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  • Working Paper 871 6

    MONETARY POLICY UNDER RATIONAL EXPECTATIONS WITH MULTIPERIOD WAGE STICKINESS AND AN ECONOMY-WIDE CREDIT MARKET

    by James G. Hoehn

    James G. Hoehn i s an economist a t t h e Federal Reserve Bank o f C leve land. The au tho r g r a t e f u l l y acknowledges the comments o f A lan C. Stockman, John L. Scadding, and W i l l i a m C. Gavin on d r a f t s .

    Working papers o f t he Federal Reserve Bank o f C leve land a re 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 d i scuss ion and c r i t i c a l comment. The views s t a t e d h e r e i n a re t hose o f the au thor and n o t n e c e s s a r i l y those o f t h e Federal Reserve Bank o f C leve land o r o f t he Board o f Governors o f t h e Federa l Reserve System.

    December 1987

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  • ABSTRACT

    The e f f e c t s o f money supp ly responses t o bo th t he c u r r e n t i n t e r e s t r a t e and

    t he lagged s t a t e o f t h e economy a re analyzed i n a dynamic IS-LM model w i t h

    m u l t i p e r i o d wage s t i c k i n e s s . A l l o w i n g p r i v a t e agents t o use the c u r r e n t

    i n t e r e s t r a t e i n f o rm ing expec ta t ions c rea tes some p o t e n t i a l l y coun te r -

    i n t u i t i v e e f f e c t s o f shocks, b u t leaves p o l i c y i m p l i c a t i o n s l a r g e l y

    una f f ec ted . A c o n f l i c t between f i r m- l e v e l and aggregate- leve l o u t p u t

    s t a b i l i z a t i o n i s found t o be i nhe ren t i n t he m u l t i p e r i o d wage c o n t r a c t i n g

    scheme. P o l i c y r u l e s t h a t s t a b i l i z e o u t p u t o r serve o t h e r o b j e c t i v e s a r e e x p l i c i t l y de r i ved . Because o f supply shocks, p r o c y c l i c a l money growth may be

    r e q u i r e d t o s t a b i l i z e f i r m ou tpu t , p r i c e s , r e a l wages, o r o u t p u t r e l a t i v e t o

    i t s f u l l - i n f o r m a t i o n l e v e l .

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  • MONETARY POLICY UNDER RATIONAL EXPECTATIONS

    WITH MULTIPERIOD WAGE STICKINESS AND AN ECONOMY-WIDE CREDIT MARKET

    I. I n t r o d u c t i o n

    T h i s a r t i c l e r e 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 a Keynesian model

    t h a t i n c o r p o r a t e s r a t i o n a l e x p e c t a t i o n s and d i s p l a y s t h e n a t u r a l r a t e

    p r o p e r t y . I m p o r t a n t f e a t u r e s a r e m u l t i p e r i o d wage s t i c k i n e s s and t h e

    a v a i l a b i l i t y , t o b o t h p r i v a t e agents and t h e po l i cymaker , o f c u r r e n t

    i n f o r m a t i o n f r o m o b s e r v a t i o n s o f t h e nominal i n t e r e s t r a t e . The model i s

    e s s e n t i a l l y a l o g - l i n e a r i z e d v e r s i o n o f t h a t o f F i s c h e r (1977), augmented b y an ( i m p l i c i t ) economy-wide c r e d i t market . As i n F i s c h e r ' s i n f l u e n t i a l paper , feedback f r o m t h e lagged s t a t e o f t h e economy i s consequen t ia l f o r o u t p u t

    b e h a v i o r because o f t h e c o n j u n c t i o n of m u l t i p e r i o d wage s t i c k i n e s s and a u t o c o r r e l a t i o n o f shocks. A t t h e same t ime , because o f i ncomp le te c u r r e n t

    i n f o r m a t i o n , p o l i c y responses t o t h e c u r r e n t i n t e r e s t r a t e a r e a l s o o f

    consequence f o r o u t p u t , as i n t h e famous a n a l y s i s o f Poole (1970). The a n a l y s i s o f t h i s a r t i c l e i s o f i n t e r e s t f r o m t h r e e d i f f e r e n t

    s t a n d p o i n t s . F i r s t , i t addresses t h e a n a l y t i c a l p rob lem o f c u r r e n t

    i n f o r m a t i o n s e t s under r a t i o n a l e x p e c t a t i o n s . The a n a l y s i s f i n d s t h a t p r i v a t e

    use o f c u r r e n t i n f o r m a t i o n f r o m t h e i n t e r e s t r a t e t o update e x p e c t a t i o n s does

    n o t n e c e s s a r i l y have t h e d r a m a t i c i m p l i c a t i o n s f o r p o l i c y t h a t Dotsey and K i n g

    (1983, 1986) o b t a i n i n c o m p l e t e l y f l e x i b l e - p r i c e models. I n p a r t i c u l a r , w h i l e p o l i c y responses t o t h e i n t e r e s t r a t e a r e i r r e l e v a n t f o r o u t p u t i n

    f l e x i b l e - p r i c e models, such responses a r e p o t e n t i a l l y i m p o r t a n t i n f l u e n c e s on

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  • -2-

    the b e h a v i o r o f o u t p u t i n s t icky- wage models.

    Second, t h i s a r t i c l e ex tends t h e c l a s s i c a n a l y s i s o f o p t i m a l p o l i c y under

    u n c e r t a i n t y , i naugura ted by Poole, t o an expanded IS-LM model i n wh ich p r i c e s

    a r e n o t f i x e d , t h e n a t u r a l r a t e p r o p o s i t i o n h o l d s , and supp ly shocks o c c u r .

    S u r p r i s i n g l y , p o l i c y r u l e s t o s t a b i l i z e o u t p u t , o r t o serve o t h e r o b j e c t i v e s , i n models w i t h p l a u s i b l e s p e c i f i c a t i o n s of commodity supp ly behav io r

    a p p a r e n t l y have n o t h e r e t o f o r e been d e r i v e d .

    A t h i r d reason t h i s a r t i c l e i s of i n t e r e s t i s t h a t i t t r e a t s t h e p r o b l e m

    o f i n c o n s i s t e n c y between t h r e e p o t e n t i a l p o l i c y o b j e c t i v e s : (1 ) s t a b i l i z a t i o n o f t o t a l o u t p u t , (2 ) s t a b i l i z a t i o n of t y p i c a l i n d i v i d u a l f i r m o u t p u t , and ( 3 ) s t a b i l i z a t i o n o f o u t p u t around i t s p e r f e c t f o r e s i g h t o r f u l l - i n f o r m a t i o n

    l e v e l . The i n c o n s i s t e n c y between t h e f i r s t and second o b j e c t i v e s has n o t been no ted before , and i s i n h e r e n t i n t h e s taggered wage c o n t r a c t i n g setup. The

    c o n f l i c t between t h e f i r s t and t h i r d o b j e c t i v e s has been no ted b e f o r e , b u t i t s i m p l i c a t i o n s f o r p o l i c y r u l e s i n s t icky- wage models have n o t been deve loped as

    f u l l y as i n t h i s a r t i c l e . The a p p r o p r i a t e response o f p o l i c y t o a commodity

    supp ly shock w i l l depend on which o b j e c t i v e i s embraced. I f t h e t h i r d o b j e c t i v e i s chosen, money shou ld be i n c r e a s e d i n response t o supp ly shocks, and t h e same may a l s o be t r u e under t h e second o b j e c t i v e . Numerical examples show t h a t t h e behav io r o f money a p p r o p r i a t e t o e i t h e r o f these o b j e c t i v e s can e a s i l y i n v o l v e a p o s i t i v e c o r r e l a t i o n between money and o u t p u t .

    I n s t u d y i n g t h e e f f e c t s o f p r i v a t e a g e n t s ' use o f c u r r e n t i n f o r m a t i o n f r o m

    t h e i n t e r e s t r a t e , t h i s a r t i c l e j o i n s B a r r o (1980) , K i n g (1983), Canzoner i , Henderson, and Rogof f (1983), and Dotsey and K i n g (1983, 1986). These p r i o r s t u d i e s make s i m p l i f y i n g assumpt ions to r e n d e r t h e a n a l y s i s t r a c t a b l e ,

    i n c l u d i n g , most i m p o r t a n t l y , l i m i t s on p o l i c y a l t e r n a t i v e s , a l l owance f o r o n l y

    a few economic d i s t u r b a n c e s , or bo th . Even these s i m p l i f i c a t i o n s have n o t

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  • always p e r m i t t e d e x p l i c i t s o l u t i o n s t o t h e model. The p resen t a r t i c l e o f f e r s

    c losed- form s o l u t i o n s w i t hou t imposing any a r b i t r a r y r e s t r i c t i o n s on monetary

    p o l i c y , enab l i ng d e r i v a t i o n and q u a l i t a t i v e c h a r a c t e r i z a t i o n o f p o l i c i e s t h a t

    s a t i s f y va r i ous o b j e c t i v e s . A lso, the a n a l y s i s here inc ludes t h r e e d i s t i n c t aggregate d is tu rbances , f o r commodity supply , commodity demand, and money

    demand.

    The expec ta t i ona l e f f e c t s o f c u r r e n t o b s e r v a t i o n o f t he i n t e r e s t r a t e

    c r e a t e t h e p o t e n t i a l f o r c o u n t e r i n t u i t i v e responses o f t he economy t o some

    d is tu rbances . For example, a p o s i t i v e shock t o t he money supp ly may reduce

    o u t p u t and p r i c e s . However, i n c o n t r a s t t o t he o t h e r s t ud ies , t h i s a r t i c l e

    f i n d s t h a t c u r r e n t i n f o r m a t i o n does n o t appear t o change t he behav io r o f

    o u t p u t i n t h e model i n a way t h a t i s l i k e l y t o be q u a n t i t a t i v e l y i m p o r t a n t ,

    nor does i t seem t o have ve ry impo r tan t o r s u r p r i s i n g i m p l i c a t i o n s f o r

    monetary p o l i c y . The conc lus ions and i n t u i t i o n s o f Poole and F i sche r

    concern ing o u t p u t - s t a b i l i z i n g p o l i c