19

c. By comparing (4.3) with (4.4), these interest rate changes have an
identical impact on ee and AL: Thus despite the flexibility of Px,» interest
rate fluctuations induced by the endogenous supply response lead to mirror
movements in ee and Ae In the presence of these latter effects, the
volatility and direction of ey (relative to the classical case) are ambiguous.
Since i, is unresponsive to ue when p = 0 in the classical case, the endogenous
supply response due to imperfect information makes i, more volatile.

M-L elasticity conditions are important in explaining the direction and
volatility of the exchange rate response to a supply shock in the presence of
imperfect information. If 1 - 662 - Ay > 0 then the exchange rate will
depreciate and the nominal interest rate will rise in response to a positive
and permanent supply shock. Since Fete is the same as in the classical case,
then e, must be less volatile under imperfect information relative to the
classical model. ?° If on the other hand 1 - 652 - Ay < 0 and |1 - 662 - A,| >
a+ b)b 18,62, the exchange rate will appreciate, the nominal rate will fall

11

and thus again ee is less volatile than the classical case. If 1 - 662 - Ay
< 0 and the exchange rate depreciates (de, /du, > 0), the exchange rate will

overshoot its long run equilibrium and will be more volatile than in the

classical case.

e. The Real Rate of Return

When the shock is transitory, tr declines as agents anticipate an
improvement in the terms of trade. Imperfect information leads agents to
believe that next period, production will expand as Px, catches up to En pPX:
This reduces the derivative [8r,/du, | and therefore for 9 = 1, imperfect

information reduces the volatility of Th When p = 0, the classical case

implied that Le was expected to adjust immediately to its long run value so


13

in Px, would be stronger in contrast to a permanent shock. Thus if the M-L
elasticity condition holds, supply side policies which are credible induce less

volatility in domestic nominal prices than credible policies. !?
III. Price Contracts

Each period agents negotiate one period (ahead) contracts set at the ex
ante market clearing price based on information one period earlier. Although
Px, is not "rigid," since contracts are renegotiated period after period, it is
invariant to contemporaneous disturbances. ! The above anticipatory pricing
mechanism implies the following path for Paes
3.1 Px, = EPs:
The equilibrium condition for exports (2.21) is replaced by the ex ante market
clearing condition,”

3.2 E E

tote * Fe-1% E>

: The solution to the system is found by replacing (2.21) with (3.2), and solving

using the method of undetermined coefficients.? The solution is,“

eo.
3.3 e, = OTC - 862 - 9) - 0) E ox,
j=0
-1 -1
+ [C1 ~ 882 - 907 = p) - bu,
-1 e jys
3.4 AL = (1 - 682) “C1 - 2° *te1-j

- -1
+ [2 - 682 = 6)9°77G = p) - by.
The distributed lags of xy one, and aL are identical to the classical case,

since contracts are renegotiated period after period. In the current period

the exchange rate is the terms of trade, since Px, is invariant to ue One


23
The real rate is defined in terms of a basket of consumer products. This
is consistent with intertemporal substitution between present and future
consumption by domestic agents.

Sstrictly speaking the foreign demand xt should also contain a term ly

representing foreign income to be symmetrical with the analysis. I assume that
the substitution always dominates the income effect, so that wos > 0.

Money demand depends on x and not I, thus we are ignoring the direct

impact of the terms of trade on money demand, a point presumably justified for
a transaction money demand. Anticipated terms of trade movements will however
effect money demand through the real interest rate. The output elasticity is
assumed to be unity so as to ease the cumbersome algebra without significant
damage to the technical propositions advocated by the model.

"currency substitution is ruled out by law, thus no stock demand for
foreign currency exists. Domestic agents will however generate a derived flow
demand for foreign currency as they purchase foreign goods and bonds.
Likewise, a flow supply of foreign currency will be generated by foreign
agents' purchase of domestic output and bonds.

Sthis result has been derived in an equilibrium context by Stockman (1978)
and used in Flood (1981).

For a similar equilibrium condition derived in an optimization context,

see Oestfeld (1982). (2.22) could be interpreted in the following way: rE
is the return on indexed bonds denominated in the domestic product x, while

re is the return on indexed bonds denominated in the foreign product, y.

10se6 for example Lucas (1973) and Barro (1976).

Myote that the lagged terms can be written in moving average form:

S__,,s . _
2.25 Pxy = (xy pu, 4] ( du,
2.26 e, = 6-1 Om .- -
t (1 ~ 082 - OC.) = py) = Cy
12 1 Cand
Lis a lag operator. The function T- pL = % pL! describes the
j=0

transition from the short run to the long run. If 9 = 1, the economy will
return back to the long run steady state in the period following the shock.
1316 the disturbance is permanent (p = 0), o> 1 - 852 is both a necessary
and sufficient condition to insure that a positive supply shock appreciates
domestic currency. If p = 1, a necessary and sufficient condition is that Ay >

1 - 662. In general, a necessary and sufficient condition is that p6,62(1 -
852) > Ay2(1 - Bdg - 6).

1 ye . . .
The converse of the proposition is untrue in general since A, > 1 - 662

is a sufficient condition. Thus if A, < 1 - 662 the volatility of Px, relative
to e, is ambiguous.

1 As long as A > 1 - 662, the exchange rate will appreciate and terms of
trade worsen in response to a positive supply shock.


domestic real balances, domestic bonds and foreign bonds. The home country is
also small in the world capital market and in terms of risk default, domestic
and foreign bonds are perfectly substitutable.

The supply of output x is exogenous to the model and its stochastic
deviation from trend growth is a result of a supply side policy rule adopted by
the fiscal authorities as well as random disturbances such as disembodied
technical growth. I adopt a version of Muth's (1960) statistical model, as
presented in Sargent (1979), to represent this output process. The output
model is as follows:

2.1 xX, =k tv

t-1 t
2.20 xfs Rte,
Ev. = Ee, =0
Eviv, = Eee, = Ev, €, =0 for all s, t s#t.
Evy. = oe; Fee, = oF

s . x
x,. is measured output, x

t is permanent output, while ee is transient output.

t
Both ee and v, are each stationary, serially:uncorrelated random processes with
mean 0 and variances of and 02 respectively. The two processes are orthogonal

at all lags. YE is a persistent disturbance as described by the random walk in

equation (2.1), while & is a temporary disturbance. Agents cannot directly

observe x. or €.. The only output information available to them is the

tt t
current and past levels of measured output as well as policy announcements by
the fiscal authorities. According to Wold's theorem there exists a random
variable uy which obeys

- = - + gs BS
2.3 ne se 7 Osgpsil,
where uy, us a stationary serially uncorrelated random process with mean zero

and variance, on. p is defined as follows ,~


20

that tT, was unresponsive to the supply side disturbance. Under imperfect
information, output is expected to expand next period as Px, catches up to
Ep Px: This will lead to an anticipated deterioration in the terms of trade

and hence re will rise according to the arbitrage equation (2.22).

IV. Conclusions

In a simple stochastic general equilibrium model I have explored how
supply side policies affect the dynamic paths of exchange rates, interest rates
and the terms of trade. The outcome -- in direction and magnitude -- generally
depends upon the type of pricing rule, the availability of information and the
credibility of the policy. However, the Marshall Lerner elasticity condition
is sufficient to guarantee that the exchange rate will initially appreciate
(depreciate) in response to a positive (negative) supply shock, irrespective of
‘the three factors above. ‘And if all prices are fully flexible, more credible
supply side policies would induce less volatile responses in nominal and real
rates than less credible policies. Moreover, if nominal prices of domestic
goods are insensitive to contemporaneous shocks due to the existence of nominal
(unindexed) contracts, credible policies will induce more volatile exchange
rate behavior than under fully flexible prices if the M-L elasticity condition
holds.

The covariation between the exchange rate and terms of trade under
flexible prices again depends on the M-L elasticity condition. If the M-L
condition holds -- this is both a necessary and sufficient condition --

positive supply shocks will induce an appreciation of the exchange rate and a

concommitant deterioration in the home terms of trade. This implies that the

domestic price level would be more volatile than the exchange rate so as to


26

relative price movements. Throughout the analysis, the covariance structure of
these shocks is assumed to be constant.

3this can be verified by noting that y appears in the denominator of (4.2)
so that 8Var Px/dy < 0.

Awhile the presence of imperfect information reduces output, it also has
an effect on interest rates (equations (4.5) and (4.6)). If i, falls in
response to a positive realization of uw it will stimulate the demand for
money. This cannot offset the imperfect information effect which reduces the
demand for money. Thus OVar Px/3y < 0 for all values of y 2 0.

Sthis can be seen by comparing these expressions to ar, /ou, and di, /du,
in (4.5) and (4.6). The first expression is boi, /au, and the second is
6168r, /du, .

by is found in A which has been defined earlier in the text.

T this can be seen in equation (4.6).

8, Proof of this is straightforward. Substitute (4.2) and (4.6) for p = 0
into the money market equilibrium condition (2.20). 8Q, /du, > 0 if
Ay > yp - 6,62), so that aA, /du, > 0.

94 fall in iL created by a positive supply shock (31, /3u, < 0) could

reduce PX, below BaP x to such an extent that the reduction in output,

“y[Px, - E,- Px] is greater than the initial disturbance u If this perverse

te
case is ruled out, then the result in the text follows.

Othe condition 1 - 862 - A; > 0 is both necessary and sufficient to

insure de, /du, > 0 and 8Var e/dy < 0. The reason is that for p = 0,
di, /eu, = 0 in the classical case. Therefore, de, /du, (classical) > e,/du,
(imperfect information).

-1
the condition |1 - 662 - Ail > (1 + b)b 6,62 is a sufficient condition.


22

*The author is Assistant Professor of Economics, Columbia Graduate School of
Business, New York, NY 10027. I am indebted to Robert Z. Lawrence, Robert
Flood, Joshua Aizenman and Guillermo Calvo for helpful conversations. The
paper was written while I was a visiting scholar to the International Finance
Division of the Board of Governors, Federal Reserve System. I am grateful to
the Board for financial support. This paper represents the views of the author
(authors) and should not be interpreted as reflecting the views of the Board of
Governors of the Federal Reserve System or other members of its staff.

I. Introduction

For an empirical and theoretical analysis of the OPEC oil price shock on
developed and developing nations see Sachs (1980).

*See for example I. Kravis and R. Lipsey (1978).

5the Meade model only considered aggregate demand side disturbances, but
has supply side implications. If output rose (say due to a multiplier effect
created by a shift in aggregate demand), the exchange rate would appreciate
only if the sum of domestic and foreign demand elasticities was greater than
unity. This has been called the Marshall Lerner (M-L) condition.

4 See J. A. Frenkel and H. G. Johnson (1976) for a critique of the
elasticity approach to the balance of payments under fixed exchange rates. For
an analysis of the monetary approach to the exchange rate see J. A. Frenkel and
H. G. Johnson (1978) and the references therein.

A rise in domestic output would stimulate the demand for money. Under

the assumption of purchasing power parity, this will unequivocally appreciate
the exchange rate.

This is ironic since the Keynesian model derives elasticity conditions
for this particular case.

This result should be compared to Obstfeld's (1980) paper in which he
describes a perfect foresight equilibrium path with full price flexibility.

Note that in traditional Keynesian type models such as Meade (1951) the
exchange rate is in fact defined as the terms of trade in the short run.

II. The Classical Model

lhe deterministic component of each variable has been deleted. In
section IV the output exogeneity assumption will be relaxed.

2See Sargent (1979) pp. 310-311 for a derivation of p.

35 can have a Bayesian interpretation -- it can be defined as agents
prior probability that a shift in measure income is in fact transitory. As
agents learn, p can be adjusted so as to incorporate new information. In the
framework presented here I abstract from this learning process since I only
seek to analyze the impact effect of a sudden policy shock.


7

Oo,
4.4 Ae L= 8525 (4 - p) = pix

t r) geo. tots

+a" [G + b)A + yC = p)[bC - 652 - Ay) + G+ »)e76,]]}u,

+ 026;, A= A, - p6,07, z=1+d(1- p),

where: Ay
A= (1 + b)Ay + y(Ay + B(1 - 659)).
Since the imperfect information disappears in the long run, the distributed
lags on past values of x, are identical to the classical case. Px, will again
decline (rise) in response to a positive (negative) supply shock. However, the
imperfect information will tend to reduce the volatility of Px, Initially,
firms respond to lower prices (relative to competitors' price) by reducing
output. The demand for money then rises by less than in the classical case for
any given nominal rate.4 Interest rates will also be influenced by the

cyclical output effect. The solution for the two polar cases is as follows:

. yO(1 = 62)(1 + b)AT Ty, for p = 0,
4.5 r=
© = @(1 = 62)(1 + ba” tu, for p= 1.
YQ. = 082 - Ay)A"7u, for p = 0,
4.6 i, = “41
-(1 - 662 - Ay)A u for p=1.

c. The Terms of Trade

The coefficient y enters both the numerator and denominator of the
equilibrium paths in (4.3) and (4.4). Thus the effect of the endogenous supply
response on the direction and volatility of ee and A, is in general ambiguous
without prior restrictions on the parameters. The expressions by(1 - 662)(1 -
p)(1 - 662 - Ay) and y(1 - 652)(1 - p)(1 + b)6,6? in the numerator of (4.3) and
(4.4) reflect adjustments in ee and A created by changes in i, and r. } If

t t

agents perceive the shock to be temporary (p = 1) these expressions will be


2.23 oA, > Sar, = 1 - 862) xe =0

where o = Bag + ay - 626(1 - 6).

@ is the elasticity of the world excess demand for x, with respect to AR:

Bag + a8 is the substitution effect while 626(1 - 6) represents the income
effect. Throughout this paper I will assume that the substitution effect
dominates the income effect, so that ¢ > 0. Any supply disturbance must be met
by either an adjustment in the real rate of return or in the terms of trade. A

positive supply shock, u, > 0 will initially raise real income and agents will

t
increase their demand for the home product by 62u, according to the absorption
effect. The excess supply (1 - 862)u, will induce a reduction in r, ora
worsening of the home terms of trade OA, > 0), so as to restore equilibrium.

The equilibrium condition in the money market is found by substituting the
interest parity condition (2.15) into (2.14) and solving (2.20). By

suppressing i* and M, this condition is,

2.24 Px, +S - b(ELe

t fet 7 er) =o

If the supply shock is positive, portfolio equilibrium will be restored by
either a reduction in Px or/and an anticipated depreciation of domestic
currency. Both of these adjustments would offset the initial increase in the
transaction demand for money in the absence of monetary accommodation.

The solution of the model is found by utilizing the method of undetermined

coefficients. !° The dynamic paths of e, and Px, are as follows: ?}

oo.
2.25 Px. = (1-p) 5 px®. - ajla +b) {bp(a - 662) + A,ZJu
t j=0 t-1-j t
for allt
1 Sj
=h- - . . Jys
2.26 e, =o C1 - 862 - 9) arn Xee1-j

+ 9°11 + by tay taza - 662 - 6) - p8,87(1 - 652)]u,,

for all t


where Pit is the nominal price of x and Pe is the price deflator, defined as a
weighted average of the nominal prices of x and the imported good, y. The
weights are the shares of consumption out of total domestic absorption, BL: P

t
is defined as,

WA

6

WA

t x 1,

2.6 PL = 6P. tt Qa - Poe 0
where Pvt is the nominal price of the imported product y. Substitution of
(2.6) into (2.5) yields,
2.7 I, = xp > (2 - 8)A,
where aL = Pye - Pot is the terms of trade -- the price of foreign goods in
terms of home goods. Aggregate domestic absorption depends negatively on the
anticipated real rate of return (to be defined below) and positively on real
income, Ti:
2.8 BL = - dir, + Sel, ; 81, 62 > 0.
Ifthe real rate of return rises (ceteris paribus) future consumption will
‘become cheaper and agents will substitute out of domestic consumption into
" future consumption. 62 is the elasticity of absorption with respect to current
income. a is defined as the difference between the nominal yield (on one
period domestic financial assets) and anticipated inflation based on

information at time t,

2.9 rial i, - CEP ead - PO)

where EL is the conditional expectation -based on information at time tf Each
period agents determine how much of their current absorption to allocate
between domestic goods and foreign goods. The demands for x and y by home
residents are derived from a C.E.S. utility function approximated in logs.

These are respectively,

d
2.10 x, = Mer, + Be a> 0


a % oF
parte - /S0+e sd.
€ €

€
By substitution of (2.3) into (2.1) and (2.2) and by extensive manipulation,

output x can be described as,

s_ ys.
2.4 X= Xt 7 PU, + uy:

By differentiation of p with respect to o2/o2 the following can be shown:

3 limit p = 1 limit p= 0.
+2, <0, 32 Pp and o2 p

Vv Vv Vv
oe a? ae”

é & €

P represents the fraction of the disturbance ue that agents regard as
transitory and (1 - p) is the fraction of uy agents regard as permanent. p can
thus be interpreted as agents' evaluation of a supply side policy rule.? The
process described in (2.4) reflects a sudden supply side policy regime in which
the government announces that it will permanently stimulate economic growth by
means of various fiscal measures and agents are uncertain as to the ability of
the government to sustain-such a policy. A policy rule designed to stimulate
output permanently is credible if agents attach a value close to zero for p.
Alternatively, (2.4) can represent disembodied technical shifts in productivity
and agents' uncertainty regarding the permanence of the shock. An important
part of the analysis will be to focus on how the credibility of policy as
measured by p affects the impact of sudden supply side policy shocks on the
exchange rate, the terms of trade and financial markets.

Real income, I, is the value of domestic product less the value of

t

servicing the net external debt. For simplicity I assume that the share of

debt service relative to output is very small so that it can be ignored. Il, is

then approximated as

s
2.5 I, ~ x, + P P


18

zero and y will then appear only in the denominators of (4.3) and (4.4). Thus
if the supply shock is temporary, imperfect information will reduce the
volatility of oa and ee (8Var A, /2Y < 0 and dVar e,/2¥ <0 for p = 1).

The derivative dA, /u, is also ambiguous. If the shock is transient
(p = 1) then 2A, /du, > 0 so that a temporary positive supply shock will worsen
the terms of trade as in the classical case.

When the shock is nontransient p # 1 and if di, /du, <0 (1 - 862 - Ay
<0), 2A, /du, is ambiguous.’ However, if 1 - 652 - Ay > O and i, /au, > 0 then
a positive supply shock will worsen the terms of trade (A, /du, >0). A
necessary and sufficient condition for the terms of trade to deteriorate in the
case of a permanent supply shock, is A; > y(jp - 6,62) where | = b/(1 + b) and
H = -(1 - 662 - Ay). As long as 8Q, /du, > 0, this condition will always be
satisfied.® If 8Q,/du, > 0, then imperfect information will reduce the
volatility of the terms of trade, regardless of the value agents attach to p.
The intuition is that suppliers initially react to the supply shock by reducing
output in response to a perceived real price decline, offsetting the primary

disturbance.?

d. The Exchange Rate and Nominal Interest Rate

As noted in section c, if p = 1, imperfect information will unambiguously
reduce the volatility of the exchange rate (8Var e/8y < 0). Since iy is the
anticipated rate of depreciation then the above conclusion also applies to i,
that is oVar i,/ey < 0 as seen in equation (4.6). The endogenous supply
response reduces both the volatility of ee and i, for policy shocks perceived
to be temporary.

For nontransitory supply shocks, imperfect information introduces a

further real interest rate and nominal interest rate effect as noted in section


Analogous to the price deflator Pe defined in (2.3), is the foreign price

deflator, Pe,

WA
2
Ee
A
me

* = OxPx* ~ @*)Py*
2.17 Pe 8 Pxé +(1- 6 dye 0
Substitute (2.6) into (2.17) and (2.16) and obtain®
- pe - = (6% -
2.18 Pp. 7 ee (6 8)A,-
2.19 says that deviations from purchasing power parity will exist and providing

domestic agents have a greater preference for home relative to foreign goods,

these deviations will be inversely related to the terms of trade, re

b. Equilibrium Conditions
The money market clears so that
_ wd

2.20 M =M-
The supply of exports in (2.12) is equal to the demand for exports (2.20),
2.21 X, = Xf.
(2.20) and (2.21) together with the interest parity condition (2.15) fully
characterize equilibrium for the quasi small open economy. There is one more
implied condition -- the interest parity equation (2.15) together with the
deviations from PPP equation (2.18) imply that real rates of return will be
equalized across countries only after adjusting for capital gains:
2.22 Fret OE Atay - ADs

where Ete - AL is the anticipated deterioration in the home country's terms

of trade.?

c. The Solution
The model has two state variables, ee and Me which are functions of
lagged and current output, ue and the parameter p. Substitute the structural

equations (2.12) and (2.13) into (2.21) and obtain


24

lorne path of the deviations from PPP can be derived as an autoregressive
moving average process. Rewrite 2.28 as

= -~ pe - = (ee - - -1)1 = p_ sayh
Al a = Pp. PE e. = (6 8)(1 - 662)6 (F = pL*t-1 + AtAy ul

The output process can be described as follows

AQ limit x, = Limit[}=hu + aay)
neil neil 4 -

Substitute A2 into Al and obtain

©
a3 a, = (OF = 6)(1 ~ 082071 = p)C Zu, 5) + Aah).
jroo? .
17 - . A
In fact, Fahey = Eee for all j. Thus Eee is agents' forecast
of the permanent terms of trade.
18hen p = 0, a supply shock will induce a classical Patinkin result sr a
once and for all increase in output will lead to an equiproportionate decline
in the price level despite the presence of liquidity preference.

1941 though the effect of p on ee is ambiguous, some elasticity conditions
de,
a=
ou,
can be derived. Differentiate ee with respect to p and obtain sign( 3p )=

sign[- A,b(1 - 052 - 6) - 6;67(1 - @52)]. If 6 > 1 - 662 the first term is
.positive while the second is negative thus the result is ambiguous. If,
however, 1 - 652 > $ and de, /du, is positive (negative) then the greater is

“p, the less (more) volatile the movement in ee: If ¢ > 1 - 66, then as p

increases, volatility will decline only if b > 6,67(1 - 06g)Aq!|1 - 062 - ol

III. Price Contracts

Isuch contracts have been explored elsewhere, for example, Green and
Lafont (1981) and Flood (1981). The length of the contract period will in
general depend on the entire covariance matrix of stochastic disturbances. I
assume that this structure remains constant.

2E Px, is derived from the ex ante equilibrium condition (3.2).

t-1"t
3the model presented is a disequilibrium model. If the product is
durable, agents would derive an optimal inventory rule. I implicitly assume
that the good sold is a service and avoid the inventory problem. See footnote
4 below.

She critical assumption is the fact that x is a nondurable product. If x

were durable the impact of u, one, would be

‘ -1 -1
ep = + ECL ~ 882 - 667°C = p) + kv) = Tu,


International Finance Discussion Papers
Number 225

June 1983

THE IMPACT OF SUPPLY SIDE POLICY RULES ON EXCHANGE RATES, INTEREST RATES
AND THE TERMS OF TRADE: AN EXPLORATION UNDER ALTERNATIVE PRICE RULES

by

Colin Lawrence*

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


ll

the terms of trade in a frictionless economy could be either negative or
positive depending on elasticity conditions. If the M-L elasticity condition
holds (A, > 1 - 662), the above covariance is independent of the degree of
permanence agents attach to the underlying movement in output. > If 1 - 662 -
Ay < 0 a negative supply shock will depreciate the exchange rate as well as
raise Px, such that the measured price level will unambiguously rise. Thus the
elasticities of goods entering international trade play a key role in the
determination of domestic inflation. Finally, by subsitution of the dynamic
path Meo (2.27) in (2.28) deviations from purchasing power parity can be
derived,

©

~ eg = (8 - 8)(1 - 682)¢71[(1 = 9) z
j=

2.28 PL -

jys cavl
ne Xea1ej + AA ul.

As long as 6* # 6 and agents perceive supply side policy as nontransient

(p.# 1) then a sudden policy shock will induce deviations from PPP which
16

persist.

d. Nominal and Real Interest Rates

Agents' optimal forecast of the terms of trade in the following period can

be found by leading (2.27) forward by one period,

Cy
- . -1 . js ol
Aeey = (1 - 862) “(G1 - p) 2p jt AA. 4].
j=0 3
. oO
By taking the conditional expectation of Mea? I obtain!’
1 a
- s :
Pawel = (1 - 662) “(1 - e) E pieeagls since Fea =0.
The real rate of return re defined in (2.22) is then
-1 ‘
2.28 re BE - Loe) = - OP(1 - 852)A; ue *for all t

All the lagged terms disappear since agents optimally forecast a once and for


10

where Ay = 9 + £,6 and Z = 1+ d(1 - p).

AL can be derived by subtracting (2.25) from (2.26),

eo.
2.27 a, = £2826 - 9) z pixS + acagtu] for all t
t o j=0 t-j-1 t
where A= 0 + (1 - p)6,62 = A, - 6,62

(2.25) supports the intuitive assertion that a negative (positive) supply
shock, ue <0 (50) will raise (lower) the nominal price of home goods.
Moreover, according to (2.27) a negative (positive) supply shock will improve
(worsen) the home country's terms of trade. In both the above cases, if the
shock is perceived as permanent (i.e. p = 0), the adjustment to the long run is
imnediate. If the shock is nonpermanent p # 0, the intial response in PxEs e
and AL will be gradually reversed towards the initial equilibrium according to
the decay function (1 - pL). 14 Equation (2.26) shows that the movement in the
exchange rate is ambiguous depending upon a general equilibrium Marshall Lerner
(M-L) condition. Inspection of (2.26) implies that the condition 1 - 852 - o<
7) (8ag + oy + 676 > 1) is sufficient (but not necessary) to guarantee that a
positive supply side shock will appreciate domestic currency. !3 By noting the
definition of ®, a sufficient condition for appreciation in response to a
positive supply shock is that the sum of domestic and foreign demand
elasticities be greater than unity (i.e. Baz + ay > 1) -- the traditional

Marshall Lerner condition.

The discussion above shows that as long as 1 - 662 - Ay < 0 a positive

supply shock will strengthen domestic currency while concommitantly worsening

the terms of trade. This implies that given high enough demand elasticities

[i.e. Ay > (1 - 662)] supply shocks induce more short run volatility in

pete 14 oye
equilibrium terms of trade. The covariation between the exchange rate and



ds.
2.11 Ye = PAL + BL B >O0 «6

The export supply schedule can be approximated (around the steady state) as
x= Mes - 6x4), where = (1 - 8). Using (2.1) and (2.10) this is,

=. . s
2.12 x, = Ba2yar, YOR, + Ox,

The foreign demand for home goods x* depends positively on the terms of trade,>

2.13 t= yaya, wag > 0.
Because the home country is small in the world y market, the price of y in
foreign currency, yy is exogenous to the home economy. Equations (2.1) -
(2.13) describe the real side of the economy.

The money demand equation for domestic agents depends inversely on iy and
positively on xP The schedule is depicted as®
2.14 Me = Px, + x8 ~ da, b> 0.
2.14 is the liquidity preference schedule along which agents optimally allocate
their existing stock of wealth between interest bearing assets (domestic and

foreign bonds) and noninterest bearing money.’ Domestic and foreign bonds are

perfect substitutes so that uncovered interest arbitrage holds at all times,

2.15 i, = is +E

ttt Meftt1 7 &

t?’
where ae is the spot exchange rate defined as the unit price of foreign

currency in terms of domestic currency. The foreign exchange market is fully

flexible with no central bank intervention. Beet 7 ey is the expected rate
of domestic currency depreciation based on information at time t. Any
deviation from (2.15) will induce incipient international capital flows in the
absence of government intervention.

Both the x and y market are perfectly arbitraged so that the law of one

price holds for each good,

= Px* ; = Py*
2.16 Px, = Pxt te and Py, Pyt te,


21

establish the new equilibrium terms of trade. This relative volatility would
be even more pronounced the more credible the supply side rule is. The reason
being that under regimes not fully credible, agents anticipate a future output
decline, which would improve the terms of trade. Arbitrage in financial
markets would then lead to an instantaneous decline in the prevailing real rate
of return. This stimulates aggregate demand thus absorbing the intial excess
supply. Under credible policy rules, the terms of trade adjust immediately to
the long run steady state preciuding a real interest rate movement.

The introduction of imperfect information leads to a confusion as to the
source of the shock. Agents attribute part of the perceived relative price
decline to negative demand shocks instead of the true supply shock and
consequently reduce output. This cyclical output response partially offsets
the intial productivity stimulus if the shock is transient. The volatility of
all prices (relative to the full current information or classical case) will be
reduced. If, however, the policy is regarded as permanent, the cyclical output
effect could dominate the initial supply shock. If this perverse result is
ruled out, imperfect information would also act as a shock absorber for

credible supply side policies.


27 ey

References

Barro, R. J. "Rational Expectations and the Role of Monetary Policy." J.
Mon. Econ. 2 (January 1976): 1-32.

Buiter, W. "Short Run and Long Run Effects of External Disturbances under a
Floating Exchange Rate." Economica 45 (1978): 251-272.

Dornbusch, R. "The Theory of Flexible Exchange Rate Regimes and Macroeconomic
Policy." Scan. J. Econ. 78 (May 1976): 225-275.

Findlay, R. and Rodriguez, C. A. "Intermediate Imports and Macroeconomic
Policy under Flexible Rates." Can. J. Econ. 10 (1977): 208-217.

Flood, R. "Explanations of Exchange Rate Volatility and Other Empirical
Regularities in Some Popular Models of the Foreign Exchange Market.”
Carnegie-Rochester Conference Series on Pubic Policy, J. Mon. Econ. 15
(1981): 219-250.

Frenkel, J. A. and Johnson, H. G. (eds.) The Monetary Approach to the Balance
of Payments. ‘Toronto: Toronto University Press, 1976.

Frenkel, J. A. and Johnson, H. G. (eds.) The Economics of Exchange Rates.
Reading: Addison-Wesley, 1978.

Green, J. and Laffont, J. “Disequilibrium Dynamics with Inventories and
Anticipatory Price Setting." Euro. Econ. Rev. 16 (1981): 199-221.

_Katseli-Papdefstratiou, L. T. “Transmission of External Price Disturbances
and the Composition of Trade." J. Int. Econ. 10 (1980): 357-375.

Kravis, I. and Lipsey, R. "Price Behavior in the Light of Balance of Payments
Theories." J. Int. Econ. 8 (1978): 193-247.

Lawrence, C. Equilibrium Models of the International Business Cycle.
Unpublished Ph.D. Dissertation, University of Chicago (December 1980).

Lucas, R. E., Jr. "Expectations and the Neutrality of Money." J. Econ.
Theory 4 (June 1972): 103-124.

Lucas, R. E., Jr. "Some International Evidence on Output Inflation Trade
Offs." Amer. Econ. Rev. 63 (June 1973): 326-334.

Meade, J. E. The Theory of International Economic Policy, Vol. I: The
Balance of Payments. London: Oxford University Press.

Mundell, R. A. International Economics. McMillan, 1968.

Obstfeld, M. "Intermediate Imports, the Terms of Trade and the Dynamics of the
Exchange Rate and the Current Account." J. Int. Econ. (1980): 461-480.


that positive (negative) supply shocks will appreciate (depreciate) the
exchange rate regardless of the underlying information structure, the pricing
rule and the perceived permanence of the shock.

A further issue addressed here is the covariation between the exchange
rate, the terms of trade and deviations from purchasing power parity.® Under
flexible prices and full current information, I show that the M-L elasticity
condition is a necessary and sufficient condition to guarantee that a slowdown
(increase) in productivity would simultaneously depreciate (appreciate) the
exchange rate and improve the domestic terms of trade. This suggests that the
exchange rate cannot be expected to play a role in accommodating terms of trade
shifts in response to supply shocks. Thus, under flexible prices, supply
shocks will induce more short run volatility in the domestic price levél than
the exchange rate if the M-L elasticity condition holds.

The structure of this paper is as follows. Section II develops the model
of a quasi small open economy under fully flexible prices. Section III
reexamines the basic postulates developed in I under anticipatory pricing in
the form of one period ahead nominal price contracts. Section IV introduces
imperfect information and endogenous output behavior. The conclusion

summarizes the main findings of the paper

II. A Classical Model

a. Structural Equations

A quasi small open economy is fully specialized in the production of good
x. Domestic agents consume x, an imported good, y and are net exporters of x.
While the economy has a large share of the world x market, it is small in the

imported good, y market. Agents hold their existing wealth in the form of


14

role of ee is to clear the money market (2.20) in the absence of a Px
adjustment. In the absence of monetary accommodation, an increase (decrease)
in the demand for money due to a positive (negative) supply shock must be
unambiguously met by a rise (fall) in it» namely the anticipated rate of
domestic currency depreciation (appreciation) .> If agents believe that the
supply shock is temporary (p = 1), an output expansion will necessarily
appreciate the spot exchange rate as seen by inspection‘of (3.3). The movement
in a is greater, the lower the interest elasticity in the demand for money and
is independent of M-L elasticity conditions. However, if a policy rule has
credibility (p = 1), again M-L elasticity conditions become important. A
sufficient condition to guarantee appreciation is the same as the flexible case
condition, namely, 1 - 662 -  < 0.

The validity of ee relative to the flexible price case is generally
ambiguous and depends again on elasticity conditions. There are four
propositions:

(1) If the shock is perceived as permanent (p = 0), the M-L condition
(1 - 652 - 6) < 0 is sufficient (but not necessary) to guarantee that ee will
exhibit more volatile behavior in the sticky price relative to the flexible
price case.©

(2) I£ the shock is transient (p = 1), the sticky price model will
exhibit more volatile exchange rate behavior if 1/b + 1 > |1 - 662 - Ay{az?.

(3) If the shock is permanent (p = 0) and if the exchange rate
depreciated in response to a positive supply shock, the terms of trade AL will
be less volatile under sticky prices.’

(4) If the shock is transient, the sticky price model will exhibit more

1 1

(less) volatile terms of trade behavior if b> (1 - 06,)a-! (bd <

(1 = @82)a7!).


16

IV. Endogenous Output Supply and Imperfect Information

a. The Structure

Domestic output is produced in decentralized markets, where producers
cannot directly observe the realized dispersion of prices across their
competitors. When current prices observed by the firm fall below (rise above)
the perceived average of competitors’ prices, the firm will contract (expand)
output. This is a cyclical phenomenon which disappears in the long run (Lucas
1972, 1973). The above supply curve is depicted as,!
41 Qe = ¥(PX, -—E

s
t-1P¥E) + Xp»

where y is a coefficient depending on the covariance structure of stochastic

shocks and x is defined according to 2.1.7

b. The Solution
Equation (4.1) is addéd to equation (2.1). Exports are redefined as x =
“HQ - ex’), The system is again solved using the method of undetermined

coefficients. The solution is,

©
-(1- js - al -
4.2 Px, = (1 eae eay-3 7 4 [bp(1 - 662) + AiZ]u,,
1 eis
=o . - . J
4.3 e, =o (1 - 862 - 6) Oe Xte1-5

+ ola lEtayz(a - 082 - 6) - p8:82(2 - 065)]
+ y(Q1 - 652)(1 ~ p)[b(1 - 662 - Ay) + (1 + b)6167) ju,

and


imported price disturbances (such as oil) on output, the exchange rate and
inflation [for example, Findlay and Rodriguez (1977), Buiter (1978) and Katseli
(1980)]. These Keynesian models postulate that elasticity conditions
underlying the demands and supplies of international goods play an important
role in describing how imported intermediate good prices affect the exchange
rate. This result contrasts sharply with the monetary approach to the exchange
rate [for example, Mundell (1968)] which views the exchange rate as the
relative price of national monies.* These models postulate that positive
supply shocks would appreciate the exchange rate irrespective of elasticity
conditions.> The above Keynesian and monetary results are derived from a
particular set of restrictive assumptions. The Keynesian models generally
assume short run price rigidities and ad hoc expectations, whereas the monetary
models abstract from imperfect substitution in consumption.

In the light of this controversy, I readdress the question as to whether
or not the Marshall Lerner (M-L) elasticity condition is at all relevant in
explaining the dynamics of exchange rate behavior in response to nonuniform
(across countries) supply shocks. This is explored under different information
structures and pricing rules adopted by rational agents facing uncertainty.
Tronically if the supply shock is regarded as transient and if domestic
(nominal) prices are set by contracts, the M-L elasticity condition is
irrelevant in determining the exchange rate path.© However, this case is an
exception. If the shock is regarded as permanent, elasticity conditions would
again play a role under a regime of price contracts. Moreover, if prices were
flexible, then regardless of the perceived persistence of the shock and
imperfections in current information, the M-L elasticity condition would again
be central in explaining the equilibrium paths of the exchange rate and

domestic interest rate.! In fact, the M-L condition is sufficient to guarantee


25

where vu, is the volume of accumulated inventory at t and k is a parameter

0 $k $1 at which rate the inventory is dissipated. k would depend on
parameters governing agents' optimal stochastic inventory rule. v depends on
the parameters of the model and for temporary disturbances is unambiguously
positive. The traditional M-L condition 602 + ay > 1 is sufficient to
guarantee that even in the presence of inventory accumulation, the exchange
rate will appreciate.

Sthe result of course resembles Dorenbusch's (1976) celebrated
overshooting hypothesis.

Scompute the short run variance of e ,in the sticky and flexible price

t
models. The solution for the case where p = 0 is,
2 i - -
pelsticky) _ [C1 = 082 - 997) - v?

of (flexible) [CQ = 02 - 6)0°1]2

2
Psa.

"The variance of the terms of trade under sticky prices is identical to
the variance of the exchange rate computed in footnote 6. The variance of A.
under flexible prices is computed from (2.27). The relative variance for
p=0 is

oisticly) _ (( - 6,)@71 - a + by]?
o2 (flexible) fa - 662)0 1]2

If - 825)! >1+t vt, e will depreciate and proposition 3 will hold.

Sohis result does depend on the assumption that agents deflate their real
rate by Px, and not Pee If (2.14) were respecified as va = - bi + P+ x the
result would always hold if de/du > 0. If de/du < 0, the result would still

hold if 8Je|/du < (1 - ey}. i.e. if the currency appreciated in response to a
positive shock, the resultant increase in real balances would not be enough to
satisfy the transaction demand for money.

Ite p=0 ee could move either way. If ee does rise, so does AE Since

the implication of 3.7 is that dr/du, > 0, AL can never overshoot its long
run equilibrium.

IV. Endogenous Output and Imperfect Information

lawrence (1980) has constructed a rational expectation model of two
countries trading in local markets for goods and global markets for foreign
exchange and international financial assets. Although no closed form solution
exists, simulation techniques generated dynamic equilibrium paths consistent
with a specification like (4.1).

2the reader should be aware that stochastic shocks (other than supply
shocks) are present in the above setting so as to create misperceptions in


I. Introduction

In the 1970s all major industrialized nations experienced a universal but
nonuniform decline in productivity. ! There were also a number of perplexing
violations of purchasing power parity accompanied by significant shifts in the
terms of trade between major trading partners.” Policy decision making shifted
from the traditional fiscal-monetary mix towards supply side policies oriented
towards revitalizing industrial sectors.

This paper explores how exogenous shifts in the rate of disembodied
technical progress and exogenous supply side policies affect the exchange rate,
the terms of trade, the nominal interest rate and the anticipated real rate of
return. In particular the analysis focuses on the uncertainty as to whether
agents perceive the supply shock to be permanent or not. I consider the role
of sudden credible policies designed to improve productivity. The type of
pricing rule adopted by agénts in an uncertain environment.is shown to play a
central role in determining how domestic and international markets respond to
supply shocks. For example if all prices are fully flexible, more credible
supply side policy rules will induce less volatility in both nominal and real
interest rates than less credible policy regimes. Also, credible policy rules
will make both “the exchange rate and nominal interest rate relatively more
volatile under price contracts than under full price flexibility.

A further purpose is to investigate how supply side shocks influence the
dynamic paths of the exchange rate and the terms of trade under different
pricing rules. Earlier Keynesian models pioneered by Meade (1951) synthesized
Joan Robinson's partial equilibrium elasticity approach to foreign exchange
markets with the closed economy Keynesian paradigm.> This framework has

recently been adopted by a growing literature concerned with the effects of


28

Obstfeld, M. “Intertemporal Price Speculation and the Optimal Current Account
Deficit." Discussion Paper Series No. 166, Columbia University, 1982.
Sachs, J. D.

"The Current Account and the Macroeconomic Adjustment in the
1970s." BPEA 12 (1981): 201-268.

Stockman, A.C. "A Theory of Exchange Rate Determination." J. Polit. Econ. 38
(August 1980): 673-398.


12

all permanent supply shock equal to (1 - p)u,. In an analegous fashion the
nominal yield iy can be found by substituting (2.26) into the interest parity
condition (2.15). The solution is,

2.29 isc pat bv) tajta - 862 - Au, for all t.
Interest rate fluctuation in response to sudden supply side policies depend
critically on the credibility of the policy. If a shock is perceived as
permanent, according to (2.28) and (2.29), agents believe that Px, e and AE
will adjust instantaneously to the new long run steady state, ‘8 Thus for

p = 0, the supply policy will not induce any response in i, and r,. In

t
contrast, government policies which lack credibility (p # 0) will induce
volatility in both real and nominal rates. If a positive contemporaneous shock
were regarded as transient, agents would anticipate an improvement in the terms

of trade as the shock decayed and r, would consequently decline according to

t
(2.28). The nominal yield i, could move either way depending again on the
general equilibrium M-L condition. If 1 - 652 - > > 0 (<0) agents will
anticipate currency appreciation (depreciation) as the supply shock decays and
as a consequence, iL will decline (rise). Thus in the event of supply side
policy rules lacking credibility, prices would all be expected to revert back
to their previous steady state levels creating volatility in financial markets
as well as in intertemporal plans of savings and investment. The terms of trade
movement (2.27) becomes more pronounced when the disturbance is perceived as
permanent. The reason being that AL bears the full burden of equilibrating the
goods market in the absence of a real rate of return effect. The impact of p

on the paths of Px and e, in response to a supply shock is generally

t
ambiguous. If however the Marshall Lerner elasticity condition holds
(1 - 052 - @ < 0) a positive supply shock will lead to a decline in i, if

p #0. This will reinforce the transaction demand for money and the adjustment


15

b. Interest Rates
Since contracts are renegotiated at the end of each period, the newly

negotiated contracts (CE, Px 4) will incorporate contemporaneous disturbances.

Agents' forecasts of deed and ret will be identical to the classical case

derived in section II. The solution of i, can be derived directly from (2.20),
~ orl

3.5 i,= b ue

i, will decline in response to a positive supply shock irrespective of agents
assessment of credibility. This contrasts sharply with the classical results
of.section II. A supply shock effects the demand for money and iL is the only
variable free to equilibrate the money market .® Recalling that permanent
disturbances (p = 0) have no impact on i, under flexible prices, then price
contracting induces greater volatility in interest rates under credible policy
regimes. Comparing (3.3) with (3.5) a statement concerning overshooting can be
deduced. If the M-L condition holds (1 - 652 - $< 0), a supply shock will
necessarily induce overshooting of the exchange rate for credible policy

” regimes. A productivity expansion would appreciate ee by more than the
anticipated appreciation so as to raise the nominal interest rate.

r, can be found by leading (3.4) forward by 1 period and taking the

conditional expectation,

“1 “1 .
3.6 Beda, = (1 > 662)6°°(1 - pC = pty tx, + (1 - 682)972 C1 - p)u,.
Subtract (3.4) from (3.6) and obtain,

_ . _ . -1
3.7 Fr, = OCR AL, 7 AR) = Ol1 - p +b Ju.

a will unambiguously rise (fall) in response to a positive (negative) supply
shock irrespective of agents’ beliefs concerning p, since agents anticipate a
worsening of the home terms of trade. If p = 0, overshooting of the terms of
trade can never occur, since agents believe that the terms of trade (3.7) will

worsen irrespective of the initial movement in Ae (3.4).