Price Rigidity

8/2/2019 Price Rigidity

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JOURNALOFMonetaryECONOMICSE L S E V I E R J o u r n a lof M onetary Economics 37 (1 996) 345-370

Nominal pr ice r ig id i ty , money supply endogene i ty ,an d b u s i n es s cyc l e sT a c k Y u n

Kore a Econ omic Research Inst i tu te , Seou l 150-756, South Ko rea(Received M ay 1994; final version received February 19 96)

A b s t r a c t

T h is p ap er in v es t ig a tes th e ab i l i t y o f n o m in a l p r i ce r ig id i ty to ex p la in th e co -m o v em en to f in f l a t io n w i th th e cy c l i ca l co m p o n en t o f o u tp u t o b se rv ed in th e p o s t -w ar U .S . d a ta . Ad y n am ic g en era l eq u i l ib r iu m m o d e l i s co n s t ru c ted w i th th e in t ro d u c t io n o f m o n o p o l i s t i cco m p e t i t io n an d n o m in a l p r i ce r ig id i ty in a s t an d ard r ea l b u s in ess cy c le m o d e l , a l lo w in gfo r an en d o g en o u s m o n ey su p p ly ru le . I t i s t h en d em o n s t ra t ed th a t s t i ck y p r i ce m o d e l scan ex p la in th e o b se rv ed as so c ia t io n s b e tw e en m o v em e n t s in in fl a t io n an d o u tp u t m u chb e t t e r th an f l ex ib le p r i ce m o d e l s . T h i s r e su l t d ep en d s l i t t le o n w h e th e r m o n ey su p p ly i sas su m ed to b e en d o g en o u s o r n o t .K e y w o r d s : N o m in a l p r i ce r ig id i ty ; In f l a t io n an d o u tp u t ; Mo n ey su p p ly en d o g en e i tyJ E L c l a s s i f i c a t i o n : E31; E32; E52

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

T h i s p a p e r a n a l y z e s t h e c h a r a c t e r o f fl u c tu a t io n s i n a g g r e g a t e e c o n o m i c a c t i v i tyi n a n e c o n o m y w i t h n o m i n a l p r i c e r i g i d it y t h at i s s u b j e c t t o b o t h t e c h n o l o g y a n dm o n e t a r y p o l i c y s h oc k s . T h e i n t r o d u c t i o n o f m o n e y a n d n o m i n a l p r ic e r i g i d i t yi n to a n o t h e r w i s e s t a n d a r d r e a l b u s i n e s s c y c l e m o d e l i s m o t i v a t e d b y a n a t t e m p tt o a c c o u n t f o r t h e o b s e r v e d c o - m o v e m e n t o f a g g r e g a t e o u t p u t w i th i n f la t io n .

T h e c o r r e l a t io n o f c h a n g e s i n th e r a te o f i n fl a ti o n w i th b u s i n e s s c y c l e s h a sb e e n m u c h r e m a r k e d . C h a d h a a n d P r a s a d ( 1 9 9 2 ) , f o r e x a m p l e , s h o w t h at t h e

This paper is based upon the second chapter of m y Ph.D. thesis at the U niversity of C hicago. I amgrateful to Lars Peter H ansen, Robert E. Lucas J r., and especially Michael Woodford for their helpfuladvice and comments. All errors are my own.0304-3932/96/$15.00 1996 Elsevier Science B .V. A ll rights reservedS S D I 0 3 0 4 - 3 9 3 2 ( 9 6 ) 0 1 2 4 6 - 9


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346 T . Y u n / J o u r n a l o f M o n e t a r y E c o n o m ic s 3 7 ( 1 9 9 6 ) 3 4 5 - 3 7 0r a t e o f i n f l a t i on i s c ons i s t e n t ly a nd u sua l ly s t r ong ly pos i t i ve ly c o r r e l a t e d w i thva r ious me a su r e s o f t he c yc l i c a l c om pon e n t o f ou tpu t . T h i s i s de m ons t r a t e d inS e c t ion 2 be low f o r t he c a se i n w h ic h , f o l l ow ing Be ve r a ge a nd N e l son ( 1981 ) ,t he c yc l i c a l c om pon e n t o f ou tpu t i s de f ine d a s the d i f f e r e nc e be tw e e n the c u r r e n tl e ve l o f ou tpu t a nd i ts p r e d i c t e d long - r un va lue , u s ing a V A R m ode l t o c ons t r uc tthe long- run forecas t .

T h i s f i n di n g is n o t e a s i l y re c o n c i l e d w i t h a m o d e l o f t e m p o r a r y m o v e m e n t s i no u t p u t d u e to t e c h n o l o g y s h o ck s , w h e n t h e e v o l u t i o n o f t h e m o n e y s u p p l y is n o ta f f ec t e d by the se shoc ks . T e c hn o log ic a l impr ov e m e n t s shou ld bo th i nc r e a se ou tpu ta nd low e r p r i c es . T h i s i s de m ons t r a t e d be low in the c a se o f a f l e x ib le p r i c e m ode ls imi l ar t o t he one a na lyz e d by Co o le y a nd H a n se n ( 1989 ) . A s those a u tho r s al sof ound , m one ta r y shoc ks ha v e l it tl e e f fe c t on ou tpu t a t bus ine s s c y c l e f r e que nc ie sin suc h a mo de l . H e n c e a ny c o r r e l a ti on be tw e e n in f l a ti on a nd t r a ns ito r y ou tpu tf luc tua t ions mu s t be d ue to t he e f fe c t s o f t e c hn o log y shoc ks , w h ic h the n l e a d toa p r e d i c t e d c o r r e l a t i on w i th t he w r ong s ign .

T h e f a il u re o f th i s s i m p l e t y p e o f m o d e l m a y s u g g e st t h at m o n e t a r y s h o c k sha ve g r e a t e r e f f e c t s on ou tpu t t ha n those p r e d i c t e d by the f l e x ib l e p r i c e mode l .I n pa rt i cu l a r , i f a n i nc r e a se d g r ow th o f m on e y sup p ly w e r e t o c a use a s ign i f ic a n tt e m por a r y inc r e a se i n ou tpu t , t he n a pos i t i ve c o r r e l a t i on be tw e e n t r a ns i to r y ou tpu tf luc tua t ions a nd in f l at i on c ou ld be c r e a t e d . T h i s r e qu i r e s a n a dd i t i ona l me c h a n i smto p r opa ga te mone ta r y shoc ks . I n t h i s mode l , f i r ms s e t p r i c e s i n a dva nc e bym a x i m i z i n g t h e i r p r es e n t d i s c o u n t v a l u e s i n m o n o p o l i s t ic a l l y c o m p e t i ti v e p r o d u c tm a r k e ts , a s i n th e m o d e l s o f B l a n c h a r d a n d K i y o t a k i ( 1 9 8 6 ) a n d S v e n s s o n ( 1 9 8 6 ) .O ne a dva n ta ge o f t h is a pp r oa c h i s t ha t the de c i s ion p r ob le ms o f the a ge n t s w hose t p r i c e s a r e ma de e xp l i ci t . I n a dd i t i on , impe r f e c t c om pe t i t i on o f t h is t yp e c a nhe lp t o e xp la in som e puz z l ing e m p i r i c al p r ope r t i e s o f t he S o low r e s idua l, w h ic hi s t a ke n to be a me a su r e o f e xog e nou s p r odu c t iv i ty c ha nge s i n s t a nda rd r e a lbus ine s s c yc l e mode l s . H a l l ( 1988 ) ha s de mons t r a t e d tha t a ga p be tw e e n p r i c ea nd ma r g ina l c o s t imp l i e s t ha t the S o low r e s idua l c a n be a n inc o r r e c t p r odu c t iv i tyc ha nge me a su r e . E va ns ( 1992 ) ha s show n tha t t he S o low r e s idua l i s G r a nge r -c a use d by nomina l va r i a b l e s suc h a s mone y a nd nomina l i n t e r e s t r a t e . T h i s i s apuz z l e f o r a mode l w i th c ompe t i t i ve f i r ms , a nd f o r a mode l w i th nomina l p r i c er ig id i ty i n w h ic h p r i c e s a r e s e t to e qu a l t he e xp e c t e d ma r g ina l c o s t .

A n u m b e r o f o t h e r a u t h o rs h a v e r e c e n t l y c o n s i d e r e d t h e c o n s e q u e n c e s o f n o m -ina l c on t r a c t o r p r i c e r i g id i ty i n c omple t e dyna mic ge ne r a l e qu i l i b r ium mode l s .T h e p a p e rs b y K i n g ( 1 9 9 0 ) a n d C h o a n d C o o l e y ( 1 9 9 2 ) h a v e e x p l o r e d t h e q u a n -t i ta t i ve imp l i c a tions o f nom ina l r i g id i ti e s i n mod e l s t ha t ha ve e x t e nd e d a s t a nda r dr e a l bus ine s s c yc l e mode l , a s t h i s pa pe r doe s . H ow e ve r , t he y do no t p r ov ide e x -p l i c it de c i s ion - the o r e t i c m ode l s o f p r i c e s e t t ing by ind iv idua l a ge n ts . T h i s p a pe rdoe s so by ha v ing f i r ms s e t p r i c e s by ma x imiz ing the i r p r e se n t d i s c oun te d va lue so f p r o f i t s t r e ams .

S ve nsson ( 1986 ) a nd H a i r a u l t a nd P o r t i e r ( 1992 ) sha r e w i th t he p r e se n t pa pe rthe a s sumpt ion tha t p r i c e s a r e s e t i n a dva nc e by monopo l i s t i c a l l y c ompe t i t i ve


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T. Y un / Journal of M oneta ry Economics 37 (1996) 345-370 347f inns . S ve nsson , howe ve r , a l lows p r i c e s to be f ixe d f o r one pe r iod on ly , a nd ha sno t e v a lua te d the qua n t i ta t ive suc c e ss o f h is m o de l . Th e a na lys i s o f Ha i r a u lt a ndP or t i e r i s c lose r in sp i r i t t o the p r e se n t pa pe r . Howe ve r , t he y ha ve a na lyz e d am o de l w i th c onv e x c os t o f p r i c e a d jus tm e n t a nd m on e y in the u t il i t y func t ion . Inth i s pa pe r , by c on t r a s t , I im pose a c a sh in a dva nc e c ons t r a in t on c onsum pt ion ,wi th s t a gge r e d m ul t i - pe r iod p r i c e se tt ing . T he s t a gge r ing use d he r e i s a n e x te ns iono f C a l v o ( 1 9 8 3 ) , w h o h a s d e v e l o p e d a c o n t in u o u s t i m e m o d e l i n w h i c h e a c h f ir mis a l lowe d to c ha nge i t s p r i c e on ly whe n a r a ndom s igna l i s r e c e ive d . M or e ove r ,H a i r a u lt a n d P o r t i e r h a v e o n l y a n a l y z e d t h e c a s e o f a n e x o g e n o u s p r o c e s s f o r th em one y supp ly , a nd ha ve e va lua te d the i r m ode l w i th r e f e r e nc e to a d i f f e r e n t s e to f da ta m om e nt s tha n those tha t a r e e m p ha s iz e d he r e . In th i s pape r , t he p r im a r ye m pha s i s i s g ive n to f a c ts a bou t the c o - m o ve m e n t o f ou tpu t a nd in f l at ion , a s theobse r ve d r e l a t ionsh ip be twe e n the se se r i e s i s t he m a in r e a son f o r the in t r oduc t iono f m on e y a nd nom ina l r ig id i t ie s in to the m ode l . W hi le the p r e d ic t ions o f them o de l a r e a na lyz e d he r e f o r a sm a l l e r num be r o f va r i a b le s , t he p r e d ic t e d jo in ts toc ha s t i c p r oc e ss f o r those va r i a b le s i s a na lyz e d in m uc h g r e a te r de ta i l .

F ina l ly , t he t e c hno logy shoc k tha t m a ke s ou tpu t t e m por a r i ly h igh m igh t a l soc a use h igh e r in fl a tion , i f t he m on e y sup p ly i s i nc re a se d , a s sugge s te d by K ing a n dP losse r ( 1984) . Th i s poss ib i l i t y i s a na lyz e d he r e by a l lowing f o r a ve r y ge ne r a lf o r m o f re s p o n s e o f m o n e y g r o w t h t o c u r r en t a n d l a g g e d t e c h n o l o g y s h o c k s .

Th e pa pe r p r oc e e d s a s f o l lows . S e c t ion 2 p r e se n t s e m pi r i c a l e v ide nc e on thec o - m o v e m e n t o f i n f l a t i o n w i t h t h e s t a t i o n a r y c o m p o n e n t o f G N P . S e c t i o n 3 d e -sc r ibe s the ba s i c f e a tu re s o f a nom ina l p r i c e r ig id i ty m ode l in w h ic h the d e g r e eo f nom ina l p r i c e r ig id i ty is de te r m ine d by the a ve r a ge f r a c t ion o f f inns tha t r e -v i se the i r p r i c e s in e a c h pe r iod a s in C a lvo ( 1983) . The m ode l a l so a l lows f o rpe r m a ne n t sh i f t in the l a bor - a ugm e n t ing t e c hno logy p r ogr e s s a s in K ing , P losse r ,a nd R e be lo ( 1 988 b) . S e c t ion 4 p r e se n ts num e r ic a l r e su lt s o f s im ula tions . I t a lsod i sc usse s how to e s t im a te m one y supp ly r u le s . S e c t ion 5 c onc lude s tha t nom ina lp r i c e r ig id i ty m ode l s c a n e xp la in the obse r ve d a s soc ia t ions be twe e n m ove m e n t sin p r i c e a nd ou tpu t m uc h be t t e r t ha n f l e x ib le p r i c e m ode l s .

2. Cycl ical beh avior of aggregate priceThis se c t ion p r e se n t s e m pi r i c a l e v ide nc e on the c o - m ove m e n t o f in f l a t ion wi th

the s t a t iona r y c om pone n t o f GNP a t t he qua r t e r ly f r e que nc y , to wh ic h the nu -m e r ic a l p r e d ic tions o f the the o r e t i c a l m o de l s w i l l be subse que n t ly c om pa r e d . T hejo in t s toc ha s ti c p r oc e ss i s c ha r a c te r i z e d by a ve c to r a u to r e g r e s s ion o f the f i rs td i f f e re nc e o f log r e a l pe r c a p i t a G NP a nd the f ir s t d i f f e re nc e o f log GN P de f l a to ri n t h e p o s t - w a r ( 1 9 4 7 - 1 9 8 7 ) U n i t e d S t a t e s .On e use f u l w a y o f de sc r ib ing the b iva r i a t e a u to r e g r e s s ive p r oc e ss i s i n t e r m sof e s t im a te d im pu l se r e sponse s to two type s o f o r thogon a l innova t ions . No te tha tth is w a y o f c ha r a c te r i z ing th e da ta r e m a ins v a l id r e ga rd le s s o f a ny s t r uc tu r a l


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348 72. Yun /Journa l o f M one tary Economics 37 (1996) 34 5~ 70i n t e rp r e t a t io n o f t h e s e i n n o v a t i o n s - w e n e e d s i m p l y t o o r t h o g o n a l i z e th e i n n o -v a t i o n s i n th e s a m e w a y a s w e r e p o r t th e n u m e r i c a l p r e d i c t i o n s o f t h e t h e o r e ti c a lm o d e l s . T h e o r t h o g o n a l i z a t i o n th a t is u s e d h e r e i s li k e t h a t o f B l a n c h a r d a n dQ u a h ( 1 9 8 9 ) ; i t i s a s s u m e d t h a t o n e i n n o v a t i o n ( t h e ' p e r m a n e n t s h o c k ' i n F i g .1 ) h a s p e r m a n e n t e f fe c ts o n th e l e v e l o f o u tp u t , w h i l e t h e o t h e r ( t h e ' t e m p o -r a r y s h o c k ' i n F ig . 1 ) l e a ds t o o n l y t e m p o r a r y m o v e m e n t s o f ou t pu t . B l a n c h a r da n d Q u a h h a v e i d e n t i f i e d t h e s e a s ' s u p p l y ' a n d ' d e m a n d ' s h o c k s , r e s p e c t i v e l y .I n fa c t, a c c o r d i n g t o al l o f t h e t h e o r e ti c a l m o d e l s w h i c h h a v e b e e n a n a l y z e d i nt h i s p a p e r , t h i s s t r u c t u r a l i n t e r p r e t a t i o n i s j u s t if i e d . T h e y a l l ( t o b e d e v e l o p e db e l o w ) i m p l y t h a t t h e p e r m a n e n t s h o c k , a s u n d e r s t o o d h e r e i n , s h o u l d c o r r e s p o n dt o a n e x o g e n o u s l a b o r - a u g m e n t i n g t e c h n o l o g y s h o c k , w h i l e t h e t e m p o r a r y s h o c ks h o u l d c o r r e s p o n d t o a n e x o g e n o u s c h a n g e i n t h e g r o w t h r a te o f m o n e y s u p p l y .H e n c e t h e e s t i m a t e d r e s p o n s e s t o t h e p e r m a n e n t a n d t e m p o r a r y s h o c k , r e s p e c -t i v e l y , a r e t o b e c o m p a r e d w i t h t h e t h e o r e t i c a l r e s p o n s e s t o t e c h n o l o g y s h o c k sa n d t o m o n e t a r y s h o c k s , r e s p e c t i v e l y .

T h e o r t h o g o n a l i z a t i o n i s c a r r i e d o u t a s f o l l o w s . L e t q~t = [A l o g Y t ~ t ] ' , w h e r eY t i s r e a l p e r c a p i t a G N P a t d a t e t a n d r~t i s t h e r a t e o f in f l a t io n ( = A l o g P t ,w h e r e P t i s th e G N P d e f l a t o r a t d a t e t ) . S i n c e 4~t i s s t a t i o n a r y , 1 a W o l d m o v i n ga v e r a g e r e p r e s e n t a t i o n c a n b e o b t a i n e d b y f ir st e s t im a t i n g 2 a v e c t o r a u t o r e g r e s s i o na n d t h e n i n v e r t i n g i t . L e t t h e e s t i m a t e b e g i v e n b y ~ t = ~ ]~ j~ o c ( j ) v t _ j , w h e r eco v ( v t ) = f2, c ( 0 ) = 2,2, 2 x 2 iden t i t y m at r ix , an d vt i s a 2 x 1 ve c to ro f r e s i d u a l s . O n t h e o t h e r h a n d , i f a s t r u c t u r a l i n t e r p r e t a t i o n i s g i v e n t o th ea b o v e e q u a t i o n , ~ t h a s t h e f o l l o w i n g r e p r e s e n t a t i o n : (Or = ~-]~j~:oa ( j ) e t - j , w h e r ec o v ( e / ) = 1 2 ,2 , a ( j ) i s a 2 x 2 m a t r i x f o r a l l j . H e r e , e t = [ e A , t E M , t i t , eA,t isp e r m a n e n t s h o c k a t d a t e t , a n d eM , i s t e m p o r a r y s h o c k a t d a t e t . W h e n t h e s et w o d i f f e r e n t r e p r e s e n t a t i o n s a r e c o m p a r e d , a ( j ) = c ( j ) a ( O ) f o r al l j . H e n c e ,t h e i d e n t i f i c a t i o n o f t h e 2 2 m a t r i x a ( 0 ) i s s u f f ic i e n t f o r i d e n t i f y i n g a l l a ( j ) ,g i v e n c ( j ) f o r al l j . T h i s i d e n t i f ic a t i o n r e q u i re s f o u r e q u a t i o n s f o r f o u r u n k n o w n s .S i n c e t h e e s t i m a t e d c o v a r i a n c e m a t r i x ( 2 g i v e s th r e e e q u a t i o n s , o n l y o n e a d d i t i o n a le q u a t i o n i s n e e d e d f o r t h e i d e n ti fi c a ti o n . H e r e , s i n c e t e m p o r a r y s h o c k s h a v e o n l y

O( )t e m p o r a r y m o v e m e n t s o f o u t pu t , t h e a d di ti o n al e q u a t i o n i s g i v e n b y ~ j = 0 a l 2 ( j )= 0 . C o n s e q u e n t l y t h i s l e a d s t h e m a t r i x , a ( O ) , t o be iden t i f i ed .I n a d d it io n , t h e o r t h o g o n a l i z a t i o n u s e d h e r e l e a d s t h e l o g a r i th m o f G N P t o

b e d e c o m p o s e d i n t o t w o t y p e s o f o r t h o g o n a l c o m p o n e n t s , s o l o g Yt - - l o g Yt +O ~ O O .l og Yt . H ere , A log Y [ = ) - ] j= o a l l ( j ) e A , t - j a n d A l o g Y t = ~ j = 0 a 1 2 ( J ) e M , t - j .

1 The stationarity of ~bt is exa mined using the Dick ey-Fuller (DF) test. The t-statistics fro m the DFregressions of A og Yt and s t are - 8. 59 and -5 .77 , respectively, wh ich are all significant at the 5percent significance level. It thus implies that the rate of inflation and the first difference o f log realGNP are stationary.2 T he lag o f bivariate vector autoregression is c hosen using the Ak aike information criteria suggestedin G ranger and N ew bold (1986). Th en, for a cho sen value, the likelihood ratio tests are perform edas su ggested in D oan (1992). As a result, the lag o f the vector autoregression is 5.


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0.02

0.01

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . i0 5 10 15 20

P~ce(Temporary)!

o,. o" .- - . - .- -" -o - .-

. . . . .

O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , I ,0 5 10 15 20

F i g . 1 . Es t i m a t ed i m p u l s e r e s p o n s es .


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350 T. Yun/Journal o f Monetary Economics 37 (1996) 345-370H e n c e l o g Y [ i s t he c om pon e n t o f ou tpu t tha t is a f f e c te d by on ly pe r m a ne n tshoc ks a nd log Y/ i s t he one tha t is a f f e cte d by o n ly t e m p or a r y shoc ks .

F ur the r m or e , f o l lowing B e ve r idge a nd Ne l son ( 1981) , one c a n de f ine the s to -c ha s t ic t r e nd o f GN P a s the long- r un f o r e c a s t o f log Yr. In th is case , log Y t c a n b er e p r e se n te d as the sum o f the r a ndom w a lk t r e nd a nd s t a t iona r y c om pon e n t . S olog Yt = log YP + log Y [ , w h e r e l o g Ytp i s t h e r a n d o m w a l k c o m p o n e n t a t d a t et and log Y7 is the s ta t ionary com po ne nt a t da te t . He re , log Y / and log Y[ a reno t ne c e ssa r i ly the sa m e b e c a use log Yt i s no t on ly a f fe c te d by t e m por a r y shoc ksbu t a l so pe r m a n e n t shoc ks , whe r e a s log Yt i s on ly a f f e cte d by t e m por a r y shoc ks .F or th i s r e a son , in subse que n t se c t ions , I e xa m ine the c o r r e l a t ions be twe e n ther a t e o f in f l a t ion a nd the se f ou r type s o f ou tpu t m e a su r e s .

The e s t im a te d im pu l se r e sponse s a r e p lo t t e d in F ig . 1 w i th two s t a nda r d e r -r o r s ba nds . T he 1 pe r c e n t inc r e a se o f s t a nda r d de v ia t ion in the pe r m a n e n t shoc kc a use s inc r e a se s in ou tpu t g r owth a nd ou tpu t l e ve l bu t g r a dua l de c l ine s in thep r i c e l e ve l t o a long- r un l e ve l . On the o the r ha nd , t e m por a r y shoc ks e xh ib i t ahum p- sha pe d e f f ec t on ou tpu t. Th i s e f f ec t r e a c he s i t s pe a k th r e e to f ive qua r -t e rs a f t e r a t e m p or a r y shoc k . Th e shoc k a l so r a i se s the r a t e o f in f la t ion a t t hein it ia l pe r iod a nd the n lowe r s i t g ra dua l ly , so the r e sponse o f the p r i c e l e ve ld isp lays gradua l inc reases to a long- run leve l . In sum, the aggrega te pr ice i sc oun te r c yc l i c a l w i th r e spe c t to pe r m a ne n t shoc ks bu t p r oc y c l i c a l t o t e m por a r yshocks .

Ta b le 2 r e por t s s t a nda r d de v ia t ions a nd c r oss - c o r re l a t ions o f in f l a tion a nd ou t -pu t m e a su r e s . T he g r ow th r a te o f GN P d i sp la ys ne ga t ive o r sm a l l pos i t ive c o r -re la t ions wi th up to th ree lags and leads o f the ra te o f inf la tion . Bes ides , thec r o s s- c o rr e la t io n s o f i n f la t io n w i t h t h e s t at io n a r y c o m p o n e n t o f G N P ( = l o g Y [ )a n d t h e c o m p o n e n t t h a t is a f fe c te d b y o n l y t e m p o r a r y s ho c k s ( = l o g Y / ) a r e c o n -s i s te n t ly pos i t ive , wh e r e a s the g r owth r a t e o f the tr e nd c om pon e n t ( = A log YP )o r t h e c o m p o n e n t th a t i s a ff e ct e d b y o n l y p e r m a n e n t s h o c k s ( = A l o g Y [ ) s h o wc ons i s t e n t ly ne ga t ive c r oss - c o r r e l a t ions w i th the r a t e o f in f l a t ion ( e xc e p t whe nthe g r ow th r a t e o f the t r e nd , wh ic h i s wh i t e no i se , l e a ds the r a t e o f in f l a tion ) . I nsum, th is cor re la t ion s t ruc ture leads one to conc lude tha t the ra te of inf la t ion hass t r ong ly pos i t ive c o r r e l a t ions w i th the c yc l i c a l c om pone n t o f ou tpu t .

3 . M o d e l

The e c o no m y c ons is t s o f in f in i t e ly l i ve d house ho lds , f i rm s , a nd gov e r nm e n t .The e c onom y a l so c on ta ins a c on t inuum of d i f f e r e n t i a t e d goods tha t a r e p r oduc e dby m o nopo l i s t i c a l ly c om pe t i t ive f ir m s . The se d i f fe r e n ti a t ed goo ds a r e a g gr e ga te dto p r oduc e a s ing le c om pos i t e good in wh ic h the u t il s o f c onsum e r s a nd a dd i t ionst o t h e a g g r e g a te c a p i ta l s t o c k d e p e n d o n l y u p o n t h e a m o u n t o f th e c o m p o s i t egood . A l so , t he de m a nd f unc t ion f a c e d by e a c h f i r m is de r ive d by spe c i f y ing a nagg rega to r for d i f fe rent ia ted good s . In re la t ion to th is , I in t roduce the agg rega to r


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T. Y un/Jo urna l o f Mo netary Economics 37 (1996) 345-370 351

o f d i f fe r e n t ia t e d goo ds use d in D ix i t a nd S t ig li t z ( 197 7) suc h tha t

O t = D t ( i ) ( e - l ) / e d i , ( 1 )wh e r e e > 1 , D t i s t h e n u m b e r o f u n i ts o f t h e c o m p o s i t e g o o d a t p e r io d t , D r ( i )i s t he de m a nd f o r good i , a nd P t ( i ) i s the p r i c e o f goo d i s e t by f i rm i . Ea c hf i r m ' s de m a nd the n i s de te r m ine d a s a so lu t ion tha t m in im iz e s the to t a l c os t o fob ta in ing D t sub je c t to the a ggr e ga to r spe c i f ie d in Eq . ( 1 ) . As a r e su l t o f c os tm in im iz a t ion , whe n the p r i c e inde x f o r the c om pos i t e good i s g ive n by

P t = P t ( i ) l - C d i , ( 2 )the de m a nd o f f ir m i t a ke s the f o l lowing f o r m :

O t ( i ) = ( P t ( i ) / P t ) - ~ D t . (3 )No te tha t the de m a nd f unc t ion in Eq . ( 3 ) ha s the c ons ta n t e l a s ti c i ty o f e.

On the o the r ha nd , f i r m i p r oduc e s good i u s ing c a p i t a l a nd l a bor a c c o r d ingto the p r odu c t ion t e c hno lo gy wi th a f ixe d l a bor c os t g ive n by

Y t ( i ) = F ( K t ( i ) , z t ( H t ( i ) - H ) ) (4 )w h e r e H t ( i ) , H , a n d Y t ( i ) r e spe c t ive ly de no te to t a l l a bo r inpu t , f ixe d l a bor c os t ,a nd ou tpu t o f fi r m i a t da te t , a nd z t de no te s the l a bor - a ugm e n t ing t e c hno logyle ve l a t da te t . He r e , t he p r od uc t ion f unc t ion F d i sp la ys the c ons ta n t re tu r nsto sca le f or capi ta l an d n e t labor , / -/ t - H , a nd the t e c hno logy p r oc e ss i s t hel o g a r i t h m i c r a n d o m w a l k g i v e n b y

z t = z t -1 exp(Tt) , (5)whe r e 7 t i s wh i t e no i se a nd i t s unc ond i t iona l m e a n i s 7z . The c os t f unc t ion o ff i rm i , then , can be wr i t ten as

T C , ( i ) = m in R t K t ( i ) + W t H t ( i ) s.t. D t ( i ) = F ( K t ( i ) , z t ( H t ( i ) - H ) ) ,Ht(i),Kt(i)w h e r e R t a n d W t a r e the no m ina l r e n ta l f o r c a p i t a l s e rv ic e a nd nom ina l wa ge a tda te t , r espec t ive ly .

In th is paper , I a ssum e tha t renta ls and wag es a re per fe c t ly f lex ib le in per fec t l yc om pe t i t ive inpu t m a r ke t s . H e nc e , m a r g ina l c o s t is i nde pe nd e n t o f the l e ve l o fou tpu t . C os t m in im iz a t ion c ond i t ions the n c a n be wr i t t e n a s

W t = M C t z , F . ( K t ( i ) , z t ( H t ( i ) - H ) ) , ( 6 )R t = M C t F K ( K t ( i ) , z t (H t ( i ) - H ) ) , ( 7 )


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352 T. Yu n/Jou rnal o f Monetary Economics 37 (1996) 345 370where F K and FI-1 deno t e t he marg ina l p roduc t o f cap i t a l and ne t l abo r , r e spec -t ively , and M C t i s the marginal cos t a t da te t . Note that the cos t min imizat ioncondi t ions speci f ied in Eqs . (6) and (7) ho ld for aggregate quant i t i es becausethe p roduc t i on func t i on F i s hom ogene ous o f deg ree 1 i n cap it a l and ne t l abo r.In add i t i on , wh en m u l t i p ly ing ne t l abo r and cap i ta l t o bo th s i des o f Eqs . (6 )and (7 ) , r e spec t i ve ly , and t hen summing up t he r e su l t i ng two equa t i ons , t he cos tfunc t i on fo r f i rm i i s g iven by T C t ( i ) = M C t D t ( i ) q - W t H . C onsequen t l y , t heins tan taneous rea l p rof i t a t da te t fo r f i rm i can be wr i t t en as

[ 'P t ( i ) ~ ) ( P t ( i ) m c t ) ( P t ( i ) ) - ~ W t H 49 ~ - - ~ t ' m c t ' L ' t ' W t = P t ', P t J k ,---~ t J D r - - (8 )w h e r e m c t ( = M C t / P t ) denotes the rea l marg inal cos t a t da te t .

Having descr ibed the ins tan taneous prof i t in per iod t , l e t ' s cons ider the pr icedec i s i on o f f irms based upon C a lvo (1983) . In each pe r i od , a f r ac ti on o f f irms ,say 1 - c~, ge t s to cha rge a ne w pr ice and the o ther f rac t ion , ~ , m us t ch argethe prev ious per iod ' s p r ices t imes average inf la t ion rc regard less of the t imeelapsed s ince the las t p r ice change, wh ere 0 < a < 1 . He nce, th i s Calvo-type s t agger ing and t he p r ice i ndex spec i fi ed i n Eq . (3 ) imp ly t ha t whe n t henew p r ice co m m i tmen t in pe r i od t i s deno t ed by Pt , , the pr ice index in eachper iod t = 0 . . . . cx~ evolves ov er t im e acco rd ing to the recurs ive form g ivenb y

P ] - e = ( 1 - a ) P ~ t ~ + a n l - ~ P ) Z ~ , (9 )w h e r e P - 1 i s g iven . Fur therm ore , s ince wi th a probab i l i ty of c~ the new pr icecommi tmen t i n pe r i od t w i l l be cha rged i n pe r i od t + k , Pt , t i s the so lu t ion to them a x i m i z a t i o n p r o b l e m g i v e n b y

P " k =o L - Z - ,where the rea l p rof i t a t da te t + k i s d i s coun t ed by i l k ( A t + k / A t ) a n d A t i s expl ic-i t ly def ined later . The ins tan taneo us rea l p rof it speci f ied in Eq . (8 ) then leads thef i rs t -order condi t ion for P t, t o be g iven by

OO ke ~ ( o: il) E t [ A t + k P t + k D t + k m c t + k ]P i t = k=0 ( 1 0 )

( ~ -- 1 ) ~ ( ~ i l r c )k E t [ A t + k P t + ~ D t + k lk=O

Here, the f i rm takes as g iven the aggregate demand, s tochas t ic d i scount fac torfor asse t p r ices , marg inal cos t , and pr ice l evel . In addi t ion , the subs t i tu t ion ofa = 0 in to Eq. (10) y ie lds the sam e opt imiza t ion cond i t ion as in fl ex ib le pr ice


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T . Y u n / J o u r n a l o f M o n e t a r y E c o n o m i c s 3 7 ( 1 9 9 6) 3 4 5 - 3 7 0 3 5 3

m o d e l s g i v e n b yP t = e M C t / ( e - 1) . (11)

The r e a l m a r g ina l c os t t he r e f o r e i s c ons ta n t ove r t im e in f l e x ib le p r i c e m ode l s ,whe r e a s i t va r i e s in s t i c ky p r i c e m ode l s .

L e t ' s t u rn t o t h e b e h a v i o r o f th e r e p r e s en t a ti v e h o u s eh o l d . T h e e c o n o m y h a sthe r e p r e se n ta t ive house ho ld wi th p r e f e r e nc e in pe r iod 0 g ive n by

O Q

E0 Z fi t U (x (C m C 2 t ) , L t + bLt-1 ) ,t= O

( 1 2 )

w h e r e Clt , C2t , a n d L t de no te c a sh a nd c r e d i t c onsum pt ion 3 goods , le isure inper io d t , and the d iscoun t fac tor , f l, and pre fe renc e param ete r , b , sa t i s fy 0 < f l< 1 and ] b ] < 1 . He re , the nonz ero va lues o f b indica te tha t the cur ren t -per iodu t i l i t y i s no t inde pe nde n t4 o f p r e v ious - pe r iod l e isu r e . A l so , i n e a c h pe r iod , t hehouse ho ld f a c e s a t im e c ons t r a in t suc h tha t

mLt + t i t 0 f o r p o s i t i v eC 1 a n d 6 '2 . I n a d d i ti o n , e v e r y d i f f er e n ti a te d g o o d c a n b e p u r c h a s e d a s a c a s h g o o d o r c r e d it g o o d a n dp r o d u c e r i p r o d u c e s b o t h c a s h g o o d i a n d c r e d i t g o o d i , se t t in g a c o m m o n p r i ce P t ( i ) . F u r t h e r m o r e ,w h i l e C lt = ( fo ~ Cl t (i ) (E --1 ) /Ed i ) e / (e - I ) a n d C 2t = ( f 01 C2t( i ) (E -1 ) /ed i ) e / (e - I ) , Ht = f o H t ( i ) d i .4 T h e n e g a t i v e v a l u e s o f b i n d i c a t e t h a t l e is u r e p r e f e re n c e s a r e c h a r a c t e r iz e d b y h a b i t p e r s i st e n c e ,w h i l e t h e p o s i t i v e v a l u e s i m p l y t h a t l e i s u r e i s d u r a b l e .


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3 5 4 T . YunlJournal o f Monetary Economics 37 (1996) 345-370b e g i n n in g o f p e r io d t + 1 i s g iv e n b y

N t+ l = B t O t + W t H t + ( R t + P t ( 1 - 6 ) ) K t + M ~- P t ( C lt - '}- C2 , -Jr"K t + l ) - ]- i f / h , ( 1 6 )

w h e r e t h e r a t e o f d e p r e c i a t i o n , 6 , sa t i sf i e s 0 < 6 < 1 , a n d Or, Kt, a n d H td e n o t e t h e g r o s s n o m i n a l i n t e r e s t r a t e i n p e r i o d t , a g g r e g a t e c a p i t a l s t o c k , a n da g g r e g a t e p r o f i t o f f ir m s g i v e n t o t h e h o u s e h o l d . T h e h o u s e h o l d t h e n d e c i d e so n c o n s u m p t i o n d e m a n d , l a b o r su p p l y , a n d d e m a n d f o r m o n e y t o m a x i m i z e t h eu t i li ty f u n c t i o n g i v e n i n E q . ( 1 2 ) s u b j e c t t o c o n s t ra i n ts ( 1 3 ) , ( 1 4 ) , ( 1 5 ) , a n d( 1 6 ) .

T h e f i r s t - o r d e r c o n d i t i o n s w i t h r e s p e c t t o c a s h a n d c r e d i t c o n s u m p t i o n g o o d si m p l y t h a tX l ( C l t , C 2 t ) / x2 ( C l t , C 2 t ) = O t, ( 1 7 )U c ( x ( C l t , C2 t ) , L t + b L t - i ) x t ( C l t , C 2 t) = A tO t , ( 1 8 )

w h e r e A t i s d e f i n e d a s At = Et(f lPtAht+l), Aht i s t h e L a g r a n g e m u l t i p l i e r f o rt h e b u d g e t c o n s t ra i n t o f t h e h o u s e h o l d s p e c i fi e d i n E q . ( 1 6 ) , a n d U c d e n o t e st h e p a r t ia l d e r i v a t i v e o f U w i t h r e s p e c t to x . N o t e t h a t, s i n c e x ( C l t , C2 t) i s h o -m o g e n e o u s o f d e g r e e 1 i n (Cl t , C2t ) , E q . ( 1 7 ) i m p l i e s t h a t t h e r at io o f c a s hc o n s u m p t i o n g o o d s t o c r e d i t c o n s u m p t i o n g o o d s ( = C l t / f 2 t ) c a n b e e x p r e s s e da s a f u n c t i o n o f t h e n o m i n a l i n t e r e s t r a t e i n a n e q u i l ib r i u m . T h i s i m p l i e s t h a t t h er a ti o o f c a sh c o n s u m p t i o n g o o d s to c o n s u m p t i o n g o o d s i s a l s o a f u n c t i o n o f t h en o m i n a l i n t e r e s t r a t e , so C l t / C t = h(Ot). F u r t h e r m o r e , f o r t h e c o n v e n i e n c e o f th ea n a l y s i s i n s u b s e q u e n t p a r ts , l e t ' s d e f i n e a n e w e n d o g e n o u s v a r i a b l e , ~ b t , s u c ht h a t

U L ( X ( C l t , C 2 t ) , L t + b Z t - 1 )~ t = U c ( x ( f l t , C 2 t ) ,Z t + b L t - 1 )" ( 1 9 )

E q s . ( 1 8 ) a n d ( 1 9 ) c a n b e s o l v e d t o y i e l d t h e f o l l o w i n g c o n s u m p t i o n d e m a n da n d l a b o r s u p p l y f u n c t i o n s :

G = C ( A t , O t , ~ t ) ,H t = - b H t - I + H S ( A t, O t , ~ t ) " ( 2 0 )

B e s i d e s , E q . ( 1 9 ) l e a d s t h e f i r s t - o r d e r c o n d i t i o n f o r l e i s u r e i n p e r i o d t t o b e g i v e nb y

A W t = A t ~ t e ( O t ) q- E t [ 3 b A t + l O t + le (O t + l ) ] ,t P t ( 2 1 )


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T. Yun /Journa l o f Mo ne tary Economics 37 (1996) 345 -370 355w he re e ( O t ) = O t / x l ( h ( O t ) , 1 - h ( O t ) ) . Also, the f i rst -order cond i t ions wi th respec tto bonds a nd inve s tme n t a re g ive n by

A , = E , [ f l ~ A t + I ] , (22)

A t = E t f l A t+ l \ P t + l + 1 - ~ . (23)In addi t ion , the cash- in-advan ce cons t ra in t holds w i th equa l i ty i f the gross nom ina linterest ra te , O r, i s grea te r than 1 . Hen ce , s ince i t i s a ssum ed throug hou t the papertha t 0 t > 1 for a ll t, the dem and for the rea l ba lance in each per iod i s g iven by

M , h / P t = h ( O t ) C ( A t , O r, bt) . (24)Fur the rmore , t he gove mme nt supp l i e s mone y th rough lump-sum t ra ns fe r , T t , sothe m on e y s toc k in pe r iod t i s g ive n by M t = M t _ l + I t , w h e r e T t = ( @ - 1 ) M r - land o~t i s the growth of money supply in per iod t .

Having descr ibed the behaviors of individua l agents , l e t ' s turn to the aggre -ga t ion o f i nd iv idua l ou tpu t s . The a ggre ga t e de ma nd , D r , i n e a c h pe r iod mus t beequa l to aggrega te output , Y t, i f the outputs of d i f fe rent f i rms a re aggrega ted ac -c o rd ing to t he fo rmula , Y t = ( f l y t ( i )( ~ _ l ) / ~ d i ) ~ / ( ~ _ l ) ' fo l l ow ing the a ggre ga to rspec i f ied in Eq. (1) . This d ef in i t ion of aggrega te output i s not use ful , however , inw r i t i ng t he e qu i l i b r ium re l a t i on be tw e e n a ggre ga t e de ma nd a nd a ggre ga t e fa c to rdemands . For us ing th i s aggrega tor , the re la t ion be tween aggrega te output andfa c to r s o f p roduc t ion i s g ive n by Y t = ( f l F ( K t ( i ) , z t ( H t ( i ) - H ) ) ( ~ - l ) / ~ d i ) ~ / ( ~ - l ) .But i t i s des i rable to be able to express aggrega te output as a func t ion ofthe agg rega te fac tor inputs only . This i s poss ib le i f one def ines the aggrega tor ,Y t* = f d Y t ( i ) d i , so tha t Y t* = F ( K t , z t (H t - H ) ) , w he re K t = f d K t ( i ) d i an dH t = f d H t ( i ) d i . The n one c a n re l a t e Yt* to Yt by using the a l ternat ive priceindex, P ? = ( f 2 P t ( i ) - ~ d i ) -1 /~ . This i s because Y t* = flo Y t ( i ) d i = ( P t / P ~ ) ~ Y t .H e nc e , t he e qu i l i b r ium re l a t i on be tw e e n a ggre ga t e de ma nd a nd a ggre ga t e fa c to rinputs can be wri t ten as

C t + K t + l - (1 - 6)Kt = ( P t / P t ) E F ( K t , z t (H t - H ) ) . (25)In addi t ion , Ca lvo- type s tagger ing impl ies tha t the a l te rna t ive pr ice index evolvesove r t ime a c c ord ing to t he fo l l ow ing e quat ion :

P ; -~ = (1 - a ) P ~ ~ + ~ u - c p ; - ; . (26)There fore , the re a re only two prede te rmined pr ices , ( P t - 1 , P [ - 1 ) , which a ffec tsubseque nt equi l ibr ium cond i t ions , regardless o f the s ize of e . This a l low s one


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3 5 6 72 Y unIJo urna l o f Monetary E conomics 37 (1996) 345 370t o c ons ide r a rb i t r a r i l y s low a d jus tme n t o f p r i c e s w i thou t ha v ing to w ork w i th alarge sta te space.

Ksymmetr ic equi l ibr ium, then, i s an a l loca t ion {Ct , H t, t+l}t=0, a sequence, ~ ooof pr ices and cos ta te var iables {P t , t, P t , P ~ Or, W t , m c t , R t , A t , t } t= 0 sa t i sfy inge qu i li b r ium c ond i t i ons (6 ) - (7 ) , (9 ) - (1 0) , (20 ) - (2 4) , a nd (25) - (26) , g ive n K o ,

-7 OOP-1 P*-I , H - l , a nd { M r , t} t= 0 . Fur the rmore , s inc e z t i s a logar i thmic randomwalk, these equi l ibr ium condi t ions lead to a de te rminis t ic s teady s ta te in whichconsumpt ion, rea l money ba lance , and capi ta l grow a t the same ra te but labori s cons tant over t ime . In th i s case , a s d i scussed in King, P losse r , and Rebe lo(1988a) , when one i s in te res ted in a s ta t ionary economy, i t i s he lpful to use there la t ions g iven by

G = c t z t , q~ t = qb tz t, K t+ l = k t+l z t , R t = r tP t , W t = w t z tP t ,A t = 2 tz ~ '7 , P t = p t z t M t , P ~ - - p T z t M t , P t,t - - p t , z t M t ,

where t / i s the inverse of the e las t ic i ty of in te r tempora l subs t i tu t ion . In par-t icula r , i f these re la t ions a re subs t i tu ted in to equi l ibr ium condi t ions , (6) - (7 ) ,(9 ) - (10) , (20 ) - (24) , a nd (25) - (26) , t he n one c a n ge t e qu i l i b r ium c ond i t i ons fo r

kn a l loca t ion {c t , I - I t , t+l}t=0, a sequenc e o f prices an d costa te variables {p t , t ,p t , P~ , Or, w t , tac t , r t , 2t , c~t}t~=o, g i v e n k 0, P - l , P *-I, H - l , a n d { w t , 7t}t~0,which in turn leads to a s teady s ta te in which c t and kt+ l a re cons tant overt ime .

The re sponse s o f mo de l e c onom ie s t o c ha nge s i n t e c hno logy p rogre s s a ndmone y supp ly a re t he n a na lyz e d us ing the me thod o f K ing , P los se r , a nd Re be lo(1988a , b) . This imp l ies tha t a s ta t ionary equi l ibr ium inv olving sm al l f luc tua t ionsaround s teady s ta te i s approximated by the solu t ion to a log- l inear approxima-t ion to the equi l ibr ium condi t ions for the t ransformed var iables . For th i s reason,le t ' s den ote the percentage devia t ions o f a ll s ta t ionary var iables a round the s teadys ta te by us ing c i rcumflex . Here , note tha t f i t = f t - This imp l ies tha t the l in-ea r ized vers ion of the soc ia l budge t cons t ra in t spec i f ied in Eq. (25) i s g ivenb y

= 1 ( # ( ? + 6 ) + ( 1 - 6 ) ) ( f ~ t- T t ) - ~ ( ? + 6 )PS l - l I2I t ~(?+--6)sc-- , t , (27)7z ?z(1 - S H ) ? A t - - S H )w h e r e / ~ ( = 1 / m c ) i s the s teady s ta te markup, sH (= w i l l y ) i s the s teady s ta tel a bor sha re , ( = r - 6 ) i s t he s te a dy s ta te g ros s re tum o n inve stme n t , a ndsc (= c / y ) i s the s teady s ta te f rac t ion of consumpt ion in output . Fur thermore ,l inear iz ing equi l ibr ium condi t ions (9) and (10) y ie lds

q--1 ^ ~zq--1 {O) ( 1 - - ~ ) ( ' ~ z - 1 - - ~ f l )E t [ A p t + I - ' ~ O ) t + l ] = ~ - A p t + - - - f f - ~ t - i t ) o ff3 m ~ c t, ( 2 8 )


13/26

T. YunlJournal of Monetary Economics 37 (1996) 345 370 3 57whe r e A f it = /3 t - f i t - 1 . A l so , the c onsu m p t ion de m a nd a n d l a bor supp ly e qua -t ions g ive n in Eq . ( 20 ) l e a d to

/Q t = - b / Q , - i + ( 1 + b ) ( c 2 ~ t + c o o t + c ( o ~ , ) , ( 2 9 )

w h e r e c j ( = j ~ H S / H S O j ) a n d c j ( = j O c / c ~ j ) denote the Fr isch e las t ic i t ie s oflabo r supply and con sum pt ion w i th respec t to j = 2 , 0 , q~. Us ing tha t E t [ f f t + l ]= 0 , t he l ine a r iz a t ion o f e qu i l ib r ium c ond i t ions f o r l e isu r e in pe r iod t a nd Eu le re qua t ions f o r inve s tm e n t a nd bonds spe c i f i e d in Eqs . ( 21 ) - ( 23 ) l e a ds to

(1 + f l b T ~ - n ) ~ t = ~ t + e o O t + f l b T l - n E t [ 2 , + l - f t t + e o O t + l + ~ t - - 1 ] , ( 3 0 )

I , ~ + 6 ^ ( 7 + 6 ) ( 1 - u ( 1 - s . ) ) ( , ~ , + ~ _ ~ , + 1 ) 1 ( 3 1 )~ t = E t ~ t+ 1 -[- ~ m c t + l q - C HK ( 1 q - ~ )

2t = Et[)~t+l + /3 t - /3 t+ l - d~t+l + Ot+l] , (3 2)whe r e C ur i s t he e l a s t i c i ty o f subs t i tu t ion be twe e n c a p i t a l a nd ne t l a bor ( n t =I - I t - H ) . The c a sh - in - a dva nc e c ons t r a in t g ive n in Eq . ( 24 ) im p l i e s tha t

[ ~ t = - ( h o + c o ) O r - c ~ 2 t - c ~ t , ( 3 3 )w h e r e h o i s the e las t ic i ty of h wi th resp ec t to 0 . F ina l ly , Eq. (6) h olds fo raggrega te quant i t ie s , so i t s l inear ized vers ion i s g iven by

f i t = n f c t + #(1 - s~/)(/~, _ it - r~t). (3 4)EH KThis se t 5 o f l i ne a r e qua t ions i s r e duc e d to the sys t e m o f l i ne a r d i f f e re nc e e qua t ionsg i v e n b y

G 1 E t [ A t + I ] = G 2 A t + G 3 B t + G 4 E t [ B t + I ] , ( 3 5 )whe r e At is t he c o lum n v e c to r c on ta in ing se ve n e ndog e nous va r i ab le s , / 3 , ~ c t ,

2 t , F i t , l e t , ! h t _ l , I 2 1 t - 1 , a nd B t i s the co lum n ve c tor co nta in ing ~2t and dh . H ere ,GI and G2 a re 7 7 matr ices and G 3 a nd G 4 a r e 7 2 matr ices . In th is case ,one c a n show tha t a u n ique s t a t iona r y so lu t ion e x i s ts w he n the m a t r ix G~ 1 G2

5 In f lexible pr ice models , Eq. (28) i s r eplaced by nfct = O.


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358 T. Yun/Journal o f Monetary Economics 37 (1996) 345-370p o sse s se s f o u r e i g e n v a l u e s t h a t a r e g r e a t e r t h a n 1 i n a b so l u t e v a l u e a n d t h r e ee i g e n v a l u e s t h a t a re l es s th a n 1 i n a b so l u t e v a l u e , f o l l o wi n g B l a n c h a r d a n d K a h n( 1 9 8 0 ) .

4 . Q uan t i ta t ive resul t sT h i s s e c t i o n b e g i n s w i t h th e d e sc r i p t i o n o f t h e c a l i b r a ti o n o f p a r a m e t e r s a n d

t h e e s t im a t i o n o f m o n e y s u p p l y p r o c e s s e s f o r n u m e r i c a l m o d e l s a n d t h e n g o e so n t o n u m e r i c a l f i n d i n g s .

4 .1 . P a r a m e t e r s v a lu e s a n d m o n e y s u p p l y r u l esFi r s t , n u m e r i c a l m o d e l s a s su m e d i v i s i b l e l a b o r su p p l y i n c o n j u n c t i o n w i t h

a log u t i l i t y func t ion , so the in t e r t empora l subs t i t u t ion has a un i t e l a s t i c i ty( c = 1 ). I n t u rn , F r i s c h e l a s ti c i ti e s f o r c o n s u m p t i o n d e m a n d a n d l a b o r su p -p ly sa tis fy c~b ---- 0, ~0 = - -e o w , c 6 = - - ~ = - - w , a n d c), = - 1 , wh e r e Cw( = H - H / H ) d e n o t e s t h e i n t e r t e m p o r a l e l a s t i c i ty o f l a b o r su p p l y . A l so , t h eh o m o g e n e i t y o f x ( c l , c 2 ) impl i e s tha t e0 = O h(O )~[1 + h ( O ) ( O - 1 ) ] a n d co =-- h o - 1 , so t h e y a r e d e t e r m i n e d b y h o , h ( O ) , a n d 0 . B e s i d e s , a b se n c e o f a r b i-t r a g e a n d E u l e r e q u a t i o n s f o r b o n d s a n d i n v e s t m e n t i m p l y t h a t 0 - - o 9 (1 - 4-F )/7 za n d f l = 7 ~/(1 + F ). Fu r t h e r m o r e , f i r m s a r e a s su m e d t o f r e e l y e n t e r m a r k e t si n t h e l o n g r u n , wh e r e a s f r e e e n t r y i s r e s t r i c t e d i n t h e sh o r t r u n . T h i s l e a d sf i x e d o v e r h e a d l a b o r t o b e g i v e n b y H o = H [ ( / ~ - 1 ) / p s n ], s o t he ra ti o o ft h e o v e r h e a d l a b o r t o t o t a l h o u r s i s d e t e r m i n e d b y t h e s t e a d y s t a t e m a r k u pa n d l a b o r sh a r e . I n su m , d e t e r m i n i s t i c s t e a d y s t a t e r e l a t i o n s l e a d o n e t o c a l i -b r a t e t h e v a l u e s o f f r e e p a r a m e t e r s su c h a s eHK, b , ew , # , 3 , 7z , ~ , SH, CO, ho,h ( O ) , e c , a n d c t o t h e r t h a n p a r a m e t e r s r e l a t e d t o m o n e y g r o w t h p a t h a n d e x -o g e n o u s t e c h n o l o g y p r o g r e s s . T h e v a l u e s f o r t h e s e p a r a m e t e r s a r e r e p o r t e d i nT a b l e 1 , w h e r e t h e y a r e t a k e n f r o m K i n g , P l o s s e r , a n d R e b e l o ( 1 9 8 8 a ) e x -c e p t f o r b, CO, h( O ), ho, I~, a n d ~ . T h e v a l u e s f o r t h e se p a r a m e t e r s a r e d e -t e r m i n e d a s f o ll o w s . T h e v a l u e o f b is g iv e n b y b = - 0 . 5 , w h i c h i n t u rni m p l i e s h a b i t p e r s i s t e n c e i n l e i su r e . A l so , t h e h a b i t p e r s i s t e n c e i n l e i su r e h a sb e e n f o u n d i n E i c h e n b a u m , H a n s e n , a n d S i n g l e t o n ( 1 9 8 8 ) a n d B r a u n a n d E v a n s( 1 9 9 1 ) . W h e n m o n e y i s d e f i n e d as M1 , t h e g r o w t h o f M1 , CO = 1 .0 15 , a n dh ( O ) ( = M 1 / P C ) = 0 .34 . In add i t ion , ho = - 7 w h i c h i s b a s e d u p o n th e e s-t i m a t e d s e m i - e l a s t i c i t y o f i n t e r e s t r a t e f o r m o n e y d e m a n d r e p o r t e d a t T a b l e 4i n L u c a s ( 1 9 8 8 ) . T h e v a l u e o f t h e s t e a d y s t a te m a r k u p t h e n i s g i v e n b y /2= 1 .2 , w h i c h is c lo s e to e s t i m a t e s o f a v e r a g e m a r k u p b y F e r n a l d a n d B a s u( 1 9 9 3 ) .

S e c o n d l y , m o n e y s u p p l y p r o c e s s e s a r e e s t i m a t e d a s f o l l o w s . W h e n t h em o n e y s u p p l y i s e x o g e n o u s , t h e c u rr e n t g r o w t h r a te o f M 1 i s r e g r e s s e d o n t h e


15/26

T . Y u n l J o u r n a l o f M o n e t a r y E c o n o m i cs 3 7 ( 1 9 9 6 ) 3 4 5 - 3 7 0Tab l e 1C a l i b r a te d p a r a m e t e r s

3 5 9

P a r a m e t e r V a l u e D e s c r i p t io n s o f p a r a m e t e r s7z 1.0043 0.025SH 0.58

0 . 0 1 6w 1.015CC 1~w 4h(O) 0.34h o -7eHK 1# 1.2b - 0 . 5

S t e a d y s t a te g r o w t h o f t re n dR a t e o f d e p r e c i a ti o n o f c a p i t al s t o c kS t ead y s t a t e l ab o r s h a re ( - w i l l Y )S t ead y s ta t e r ea l r a t e o f r e t u rn ( = r - 6 )S t e a d y s t a t e g r o w t h o f M 1I n t e r te m p o r a l e l a s ti c it y o f c o n s u m p t i o nIn t e r t em p o ra l e l a s t i c i t y o f l ab o r s u p p l yI n v e r s e o f s t e a d y s t a t e c o n s u m p t i o n v e l o c i t y ( = M 1 / P C )S e m i - i n t e r e s t e l a s t i c i t y o f d e m a n d f o r m o n e y ( p e r c e n t )E l as t i c i t y o f s u b s t i t u t i o n b e t ween cap i t a l an d n e t l ab o rS t ead y s t a t e m ark u pD e g r e e o f h a b i t p e r s i s t e n c e i n l e i s ur e

T a b l e 2E s t i m a t e d s t a n d a r d d e v i a t io n s a n d c r o s s - c o r re l a t io n sP a n e l 1 . E s t i m a t e d s t a n d a r d d e v i a t i o n sP e r c e n t a g e ( q u a r t e r ) A l o g Y A l o g Y P A lo g y r lo g Y'~ lo g y dEs t i m a t es f ro m V A R 1 .1 1 0 1 .5 9 5 0 . 7 8 6 3 .1 6 8 2 . 4 2 7 0 . 8 0 0Pa n e l 2 . Es t i m a t ed c r o s s -co r r e l a ti o n s

- 3 - 2 - 1 0 1 2 3co r ( f f t + j , A l o g Y t) - 0 . 2 0 0 - 0 . 1 0 4 - 0 . 0 4 8 - 0 . 0 2 5 0 .0 26 0 .0 1 4 - 0 . 0 2 8c o r ( x t + j , d l o g Ytp ) 0 0 0 - 0 . 4 5 1 - 0 . 1 7 7 - 0 .1 5 1 - 0 . 1 6 9co r (~ t + j , d l o g Y ~ ) - 0 . 0 6 3 - 0 . 1 2 1 - 0 . 1 6 8 - 0 , 5 3 0 - 0 . 2 5 2 - 0 . 2 2 3 - 0 . 2 3 2cor( f f t+ j , log YT) 0 .744 0 .814 0 .850 0 .867 0 .649 0 .550 0 .469cor(:fft+j , log y d ) 0.596 0.66 7 0.675 0,643 0.483 0.400 0.311Y: real output , r~: rate of inflat ion, Y P : t r e n d c o m p o n e n t o f r e a l o ut p u t, y s : s t a ti o n a r y c o m p o n e n t o freal ou tput , y r : c o m p o n e n t o f r e al o u t p u t t h a t i s a f fe c t e d b y o n l y p e r m a n e n t s h o c k s , y d : c o m p o n e n to f r ea l o u t p u t t h a t i s a f f ec t ed b y o n l y t r an s i t o ry s h o ck s .

prev ious pe r i od ' s g rowth r a t e o f M1 to e s t ima t e the m on ey supp ly p roces s 6 g ivenb y

log cot = -0 . 00 00 3 + 0 .603 log w t - i + M , t , (36 )(0 .00064) (0 .063) (0 .00814)

where the numbers in paren theses denote s tandard er rors .

6 T h e d a t a o n M 1 i n t h e p o s t - w a r U . S . A . i s o b t a i n e d fr o m C I T I B A S E ( 1 9 5 9 - 1 9 8 7 : F M 1 ) a n d f r o mS u r v e y o f C u r r e n t B u s i n e s s ( 1 9 4 7 - 1 9 5 9 ) .


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3 6 0 T. Yun /Journa l of Monetary Economics 37 (1996 ) 345-370O n the o the r ha nd , w he n i t i s no t e xoge nous , t he mone y supp ly p r oc e s s i s a s

fo l lows:kl k2 k3

(Dt-~- Z 1)c'J(f)t--J @ ~ VA'j~t-J -'~ Z VM'jEM't-J"j - 1 j = O j = O

( 3 7 )

I n th i s c a se , one c a n e s t ima te the pa r a me te r s i n Eq . ( 37 ) u s ing the b iva r i a t eve c to r a u to r e g r e s s ion de sc r ibe d in S e c t ion 2 . I n pa r t i c u la r , no te tha t t he g r ow thr a te o f n o m i n a l G N P d e r i v e d f ro m m o d e l s c a n b e w r i t te n a s d Y t N 'p = u A ( L ; v ) ~+ U M ( L ; V )e M , , w h e r e u A ( L ; v ) an d U M ( L ; v ) a r e r at io s o f po lynom ia l s i n t helag opera tor , L , and v i s the vec tor of pa ram ete r s in Eq . (3 7) . Bes ides , the es -t i m a t e d g r o w t h r at e o f n o m i n a l G N P c a n b e w r it te n a s A Y N 'e = e A ( L ; f ) A Y t p+ e M ( L ; f ) ~ M , t , w h e r e e A ( L ; f ) a n d e M ( L ; 6 ) a r e ra t io s o f po lyno m ia l s i n t hel ag ope r a to r a nd 1) i s t he v e c to r o f e s t ima te d c oe f f ic i e n t s o f t he ve c to r a u -t o r e g r e s s i o n i n S e c t i o n 2 . A n e n d o g e n o u s m o n e y s u p p l y p r o c e s s t h e n c a n b ee s t ima te d by c a l c u la t ing a ve c to r v to so lve the f o l low ing e qua t ions f o r v ,g i v e n L :

u A ( L ; v ) = e A ( L ; ~ ) an d u ~ ( L ; v ) = e M ( L ; ~ ). ( 3 8 )Th i s imp l i e s t ha t t he e nd oge no us m on e y supp ly p r oc e s s 7 i s c a l c u la te d by se t ti ngt h e m o d e l ' s i m p u l s e r e sp o n s e f u n c t i o n o f n o m i n a l G N P t o e q u a l t h e e s ti m a t e di m p u l s e r e s p o n s e f u n c t io n o f n o m i n a l G N P .4 .2 . N u m e r i c a l r e s u l t s

This s e c t ion p r e se n t s some qua n t i t a t ive p r ope r t i e s de r ive d f r om nume r i c a lso lu t ions f o r the m ode l e c ono m ie s de sc r ibe d in S e c t ion 3.

F igs . 2 a nd 3 sho w impu l se r e spon se s o f ou tpu t a nd in fl a tion in f le x ib l e a nds t i c k y p r i c e m o d e l s w i t h e x o g e n o u s m o n e y s u p p l y r e s p e c t i v e l y . F i g . 2 d e m o n -s t ra t es t he sm a l l e f f e ct o f a m one ta r y shoc k on ou tpu t i n t he f l e x ib l e p r i c e mo de l ,w he r e a s in F ig . 3 , w i th s t i c ky p r i c e s , a n e xoge nous e xpa ns ion in the mone y sup -p ly l e a ds to a g r a dua l i nc r e a se in the p r i c e l e ve l a nd a t e mpor a r y inc r e a se inou tpu t. B e s ide s , i n bo th F igs . 2 a nd 3 , a pos i ti ve t e c hno logy shoc k induc e s g r a d -ua l de c r e a se s in t he p r i c e l e ve l t o a l ong - r un l e ve l w h i l e i t a l so inc r e a se s ou tpu tin the long r un . H e nc e , w he n the pe r ma ne n t shoc k in S e c t ion 2 c o r r e sponds toa n e x o g e n o u s l a b o r -a u g m e n t i n g t e c h n o l o g y s h o c k a n d t h e t e m p o r a r y s h o c k c o r r e -sponds to a n e xog e nou s c ha nge in the g r ow th r a te o f m on e y supp ly , the se f igu re s

7 T h e i m p u l s e r e s p o n s e s o f t h e e n d o g e n o u s m o n e y s u p p l y p r o c e s s e s f o r f le x i b le a n d s t i c k y p r ic em o d e l s a r e p r e s e n t e d in F i g . 4 . T e c h n i c a l a p p e n d i x o n t h e c a l c u l a ti o n o f t h e e n d o g e n o u s m o n e ys u p p l y p r o c e s s e s i s a v a i l a b l e f r o m t h e a u t h o r u p o n r e q u e s t .


17/26

T . Y u n / J o u r n a l o f M o n e t a r y E c o n o m ic s 3 7 ( 1 9 9 6 ) 3 4 5 - 3 7 0 361

0,020 . 015

0,010,005

0

-0 .005

Growth of Nominal GNP(Technology) Gro~(h o f Nominal GNP(Mone y)0.02

0.0150.01

0.0050

-0.0050 5 10 15 20 0 5 10 15

0.03

0.02

0,01

0

-0.01

0.O05

0

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GNP(Technology) ONP(Money)

0 5 1 0 1 5 2 0 5 1 0 t 5

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0.00(12O.OOO15

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0 . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . .5 1 0 1 5 2 0 0 5 t 0 1 5F i g . 2 . F l e x ib l e p r ic e m o d e l w i t h e x o g e n o u s m o n e y s u p p ly .

20

2 0

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18/26

3 6 2 T . Y u n / Jo u r n a l f M o n e ta r y c o n o m ic s 7 ( 1 9 9 6 )3 4 5 - 3 7 0Gro wth o f Nominal GNP(Technology)

O.O20.015 f ~

o . o t ' ~G ~ l i

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0.005

0

.0 .005

-0.01

Inf lat ion(Money I

5 1 0 1 5 20

0-0.01

-0.02-0.03.0.04

Pdce(Techndowl0 . ~

GO2

0.01

00 5 10 15 20

Pdce(Money)

~_ _ . . _ _ . . ~ y . 7 . . . . . . . . . . .

5 10 15 Z O

, a : 0 . 2 6 - - - - - - a : 0 . 6 . . . . . a R 0. ?6 [

F i g . 3. N o m i n a l p r ic e r ig i d i t y m o d e l w i t h e x o g e n o u s m o n e y s u p p l y .


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T. Yun/Journal o f Monetary Economics 37 (1996) 345-370 363im ply tha t s t i c ky p r i c e m ode l s f i t t he e m pi r i c a l e v ide nc e p r e se n te d in S e c t ion 2be t te r than f lex ib le pr ice mo de ls . In par t icu la r , the d i f fe rence be tw een f lexib lea nd s t i c ky p r i c e m o de l s in t e r m s o f the r e a l e f fe c t o f m on e y sup p ly shoc ks i sa s soc ia t e d wi th the r e sponse o f the l a bor de m a n d sc he du le to a m on e ta r y shoc kin s t i c ky p r ic e m o de l s . Th e s lugg i sh p r i c e a d jus tm e n t o f the type c ons id e r e d he r ec a use s pos i t ive va r i a tions o f r e a l m a r g ina l c os t i n r e sponse to a pos i t ive m o ne ta r yshoc k . The y sh i f t up the l a bor de m a nd c u r ve in the in i t i a l pe r iod g ive n p r e de te r -m ine d c a p i t a l , a nd the n r a i se ou tpu t by s t im u la t ing e qu i l ib r ium e m ploym e n t . No tehe r e tha t t o a c h ie ve a n inc r e a se in bo th r e a l wa ge a nd e m ploym e n t invo lve s ar e l a t ive ly we a ke r w e a l th e f f e c t t o the e x te n t tha t t he sh i f t - up o f the l a bor supp lyc ur ve induc e d b y the we a l th e f f e c t doe s n o t o f f se t t he va r i a t ion o f l abor de m a nddue to the m a r g ina l c os t . I n a dd i t ion , t he m a r g ina l c os t be c om e s m or e va r i -able as no m ina l p r ice r ig id i ty r ises . F ig . 3 a lso show s tha t the in i t ia l e f fec t o f at e c hn o log y shoc k on o u tpu t de c r e a se s a s the de g r e e o f nom ina l r ig id i ty inc re a se s .A r e a son f o r i t is t ha t t e c hno log ic a l im pr o ve m e n t s de c r e a se m a r g ina l c os t , so the sene ga t ive m o ve m e n t s o f m a r g ina l c os t o f fse t i nc r e a se s in e qu i l ib r ium e m p loym e n tdue to pos i t ive t e c hno logy shoc ks . M or e ove r , t he m a g n i tude o f th is a dve r se e f f e c tinc r e ase s a s the d e g r e e o f nom ina l p r i c e r ig id i ty g r ows .

F ur the r m o r e , F ig . 4 p r e se n t s the im pu l se r e sponse s o f the e ndoge nous m on e ysupp ly p r oc e sse s in bo th f l e x ib le a nd s t i c ky p r i c e m ode l s tha t a r e c a l c u la t e d a sde sc r ibe d in S e c t ion 4 .1 . G ive n the se e ndoge nous m one y supp ly p r oc e sse s , F igs .5 a nd 6 r e spe c t ive ly d i sp la y the im pu l se r e spon se s o f ou tpu t a nd in f la t ion inf l e x ib le a nd s t i c ky p r i c e m ode l s . The in t r oduc t ion o f e ndoge ne i ty in the m one ysupp ly b y i t s e l f doe s no t m a ke a s ign if i ca n t d if f e re nc e in t e r m s o f the r e a l e f f e c to f a m o ne ta r y shoc k in f l e x ib le a nd s t i c ky p r i c e m ode l s , a s F igs . 5 a nd 6 a r ecompared wi th F igs . 2 and 3 , respec t ive ly . Bes ides , in F igs . 5 and 6 , a pos i -t ive t e c hno logy shoc k induc e s g r a dua l de c r e a se s in the p r i c e l e ve l t o a long- r unleve l whi le i t a l so inc reases output in the long run . Hence these f igures implytha t , e ve n wi th the e ndoge nous m one y supp ly p r oc e sse s in F ig . 4 , s t i c ky p r i c em o de l s f it the e m pi r i c a l e v ide n c e p r e se n te d in S e c t ion 2 be t t e r tha n f l e x ib le p r i c em o d e l s .The s t a nda rd de v ia t ions o f ou tpu t m e a su r e s a nd in fl a tion in num e r ic a l m ode l sa r e r e por t e d in T a b le 3 in wh ic h the s t a ndar d de v ia t ion o f the d i f f e r enc e d t r e ndc om pone n t o f log ou tpu t in m ode l e c onom ie s i s s e t t o e qua l the e s t im a te d one .Ta b le 3 a l so show s sm a l l e f fe c t s o f m on e ta r y shoc ks in f le x ib le p r i c e m ode l swi th e xoge nous a nd e ndoge nous m one y supp ly . A l so , a n inc r e a se in nom ina lp r i c e r ig id i ty l e ads to l a r ge r st a nda r d de v ia t ions o f ou tpu t m e a su r e s bu t l e s svo la t i le in f la t ion . Th e d yna m ic c o r r e l a t ions o f in f l at ion a nd ou tpu t m e a su r e s a r ethe n r e por t e d in Ta b le s 4 a nd 5 . Ac c or d ing to the se t a b le s , w i th s t i c ky p r i c e s ,the r a t e o f in f la t ion i s pos i t ive ly c o r re l a t e d wi th two m e a sur e s o f s t a t iona r y c om -pone n t s o f ou tpu t ( log Y7 a nd log Yy) bu t ne ga t ive ly wi th two m e a sur e s o fou tpu t c on ta in ing pe r m a ne n t shoc ks ( log Ytp a nd log Yt r ). On the o the r ha nd ,f l e x ib le p r i c e m ode l s d i sp la y ne ga t ive c r oss - c o r r e l a t ions o f in f l a t ion wi th the


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364 7~ Yun/Journal of Monetary Economics 37 (1996) 345-370

0,003

0.001-GO01-0.003-GO05-0.007

F l e x i b le P r i c e ( T e c h n o l o g y )

/. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , , i , i ,

0 5 10 15 20

0 .020 . 0 / 5

0 . 0 /0.0O5

0

- 0 . 0 0 5

F l e x ib l e P r i c e ( M o n e y )

. . . . . . . . . . . . . . . . . . . . . . . . . . , i , l |0 5 1 0 1 5 2 0

Nom inal RJgidity~echnoiocjy:.a = 0.25)

0 O O 3

000'1-0.00/..0.01~-O.O05-O.a07

0

f

5 10 15 20

0.020,015

0.010,005

0- 0 . 0 0 5

N o m i n a l R i g i d i t y ( M o n e y : a = 0 .2 5 )

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , = , l ,5 10 15 20

0,0030.001

-0.001-0.003-0,005-0,007

0 .02

N o m i n a l R i g i d i t y ( T e c h n o l o g y : a = 0 . 5)

5 10 15 20N o m i n a l R i g i d i t y ( T e c h n o l g y : a = 0 . 7 5)

0.020,015

0,010.005

0.0,005

0 .02

N o m i n a l R i g i d i t y ( M o n e y : a = 0 .6 )

5 10 15N o m i n a l R i g i d i t y ( M o n e y : a = 0 . 7 5)

20

0.015O,01

O.OO5

..0.005 0 5 10 15

0,015O.01

O.OO50

-O,OO520

h , ,

. . . . . . . . . . . . . i , , , i , , , i , , ,5 10 15 20

Fig. 4. Impulse responses of money supply growth rate in endogenous money supply models.


21/26

T. Yun/Journal of Monetary Economics 37 (1996) 345-370 365Growth of Nominal GNP(Technology)

0.02 0.02G r o w t h o f N o m in a l G N l~ M o n e y )

~ 0 1 5~ 0 1

~ 0 0 50

.GO050 5 10 15 20

0.015

0.010.005

0-0 .005

0 5 1 0 1 5 2 0

0.03

0.02

0 . 0 t

0

-0 .0 /

GNP(Technology)

0 5 10 15 20

0.00020,00015

0.00010.00005

0-0.00005

-0.0001

GNP(Money)

f | , | , | , r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0 5 1 0 1 5 2 0

0.005Inf lat ion(Technology)

0,015I n f la t ion(Money)

0-GO05

-GO/- G 0 / 5

5 1 0 1 5 2 0

0.010.005

0-0 .005

-0.015 1 0 1 5 2 0

0-0.01-0.02-0.03-0.04

Pr i c e ( Te c h n o lo g y ) P r i c e ( M o n e y )

0 5 10 15 20

0,03

0.02

0.01

5 10 15 20

F i g . 5 . F l e x i b l e p r i c e m o d e l w i t h e n d o g e n o u s m o n e y s u p p l y .


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366 T. Yun/Journal o f Monetary Economics 37 (1996) 345-370Grow th olr Nom inal GN P(Technology)

0.020 . 0 1 5

O.01GO05

o ~-~..~-0,005 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0 5 t 0 1 5 2 0

0.0;r0.015

0.0t0.005

0-0.006

Growth of Nominal GNP(Money)

0 5 1 0 1 5 2 0

0.03GNP(Technology)

0.O20.0/

0

-GO/ 0 5 1 0 1 5 2 0

ONP(Money}O.O25

G 0 t 5

O.O05.0.005

0

. * - .

5 1 0 1 5 2 0

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.-G006-GO/

-0.0/5

Inflation(Technology)

5 1 0 1 5 20Pflce(Techndogy)

.0,01

.0.02 I

..0.O3-0.04

0

0.0f$0.0f

0.0050

-0,006-GO/

inflation(Money)

GO9

5 1 0 1 5 2 0Prk : (M oney )

GO2

G O t I o

5 1 0 1 5 2 0 0 $ t 0 1 5 2 0

I a = 0 . 2 5 - - a - 0 . 7 6 JF i g . 6 . N o m i n a l p r i c e r i g i d i t y m o d e ] w i t h e n d o g e n o u s m o n e y s u p p l y .


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7~ Y u n / J o u r n a l o f M o n e t a r y E c o n om i c s 3 7 ( 1 9 9 6 ) 3 4 5 0 7 0T a b l e 3S tan d ard d ev iat ion s of inflation and output m e a s u r e s

367

Pane l 1 . Exogenous money supp lyPercen tage (q u arter ) A log Y A log YP A log Yr log ys log y dExogenous money

a n d c~ : 0 0.927 1.595 0.927 2.374 0.004 1.459Exogenous money

a n d c~ : 0.25 0.878 1.595 0.852 2.435 0.224 1.440Exogenous money

a n d ~ = 0.5 1.105 1.595 0.657 2.764 0.922 1.379Exogenous money

a n d ~ = 0.75 3.873 1.595 1.523 5.186 3.628 1.135

Pane l 2 . Endogenous mon ey supp lyP e r c e n t a g e ( q u a r t e r ) A log Y A log Y P A log y r log ys log y aEndogenous money

a n d c~ = 0 0.928 1.595 0.928 2.374 0.005 1.573Endogenous money

a n d ~ = 0.25 0.832 1.595 0.820 2.450 0.198 1.440Endogenous money

a n d c~ : 0.5 0.756 1.595 0.620 2.750 0.708 1.180Endogenous money

a n d ~ = 0.75 0.905 1.595 0.425 3.723 1.835 0.847Y: real output, r~: rate of inflation, YP: trend component of real output, Y~: stationary component ofreal output, yr: component of real output that is affected by only p e r m a n e n t s h o c k s , yd : componentof real output th at i s a f fec ted by only tran s i tory sh ock s .

c o m p o n e n t o f G N P o n l y w i t h t e m p o r a r y s h o c k s ( l og Y / ) fo r some l ags o r l eads o finflat ion.

5 . C o n c l u s i o nT h i s p a p e r h a s c o n s i d e r e d w h e t h e r n o m i n a l p r i c e r i g i d i t y i s c o n s i s t e n t w i t h t h e

p o s i t iv e c o - m o v e m e n t o f i n fl a ti o n a n d o u t p u t o b s e r v e d i n t h e U . S . e c o n o m y . T h ev a r i o u s k i n d s o f c r i t e r i a u s e d h e r e f o r t h i s p u r p o s e l e a d o n e t o c o n c l u d e t h a tn o m i n a l p r i c e r ig i d i ty m o d e l s c a n p r o v i d e a b e tt e r u n d e r s t a n d i n g o f t h e o b s e r v e da s s o c i a t i o n s b e t w e e n o u t p u t a n d i n fl a ti o n t h a n f l ex i b l e p r ic e m o d e l s . H o w e v e r , i ts h o u l d b e n o t e d t h a t t h i s c o n c l u s i o n d e p e n d s c r i t ic a l ly o n t h e d e g r e e o f n o m i n a lp r i c e r i g i d i t y .

F u r t h er m o r e , t h e q u a n t i t a ti v e r es u lt s i n t h i s p a p e r d o n o t m e a n t h a t m o n e ys u p p l y s h o c k s a re th e o n l y n o m i n a l d i s t u r b a n c es t h a t m a tt er . F o r e x a m p l e , w h e nt h e m o n e t a r y a u th o r i t y a c c o m m o d a t e s f lu c t u a t io n s i n a g g r e g a t e m o n e y d e m a n d ,a g g r e g a t e d e m a n d d i s t u r b a n c e s a f f e c t i n g t h e m o n e y d e m a n d c a n b e p r o p a g a t e d


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368 T Yu n/Jo urna l o f Monetary Economics 37 (1996) 345 370Tab le 4Cross-correlat ions of inflat ion an d output measures w ith exog enou s m one y supply

- 3 - 2 - 1 0 1 2 3Panel 1. Exogenous money and flexible priceco r( ff t+ j, A log l (t ) -0 .01 9 -0 .02 0 -0 .0 31 0 .378 -0 .0 35 -0 .03 4 -0 .0 33co r( r~ t+ j, A log Y t ) 0 0 0 -0 .37 8 -0 .03 3 -0 .03 5 -0 .02 4cor(fft+j, A log Y [) - 0 . 0 1 7 - 0 . 0 2 1 - 0 . 0 3 2 - 0 . 3 7 8 - 0 . 0 3 5 - 0 . 0 3 4 - 0 . 0 3 3co r(~ t+j , log Yt ) 0.172 0.179 0.187 0.199 0.098 0.094 0.091cor(fft+j, log Yt ) 0.274 0.223 0.134 -0 .0 0 8 0.022 0.013 0.008Panel 2. Exogenous mon ey and c~ = 0.2 5cor(t+j, A lo g Yt) - 0 . 0 4 2 - 0 . 0 7 3 - 0 . 1 6 8 - 0 . 2 0 9 - 0 . 0 1 2 - 0 . 0 2 1 - 0 . 0 2 6cor(fft+j, A log Ytp ) 0 0 0 - 0 . 3 7 1 - 0 . 0 2 5 - 0 . 0 2 5 - 0 . 0 2 5cor(t+j, A lo g Y [) - 0 . 0 2 1 - 0 . 0 3 0 - 0 . 0 6 0 - 0 . 3 7 9 - 0 . 0 3 8 - 0 . 0 3 8 - 0 . 0 3 7cor(r?t+j, log Yt ) 0.187 0.212 0.228 0.289 0.122 0.109 0.104cor(~t+j , log Yff ) 0.183 0.266 0.440 0.870 0.248 0.150 0.091Panel 3. Exogenous money and c~ = 0.5cor(r~t+j , A log Yt) -0 .09 1 -0 .1 87 -0 .4 77 0 .306 0 .053 0 .021 -0 .0 01cor(r~t+j, A log Y f ) 0 0 0 - 0 . 3 7 4 - 0 . 0 2 5 - 0 . 0 2 6 - 0 . 0 2 6cor(fft+j, A log Y [) - 0 . 0 3 6 - 0 . 0 6 9 - 0 . 1 9 1 - 0 . 3 5 1 - 0 . 0 5 0 - 0 . 0 5 1 - 0 . 0 4 9cor(~t+j , log YT) 0.220 0.256 0.363 0.522 0.184 0.148 0.125cor(~t+j , log Yff) 0.181 0.264 0.439 0.876 0.259 0.159 0.098Panel 4. Exogenous money and ~ = 0.75cor(r~t+j, A log l~ t ) -0 .0 88 -0 .1 96 -0 .5 53 0 .601 0 .093 0 .055 0 .031cor(r~t+j, A log Ytp ) 0 0 0 - 0 . 3 7 0 - 0 . 0 2 5 - 0 . 0 3 2 - 0 . 0 3 3c or (r ~t+ j, A l o g Y ~) - 0 . 0 3 1 - 0 . 0 8 8 - 0 . 3 2 3 0 .1 50 - 0 . 3 0 5 - 0 . 0 2 7 - 0 . 0 2 6co r(~ t+j , log YT) 0.243 0.308 0.455 0.867 0.305 0.228 0.177cor(fft+j, log Yff) 0.187 0.267 0.440 0.894 0.316 0.228 0.133Y: real output, 7~: rate of inflation, YP: t rend component of rea l ou tput , ys : s t a ti ona ry com ponen t o freal output, yr : component of rea l ou tput tha t i s a ffec ted by only permanent shocks, ya : c o m p o n e n tof real output that is affected by only transi tory shocks.

t h r o u g h t h i s k i n d o f a c c o m m o d a t i o n . H o w e v e r , t h e i n c o r p o r a t i o n o f t h e s e k i n d s o fd e m a n d d i s t u r b a n c e s i n to a m o d e l r e q u i r e s m o r e d e v e l o p e d i d e n t i f ic a t i o n s c h e m e sf o r t h e v a r i o u s p o s s i b l e n o m i n a l d i s t u r b a n c e s i n o r d e r to e s t i m a t e a n e n d o g e -n o u s m o n e y s u p p l y d e c i s i o n r u l e r e s p o n d i n g t o t h e s e d i s tu r b a n c e s . T h u s ,d e v e l o p i n g m o d e l s w i t h n o m i n a l d i s t u r b a n c e s o th e r t h a n m o n e y s u p p l ys h o c k s a s w e l l a s s u c h i d e n t i f i c a t i o n s c h e m e s m a y b e f u t u re r e s e a r c hs u b j e c t s .


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T . Y u n / J o u r n a l o f M o n e t a r y E c o n o m ic s 3 7 ( 1 9 9 6 ) 3 4 5 3 7 0Tab l e 5C r o s s - c o r r e la t i o n s o f i n f la t io n a n d o u t p u t m e a s u r e s w i t h e n d o g e n o u s m o n e y s u p p l y

36 9

P a n e l l . E n d o g e n o u s m o n e y a n d f l e x i b l e p ri c ec or( r~ t+ j, A l o g Y t) - 0 . 0 2 0 - 0 . 0 2 4 - 0 . 0 4 1 - 0 . 5 8 6 - 0 . 0 4 1 - 0 . 0 2 5 - 0 . 0 2 2c o r ( f ft + j , A l o g Y t ) 0 0 0 - 0 . 5 8 2 - 0 . 0 3 6 0 . 02 0 - 0 . 0 1 6c o r ( ~ t + j , A l o g Y [ ) - -0 .0 2 0 - 0 . 0 2 5 - - 0 .0 4 2 - 0 . 5 8 6 - 0 . 0 4 2 - 0 . 0 2 5 - 0 . 0 2 1co r (~ t + j , l o g ]I7) 0.193 0 .200 0 .210 0 .226 0 .063 0 .055 0 .052c o r ( ~ t + j , l o g Yt ) 0 .3 25 0 .2 28 0 . 11 5 - - 0 . 0 2 7 - 0 . 0 4 4 - 0 . 0 6 4 - 0 . 0 4 7P a n e l 2 . E n d o g e n o u s m o n e y a n d ~ - 0.25c or (r~ t+ j, A l o g l it ) - 0 . 0 7 4 - 0 . 0 8 4 - 0 . 1 4 8 - 0 . 4 1 6 - 0 . 0 5 8 - 0 . 0 0 3 - 0 . 0 0 9co r ( f f t + j , A l o g Ytp ) 0 0 0 - 0 . 5 5 3 - 0 . 0 9 9 - 0 . 0 4 0 - 0 . 0 2 4cor (~ t+ j , z ] log Y [ ) - -0 . 0 3 6 - -0 . 0 6 0 - -0 . 1 1 8 - -0 . 5 8 4 0 . 1 1 8 - -0 . 0 6 0 - -0 . 0 3 8cor(r~t+j , log Yt ) 0.240 0.278 0.323 0.395 0.16 0 0.108 0.071cor(7~t+j , log l~ff) 0.198 0.397 0.578 0.787 0.471 0.29 6 0.092P a n e l 3. E n d o g e n o u s m o n e y a n d ~ - 0.5co r ( f f t + j , A lo g Y t) - 0 . 2 4 3 - 0 . 4 5 1 - 0 . 3 2 1 0 .1 95 0 .0 02 0 .0 9 3 0 . 05 8cor(r?t+j, A log YI ) 0 0 0 - 0 . 4 6 2 - -0 .1 9 2 - 0 . 1 0 1 - 0 . 0 6 0cor(r?t+j, A lo g Y [ ) - 0 . 0 8 2 - 0 . 1 3 0 0 .3 12 - 0 . 5 2 0 - 0 . 2 3 4 5 - 0 . 1 3 2 - 0 . 0 8 5cor(r?t+j , log Yt ) 0.317 0.384 0.453 0.81 6 0.327 0.215 0.131co r (~ t + j , l o g Yf f ) 0.335 0 .523 0 .677 0 .816 0 .569 0 .361 0 .146

Pa n e l 4 . En d o g en o u s mo n ey a n d c~ - 0.75cor(Tft+j , A log Y t ) - 0 . 3 9 7 - 0 . 3 3 9 - 0 . 2 8 5 - 0 . 0 5 8 0 .1 9 7 0 .2 3 0 0 .1 6 4co r( r~ t+ j, A l o g Y t ) 0 0 0 -0 . 2 8 6 -0 . 2 9 8 - -0 . 1 4 3 0 . 1 5 8cor(Tft+j , A log Y [ ) - 0 . 2 2 6 - 0 . 2 7 3 - 0 . 3 8 3 - - 0 .5 0 0 0 .3 8 8 - - 0 .2 7 7 - 0 . 2 3 2co r (~ t + j , l o g Y T ) 0.529 0 .626 0.708 0 .778 0 .641 0 .465 0 .349cor(r~ t+/ , log Yt ) 0 .518 0 .662 0 .766 0 .818 0 .671 0 .486 0 .308Y: real output , r?: rate of inflat ion, Y P : t r e n d c o m p o n e n t o f r e a l o u tp u t , ys: s t a t i o n a r y c o m p o n e n t o freal ou tput , y r : c o m p o n e n t o f r e al o u t p u t t h a t i s a f fe c t e d b y o n l y p e r m a n e n t s h o c k s , y a : c o m p o n e n to f r ea l o u t p u t t h a t i s a f f ec t ed b y o n l y t r an s i t o ry s h o ck s .

R e f e r e n c e s

B as u , S u s an t o an d J . G . F e rn a l d , 1 9 9 3 , C o n s t an t r e t u rn s an d s m a l l m ark u p s i n U . S . m an u fac t u r i n g ,M i m e o . ( U n i v e r s i t y o f M i c h i g a n , A n n A r b o r , M I ) .

B e v e r i d g e , S . a n d C . N e l s o n , 1 9 81 , A n e w a p p r o a c h t o d e c o m p o s i t i o n o f e c o n o m i c ti m e s e r ie s i n top e r m a n e n t a n d t r a n si to r y c o m p o n e n t w i t h p a r t ic u l a r a t te n t io n t o m e a s u r e m e n t o f t h e b u s i n e s s c y c l e ,J o u m a l o f M o n e t a r y E c o n o m i c s 7 , 15 1 1 7 4 .

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