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Federal Reserve Bank of Chicago

Fiscal Consequences of Paying Interest
on Reserves
Marco Bassetto and Todd Messer

May 2013
WP 2013-04

Fiscal Consequences of Paying Interest on Reserves∗
Marco Bassetto and Todd Messer†

Abstract
We review the role of the central bank’s (CB) balance sheet in a textbook monetary
model, and explore what changes if the central bank is allowed to pay interest on its
liabilities. When the central bank cannot pay interest, away from the zero lower bound its
(real) balance sheet is limited by the demand for money. Furthermore, if securities are not
marked to market and the central bank holds its bonds to maturity, it is impossible for the
central bank to make losses, and it always obtains profits from being a monopoly provider
of money. When the option of paying interest on liabilities is allowed, the limit on the CB’s
balance sheet is lifted. In this case, the CB is free to take on interest rate risk, e.g, by
buying long-term securities and financing those purchases with short-term debt that pays
the market interest rate. This is a risky enterprise that can lead to additional profits but
also to losses. To the extent that losses exceed the profits of the monopoly operations, the
CB faces two options: either it is recapitalized by Treasury, or it increases its monopoly
profits by raising the inflation tax.
∗

We are indebted to Fernando Alvarez, Gadi Barlevy, Mariacristina De Nardi, Fran¸ois Velde, and seminar
c

participants at the Federal Reserve Bank of Chicago for valuable suggestions. The views expressed herein are
those of the authors and not necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve
System.
†
Federal Reserve Bank of Chicago

1

1

Introduction

The financial crisis of 2008 and its aftermath have brought about dramatic changes in the balanced sheet of the central banks (CBs) of the largest economies in the world. Faced with the
inability to wield their traditional policy instrument, which effectively hit the zero lower bound
on short-term rates, CBs greatly expanded their balance sheet. While these purchases entailed
a variety of assets in the immediate aftermath of 2008, they have since concentrated on bonds
(particularly long-term) issued or guaranteed by the governments of their economies; as an example, Figures 1 and 2 show the case of the Federal Reserve in the United States. This expansion
Federal Reserve Balance Sheet − Assets
3.5
Loans to Govt.
Loans to Private
Other
3

Dollars in Trillions

2.5

2

1.5

1

0.5

0

Jan−08

Jan−10

Jan−12

Figure 1: Federal Reserve Assets by Major Category since 2007
was financed in large part by deposits, as shown in Figure 3.1 At the beginning of the crisis,
in September 2008, while the Fed funds rate was still well above zero and the Fed was not yet
allowed to pay interest on reserves, these deposits were held by the U.S. Treasury; but since then
they have been largely deposits of commercial banks. Not since the Great Depression has the
balance of deposits of commercial banks been so large compared to their minimum required reserves. With slight differences in timing, a very similar picture arises in the case of the European
1

See the appendix for definitions.

2

Central Bank and the Bank of England (Figures 4 and 5 in the appendix).
Federal Reserve Maturity Structure − Assets
3.5
<1 Year
1 to 10 Years
>10 Years
3

Dollars in Trillions

2.5

2

1.5

1

0.5

0

Jan−08

Jan−10

Jan−12

Figure 2: Maturity Structure of Federal Reserve Assets since 2007.2
Just as it took years for the expansion in the CBs’ assets to take place, it is likely that
years will also pass before their balance sheet will return to resemble its pre-2008 composition,
with liabilities dominated by currency notes.3 During this transition, excess reserves deposited
by commercial banks will have to be paid the market short-term rate. If the transition will
not be complete by the time when CBs will desire to lift short-term rates from zero to contain
inflationary pressures, paying interest on reserves will thus be necessary.
Our goal is not to assess the role that large-scale asset purchases played in the pursuit of
monetary policy objectives; indeed, our analysis is based on a simplified model where no such role
is present. Our goal is to review instead the fiscal implications of such purchases. The starting
point of our analysis is Sargent and Wallace’s [14] insight that monetary and fiscal authorities
are eventually forced to coordinate because they face a single, consolidated budget constraint, to
which seigniorage revenues contribute.4 We go beyond Sargent and Wallace by unbundling the
2

This graph only includes Liquidity and Credit Facilities, Securities held Outright, TALF, Repurchase agree-

ments, and central bank liquidity swaps, for which maturity data is readily available.
3
Bank excess reserves remained elevated into the 1940s in the aftermath of the Great Depression.
4
The role of nominal debt in this connection has been explored more recently by Leeper [11], Sims [15],

3

Federal Reserve Balance Sheet − Liabilities
3.5
Currency
Reverse Repos and Deposits
Capital
3

Dollars in Trillions

2.5

2

1.5

1

0.5

0

Jan−08

Jan−10

Jan−12

Figure 3: Federal Reserve Liabilities by Major Category since 2007
budget constraints of the government and the CB. In a world in which the latter is simply an
agency under direct control of the executive, there is no reason to distinguish between CB and
Treasury liabilities. But things change when monetary policy is conducted by an “independent”
CB, formally tasked with objectives, such as price and macroeconomic stability, that may conflict
with the desires of fiscal authorities. In this case, it is conceivable that the magnitude of its profits
and losses, as well as its transfers to fiscal authorities, may ultimately have an effect on the way
fiscal-monetary coordination will occur. The CB may find it easier to concentrate on its mandate
if it generates a steady stream of profits that can be transferred to Treasury. In contrast, it might
find its independence under threat when it books losses, particularly in the extreme case in which
these were so large as to require reverse transfers.
To analyze the implications of different asset-management policies of the CB, we rely on a
highly stylized, commonly used model of a monetary economy.5 After displaying the linkages
between the budget constraints of Treasury and the central bank, confirming Sargent and Wallace [14], we focus on the way different balance sheet choices of the CB affect the riskiness of
Woodford [18], Bassetto [2, 3], and Cochrane [6], among others. Sims [16, 17] has discussed in greater detail how
the balance sheet of the CB affects its ability to achieve price level determinacy.
5
Our model is based on Lucas and Stokey [12].

4

its position. Through a sequence of propositions, we show how increasingly aggressive portfolio management strategies by the CB increase the risk of losses that would reduce (and, in
extreme circumstances, erase or more than erase) the seigniorage transfers that the can be paid
to Treasury.
We identify quantitative easing, defined as purchases of long-term bonds financed with the
creation of excess reserves, as a qualitative breakpoint in the fiscal risk implied by CB policy.
To better understand this breakpoint, an analogy with an individual investor is helpful. An
individual investor buying bonds using its own assets may face losses on its portfolio, but may
never lose more than the entire value of its initial capital. In contrast, an investor taking a
leveraged position in bonds may lose more than its capital (although, of course, such a loss may
be extremely unlikely if the leverage ratio is small). Compared to the portfolio of an individual
investor, the balance sheet of a central bank is more complicated, in that it involves a significant
amount of liabilities (currency) that pay no interest. Moreover, unlike the period of the gold
standard, contemporary CBs do not back their currencies with assets, but rather money is
irredeemable and takes value simply because of the liquidity services that it provides (money
is “fiat”). For this reason, in computing the point at which a CB position becomes leveraged,
liabilities in the form of currency (and required reserves) can be neglected.
Our paper is closely related to independent work by Hall and Reis [9], who also identify
excess reserves as a force driving the CB to potential losses and study the implications for the
conduct of monetary policy; Hall and Reis show that quantitatively the Federal Reserve and the
European Central Bank are unlikely to face losses that would threaten their ability to keep prices
stable in the absence of a recapitalization.6 In our work, we discuss the budget constraints of the
fiscal, as well as the monetary authorities, and emphasize the similarity in the debt instruments
managed by the central bank and Treasury. We are ultimately interested in the question of how
the power to take fiscal risk is allocated across the two agencies, how coordination should be
managed, and what institutional rules could foster proper management. Answering this question
requires an explicit theory of the objectives of fiscal and monetary authorities, and the way
6

Similar projections are also contained in Carpenter et al. [5] and Greenlaw et al. [8].

5

different asset-management constraints affect their strategic interaction; we leave this step to
future research.

2

The Setup

Our analysis is based on a very stylized model based on an economy that features flexible prices
and special assumptions about preferences, but the implications we discuss generalize to much
richer environments, with more complex preferences and potentially many other frictions. We
relegate the full description of the microfoundations of the model to the appendix and concentrate
here on the essential elements.
The economy features a continuum of private households and a government, separated into
two agencies: “Treasury” and the “central bank” (CB). For each one of these two agencies, we
keep the model as simple as possible by only including their functions and the budget items that
are relevant for our discussion.
Treasury issues government bonds of different maturities. We assume that there are just two
maturities: one-period bonds, and consols, that promise a payment into the indefinite future.
We denote by Bt the nominal amount of one-period bonds that are issued in period t and need
to be repain in period t + 1, and by Dt the coupons due at the beginning of period t on all
outstanding consols. Let Rt be the nominal interest rate between periods t and t + 1 and Qt be
the price of a consol in period t. To repay its debts, Treasury has the power to levy (lump-sum)
taxes; let Tt be their nominal amount in period t. We abstract from government spending.
The CB’s liabilities are “money” and “excess reserves.” Money is interpreted here in the
narrow sense of currency held by the private sector and required reserves. It has the unique
feature of being monopolistically provided by the CB and it thus represents the source of CB
profits. In contrast, excess reserves do not provide households any liquidity services beyond those
that are also provided by short-term government debt; as a consequence, households will only
hold them if they pay the same interest rate Rt as one-period debt. We let Mt be money that
can be used in transactions in period t and Xt be the amount of excess reserves at the beginning

6

of period t. On the asset side, the CB may hold government debt of either maturity.7 We
assume that the CB cannot (or does not) sell government bonds short. Otherwise, the CB could
circumvent a ban on paying interest on reserves simply by selling short-term Treasury bonds
short. Treasury and the CB are linked by remittances (seigniorage), whose amount in period t
is St . When St > 0, these represent distributions of profits from the CB to Treasury; this is the
ordinary direction of transfers that we observe in the data. St < 0 indicates a recapitalization of
the CB by Treasury.
The actions of Treasury and the CB are subject to their budget constraint. It is customary
in macroeconomic models to lump the two constraints into one, since in practice Treasury is a
residual claimant of the profits of the CB (through the seigniorage payments St ) and, from a
purely economic perspective, the distinction between the two agencies is superfluous. However,
as we emphasized in the introduction, there are several reasons why the balance sheet of the
CB may affect its ability and/or willingness of entertaining alternative policy options and its
independence. We thus consider the two as separate budget constraints.
On a period-by-period basis, the budget constraint for Treasury is given by the following:
Bt−1 + Dt−1 =

Bt
+ Qt (Dt − Dt−1 ) + St + Tt .
1 + Rt

(1)

At each period t, the left-hand side of equation (1) represents the Treasury’s repayment commitments: Bt−1 to the holders of short-term debt, and a coupon Dt−1 to the holders of consols. The
right-hand side represents the sources of funds: taxes from the private sector (Tt ), seigniorage
transfers from the central bank to Treasury (St ), new issuance (or repurchase, if negative) of
consols (Dt − Dt−1 , valued at the consol price Qt ), and new issuance of short-term debt (Bt ,
discounted at the current short-term nominal interest rate Rt ).
For the central bank, the budget constraint in period t is
Mt − Mt−1
7

B
Bt
Xt
B
B
B
B
=
− Bt−1 + Qt (Dt − Dt−1 ) − Dt−1 + St −
+ Xt−1
1 + Rt
1 + Rt

(2)

We assume that the central bank only holds government debt. The analysis could readily be extended to the

case in which the assets include privately-issued debt; in this case, in addition to interest-rate risk discussed in
this paper, the central bank is also subject to credit risk.

7

B
B
Here, Bt and Dt are central bank holdings of short-term and long-term Treasury debt respec-

tively. Equation (2) shows all the possible sources of growth in the supply of money (as defined
above). The central bank must increase the money supply if it decides to acquire more short-term
debt than needed to roll over existing debt; similarly, it grows the money supply if it purchases
new consols with value in excess of the coupon payment on existing holdings, or if it increases its
remittances to Treasury. Finally, the money supply increases if the central bank uses it to repay
some of its own interest-bearing liabilities (excess reserves), rather than rolling them over. A
contraction in the money supply can be achieved by any combination of these factors in reverse.
The economy starts at time 0 with some initial stock of bonds, money, and excess reserves,
B
B
described by (B−1 , D−1 , B−1 , D−1 , X−1 , M−1 ).

From the terms in equation (2) it will be useful to identify the profits of the CB, which we
define in two ways, depending on whether assets are carried at their historical cost or marked to
market. In period t, profits at historical cost are given by
ΠHC :=
t

Rt−1
B
B
B
¯
B
B
(B B − Xt−1 ) + Dt−1 + (Qt − Qt−1 )(Dt−1 − Dt )IDt−1 >Dt ,
1 + Rt−1 t−1

(3)

B
B
¯
B
B
where IDt−1 >Dt is an indicator function that is 1 if Dt−1 > Dt and 0 otherwise, and Qt is the

average historical cost of consols held by the central bank at the end of period t − 1.8 The
first term of equation (3) represents net interest receipts on short-term debt instruments: the
CB earns profits from its holdings of government debt, but makes losses when it pays interest
on excess reserves. The second term represents the coupon payments on consols held at the
beginning of the period. Finally, the last term, which is present only if the central bank sells
long-term debt during the period, represents the realized capital gain (or loss, if negative) on the
sale.
The corresponding expression for profits when assets are marked to market is9
ΠM M :=
t
8

Rt−1
B
B
B
(Bt−1 − Xt−1 ) + Dt−1 + (Qt − Qt−1 )Dt−1 .
1 + Rt−1

(4)

D
D
¯
¯
¯
¯
¯
Starting from some initial condition Q−1 , Qt is defined recursively as Qt = Qt−1 if Bt ≤ Bt−1 , and Qt =

D
D ¯
D
D
(Bt−1 /Bt )Qt−1 + (1 − Bt−1 /Bt )Qt otherwise.
9
Since we assumed all of the CB liabilities to be short term, there is no issue of marking liabilities to market.

8

Compared to equation (3), the first two terms are identical, but now profits (or losses) are
measured taking into account both realized and unrealized capital gains.
The flow budget equations above will play an important role in our discussion of payments
across different actors. Of independent interest are the present-value budget constraints, which
can be computed by rolling equations (1) and (2) forward and imposing long-run balance:
∞

Bt−1 + (1 + Qt )Dt−1 =

PVt (Ss + Ts )

(5)

s=t

and

∞
B
Bt−1

+ (1 +

B
Qt )Dt−1

∞

− Xt−1 +

PVt (Ms − Ms−1 ) =
s=t

PVt (Ss ) ,

(6)

s=t

where the function PVt represents the present value computed as of time t; details of the PV
function are provided in the appendix.
Equation (5) shows that the value of government debt at the beginning of period t is equal
to the present value of future taxes and seigniorage transfers that will be used to repay it.
In equation (6), the left-hand side represents the net value of the central bank at the beginning
of period t. This is represented by two components. The first component represents the value
of holdings of government debt (which are assets for the CB), net of money and excess reserves
(liabilities). The second component, represented by the infinite sum, stems from the monopoly
privilege granted to the central bank to issue money, a liability that carries no interest but is
still valued by the private sector for its liquidity services. This term captures the present value
of monopoly profits that will accrue to the central bank from period t onwards. The net value
of the CB matches the present value of seigniorage distributed to Treasury, the right-hand side
of equation (6).10
We complete the description of the economy by the following three equations, that characterize the behavior of the private sector in each period t (a full description of the microfoundations
of these equations appears in the appendix):
Mt
= L(Rt ),
Pt
10

(7)

It is natural to think of these as dividend payments, treating Treasury as the true owner of the CB. Alterna-

tively, this can be viewed as a tax on the CB.

9

1 = βt Et

Pt
(1 + Rt+1 ) ,
Pt+1

(8)

and
Qt =

1
1 + Rt

1 + βt Et (1 + Rt+1 )

Pt
Qt+1
Pt+1

,

(9)

where Et represents the expected value as of time t, Pt is the price level in period t, and βt is an
exogenous shock to the real interest rate,11 which is the only source of extrinsic uncertainty in
the model.
Equation (7) represents money demand, and shows that real money balances (money divided
by the price level) are a (decreasing) function of the opportunity cost of holding money, which
is the nominal interest rate.
Equation (8) is a Fisher equation that relates nominal interest rates and inflation: in highinflation environments, households require higher nominal rates to willingly hold government
debt (or central bank excess reserves).12
Finally, equation (9) recursively links the price of a consol to current and future expected
interest rates. In the absence of uncertainty, the equation would simplify to Qt = (1 + Qt+1 )/(1 +
Rt ): the value of a consol in period t would be equal to the discounted value of its dividend in
period t + 1 (which is 1) and its price in period t + 1 (Qt+1 ). In the presence of uncertainty,
the more-complicated expression (9) takes into account of the covariance between future interest
rates and inflation, and it encompasses a risk premium that may make long-term rates higher
than short-term rates on average.
An additional condition, that we directly imposed, states that any excess reserves held by
the public must yield the same return as short-term debt. Hence, if the short-term rate Rt is
greater than zero and the CB is not allowed to pay interest on reserves, Xt will necessarily be
zero.
11

As commonly done in the literature (e.g., Eggertsson and Woodford [7]), this is introduced as a preference

shock. In practice, it is a shortcut for a shock that affects financial intermediation, and, through that channel,
the desire of households to save and (in a richer model) to invest.
12
Equation (8) links inflation between period t and t + 1 to the nominal interest rate between period t + 1 and
t + 2. As discussed in Carlstrom and Fuerst [4], this is a consequence of assuming the “cash-in-advance” timing.
Our results would be equivalent under alternative timing assumptions in which Rt+1 is replaced by Rt .

10

B
B
A (competitive) equilibrium C is thus a sequence of asset balances (Mt , Xt , Bt , Dt , Bt , Dt )∞ ,
t=0

of taxes and seigniorage transfers (Tt , St )∞ , of asset prices (Rt , Qt ) and present-value operators
t=0
P Vt such that equations (1), (2), (5), (6), (7), (8), (9), and (12) hold. Whenever these equations
are satisfied, households find it optimal to hold money and excess reserves in amounts Mt and
B
B
Xt respectively, as well as short-term bonds and consols in amounts Bt − Bt and Dt − Dt (what

is issued by Treasury, net of CB holdings).

3

Properties of Equilibria

Having characterized the equilibrium conditions, we are now ready to study its properties. Our
first step is to establish an economic equivalence proposition. This proposition formally states
that, in our simple model, the timing of taxes and seigniorage transfers from the CB to Treasury
is irrelevant; only their present values matter. Since taxes are non-distorting in our economy,
Ricardian equivalence holds, as in Barro [1].13 Furthermore, the dividend policy followed by the
CB in distributing its profits to Treasury is economically irrelevant: as an example, in a period
in which the CB makes large profits, it does not matter whether it immediately distributes them
to Treasury or whether instead it distributes them over time, purchasing short-term Treasury
debt with the retained earnings in the meantime.
Proposition 1 Let C1 be a competitive equilibrium. It is then possible to construct many other
equilibria as follows:
1. By changing the timing of taxes:
• Given some arbitrary period t1 and some arbitrary state of nature realized in period
t1 , increase (decrease) taxes in period t1 by ∆T ;
13

The proposition would be simpler to state if the economy featured complete markets; in this case, taxes and

seigniorage payments could be varied in arbitrary ways both across time and states of nature as long as their
present values are unaffected. Since we do not allow arbitrary contingent contracts across agents, the proposition
considers only a specific class of tax and payment shifts, that can be financed with appropriate issuance of
short-term debt.

11

• In each subsequent period s up to some other arbitrary period t2 > t1 , increase (des
v=t1 (1

crease) short-term borrowing by Treasury (Bs ) by ∆T
• Decrease (increase) taxes in period t2 by ∆T

t2 −1
v=t1 (1

+ Rv );

+ Rv ).

2. By changing the timing of seigniorage remittances:
• Given some arbitrary period t1 and some arbitrary state of nature realized in period
t1 , increase (decrease) seigniorage transfers in period t1 (St1 ) by ∆S;
• In each subsequent period s up to some other arbitrary period t2 > t1 , decrease (increase) short-term borrowing by Treasury (Bs ) by ∆S

s
v=t1 (1

+ Rv );

• Between periods t1 and t2 , decrease (increase) holdings of short-term debt the CB
B
(Bs ) by ∆S

s
v=t1 (1

+ Rv ); alternatively, increase (decrease) excess reserves (Xs ) by

the same amount;
• Decrease (increase) seigniorage transfers in period t2 by ∆S

t2 −1
v=t1 (1

+ Rv ).

Proof. Equations (5), (6), (7), (8), (9), and (12) are unaffected by these changes, since
they are constructed in a way that alters only the timing, but not the present value of taxes and
seigniorage revenues. Similarly, it is straightforward to verify that the debt adjustments described
in the proposition are exactly those that are needed to ensure that equations (1) and (2) continue
to hold. The new sequences thus satisfy all the conditions for a competitive equilibrium. QED.
The economic equivalence of proposition 1 ignores the reality that Treasury and the CB
may make decisions over time, rather than committing to their entire future strategy at time
0, and at times they may have conflicting objectives. Specifically, it is likely that Treasury
will be mostly be concerned with the fiscal implications of the seigniorage transfers, while an
independent central bank is typically tasked with price and macroeconomic stability. The main
rationale for segregating monetary policy in an independent actor is precisely to insulate it from
the temptation to resort to the printing press to inflate debt away and to raise seigniorage
revenues.
When conflict is present, who controls the size and timing of seigniorage transfers may be
important, and this in turn is likely to depend on the balance sheet of the CB. To illustrate this
12

point with an extreme example, suppose that at time 0 the CB disburses to Treasury more than
the value of its initial net assets, plus the entire present value of future seigniorage profits:
∞

S0 >

B
B−1

+ (1 +

B
Q0 )D−1

− X−1 +

PV0 (Ms − Ms−1 )
s=0

Using equations (2) and (6) it is easy to verify that, at least in some states of the world, this
dividend policy leads the CB to start period 1 with net liabilities that exceed the present value
of its future seigniorage profits:
∞

X0 −

B
B0

− (1 +

B
Q1 )D0

PV1 (Ms − Ms−1 ) .

>
s=1

This situation is only sustainable if Treasury recapitalizes the CB by sending some reverse transfers in period 1 or in one of the later periods. But by having to rely on transfers from Treasury
the CB may see its independence reduced, and this may affect the balance of powers between
the two government agencies if their objectives conflict in the future. It is thus quite possible
that such a dividend policy would generate incentives to pursue a different monetary-fiscal policy
than the one that would be selected if the central bank does not disburse immediately its entire
present value of its future profits, and retains instead assets and profits, disbursing the proceeds
over time; in particular, a temptation might emerge to resolve the imbalance by printing extra
money and thereby raising seigniorage instead.
We already observed from equation (6) that the present value of seigniorage transfers from
the CB to Treasury arises from two distinct sources: the value of its asset portfolio, and the
monopoly profits on money issuance. In the discussion that follows, a special case will play a
prominent role:
Definition 1 We define money to be fiat whenever monetary policy is such that Ms ≥ Ms−1 in
every period.
We call money fiat in this case because the value of money derives value uniquely from its
liquidity services, and not from the CB assets: the CB never uses its assets to redeem any money
that it issued in the past. The case of fiat money is particularly relevant because it describes well
13

the behavior of most contemporary CBs: they increase the money supply both to accommodate
real growth, as well as to allow some inflation.
We now proceed as follows:
• We fix an arbitrary desired path for prices (and thus inflation), Pt , as well as an initial
nominal interest rate R0 ; in equilibrium, this determines all future nominal interest rates,
present values, and money balances (from equations (7), (8), and (12));14
• We then study the profits of the central bank and the evolution of its net worth under
different policy scenarios that are consistent with the desired path. While Mt and Rt are
set by the requirements of the desired path, the CB and Treasury still have freedom in
setting different paths for short and long-term debt, excess reserves, taxes, and seigniorage
transfers. Through a sequence of simple propositions, we illustrate how the timing and
riskiness of the CB profits depend on its choices of asset holdings and reserves.
In particular, we will be interested in two related, but distinct questions:
1. When will the CB be able to guarantee a positive stream of payments to Treasury all along
the desired path?15
2. When will the CB be able to always book positive profits all along the path?
We will consider a sequence of asset-management strategies on the part of the CB, starting
from the most conservative policy, where CB profits are guaranteed to be positive independent
of the accounting criterion, to the least restrictive one, where the CB is potentially exposed to
unbounded losses. We will do so first for the simpler case in which the desired path features
nominal interest rates that are always strictly positive. We will then expand the discussion
to situations in which the short-term rate may occasionally drop to zero, in which case the
distinction between the powers that the CB has with or without the ability to pay interest on
reserves is blurred.
14
15

Fiat money will characterize a subset of these possible desired paths.
Throughout the paper, “positive” [“negative”] means greater or equal [less or equal] than 0. Whenever a

quantity is strictly greater [smaller] than 0, we will call it “strictly positive” [“strictly negative”].

14

3.1
3.1.1

Rt > 0 Always
Bills Only

We call the most conservative asset-management strategy bills only: it entails investing the entire
portfolio of assets in short-term securities.16
Proposition 2 Suppose that the CB is not allowed (or never chooses) to pay interest on reserves,
and that it invests all of its assets in short-term securities. Then its profits are always positive,
whether they are measured at historical prices or marked to market.
Proof. With Rt > 0, excess reserves will always be 0 if the CB does not pay interest on them:
the private sector will find it preferable to invest in government bonds any funds that are not
B
needed for liquidity services. Furthermore, Dt = 0 in any period t. From equations (3) and (4)

we thus obtain
ΠHC = ΠM M =
t
t

Rt
B B ≥ 0.
1 + Rt t

(10)

QED.
In general, the profits from equation (10) will always be strictly positive, because the CB
holds some assets on its balance sheet. However, they could be 0 if the CB chooses (or is
forced to) immediately remit to Treasury a payment equal to its assets in every period. If CB
independence is related to its profit stream, the bills-only policy coupled with no excess reserves
gives the best case scenario, since the CB is guaranteed to never record losses, either at historical
prices or marking its assets to market. When money is fiat, this policy can also guarantee a
positive stream of seigniorage transfers, as we establish below:
Proposition 3 Suppose that the CB is not allowed (or never chooses) to pay interest on reserves,
and that it invests all of its assets in short-term securities. In addition, suppose that money is
fiat. Then the CB can guarantee a positive stream of seigniorage transfers to Treasury.
16

The bills only doctrine was introduced in the United States in the aftermath of the Treasury accord of 1951,

which freed the Federal Reserve from pegging interest rates on government debt. For a presentation of the
arguments discussed at the time, see e.g. Young and Yager [19].

15

Proof. In the appendix.
Intuitively, since its portfolio of assets is not needed to redeem money issues when money is
fiat, the CB can simply pay to Treasury its profits from equation (10) plus the value of any new
money that it issued during the period.
3.1.2

Buy and Hold

In the strategy that we call buy and hold, the CB invests in both long and short-term debt, but
it holds all of its debt to maturity.
Proposition 4 Suppose that the CB is not allowed (or never chooses) to pay interest on reserves.
Suppose further that its assets are invested in both short and long-term debt, but that the CB
holds long-term debt to maturity.17 Then its profits at historical prices are always positive.
Proof. As before, no interest payment on reserves implies Xt = 0 in all periods. Furthermore,
B
B
since the CB holds its debt to maturity, Dt ≥ Dt−1 in all periods. Equation (3) then implies

ΠHC =
t

Rt−1
B
Bt−1 + Dt−1 ≥ 0.
1 + Rt−1

QED.
While the value of the CB portfolio can now fluctuate with movements in long-term rates,
the CB is still investing in assets that command a positive interest rate, and issuing money that
pays no interest rate. Under the “buy and hold” strategy, at historical cost the CB simply books
as profits the interest on short-term debt and the coupon paid by long-term debt.
We do not discuss here the profits and losses that the CB faces when its assets are marked to
market, nor its ability to pay positive seigniorage transfers: this is because the implications of
“buy and hold” on these two subjects are the same as “unlevered active trading,” the strategy
to which we turn next.
17

In the case of consols, this means that the stock of consols held by the CB never declines in nominal terms;

the CB uses only the coupon payments from the consols (along with maturing short-term debt) for reinvestment
into new government bonds or for paying seigniorage transfers.

16

3.1.3

Unlevered Active Trading

Here, we do not make any assumption of the CB’s portfolio, other than imposing that it does
not pay interest on reserves.
Proposition 5 Suppose that the CB is not allowed (or never chooses) to pay interest on reserves.
Then the CB losses, whether at historical prices or marked to market, cannot exceed the value
of the CB portfolio in the previous period (evaluated at historical prices or marked to market,
respectively).
Proof. Once again, no interest on reserves implies Xt = 0. From equation (3),
ΠHC =
t

Rt−1
B
B
B
B
B
B
¯
¯
¯
B
B
B B +Dt−1 +(Qt −Qt−1 )(Dt−1 −Dt )IDt−1 >Dt ≥ −Qt−1 Dt−1 ≥ −Bt−1 −Qt−1 Dt−1 .
1 + Rt−1 t−1

From equation (4),
ΠM M =
t

Rt−1
B
B
B
B
B
B B + Dt−1 + (Qt − Qt−1 )Dt−1 ≥ −Qt−1 Dt−1 ≥ −Bt−1 − Qt−1 Dt−1 .
1 + Rt−1 t−1

QED.
When the CB invests in long-term securities, movements in long-term interest rates affect the
value of its portfolio. Under “buy and hold,” these changes are reflected in the CB’s accounting
only if it marks its assets to market, while active trading may lead the CB to realize its losses
and thus book them even if it values its assets at historical cost.
In either case, the CB can do no worse than losing all of its investments, which would happen
in the extreme circumstance in which all of its assets are long term and the long-term interest
rate becomes so large that Qt becomes close to 0.18 Not surprisingly, in the case of fiat money,
when assets are not needed to redeem previously issued money, such a loss would not threaten
the CB’s ability to pay positive seigniorage transfers, as the following proposition formally states:
Proposition 6 Suppose that the CB is not allowed (or never chooses) to pay interest on reserves,
and that money is fiat. Then the CB can guarantee a positive stream of seigniorage transfers to
Treasury.
18

To be precise, even in this extreme circumstance the CB would still have positive assets left, from the coupon

B
payment Dt−1 .

17

Proof. In the appendix.
Even though under fiat money the CB can arrange its payments to Treasury so as to never
need to require a reverse transfer (a “bailout”), the potential loss of value of its portfolio will
still translate into a smaller present-value of seigniorage transfers to Treasury (equation (6)); this
risk may be undesirable to the fiscal authorities.
3.1.4

Quantitative Easing

In our final step, we consider the case in which the CB issues interest-bearing reserves. To the
extent that these reserves are invested in short-term government debt, this policy has no effect:
the CB buys a debt instrument that promises to pay 1£ in the subsequent period and finances
the purchase by issuing a promise to deliver the same amount.19 But when the CB uses excess
reserves to finance purchases of long-term debt, it is effectively taking a levered bet on long-term
interest rates. Because of its leverage, the CB can no longer guarantee that the value of its
portfolio will remain positive, independent of movements in long-term rates. If the CB position
is sufficiently large, the losses from this bet will thus need to be covered with profits from the
monopoly over the issuance of money, or, in extreme circumstances in which not even those are
sufficient, with transfers from Treasury. This intuition is formalized in the following proposition.
Proposition 7 Suppose that the CB is allowed to pay interest on reserves, and that the path of
future long-term interest rates is uncertain. Then the CB is free to choose policies that entail
the risk of arbitrarily large losses. Some of these trading strategies will require transfers from
Treasury to the CB to keep inflation at the preset desired path.
Proof. In the appendix.
In our highly stylized model, where there is no cost of raising taxes, fiscal losses (whether
incurred by the CB or by Treasury) carry no welfare consequences. This is no longer the case
19

In practice, excess reserves held by banks at the CB are overnight loans, while government debt is of longer

maturity. At the height of a financial crisis, this difference may be important. For the fiscal implications considered
here, a CB policy of purchasing short-term debt (e.g., of a 3-month maturity) by issuing overnight reserves will
still carry very low interest rate risk.

18

in environments where taxes are distortionary. Long-term debt will be particularly helpful if
strains on the government budget are associated with higher long-term interest rates, a likely
event in practice. Lustig, Sleet, and Yeltekin [13] study the case of distortionary taxes in detail
and formally prove that the maturity structure that minimizes expected distortions arising from
taxes and inflation involves issuing only long-term debt. In this case, expected tax distortions
increase if the CB engages in maturity transformation by replacing long-term debt issued by
Treasury with short-term obligations of its own.
The fact that the CB can take risks large enough that would require a recapitalization does
not need that it will do so. As an example, Carpenter et al. [5] and Greenlaw et al. [8] compute
some projections of the balance sheet of the Federal Reserve; under adverse scenarios, they
establish that these could lead to losses according to the accounting developed here,20 but these
losses would be very minor compared to the present value of seigniorage revenues going forward.
In proposition 7, as well as in all previous propositions, we kept the stochastic process for
inflation, nominal interest rates, and money fixed. Because of this assumption, the CB profits and
losses only had fiscal implications, affecting the size (and, in extreme cases, the sign) of seigniorage
transfers to Treasury, and from there would spill over to taxes. But inflation, (nominal) interest
rates, and the money supply are under CB control. This suggests that a CB facing losses always
faces a second alternative: resorting to the printing press. To better understand this alternative,
suppose that a CB starts period t in a situation such that, at the desired path of inflation,
nominal interest rates, and money balances, the left-hand side of equation (6) is negative, which
would require (sooner or later) a transfer from Treasury. The CB liabilities are made of 2 items,
both of which can be discharged with no need of transfers from Treasury, provided the CB is
willing to let money grow sufficiently fast and suffer the inflationary consequences:
• Promises to decrease the money supply (when Ms < Ms−1 ) can be avoided simply by
never repurchasing previously issued money, but rather choosing an increasing path for the
20

What is called losses in this paper is called a “deferred asset” in Carpenter et al. [5] and Greenlaw et al. [8].

This is consistent with a view that seigniorage payments are not profits distributed to Treasury, but rather a
tax paid by the Federal Reserve. According to this interpretation, current losses could be used to reduce future
seigniorage payments, and thus future tax liabilities, thereby resulting in a “deferred asset.”

19

money supply.
• Excess reserves Xt are simply a promise to deliver money, so they can be discharged
by increasing the money supply by Xt in period t (in equation (6), this will generate a
corresponding increase in the profits from the monopoly issuance of money).

3.2

The Zero Lower Bound

Propositions 2-7 rely on the fact that excess reserves are necessarily zero unless the CB pays
interest on them. However, whenever the nominal interest rate Rt is at 0, this is no longer the
case: the distinction between paying or not paying interest on excess reserves is lost. This has
effectively been the case in the last few years.
The following proposition shows that excess reserves cannot cause losses on the CB balance
sheet, whenever they are invested according to the “bills only” doctrine. This result is intuitive:
any excess reserves are matched by assets of the same maturity, and hence no loss can arise from
their issuance. The only qualification that is required for the case in which Rt may hit zero is
that the CB should never distribute transfers to Treasury in such an amount that it would lead
its portfolio of assets to have negative value.21
Proposition 8 Suppose that the CB invests all of its assets in short-term securities, and that
its dividend policy is such that Bt − Xt ≥ 0 always. Then its profits are always positive, whether
they are measured at historical prices or marked to market. When money is fiat and the CB
starts from an initial portfolio of positive value, this policy can be achieved while paying positive
transfers in every period, St ≥ 0.
B
Proof. After imposing Dt = 0, equations (3) and (4) imply

ΠHC = ΠM M =
t
t

Rt
B
(Bt − Xt ),
1 + Rt

B
which is positive whenever Bt − Xt is positive. If the CB starts from an initial condition

B−1 − X−1 ≥ 0 and the money supply is an increasing sequence (money is fiat), equation (2)
21

In the case of Rt > 0, this was guaranteed, since we necessarily had Xt = 0.

20

B
implies that the CB can set St = Mt − Mt−1 + Bt−1 − Xt−1 ≥ 0 and still retain a portfolio of
B
zero value (Bt = Xt ) from period 0 onwards. QED.

While the bills-only doctrine ensures the CB against losses on its balance sheet, it also makes
monetary policy particularly ineffective when short-term nominal interest rates are 0, since it is
unlikely that swapping Treasury short-term liabilities for CB short-term liabilities would have
any effect.
When the CB buys long-term debt, it is straightforward to verify that propositions 4-6 continue to be true if the CB limits its creations of excess reserves to the amount of short-term
bills in its portfolio. Further quantitative easing beyond this value involves taking leveraged
interest-rate risk, and may cause losses that would need to be repaid with profits from money
issuance and/or transfers from Treasury, even if the risk is originally taken at a time in which
short-term rates are zero.

4

Conclusion

We have analyzed simple conditions under which central bank policy ensures positive profits
and/or positive transfers to Treasury. We did so by use of a highly stylized model, where the
results are particularly transparent and easy to derive. Nonetheless, the implications apply
equally well to much richer environments featuring nominal frictions, an explicit banking sector,
and transaction or regulatory costs that may segment markets for government debt of different
maturities. In these environments, more interesting roles for monetary policy and quantitative
easing emerge, which are not present in our simple setup;22 a trade-off would then emerge between
the pursuit of these roles and the minimization of fiscal risks.
To the extent that financial market imperfections warrant a role for adjusting the maturity
structure of the liabilities of the central bank and Treasury, an expansion of the balance sheet
of the central banks financed with excess reserves held by commercial banks is only one of
many potential arrangements. As an example, on September 17, 2008, with the Fed funds
22

Optimal monetary policy in our stylized economy would call for the “Friedman rule,” where the CB pursues

a deflationary policy by repurchasing money over time and keeping nominal interest rates at zero.

21

target rate still at 2% and while the Federal Reserve did not yet have power to pay interest
on reserves (and thus to raise funds from commercial banks at that rate), the U.S. Department
of Treasury announced a Supplementary Financing Program,23 whereby T-Bills would be sold
and the cash proceeds would be deposited at the Federal Reserve, which could in turn use the
cash to buy privately-issued and mortgage-backed securities, without increasing the overall level
of the monetary base. The Treasury deposits with the Federal Reserve did not earn interest;
this represented an alternative funding mechanism for quantitative easing that shifted interest
rate risk from monetary to fiscal authorities. Similarly, to the extent that a policy of lowering
long-term interest rates by shifting the maturity structure held of government debt held by the
public is desirable, this goal could be attained either by the policy of quantitative easing pursued
by the Federal Reserve and the Bank of England, or by the Treasury’s choice of concentrating
its issued of debt at the short end of the maturity structure. While the two options have similar
implications for the portfolio of securities available to the private sector, they allocate fiscal risk
differently between the central bank and the government. A goal of this paper is to stimulate
further analysis on how the allocation of this risk is likely to affect macroeconomic outcomes,
and ultimately on the optimal allocation of this risk.

A

Model Microfoundations.

We consider a model economy populated by a continuum of identical households that consume
a single good in each period, produced by working. The consumer’s preferences are given by
∞

t−1

u(c0 ) − φy0 + E0

βs
t=1

[u(ct ) − φyt ],

s=0

where ct is consumption in period t and yt is labor supplied in period t. While we allow for
periods in which the discount factor βs is greater than 1, so that the zero-bound on nominal
interest rates may be binding for a central bank that attempts to target stable prices, we assume
¯
¯
that there is a period T and a value β < 1 such that βs ≤ β with probability 1 when s > T . This
assumption could be relaxed, but is convenient to ensure that, in an equilibrium, present-value
23

See http://www.treasury.gov/press-center/press-releases/Pages/hp1144.aspx

22

budget constraints will have to be well defined. There is a technology with constant returns to
scale that produces one unit of the consumption good for each unit of time worked.
In each period, each household cannot consume what it produces, but it rather has to purchase
its consumption from an anonymous market with money acquired beforehand; this imposes the
following cash-in-advance constraint:24
m t ≥ Pt ct ,
where mt are money balances held by the individual household (we thus use lowercase letters
for variables that are chosen individually by each household, and uppercase letters for aggregate
equilibrium values).
In each period, the household budget constraint is given by
bt + x t
+ Qt dt + mt + Tt ≤ mt−1 + Pt−1 (yt−1 − ct−1 ) + bt−1 + xt−1 + (1 + Qt )dt−1 ,
1 + Rt

(11)

where bt and dt are household holdings of short and long-term bonds, and xt are holdings of
excess reserves. We also impose a lower bound on household indebtedness in each period (i.e.,
the lower bound affects bt−1 + xt−1 + (1 + Qt )dt−1 ); the lower bound is chosen so as to never be
binding in equilibrium, but is there simply to prevent houshold from rolling over their debt into
the indefinite future without ever repaying it, imposing a transversality condition.
Manipulation of the first-order (necessary) conditions of the household problem yields equations (7), (8), and (9), as well as the following expression for the present-value function:
P Vt (wt+k ) =

1
Et (zt+k wt+k ),
zt

(12)

where wt+k is an arbitrary payoff realized at time t + k, and
z0 = u (C0 )/P0 ,
(13)

t−1

βs

zt =

u (Ct )/Pt

s=0
24

See Lucas and Stokey [12] for an early formulation of this model, and Lagos and Wright [10] for a deeper

justification of this constraint.

23

These conditions are also sufficient for a competitive equilibrium when the budget constraints
(in flow and present-value form) and the transversality condition are satisfied; the transversality
condition is in turn implied by the present-value budget constraints (5) and (6).

B

Proofs

B.1

Proof of Propositions 3 and 6

Substitute Xt = Xt−1 = 0 in equation (2). In period t, any choice of 0 ≤ St ≤ Mt − Mt−1 +
B
B
B
B
Bt−1 + (1 + Qt )Dt−1 ensures that Qt Dt + Bt ≥ 0, leaving enough resources to ensure that the

CB starts period t + 1 with a portfolio of positive value, in addition to the present value of future
revenues from money issuance. QED.

B.2

Proof of Proposition 7

Consider an arbitrary period t for which the future price of long-term bonds Qt+1 is uncertain.
The CB balance available for investment in period t are given by Vt , defined as
B
B
Vt := Bt−1 + (1 + Qt )Dt−1 − St − Xt−1 − (Mt − Mt−1 ),

where Mt−1 , Mt , Rt , and Qt are dictated by the desired equilibrium path. This balance can be
allocated in any way that satisfies the budget constraint (2):
B
Bt − Xt
B
+ Qt Dt = Vt
1 + Rt

(14)

The value of this portfolio in period t + 1 (after some algebra, and using equation (9) will be
B
B
Bt − Xt + (1 + Qt+1 )Dt = (1 + Rt )Vt + Qt+1 − βt Et (1 + Rt+1 )

Pt
Qt+1
Pt+1

B
Dt .

(15)

If Qt+1 is known as of time t, equation (8) implies that the term within brackets is 0, and it does
not matter whether the CB invests in long or short-term bonds: with no uncertainty about the
price Qt+1 , short and long-term bonds must yield exactly the same rate of return between periods
t and t + 1. However, when Qt+1 is uncertain, the term in brackets will be strictly negative (and
24

strictly positive) with probability greater than 0.25 Provided that the CB chooses to a sufficiently
B
long position in Dt , the value of its portfolio could thus turn strictly negative, and unboundedly

so. Using equation (15) in the present-value budget constraint of the CB (equation 6) as of
period t + 1, we obtain
(1+Rt )Vt + Qt+1 − βt Et

∞

Pt
(1 + Rt+1 )
Qt+1
Pt+1

B
Dt

=

∞

PVt+1 (Ms − Ms−1 ) .

PVt+1 (Ss )−
s=t+1

s=t+1

(16)
B
For intermediate values of Dt , even if the value of the portfolio at t + 1 (the left-hand side of

equation (16)) is strictly negative, the present value of profits from money issuance may ensure
that

∞
s=t+1

B
PVt+1 (Ss ) > 0. But for Dt large enough, there are states of the world in period

t + 1 in which

∞
s=t+1

PVt+1 (Ss ) < 0: in these states, the fiscal risk taken by the CB is so large

that a transfer from Treasury to the CB is eventually needed to achieve the desired path for
inflation and money.
When marked to market, CB profits are given by
B
B
ΠM M = Bt −Xt +(1+Qt+1 )Dt −
t

B
Pt
Bt − Xt
B
−Qt Dt = Rt Vt + Qt+1 − βt Et (1 + Rt+1 )
Qt+1
1 + Rt
Pt+1

B
once again, arbitrarily high losses are possible provided Dt is sufficiently large. Profits at

historical prices will coincide with profits marked to market if the CB starts period t with no
long-term debt and sells all of its long-term debt in period t + 1, so unboundedly large losses are
possible even in this case.26

C

Description of Data

The graphs pertaining to the assets and liabilities for the Federal Reserve and the liabilities of
the European Central Bank and the Bank of England were compiled using data directly from
25

That this term cannot always take the same sign follows from a simple no-arbitrage argument, which is

omitted here for brevity.
26
With some additional algebra that we can skip here, it is possible to prove that unboundedly large losses at
historical cost are possible even if the CB follows a “buy and hold” strategy. These losses occur in subsequent
periods, in which the short-term interest rate paid on excess reserves may exceed the rate of return on the CB’s
holdings of long-term debt.

25

B
Dt ;

their web sites. For the Federal Reserve, data comes from the Federal Reserve’s balance sheet.27
For the European Central Bank, data comes from the ECB Eurosystem Statistical Warehouse.28
Finally, for the Bank of England, data comes from the Statistical Interactive Database.29
To construct the Federal Reserve graph of assets, we constructed three categories - Loans to
Government, Loans to Private Institutions, and Other. In the “Loans to Government” category,
we include all securities held outright (Treasury bills, Treasury notes, Treasury bonds, agency
debt, mortgage-backed securities, unamortized premiums and unamortized discounts).30 In the
“Loans to Private Institutions category,” we include Maiden Lane I, Maiden Lane II, Maiden
Lane III, TALF, CPFF, and TAF. Finally, in the “Other” category, we include gold stock, special
drawing rights, Treasury currency outstanding, float, central bank liquidity swaps, and foreign
currency denominated assets, and other assets.
The basic construction of the three liabilities graphs all follow a similar breakdown - currency
that does not pay interest, liabilities that could pay interest, and other (mostly capital).
To construct the Federal Reserve graph of liabilities, we constructed three categories - Currency, Reverse Repos and Deposits, and Capital. In the Currency category, we include currency
in circulation. In the Reverse Repos and Deposits category, we include reverse repurchase agreements, Treasury Cash Holdings, Deposits, and Reserves. Finally, in the Capital category, we
include other liabilities and capital.
To construct the European Central Bank graph of liabilities, we constructed three categories
- Currency, Deposits and Other, and Capital and Reserves. In the Currency category, we include
banknotes in circulation. In the Deposits and Other category, we include current accounts, the
deposit facility, fixed-term deposits, fine tuning reverse operations, deposits related to margin
calls, other liabilities denominated in world, debt certificates issued, other euro-denominated liabilities, and Special Drawing Rights allocated by the IMF. In the Capital and Reserves category,
27

http://www.federalreserve.gov/monetarypolicy/bst fedsbalancesheet.htm
http://sdw.ecb.europa.eu/browse.do?node=bbn129
29
http://www.bankofengland.co.uk/boeapps/iadb/BankStats.asp?Travel=NIxSTxTBx
30
Agency debt and mortgage-backed securities are technically not issued by the government, but we treat them
28

as part of the loans to the government, since their repayment was guaranteed by the government during the
financial crisis, and it is widely believed that they will continue to be guaranteed in the future.

26

ECB Balance Sheet − Liabilities
3.5
Currency
Deposits and Other
Capital and Reserves
3

Euros in Trillions

2.5

2

1.5

1

0.5

0
Jan−07

Jan−08

Jan−09

Jan−10

Jan−11

Jan−12

Jan−13

Figure 4: ECB Liabilities since 2007
we include all other liabilities, revaluation accounts, and capital and reserves.
To construct the Bank of England graph of liabilities, we constructed three categories - Sterling Notes, Reserve Balances, and Other. In the Sterling Notes category, we include sterling
notes in circulation. In the Reserve Balances category, we include sterling reserve balance liabilities. Finally, in the Other category, we include standing facility deposits, short-term open
market operations, foreign currency public securities issued, cash deposit ratios from MFIs, and
all other liabilities.
To construct the Federal Reserve maturity structure, we only include Liquidity and Credit
Facilities, Securities held Outright, TALF, Repurchase agreements, and central bank liquidity
swaps.

27

Bank of England Balance Sheet − Liabilities
0.45
Sterling Notes
Reserve Balances
Other

0.4

0.35

Pounds in Trillions

0.3

0.25

0.2

0.15

0.1

0.05

0

Jan−08

Jan−10

Jan−12

Figure 5: Bank of England Liabilities since 2007

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30

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Eric French and Christopher Taber

WP-10-08

Public Pensions and Labor Supply Over the Life Cycle
Eric French and John Jones

WP-10-09

Explaining Asset Pricing Puzzles Associated with the 1987 Market Crash
Luca Benzoni, Pierre Collin-Dufresne, and Robert S. Goldstein

WP-10-10

Prenatal Sex Selection and Girls’ Well‐Being: Evidence from India
Luojia Hu and Analía Schlosser

WP-10-11

Mortgage Choices and Housing Speculation
Gadi Barlevy and Jonas D.M. Fisher

WP-10-12

Did Adhering to the Gold Standard Reduce the Cost of Capital?
Ron Alquist and Benjamin Chabot

WP-10-13

Introduction to the Macroeconomic Dynamics:
Special issues on money, credit, and liquidity
Ed Nosal, Christopher Waller, and Randall Wright

WP-10-14

Summer Workshop on Money, Banking, Payments and Finance: An Overview
Ed Nosal and Randall Wright

WP-10-15

Cognitive Abilities and Household Financial Decision Making
Sumit Agarwal and Bhashkar Mazumder

WP-10-16

1

Working Paper Series (continued)
Complex Mortgages
Gene Amromin, Jennifer Huang, Clemens Sialm, and Edward Zhong

WP-10-17

The Role of Housing in Labor Reallocation
Morris Davis, Jonas Fisher, and Marcelo Veracierto

WP-10-18

Why Do Banks Reward their Customers to Use their Credit Cards?
Sumit Agarwal, Sujit Chakravorti, and Anna Lunn

WP-10-19

The impact of the originate-to-distribute model on banks
before and during the financial crisis
Richard J. Rosen

WP-10-20

Simple Markov-Perfect Industry Dynamics
Jaap H. Abbring, Jeffrey R. Campbell, and Nan Yang

WP-10-21

Commodity Money with Frequent Search
Ezra Oberfield and Nicholas Trachter

WP-10-22

Corporate Average Fuel Economy Standards and the Market for New Vehicles
Thomas Klier and Joshua Linn

WP-11-01

The Role of Securitization in Mortgage Renegotiation
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
and Douglas D. Evanoff

WP-11-02

Market-Based Loss Mitigation Practices for Troubled Mortgages
Following the Financial Crisis
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
and Douglas D. Evanoff

WP-11-03

Federal Reserve Policies and Financial Market Conditions During the Crisis
Scott A. Brave and Hesna Genay

WP-11-04

The Financial Labor Supply Accelerator
Jeffrey R. Campbell and Zvi Hercowitz

WP-11-05

Survival and long-run dynamics with heterogeneous beliefs under recursive preferences
Jaroslav Borovička

WP-11-06

A Leverage-based Model of Speculative Bubbles (Revised)
Gadi Barlevy

WP-11-07

Estimation of Panel Data Regression Models with Two-Sided Censoring or Truncation
Sule Alan, Bo E. Honoré, Luojia Hu, and Søren Leth–Petersen

WP-11-08

Fertility Transitions Along the Extensive and Intensive Margins
Daniel Aaronson, Fabian Lange, and Bhashkar Mazumder

WP-11-09

Black-White Differences in Intergenerational Economic Mobility in the US
Bhashkar Mazumder

WP-11-10

2

Working Paper Series (continued)
Can Standard Preferences Explain the Prices of Out-of-the-Money S&P 500 Put Options?
Luca Benzoni, Pierre Collin-Dufresne, and Robert S. Goldstein
Business Networks, Production Chains, and Productivity:
A Theory of Input-Output Architecture
Ezra Oberfield

WP-11-11

WP-11-12

Equilibrium Bank Runs Revisited
Ed Nosal

WP-11-13

Are Covered Bonds a Substitute for Mortgage-Backed Securities?
Santiago Carbó-Valverde, Richard J. Rosen, and Francisco Rodríguez-Fernández

WP-11-14

The Cost of Banking Panics in an Age before “Too Big to Fail”
Benjamin Chabot

WP-11-15

Import Protection, Business Cycles, and Exchange Rates:
Evidence from the Great Recession
Chad P. Bown and Meredith A. Crowley

WP-11-16

Examining Macroeconomic Models through the Lens of Asset Pricing
Jaroslav Borovička and Lars Peter Hansen

WP-12-01

The Chicago Fed DSGE Model
Scott A. Brave, Jeffrey R. Campbell, Jonas D.M. Fisher, and Alejandro Justiniano

WP-12-02

Macroeconomic Effects of Federal Reserve Forward Guidance
Jeffrey R. Campbell, Charles L. Evans, Jonas D.M. Fisher, and Alejandro Justiniano

WP-12-03

Modeling Credit Contagion via the Updating of Fragile Beliefs
Luca Benzoni, Pierre Collin-Dufresne, Robert S. Goldstein, and Jean Helwege

WP-12-04

Signaling Effects of Monetary Policy
Leonardo Melosi

WP-12-05

Empirical Research on Sovereign Debt and Default
Michael Tomz and Mark L. J. Wright

WP-12-06

Credit Risk and Disaster Risk
François Gourio

WP-12-07

From the Horse’s Mouth: How do Investor Expectations of Risk and Return
Vary with Economic Conditions?
Gene Amromin and Steven A. Sharpe

WP-12-08

Using Vehicle Taxes To Reduce Carbon Dioxide Emissions Rates of
New Passenger Vehicles: Evidence from France, Germany, and Sweden
Thomas Klier and Joshua Linn

WP-12-09

Spending Responses to State Sales Tax Holidays
Sumit Agarwal and Leslie McGranahan

WP-12-10

3

Working Paper Series (continued)
Micro Data and Macro Technology
Ezra Oberfield and Devesh Raval

WP-12-11

The Effect of Disability Insurance Receipt on Labor Supply: A Dynamic Analysis
Eric French and Jae Song

WP-12-12

Medicaid Insurance in Old Age
Mariacristina De Nardi, Eric French, and John Bailey Jones

WP-12-13

Fetal Origins and Parental Responses
Douglas Almond and Bhashkar Mazumder

WP-12-14

Repos, Fire Sales, and Bankruptcy Policy
Gaetano Antinolfi, Francesca Carapella, Charles Kahn, Antoine Martin,
David Mills, and Ed Nosal

WP-12-15

Speculative Runs on Interest Rate Pegs
The Frictionless Case
Marco Bassetto and Christopher Phelan

WP-12-16

Institutions, the Cost of Capital, and Long-Run Economic Growth:
Evidence from the 19th Century Capital Market
Ron Alquist and Ben Chabot

WP-12-17

Emerging Economies, Trade Policy, and Macroeconomic Shocks
Chad P. Bown and Meredith A. Crowley

WP-12-18

The Urban Density Premium across Establishments
R. Jason Faberman and Matthew Freedman

WP-13-01

Why Do Borrowers Make Mortgage Refinancing Mistakes?
Sumit Agarwal, Richard J. Rosen, and Vincent Yao

WP-13-02

Bank Panics, Government Guarantees, and the Long-Run Size of the Financial Sector:
Evidence from Free-Banking America
Benjamin Chabot and Charles C. Moul
Fiscal Consequences of Paying Interest on Reserves
Marco Bassetto and Todd Messer

WP-13-03

WP-13-04

4