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Federal Reserve Bank of Chicago
Inside-Outside Money Competition
Ramon Marimon, Juan Pablo Nicolini and
Pedro Teles
WP 2003-09
Inside-Outside Money Competition∗
Ramon Marimona,b,c, Juan Pablo Nicolinid and Pedro Telese,c†
a
Universitat Pompeu Fabra.
b
Centre for Economic Policy Research.
c
National Bureau of Economic Research.
d
Universidad Torcuato Di Tella.
e
Federal Reserve Bank of Chicago.
Revised, July, 2003
Abstract
We study how competition from privately supplied currency substitutes
affects monetary equilibria. Whenever currency is inefficiently provided,
inside money competition plays a disciplinary role by providing an upper
bound on equilibrium inflation rates. Furthermore, if “inside monies” can
be produced at a sufficiently low cost, outside money is driven out of circulation. Whenever a ’benevolent’ government can commit to its fiscal policy,
sequential monetary policy is efficient and inside money competition plays
no role.
∗
A previous version of this paper was circulated with the title: ”Electronic Money: Sustaining
Low Inflation?”. We thank Isabel Correia, Giorgia Giovanetti, Robert King, Sérgio Rebelo, Neil
Wallace and participants at seminars where this work was presented for helpful comments and
suggestions. We are particularly grateful to an anonymous referee, for many useful comments and
suggestions. Teles thanks hospitality at the European University Institute (European Forum),
and the financial support of Praxis XXI. Marimon thanks the support of CREA (Generalitat
de Catalunya). The opinions expressed herein do not necessarily represent those of the Federal
Reserve Bank of Chicago or the Federal Reserve System.
†
Corresponding author: Pedro Teles, Federal Reserve Bank of Chicago, 230 S. LaSalle St.,
Chicago, Il 60604, USA. Tel.: +1-312-3222947; fax.: +1-312-3222357; pteles@frbchi.org. Teles
is on leave from Banco de Portugal and Universidade Catolica Portuguesa.
Key words: Electronic money; Inside Money; Currency competition;
Reputation; Inflation
JEL classification: E40; E50; E58; E60
2
1. Introduction
Payment systems have gone through a major transformation in the last two
decades. In particular, electronic payments have risen in most developed countries
and are expected to rise even more in the future.1 The development of the technology to transfer information electronically has increased substitutability between
deposits and currency in transactions and has substantially reduced the cost of
transactions using deposits.2 Deposits used for electronic payments3 are highly
substitutable for currency because the settling value is ultimately a liability of
the financial institution that issues the electronic card (checks, in contrast, are
a liability of the purchaser). Clearing electronic transactions is also considerably
less expensive than clearing checks (1/3 to 1/2 of the cost of checks, according to
Humphrey et al, 1996). Furthermore, in contrast to currency, deposits used for
electronic transactions can pay nominal interest on the average balance at a very
low cost.
In spite of the technological developments leading to a widespread use of different forms of electronic money, there has been little theoretical attention on a
range of issues raised by this. How is monetary policy affected by the increased
competition from inside money? Does the increased efficiency in the supply of
inside money induce lower inflation rates? Can the increasing efficiency in the
supply of inside money result in a cashless economy? In other words, will inside
money drive outside money out? In this paper we investigate the theoretical issues
associated with competition between currency and currency substitutes, between
outside and inside money.
At first glance, competition between suppliers of currency substitutes and between them and the monopolist supplier of currency should induce a lower price
for the use of money and, therefore, lower inflation rates as well as nominal interest
rates. However, one reason for high inflation rates, emphasized in the literature,
is the time inconsistency of monetary policy; and it is unclear whether expos1
For example, Humphrey et al. (1996) find that “in all (fourteen) developed countries but
the United States, electronic payments have been either the sole or the primary reason for the
34 percent rise in total non-cash payments between 1987 and 1993”( p. 935).
2
According to Humphrey et al. ( 2003), there has been a major reduction in the operating
costs of providing bank payments and other services, associated with the development of electronic payments. They estimate those costs to have fallen by 24% relative to banks’ total assets
in 12 European countries over 1987-1999.
3
We call these deposits used for electronic payments, electronic money, which are privately
issued currency substitutes, a form of inside money.
3
ing monetary authorities to competition will discipline them or possibly worsen
the time consistency problem. In other words, the role of competition cannot be
analyzed independently of the commitment problem. The aim of this paper is
to study these issues in the context of a dynamic monetary general equilibrium
model where currency is the unique outside money and where competitively supplied inside monies are perfect substitutes for currency. To this end, we consider
monetary regimes that differ in two dimensions regarding the monetary authority:
the objective function (whether the aim is to maximize transfers or welfare) and
the ability to commit to a policy (whether there is full commitment or policies
are sequentially redesigned).
We start the analysis in Section 2 by describing the competitive equilibria for
given monetary policies. In Section 3, we show that a government that maximizes
transfers (or revenues) and is able to commit to its policies will be induced by
competition from currency substitutes to set a low stationary inflation rate. This
inflation rate is driven down with the reduction of financial intermediation costs,
and approaches a negative number, corresponding to the Friedman rule, as the intermediation costs approach zero. Since these low inflation equilibrium outcomes
are time inconsistent we analyze, in Section 4, the set of sustainable equilibria,
in particular, whether the commitment solution can be sustained through reputation, and how competition from currency substitutes affects the set of sustainable
equilibria. We show that the set of sustainable equilibria with valued currency
is characterized by inflation rates which are nonnegative and are bounded above.
The zero lower bound results from the need of future positive rents for the reputation mechanism to work. The upper bound results from inside money competition
since it limits the expected revenues that can be obtained from outside money.
When the production of inside money is sufficiently efficient the corresponding
upper bound would become negative and, as a result, there is no equilibrium with
valued currency.
Competition between outside and inside money is an interplay between two
sources of inefficiency, one resulting from lack of commitment affecting the supply of outside money and the other an assumed technological inferiority in the
supply of inside money. Outside money is produced at zero cost but, without
commitment, requires inflationary rents to exist in equilibrium. Inside money is
produced competitively but at a positive cost. In equilibrium, whether inside
or outside money circulates is determined by which of the two sources of inefficiency is dominant. In summary, inside money competition enhances efficiency
by constraining the inflation rates that can be sustained in equilibria with valued
4
currency. However, as the intermediation costs are reduced, outside money may
be driven out of circulation. In this case, because the economy would be using a
more costly technology to supply money, there would be a welfare loss.
In Section 5 we analyze the case of a “representative” government. With
full commitment, the Ramsey planner chooses to implement the Friedman rule.
Therefore, with commitment, there is no disciplinary role for competition from
currency substitutes. However, even if the monetary authority can not commit to
future decisions, as long as the fiscal authority is committed to an expenditure
and tax policy, it is a time-consistent monetary policy to maintain the Friedman
rule. This is due to the fact that, once there is commitment to fiscal policy, the
zero bound on interest rates leaves no room for enhancing welfare by changing
the time pattern of government revenues. It follows that in this regime, inside
money competition plays no role independently of whether there is commitment
to monetary policy. Only the ’technologically efficient’ outside money circulates.
In our model we abstract from some aspects that distinguish different “currency substitutes”. Deposits can be used for transactions through electronic payments in many different ways. Our model allows for the use of deposits for transactions through an arrangement that most resembles debit cards, which allow
buyers to make purchases directly using funds from some form of deposit account.
Reloadable cash cards would also fit our description of currency substitutes, but
these cards are not widely used and do not typically pay interest, although they
could.
In our set up, currency substitutes are assumed to be fully backed, default free
deposits that are perfect substitutes for currency. The suppliers of these deposits
are price takers. Relaxing these assumptions can significantly alter the results. If
the suppliers of currency substitutes can default on nominal contracts, then they
will, unless the resulting loss of future profits prevents them from doing so. If the
suppliers of inside monies were not price takers, then they would have an incentive
to overissue in order to devalue outstanding balances. In Marimon, Nicolini and
Teles (2000), we analyze a monetary arrangement of that type as an example of
how the reputation and the competition mechanisms interact.
That alternative environment is also analyzed in Klein (1974), with ”...one
dominant money (currency supplied by a government monopoly) and many privately produced nondominant monies (deposits supplied by different commercial
banks).” Klein asked most of the questions that we address in this paper. In
particular, he made it clear that competition between the private issuers of currency substitutes and between them and the monopolist issuer of currency did
5
not dismiss and could even raise intertemporal consistency problems. However,
he did not provide a full characterization of the equilibrium set as we do in this
paper. To our knowledge, Taub (1985) has been the only previous attempt to
study “currency competition” taking into account reputational aspects using a
dynamic general equilibrium framework.4
2. Competitive monetary equilibria
In this section we describe the economic environment and characterize its monetary equilibria for a given policy. The economy is populated by a large number of
identical infinitely lived households, financial intermediaries, and a government.
The households have preferences defined over consumption of a cash good, c1t ,
consumption of a credit good, c2t , and total labor, nt , for any period t ≥ 0,
V =
∞
X
t=0
β t [u(c1t ) + u(c2t ) − αnt ].
(2.1)
Assuming that leisure enters linearly into the utility function is in no way essential,
but significantly simplifies the analysis. The function u is increasing, strictly
concave, and differentiable.
The households are endowed with a unit of time that can be used for leisure or
total labor, nt , which can be allocated to the production of the consumption good
or the production of deposits, net . The production technology of the consumption
good is linear with unitary coefficients. Thus, feasibility requires that
c1t + c2t = nt − net
We use the timing of transactions as found in Svensson (1985). The goods
market meets in the beginning of the period. The cash good, c1t , must be purchased
using either currency, Mt , or privately issued currency substitutes, Et , which have
been carried over from the previous period. Currency substitutes are deposits that
the buyers can easily access, for example using electronic cards. The credit good,
wages, and government transfers are paid at the end of the period in the assets
market where the households can adjust their portfolios of currency, deposits,
and real bonds. In principle, currency and currency substitutes do not have
4
In contrast with this paper, Taub (1985) only considers time-consistent stationary policies
and therefore cannot provide a full characterization of equilibria with reputation and competition.
6
to be traded at par. In other words, there are two nominal units of account
corresponding to the two payment systems. Goods are priced in units of these
two assets; that is, Ptm is the price of goods in currency and Pte the corresponding
price in privately issued currency substitutes. The corresponding exchange rate in
period t is εt = Ptm / Pte , which denotes the price of deposits in units of currency.
We focus our attention on three types of equilibria. In the first type of equilibria,
both currency and deposits are valued, meaning that if the supply was positive and
finite, the price would be finite. Because of perfect substitutability the exchange
rate is indeterminate. We look at equilibria where the two monies trade at par,
εt = 1, and where the supply and demand of deposits is zero, Et = 0, t ≥ 0. In
the second type of equilibria, currency is never valued. Only deposits are used for
transactions. If Mt > 0, then εt = ∞. Finally, we also consider a third type of
equilibria where deposits have zero value, but currency is valued. In this case, if
Et > 0, then εt = 0. There are no equilibria where both monies have zero value.
We use Pt to denote the price of goods in the relevant unit of account. Thus, when
currency is valued, including the case in which deposits are also valued, εt = 1,
t ≥ 0, then Pt = Ptm , and when only inside money circulates, then Pt = Pte .5
The representative household is endowed with initial holdings of money M0 and
of real bonds valued at R0 bh0 , as well as initial deposits that are assumed to be zero,
I0f E0 = 0. We assume for convenience that R0 = β −1 . The ©household chooses
ª
sequences of consumptions and labor {c1t , c2t , nt } and portfolios Mt+1 , bht+1 , Eo
t+1 ,
n
t ≥ 0, treating parametrically prices and interest rates
{gt }∞
t=0 ,
f
Pt , εt , Rt+1 , It+1
∞
,
t=0
{Πt }∞
t=0 .
government transfers
and dividends from financial intermediaries
f
It+1 is the gross interest on deposits held from period t to t+1 in units of deposits.
If both outside and inside money are valued forever, i.e., εt = 1, t ≥ 0, the
household intertemporal budget and cash-in-advance constraints for t ≥ 0 are
Mt+1 + Pt bht+1 + Et+1 ≤ Mt + Pt Rt bht + Itf Et − Pt (c1t + c2t ) + Pt nt + Pt gt + Πt (2.2)
Pt c1t ≤ Mt + Et
(2.3)
and a no-Ponzi scheme condition that guarantees that the present value budget is
5
In our environment with a dominant money (currency) and privately issued deposits, it
would be natural to assume a one-sided convertibility legal requirement in that deposits are
convertible on demand into currency at a one-to-one fixed exchange rate. This convertibility
requirement implies that, in equilibrium, εt ≥ 1. If εt < 1, depositors would exercise their option
to convert their deposits at par value.
7
satisfied.6 Notice that there is no nominal interest paid on currency, while deposits
Et+1 are remunerated by financial intermediaries at the gross nominal interest rate,
f
It+1
. The nominal interest rate on bonds is given by It+1 ≡ PPt+1
Rt+1 .
t
Since currency does not pay nominal interest, in the equilibria where both
f
currency and deposits are valued, and εt = 1, t ≥ 0, it must be that It+1
= 1,
t ≥ 0. Then an equilibrium allocation must satisfy, for t ≥ 0,
u0 (c1t+1 )
= It+1 ,
α
u0 (c2t )
= 1,
α
Rt+1 = β −1
(2.4)
(2.5)
(2.6)
In an equilibrium where currency is never valued and where only deposits are
used for transactions, the equation (2.4) is replaced with
u0 (c1t+1 )
f
= 1 + It+1 − It+1
α
(2.7)
meaning that the cost of holding inside money is the difference between the return
on bonds and the return on deposits. To simplify notation, from now on we use
the fact that in equilibrium the real rate of return on bonds always satisfies (2.6).
Private issuers of inside money The financial intermediation sector is competitive. A representative issuer of inside money offers deposits Et+1 at a gross inf
. We assume that their contracts are enforceable, possibly through
terest rate It+1
banking regulation. The financial intermediation technology is such that they
must pay a real cost, in units of labor, for the supply of deposits, at redemption
time, as a fraction of the real value of the outstanding deposits: net = θ EPtt . The
financial intermediary holds the total amount deposited, Et+1 , as bonds, Pt bet+1 ,
which pay gross interest It+1 . The cash flow of the financial intermediary in period
t ≥ 0 is
Πt = Et+1 − Et Itf − Pt bet+1 + Pt bet β −1 − Pt net
6
If inside money is not valued, i.e., εt = 0, t ≥ 0, Et must be replaced by εt Et in the
constraints and, similarly, if currency is not valued, i.e., εt = ∞, t ≥ 0, Mt must be replaced by
Mt /εt .
8
Free entry in the financial intermediation sector results in Πt+1 = 0, t ≥ 0, which,
given that Et+1 = Pt bet+1 and Pt net = Et θ, implies
f
It+1 − It+1
= θ, t ≥ 0
(2.8)
Recall that we assume that financial intermediaries are price takers and honor
their liabilities. If they were not price takers, then it would be optimal to surprise
the households and overissue. This overissuing would have an impact on the price
level and would reduce the real value of the nominal liabilities of the financial
intermediary. Similarly, if the deposit contracts could not be enforced then they
would have an incentive, in any given period, to default on deposits.7
Government Given (M0 , R0 d0 ) , a government policy consists of a sequence of
∞
transfers {gt }∞
t=0 , that can be negative, and a monetary and debt policy {Mt+1 , dt+1 }t=0 .
For now, we abstract from sources of revenues other than seigniorage; therefore,
in the equilibria where both currency and deposits are valued, the intertemporal
budget constraint of the government is
Mt+1 + Pt dt+1 ≥ Mt + Pt Rt dt + Pt gt
(2.9)
together with a no-Ponzi games condition.
In setting its policy, the government takes into account the competitive behavior of the private sector. Using (2.6), the present value budget constraint can
be written as
∞
X
t=0
β t gt ≤
∞
X
t=0
β t+1 (It+1 − 1)m(It+1 ) −
M0
− R0 d0
P0
(2.10)
and m(I) is defined implicitly by (2.4) together with the
where It+1 = β −1 PPt+1
t
cash-in-advance constraint, i.e., m(I) = u0−1 (αI). In the equilibria where currency
is not valued the budget constraint would be
∞
X
t=0
β t gt ≤ −R0 d0
(2.11)
It is well known, that, in general, for a given money supply policy {Mt+1 }∞
t=0
there are multiple competitive equilibria, with different paths for the initial price
7
Marimon, Nicolini and Teles (1999) study the case of private issuers of currency who are
neither price takers nor necessarily credible.
9
level and interest rates (P0 , {It+1 }∞
t=0 ). We will focus our attention on equilibria
with constant rates of money growth, from period t = 1 on. In this case, in
addition to stationary equilibria there may be multiple non stationary equilibria.
We only consider the equilibria that are stationary from period t = 1 on.
³
´
Competitive equilibria Given M0 , R0 d0 , R0 bh0 , R0 be0 , I0f E0 and a prespecified government policy {Mt+1 , dt+1 , gt }∞
t=0 , a competitive equilibrium where inside
and outside money are
= 1, t ≥ 0)8 consists of sequences of price levn valued (i.e. εot ∞
ª∞
©
f
els and interest rates Pt , Rt+1 , It+1
, households’ allocations c1t , c2t , nt , Mt+1 , Et+1 , bht+1 t=0
t=0 ©
ª∞
and financial intermediaries’ allocations net , Et+1 , bet+1 t=0 , such that households
maximize their utility subject to their budget constraints, financial intermediaries
maximize profits, and markets clear; that is, for t ≥ 0, c1t + c2t = nt − net ; net = θ EPtt ;
dt = bht + bet .
Equilibria with valued currency As previously mentioned, we are interested
in the characterization of stationary equilibria (from period one on) where one or
both forms of monies are valued. In equilibria where currency is held, the cost of
holding currency must be less than or equal to the cost of holding deposits;
f
≤1
It+1
f
must hold. Since the cost of holding deposits is It+1 − It+1
= θ, in a stationary
equilibrium with valued currency it must be that either It+1 = I < 1 + θ, t ≥ 0 or
It+1 = 1 + θ, t ≥ 0. In equilibria with I < 1 +θ, t ≥ 0, deposits do not have value.
This means that if the supply of deposits is positive, Et > 0, the exchange rate
must be εt = 0. When It+1 = 1 + θ, t ≥ 0, the households are indifferent between
holding currency and deposits. We will assume that only currency is held, so that
Et = 0.
Cashless equilibria In an equilibrium where currency is not valued and only
deposits are used for transactions, the price level is Pt = Pte , and both the nominal
interest rate on deposits, Itf , and on bonds, It , are in units of deposits. There
is a unique such equilibrium, up to the determination of all nominal variables.
8
The competitive equilibria where either only outside money or only inside money is valued
are defined analogously.
10
,
Furthermore there is no equilibrium where neither currency nor deposits are valued.9 In the equilibrium with valued deposits, if the supply of currency is positive,
Mt > 0, then εt = ∞. The incremental cost of the cash good is equal to the difference between the interest rate on bonds and the one on deposits, that is, the
f
intermediation cost, θ (i.e., It+1 − It+1
= θ, t ≥ 0).
In this economy with inside money, the nominal supply of deposits is indeterminate. It follows that price levels are also indeterminate. The interest
rates are also indeterminate, but the difference between the two interest rates
is not, and that is what is relevant to determining the allocations. All of the
real quantities except the initial consumption of the cash good are determined by
u0 (c2t ) = α; u0 (c1t+1 ) = α(1 + θ) and nt = c2t + c1t (1 + θ), t ≥ 0. Since c10 = EP00 I0f , the
initial consumption is indeterminate if E0 I0f > 0. Assuming E0 I0f = 0 avoids this
indeterminacy without affecting the characterization of equilibria from period one
on.10
3. Equilibria with commitment
In this section, we consider full commitment policies under the assumption that the
government chooses the policy ({Mt+1 } , {dt+1 } , {gt }) that maximizes its preferences for revenues (or transfers).
More precisely, we assume that the government’s
P
t
problem is to maximize ∞
β
G(g
t ) (where, for standard reasons, the function
t=0
G is assumed to be increasing and strictly concave), subject to (2.10). Thus, given
that in equilibrium the gross real interest rate is constant and equal to β −1 , the
government will always choose a constant sequence of transfers. Therefore, the
value to the government of different allocations can be measured in terms of g.
In the full commitment optimal program the value of the outstanding initial
0
= 0. The choices of interest rates are likely to be
money balances is zero, M
P0
constrained by the presence of currency substitutes. To see this, notice that
without inside money competition, revenues from the inflation tax are given by
f (I) = (I − 1)m(I). We assume that the function f (I) has a unique maximum I ∗ ,
and that f 0 (I) > 0 for I ∗ > I ≥ 1 and f 0 (I) < 0 for I > I ∗ . If, for example, u is of
9
The formal treatment of the existence and non-uniqueness of monetary equilibria in
economies with inside money only is, to our knowledge, best performed by Drèze and Polemarchakis (2000).
10
This cashless economy is not the limit of economies with well defined currency demands, as
in Woodford (1998) and, therefore, it is not possible to determine the initial price level in our
cashless equilibrium as the limit of a sequence of equilibria with valued currency.
11
the CRRA form then f satisfies these assumptions. It follows that an optimal plan
is stationary It+1 = I, t ≥ 0. Furthermore, whenever f 0 (1 + θ) ≥ 0, i.e., revenues
from the inflation tax are non-decreasing at 1 + θ, the unconstrained choice of the
interest rate is greater than or equal to 1 + θ. Inside money competition prompts
f
the government to choose I = 1 + θ. Condition (2.8) implies that It+1
= 1. More
formally,
Proposition 1 Assume there exists I ∗ > 1 +θ such that f 0 (I) > 0 for I ∗ > I ≥ 1
and f 0 (I) < 0 for I > I ∗ . Then, the commitment solution for the revenue
f
maximizing government is It+1 = 1 + θ, resulting in It+1
= 1 for t ≥ 0.
It follows as a corollary that as the intermediation costs are reduced (i.e.,
θ & 0) — for example, because the suppliers of currency substitutes become more
efficient —, the commitment equilibrium approaches the Friedman rule, where the
rents to the monopolist supplier of currency are zero.
The commitment solution is time inconsistent. In this solution, at time zero,
the government runs a big open market operation holding real bonds issued by
the private sector that are exchanged for currency so that the real value of the
outstanding money stock is zero. In addition, monetary policy from time one on
is such that the gross nominal interest rate is constant over htime and seti at 1 + θ.
t
+ β −1 dt , so that
At time t ≥ 1, the government has outstanding liabilities M
Pt
if it was able to commit from time t on, it would be optimal to revise the plan
t
by setting M
= 0, thereby conducting another big open market operation. The
Pt
interest rate plan It = 1 + θ will not necessarily be optimal for a government that
can decide sequentially. Therefore, we turn our attention to an economy without
a fully committed monetary authority.
4. Equilibria without commitment
In this section, we define and characterize equilibria when the government makes
choices sequentially. These decisions depend on the history of the economy, which
is given by
n
o
h0 = M0 , R0 d0 , R0 bh0 , R0 be0 , I0f E0 and h1t+1 = {ht , Mt+1 , dt+1 , gt } , for t ≥ 0.
©
ª
and ht+1 = h1t+1 , bht+1 , bet+1 , Et+1 , for t ≥ 0.
12
Given a history ht at the beginning of period t, the government moves first and
chooses the policy for the period (gt , Mt+1 , dt+1 ).11 Thus, h1t+1 is known within
period t, at the time households make their choices.
A sequential policy for the government is a sequence of functions σ = {σ t }∞
t=0 ,
where σ t (ht ) specifies the choice of a government action (gt , Mt+1 , dt+1 ) as a function of the history ht . As in the commitment case, the government takes the
competitive behavior of the private sector as a given when choosing a policy. An
allocation rule for the private sector η is a sequence of functions {ηt }∞
t=0 , where
1
η t (ht+1 ) specifies a one-period allocation for households and financial intermedid
aries (c1t , c2t , nt , Mt+1
, Et+1 , bht+1 , bet+1 ) as a function of the history h1t+1 . If σ t (ht )
denotes the continuation of σ from ht , sequential rationality implies that for each
(t, ht ), σ t (ht ) is optimal (i.e., maximizes transfer revenues subject to (2.10)) given
the allocation rules of the households.
A Sustainable Equilibrium (SE) is a pair (σ, η)nsuch that: i) (σ,oη) defines a
∞
f
, and ii)
competitive equilibrium, with corresponding prices Pt , εt , Rt+1 , It+1
t=0
for each (t, ht ), σ t (ht ) is optimal given η.
In order to characterize the set of sustainable equilibrium values, we first need
to identify the worst one.
Proposition 2. The value of a competitive equilibrium where currency is not
held and deposits are used for transactions is the value of the worst sustainable equilibrium.
Proof. Let η be the allocation rule for the private sector corresponding to an
equilibrium where only inside money is valued (as defined in Section 2). Let the
b)Mt , where (1 + µ
b)β −1 >
strategy of the government σ be given by Mt+1 = (1 + µ
1 + θ, dt = d0 , gt = −(β −1 − 1)d0 , for all t. Currency is dominated and is not
held in the equilibrium defined by (σ, η). Since currency is not valued, such a
policy is sequentially rational for the government. It follows that the value of this
equilibrium outcome, measured by the constant flow of government transfers, is
V W SE (d0 ) = −(β −1 − 1)d0
(4.1)
where W SE stands for worst sustainable equilibrium. In fact the government can
always guarantee this payoff, so that that there is no sustainable equilibrium with
a value lower than V W SE (d0 ).
11
The implementation of the policy has to obey the timing of transactions spelled out in
Section 2 where good markets open first and asset markets open at the end of the period, taken
from Svensson (1986).
13
In line with Chari and Kehoe (1990), we apply Abreu (1988)’s optimal penal
codes and use the reversion to the worst sustainable equilibrium as the means of
supporting equilibrium outcomes. As mentioned above, we will concentrate on
stationary equilibria, except for the initial big open market operation.
More explicitly, consider the following government strategy σ: M1 = BM0 ,
0
0
0
Mt+1 = (1 + µ )Mt , t ≥ 1, gt = g = µ m(I ) − d1 (β −1 − 1), and dt+1 = d1 =
0
d0 − βm(I ), for all t ≥ 0, as long as Ms = (1 + µ0 )Ms−1 , for 2 ≤ s ≤ t, and
M1 = BM0 , where I 0 = (1 + µ0 )β −1 ≤ 1 + θ. If M1 6= BM0 , then for t ≥ 1,
Mt+1 = (1 + µ
b)Mt , gt = −d1 (β −1 − 1), and dt+1 = d1 , where (1 + µ
b)β −1 > 1 + θ;
and if Ms 6= (1 +µ0 )Ms−1 for at least one s ≥ 2, then, for t ≥ s, Mt+1 = (1 + µ
b)Mt ,
gt = gs = −ds (β −1 − 1), and dt+1 = ds , where (1 + µ
b)β −1 > 1 + θ. We consider the
limiting equilibria as B → ∞. For I 0 = 1 + θ, the limiting strategy corresponds to
following the policy achieved under full commitment (Proposition 1), as long as
such a full commitment path has been followed previously, while a deviation to an
inside money equilibrium -without cash, as in Proposition 2- follows if a deviation
from the full commitment path is observed.
As we have seen (Proof of Proposition 1), the value for the government after a
deviation is V W SE (dt ). Therefore, it is not profitable for the government to deviate
0
from the path of constant growth of the money supply µ if V (I 0 ; dt ) ≥ V W SE (dt ),
t ≥ 1, where
´
³
0
0
0
V (I ; dt ) = β(I 0 − 1)m(I ) − (1 − β) m(I ) + dt β −1 , t ≥ 1
0
= (βI 0 − 1) m(I ) + V W SE (dt ), t ≥ 1
0
0
0
At t = 0, the value of the equilibrium with I , V (I ; d0 ) = β(I 0 − 1)m(I ) − (1 −
β)d0 β −1 is always higher than V W SE (d0 ). V (I 0 ; dt ) ≥ V W SE (dt ), for all t, only
if βI 0 − 1 = π 0 ≥ 0, where π 0 is the, constant, inflation rate when I 0 is the gross
nominal interest rate.
So far, we have shown that sustainability requires the inflation rate to be
nonnegative.12 In addition, competition from currency substitutes requires I 0 =
(1 + π 0 )β −1 ≤ 1 + θ. Thus, the set of (from period one) stationary sustainable
competitive outcomes with valued currency is characterized by inflation rates satisfying
12
If there was nominal debt, the corresponding lower bound on inflation rates would be stricly
positive.
14
0 ≤ π ≤ β (1 + θ) − 1
(4.2)
In the absence of competition from currency substitutes, the set of sustainable
equilibria is a very large one that includes the commitment solution, i.e. the
stationary inflation rate that allows achieving the maximum of the Laffer curve.
As long as that value is positive, the equilibrium is sustainable. The punishment is
autarchy, but from the perspective of a revenue maximizing government, autarchy
has the same value as the deposits-only equilibrium.
Competition reduces the set of sustainable inflation rates by imposing an upper
bound on equilibrium inflation when currency is valued. Thus, competition from
currency substitutes allows to reduce the maximum level of the inflation rate in a
sustainable equilibrium.
Because competition from currency substitutes reduces the future gains from
issuing currency, it is more difficult to sustain equilibria where currency has value.
If the supply of currency substitutes is very efficient, the set of sustainable equilibria with valued currency may be empty. That would be the case if, under
commitment, competition from currency substitutes drove the inflation rates into
negative numbers, which would happen if θ < β −1 − 1. In that case, there would
be no sustainable equilibrium with valued currency but there would still be a sustainable equilibrium outcome with deposits being used for transactions. In this
equilibrium, the cost of transactions is given by the real intermediation cost θ.
It follows that, with limited commitment, relatively less efficient competitors can
drive currency out of circulation.
Proposition 3. The policy with full commitment (of Proposition 1), characterized by It+1 = 1 + θ, is sustainable if the intermediation cost θ satisfies
θ ≥ β −1 − 1; i.e., if the equilibrium inflation rate is non-negative, π > 0. If
θ < β −1 − 1, there is no sustainable equilibrium with valued currency, but
there is a sustainable equilibrium with (only) inside money.
When the policy with full commitment is sustainable, the set of sustainable
equilibria can be relatively large although, as (4.2) shows, it shrinks with the
costs of supplying inside money. Efficiency is thus enhanced as these costs are
reduced, to the point where outside money is driven out of circulation. At this
point there would be a discrete loss of welfare, because of the use of a relatively
more costly technology to supply money. In turn, this cost would be minimized
as the inside-money technology becomes increasingly efficient.
15
5. The case of a representative government
In this section we show how the results we have obtained so far are modified
when we assume that the government maximizes welfare. As in the standard
Ramsey problem, we assume exogenous -per period- government expenditures, g.
As the ability to collect seigniorage will be limited by the efficiency of the financial
intermediaries, we allow for the government to levy consumption taxes, τ t , as well
as taxes on the production of inside money, τ et , to ensure that expenditures can
be financed. In this paper we concentrate on the choice of monetary policy and
therefore we maintain full commitment on the choice of tax policy, in addition to
exogeneity of expenditures. We allow for monetary policy to be chosen with and
without commitment.
As in the previous section, the timing of events is as in Svensson (1985).
Nicolini (1998) shows that with this timing, the time inconsistency problem of a
Ramsey government is of a different nature than in the classic papers of Calvo
(1978) and Lucas and Stokey (1983), since there are costs of unanticipated inflation. The two main differences that this timing introduces are that the optimal
deviation for inflation is always finite and that for the government to be willing
to deviate from the Ramsey policy and inflate at a higher rate, the price elasticity
of consumption has to be larger than one. We will assume that this is indeed the
case. Nicolini (1998) obtains these results in an environment where seigniorage is
the sole source of revenue. In our set up there are alternative taxes which implies
that the optimal monetary policy is characterized by the Friedman rule. As we
show in this section, in our economy, when there is commitment to tax policy, the
monetary policy is time consistent.
The consumer’s problem is the same as before, except for the presence of a tax
on consumption. We simplify the analysis in this section by assuming preferences
of the form (2.1), but with the additional restriction of constant relative risk
00
aversion (CRRA), i. e., − uu0(c(ctt)c) t = ρ > 0), where 1/ρ is the price elasticity of ct .
For the reasons stated above, we assume that ρ < 1. If εt = ε ∈ {0, 1}, t ≥ 0, the
budget and cash-in-advance constraints are
Mt+1 + Pt bht+1 + εt Et+1 ≤ Pt nt − (1 + τ t )Pt (c1t + c2t ) + Mt + Pt Rt bht + Itf εt Et (5.1)
(1 + τ t )Pt c1t ≤ Mt + εt Et
for t ≥ 0, M0 , R0 bh0 , E0 = 0 given. Again, we assume that R0 = β −1 .
16
(5.2)
The tax on consumption imposes a distortion between consumption and leisure,
shown in the following first order conditions for t ≥ 0:
u0 (c2t )
= 1 + τ t, t ≥ 0
α
(5.3)
As before, when currency has value, the marginal rate of substitution between the
two consumption goods is such that
u0 (c1t+1 )
= It+1 , t ≥ 0.
u0 (c2t+1 )
(5.4)
When only inside money circulates the consumptions of the two goods satisfy
u0 (c1t+1 )
f
,t≥0
= 1 + It+1 − It+1
2
0
u (ct+1 )
(5.5)
Since there are consumption taxes the real value of deposits is (1+τEtt )Pt . The
financial intermediation technology is described by net = θ (1+τEtt )Pt . The financial
intermediaries pay a tax on time used to produce money, τ et . Free entry in the
financial intermediation sector results in
¡
¢
1 + τ et+1 θ
f
It+1 − It+1 =
, t≥0
(5.6)
1 + τ t+1
If, as it will be shown to be the case, τ et+1 = τ t+1 , then (5.5) and (5.6) imply
u0 (c1t+1 )
= 1 + θ, t ≥ 0.
u0 (c2t+1 )
(5.7)
5.1. Optimal policy under commitment
The optimal policy under commitment is the solution of a dynamic Ramsey problem, as in Lucas and Stokey (1983); like they did, we follow the primal approach.
The objective of the government is to maximize the welfare of the representative
household, subject to feasibility and other competitive equilibrium constraints.
These other competitive equilibrium constraints are consolidated in an implementability condition.
f
We first consider the case where It+1
≤ 1 and only currency is used for transactions. The budget constraint of the households, from any period t ≥ 0 on, can be
17
written as follows, provided that the cash-in-advance constraint is satisfied with
equality for all t ≥ 0:
∞
X
s=1
£
¡
©
¤
ª
¢
β s (1 + τ t+s ) It+s c1t+s + c2t+s − nt+s +(1+τ t ) c1t + c2t −nt ≤ (1+τ t )c1t +bht β −1
(5.8)
This constraint, for t = 0, satisfied with equality, together with (5.3) and (5.4),
can be used to build the following implementability condition, which is a necessary
condition for the optimal solution to be decentralized as a competitive equilibrium
with taxes:
∞
X
t=1
β t [u0 (c1t )c1t + u0 (c2t )c2t − αnt ] + u0 (c20 )c20 − αn0 − αd0 β −1 = 0
(5.9)
We can now define the Ramsey problem as the maximization of the utility
function subject to (5.9) and
c1t + c2t + g − nt ≤ 0, t ≥ 0.
(5.10)
In the following proposition we characterize the Ramsey solution.
Proposition 4. Let the utility function u be CRRA and ρ < 1. The Ramsey
solution is such that It+1 = 1 and τ ct = τ R , for t ≥ 0. Furthermore, c10 ≡ cR
0 <
2
1
R
ct = ct+1 = c , t ≥ 0.
Proof. The result follows directly from the first order conditions of the Ramsey
problem. Let γ ≥ 0 be the Lagrange multiplier associated with condition (5.9).
u0 (c1 )
u0 (c1 )
1+γ(1−ρ)
Then, u0 (c02 ) = 1 + γ(1 − ρ), and, for t ≥ 0, It+1 = u0 (ct+1
2 ) = 1+γ(1−ρ) = 1 and
0
u0 (c2t )
α
t+1
1+γ
.
1+γ(1−ρ)
1 + τt =
=
We have set up the Ramsey problem assuming that the cash-in-advance con0 1
(1+τ t )Pt
straints were satisfied with equality. That is indeed the case if βuu0 (c(c1t ) ) ≥ (1+τ
,
t+1 )Pt+1
t+1
1
t
t ≥ 0. At the Ramsey optimum β PPt+1
= It+1
= 1, and τ t = τ R . The time zero
cash-in-advance constraint is satisfied with equality if c10 ≤ c11 , which is the case
provided ρ ≤ 1.
f
≤ 1. Suppose
We have also assumed that the optimal policy resulted in It+1
f
that It+1 > 1, t ≥ 0. In that case only inside money circulates and the Ramsey
problem is the one in the cashless economy.
18
The budget constraint of the households in the cashless economy after a deviation at some period t ≥ 0 can be written as
∞
X
s=1
n
h³
³
´´
i
o
f
β s (1 + τ t+s ) 1 + It+s − It+s
c1t+s + c2t+s − nt+s +(1+τ t )c2t −nt ≤ dt β −1
(5.11)
with c1t = 0, since Et = 0. For t = 0, this budget constraint and the first order
conditions (5.5), (5.6), (5.3) can be summarized in the single implementability
condition, (5.9), together with c10 = 0. The feasibility condition is
(1 + θ) c1t + c2t + g − nt ≤ 0, t ≥ 0.
(5.12)
The Ramsey problem is to maximize the utility function, subject to feasibility,
(5.12) and implementability, (5.9), with c10 = 0.
The solution is given by a constant consumption tax, τ t = τ , t ≥ 0, and by a
tax on the production of money that equals the consumption tax, τ et+1 = τ t+1 = τ ,
t ≥ 0. This way both cash and credit goods are taxed at the same rate, τ .
u0 (c1 )
1
Using (5.7), u0 (ct+1
2 ) = 1+θ, for t ≥ 0 and c0 = 0. However, these marginal rates
t+1
of substitution and initial consumption were a feasible solution to the Ramsey
f
problem, as set up above, by choosing It+1 = 1 + θ (resulting in It+1
= 1) and
a zero
initial
price
of
money.
That
(suboptimal)
policy
would
increase
revenues,
P∞ t+1 1
by t=0 β θct+1 , and save on intermediation costs, relatively to a policy that
f
f
implies It+1
> 1. It follows that the Ramsey solution is such that It+1
≤ 1, t ≥ 0,
so that currency substitutes will not be held, and only currency will be used for
transactions.
This proposition states that under commitment, a benevolent government will
follow the Friedman rule, It+1 = 1, t ≥ 0. The Friedman rule means that both
cash and credit goods, from period one on, are taxed at the same rate. This is
the optimal taxation solution since the utility function is homothetic in the two
goods and separable in leisure - which are the conditions for uniform taxation
of Atkinson and Stiglitz (1972), as highlighted by Lucas and Stokey (1983) and
Chari, Christiano and Kehoe (1993). It also follows from standard optimal taxation principles that, since the price elasticity is greater than one (ρ < 1), the
consumption in period 0 of the cash good is lower than the consumption from
period 1 on. That is, there is a higher tax on the initial cash good (with a price
elasticity of one).13
13
See Nicolini (1998) for a further discussion of this.
19
Under the Friedman rule the price level will be decreasing at the rate of time
preference, Pt+1 = βPt , t ≥ 0. The following path for the money supply supports
R
the optimal allocation and prices: Mt+1 = βMt , t ≥ 1, and M1 = β ccR M0 . Notice
0
that the growth rate of money is higher at time zero than from time one on.
5.2. Optimal monetary policy without commitment
In this section we discuss the implications of relaxing the assumption that the
government is able to commit to monetary policy. We maintain the assumption
of commitment to fiscal policy while monetary policy is sequentially decided and
implemented. Such a regime is consistent with an institutional arrangement where
there exists a well developed commitment technology for fiscal policy (e.g., fiscal
policies are infrequently revised and have to be approved by parliaments), while
that may not be the case for monetary policy. As we will see, once the government
is committed to an optimal fiscal policy, there are no incentives for the monetary
policy to deviate from the optimal Friedman rule. The reason is that government
expenditures and alternative tax revenues are determined in period zero, and,
furthermore, the monetary authority can not reduce revenues in future periods.
Thus, it has no incentive to increase revenues either. The following proposition
states the time consistency of monetary policy.
Proposition 5 Assume that the government can commit to tax policy. Then,
monetary policy is time consistent.
Proof. In each period t ≥ 1, the problem of a government that considers revising
the Ramsey monetary policy is to maximize
∞
X
s=0
¡
¢
β s [u(c1t+s ) + u(cR ) − α c1t+s + cR + g ]
subject to the implementability condition
½· 0 1
¸
¾
∞
X
u (ct+s )
s
−1
1
R R
β
− 1 ct+s + τ c − g + τ R cR − g − c1t − dR
= 0 (5.13)
1β
α
s=1
and subject to the restriction that the nominal interest rate is non-negative. Given
(5.4), the latter restriction can be written as c1t+s ≤ cR . Let ϕt+s be the multipliers
20
of these constraints and γ, the multiplier of the implementability condition. Then
the first order conditions are
¡ ¢
u0 c1t = α + γ
¡
¢ α + γ + ϕt+s
u0 c1t+s =
,s≥1
1 + αγ [1 − ρ]
If the constraint that the nominal interest rate ¡cannot
¢ be negative is not binding,
so that ϕt+s = 0, s ≥ 1, then since ρ < 1, u0¡ c1t+s¢ < u0 (c1t ), s ≥ 1. Therefore
c1t < c1t+s ≤ cR , s ≥ 1, but, then, since u0 c1t+s − α > 0, s ≥ 0, there are
no incentives to deviate from the full commitment path with c1t+s = cR , s ≥ 0.
Similarly, if -as it is the case— the zero bound constraint is binding, so that c1t+s =
cR , s ≥ 1, in order to satisfy the budget constraint it must be that c1t ≤ cR . It
follows that c1t = cR . Since there are no incentives to deviate from period t ≥ 1
on, the Ramsey policy is time consistent.
6. Concluding Remarks
The development of electronic payment systems has drastically reduced intermediation costs for the banking system, making inside money a closer substitute for
outside money. Somewhat surprisingly, little attention has been paid to how those
developments may affect the conduct of monetary policy. This paper sheds light
on this and related issues.
We have shown that inside money competition may enhance efficiency, and
that would certainly be the case if the provision of increasingly efficient inside
money would compete with a fully committed central bank aiming at maximizing
revenues. In this case, lower costs of producing inside money drive down inflation
rates and, in the zero-cost limit, the Friedman rule is implemented. There are
however two main qualifications to the view that inside-outside money competition
works as standard product competition.
The first qualification is that competitive pressure may be exercised as an interplay between two forms of inefficiency; between the inefficiency of using costly
produced inside money and the inefficiency generated by pursuing sequential monetary policies when there is limited commitment. This is the case when a revenue
maximizer central bank can not commit to future interest rates. As the supply of
inside money becomes increasingly efficient, equilibrium inflation rates are driven
down to the point where the inflationary rents supporting valued currency vanish,
21
and the more efficient -even if more costly— inside money drives outside money
out.
The second qualification is that the competitive pressure from inside money
may be irrelevant when there is a benevolent government that delegates the implementation of monetary policy maintaining full commitment to fiscal policy. In
this context monetary policy is efficient and time consistent. A Ramsey government chooses the Friedman rule with full commitment and, therefore, there is no
disciplinary role for inside money competition. It turns out that such efficient
policy is time consistent when there is commitment to fiscal policy. The time
consistency of the Friedman rule results from the fact that there is no incentive
to raise initial revenues, when the zero bound on interest rates does not allow for
revenues to be reduced in the future. It follows that, even without commitment,
there is no disciplinary role for inside money competition.
Although we do not analyze it in this paper, it should be clear that if the
Ramsey solution implies an inflationary policy -for example, if seigniorage has to
be collected because other taxes are not available— or if there is no commitment to
a tax policy, then the Friedman rule is no longer time-consistent and inside money
competition may affect equilibrium outcomes. In particular, in our economies
the loss of confidence on outside money, following a deviation of the monetary
authority, is characterized by a shift to a cashless economy. Since the technological
inferiority of the inside money determines the welfare in the cashless economy, it
follows that inside money competition would determine the sustainability of the
Ramsey policy in these contexts.
Can the observed increased efficiency in the provision of currency substitutes
justify the low inflation rates in most developed economies in the last two decades?
Possibly, as we have seen, but then we should also be aware that the pressure for
low inflation rates can threat the value of currency. We have also learnt that low
inflation rates can also be the outcome of properly motivated and designed fiscal
and monetary institutions, even when the latter are allowed to make discretionary
choices.
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22
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[6] Drèze, J. H. and H. M. Polemarchakis, 2000, Monetary equilibria, mimeo,
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24
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WP-01-21
Is the United States an Optimum Currency Area?
An Empirical Analysis of Regional Business Cycles
Michael A. Kouparitsas
WP-01-22
A Note on the Estimation of Linear Regression Models with Heteroskedastic
Measurement Errors
Daniel G. Sullivan
WP-01-23
The Mis-Measurement of Permanent Earnings: New Evidence from Social
Security Earnings Data
Bhashkar Mazumder
WP-01-24
Pricing IPOs of Mutual Thrift Conversions: The Joint Effect of Regulation
and Market Discipline
Elijah Brewer III, Douglas D. Evanoff and Jacky So
WP-01-25
Opportunity Cost and Prudentiality: An Analysis of Collateral Decisions in
Bilateral and Multilateral Settings
Herbert L. Baer, Virginia G. France and James T. Moser
WP-01-26
Outsourcing Business Services and the Role of Central Administrative Offices
Yukako Ono
WP-02-01
Strategic Responses to Regulatory Threat in the Credit Card Market*
Victor Stango
WP-02-02
The Optimal Mix of Taxes on Money, Consumption and Income
Fiorella De Fiore and Pedro Teles
WP-02-03
Expectation Traps and Monetary Policy
Stefania Albanesi, V. V. Chari and Lawrence J. Christiano
WP-02-04
Monetary Policy in a Financial Crisis
Lawrence J. Christiano, Christopher Gust and Jorge Roldos
WP-02-05
Regulatory Incentives and Consolidation: The Case of Commercial Bank Mergers
and the Community Reinvestment Act
Raphael Bostic, Hamid Mehran, Anna Paulson and Marc Saidenberg
Technological Progress and the Geographic Expansion of the Banking Industry
Allen N. Berger and Robert DeYoung
WP-02-06
WP-02-07
4
Working Paper Series (continued)
Choosing the Right Parents: Changes in the Intergenerational Transmission
of Inequality Between 1980 and the Early 1990s
David I. Levine and Bhashkar Mazumder
WP-02-08
The Immediacy Implications of Exchange Organization
James T. Moser
WP-02-09
Maternal Employment and Overweight Children
Patricia M. Anderson, Kristin F. Butcher and Phillip B. Levine
WP-02-10
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
5
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
6
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
7
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