Iv. Fiscal Policy

I turn now to a discussion of the effects of fiscal policy in the
open-economy stock-market model. I am particularly interested in
analysing anticipated, and/or transitory fiscal disturbances, for which
the analysis quickly becomes algebraically cumbersome. To preserve
analytical tractability, I limit myself in this paper to the case in
which o is very large, so that output adjusts instantaneously to
aggregate demand. This permits graphical analysis of the model. My
earlier paper contains some results for the more general case, and the
simulation results in Section V also examine the case in which o is
finite.

Fiscal policy has no effect on the price level in this model,
because, as in the static Mundell-Fleming model, steady state internal
balance is achieved through exchange rate fluctuations with no changes
in the real money supply.9/ The inflation equation (5) then implies
that the price level is fixed even in the short run.

With prices fixed and output equal to aggregate demand, the

economy can be represented with two, rather than four dynamic equations:

ol

rtad yall q-

a

(22) =

o
ol

ac Ye 6-

where all of the parameters are defined as in Section II, except that

the parameters a and Y, should be interpreted as the "a" and "Y" in


39

NOISNVdXa AWVIAS

[

LAV SYVHA PAWIL

| z i
TTT ecemetrrmed

aseo ,,puog pexepul,,

aseo oseg

9Sed |, Jax1BU-yD0}s-3u01Ig,,

(ALVES AVALS FHL WOWd NOILVIAGG INTOUTa)
(AVY ASNVHOX] 1W3y)
NOISNVdX4 AUV.LANOW GALVdIOILNVNN

ANIN FuNSIA



35

In our model, G is about 1.0, so a 19 percent increase in q
corresponds to a change in the level of about .10. Thus, "a" in
equation (1) which is the percentage change in aggregate demand from a
unit change in the level (not the log) of the stock market, is
(.0127.10) = 12.

Finally, we need to make assumptions about the dynamic adjustment
of prices and output. I assume that 6, the price adjustment parameter,
is about 1/3. This implies, for example, that a one percent increase in
the money supply leads to an increase in the price level of .3 percent
at the end of one year, and .5 percent at the end of the second year.
Thus, it is assumed that money exhibits substantial non=neutrality in
the short run. I assume that o is about 6, which implies fairly rapid
adjustment of output to aggregate demand. This parameter was chosen
rather arbitrarily and after some experimentation. It results in an
output peak about one year after the beginning of a monetary expansion.

Application to a Monetary Expansion: With these Parameters, I

similate the model for an unanticipated monetary expansion of one
percent. Figures Six through Nine depict the results. They are
qualitatively very similar. In each ease, the sudden increase in the
money supply leads to a drop of about 0.7 percentage points in the real
interest rate. The decline in interest rates leads to a stock price
increase and depreciation of the real exchange rate. Output increases
transitorily, but as the price level rises, real balances fall, the
interest rate rises, and the economy returns to its original steady

state.


MOOHS TVOSI4 AHL dO LNAWADNNONNV YALAV SUVAA PAWL
oa4 oO S‘l or $10 0
n n
TUT TTT TTT TTT TTT UT TTT TTT TTT TTT TTT TTT TT TTT TT TT
red i
£°0-[— cm
p0-K 4
T°0-[— ‘ 4
rer.
Z0f- 4
bo
sv
S*Of—- |
upuoq pexepur,,
8°Oo;-
aseo aseg .
N
Vy =
ase ,,Jey1eU yO}s Bu0I}S,, Ny
ee alae
ete 4
pq =

(HLVLS KGVALS WOUd NOILVIAGG LNAIUAd)

dlY¥d MOOLS

NOISNVdX4 1VOSI4 GALVdISILNV

AATAML AANDIA


below the steady state implies that the home interest rate is below the
world interest rate. The interest rate differential must be offset by
anticipated appreciation. But, because there is only one stable root in
the fixed-price version of the model, the convergence to the steady
state is necessarily monotonic, which means that the exchange rate can
only converge to its steady state if it starts out by a jump
depreciation that is larger than the steady state depreciation. That
is, the real exchange rate must overshoot. We shall see below that: this
familiar chain of reasoning can break down in a model with slight:.y more

complicated dynamics.

III. Monetary Policy
The first application of the model developed above is to analyze
a change in the money supply. We suppose that at time zero the economy
is in steady state, and is disturbed by an unanticipated increase in the
money supply of m. The new steady state is identical to the old, except
that the price level is increased by i. The dynamics are as follows:
The solution for prices is trivial, because of the simple price

adjustment equation (5). The solution is:

“st
(16) [p(t)-p(0)] = mi-e  )

So, the steady state price level adjusts monotonically from its old
steady state to its new steady state regardless of output dynamics or,

for that matter, anything else.


T2

large eigenvalue (for which I will henceforth use the shorthand phrase "large
eigenvector) is positive, and that the eigenvector corresponding to the small
eigenvalue is negative, and lies between the 6-0 schedule and the q=0
schedule.

The slope of the 8=0 schedule is -a/Y. The slope of the q=0 schedule
is -a/Y-P/YA. With A positive, it follows immediately that the 4=0
schedule is negatively sloped and steeper than the 6=0 schedule. The large
eigenvector has slope ($,-(F+as)). I showed above that, in the good
news case, this is positive (B9b). The small eigenvector has slope
($,-(P+aA)), which is negative (B9b). It can also be written
(-a/Y+($,-F)/YA). We have shown (B9a) that ($,-7) is negative, so
the small eigenvector is steeper than the 8=0 schedule. Since 9, is
positive, it is also obvious that the small eigenvector is less steep than
the q=0 schedule.

This justifies the way I have drawn Figure Three. Now I use
(B17)-(B19) to prove some of the key conclusions that I drew from that

graphical analysis.

In_the bad news case: output is always below steady state between the
announcement and implementation of the fiscal expansion, and is always above
the steady state during the fiscal expansion.

It was demonstrated above that ($,-F)<0<(¢,-F). It follows
by inspection of equation (B19) that output is below steady state between

time zero and T,, and above the steady state between time T, and time 1T,.


54

Appendix A: Monetary Expansion:

We suppose at time zero the economy is in steady state, when
there is an unanticipated and permanent increase in the money supply of m.
The only change in the steady state is an increase in the price level equal
to wm. This appendix provides analytical justification for the discussion
of dynamics in Section III of the main text of this paper. The solution

for (12) can be written:

y(t)-y¥ 1 V(F+5)+adq
a(t)-g ~A/ (FHA) 64(b-5/0)+Ya,
mht “ét
= ke + k,e (A1)
6(t)-5 ~e/) (F+S) (b-S/a)-aa,
p(t)-p io) “2
where = 2 = 6/(hn+8)[(F+5)(b-8/0-cY/5) +a(cq-a4)] (Ala)
and A = (eG-a,) (Alb)

We know that the constants associated with the positive eigenvalues are

zero by the assumption that the economy converges to a steady state, ie

,
that it is on its saddle path. The constants k, and kz are determined by
the requirement that neither the price level nor output can jump at time

zero. That is, y(0) = y, and p(0) = p, Solving for k, and k,,

we have:


52

References

Austin, G.A., and W.H. Buiter (1982) "'Saddlepoint': A Programme for
Solving Continuous=Time Rational Expectations Models,"
University of Bristol Working Paper No. 82/132, (November )

Blanchard, Olivier J. (1981) "Output, the Stock Market, and Interest
Rates," American Economic Review 71,1 (March) 1327143

(1984) "Current and Anticipated Deficits, Interest Rates, and
Economic Activity," European Economic Review 25,1 7727

Branson, W.H. and W.H. Buiter (1983) "Monetary and Fiscal Policy with
Flexible Exchange Rates," in J.S. Bhandari and B.H. Putinam
(eds.) Economic Interdependence and Flexible Exchange Rates,
MIT Press, Cambridge, MA

o>oes A, Fraga, and R.A. Johnson (1985) "Expected Fiscal Policy and the
Recession of 1982," International Finance Discussion
Paper No. 272, Federal Reserve Board (December )

Burgstaller, André (1983) "Contractionary Effects of an Anticipated
Fiscal Stimulus in the Flexible Exchange=Rate Economy,"
manuscript, Columbia University.

Cardoso, Eliana A. (1983) "Exchange Rate Dynamics and the Stock Market,"
manuscript, Boston University

Dooley, M. and P. Isard (1986) "Tax Avoidance and Exchange Rate
Determination," manuscript, International Monetary Fund.

Dornbusch, Rudiger (1982) "Exchange Risk and the Macroeconomics of
Exchange Rate Determination," in R. Hawkins et. al. (eds.)
Internationalization of Financial Markets and National
Economic Policy, JAI Press ”

eee toT (1986) "The Dollar and the Exchange Rate System," manuscript,
Massachusetts Institute of Technology

Fama, Eugene F. (1981) "Stock Returns, Real Activity, Inflation and
Money," American Economic Review 71,4 (September) 545-565

Fischer, Stanley (1984) "Investment and Lagged Q," manuscript,
Massachusetts Institute of Technology

iaaianel and Robert C. Merton (1984) "Macroeconomics and Finance, the
Role of the Stock Market," manuscript, Massachusetts Institute
of Technology


58

We begin the analysis of (A9) by making two observations; first,
the solution is the sum of two declining exponentials, so that the time
path for the real exchange rate can have at most one "hump", that is,
one point at which the time derivative equals zero. Second, because
both output and the price level are sticky, the home interest rate
necessarily falls below the world rate at time zero, which means that
just after the monetary expansion (and after the exchange rate jumps)

the exchange rate has to be appreciating. Formally:

ic} = (r-r) te

t-0 = -m (h+8) <0 (A10)

0

These two facts allow us to narrow the possible time paths for

@(t) down to three, illustrated below:

Figure A2

ol

We begin to expand upon these general observations by figuring out
what happens at time zero, just after the increase in the money supply;
does the exchange rate initially depreciate (the standard result) or

does it appreciate? From (26), we have:


62

parameters that enter into condition (A14a), and it may be that A
depends on them in some way that makes (A14a) impossible. The easiest
way to prove that (B) or (C) can indeed occur is to construct an example
of an economy for which (Al4a) holds. This turns out to be possible,
and in fact holds for the base case of the empirical section of the

text, so the result is of at least theoretical interest.

4. Stock price dynamics

Using (A1), (A3), and (A4), we can derive the solution for the

time path of stock prices. It is:

oo. ~ ~ = St .
Ca(t)-q] = B | (ara dvs dyradale 41 55(p-6/0)+¥a, Je 8 (a16)
(rtd)

This is not particularly revealing, so we begin by establishing

the direction of the jump at t=O. Using (A16), we obtain:

fa_ | (eqray )L¥(r+8)+a6q]

Ca(o)- ql = 5 G + [8q(b-S/0)+¥a4 ] (a17)
r+h)
= HWS)
comm (A1T*)

where W(6) is defined implicitly in (A17).
As with the exchange rate, we have three bits of information about

Q(6) and W(6).


dependence between the real exchange rate and real balances. In this
ease, a fiscal expansion leads to a transitory increase in output
because the induced appreciation reduces the CPI, and raises real
balances. Another factor that would lead to short-run output effects
from a permanent, unanticipated fiscal expansion is sluggish adjustment
of net exports to the real exchange rate. However, in any case equation
(11) holds as a steady state relation.

1/ This distinction is discussed in more detail in Blanchard (1981) and
an earlier version of this paper.

8/ I discuss the analytical solutions for output, the real exchange
rate, and the stock price in Appendix A, available from the author.

9/ This result depends upon the money demand assumption that I have
adopted. See footnote 6.

lo/ In Figure Two I have considered only those cases in which the
positive roots are not complex. Appendix B discusses the assumptions
under which the roots are real. Section V shows that, for plausible
parameter estimates, the qualitative properties of the model are not
much affected when the roots are complex.

11/ See footnote 6 for appropriate qualifications.

jes See Appendix B for a more comprehensive discussion. In the case of
real roots, there are actually three distinct subcases, of which I
describe only two in the text of the paper. In the third subcase
described more fully in Appendix B, an anticipated fiscal expansion is
necessarily contractionary, as in the bad news case. The dynamics for
this case look like those of Figure Four, except that the curve ‘.abelled
(A) cuts through the SS, curve from below the 9=0 curve.

13/ To interpret this condition, consider a one-period, unit increase
in output. The stock price would, through interest rate and proit
effects, increase by =A, which would, in turn, raise aggregate demand by
zak. The one-period, unit increase in output would raise the real
interest rate, and lower the real exchange rate, by c. This, in turn,
would lower aggregate demand by cY. If =aA>cY, then the favorab..e
effect on aggregate demand from the stock market increase would be
larger than the unfavorable impact of the real exchange rate
appreciation.

14/7 In the closed economy case analysed by Blanchard (1981), an
anticipated fiscal policy expansion was necessarily expansionary in the
"good news" case. There are two sources of difference between his
analysis and that of this paper. First, he analysed fiscal policy
shocks under the assumption of fixed prices, so that output and profits
were permanently increased by the fiscal expansion. Second, with no
foreign sector, there was in his model no possibility of crowding out
through net exports that is an important part of this model.


22

Figure Three
Dynamic Adjustment to a Future, Transitory Fiscal Expansion
Bad News Case

al


40

In the base case, output peaks about 0.62 percent above the
steady state, roughly one year after the monetary shock. The increase
is only 0.47 percent in the "indexed bond" case, and it is 0.67 percent
in the "strong stock market" case. Thus, the stronger the impact. of
output on the stock market, the larger the impact of monetary policy on
output.

This is because the cases with stronger output-profit effects
result in larger stock price increases. In the "indexed bond" case, the
"stock price," rises only 1.2 percent. (This should be interpreted as a
decrease in the long real interest rate on an indexed perpetuity of 1.2
percent, or about .10 percentage points.) In the "base case", the stock
price jumps 1.9 percent, and in the "strong stock" case, the stock price
Jumps 2.1 percent.

The higher is output, the higher is the real interest rate and
therefore the less is the exchange rate depreciation induced by tre
monetary expansion, In the "indexed bond" case the real exchange rate
depreciates 1.5 percent, and then gradually appreciates to the steady
state. In the "base case," the initial depreciation is 1.35 percent,
and in the "strong stock" case, it is 1.30 percent.

Thus, for the chosen parameter values, the impact of introcucing
a stock market is quantitative, not qualitative. In particular, while
the stock market tends to reduce the extent of the real exchange rate
overshooting after a monetary expansion, it does not lead to the
"reverse overshooting" possibility indicated in the theoretical section.
It is somewhat interesting to note that this is not because the stock

market is too unimportant, in particular, condition (21) does hold for


val

where A is the radical in equations (B7a) and (37b), D is the length of the
fiscal expansion (T,-T,), and the carat denotes a deviation from the original
steady state.

Now we are in a position to prove (B12c). Using (B17) and (B18), we

can write the slope of the equilibrium trajectory in (q,6) space as follows:

O-

40 | | (e/YAIL-61(¢,-(r+ad)) + 62(d27(rtad))]
{9 ket, og tet, [ea/AI-0,+62)

Using the fact that $,=$,+A, this expression simplifies to:

as =f
dq =T, nN

This is greater than the slope of the 6=0 schedule if (e/A)>(-a/Y), which,

with A regative, occurs if (aA+cY)<0.

Discussion of the Analysis in the Text:

We can use these results to explain the graphical analysis and formally prove
some key assertions made in the text of the paper. The discussion is simple
for the "bad news" case, but in the "good news" case there are three subcases

to be ccnsidered separately. We begin with the "bad news" case.

Bad News: Case:
First, I discuss why Figure Three is drawn as it is. The key
features: of Figure Three are that the q=0 schedule is negatively sloped and

steeper than the 6=0 schedule, that the eigenvector corresponding to the


on capital stocks located in different countries. I do, however,
present a model that is capable of answering questions of a
macroeconomic nature related to changes in the expected profitability or
riskiness of a country's capital stock, and which accounts for the link
between output, profitability and asset prices.

The reader is forewarned that the following analysis becomes
somewhat taxonomic at times, with the results depending upon which of
several cases are being considered. I try to avoid simply listing a
series of cases, but to some extent it is necessary to distinguish
between cases that lead to qualitatively different behavior. The reader
may find it helpful to bear in mind that the multiplicity of distinct
cases results primarily from two sources. First, the effect of an
increase in output on the stock market is uncertain, because higher
outfut leads to both high profits and high interest rates, so we must
distinguish between cases in which. output is "good" for the stock
market, and others in which it is "bad". Second, we must occasionally
distinguish between those cases in which the stock market or the real
exchange rate are more influential (in a sense that is defined more
precisely below).

The paper is organized as follows. In Section II the model is
outlined, and its general properties discussed. In Sections III and
IV the implications of the model are further explored by using it to
analyze the impact of changes in monetary and fiscal policy,
respectively. In Section V the analysis is given some empirical content

by simulating the model for parameter values that might roughly


74

place. (C) The stock market is necessarily above the steady state before
implementation of the fiscal expansion if there is a long delay before the
expansion will happen.

(A) In the bad news case, A>0. The negativity of (B17) for T,<t<T,
follows from this and the fact that $.>6,.
(B) For given D, consider the case in which (T,-t) goes to zero.

Then, we can write (B17) as follows:

Q(t)=|—-][(1-e )- (Ire )J =/—]le -e ]

ga ~o,D “2D BA) -o2D oD
A A

With A>O0 and $,>$,, this is necessarily negative.

(C) For given D, consider the case in which (T,-t) goes to infinity.
Then, q goes to zero, (which just implies that a fiscal expansion that's
very far into the future has essentially no impact on today's equilibrium.)

To determine the sign of Q(t) as (T,-t) approaches infinity, write (B17) as

follows:
7 BA] ~$,(T,-t) ~o,D “2D —(62791 (Ty -t)
q(t)=+ —~-Je [(1-e  )- (1-e )e ]
A

As (T,~t) goes to infinity, the second term in the square brackets goes to

zero, and it is obvious that q(t) is positive.

Good News Case:
I turn now to the good news case. I confine myself to the case in
which the positive roots 9, and $2 are not complex. This requires that:

Pr is either "big enough" or "small enough," as specified in (B8a) and


73

in_the bad news case: the real exchange rate is appreciated relative
to the original steady state both in anticipation of and after implementation
of the fiscal expansion.

It was demonstrated above that (9,-(P+aA))<0<($,-(Ftad)).
The negativity of the real exchange rate for t<T, then follows from

inspection of equation (B18). For T,<t<T,, first define:

u

23 = (oy-(Ptad)) i= 1, 2

vt

In this case, z,<0, z,>0. Differentiate (B18) with respect to T, to obtain:

~biT. “ba?
G(t.) 8 1 Cone -e )- ave) <0
dT, YA

(Tit) i=, 2

where I used the fact that z,=Z,+A, and $,=$,+A. So, as T,-t increases, the
real exciange rate decreases (a fact that is also apparent from Figure Three
in the text.) So, if the real exchange rate is below the steady state when
T, approaches t, then it will be even further below if for T, larger than t.
So, consider the limit of (B18) as T,+0. This is:

tim 28). 8 4,2,-9,.2,1/6, <0

T,70 treet te YA

where I rave used l'Hospital's rule and omitted some algebra. This means
that, for very small (T,-t) the real exchange rate is below the steady state
which, combined with the derivative condition above, establishes that the

real exchange rate is below the steady state for all t less than T,.

In

=aathe bad news case: (A) The stock market is necessarily below its
steady state after implementation of the fiscal expansion. (B) The stock
market is necessarily below the steady state before implementation of the
fiscal policy if there is a short delay before the fiscal expansion will take



inconsistent with the assumption of saddlepoint stability, so we arrive at a
contradiction. Thus, Case 4 is inconsistent with the assumptions of
saddlepath stability and real roots, so I rule it out.

Now I examine cases 1-3 individually. The purpose of the discussion
is to justify the graphical analysis used in the paper, and to prove some of
the key assertions made in the paper.

Good News Case 1: [adA+cY<0, f+aA>cY] This is the Case 1 of the
paper, and corresponds to Figure Four. The key features of Figure Four are
(i) the eigenvectors are positive, and (ii) the trajectory labelled (A)
approaches SS, after passing above the b=0 schedule. From the geometry, it's
obvious that (ii) can happen only if the slope of the equilibrium trajectory
at SS, is greater than the slope of the 8=0 schedule, It was shown above
that this can only happen if aA+cY<0. Since that is assumed in this case, it
was correct to draw the trajectory (A) as in Figure Four. As for the
positive eigenvectors, that is guaranteed ‘by the assumption that
Frad>cy.

Now I prove some of the key assertions derived from Figure Four in

the text of the paper.

In_the good news case 1: (A) If the delay between announcement and
implementation of the fiscal expansion is large enough, then output falls in

anticipation of the fiscal stimulus, (B) If the expected duration of the
fiscal stimulus is long enough, then output falls in anticipation of the
fiscal stimulus, (C) If the expected duration of the expansion is short
enough, and the delay between enactment and implementation is short enough,
then output increases in anticipation of the stimulus, (D) After the fiscal
expansion is implemented, output is above the steady state level.

(A) Take the limit as T,=(T,-t) goes to infinity. Then, from (B19),

output is:


33

In equations (25) and (26) I present estimates of the sensitivity
of real corporate profits (deflated with the GNP deflator) to eyclical

fluctuations in real output, where Y is real GNP and Y is potential

real GNP:

(25) log(m) = .31 + .65 log(¥) + 4.5 log(y/¥) 1948 :1-1985 :3
(0.3) (4.1) (14.5) p = .935

(26) log(m) = -7.5 + 1.61 log(¥) + 4.5 log(y/¥) 1960 :1-1985 :3
(1.2) (2.1) (11.3) p = .976

The estimated relationship between real profits and potential
output is somewhat sensitive to the time-period of estimation, inclusion
of a trend and lagged variables, and estimation in differences.

However, the estimated elasticity of profits with respect to cyclical
fluctuations in output, which is the parameter of interest, was very
robust to all the variations I tried.

With J=0, it follows that a, is the share of steady state
profits in steady state output. Corporate profits in late 1985 were
slightly over 7.5 percent of ‘out put.17/ Equations (25) and (26)
Suggest, then, that the steady state share of profits in output, a,, is
roughly .085. The elasticity of profits with respect to output is
&,/a9, which assuming the elasticity is 4.5, implies an estimate for a,
of about 0.4." This will be my "base case," below. In the "indexed
bond" case, I will set a, equal to 0. In my "strong stock" case, I will
set a, equal to 0.5

I assume that the required real rate of return on equity is about

-085. This is above the historical rate of return on equity, but real


19

equation (1) divided by "b." This redefinition is not substantive, it
merely simplifies the notation. I show in Appendix B that, under

condition (15), there are two positive roots to the characteristic

equation for the Jacobian in (22), so that the saddle "path" is a point

in (6,q) space. The dynamics are shown graphically in Figure Two. 1o/

Figure Two
Bad News Good News Case 1 Good News Case 2
t) () .

. \

N a \

[ BB

OZ i
\ \
60 q “4 q oO

The 6=0 schedule is also the locus of points for which output
equals steady-state output. This is because the 8=0 schedule is the
locus of points for which r=r*, With a constant price level and money
supply, the domestic real interest rate depends only upon real output.
Thus, the interest rate is above the world rate when output is above the
steady state level, and conversely.

An increase in the real exchange rate raises net exports, and
aggregate demand. To keep output and the real interest rate at their
steady state, an increase in @ must therefore be offset by a decrease in

the stock price. Thus, the 6=0 schedule is downward sloping. Above it,


Good news case: We can characterize the "bad news" economy's
reaction to an anticipated fiscal expansion as follows. The real
exchange rate must appreciate during the future fiscal expansion.
Because asset markets are ‘forward-looking, it jump-appreciates part of
the wey upon announcement of the fiscal expansion. This reduces net
exports and, because the fiscal stimulus has not yet arrived, results in
a recession until the fiscal expansion is implemented. When the future
fiscal. expansion is announced, the stock price can either fall
(intensifying the anticipatory recession) or rise (offsetting the fiscal
expansion). It cannot, however, rise enough to reverse the impact on
aggregate demand of the exchange rate appreciation. (This is easy to
understand. The stock price only rises when the favorable impact of the
initial recession overwhelms the unfavorable effect of the future boom.
Thus, an increase in the stock market is inconsistent with an expansion
of output between period T, and T,.)

All of these results can be reversed in the "good news" case. A
future fiscal expansion can lead to a transitory appreciation, as in the
"bad news" case, or a jump depreciation. Output can either fall or rise
in anticipation of the fiscal expansion, and in the case in which output
rises it can be due either to an investment boom associated with high
stock prices, or to an increase in net exports associated with real
exchange rate depreciation. Unlike in the "bad news" case, there can be
a temporary period after the fiscal expansion is implemented in which
the economy goes into recession.

The task of the following discussion is to bring some order into

this list of possibilities, to provide greater insights into the.


2i

good news case, and show that some of the propositions that have become
commenplace in the literature can, under some circumstances, be
reversed.

Bad news case: Figure Three illustrates the dynamic adjustment
path to an anticipated, transitory fiscal expansion. Before and after
the ®iscal expansion, the economy is governed by dynamics summarized in
the upper schedules, and during the fiscal expansion it is governed by
the dynamics summarized by the lower schedules. In the case of an
unanticipated, permanent fiscal expansion, the econony jumps from SS, to
SS,, and remains there. Thus, the only effect is on the real exchange
rate and, therefore, the composition of aggregate demand.11/ Output,
interest rates and the stock price are unaffected.

Anticipated or transitory fiscal expansions lead to more
interesting asset price dynamics, which we now explore, By ruling out
anticipated asset price jumps, we know that at time T,, when the fiscal
expansion ends, the economy must be at point SS. This means that
during the fiscal expansion, (between T, and T,), the economy must be
somewhere on the curve labelled (A). This is the locus of points for
which the economy's dynamics (as influenced by the fiscal expansion)
lead through the point SS,. Where on this trajectory the economy will
be at time T, depends upon the length of the fiscal expansion, (T2°T,).
If the expansion lasts for a very long time, the economy must be very
close to SS, at time T,. If the expansion is very short, the economy

must be somewhere near SS, at time T,.


34

interest rates have, for the past several years, also been substantially
above historical levels, Thus, the steady state value of the stock
market, 9, is (.085/.085) or 1.0 times steady state real output.

A reasonable rule of thumb for the U.S. is that it takes a 12
percent real depreciation to improve the trade balance by one percent of
GNP. (This is consistent with Dornbusch (1986), Dornbusch and Frankel
(1985), and the results of the Federal Reserve Board's multi-country
model.) This implies that a one percent increase in the real exchange
rate increases net exports, and therefore aggregate demand, by roughly
-085 percent of GNP, or $3.5 billion. So, Y in equation (1) is set at
+085.

There is less empirical evidence on the impact of the stock
market on aggregate demand. With no pretentions that these estimates
are definitive, I offer the following approximations. Summers (981)
estimates that a 10 percent increase in the stock market raises the
ratio of investment to the capital stock by about .009. The ratio of
the capital stock to output is about 0.8, so a 10 percent increase in
the stock market raises investment by about 0.72 percent of GNP.

In our model, the stock market is about 1.0 times steady state
output, so a 10 percent increase in the stock market would increzse
wealth by .10 times output. If we assume that the marginal propensity
to consume out of wealth is about +05, the implied change in consumption
demand is about 0.50 percent of output. Thus, a 10 percent increase in
the stock market is assumed to raise aggregate demand by roughly 1.2

percent of output.


16

If this reversal of the interest differential is large, and
oceurs quickly enough, then immediately after the monetary expansion,
the long real interest rate actually rises, even though the short rate
necessarily falls. As summarized in equation (8a), with no change in
the steady state real exchange rate, this increase in the long, real
rate to a level above the foreign interest rate generates a jump
exchange rate appreciation. Hence, if (21) holds and price adjustment
is slow enough, the rise in the long, real interest rate induced by an
expansionary monetary policy creates an exchange rate appreciation. (In
Section V the plausibility of condition (21) being satisfied is
examined.)

This "reverse overshooting" scenario thus requires a rapid, large
increase in output which, because the real exchange rate has
appreciated, requires an increase in the stock market that is both large
and effective in increasing aggregate demand. It is easy to see hcw
these requirements relate to condition (21).

I have already noted that a large a, implies that output
expansion will have a large effect on the stock price, and that a large
value for "a" implies that an increase in the stock market will have a
large effect on output. (21) is also more likely to hold if A is large,
which is to say, if output can adjust rapidly. This is necessary to
ensure that the real interest differential is quickly reversed. A small
b, which is to say a large 8, also increases the likelihood that (21)
will hold. This is because, through the simple Keynsian multiplier
process, it reinforces the positive effect of output on aggregate demand

that is at the center of the intuitive explanation offered above.


ie)

(B8b). In terms of the phase diagrams, it requires that the eigenvectors be
steep enough, whether positively or negatively sloped.
I begin by splitting the parameter space into four regions, depending

upon the sign of (adtcY), and of (F+aA-cY). I denote the cases as

follows:

ad+cY<0 abt cY>0
(r+ad) >cY Case 1 Case 3
(r+ab)<ey Case 4 Case 2

Case 4 will be ruled out by the assumption of real roots and
saddlepath stability. Case 1 is the one in which the possibility of an
investment-led anticipatory expansion exists. Case 2 is the one in which the
possibility of a net export-led anticipatory boom exists. In Case 3, (not
discussed in the text of the paper), neither possibility exists.

First, I demonstrate that Case 4 can be ruled out. With

F<(cY-ad), the assumption of real roots implies (B8b) that

B20) P < (eY-ad) - 2v-abeyY

Suppose that (adt+tcY)<0. Then, adding aA+cY to both sides of (B20), we
obtain:

B21) PradtoY< 2(cY-¥=aley )

By assumption, -aA>cY, which implies that the right side of (B21) is negative

which, in turn, implies that the left side is negative. But this is


60

Las)

Figure A3:
Q and Q as Functions of 6
as),
Q(s)
(8) 2(6) 2(8)
ty) él 6% a éL 6* é
(5) Q(8)
Note that 2(6) is always greater than zero when 6 is less than A, and
vice versa, and that when 6 equals 4, both Q(6) and 2(6) are equal to
zero. This is the diagramatic correspondent of facts (1) and (2) above.
Fact (2) was discussed in the section on exchange rate dynamics, and
also implies that 2(A)=0. That Q(\)=0 is trivial to show; note that 2

= Q (=0) when A=6.

(3).

value of 6 for which Q and Q are of opposite signs.

I have also drawn all of the Q() schedules concave, which is fact

This fact is easily verified by differentiating Q(6) twice.

Now, consider case (A).

In this case Q(0) > 0. and there is no

This means that the

exchange rate necessarily depreciates at the moment that the money

supply is increased.

The condition for case (A) is:


Note that when a, is zero, the "stock" looks exactly like an
indexed perpetuity, so that the model reduces to a standard open-
economy IS-LM analysis, in which the interest rate that affects
aggregate demand is the real rate on an indexed consol. Thus, a, is a
natural measure of how different the present model is from those that,
have been analysed in the past. Consequently, it will be a key
parameter in the analysis that follows.

The steady state: Steady state output is by assumption
exogenously given, and the steady state interest rate is the foreign
interest rate, which is also exogenously given. From (7), the steady
state stock market is the present value of steady state profits,

discounted at the steady state (foreign) rate of interest.

(10) Q=a/r = (a, + ay)/r

The steady state price level was defined in equation (6). Note that
there is no allowance in this simple framework for non-zero monetary
growth and inflation; extending the model to incorporate this
possibility would be straightforward. Finally, the steady state real
exchange rate is determined by imposing equilibrium in the goods mar<et.
In steady state, output and aggregate demand must be equal to the
full-employment level of output. Imposing these equalities, and

rearranging (1), we obtain:

(11) 8 = (by - aq -g)/Y


31

rate. If this recession lasts long enough, its depressing effect on the
time-T, long real interest rate will be larger than the effect of high
real interest rates between time T, and T,, so upon announcement of the
future fiscal expansion the long real interest rate will fall, rather
than iricrease, Thus, by equation (8a), the real exchange rate must
depreciate. We are, by the assumption that ad+cY>0 (and cY>r+ad, see
footnote 15), in a case in which the effect of the exchange rate on
output is strong, so this exchange rate depreciation leads to a
transitory increase in output. As time passes, the stock price
declines, and eventually the real exchange rate starts to appreciate,
and the economy passes through a period of recession until the fiscal

expansion is implemented.
V. Simulation results

The previous sections explored the theoretical properties of the
open-economy stock-market model. It was demonstrated that the
qualitative behavior of the model depends, inter alia, upon the relative
importance of interest rate versus stock market effects on equity
valuation, exchange rate versus stock price effects on aggregate demand,
and relative speeds of adjustment of output and the price level.

This section makes a preliminary attempt to determine the
empirical importance of the theoretical possibilities delineated in
sections III and IV. The intention is not to put forth a realistic
forecasting model of the United States economy; no four equation dynamic
system can fulfil such an ambitious goal. Rather it is to see if the

introduction of a stock market significantly alters the response to


67

To prove (B9a), use (B7a), and rearrange the term under the radical
to obtair:
Bl0a)  ¢,-P = %& [(adtoy-r) - Y(abteY-r)*+4rad

In the bad news case, A is positive, so the radical is larger in absolute
value than is (aAt+cY-F). Thus, ($,-PF) must be negative. As for

go, we have:

B10b) dar = % C(adtoY-r) + Y(ad+eY-r)**4rad J

Again, the radical is larger in absolute value than the first term in
parentheses, so (¢,-F) is necessarily positive.

(B9b) is proved by exactly the same logic, where:

Blla) 0, 7(Ptad)

¥% C(eY-(r+ad))- Y(CeY-(rtah)) **4e¥ad ]

Bl1b) 6,-(r+ad)

¥% [(eY-(rtad))+ YCeY—(r+ab)) +40 Vad

wu

(B9¢c) holds trivially, because in the bad news case A>0. (B9d) holds
because she term under the radical in equation (310) is by inspection
positive,

‘Turning now to the good news case, we will need the following facts:
B12a) ‘by and $2 are less than (Ftad) if (F+aA)>cY, and conversely
B12b) , and $, are less than P if (aA+cY)<f, and conversely.

B12c) The slope of the equilibrium trajectory in (q,6) space as it passes
through the original steady state, SS,, is greater than the slope of
the @=0 schedule if (ad+cY)<0
To prove (B12a) and (B12b), consider equations (B10) and (B11). With

A less tian zero, the term in parentheses is larger in absolute value than is


69

original steady state minus g/Y. So, we can write the solution to the

problem as follows:

git bat
- ke + k,e t<Ty
B14) [a(t)-q] =
git oot
ke + ke T,<t<T,
dit bat
_ 8,k,e + S,k,e t<T,
B15) Ce(t)-e] =
git bat
8,k,e + S,k,e —g/Y T,<t<T,

where the barred values denote original steady states, ie, the steady state
in the absence of the fiscal expansion. After T,, when the fiscal expansion

has ended, both q(t) and 6(t) return to their original steady state values.

Four conditions determine the four constants, k, through k,: neither
the stock market nor the exchange rate can jump at time T,, when the fiscal
expansion begins, nor can either jump at T,, when the fiscal expansion ends.

These conditions imply:


70

git. bal oT, bal
Bl6a) k,e + k2e = k3e + kye
oT, b2T oT, bol
B16b) s,k,e + s,k,e = 8,k3,e + s,kye - B/Y
oiT2 baT2
Bi6c) kse + kye =0
oiT2 baT2
B16d) = s,k3e + sokye - g/Y =0

Solving (316a) through (B16d) for k, through k,, and substituting
these constants into (B1), (B14), and (B15), we obtain solutions for the time

path of output and asset prices:

A “1D -$,(T,-t) —2D -$2(T,-t)
S21 [(1-e de - (Ire de ] t<T,
A
BIT) q(t)=
gh] oa (Tent) ~o2(T2-t)
= =| [-e +e J T,<t<T,
A
g | - ~$,D -¢,(T,-t) . “2D ~b2(Ti-t)
—= | [(oi-(r+ad))(1-e ee — (da-(r+ad))(1-e de
YA
B18) 0(t)= .
g . -$,(T2-t) _ -b2(T2-t)
—= | [-(¢.-(r+ad))e + (g2-(r+ad))e - AJ T,<t<T,
YA
3 | -. 7D -o,(T,-t) -. ~b2D ~62(T,-t)
=| Cldi-r)(i-e de - (gar)(1-e de ] t<T,
A
P19) 9(t)e
3 | _ 71 (T2-t) _ 72 (T2-t)
_ [-(¢:-r)e + (o2-rie j 1, <t<T,

t<T,


28

somewhere on curve (B), which lies entirely below the 6=0 schedule.
Thus, if the fiscal expansion is expected to last long enough, output
necessarily falls before implementation of the expansion.

On the other hand, suppose that the fiscal expansion is expected
to last for a shorter period of time, so that at time T, the economy
lands at point (b). Then the economy must be somewhere on curve (C)
between T, and T,. If the delay between announcement and implementation
is long, then at time T, the economy jumps to a point on (C) that is
close to SS,. These points lie below the 6=0 schedule, which indicates
that output falls at time T,. If, however, the delay between
announcement and implementation is short enough, the economy jumps at T,
to a point on (C) like (c), which is above the 6=0 schedule, indicating
that there is an increase in output at time T,. Thus, if the fiscal
expansion is expected to be fairly short, the delay between announcement
and implementation is short, and aA+cY<0, then output increases upon
announcement of a future fiscal expansion.14/

This reversal of the "anticipatory recession" result occurs for a
perfectly intuitive reason. Stock-holders look forward to the increase
in output during the fiscal expansion, which is good for the stock
market. The shorter the fiscal expansion, the larger the output
increase, and the closer the fiscal expansion is, the more it counts in
investors' present-value calculations. In addition, if the expansion is
short, then the real interest rate only increases for a short period of
time, which implies that the long real interest rate does not increase

much, and therefore that the real exchange rate does not appreciate much.


80

Thus, if the delay until the fiscal expansion takes place is short enough,
then the stock price is necessarily above the steady state.
(B) When T,<t<T,, q(t) is positive by inspection of equation (B17).
Good News Case 2: [aAt+cY>0, F+ad<cY] This is Case 2 of the
text of the paper, and corresponds to Figure Five. The important assumption
in Figure Five is that the eigenvectors are negatively sloped, and steeper
than the 8=0 eurve, I first prove that aA+cy>?P in this case:
1. ad+tcY>0 + eY>-ad

2. F<cY-aA + F<eY-ad-2¥-adeY by the assumption of real
roots. Adding 2aA to both sides and rearranging, this implies:

3. adtcY> F+2(cY+ah)>F

It was shown above that this implies that ($4-F)>0 which in turn implies
that j-(F+ad)>0. The fact that ($4-7)>0 implies that the
eigenvectors are not only negatively sloped, but also steeper than the 8=0
schedule.
Now I prove some of the assertions made in the text about this case,
In the good news case 2: If there isa long enough period of time_

before the anticipated fiscal expansion will be implemented, then output
increases. If the delay before implementation is short, then output must be

below steady state.
First take the case in which (T,-t) is very large. Then, (B19) can

be written:

- “oiTy _ ~g,D _ ~b2D ~(62761)T,
B34) y(t) = (g/A)e [(dier)(i-e =) = (g.-P)(1-e De ]

As (T,-t)=T, goes to infinity, this becomes positive because (¢,-F)>0.
If instead we take the limit of (B34) as T,70, we obtain:

. _ dD _ “2D
B35) f(t) = (g/A) C(@i-P)U-e) - (be-F)(I-e )


constrained, so that current income, and not just the capitalized value
of lifetime income, determines consumption. The real exchange rate
determines net exports through relative prices and, conceivably, a
wealth effect, the sign of which would depend upon the currency
denomination of assets held by domestic investors relative to the weight
of foreign goods in the consumption basket. Here I simply assume that
an exchange rate depreciation, an increase in 6, raises aggregate demand.
Output dynamics: Output is assumed to adjust to the discrepancy

between aggregate demand and output.

(2) y= o(d - y) = olaq- by + Yo + g)

where b = 1 - 8, and a dot on top of a variable denotes a time
derivative. Blanchard (1981) offers two rationalizations for this form-
ulation: that output might adjust slowly to aggregate spending with the
residual demand being satisfied with inventory fluctuations, or that
aggregate spending itself may adjust to the target level, d, with a lag.
In some instances below I consider the special case in which o is very
large, so that output always equals aggregate demand.3/

Money demand: I adopt the standard liquidity formulation of
money demand, solved for the nominal interest rate, i. Money supply is

exogenously given.

(3) i = cy - h(m-p)

(4) r=i-p


correspond to those of the U.S. economy. Section VI presents the
conclusions of the study.
II. The Model

As noted above, the model follows Blanchard (1981) very closely,
including, wherever possible, notation. It focusses on the joint
determination of output and asset prices. Asset prices determine
aggregate demand, and therefore output. Output, through both
profitability and interest-rate channels, is a key determinant of asset
prices. The price level is sticky, and output is demand determined in
the short run. In the long run it is assumed that output converges to
an exogenously-determined full-employment level.2/ There are four
assets held by risk neutral investors: money, domestic bonds, foreign
bonds, and shares in the stock market, the last of which are claims on
the economy's profits.

Aggregate demand: Equation (1) relates the log of real aggregate
demand, d, to the real value of the stock market, q, the log of real
output, y, the log of the real exchange rate, 6, and a measure of fiscal
policy, g. (All parameters in the following structural equations are

positive.)

Q) d= aq+ By + YO +g

The stock market affects aggregate demand both because it is part
of wealth, and because it determines the market valuation of capital
relative to replacement cost, determining investment demand. Output

influences aggregate demand to the extent that workers are liquidity


Condit:on (21) is unlikely to hold if Y is large, because in that case
an exchange rate appreciation would have an important dampening effect
on output, reducing the likelihood of the strong, rapid output increase
needed to bring about reversal of the interest rate differential.

Finally, the "reverse overshooting" scenario requires slow price
adjustment. This is also easy to understand. If price adjustment were
very rapid, then money would be approximately neutral and monetary
expansi.on would have only a small effect on output and interest rates.
There would not be a substantial effect on the stock price, because
output would not increase enough, or for a long enough period of time,
to significantly raise the discounted value of a claim on future
profits, thus eliminating the strong stock price-output-stock price
feedback that generates the "reverse overshooting" scenario.

The difference between the real exchange rate's dynamics in cases
A and B in Figure One is in the convergence to steady state. In Case A,
the real exchange rate converges monotonically, and never falls below
the steady state. In Case B, the real exchange rate intially
depreciates, and gradually appreciates over time until it falls below
the steady state level. After a while, the real exchange rate stops
appreciating, and gradually depreciates, approaching the steady state
from below. The reason for Case B's overshooting the steady state is
that, in that case, output increase fast relative to the increase in the
price level. This leads to an increase in the interest rate, which
eventually rises above the world rate. When this happens, asset market
equilibrium requires expected depreciation of the home currency. Thus,

the real exchange rate must converge to the steady state from below.


Equation (7) requires that the expected real return on a share of the
stock market, which consists of both capital gains and profits (nm),
equal. the real return on domestic bonds. 5/ Equation (8) is the open
interest parity condition, where r* is the foreign real interest rate.
r* is exogenously given, and as discussed below it is the steady state
interest rate to which the small economy must converge. Henceforth, I
will therefore use r* and * interchangably. Equation (9) gives
real profits as a function of real output.

For future discussion, it is useful to note that equation (7) can
be solved forward, under the appropriate transversality condition, to
obtain an expression for the stock price as the present value of

anticipated future profits, discounted at the real interest rate.

T
7 -f r(s)ds

(1a) a(t) = S w(t) e * dt
t

Similarly, (8) can be solved forward for the current value of the

real exchange rate as follows:

(8a) a(t) = 8 - Sf (w(t) - Pr) dt
t

So the current real exchange rate equals the steady state real exchange
rate minus the difference between the home-currency and the foreign-
currency interest rate, where the interest rate is the real rate ona

very long zero-coupon bond.


82

must fall in anticipation of the fiscal expansion. The exchange rate must
appreciate, and the stock price dyamics are qualitatively the same as in

cases 1 and 2.


For illustrative purposes, let us suppose that (T,-T,) is such
that at time T, the economy is at point (a) in Figure Three. The
economy's behavior before the fiscal expansion, (between T, andT,), is
determined by the requirement that there be no anticipated jump in asset
prices at time T,. Thus, between T, and T,, the economy must be
somewhere on the trajectory labelled (B). To which point on this
trajectory the economy must jump at time Ty depends upon how long is the
delay between announcement and implementation of the fiscal expansion,
(T,-T,). If the delay is very long, then the economy must jump to a
point near SS, after the fiscal policy change is announced. If the
delay is very short, it must jump to a point on (3) near (a).

We can use Figure Three to deduce the following characteristics
of the equilibrium: (These assertions are proven in Appendix B.)

1. Output always falls in anticipation of the fiscal expansion,
and rises above the steady state level during the fiscal expansion. We
knew that this is so because (B) lies entirely below the 6=0 schedule,
and (A) lies above the 6=0' schedule.

The size of the recession between T, and T, is increasing in the
length of the fiscal expansion and decreasing in the delay between the
announcement and the implementation of the fiscal expansion, The size
of the boom during the fiscal expansion depends upon the length of the
fiscal expansion. Long expansions lead to small output effects, because
they generate larger exchange rate appreciations, while short fiscal
expansions generate small exchange rate appreciations, and therefore

have a larger effect on output. (In the limit, as the length of the


International Finance Discussion Papers
Number 278

April 1986

THE STOCK MARKET AND EXCHANGE RATE DYNAMICS
by

Michael K. Gavin

NOTE: International Finance Discussion Papers are preliminary meterials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an
acknowledgement by a writer that he has had access to unpublished
material) should be cleared with the author or authors.


46

offset the unfavorable impact on aggregate demand of the exchang2 rate
appreciation. In fact, to a first approximation output is unchanged
between announcement and implementation of the fiscal expansion.

After the fiscal expansion arrives, output increases in all cases.
The stronger the impact of output on profits, the larger the increase in
output, which makes intuitive sense.

The real exchange rate initially appreciates in all three cases,
The extent of the appreciation depends upon the strength of the stock
market effects: strong stock market effects imply higher future output
and interest rates, and therefore generate larger appreciations.

The stock price initially falls in the "indexed bond" case,
because the fiscal expansion means higher real interest rates wich, by
assumption, no impact on profitability. The 0.9 percent decline in the
"stock market" can be interpreted as a 0.75 percentage point increase in
the internal rate of return on an indexed bond. In the other two cases,
the value of the stock market increases. In these cases, the higher
profits due to higher future output more than compensate for the higher
real interest rates.

VI. Conclusion

This paper analysed a model of the small, open economy in which
the stock market, rather than the bond market, determines aggregate
demand. It was shown that the asset price and output dynamics can
differ in interesting ways from more conventional dynamic,
Mundell-Fleming models. In particular, if the stock market effects are

large enough, and if money is not "too neutral," then expansionary


The cubic part of (13) can be rearranged as follows:

(4) Ae + (bo = F)A? = oLa(eg - a) + bP + cY]A + cYor = 0

If: (15) a(eq-a,) + br + ey>O

then the coefficients of the polynomial change sign twice, and we are
guaranteed two positive roots. This condition is similar to the one
found in Blanchard (1981), which is, in turn, satisfied if the IS curve
cuts the LM curve from above. I assume that the slightly weaker
condition (15) is satisfied. Thus, equation (13) has two positive roots
and two negative roots. The negative roots will be denoted -\ and -é
for the remainder of the paper.

The two positive and two negative roots, combined with the
assumption that output and the price level are predetermined while the
stock price and exchange rate can jump, ensures a unique equilibrium to
(12).

The characteristic vectors that correspond to the negative roots

-h and ~-6 are proportional to:


As in the static Mundell-Flemming model, a permanent fiscal expansion
has no effect on output or the interest rate, it merely induces an
exchange rate appreciation sufficient to crowd out enough net exports to
undo the expansionary impact of the fiscal stimulus.6/

Dynamics: Equation (12) is a linearized version of equations (1)
to (9), which I will use to examine the dynamic properties of the model

in the neighborhood of the steady state.

ri4T 1 [..-]
yle= -bo ao Yo 0 yr-y
te) | afr fiedn ad F 0 th aya a-4
6{ = e 0) 0) (h + 6) e- 68
| >| -| 0 0 0 -5 |p -P

The characteristic equation for the Jacobian in (12) is:

(13) (8 + A) {AL (bo + ADCP = A) + agl(eq -a)] - cYo(F - A)} = 0

where A is an eigenvalue of the dynamic system.

Because of the way that the price dynamics were specified, (12)
is block recursive, so (13) factors naturally into a cubic and a linear
term. By inspection, therefore, one root of (13) is -6, which is, of

course, negative.


te(o)-3) = [ c+sycb-sor8¥(67a)3 + aleq(s/x)-a, 1 (11)
= '
* TG Q(6) (a11")

Q(S) is defined implicitly in (A11), and for the rest of this discussion
I am viewing 2 (equation (Ala)) as a function of 6.

From (A11') we see that when 2(6) and Q(6) are the same sign, the
exchange rate's initial jump is a depreciation. When they are of
opposite sign the exchange rate initially appreciates. I now
investigate conditions under which Q(6) and (8) are of opposite sign,
to see if there are any conditions under which a monetary expansion
leads to a jump appreciation as in Figure A2-C.

There are three facts about the functions Q(8) and 9(8) that will

help us.
1. MA) = QQ) = 0 (A12a)
2. 2(6) > 0asr>6 (A12b)
< <

3. Qn(6) < 0 (A12¢)

These facts narrow the list of possibilities to three, described in the

following diagrams:


42

NOOHS ‘TVOSId AHL JO INIWAONNONNV JHL WalAV SUVaA SOWIL

O°” S°E oF Ss"

‘ ST s°0

0

ee Phim

MTT Trt TTT TT

s°8

ese to

6°8

T6 LL

S°6

26 LL

ase ,,puoq paxepuy,,

aseo aseg

9sed ,,Jex1eW Y03s B8u0lIs¢,,

(4S°8 SI ALVLS AGVALS +SINIOd OVINE)

3LlVY LSSYALNI vay
NOISNVdX4 IVOSI4 GALVdIOILNV

NGL aunold



IFDP
NUMBER

284

283

282

281

280

279

278

277

276

275

274

273

83

International Finance Discussion Papers

TITLES

1986

Labor Market Rigidities and Unemployment:
the Case of Severance Costs

A Framework for Analyzing the Process
of Financial Innovation

Is the ECU an Optimal Currency Basket?

Are Foreign Exchange Forecasts Rational?
New Evidence from Survey Data

Taxation of Capital Gains on Foreign
Exchange Transactions and the Non-neutrality
of Changes in Anticipated Inflation

The Prospect of a Depreciating Dollar
and Possible Tension Inside the EMS

The Stock Market and Exchange Rate Dynamics

Can Debtor Countries Service Their Debts?
Income and Price Elasticities for Exports
of Developing Countries

Post-simulation Analysis of Monte Carlo
Experiments: Interpreting Pesaran's (1974)
Study of Non-nested Hypothesis Test Statistics

A Method for Solving Systems of First Order
Linear Homogeneous Differential Equations
When the Elements of the Forcing Vector
are Modelled as Step Functions

International Comparisons of Fiscal Policy:
The OECD and the IMF Measures of Fiscal
Impulse

An Analysis of the Welfare Implications of
Alternative Exchange Rate Regimes: An
Intertemporal Model with an Application

AUTHOR(s)

Michael K. Gavin
Allen B. Frankel
Catherine L. Mann
Hali J. Edison

Kathryn M. Dominguez

Garry J. Schinasi

Jacques Melitz
Michael K. Gavin
Jaime Marquez

Caryl McNeilly

Neil R. Ericsson

Robert A. Johnson

Garry Schinasi

Andrew Feltenstein
David Lebow
Anne Sibert

Please address requests for copies to International Finance Discussion

Papers, Division of International Finance, Stop 24, Board of Governors of
the Fejeral Reserve System, washington, D.C. 20551.


Ea]

30.

Figure Five
Dynamic Adjustment to a Future, Transitory Fiscal Expansicn
Good News Case 2

al


47

monetary policy can lead to real exchange rate appreciation, rather than
depreciation. Unlike in models with only a bond market, anticipated
fiscal policy can lead to an anticipatory expansion, rather than
contraction, Furthermore, if the delay between announcement and
implementation of the fiscal expansion is long enough, the anticipated
fiscal policy can lead to exchange rate depreciation, rather than
appreciation.

The model was simulated for plausible parameter values. The
results indicated that, for monetary policy, the behavior of the model
was qualitatively similar to that of models without a stock market. The
stronger the stock market effects, the larger the impact of the monetary
expansion on output, and the smaller the real exchange rate depreciation.
Simulations for fiscal policy shocks suggest that stock market effects
may be more important in this case. The reversal of the "anticipatory
recession" result in, for example, Branson, Fraga and Johnson (1985)
appears to be plausible. This is buttressed by the presumption that
certain sensible modifications to the model would tend to strengthen the
positive impact of an expected future fiscal expansion on current
output.

A variety of extensions to the model would be worth considering,
although they would likely require simulation methods. It would be
useful to deflate nominal money with an expenditure deflator, like the
CPI, and to recognize the lag between changes in the real exchange rate
and net exports. Both of these would tend to increase the expansionary
influence of transitory fiscal expansions, making it more likely that an

anticipated fiscal expansion would lead to an anticipatory output


29

With a large increase in the stock price and a small exchange rate
appreciation, output expands immediately.

A less intuitive possibility is illustrated in Figure Five, which
depicts one case in which aAtcY>0.15/ This is the case in which the
exchange rate is more "influential" than the stock price. Note that
(A), the curve upon which the economy must be during the fiscal
expansion, lies entirely below the 6=0 schedule. This means that, if
the delay between announcement and implementation of the fiscal
expansion is short enough, then output must fall upon announcement of
the future fiscal expansion. However, consider a point like (b), which
is where the economy must jump if the delay between announcement and
implementation is long. This segment of curve (B) lies above the 8=0
schedule, which implies that output is above steady state. Thus, as in
Figure Four, output may increase upon announcement of a future fiscal
expansion, but only if the delay between announcement and implementation
is long enough. The output expansion is, unlike in Figure Four,
characterized by a decline in the stock market, and a real exchange rate
depreciation.

The intuition behind this outcome is as follows. When the fiscal
expansion is implemented, the economy will travel from a point like (a)
back to SS,. During that period of time, the short, real interest rate
will be above the world rate. This period of high real interest rates
tends to increase the time-T, long, real interest rate, thus providing a
force for exchange rate appreciation. There is, however an offsetting
effect. Before the fiscal expansion is implemented, the economy must go

through a recession in which the real interest rate is below the world


66

quadratic in F, we can determine conditions on F such that the

roots are real.

B8') r? + 2(ad-cY)r + (ad+cY)? > 0

By inspection it is obvious that this holds for very small and very large

values of F. Specifically, the roots are real in the good news case if:

B8a) Yr > (eY-ad) + 2 Y=akeY¥

or:

B8b) Yr < (cY-aA) - 2 Y-ahcY

It will be assumed in what follows that one of these conditions is met. When
it matters, I will specify whether I am assuming (B8a) or (B8b). This is a
restrictive assumption, but it makes the analysis much easier. The
simulations in Section V of the text showed that complex roots are possible,
but also that the dynamic behavior of the model was, at least for that set of
parameters, well described by the following analysis.

We will need some basic relations between the eigenvalues aid the
structural parameters of the model, which I now establish.

In the bad news case, we have the following important facts:

B9a) $1 <P<o,
B9b) 61 <(F+ad)<o.
B9c) ad+cY>0

B9d) Both $, and 9, are necessarily real.


Note that real balances are deflated with the price of home output
(value-added), rather than an expenditure deflator which would, given
wages, depend upon the real exchange rate. The consequences of making
the alternative assumption are well established in the literature, [see,
for example, Branson and Buiter (1983) or Henderson (1983)], so for now
I make the simpler assumption embodied in (3).

Price dynamics: Equation (5) gives the price adjustment

equation, and equation (6) defines the steady state price level:

(5) p = -8(p - p)

(6) Pp = m+ (r - cy)/h

The steady state price level is that which secures money market
equilibrium at the steady state interest rate and level of output.4/
This formulation was chosen for analytical tractability. Alternative
specifications, such as a more standard Phillips curve framework, can be
explored in a simulation model.

Asset _market equilibrium: Assuming perfect foresight, the

equilibrium conditions are:

(7) q/q+ t/q=r


20

output is high, and the domestic interest rate is above the world vate;
therefore asset market equilibrium requires that the real exchange rate
be depreciating (8>0). Conversely, below the 6=0 schedule, the real
exchange rate must be appreciating.

The slope of the §=0 schedule depends upon the size of A. If A
is positive (the bad news case) then the schedule is a negatively sloped
curve that is steeper than the 6=0 curve. In the "good news" case, when
A is negative, the schedule is either negatively sloped and less steep
than the 8=0 schedule, or it is positively sloped. Above the 4-0
schedule, the real exchange rate depreciation leads to higher output,
raising both the interest rate and profits. In the bad news case, the
adverse interest rate effect dominates; thus, asset market equilitrium
requires expected capital gains (§>0). In the good news case, the
favorable profitability effect dominates, so that asset mar ket
equilibrium requires expected capital losses in the stock market (§<o).

The remainder of this section uses these phase diagrams to
consider the following experiment. At time T,, it is announced that
there will be a fiscal expansion beginning at time T, and lasting until
T,. After T, fiscal policy returns to the original setting. (There is
nothing restrictive about the assumption that the fiscal expansion is
"transitory" or "anticipated." A permanent fiscal expansion is the
special case in which T, is infinite, and an unanticipated fiscal
expansion is the case in which (T,-T,) is zero.)

I begin by discussing the bad news case, and show that in ‘hat
case the predictions of the model are essentially identical to those

from a standard, dynamic Mundell-Fleming analysis. I then consider the


84

International Finance Discussion Papers

IFDP
NUMBER TITLES
1985
(partial listing)

272 Expected Fiscal Policy and the Recession
of 1982

271 lections and Macroeconomic Policy Cycles

270 Assertion without Empirical Basis: An
Econometric Appraisal of Monetary Trends
in ... the United Kingdom by Milton Friedman
and Anna J. Schwartz

269 Canadian Financial Markets: The Government's
Proposal for Reform

268 vias It Real? The Exchange Rate Interest
Differential Relation, 1973-1984

267 The U.K. Sector of the Federal Reserve's
Multicountry Model: The Effects of
Monetary and Fiscal Policies

266 Optimal Currency Basket in a world of
Generalized Floating: An Application to
the Nordic Countries

265 Money Demand in Open Economies: A Currency
Substitution Model for Venezuela

264 Comparing Costs of Note Issuance Facilities
and Eurocredits

263 Some Implications of the President's Tax
Proposals for U.S. Banks with Claims on
Developing Countries

262 Monetary Stabilization Policy in an Open
Economy

261 Anticipatory Capital Flows and the Behaviour

. of the Dollar

260 Simulating Exchange Rate Shocks in the MPS
and MCM Models: An Evaluation

259 Trade Policy for the Multiple Product

Declining Industry

AUTHOR(S)

William H. Branson
Arminio Fraga
Robert A. Johnson

Kenneth Rogoff
Anne Sibert

David F. Hendry
Neil R. Ericsson

Garry J. Schinasi
Richard Meese
Kenneth Rogoff

Hali J. Edison

Hali J. Edison
Erling Vardal

Jaime Marquez
Rodney H. Mills

Allen B. Frankel

Marcus H. Miller
Arnold Kling
Arnold Kling

Catherine Mann


Figure Al

C(X)

This shows that, for positive X, -X < -\ implies that C(-X) < 0 and
conversely. This matters because it turns out that Q, viewed as a
function of 6, has the same sign as C(-é). It follows that \ > 6,
implies (and is implied by) 2 > 0, and the converse. This allows us to

conclude that output necessarily rises after the monetary stimulus.

3. Exchange rate dynamics

As noted above, the steady state real exchange rate is unchanged
by the more expansionary monetary policy. From (A1), (A3), and (A4), we

obtain the solution for the real exchange rate's dynamics:

[o(t)-6] =

“At
— + £(F+8) (b-8/ate¥/6)-aa, re | (a9)

Slp>


81

— 72D ~o,D “2D
= (g/A) C(gicr)(e  -e =) = A(tre 1 << 0

So, if the delay between announcement and implementation is short, then

output; is below the steady state.

In_the good news case 2: If the length of time before the fiscal
expansion is to be implemented is very long, then the exchange rate

depreciates in anticipation of the fiscal expansion. If it is short, then
the real exchange rate must appreciate.

(B18) can be written as follows:

“$:T, _ ~o1D _ —b2D ~(b2-b1 71
B36) a(t) = (g/YA)e [C(o.-(rtad))(i-e = )-(ga-(rtad))(1-e de

As T, gets very large, this becomes positive. As T, goes to zero, this is:

_ —$,D _ “2D
B37) 8(t) = (g/YA)E(o:-(rtad))(1-e =) - (2-(r+ad))(1-e

_ —b2D —$,D “2D
= (g/YA)[(o,-(rtad))(e -e )- A(Im-e J] <0

I forego a discussion of the stock price dynamics because they are
qualitatively the same as in the good news case 1. (This can be seen by
inspection of equation (B17), or by comparing Figures Four and Five in the

text of the paper.

Good News Case 3: [ad+cY>0, (Fr+aA>cY] This third and final
ease is the same as case 1, except that aAtcY>0. For comparison, see Figure
B-One. The eigenvectors look much like in case 1. The difference is that,
while in case 1 the equilibrium trajectory approaches SS, after crossing
above the 8=0 schedule, in case 3 the trajectory passes through SS, from

below the 6=0 schedule. This implies that the possibility of an anticipatory

boom that is present in case 1 is not present in case 3. In fact, output


64

Appendix B: Fiscal Policy

Preliminaries:

This appendix provides analytical support for the intuitive and
graphical arguments in Section IV. I consider the case in which o is very
large, so that output equals aggregate demand. Then, equation (1) of the

paper becomes:

B1) (y - y) = a(q - q) + ¥(8 - @)

where the a and Y in equation (B1) equal the a and Y in equation (1) divided
by (1-8).

As explained in the text of the paper, the price level is constant.
Without loss of generality, I set p=m, in which case money market equilibrium

can be written:

B2) (r - P) = ely - y)

The equations for asset market equilibrium are:

B3) 6 = (r-P) = ely - y)

Bu) q

rq- 7

Linearizing (B4) around the steady state, and substituting the expression for

tw, we have:


37

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(Ty-t)22

The second term in square brackets approaches zero as (T,-t) becomes large,
and the first term is negative by the assumption that ad+cY<0 (B12a). Thus,
for large enough (T,-t), output is below the steady state.

(B) Take the limit as (T,-T,) goes to infinity. Then, from (B19):

a _ 7o,(T7t) _ 7$2(Ti-t)
B23) lim 9(t) = (g/A)C (gi -re - (o,-r)e ]

D>

_ 71 (Tint) -o2(T-t) ~2(T,-t)
(g/A)E(d.-) (e -e ) - he 1<o

(C) Now we examine the behavior of output as (T,-T,) and (T,-t)
become small. Taking the limit of (B19) as (T,-t) goes to zero, we obtain:

m -o,D _ _ “bed “o,D
B24) H(t) = (g/A)-e LU (di-e) - (deer) (ime (ire)

where D=(T,-T,). Using 1'Hospital's rule, and taking the limit as D goes to

zero, we see that the term in square brackets goes to:

B25) Lim Le] = C (i-P) - (2-P) (42/61) J

Deo

Using the facts that $2=6,+A, and that 4<0, it is easy to show that this is
positive if aA+cY<0, which we have assumed to be true in this case.
(D) Using (B19), we can show that for T,<t<T, output is:

_ bi (T27t) -b2 (Tat) ~b2(T27t)
B26) = F(t) = (g/A)E-(o.-1P) (e -e ) + he

Noting that $,-7<O and $1<,, (B26) is positive by inspection.


38

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THSTA Funda


Frankel, Jeffrey (1982) "In Search of the Exchange Risk Premium: A Six-
Currency Test Assuming Mean-Variance Optimization," Journal of
International Money and Finance 1, 255-274

Hayashi, Fumio (1982) "Tobin's Marginal q and Average q: A Neoclassical
Interpretation," Econometrica 50,1 (January) 213-224

Henderson, D.W. (1983) "Comment," in Douglas Purvis (ed.) The Canadian
Balance of Payments: Perspectives and Policy Issues, Institute
for Research on Public Policy, Montreal.

Johnson, R.A. (1985) "A Note on the Solution of Linear Saddlepaths When
the Forcing Vectors are Modelled as Step Functions,"
manuscript, Federal Reserve Board.

Judd, John P. and John L. Scadding (1982) "The Search for a Stable Money
Demand Function: A Survey of the Post-1973 Literature,"
Journal of Economic Literature XX (September) 993-1023

Krugman, Paul (1981) "Consumption Preferences, Asset Demands and
Distribution Effects in International Financial Markets,"
National Bureau of Economic Research, #651

Summers, Lawrence H. (1981) "Taxation and Corporate Investment: A
q-Theory Approach," Brookings Papers on Economic Activity
1:1981 67-127

Tobin, James (1978) "Monetary Policies and the Economy: The Transmission
Mechanism," Southern Economic Journal (January) 421-431



26

interaction of stock prices and exchange rate movements. To do so, I
eschew a comprehensive listing of all the possible outcomes, and fccus
on two interesting cases; one in which the stock market is more
"influential" then is the real exchange rate, and one in which the
reverse is true. In particular, I do not discuss cases in which the
economy's dynamics are eyelical.12/ A more complete taxonomy of
possible cases is given in Appendix B.

Figure Four illustrates the dynamic adjustment of the economy to
an anticipated, transitory fiscal expansion in the strong-stock~mar ket
ease. In this case, adt+cY<0.13/ Thus, the effect of output on the
stock market (A) and the stock market on output (a) must be large
relative to the effect of output on the exchange rate (c) and the e*fect
of the exchange rate on output (Y). As in Figure Three, the economy
must be on the curve (A) between T, and T,, and on a curve like (B)
between time T, and T,.

We can see from Figure Four that, in this case as in the "bad
news" case, the exchange rate must always appreciate relative to the
original steady state, both in anticipation of and during the fiscal
expansion. Output is always above the steady state during the fiscal
expansion,

Whether output rises or falls in anticipation of the fiscal
expansion depends upon the length of the expansion, and the delay
between announcement and implementation. Suppose the expansion is
expected to last for a fairly long time, so that the economy lands at a

point like (a) at time T,. Then between T, and T, the economy must be


56

then falling asymptotically and monotonically toward full-employment
output.
From (A6), it is not immediately obvious whether output rises or

falls after the monetary stimulus. Observe that:

; _ Ly(r+s)+adq] (a-8) fi

¥| to a (48)

Therefore, if (A-S) and 2 have the same sign, output rises after
the monetary expansion. However, if (A-é) and 2 are of opposite signs,
then output initially declines after the monetary expansion. However,
it is possible to show that \ > § implies 2 > 0, and the converse.

This implies that, in this model, a monetary expansion necessarily
results in a transitory increase in output.

To see this, recall that -\ is the negative root of the cubic
part of the characteristic equation (14). I showed above that there are
two positive roots and one negative root to this equation. Dencte the
polynomial in (14) as C(X). By inspection, C(0)>0, so the polynomial

looks like the following:


a

BUY) q = (Fead)(q - q) + ¥AC(8 - 8)

where A=(cq-a,)

(B1)-(B4') can be summarized as follows:

q reas YA | | 9-4
B5) =

8 ac ey | | 0-6

The characteristic equation for (B5) is:
B6 ) 62 - o(FtabtcY) + Ye = 0

If (rtak+eY)>0, then (B6) has two positive real roots, or a pair of
complex roots with a positive real part. (In either case, the saddle point
stability of the system is guaranteed.) I assume this condition throughout ,

and denote the roots 4, and $2, with $,<d2. The roots are:

BTa) 61 = % L(rtadtcy) - Y (rtabtoyY)® — Unc J
B7b) da. = % L(Ptadtcy) + / (rtadtey)” — UrcY ]

The roots are real if:

B8) (PtadtcY)? - Urey > 0

If A>O (the bad news case) then (B8) necessarily holds, so the roots are
necessarily real. In the good news case, the roots might be complex. To

keep the analysis tractable, I rule out complex roots. Writing (B8) as a


profits of firms, forms the link between future profit and interest vate
fluctuations, and current investment and consumption decisions.1/ This
theoretical link between the stock market and the macroeconomy has an
empirical counterpart. For example Fischer and Merton (1984) document a
strong empirical link between movements in the stock market and
subsequent movements in output, and numerous studies of both investment
and consumption find significant stock market effects. One motivation
for this paper, then, is to determine how the introduction of a stoc<x
market alters the output and asset price dynamics of an otherwise
conventional macroeconomic model of the open economy.

A second motivation is more directly related to the literature on
asset preferences and exchange rate determination. In recent years, it
has become apparent that models of exchange rate risk premia that focus
on the currency denomination of outside assets (usually defined, for
empirical purposes, as the stock of government debt plus high-powered
money) have not performed well. [See Kruginan (1981) and Frankel
(1982).] One response to these failures has been to place more emphasis
on models in which the location, not just the currency denomination, of
assets matters, [See especially Dooley and Isard (1986) and Isard
(1986).]

One such asset is marketable claims on the productivity of
physical assets; for short, the stock market. Returns on capital are
country-specific for a variety of reasons, including the uncertain
prospect of changes in tax and repatriation rules, and country-specific
fluctuations in the macroeconomic environment. In the following,

nonstochastic, model I do not analyse the determination of risk premia


45

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68

the radical. Thus, the signs of both 9, and 4, are unchanged by the addition
or subtraction of the radical. (B12a) and (B12b) follow immediately.

I defer a proof of (B12c) until after I have derived analytical
solutions for the time paths of 6(t) and q(t), immediately below.

Finally, we need to discuss the eigenvectors of the system, I
normalize so that the first element of the eigenvector, that which multiplies
the stock price, is 1. Denote the second element of the eigenvector
corresponding to the small eigenvalue s,, and the second element of the
eigenvector corresponding to the large eigenvalue s,. Simple algebra taen

establishes that:

B13) 8, = (6,-(P+aA))/YA, —S9= (627(PtaA))/YA

Analytical Solution for the Anticipated, Transitory Fiscal Expansion

At time zero the economy is in steady state. It is announced that,
at time T,, there will be a fiscal expansion of amount g, lasting until. time
T,, when fiscal policy will go back to its original setting. If T, is very
close to zero, then this is the same as an unanticipated fiscal policy change.
If (T,-T,) is very large, then the analysis is the same as for a permanent
fiscal policy change. Thus, there is nothing restrictive about either the
"transitory" or "anticipated" assumptions.

The only change in the stationary state is a reduction in the steady
state real exchange of g/Y between time T,; and T,. Thus, equation (B5)

holds, except that between T, and T, the steady state exchange rate is the


Output is "humpbacked," rising from the initial steady state, to

a maximum at time t*, where:

» log(6/A)
(17) t = (82)

ther, falling asymptotically and monotonically toward the unchanged
steedy state.8/ This is not the truly cyclical behavior that would arise
from a multiplier-accelerator framework, or a more conventional Phillips
curve equation; however, there is a family resemblance.

The solution for the stock price dynamics can be briefly
summarized. The steady state value of the stock market is unchanged by
the monetary expansion, but the stock price necessarily increases after
the monetary expansion. This is intuitively appealing, since
profitability necessarily increases, and the interest rate declines at
least transitorily. However, as will be discussed below, it is possible
that the long real interest rate increases after the monetary expansion,
so this result is less obvious than it might appear at first glance. In
the longer version of the paper I discuss other aspects of stock price
dynamics in more detail; they are not, however, of central interest so I
forego the discussion in this version of the Paper.

So far the model has exhibited no surprising properties. The
exchange rate dynamics, however, are somewhat more interesting. The
steady state real exchange rate is unchanged by the more expansionary
monetary policy, although the nominal exchange rate would, of course,
depreciate in proportion to the increase in the money supply. I begin

the ciscussion of dynamics with two observations: first, the solution


a
a

ky = (fi/a) {y(r+6)+a6q} (a3)

ka = h/ (A4)
With (A1) through (A4) we can discuss the dynamics in more detail

1. Price dynamics
These dynamics are trivial, because of the Simple price adjustment
equation (5). The solution is simply:

[p(t)-p) = ~m e St (A5)

where § is the new steady-state price level. So the price level
adjusts monotonically from its old steady state, p(0), toward its new
steady state, p, regardless of output dynamics or, for that matter,

anything else.

2. Output dynamics

The solution for output- can be written:

mat

Ly(t)-y] = 2 Ly(res)easqy(e ®t et) (a6)

Assuming i # 6, output is "hump-backed," starting at y, rising to
a maximum at time tmay where:

log (8/))

t = (a
max (8 - A) 7)



41

Q(0) = r(bteY/A)-aa, > 0 (A13)

Now consider case (B). Here things are more interesting; when 6 is less
than 6*, Q(5) and 2(6) have opposite signs. This means that, in this
case, there is a critical price adjustment parameter 6* such that if

6<6*, the exchange rate initially appreciates when the money stock is

increased. The conditions for case (B) are:

Q(0) = r(bteY/A)-aa, <0 (At4a)

Q'(A) = -(2\#r=ba) + co(¥taq)/A < 0 (A14b)

Case (C) is qualitatively the same as case (B), except that the critical
speed of price adjustment is in this case greater than A. The

conditions for case (C) are:

Q(0) = r(bteY/A)-aa, < 0 (A15a)

Q'(A) = -(2A+r-ba) + co(Y+aq)/A > 0 (A15b)

So, if price adjustment is slow enough, and condition (Al4a)
holds, then the exchange rate initially jump appreciates after a
monetary expansion. On the other hand, if price adjustment is fast, or
if condition (Al4a) does not hold, then the exchange rate must jump
depreciate after an unanticipated monetary expansion.

A question is whether case (B) or (C) is indeed possible. The

issue here is that A is a complicated function of the various structural


15

(21) P(bteY/A) = aa, <0

then there is some 6* such that if 6 (the price adjustment parameter) is
less than 6*, the real exchange rate jump appreciates after a monetary
expansion, as in Figure One (C) above.

This counterintuitive result is clearly linked to the presence of
the stock market: it requires that aa, be a big number, where a is the
impact of the stock market on aggregate demand, and a, is the impact of
output on the stock market. In particular, in the case in which the
return on the domestic asset is insensitive to cutput (the "indexed
bond" case, with a,=0) this result would be impossible.

The intuitive explanation for this apparently perverse "reverse
overshooting" is as follows. In this scenario, the monetary expansion
leads to a transitory decline in the short real interest rate, both
because of liquidity and inflation effects. Aggregate demand and out put.
inerease, as a result of a large increase in the value of the stock
market. The increase in the stock market is large, and the impact
aggregate demand important, because a and a1 are large. As output and
the price level increase, the demand for real balances inereases while
the supply declines, requiring an equilibrating increase in the nominal
interest rate. This combines with a gradually declining rate of
inflation to generate a sharp increase in the short real interest rate
from its initial position below the world rate, to a level above the

world rate.


The Stock Market and Exchange Rate Dynamics
by

Michael K. Gavin*

I, Introduction

This paper articulates a model of the small, open economy in
which the price of shares in the stock market, rather than the real
interest rate, determines domestic aggregate demand. The model builds
upon Blanchard's 1981 analysis, and apart from the introduction of
stock-market effects on aggregate demand, is also in the spirit of the
dynamic, Mundell-Fleming analyses that are well-established in the
international macroeconomics literature. Indeed, the model includes as
a special case one version of this "standard" framework. It differs
from Blanchard's analysis in the assumption that the economy is open.
Despite this close kinship to the two strands of the literature, I show
below that the open-economy stock~-market model can, in some
circumstances, exhibit output and asset-price dynamics that differ
significantly, and in an economically illuminating way, from those that
are in the literature.

There are two motivations for introducing the stock price into a
macroeconomic model. The first derives from the observation that
movements in current and expected future profitability, as well as
interest rates, are widely believed to affect investment and
consumption, through both relative price and wealth effects. The stock

market, broadly interpreted as all marketable claims on the future


36

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78

In the good news case 1: The real exchange rate is appreciated
relative to the steady state both in anticipation of and after the
implementation of the fiscal expansion.

First consider t<T,. For notational simplicity, define:

zi = (oj-(Frad)) i = 1,2
Ty = Ty-t, i= 1,2

In this case, 2j<0. Differentiate (B18) with respect to D to obtain:
de wit, ~b2T2

B27) — = ome 7 o222€
dD

“bit, ~d2T2
= $12, (e -e )- eYA <0

where I have used the fact that T,=T,+D. Since dé/dD<0, we can consider the
ease in which D*0: if in that case the exchange rate deviation is negative,
it must be even more negative for D larger than zero. Using (B18), we can
compute the exchange rate deviation for very small D. Using l'Hospital's
rule, we have:

seid “bit, eT)

B28) lim o(t) = 8&2 Eze ~ 22(b2/be J
D>0 YA

The term in square brackets can be written:

“bit, “b2T1
B29) Ce] = ¢,z,(e -e )- acy <0

where the inequality holds because in this case z,<0. This proves tha
between time zero and T,, the real exchange rate is necessarily below the
original steady state. Now consider T,<t<T,. Differentiating (B18) with

respect to T,, and rearranging, we have:


24

fiscal expansion goes to infinity, the effect on output goes to zero, as
in the static Mundell-Fleming model.)

2. The real exchange rate necessarily appreciates relative to
the original steady state both before and during the fiscal expansion.
The exchange rate appreciation is increasing in the length of the fiscal
expansion, and decreasing in the delay between announcement and
implementation of. the fiscal expansion.

3. The stock price is necessarily below the steady state during
the fiscal expansion (between T, and T,). This is because during the
fiscal expansion output is above the steady state, leading to higher
profits and interest rates. In the bad news case, the interest rate
effect dominates, so the increase in output leads to a fall in the stock
price.

Before the fiscal expansion the stock price is above the steady
state if the delay is long, and below it if the delay is short. This is
because there are two offsetting effects on the stock price. Between T,
and T, output and interest rates are low, which is good for the stock
market. But stock-holders must also look forward to the period after T,
during which output and interest rates will be high. If the period of
time between announcement and implementation of the fiscal expansion
(T,-T,) is long, the favorable effect of the anticipatory recession will
dominate, and the stock market will rise. But,.if delay is short, the
recession will be short and the subsequent boom is imminent.
Consequently, the adverse second-period effects will dominate, and the

stock price will fall upon announcement of the future fiscal expansion.


ABSTRACT

This paper articulates a model of the small, open economy in
which the stock market, rather than the bond market, determines domestic
aggregate demand. It resembles in many respects the widely adopted
dynamic Mundell-Fleming approach, but can, in some circumstances,
exhibit output and asset price dynamics that differ in economically
illuminating ways from that more standard framework. In particular, if
the stock market effects are important enough, then a monetary expansion
can result in real exchange rate appreciation, rather than depreciation.
Anticipated fiscal expansion can, if the favorable effects on future
product:.vity lead to strong enough stock market effects, lead to an
output expansion, rather than a contraction as in, for example,
Burgstaller (1933), Blanchard (1984) and Branson, Fraga and Johnson
(1985). Furthermore, if the delay between announcement and
implementation of the fiscal expansion is long enough, an anticipated
fiscal expansion can lead to exchange rate depreciation, rather than
appreciation.


48

expansion, rather than recession. Working against this is the fact that
investment, too, responds to changes in q with a lag.

There are several long-run issues that could be addressec. The
effect of different rates of capital accumulation on full-employment
output is a potentially important consideration. In addition, the
wealth effects of alternative current account and capital accumulation
paths should be modelled.

Finally, it would be possible to relax the small-country
assumption, by creating a two-country version of the model. And, it
would be possible to add risk premia to equations (7) and (8), which
would allow the exploration of "safe-haven," or "location" vs.

"currency-denomination" risk.


32

various shocks, in a very stylized model that resembles in certain
important respects the U.S. economy. The hope is that this will
contribute to our understanding of the more difficult question of how
the stock market would affect a more fully articulated model of the
economy.

The section is organized as follows. First I discuss empirical
estimates of the model's parameters. Then I simulate the model for a
monetary and a fiscal policy shock, using the solution algorithm
developed by Austin and Buiter (1982) and Johnson (1985). For each
shock, I consider three cases: one in which stock market effects are
negligible (the "indexed bond" case); one in which stock market effects
are given by my best estimate (the base case), and one in which stock
market effects are somewhat larger than my best estimate.

Parameter estimates: I choose units in what follows so thet
steady state real output is equal to one. Thus JY, the log of
steady state real output, is zero. In the following empirical
discussion, I will use capital letters to correspond to the level of the
variable that is expressed in logs in the model. Thus, y = log(Y), and
so on. We need to make assumptions about money demand, the sensitivity
of profits to cyclical fluctuations in output, the impact of asset.
prices on goods markets, the speed of adjustment of the price level, and
the speed of adjustment of output.

A simple average of the money demand estimates surveyed in Judd
and Scadding (1982, Table 1) implies a long-run income elasticity of
0.725, and an interest elasticity of -0.275. These elasticities imply

that "ce" in equation (3) is .225, and "h" is .310.16/


yy

these parameter values. However, the critical price adjustment
parameter, 6*, below which the actual price adjustment parameter must
lie to obtain the "reverse overshooting," is very low indeed, on the
order of .05. Thus, the empirical results are qualitatively similar to
the "indexed bond" case not because stock market effects are too small,
but rather because price adjustment is too fast, or, put another way,
money is too neutral.

Application to an Anticipated Fiscal Expansion: I now consider

the simulated impact of an anticipated, transitory fiscal expansion. At
time zero, it is learned that in six months there will be an increase in
g equal to 2 percent of GNP, an expansion that will last for a year.
After that year, fiscal. policy returns to its original setting.

Figures 10 through 13 summarize the results of this experiment.
In the "indexed bond" case, output falls upon announcement of the future
fiscal expansion, as a result both of exchange rate appreciation, and a
decline in the "stock market," which is in this context an increase in
the long, real interest rate. Output continues to fall until the
arrival of the fiscal stimulus, hitting a trough of about 0.33 percent
below steady state. In the "strong stock market" ease, output actually
rises in anticipation of the fiscal stimulus. The real exchange rate
appreciates in this case, but its effect on aggregate demand is more
than offset by an increase in the value of the stock market. In this
case the stock market, looking forward to the high profits to be made
after the arrival of the fiscal stimulus, increases immediately. In

the "base case," the stock price increases but not enough to completely


27

Figure Four
Dynamic Adjustment to a Future, Transitory Fiscal Expansion
Good News Case 1

=0

al


11

A -6
l 1 7 r y(F+6)+a8q 7
-(eqra, )/ (P+d) 8q(b-8/0)+¥a,
-c/) (F+8) (b-6/a)-aa,
L ) | C-s/¢ne8) IC (rss) (b-6 /oteY¥/8)+a(cq-a,)]

The first eigenvector is easy to interpret, as it corresponds
exactly to the fixed-price analysis in Blanchard (1981), with the

addition of a real exchange rate. The sign of the second element

depends upon the sign of (cq-a,). Because this term crops up repeatedly

in the remainder of the paper, I denote it A. If A is greater than
zero, we are in the "bad news case," in which an increase in output
raises interest rates proportionately more than it raises profits, so
that an increase in output causes a fall in the stock market. If A is
less than zero, we are in the "good news case," in which an increase in
output raises the value of the stock market.7/

The third element of the eigenvector, which applies to the real
excnange rate, is necessarily negative. This is the slope of the saddle
path in (@,y) space, so its negativity indicates that there is
necessarily real exchange rate overshooting in the fixed-price version

of this model. This is easy to understand: with prices fixed, output


63

1. QCA) = WA) = 0 (A18a)

2. 2(6)>O0asr>sé (A1Tb)
< <

3. W"(6) <0 (A18¢)

There are again three cases, which are depicted in Figure A3. (Simply
relabel the Q(6) curve as W(S)). To see which of the three are relevant,

evaluate W(S) at 5=0:

w(o) = y] 92 9ve yg (a19)
(r + X)
- r a
= Y]eq} ——-| + a} o-— >0 (A19"')
r+) r+)

Unlike in the case of the real exchange rate, W(0) is necessarily positive.
Trat means that only case (A) in Figure A3 is relevant, which is to say that the
price of shares in the stock market must jump upward just after the increase in

the money supply.


79

“o:T, —b2T2
eo ) = aey] <0
aT, YA

B30)

So, as T, decreases, the real exchange rate increases. (This is apparent from
Figure Four.) So we consider the case in which T,*t. If the real exchange
rate is below the steady state in this case, it must be below the steady
state in all cases. We have from equation (B18):
p31) tim 88) _ ogg, z,1/8, <0

T2700 y_séiT2 YA
where I nave used l'Hospital's rule and omitted some of the algebra. This
establishes that for all t between time T, and T,, the real exchange rate is
necessarily below the original steady state.

An_the good news case 1: (A) Before the fiscal expansion arrives, the
Stock price is above the steady state if the length of time until the fiscal
expansion is implemented is not too long, and it is below the Steady state if

the delay is long, (B) After the arrival of the fiscal stimulus, the stock
price is necessarily above the steady state.

(A) Consider first the case in which T,-t is large. (B17) can be

written as follows:

a “itr —o,D ~b2D -(b27o) Ty
B32) q(t) = [gA/Al]e [(1-e )- (Ire )e

As (T,-t)=T, gets large, the second term in Square brackets goes to zero.
With A<O, q(t) becomes negative. Now consider the case in which (T,-t) is

very small, Taking the limit of (B17) as T,*t, we have:

B33) lim = 84 (

Tyet A

~b2D -o,D
e -e )>0


49

Footnotes

* Division of International Finance, Federal Reserve Board. This paper
reflects the views of the author, and should not be construed as
reflecting the views of the Board of Governors, or of any other members
of its staff. I am especially indebted to Rudiger Dornbusch and Dale
Henderson for encouragement and many useful comments. Helpful
conversations with Olivier Blanchard and Stanley Fischer are also

gratefully acknowledged. I am, of course, soley responsible for any
remaining errors.

4/ The standard references are Tobin (1978) and Hayashi (1982) Unlike
these papers, I do not make the important distinction between average q,
which affects wealth, and marginal q, which affects the investment
decision.

2/ The small country assumption, which fixes the real interest rate
‘and, therefore, given the profitability function, the level of
investment, makes this assumption more palatable than it might be ina
closed economy. However, for experiments in which the steady-state
capital stock is potentially affected, (for example, changes in the
profitability of capital or the steady state real interest rate), the
exogeneity of potential output would be a questionable assumption.

3/ It is noteworthy that, while output is "sticky," it is assumed that
‘the composition of output can be shifted instantaneously between, for
example, net exports and government consumption. It would be more
real: stic to make investment adjust slowly to changes in q (see Fischer
(198!.)) and net exports respond slowly to changes in the real exchange
rate (see the long literature on net exports and the real exchange rate,
one example of which is Dornbusch (1986)). Such dynamics would alter
the nodel's properties significantly. They would also make the model
analytically intractable, although more realistic models can be explored
with simulation methods. Branson, Fraga, and Johnson (1985) includes
some of these dynamic complications.

4/ Money demand depends upon the nominal, not the real interest rate.
However, for tractability I have assumed that in the steady state
monetary growth and inflation are zero, so that the steady nominal
interest rate is equal to the steady state real interest rate.

5/ “in equations (7) and (8) I have assumed risk neutrality. However,
Zt would be very easy to introduce separate risk premia in equation (8),
corresponding to currency-risk, and equation (7), corresponding to
"safa-haven" or "country-risk," considerations.

6/ ‘This result holds even in the short run because of the money demand
‘Specification that I have adopted. It is well understood (see for
exam>le Branson and Buiter (1983) or Henderson (1983)) that deflating
nominal balances with an expenditure deflator like the CPI introduces a


15/ There are actually two subeases to consider when aA+cY>0, depending
upon whether (#+aA) is greater than or less than cY. In the case
discussed in the text, (F+aA)<cY. When the reverse is true, an
anticipated fiscal expansion is necessarily contractionary. See
Appendix B for further discussion.

167 To see this, note that the money demand function can be written:

(m=p) = .725y > .275log(i) + const
log(i) = (.725/.275)y = (1/.275)(m=p) + const

Lirearizing about the steady state:

Vi = (.725/.275)F¥ = (1/.275) (fi=p)

i= T+ 90(.725/.275)9 = (1/.275) (=p) ]

17/7 It would also be possible to assume that non-corporate capital
Income is capitalized and considered part of "the stock market." For
that matter, in a model with forward=looking wage earners who are not
liquidity constrained, it would be appropriate to assume that labor
income is capitalized as well. These broader definitions of "the stock
market" would presumably make the stock>market transmission mechanism
more powerful than my narrow definition.


14

is the sum of two declining exponentials, so the time path for the real
exchange rate can have at most one "hump," that is, one point at which
the time derivative switches sign. Second, because both output and the
price level are "sticky," the home interest rate necessarily falls below
the world rate just after the increase in the money supply, which
implies that the rate of change of the real exchange rate at time zero
is negative.

These two observations restrict the possible time paths for @(t)

to three, which are illustrated in Figure One:

Figure One
Possible Time Paths for the Real Exchange Rate

Case A Case B Case C

In cases A and B, the exchange rate's initial jump is a
depreciation, the standard case. They are discussed in more detail.
below, but for now consider case C. In this case, the increased money
supply results in a jump appreciation of the exchange rate. These
diagrams alone do not establish that case C is possible, but I show in

appendix A that if: