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Working Paper 8710
MONETARY POLICY I N AN ECONOMY
WITH NOMINAL WAGE CONTRACTS
by Charles T. Carlstrom
Charles T. Carl strom i s an economist a t the Federal Reserve Bank o f
Cleveland. The author thanks seminar p a r t i c i p a n t s a t t h e Bank f o r many
h e l p f u l comments. Working papers a r e p r e l i m i n a r y m a t e r i a l s c i r c u l a t e d t o
s t i m u l a t e discussion and c r i t i c a l comment. The views s t a t e d h e r e i n are
those o f t h e author and n o t n e c e s s a r i l y those of the Federal Reserve Bank o f
Cleveland o r o f the Board o f Governors o f the Federal Reserve System.
December 1987
-
-
Abstract
T h i s paper c o n s i d e r s t h e r o l e o f monetary p o l i c y i n an economy w i t h
r a t i o n a l e x p e c t a t i o n s and a nominal wage c o n t r a c t i n g c o n s t r a i n t .
To t h i s
end, a monetary economy w i t h nominal wage c o n t r a c t i n g i s c o n s t r u c t e d i n a
simple n e o c l a s s i c a l growth model.
I t i s shown t h a t when u t i l i t y i s
l o g a r i t h m i c i n consumption t h a t a money supply r u l e designed t o e i t h e r peg
nominal i n t e r e s t r a t e s o r t a r g e t nominal o u t p u t w i l l be o p t i m a l f o r t h i s
economy.
I n more general f o r m u l a t i o n s o f u t i l i t y no s p e c i f i c p o l i c y
reccomendations can be made, o p t i m a l monetary p o l i c y can be e i t h e r
p r o c y c l i c a l o r c o u n t e r c y c l i c a l depending on t h e e x a c t f o r m o f t h e u t i l i t y
function.
I. I n t r o d u c t i o n
This paper c o n s i d e r s t h e r o l e o f monetary p o l i c y i n an economy w i t h
r a t i o n a l e x p e c t a t i o n s and a nominal wage- contracting c o n s t r a i n t .
Building
upon t h e work o f F i s c h e r (1977), households and f i r m s a r e (by assumption)
r e q u i r e d t o agree on a nominal wage b e f o r e t h e r e a l i z a t i o n o f t h e r e a l and
monetary shocks. The p r o t o t y p e o f t h e model developed i s f r o m P r e s c o t t
(1983).
P r e s c o t t r e c o n s i d e r e d t h e nominal wage- contracting model o f F i s c h e r
and p u t F i s c h e r ' s system o f e q u a t i o n s i n t o a s i m p l e n e o c l a s s i c a l growth model
w i t h r a t i o n a l expectations.
P r e s c o t t ' s model i s m o d i f i e d t o i n c l u d e economy-wide s u p p l y shocks and
p o s s i b l e p o l i c y responses c o n d i t i o n a l on these shocks.
I n a d d i t i o n , money i s
i n t r o d u c e d i n t o t h e system by i n c l u d i n g r e a l balances i n t h e u t i l i t y f u n c t i o n
i n s t e a d o f a cash- in- advance c o n s t r a i n t .
T h i s i s done so t h a t t h e
i n t r o d u c t i o n o f money does n o t i n f l u e n c e any r e a l q u a n t i t i e s (assuming t h a t
u t i l i t y i s separable).
The o p t i m a l monetary p o l i c y w i l l depend on t h e money
demand equation, so i n c l u d i n g r e a l balances i n t h e u t i l i t y f u n c t i o n a l s o
a l l o w s one t o e a s i l y c o n s i d e r d i f f e r e n t f o r m u l a t i o n s f o r money demand.
Because nominal wages a r e c o n t r a c t e d p r i o r t o money s u p p l y
announcements, monetary p o l i c y can have r e a l e f f e c t s
l e v e l and, hence, r e a l wages.
by in f 1uenci ng t h e p r i ce
S i m i l a r l y , s i n c e wages a r e c o n t r a c t e d p r i o r t o
t h e observance o f t h e p r o d u c t i v i t y shocks, employment cannot a d j u s t t o i t s
f i r s t b e s t ( f l e x wage) l e v e l .
Assuming t h a t monetary p o l i c y can be made a f t e r
t h e r e a l shock i s observed, monetary p o l i c y can p o t e n t i a l l y i n c r e a s e t h e
w e l f a r e o f t h e r e p r e s e n t a t i v e consumer.
The money s u p p l y can be i n f l a t e d o r
d e f l a t e d t o i n c r e a s e o r decrease t h e r e a l wage and t o mimic t h e spot- market
wage t h a t would a r i s e w i t h o u t an ad hoc nominal wage- contracting c o n s t r a i n t .
Although monetary p o l i c y can s t a b i l i z e o u t p u t , i t w i l l n o t g e n e r a l l y be
d e s i r a b l e t o do so.
The money-supply r u l e , which maximizes t h e u t i l i t y o f t h e
r e p r e s e n t a t i v e consumer and p r o v i d e s t h a t t h e f i r m e a r n z e r o p r o f i t s , may be
e i t h e r procycPica1 o r c o u n t e r c y c l i c a l .
The c o r r e c t monetary response w i l l
depend on t h e consumption e l a s t i c i t y o f money demand and the consumer's
r e l a t i v e degree o f r i s k a v e r s i o n .
Assuming u t i l i t y i s l o g a r i t h m i c i n consumption, a p o l i c y r u l e designed
e i t h e r t o peg t h e nominal i n t e r e s t r a t e a t a g i v e n l e v e l o r t o s t a b i l i z e
nominal o u t p u t w i l l produce t h e f i r s t b e s t ( f l e x wage) q u a n t i t i e s .
The
Federal Reserve Board c u r r e n t l y t a r g e t s t h e nominal i n t e r e s t r a t e , w h i l e
s e v e r a l economists have l o n g advocated a p o l i c y r u l e t o t a r g e t nominal
output.
I n t h e s p e c i a l case i n which u t i l i t y i s l o g a r i t h m i c i n consumption
b o t h p o l i c y r u l e s a r e i d e n t i c a l as w e l l as o p t i m a l .
These r u l e s amount t o
p u r s u i n g a p r o c y c l i c a l ( c o u n t e r c y c l i c a l ) money s u p p l y r u l e i f t h e income
e l a s t i c i t y o f money demand i s g r e a t e r ( l e s s ) t h a n one.
The case i n which u t i l i t y i s n o t l o g a r i t h m i c i n consumption, b u t i s
l o g a r i t h m i c i n r e a l money balances, leads t o s i m i l a r p o l i c y c o n c l u s i o n s .
The
o p t i m a l p o l i c y can be e i t h e r p r o c y c l i c a l o r c o u n t e r c y c l i c a l depending on t h e
r e l a t i v e degree o f r i s k a v e r s i o n o f t h e r e p r e s e n t a t i v e household.
Procyclical
( c o u n t e r c y c l i c a l ) monetary p o l i c y would be f a v o r e d i f t h e degree o f r e l a t i v e
r i s k a v e r s i o n i s g r e a t e r ( l e s s ) than one.
The s t r u c t u r e o f t h e paper i s as f o l l o w s : s e c t i o n I1 d e s c r i b e s t h e
environment i n terms o f t a s t e s , technology, and endowments and t h e n d e f i n e s an
e q u i l i b r i u m f o r t h i s economy.
S e c t i o n I11 c h a r a c t e r i z e s t h e e q u i l i b r i u m and
discusses t h e a p p r o p r i a t e p o l i c y response t o v a r i o u s p r o d u c t i v i t y shocks.
f i n a l s e c t i o n discusses whether nominal c o n t r a c t i n g models can be used f o r
The
p o l i c y purposes g i v e n t h e c u r r e n t i n f o r m a t i o n on t h e f o r m o f t h e u t i l i t y
f u n c t i o n and t h e e m p i r i c a l v a l i d i t y o f nominal c o n t r a c t i n g models.
11. An Economy w i t h Nominal Wage C o n t r a c t s
The e v o l u t i o n o f t h e economy i s as f o l l o w s :
t h e r e p r e s e n t a t i v e household
e n t e r s i n t o each p e r i o d w i t h cash and c a p i t a l c a r r i e d o v e r f r o m t h e p r e v i o u s
p e r i o d (except f o r t h e i n i t i a l p e r i o d , where cash and c a p i t a l a r e g i v e n as
endowments).
The worker t h e n s i g n s a c o n t r a c t w i t h a f i r m s p e c i f y i n g t h e
nominal h o u r l y wage t h a t w i l l be p a i d i n t h e coming p e r i o d .
By assumption,
t h i s wage c o n t r a c t cannot be indexed t o e i t h e r t h e monetary i n j e c t i o n or t h e
price level.
However, t h e number o f hours worked can be made c o n d i t i o n a l o n
b o t h p r o d u c t i v i t y shocks and monetary shocks.
Hours a r e a l l o w e d t o depend o n
t h e monetary shock i n o r d e r f o r monetary i n j e c t i o n s t o have r e a l e f f e c t s .
A f t e r t h e shocks o c c u r , t h e household r e n t s c a p i t a l s t o c k t o a f i r m ( n o t
n e c e s s a r i l y i t s employer) f o r a r e n t a l r a t e , u, and works t h e number o f h o u r s
s p e c i f i e d by t h e c o n t r a c t , c o n t i n g e n t upon t h e r e a l i z a t i o n s o f t h e monetary
i n j e c t i o n and t h e p r o d u c t i v i t y shock.
A t t h e end o f t h e p e r i o d , t h e household r e c e i v e s i t s r e n t a l and wage
payments i n cash f r o m t h e f i r m ( s > .
For s i m p l i c i t y , i t i s assumed t h a t c a p i t a l
d e p r e c i a t e s c o m p l e t e l y a f t e r one p e r i o d .
t h e purchase p r i c e o f c a p i t a l .
The r e n t a l p r i c e o f c a p i t a l i s t h u s
The household t h e n combines t h e wage and
r e n t a l payments w i t h t h e i n i t i a l c u r r e n c y h o l d i n g s and any lump-sum monetary
t r a n s f e r s f r o m t h e monetary a u t h o r i t i e s t o choose t h e amount o f consumption
f o r t h a t p e r i o d and t h e amount o f c a p i t a l and cash i t wishes t o c a r r y o v e r
i n t o the next period.
Money w i l l be h e l d i n e q u i l i b r i u m because o f t h e
u t i l i t y i t p r o v i d e s t h e household.
The p e r c a p i t a money stock e v o l v e s a c c o r d i n g t o t h e f o l l o w i n g f o r m u l a :
M,,
=
M,(l+x),
where x i s a random v a r i a b l e and M, i s t h e economy-wide
money s t o c k (which, i n e q u i l i b r i u m , w i l l be equal t o t h e amount h e l d b y t h e
r e p r e s e n t a t i v e consumer) a t t h e b e g i n n i n g o f p e r i o d t.
Increases i n t h e money
s t o c k a r e b r o u g h t about by lump-sum t r a n s f e r s t o t h e household(s) from t h e
monetary a u t h o r i t i e s .
I t i s assumed t h a t t h e p r o b a b i l i t y d e n s i t y f u n c t i o n o f
t h e monetary i n j e c t i o n s , x, i s f(x:K,,M,,B,),
where 8, i s t h e
p r o d u c t i v e shock r e a l i z e d i n p e r i o d t .
C o n d i t i o n i n g t h e d i s t r i b u t i o n on K , M, and 8 i s due t o t h e assumption
t h a t t h e monetary a u t h o r i t i e s can choose t h e money supply a f t e r o b s e r v i n g t h e
s t a t e o f t h e economy i n t h a t p e r i o d .
W i t h o u t t h e r e a l shock, t h e o p t i m a l
monetary p o l i c y would be t o m a i n t a i n a c o n s t a n t money s t o c k o r g i v e n t h a t t h e
monetary a u t h o r i t i e s have t h e necessary revenues t o d e f l a t e t h e money s t o c k a t
the r a t e o f time preference.
The p r o d u c t i v i t y shock, 8, i s assumed t o be a s t r i c t l y p o s i t i v e random
v a r i a b l e t h a t i s i d e n t i c a l l y , independently d i s t r i b u t e d over time w i t h a
Furthermore, i t i s assumed t h a t 8
p r o b a b i l i t y density function o f g(8).
affects production m u l t i p l i c a t i v e l y .
have t h e f o r m
8F(kt,ht),
The p r o d u c t i o n f u n c t i o n i s assumed t o
where F(.,.)
degree one i n l a b o r , h, and c a p i t a l , k .
i s assumed t o be homogeneous of
The technology i s f u r t h e r assumed t o
have t h e f o r m t h a t c a p i t a l and t h e consumption good can be transformed w i t h o u t
c o s t f r o m one t o another.
Firms a r e assumed t o be p r o f i t maximizers o p e r a t i n g i n a p u r e l y
c o m p e t i t i v e environment.
T h i s ensures t h a t c a p i t a l and l a b o r w i l l be chosen
i n such a way t h a t t h e value o f t h e marginal p r o d u c t i v i t y o f c a p i t a l i s equal
t o t h e r e n t a l p r i c e o f c a p i t a l and t h a t t h e v a l u e o f t h e m a r g i n a l p r o d u c t i v i t y
o f l a b o r i s equal t o t h e wage r a t e .
The c o n s t a n t - r e t u r n s - t o - s c a l e assumption
ensures t h a t , i n e q u i l i b r i u m , f i r m s w i l l e a r n z e r o p r o f i t s .
n o t necessary.
The assumption i s
However, i t s i m p l i f i e s t h e a n a l y s i s s i n c e t h e d i v i d e n d s
households r e c e i v e f r o m f i r m s no l o n g e r have t o be considered.
The r e p r e s e n t a t i v e household i s assumed t o have p r e f e r e n c e s o v e r
consumption, c,,
balances , m,
+
l e i s u r e , 1-ht (where 0 < h, < I >and
, r e a l money
, /pt ,
as f o l lows :
where 0 < I3 < 1 i s t h e d i s c o u n t f a c t o r and u ( . , . >
and H ( . )
have a l l o f t h e
usual p r o p e r t i e s : concave, t w i c e d i f f e r e n t i a b l e , and i n c r e a s i n g i n t h e i r
arguments.
The above e x p e c t a t i o n i s taken t o be c o n d i t i o n a l on t h e
i n f o r m a t i o n s e t a t t i m e zero, t h e i n i t i a l c o n d i t i o n s KO and M o .
Capital
l e t t e r s denote aggregate v a r i a b l e s o v e r which t h e i n d i v i d u a l has no c o n t r o l ,
w h i l e lower- case l e t t e r s r e p r e s e n t a choice v a r i a b l e f o r t h e i n d i v i d u a l .
However, i n e q u i l i b r i u m , t h e q u a n t i t i e s chosen by t h e i n d i v i d u a l w i l l be equal
t o t h o s e f o r t h e economy as a whole.
The e q u i l i b r i u m c o n t r a c t w i l l be chosen so i t maximizes t h e u t i l i t y o f
t h e r e p r e s e n t a t i v e consumer, s u b j e c t t o t h e c a p i t a l and 1abor t h e f i r m w i 11
h i r e a t t h e chosen r e n t a l and wage r a t e s , and s u b j e c t t o t h e budget c o n s t r a i n t
for the individual.
The f o l l o w i n g i s t h e p l a n n i n g problem f o r t h i s economy:
Problem H:
max
w,,ut(.>,ct(.)
mt+l(.>,kt+l(.)
E , { ~ R ' ~ u ( c,1-h,)
,
+ H(mt+~lpt)l1
0
C o n s t r a i n t s 1 and 2 are the " r e a c t i o n f u n c t i o n s " f o r the f i r m , which
s p e c i f y how much l a b o r and c a p i t a l w i l l be chosen by the f i r m a t v a r i o u s wage
and r e n t a l r a t e s .
C o n s t r a i n t 3 i s the budget c o n s t r a i n t f o r the worker.
notation ut(.>, ct(.>,
...
The
e t c . denotes the r e n t a l r a t e on c a p i t a l ,
consumption, next p e r i o d ' s c a p i t a l , and next p e r i o d ' s money stock are a l l
chosen c o n d i t i o n a l on k t , M,,
denotes w(kt,m,,,Mt>
m t , 8,,
x,.
The wage r a t e , w,,
since, by assumption, wages cannot depend on x o r
8.
The p r i c e o f consumption and c a p i t a l , p,,
f i r m and worker i n problem H .
i s taken as given by t h e
I n e q u i l i b r i u m , p t w i l l be chosen i n such a
way t h a t the money market c l e a r s , M, = m,.
The household's budget c o n s t r a i n t consists o f income from c a p i t a l and
l a b o r as w e l l as money c a r r i e d over from the previous p e r i o d and the lump-sum
t r a n s f e r from the monetary a u t h o r i t i e s , M t x .
The household spends i t s
income on c u r r e n t consumption as w e l l as on t h e c a p i t a l and c u r r e n c y i t wishes
t o c a r r y over i n t o the next period.
The problem i s s t a t e d i n t h i s form i n s t e a d o f t h e " d u a l " f o r m u l a t i o n
s i n c e c o m p e t i t i o n by f i r m s f o r workers and c a p i t a l ensures t h a t t h e wage r a t e
and r e n t a l r a t e o f c a p i t a l w i l l be chosen o p t i m a l l y f r o m t h e h o u s e h o l d ' s p o i n t
o f view.
Otherwise, a f i r m c o u l d e n t e r and make p o s i t i v e p r o f i t s w h i l e t h e
household remains a t l e a s t as w e l l o f f as b e f o r e .
We a r e now r e a d y t o d e f i n e an e q u i l i b r i u m f o r t h i s economy:
D e f i n i t i o n o f Equi 1i b r i u m :
A s t a t i o n a r y e q u i l i b r i u m f o r t h i s economy r e q u i r e s t h a t t h e f o l l o w i n g
conditions are satisfied:
1) w,,
u,(.),
kt+,(.),
Problem H f o r t = 1 , 2,
ht(.),
ct(.),
m t + , ( . ) a r e chosen t o s a t i s f y
....
2) P, i s chosen such t h a t t h e money market c l e a r s :
3 ) The u n i t o f account does n o t m a t t e r , t h a t i s P,, W,, U t a r e
homogenous o f degree one i n l a s t p e r i o d ' s money s t o c k M,.
T h i s completes t h e d e f i n i t i o n o f e q u i l i b r i u m .
The n e x t s e c t i o n
c o n s i d e r s v a r i o u s f u n c t i o n a l forms f o r t h e p r o d u c t i o n f u n c t i o n and t h e u t i l i t y
f u n c t i o n i n o r d e r t o t a l k a b o u t t h e o p t i m a l monetary p o l i c y .
111. Real Shocks and Monetary P o l i c y
I n t h i s s e c t i o n , t h e u t i l i t y i s assumed t o have a c o n s t a n t i n t e r t e m p o r a l
e l a s t i c i t y o f s u b s t i t u t i o n , w h i l e t h e p r o d u c t i o n f u n c t i o n i s assumed t o be
Cobb-Douglas.
u(c,l-h)
The forms f o r b o t h a r e as f o l l o w s :
=
LC'-" - ll/(l-a)
+ v(1-h)
H(mt+l / p t > = C(mt+ / p t ) ' - b - l l / ( l - b )
F(k,h)
= kah
-OE
where 0 < a < 1, a
.
W i t h these f u n c t i o n a l forms, t h e f i r s t - o r d e r c o n d i t i o n s f o r Problem H a r e
as f o l l o w s :
(3.6)
A,,
(3.8)
l i m BtEt+l(A3tptkt+l)
t*°~
=
m;:l(l/pt>l-b
where E t ( . ) = E,,e(.:Kt,Mt)
+
=
REt+i(A3t+i)
0
and A i (i = 1,2,3> i s t h e c o s t a t e
v a r i a b l e associated w i t h t h e i
constraint.
E q u a t i o n 3.1 s t a t e s t h a t t h e m a r g i n a l u t i l i t y o f r e a l b a l a n c e s i s e q u a l
t o t h e m a r g i n a l u t i l i t y of consumption.
market c l e a r s .
E q u a t i o n 3.2 s t a t e s t h a t t h e c a p i t a l
C o n d i t i o n 3.3 i s i d e n t i c a l e x c e p t t h a t , because o f t h e n o m i n a l
w a g e - c o n t r a c t i n g c o n s t r a i n t , t h e l a b o r m a r k e t w i l l o n l y c l e a r " on a v e r a g e ."
E q u a t i o n 3.4 s t a t e s t h a t i n v e s t m e n t o c c u r s u n t i l t h e m a r g i n a l c o s t o f
i n v e s t i n g i n terms o f forgone consumption i s equal t o t h e d i s c o u n t e d e x p e c t e d
b e n e f i t s due t o i n c r e a s e d p r o d u c t i o n n e x t p e r i o d .
E q u a t i o n 3.6 i s t h e demand
f o r nominal cash b a l a n c e s , w h i l e e q u a t i o n s 3.7 and 3.8 a r e t h e t e r m i n a l or
t r a n s v e r s a l it y condi t i o n .
Because o f t h e nominal c o n t r a c t i n g c o n s t r a i n t , employment i n c r e a s e s
(decreases) w i t h money s u p p l y i n c r e a s e s t h a t a r e l a r g e r ( s m a l l e r ) t h a n
expected.
U s i n g e q u a t i o n s 3.1,
3.3, and 3.5 we can see t h a t , o n average,
r e p r e s e n t a t i v e worker w i l l be n e i t h e r o v e r - or underemployed.
the
Overemployment
(underemployment) i s d e f i n e d as when t h e w o r k e r i s w o r k i n g more ( l e s s ) t h a n he
w o u l d w i s h t o (ex p o s t ) i n a s p o t m a r k e t a t t h e p r e v a i l i n g wage r a t e .
Underemployment o c c u r s when monetary i n j e c t i o n s a r e s m a l l e r t h a n e x p e c t e d ,
w h i l e overemployment o c c u r s when monetary i n j e c t i o n s a r e l a r g e r t h a n
expected.
A l t h o u g h underemployment i s a k i n t o i n v o l u n t a r y unemployment, t h e
t w o s h o u l d n o t be t r e a t e d synonymously, s i n c e by d e f i n i t i o n t h e r e i s o n l y one
w o r k e r i n t h i s a r t i f i c i a l economy.
As w i l l be seen, t h e money s u p p l y r u l e t h a t maximizes t h e u t i l i t y o f t h e
r e p r e s e n t a t i v e worker w i l l e l i m i n a t e overemployment and underemployment.
However, s i n c e underemployment and overemployment a r e n o t o b s e r v a b l e , i t i s
n e c e s s a r y t o d i s c u s s what t h e money s u p p l y r u l e s h o u l d be w i t h r e s p e c t t o
o b s e r v a b l e v a r i a b l e s , namely o u t p u t and p r i c e s .
U s i n g t h e t r a n s v e r s a l i t y c o n d i t i o n s e q u a t i o n s , 3 . 4 and 3.6 can be s o l v e d
recursively yielding:
(3.4')
yt~;a
C ( U R > ~ E ~(c;;:)
+~
=
S
and
=o
Equation 3.6'
shows t h a t t h e m a r g i n a l u t i l i t y of nominal cash balances,
X3, i s d e c r e a s i n g i n b o t h c u r r e n t and expected f u t u r e monetary
injections.
Combining 3 . 6 ' w i t h 3.1 g i v e s t h e demand f o r r e a l cash balances
o r e q u i v a l e n t l y shows how t h e p r i c e l e v e l - i s determined i n e q u i l i b r i u m , g i v e n
the market- clearing c o n d i t i o n m t + , = M t + l :
S
00
where Bt
=
C R s E , + , I I { C I I ( l + ~ i ) l ' - b [ l / ( l + ~ i)Ib}
s=o
I
=o
p t + i + l = p t + i ( l + ~ i )and M t + i + l = M t + i ( l + x i ) .
Equation 3.9 shows t h a t r e a l money balances a r e d e c r e a s i n g i n t h e
e x p e c t a t i o n o f f u t u r e monetary i n j e c t i o n s .
I t also indicates t h a t the
consumption e l a s t i c i t y o f money demand i s g r e a t e r ( l e s s ) t h a n one when a > ( < I
b, o r when t h e d e s i r e t o smooth consumption i s g r e a t e r ( l e s s ) than t h e d e s i r e
t o smooth r e a l cash balances o v e r time.
The i n t u i t i o n b e h i n d t h i s r e s u l t can
be seen most c l e a r l y if one assumes t h a t B t i s c o n s t a n t .
I n t h i s case, when
t h e d e s i r e t o smooth consumption and t h e d e s i r e t o smooth r e a l cash balances
a r e equal, a = b, money balances a r e p r o p o r t i o n a l t o consumption.
Similarly,
when t h e d e s i r e t o smooth consumption o v e r time i s g r e a t e r t h a n i t i s t o
smooth r e a l balances o v e r t i m e , a > b, increases o r decreases i n consumption
w i 11 be m a g n i f i e d t h r o u g h t h e p r i c e l e v e l so t h a t t h e t i m e s e r i e s f o r
consumption w i l l be smoother t h a n i t i s f o r r e a l money balances.
The nominal i n t e r e s t r a t e i n t h i s economy i s g i v e n by t h e f o l l o w i n g
equation:
One, p l u s t h e nominal r a t e o f i n t e r e s t , e q u a l s t h e r a t i o o f t h e m a r g i n a l
u t i l i t y o f nominal balances today and t h e p r e s e n t d i s c o u n t e d v a l u e o f what i t
i s expected t o be tomorrow.
The o p t i m a l money s u p p l y r u l e when wages a r e
f l e x i b l e i s t h e FriedmanISidrauski r u l e o f d e f l a t i n g t h e money supply such
t h a t t h e nominal i n t e r e s t r a t e approaches zero, o r e q u i v a l e n t l y such t h a t t h e
marginal u t i l i t y o f nominal cash balances grows a t t h e r a t e o f t i m e
preference.
T h i s w i l l e n t a i l d e f l a t i n g t h e money s u p p l y a t a c o n s t a n t r a t e
o n l y when b = 1.
I V . Optimal Monetary P o l i c y
This s e c t i o n c o n s i d e r s t h e o p t i m a l monetary p o l i c y i n response t o r e a l
p r o d u c t i v i t y shocks.
We proceed b y f i n d i n g t h e money supply r u l e t h a t
reproduces t h e q u a n t i t i e s t h a t would be chosen i n a w o r l d w i t h f l e x i b l e
wages.
Since r e a l money balances e n t e r s e p a r a b l y i n t h e u t i 1 it y f u n c t i o n ,
t h i s a l s o reproduces t h e q u a n t i t i e s t h a t would be chosen by t h e s o c i a l p l a n n e r
i n t h e standard o p t i m a l growth model w i t h o u t money.
The f i r s t s t e p i n d i s c u s s i n g t h e o p t i m a l money supply r u l e i s t o r e s t a t e
t h e f i r s t - o r d e r c o n d i t i o n s o f problem H when t h e nominal wage- contracting
constraint i s l i f t e d .
These f i r s t - o r d e r c o n d i t i o n s a r e i d e n t i c a l t o t h o s e
g i v e n by equations 3.1
-
3.8 ( i n c l u d i n g 3 . 4 ' and 3 . 6 ' 1 , except f o r t h e
f i r s t - o r d e r c o n d i t i o n w i t h r e s p e c t t o choosing t h e o p t i m a l wage, e q u a t i o n
3.3.
T h i s , i n t u r n , a f f e c t s t h e l a b o r s u p p l y t h a t w i l l be chosen, e q u a t i o n
3.5.
When r e a l i n s t e a d o f nominal wages a r e chosen equations 3.3 and 3 . 5
become :
(4.1) X l t = X 3 t h t and
(4.2) ~ ' ( 1 - h t ) = X,tWt.
Since X3 i s t h e m a r g i n a l u t i l i t y o f consumption d i v i d e d by t h e p r i c e
l e v e l , e q u a t i o n 4.2 i n d i c a t e s t h a t workers w i l l never be underemployed o r
overemployed.
This, o f course, i s n o t s u r p r i s i n g .
The o p t i m a l money s u p p l y r u l e due t o t h e nominal c o n t r a c t i n g c o n s t r a i n t
w i l l be discussed i n two stages: t h e f i r s t stage l e t s "b" v a r y b u t s e t s a = l ,
i . e . u t i l i t y i s l o g a r i t h m i c i n consumption.
The second case l e t s " a" v a r y b u t
s e t s b = l , i . e . u t i l i t y i s l o g a r i t h m i c i n r e a l money balances.
A. L o g a r i t h m i c Consumption, a=l
S e t t i n g a=l and r e p l a c i n g equations 3.3,
3.5 w i t h 4.1 and 4.2,
f i r s t - o r d e r c o n d i t i o n s w i t h f l e x i b l e wages become:
(4.3) .ct = (1-a8)yt
(4.4) k t + , = aBy,
(4.5) ~ ' ( 1 - h t ) h t = ( 1 - a ) l ( l - a B )
(4.6) m t + / p t = B l ' b ~ : " b .
and
the
03
where
A,,
=
~ ~ ~ ~ ~ + ~ ( m ; ~ , + , ( l l p ,and
+~)'-~~
s=o
The f i r s t t h r e e a r e standard when u t i l i t y i s l o g a r i t h m i c i n
consumption.
Consumption and investment a r e p r o p o r t i o n a l t o o u t p u t , w h i l e
l a b o r supply i s c o n s t a n t , because w i t h l o g a r i t h m i c consumption and 100 p e r c e n t
d e p r e c i a t i o n o f c a p i t a l , t h e income and s u b s t i t u t i o n e f f e c t s cancel o u t .
From e q u a t i o n s 4.3 and 3.10,
t h e FriedmanISidrauski r u l e t o pursue a
monetary p o l i c y such t h a t t h e nominal i n t e r e s t r a t e i s near z e r o i m p l i e s t h a t
t h e monetary a u t h o r i t i e s should pursue a p o l i c y o f d e f l a t i n g nominal income a t
t h e household's r a t e o f time p r e f e r e n c e .
I f t h e government wishes t o c o l l e c t
a g i v e n amount o f t a x revenue o v e r t i m e v i a t h e i n f l a t i o n t a x , i t s h o u l d l e t
nominal o u t p u t grow a t a predetermined r a t e .
The employment l e v e l t h a t r e s u l t s w i t h a nominal c o n t r a c t i n g c o n s t r a i n t
can be seen by n o t i n g t h a t A3wh = ( 1 - a ) L p y .
Labor supply i s then:
Since wages by assumption cannot be indexed t o monetary and p r o d u c t i v i t y
shocks, employment responds t o monetary and r e a l shocks o n l y t h r o u g h t h e i r
e f f e c t on t h e m a r g i n a l u t i l i t y o f nominal balances.
Equation 4.7 i n d i c a t e s
t h a t employment responds n e g a t i v e l y t o p o s i t i v e p r o d u c t i v i t y shocks when b <
1, w h i l e employment increases w i t h p o s i t i v e p r o d u c t i v i t y shocks when b > 1.
These r e s u l t s can be seen f r o m e q u a t i o n 4.6,
which shows t h a t p r i c e s and
p r o d u c t i v i t y shocks a r e n e g a t i v e l y r e l a t e d .
Not s u r p r i s i n g l y , e q u a t i o n 4.7
a l s o shows t h a t employment increases w i t h monetary i n n o v a t i o n s .
From e q u a t i o n
4.6 t h i s i n d i c a t e s t h a t g i v e n a c o n s t a n t money supply, employment w i l l be
p r o c y c l i c a l ( c o u n t e r c y c l i c a l ) when t h e income e l a s t i c i t y o f money demand i s
l e s s ( g r e a t e r ) than u n i t y .
The reason f o r t h i s can be seen by r e c a l l i n g t h e
second c o n s t r a i n t i n problem H, w t
=
ptetFl(kt,lt).
When t h e
income e l a s t i c i t y i s g r e a t e r than one, t h e percentage decrease i n p r i c e s w i l l
be g r e a t e r t h a n t h e percentage i n c r e a s e i n o u t p u t .
Therefore,
py and, hence,
8p w i l l n e c e s s a r i l y decrease w i t h p r o d u c t i v i t y shocks, i m p l y i n g t h a t
employment w i l l decrease when p r o d u c t i v i t y i n c r e a s e s .
The above argument can
be r e v e r s e d when t h e income e l a s t i c i t y o f money demand i s l e s s t h a n one t o
show t h a t employment w i l l i n c r e a s e w i t h i n c r e a s e s i n p r o d u c t i v i t y .
Since employment i s c o n s t a n t when wages a r e f l e x i b l e and u t i l i t y i s
l o g a r i t h m i c i n consumption, t h e o p t i m a l monetary p o l i c y can be e i t h e r
procyclical o r countercyclical.
The o p t i m a l monetary p o l i c y w i l l be
p r o c y c l i c a l when t h e income e l a s t i c i t y o f money demand i s l e s s t h a n one ( a = l ,
b > l ) and c o u n t e r c y c l i c a l when t h e income e l a s t i c i t y of money demand i s g r e a t e r
t h a n one ( a = l , b c l ) .
E q u i v a l e n t l y , when p r o d u c t i v i t y i n c r e a s e s by 1 p e r c e n t ,
i n s t e a d o f r e a l wages i n c r e a s i n g by 1 p e r c e n t as t h e y would w i t h f l e x i b l e
wages, t h e y i n c r e a s e by more t h a n 1 p e r c e n t when t h e income e l a s t i c i t y o f
money demand i s g r e a t e r t h a n one.
Monetary p o l i c y should then be p r o c y c l i c a l
i n o r d e r t o reduce r e a l wages t o t h e i r s p o t market l e v e l .
This a l s o serves t o
i n c r e a s e employment and t o reduce o r e l i m i n a t e underemployment.
Underemployment e x i s t s i n t h i s case s i n c e t h e i n c r e a s e i n r e a l wages i s more
than i s optimal.
S i m i l a r l y , when t h e income e l a s t i c i t y o f money demand i s
l e s s than one, r e a l wages do n o t increase as much as t h e y would w i t h f l e x i b l e
wages, so t h a t t h e government should pursue a c o u n t e r c y c l i c a l monetary p o l i c y .
One c a v e a t t o t h e p o s s i b i l i t y o f p r o c y c l i c a l monetary p o l i c y s h o u l d be
noted.
P r o c y c l i c a l monetary p o l i c y a p p l i e s o n l y i f t h e i n c r e a s e o r decrease
i n o u t p u t was caused by r e a l f a c t o r s and n o t by r e c k l e s s monetary p o l i c y .
C a l l i n g f o r e i t h e r p r o c y c l i c a l o r c o u n t e r c y c l i c a l monetary p o l i c y
p r o v i d e s d i r e c t i o n a l guidance; however, i t begs t h e c r u c i a l question: By how
much?
W i t h o u t answering t h i s q u e s t i o n , Friedman's 4 p e r c e n t money s u p p l y r u l e
m i g h t be c a l l e d f o r on grounds t h a t t h e c u r e m i g h t be worse than t h e d i s e a s e .
F o r t u n a t e l y , when u t i l i t y i s l o g a r i t h m i c i n consumption, a simple money s u p p l y
r u l e t o t a r g e t nominal o u t p u t w i l l achieve t h e f i r s t b e s t a l l o c a t i o n .
Comparing equations 4.5 and 4.7 i m p l i e s t h a t a p o l i c y o f s t a b i l i z i n g t h e
m a r g i n a l u t i l i t y o f nominal balances, X 3 , ( o r l e t t i n g i t grow o r s h r i n k a t
a predetermined r a t e ) w i l l achieve t h e f i r s t b e s t employment l e v e l .
From t h e
f i r s t - o r d e r c o n d i t i o n s f r o m problem H, t h i s i s e q u i v a l e n t t o s t a b i l i z i n g
nominal consumption o r nominal o u t p u t .
To ensure t h a t employment w i l l indeed
be a t i t s f i r s t b e s t l e v e l , e q u a t i o n s 3.3 and 3.5 i m p l y t h a t employment w i l l
be d e t e r m i n i s t i c and t h a t employment w i l l be chosen such t h a t ~ ' ( 1 - h ) = X3w
o r , e q u i v a l e n t l y , t h a t employment w i l l be chosen such t h a t t h e r e i s n o t any
under- loveremployment.
From e q u a t i o n 3.1 t h i s i m p l i e s t h a t e q u a t i o n 4.5 w i l l
a l s o be s a t i s f i e d .
P u r s u i n g a p o l i c y t o s t a b i l i z e nominal o u t p u t i m p l i e s a p r o c y c l i c a l
monetary p o l i c y when t h e income e l a s t i c i t y o f money demand i s g r e a t e r t h a n
one, o r a c o u n t e r c y c l i c a l monetary p o l i c y when t h e income e l a s t i c i t y o f money
demand i s l e s s than one.
R e c a l l t h a t p r i c e s f a l l more ( i n percentage terms)
t h a n t h e percentage i n c r e a s e i n o u t p u t when t h e income e l a s t i c i t y o f money
demand i s g r e a t e r than one.
Therefore, nominal o u t p u t w i l l f a l l ( r i s e ) when
t h e r e i s a good (bad) p r o d u c t i v i t y shock.
S t a b i l i z i n g nominal o u t p u t i n t h i s
case n e c e s s i t a t e s p u r s u i n g a p r o c y c l i c a l monetary p o l i c y .
Similarly, i f the
income e l a s t i c i t y o f money demand i s l e s s than one, p r o d u c t i v i t y and nominal
o u t p u t move t o g e t h e r , so s t a b i l i z i n g nominal o u t p u t w i l l e n t a i l a
c o u n t e r c y c l i c a l monetary p o l i c y .
Recalling our e a r l i e r r e s u l t , t h i s policy w i l l also s a t i s f y the
F r i e d m a n l s i d r a u s k i money supply r u l e .
S i m i l a r l y , f r o m e q u a t i o n 3.10,
a pol i c y
t o t a r g e t t h e nominal i n t e r e s t r a t e w i l l ensure t h a t q u a n t i t i e s a r e chosen a t
t h e i r o p t i m a l l e v e l , suggesting t h a t t h e Federal Reserve Bank's c u r r e n t p o l i c y
may be c o r r e c t .
T h i s p o l i c y a l s o r e q u i r e s t h e monetary a u t h o r i t i e s t o r e a c t
t o y e s t e r d a y ' s r e c e s s i o n s and booms, because investment causes independent
p r o d u c t i v i t y shocks t o t r a n s l a t e i n t o s e r i a l l y c o r r e l a t e d o u t p u t o v e r t i m e .
Since wage s e t t e r s can r e a d i l y observe t h e c u r r e n t c a p i t a l s t o c k t h a t was
c a r r i e d o v e r f r o m t h e p r e v i o u s p e r i o d , these monetary supply changes w i l l be
c o m p l e t e l y a n t i c i p a t e d and r e f l e c t e d i n t h e agreed- upon nominal wage r a t e .
U n f o r t u n a t e l y , as w i l l be seen i n t h e n e x t subsection, t h e r e s u l t t h a t
t a r g e t i n g nominal i n t e r e s t r a t e s o r t a r g e t i n g nominal o u t p u t i s o p t i m a l
depends on t h e assumption t h a t u t i l i t y i s l o g a r i t h m i c i n consumption.
However, t h e r e s u l t t h a t t h e o p t i m a l monetary p o l i c y m i g h t be p r o c y c l i c a l i s
s t i l l t r u e depending on t h e e l a s t i c i t y o f s u b s t i t u t i o n o f consumption o v e r
time, t h a t i s whether
a < ( > I 1.
B. L o g a r i t h m i c Real Balances, b=l
T h i s subsection c o n s i d e r s t h e case when u t i l i t y i s l o g a r i t h m i c i n r e a l
money balances, b u t " a" i s a l l o w e d t o v a r y .
case w i l l no l o n g e r be c o n s t a n t .
The o p t i m a l l a b o r s u p p l y i n t h i s
Whether t h e s u b s t i t u t i o n e f f e c t o r t h e
income e f f e c t dominates w i l l depend on the s u b s t i t u t a b i l i t y o f consumption
From equations 3.3' and 3.4',
over time.
t h e optimal ( f l e x wage) l a b o r supply
is
From equation 4.8 l a b o r supply when wages are f l e x i b l e w i l l increase
(decrease) w i t h p o s i t i v e p r o d u c t i v i t y shocks when a <
(>)
1.
This r e s u l t s
because o f the assumed c o n c a v i t y o f v(.) and because both c u r r e n t and expected
f u t u r e consumption increase w i t h p o s i t i v e p r o d u c t i v i t y shocks.
The way i n which the economy evolves given the presence o f a nominal
c o n t r a c t i n g c o n s t r a i n t i s s i m i l a r t o before.
The f o l l o w i n g equations express
t h e way i n which o u t p u t i s d i v i d e d between consumption and investment, t h e
money demand f u n c t i o n , and t h e number o f hours worked when t h e economy i s
s u b j e c t t o nominal wage c o n t r a c t i n g and b = l .
00
where
Dt
=
C ( ~ R ) ~ E ~ + ~ ( C and
~;~)
s=o
Since n e i t h e r X 3 t nor w t i s a f f e c t e d by p r o d u c t i v i t y shocks
e q u a t i o n 4.5 shows t h a t as w i t h f l e x i b l e wages, employment w i l l i n c r e a s e
(decrease) w i t h i n c r e a s e s i n p r o d u c t i v i t y when a < 0 ) 1.
The b o r d e r l i n e case
i s when a = l , o r when u t i l i t y i s l o g a r i t h m i c i n b o t h consumption and r e a l
money.
This i s t h e o n l y case i n which t h e monetary a u t h o r i t i e s should t a r g e t
t h e money supply.
The reason t h a t employment can e i t h e r i n c r e a s e o r decrease
w i t h p o s i t i v e p r o d u c t i v i t y shocks i s again because, t h e income e l a s t i c i t y o f
money demand i s g r e a t e r ( l e s s ) t h a n one when a < ( > I 1.
However, employment would i n c r e a s e o r decrease more t h a n would be
o p t i m a l g i v e n an i n c r e a s e i n p r o d u c t i v i t y .
Using an a s t e r i s k t o denote t h e
o p t i m a l l e v e l , e q u a t i o n s 4.5 and 4.9 show t h a t employment can o n l y be a t t h e
o p t i m a l l e v e l when v l ( l - h * )
depend on 8.
= X3w.
However, when b = l , X3 does n o t
Therefore, employment w i 11 be o p t i m a l o n l y when h * i s
c o n s t a n t , t h a t i s when a = l .
T h i s i s because i n a s p o t market, workers choose
t h e i r l a b o r supply so t h a t v l ( l - h )
= X3w,
i m p l y i n g t h a t a worker would n o t
want t o change t h e number o f hours he works when p r o d u c t i v i t y changes.
< 1, h * increases w i t h 8, i m p l y i n g t h a t v l ( l - h * )
> X3w.
When a
Thus
overemployment o c c u r s when p r o d u c t i v i t y i s g r e a t e r t h a n expected, and
underemployment o c c u r s when p r o d u c t i v i t y i s l e s s t h a n expected.
When r e a l
wages a r e t o o low i n booms and t o o h i g h i n r e c e s s i o n s , t h e monetary a u t h o r i t y
s h o u l d pursue a c o u n t e r c y c l i c a l monetary p o l i c y .
vl(l-h*)
S i m i l a r l y , when a > 1,
< ( > I X3w w i t h good (bad) p r o d u c t i v i t y shocks.
I n this
s i t u a t i o n , i t would be o p t i m a l t o f o l l o w a p r o c y c l i c a l money s u p p l y r u l e .
V . Conclusions
This paper showed t h a t o p t i m a l monetary p o l i c y i n a model where wages
a r e " s t i c k y " because o f a nominal c o n t r a c t i n g c o n s t r a i n t can be e i t h e r
p r o c y c l i c a l o r c o u n t e r c y c l i c a l (as measured a g a i n s t o u t p u t ) .
Perhaps t h e
p o s s i b i l i t y f o r unconventional monetary p o l i c y a r i s i n g f r o m such a model i s
n o t a l t o g e t h e r s u p r i s i n g ; however, i t p o i n t s t o t h e need f o r d i s c u s s i n g t h e
p o l i c y i m p l i c a t i o n s o f macroeconomic models i n an o p t i m i z i n g framework.
The
p o l i c y o b j e c t i v e s t h a t a r e f r e q u e n t l y thought t o f o l l o w f r o m nominal
c o n t r a c t i n g models, namely s t a b i l i z i n g o u t p u t , p r i c e s , o r a c o n s t a n t money
supply, a r e o p t i m a l o n l y i n extreme cases.
For example, i f t h e r e a r e no r e a l
shocks, a l l t h r e e o b j e c t i v e s produce t h e o p t i m a l monetary p o l i c y .
When a=b=l,
a money supply r u l e a l s o i s o p t i m a l , o r when " a" approaches i n f i n i t y , so t h a t
t h e household i s i n f i n i t e l y r i s k - a v e r s e ( a "maxi- min" u t i l i t y f u n c t i o n ) , a
p o l i c y r u l e t o s t a b i l i z e prices i s also optimal.
However, i n a d d i t i o n t o these extreme cases, a s l i g h t l y more g e n e r a l
case when u t i l i t y i s l o g a r i t h m i c i n consumption r e s u l t s i n a w e l l - d e f i n e d
p o l i c y r u l e f o r t h i s economy.
This case i n d i c a t e s t h a t a p o l i c y r u l e designed
e i t h e r t o s t a b i l i z e nominal o u t p u t o r t o peg t h e nominal i n t e r e s t r a t e w i l l be
optimal.
Both o f these p o l i c i e s a c t u a l l y correspond t o e i t h e r a p r o c y c l i c a l
o r c o u n t e r c y c l i c a l money supply r u l e , depending on " b" , o r t h e income
e l a s t i c i t y o f money demand.
Although t h i s paper discusses o p t i m a l monetary p o l i c y , a c t u a l p o l i c y
p r e s c r i p t i o n s should be tempered w i t h t h e r e l i a n c e o f these p o l i c y r u l e s on
the form o f the u t i l i t y function.
P o l i c y c o n c l u s i o n s f r o m t h e model a r e
t e n t a t i v e a t best, g i v e n t h a t t h e model assumes t h a t nominal w a g e - c o n t r a c t i n g
e x i s t s b u t does n o t e x p l a i n why p a r t i e s c o n t r a c t i n nominal i n s t e a d o f r e a l
terms.
For example, i t i s l i k e l y t h a t an e x p l a n a t i o n f o r nominal c o n t r a c t i n g
w i l l be t o have n o i s y o b s e r v a t i o n s o f t h e p r i c e l e v e l s i m i l a r t o Lucas (1972).
The c o r r e c t p o l i c y p r e s c r i p t i o n , i f t h i s were t h e case, would undoubtedly c a l l
f o r a we1 1- d e f i n e d money supply r u l e .
Given t h e l i m i t e d d a t a a v a i l a b l e , t h e model t e n t a t i v e l y suggests t h a t
t h e p r o p e r monetary p o l i c y i n a w o r l d w i t h nominal wage c o n t r a c t s i s
procyclical.
T h i s r e s t s on s t u d i e s ( f o r example, Grossman and S h i l l e r [19811,
and F r i e n d and Blume [19751> t h a t e s t i m a t e t h e r e l a t i v e degree of r i s k
a v e r s i o n , " a" , t o be between two and f o u r .
However, g i v e n t h e l a c k of d a t a on
"b", t h e p o l i c y r u l e f o r when u t i l i t y i s l o g a r i t h m i c i n consumption would
p r o b a b l y be p r e f e r r e d , because t h e o p t i m a l p o l i c y i s w e l l - d e f i n e d and i s
independent o f " b" i n t h i s s p e c i a l case.
Monetary p o l i c y designed t o peg t h e
nominal i n t e r e s t r a t e o r t o t a r g e t nominal o u t p u t w i l l be o p t i m a l i n t h i s case.
T h i s paper has sought t o map F i s c h e r i n t o an o p t i m i z a t i o n framework, and
t o d i s c u s s whether these d i f f e r e n c e s have d i f f e r e n t p o l i c y i m p l i c a t i o n s .
The
f i r s t d i f f e r e n c e i s t h a t F i s c h e r ' s two- period nominal c o n t r a c t s a r e c o l l a p s e d
i n t o one p e r i o d .
I n F i s c h e r ' s model, policymakers cannot a c t i n s t a n t a n e o u s l y
t o economy-wide shocks, as t h e y can i n t h i s paper.
P o l i c y i n h i s paper
r e s u l t e d f r o m t h e assumption t h a t shocks were c o r r e l a t e d over time, which
a l l o w e d p o l i c y m a k e r s t o use i n f o r m a t i o n about t h e p r e v i o u s p e r i o d ' s shock i n
o r d e r t o p r e d i c t t h e shock t h a t would o c c u r i n t h e c u r r e n t p e r i o d .
T h i s paper
has one- period wage c o n t r a c t s ; however, i t r e t a i n s t h e essence o f F i s c h e r ' s
paper s i n c e c o n t r a c t s a r e drawn up i n advance o f b o t h monetary and r e a l
shocks.
Policymakers a r e assumed t o have p e r f e c t i n f o r m a t i o n i n which t o
r e a c t t o o u t s i d e shocks i n s t e a d o f a n o i s y s i g n a l , as i n F i s c h e r ' s o r i g i n a l
paper.
I n c o r p o r a t i n g t h i s element does n o t seem t o a f f e c t t h e p o l i c y r u l e s
d e r i v e d i n t h i s paper.
However, t h i s d i f f e r e n c e would make i t even h a r d e r t o
p r e s c r i b e monetary p o l i c y .
The second d i f f e r e n c e between t h e o p t i m i z a t i o n model s e t up i n t h i s
paper and t h e s e t o f e q u a t i o n s formulated by F i s c h e r i s t h e type of shocks
- 21 assumed to affect the economy. Real productivity shocks are assumed in this
paper, while Fischer had shocks affecting aggregate demand, aggregate supply,
and money demand. Keynesians might not accept that shifts in the aggregate
supply schedule are caused by real productivity shocks. However, given that
Fischer assumed rational expectations, it seems reasonable to treat shocks t o
aggregate supply as productivity shocks. Assumed shocks to aggregate demand
would have to be modeled as shocks to the utility function.
Although the model shows that a procyclical money supply with respect to
output may be optimal, it nevertheless has conventional countercyclical
monetary policy implications with respect to employment. Similarly, using the
evidence we have on "a", the model suggests that given a constant money
supply, employment would be countercyclical. However, this result depends on
the assumption of 100 percent depreciation as well as the assumption that
consumption and leisure are separable.
If nominal contracting models are going to be useful for policy
analysis, then future work is necessary in order to address two concerns.
first is to build a model in which nominal contracts arise endogenously.
The
The
second area of future research is to determine if nominal contracts are
empirically relevant for the study of business cycles. This question has been
tested by Ahmed (1985), who showed that in Canada the amount to which
employment and output responded to money shocks was insignificantly correlated
with the amount of indexing in labor contracts. This provides some evidence
against nominal contracting models. However, future work is still needed
because industries that naturally respond more to monetary disturbances would
probably have larger incentives to index their wage contracts. Until such
work is done, nominal wage-contracting models should not be used for policy
analysi s.
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