-18-

also discuss the relationship between exchange rate volatility and
contract length.

The Gray-Canzoneri Model:

Suppose first that the length of the contract is given; we will
return to the subject of contract length later. Perhaps the most natural
extension of the model described above is to assume that a series of base
wages is specified in the contract, a separate wage for each period
covered by the contract. When the contract is negotiated, the time paths
of prices and exchange rates are predicted, and nominal wages are set at
levels that are expected to clear the market each period; the contract
may also include indexing provisions. As before, price and exchange rate
prediction errors will cause fluctuations in employment and output.

The basic difference here is in the information set that is
reflected in the predictions. As we pass through the contract period
the information on which the predictions were based becomes more and more
dated; Canzoneri (1980) has shown that prediction errors (or more
precisely, their variance) will get bigger, and fluctuations in
employment and output will become larger. In addition, if the movements
in prices and exchange rates are serially correlated, then the prediction
errors and the associated fluctuations in employment and output will be
serially correlated ;!4 the model implies "cycles" or persistence.

Gray (1978) and Canzoneri (1980) have suggested that the length of
contracts is determined by comparing the costs of more frequent
negotiations with the benefits. The benefits of more frequent

contracting accrue from more informed price and exchange rate


-39-

Canzoneri [1980] or Gray [1976] (see section 1). In the present context
such a contracting scheme would allow laborers and firms to enter into
contracts at the beginning of a given period [before exchange rate and other
variables are realized] and predict the exchange rate so as to set nominal
wages for each period at values expected to clear the labor market.
Moreover, firms and laborers would be able to enter into new contracts at
discrete intervals at which point they would repeat the process of setting
nominal wages described above. Thus, under this type of contracting only
changes in the exchange rate not anticipated at the time the contract is
negotiated will affect the firms demand for labor.

In sum, this section has investigated how the firm's decision-
makers will dynamically adjust employment and output given either an
anticipated change in the exchange rate or an unanticipated exchange rate
shock. In particular it was found that such decisions were affected
importantly by the firm's perceptions about (1) the degree of serial
correlation (or persistence) in the exchange rate process and (2) upon
the costs of adjusting labor. Moreover, as in section 1 above, whether
anticipated exchange rate changes or unanticipated exchange rate shocks
will both affect the firms intertemporial chéices of employment and output
depended critically on the assumptions made about the nature of firm-labor

wage contracts.


=35-

The decision-makers expectation about future exchange rates (i.e.
wage rates) will be influenced by the degree of serial correlation (p)
in the exchange rate process. Moreover, as i (the number of steps in the
forecast) becomes large the firms decision-maker's best forecast will tend
to the asymptotic mean of the exchange rate process S*, Substituting (37)
into (36) and using the method of undetermined coefficients (see Appendix
B)27 results in a reduced form employment rule of the form

cd q

(38) Ne=N-c Er agri piz
q=o i=o 1

- il
where N= F (£9 ~ S*) is the steady state value of employment.
1

c =_Al [__1__]> and *1 is defined as in section 2b.
d= 1=(d,b)e

Equation (38) suggests that the demand for labor depends upon an
infinite moving average of innovations or shocks (as represented by the Zt-q)
in the real wage (or exchange rate) process. These shocks are discounted by
p (the degree of persistence of the shock) which the firm's decision-makers
are assumed to know and )j, the stable root, which is itself a function
of the discount factor b, the real cost of adjusting labor d, and fj, a
parameter in the production function. Equation (38) also implies that both
the anticipated component of the exchange rate process (S*(1-p) + pSt_y)
and the unanticipated shocks (Zz) will alter the firm's demand for labor
and the level of output produced. The fact that anticipated changes in the
exchange rate affect the firm's choice of employment and output stems from
our assumption that wage earners and firms enter into wage contracts in

which wages are fixed for all periods in the contract.


-44-

distributed, yields:

(42) E[UCn)] = (1/o,¥2pt) f= exp (-8n) exp[-(1-0)2/20,7]dm.

where pi = 3.1417...., 7 E(n], and On? = variance of profits. After some

substitution [see Sargent 1979), p. 150], this reduces to:
(43) B[U(n)] = -exp [-0(7 - 60,2/2)].

To maximize the expected utility of profits it is then necessary

for the decision-maker to maximize the term in parenthesis in equation (43)
a 2
(44) V=T- 60,2/2.

By making explicit assumptions about the form of the utility function and the
probability density function of profits (or the exchange rate in the present
context), one can therefore express the decision~maker's problem as the
maximization of a function that is positively related to the expected level
of profits and inversely related to the variance of profits.

The expected value of profits is given by:

(45) E{w] = E[SY - WN - RK]
= E(S£(K,N) - WN - RK]

= S £(K,N) - WN - RK

because S, which is distributed as N(S, og) is the only stochastic variable
in the model. The variance of profits is therefore equal to a simple function
of the variance of the exchange rate and all covariances are therefore zero:

2

(46) 9,2 = En - n]? = £709.

1


-12-

FIGURE 1.c

marginal
cost

Peteer* (Set ft-1)

Pelt-1

<


-A6-

(A199) F(t+j) = w+ a(-1)tt5

Then from (Al5) we see that the firm's labor demand rule is given by:

P-1
(420) yy, = 10-1 Baw ta)
Jo fy «fy %0
P-1
Since qq = 1 and since the period of this particular specification of F
2=0

is two, (A20) can be rewritten as:

fp-w oa tt
C21) Nea = a - F Bo7 ay} (-1)

From (Al6) we can see that

(022) go = q) = 1/dy — (+b) + Ayb
07 41 Th Citb) +4q>

Using (A5) we can obtain:

£
(A23) g -q. = 1
do ~ 41" FF Barby

Therefore,

_- ac-yt*d

(A24) y fo ¥
FL «FyF2aci+b)

t+j =

This is the expression for labor demand given in the text. This expression
for N puts the firm's employment rule in terms of clearly interpretable

parameters.


-54-

4, Summary and Implied Measures of Volatility

Exchange rates can play an important role in a firm's price and
cost structure. Consequently, exchange rate movements may affect the firm's
short-run employment decisions, and exchange rate volatility may affect its
scale of operation. In this paper, we have discussed a number of ways in
which exchange rate fluctuations can be transmitted to real economic activity,
and our examples suggest several measures of volatility. Some of these
measures have been long recognized; others are new.

In section 1, we focused primarily on exchange rate prediction
errors in contracting models like Gray's (1976). Nominal wages are set at
levels that are expected to clear the labor market. An unanticipated
depreciation will raise the price of an internationally traded good and result
in an unexpectedly low real wage, causing the firm to employ more labor.
Through its effects on the price structure, an unanticipated depreciation
tends to be expansionary; however, the depreciation can also affect the firm's
cost structure. If the nominal wage is indexed to a basket that includes
foreign goods, then labor costs will rise; if the price of another factor of
production, say oil, is fixed in terms of a foreign currency, then oil costs
in domestic currency will also rise. These effects are both contractionary.
Taken as a whole, these results suggests that prediction errors are an
important measure of exchange rate variability, though a given prediction
error may have different implications for different firms.

When using this measure of exchange rate variability (or any of the
others suggested in this paper), it is important to remember that the cesults
reported above are partial equilibrium in nature; it is assumed that the

unanticipated depreciation is not accompanied by other price changes. In


-52-

function given by equation (44) above. Computing the variance of profits

results, after some manipulation, in the following expression.

(60) 9,2 = Bln-t]2 = (20g + 5? 08) (Kyaw)?

Using equations (57) and (60) to substitute for 7 and on?

respectively, in equation (44) yields the following expression for the

optimal capital stock, K:
(61) K= (03 + 32 = 4Rgu)/{aRyw + OL(og/2) + (S? 0§/4]/W}

Equation (61) shows that as the degree of risk aversion increases,
the optimal capital stock declines. We know from equation (55) that labor
employed, on average, will also decline, and therefore the average level of
output will decline.

Of primary interest here is the impact of an increase in the exchange
rate variability on the level of factors employed and on the level of output.
Inspection of equation (61) shows that if 0 is large, we get the standard
result that an increase in exchange rate variability will reduce the optimal
capital stock and thereby reduce the average level of output of the firm.

However, if © is small, then greater exchange rate variability can
increase the optimal capital stock and thus the firm's average output: leve1.33
Basically, what is going on is that there are two forces at work. On the
other hand, if, as in the case here, the firm can adjust in part to both
high and low prices, its expected profits will be larger with greater
exchange rate variability; it can increase output, and therefore increase
profits when the price is high, and vice versa. 34 When increased exchange

rate variability raises both the expected value and the variability of


FOOTNOTES
1. The macroeconomic literature generally ascribes price stickiness to
the "costs" of wage or price setting (see for example Gray (1978),
Canzoneri (1980) or Mussa (1981)), or it simply asserts sluggish price
adjustment (see Dornbusch (1976)) or the existence of “information
islands" (see Lucas (1972) and Barro (1976)) or "contracts" (see Gray
(1976), Fischer (1977), or Taylor (1979)). The positive implications of
all of these views of price stickiness are similar: monetary
disturbances can have transitory real effects. However, the normative
implications can vary widely.
2. If labor supply were a function of a real wage defined in terms of
a bundle of consumer goods, then the supply curve would be upward
sloping, and it would in Figure l.a shift with the terms of trade; the
market clearing solution (v,n) would also be a function of the terms of
trade. See Salop (1974) Flood and Marion (1982) and Marston (1982) for
discussions of this more complicated framework.
3. Fischer (1977) assumes the goal is to maintain a constant rate of
employment. Canzoneri (1980) assumes a union imposed real wage target.
In any case, the nominal wage is set on the basis of predicted prices and
exchange rates, and the results, for our purposes anyway, are quite
similar.
4. Fischer (1977) and Canzoneri (1980) make the same assumption.
Barro (1977) has pointed out that there are other contracts that would
probably be preferred by both the firm and its workers. For example,
workers may be willing to trade a lower expected real wage for more

employment stability (see Sargent's (1979) discussion of implicit labor


-62-

22. In Appendix A we generalize the cyclical process of the exchange
rate by allowing the period of the cycle to be any integer greater than
zero (we have implicitly assumed a period of two for the exchange rate

cycle presented in this section). The results obtained there correspond

to those presented here.

23. The sum of two convex functions is convex.
24. See Appendix A for the derivation.
25. Assuming that the exchange rate is generated by a process like

(34) allows us to investigate the effects of changes in the persistence
(i.e., changes inp) and hence in the variability of the exchange rate
without allowing the mean to change as in the work of Rothschild and
Stiglitz [1970] on mean preserving spreads.

26. The reader should note that in general the conditional expectation
EW yj| Ae! is not a linear function in the variables contained in Mu.
However, a sufficient condition for this to be the case is that the variates
in Wy and those in SL. follow a multivariate normal distribution. In the
present context given a simple first order Markov process generating the
exchange rate where Se, contains contemporaneous and lagged values of the
exchange rate (or real wages) one needs to assume that the exchange rate

is distributed normally, implying in the present context that the real

wage rate will also be distributed normally.

27. The method of undetermined coefficients is one method of solving

a difference equation (see Appendix B), to obtain a particular solution.

28. See, for example, Hooper and Kohlhagen []978] and section 3 bellow.
29. Some authors, e.g., Batra (1975), introduce uncertainty by specifying
a randon term in the production function.

30. These are referred to as “commitment models" by Pomery (1979).


-50-

a nonlinear term for the cost of capital as a proxy for the cost of adjust-
ing the capital stock. This term can be thought of as reflecting an upward
sloping supply schedule for capital facing the firms. It is necessary in
order to have the size of the firm well-defined. This nonlinear term is

embodied in the profit function given below:

(52) 1 = S£(K,N) - WN-R

2
~ Rk.

We further simplify the exposition by assuming that the production function

is Cobb-Douglas (Hartman (1976) uses a CES function):
(53) £(K,N) = K@ Ni-@ = K(N/K)1~0

The decision-making problem of the firm can be decomposed into
two stages. First, the firm decides on a profit-maximizing employment rule
which can be used to determine the optimum level of labor employed each
period in response to the actual realization of the exchange rate. The
level of employment is based on a given level of the capital stock. Second,
the firm chooses the level of the capital stock that maximizes the expected
utility of profits, where the employment rule is part of the second-stage
process.

The profit-maximizing employment rule is the standard "marginal
product equals real wage" condition because there is no uncertainty within
the period; the firm knows the price in the current period, and because of
the assumption of costless adjustment of labor, varys labor input so that

equation (54) holds:

(54) 3£/8N = (1-a) (K/N)* = W/S,


-22-

Two kinds of exchange rate processes are investigated here. One
exhibits predictable and persistent cycling. With this kind of exchange
rate variability we find that, even in the presence of adjustment costs, the
firm will vary the quantity of labor it employs over the exchange rate cycle.
Furthermore, we find that with finite adjustment costs, the firm's present
value increases with increases in exchange rate variability. The other
exchange rate process is stochastic, covariance stationary, and serially
correlated. In this case we find that both the persistence of the exchange
rate shocks and the size of the adjustment costs will affect the firm's
demand for labor and supply of output.

In section 2a we present the assumptions common to the analysis in
section 2b and 2c. In the later two sections we discuss the results of our

investigations of the two exchange rate processes.

2a. Assumptions

To evaluate the results presented in section 2b and 2c it is useful
to set out the assumptions which underly our model of the firm. As in the
work of Sargent (1979) the firm is assumed to face a quadratic production
function which can be expressed as

(18) F(N,) = fgN, - 1/2£,N2
where fg, f) are assumed to be greater than zero. The firm employs a single
variable factor of production, labor (Nt), and has a fixed capital stock.
Note that the marginal product of labor will be positive as long as (f9/£1) > Ne
and that the production function is concave in Nt. We adopt this specification
primarily because it makes it less difficult to obtain an explicit solution to

the firms dynamic optimization problem.


-40-

3. Exchange Rate Variability and Expected Utility Maximization

In this section we take explicit account of the firm's attitude
toward risk, and particularly, how its attitude affects the relationship
between exchange rate variability and output and employment. We first
assume, as in section lb, that nominal wages are set for the duration of
the period, i.e., we define the period to be the length of the wage con-
tract. We also initially assume that over the period they are committed
to a fixed nominal wage, firms are also committed both to the existing
stock of capital and the level of labor employed because of high costs
of adjusting both factors of production. The assumption of fixed labor
inputs differs from that in section 1 and is the same as an extreme case
considered in section 2. The firm is assumed to maximize the expected
utility of profits, where the firm's attitude toward risk is reflected
in whether marginal utility is decreasing, constant, or increasing. We
illustrate the standard result in the literature--that an increase in
exchange rate variability reduces output and employment if the firm is
risk averse--in a simple model that embodies explicit assumptions about
the form of the utility function (expotential) and the probability density
function of the exchange rate (normal).

In the second part of this section we maintain the assumption of
a fixed nominal wage but relax the assumption of fixed labor inputs and
instead assume that the firm adjusts the number of workers employed in
response to actual exchange rate realizations because costs of adjustment
are not infinite. The approach taken here is similar to that in section 2
which explicitly considers alternative assumptions concerning the costs of

adjusting labor inputs. As in that section, the firm's profit function is


-A5-

and

a4
a >§- 4 « ob for i=0,1,2,..., Pol

Therefore, qq -> 1 and all other qy -> 0.
To see what happens as \j-> 1, we must rewrite (A16) substituting

the expression for %g shown in (Al7) and using the fact that

P-1
1-(yb)P = (1-ab)(-E (Ay) *)
0

1 -aP = (1-a,)(2P-1,4),
1 iv) 1
These substitutions yield:

' 7
G=aOy)) | Geybay

72, z 2 z
(2 dpb) (ZC, b) ) (1 AD) CEA, )

(A18) 4a =

From (Al8), then, we can see that as 4ya-> i,

q >So+12 for 1=0,1,2,...,P+1
i P

This result can now be used to make a more general claim. Since
as adjustment costs (d) approach zero, we can see that for any general
periodic function, as d-> 0, the firm's decision-makers need not concern
themselves with any but the current wage rate in the cycle. Similarly,
as d increases without bound,A, approaches unity and we can see that
firms give equal weight to all the values of the wage rate that occur in
the cycle.

To derive the specific labor demand rule discussed in the text,

let us set


increased risk has to be weighed against the expected profitability of being
able to exploit the wider fluctuations in the exchange rate.

In section 4 we summarize our results and describe different measures
of exchange rate volatility that are suggested by the models presented in the
first three sections. Prediction errors, time series properties, and variances
are all measures of volatility that have implications for firms' employment

and output decisions.


-A8-

(£9)? a? 2 - £, -4d
2EyCi-b) ~ ZC-byTE, + 24TH] af) + 24(a4b)) ~ Fy ~Aa)

__alég “#)C1)* 14 fit 2a(1+b) _
Ci+b) [£1 + 2d(1+b)]) fy

(026) ye (£99? a*[f, + 4db] _ alfg-@(-))*
t” 2FyC=b) » D-b) TE, + 2d +H) #Cit6)
where
ave, [£ + 4dbla (fom DS

3a“ (T=by fy + 2aC1¥b)]* =F, +b)

Thus, the value of the present value function depends on whether it is even
or odd. When t is odd, the present value calculation begins in a period
in which the wage rate is low and employment and output are high. In this
case, variability (i.e., a# 0) can only increase the present value of the
firm.

When t is even, however, it is possible that variability will
decrease the present value. In the neighborhood of a = 0, an increase ina
will decrease the present value. However, for large enough values of a, an
increase in a will cause the present value to rise and it may be true that
the present value at some big enough value of a will be larger than the
present value at a=0-

One can see that, on average, the present value of the firm is higher
with variability than without it:

(fg-u)? a*[£1 + 4db]

vk = +
t+(t+1) 2£,(1-b) 2(1-b) [£7 + 2d(1+b)]
2



-A7-

*
To find the present value v_ that corresponds to the firm's choice
of Ne+j, we can substitute (A24) the expression for wt+j into (Al) to obtain

(A25) ve = F $6 ~ we a(-1)*5] (£9 - W)/f, - a(-1)t*5/(£) + 24(1+b))
t  4=0

2

£) | fo-7 a (-1)t43
v |e” Fp ye 2acieby

d | -2a (-1)t+3
2 | f, + 2d(tb)

EG for? _ (forays alto Cts a?
5-0 f Fy + 2d(i+b) Fy Fy + 2a)
£1, | (£g-)?_ 2¢£g-a(-1)**5 . a?

~F | Fi? F,[f, + 2dCitb)] TE, + 2d(1tb)]¢

_d 4a
2 | + 2d0+b)]7

which after some further manipulation can be written as:

vp = for (fpw)a-Dt —_altgw)(-Dt . a?
t £,(1-b) (1+b) [£) + 2d(1+b)] £,(1+b) (1=b) [£ + 2d(1+b)]
(Eg-w)? a(£g-w)(-1)* af,

~ 3, C=by ” asbytey + 2dCi+b)) — WCIHbYTE, + 2aCI4b))2

-2da2
(1=b)[£y + 2d(1+b)] 2


-B2-

Now substituting (Bl) into (B2) yields

o i

(B3) xf _ MM 1S
Nt d(1=%;) + Neer — G (SZ) G2)

_« . ~
S* LE (1/ag)t pL + E (1/dp)FptsE]
i=0 i=0

bo + AyNe-z — (A1/d) © (1/(1-(1/A2) 0) S#

where,

bo = Cayfg/d(1-agb) = (Aa/4) [S*CL/(-(1/2)) = 1/2)

since 0 < (1/\2) < 1 and 0 <[{p|<1. Now to obtain a solution for the
difference equation in (B3) in terms of all past shocks to the exchange rate
process we first note that the moving average representation of the exchange

rate process can be written as

©
(B4) S, = S*# +E pty
i=0

substituting (B4) into (B3) yields

«
= i
(B5) Ny = Cy + AQN_y - % te Zend

where Cj = bg - C2 *S*

Mos 1
d CI=(7%3) 0)

and Cy =

Now suppose our hypothesized solution to (B5) is
_
(B6) Ne = N+ 2 O42e-4
i=0
substituting (B6) into (B5) for Ne, and N¢- and solving for the o's in terms

of the structural parameters in the model using the method of undetermined


=33-

2c. Exchange Rate Variability and Adjustment Costs: The Stochastic Case

In this section we examine the implications of relaxing several of
the assumptions made in section 2b. First, we no longer assume that the
exchange rate is characterized by a cyclical nonstochastic process. Instead
we assume that the exchange rate follows a stochastic process which permits
an examination of the effects of both unanticipated and anticipated exchange
rate movements upon the firm's demand for labor and production. Second, we
briefly consider the implications of relaxing the assumption that the firm's
decision-makers maximize a quadratic objective function. Finally, we explore
the implications of allowing firms and laborers to enter into wage contracts
of the Canzoneri-Gray type, discussed in section 1, rather than engage in
long term contracts in which the nominal wage rate is fixed for all periods
in the contract.

Given our assumptions outlined in section 2a we now also assume
that the exchange rate (or real wage rate) follows a covariance stationary

first-order autoregressive process
(34) (We/Pe) = Se* = S*(1-p) + pS* 1 +2
t-

where 0 <p < 1. The mean of the exchange rate process is S*25 and
o9/(1 =p?) is the variance. Finally the error term (24) is assumed
to be a white noise process such that E(Z_) = 0, E(Ze 25) =(0, j#e.
of, jze
The simple stochastic process in (34) can be viewed as having both a pre-
dictable component based on the firm's knowledge of the autoregressive (p)
and drift (S*(1-p)) parameters and an unpredictable component as represented by

the error term (Zt).


-19-

predictions, smaller prediction errors (on average), and less deviation
from the market clearing solution. !®

According to this view, a volatile, hard to predict exchange rate
would result in short contracts. A monetary policy that was successful
in reducing this volatility would reduce the benefits of frequent
recontracting and allow the firm and its workers to economize on the
costs of negotiation. Contracts would become longer, and fluctuations in
employment and output would be smaller, though more inertia ridden.

The Mussa-Taylor Model:

The Gray-Canzoneri model focuses on the bargaining costs of
contract renegotiation; it assumes that there is little or no cost to
specifying different wage settings for the various periods covered by the
contract. The Mussa (1981) model, by contract, attributes the same cost
to each and every change in wage setting. His is thus a model with one
fixed wage for all of the periods in the contract. Given that
restriction, his model is much like the Gray-Canzoneri model: The wage
is set at the best level on the basis of expected inflation, etc., and
the length of the contract is determined by weighing the costs of more
frequent wage settings against the benefits.

It is not clear what employment rule Mussa himself would combine
with his wage setting scheme! ® However, we will continue to use the
period by period profit maximizing labor demand curve in Figure 1.a.
This model will of course have the same implications for the relationship
between price and exchange rate prediction errors and employment and

output fluctuations. What's new is that anticipated movements in prices


~25-

2b. Exchange Rate Variability and Adjustment Costs: The Certainty Case

In this section we investigate how perfectly predictable exchange
rate variability affects a firm's output and employment decisions. We
hypothesize a cyclical exchange rate path which the firm's decision-makers
can predict without error, and consider their employment rule under three
different adjustment cost assumptions: zero adjustment costs, positive but
finite adjustment costs, and infinite adjustment costs. We find that the
adjustment cost assumption made influences the output and employment responses
of the firm to increased variability. In addition, we look at the effect of
exchange rate variability on the firm's present value and find that, because
of the convexity of the firm's profit function, the average present value
over the exchange rate cycle may increase as the variability of the exchange
rate increases.

Since we are interested in examining exchange rate paths which
exhibit variability, we make the following simple assumption about the exchange

rate path S*
t

(21) S* = S* + a(-1)* = w/P S*>a>do
t t

t= 0, 1, 2, «.

In this simple process s* takes only two values as time progresses - a high
value (S* + a) when t is even and a low value (S* - a) when t is odd. S*
represents some positive mean around which st cycles with amplitude (a) and
a frequency of two periods.22 Amplitude and frequency are the measures of
exchange rate variability focused upon here. Given our assumptions about
the nominal wage rate and the foreign currency price of output, the real

wage rate path is thus identical to the exchange rate path.


-21-

2. Effects of Exchange Rate Dynamics and Adjustment Costs

In the previous section we looked at models of contracting and
employment that are explicitly intertemporal: the firm and its employees
make nominal wage rate and indexing decisions in one period and follow
through with the consequences of those decisions for employment and output in
subsequent periods. We saw how different contracting arrangement can lead,
in the context of exchange rate variability, to different effects on output
and employment. Implicit in the previous section is the assumption that
after the contract is settled, the costs to the firm of adjusting its output
and employment to unpredicted or predicted changes in the exchange rate are
Zero.

In this section we also investigate models which are explicitly
intertemporal. We assume, for simplicity, a contracting arrangement in which
one nominal wage rate is fixed over an indefinite horizon. This kind of
assumption is more closely allied with the Mussa-Taylor model of contracting
than it is with the Canzoneri-Gray model. With this simple kind of long-term
contract, our model falls into the class of models for which perfectly
predictable fluctuations in nominal magnitudes can generate real effects.

Instead of assuming zero costs of adjustment, we now explore a
model of the firm in which the firm's decision-makers 1) consider explicitly
the costs of adjusting their labor force and 2) view the exchange rate as a
time series which, in the presence of the fixed nominal wage rate, generates
a well-defined real wage rate process. The firm's decision-makers use their
knowledge of this real wage process to choose the quantities of labor they

employ in the periods over their planning horizon.


=34-
The firm maximizes

(35) max Vy = ,E t dma (j = 0, 1, 2, oe)
j=0

where}; is defined in equation (19), O< b< 1, and (B= E((%],
where the information set of the firm % is assumed to contain all the
variables in the model dated t and earlier. In contrast to section 2b above
the firm's decision-makers maximize the expected present value of profits.
They do not know with certainty the future exchange rate (or the real wage
rate), but they can form expectations conditioned on information at time t.
Given their forecasts of the exchange rate, they must then pick a sequence of
Ne+j (j=0, 1, 2, ..-) and associated sequence of output such that they maxi-
mize the firm's present value. More formally this can be seen by representing

the firm's optimal employment rule (see Sargent [1979]) as

ume

i *
(36) _ rfo 4 MWNetj-a 7 Oy e+g Staj+i

Ney, = — 2 —
tty d(=7b) q i=0

(j = 0, 1, 2, ..-)

where all parameters are defined as in section 2b ahove. Thus, given finite
adjustment costs (0 < d <@) the firm's decision-makers will determine the
level of employment and output by forming forecasts of the real wage rate
based on information through the current period. If the firm's decision-
makers are assumed to form linear least squares predictions 26 of the
exchange rate we have (see Appendix B)

(37), ES* = S*(1-p!) + pis,,;
ce ety ti tty


-16-

its fixed capital stock, to produce output. This composite input
replaces N in equation (1), and if q is the (log of) the domestic price
of oil, then g(w-p) + (1-8)(q-p) replaces w-p in equation (4) the real
cost of a unit of the variable input; g is labor's share of the composite
input bill at full employment. The base wage is set to clear the labor

market, so

(15) ew, + (1-8) diye = 1 + Peje-a

and equation (5) is replaced by
(16), = 9 + Pigg ~ CO-8Y/8) (eyed ~ Pefe ea)

and assuming no wage indexation, employment (of both oil and labor) will

be
(17) ny, = fi + (1/a)EB, - (1-8 )a]

where once again a "~" denotes a one-period prediction error.

Canzoneri and Gray (1983) focus upon an important asymmetry in the
pricing of oil. In the short-run, the price of oil is fixed in terms of
u.S. dollars. For U.S. firms then, 4 is simply an error in predicting
the price setting behavior of oil producers. For other firms, the
domestic price of oil, Gee also includes a prediction error for the value

of the dollar. In this way, the volatility of the dollar per se has


Appendix B

In this appendix we use the model of the firm in Sargent [1979] to
derive equations (37) and (38) in the text. The formal derivation of equation
(36) in the text can be found in Sargent [1979] p. 156. Equation (37) in the
text can be obtained by noting that the i- step ahead predictor for the real

wage (or exchange rate) process in equation (34) can be written as

(Bl) ES*

"

t

rt = SAC) Ctete.etotapinly +ptst

"

Sept) + pist

Moreover in the limit as the number of periods ahead (i) for which the
forecast is being made becomes large

4 *
= ‘im ,ES;,) = S* so that the mean of the real wage process

will tend to become the optimal forecast for real wages when i is large.

This result is due to the fact that we are considering a covariance stationary
invertible first order autoregressive process where 0 <[el< 1. Note also

that although changes in the autoregressive parameter » will not effect the

mean of the exchange rate process (as i=>) the variance of the process
* oy 2
can be written as var (S,) = — suggesting that changes in
2
the autoregressive parameter will effect the variance of the exchange rate
or the real wage rate.

Now to obtain equation (38) in the text we first write equation (36),

letting j=0, as

a8

ue N (19g) LES
(2) y - 21f0 ton Mey eh 2) ESE
©" Fey 1 Ne-1 - + i=o


-60-

10. Again, one must remember the partial equilibrium nature of the
exercise. Suppose, for example, that all contracts were fully indexed
and that the depreciation was caused by an unanticipated increase in the
home money supply. In this case, all prices (and the exchange rate)
would increase proportionately, and there would be no effect on
employment or output.

11. See also Daniel (1981) where the fixed proportions assumption is
relaxed.

12. The phrase “third oil shock" appears to have originated with the
French. In at least one instance, it is attributed to the French
Minister of Economy and Finance, Delors, by Le Figaro (December 6,
1981).

13. In addition, the length of the contract may have important
implications for monetary policy; see Fischer (1977) and Canzoneri
(1980).

14. This is one reason why indexing provisions in long-term contracts
may look like "catch-up" clauses.

15. Christofides and Wilton (forthcoming) provide empirical support for
their hypothesis.

16. Mussa talks about wage setting, but most of his analysis is
centered on the example of a price setting firm. We may be doing him a
disservice in what follows.

17. Begg (1982) discusses these rather anomalous results in some

detail.


Later, during the contract period, actual prices and exchange rates
will become known, and wage setters’ prediction errors will of course

lead to a divergence between the actual real wage and v; that is,

(6) We - PE =v - (Py - Peiea)
=v COPE - Pegg) + (Se > Seie-n)4

Clearly, labor and management can not both be on their notional supply
and demand curves in this situation, so the contract must also specify
(perhaps implicitly) an employment rule stating how much labor is to be
utilized at the actual real wage. One can imagine various employment.
rules that might be instituted; however, we will again follow Gray (1976)
in assuming that essentially management wins out. During the contract
period, the firm employs, and workers willingly supply, the profit
maximizing amount of labor; the notional demand curve in Figure l.a is
also the employment rule.‘

The practical import of all this is that unanticipated exchange
rate movements cause fluctuations in employment and output. The effect
of an unanticipated depreciation (a rise in s, with no change in p*)
is depicted in Figure 1.b. The actual real wage, v - (s, - St[t-1)> is
lower than was intended because the price of output, p = p* +s, is
higher than was anticipated. Consequently, the firm employs more labor
than was orignally envisioned. In view of (4) and (6), the general

result is

(7) n= m+ (1/a) (Py - Pelt-1)


-31-

exchange rate. We have also seen that increases in the amplitude of the
exchange rate cycle will, if the firm faces adjustment costs which are zero
or finite, increase a firm's present value. All of these results are driven
by the fact that the firm's profit function is convex in the real wage rate.
A closer examination of what this convexity means in terms of the firm's
behavior will reveal the relationships between this convexity and adjustment
costs.

Consider first the case in which adjustment costs are infinite.

In this case the firm does not vary its employment and output; it employs
the quantity of labor it would have chosen had the amplitude of the exchange
rate process been zero (i.e., Ne =). With employment and output fixed,
the reduction in costs the firm enjoys when the real wage rate is low just
offsets the increase in costs it bears when the real wage rate is high.
Consequently, the sum of profits across the cycle equals the sum of profits
the firm would have earned had the exchange rate stayed constant at 3s.

Now consider the case in which adjustment costs are finite. When
the real wage rate is low and the firm is employing N, the marginal product
of labor is greater than the real wage rate. If the firm can adjust at all,
it can increase its profits by increasing employment and output. Since, with
quadratic adjustment costs, the marginal cost of adjusting the labor force
approaches zero as the adjustment gets smaller, the firm can always profit
by adjusting its employment at least a small amount, no matter how large
dis. Similarly, when the real wage rate is high and the firm employs N,
the marginal product of labor is below the real wage rate and the firm can
reduce its losses if it can cut back on employment and output. Once again,

if the firm has the ability to adjust, it can gain from adjusting its


Appendix A

This model of the firm is taken directly from Sargent [1979]. His
discussion begins on page 196. Since we are not interested in productivity
shocks here we set his attj = 0 for all t and j. Sargent states the problem
of the firm as:

(Al) Max vy = 2 bi {fouys - 1/2E\N?

ONt+j 4

- - 22
1/24(Ne45 ~ Neag-1)” ~ WeagNeaz?

where all variables are defined as in Section 2a and we = (We/P_) is the real
wage as defined in equation (21).
Sargent demonstrates that the demand schedule for employment found

by maximizing over the Ne+j can be written as

«
= i

(02) Neag = AL Meggan 7 Oy/d) ECQ/29) (rrjti 7 £0)

j=0, 1, 2, ...

where \j and Az are the roots of the difference equation and the following
conditions are known to hold:

(A3) O< AY<1< Ag,

(A4) 1/AQ = yb

(AS) (£/d) + (1+b) = Ayb + 1/Az.

Equation (A2) can be rewritten as

(A6) Negj = AINe+j-1 + Arfo/d(1 - 1/2)

- (A/a) B AD9)* Meajaie


-A3-

© ©
S= EF APE (1/dy)P.
n=0 1 n=0

From (A10) we can see that labor's marginal product equals a weighted average
of all past and future real wage rates, i.e.,
; ©
(All) £9 - £1Ne4j = EZ Zeweajage
Jaco

If we examine the weights, Zg, more closely we see they can be written as:

w7*249 for 2 < 0
1
(A1l2) Zg =

(1/A9)"%q for & > 0.

where Zo = (1 — Az) [1 ~ (1/d2)]/[1 - Aq/d2)]-

Thus Zo > 24 ¥i#0
25 > 2541 ¥ 520
Ze > Lay ¥k <0
Ze > Zo ¥k <0

because Z, = xKZo > (bd) 2,

= (1/d9)*z9 = 2y
The weight on the current wage rate is the largest. More recent wage rates
are weighted more heavily than those further into the future or past. And
this last inequality implies that each weight over history is largest than
its corresponding weight over the future.

If we let the wage rate path follow some periodic function, F,
such that

(A13) Wegy = F(t+j) = F(t+j+P)
tt+i


-A4-

when P is the period of the function, then (All) becomes
©
(A14) fo - £1Ne¢j = 2 By F(t+j+2)
=-0
Since F(t+j+%) takes the same value every P time periods, we can partition
the summation in (Al4) into P summations, as follows:

P-1
(ALS) £0 — £1Ne+j = 2 ay F(tti+2)
£=0

°
where qq = 2 Zgp4i i= 0, 1, 2, eooee, PHl

Rao

We can see, therefore, that if the wage rate follows a periodic function, the
firm will hire labor such that the marginal product of labor equals a weighted
average of the values the wage rate takes across its cycle.

If we look more closely at the weights, qi, we can derive a further
result: that for any function F of any period P, as \j varies from zero to
one, the values the weights take vary from qg = 1 and qizo = 0 to qy = 1/P
for all i. In other words, the weight shifts from being concentrated
completely on qq to being divided equally across all weights. To see this,

break up the summation in (A15) for qq to obtain

P-i

i
(A16) qq= 9 San + jie
1

Now as jj —> 0,

A17) @. = (b= AVC = Ab) =
(Al7) 2) = 325) >1


~28-

is also convex in the real wage rate.23 Consequently, the average present

value of the firm over the cycle increases with increases in a.24

a2, 2
(PVE + PVE41) | (Eo ~5#)" + a
z 21 (1b)

(27)

Next consider the case in which adjustment costs are positive and
finite (i.e. O< d< ©). In this case the firm's labor demand is given
by (see Appendix A for derivation):

fy ~ (4St4j * GSt4jen) + 02, ¢45
é
1

(28) Neay =

f= 0, 1, 2, ceeee

hn £1 + (14d)
where 4. ~ Fy + ad(i*b)

_ d(1+b)
4 ~ Fp ¥ 2d)

qota1 = 1

o< ysl

Here the firm's employment rule is expressed in terms of a weighted average
of the two values the real wage takes over the exchange rate cycle and is
similar in form to (23). The term cagts reflects the effects of initial
conditions on the firm's adjustment problem: dy is the stable root of the
second-order difference equations generated by the maximization problem and
c is a constant determined by initial conditions. By picking t+j large
enough so that the effects of initial conditions are negligible, we can
look at the firm in a kind of “steady-state,” i.e., we can see how the

firm responds to pure cyclical variation.


-5-

fluctuations, but empirical work has yet to differentiate strongly
between them.
l.a A Simple Contracting Model

Figure l.a illustrates the notional supply and demand for labor at
the firm we are considering. The real wage v is the market clearing
wage; n is the equilibrium rate of employment, sometimes called the
"natural" rate. For simplicity, we assume that labor supply is
inelastic. The labor demand curve is a graph of the marginal product
of labor, which is appropriate for a price taking, profit maximizing
firm.

More explicitly, if the firm's technology is Cobb-Douglas

(1) = Ken(t-9)

(where Y is output, N is employment, and K is the capital stock), and if
the capital stock is fixed (at, say, K = 1) while there is no cost to
adjusting employment, then the profit maximizing rate of employment is

given by
- oO
(2) We/P, = (l-a)NE

(where Wis the nominal wage rate and Ph is the domestic price of
output). We will find it more convenient to work with linear models, and
equations (1) and (2) have natural log-linear representations. Letting
small letters denote the logarithms of the corresponding capital letters,

(1) and (2) become


1. The Effects of Exchange Rate Prediction Errors

In this section we are concerned with the effects of unexpected
exchange rate movements on a firm and its employees. Unexpected exchange
rate movements can occur for a variety of reasons, and their effects,
both positive and normative, will generally depend upon the source of the
disturbance. Here we will assume that that source is external to the
firm and the industry in which it operates.

Monetary disturbances would have no effect on employment or output
were it not for some sort of price stickiness. | Here we attribute that
stickiness to wage contracting. In section 1.a we develop the basic
contracting framework that we will extend and use repeatedly throughout
the rest of the paper to describe different ways in which exchange rate
volatility affects unemployment, output and investment decisions.

In section l.a we describe the simplest of contracting models and
show how unexpected exchange rate movements lead to fluctuations in the
price of the firm's product, and thus to fluctuations in employment and
output. In section 1.b we extend the model to include wage indexing and
imported intermediate goods, like oil; exchange rate fluctuations have
had important cost implications in recent years via both of these
channels. In section 1.c we extend the model to include long-term
contracts, contracts that last for more than one period. There appear to
be two relevant ways of doing this, both on theoretical and empirical
grounds. The two approaches have very different implications for the way

exchange rate volatility is transmitted to employment and output


-17-

become more important in the last decade. It has also been the source of
international disputes; indeed some European policy maker's view the
strong U.S. dollar as the "third oi] shock "22
Summarizing, an unanticipated depreciation will, ceteris paribus
increase the price the firm receives for its product if the good is traded
internationally; however, it may also increase the price it has to pay
for its labor and oil inputs. If indexing and the dollar pricing of oil
play an important role in the firm's cost structure, then employment and out-
put will not increase much. Again, the key word is unanticipated. If the

depreciation had been foreseen, a higher base wage would have been specified

in the contract, and employment and output would have been unaffected.

l.c. Long-term Contracting

In sections 1.a and 1.b, we asumed that contracts lasted only one
period, or more precisely, we defined a period to be the length of a
contract. If we were doing emperical work with quarterly (or even
yearly) data, then this assumption would probably not be appropriate. '°
Most union contracts in the U.S. last for three years; most other workers
are not covered by formal contracts, but are subject to annual salary and
performance reviews.

In this section, we describe two of the ways long-term contracts
have been modeled and discuss the implications of multiple period

contracts for exchange rate volatility and employment fluctuations. We


-7-

(3) yy = (l-a)ny
and

(4) w

t 7 Pt log (l-a) - an,

[log (1-a) - an] - a(n,-n)

The bracketed term, log (1-a) - af, is the market clearing wage v in
Figure l.a.

The firm's product is sold on world markets, so the good's price p
is equal to p* +s, where p* is "the" world price and s is "the" exchange
rate. (For present purposes we are aggregating the "rest of world" into
one entity.) Volatility in s that is not offset by movements in p* is
passed on to the domestic price of output.

Following Gray (1976), we simply postulate that the firm and its
workers must get together at the beginning of each period, before goods
prices and exchange rates are known, and set the nominal wage in a labor
contract. Their goal is to achieve the market clearing solution; that
is, they predict prices and exchange rates as best they can and set the
nominal wage at a level that is expected to result in the market clearing
real wage v3 If PElt-1 and Stlt-1 are the price and exchange rate

expected to prevail, then the wage set in the contract is

(5) Wet vt Perey = Yt (PE ey + Steen)

The symbol "|t-1" denotes an expectation based upon information available

at the end of period t-1.


-23-

The firm is also assumed to be subject to real quadratic costs in
adjusting its labor force which can be expressed as d/2(Ne 4, - Nosy)” where
d > 0. Two possible interpretations can be given to these costs. First,
such costs could be interpreted as being part of the production function and
therefore technological in nature. In this case, as in Sargent [1979], the
cost is specified in terms of the firm's own output. Second, these adjustment
costs might conceivably be related to unemployment insurance and financial
costs other than wages which arise when the firm alters its demand for labor
from period to period. Given this interpretation, the cost might be specified
in terms of a basket of consumption goods. We have chosen the first
interpretation.

The firm is assumed to maximize the expected present value of

profits. Profits (mE 45) are defined in terms of output 18 as:

(19) teay = FoNeag 7 1/28 NEay ~ 1/2404 — Neagen)?

~ Weg /Pety Ne+y

The only new term introduced in (19) is the firm's real wage bill
Westy Pets Ne+j where We+j is the contract wage.

The assumption that both the firm's production function and costs
of adjusting labor are quadratic result in a quadratic objective function.
This is a convenient representation because when the firm maximizes the
expected present value of profits with respect to its choice of employment
(Ne), we obtain linear first order conditions which make it straightforward
to obtain reduced-form expressions for the firm's employment rule. The
quadratic nature of the firm's objective function also results in the

“separation principle", applicable in the stochastic case, where we can


International Finance Discussion Papers
Number 240

April 1984

THE EFFECTS OF EXCHANGE RATE VARIABILITY ON OUTPUT AND EMPLOYMENT
by

Matthew B. Canzoneri, Peter 8. Clark, Thomas C. Glaessner
: and Michael P. Leahy

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 materials)
should be cleared with the author or authors.


-46-

_
wie
>
an
“i

1
fy B NN

Nz Ny
Figure 3. Effects of Exchange Rate Variability on Labor
Demand.

Figure 3 depicts a specific example of the general result that if
the decision-maker is risk averse, i.e., has a utility function characterized
by decreasing marginal utility, the firm will produce at a lower level of
output, and hire fewer factors of production, when the price of output is
unpredictable compared to a situation where the price is known with certainty.
When the firm must make its hiring and production decisions before the actual
realization of the price of output, the equilibrium position of the firm is
where production takes place such that the average, i.e., expected price,
exceeds the marginal cost of production. This condition is shown in Figure 3
as the marginal product of labor exceeding the expected real wage, which
implies that the expected exchange rate, Ss, exceeds the marginal cost of labor.

Under uncertainty, a risk-averse firm will produce less than when
the price is certain because by lowering output the firm reduces the
variability of profits. Consider a risk-averse firm facing an initially
certain price. Output will be determined where price equals marginal cost.

If the price now becomes variable but the expected price and expected profits


-10-

= + (a) COO$ ~ PH gg) + SE - Stead]

Exchange rate prediction errors lead to fluctuations in employment about
its “natural” rate.

It should be noted that an unanticipated increase in s will often
be accompanied by an unanticipated movement in p*. Canzoneri and
Underwood (1982) have shown that if the depreciation is due to an
unanticipated increase in the rate of growth of the home money supply»
both s and p will increase, but because of the wage stickiness, the
increase in s will be larger 5 This means that p*, the foreign price of

the firm's output, must be unexpectedly low, for

(8) PE - Pegg = (Py Pepeen) ~ (Se - Septet)

In this case, just looking at Sp- Seite in Figure 1.b will overstate
the impact on employment. Indeed, suppose that the depreciation is due
to an unanticipated decrease in the rate of growth of the foreign money
supply. In this case, p will be unexpectedly low and employment will
actually fal1.® The fall in p* outweighs the rise in s and reverses the
effect on employment illustrated in Figure 1.b.

These two examples illustrate an important caveat for studies such
as this. There can be no fixed relationship between two endogenous vari-
ables such as the exchange rate and employment. Both are fluctuating in
response to some truly exogenous disturbance (or group of disturbances),
and the very sign of the covariance between the two will depend upon the

source of the disturbance. The exchange rate is exogenous to the price


FIGURE 1.b

labor supply

v-(SerSt ter)

labor demand



-59-

contracts); that is, the actual employment rule may lie "below" the labor
demand curve in Figure l.a and be "steeper". Our view is that
modifications of this sort would probably not seriously alter the basic
discussion above; however, this remains a controversial point in contract
theory. The comments of Fischer (1980) and Waldo (1981) on Barro's
criticism are also relevant.

5. This is essentially Dornbush's (1976) "overshooting" result in a
wage contracting framework.

6. This need not be so, from a theoretical point of view anyway. The
contractionary foreign monetary policy may actually be inflationary at
home. Canzoneri and Gray (1983) describe the transmission mechanisms
that tend to produce positive or negative spillovers for monetary policy.
7. In practice, it may be difficult to make this distinction when
observing actual labor contracts.

8. Gray (1976) derived optimal indexing rules for closed economies.
Marston (1982), Turnovsky (1982) and Flood and Marion (1982) have
extended her work to open economies.

9. In the simple model described above, full indexation to P would
always achieve the full employment solution. However, adding
productivity shocks (which shift the labor demand curve in Figure l.a)
and an elastic labor supply curve (see footnote 2) would complicate the
situation considerably. The equilibrium solution (v, nm) would shift with
both productivity disturbances and the terms of trade, and full

indexation to either P or I would not be optimal.


-42-

P=S, Henceforth we shall make this substitution and define the price of
output as equal to the exchange rate.
The firm is a price taker both with regard to its sale price
and with respect to the prices, R and W, of the two inputs, K and N,
respectively. The prices of the two inputs are assumed to be non-stochastic,
and the labor-contracting assumptions are the same as in the first section
of the paper. Uncertainty enters through the price of output being a random
variable with the mean and variance known to the decisionmaker.29
Consistent with the standard approach using expected utility
maximization, we assume initially that decisions concerning the volume of
output and the hiring of both inputs are made prior to the realization of
the market price.30 We later partially relax this assumption by assuming
that the firm adjusts output and the labor input each period in response
to the observed exchange rate each period, but varies the capital stock
only in the long run when there is a change in the mean and/or variance
of the exchange rate. The assumption of short-run fixity of both labor
and capital in the standard model appears to reflect an implicit assumption
that the costs of adjusting capital and labor are so large in the short run
that factor inputs are varied in some unspecifed manner only over some
longer-run period as the average level and variability of the firm's price
changes. The reasons for the short-run fixity of labor presumably include
the explicit and implicit costs of hiring and firing labor, the need to
train labor, and union rules specifying the conditions under which labor
can be hired or fired. Because these costs of adjusting labor would appear
to be lower than adjusting capital in the short run, and because there is

a clear profit incentive to adjust output, and therefore, labor input in


~30-
increases with increases in a. Equation (32) shows the expression for the

average present value over the cycle.

* * —- 2 2
(32) (PVE + PVE 47) _ (£5-S*) + a [£1 + 4db]
2 | BE C=by © PHBE FAA]

Finally, consider the case in which adjustment costs are infinite.

As d increases without bound, the second term of (30) vanishes and the firm's

labor demand is given hy:

(33) Netz =

Since adjustment costs are infinite, the firm's decision-makers choose a
quantity of labor, N, and keep it constant throughout their planning horizon.
They will pick N such that labor's marginal product, fo-f1N, equals the
average real wage rate over the cycle.

From (33) then, we can see that 1) the firm's output and employment
do not vary over the exchange rate cycle and 2) an increase in the amplitude
of the exchange rate cycle has no effect on output and employment. Further-
more, as d increases without bound, the second term of (32) vanishes and
we can see that the average present value of the firm over the cycle neither
increases nor decreases with increases in a. This case corresponds to the
model of the firm commonly used in studies employing risk aversion to
generate effects from increased variability. As is discussed in section 3,
implicit in those studies is an assumption of infinite adjustment costs.

In this section we have seen how exchange rate cycling affects a
firm's output and employment decisions under three different adjustment cost
assumptions. We have found that as long as adjustment costs are zero or

finite, the firm will adjust its output and employment to changes in the


-47-

are unchanged, the firm will no longer be in equilibrium; expected utility
will be reduced because the utility of the extra profits is less than the
loss in utility from a reduction in profits of the same magnitude. To
moderate the loss in expected utility, the firm reduces the level of output
because this action will directly reduce the variability in profits [see
equation (46)] and thereby increase the expected utility of profits relative
to the position of higher output associated with the certain price.

Now let us consider what happens when there is an increase in the
variance of the exchange rate, i-e., when there are larger exchange rate
fluctuations. Here we assume that the firm adjusts both capital and labor
in response to a perceived change in the variance of the exchange rate. The
first-order condition for capital employment is similar to equation (48), and

is given by:
(50) aV/8K = Sty - R - Of fy og = 0

The equilibrium condition for capital employment is:
(51) R/S = (1-6f 08/8) Ex.

If the production function is homogeneous of degree one, then
because factor prices are assumed to be unchanged, it follows that the firm
will continue to hire capital and labor in the same proportion and that the
marginal products fx and fy will be functions of the unchanged capital-labor
ratio. Consequently, for production functions homogeneous of degree one,
f, and fy will be constant. Because the only two variables that change in

equations (49) and ( 51) are f, i-e., output, and og, it follows that an


-29-

From (28) we can see that the firm's decision-makers choose the
quantity of labor they desire such that in each period labor's marginal
product equals a weighted average of the values the wage rate takes over
the cycle. By substituting into (28) the expression for the exchange rate
process (21) and by suppressing the term c i, we can see more clearly
the effect of increases in variability on the firm's employment rule in the

steady state.

fy - (5 + alagraqy (9)
(29) N= 27 So“)
tty ty
-_ tti
N- a(-1) 3
(30) = ;
Fj F2d(ib) f= 0,1, 2, eee

With adjustment costs the firm's production function is given by

= - 2
(31) Yeas = EoNe ay V2 1/24(N

2
+5 7 Neaj-1)°>

Comparing (30) with (23), we can make the following observations. 1) With
adjustment costs the firm's output and employment still cycle with the same
frequency as the exchange rate, but the amplitude of the cycling is diminished.
2) An increase in the amplitude of the exchange rate cycle brings about an
increase in the amplitude of the output and employment cycles. 3) Again,
because of the concavity of the production function, average output falls as
the amplitude of the exchange rate cycle increases, even though average
employment remains fixed at N.

By substituting into the firm's present value function its
employment rule (30) and the wage rate process, we can show that, even with

adjustment costs, the average present value of the firm over the cycle


-66-

Pomery, John, “Uncertainty and International Trade,” in R. Dornbusch and
J. Frenkel, eds., International Economic Policy ~ Theory and
Evidence, John Hopkins University Press, Baltimore and London, 1979.

Poole, W., “Optimal Choice of Monetary Policy Instruments in a Simple
Stochastic Macro Model,” Quarterly Journal of Economics, May 1970,
pp- 197-216.

Pratt, J.W., Risk Aversion in the Small and in the Large,” Econometrica,
32, (January/April 1964), pp. 122-36.

Rothschild, M., Stiglitz J.E., “Increasing Risk: I.A. Definition”
1970, Vol. 2., pp. 225-243.

Salop, J., "Devaluation and the Balance of Trade Under Flexible Wages,"
in G. Horwich, and P. Samuelson, eds., Trade Stability and Macro-
economics, (Academic Press, New York), 1974.

Samuelson, Paul A., “The Consumer Does Benefit From Feasible Price
Stability," Quarterly Journal of Economics, 1972, Vol. 86,
ppe 476-93.

Sandmo, Agnar, "On the Theory of the Competitive Firm Under Uncertainty,”
American Economic Review, (March 1971), pp. 65-73.

Sargent, T., Macroeconomic Theory, Academic Press, New York, 1979.

Sikdar, Soumyen, “Timing of Decisions and the Competitive Firm Under Input Price
Uncertainty,” Economic Letters, 14, 1984, pp. 321-325.

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

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

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

Varian, Hal R., Microeconomic Analysis, 1978, New York: W.W. Norton
and Co.

Waldo, D., "Sticky Nominal Wages and the Optimal Employment Rule,"
Journal of Monetary Economics, May 1981, pp. 339-354.



FIGURE 1.a

labor supply

labor demand



-20-

and exchange rates will also affect employment and output; this wage
setting model does not incorporate the "natural rate" hypothesis (though
it is perfectly consistent with the "rational expectations" hypothesis).
Consider for example the effect of a fully anticipated series of
depreciations (with no change in P* or P**), Since just one nominal wage
is specified for the duration of the contract, the real wage in Figure
1.b will start high (too high for market clearing) and be inflated away,
period by period; employment will be low in the early periods, and high
in later periods. |”

Taylor's (1979,1980) contracting model also assumes that one wage
is set for the life of the contract; indeed, this is the source (when
combined with overlapping contracts) of the persistence effects that are
thought to be a virtue of his model. Taylor uses a different employment
rule, and his wage setters appear (on the surface anyway) to have
different motivations; it is possible however that his model could be
explained in a way that is quite consistent with Mussa (1981).

Canzoneri and Underwood (1982) compare the effects of exchange rate
volatility in Taylor's model with those in the Gray-Canzoneri model.
Aside from the fact that Taylor's model does not incorporate the "natural
rate" hypothesis, the basic difference is that exchange rate movements
have longer lasting effects on employment and output. The effect

persists even after all of the contracts have been negotiated.


-57-

in the variance of the exchange rate; a low degree of risk aversion will lead
the firm to expand its scale of operations.

Our paper has focused on only a few of the channels through which
variability in exchange rates affects the behavior of firms. We have, for
example, deliberately ignored the financial structure of the firm. It would
be useful to extend the work of this paper by integrating financial considerations
into the models developed here to gain further insights into how firms make
production and employment decisions in response to increased variability in

exchange rates.


REFERENCES

Arrow, K.J., Aspects of the Theory of Risk Bearing. Helsinki:
Jahnssonin Saatio, 1965.

Barro, R. “Rational Expectations and the Role of Monetary Policy,”
Journal of Monetary Economics, Jan. 1976, p. 1-32.

Batra, Raveendra, N., The Pure Theory of International Trade Under
Uncertainty, New York: John Wiley and Sons, 1975.

Batra, R.N., and Ullah, Aman, "Competitive Firm and the Theory of Input
Demand Under Uncertainty,” Journal of Political Economy, 82, 1974
(May/June), pp. 537-548.

Begg, D., “Rational Expectations, Wage Rigidity and Involuntary Unemployment:
A Particular Theory," Oxford Economic Papers, March 1982, p. 23-48.

Blinder, A.S., “Inventories and Sticky Prices," American Economic Review,
Volume 72, No. 3, (June 1982) pp. 334-348.

Canzoneri, Matthew and Jo Anna Gray, “Some Aspects of the Adjustment
Problem in an Interdependent World." In The Future of the
International Monetary System, edited by Tamir Agmon, Robert Hawkins
and Richard Levich, forthcoming in 1984.

Canzoneri, M. and J. Underwood, “Wage Contracting, Exchange Rate Volatility,
and Exchange Intervention Policy,” working paper, December 1982.

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

Christofides, L. and Wilton, D., "The Determinants of Contract Length:
an Empirical Analysis Based on Canadian Macro Data,” Journal of

Monetary Economics, forthcoming.

Clark, Peter B., “Uncertainty, Exchange Risk, and the Level of International
Trade," Western Economic Journal, Vol. 11 (1973), pp. 302-313.

Coes, Donald, “The Crawling Peg and Exchange Rate Uncertainty," in John
Williamson, ed., Exchange Rate Rules, London, McMillan Press, 1981.

Cushman, David 0., “The Effects of Real Exchange Rate Risk on International
Trade," Journal of International Economics, 15, No. 1/2 (August 1983),
pp. 45-64.

Daniel, Betty C., "The International Transmission of Economic Disturbances
Under Flexible Exchange Rates," International Economic Review, 22,
No. 3 (October 1981), pp. 491-509.

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

Fama, E.F., Miller, M.H., The Theory of Finance, Holt, Rinehart and Winston,
Inc., 1972.


-37-

rather than at point a. Over time this shock would be discounted at a rate
which would depend upon (1) the persistence of the shock (i.e., the size of p)
and (2) upon the structural parameters affecting the root i, in the model

(as suggested above).

Figure 2 illustrates the effect of letting the persistence (or
permanence) of a given unanticipated exchange rate (or real wage) shock
increase (i.e., an increase in the size of p). In this case if there
initially was a positive exchange rate (or real wage) shock (increase in Z_)
without any change in the persistence of the shock we would move from point
a to b as in figure 1. However, suppose that given the same real wage shock,
the firm perceives the shock to be more persistent or permanent (e.ge, 0
has risen). In this case they will move from a to c so that their demand for
labor will fall by more than it would have otherwise. Thus, as shocks are
viewed as more permanent (thereby increasing the variance of the exchange
rate process) firms will tend to adjust their demand for labor by larger
amounts initially (e.g. at time ty) in response to the unanticipated shock.

Figure 3 illustrates how the firm's decision makers will react
to an exchange rate shock as adjustment costs rise. Note that for a given
level of adjustment costs the firm's decision makers would reduce their demand
for labor initially to b; however, if these costs were higher the firm would
only reduce its employment to point c. Equation (38) also reveals that
when adjustment costs are infinite (d«) the demand for labor is simply
equal to WN (the steady state level of employment). Alternatively as d-> 0
a case synonymous with that of section 1 the firm will only be concerned

with the exchange rate shock in the current period.


-B3-

coefficients yields

o q .
(B88) Ne=N-c 5 £ aged piz,_
q=0 i=0 t 4
c 1
where N = —1 (£9 - 8*)

=X Fy
by using the fact that

1 nT

i = FCESTE DIGESTS) as indicated in equation (A8) of appendix A.

oy 1
Also C = = =e where it should be observed that

|ai| < 1 and we have assumed that the effects of any initial conditions on
the firms employment rule are negligible. Note that equation (B8) corresponds
to equation (38) in the text.

Some of the results regarding the effects of unanticipated exchange
rate shocks on firm behavior described graphically in the text can be obtained
more formally by deriving the variance of the demand for labor by using

equation (B8). Thus we have

(B9) Var(N,)

E(N, - WJ?

o _
EIN - CE oy Zig - NI?
&0

°
of(-C)2 £ g,2 since E[Z,Z,] = 0 for s#t.

substituting for $g we obtain:


=38-

The results presented above are heavily dependent upon the
assumptions that (1) the firm's decision-makers maximize a quadratic objective
function and (2) that labor contracts specify that the nominal wage be fixed
at the same rate for all periods in the contract. The first of these two
assumptions is critical because it limits the ways in which variability
effects the firm's demand for labor. For example, changes in the variance of
unanticipated exchange rate shocks (%) do not enter directly into the
parameters or as an independent variable in the firms employment rule (see
equations (36) and (38) above). Instead only changes in the extent of serial
correlation in the exchange rate process effect the firm's decision-makers
forecasts of the real wage rate and hence the level of employment and output.
In the present context the variance of the exchange rate could enter into
the firms optimal employment rule if either the production function or
adjustment costs were of a higher order than quadratic (e.g., cubic). This
is due to the fact that the first order conditions of the firm's maximization
problem would no longer be linear, so that when conditional expectations were
taken, conditional variances would enter the firm's employment rule.
Relaxation of the quadratic assumption would allow higher moments to affect
the firms employment rule without assuming that the firm's decision-makers
are risk averse or that they maximize expected utility, two assumptions which
have been prevelant in most of the literature explaining the relationship
between exchange rate variability and trade flows. 28

Finally having derived results for a simple model of the firm
given a stochastic exchange rate process and long term wage contracts in
which the nominal wage is indefinitely fixed at one level, we investigate the

implications of adopting the sort of contracting scheme developed in


-53-

profits, the effects on the optimum capital stock, and therefore on the
level of output, depends on the size of 6. With relatively low risk
aversion, i.e., small 8, the positive effect on utility of greater price
variability on expected profits outweighs the negative impact of utility
of greater variability of profits, and the firm will raise the average
capital stock and level of output.

A similar result was derived by Hartman (1976). Using a CES
production function, he showed that with low elasticity of substitution
between capital and labor and returns to scale approaching unity, increased
uncertainty could increase the expected value of profits. Using a general
concave utility function, he shows that if U"(m) is sufficiently small,
the higher expected profits dominate the increased variability of profits,
and greater price variability raises output. The advantage of the approach
taken here is that it provides an explicit solution for the capital stock
in terms of measurable parameters, the mean and variance of the exchange
rate.

A recent contribution to the literature on the behavior of the
firm under uncertainty [Pindyck (1982)] has also shown that under certain
conditions, increased price variability can result in increased average
investment and output. Pindyck assumes that the price of the firm's output
follows a random walk and that it faces increasing marginal adjustment
costs, i.e., CM/#(I) > 0. Pindyck finds that with risk aversion, increased
uncertainty will raise the target capital stock and output even if cTM(I) = 0.
Increasing marginal adjustment costs reinforce the tendency to hold a higher

capital stock.


-26-

We derive the firm's labor demand expression from the following
maximization problem:

(22) mx PV, = 5 bi x

jo

Nety
where O< b<1

TMety is the profit function discussed in section 2a. In this section, the
firm's decision-makers know with certainty that the exchange rate S; follows
the process given in (21). Given this information, they must pick a sequence
of Ne+j (j = 0, 1, 2, ...), and by so doing an output sequence, such that
they maximize the firm's present value.

Nosy = fo - St4 =N-2 (-1) tt

(23) fy fy]
j=0,1, 2, ...

£,8*

here N =
where fy

In this case the firm chooses the quantity of labor it desires such that in
each period labor's marginal product, fof Net y> equals the real wage rate
St+j- This period-by-period profit maximization is what we would expect when
the firm's decision-making in one period has no effect on profits in other
periods. Using (23) and the fact that output, Y~, is given by the firm's

production function

= - 2
(24) Yeas = EoNtty 7 MV 2ENeay>


-56-

In section 2, we focused primarily on time series properties of
exchange rate movements and their implications for employment decisions in
firms facing fixed money wage rates and fixed costs of adjustment. If the
firm's product is traded internationally, then exchange rate cycles produce
cycles in the price the firm receives and in the real wage it has to pay.
However, because the firm's profit function is convex in the real wage, it
will actually benefit from this cycling even if there are (finite) costs of
adjusting employment from period to period. If, for example, the amplitude
of the exchange rate cycle increases, the firm can actually increase its
average profits by allowing employment to adjust optimally. We found that an
increase in the amplitude of the exchange rate cycle will lead to an increase
in the amplitude of the employment cycle, and that an increase in the
persistence of shocks to the exchange rate cycle will lead to bigger and longer
lasting effects in the employment cycle. Here again, all of our results are
partial equilibrium in nature.

In section 3, we focused primarily on variances of exchange rates
and their implications for the investment decisions of a risk averse firm
facing infinite short-run adjustment costs for its capital stock. Suppose
the variance of exchange rate fluctuations increases, increasing with it the
variance of real wage fluctuations. Here again, the convexity of the profit
function will allow the firm to increase the expected value of its short-run
profits by varying employment optimally. In the long run, this tends to make
the firm want to increase its capital stock. However, the variance of profits
is also increased, and this tends to make a risk averse firm want to contract
its scale of operations. In theory, either effect can dominate. A high

degree of risk aversion will lead the firm to contract in response to an increase


-65-

Fischer, S., “Long-Term Contracting, Sticky Prices and Monetary Policy:
A Comment,” Journal of Monetary Economics, 3, 1977b, p. 317-23.

Fischer, S., “Long-Term Contracts, Rational Expectations, and the Optimal
Policy Rule," Journal of Political Economy, 85, Feb. 1977a, p. 19-
205.

Flood, R.P., and Hodrick R., “Optimal Price and Inventory Adjustment in an
Open-Economy Model of the Business Cycle," Unpublished Manuscript,
August, 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.

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

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

Journal of Monetary
Hartman, Richard, “Factor Demand with Output Price Uncertainty,” American
Economic Review, September, 1976.

Helpman, E., and Razin, A., A Theory of International Trade Under
Uncertainty, Academic Press, New York, 1978.

Hooper, P., and Kohlagen, S., "The Effects of Exchange Rate Uncertainty
on the Prices and Volume of International Trade," Journal of Inter-
national Economics, Vol. 8, 1978, pp- 483-511.

Horowitz, Ira, Decision Making and the Theory of the Firm, Holt, Rinehart
and Winston, Inc., New York, 1970.

Justice, G., "The Impact of Exchange Rate Variability on International Trade
Flows,” Bank of England Discussion Papers No. 4, December 1983.

Lucas, R., "Expectations and the Neutrality of Money, Journal of Economic
Theory, April 1972, p. 103-24.

Marston, R., “Real Wages and the Terms of Trade: Alternative Indexation
Rules for an Open Economy,” unpublished manuscript, May 1982.

Mussa, M., “Sticky Prices and Disequilibrium Adjustment in a Rational
Model of the Inflationary Process, American Economic Review,
December 1981, p. 1020-1026.

Oi, Walter, “The Desirability of Price Instability Under Perfect Competition,”
Econometrica, 29, pp. 58-64.

Pindyck, R.S., “Adjustment Costs, Uncertainty, and the Behavior of the Firm,”
American Economic Review, Vol. 72, No. 3 (June, 1982), 415-427.



of movements in one endogenous variable (here, the exchange rate) for
movements in another (here, real economic activity) generally depend upon
the source of the exogenous disturbance. We give examples of this problem
in section l.

The paper is organized as follows: The analysis focuses on the
implications of different assumptions about labor contracts and the costs of
adjustment. In section 1, we develop two contracting models and explore
the static effects of exchange rate fluctuations on real economic activity.
In the Gray-Fischer-Canzoneri model, exchange rate prediction errors cause
fluctuations in employment and output, whereas in the Mussa-Taylor model
anticipated exchange rate movements also affect the firm's employment and
output decisions.

In section 2, we use the same contracting models to describe the
dynamic effects of exchange rate fluctuations on employment and output. We
show that the time series properties of employment and output depend upon
the time series properties of the exchange rate, the cost of adjusting
factor inputs, and the form of the labor contract. We also show that exchange
rate volatility can be profitably exploited by an individual firm when the
firm can adjust its output to price changes each period.

In section 3, we examine the implications of risk aversion. We
illustrate the standard result that, given an increase in exchange rate
variability, a risk averse firm will reduce its scale of operations if
adjustment costs prohibit its responding to actual realizations of the exchange
rate. However, we also show that if this last assumption is relaxed and the
firm is able to adjust its labor input in response to exchange movements,

then it may well want to increase its scale of operations. Aversion to the


-45-

Substituting the right-hand side of (45) and (46) into equation

(44) gives the following expression for the objective function of the firm:
(47) V= 3S £ - WN RK~- 0 £2 08/2

Maximizing V with respect to the quantity of labor employed, holding capital

constant, gives:
Ss 2.
(48) V/ N= 8 fy - W- Of fyog = 0,
which can be re-arranged to yield an expression for the real wage .32
(49) W/S = (1-0f 08/8) fy.

Let B = Of o&/S. Because W/S > 0, the values of the variables that
determine § are such that 8 <1. The equilibrium employment condition
given by equation (49) reduces to the standard non-stochastic real wage =
marginal product-of-labor expression if the variance of the exchange rate
is zero, i.e., 0 = 0, or if the decision-maker becomes risk neutral
iee., 0 -> 0.

The equilibrium condition given by equation (49) is depicted in
Figure 3. The AA line gives the marginal product of labor, fy, associated
with a given capital stock. The BB line depicts the “adjusted” demand
schedule for labor, where the adjustment factor is equal to 1-8. The
equilibrium quantity of labor demanded is Nj, which is determined by the

intersection of the BB schedule and the given expected real wage.


-43-

order to take advantage of price fluctuations, we consider below the case
where the firm maximizes the expected utility of profits each period by
varying the level of labor input.

We first use a general production function, Y = f£(K, N), where
first and second derivatives with respect of each factor are positive and

e
negative, respectively. The profit function of the firm is given by:
(40) nm = SY - WN - RK.

The firm maximizes the expected utility of profits. Rather than attempt

to derive the most general result possible, which has already been done by,
e.g. Batra and Ullah (1974), we illustrate our points and pay the price of
some loss in generality for a gain in terms of concreteness and simplicity.
We assume a given utility function--the expotential—-and a specific
probability density function for the exchange rate--the normal distribution.
These two assumptions make it possible to relate the level of output and
employment to explicit expressions involving the mean and variance of the
exchange rate.

The utility function of the firm is given by
(41) U(m) = - exp (-6r),

where 9 > 0. This utility function exhibits positive but declining marginal
utility because U'(m) = 6 exp(-91) > 0 and U"(m) = -092 exp(-@m) < 0.
Also, where R,(TM) denotes the level of absolute risk aversion, the
expotential utility function is characterized by constant absolute risk
aversion = @ because R,(m) = -U"(m)/U'(m) = g3l

Taking the expectation of the utility of profits, where profits

are distributed normally because the exchange rate is assumed to be normally


~A2-

Solving for Ne+j> finally, we get:

(AT) Nesey = Azfo/a(1 - 1/22)(1-a1)

=0 1

+ catti,
1

= ©
Qy/a) BAKE (1/A9)4 weg aine
1 k i=0 2 ttjti

As in the text, we will henceforth assume that t+j is large enough so that

the effect of any initial conditions on the firm's employment rule are

negligible. To simplify (A7), we note that

(A8) g/d = (l= Ayb) (1 1)/f1-

Substituting from (A4) into (A8), we get:

(A9) g/d = (1 = 1/A2)(1 = A2)/£1-

Using (A9) and the fact that

1/1 = Wry) = E sag)! and 1/(1= 44) = E
i=0 i=0

(A7) in the following form:

o
(A10) Ne+g = f/f. = (1/£1) 2 Ze weajee
Lao

where:
(1/s) © (A,)4°% (1/Ag)? for & < 0
i=0
Zg =
(1/8) © (A,)4(1/A9)4** for 2 > 0
1=0
Py
Eo Zgsl

(A5) can be rewritten as:

i, we can rewrite
1


~13-

contract, as shown in equation (5), and the market clearing solution
would have obtained. This contracting model incorporates the “natural
rate" hypothesis; perfectly anticipated movements in prices or exchange
rates have no effect upon employment or output. Later we will describe a
contracting model in which perfectly anticipated exchange rate
fluctuations can have real effects.

1.b. Indexing and Imported Intermediate Goods

Wage indexing has become an important feature in the cost structure
of many economies recently. When added to the contracting framework
described above, it becomes a new channel for unanticipated exchange rate
fluctuations to affect real wages and employment.

It will be recalled that anticipated inflation and exchange rate
depreciation are already reflected in the base wage set in the contract;
so, for example, indexing clauses designed to capture expected losses in
purchasing power have already been accounted for. In the view of wage
contracting taken here, this kind of indexing does not affect employment
or output, though it may well be an important factor in inflation.

Instead, the indexing we want to discuss here is an explicit
contract provision for modifying the base wage as actual price and
exchange rate data become available.” The goal once again is to achieve
the market clearing solution, and the basic idea is that movements in P
or some index of prices, C, can act as signals for wage setting, much as
interest rate movements are taken as indicators for monetary policy.
Unfortunately, movements in P and C are both imperfect signals; neither
tells one how to adjust the base wage to achieve the market clearing

solution in all circumstances. The problem is analogous to Poole's


-55-

general equilibrium, this will not be the case; all prices and exchange rates
will move in response to some exogenous shock, and these additional price
movements may augment or conteract the exchange rate effects described above.
Even if structural features like indexing and the dollar pricing of oil remain
unchanged, in general equilibrium there is no fixed relationship between a
firm's employment decisions and exchange rate prediction errors, such as

given by the following equation:
(62) ny = n= P(e, - Se[e-1)>

The two-country model of Canzoneri and Gray (1984) provides a simple
example of this problem. In their model, an unanticipated increase in the
home money supply, m, depreciates the home currency and is expansionary both
at home and abroad; similarly, an unanticipated increase in the foreign money

supply, m, appreciates the home currency and is expansionary in both countries:

(63) on, - A= 4 (me-mfe) + Oy (mg-me | 1)

eos
me 70

wok
(meme | pay) + %2CmeMe | p-1)
* *
Se 7 Sefenn = Sg l (mpm fey) ~ Cmemme|_-1)]

where %; > %2 > 0 and %3 > 0. If a data sample is generated by home
monetary disturbances, then the observed correlation in equation (62) will be
» = %)/43, If the data are generated by foreign monetary disturbances,

then the observed correlation will be ¥» = -42/%3. Both the sign and the
size of the coefficient »¥ in equation (62) depend upon the source of the

disturbance generating the fluctuations.


-61-

18. Firms are concerned with real profits where nominal profits are
deflated in each period by the price of the firm's output (P,). Alter-
natively, we could have deflated nominal profits by a general price
level (PI) which can be viewed as constant over time or it could be
assumed to grow at some rate which would become part of the discount
factor used to compute the present value of future profits.

19. Relaxation of the assumption of a quadratic objective function is
explored in section 2c below.

20. Relaxing assumptions about world prices and nominal wages being
fixed would lead to more complicated processes generating real wages.
In this case the covariances between components of the real wage become
important in affecting the behavior of the firm, as in Section 1. For
our purposes, it is more convenient to look at the foreign currency
price of the domestic currency, Se » rather than its reciprocal, S,.
21. Blinder [1982] and Flood and Hodrick [1982] develop similar models
to those considered below except that the firm is monopolist in output
markets and is subject to demand rather than exchange rate shocks. In
their models firms adjust inventories rather than labor intertemporally
in response to exogenous shocks} however, the results of their analysis
do not differ significantly from that presented below for the case of a
stochastic real wage process (section 2c). Moreover, these authors do
not consider how purely deterministic movements in exogenous variables

will affect decision variables, as we do in section 2b.


-15-

(14) ny = 8 + (1-2)(1/a)B, + 2(1/a)Ev1 (By - 7.) + v2, - Te - S,)7

As before, employment and output depend on own price prediction errors,
Bee but now they also depend upon the relative price prediction errors
Pe -i, and Pe - is - 8.

Consider once again the effect of an unanticipated depreciation.
If the domestic price of output remained constant (that is, if a negative
p* offset the positive $, so that p = p* + § = 0), then the only effect
on the real wage and employment would be through the indexing clause.
The price of foreign goods would rise, and this would be passed on to the
nominal and then the real wage; employment and output would fall. If, at
the opposite extreme, the domestic price of output rose by the full
amount of the depreciation, then the real wage would have to fall.
However, it would not fall in proportion with the rise in the domestic
price, because the higher cost of domestic and foreign goods would be
passed on to a higher nominal wage. Employment and output would rise,
but not by as much as if there had been no indexing. 1°

Oil and other imported intermediate goods have also become an
important factor in many firm's cost structure. Canzoneri and Gray
(1983) provide a simple model in which oil and labor are used in fixed

13)

proportions. One unit of oi] and one unit of labor combine to form

one unit of the variable composite input which the firm uses, along with


The Effects of Exchange Rate Variability on Output and Employment
by

Matthew B. Canzoneri, Peter B. Clark,
Thomas C. Glaessner, and Michael P. Leahy*

The current regime of flexible exchange rates has focused attention
upon the relationship between the volatility of exchange rate movements and
the level of real economic activity. The concern is that exchange rate
variability may decrease international trade flows, and may even affect
employment and output at firms that are not directly involved in international
markets.

In this paper, we survey the theoretical underpinnings of the
relationship between exchange rate variability and a firm's employment and
output decisions. Using simple models, we catalogue the different ways in
which exchange rate movements affect the cost and revenue structure of the
firm. (No attempt is made to integrate the financial structure of the firm
into these models; such an extension would be most useful.)

Few of our results are really new. Rather, we hope that our survey
will be helpful in developing empirical models of trade flows; we also think
that our work points to certain measures of exchange rate volatility that are
relevant: to discussions of regime design. Some of these measures are already
familiar from existing empirical work on trade flows and from the literature
on rational expectations; others, particularly those suggested by section 2,

ate new. Care must be taken in the use of these measures. The implications

*The first three authors are on the staff of the Federal Reserve Board.
Michael Leahy is a graduate student at the University of Wisconsin. The
views expressed are those of the authors and do not necessarily represent
those of the Board of Governors or the Staff of the Federal Reserve Systen.


-36-

The effect on the firm's demand for labor of an unanticipated
exchange rate (or real wage) shock is illustrated in figures 1-3 below. In
figure 1, a positive real wage shock which is unanticipated at time t,

would cause the firm to employ the level of labor at point b

Figure 1
Ne
a N
be”
ty 2 t
Figure 2
Ne
a N
’g- 7-7
uf
ey
ty t2 t
Figure 3
Ne
a V
c aa -7 °
ad
,
b b-
t



=B4-

g o o o |

[rf £ ayCt pt]? = 2 d2 +p? fala + ot 5 abe
£=0 1=0 j-o } jeoot jeo 1

+ seseeeeeeed = 1/(1-A2)(1/(1-p2)

so we have
(B9") Var(N,) = 02 (-6)?(1/1-4f )(A/1-67)
where

var (WN, )/ 302 = (-¢)2(1/1-a2)(1/1-p2) > 0

a Var (Ne)/2p > O by inspection of (B9)'


=24-

first obtain optimal linear forecasts of the exogenous variables and then
solve a nonstochastic optimization problem. 19

In our model of the firm, assumptions about the nature of labor
contracts and commodity arbitrage imply that exchange rate variability
results in associated variability in real wages. In particular we assume
that firms enter into long term contracts with labor in which laborers and
firms agree on a nominal wage rate which is assumed to be fixed over the
firm's entire planning horizon. Moreover, the firm's output is sold on
domestic and world markets and is subject to commodity arbitrage so that

R= prs, where Pe and S, are defined as in section 1 above. Under

t

these two assumptions the real wage rate can be written as:

(20) (Wy /P_) = (W/PA)SE = St

where (W/P*) = 1 and st = (1/S,)-

For convenience we define the units of the nominal wage rate W and
the foreign currency price of output, p*, such that their ratio equals one.
Thus equation (20) implies that the real wage process will be generated by
whatever assumptions are made about the process generating st = (1/8,)-2°
Finally the firm is assumed to be a perfect competitor on both domestic and
foreign output markets so that it views the real wage rate as an exogenous
process which will be assumed to be either stochastic or purely deter-

ministic.21l


Title: The Effects of Exchange Rate Variability on Output and Employment

Authors: Matthew B. Canzoneri, Peter 8. Clark, Thomas C. Glaessner, and Michael
P. Leahy

Address: Board of Governors of the Federal Reserve System
Washington, D.C. 20551

Date: April 1984
Series Number: International Finance Discussion Papers, No. 240
Pages: 78
Price: No charge
JEL Subject Classification: 431
Keywords: Exchange rate variability, Output, Employment, Labor contracts,
Adjustment costs, Expected utility maximization

This paper is a theoretical analysis of the effects of exchange rate
variability on a firm's employment and output decisions. In section 1, two
contracting models are developed and the static effects are explored. In the
Gray-Fischer-Canzoneri model, only exchange rate prediction errors have effects,
whereas in the Mussa-Taylor model anticipated exchange rate movements also have
effects. In section 2, the same contracting models are used to describe the
dynamic effects. The time series properties of employment and output depend upon
the time series properties of the exchange rate, the cost of adjusting factor
inputs, and the form of the labor contract. Also, exchange rate volatility can
be profitably exploited by an individual firm that can adjust its output to price
changes each period. In section 3, the implications of risk aversion are
examined. Given an increase in exchange rate variability, a risk-averse firm
will reduce its scale of operations if adjustment costs prohibit its responding
to realizations of the exchange rate. However, if the firm is able to adjust its
labor input in response to exchange rate movements, then it may well want to
increase its scale of operations. Aversion to the increased risk has to be
weighed against the expected profitability of being able to exploit wider

fluctuations in the exchange rate.


-48-

increase in the latter must reduce the former, i.e., greater exchange rate
variability reduces output.

This result is depicted in Figure 3. An increase in og affects
both the marginal-product-of-labor and "adjusted" demand-for-labor schedules,
shifting both down and to the left, the former because the capital stock has
declined, and the latter because of the argument in the above paragraph. The
new equilibrium at the unchanged real wage and marginal product of labor is
characterized by less labor employed, Ng. This effect is a specific example
of the impact of a marginal increase in uncertainty. The more general result
regarding the effects of an increase in variability or uncertainty is in terms
of a mean preserving spread in the probability density function of the price
of output. Using this technique, Batra and Ullah (1974) show that under the
hypothesis of decreasing absolute risk aversion, increased variability leads
to a decline in output and reduction in factor demand.

A major difference between the model and those in the first two
sections of the paper is that there is no adjustment in the expected utility
model to individual realizations of the exchange rate, whereas in the models
in sections 1 and 2 there is full or partial adjustment by the firm to the
exchange rate change when it occurs. In terms of Figure 3, deviations of S
from S and the resulting changes in the real wage do not induce any change
in the behavior of the firm; desired and actual labor demand remains at Nj.
At the other extreme, in the approach taken in the first section of the paper,
the firm always adjusts fully to the change in the price of its output
generated by fluctuations in the exchange rate, and moves up and down its

demand-for-labor schedule.


-32-

employment. Since the marginal costs of adjusting are arbitrarily small
for small enough adjustments, firms can reduce their losses by reducing
output and employment. Thus, if a firm has the ability to adjust, its
profits over the exchange rate cycle are higher than the profits the firm
would have earned had the exchange rate stayed constant. Put another way,
if a firm has the ability to adjust, its profit function will be convex in
the real wage rate, and its profits will increase as the amplitude of the
real wage rate cycle increases.

In this section, then we have isolated another channel through which
exchange rate variability affects firm behavior. Our analysis suggests that
exchange rate variability is not necessarily costly to firms. Firms with any
ability to adjust to changes in the exchange rate can gain from exchange rate
variability in this model. While this analysis is a partial equilibrium
result, there is nevertheless the possibility that in a general equilibrium
analysis in which agents have varying degrees of flexibility, exchange rate
variability may bring about transfers of income from those who find

adjustment costly or impossible to those who find adjustment less costly.


-41-

convex in the exchange rate and the expected value of profits is a positive
function of the variance of profits. We find that if the firm is risk
averse, an increase in exchange rate variability does not necessarily reduce
output and employment, a result at variance with the standard one.
3a. Exchange Rate Variability and Expected Utility Maximization - The
Standard Results

An exposition of the theory of the firm under uncertainty with
expected utility maximization has been done along general lines by Sandmo
(1971) and Batra and Ullah (1975) and Helpman and Razin (1978). A recent
survey of the literature on the effects of uncertainty on international
trade, with emphasis on the real side, has recently been provided by
Pomery (1979). Specific applications of the expected utility maximization
approach to the effects of exchange rate variability on the level of trade
have been done by Clark (1973), Coes (1981), and Hooper and Kohlhagen (1978).
Cushman (1983) and Justice (1983) also provide empirical evidence on the
impact of exchange rate variability on trade flows.

Here we illustrate the connection between exchange rate variability
and output and employment, rather than focusing specifically on the impact
on the level of trade flows. We assume the same market structure described

above that generates variability in the price of output, i.e.,

(39) P=S °* P*

where P* = price of the same commodity in foreign currency and assumed to be
fixed. As before, the firm is assumed to be a price taker on domestic and
world markets, and commodity arbitrage ensures that the domestic~currency
price varies in proportion to the exchange rate. We can without loss of

generality define the unit of output such that P* = 1.0, and consequently


-27-

we can make the following observations. 1) The firm's output and employment
vary with the same frequency as the exchange rate. 2) An increase in the
amplitude of the exchange rate cycle brings about an increase in the amplitude
of the output and employment cycle. 3) Because of the concavity of the
production function, average output falls as exchange rate variability
increases, even though average employment remains fixed at N as a increases.

By substituting the firm's employment rule (23) and the exchange
(or real wage) rate process (21) into its profit function, we obtain:

- 2 2 -
(sy tho (for) 8 (ES a(-1)*
ct. -

aa fy

’

*
where TM, is the maximized value of profits for the given wage rate path.
We can see that the profits of the firm over the cycle, and average profits,

increase with increases in a.

(26)

(rf + 1H) (Ego Bay? +a”
2 2f)

The formal reason why average profits increase with increases in
exchange rate variability is that the firm's profit function is convex in
the real wage rate. Oi [1961] contains an early discussion of this property
in connection with a firm's profit function. See also Samuelson [1972] and
Chapter 1.9 in Varian [1978]. We will be able to discuss more clearly what
this convexity means in terms of the behavior of the firm after we have
presented the next two cases. Before we go on to the case of positive but
finite adjustment costs, however, let us note that because the firm's profit

function is convex in the real wage rate, the firm's present value function


-ll-

taking firm, and we discuss the impact, ceteris paribus, of exchange rate
volatility on the firm's employment. This is a standard partial
equilibrium exercise, but we must recognize that, in the case of the
exchange rate anyway, the “ceteris paribus" qualification is very
important.

Fluctuations in employment will of course lead to fluctuations in
output. In fact, our simple contracting model can be explained in terms
of the price-marginal cost diagram illustrated in Figure l.c. The (log

of) the marginal cost curve for the firms is

(9) c'(¥,) = wy, - log (1-a) + Ca/(1-a) ly,
(wy - v) + La/(1-a)1(y, - ¥)

a"

where y = (l-a)n is the equilibrium or “natural” rate of output. The

position of the marginal cost curve is determined by the We set in the

contract. It is clear from (5) and (9) that We is set so that

c'(y) = Pelt-1° In other words, w, is set in the contract so that the

t
marginal cost curve in Figure 1.c will intersect the expected price,
Peit-1? at the equilibrium rate of output, y. The unanticipated
depreciation analyzed in Figure 1.b causes the actual price to be higher

than expected and increases output. The general result is

"

(10) yg = ¥ + [(1-a)/al(P - Pepe _y)

=F + [(l-a)/aI(Of = PR Ey) + Se = Styeea)]

The key word here is unanticipated. If the depreciation had been

accurately predicted, a higher nominal wage would have been set in the


-63-

31. Following Pratt (1964) and Arrow (1965), a decision-maker's attitude
toward risk can be defined as:

Rg(TM = - U" (m) / U' (7)
where Rg (") is the absolute risk-aversion function. For risk-averse
decision-makers, Rg (") is decreasing in ".
32. A similar expression can be derived for the real return on capital.
33. Hartman (1976, p. 681) derives the same result.
34, This result is similar to that shown in Appendix A, where it is
demonstrated that the present value of the firm increases as long as it can
adjust to some extent within the period in response to exchange rate flucu-
ations. A recent contribution to the literature by Sikdar (1984) has also
provided a result similar to that given here. Sikdar finds that if a firm
postpones the choice of the input mix and level of output until the actual
value of a random input price becomes known, then uncertainty may induce a
risk-neutral or risk-averse firm to produce more than in the case of
certainty, and increased risk in the form of a mean-preserving spread in a
random input price may lead to an expansion of production by a risk-neutral

firm,


-49-

The extreme assumption in the expected utility approach of no
adjustment to actual exchange rate movements (that do not change the mean
value, ‘S) is consistent with the treatment of uncertainty. The idea is
that because of the implicit assumption of very large adjustment costs,
firms must make commitments in hiring capital and labor, and therefore
output--these models do not allow for inventory changes--without knowing
the actual prices at which output will be sold. The uncertainty is generated
by the lag between the time factors are hired and the time the price level
becomes known. The level of uncertainty in terms of the variability in the
actual price relative to its expected value depends on the length of this lag,
and therefore on the costs of adjustment. If the firm could adjust capital
and labor costlessly in response to the price of output generated by the
exchange rate each period, there would be no uncertainty of the kind that is
assumed by the expected utility approach. A move in this direction is in

fact described below.

3b. Adjustment of Labor Input to Realized Exchange Rates
In this section we relax the assumption that neither labor nor
capital are adjusted to the current price, i.e., exchange rate realization.
Here we assume instead that labor can be adjusted costlessly in the short
run when the current exchange rate is observed. We still maintain the
assumption that capital is a fixed factor that is adjusted only in the long
run, i.e., the capital stock is chosen before the exchange rate is observed
and is altered only in response to the mean and variance of the exchange rate.
Our approach is similar to that of Hartman (1976). We differ in

that we use a specific utility function, again the exponential, and we include


-51-

where K is the capital stock fixed in the short run, W is, as before, the
fixed nominal wage, and S is the actual current-period exchange rate. The

profit-maximizing employment rule derived from equation (54) is:
(55) N= (1-a)2/@ (s/wyl/o &

To further simplify the exposition we assume that a =1/2. Using

equations (52), (53), and (55) give the following expression for profits:

<4

(56) 1 =82(1/4 W) K - Rok
Expected profits are given by:

(57) Ef] = 7 = (og +32) (1/4W) K

E-R¥w
- RoK - RK

In the risk-neutral case, the firm chooses the level of the

capital stock that maximizes the expected value of profits. This gives:
(58) d E{w]/d K = (0g + 8%) (1/4 W) — Ro ~ 2Ry K= 0.
Solving for K yields:
(59) K= [Cog + 37)/8 RyW] - Ro/2Ry

Note that as Ry —> 0, K— », Also note that the optimal capital stock
is positively telated to the variance of the exchange rate.

Where the decision-maker is risk averse, we again assume that, as
above, the exchange rate is distributed as NG, og) and that the utility

function is expotential, so that it is necessary to maximize the objective


-14-

(1970). Just as Poole's optimal combination policy depends upon the
relative sizes of disturbances in the IS and LM curves, so the optimal
indexing scheme will depend upon the sizes of various disturbances
affecting equilibrium in the labor market ,° and just as pegging the
interest rate is not generally optimal for monetary policy, so full
indexation to P or C (which amounts to pegging W/P or W/C) is not

generally optimal for wage policy.?

Suppose the labor contract calls for partial indexation of W to C,

where

YoY. Y2
(11) C =P (I) (I*S) 5 Yo t+¥1 + ¥2 = 1

I is an index of home goods, other than Y, and I* is an index of foreign

goods. If (5) is modified to

(12) Wav + Pelt-1 + alc, - Celta)

where Q is an indexing parameter (0 < 2 < 1), then the real wage is
(13) wy = Pp =v = (1-2)P, - Of (BE - TE) + v2(B, - TF - §,)]

where i is the log of I, a "+" denotes a prediction error (e.g. x =X

Xejt-1) and the general result for employment is