekly log

returns over the calendar year (as opposed to the government fiscal year), in order to match the timing of

the non-M1 M2 yield which is a calendar year average.

Slope: As for Table I, with the exception that we here use calendar year averages: (annual calendar

year average of 10-year monthly yields)-(annual calendar year average of 3-month monthly yields), in order

to match the timing of the non-M1 M2 yield which is a calendar year average.

45
Table VI: Same data as Table I.

Table VII:

The data in this table are all from Flow of Funds Accounts of the United States and are end of year, from

1945-2008. Treasury holdings are from Table L. 209 and Table L. 107, holdings of agency- and GSE-backed

securities are from Table L. 210 and L. 107, holdings of corporate bonds are from Table L. 212 (we denote

these long-term corporate bonds in the table to distinguish them from commercial paper), and holdings of

commercial paper are from Table L. 208 (we denote these short-term corporate bonds in the table).

46
Figure 1: Corporate Bond Spread and Government Debt

A. Scatter plot

1919

1920

1921 1922

1923

1924

1925

1926

1927

1928

1929

1930

1931

1932

1933

1934

1935

1936

1937

1938 1939

1940

1941

1942

1943 1944 1945

1947 1946

19491948

1951 1950 1952

1953

1954

1955

1956

1957

1958

1959

1960

1961

1962

1963 1964

1965

1966

1967

1968

1969

1970

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004 2005

2006

2007

2008

0 .5 1 1.5 2

Aaa−Treasury spread

0 .2 .4 .6 .8 1 1.2

Debt/gdp

B. Time series plot

0 .5 1 1.5 2

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Year

Aaa−Treasury spread Debt/gdp

Figure 1A plots the Aaa-Treasury corporate bond spread (y-axis) against the Debt-to-GDP ratio (x-axis)

while Figure 1B is a time-series graph of the same two time series. Both figures are based on annual

observations from 1919 to 2008. The corporate bond spread is the difference between the percentage yield

on Moody’s Aaa long maturity bond index and the percentage yield on long maturity Treasury bonds.

47
Figure 2: Money and Government Debt

A. Scatter plot

1934

1935

1936

1937

1938

1939

1940

1941

1942

1943

1944

1945

1946

19491948 1947

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

B. Time series plot

.2 .4 .6 .8 1 1.2

1930 1940 1950 1960 1970 1980 1990 2000 2010

Year

non−M1M2/gdp Debt/gdp

Figure 2A plots the quantity of small time and savings deposits, measured as M2 minus M1 minus Treasury

holdings of retail money market funds divided by GDP, against the Debt-to-GDP ratio while Figure 2B is a

time-series graph of the same two time series. Both figures are based on annual observations from 1934 to

2008.

48
Table I

Impact of Treasury Supply on Bond Spreads: Log Specification

The dependent variables are short and long-term yield spreads between corporate and Treasury bonds, both measured in percentaare the log of the ratio of the market value of Treasury debt outstanding to US GDP, and controls for the default risk and risk premis the expected default frequency for corporate bonds. Volatility is the annualized standard deviation of weekly log stock returns 

the slope of the Treasury yield curve measured as the spread between the 10-year Treasury yield and the 3-month Treasury yielthe precise definitions of all variables. EDF, volatility, and slope controls are demeaned. Regressions are estimated by ordinary lea

are adjusted assuming errors are AR(1). We use the Box-Jenkins methodology for identifying the error structure. ρ denotes the fi

error terms. t-statistics in brackets.

Panel A: Aaa-Treasury Panel B: Baa-Treasury Panel C: CP-Bills 

(1) (2) (3) (4) (5) (6) (7) (8) 

Period 1919-2008 1969-2007 1926-2008 1969-2007 1926-2008 1920-2008 1969-2007 1926-200log(Debt/GDP) -0.744 -0.910 -0.797 -1.752 -1.304 -0.728 -1.006 -0.550 

[-4.32] [-3.35] [-5.06] [-5.98] [-7.54] [-4.37] [-2.21] [-3.52] 

EDF 0.953 1.206 0.024 

[3.57] [3.71] [0.05] 

V olatility 1.294 6.364 1.947

[1.90] [6.88] [2.33]

Slope 0.045 0.080 0.175 0.309 -0.123 -0.085 

[1.05] [1.86] [2.04] [4.64] [-1.30] [-1.42] 

Intercept 0.111 0.052 0.078 0.208 0.737 0.095 -0.269 0.229 

[0.62] [0.18] [0.49] [0.66] [4.34] [0.56] [-0.55] [1.49] 

R2 0.447 0.623 0.568 0.669 0.690 0.224 0.211 0.259 

ρ 0.572 0.402 0.528 0.066 0.012 0.183 -0.023 0.018 

N 90 39 83 39 83 89 39 83 

49
Table II

Impact of Treasury Supply on Bond Returns

The dependent variable is the annual percentage excess return on long

term corporate bonds over long term government bonds. Return data

are from Ibbotson, beginning in 1926 and ending in 2003. Controls include the annual percentage excess return on corporate junk bonds over

corporate Baa-rated bonds (CreditHedge), the spread between the 10-

year Treasury yield and the 3-month Treasury yield (Slope), and the

excess return on long term government bonds over short term government bonds (DurationHedge). The data appendix provides the precise definitions of all variables. Regressions are estimated by ordinary

least squares. The standard errors are adjusted assuming errors are

ARMA(1,1). t-statistics in brackets.

(1) (2) (3)

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]

R2 0.009 0.100 0.162

N 78 78 78

50
Table III

Impact of Treasury Supply on the Price of Safety and the Price of Liquid

The dependent variables are: The spread between Baa-rated corporate bonds and Aaa-rated bonds (column (1) and (2)), thA1/P1-rated commercial paper (column (3) and (4)), the spread between the interest rate on FDIC insured 6 month CDs and 6

and the spread between the average interest rate paid by banks on time and savings deposits and 6-month Treasury bills (column log of the ratio of the market value of Treasury debt outstanding to US GDP, the log of the ratio of the market value of Treasury d

than 10 years to US GDP, the log of the ratio of the market value of Treasury debt with remaining maturity less than 1 year to 

deviation of weekly log stock returns on the S&P500 index (V olatility), and the slope of the Treasury yield curve measured as the s

yield and the 3-month Treasury yield in column (1)-(4) and as the spread between the 10-year Treasury yield and the 6-month Tr

data appendix provides the precise definitions of all variables. Regressions are estimated by ordinary least squares or instrume

instruments Debt/GDP, (Debt/GDP)2, and (Debt/GDP)3, as indicated. The standard errors are adjusted assuming errors are 

the Box-Jenkins methodology for identifying the error structure. t-statistics in brackets.

Panel A: Price of Safety Panel 

Assets with similar liquidity and different safety: Assets with sim

SBaa−Aaa SP2−P1 SFDIC insured CDs-B

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

Period 1926-2008 1926-2008 1974-2007 1974-2007 1984-2008 

log(Debt/GDP) -0.506 -0.879 -1.904 

[-3.42] [-4.47] [-1.83] 

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

(Debt/GDP), (Debt/GDP)2, (Debt/GDP)3 [-2.40]log(Debt ≤ 1 year mat/GDP) instr. by -1.453(Debt/GDP), Debt/GDP)2, (Debt/GDP)3 [-2.94]V olatility 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 0.137 

[4.15] [3.24] [0.40] [1.14] [1.32] 

Constant 0.660 0.241 -0.500 -2.662 -1.500 

[4.52] [0.648] [-2.45] [-2.56] [-1.63] 

N 83 83 34 34 25 

R2 0.600 0.486 0.271 Estimation method OLS IV OLS IV OLS Error term AR(1) AR(1) AR(1) AR(1) i.i.d. 

51
Table IV

Demand Curve Estimate of Long-term Holders

The dependent variable is the spread between Baa bonds and Aaa bonds. The independent variables are the

log of the ratio of the Treasury holdings of public and private pension funds and insurance companies to GDP

(log(DebtGROUP /GDP)), the annualized standard deviation of weekly log stock returns on the S&P500 index

(V olatility), and the slope of the Treasury yield curve measured as the spread between the 10-year Treasury yield and

the 6-month Treasury yield (Slope). The data appendix provides the precise definitions of all variables. The estimation is by instrumental variables (2SLS), where we use instruments Debt/GDP, (Debt/GDP)

2

, and (Debt/GDP)

3

.

Standard errors are adjusted assuming an AR(2) error structure. t-statistics in brackets.

Period log(DebtGROUP /GDP) V olatility Slope Constant N

1945-2008 -0.372 [-1.95] 3.484 [2.56] 0.207 [3.35] -0.266 [-0.44] 64

52
Table V

Response of Money to Treasury Supply, 1934-2008

Panel A presents reduced form regressions between measures of money and Treasury supply. The money measures include small tim

and non-Treasury retail money market fund holdings (non-M1 M2, minus retail money market fund Treasury holdings) and sm

savings deposits, non-Treasury retail and institutional money market fund holdings, repos and Eurodollars (non-M1 M3, minus 

money market fund Treasury holdings). Panel B presents structural instrumental variables estimates of the supply response of t

the first stage, the spread between Baa bond yields and the interest rate on non-M1 M2 is regressed on log(Debt/GDP) and c

stage, log(non − M1M2/GDP) is regressed on the fitted values of the spread and controls. The data appendix provides the p

variables. The regressions in Panel B exclude the Regulation Q period of 1966-1983. Errors are adjusted assuming serial correlat

AR(1), as indicated. We use the Box-Jenkins methodology to identify the error structure. t-statistics in brackets.

Panel A: Reduced Form Panel B: Structur

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

1st Stage of IV 

Dep. Var. non-M1 M2/GDP non-M1 M2/GDP non-M1 M3/GDP SBaa−(non−M1M2) log

Period 1926-2008 1959-2005 1959-2005 1935-1965, 

1984-2008 

Debt/GDP -0.305 -0.352 -0.553 Log(Debt/gdp) -1.587 SBa

[-5.52] [-4.16] [-3.34] [-2.10] 

Y ear 0.001 0.007 V olatility 7.942 V ol

[1.86] [5.99] [2.81] 

Slope 0.440 Slop

[2.27] 

Intercept 0.502 -1.467 -12.161 Intercept 2.279 Inte

[18.26] [-1.38] [-5.69] [3.94] 

R2 0.601 0.534 0.802

N 75 47 47 56 

Estimation method OLS OLS OLS OLS 

Standard errors AR(2) AR(2) AR(2) AR(1) 

53
Table VI

Impact of Treasury Supply on Bond Spreads: Piecewise Linear Specification

This table estimates a piecewise linear specification for the relation between Treasury supply and

bond spread. The function estimated is b0 + b1 × max[b2 − Debt/GDP, 0]. The dependent variables

are long-term yield spreads between corporate and Treasury bonds, measured in percentage units.

Independent variables are the log of the ratio of the market value of Treasury debt outstanding

to US GDP, and controls for the default risk and risk premium on corporate bonds. Volatility is

the annualized standard deviation of weekly log stock returns on the S&P500 index. Slope is the

slope of the Treasury yield curve measured as the spread between the 10-year Treasury yield and

the 3-month Treasury yield. The data appendix provides the precise definitions of all variables.

Volatility and slope are demeaned. Regressions are estimated by non-linear least squares. The

standard errors are adjusted assuming errors are AR(1). We use the Box-Jenkins methodology for

identifying the error structure. t-statistics in brackets.

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 ]

V olatility 1.189 6.236

[ 1.90 ] [ 7.05 ]

Slope 0.095 0.330

[ 2.38 ] [ 5.03 ]

R2 0.477 0.612 0.290 0.704

N 90 83 90 83

54
Table VII

Debt Holdings, by Group

Panel A of this table presents statistics on the fraction of Treasury securities held by various groups. Panel

B presents the bond portfolio composition of each of the groups, broken down into Treasury, Agency, and

short and long-term corporate bonds. The data are from the Flow of Funds Accounts of the Federal Reserve,

and are annual (end of year) from 1945 to 2008. Mutual funds include closed-end funds and exchange traded

funds.

Group 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

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

55