econstor www.econstor.eu Der Open-Access-Publikationsserver der ZBW – Leibniz-Informationszentrum Wirtschaft The Open Access Publication Server of the ZBW – Leibniz Information Centre for Economics Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. zbw Leibniz-Informationszentrum Wirtschaft Leibniz Information Centre for Economics Bassetto, Marco; Phelan, Christopher Working Paper Speculative runs on interest rate pegs: The frictionless case Working Paper, Federal Reserve Bank of Chicago, No. 2012-16 Provided in Cooperation with: Federal Reserve Bank of Chicago Suggested Citation: Bassetto, Marco; Phelan, Christopher (2012) : Speculative runs on interest rate pegs: The frictionless case, Working Paper, Federal Reserve Bank of Chicago, No. 2012-16 This Version is available at: http://hdl.handle.net/10419/70489
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Der Open-Access-Publikationsserver der ZBW – Leibniz-Informationszentrum WirtschaftThe Open Access Publication Server of the ZBW – Leibniz Information Centre for Economics
Standard-Nutzungsbedingungen:
Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichenZwecken und zum Privatgebrauch gespeichert und kopiert werden.
Sie dürfen die Dokumente nicht für öffentliche oder kommerzielleZwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglichmachen, vertreiben oder anderweitig nutzen.
Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen(insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten,gelten abweichend von diesen Nutzungsbedingungen die in der dortgenannten Lizenz gewährten Nutzungsrechte.
Terms of use:
Documents in EconStor may be saved and copied for yourpersonal and scholarly purposes.
You are not to copy documents for public or commercialpurposes, to exhibit the documents publicly, to make thempublicly available on the internet, or to distribute or otherwiseuse the documents in public.
If the documents have been made available under an OpenContent Licence (especially Creative Commons Licences), youmay exercise further usage rights as specified in the indicatedlicence.
zbw Leibniz-Informationszentrum WirtschaftLeibniz Information Centre for Economics
Bassetto, Marco; Phelan, Christopher
Working Paper
Speculative runs on interest rate pegs: Thefrictionless case
Working Paper, Federal Reserve Bank of Chicago, No. 2012-16
Provided in Cooperation with:Federal Reserve Bank of Chicago
Suggested Citation: Bassetto, Marco; Phelan, Christopher (2012) : Speculative runs on interestrate pegs: The frictionless case, Working Paper, Federal Reserve Bank of Chicago, No.2012-16
This Version is available at:http://hdl.handle.net/10419/70489
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Speculative Runs on Interest Rate Pegs The Frictionless Case
Marco Bassetto and Christopher Phelan
WP 2012-16
Speculative Runs on Interest Rate Pegs
The Frictionless Case∗
Marco Bassetto† and Christopher Phelan‡
Abstract
In this paper we show that interest rate rules lead to multiple equilibria when the central
bank faces a limit to its ability to print money, or when private agents are limited in the
amount of bonds that can be pledged to the central bank in exchange for money. Some of
the equilibria are familiar and common to the environments where limits to money growth
are not considered. However, new equilibria emerge, where money growth and inflation
are higher. These equilibria involve a run on the central bank’s interest target: households
borrow as much as possible from the central bank, and the shadow interest rate in the
private market is different from the policy target.
1 Introduction
Until the last couple of years, most central banks around the world conducted monetary policy
by setting targets for short-term interest rates, and letting the quantity of money adjust in
response to demand. Maneuvering interest rates as a way to achieve low and stable inflation is
now regarded as a success story. Yet this was not always the case. As mentioned by Sargent [8],
∗For valuable suggestions, we thank Fernando Alvarez, Gadi Barlevy, Robert Barsky, Mariacristina De Nardi,
Robert E. Lucas, Jr., and Thomas J. Sargent. The views expressed herein are those of the authors and not
necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve System.†Federal Reserve Bank of Chicago‡University of Minnesota and Federal Reserve Bank of Minneapolis
1
the German Reichsbank also discounted treasury and commercial bills at fixed nominal interest
rates in 1923; but, rather than contributing to stabilizing the value of the mark, the policy added
fuel to the hyperinflation by causing the Reichsbank to greatly increase the money supply and
transferring this money to the government and to those private entities lucky enough to borrow
from the Reichsbank at the official discount rate. In our paper, we study the extent to which
setting a short-term interest rate can be used as a way of implementing a unique equilibrium in
a monetary economy.
We start our analysis in a simple environment where both the central bank and Treasury
trade with all agents in the economy in every period and prices are flexible. In this setup, we
consider the properties of an interest rate rule, whereby the central bank sets a price at which
private agents are free to trade currency for one-period debt; this price need not be fixed, but
rather may depend in arbitrary ways on all the information that the central bank has at the
moment it makes its decision. We show that setting a policy rate in this way leads to multiple
equilibria when the central bank faces a limit to its ability to print money, or when private
agents are limited in the amount of bonds that can be pledged to the central bank in exchange
for money. Some of the equilibria are familiar and common to the environments where limits
to money growth are not considered. However, new equilibria emerge, where money growth
and inflation are higher. These equilibria involve a run on the central bank’s interest target:
households borrow as much as possible from the central bank, and the shadow interest rate in
the private market is different from the policy target.
To the extent that monetary policy is primarily conducted by open market operations that
exchange money for government bonds (or government-backed bonds), fiscal policy plays a promi-
nent role in defining the characteristics of equilibria that feature runs. This happens because
the amount of bonds held by the private sector determines the size of the run in the event of a
run. This is a new channel by which excessive deficits threaten price stability, and is indepen-
dent of the familiar unpleasant monetarist arithmetic of Sargent and Wallace [9] and the fiscal
theory of the price level (Leeper [6], Sims [10], Woodford [11]). In fact, we deliberately rule out
these alternative channels of monetary-fiscal interaction by postulating fiscal rules that ensure
2
long-term budget balance independently of the path of inflation.
Our research implies that interest-rate targets are an incomplete description of the way mod-
ern central banks have succeeded in establishing low and stable inflation, and suggests a new
role for the “twin-pillar” doctrine of paying attention to monetary aggregates (both broad and
narrow) as well as interest rates in designing appropriate monetary policy rules.1
2 The basic cash-in-advance model
Consider a version of the cash-in-advance model. There are a continuum of households of unit
mass and a government/monetary authority. Time is discrete with dates t ∈ {0, 1, 2, . . .}. In
each period, the timing is as follows: First, households pay lump sum nominal taxes Tt levied
by the government and asset markets open. In these asset markets, households can buy (or
sell) government bonds, acquire money, as well as trade zero-net supply securities with other
households. At this same time, the government can print and destroy money, borrow and lend.
After the asset markets, a goods market opens. In the goods market, households produce
the consumption good using their own labor for the use of other households (but, as usual, not
their own household) and the government. Each household has one unit of time and a constant-
returns-to-scale technology that converts units of time into units of the consumption good one
for one. Households use money to purchase units of the consumption good produced by other
households. The government uses either money or bonds (it is immaterial which) to purchase
Gt = G ∈ (0, 1) units of the consumption good.
Let Mt denote the amount of money in circulation at the end of the asset market in period
t, after taxes are paid. Let Bt−1 be the nominal amount of government bonds payable at date t.
(If Bt−1 < 0 this implies households have agreed to pay the government Bt−1 dollars at date t.)
The households start with initial nominal claims W−1 against the government.2
Consider a price sequence {Pt, Rt, Rt}∞t=0, where Pt is the nominal price of a unit of the
consumption good at date t, Rt is the nominal risk-free rate between period t and t+ 1 at which
1For a discussion of the twin-pillar doctrine, see Lucas [7].2These claims represent money and maturing bonds, before paying period 0 taxes.
3
the government trades with private agents, and Rt is the rate at which households trade with
each other. A government policy {Tt,Mt, Bt}∞t=0 is said to be feasible given {Pt, Rt, Rt}∞t=0 if for
all t > 0
Bt = (1 +Rt)[Pt−1G− Tt −Mt +Mt−1 +Bt−1
], (1)
with the initial condition
B0 = (1 +R0)[W−1 −M0 − T0]. (2)
In what follows, we use lower-case letters to indicate individual household choices and upper-
case variables to indicate aggregates: as an example, mt are individual money holdings, and Mt
are aggregate money holdings. In equilibrium, lower and upper-case variables will coincide, since
we consider a representative household.
Households are subject to a cash-in-advance constraint: their consumption must be purchased
with money. A household’s path is given by {ct, yt, bt, bt,mt}∞t=0, where bt are holdings of privately-
issued bonds maturing in period t + 1.3 In addition, households are potentially constrained in
their holdings of government securities to a set Bt. We will first explore the case in which Btis the entire real line, and we will then explore the implications of setting a limit to private
NecSufConditionsDynOpt.pdf, 2008. Mimeo, University of Chicago.
[5] Sanford Grossman and Laurence Weiss. A Transactions-Based Model of the Monetary
Transmission Mechanism. American Economic Review, 73(5):871–880, 1983.
[6] Eric Leeper. Equilibria under ‘Active’ and ‘Passive’ Monetary Policies. Journal of Monetary
Economics, 27(1):129–147, 1991.
[7] Robert E. Lucas, Jr. Panel Discussion: Central Banking: Is Science Replacing Art? In
Monetary Policy. A Journey from Theory to Practice. An ECB Colloquium held in honour
of Otmas Issing 16-17 March 2006, pages 168–171. European Central Bank, 2007.
[8] Thomas J. Sargent. The Ends of Four Big Inflations. In Robert E. Hall, editor, Inflation:
Causes and Effects, pages 41–97. The University of Chicago Press, 1983.
[9] Thomas J. Sargent and Neil Wallace. Some Unpleasant Monetarist Arithmetic. Federal
Reserve Bank of Minneapolis Quarterly Review, 5(1):1–17, 1981.
[10] Christopher A. Sims. A Simple Model for Study of the Determination of the Price Level
and the Interaction of Monetary and Fiscal Policy. Economic Theory, 4(3):381–399, 1994.
25
[11] Michael Woodford. Monetary Policy and Price Level Determinacy in a Cash-in-Advance
Economy. Economic Theory, 4(3):345–380, 1994.
26
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