Hysteresis Us Germ

8/3/2019 Hysteresis Us Germ

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em pec (1990) 1 5 :18 5-19 8

T e s t i n g f o r H y s t e r e s i s i n U n e m p l o y m e n tA n U n o b s e rv e d C o m p o n e n t s A p p r o a c h 1B y A . J a e g e r 2 a nd M . P a r k i n s o n 3

Abstract: W e s ugges t a new tes t fo r hys te res i s in unem ploym en t bas ed on an unobs erved com po-nents m ode l . Obs erved une m plo ym e n t r a tes a r e decom pos ed in to a na tu ra l r a te com pone n t and acyc l ica l com p onen t . T he im pac t o f l agged cyc l ica l s hocks on the cu r ren t na tu ra l com pon en t i s them eas ure o f hys te resi s . T o iden t i fy the two com ponen ts o f unem ploym en t , we as s um e tha t the cyc-l i cal com poen tn i s co r re la ted w i th capa c i ty u t i li za t ion . T he m od e l i s app l ied to U . S . and Germ and a t a . W e f i n d n o e v i d e n c e o f h y s t e r e s i s i n U . S . d a t a . G e r m a n u n e m p l o y m e n t r a t e s e x h i b i ts ubs tan t ia l hys te res i s . A s hock o f 1 . 0 pe rcen t to the cu r ren t cy c l ica l com ponen t pe rm an en t ly in -c reas es fu tu re Germ an na tu ra l r a tes by abou t 0 . 5 pe rcen t . Fo r bo th cou n t r i es , na tu ra l r a te s hocksturn ou t to be an im por tan t im pu ls e m ech an is m to exp la in m ovem en ts in obs erved unem ploym en trates.

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

O v e r th e l a s t 15 y e a rs , h i g h a n d p e r s i s t e n t u n e m p l o y m e n t h a s s u r f a c e d a s t h e m a j o rm a c r o e c o n o m i c p r o b l e m i n m a n y E u r o p e a n e c o n o m i e s ( in p a r t i c u l a r i n G e r m a n y ,F r a n c e , I t a ly a n d th e U n i t e d K i n g d o m ) a s w e l l a s i n A u s t r a l i a a n d C a n a d a . I nc o n t r a s t , th e U . S . h a s e x p e r i e n c e d l a r g e s w i n g s i n it s u n e m p l o y m e n t r a te w i t h a na p p a r e n t t e n d e n c y o f o b s e r v e d u n e m p l o y m e n t t o m o v e b a c k t o w a r d s o m e r e l a t i v e l ys t ab l e u n d e r l y i n g r a t e . B y w a y o f f u r t h e r c o n t r as t , J a p a n a n d s o m e E u r o p e a n e c o -n o m i e s , n o t a b l y A u s t r i a , N o r w a y , S w e d e n , a n d S w i t z e r l a n d , h a v e e n j o y e d b a s i -c a l l y s t a b le u n e m p l o y m e n t r a te s o v e r t h e s a m e t i m e p e r i o d . E x p l a i n i n g t h i s d iv e r -

1 W e w o u l d l i k e to t h a n k B e n B e r n a n k e, J o h n C a m p b e l l , W h i t n e y N e w e y , P i e r r e P e r ro n , M a r kSchankerm an , and two anonym ous r e fe rees fo r he lp fu l com m ents . A l l r em ain ing e r ro r s a r e ou rown . T he f i r s t au tho r acknow ledges f inanc ia l s uppor t by the E rwin Sc hroed inger Founda t ion andthe s econd au thor by the Aus t r a l i an T reas u ry . T he v iew s expres s ed here in a re ou r own and s ho u ldno t be a t t r ibu ted to the s pons or ing bod ies .2 A lber t J aeger, In s t i tu te fo r Advan ced S tud ies , S tum pergas s e 56 , A-106 0 Vienna , Aus t r i a .3 Mar t in Park inson , Depar tm e n t o f E conom ics , P r ince ton Univer s i ty , P r ince ton , NJ 08540 , USA ,and Aus t r a l i an T reas u ry , Canber ra , AC T 2600 , Aus t r a l i a .

0377-7332 /90 /2 /185-198 $2 . 50 9 1990 Phys ica -Ver lag Heide lberg


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186 A. Jaeg er and M. Parkinson

s it y o f e x p e r i e n c e h a s p u t m a c r o e c o n o m i c t h e o r y t o a s e v e r e t es t, a n d s e v e r a l c o m -m e n t a t o r s h a v e a l r e a d y e x p r e s s e d d o u b t t h a t it h as m e t t h is c h a l l e n g e a d e q u a t e l y(see B l inde r 1988) .As a ma t te r o f t axono m y, s t anda rd theor ies o f unem ploy m ent sugges t tha t h ighobse rv ed unem ploy m ent can be the re su l t o f st ructu ral fac to rs tha t have changed thena tu ra l ra te o f unem ploy m ent o r o f cyc l i ca l fac to rs tha t have t empora r i ly d r iven un-employment above the na tu ra l ra te . The re la t ive ly low and s t ab le in f l a t ion ra te s o ft h e 1 9 8 0 s a r e w i d e l y i n t e r p r e te d a s c a s ti n g d o u b t o n t h e p o s s i b i l it y t h a t c y c l i c a lfac to rs a re re spon s ib le fo r h igh un em ploy m ent ra te s . The p res s ing ques t ion then i s:W h y h a v e n a t u ra l r a t es m o v e d u p s o s h ar p l y i n m a n y c o u n t r i e s o v e r th e la s t 1 5yea rs?

A c c o r d i n g t o o n e i n f l u e n t i a l v i e w , u n e m p l o y m e n t i n c r e a s e d b e c a u s e t h es t ruc tu ra l de te rminan t s o f the na tu ra l ra te changed . B runo and S achs (1985 ) a rguet h a t i n c r e a s e d , , w a g e g a p s " l e d t o u p w a r d p r e s s u r e o n t h e n a t u r a l r a t e i n m a n yc o u n t r i e s d u r i n g t h e 1 9 7 0 s. L a y a r d a n d N i c k e l l ( 1 9 8 6 ) r e p o r t t h a t p a rt o f t h e i n-c rease in Br it i sh u nem ploy m ent can b e t raced to changes in s t ruc tu ra l fac to rs inc lu -d i ng u n e m p l o y m e n t b e n e f i ts , e m p l o y m e n t p r o t e c ti o n l a w s , a n d u n i o n m i li ta n c y .L ind bec k (1985 ) a t t r ibu te s the inc rease in na tu ra l ra te s to the deb i li t a ting e f fe c t s o fi n c r e a s ed g o v e r n m e n t i n t er v e n ti o n . C o e ( 1 9 8 9 ) i n v e s t ig a t e s L i n d b e c k ' s h y p o t h e s i sf o r C a n a d a a n d c o n c l u d e s t h at t h e in c r e a s e d g e n e r o s i t y o f th e u n e m p l o y m e n t i n -su rance sys tem w as a m a jo r cause fo r the r is e in the na tu ral ra te dur ing the 1970s .

T h e m a i n a l t e r n a ti v e h y p o t h e s i s t o t h e s tr u c tu r a l v i e w i s b a s e d o n t h e c o n c e p to f hys te re s i s in the na tu ra l ra te . F i r s t app l i ed in unam bigu ous t e rms to the l abormarke t by Hargreaves Heap (1980) , th i s hypo thes i s pos tu la te s tha t the na tu ra l ra ted e p e n d s o n t h e p r ev i o u s h i st o r y o f u n e m p l o y m e n t . T h r e e m a j o r m e c h a n i s m s f o rt hi s h i s to r y d e p e n d e n c e h a v e b e e n s u g g e s t e d - t h e e r o s io n o f h u m a n c a p i ta l d u e t ou n e m p l o y m e n t , a s h o r t a g e o f p h y s i c a l c a p it a l, a n d s o c a l le d , , in s i d e r - o u ts i d e r "me chan i sms a s soc ia ted wi th and so ca l l ed , , ind ide r -ou t s ide r" m echan i sms a s soc ia -t e d w i t h w a g e d e t e r m i n a t i o n . B l a n c h a r d a n d S u m m e r s ( 1 9 8 6 ) a n d G o r d o n ( 1 9 8 8 )f ind tha t the hys te re s i s hypo thes i s i s we l l suppo r ted fo r s eve ra l European coun t r i e sb y e m p i r i c a l e v i d e n c e f r o m w a g e - p r i c e s y s t e m s . S o m e s u p p o r t in g e v i d e n c e i s a ls or e p o r t e d b y F r a n z ( 1 9 8 7 ) f o r G e r m a n y a n d G r e g o r y ( 1 9 8 6 ) f o r A u s t r a l i a . C o e(1987) repor t s mixed re su l t s in a s tudy o f wage equa t ions fo r 12 OEC D coun t r ie s .

I n t hi s p a p e r w e a d o p t a n u n o b s e r v e d c o m p o n e n t s (UC) a p p r o a c h t o t e st f o rh y s t e re s i s i n u n e m p l o y m e n t . U n o b s e r v e d c o m p o n e n t s m o d e l s h a v e b e e n s u g g e s t e db y W a t s o n a n d E n g l e ( 1 9 8 3 ) a n d H a r v e y a n d T o d d ( 1 9 8 3 ) a s f le x i b l e i n s tr u m e n t sf o r e x t r a c t i n g i n f o r m a t i o n f r o m o b s e r v e d v a r i a b l e s ( e . g . t h e u n e m p l o y m e n t r a t e )r e g a rd i n g t h e p ro p e r t i e s o f u n o b s e r v a b l e v a r i a b l e s ( e. g. t h e n at u r al u n e m p l o y m e n tra te ) . Our app l i ca t ion o f UCm o d e l s t o l a b o r m a r k e t s i s c l o s e ly r e la t e d t o w o r k b yCla rk (198 9) . The bas ic idea in s t a ti s ti ca l t e rms i s to d i s en tang le the nons ta t iona ryn a tu r al r a t e c o m p o n e n t a n d t h e s t a ti o n a ry c y c l i ca l c o m p o n e n t o f u n e m p l o y m e n t b yus ing the in fo rma t ion con ta ined in a va r iab le tha t i s co r re la ted wi th the cyc l i ca l


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Testing for Hysteresis in Unemployment 187

component of unemployment. Preferably, the variable used to achieve the decom-position should be stationary to obviate the need to decompose this variable itselfinto a stationary and nonstationary part. For this reason, we use capacity utilizationto identify the decomposition. Other variables such as Gross National Productcould be used for the decomposition. The difficulty with GNP, however, is that itis itself nonstationary and has first to be decomposed into a stationary and nonsta-tionary component. Regardless of the variable used to achieve the decomposition ofunemployment into its natural and cyclical components, the measure of hysteresisdefined in this paper is given by the impact on the current natural rate of lagged cyc-lical shocks.

We use the UC approach to provide information on the importance ofhysteresis effects relative to structural factors for explaining persistently highunemployment. The UC approach is not a substitute for work that tries to pin downthe economic forces behind the movements in the natural rate, but it can provide aclue on where the search for these forces is most likely to be successful.

In the empirical section of the paper we apply the UC model to seasonallyadjusted quarterly postwar time series on unemployment rates and capacityutilization from the U.S. and Germany, Our results indicate no evidence in favor ofhysteresis for U.S. data. For Germany, the results show that shocks to the cyclicalCOmponent of unemployment have a substantial long term effect on the natural rate.A shock of 1.0 percent to the current cyclical component permanently increasesfuture German natural rates by about 0.5 percent. For both countries, currentshocks to the natural rate turn out to be an important impulse mechanism to explainmovements in observed unemployment rates.

Section 2 Outlines an operational definition of hysteresis in terms ofUnobserved components of unemployment. Section 3 discusses the estimation ofthe UC model. In section 4, we offer a critical appraisal of alternative approaches totesting hysteresis from the viewpoint of the UC approach. Empirical results arepresented in section 5, and section 6 concludes.

2 M e a s u r i n g H y s t e r e s isAssume the unemploy ment rate to be the sum of a cyclical (,,transitory" or,,stationary") component, U~t, and a natural (,,permanent" or ,,nonstationary") com-ponent, UN,

u , = v f + v f . (1 )The cyclical component is assumed to be generated by a stationary process and

to follow an autoregressive process of order two with the suitable s tationarity con-


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188 A. Jaeger and M. Parkinson

di t ions im po sed on the co eff ic ien ts ~bl and ~bl

U tC = ~ l U t C 1 + ~ 2 u t C 1 + E C . (2 )T h e a s s u m p t i o n o f a s e c o n d o r d e r a u t o r e g r e s s i v e r e p r e s e n t a t i o n f o r t h e c y c l i c a lc o m p o n e n t c a n e a s i l y b e r e l a x e d , b u t w e f i n d t h a t s e c o n d o r d e r p r o c e s s e s t y p i c a ll yf i t we l l fo r the unem ploy me nt da ta u sed in th is pape r .

The na tu ra l ra te com pon ent i s a s sum ed to evo lve a sU t N =U ?_ 1 -I-EN +OSL l , (3 )

i .e . a s a r a n d o m w a l k p l u s t h e e f f e c t o f la g g e d s h o c k s t o th e c y c l i c a l c o m p o n e n t o fu n e m p l o y m e n t . T h e c o e f f i c i e n t 0 m e a s u r e s i n p e r c e n t a g e p o i n t s b y h o w m u c h t h ena tura l ra te inc reases in a l l fu tu re pe r iods i f the eco no m y exper ience s a 1 .0 pe rcen tc y c l ic a l s h o c k i n u n e m p l o y m e n t . O u r m e a s u r e o f h y s t e re s i s is a n a l o g o u s t o m e a s u -r e s o f p e r s i st e n c e in G N P ( s e e C a m p b e l l a n d M a n k i w 1 98 7) .

Pe rm anent and cyc l ica l shocks a re a s sum ed to be unco r re la ted a t a ll l eads andlags. The p rese nce o f the cyc l ica l shock lagg ed on ce in (3 ) cap tures the no t ion tha thys te res i s occu rs i f the na tu ra l ra te i s depend en t on the h i s to ry o f cyc l i ca l shocks .As a spec ia l case , the na tu ra l ra te component may be cons tan t (va r iance (e~ t ) = 0and 0 = 0 ) . By ru l ing ou t a d r i f t t e rm in (3 ), w e a p r io r i exc lude the po ss ib i l i ty tha tune mp loym ent fo l low s a de te rmin i s t i c t rend . A fu r the r re s tr i c tion im posed b y (3 ) isthat perm ane nt sho cks , e~vt, incre ase the c urren t an d a l l future n atura l ra tes b y ex-ac t ly the am ount o f the cur ren t shock . I t shou ld be kep t in mind tha t these a s sum p-t io n s w i l l g i v e o n e p o s s i b l e d e c o m p o s i t i o n o f u n e m p l o y m e n t i n it s p e r m a n e n t a n dt r an s i to r y c o m p o n e n t . O t h e r r e s e a rc h e r s m i g h t p r e f e r d i f f e re n t d e c o m p o s i t i o n s o nan a pr ior i bas is (see Qua h 1988).

M e a s u r i n g h y s t e r e s i s b y t h e e f f e c t o f o n c e - l a g g e d c y c l i c a l s h o c k s o n t h ecur ren t na tu ra l ra te may no t cap ture phys ica l and human cap i ta l channe l s caus inghys te res i s adequa te ly i f the re a re long t ime lags invo lved be fo re hum an or phys ica lcap i ta l decays . In p r inc ip le , the mo de l c ou ld be gene ra l ized by inc lud ing h ighe r l agso f th e c y c l i c a l s h o c k i n ( 3 ) a n d b y i m p o s i n g a d is t r i b u t e d l a g s t r u c tu r e o n t h egenera l i zed m ode l (e .g . a K oy ck lag s truc tu re ) . The m ode l a s adop ted in th i s pape rs h o u l d b e a b l e t o c a p t u r e h y s t e r e s i s e f f e c t s w o r k i n g t h r o u g h i n s i d e r - o u t s i d e rm e c h a n i s m s i n w a g e b a r g a i n i n g ( s e e L i n d b e c k a n d S n o w e r 1 9 8 6 ) . T h e i n s i d e r -o u t s i d e r h y p o t h e s i s a s s e r t s i n i t s m o s t s i m p l i f i e d f o r m t h a t w a g e s a r e s e t b ybarga in ing be tween f i rms and the i r employees ( the ins ide rs ) wi thou t rega rd fo r theu n e m p l o y e d ( t h e o u t si d e rs ) . T h e e m p l o y e d w i s h to e n s u re t o r em a i n e m p l o y e d b u thave no in te res t in ensur ing the em ploy me nt o f the ou t s ide rs . The m a jor impl ica t iono f th e i n s i d e r - o u t si d e r h y p o t h e s i s i s th a t i n r e s p o n s e t o a n a d v e r s e s h o c k w h i c hr e d u c e s e m p l o y m e n t s o m e o f th e p r e v i o u s in s i de r s b e c o m e o u t s id e r s a n d th e n e w ,


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Testing for Hy steresis n Unem ployment 189

S m a l le r , g r o u p o f i n s i d e r s s e t s t h e w a g e t o e n s u r e t h e n e w l o w e r l e v e l o fe m p l o y m e n t . H e n c e a n y g i v e n c y c l i c a l s h o c k t o u n e m p l o y m e n t w i l l a t l e a s t b epart ia l ly permanent , ra is ing next per iod ' s na tura l ra te .

3 E s t im a t i o n o f t h e U n o b s e r v e d C o m p o n e n t s M o d e l

T h e d i s c u s s i o n o f i d e n t i f ic a t i o n o f UC m o d e l s i n W a t s o n ( 1 9 8 6 ) s h o w s t h a t t h esys tem (1) to (3 ) i s no t iden t i f ied beca use the cyc l ica l and the pe rman ent com pon enta re ne i the r pe r fec t ly cor re la ted nor uncor re la ted . Addi t iona l iden t i fy ing in format ionb e a ri n g e i th e r o n t h e c y c l i ca l o r th e p e r m e n e n t c o m p o n e n t o f u n e m p l o y m e n t h a s t obe b rought in to the mode l . We use capac i ty u t i l i za t ion (CUt ) t o p i c k u p t h e m o v e -m e n t s in t h e c y c l i c a l c o m p o n e n t o f u n e m p l o y m e n t . C a p a c i t y u t i li z at io n i s a s s u m e dto be s ta t iona ry , an a s sump t ion tha t wi l l be t e s ted be low , and to be cor re la ted w i ththe cyc lica l com pone nt in unemp loyment .

To es t ima te the m ode l , w e w r i t e it in s t a te space fo rm. The t rans i t ion equa t ionsare se t up as

~ ' , ~ / = ~ ' ~ = / ~ ' , ~ - , / + P , ~ /~ ' ~ - ' / o / ~ ' , ~ - = / / ~ /j o o L F , _ , j L O ~ C j

(4 )

W r i t in g o u t t h e tr a n s it i o n e q u a t i o n s ( 4 ) i n e q u a t i o n f o r m a n d s u b s t i t u t io n s h o w stha t (4 ) is equ iva len t to equa t ions (2 ) and (3 ). The mea surem ent eq ua t ions a re g ivenb y

F " : 70 0 0 1a0 a , / . t~_~ / Lv ,u

L , JT h e s h o c k vt d e n o t e s a m e a s u r e m e n t e r r o r i n t h e e q u a t i o n l i n k i n g c a p a c i t y

u t il iz a ti o n a n d c y c l i c a l u n e m p l o y m e n t . T h e v a r i a n c e - c o v a r i a n c e m a t r ix ( E ) o f t h eth ree shocks i s g iven b y

I; = [ ~ o oo a~ (6 )


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190 A . J aege r and M . P a rk ins on

and the cyc l i ca l com po nen t bu t found th i s type o f co r re l a t ion to be in s ign i f i c an t ino u r e m p i r i c al w o r k w i t h U . S . a n d G e r m a n d a t a . A l l s h o c k s a re a s s u m e d t o b e u n -co r re l a t ed ove r t ime and no rm a l ly d i s t r ibu ted .Th e pa ra m e te r s to be e s t im a ted a re ~b l, ~b2, 0 , a0 , a l , ~ , cr2 , and or2 . W e usethe Ka lm an f i lt e r to ca lcu la te the l ike l ihood fo r obs e rv ing a sam ple o f obse rva t ionso n u n e m p l o y m e n t a n d c a p a c i t y u t il iz a ti o n g i v e n a f ix e d p a r a m e t e r v e c t o r . H a r v e y(1981 , chap te r 4 ) i s a s t r a igh t fo rward gu ide fo r se t t ing up the p red ic t ion and u pda -t in g e q u a t i o n s o f t h e K a l m a n f il te r . T h e l i k e li h o o d i s m a x i m i z e d b y t h e m e t h o d o fs c o r i n g w i t h m o d i f i e d s t e p s i z e s u g g e s t e d i n B e r n d t e t . a l . ( 1 9 7 4 ) . T h e p r o g r a mu s e d f o r e s ti m a t i o n i s w r i tt e n i n G A U S S .

4 Al t e r n a t iv e A p p r o a c h e s fo r T e s t in g Hy s te r e s isT h e U C approa ch p rov id es a u se fu l pe r spec t iv e fo r a c r i ti c a l app ra i sa l o f o the r ap -p roaches fo r t e s t ing hys te re s i s . The U C approa ch sugg es t s tha t a l l t e s ts o f hys te re -s i s mus t a t l e a s t imp l i c i t ly d i sen tang le the cyc l i ca l and na tu ra l componen t in un -e m p l o y m e n t b y u s i n g i n f o r m a t i o n i n v a r i a b l e s th a t m o v e e i t h e r w i th t h e n a tu r a l o rt h e c y c l i c a l c o m p o n e n t . F r o m t h i s p o i n t o f v i e w i t f o l l o w s i m m e d i a t e l y t h a t t h eu n i v a r ia t e p r o p e r t i e s o f th e o b s e r v e d u n e m p l o y m e n t s e ri e s, e .g . t h e p e r s i s t e n c e o fu n e m p l o y m e n t , c a n p r o v i d e n o i n f o rm a t i o n o n t h e e x i s t e n c e o f h y s t e r e s i s e ff e c t s .H i g h p e r s i s t e n c e o f u n e m p l o y m e n t c a n b e d u e e i th e r t o n at u ra l r a t e s h o c k s o rhys te re s i s e f fec t s o r bo th .

M o s t a u t h o r s h a v e t a k e n t h e f o l l o w i n g s t y l i z e d a p p r o a c h f o r t e st in g h y s t e r e s is( see the d i scuss ion o f F ranz 1987 by W yp losz 1987) . A Ph i l l ip s cu rve is pos tu la t ed

= + 3 ( u ? - u t ) , (7 )wh e re r rt and ~ a re the ac tua l and exp ec ted ra t e s o f in f la t ion . O the r va r i ab le s m aybe inc luded w i thou t a f fec t ing the a rgumen t . The na tu ra l r a t e i s a ssumed to be de -t e rmined by

uN = cUt -1 + bZt 9 ( 8 )

T h e v e c t o r Z t con ta ins va r i ab le s exp la in ing sh i f t s in the na tu ra l r a t e due to, ,s t ruc tu ra l f a c to r s" . T he v ec to r o f s t ruc tu ra l f a c to r s , Z , m ay inc lud e chan ges in thec o m p o s i t i o n o f t h e la b o u r f o r c e b y d e m o g r a p h i c a n d s k i l l c a t e g o r y ( w h a t i s c o m -m o n l y r e f e r r e d t o a s , ,m i s m a t c h " ) a n d c a u s e s o f d is t o r ti o n s i n t h e l a b o u r m a r k e ts u c h a s u n e m p l o y m e n t r e p l a c e m e n t r a t i o s , m i n i m u m w a g e s , l a b o u r t a x e s ,employmen t secu r i ty l eg i s l a t ion , and soc ia l obs tac le s to l abour mob i l i ty . In se r t ing


7/14

Testing for Hy steresis in Une mp loym ent 191

(8) in to (7) g ives

rot = r c~ - f l U t + f l c U t _ l + f l b Z , . (9 )T h e h y p o t h e s i s c = 1 i s ta k e n t o r e p r e s e n t t h e c a s e o f a , , h y st e re s i s e c o n o m y " . T od i s c u s s th e p r o p e r t i e s o f th i s t e st i t is u s e f u l t o re w r i t e ( 9 ) w i t h t h e u n e m p l o y m e n tr a te a s the dep end en t va r i ab l e

u t = c u , _ ~ + b Z , + ( 1 / f l ) ( : r - z c ~) ( l o )W e n o t e t h e f o l l o w i n g p r o p e r t ie s o f t h i s a l t e rn a t i v e t es t f o r h y s t e re s i s :F i r s t, t h e h y s t e r e s i s h y p o t h e s i s i s a p o i n t h y p o t h e s i s . I t c o r r e s p o n d s t o t h e e x -

t r e m e h y p o t h e s i s 0 = 1 i n t h e U C a p p ro a c h. P a s t s h o c k s t o c y c l ic a l u n e m p l o y m e n ta r e a s sum ed t o be fu l l y r e f l ec t ed i n the n a t u r a l r a te .

S e c o n d , f r o m e q u a t i o n ( 1 0 ) w e s e e t h a t th e t e s t c = l i s b a s i c a l l y a u n i t r o o tt es t. T h e t e s t d o e s n o t s u p p l y a m e a s u r e o f t h e e c o n o m i c s i g n i f i c a n c e o f h y s t e r e s i s .F r o m t h e li t e ra t u r e o n u n i t r o o ts i n G N P w e k n o w t h a t th e f i n d i n g o f a u n i t r o o t g i -v e s n o i n d i c a t i o n o f t h e e c o n o m i c s i g n i fi c a n c e o f p e r m a n e n t s h o c k s t o G N P ( s eeC a m p b e l l a n d M a n k i w 1 9 87 ).

T h i r d , t h e s t a t i s t ic a l d i s tr i b u t i o n s o f t h e e s t i m a t e s f r o m t h e P h i l l ip s c u r v e a p -p r o ac h a r e p r e s u m a b l y n o n s t a n d a r d . I f w e a s s u m e t h e u n e m p l o y m e n t r a te t o h a v e au n i t r o o t a n d b = 0 , t h e t e s t is b i a s e d a g a i n s t f i n d i n g h y s t e r e s i s s i n c e u n d e r t h e n u l lo f c = 1 t h e c r i ti c a l v a l u e s f o r t h e r e s u l t i n g t e s t s ta t i st i c m u s t b e t a k e n f r o m F u l l e r( 1 9 7 6 ) a n d n o t , a s is u s u a l p r a c t ic e , f r o m t h e s t a n d a r d S t u d e n t - t d i s t r ib u t i o n . F u r -t h e r m o r e , i f t he n a t u r a l r a t e i s in f a c t s h i f t e d b y a v e c t o r o f p r e s u m a b l y n o n s t a -t i o n a r y v a r i a b l e s Z t , i .e . b i s d i f f e r e n t f r o m z e r o , t h e r e l e v a n t d i s t r i b u t i o n s o f t h et e st s ta t is t ic s o f t h e c o e f f i c i e n t s c a n d b m i g h t a l s o b e n o n s t a n d a r d .

F o u r t h , t h e P h i l li p s c u r v e a p p r o a c h w o r k s b y u s i n g , , i n f o r m a t i o n v a r ia b l e s " ,Z t , co r r e l a t ed w i t h t he na t u r a l r a t e . Fa i l ue t o spec i fy Z t cor r e c t l y , o r no t a t a ll a s i nB l a n c h a r d a n d S u m m e r s ( 1 9 8 6 ) , w i ll l e a d to f i n d i n g h y s t e r e s i s b y d e f a u l t i f u n -e m p l o y m e n t h a s a u n i t ro o t. I f Z t i s c o r r e c tl y s p e c i f i e d , h o w e v e r , t h e P h i l l i p s c u r v ea p p r o a c h c o u l d i n p r i n c i p le p r o v i d e t h e r e l e v a n t i n f o r m a t i o n f o r e c o n o m i c p o l i c y o nw h a t a c t u a l l y m o v e d t h e n a t u r a l r at e.

5 E m p i r i ca l R esu l t sT h e e m p i r i c a l a n a l y s i s u s e s s e a s o n a l l y a d j u s te d , q u a r t e r l y d a t a f o r th e U . S . a n dG e r m a n y . T h e s a m p l e p e r i o d f o r t h e U . S . d a t a is 1 9 5 4 . 1 t o 1 9 8 9 . 1 . D a t a f o r t h eu n e m p l o y m e n t ra t e a r e f r o m v a r i o u s i ss u e s o f t h e B u r e a u o f L a b o r S t a ti st ic s B u l l e -t in . D a t a on capa c i t y u t i l iza t i on a re t aken f ro m va r i ou s i s sues o f the Fed e ra l R ese rve


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Test ing for Hysteresi s in Un em ploym ent 193

T a b l e I . Augm ented Dickey-Fuller (ADF ) tests fo r unit rootsaA . ) U . S . D a t a : 1 9 5 4 . 1 - 1 9 8 9 . 1

U n e m p l o y m e n t R a t e

A U t - . 2 4 - . 0 4 U + 7 8 A U _ . - . 2 2 A U . ^(. ii ) (.o2~ -I i.os) =-~ (.o9) ~-~R 2 - . 4 6 A D F - - 2 . 4 3

C a p a c i t y U t i l i z a t i o n

A C U t - 9 . 2 2 -( 2 , 8 9 )

R 2 - .3 4

B .

U n e m p l o y m e n t R a t e

. I I C U _ . + . 5 g * c u - . 2 7 A C U ( . 0 4 ) ~ - ~ ( . 0 8 ) t - i ( . I 0 ) t - 2

t . 2 6 A C U _ ~ - 1 7 A C U _ .~ ' ~ i . 0 9 ) = - 4.og)A D F = - 3 . 2 1

G e r m a n D a t a : 1 9 6 2 . 1 - 1 9 8 9 .1

* U t = . 0 4 - . 0 0 8 U + " 8 2 A U t I( . 0 3 ) ( . 0 0 5 ) t - I ( . 0 6 ) - - "

R 2 = . 6 4 A D F = - 1 . 0 2

C a p a c i t y U t i l i z a t i o n

A C U t - 8 . 7 5 - . I I C U _ ~ * . 1 9 A C U . . + . 3 2 A C U( 2 . 8 6 ) ( . ~3 3 ) ~ - ~ ( . 0 9 ) t - ~ ( . 0 9 ) t - 2

R 2 = . 1 8 A D F = - 3 . 0 7

a Standa rd errors in pa rentheses below co efficient estimates. Critical values fo r argum ented Dicke y-Fuller test statistic (A DF) from F uller (1976, p. 373) are -3.51 (1%), -2.89 (5%), and -2.58(t0%).

B u l l e ti n . F i g u r e la p lo t s th e U . S . u n e m p l o y m e n t r a t e a n d t h e m e a n a d j u s t e d c a p a -c i ty u ti l iz a t io n r a te . T h e u n e m p l o y m e n t a n d c a p a c i t y u t il i z at i o n s e r ie s f o r G e r m a n yr u n f r o m 1 9 6 2. 1 to 1 9 8 9 . 1 . T h e s e d a ta a re t a k e n f ro m O E C D M a i n E c o n o m i cI n d i c a to r s . B e c a u s e t h e G e r m a n c a p a c i t y u t i l i z a ti o n s e r ie s i s s e a s o n a l l y u n a d j u s t e dW e h a v e a d j u s t e d t h e s e r i e s b y C e n s u s X - 1 1. T h e G e r m a n s e r ie s a r e p l o t t e d i n f i -g u r e l b . T h e c a p a c i t y u t i l iz a t i o n s e r ie s r e f e r t o t h e m a n u f a c t u r i n g s e c t o r , an d f i g u -r e s l a a n d l b s u g g e s t a c l o s e i n v e r s e re l a t i o n s h i p b e t w e e n t h e s e s e r i e s a n d t h e u n -e m p l o y m e n t r at e s f o r b o t h c o u n t r i e s.


10/14

1 9 4 A . J a e g e r a n d M . P a r k i n s o n

T a b l e 2 . E s t i m a t e s f o r u n o b s e r v e d c o m p o n e n t s m o d e l su . s . ~ . 1 9 s a . 1 - 1 9 8 9 . 1

L o g L i k e l i h o o d 7 6 . 3 2

P a r a m e t e r s

a 1~ Na Ca v

L i k e l i h o o d R a t i o

~ i 1 . 6 3 ( . 0 5 )~ 2 - . 7 2 ( . 0 6 )O . I I ( . 0 9 )a 0 - . 7 9 ( . 0 6 )

. 3 6 ( . 0 5 )- . 1 8- . 2 3

. 0 0 4

T e s t ( N u l l : O ~ 0 ) 2 . 3 4 b

G e r m a n y 1 9 62 . ,i - 1 9 8 9 . 1

L o g L i k e l i h o o d 8 2 . 9 7P a r a m e t e r s 0 1 1 . 7 8 ( . 0 8 )

~ 2 - . 8 3 ( . 0 7 )e . 5 O ( . 3 O )a 0 - 1 . 3 8 ( . 2 6 )a I , 9 3 ( , 2 8 )a p - . 1 8a C - .09o v 0 3

L i k e l i h o o d R a t i o T e s t ( N u l l 8 = O ) 4 . 2 9 b

a C a pa c i ty u t i l i z a t ion ha s be e n sc a l e d by a f a c to r o f 10 . Asy m p to t i c s t a nda r d e r r o r s i n pa r e n the se s .b D i s t r ibu te d a s C h i - S qu a r e w i th 1 de g r e e o f f r e e do m u nde r t he nu l l . C r i t i c a l va lue s a r e 6 . 63 ( 1%) ,3 .84 (5%) , and 2 .71 (10%) .

As a f i r s t s t ep , we t e s t two impor tan t a s sumpt ions conce rn ing the s t a t iona r i typrope r t i e s o f the va r iab le s in the UC m o d e l . U n e m p l o y m e n t s h o u l d h av e a u n it ro o tin l eve l s whi le capac i ty u t i l i za t ion shou ld b e s t a t iona ry in l eve l s . W e te s t fo r un i tr o o t s u s i n g a u g m e n t e d D i c k e y - F u l l e r t e s t s . S t a r t i n g w i t h r e g r e s s i o n s i n c l u d i n g 6lagged au toregress iv e te rms , lags ins ignif icant a t the 5 perce nt level w ere e l iminatedin a s t epwise reg res s ion p roced ure s t a r ting w i th the h ighes t l ag . Tab le 1 repor t s theresu l ts w i th on ly the s ign i f ican t l ags inc luded . Th e nu l l o f a un i t roo t can no t be re -j e c t e d f o r t h e u n e m p l o y m e n t r a t es e v e n a t th e 1 0 p e r c e n t s i g n i f ic a n c e l e v e l. C a p a -c i ty u t il i za t ion m easures a re judge d s t a tiona ry a t the conven t iona l 5 pe rcen t s ign i f i -cance level .

W e e x c l u d e d a t i m e t r e n d f r o m t h e D i c k e y - F u l l e r r e g r e s s i o n s o n t h eas sumpt ion tha t ne i the r unemployment nor capac i ty u t i l i za t ion i s de te rmin i s t i ca l lygrow ing o r fa l ling ov e r time . Th i s po in t i s impor tan t s ince o the r re sea rche rs appea r


11/14

Testing for Hysteresis in Unemployment 195

to assume the unemployment rate to have a deterministic trend (see e.g. Blanchardand Quah 1988 and Clark 1989). We find the assumption of a deterministic upwardor downward trend in unemployment unattractive on an a priori basis.Table 2 reports estimates of the parameters and test statistics for the UC model.We first discuss the U.S. results.

The point estimate of the hysteresis coeffic ient 0 for the U.S. is 0.11 A likeli-hood ratio test of the hypothesis that 0 = 0.0 cannot reject the null even at the 10percent level. This finding suggests that hysteresis effects in the U.S. unemploy-ment rate are neither economically important nor statistically significant. These re-suits are consistent with conventional wisdom in the sense that they suggest a U.S.natural unemployment rate that is shifted over time by structural facgtors with largebut independent movements of the actual unemployment rate around the naturalrate. In figure 2a, we plot the natural rate component o f U.S. unemployment deri-ved from smoothed Kalman filter estimates along with the actual unemploymentrate. As an aside, we note from figure 2a that by the time the Kennedy-Johnson taxcuts were implemented as a countercyclical measure in February 1964, the actualrate of unemployment was already below the natural rate. By contrast, the ReaganEconomic Recovery Tax Act o f 1981 introduced tax cuts which took effect in 1982,a time when the actual unemployment rate exceeded the natural rate by more thantwo percentage points.p I H .[RCEN 1 2 . - -T

I 0 . - -

6 . - -

2 . i , i , i , i , i , i , i , i , i , i , i , i , i

5 ~ 5 6 58 6 0 6 2 5 ~ 8 6 6 8 7 0 7 2 7 ~ 7 6 7 8~ E R R

- - A t | O A k U N [~ P LO Y N [ N I ~ A I E. . . . N & I U R A L U N [ H P L O V N ( N I R A I l

F i g , 2 a . U . S . A c t u a l a n d n a t u r a l u n e m p l o y m e n t r a te . 1 9 5 4 . 1 - 1 9 8 9 . 1

' I ' I ' I ' I ' I 'B 0 8 2 B " i 8 6 8 8


12/14


The results for Germany suggest a different interpretation. The hysteresiscoefficient 0 is estimated to be about 0.50, implying that a positive 1 percent shockin cyclical unemployment will increase future natural rates by about 0.50 percent. Alikelihood ratio test of 0 = 0.0 rejects the null at the 5 percent significance level butnot at a 1 percent level. We conclude from these results that the evidence in a formalstatistical sense is not overwhelming but accepting the point estimate o f 0 would in-dicate substantial hysteresis in the German unemployment rate. It is important tonote, however, that hysteresis is only a partial explanation for the increase in theGerman natural rate given the substantial variance of the shocks to the natural rate.Figure 2b plots the natural and actual unemployment rate for Germany.

In both countries, a 1 percent change in cyclica l unemployment is associatedwith a steady state change in capacity utilization of some 4 percent. Judging fromthe standard deviation of measurement error in the equat ion linking capacity utiliza-tion and cyclical unemployment (Cry), movements in the U.S. cyclical componentappear to be much more closely related to capacity utilization than in the Germancase.

J

12

10

/ , , 'i

i . , , i , , , i . , . i , , . i , , , i , , . i . , . i , , , i , , , i . ~ . 1 . , . i , ' , ' . i , , , i ' ~ j62 6H 66 68 70 72 7't 76 78 80

Y E R RA C | U A L U N [M P L O V H E N ! R A I E

. . . . . N A T U R A L U N E H P L O Y H [ H r R A T E

Fig. 2b. German actual and natural unemploymen t rate. 1962.1-1989.1

82 84 86 88


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T es t ing fo r Hys te res i s in Une m plo ym e nt 197

6 C o n c l u s i o n

W e sugges t ed i n th i s paper a new t e st for hys t eres is i n unem pl oym ent . Th e obser -ved unem ploym ent rate i s deco m pos ed into a natural rate comp onen t and a cyc l icalCOmponent. Th e imp act of lagged cyc l ica l sho cks on the current natural com po nen tSupplies a measure o f hysteres i s . T he em pir ical resul t s for U .S. and Germ an dataprov ide no ev i den ce f or hys t eres is i n t he U. S . unem pl oym ent ra te but an econ om i -ca l ly s i gn i f icant hys t eres i s e f f ec t for the G erm an un em pl oym ent ra te . A shock o f1.0 percent to the current cy cl ica l com po ne nt permanently increa ses future Germannatural rates by a bout 0.5 percent. For both cou ntries , current shock s to the naturalrate turn out to be an important imp ulse m echan ism to explain mo vem ents in obser-ved unemployment rates .

R e f e r e n c e s

B e r n d t E K , H a l l R E , H a l l B H , H a u s m a n J ( 1 9 7 4 ) E s t i m a t i o n a n d i n f e r e n c e i n n o n l i n e a rs t ruc tu ra l m ode ls . Anna ls o f E conom ic and S oc ia l Me asurem ent 3 :65 3-66

Blanchard O J , Quah D (1988) T he dynam ic e f fec t s o f aggrega te dem and and su pp ly d i s tu rbances .N B E R W o r k i n g P a p e r N o . 2 7 3 7Blanchard O J , Sum m ers L H (1986) Hys te res i s and the E uropean unem ploym ent p rob lem . NBE RMac roeconom ics Annu a l 1986 , MIT P res s

B l i n d e r A S ( 1 98 8) T h e c h a l l e n g e o f h ig h u n e m p l o y m e n t . A m e r i c a n E c o n o m i c R e v i e w 7 8 : 1 - 1 5Bruno M, Sachs JD (1985) E cono m ics o f W or ldwise S tag f la t ion . Harvard U niver s i ty P res sCam pbel l J Y , M ank iw NG (1987) Are ou tpu t f luc tua t ions t r ans i to ry? Quar te r ly Journa l o f E co-

n o m i c s 1 0 2 : 8 5 7 - 8 8 0Clark P K (1989) T rend rever s ion in r ea l ou tpu t and une m ploym ent . Journa l o f E cono m et r ics ,

4 0 : 1 5 - 3 2Coe D T (1988) Hy s te res i s E f fec t s in Agg rega te Wag e E qua t ions . In : R Cros s ( ed . ) Un em p loy-

m ent , Hys te res i s and the Natu ra l Ra te H ypo thes i s , Bas i l B lackw el lC o e D T ( 1 9 8 9 ) S t r u c t u r a l d e t e r m i n a n t s o f th e n a t u r a l r a te o f u n e m p l o y m e n t i n C a n a d a . I M F

W o r k i n g P a p e r.F ranz W (1987) Hys te res i s , pe r s i s tence , and the N AIR U: A n em pi r ica l ana lys i s fo r the Rep ub l ic

o f G e r m a n y I n : R L a y a r d , L C a l m f o r s ( e d s. ) T h e F i g h t A g a i n s t U n e m p l o y m e n t , C e n t re f o rE uropean Po l icy S tud ies , M IT P res s

Fu l le r W A (1976) In t roduc t ion to S ta t i s t i ca l T im e S er ies . John W i ley & SonsG o r d o n R J ( 1 98 8 ) B a c k t o th e f u t u re : E u r o p e a n u n e m p l o y m e n t t o d a y v i e w e d f r o m A m e r i c a in

1939 . Brook ing Paper s on E conom ic Act iv i ty 19 :1271-312Grego ry R G (1986) Wa ge po l icy and unem ploy m ent in Aus t ra l i a . E cono m ica (Supp lem ent ) : 53 -

74Hargreaves Heap S P (1980) Choos ing the wrong na tu ra l ra te , acce le ra t ing in f la t ion o r dece le ra t ingu n e m p l o y m e n t a n d g r o w th ? E c o n o m i c J o u r na l 9 0 : 6 1 1 - 2 0Harvey A C (1981) T im e Se r ies Mo dels . Ph i l ip A l lan


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Harvey A C, Todd P H J (1983) Forecasting economic time series with structural and Box-Jenkinsmodels: A case study. Journal of Business and Economic Statistics, 1:299-315

Layard R, Nickell S J (1986) Unemployment in Britain. Economica 53 (Supplement): 121-170Lindbeck A (1985) What is wrong with the West European economies? World Economy 8: 153-

70Lindbeck A, Snower D J (1986) Wage setting, unemployment and insider-outsider relations.

American Economic Review 76/2:235-39Quah D (1988) The relative importance of permanent and transitory components: identification and

some theoretical bounds, mimeo, MIT.Watson M W (1986) Univariate detrending methods with stochastic trends. Journal of Monetary

Economics 18:49-76Watson M W, Engle R E (1983) Alternative algorithms for the estimation of dynamic factor, MI-

MIC, and varying coefficient regression models. Journal of Econometrics, 23:385-400Wyplosz C (1987) Comments. In: R Layard, L Calmfors (eds.) The Fight Against Unemploy-ment, Centre for European Policy Studies, MIT Press

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