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\begin{document}
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\title{The Precarious Fiscal Foundations of EMU}%
\author{Christopher A. Sims}%
\address{Department of Economics, Yale University}%
\email{sims@econ.yale.edu}%

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\begin{abstract}
After a brief overview of the fiscal theory of the price level, we consider
insights it provides into monetary policy formation under certain kinds of
deflationary and inflationary stress.  Then we consider how the institutions of
the EMU are equipped---or unequipped---to deal with such stress.  The
conclusion is that fiscal institutions as yet unspecified will have to arise or
be invented in order for EMU to be a long term success.
\end{abstract}
\maketitle
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\section{Introduction}
Conventional macroeconomic models specify carefully the connection of monetary
policy to the evolution of the price level, while ordinarily leaving the
government budget constraint and evolution of the stock of government debt
entirely hidden.  It has been recognized, at least since \citeasnoun{UnplArith},
that sufficiently irresponsible fiscal policy could cause problems for monetary
policy, but this has been treated as no more than an important footnote to the central role
of monetary policy.  Recently a number of economists have begun to take the
view that fiscal policy plays a role at least as important as monetary policy
in determining the price level.

Development of this view has required new models and new forms of analysis of
the models, but it is far from a merely technical advance.  It has made us
realize that there are a wider range of policy approaches to price stability
than are apparent from conventional models.  It has also made us aware that
conventional prescriptions for good monetary policy---commitment to control of
monetary aggregates or to vigorous use of interest rate policy to counter
inflation---are not by themselves guarantors of price stability.

The European Monetary Union has the appearance of an attempt to create a
central bank and a monetary unit that have no corresponding fiscal authority
behind them.  In the light of this new fiscal approach to the price level, such
an attempt appears to carry with it great dangers.  This paper outlines the
fiscal theory of the price level (FTPL) and examines a number of hazards for
EMU that the theory brings out.

\section{The Fiscal Theory of the Price Level}
\label{sec:FTPL} In one sense the fiscal theory of the price level is very simple.
If we pretend for a moment that there is no money, just interest-bearing debt
(of zero term), the instantaneous government budget constraint is
\begin{equation}\label{eq:GBCnoM}
  \frac{\dot{B}}{P}+\tau=\frac{rB}{P}\:,
\end{equation}
where $B$ is nominal government debt, $P$ is the price level, $r$ is the
nominal interest rate, and $\tau$ is the real primary surplus.  A dot over a variable
indicates the derivative of the variable with respect to time.  Now we introduce $b=B/P$
to stand for the real value of the debt and
\begin{equation}\label{eq:realR}
  \rho=r-\frac{\Hat{\Dot{P}}}{P}
\end{equation}
to stand for the real interest rate.  We use $\Hat{\Dot{P}}$ to stand for the
right derivative of $P$ with respect to time, i.e. the expected rate of change
from the current time onward.\footnote{The model we are considering here is not
stochastic.  We assume that all time paths in it are continuous and
differentiable and perfectly anticipated, except at the initial date (taken as
$t=0$). At $t=0$, discontinuity is possible in some variables, but
right-derivatives still exist. }  This allows us to rewrite \eqref{eq:GBCnoM}
as
\begin{equation}\label{eq:GBCnoMr}
  \dot{b} +\tau = \left(\rho+\frac{\Hat{\Dot{P}}-\Dot{P}}{P}\right) b\:.
\end{equation}
Though it is important to bear in mind that an unanticipated disturbance
creates a non-zero value for $\Hat{\Dot{P}}-\Dot{P}$, along perfect-foresight
solution paths the term is zero, allowing us to reduce \eqref{eq:GBCnoMr} to
\begin{equation}\label{eq:GBCnoMr2}
  \dot{b}=\rho b -\tau \:.
\end{equation}
In the simple case where $\rho$ and $\tau$ are constant, we conclude that if
$b$ cannot grow explosively, the only possible value for it is
\begin{equation}\label{eq:bval}
  b=\frac{\tau}{\rho} \:.
\end{equation}
More generally, $b$ must be the discounted present value of current
and future primary surpluses.  Equation \eqref{eq:bval} can be thought of as determining
the price level if we rearrange it as
\begin{equation}\label{eq:Peq}
  P=\frac{\rho B}{\tau}\:.
\end{equation}
In words, the price level is determined by the ratio of nominal government
liabilities to the primary surplus.

A relationship of this form exists in nearly every general equilibrium model including
government debt.  It is implicit in most standard macroeconomic models.  In
models with money, it coexists with the ``demand for money" equation derived
from bond/money arbitrage, which can also be rearranged so as to appear to be
determining the price level:
\begin{equation}\label{eq:MD}
  \frac{M}{P}=L(r,Y)\quad\rightarrow\quad P=\frac{M}{L(r,Y)}\:.
\end{equation}
In fact, neither of these equations stands alone, generally, in determining the
price level.  Each must be understood as a component of a general equilibrium
system.

When money is present, the real version of the government budget constraint \eqref{eq:GBCnoMr}
emerges as
\begin{equation}\label{eq:GBCr}
  \dot{b}=\left(\rho+\frac{\Hat{\Dot{P}}-\dot{P}}{P}\right)
  b -\tau -\frac{\dot{M}}{P}\:,
\end{equation}
which can also be written as
\begin{equation}\label{eq:GBCr2}
  \dot{b}+\dot{m}=\left(\rho+\frac{\Hat{\Dot{P}}-\dot{P}}{P}\right)
  (b+m)-\tau-rm \:.
\end{equation}
Comparing the last terms on the right sides of \eqref{eq:GBCr} and
\eqref{eq:GBCr2}, we see that we can think of the government budget constraint
as being written in terms of $b+m$, total real government liabilities, if we
count as part of revenue the seignorage term $rm$, the real interest payments
avoided by maintaining money balances.  Instead, we can think of the constraint
as written in terms of interest bearing debt $b$ alone, in which case we have
to count $\dot{M}/P$, the more standard notion of seignorage as expenditure
financed with newly issued money, as the seignorage term.  The two versions of
seignorage are not generally identical.

Naive discussions of fiscal policy sometimes, misreading the implications of
``Ricardian equivalence", take it to be true that whenever the government
issues additional debt, it is implicitly committing itself to raising
additional future revenue, in real terms, in order that the new debt have
value.  But in fact the new debt commits the government only to raising
additional future revenue in \emph{nominal} terms.  If asset market
participants believe that there is no commitment to additional real revenues,
the effect is not to make the new debt valueless, but simply to dilute the
value of all outstanding nominal debt.  This situation is perfectly analogous
to what would happen to the value of a private company's stock if it were to
issue new shares that were seen by market participants to be devoted to
non-productive expenditures.

To trace out the equilibrium implications of this
basic point, we consider fiscal behavior rules of two simple forms,
\begin{align}
   \tau&=-\phi_0+\phi_1 b \label{eq:Fpol}\\
   \intertext{or}
   \tau&=-\phi_0+\phi_1\cdot(b+m) \label{eq:FpolBSU}\:,
\end{align}
combined with monetary policy characterized by one of
\begin{align}
   M&\equiv\bar{M} \label{eq:MpolB} \\
   \intertext{or}
   r&=\theta (P-\bar{P}) +\beta \label{eq:MpolA}\:.
\end{align}
\citeasnoun{LeeperActPass} and most of the subsequent literature concentrated
on fiscal policies of the form \eqref{eq:Fpol}, while
\citeasnoun{BenhabibMultEq} have recently shown the importance of considering
fiscal policies of the form \eqref{eq:FpolBSU} when analyzing situations where
the nominal interest rate may approach zero.\footnote{That the results of
\citename{BenhabibMultEq} depend on their use of \eqref{eq:FpolBSU} in place of
\eqref{eq:Fpol} is not made explicit in their paper.}

Here we will summarize conclusions and try to support them with heuristics.  In
the Appendix we give detailed arguments.

Paralleling the conclusions of \citeasnoun{LeeperActPass}, we find that a
complete model has a unique path along which $b$ and $m$ are stable, associated
with a unique corresponding initial $P$, if fiscal policy of the form
\eqref{eq:Fpol}, with $\phi_1>\rho$, is combined with either \eqref{eq:MpolB}
or \eqref{eq:MpolA} with $\theta>0$.  This form of fiscal policy is what Leeper
calls ``passive" and Woodford calls ``Ricardian", while the monetary policy is
what Leeper calls ``active".\footnote{Woodford's usage is more suggestive of the
nature of the policy, but may be confusing, as no violation of Ricardian
equivalence is implied by ``non-Ricardian" fiscal policies.}  There is also a
unique price path associated with stable $b$ and $m$ when fiscal policy of the
form \eqref{eq:Fpol} with $\phi_1\le \rho$ (active fiscal policy, in Leeper's
terminology) is combined with monetary policy of the form \eqref{eq:MpolA} with
$\theta\le 0$ (passive monetary policy in Leeper's terminology.

Roughly speaking, these results can be explained by the fact that, with
seignorage small, the government budget constraint is an unstable differential
equation in real debt unless $\tau$ responds sufficiently positively to the
level of debt, i.e. $\phi_1>\rho$.  At the same time, the consumer's first order
condition, relating the rate of growth of consumption to the real interest
rate, becomes an unstable equation in prices if policy makes the nominal
interest rate $r$ respond positively to the price level.  If both these
equations (the government budget constraint with the fiscal policy rule used to
substitute out $\tau$ and the consumer's FOC with the monetary policy rule used
to substitute out $r$) are unstable, the model has no stable solution.  If
neither is unstable, the model has a continuum of stable solutions and
(therefore) an indeterminate price level.  If just one is unstable, the model
has a unique stable solution.

The more recent literature has moved beyond Leeper's analysis, however, to
recognize that it can occur that paths on which $m$ or $b$
explodes exponentially upward or downward may fail to violate transversality or
solvency constraints and thus may be legitimate equilibria.  This substantially
alters conclusions about the nature of policies that deliver a determinate
price level.  Furthermore, it turns out that conclusions here depend in detail
on the nature of transactions technology, of solvency constraints, and of
policy (whether fiscal policy is of the form \eqref{eq:Fpol} or
\eqref{eq:FpolBSU}).

If money is not essential, in the sense that the economy has a well-defined
equilibrium in which money has lost all value (a barter equilibrium), then
equilibria in which the price level explodes upward while real balances shrink
toward zero are usually possible.  This may render the price level
indeterminate under most combinations of active monetary with passive fiscal
policies.  The indeterminacy can be resolved by postulating that it is
generally believed that when inflation or the price level become high enough,
the passive fiscal rule will be abandoned, being replaced with, say, a policy
that redeems government liabilities at a fixed floor real value.  If such a
policy is understood to be in place, the circumstances that would trigger the
switch in fiscal policy will never arise, as only stable price paths will be
consistent with equilibrium.  But note that the credibility of such a
``backstop" policy depends on the existence of a fiscal authority that can be
seen to be committed to it.  A commitment of the central bank to keep monetary
policy active cannot by itself remove the indeterminacy.

As pointed out by \citeasnoun{BenhabibMultEq}, a combination of
\eqref{eq:MpolB} with a ``passive" form of \eqref{eq:FpolBSU} ($\phi_1>\rho$)
does not imply a uniquely determined price level, because of the possibility of
liquidity traps, in which prices spiral downward with nominal interest rates
zero.  Along an equilibrium path descending in to a liquidity trap under these
policies, real balances increase without bound.  Government \emph{lending} also
increases without bound, leaving the net worth of the public bounded as $M/P$
rises. There is thus no conflict with transversality conditions on such a path.
But this conclusion depends on the idea that, despite the absence of
interest-bearing debt, the government feels obliged to tax to back the value of
its outstanding non-interest-bearing liabilities.  While this may seem
far-fetched, the actions of the US Federal Reserve in the Great Depression
suggest that it was concerned about the inflationary potential of excess
reserves and applied the implicit tax of a reserve requirement increase to
absorb the excess.  Also, with policy characterized by \eqref{eq:Fpol} and
$\phi_1>\rho$, and with initial $b>\bar b$, the real primary surplus is implied
to be falling, regardless of what happens to the price level.  In a
deflationary spiral, a fixed nominal primary surplus would grow in real value.
If fiscal authorities display some money illusion and are therefore slow to cut
the nominal primary surplus, fiscal policy could behave more like what is
implied by \eqref{eq:FpolBSU} than by \eqref{eq:Fpol}, and a deflationary
spiral would be possible.

The liquidity trap indeterminacy of \citename{BenhabibMultEq} does not arise
if the fiscal policy is set according to \eqref{eq:Fpol} with
$\phi_1>\rho$.  In this case $b$ tends, as $P$ spirals downward, to some
positive limit, regardless of initial conditions, while $M/P$, and thus private
net worth, grows without bound. This would violate the representative agent's
transversality condition, and therefore deflationary spiral paths are not
equilibria of the model under this policy configuration.

The principle here is that along a deflationary path, active monetary policy
generates expansionary pressure by forcing a rise in the real value of
high-powered money $M$.  But this expansionary pressure can be completely
offset by misguided fiscal policy motivated by a desire to absorb ``excess
liquidity" or by sluggish adjustment of fiscal instruments to price declines.

\section{Liquidity Traps}
\label{sec:LT}
The analytical results cited in the previous section suggest that a central
bank may have difficulty halting a deflationary spiral if inappropriate fiscal
policies are followed.  We can make this difficulty more concrete by
considering particular historical circumstances.

In a recent paper \cite{CapeConf} I showed that postwar US monetary policy
reactions would have implied negative interest rates during the 1930's in the
US.  Since this was infeasible, what could the US monetary authorities have
done instead, and why did they not take effective action? This is of course a
question that has already been debated at length.  One suggestion is that the
Fed could have engaged in more aggressive open market operations.  But banks
already had large amounts of excess reserves in the form of
non-interest-bearing deposits with the Fed.  Would actions that replaced their
nearly non-interest-bearing holdings of government securities with additional
non-interest-bearing reserve deposits have been likely to change bank behavior?
It seems unlikely.  When interest rates are zero, open market operations are
pointless.

The banks were not lending because they had portfolios of loans of
questionable liquidity and depositors who were alert for any sign of distress
in their banks.  The Federal Reserve could have taken action to give the banks
increased confidence in lending, by moving aggressively to discount bank loans.
By greatly reducing bank concerns about solvency, such actions would probably
have increased bank lending and reduced public fears of bank failure.  In fact,
simply by making clear that it was ready to discount loans it might have had
substantial effects before it actually discounted very many loans.

But to be successful such a policy move would have had to be bold and broad. If
it were limited only to banks that were in distress, the stigma of coming to
the discount window would have discouraged banks from using it.  If it were
limited only to the very soundest of loans in bank portfolios, it would have
helped little to relieve concerns about solvency.  Discounting a substantial
volume of somewhat dubious loans would clearly have been risky, and would
thereby have acquired a fiscal dimension.  The Federal Reserve System would
have been taking on risk, and if the result was substantial losses, there would
have been a need for Congressional approval of appropriations to restore
Federal Reserve solvency.\footnote{It is sometimes suggested that a central
bank cannot have a solvency problem because it can always ``print money".  But
if the asset side of the bank's balance sheet deteriorates, and at the same
time the demand for high-powered money drops, the bank's ability to absorb
high-powered money via open market operations, and thereby preserve the value
of the currency, is compromised.  Being able to ``print money" is no help, of
course.  It is previously printed money that the public is attempting to
convert into something it values more---interest-bearing securities.}

We see this tension, in which policy to shore up a banking system, even if
undertaken by the central bank, is forced to be in some sense fiscal policy, in
two recent examples.  In Mexico, the central bank in 1994 in effect discounted
loans with a face value now of \$60 billion, exchanging them for government
bonds.  The bank did not obtain legislative approval at the time, and it has
this year (1998) tried to obtain legislative approval for completing the
bailout---effectively permanently lodging ownership of the questionable loans
with the government.  The result has been an extended political battle that is
having its own repercussions on the central bank and the banking system in
Mexico.

In Japan, similar concerns about banking system solvency have taken a long time
to resolve.  Unlike in Mexico, the Japanese environment has been deflationary,
with short term interest rates close to zero.  Conventional monetary policy has
been powerless, therefore, to reinvigorate bank lending.  In this case, the
central bank has not undertaken any quasi-fiscal actions on its own, as the
need for a fiscal component in the resolution has been apparent.


\section{Inflationary Shifts in Demand for Government Liabilities}
Another kind of test of a monetary authority's ability to maintain stability is a
sudden drop in demand for the liabilities of the government.  This will of
course be inflationary if not counteracted by policy.  If the decline has
occurred because of a reduced need for transactions balances, it can be offset
by letting the public adjust its portfolio to hold less money and more
government debt.  This is the kind of thing that open market operations are
meant to accomplish.  We are not used to thinking of open market operations as
having a fiscal dimension, but they do in fact.  When the central bank sells
interest-bearing government debt to absorb non-interest-bearing liabilities, it
increases the level of current and future interest expenses and thereby
requires expenditure cuts or tax increases.  If the monetary authority's action
is not backed up in this way by fiscal policy, it will not have the desired
anti-inflationary effect.

An historical example here is instructive.  From 1890 to 1894 in the US, gold
reserves shrank rapidly.  US paper currency supposedly backed by gold was being
presented at the Treasury and gold was being requested in return.  Grover
Cleveland, then the president, repeatedly issued bonds for the purpose of
buying gold to replenish reserves.  This strategy eventually succeeded.  From
one point of view, it was simply an open market operation: sale of bonds to
absorb high-powered money.  But at the time, the US had no central bank.
Cleveland issued the bonds under dubious legal authority, without consulting
Congress, and there resulted a major legal and political dispute---luckily
after the fact.  The argument of Cleveland's opponents, which was surely
correct in principle, was that while the issuance of the bonds was not directly
a purchase of goods and services, it nonetheless imposed fiscal obligations,
and Congress was constitutionally charged with deciding such issues.

Nowadays in the US at least, the legal situation is much clearer.  There is a
continually adjusted upper bound on US government debt, set by Congress, and
the president could not exceed it without Congressional authority.  It is
therefore not a mere accounting fiction that the Federal Reserve holds US
government debt on the asset side of its balance sheets.  Sale of these bonds
imposes fiscal obligations as surely as did Cleveland's bond sales, but it is
understood that the Federal Reserve can sell or buy bonds routinely, without
consulting Congress.

\section{Exchange Rate Determination}

There has been some controversy surrounding the application of FTPL to
determination of exchange rates.\footnote{See \citeasnoun{BerginEMU},
\citeasnoun{WoodEMU} and \citeasnoun{Dupor}.}  The main difficulty is that in a
multi-country model, if the governments are given arbitrary decision rules like
\eqref{eq:MpolA}, \eqref{eq:MpolB} and \eqref{eq:Fpol}, they need not end up
satisfying ``transversality conditions".  That is, while we can be sure that
optimizing individuals will not accumulate wealth indefinitely without spending
it, non-optimizing governments might do so.  But since doing so would reduce
the welfare of their own citizens, equilibria in which this occurs are
unappealing as descriptors of possible reality.  The elements going in to this
discussion are described clearly by \citeasnoun{BerginEMU}.

Once we accept the view that it is unrealistic to consider equilibria in which
any government accumulates indefinitely large amounts of the debt issued by
other governments, FTPL produces a simple message about exchange rate
determination.  In simple multicountry extensions of the model of section
\ref{sec:FTPL}, domestic price levels are determined by the ratio of nominal
government liabilities to discounted future primary surpluses, and exchange
rates are then determined by the ratios of price levels.  If borrowing takes
place both in foreign and domestic currency, fluctuations in the country's
fiscal status are magnified, because it is the ratio of domestic debt to the primary surplus
after dollar interest is subtracted that determines the price level.  Foreign
currency borrowing therefore acts as leverage in the FTPL relationship.

When we view exchange rate determination from the FTPL viewpoint, new
possibilities arise for the type of speculative attack multiple equilibria that
have now been widely studied in the international macroeconomics literature.
That literature focuses mainly on the possibility that monetary policy could
respond to an exchange rate change brought on by a speculative attack.  But the
possibility of a fiscal shift in response to a speculative attack can equally
well produce multiple equilibria.  Indeed one aspect of the recent Asian
financial crises may be precisely such a mechanism:  devaluation can lead to
financial distress in large companies or banks and thereby to government
bailouts that produce sudden increases in the liabilities of the government.
Simple models demonstrating that this can lead to multiple equilibria with
speculative attacks are displayed in \citeasnoun{HongKong}.

\section{EMU: Monetary Policy without Fiscal Backing?}

It is striking that the Maastricht accords spell out in great detail the
institutional arrangements for a common monetary system while providing no
correspondingly detailed structures for coordination of fiscal policy.  The
accords even seem to reflect a belief that eliminating relationships between
fiscal authorities and the central bank guarantees monetary stability.  The
European Central Bank is designed to be ``independent" of fiscal authorities in
the sense of being disconnected from them.  Yet the fiscal theory of the price
level suggests that this is a mistaken definition of central bank independence.
A truly independent central bank is one that can act, even under inflationary
or deflationary stress, without any worry about whether the necessary fiscal
backing for its actions will be forthcoming.  What kind of problems is the
Maastricht structure likely to engender?

Before I proceed, let me note that I am only going to describe what seem to me
to be potential hazards and pressures on the system.  I think it is unlikely
that EMU can long survive with the degree of vagueness and weakness in the
associated fiscal structure that currently characterize it.  This does not
mean, though, that the EMU cannot long survive.  One possible response to
pressures as they arise is that fiscal institutions can emerge and adapt as
necessary in order that EMU survive.

\subsection{The Fiscal Criteria as Passive Fiscal Policy}
The criteria for fiscal behavior set out in the treaty amount to a commitment
that each country individually will follow a passive fiscal policy, raising the
primary surplus by more than enough to offset the increased interest payments
when real debt grows.  As we noted in \ref{sec:FTPL}, such a fiscal policy
implies a unique stable price path when it is coupled with an active monetary
policy, one that stabilizes a monetary aggregate or increases interest rates
when the price level rises.  However, this policy combination also allows
unstable equilibria, in which a self-reinforcing, accelerating inflation wipes
out the real value of the money stock while leaving the real value of the stock
of interest-bearing debt unchanged.  No amount of ``commitment" or
``credibility" on the part of the monetary authority can rule out such
equilibria.  What is required to rule them out is widespread belief in a fiscal
commitment to a floor value for the currency.

Such a commitment is plausible in a country with a single monetary and a single
fiscal authority.  But in EMU, a coordination problem would arise.  The
commitment would after all require raising taxes to preserve the value of the
currency.  Any single country in the EMU might well worry that if it moves
first with such a backup tax, it could end up carrying the burden for the rest
of Europe.  Indeed, there might be a question whether any single country,
certainly among those with smaller economies, has the fiscal resources to
credibly promise such a backup.  To succeed, therefore, such an implicit or
explicit fiscal backup commitment would have to involve coordination, with at
least several countries jointly taking on the task.  This would require
political skill, and since it has not been done before and would not need to be
done in equilibrium, it might be hard to convince the markets that this
political process could carry forward with the required speed if an
accelerating inflation did begin.

\subsection{A Deflationary Depression Scenario}
As we have noted in sections \ref{sec:FTPL} and \ref{sec:LT}, the zero lower bound on
interest rates can make the active-monetary, passive-fiscal policy combination
untenable as deflation pushes interest rates toward zero.  What is required to
break out of such a situation is fiscal action that prevents continued rise in
the real value of government liabilities and high real returns on them.  This
will mean reducing primary surpluses and convincing the public that these
reductions will be long-lasting.  Standard passive fiscal policy is counter to
what is needed in this situation.  The real value of government liabilities
will be high and rising.  With the economy generally in distress, policy-makers
might not find it difficult to put the fact of rising real government
liabilities aside and undertake fiscal expansion.  But if the Maastricht rules are taken
seriously, they will point in precisely the wrong direction in such a
situation.

Here what is a weakness of the EMU system in other circumstances---the fiscal
free rider problem---would work toward resolving the difficulty.  Even one
country that is sufficiently fiscally expansive despite the Maastricht rules,
could undo the liquidity trap, with the resultant reversal of deflation
benefiting all members of the EMU.  On the other hand, if the logical
foundations of the need for fiscal coordination are not understood, the need to
break the Maastricht rules in this situation could undermine adherence to them
more generally.

\subsection{Fiscal Free-Riding and Country Bankruptcy}
Some writing about EMU assumes that it will permanently eliminate nominal interest
differentials across countries on government debt.  Monetary policy under EMU is often
described as decision-making on interest rates being made at the European
Central Bank (ECB) and implementation of those decisions in individual
countries being carried out by country central banks.  If the rates are not
truly to be uniform across countries, difficult questions of interpretation
will arise in implementing the ECB rate decisions in individual countries.

But a policy of eliminating cross-country rate differentials amounts to a
policy of accommodating debt issue by fiscally expansive
countries.\footnote{The treaty language emphasizes that the ECB and the country
central banks will not ``directly" buy government debt.  However, use of
repurchase agreements with government debt as collateral seems definitely to be
contemplated.  In its effect on the market for government debt, a repurchase
agreement is not very different from an outright purchase.}  With such a policy
in place, the benefits to a country of running a fiscal deficit unbacked by
future taxes are greater than for a country not in a monetary union.  The
isolated country faces the full inflationary consequences of its unbacked
fiscal expansion.  The EMU member spreads the inflationary consequences over
its EMU partners and, if not forced to undo the effects of its initial
expansion by later fiscal contraction, attains a permanent increase in wealth
at the expense of other EMU members.\footnote{A simple model laying this out is
in \citeasnoun{HongKong}.}

So if it is to succeed in maintaining uniform interest rates without generating
fiscal imbalances, the EMU will have to find ways to enforce fiscal discipline
on its member states, even when those states are under economic stress.  The
treaty language mentions the possibility of fines and required
non-interest-bearing deposits for fiscally recalcitrant states.  These measures
do not seem likely to be widely useful.  A state in such distress is not likely
to have reached its condition through frivolous excess.  More likely, it will
have undergone unusual economic hardship.  At such a juncture, trying to
encourage greater fiscal stringency by adding an item to the expense side of
the country's budget is likely to be counterproductive.

But one could take another view entirely of how the system will work---and one
difficulty in understanding how it will work is that people seem to take both
these contradictory views.  The other view is that there is no need for the
Maastricht criteria or for concern about fiscal discipline.  The markets will
take care of the fiscal discipline.  The strict language forbidding the ECB to
buy government debt suggests that interest rate uniformity may not be a central
tenet of policy.  Interest rate differentials across countries may persist,
reflecting market judgments of the relative risks that the countries will
default on their debts.  US states, which have no independent monetary policies
and have occasionally through history defaulted, are pointed to as an example.

This view seems to me naive, at least as it applies to the first decade or two after
the EMU begins.  Country default, if it occurs, will be a major blow to the
defaulting country's economy and financial system.  EMU members are all
sovereign states with recent histories of having run their own monetary
systems.  They will all still have central banks, of a sort, and central
bankers.  If a country were in such distress that its interest rates
rise substantially above those of other EMU members and that it thereby came
to the brink of default, it seems very likely that it would leave the EMU and
restart its independent monetary system.  It would thereby revive the option of gentle,
uniform, and partial default via inflationary finance and devaluation.  If
markets put some credence in this scenario, they will react to an EMU member's
fiscal distress much the way they have historically reacted to a fragile
commitment to a fixed exchange rate.  Rising interest rates on debt will fuel
speculation that drives the rates up even faster, increasing fiscal distress
further, in a rapid spiral leading to crisis.

Even one such crisis would threaten the future of EMU, as it would likely breed
contagion effects in other countries.  It seems to me, therefore, that the EMU
must pay attention to fiscal coordination and to attempts to keep interest
rates uniform.  Country bankruptcy may have to be contemplated as a remote
possibility, but welcoming its threat as a source of fiscal discipline seems
foolhardy.

\section{Inflationary Shifts in Demand for EMU Government Liabilities}
Where is the EMU's Grover Cleveland?  Presumably despite being forbidden to
hold government debt, the country central banks and the ECB will strive to hold
assets whose value is closely tied to their Euro-denominated liabilities.  Very
likely these will be government debt repurchase agreements, and very likely
country central banks will tend to specialize in repurchase agreements for their
own country's government debt.  There should therefore be adequate stocks of
interest-bearing assets on hand to meet demand under sudden portfolio shifts.

Note, though, that this comforting thought is predicated on country default
risk being a remote possibility.  One type of shift in demand for EMU
government liabilities might come from a widespread increase in concern about
country default risk.  Such concern would not divide itself evenly across
countries, so the demand to exchange reserves for interest-bearing debt would
vary across countries, and those most heavily hit would likely face rising
interest rates if there were no automatic interest-smoothing mechanisms in
place.  Country default risk might therefore be associated with country central
bank failure risk.  Once this possibility came seriously to the fore, a
coordinated fiscal mechanism to provide credit and/or recapitalization to the
distressed bank or banks would be essential.
\section{Conclusion}

Human institutions are never perfect, and it is difficult to predict how they
will actually work from their paper constitutions.  Despite its emphasis on what could
go wrong, this paper is not meant to be nihilistic.  The EMU is more likely to
succeed if those running it have thought carefully about all the ways it might
fail.  It seems to me that the FTPL is a useful tool to deploy in that
enterprise.

\appendix
\section{Detailed Analysis of the Model}
   \label{sec:AppFOC}

To consider questions of uniqueness and existence of equilibrium we have to
complete the model.  Here I present a simple, unrealistic model in which the
central issues can be discussed.  The model differs from that in
\citeasnoun{CASMandF} only in that this paper's model is in continuous time.
It differs from that in \citeasnoun{HongKong} in that it incorporates money
explicitly.

We postulate a representative agent who solves
\begin{equation}\label{eq:obj}
  \max_{C,M,B}\int_0^{\infty}e^{-\beta t} \frac{C^{1-\gamma}}{1-\gamma}dt
\end{equation}
subject to
\begin{gather}\label{eq:constraint}
  C\cdot\left(1+\psi(V)\right) + \frac{\dot{M}+\dot{B}}{P}+\tau \le rB+Y
  \text{  ,}\\
  \intertext{and}
  \label{eq:Ge0} M\ge 0\:,\quad\quad B+M \ge 0\:.
\end{gather}
The inequality \eqref{eq:constraint} is a budget constraint of usual form,
except perhaps for the term in $V$, which we define as velocity
\begin{equation}\label{eq:Vdef}
  V=\frac{PC}{M}\:.
\end{equation}
The factor $1+\psi(V)$ in front of $C$ represents the effect of transactions
costs on the amount of utility-yielding consumption obtained from a given
amount of expenditure.  It is natural to suppose $\psi(0)=0$ --- i.e. that
transactions costs approach zero as real balances become arbitrarily large
relative to consumption.  It is also natural to assume $\psi'>0$.  Existence and
uniqueness of equilibrium may depend on further restrictions on the form of $\psi$,
which we will discuss further below.

The two constraints in \eqref{eq:Ge0} are, first, a
statement that there is no such thing as negative money, and, second, a
borrowing constraint.  Even if the government does lend to the public, we
assume it does insofar as the loan is backed by money holdings.  While this
form of the constraint is somewhat arbitrary, some such constraint, bounding
borrowing, is required to make the consumers' problem well-defined.

To keep the model very simple, we assume the endowment stream $Y$ is constant.

Note that the government budget constraint \eqref{eq:GBCr} and
\eqref{eq:constraint} together imply the social resource constraint
\begin{equation}\label{eq:SRC}
  C\cdot(1+\psi( V))\le Y \:.
\end{equation}
Thus, if it could be arranged, it would be optimal to set $V=0$ --- i.e. to
saturate the economy with money.  Money balances in fact consume no resources,
yet they provide transactions services.  However, in any equilibrium with
valued money, individuals perceive that they are sacrificing current
consumption in refraining from consuming their money balances.  This is an
externality that cannot be removed.  It can be made small by policies that make
the real rate of return on money approach the discount rate $\beta$.  This
would require negative inflation rates.  Our interest here, though, is not in
optimal policy for this unrealistic model.  It is in using this easily
analyzed, simple model as a guide to understanding more realistic models in
which positive inflation rates are the focus.

The first order conditions for an optimum for an agent maximizing
\eqref{eq:obj} subject to \eqref{eq:constraint} and \eqref{eq:Vdef} are,
assuming an interior solution,
\begin{align}
   \partial C\tcol& & &U' = \lambda\cdot(1+\psi ' \cdot V+\psi) \label{eq:DC}\\
   \partial B\tcol&&&
   -\frac{\dot\lambda}{P}+\frac{\lambda\dot{P}}{P^2}+\frac{\lambda\beta}{P}=r\frac{\lambda}{P}
   \label{eq:DB}\\
   \partial M\tcol&&& -\frac{\dot\lambda}{P}+\frac{\lambda\dot{P}}{P^2}+\frac{\lambda\beta}{P}=
      \lambda \psi ' \frac{V^2}{P}\:.\label{eq:DM}
\end{align}

Equating the right-hand sides of \eqref{eq:DB} and \eqref{eq:DM} gives us the
usual liquidity preference function
\begin{equation}\label{eq:LP}
  r=\psi '\cdot V^2\:.
\end{equation}
We can simplify \eqref{eq:DB} to the form
\begin{equation}\label{eq:DBSimp}
  -\frac{\dot{\lambda}}{\lambda}=r-\beta-\frac{\dot P}{P} \:.
\end{equation}

We can now collect a set of 6 equations in the six variables $C$, $P$, $M$,
$V$, $r$, $\tau$ and $b$.  The equations are \eqref{eq:Vdef}, \eqref{eq:GBCr},
\eqref{eq:MpolA} or \eqref{eq:MpolB}, \eqref{eq:Fpol} or \eqref{eq:FpolBSU}, \eqref{eq:LP},
\eqref{eq:DBSimp} and \eqref{eq:SRC}.  Note that just two of these,
\eqref{eq:GBCr} and \eqref{eq:DBSimp}, are differential equations, so that in
principle the system can be reduced to a two-dimensional differential equation
system.

In order to gain insight into how the system behaves, we specialize to the case
of CRRA utility, i.e.
\begin{equation}\label{eq:CRRA}
  U(C)=\frac{C^{1-\gamma}}{1-\gamma}
\end{equation}
and a particular choice of $\psi$, starting with $\psi(V)=\kappa V$.  Consider
first the case of fixed-$M$ monetary policy, given by \eqref{eq:MpolB},
accompanied by one of the fiscal policies \eqref{eq:Fpol} or \eqref{eq:FpolBSU}
with $\phi_1>\beta$.  Our simplifications let us rewrite \eqref{eq:DBSimp} as
\begin{equation}\label{eq:DBMbar}
  \gamma\frac{\dot{C}}{C}+\frac{2\kappa\dot{V}}{1+2\kappa V} = \kappa
  V^2-\beta-\frac{\dot{P}}{P}\:.
\end{equation}
The social resource constraint \eqref{eq:SRC} (with $Y$ constant) lets us conclude that
\begin{equation}\label{eq:cdot}
  \frac{\dot{C}}{C}=-\frac{\kappa \dot{V}}{1+\kappa V}\:,
\end{equation}
and the definition of $V$ together with the constancy of $M$ \eqref{eq:Vdef} gives us
\begin{equation}\label{eq:pdot}
  \frac{\dot{P}}{P}=\frac{\dot{V}}{V}-\frac{\dot{C}}{C} \:.
\end{equation}
Using these relations in \eqref{eq:DBMbar} produces
\begin{equation}\label{eq:dV}
  \frac{\dot{V}}{V}\left(1+\frac{(1-\gamma)\kappa V}{1+\kappa V}+\frac{2\kappa V}{1+2\kappa V}\right)
  =\kappa V^2-\beta \:.
\end{equation}

So long as $\gamma\le 3$, the expression in the large parenthesis in
\eqref{eq:dV} is always positive.  Thus in this case $V$ has a unique,
unstable, fixed point at $V=\bar{V}=\sqrt{\beta/\kappa}$.  If at some initial
date $t=0$ we had $V(0)<\bar{V}$, $\dot{V}(0)$ would be negative, and $V$ would
drop toward zero.  As $V$ approached zero, $\dot{V}/V$ would approach $-\beta$.
But with $V$ approaching zero, $C$ would have to approach $Y$ (by the SRC
\eqref{eq:SRC}), and since $M$ is constant, the only way for $V$ to be
approaching zero then is for $P$ to approach zero.  This would imply
$M/P\to\infty$.

Under the fiscal policy \eqref{eq:Fpol} with $\phi_1>\rho$, the real government
budget constraint \eqref{eq:GBCr}, with $\tau$ substituted out and using the fact that $\dot
M=0$, becomes
\begin{equation}\label{eq:StabGBCr}
  \dot b = -(\phi_1 -\rho)b +\phi_0\:.
\end{equation}
This equation is stable in $b$, so along any equilibrium path $b$ is bounded.
Thus the fact that if $P\to 0$, $M/P\to \infty$ implies that consumer net worth
goes to infinity.  This is incompatible with consumer optimization if (as it
must) $C$ remains bounded.

But if instead fiscal policy is given by \eqref{eq:FpolBSU}, we can rewrite the
government budget constraint \eqref{eq:GBCr2}, substituting out $\tau$ with the fiscal policy
rule and $r$ with the liquidity preference relation \eqref{eq:LP}, as
\begin{equation}\label{eq:StabGBCr2}
  \dot b + \dot m = -(\phi_1 - \rho)(b+m) +\phi_0 - \kappa\frac{C^2}{m}\:.
\end{equation}
The boundedness of $C$ and the fixity of $M$ imply that as $P\to 0$, the last
term in \eqref{eq:StabGBCr2} also goes to zero, leaving the behavior of $b+m$
determined by a stable linear differential equation.  Thus $b+m$ remains
bounded even though $m\to\infty$.  This can occur, because government can use
primary surpluses to make $b$ negative by purchasing private assets and lending
to the public.  But then the net worth of the representative consumer remains
bounded, and paths with $P$ approaching zero violate no transversality
condition of private agents.

If initially $V(0)>\bar{V}$, $\dot{V}(0)>0$, and $V$ would increase without
bound.  By the social resource constraint \eqref{eq:SRC}, this would imply $C$
shrinking toward zero and thus $P\to\infty$ very rapidly.  It turns out that
not only does $V\to\infty$, it increases so rapidly that it reaches $\infty$ in
finite time.  A plot of a typical time path, with $\gamma=2$, $\kappa=.01$,
$\beta=.05$, $V(0)=\sqrt{\beta/\gamma}+.1$ is displayed in Figure
\ref{fig:Vpath}.  There are no apparent incentives for individuals to trade so
as to undermine the equilibrium represented by this path of $V$, despite the
fact that it ends in finite time.  At the end of the path, real balances have
disappeared and the economy has been reduced to barter.  This reduces $C$ to
zero, and utility either to 0 (if $0<\gamma<1$) or to $-\infty$ (if $\gamma\ge
1$), but it is not physically unsustainable.  Thus if we maintain the
assumption that fiscal policy sticks to its passive form \eqref{eq:Fpol} with
$\phi_1>\beta$, the initial price level is indeterminate.  A fully credible
commitment by the monetary authority to keep $M$ constant cannot prevent an
equilibrium in which inflation accelerates so rapidly as to make real balances
disappear in finite time.

\begin{figure}[p]
  \centering
  \includegraphics*[width=.95\textwidth]{vexplode}
  \caption{Time Path of $V$ with $\gamma=2$}\label{fig:Vpath}
\end{figure}

A different situation arises if $\gamma>3$.  Then the term in the large
parenthesis in \eqref{eq:dV} becomes negative for $V$ above some critical
value $\Bar{\Bar{V}}$.  If $V(0)>\Bar{\Bar{V}}$, $V$ decreases rapidly toward
$\Bar{\Bar{V}}$.  If $V(0)<\Bar{\Bar{V}}$, $V$ increases rapidly, reaching
$\Bar{\Bar{V}}$ in finite time.  A plot of such a path appears in Figure
\ref{fig:Vbound}. These solutions to \eqref{eq:dV} cannot be equilibria of
the economy, however.  At the time, say $t=T$, at which $V$ reaches
$\Bar{\Bar{V}}$, $\dot{V}(T)=\infty$ is required to make individuals satisfied
with real balances as small as implied by this high level of $V$.  But if $V$
actually continues growing, it crosses into the region in which $\dot{V}$, and
hence $\dot{P}$, becomes negative.  So $V$ cannot in fact grow, and thus in
turn $P$ cannot grow as fast as required.  This reverses the growth of $P$, and
if this reversal is anticipated, it creates an incentive to speculation that
will undermine any potential equilibrium that begins with $V(0)>\bar{V}$.  Thus
with $\gamma>3$, there is a unique equilibrium $P(0)$, given by
\begin{equation}\label{eq:Pbar}
  \bar{P}=(1+\kappa \bar{V})\frac{\bar{M}\bar{V}}{Y} \:.
\end{equation}
\begin{figure}[p]
  \centering
  %\includegraphics*[width=.8\textwidth]{vbound.png}
  \includegraphics*[width=.95\textwidth]{vbound}
  \caption{Time Path of $V$ with $\gamma=5$}\label{fig:Vbound}
\end{figure}

The drastic behavior of the economy when $V(0)>\bar{V}$ in these examples depends on
the fact that they assume transactions costs are capable of driving $C$ to
zero, while $Y$ remains constant.\footnote{More precisely, the drastic behavior
arises from the insufficiently rapid rate of decline of $\psi^\prime$ as $V\to
\infty$.  The distinction between economies that can smoothly approach $V=0$
over an infinite time span and those in which upward-explosive paths for $V$
are either unsustainable as equilibria or last a finite time is only
approximately the distinction between economies with and without barter
equilibria.}  Under the more moderate assumption that there is a non-zero level
of $C$ attainable with $M/P=0$, we get different results.  For example, if
\begin{equation}\label{eq:psi2}
  \psi(V)=\frac{\kappa V}{1+V}\:,
\end{equation}
the analogue of equation \eqref{eq:dV} becomes
\begin{multline}\label{eq:dVb}
  \frac{\dot{V}}{V}\cdot\left(1+\frac{\kappa
  V}{(1+V)(1+(1+\kappa)V)}+\frac{2\kappa V}{(1+V)(1-\kappa
  +2V+(1+\kappa)V^2)}\right)\\
  = \frac{\kappa V^2}{(1+V)^2}-\beta \:.
\end{multline}

As can be seen from the right-hand side of \eqref{eq:dVb}, there will be no
steady-state value of $V$ in this economy if $\kappa<\beta$, i.e. if
transactions costs are a small fraction of output in barter equilibrium, so
money is not very important to the economy.  For large $\gamma$ and $\kappa$,
the term in the large parenthesis in \eqref{eq:dVb} may change signs at some
positive value of $V$, which makes analysis of the economy's behavior
complicated.  But at levels of risk aversion $\gamma$ usually taken to be
realistic, there is a single steady state $\bar{V}$ for $V$.  Values of $V(0)$
less than $\bar{V}$ imply steady shrinkage of $V$ toward zero, which is
inconsistent with optimizing behavior just as in the case with $\psi(V)=\kappa
V$ that we have already discussed.  Values of $V(0)$ above $\bar{V}$, however,
now lead to steady growth of $V$ (and therefore also $P$), with the exponential
growth rate eventually approaching $\kappa-\beta$.  Thus the economy smoothly
approaches barter equilibrium as real balances shrink toward zero over an
infinite time span.  This occurs without galloping inflation---just a steady,
possibly (if $\kappa-\beta$ is small) even slow, inflation that eats
away at the value of real balances.  Since this is true whatever the initial
value of $V$, the initial price level is indeterminate, regardless of which of
the two fiscal rules \eqref{eq:Fpol} or \eqref{eq:FpolBSU} is being followed.

No such cases of price level indeterminacy arise if monetary policy, instead of
fixing $M$, fixes $r=\bar{r}$, while fiscal policy, instead of making $\tau$
respond to $b$, fixes $\tau=\bar{\tau}$.  Then the fixed-$r$ policy fixes $V$
at a constant level by the liquidity preference relation
\eqref{eq:LP}.\nolinebreak \footnote{Note, though, that there will be an upper
bound on feasible $r$'s, given by $\kappa$. An attempt to set $\bar{r}>\kappa$
in this model leads to nonexistence.  The fixed-$M$ policy leads to
non-existence when the equilibrium $r$ it requires, which is $r=\beta$, is too
high relative to $\kappa$.} Then the social resource constraint \eqref{eq:SRC}
determines a constant $C$  and the definition of $V$ \eqref{eq:Vdef} in turn
fixes a constant level of real balances $M/P=\bar{m}$.  The first-order conditions
\eqref{eq:DBSimp} and \eqref{eq:DC}, together with the constancy of $C$ and
$V$, imply that the inflation rate $\dot{P}/P$ is constant at $\bar{r}-\beta$.
This means that we can write the government budget constraint \eqref{eq:GBCr2}
as
\begin{equation}\label{eq:GBCr3}
  \dot{b}=\beta b - (\bar{\tau}+(\bar{r}-\beta)\bar{m})\:.
\end{equation}
This is an unstable equation in $b$, with the unique constant solution
\begin{equation}\label{eq:bbar}
  b=\bar{b}=\frac{\bar{\tau}+(\bar{r}-\beta)\bar{m}}{\beta}\:.
\end{equation}
Given the initial $B(0)$, this unique $b$ determines a unique initial $P(0)$,
which will in equilibrium remain constant.

Ruling out the unstable solutions to \eqref{eq:GBCr3} requires assuring
ourselves that explosively increasing or decreasing $b$ is not consistent with
equilibrium.  The explosively increasing solutions are ruled out by the fact
that they would require individuals to maintain constant consumption despite
unboundedly large real wealth (including the negative component of wealth from
anticipated future taxes, which here remains constant).  This cannot be
optimal, and if individuals thought they were starting on such a path, they
would try to increase their consumption, thereby raising the price level and
bringing initial $b$ back toward $\bar{b}$.

Explosively decreasing solutions would require $b$ at some point to become
less than $m$, though we have assumed that individuals know that they are
constrained not to borrow more than this from the government.  Individuals would see such
paths as infeasible, therefore.  They would involve projecting constant
consumption despite the fact that the individual's income and wealth are not
sufficient to sustain the constant level of consumption.  An individual who
thought he was starting down such a path would cut back consumption in an
attempt to get back on a sustainable path, and this would tend to reduce prices
and bring $b(0$) back up toward $\bar{b}$.

That this model produces much better results from a policy of $r\equiv
\bar{r}$, $\tau\equiv \bar{\tau}$ than from conventionally ``responsible"
policies that set $M\equiv \bar{M}$ and make $\tau$ respond to the level of
real debt does not mean that the conventional policies are wrong.  Uniqueness
of equilibrium can be attained with conventional policies if they are
understood as nonlinear, so that at very high or low price levels policy would
change. The equilibria with explosive inflation can be eliminated by a
``backstop" fiscal policy of taxing to guarantee some minimum real value for
government nominal liabilities.  Furthermore, once such a backstop policy is in
place and understood by the public, it is never invoked in equilibrium.

The cases of non-existence of equilibrium with fixed $M$ that arise with low
$\kappa$ in our example with bounded $\psi$ can be eliminated by a policy that
commits to cutting the interest rate to a fixed level less than $\kappa$ if
real balances reach some high trigger level.  The switch in monetary policy of
course would have to be accompanied by a corresponding switch in fiscal policy.
In this kind of deflationary scenario, the switch would involve committing not
to further increase taxes if deflation created further rises in $b$.  This is
not really a ``backstop" policy, however, since instead of eliminating the bad
behavior of the economy without ever being invoked in equilibrium, it does so
by being invoked with certainty.
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