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\begin{document}
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\title[ISLM]{Whither ISLM}%
\author{Christopher A. Sims}%
\address{Department of Economics, Yale University}%
\email{sims@econ.yale.edu}%

\thanks{\copyright 1998 by Christopher A. Sims.  This material may be reproduced for
educational and research purposes so long as the copies are not sold, even to recover costs,
the document is not altered, and this copyright notice is included in the copies.}%
%\subjclass{}%
\keywords{ISLM,fiscal theory of the price level, Keynes}%

\date{\today}%
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\begin{abstract}
ISLM inhibits attention to expectations in macroeconomics, going against
the spirit of Keynes's own approach.  This can lead to mistaken policy conclusions
and to unnecessarily weak responses to classical critiques of Keynesian
modeling.  A coherent Keynesian approach, accounting for endogenous
expectations, implies very strong effects of monetary and fiscal policy
and leads to greater attention to the role of the government budget
constraint in making the effects of monetary policy conditional on
prevailing fiscal responses, and vice versa.
\end{abstract}
\maketitle
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\section{Introduction}
Keynes considered expectations a central factor in macroeconomic dynamics.
Much of his discussion of them treats them as volatile but exogenous
(``animal spirits"), but in places he elaborates on the importance of
particular types of endogenous expectations.  Since the equations he wrote
down did not include an explicit role for expectations, the ISLM
codification of Keynesian orthodoxy could plausibly ignore them, and did
so.  This not only distorted Keynes's thinking, it ironically weakened
Keynesian orthodoxy in the face of the rational expectations critique. The
standard Keynesian position came to be that
expectations, or at least endogenous expectations, were not as important
as the RE critics made them out to be.  This was a substantively weak
position in itself, and it had the further weakening effect of keeping
Keynesian attention away from developing a strong response to Keynes's new
classical critics.

The fact is that it is possible to develop general equilibrium models with
endogenous expectations and price and wage stickiness that are completely
in line with the way Keynes thought about the economy.  Such models
deliver the Keynesian conclusion that monetary and (under some conditions)
fiscal policy have powerful real effects and that there is no automatic
tendency of the economy toward optimal behavior in the absence of good
monetary and fiscal policy.  The models are not subject to some of the
standard criticisms of Keynesian models as incomplete or internally
inconsistent.  But we do not arrive at these models by modifying or
modernizing ISLM.  They represent a different approach to modeling
entirely.

ISLM continues to be used, especially in undergraduate teaching, because
sophomores and juniors---and their professors---can understand it and
because it claims to give answers to interesting and important questions.
But an appealing, teachable, falsehood is still a falsehood.  Finding
equally teachable simplifications that are not so distorted is not easy,
but we need to proceed in that direction.

\section{Critique of ISLM and ASAD}
The most common intermediate textbook approach to Keynesian modeling has
an investment function that depends on an interest rate and output, but
not explicitly on expected future values of anything. It is part of an IS
sector derived entirely in real terms.  This means the IS curve relates
the \emph{real} rate of interest to output, while of course in the
standard derivation the LM curve relates the \emph{nominal} rate to
output.  The combined IS and LM curves imply a single number---output or
labor---as a solution, reflecting what is known as aggregate demand.
Aggregate demand then feeds in to the Phillips Curve, which generates wage
and/or price dynamics, without any explicit feedback into the ISLM part of
the model.  The rational expectations critique of Keynesian modeling is
often taken to be focused on the Phillips Curve, and sophisticated
textbook modeling often explicitly allows for rational expectations, or at
least long-run rational expectations, in the Phillips Curve.  It is much
less common for textbook modeling to allow for an explicit real/nominal
interest rate distinction\footnote{\citeasnoun{DornFisch} include an
appendix discussing a version of ISLM that distinguishes real and nominal
rates, but the resulting model, as it does not include other
forward-looking aspects of investment and consumption, is ill-behaved.},
and still less so for there to be explicit treatment of the role of
expectations in forming the real rate.

The set of modeling choices that lead to this standard setup seems hard to
justify.  If money illusion, lack of foresight, and decision-making
inertia are important in macroeconomic dynamics, it seems more likely that
they are important in labor markets than in the majority (value-weighted)
of investment and savings decisions.  One would think therefore that the
first place to examine the implications of forward-looking behavior would
be in savings and investment decisions, and that ``irrational" inertial
elements in labor-market behavior might be well worth retaining.

These modeling choices are nonetheless understandable.  It is essential to
Keynesian reasoning about the business cycle that adjustment of the
capital stock is costly, so that a rise in the marginal product of capital
can lead to a sustained rise in investment.  This implies that the
expected growth rate of the relative price of capital goods is an
essential determinant of investment.  There will be no way to write down
the real rate of interest as a function of $K$, $L$, and $I$ based on
production technology and firm optimization alone.  When this fact is augmented
by the need to distinguish real from nominal rates, we are confronted with
an essentially multivariate rational expectations system.  Even today
graduate students in economics are often not taught how to handle such
systems as part of their core training in macroeconomic theory.  The
prospect of explaining such systems to undergraduates with only a shaky
grasp of calculus is daunting.

Besides the fact that the ISLM framework mishandles expectations, there is
reason to regret the mental habit of breaking models into IS, LM, and
AS sectors.  Both for econometric and analytic purposes, the reason for
breaking a model into ``structural" blocks is that it is useful to
consider perturbations in one block while the other blocks hold
constant.\footnote{This is an old point, made precisely by
\citeasnoun{HurwiczID}, for example.}  This may be because we think
historical stochastic disturbances in the separate blocks are more or less
unrelated, because we contemplate taking policy measures that affect one
block but not others, or some mixture of these reasons.  In academic
exercises we do move around the IS, LM, and AS curves independently.  But
what is the basis for thinking such exercises useful?

These blocks do not correspond to the behavior of distinct groups of
economic agents.  In discussing IS, Keynesian modelers do distinguish the
behavior of firms, who control production technology, from that of
workers, who control labor supply and consumption, and this distinction is
clearly justifiable.  But the arbitrage condition relating bond interest
rates to money holdings that goes in to the LM curve is generated by the
behavior of some mixture of firms and workers.  What reason is there to
think that the disturbances to this block will be distinguishable from
those to the IS block?  The same goes for AS.  Despite their names, the
Keynesian AS/AD distinction carries nothing like the microeconomic SS/DD
distinction between technological and taste influences on equilibrium.
Keynesian ``AS" describes price and wage setting behavior, and this
behavior involves the same workers and firms that are making investment
and consumption decisions and monitoring their real balances.

It is standard to assume that the block distinctions do correspond to
components of the economy that can be separately disturbed by monetary and
fiscal policy actions.  Only the IS block contains $G$ and $T$ variables that
are thought of as controlled by a fiscal authority, while only the LM block
contains $M$, controlled by a monetary authority.  Monetary policy
intervention is modeled as a shift in LM, fiscal policy intervention as
a shift in IS.  A Keynesian model that takes endogenous
expectation formation seriously will still contain a block that, in terms
of raw variable counts and which variables appear where, will look in
these respects like ISLM.  Indeed some writers take modern models with
forward-looking components and label the components with ISLM terminology.
But in models with careful dynamics, these equations are differential or
difference equations with forward-looking terms.  They cannot be used to
produce relationships among current levels of variables that correspond to
IS and LM.  Furthermore, the absence of $M$ from the IS block depends on
ignoring the existence of the government budget constraint as a separate
relationship connecting monetary and fiscal variables.

Ideally at this point the paper would go into a discussion of how to get
the ideas of Keynesian economics across to a non-technical audience.
There are existing approaches to this, and I have some ideas of my own,
but it is far from a solved problem.

Instead we proceed directly to laying out a complete Keynesian model with
endogenous expectations, observing in what respects it emerges as
familiar and unfamiliar.

\section{A Coherent Keynesian Model}
The actors in this model are a representative consumer-worker-investor, a
representative firm, and a government that sets fiscal and monetary
policy.  The worker saves in the form of bonds and money and receives
dividends as equity-holder in the firm.  The firm hires workers and
invests to maintain or increase its capital stock.  It borrows and lends
in the same bond market that workers participate in.  Investment and
consumption goods are not perfect substitutes, so the capital stock does
not adjust instantly in response to shifts in the marginal product of
capital.

Both firms and workers are dynamic optimizers.  The distinction between
the Keynesian model as presented here and a classical version of the same
model is that both workers and firms consider employment $L$ not to be
under their direct control, so that firm and worker first-order conditions
(FOC's) with respect to $L$ do not take their places among the model's
behavioral equations.  Instead there is a Phillips Curve and a Markup
Equation.  The former makes nominal wages rise when workers feel
overworked -- measured by when the marginal utility of leisure exceeds the
real wage.  The latter makes prices rise when firms feel that revenues are
not covering costs---measured by when the marginal product of labor falls
below the real wage.

A model like this does not have an elaborate story, based on
forward-looking optimizing behavior, for its price and wage dynamics.  New
Keynesian style models do provide such stories.  The stories are arguably
in disagreement with microeconomic evidence, however.  Actual industries have highly skewed
distributions of firm sizes, and regular turnover of firms, with entry and exit decisions
a key component of competition.  None of these elements is present in the microeconomics
underlying New Keynesian  macroeconomics.  Our objective here
is to show that the somewhat old-fashioned and somewhat more transparent
``disequilibrium" style of modeling can incorporate dynamically optimizing
agents and in the end give results for macroeconomic behavior similar to
those from New Keynesian models.  Both types of model imply strong, quick
responses of real variables to nominal disturbances---in particular to
monetary policy.  In fact, the empirical weakness of these models is that
they imply stronger real effects of monetary policy than clearly emerge in the
data.

The model of this section includes money illusion in the Phillips Curve.
There is no a priori argument that this must be irrational, however, so
long as fluctuations in prices are stationary, as is assumed here.  The
assumption of a real cost to nominal changes in prices, as in New
Keynesian models, is a similarly arbitrary introduction of non-neutrality,
with no greater a priori justification.  Both kinds of assumption would
need to be reconsidered if the models containing them were being used to
project the effects of large and permanent changes in the inflation rate.
It is useful to recognize where we are introducing non-neutrality into a
model and to bear in mind the limitations of non-neutrality assumptions.
But it was one of Keynes's central insights that in this respect a little
ad hockery is not too high a price to pay for maintaining a model's grip on
reality.

\subsection{Consumer}

\noindent\emph{Optimization problem:}
\begin{equation}\label{eq:CICobj}
   \max_{C,L,V,M,B_C} \int\limits_0^\infty  {e^{-\beta t}{\frac{C_t^{\mu _0}
\left( {1-L_t} \right)^{\mu _1}}{\mu _0+\mu _1}}dt}
\end{equation}
subject to
\begin{align}
   \lambda&\text{:} &  PC^*+\dot B_C+\dot M+\tau &\le WL+\pi +rB_C \label{eq:CIClambda}\\
   \psi_C&\text{:} & C^*&\ge C\cdot \left( {1+\gamma V} \right) \label{eq:CICpsiC}\\
   \psi_V&\text{:} & V&\ge {\frac{PC^*} M} \label{eq:CICpsiV}\:.
\end{align}

Note that the demand for money arises out of the $\gamma V$ term in
\eqref{eq:CIClambda}.  This term implies that the budgetary cost of the
consumption $C$ that enters utility is blown up by a transactions cost
factor $(1+\gamma V)$ before it enters the budget constraint (as
$\Cstar$). Larger real balances therefore make possible increased
consumption.

\noindent\emph{FOC's:}
\begin{align}
   \partial C&\text{:}& \frac{\mu _0U} C &=\left( {1+\gamma V} \right)\psi _C
   \label{eq:CICdC}\\
   \intertext{where $U$ is instantaneous utility, the undiscounted integrand in \eqref{eq:CICobj}.}
   \partial L&\text{:} & \frac{\mu_1U}{1-L}&=W\lambda \label{eq:CICdL} \\
   \intertext{(Equation above not used directly.)}
   \partial \Cstar &\text{:}& P\lambda +{\frac{P\psi _V}  M}&=\psi _C
   \label{eq:CICdCstar}\\
   \partial B_C&\text{:}& -\dot \lambda +\beta \lambda &=r\lambda \label{eq:CICdBC}\\
   \partial M&\text{:}& -\dot \lambda +\beta \lambda &=\psi _V{\frac{PC^*} {M^2}}
   \label{eq:CICdM}\\
   \partial V&\text{:}& \gamma C\psi _C&=\psi _V \label{eq:CICdV} \:.
\end{align}

\subsection{Firm}

\noindent\emph{Optimization problem:}

\begin{equation}\label{eq:CIFobj}
   \max_{\pi,I,K,L,\Cstar,B_F} \int\limits_0^\infty  {e^{-\beta t}\phi \left( {\pi _t} \right)dt}
\end{equation}
subject to
\begin{align}
   \zeta&\text{:} &\pi &\le PC^*-WL+\dot B_F-rB_F \label{eq:CIFzeta}\\
   \omega&\text{:}& C^*+\left( {1+\xi {\frac I  K}} \right)I&\le AK^\alpha L^{1-\alpha
   }\label{eq:CIFomega}\\
   \sigma_K&\text{:}& \dot K&\le I-\delta K \label{eq:CIFsigmaK}
\end{align}.

\noindent\emph{FOC's:}
\begin{align}
   \partial I&\tcol & \sigma _K&=\left( {1+2\xi {\frac I  K}} \right)\omega
   \label{eq:CIFdI}\\
   \partial K&\tcol & -\dot \sigma _K+\left( {\beta +\delta } \right)\sigma _K&=\omega \cdot \left( {\alpha \cdot A\cdot \left( {{\frac K  L}} \right)^{\alpha -1}+\xi {\frac{I^2} {K^2}}}
   \right)\label{eq:CIFdK}\\
   \partial L &\tcol & \zeta W&=\omega \cdot (1-\alpha)\cdot A\cdot \left( \frac{K}{L}
   \right)^\alpha \label{eq:CIFdL}\\
   \intertext{Equation above not used directly.}
   \partial B_F&\tcol & -{\frac{\dot \zeta } \zeta }&=r-\beta \label{eq:CIFdBF} \\
   \partial \Cstar&\tcol & P\zeta &= \omega \:. \label{eq:CIFdCstar}
\end{align}

\subsection{Price and Wage Adjustment}
\begin{align}
   \text{Phillips Curve}&\tcol
   &\frac{\dot{W}}{W}&=\eta_L\frac{\mu_1U}{(1-L)W\lambda}
      \label{eq:PhC}\\
   \text{Markup Equation}&\tcol &\frac{\dot{P}}{P}
      &=-\eta_C \log\left(\frac{A\left(\dfrac{K}{L}\right)^\alpha \omega}{W \zeta}\right)
   \label{eq:Mkup}
\end{align}
These equations can only be interpreted as temporary local approximations.
Certainly the expected ``normal" rate of inflation will change over time if
the economy's actual inflation level drifts.  This normal level of inflation
will tend to become the reference point for price adjustment, shutting off, or
at least greatly attenuating, long run effects of changes in the inflation
rate on real equilibrium.  However, as we have already noted, this caveat
applies equally to other, ``micro-founded" models of wage and price
adjustment.  Theories that postulate a cost of adjustment for prices, or that
postulate an exogenously determined contract length or mean time between
opportunities to adjust price, will not be quantitatively stable if the
inflation rate drifts.  It is a fact that contract lengths change when the
inflation environment changes. Whatever the costs of price adjustment are,
institutions will adapt to change those costs if the inflation rate drifts.
The question of which type of potentially unstable description of price
adjustment is best is empirical, and as yet has no clear answer.

\subsection{Government}

\noindent\emph{Constraint:}
\begin{equation}\label{eq:CIGBC}
{\frac{\dot B_C-\dot B_F+\dot M} P}+\tau =r{\frac{B_C-B_F} P}
\end{equation}

\noindent\emph{Behavior:}
Monetary and fiscal policy equations must be specified jointly in a model
like this, as was explained in \citeasnoun{LeeperActPass}.  Monetary
policy can be given the form
\begin{equation}\label{eq:Mpol}
  \dot r = -\theta_1 r + \theta_2 \log M + \eps_M
\end{equation}
and fiscal policy the form
\begin{equation}\label{eq:Fpol}
  \tau = -\phi_0+\phi_1 \frac{B}{P}+\eps_F \:.
\end{equation}

This model behaves as \citeasnoun{LeeperActPass} would suggest:  Existence
and uniqueness of equilibrium requires a combination of active fiscal with
passive monetary policy, or vice versa.  Active monetary policy combined
with active fiscal policy leads to non-existence, while passive monetary
policy combined with passive fiscal policy leads to non-uniqueness.  In
Leeper's definition, ``active" monetary policy increases interest rates
with the price level, or else increases them more than one-for-one with
the inflation rate.  Active fiscal policy commits to a level or path of
$\tau$, the real primary surplus, that does not respond strongly to
$B/P$---in particular with a coefficient less than the steady-state real
rate ($\beta$ in this model).  Passive monetary policy pegs $r$ or
otherwise makes it respond to inflation by too little to make inflation
increases raise the real rate of interest.  Passive fiscal
policy\footnote{Woodford calls such fiscal policies ``Ricardian", though
the Ricardian equivalence proposition does not rest on policy taking this
form.} commits to increasing $\tau$ with $B/P$ by enough so that the
increased interest expense in the budget is more than offset.
\subsection{Can this Model be ISLM'd?}
Because it has firms that make an investment decision, consumers who make
savings and money-holding decisions, and a government that controls interest
rates and deficits, this model has at least the sectoral structure of an ISLM
model.  And indeed we can derive analogues of the elements of the ISLM model.

There is a standard liquidity preference, or
money demand, relation in this model, which emerges if we equate the
right-hand sides of \eqref{eq:CICdBC} and \eqref{eq:CICdM}, then use
\eqref{eq:CICdCstar} and \eqref{eq:CICdV} to eliminate the Lagrange
multipliers.  The result is
\begin{equation}\label{eq:L}
  r=\gamma V^2\:.
\end{equation}

From \eqref{eq:CICdC}, \eqref{eq:CICdCstar} and \eqref{eq:CICdV} we can get an
expression for $\lambda P$ as
\begin{equation}\label{eq:lambdaDef}
  \lambda P = \frac{D_C U}{(1+\gamma V)^2}\:.
\end{equation}
In a model where for simplicity the dependence of transactions demand on $C$
(or on any other measure of aggregate activity) were suppressed, the
right-hand side of \eqref{eq:lambdaDef} would be just the marginal utility of
consumption.

Substituting \eqref{eq:lambdaDef} into \eqref{eq:CICdBC} gives us the usual
forward-looking consumption Euler equation:
\begin{equation}\label{eq:cEuler}
  \frac{-\tfrac{d}{dt}D_CU}{D_CU} = r - \beta -\frac{\dot P}{P} -\frac{2\gamma
  \dot V}{1+\gamma V}\:.
\end{equation}
The only non-standard (for rational expectations models) element of this
equation is the term in $V$ on the right-hand side.  This term is important,
though, as it implies (after substituting for $V$ using the money demand
equation) that there is strong dependence of the rate of growth of $D_CU$ on
$\dot r$ as well as on $r$ itself.

To derive an investment function, we introduce
\begin{equation}\label{eq:Pkdef}
  P_K = 1+2\xi\frac{I}{K}\:,
\end{equation}
the price of capital goods in terms of consumption goods (if they were
traded). Then from \eqref{eq:CIFdI}, \eqref{eq:CIFdK}, \eqref{eq:CIFdBF}, and
\eqref{eq:CIFdCstar} we can derive
\begin{equation}\label{eq:Ieq}
  \frac{\alpha  A\left(\dfrac{K}{L}\right)^{\alpha-1}+\xi\dfrac{I^2}{K^2}}
  {P_K}=r-\beta-\frac{\dot P}{P}-\frac{\dot P_K}{P_K}\:.
\end{equation}
This equation matches the real interest rate in terms of capital goods prices
to the marginal product of savings (i.e., of capital measured in consumption
goods units).

We have arrived at a pair of equations that characterizes household savings
behavior (\eqref{eq:cEuler} and \eqref{eq:CIClambda}), an investment equation,
and a money demand equation.  Is it useful to think of this as a version of
ISLM?  There is no harm in observing that there are parallels between this
system and ISLM, but the difference between this system and the usual
aggregate supply vs. aggregate demand (ASAD) reasoning that emerges from
traditional ISLM are great --- so great, I would argue, that to label this
system ``modern ISLM", or the like, is a barrier to understanding.  Perhaps
equally important, calling a system like this ISLM legitimizes the version of
ISLM taught in undergraduate textbooks, as if it was a simplified distillation
of this kind of model, which it is not.

There are two crucial characteristics of this system that make an ASAD
interpretation of it untenable.  The inflation rate as well as the interest
rate (or equivalently, real and nominal rates separately) enter the
``aggregate demand" portion of the model; and investment depends on the
expected rate of growth of real capital goods prices.  The wage and price
dynamics equations do provide growth rates for $W$ and $P$ as functions of
real variables and the price and wage levels, but even holding $P$ and $W$
levels fixed, there is no possibility of solving the ``ISLM" sectors of the
model for $C$ and $L$, treating these as determined by ``demand", and then
reading off $\dot W$ and $\dot P$ recursively from ``aggregate supply" in the
form of the Phillips curve and markup equations, \eqref{eq:PhC} and
\eqref{eq:Mkup}. The system is fundamentally simultaneous, and fundamentally
forward looking. The price level is predetermined, but the inflation rate is
not and appears in both ``aggregate demand" and ``aggregate supply" portions
of the model. As current levels of $C$ and $L$ change, expectations about
their future paths necessarily change also, which will affect $\dot P_K/P_K$.
Thus we cannot even derive aggregate demand as a schedule connecting $C$ and
$L$ to the inflation rate.  The effects of given changes in the current values
of the interest rate or the government's primary surplus can be drastically
different according to how persistent they are expected to be.

\subsection{Responses to Policy}
With a ``standard" active-money, passive-fiscal policy combination, the
response of the economy to a monetary policy expansion takes the form
shown in Figures \ref{fig:stdNom} and \ref{fig:stdReal}.\footnote{All the
responses shown are based on linearization of the model about its
steady-state.  The calculations were carried out with the matlab program
\texttt{gensysct.m}, available through the author's web page at
\texttt{www.princeton.edu/$\sim$csims}.  The complete set of parameter values
used to generate the responses are shown in the appendix.}
The policy parameters underlying these responses are $\theta_1=.2$,
$\theta_2=.01$, $\phi_0=.4$, $\phi_1=.06$.  An interest rate reduction,
initially of about 1 percentage point, produces an instant 18\% rise in
$M$, humpshaped responses of wages and prices peaking at about 6\% and
2\%, respectively, and immediate expansions in employment, consumption and
investment.  The initial expansion in $L$ is 16\%, roughly the same as
that in $M$.  With this policy configuration, the model is Ricardian, so
that disturbances to the fiscal policy equation affect nothing except the
time paths of $\tau$ and $B/P$.

\begin{figure}[p]
  \centering
  \includegraphics[height=.35\textheight]{imp3_1b.eps}
  %%\rule{0pt}{.4\textheight}
   \caption{Nominal Variables}\label{fig:stdNom}
   \bigskip
  \parbox{.6\textwidth}{\footnotesize Note: All variables in log units except $r$, which is in
   natural units (not per cent).}
\end{figure}

\begin{figure}[p]
  \centering
  \includegraphics[height=.35\textheight]{imp3_1a.eps}
  %\rule{0pt}{.4\textheight}
   \caption{Real Variables}\label{fig:stdReal}
   \bigskip
   \parbox{.6\textwidth}
  {\footnotesize Note: All variables in log units except $I$, which is scaled
   so that the units are \% of steady-state $C$.}
\end{figure}

The model also has a well-behaved equilibrium when monetary policy is
passive and fiscal policy is active.  For this case we set $\theta_2=0$,
$\phi_0=-.4$, and $\phi_1=0$, with all other parameters in the model the
same as for the previous case.  The responses are shown in
Figures \ref{fig:rpegNomM} and \ref{fig:rpegRealM}.  Here monetary
``expansion", while lowering $r$ and raising $M$ as would be expected,
produces contractionary effects on prices, wages, and employment.  This
reflects the fact that, unlike the preceding case, here the fiscal
authorities do not ``back up" the monetary expansion with a tax decrease.
The monetary expansion, by lowering interest rates, lowers the
conventional deficit, or increases the surplus, and thereby starts to
contract the volume of outstanding government liabilities.  This is
deflationary.  With passive fiscal policy, this effect would be offset by
tax cuts as the debt declined.  Since that does not happen here, the
effect of the interest rate decline is contractionary.
\begin{figure}[p]
  \centering
  \includegraphics[height=.35\textheight]{imp351b.eps}
  %\rule{0pt}{.4\textheight}
   \caption{Nominal Variables}\label{fig:rpegNomM}
   \bigskip
   \begin{parbox}{.6\textwidth}
  {\footnotesize Note: All variables in log units except $r$, which is in
   natural units (not per cent).}
   \end{parbox}
\end{figure}
\begin{figure}[p]
  \centering
  \includegraphics[height=.35\textheight]{imp351a.eps}
  %\rule{0pt}{.4\textheight}
   \caption{Nominal Variables}\label{fig:rpegRealM}
   \bigskip
   \begin{parbox}{.6\textwidth}
  {\footnotesize Note: All variables in log units except $I$, which is scaled
   so that the units are \% of steady-state $C$}
   \end{parbox}
\end{figure}

That this seems bizarre or counterintuitive to many macro-economists
probably reflects in part economists' widespread training in ISLM. That an
interest rate increase engineered by the central bank could exacerbate
rather than reduce inflation, is commonly recognized in current policy
discussions, even though it is not mentioned in most (any?) intermediate
macro textbooks. It is particularly likely to occur in economies where the
political ability to adjust taxes to public obligations is weak, as in
many poorer countries.

With this combination of policy reaction functions, a positive disturbance
to the fiscal policy equation has a contractionary effect.  The responses
are displayed in Figures \ref{fig:rpegNomF} and \ref{fig:rpegRealF}.
Money does decline in reaction to the fiscal contraction, and it is a
necessary aspect of the equilibrium that monetary policy ``accommodates"
fiscal policy in this respect, allowing $M$ to drop to maintain its
commitment to a fixed $r$.
\begin{figure}[p]
  \centering
  \includegraphics[height=.35\textheight]{imp352b.eps}
  %\rule{0pt}{.4\textheight}
   \caption{Nominal Variables}\label{fig:rpegNomF}
   \bigskip
   \begin{parbox}{.6\textwidth}
  {\footnotesize Note: All variables in log units except $r$, which is in
   natural units (not per cent).}
   \end{parbox}
\end{figure}
\begin{figure}[p]
  \centering
  \includegraphics[height=.35\textheight]{imp352a.eps}
  %\rule{0pt}{.4\textheight}
   \caption{Nominal Variables}\label{fig:rpegRealF}
   \bigskip
   \begin{parbox}{.6\textwidth}
  {\footnotesize Note: All variables in log units except $I$, which is scaled
   so that the units are \% of steady-state $C$}
   \end{parbox}
\end{figure}

\section{Conclusion}

\begin{itemize}
  \item Keynesian reasoning ought to be essentially forward looking and to
  emphasize expectational factors in savings and investment decisions.
  Traditional ISLM hides and inhibits development of this aspect of Keynesian modeling.

  \item ISLM ignores connections between monetary and fiscal policy that
  are enforced by the government budget constraint.  In many policy
  contexts, this is a major gap.

  \item It remains to be seen whether there is a way to capture these
  aspects of Keynesian modeling in a package as neat and non-technical as
  ISLM, but that should not be an excuse for continuing to make ISLM the
  core of our teaching and informal policy discussion.

\end{itemize}
\newpage
\appendix
\section{Parameter settings}
\begin{center}
\begin{tabular}{r@{: }r@{.}l}
  % after \\: \hline or \cline{col1-col2} \cline{col3-col4} ...
  $\alpha$& 0&3\\
      $\beta$& 0&05\\
     $\gamma$& 0&01\\
     $\delta$& 0&07\\
         $A$& 12&211\\
        $\xi$& 1&0\\
       $\mu_0$& -0&9\\
       $\mu_1$& -0&3\\
    $\theta_1$& 0&2\\
    $\theta_2$& 0&01/0.0\\
      $\eta_C$& 0&5\\
      $\eta_L$& 0&5\\
      $\phi_0$& 0&4/-0.4\\
      $\phi_1$& 0&06/0.0
\end{tabular}
\end{center}
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\end{document}
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