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Federal Reserve Bank of Chicago
Nominal Debt as a Burden on
Monetary Policy
Javier Díaz-Giménez, Giorgia Giovannetti,
Ramon Marimon, and Pedro Teles
WP 2004-10
Nominal Debt as a Burden on Monetary Policy∗
Javier Díaz-Giménez
Ramon Marimon
Giorgia Giovannetti
Pedro Teles†
This version: July 7, 2004
Abstract
We study the effects of nominal debt on the optimal sequential choice of monetary and debt policy. When the stock of debt is nominal, the incentive to generate
unanticipated inflation increases the cost of the outstanding debt even if no unanticipated inflation episodes occur in equilibrium. Without full commitment, the
optimal sequential policy is to deplete the outstanding stock of debt progressively
until these extra costs disappear. Nominal debt is therefore a burden on monetary
policy, not only because it must be serviced, but also because it creates a time
inconsistency problem that distorts interest rates. The introduction of alternative
forms of taxation may lessen this burden, if there is enough commitment to fiscal
policy.
Key words: Nominal debt; monetary policy; time-consistency; Markov-perfect
equilibrium.
JEL classification: E40; E50; E63.
1
Introduction
Fiscal discipline has often been seen as a precondition to sustain price stability. Such
is, for example, the rationale behind the Growth and Stability Pact in Europe. More
precisely, it is understood that an economy with a large stock of nominally denominated
government debt can benefit from inflation surprises that reduce the need for distortionary taxation in the future. This means that optimal monetary policy under full
∗
We would like to thank Jośe-Victor Ríos-Rull, Jaume Ventura, Juan Pablo Nicolini and Isabel
Correia for their comments, as well as the participants in seminars and conferences where this work
has been presented.
†
J. Díaz-Giménez: Universidad Carlos III and CAERP; G. Giovannetti: Università di Firenze;
R. Marimon: Universitat Pompeu Fabra, CREi, CREA, CEPR and NBER, and P. Teles: Federal
Reserve Bank of Chicago and CEPR.
1
commitment (the Ramsey policy) can be time inconsistent. In other words, if a government with the ability to honor its commitments were to re-optimize at a later date, it
may choose to deviate from its original plan. In this context, a constraint on the level
of debt may reduce the impact of such time-inconsistency distortions.
In this paper we study the effects of nominal debt on the optimal sequential choice
of monetary and debt policy. We analyze a very stylized monetary model to show how
optimal monetary policy differs depending on whether there is indexed or nominal debt
and on the degree of commitment of monetary authorities. The structure of the optimal
taxation problems that we solve is the following: first, we assume that the government
has to finance a given constant flow of expenditures with revenues levied using only
seigniorage. To solve these optimal taxation problems, the government chooses the paths
of seigniorage that maximize the household’s utility subject to the implementability
and budget constraints. Unexpected inflation is costly, because we assume that the
consumption good must be purchased with cash carried over from the previous period,
as in Svensson (1985). This timing of the cash-in-advance constraint implies that, if the
government decided to surprise the household with an unexpected increase in inflation in
any given period, the household’s consumption would be smaller than planned because
its predetermined cash balances would be insufficient to purchase the intended amount
of consumption. When considering whether or not to carry out such a surprise inflation,
the government compares the reduction in the household’s current utility that results
from this lower level of consumption with the increase in the household’s future utility
that results from the reduction in future seigniorage.
After describing the model economy in Section 2, in Section 3 we characterize optimal
policy with full commitment, in the benchmark case where the outstanding stock of
government debt is indexed. Our results build on those of Nicolini (1998), who shows
that, when the utility function is logarithmic in consumption and linear in leisure and
the stock of government debt is indexed, the optimal monetary policy –in an economy
similar to ours– is to abstain from inflation surprises. This result follows from applying
optimal taxation principles and it means that, in this model economy, the solution to
the Ramsey problem is time consistent. The solution to this problem is stationary, and
there is a unique interest rate that balances the government budget.
Next we study the optimal monetary policy when the outstanding stock of government debt is nominal. In Section 4, we assume that there is full commitment to
monetary policy. We show that interest rates are kept constant from period one onwards, but that the initial interest rate is higher, since it is optimal to cancel part of the
inherited stock of nominal debt. In this case, after period zero, the interest rate is lower
than the one that obtains in the equilibrium with indexed debt, since the government
cannot reduce the inherited stock of debt by increasing the initial price. We characterize
the rational expectations Ramsey equilibrium in which there are no surprise inflations
even in period zero. This equilibrium has the property that initial real liabilities are the
same as in the case of indexed debt. Since there is no ‘free lunch’ surprise inflation, the
equilibrium that obtains with nominal debt and full commitment is less efficient than
the time consistent equilibrium with indexed debt.
2
With these regimes as reference, in Section 5 we present the main result of the paper.
We study optimal policy in the absence of commitment. In this case, we restrict our
attention to a Markov perfect equilibrium. We call this equilibrium recursive as in Cole
and Kehoe (1996) and Obstfeld (1997). Two interesting features of the optimal policy
under this recursive equilibrium are that the optimal inflation tax is non-stationary and
that it converges to the inflation tax that obtains when there is no government debt.
This result arises because, in the recursive equilibrium, it is optimal for the government
to asymptotically deplete the stock of nominal government debt. An implication of this
result is that, in this economy, the optimal nominal interest is initially higher than the
one prevailing when debt is indexed while, in the limit, it is lower. This decreasing path
for the nominal interest rate is another indication that nominal debt is indeed a burden
for monetary policy. Not only debt has to be serviced, but it also distorts interest
rates. In fact, it is because the optimal policy endogenizes these distortions that it
asymptotically monetizes the debt as the way to eliminate distortions. In Section 6,
we carry out a numerical example and we describe our findings comparing the different
regimes.
In Section 7 we ask whether these results are robust to the introduction of additional
taxes. This is important since, in advanced economies, seigniorage is a minor source
of tax revenue and we would like to know if our results still hold when government
outlays are financed with other taxes. Specifically, we study the case of consumption
taxes. We impose the natural assumption that taxes are chosen before the monetary
policy decisions are made. We find that the same equilibria arise when there are both
seigniorage and consumption taxes as when there is only seigniorage. However, the
fiscal authority can constrain the monetary authority to follow the Friedman rule, of
zero nominal rates, from the outset. In this case, since monetary distortions resulting in
negative interest rates are not equilibrium rates, the monetary authority has no incentive
to monetize the debt and, as a result, implements the optimal equilibrium that obtains
with indexed debt (see Marimon, Nicolini and Teles, 2003).
The relationship between fiscal and monetary policy has been addressed in the unpleasant monetarist arithmetic literature of Sargent and Wallace (1981), and in the fiscal
theory of the price level of Sims (1994) and Woodford (1996). In these approaches, however, policies are taken to be exogenous. This is not the case in our analysis, nor in the
related work of Chari and Kehoe (1999), Rankin (2002) and Obstfeld (1997). These last
two papers are the closest to ours. Both, however, assume that debt is real and only
focus on monetary policy. They aim at characterizing the Markov perfect equilibrium
when the source of the time inconsistency of monetary policy is related to the depletion
of the real value of money balances. This source of time inconsistency is ambiguous:
while in Lucas and Stokey (1983) the government would want to completely deplete
the outstanding money balances, in Svensson (1985)’s set up, as was shown in Nicolini (1998), under certain elasticity conditions, the government problem would be time
consistent. This ambiguity led Obstfeld (1997) to consider an ad-hoc cost of a surprise
inflation. Our analysis differs from Obstfeld’s both because we consider nominal debt
and because, in our model economy, the cost of unanticipated inflation arises from the
timing of the cash-in-advance constraint rather than being imposed ad-hoc. In a similar
3
framework, Rankin (2002) shows that the size of the initial debt matters for the direction of the time inconsistency problem, but he does not provide a full characterization
of the resulting dynamic equilibrium. He shows that, for general preferences, there can
be a value of debt where the elasticity is unitary and, therefore, there exists a steady
state with positive debt.
Finally, an additional contribution of this paper is the full characterization and the
computation of the optimal policy in a recursive equilibrium with a state variable. In
this respect, our work is closely related to the recent work of Krusell, Martín and RíosRull (2003) who characterize recursive equilibria in the context of an optimal labor
taxation problem.
2
The model economy
In our model economy there is a representative household and a government. The
g
g
government issues currency, Mt+1
, and nominal debt, Bt+1
, to finance an exogenous and
constant level of public consumption, g. Initially, we abstract from all other sources of
public revenues. In each period t ≥ 0 the government budget constraint is the following:
g
g
Mtg + Btg (1 + it ) + pt g ≤ Mt+1
+ Bt+1
(1)
where it is the nominal interest rate paid on debt issued by the government at time
t − 1, and pt is the price of one unit of the date t composite good. The initial stock of
currency, M0g , and initial debt liabilities, B0g (1 + i0 ), are given. A government policy is,
g
g
therefore, a specification of {Mt+1
, Bt+1
, g} for t ≥ 0.
We assume that the household’s preferences over consumption and labor can be
represented by the following utility function:
∞
X
t=0
β t [u(ct ) − αnt ]
(2)
where ct > 0 denotes consumption at time t, nt denotes labor at time t, and 0 < β < 1
is the time discount factor. We assume that the utility of consumption satisfies the
standard assumptions of being strictly increasing and strictly concave. For reasons that
will become clear below, in most of this article we assume that the utility is logarithmic
in consumption, i.e., u(c) = log(c).
We assume that consumption in period t must be purchased using currency carried over from period t − 1 as in Svensson (1985). This timing of the cash-in-advance
constraint implies that the representative household takes both M0 and B0 (1 + i0 ) as
given when solving its maximization problem, and it is crucial to obtain the results
4
that we report here. The specific form of the cash-in-advance constraint faced by the
representative household is:
pt ct ≤ Mt
(3)
for every t ≥ 0.
To simplify the productive side of this economy, we assume that labor can be transformed into either the private consumption good or the public consumption good on a
one-to-one basis. Consequently, the competitive equilibrium real wage is wt∗ = 1, and
the economy’s resource constraint is:
ct + g ≤ nt
(4)
both for every t ≥ 0.
Each period the representative household also faces the following budget constraint:
Mt+1 + Bt+1 ≤ Mt − pt ct + Bt (1 + it ) + pt nt
(5)
where Mt+1 and Bt+1 denote, respectively, the currency and the stock of nominal government debt that the household carries over from period t to period t + 1.
Finally, we assume that the representative household faces a no-Ponzi games condition:
lim β T BT +1 = 0
(6)
T −→∞
2.1
A competitive equilibrium
Definition 1 A competitive equilibrium for an economy with nominal debt is a govg
g
∞
ernment policy, {Mt+1
, Bt+1
, g, }∞
t=0 , an allocation {Mt+1 , Bt+1 , ct , nt }t=0 , and a price
vector, {pt , it+1 }∞
t=0 , such that:
(i) given M0g and B0g (1 + i0 ), the government policy and the price vector satisfy the
government budget constraint described in expression (1);
(ii) when households take M0 , B0 (1 + i0 ) and the price vector as given, the allocation
maximizes the problem described in expression (2), subject to the cash-in-advance
constraint described in expression (3), the household budget constraint described
in expression (5), and the no-Ponzi games condition described in expression (6);
and
5
(iii) the price vector is such that all markets clear, that is: Mtg = Mt , Btg = Bt ,
and g and {ct , nt }∞
t=0 satisfy the economy’s resource constraint described in expression (4), for every t ≥ 0.
When the debt is indexed, outstanding government liabilities are fixed in real terms.
g
/pt be the real value of the end-of-period stock of debt. A competitive
Let bt+1 = Bt+1
g
equilibrium for an economy with indexed debt is defined as a government policy, {Mt+1
,
g
∞
∞
∞
bt+1 , g, }t=0 , an allocation {Mt+1 , bt+1 , ct , nt }t=0 , and a price vector, {pt , it+1 }t=0 , such
that the corresponding (i), (ii) and (iii) are satisfied when nominal liabilities are replaced
by real liabilities. In particular, the initial government liabilities are given by M0g and
boβ −1
Given our assumptions on the utility of consumption u, it is straightforward to show
that the competitive equilibrium allocation of this economy satisfies both the economy’s
resource constraint (4) and the household’s budget constraint (5) with equality, and
that the first order conditions of the Lagrangian of the household’s problem are both
necessary and sufficient to characterize the solution to the household’s problem. Furthermore, it is also straightforward to show that, when it+1 > 0, the cash-in-advance
constraint (3) is binding.
The competitive equilibrium allocation of an economy with nominal debt can be
completely characterized by the following conditions that must hold for every t ≥ 0:
u0 (ct+1 )
= 1 + it+1 ,
α
(7)
pt+1
,
pt
(8)
1 + it+1 = β −1
ct =
Mt
,
pt
(9)
the government budget constraint (1), the resource constraint (4), and the no-Ponzi
games condition (6).
These conditions imply that the intertemporal government budget constraint described in expression (10) is also satisfied in equilibrium.
∞
X
t=0
β
t
µ
β
− nt
α
¶
=
B0 (1 + i0 )
.
p0
(10)
The competitive equilibrium allocation of an economy with indexed debt is also
completely characterized by (7), (8) and (9) with (8) –and, correspondingly, (7)— also
being satisfied in period zero (i.e., for t = −1). In other words, when debt is indexed
6
and pt−1 is given, the government policy must be such that it adjusts to pt in order
to satisfy Fisher’s equation even in period zero. The present value budget government
constraint is the same as (10) in its revenue side,P
while its
are given in real
¡ liabilities
¢
t β
−1
terms, independently of the initial price. That is, ∞
β
−
n
=
boβ
.
t
t=0
α
Therefore, in order to make meaningful comparisons, we will confront an indexed
debt economy with initial liabilities b0 β −1 with a nominal debt economy for which its
0)
real liabilities B0 (1+i
are equal to b0 β −1 in equilibrium.
p0
3
Optimal policy with indexed debt
In this section we study the optimal policy when the stock of government debt is indexed
(I). This is the benchmark against which we compare the optimal policy that obtains
when the stock of government debt is nominal –that is, not indexed– which is the
main focus of this article.
In the model economy with indexed government debt, the definition of an optimal
monetary equilibrium is the following
Definition 2 For a given level of government expenditures, g, and initial values of currency, M0 , and real government debt, b0 , an optimal monetary equilibrium with indexed
debt (I) is a government policy, a price vector, and an implied allocation, such that: (i)
the household utility is maximized, (ii) the government policy, the allocation, and the
price vector are a competitive equilibrium with indexed debt.
We follow the standard implementability approach of letting the government choose
the allocation directly. That is, we use expressions (7), (8), and (9) and the equilibrium
g
conditions Mtg = Mt and Btg = Bt to replace the prices and the variables Mt+1
/pt ,
g
g
g
Mt /pt , Mt and Bt in expression (1).
Consequently, the household’s utility is maximized when the government chooses
the policy that implements the consumption and real debt sequences that maximize
expression (2), subject to the following implementability condition:
u0 (ct+1 ) ct+1
β
+ bt+1 = ct + bt β −1 + g, t ≥ 0
α
(11)
and the no -Ponzi games condition (6).
This problem is recursive only when u(c) = ln(c). In this case, the price elasticity
is unitary and, as Nicolini (1998) has shown, the optimal monetary policy is timeconsistent. This problem can be written recursively as follows:
V (b) = max
{log(c) − α(c + g) + βV (b0 )}
0
c,b
7
(12)
subject to:
b0 = c + β −1 b − γ,
where γ ≡
β
α
(13)
− g.
The first order condition for c is:
1
− α = −βV 0 (b0 )
c
(14)
The interpretation of this equation is that the marginal gain of increasing consumption
is equated to the marginal cost of increasing future debt. Using the envelope theorem,
we obtain that
V 0 (b) = V 0 (b0 ),
(15)
and, substituting expression (14) into this expression:
1
1
−α = 0 −α
c
c
(16)
which implies that the optimal level of consumption, c∗I , is constant and equal to:
¡
¢
c∗I = γ − β −1 − 1 b0 .
(17)
Notice that expression (15) implies that the real value of the government debt is stationary and, consequently, that b∗I = b0 .
Finally, the stationary value of the nominal interest rate is:
£
¡
¢ ¤−1
1 + i∗I = αγ − α β −1 − 1 b0
.
(18)
and the evolution of prices and currency are given recursively by: p∗I,0 = M0 /c∗I and
∗
∗
= βp∗I,t /α, and p∗I,t = MI,t
/c∗I .1
MI,t+1
4
Optimal policy with nominal debt and full commitment
In this section we study the optimal monetary policy that obtains when the outstanding
stock of government is nominal –i.e., not indexed– and the government can fully
1
Notice that this last equality has been obtained from expressions (7), (8) and (9).
8
commit to the Ramsey monetary policy (R) after a given initial period that we denote
by t = 0. When the stock of debt is not indexed, the fact that consumption must be
purchased with currency carried over from the previous period, implies that seigniorage
at t = 0 is a tax that can be levied without affecting the commitment to future interest
rates. This may create an incentive for a Ramsey government to increase the initial
seigniorage tax at t = 0, and to use its proceeds to reduce the outstanding stock of debt.
Rational forward-looking households are aware of this incentive and, therefore, they
would have anticipated it when making their previous period decisions. In terms of the
initial level of consumption, this implies that the resulting optimal c0 must have been
correctly anticipated by the households or, equivalently, that the ex-ante and the ex-post
real interest rates must coincide in a rational expectations equilibrium (see Chari and
Kehoe, 1999).
To clarify this further, consider the government budget constraint in period zero:
p0 g + M0g + B0g (1 + i0 ) = M1g + B1g
(19)
Using the optimality conditions (7), (8), and (9) and the definition of b1 , expression (19)
can be rewritten as:
g + c0 +
B0g (1 + i0 )c0
β
= + b1
g
M0
α
(20)
When debt is nominal, a fully committed Ramsey government would choose the value
of c0 = c∗R,0 that maximizes the representative household utility subject to (20), and
the additional implementability constraints, one for each t > 0, that we describe below.
This optimal choice would result in p∗R,0 = M0 /c∗R,0 and the initial real liabilities would
∗
∗
), where rR,0
is the ex-post real interest rate that is
be B0g (1 + i0 )/p∗R,0 = b0 (1 + rR,0
consistent with c0 = c∗R,0 .
Let p0 and c0 be such that they satisfy:
B0g (1 + i0 )
B0g (1 + i0 )
=
c0 = b0 β −1 .
p0
M0g
(21)
That is, p0 is the price that satisfies Fisher’s equation (8) in period zero, and c0 is the
optimal consumption plan for t = 0 that is consistent with an initial real interest rate
r0 = β −1 .
Now we impose the additional consistency condition that p0 = p0 in equilibrium. In
other words, we impose the condition that the decisions taken in the past must satisfy an
ex-post, rational expectations, consistency condition in period zero. This requires that
there must be a fixed point between expectations and realizations –or, equivalently,
between the ex-ante and the ex-post real interest rates– implicitly defined by c0 = c0 .
9
Notice that imposing this additional consistency restriction in period zero prevents
the “free lunches” that would result from surprise inflations, and allows us to compare
the optimal policies that obtain in model economies with indexed debt and those in
model economies with nominal debt. We can compare equilibria that result under
different regimes having the same initial real government liabilities.2
Definition 3 A full commitment Ramsey equilibrium with nominal debt (R) is a
competitive equilibrium with nominal debt and a value for the expected consumption at
time t = 0, c0 , that satisfy the following conditions:
(i) given c̄0 , the equilibrium allocation solves the following problem:
Max
∞
X
t=0
β t [log(ct ) − α(ct + g)]
(22)
subject to the implementability constraints
γ + b1 − c0 − c0 b0
β −1
=0
c0
(23)
γ + bt+1 − ct − β −1 bt = 0, for t ≥ 1
(24)
(ii) c0 = c0 .
This full commitment Ramsey equilibrium is characterized by the following conditions:
1
c∗R,0
−α =
"
1
c∗R,1
−α
#"
β −1
1 + b0 ∗
cR,0
#
(25)
ct+1 = c∗R,1 , for t ≥ 1.
(26)
Notice that, as long as b0 > 0, c∗R,0 is smaller than c∗R,1 , and:
c∗R,0 = c∗R,1 − β −1 b0 (1 − αc∗R,1 ).
(27)
Moreover, from (23) and (24), we obtain that:
2
£
¡
¢ ¤−1
c∗R,1 = γ 1 + α β −1 − 1 b0
(28)
Notice that, when the utility function is logarithmic in consumption, there is a one-to-one mapping
between initial conditions (B0 , M0 ) and b0 . Specifically, b0 β −1 = B0 /(αM0 ). This follows from the
equalities (1 + i0 )/p0 = (1 + i0 )c0 /M0 = 1/(αM0 ).
10
Finally, rewriting (25), the path of the nominal interest rate is:
i∗R,1 =
1+
i0
(1+i0 )B0
M0
(29)
It is useful to compare the full commitment Ramsey equilibrium allocation with the
one that obtains when debt is indexed, since indexed debt can be viewed as an extreme
form of commitment. The full commitment Ramsey equilibrium with nominal debt is
characterized by an ex-post nominal interest rate higher than the one resulting in the
optimal equilibrium with indexed debt in period t = 0, and lower afterwards.
The reason for this is that the government wants to take advantage of the lump-sum
character of monetizing part of the outstanding stock of nominal debt, since there is
no time zero indexation that the government must internalize. In other words, in our
economy with unitary price elasticity (u(c) = ln(c)), nominal debt adjusts less than
one-to-one to any price change. It follows that to cancel part of the stock of nominal
debt in the initial period is part of the optimal tax policy. This is because in the full
commitment Ramsey equilibrium expectations are given and the initial price increase
does not question the commitment to the new optimal monetary policy.
When the stock of debt is indexed, the first order condition (16) requires that the
marginal values of consumption are equated, even in period zero. In contrast, when the
stock of debt is nominal and there is full commitment, the first order condition (25)
shows that the marginal value of consumption in period zero is discounted, since a
marginal reduction in c0 , results in a lower b1 .
Moreover, notice that, for any given b0 , the indexed debt solution, c∗I , is a feasible
solution for a fully committed Ramsey planner.3 However, when debt is nominal debt,
the fully committed Ramsey planner has an additional taxation instrument, namely to
monetize part of the outstanding stock of debt, and c∗I is not a best reply to the expectations c0 = c∗I . As it often happens with Nash equilibria, the fact that the government
has an additional taxation instrument does not imply that the Ramsey equilibrium that
obtains when the stock of debt is nominal (i.e., c0 = c∗R,0 ) is more efficient than the
equilibrium that obtains when the stock of debt is indexed. In fact, as the following
proposition states, the converse is true.
Proposition 4 Assume u(c) = log(c). Then, for any given b0 > 0, the optimal policy
that obtains in an equilibrium with indexed debt is more efficient than the optimal policy
that obtains in a full commitment Ramsey equilibrium with nominal debt.
Proof. It is enough to show that the household’s value obtained in the full commitment
Ramsey equilibrium is lower than the value achieved in the equilibrium with indexed
3
In this case the expected initial consumption would be c0 = c∗I .
11
debt. That is,
¤ª
©
£
log(c∗R,0 ) − α(c∗R,0 + g) + β(1 − β)−1 log(c∗R,1 ) − α(c∗R,1 + g)
ª
©
< (1 − β)−1 [log(c∗I ) − α(c∗I + g)]
Since preferences are linear in labor and strictly concave in consumption, the above
inequality follows from Jensen’s inequality as long as that c∗I = (1 − β)c∗R,0 + βc∗R,1 . But
this equality follows immediately from the definitions of c∗R,0 , c∗R,1 , and c∗I , i.e.,
(1 − β)c∗R,0 + βc∗R,1
£
¡
¢¤
= (1 − β) c∗R,1 − b0 β −1 1 − αc∗R,1 + βc∗R,1
¡
¡
¢ ¢
= γ − β −1 − 1 b0
= c∗I
5
Optimal policy with nominal debt and no commitment
When the government cannot commit to its monetary policy, the incentive to monetize
part of the debt discussed in the previous section arises every period and, consequently,
the price level each period becomes a function pt = p(bt , Mt ). Since the representative
household has rational expectations, it takes as given the government policy function.
Furthermore, its expected future prices, p¯t , are formed in period t − 1, and they are the
same function of the state of the economy at the beginning of period t, i.e. p¯t = p(bt , Mt ).
Consequently, in this case, the nominal interest rate will satisfy the following version
of the equilibrium Fisher’s equation:
1 + it =
pt
p(bt , Mt )
=
βpt−1
βpt−1
(30)
The implementability condition which, in general, can be written as:
γ + bt+1 = ct + bt (1 + it )
pt−1
pt
(31)
Using (30), becomes:
γ + bt+1 = ct + bt β −1
pt
pt
(32)
12
And, since from the cash-in-advance constraint we have that ct = Mt /pt and, consequently, that ct = Mt /pt , it can be rewritten as:
γ + bt+1 = ct + bt β −1
ct
ct
(33)
Notice that, once again, the optimal policy problem can be written as a recursive
dynamic program with a single state variable bt . Specifically, the government has to
find a policy, c = C (b), that solves the following problem:
V (b) = Max{log(c) − α (c + g) + βV (b0 )}
(34)
s.t.
b0 ≤ c + bβ −1
c
−γ
C (b)
(35)
and C (b) = C (b).
Definition 5 A recursive monetary equilibrium for this economy (M) is a value function
V (b), policy functions {C ∗ (b), b∗ (b)}, and a function C(b) such that:
(i) Given function C(b), the value function and the policy functions solve the problem
described in (34) and (35), and
(ii) C ∗ (b) = C(b)
To characterize the recursive monetary equilibrium, notice that the first order conditions of the problem described in expressions (34) and (35) are, first:
¸
·
1
−1 1
0 0
− α = −βV (b ) 1 + bβ
c
C (b)
(36)
This condition equates the marginal gain of one additional unit of consumption to its
marginal cost associated with higher debt needed to finance this consumption, plus the
additional debt that results from the lower current period price level.
Second, using the envelope theorem,
"
0
c
c bC (b)
V 0 (b) = V 0 (b0 )
−
C (b) C (b) C (b)
#
13
(37)
Given that in equilibrium c = C (b), it can be rewritten as:
V 0 (b) = V 0 (b0 ) [1 − ²c (b)]
(38)
where ²c (b) is the elasticity of function C (b). That is, the marginal increase of bt has
value V 0 (bt ), but the corresponding increase of bt+1 has two components, the direct effect
of increasing the stock of debt –as in the indexed debt case– and the indirect effect
that arises from the fact that higher values of debt are associated with higher interest
rates, ²c (b) ≤ 0. This higher costs arise because a larger stock of nominal debt increases
the incentive to monetize the debt and, along a rational expectations equilibrium path,
these additional distortions are anticipated.
Using expression (36), (38) becomes
1
1
−α
0 − α
0
£ c −1 1 ¤ = £ c
¤
−1 1 [1 − ²c (b )]
0
1 + bβ c
1 + b β c0
(39)
or, equivalently,
1
c
h
1+
−α
(1+i)B
M
1
c0
i=h
1+
−α
(1+i0 )B 0
M0
i [1 − ²c (b0 )]
(40)
In contrast with expression (16), characterizing the optimal policy with indexed debt,
where the marginal values of consumption are simply equated, expression (40) shows
that in a recursive monetary equilibrium with nominal debt, the marginal values of
consumption must be discounted, since a higher consumption means a lower price and,
therefore, higher debt in the future.
Recall that, this discounting already showed up when the fully committed Ramsey
planner evaluated the marginal value of consumption in period zero according to expression (25). Now, the uncommitted recursive planner reoptimizes every period and,
therefore, the marginal values of consumption must be discounted every period, as long
as there is outstanding debt.
Condition (40) also shows that the discounted marginal values of consumption are
distorted further by the incentive to increase the current price that arises when the
end-of-period stock of debt, b0 , is positive: [1 − ²c (bt+1 )].
In the previous section we have shown that the optimal policy with indexed debt
is more efficient than the optimal policy followed by a fully committed Ramsey planner. That the latter is more efficient than the optimal policy in a non-commitment
recursive monetary equilibrium follows from the standard argument of comparing the
commitment and non-commitment policies achieved with the same tax instruments and
rational expectations consistency conditions. Namely, the Ramsey planner can choose
the recursive equilibrium allocation –satisfying the required consistency condition–
but the recursive equilibrium allocation is dominated by the Ramsey equilibrium allocation.
14
6
Numerical solutions
To carry out our numerical example, we use the following values for the model economy
parameters: α = 0.45, β = 0.98, b0 = 0.17865 and g = 0.00822. Notice that our period
corresponds to a year and that we choose a very high level of nominal debt in relation to
government expenditures (b ' 22g). As we will see, results for lower values of the initial
stock of debt can be obtained from our calculations. The results that we obtain for the
time paths of the stocks of debt, nominal interest rates, and consumption in the three
cases analyzed in the previous sections are reported in Figures 1, 2 and 3, respectively.
The optimal monetary policy with indexed debt is stationary, while this is not the
case when debt is nominal (see Figure 2). When the debt is indexed, its stock is timeinvariant, while when the debt is nominal, it is optimal to reduce the initial stock. Under
full commitment this reduction is only carried out in the first period, while under no
commitment, the stock of debt is depleted progressively until it is completely cancelled
(see Figure 1).
The long-run interest rate that obtains when debt is indexed is higher than those
that obtain when debt is nominal. In this latter case, the long-run interest rate under
full commitment is higher than the one that obtains when there is no commitment (see
Figure 2).
Finally, when we compare the welfare levels in the three different regimes, we find
that the value of the optimal consumption path is highest in the economy with indexed
debt and no taxes. In particular, the value of the optimal consumption is 0.012%
smaller when there is nominal debt and full commitment, and 0.133% smaller when
there is nominal debt and no commitment.
The algorithm used to compute the solution is described in the Appendix and the
code that implements the algorithm can be obtained from the first author upon request.
7
Additional taxes
In most advanced economies, seigniorage is a minor source of revenue, and government
liabilities are financed mostly with consumption and income taxes. This leads us to
generalize our model economy to include consumption taxes, τ .4 In this economy, a
fiscal policy is a sequence {τ t }∞
t=0 .
We make the natural assumption that tax policy precedes monetary policy; tax rates
are announced at the beginning of the period, before the monetary policy decisions are
made. That is, given the current state of the economy (bt , Mt , t), the fiscal authority
chooses τ t = τ (bt , Mt , t) and then the monetary authority chooses pt = p(bt , Mt , τ t , t).
4
As it will become clear from our analysis, the introduction of other taxes does not change the
nature of the main results reported in this section.
15
In this section we first study the case of an arbitrary fiscal policy that allows the
monetary policy to adapt to it optimally choosing a path of nonnegative interest rates.
Next we study the case in which the fiscal authority can fully commit to an optimal
policy, and we show that is part of such policy to finance all the outstanding government liabilities with the consumption tax, and to constrain the monetary authority to
implement a zero nominal interest rate.
7.1
The model economy with consumption taxes
When the government levies consumption taxes, the household problem becomes:
max
∞
X
t=0
β t [u(ct ) − αnt ]
(41)
subject to:
pt (1 + τ t )ct ≤ Mt
(42)
Mt+1 + Bt+1 ≤ Mt − pt (1 + τ t )ct + Bt (1 + it ) + pt nt
(43)
and to:
lim β T BT +1 = 0
(44)
T −→∞
Now, expressions (7), (8) and (9), that characterize the households’s optimal choice,
become:
u0 (ct+1 )
= (1 + it+1 )(1 + τ t+1 )
α
1 + it+1 = β −1
(45)
pt+1
pt
(46)
and
ct ≤
Mt
pt (1 + τ t )
(47)
These conditions must hold for every t ≥ 0. Notice that expression (45) reflects the
fact that the household makes its plans based on its expectations about both interest
16
rates and taxes. The intertemporal condition (46) is exactly the same as expression
(45)5 and the cash-in-advance constraint (47) now includes consumption taxes.
The intertemporal government budget constraint in this economy is now:
g
g
pt g + Mtg + Btg (1 + it ) ≤ pt τ t ct + Mt+1
+ Bt+1
(48)
and the feasibility condition (4) does not change.
7.2
Optimal monetary policy when the fiscal authority moves
first
We now consider the general case in which: (i) the fiscal authority moves first and its
policy rule is τ t = τ (bt , Mt , t); (ii) the monetary authority moves last and its policy rule
is pt = p(bt , Mt , τ t , t), and (iii) the household makes its plans in period t − 1 based on
expectations pt = p(bt , Mt , τ t , t). Specifically we assume that for all t ≥ 0, the following
rational expectations condition is satisfied:
1 + it =
pt
p(bt , Mt , τ t , t)
=
βpt−1
βpt−1
(49)
planned consumption c̄t satisfies (45), and the cash-in-advance constraint (47) is satisfied
with equality for it > 0.
With this general formulation, when the stock of debt is indexed, pt = pt must be
satisfied for all t ≥ 0. When the stock of debt is nominal and the monetary authority
is fully committed, pt = pt must be satisfied for all t ≥ 1, while p0 = p0 must be
satisfied only in equilibrium. Finally, when the stock of debt is nominal and there is
no commitment to monetary policy, pt = pt , must be satisfied for all t ≥ 0 only in
equilibrium.
In the economy with consumption taxes the general implementability condition is
u0 (ct+1 ) ct+1
β
ct
+ bt+1 = bt β −1 + ct + g
α
c̄t
(50)
which, when the utility of consumption is logarithmic, simplifies to:
γ + bt+1 − ct − bt β −1
ct
=0
c̄t
(51)
5
Notice that when the government uses labor taxes, τ nt = τ n (bt , Mt , t), expression (46) becomes
pt+1(1−τ n )
and, therefore, the equilibrium nominal interest rate will be affected by fiscal
1 + it+1 = β −1 pt (1−τt+1
n)
t
policy. As far as our results are concerned, this change makes a difference only when the stock of debt
is indexed debt and the fiscal authority is not fully committed.
17
Notice that this expression is exactly the same as expression (33).
Now the following additional restrictions must be satisfied: (i) when the stock of
debt is indexed, cc̄tt = 1 must be satisfied for all t ≥ 0 along any path (i.e. both in and
out of equilibrium); (ii) when the stock of debt is nominal and there is full commitment
to monetary policy, cc̄tt = 1 must be satisfied for all t ≥ 1 along any path, while c̄c00 = 1
is only a Ramsey equilibrium restriction; and (iii) when the stock of debt is nominal
and there is no commitment to monetary policy, c̄ctt = 1 for all t ≥ 0 is only a recursive
equilibrium restriction.
Consequently, the monetary authority faces the same problem with consumption
taxes than the one faced when there was only seigniorage, for any level of monetary
commitment. Therefore, the allocations that obtain for the various types of debt and
monetary policy commitment technologies are exactly the same as those that obtained
before. This result is established in the following subsections:
Consumption taxes and indexed debt. In this ¡case policies
¢ are stationary and we
−1
∗
obtain the stationary equilibrium allocation c = γ − β − 1 b0 described in Section 3.
Notice, however that now interest rates ı̃t = i(bt , τ t ) are set as to satisfy:6
u0 (c∗ )
= [1 + i(bt , τ t )](1 + τ t )
α
(52)
And when the stock of debt is indexed the time-invariant equilibrium nominal interest
rate is:
£ ¡
¡
¢ ¢
¤−1
ı̃I,t = ı̃I (b0 , τ t ) = α γ − β −1 − 1 b0 (1 + τ t )
−1
(53)
Where, as we have already mentioned, we assume that ı̃I (b0 , τ t ) ≥ 0. The equilibrium
M̃t
paths of prices and currency are recursively given recursively by: p̃t = c∗ (1+τ
and
t)
M̃t+1 = αβ p̃t .
Consumption taxes, nominal debt and full commitment to monetary policy.
In this case we obtain the Ramsey equilibrium allocation c∗0 = c∗1 − β −1 b0 (1 − αc∗1 ) and
£
¡
¢ ¤−1
c∗1 = γ 1 + α β −1 − 1 b0
described in Section 4.
Now, the equilibrium interest rates are
ı̃R,0 = ı̃R (b0 , τ 0 , 0) = [αc∗0 (1 + τ 0 )]−1 − 1
(54)
ı̃R,t = ı̃R (bt , τ t , t) = [αc∗1 (1 + τ t )]−1 − 1
(55)
and
6
Henceforth we use tildes to distinguish the variables of the model economy with consumption taxes
from the corresponding variables of the model economy without consumption taxes.
18
for all t ≥ 1, and where we assume that with ı̃R (bt , τ t , t) ≥ 0 for all t.
Finally, the intertemporal condition between interest rates in period zero –that
corresponds to expression (29)– is
(1 + ı̃R,0 )(1 + τ 0 ) − 1
= (1 + ı̃R,1 )(1 + τ 1 ) − 1
B0
1 + (1 + ı̃R,0 )(1 + τ 0 ) M
0
(56)
Consumption taxes, nominal debt and no commitment to monetary policy.
In this case policies are also stationary and we obtain the recursive equilibrium allocation
described in Section 5. Specifically, the intertemporal condition (40) now takes the form:
1
1
−α
−α
c
c0
£
¤
£
¤ [1 − ²c (b0 )]
=
B
B0
0
c0
1 + (1 + ı̃M ) (1 + τ ) M
1 + (1 + ı̃M ) (1 + τ ) M 0
(57)
It follows that in the economy with nominal debt and no commitment to monetary
policy, the path of depletion of the stock of debt in real terms coincides with the one
characterized in Section 5 and computed in Section 6 even though the consumption tax
revenues would allow for a faster debt depletion rate.
7.3
Optimal fiscal policy with commitment
In the three regimes discussed in the previous section exactly how the equilibrium allocations are supported is indeterminate since the household only cares about the effective
nominal rate of return, (1 + i) (1 + τ ). For instance, it is always possible to set taxes
in a way that the resulting monetary policy follows the Friedman rule of zero nominal
interest rates even though in our economy there is no efficiency gain from following such
a rule.7 More precisely, as long as monetary responses to realized fiscal policies result in
non-negative interest rates, fiscal policy is not effective in this economy since the monetary authority can adapt to any fiscal policy in order to support the allocation that
obtained in the economy without consumption taxes. Moreover, such adaptation is the
optimal policy in every case. But this may not be the only scenario in which monetary
authorities operate.
To see this, suppose that the stock of debt is nominal and that there is full commitment to monetary policy. Let the fiscal authority set τ (bt , Mt , t) = τ ∗ (b0 ), where
7
This may not be true in a more general model economy. For instance, this is not true if we introduce
a distinction between cash and credit goods. In this case, the Friedman rule would eliminate the distortion between cash and credit goods created by the cash-in-advance constraint. This notwithstanding,
the distortions introduced by the presence of a positive stock of nominal debt would still be there, just
as in the economy with only cash goods.
19
τ ∗ (b0 ) corresponds to the tax rate that fully finances the government liabilities in the
allocation that obtains with indexed debt. That is,
¡
¢
u0 (γ − β −1 − 1 b0 )
u0 (c∗ )
(1 + τ (b0 )) =
=
α
α
∗
(58)
If the monetary authority tries to monetize part of the existing stock of nominal debt
and to use the resulting revenues to increase future consumption —say, maintaining
a constant c1 — then, it must be the case that c0 < c∗ < c1 . But such allocation
requires that (1 + ı̃R,0 )(1 + τ ∗ (b0 )) > (1 + τ ∗ (b0 )) > (1 + ı̃R,1 )(1 + τ ∗ (b0 )) which implies
ı̃R,0 > 0 > ı̃R,1 . However negative interest rates cannot be an equilibrium in this
economy since then the household would like to borrow unboundly. Therefore, given
that it is not possible to raise future consumption with negative taxes, there is no gain
in partially monetizing the stock of nominal debt in period zero. It follows that, if the
fiscal authority wants to maximize expression (2), it will set τ (bt , Mt , t) = τ ∗ (b0 ). The
same argument applies when there is no commitment to monetary policy.8 The following
proposition summarizes this result:
Proposition 6 Assume that fiscal authorities maximize the welfare of the representative
household and can fully commit to their policies. Then the equilibrium allocation is the
optimal equilibrium allocation that obtains when the stock of debt is indexed, regardless
of the nature of the debt and independently of the degree of commitment of the monetary
authority.
8
Concluding comments
This paper discusses the different ways in which nominal and indexed debt affect the
sequential choice of optimal monetary and debt policies in a general equilibrium monetary model where the costs of an unanticipated inflation arise from a cash-in-advance
constraint with the timing as in Svensson (1985) and government expenditures are exogeneous. In our environment, as in Nicolini (1998), when the utility function is logarithmic
in consumption and linear in leisure and debt is indexed, there is no time-inconsistency
problem. In this case, the optimal monetary policy is to maintain the initial level of
indexed debt, independently of the level of commitment of a Ramsey government.
In contrast, for the same specification of preferences, when the initial stock of government debt is nominally denominated a time inconsistency problem arises. In this case,
the government is tempted to inflate away its nominal debt liabilities. When the government cannot commit to its planned policies, the optimal sequential policy consists
in progressively depleting the outstanding stock of debt, so that it converges asymptotically to zero. Optimal nominal interest rates in this case are also decreasing, and
converge to zero, as long as there is no need to use seigniorage to finance government
8
Marimon, Nicolini, and Teles (2003) make a similar argument.
20
expenditures different from debt servicing. Hence, the optimal monetary policy in this
economy coincides in the long term with the one that obtains in an economy which has
no outstanding debt and from which these time-inconsistency distortions are obviously
absent.
Such equilibrium path is not chosen when the initial stock of government debt is
nominally denominated and the government can fully commit to its planned policies.
In this case, it is optimal to increase the inflation tax in the first period and to keep a
lower and constant inflation tax from there on.
We show that in the rational expectations equilibria, for a given initial level of
outstanding debt, the most efficient equilibrium is the one that obtains when debt is
indexed, the equilibrium with nominal debt and full commitment comes second, and
the equilibrium with nominal debt and no commitment is the least efficient. This result
highlights the sense in which nominal debt is indeed a burden on optimal monetary
policy.
It should be noted that the source of the inefficiencies and of the monetary policy
distortions discussed in this paper is not the desire to run a soft budgetary policy that
increases the debt liabilities of the government. Every policy discussed in this article is
an optimal policy, subject to the appropriate institutional and commitment constraints,
and is implemented by a benevolent and far-sighted government who does not face
either uncertainty or the need for public investments and who would, therefore, prefer
to reduce debt liabilities. The source of the inefficiencies is the distortion created by
the lack of commitment when there is an outstanding stock of nominal debt. Therefore,
our results highlight the need to implement policy and institutional arrangements that
either guarantee high commitment levels or that reduce the allowed levels of nominal
debt. However, they also show that a constraint on deficits may be ineffective to reduce
the distortions created by nominal debt since they are independent of the size of the
deficits.
The introduction of additional forms of taxation further clarifies the interplay between the various forms of debt and commitment possibilities. Under the natural assumption that monetary choices are made after the tax rates have been decided, we
show that the equilibrium allocations obtained when we introduce consumption taxes
are the same as those obtained when there is only seigniorage, provided there is enough
seigniorage as to allow for an optimal monetary policy with non negative interest rates.
However, as in Marimon, Nicolini and Teles (2003), if there is full commitment to an
optimal fiscal policy, the fiscal authorities, anticipating monetary policy distortions,
choose to fully finance government liabilities and the resulting monetary policy is the
Friedman rule of zero nominal interest rates and, as a result, the efficient equilibrium
that obtains in the economy with indexed debt.
In summary, we show that fiscal discipline may be needed to achieve efficiency and
price stability, even when monetary authorities pursue optimal policies. However, our
analysis shows that fiscal discipline applies to the level of the debt and not to the level
of the deficit or, alternatively, to the issuing of indexed debt. In contrast, for reasons
21
beyond the scope of this paper, the use of nominal government debt and of ‘constraints
on fiscal deficits’ (as in the EU Growth and Stability Pact) is widespread.
References
[1] Chari, V.V. and Patrick J. Kehoe. 1999. “Optimal Fiscal and Monetary Policy”, National
Bureau of Economic Research, WP 6891, January.
[2] Cole, Harold and Timothy Kehoe, 1996, “A self-fulfilling model of Mexico’s 1994-1995
debt crisis”, Journal of International Economics, 41, 309-330.
[3] Krusell, Per, Fernando Martín and José-Víctor Ríos-Rull, 2003, “On the Determination
of Government Debt,” work in progress.
[4] Lucas, Robert E., Jr. and Nancy L. Stokey, 1983, “Optimal Fiscal and Monetary Theory
in an Economy without Capital”, Journal of Monetary Economics, 12, 55-93.
[5] Marimon, Ramon, Juan Pablo Nicolini and Pedro Teles, 2003, “Inside-Outside Money
Competition,” Journal of Monetary Economics, 50:8.
[6] Nicolini, Juan Pablo, 1998, “More on the Time Inconsistency of Optimal Monetary Policy”, Journal of Monetary Economics
[7] Obstfeld Maurice, 1997, “Dynamic Seigniorage Theory”, Macroeconomic Dynamics, 588614.
[8] Rankin, Neil, 2002, “Time Consistency and Optimal Inflation-Tax Smoothing: Is There
Really a Deflation Bias?, mimeo, University of Warwick.
[9] Sargent, Thomas, J. and Neil Wallace, 1981, “Some Unpleasant Monetarist Arithmetic,”
Quarterly Review, Federal Reserve bank of Minneapolis, 5,3, 1-17. [Reprinted, 1993, in
Rational Expectations and Inflation, 2nd ed., New York, Harper Collins].
[10] Sims,Christopher A., 1994, “A Simple Model for the Study of the Determination
of the Price Level and the Interaction of Monetary and Fiscal Policy,” Economic
Theory 4, 381—399.
[11] Svensson, L.E.O., 1985, “Money and Asset Prices in a Cash-in-Advance Economy”, Journal of Political Economy, 93, 919—944.
[12] Woodford, Michael. 1996. “Control of the Public Debt: A Requirement for Price Stability?”, NBER Working Paper 5684
22
Appendix: Computation
In order to compute the recursive monetary equilibrium defined in Section 5, we must
solve the following dynamic program:
{log(c) − α (c + g) + βV (b0 )}
V (b) = max
0
(59)
c
β
+g−
α
C (b)
(60)
c,b
s.t.
b0 ≤ c + bβ −1
for a given C (b).
However, computational considerations lead us to solve the following transformed problem:
V (x) = max
{log(c) − α (c + g) + βV (x0 )}
0
c,x
(61)
s.t.
βx0 Ĉ(x0 ) ≤ c(1 + x) + g −
β
α
(62)
for a given Ĉ (b) and where x = b/β Ĉ(x).
In order to solve this problem we use the following algorithm:
• Step 1: Define a discrete grid on x
• Step 2: Define a decreasing discrete function Ĉ0 (x)
• Step 3: Iterate on the Bellman operator described in equations (35) and (62) until
we find the converged V ∗ (x), x0 ∗ (x),c∗ (x)
• Step 4: If c∗ (x) = Ĉ0 (x), we are done. Else, let Ĉ0 (b) = c∗ (b) and go to Step 3.
Finally, to recover the policy functions of the original problem we undo the transformation as follows: From x = b/β Ĉ(x), we obtain that b̂(x) = βxĈ(x), which can be
computed directly from the solution to the transformed problem described above. Next
we invert b̂(x) and we obtain x = b̂−1 (b). Finally, we use this expression to obtain
C(b) = Ĉ[b̂−1 (b)] and b0 (b) = b̂{x0 [b̂−1 (b)]}.
23
Figure 1: The optimal stocks of indexed debt and of nominal debt with full commitment
and with no commitment
0.35
0.30
0.25
bind
0.20
bram
0.15
brec
0.10
0.05
0.00
0
10
20
30
40
50
21
60
70
80
90
100
Figure 2: The optimal paths of nominal interest rates with indexed debt and with
nominal debt with full commitment and with no commitment
0.70
0.60
iind
iram
0.50
irec
0.40
0.30
0.20
0.10
0.00
0
10
20
30
40
50
22
60
70
80
90
100
Figure 3: The optimal paths of consumption with indexed debt and with nominal debt
with full commitment and with no commitment
0.22
0.20
0.18
cind
0.16
cram
crec
0.14
0.12
0
10
20
30
40
50
23
60
70
80
90
100
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The Costs and Benefits of Moral Suasion: Evidence from the Rescue of
Long-Term Capital Management
Craig Furfine
WP-02-11
On the Cyclical Behavior of Employment, Unemployment and Labor Force Participation
Marcelo Veracierto
WP-02-12
Do Safeguard Tariffs and Antidumping Duties Open or Close Technology Gaps?
Meredith A. Crowley
WP-02-13
Technology Shocks Matter
Jonas D. M. Fisher
WP-02-14
Money as a Mechanism in a Bewley Economy
Edward J. Green and Ruilin Zhou
WP-02-15
Optimal Fiscal and Monetary Policy: Equivalence Results
Isabel Correia, Juan Pablo Nicolini and Pedro Teles
WP-02-16
Real Exchange Rate Fluctuations and the Dynamics of Retail Trade Industries
on the U.S.-Canada Border
Jeffrey R. Campbell and Beverly Lapham
WP-02-17
Bank Procyclicality, Credit Crunches, and Asymmetric Monetary Policy Effects:
A Unifying Model
Robert R. Bliss and George G. Kaufman
WP-02-18
Location of Headquarter Growth During the 90s
Thomas H. Klier
WP-02-19
The Value of Banking Relationships During a Financial Crisis:
Evidence from Failures of Japanese Banks
Elijah Brewer III, Hesna Genay, William Curt Hunter and George G. Kaufman
WP-02-20
On the Distribution and Dynamics of Health Costs
Eric French and John Bailey Jones
WP-02-21
The Effects of Progressive Taxation on Labor Supply when Hours and Wages are
Jointly Determined
Daniel Aaronson and Eric French
WP-02-22
3
Working Paper Series (continued)
Inter-industry Contagion and the Competitive Effects of Financial Distress Announcements:
Evidence from Commercial Banks and Life Insurance Companies
Elijah Brewer III and William E. Jackson III
WP-02-23
State-Contingent Bank Regulation With Unobserved Action and
Unobserved Characteristics
David A. Marshall and Edward Simpson Prescott
WP-02-24
Local Market Consolidation and Bank Productive Efficiency
Douglas D. Evanoff and Evren Örs
WP-02-25
Life-Cycle Dynamics in Industrial Sectors. The Role of Banking Market Structure
Nicola Cetorelli
WP-02-26
Private School Location and Neighborhood Characteristics
Lisa Barrow
WP-02-27
Teachers and Student Achievement in the Chicago Public High Schools
Daniel Aaronson, Lisa Barrow and William Sander
WP-02-28
The Crime of 1873: Back to the Scene
François R. Velde
WP-02-29
Trade Structure, Industrial Structure, and International Business Cycles
Marianne Baxter and Michael A. Kouparitsas
WP-02-30
Estimating the Returns to Community College Schooling for Displaced Workers
Louis Jacobson, Robert LaLonde and Daniel G. Sullivan
WP-02-31
A Proposal for Efficiently Resolving Out-of-the-Money Swap Positions
at Large Insolvent Banks
George G. Kaufman
WP-03-01
Depositor Liquidity and Loss-Sharing in Bank Failure Resolutions
George G. Kaufman
WP-03-02
Subordinated Debt and Prompt Corrective Regulatory Action
Douglas D. Evanoff and Larry D. Wall
WP-03-03
When is Inter-Transaction Time Informative?
Craig Furfine
WP-03-04
Tenure Choice with Location Selection: The Case of Hispanic Neighborhoods
in Chicago
Maude Toussaint-Comeau and Sherrie L.W. Rhine
WP-03-05
Distinguishing Limited Commitment from Moral Hazard in Models of
Growth with Inequality*
Anna L. Paulson and Robert Townsend
WP-03-06
Resolving Large Complex Financial Organizations
Robert R. Bliss
WP-03-07
4
Working Paper Series (continued)
The Case of the Missing Productivity Growth:
Or, Does information technology explain why productivity accelerated in the United States
but not the United Kingdom?
Susanto Basu, John G. Fernald, Nicholas Oulton and Sylaja Srinivasan
WP-03-08
Inside-Outside Money Competition
Ramon Marimon, Juan Pablo Nicolini and Pedro Teles
WP-03-09
The Importance of Check-Cashing Businesses to the Unbanked: Racial/Ethnic Differences
William H. Greene, Sherrie L.W. Rhine and Maude Toussaint-Comeau
WP-03-10
A Structural Empirical Model of Firm Growth, Learning, and Survival
Jaap H. Abbring and Jeffrey R. Campbell
WP-03-11
Market Size Matters
Jeffrey R. Campbell and Hugo A. Hopenhayn
WP-03-12
The Cost of Business Cycles under Endogenous Growth
Gadi Barlevy
WP-03-13
The Past, Present, and Probable Future for Community Banks
Robert DeYoung, William C. Hunter and Gregory F. Udell
WP-03-14
Measuring Productivity Growth in Asia: Do Market Imperfections Matter?
John Fernald and Brent Neiman
WP-03-15
Revised Estimates of Intergenerational Income Mobility in the United States
Bhashkar Mazumder
WP-03-16
Product Market Evidence on the Employment Effects of the Minimum Wage
Daniel Aaronson and Eric French
WP-03-17
Estimating Models of On-the-Job Search using Record Statistics
Gadi Barlevy
WP-03-18
Banking Market Conditions and Deposit Interest Rates
Richard J. Rosen
WP-03-19
Creating a National State Rainy Day Fund: A Modest Proposal to Improve Future
State Fiscal Performance
Richard Mattoon
WP-03-20
Managerial Incentive and Financial Contagion
Sujit Chakravorti, Anna Llyina and Subir Lall
WP-03-21
Women and the Phillips Curve: Do Women’s and Men’s Labor Market Outcomes
Differentially Affect Real Wage Growth and Inflation?
Katharine Anderson, Lisa Barrow and Kristin F. Butcher
WP-03-22
Evaluating the Calvo Model of Sticky Prices
Martin Eichenbaum and Jonas D.M. Fisher
WP-03-23
5
Working Paper Series (continued)
The Growing Importance of Family and Community: An Analysis of Changes in the
Sibling Correlation in Earnings
Bhashkar Mazumder and David I. Levine
WP-03-24
Should We Teach Old Dogs New Tricks? The Impact of Community College Retraining
on Older Displaced Workers
Louis Jacobson, Robert J. LaLonde and Daniel Sullivan
WP-03-25
Trade Deflection and Trade Depression
Chad P. Brown and Meredith A. Crowley
WP-03-26
China and Emerging Asia: Comrades or Competitors?
Alan G. Ahearne, John G. Fernald, Prakash Loungani and John W. Schindler
WP-03-27
International Business Cycles Under Fixed and Flexible Exchange Rate Regimes
Michael A. Kouparitsas
WP-03-28
Firing Costs and Business Cycle Fluctuations
Marcelo Veracierto
WP-03-29
Spatial Organization of Firms
Yukako Ono
WP-03-30
Government Equity and Money: John Law’s System in 1720 France
François R. Velde
WP-03-31
Deregulation and the Relationship Between Bank CEO
Compensation and Risk-Taking
Elijah Brewer III, William Curt Hunter and William E. Jackson III
WP-03-32
Compatibility and Pricing with Indirect Network Effects: Evidence from ATMs
Christopher R. Knittel and Victor Stango
WP-03-33
Self-Employment as an Alternative to Unemployment
Ellen R. Rissman
WP-03-34
Where the Headquarters are – Evidence from Large Public Companies 1990-2000
Tyler Diacon and Thomas H. Klier
WP-03-35
Standing Facilities and Interbank Borrowing: Evidence from the Federal Reserve’s
New Discount Window
Craig Furfine
WP-04-01
Netting, Financial Contracts, and Banks: The Economic Implications
William J. Bergman, Robert R. Bliss, Christian A. Johnson and George G. Kaufman
WP-04-02
Real Effects of Bank Competition
Nicola Cetorelli
WP-04-03
Finance as a Barrier To Entry: Bank Competition and Industry Structure in
Local U.S. Markets?
Nicola Cetorelli and Philip E. Strahan
WP-04-04
6
Working Paper Series (continued)
The Dynamics of Work and Debt
Jeffrey R. Campbell and Zvi Hercowitz
WP-04-05
Fiscal Policy in the Aftermath of 9/11
Jonas Fisher and Martin Eichenbaum
WP-04-06
Merger Momentum and Investor Sentiment: The Stock Market Reaction
To Merger Announcements
Richard J. Rosen
WP-04-07
Earnings Inequality and the Business Cycle
Gadi Barlevy and Daniel Tsiddon
WP-04-08
Platform Competition in Two-Sided Markets: The Case of Payment Networks
Sujit Chakravorti and Roberto Roson
WP-04-09
Nominal Debt as a Burden on Monetary Policy
Javier Díaz-Giménez, Giorgia Giovannetti, Ramon Marimon, and Pedro Teles
WP-04-10
7
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