-19-

asset sector may not provide a robust explanation of portfolio manager's
behavior. The specific results we derive below are incomplete at best
and should be viewed accordingly. However, we think that they provide an
interesting and important complement to the positive implications of wage
contracting discussed in the last section.

Wage setters in our model are worried about their price prediction
errors. Those covered by one-period contracts are interested only in
one-period price prediction errors; those covered by two-period contracts
are interested in both one and two-period price prediction errors.

Serial correlation in disturbances, lags in the economic struture and
monetary policy can all cause the two to differ. Portfolio managers

worry about unanticipated changes in the real interest rate,

(27) Lig ~ (Piggy - PI_ID - Gy - CPigagye - PHED = -Otearye > Pte)

where
pi, = (1 - o)PE + wle, + pe

pi is a price index, and w is thé share of foreign goods in portfolio
managers' market basket. So porfolio managers are interested in the

one-period price index prediction error2o/2z/

(28) Dig = Pages = oC, - eepeen) + (1 = ©), - Peer)

which depends upon both price and exchange rate prediction errors.
III.B. Wage Contracting and Agents' Normative Measures of Volatility

The one-period price and exchange rate prediction errors that are


The fixed wage model is solved in a similar manner. First assuming
that 9 = 0, we postulate that

+ EnV, = E42 - €,U

(5A) e t 7 5M S61

ot
(6A) Pez mM +m 7 +0

We can then substitute for Cpe Pes and Peitet in the goods market
equilibrium condition,

9(PE = Perea) - Sleep - PE) - Upp > UE EO

We can then solve for the e's in terms of the m's. (Since this equation
must hold for all possible values of the shocks, the coefficient of each
shock must equal zero.) We can rewrite the money market equilibrium

condition, equation (4) in the main text, as
(1+ 0)PE = Meare — ee) tM tM tM t Perey

We can solve for Pe substituting for etait - e& and Pelee using
(5A) and (6A) and writing the e's in terms of the m's. We can equate the
coefficients from this equation with those in (6A) and solve for the m's.
The model with » different from zero is solved in the same way.

The neo-Keynesian contracting model is solved in two steps. First

we postulate a solution for Xp

t-1 2 t-1 3t


-F7-

4 = (1 + @)/ (6 + 66) = 1/6; with this policy, temporary goods market
disturbances (rather than permanent ones) would be totally absorbed by
the exchange rate. Turnovsky ( ) and Buiter and Eaton (1980) have

found similar results.


-13-

the decrease in price level undershooting, and the existence of two-
period contracts helps explain the fact that exchange rates are more
volatile than prices.

The reason for these results is that portfolio managers see the
permanent monetary disturbance and understand that it will also affect
the future output of firms with contracts that carry over to the next
period. This recognition affects their exchange rate predictions, and
thus their current demands for money and bonds. For example, for a
positive disturbance, the existence of two-period contracts decreases the
expected rate of appreciation of the home currency and lowers the current
demand for it; this then increases the impact on the current price level,
“output and exchange rate.

Summarizing, neo-Classical contracting helps explain the stylized
fact that exchange rates are more volatile than prices in the presence of
monetary disturbances. Increasing the length of some of the contracts
goes even further in explaining the fact in the presence of permanent
monetary disturbances. This form of contracting does little to help
explain the stylized fact in the presence of goods market disturbances,
but then goods market disturbances already had more impact on exchange
rates than on prices in the flexible-wage model; there wasn't really a
paradox to be explained. Neo-classical contracting can also help explain
persistence. The economy is fully adjusted to a permanent monetary
disturbance only after the last existing contract is renegotiated.
Persistence may however be better explained by the neo-Keynesian
contracting model discussed in the next section; there temporary and
permanent disturbances are ‘passed from one contract to the next

successively through time.


-23-

(36) My ryt 8[n3(m, + V4) + 142]

It is clear from (36) that tie cyclical effects in output and employment
have been eliminated, even though two-period contracts still exist .22/
The lagged feedback policy (33) reduces two-period price prediction

errors to one-period price prediction errors.
(37) PL - Pelt-2 = Peo Pelt = 1, (m, + ‘4 ) + TAZ

It converts the permanent monetary disturbances into temporary ones.
Hence, there is no useful information embodied in one-period price
predictions that is not already embodied in two-period price predictions.
And in addition, one-period errors are smaller because temporary monetary
disturbances have less impact on the price level than permanent ones;
that is, 3 is less than 1 32! So the feedback policy (33) benefits
both one and two-period wage contractors if permanent monetary
disturbances are an important determinant of price fluctuations.

Portfolio managers are also better off in this case because
(38) e- ete = e€(m, + V4) + e42y

Temporary monetary disturbances also have less impact on the exchange
rate, so both components of the price index prediction error (28) are
reduced. 24/

Exchange Intervention Policy:

A policy of the form


References

Barro, R., “Long-term Contracting, Sticky Prices, and Monetary Policy,

Journal of Monetary Economics, 3, 1977, p. 305-16.

Bhandari, "A Stochastic Macroequilibrium Approach 20 a Floating Exchange
Rate Economy with Interest-Bearing Assets," Weltwirtschaftliches
Archiv, Band 117, Heft 1, 1981, p. 1-19.

Buiter, W. H. and J. Eaton “Policy Decentralization and Exchange Rate
Management in Interdependent Economies," N.B.E.R. Working Paper No.
531, August 1980.

Canzoneri, M. “The Returns to Labor and the Cyclical Behavior of Real

Wages: The Canadian Case," The Review of Economics and Statistics,

LX No. 1, February 1978, p. 19-24.

Canzoneri, M. "Labor Contracts and Monetary Policy," Journal of Monetary
Economics, 6, 1980, p. 241-255.

Dornbusch, R. "Expectations and Exchange Rate Dynamics," Journal of
Political Economy, 84, 1976, p. 1161-76.

Fischer, S. “Long Term Contracts, Rational Expectations, and the Optimal

Policy Rule," Journal of Political Economy, 85, Feb. 1977a, p. 19

205.
Fischer, S., “Long-term Contracting, Sticky Prices and Monetary Policy:

A Comment," Journal of Monetary Economics, 3, 1977b, p. 317-23.

Flood, R. and R. Hodrick, “Exchange-Rate and Price Dynamics with
Asymmetric Information," unpublished manuscript, June 1982.

Flood, R. and N. Marion, "The Transmission of Disturbances under
Alternative Exchange Rate Regimes with Optimal Indexing," Quarterly

Journal of Economics, 97, 1982, p. 43-66.


-4-
(1) yy = ¥ ~ (PE = ey = PE) + Uy + 2

where y, p, e and p* are (the logs of) output, its home currency price,
the exchange rate, and the foreign currency price of foreign output, and

u and Z are disturbance terms 2/ Supply of the product is fixed at its

full-employment or "natural" rate, y.

This is a consequence of the flexible-wage assumption; the nominal wage
moves each period to clear the labor market.2/ .

Incipient capital movements insure that

= r* -
(3) re TE * Cae 7 et
where r and r* are the nominal rates of return on domestic and foreign

bonds, and e is the expected rate of depreciation of the

te1|t 7
domestic currency. Expectations are assumed to be "rational ;" etal lt is
the expected value of next period's exchange rate based upon complete
current and lagged information. Home country residents hold the entire
domestic money stock; money demand is given by

(4) om = Pp = ATE + YE > ME

where m is the (log of the) domestic money stock, and V is a velocity

4/

disturbance.—


-F5-

is apparent from the fact that d(e, - 1)/do = (1 + 8/8)dn, /do.

17/ As shown in footnote 16, da /d¢ > 0; so the immediate impact on
output is bigger for larger 9. From equation (1), this means that the
immediate impact on e - p must also be bigger.

18/ These latter features are not necessary. We could, as in the last
section, specify an employment rule and let the price level move to clear
the goods market. Taylor however wanted a model that de-emphasized the
cyclical role of real wages; see footnote 13.

19/ Taylor (1979, 1980) uses Veter and Yea feet to measure expected
demand pressure. In his model these measures reduce to expected real
balances, but in ours they do not (except in special cases where eat [tel
- Melt = 0). Our specification is necessary to retain the simplicty of
Taylor's solution. In particular, if we had used Veal [t-1 and Yefter we

would have had to solve the following cubic equation in a:
2 2
a= .5(1 - .5y)(a” +1) - .5ya + .25yp(1 - 6)(1 - a%)(a + 1)

20/ Derivation of this solution is discussed in an appendix.

21/ We will assume y is less than two. If y is greater than two, the
moderating effect of expected demand pressures is so great that a is
negative.

22/ The moving average representations for % disturbances are given in
an appendix.

23/ The normative implications of the neo-Keynesian contracting model
discussed in section II.C. are less clear to us; so we restrict our

attention here to the neo-Classical model.


relevant to portfolio managers can be calculated from equations (15) and

(16):
(29) Pe ~ Peyear = MMe + 73M + 142
(30) e - et |t-1 = eym, - (1/8)u, + E3VE = E42

We showed in section II.B. that wage contracting causes the
exchange rate and price level to overshoot and undershoot respectively
their flexible-wage values in response to both permanent and temporary
monetary disturbances 22/ The price levels undershooting will help
portfolio managers, but the exchange rate's overshoot ing will hurt them.
On balance, wage contracting will be beneficial to portfolio managers if
(1 - w), the share of the domestic good in their market basket, is large
enough. Increasing 9, the proportion of contracts that last two periods,
will hurt portfolio managers because it increases the exchange rate
overshooting and decreases the price level undershooting in response to
permanent monetary disturbances .22/

Wage contracting does not matter to portfolio managers in the case
of permanent goods market disturbances; they are always absorbed by the
exchange rate. However, temporary goods market disturbances have less
impact on both the price level and the exchange rate with wage
contracting. It is difficult to assess the implications of this for
portfolio managers since a positive price prediction error tends to
cancel the negative exchange rate prediction error in the price index
prediction error .22/ However, we might expect that wage contracting

benefits portoflio managers in the case of goods market disturbances.


-26-
where
fp - eg = {6(1 + A +g) + O[6(1 + g) + A]}n/8(1 + g)

in addition to the price prediction error (43), as both are components in
their price index prediction error (28).

A strong intervention policy will always reduce exchange rate
fluctuations and make the exchange rate more predictable. In the case of
monetary disturbances, this will benefit both wage setters and portfolio
managers. Monetary disturbances make the price level and the exchange
rate fluctuate in the same direction; so there is no cancellation in
(28). A strong intervention policy will make both fluctuate less and in
this way decrease portfolio managers price index prediction errors.

However, unlike wage setters, portfolio managers will probably
favor some intervention in the case of goods market disturbances. Goods
market disturbances make the price level and the exchange rate fluctuate
in opposite directions, so price and exchange rate prediction errors tend
to cancel in (28). With no intervention at all, permanent goods market
disturbances are absorbed totally by the exchange rate. Some
intervention to stabilize the exchange rate will make part of the
disturbance be absorbed by the price level. Thus, with some
intervention, a smaller exchange rate prediction error in (28) will be
further offset by a price prediction error in the opposite direction.
This will clearly benefit portfolio managers. The case for temporary
disturbances is less clear since the effect is shared with no
intervention. The more important is the foreign good in the portfolio
managers’ market basket, the more likely are they to benefit from some

intervention in this case as well.


-22-

III.C. Wage Contracting and Monetary Policy

Wage contracting slows adjustment in the labor market, and this
introduces persistence and exchange rate overshooting. A lagged feedback
rule for monetary policy can take the persistence out of deviations in
employment and output about their natural rates, and an exchange
intervention policy can smooth exchange rate fluctuations. In this
section, we examine the effects of these two policies on the various
agents in our economy. Once again, the results depend upon whether
monetary or goods market disturbances are the primary causes of price and
exchange rate flucutations.
Counter-cyclical Policies:

Let the money supply process be represented by

(32) m= My
where hy represents "policy". It should be obvious that the lagged

feedback rule

(33) h = -m

t os

t-i

offsets all expected effects due to permanent monetary disturbances. If

it were imposed, equations (15), (16) and (17) would reduce to

(34) P= 1, (my + %) + 42,

(35) e, = e,(m +) - (1/8)35 Uy 7 &qzt


-F6-

24/ Equation (3) asserts that risk neutral agents dominate the market;
but that does not preclude the existence of risk averse agents. More
generally, similar results would be obtained in a model in which bonds
were imperfect substitutes.

25/ See footnote 6.

26/ Here, as above, we have set Pe equal to zero.

27/ Labor suppliers would be more like portfolio managers in this if we
had not assumed that labor supply is perfectly inelastic; see footnote 3.
Labor demanders would remain interested in own-price prediction errors.
28/ See footnote 9.

29/ See footnote 16.

30/ Ey falls less than 1,; see footnote 10. So it is possible that

re
portfolio managers will be worse off if w is large enough.

31/ See footnote 16 and the definition of 1%, in equation (15).

32/ Indeed, one might expect the number of two-period contracts to grow

as a result of this policy because, as shown below, the variance of two- ;
period prediction errors -is diminished; see Canzoneri (1980).

33/ When @ = 0, 1) = TM3(1 +i) > 13. Since dn, /dg > 0 (see footnote 6)

and dn 4/do = 0, TM > 1, for all $ between zero and one.

3
34 e,= T+ (6/6) In, >—+ (8/6)In, = €, since TM) > 13.

35/ dn 4/dg is clearly negative, and TM37 Oasgro,

36/ dm ,/dg = 6(1 + @)n2 > 0, and for permanent disturbances Tr = Te = 0
if g is set equal to zero.

37/ | Wage setters would actually prefer a policy that destabilized

exchange rates in the case of temporary goods market disturbances.

Setting g = -A would make TM|]F 0, but it would also increase £4 to


-17-

(24) Pp = re eaT Mey where m = -5(1 - a)

n, 21 - aT + a) i>2
(25) e = 25 _g&jTM_5 where Ey = By > &

e, = 1 +801"! i>]
(26) y, = ¥ + Zy_qnym,_; where Ng = 6By > ny

ny = 6[.5() +a) +8,]0°) 421

i 1

Permanent monetary disturbances are neutral in the long-run; that
is, W.. TM,, and e, are all equal to one,-and n,. is equal to zero.

However it takes an infinite amount of time for a given disturbance to
work its way through the system.

Hence, the present model produces overshooting patterns for the
exchange rate that are very similar to Dornbusch's. In response to a
positive disturbance, the exchange rate overshoots its long-run value,
and the price level undershoots; after one period, both begin a smooth
exponential decay to their long-run values. The real exchange rate and
output similarly go positive and then decay back to their natural rates.
Smaller values of y imply larger values of a, more overshooting of the
exchange rate and output, and a slower decay to the long run values.

III. THE NORMATIVE IMPLICATIONS OF WAGE CONTRACTING AND MONETARY POLICY

In this paper we have abscribed the slow adjustment in the goods
market, and the consequent overshooting of the exchange rate, to wage
contracting. The neo-Classical, of contracting model discussed in section
II.B suggests certain measures of volatility in exchange rates and prices
that may be relevant from a normative point of view, 22/ and these

measures are not necessarily the ones that were focused upon in the last


-9-

We consider first the case in which » is equal to zero; all
contracts last just one period. In this case, we have

Solution to Neo-Classical Contracting Model, 9 = 0:

(12) Pp = mI, +0, Mm. + mV, + 142

(13) 7 My + &3%E 7 (1/8)2 Ung 7 Eq2t

o
"
my
se
+
um

where

mF 1a a ey = 01 + (6/6)

1, = 1 = 6) e, = [) + (6/6)}0

3 =? +A) +6 3 3

Tm] [e/(1 - p)In, 4 = (1/6) - [1 + (8/6) Inq >0
and

p= a/(A +6) <1
The derivation of this solution is discussed in an appendix.

The first thing to note is that contracting decreases the impact of
monetary disturbances on the price level and (if 6 <1) increases the

9/

impact of monetary disturbances on the exchange rate.— In this way,
contracting can explain the stylized fact that exchange rates are more
volatile than prices. Contracting does little however to help explain
our stylized fact in the case of goods market disturbances. Permanent
goods market disturbances are still totally absorbed by the exchange

rate, and contracting mutes the impact of temporary disturbances on both


-F3-

8/ See Gray (1978) and Canzoneri (1981) for a discussion of the
determinants of 9.

9/ Starting with permanent disturbances, vy is clearly less than 1, and

cy = 1+ (1 = 6)o0/aL(1 ~ p)(1 + x) + 81

is greater than 1 if 6 <1. Similarly, for temporary disturbances

3 = [1/(1 + 4)] - @/(1 + AED = p)(1 + A) + 09

is less than 1/(1 +), and

e€, = [1/(1 + A)] + (1 - 6)0(1 ~ 0)/6(1 + A)E(T ~ o)(1 + A) + 8)

is greater than 1/(1 +A) if 6< 1.

10/ Contracting does make the condition for Z, to have a greater impact

t

£4 >] if 4<1 +6. In the flexible

wage model, the conditon was A < 1.

on e, than Pe less stringent.

ll/_ It may be interesting to note that Dornbusch (1976) gets precisely
the same condition for overshooting in his fixed-price model. A small 6
keeps demand from increasing too much in equation (1) in response to the
decrease in the terms of trade.

12/ The coefficients for the monetary disturbances in equation (14)

depend directly upon 6; that is,

d(er,)/de = (1 ~ 9)2(1 + a)2/E(1 = p)(1 +a) + 8]? > 0


-27-

Summarizing, if monetary disturbances are the primary cause of
price and exchange rate fluctuations, then both portfolio managers and
wage setters will favor a strong exchange intervention policy to control
the exchange rate's overshooting. Such a policy will stabilize the price.
level, the exchange rate and the price index; it will make both the price
level and the real rate of interest more predictable. If however goods
market disturbances are the primary source of price and exchange rate
fluctuations, then the monetary authorities may have to choose between
Portfolio managers and wage setters. Intervention shifts the effects of
these disturbances from the exchange rate to the price level, increasing
price prediction errors, but quite possibly making the real interest rate

more predictable.


-6-

increase produces an expected rate of depreciation and a temporary
increase in the terms of trade that is absorbed by both the price level
and the exchange rate.

The important thing to note is that in our benchmark case monetary
disturbances, be they permanent or temporary, have an equal impact on the
exchange rate and the price level. This result is inconsistent with our
stylized fact that exchange rates are more volatile than prices, and it
is the paradox that the “sticky-price" models of Dornbusch (1976) and
others were built to explain.

However, it is also interesting to note that goods market
disturbances may have more impact on exchange rates than prices.
Permanent disturbances are totally absorbed by the exchange rate, and
temporary disturbances have a larger impact on the exchange rate than the
price level if the interest semi-elasticity of money demand is small (A <
1). If price and exchange rate movements are primarily determined by
goods market disturbances, then our flexible-wage model is probably not
inconsistent with our stylized fact.

In summary, our benchmark flexible-wage economy is inconsistent
with the stylized fact that exchange rates are more volatile than prices
if the monetarist view prevails and exchange rate movements are primarily
monetary phenomena. If instead exchange rate movements result from goods
market disturbances, then we may have no paradox to explain.

The flexible-wage model is definitely inconsistent with our second
stylized fact concerning persistence. The effects of both monetary and
goods market disturbances are immediate and complete within the period in
which they occur. The system requires no further a‘justment.

II.B. A Neo-Classical Contracting Model

Fischer (1977), Gray (1976, 1980) and Canzoneri (1981) have


-5-

We want to model both temporary and permanent monetary and goods
market disturbances. A "~" over a disturbance indicates that it is
serially uncorrelated and normally distributed. ¥V is a temporary
monetary disturbance, and Z is a temporary goods market disturbance. m

and u are assumed to follow a random walk,

(5) mM = m7 +m and UL = Ub, + Up»

"

so m and u are permanent monetary and goods market disturbances.
For simplicity, we set Pt and rt equal to zero; then we have

Solution to Flexible-Wage Model:

(6) Pp = 2y My + CIT + aI, + Lae + a),

won
TM,

(7) ey = 25

Fy My + O/C FAD, - (1/8)25 Oy - C1761 + a) Iz,
Solution techniques are discussed in an appendix.

Money is of course neutral in this frictionless economy. A
permanent increase in the money supply produces permanent and
proportionate increases in the price level and the exchange rate; it has
no effect on the expected rate of depreciation, tart - et. By
contrast, a temporary increase (which is equivalent to a positive v4)
produces an expected rate of appreciation, and therefore has less than
proportionate effects on the price level and the exchange rate. A
permanent increase in demand for the home good is immediately offset by a
permanent increase in the terms of trade, which is achieved by a

permanent appreciation of the exchange rate; there is however no change

in the expected rate of appreciation or in the price level. A temporary


-18-

section; there we were engaged in explaining certain stylized facts that
are of interest to the observing economist.

Here we begin by identifying the measures of volatility that would
seem to be relevant to the wage setters and the portfolio managers in our
economy. Then we examine the implications of wage contracting and
monetary policy for these normative measures of volatility. We consider
two kinds of policy. One offsets the cycling of employment and output
brought on by long-term contracting; the other smooths the exchange rate
overshooting. Not surprisingly, we find some tradeoffs between the
interests of wage setters and portfolio managers. Once again, the
results depend crucially upon whether economic fluctuations are caused by
monetary disturbances or by goods market disturbances.

III.A. Normative Measures of Volatility

The agents in our simple economy make decisions on the basis of
their expectations of future prices and exchange rates. Wage setters are
worried about price. prediction errors and the deviations from full-
employment that they cause. Portfolio managers are worried about the
variability of real interest rates. 24/

We realize that we are on precarious ground here. We have only
modeled certain kinds of agents with certain kinds of problems. There
are undoubtedly other agents in the real world for whom the size of
prediction errors is not the only relevant measure of volatility. Some
firms for example may have to incur adjustment or inventory costs for
even perfectly foreseen fluctuations in demand. What's more, our labor
contracts were not derived explicitly from a utility maximizing
framework, and their form may not be invariant in some of the policy

experiments we want to perform. 22/ Similarly, our specification of the


-8-

maximizing firm's demand curve, but there are other possibilities .£/ The

output supply curve in period t + i for firms under this contract is

(10) Yay = Y + Peay ~ Praaye)

and the slope of this curve, ©, depends positively upon the marginal
productivity of Tabor.2/

The aggregate supply curve we use in place of equation (2) is

(11) ve = ¥ + (1 ~ 6)0(Pe-Peig_y) + 40-52 (PEPE ye) + -50(PE-Pe ita)

We assume that some firms are covered by contracts that last only one
period while others are covered by contracts lasting two periods; ¢ is
the fraction of firms covered by two-period contracts. If is equal to
zero all of the contracts are renegotiated at the end of each period, and
output fluctuates about its "natural rate" with one-period price
prediction errors. If ¢ is greater than zero, all of the one-period
contracts and half of the two-period contracts are being renegotiated at
the end of each period; the other half of the two-period contracts are
going into their second and final period. The second term on the RHS of
(11) comes from the one-period contracts; the third is due to the two-
period contracts.

By increasing ¢ from zero to one, we can increase the inertia in
the labor market and assess its implications for the volatility of price
and exchange rate movements and for the persistence of effects.2/ We
could also include contracts that lasted more than two periods, but the

implications of such an extension will be obvious.


-24-

(39) h, = -m

t g>o0

t-1 7 9%

can control the exchange rate's overshooting in addition to removing the
cyclical effects on output and employment. If it is imposed (and
assuming for simplicity that is equal to zero), then (34), (35) and

(36) become
(40) Ph = 73 (m, + 79) tmy2y + meu, MEU,

(41)

i)

(42) yy 2 V+ olny (i, + Vy) + yz + (ng - ug )iI

where
m3 = 6n £3 = (6 + 6)n
my = (A+ 9)n 4 = (1+ 8)n
m7, = 9/8(1 +g) eg = 1/8(1 +g)
1). = (6+ +4 g)enn, &5 = qa - 8) gene,
and

n= I/[6(1 +A +g) + 0(6+A+g)]

For large values of g, all exchange rate fluctuations are eliminated.


International Finance Disucssion Papers
Number. 212

December 1982

WAGE CONTRACTING, EXCHANGE RATE VOLATILITY, AND
EXCHANGE INTERVENTION POLICY

by

Matthew B. Canzoneri and John M. Underwood

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.


-l1-

(14) y zy + Onn + Ona¥y + OnyZ,

The impact of monetary disturbances on output and the amount of exchange
rate overshooting and price level undershooting all depend upon the size
of 9.t2/ A bigger 6 implies a more elastic supply of output. Thus, in
response to an unanticipated increase in the money supply, the increase
in output does more to equilibrate the money market, and the price level
does less; in terms of Figure 1, the price level undershoots more. And
with a bigger supply effect, the terms of trade must fall further to
equilibrate the goods market; the exchange rate overshoots more to
produce this terms of trade effect.

So 6 is an important parameter in this explanation of output, price
and exchange rate fluctuations in response to monetary disturbances. As
stated above, a large 6 is implied by a high marginal productivity of
labor and a relativley wage-elastic employment rule w3/14/

One-period contracts do allow deviations in output from its full-
employment level, but they do not explain the persistence in these
deviations that we have taken as our second stylized fact. Similarly, it
is clear from equations (12) and (13) that the price level and the
exchange rate adjust fully to any disturbance after only one period.

With ¢ > 0, some contracts last two periods, and we have

Solution to Neo-Classical Contracting Model, ¢ > 0:

(15) Pe = mM, + Tom,» +5

(16) eg = em + ep) + 2p My

+ 63M, - (1/8)25 Ung 7 &q2e


-10-
the price level and the exchange rate L0/

These results for monetary disturbances can be explained in terms
of "overshooting" of the exchange rate and “undershooting" of the price
level. Figure 1 shows how a permanent increase in the money supply at
time to affects the price level and the exchange rate over time. (The
analysis of temporary monetary disturbances is analogous.) In the

flexible-wage model, the full effect of m On Py and e is immediate and
0

permanent, as represented by the solid line in Figure 1. With one-period
contracts however, the price level will undershoot in the first period;
this is represented by a dashed line in Figure 1. The rising price level
and falling real wage increase output and therefore money demand;
consequently, a less than proportionate increase in the price level is
needed to equilibrate the money market. The exchange rate will
overshoot, as shown by the dotted line in Figure 1, if 6 is less than
one. The less than proportionate increase in the price level leaves an
increase in the real supply of money that must be accomodated by an
increase in demand. The increase in output raises transactions demand,
and if this is not sufficient to fill the gap, the interest rate falls.
It is clear from the interest parity equation, equation (3), that this
requires the exchange rate to overshoot and create the expectation of an
appreciation; otherwise, risk neutral portfolio managers would not hold
domestic bonds. The condition on 6, which we assume to hold, keeps the
output effect on money demand from reversing this result by limiting the
effect of the fall in the terms of trade on demand for the domestic

WW/

good.—'

From (11) and (12), output is given by


-F2-
m, ~ Pig = Ary + (DE + YE = PIE) - VE

where pi is an index of domestic and foreign good prices. Letting n= 1,

this specification becomes (4) above.

5/ See footnote 3.

6/ Barro (1977) and Waldo (1981), following the spirit of the “implicit
contracts" literature, suggest that colluding suppliers and demanders of
labor will settle upon some other rule. Barro (1977) is justly critical
of this kind of contracting model because of its lack of utility
maximizing foundation, but see also Fischer's (1977b) response.

J/ Assuming that the production function is Cobb-Douglas, the first-

order condition for profit maximization (in logs) is:

(YT) = Pt Peete - Prag > IY

where y is labor's share of output. Choosing units so that n 0,

tei lt ~

Iny = w - p and

>
"

ty 7 EV oes > Praia ye)
making
Yeag = CY/0 ~ 9) TPE - Peaayt)

Hence, @ = w/(1 - y) and de/dy = 1/(1 - y)2> 0 foro<y <1.


Footnotes

1/  Dornbusch's (1976) paper stimulated many others. Weber (1981) and
Bhandari (1981) for example replaced Dornbusch's Phillips Curve with the
two familiar versions of the Lucas supply hypothesis. Flood and Hodrick
(1982) use information asymmetries to try to explain some of the same
stylized facts.

2/ Dornbusch's (1976) specification included the real interest rate. We
have left it out for simplicity.

3/ More generally, full-employment output will not be a time-invariant
constant. It will fluctuate with the terms of trade and with
productivity disturbances.

Salop (1974) initiated a host of papers investigating
the implications of the fact that labor supply is a function of wages
deflated by an index of prices while labor demand is a function of wages
deflated by just the price of the domestic product; one implication is
that full-employment output depends upon the terms of trade, Gray (1976)
initiated a host of papers investigating the implications of productivity
disturbances and indexing in contracting models. Flood and Marion
(1982), Marston (1982) and Turnovsky (1982) are a recent examples of
both; our paper is an example of neither.

We assume that labor supply is perfectly inelastic, avoiding the
issues raised by Salop, and that there are no productivity disturbances,
avoiding the issues raised by Gray.

4/ The income elasticity of demand has been set equal to one so that the
money supply is effectively deflated by the price of domestic output.

More generally we would have


developed contracting models in which the nominal wage must be specified
in a labor contract before markets meet and production occurs. Ina
popular version of these models, there is a supply of labor derived from
utility maximization and a demand for labor derived from profit
maximization, and wage setters choose the wage that is expected to clear
the market.

If labor supply is perfectly inelastic, and if there are no
Productivity disturbances, then the market clearing real wage is a time-
invariant constant, w - pv! The labor contract specifies nominal wage
rates, so the wage setters must first predict the price levels that will
Prevail during the contract period and then set the wage rates

accordingly. For example, the contract wage for period t + i will be

(8) yy WP + Peailt

in a contract negotiated at the end of period t; wage setters expect this
wage to clear the market in period t + i.

Of course, the real wage that actually obtains in period t + i will
not be the market clearing one unless the wage setters predict the price

level perfectly; that is,

(9) w wW

tei 7 Pte Pe Peay - Pesilt)

With probability one, the plans of both suppliers and demanders of labor
can not be realized. So the contract also specifies (perhaps implicitly)
an employment rule that relates employment in period t + i the real wage
that actually obtains in period t + i. We follow the authors referred to

above in assuming that the employment rule is identical to the profit


-21-

For wage setters covered by one-period contracts, the relevant
measure of volatility is the size of the one-period price prediction
error (29). For wage setters covered by two-period contracts, the

relevant measure may be taken to be

(31) -5(Pp = Pee ig) + -5(Peay > Pearpeed) = 5% (E47 + Me)
+ .5rom, + +53 (Vey + Yt) + 54 (2444 + ts

the average price prediction error over the life of the contract.

Wage setters must benefit from wage contracting; otherwise they
would not do it. The interesting question here is how contractors under
‘existing one and two-period contracts are affected by an increase in 9,
that is, by the conversion of other one-period contracts to two-period
contracts. We showed in section IJ.B. that increasing ¢ magnified the
immediate impact of permanent monetary disturbances on prices, but muted
the lagged effect; that is, dn, /d¢ is positive, but day /d¢ is
negative.2// So an increase in » makes one-period contractors worse off,
and probably two-period contractors as well.

Summarizing, the existence of wage contracting will probably
benefit both wage setters and portfolio managers, especially if goods
market disturbances are an important source of price and exchange rate
fluctuations. However, an increase in 9, the conversion of some one-
period contracts to two-period contracts, will hurt both portfolio
managers and wage setters under existing contracts if monetary
disturbances are an important source of price and exchange rate

fluctuations.


-A4-

Appendix: Moving Average Representation of the Solution to the Neo-
Keynesian Contracting Model with Wage Disturbances

The following equations show how disturbances to the wage setting
process affect wages, prices, the exchange rate, and output under the
assumption that all other disturbances are zero.

wo in ~ © j-l~
inn * *tei i ine a Ol

x
+
r

~ © j-l~
= 65k, + .5(1 + a) Ey al” 'X

Bo]
+
"

t-i

~ 2 j-l~
YE -5(8, + +5) XK - 5(8, + .5(1 + a))E5 a’ Xe

With y < 2 (see footnote 21 of the main text), 0 < a <1, and the effect
of a wage disturbance on wage setting dies out monotonically. The price
of the home good rises for two periods and then drops monotonically. The
exhange rate may appreciate and output may fall for two periods before

decaying monotonically to their long-run values.


Appendix: Model Solutions

We solve the models given in the paper by the method of
undetermined coefficients. We postulate that the dependent variables of
interest, the exchange rate and the home good price, are linear functions
of current and lagged disturbances. For example we might postulate that,

given the flexible wage model,

(1A) ee = M + M1 + €3M4 - 42, - ep - ecuy |
From the money market equilibrium condition we have
(2A) p, = Meare - e) +m tm + My

We note that

(3A) eat|t ~ = -€g¥, + € 42, + (e, - 6 )Ub

From equation (1) in the main text, the goods market equilibrium

condition is,
(4A) ep = PE - 1/8 (uy _y + Uy + 2)

Using (2A) and (3A) we can solve (4A) for e, as a function of the
exogenous shocks. We equate the coefficients in this solution to those
in (1A) and solve for the e's. The resulting values are those in text
equation (7). Knowing the e's, we can use (2A) and (3A) to solve for

text equation (8).


Figure 1

Cr Pt

to to+1 to+2

Figure 2

Ct Pt



-3-

(5) An intervention policy that leans against the wind to stabilize
exchange rate fluctuations will benefit both labor market participants
and portfolio managers if the monetarist assertion is correct. If
instead goods market disturbances are the primary source of price and
exchange rate fluctuations, then such a policy may benefit portfolio
managers at the expense of labor market participants by stabilizing the
real interest rate but destabilizing employment.
II. THE POSITIVE IMPLICATIONS OF WAGE CONTRACTING

First we show how monetary and goods market disturbances affect the
exchange rate and price level in the flexible-wage economy that we take
as a benchmark, Then we impose two different forms of contracting on the
labor market and examine their implications for the volatility of
exchange rate and price level movements. In particular, we want to see
whether either form of contracting helps to explain our stylized facts by
increasing exchange rate volatility and/or decreasing price level
volatility and by imparting more persistence to the effects of
disturbances. The economy operates quite differently under these two
forms of contracting; in fact, they really constitute two different views
of the supply side of the economy. So we are also interested in
identifying the particular features in the economy that are important if
a given form of contracting is to help explain the stylized facts.
II.A. A Flexible-wage Model: The Benchmark Case

Our basic framework is similar to Dornbusch's (1976). We consider
a single country that produces a differentiated product, but whose bonds
are perfect substitutes for foreign bonds. Demand for the country's

product is given by


-14-

II.C. A Neo-Keynesian Contracting Model

Taylor (1979, 1980) has developed a contracting model that is less
neo-classical in nature and more closely related to Dornbusch's (1976)
sticky-price model. In Taylor's model, wages are set (with some
modification for demand conditions) to preserve the relative wage
structure over contracts. Contracting is once again staggered, with say
half of the contracts being renegotiated each period. This is an
important feature in Taylor's model because it allows the effects of a
disturbance to be passed from one contract to the next; that is,
disturbances affecting existing contracts are passed on to new contracts
by the attempts of wage setters to preserve the relative wage structure
over all contracts. The staggering of contracts is the source of the
strong persistence of effects in Taylor's model. Price in Taylor's model
is a constant markup over the average wage, and employment is determined
by the demand for output; these features give the model a neo-Keynesian
flavor despite its incorporation of "rational" expectations
formation.12/

More specifically, the demand side of the economy -- equations (1),
(3) and (4) -- is retained (though we will drop the permanent goods
market disturbance, u,, for simplicty of exposition), and the supply side

is replaced by

(18) xy = -80xg y+ Xearpeer) + -S¥L(TM ~ Pepe, +O = Pleat year] + %

(19) Pe = ME = 25 (X, + Xt.)

All contracts specify a fixed nominal wage for two periods; half of the

contracts are renogotiated at the beginning of each period. x, is the

t


-16-

[.5(1 - 6) + By V/(5 + 2) By=1 +B,

1/(6 + A) 8

1/(6 + 2)

85

The absolute value of a is less than one for all positive values of
yY, so the wage-price process is stable. A positive wage disturbance
increases expected future prices and lowers expected future real
balances; this has a moderating effect on next period's contract wage.
The larger is y, the smaller is a and the stronger is the moderating
influence.2-/

Permanent monetary disturbances and temporary wage disturbances
“generate persistent effects on all variables in the model, effects that
last even after all of the existing contracts have been renegotiated.
Any disturbance that gets into the wage setting process will
have persistent effects. Permanent disturbances get in because they
affect expected future real balances. Temporary monetary and goods
market disturbances would get in if they were correlated with Xe that
is, if current actual demand conditions affected the wage setting
process.

To illustrate how permanent monetary disturbances pass through the
economy, we have solved equations (20), (21), (22) and (1) for their
moving average representations under the assumption that all other

disturbances are equal to zero:22/

(23) x, = rea Meg where Ww, = 1-0

t


-2-

example suggest which agents are helped or hurt by exchange rate
overshooting. We can also suggest which agents would be helped or hurt
by an intervention policy that curbed the exchange rate overshooting.
Some monetarists assert that price and exchange rate fluctuations
are due primarily to monetary disturbances. It turns out that most of
our results depend crucially upon the validity of this assertion. Our
basic conclusions may be summarized as follows:
(1) If goods market disturbances, rather than monetary disturbances,
are the primary source of price and exchange rate fluctuations, then a
frictionless model of the economy may not be inconsistent with the
observation that exchange rates are more volatile than prices. This
real-world fact may not be a paradox that needs to be explained.
(2) If on the other hand the monetarist assertion is correct, then a
frictionless economy can not explain the observed volatility of exchange
rates relative to prices, but both contracting models can. In addition,
increasing the degree of inertia embodied in the contracts increases the
volatility of exchange rates relative to prices.
(3) Taylor's contracting model implies more persistence than Gray's and
is more closely related to Nornbusch's fixed-price model.
(4) The existence of wage contracting presumably benefits labor market
participants and may also benefit portfolio managers by stabilizing the
real interest rate, especially if goods market disturbances are an
important source of price and exchange rate variation. If however the
monetarist assertion is correct, then the conversion of some one-period
contracts to two-period contracts will hurt both portfolio managers and
the labor market participants under existing contracts by destabilizing

both the real interest rate and employment.


-A3-

Using the above equation and equations (18) and (19) from the main
text, we can solve for the a's. We then postulate a solution for ee

Se = By Xe + BoM 1 - Bax + Bam + Bove - 8674

We use this equation together with the money market equilibrium

condition, to solve for the B's.


The one-period price prediction errors of interest to wage setters

(43) PE Pelt-1 = 13 (m, + Yt) + 142, + (a, - 7. )Uy
where
4,2 9(1 + 44 g)n/(l +9)

If price fluctuations are caused by monetary disturbances, then wage
setters would favor a strong intervention policy to smooth, or even
‘eliminate, exchange rate fluctuations 22/ Monetary disturbances and
monetary policy push the exchange rate and the price level in the same
direction; so a monetary policy that stabilizes the exchange rate will
also stabilize the price level and make it more predictable. Goods
market disturbances on the other hand either move the exchange rate and
the price level in opposite directions (in the case of temporary
disturbances) or are totally absorbed by the exchange rate (in the case
of permanent disturbances). In either case, a monetary policy that
stabilizes the exchange rate will destabilize the price level and make it
less predictable .20/ Wage setters would prefer that monetary policy
allow the exchange rate to fluctuate freely and absorb some of the impact
of these disturbances. 2//

Portfolio managers are worried about the one-period exchange rate

prediction error

(44) ee - a = e3(m, + v4) 7 &42, - (e, - & 6),


I. INTRODUCTION AND SUMMARY

A frictionless model of the economy, with wages and prices moving
each period to clear the labor and goods markets, is generally considered
to be inconsistent with certain stylized facts about the real world. In
such a model, employment and output adjust immediately to any economic
disturbance; there is no persistence of effects, no business cycle.

Also, money is neutral in such an economy, and if monetary disturbances
are the primary source of exchange rate and price level movements, the
model is incapable of explaining the apparent fact that exchange rates
are more volatile than prices. Dornbusch's (1976) approach to this
Problem was to postulate that the goods market clears more slowly than
the money market. Representing price stickiness by a Phillips Curve, and
assuming that the money market clears instantaneously, he derived his
celebrated "overshooting" result for the exchange rate.

In this paper, we attribute the slow adjustment in the real side of
the economy to wage contracting./ We consider both the neo-Classicial
contracting model of Gray (1976), Fischer (1977a) and Canzoneri (1980)
and the neo-Keynesian model of Taylor (1980). This approach has a number
of advantages. We do not have to assume that prices are fixed in the
short-run; so the question of the relative variability of prices and
exchange rates has more meaning. We can identify the degree of inertia
imposed upon the real side of the economy with either the average length
of contracts or the sensitivity of wages to expected demand conditions,
and we can vary the degree of inertia to assess the effect of slower
adjustment on persistence and the relative variablity of prices and
exchange rates. More importantly, and also more controversially, we can

give these positive results a normative interpretation. We can for


-F4-
= 2 2
d(6n3)/de = (1 - »)°(1 + A)/E = p)(1 +a) + 8] > 0
Exchange rate overshooting depends directly upon 0,

d(eq ~ 1)/d8 = (1 = 8)(0/a)(1 = »)(1 + AY/EM = 9)(1 +a) + 87" > 0

as does price level undershooting
d(1 = 1y)/d0 = (1 ~ p)(1 + a)/E(1 - p)(1 +a) +e]? > 0

13/ A relatively elastic employment rule is also consistent with another
stylized fact. Real wages do not seem to follow a strongly
countercyclical pattern. However, a formal empirical application of this
model may benefit from the disaggregation suggested by Lucas, Sargent and
Wallace; see Canzoneri (1978) and the references therein.

14/ The "implicit contracts" literature referred to in footnote 6
suggests instead that the employment rule should be relatively inelastic
as wage setters try to smooth employment variation.

15/ Permanent goods market disturbances would have the same effect if
they were not totally absorbed by ‘the exchange rate.

16/ For permanent monetary disturbances, the increased impact on the
price level is shown by

dry -50(1_- 6)o(1 - o)2(1 + a)E(1 - p)(1 +a) + 0]

aT o)@(1 + )% + o(1 - p)(1 +2) + .540E(1 - p)(T +a) + 010-

which is positive for all g. The increase in exchange rate overshooting


-R2-

Gray, J., "Wage Indexation: A Macroeconomic Approach," Journal of
Monetary Economics, 2, 1976, p. 221-35.

Gray, J., "On Indexation and Contract Length," Journal of Political
Economy, Feb. 1978, p. 1-18.

Marston, R., "Real Wages and the Terms of Trade: Alternative Indexation
Rules for an Open Economy," unpublished manuscript, May 1982.
Salop, J., “Devaluation and the Balance of Trade under Flexible Wages,"
in G. Horwich, and P. Samuelson, eds. Trade Stability and

Macroeconomics (Academic Press, New York), 1974.

Taylor, J., "Staggered Wage Setting in a Macro Model," American Economic
Review, 69, 1979, p. 108-113.

Taylor, J. “Aggregate Dynamics and Staggered Contracts," Journal of
Political Economy, 88, 1980, p. 1-23.

Turnovsky, S., "Wage Indexation and Exchange Market Intervention in a
Small Open Economy," unpublished manuscript, University of
Illinois, Oct. 1982.

Turnovsky, S. “Exchange Market Intervention in a Small Open Economy," in

J. Bhandari and B. H. Putnam eds., The International Transmission

of Economic Disturbances, forthcoming.

Waldo, 0., “Sticky Nominal Wages and the Optimal Employment Rule,"

Journal of Monetary Economics, May 1981, p. 339-354.

Weber, W. "Output Variability under Monetary Policy and Exchange Rate

Rules," Journal of Political Economy, Vol. 89, No. 4, Aug. 1981,

p. 733- 758.




-12-

where
i: (1_~ p)2(1 + ay? + .590(1 - ») + .5400(1 - »)(1 + A)
Ta = 5)*(1 + a)® + (1 - p)(1 +) + .590(7 - p)(1 +A) + 25902
2 1 -o)(l +2 ce, = [1 + .54(8/6)]
TM) = =? + XA) + 590 20 230 172

and Tas Tyr &3 and &, are as defined in (12) and (13).
With two-period contracts, it takes two periods for the price level
and the exchange rate to adjust to a permanent monetary disturbance. A
permanent disturbance that occurs in the first period of a two-period
contract will also cause a price prediction error in the second period of
15/

the contract.— This implies a positive correlation in the deviations

from full-employment for firms covered by two-period contracts.

(17) MY zyt 8(mym, + mV, + 1424) + Spon om

Output cycles about its natural rate.

The size of $, the proportion of contracts lasting two periods,
also affects the magnitude of the immediate impact of a permanent
monetary disturbance on the price level, the exchange rate and output.
Figure 2 shows how price level undershooting and exchange rate
overshooting are affected. 16/ (The solid lines reproduce the results for
the case ¢ = 0; the dashed and dotted lines obtain if ¢ > 0.) The
overshooting of the exchange rate increases. It also turns out that the

immediate impact on output and the real exchange rate, e - p, is

magnified 2/ So the increase in exchange rate overshooting outweighs


-15-

(log of the) wage specified in a contract negotiated at the beginning of
period t. The first term in the wage-setting equation (18) reflects the
fact that wage setters try to maintain their own wage relative to the
wages that will exist in other contracts during the two periods covered
by the contract. The second term says that expected demand pressures, as
measured by expected real balances, are also taken into account ;,12/ Y
measures the importance of demand conditions in the negotiations, and it
is an important parameter in Taylor's contracting model. % isa
disturbance in the wage setting process; we assume initially that it is
independent of i » Vee and cn even though this implies (perhaps
unrealistically) that current actual demand conditions play no role in
the wage-setting process. Equation (19) is the price-setting equation;

w,is the average wage across contracts at time t.

This model can be solved for-20/

t

Solution to Neo-Keynesian Contracting Model:

(20) x = ax) + (1 - a)m_) + Xe

(21) Py = aPy_y + -5(1 - a)(m - m_{) + -5(X, + X_1)
(22) = 81% 1 + B2Mea1 = Bake Bah, * BaME - Bg%
where

a= (1 + .5y = ¥2y)/(1 - .5y)

By = -5(1 - 6)(1 + a)/[6 + A(] - a)] Bo = 1 +8,