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Working Paper 8801 TOBIN'S Q, INVESTMENT, AND THE ENDOGENOUS ADJUSTMENT OF FINANCIAL STRUCTURE b y W i l l i a m P. Osterberg W i l l i a m P. Osterberg i s an economist a t t h e Federal Reserve Bank o f Cleveland. T h i s paper i s based on t h e f i r s t c h a p t e r o f t h e a u t h o r ' s Ph.D. d i s s e r t a t i o n . The a u t h o r i s g r a t e f u l t o W i l l i a m Brock, C h r i s F l i n n , Mark G e r t l e r , and Donald Hester for numerous he1p f u l comments and suggestions. Working papers o f t h e Federal Reserve Bank o f Cleveland are p r e l i m i n a r y m a t e r i a l s c i r c u l a t e d t o s t i m u l a t e d i s c u s s i o n and c r i t i c a l comment. The views s t a t e d h e r e i n a r e those o f t h e a u t h o r and n o t n e c e s s a r i l y those o f t h e Federal Reserve Bank of C l e v e l a n d o r o f t h e Board o f Governors of t h e Federal Reserve System. A p r i l 1988 ABSTRACT This paper asks whether q t h e o r y must be modified t o take account of f i n a n c i a l s t r u c t u r e by analyzing a q model o f investment i n which f i n a n c i a l s t r u c t u r e a f f e c t s f i r m value. The model i s a p e r f e c t f o r e s i g h t model o f general e q u i l i b r i u m s i m i l a r t o t h a t o f Brock and Turnovsky (1981), except t h a t there i s a debt- related agency c o s t . The combination o f the agency c o s t and taxes t h a t favor debt y i e l d s an i n t e r i o r s o l u t i o n f o r the debt- to- equity r a t i o , which v a r i e s endogenously. We f i n d t h a t although q i s i n f l u e n c e d by f i n a n c i a l s t r u c t u r e , i t i s s t i l l a " s u f f i c i e n t s t a t i s t i c " f o r investment. However, the model i m p l i e s t h a t analyses which i g n o r e the endogenous adjustment o f f i n a n c i a l s t r u c t u r e w i l l s y s t e m a t i c a l l y e r r i n p r e d i c t i n g investment. To i l l u s t r a t e these p o i n t s , we examine the comparative s t a t i c s and dynamics o f changing the corporate tax r a t e . corporate tax r a t e lowers the c o s t o f c a p i t a l . An u n a n t i c i p a t e d increase i n t h e The presence o f r e a l agency costs, however, may cause the c a p i t a l stock t o d e c l i n e . TOBIN'S Q, INVESTMENT, AND THE ENDOGENOUS ADJUSTMENT OF FINANCIAL STRUCTURE I. I n t r o d u c t i o n Analyses o f the l i n k between f i n a n c i a l markets and t h e investment decisions o f f i r m s have g e n e r a l l y d i f f e r e d between t h e f i e l d s o f macroeconomics and finance. Macroeconomic analyses o f investment now focus on the r e l a t i o n between T o b i n ' s q and the r a t e o f investment. finance, I n the f i e l d of analyses tend t o focus on the r e l a t i o n s between t h e cost of c a p i t a l , f i r m s ' value, and f i r m s ' f i n a n c i n g decisions i n t h e presence o f c a p i t a l market imperfections. These l a t t e r analyses t y p i c a l l y describe f i n a n c i n g d e c i s i o n s by the 1everage or debt- to- equi t y r a t i o . ' Most q models ( f o r example, see Abel and Blanchard C19831, Hayashi C19821, o r Von Furstenberg C19771) assume t h a t n e i t h e r the market value o f a f i r m nor i t s cost o f c a p i t a l i s a f f e c t e d by the d e c i s i o n o f how investment i s financed. Analyses o f c a p i t a l market i m p e r f e c t i o n s (see Bradley,' J a r r e l l , and Kim C198411, on t h e o t h e r hand, f a i l t o p r o v i d e i n s i g h t about the dynamic r e l a t i o n between f i n a n c i a l s t r u c t u r e and investment. I n t h i s paper, we i n v e s t i g a t e whether q theory needs t o be m o d i f i e d t o take account o f f i n a n c i a l structure. The f a i l u r e o f q t o perform w e l l e m p i r i c a l l y i s another source o f m o t i v a t i o n t o modify q theory. Although q theory i m p l i e s t h a t past values o f q should n o t m a t t e r i n a r e g r e s s i o n o f investment r a t e s on c u r r e n t and p a s t q, most e m p i r i c a l t e s t s (see Abel and Blanchard C19831, Hayashi C19821, o r Von Furstenberg C19771) f i n d t h a t c u r r e n t q has low explanatory power and t h a t r e s i d u a l s are h i g h l y c o r r e l a t e d . These e m p i r i c a l r e s u l t s suggest t h a t we examine 1i n k s between f i n a n c i a l markets and investment o t h e r than q. I n t h i s paper, the debt- to- equity r a t i o a f f e c t s f i r m value and i s determinate, l y i n g between 0 and i n f i n i t y . The optimal debt- to- equi t y r a t i o , chosen by f i r m s , i s determined by agency costs o f debt together w i t h t a x r a t e s f a v o r i n g debt. The agency c o s t o f debt a r i s e s from the presence of bond covenants and o t h e r l e g a l o r i n s t i t u t i o n a l r e s t r i c t i o n s on f i r m s . Jensen and Meckl i n g (1976) and o t h e r s have shown how agency problems may be r e l a t e d t o financial structure. Tax r a t e s f a v o r debt issue, since corporate i n t e r e s t payments are tax- deductib l e f o r f i r m s . D i f f e r e n c e s between the personal income t a x r a t e , the c a p i t a l gains tax r a t e , and the corporate tax r a t e have a1 1 been c i t e d as determinants o f an optimal f i n a n c i a l s t r u c t u r e f o r firms and t a x c l i e n t e l es among i n v e s t o r s (see M i 1l e r C19771). Reasonable values f o r a1 1 t h r e e t a x r a t e s imply t h a t tax r a t e s f a v o r debt over e q u i t y . The model u t i 1i z e s frameworks developed by Abel and Blanchard ( 1 983) and Brock and Turnovsky (1981). I n t h i s dynamic, general e q u i l i b r i u m model of savings and investment, the r e l a t i o n between i n v e s t o r s ' p o r t f o l i o d e c i s i o n s and the decisions o f f i r m s i s c l e a r l y exposed. The l i n k between households and f i r m s i s the c o s t o f c a p i t a l , d r i v e n by the r a t e s o f r e t u r n r e q u i r e d by households. Firms, f a c i n g t a x r a t e s f a v o r i n g debt, and a cost of debt, choose the debt- to- equity r a t i o i n o r d e r t o t o minimize the cost o f c a p i t a l . V a r i a t i o n s i n t a x r a t e s o r i n the i n t e r e s t r a t e a f f e c t the trade- off between debt and e q u i t y and, thus, the optimal debt- to- equity r a t i o . We f i n d t h a t even i f f i n a n c i a l s t r u c t u r e a f f e c t s f i r m value, q i s a " s u f f i c i e n t s t a t i s t i c " f o r investment. Thus, u n l i k e C h i r i n k o (1987), we conclude t h a t f i n a n c i a l s t r u c t u r e does n o t e x p l a i n the poor performance of T o b i n ' s q. F i n a n c i a l s t r u c t u r e a f f e c t s q, however, because q i s the present discounted value o f a f t e r - t a x marginal products o f c a p i t a l and because t h e d i s c o u n t r a t e ( c o s t o f c a p i t a l 1 v a r i e s w i t h the debt- to- equi t y r a t i o . Indeed, the endogenous adjustment o f f i n a n c i a l s t r u c t u r e has r e a l e f f e c t s . For example, when i n t e r e s t r a t e s r i s e , f i r m s o f f s e t p a r t o f the e f f e c t on t h e c o s t of c a p i t a l by i n c r e a s i n g the debt- to- equity r a t i o t o take advantage o f t h e i n t e r e s t - d e d u c t i b i l i t y o f debt. This i m p l i e s t h a t models i g n o r i n g r e a l effects o f financial structure w i l l systematically e r r i n predicting investment. I n a d d i t i o n , one f a c t o r t h a t may p o t e n t i a l l y break the l i n k between marginal q and investment i s uncovered. U n a n t i c i p a t e d changes i n t h e corporate t a x r a t e may cause marginal q and investment t o move i n o p p o s i t e directions. The comparative s t a t i c s and dynamics o f an u n a n t i c i p a t e d change i n t h e corporate tax r a t e a r e analyzed t o demonstrate the s i g n i f i c a n c e o f t h e endogenous adjustment o f f i n a n c i a l s t r u c t u r e . 11. D e s c r i p t i o n o f the Model The model i s a v a r i a n t o f the p e r f e c t f o r e s i g h t models o f general e q u i l i b r i u m o f Abel-Blanchard (A-B> and Brock-Turnovsky (B-TI. F o l l o w i n g B-T, I i n d i c a t e the way i n which consumers' demand f o r savings i n f l u e n c e s t h e c o s t o f capital. The a p p r o p r i a t e form f o r the c o s t o f c a p i t a l i s determined e x p l i c i t l y from the f i r m s assumed o b j e c t i v e . costs i n t h e model i s i n t h e s p i r i t o f A-B. The i n c o r p o r a t i o n o f adjustment Costly financial structure provides t h e unique l i n k between f i n a n c i a l markets and r e a l decisions. The model c o n s i s t s o f t h r e e sectors: consumers, f i r m s , and government. Because a l l consumers are assumed t o be i d e n t i c a l , t h e a n a l y s i s i s conducted i n terms o f a r e p r e s e n t a t i v e consumer. S i m i l a r l y , a l l f i r m s are assumed t o be i d e n t i c a l , and the corporate s e c t o r i s aggregated t o a s i n g l e f i r m . Both t h e consumer and the f i r m a r e i n f i n i t e l y l i v e d and solve e x p l i c i t maximization problems by making f o r e c a s t s o f v a r i a b l e s r e l e v a n t t o these decisions. I assume t h a t a l l expectations o r f o r e c a s t s are f u l f i l l e d , t h a t a l l markets c l e a r , and t h a t a l l supply and demand f u n c t i o n s o f f i r m s and households a r e d e r i v e d from maximizing behavior under p e r f e c t competition. The consumer saves i n the form o f e i t h e r bonds o r e q u i t i e s . Being concerned o n l y w i t h r a t e s of r e t u r n on a l t e r n a t i v e assets, t h e consumer's problem i m p l i e s t h a t i f debt and e q u i t y are t o c o e x i s t , then a f t e r - t a x r a t e s of r e t u r n must be equal. Since t h e r e t u r n s are equal, the consumer would seem t o be i n d i f f e r e n t about the debt- to- equity r a t i o . The f i r m , however, i s n o t i n d i f f e r e n t about the debt- to- equity r a t i o . The f i r m maximizes i t s market value by choosing sequences o f n o t i o n a l demands and supplies. Given a s e t o f f i n a n c i a l / a c c o u n t i n g c o n s t r a i n t s , market value maximization i s e q u i v a l e n t t o maximization o f a p a r t i c u l a r present d i scounted value. The d i scount r a t e i ncorporates the r a t e o f r e t u r n r e q u i r e d by t h e consumer, the t a x r a t e s f a c i n g the consumer and the f i r m , and the agency c o s t o f debt. Because o f t h e presence o f an agency c o s t and a t a x s t r u c t u r e t h a t f a v o r s debt, t h e r e i s an optimal debt- to- equity r a t i o which minimizes the cost o f c a p i t a l and l i e s between 0 and i n f i n i t y . Without t h e agency c o s t , the optimal debt- to- equity r a t i o would be 0 o r i n f i n i t y , depending on the tax r a t e s . The government sets t h e t a x r a t e s T, T,, and consumption goods, b u t issues no money o r debt. statement i d e n t i t y r e q u i r e s t h a t t h e lump-sum t a x 111. A. T,, and consumes The government income T v a r y endogenously. The S t r u c t u r e The Consumer The u t i l i t y o f the consumer i s a f u n c t i o n o n l y o f consumption: t h e r e i s no d i s u t i 1it y associated w i t h l a b o r . The f i r m determines employment. Individual consumers view themselves as unable t o i n f l u e n c e the s i z e o f the lump sum tax. The household's o b j e c t i v e i s t o choose the sequence t = CO, { c t , bz, E;), m) t o solve m (1) MAX S e-"U(ct)dt 0 subject t o (3) lim t- get b t -> 0, l i m get ztEt 2 0, t- and (4) bt=o = bo, E L 0 = Eo. c t = r e a l p r i v a t e consumption t t = r e a l employment b t = demand f o r r e a l corporate bonds Et = number o f shares o f e q u i t y demand z, = r e l a t i v e p r i c e o f e q u i t y i n terms o f o u t p u t w t = r e a l wage r a t e s t = r e a l i n t e r e s t r a t e on p r i v a t e bonds r, = t a x r a t e on c a p i t a l gains r, = t a x r a t e on wage and i n t e r e s t income lump sum tax determined as r e s i d u a l from government income i d e n t i t y r = d = d i v i d e n d pay.out r a t e : = D/zE D '= r e a l dividends I3 = r a t e o f time discount 8 = r a t e o f r e t u r n on consumption, d e f i n e d below The u t i l i t y f u n c t i o n U ( c t ) has the usual concavity p r o p e r t i e s : < 0, U1(0) 0, U"( > Expression (2) i s the intertemporal budget = c o n s t r a i n t f a c i n g the consumer. Income i s received as l a b o r income, i n t e r e s t income, d i v i d e n d income, and c a p i t a l gains. income are taxed a t the r a t e 2,. U1( T,. Labor, i n t e r e s t , and dividend C a p i t a l gains are taxed a t the r a t e A l l c a p i t a l gains and losses on e q u i t y are immediately r e a l i z e d . With t h i s income, the household consumes o r purchases bonds o r e q u i t i e s . Expression ( 3 ) s t a t e s t h a t t h e values o f debt and e q u i t y are bounded. bonds mature instantaneously. stock o f debt and equities, All Expression ( 4 ) s t a t e s i n i t i a l conditions on t h e The outcome o f t h i s o p t i m i z a t i o n problem w i l l be sequences o f n o t i o n a l demands, where unambiguous t s u b s c r i p t s are omitted. This problem leads t o t h e f o r m u l a t i o n o f the f o l l o w i n g Hamiltonian: (5) H = e-" U { [ ( ~ O + ~ b ~ + d z E ~ ) ( l - r , )T- - bd - , ~ E ~ zid - TI + a(bd) + ((id)) where a and ( are t h e c o s t a t e v a r i a b l e s associated w i t h b and E, respectively. I f both debt and e q u i t y are t o be h e l d by the household, then a f t e r - t a x r a t e s o f r e t u r n must be equal. The existence o f both debt and e q u i t y w i 11 be optimal f o r the f i r m and, hence, both assets w i 11 be h e l d by the household. This i m p l i e s t h a t c o n d i t i o n (6) w i l l hold: (6) ~(1-T,) = 8 = (~-T,)z/z + d(1-2,). 8 i s the r a t e of r e t u r n on consumption: B. 8 = 13 - U,,c/U,. TheFirm The f i r m maximizes t h e market value o f debt p l u s e q u i t y a t time t = 0, V,=, = bt,o + zt,oEt,o. Given a s e t o f f i n a n c i a l and production c o n s t r a i n t s , and numerical values f o r KO, b o , and Eo, maximizing V t Z o i s e q u i v a l e n t t o maximizing a p a r t i c u l a r present discounted value. equivalence i s demonstrated i n appendix A. This The appropriate discount r a t e o r c o s t o f c a p i t a l i s determined by t h i s equivalence. These c o n s t r a i n t s are: y s = F(Kd, Id) (7) where Id = r e a l l a b o r demand by the f i r m K d = r e a l c a p i t a l demand by the f i r m n = r e a l gross p r o f i t s 6 = exogenous r a t e o f d e p r e c i a t i o n b s = r e a l supply o f corporate bonds X = bIzE, t h e debt- to- equity r a t i o y s = r e a l o u t p u t , the supply o f goods q( 1 = adjustment c o s t of i n v e s t i n g a(X)b = c o s t o f m a i n t a i n i n g the bond p o r t f o l i o RE = r e t a i n e d earnings Es = r e a l supply o f e q u i t i e s 2, = corporate t a x r a t e Expression ( 7 ) i s a production f u n c t i o n w i t h p o s i t i v e b u t d i m i n i s h i n g marginal p r o d u c t i v i t i e s and constant r e t u r n s t o scale. Expression (8) defines r e a l gross p r o f i t s as revenue minus the wage b i l l and adjustment costs associated w i t h gross investment. Expression (9) i n d i c a t e s t h a t gross p r o f i t s go t o bondholders as i n t e r e s t , t o the government as taxes, t o stockholders as dividends, i n t o r e t a i n e d earnings, o r are absorbed by the agency cost. Dividends a r e p a i d o u t a t a f i x e d r a t e d. taxable income. I n t e r e s t payments are deducted from Expression (10) s t a t e s t h a t a l l investment must be f i n a n c e d through r e t a i n e d earnings o r debt issue. There i s no e q u i t y issue, although there i s an i n i t i a l stock o f e q u i t y , Eo. Expression (11) s t a t e s t h a t a l l investment i s n e t investment o r replacement investment where d e p r e c i a t i o n occurs a t a constant r a t e 6. There i s no deduction f o r depreciation. Expression (12) s t a t e s the i n i t i a l c o n d i t i o n s f o r c a p i t a l , e q u i t y , and debt. The adjustment c o s t q(I,K) i s deducted f r o m t a x a b l e income, since increases i n the r a t e o f investment draw resources o f the f i r m away from productive a c t i v i t i e s . The adjustment c o s t f u n c t i o n q(I,K) i s assumed t o be 1i n e a r l y homogenous so t h a t i t can be w r i t t e n as h ( I / K ) I w i t h the p r o p e r t i e s h(0) = 0, hl(O> > 0, 2 h 1 ( + ( I / K ) h t ( 1 > 0. This i s s i m i l a r t o f o r m u l a t i o n s o f adjustment costs proposed by Hayashi (1 982) and o t h e r s . The c o s t a(X)b i s assumed n o t t o reduce o u t p u t by drawing on p r o d u c t i v e resources. While o n l y the i n t e r e s t r a t e on debt i s tax- deductible, the gross cost o f debt t o t h e f i r m i s Cs + g t X ) l b . The s i z e o f the f i r m does n o t a f f e c t t h i s cost d i r e c t l y , b u t t h e f i r m ' s value does. I f the f i r m ' s value increases due t o increases i n e q u i t y share p r i c e s , the debt- to- equity r a t i o fa1 1s. For a g i v e n f i r m value, increases i n debt lead t o an increase i n t h e agency cost. This c o s t i s b e s t viewed as an agency c o s t . Smith and Warner (1979) p o i n t o u t t h a t t h e existence o f bond covenants can be viewed as a method o f c o n t r o l l i n g the c o n f l i c t between bondholders and stockholders. I t i s assumed here t h a t bond covenants succeed i n e l i m i n a t i n g t h e c o n f l i c t , and thus firm- value maximization, r a t h e r than equity- value maximization, i s the proper f i r m objective. Without such r e s t r i c t i o n s , Bond covenants t y p i c a l l y r e s t r i c t debt issue. For stockholders would issue more debt and i n c u r g r e a t e r agency costs. example, i t may be t h a t the i n c e n t i v e f o r stockholders t o s h i f t t o higher- variance investment p r o j e c t s increases w i t h the face value of debt (see Barnea, Haugen, and Senbet C19851). of the f i r m , I f such a s h i f t decreases the t o t a l value then bondholders, a n t i c i p a t i n g such actions, would demand h i g h e r interest rates. The increase i n the i n t e r e s t r a t e demanded by bondholders i s a type o f agency cost. Here I assume t h a t bond covenants are n e g o t i a t e d t o r e s t r i c t the l e v e l o f debt, f o r a given value o f e q u i t y . The higher t h e debt- to- equity r a t i o , the more 1 i k e l y t h a t the covenant w i 11 be v i o l a t e d , r e s u l t i n g i n r e s t r i c t i o n s on investment a c t i v i t i e s and a decrease i n f i r m value. Thus, the c o s t o f i s s u i n g b u n i t s o f debt increases w i t h t h e debt- to- equity r a t i o . I assume t h a t a(0) > 0, a ' ( 1 > 0, and a " ( Appendix A demonstrates how expressions (7)-(12) can be used t o d e r i v e expression (13): Y, t h e cash f l o w , i s defined as r, t h e c o s t o f c a p i t a l , i s defined as Now t h e f i r m ' s problem i s t o choose the sequence a (16) MAX subject t o J'e 0 - SiT(z>dz = Y( t 1 d t KO, b t Z o = b o . 1 > 0. Kt, c:, bs) Note t h a t Y i s s o l e l y a f u n c t i o n o f " r e a l " v a r i a b l e s Kt and It, whereas r i s a f u n c t i o n o f o n l y " f i n a n c l a l " v a r i a b l e s summarized by 1,. These considerations imply t h a t the f i r m can optimize i n t h e f o l l o w i n g sequence: first, choose K: and It t o maximize Y(t), then choose At t o minimize T ( t ) . I f a(X) = 0, the f i r m would choose X as f o l l o w s : (17) s e t X = rn if (1 = T,) > (1 - ~ , )-(Tl ~ - T,) < (1 (18) s e t X = 0 i f (1 where T, = dr,+ (;/z)T, d + ilz - ~,)(1- ) T,) i s the marginal t a x r a t e on e q u i t y income. Expressions (17) and (18) imply t h a t i f the a f t e r - t a x income from bonds exceeds the a f t e r - t a x i ncome from e q u i t y , i n v e s t o r s p r e f e r debt f inance. Given reasonable values o f d, T, T,, and T,, (17) i s l i k e l y t o be the case and w i l l be a ~ s u m e d . ~C o n d i t i o n (17) i n c o n j u n c t i o n w i t h a c o s t t o debt a(X)b r e s u l t s i n an optimal X: 0 < X < The f i r m ' s problem leads t o the f o l l o w i n g Hamiltonian f o r m u l a t i o n : where q'and Q are the c o s t a t e v a r i a b l e s associated w i t h K and b, respectively. Expressions (20) through (23) a r e the o p t i m a l it y c o n d i t i o n s f o r the f i r m . (24) (TVC) l i m p t q t K t = 0 = l i m ptQtbt tt- -Sh T ( ~ > d z where p , = e Expression (21) s t a t e s t h a t marginal q d i f f e r s from one by the a f t e r - t a x d e c l i n e i n r e a l cash f l o w due t o i n s t a l l a t i o n costs and i m p l i e s t h a t the Expression (22) i s investment r a t e i s an i n c r e a s i n g f u n c t i o n o f marginal q. t h e a r b i t r a g e c o n d i t i o n t h a t t h e shadow r e t u r n from h o l d i n g c a p i t a l must equal t h e r e q u i r e d r e t u r n on c a p i t a l , (r + 6)q. Expression (22) can be i n t e g r a t e d s u b j e c t t o the t r a n s v e r s a l i t y c o n d i t i o n (24) t o o b t a i n Thus, q equals the present discounted sum o f a f t e r - t a x marginal products of a u n i t o f c a p i t a l i n s t a l l e d a t time t. T, r depends on tax r a t e s and Expression (23) s t a t e s the r e l a t i o n between X, t h e debt cost, so does q. 8, and Since when the f i r m chooses X so as t o minimize r. Since t h e r e i s no e q u i t y issue, X i s adjusted by v a r y i n g the b versus RE f i n a n c i n g m i x . Having chosen the p a t h o f the c a p i t a l stock, employment, and t h e debt- to- equi t y r a t i o , the f i r m has maximized V t = o , and the r e s u l t i n g i n i t i a l share p r i c e i s determined by the c o n d i t i o n b t Z o + zt,oEt=o = V t Z o . C. Government The government i s c h a r a c t e r i z e d by an income statement i d e n t i t y : (26) r, [ w l + sb + dzEl The government sets T, + T, T E ;, T,, + T,[Y and g. v a r i e s so as t o s a t i s f y the i d e n t i t y . impact o f a change i n T - w l - q(I,K) - s b l + r = g. The lump sum tax Although T T a d j u s t s endogenously, t h e i s ignored i n the dynamic a n a l y s i s t h a t follows because i n d i v i d u a l consumers take T as given p a r a m e t r i c a l l y . IV. Perfect Foresight Equilibrium A p e r f e c t f o r e s i g h t e q u i l i b r i u m i s a sequence o f p r i c e s and q u a n t i t i e s f o r which n o t i o n a l demands and suppl i e s f o r bonds and e q u i t i e s a r e equal i n t h e p r e s e n t and f u t u r e . Given t h e o p t i m a l i t y c o n d i t i o n s o f consumers and f i r m s and t h e government income statement i d e n t i t y , expressions (27)-(32) t h e sequence o f v a r i a b l e s , {Kt, c t ) , t=[O, determine a). Here I have simp1 i f i e d t h e model b y s e t t i n g assume t h a t employment i s g i v e n exogenously. T, = TC = 0. I a1 so Together w i t h expression (201, t h i s i s analogous t o assuming t h a t t h e r e a l wage a d j u s t s t o e q u i l i b r a t e t h e l a b o r market. So, c o n d i t i o n (20) i s n o t needed below. Expression (28) i s a r e s t a t e m e n t o f t h e m a t e r i a l balance c o n s t r a i n t which uses t h e f a c t s : CXl(1 + b = X I I V , V = qK. Expression (31) g i v e s t h e o p t i m a l d e b t - t o - e q u i t y r a t i o and i n d i c a t e s t h a t a h i g h e r i n t e r e s t r a t e or c o r p o r a t e t a x r a t e means a h i g h e r d e b t - t o - e q u i t y r a t i o as t h e v a l u e o f t h e i n t e r e s t d e d u c t i o n r i s e s . To see t h a t (31) i m p l i e s an o p t i m a l X, d e r i v e e x p r e s s i o n (33) f r o m e x p r e s s i o n (32) f o r g i v e n and 8. T, Figure 1 shows how expression (33) i m p l i e s t h a t an increase i n from T, T,O t o .rPl leads t o an increase i n the optimal X from Xz t o 1:. An increase i n T, makes a higher X optimal. Expressions (31) and (32) together show t h a t t h e minimized cost o f c a p i t a l i s equal t o (34) r = 8 - ~'(x)x'. The decrease i n the c o s t o f c a p i t a l due t o an increase i n by the T,I l i n e i n f i g u r e 1. T, i s indicated However, expression (28) i n d i c a t e s t h a t an increase i n the debt- to- equity r a t i o , which reduces t h e c o s t o f c a p i t a l , may increase the debt cost. The change i n a(X)b depends on t h e change i n X, t h e response o f q, and t h e response o f K. These r e l a t i o n s h i p s a r e examined below. V. Steady State and Comparative Results I n the steady s t a t e , K = 0 and c = 0. The f i r s t c o n d i t i o n i m p l i e s t h a t I = 6K and thus I I K = 6. The second impl i e s t h a t 8 = B: the steady s t a t e i n t e r e s t r a t e i s the r a t e o f time preference o f consumers. The c o n d i t i o n t h a t 8 = B, t o g e t h e r w i t h (301, impl i e s t h a t q = 0. The debt- to- equi t y r a t i o must a1 so be constant i n the steady s t a t e . t h a t d=B. Expressions (35)-(38) describe the steady s t a t e : This impl i e s - 14 - Figure 1 The E f f e c t o f an Increase i n T, on t h e Cost o f C a p i t a l ( T I The impact o f i n c r e a s i n g the corporate t a x r a t e i s given by: where dq = - Ch(S)+6h1(6>1 < 0, dz P a a @= @ < 0, < 0, and dzP dX dzP dl The s i g n of dK/dzp i s unclear because o f two competing e f f e c t s . F i r s t , the increase i n X optimal. T, reduces the c o s t o f c a p i t a l by making a g r e a t e r This i s c l e a r from expression (34). Second, the r e d u c t i o n i n The s i g n the a f t e r - t a x r e t u r n from a u n i t o f c a p i t a l reduces steady s t a t e q. of dc/dzp i s a l s o unclear. would be -CF,-6-h(6)I I n the absence o f the agency cost, d c / d ~ p dK/dzP. Then the requirement f o r steady s t a t e c t o change i n the same d i r e c t i o n as K would be: < 0, where A(X>H( t h e analogous v e r s i o n i s FK-6-h(6>6-AtX>H( the p e r - u n i t o f c a p i t a l agency cost. FK-6-h(6)6 < 0. ) Here, is This c o n d i t i o n , however, i s n o t s u f f i c i e n t f o r steady s t a t e K and c t o move i n the same d i r e c t i o n , since the increase i n z P a l s o a f f e c t s X, q, and K. Note t h a t d c / d ~ pcan be w r i t t e n as: where the l a s t t h r e e terms equal dEa(X>bl/dz,. Although X w i l l increase, t o t a l agency costs may f a l l , since the value o f the f i r m may f a l l . VI. Dynamic Behavior As i s w e l l known, i n dynamic r a t i o n a l - e x p e c t a t i o n s models, endogenous v a r i a b l e s may overshoot the new steady s t a t e . Consequently, i t i s useful t o d i s t ingui sh between s hort- run and 1ong-run responses t o pol i cy changes. In t h i s s e c t i o n I describe the movement o f the system about the steady s t a t e i n response t o an u n a n t i c i p a t e d increase i n T,. The movement can be described by changes i n the r a t e o f investment, x = I I K , and the c a p i t a l stock. This s i m p l i f i c a t i o n recognizes t h a t the c o s t o f c a p i t a l v a r i e s w i t h the i n t e r e s t r a t e and the debt- to- equity r a t i o , both o f which vary w i t h t h e r a t e of change o f consumption and marginal u t i l i t y . The f o l l o w i n g system i s derived i n appendix B by expanding t h e system described by expressions (27)-(32) about the steady s t a t e : X ~ X * (42) (47) - A1 n2 KIK K * o C1 = 1 + H(G,T,)KA'~K zE X- X* K- K* Ucc Uc Here I have made use o f t h e f o l l o w i n g d e f i n i t i o n s : 1) H O = l + ( l - ~ , ) q , = q; 2) H I 0 = dHO1dx; 3) r ' = d r l d e ; 4) A ' ( > = dA(X)/dX; and 5) h ' 0 = dh(x)/dx. Since investment (I) can change instantaneously, x i s the "jump" v a r i a b l e f o r which d i s c o n t i n u i t i e s can occur. Since K i s predetermined w h i l e x depends on the f u t u r e p a t h o f the system, i n o r d e r f o r the system t o be s t a b l e , t h e r e must be one p o s i t i v e and one negative eigenvalue f o r the m a t r i x i n (42). This c o n d i t i o n assures me o f a jump o n t o the s t a b l e arm o f the system i n i t s movement toward t h e new steady s t a t e . < 0, -Kn2 < 0, (48) d e t From (43)-(471, To assure t h i s s t a b i l i t y I assume t h a t : n2 > 0. i t i s c l e a r t h a t expression (49) i s s u f f i c i e n t f o r (48) t o hol d. (49) C1 > 0 The second term i n C1 r e f l e c t s t h a t an increase i n consumption accompanies a r i s i n g i n t e r e s t r a t e and an increase i n e q u i t y values. An increase i n e q u i t y values reduces the r a t e o f change o f the debt- to- equi t y r a t i o , thus reducing the r a t e o f change o f the debt cost. Condition (49) s t a t e s t h a t the d i r e c t e f f e c t o f r i s i n g consumption on aggregate demand outweighs t h e i n d i r e c t e f f e c t o p e r a t i n g through the debt cost. So, t o assure C1 > 0, I assume t h a t the r a t e o f change o f demand f o r goods v a r i e s p o s i t i v e l y w i t h the r a t e o f change o f consumption. Note t h a t f o r the s t a b l e eigenvalue Q < 0 and the corresponding eigenvector, (XI, X2I1, Expression (50) imp1 i e s t h a t t h e movement o f x and K f r o m t h e i r steady s t a t e values can be d e s c r i b e d b y expression (51): (51) x t - x* = ylw2eat, K t - K* = Y , ( n - v1)eQt. Y1 i s a c o n s t a n t determined f r o m t h e f a c t t h a t K remains f i x e d a t t h e t i m e of t h e announcement and implementation o f an u n a n t i c i p a t e d change i n Having determined Yl as d e s c r i b e d i n appendix B, t h e movements o f 2,. x and K about t h e steady s t a t e a r e described b y expressions (52) and (53). (52) xt - x* = (- d K / d ~ , ) d ~ , w ~ e ' ~ / ( Q- w,) (53) Kt - K* = (- dK/d~,)d~,e~' These i m p l y x t - x ZO as dK/d-~, ZO. I n o t h e r words, i f t h e steady s t a t e c a p i t a l s t o c k increases, investment i s above i t s steady s t a t e v a l u e d u r i n g t h e adjustment p e r i o d . I n f a c t , x must immediately i n c r e a s e a t t i m e t = 0. The jump is computed as : VII. Dynamic R e l a t i o n s h i p s Between T o b i n ' s q , t h e Debt- to- Equity R a t i o , and t h e Rate o f Investment Because t h e movements o f q and x a r e c l o s e l y r e l a t e d by e x p r e s s i o n (211, on t h e s t a b l e adjustment path, s i g n [;I = sign Cql. The new steady s t a t e v a l u e o f q w i 11 be lower, s i n c e z P has increased. I n i t i a l l y , however, q and x may jump i n d i f f e r e n t d i r e c t i o n s . The i n c r e a s e i n t h e r a t e a t which c u r r e n t r e t u r n s a r e taxed tends t o decrease q a t t h e t i m e o f t h e announcement. The movement o f q a l o n g t h e s t a b l e arm can be d e s c r i b e d by expresssion (561, where q: i s t h e new steady s t a t e value: The jump i n q a t t = 0 i s If steady s t a t e K increases, q may e i t h e r r i s e o r f a l l i n i t i a l l y . These r e s u l t s a r e However, i f steady s t a t e K f a l l s , q must immediately f a l l . depicted i n f i g u r e 2. The i n i t i a l movement i n X can be i n f e r r e d d i r e c t l y from the jump i n q u s i n g the f o l l o w i n g r e l a t i o n s : a) X = b/zE, b) V = b + zE, c) V = qK. v a r i a b l e s b, E, and K a r e predetermined. opposite i n s i g n t o t h a t o f q. The These i m p l y t h a t t h e jump i n . X i s An increase i n the market value o f e x i s t i n g c a p i t a l w i l l be immediately r e f l e c t e d i n a higher p r i c e o f e q u i t y and a lower debt- to- equity r a t i o . Once t h i s i n i t i a l adjustment has been made, however, subsequent movements i n X are govern,ed by r e l a t i o n (31): 82, = a(X) + al(X)X(l + X I . In f a c t , the i n i t i a l r e a c t i o n o f the i n t e r e s t r a t e i s a l s o governed by (31). Thus, X and 8 may i n i t i a l l y jump i n opposite d i r e c t i o n s . To demonstrate the dynamics o f these r e l a t i o n s , two p o s s i b l e cases a r e examined below. Case I: d K / d ~ , > 0. As noted above, x w i l l immediately increase w h i l e t h e movement of q i s unclear. I f q immediately increases, then the debt- to- equity r a t i o drops. Then, from (311, i n o r d e r t o be on t h e s t a b l e path, t h e i n t e r e s t r a t e must i n i t i a l l y f a l l , given t h e h i g h e r consumption i s f a l l i n g . T,. When the i n t e r e s t r a t e i s below 6, This i s seen from expresssion (27): As t h e i n t e r e s t r a t e r i s e s toward O , X r i s e s toward i t s higher steady s t a t e level. The s i g n o f t h e i n i t i a l change i n c i s indeterminate, as i s t h e s i g n of t h e comparative s t a t i c r e s u l t , because o f the presence o f debt costs t h a t may move i n the o p p o s i t e d i r e c t i o n o f the c a p i t a l stock. The former case i s depicted i n f i g u r e 3. Case 11: dK/dr, < 0. Here t h e i n i t i a l impact on q i s c l e a r . Both t h e drop i n investment and t h e higher t a x r a t e r e q u i r e q t o f a l l . I n t h i s case, i t i s c l e a r t h a t t h e new steady s t a t e f i r m value w i l l be lower. As a r e s u l t o f t h e change i n T,, t h e r e l a t i o n s h i p between X and 8 has been a l t e r e d , and the d i r e c t i o n of t h e jump i n 8 i s indeterminate. 4. Two p o s s i b i l i t i e s a r e p i c t u r e d i n f i g u r e The ambiguity r e g a r d i n g t h e path o f X and 8 i n f i g u r e 4 can be r e s o l v e d by r e s t r i c t i n g t h e response o f the system t o t h e change i n T,. Expressions (87) and (88) i n appendix B imply expression (58): Here IT, > 0 and C1 > 0 i m p l y t h a t i f d K / d ~ , > 0, as K increases toward the new steady s t a t e , c > 0. determined through i n s p e c t i o n o f B 2 . The s i g n o f IT, = B2/B1 can be B2 i s t h e response o f q t o an a increase i n x. I f an increase i n t h e l e v e l o f investment decreases x, q w i l l a l s o decrease. This i s c l e a r from expression (29) and w i l l be assumed, i m p l y i n g n , < 0. Figure 3 The E f f e c t o f an Increase i n T, on q, X, x , and 8 When d K / d ~ , > 0 and q,-q* 1 ,,, > 0 Figure 4 The E f f e c t o f an I n c r e a s e i n T, on q, A, x , and 8 When dK/dr, and q,-q* 1 t = o > 0 The f i r s t term i n t h e c o e f f i c i e n t f o r (x - x*) i n expression (58) This represents t h e response o f excess supply o f goods t o an increase i n K. w i l l be assumed p o s i t i v e , assuring us t h a t (c - c*) v a r i e s p o s i t i v e l y w i t h Thus, (58) i m p l i e s t h a t i f d K / d ~ , < 0, (c (x-x*). - c * ) > 0. This, i n turn, t e l l s us t h a t p a t h A i s the a p p r o p r i a t e path f r o m f i g u r e 4. VIII. The D i s t i n c t i o n Between the Cost o f C a p i t a l and t h e I n t e r e s t Rate This model p r e d i c t s t h a t the i n t e r e s t r a t e and t h e debt- to- equity r a t i o are p o s i t i v e l y c o r r e l a t e d . However, t h i s i s n o t the r e s u l t o f bankruptcy r i s k , b u t r a t h e r the i n t e r e s t deduction f o r debt. While t h e c o s t o f c a p i t a l i s p o s i t i v e l y c o r r e l a t e d w i t h the debt- to- equity r a t i o , t h e r a t i o between t h e c o s t o f c a p i t a l and the i n t e r e s t r a t e i s given by expression (34). (34) r = 8 - a1(X)X2. Since the debt- to- equity r a t i o r i s e s w i t h the i n t e r e s t r a t e , the gap between the c o s t o f c a p i t a l and the i n t e r e s t r a t e a l s o r i s e s w i t h 8. This i m p l i e s t h a t models t h a t use the i n t e r e s t r a t e as t h e discount r a t e o v e r s t a t e the cost o f c a p i t a l by an i n c r e a s i n g amount as the i n t e r e s t r a t e r i s e s . We would expect t h a t these models would understate investment. Using expressions (231, (341, and (581, i t i s s t r a i g h t f o r w a r d t o show how the gap between r and 8 v a r i e s . Together w i t h (581, (59) i m p l i e s : Expressions (23) and (34) imply: Given the assumptions above, i f d K / d ~ , > 0, dCT r- - 81 < 0. Since 8 = -a1(X)X2 < 0, i f t h e c a p i t a l stock i s r i s i n g , t h e absolute value of the gap between t h e c o s t o f c a p i t a l .and the i n t e r e s t r a t e i s r i s i n g . IX. Summary Previous q models o f investment have imp1i c i t l y assumed t h a t f i n a n c i a l decisions have no impact on t h e c o s t o f the c a p i t a l . Here we show how f i n a n c i a l s t r u c t u r e a f f e c t s t h e c o s t o f c a p i t a l and t h e time paths o f investment, q and X. I n t h i s paper, the presence o f a debt c o s t together w i t h a tax code t h a t f a v o r s debt r e s u l t s i n an optimal debt- to- equi t y r a t i o t h a t covaries w i t h the i n t e r e s t r a t e . We f i n d t h a t q i s s t i l l a " s u f f i c i e n t s t a t i s t i c " f o r investment, although f i n a n c i a l s t r u c t u r e has r e a l e f f e c t s . In a d d i t i o n , the gap between t h e c o s t o f c a p i t a l and the i n t e r e s t r a t e covaries w i t h i n t e r e s t r a t e s and f i n a n c i a l s t r u c t u r e . As the debt- to- equity r a t i o r i s e s , however, the increase i n the cost o f debt reduces t h e amount o f o u t p u t avai 1able f o r consumption o r investment. The a n a l y s i s i m p l i e s t h a t models t h a t ignore the endogenous adjustment o f f in a n c i a i s t r u c t u r e w i 11 systematical l y e r r i n p r e d i c t i n g the response o f investment t o changes i n t a x r a t e s o r i n t e r e s t r a t e s . For example, a change i n t h e corporate tax r a t e a f f e c t s both the c o s t o f c a p i t a l and the gap between t h e c o s t o f c a p i t a l and t h e i n t e r e s t r a t e . I n a d d i t i o n , t h e presence of r e a l c o s t s t o f i n a n c i a l s t r u c t u r e may imply t h a t the c a p i t a l stock would d e c l i n e i n s p i t e o f a lower c o s t o f c a p i t a l . Appendix A Here I d e r i v e t h e a p p r o p r i a t e form f o r the c o s t of c a p i t a l through t h e use o f the c o n s t r a i n t s (7)-(12) V(0). maximization o f F i r s t , use (8) and ( 9 ) t o w r i t e - 1 , K l - T , Note t h a t V = b + zE i m p l i e s A and t h e assumed f i r m o b j e c t i v e : y w - ) = - (s(l T,) + a(X))b + dzE + RE. * Expressions (10) and (B1) imply (83): where ( y - wC - *(I,K))(l f l o w o f the f i r m . - r,) -I i s d e f i n e d as Y, t h e r e a l cash Using (61, (A41 can be r e w r i t t e n as Using the d e f i n i t i o n o f 1, (A51 can be w r i t t e n as F i n a l l y , d e f i n i n g the c o s t o f c a p i t a l r as (A61 can be w r i t t e n as which i s a l i n e a r d i f f e r e n t i a l equation i n V t h a t can be i n t e g r a t e d t o show that r i s t h e discount f a c t o r which maintains the e q u a l i t y between the i n t e g r a l i n expression (13) and b t = o + Z,=~E,=,. Appendix B Here I d e r i v e expressions (42)-(47) (271432) about t h e steady s t a t e . where H(x,T,> = 1 + (1-2,) o f t h e t e x t by expanding t h e system F i r s t note t h a t (29) i m p l i e s [h(x) + h l ( x ) l and H'(x,T,) = dH( )/dx. Together w i t h (301, t h i s i m p l i e s Since €3 = I3 - Uccc/Uc, i n o r d e r for (B2) t o y i e l d a r e l a t i o n f o r x, I r e q u i r e an expression for ;. An expression for ;can be derived f r o m (28). Take t h e time d e r i v a t i v e o f (28): Here I have used t h e f a c t t h a t K = K(x-6) and I = xK. The l a s t term on t h e r i g h t i s an expression f o r qKdCA(X>l/dt t h a t makes use o f t h e f o l l o w i n g facts: These y i e l d the f o l l o w i n g expression f o r ;: Now l i n e a r i z e (2) about t h e steady s t a t e t o o b t a i n an expression f o r ( x where A l = (x,~,), A2 = (r + &)H(X,T~) . x*): - - (1 - T ~ ) ( F K + x Z h ' ( x ) ) and, since a l l c o e f f i c i e n t s are evaluated a t the steady state, A, = q = 0. So we have: . - H( ) r t ( - u c c ~ / u c ) (-~ CI*). From (B4) I derive: This expression makes use o f the f a c t t h a t i n t h e steady s t a t e x-6 = x = d-8 = 0. d-8 = 0 stems from the requirement t h a t i n the steady s t a t e , X = 0, and thus z/z = 0. This i m p l i e s t h a t 8 = 8 = d. r e s u l t i n g expression f o r ( x (88) ( x 1 x*) = r l ( x - 1 x*) The is: x*) + n 2 ( K - K*), where rl and n2 are defined as i n t h e t e x t . I n t h i s s e c t i o n t h e d e t e r m i n a t i o n o f the constant Y, i n expression (51) i n the t e x t i s described. Expressions (89)-(811) are i m p l i e d by the f a c t t h a t c a p i t a l stock remains f i x e d a t t h e time o f t h e announced change, b u t e v e n t u a l l y changes by ( d K / d ~ , ) d ~ , . (B9) Kt - Kl 1 t , o = K* (B10) Kt - Kl It = o = (B11) Y1 = (-dKld~,)d~,/(Q - nl) - K: = (-dK/dz,)d~, YltQ - IT, = (-dK/d~,)d~, Footnotes 1. As an example o f more r e c e n t developments, Bernanke and G e r t l e r (1986) have incorporated f i nanci a1 s t r u c t u r e i n t o a s t o c h a s t i c general e q u i l i b r i u m model. 2. C h i r i n k o (1 987) and Hayashi (1985) have incorporated f i n a n c i a l s t r u c t u r e i n t o q frameworks. Chirinko, however, ignores tax e f f e c t s and i n v e s t i g a t e s whether the debt versus e q u i t y choice can e x p l a i n the poor performance o f q, defined as the market value o f e q u i t y d i v i d e d by t h e replacement value o f c a p i t a l . The a n a l y s i s o f t h i s paper, as do o t h e r s , defines q as the market value o f debt and e q u i t y d i v i d e d .by the replacement cost o f c a p i t a l . U t i l i z i n g a p a r t i a l e q u i l i b r i u m framework, Hayashi (1985) shows how the f i r m ' s choice o f f i n a n c i a l p o l i c y depends on the l e v e l o f p r o f i t s r e l a t i v e t o investment. He f i n d s t h a t o n l y when incremental investment i s e n t i r e l y debt- financed i s t h e l i n k between q and investment broken. C h i r i n k o and King (1985) take i n t o account the r o l e o f debt i n the response o f investment by equity- maximizing f i r m s t o changes i n inflation. 3. A series o f a r t i c l e s (see Auerbach C19831 f o r a review) has concluded t h a t bankruptcy r i s k and tax r a t e s t h a t vary across i n v e s t o r s and types of income can l e a d t o a determinate debt- to- equi t y r a t i o and a c o s t of c a p i t a l t h a t v a r i e s w i t h the debt- to- equity r a t i o . However, i f w i t h bankruptcy r i s k a f i r m ' s decisions i n f l u e n c e the i m p l i c i t p r i c e s o f the Arrow-Debreu s t a t e contingent commodities, the cost of c a p i t a l i s n o t well- defined. 4. I f a(X>b were t r e a t e d as a deduction from taxable income o r as a c o s t t h a t reduced taxable revenue, the form f o r the optimal c o s t of c a p i t a l would be somewhat d i f f e r e n t . To see t h i s , replace (14) by the f o l l o w i n g : and proceed as i n appendix B. The r e s u l t i n g expression f o r r is A t the optimal debt- to- equity r a t i o , the c o n d i t i o n t h a t dT/dX = 0 implies t h a t which y i e l d s r = 8 - ( l - - t , ) ~ ~ a ' ( ~ ) .I t can be shown t h a t an increase i n 2, s t i 11 w i 11 decrease the steady s t a t e c o s t o f c a p i t a l . 5. The f o r m u l a t i o n o f the adjustment t h e form G(B,K,I) w i t h Ga > 0, G K GnQ<O and G(I,K,I) homogeneous o f assumption t h a t G a l = 0, G(8,K,I) F(K,Q> - q(I,K). cost i m p l i e s a p r o d u c t i o n f u n c t i o n o f < 0, G I < O , G K K < 0, degree one. Then w i t h the can be w r i t t e n as G(Q,K,I) = 6. C h i r i n k o (1982) estimates T C a t .033 when r a t e s a p p l i c a b l e t o v a r i o u s i n v e s t o r classes a r e weighted by t r a n s a c t i o n s shares. The e s t i m a t e when weights r e f l e c t SEC market value data i s .031. Feldstein, Poterba, and Dicks- Mireaux (1981) estimate z c a t .083. While Gordon and M a l k i e l (1981) argue t h a t t h e r a t e on d i v i d e n d and i n t e r e s t income should be approximately equal f o r r e l e v a n t i n v e s t o r s , o t h e r researchers disagree. F e l d s t e i n , Poterba, and Dicks-Mireaux estimate t h e dividend t a x r a t e a t .349 i n 1979, and estimate t h e t a x r a t e on i n t e r e s t income a t .317. C h i r i n k o estimates the d i v i d e n d t a x r a t e a t . I 6 8 w i t h t r a n s a c t i o n s weights, and .278 when r a t e s are weighted by market shares. Gordon and M a l k i e l estimate t h e dividend and i n t e r e s t income t a x r a t e a t .44. The f e d e r a l corporate t a x r a t e i s .48. F e l d s t e i n , Poterba, and Dicks- Mireaux estimate the corporate t a x r a t e i n c l u s i v e o f s t a t e and l o c a l government corporate taxes a t .472. References Abel , Andrew B. "Dynamic E f f e c t s o f Permanent and Temporary Tax Pol i c i es i n a q Model o f Investment," Journal of Monetary Economics, v o l . 9 (May 1 982 1, 353-373. Abel, Andrew B.$ and O l i v i e r J. Blanchard. "An I n t e r t e m p o r a l Model o f Savings and Investment," Econometrica, v o l . 51, no. 3 (19831, 675-692. . "The Present Value o f P r o f i t s and C y c l i c a l Movements i n Investment," Econometrica, v o l . 54, no. 2 (March 19861, 249-273. Auerbach, Alan J. " Taxation, Corporate F i n a n c i a l P o l i c y and the Cost of C a p i t a l , " Journal o f Economic L i t e r a t u r e , v o l . 21, no. 3 (September 19831, 905-940. Barnea, Ami r , Robert A. Haugen, and Lemma W. Senbet. Agency Problems and F i n a n c i a l Contracting. Englewood C l i f f s , NJ: Prentice- Hall, I n c . , 1985. Bernanke, Ben, and Mark G e r t l e r . "Agency Costs, C o l l a t e r a l , and Business F l u c t u a t i o n s , " N a t i o n a l Bureau o f Economic Research Working Paper No. 2015 (September 19861. Blanchard, 01 i v i e r J. "Output, the Stock Market, and I n t e r e s t Rates," American Economic Review, v o l . 71, no. 1 (March 1981), 132-143. Bradley, Michael, Gregg A. J a r r e l l , and E. Han Kim. "On the Existence o f an Optimal C a p i t a l S t r u c t u r e : Theory and Evidence," Journal o f Finance, v o l . 39, no. 3 ( J u l y 19841, 857-878. Brock, W i l l i a m A., and Stephen J. Turnovsky. "The A n a l y s i s o f Macroeconomic P o l i c i e s i n P e r f e c t F o r e s i g h t E q u i l i b r i u m , " I n t e r n a t i o n a l Economic Review, v o l . 22, no. 1 (February 19811, 179-209. C h i r i n k o , Robert. " F i n a n c i a l Variables, Non-Neutral Taxes, and C a p i t a l Formation," Northwestern U n i v e r s i t y , mimea, June 1982. . "Tobin's q and F i n a n c i a l P o l i c y , " Journal o f Monetary Economics, v o l . 19 (January 19871, 69-87. , and Stephen R. King. "Hidden S t i m u l i t o C a p i t a l Formation: Debt and t h e Incomplete Adjustment o f F i n a n c i a l Returns," National Bureau o f Economic Research Working Paper No. 1684 (August 19851. Di x i t, Avi nash. "A S o l u t i o n Technique f o r Rational Expectations Model s w i t h Appl ic a t i o n s t o Exchange Rate and I n t e r e s t Rate Determination," U n i v e r s i t y o f Warwick, p r e l i m i n a r y paper, 1980. F e l d s t e i n , M a r t i n , James Poterba, and Louis Dicks- Mireaux. "The E f f e c t i v e Tax Rate and the Pretax Rate o f Return," National Bureau o f Economic Research Working Paper No. 740 (August 1981). G e r t l e r , Mark. " A Model o f Income E f f e c t s i n t h e Business Cycle," S o c i a l Systems Research I n s t i t u t e Working Paper No. 8415, Madison, Wisconsin, August 1984. Gordon, Roger H., and Burton G . M a l k i e l . " Corporation Finance," i n Henry J. Aaron and Joseph A. Pechman, Eds., How Taxes A f f e c t Economic Behavior, Washington, D.C.: The Brookings I n s t i t u t i o n , 131-198. Hayashi, Fumio. " T o b i n ' s Marginal q and Average q: A Neoclassical I n t e r p r e t a t i o n , " Econometrica, v o l . 50, no. 1 (January 19821, 213-224. . "Corporate Finance Side o f t h e Q Theory o f Investment," Journal o f P u b l i c Economics, v o l . 27, no. 3 (19851, 261-280. Jensen. Michael C.. and W i l l i a m H. Mecklina. "Theorv o f the Firm: Managerial ~ e h a v i o r , ~ ~ e Costs n c ~and Ownership s t r u c t u r e ,"-Journal o f F i nanci a i Economics, v o l . 3, no. 4 (October 19761, 305-360. Kalay, Avner. "Stockholder- Bondholder C o n f l i c t and Dividend C o n s t r a i n t s , " Journal o f F i n a n c i a l Economics, v o l . 10, no. 2 ( J u l y 19821, 47-56. M i l l e r , Merton H. "Debt and Taxes," 19771, 261-275. Journal o f Finance, v o l . 32, no. 2 (May M o d i g l i a n i , Franco, and Merton H. M i l l e r . "The Cost o f C a p i t a l , C o r p o r a t i o n Finance and t h e Theory o f Investment," American Economic Review, v o l . 48, no. 3 (June 19581, 261-297. Myers, Stewart C. "Determinants o f Corporate Borrowing," Journal of F i n a n c i a l Economics, v o l . 5, no. 2 (November 19771, 147-175. . "The C a p i t a l S t r u c t u r e Puzzle," Journal o f Finance, v o l . 34, no. 3 ( J u l y 19841, 575-592. Sargent, Thomas J. " ' T o b i n ' s q ' and t h e Rate o f Investment i n General E q u i l i b r i u m , " i n K a r l Brunner and A l l a n H. M e l t z e r , Eds., On t h e S t a t e o f Macroeconomics, Amsterdam, Holland: North- Holland P u b l i s h i n g Co., 1980, 107-1 54. Smith, C l i f f o r d W., and J e r o l d B. Warner. "On F i n a n c i a l C o n t r a c t i n g : An A n a l y s i s o f Bond Covenants," Journal o f F i n a n c i a l Economics, v o l . 7, no. 2 (June 19791, 117-161. Steigum, E r l i n g J r . " A F i n a n c i a l Theory o f Investment Behavior," Econornetrica, v o l . 51, no. 3 (May 19831, 637-645. Summers, Lawrence H. "Taxation and Corporate Investment: a q-Theory Approach," Brookings Papers on Economic A c t i v i t y , v o l . 1 (19811, 67-127. Von Furstenberg, George M. "Corporate Investment: Does Market V a l u a t i o n M a t t e r i n the Aggregate?" Brookings Papers on Economic A c t i v i t y , v o l . 2 (19771, 347-397.