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JOURNALOFPUBLICECONOMICSEI~SEVIER Jo urn al of Public Ec ono m ics 56 (1995) 311-325

C o r p o r a t e i n c o m e t a x c o m p e t i t i o n , d o u b l e t a x a t i o nt r e a t i e s , an d f or e i gn d i r e c t i n ve s t m e n t

Eckhard JanebaDepartment of Econom ics, Indiana U niversi(v, Bloomington, IN 47405, US A

Received F ebru ary 1992, f inal version received Oc tober 1993

A b s t r a c t

I n t h e p r e s e n c e o f i n t e r n a t i o n a l c a p i t a l m o b i l i t y , f o r e i g n d i r e c t i n v e s t m e n t i si n f l u e n c e d b y c o r p o r a t e i n c o m e t a x r a t e s a n d t h e r u l e s o f h o w t a x e s p a i d in th e h o s tc o u n t r y a r e t r e a t e d a t h o m e . I n th i s p a p e r t h e e x e m p t i o n , c r e d i t a n d d e d u c t i o nm e t h o d s a r e c o n s i d e r e d a s t a x ru l e s. T a x c o m p e t i t i o n i s m o d e l e d a s a n o n - c o -o p e r a t i v e g a m e w i t h r e s p e c t t o b o t h c o r p o r a t e t a x r a t e s a n d t h e f o r m o f d o u b l et a x a t i o n r e l ie f . T h e s u b g a m e p e r f e c t e q u i li b r iu m i s s h o w n t o b e i n d e p e n d e n t o f th et a x r u l e s . S i n c e c a p i t a l i s i n e f f ic i e n t ly a l l o c a t e d , t h e f e a s i b i l it y a n d t h e c o n t e n t o f ac o o p e r a t i v e c o n t r a c t b e t w e e n g o v e r n m e n t s a r e a n a l y z e d . I t is a r g u e d t h a t o n l y t h ec r e d i t m e t h o d r e q u i r e s n e i th e r c o m p e n s a t o r y p a y m e n t s n o r f ul ly h a r m o n i z e d t a xr a t e s . T h i s i s c o n s i s t e n t w i t h t h e o b s e r v a t i o n t h a t t a x c r e d i t s a r e v e r y o f t e n a d o p t e di n d o u b l e t a x a t i o n t r e a t i e s .K e y w o r d s : T a x c o m p e t i t i o n ; T a x h a r m o n i z a t i o n ; D o u b l e t a x a t i o n ; F o r e i g n d i r e c ti n v e s t m e n tJ E L classif ication: F 2 0 ; H 8 7

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

I n a n i n t e r d e p e n d e n t w o r l d e c o n o m y a g o v e r n m e n t ' s a b i l i t y t o p u r s u e a na u t o n o m o u s t a x p o l i cy is r e s t r i c t e d b y t h e m o b i l i t y o f fa c t o r s o f p r o d u c t i o na n d g o o d s . T a x p o l i c y i s o f t e n u s e d t o a t t r a c t b u s i n e s s w h i c h c r e a t e s j o b sa n d i n c r e a s e s d o m e s t i c w e l f a r e . T h e r e f o r e , i n r e c e n t y e a r s t h e t o p i c o f t a x0047-2727/95/$09.50 1995 Else vier Science B.V. A ll r ights rese rvedS S D I 0 0 4 7 - 2 7 2 7 ( 9 4 ) 0 1 4 2 4 - M

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312 E . J a n e b a / J o u r n a l o f P u b l i c E c o n o m i c s 5 6 ( 1 9 9 5 ) 3 1 1 - 3 2 5c o m p e t i t i o n c a m e o n t h e p o li ti c al a n d r e s e a r c h a g e n d a . I n th e l i t e r a tu r e t h eq u e s t i o n w a s r a i s e d w h e t h e r c a p i t a l i n c o m e t a x e s c a n b e s u s t a i n e d a t a l lw h e n c a p i ta l is v e r y m o b i le : i n t h e w o r d s o f R o g e r G o r d o n ( 1 9 90 ) , " C a nc a p i t a l i n c o m e t a x e s s u r v i v e i n o p e n e c o n o m i e s ? " . T h e q u e s t i o n i s r e a s o n -a b l e s i nc e f o r e ig n e a r n in g s c a n n o t b e m o n i t o r e d a n d t h e r e f o r e c a n n o t b ee f f e c t i v e ly t a x e d . P r o b l e m s o f m o n i t o r i n g a r e p a r t i c u la r l y r e l e v a n t w h e nf o r e i g n i n v e s t m e n t t a k e s t h e f o r m o f p o r t f o l i o i n v e s tm e n t . ~ I n t h a t c a s et a x a t i o n o f d o m e s t i c a l ly g e n e r a t e d c a p it a l i n c o m e i s p r o b l e m a t i c s i nc e t h es a m e n e t r e t u r n a s a b r o a d m u s t b e o f f e r e d . T a x a t i o n in c r e a s e s t h e d o m e s t i cg r o s s r a t e o f r e t u r n a b o v e t h e w o r l d l e v e l , w h i c h c a u s e s i n e f f ic i e n c ie s .T h e r e f o r e , t a x i n g m o b i l e f a c t o r s m i g ht n o t b e a t oo l f o r r a is in g r e v e n u e .

I t ha s b e e n r e c o g n i z e d , h o w e v e r , t h a t t h e t a x a t i o n o f i n c o m e f r o m f o r e i g nd i r e c t i n v e s t m e n t i s d i f f e r e n t s in c e a c o r p o r a t e f i rm u n d e r t a k e s t h e i n v e s t-m e n t . T h e f ir m is w e l l m o n i t o r e d a n d i s u s u al ly i n t e r e s t e d i n d o c u m e n t i n gt h e f o r e i g n d i r e c t i n v e s t m e n t . O n t h e o t h e r h a n d , t a x a t i o n o f f o r e i g n d i r e c ti n v e s t m e n t i n c o m e i s m o r e c o m p l i c a t e d d u e t o t h e m a n y p o s s ib l e p ro v i si o n so f d o u b l e t a x a t i o n t r e a t ie s . A g o o d d e s c r i p t i o n o f t h e s e c o m p l e x p ro v i s io n sis g i v e n i n A l w o r t h ( 1 9 8 8 ). S i n c e g o v e r n m e n t s a r e i n t e r e s t e d in p r o m o t i n gd o m e s t i c p r o d u c t i o n a n d i n i n c r e a s i n g n a t i o n a l w e l f a r e t h e s t r a t e g i c u s e o fc o r p o r a t e t a x a t i o n in o p e n e c o n o m i e s ha s b e e n a n a l y z e d in th e s e m i n a lp a p e r b y H a m a d a ( 1 96 6 ), a n d m o r e r e c e n t l y in B o n d a n d S a m u e l s o n( 1 9 8 9 ), G o r d o n ( 1 9 9 0 ) , a n d M i n t z a n d T u l k e n s ( 1 99 0 ).

T h i s p a p e r a l s o a d d r e s s e s t h e s t r a t e g i c us e o f c o r p o r a t e t a x a t i o n i n a ni n t e r n a t i o n a l f r a m e w o r k . I n c o n t r a s t t o B o n d a n d S a m u e l s o n ( 1 9 8 9 ) , b u t i nl i n e w i t h G o r d o n ( 1 9 9 0 ) a n d B o n d ( 1 9 9 1 ) , it is a s s u m e d t h a t t h e c a p i t a le x p o r t i n g c o u n t r y c a n n o t d i s c r i m i n a t e a g a i n s t o u t fl o w i n g c a p i t a l b y c h o o s i n gd i f f e r e n t ta x r a t e s . F o r e i g n i n v e s t m e n t i n c o m e i s n o t , h o w e v e r , t r e a t e d int h e s a m e w a y a s i n c o m e f r o m d o m e s t i c i n v e s t m e n t , s i n c e d o u b l e t a x a t i o nr e l i e f f o r t a x e s p a i d i n t h e h o s t c o u n t r y i s o n l y p a r t ia l l y o f f s e tt i n g . A r e a s o nw h y g o v e r n m e n t s d o n o t d i s c r i m i n a t e a g a i n s t f o r e i g n d i r e c t i n v e s t m e n t b yc h o o s i n g d i f f e r e n t t a x r a t e s c o u l d b e t h e f o l l o w i n g : w i t h d i s c r i m i n a t i o n ,c h a n g e s i n t h e c a p i t a l e x p o r t i n g c o u n t r y ' s t a x r a t e a lw a y s i n d u c e a r e a l l o c a -t i o n o f c a p i t a l. A l t h o u g h n o t e x p l i c it l y m o d e l e d i n t h e p a p e r , a c h a n g e i nt h e l o c a t i o n o f c a p i ta l is li k e ly t o b e c o s t l y s in c e ( f o r e i g n d i r e c t ) i n v e s t m e n tis r a t h e r a l o n g - r u n d e c i s i o n w i t h c o m m i t m e n t c h a r a c t e r . W i t h n o n - d i sc r i m i -n a t i o n , c h a n g e s i n th e t a x r a t e l e a d o n l y in s o m e c a s e s t o r e a l l o c a t i o n s ( a sw i l l b e c o m e c l e a r e r l a t e r ) .

~A good exa m ple was the at tempt of the G erm an gove rnm ent to introduce a 10%withholding tax on interest inco m e in 1989. Sinc e save rs co uld export their cap ital toLuxemburg, they were able to evad e German taxation.

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E. Janeba / Journal of Public Economics 56 (1995) 311-325 313F o r e i g n d i r e c t i n v e s t m e n t i s a f f e c t e d b y t h e g o v e r n m e n t ' s d e c i s i o n o n

b o t h t h e c o r p o r a t e t a x r a te a n d t h e f o r m o f d o u b l e t a x a t i o n r e li e f. D o u b l et a x a t i o n r e l i e f c a n t a k e o n e o f th r e e f o r m s . T h e c a p it a l e x p o r t in g c o u n t r ym a y a l l o w f o r e i t h e r a d e d u c t i o n o f t a x e s p a i d in th e h o s t c o u n t r y , o r ac r e d i t u p t o t h a t a m o u n t w h i c h w o u l d h a v e b e e n i n c u r r e d u n d e r p u r ed o m e s t i c t a x a t i o n , o r c o m p l e t e l y e x e m p t f r o m t a x a t i o n. I n th is p a p e r b o t ht h e c o r p o r a t e i n c o m e t a x r a t e a n d t h e m e t h o d o f h o w h o s t c o u n t r y t a x e s ar et r e a t e d a t h o m e ( t h e t a x r u l e ) a re d e c i s i o n v a r i a b l e s o f t h e g o v e r n m e n t s . I tis s h o w n t h a t in e q u i l ib r i u m o f t h e n o n - c o o p e r a t i v e g a m e t h e n a t i o n a li n c o m e l e v e ls a r e i n d e p e n d e n t o f t h e t a x r u le s c h o s e n b y b o t h c o u n t r ie s . As i m p l i f y in g b u t i n t u i ti v e e x p l a n a t i o n is t h a t t h e c a p i t a l e x p o r t i n g c o u n t r yp r e f e r s le s s c a p i t a l o u t f lo w w h e n t h e h o s t c o u n t r y ta x e s f o r e i g n i n v e s t m e n ti n c o m e . T h i s r e d u c e s t h e e x p o r t i n g c o u n t r y ' s t a x r a t e d o w n t o z e r o , s u c ht h a t t h e f o r m o f d o u b l e t a x a t i o n r e l i e f b e c o m e s i r r e l ev a n t .

S i n c e i n e q u i l i b r i u m t h e w o r l d c a p i t a l s t o c k i s i n e f f i c i e n t l y a l l o c a t e d , t h eq u e s t i o n o f w h e t h e r c o o p e r a t i o n b e t w e e n g o v e r n m e n t s c a n yi e ld a P a r e t o -i m p r o v e m e n t is a d d r e s s e d . I t w i ll b e a r g u e d t h a t t a x r u le s d i f f e r g r e a t l yr e g a r d i n g t h e c o n t e n t o f a c o o p e r a t i v e c o n t ra c t . T h e c r e d i t m e t h o d h a s t h es m a l l e st r e q u i r e m e n t f o r a P a r e t o - i m p r o v e m e n t s in c e n e i t h e r a c o m p e n s a t -o r y p a y m e n t n o r fu l ly h a r m o n i z e d t a x r a t e s a re n e c e s s a r y . T h e e x e m p t i o nm e t h o d r e q u ir e s h a r m o n i z e d t ax ra t es , w h e r e a s u n d e r t h e d e d u c t i o n m e t h o da n e f f i c ie n t c a p i t a l a l l o c a t i o n is c o m p a t i b l e w i th a P a r e t o - i m p r o v e m e n t o n l yw h e n a s i d e p a y m e n t is m a d e . T h e s e r e s u l t s s e e m t o b e c o n s i s t e n t w i th t h eo b s e r v a t i o n t h a t i n d o u b l e t a x a t i o n t r e a t i e s t h e c r e d i t a n d e x e m p t i o nm e t h o d s a r e a l m o s t a l w a y s a g r e e d o n .

T h e p a p e r i s o r g a n i z e d a s f o l l o w s : S e c t i o n 2 p r e s e n t s t h e b a s i c f r a m e w o r ka n d a n a l y z e s a n o n - c o o p e r a t i v e t h r e e - s t a g e g a m e i n w h i c h g o v e r n m e n t sc h o o s e a ta x r u l e a n d a c o r p o r a t e i n c o m e t a x r a te . T h e f e a s i b i li t y a n d t h ec o n t e n t o f a c o o p e r a t i v e c o n t r a c t b e t w e e n g o v e r n m e n t s a r e i n v e s ti g a t ed i nS e c t i o n 3 . F i n a l l y , S e c t i o n 4 s e t s o u t s o m e c o n c l u s i o n s .

2. Non-cooperative fiscal policyA c c o r d i n g t o R u f fi n (1 9 8 8 ), t h e M a c D o u g a l l - K e m p m o d e l is t h e s i m p le s t

f o r a n a l y z i n g in t e r n a t i o n a l c a p i t a l m o v e m e n t s . H e r e i t is u s e d t o a n a l y z ei n t e r n a t i o n a l c o r p o r a t e i n c o m e t ax c o m p e t i t io n . T h e r e a r e tw o c o u n t r i e s ,t h e h o m e a n d t h e f o r e i g n c o u n t r y ( al l f o r e i g n v a r i a b l e s a r e i n d e x e d w i t h a na s t e r i sk ) . O n e g o o d is p r o d u c e d b y u se o f t h e f a c t o r s , c a p it a l K(K*) a n dl a b o r L (L * ) , u n d e r c o n d i t i o n s o f p e r f e c t c o m p e t i t i o n in a ll m a r k e t s . T h ep r o d u c t i o n f u n c t i o n F(F*) is h o m o g e n e o u s o f d e g r e e o n e , s t r ic t ly qu a s i -c o n c a v e a n d s a ti sf ie s t h e s t a n d a r d I n a d a c o n d i t i o n s . E a c h c o u n t r y h a s

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314 E . J a n e b a / J o u r n a l o f P u b l i c E c o n o m i c s 5 6 ( 1 9 9 5 ) 3 1 1 - 3 2 5s t ri c tl y p o s i t i v e e n d o w m e n t s o f c a p i ta l a n d l a b o r , ( K , K * , L , L * ) , w h i ch a r ei n e l a s ti c a l ly s u p p l ie d . C a p i t a l , h o w e v e r , is i n t e r n a t i o n a l l y m o b i l e w h e r e a sl a b o r i s n o t . e

I t is a s s u m e d t h a t t h e r e t u r n o n i n v e s t m e n t i n t he h o m e c o u n t r y is b e l o wt h a t i n t h e f o r e i g n c o u n t r y w h e n n o c a p i t a l is t r a d e d , i .e . r = F K [ K , L ] 0 d e n o t e c a p i t a l e x p o r t s , w h e r e a s Z < 0r e p r e s e n t s c a p i t a l im p o r t s f o r t h e h o m e c o u n t r y . I n a f r e e - t r a d e e q u i li b r iu m ,f i r m s h i r e c a p i t a l a n d l a b o r u n t i l e a c h l a b o r m a r k e t c l e a r s ( a n d l a b o r i s p a i di t s m a r g i n a l p r o d u c t ) ; w o r l d c a p i t a l d e m a n d e q u a l s w o r l d c a p i t a l s u p p l y , a n dt h e f o l l o w i n g i n t e r n a t i o n a l c a p i t a l m a r k e t e q u i l i b r i u m c o n d i t i o n h o l d s

F K [ / ~ - Z ] = F ~ :[ R * + Z ] , ( 2 )w h e r e Z > 0 . T h e p r o p e r t i e s o f t h e p r o d u c t i o n f u n c t io n s e n s u r e t h ee x i s t e n c e o f a u n i q u e e q u i l i b r iu m .

C o r p o r a t e i n c o m e t a x e s h a v e b e e n l o w e r e d i n m o s t W e s t e r n c o u n t r i e sd u r i n g t h e l a s t d e c a d e ( O E C D , 1 9 9 0 ) . T h i s p r o c e s s i s o f t e n c a l l e d ( c o r p o -r a t e ) t a x c o m p e t i t i o n a n d c a n b e i d e n ti f ie d w i th n o n - c o o p e r a t i v e b e h a v i o r .T h e r e f o r e , i t is i n t e r e s ti n g a n d n e c e s s a r y t o m a k e t a x r a t e s a n e n d o g e n o u sg o v e r n m e n t d e c i s i o n v a r i a b le . I t w il l b e a s s u m e d t h a t e a c h g o v e r n m e n t h a sa n o n - d i s c r i m i n a t o r y c o r p o r a t e i n c o m e t a x r a t e , t ~ [ 0, /m a x ] w h e r e tm ax < 1,a n d t * E [ 0, t'm ax] w h e r e /* ax < 1 , r e s p e c t i v e l y . H o w e v e r , c o r p o r a t e i n c o m et a x r a t e c h a n g e s b y g o v e r n m e n t s a r e e m b e d d e d w i th i n e xi s ti n g r u le s f o rd o u b l e t a x a t i o n . H e n c e , t a x r u le s s h o u l d a ls o b e s e e n a s d e c i s i o n v a r i a b l e so f g o v e r n m e n t s . E a c h g o v e r n m e n t a p p l ie s o n e o f t h r e e a l t e r n a t iv e r u le s o fh o w t o t r e a t f o r e i g n i n v e s t m e n t i n c o m e . F i r s t , i t c a n c r e d i t t h e f o r e i g n t a xp a i d u p t o t h a t a m o u n t w h i c h w o u l d h a v e b e e n i n c u r r e d u n d e r p u r ed o m e s t i c t a x a t i o n . T h i s l e a d s t o t a x a t i o n a t t h e h i g h e r o f t h e t w o r a t e s a n d isc a l l e d t h e c r e d i t -c u r e - l i m i t a t i o n m e t h o d , c c l. S e c o n d , f o r e i g n i n v e s t m e n t

2 M oreover, it is assume d that all foreign direct investment is equity-financedand the returnis repatriated to capital owners. These assumptions correspond to those m ade in Bo nd andSam uelson (1989). Em pirical evidence suggests that foreign direc t investment is financed atleast pa rt ial ly by ho st country sources. As argu ed by Sin n (1990), howev er, new foreignsubsidiaries cannot be financed by retained profits, and usually obtain transfers fro m the parentfirm. In later phases retained ea rnings or hos t country sources are us ed for tax reasons.

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E. Janeba / Journal o f Publ ic Economics 56 (1995) 311-325 315i n c o m e c a n b e c o m p l e t e l y e x e m p t e d f r o m d o m e s t i c t a x a t io n , s u c h th a t o n l yt h e f o r e i g n t a x i s r e l e v a n t . T h i s is c a l l e d t h e e x e m p t i o n m e t h o d , e x . F i n a l l y ,t h e g o v e r n m e n t c a n a l lo w t h e f o re i g n t a x t o b e d e d u c t e d f r o m i n c o m eb e f o r e t h e d o m e s t i c c o r p o r a t e t a x is a p p l i e d . T h i s is c a l l e d t h e d e d u c t i o nm e t h o d , d e d . H e n c e , f o r a c a p i ta l o w n e r in th e h o m e c o u n t r y t h e ta x f a c t o ro n a d i r e c t i n v e s t m e n t i n t h e f o r e i g n c o u n t r y is { 1 - m a x ( t , t * )} u n d e r t h ec r e d i t m e t h o d , ( 1 - t* ) u n d e r th e e x em p t i o n m e t h o d , a n d ( 1 - t ) ( 1 - t * )u n d e r t h e d e d u c t i o n m e t h o d . T a x f a c t o r s f o r a f o re i g n c a p it a l o w n e ri n v e s ti n g in t h e h o m e c o u n t r y c a n b e w r i t te n a n a l o g ou s l y .

I t is a s s u m e d t h a t g o v e r n m e n t s m a x i m i z e n a t io n a l i n c o m e , d e f i n e d as th es u m o f d o m e s t i c o u t p u t a n d n e t f a c t o r p a y m e n t s t o th e o t h e r c o u n t r y . F o rZ > 0 , a n d f o r g i v e n t a x ru l e c o m b i n a t i o n s , n a t i o n a l i n c o m e o f t h e h o m ea n d t h e f o r e i g n c o u n t r y , r e s p e c t i v e ly , a r e t h e r e f o r e

Y ( t , t * ) = F [ K - Z ( t , t * )] + (1 - t * ) F ~ : [ g * + Z ( t , t * ) ] Z ( t , t * ) ( 3 )r * ( t , t * ) = F * [ / * + Z ( t , t * ) ] - ( 1 - t * ) F ~ [ / ~ * + Z ( t , t * ) l Z ( t , t * ) ( 4 )

A l t h o u g h t h e t a x ra t e a n d t h e t a x r u l e a re b o t h e l e m e n t s o f a t a x s y s te m ,t h e y a r e d i s t i n c t i n n a t u r e . T h e d e c i s i o n o n a t a x r u l e i s a l o n g - r u n d e c i s i o ns i n c e t h e t a x r u l e is c h a n g e d l es s o f t e n t h a n t h e c o r p o r a t e t a x r a t e . F o r e i g nd i r e c t i n v e s t m e n t s e e m s t o b e m o r e s e n s i t i v e t o t h e t a x r u l e t h a n t o t h e t a xr a t e b e c a u s e t h e l a t t e r a f fe c t s b o t h t y p e s o f i n v e s t m e n t , w h e r e a s t h e f o r m e ra p p l i e s o n l y t o f o r e i g n d i r e c t in v e s t m e n t . I n th e f o l l o w i n g t h r e e - s t a g e g a m et h e c o r p o r a t e i n c o m e t a x r a t e a n d t h e t a x r u l e a r e m a d e e n d o g e n o u s , a n d a l la c t i on s t a k e n b y g o v e r n m e n t s a r e o b s e r v a b l e i n s u b s e q u e n t s t ag e s . T h es t r u c t u r e o f th e g a m e is a s fo l lo w s :

F i r s t s ta g e: G o v e r n m e n t s s i m u l t a n e o u s l y c h o o s e a t ax r u l e.S e c o n d s ta g e: G o v e r n m e n t s s i m u l t a n e o u s l y c h o o s e a c o r p o r a t e i n c o m e

t a x r a t e .T h i r d s ta g e : M a r k e t e q u i l ib r i u m i s d e t e r m i n e d .

B o t h g o v e r n m e n t s c h o o s e a t a x r u le in t h e fi rs t s t a g e b e c a u s e c a p i t a l d o e sn o t a l w a y s fl o w f r o m t h e h o m e t o t h e f o r e ig n c o u n t r y . T h e r e e x is t t a x r ul ea n d t a x r a t e c o m b i n a t i o n s w h i c h m a y t r a n s f o r m t h e h o m e c o u n t r y , t h e' p o t e n t i a l ' c a p i t a l e x p o r t e r , i n t o a n e t c a p it a l i m p o r t e r , a s w i ll b e s h o w nb e l o w .2 . 1 . T h e c a p i t a l m a r k e t e q u i l i b r i u m w i t h t a x a t io n - t h e t h i r d s t a g e

C o r p o r a t e t a x a t i o n a c c o r d i n g t o d i f f e r e n t t a x r u l e s c h a n g e s t h e c a p i t a lm a r k e t e q u i l i b r i u m . I t is a s s u m e d t h a t s h o r t s a l es o f a s s e ts a r e n o t a l l o w e d ,o t h e r w i s e , c a p i ta l o w n e r s c o u l d b o r r o w a t t h e l o w e r r a te o f r e t u r n a n d

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3 16 E . J a n e b a / J o u r n a l o f P u b l i c E c o n o m i c s 5 6 ( 1 9 9 5 ) 3 1 1 - 3 2 5

i n v e s t i n t h e o t h e r c o u n t r y . M o s t l ik e l y , n o e q u i l i b r i u m e x is ts . 3 W i t h t h en o - s h o r t - s a l e s a s s u m p t i o n t h e r e e x i st s a u n i q u e e q u i l i b r i u m . N o n - d i s -c r i m i n a t o r y t a x e s s h i f t t h e n e t - o f - t a x c u r v e s s u c h t h a t d o m e s t i c i n v e s t m e n tc a n n o t b e s t r ic t ly i n f e r i o r f o r c a p i t a l o w n e r s i n b o t h c o u n t r i e s .

R e g a r d i n g Z , t h e r e e x i s t t h r e e t y p e s o f e q u i l i b r i u m . M o s t n a t u r a l i s t h ec a s e w h e r e Z > 0 , i . e . t h e h o m e c o u n t r y e x p o r t s c a p i t a l . F o r e a c h t a x r u l ec h o s e n b y t h e h o m e c o u n t r y , t h e r e s p e c t i v e ca p i ta l m a r k e t e q u i l ib r i u mc o n d i t i o n i s

cc l : (1 - t ) F k [ K - Z ( t , t * ) ] = { 1 - m a x ( t , t * ) ) / ~ r [ / ~ * + Z ( t , t * ) ]( 5 a )

e x : ( 1 - t ) F k [ K - Z ( t , t * )] = (1 - t * ) ~ [ k * + Z ( t , t * ) ] ( 5 b )d e d : ( 1 - t ) F ~ [ R - Z ( t , t * ) l = (1 - t ) ( 1 - t * ) F ~ [ / ~ * + Z ( t , t * ) ] .

(5c)F o r e i g n d i r e c t i n v e s t m e n t i s c a r r i e d o u t u n ti l th e n e t r e t u r n o n d o m e s t i c a n df o r e i g n i n v e s t m e n t f o r t h e h o m e c o u n t r y fi rm is t h e s a m e . F o r e x a m p l e , Z isp o s i t i v e i n t h e f i r s t t w o c a s e s w h e n t a x r a t e s a r e i d e n t i c a l . A l t e r n a t i v e l y ,t h e r e e x i s t e q u i l i b r ia w i t h Z = 0 a n d Z < O . I n t h e f o r m e r c a s e , c a p i ta lo w n e r s i n o n e c o u n t r y a r e e i t h e r i n d i f f e r e n t t o i n v e s t i n g i n a n y c o u n t r y , o r ,c a p i t a l o w n e r s i n b o t h c o u n t r i e s s t r i c t l y p r e f e r t o i n v e s t t h e i r c a p i t a ld o m e s t i c a l l y . 4 T h e c a s e Z < 0 c a n a l so o c c u r a s t h e f o l lo w i n g l e m m a s h o w s .

J L e m m a . T h e h o m e c o u n t r y i m p o r t s c a p i t a l ( Z < O ) i f, a n d o n l y i f, t h e f o r e i g nc o u n t r y a p p l i e s t h e e x e m p t i o n m e t h o d a n d t* > 1 - (1 - t )c .P r o o f . I f t h e f o r e i g n c o u n t r y a p p l i e s e x , t h e c o n d i t i o n o n t a x r a t e i m p l i e sZ < 0 s i n c e ( 1 - t)c > (1 - t* ) :> (1 - t )F K [ / ] > (1 - t* ) /~ r [ / *] .

T o p r o v e t h e o t h e r d i r ec t io n , i t f o ll o w s im m e d i a t e l y b y th e a b o v ea r g u m e n t th a t f o r t * ~ < l - ( 1 - t ) c , t h e f o r e ig n c o u n t r y w ill n o t i n v e sta b r o a d u n d e r e x . I f t h e f o r e i g n c o u n t r y a p p l i e s c cl o r d e d , t h e n Z c a n n e v e rb e n e g a t i v e . T h i s w i ll b e p r o v e d b y c o n t r a d i c t i o n . A s s u m e t h a t t h e fo r e i g n

3 F o r a d i s c u s s i o n o f c a p it a l m a r k e t e q u i l i b r ia w i t h s h o r t s a l e s s e e S l e m r o d ( 1 9 88 ) a n dH o d d e r a n d S e n b e t ( 1 9 9 0 ) .

4 T o d e m o n s t r a t e s u c h a c as e s u p p o s e t h a t t h e h o m e c o u n t r y a p p l i e s t h e e x e m p t i o n m e t h o da n d t a x r a t e s a r e s u c h t h a t ( 1 - t )F K [/ ~ ] > ( I - t * ) ~ [ / ~ * ] . C l e a rl y , i n v es t in g a b r o a d is n o tp r o f i t a b l e f o r h o m e c o u n t r y f i rm s , s i n c e t h e m a r g i n a l l o s s o n t h e l e f t - h a n d s i d e is l a r g e r t h a n t h em a r g i n a l g a i n o n t h e r i g h t - h a n d s i d e. I f t h e f o r e ig n c o u n t r y a p p l i e s t h e d e d u c t i o n m e t h o d a n d i ft h e f o l lo w i n g i n e q u a li t y h o ld s ( 1 - t * ) ~ [ / ~ * ] > ( 1 - t * ) ( 1 - t ) F K [ k ] , t h e n t h e e q u il i b ri u m i sc h a r a c t e r i z e d b y Z = 0 . T h e p r e c e d i n g t w o i n e q u a l i t i e s i m p l y 1 > ( 1 - t) c > ( 1 - t * ) , w h i c h is b ya s s u m p t i o n a p o s s i b l e c o n f i g u r a t i o n o f t h e p a r a m e t e r c a n d t a x r a te s .

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E. Janeba / Journal o f Public Economics 56 (1995) 311-3 25 317c o u n t r y a p p l i e s c c l a n d Z < 0 . T h e n i t m u s t h o l d ( 1 - t * ) < {1 - m a x ( t , t * ) } c .I f t ~< t * , i t f o l l o w s t h a t 1 < c , w h i c h i s n o t p o s s i b l e b y a s s u m p t i o n . H o w e v e r ,t > t * w o u l d r e q u i r e ( 1 - t * ) < ( 1 - t ) c , o r a t l e a s t ( 1 - t * ) < ( 1 - t ) . B u t t h i si m p l i e s t < t* , a c o n t r a d i c t i o n . A s s u m e t h a t t h e f o r e i g n c o u n t r y a p p l i e s d e d .Z < 0 r e q u i r e s 1 < ( 1 - t ) c , w h i c h i s i m p o s s i b l e . [ ]

T h e r e is a g o o d i n t u i t iv e e x p l a n a t i o n f o r th i s r e s u lt . T h e r e v e r s a l o f c a p i t a lf l o w s c a n n o t o c c u r i f t h e f o r e i g n c o u n t r y a p p l i e s d e d o r c c l. T h e d i f f e r e n c ei n t h e m a r g i n a l p r o d u c t o f c a p i t a l , w h i c h a l r e a d y e x is t s w i t h o u t t a x a t i o n , i sn o t c o m p e n s a t e d b y t a x e s , b e c a u s e u n d e r d e d t h e f o r ei g n t ax t* d o e s n o tm a t t e r , w h e r e a s u n d e r c c l - i f i t m a t t e r s - i t is b e lo w t ha t in t he h o m ec o u n t r y . T h e e x e m p t i o n m e t h o d , w h i ch f o r g iv e n ta x ra t e s a n d c a p it a l f lo w sy i e l d s t h e h i g h e s t n e t r e t u r n , is h o w e v e r n o t s u f f i c ie n t f o r a r e v e r s a l . S i n c e int h i s c a s e t* d o e s n o t a f f e c t t h e n e t r e t u r n o n t h e i n v e s t m e n t a b r o a d , o n l y as u f f i c i e n t l y h i g h f o r e i g n t a x r a t e d i s c r i m i n a t e s i n v e s t m e n t i n t h e f o r e i g nc o u n t r y a n d l e a d s t o Z < 0 . T h e l e m m a i m p l i e s th a t a ' p o t e n t i a l ' c a p i t a li m p o r t e r c a n p r e s e r v e t h a t s ta t u s in d e p e n d e n t l y o f c a nd t h e t a x ra t e s b ys t i c k i n g t o th e d e d u c t i o n o r th e c r e d i t m e t h o d .2 . 2 . C h o o s i n g t a x r a te s - t h e s e c o n d s t a g e

I f t a x e s i n f l u e n c e c a p i t a l f l o w s ( w h i c h i s n o t t h e c a s e f o r ( e q . 5 a ) i f t > t * ) ,a n i n c r e a s e i n t h e c o r p o r a t e i n c o m e t a x a l w a y s d r i v e s c a p i t a l o u t o f th ec o u n t r y : Z i n c r e a s e s ( d e c r e a s e s ) i f t h e h o m e ( f o r e i g n ) c o u n t r y i n c r e a s e i tst a x r a t e . T w o d i f f e r e n t c a s e s h a v e t o b e c o n s i d e r e d . F i rs t , b o t h c o u n t r i e s 't a x r a t e s i n f l u e n c e Z . T h i s i s t h e c a s e i n ( 5 a ) f o r t < t * a n d ( 5 b ) . T h e n , b yt o t a l d i f f e r e n t i a t i o n o f t h e c a p i t a l m a r k e t e q u i l i b r i u m t h e f o l lo w i n g d e r i v a -t i v e s r e s u l t :

- F K Z e *Z , - (1 - t ) F K ~ + (1 - t * ) F * ~ K - - ( 1 - - t ) ( e + * ) > 0 , ( 6 )

- Z *Z, . = ( 1 - t ) F K t~ + (1 - - t*)F*KK (1 - - t * ) ( + * ) < 0 , ( 7 )

w h e r e u s e o f t h e d e f i n i t io n o f th e e l a s t ic i ty o f s u p p l y a n d d e m a n d o fe x p o r t e d c a p i t a l , = - - -- F K / F K K Z a n d e *---- * *F ~ / F K ~ Z , h a s b e e n m a d e ( f o rZ # 0 ) . T h e s e r e l a t e t h e r e l a t i v e c h a n g e i n n e t c a p i t a l e x p o r t s t o a r e l a t i v ec h a n g e i n t h e g r o s s r e t u r n , i .e . t h e m a r g i n a l p r o d u c t o f c a p i ta l . W h e n t h eh o m e c o u n t r y e x p o r t s c a p i t a l ( Z > 0 ) , t h e n > 0 d e n o t e s a ca p i t a l s u p p l ye l a s t i c i t y , w h e r e a s f o r Z < 0 , < 0 is a d e m a n d e l a s t i c it y , a n d v i c e v e r s a f o rt h e f o r e i g n c o u n t r y . I n t h e s e c o n d c a s e , a s fo r ( 5 c) , o n l y t h e f o r e i g n t a x r a t ei s r e l e v a n t : Z , = 0 a n d Z , . c a n b e w r i t t e n a s i n ( 7 ) , w h e r e Z , a n d *d e p e n d o n l y o n t* .

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318 E . J a n e b a / J o u r n a l o f P u b l ic E c o n o m i c s 5 6 ( 1 9 95 ) 3 1 1 - 3 2 5At this point the subgame perfect equilibrium of the full game can already

be characterized due to the following neutrality theorem.

Pr o p o s i t i o n 1 : Fo r eve r y co m b i n a t i o n o f t a x r u l e s t h e s u b g a m e N a s h -eq u i l i b r i u m i n t a x r a te s y i e ld s t h e s a m e n a t i o n a l i n co m e p a i r [ Y , Y*] a n d t h es a m e ca p i ta l f l o w Z , w h er e 0 < Z < Z . T h e e q u i l ib r i u m t a x ra te s ar e

, . ( = 0~*= l + ~ , t E[0 , tmax]

i f t h e h o m e co u n t r y ch o o s es ex o r ccli f t h e h o m e co u n t r y ch o o s es d ed .

T h e f o r e i g n co u n t r y g a i n s w h er ea s t h e h o m e co u n t r y l o se s co m p a r e d t o t h ef r ee - t r a d e eq u i l i b r i u m .

The proof of the surprising result that governments are indifferent as towhich rule to choose is relegated to the appendix. Here, some intuition isattempted. For any home tax rate the foreign country faces a trade-off. Byincreasing its tax t* the foreign country lowers the return which has to bepaid to the home country. However, it also reduces capital inflows whichdrives up the marginal product of capital and reduces revenues. A small taxincrease above zero is always welfare-improving for the foreign country.Why does the foreign country not find a reversal of capital flows optimal(recall from the lemma that the foreign country effectively controls Z)? If areversal occurs, foreign capital owners are indifferent in equilibrium toinward and outward investment. To induce such a situation the foreign taxrate has to be higher than the home tax rate. From the foreign country'spoint of view this means, however, that the marginal gain from a unit ofcapital in the foreign country is higher than in the home country.

Now consider the home country. Why is t'= 0 optimal under ex and ccl?Take first the case when the home country is a capital importer. Then, forsimilar reasons as above, a positive tax rate t would be optimal. From theargument above it follows that the foreign country does not allow for such asituation. When the home country is confronted with outflow of capital andbad terms of trade, its dominant strategy is not to drive even more capitalout of the country. Increasing its own tax lowers the return on the existingcapital exported.Under ded the home country tax rate does not matter for the location ofcapital. The home tax rate simply redistributes income from capital ownersto the government and national income remains unaffected. Again, theforeign tax rate determines the capital market equilibrium. Since the capitalflow and the foreign tax rate are the same in all subgames, national incomelevels are the same. The foreign country improves upon the free-tradeequilibrium since its tax rate is positive although t'= 0. Since free-t rade is

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E . J a n e b a / J o u r n a l o f P u b l i c E c o n o m i c s . 56 ( 1 9 9 5) 3 1 1 - 3 2 5 319e q u i v a l e n t t o jo i n t o u t p u t m a x i m i z a t i o n , t h e h o m e c o u n t r y m u s t b e w o r s eo f f .5

3 . Can f i sca l coopera t ion be Pare to- improving?S i n c e th e n o n - c o o p e r a t i v e N a s h - e q u i l i b r i u m y i e l d s a n i n e ff i c i e n t a l l o c a t io n

o f t h e w o r l d ' s c a p i ta l s t o c k , c o o p e r a t i o n m i g h t b e w e l f a r e - i m p r o v i n g fo rb o t h c o u n t r i e s . O f c o u r s e , i f t h e g o v e r n m e n t h a d a l u m p - s u m t a x , t h e n -w i t h z e r o c o r p o r a t e t a x e s a n d a c o m p e n s a t o r y p a y m e n t f r o m t h e h o m e t o

t h e f o r e i g n c o u n t r y - a P a r e t o - i m p r o v e m e n t w o u l d b e p o s s ib l e . T h e m o r ei n t e r e s t i n g a n d p o l i t i c a l ly r e l e v a n t q u e s t i o n i s, h o w e v e r , w h e t h e r t h e r e e x i s t sa c o n t r a c t w h i c h r e q u i r e s n e i t h e r a s i de p a y m e n t n o r f ul l h a r m o n i z a t i o n o ft a x r a t e s . T h e l a t t e r a s p e c t s c a p t u r e t h e i d e a o f n a t i o n a l s o v e r e i g n t y . O n af o r m a l l e v e l , p r e f e r r i n g m o r e s o v e r e i g n t y a t a g i v e n in c o m e l e v e l c a n b ed e s c r i b e d b y l e x i c o g r a p h i c p r e f e r e n c e s . F i r s t p r i o r i t y is g i v e n t o n a t i o n a li n c o m e . I f t w o s i t u a t io n s g iv e t h e s a m e l e v e l o f i n c o m e , g o v e r n m e n t s p r e f e rf e w e r r e s t r i c t i o n s o n t h e i r p o l i c y c h o i c e , i . e . n o c o m p e n s a t o r y p a y m e n t s a n dm o r e f l e x i b i l i ty i n c h o o s i n g t a x r a t e s .

T h e i d e a o f c o o p e r a t i o n w i t h o u t c o m p e n s a t o r y p a y m e n t s g o e s b a c k t oH a m a d a ( 1 9 6 6 ) . H e a n a l y z e d o n l y t h e c r e d i t m e t h o d a n d a s s u m e d t h a tm a r g i n a l p r o d u c t o f c a p i t a l is l i n e a r i n t h e n e i g h b o r h o o d o f t h e n o n -c o o p e r a t i v e e q u i l i b r i u m . 6 H e r e t h e t h r e e t a x r u le s w i l l b e c o m p a r e d a n d ar e s u l t o n c o o p e r a t i o n w i l l b e p r e s e n t e d w i t h o u t fu r t h e r a s s u m p t i o n s . Ac o o p e r a t i v e c o n t r a c t s p e c if i e s a ta x ru l e a n d a t a x r a t e c o m b i n a t i o n s u c h t h a tn a t i o n a l i n c o m e l e v e l s a r e h i g h e r th a n in t h e N a s h - e q u i l i b r i u m a n d c a p i t a l i se f f i c i e n t l y a l l o c a t e d . T h i s i s i l l u s t r a t e d in F i g . 1 . T h e l in e p a s s i n g t h r o u g h t h e

5 M aximum tax ra tes equal to o ne w ere excluded, I f i t were assumed that n o capi ta l is t radedwhen the n et re turn i s zero , a utarky would be a second N ash-equi l ibr ium when the credi t or thededuct ion method is adopted by the home country . However , s ince income levels are h igherunde r the t rade equi l ibr ium than unde r au tarky ( th is d i rect ly follows f rom the prope r t ies of theprodu ct ion functions) , the form er equi l ibr ium Pareto-dom inates the la t ter . Subsidies w ere a lsoexcluded since no other taxes were considered. S imi lar ly a non-negat ive government budgetconst raint was impl ic i t ly assumed . The governm ent would receive a lump-sum tax when taxinglabor . T he assumpt ion of inelast ic labor supply, howev er , was made for s impl ic i ty . M oreove r ,negat ive corp orate tax ra tes should be unde rstood as negat ive effect ive tax ra tes . S ince the taxbase was not ex pl ic i t ly mo deled , negat ive tax ra tes are di ff icult to just i fy and to in terpret .However , even i f one considered subsidies (and a lump-sum tax) the home country need notimprove i t s s i tuat ion compared to the case wi th non-negat ive tax ra tes . In any case, theNash-equi l ibr ia in a l l subgames would be s t i l l character ized by a posi t ive but too- low capi ta lf low. All quali tat ive results concerning the following Section 3 remain valid.6 M oreo ver , H am ada did not impo se a non-negat iv i ty const ra int on tax ra tes . Therefore , heimpl ic i t ly assumed that a lump -sum tax i s avai lable , which m akes the problem t r iv ia l as arguedabove .

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320 E. J ane ba / J ourna l o f Pub l ic Ec onom i c s 56 (1995) 3 l l -3 2 5y-

? .

Y ~ vFig. 1. Pareto-improving and Pareto-optimal allocations.

f r e e - t r a d e e q u i l i b r iu m w i t h s lo p e - 1 d e s c r ib e s th e s e t o f P a r e t o - o p t i m a la l l o c a t i o n s i n t h e e c o n o m y ( w h e n s i d e p a y m e n t s a r e p o s s i b l e ) . T h e s h a d e da r e a c o n t a i n s t h e s e t o f a l l o c a t i o n s w h i c h i m p r o v e u p o n t h e N a s h - e q u i l i b -r i u m .T o t h e i n v e s t i g a t e t h e p r o b l e m , f i r st t o b e c o n s i d e r e d a r e f is c al p o l ic i e sw h i c h a r e c o m p a t i b l e w i th f r e e - t r a d e c a p i ta l f lo w s. T h e f r e e - t r a d e e q u i l ib -r i u m y i e l d s a n e f f ic i e n t c a p i t a l a l l o c a t i o n s in c e t h e r e is n o d i f f e r e n c eb e t w e e n t h e s o c ia l a n d t h e p r i v a t e r e t u r n o n i n v e s t m e n t . W i t h t a x a t i o n t hi sis u s u a ll y n o l o n g e r tr u e . H o w e v e r , u n d e r e a c h t a x r u l e c h o s e n b y t h e h o m ec o u n t r y t h e r e e x is t ta x r a t e c o m b i n a t i o n s w h i c h r e s u l t in a f r e e - t r a d e c a p i t a lf lo w . U n d e r e x e m p t i o n t h is i s t h e c a s e f o r t = t * , u n d e r c r e d i t f o r t i> t * , a n du n d e r d e d u c t i o n t * - - 0 m u s t h o l d . T h e r e a s o n is s t r a ig h t f o rw a r d : c a p i ta l ise f f i c i e n t ly a l l o c a t e d i f i n e q u i l i b r i u m t h e m a r g i n a l r e t u r n o n c a p i t a l is e q u a li n b o t h c o u n t r i e s . T h i s is s a t i sf i e d if f o r e a c h t a x r u l e i n E q . ( 5 ) t a x e s c a n c e l .V e r y o f t e n i d e n t i c a l ta x r a t e s a r e c l a i m e d t o b e n e c e s s a r y t o a c h i e v e a ne f f i c i e n t a l l o c a t io n : a s c a n n o w b e s e e n , e f f i c ie n c y c r i ti c a ll y d e p e n d s o n t h et a x r u l e t h a t i s a p p l i e d . I d e n t i c a l t a x r a t e s a r e s u f f i c i e n t f o r e f f i c i e n c y o n l y i ft h e h o m e c o u n t r y c h o o s e s cc l o r e x . T h e y a r e a l s o n e c e s s a r y u n d e r e x , b u ta r e n e i t h e r n e c e s s a r y n o r s u f fi c ie n t u n d e r t h e d e d u c t i o n m e t h o d .

U n d e r t h e r e q u i r e m e n t o f a n e ff ic i e nt t a x s tr u c t u r e n a t i o n a l i n c o m e l e v e ls(Ye , Y~) a r e e q u i v a l e n t t o a f r e e - t r a d e i n c o m e l e v e l s ( Y 0 , Y ~ ) o n l y f o r s o m ep a r t i c u l a r t a x ra t e c o n s t e ll a t io n s . W h e n t h e h o m e c o u n t r y a d o p t s t h ee x e m p t i o n o r t h e c r e d i t m e t h o d t h e f o ll o w i n g r e l a t i o n s h ip h o l d s:

reex = - - E V i C t = F [ / ~ - Z ] + (1 - t* )F~: [ /~* + Z]Z Y ~ , ( 9 )

w h e r e e q u a l i t y ho l d s in ( 8 ) a n d ( 9 ) if t * = 0 . T h e e x e m p t i o n a n d c r e d i tm e t h o d s a r e e q u i v a l e n t u n d e r e f f ic i e n t t a x s t r u c t u r e s a s f a r as n a t i o n a li n c o m e i s c o n c e r n e d . F o r a g i v e n f o r e i g n ta x r a t e t h e y d i f f e r r e g a r d i n g t h e

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E. Janeba / Journal of Public Econom ics 56 (1995) 311-325 321d i s t r ib u t i o n o f th e n e t - o f - f o r e i g n -t a x r e t u r n b e t w e e n t h e h o m e c o u n t r yg o v e r n m e n t a n d t h e h o m e c a p i ta l o w n e r s . I n c o n t r a s t t o e x a n d c c l, u n d e rt h e d e d u c t i o n m e t h o d a z e r o f o re i g n ta x r a t e i s a n e c e s s a r y c o n d i t i o n t or e a c h e f f i c i e n c y , w h i c h l e a d s " , ,ded , ,O r e = Y 0 a n d Y E = Y 0 . H e n c e , o n e c a nd i r e c tl y c o n c l u d e t h a t u n d e r t h e d e d u c t i o n m e t h o d t h e r e n e v e r e x is ts ac o o p e r a t i v e c o n t r a c t w h i c h a ll ow s a P a r e t o - i m p r o v e m e n t a n d a n e f fi c ie n tc a p i t a l a l l o c a t i o n .

C o n s i d e r n e x t th e e x e m p t i o n m e t h o d c h o s e n b y th e h o m e c o u n t r y . T h eq u e s t i o n is w h e t h e r t h e r e e x i s t e q u a l t a x r a t e s t = t* s u c h t h a t a t l e a s t t h el o w e r r i g h t c o r n e r o f th e s h a d e d a r e a i n F i g. 1 is a tt a i n a b l e , t h a t is f o r m a l l y

Y~./> I7 * = F * [ /< * + 2 1 - (1 - 7 * )F ~ :[ /< * + 2 1 2 . (1 0 )Y*E i s m o n o t o n i c a l l y i n c r e a s i n g i n t * . C l e a r l y , f o r t* c l o s e t o o n e , Y~-c o n v e r g e s t o F * [ / ~ * + Z ] w h i c h is l a r g e r t h a n t h e r i g h t - h a n d s id e o f ( 1 0 ) ,s i nc e f r o m P r o p o s i t i o n 1 , Z > Z . H o w e v e r , c a n a ll e f fi c ie n t P a r e t o - i m -p r o v e m e n t s b e i m p l e m e n t e d ? I f t hi s is t h e c a s e it m u s t h o l d t h a t

l ie = Y0 + r ~ - YE ~< 17 (1 1)w h i c h i s , f o r t* s u f f i c i e n t ly c l o s e t o o n e , e q u i v a l e n t t o

F [ K - Z ] - F [ K - Z ] - (1 - 7 * ) ~ [ g * + 2 ] 2 ~

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322 E. J ane ba / J ourna l o f Pub l i c Ec onom i c s 56 (1995) 3 11 -32 5E C m e m b e r s ta t es ( C o u n c i l o f t h e E u r o p e a n C o m m u n i t i e s , 1 99 0) . U s u a l l yi n d o u b l e t a x a t i o n t r e a t i e s , u p p e r l im i t s f o r w i t h h o l d i n g t a x e s a r e f ix e d . I nW e s t e r n c o u n t r i e s , w i t h h o l d i n g t a x e s o n d i v i d e d r e p a t r ia t i o n s o f f o r e ig ns u b s i d i a r i e s a r e t y p i c a l ly v e r y lo w ( O E C D , 1 9 9 0 ), 5 t o 1 0 % , o r e v e n z e r o a sr u l e d b y t h e E C C o u n c i l D i r e c t i v e . A l t h o u g h n o w i t h h o l d in g t a x w a sa s s u m e d , t h e o b s e r v a t i o n c a n b e r a t i o n a li z e d w i th i n t h e m o d e l . A s l o n g a st h e w i t h h o l d i n g t a x i s l e v i e d o n t o p o f t h e c o r p o r a t e t a x r a t e , t h e f o r e i g nc o u n t r y t a x t* c a n b e i n t e r p r e t e d a s t h e s u m o f b o t h t a x ra t e s . I f t h e f o r e i g ng o v e r n m e n t w a n t s t o r e m a i n f l e x i b le i n r a i si n g r e v e n u e s , i t i s b e t t e r t o a d j u s tt h e w i t h h o l d i n g t a x r a t h e r t h a n t h e c o r p o r a t e t a x . S i n c e u n d e r t h e c r e d i tm e t h o d t h e h o s t c o u n t r y t ax h a s to b e s m a l l e r t h a n t h e h o m e c o u n t r y ta x ,l o w o r z e r o w i t h h o l d i n g t a x e s a r e t h e c o n s e q u e n c e . C o r p o r a t e t a x r a t e s c a nb e c h a n g e d a s l o n g a s b o t h c o u n t r i e s i m p r o v e u p o n t h e N a s h - e q u i l i b r i u m .

4 . C o n c l u s i o n s

I n t hi s p a p e r , t a x c o m p e t i t i o n w a s i n t e r p r e t e d a s a n o n - c o o p e r a t i v e g a m eb e t w e e n g o v e r n m e n t s t h a t i n f lu e n c e th e l o c a t io n o f i n v e s t m e n t b y t h e u s e o fb o t h t a x r a t e s a n d t h e f o r m o f d o u b l e t a x a t i o n r e l i e f . I n e q u i l i b r i u m , a l ld i f f e r e n t t a x r u le c o m b i n a t i o n s l e a d t o t h e s a m e p a i r o f n a t i o n a l i n c o m el e v e ls . W h e n t h e c o r p o r a t e t a x r a t e o f t h e c a p i ta l e x p o r t i n g c o u n t r y a f fe c t sc a p i t a l f l o w s a s u n d e r t h e c r e d i t a n d e x e m p t i o n m e t h o d s , i t i s d r i v e n d o w nt o z e r o . T h e c a p i t a l i m p o r t i n g c o u n t r y s e ts a p o s i t iv e t a x r a t e , t h e r e b yi m p r o v i n g t h e t e r m s o f t r a d e . T h e r e s u lt is in c o n t ra s t t o B o n d a n dS a m u e l s o n ( 1 9 8 9 ), w h o a s s u m e t h a t t h e c a p i t al e x p o r t i n g c o u n t r y c a n f ul lyd i s c r i m i n a t e a g a i n s t f o r e i g n d i r e c t i n v e s t m e n t b y c h o o s i n g a d i f f e r e n t t a xr a t e o n f o r e i g n s o u r c e i n c o m e . I n t h e i r m o d e l t h e d e d u c t i o n m e t h o d w a sp r e f e r r e d t o t h e c r e d i t m e t h o d s i n c e t h e f o r m e r , b u t n o t t h e l a t t e r , a l l o w st r a d e i n c a p i t a l. T h i s f o r m o f d i s c r im i n a t i o n , h o w e v e r , is n o t a p p l i e d inp r a c t i c e . T r a d e i n c a p i t a l c a n b e o b s e r v e d u n d e r t h e c r e d i t m e t h o d e v e nw h e n n o d o u b l e t a x a t i o n t r e a t y ha s b e e n s i gn e d . M o r e o v e r , a c c o r d i n g toA l w o r t h ( 1 9 88 ) t h e d e d u c t i o n s y s t e m is u s e d a l m o s t n o w h e r e .

T a x c o m p e t i t i o n l e a d s t o a n i n e f f i c ie n t a l l o c a t i o n o f t h e w o r l d ' s c a p i ta ls t o c k , w h i c h r a i se s t h e i ss u e o f c o o p e r a t i o n . I n fa c t , d o u b l e t a x a t i o n t r e a t i e sc a n b e u n d e r s t o o d a s a f o r m o f c o o p e r a t i o n . G o v e r n m e n t s s ig n a c o n t r a c tw h i c h s p e c if i e s ( w i t h h o l d i n g ) t a x r a t e s a n d t h e f o r m o f d o u b l e t a x a t i o n r e l i e fs u c h t h a t b o t h c o u n t r i e s b e n e f i t. T h e c l e a r a d v a n t a g e o f t h e c r e d i t o v e r t h ee x e m p t i o n a n d d e d u c t i o n m e t h o d s is t h a t n e i t h e r fu l ly h a r m o n i z e d t a x r a t e s( a s u n d e r e x e m p t i o n ) n o r s i d e p a y m e n t s ( a s u n d e r d e d u c t i o n ) a r e n e c e s s a r y .I n th is s e n s e , t h e a d o p t i o n o f t h e p r e s e n t E C l aw ( C o u n c i l o f t h e E u r o p e a nC o m m u n i t i e s , 1 9 90 ), w h i ch a ll ow s f o r t h e c r e d it a n d e x e m p t i o n m e t h o d so n l y , s e e m s t o b e a g o o d d e c is i on . T h e D i r e c t i v e i n t e n d s t o l o w e r d o u b l e

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E . J a n e b a / J o u r n a l o f P u b l i c E c o n o m i c s 5 6 ( 1 9 0 5) 3 1 1 - 3 2 5 323t a x a t i o n f o r a g i v e n c a p it a l fl ow . I n t h e l i g h t o f th e a b o v e r e s u l t, h o w e v e r ,t h e m e r i t o f t h e c r e d it a n d e x e m p t i o n m e t h o d s is to m a k e a n i n d iv i d u a ll yr a t i o n a l a n d e f f ic i e n t a l l o c a ti o n p o s s i b le w i t h o u t s i d e p a y m e n t s .

A c k n o w l e d g m e n t sF i n a n c i a l s u p p o r t b y D e u t s c h e F o r s c h u n g s g e m e i n s c h a f t , S o n d e r -

f o r s c h u n g s b e r e i c h 3 0 3 a t t h e U n i v e r s i t y o f B o n n , i s g r a t e f u l l y a c k n o w l -e d g e d . I w o u l d l ik e t o t h a n k D i e t e r B 6 s G / i n th e r L a n g , L u d g e r L i n n e m a n n ,L o r e n z N e t t , W o l f g a n g P e t e rs a n d t w o a n o n y m o u s r e f e r e es f o r u se f ulc o m m e n t s a n d f o r i m p r o v i n g t h e e x p o s i t i o n c o n s i d e r a b l y . I n p a r t i c u l a r Iw i s h t o t h a n k L a r r y S a m u e l s o n f o r v a l u a b l e d i s c u s s i o n s a n d f o r e n c o u r a g i n gm e t o u n d e r t a k e t h i s r e s e a r c h .

A p p e n d i x : P r o o f o f P r o p o s i t i o n 1R a t h e r t h a n e a c h s u b g a m e b e i n g a n a ly z e d i n d iv i d u a ll y , t h e p r o o f isp e r f o r m e d d i r e c t ly b y a c h a r a c t e r i z a t io n o f t h e e q u i l ib r i u m i n s e v e r al s t e p s.F a c t 1 : I f a n e q u i l i b r i u m e x i st s , t h e n Z > O .

T o p r o v e F a c t 1 , i t w i ll f ir s t b e s h o w n t h a t Z < 0 i s n o t c o m p a t i b l e w i t h a ne q u i l i b r i u m . F r o m t h e l e m m a i t is k n o w n t h a t Z < 0 r e q u i r e s t h e f o r e i g nc o u n t r y t o a d o p t t h e e x e m p t i o n m e t h o d ; h e n c e Z , . < 0 . I n t h i s c a s e f o r e i g ni n c o m e i s d e c r e a s i n g i n t *. T o s e e t h is , d i f f e r e n t i a t e f o r e i g n n a t i o n a l i n c o m e ,w h i c h g i v e s

Y,* = [ - (1 - t * ) F ~ Z + t * F ~ ] Z , , + G Z (13)[- E*(1 - t*( 1 + e) ) ( 1 4 )

w h e r e t h e s e c o n d l i n e f o l lo w s b y u s e o f (7 ) . I f Z < 0 , t h e n E a n d E * a r en e g a t i v e a n d t h e t e r m i n b r a c k e t s i s p o s i ti v e . F o r e i g n n a t i o n a l i n c o m e isd e c r e a s i n g i n t* , h e n c e a r e d u c t i o n o f t h e f o r e i g n t a x is b e n e fi c ia l a n d c a p i t a lf l o w s a r e n o n - n e g a t i v e i f a n e q u i l i b r i u m e x i s t s . I n t h e n e x t s t e p i t is s h o w nt h a t a u t a r k y ( Z = 0 ) i s n o t o p t i m a l f o r t h e f o r e i g n c o u n t r y . F o r Z = 0 , (1 3 )r e d u c e s t o

Y**lz=0 = t*IaKZ, , . ( 1 5 )A s m a l l r e d u c t i o n o f t * , w h i c h m a k e s Z p o s i t i v e ( t h e l e f t- s i d e d e r i v a t i v e a t

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3 2 4 E . J a n e b a / J o u r n a l o f P u b l i c E c o n o m i c s 5 6 ( 1 9 9 5) 3 1 1 - 3 2 5

Z = 0 ) , i n c r e a s e s n a t i o n a l i n c o m e s i nc e Z , . i s n e g a t i v e ] H e n c e , f o r a n y t t h eo p t i m a l f o r e i g n t a x i m p l ie s Z > 0 . M o r e o v e r t h e L e m m a a n d F a c t 1 i m p l yt h a t t h e f o r e i g n c o u n t r y ' s c h o i c e o f d o u b l e t a x a t i o n r e l i e f i s n o t r e l e v a n t f o rt h e e q u i l i b r iu m . T h e r e f o r e t h e h o m e c o u n t r y 's d e c is i on o n d o u b l e t a x a t i o nr e l i e f is c o n s i d e r e d . F a c t 2 d e a l s w i t h th e c a s e i n w h i c h t h e h o m e c o u n t r yc h o o s e s e i t h e r a t a x c r e d i t o r t h e e x e m p t i o n r u l e .F a c t 2: I f a n e q u i l i b r i u m e x i st s u n d e r c c l o r e x , t h e n 7 = O.

D i f f e r e n t i a t i n g h o m e n a t i o n a l i n c o m e y i e l d sY , = [ - F K + (1 - t * ) ( F * r x Z + P r ) ] Z , . ( 1 6 )

H o m e t a x a t i o n d r i ve s c a p i ta l o u t o f t h e c o u n t r y u n d e r t h e e x e m p t i o n o rc r e d i t m e t h o d s ( w h e n t < t * ) . H e n c e , t h e c a p i ta l m a r k e t i s in e q u i li b r iu mw h e n ( 5 b) h o ld s . T h e r e f o r e , ( 1 6 ) c a n be r e w r i t t e n as

Y , [ - -t F K + ( 1 - - * t ) F K r Z ] Z , . ( 1 7 )S i n c e n a t io n a l i n c o m e i s d e c r e a s i n g in t w h e n Z > 0 , t h e h o m e c o u n t r yc h o o s e s i ts t a x r a t e s u c h t h a t Z ~ 0 f o r a n yh o m e t a x r a t e , h o w e v e r , t h e n t = 0 m u s t h o l d in e q u i li b r iu m . A s s u m e i nc o n t r a s t t h a t i n t h e c a s e o f p o s i t i v e c a p i t a l fl ow s t ' > 0 is a b e s t r e s p o n s e f o rs o m e t * . T h e n Z , = 0 m u s t h o l d f o r a l l t ~< T. S i n c e Z , = 0 h o l d s o n l y i f t / > t*u n d e r c c l , a p o s i t i v e h o m e t a x is n o t a b e s t r e s p o n s e w h e n t* > 0 . I f t * = 0,t h e n Z t - - 0 f o r a l l t . In t h a t c a s e , h o w e v e r , a s t r i c t ly p o s i t i v e h o m e t a x i s n o ta n e q u i l i b r i u m . A s s u m e o n t h e c o n t r a r y t > 0 a n d t* = 0 is a n e q u i l i b r iu m .S i n c e Z , . = 0 , f o r e i g n n a t i o n a l i n c o m e is i n c r e a s in g i n t h e f o r e i g n t a x(Y,** = ~ Z > 0 ) , w h i c h c o n t r a d i c t s t h e a s s u m p t i o n .F a c t 3 : A n e q u i l i b r i u m c h a r a c t e r i z e d b y Z ( O , t * ) > 0 e x i st s u n d e r c c l a n d e x .

S i n c e i n e q u i l i b r i u m t = 0 f o r a l l t * ( w h i c h i m p l i e s Z ( 0 , t * ) > 0 ) , t h e p r o o fo f e x i s t e n c e r e d u c e s t o s h o w i n g t h a t Z ( 0 , t * ) > 0 is p r o o f . T h e a s s u m p t i o nm a d e i n E q . ( 1 ) a n d e n s u r e t h a t p o s i t i v e c a p i t a l f lo w s a r e c o m p a t i b l e w i t h as m a l l b u t p o s i t i v e f o r e i g n t a x r a t e .F a c t 4: T h e r e e x is ts a n e q u i li b r i u m u n d e r d e d i n d e p e n d e n t o f t, w h i c h h a s t hes a m e p r o p e r t ie s r e g a r d in g ( Y , Y * ) a n d Z a s u n d e r c c l a n d e x .

U n d e r t h e d e d u c t i o n m e t h o d t h e h o m e t ax r a te d o e s n o t a f fe c t t h ee q u i l i b r iu m i n th e c a p i ta l m a r k e t . T h e c a p it a l m a r k e t e q u i l i b r iu m c o n d i t io n s

7 I t is e a s i l y c h e c k e d t h a t t * i s s t r ic t l y p o s i t i v e w h e n Z c o n v e r g e s t o z e r o .

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E. Janeba / Journal of Public Economics 56 (1995) 311-325 325(5a), (5b) an d (5c) are identica l for all tax rules since unde r the credit an dexe mpt ion me thod s the h ome tax is zero. Equ il i br i um capital f lows andnational income levels depend only on the foreign tax.

F a c t 5: T h e o p t i m a l f o r e i g n t a x in e q u i l i b r i u m i s c h a r a c t e r i z e d b y 7* = (1 +5) -1 .With

op t ima lwr i t tenimplies:

a zero or ir relevant home tax rate, the prob lem reduces to antax choice for the foreign country. The optimal tax rate can be

as an inverse elast ici ty rule by the use of (14) . This immediately

F a c t 6 :i n c o m e

E q u i l i b r i u m c a p it a l f l o w s a r e to o l o w , 0 < Z < Z , a n d n a t i o n a ll eve l s a re cha rac t e r i z ed by Y < Yo an d Y* > Y~*~.

This complet es the proof. [ ]

R e f e r e n c e s

Alworth, J.S., 1988, The finance, investment and taxation decisions of multinationals (BasilBlackwell, Oxford).Bond, E.W., 1991, Optimal tax and Tariff policies with tax credits, Journal of InternationalEconomics 30, 317-329.Bond, E.W. and L. Samuelson, 1989, Strategic behavior and the rules for international taxationof capital, Economic Journal 99, 1099-1111.Council of the European Communities, 1990, Council Directive of July 23, 1990 on thecommon system of taxation applicable in the case of parent companies and subsidiaries ofdifferent Member States, Official Journal of the European Communities, No. L 225/6-9 of20.8.1990.Gordon, R.H. 1990, Can capital income taxes survive in open economies?, NBER WorkingPaper No. 3416.Hamada, K., 1966, Strategic aspects of taxation on foreign investment income, QuarterlyJournal of Economics 80, 361-375.Hodder, J.E. and L.W. Senbet, 1990, International capital structure equilibrium, Journal ofFinance 45, 1495-1516.Mintz, J.M. and H. Tulkens, 1990, Strategic use of tax rates and credits in a model ofinternational corporate income tax competition, CORE Discussion Paper No. 9073.OECD, 1990, Taxation and international capital flows: A symposium of OECD and non-OECD countries, Paris.Ruffin, R.J., 1988, International factor movements, in: R.W. Jones and P.B. Kenen, eds.,Handbook of International Economics, Vol. 1 (North-Holland, Amsterdam) 237-288.Sinn, H.-W., 1990, Taxation and the birth of foreign subsidiaries. Discussion Paper No. 90-30,University of Munich.Slemrod, J., 1988, Effect of taxation with international capital mobility, in: H.J. Aaron, H.Galper, J.A. Pechman, eds., Uneasy compromise: Problems of hybrid income-consumptiontax, (The Brookings Institution, Washington D.C.) 115-155.